LMFDB - Embedded newform 804.2.bd.a.35.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(23,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 33, 28]))

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

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

chi := DirichletCharacter("804.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.bd (of order $66$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$2640$
Relative dimension:	$132$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			35.20
Character	$\chi$	$=$	804.35
Dual form			804.2.bd.a.23.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28787 + 0.584297i) q^{2} +(-1.68798 + 0.388227i) q^{3} +(1.31719 - 1.50499i) q^{4} +(-0.837417 - 0.382435i) q^{5} +(1.94705 - 1.48627i) q^{6} +(3.05562 - 3.20464i) q^{7} +(-0.817004 + 2.70786i) q^{8} +(2.69856 - 1.31064i) q^{9} +O(q^{10})$	\(q+(-1.28787 + 0.584297i) q^{2} +(-1.68798 + 0.388227i) q^{3} +(1.31719 - 1.50499i) q^{4} +(-0.837417 - 0.382435i) q^{5} +(1.94705 - 1.48627i) q^{6} +(3.05562 - 3.20464i) q^{7} +(-0.817004 + 2.70786i) q^{8} +(2.69856 - 1.31064i) q^{9} +(1.30194 + 0.00322483i) q^{10} +(2.13552 - 0.203917i) q^{11} +(-1.63912 + 3.05177i) q^{12} +(-2.08322 + 0.401508i) q^{13} +(-2.06276 + 5.91254i) q^{14} +(1.56202 + 0.320435i) q^{15} +(-0.530004 - 3.96473i) q^{16} +(-1.63403 - 3.16958i) q^{17} +(-2.70958 + 3.26469i) q^{18} +(2.30859 + 2.42118i) q^{19} +(-1.67860 + 0.756564i) q^{20} +(-3.91370 + 6.59565i) q^{21} +(-2.63111 + 1.51039i) q^{22} +(2.93067 + 1.17326i) q^{23} +(0.327822 - 4.88800i) q^{24} +(-2.71929 - 3.13823i) q^{25} +(2.44831 - 1.73431i) q^{26} +(-4.04629 + 3.25999i) q^{27} +(-0.798121 - 8.81982i) q^{28} +(-8.62550 + 4.97993i) q^{29} +(-2.19889 + 0.500004i) q^{30} +(1.08798 - 5.64497i) q^{31} +(2.99916 + 4.79636i) q^{32} +(-3.52554 + 1.17327i) q^{33} +(3.95639 + 3.12723i) q^{34} +(-3.78440 + 1.51504i) q^{35} +(1.58202 - 5.78768i) q^{36} +(-0.0290824 + 0.0503722i) q^{37} +(-4.38785 - 1.76925i) q^{38} +(3.36056 - 1.48650i) q^{39} +(1.71975 - 1.95516i) q^{40} +(3.16113 + 0.150583i) q^{41} +(1.18650 - 10.7811i) q^{42} +(2.25726 - 3.51237i) q^{43} +(2.50599 - 3.48253i) q^{44} +(-2.76105 + 0.0655280i) q^{45} +(-4.45984 + 0.201378i) q^{46} +(-0.135786 + 0.106783i) q^{47} +(2.43385 + 6.48663i) q^{48} +(-0.599845 - 12.5923i) q^{49} +(5.33574 + 2.45274i) q^{50} +(3.98873 + 4.71581i) q^{51} +(-2.13974 + 3.66410i) q^{52} +(-5.17743 - 8.05623i) q^{53} +(3.30627 - 6.56267i) q^{54} +(-1.86630 - 0.645933i) q^{55} +(6.18127 + 10.8924i) q^{56} +(-4.83683 - 3.19065i) q^{57} +(8.19872 - 11.4533i) q^{58} +(8.26955 - 9.54357i) q^{59} +(2.53973 - 1.92875i) q^{60} +(11.0474 + 1.05490i) q^{61} +(1.89717 + 7.90567i) q^{62} +(4.04564 - 12.6527i) q^{63} +(-6.66501 - 4.42466i) q^{64} +(1.89807 + 0.460468i) q^{65} +(3.85488 - 3.57098i) q^{66} +(-6.69669 + 4.70684i) q^{67} +(-6.92252 - 1.71574i) q^{68} +(-5.40241 - 0.842680i) q^{69} +(3.98856 - 4.16239i) q^{70} +(1.27422 + 0.656908i) q^{71} +(1.34430 + 8.37812i) q^{72} +(-0.405416 - 0.0387126i) q^{73} +(0.00802186 - 0.0818653i) q^{74} +(5.80846 + 4.24157i) q^{75} +(6.68473 - 0.285250i) q^{76} +(5.87185 - 7.46666i) q^{77} +(-3.45939 + 3.87798i) q^{78} +(-2.72312 - 0.942482i) q^{79} +(-1.07242 + 3.52282i) q^{80} +(5.56444 - 7.07368i) q^{81} +(-4.15909 + 1.65311i) q^{82} +(-5.41507 - 7.60441i) q^{83} +(4.77131 + 14.5778i) q^{84} +(0.156206 + 3.27917i) q^{85} +(-0.854781 + 5.84237i) q^{86} +(12.6263 - 11.7547i) q^{87} +(-1.19255 + 5.94928i) q^{88} +(-5.56546 - 0.800192i) q^{89} +(3.51758 - 1.69767i) q^{90} +(-5.07885 + 7.90284i) q^{91} +(5.62601 - 2.86522i) q^{92} +(0.355045 + 9.95099i) q^{93} +(0.112481 - 0.216862i) q^{94} +(-1.00731 - 2.91043i) q^{95} +(-6.92460 - 6.93181i) q^{96} +(-2.40390 + 4.16367i) q^{97} +(8.13016 + 15.8667i) q^{98} +(5.49555 - 3.34918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{19}{33}\right)$	$-1$

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 $

$2$	−1.28787	+	0.584297i	−0.910658	+	0.413161i
$2$	−1.28787	+	0.584297i	−0.910658	+	0.413161i
$3$	−1.68798	+	0.388227i	−0.974556	+	0.224143i
$3$	−1.68798	+	0.388227i	−0.974556	+	0.224143i
$4$	1.31719	−	1.50499i	0.658597	−	0.752496i
$5$	−0.837417	−	0.382435i	−0.374504	−	0.171030i	0.219266	−	0.975665i	$-0.429634\pi$
$5$	−0.837417	−	0.382435i	−0.374504	−	0.171030i	−0.593770	+	0.804635i	$0.702361\pi$
$6$	1.94705	−	1.48627i	0.794880	−	0.606766i
$7$	3.05562	−	3.20464i	1.15492	−	1.21124i	0.181208	−	0.983445i	$-0.441999\pi$
$7$	3.05562	−	3.20464i	1.15492	−	1.21124i	0.973709	−	0.227797i	$-0.0731522\pi$
$8$	−0.817004	+	2.70786i	−0.288855	+	0.957373i
$9$	2.69856	−	1.31064i	0.899520	−	0.436880i
$10$	1.30194	+	0.00322483i	0.411708	+	0.00101978i
$11$	2.13552	−	0.203917i	0.643882	−	0.0614833i	0.231993	−	0.972717i	$-0.425475\pi$
$11$	2.13552	−	0.203917i	0.643882	−	0.0614833i	0.411889	+	0.911234i	$0.364869\pi$
$12$	−1.63912	+	3.05177i	−0.473173	+	0.880970i
$13$	−2.08322	+	0.401508i	−0.577782	+	0.111358i	−0.469766	−	0.882791i	$-0.655662\pi$
$13$	−2.08322	+	0.401508i	−0.577782	+	0.111358i	−0.108015	+	0.994149i	$0.534450\pi$
$14$	−2.06276	+	5.91254i	−0.551297	+	1.58019i
$15$	1.56202	+	0.320435i	0.403311	+	0.0827361i
$16$	−0.530004	−	3.96473i	−0.132501	−	0.991183i
$17$	−1.63403	−	3.16958i	−0.396311	−	0.768735i	0.603275	−	0.797533i	$-0.293862\pi$
$17$	−1.63403	−	3.16958i	−0.396311	−	0.768735i	−0.999585	+	0.0287983i	$0.990832\pi$
$18$	−2.70958	+	3.26469i	−0.638653	+	0.769495i
$19$	2.30859	+	2.42118i	0.529628	+	0.555458i	0.933138	−	0.359517i	$-0.117059\pi$
$19$	2.30859	+	2.42118i	0.529628	+	0.555458i	−0.403511	+	0.914975i	$0.632210\pi$
$20$	−1.67860	+	0.756564i	−0.375347	+	0.169173i
$21$	−3.91370	+	6.59565i	−0.854040	+	1.43929i
$22$	−2.63111	+	1.51039i	−0.560954	+	0.322017i
$23$	2.93067	+	1.17326i	0.611087	+	0.244642i	0.656500	−	0.754326i	$-0.272036\pi$
$23$	2.93067	+	1.17326i	0.611087	+	0.244642i	−0.0454129	+	0.998968i	$0.514460\pi$
$24$	0.327822	−	4.88800i	0.0669164	−	0.997759i
$25$	−2.71929	−	3.13823i	−0.543859	−	0.627647i
$26$	2.44831	−	1.73431i	0.480153	−	0.340126i
$27$	−4.04629	+	3.25999i	−0.778709	+	0.627386i
$28$	−0.798121	−	8.81982i	−0.150831	−	1.66679i
$29$	−8.62550	+	4.97993i	−1.60171	+	0.924750i	−0.610570	+	0.791962i	$0.709060\pi$
$29$	−8.62550	+	4.97993i	−1.60171	+	0.924750i	−0.991144	+	0.132788i	$0.957607\pi$
$30$	−2.19889	+	0.500004i	−0.401461	+	0.0912877i
$31$	1.08798	−	5.64497i	0.195407	−	1.01387i	−0.743250	−	0.669014i	$-0.766717\pi$
$31$	1.08798	−	5.64497i	0.195407	−	1.01387i	0.938657	−	0.344853i	$-0.112071\pi$
$32$	2.99916	+	4.79636i	0.530181	+	0.847885i
$33$	−3.52554	+	1.17327i	−0.613718	+	0.204241i
$34$	3.95639	+	3.12723i	0.678515	+	0.536315i
$35$	−3.78440	+	1.51504i	−0.639680	+	0.256089i
$36$	1.58202	−	5.78768i	0.263670	−	0.964613i
$37$	−0.0290824	+	0.0503722i	−0.00478111	+	0.00828113i	−0.868406	−	0.495854i	$-0.834855\pi$
$37$	−0.0290824	+	0.0503722i	−0.00478111	+	0.00828113i	0.863625	+	0.504135i	$0.168189\pi$
$38$	−4.38785	−	1.76925i	−0.711803	−	0.287011i
$39$	3.36056	−	1.48650i	0.538120	−	0.238031i
$40$	1.71975	−	1.95516i	0.271917	−	0.309137i
$41$	3.16113	+	0.150583i	0.493685	+	0.0235171i	0.292949	−	0.956128i	$-0.405363\pi$
$41$	3.16113	+	0.150583i	0.493685	+	0.0235171i	0.200736	+	0.979645i	$0.435667\pi$
$42$	1.18650	−	10.7811i	0.183080	−	1.66356i
$43$	2.25726	−	3.51237i	0.344229	−	0.535631i	−0.625370	−	0.780328i	$-0.715052\pi$
$43$	2.25726	−	3.51237i	0.344229	−	0.535631i	0.969600	+	0.244697i	$0.0786885\pi$
$44$	2.50599	−	3.48253i	0.377793	−	0.525012i
$45$	−2.76105	+	0.0655280i	−0.411594	+	0.00976834i
$46$	−4.45984	+	0.201378i	−0.657568	+	0.0296916i
$47$	−0.135786	+	0.106783i	−0.0198064	+	0.0155760i	−0.628013	−	0.778203i	$-0.716132\pi$
$47$	−0.135786	+	0.106783i	−0.0198064	+	0.0155760i	0.608207	+	0.793779i	$0.291889\pi$
$48$	2.43385	+	6.48663i	0.351297	+	0.936264i
$49$	−0.599845	−	12.5923i	−0.0856921	−	1.79890i
$50$	5.33574	+	2.45274i	0.754588	+	0.346870i
$51$	3.98873	+	4.71581i	0.558534	+	0.660345i
$52$	−2.13974	+	3.66410i	−0.296728	+	0.508119i
$53$	−5.17743	−	8.05623i	−0.711174	−	1.10661i	−0.989276	−	0.146057i	$-0.953342\pi$
$53$	−5.17743	−	8.05623i	−0.711174	−	1.10661i	0.278102	−	0.960552i	$-0.410295\pi$
$54$	3.30627	−	6.56267i	0.449926	−	0.893066i
$55$	−1.86630	−	0.645933i	−0.251652	−	0.0870976i
$56$	6.18127	+	10.8924i	0.826007	+	1.45556i
$57$	−4.83683	−	3.19065i	−0.640654	−	0.422612i
$58$	8.19872	−	11.4533i	1.07654	−	1.50390i
$59$	8.26955	−	9.54357i	1.07660	−	1.24247i	0.107922	−	0.994159i	$-0.465580\pi$
$59$	8.26955	−	9.54357i	1.07660	−	1.24247i	0.968681	−	0.248307i	$-0.0798742\pi$
$60$	2.53973	−	1.92875i	0.327878	−	0.249000i
$61$	11.0474	+	1.05490i	1.41448	+	0.135066i	0.774133	−	0.633023i	$-0.218186\pi$
$61$	11.0474	+	1.05490i	1.41448	+	0.135066i	0.640343	+	0.768089i	$0.278792\pi$
$62$	1.89717	+	7.90567i	0.240941	+	1.00402i
$63$	4.04564	−	12.6527i	0.509703	−	1.59410i
$64$	−6.66501	−	4.42466i	−0.833126	−	0.553083i
$65$	1.89807	+	0.460468i	0.235427	+	0.0571140i
$66$	3.85488	−	3.57098i	0.474503	−	0.439558i
$67$	−6.69669	+	4.70684i	−0.818131	+	0.575032i
$67$	−6.69669	+	4.70684i	−0.818131	+	0.575032i
$68$	−6.92252	−	1.71574i	−0.839479	−	0.208064i
$69$	−5.40241	−	0.842680i	−0.650374	−	0.101447i
$70$	3.98856	−	4.16239i	0.476724	−	0.497500i
$71$	1.27422	+	0.656908i	0.151223	+	0.0779607i	0.532177	−	0.846633i	$-0.321374\pi$
$71$	1.27422	+	0.656908i	0.151223	+	0.0779607i	−0.380954	+	0.924594i	$0.624404\pi$
$72$	1.34430	+	8.37812i	0.158427	+	0.987371i
$73$	−0.405416	−	0.0387126i	−0.0474504	−	0.00453096i	0.0713038	−	0.997455i	$-0.477284\pi$
$73$	−0.405416	−	0.0387126i	−0.0474504	−	0.00453096i	−0.118754	+	0.992924i	$0.537890\pi$
$74$	0.00802186	−	0.0818653i	0.000932523	−	0.00951665i
$75$	5.80846	+	4.24157i	0.670704	+	0.489775i
$76$	6.68473	−	0.285250i	0.766791	−	0.0327204i
$77$	5.87185	−	7.46666i	0.669159	−	0.850905i
$78$	−3.45939	+	3.87798i	−0.391699	+	0.439095i
$79$	−2.72312	−	0.942482i	−0.306375	−	0.106038i	0.169554	−	0.985521i	$-0.445767\pi$
$79$	−2.72312	−	0.942482i	−0.306375	−	0.106038i	−0.475930	+	0.879483i	$0.657888\pi$
$80$	−1.07242	+	3.52282i	−0.119900	+	0.393864i
$81$	5.56444	−	7.07368i	0.618271	−	0.785965i
$82$	−4.15909	+	1.65311i	−0.459295	+	0.182555i
$83$	−5.41507	−	7.60441i	−0.594381	−	0.834692i	0.402349	−	0.915486i	$-0.368194\pi$
$83$	−5.41507	−	7.60441i	−0.594381	−	0.834692i	−0.996731	+	0.0807943i	$0.974254\pi$
$84$	4.77131	+	14.5778i	0.520593	+	1.59057i
$85$	0.156206	+	3.27917i	0.0169429	+	0.355676i
$86$	−0.854781	+	5.84237i	−0.0921734	+	0.629999i
$87$	12.6263	−	11.7547i	1.35368	−	1.26023i
$88$	−1.19255	+	5.94928i	−0.127126	+	0.634195i
$89$	−5.56546	−	0.800192i	−0.589938	−	0.0848202i	−0.159120	−	0.987259i	$-0.550866\pi$
$89$	−5.56546	−	0.800192i	−0.589938	−	0.0848202i	−0.430818	+	0.902439i	$0.641775\pi$
$90$	3.51758	−	1.69767i	0.370785	−	0.178950i
$91$	−5.07885	+	7.90284i	−0.532408	+	0.828443i
$92$	5.62601	−	2.86522i	0.586552	−	0.298720i
$93$	0.355045	+	9.95099i	0.0368164	+	1.03187i
$94$	0.112481	−	0.216862i	0.0116015	−	0.0223676i
$95$	−1.00731	−	2.91043i	−0.103348	−	0.298604i
$96$	−6.92460	−	6.93181i	−0.706739	−	0.707475i
$97$	−2.40390	+	4.16367i	−0.244079	+	0.422757i	−0.961872	−	0.273499i	$-0.911819\pi$
$97$	−2.40390	+	4.16367i	−0.244079	+	0.422757i	0.717793	+	0.696256i	$0.245152\pi$
$98$	8.13016	+	15.8667i	0.821270	+	1.60278i
$99$	5.49555	−	3.34918i	0.552324	−	0.336605i
$100$	−8.30485	−	0.0411416i	−0.830485	−	0.00411416i
$101$	17.6548	−	4.28301i	1.75672	−	0.426175i	0.777483	−	0.628904i	$-0.216496\pi$
$101$	17.6548	−	4.28301i	1.75672	−	0.426175i	0.979235	+	0.202729i	$0.0649810\pi$
$102$	−7.89238	−	3.74272i	−0.781462	−	0.370585i
$103$	0.293281	−	1.52169i	0.0288979	−	0.149936i	−0.964614	−	0.263667i	$-0.915068\pi$
$103$	0.293281	−	1.52169i	0.0288979	−	0.149936i	0.993512	+	0.113731i	$0.0362801\pi$
$104$	0.614773	−	5.96910i	0.0602834	−	0.585319i
$105$	5.79981	−	4.02657i	0.566003	−	0.392953i
$106$	11.3751	+	7.35018i	1.10484	+	0.713913i
$107$	−7.66719	−	16.7888i	−0.741215	−	1.62304i	−0.781545	−	0.623849i	$-0.785568\pi$
$107$	−7.66719	−	16.7888i	−0.741215	−	1.62304i	0.0403295	−	0.999186i	$-0.487159\pi$
$108$	−0.423483	+	10.3837i	−0.0407497	+	0.999169i
$109$	−5.08438	−	5.86769i	−0.486995	−	0.562023i	0.458065	−	0.888919i	$-0.348543\pi$
$109$	−5.08438	−	5.86769i	−0.486995	−	0.562023i	−0.945060	+	0.326896i	$0.893997\pi$
$110$	2.78096	−	0.258600i	0.265154	−	0.0246566i
$111$	0.0295347	−	0.0963178i	0.00280331	−	0.00914208i
$112$	−14.3250	−	10.4162i	−1.35359	−	0.984243i
$113$	−13.6754	−	9.73823i	−1.28648	−	0.916096i	−0.287348	−	0.957826i	$-0.592774\pi$
$113$	−13.6754	−	9.73823i	−1.28648	−	0.916096i	−0.999129	+	0.0417304i	$0.986713\pi$
$114$	8.09348	+	1.28298i	0.758024	+	0.120162i
$115$	−2.00550	−	2.10330i	−0.187013	−	0.196134i
$116$	−3.86668	+	19.5408i	−0.359013	+	1.81432i
$117$	−5.09546	+	3.81385i	−0.471076	+	0.352590i
$118$	−5.07378	+	17.1227i	−0.467079	+	1.57627i
$119$	−15.1503	−	4.44854i	−1.38883	−	0.407797i
$120$	−2.14387	+	3.96792i	−0.195707	+	0.362220i
$121$	−6.28237	+	1.21083i	−0.571125	+	0.110075i
$122$	−14.8440	+	5.09641i	−1.34391	+	0.461407i
$123$	−5.39438	+	0.973055i	−0.486395	+	0.0877374i
$124$	−7.06256	−	9.07292i	−0.634237	−	0.814772i
$125$	2.37384	+	8.08456i	0.212323	+	0.723105i
$126$	2.18273	+	18.6589i	0.194453	+	1.66227i
$127$	5.84447	−	6.12951i	0.518613	−	0.543906i	−0.411389	−	0.911460i	$-0.634956\pi$
$127$	5.84447	−	6.12951i	0.518613	−	0.543906i	0.930002	+	0.367554i	$0.119805\pi$
$128$	11.1690	+	1.80402i	0.987205	+	0.159455i
$129$	−2.44662	+	6.80514i	−0.215413	+	0.599159i
$130$	−2.71351	+	0.516019i	−0.237991	+	0.0452579i
$131$	−1.87240	−	13.0229i	−0.163593	−	1.13781i	−0.891791	−	0.452447i	$-0.850551\pi$
$131$	−1.87240	−	13.0229i	−0.163593	−	1.13781i	0.728199	−	0.685366i	$-0.240358\pi$
$132$	−2.87805	+	6.85134i	−0.250502	+	0.596333i
$133$	14.8132			1.28447
$134$	5.87423	−	9.97464i	0.507457	−	0.861677i
$135$	4.63517	−	1.18253i	0.398932	−	0.101776i
$136$	9.91778	−	1.83517i	0.850442	−	0.157364i
$137$	2.19601	−	0.315739i	0.187618	−	0.0269754i	−0.0478653	−	0.998854i	$-0.515242\pi$
$137$	2.19601	−	0.315739i	0.187618	−	0.0269754i	0.235483	+	0.971878i	$0.424333\pi$
$138$	7.44995	−	2.07136i	0.634182	−	0.176326i
$139$	15.8148	+	7.22237i	1.34139	+	0.612593i	0.951324	−	0.308193i	$-0.0997241\pi$
$139$	15.8148	+	7.22237i	1.34139	+	0.612593i	0.390068	+	0.920786i	$0.372451\pi$
$140$	−2.70465	+	7.69110i	−0.228585	+	0.650016i
$141$	0.187748	−	0.232964i	0.0158112	−	0.0196191i
$142$	−2.02486	−	0.101483i	−0.169922	−	0.00851630i
$143$	−4.36688	+	1.28223i	−0.365177	+	0.107226i
$144$	−6.62659	−	10.0044i	−0.552216	−	0.833701i
$145$	9.12764	−	0.871584i	0.758009	−	0.0723811i
$146$	0.544741	−	0.187027i	0.0450831	−	0.0154785i
$147$	5.90120	+	21.0227i	0.486723	+	1.73392i
$148$	0.0375026	+	0.110119i	0.00308270	+	0.00905170i
$149$	−2.16762	+	7.38224i	−0.177579	+	0.604777i	0.821808	+	0.569764i	$0.192965\pi$
$149$	−2.16762	+	7.38224i	−0.177579	+	0.604777i	−0.999387	+	0.0350129i	$0.988853\pi$
$150$	−9.95886	−	2.06870i	−0.813137	−	0.168909i
$151$	3.58101	+	6.94618i	0.291418	+	0.565272i	0.988410	−	0.151806i	$-0.0485091\pi$
$151$	3.58101	+	6.94618i	0.291418	+	0.565272i	−0.696992	+	0.717079i	$0.745479\pi$
$152$	−8.44236	+	4.27323i	−0.684766	+	0.346605i
$153$	−8.56370	−	6.41166i	−0.692334	−	0.518352i
$154$	−3.19940	+	13.0470i	−0.257815	+	1.05135i
$155$	−3.06993	+	4.31111i	−0.246583	+	0.346277i
$156$	2.18933	−	7.01563i	0.175287	−	0.561700i
$157$	3.76585	+	1.50762i	0.300547	+	0.120321i	0.517035	−	0.855964i	$-0.327036\pi$
$157$	3.76585	+	1.50762i	0.300547	+	0.120321i	−0.216487	+	0.976285i	$0.569460\pi$
$158$	4.05771	−	0.377324i	0.322814	−	0.0300183i
$159$	11.8670	+	11.5887i	0.941118	+	0.919047i
$160$	−0.677246	−	5.16353i	−0.0535410	−	0.408213i
$161$	12.7149	−	5.80671i	1.00208	−	0.457633i
$162$	−3.03312	+	12.3612i	−0.238304	+	0.971191i
$163$	−19.9812	+	11.5361i	−1.56505	+	0.903581i	−0.568315	+	0.822811i	$0.692405\pi$
$163$	−19.9812	+	11.5361i	−1.56505	+	0.903581i	−0.996733	+	0.0807700i	$0.974262\pi$
$164$	4.39044	−	4.55912i	0.342836	−	0.356008i
$165$	3.40105	+	0.365774i	0.264771	+	0.0284754i
$166$	11.4171	+	6.62944i	0.886140	+	0.514544i
$167$	−1.21258	−	4.99832i	−0.0938322	−	0.386782i	0.905459	−	0.424434i	$-0.139527\pi$
$167$	−1.21258	−	4.99832i	−0.0938322	−	0.386782i	−0.999291	+	0.0376528i	$0.988012\pi$
$168$	−14.6626	−	15.9864i	−1.13124	−	1.23338i
$169$	−7.89018	+	3.15875i	−0.606937	+	0.242981i
$170$	−2.11718	−	4.13185i	−0.162380	−	0.316899i
$171$	9.40318	+	3.50797i	0.719079	+	0.268261i
$172$	−2.31284	−	8.02363i	−0.176352	−	0.611796i
$173$	−12.3934	+	4.28941i	−0.942255	+	0.326118i	−0.754650	−	0.656127i	$-0.772194\pi$
$173$	−12.3934	+	4.28941i	−0.942255	+	0.326118i	−0.187604	+	0.982245i	$0.560072\pi$
$174$	−9.39278	+	22.5160i	−0.712064	+	1.70693i
$175$	−18.3661	−	0.874883i	−1.38834	−	0.0661349i
$176$	−1.94031	−	8.35867i	−0.146256	−	0.630058i
$177$	−10.2538	+	19.3198i	−0.770720	+	1.45217i
$178$	7.63511	−	2.22134i	0.572276	−	0.166497i
$179$	−1.42746	+	9.92822i	−0.106694	+	0.742070i	0.864302	+	0.502973i	$0.167760\pi$
$179$	−1.42746	+	9.92822i	−0.106694	+	0.742070i	−0.970996	+	0.239097i	$0.923149\pi$
$180$	−3.53822	+	4.24168i	−0.263723	+	0.316156i
$181$	6.29770	−	4.95256i	0.468104	−	0.368121i	−0.356068	−	0.934460i	$-0.615883\pi$
$181$	6.29770	−	4.95256i	0.468104	−	0.368121i	0.824173	+	0.566339i	$0.191641\pi$
$182$	1.92326	−	13.1453i	0.142562	−	0.974398i
$183$	−19.0574	+	2.50826i	−1.40876	+	0.185416i
$184$	−5.57140	+	6.97729i	−0.410729	+	0.514372i
$185$	0.0436182	−	0.0310604i	0.00320687	−	0.00228360i
$186$	−6.27159	−	12.6081i	−0.459855	−	0.924469i
$187$	−4.13583	−	6.43547i	−0.302442	−	0.470608i
$188$	−0.0181484	+	0.345011i	−0.00132361	+	0.0251625i
$189$	−1.91682	+	22.9282i	−0.139428	+	1.66778i
$190$	2.99783	+	3.15967i	0.217486	+	0.229227i
$191$	−2.06206	−	1.62162i	−0.149205	−	0.117336i	0.540766	−	0.841173i	$-0.318134\pi$
$191$	−2.06206	−	1.62162i	−0.149205	−	0.117336i	−0.689971	+	0.723837i	$0.742377\pi$
$192$	12.9682	+	4.88121i	0.935898	+	0.352271i
$193$	1.33074	−	1.53576i	0.0957890	−	0.110546i	−0.705831	−	0.708380i	$-0.749426\pi$
$193$	1.33074	−	1.53576i	0.0957890	−	0.110546i	0.801620	+	0.597834i	$0.203972\pi$
$194$	0.663073	−	6.76684i	0.0476059	−	0.485831i
$195$	−3.38268	−	0.0403765i	−0.242239	−	0.00289142i
$196$	−19.7414	−	15.6837i	−1.41010	−	1.12027i
$197$	6.64729	−	12.8939i	0.473600	−	0.918655i	−0.524151	−	0.851625i	$-0.675617\pi$
$197$	6.64729	−	12.8939i	0.473600	−	0.918655i	0.997751	−	0.0670299i	$-0.0213523\pi$
$198$	−5.12062	+	7.52432i	−0.363906	+	0.534730i
$199$	−4.74106	−	1.15017i	−0.336085	−	0.0815333i	0.0641652	−	0.997939i	$-0.479562\pi$
$199$	−4.74106	−	1.15017i	−0.336085	−	0.0815333i	−0.400250	+	0.916406i	$0.631077\pi$
$200$	10.7196	−	4.79952i	0.757988	−	0.339377i
$201$	9.47655	−	10.5449i	0.668425	−	0.743780i
$202$	−20.2344	+	15.8316i	−1.42369	+	1.11391i
$203$	−10.3973	+	42.8584i	−0.729751	+	3.00807i
$204$	12.3512	+	0.208626i	0.864756	+	0.0146067i
$205$	−2.58959	−	1.33503i	−0.180865	−	0.0932423i
$206$	0.511411	+	2.13109i	0.0356317	+	0.148480i
$207$	9.44632	−	0.674936i	0.656564	−	0.0469113i
$208$	2.69599	+	8.04661i	0.186933	+	0.557932i
$209$	5.42376	+	4.69972i	0.375169	+	0.325086i
$210$	−5.11666	+	8.57450i	−0.353083	+	0.591696i
$211$	−6.46561	+	8.22170i	−0.445111	+	0.566005i	−0.955897	−	0.293703i	$-0.905112\pi$
$211$	−6.46561	+	8.22170i	−0.445111	+	0.566005i	0.510785	+	0.859708i	$0.329355\pi$
$212$	−18.9442	−	2.81963i	−1.30110	−	0.193653i
$213$	−2.40590	−	0.614160i	−0.164849	−	0.0420816i
$214$	19.6840	+	17.1418i	1.34557	+	1.17179i
$215$	−3.23352	+	2.07806i	−0.220524	+	0.141722i
$216$	−5.52176	−	13.6202i	−0.375708	−	0.926738i
$217$	−14.7657	−	20.7355i	−1.00236	−	1.40762i
$218$	9.97647	+	4.58600i	0.675692	+	0.310603i
$219$	0.699364	−	0.0920477i	0.0472587	−	0.00622000i
$220$	−3.43040	+	1.95795i	−0.231278	+	0.132005i
$221$	4.67666	+	5.94685i	0.314586	+	0.400029i
$222$	0.0182416	+	0.141301i	0.00122430	+	0.00948353i
$223$	24.8510	+	3.57303i	1.66415	+	0.239268i	0.909152	−	0.416464i	$-0.136731\pi$
$223$	24.8510	+	3.57303i	1.66415	+	0.239268i	0.754994	+	0.655732i	$0.227640\pi$
$224$	24.5349	+	5.04463i	1.63931	+	0.337059i
$225$	−11.4513	−	4.90469i	−0.763418	−	0.326979i
$226$	23.3021	+	4.55101i	1.55004	+	0.302729i
$227$	−1.11161	+	23.3356i	−0.0737802	+	1.54884i	0.593991	+	0.804471i	$0.297551\pi$
$227$	−1.11161	+	23.3356i	−0.0737802	+	1.54884i	−0.667772	+	0.744366i	$0.732752\pi$
$228$	−11.1730	+	3.07669i	−0.739947	+	0.203759i
$229$	−4.02184	−	11.6203i	−0.265770	−	0.767893i	−0.996373	−	0.0850904i	$-0.972882\pi$
$229$	−4.02184	−	11.6203i	−0.265770	−	0.767893i	0.730603	−	0.682803i	$-0.239239\pi$
$230$	3.81176	+	1.53696i	0.251340	+	0.101344i
$231$	−7.01280	+	14.8832i	−0.461409	+	0.979242i
$232$	−6.43789	−	27.4253i	−0.422668	−	1.80056i
$233$	−4.08281	−	10.1984i	−0.267474	−	0.668118i	0.732445	−	0.680826i	$-0.238379\pi$
$233$	−4.08281	−	10.1984i	−0.267474	−	0.668118i	−0.999919	+	0.0127081i	$0.995955\pi$
$234$	4.33385	−	7.88899i	0.283312	−	0.515719i
$235$	0.154547	−	0.0374928i	0.0100816	−	0.00244576i
$236$	−3.47040	−	25.0163i	−0.225904	−	1.62842i
$237$	4.96248	+	0.533701i	0.322348	+	0.0346676i
$238$	22.1109	−	3.12318i	1.43323	−	0.202446i
$239$	1.81227	+	3.13895i	0.117226	+	0.203041i	0.918667	−	0.395032i	$-0.129266\pi$
$239$	1.81227	+	3.13895i	0.117226	+	0.203041i	−0.801441	+	0.598073i	$0.795933\pi$
$240$	0.442566	−	6.36280i	0.0285675	−	0.410717i
$241$	8.26298	+	18.0934i	0.532265	+	1.16550i	0.964584	+	0.263778i	$0.0849685\pi$
$241$	8.26298	+	18.0934i	0.532265	+	1.16550i	−0.432318	+	0.901721i	$0.642304\pi$
$242$	7.38336	−	5.23016i	0.474621	−	0.336207i
$243$	−6.64647	+	14.1005i	−0.426371	+	0.904548i
$244$	16.1392	−	15.2368i	1.03321	−	0.975434i
$245$	−4.31342	+	10.7744i	−0.275574	+	0.688351i
$246$	6.37868	−	4.40509i	0.406690	−	0.280858i
$247$	−5.78144	−	4.11694i	−0.367864	−	0.261955i
$248$	14.3969	+	7.55806i	0.914205	+	0.479937i
$249$	12.0928	+	10.7338i	0.766349	+	0.680228i
$250$	−7.78097	−	9.02479i	−0.492112	−	0.570778i
$251$	13.6185	−	7.02080i	0.859589	−	0.443149i	0.0287006	−	0.999588i	$-0.490863\pi$
$251$	13.6185	−	7.02080i	0.859589	−	0.443149i	0.830888	+	0.556439i	$0.187833\pi$
$252$	−13.7134	−	22.7548i	−0.863863	−	1.43342i
$253$	6.49774	+	1.90791i	0.408510	+	0.119949i
$254$	−3.94544	+	11.3089i	−0.247559	+	0.709583i
$255$	−1.53673	−	5.47453i	−0.0962341	−	0.342828i
$256$	−15.4382	+	4.20265i	−0.964887	+	0.262666i
$257$	−2.53463	−	26.5438i	−0.158106	−	1.65576i	−0.631847	−	0.775093i	$-0.717703\pi$
$257$	−2.53463	−	26.5438i	−0.158106	−	1.65576i	0.473742	−	0.880664i	$-0.342903\pi$
$258$	−0.825313	−	10.1937i	−0.0513817	−	0.634629i
$259$	0.0725601	+	0.247117i	0.00450866	+	0.0153551i
$260$	3.19313	−	2.25006i	0.198030	−	0.139543i
$261$	−16.7495	+	24.7436i	−1.03677	+	1.53159i
$262$	10.0206	+	15.6776i	0.619076	+	0.968568i
$263$	3.10981	−	6.80953i	0.191759	−	0.419894i	−0.789193	−	0.614146i	$-0.789501\pi$
$263$	3.10981	−	6.80953i	0.191759	−	0.419894i	0.980952	+	0.194252i	$0.0622280\pi$
$264$	−0.296677	−	10.5052i	−0.0182592	−	0.646553i
$265$	1.25467	+	8.72645i	0.0770740	+	0.536062i
$266$	−19.0774	+	8.65533i	−1.16971	+	0.530692i
$267$	9.70505	−	0.809955i	0.593939	−	0.0495684i
$268$	−1.73707	+	16.2783i	−0.106108	+	0.994355i
$269$		−	9.70930i		−	0.591987i	−0.955190	−	0.295993i	$-0.904349\pi$
$269$		−	9.70930i		−	0.591987i	0.955190	−	0.295993i	$-0.0956506\pi$
$270$	−5.27852	+	4.23125i	−0.321241	+	0.257506i
$271$	23.3389	−	3.35563i	1.41774	−	0.203840i	0.609541	−	0.792754i	$-0.291354\pi$
$271$	23.3389	−	3.35563i	1.41774	−	0.203840i	0.808195	+	0.588915i	$0.200445\pi$
$272$	−11.7005	+	8.15838i	−0.709446	+	0.494674i
$273$	5.50490	−	15.3116i	0.333171	−	0.926699i
$274$	−2.64368	+	1.68975i	−0.159711	+	0.102082i
$275$	−6.44703	−	6.14723i	−0.388771	−	0.370692i
$276$	−8.38425	+	7.02061i	−0.504672	+	0.422591i
$277$	−9.14238	+	2.68444i	−0.549312	+	0.161293i	−0.544599	−	0.838696i	$-0.683318\pi$
$277$	−9.14238	+	2.68444i	−0.549312	+	0.161293i	−0.00471271	+	0.999989i	$0.501500\pi$
$278$	−24.5873	−	0.0609015i	−1.47465	−	0.00365263i
$279$	−4.46256	−	16.6592i	−0.267166	−	0.997363i
$280$	−1.01066	−	11.4854i	−0.0603984	−	0.686385i
$281$	4.89354	+	25.3901i	0.291924	+	1.51465i	0.770979	+	0.636861i	$0.219767\pi$
$281$	4.89354	+	25.3901i	0.291924	+	1.51465i	−0.479055	+	0.877785i	$0.659020\pi$
$282$	−0.105674	+	0.409727i	−0.00629279	+	0.0243989i
$283$	−0.256587	+	0.873855i	−0.0152525	+	0.0519453i	−0.966768	−	0.255657i	$-0.917708\pi$
$283$	−0.256587	+	0.873855i	−0.0152525	+	0.0519453i	0.951515	+	0.307602i	$0.0995265\pi$
$284$	2.66704	−	1.05242i	0.158260	−	0.0624498i
$285$	2.83023	+	4.52168i	0.167648	+	0.267841i
$286$	4.87474	−	4.20289i	0.288250	−	0.248522i
$287$	10.1418	−	9.67016i	0.598650	−	0.570812i
$288$	14.3797	+	9.01244i	0.847332	+	0.531063i
$289$	2.48481	−	3.48942i	0.146165	−	0.205260i
$290$	−11.2459	+	6.45574i	−0.660382	+	0.379094i
$291$	2.44128	−	7.96146i	0.143111	−	0.466709i
$292$	−0.592274	+	0.559157i	−0.0346602	+	0.0327222i
$293$	−8.62141	+	7.47049i	−0.503668	+	0.436431i	−0.869268	−	0.494341i	$-0.835409\pi$
$293$	−8.62141	+	7.47049i	−0.503668	+	0.436431i	0.365600	+	0.930772i	$0.380864\pi$
$294$	−19.8834	−	23.6263i	−1.15963	−	1.37791i
$295$	−10.5749	+	4.82937i	−0.615692	+	0.281177i
$296$	−0.112640	−	0.119905i	−0.00654709	−	0.00696935i
$297$	−7.97615	+	7.78687i	−0.462823	+	0.451840i
$298$	−1.52182	−	10.7739i	−0.0881567	−	0.624113i
$299$	−6.57631	−	1.26748i	−0.380318	−	0.0733003i
$300$	14.0344	−	3.15472i	0.810277	−	0.182138i
$301$	−4.35855	−	17.9662i	−0.251223	−	1.03555i
$302$	−8.67049	−	6.85337i	−0.498931	−	0.394367i
$303$	−28.1382	+	14.0837i	−1.61650	+	0.809088i
$304$	8.37578	−	10.4362i	0.480384	−	0.598557i
$305$	−8.84786	−	5.10831i	−0.506627	−	0.292501i
$306$	14.7752	+	3.25361i	0.844643	+	0.185996i
$307$	−2.14171	+	0.741252i	−0.122234	+	0.0423055i	−0.387500	−	0.921870i	$-0.626661\pi$
$307$	−2.14171	+	0.741252i	−0.122234	+	0.0423055i	0.265266	+	0.964175i	$0.414540\pi$
$308$	−3.50291	−	18.6721i	−0.199597	−	1.06394i
$309$	0.0957076	+	2.68244i	0.00544462	+	0.152599i
$310$	1.43468	−	7.34588i	0.0814845	−	0.417218i
$311$	18.7528	+	12.0517i	1.06337	+	0.683389i	0.950659	−	0.310238i	$-0.100409\pi$
$311$	18.7528	+	12.0517i	1.06337	+	0.683389i	0.112715	+	0.993627i	$0.464045\pi$
$312$	1.27964	+	10.3144i	0.0724456	+	0.583938i
$313$	0.418423	−	2.91019i	0.0236506	−	0.164494i	−0.974573	−	0.224070i	$-0.928066\pi$
$313$	0.418423	−	2.91019i	0.0236506	−	0.164494i	0.998224	+	0.0595758i	$0.0189748\pi$
$314$	−5.73080	+	0.258766i	−0.323408	+	0.0146030i
$315$	−8.22674	+	9.04842i	−0.463524	+	0.509821i
$316$	−5.00531	+	2.85685i	−0.281571	+	0.160710i
$317$	31.8911	−	1.51916i	1.79118	−	0.0853246i	0.874522	−	0.484986i	$-0.161175\pi$
$317$	31.8911	−	1.51916i	1.79118	−	0.0853246i	0.916663	+	0.399662i	$0.130872\pi$
$318$	−22.0544	−	7.99086i	−1.23675	−	0.448105i
$319$	−17.4044	+	12.3936i	−0.974459	+	0.693909i
$320$	3.88924	+	6.25422i	0.217415	+	0.349622i
$321$	19.4599	+	25.3626i	1.08615	+	1.41560i
$322$	−12.9823	+	14.9075i	−0.723473	+	0.830765i
$323$	3.90182	−	11.2736i	0.217103	−	0.627277i
$324$	−3.31639	−	17.6918i	−0.184244	−	0.982881i
$325$	6.92492	+	5.44581i	0.384125	+	0.302079i
$326$	18.9925	−	26.5320i	1.05190	−	1.46947i
$327$	10.8603	+	7.93065i	0.600578	+	0.438566i
$328$	−2.99041	+	8.43686i	−0.165118	+	0.465848i
$329$	−0.0727083	+	0.761436i	−0.00400854	+	0.0419793i
$330$	−4.59381	+	1.51616i	−0.252881	+	0.0834617i
$331$	14.1839	−	27.5129i	0.779618	−	1.51225i	−0.0774219	−	0.996998i	$-0.524669\pi$
$331$	14.1839	−	27.5129i	0.779618	−	1.51225i	0.857040	−	0.515250i	$-0.172301\pi$
$332$	−18.5773	−	1.86683i	−1.01956	−	0.102455i
$333$	−0.0124607	+	0.174049i	−0.000682843	+	0.00953782i
$334$	4.48214	+	5.72865i	0.245252	+	0.313458i
$335$	7.40798	−	1.38054i	0.404741	−	0.0754269i
$336$	28.2243	+	12.0210i	1.53976	+	0.655802i
$337$	2.00913	−	8.28174i	0.109444	−	0.451135i	−0.890549	−	0.454888i	$-0.849679\pi$
$337$	2.00913	−	8.28174i	0.109444	−	0.451135i	0.999993	+	0.00375270i	$0.00119452\pi$
$338$	8.31584	−	8.67826i	0.452322	−	0.472035i
$339$	26.8645	+	11.1288i	1.45908	+	0.604432i
$340$	5.14087	+	4.08421i	0.278803	+	0.221497i
$341$	1.17229	−	12.2768i	0.0634831	−	0.664825i
$342$	−14.1597	+	0.976461i	−0.765670	+	0.0528010i
$343$	−18.7619	−	16.2572i	−1.01305	−	0.877809i
$344$	7.66681	+	8.98197i	0.413367	+	0.484275i
$345$	4.20180	+	2.77175i	0.226217	+	0.149226i
$346$	13.4548	−	12.7656i	0.723333	−	0.686284i
$347$	9.89175	−	28.5803i	0.531017	−	1.53427i	−0.286333	−	0.958130i	$-0.592436\pi$
$347$	9.89175	−	28.5803i	0.531017	−	1.53427i	0.817350	−	0.576142i	$-0.195443\pi$
$348$	−1.05940	−	34.4857i	−0.0567898	−	1.84863i
$349$	−21.8312	+	14.0300i	−1.16859	+	0.751010i	−0.973255	−	0.229725i	$-0.926217\pi$
$349$	−21.8312	+	14.0300i	−1.16859	+	0.751010i	−0.195339	+	0.980736i	$0.562581\pi$
$350$	24.1642	−	9.60450i	1.29163	−	0.513382i
$351$	7.12040	−	8.41590i	0.380059	−	0.449207i
$352$	7.38280	+	9.63112i	0.393505	+	0.513340i
$353$	35.2671	−	1.67998i	1.87708	−	0.0894164i	0.922255	−	0.386583i	$-0.126345\pi$
$353$	35.2671	−	1.67998i	1.87708	−	0.0894164i	0.954826	+	0.297167i	$0.0960417\pi$
$354$	1.91694	−	30.8726i	0.101884	−	1.64086i
$355$	−0.815832	−	1.03741i	−0.0432999	−	0.0550602i
$356$	−8.53507	+	7.32197i	−0.452358	+	0.388064i
$357$	27.3005	+	1.62728i	1.44490	+	0.0861246i
$358$	−3.96265	−	13.6203i	−0.209433	−	0.719853i
$359$	−15.3118	−	9.84031i	−0.808127	−	0.519352i	0.0701313	−	0.997538i	$-0.477658\pi$
$359$	−15.3118	−	9.84031i	−0.808127	−	0.519352i	−0.878259	+	0.478186i	$0.841295\pi$
$360$	2.07835	−	7.53008i	0.109539	−	0.396870i
$361$	0.371532	−	7.79941i	0.0195543	−	0.410495i
$362$	−5.21681	+	10.0580i	−0.274190	+	0.528635i
$363$	10.1344	−	4.48284i	0.531920	−	0.235288i
$364$	5.20389	+	18.0532i	0.272758	+	0.946244i
$365$	0.324697	+	0.187464i	0.0169954	+	0.00981232i
$366$	23.0778	−	14.3655i	1.20629	−	0.750895i
$367$	7.57098	+	18.9114i	0.395202	+	0.987167i	0.983885	+	0.178803i	$0.0572225\pi$
$367$	7.57098	+	18.9114i	0.395202	+	0.987167i	−0.588683	+	0.808364i	$0.700353\pi$
$368$	3.09841	−	12.2412i	0.161516	−	0.638115i
$369$	8.72785	−	3.73674i	0.454354	−	0.194527i
$370$	−0.0380258	+	0.0654875i	−0.00197687	+	0.00340453i
$371$	−41.6376	−	8.02499i	−2.16172	−	0.416637i
$372$	15.4438	+	12.5730i	0.800725	+	0.651882i
$373$	9.71542	+	16.8276i	0.503045	+	0.871300i	0.999994	+	0.00351989i	$0.00112042\pi$
$373$	9.71542	+	16.8276i	0.503045	+	0.871300i	−0.496949	+	0.867780i	$0.665546\pi$
$374$	9.08662	+	5.87147i	0.469858	+	0.303606i
$375$	−7.14564	−	12.7250i	−0.368999	−	0.657116i
$376$	−0.178217	−	0.454932i	−0.00919082	−	0.0234613i
$377$	15.9693	−	13.8375i	0.822463	−	0.712668i
$378$	−10.9283	−	30.6484i	−0.562091	−	1.57639i
$379$	11.6391	−	29.0730i	0.597860	−	1.49338i	−0.252722	−	0.967539i	$-0.581326\pi$
$379$	11.6391	−	29.0730i	0.597860	−	1.49338i	0.850582	−	0.525843i	$-0.176250\pi$
$380$	−5.70699	−	2.31760i	−0.292763	−	0.118891i
$381$	−7.48572	+	12.6155i	−0.383505	+	0.646311i
$382$	3.60317	+	0.883574i	0.184354	+	0.0452076i
$383$	−12.7515	+	12.1586i	−0.651574	+	0.621274i	−0.941996	−	0.335624i	$-0.891053\pi$
$383$	−12.7515	+	12.1586i	−0.651574	+	0.621274i	0.290422	+	0.956899i	$0.406204\pi$
$384$	−19.5533	+	1.29093i	−0.997828	+	0.0658777i
$385$	−7.77270	+	4.00710i	−0.396133	+	0.204221i
$386$	−0.816478	+	2.75540i	−0.0415576	+	0.140246i
$387$	1.48790	−	12.4368i	0.0756343	−	0.632198i
$388$	3.09990	+	9.10221i	0.157374	+	0.462095i
$389$	7.01550	+	36.3999i	0.355700	+	1.84555i	0.513517	+	0.858079i	$0.328342\pi$
$389$	7.01550	+	36.3999i	0.355700	+	1.84555i	−0.157817	+	0.987468i	$0.550446\pi$
$390$	4.38003	−	1.92449i	0.221791	−	0.0974504i
$391$	−1.07006	−	11.2061i	−0.0541151	−	0.566719i
$392$	34.5882	+	8.66366i	1.74697	+	0.437581i
$393$	8.21641	+	21.2554i	0.414463	+	1.07219i
$394$	−1.02692	+	20.4896i	−0.0517352	+	1.03225i
$395$	1.91995	+	1.83067i	0.0966032	+	0.0921109i
$396$	2.19822	−	12.6823i	0.110465	−	0.637308i
$397$	−4.84159	+	10.6016i	−0.242992	+	0.532079i	−0.991354	−	0.131212i	$-0.958113\pi$
$397$	−4.84159	+	10.6016i	−0.242992	+	0.532079i	0.748362	+	0.663290i	$0.230841\pi$
$398$	6.77789	−	1.28893i	0.339745	−	0.0646080i
$399$	−25.0044	+	5.75090i	−1.25179	+	0.287905i
$400$	−11.0010	+	12.4445i	−0.550051	+	0.622227i
$401$			10.9560i			0.547117i	0.961855	+	0.273558i	$0.0882007\pi$
$401$			10.9560i			0.547117i	−0.961855	+	0.273558i	$0.911799\pi$
$402$	−6.04317	+	19.1175i	−0.301406	+	0.953496i
$403$			12.1966i			0.607554i
$404$	16.8089	−	32.2119i	0.836273	−	1.60260i
$405$	−7.36498	+	3.79558i	−0.365969	+	0.188604i
$406$	−11.6517	−	61.2710i	−0.578264	−	3.04083i
$407$	−0.0518341	+	0.113501i	−0.00256932	+	0.00562603i
$408$	−16.0286	+	6.94808i	−0.793532	+	0.343981i
$409$	18.0632	+	17.2232i	0.893168	+	0.851634i	0.989621	−	0.143704i	$-0.0459012\pi$
$409$	18.0632	+	17.2232i	0.893168	+	0.851634i	−0.0964528	+	0.995338i	$0.530750\pi$
$410$	4.11510	+	0.206243i	0.203230	+	0.0101856i
$411$	−3.58425	+	1.38551i	−0.176798	+	0.0683423i
$412$	−1.90382	−	2.44574i	−0.0937945	−	0.120493i
$413$	−5.31512	−	55.6625i	−0.261540	−	2.73897i
$414$	−11.7712	+	6.38868i	−0.578524	+	0.313987i
$415$	1.62648	+	8.43897i	0.0798407	+	0.414253i
$416$	−8.17368	−	8.78769i	−0.400748	−	0.430852i
$417$	−29.4990	−	6.05149i	−1.44457	−	0.296343i
$418$	−9.73110	−	2.88351i	−0.475964	−	0.141037i
$419$	3.61464	−	1.86348i	0.176587	−	0.0910369i	−0.367667	−	0.929958i	$-0.619843\pi$
$419$	3.61464	−	1.86348i	0.176587	−	0.0910369i	0.544254	+	0.838921i	$0.316813\pi$
$420$	1.57951	−	14.0324i	0.0770721	−	0.684713i
$421$	−14.5607	+	13.8836i	−0.709646	+	0.676647i	−0.956277	−	0.292463i	$-0.905525\pi$
$421$	−14.5607	+	13.8836i	−0.709646	+	0.676647i	0.246630	+	0.969110i	$0.420677\pi$
$422$	3.52292	−	14.3663i	0.171493	−	0.699339i
$423$	−0.226472	+	0.466128i	−0.0110115	+	0.0226639i
$424$	26.0451	−	7.43777i	1.26486	−	0.361210i
$425$	−5.50346	+	13.7470i	−0.266957	+	0.666826i
$426$	3.45732	−	0.614804i	0.167508	−	0.0297873i
$427$	37.1373	−	32.1797i	1.79720	−	1.55728i
$428$	−35.3662	−	10.5750i	−1.70949	−	0.511164i
$429$	6.87341	−	3.85972i	0.331851	−	0.186349i
$430$	2.95014	−	4.56560i	0.142268	−	0.220173i
$431$	−3.52133	−	6.09913i	−0.169617	−	0.293785i	0.768668	−	0.639647i	$-0.220920\pi$
$431$	−3.52133	−	6.09913i	−0.169617	−	0.293785i	−0.938285	+	0.345863i	$0.887586\pi$
$432$	15.0695	+	14.3146i	0.725034	+	0.688714i
$433$	−22.0536	−	4.25048i	−1.05983	−	0.204265i	−0.370587	−	0.928798i	$-0.620843\pi$
$433$	−22.0536	−	4.25048i	−1.05983	−	0.204265i	−0.689240	+	0.724533i	$0.742055\pi$
$434$	31.1319	+	18.0770i	1.49438	+	0.867722i
$435$	−15.0689	+	5.01481i	−0.722499	+	0.240442i
$436$	−15.5279	−	0.0769243i	−0.743653	−	0.00368401i
$437$	3.92504	+	9.80429i	0.187760	+	0.469003i
$438$	−0.846904	+	0.527182i	−0.0404666	+	0.0251897i
$439$	20.6935	+	11.9474i	0.987648	+	0.570219i	0.904570	−	0.426324i	$-0.140192\pi$
$439$	20.6935	+	11.9474i	0.987648	+	0.570219i	0.0830775	+	0.996543i	$0.473525\pi$
$440$	3.27387	−	4.52595i	0.156076	−	0.215766i
$441$	−18.1227	−	33.1949i	−0.862985	−	1.58071i
$442$	−9.49763	−	4.92619i	−0.451756	−	0.234315i
$443$	−1.04724	+	21.9843i	−0.0497560	+	1.04451i	0.826584	+	0.562814i	$0.190281\pi$
$443$	−1.04724	+	21.9843i	−0.0497560	+	1.04451i	−0.876340	+	0.481694i	$0.840022\pi$
$444$	−0.106055	−	0.171319i	−0.00503314	−	0.00813042i
$445$	4.35459	+	2.79852i	0.206427	+	0.132663i
$446$	−34.0924	+	9.91879i	−1.61432	+	0.469668i
$447$	0.792916	−	13.3026i	0.0375036	−	0.629192i
$448$	−34.5452	+	7.83888i	−1.63211	+	0.370352i
$449$	−7.53630	−	9.58318i	−0.355660	−	0.452258i	0.574995	−	0.818157i	$-0.305004\pi$
$449$	−7.53630	−	9.58318i	−0.355660	−	0.452258i	−0.930655	+	0.365899i	$0.880762\pi$
$450$	17.6135	−	0.374371i	0.830308	−	0.0176480i
$451$	6.78134	−	0.323035i	0.319321	−	0.0152111i
$452$	−32.6692	+	7.75429i	−1.53663	+	0.364731i
$453$	−8.74137	−	10.3348i	−0.410705	−	0.485570i
$454$	−12.2033	−	30.7026i	−0.572730	−	1.44094i
$455$	7.27543	−	4.67564i	0.341078	−	0.219197i
$456$	12.5916	−	10.4907i	0.589654	−	0.491272i
$457$	1.53046	−	4.42196i	0.0715917	−	0.206851i	−0.903528	−	0.428529i	$-0.859032\pi$
$457$	1.53046	−	4.42196i	0.0715917	−	0.206851i	0.975120	+	0.221678i	$0.0711533\pi$
$458$	11.9693	+	12.6155i	0.559289	+	0.589482i
$459$	16.9446	+	7.49810i	0.790904	+	0.349981i
$460$	−5.80708	+	0.247799i	−0.270756	+	0.0115537i
$461$	−5.59855	−	4.85117i	−0.260750	−	0.225941i	0.514668	−	0.857390i	$-0.327915\pi$
$461$	−5.59855	−	4.85117i	−0.260750	−	0.225941i	−0.775418	+	0.631448i	$0.782461\pi$
$462$	0.335335	−	23.2651i	0.0156012	−	1.08239i
$463$	−2.23759	+	23.4331i	−0.103990	+	1.08903i	0.781353	+	0.624089i	$0.214530\pi$
$463$	−2.23759	+	23.4331i	−0.103990	+	1.08903i	−0.885343	+	0.464939i	$0.846076\pi$
$464$	24.3156	+	31.5584i	1.12883	+	1.46506i
$465$	3.50829	−	8.46891i	0.162693	−	0.392736i
$466$	11.2170	+	10.7486i	0.519617	+	0.497917i
$467$	−4.21534	+	17.3759i	−0.195063	+	0.804059i	0.787223	+	0.616669i	$0.211518\pi$
$467$	−4.21534	+	17.3759i	−0.195063	+	0.804059i	−0.982285	+	0.187391i	$0.939997\pi$
$468$	−0.971897	+	12.6922i	−0.0449259	+	0.586697i
$469$	−5.37879	+	35.8428i	−0.248369	+	1.65507i
$470$	−0.177129	+	0.138587i	−0.00817036	+	0.00639255i
$471$	−6.94198	−	1.08283i	−0.319869	−	0.0498940i
$472$	19.0864	+	30.1899i	0.878522	+	1.38960i
$473$	4.10419	−	7.96101i	0.188711	−	0.366048i
$474$	−6.70284	+	2.21223i	−0.307872	+	0.101611i
$475$	1.32049	−	13.8288i	0.0605883	−	0.634510i
$476$	−26.6510	+	16.9416i	−1.22154	+	0.776515i
$477$	−24.5304	−	14.9545i	−1.12317	−	0.684718i
$478$	−4.16804	−	2.98363i	−0.190642	−	0.136468i
$479$	3.72998	+	2.93329i	0.170427	+	0.134025i	0.699729	−	0.714408i	$-0.253304\pi$
$479$	3.72998	+	2.93329i	0.170427	+	0.134025i	−0.529302	+	0.848433i	$0.677546\pi$
$480$	3.14780	+	8.45302i	0.143677	+	0.385826i
$481$	0.0403602	−	0.116613i	0.00184027	−	0.00531710i
$482$	−21.2135	−	18.4738i	−0.966250	−	0.841460i
$483$	−19.2082	+	14.7379i	−0.874004	+	0.670597i
$484$	−6.45281	+	11.0498i	−0.293310	+	0.502264i
$485$	3.60540	−	2.56739i	0.163713	−	0.116579i
$486$	0.320870	−	22.0431i	0.0145550	−	0.999894i
$487$	−0.765107	+	0.0364465i	−0.0346703	+	0.00165155i	−0.0649099	−	0.997891i	$-0.520676\pi$
$487$	−0.765107	+	0.0364465i	−0.0346703	+	0.00165155i	0.0302396	+	0.999543i	$0.490373\pi$
$488$	−11.8823	+	29.0530i	−0.537887	+	1.31517i
$489$	29.2492	−	27.2300i	1.32270	−	1.23139i
$490$	−0.740351	−	16.3963i	−0.0334457	−	0.740709i
$491$	−1.25394	+	8.72134i	−0.0565895	+	0.393588i	0.941766	+	0.336268i	$0.109165\pi$
$491$	−1.25394	+	8.72134i	−0.0565895	+	0.393588i	−0.998356	+	0.0573205i	$0.981744\pi$
$492$	−5.64100	+	9.40021i	−0.254316	+	0.423794i
$493$	29.8786	+	19.2018i	1.34566	+	0.864806i
$494$	9.85123	+	1.92399i	0.443228	+	0.0865643i
$495$	−5.88291	+	0.702962i	−0.264417	+	0.0315958i
$496$	−22.9574	−	1.32169i	−1.03082	−	0.0593454i
$497$	5.99871	−	2.07617i	0.269079	−	0.0931291i
$498$	−21.8456	−	6.75792i	−0.978925	−	0.302830i
$499$	−16.2697	−	9.39329i	−0.728330	−	0.420501i	0.0894811	−	0.995989i	$-0.471479\pi$
$499$	−16.2697	−	9.39329i	−0.728330	−	0.420501i	−0.817811	+	0.575487i	$0.804812\pi$
$500$	15.2940	+	7.07631i	0.683969	+	0.316462i
$501$	3.98729	+	7.96631i	0.178139	+	0.355909i
$502$	−13.4365	+	16.9991i	−0.599700	+	0.758706i
$503$	7.58770	+	31.2769i	0.338319	+	1.39457i	0.846073	+	0.533067i	$0.178961\pi$
$503$	7.58770	+	31.2769i	0.338319	+	1.39457i	−0.507754	+	0.861502i	$0.669524\pi$
$504$	30.9566	+	21.2924i	1.37891	+	0.948437i
$505$	−16.4224	−	3.16516i	−0.730787	−	0.140848i
$506$	−9.48300	+	1.33948i	−0.421571	+	0.0595473i
$507$	12.0922	−	8.39510i	0.537032	−	0.372839i
$508$	−1.52656	−	16.8696i	−0.0677302	−	0.748469i
$509$	−12.0448	+	5.50065i	−0.533874	+	0.243812i	−0.664063	−	0.747677i	$-0.731169\pi$
$509$	−12.0448	+	5.50065i	−0.533874	+	0.243812i	0.130188	+	0.991489i	$0.458442\pi$
$510$	5.17786	+	6.15254i	0.229279	+	0.272439i
$511$	−1.36286	+	1.18092i	−0.0602893	+	0.0522410i
$512$	17.4267	−	14.4329i	0.770159	−	0.637852i
$513$	−17.2343	−	2.27081i	−0.760912	−	0.100259i
$514$	18.7737	+	32.7039i	0.828074	+	1.44251i
$515$	−0.827546	+	1.16213i	−0.0364660	+	0.0512094i
$516$	7.01902	+	12.6458i	0.308995	+	0.556701i
$517$	−0.268198	+	0.255727i	−0.0117953	+	0.0112468i
$518$	−0.237837	−	0.275857i	−0.0104500	−	0.0121204i
$519$	19.2546	−	12.0519i	0.845183	−	0.529020i
$520$	−2.79762	+	4.76352i	−0.122684	+	0.208894i
$521$	−5.71376	+	19.4593i	−0.250324	+	0.852526i	0.734446	+	0.678667i	$0.237442\pi$
$521$	−5.71376	+	19.4593i	−0.250324	+	0.852526i	−0.984771	+	0.173859i	$0.944376\pi$
$522$	7.11351	−	41.6531i	0.311350	−	1.82311i
$523$	−1.39517	−	7.23881i	−0.0610063	−	0.316531i	0.938587	−	0.345042i	$-0.112135\pi$
$523$	−1.39517	−	7.23881i	−0.0610063	−	0.316531i	−0.999593	+	0.0285114i	$0.990923\pi$
$524$	−22.0656	−	14.3357i	−0.963941	−	0.626257i
$525$	31.3412	−	5.65342i	1.36784	−	0.246735i
$526$	−0.0262230	+	10.5868i	−0.00114338	+	0.461607i
$527$	−19.6700	+	5.77562i	−0.856837	+	0.251590i
$528$	6.52027	+	13.3560i	0.283758	+	0.581245i
$529$	−9.43360	−	8.99492i	−0.410156	−	0.391083i
$530$	−6.71469	−	10.5054i	−0.291668	−	0.456325i
$531$	9.80767	−	36.5923i	0.425617	−	1.58797i
$532$	19.5119	−	22.2938i	0.845947	−	0.966559i
$533$	−6.64579	+	0.955520i	−0.287861	+	0.0413882i
$534$	−12.0255	+	6.71375i	−0.520396	+	0.290532i
$535$			16.9914i			0.734604i
$536$	−7.27425	−	21.9792i	−0.314200	−	0.949357i
$537$	−1.44488	−	17.3128i	−0.0623510	−	0.747103i
$538$	5.67312	+	12.5043i	0.244586	+	0.539097i
$539$	−3.84876	−	26.7687i	−0.165778	−	1.15301i
$540$	4.32571	−	8.53350i	0.186149	−	0.367224i
$541$	10.6643	−	23.3516i	0.458495	−	1.00397i	−0.529332	−	0.848414i	$-0.677558\pi$
$541$	10.6643	−	23.3516i	0.458495	−	1.00397i	0.987828	−	0.155551i	$-0.0497151\pi$
$542$	−28.0967	+	17.9584i	−1.20685	+	0.771381i
$543$	−8.70767	+	10.8048i	−0.373682	+	0.463677i
$544$	10.3017	−	17.3435i	0.441682	−	0.743594i
$545$	2.01373	+	6.85815i	0.0862589	+	0.293771i
$546$	1.85696	+	22.9358i	0.0794704	+	0.981560i
$547$	3.32909	+	34.8638i	0.142342	+	1.49067i	0.731051	+	0.682323i	$0.239030\pi$
$547$	3.32909	+	34.8638i	0.142342	+	1.49067i	−0.588709	+	0.808345i	$0.700364\pi$
$548$	2.41739	−	3.72087i	0.103266	−	0.158948i
$549$	31.1947	−	11.6325i	1.33136	−	0.496462i
$550$	11.8947	+	4.14982i	0.507193	+	0.176949i
$551$	−31.9701	−	9.38727i	−1.36197	−	0.399911i
$552$	6.69565	−	13.9405i	0.284986	−	0.593347i
$553$	−11.3412	+	5.84677i	−0.482275	+	0.248630i
$554$	10.2056	−	8.79907i	0.433596	−	0.373837i
$555$	−0.0615682	+	0.0693631i	−0.00261342	+	0.00294430i
$556$	31.7007	−	14.2879i	1.34441	−	0.605941i
$557$	17.5298	+	12.4829i	0.742761	+	0.528918i	0.887644	−	0.460531i	$-0.152341\pi$
$557$	17.5298	+	12.4829i	0.742761	+	0.528918i	−0.144882	+	0.989449i	$0.546280\pi$
$558$	15.4811	+	18.8474i	0.655368	+	0.797874i
$559$	−3.29213	+	8.22335i	−0.139242	+	0.347810i
$560$	8.01249	+	14.2011i	0.338590	+	0.600108i
$561$	9.47963	+	9.25731i	0.400230	+	0.390844i
$562$	−21.1376	−	29.8397i	−0.891635	−	1.25871i
$563$	−3.65975	−	8.01374i	−0.154240	−	0.337739i	0.816700	−	0.577063i	$-0.195801\pi$
$563$	−3.65975	−	8.01374i	−0.154240	−	0.337739i	−0.970940	+	0.239324i	$0.923074\pi$
$564$	−0.103309	−	0.589418i	−0.00435008	−	0.0248190i
$565$	7.72779	+	13.3849i	0.325111	+	0.563108i
$566$	−0.180142	−	1.27533i	−0.00757192	−	0.0536061i
$567$	−5.66581	−	39.4466i	−0.237942	−	1.65660i
$568$	−2.81986	+	2.91372i	−0.118319	+	0.122257i
$569$	−8.97741	+	2.17790i	−0.376352	+	0.0913021i	−0.419473	−	0.907768i	$-0.637785\pi$
$569$	−8.97741	+	2.17790i	−0.376352	+	0.0913021i	0.0431207	+	0.999070i	$0.486270\pi$
$570$	−6.28696	−	4.16962i	−0.263332	−	0.174646i
$571$	−11.4881	−	28.6960i	−0.480763	−	1.20089i	−0.948431	−	0.316985i	$-0.897330\pi$
$571$	−11.4881	−	28.6960i	−0.480763	−	1.20089i	0.467667	−	0.883905i	$-0.345095\pi$
$572$	−3.82227	+	8.26106i	−0.159817	+	0.345412i
$573$	4.11028	+	1.93672i	0.171709	+	0.0809076i
$574$	−7.41099	+	18.3797i	−0.309329	+	0.767153i
$575$	−4.28738	−	12.3876i	−0.178796	−	0.516598i
$576$	−23.7851	−	3.20479i	−0.991044	−	0.133533i
$577$	1.39929	−	29.3748i	0.0582534	−	1.22289i	−0.760729	−	0.649070i	$-0.775158\pi$
$577$	1.39929	−	29.3748i	0.0582534	−	1.22289i	0.818982	−	0.573819i	$-0.194539\pi$
$578$	−1.16124	+	5.94577i	−0.0483010	+	0.247312i
$579$	−1.65005	+	3.10897i	−0.0685736	+	0.129204i
$580$	10.7111	−	14.8851i	0.444756	−	0.618069i
$581$	−40.9158	−	5.88281i	−1.69747	−	0.244060i
$582$	1.50782	+	11.6797i	0.0625011	+	0.484140i
$583$	−12.6993	−	16.1484i	−0.525950	−	0.668800i
$584$	0.436055	−	1.06618i	0.0180441	−	0.0441189i
$585$	5.72557	−	1.24509i	0.236723	−	0.0514783i
$586$	6.73822	−	14.6585i	0.278353	−	0.605535i
$587$	6.76114	+	9.49470i	0.279062	+	0.391888i	0.930189	−	0.367081i	$-0.119643\pi$
$587$	6.76114	+	9.49470i	0.279062	+	0.391888i	−0.651127	+	0.758969i	$0.725703\pi$
$588$	39.4120	+	18.8097i	1.62532	+	0.775697i
$589$	16.1792	−	10.3978i	0.666653	−	0.428432i
$590$	10.7972	−	12.3984i	0.444513	−	0.510436i
$591$	−6.21471	+	24.3454i	−0.255639	+	1.00144i
$592$	0.215126	+	0.0886064i	0.00884162	+	0.00364170i
$593$	−8.19663	+	10.4229i	−0.336595	+	0.428016i	−0.924657	−	0.380800i	$-0.875649\pi$
$593$	−8.19663	+	10.4229i	−0.336595	+	0.428016i	0.588062	+	0.808816i	$0.299891\pi$
$594$	5.72235	−	14.6889i	0.234791	−	0.602692i
$595$	10.9859	+	9.51931i	0.450377	+	0.390254i
$596$	8.25504	+	12.9861i	0.338140	+	0.531931i
$597$	8.44934	+	0.100854i	0.345809	+	0.00412766i
$598$	9.20999	−	2.21018i	0.376624	−	0.0903809i
$599$	26.6777	+	13.7533i	1.09002	+	0.561944i	0.906985	−	0.421163i	$-0.138378\pi$
$599$	26.6777	+	13.7533i	1.09002	+	0.561944i	0.183034	+	0.983107i	$0.441408\pi$
$600$	−16.2311	+	12.2631i	−0.662633	+	0.500640i
$601$	−1.23904	+	5.10741i	−0.0505417	+	0.208336i	−0.991483	−	0.130233i	$-0.958428\pi$
$601$	−1.23904	+	5.10741i	−0.0505417	+	0.208336i	0.940942	+	0.338568i	$0.109943\pi$
$602$	16.1108	+	20.5913i	0.656628	+	0.839240i
$603$	−11.9024	+	21.4786i	−0.484704	+	0.874678i
$604$	15.1708	+	3.76008i	0.617292	+	0.152995i
$605$	5.72402	+	1.38863i	0.232715	+	0.0564560i
$606$	28.0091	−	34.5790i	1.13779	−	1.40468i
$607$	15.5369	−	30.1373i	0.630621	−	1.22323i	−0.329633	−	0.944109i	$-0.606925\pi$
$607$	15.5369	−	30.1373i	0.630621	−	1.22323i	0.960255	−	0.279126i	$-0.0900446\pi$
$608$	−4.68903	+	18.3344i	−0.190165	+	0.743556i
$609$	0.911700	−	76.3808i	0.0369440	−	3.09510i
$610$	14.3796	+	1.40904i	0.582214	+	0.0570503i
$611$	0.239998	−	0.276973i	0.00970928	−	0.0112051i
$612$	−20.9296	+	4.44291i	−0.846027	+	0.179594i
$613$	−2.04880	−	1.61119i	−0.0827503	−	0.0650755i	0.575927	−	0.817501i	$-0.304641\pi$
$613$	−2.04880	−	1.61119i	−0.0827503	−	0.0650755i	−0.658677	+	0.752426i	$0.728884\pi$
$614$	2.32512	−	2.20603i	0.0938341	−	0.0890279i
$615$	4.88948	+	1.24815i	0.197163	+	0.0503303i
$616$	15.4213	+	22.0004i	0.621344	+	0.886423i
$617$	25.6606	+	39.9286i	1.03306	+	1.60747i	0.764965	+	0.644072i	$0.222756\pi$
$617$	25.6606	+	39.9286i	1.03306	+	1.60747i	0.268090	+	0.963394i	$0.413607\pi$
$618$	−1.69060	−	3.39870i	−0.0680059	−	0.136716i
$619$	15.9680	−	11.3708i	0.641809	−	0.457030i	−0.212244	−	0.977217i	$-0.568077\pi$
$619$	15.9680	−	11.3708i	0.641809	−	0.457030i	0.854053	+	0.520187i	$0.174138\pi$
$620$	2.44450	+	10.2988i	0.0981736	+	0.413609i
$621$	−15.6832	+	4.80660i	−0.629344	+	0.192882i
$622$	−31.1929	−	4.56375i	−1.25072	−	0.182990i
$623$	−19.5703	+	15.3902i	−0.784067	+	0.616597i
$624$	−7.67469	−	12.5359i	−0.307233	−	0.501836i
$625$	−1.85087	+	12.8731i	−0.0740347	+	0.514923i
$626$	1.16155	+	3.99242i	0.0464247	+	0.159569i
$627$	−10.9798	−	5.82738i	−0.438489	−	0.232723i
$628$	7.22930	−	3.68175i	0.288481	−	0.146918i
$629$	0.207180	+	0.00986920i	0.00826081	+	0.000393511i
$630$	5.30796	−	16.4600i	0.211474	−	0.655783i
$631$	14.0934	−	4.87777i	0.561049	−	0.194181i	−0.0318006	−	0.999494i	$-0.510124\pi$
$631$	14.0934	−	4.87777i	0.561049	−	0.194181i	0.592849	+	0.805313i	$0.298003\pi$
$632$	4.77691	−	6.60382i	0.190015	−	0.262686i
$633$	7.72194	−	16.3882i	0.306920	−	0.651372i
$634$	−40.1838	+	20.5904i	−1.59590	+	0.817749i
$635$	−7.23840	+	2.89782i	−0.287247	+	0.114996i
$636$	33.0722	−	2.59520i	1.31140	−	0.102906i
$637$	6.30551	+	25.9917i	0.249834	+	1.02983i
$638$	15.1730	−	26.1306i	0.600703	−	1.03452i
$639$	4.29954	+	0.102655i	0.170087	+	0.00406099i
$640$	−8.66314	−	5.78212i	−0.342441	−	0.228558i
$641$	−14.9701	+	8.64296i	−0.591281	+	0.341377i	−0.765604	−	0.643312i	$-0.777560\pi$
$641$	−14.9701	+	8.64296i	−0.591281	+	0.341377i	0.174323	+	0.984689i	$0.444226\pi$
$642$	−39.8811	−	21.2932i	−1.57398	−	0.840375i
$643$	−38.6678	+	17.6590i	−1.52491	+	0.696402i	−0.989006	−	0.147878i	$-0.952756\pi$
$643$	−38.6678	+	17.6590i	−1.52491	+	0.696402i	−0.535902	+	0.844280i	$0.680028\pi$
$644$	8.00895	−	26.7844i	0.315597	−	1.05545i
$645$	4.65136	−	4.76306i	0.183147	−	0.187545i
$646$	1.56210	+	16.7986i	0.0614599	+	0.660934i
$647$	29.8706	+	11.9584i	1.17433	+	0.470132i	0.875050	−	0.484032i	$-0.160828\pi$
$647$	29.8706	+	11.9584i	1.17433	+	0.470132i	0.299283	+	0.954164i	$0.403252\pi$
$648$	14.6084	+	20.8470i	0.573871	+	0.818946i
$649$	15.7137	−	22.0667i	0.616815	−	0.866195i
$650$	−12.1003	−	2.96726i	−0.474614	−	0.116386i
$651$	32.9743	+	29.2687i	1.29236	+	1.14713i
$652$	−8.95728	+	45.2669i	−0.350794	+	1.77279i
$653$	4.10495	+	7.96248i	0.160639	+	0.311596i	0.955394	−	0.295334i	$-0.0954310\pi$
$653$	4.10495	+	7.96248i	0.160639	+	0.311596i	−0.794755	+	0.606930i	$0.792401\pi$
$654$	−18.6205	−	3.86794i	−0.728119	−	0.151249i
$655$	−3.41242	+	11.6216i	−0.133334	+	0.454095i
$656$	−1.07839	−	12.6128i	−0.0421040	−	0.492448i
$657$	−1.14478	+	0.426887i	−0.0446621	+	0.0166545i
$658$	−0.351266	−	1.02311i	−0.0136938	−	0.0398850i
$659$	−15.1677	+	1.44834i	−0.590848	+	0.0564192i	−0.386198	−	0.922416i	$-0.626212\pi$
$659$	−15.1677	+	1.44834i	−0.590848	+	0.0564192i	−0.204650	+	0.978835i	$0.565606\pi$
$660$	5.03033	−	4.63676i	0.195805	−	0.180486i
$661$	−13.1905	+	3.87309i	−0.513052	+	0.150646i	−0.528003	−	0.849243i	$-0.677059\pi$
$661$	−13.1905	+	3.87309i	−0.513052	+	0.150646i	0.0149509	+	0.999888i	$0.495241\pi$
$662$	−2.19122	+	43.7206i	−0.0851642	+	1.69925i
$663$	−10.2028	−	8.22257i	−0.396245	−	0.319338i
$664$	25.0158	−	8.45043i	0.970801	−	0.327940i
$665$	−12.4048	−	5.66510i	−0.481039	−	0.219683i
$666$	−0.0856486	−	0.231432i	−0.00331881	−	0.00896781i
$667$	−31.1213	+	4.47456i	−1.20502	+	0.173256i
$668$	−9.11963	−	4.75883i	−0.352849	−	0.184125i
$669$	−43.3352	+	3.61662i	−1.67543	+	0.139827i
$670$	−8.73383	+	6.10641i	−0.337417	+	0.235911i
$671$	23.8070			0.919061
$672$	−43.3729	+	1.00988i	−1.67315	+	0.0389570i
$673$	1.91728	+	13.3350i	0.0739057	+	0.514026i	0.992825	+	0.119579i	$0.0381545\pi$
$673$	1.91728	+	13.3350i	0.0739057	+	0.514026i	−0.918919	+	0.394446i	$0.870936\pi$
$674$	2.25151	+	11.8397i	0.0867250	+	0.456048i
$675$	21.2337	+	3.83332i	0.817284	+	0.147545i
$676$	−5.63900	+	16.0354i	−0.216884	+	0.616744i
$677$	28.2281	−	29.6048i	1.08490	−	1.13781i	0.0950770	−	0.995470i	$-0.469690\pi$
$677$	28.2281	−	29.6048i	1.08490	−	1.13781i	0.989818	−	0.142336i	$-0.0454613\pi$
$678$	−41.1004	+	1.36451i	−1.57845	+	0.0524037i
$679$	5.99769	+	20.4263i	0.230170	+	0.783888i
$680$	−9.00714	−	2.25611i	−0.345408	−	0.0865178i
$681$	−7.18314	−	39.8216i	−0.275258	−	1.52597i
$682$	5.66354	+	16.4958i	0.216868	+	0.631657i
$683$	15.4453	−	2.97684i	0.590998	−	0.113905i	0.115020	−	0.993363i	$-0.463307\pi$
$683$	15.4453	−	2.97684i	0.590998	−	0.113905i	0.475977	+	0.879458i	$0.342095\pi$
$684$	17.6653	−	9.53104i	0.675449	−	0.364429i
$685$	−1.95973	−	0.575427i	−0.0748773	−	0.0219859i
$686$	33.6618	+	9.97463i	1.28521	+	0.380833i
$687$	11.3001	+	18.0535i	0.431126	+	0.688784i
$688$	−15.1220	−	7.08787i	−0.576519	−	0.270222i
$689$	14.0204	+	14.7041i	0.534133	+	0.560183i
$690$	−7.03087	−	1.11454i	−0.267661	−	0.0424297i
$691$	−27.7361	−	19.7508i	−1.05513	−	0.751356i	−0.0856019	−	0.996329i	$-0.527281\pi$
$691$	−27.7361	−	19.7508i	−1.05513	−	0.751356i	−0.969530	+	0.244974i	$0.921221\pi$
$692$	−9.86901	+	24.3020i	−0.375164	+	0.923823i
$693$	6.05942	−	27.8451i	0.230178	−	1.05775i
$694$	3.96017	+	42.5873i	0.150326	+	1.61659i
$695$	−10.4815	−	12.0963i	−0.397585	−	0.458837i
$696$	21.5143	+	43.7940i	0.815497	+	1.66001i
$697$	−4.68809	−	10.2655i	−0.177574	−	0.388833i
$698$	19.9179	−	30.8247i	0.753903	−	1.16673i
$699$	10.8510	+	15.6296i	0.410423	+	0.591166i
$700$	−25.5083	+	26.4884i	−0.964124	+	1.00117i
$701$	−6.55032	+	33.9863i	−0.247402	+	1.28364i	0.619433	+	0.785050i	$0.287363\pi$
$701$	−6.55032	+	33.9863i	−0.247402	+	1.28364i	−0.866835	+	0.498595i	$0.833850\pi$
$702$	−4.25273	+	14.9990i	−0.160509	+	0.566100i
$703$	−0.189100	+	0.0458751i	−0.00713203	+	0.00173021i
$704$	−15.1355	−	8.08983i	−0.570440	−	0.304897i
$705$	−0.246317	+	0.123287i	−0.00927684	+	0.00464324i
$706$	−44.4377	+	22.7701i	−1.67244	+	0.856963i
$707$	40.2209	−	69.6646i	1.51266	−	2.62001i
$708$	15.5700	+	40.8798i	0.585156	+	1.53636i
$709$	11.2714	+	32.5665i	0.423305	+	1.22306i	0.932109	+	0.362177i	$0.117966\pi$
$709$	11.2714	+	32.5665i	0.423305	+	1.22306i	−0.508805	+	0.860882i	$0.669912\pi$
$710$	1.65684	+	0.859362i	0.0621801	+	0.0322513i
$711$	−8.58376	+	1.02569i	−0.321916	+	0.0384665i
$712$	6.71381	−	14.4167i	0.251611	−	0.540290i
$713$	9.81155	−	15.2671i	0.367446	−	0.571756i
$714$	−36.1102	+	13.8559i	−1.35139	+	0.518545i
$715$	4.14727	+	0.596287i	0.155099	+	0.0222999i
$716$	13.0616	+	15.2257i	0.488137	+	0.569011i
$717$	−4.27770	−	4.59491i	−0.159754	−	0.171600i
$718$	25.4692	+	3.72634i	0.950503	+	0.139066i
$719$	−0.935991	−	19.6489i	−0.0349066	−	0.732779i	−0.946697	−	0.322124i	$-0.895603\pi$
$719$	−0.935991	−	19.6489i	−0.0349066	−	0.732779i	0.911791	−	0.410655i	$-0.134700\pi$
$720$	1.72317	+	10.9121i	0.0642188	+	0.406670i
$721$	−3.98031	−	5.58956i	−0.148234	−	0.208166i
$722$	4.07869	+	10.2617i	0.151793	+	0.381900i
$723$	−20.9721	−	27.3334i	−0.779961	−	1.01654i
$724$	0.841713	−	16.0015i	0.0312820	−	0.594690i
$725$	39.0835	+	13.5269i	1.45152	+	0.502377i
$726$	−10.4325	+	11.6948i	−0.387186	+	0.434036i
$727$	−15.2052	+	19.3350i	−0.563930	+	0.717095i	−0.981481	−	0.191558i	$-0.938646\pi$
$727$	−15.2052	+	19.3350i	−0.563930	+	0.717095i	0.417551	+	0.908653i	$0.362888\pi$
$728$	−17.2503	−	20.2095i	−0.639340	−	0.749012i
$729$	5.74492	−	26.3817i	0.212775	−	0.977101i
$730$	−0.527701	−	0.0517087i	−0.0195311	−	0.00191382i
$731$	−14.8212	−	1.41525i	−0.548180	−	0.0523449i
$732$	−21.3273	+	31.9851i	−0.788281	+	1.18220i
$733$	−22.5536	−	11.6272i	−0.833035	−	0.429459i	−0.0117179	−	0.999931i	$-0.503730\pi$
$733$	−22.5536	−	11.6272i	−0.833035	−	0.429459i	−0.821317	+	0.570472i	$0.806760\pi$
$734$	−20.8003	−	19.9316i	−0.767753	−	0.735690i
$735$	3.09805	−	19.8616i	0.114273	−	0.732605i
$736$	3.16215	+	17.5754i	0.116558	+	0.647836i
$737$	−13.3411	+	11.4171i	−0.491425	+	0.420555i
$738$	−9.05692	+	9.91208i	−0.333390	+	0.364869i
$739$	35.3350	+	8.57218i	1.29982	+	0.315333i	0.825191	−	0.564854i	$-0.191067\pi$
$739$	35.3350	+	8.57218i	1.29982	+	0.315333i	0.474628	+	0.880186i	$0.342583\pi$
$740$	0.0107080	−	0.106557i	0.000393632	−	0.00391713i
$741$	11.3573	+	4.70481i	0.417220	+	0.172835i
$742$	58.3126	−	13.9936i	2.14072	−	0.513723i
$743$	49.4569	+	4.72256i	1.81440	+	0.173254i	0.946332	−	0.323196i	$-0.104757\pi$
$743$	49.4569	+	4.72256i	1.81440	+	0.173254i	0.868065	+	0.496450i	$0.165363\pi$
$744$	−27.2360	−	7.16859i	−0.998519	−	0.262813i
$745$	4.63843	−	5.35304i	0.169939	−	0.196120i
$746$	−22.3445	−	15.9950i	−0.818089	−	0.585618i
$747$	−24.5795	−	13.4237i	−0.899318	−	0.491148i
$748$	−15.1330	−	2.25237i	−0.553318	−	0.0823549i
$749$	−77.2302	−	26.7296i	−2.82193	−	0.976679i
$750$	16.6378	+	12.2129i	0.607527	+	0.445952i
$751$	21.8002	+	33.9218i	0.795501	+	1.23782i	0.967536	+	0.252733i	$0.0813296\pi$
$751$	21.8002	+	33.9218i	0.795501	+	1.23782i	−0.172035	+	0.985091i	$0.555034\pi$
$752$	0.495335	+	0.481760i	0.0180630	+	0.0175680i
$753$	−20.2620	+	17.1380i	−0.738389	+	0.624545i
$754$	−12.4811	+	27.1517i	−0.454536	+	0.988806i
$755$	−0.342328	−	7.18635i	−0.0124586	−	0.261538i
$756$	31.9820	+	33.0857i	1.16317	+	1.20331i
$757$	−29.3391	+	23.0725i	−1.06635	+	0.838584i	−0.987392	−	0.158295i	$-0.949400\pi$
$757$	−29.3391	+	23.0725i	−1.06635	+	0.838584i	−0.0789540	+	0.996878i	$0.525158\pi$
$758$	1.99772	+	44.2429i	0.0725606	+	1.60697i
$759$	−11.7088	−	0.697913i	−0.425001	−	0.0253326i
$760$	8.70401	−	0.349820i	0.315727	−	0.0126893i
$761$	−3.98456	+	6.20010i	−0.144440	+	0.224753i	−0.905934	−	0.423419i	$-0.860830\pi$
$761$	−3.98456	+	6.20010i	−0.144440	+	0.224753i	0.761494	+	0.648172i	$0.224466\pi$
$762$	2.26940	−	20.6209i	0.0822119	−	0.747017i
$763$	−34.3398	−	1.63581i	−1.24318	−	0.0592202i
$764$	−5.15666	+	0.967395i	−0.186561	+	0.0349991i
$765$	4.71934	+	8.64430i	0.170628	+	0.312535i
$766$	9.31805	−	23.1093i	0.336675	−	0.834973i
$767$	−13.3955	+	23.2016i	−0.483683	+	0.837763i
$768$	24.4278	−	13.0875i	0.881462	−	0.472255i
$769$	−6.08620	+	2.43655i	−0.219474	+	0.0878641i	−0.478794	−	0.877927i	$-0.658926\pi$
$769$	−6.08620	+	2.43655i	−0.219474	+	0.0878641i	0.259320	+	0.965791i	$0.416502\pi$
$770$	7.66884	−	9.70218i	0.276366	−	0.349642i
$771$	14.5834	+	43.8214i	0.525209	+	1.57819i
$772$	−0.558461	−	4.02565i	−0.0200994	−	0.144886i
$773$	−3.74273	+	19.4192i	−0.134617	+	0.698458i	0.850419	+	0.526107i	$0.176349\pi$
$773$	−3.74273	+	19.4192i	−0.134617	+	0.698458i	−0.985035	+	0.172352i	$0.944863\pi$
$774$	5.35057	+	16.8863i	0.192322	+	0.606965i
$775$	−20.6738	+	11.9360i	−0.742624	+	0.428754i
$776$	−9.31065	−	9.91116i	−0.334233	−	0.355790i
$777$	−0.218418	−	0.388959i	−0.00783569	−	0.0139538i
$778$	−30.3034	−	42.7790i	−1.08643	−	1.53370i
$779$	6.93317	+	8.00131i	0.248407	+	0.286677i
$780$	−4.51641	+	5.03772i	−0.161713	+	0.180379i
$781$	2.85508	+	1.14300i	0.102163	+	0.0408998i
$782$	7.92580	+	13.8068i	0.283426	+	0.493729i
$783$	18.6667	−	48.2693i	0.667094	−	1.72500i
$784$	−49.6071	+	9.05219i	−1.77168	+	0.323293i
$785$	−2.57702	−	2.70270i	−0.0919777	−	0.0964634i
$786$	−23.0011	−	22.5733i	−0.820423	−	0.805163i
$787$	19.8504	+	38.5044i	0.707590	+	1.37253i	0.918655	+	0.395061i	$0.129277\pi$
$787$	19.8504	+	38.5044i	0.707590	+	1.37253i	−0.211064	+	0.977472i	$0.567693\pi$
$788$	−10.6495	−	26.9879i	−0.379373	−	0.961405i
$789$	−2.60565	+	12.7017i	−0.0927636	+	0.452191i
$790$	−3.54229	−	1.23583i	−0.126029	−	0.0439689i
$791$	−72.9945	+	14.0685i	−2.59539	+	0.500220i
$792$	4.57921	+	17.6175i	0.162715	+	0.626010i
$793$	−23.4378	+	2.23803i	−0.832299	+	0.0794749i
$794$	0.0408259	−	16.4823i	0.00144886	−	0.584937i
$795$	−5.50571	−	14.2430i	−0.195268	−	0.505147i
$796$	−7.97589	+	5.62026i	−0.282698	+	0.199205i
$797$	−30.7204	+	32.2186i	−1.08817	+	1.14124i	−0.0989088	+	0.995097i	$0.531535\pi$
$797$	−30.7204	+	32.2186i	−1.08817	+	1.14124i	−0.989263	+	0.146145i	$0.953313\pi$
$798$	28.8421	−	22.0164i	1.02100	−	0.779373i
$799$	0.560337	+	0.255897i	0.0198233	+	0.00905299i
$800$	6.89650	−	22.4548i	0.243828	−	0.793896i
$801$	−16.0675	+	5.13495i	−0.567717	+	0.181435i
$802$	−6.40157	−	14.1099i	−0.226047	−	0.498237i
$803$	−0.873667			−0.0308310
$804$	−3.38754	−	28.1518i	−0.119469	−	0.992838i
$805$	−12.8684			−0.453551
$806$	−7.12642	−	15.7075i	−0.251017	−	0.553274i
$807$	3.76942	+	16.3891i	0.132690	+	0.576924i
$808$	−2.82626	+	51.3059i	−0.0994274	+	1.80494i
$809$	−21.7183	−	9.91842i	−0.763575	−	0.348713i	−0.00473416	−	0.999989i	$-0.501507\pi$
$809$	−21.7183	−	9.91842i	−0.763575	−	0.348713i	−0.758841	+	0.651276i	$0.774234\pi$
$810$	7.26736	−	9.19153i	0.255349	−	0.322958i
$811$	5.56966	−	5.84129i	0.195577	−	0.205116i	−0.618642	−	0.785673i	$-0.712317\pi$
$811$	5.56966	−	5.84129i	0.195577	−	0.205116i	0.814219	+	0.580557i	$0.197165\pi$
$812$	50.8063	+	72.1008i	1.78295	+	2.53024i
$813$	−38.0929	+	14.7250i	−1.33597	+	0.516429i
$814$	0.000437084	−	0.176460i	1.53198e−5	−	0.00618494i
$815$	21.1444	−	2.01905i	0.740657	−	0.0707241i
$816$	16.5829	−	18.3136i	0.580517	−	0.641105i
$817$	13.7152	−	2.64339i	0.479834	−	0.0924804i
$818$	−33.3265	−	11.6269i	−1.16523	−	0.406526i
$819$	−3.34778	+	27.9828i	−0.116981	+	0.977799i
$820$	−5.42020	+	2.13883i	−0.189282	+	0.0746911i
$821$	−17.5965	−	34.1324i	−0.614121	−	1.19123i	−0.966812	−	0.255489i	$-0.917764\pi$
$821$	−17.5965	−	34.1324i	−0.614121	−	1.19123i	0.352691	−	0.935740i	$-0.385267\pi$
$822$	3.80647	−	3.87862i	0.132766	−	0.135282i
$823$	2.37692	+	2.49284i	0.0828541	+	0.0868949i	0.763856	−	0.645387i	$-0.223304\pi$
$823$	2.37692	+	2.49284i	0.0828541	+	0.0868949i	−0.681002	+	0.732282i	$0.738455\pi$
$824$	3.88090	+	2.03739i	0.135198	+	0.0709758i
$825$	13.2690	+	7.87350i	0.461967	+	0.274120i
$826$	39.3686	+	68.5802i	1.36981	+	2.38621i
$827$	8.12895	+	3.25434i	0.282671	+	0.113165i	0.508666	−	0.860964i	$-0.330139\pi$
$827$	8.12895	+	3.25434i	0.282671	+	0.113165i	−0.225994	+	0.974129i	$0.572563\pi$
$828$	11.4269	−	15.1057i	0.397111	−	0.524958i
$829$	1.27838	+	1.47532i	0.0443998	+	0.0512401i	0.777515	−	0.628864i	$-0.216480\pi$
$829$	1.27838	+	1.47532i	0.0443998	+	0.0512401i	−0.733115	+	0.680104i	$0.761934\pi$
$830$	−7.02555	−	9.91791i	−0.243860	−	0.344256i
$831$	14.3900	−	8.08061i	0.499183	−	0.280313i
$832$	15.6612	+	6.54150i	0.542955	+	0.226786i
$833$	−38.9321	+	22.4774i	−1.34892	+	0.778797i
$834$	41.5266	−	9.44267i	1.43795	−	0.326973i
$835$	−0.896100	+	4.64941i	−0.0310108	+	0.160899i
$836$	14.2172	−	1.97229i	0.491711	−	0.0682129i
$837$	14.0003	+	26.3880i	0.483921	+	0.912103i
$838$	−3.56635	+	4.51193i	−0.123197	+	0.155862i
$839$	28.4847	−	11.4036i	0.983402	−	0.393695i	0.176449	−	0.984310i	$-0.443539\pi$
$839$	28.4847	−	11.4036i	0.983402	−	0.393695i	0.806953	+	0.590615i	$0.201115\pi$
$840$	6.16493	+	18.9948i	0.212710	+	0.655383i
$841$	35.0995	−	60.7941i	1.21033	−	2.09635i
$842$	10.6401	−	26.3880i	0.366682	−	0.909392i
$843$	−18.1173	−	40.9582i	−0.623994	−	1.41067i
$844$	3.85713	+	20.5603i	0.132768	+	0.707713i
$845$	7.81539	+	0.372293i	0.268857	+	0.0128073i
$846$	0.0193082	−	0.732637i	0.000663830	−	0.0251886i
$847$	−15.3163	+	23.8326i	−0.526274	+	0.818898i
$848$	−29.1967	+	24.7969i	−1.00262	+	0.851530i
$849$	0.0938595	−	1.57466i	0.00322125	−	0.0540423i
$850$	−0.944609	−	20.9199i	−0.0323998	−	0.717547i
$851$	−0.144331	+	0.113503i	−0.00494759	+	0.00389083i
$852$	−4.09334	+	2.81189i	−0.140235	+	0.0963337i
$853$	1.91324	+	40.1639i	0.0655081	+	1.37519i	0.757290	+	0.653079i	$0.226523\pi$
$853$	1.91324	+	40.1639i	0.0655081	+	1.37519i	−0.691782	+	0.722106i	$0.743174\pi$
$854$	−29.0253	+	63.1423i	−0.993227	+	2.16068i
$855$	−6.53281	−	6.53374i	−0.223417	−	0.223449i
$856$	51.7259	−	7.04516i	1.76795	−	0.240798i
$857$	−10.0181	−	15.5885i	−0.342213	−	0.532494i	0.626903	−	0.779097i	$-0.284322\pi$
$857$	−10.0181	−	15.5885i	−0.342213	−	0.532494i	−0.969117	+	0.246603i	$0.920686\pi$
$858$	−6.59680	+	8.98692i	−0.225211	+	0.306808i
$859$	6.83976	+	2.36726i	0.233369	+	0.0807700i	0.441250	−	0.897384i	$-0.354535\pi$
$859$	6.83976	+	2.36726i	0.233369	+	0.0807700i	−0.207880	+	0.978154i	$0.566656\pi$
$860$	−1.13171	+	7.60363i	−0.0385910	+	0.259282i
$861$	−13.3649	+	20.2604i	−0.455475	+	0.690471i
$862$	8.09871	+	5.79735i	0.275843	+	0.197459i
$863$	9.44061	−	10.8950i	0.321362	−	0.370872i	−0.571965	−	0.820278i	$-0.693819\pi$
$863$	9.44061	−	10.8950i	0.321362	−	0.370872i	0.893328	+	0.449406i	$0.148364\pi$
$864$	−27.7715	−	9.63023i	−0.944807	−	0.327627i
$865$	12.0189	+	1.14766i	0.408654	+	0.0390218i
$866$	30.8856	−	7.41180i	1.04953	−	0.251863i
$867$	−2.83962	+	6.85475i	−0.0964385	+	0.232800i
$868$	−50.6560	−	5.09042i	−1.71938	−	0.172780i
$869$	−6.00746	−	1.45739i	−0.203789	−	0.0494387i
$870$	16.4766	−	15.2631i	0.558608	−	0.517468i
$871$	12.0608	−	12.4942i	0.408666	−	0.423349i
$872$	20.0428	−	8.97387i	0.678736	−	0.303893i
$873$	−1.02998	+	14.3866i	−0.0348596	+	0.486912i
$874$	−10.7835	−	10.3332i	−0.364759	−	0.349526i
$875$	33.1617	+	17.0960i	1.12107	+	0.577952i
$876$	0.782667	−	1.17378i	0.0264439	−	0.0396584i
$877$	35.9117	+	3.42915i	1.21265	+	0.115794i	0.681716	−	0.731617i	$-0.261234\pi$
$877$	35.9117	+	3.42915i	1.21265	+	0.115794i	0.530937	+	0.847411i	$0.321840\pi$
$878$	−33.6313	−	3.29548i	−1.13500	−	0.111217i
$879$	11.6525	−	15.9571i	0.393030	−	0.538220i
$880$	−1.57180	+	7.74173i	−0.0529855	+	0.260974i
$881$	28.1345	−	35.7759i	0.947875	−	1.20532i	−0.0307199	−	0.999528i	$-0.509780\pi$
$881$	28.1345	−	35.7759i	0.947875	−	1.20532i	0.978595	−	0.205794i	$-0.0659776\pi$
$882$	42.7352	+	32.1615i	1.43897	+	1.08293i
$883$	−20.5367	−	7.10781i	−0.691114	−	0.239197i	−0.0411400	−	0.999153i	$-0.513099\pi$
$883$	−20.5367	−	7.10781i	−0.691114	−	0.239197i	−0.649974	+	0.759957i	$0.725220\pi$
$884$	15.1100	+	0.794821i	0.508205	+	0.0267327i
$885$	15.9753	−	12.2573i	0.537002	−	0.412026i
$886$	−11.4967	−	28.9248i	−0.386239	−	0.971746i
$887$	7.37535	+	10.3572i	0.247640	+	0.347762i	0.919621	−	0.392807i	$-0.128496\pi$
$887$	7.37535	+	10.3572i	0.247640	+	0.347762i	−0.671981	+	0.740568i	$0.734556\pi$
$888$	0.236685	+	0.158668i	0.00794264	+	0.00532454i
$889$	−1.78439	−	37.4589i	−0.0598465	−	1.25633i
$890$	−7.24329	−	1.05975i	−0.242796	−	0.0355228i
$891$	10.4405	−	16.2406i	0.349770	−	0.544082i
$892$	38.1110	−	32.6942i	1.27605	−	1.09468i
$893$	−0.572017	−	0.0822437i	−0.0191418	−	0.00275218i
$894$	6.75151	+	17.5953i	0.225804	+	0.588474i
$895$	4.99228	−	7.76814i	0.166874	−	0.259660i
$896$	39.9094	−	30.2801i	1.33328	−	1.01159i
$897$	11.5928	−	0.413622i	0.387071	−	0.0138104i
$898$	15.3052	+	7.93841i	0.510740	+	0.264908i
$899$	18.7272	+	54.1088i	0.624588	+	1.80463i
$900$	−22.4651	+	10.7737i	−0.748835	+	0.359122i
$901$	−17.0748	+	29.5744i	−0.568843	+	0.985265i
$902$	−8.54471	+	4.37835i	−0.284508	+	0.145783i
$903$	14.3321	+	28.6345i	0.476943	+	0.952896i
$904$	37.5427	−	29.0750i	1.24865	−	0.967020i
$905$	−7.16783	+	1.73890i	−0.238267	+	0.0578029i
$906$	17.2963	+	8.20224i	0.574631	+	0.272501i
$907$	1.06933	−	5.54823i	0.0355066	−	0.184226i	−0.959845	−	0.280530i	$-0.909490\pi$
$907$	1.06933	−	5.54823i	0.0355066	−	0.184226i	0.995352	+	0.0963037i	$0.0307020\pi$
$908$	33.6557	+	32.4105i	1.11690	+	1.07558i
$909$	42.0290	−	34.6970i	1.39401	−	1.15083i
$910$	−6.63782	+	10.2726i	−0.220041	+	0.340534i
$911$	10.3447	+	22.6518i	0.342737	+	0.750488i	0.999995	−	0.00317688i	$-0.00101123\pi$
$911$	10.3447	+	22.6518i	0.342737	+	0.750488i	−0.657258	+	0.753665i	$0.728284\pi$
$912$	−10.0865	+	20.8678i	−0.333999	+	0.691002i
$913$	−13.1146	−	15.1351i	−0.434031	−	0.500899i
$914$	0.612720	+	6.58913i	0.0202670	+	0.217949i
$915$	16.9182	+	5.18775i	0.559298	+	0.171502i
$916$	−22.7860	−	9.25339i	−0.752872	−	0.305741i
$917$	−47.4550	−	33.7925i	−1.56710	−	1.11593i
$918$	−26.2034	+	0.244115i	−0.864842	+	0.00805700i
$919$	5.77001	+	6.05141i	0.190335	+	0.199618i	0.811986	−	0.583676i	$-0.198386\pi$
$919$	5.77001	+	6.05141i	0.190335	+	0.199618i	−0.621651	+	0.783294i	$0.713538\pi$
$920$	7.33395	−	3.71219i	0.241793	−	0.122387i
$921$	3.32739	−	2.08269i	0.109641	−	0.0686269i
$922$	10.0447	+	2.97643i	0.330804	+	0.0980236i
$923$	−2.91825	−	0.856874i	−0.0960552	−	0.0282044i
$924$	13.1619	+	30.1583i	0.432994	+	0.992134i
$925$	0.237163	−	0.0457094i	0.00779788	−	0.00150292i
$926$	−10.8102	−	31.4861i	−0.355245	−	1.03470i
$927$	−1.20295	−	4.49075i	−0.0395100	−	0.147496i
$928$	−49.7548	−	26.4354i	−1.63328	−	0.867784i
$929$	6.73769	+	22.9465i	0.221057	+	0.752849i	0.993099	+	0.117279i	$0.0374170\pi$
$929$	6.73769	+	22.9465i	0.221057	+	0.752849i	−0.772043	+	0.635571i	$0.780765\pi$
$930$	0.430155	+	12.9567i	0.0141053	+	0.424867i
$931$	29.1035	−	30.5228i	0.953827	−	1.00035i
$932$	−20.7263	−	7.28863i	−0.678914	−	0.238747i
$933$	−36.3332	−	13.0627i	−1.18950	−	0.427653i
$934$	−4.72388	−	24.8408i	−0.154570	−	0.812815i
$935$	1.00226	+	6.97086i	0.0327773	+	0.227971i
$936$	−6.16435	−	16.9137i	−0.201488	−	0.552842i
$937$	13.7187			0.448171			0.224086	−	0.974569i	$-0.428060\pi$
$937$	13.7187			0.448171			0.224086	+	0.974569i	$0.428060\pi$
$938$	−14.0157	−	49.3035i	−0.457630	−	1.60982i
$939$	0.423527	+	5.07479i	0.0138213	+	0.165610i
$940$	0.147142	−	0.281978i	0.00479925	−	0.00919710i
$941$	31.5465	−	4.53570i	1.02839	−	0.147860i	0.392587	−	0.919715i	$-0.371580\pi$
$941$	31.5465	−	4.53570i	1.02839	−	0.147860i	0.635798	+	0.771855i	$0.280671\pi$
$942$	9.57302	−	2.66165i	0.311906	−	0.0867211i
$943$	9.08755	+	4.15015i	0.295931	+	0.135147i
$944$	−42.2206	−	27.7284i	−1.37416	−	0.902483i
$945$	10.3737	−	18.4674i	0.337458	−	0.600745i
$946$	−0.634041	+	12.6508i	−0.0206144	+	0.411312i
$947$	28.1877	−	8.27664i	0.915976	−	0.268955i	0.210422	−	0.977611i	$-0.432516\pi$
$947$	28.1877	−	8.27664i	0.915976	−	0.268955i	0.705554	+	0.708656i	$0.250698\pi$
$948$	7.33976	−	6.76550i	0.238384	−	0.219733i
$949$	0.860115	−	0.0821311i	0.0279205	−	0.00266609i
$950$	6.37953	+	18.5812i	0.206979	+	0.602854i
$951$	−53.2418	+	14.9453i	−1.72649	+	0.484635i
$952$	24.4239	−	37.3905i	0.791584	−	1.21183i
$953$	10.1438	−	34.5467i	0.328591	−	1.11908i	−0.615155	−	0.788406i	$-0.710907\pi$
$953$	10.1438	−	34.5467i	0.328591	−	1.11908i	0.943746	−	0.330672i	$-0.107275\pi$
$954$	40.3297	+	4.92629i	1.30572	+	0.159494i
$955$	1.10664	+	2.14658i	0.0358100	+	0.0694616i
$956$	7.11120	+	1.40714i	0.229993	+	0.0455103i
$957$	24.5667	−	27.6770i	0.794130	−	0.894672i
$958$	−6.51762	−	1.59826i	−0.210575	−	0.0516375i
$959$	5.69835	−	8.00221i	0.184009	−	0.258405i
$960$	−8.99302	−	9.04710i	−0.290249	−	0.291994i
$961$	−1.90262	−	0.761694i	−0.0613749	−	0.0245708i
$962$	0.0161583	+	0.173764i	0.000520963	+	0.00560239i
$963$	−42.6945	−	35.2567i	−1.37581	−	1.13613i
$964$	38.1144	+	11.3968i	1.22758	+	0.367066i
$965$	−1.70172	+	0.777148i	−0.0547802	+	0.0250173i
$966$	16.1263	−	30.2037i	0.518854	−	0.971789i
$967$	22.5711	−	13.0315i	0.725839	−	0.419063i	−0.0910589	−	0.995846i	$-0.529025\pi$
$967$	22.5711	−	13.0315i	0.725839	−	0.419063i	0.816898	+	0.576782i	$0.195692\pi$
$968$	1.85397	−	18.0010i	0.0595889	−	0.578575i
$969$	−2.20949	+	20.5443i	−0.0709790	+	0.659979i
$970$	−3.14315	+	5.41308i	−0.100920	+	0.173804i
$971$	−7.93540	−	32.7102i	−0.254659	−	1.04972i	−0.945217	−	0.326442i	$-0.894150\pi$
$971$	−7.93540	−	32.7102i	−0.254659	−	1.04972i	0.690558	−	0.723277i	$-0.257365\pi$
$972$	12.4665	+	28.5760i	0.399862	+	0.916575i
$973$	71.4691	−	28.6119i	2.29119	−	0.917256i
$974$	0.964059	−	0.493988i	0.0308904	−	0.0158284i
$975$	−13.8033	−	6.50399i	−0.442061	−	0.208294i
$976$	−1.67278	−	44.3591i	−0.0535444	−	1.41990i
$977$	−17.4802	+	6.04997i	−0.559243	+	0.193556i	−0.592043	−	0.805906i	$-0.701679\pi$
$977$	−17.4802	+	6.04997i	−0.559243	+	0.193556i	0.0328006	+	0.999462i	$0.489557\pi$
$978$	−21.7586	+	52.1589i	−0.695764	+	1.66786i
$979$	−12.0483	−	0.573931i	−0.385065	−	0.0183429i
$980$	10.5338	+	20.6836i	0.336489	+	0.660714i
$981$	−21.4109	−	9.17051i	−0.683598	−	0.292792i
$982$	−3.48095	−	11.9646i	−0.111082	−	0.381805i
$983$	7.09884	−	49.3735i	0.226418	−	1.57477i	−0.486600	−	0.873625i	$-0.661763\pi$
$983$	7.09884	−	49.3735i	0.226418	−	1.57477i	0.713018	−	0.701146i	$-0.247328\pi$
$984$	1.77234	−	15.4022i	0.0565000	−	0.491005i
$985$	−10.4976	+	8.25544i	−0.334483	+	0.263040i
$986$	−49.6992	−	7.27136i	−1.58274	−	0.231567i
$987$	−0.172880	−	1.31352i	−0.00550283	−	0.0418097i
$988$	−13.8112	+	3.27821i	−0.439394	+	0.104294i
$989$	10.7362	−	7.64523i	0.341392	−	0.243104i
$990$	7.16566	−	4.34269i	0.227739	−	0.138020i
$991$	16.0578	+	24.9864i	0.510092	+	0.793718i	0.996808	−	0.0798421i	$-0.0254416\pi$
$991$	16.0578	+	24.9864i	0.510092	+	0.793718i	−0.486716	+	0.873560i	$0.661805\pi$
$992$	30.3383	−	11.7118i	0.963243	−	0.371851i
$993$	−13.2609	+	51.9479i	−0.420822	+	1.64852i
$994$	−6.51242	+	6.17886i	−0.206562	+	0.195981i
$995$	3.53038	+	2.77632i	0.111920	+	0.0880152i
$996$	32.0828	−	4.06104i	1.01658	−	0.128679i
$997$	−33.9486	+	39.1788i	−1.07516	+	1.24081i	−0.106006	+	0.994365i	$0.533806\pi$
$997$	−33.9486	+	39.1788i	−1.07516	+	1.24081i	−0.969158	+	0.246440i	$0.920739\pi$
$998$	26.4416	+	2.59097i	0.836994	+	0.0820158i
$999$	−0.0465371	−	0.298629i	−0.00147237	−	0.00944819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.bd.a.35.20	yes	2640
3.2	odd	2	inner	804.2.bd.a.35.113	yes	2640
4.3	odd	2	inner	804.2.bd.a.35.38	yes	2640
12.11	even	2	inner	804.2.bd.a.35.95	yes	2640
67.23	even	33	inner	804.2.bd.a.23.95	yes	2640
201.23	odd	66	inner	804.2.bd.a.23.38	yes	2640
268.23	odd	66	inner	804.2.bd.a.23.113	yes	2640
804.23	even	66	inner	804.2.bd.a.23.20	✓	2640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.bd.a.23.20	✓	2640	804.23	even	66	inner
804.2.bd.a.23.38	yes	2640	201.23	odd	66	inner
804.2.bd.a.23.95	yes	2640	67.23	even	33	inner
804.2.bd.a.23.113	yes	2640	268.23	odd	66	inner
804.2.bd.a.35.20	yes	2640	1.1	even	1	trivial
804.2.bd.a.35.38	yes	2640	4.3	odd	2	inner
804.2.bd.a.35.95	yes	2640	12.11	even	2	inner
804.2.bd.a.35.113	yes	2640	3.2	odd	2	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.bd (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28787 + 0.584297i) q^{2} +(-1.68798 + 0.388227i) q^{3} +(1.31719 - 1.50499i) q^{4} +(-0.837417 - 0.382435i) q^{5} +(1.94705 - 1.48627i) q^{6} +(3.05562 - 3.20464i) q^{7} +(-0.817004 + 2.70786i) q^{8} +(2.69856 - 1.31064i) q^{9} +O(q^{10})\)	\(q+(-1.28787 + 0.584297i) q^{2} +(-1.68798 + 0.388227i) q^{3} +(1.31719 - 1.50499i) q^{4} +(-0.837417 - 0.382435i) q^{5} +(1.94705 - 1.48627i) q^{6} +(3.05562 - 3.20464i) q^{7} +(-0.817004 + 2.70786i) q^{8} +(2.69856 - 1.31064i) q^{9} +(1.30194 + 0.00322483i) q^{10} +(2.13552 - 0.203917i) q^{11} +(-1.63912 + 3.05177i) q^{12} +(-2.08322 + 0.401508i) q^{13} +(-2.06276 + 5.91254i) q^{14} +(1.56202 + 0.320435i) q^{15} +(-0.530004 - 3.96473i) q^{16} +(-1.63403 - 3.16958i) q^{17} +(-2.70958 + 3.26469i) q^{18} +(2.30859 + 2.42118i) q^{19} +(-1.67860 + 0.756564i) q^{20} +(-3.91370 + 6.59565i) q^{21} +(-2.63111 + 1.51039i) q^{22} +(2.93067 + 1.17326i) q^{23} +(0.327822 - 4.88800i) q^{24} +(-2.71929 - 3.13823i) q^{25} +(2.44831 - 1.73431i) q^{26} +(-4.04629 + 3.25999i) q^{27} +(-0.798121 - 8.81982i) q^{28} +(-8.62550 + 4.97993i) q^{29} +(-2.19889 + 0.500004i) q^{30} +(1.08798 - 5.64497i) q^{31} +(2.99916 + 4.79636i) q^{32} +(-3.52554 + 1.17327i) q^{33} +(3.95639 + 3.12723i) q^{34} +(-3.78440 + 1.51504i) q^{35} +(1.58202 - 5.78768i) q^{36} +(-0.0290824 + 0.0503722i) q^{37} +(-4.38785 - 1.76925i) q^{38} +(3.36056 - 1.48650i) q^{39} +(1.71975 - 1.95516i) q^{40} +(3.16113 + 0.150583i) q^{41} +(1.18650 - 10.7811i) q^{42} +(2.25726 - 3.51237i) q^{43} +(2.50599 - 3.48253i) q^{44} +(-2.76105 + 0.0655280i) q^{45} +(-4.45984 + 0.201378i) q^{46} +(-0.135786 + 0.106783i) q^{47} +(2.43385 + 6.48663i) q^{48} +(-0.599845 - 12.5923i) q^{49} +(5.33574 + 2.45274i) q^{50} +(3.98873 + 4.71581i) q^{51} +(-2.13974 + 3.66410i) q^{52} +(-5.17743 - 8.05623i) q^{53} +(3.30627 - 6.56267i) q^{54} +(-1.86630 - 0.645933i) q^{55} +(6.18127 + 10.8924i) q^{56} +(-4.83683 - 3.19065i) q^{57} +(8.19872 - 11.4533i) q^{58} +(8.26955 - 9.54357i) q^{59} +(2.53973 - 1.92875i) q^{60} +(11.0474 + 1.05490i) q^{61} +(1.89717 + 7.90567i) q^{62} +(4.04564 - 12.6527i) q^{63} +(-6.66501 - 4.42466i) q^{64} +(1.89807 + 0.460468i) q^{65} +(3.85488 - 3.57098i) q^{66} +(-6.69669 + 4.70684i) q^{67} +(-6.92252 - 1.71574i) q^{68} +(-5.40241 - 0.842680i) q^{69} +(3.98856 - 4.16239i) q^{70} +(1.27422 + 0.656908i) q^{71} +(1.34430 + 8.37812i) q^{72} +(-0.405416 - 0.0387126i) q^{73} +(0.00802186 - 0.0818653i) q^{74} +(5.80846 + 4.24157i) q^{75} +(6.68473 - 0.285250i) q^{76} +(5.87185 - 7.46666i) q^{77} +(-3.45939 + 3.87798i) q^{78} +(-2.72312 - 0.942482i) q^{79} +(-1.07242 + 3.52282i) q^{80} +(5.56444 - 7.07368i) q^{81} +(-4.15909 + 1.65311i) q^{82} +(-5.41507 - 7.60441i) q^{83} +(4.77131 + 14.5778i) q^{84} +(0.156206 + 3.27917i) q^{85} +(-0.854781 + 5.84237i) q^{86} +(12.6263 - 11.7547i) q^{87} +(-1.19255 + 5.94928i) q^{88} +(-5.56546 - 0.800192i) q^{89} +(3.51758 - 1.69767i) q^{90} +(-5.07885 + 7.90284i) q^{91} +(5.62601 - 2.86522i) q^{92} +(0.355045 + 9.95099i) q^{93} +(0.112481 - 0.216862i) q^{94} +(-1.00731 - 2.91043i) q^{95} +(-6.92460 - 6.93181i) q^{96} +(-2.40390 + 4.16367i) q^{97} +(8.13016 + 15.8667i) q^{98} +(5.49555 - 3.34918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more