LMFDB - Embedded newform 503.2.c.a.2.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [503,2,Mod(2,503)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(503, base_ring=CyclotomicField(502))

chi = DirichletCharacter(H, H._module([202]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("503.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.c (of order $251$, degree $250$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.01647522167$
Analytic rank:	$0$
Dimension:	$10250$
Relative dimension:	$41$ over $\Q(\zeta_{251})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{251}]$

Embedding invariants

Embedding label			2.10
Character	$\chi$	$=$	503.2
Dual form			503.2.c.a.252.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.994976 - 1.22503i) q^{2} +(-1.98352 + 1.71676i) q^{3} +(-0.100616 + 0.480254i) q^{4} +(-1.27158 - 4.01588i) q^{5} +(4.07664 + 0.721744i) q^{6} +(1.44819 - 4.20490i) q^{7} +(-2.11761 + 1.09069i) q^{8} +(0.556781 - 3.84146i) q^{9} +O(q^{10})$	\(q+(-0.994976 - 1.22503i) q^{2} +(-1.98352 + 1.71676i) q^{3} +(-0.100616 + 0.480254i) q^{4} +(-1.27158 - 4.01588i) q^{5} +(4.07664 + 0.721744i) q^{6} +(1.44819 - 4.20490i) q^{7} +(-2.11761 + 1.09069i) q^{8} +(0.556781 - 3.84146i) q^{9} +(-3.65440 + 5.55343i) q^{10} +(0.114889 - 0.0371709i) q^{11} +(-0.624904 - 1.12533i) q^{12} +(3.46878 - 1.17043i) q^{13} +(-6.59206 + 2.40970i) q^{14} +(9.41649 + 5.78260i) q^{15} +(4.34194 + 1.90284i) q^{16} +(-0.419893 - 0.209661i) q^{17} +(-5.25989 + 3.14009i) q^{18} +(-2.54124 - 5.70132i) q^{19} +(2.05658 - 0.206618i) q^{20} +(4.34627 + 10.8267i) q^{21} +(-0.159848 - 0.103759i) q^{22} +(1.36173 - 4.70690i) q^{23} +(2.32788 - 5.79883i) q^{24} +(-10.4217 + 7.33518i) q^{25} +(-4.88517 - 3.08481i) q^{26} +(1.24701 + 1.94769i) q^{27} +(1.87371 + 1.11858i) q^{28} +(-0.296587 + 2.48256i) q^{29} +(-2.28532 - 17.2891i) q^{30} +(0.314516 + 3.85739i) q^{31} +(-0.722505 - 2.61976i) q^{32} +(-0.164072 + 0.270966i) q^{33} +(0.160942 + 0.722990i) q^{34} +(-18.7279 - 0.468906i) q^{35} +(1.78885 + 0.653909i) q^{36} +(2.57013 + 3.24659i) q^{37} +(-4.45582 + 8.78578i) q^{38} +(-4.87104 + 8.27662i) q^{39} +(7.07279 + 7.11719i) q^{40} +(-0.941818 + 4.79360i) q^{41} +(8.93861 - 16.0966i) q^{42} +(0.353129 - 1.92435i) q^{43} +(0.00629175 + 0.0589160i) q^{44} +(-16.1349 + 2.64875i) q^{45} +(-7.12099 + 3.01509i) q^{46} +(-12.5580 + 0.471759i) q^{47} +(-11.8790 + 3.67971i) q^{48} +(-10.0685 - 7.86862i) q^{49} +(19.3551 + 5.46852i) q^{50} +(1.19280 - 0.304987i) q^{51} +(0.213091 + 1.78366i) q^{52} +(2.81691 - 6.31978i) q^{53} +(1.14523 - 3.46553i) q^{54} +(-0.295365 - 0.414117i) q^{55} +(1.51953 + 10.4839i) q^{56} +(14.8284 + 6.94599i) q^{57} +(3.33631 - 2.10676i) q^{58} +(0.698148 - 1.67805i) q^{59} +(-3.72457 + 3.94048i) q^{60} +(4.97693 + 8.21943i) q^{61} +(4.41249 - 4.22330i) q^{62} +(-15.3467 - 7.90438i) q^{63} +(3.01507 - 4.22728i) q^{64} +(-9.11115 - 12.4419i) q^{65} +(0.495190 - 0.0686115i) q^{66} +(10.5807 - 6.49752i) q^{67} +(0.142938 - 0.180560i) q^{68} +(5.37957 + 11.6740i) q^{69} +(18.0594 + 23.4088i) q^{70} +(2.23981 + 14.1991i) q^{71} +(3.01079 + 8.74200i) q^{72} +(4.23387 + 4.05235i) q^{73} +(1.41996 - 6.37878i) q^{74} +(8.07884 - 32.4409i) q^{75} +(2.99377 - 0.646796i) q^{76} +(0.0100817 - 0.536929i) q^{77} +(14.9857 - 2.26787i) q^{78} +(-0.436680 - 7.74488i) q^{79} +(2.12049 - 19.8563i) q^{80} +(5.34844 + 1.58367i) q^{81} +(6.80940 - 3.61577i) q^{82} +(-3.77782 - 7.22337i) q^{83} +(-5.63687 + 0.997974i) q^{84} +(-0.308047 + 1.95284i) q^{85} +(-2.70875 + 1.48209i) q^{86} +(-3.67366 - 5.43337i) q^{87} +(-0.202749 + 0.204022i) q^{88} +(2.51405 + 9.58219i) q^{89} +(19.2986 + 17.1303i) q^{90} +(0.101890 - 16.2809i) q^{91} +(2.12349 + 1.12757i) q^{92} +(-7.24604 - 7.11126i) q^{93} +(13.0728 + 14.9145i) q^{94} +(-19.6644 + 17.4550i) q^{95} +(5.93060 + 3.95599i) q^{96} +(-0.660930 - 2.80315i) q^{97} +(0.378599 + 20.1633i) q^{98} +(-0.0788224 - 0.462039i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10250 q - 249 q^{2} - 249 q^{3} - 285 q^{4} - 245 q^{5} - 237 q^{6} - 247 q^{7} - 239 q^{8} - 280 q^{9}+O(q^{10}) $ 10250 * q - 249 * q^2 - 249 * q^3 - 285 * q^4 - 245 * q^5 - 237 * q^6 - 247 * q^7 - 239 * q^8 - 280 * q^9	\( 10250 q - 249 q^{2} - 249 q^{3} - 285 q^{4} - 245 q^{5} - 237 q^{6} - 247 q^{7} - 239 q^{8} - 280 q^{9} - 233 q^{10} - 239 q^{11} - 239 q^{12} - 245 q^{13} - 223 q^{14} - 231 q^{15} - 263 q^{16} - 243 q^{17} - 217 q^{18} - 229 q^{19} - 195 q^{20} - 215 q^{21} - 233 q^{22} - 241 q^{23} - 181 q^{24} - 280 q^{25} - 215 q^{26} - 237 q^{27} - 185 q^{28} - 217 q^{29} - 159 q^{30} - 219 q^{31} - 185 q^{32} - 209 q^{33} - 167 q^{34} - 187 q^{35} - 203 q^{36} - 237 q^{37} - 161 q^{38} - 197 q^{39} - 135 q^{40} - 209 q^{41} - 117 q^{42} - 221 q^{43} - 147 q^{44} - 167 q^{45} - 167 q^{46} - 195 q^{47} - 141 q^{48} - 234 q^{49} - 145 q^{50} - 177 q^{51} - 179 q^{52} - 211 q^{53} - 83 q^{54} - 165 q^{55} - 125 q^{56} - 177 q^{57} - 205 q^{58} - 189 q^{59} - 27 q^{60} - 193 q^{61} - 143 q^{62} - 159 q^{63} - 185 q^{64} - 155 q^{65} - 97 q^{66} - 201 q^{67} - 155 q^{68} - 113 q^{69} - 123 q^{70} - 153 q^{71} - 21 q^{72} - 213 q^{73} - 83 q^{74} - 161 q^{75} - 97 q^{76} - 139 q^{77} - 43 q^{78} - 191 q^{79} + 3 q^{80} - 188 q^{81} - 97 q^{82} - 161 q^{83} + 67 q^{84} - 159 q^{85} - 121 q^{86} - 121 q^{87} - 143 q^{88} - 155 q^{89} + 115 q^{90} - 137 q^{91} - 119 q^{92} - 123 q^{93} - 99 q^{94} - 181 q^{95} + 67 q^{96} - 229 q^{97} - 63 q^{98} - 85 q^{99}+O(q^{100}) \) 10250 * q - 249 * q^2 - 249 * q^3 - 285 * q^4 - 245 * q^5 - 237 * q^6 - 247 * q^7 - 239 * q^8 - 280 * q^9 - 233 * q^10 - 239 * q^11 - 239 * q^12 - 245 * q^13 - 223 * q^14 - 231 * q^15 - 263 * q^16 - 243 * q^17 - 217 * q^18 - 229 * q^19 - 195 * q^20 - 215 * q^21 - 233 * q^22 - 241 * q^23 - 181 * q^24 - 280 * q^25 - 215 * q^26 - 237 * q^27 - 185 * q^28 - 217 * q^29 - 159 * q^30 - 219 * q^31 - 185 * q^32 - 209 * q^33 - 167 * q^34 - 187 * q^35 - 203 * q^36 - 237 * q^37 - 161 * q^38 - 197 * q^39 - 135 * q^40 - 209 * q^41 - 117 * q^42 - 221 * q^43 - 147 * q^44 - 167 * q^45 - 167 * q^46 - 195 * q^47 - 141 * q^48 - 234 * q^49 - 145 * q^50 - 177 * q^51 - 179 * q^52 - 211 * q^53 - 83 * q^54 - 165 * q^55 - 125 * q^56 - 177 * q^57 - 205 * q^58 - 189 * q^59 - 27 * q^60 - 193 * q^61 - 143 * q^62 - 159 * q^63 - 185 * q^64 - 155 * q^65 - 97 * q^66 - 201 * q^67 - 155 * q^68 - 113 * q^69 - 123 * q^70 - 153 * q^71 - 21 * q^72 - 213 * q^73 - 83 * q^74 - 161 * q^75 - 97 * q^76 - 139 * q^77 - 43 * q^78 - 191 * q^79 + 3 * q^80 - 188 * q^81 - 97 * q^82 - 161 * q^83 + 67 * q^84 - 159 * q^85 - 121 * q^86 - 121 * q^87 - 143 * q^88 - 155 * q^89 + 115 * q^90 - 137 * q^91 - 119 * q^92 - 123 * q^93 - 99 * q^94 - 181 * q^95 + 67 * q^96 - 229 * q^97 - 63 * q^98 - 85 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/503\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{101}{251}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.994976	−	1.22503i	−0.703555	−	0.866228i	0.292381	−	0.956302i	$-0.405553\pi$
$2$	−0.994976	−	1.22503i	−0.703555	−	0.866228i	−0.995935	+	0.0900739i	$0.971290\pi$
$3$	−1.98352	+	1.71676i	−1.14519	+	0.991169i	−0.145188	+	0.989404i	$0.546379\pi$
$3$	−1.98352	+	1.71676i	−1.14519	+	0.991169i	−0.999998	+	0.00176497i	$0.999438\pi$
$4$	−0.100616	+	0.480254i	−0.0503080	+	0.240127i
$5$	−1.27158	−	4.01588i	−0.568667	−	1.79596i	−0.604506	−	0.796601i	$-0.706629\pi$
$5$	−1.27158	−	4.01588i	−0.568667	−	1.79596i	0.0358388	−	0.999358i	$-0.488590\pi$
$6$	4.07664	+	0.721744i	1.66428	+	0.294651i
$7$	1.44819	−	4.20490i	0.547365	−	1.58930i	−0.238656	−	0.971104i	$-0.576707\pi$
$7$	1.44819	−	4.20490i	0.547365	−	1.58930i	0.786021	−	0.618200i	$-0.212138\pi$
$8$	−2.11761	+	1.09069i	−0.748689	+	0.385617i
$9$	0.556781	−	3.84146i	0.185594	−	1.28049i
$10$	−3.65440	+	5.55343i	−1.15562	+	1.75615i
$11$	0.114889	−	0.0371709i	0.0346405	−	0.0112075i	−0.290455	−	0.956889i	$-0.593807\pi$
$11$	0.114889	−	0.0371709i	0.0346405	−	0.0112075i	0.325096	+	0.945681i	$0.394604\pi$
$12$	−0.624904	−	1.12533i	−0.180394	−	0.324854i
$13$	3.46878	−	1.17043i	0.962066	−	0.324620i	0.205587	−	0.978639i	$-0.434089\pi$
$13$	3.46878	−	1.17043i	0.962066	−	0.324620i	0.756479	+	0.654019i	$0.226918\pi$
$14$	−6.59206	+	2.40970i	−1.76180	+	0.644019i
$15$	9.41649	+	5.78260i	2.43133	+	1.49306i
$16$	4.34194	+	1.90284i	1.08548	+	0.475711i
$17$	−0.419893	−	0.209661i	−0.101839	−	0.0508502i	0.395083	−	0.918645i	$-0.370716\pi$
$17$	−0.419893	−	0.209661i	−0.101839	−	0.0508502i	−0.496922	+	0.867795i	$0.665537\pi$
$18$	−5.25989	+	3.14009i	−1.23977	+	0.740126i
$19$	−2.54124	−	5.70132i	−0.583001	−	1.30797i	−0.929119	−	0.369781i	$-0.879433\pi$
$19$	−2.54124	−	5.70132i	−0.583001	−	1.30797i	0.346118	−	0.938191i	$-0.387500\pi$
$20$	2.05658	−	0.206618i	0.459866	−	0.0462011i
$21$	4.34627	+	10.8267i	0.948435	+	2.36258i
$22$	−0.159848	−	0.103759i	−0.0340797	−	0.0221215i
$23$	1.36173	−	4.70690i	0.283941	−	0.981456i	−0.683834	−	0.729638i	$-0.739689\pi$
$23$	1.36173	−	4.70690i	0.283941	−	0.981456i	0.967774	−	0.251818i	$-0.0810286\pi$
$24$	2.32788	−	5.79883i	0.475177	−	1.18368i
$25$	−10.4217	+	7.33518i	−2.08433	+	1.46704i
$26$	−4.88517	−	3.08481i	−0.958061	−	0.604981i
$27$	1.24701	+	1.94769i	0.239987	+	0.374833i
$28$	1.87371	+	1.11858i	0.354098	+	0.211392i
$29$	−0.296587	+	2.48256i	−0.0550749	+	0.460999i	0.938277	+	0.345884i	$0.112421\pi$
$29$	−0.296587	+	2.48256i	−0.0550749	+	0.460999i	−0.993352	+	0.115115i	$0.963276\pi$
$30$	−2.28532	−	17.2891i	−0.417240	−	3.15653i
$31$	0.314516	+	3.85739i	0.0564887	+	0.692807i	0.962803	+	0.270204i	$0.0870910\pi$
$31$	0.314516	+	3.85739i	0.0564887	+	0.692807i	−0.906315	+	0.422604i	$0.861116\pi$
$32$	−0.722505	−	2.61976i	−0.127722	−	0.463113i
$33$	−0.164072	+	0.270966i	−0.0285613	+	0.0471692i
$34$	0.160942	+	0.722990i	0.0276014	+	0.123992i
$35$	−18.7279	−	0.468906i	−3.16559	−	0.0792596i
$36$	1.78885	+	0.653909i	0.298142	+	0.108985i
$37$	2.57013	+	3.24659i	0.422527	+	0.533737i	0.948505	−	0.316761i	$-0.102595\pi$
$37$	2.57013	+	3.24659i	0.422527	+	0.533737i	−0.525978	+	0.850498i	$0.676301\pi$
$38$	−4.45582	+	8.78578i	−0.722829	+	1.42524i
$39$	−4.87104	+	8.27662i	−0.779991	+	1.32532i
$40$	7.07279	+	7.11719i	1.11831	+	1.12533i
$41$	−0.941818	+	4.79360i	−0.147087	+	0.748635i	0.833495	+	0.552527i	$0.186336\pi$
$41$	−0.941818	+	4.79360i	−0.147087	+	0.748635i	−0.980582	+	0.196108i	$0.937170\pi$
$42$	8.93861	−	16.0966i	1.37926	−	2.48376i
$43$	0.353129	−	1.92435i	0.0538517	−	0.293461i	−0.945644	−	0.325202i	$-0.894568\pi$
$43$	0.353129	−	1.92435i	0.0538517	−	0.293461i	0.999496	+	0.0317417i	$0.0101054\pi$
$44$	0.00629175	+	0.0589160i	0.000948517	+	0.00888193i
$45$	−16.1349	+	2.64875i	−2.40524	+	0.394852i
$46$	−7.12099	+	3.01509i	−1.04993	+	0.444551i
$47$	−12.5580	+	0.471759i	−1.83177	+	0.0688132i	−0.930898	−	0.365280i	$-0.880973\pi$
$47$	−12.5580	+	0.471759i	−1.83177	+	0.0688132i	−0.900868	+	0.434093i	$0.857069\pi$
$48$	−11.8790	+	3.67971i	−1.71459	+	0.531120i
$49$	−10.0685	−	7.86862i	−1.43835	−	1.12409i
$50$	19.3551	+	5.46852i	2.73723	+	0.773365i
$51$	1.19280	−	0.304987i	0.167026	−	0.0427067i
$52$	0.213091	+	1.78366i	0.0295504	+	0.247349i
$53$	2.81691	−	6.31978i	0.386932	−	0.868088i	−0.610189	−	0.792256i	$-0.708906\pi$
$53$	2.81691	−	6.31978i	0.386932	−	0.868088i	0.997121	−	0.0758320i	$-0.0241613\pi$
$54$	1.14523	−	3.46553i	0.155846	−	0.471599i
$55$	−0.295365	−	0.414117i	−0.0398270	−	0.0558395i
$56$	1.51953	+	10.4839i	0.203056	+	1.40097i
$57$	14.8284	+	6.94599i	1.96407	+	0.920019i
$58$	3.33631	−	2.10676i	0.438079	−	0.276631i
$59$	0.698148	−	1.67805i	0.0908911	−	0.218463i	−0.871350	−	0.490662i	$-0.836755\pi$
$59$	0.698148	−	1.67805i	0.0908911	−	0.218463i	0.962241	+	0.272199i	$0.0877509\pi$
$60$	−3.72457	+	3.94048i	−0.480839	+	0.508714i
$61$	4.97693	+	8.21943i	0.637230	+	1.05239i	0.993034	+	0.117829i	$0.0375936\pi$
$61$	4.97693	+	8.21943i	0.637230	+	1.05239i	−0.355804	+	0.934561i	$0.615793\pi$
$62$	4.41249	−	4.22330i	0.560386	−	0.536360i
$63$	−15.3467	−	7.90438i	−1.93350	−	0.995858i
$64$	3.01507	−	4.22728i	0.376883	−	0.528410i
$65$	−9.11115	−	12.4419i	−1.13010	−	1.54323i
$66$	0.495190	−	0.0686115i	0.0609537	−	0.00844549i
$67$	10.5807	−	6.49752i	1.29264	−	0.793799i	0.305272	−	0.952265i	$-0.401252\pi$
$67$	10.5807	−	6.49752i	1.29264	−	0.793799i	0.987364	+	0.158466i	$0.0506548\pi$
$68$	0.142938	−	0.180560i	0.0173338	−	0.0218961i
$69$	5.37957	+	11.6740i	0.647624	+	1.40538i
$70$	18.0594	+	23.4088i	2.15851	+	2.79789i
$71$	2.23981	+	14.1991i	0.265817	+	1.68513i	0.648474	+	0.761237i	$0.275407\pi$
$71$	2.23981	+	14.1991i	0.265817	+	1.68513i	−0.382657	+	0.923890i	$0.624991\pi$
$72$	3.01079	+	8.74200i	0.354825	+	1.03025i
$73$	4.23387	+	4.05235i	0.495538	+	0.474291i	0.897280	−	0.441461i	$-0.145540\pi$
$73$	4.23387	+	4.05235i	0.495538	+	0.474291i	−0.401743	+	0.915753i	$0.631595\pi$
$74$	1.41996	−	6.37878i	0.165067	−	0.741518i
$75$	8.07884	−	32.4409i	0.932864	−	3.74595i
$76$	2.99377	−	0.646796i	0.343409	−	0.0741926i
$77$	0.0100817	−	0.536929i	0.00114892	−	0.0611888i
$78$	14.9857	−	2.26787i	1.69680	−	0.256785i
$79$	−0.436680	−	7.74488i	−0.0491303	−	0.871367i	−0.922903	−	0.385033i	$-0.874190\pi$
$79$	−0.436680	−	7.74488i	−0.0491303	−	0.871367i	0.873773	−	0.486335i	$-0.161666\pi$
$80$	2.12049	−	19.8563i	0.237078	−	2.22001i
$81$	5.34844	+	1.58367i	0.594271	+	0.175964i
$82$	6.80940	−	3.61577i	0.751973	−	0.399294i
$83$	−3.77782	−	7.22337i	−0.414670	−	0.792868i	0.585167	−	0.810913i	$-0.301029\pi$
$83$	−3.77782	−	7.22337i	−0.414670	−	0.792868i	−0.999837	+	0.0180445i	$0.994256\pi$
$84$	−5.63687	+	0.997974i	−0.615033	+	0.108888i
$85$	−0.308047	+	1.95284i	−0.0334124	+	0.211816i
$86$	−2.70875	+	1.48209i	−0.292092	+	0.159818i
$87$	−3.67366	−	5.43337i	−0.393857	−	0.582519i
$88$	−0.202749	+	0.204022i	−0.0216132	+	0.0217488i
$89$	2.51405	+	9.58219i	0.266489	+	1.01571i	0.956458	+	0.291871i	$0.0942776\pi$
$89$	2.51405	+	9.58219i	0.266489	+	1.01571i	−0.689969	+	0.723839i	$0.742376\pi$
$90$	19.2986	+	17.1303i	2.03425	+	1.80569i
$91$	0.101890	−	16.2809i	0.0106809	−	1.70670i
$92$	2.12349	+	1.12757i	0.221390	+	0.117557i
$93$	−7.24604	−	7.11126i	−0.751379	−	0.737403i
$94$	13.0728	+	14.9145i	1.34835	+	1.53831i
$95$	−19.6644	+	17.4550i	−2.01753	+	1.79085i
$96$	5.93060	+	3.95599i	0.605289	+	0.403757i
$97$	−0.660930	−	2.80315i	−0.0671072	−	0.284617i	0.929298	−	0.369330i	$-0.120413\pi$
$97$	−0.660930	−	2.80315i	−0.0671072	−	0.284617i	−0.996405	+	0.0847132i	$0.973003\pi$
$98$	0.378599	+	20.1633i	0.0382443	+	2.03680i
$99$	−0.0788224	−	0.462039i	−0.00792195	−	0.0464367i
$100$	−2.47416	−	5.74307i	−0.247416	−	0.574307i
$101$	2.35203	−	0.927150i	0.234036	−	0.0922549i	−0.246797	−	0.969067i	$-0.579378\pi$
$101$	2.35203	−	0.927150i	0.234036	−	0.0922549i	0.480833	+	0.876812i	$0.340334\pi$
$102$	−1.56043	−	1.15777i	−0.154506	−	0.114636i
$103$	7.80176	−	1.58361i	0.768730	−	0.156038i	0.201378	−	0.979514i	$-0.435458\pi$
$103$	7.80176	−	1.58361i	0.768730	−	0.156038i	0.567352	+	0.823476i	$0.307968\pi$
$104$	−6.06895	+	6.26188i	−0.595109	+	0.614028i
$105$	37.9522	−	31.2211i	3.70375	−	3.04687i
$106$	−10.5447	+	2.83723i	−1.02419	+	0.275576i
$107$	−10.4626	−	0.393045i	−1.01146	−	0.0379971i	−0.473352	−	0.880873i	$-0.656956\pi$
$107$	−10.4626	−	0.393045i	−1.01146	−	0.0379971i	−0.538108	+	0.842876i	$0.680861\pi$
$108$	−1.06085	+	0.402913i	−0.102081	+	0.0387703i
$109$	6.71746	+	7.10688i	0.643416	+	0.680715i	0.963816	−	0.266567i	$-0.0858893\pi$
$109$	6.71746	+	7.10688i	0.643416	+	0.680715i	−0.320401	+	0.947282i	$0.603818\pi$
$110$	−0.213425	+	0.773868i	−0.0203493	+	0.0737854i
$111$	−10.6715	−	2.02740i	−1.01290	−	0.192432i
$112$	14.2892	−	15.5017i	1.35021	−	1.46478i
$113$	0.723862	+	1.47268i	0.0680952	+	0.138539i	0.928819	−	0.370534i	$-0.120825\pi$
$113$	0.723862	+	1.47268i	0.0680952	+	0.138539i	−0.860724	+	0.509072i	$0.829989\pi$
$114$	−6.24482	−	25.0763i	−0.584881	−	2.34861i
$115$	−20.6339	+	0.516629i	−1.92412	+	0.0481759i
$116$	−1.16242	−	0.392222i	−0.107928	−	0.0364169i
$117$	−2.56483	−	13.9769i	−0.237119	−	1.29216i
$118$	−2.75030	+	0.814364i	−0.253186	+	0.0749683i
$119$	−1.48969	+	1.46198i	−0.136560	+	0.134020i
$120$	−26.2475	−	1.97484i	−2.39606	−	0.180278i
$121$	−8.90353	+	6.43480i	−0.809411	+	0.584982i
$122$	5.11714	−	14.2750i	0.463284	−	1.29240i
$123$	−6.36133	−	11.1251i	−0.573582	−	1.00311i
$124$	−1.88417	−	0.237068i	−0.169203	−	0.0212893i
$125$	25.9529	+	19.7643i	2.32130	+	1.76777i
$126$	5.58644	+	26.6648i	0.497679	+	2.37549i
$127$	−2.33759	+	1.31729i	−0.207428	+	0.116891i	−0.591163	−	0.806552i	$-0.701331\pi$
$127$	−2.33759	+	1.31729i	−0.207428	+	0.116891i	0.383735	+	0.923443i	$0.374638\pi$
$128$	−13.6030	+	0.852407i	−1.20234	+	0.0753429i
$129$	2.60320	+	4.42322i	0.229199	+	0.389443i
$130$	−6.17635	+	23.5409i	−0.541702	+	2.06467i
$131$	15.9436	−	10.6352i	1.39300	−	0.929198i	0.393048	−	0.919518i	$-0.371421\pi$
$131$	15.9436	−	10.6352i	1.39300	−	0.929198i	0.999953	−	0.00968029i	$-0.00308138\pi$
$132$	−0.113624	−	0.106060i	−0.00988972	−	0.00923132i
$133$	−27.6537	+	2.42907i	−2.39788	+	0.210627i
$134$	−18.4872	−	6.49679i	−1.59705	−	0.561238i
$135$	6.23602	−	7.48449i	0.536711	−	0.644162i
$136$	1.11785	−	0.0139920i	0.0958545	−	0.00119981i
$137$	−2.19770	−	5.67913i	−0.187762	−	0.485200i	0.806617	−	0.591074i	$-0.201296\pi$
$137$	−2.19770	−	5.67913i	−0.187762	−	0.485200i	−0.994380	+	0.105874i	$0.966236\pi$
$138$	8.94847	−	18.2055i	0.761744	−	1.54975i
$139$	−15.5556	−	3.36074i	−1.31941	−	0.285055i	−0.503880	−	0.863774i	$-0.668095\pi$
$139$	−15.5556	−	3.36074i	−1.31941	−	0.285055i	−0.815527	+	0.578719i	$0.803553\pi$
$140$	2.10952	−	8.94696i	0.178287	−	0.756156i
$141$	24.0991	−	22.4947i	2.02951	−	1.89439i
$142$	15.1658	−	16.8716i	1.27269	−	1.41584i
$143$	0.355020	−	0.263408i	0.0296882	−	0.0220273i
$144$	9.72721	−	15.6199i	0.810601	−	1.30166i
$145$	10.3468	−	1.96571i	0.859255	−	0.163243i
$146$	0.751649	−	9.21862i	0.0622069	−	0.762938i
$147$	33.4795	−	1.67756i	2.76134	−	0.138363i
$148$	−1.81779	+	0.907656i	−0.149421	+	0.0746089i
$149$	2.54942	−	3.98190i	0.208857	−	0.326210i	−0.721801	−	0.692100i	$-0.756686\pi$
$149$	2.54942	−	3.98190i	0.208857	−	0.326210i	0.930658	+	0.365890i	$0.119235\pi$
$150$	−47.7794	+	22.3811i	−3.90117	+	1.82741i
$151$	10.1195	+	15.3781i	0.823510	+	1.25145i	0.965192	+	0.261543i	$0.0842312\pi$
$151$	10.1195	+	15.3781i	0.823510	+	1.25145i	−0.141681	+	0.989912i	$0.545251\pi$
$152$	11.5997	+	9.30148i	0.940862	+	0.754450i
$153$	−1.03919	+	1.49627i	−0.0840138	+	0.120966i
$154$	−0.667787	+	0.521882i	−0.0538118	+	0.0420544i
$155$	15.0909	−	6.16803i	1.21213	−	0.495428i
$156$	−3.48477	−	3.17210i	−0.279005	−	0.253971i
$157$	2.75239	−	5.78137i	0.219665	−	0.461404i	−0.763096	−	0.646285i	$-0.776322\pi$
$157$	2.75239	−	5.78137i	0.219665	−	0.461404i	0.982761	+	0.184881i	$0.0591901\pi$
$158$	−9.05324	+	8.24092i	−0.720237	+	0.655613i
$159$	5.26212	+	17.3713i	0.417313	+	1.37764i
$160$	−9.60195	+	6.23273i	−0.759101	+	0.492741i
$161$	−17.8200	−	12.5424i	−1.40441	−	0.988484i
$162$	−3.38152	−	8.12772i	−0.265677	−	0.638574i
$163$	−0.109468	−	0.0415759i	−0.00857417	−	0.00325648i	0.350764	−	0.936464i	$-0.385922\pi$
$163$	−0.109468	−	0.0415759i	−0.00857417	−	0.00325648i	−0.359338	+	0.933207i	$0.616998\pi$
$164$	−2.20738	−	0.934625i	−0.172368	−	0.0729819i
$165$	1.29680	+	0.314340i	0.100956	+	0.0244713i
$166$	−5.09002	+	11.8150i	−0.395062	+	0.917025i
$167$	0.107071	−	3.42070i	0.00828542	−	0.264702i	−0.986566	−	0.163361i	$-0.947766\pi$
$167$	0.107071	−	3.42070i	0.00828542	−	0.264702i	0.994852	−	0.101341i	$-0.0323132\pi$
$168$	−21.0123	−	18.1863i	−1.62113	−	1.40311i
$169$	0.320091	−	0.243763i	0.0246224	−	0.0187510i
$170$	2.69879	−	1.56566i	0.206988	−	0.120081i
$171$	−23.3163	+	6.58769i	−1.78304	+	0.503774i
$172$	0.888646	+	0.363212i	0.0677586	+	0.0276947i
$173$	−10.1550	−	21.3305i	−0.772070	−	1.62173i	−0.783186	−	0.621787i	$-0.786407\pi$
$173$	−10.1550	−	21.3305i	−0.772070	−	1.62173i	0.0111156	−	0.999938i	$-0.496462\pi$
$174$	−3.00085	+	9.90642i	−0.227494	+	0.751004i
$175$	15.7512	+	54.4448i	1.19068	+	4.11564i
$176$	0.569573	+	0.0572230i	0.0429332	+	0.00431334i
$177$	1.49601	+	4.52699i	0.112447	+	0.340269i
$178$	9.23706	−	12.6138i	0.692347	−	0.945448i
$179$	−2.20740	+	4.09501i	−0.164989	+	0.306076i	−0.949345	−	0.314234i	$-0.898252\pi$
$179$	−2.20740	+	4.09501i	−0.164989	+	0.306076i	0.784357	+	0.620310i	$0.212993\pi$
$180$	0.351353	−	8.01533i	0.0261883	−	0.597427i
$181$	−1.81041	−	26.2574i	−0.134567	−	1.95170i	−0.274613	−	0.961555i	$-0.588550\pi$
$181$	−1.81041	−	26.2574i	−0.134567	−	1.95170i	0.140046	−	0.990145i	$-0.455275\pi$
$182$	−20.0460	+	16.0743i	−1.48591	+	1.19151i
$183$	−23.9826	−	7.75924i	−1.77284	−	0.573580i
$184$	2.25014	+	11.4526i	0.165882	+	0.844298i
$185$	9.76982	−	14.4497i	0.718292	−	1.06236i
$186$	−1.50188	+	15.9522i	−0.110123	+	1.16967i
$187$	−0.0560346	−	0.00848001i	−0.00409765	−	0.000620120i
$188$	1.03697	−	6.07847i	0.0756286	−	0.443318i
$189$	9.99575	−	2.42294i	0.727084	−	0.176243i
$190$	40.9486	+	6.72226i	2.97072	+	0.487684i
$191$	1.06702	−	18.9245i	0.0772069	−	1.36933i	−0.688078	−	0.725637i	$-0.741545\pi$
$191$	1.06702	−	18.9245i	0.0772069	−	1.36933i	0.765285	−	0.643692i	$-0.222598\pi$
$192$	1.27676	+	13.5610i	0.0921420	+	0.978682i
$193$	5.34147	+	2.92258i	0.384487	+	0.210372i	0.660575	−	0.750760i	$-0.270313\pi$
$193$	5.34147	+	2.92258i	0.384487	+	0.210372i	−0.276087	+	0.961133i	$0.589038\pi$
$194$	−2.77634	+	3.59873i	−0.199330	+	0.258374i
$195$	39.4319	+	9.03717i	2.82378	+	0.647165i
$196$	4.79198	−	4.04372i	0.342284	−	0.288837i
$197$	1.48609	−	0.111812i	0.105880	−	0.00796631i	−0.0219817	−	0.999758i	$-0.506998\pi$
$197$	1.48609	−	0.111812i	0.105880	−	0.00796631i	0.127861	+	0.991792i	$0.459189\pi$
$198$	−0.487586	+	0.556278i	−0.0346512	+	0.0395330i
$199$	−0.101312	−	16.1886i	−0.00718182	−	1.14758i	−0.822570	−	0.568665i	$-0.807460\pi$
$199$	−0.101312	−	16.1886i	−0.00718182	−	1.14758i	0.815388	−	0.578915i	$-0.196524\pi$
$200$	14.0686	−	26.8998i	0.994801	−	1.90211i
$201$	−9.83235	+	31.0524i	−0.693521	+	2.19027i
$202$	−3.47600	−	1.95882i	−0.244571	−	0.137822i
$203$	10.0094	+	4.84234i	0.702522	+	0.339866i
$204$	0.0264560	+	0.603535i	0.00185229	+	0.0422559i
$205$	20.4482	−	2.31321i	1.42816	−	0.161562i
$206$	−9.70254	−	7.98174i	−0.676008	−	0.556114i
$207$	−17.3232	−	7.85176i	−1.20404	−	0.545735i
$208$	17.2884	+	1.51859i	1.19873	+	0.105296i
$209$	−0.503885	−	0.560561i	−0.0348544	−	0.0387748i
$210$	−76.0084	−	15.4283i	−5.24508	−	1.06465i
$211$	−15.8448	+	10.8582i	−1.09080	+	0.747512i	−0.969497	−	0.245103i	$-0.921178\pi$
$211$	−15.8448	+	10.8582i	−1.09080	+	0.747512i	−0.121305	+	0.992615i	$0.538708\pi$
$212$	2.75167	+	1.98870i	0.188985	+	0.136584i
$213$	−28.8192	−	24.3191i	−1.97466	−	1.66631i
$214$	9.92857	+	13.2081i	0.678703	+	0.902888i
$215$	−8.17700	+	1.02884i	−0.557667	+	0.0701661i
$216$	−4.76501	−	2.76435i	−0.324218	−	0.188090i
$217$	16.6754	+	4.26373i	1.13200	+	0.289441i
$218$	2.02244	−	15.3003i	0.136977	−	1.03627i
$219$	−15.3549	−	0.769388i	−1.03759	−	0.0519904i
$220$	0.228600	−	0.100183i	0.0154122	−	0.00675436i
$221$	−1.70191	−	0.235810i	−0.114483	−	0.0158623i
$222$	8.13428	+	15.0902i	0.545937	+	1.01279i
$223$	−18.0961	+	8.75451i	−1.21180	+	0.586245i	−0.927980	−	0.372631i	$-0.878456\pi$
$223$	−18.0961	+	8.75451i	−1.21180	+	0.586245i	−0.283824	+	0.958876i	$0.591603\pi$
$224$	−12.0622	−	0.755857i	−0.805939	−	0.0505028i
$225$	22.3752	+	44.1185i	1.49168	+	2.94123i
$226$	1.08386	−	2.35204i	0.0720973	−	0.156455i
$227$	1.82383	−	0.417993i	0.121052	−	0.0277432i	−0.162435	−	0.986719i	$-0.551935\pi$
$227$	1.82383	−	0.417993i	0.121052	−	0.0277432i	0.283487	+	0.958976i	$0.408509\pi$
$228$	−4.82781	+	6.42250i	−0.319729	+	0.425341i
$229$	−8.32575	+	14.5606i	−0.550181	+	0.962190i	0.447510	+	0.894279i	$0.352311\pi$
$229$	−8.32575	+	14.5606i	−0.550181	+	0.962190i	−0.997691	+	0.0679115i	$0.978366\pi$
$230$	21.1631	+	24.7632i	1.39546	+	1.63283i
$231$	0.901779	+	1.08232i	0.0593327	+	0.0712113i
$232$	−2.07964	−	5.58058i	−0.136535	−	0.366383i
$233$	21.5168	+	0.269325i	1.40961	+	0.0176441i	0.713684	−	0.700467i	$-0.247025\pi$
$233$	21.5168	+	0.269325i	1.40961	+	0.0176441i	0.695928	+	0.718112i	$0.254993\pi$
$234$	−14.5701	+	17.0486i	−0.952480	+	1.11450i
$235$	17.8629	+	49.8314i	1.16525	+	3.25064i
$236$	0.735643	+	0.504126i	0.0478863	+	0.0328158i
$237$	14.1622	+	14.6125i	0.919936	+	0.949181i
$238$	3.27318	+	0.370281i	0.212169	+	0.0240017i
$239$	−0.218309	+	3.16625i	−0.0141212	+	0.204808i	0.985301	+	0.170826i	$0.0546436\pi$
$239$	−0.218309	+	3.16625i	−0.0141212	+	0.204808i	−0.999422	+	0.0339820i	$0.989181\pi$
$240$	29.8824	+	43.0258i	1.92890	+	2.77730i
$241$	−25.9048	−	8.02442i	−1.66868	−	0.516898i	−0.690265	−	0.723557i	$-0.742506\pi$
$241$	−25.9048	−	8.02442i	−1.66868	−	0.516898i	−0.978413	+	0.206659i	$0.933741\pi$
$242$	16.7416	+	4.50463i	1.07619	+	0.289568i
$243$	−19.6468	+	8.90492i	−1.26034	+	0.571251i
$244$	−4.44817	+	1.56318i	−0.284765	+	0.100072i
$245$	−18.7966	+	50.4394i	−1.20087	+	3.22246i
$246$	−7.29920	+	18.8620i	−0.465380	+	1.20260i
$247$	−15.4880	−	16.8023i	−0.985479	−	1.06910i
$248$	−4.87323	−	7.82541i	−0.309451	−	0.496914i
$249$	19.8942	+	7.84211i	1.26074	+	0.496973i
$250$	−1.61069	−	51.4581i	−0.101869	−	3.25450i
$251$	0.778633	−	0.958666i	0.0491469	−	0.0605105i	−0.751063	−	0.660231i	$-0.770459\pi$
$251$	0.778633	−	0.958666i	0.0491469	−	0.0605105i	0.800210	+	0.599720i	$0.204721\pi$
$252$	5.34023	−	6.57498i	0.336403	−	0.414185i
$253$	−0.0185111	−	0.591390i	−0.00116378	−	0.0371804i
$254$	3.93957	+	1.55295i	0.247191	+	0.0974405i
$255$	−2.74154	−	4.40234i	−0.171682	−	0.275686i
$256$	7.54046	+	8.18030i	0.471279	+	0.511269i
$257$	1.86463	−	4.81842i	0.116312	−	0.300565i	−0.862261	−	0.506464i	$-0.830952\pi$
$257$	1.86463	−	4.81842i	0.116312	−	0.300565i	0.978573	+	0.205899i	$0.0660119\pi$
$258$	2.82847	−	7.59001i	0.176093	−	0.472533i
$259$	17.3737	−	6.10547i	1.07955	−	0.379376i
$260$	6.89200	−	3.12381i	0.427424	−	0.193730i
$261$	9.37152	+	2.52157i	0.580082	+	0.156081i
$262$	−28.8919	−	8.94971i	−1.78495	−	0.552915i
$263$	4.86859	+	7.00997i	0.300210	+	0.432253i	0.942499	−	0.334209i	$-0.108469\pi$
$263$	4.86859	+	7.00997i	0.300210	+	0.432253i	−0.642289	+	0.766463i	$0.722015\pi$
$264$	0.0519013	−	0.752753i	0.00319430	−	0.0463287i
$265$	−28.9614	−	3.27628i	−1.77909	−	0.201260i
$266$	30.4905	+	31.4598i	1.86949	+	1.92892i
$267$	−21.4369	−	14.6904i	−1.31192	−	0.899041i
$268$	2.05587	+	5.73517i	0.125582	+	0.350331i
$269$	−5.42348	+	6.34606i	−0.330675	+	0.386926i	−0.900511	−	0.434833i	$-0.856808\pi$
$269$	−5.42348	+	6.34606i	−0.330675	+	0.386926i	0.569836	+	0.821759i	$0.307007\pi$
$270$	−15.3734	−	0.192429i	−0.935597	−	0.0117108i
$271$	−4.60414	−	12.3549i	−0.279682	−	0.750508i	−0.998471	−	0.0552796i	$-0.982395\pi$
$271$	−4.60414	−	12.3549i	−0.279682	−	0.750508i	0.718789	−	0.695228i	$-0.244697\pi$
$272$	−1.42420	−	1.70933i	−0.0863546	−	0.103643i
$273$	27.7482	+	32.4684i	1.67940	+	1.96508i
$274$	−4.77045	+	8.34285i	−0.288193	+	0.504010i
$275$	−0.924682	+	1.23012i	−0.0557604	+	0.0741788i
$276$	−6.14775	+	1.40897i	−0.370051	+	0.0848099i
$277$	6.22364	−	13.5057i	0.373942	−	0.811477i	−0.625568	−	0.780170i	$-0.715133\pi$
$277$	6.22364	−	13.5057i	0.373942	−	0.811477i	0.999510	−	0.0313072i	$-0.00996701\pi$
$278$	11.3604	+	22.3999i	0.681352	+	1.34346i
$279$	14.9931	+	0.939519i	0.897615	+	0.0562476i
$280$	40.1699	−	19.4333i	2.40061	−	1.16136i
$281$	8.19233	+	15.1978i	0.488713	+	0.906627i	0.998915	+	0.0465721i	$0.0148297\pi$
$281$	8.19233	+	15.1978i	0.488713	+	0.906627i	−0.510202	+	0.860055i	$0.670429\pi$
$282$	−51.5347	−	7.14044i	−3.06885	−	0.425207i
$283$	26.7389	−	11.7183i	1.58946	−	0.696579i	0.595204	−	0.803575i	$-0.297071\pi$
$283$	26.7389	−	11.7183i	1.58946	−	0.696579i	0.994260	+	0.106995i	$0.0341230\pi$
$284$	−7.04455	−	0.352982i	−0.418017	−	0.0209456i
$285$	9.03886	−	68.3814i	0.535416	−	4.05056i
$286$	−0.675920	−	0.172825i	−0.0399680	−	0.0102194i
$287$	18.7927	+	10.9023i	1.10930	+	0.643543i
$288$	−10.4660	+	1.31684i	−0.616715	+	0.0775956i
$289$	−10.0824	−	13.4128i	−0.593085	−	0.788989i
$290$	−12.7029	−	10.7193i	−0.745939	−	0.629461i
$291$	6.12330	+	4.42546i	0.358954	+	0.259425i
$292$	−2.37215	+	1.62560i	−0.138820	+	0.0951312i
$293$	−3.64590	−	0.740051i	−0.212996	−	0.0432342i	0.0912491	−	0.995828i	$-0.470914\pi$
$293$	−3.64590	−	0.740051i	−0.212996	−	0.0432342i	−0.304245	+	0.952594i	$0.598404\pi$
$294$	−35.3664	−	39.3443i	−2.06261	−	2.29461i
$295$	−7.62659	−	0.669912i	−0.444037	−	0.0390038i
$296$	−8.98357	−	4.07181i	−0.522159	−	0.236669i
$297$	0.215666	+	0.177416i	0.0125142	+	0.0102947i
$298$	−7.41457	+	0.838778i	−0.429514	+	0.0485891i
$299$	−0.785570	−	17.9210i	−0.0454307	−	1.03640i
$300$	14.7670	+	7.14397i	0.852573	+	0.412457i
$301$	−7.58031	−	4.27170i	−0.436922	−	0.246217i
$302$	8.77007	−	27.6975i	0.504661	−	1.59381i
$303$	−3.07361	+	5.87688i	−0.176574	+	0.337618i
$304$	−0.185183	−	29.5903i	−0.0106210	−	1.69712i
$305$	26.6797	−	30.4384i	1.52768	−	1.74290i
$306$	2.86695	−	0.215707i	0.163892	−	0.0123312i
$307$	−2.62659	+	2.21645i	−0.149907	+	0.126499i	−0.716760	−	0.697319i	$-0.754376\pi$
$307$	−2.62659	+	2.21645i	−0.149907	+	0.126499i	0.566853	+	0.823819i	$0.308161\pi$
$308$	0.256848	+	0.0588655i	0.0146353	+	0.00335417i
$309$	−12.7563	+	16.5348i	−0.725678	+	0.940634i
$310$	−22.5711	−	12.3498i	−1.28195	−	0.701420i
$311$	−0.740623	−	7.86650i	−0.0419969	−	0.446068i	−0.991292	−	0.131682i	$-0.957962\pi$
$311$	−0.740623	−	7.86650i	−0.0419969	−	0.446068i	0.949295	−	0.314386i	$-0.101799\pi$
$312$	1.28776	−	22.8395i	0.0729050	−	1.29303i
$313$	−6.61703	−	1.08627i	−0.374017	−	0.0613998i	−0.0279489	−	0.999609i	$-0.508898\pi$
$313$	−6.61703	−	1.08627i	−0.374017	−	0.0613998i	−0.346068	+	0.938210i	$0.612483\pi$
$314$	−9.82093	+	2.38056i	−0.554227	+	0.134343i
$315$	−12.2286	+	71.6814i	−0.689005	+	4.03879i
$316$	3.76345	+	0.569542i	0.211710	+	0.0320393i
$317$	1.75560	−	18.6470i	0.0986041	−	1.04732i	−0.797453	−	0.603381i	$-0.793820\pi$
$317$	1.75560	−	18.6470i	0.0986041	−	1.04732i	0.896057	−	0.443939i	$-0.146419\pi$
$318$	16.0448	−	23.7303i	0.899745	−	1.33073i
$319$	0.0582042	+	0.296244i	0.00325881	+	0.0165865i
$320$	−20.8102	−	6.73284i	−1.16332	−	0.376377i
$321$	21.4276	−	17.1822i	1.19597	−	0.959014i
$322$	2.36559	+	34.3095i	0.131829	+	1.91199i
$323$	−0.128294	+	2.92674i	−0.00713848	+	0.162848i
$324$	−1.29870	+	2.40926i	−0.0721502	+	0.133848i
$325$	−27.5650	+	37.6420i	−1.52903	+	2.08800i
$326$	0.0579860	+	0.175468i	0.00321155	+	0.00971830i
$327$	−25.5250	−	2.56440i	−1.41153	−	0.141812i
$328$	−3.23392	−	11.1782i	−0.178564	−	0.617214i
$329$	−16.2026	+	53.4882i	−0.893279	+	2.94890i
$330$	−0.905209	−	1.90138i	−0.0498301	−	0.104668i
$331$	−0.888592	−	0.363190i	−0.0488414	−	0.0199627i	0.353790	−	0.935325i	$-0.384893\pi$
$331$	−0.888592	−	0.363190i	−0.0488414	−	0.0199627i	−0.402632	+	0.915362i	$0.631905\pi$
$332$	3.84916	−	1.08753i	0.211250	−	0.0596858i
$333$	13.9027	−	8.06542i	0.761862	−	0.441983i
$334$	−4.29700	+	3.27235i	−0.235121	+	0.179055i
$335$	−39.5475	−	34.2287i	−2.16071	−	1.87011i
$336$	−1.73029	+	55.2791i	−0.0943951	+	3.01572i
$337$	−11.6411	+	27.0216i	−0.634133	+	1.47196i	0.232287	+	0.972647i	$0.425379\pi$
$337$	−11.6411	+	27.0216i	−0.634133	+	1.47196i	−0.866421	+	0.499315i	$0.833585\pi$
$338$	−0.617100	−	0.149583i	−0.0335658	−	0.00813625i
$339$	−3.96404	−	1.67841i	−0.215297	−	0.0911585i
$340$	−0.906865	−	0.344428i	−0.0491817	−	0.0186792i
$341$	0.179517	+	0.431482i	0.00972140	+	0.0233661i
$342$	31.2693	+	22.0086i	1.69085	+	1.19009i
$343$	−21.5556	+	13.9920i	−1.16389	+	0.755496i
$344$	1.35108	+	4.46018i	0.0728452	+	0.240477i
$345$	40.0409	−	36.4481i	2.15573	−	1.96230i
$346$	−16.0265	+	33.6635i	−0.861591	+	1.80976i
$347$	−18.8170	−	17.1286i	−1.01015	−	0.919511i	−0.0133860	−	0.999910i	$-0.504261\pi$
$347$	−18.8170	−	17.1286i	−1.01015	−	0.919511i	−0.996763	+	0.0803990i	$0.974381\pi$
$348$	2.97903	−	1.21760i	0.159693	−	0.0652704i
$349$	13.2329	−	10.3417i	0.708342	−	0.553576i	−0.195886	−	0.980627i	$-0.562758\pi$
$349$	13.2329	−	10.3417i	0.708342	−	0.553576i	0.904228	+	0.427051i	$0.140447\pi$
$350$	51.0245	−	73.4670i	2.72738	−	3.92698i
$351$	6.60525	+	5.29655i	0.352562	+	0.282709i
$352$	−0.180387	−	0.274127i	−0.00961467	−	0.0146110i
$353$	10.6684	−	4.99735i	0.567822	−	0.265982i	−0.118896	−	0.992907i	$-0.537935\pi$
$353$	10.6684	−	4.99735i	0.567822	−	0.265982i	0.686717	+	0.726925i	$0.259051\pi$
$354$	4.05721	−	6.33690i	0.215638	−	0.336803i
$355$	54.1740	−	27.0501i	2.87526	−	1.43567i
$356$	−4.85483	+	0.243262i	−0.257306	+	0.0128928i
$357$	0.444966	−	5.45730i	0.0235501	−	0.288831i
$358$	7.21283	−	1.37031i	0.381210	−	0.0724230i
$359$	−17.0416	+	27.3654i	−0.899423	+	1.44429i	−0.00354310	+	0.999994i	$0.501128\pi$
$359$	−17.0416	+	27.3654i	−0.899423	+	1.44429i	−0.895880	+	0.444296i	$0.853454\pi$
$360$	31.2784	−	23.2071i	1.64852	−	1.22312i
$361$	−13.3454	+	14.8465i	−0.702391	+	0.781394i
$362$	−30.3649	+	28.3433i	−1.59594	+	1.48969i
$363$	6.61335	−	28.0487i	0.347111	−	1.47218i
$364$	7.80871	+	1.68705i	0.409287	+	0.0884256i
$365$	10.8901	−	22.1556i	0.570012	−	1.15968i
$366$	14.3568	+	37.0997i	0.750441	+	1.93923i
$367$	−2.68944	+	0.0336636i	−0.140387	+	0.00175722i	−0.0826788	−	0.996576i	$-0.526348\pi$
$367$	−2.68944	+	0.0336636i	−0.140387	+	0.00175722i	−0.0577086	+	0.998333i	$0.518379\pi$
$368$	14.8691	−	17.8459i	0.775103	−	0.930281i
$369$	17.8901	+	6.28694i	0.931319	+	0.327285i
$370$	−27.4220	+	2.40872i	−1.42560	+	0.125224i
$371$	−22.4946	−	20.9971i	−1.16786	−	1.09011i
$372$	4.14428	−	2.76443i	0.214871	−	0.143329i
$373$	−3.23792	+	12.3412i	−0.167653	+	0.639001i	0.829144	+	0.559034i	$0.188828\pi$
$373$	−3.23792	+	12.3412i	−0.167653	+	0.639001i	−0.996798	+	0.0799667i	$0.974519\pi$
$374$	0.0453648	+	0.0770815i	0.00234576	+	0.00398579i
$375$	−85.4086	+	5.35199i	−4.41048	+	0.276375i
$376$	26.0783	−	14.6958i	1.34489	−	0.757879i
$377$	1.87688	+	8.95858i	0.0966641	+	0.461390i
$378$	−12.9137	−	9.83435i	−0.664210	−	0.505824i
$379$	−8.72967	−	1.09837i	−0.448413	−	0.0564196i	−0.102599	−	0.994723i	$-0.532716\pi$
$379$	−8.72967	−	1.09837i	−0.448413	−	0.0564196i	−0.345814	+	0.938303i	$0.612397\pi$
$380$	−6.40427	−	11.2002i	−0.328532	−	0.574557i
$381$	2.37519	−	6.62595i	0.121685	−	0.339457i
$382$	−24.2448	+	17.5223i	−1.24047	+	0.896518i
$383$	25.4399	+	1.91408i	1.29992	+	0.0978050i	0.706859	−	0.707354i	$-0.250111\pi$
$383$	25.4399	+	1.91408i	1.29992	+	0.0978050i	0.593059	+	0.805159i	$0.297920\pi$
$384$	25.5184	−	25.0437i	1.30223	−	1.27801i
$385$	−2.16907	+	0.642261i	−0.110546	+	0.0327326i
$386$	−1.73438	−	9.45137i	−0.0882776	−	0.481062i
$387$	−7.19570	−	2.42797i	−0.365778	−	0.123421i
$388$	1.41273	−	0.0353716i	0.0717203	−	0.00179572i
$389$	5.87194	+	23.5790i	0.297719	+	1.19550i	0.913253	+	0.407392i	$0.133562\pi$
$389$	5.87194	+	23.5790i	0.297719	+	1.19550i	−0.615534	+	0.788110i	$0.711060\pi$
$390$	−28.1630	−	57.2971i	−1.42609	−	2.90135i
$391$	−1.55864	+	1.69089i	−0.0788236	+	0.0855121i
$392$	29.9034	+	5.68110i	1.51035	+	0.286939i
$393$	−13.3665	+	48.4664i	−0.674253	+	2.44480i
$394$	−1.61560	−	1.70926i	−0.0813927	−	0.0861111i
$395$	−30.5473	+	11.6019i	−1.53700	+	0.583754i
$396$	0.229827	+	0.00863381i	0.0115492	+	0.000433865i
$397$	0.250077	−	0.0672874i	0.0125510	−	0.00337706i	−0.253545	−	0.967323i	$-0.581597\pi$
$397$	0.250077	−	0.0672874i	0.0125510	−	0.00337706i	0.266096	+	0.963946i	$0.414266\pi$
$398$	−19.7308	+	16.2314i	−0.989013	+	0.813606i
$399$	50.6815	−	52.2927i	2.53725	−	2.61791i
$400$	−59.2079	+	12.0181i	−2.96039	+	0.600905i
$401$	−4.71365	−	3.49731i	−0.235388	−	0.174647i	0.471729	−	0.881744i	$-0.343630\pi$
$401$	−4.71365	−	3.49731i	−0.235388	−	0.174647i	−0.707117	+	0.707096i	$0.750005\pi$
$402$	47.8232	−	18.8515i	2.38520	−	0.940227i
$403$	5.60581	+	13.0123i	0.279245	+	0.648189i
$404$	0.208615	+	1.22286i	0.0103790	+	0.0608394i
$405$	−0.441110	−	23.4925i	−0.0219189	−	1.16735i
$406$	−4.02710	−	17.0799i	−0.199862	−	0.847659i
$407$	0.415960	+	0.277465i	0.0206184	+	0.0137534i
$408$	−2.19325	+	1.94682i	−0.108582	+	0.0963820i
$409$	3.39012	+	3.86773i	0.167631	+	0.191247i	0.829723	−	0.558176i	$-0.188499\pi$
$409$	3.39012	+	3.86773i	0.167631	+	0.191247i	−0.662092	+	0.749423i	$0.730331\pi$
$410$	−23.1792	−	22.7480i	−1.14474	−	1.12345i
$411$	14.1089	+	7.49175i	0.695938	+	0.369541i
$412$	−0.0244457	+	3.90616i	−0.00120435	+	0.192443i
$413$	−6.04498	−	5.36578i	−0.297454	−	0.264033i
$414$	7.61751	+	29.0338i	0.374380	+	1.42693i
$415$	−24.2044	+	24.3564i	−1.18815	+	1.19561i
$416$	−5.57247	−	8.24174i	−0.273213	−	0.404084i
$417$	36.6244	−	20.0390i	1.79350	−	0.981315i
$418$	−0.185351	+	1.17502i	−0.00906582	+	0.0574721i
$419$	15.6367	−	2.76839i	0.763904	−	0.135245i	0.221269	−	0.975213i	$-0.428980\pi$
$419$	15.6367	−	2.76839i	0.763904	−	0.135245i	0.542636	+	0.839968i	$0.317426\pi$
$420$	11.1755	+	21.3680i	0.545307	+	1.04265i
$421$	−0.498853	+	0.264889i	−0.0243126	+	0.0129099i	−0.481092	−	0.876670i	$-0.659760\pi$
$421$	−0.498853	+	0.264889i	−0.0243126	+	0.0129099i	0.456780	+	0.889580i	$0.349003\pi$
$422$	29.0669	+	8.60671i	1.41495	+	0.418968i
$423$	−5.17978	+	48.5036i	−0.251850	+	2.35832i
$424$	0.927794	+	16.4552i	0.0450577	+	0.799135i
$425$	5.91388	−	0.894979i	0.286865	−	0.0434129i
$426$	−1.11724	+	59.5013i	−0.0541302	+	2.88285i
$427$	41.7695	−	9.02419i	2.02137	−	0.436711i
$428$	1.24147	−	4.98517i	0.0600087	−	0.240967i
$429$	−0.251981	+	1.13196i	−0.0121658	+	0.0546514i
$430$	9.39628	+	8.99342i	0.453129	+	0.433701i
$431$	1.32000	+	3.83270i	0.0635823	+	0.184615i	0.972770	−	0.231771i	$-0.0744520\pi$
$431$	1.32000	+	3.83270i	0.0635823	+	0.184615i	−0.909188	+	0.416386i	$0.863297\pi$
$432$	1.70829	+	10.8296i	0.0821903	+	0.521040i
$433$	−15.2589	−	19.7788i	−0.733297	−	0.950509i	0.266615	−	0.963803i	$-0.414095\pi$
$433$	−15.2589	−	19.7788i	−0.733297	−	0.950509i	−0.999912	+	0.0132943i	$0.995768\pi$
$434$	−11.3685	−	24.6702i	−0.545703	−	1.18421i
$435$	−17.1485	+	21.6619i	−0.822205	+	1.03861i
$436$	−4.08899	+	2.51102i	−0.195827	+	0.120256i
$437$	−30.2960	+	4.19769i	−1.44926	+	0.200803i
$438$	14.3352	+	19.5757i	0.684963	+	0.935364i
$439$	1.53064	−	2.14603i	0.0730534	−	0.102425i	−0.775997	−	0.630737i	$-0.782753\pi$
$439$	1.53064	−	2.14603i	0.0730534	−	0.102425i	0.849050	+	0.528312i	$0.177175\pi$
$440$	1.07714	+	0.554788i	0.0513507	+	0.0264485i
$441$	−35.8329	+	34.2966i	−1.70633	+	1.63317i
$442$	1.40449	+	2.31952i	0.0668046	+	0.110328i
$443$	16.6213	−	17.5848i	0.789701	−	0.835481i	−0.199826	−	0.979831i	$-0.564038\pi$
$443$	16.6213	−	17.5848i	0.789701	−	0.835481i	0.989527	+	0.144350i	$0.0461093\pi$
$444$	2.04739	−	4.92105i	0.0971649	−	0.233543i
$445$	35.2841	−	22.2806i	1.67263	−	1.05620i
$446$	28.7297	+	13.4577i	1.36039	+	0.637243i
$447$	1.77912	+	12.2749i	0.0841497	+	0.580583i
$448$	−13.4089	−	18.8000i	−0.633511	−	0.888215i
$449$	5.26913	−	15.9446i	0.248666	−	0.752474i	−0.747442	−	0.664327i	$-0.768718\pi$
$449$	5.26913	−	15.9446i	0.248666	−	0.752474i	0.996107	−	0.0881471i	$-0.0280945\pi$
$450$	31.7837	−	71.3072i	1.49830	−	3.36145i
$451$	0.0699777	+	0.585742i	0.00329512	+	0.0275815i
$452$	−0.780095	+	0.199462i	−0.0366926	+	0.00938190i
$453$	−46.4727	−	13.1302i	−2.18348	−	0.616910i
$454$	−2.32672	−	1.81836i	−0.109199	−	0.0853397i
$455$	−65.5118	+	20.2933i	−3.07124	+	0.951362i
$456$	−38.9767	+	1.46422i	−1.82525	+	0.0685684i
$457$	−4.52646	+	1.91654i	−0.211739	+	0.0896521i	−0.493183	−	0.869926i	$-0.664167\pi$
$457$	−4.52646	+	1.91654i	−0.211739	+	0.0896521i	0.281444	+	0.959578i	$0.409187\pi$
$458$	26.1211	−	4.28813i	1.22056	−	0.200371i
$459$	−0.115257	−	1.07927i	−0.00537975	−	0.0503760i
$460$	1.82799	−	9.96150i	0.0852305	−	0.464457i
$461$	10.1673	−	18.3092i	0.473537	−	0.852745i	−0.526460	−	0.850200i	$-0.676481\pi$
$461$	10.1673	−	18.3092i	0.473537	−	0.852745i	0.999997	−	0.00254454i	$-0.000809954\pi$
$462$	0.428625	−	2.18159i	0.0199414	−	0.101497i
$463$	18.5491	+	18.6656i	0.862051	+	0.867462i	0.992280	−	0.124022i	$-0.0395792\pi$
$463$	18.5491	+	18.6656i	0.862051	+	0.867462i	−0.130229	+	0.991484i	$0.541571\pi$
$464$	−6.01169	+	10.2147i	−0.279086	+	0.474208i
$465$	−19.3441	+	38.1418i	−0.897061	+	1.76878i
$466$	−21.0788	−	26.6267i	−0.976455	−	1.23346i
$467$	−12.6764	−	4.63380i	−0.586593	−	0.214427i	0.0328604	−	0.999460i	$-0.489538\pi$
$467$	−12.6764	−	4.63380i	−0.586593	−	0.214427i	−0.619454	+	0.785033i	$0.712646\pi$
$468$	6.97050	+	0.174526i	0.322211	+	0.00806748i
$469$	−11.9986	−	53.9004i	−0.554044	−	2.48889i
$470$	43.2718	−	71.4638i	1.99598	−	3.29638i
$471$	4.46577	+	16.1927i	0.205772	+	0.746118i
$472$	0.351821	+	4.31491i	0.0161939	+	0.198610i
$473$	−0.0309591	−	0.234214i	−0.00142350	−	0.0107692i
$474$	3.80964	−	31.8882i	0.174982	−	1.46468i
$475$	68.3041	+	40.7767i	3.13401	+	1.87096i
$476$	−0.552235	−	0.862528i	−0.0253117	−	0.0395339i
$477$	−22.7088	−	14.3398i	−1.03976	−	0.656573i
$478$	4.09597	−	2.88291i	0.187345	−	0.131861i
$479$	10.8123	−	26.9337i	0.494025	−	1.23063i	−0.447681	−	0.894193i	$-0.647750\pi$
$479$	10.8123	−	26.9337i	0.494025	−	1.23063i	0.941706	−	0.336438i	$-0.109222\pi$
$480$	8.34559	−	28.8470i	0.380922	−	1.31668i
$481$	12.7151	+	8.25354i	0.579761	+	0.376329i
$482$	15.9445	+	39.7184i	0.726254	+	1.80912i
$483$	56.8787	−	5.71440i	2.58807	−	0.260014i
$484$	−2.19450	−	4.92340i	−0.0997499	−	0.223791i
$485$	−10.4167	+	6.21865i	−0.472999	+	0.282374i
$486$	30.4569	+	15.2077i	1.38155	+	0.689836i
$487$	−21.1965	−	9.28934i	−0.960507	−	0.420940i	−0.138465	−	0.990367i	$-0.544217\pi$
$487$	−21.1965	−	9.28934i	−0.960507	−	0.420940i	−0.822042	+	0.569427i	$0.807165\pi$
$488$	−19.5040	−	11.9773i	−0.882906	−	0.542186i
$489$	0.288507	−	0.105463i	0.0130467	−	0.00476918i
$490$	80.4921	−	27.1596i	3.63626	−	1.22695i
$491$	16.8286	+	30.3049i	0.759464	+	1.36764i	0.924434	+	0.381343i	$0.124538\pi$
$491$	16.8286	+	30.3049i	0.759464	+	1.36764i	−0.164970	+	0.986299i	$0.552753\pi$
$492$	5.98291	−	1.93569i	0.269730	−	0.0872677i
$493$	0.645031	−	0.980226i	0.0290507	−	0.0441472i
$494$	−5.17307	+	35.6912i	−0.232747	+	1.60582i
$495$	−1.75527	+	0.904061i	−0.0788934	+	0.0406345i
$496$	−5.97440	+	17.3470i	−0.268259	+	0.778904i
$497$	62.9497	+	11.1449i	2.82368	+	0.499916i
$498$	−10.1874	−	32.1737i	−0.456507	−	1.44174i
$499$	2.22036	−	10.5981i	0.0993968	−	0.474434i	−0.899870	−	0.436157i	$-0.856339\pi$
$499$	2.22036	−	10.5981i	0.0993968	−	0.474434i	0.999267	−	0.0382767i	$-0.0121868\pi$
$500$	−12.1031	+	10.4754i	−0.541269	+	0.468473i
$501$	5.66012	+	6.96884i	0.252876	+	0.311345i
$502$	−1.94912			−0.0869934
$503$	−11.8158	−	19.0627i	−0.526843	−	0.849963i
$503$	−11.8158	−	19.0627i	−0.526843	−	0.849963i
$504$	41.1195			1.83161
$505$	−6.71412	−	8.26653i	−0.298774	−	0.367856i
$506$	−0.706053	+	0.611095i	−0.0313879	+	0.0271665i
$507$	−0.216425	+	1.03303i	−0.00961179	+	0.0458783i
$508$	−0.397436	−	1.25518i	−0.0176334	−	0.0556895i
$509$	19.8756	+	3.51886i	0.880971	+	0.155971i	0.596403	−	0.802685i	$-0.296596\pi$
$509$	19.8756	+	3.51886i	0.880971	+	0.155971i	0.284568	+	0.958656i	$0.408150\pi$
$510$	−2.66525	+	7.73870i	−0.118019	+	0.342675i
$511$	23.1712	−	11.9345i	1.02503	−	0.527949i
$512$	−1.39155	+	9.60090i	−0.0614985	+	0.424304i
$513$	7.93543	−	12.0591i	0.350358	−	0.532424i
$514$	−7.75798	+	2.50999i	−0.342190	+	0.110711i
$515$	−16.2802	−	29.3173i	−0.717389	−	1.29187i
$516$	−2.38619	+	0.805149i	−0.105046	+	0.0354447i
$517$	−1.42524	+	0.520991i	−0.0626820	+	0.0229131i
$518$	−24.7658	−	15.2085i	−1.08815	−	0.668223i
$519$	56.7618	+	24.8758i	2.49157	+	1.09192i
$520$	32.8641	+	16.4097i	1.44119	+	0.719614i
$521$	25.4228	−	15.1771i	1.11379	−	0.664919i	0.166740	−	0.986001i	$-0.446676\pi$
$521$	25.4228	−	15.1771i	1.11379	−	0.664919i	0.947052	+	0.321082i	$0.104046\pi$
$522$	−6.23544	−	13.9893i	−0.272918	−	0.612295i
$523$	−29.7779	+	2.99168i	−1.30210	+	0.130817i	−0.726641	−	0.687017i	$-0.758920\pi$
$523$	−29.7779	+	2.99168i	−1.30210	+	0.130817i	−0.575454	+	0.817834i	$0.695175\pi$
$524$	3.50339	+	8.72705i	0.153046	+	0.381243i
$525$	−124.711	−	80.9514i	−5.44284	−	3.53301i
$526$	3.74331	−	12.9389i	0.163216	−	0.564164i
$527$	0.676681	−	1.68563i	0.0294767	−	0.0734273i
$528$	−1.22800	+	0.864314i	−0.0534417	+	0.0376145i
$529$	−0.853332	−	0.538848i	−0.0371014	−	0.0234282i
$530$	24.8024	+	38.7385i	1.07735	+	1.68269i
$531$	−6.05744	−	3.61621i	−0.262870	−	0.156930i
$532$	1.61583	−	13.5252i	0.0700553	−	0.586392i
$533$	2.34364	+	17.7303i	0.101514	+	0.767984i
$534$	3.33299	+	40.8776i	0.144233	+	1.76895i
$535$	11.7256	+	42.5165i	0.506943	+	1.83815i
$536$	−15.3190	+	25.2995i	−0.661681	+	1.09277i
$537$	−2.65171	−	11.9121i	−0.114430	−	0.514045i
$538$	13.1704	+	0.329757i	0.567814	+	0.0142168i
$539$	−1.44925	−	0.529766i	−0.0624234	−	0.0228186i
$540$	2.96701	+	3.74793i	0.127680	+	0.161285i
$541$	2.04154	−	4.02541i	0.0877725	−	0.173066i	−0.843763	−	0.536716i	$-0.819665\pi$
$541$	2.04154	−	4.02541i	0.0877725	−	0.173066i	0.931536	+	0.363650i	$0.118470\pi$
$542$	−10.5541	+	17.9331i	−0.453340	+	0.770291i
$543$	48.6686	+	48.9741i	2.08857	+	2.10168i
$544$	−0.245887	+	1.25150i	−0.0105423	+	0.0536577i
$545$	19.9986	−	36.0135i	0.856647	−	1.54265i
$546$	12.1660	−	66.2977i	0.520657	−	2.83728i
$547$	3.15374	+	29.5317i	0.134844	+	1.26268i	0.835623	+	0.549304i	$0.185107\pi$
$547$	3.15374	+	29.5317i	0.134844	+	1.26268i	−0.700778	+	0.713379i	$0.747164\pi$
$548$	2.94855	−	0.484043i	0.125956	−	0.0206773i
$549$	34.3457	−	14.5422i	1.46584	−	0.620648i
$550$	2.42697	−	0.0911729i	0.103486	−	0.00388763i
$551$	14.9076	−	4.61784i	0.635083	−	0.196727i
$552$	−24.1245	−	18.8536i	−1.02681	−	0.802461i
$553$	−33.1989	−	9.37988i	−1.41176	−	0.398873i
$554$	−22.7372	+	5.81367i	−0.966013	+	0.246999i
$555$	5.42788	+	45.4336i	0.230401	+	1.92855i
$556$	3.17915	−	7.13248i	0.134826	−	0.302484i
$557$	−9.33598	+	28.2511i	−0.395578	+	1.19704i	0.539313	+	0.842105i	$0.318684\pi$
$557$	−9.33598	+	28.2511i	−0.395578	+	1.19704i	−0.934891	+	0.354934i	$0.884503\pi$
$558$	−13.7669	−	19.3018i	−0.582798	−	0.817112i
$559$	−1.02740	−	7.08846i	−0.0434544	−	0.299810i
$560$	−80.4231	−	37.6722i	−3.39850	−	1.59194i
$561$	0.125704	−	0.0793773i	0.00530722	−	0.00335131i
$562$	10.4667	−	25.1573i	0.441509	−	1.06120i
$563$	−4.05542	+	4.29051i	−0.170915	+	0.180824i	−0.806549	−	0.591167i	$-0.798667\pi$
$563$	−4.05542	+	4.29051i	−0.170915	+	0.180824i	0.635633	+	0.771991i	$0.280739\pi$
$564$	8.37840	+	13.8370i	0.352794	+	0.582642i
$565$	4.99369	−	4.77958i	0.210086	−	0.201079i
$566$	−40.9598	−	21.0966i	−1.72167	−	0.886757i
$567$	14.4048	−	20.1962i	0.604943	−	0.848161i
$568$	−20.2299	−	27.6253i	−0.848827	−	1.15913i
$569$	28.7707	−	3.98636i	1.20613	−	0.167117i	0.494190	−	0.869354i	$-0.335465\pi$
$569$	28.7707	−	3.98636i	1.20613	−	0.167117i	0.711943	+	0.702237i	$0.247815\pi$
$570$	−92.7628	+	56.9650i	−3.88541	+	2.38600i
$571$	20.9895	−	26.5140i	0.878385	−	1.10958i	−0.114841	−	0.993384i	$-0.536636\pi$
$571$	20.9895	−	26.5140i	0.878385	−	1.10958i	0.993227	−	0.116193i	$-0.0370692\pi$
$572$	0.0907821	+	0.197003i	0.00379579	+	0.00823709i
$573$	30.3723	+	39.3689i	1.26882	+	1.64466i
$574$	−5.34263	−	33.8692i	−0.222997	−	1.41367i
$575$	20.3345	+	59.0422i	0.848006	+	2.46223i
$576$	−14.5602	−	13.9359i	−0.606675	−	0.580664i
$577$	−3.77462	+	16.9564i	−0.157139	+	0.705905i	0.831491	+	0.555538i	$0.187488\pi$
$577$	−3.77462	+	16.9564i	−0.157139	+	0.705905i	−0.988630	+	0.150367i	$0.951954\pi$
$578$	−6.39933	+	25.6968i	−0.266177	+	1.06884i
$579$	−15.6123	+	3.37299i	−0.648824	+	0.140177i
$580$	−0.0970166	+	5.16687i	−0.00402840	+	0.214543i
$581$	−35.8446	+	5.42456i	−1.48708	+	0.225048i
$582$	−0.671209	−	11.9045i	−0.0278225	−	0.493456i
$583$	0.0887207	−	0.830782i	0.00367444	−	0.0344075i
$584$	−13.3856	−	3.96346i	−0.553898	−	0.164009i
$585$	−52.8680	+	28.0727i	−2.18582	+	1.16066i
$586$	2.72100	+	5.20267i	0.112403	+	0.214920i
$587$	9.16138	−	1.62197i	0.378131	−	0.0669458i	0.0179760	−	0.999838i	$-0.494278\pi$
$587$	9.16138	−	1.62197i	0.378131	−	0.0669458i	0.360155	+	0.932893i	$0.382724\pi$
$588$	−2.56292	+	16.2475i	−0.105693	+	0.670034i
$589$	21.1929	−	11.5957i	0.873240	−	0.477793i
$590$	6.76762	+	10.0094i	0.278618	+	0.412079i
$591$	−2.75574	+	2.77304i	−0.113356	+	0.114067i
$592$	4.98159	+	18.9871i	0.204742	+	0.780364i
$593$	5.95803	+	5.28860i	0.244667	+	0.217177i	0.777235	−	0.629210i	$-0.216622\pi$
$593$	5.95803	+	5.28860i	0.244667	+	0.217177i	−0.532568	+	0.846387i	$0.678773\pi$
$594$	0.00275814	−	0.440722i	0.000113168	−	0.0180830i
$595$	7.76540	+	4.12340i	0.318351	+	0.169043i
$596$	1.65581	+	1.62501i	0.0678246	+	0.0665631i
$597$	27.9928	+	31.9365i	1.14567	+	1.30707i
$598$	−21.1722	+	18.7933i	−0.865795	+	0.768516i
$599$	−36.9992	−	24.6803i	−1.51175	−	1.00841i	−0.987637	−	0.156758i	$-0.949896\pi$
$599$	−36.9992	−	24.6803i	−1.51175	−	1.00841i	−0.524111	−	0.851650i	$-0.675602\pi$
$600$	18.2751	+	77.5088i	0.746077	+	3.16428i
$601$	−0.474103	−	25.2496i	−0.0193391	−	1.02995i	−0.866669	−	0.498884i	$-0.833743\pi$
$601$	−0.474103	−	25.2496i	−0.0193391	−	1.02995i	0.847330	−	0.531067i	$-0.178209\pi$
$602$	2.30926	+	13.5364i	0.0941184	+	0.551701i
$603$	−19.0689	−	44.2630i	−0.776544	−	1.80253i
$604$	−8.40359	+	3.31262i	−0.341937	+	0.134789i
$605$	37.1629	+	27.5732i	1.51089	+	1.12101i
$606$	10.2575	−	2.08209i	0.416684	−	0.0845792i
$607$	−15.7078	+	16.2071i	−0.637558	+	0.657826i	−0.957104	−	0.289744i	$-0.906430\pi$
$607$	−15.7078	+	16.2071i	−0.637558	+	0.657826i	0.319546	+	0.947571i	$0.396470\pi$
$608$	−13.1001	+	10.7767i	−0.531277	+	0.437052i
$609$	−28.1670	+	7.57881i	−1.14138	+	0.307109i
$610$	−63.8337	−	2.39801i	−2.58455	−	0.0970928i
$611$	−43.0086	+	16.3347i	−1.73994	+	0.660831i
$612$	−0.614029	−	0.649625i	−0.0248206	−	0.0262595i
$613$	1.79047	−	6.49214i	0.0723163	−	0.262215i	−0.918895	−	0.394502i	$-0.870917\pi$
$613$	1.79047	−	6.49214i	0.0723163	−	0.262215i	0.991211	+	0.132287i	$0.0422320\pi$
$614$	5.32862	+	1.01234i	0.215045	+	0.0408548i
$615$	−36.5881	+	39.6928i	−1.47537	+	1.60057i
$616$	0.564274	+	1.14800i	0.0227352	+	0.0462544i
$617$	1.25065	+	5.02202i	0.0503491	+	0.202179i	0.990258	−	0.139248i	$-0.0444684\pi$
$617$	1.25065	+	5.02202i	0.0503491	+	0.202179i	−0.939908	+	0.341427i	$0.889090\pi$
$618$	32.9479	−	0.824944i	1.32536	−	0.0331841i
$619$	−1.87082	−	0.631251i	−0.0751945	−	0.0253721i	0.281861	−	0.959455i	$-0.409048\pi$
$619$	−1.87082	−	0.631251i	−0.0751945	−	0.0253721i	−0.357056	+	0.934083i	$0.616219\pi$
$620$	1.44383	+	7.86806i	0.0579857	+	0.315989i
$621$	10.8657	−	3.21732i	0.436024	−	0.129107i
$622$	−8.89981	+	8.73427i	−0.356850	+	0.350212i
$623$	43.9330	+	3.30549i	1.76014	+	0.132432i
$624$	−36.8989	+	26.6677i	−1.47714	+	1.06756i
$625$	24.8676	−	69.3720i	0.994705	−	2.77488i
$626$	5.25307	+	9.18689i	0.209955	+	0.367182i
$627$	1.96181	+	0.246837i	0.0783472	+	0.00985770i
$628$	2.49959	+	1.90355i	0.0997446	+	0.0759598i
$629$	−0.398497	−	1.90208i	−0.0158891	−	0.0758409i
$630$	99.9792	−	56.3409i	3.98327	−	2.24467i
$631$	26.9541	−	1.68903i	1.07303	−	0.0672394i	0.483777	−	0.875191i	$-0.339265\pi$
$631$	26.9541	−	1.68903i	1.07303	−	0.0672394i	0.589248	+	0.807952i	$0.299424\pi$
$632$	9.37198	+	15.9244i	0.372797	+	0.633438i
$633$	12.7876	−	48.7392i	0.508261	−	1.93721i
$634$	−24.5899	+	16.4027i	−0.976591	+	0.651433i
$635$	8.26252	+	7.71245i	0.327888	+	0.306059i
$636$	−8.87210	+	0.779317i	−0.351802	+	0.0309019i
$637$	−44.1350	−	15.5100i	−1.74869	−	0.614528i
$638$	0.304996	−	0.366058i	0.0120749	−	0.0144924i
$639$	55.7925	−	0.698353i	2.20712	−	0.0276264i
$640$	20.7204	+	53.5440i	0.819046	+	2.11651i
$641$	1.32054	−	2.68662i	0.0521582	−	0.106115i	−0.869800	−	0.493405i	$-0.835752\pi$
$641$	1.32054	−	2.68662i	0.0521582	−	0.106115i	0.921958	+	0.387290i	$0.126589\pi$
$642$	−42.3686	−	9.15364i	−1.67216	−	0.361265i
$643$	6.24827	−	26.5003i	0.246408	−	1.04507i	−0.697949	−	0.716148i	$-0.745904\pi$
$643$	6.24827	−	26.5003i	0.246408	−	1.04507i	0.944357	−	0.328924i	$-0.106686\pi$
$644$	7.81654	−	7.29615i	0.308015	−	0.287509i
$645$	14.4530	−	16.0786i	0.569086	−	0.633095i
$646$	3.71300	−	2.75488i	0.146086	−	0.108389i
$647$	−16.0588	+	25.7872i	−0.631338	+	1.01380i	0.365222	+	0.930920i	$0.380993\pi$
$647$	−16.0588	+	25.7872i	−0.631338	+	1.01380i	−0.996560	+	0.0828788i	$0.973589\pi$
$648$	−13.0532	+	2.47988i	−0.512779	+	0.0974187i
$649$	0.0178352	−	0.218741i	0.000700094	−	0.00858632i
$650$	73.5392	−	3.68483i	2.88444	−	0.144531i
$651$	−40.3958	+	20.1704i	−1.58324	+	0.790542i
$652$	0.0309812	−	0.0483891i	0.00121332	−	0.00189506i
$653$	−33.6420	+	15.7588i	−1.31651	+	0.616689i	−0.949570	−	0.313554i	$-0.898480\pi$
$653$	−33.6420	+	15.7588i	−1.31651	+	0.616689i	−0.366944	+	0.930243i	$0.619596\pi$
$654$	22.2553	+	33.8204i	0.870250	+	1.32248i
$655$	−62.9831	−	50.5043i	−2.46096	−	1.97337i
$656$	−13.2108	+	19.0214i	−0.515795	+	0.742660i
$657$	17.9243	−	14.0080i	0.699293	−	0.546504i
$658$	81.6459	−	33.3708i	3.18289	−	1.30093i
$659$	−3.35368	−	3.05276i	−0.130641	−	0.118919i	0.605200	−	0.796074i	$-0.293093\pi$
$659$	−3.35368	−	3.05276i	−0.130641	−	0.118919i	−0.735841	+	0.677155i	$0.763213\pi$
$660$	−0.281442	+	0.591165i	−0.0109551	+	0.0230111i
$661$	0.0844367	−	0.0768605i	0.00328421	−	0.00298953i	−0.671508	−	0.740998i	$-0.734353\pi$
$661$	0.0844367	−	0.0768605i	0.00328421	−	0.00298953i	0.674792	+	0.738008i	$0.264233\pi$
$662$	0.439209	+	1.44992i	0.0170703	+	0.0563527i
$663$	3.78060	−	2.45403i	0.146826	−	0.0953067i
$664$	15.8784	+	11.1759i	0.616202	+	0.433708i
$665$	44.9187	+	107.965i	1.74187	+	4.18672i
$666$	−23.7132	−	9.00630i	−0.918869	−	0.348987i
$667$	11.2813	+	4.77659i	0.436813	+	0.184950i
$668$	1.63203	+	0.395599i	0.0631451	+	0.0153062i
$669$	20.8646	−	48.4313i	0.806672	−	1.87246i
$670$	−2.58245	+	82.5037i	−0.0997686	+	3.18740i
$671$	0.877320	+	0.759328i	0.0338686	+	0.0293135i
$672$	25.2232	−	19.2086i	0.973006	−	0.740986i
$673$	−25.7853	+	14.9590i	−0.993950	+	0.576625i	−0.907687	−	0.419647i	$-0.862154\pi$
$673$	−25.7853	+	14.9590i	−0.993950	+	0.576625i	−0.0862630	+	0.996272i	$0.527493\pi$
$674$	44.6850	−	12.6251i	1.72120	−	0.486301i
$675$	−27.2826	−	11.1511i	−1.05011	−	0.429205i
$676$	0.0848618	+	0.178251i	0.00326392	+	0.00685582i
$677$	1.89943	−	6.27041i	0.0730011	−	0.240992i	−0.912938	−	0.408099i	$-0.866192\pi$
$677$	1.89943	−	6.27041i	0.0730011	−	0.240992i	0.985939	+	0.167108i	$0.0534427\pi$
$678$	1.88802	+	6.52604i	0.0725090	+	0.250631i
$679$	−12.7441	−	1.28036i	−0.489075	−	0.0491357i
$680$	−1.47762	−	4.47135i	−0.0566641	−	0.171468i
$681$	−2.90001	+	3.96017i	−0.111129	+	0.151754i
$682$	0.349964	−	0.649229i	0.0134008	−	0.0248603i
$683$	−1.82408	+	41.6122i	−0.0697963	+	1.59225i	0.568649	+	0.822580i	$0.307466\pi$
$683$	−1.82408	+	41.6122i	−0.0697963	+	1.59225i	−0.638445	+	0.769667i	$0.720422\pi$
$684$	−0.817770	−	11.8606i	−0.0312682	−	0.453500i
$685$	−20.0122	+	16.0472i	−0.764626	+	0.613131i
$686$	38.5879	+	12.4846i	1.47329	+	0.476664i
$687$	−8.48266	−	43.1745i	−0.323634	−	1.64721i
$688$	5.19500	−	7.68346i	0.198058	−	0.292929i
$689$	2.37433	−	25.2189i	0.0904550	−	0.960764i
$690$	−84.4898	−	12.7863i	−3.21647	−	0.486766i
$691$	−1.44630	+	8.47787i	−0.0550197	+	0.322513i	−0.999989	−	0.00464520i	$-0.998521\pi$
$691$	−1.44630	+	8.47787i	−0.0550197	+	0.322513i	0.944969	+	0.327159i	$0.106091\pi$
$692$	11.2658	−	2.73079i	0.428261	−	0.103809i
$693$	−2.05698	−	0.337681i	−0.0781382	−	0.0128274i
$694$	−2.26062	+	40.0940i	−0.0858119	+	1.52195i
$695$	6.28377	+	66.7428i	0.238357	+	2.53170i
$696$	13.7055	+	7.49896i	0.519506	+	0.284247i
$697$	1.40049	−	1.81534i	0.0530475	−	0.0687608i
$698$	−25.8353	−	5.92104i	−0.977880	−	0.224115i
$699$	−43.1414	+	36.4049i	−1.63176	+	1.37696i
$700$	−27.7321	+	2.08655i	−1.04818	+	0.0788641i
$701$	12.1567	−	13.8693i	0.459151	−	0.523837i	−0.475350	−	0.879797i	$-0.657679\pi$
$701$	12.1567	−	13.8693i	0.459151	−	0.523837i	0.934501	+	0.355960i	$0.115846\pi$
$702$	−0.0836199	−	13.3616i	−0.00315603	−	0.504300i
$703$	11.9785	−	22.9035i	0.451779	−	0.863823i
$704$	0.189267	−	0.597742i	0.00713328	−	0.0225283i
$705$	−120.980	−	68.1753i	−4.55637	−	2.56763i
$706$	−16.7367	−	8.09688i	−0.629895	−	0.304730i
$707$	−0.492389	−	11.2327i	−0.0185182	−	0.422451i
$708$	−2.32463	+	0.262975i	−0.0873648	+	0.00988320i
$709$	−16.6533	−	13.6998i	−0.625429	−	0.514506i	0.268170	−	0.963372i	$-0.413581\pi$
$709$	−16.6533	−	13.6998i	−0.625429	−	0.514506i	−0.893599	+	0.448866i	$0.851828\pi$
$710$	−87.0391	−	39.4506i	−3.26652	−	1.48055i
$711$	−29.9948	−	2.63471i	−1.12489	−	0.0988095i
$712$	−15.7750	−	17.5493i	−0.591192	−	0.657688i
$713$	18.5846	+	3.77234i	0.696000	+	0.141275i
$714$	−7.12810	+	4.88479i	−0.266762	+	0.182809i
$715$	−1.50925	−	1.09077i	−0.0564428	−	0.0407926i
$716$	−1.74454	−	1.47214i	−0.0651967	−	0.0550163i
$717$	−5.00266	−	6.65511i	−0.186828	−	0.248540i
$718$	50.4795	−	6.35137i	1.88388	−	0.237031i
$719$	−5.02518	−	2.91529i	−0.187408	−	0.108722i	0.405148	−	0.914251i	$-0.367220\pi$
$719$	−5.02518	−	2.91529i	−0.187408	−	0.108722i	−0.592556	+	0.805529i	$0.701881\pi$
$720$	−75.0967	−	19.2014i	−2.79869	−	0.715595i
$721$	4.63950	−	35.0990i	0.172784	−	1.30716i
$722$	31.4658	+	1.57666i	1.17104	+	0.0586772i
$723$	65.1587	−	28.5557i	2.42328	−	1.06200i
$724$	12.7924	+	1.77246i	0.475425	+	0.0658730i
$725$	−15.1191	−	28.0479i	−0.561509	−	1.04167i
$726$	−40.9407	+	19.8063i	−1.51945	+	0.735079i
$727$	7.13514	+	0.447112i	0.264628	+	0.0165825i	0.194303	−	0.980942i	$-0.437756\pi$
$727$	7.13514	+	0.447112i	0.264628	+	0.0165825i	0.0703253	+	0.997524i	$0.477596\pi$
$728$	17.5416	+	34.5878i	0.650136	+	1.28191i
$729$	16.6787	−	36.1939i	0.617731	−	1.34051i
$730$	−37.9767	+	8.70366i	−1.40558	+	0.322137i
$731$	−0.551738	+	0.733984i	−0.0204068	+	0.0271474i
$732$	6.13944	−	10.7370i	0.226920	−	0.396852i
$733$	18.8609	+	22.0693i	0.696644	+	0.815149i	0.990032	−	0.140844i	$-0.0449817\pi$
$733$	18.8609	+	22.0693i	0.696644	+	0.815149i	−0.293387	+	0.955994i	$0.594783\pi$
$734$	2.71716	+	3.26115i	0.100292	+	0.120371i
$735$	−49.3087	−	132.317i	−1.81878	−	4.88058i
$736$	−13.3148	−	0.166661i	−0.490791	−	0.00614321i
$737$	0.974090	−	1.13979i	0.0358811	−	0.0419847i
$738$	−10.0985	−	28.1712i	−0.371730	−	1.03700i
$739$	−28.3816	−	19.4495i	−1.04403	−	0.715462i	−0.0843190	−	0.996439i	$-0.526871\pi$
$739$	−28.3816	−	19.4495i	−1.04403	−	0.715462i	−0.959715	+	0.280977i	$0.909342\pi$
$740$	5.95650	+	6.14586i	0.218965	+	0.225926i
$741$	59.5662	+	6.73846i	2.18822	+	0.247544i
$742$	−3.34044	+	48.4482i	−0.122631	+	1.77859i
$743$	−10.3721	−	14.9341i	−0.380515	−	0.547879i	0.584053	−	0.811716i	$-0.301466\pi$
$743$	−10.3721	−	14.9341i	−0.380515	−	0.547879i	−0.964567	+	0.263837i	$0.915012\pi$
$744$	23.1005	+	7.15572i	0.846904	+	0.262341i
$745$	−19.2326	−	5.17488i	−0.704630	−	0.189593i
$746$	18.3400	−	8.31261i	0.671474	−	0.304346i
$747$	−29.8517	+	10.4905i	−1.09222	+	0.383828i
$748$	0.00971053	−	0.0260576i	0.000355052	−	0.000952759i
$749$	−16.8046	+	43.4251i	−0.614027	+	1.58672i
$750$	91.5358	+	99.3031i	3.34242	+	3.62604i
$751$	−9.15944	−	14.7082i	−0.334233	−	0.536709i	0.638207	−	0.769865i	$-0.279677\pi$
$751$	−9.15944	−	14.7082i	−0.334233	−	0.536709i	−0.972439	+	0.233156i	$0.925095\pi$
$752$	−55.4235	−	21.8475i	−2.02109	−	0.796696i
$753$	0.101361	+	3.23826i	0.00369379	+	0.118009i
$754$	9.10710	−	11.2128i	0.331661	−	0.408346i
$755$	48.8891	−	60.1931i	1.77926	−	2.19065i
$756$	0.157891	+	5.04428i	0.00574244	+	0.183459i
$757$	7.90923	+	3.11775i	0.287466	+	0.113317i	0.506057	−	0.862500i	$-0.331102\pi$
$757$	7.90923	+	3.11775i	0.287466	+	0.113317i	−0.218591	+	0.975816i	$0.570146\pi$
$758$	7.34027	+	11.7870i	0.266611	+	0.428122i
$759$	1.05199	+	1.14125i	0.0381848	+	0.0414249i
$760$	22.6037	−	58.4107i	0.819923	−	2.11878i
$761$	−13.7159	+	36.8057i	−0.497200	+	1.33420i	0.409455	+	0.912331i	$0.365719\pi$
$761$	−13.7159	+	36.8057i	−0.497200	+	1.33420i	−0.906655	+	0.421874i	$0.861373\pi$
$762$	−10.4802	+	3.68298i	−0.379659	+	0.133420i
$763$	39.6119	−	17.9541i	1.43405	−	0.649984i
$764$	8.98120	+	2.41655i	0.324928	+	0.0874276i
$765$	7.33025	+	2.27066i	0.265026	+	0.0820958i
$766$	−22.9673	−	33.0691i	−0.829842	−	1.19484i
$767$	0.457675	−	6.63791i	0.0165257	−	0.239681i
$768$	−29.0002	−	3.28067i	−1.04646	−	0.118381i
$769$	−21.5661	−	22.2517i	−0.777695	−	0.802418i	0.206698	−	0.978405i	$-0.433728\pi$
$769$	−21.5661	−	22.2517i	−0.777695	−	0.802418i	−0.984393	+	0.175987i	$0.943688\pi$
$770$	2.94496	+	2.01814i	0.106129	+	0.0727287i
$771$	4.57353	+	12.7586i	0.164712	+	0.459488i
$772$	−1.94102	+	2.27120i	−0.0698588	+	0.0817424i
$773$	3.15310	+	0.0394672i	0.113409	+	0.00141954i	0.0692004	−	0.997603i	$-0.477955\pi$
$773$	3.15310	+	0.0394672i	0.113409	+	0.00141954i	0.0442088	+	0.999022i	$0.485923\pi$
$774$	4.18521	+	11.2307i	0.150434	+	0.403681i
$775$	−31.5724	−	37.8933i	−1.13411	−	1.36117i
$776$	4.45696	+	5.21513i	0.159996	+	0.187212i
$777$	−23.9794	+	41.9367i	−0.860257	+	1.50447i
$778$	23.0426	−	30.6539i	0.826116	−	1.09899i
$779$	29.7232	−	6.81210i	1.06495	−	0.244069i
$780$	−8.30761	+	18.0280i	−0.297460	+	0.645507i
$781$	0.785126	+	1.54807i	0.0280940	+	0.0553944i
$782$	3.62220	+	0.226979i	0.129530	+	0.00811676i
$783$	−5.20510	+	2.51812i	−0.186015	+	0.0899902i
$784$	−28.7440	−	53.3238i	−1.02657	−	1.90442i
$785$	−26.7172	−	3.70183i	−0.953578	−	0.132124i
$786$	72.6722	−	31.8485i	2.59213	−	1.13600i
$787$	−31.2290	−	1.56479i	−1.11319	−	0.0557788i	−0.515043	−	0.857164i	$-0.672224\pi$
$787$	−31.2290	−	1.56479i	−1.11319	−	0.0557788i	−0.598148	+	0.801385i	$0.704097\pi$
$788$	−0.0958262	+	0.724951i	−0.00341367	+	0.0258253i
$789$	−21.6913	−	5.54625i	−0.772232	−	0.197452i
$790$	44.6065	+	25.8778i	1.58703	+	0.920691i
$791$	7.24079	−	0.911042i	0.257453	−	0.0323929i
$792$	0.670856	+	0.892449i	0.0238378	+	0.0317118i
$793$	26.8842	+	22.6862i	0.954685	+	0.805611i
$794$	−0.331249	−	0.239402i	−0.0117556	−	0.00849607i
$795$	63.0701	−	43.2211i	2.23687	−	1.53289i
$796$	7.78483	+	1.58018i	0.275926	+	0.0560079i
$797$	−19.4146	−	21.5983i	−0.687701	−	0.765052i	0.293933	−	0.955826i	$-0.405036\pi$
$797$	−19.4146	−	21.5983i	−0.687701	−	0.765052i	−0.981634	+	0.190774i	$0.938900\pi$
$798$	−114.487	−	10.0564i	−4.05280	−	0.355994i
$799$	5.37191	+	2.43482i	0.190044	+	0.0861379i
$800$	26.7461	+	22.0026i	0.945619	+	0.777908i
$801$	38.2094	−	4.32246i	1.35006	−	0.152727i
$802$	0.405655	+	9.25411i	0.0143242	+	0.326774i
$803$	0.637057	+	0.308195i	0.0224812	+	0.0108760i
$804$	−13.9237	−	7.84640i	−0.491053	−	0.276721i
$805$	−27.7095	+	87.5118i	−0.976631	+	3.08439i
$806$	10.3628	−	19.8142i	0.365015	−	0.697926i
$807$	−0.137045	−	21.8983i	−0.00482421	−	0.770858i
$808$	−3.96945	+	4.52868i	−0.139645	+	0.159318i
$809$	33.3700	−	2.51073i	1.17323	−	0.0882727i	0.525941	−	0.850521i	$-0.323713\pi$
$809$	33.3700	−	2.51073i	1.17323	−	0.0882727i	0.647284	+	0.762249i	$0.275905\pi$
$810$	−28.3401	+	23.9148i	−0.995771	+	0.840281i
$811$	10.7701	+	2.46833i	0.378188	+	0.0866747i	0.408242	−	0.912874i	$-0.366142\pi$
$811$	10.7701	+	2.46833i	0.378188	+	0.0866747i	−0.0300546	+	0.999548i	$0.509568\pi$
$812$	−3.33266	+	4.31984i	−0.116953	+	0.151597i
$813$	30.3428	+	16.6020i	1.06417	+	0.582259i
$814$	−0.0739668	−	0.785635i	−0.00259253	−	0.0275365i
$815$	−0.0277673	+	0.492477i	−0.000972647	+	0.0172507i
$816$	5.75942	+	0.945485i	0.201620	+	0.0330986i
$817$	−11.8687	+	2.87694i	−0.415234	+	0.100651i
$818$	1.36500	−	8.00130i	0.0477260	−	0.279759i
$819$	−62.4857	−	9.45629i	−2.18343	−	0.330430i
$820$	−0.946484	+	10.0530i	−0.0330527	+	0.351068i
$821$	3.76478	−	5.56814i	0.131392	−	0.194330i	−0.757001	−	0.653414i	$-0.773336\pi$
$821$	3.76478	−	5.56814i	0.131392	−	0.194330i	0.888393	+	0.459084i	$0.151822\pi$
$822$	−4.86035	−	24.7379i	−0.169524	−	0.862833i
$823$	13.8495	+	4.48082i	0.482763	+	0.156191i	0.539137	−	0.842218i	$-0.318751\pi$
$823$	13.8495	+	4.48082i	0.482763	+	0.156191i	−0.0563736	+	0.998410i	$0.517954\pi$
$824$	−14.7939	+	11.8628i	−0.515369	+	0.413259i
$825$	−0.277685	−	4.02741i	−0.00966774	−	0.140217i
$826$	−0.558639	+	12.7441i	−0.0194375	+	0.443424i
$827$	8.37308	−	15.5332i	0.291161	−	0.540141i	−0.692222	−	0.721684i	$-0.743368\pi$
$827$	8.37308	−	15.5332i	0.291161	−	0.540141i	0.983383	+	0.181543i	$0.0581093\pi$
$828$	5.51383	−	7.52951i	0.191619	−	0.261669i
$829$	8.75432	+	26.4910i	0.304050	+	0.920070i	0.982635	+	0.185549i	$0.0594062\pi$
$829$	8.75432	+	26.4910i	0.304050	+	0.920070i	−0.678585	+	0.734522i	$0.737407\pi$
$830$	53.9202	+	5.41717i	1.87160	+	0.188033i
$831$	10.8412	+	37.4732i	0.376078	+	1.29993i
$832$	5.51084	−	18.1924i	0.191054	−	0.630709i
$833$	2.57795	+	5.41495i	0.0893205	+	0.187617i
$834$	−60.9888	−	24.9277i	−2.11187	−	0.863175i
$835$	−13.8733	+	3.91970i	−0.480105	+	0.135647i
$836$	0.319910	−	0.185591i	0.0110643	−	0.00641880i
$837$	−7.12078	+	5.42278i	−0.246130	+	0.187439i
$838$	−18.9495	−	16.4010i	−0.654601	−	0.566563i
$839$	0.443077	−	14.1554i	0.0152967	−	0.488698i	−0.961534	−	0.274685i	$-0.911426\pi$
$839$	0.443077	−	14.1554i	0.0152967	−	0.488698i	0.976831	−	0.214013i	$-0.0686534\pi$
$840$	−46.3154	+	107.508i	−1.59803	+	3.70939i
$841$	22.1087	+	5.35907i	0.762369	+	0.184796i
$842$	0.820844	+	0.347552i	0.0282881	+	0.0119774i
$843$	−42.3406	−	16.0810i	−1.45829	−	0.553859i
$844$	−3.62047	−	8.70205i	−0.124622	−	0.299537i
$845$	−1.38595	−	0.975485i	−0.0476780	−	0.0335577i
$846$	64.5721	−	41.9145i	2.22004	−	1.44105i
$847$	14.1637	+	46.7573i	0.486671	+	1.60660i
$848$	24.2564	−	22.0799i	0.832967	−	0.758228i
$849$	−32.9198	+	69.1476i	−1.12980	+	2.37314i
$850$	−6.98055	−	6.35421i	−0.239431	−	0.217948i
$851$	18.7812	−	7.67636i	0.643812	−	0.263142i
$852$	14.5790	−	11.3936i	0.499468	−	0.390339i
$853$	−15.2819	+	22.0035i	−0.523244	+	0.753386i	−0.991486	−	0.130215i	$-0.958433\pi$
$853$	−15.2819	+	22.0035i	−0.523244	+	0.753386i	0.468242	+	0.883600i	$0.344888\pi$
$854$	−52.6145	−	42.1900i	−1.80043	−	1.44371i
$855$	56.1039	+	85.2588i	1.91871	+	2.91579i
$856$	22.5845	−	10.5791i	0.771921	−	0.361588i
$857$	−6.96677	+	10.8813i	−0.237980	+	0.371698i	−0.940403	−	0.340062i	$-0.889552\pi$
$857$	−6.96677	+	10.8813i	−0.237980	+	0.371698i	0.702423	+	0.711760i	$0.252102\pi$
$858$	1.63740	−	0.817586i	0.0558999	−	0.0279119i
$859$	11.0312	−	0.552743i	0.376381	−	0.0188593i	0.139042	−	0.990286i	$-0.455598\pi$
$859$	11.0312	−	0.552743i	0.376381	−	0.0188593i	0.237338	+	0.971427i	$0.423725\pi$
$860$	0.328635	−	4.03055i	0.0112064	−	0.137441i
$861$	−55.9923	+	10.6375i	−1.90821	+	0.362526i
$862$	3.38181	−	5.43049i	0.115185	−	0.184963i
$863$	33.9299	−	25.1744i	1.15499	−	0.856948i	0.163423	−	0.986556i	$-0.447746\pi$
$863$	33.9299	−	25.1744i	1.15499	−	0.856948i	0.991565	+	0.129608i	$0.0413719\pi$
$864$	4.20151	−	4.67409i	0.142938	−	0.159016i
$865$	−72.7478	+	67.9047i	−2.47350	+	2.30883i
$866$	−9.04740	+	38.3721i	−0.307443	+	1.30394i
$867$	43.0253	+	9.29550i	1.46121	+	0.315692i
$868$	−3.72549	+	7.57943i	−0.126451	+	0.257263i
$869$	−0.338054	−	0.873573i	−0.0114677	−	0.0296339i
$870$	43.5989	−	0.545725i	1.47814	−	0.0185018i
$871$	29.0971	−	34.9225i	0.985919	−	1.18330i
$872$	−21.9764	−	7.72296i	−0.744214	−	0.261532i
$873$	−11.1362	+	0.978193i	−0.376903	+	0.0331068i
$874$	35.2861	+	32.9370i	1.19357	+	1.11411i
$875$	120.692	−	80.5071i	4.08012	−	2.72164i
$876$	1.91445	−	7.29682i	0.0646832	−	0.246537i
$877$	10.3271	+	17.5472i	0.348720	+	0.592528i	0.983660	−	0.180034i	$-0.0576206\pi$
$877$	10.3271	+	17.5472i	0.348720	+	0.592528i	−0.634940	+	0.772561i	$0.718975\pi$
$878$	−4.15191	+	0.260172i	−0.140120	+	0.00878040i
$879$	8.50220	−	4.79121i	0.286772	−	0.161604i
$880$	−0.494456	−	2.36010i	−0.0166681	−	0.0795590i
$881$	20.1700	+	15.3603i	0.679545	+	0.517503i	0.887600	−	0.460614i	$-0.152371\pi$
$881$	20.1700	+	15.3603i	0.679545	+	0.517503i	−0.208056	+	0.978117i	$0.566714\pi$
$882$	77.6673	+	9.77216i	2.61519	+	0.329046i
$883$	−28.3373	−	49.5579i	−0.953625	−	1.66776i	−0.718165	−	0.695873i	$-0.755018\pi$
$883$	−28.3373	−	49.5579i	−0.953625	−	1.66776i	−0.235459	−	0.971884i	$-0.575660\pi$
$884$	0.284488	−	0.793623i	0.00956837	−	0.0266924i
$885$	16.2776	−	11.7642i	0.547165	−	0.395450i
$886$	−38.0798	−	2.86510i	−1.27931	−	0.0962548i
$887$	−1.30321	+	1.27897i	−0.0437576	+	0.0429437i	−0.721988	−	0.691906i	$-0.756771\pi$
$887$	−1.30321	+	1.27897i	−0.0437576	+	0.0429437i	0.678230	+	0.734850i	$0.262747\pi$
$888$	24.8094	−	7.34606i	0.832549	−	0.246518i
$889$	2.15381	+	11.7370i	0.0722365	+	0.393647i
$890$	−62.4014	−	21.0555i	−2.09170	−	0.705781i
$891$	0.673345	−	0.0168591i	0.0225579	−	0.000564802i
$892$	−2.38363	−	9.57155i	−0.0798098	−	0.320479i
$893$	34.6024	+	70.3980i	1.15793	+	2.35578i
$894$	13.2670	−	14.3927i	0.443714	−	0.481365i
$895$	19.2520	+	3.65753i	0.643523	+	0.122258i
$896$	−16.1154	+	58.4336i	−0.538378	+	1.95213i
$897$	32.3242	+	34.1981i	1.07927	+	1.14184i
$898$	−24.7753	+	9.40969i	−0.826764	+	0.314006i
$899$	−9.66947	−	0.363249i	−0.322495	−	0.0121150i
$900$	−23.4394	+	6.30677i	−0.781312	+	0.210226i
$901$	−2.50781	+	2.06304i	−0.0835472	+	0.0687297i
$902$	0.647927	−	0.668525i	0.0215736	−	0.0222594i
$903$	22.3692	−	4.54053i	0.744399	−	0.151099i
$904$	−3.13910	−	2.32907i	−0.104405	−	0.0774636i
$905$	−103.145	+	40.6588i	−3.42865	+	1.35154i
$906$	30.1543	+	69.9947i	1.00181	+	2.32542i
$907$	−5.44510	−	31.9179i	−0.180801	−	1.05982i	−0.921615	−	0.388106i	$-0.873129\pi$
$907$	−5.44510	−	31.9179i	−0.180801	−	1.05982i	0.740813	−	0.671711i	$-0.234440\pi$
$908$	0.0172362	+	0.917958i	0.000572003	+	0.0304635i
$909$	−2.25205	−	9.55145i	−0.0746957	−	0.316802i
$910$	90.0425	+	60.0627i	2.98488	+	1.99106i
$911$	−20.0138	+	17.7651i	−0.663087	+	0.588584i	−0.926589	−	0.376075i	$-0.877274\pi$
$911$	−20.0138	+	17.7651i	−0.663087	+	0.588584i	0.263503	+	0.964659i	$0.415122\pi$
$912$	51.1667	+	58.3751i	1.69430	+	1.93299i
$913$	−0.702531	−	0.689464i	−0.0232504	−	0.0228179i
$914$	6.85155	+	3.63815i	0.226629	+	0.120339i
$915$	−0.664485	+	106.178i	−0.0219672	+	3.51013i
$916$	−6.15507	−	5.46350i	−0.203369	−	0.180519i
$917$	−21.6304	−	82.4432i	−0.714299	−	2.72251i
$918$	−1.20746	+	1.21504i	−0.0398522	+	0.0401024i
$919$	23.8119	+	35.2180i	0.785481	+	1.16173i	0.983389	+	0.181513i	$0.0580993\pi$
$919$	23.8119	+	35.2180i	0.785481	+	1.16173i	−0.197908	+	0.980221i	$0.563415\pi$
$920$	43.1312	−	23.5992i	1.42199	−	0.778043i
$921$	1.40479	−	8.90559i	0.0462895	−	0.293449i
$922$	−32.5455	+	5.76200i	−1.07183	+	0.189761i
$923$	24.3886	+	46.6321i	0.802760	+	1.53491i
$924$	−0.610521	+	0.324184i	−0.0200847	+	0.0106649i
$925$	−50.5994	−	14.9825i	−1.66370	−	0.492621i
$926$	4.40997	−	41.2950i	0.144921	−	1.35704i
$927$	−1.73952	−	30.8519i	−0.0571334	−	1.01331i
$928$	6.71800	−	1.01667i	0.220529	−	0.0333739i
$929$	−0.243421	+	12.9640i	−0.00798638	+	0.425335i	0.972951	+	0.231011i	$0.0742035\pi$
$929$	−0.243421	+	12.9640i	−0.00798638	+	0.425335i	−0.980937	+	0.194324i	$0.937749\pi$
$930$	65.9718	−	14.2530i	2.16330	−	0.467376i
$931$	−19.2750	+	77.3997i	−0.631714	+	2.53667i
$932$	−2.29428	+	10.3064i	−0.0751516	+	0.337598i
$933$	14.9739	+	14.3319i	0.490223	+	0.469205i
$934$	6.93615	+	20.1395i	0.226958	+	0.658985i
$935$	0.0371976	+	0.235811i	0.00121649	+	0.00771185i
$936$	20.6757	+	26.8001i	0.675807	+	0.875990i
$937$	1.51714	+	3.29228i	0.0495627	+	0.107554i	0.931396	−	0.364006i	$-0.118591\pi$
$937$	1.51714	+	3.29228i	0.0495627	+	0.107554i	−0.881834	+	0.471560i	$0.843691\pi$
$938$	−54.0914	+	68.3283i	−1.76615	+	2.23100i
$939$	14.9899	−	9.20517i	0.489176	−	0.300400i
$940$	−25.7290	+	3.56491i	−0.839188	+	0.116274i
$941$	4.01280	+	5.47976i	0.130814	+	0.178635i	0.867252	−	0.497870i	$-0.165884\pi$
$941$	4.01280	+	5.47976i	0.130814	+	0.178635i	−0.736438	+	0.676505i	$0.763494\pi$
$942$	15.3932	−	21.5820i	0.501537	−	0.703181i
$943$	21.2805	+	10.9606i	0.692989	+	0.356928i
$944$	6.22438	−	5.95751i	0.202586	−	0.193900i
$945$	−22.4406	−	37.0608i	−0.729993	−	1.20559i
$946$	−0.256116	+	0.270963i	−0.00832703	+	0.00880976i
$947$	−5.89746	+	14.1750i	−0.191642	+	0.460624i	−0.989913	−	0.141673i	$-0.954752\pi$
$947$	−5.89746	+	14.1750i	−0.191642	+	0.460624i	0.798272	+	0.602297i	$0.205748\pi$
$948$	−8.44264	+	5.33122i	−0.274204	+	0.173150i
$949$	19.4294	+	9.10122i	0.630704	+	0.295438i
$950$	−18.0083	−	124.247i	−0.584266	−	4.03109i
$951$	28.5301	+	40.0006i	0.925151	+	1.29711i
$952$	1.56002	−	4.72070i	0.0505605	−	0.152999i
$953$	7.29836	−	16.3740i	0.236417	−	0.530406i	−0.755818	−	0.654782i	$-0.772761\pi$
$953$	7.29836	−	16.3740i	0.236417	−	0.530406i	0.992235	+	0.124376i	$0.0396929\pi$
$954$	5.02803	+	42.0867i	0.162789	+	1.36261i
$955$	−77.3554	+	19.7789i	−2.50316	+	0.640032i
$956$	−1.49864	−	0.423420i	−0.0484695	−	0.0136944i
$957$	−0.624028	−	0.487684i	−0.0201720	−	0.0157646i
$958$	−43.7525	+	13.5530i	−1.41358	+	0.437878i
$959$	−27.0629	+	1.01666i	−0.873906	+	0.0328296i
$960$	52.8360	−	22.3712i	1.70527	−	0.722028i
$961$	15.8100	−	2.59542i	0.510001	−	0.0837234i
$962$	−2.54042	−	23.7885i	−0.0819065	−	0.766973i
$963$	−7.33526	+	39.9729i	−0.236375	+	1.28811i
$964$	6.46020	−	11.6335i	0.208069	−	0.374690i
$965$	4.94466	−	25.1670i	0.159174	−	0.810155i
$966$	−63.5933	−	63.9925i	−2.04608	−	2.05892i
$967$	18.0127	−	30.6062i	0.579249	−	0.984230i	−0.417880	−	0.908502i	$-0.637227\pi$
$967$	18.0127	−	30.6062i	0.579249	−	0.984230i	0.997129	−	0.0757277i	$-0.0241280\pi$
$968$	11.8359	−	23.3374i	0.380419	−	0.750092i
$969$	−4.77003	−	6.02550i	−0.153235	−	0.193567i
$970$	17.9824	+	6.57340i	0.577381	+	0.211059i
$971$	15.6315	+	0.391378i	0.501638	+	0.0125599i	0.275048	−	0.961430i	$-0.411306\pi$
$971$	15.6315	+	0.391378i	0.501638	+	0.0125599i	0.226589	+	0.973990i	$0.427242\pi$
$972$	−2.29984	−	10.3314i	−0.0737675	−	0.331380i
$973$	−36.6591	+	60.5427i	−1.17524	+	1.94091i
$974$	9.71032	+	35.2091i	0.311139	+	1.12817i
$975$	−9.94625	−	121.986i	−0.318535	−	3.90668i
$976$	5.96920	+	45.1586i	0.191069	+	1.44549i
$977$	−0.247224	+	2.06937i	−0.00790941	+	0.0662050i	−0.996342	−	0.0854565i	$-0.972765\pi$
$977$	−0.247224	+	2.06937i	−0.00790941	+	0.0662050i	0.988432	+	0.151661i	$0.0484624\pi$
$978$	−0.416253	−	0.248497i	−0.0133103	−	0.00794607i
$979$	0.645017	+	1.00744i	0.0206148	+	0.0321980i
$980$	−22.3325	−	14.1021i	−0.713385	−	0.450477i
$981$	31.0409	−	21.8479i	0.991061	−	0.697549i
$982$	20.3804	−	50.7682i	0.650365	−	1.62008i
$983$	0.983648	−	3.40003i	0.0313735	−	0.108444i	−0.943389	−	0.331688i	$-0.892382\pi$
$983$	0.983648	−	3.40003i	0.0313735	−	0.108444i	0.974763	+	0.223244i	$0.0716647\pi$
$984$	25.6048	+	16.6204i	0.816252	+	0.529838i
$985$	−2.33871	−	5.82579i	−0.0745174	−	0.185625i
$986$	−1.84260	+	0.185119i	−0.0586803	+	0.00589540i
$987$	−59.6879	−	133.911i	−1.89989	−	4.26243i
$988$	9.62769	−	5.74760i	0.306298	−	0.182856i
$989$	−8.57686	−	4.28260i	−0.272728	−	0.136179i
$990$	2.85395	+	1.25074i	0.0907046	+	0.0397511i
$991$	−24.4922	−	15.0405i	−0.778021	−	0.477777i	0.0765795	−	0.997063i	$-0.475600\pi$
$991$	−24.4922	−	15.0405i	−0.778021	−	0.477777i	−0.854600	+	0.519287i	$0.826198\pi$
$992$	9.87821	−	3.61094i	0.313633	−	0.114647i
$993$	2.38605	−	0.805100i	0.0757190	−	0.0255491i
$994$	−48.9806	−	88.2042i	−1.55357	−	2.79767i
$995$	−64.8828	+	20.9919i	−2.05692	+	0.665489i
$996$	−5.76787	+	8.76520i	−0.182762	+	0.277736i
$997$	6.82601	−	47.0955i	0.216182	−	1.49153i	−0.542494	−	0.840060i	$-0.682520\pi$
$997$	6.82601	−	47.0955i	0.216182	−	1.49153i	0.758676	−	0.651469i	$-0.225847\pi$
$998$	−15.1922	+	7.82481i	−0.480899	+	0.247690i
$999$	−3.11837	+	9.05436i	−0.0986608	+	0.286467i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.c.a.2.10	✓	10250
503.252	even	251	inner	503.2.c.a.252.10	yes	10250

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.c.a.2.10	✓	10250	1.1	even	1	trivial
503.2.c.a.252.10	yes	10250	503.252	even	251	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.c (of order \(251\), degree \(250\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.994976 - 1.22503i) q^{2} +(-1.98352 + 1.71676i) q^{3} +(-0.100616 + 0.480254i) q^{4} +(-1.27158 - 4.01588i) q^{5} +(4.07664 + 0.721744i) q^{6} +(1.44819 - 4.20490i) q^{7} +(-2.11761 + 1.09069i) q^{8} +(0.556781 - 3.84146i) q^{9} +O(q^{10})\)	\(q+(-0.994976 - 1.22503i) q^{2} +(-1.98352 + 1.71676i) q^{3} +(-0.100616 + 0.480254i) q^{4} +(-1.27158 - 4.01588i) q^{5} +(4.07664 + 0.721744i) q^{6} +(1.44819 - 4.20490i) q^{7} +(-2.11761 + 1.09069i) q^{8} +(0.556781 - 3.84146i) q^{9} +(-3.65440 + 5.55343i) q^{10} +(0.114889 - 0.0371709i) q^{11} +(-0.624904 - 1.12533i) q^{12} +(3.46878 - 1.17043i) q^{13} +(-6.59206 + 2.40970i) q^{14} +(9.41649 + 5.78260i) q^{15} +(4.34194 + 1.90284i) q^{16} +(-0.419893 - 0.209661i) q^{17} +(-5.25989 + 3.14009i) q^{18} +(-2.54124 - 5.70132i) q^{19} +(2.05658 - 0.206618i) q^{20} +(4.34627 + 10.8267i) q^{21} +(-0.159848 - 0.103759i) q^{22} +(1.36173 - 4.70690i) q^{23} +(2.32788 - 5.79883i) q^{24} +(-10.4217 + 7.33518i) q^{25} +(-4.88517 - 3.08481i) q^{26} +(1.24701 + 1.94769i) q^{27} +(1.87371 + 1.11858i) q^{28} +(-0.296587 + 2.48256i) q^{29} +(-2.28532 - 17.2891i) q^{30} +(0.314516 + 3.85739i) q^{31} +(-0.722505 - 2.61976i) q^{32} +(-0.164072 + 0.270966i) q^{33} +(0.160942 + 0.722990i) q^{34} +(-18.7279 - 0.468906i) q^{35} +(1.78885 + 0.653909i) q^{36} +(2.57013 + 3.24659i) q^{37} +(-4.45582 + 8.78578i) q^{38} +(-4.87104 + 8.27662i) q^{39} +(7.07279 + 7.11719i) q^{40} +(-0.941818 + 4.79360i) q^{41} +(8.93861 - 16.0966i) q^{42} +(0.353129 - 1.92435i) q^{43} +(0.00629175 + 0.0589160i) q^{44} +(-16.1349 + 2.64875i) q^{45} +(-7.12099 + 3.01509i) q^{46} +(-12.5580 + 0.471759i) q^{47} +(-11.8790 + 3.67971i) q^{48} +(-10.0685 - 7.86862i) q^{49} +(19.3551 + 5.46852i) q^{50} +(1.19280 - 0.304987i) q^{51} +(0.213091 + 1.78366i) q^{52} +(2.81691 - 6.31978i) q^{53} +(1.14523 - 3.46553i) q^{54} +(-0.295365 - 0.414117i) q^{55} +(1.51953 + 10.4839i) q^{56} +(14.8284 + 6.94599i) q^{57} +(3.33631 - 2.10676i) q^{58} +(0.698148 - 1.67805i) q^{59} +(-3.72457 + 3.94048i) q^{60} +(4.97693 + 8.21943i) q^{61} +(4.41249 - 4.22330i) q^{62} +(-15.3467 - 7.90438i) q^{63} +(3.01507 - 4.22728i) q^{64} +(-9.11115 - 12.4419i) q^{65} +(0.495190 - 0.0686115i) q^{66} +(10.5807 - 6.49752i) q^{67} +(0.142938 - 0.180560i) q^{68} +(5.37957 + 11.6740i) q^{69} +(18.0594 + 23.4088i) q^{70} +(2.23981 + 14.1991i) q^{71} +(3.01079 + 8.74200i) q^{72} +(4.23387 + 4.05235i) q^{73} +(1.41996 - 6.37878i) q^{74} +(8.07884 - 32.4409i) q^{75} +(2.99377 - 0.646796i) q^{76} +(0.0100817 - 0.536929i) q^{77} +(14.9857 - 2.26787i) q^{78} +(-0.436680 - 7.74488i) q^{79} +(2.12049 - 19.8563i) q^{80} +(5.34844 + 1.58367i) q^{81} +(6.80940 - 3.61577i) q^{82} +(-3.77782 - 7.22337i) q^{83} +(-5.63687 + 0.997974i) q^{84} +(-0.308047 + 1.95284i) q^{85} +(-2.70875 + 1.48209i) q^{86} +(-3.67366 - 5.43337i) q^{87} +(-0.202749 + 0.204022i) q^{88} +(2.51405 + 9.58219i) q^{89} +(19.2986 + 17.1303i) q^{90} +(0.101890 - 16.2809i) q^{91} +(2.12349 + 1.12757i) q^{92} +(-7.24604 - 7.11126i) q^{93} +(13.0728 + 14.9145i) q^{94} +(-19.6644 + 17.4550i) q^{95} +(5.93060 + 3.95599i) q^{96} +(-0.660930 - 2.80315i) q^{97} +(0.378599 + 20.1633i) q^{98} +(-0.0788224 - 0.462039i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10250 q - 249 q^{2} - 249 q^{3} - 285 q^{4} - 245 q^{5} - 237 q^{6} - 247 q^{7} - 239 q^{8} - 280 q^{9}+O(q^{10}) \) 10250 * q - 249 * q^2 - 249 * q^3 - 285 * q^4 - 245 * q^5 - 237 * q^6 - 247 * q^7 - 239 * q^8 - 280 * q^9	\( 10250 q - 249 q^{2} - 249 q^{3} - 285 q^{4} - 245 q^{5} - 237 q^{6} - 247 q^{7} - 239 q^{8} - 280 q^{9} - 233 q^{10} - 239 q^{11} - 239 q^{12} - 245 q^{13} - 223 q^{14} - 231 q^{15} - 263 q^{16} - 243 q^{17} - 217 q^{18} - 229 q^{19} - 195 q^{20} - 215 q^{21} - 233 q^{22} - 241 q^{23} - 181 q^{24} - 280 q^{25} - 215 q^{26} - 237 q^{27} - 185 q^{28} - 217 q^{29} - 159 q^{30} - 219 q^{31} - 185 q^{32} - 209 q^{33} - 167 q^{34} - 187 q^{35} - 203 q^{36} - 237 q^{37} - 161 q^{38} - 197 q^{39} - 135 q^{40} - 209 q^{41} - 117 q^{42} - 221 q^{43} - 147 q^{44} - 167 q^{45} - 167 q^{46} - 195 q^{47} - 141 q^{48} - 234 q^{49} - 145 q^{50} - 177 q^{51} - 179 q^{52} - 211 q^{53} - 83 q^{54} - 165 q^{55} - 125 q^{56} - 177 q^{57} - 205 q^{58} - 189 q^{59} - 27 q^{60} - 193 q^{61} - 143 q^{62} - 159 q^{63} - 185 q^{64} - 155 q^{65} - 97 q^{66} - 201 q^{67} - 155 q^{68} - 113 q^{69} - 123 q^{70} - 153 q^{71} - 21 q^{72} - 213 q^{73} - 83 q^{74} - 161 q^{75} - 97 q^{76} - 139 q^{77} - 43 q^{78} - 191 q^{79} + 3 q^{80} - 188 q^{81} - 97 q^{82} - 161 q^{83} + 67 q^{84} - 159 q^{85} - 121 q^{86} - 121 q^{87} - 143 q^{88} - 155 q^{89} + 115 q^{90} - 137 q^{91} - 119 q^{92} - 123 q^{93} - 99 q^{94} - 181 q^{95} + 67 q^{96} - 229 q^{97} - 63 q^{98} - 85 q^{99}+O(q^{100}) \) 10250 * q - 249 * q^2 - 249 * q^3 - 285 * q^4 - 245 * q^5 - 237 * q^6 - 247 * q^7 - 239 * q^8 - 280 * q^9 - 233 * q^10 - 239 * q^11 - 239 * q^12 - 245 * q^13 - 223 * q^14 - 231 * q^15 - 263 * q^16 - 243 * q^17 - 217 * q^18 - 229 * q^19 - 195 * q^20 - 215 * q^21 - 233 * q^22 - 241 * q^23 - 181 * q^24 - 280 * q^25 - 215 * q^26 - 237 * q^27 - 185 * q^28 - 217 * q^29 - 159 * q^30 - 219 * q^31 - 185 * q^32 - 209 * q^33 - 167 * q^34 - 187 * q^35 - 203 * q^36 - 237 * q^37 - 161 * q^38 - 197 * q^39 - 135 * q^40 - 209 * q^41 - 117 * q^42 - 221 * q^43 - 147 * q^44 - 167 * q^45 - 167 * q^46 - 195 * q^47 - 141 * q^48 - 234 * q^49 - 145 * q^50 - 177 * q^51 - 179 * q^52 - 211 * q^53 - 83 * q^54 - 165 * q^55 - 125 * q^56 - 177 * q^57 - 205 * q^58 - 189 * q^59 - 27 * q^60 - 193 * q^61 - 143 * q^62 - 159 * q^63 - 185 * q^64 - 155 * q^65 - 97 * q^66 - 201 * q^67 - 155 * q^68 - 113 * q^69 - 123 * q^70 - 153 * q^71 - 21 * q^72 - 213 * q^73 - 83 * q^74 - 161 * q^75 - 97 * q^76 - 139 * q^77 - 43 * q^78 - 191 * q^79 + 3 * q^80 - 188 * q^81 - 97 * q^82 - 161 * q^83 + 67 * q^84 - 159 * q^85 - 121 * q^86 - 121 * q^87 - 143 * q^88 - 155 * q^89 + 115 * q^90 - 137 * q^91 - 119 * q^92 - 123 * q^93 - 99 * q^94 - 181 * q^95 + 67 * q^96 - 229 * q^97 - 63 * q^98 - 85 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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