LMFDB - Embedded newform 50.3.f.b.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,3,Mod(3,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("50.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	50.f (of order $20$, degree $8$, 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:	$1.36240132180$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			27.1
Character	$\chi$	$=$	50.27
Dual form			50.3.f.b.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39680 + 0.221232i) q^{2} +(-2.14176 - 4.20343i) q^{3} +(1.90211 + 0.618034i) q^{4} +(-1.43099 - 4.79085i) q^{5} +(-2.06168 - 6.34519i) q^{6} +(8.41873 + 8.41873i) q^{7} +(2.52015 + 1.28408i) q^{8} +(-7.79165 + 10.7243i) q^{9} +O(q^{10})$	\(q+(1.39680 + 0.221232i) q^{2} +(-2.14176 - 4.20343i) q^{3} +(1.90211 + 0.618034i) q^{4} +(-1.43099 - 4.79085i) q^{5} +(-2.06168 - 6.34519i) q^{6} +(8.41873 + 8.41873i) q^{7} +(2.52015 + 1.28408i) q^{8} +(-7.79165 + 10.7243i) q^{9} +(-0.938916 - 7.00845i) q^{10} +(-8.83615 + 6.41984i) q^{11} +(-1.47600 - 9.31908i) q^{12} +(13.8302 - 2.19049i) q^{13} +(9.89681 + 13.6218i) q^{14} +(-17.0732 + 16.2759i) q^{15} +(3.23607 + 2.35114i) q^{16} +(4.53099 - 8.89257i) q^{17} +(-13.2560 + 13.2560i) q^{18} +(-14.9790 + 4.86698i) q^{19} +(0.239013 - 9.99714i) q^{20} +(17.3567 - 53.4184i) q^{21} +(-13.7626 + 7.01241i) q^{22} +(-1.69189 + 10.6822i) q^{23} -13.3434i q^{24} +(-20.9046 + 13.7113i) q^{25} +19.8027 q^{26} +(19.8308 + 3.14088i) q^{27} +(10.8103 + 21.2164i) q^{28} +(4.11402 + 1.33673i) q^{29} +(-27.4486 + 18.9571i) q^{30} +(4.02808 + 12.3972i) q^{31} +(4.00000 + 4.00000i) q^{32} +(45.9102 + 23.3924i) q^{33} +(8.29622 - 11.4188i) q^{34} +(28.2858 - 52.3800i) q^{35} +(-21.4486 + 15.5833i) q^{36} +(-3.95354 - 24.9617i) q^{37} +(-21.9995 + 3.48437i) q^{38} +(-38.8285 - 53.4428i) q^{39} +(2.54554 - 13.9112i) q^{40} +(-21.6147 - 15.7040i) q^{41} +(36.0617 - 70.7751i) q^{42} +(21.2302 - 21.2302i) q^{43} +(-20.7750 + 6.75022i) q^{44} +(62.5282 + 21.9824i) q^{45} +(-4.72648 + 14.5466i) q^{46} +(-46.4137 + 23.6489i) q^{47} +(2.95199 - 18.6382i) q^{48} +92.7500i q^{49} +(-32.2329 + 14.5272i) q^{50} -47.0836 q^{51} +(27.6604 + 4.38098i) q^{52} +(-15.6773 - 30.7684i) q^{53} +(27.0048 + 8.77439i) q^{54} +(43.4009 + 33.1460i) q^{55} +(10.4061 + 32.0267i) q^{56} +(52.5394 + 52.5394i) q^{57} +(5.45074 + 2.77729i) q^{58} +(8.92677 - 12.2866i) q^{59} +(-42.5342 + 20.4068i) q^{60} +(-47.6752 + 34.6380i) q^{61} +(2.88379 + 18.2075i) q^{62} +(-155.881 + 24.6891i) q^{63} +(4.70228 + 6.47214i) q^{64} +(-30.2852 - 63.1240i) q^{65} +(58.9524 + 42.8314i) q^{66} +(-44.1187 + 86.5878i) q^{67} +(14.1144 - 14.1144i) q^{68} +(48.5255 - 15.7669i) q^{69} +(51.0978 - 66.9068i) q^{70} +(20.2698 - 62.3839i) q^{71} +(-33.4069 + 17.0217i) q^{72} +(12.5050 - 78.9533i) q^{73} -35.7412i q^{74} +(102.407 + 58.5046i) q^{75} -31.4998 q^{76} +(-128.436 - 20.3423i) q^{77} +(-42.4125 - 83.2392i) q^{78} +(16.9345 + 5.50235i) q^{79} +(6.63320 - 18.8680i) q^{80} +(7.59667 + 23.3801i) q^{81} +(-26.7172 - 26.7172i) q^{82} +(88.9040 + 45.2989i) q^{83} +(66.0288 - 90.8808i) q^{84} +(-49.0868 - 8.98217i) q^{85} +(34.3512 - 24.9576i) q^{86} +(-3.19239 - 20.1559i) q^{87} +(-30.5120 + 4.83262i) q^{88} +(-6.44619 - 8.87242i) q^{89} +(82.4764 + 44.5382i) q^{90} +(134.874 + 97.9917i) q^{91} +(-9.82014 + 19.2731i) q^{92} +(43.4834 - 43.4834i) q^{93} +(-70.0626 + 22.7647i) q^{94} +(44.7518 + 64.7977i) q^{95} +(8.24670 - 25.3807i) q^{96} +(117.203 - 59.7179i) q^{97} +(-20.5192 + 129.553i) q^{98} -144.783i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9	\( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9} - 32 q^{11} + 4 q^{12} + 2 q^{13} + 30 q^{14} - 20 q^{15} + 24 q^{16} - 92 q^{17} - 136 q^{18} - 230 q^{19} - 20 q^{20} + 68 q^{21} - 48 q^{22} - 18 q^{23} + 40 q^{25} + 36 q^{26} + 260 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} - 132 q^{31} + 96 q^{32} + 364 q^{33} + 150 q^{34} + 50 q^{35} - 108 q^{36} - 192 q^{37} + 20 q^{38} - 80 q^{39} + 20 q^{40} + 168 q^{41} - 8 q^{42} - 78 q^{43} - 40 q^{44} - 310 q^{45} + 26 q^{46} - 22 q^{47} - 8 q^{48} - 30 q^{50} + 168 q^{51} + 4 q^{52} - 108 q^{53} - 80 q^{54} - 40 q^{55} - 48 q^{56} + 280 q^{57} + 40 q^{58} + 450 q^{59} - 100 q^{60} - 492 q^{61} - 458 q^{62} - 558 q^{63} + 120 q^{65} + 202 q^{66} - 572 q^{67} - 136 q^{68} - 670 q^{69} - 260 q^{70} - 2 q^{71} + 128 q^{72} + 262 q^{73} + 140 q^{75} - 40 q^{76} + 496 q^{77} - 62 q^{78} - 360 q^{79} - 80 q^{80} - 46 q^{81} + 272 q^{82} + 772 q^{83} + 620 q^{84} + 490 q^{85} - 264 q^{86} + 210 q^{87} - 84 q^{88} + 900 q^{89} + 1110 q^{90} + 798 q^{91} - 16 q^{92} + 294 q^{93} - 190 q^{94} + 16 q^{96} + 378 q^{97} + 106 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9 - 32 * q^11 + 4 * q^12 + 2 * q^13 + 30 * q^14 - 20 * q^15 + 24 * q^16 - 92 * q^17 - 136 * q^18 - 230 * q^19 - 20 * q^20 + 68 * q^21 - 48 * q^22 - 18 * q^23 + 40 * q^25 + 36 * q^26 + 260 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 - 132 * q^31 + 96 * q^32 + 364 * q^33 + 150 * q^34 + 50 * q^35 - 108 * q^36 - 192 * q^37 + 20 * q^38 - 80 * q^39 + 20 * q^40 + 168 * q^41 - 8 * q^42 - 78 * q^43 - 40 * q^44 - 310 * q^45 + 26 * q^46 - 22 * q^47 - 8 * q^48 - 30 * q^50 + 168 * q^51 + 4 * q^52 - 108 * q^53 - 80 * q^54 - 40 * q^55 - 48 * q^56 + 280 * q^57 + 40 * q^58 + 450 * q^59 - 100 * q^60 - 492 * q^61 - 458 * q^62 - 558 * q^63 + 120 * q^65 + 202 * q^66 - 572 * q^67 - 136 * q^68 - 670 * q^69 - 260 * q^70 - 2 * q^71 + 128 * q^72 + 262 * q^73 + 140 * q^75 - 40 * q^76 + 496 * q^77 - 62 * q^78 - 360 * q^79 - 80 * q^80 - 46 * q^81 + 272 * q^82 + 772 * q^83 + 620 * q^84 + 490 * q^85 - 264 * q^86 + 210 * q^87 - 84 * q^88 + 900 * q^89 + 1110 * q^90 + 798 * q^91 - 16 * q^92 + 294 * q^93 - 190 * q^94 + 16 * q^96 + 378 * q^97 + 106 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{1}{20}\right)$

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 $

$2$	1.39680	+	0.221232i	0.698401	+	0.110616i
$2$	1.39680	+	0.221232i	0.698401	+	0.110616i
$3$	−2.14176	−	4.20343i	−0.713918	−	1.40114i	−0.907497	−	0.420059i	$-0.862009\pi$
$3$	−2.14176	−	4.20343i	−0.713918	−	1.40114i	0.193578	−	0.981085i	$-0.437991\pi$
$4$	1.90211	+	0.618034i	0.475528	+	0.154508i
$5$	−1.43099	−	4.79085i	−0.286197	−	0.958171i
$5$	−1.43099	−	4.79085i	−0.286197	−	0.958171i
$6$	−2.06168	−	6.34519i	−0.343613	−	1.05753i
$7$	8.41873	+	8.41873i	1.20268	+	1.20268i	0.973350	+	0.229326i	$0.0736521\pi$
$7$	8.41873	+	8.41873i	1.20268	+	1.20268i	0.229326	+	0.973350i	$0.426348\pi$
$8$	2.52015	+	1.28408i	0.315018	+	0.160510i
$9$	−7.79165	+	10.7243i	−0.865739	+	1.19159i
$10$	−0.938916	−	7.00845i	−0.0938916	−	0.700845i
$11$	−8.83615	+	6.41984i	−0.803287	+	0.583622i	−0.911876	−	0.410465i	$-0.865366\pi$
$11$	−8.83615	+	6.41984i	−0.803287	+	0.583622i	0.108590	+	0.994087i	$0.465366\pi$
$12$	−1.47600	−	9.31908i	−0.123000	−	0.776590i
$13$	13.8302	−	2.19049i	1.06386	−	0.168499i	0.400122	−	0.916462i	$-0.368968\pi$
$13$	13.8302	−	2.19049i	1.06386	−	0.168499i	0.663741	+	0.747963i	$0.268968\pi$
$14$	9.89681	+	13.6218i	0.706915	+	0.972985i
$15$	−17.0732	+	16.2759i	−1.13821	+	1.08506i
$16$	3.23607	+	2.35114i	0.202254	+	0.146946i
$17$	4.53099	−	8.89257i	0.266529	−	0.523092i	−0.718490	−	0.695537i	$-0.755167\pi$
$17$	4.53099	−	8.89257i	0.266529	−	0.523092i	0.985019	+	0.172445i	$0.0551666\pi$
$18$	−13.2560	+	13.2560i	−0.736442	+	0.736442i
$19$	−14.9790	+	4.86698i	−0.788370	+	0.256157i	−0.675410	−	0.737443i	$-0.736033\pi$
$19$	−14.9790	+	4.86698i	−0.788370	+	0.256157i	−0.112960	+	0.993600i	$0.536033\pi$
$20$	0.239013	−	9.99714i	0.0119506	−	0.499857i
$21$	17.3567	−	53.4184i	0.826509	−	2.54373i
$22$	−13.7626	+	7.01241i	−0.625574	+	0.318746i
$23$	−1.69189	+	10.6822i	−0.0735606	+	0.464443i	0.923220	+	0.384271i	$0.125547\pi$
$23$	−1.69189	+	10.6822i	−0.0735606	+	0.464443i	−0.996781	+	0.0801725i	$0.974453\pi$
$24$		−	13.3434i		−	0.555977i
$25$	−20.9046	+	13.7113i	−0.836182	+	0.548452i
$26$	19.8027			0.761641
$27$	19.8308	+	3.14088i	0.734473	+	0.116329i
$28$	10.8103	+	21.2164i	0.386083	+	0.757730i
$29$	4.11402	+	1.33673i	0.141863	+	0.0460940i	0.379088	−	0.925361i	$-0.376238\pi$
$29$	4.11402	+	1.33673i	0.141863	+	0.0460940i	−0.237225	+	0.971455i	$0.576238\pi$
$30$	−27.4486	+	18.9571i	−0.914954	+	0.631902i
$31$	4.02808	+	12.3972i	0.129938	+	0.399908i	0.994768	−	0.102156i	$-0.0325741\pi$
$31$	4.02808	+	12.3972i	0.129938	+	0.399908i	−0.864830	+	0.502064i	$0.832574\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	45.9102	+	23.3924i	1.39122	+	0.708862i
$34$	8.29622	−	11.4188i	0.244006	−	0.335846i
$35$	28.2858	−	52.3800i	0.808166	−	1.49657i
$36$	−21.4486	+	15.5833i	−0.595794	+	0.432870i
$37$	−3.95354	−	24.9617i	−0.106852	−	0.674640i	−0.981728	−	0.190291i	$-0.939057\pi$
$37$	−3.95354	−	24.9617i	−0.106852	−	0.674640i	0.874875	−	0.484348i	$-0.160943\pi$
$38$	−21.9995	+	3.48437i	−0.578933	+	0.0916940i
$39$	−38.8285	−	53.4428i	−0.995603	−	1.37033i
$40$	2.54554	−	13.9112i	0.0636385	−	0.347779i
$41$	−21.6147	−	15.7040i	−0.527187	−	0.383024i	0.292117	−	0.956382i	$-0.405640\pi$
$41$	−21.6147	−	15.7040i	−0.527187	−	0.383024i	−0.819305	+	0.573359i	$0.805640\pi$
$42$	36.0617	−	70.7751i	0.858612	−	1.68512i
$43$	21.2302	−	21.2302i	0.493726	−	0.493726i	−0.415752	−	0.909478i	$-0.636481\pi$
$43$	21.2302	−	21.2302i	0.493726	−	0.493726i	0.909478	+	0.415752i	$0.136481\pi$
$44$	−20.7750	+	6.75022i	−0.472160	+	0.153414i
$45$	62.5282	+	21.9824i	1.38952	+	0.488497i
$46$	−4.72648	+	14.5466i	−0.102750	+	0.316231i
$47$	−46.4137	+	23.6489i	−0.987525	+	0.503169i	−0.871668	−	0.490097i	$-0.836961\pi$
$47$	−46.4137	+	23.6489i	−0.987525	+	0.503169i	−0.115857	+	0.993266i	$0.536961\pi$
$48$	2.95199	−	18.6382i	0.0614999	−	0.388295i
$49$			92.7500i			1.89286i
$50$	−32.2329	+	14.5272i	−0.644658	+	0.290544i
$51$	−47.0836			−0.923208
$52$	27.6604	+	4.38098i	0.531931	+	0.0842496i
$53$	−15.6773	−	30.7684i	−0.295797	−	0.580535i	0.694501	−	0.719492i	$-0.255625\pi$
$53$	−15.6773	−	30.7684i	−0.295797	−	0.580535i	−0.990298	+	0.138957i	$0.955625\pi$
$54$	27.0048	+	8.77439i	0.500089	+	0.162489i
$55$	43.4009	+	33.1460i	0.789108	+	0.602655i
$56$	10.4061	+	32.0267i	0.185824	+	0.571906i
$57$	52.5394	+	52.5394i	0.921744	+	0.921744i
$58$	5.45074	+	2.77729i	0.0939784	+	0.0478844i
$59$	8.92677	−	12.2866i	0.151301	−	0.208248i	−0.726638	−	0.687021i	$-0.758918\pi$
$59$	8.92677	−	12.2866i	0.151301	−	0.208248i	0.877939	+	0.478772i	$0.158918\pi$
$60$	−42.5342	+	20.4068i	−0.708904	+	0.340113i
$61$	−47.6752	+	34.6380i	−0.781560	+	0.567837i	−0.905447	−	0.424460i	$-0.860464\pi$
$61$	−47.6752	+	34.6380i	−0.781560	+	0.567837i	0.123887	+	0.992296i	$0.460464\pi$
$62$	2.88379	+	18.2075i	0.0465127	+	0.293670i
$63$	−155.881	+	24.6891i	−2.47430	+	0.391890i
$64$	4.70228	+	6.47214i	0.0734732	+	0.101127i
$65$	−30.2852	−	63.1240i	−0.465926	−	0.971138i
$66$	58.9524	+	42.8314i	0.893218	+	0.648961i
$67$	−44.1187	+	86.5878i	−0.658488	+	1.29236i	0.284227	+	0.958757i	$0.408263\pi$
$67$	−44.1187	+	86.5878i	−0.658488	+	1.29236i	−0.942715	+	0.333599i	$0.891737\pi$
$68$	14.1144	−	14.1144i	0.207564	−	0.207564i
$69$	48.5255	−	15.7669i	0.703268	−	0.228506i
$70$	51.0978	−	66.9068i	0.729969	−	0.955811i
$71$	20.2698	−	62.3839i	0.285490	−	0.878647i	−0.700762	−	0.713395i	$-0.747156\pi$
$71$	20.2698	−	62.3839i	0.285490	−	0.878647i	0.986251	−	0.165252i	$-0.0528436\pi$
$72$	−33.4069	+	17.0217i	−0.463985	+	0.236412i
$73$	12.5050	−	78.9533i	0.171301	−	1.08155i	−0.740842	−	0.671679i	$-0.765573\pi$
$73$	12.5050	−	78.9533i	0.171301	−	1.08155i	0.912143	−	0.409872i	$-0.134427\pi$
$74$		−	35.7412i		−	0.482989i
$75$	102.407	+	58.5046i	1.36543	+	0.780062i
$76$	−31.4998			−0.414470
$77$	−128.436	−	20.3423i	−1.66800	−	0.264185i
$78$	−42.4125	−	83.2392i	−0.543750	−	1.06717i
$79$	16.9345	+	5.50235i	0.214361	+	0.0696500i	0.414229	−	0.910173i	$-0.364051\pi$
$79$	16.9345	+	5.50235i	0.214361	+	0.0696500i	−0.199868	+	0.979823i	$0.564051\pi$
$80$	6.63320	−	18.8680i	0.0829151	−	0.235850i
$81$	7.59667	+	23.3801i	0.0937860	+	0.288644i
$82$	−26.7172	−	26.7172i	−0.325820	−	0.325820i
$83$	88.9040	+	45.2989i	1.07113	+	0.545769i	0.898390	−	0.439198i	$-0.144737\pi$
$83$	88.9040	+	45.2989i	1.07113	+	0.545769i	0.172742	+	0.984967i	$0.444737\pi$
$84$	66.0288	−	90.8808i	0.786057	−	1.08191i
$85$	−49.0868	−	8.98217i	−0.577492	−	0.105673i
$86$	34.3512	−	24.9576i	0.399433	−	0.290205i
$87$	−3.19239	−	20.1559i	−0.0366941	−	0.231677i
$88$	−30.5120	+	4.83262i	−0.346727	+	0.0549162i
$89$	−6.44619	−	8.87242i	−0.0724291	−	0.0996901i	0.771265	−	0.636514i	$-0.219624\pi$
$89$	−6.44619	−	8.87242i	−0.0724291	−	0.0996901i	−0.843695	+	0.536824i	$0.819624\pi$
$90$	82.4764	+	44.5382i	0.916404	+	0.494869i
$91$	134.874	+	97.9917i	1.48213	+	1.07683i
$92$	−9.82014	+	19.2731i	−0.106741	+	0.209490i
$93$	43.4834	−	43.4834i	0.467564	−	0.467564i
$94$	−70.0626	+	22.7647i	−0.745347	+	0.242178i
$95$	44.7518	+	64.7977i	0.471071	+	0.682081i
$96$	8.24670	−	25.3807i	0.0859032	−	0.264383i
$97$	117.203	−	59.7179i	1.20828	−	0.615649i	0.270446	−	0.962735i	$-0.412829\pi$
$97$	117.203	−	59.7179i	1.20828	−	0.615649i	0.937833	+	0.347087i	$0.112829\pi$
$98$	−20.5192	+	129.553i	−0.209380	+	1.32197i
$99$		−	144.783i		−	1.46245i
$100$	−48.2369	+	13.1607i	−0.482369	+	0.131607i
$101$	85.6222			0.847745			0.423872	−	0.905722i	$-0.360670\pi$
$101$	85.6222			0.847745			0.423872	+	0.905722i	$0.360670\pi$
$102$	−65.7665	−	10.4164i	−0.644769	−	0.102121i
$103$	−54.4018	−	106.770i	−0.528173	−	1.03660i	−0.988834	−	0.149022i	$-0.952388\pi$
$103$	−54.4018	−	106.770i	−0.528173	−	1.03660i	0.460661	−	0.887576i	$-0.347612\pi$
$104$	37.6669	+	12.2387i	0.362182	+	0.117680i
$105$	−280.757	−	6.71237i	−2.67388	−	0.0639274i
$106$	−15.0911	−	46.4456i	−0.142369	−	0.438166i
$107$	−132.988	−	132.988i	−1.24288	−	1.24288i	−0.958801	−	0.284080i	$-0.908312\pi$
$107$	−132.988	−	132.988i	−1.24288	−	1.24288i	−0.284080	−	0.958801i	$-0.591688\pi$
$108$	35.7792	+	18.2304i	0.331289	+	0.168800i
$109$	3.40517	−	4.68682i	0.0312401	−	0.0429983i	−0.793111	−	0.609077i	$-0.791540\pi$
$109$	3.40517	−	4.68682i	0.0312401	−	0.0429983i	0.824351	+	0.566078i	$0.191540\pi$
$110$	53.2896	+	55.9001i	0.484451	+	0.508183i
$111$	−96.4572	+	70.0802i	−0.868984	+	0.631354i
$112$	7.44996	+	47.0372i	0.0665175	+	0.419975i
$113$	93.3335	−	14.7826i	0.825961	−	0.130819i	0.270877	−	0.962614i	$-0.412686\pi$
$113$	93.3335	−	14.7826i	0.825961	−	0.130819i	0.555083	+	0.831795i	$0.312686\pi$
$114$	61.7638	+	85.0106i	0.541788	+	0.745707i
$115$	53.5979	−	7.18046i	0.466069	−	0.0624388i
$116$	6.99919	+	5.08521i	0.0603378	+	0.0438380i
$117$	−84.2687	+	165.387i	−0.720246	+	1.41356i
$118$	15.1871	−	15.1871i	0.128705	−	0.128705i
$119$	113.009	−	36.7190i	0.949658	−	0.308563i
$120$	−63.9265	+	19.0943i	−0.532721	+	0.159119i
$121$	−0.527824	+	1.62448i	−0.00436218	+	0.0134254i
$122$	−74.2558	+	37.8352i	−0.608654	+	0.310125i
$123$	−19.7173	+	124.490i	−0.160303	+	1.01211i
$124$			26.0703i			0.210244i
$125$	95.6029	+	80.5300i	0.764823	+	0.644240i
$126$	−223.197			−1.77140
$127$	227.247	+	35.9923i	1.78934	+	0.283404i	0.960946	−	0.276737i	$-0.0892532\pi$
$127$	227.247	+	35.9923i	1.78934	+	0.283404i	0.828397	+	0.560141i	$0.189253\pi$
$128$	5.13632	+	10.0806i	0.0401275	+	0.0787546i
$129$	−134.710	−	43.7699i	−1.04426	−	0.339301i
$130$	−28.3374	−	94.8717i	−0.217980	−	0.729782i
$131$	−22.6296	−	69.6469i	−0.172745	−	0.531656i	0.826778	−	0.562528i	$-0.190171\pi$
$131$	−22.6296	−	69.6469i	−0.172745	−	0.531656i	−0.999523	+	0.0308728i	$0.990171\pi$
$132$	72.8691	+	72.8691i	0.552039	+	0.552039i
$133$	−167.078	−	85.1305i	−1.25623	−	0.640079i
$134$	−80.7811	+	111.186i	−0.602844	+	0.829743i
$135$	−13.3300	−	99.5009i	−0.0987410	−	0.737043i
$136$	22.8375	−	16.5924i	0.167923	−	0.122003i
$137$	11.3116	+	71.4189i	0.0825667	+	0.521306i	0.993958	+	0.109764i	$0.0350095\pi$
$137$	11.3116	+	71.4189i	0.0825667	+	0.521306i	−0.911391	+	0.411542i	$0.864990\pi$
$138$	71.2687	−	11.2879i	0.516440	−	0.0817960i
$139$	−31.0454	−	42.7304i	−0.223349	−	0.307413i	0.682607	−	0.730786i	$-0.260846\pi$
$139$	−31.0454	−	42.7304i	−0.223349	−	0.307413i	−0.905956	+	0.423373i	$0.860846\pi$
$140$	86.1754	−	82.1511i	0.615539	−	0.586793i
$141$	198.813	+	144.446i	1.41002	+	1.02444i
$142$	42.1142	−	82.6537i	0.296579	−	0.582068i
$143$	−108.143	+	108.143i	−0.756247	+	0.756247i
$144$	−50.4286	+	16.3853i	−0.350199	+	0.113786i
$145$	0.516953	−	21.6225i	0.00356520	−	0.149121i
$146$	34.9339	−	107.516i	0.239274	−	0.736408i
$147$	389.868	−	198.648i	2.65216	−	1.35135i
$148$	7.90708	−	49.9234i	0.0534262	−	0.337320i
$149$			250.778i			1.68307i	0.540202	+	0.841536i	$0.318348\pi$
$149$			250.778i			1.68307i	−0.540202	+	0.841536i	$0.681652\pi$
$150$	130.099	+	104.375i	0.867327	+	0.695834i
$151$	−279.436			−1.85057			−0.925286	−	0.379269i	$-0.876175\pi$
$151$	−279.436			−1.85057			−0.925286	+	0.379269i	$0.876175\pi$
$152$	−43.9989	−	6.96874i	−0.289467	−	0.0458470i
$153$	60.0626	+	117.879i	0.392566	+	0.770454i
$154$	−174.899	−	56.8283i	−1.13571	−	0.369015i
$155$	53.6288	−	37.0381i	0.345992	−	0.238955i
$156$	−40.8267	−	125.652i	−0.261710	−	0.805459i
$157$	−181.969	−	181.969i	−1.15904	−	1.15904i	−0.984682	−	0.174358i	$-0.944215\pi$
$157$	−181.969	−	181.969i	−1.15904	−	1.15904i	−0.174358	−	0.984682i	$-0.555785\pi$
$158$	22.4368	+	11.4321i	0.142005	+	0.0723553i
$159$	−95.7558	+	131.797i	−0.602238	+	0.828909i
$160$	13.4395	−	24.8874i	0.0839967	−	0.155546i
$161$	−104.174	+	75.6869i	−0.647044	+	0.470105i
$162$	5.43862	+	34.3381i	0.0335717	+	0.211963i
$163$	56.7560	−	8.98926i	0.348196	−	0.0551488i	0.0201130	−	0.999798i	$-0.493597\pi$
$163$	56.7560	−	8.98926i	0.348196	−	0.0551488i	0.328083	+	0.944649i	$0.393597\pi$
$164$	−31.4080	−	43.2293i	−0.191512	−	0.263594i
$165$	46.3728	−	253.423i	0.281047	−	1.53590i
$166$	114.160	+	82.9419i	0.687710	+	0.499650i
$167$	97.8251	−	191.993i	0.585779	−	1.14966i	−0.387894	−	0.921704i	$-0.626797\pi$
$167$	97.8251	−	191.993i	0.585779	−	1.14966i	0.973672	−	0.227952i	$-0.0732028\pi$
$168$	112.335	−	112.335i	0.668660	−	0.668660i
$169$	25.7479	−	8.36602i	0.152355	−	0.0495031i
$170$	−66.5774	−	23.4059i	−0.391632	−	0.137682i
$171$	64.5164	−	198.561i	0.377289	−	1.16118i
$172$	53.5033	−	27.2613i	0.311066	−	0.158496i
$173$	−39.6355	+	250.249i	−0.229107	+	1.44653i	0.558067	+	0.829796i	$0.311543\pi$
$173$	−39.6355	+	250.249i	−0.229107	+	1.44653i	−0.787175	+	0.616730i	$0.788457\pi$
$174$		−	28.8601i		−	0.165863i
$175$	−291.421	−	60.5582i	−1.66527	−	0.346047i
$176$	−43.6883			−0.248229
$177$	−70.7651	−	11.2081i	−0.399803	−	0.0633225i
$178$	−7.04119	−	13.8191i	−0.0395572	−	0.0776355i
$179$	176.540	+	57.3613i	0.986256	+	0.320454i	0.757361	−	0.652997i	$-0.226489\pi$
$179$	176.540	+	57.3613i	0.986256	+	0.320454i	0.228896	+	0.973451i	$0.426489\pi$
$180$	105.350	+	80.4575i	0.585277	+	0.446986i
$181$	−54.7245	−	168.425i	−0.302346	−	0.930524i	−0.980654	−	0.195747i	$-0.937287\pi$
$181$	−54.7245	−	168.425i	−0.302346	−	0.930524i	0.678309	−	0.734777i	$-0.262713\pi$
$182$	166.713	+	166.713i	0.916008	+	0.916008i
$183$	247.707	+	126.213i	1.35359	+	0.689689i
$184$	−17.9806	+	24.7482i	−0.0977207	+	0.134501i
$185$	−113.930	+	54.6607i	−0.615839	+	0.295463i
$186$	70.3577	−	51.1178i	0.378267	−	0.274827i
$187$	17.0524	+	107.664i	0.0911891	+	0.575745i
$188$	−102.900	+	16.2977i	−0.547340	+	0.0866901i
$189$	140.508	+	193.392i	0.743426	+	1.02324i
$190$	48.1740	+	100.410i	0.253548	+	0.528474i
$191$	−188.360	−	136.852i	−0.986179	−	0.716501i	−0.0270979	−	0.999633i	$-0.508627\pi$
$191$	−188.360	−	136.852i	−0.986179	−	0.716501i	−0.959081	+	0.283132i	$0.908627\pi$
$192$	17.1340	−	33.6275i	0.0892398	−	0.175143i
$193$	150.137	−	150.137i	0.777914	−	0.777914i	−0.201562	−	0.979476i	$-0.564602\pi$
$193$	150.137	−	150.137i	0.777914	−	0.777914i	0.979476	+	0.201562i	$0.0646017\pi$
$194$	176.921	−	57.4851i	0.911964	−	0.296315i
$195$	−200.474	+	262.498i	−1.02807	+	1.34614i
$196$	−57.3226	+	176.421i	−0.292462	+	0.900107i
$197$	−207.677	+	105.817i	−1.05420	+	0.537141i	−0.893128	−	0.449802i	$-0.851494\pi$
$197$	−207.677	+	105.817i	−1.05420	+	0.537141i	−0.161070	+	0.986943i	$0.551494\pi$
$198$	32.0305	−	202.233i	0.161770	−	1.02138i
$199$		−	158.777i		−	0.797875i	−0.916978	−	0.398938i	$-0.869379\pi$
$199$		−	158.777i		−	0.797875i	0.916978	−	0.398938i	$-0.130621\pi$
$200$	−70.2889	+	7.71136i	−0.351445	+	0.0385568i
$201$	458.457			2.28088
$202$	119.597	+	18.9424i	0.592066	+	0.0937740i
$203$	23.3813	+	45.8883i	0.115179	+	0.226051i
$204$	−89.5583	−	29.0993i	−0.439011	−	0.142643i
$205$	−44.3052	+	126.025i	−0.216123	+	0.614756i
$206$	−52.3678	−	161.171i	−0.254212	−	0.782386i
$207$	−101.376	−	101.376i	−0.489741	−	0.489741i
$208$	49.9057	+	25.4282i	0.239931	+	0.122251i
$209$	101.112	−	139.168i	0.483788	−	0.665877i
$210$	−390.677	−	71.4882i	−1.86037	−	0.340420i
$211$	120.250	−	87.3667i	0.569905	−	0.414060i	−0.265166	−	0.964203i	$-0.585427\pi$
$211$	120.250	−	87.3667i	0.569905	−	0.414060i	0.835071	+	0.550143i	$0.185427\pi$
$212$	−10.8040	−	68.2140i	−0.0509624	−	0.321764i
$213$	−305.640	+	48.4085i	−1.43493	+	0.227270i
$214$	−156.337	−	215.179i	−0.730547	−	1.00551i
$215$	−132.091	−	71.3308i	−0.614377	−	0.331771i
$216$	45.9433	+	33.3798i	0.212700	+	0.154536i
$217$	−70.4570	+	138.280i	−0.324686	+	0.637233i
$218$	5.79323	−	5.79323i	0.0265744	−	0.0265744i
$219$	−358.657	+	116.535i	−1.63770	+	0.532122i
$220$	62.0681	+	89.8707i	0.282128	+	0.408503i
$221$	43.1855	−	132.911i	0.195409	−	0.601408i
$222$	−150.236	+	76.5489i	−0.676737	+	0.344815i
$223$	−61.3358	+	387.259i	−0.275048	+	1.73659i	0.333215	+	0.942851i	$0.391866\pi$
$223$	−61.3358	+	387.259i	−0.275048	+	1.73659i	−0.608263	+	0.793735i	$0.708134\pi$
$224$			67.3498i			0.300669i
$225$	15.8372	−	331.020i	0.0703875	−	1.47120i
$226$	133.639			0.591322
$227$	96.9149	+	15.3498i	0.426938	+	0.0676203i	0.366206	−	0.930534i	$-0.380657\pi$
$227$	96.9149	+	15.3498i	0.426938	+	0.0676203i	0.0607318	+	0.998154i	$0.480657\pi$
$228$	67.4648	+	132.407i	0.295898	+	0.580733i
$229$	166.723	+	54.1716i	0.728048	+	0.236557i	0.649509	−	0.760354i	$-0.274974\pi$
$229$	166.723	+	54.1716i	0.728048	+	0.236557i	0.0785390	+	0.996911i	$0.474974\pi$
$230$	76.4543	+	1.82788i	0.332410	+	0.00794730i
$231$	189.571	+	583.440i	0.820655	+	2.52572i
$232$	8.65147	+	8.65147i	0.0372908	+	0.0372908i
$233$	−247.354	−	126.033i	−1.06161	−	0.540916i	−0.166167	−	0.986098i	$-0.553139\pi$
$233$	−247.354	−	126.033i	−1.06161	−	0.540916i	−0.895440	+	0.445182i	$0.853139\pi$
$234$	−154.296	+	212.370i	−0.659383	+	0.907562i
$235$	179.716	+	188.520i	0.764749	+	0.802212i
$236$	24.5733	−	17.8535i	0.104124	−	0.0756506i
$237$	−13.1408	−	82.9677i	−0.0554464	−	0.350074i
$238$	165.975	−	26.2879i	0.697374	−	0.110453i
$239$	87.3521	+	120.230i	0.365490	+	0.503054i	0.951668	−	0.307128i	$-0.0993681\pi$
$239$	87.3521	+	120.230i	0.365490	+	0.503054i	−0.586178	+	0.810182i	$0.699368\pi$
$240$	−93.5169	+	12.5284i	−0.389654	+	0.0522016i
$241$	−29.7040	−	21.5812i	−0.123253	−	0.0895488i	0.524451	−	0.851441i	$-0.324271\pi$
$241$	−29.7040	−	21.5812i	−0.123253	−	0.0895488i	−0.647704	+	0.761892i	$0.724271\pi$
$242$	−1.09665	+	2.15230i	−0.00453162	+	0.00889380i
$243$	209.782	−	209.782i	0.863300	−	0.863300i
$244$	−112.091	+	36.4206i	−0.459389	+	0.149265i
$245$	444.352	−	132.724i	1.81368	−	0.541730i
$246$	−55.0822	+	169.526i	−0.223911	+	0.689129i
$247$	−196.502	+	100.123i	−0.795555	+	0.405355i
$248$	−5.76757	+	36.4150i	−0.0232563	+	0.146835i
$249$		−	470.721i		−	1.89045i
$250$	115.723	+	133.635i	0.462890	+	0.534540i
$251$	−354.053			−1.41057			−0.705286	−	0.708923i	$-0.749181\pi$
$251$	−354.053			−1.41057			−0.705286	+	0.708923i	$0.749181\pi$
$252$	−311.761	−	49.3782i	−1.23715	−	0.195945i
$253$	−53.6282	−	105.251i	−0.211969	−	0.416013i
$254$	309.456	+	100.548i	1.21833	+	0.395859i
$255$	67.3760	+	225.571i	0.264219	+	0.884590i
$256$	4.94427	+	15.2169i	0.0193136	+	0.0594410i
$257$	125.873	+	125.873i	0.489778	+	0.489778i	0.908236	−	0.418458i	$-0.137429\pi$
$257$	125.873	+	125.873i	0.489778	+	0.489778i	−0.418458	+	0.908236i	$0.637429\pi$
$258$	−178.480	−	90.9399i	−0.691782	−	0.352480i
$259$	176.862	−	243.429i	0.682864	−	0.939882i
$260$	−18.5930	−	138.786i	−0.0715117	−	0.533793i
$261$	−46.3904	+	33.7046i	−0.177741	+	0.129136i
$262$	−16.2010	−	102.289i	−0.0618360	−	0.390417i
$263$	102.171	−	16.1822i	0.388482	−	0.0615295i	0.0408614	−	0.999165i	$-0.486990\pi$
$263$	102.171	−	16.1822i	0.388482	−	0.0615295i	0.347620	+	0.937635i	$0.386990\pi$
$264$	85.6628	+	117.905i	0.324480	+	0.446609i
$265$	−124.973	+	119.137i	−0.471595	+	0.449572i
$266$	−214.541	−	155.874i	−0.806547	−	0.585991i
$267$	−23.4884	+	46.0987i	−0.0879717	+	0.172654i
$268$	−137.433	+	137.433i	−0.512810	+	0.512810i
$269$	23.0012	−	7.47355i	0.0855064	−	0.0277827i	−0.265951	−	0.963986i	$-0.585686\pi$
$269$	23.0012	−	7.47355i	0.0855064	−	0.0277827i	0.351458	+	0.936204i	$0.385686\pi$
$270$	3.39333	−	141.932i	0.0125679	−	0.525674i
$271$	54.0115	−	166.230i	0.199305	−	0.613396i	−0.800595	−	0.599206i	$-0.795483\pi$
$271$	54.0115	−	166.230i	0.199305	−	0.613396i	0.999899	−	0.0141902i	$-0.00451704\pi$
$272$	35.5703	−	18.1240i	0.130773	−	0.0666322i
$273$	123.034	−	776.808i	0.450675	−	2.84545i
$274$			102.261i			0.373214i
$275$	96.6915	−	255.359i	0.351606	−	0.928578i
$276$	102.045			0.369730
$277$	365.152	+	57.8343i	1.31824	+	0.208788i	0.775624	−	0.631195i	$-0.217435\pi$
$277$	365.152	+	57.8343i	1.31824	+	0.208788i	0.542613	+	0.839983i	$0.317435\pi$
$278$	−33.9110	−	66.5541i	−0.121982	−	0.239403i
$279$	−164.336	−	53.3960i	−0.589018	−	0.191384i
$280$	138.544	−	95.6840i	0.494802	−	0.341729i
$281$	89.3268	+	274.920i	0.317889	+	0.978362i	0.974549	+	0.224175i	$0.0719688\pi$
$281$	89.3268	+	274.920i	0.317889	+	0.978362i	−0.656660	+	0.754187i	$0.728031\pi$
$282$	245.747	+	245.747i	0.871443	+	0.871443i
$283$	−260.171	−	132.564i	−0.919334	−	0.468424i	−0.0707553	−	0.997494i	$-0.522541\pi$
$283$	−260.171	−	132.564i	−0.919334	−	0.468424i	−0.848578	+	0.529070i	$0.822541\pi$
$284$	77.1108	−	106.134i	0.271517	−	0.373711i
$285$	176.525	−	326.892i	0.619388	−	1.14699i
$286$	−174.979	+	127.130i	−0.611816	+	0.444511i
$287$	−49.7605	−	314.176i	−0.173382	−	1.09469i
$288$	−74.0638	+	11.7305i	−0.257166	+	0.0407311i
$289$	111.322	+	153.222i	0.385197	+	0.530179i
$290$	5.50566	−	30.0880i	0.0189851	−	0.103752i
$291$	−502.040	−	364.754i	−1.72522	−	1.25345i
$292$	72.5817	−	142.450i	0.248567	−	0.487841i
$293$	−97.8910	+	97.8910i	−0.334099	+	0.334099i	−0.854141	−	0.520042i	$-0.825916\pi$
$293$	−97.8910	+	97.8910i	−0.334099	+	0.334099i	0.520042	+	0.854141i	$0.325916\pi$
$294$	588.516	−	191.220i	2.00176	−	0.650410i
$295$	−71.6376	−	25.1848i	−0.242839	−	0.0853723i
$296$	22.0893	−	67.9838i	0.0746259	−	0.229675i
$297$	−195.392	+	99.5570i	−0.657884	+	0.335209i
$298$	−55.4800	+	350.287i	−0.186174	+	1.17546i
$299$			151.443i			0.506499i
$300$	158.632	+	174.573i	0.528772	+	0.581911i
$301$	357.463			1.18759
$302$	−390.318	−	61.8202i	−1.29244	−	0.204703i
$303$	−183.382	−	359.907i	−0.605221	−	1.18781i
$304$	−59.9161	−	19.4679i	−0.197092	−	0.0640392i
$305$	234.168	+	178.838i	0.767765	+	0.586355i
$306$	57.8169	+	177.942i	0.188944	+	0.581510i
$307$	158.687	+	158.687i	0.516896	+	0.516896i	0.916631	−	0.399735i	$-0.130898\pi$
$307$	158.687	+	158.687i	0.516896	+	0.516896i	−0.399735	+	0.916631i	$0.630898\pi$
$308$	−231.728	−	118.071i	−0.752363	−	0.383348i
$309$	−332.283	+	457.349i	−1.07535	+	1.48009i
$310$	83.1029	−	39.8705i	0.268074	−	0.128615i
$311$	−108.299	+	78.6839i	−0.348229	+	0.253003i	−0.748126	−	0.663557i	$-0.769046\pi$
$311$	−108.299	+	78.6839i	−0.348229	+	0.253003i	0.399897	+	0.916560i	$0.369046\pi$
$312$	−29.2287	−	184.543i	−0.0936817	−	0.591483i
$313$	455.593	−	72.1588i	1.45557	−	0.230539i	0.622027	−	0.782996i	$-0.286310\pi$
$313$	455.593	−	72.1588i	1.45557	−	0.230539i	0.833542	+	0.552457i	$0.186310\pi$
$314$	−213.918	−	294.433i	−0.681267	−	0.937683i
$315$	341.345	+	711.472i	1.08363	+	2.25864i
$316$	28.8107	+	20.9322i	0.0911730	+	0.0662411i
$317$	−30.6244	+	60.1038i	−0.0966070	+	0.189602i	−0.934252	−	0.356613i	$-0.883932\pi$
$317$	−30.6244	+	60.1038i	−0.0966070	+	0.189602i	0.837645	+	0.546214i	$0.183932\pi$
$318$	−162.910	+	162.910i	−0.512294	+	0.512294i
$319$	−44.9337	+	14.5998i	−0.140858	+	0.0457675i
$320$	24.2782	−	31.7895i	0.0758692	−	0.0993421i
$321$	−274.179	+	843.835i	−0.854139	+	2.62877i
$322$	−162.255	+	82.6731i	−0.503898	+	0.256749i
$323$	−24.5899	+	155.254i	−0.0761296	+	0.480663i
$324$			49.1667i			0.151749i
$325$	−259.080	+	235.421i	−0.797169	+	0.724373i
$326$	81.2656			0.249281
$327$	−26.9938	−	4.27539i	−0.0825498	−	0.0130746i
$328$	−34.3070	−	67.3313i	−0.104595	−	0.205278i
$329$	−589.838	−	191.650i	−1.79282	−	0.582523i
$330$	120.839	−	343.723i	0.366179	−	1.04159i
$331$	60.5799	+	186.446i	0.183021	+	0.563280i	0.999909	−	0.0135163i	$-0.00430251\pi$
$331$	60.5799	+	186.446i	0.183021	+	0.563280i	−0.816888	+	0.576797i	$0.804303\pi$
$332$	141.109	+	141.109i	0.425028	+	0.425028i
$333$	298.501	+	152.094i	0.896399	+	0.456738i
$334$	179.117	−	246.534i	0.536279	−	0.738124i
$335$	477.963	+	87.4603i	1.42675	+	0.261075i
$336$	181.762	−	132.058i	0.540957	−	0.393028i
$337$	57.2501	+	361.463i	0.169881	+	1.07259i	0.914348	+	0.404929i	$0.132704\pi$
$337$	57.2501	+	361.463i	0.169881	+	1.07259i	−0.744466	+	0.667660i	$0.767296\pi$
$338$	37.8156	−	5.98941i	0.111881	−	0.0177201i
$339$	−262.035	−	360.660i	−0.772965	−	1.06390i
$340$	−87.8173	−	47.4224i	−0.258286	−	0.139478i
$341$	−115.180	−	83.6835i	−0.337773	−	0.245406i
$342$	134.045	−	263.078i	0.391944	−	0.769233i
$343$	−368.319	+	368.319i	−1.07382	+	1.07382i
$344$	80.7646	−	26.2420i	0.234781	−	0.0762849i
$345$	−144.976	−	209.916i	−0.420221	−	0.608453i
$346$	−110.726	+	340.780i	−0.320017	+	0.984912i
$347$	−420.726	+	214.371i	−1.21247	+	0.617783i	−0.938940	−	0.344081i	$-0.888190\pi$
$347$	−420.726	+	214.371i	−1.21247	+	0.617783i	−0.273527	+	0.961864i	$0.588190\pi$
$348$	6.38477	−	40.3119i	0.0183470	−	0.115839i
$349$		−	436.033i		−	1.24938i	−0.780874	−	0.624689i	$-0.785226\pi$
$349$		−	436.033i		−	1.24938i	0.780874	−	0.624689i	$-0.214774\pi$
$350$	−393.661	−	149.059i	−1.12474	−	0.425884i
$351$	281.144			0.800979
$352$	−61.0240	−	9.66525i	−0.173364	−	0.0274581i
$353$	233.399	+	458.071i	0.661186	+	1.29765i	0.941263	+	0.337673i	$0.109640\pi$
$353$	233.399	+	458.071i	0.661186	+	1.29765i	−0.280077	+	0.959977i	$0.590360\pi$
$354$	−96.3652	−	31.3110i	−0.272218	−	0.0884490i
$355$	−327.878	−	7.83895i	−0.923600	−	0.0220816i
$356$	−6.77792	−	20.8603i	−0.0190391	−	0.0585964i
$357$	−396.384	−	396.384i	−1.11032	−	1.11032i
$358$	233.901	+	119.179i	0.653355	+	0.332901i
$359$	251.399	−	346.021i	0.700275	−	0.963846i	−0.299677	−	0.954041i	$-0.596879\pi$
$359$	251.399	−	346.021i	0.700275	−	0.963846i	0.999952	−	0.00980492i	$-0.00312105\pi$
$360$	129.353	+	135.690i	0.359315	+	0.376917i
$361$	−91.3715	+	66.3853i	−0.253107	+	0.183893i
$362$	−39.1784	−	247.363i	−0.108228	−	0.683323i
$363$	7.95885	−	1.26056i	0.0219252	−	0.00347261i
$364$	195.983	+	269.748i	0.538416	+	0.741066i
$365$	−396.148	+	53.0716i	−1.08534	+	0.145402i
$366$	318.076	+	231.095i	0.869059	+	0.631408i
$367$	78.1469	−	153.372i	0.212934	−	0.417907i	−0.759692	−	0.650283i	$-0.774650\pi$
$367$	78.1469	−	153.372i	0.212934	−	0.417907i	0.972626	+	0.232377i	$0.0746501\pi$
$368$	−30.5904	+	30.5904i	−0.0831262	+	0.0831262i
$369$	336.828	−	109.442i	0.912813	−	0.296591i
$370$	−171.231	+	51.1451i	−0.462786	+	0.138230i
$371$	127.048	−	391.013i	0.342447	−	1.05394i
$372$	109.585	−	55.8362i	0.294582	−	0.150097i
$373$	88.8954	−	561.263i	0.238325	−	1.50473i	−0.520741	−	0.853714i	$-0.674344\pi$
$373$	88.8954	−	561.263i	0.238325	−	1.50473i	0.759067	−	0.651013i	$-0.225656\pi$
$374$			154.158i			0.412188i
$375$	133.744	−	574.336i	0.356651	−	1.53156i
$376$	−147.336			−0.391852
$377$	59.8258	+	9.47548i	0.158689	+	0.0251339i
$378$	153.477	+	301.215i	0.406023	+	0.796866i
$379$	121.129	+	39.3572i	0.319602	+	0.103845i	0.464425	−	0.885613i	$-0.346261\pi$
$379$	121.129	+	39.3572i	0.319602	+	0.103845i	−0.144823	+	0.989458i	$0.546261\pi$
$380$	45.0757	+	150.911i	0.118620	+	0.397133i
$381$	−335.415	−	1032.30i	−0.880355	−	2.70945i
$382$	−232.826	−	232.826i	−0.609492	−	0.609492i
$383$	41.3418	+	21.0647i	0.107942	+	0.0549992i	0.507128	−	0.861871i	$-0.330707\pi$
$383$	41.3418	+	21.0647i	0.107942	+	0.0549992i	−0.399186	+	0.916870i	$0.630707\pi$
$384$	31.3723	−	43.1803i	0.0816988	−	0.112449i
$385$	86.3334	+	644.428i	0.224243	+	1.67384i
$386$	242.927	−	176.497i	0.629346	−	0.457246i
$387$	62.2606	+	393.098i	0.160880	+	1.01576i
$388$	259.841	−	41.1548i	0.669694	−	0.106069i
$389$	80.1323	+	110.293i	0.205996	+	0.283529i	0.899497	−	0.436926i	$-0.143933\pi$
$389$	80.1323	+	110.293i	0.205996	+	0.283529i	−0.693502	+	0.720455i	$0.743933\pi$
$390$	−338.095	+	322.306i	−0.866910	+	0.826426i
$391$	87.3263	+	63.4462i	0.223341	+	0.162267i
$392$	−119.098	+	233.744i	−0.303822	+	0.596285i
$393$	−244.289	+	244.289i	−0.621600	+	0.621600i
$394$	−313.494	+	101.860i	−0.795669	+	0.258529i
$395$	2.12793	−	89.0045i	0.00538716	−	0.225328i
$396$	89.4806	−	275.393i	0.225961	−	0.695437i
$397$	341.113	−	173.806i	0.859227	−	0.437798i	0.0318816	−	0.999492i	$-0.489850\pi$
$397$	341.113	−	173.806i	0.859227	−	0.437798i	0.827345	+	0.561694i	$0.189850\pi$
$398$	35.1265	−	221.780i	0.0882576	−	0.557237i
$399$			884.630i			2.21712i
$400$	−99.8857	−	4.77889i	−0.249714	−	0.0119472i
$401$	424.132			1.05768			0.528842	−	0.848720i	$-0.322626\pi$
$401$	424.132			1.05768			0.528842	+	0.848720i	$0.322626\pi$
$402$	640.374	+	101.425i	1.59297	+	0.252302i
$403$	82.8650	+	162.632i	0.205620	+	0.403553i
$404$	162.863	+	52.9175i	0.403127	+	0.130984i
$405$	101.140	−	69.8512i	0.249729	−	0.172472i
$406$	22.5071	+	69.2696i	0.0554361	+	0.170615i
$407$	195.184	+	195.184i	0.479568	+	0.479568i
$408$	−118.658	−	60.4590i	−0.290827	−	0.148184i
$409$	−41.4213	+	57.0116i	−0.101275	+	0.139393i	−0.856647	−	0.515904i	$-0.827456\pi$
$409$	−41.4213	+	57.0116i	−0.101275	+	0.139393i	0.755372	+	0.655296i	$0.227456\pi$
$410$	−89.7663	+	166.230i	−0.218942	+	0.405439i
$411$	275.978	−	200.509i	0.671478	−	0.487858i
$412$	−37.4912	−	236.710i	−0.0909980	−	0.574539i
$413$	178.590	−	28.2859i	0.432421	−	0.0684888i
$414$	−119.175	−	164.030i	−0.287862	−	0.396209i
$415$	89.7998	−	490.748i	0.216385	−	1.18253i
$416$	64.0828	+	46.5589i	0.154045	+	0.111920i
$417$	−113.123	+	222.015i	−0.271277	+	0.532411i
$418$	172.021	−	172.021i	0.411535	−	0.411535i
$419$	−426.885	+	138.703i	−1.01882	+	0.331034i	−0.770360	−	0.637609i	$-0.779924\pi$
$419$	−426.885	+	138.703i	−1.01882	+	0.331034i	−0.248458	+	0.968643i	$0.579924\pi$
$420$	−529.883	−	186.285i	−1.26163	−	0.443536i
$421$	96.5333	−	297.099i	0.229295	−	0.705698i	−0.768532	−	0.639811i	$-0.779012\pi$
$421$	96.5333	−	297.099i	0.229295	−	0.705698i	0.997827	−	0.0658866i	$-0.0209876\pi$
$422$	187.294	−	95.4309i	0.443824	−	0.226140i
$423$	108.021	−	682.018i	0.255369	−	1.61234i
$424$		−	97.6716i		−	0.230358i
$425$	27.2103	+	248.021i	0.0640241	+	0.583579i
$426$	−437.627			−1.02729
$427$	−692.972	−	109.756i	−1.62289	−	0.257040i
$428$	−170.767	−	335.150i	−0.398989	−	0.783060i
$429$	686.189	+	222.956i	1.59951	+	0.519712i
$430$	−168.725	−	128.858i	−0.392383	−	0.299669i
$431$	−6.66936	−	20.5262i	−0.0154742	−	0.0476245i	0.943021	−	0.332732i	$-0.107971\pi$
$431$	−6.66936	−	20.5262i	−0.0154742	−	0.0476245i	−0.958495	+	0.285108i	$0.907971\pi$
$432$	56.7890	+	56.7890i	0.131456	+	0.131456i
$433$	−489.321	−	249.322i	−1.13007	−	0.575800i	−0.214008	−	0.976832i	$-0.568652\pi$
$433$	−489.321	−	249.322i	−1.13007	−	0.575800i	−0.916064	+	0.401032i	$0.868652\pi$
$434$	−129.006	+	177.562i	−0.297250	+	0.409129i
$435$	−91.9959	+	44.1371i	−0.211485	+	0.101465i
$436$	9.37364	−	6.81035i	0.0214992	−	0.0156201i
$437$	−26.6471	−	168.243i	−0.0609774	−	0.384996i
$438$	−526.755	+	83.4297i	−1.20264	+	0.190479i
$439$	117.604	+	161.869i	0.267892	+	0.368721i	0.921676	−	0.387959i	$-0.126820\pi$
$439$	117.604	+	161.869i	0.267892	+	0.368721i	−0.653785	+	0.756680i	$0.726820\pi$
$440$	66.8146	+	139.263i	0.151851	+	0.316507i
$441$	−994.678	−	722.676i	−2.25551	−	1.63872i
$442$	89.7258	−	176.097i	0.202999	−	0.398409i
$443$	100.812	−	100.812i	0.227566	−	0.227566i	−0.584109	−	0.811675i	$-0.698556\pi$
$443$	100.812	−	100.812i	0.227566	−	0.227566i	0.811675	+	0.584109i	$0.198556\pi$
$444$	−226.784	+	73.6867i	−0.510776	+	0.165961i
$445$	−33.2820	+	43.5791i	−0.0747911	+	0.0979305i
$446$	−171.348	+	527.354i	−0.384188	+	1.18241i
$447$	1054.13	−	537.104i	2.35822	−	1.20158i
$448$	−14.8999	+	94.0744i	−0.0332588	+	0.209987i
$449$			594.424i			1.32389i	0.749554	+	0.661943i	$0.230268\pi$
$449$			594.424i			1.32389i	−0.749554	+	0.661943i	$0.769732\pi$
$450$	95.3536	−	458.866i	0.211897	−	1.01970i
$451$	291.808			0.647023
$452$	186.667	+	29.5652i	0.412980	+	0.0654097i
$453$	598.485	+	1174.59i	1.32116	+	2.59292i
$454$	131.975	+	42.8813i	0.290694	+	0.0944522i
$455$	276.461	−	786.386i	0.607606	−	1.72832i
$456$	64.9423	+	199.872i	0.142417	+	0.438315i
$457$	−120.448	−	120.448i	−0.263562	−	0.263562i	0.562937	−	0.826500i	$-0.309671\pi$
$457$	−120.448	−	120.448i	−0.263562	−	0.263562i	−0.826500	+	0.562937i	$0.809671\pi$
$458$	220.895	+	112.551i	0.482303	+	0.245745i
$459$	117.784	−	162.115i	0.256609	−	0.353192i
$460$	106.387	+	19.4673i	0.231276	+	0.0423202i
$461$	306.035	−	222.347i	0.663850	−	0.482315i	−0.204111	−	0.978948i	$-0.565430\pi$
$461$	306.035	−	222.347i	0.663850	−	0.482315i	0.867961	+	0.496632i	$0.165430\pi$
$462$	135.718	+	856.890i	0.293762	+	1.85474i
$463$	−50.4954	+	7.99769i	−0.109061	+	0.0172736i	−0.210727	−	0.977545i	$-0.567583\pi$
$463$	−50.4954	+	7.99769i	−0.109061	+	0.0172736i	0.101665	+	0.994819i	$0.467583\pi$
$464$	10.1704	+	13.9984i	0.0219190	+	0.0301689i
$465$	−270.547	−	146.099i	−0.581821	−	0.314190i
$466$	−317.623	−	230.766i	−0.681593	−	0.495207i
$467$	−311.558	+	611.468i	−0.667149	+	1.30935i	0.270819	+	0.962630i	$0.412705\pi$
$467$	−311.558	+	611.468i	−0.667149	+	1.30935i	−0.937968	+	0.346723i	$0.887295\pi$
$468$	−262.503	+	262.503i	−0.560904	+	0.560904i
$469$	−1100.38	+	357.536i	−2.34623	+	0.762337i
$470$	209.321	+	303.084i	0.445364	+	0.644859i
$471$	−375.162	+	1154.63i	−0.796522	+	2.45144i
$472$	38.2738	−	19.5015i	0.0810886	−	0.0413167i
$473$	−51.2989	+	323.888i	−0.108454	+	0.684753i
$474$		−	118.797i		−	0.250626i
$475$	246.397	−	307.124i	0.518731	−	0.646576i
$476$	237.650			0.499265
$477$	452.120	+	71.6088i	0.947842	+	0.150123i
$478$	95.4149	+	187.262i	0.199613	+	0.391762i
$479$	54.9406	+	17.8513i	0.114698	+	0.0372678i	0.365804	−	0.930692i	$-0.380794\pi$
$479$	54.9406	+	17.8513i	0.114698	+	0.0372678i	−0.251105	+	0.967960i	$0.580794\pi$
$480$	−133.396	−	3.18926i	−0.277909	−	0.00664429i
$481$	−109.357	−	336.565i	−0.227353	−	0.699720i
$482$	−36.7162	−	36.7162i	−0.0761747	−	0.0761747i
$483$	541.260	+	275.786i	1.12062	+	0.570985i
$484$	−2.00796	+	2.76372i	−0.00414868	+	0.00571017i
$485$	−453.816	−	476.047i	−0.935703	−	0.981540i
$486$	339.434	−	246.614i	0.698425	−	0.507435i
$487$	45.4546	+	286.989i	0.0933360	+	0.589300i	0.989382	+	0.145339i	$0.0464272\pi$
$487$	45.4546	+	286.989i	0.0933360	+	0.589300i	−0.896046	+	0.443961i	$0.853573\pi$
$488$	−164.626	+	26.0743i	−0.337349	+	0.0534309i
$489$	−159.343	−	219.317i	−0.325855	−	0.448501i
$490$	650.034	−	87.0844i	1.32660	−	0.177723i
$491$	210.550	+	152.974i	0.428819	+	0.311555i	0.781177	−	0.624310i	$-0.214620\pi$
$491$	210.550	+	152.974i	0.428819	+	0.311555i	−0.352357	+	0.935865i	$0.614620\pi$
$492$	−114.443	+	224.608i	−0.232609	+	0.456520i
$493$	30.5275	−	30.5275i	0.0619219	−	0.0619219i
$494$	−296.625	+	96.3792i	−0.600455	+	0.195100i
$495$	−693.632	+	207.182i	−1.40128	+	0.418549i
$496$	−16.1123	+	49.5886i	−0.0324845	+	0.0999770i
$497$	695.839	−	354.548i	1.40008	−	0.713376i
$498$	104.138	−	657.504i	0.209113	−	1.32029i
$499$			58.9853i			0.118207i	0.998252	+	0.0591035i	$0.0188242\pi$
$499$			58.9853i			0.118207i	−0.998252	+	0.0591035i	$0.981176\pi$
$500$	132.077	+	212.263i	0.264155	+	0.424526i
$501$	−1016.54			−2.02903
$502$	−494.542	−	78.3278i	−0.985144	−	0.156032i
$503$	−381.004	−	747.763i	−0.757464	−	1.48661i	−0.870049	−	0.492965i	$-0.835913\pi$
$503$	−381.004	−	747.763i	−0.757464	−	1.48661i	0.112585	−	0.993642i	$-0.464087\pi$
$504$	−424.545	−	137.943i	−0.842351	−	0.273696i
$505$	−122.524	−	410.204i	−0.242622	−	0.812284i
$506$	−51.6230	−	158.879i	−0.102022	−	0.313991i
$507$	−90.3118	−	90.3118i	−0.178130	−	0.178130i
$508$	410.004	+	208.908i	0.807095	+	0.411235i
$509$	−327.038	+	450.129i	−0.642510	+	0.884340i	−0.998746	−	0.0500563i	$-0.984060\pi$
$509$	−327.038	+	450.129i	−0.642510	+	0.884340i	0.356236	+	0.934396i	$0.384060\pi$
$510$	44.2075	+	329.983i	0.0866814	+	0.647026i
$511$	769.962	−	559.410i	1.50678	−	1.09474i
$512$	3.53971	+	22.3488i	0.00691349	+	0.0436501i
$513$	−312.332	+	49.4685i	−0.608835	+	0.0964299i
$514$	147.972	+	203.667i	0.287884	+	0.396238i
$515$	−433.669	+	413.417i	−0.842076	+	0.802752i
$516$	−229.182	−	166.510i	−0.444151	−	0.322695i
$517$	258.296	−	506.934i	0.499605	−	0.980530i
$518$	300.895	−	300.895i	0.580879	−	0.580879i
$519$	1136.79	−	369.367i	2.19035	−	0.711689i
$520$	4.73310	−	197.970i	0.00910211	−	0.380712i
$521$	−261.077	+	803.512i	−0.501107	+	1.54225i	0.306110	+	0.951996i	$0.400972\pi$
$521$	−261.077	+	803.512i	−0.501107	+	1.54225i	−0.807218	+	0.590254i	$0.799028\pi$
$522$	−72.2548	+	36.8157i	−0.138419	+	0.0705281i
$523$	16.0763	−	101.502i	0.0307386	−	0.194076i	−0.967541	−	0.252716i	$-0.918676\pi$
$523$	16.0763	−	101.502i	0.0307386	−	0.194076i	0.998279	+	0.0586397i	$0.0186763\pi$
$524$		−	146.462i		−	0.279508i
$525$	369.601	+	1354.67i	0.704002	+	2.58033i
$526$	146.292			0.278122
$527$	128.494	+	20.3514i	0.243821	+	0.0386175i
$528$	93.5697	+	183.641i	0.177215	+	0.347805i
$529$	391.862	+	127.324i	0.740760	+	0.240688i
$530$	−200.919	+	138.762i	−0.379092	+	0.261816i
$531$	62.2113	+	191.467i	0.117159	+	0.360577i
$532$	−265.188	−	265.188i	−0.498473	−	0.498473i
$533$	−333.335	−	169.843i	−0.625394	−	0.318654i
$534$	−43.0072	+	59.1943i	−0.0805378	+	0.110851i
$535$	−446.823	+	827.431i	−0.835183	+	1.54660i
$536$	−222.371	+	161.562i	−0.414872	+	0.301422i
$537$	−136.991	−	864.927i	−0.255104	−	1.61067i
$538$	33.7815	−	5.35047i	0.0627909	−	0.00994511i
$539$	−595.440	−	819.553i	−1.10471	−	1.52051i
$540$	36.1397	−	197.500i	0.0669253	−	0.365741i
$541$	400.700	+	291.125i	0.740665	+	0.538124i	0.892919	−	0.450217i	$-0.148653\pi$
$541$	400.700	+	291.125i	0.740665	+	0.538124i	−0.152255	+	0.988341i	$0.548653\pi$
$542$	112.219	−	220.242i	0.207046	−	0.406350i
$543$	−590.756	+	590.756i	−1.08795	+	1.08795i
$544$	53.6942	−	17.4463i	0.0987027	−	0.0320704i
$545$	−27.3266	−	9.60691i	−0.0501406	−	0.0176274i
$546$	343.709	−	1057.83i	0.629504	−	1.93741i
$547$	−548.489	+	279.469i	−1.00272	+	0.510912i	−0.876660	−	0.481110i	$-0.840234\pi$
$547$	−548.489	+	279.469i	−1.00272	+	0.510912i	−0.126062	+	0.992022i	$0.540234\pi$
$548$	−22.6233	+	142.838i	−0.0412834	+	0.260653i
$549$		−	781.170i		−	1.42290i
$550$	191.552	−	335.295i	0.348277	−	0.609627i
$551$	−68.1298			−0.123648
$552$	142.537	+	22.5757i	0.258220	+	0.0408980i
$553$	96.2441	+	188.890i	0.174040	+	0.341573i
$554$	497.250	+	161.566i	0.897563	+	0.291636i
$555$	473.773	+	361.828i	0.853645	+	0.651943i
$556$	−32.6431	−	100.465i	−0.0587106	−	0.180693i
$557$	−65.6218	−	65.6218i	−0.117813	−	0.117813i	0.645742	−	0.763555i	$-0.276548\pi$
$557$	−65.6218	−	65.6218i	−0.117813	−	0.117813i	−0.763555	+	0.645742i	$0.776548\pi$
$558$	−217.732	−	110.940i	−0.390201	−	0.198817i
$559$	247.114	−	340.123i	0.442064	−	0.608449i
$560$	214.688	−	103.001i	0.383371	−	0.183931i
$561$	416.038	−	302.269i	0.741600	−	0.538804i
$562$	63.9510	+	403.770i	0.113792	+	0.718453i
$563$	944.052	−	149.523i	1.67682	−	0.265583i	0.755718	−	0.654897i	$-0.227288\pi$
$563$	944.052	−	149.523i	1.67682	−	0.265583i	0.921105	+	0.389314i	$0.127288\pi$
$564$	288.893	+	397.627i	0.512221	+	0.705012i
$565$	−204.380	−	425.994i	−0.361735	−	0.753971i
$566$	−334.081	−	242.724i	−0.590249	−	0.428841i
$567$	−132.877	+	260.785i	−0.234351	+	0.459939i
$568$	131.189	−	131.189i	0.230966	−	0.230966i
$569$	675.070	−	219.343i	1.18641	−	0.385489i	0.351668	−	0.936125i	$-0.385615\pi$
$569$	675.070	−	219.343i	1.18641	−	0.385489i	0.834746	+	0.550635i	$0.185615\pi$
$570$	318.890	−	417.550i	0.559456	−	0.732544i
$571$	29.6017	−	91.1046i	0.0518418	−	0.159553i	−0.921784	−	0.387704i	$-0.873268\pi$
$571$	29.6017	−	91.1046i	0.0518418	−	0.159553i	0.973626	+	0.228152i	$0.0732682\pi$
$572$	−272.537	+	138.864i	−0.476463	+	0.242770i
$573$	−171.825	+	1084.86i	−0.299869	+	1.89330i
$574$		−	449.850i		−	0.783710i
$575$	−111.098	−	246.505i	−0.193215	−	0.428704i
$576$	−106.048			−0.184110
$577$	−190.430	−	30.1612i	−0.330035	−	0.0522725i	−0.0107820	−	0.999942i	$-0.503432\pi$
$577$	−190.430	−	30.1612i	−0.330035	−	0.0522725i	−0.319253	+	0.947669i	$0.603432\pi$
$578$	121.597	+	238.648i	0.210376	+	0.412886i
$579$	−952.650	−	309.535i	−1.64534	−	0.534602i
$580$	14.3467	−	40.8089i	0.0247358	−	0.0703602i
$581$	367.100	+	1129.82i	0.631842	+	1.94461i
$582$	−620.556	−	620.556i	−1.06625	−	1.06625i
$583$	336.055	+	171.228i	0.576423	+	0.293702i
$584$	132.897	−	182.917i	0.227563	−	0.313213i
$585$	912.931	+	167.053i	1.56057	+	0.285561i
$586$	−158.391	+	115.078i	−0.270292	+	0.196378i
$587$	−66.5873	−	420.416i	−0.113437	−	0.716211i	−0.977201	−	0.212315i	$-0.931900\pi$
$587$	−66.5873	−	420.416i	−0.113437	−	0.716211i	0.863765	−	0.503896i	$-0.168100\pi$
$588$	864.345	−	136.899i	1.46997	−	0.232821i
$589$	−120.673	−	166.093i	−0.204878	−	0.281991i
$590$	−94.4919	−	51.0268i	−0.160156	−	0.0864860i
$591$	889.587	+	646.323i	1.50522	+	1.09361i
$592$	45.8945	−	90.0730i	0.0775245	−	0.152150i
$593$	161.153	−	161.153i	0.271759	−	0.271759i	−0.558049	−	0.829808i	$-0.688450\pi$
$593$	161.153	−	161.153i	0.271759	−	0.271759i	0.829808	+	0.558049i	$0.188450\pi$
$594$	−294.949	+	95.8346i	−0.496547	+	0.161338i
$595$	−337.630	−	488.867i	−0.567445	−	0.821625i
$596$	−154.989	+	477.007i	−0.260049	+	0.800348i
$597$	−667.409	+	340.062i	−1.11794	+	0.569618i
$598$	−33.5040	+	211.536i	−0.0560268	+	0.353739i
$599$		−	302.025i		−	0.504216i	−0.967699	−	0.252108i	$-0.918876\pi$
$599$		−	302.025i		−	0.504216i	0.967699	−	0.252108i	$-0.0811238\pi$
$600$	182.956	+	278.939i	0.304926	+	0.464898i
$601$	−147.116			−0.244786			−0.122393	−	0.992482i	$-0.539057\pi$
$601$	−147.116			−0.244786			−0.122393	+	0.992482i	$0.539057\pi$
$602$	499.305	+	79.0822i	0.829411	+	0.131366i
$603$	−584.835	−	1147.80i	−0.969876	−	1.90349i
$604$	−531.520	−	172.701i	−0.880000	−	0.285929i
$605$	8.53794	+	0.204126i	0.0141123	+	0.000337399i
$606$	−176.525	−	543.289i	−0.291296	−	0.896517i
$607$	−166.801	−	166.801i	−0.274796	−	0.274796i	0.556231	−	0.831028i	$-0.312247\pi$
$607$	−166.801	−	166.801i	−0.274796	−	0.274796i	−0.831028	+	0.556231i	$0.812247\pi$
$608$	−79.3840	−	40.4482i	−0.130566	−	0.0665266i
$609$	142.812	−	196.563i	0.234502	−	0.322764i
$610$	287.522	+	301.607i	0.471348	+	0.494438i
$611$	−590.108	+	428.739i	−0.965807	+	0.701700i
$612$	41.3923	+	261.341i	0.0676345	+	0.427027i
$613$	−688.785	+	109.093i	−1.12363	+	0.177965i	−0.690476	−	0.723355i	$-0.742599\pi$
$613$	−688.785	+	109.093i	−1.12363	+	0.177965i	−0.433153	+	0.901320i	$0.642599\pi$
$614$	186.548	+	256.761i	0.303824	+	0.418177i
$615$	624.628	−	83.6808i	1.01566	−	0.136066i
$616$	−297.557	−	216.188i	−0.483047	−	0.350954i
$617$	393.489	−	772.265i	0.637745	−	1.25165i	−0.315350	−	0.948975i	$-0.602122\pi$
$617$	393.489	−	772.265i	0.637745	−	1.25165i	0.953095	−	0.302670i	$-0.0978781\pi$
$618$	−565.314	+	565.314i	−0.914748	+	0.914748i
$619$	114.108	−	37.0760i	0.184343	−	0.0598966i	−0.215391	−	0.976528i	$-0.569103\pi$
$619$	114.108	−	37.0760i	0.184343	−	0.0598966i	0.399734	+	0.916631i	$0.369103\pi$
$620$	124.899	−	37.3062i	0.201450	−	0.0601713i
$621$	−67.1031	+	206.522i	−0.108057	+	0.332564i
$622$	−168.680	+	85.9467i	−0.271189	+	0.138178i
$623$	20.4258	−	128.963i	0.0327861	−	0.207004i
$624$		−	264.236i		−	0.423455i
$625$	249.001	−	573.257i	0.398402	−	0.917211i
$626$	652.337			1.04207
$627$	−801.541	−	126.952i	−1.27837	−	0.202475i
$628$	−233.663	−	458.589i	−0.372075	−	0.730238i
$629$	−239.887	−	77.9440i	−0.381378	−	0.123917i
$630$	319.391	+	1069.30i	0.506970	+	1.69730i
$631$	40.7698	+	125.476i	0.0646113	+	0.198853i	0.978151	−	0.207897i	$-0.0666619\pi$
$631$	40.7698	+	125.476i	0.0646113	+	0.198853i	−0.913539	+	0.406750i	$0.866662\pi$
$632$	35.6120	+	35.6120i	0.0563480	+	0.0563480i
$633$	−624.786	−	318.344i	−0.987024	−	0.502914i
$634$	−56.0731	+	77.1780i	−0.0884434	+	0.121732i
$635$	−152.753	−	1140.21i	−0.240555	−	1.79561i
$636$	−263.593	+	191.512i	−0.414455	+	0.301119i
$637$	203.168	+	1282.75i	0.318945	+	2.01374i
$638$	−65.9934	+	10.4523i	−0.103438	+	0.0163830i
$639$	511.088	+	703.453i	0.799825	+	1.10087i
$640$	40.9446	−	39.0325i	0.0639760	−	0.0609883i
$641$	144.903	+	105.278i	0.226058	+	0.164241i	0.695050	−	0.718962i	$-0.255382\pi$
$641$	144.903	+	105.278i	0.226058	+	0.164241i	−0.468991	+	0.883203i	$0.655382\pi$
$642$	−569.656	+	1118.01i	−0.887315	+	1.74145i
$643$	40.3319	−	40.3319i	0.0627245	−	0.0627245i	−0.675049	−	0.737773i	$-0.735877\pi$
$643$	40.3319	−	40.3319i	0.0627245	−	0.0627245i	0.737773	+	0.675049i	$0.235877\pi$
$644$	−244.928	+	79.5820i	−0.380323	+	0.123574i
$645$	−16.9272	+	708.009i	−0.0262437	+	1.09769i
$646$	−68.6943	+	211.419i	−0.106338	+	0.327275i
$647$	−96.4539	+	49.1457i	−0.149079	+	0.0759594i	−0.526938	−	0.849903i	$-0.676660\pi$
$647$	−96.4539	+	49.1457i	−0.149079	+	0.0759594i	0.377860	+	0.925863i	$0.376660\pi$
$648$	−10.8772	+	68.6761i	−0.0167858	+	0.105982i
$649$			165.875i			0.255586i
$650$	−413.966	+	271.520i	−0.636871	+	0.417723i
$651$	732.150			1.12465
$652$	113.512	+	17.9785i	0.174098	+	0.0275744i
$653$	−350.044	−	687.000i	−0.536055	−	1.05207i	−0.987181	−	0.159607i	$-0.948977\pi$
$653$	−350.044	−	687.000i	−0.536055	−	1.05207i	0.451126	−	0.892460i	$-0.351023\pi$
$654$	−36.7591	−	11.9438i	−0.0562066	−	0.0182626i
$655$	−301.285	+	208.079i	−0.459978	+	0.317678i
$656$	−33.0243	−	101.638i	−0.0503419	−	0.154936i
$657$	749.283	+	749.283i	1.14046	+	1.14046i
$658$	−781.488	−	398.188i	−1.18767	−	0.605149i
$659$	−697.843	+	960.499i	−1.05894	+	1.45751i	−0.178152	+	0.984003i	$0.557012\pi$
$659$	−697.843	+	960.499i	−1.05894	+	1.45751i	−0.880790	+	0.473506i	$0.842988\pi$
$660$	244.831	−	453.380i	0.370955	−	0.686939i
$661$	−1026.11	+	745.510i	−1.55235	+	1.12785i	−0.610409	+	0.792086i	$0.708995\pi$
$661$	−1026.11	+	745.510i	−1.55235	+	1.12785i	−0.941946	+	0.335766i	$0.891005\pi$
$662$	43.3704	+	273.830i	0.0655142	+	0.413641i
$663$	−651.176	+	103.136i	−0.982166	+	0.155560i
$664$	165.884	+	228.320i	0.249825	+	0.343855i
$665$	−168.762	+	922.267i	−0.253777	+	1.38687i
$666$	383.299	+	278.483i	0.575524	+	0.418142i
$667$	−21.2397	+	41.6852i	−0.0318436	+	0.0624965i
$668$	304.732	−	304.732i	0.456186	−	0.456186i
$669$	1759.18	−	571.593i	2.62957	−	0.854399i
$670$	648.271	+	227.905i	0.967568	+	0.340157i
$671$	198.894	−	612.134i	0.296415	−	0.912271i
$672$	283.100	−	144.247i	0.421280	−	0.214653i
$673$	−2.43582	+	15.3791i	−0.00361934	+	0.0228516i	−0.989432	−	0.144998i	$-0.953682\pi$
$673$	−2.43582	+	15.3791i	−0.00361934	+	0.0228516i	0.985813	+	0.167850i	$0.0536824\pi$
$674$			517.557i			0.767889i
$675$	−457.619	+	206.247i	−0.677954	+	0.305551i
$676$	54.1460			0.0800976
$677$	−75.1252	−	11.8987i	−0.110968	−	0.0175756i	0.100704	−	0.994916i	$-0.467891\pi$
$677$	−75.1252	−	11.8987i	−0.110968	−	0.0175756i	−0.211671	+	0.977341i	$0.567891\pi$
$678$	−286.222	−	561.742i	−0.422156	−	0.828528i
$679$	1489.45	+	483.951i	2.19359	+	0.712742i
$680$	−112.172	−	85.6677i	−0.164959	−	0.125982i
$681$	−143.046	−	440.250i	−0.210053	−	0.646476i
$682$	−142.371	−	142.371i	−0.208755	−	0.208755i
$683$	−96.1264	−	48.9789i	−0.140741	−	0.0717114i	0.382202	−	0.924079i	$-0.375166\pi$
$683$	−96.1264	−	48.9789i	−0.140741	−	0.0717114i	−0.522943	+	0.852368i	$0.675166\pi$
$684$	245.435	−	337.812i	0.358823	−	0.493878i
$685$	325.971	−	156.392i	0.475869	−	0.228309i
$686$	−595.953	+	432.985i	−0.868737	+	0.631174i
$687$	−129.373	−	816.831i	−0.188316	−	1.18898i
$688$	118.618	−	18.7872i	0.172410	−	0.0273070i
$689$	−284.218	−	391.192i	−0.412507	−	0.567768i
$690$	−156.063	−	325.285i	−0.226178	−	0.471428i
$691$	−585.805	−	425.612i	−0.847764	−	0.615937i	0.0767647	−	0.997049i	$-0.475541\pi$
$691$	−585.805	−	425.612i	−0.847764	−	0.615937i	−0.924529	+	0.381113i	$0.875541\pi$
$692$	−230.054	+	451.506i	−0.332448	+	0.652465i
$693$	1218.89	−	1218.89i	1.75885	−	1.75885i
$694$	−635.097	+	206.355i	−0.915125	+	0.297342i
$695$	−160.289	+	209.881i	−0.230632	+	0.301987i
$696$	17.8365	−	54.8952i	0.0256272	−	0.0788724i
$697$	−237.585	+	121.055i	−0.340867	+	0.173681i
$698$	96.4643	−	609.052i	0.138201	−	0.872567i
$699$			1309.67i			1.87363i
$700$	−516.890	−	295.297i	−0.738414	−	0.421853i
$701$	−388.344			−0.553986			−0.276993	−	0.960872i	$-0.589338\pi$
$701$	−388.344			−0.553986			−0.276993	+	0.960872i	$0.589338\pi$
$702$	392.702	+	62.1979i	0.559405	+	0.0886010i
$703$	180.708	+	354.660i	0.257053	+	0.504495i
$704$	−83.1002	−	27.0009i	−0.118040	−	0.0383535i
$705$	407.522	−	1159.19i	0.578046	−	1.64424i
$706$	224.672	+	691.469i	0.318232	+	0.979418i
$707$	720.830	+	720.830i	1.01956	+	1.01956i
$708$	−127.676	−	65.0542i	−0.180334	−	0.0918845i
$709$	326.398	−	449.248i	0.460364	−	0.633637i	−0.514220	−	0.857658i	$-0.671919\pi$
$709$	326.398	−	449.248i	0.460364	−	0.633637i	0.974584	+	0.224021i	$0.0719186\pi$
$710$	−456.247	−	83.4865i	−0.642601	−	0.117587i
$711$	−190.956	+	138.738i	−0.268574	+	0.195131i
$712$	−4.85246	−	30.6372i	−0.00681525	−	0.0430298i
$713$	−139.244	+	22.0541i	−0.195293	+	0.0309314i
$714$	−465.977	−	641.363i	−0.652629	−	0.898267i
$715$	672.850	+	363.347i	0.941049	+	0.508178i
$716$	300.348	+	218.215i	0.419480	+	0.304770i
$717$	318.291	−	624.681i	0.443921	−	0.871243i
$718$	427.705	−	427.705i	0.595689	−	0.595689i
$719$	−208.554	+	67.7632i	−0.290061	+	0.0942465i	−0.450433	−	0.892810i	$-0.648730\pi$
$719$	−208.554	+	67.7632i	−0.290061	+	0.0942465i	0.160372	+	0.987057i	$0.448730\pi$
$720$	150.662	+	218.149i	0.209253	+	0.302985i
$721$	440.870	−	1356.86i	0.611470	−	1.88191i
$722$	−142.314	+	72.5129i	−0.197111	+	0.100433i
$723$	−27.0965	+	171.081i	−0.0374779	+	0.236626i
$724$		−	354.185i		−	0.489205i
$725$	−104.330	+	28.4648i	−0.143903	+	0.0392619i
$726$	11.3958			0.0156967
$727$	92.9105	+	14.7156i	0.127800	+	0.0202415i	0.220007	−	0.975498i	$-0.429392\pi$
$727$	92.9105	+	14.7156i	0.127800	+	0.0202415i	−0.0922068	+	0.995740i	$0.529392\pi$
$728$	214.073	+	420.142i	0.294057	+	0.577118i
$729$	−1120.68	−	364.132i	−1.53729	−	0.499496i
$730$	−565.082	−	13.5100i	−0.774084	−	0.0185069i
$731$	−92.5974	−	284.985i	−0.126672	−	0.389857i
$732$	393.163	+	393.163i	0.537108	+	0.537108i
$733$	−57.0412	−	29.0639i	−0.0778188	−	0.0396507i	0.414648	−	0.909982i	$-0.363905\pi$
$733$	−57.0412	−	29.0639i	−0.0778188	−	0.0396507i	−0.492467	+	0.870331i	$0.663905\pi$
$734$	143.086	−	196.942i	0.194941	−	0.268313i
$735$	−1509.59	−	1583.54i	−2.05386	−	2.15448i
$736$	−49.4964	+	35.9612i	−0.0672505	+	0.0488604i
$737$	−166.040	−	1048.34i	−0.225292	−	1.42244i
$738$	494.694	−	78.3519i	0.670317	−	0.106168i
$739$	707.012	+	973.119i	0.956715	+	1.31681i	0.948479	+	0.316839i	$0.102622\pi$
$739$	707.012	+	973.119i	0.956715	+	1.31681i	0.00823572	+	0.999966i	$0.497378\pi$
$740$	−250.490	+	33.5580i	−0.338501	+	0.0453486i
$741$	841.718	+	611.544i	1.13592	+	0.825296i
$742$	263.965	−	518.061i	0.355748	−	0.698195i
$743$	−235.132	+	235.132i	−0.316463	+	0.316463i	−0.847407	−	0.530944i	$-0.821837\pi$
$743$	−235.132	+	235.132i	−0.316463	+	0.316463i	0.530944	+	0.847407i	$0.321837\pi$
$744$	165.421	−	53.7485i	0.222340	−	0.0722426i
$745$	1201.44	−	358.859i	1.61267	−	0.481690i
$746$	248.338	−	764.307i	0.332893	−	1.02454i
$747$	−1178.51	+	600.479i	−1.57765	+	0.803855i
$748$	−34.1047	+	215.329i	−0.0455945	+	0.287873i
$749$		−	2239.18i		−	2.98956i
$750$	313.876	−	772.645i	0.418501	−	1.03019i
$751$	−1331.68			−1.77321			−0.886607	−	0.462523i	$-0.846944\pi$
$751$	−1331.68			−1.77321			−0.886607	+	0.462523i	$0.846944\pi$
$752$	−205.800	−	32.5955i	−0.273670	−	0.0433451i
$753$	758.296	+	1488.24i	1.00703	+	1.97641i
$754$	81.4686	+	26.4707i	0.108049	+	0.0351071i
$755$	399.870	+	1338.74i	0.529629	+	1.77316i
$756$	147.738	+	454.692i	0.195421	+	0.601445i
$757$	699.634	+	699.634i	0.924219	+	0.924219i	0.997324	−	0.0731053i	$-0.0232909\pi$
$757$	699.634	+	699.634i	0.924219	+	0.924219i	−0.0731053	+	0.997324i	$0.523291\pi$
$758$	160.486	+	81.7719i	0.211723	+	0.107878i
$759$	−327.558	+	450.845i	−0.431565	+	0.593998i
$760$	29.5756	+	220.765i	0.0389153	+	0.290480i
$761$	412.515	−	299.710i	0.542069	−	0.393836i	−0.282784	−	0.959184i	$-0.591258\pi$
$761$	412.515	−	299.710i	0.542069	−	0.393836i	0.824853	+	0.565347i	$0.191258\pi$
$762$	−240.131	−	1516.13i	−0.315132	−	1.98967i
$763$	68.1243	−	10.7898i	0.0892848	−	0.0141413i
$764$	−273.703	−	376.720i	−0.358250	−	0.493089i
$765$	478.795	−	456.435i	0.625875	−	0.596647i
$766$	53.0861	+	38.5693i	0.0693030	+	0.0503516i
$767$	96.5454	−	189.481i	0.125874	−	0.247042i
$768$	53.3738	−	53.3738i	0.0694971	−	0.0694971i
$769$	−508.350	+	165.173i	−0.661053	+	0.214789i	−0.620282	−	0.784379i	$-0.712982\pi$
$769$	−508.350	+	165.173i	−0.661053	+	0.214789i	−0.0407717	+	0.999168i	$0.512982\pi$
$770$	−21.9773	+	919.238i	−0.0285419	+	1.19382i
$771$	259.509	−	798.687i	0.336588	−	1.03591i
$772$	378.368	−	192.788i	0.490114	−	0.249726i
$773$	32.8579	−	207.456i	0.0425069	−	0.268378i	−0.957277	−	0.289173i	$-0.906620\pi$
$773$	32.8579	−	207.456i	0.0425069	−	0.268378i	0.999784	+	0.0207948i	$0.00661968\pi$
$774$			562.854i			0.727201i
$775$	−254.186	−	203.927i	−0.327982	−	0.263131i
$776$	372.051			0.479448
$777$	−1402.03	−	222.060i	−1.80442	−	0.285792i
$778$	87.5287	+	171.785i	0.112505	+	0.220803i
$779$	400.198	+	130.032i	0.513732	+	0.166922i
$780$	−543.556	+	375.401i	−0.696867	+	0.481283i
$781$	221.388	+	681.363i	0.283468	+	0.872423i
$782$	107.941	+	107.941i	0.138032	+	0.138032i
$783$	77.3856	+	39.4300i	0.0988322	+	0.0503575i
$784$	−218.068	+	300.145i	−0.278148	+	0.382838i
$785$	−611.393	+	1132.18i	−0.778844	+	1.44227i
$786$	−395.268	+	287.179i	−0.502885	+	0.365367i
$787$	−45.4625	−	287.039i	−0.0577668	−	0.364725i	−0.999590	−	0.0286178i	$-0.990889\pi$
$787$	−45.4625	−	287.039i	−0.0577668	−	0.364725i	0.941824	−	0.336108i	$-0.109111\pi$
$788$	−460.424	+	72.9239i	−0.584294	+	0.0925431i
$789$	−286.846	−	394.809i	−0.363556	−	0.500392i
$790$	22.6629	−	123.851i	0.0286872	−	0.156773i
$791$	910.200	+	661.299i	1.15070	+	0.836029i
$792$	185.912	−	364.873i	0.234738	−	0.460699i
$793$	−583.483	+	583.483i	−0.735792	+	0.735792i
$794$	514.919	−	167.307i	0.648512	−	0.210714i
$795$	768.443	+	270.153i	0.966595	+	0.339815i
$796$	98.1297	−	302.012i	0.123278	−	0.379412i
$797$	−218.799	+	111.484i	−0.274528	+	0.139879i	−0.585835	−	0.810430i	$-0.699233\pi$
$797$	−218.799	+	111.484i	−0.274528	+	0.139879i	0.311307	+	0.950309i	$0.399233\pi$
$798$	−195.708	+	1235.65i	−0.245248	+	1.54844i
$799$			519.890i			0.650676i
$800$	−138.463	−	28.7731i	−0.173079	−	0.0359663i
$801$	145.377			0.181494
$802$	592.428	+	93.8314i	0.738688	+	0.116997i
$803$	396.372	+	777.923i	0.493613	+	0.968771i
$804$	872.038	+	283.342i	1.08462	+	0.352416i
$805$	511.677	+	390.776i	0.635623	+	0.485436i
$806$	79.7668	+	245.497i	0.0989662	+	0.304587i
$807$	−80.6775	−	80.6775i	−0.0999721	−	0.0999721i
$808$	215.781	+	109.946i	0.267055	+	0.136071i
$809$	162.358	−	223.466i	0.200689	−	0.276225i	−0.696796	−	0.717269i	$-0.745392\pi$
$809$	162.358	−	223.466i	0.200689	−	0.276225i	0.897485	+	0.441044i	$0.145392\pi$
$810$	156.726	−	75.1929i	0.193489	−	0.0928307i
$811$	449.536	−	326.607i	0.554298	−	0.402721i	−0.275070	−	0.961424i	$-0.588701\pi$
$811$	449.536	−	326.607i	0.554298	−	0.402721i	0.829368	+	0.558703i	$0.188701\pi$
$812$	16.1133	+	101.735i	0.0198439	+	0.125290i
$813$	−814.418	+	128.991i	−1.00174	+	0.158661i
$814$	229.453	+	315.814i	0.281883	+	0.387978i
$815$	−124.283	−	259.046i	−0.152495	−	0.317848i
$816$	−152.366	−	110.700i	−0.186723	−	0.135662i
$817$	−214.681	+	421.335i	−0.262767	+	0.515710i
$818$	−70.4702	+	70.4702i	−0.0861494	+	0.0861494i
$819$	−2101.78	+	682.910i	−2.56628	+	0.833834i
$820$	−162.161	+	212.332i	−0.197757	+	0.258941i
$821$	190.467	−	586.197i	0.231994	−	0.714004i	−0.765512	−	0.643422i	$-0.777514\pi$
$821$	190.467	−	586.197i	0.231994	−	0.714004i	0.997506	−	0.0705823i	$-0.0224858\pi$
$822$	429.845	−	219.017i	0.522926	−	0.266444i
$823$	−98.2286	+	620.191i	−0.119354	+	0.753573i	0.853318	+	0.521391i	$0.174587\pi$
$823$	−98.2286	+	620.191i	−0.119354	+	0.753573i	−0.972672	+	0.232182i	$0.925413\pi$
$824$		−	338.931i		−	0.411324i
$825$	−1280.47	+	140.480i	−1.55209	+	0.170279i
$826$	255.713			0.309580
$827$	343.416	+	54.3917i	0.415255	+	0.0657699i	0.360566	−	0.932734i	$-0.382583\pi$
$827$	343.416	+	54.3917i	0.415255	+	0.0657699i	0.0546886	+	0.998503i	$0.482583\pi$
$828$	−130.175	−	255.483i	−0.157216	−	0.308555i
$829$	−1330.60	−	432.337i	−1.60506	−	0.521516i	−0.636709	−	0.771104i	$-0.719705\pi$
$829$	−1330.60	−	432.337i	−1.60506	−	0.521516i	−0.968352	+	0.249588i	$0.919705\pi$
$830$	234.002	−	665.612i	0.281930	−	0.801942i
$831$	−538.963	−	1658.76i	−0.648571	−	1.99610i
$832$	79.2107	+	79.2107i	0.0952052	+	0.0952052i
$833$	824.786	+	420.249i	0.990139	+	0.504501i
$834$	−207.127	+	285.085i	−0.248353	+	0.341829i
$835$	−1059.79	−	193.927i	−1.26921	−	0.232248i
$836$	278.337	−	202.223i	0.332938	−	0.241894i
$837$	40.9419	+	258.497i	0.0489150	+	0.308837i
$838$	−626.959	+	99.3006i	−0.748161	+	0.118497i
$839$	−364.766	−	502.058i	−0.434763	−	0.598400i	0.534275	−	0.845311i	$-0.320585\pi$
$839$	−364.766	−	502.058i	−0.434763	−	0.598400i	−0.969038	+	0.246910i	$0.920585\pi$
$840$	−698.930	−	377.430i	−0.832059	−	0.449322i
$841$	−665.245	−	483.329i	−0.791017	−	0.574707i
$842$	200.566	−	393.632i	0.238201	−	0.467497i
$843$	964.290	−	964.290i	1.14388	−	1.14388i
$844$	282.725	−	91.8628i	0.334982	−	0.108842i
$845$	−76.9253	−	111.383i	−0.0910359	−	0.131814i
$846$	301.768	−	928.746i	0.356700	−	1.09781i
$847$	−18.1196	+	9.23242i	−0.0213927	+	0.0109001i
$848$	21.6081	−	136.428i	0.0254812	−	0.160882i
$849$			1377.53i			1.62254i
$850$	−16.8628	+	352.456i	−0.0198385	+	0.414654i
$851$	273.335			0.321192
$852$	−611.279	−	96.8171i	−0.717464	−	0.113635i
$853$	−423.706	−	831.570i	−0.496725	−	0.974877i	−0.994215	−	0.107408i	$-0.965745\pi$
$853$	−423.706	−	831.570i	−0.496725	−	0.974877i	0.497490	−	0.867470i	$-0.334255\pi$
$854$	−943.664	−	306.615i	−1.10499	−	0.359034i
$855$	−1043.60	−	24.9505i	−1.22058	−	0.0291819i
$856$	−164.382	−	505.917i	−0.192036	−	0.591025i
$857$	883.165	+	883.165i	1.03053	+	1.03053i	0.999519	+	0.0310117i	$0.00987291\pi$
$857$	883.165	+	883.165i	1.03053	+	1.03053i	0.0310117	+	0.999519i	$0.490127\pi$
$858$	909.145	+	463.233i	1.05961	+	0.539898i
$859$	684.349	−	941.925i	0.796681	−	1.09654i	−0.196563	−	0.980491i	$-0.562978\pi$
$859$	684.349	−	941.925i	0.796681	−	1.09654i	0.993244	−	0.116046i	$-0.0370219\pi$
$860$	−207.167	−	217.316i	−0.240892	−	0.252693i
$861$	−1214.04	+	882.052i	−1.41004	+	1.02445i
$862$	−4.77473	−	30.1465i	−0.00553913	−	0.0349727i
$863$	1452.01	−	229.977i	1.68252	−	0.266485i	0.759295	−	0.650746i	$-0.225544\pi$
$863$	1452.01	−	229.977i	1.68252	−	0.266485i	0.923224	+	0.384261i	$0.125544\pi$
$864$	66.7595	+	91.8866i	0.0772680	+	0.106350i
$865$	1255.62	−	168.215i	1.45159	−	0.194468i
$866$	−628.327	−	456.506i	−0.725551	−	0.527143i
$867$	405.632	−	796.098i	0.467857	−	0.918221i
$868$	−219.479	+	219.479i	−0.252856	+	0.252856i
$869$	−184.960	+	60.0971i	−0.212842	+	0.0691566i
$870$	−138.265	+	41.2984i	−0.158925	+	0.0474695i
$871$	−420.501	+	1294.17i	−0.482780	+	1.48584i
$872$	14.5998	−	7.43896i	0.0167429	−	0.00853092i
$873$	−272.773	+	1722.22i	−0.312455	+	1.97276i
$874$		−	240.898i		−	0.275627i
$875$	126.895	+	1482.82i	0.145023	+	1.69465i
$876$	−754.229			−0.860992
$877$	1629.98	+	258.163i	1.85859	+	0.294371i	0.982285	−	0.187393i	$-0.0600039\pi$
$877$	1629.98	+	258.163i	1.85859	+	0.294371i	0.876301	+	0.481764i	$0.160004\pi$
$878$	128.460	+	252.116i	0.146309	+	0.287148i
$879$	621.137	+	201.820i	0.706640	+	0.229601i
$880$	62.5174	+	209.304i	0.0710425	+	0.237846i
$881$	−16.0890	−	49.5167i	−0.0182622	−	0.0562051i	0.941510	−	0.336985i	$-0.109407\pi$
$881$	−16.0890	−	49.5167i	−0.0182622	−	0.0562051i	−0.959772	+	0.280779i	$0.909407\pi$
$882$	−1229.49	−	1229.49i	−1.39398	−	1.39398i
$883$	905.982	+	461.621i	1.02603	+	0.522787i	0.884202	−	0.467105i	$-0.154703\pi$
$883$	905.982	+	461.621i	1.02603	+	0.522787i	0.141825	+	0.989892i	$0.454703\pi$
$884$	164.287	−	226.122i	0.185845	−	0.255794i
$885$	47.5675	+	355.064i	0.0537486	+	0.401202i
$886$	163.117	−	118.511i	0.184105	−	0.133760i
$887$	36.9127	+	233.058i	0.0416153	+	0.262748i	0.999720	−	0.0236702i	$-0.00753517\pi$
$887$	36.9127	+	233.058i	0.0416153	+	0.262748i	−0.958105	+	0.286419i	$0.907535\pi$
$888$	−333.075	+	52.7539i	−0.375084	+	0.0594075i
$889$	1610.12	+	2216.14i	1.81116	+	2.49284i
$890$	−56.1295	+	53.5083i	−0.0630669	+	0.0601217i
$891$	−217.222	−	157.821i	−0.243796	−	0.177128i
$892$	−356.007	+	698.702i	−0.399111	+	0.783299i
$893$	580.132	−	580.132i	0.649644	−	0.649644i
$894$	1591.23	−	517.022i	1.77990	−	0.578325i
$895$	22.1834	−	927.860i	0.0247859	−	1.03672i
$896$	−41.6245	+	128.107i	−0.0464559	+	0.142977i
$897$	636.581	−	324.354i	0.709678	−	0.361599i
$898$	−131.506	+	830.293i	−0.146443	+	0.924603i
$899$			56.3866i			0.0627214i
$900$	234.706	−	619.850i	0.260784	−	0.688722i
$901$	−344.643			−0.382512
$902$	407.597	+	64.5571i	0.451882	+	0.0715711i
$903$	−765.599	−	1502.57i	−0.847839	−	1.66398i
$904$	254.196	+	82.5934i	0.281191	+	0.0913643i
$905$	−728.589	+	503.191i	−0.805070	+	0.556012i
$906$	576.108	+	1773.08i	0.635880	+	1.95704i
$907$	−757.766	−	757.766i	−0.835464	−	0.835464i	0.152794	−	0.988258i	$-0.451173\pi$
$907$	−757.766	−	757.766i	−0.835464	−	0.835464i	−0.988258	+	0.152794i	$0.951173\pi$
$908$	174.856	+	89.0937i	0.192573	+	0.0981209i
$909$	−667.139	+	918.238i	−0.733926	+	1.01016i
$910$	560.135	−	1037.26i	0.615533	−	1.13985i
$911$	−787.930	+	572.465i	−0.864907	+	0.628392i	−0.929215	−	0.369538i	$-0.879516\pi$
$911$	−787.930	+	572.465i	−0.864907	+	0.628392i	0.0643086	+	0.997930i	$0.479516\pi$
$912$	46.4935	+	293.549i	0.0509798	+	0.321874i
$913$	−1076.38	+	170.482i	−1.17895	+	0.186727i
$914$	−141.595	−	194.889i	−0.154918	−	0.213226i
$915$	250.203	−	1367.34i	0.273446	−	1.49436i
$916$	283.646	+	206.081i	0.309657	+	0.224979i
$917$	395.825	−	776.851i	0.431653	−	0.847166i
$918$	200.385	−	200.385i	0.218285	−	0.218285i
$919$	−1014.37	+	329.588i	−1.10377	+	0.358638i	−0.803554	−	0.595232i	$-0.797060\pi$
$919$	−1014.37	+	329.588i	−1.10377	+	0.358638i	−0.300220	+	0.953870i	$0.597060\pi$
$920$	144.295	+	50.7282i	0.156842	+	0.0551393i
$921$	327.161	−	1006.90i	0.355224	−	1.09327i
$922$	476.661	−	242.871i	0.516985	−	0.263417i
$923$	143.684	−	907.184i	0.155670	−	0.982864i
$924$			1226.93i			1.32785i
$925$	424.904	+	467.605i	0.459356	+	0.505519i
$926$	−72.3014			−0.0780793
$927$	1568.91	+	248.491i	1.69246	+	0.268059i
$928$	11.1092	+	21.8030i	0.0119711	+	0.0234946i
$929$	−1611.25	−	523.525i	−1.73439	−	0.563536i	−0.740315	−	0.672261i	$-0.765323\pi$
$929$	−1611.25	−	523.525i	−1.73439	−	0.563536i	−0.994072	+	0.108724i	$0.965323\pi$
$930$	−345.579	−	263.924i	−0.371590	−	0.283790i
$931$	−451.412	−	1389.30i	−0.484868	−	1.49227i
$932$	−392.603	−	392.603i	−0.421248	−	0.421248i
$933$	562.693	+	286.706i	0.603100	+	0.307295i
$934$	−570.462	+	785.173i	−0.610773	+	0.840656i
$935$	491.402	−	235.762i	0.525564	−	0.252151i
$936$	−424.739	+	308.591i	−0.453781	+	0.329691i
$937$	64.1780	+	405.204i	0.0684930	+	0.432448i	0.997976	+	0.0635842i	$0.0202531\pi$
$937$	64.1780	+	405.204i	0.0684930	+	0.432448i	−0.929483	+	0.368864i	$0.879747\pi$
$938$	−1616.12	+	255.968i	−1.72294	+	0.272887i
$939$	−1279.08	−	1760.51i	−1.36218	−	1.87487i
$940$	225.328	+	469.656i	0.239711	+	0.499635i
$941$	186.657	+	135.614i	0.198360	+	0.144117i	0.682532	−	0.730856i	$-0.260879\pi$
$941$	186.657	+	135.614i	0.198360	+	0.144117i	−0.484171	+	0.874973i	$0.660879\pi$
$942$	−779.468	+	1529.79i	−0.827460	+	1.62398i
$943$	204.323	−	204.323i	0.216673	−	0.216673i
$944$	57.7753	−	18.7723i	0.0612026	−	0.0198859i
$945$	725.449	−	949.893i	0.767671	−	1.00518i
$946$	−143.309	+	441.059i	−0.151489	+	0.466236i
$947$	817.953	−	416.768i	0.863731	−	0.440093i	0.0347672	−	0.999395i	$-0.488931\pi$
$947$	817.953	−	416.768i	0.863731	−	0.440093i	0.828964	+	0.559303i	$0.188931\pi$
$948$	26.2816	−	165.935i	0.0277232	−	0.175037i
$949$		−	1119.33i		−	1.17949i
$950$	412.114	−	374.480i	0.433804	−	0.394190i
$951$	318.232			0.334629
$952$	331.950	+	52.5757i	0.348687	+	0.0552266i
$953$	−734.794	−	1442.12i	−0.771033	−	1.51324i	−0.856070	−	0.516860i	$-0.827101\pi$
$953$	−734.794	−	1442.12i	−0.771033	−	1.51324i	0.0850372	−	0.996378i	$-0.472899\pi$
$954$	615.681	+	200.047i	0.645368	+	0.209693i
$955$	−386.096	+	1098.24i	−0.404288	+	1.14999i
$956$	91.8474	+	282.677i	0.0960747	+	0.295688i
$957$	157.606	+	157.606i	0.164688	+	0.164688i
$958$	72.7919	+	37.0893i	0.0759831	+	0.0387153i
$959$	−506.027	+	696.486i	−0.527661	+	0.726263i
$960$	−185.623	−	33.9663i	−0.193357	−	0.0353815i
$961$	640.001	−	464.988i	0.665974	−	0.483859i
$962$	−78.2907	−	494.308i	−0.0813833	−	0.513834i
$963$	2462.40	−	390.006i	2.55701	−	0.404991i
$964$	−43.1625	−	59.4081i	−0.0447744	−	0.0616266i
$965$	−934.131	−	504.442i	−0.968011	−	0.522738i
$966$	695.021	+	504.962i	0.719484	+	0.522735i
$967$	525.750	−	1031.84i	0.543692	−	1.06706i	−0.441765	−	0.897131i	$-0.645648\pi$
$967$	525.750	−	1031.84i	0.543692	−	1.06706i	0.985457	−	0.169924i	$-0.0543524\pi$
$968$	−3.41615	+	3.41615i	−0.00352908	+	0.00352908i
$969$	705.266	−	229.155i	0.727829	−	0.236486i
$970$	−528.574	−	765.342i	−0.544922	−	0.789012i
$971$	49.0351	−	150.914i	0.0504996	−	0.155422i	−0.922627	−	0.385695i	$-0.873962\pi$
$971$	49.0351	−	150.914i	0.0504996	−	0.155422i	0.973126	+	0.230273i	$0.0739619\pi$
$972$	528.681	−	269.377i	0.543911	−	0.277136i
$973$	98.3724	−	621.099i	0.101102	−	0.638334i
$974$			410.923i			0.421892i
$975$	1544.46	+	584.810i	1.58406	+	0.599805i
$976$	−235.719			−0.241515
$977$	−1513.70	−	239.746i	−1.54933	−	0.245390i	−0.677620	−	0.735412i	$-0.736989\pi$
$977$	−1513.70	−	239.746i	−1.54933	−	0.245390i	−0.871710	+	0.490022i	$0.836989\pi$
$978$	−174.051	−	341.594i	−0.177966	−	0.349278i
$979$	113.919	+	37.0145i	0.116363	+	0.0378085i
$980$	927.235	+	22.1685i	0.946158	+	0.0226209i
$981$	23.7309	+	73.0361i	0.0241905	+	0.0744507i
$982$	260.254	+	260.254i	0.265025	+	0.265025i
$983$	−1640.80	−	836.029i	−1.66918	−	0.850487i	−0.993569	−	0.113224i	$-0.963882\pi$
$983$	−1640.80	−	836.029i	−1.66918	−	0.850487i	−0.675606	−	0.737263i	$-0.736118\pi$
$984$	−209.545	+	288.414i	−0.212952	+	0.293104i
$985$	804.135	+	843.528i	0.816381	+	0.856374i
$986$	49.3946	−	35.8872i	0.0500959	−	0.0363968i
$987$	457.701	+	2889.81i	0.463730	+	2.92787i
$988$	−435.648	+	68.9999i	−0.440939	+	0.0698380i
$989$	190.866	+	262.705i	0.192989	+	0.265627i
$990$	−1014.70	+	135.939i	−1.02495	+	0.137312i
$991$	852.332	+	619.255i	0.860072	+	0.624879i	0.927905	−	0.372818i	$-0.121608\pi$
$991$	852.332	+	619.255i	0.860072	+	0.624879i	−0.0678324	+	0.997697i	$0.521608\pi$
$992$	−33.4763	+	65.7009i	−0.0337463	+	0.0662308i
$993$	653.965	−	653.965i	0.658575	−	0.658575i
$994$	1050.39	−	341.291i	1.05673	−	0.343352i
$995$	−760.678	+	227.208i	−0.764501	+	0.228350i
$996$	290.922	−	895.364i	0.292090	−	0.898960i
$997$	−1164.89	+	593.541i	−1.16839	+	0.595327i	−0.926986	−	0.375097i	$-0.877610\pi$
$997$	−1164.89	+	593.541i	−1.16839	+	0.595327i	−0.241409	+	0.970423i	$0.577610\pi$
$998$	−13.0494	+	82.3908i	−0.0130756	+	0.0825560i
$999$		−	507.427i		−	0.507935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.3.f.b.27.1	yes	24
4.3	odd	2		400.3.bg.b.177.3		24
5.2	odd	4		250.3.f.d.93.1		24
5.3	odd	4		250.3.f.f.93.3		24
5.4	even	2		250.3.f.e.157.3		24
25.9	even	10		250.3.f.d.207.1		24
25.12	odd	20		250.3.f.e.43.3		24
25.13	odd	20	inner	50.3.f.b.13.1	✓	24
25.16	even	5		250.3.f.f.207.3		24
100.63	even	20		400.3.bg.b.113.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.b.13.1	✓	24	25.13	odd	20	inner
50.3.f.b.27.1	yes	24	1.1	even	1	trivial
250.3.f.d.93.1		24	5.2	odd	4
250.3.f.d.207.1		24	25.9	even	10
250.3.f.e.43.3		24	25.12	odd	20
250.3.f.e.157.3		24	5.4	even	2
250.3.f.f.93.3		24	5.3	odd	4
250.3.f.f.207.3		24	25.16	even	5
400.3.bg.b.113.3		24	100.63	even	20
400.3.bg.b.177.3		24	4.3	odd	2

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	50.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39680 + 0.221232i) q^{2} +(-2.14176 - 4.20343i) q^{3} +(1.90211 + 0.618034i) q^{4} +(-1.43099 - 4.79085i) q^{5} +(-2.06168 - 6.34519i) q^{6} +(8.41873 + 8.41873i) q^{7} +(2.52015 + 1.28408i) q^{8} +(-7.79165 + 10.7243i) q^{9} +O(q^{10})\)	\(q+(1.39680 + 0.221232i) q^{2} +(-2.14176 - 4.20343i) q^{3} +(1.90211 + 0.618034i) q^{4} +(-1.43099 - 4.79085i) q^{5} +(-2.06168 - 6.34519i) q^{6} +(8.41873 + 8.41873i) q^{7} +(2.52015 + 1.28408i) q^{8} +(-7.79165 + 10.7243i) q^{9} +(-0.938916 - 7.00845i) q^{10} +(-8.83615 + 6.41984i) q^{11} +(-1.47600 - 9.31908i) q^{12} +(13.8302 - 2.19049i) q^{13} +(9.89681 + 13.6218i) q^{14} +(-17.0732 + 16.2759i) q^{15} +(3.23607 + 2.35114i) q^{16} +(4.53099 - 8.89257i) q^{17} +(-13.2560 + 13.2560i) q^{18} +(-14.9790 + 4.86698i) q^{19} +(0.239013 - 9.99714i) q^{20} +(17.3567 - 53.4184i) q^{21} +(-13.7626 + 7.01241i) q^{22} +(-1.69189 + 10.6822i) q^{23} -13.3434i q^{24} +(-20.9046 + 13.7113i) q^{25} +19.8027 q^{26} +(19.8308 + 3.14088i) q^{27} +(10.8103 + 21.2164i) q^{28} +(4.11402 + 1.33673i) q^{29} +(-27.4486 + 18.9571i) q^{30} +(4.02808 + 12.3972i) q^{31} +(4.00000 + 4.00000i) q^{32} +(45.9102 + 23.3924i) q^{33} +(8.29622 - 11.4188i) q^{34} +(28.2858 - 52.3800i) q^{35} +(-21.4486 + 15.5833i) q^{36} +(-3.95354 - 24.9617i) q^{37} +(-21.9995 + 3.48437i) q^{38} +(-38.8285 - 53.4428i) q^{39} +(2.54554 - 13.9112i) q^{40} +(-21.6147 - 15.7040i) q^{41} +(36.0617 - 70.7751i) q^{42} +(21.2302 - 21.2302i) q^{43} +(-20.7750 + 6.75022i) q^{44} +(62.5282 + 21.9824i) q^{45} +(-4.72648 + 14.5466i) q^{46} +(-46.4137 + 23.6489i) q^{47} +(2.95199 - 18.6382i) q^{48} +92.7500i q^{49} +(-32.2329 + 14.5272i) q^{50} -47.0836 q^{51} +(27.6604 + 4.38098i) q^{52} +(-15.6773 - 30.7684i) q^{53} +(27.0048 + 8.77439i) q^{54} +(43.4009 + 33.1460i) q^{55} +(10.4061 + 32.0267i) q^{56} +(52.5394 + 52.5394i) q^{57} +(5.45074 + 2.77729i) q^{58} +(8.92677 - 12.2866i) q^{59} +(-42.5342 + 20.4068i) q^{60} +(-47.6752 + 34.6380i) q^{61} +(2.88379 + 18.2075i) q^{62} +(-155.881 + 24.6891i) q^{63} +(4.70228 + 6.47214i) q^{64} +(-30.2852 - 63.1240i) q^{65} +(58.9524 + 42.8314i) q^{66} +(-44.1187 + 86.5878i) q^{67} +(14.1144 - 14.1144i) q^{68} +(48.5255 - 15.7669i) q^{69} +(51.0978 - 66.9068i) q^{70} +(20.2698 - 62.3839i) q^{71} +(-33.4069 + 17.0217i) q^{72} +(12.5050 - 78.9533i) q^{73} -35.7412i q^{74} +(102.407 + 58.5046i) q^{75} -31.4998 q^{76} +(-128.436 - 20.3423i) q^{77} +(-42.4125 - 83.2392i) q^{78} +(16.9345 + 5.50235i) q^{79} +(6.63320 - 18.8680i) q^{80} +(7.59667 + 23.3801i) q^{81} +(-26.7172 - 26.7172i) q^{82} +(88.9040 + 45.2989i) q^{83} +(66.0288 - 90.8808i) q^{84} +(-49.0868 - 8.98217i) q^{85} +(34.3512 - 24.9576i) q^{86} +(-3.19239 - 20.1559i) q^{87} +(-30.5120 + 4.83262i) q^{88} +(-6.44619 - 8.87242i) q^{89} +(82.4764 + 44.5382i) q^{90} +(134.874 + 97.9917i) q^{91} +(-9.82014 + 19.2731i) q^{92} +(43.4834 - 43.4834i) q^{93} +(-70.0626 + 22.7647i) q^{94} +(44.7518 + 64.7977i) q^{95} +(8.24670 - 25.3807i) q^{96} +(117.203 - 59.7179i) q^{97} +(-20.5192 + 129.553i) q^{98} -144.783i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9	\( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9} - 32 q^{11} + 4 q^{12} + 2 q^{13} + 30 q^{14} - 20 q^{15} + 24 q^{16} - 92 q^{17} - 136 q^{18} - 230 q^{19} - 20 q^{20} + 68 q^{21} - 48 q^{22} - 18 q^{23} + 40 q^{25} + 36 q^{26} + 260 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} - 132 q^{31} + 96 q^{32} + 364 q^{33} + 150 q^{34} + 50 q^{35} - 108 q^{36} - 192 q^{37} + 20 q^{38} - 80 q^{39} + 20 q^{40} + 168 q^{41} - 8 q^{42} - 78 q^{43} - 40 q^{44} - 310 q^{45} + 26 q^{46} - 22 q^{47} - 8 q^{48} - 30 q^{50} + 168 q^{51} + 4 q^{52} - 108 q^{53} - 80 q^{54} - 40 q^{55} - 48 q^{56} + 280 q^{57} + 40 q^{58} + 450 q^{59} - 100 q^{60} - 492 q^{61} - 458 q^{62} - 558 q^{63} + 120 q^{65} + 202 q^{66} - 572 q^{67} - 136 q^{68} - 670 q^{69} - 260 q^{70} - 2 q^{71} + 128 q^{72} + 262 q^{73} + 140 q^{75} - 40 q^{76} + 496 q^{77} - 62 q^{78} - 360 q^{79} - 80 q^{80} - 46 q^{81} + 272 q^{82} + 772 q^{83} + 620 q^{84} + 490 q^{85} - 264 q^{86} + 210 q^{87} - 84 q^{88} + 900 q^{89} + 1110 q^{90} + 798 q^{91} - 16 q^{92} + 294 q^{93} - 190 q^{94} + 16 q^{96} + 378 q^{97} + 106 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9 - 32 * q^11 + 4 * q^12 + 2 * q^13 + 30 * q^14 - 20 * q^15 + 24 * q^16 - 92 * q^17 - 136 * q^18 - 230 * q^19 - 20 * q^20 + 68 * q^21 - 48 * q^22 - 18 * q^23 + 40 * q^25 + 36 * q^26 + 260 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 - 132 * q^31 + 96 * q^32 + 364 * q^33 + 150 * q^34 + 50 * q^35 - 108 * q^36 - 192 * q^37 + 20 * q^38 - 80 * q^39 + 20 * q^40 + 168 * q^41 - 8 * q^42 - 78 * q^43 - 40 * q^44 - 310 * q^45 + 26 * q^46 - 22 * q^47 - 8 * q^48 - 30 * q^50 + 168 * q^51 + 4 * q^52 - 108 * q^53 - 80 * q^54 - 40 * q^55 - 48 * q^56 + 280 * q^57 + 40 * q^58 + 450 * q^59 - 100 * q^60 - 492 * q^61 - 458 * q^62 - 558 * q^63 + 120 * q^65 + 202 * q^66 - 572 * q^67 - 136 * q^68 - 670 * q^69 - 260 * q^70 - 2 * q^71 + 128 * q^72 + 262 * q^73 + 140 * q^75 - 40 * q^76 + 496 * q^77 - 62 * q^78 - 360 * q^79 - 80 * q^80 - 46 * q^81 + 272 * q^82 + 772 * q^83 + 620 * q^84 + 490 * q^85 - 264 * q^86 + 210 * q^87 - 84 * q^88 + 900 * q^89 + 1110 * q^90 + 798 * q^91 - 16 * q^92 + 294 * q^93 - 190 * q^94 + 16 * q^96 + 378 * q^97 + 106 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more