LMFDB - Embedded newform 403.2.bi.b.14.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(14,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 22]))

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

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

chi := DirichletCharacter("403.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bi (of order $15$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$17$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			14.13
Character	$\chi$	$=$	403.14
Dual form			403.2.bi.b.144.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.477192 - 1.46864i) q^{2} +(1.45858 - 1.61992i) q^{3} +(-0.311171 - 0.226079i) q^{4} +(1.14752 - 1.98757i) q^{5} +(-1.68306 - 2.91515i) q^{6} +(-0.410673 + 3.90729i) q^{7} +(2.01809 - 1.46623i) q^{8} +(-0.183091 - 1.74199i) q^{9} +O(q^{10})$	\(q+(0.477192 - 1.46864i) q^{2} +(1.45858 - 1.61992i) q^{3} +(-0.311171 - 0.226079i) q^{4} +(1.14752 - 1.98757i) q^{5} +(-1.68306 - 2.91515i) q^{6} +(-0.410673 + 3.90729i) q^{7} +(2.01809 - 1.46623i) q^{8} +(-0.183091 - 1.74199i) q^{9} +(-2.37144 - 2.63375i) q^{10} +(0.296236 - 0.131893i) q^{11} +(-0.820097 + 0.174317i) q^{12} +(-0.978148 - 0.207912i) q^{13} +(5.54245 + 2.46766i) q^{14} +(-1.54594 - 4.75792i) q^{15} +(-1.42807 - 4.39513i) q^{16} +(0.566184 + 0.252081i) q^{17} +(-2.64574 - 0.562369i) q^{18} +(-5.15531 + 1.09579i) q^{19} +(-0.806422 + 0.359042i) q^{20} +(5.73049 + 6.36435i) q^{21} +(-0.0523423 - 0.498004i) q^{22} +(-5.14052 + 3.73480i) q^{23} +(0.568377 - 5.40775i) q^{24} +(-0.133614 - 0.231426i) q^{25} +(-0.772112 + 1.33734i) q^{26} +(2.20158 + 1.59954i) q^{27} +(1.01115 - 1.12299i) q^{28} +(-0.934493 + 2.87608i) q^{29} -7.72540 q^{30} +(-5.56769 + 0.0282715i) q^{31} -2.14736 q^{32} +(0.218429 - 0.672254i) q^{33} +(0.640396 - 0.711232i) q^{34} +(7.29475 + 5.29994i) q^{35} +(-0.336855 + 0.583450i) q^{36} +(-1.95368 - 3.38387i) q^{37} +(-0.850737 + 8.09422i) q^{38} +(-1.76351 + 1.28126i) q^{39} +(-0.598423 - 5.69362i) q^{40} +(6.12974 + 6.80776i) q^{41} +(12.0815 - 5.37904i) q^{42} +(-0.836883 + 0.177885i) q^{43} +(-0.121998 - 0.0259315i) q^{44} +(-3.67243 - 1.63507i) q^{45} +(3.03209 + 9.33181i) q^{46} +(-2.06311 - 6.34959i) q^{47} +(-9.20270 - 4.09731i) q^{48} +(-8.25124 - 1.75386i) q^{49} +(-0.403642 + 0.0857967i) q^{50} +(1.23418 - 0.549490i) q^{51} +(0.257367 + 0.285834i) q^{52} +(-0.803351 - 7.64338i) q^{53} +(3.39973 - 2.47005i) q^{54} +(0.0777917 - 0.740139i) q^{55} +(4.90021 + 8.48740i) q^{56} +(-5.74433 + 9.94948i) q^{57} +(3.77800 + 2.74488i) q^{58} +(-1.87676 + 2.08435i) q^{59} +(-0.594612 + 1.83003i) q^{60} +7.59240 q^{61} +(-2.61533 + 8.19045i) q^{62} +6.88167 q^{63} +(1.83143 - 5.63656i) q^{64} +(-1.53568 + 1.70555i) q^{65} +(-0.883070 - 0.641588i) q^{66} +(4.43665 - 7.68450i) q^{67} +(-0.119190 - 0.206443i) q^{68} +(-1.44778 + 13.7747i) q^{69} +(11.2647 - 8.18430i) q^{70} +(-0.603291 - 5.73993i) q^{71} +(-2.92365 - 3.24705i) q^{72} +(-3.68467 + 1.64052i) q^{73} +(-5.90198 + 1.25451i) q^{74} +(-0.569777 - 0.121110i) q^{75} +(1.85192 + 0.824527i) q^{76} +(0.393688 + 1.21165i) q^{77} +(1.04019 + 3.20137i) q^{78} +(-0.979003 - 0.435880i) q^{79} +(-10.3744 - 2.20514i) q^{80} +(10.9422 - 2.32585i) q^{81} +(12.9232 - 5.75380i) q^{82} +(-5.66791 - 6.29485i) q^{83} +(-0.344316 - 3.27594i) q^{84} +(1.15074 - 0.836059i) q^{85} +(-0.138104 + 1.31397i) q^{86} +(3.29597 + 5.70879i) q^{87} +(0.404446 - 0.700521i) q^{88} +(-0.533527 - 0.387630i) q^{89} +(-4.15379 + 4.61325i) q^{90} +(1.21407 - 3.73652i) q^{91} +2.44394 q^{92} +(-8.07513 + 9.06044i) q^{93} -10.3098 q^{94} +(-3.73787 + 11.5040i) q^{95} +(-3.13209 + 3.47854i) q^{96} +(4.46924 + 3.24709i) q^{97} +(-6.51321 + 11.2812i) q^{98} +(-0.283995 - 0.491893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9	\( 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9} + 7 q^{10} + 5 q^{11} + 28 q^{12} + 17 q^{13} - 3 q^{14} + 17 q^{15} - 78 q^{16} - 12 q^{17} + 34 q^{18} - 23 q^{19} + 8 q^{20} - 38 q^{21} + 8 q^{22} + 9 q^{23} + 46 q^{24} - 69 q^{25} - 12 q^{26} - 58 q^{27} + 7 q^{28} + 18 q^{29} + 60 q^{30} + 14 q^{31} + 212 q^{32} - 41 q^{33} - 30 q^{35} - 106 q^{36} + 6 q^{37} - 62 q^{38} + 6 q^{39} + 39 q^{40} - 5 q^{41} + 37 q^{42} + q^{43} - 88 q^{44} - 168 q^{45} + 6 q^{46} - 81 q^{47} - 101 q^{48} + 117 q^{49} - 20 q^{50} + 35 q^{51} + 7 q^{52} + 25 q^{53} + 57 q^{54} + 19 q^{55} - 63 q^{56} - 20 q^{57} - 44 q^{58} + 9 q^{59} + 113 q^{60} + 8 q^{61} + 57 q^{62} + 112 q^{63} - 146 q^{64} - 5 q^{65} + 70 q^{66} - 99 q^{67} - 56 q^{68} - 65 q^{69} + 169 q^{70} - q^{71} - 43 q^{72} + 50 q^{73} - 26 q^{74} - 18 q^{75} - 94 q^{76} + 114 q^{77} - 17 q^{79} + 217 q^{80} + 54 q^{81} - 25 q^{82} - 53 q^{83} - 22 q^{84} + 2 q^{85} - 54 q^{86} - 28 q^{87} + 70 q^{88} - 101 q^{89} + 165 q^{90} - 4 q^{91} + 64 q^{92} + 61 q^{93} - 90 q^{94} - 33 q^{95} - 217 q^{96} + 73 q^{97} + 33 q^{98} - 15 q^{99}+O(q^{100}) \) 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9 + 7 * q^10 + 5 * q^11 + 28 * q^12 + 17 * q^13 - 3 * q^14 + 17 * q^15 - 78 * q^16 - 12 * q^17 + 34 * q^18 - 23 * q^19 + 8 * q^20 - 38 * q^21 + 8 * q^22 + 9 * q^23 + 46 * q^24 - 69 * q^25 - 12 * q^26 - 58 * q^27 + 7 * q^28 + 18 * q^29 + 60 * q^30 + 14 * q^31 + 212 * q^32 - 41 * q^33 - 30 * q^35 - 106 * q^36 + 6 * q^37 - 62 * q^38 + 6 * q^39 + 39 * q^40 - 5 * q^41 + 37 * q^42 + q^43 - 88 * q^44 - 168 * q^45 + 6 * q^46 - 81 * q^47 - 101 * q^48 + 117 * q^49 - 20 * q^50 + 35 * q^51 + 7 * q^52 + 25 * q^53 + 57 * q^54 + 19 * q^55 - 63 * q^56 - 20 * q^57 - 44 * q^58 + 9 * q^59 + 113 * q^60 + 8 * q^61 + 57 * q^62 + 112 * q^63 - 146 * q^64 - 5 * q^65 + 70 * q^66 - 99 * q^67 - 56 * q^68 - 65 * q^69 + 169 * q^70 - q^71 - 43 * q^72 + 50 * q^73 - 26 * q^74 - 18 * q^75 - 94 * q^76 + 114 * q^77 - 17 * q^79 + 217 * q^80 + 54 * q^81 - 25 * q^82 - 53 * q^83 - 22 * q^84 + 2 * q^85 - 54 * q^86 - 28 * q^87 + 70 * q^88 - 101 * q^89 + 165 * q^90 - 4 * q^91 + 64 * q^92 + 61 * q^93 - 90 * q^94 - 33 * q^95 - 217 * q^96 + 73 * q^97 + 33 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{11}{15}\right)$

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 $

$2$	0.477192	−	1.46864i	0.337425	−	1.03849i	−0.628090	−	0.778141i	$-0.716163\pi$
$2$	0.477192	−	1.46864i	0.337425	−	1.03849i	0.965515	−	0.260347i	$-0.0838371\pi$
$3$	1.45858	−	1.61992i	0.842112	−	0.935260i	−0.156514	−	0.987676i	$-0.550026\pi$
$3$	1.45858	−	1.61992i	0.842112	−	0.935260i	0.998625	+	0.0524160i	$0.0166922\pi$
$4$	−0.311171	−	0.226079i	−0.155585	−	0.113039i
$5$	1.14752	−	1.98757i	0.513187	−	0.888867i	−0.486696	−	0.873572i	$-0.661798\pi$
$5$	1.14752	−	1.98757i	0.513187	−	0.888867i	0.999883	−	0.0152951i	$-0.00486878\pi$
$6$	−1.68306	−	2.91515i	−0.687107	−	1.19010i
$7$	−0.410673	+	3.90729i	−0.155220	+	1.47682i	0.588593	+	0.808429i	$0.299682\pi$
$7$	−0.410673	+	3.90729i	−0.155220	+	1.47682i	−0.743813	+	0.668388i	$0.766985\pi$
$8$	2.01809	−	1.46623i	0.713502	−	0.518390i
$9$	−0.183091	−	1.74199i	−0.0610303	−	0.580665i
$10$	−2.37144	−	2.63375i	−0.749915	−	0.832865i
$11$	0.296236	−	0.131893i	0.0893186	−	0.0397672i	−0.361591	−	0.932337i	$-0.617766\pi$
$11$	0.296236	−	0.131893i	0.0893186	−	0.0397672i	0.450910	+	0.892570i	$0.351100\pi$
$12$	−0.820097	+	0.174317i	−0.236741	+	0.0503210i
$13$	−0.978148	−	0.207912i	−0.271289	−	0.0576643i
$13$	−0.978148	−	0.207912i	−0.271289	−	0.0576643i
$14$	5.54245	+	2.46766i	1.48128	+	0.659510i
$15$	−1.54594	−	4.75792i	−0.399160	−	1.22849i
$16$	−1.42807	−	4.39513i	−0.357016	−	1.09878i
$17$	0.566184	+	0.252081i	0.137320	+	0.0611387i	0.474246	−	0.880392i	$-0.342721\pi$
$17$	0.566184	+	0.252081i	0.137320	+	0.0611387i	−0.336926	+	0.941531i	$0.609387\pi$
$18$	−2.64574	−	0.562369i	−0.623607	−	0.132552i
$19$	−5.15531	+	1.09579i	−1.18271	+	0.251393i	−0.756968	−	0.653452i	$-0.773320\pi$
$19$	−5.15531	+	1.09579i	−1.18271	+	0.251393i	−0.425741	+	0.904845i	$0.639987\pi$
$20$	−0.806422	+	0.359042i	−0.180321	+	0.0802843i
$21$	5.73049	+	6.36435i	1.25050	+	1.38882i
$22$	−0.0523423	−	0.498004i	−0.0111594	−	0.106175i
$23$	−5.14052	+	3.73480i	−1.07187	+	0.778761i	−0.976248	−	0.216657i	$-0.930485\pi$
$23$	−5.14052	+	3.73480i	−1.07187	+	0.778761i	−0.0956242	+	0.995418i	$0.530485\pi$
$24$	0.568377	−	5.40775i	0.116020	−	1.10385i
$25$	−0.133614	−	0.231426i	−0.0267228	−	0.0462852i
$26$	−0.772112	+	1.33734i	−0.151424	+	0.262273i
$27$	2.20158	+	1.59954i	0.423694	+	0.307832i
$28$	1.01115	−	1.12299i	0.191088	−	0.212225i
$29$	−0.934493	+	2.87608i	−0.173531	+	0.534074i	−0.999563	−	0.0295491i	$-0.990593\pi$
$29$	−0.934493	+	2.87608i	−0.173531	+	0.534074i	0.826032	+	0.563623i	$0.190593\pi$
$30$	−7.72540			−1.41046
$31$	−5.56769	+	0.0282715i	−0.999987	+	0.00507772i
$31$	−5.56769	+	0.0282715i	−0.999987	+	0.00507772i
$32$	−2.14736			−0.379603
$33$	0.218429	−	0.672254i	0.0380236	−	0.117024i
$34$	0.640396	−	0.711232i	0.109827	−	0.121975i
$35$	7.29475	+	5.29994i	1.23304	+	0.895854i
$36$	−0.336855	+	0.583450i	−0.0561425	+	0.0972417i
$37$	−1.95368	−	3.38387i	−0.321183	−	0.556305i	0.659550	−	0.751661i	$-0.270747\pi$
$37$	−1.95368	−	3.38387i	−0.321183	−	0.556305i	−0.980732	+	0.195356i	$0.937414\pi$
$38$	−0.850737	+	8.09422i	−0.138008	+	1.31306i
$39$	−1.76351	+	1.28126i	−0.282387	+	0.205166i
$40$	−0.598423	−	5.69362i	−0.0946190	−	0.900240i
$41$	6.12974	+	6.80776i	0.957304	+	1.06319i	0.997949	+	0.0640206i	$0.0203923\pi$
$41$	6.12974	+	6.80776i	0.957304	+	1.06319i	−0.0406442	+	0.999174i	$0.512941\pi$
$42$	12.0815	−	5.37904i	1.86422	−	0.830003i
$43$	−0.836883	+	0.177885i	−0.127623	+	0.0271272i	−0.271281	−	0.962500i	$-0.587447\pi$
$43$	−0.836883	+	0.177885i	−0.127623	+	0.0271272i	0.143657	+	0.989628i	$0.454114\pi$
$44$	−0.121998	−	0.0259315i	−0.0183919	−	0.00390932i
$45$	−3.67243	−	1.63507i	−0.547453	−	0.243742i
$46$	3.03209	+	9.33181i	0.447057	+	1.37590i
$47$	−2.06311	−	6.34959i	−0.300935	−	0.926184i	−0.981163	−	0.193183i	$-0.938119\pi$
$47$	−2.06311	−	6.34959i	−0.300935	−	0.926184i	0.680228	−	0.733001i	$-0.261881\pi$
$48$	−9.20270	−	4.09731i	−1.32830	−	0.591395i
$49$	−8.25124	−	1.75386i	−1.17875	−	0.250551i
$50$	−0.403642	+	0.0857967i	−0.0570835	+	0.0121335i
$51$	1.23418	−	0.549490i	0.172819	−	0.0769440i
$52$	0.257367	+	0.285834i	0.0356903	+	0.0396381i
$53$	−0.803351	−	7.64338i	−0.110349	−	1.04990i	−0.899865	−	0.436169i	$-0.856335\pi$
$53$	−0.803351	−	7.64338i	−0.110349	−	1.04990i	0.789516	−	0.613730i	$-0.210332\pi$
$54$	3.39973	−	2.47005i	0.462645	−	0.336131i
$55$	0.0777917	−	0.740139i	0.0104894	−	0.0998003i
$56$	4.90021	+	8.48740i	0.654817	+	1.13418i
$57$	−5.74433	+	9.94948i	−0.760856	+	1.31784i
$58$	3.77800	+	2.74488i	0.496076	+	0.360420i
$59$	−1.87676	+	2.08435i	−0.244333	+	0.271359i	−0.852820	−	0.522204i	$-0.825110\pi$
$59$	−1.87676	+	2.08435i	−0.244333	+	0.271359i	0.608488	+	0.793563i	$0.291777\pi$
$60$	−0.594612	+	1.83003i	−0.0767641	+	0.236256i
$61$	7.59240			0.972107			0.486054	−	0.873929i	$-0.338436\pi$
$61$	7.59240			0.972107			0.486054	+	0.873929i	$0.338436\pi$
$62$	−2.61533	+	8.19045i	−0.332148	+	1.04019i
$63$	6.88167			0.867009
$64$	1.83143	−	5.63656i	0.228929	−	0.704570i
$65$	−1.53568	+	1.70555i	−0.190478	+	0.211547i
$66$	−0.883070	−	0.641588i	−0.108698	−	0.0789740i
$67$	4.43665	−	7.68450i	0.542023	−	0.938811i	−0.456765	−	0.889587i	$-0.650992\pi$
$67$	4.43665	−	7.68450i	0.542023	−	0.938811i	0.998788	−	0.0492235i	$-0.0156747\pi$
$68$	−0.119190	−	0.206443i	−0.0144539	−	0.0250348i
$69$	−1.44778	+	13.7747i	−0.174292	+	1.65828i
$70$	11.2647	−	8.18430i	1.34639	−	0.978211i
$71$	−0.603291	−	5.73993i	−0.0715974	−	0.681204i	−0.970178	−	0.242395i	$-0.922067\pi$
$71$	−0.603291	−	5.73993i	−0.0715974	−	0.681204i	0.898580	−	0.438809i	$-0.144600\pi$
$72$	−2.92365	−	3.24705i	−0.344556	−	0.382668i
$73$	−3.68467	+	1.64052i	−0.431258	+	0.192008i	−0.610873	−	0.791729i	$-0.709181\pi$
$73$	−3.68467	+	1.64052i	−0.431258	+	0.192008i	0.179615	+	0.983737i	$0.442515\pi$
$74$	−5.90198	+	1.25451i	−0.686092	+	0.145833i
$75$	−0.569777	−	0.121110i	−0.0657922	−	0.0139846i
$76$	1.85192	+	0.824527i	0.212429	+	0.0945797i
$77$	0.393688	+	1.21165i	0.0448649	+	0.138080i
$78$	1.04019	+	3.20137i	0.117778	+	0.362484i
$79$	−0.979003	−	0.435880i	−0.110146	−	0.0490403i	0.350924	−	0.936404i	$-0.385868\pi$
$79$	−0.979003	−	0.435880i	−0.110146	−	0.0490403i	−0.461070	+	0.887364i	$0.652534\pi$
$80$	−10.3744	−	2.20514i	−1.15989	−	0.246542i
$81$	10.9422	−	2.32585i	1.21581	−	0.258427i
$82$	12.9232	−	5.75380i	1.42713	−	0.635401i
$83$	−5.66791	−	6.29485i	−0.622134	−	0.690950i	0.346893	−	0.937905i	$-0.387237\pi$
$83$	−5.66791	−	6.29485i	−0.622134	−	0.690950i	−0.969027	+	0.246955i	$0.920570\pi$
$84$	−0.344316	−	3.27594i	−0.0375679	−	0.357435i
$85$	1.15074	−	0.836059i	0.124815	−	0.0906834i
$86$	−0.138104	+	1.31397i	−0.0148921	+	0.141689i
$87$	3.29597	+	5.70879i	0.353365	+	0.612046i
$88$	0.404446	−	0.700521i	0.0431141	−	0.0746758i
$89$	−0.533527	−	0.387630i	−0.0565538	−	0.0410887i	0.559149	−	0.829067i	$-0.311128\pi$
$89$	−0.533527	−	0.387630i	−0.0565538	−	0.0410887i	−0.615703	+	0.787978i	$0.711128\pi$
$90$	−4.15379	+	4.61325i	−0.437848	+	0.486279i
$91$	1.21407	−	3.73652i	0.127269	−	0.391694i
$92$	2.44394			0.254798
$93$	−8.07513	+	9.06044i	−0.837352	+	0.939524i
$94$	−10.3098			−1.06337
$95$	−3.73787	+	11.5040i	−0.383497	+	1.18028i
$96$	−3.13209	+	3.47854i	−0.319668	+	0.355027i
$97$	4.46924	+	3.24709i	0.453782	+	0.329692i	0.791087	−	0.611703i	$-0.209515\pi$
$97$	4.46924	+	3.24709i	0.453782	+	0.329692i	−0.337305	+	0.941395i	$0.609515\pi$
$98$	−6.51321	+	11.2812i	−0.657934	+	1.13957i
$99$	−0.283995	−	0.491893i	−0.0285425	−	0.0494371i
$100$	−0.0107438	+	0.102220i	−0.00107438	+	0.0102220i
$101$	13.8241	−	10.0438i	1.37555	−	0.999394i	0.378267	−	0.925696i	$-0.376520\pi$
$101$	13.8241	−	10.0438i	1.37555	−	0.999394i	0.997281	−	0.0736975i	$-0.0234799\pi$
$102$	−0.218068	−	2.07478i	−0.0215919	−	0.205434i
$103$	2.21052	+	2.45503i	0.217809	+	0.241902i	0.842141	−	0.539258i	$-0.181295\pi$
$103$	2.21052	+	2.45503i	0.217809	+	0.241902i	−0.624331	+	0.781160i	$0.714629\pi$
$104$	−2.27884	+	1.01460i	−0.223458	+	0.0994900i
$105$	19.2254	−	4.08649i	1.87621	−	0.398801i
$106$	−11.6088	−	2.46752i	−1.12754	−	0.239666i
$107$	11.0053	+	4.89986i	1.06392	+	0.473687i	0.862625	−	0.505844i	$-0.168819\pi$
$107$	11.0053	+	4.89986i	1.06392	+	0.473687i	0.201294	+	0.979531i	$0.435485\pi$
$108$	−0.323445	−	0.995462i	−0.0311235	−	0.0957883i
$109$	1.10096	+	3.38841i	0.105453	+	0.324551i	0.989837	−	0.142210i	$-0.0454209\pi$
$109$	1.10096	+	3.38841i	0.105453	+	0.324551i	−0.884384	+	0.466761i	$0.845421\pi$
$110$	−1.04988	−	0.467436i	−0.100102	−	0.0445683i
$111$	−8.33119	−	1.77085i	−0.790762	−	0.168082i
$112$	17.7595	−	3.77491i	1.67812	−	0.356695i
$113$	11.9822	−	5.33481i	1.12719	−	0.501857i	0.243485	−	0.969905i	$-0.421709\pi$
$113$	11.9822	−	5.33481i	1.12719	−	0.501857i	0.883703	+	0.468048i	$0.155043\pi$
$114$	11.8711	+	13.1842i	1.11183	+	1.23481i
$115$	1.52432	+	14.5029i	0.142143	+	1.35240i
$116$	0.941007	−	0.683681i	0.0873703	−	0.0634782i
$117$	−0.183091	+	1.74199i	−0.0169268	+	0.161047i
$118$	2.16560	+	3.75092i	0.199359	+	0.345300i
$119$	−1.21747	+	2.10872i	−0.111605	+	0.193306i
$120$	−10.0960	−	7.33520i	−0.921638	−	0.669609i
$121$	−7.29008	+	8.09645i	−0.662734	+	0.736041i
$122$	3.62303	−	11.1505i	0.328014	−	1.00952i
$123$	19.9687			1.80052
$124$	1.73889	+	1.24994i	0.156157	+	0.112248i
$125$	10.8619			0.971520
$126$	3.28387	−	10.1067i	0.292551	−	0.900378i
$127$	9.08344	−	10.0882i	0.806025	−	0.895181i	−0.190222	−	0.981741i	$-0.560921\pi$
$127$	9.08344	−	10.0882i	0.806025	−	0.895181i	0.996247	+	0.0865601i	$0.0275875\pi$
$128$	−10.8787	−	7.90381i	−0.961547	−	0.698605i
$129$	−0.932502	+	1.61514i	−0.0821022	+	0.142205i
$130$	1.77203	+	3.06925i	0.155417	+	0.269191i
$131$	−1.19130	+	11.3344i	−0.104084	+	0.990295i	0.810456	+	0.585800i	$0.199219\pi$
$131$	−1.19130	+	11.3344i	−0.104084	+	0.990295i	−0.914540	+	0.404495i	$0.867447\pi$
$132$	−0.219951	+	0.159804i	−0.0191443	+	0.0139091i
$133$	−2.16444	−	20.5933i	−0.187681	−	1.78567i
$134$	−9.16867	−	10.1828i	−0.792052	−	0.879663i
$135$	5.70556	−	2.54028i	0.491056	−	0.218632i
$136$	1.51222	−	0.321432i	0.129672	−	0.0275626i
$137$	−18.8731	−	4.01160i	−1.61244	−	0.342734i	−0.688487	−	0.725249i	$-0.741725\pi$
$137$	−18.8731	−	4.01160i	−1.61244	−	0.342734i	−0.923949	+	0.382515i	$0.875058\pi$
$138$	19.5393	+	8.69946i	1.66330	+	0.740547i
$139$	4.93055	+	15.1747i	0.418204	+	1.28710i	0.909353	+	0.416024i	$0.136577\pi$
$139$	4.93055	+	15.1747i	0.418204	+	1.28710i	−0.491149	+	0.871075i	$0.663423\pi$
$140$	−1.07171	−	3.29837i	−0.0905758	−	0.278764i
$141$	−13.2950	−	5.91933i	−1.11964	−	0.498497i
$142$	−8.71780	−	1.85303i	−0.731581	−	0.155502i
$143$	−0.317185	+	0.0674197i	−0.0265243	+	0.00563792i
$144$	−7.39483	+	3.29239i	−0.616236	+	0.274366i
$145$	4.64404	+	5.15773i	0.385666	+	0.428326i
$146$	0.651048	+	6.19431i	0.0538811	+	0.512644i
$147$	−14.8762	+	10.8082i	−1.22697	+	0.891444i
$148$	−0.157094	+	1.49465i	−0.0129130	+	0.122859i
$149$	−9.23305	−	15.9921i	−0.756401	−	1.31012i	−0.944675	−	0.328008i	$-0.893623\pi$
$149$	−9.23305	−	15.9921i	−0.756401	−	1.31012i	0.188274	−	0.982117i	$-0.439711\pi$
$150$	−0.449760	+	0.779007i	−0.0367228	+	0.0636057i
$151$	−13.1326	−	9.54137i	−1.06871	−	0.776466i	−0.0930326	−	0.995663i	$-0.529656\pi$
$151$	−13.1326	−	9.54137i	−1.06871	−	0.776466i	−0.975681	+	0.219198i	$0.929656\pi$
$152$	−8.79719	+	9.77027i	−0.713546	+	0.792474i
$153$	0.335461	−	1.03244i	0.0271204	−	0.0834680i
$154$	1.96734			0.158533
$155$	−6.33286	+	11.0986i	−0.508667	+	0.891461i
$156$	0.838418			0.0671272
$157$	−6.14279	+	18.9056i	−0.490248	+	1.50883i	0.333985	+	0.942578i	$0.391606\pi$
$157$	−6.14279	+	18.9056i	−0.490248	+	1.50883i	−0.824233	+	0.566250i	$0.808394\pi$
$158$	−1.10732	+	1.22981i	−0.0880940	+	0.0978383i
$159$	−13.5534	−	9.84711i	−1.07485	−	0.780927i
$160$	−2.46414	+	4.26802i	−0.194807	+	0.337416i
$161$	−12.4819	−	21.6193i	−0.983711	−	1.70384i
$162$	1.80571	−	17.1801i	0.141870	−	1.34980i
$163$	−13.0287	+	9.46591i	−1.02049	+	0.741427i	−0.966383	−	0.257108i	$-0.917230\pi$
$163$	−13.0287	+	9.46591i	−1.02049	+	0.741427i	−0.0541040	+	0.998535i	$0.517230\pi$
$164$	−0.368304	−	3.50418i	−0.0287597	−	0.273631i
$165$	−1.08550	−	1.20557i	−0.0845059	−	0.0938534i
$166$	−11.9496	+	5.32029i	−0.927467	+	0.412935i
$167$	6.39282	−	1.35884i	0.494691	−	0.105150i	0.0461910	−	0.998933i	$-0.485292\pi$
$167$	6.39282	−	1.35884i	0.494691	−	0.105150i	0.448500	+	0.893783i	$0.351958\pi$
$168$	20.8962	+	4.44163i	1.61218	+	0.342679i
$169$	0.913545	+	0.406737i	0.0702727	+	0.0312874i
$170$	−0.678752	−	2.08898i	−0.0520579	−	0.160218i
$171$	2.85276	+	8.77989i	0.218156	+	0.671415i
$172$	0.300629	+	0.133849i	0.0229228	+	0.0102059i
$173$	−7.20501	−	1.53147i	−0.547787	−	0.116436i	−0.0742990	−	0.997236i	$-0.523672\pi$
$173$	−7.20501	−	1.53147i	−0.547787	−	0.116436i	−0.473488	+	0.880800i	$0.657005\pi$
$174$	9.95699	−	2.11642i	0.754837	−	0.160446i
$175$	0.959120	−	0.427028i	0.0725026	−	0.0322803i
$176$	−1.00273	−	1.11365i	−0.0755837	−	0.0839442i
$177$	0.639074	+	6.08038i	0.0480357	+	0.457030i
$178$	−0.823886	+	0.598588i	−0.0617529	+	0.0448661i
$179$	−2.52113	+	23.9869i	−0.188438	+	1.79287i	0.336455	+	0.941699i	$0.390772\pi$
$179$	−2.52113	+	23.9869i	−0.188438	+	1.79287i	−0.524893	+	0.851168i	$0.675895\pi$
$180$	0.773098	+	1.33904i	0.0576233	+	0.0998065i
$181$	10.9629	−	18.9882i	0.814862	−	1.41138i	−0.0945643	−	0.995519i	$-0.530146\pi$
$181$	10.9629	−	18.9882i	0.814862	−	1.41138i	0.909427	−	0.415864i	$-0.136521\pi$
$182$	−4.90828	−	3.56608i	−0.363826	−	0.264335i
$183$	11.0741	−	12.2991i	0.818623	−	0.909173i
$184$	−4.89795	+	15.0743i	−0.361082	+	1.11130i
$185$	−8.96756			−0.659308
$186$	9.45318	+	16.1831i	0.693141	+	1.18660i
$187$	0.200972			0.0146965
$188$	−0.793530	+	2.44223i	−0.0578741	+	0.178118i
$189$	−7.15401	+	7.94533i	−0.520377	+	0.577938i
$190$	15.1116	+	10.9792i	1.09631	+	0.796514i
$191$	−2.84794	+	4.93278i	−0.206070	+	0.356924i	−0.950473	−	0.310807i	$-0.899401\pi$
$191$	−2.84794	+	4.93278i	−0.206070	+	0.356924i	0.744403	+	0.667730i	$0.232734\pi$
$192$	−6.45948	−	11.1881i	−0.466173	−	0.807435i
$193$	2.03889	−	19.3988i	0.146763	−	1.39635i	−0.634872	−	0.772618i	$-0.718947\pi$
$193$	2.03889	−	19.3988i	0.146763	−	1.39635i	0.781634	−	0.623737i	$-0.214386\pi$
$194$	6.90150	−	5.01424i	0.495499	−	0.360001i
$195$	0.522932	+	4.97536i	0.0374479	+	0.356293i
$196$	2.17104	+	2.41118i	0.155074	+	0.172227i
$197$	−8.92236	+	3.97249i	−0.635692	+	0.283028i	−0.699170	−	0.714955i	$-0.746447\pi$
$197$	−8.92236	+	3.97249i	−0.635692	+	0.283028i	0.0634788	+	0.997983i	$0.479780\pi$
$198$	−0.857936	+	0.182360i	−0.0609708	+	0.0129598i
$199$	−9.55387	−	2.03074i	−0.677256	−	0.143955i	−0.143573	−	0.989640i	$-0.545859\pi$
$199$	−9.55387	−	2.03074i	−0.677256	−	0.143955i	−0.533683	+	0.845685i	$0.679192\pi$
$200$	−0.608968	−	0.271130i	−0.0430605	−	0.0191718i
$201$	−5.97705	−	18.3955i	−0.421588	−	1.29752i
$202$	−8.15401	−	25.0955i	−0.573714	−	1.76571i
$203$	−10.8539	−	4.83246i	−0.761794	−	0.339173i
$204$	−0.508268	−	0.108036i	−0.0355858	−	0.00756400i
$205$	20.5649	−	4.37120i	1.43631	−	0.305298i
$206$	4.66041	−	2.07495i	0.324706	−	0.144569i
$207$	7.44719	+	8.27094i	0.517615	+	0.574870i
$208$	0.483059	+	4.59600i	0.0334941	+	0.318675i
$209$	−1.38266	+	1.00456i	−0.0956407	+	0.0694870i
$210$	3.17261	−	30.1854i	0.218931	−	2.08299i
$211$	−10.9680	−	18.9971i	−0.755068	−	1.30782i	−0.945340	−	0.326085i	$-0.894270\pi$
$211$	−10.9680	−	18.9971i	−0.755068	−	1.30782i	0.190272	−	0.981731i	$-0.439063\pi$
$212$	−1.47803	+	2.56002i	−0.101511	+	0.175823i
$213$	−10.1782	−	7.39486i	−0.697396	−	0.506688i
$214$	12.4478	−	13.8247i	0.850912	−	0.945034i
$215$	−0.606783	+	1.86749i	−0.0413823	+	0.127362i
$216$	6.78828			0.461884
$217$	2.17604	−	21.7662i	0.147719	−	1.47759i
$218$	5.50174			0.372625
$219$	−2.71688	+	8.36168i	−0.183589	+	0.565030i
$220$	−0.191536	+	0.212723i	−0.0129134	+	0.0143418i
$221$	−0.501401	−	0.364289i	−0.0337279	−	0.0245047i
$222$	−6.57632	+	11.3905i	−0.441374	+	0.764482i
$223$	7.01555	+	12.1513i	0.469796	+	0.813711i	0.999404	−	0.0345321i	$-0.0109941\pi$
$223$	7.01555	+	12.1513i	0.469796	+	0.813711i	−0.529607	+	0.848243i	$0.677661\pi$
$224$	0.881862	−	8.39035i	0.0589219	−	0.560604i
$225$	−0.378679	+	0.275126i	−0.0252453	+	0.0183418i
$226$	−2.11714	−	20.1433i	−0.140830	−	1.33991i
$227$	9.38702	+	10.4253i	0.623039	+	0.691955i	0.969215	−	0.246215i	$-0.0791869\pi$
$227$	9.38702	+	10.4253i	0.623039	+	0.691955i	−0.346177	+	0.938169i	$0.612520\pi$
$228$	4.03684	−	1.79731i	0.267346	−	0.119030i
$229$	−6.75126	+	1.43502i	−0.446136	+	0.0948291i	−0.425501	−	0.904958i	$-0.639902\pi$
$229$	−6.75126	+	1.43502i	−0.446136	+	0.0948291i	−0.0206349	+	0.999787i	$0.506569\pi$
$230$	22.0270	+	4.68198i	1.45242	+	0.308721i
$231$	2.53699	+	1.12954i	0.166922	+	0.0743184i
$232$	2.33109	+	7.17436i	0.153044	+	0.471020i
$233$	8.41317	+	25.8931i	0.551165	+	1.69631i	0.705861	+	0.708350i	$0.250560\pi$
$233$	8.41317	+	25.8931i	0.551165	+	1.69631i	−0.154696	+	0.987962i	$0.549440\pi$
$234$	2.47100	+	1.10016i	0.161534	+	0.0719197i
$235$	−14.9877	−	3.18573i	−0.977690	−	0.207814i
$236$	1.05522	−	0.224294i	0.0686889	−	0.0146003i
$237$	−2.13404	+	0.950138i	−0.138621	+	0.0617181i
$238$	2.51600	+	2.79430i	0.163088	+	0.181127i
$239$	−1.30799	−	12.4447i	−0.0846068	−	0.804980i	−0.951740	−	0.306904i	$-0.900707\pi$
$239$	−1.30799	−	12.4447i	−0.0846068	−	0.804980i	0.867134	−	0.498075i	$-0.165960\pi$
$240$	−18.7040	+	13.5892i	−1.20734	+	0.877181i
$241$	2.10498	−	20.0275i	0.135594	−	1.29009i	−0.689166	−	0.724603i	$-0.742023\pi$
$241$	2.10498	−	20.0275i	0.135594	−	1.29009i	0.824760	−	0.565483i	$-0.191310\pi$
$242$	8.41204	+	14.5701i	0.540747	+	0.936601i
$243$	8.11051	−	14.0478i	0.520289	−	0.901168i
$244$	−2.36253	−	1.71648i	−0.151246	−	0.109886i
$245$	−12.9544	+	14.3873i	−0.827625	+	0.919171i
$246$	9.52891	−	29.3270i	0.607541	−	1.86982i
$247$	5.27048			0.335353
$248$	−11.1947	+	8.22056i	−0.710861	+	0.522006i
$249$	−18.4642			−1.17012
$250$	5.18322	−	15.9523i	0.327815	−	1.00891i
$251$	−0.364598	+	0.404927i	−0.0230132	+	0.0255588i	−0.754542	−	0.656252i	$-0.772141\pi$
$251$	−0.364598	+	0.404927i	−0.0230132	+	0.0255588i	0.731528	+	0.681811i	$0.238807\pi$
$252$	−2.14137	−	1.55580i	−0.134894	−	0.0980061i
$253$	−1.03021	+	1.78438i	−0.0647689	+	0.112183i
$254$	−10.4814	−	18.1543i	−0.657662	−	1.13910i
$255$	0.324095	−	3.08356i	0.0202956	−	0.193100i
$256$	−7.20960	+	5.23808i	−0.450600	+	0.327380i
$257$	−0.541276	−	5.14989i	−0.0337639	−	0.321242i	−0.998348	−	0.0574646i	$-0.981698\pi$
$257$	−0.541276	−	5.14989i	−0.0337639	−	0.321242i	0.964584	−	0.263777i	$-0.0849683\pi$
$258$	1.92709	+	2.14024i	0.119975	+	0.133246i
$259$	14.0241	−	6.24393i	0.871415	−	0.387979i
$260$	0.863449	−	0.183532i	0.0535488	−	0.0113822i
$261$	5.18120	+	1.10130i	0.320708	+	0.0681687i
$262$	16.0778	+	7.15829i	0.993289	+	0.442241i
$263$	−3.43543	−	10.5732i	−0.211838	−	0.651969i	−0.999363	−	0.0356871i	$-0.988638\pi$
$263$	−3.43543	−	10.5732i	−0.211838	−	0.651969i	0.787525	−	0.616282i	$-0.211362\pi$
$264$	−0.544870	−	1.67694i	−0.0335344	−	0.103208i
$265$	−16.1136	−	7.17423i	−0.989849	−	0.440709i
$266$	−31.2771	−	6.64815i	−1.91772	−	0.407624i
$267$	−1.40612	+	0.298880i	−0.0860532	+	0.0182912i
$268$	−3.11786	+	1.38816i	−0.190453	+	0.0847953i
$269$	−14.3868	−	15.9782i	−0.877179	−	0.974206i	0.122654	−	0.992449i	$-0.460859\pi$
$269$	−14.3868	−	15.9782i	−0.877179	−	0.974206i	−0.999834	+	0.0182432i	$0.994193\pi$
$270$	−1.00812	−	9.59164i	−0.0613523	−	0.583728i
$271$	−13.6655	+	9.92859i	−0.830122	+	0.603119i	−0.919594	−	0.392871i	$-0.871482\pi$
$271$	−13.6655	+	9.92859i	−0.830122	+	0.603119i	0.0894720	+	0.995989i	$0.471482\pi$
$272$	0.299383	−	2.84844i	0.0181528	−	0.172712i
$273$	−4.28204	−	7.41671i	−0.259161	−	0.448880i
$274$	−14.8977	+	25.8035i	−0.900002	+	1.55885i
$275$	−0.0701046	−	0.0509340i	−0.00422747	−	0.00307144i
$276$	3.56468	−	3.95898i	0.214569	−	0.238303i
$277$	−1.94169	+	5.97590i	−0.116665	+	0.359057i	−0.992291	−	0.123933i	$-0.960449\pi$
$277$	−1.94169	+	5.97590i	−0.116665	+	0.359057i	0.875626	+	0.482990i	$0.160449\pi$
$278$	24.6390			1.47775
$279$	1.06864	+	9.69371i	0.0639780	+	0.580347i
$280$	22.4924			1.34418
$281$	1.98650	−	6.11381i	0.118504	−	0.364719i	−0.874157	−	0.485643i	$-0.838586\pi$
$281$	1.98650	−	6.11381i	0.118504	−	0.364719i	0.992662	+	0.120924i	$0.0385856\pi$
$282$	−15.0377	+	16.7010i	−0.895480	+	0.994531i
$283$	24.9033	+	18.0933i	1.48035	+	1.07553i	0.977445	+	0.211191i	$0.0677343\pi$
$283$	24.9033	+	18.0933i	1.48035	+	1.07553i	0.502902	+	0.864344i	$0.332266\pi$
$284$	−1.10995	+	1.92249i	−0.0658634	+	0.114079i
$285$	13.1835	+	22.8345i	0.780923	+	1.35260i
$286$	−0.0523423	+	0.498004i	−0.00309506	+	0.0294476i
$287$	−29.1172	+	21.1549i	−1.71874	+	1.24873i
$288$	0.393162	+	3.74068i	0.0231673	+	0.220422i
$289$	−11.1182	−	12.3480i	−0.654012	−	0.726354i
$290$	9.79096	−	4.35922i	0.574945	−	0.255982i
$291$	11.7788	−	2.50365i	0.690483	−	0.146767i
$292$	1.51745	+	0.322543i	0.0888019	+	0.0188754i
$293$	30.3623	+	13.5182i	1.77378	+	0.789740i	0.984424	+	0.175809i	$0.0562542\pi$
$293$	30.3623	+	13.5182i	1.77378	+	0.789740i	0.789360	+	0.613931i	$0.210412\pi$
$294$	8.77459	+	27.0054i	0.511745	+	1.57499i
$295$	1.98916	+	6.12202i	0.115814	+	0.356438i
$296$	−8.90423	−	3.96442i	−0.517548	−	0.230427i
$297$	0.863156	+	0.183469i	0.0500854	+	0.0106460i
$298$	−27.8927	+	5.92877i	−1.61578	+	0.343444i
$299$	5.80469	−	2.58442i	0.335694	−	0.149461i
$300$	0.149918	+	0.166500i	0.00865550	+	0.00961290i
$301$	−0.351363	−	3.34300i	−0.0202522	−	0.192687i
$302$	−20.2796	+	14.7340i	−1.16696	+	0.847847i
$303$	3.89343	−	37.0435i	0.223672	−	2.12810i
$304$	12.1783	+	21.0934i	0.698473	+	1.20979i
$305$	8.71245	−	15.0904i	0.498873	−	0.864074i
$306$	−1.35621	−	0.985346i	−0.0775295	−	0.0563285i
$307$	−2.02199	+	2.24565i	−0.115401	+	0.128166i	−0.798077	−	0.602555i	$-0.794149\pi$
$307$	−2.02199	+	2.24565i	−0.115401	+	0.128166i	0.682676	+	0.730721i	$0.260816\pi$
$308$	0.151423	−	0.466033i	0.00862815	−	0.0265547i
$309$	7.20118			0.409661
$310$	13.2779	+	14.5969i	0.754135	+	0.829047i
$311$	−14.8323			−0.841060			−0.420530	−	0.907279i	$-0.638156\pi$
$311$	−14.8323			−0.841060			−0.420530	+	0.907279i	$0.638156\pi$
$312$	−1.68029	+	5.17141i	−0.0951278	+	0.292773i
$313$	2.72249	−	3.02363i	0.153884	−	0.170906i	−0.661273	−	0.750145i	$-0.729984\pi$
$313$	2.72249	−	3.02363i	0.153884	−	0.170906i	0.815158	+	0.579239i	$0.196650\pi$
$314$	24.8343	+	18.0432i	1.40148	+	1.01823i
$315$	7.89686	−	13.6778i	0.444938	−	0.770655i
$316$	0.206094	+	0.356965i	0.0115937	+	0.0200808i
$317$	−3.01886	+	28.7225i	−0.169556	+	1.61322i	0.496992	+	0.867755i	$0.334438\pi$
$317$	−3.01886	+	28.7225i	−0.169556	+	1.61322i	−0.666548	+	0.745462i	$0.732229\pi$
$318$	−20.9295	+	15.2062i	−1.17367	+	0.852719i
$319$	0.102503	+	0.975250i	0.00573906	+	0.0546035i
$320$	−9.10144	−	10.1082i	−0.508786	−	0.565064i
$321$	23.9894	−	10.6808i	1.33896	−	0.596143i
$322$	−37.7073	+	8.01493i	−2.10135	+	0.446655i
$323$	−3.19508	−	0.679136i	−0.177779	−	0.0377881i
$324$	−3.93073	−	1.75007i	−0.218374	−	0.0972264i
$325$	0.0825779	+	0.254149i	0.00458060	+	0.0140976i
$326$	7.68486	+	23.6516i	0.425625	+	1.30994i
$327$	7.09479	+	3.15880i	0.392343	+	0.174682i
$328$	22.3521	+	4.75109i	1.23419	+	0.262335i
$329$	25.6570	−	5.45356i	1.41452	−	0.300664i
$330$	−2.28854	+	1.01892i	−0.125980	+	0.0560899i
$331$	−9.20920	−	10.2279i	−0.506184	−	0.562174i	0.434843	−	0.900506i	$-0.356804\pi$
$331$	−9.20920	−	10.2279i	−0.506184	−	0.562174i	−0.941027	+	0.338332i	$0.890137\pi$
$332$	0.340555	+	3.24017i	0.0186904	+	0.177827i
$333$	−5.53698	+	4.02285i	−0.303425	+	0.220451i
$334$	1.05495	−	10.0372i	0.0577244	−	0.549211i
$335$	−10.1823	−	17.6363i	−0.556319	−	0.963572i
$336$	19.7887	−	34.2750i	1.07956	−	1.86985i
$337$	−3.13841	−	2.28019i	−0.170960	−	0.124210i	0.499015	−	0.866593i	$-0.333695\pi$
$337$	−3.13841	−	2.28019i	−0.170960	−	0.124210i	−0.669975	+	0.742384i	$0.733695\pi$
$338$	1.03329	−	1.14758i	0.0562034	−	0.0624202i
$339$	8.83501	−	27.1914i	0.479852	−	1.47683i
$340$	−0.547091			−0.0296702
$341$	−1.64562	+	0.742714i	−0.0891155	+	0.0402202i
$342$	14.2558			0.770868
$343$	1.74289	−	5.36407i	0.0941074	−	0.289633i
$344$	−1.42808	+	1.58605i	−0.0769972	+	0.0855140i
$345$	25.7168	+	18.6844i	1.38455	+	1.00593i
$346$	−5.68736	+	9.85080i	−0.305754	+	0.529582i
$347$	18.2117	+	31.5436i	0.977656	+	1.69335i	0.670876	+	0.741570i	$0.265918\pi$
$347$	18.2117	+	31.5436i	0.977656	+	1.69335i	0.306780	+	0.951780i	$0.400748\pi$
$348$	0.265026	−	2.52156i	0.0142069	−	0.135170i
$349$	−17.5354	+	12.7402i	−0.938647	+	0.681967i	−0.948095	−	0.317988i	$-0.896993\pi$
$349$	−17.5354	+	12.7402i	−0.938647	+	0.681967i	0.00944725	+	0.999955i	$0.496993\pi$
$350$	−0.169468	−	1.61238i	−0.00905844	−	0.0861853i
$351$	−1.82091	−	2.02232i	−0.0971929	−	0.107944i
$352$	−0.636125	+	0.283221i	−0.0339056	+	0.0150957i
$353$	18.0655	−	3.83995i	0.961531	−	0.204380i	0.299701	−	0.954033i	$-0.403113\pi$
$353$	18.0655	−	3.83995i	0.961531	−	0.204380i	0.661830	+	0.749654i	$0.269780\pi$
$354$	9.23488	+	1.96293i	0.490828	+	0.104329i
$355$	−12.1008	−	5.38761i	−0.642243	−	0.285945i
$356$	0.0783831	+	0.241238i	0.00415430	+	0.0127856i
$357$	1.64018	+	5.04794i	0.0868074	+	0.267166i
$358$	34.0252	+	15.1490i	1.79829	+	0.800650i
$359$	−13.6272	−	2.89656i	−0.719218	−	0.152875i	−0.166258	−	0.986082i	$-0.553168\pi$
$359$	−13.6272	−	2.89656i	−0.719218	−	0.152875i	−0.552960	+	0.833208i	$0.686502\pi$
$360$	−9.80868	+	2.08490i	−0.516963	+	0.109884i
$361$	8.01908	−	3.57033i	0.422057	−	0.187912i
$362$	−22.6556	−	25.1615i	−1.19075	−	1.32246i
$363$	2.48242	+	23.6186i	0.130293	+	1.23966i
$364$	−1.22253	+	0.888221i	−0.0640781	+	0.0465555i
$365$	−0.967595	+	9.20605i	−0.0506462	+	0.481867i
$366$	−12.7785	−	22.1330i	−0.667941	−	1.15691i
$367$	9.62857	−	16.6772i	0.502607	−	0.870542i	−0.497388	−	0.867528i	$-0.665707\pi$
$367$	9.62857	−	16.6772i	0.502607	−	0.870542i	0.999995	−	0.00301350i	$-0.000959228\pi$
$368$	23.7560	+	17.2597i	1.23837	+	0.899725i
$369$	10.7368	−	11.9244i	0.558935	−	0.620760i
$370$	−4.27924	+	13.1702i	−0.222467	+	0.684684i
$371$	30.1948			1.56764
$372$	4.56112	−	0.993728i	0.236483	−	0.0515224i
$373$	5.26547			0.272636			0.136318	−	0.990665i	$-0.456473\pi$
$373$	5.26547			0.272636			0.136318	+	0.990665i	$0.456473\pi$
$374$	0.0959021	−	0.295156i	0.00495898	−	0.0152622i
$375$	15.8430	−	17.5954i	0.818128	−	0.908623i
$376$	−13.4735	−	9.78906i	−0.694842	−	0.504832i
$377$	1.51204	−	2.61893i	0.0778741	−	0.134882i
$378$	8.25503	+	14.2981i	0.424593	+	0.735417i
$379$	1.67763	−	15.9616i	0.0861740	−	0.819891i	−0.863014	−	0.505180i	$-0.831426\pi$
$379$	1.67763	−	15.9616i	0.0861740	−	0.819891i	0.949188	−	0.314710i	$-0.101907\pi$
$380$	3.76392	−	2.73465i	0.193085	−	0.140284i
$381$	−3.09309	−	29.4288i	−0.158464	−	1.50768i
$382$	5.88549	+	6.53650i	0.301128	+	0.334436i
$383$	4.06902	−	1.81164i	0.207917	−	0.0925706i	−0.300136	−	0.953896i	$-0.597032\pi$
$383$	4.06902	−	1.81164i	0.207917	−	0.0925706i	0.508053	+	0.861326i	$0.330365\pi$
$384$	−28.6709	+	6.09419i	−1.46311	+	0.310993i
$385$	2.85999	+	0.607910i	0.145759	+	0.0309820i
$386$	−27.5170	−	12.2513i	−1.40058	−	0.623577i
$387$	0.463100	+	1.42528i	0.0235407	+	0.0724508i
$388$	−0.656598	−	2.02080i	−0.0333337	−	0.102591i
$389$	0.0853054	+	0.0379804i	0.00432516	+	0.00192568i	0.408898	−	0.912580i	$-0.365913\pi$
$389$	0.0853054	+	0.0379804i	0.00432516	+	0.00192568i	−0.404573	+	0.914506i	$0.632580\pi$
$390$	7.55658	+	1.60620i	0.382642	+	0.0813331i
$391$	−3.85195	+	0.818758i	−0.194802	+	0.0414064i
$392$	−19.2233	+	8.55876i	−0.970923	+	0.432283i
$393$	16.6233	+	18.4620i	0.838532	+	0.931285i
$394$	1.57650	+	14.9994i	0.0794230	+	0.755659i
$395$	−1.98977	+	1.44565i	−0.100116	+	0.0727386i
$396$	−0.0228358	+	0.217268i	−0.00114754	+	0.0109181i
$397$	0.643645	+	1.11483i	0.0323036	+	0.0559515i	0.881725	−	0.471763i	$-0.156382\pi$
$397$	0.643645	+	1.11483i	0.0323036	+	0.0559515i	−0.849422	+	0.527715i	$0.823049\pi$
$398$	−7.54146	+	13.0622i	−0.378019	+	0.654748i
$399$	−36.5165	−	26.5308i	−1.82811	−	1.32820i
$400$	−0.826338	+	0.917742i	−0.0413169	+	0.0458871i
$401$	0.00166477	−	0.00512363i	8.31346e−5	−	0.000255862i	−0.951015	−	0.309145i	$-0.899957\pi$
$401$	0.00166477	−	0.00512363i	8.31346e−5	−	0.000255862i	0.951098	+	0.308889i	$0.0999572\pi$
$402$	−29.8686			−1.48971
$403$	5.45190	+	1.12993i	0.271579	+	0.0562861i
$404$	−6.57234			−0.326986
$405$	7.93370	−	24.4174i	0.394228	−	1.21331i
$406$	−12.2766	+	13.6345i	−0.609275	+	0.676669i
$407$	−1.02506	−	0.744749i	−0.0508103	−	0.0369158i
$408$	1.68500	−	2.91850i	0.0834199	−	0.144487i
$409$	12.6296	+	21.8751i	0.624494	+	1.08166i	0.988638	+	0.150313i	$0.0480282\pi$
$409$	12.6296	+	21.8751i	0.624494	+	1.08166i	−0.364144	+	0.931343i	$0.618638\pi$
$410$	3.39365	−	32.2884i	0.167600	−	1.59461i
$411$	−34.0264	+	24.7216i	−1.67840	+	1.21943i
$412$	−0.132819	−	1.26369i	−0.00654352	−	0.0622574i
$413$	−7.37343	−	8.18902i	−0.362823	−	0.402955i
$414$	15.7008	−	6.99045i	0.771652	−	0.343562i
$415$	−19.0155	+	4.04187i	−0.933433	+	0.198407i
$416$	2.10043	+	0.446461i	0.102982	+	0.0218895i
$417$	31.7733	+	14.1464i	1.55595	+	0.692752i
$418$	0.815551	+	2.51001i	0.0398899	+	0.122768i
$419$	5.42122	+	16.6848i	0.264844	+	0.815106i	0.991729	+	0.128347i	$0.0409671\pi$
$419$	5.42122	+	16.6848i	0.264844	+	0.815106i	−0.726885	+	0.686759i	$0.759033\pi$
$420$	−6.90626	−	3.07487i	−0.336991	−	0.150038i
$421$	24.2041	+	5.14475i	1.17964	+	0.250740i	0.755679	−	0.654942i	$-0.227307\pi$
$421$	24.2041	+	5.14475i	1.17964	+	0.250740i	0.423959	+	0.905682i	$0.360640\pi$
$422$	−33.1339	+	7.04282i	−1.61293	+	0.342839i
$423$	−10.6832	+	4.75647i	−0.519436	+	0.231268i
$424$	−12.8282	−	14.2471i	−0.622991	−	0.691901i
$425$	−0.0173118	−	0.164711i	−0.000839748	−	0.00798966i
$426$	−15.7174	+	11.4193i	−0.761508	+	0.553268i
$427$	−3.11799	+	29.6657i	−0.150890	+	1.43562i
$428$	−2.31676	−	4.01275i	−0.111985	−	0.193964i
$429$	−0.353425	+	0.612150i	−0.0170635	+	0.0295549i
$430$	2.45312	+	1.78230i	0.118300	+	0.0859500i
$431$	−14.8271	+	16.4672i	−0.714197	+	0.793196i	−0.985568	−	0.169279i	$-0.945856\pi$
$431$	−14.8271	+	16.4672i	−0.714197	+	0.793196i	0.271372	+	0.962475i	$0.412523\pi$
$432$	3.88620	−	11.9605i	0.186975	−	0.575450i
$433$	−4.72688			−0.227160			−0.113580	−	0.993529i	$-0.536232\pi$
$433$	−4.72688			−0.227160			−0.113580	+	0.993529i	$0.536232\pi$
$434$	−30.9284	−	13.5825i	−1.48461	−	0.651979i
$435$	15.1288			0.725370
$436$	0.423461	−	1.30328i	0.0202801	−	0.0624157i
$437$	22.4084	−	24.8870i	1.07194	−	1.19051i
$438$	10.9839	+	7.98025i	0.524830	+	0.381311i
$439$	−4.51824	+	7.82582i	−0.215644	+	0.373506i	−0.953472	−	0.301483i	$-0.902518\pi$
$439$	−4.51824	+	7.82582i	−0.215644	+	0.373506i	0.737828	+	0.674989i	$0.235852\pi$
$440$	−0.928222	−	1.60773i	−0.0442512	−	0.0766454i
$441$	−1.54448	+	14.6947i	−0.0735466	+	0.699749i
$442$	−0.774275	+	0.562544i	−0.0368285	+	0.0267575i
$443$	2.20531	+	20.9821i	0.104778	+	0.996892i	0.912985	+	0.407994i	$0.133771\pi$
$443$	2.20531	+	20.9821i	0.104778	+	0.996892i	−0.808207	+	0.588898i	$0.799562\pi$
$444$	2.19207	+	2.43454i	0.104031	+	0.115538i
$445$	−1.38268	+	0.615607i	−0.0655451	+	0.0291826i
$446$	21.1937	−	4.50486i	1.00355	−	0.213311i
$447$	−39.3730	−	8.36900i	−1.86228	−	0.395840i
$448$	21.2716	+	9.47072i	1.00499	+	0.447449i
$449$	−7.54549	−	23.2226i	−0.356094	−	1.09594i	−0.955373	−	0.295403i	$-0.904546\pi$
$449$	−7.54549	−	23.2226i	−0.356094	−	1.09594i	0.599279	−	0.800540i	$-0.295454\pi$
$450$	0.223360	+	0.687433i	0.0105293	+	0.0324059i
$451$	2.71375	+	1.20824i	0.127785	+	0.0568937i
$452$	−4.93459	−	1.04888i	−0.232104	−	0.0493351i
$453$	−34.6111	+	7.35682i	−1.62617	+	0.345654i
$454$	19.7905	−	8.81131i	0.928816	−	0.413535i
$455$	−6.03342	−	6.70079i	−0.282851	−	0.314138i
$456$	2.99562	+	28.5014i	0.140283	+	1.33470i
$457$	25.7691	−	18.7224i	1.20543	−	0.875795i	0.210620	−	0.977568i	$-0.432452\pi$
$457$	25.7691	−	18.7224i	1.20543	−	0.875795i	0.994808	+	0.101773i	$0.0324517\pi$
$458$	−1.11410	+	10.6000i	−0.0520586	+	0.495305i
$459$	0.843285	+	1.46061i	0.0393612	+	0.0681756i
$460$	2.80447	−	4.85749i	0.130759	−	0.226482i
$461$	1.26584	+	0.919684i	0.0589559	+	0.0428339i	0.616873	−	0.787063i	$-0.288399\pi$
$461$	1.26584	+	0.919684i	0.0589559	+	0.0428339i	−0.557917	+	0.829897i	$0.688399\pi$
$462$	2.86952	−	3.18693i	0.133502	−	0.148269i
$463$	−8.15782	+	25.1072i	−0.379126	+	1.16683i	0.561526	+	0.827459i	$0.310214\pi$
$463$	−8.15782	+	25.1072i	−0.379126	+	1.16683i	−0.940652	+	0.339371i	$0.889786\pi$
$464$	13.9753			0.648785
$465$	8.74184	+	26.4469i	0.405393	+	1.22645i
$466$	42.0424			1.94758
$467$	5.11909	−	15.7549i	0.236883	−	0.729052i	−0.759983	−	0.649943i	$-0.774793\pi$
$467$	5.11909	−	15.7549i	0.236883	−	0.729052i	0.996866	−	0.0791086i	$-0.0252074\pi$
$468$	0.450800	−	0.500664i	0.0208383	−	0.0231432i
$469$	28.2036	+	20.4911i	1.30232	+	0.946191i
$470$	−11.8307	+	20.4914i	−0.545710	+	0.945198i
$471$	21.6657	+	37.5261i	0.998303	+	1.72911i
$472$	−0.731332	+	6.95816i	−0.0336623	+	0.320275i
$473$	−0.224453	+	0.163075i	−0.0103204	+	0.00749819i
$474$	0.377067	+	3.58755i	0.0173192	+	0.164782i
$475$	0.942416	+	1.04666i	0.0432410	+	0.0480240i
$476$	0.855579	−	0.380928i	0.0392154	−	0.0174598i
$477$	−13.1676	+	2.79887i	−0.602904	+	0.128151i
$478$	−18.9010	−	4.01753i	−0.864510	−	0.183757i
$479$	5.92465	+	2.63782i	0.270704	+	0.120525i	0.537600	−	0.843200i	$-0.319331\pi$
$479$	5.92465	+	2.63782i	0.270704	+	0.120525i	−0.266896	+	0.963725i	$0.585998\pi$
$480$	3.31969	+	10.2169i	0.151522	+	0.466338i
$481$	1.20744	+	3.71612i	0.0550545	+	0.169440i
$482$	−28.4088	−	12.6484i	−1.29399	−	0.576120i
$483$	−53.2273	−	11.3138i	−2.42193	−	0.514796i
$484$	4.09889	−	0.871247i	0.186313	−	0.0396021i
$485$	11.5824	−	5.15680i	0.525928	−	0.234158i
$486$	−16.7610	−	18.6150i	−0.760293	−	0.844391i
$487$	−1.87036	−	17.7953i	−0.0847542	−	0.806382i	−0.951503	−	0.307638i	$-0.900461\pi$
$487$	−1.87036	−	17.7953i	−0.0847542	−	0.806382i	0.866749	−	0.498744i	$-0.166205\pi$
$488$	15.3221	−	11.1322i	0.693601	−	0.503931i
$489$	−3.66942	+	34.9122i	−0.165937	+	1.57878i
$490$	14.9481	+	25.8909i	0.675287	+	1.16963i
$491$	17.2524	−	29.8821i	0.778591	−	1.34856i	−0.154163	−	0.988045i	$-0.549268\pi$
$491$	17.2524	−	29.8821i	0.778591	−	1.34856i	0.932754	−	0.360514i	$-0.117399\pi$
$492$	−6.21369	−	4.51451i	−0.280135	−	0.203530i
$493$	−1.25410	+	1.39282i	−0.0564818	+	0.0627294i
$494$	2.51503	−	7.74046i	0.113157	−	0.348260i
$495$	−1.30356			−0.0585907
$496$	8.07529	+	24.4304i	0.362591	+	1.09696i
$497$	22.6753			1.01713
$498$	−8.81098	+	27.1174i	−0.394829	+	1.21516i
$499$	−14.9302	+	16.5817i	−0.668369	+	0.742299i	−0.978011	−	0.208554i	$-0.933124\pi$
$499$	−14.9302	+	16.5817i	−0.668369	+	0.742299i	0.309642	+	0.950853i	$0.399791\pi$
$500$	−3.37991	−	2.45565i	−0.151154	−	0.109820i
$501$	7.12324	−	12.3378i	0.318243	−	0.551212i
$502$	0.420711	+	0.728692i	0.0187772	+	0.0325231i
$503$	0.119200	−	1.13411i	0.00531488	−	0.0505677i	−0.991543	−	0.129779i	$-0.958573\pi$
$503$	0.119200	−	1.13411i	0.00531488	−	0.0505677i	0.996858	+	0.0792108i	$0.0252400\pi$
$504$	13.8878	−	10.0901i	0.618613	−	0.449448i
$505$	−4.09925	−	39.0018i	−0.182414	−	1.73556i
$506$	2.12901	+	2.36451i	0.0946462	+	0.105115i
$507$	1.99136	−	0.886610i	0.0884394	−	0.0393757i
$508$	−5.10722	+	1.08557i	−0.226596	+	0.0481645i
$509$	11.2237	+	2.38567i	0.497481	+	0.105743i	0.449817	−	0.893121i	$-0.351489\pi$
$509$	11.2237	+	2.38567i	0.497481	+	0.105743i	0.0476638	+	0.998863i	$0.484822\pi$
$510$	−4.37400	−	1.94743i	−0.193684	−	0.0862336i
$511$	−4.89679	−	15.0708i	−0.216621	−	0.666692i
$512$	−4.05804	−	12.4894i	−0.179342	−	0.551957i
$513$	−13.1026	−	5.83365i	−0.578494	−	0.257562i
$514$	−7.82166	−	1.66254i	−0.344998	−	0.0733317i
$515$	7.41617	−	1.57636i	0.326795	−	0.0694625i
$516$	0.655316	−	0.291766i	0.0288487	−	0.0128443i
$517$	−1.44863	−	1.60887i	−0.0637108	−	0.0707580i
$518$	−2.47793	−	23.5760i	−0.108874	−	1.03587i
$519$	−12.9899	+	9.43775i	−0.570195	+	0.414271i
$520$	−0.598423	+	5.69362i	−0.0262426	+	0.249682i
$521$	−6.31318	−	10.9347i	−0.276585	−	0.479060i	0.693949	−	0.720025i	$-0.255869\pi$
$521$	−6.31318	−	10.9347i	−0.276585	−	0.479060i	−0.970534	+	0.240965i	$0.922536\pi$
$522$	4.08984	−	7.08381i	0.179007	−	0.310050i
$523$	−32.0501	−	23.2858i	−1.40145	−	1.01822i	−0.994497	−	0.104769i	$-0.966590\pi$
$523$	−32.0501	−	23.2858i	−1.40145	−	1.01822i	−0.406957	−	0.913447i	$-0.633410\pi$
$524$	2.93317	−	3.25762i	0.128136	−	0.142310i
$525$	0.707204	−	2.17655i	0.0308649	−	0.0949924i
$526$	−17.1676			−0.748542
$527$	−3.15946	−	1.38750i	−0.137628	−	0.0604406i
$528$	−3.26658			−0.142160
$529$	5.36877	−	16.5234i	0.233425	−	0.718407i
$530$	−18.2257	+	20.2416i	−0.791672	+	0.879241i
$531$	3.97454	+	2.88767i	0.172480	+	0.125314i
$532$	−3.98220	+	6.89737i	−0.172650	+	0.299039i
$533$	−4.58038	−	7.93344i	−0.198398	−	0.343636i
$534$	−0.232040	+	2.20772i	−0.0100414	+	0.0955372i
$535$	22.3676	−	16.2510i	0.967035	−	0.702592i
$536$	−2.31367	−	22.0131i	−0.0999355	−	0.950823i
$537$	35.1796	+	39.0709i	1.51811	+	1.68603i
$538$	−30.3315	+	13.5045i	−1.30768	+	0.582219i
$539$	−2.67564	+	0.568724i	−0.115248	+	0.0244967i
$540$	−2.34971	−	0.499446i	−0.101115	−	0.0214927i
$541$	−4.32573	−	1.92594i	−0.185977	−	0.0828025i	0.311635	−	0.950202i	$-0.399123\pi$
$541$	−4.32573	−	1.92594i	−0.185977	−	0.0828025i	−0.497613	+	0.867399i	$0.665790\pi$
$542$	8.06049	+	24.8076i	0.346228	+	1.06558i
$543$	−14.7691	−	45.4548i	−0.633805	−	1.95065i
$544$	−1.21580	−	0.541309i	−0.0521270	−	0.0232084i
$545$	7.99807	+	1.70004i	0.342600	+	0.0728218i
$546$	−12.9359	+	2.74960i	−0.553604	+	0.117672i
$547$	19.8658	−	8.84485i	0.849402	−	0.378178i	0.0645901	−	0.997912i	$-0.479426\pi$
$547$	19.8658	−	8.84485i	0.849402	−	0.378178i	0.784812	+	0.619734i	$0.212759\pi$
$548$	4.96581	+	5.51510i	0.212129	+	0.235593i
$549$	−1.39010	−	13.2259i	−0.0593280	−	0.564468i
$550$	−0.108257	+	0.0786535i	−0.00461611	+	0.00335380i
$551$	1.66601	−	15.8511i	0.0709746	−	0.675278i
$552$	17.2751	+	29.9214i	0.735279	+	1.27354i
$553$	2.10516	−	3.64624i	0.0895205	−	0.155054i
$554$	7.84992	+	5.70330i	0.333511	+	0.242310i
$555$	−13.0799	+	14.5267i	−0.555211	+	0.616624i
$556$	1.89643	−	5.83661i	0.0804265	−	0.247527i
$557$	−25.5119			−1.08097			−0.540486	−	0.841353i	$-0.681760\pi$
$557$	−25.5119			−1.08097			−0.540486	+	0.841353i	$0.681760\pi$
$558$	14.7466	+	3.05630i	0.624272	+	0.129383i
$559$	0.855579			0.0361871
$560$	12.8766	−	39.6301i	0.544135	−	1.67468i
$561$	0.293134	−	0.325558i	0.0123761	−	0.0137451i
$562$	−8.03107	−	5.83492i	−0.338770	−	0.246131i
$563$	−7.06296	+	12.2334i	−0.297668	+	0.515577i	−0.975602	−	0.219546i	$-0.929542\pi$
$563$	−7.06296	+	12.2334i	−0.297668	+	0.515577i	0.677934	+	0.735123i	$0.262876\pi$
$564$	2.79879	+	4.84765i	0.117850	+	0.204123i
$565$	3.14652	−	29.9372i	0.132375	−	1.25947i
$566$	38.4563	−	27.9401i	1.61644	−	1.17441i
$567$	4.59408	+	43.7097i	0.192933	+	1.83564i
$568$	−9.63354	−	10.6991i	−0.404214	−	0.448925i
$569$	10.8307	−	4.82215i	0.454047	−	0.202155i	−0.166954	−	0.985965i	$-0.553393\pi$
$569$	10.8307	−	4.82215i	0.454047	−	0.202155i	0.621001	+	0.783810i	$0.286726\pi$
$570$	39.8268	−	8.46545i	1.66816	−	0.354579i
$571$	7.00670	+	1.48932i	0.293221	+	0.0623261i	0.352174	−	0.935935i	$-0.385443\pi$
$571$	7.00670	+	1.48932i	0.293221	+	0.0623261i	−0.0589524	+	0.998261i	$0.518776\pi$
$572$	0.113941	+	0.0507297i	0.00476410	+	0.00212112i
$573$	3.83675	+	11.8083i	0.160282	+	0.493298i
$574$	17.1745	+	52.8578i	0.716852	+	2.20624i
$575$	1.55117	+	0.690627i	0.0646884	+	0.0288012i
$576$	−10.1542	−	2.15834i	−0.423091	−	0.0899307i
$577$	−15.9696	+	3.39445i	−0.664824	+	0.141313i	−0.527950	−	0.849276i	$-0.677039\pi$
$577$	−15.9696	+	3.39445i	−0.664824	+	0.141313i	−0.136875	+	0.990588i	$0.543706\pi$
$578$	−23.4404	+	10.4363i	−0.974990	+	0.434094i
$579$	−28.4505	−	31.5975i	−1.18236	−	1.31315i
$580$	−0.279036	−	2.65485i	−0.0115864	−	0.110237i
$581$	26.9235	−	19.5610i	1.11697	−	0.811529i
$582$	1.94375	−	18.4935i	0.0805710	−	0.766582i
$583$	−1.24609	−	2.15829i	−0.0516077	−	0.0893872i
$584$	−5.03061	+	8.71328i	−0.208168	+	0.360558i
$585$	3.25223	+	2.36288i	0.134463	+	0.0976931i
$586$	34.3420	−	38.1407i	1.41866	−	1.57558i
$587$	−4.86765	+	14.9811i	−0.200909	+	0.618335i	0.798947	+	0.601401i	$0.205391\pi$
$587$	−4.86765	+	14.9811i	−0.200909	+	0.618335i	−0.999857	+	0.0169341i	$0.994609\pi$
$588$	7.07254			0.291667
$589$	28.6722	−	6.24680i	1.18142	−	0.257395i
$590$	9.94028			0.409235
$591$	−6.57887	+	20.2477i	−0.270619	+	0.832878i
$592$	−12.0826	+	13.4191i	−0.496591	+	0.551520i
$593$	11.1314	+	8.08746i	0.457113	+	0.332112i	0.792398	−	0.610005i	$-0.208832\pi$
$593$	11.1314	+	8.08746i	0.457113	+	0.332112i	−0.335285	+	0.942117i	$0.608832\pi$
$594$	0.681342	−	1.18012i	0.0279558	−	0.0484209i
$595$	2.79415	+	4.83961i	0.114549	+	0.198405i
$596$	−0.742422	+	7.06367i	−0.0304108	+	0.289339i
$597$	−17.2247	+	12.5145i	−0.704961	+	0.512184i
$598$	−1.02564	−	9.75829i	−0.0419415	−	0.399046i
$599$	−20.5198	−	22.7895i	−0.838416	−	0.931155i	0.160017	−	0.987114i	$-0.448845\pi$
$599$	−20.5198	−	22.7895i	−0.838416	−	0.931155i	−0.998433	+	0.0559590i	$0.982178\pi$
$600$	−1.32744	+	0.591013i	−0.0541924	+	0.0241280i
$601$	−37.4712	+	7.96475i	−1.52848	+	0.324889i	−0.894007	−	0.448054i	$-0.852117\pi$
$601$	−37.4712	+	7.96475i	−1.52848	+	0.324889i	−0.634476	+	0.772943i	$0.718784\pi$
$602$	−5.07734	−	1.07922i	−0.206937	−	0.0439858i
$603$	−14.1987	−	6.32165i	−0.578214	−	0.257437i
$604$	1.92937	+	5.93799i	0.0785049	+	0.241613i
$605$	7.72671	+	23.7804i	0.314135	+	0.966809i
$606$	−52.5459	−	23.3949i	−2.13453	−	0.950354i
$607$	−19.3968	−	4.12293i	−0.787294	−	0.167344i	−0.203315	−	0.979113i	$-0.565172\pi$
$607$	−19.3968	−	4.12293i	−0.787294	−	0.167344i	−0.583979	+	0.811769i	$0.698505\pi$
$608$	11.0703	−	2.35306i	0.448960	−	0.0954293i
$609$	−23.6595	+	10.5339i	−0.958730	+	0.426854i
$610$	−18.0049	−	19.9965i	−0.728998	−	0.809634i
$611$	0.697870	+	6.63979i	0.0282328	+	0.268617i
$612$	−0.337799	+	0.245425i	−0.0136547	+	0.00992073i
$613$	4.41297	−	41.9866i	0.178238	−	1.69582i	−0.430611	−	0.902538i	$-0.641702\pi$
$613$	4.41297	−	41.9866i	0.178238	−	1.69582i	0.608849	−	0.793286i	$-0.291632\pi$
$614$	2.33318	+	4.04119i	0.0941596	+	0.163089i
$615$	22.9146	−	39.6892i	0.924004	−	1.60042i
$616$	2.57105	+	1.86797i	0.103590	+	0.0752628i
$617$	28.2984	−	31.4286i	1.13925	−	1.26527i	0.179703	−	0.983721i	$-0.442486\pi$
$617$	28.2984	−	31.4286i	1.13925	−	1.26527i	0.959548	−	0.281545i	$-0.0908469\pi$
$618$	3.43634	−	10.5760i	0.138230	−	0.425428i
$619$	−25.7967			−1.03686			−0.518429	−	0.855121i	$-0.673483\pi$
$619$	−25.7967			−1.03686			−0.518429	+	0.855121i	$0.673483\pi$
$620$	4.47976	−	2.02184i	0.179911	−	0.0811989i
$621$	−17.2912			−0.693874
$622$	−7.07783	+	21.7833i	−0.283795	+	0.873432i
$623$	1.73369	−	1.92546i	0.0694588	−	0.0771418i
$624$	8.14972	+	5.92112i	0.326250	+	0.237035i
$625$	13.1324	−	22.7459i	0.525295	−	0.909837i
$626$	−3.14149	−	5.44122i	−0.125559	−	0.217475i
$627$	−0.389415	+	3.70503i	−0.0155517	+	0.147965i
$628$	6.18560	−	4.49410i	0.246832	−	0.179334i
$629$	−0.253131	−	2.40838i	−0.0100930	−	0.0960284i
$630$	−16.3195	−	18.1246i	−0.650183	−	0.722101i
$631$	−0.171406	+	0.0763148i	−0.00682356	+	0.00303804i	−0.410146	−	0.912020i	$-0.634522\pi$
$631$	−0.171406	+	0.0763148i	−0.00682356	+	0.00303804i	0.403322	+	0.915058i	$0.367855\pi$
$632$	−2.61481	+	0.555796i	−0.104012	+	0.0221084i
$633$	−46.7715	−	9.94159i	−1.85900	−	0.395143i
$634$	40.7426	+	18.1398i	1.61809	+	0.720422i
$635$	−9.62748	−	29.6303i	−0.382055	−	1.17584i
$636$	1.99120	+	6.12827i	0.0789560	+	0.243002i
$637$	7.70628	+	3.43106i	0.305334	+	0.135943i
$638$	1.48121	+	0.314841i	0.0586417	+	0.0124647i
$639$	−9.88846	+	2.10186i	−0.391181	+	0.0831482i
$640$	−28.1929	+	12.5523i	−1.11442	+	0.496172i
$641$	0.452420	+	0.502463i	0.0178695	+	0.0198461i	0.752013	−	0.659148i	$-0.229083\pi$
$641$	0.452420	+	0.502463i	0.0178695	+	0.0198461i	−0.734144	+	0.678994i	$0.762416\pi$
$642$	−4.23872	−	40.3287i	−0.167289	−	1.59165i
$643$	39.9949	−	29.0580i	1.57725	−	1.14594i	0.657477	−	0.753475i	$-0.271624\pi$
$643$	39.9949	−	29.0580i	1.57725	−	1.14594i	0.919768	−	0.392461i	$-0.128376\pi$
$644$	−1.00366	+	9.54918i	−0.0395497	+	0.376290i
$645$	2.14013	+	3.70682i	0.0842676	+	0.145956i
$646$	−2.52208	+	4.36836i	−0.0992297	+	0.171871i
$647$	1.38643	+	1.00730i	0.0545063	+	0.0396011i	0.614705	−	0.788757i	$-0.289275\pi$
$647$	1.38643	+	1.00730i	0.0545063	+	0.0396011i	−0.560199	+	0.828358i	$0.689275\pi$
$648$	18.6722	−	20.7376i	0.733514	−	0.814650i
$649$	−0.281052	+	0.864991i	−0.0110323	+	0.0339538i
$650$	0.412659			0.0161858
$651$	−32.0855	−	35.2728i	−1.25753	−	1.38245i
$652$	6.19419			0.242583
$653$	9.26337	−	28.5097i	0.362504	−	1.11567i	−0.589026	−	0.808114i	$-0.700488\pi$
$653$	9.26337	−	28.5097i	0.362504	−	1.11567i	0.951529	−	0.307558i	$-0.0995117\pi$
$654$	8.02473	−	8.91236i	0.313792	−	0.348501i
$655$	21.1609	+	15.3743i	0.826826	+	0.600724i
$656$	21.1674	−	36.6630i	0.826447	−	1.43145i
$657$	3.53240	+	6.11830i	0.137812	+	0.238698i
$658$	4.23395	−	40.2834i	0.165057	−	1.57041i
$659$	32.3758	−	23.5224i	1.26118	−	0.916303i	0.262368	−	0.964968i	$-0.415497\pi$
$659$	32.3758	−	23.5224i	1.26118	−	0.916303i	0.998815	+	0.0486648i	$0.0154966\pi$
$660$	0.0652220	+	0.620546i	0.00253876	+	0.0241547i
$661$	14.2638	+	15.8416i	0.554798	+	0.616165i	0.953675	−	0.300839i	$-0.0972667\pi$
$661$	14.2638	+	15.8416i	0.554798	+	0.616165i	−0.398877	+	0.917004i	$0.630600\pi$
$662$	−19.4156	+	8.64440i	−0.754610	+	0.335974i
$663$	−1.32145	+	0.280883i	−0.0513209	+	0.0109086i
$664$	−20.6680	−	4.39313i	−0.802075	−	0.170486i
$665$	−43.4143	−	19.3293i	−1.68353	−	0.749558i
$666$	3.26594	+	10.0515i	0.126553	+	0.389489i
$667$	−5.93780	−	18.2747i	−0.229912	−	0.707598i
$668$	−2.29646	−	1.02245i	−0.0888528	−	0.0395598i
$669$	29.9168	+	6.35902i	1.15665	+	0.245854i
$670$	−30.7603	+	6.53830i	−1.18837	+	0.252597i
$671$	2.24914	−	1.00138i	0.0868272	−	0.0386580i
$672$	−12.3054	−	13.6665i	−0.474692	−	0.527198i
$673$	4.57676	+	43.5450i	0.176421	+	1.67854i	0.621786	+	0.783187i	$0.286407\pi$
$673$	4.57676	+	43.5450i	0.176421	+	1.67854i	−0.445365	+	0.895349i	$0.646926\pi$
$674$	−4.84640	+	3.52112i	−0.186676	+	0.135628i
$675$	0.0760139	−	0.723224i	0.00292578	−	0.0278369i
$676$	−0.192314	−	0.333098i	−0.00739670	−	0.0128115i
$677$	−12.0554	+	20.8805i	−0.463325	+	0.802502i	−0.999124	−	0.0418432i	$-0.986677\pi$
$677$	−12.0554	+	20.8805i	−0.463325	+	0.802502i	0.535799	+	0.844345i	$0.320010\pi$
$678$	−35.7185	−	25.9510i	−1.37176	−	0.996642i
$679$	−14.5227	+	16.1291i	−0.557331	+	0.618979i
$680$	1.09644	−	3.37449i	0.0420464	−	0.129406i
$681$	30.5799			1.17183
$682$	0.305505	+	2.77125i	0.0116984	+	0.106117i
$683$	42.8349			1.63903			0.819517	−	0.573055i	$-0.194242\pi$
$683$	42.8349			1.63903			0.819517	+	0.573055i	$0.194242\pi$
$684$	1.09725	−	3.37699i	0.0419544	−	0.129122i
$685$	−29.6306	+	32.9081i	−1.13213	+	1.25735i
$686$	−7.04622	−	5.11938i	−0.269026	−	0.195459i
$687$	−7.52263	+	13.0296i	−0.287006	+	0.497110i
$688$	1.97695	+	3.42418i	0.0753706	+	0.130546i
$689$	−0.803351	+	7.64338i	−0.0306052	+	0.291189i
$690$	39.7125	−	28.8529i	1.51183	−	1.09841i
$691$	2.87673	+	27.3703i	0.109436	+	1.04121i	0.902092	+	0.431544i	$0.142031\pi$
$691$	2.87673	+	27.3703i	0.109436	+	1.04121i	−0.792656	+	0.609670i	$0.791302\pi$
$692$	1.89576	+	2.10545i	0.0720658	+	0.0800372i
$693$	2.03860	−	0.907643i	0.0774400	−	0.0344785i
$694$	55.0168	−	11.6942i	2.08841	−	0.443905i
$695$	35.8186	+	7.61348i	1.35868	+	0.288796i
$696$	15.0220	+	6.68820i	0.569406	+	0.253516i
$697$	1.75445	+	5.39964i	0.0664545	+	0.204526i
$698$	10.3431	+	31.8328i	0.391492	+	1.20489i
$699$	54.2159	+	24.1385i	2.05064	+	0.913002i
$700$	−0.394992	−	0.0839581i	−0.0149293	−	0.00317332i
$701$	35.9346	−	7.63813i	1.35723	−	0.288488i	0.528879	−	0.848697i	$-0.322612\pi$
$701$	35.9346	−	7.63813i	1.35723	−	0.288488i	0.828352	+	0.560209i	$0.189279\pi$
$702$	−3.83899	+	1.70923i	−0.144894	+	0.0645108i
$703$	13.7798	+	15.3041i	0.519717	+	0.577204i
$704$	−0.200886	−	1.91131i	−0.00757119	−	0.0720351i
$705$	−27.0214	+	19.6322i	−1.01768	+	0.739391i
$706$	2.98120	−	28.3642i	0.112199	−	1.06750i
$707$	33.5668	+	58.1394i	1.26241	+	2.18656i
$708$	1.17578	−	2.03652i	0.0441887	−	0.0765371i
$709$	−27.3533	−	19.8734i	−1.02728	−	0.746359i	−0.0595139	−	0.998227i	$-0.518955\pi$
$709$	−27.3533	−	19.8734i	−1.02728	−	0.746359i	−0.967762	+	0.251868i	$0.918955\pi$
$710$	−13.6869	+	15.2008i	−0.513659	+	0.570476i
$711$	−0.580054	+	1.78522i	−0.0217537	+	0.0669511i
$712$	−1.64506			−0.0616513
$713$	28.5152	−	20.9396i	1.06790	−	0.784193i
$714$	8.19631			0.306739
$715$	−0.229975	+	0.707791i	−0.00860059	+	0.0264699i
$716$	6.20744	−	6.89406i	0.231983	−	0.257643i
$717$	−22.0672	−	16.0327i	−0.824113	−	0.598753i
$718$	−10.7568	+	18.6314i	−0.401441	+	0.695316i
$719$	0.731100	+	1.26630i	0.0272654	+	0.0472251i	0.879336	−	0.476202i	$-0.157987\pi$
$719$	0.731100	+	1.26630i	0.0272654	+	0.0472251i	−0.852071	+	0.523427i	$0.824653\pi$
$720$	−1.94189	+	18.4758i	−0.0723698	+	0.688553i
$721$	−10.5003	+	7.62894i	−0.391053	+	0.284117i
$722$	−1.41690	−	13.4809i	−0.0527316	−	0.501707i
$723$	−29.3727	−	32.6216i	−1.09238	−	1.21321i
$724$	−7.70415	+	3.43011i	−0.286323	+	0.127479i
$725$	0.790459	−	0.168017i	0.0293569	−	0.00624001i
$726$	35.8720	+	7.62482i	1.33133	+	0.282984i
$727$	14.2812	+	6.35840i	0.529660	+	0.235820i	0.654101	−	0.756407i	$-0.273047\pi$
$727$	14.2812	+	6.35840i	0.529660	+	0.235820i	−0.124441	+	0.992227i	$0.539714\pi$
$728$	−3.02849	−	9.32074i	−0.112243	−	0.345450i
$729$	−0.555828	−	1.71066i	−0.0205862	−	0.0633579i
$730$	13.0587	+	5.81410i	0.483324	+	0.215190i
$731$	−0.518671	−	0.110247i	−0.0191837	−	0.00407763i
$732$	−6.22650	+	1.32348i	−0.230138	+	0.0489174i
$733$	4.89036	−	2.17733i	0.180630	−	0.0804215i	−0.314429	−	0.949281i	$-0.601813\pi$
$733$	4.89036	−	2.17733i	0.180630	−	0.0804215i	0.495059	+	0.868859i	$0.335146\pi$
$734$	−19.8982	−	22.0992i	−0.734455	−	0.815695i
$735$	4.41123	+	41.9701i	0.162711	+	1.54809i
$736$	11.0385	−	8.01996i	0.406886	−	0.295620i
$737$	0.300765	−	2.86159i	0.0110788	−	0.105408i
$738$	−12.3892	−	21.4587i	−0.456053	−	0.789907i
$739$	−11.8624	+	20.5463i	−0.436366	+	0.755809i	−0.997406	−	0.0719800i	$-0.977068\pi$
$739$	−11.8624	+	20.5463i	−0.436366	+	0.755809i	0.561040	+	0.827789i	$0.310402\pi$
$740$	2.79044	+	2.02737i	0.102579	+	0.0745278i
$741$	7.68742	−	8.53775i	0.282404	−	0.313642i
$742$	14.4087	−	44.3454i	0.528960	−	1.62797i
$743$	42.7429			1.56808			0.784042	−	0.620707i	$-0.213154\pi$
$743$	42.7429			1.56808			0.784042	+	0.620707i	$0.213154\pi$
$744$	−3.01167	+	30.1248i	−0.110413	+	1.10443i
$745$	−42.3805			−1.55270
$746$	2.51264	−	7.73310i	0.0919942	−	0.283129i
$747$	−9.92785	+	11.0260i	−0.363241	+	0.403420i
$748$	−0.0625366	−	0.0454355i	−0.00228656	−	0.00166129i
$749$	−23.6647	+	40.9885i	−0.864691	+	1.49769i
$750$	−18.2813	−	31.6641i	−0.667538	−	1.15621i
$751$	−0.565248	+	5.37797i	−0.0206262	+	0.196245i	−0.999983	−	0.00589596i	$-0.998123\pi$
$751$	−0.565248	+	5.37797i	−0.0206262	+	0.196245i	0.979356	+	0.202141i	$0.0647899\pi$
$752$	−24.9611	+	18.1353i	−0.910236	+	0.661325i
$753$	0.124153	+	1.18124i	0.00452438	+	0.0430466i
$754$	−3.12475	−	3.47039i	−0.113797	−	0.126384i
$755$	−34.0340	+	15.1529i	−1.23862	+	0.551471i
$756$	4.02239	−	0.854985i	0.146293	−	0.0310955i
$757$	−42.0335	−	8.93449i	−1.52773	−	0.324730i	−0.634002	−	0.773332i	$-0.718589\pi$
$757$	−42.0335	−	8.93449i	−1.52773	−	0.324730i	−0.893732	+	0.448602i	$0.851922\pi$
$758$	−22.6413	−	10.0806i	−0.822370	−	0.366143i
$759$	1.38790	+	4.27152i	0.0503777	+	0.155047i
$760$	9.32409	+	28.6966i	0.338220	+	1.04094i
$761$	7.94491	+	3.53730i	0.288003	+	0.128227i	0.545653	−	0.838011i	$-0.316282\pi$
$761$	7.94491	+	3.53730i	0.288003	+	0.128227i	−0.257650	+	0.966238i	$0.582948\pi$
$762$	−44.6965	−	9.50053i	−1.61918	−	0.344168i
$763$	−13.6916	+	2.91025i	−0.495671	+	0.105358i
$764$	2.00139	−	0.891078i	0.0724079	−	0.0322381i
$765$	−1.66710	−	1.85150i	−0.0602741	−	0.0669412i
$766$	−0.718959	−	6.84044i	−0.0259770	−	0.247155i
$767$	2.26911	−	1.64860i	0.0819327	−	0.0595276i
$768$	−2.03052	+	19.3191i	−0.0732701	+	0.697119i
$769$	22.8718	+	39.6152i	0.824780	+	1.42856i	0.902088	+	0.431553i	$0.142034\pi$
$769$	22.8718	+	39.6152i	0.824780	+	1.42856i	−0.0773078	+	0.997007i	$0.524632\pi$
$770$	2.25757	−	3.91022i	0.0813571	−	0.140915i
$771$	−9.13190	−	6.63471i	−0.328877	−	0.238943i
$772$	−5.02010	+	5.57538i	−0.180677	+	0.200662i
$773$	−16.3378	+	50.2826i	−0.587630	+	1.80854i	0.000809924		1.00000i	$0.499742\pi$
$773$	−16.3378	+	50.2826i	−0.587630	+	1.80854i	−0.588440	+	0.808541i	$0.700258\pi$
$774$	2.31421			0.0831826
$775$	0.750463	+	1.28473i	0.0269574	+	0.0461489i
$776$	13.7803			0.494684
$777$	10.3406	−	31.8251i	0.370968	−	1.14172i
$778$	0.0964867	−	0.107159i	0.00345922	−	0.00384185i
$779$	−39.0606	−	28.3792i	−1.39949	−	1.01679i
$780$	0.962103	−	1.66641i	0.0344488	−	0.0596671i
$781$	−0.935772	−	1.62080i	−0.0334845	−	0.0579969i
$782$	−0.635655	+	6.04785i	−0.0227310	+	0.216271i
$783$	−6.65777	+	4.83715i	−0.237929	+	0.172866i
$784$	4.07488	+	38.7699i	0.145532	+	1.38464i
$785$	30.5271	+	33.9038i	1.08956	+	1.21008i
$786$	35.0466	−	15.6037i	1.25007	−	0.556567i
$787$	22.0433	−	4.68545i	0.785758	−	0.167018i	0.202476	−	0.979287i	$-0.435101\pi$
$787$	22.0433	−	4.68545i	0.785758	−	0.167018i	0.583283	+	0.812269i	$0.301768\pi$
$788$	3.67447	+	0.781033i	0.130898	+	0.0278232i
$789$	−22.1385	−	9.85670i	−0.788152	−	0.350908i
$790$	1.17365	+	3.61211i	0.0417565	+	0.128513i
$791$	15.9239	+	49.0087i	0.566189	+	1.74255i
$792$	−1.29435	−	0.576284i	−0.0459929	−	0.0204773i
$793$	−7.42649	−	1.57855i	−0.263722	−	0.0560559i
$794$	1.94443	−	0.413300i	0.0690051	−	0.0146675i
$795$	−35.1246	+	15.6385i	−1.24574	+	0.554640i
$796$	2.51378	+	2.79183i	0.0890985	+	0.0989539i
$797$	2.40014	+	22.8358i	0.0850172	+	0.808885i	0.951079	+	0.308948i	$0.0999769\pi$
$797$	2.40014	+	22.8358i	0.0850172	+	0.808885i	−0.866062	+	0.499937i	$0.833356\pi$
$798$	−56.3896	+	40.9695i	−1.99617	+	1.45030i
$799$	0.432515	−	4.11511i	0.0153013	−	0.145582i
$800$	0.286917	+	0.496954i	0.0101440	+	0.0175700i
$801$	−0.577566	+	1.00037i	−0.0204073	+	0.0353464i
$802$	−0.00673038	−	0.00488991i	−0.000237658	−	0.000172669i
$803$	−0.875159	+	0.971962i	−0.0308837	+	0.0342998i
$804$	−2.29894	+	7.07541i	−0.0810774	+	0.249531i
$805$	−57.2930			−2.01931
$806$	4.26107	−	7.46771i	0.150090	−	0.263039i
$807$	−46.8676			−1.64982
$808$	13.1718	−	40.5385i	0.463381	−	1.42614i
$809$	−7.53661	+	8.37025i	−0.264973	+	0.294282i	−0.860919	−	0.508742i	$-0.830111\pi$
$809$	−7.53661	+	8.37025i	−0.264973	+	0.294282i	0.595946	+	0.803025i	$0.296777\pi$
$810$	−32.0746	−	23.3036i	−1.12699	−	0.818803i
$811$	−16.9162	+	29.2998i	−0.594010	+	1.02885i	0.399676	+	0.916656i	$0.369123\pi$
$811$	−16.9162	+	29.2998i	−0.594010	+	1.02885i	−0.993686	+	0.112198i	$0.964211\pi$
$812$	2.28490	+	3.95756i	0.0801841	+	0.138883i
$813$	−3.84878	+	36.6187i	−0.134983	+	1.28427i
$814$	−1.58292	+	1.15006i	−0.0554813	+	0.0403095i
$815$	3.86339	+	36.7577i	0.135329	+	1.28757i
$816$	−4.17757	−	4.63966i	−0.146244	−	0.162421i
$817$	4.11946	−	1.83410i	0.144122	−	0.0641672i
$818$	38.1535	−	8.10978i	1.33401	−	0.283552i
$819$	−6.73129	−	1.43078i	−0.235210	−	0.0499955i
$820$	−7.38743	−	3.28910i	−0.257980	−	0.114860i
$821$	−0.852795	−	2.62463i	−0.0297628	−	0.0916003i	0.935072	−	0.354459i	$-0.115335\pi$
$821$	−0.852795	−	2.62463i	−0.0297628	−	0.0916003i	−0.964834	+	0.262858i	$0.915335\pi$
$822$	20.0701	+	61.7696i	0.700027	+	2.15446i
$823$	−47.8449	−	21.3019i	−1.66777	−	0.742539i	−0.667772	−	0.744366i	$-0.732752\pi$
$823$	−47.8449	−	21.3019i	−1.66777	−	0.742539i	−0.999998	+	0.00182722i	$0.999418\pi$
$824$	8.06067	+	1.71335i	0.280807	+	0.0596873i
$825$	−0.184762	+	0.0392724i	−0.00643259	+	0.00136729i
$826$	−15.5453	+	6.92121i	−0.540890	+	0.240820i
$827$	9.67730	+	10.7477i	0.336513	+	0.373735i	0.887523	−	0.460763i	$-0.152424\pi$
$827$	9.67730	+	10.7477i	0.336513	+	0.373735i	−0.551010	+	0.834498i	$0.685758\pi$
$828$	−0.447463	−	4.25733i	−0.0155504	−	0.147952i
$829$	−37.6536	+	27.3570i	−1.30776	+	0.950147i	−0.999999	−	0.00131552i	$-0.999581\pi$
$829$	−37.6536	+	27.3570i	−1.30776	+	0.950147i	−0.307766	+	0.951462i	$0.599581\pi$
$830$	−3.13796	+	29.8557i	−0.108920	+	1.03631i
$831$	6.84836	+	11.8617i	0.237567	+	0.411478i
$832$	−2.96332	+	5.13261i	−0.102735	+	0.177941i
$833$	−4.22961	−	3.07299i	−0.146547	−	0.106473i
$834$	35.9380	−	39.9132i	1.24443	−	1.38208i
$835$	4.63512	−	14.2654i	0.160405	−	0.493676i
$836$	0.657354			0.0227351
$837$	−12.3029	−	8.84352i	−0.425252	−	0.305677i
$838$	27.0910			0.935843
$839$	−14.6539	+	45.1002i	−0.505910	+	1.55703i	0.293325	+	0.956013i	$0.405238\pi$
$839$	−14.6539	+	45.1002i	−0.505910	+	1.55703i	−0.799235	+	0.601018i	$0.794762\pi$
$840$	32.8069	−	36.4358i	1.13195	−	1.25715i
$841$	16.0630	+	11.6704i	0.553895	+	0.402428i
$842$	19.1058	−	33.0923i	0.658430	−	1.14043i
$843$	−7.00640	−	12.1354i	−0.241313	−	0.417967i
$844$	−0.881928	+	8.39098i	−0.0303572	+	0.288830i
$845$	1.85673	−	1.34899i	0.0638734	−	0.0464068i
$846$	1.88763	+	17.9596i	0.0648980	+	0.617464i
$847$	−28.6414	−	31.8094i	−0.984129	−	1.09299i
$848$	−32.4464	+	14.4461i	−1.11421	+	0.496080i
$849$	65.6331	−	13.9507i	2.25252	−	0.478788i
$850$	−0.250163	−	0.0531738i	−0.00858053	−	0.00182385i
$851$	22.6810	+	10.0982i	0.777495	+	0.346163i
$852$	1.49532	+	4.60213i	0.0512289	+	0.157666i
$853$	−11.7997	−	36.3158i	−0.404014	−	1.24343i	−0.921716	−	0.387866i	$-0.873212\pi$
$853$	−11.7997	−	36.3158i	−0.404014	−	1.24343i	0.517701	−	0.855561i	$-0.326788\pi$
$854$	42.0805	+	18.7355i	1.43997	+	0.641114i
$855$	20.7242	+	4.40507i	0.708753	+	0.150650i
$856$	29.3939	−	6.24787i	1.00466	−	0.213548i
$857$	8.11571	−	3.61335i	0.277227	−	0.123430i	−0.263414	−	0.964683i	$-0.584848\pi$
$857$	8.11571	−	3.61335i	0.277227	−	0.123430i	0.540641	+	0.841253i	$0.318182\pi$
$858$	0.730379	+	0.811169i	0.0249347	+	0.0276928i
$859$	−4.34742	−	41.3630i	−0.148332	−	1.41129i	−0.774981	−	0.631985i	$-0.782241\pi$
$859$	−4.34742	−	41.3630i	−0.148332	−	1.41129i	0.626649	−	0.779302i	$-0.284426\pi$
$860$	0.611012	−	0.443927i	0.0208354	−	0.0151378i
$861$	−8.20062	+	78.0237i	−0.279476	+	2.65904i
$862$	17.1090	+	29.6337i	0.582737	+	1.00933i
$863$	9.58813	−	16.6071i	0.326384	−	0.565313i	−0.655408	−	0.755275i	$-0.727503\pi$
$863$	9.58813	−	16.6071i	0.326384	−	0.565313i	0.981791	+	0.189962i	$0.0608365\pi$
$864$	−4.72758	−	3.43479i	−0.160836	−	0.116854i
$865$	−11.3118	+	12.5630i	−0.384613	+	0.427156i
$866$	−2.25563	+	6.94211i	−0.0766494	+	0.235903i
$867$	−36.2196			−1.23008
$868$	−5.59800	+	6.28105i	−0.190008	+	0.213193i
$869$	−0.347505			−0.0117883
$870$	7.21933	−	22.2188i	0.244758	−	0.753289i
$871$	−5.93739	+	6.59414i	−0.201181	+	0.223434i
$872$	7.19002	+	5.22386i	0.243485	+	0.176902i
$873$	4.83813	−	8.37989i	0.163746	−	0.283616i
$874$	−25.8571	−	44.7858i	−0.874630	−	1.51490i
$875$	−4.46070	+	42.4407i	−0.150799	+	1.43476i
$876$	2.73581	−	1.98768i	0.0924345	−	0.0671576i
$877$	−4.39715	−	41.8361i	−0.148481	−	1.41270i	−0.774341	−	0.632769i	$-0.781918\pi$
$877$	−4.39715	−	41.8361i	−0.148481	−	1.41270i	0.625860	−	0.779936i	$-0.284748\pi$
$878$	9.33728	+	10.3701i	0.315118	+	0.349974i
$879$	66.1842	−	29.4671i	2.23234	−	0.993900i
$880$	−3.36410	+	0.715062i	−0.113404	+	0.0241047i
$881$	−24.1862	−	5.14094i	−0.814855	−	0.173203i	−0.218410	−	0.975857i	$-0.570087\pi$
$881$	−24.1862	−	5.14094i	−0.814855	−	0.173203i	−0.596445	+	0.802654i	$0.703421\pi$
$882$	20.8443	+	9.28049i	0.701864	+	0.312490i
$883$	−1.32298	−	4.07170i	−0.0445217	−	0.137024i	0.926325	−	0.376726i	$-0.122950\pi$
$883$	−1.32298	−	4.07170i	−0.0445217	−	0.137024i	−0.970846	+	0.239702i	$0.922950\pi$
$884$	0.0736633	+	0.226712i	0.00247756	+	0.00762516i
$885$	12.8185	+	5.70717i	0.430890	+	0.191844i
$886$	31.8677	+	6.77368i	1.07062	+	0.227566i
$887$	21.8608	−	4.64666i	0.734015	−	0.156020i	0.174285	−	0.984695i	$-0.444238\pi$
$887$	21.8608	−	4.64666i	0.734015	−	0.156020i	0.559729	+	0.828676i	$0.310905\pi$
$888$	−19.4096	+	8.64169i	−0.651342	+	0.289996i
$889$	35.6871	+	39.6346i	1.19691	+	1.32930i
$890$	0.244306	+	2.32442i	0.00818917	+	0.0779148i
$891$	2.93473	−	2.13220i	0.0983170	−	0.0714315i
$892$	0.564115	−	5.36719i	0.0188880	−	0.179707i
$893$	17.5938	+	30.4734i	0.588755	+	1.01975i
$894$	−31.0796	+	53.8314i	−1.03946	+	1.80039i
$895$	44.7826	+	32.5364i	1.49692	+	1.08757i
$896$	35.3501	−	39.2602i	1.18096	−	1.31159i
$897$	4.28007	−	13.1727i	0.142907	−	0.439824i
$898$	−37.7064			−1.25828
$899$	5.12166	−	16.0395i	0.170817	−	0.534948i
$900$	0.180034			0.00600113
$901$	1.47191	−	4.53007i	0.0490364	−	0.150918i
$902$	3.06945	−	3.40897i	0.102201	−	0.113506i
$903$	−5.92787	−	4.30685i	−0.197267	−	0.143323i
$904$	16.3591	−	28.3347i	0.544094	−	0.942399i
$905$	−25.1602	−	43.5788i	−0.836354	−	1.44861i
$906$	−5.71158	+	54.3421i	−0.189755	+	1.80539i
$907$	−14.8618	+	10.7977i	−0.493478	+	0.358533i	−0.806520	−	0.591206i	$-0.798652\pi$
$907$	−14.8618	+	10.7977i	−0.493478	+	0.358533i	0.313042	+	0.949739i	$0.398652\pi$
$908$	−0.564018	−	5.36627i	−0.0187176	−	0.178086i
$909$	−20.0273	−	22.2425i	−0.664263	−	0.737738i
$910$	−12.7202	+	5.66339i	−0.421670	+	0.187739i
$911$	17.1307	−	3.64123i	0.567564	−	0.120639i	0.0848126	−	0.996397i	$-0.472971\pi$
$911$	17.1307	−	3.64123i	0.567564	−	0.120639i	0.482751	+	0.875757i	$0.339638\pi$
$912$	51.9326	+	11.0386i	1.71966	+	0.365525i
$913$	−2.50928	−	1.11721i	−0.0830452	−	0.0369741i
$914$	−15.1997	−	46.7798i	−0.502761	−	1.54734i
$915$	−11.7374	−	36.1240i	−0.388026	−	1.19422i
$916$	2.42522	+	1.07978i	0.0801316	+	0.0356769i
$917$	−43.7977	−	9.30950i	−1.44633	−	0.307427i
$918$	2.54753	−	0.541494i	0.0840810	−	0.0178720i
$919$	−39.3529	+	17.5210i	−1.29813	+	0.577966i	−0.935289	−	0.353884i	$-0.884861\pi$
$919$	−39.3529	+	17.5210i	−1.29813	+	0.577966i	−0.362843	+	0.931850i	$0.618194\pi$
$920$	24.3408	+	27.0331i	0.802491	+	0.891256i
$921$	0.688530	+	6.55092i	0.0226878	+	0.215860i
$922$	1.95473	−	1.42020i	0.0643758	−	0.0467717i
$923$	−0.603291	+	5.73993i	−0.0198576	+	0.188932i
$924$	−0.534072	−	0.925040i	−0.0175697	−	0.0304316i
$925$	−0.522077	+	0.904264i	−0.0171658	+	0.0297320i
$926$	32.9807	+	23.9619i	1.08381	+	0.787436i
$927$	3.87193	−	4.30021i	0.127171	−	0.141237i
$928$	2.00669	−	6.17596i	0.0658729	−	0.202736i
$929$	−46.9581			−1.54064			−0.770322	−	0.637655i	$-0.779904\pi$
$929$	−46.9581			−1.54064			−0.770322	+	0.637655i	$0.779904\pi$
$930$	43.0126	−	0.218409i	1.41044	−	0.00716191i
$931$	44.4596			1.45710
$932$	3.23594	−	9.95921i	0.105997	−	0.326225i
$933$	−21.6340	+	24.0270i	−0.708267	+	0.786610i
$934$	−20.6956	−	15.0363i	−0.677182	−	0.492001i
$935$	0.230620	−	0.399445i	0.00754207	−	0.0130632i
$936$	2.18467	+	3.78395i	0.0714080	+	0.123682i
$937$	2.64597	−	25.1747i	0.0864401	−	0.822423i	−0.862307	−	0.506386i	$-0.830981\pi$
$937$	2.64597	−	25.1747i	0.0864401	−	0.822423i	0.948747	−	0.316037i	$-0.102352\pi$
$938$	43.5526	−	31.6428i	1.42204	−	1.03318i
$939$	−0.927064	−	8.82042i	−0.0302536	−	0.287844i
$940$	3.94351	+	4.37971i	0.128623	+	0.142850i
$941$	27.7222	−	12.3427i	0.903719	−	0.402361i	0.0983611	−	0.995151i	$-0.468640\pi$
$941$	27.7222	−	12.3427i	0.903719	−	0.402361i	0.805358	+	0.592789i	$0.201973\pi$
$942$	65.4512	−	13.9121i	2.13251	−	0.453280i
$943$	−56.9357	−	12.1021i	−1.85408	−	0.394097i
$944$	11.8411	+	5.27201i	0.385396	+	0.171589i
$945$	7.58249	+	23.3365i	0.246658	+	0.759137i
$946$	0.132392	+	0.407460i	0.00430443	+	0.0132477i
$947$	12.6916	+	5.65067i	0.412422	+	0.183622i	0.602450	−	0.798156i	$-0.294191\pi$
$947$	12.6916	+	5.65067i	0.412422	+	0.183622i	−0.190028	+	0.981779i	$0.560858\pi$
$948$	0.878858	+	0.186807i	0.0285440	+	0.00606721i
$949$	3.94523	−	0.838585i	0.128068	−	0.0272216i
$950$	1.98688	−	0.884617i	0.0644630	−	0.0287008i
$951$	42.1249	+	46.7844i	1.36599	+	1.51709i
$952$	0.634901	+	6.04068i	0.0205773	+	0.195780i
$953$	3.94670	−	2.86744i	0.127846	−	0.0928856i	−0.522025	−	0.852930i	$-0.674823\pi$
$953$	3.94670	−	2.86744i	0.127846	−	0.0928856i	0.649871	+	0.760045i	$0.274823\pi$
$954$	−2.17294	+	20.6742i	−0.0703516	+	0.669350i
$955$	6.53615	+	11.3210i	0.211505	+	0.366337i
$956$	−2.40647	+	4.16813i	−0.0778308	+	0.134807i
$957$	1.72933	+	1.25643i	0.0559014	+	0.0406148i
$958$	6.70121	−	7.44245i	0.216506	−	0.240455i
$959$	23.4251	−	72.0952i	0.756437	−	2.32807i
$960$	−29.6496			−0.956936
$961$	30.9984	−	0.314815i	0.999948	−	0.0101553i
$962$	6.03384			0.194539
$963$	6.52056	−	20.0682i	0.210122	−	0.646689i
$964$	−5.18281	+	5.75609i	−0.166927	+	0.185391i
$965$	−36.2167	−	26.3130i	−1.16586	−	0.847044i
$966$	−42.0156	+	72.7731i	−1.35183	+	2.34144i
$967$	19.7556	+	34.2177i	0.635297	+	1.10037i	0.986452	+	0.164050i	$0.0524557\pi$
$967$	19.7556	+	34.2177i	0.635297	+	1.10037i	−0.351155	+	0.936317i	$0.614211\pi$
$968$	−2.84079	+	27.0283i	−0.0913063	+	0.868722i
$969$	−5.76043	+	4.18520i	−0.185052	+	0.134448i
$970$	−2.04650	−	19.4711i	−0.0657091	−	0.625181i
$971$	−13.1689	−	14.6255i	−0.422610	−	0.469356i	0.493812	−	0.869569i	$-0.335603\pi$
$971$	−13.1689	−	14.6255i	−0.422610	−	0.469356i	−0.916422	+	0.400212i	$0.868936\pi$
$972$	−5.69967	+	2.53766i	−0.182817	+	0.0813953i
$973$	−61.3168	+	13.0333i	−1.96572	+	0.417828i
$974$	−27.0275	−	5.74487i	−0.866017	−	0.184077i
$975$	0.532146	+	0.236927i	0.0170423	+	0.00758773i
$976$	−10.8424	−	33.3696i	−0.347058	−	1.06814i
$977$	1.41216	+	4.34617i	0.0451788	+	0.139046i	0.971101	−	0.238667i	$-0.0767105\pi$
$977$	1.41216	+	4.34617i	0.0451788	+	0.139046i	−0.925923	+	0.377713i	$0.876710\pi$
$978$	49.5226	+	22.0489i	1.58356	+	0.705045i
$979$	−0.209176	−	0.0444617i	−0.00668529	−	0.00142100i
$980$	7.28369	−	1.54820i	0.232669	−	0.0494553i
$981$	5.70101	−	2.53825i	0.182019	−	0.0810402i
$982$	−35.6534	−	39.5971i	−1.13775	−	1.26360i
$983$	−2.76186	−	26.2773i	−0.0880896	−	0.838117i	−0.945967	−	0.324262i	$-0.894884\pi$
$983$	−2.76186	−	26.2773i	−0.0880896	−	0.838117i	0.857878	−	0.513854i	$-0.171783\pi$
$984$	40.2987	−	29.2787i	1.28468	−	0.933371i
$985$	−2.34302	+	22.2923i	−0.0746547	+	0.710292i
$986$	1.44711	+	2.50647i	0.0460854	+	0.0798222i
$987$	28.5884	−	49.5166i	0.909980	−	1.57613i
$988$	−1.64002	−	1.19154i	−0.0521760	−	0.0379081i
$989$	3.63765	−	4.04001i	0.115670	−	0.128465i
$990$	−0.622048	+	1.91447i	−0.0197700	+	0.0608457i
$991$	46.3729			1.47308			0.736542	−	0.676391i	$-0.236457\pi$
$991$	46.3729			1.47308			0.736542	+	0.676391i	$0.236457\pi$
$992$	11.9558	−	0.0607091i	0.379598	−	0.00192752i
$993$	−30.0006			−0.952042
$994$	10.8205	−	33.3020i	0.343205	−	1.05627i
$995$	−14.9995	+	16.6586i	−0.475516	+	0.528114i
$996$	5.74553	+	4.17437i	0.182054	+	0.132270i
$997$	8.90094	−	15.4169i	0.281896	−	0.488258i	−0.689956	−	0.723851i	$-0.742370\pi$
$997$	8.90094	−	15.4169i	0.281896	−	0.488258i	0.971852	+	0.235594i	$0.0757035\pi$
$998$	17.2280	+	29.8398i	0.545344	+	0.944564i
$999$	1.11146	−	10.5749i	0.0351651	−	0.334574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bi.b.14.13	✓	136
31.20	even	15	inner	403.2.bi.b.144.13	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bi.b.14.13	✓	136	1.1	even	1	trivial
403.2.bi.b.144.13	yes	136	31.20	even	15	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bi (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.477192 - 1.46864i) q^{2} +(1.45858 - 1.61992i) q^{3} +(-0.311171 - 0.226079i) q^{4} +(1.14752 - 1.98757i) q^{5} +(-1.68306 - 2.91515i) q^{6} +(-0.410673 + 3.90729i) q^{7} +(2.01809 - 1.46623i) q^{8} +(-0.183091 - 1.74199i) q^{9} +O(q^{10})\)	\(q+(0.477192 - 1.46864i) q^{2} +(1.45858 - 1.61992i) q^{3} +(-0.311171 - 0.226079i) q^{4} +(1.14752 - 1.98757i) q^{5} +(-1.68306 - 2.91515i) q^{6} +(-0.410673 + 3.90729i) q^{7} +(2.01809 - 1.46623i) q^{8} +(-0.183091 - 1.74199i) q^{9} +(-2.37144 - 2.63375i) q^{10} +(0.296236 - 0.131893i) q^{11} +(-0.820097 + 0.174317i) q^{12} +(-0.978148 - 0.207912i) q^{13} +(5.54245 + 2.46766i) q^{14} +(-1.54594 - 4.75792i) q^{15} +(-1.42807 - 4.39513i) q^{16} +(0.566184 + 0.252081i) q^{17} +(-2.64574 - 0.562369i) q^{18} +(-5.15531 + 1.09579i) q^{19} +(-0.806422 + 0.359042i) q^{20} +(5.73049 + 6.36435i) q^{21} +(-0.0523423 - 0.498004i) q^{22} +(-5.14052 + 3.73480i) q^{23} +(0.568377 - 5.40775i) q^{24} +(-0.133614 - 0.231426i) q^{25} +(-0.772112 + 1.33734i) q^{26} +(2.20158 + 1.59954i) q^{27} +(1.01115 - 1.12299i) q^{28} +(-0.934493 + 2.87608i) q^{29} -7.72540 q^{30} +(-5.56769 + 0.0282715i) q^{31} -2.14736 q^{32} +(0.218429 - 0.672254i) q^{33} +(0.640396 - 0.711232i) q^{34} +(7.29475 + 5.29994i) q^{35} +(-0.336855 + 0.583450i) q^{36} +(-1.95368 - 3.38387i) q^{37} +(-0.850737 + 8.09422i) q^{38} +(-1.76351 + 1.28126i) q^{39} +(-0.598423 - 5.69362i) q^{40} +(6.12974 + 6.80776i) q^{41} +(12.0815 - 5.37904i) q^{42} +(-0.836883 + 0.177885i) q^{43} +(-0.121998 - 0.0259315i) q^{44} +(-3.67243 - 1.63507i) q^{45} +(3.03209 + 9.33181i) q^{46} +(-2.06311 - 6.34959i) q^{47} +(-9.20270 - 4.09731i) q^{48} +(-8.25124 - 1.75386i) q^{49} +(-0.403642 + 0.0857967i) q^{50} +(1.23418 - 0.549490i) q^{51} +(0.257367 + 0.285834i) q^{52} +(-0.803351 - 7.64338i) q^{53} +(3.39973 - 2.47005i) q^{54} +(0.0777917 - 0.740139i) q^{55} +(4.90021 + 8.48740i) q^{56} +(-5.74433 + 9.94948i) q^{57} +(3.77800 + 2.74488i) q^{58} +(-1.87676 + 2.08435i) q^{59} +(-0.594612 + 1.83003i) q^{60} +7.59240 q^{61} +(-2.61533 + 8.19045i) q^{62} +6.88167 q^{63} +(1.83143 - 5.63656i) q^{64} +(-1.53568 + 1.70555i) q^{65} +(-0.883070 - 0.641588i) q^{66} +(4.43665 - 7.68450i) q^{67} +(-0.119190 - 0.206443i) q^{68} +(-1.44778 + 13.7747i) q^{69} +(11.2647 - 8.18430i) q^{70} +(-0.603291 - 5.73993i) q^{71} +(-2.92365 - 3.24705i) q^{72} +(-3.68467 + 1.64052i) q^{73} +(-5.90198 + 1.25451i) q^{74} +(-0.569777 - 0.121110i) q^{75} +(1.85192 + 0.824527i) q^{76} +(0.393688 + 1.21165i) q^{77} +(1.04019 + 3.20137i) q^{78} +(-0.979003 - 0.435880i) q^{79} +(-10.3744 - 2.20514i) q^{80} +(10.9422 - 2.32585i) q^{81} +(12.9232 - 5.75380i) q^{82} +(-5.66791 - 6.29485i) q^{83} +(-0.344316 - 3.27594i) q^{84} +(1.15074 - 0.836059i) q^{85} +(-0.138104 + 1.31397i) q^{86} +(3.29597 + 5.70879i) q^{87} +(0.404446 - 0.700521i) q^{88} +(-0.533527 - 0.387630i) q^{89} +(-4.15379 + 4.61325i) q^{90} +(1.21407 - 3.73652i) q^{91} +2.44394 q^{92} +(-8.07513 + 9.06044i) q^{93} -10.3098 q^{94} +(-3.73787 + 11.5040i) q^{95} +(-3.13209 + 3.47854i) q^{96} +(4.46924 + 3.24709i) q^{97} +(-6.51321 + 11.2812i) q^{98} +(-0.283995 - 0.491893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9	\( 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9} + 7 q^{10} + 5 q^{11} + 28 q^{12} + 17 q^{13} - 3 q^{14} + 17 q^{15} - 78 q^{16} - 12 q^{17} + 34 q^{18} - 23 q^{19} + 8 q^{20} - 38 q^{21} + 8 q^{22} + 9 q^{23} + 46 q^{24} - 69 q^{25} - 12 q^{26} - 58 q^{27} + 7 q^{28} + 18 q^{29} + 60 q^{30} + 14 q^{31} + 212 q^{32} - 41 q^{33} - 30 q^{35} - 106 q^{36} + 6 q^{37} - 62 q^{38} + 6 q^{39} + 39 q^{40} - 5 q^{41} + 37 q^{42} + q^{43} - 88 q^{44} - 168 q^{45} + 6 q^{46} - 81 q^{47} - 101 q^{48} + 117 q^{49} - 20 q^{50} + 35 q^{51} + 7 q^{52} + 25 q^{53} + 57 q^{54} + 19 q^{55} - 63 q^{56} - 20 q^{57} - 44 q^{58} + 9 q^{59} + 113 q^{60} + 8 q^{61} + 57 q^{62} + 112 q^{63} - 146 q^{64} - 5 q^{65} + 70 q^{66} - 99 q^{67} - 56 q^{68} - 65 q^{69} + 169 q^{70} - q^{71} - 43 q^{72} + 50 q^{73} - 26 q^{74} - 18 q^{75} - 94 q^{76} + 114 q^{77} - 17 q^{79} + 217 q^{80} + 54 q^{81} - 25 q^{82} - 53 q^{83} - 22 q^{84} + 2 q^{85} - 54 q^{86} - 28 q^{87} + 70 q^{88} - 101 q^{89} + 165 q^{90} - 4 q^{91} + 64 q^{92} + 61 q^{93} - 90 q^{94} - 33 q^{95} - 217 q^{96} + 73 q^{97} + 33 q^{98} - 15 q^{99}+O(q^{100}) \) 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9 + 7 * q^10 + 5 * q^11 + 28 * q^12 + 17 * q^13 - 3 * q^14 + 17 * q^15 - 78 * q^16 - 12 * q^17 + 34 * q^18 - 23 * q^19 + 8 * q^20 - 38 * q^21 + 8 * q^22 + 9 * q^23 + 46 * q^24 - 69 * q^25 - 12 * q^26 - 58 * q^27 + 7 * q^28 + 18 * q^29 + 60 * q^30 + 14 * q^31 + 212 * q^32 - 41 * q^33 - 30 * q^35 - 106 * q^36 + 6 * q^37 - 62 * q^38 + 6 * q^39 + 39 * q^40 - 5 * q^41 + 37 * q^42 + q^43 - 88 * q^44 - 168 * q^45 + 6 * q^46 - 81 * q^47 - 101 * q^48 + 117 * q^49 - 20 * q^50 + 35 * q^51 + 7 * q^52 + 25 * q^53 + 57 * q^54 + 19 * q^55 - 63 * q^56 - 20 * q^57 - 44 * q^58 + 9 * q^59 + 113 * q^60 + 8 * q^61 + 57 * q^62 + 112 * q^63 - 146 * q^64 - 5 * q^65 + 70 * q^66 - 99 * q^67 - 56 * q^68 - 65 * q^69 + 169 * q^70 - q^71 - 43 * q^72 + 50 * q^73 - 26 * q^74 - 18 * q^75 - 94 * q^76 + 114 * q^77 - 17 * q^79 + 217 * q^80 + 54 * q^81 - 25 * q^82 - 53 * q^83 - 22 * q^84 + 2 * q^85 - 54 * q^86 - 28 * q^87 + 70 * q^88 - 101 * q^89 + 165 * q^90 - 4 * q^91 + 64 * q^92 + 61 * q^93 - 90 * q^94 - 33 * q^95 - 217 * q^96 + 73 * q^97 + 33 * q^98 - 15 * q^99

Introduction

L-functions

Modular forms

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