LMFDB - Embedded newform 363.2.f.e.239.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(161,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("363.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.f (of order $10$, degree $4$, not 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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			239.1
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	363.239
Dual form			363.2.f.e.161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53884 + 1.11803i) q^{2} +(-0.0877853 + 1.72982i) q^{3} +(0.500000 - 1.53884i) q^{4} +(-1.53884 + 2.11803i) q^{5} +(-1.79892 - 2.76007i) q^{6} +(-0.690983 - 0.224514i) q^{7} +(-0.224514 - 0.690983i) q^{8} +(-2.98459 - 0.303706i) q^{9} +O(q^{10})$	\(q+(-1.53884 + 1.11803i) q^{2} +(-0.0877853 + 1.72982i) q^{3} +(0.500000 - 1.53884i) q^{4} +(-1.53884 + 2.11803i) q^{5} +(-1.79892 - 2.76007i) q^{6} +(-0.690983 - 0.224514i) q^{7} +(-0.224514 - 0.690983i) q^{8} +(-2.98459 - 0.303706i) q^{9} -4.97980i q^{10} +(2.61803 + 1.00000i) q^{12} +(-1.80902 - 2.48990i) q^{13} +(1.31433 - 0.427051i) q^{14} +(-3.52874 - 2.84786i) q^{15} +(3.73607 + 2.71441i) q^{16} +(2.12663 + 1.54508i) q^{17} +(4.93236 - 2.86951i) q^{18} +(-4.04508 + 1.31433i) q^{19} +(2.48990 + 3.42705i) q^{20} +(0.449028 - 1.17557i) q^{21} -1.76393i q^{23} +(1.21499 - 0.327712i) q^{24} +(-0.572949 - 1.76336i) q^{25} +(5.56758 + 1.80902i) q^{26} +(0.787361 - 5.13615i) q^{27} +(-0.690983 + 0.951057i) q^{28} +(-1.17557 + 3.61803i) q^{29} +(8.61418 + 0.437153i) q^{30} +(0.690983 - 0.502029i) q^{31} -7.33094 q^{32} -5.00000 q^{34} +(1.53884 - 1.11803i) q^{35} +(-1.95965 + 4.44095i) q^{36} +(0.927051 - 2.85317i) q^{37} +(4.75528 - 6.54508i) q^{38} +(4.46589 - 2.91071i) q^{39} +(1.80902 + 0.587785i) q^{40} +(-0.951057 - 2.92705i) q^{41} +(0.623345 + 2.31105i) q^{42} +1.62460i q^{43} +(5.23607 - 5.85410i) q^{45} +(1.97214 + 2.71441i) q^{46} +(6.96767 - 2.26393i) q^{47} +(-5.02343 + 6.22446i) q^{48} +(-5.23607 - 3.80423i) q^{49} +(2.85317 + 2.07295i) q^{50} +(-2.85941 + 3.54306i) q^{51} +(-4.73607 + 1.53884i) q^{52} +(-2.85317 - 3.92705i) q^{53} +(4.53077 + 8.78402i) q^{54} +0.527864i q^{56} +(-1.91846 - 7.11267i) q^{57} +(-2.23607 - 6.88191i) q^{58} +(-2.48990 - 0.809017i) q^{59} +(-6.14677 + 4.00624i) q^{60} +(-2.50000 + 3.44095i) q^{61} +(-0.502029 + 1.54508i) q^{62} +(1.99411 + 0.879937i) q^{63} +(3.80902 - 2.76741i) q^{64} +8.05748 q^{65} -8.32624 q^{67} +(3.44095 - 2.50000i) q^{68} +(3.05129 + 0.154847i) q^{69} +(-1.11803 + 3.44095i) q^{70} +(-6.06961 + 8.35410i) q^{71} +(0.460226 + 2.13049i) q^{72} +(-14.4721 - 4.70228i) q^{73} +(1.76336 + 5.42705i) q^{74} +(3.10059 - 0.836305i) q^{75} +6.88191i q^{76} +(-3.61803 + 9.47214i) q^{78} +(6.28115 + 8.64527i) q^{79} +(-11.4984 + 3.73607i) q^{80} +(8.81553 + 1.81288i) q^{81} +(4.73607 + 3.44095i) q^{82} +(-11.7229 - 8.51722i) q^{83} +(-1.58450 - 1.27877i) q^{84} +(-6.54508 + 2.12663i) q^{85} +(-1.81636 - 2.50000i) q^{86} +(-6.15537 - 2.35114i) q^{87} +9.47214i q^{89} +(-1.51240 + 14.8626i) q^{90} +(0.690983 + 2.12663i) q^{91} +(-2.71441 - 0.881966i) q^{92} +(0.807763 + 1.23935i) q^{93} +(-8.19098 + 11.2739i) q^{94} +(3.44095 - 10.5902i) q^{95} +(0.643548 - 12.6812i) q^{96} +(5.35410 - 3.88998i) q^{97} +12.3107 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{4} + 10 q^{6} - 10 q^{7} - 10 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^4 + 10 * q^6 - 10 * q^7 - 10 * q^9	$ 8 q + 4 q^{3} + 4 q^{4} + 10 q^{6} - 10 q^{7} - 10 q^{9} + 12 q^{12} - 10 q^{13} + 4 q^{15} + 12 q^{16} + 20 q^{18} - 10 q^{19} + 20 q^{24} - 18 q^{25} - 2 q^{27} - 10 q^{28} + 30 q^{30} + 10 q^{31} - 40 q^{34} - 6 q^{37} + 10 q^{39} + 10 q^{40} - 10 q^{42} + 24 q^{45} - 20 q^{46} - 14 q^{48} - 24 q^{49} + 10 q^{51} - 20 q^{52} - 10 q^{57} - 8 q^{60} - 20 q^{61} - 10 q^{63} + 26 q^{64} - 4 q^{67} + 34 q^{69} + 20 q^{72} - 80 q^{73} + 6 q^{75} - 20 q^{78} + 10 q^{79} - 2 q^{81} + 20 q^{82} - 10 q^{84} - 30 q^{85} + 30 q^{90} + 10 q^{91} - 70 q^{94} + 30 q^{96} + 16 q^{97}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^4 + 10 * q^6 - 10 * q^7 - 10 * q^9 + 12 * q^12 - 10 * q^13 + 4 * q^15 + 12 * q^16 + 20 * q^18 - 10 * q^19 + 20 * q^24 - 18 * q^25 - 2 * q^27 - 10 * q^28 + 30 * q^30 + 10 * q^31 - 40 * q^34 - 6 * q^37 + 10 * q^39 + 10 * q^40 - 10 * q^42 + 24 * q^45 - 20 * q^46 - 14 * q^48 - 24 * q^49 + 10 * q^51 - 20 * q^52 - 10 * q^57 - 8 * q^60 - 20 * q^61 - 10 * q^63 + 26 * q^64 - 4 * q^67 + 34 * q^69 + 20 * q^72 - 80 * q^73 + 6 * q^75 - 20 * q^78 + 10 * q^79 - 2 * q^81 + 20 * q^82 - 10 * q^84 - 30 * q^85 + 30 * q^90 + 10 * q^91 - 70 * q^94 + 30 * q^96 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−1.53884	+	1.11803i	−1.08813	+	0.790569i	−0.979082	−	0.203468i	$-0.934779\pi$
$2$	−1.53884	+	1.11803i	−1.08813	+	0.790569i	−0.109044	+	0.994037i	$0.534779\pi$
$3$	−0.0877853	+	1.72982i	−0.0506828	+	0.998715i
$3$	−0.0877853	+	1.72982i	−0.0506828	+	0.998715i
$4$	0.500000	−	1.53884i	0.250000	−	0.769421i
$5$	−1.53884	+	2.11803i	−0.688191	+	0.947214i	−0.999996	−	0.00293261i	$-0.999067\pi$
$5$	−1.53884	+	2.11803i	−0.688191	+	0.947214i	0.311805	+	0.950146i	$0.399067\pi$
$6$	−1.79892	−	2.76007i	−0.734404	−	1.12680i
$7$	−0.690983	−	0.224514i	−0.261167	−	0.0848583i	0.175507	−	0.984478i	$-0.443844\pi$
$7$	−0.690983	−	0.224514i	−0.261167	−	0.0848583i	−0.436674	+	0.899620i	$0.643844\pi$
$8$	−0.224514	−	0.690983i	−0.0793777	−	0.244299i
$9$	−2.98459	−	0.303706i	−0.994862	−	0.101235i
$10$		−	4.97980i		−	1.57475i
$11$		0			0
$11$		0			0
$12$	2.61803	+	1.00000i	0.755761	+	0.288675i
$13$	−1.80902	−	2.48990i	−0.501731	−	0.690574i	0.480767	−	0.876849i	$-0.340358\pi$
$13$	−1.80902	−	2.48990i	−0.501731	−	0.690574i	−0.982498	+	0.186275i	$0.940358\pi$
$14$	1.31433	−	0.427051i	0.351269	−	0.114134i
$15$	−3.52874	−	2.84786i	−0.911117	−	0.735314i
$16$	3.73607	+	2.71441i	0.934017	+	0.678603i
$17$	2.12663	+	1.54508i	0.515783	+	0.374738i	0.815013	−	0.579443i	$-0.196730\pi$
$17$	2.12663	+	1.54508i	0.515783	+	0.374738i	−0.299230	+	0.954181i	$0.596730\pi$
$18$	4.93236	−	2.86951i	1.16257	−	0.676351i
$19$	−4.04508	+	1.31433i	−0.928006	+	0.301527i	−0.733747	−	0.679423i	$-0.762230\pi$
$19$	−4.04508	+	1.31433i	−0.928006	+	0.301527i	−0.194259	+	0.980950i	$0.562230\pi$
$20$	2.48990	+	3.42705i	0.556758	+	0.766312i
$21$	0.449028	−	1.17557i	0.0979859	−	0.256531i
$22$		0			0
$23$		−	1.76393i		−	0.367805i	−0.982944	−	0.183903i	$-0.941127\pi$
$23$		−	1.76393i		−	0.367805i	0.982944	−	0.183903i	$-0.0588731\pi$
$24$	1.21499	−	0.327712i	0.248008	−	0.0668939i
$25$	−0.572949	−	1.76336i	−0.114590	−	0.352671i
$26$	5.56758	+	1.80902i	1.09189	+	0.354777i
$27$	0.787361	−	5.13615i	0.151528	−	0.988453i
$28$	−0.690983	+	0.951057i	−0.130584	+	0.179733i
$29$	−1.17557	+	3.61803i	−0.218298	+	0.671852i	0.780605	+	0.625025i	$0.214911\pi$
$29$	−1.17557	+	3.61803i	−0.218298	+	0.671852i	−0.998903	+	0.0468274i	$0.985089\pi$
$30$	8.61418	+	0.437153i	1.57273	+	0.0798128i
$31$	0.690983	−	0.502029i	0.124104	−	0.0901670i	−0.524002	−	0.851717i	$-0.675561\pi$
$31$	0.690983	−	0.502029i	0.124104	−	0.0901670i	0.648106	+	0.761550i	$0.275561\pi$
$32$	−7.33094			−1.29594
$33$		0			0
$34$	−5.00000			−0.857493
$35$	1.53884	−	1.11803i	0.260112	−	0.188982i
$36$	−1.95965	+	4.44095i	−0.326608	+	0.740159i
$37$	0.927051	−	2.85317i	0.152406	−	0.469058i	−0.845483	−	0.534003i	$-0.820687\pi$
$37$	0.927051	−	2.85317i	0.152406	−	0.469058i	0.997889	+	0.0649448i	$0.0206871\pi$
$38$	4.75528	−	6.54508i	0.771409	−	1.06175i
$39$	4.46589	−	2.91071i	0.715115	−	0.466086i
$40$	1.80902	+	0.587785i	0.286031	+	0.0929370i
$41$	−0.951057	−	2.92705i	−0.148530	−	0.457129i	0.848918	−	0.528525i	$-0.177255\pi$
$41$	−0.951057	−	2.92705i	−0.148530	−	0.457129i	−0.997448	+	0.0713961i	$0.977255\pi$
$42$	0.623345	+	2.31105i	0.0961842	+	0.356602i
$43$			1.62460i			0.247749i	0.992298	+	0.123874i	$0.0395320\pi$
$43$			1.62460i			0.247749i	−0.992298	+	0.123874i	$0.960468\pi$
$44$		0			0
$45$	5.23607	−	5.85410i	0.780547	−	0.872678i
$46$	1.97214	+	2.71441i	0.290776	+	0.400218i
$47$	6.96767	−	2.26393i	1.01634	−	0.330228i	0.246963	−	0.969025i	$-0.420567\pi$
$47$	6.96767	−	2.26393i	1.01634	−	0.330228i	0.769376	+	0.638797i	$0.220567\pi$
$48$	−5.02343	+	6.22446i	−0.725070	+	0.898423i
$49$	−5.23607	−	3.80423i	−0.748010	−	0.543461i
$50$	2.85317	+	2.07295i	0.403499	+	0.293159i
$51$	−2.85941	+	3.54306i	−0.400398	+	0.496127i
$52$	−4.73607	+	1.53884i	−0.656774	+	0.213399i
$53$	−2.85317	−	3.92705i	−0.391913	−	0.539422i	0.566778	−	0.823870i	$-0.308190\pi$
$53$	−2.85317	−	3.92705i	−0.391913	−	0.539422i	−0.958691	+	0.284448i	$0.908190\pi$
$54$	4.53077	+	8.78402i	0.616560	+	1.19535i
$55$		0			0
$56$			0.527864i			0.0705388i
$57$	−1.91846	−	7.11267i	−0.254106	−	0.942096i
$58$	−2.23607	−	6.88191i	−0.293610	−	0.903639i
$59$	−2.48990	−	0.809017i	−0.324157	−	0.105325i	0.142418	−	0.989807i	$-0.454512\pi$
$59$	−2.48990	−	0.809017i	−0.324157	−	0.105325i	−0.466575	+	0.884482i	$0.654512\pi$
$60$	−6.14677	+	4.00624i	−0.793545	+	0.517204i
$61$	−2.50000	+	3.44095i	−0.320092	+	0.440569i	−0.938495	−	0.345292i	$-0.887780\pi$
$61$	−2.50000	+	3.44095i	−0.320092	+	0.440569i	0.618403	+	0.785861i	$0.287780\pi$
$62$	−0.502029	+	1.54508i	−0.0637577	+	0.196226i
$63$	1.99411	+	0.879937i	0.251235	+	0.110862i
$64$	3.80902	−	2.76741i	0.476127	−	0.345927i
$65$	8.05748			0.999407
$66$		0			0
$67$	−8.32624			−1.01721			−0.508606	−	0.860999i	$-0.669839\pi$
$67$	−8.32624			−1.01721			−0.508606	+	0.860999i	$0.669839\pi$
$68$	3.44095	−	2.50000i	0.417277	−	0.303170i
$69$	3.05129	+	0.154847i	0.367333	+	0.0186414i
$70$	−1.11803	+	3.44095i	−0.133631	+	0.411273i
$71$	−6.06961	+	8.35410i	−0.720330	+	0.991449i	0.279183	+	0.960238i	$0.409937\pi$
$71$	−6.06961	+	8.35410i	−0.720330	+	0.991449i	−0.999513	+	0.0312115i	$0.990063\pi$
$72$	0.460226	+	2.13049i	0.0542381	+	0.251080i
$73$	−14.4721	−	4.70228i	−1.69384	−	0.550360i	−0.706321	−	0.707891i	$-0.749647\pi$
$73$	−14.4721	−	4.70228i	−1.69384	−	0.550360i	−0.987514	+	0.157531i	$0.949647\pi$
$74$	1.76336	+	5.42705i	0.204986	+	0.630882i
$75$	3.10059	−	0.836305i	0.358026	−	0.0965682i
$76$			6.88191i			0.789409i
$77$		0			0
$78$	−3.61803	+	9.47214i	−0.409662	+	1.07251i
$79$	6.28115	+	8.64527i	0.706685	+	0.972668i	0.999862	+	0.0166102i	$0.00528743\pi$
$79$	6.28115	+	8.64527i	0.706685	+	0.972668i	−0.293177	+	0.956058i	$0.594713\pi$
$80$	−11.4984	+	3.73607i	−1.28556	+	0.417705i
$81$	8.81553	+	1.81288i	0.979503	+	0.201431i
$82$	4.73607	+	3.44095i	0.523011	+	0.379990i
$83$	−11.7229	−	8.51722i	−1.28676	−	0.934886i	−0.287026	−	0.957923i	$-0.592667\pi$
$83$	−11.7229	−	8.51722i	−1.28676	−	0.934886i	−0.999735	+	0.0230363i	$0.992667\pi$
$84$	−1.58450	−	1.27877i	−0.172883	−	0.139525i
$85$	−6.54508	+	2.12663i	−0.709914	+	0.230665i
$86$	−1.81636	−	2.50000i	−0.195863	−	0.269582i
$87$	−6.15537	−	2.35114i	−0.659925	−	0.252069i
$88$		0			0
$89$			9.47214i			1.00404i	0.864855	+	0.502022i	$0.167410\pi$
$89$			9.47214i			1.00404i	−0.864855	+	0.502022i	$0.832590\pi$
$90$	−1.51240	+	14.8626i	−0.159420	+	1.56666i
$91$	0.690983	+	2.12663i	0.0724347	+	0.222931i
$92$	−2.71441	−	0.881966i	−0.282997	−	0.0919513i
$93$	0.807763	+	1.23935i	0.0837612	+	0.128515i
$94$	−8.19098	+	11.2739i	−0.844835	+	1.16282i
$95$	3.44095	−	10.5902i	0.353035	−	1.08653i
$96$	0.643548	−	12.6812i	0.0656819	−	1.29427i
$97$	5.35410	−	3.88998i	0.543627	−	0.394968i	−0.281803	−	0.959472i	$-0.590933\pi$
$97$	5.35410	−	3.88998i	0.543627	−	0.394968i	0.825430	+	0.564504i	$0.190933\pi$
$98$	12.3107			1.24357
$99$		0			0
$100$	−3.00000			−0.300000
$101$	−10.0984	+	7.33688i	−1.00482	+	0.730047i	−0.963117	−	0.269083i	$-0.913279\pi$
$101$	−10.0984	+	7.33688i	−1.00482	+	0.730047i	−0.0417064	+	0.999130i	$0.513279\pi$
$102$	0.438926	−	8.64912i	0.0434602	−	0.856391i
$103$	−2.09017	+	6.43288i	−0.205951	+	0.633851i	0.793722	+	0.608280i	$0.208140\pi$
$103$	−2.09017	+	6.43288i	−0.205951	+	0.633851i	−0.999673	+	0.0255706i	$0.991860\pi$
$104$	−1.31433	+	1.80902i	−0.128880	+	0.177389i
$105$	1.79892	+	2.76007i	0.175556	+	0.269356i
$106$	8.78115	+	2.85317i	0.852901	+	0.277124i
$107$	−0.0530006	−	0.163119i	−0.00512376	−	0.0157693i	0.948462	−	0.316891i	$-0.102639\pi$
$107$	−0.0530006	−	0.163119i	−0.00512376	−	0.0157693i	−0.953586	+	0.301122i	$0.902639\pi$
$108$	−7.51005	−	3.77970i	−0.722654	−	0.363702i
$109$			7.60845i			0.728758i	0.931251	+	0.364379i	$0.118719\pi$
$109$			7.60845i			0.728758i	−0.931251	+	0.364379i	$0.881281\pi$
$110$		0			0
$111$	4.85410	+	1.85410i	0.460731	+	0.175984i
$112$	−1.97214	−	2.71441i	−0.186349	−	0.256488i
$113$	−18.9681	+	6.16312i	−1.78437	+	0.579777i	−0.999219	−	0.0395244i	$-0.987416\pi$
$113$	−18.9681	+	6.16312i	−1.78437	+	0.579777i	−0.785153	+	0.619302i	$0.787416\pi$
$114$	10.9044	+	8.80037i	1.02129	+	0.824230i
$115$	3.73607	+	2.71441i	0.348390	+	0.253120i
$116$	4.97980	+	3.61803i	0.462363	+	0.335926i
$117$	4.64297	+	7.98073i	0.429243	+	0.737819i
$118$	4.73607	−	1.53884i	0.435990	−	0.141662i
$119$	−1.12257	−	1.54508i	−0.102906	−	0.141638i
$120$	−1.17557	+	3.07768i	−0.107314	+	0.280953i
$121$		0			0
$122$		−	8.09017i		−	0.732450i
$123$	5.14677	−	1.38821i	0.464069	−	0.125171i
$124$	−0.427051	−	1.31433i	−0.0383503	−	0.118030i
$125$	−7.83297	−	2.54508i	−0.700602	−	0.227639i
$126$	−4.05242	+	0.875402i	−0.361019	+	0.0779870i
$127$	7.76393	−	10.6861i	0.688938	−	0.948241i	−0.311060	−	0.950390i	$-0.600684\pi$
$127$	7.76393	−	10.6861i	0.688938	−	0.948241i	0.999998	+	0.00214903i	$0.000684058\pi$
$128$	1.76336	−	5.42705i	0.155860	−	0.479688i
$129$	−2.81027	−	0.142616i	−0.247431	−	0.0125566i
$130$	−12.3992	+	9.00854i	−1.08748	+	0.790101i
$131$	−4.08174			−0.356623			−0.178312	−	0.983974i	$-0.557064\pi$
$131$	−4.08174			−0.356623			−0.178312	+	0.983974i	$0.557064\pi$
$132$		0			0
$133$	3.09017			0.267952
$134$	12.8128	−	9.30902i	1.10685	−	0.804177i
$135$	9.66692	+	9.57138i	0.831996	+	0.823774i
$136$	0.590170	−	1.81636i	0.0506067	−	0.155751i
$137$	5.11855	−	7.04508i	0.437308	−	0.601902i	−0.532304	−	0.846554i	$-0.678673\pi$
$137$	5.11855	−	7.04508i	0.437308	−	0.601902i	0.969611	+	0.244651i	$0.0786735\pi$
$138$	−4.86858	+	3.17316i	−0.414441	+	0.270118i
$139$	1.64590	+	0.534785i	0.139603	+	0.0453598i	0.377985	−	0.925812i	$-0.376617\pi$
$139$	1.64590	+	0.534785i	0.139603	+	0.0453598i	−0.238382	+	0.971171i	$0.576617\pi$
$140$	−0.951057	−	2.92705i	−0.0803789	−	0.247381i
$141$	3.30455	+	12.2516i	0.278293	+	1.03177i
$142$		−	19.6417i		−	1.64829i
$143$		0			0
$144$	−10.3262	−	9.23607i	−0.860520	−	0.769672i
$145$	−5.85410	−	8.05748i	−0.486157	−	0.669137i
$146$	27.5276	−	8.94427i	2.27820	−	0.740233i
$147$	7.04029	−	8.72353i	0.580674	−	0.719504i
$148$	−3.92705	−	2.85317i	−0.322802	−	0.234529i
$149$	−0.138757	−	0.100813i	−0.0113674	−	0.00825893i	0.582087	−	0.813126i	$-0.302236\pi$
$149$	−0.138757	−	0.100813i	−0.0113674	−	0.00825893i	−0.593454	+	0.804868i	$0.702236\pi$
$150$	−3.83630	+	4.75351i	−0.313233	+	0.388122i
$151$	16.7082	−	5.42882i	1.35969	−	0.441791i	0.463753	−	0.885964i	$-0.346502\pi$
$151$	16.7082	−	5.42882i	1.35969	−	0.441791i	0.895941	+	0.444173i	$0.146502\pi$
$152$	1.81636	+	2.50000i	0.147326	+	0.202777i
$153$	−5.87785	−	5.25731i	−0.475196	−	0.425028i
$154$		0			0
$155$			2.23607i			0.179605i
$156$	−2.24617	−	8.32766i	−0.179838	−	0.666746i
$157$	−1.14590	−	3.52671i	−0.0914526	−	0.281462i	0.894860	−	0.446346i	$-0.147275\pi$
$157$	−1.14590	−	3.52671i	−0.0914526	−	0.281462i	−0.986313	+	0.164884i	$0.947275\pi$
$158$	−19.3314	−	6.28115i	−1.53792	−	0.499702i
$159$	7.04358	−	4.59075i	0.558592	−	0.364070i
$160$	11.2812	−	15.5272i	0.891853	−	1.22753i
$161$	−0.396027	+	1.21885i	−0.0312113	+	0.0960586i
$162$	−15.5926	+	7.06633i	−1.22507	+	0.555183i
$163$	10.0172	−	7.27794i	0.784609	−	0.570052i	−0.121750	−	0.992561i	$-0.538850\pi$
$163$	10.0172	−	7.27794i	0.784609	−	0.570052i	0.906359	+	0.422509i	$0.138850\pi$
$164$	−4.97980			−0.388857
$165$		0			0
$166$	27.5623			2.13925
$167$	−0.0857567	+	0.0623059i	−0.00663605	+	0.00482138i	−0.591098	−	0.806600i	$-0.701305\pi$
$167$	−0.0857567	+	0.0623059i	−0.00663605	+	0.00482138i	0.584462	+	0.811421i	$0.301305\pi$
$168$	−0.913112	−	0.0463387i	−0.0704481	−	0.00357511i
$169$	1.09017	−	3.35520i	0.0838592	−	0.258092i
$170$	7.69421	−	10.5902i	0.590119	−	0.812229i
$171$	12.4721	−	2.69421i	0.953764	−	0.206031i
$172$	2.50000	+	0.812299i	0.190623	+	0.0619372i
$173$	6.84915	+	21.0795i	0.520731	+	1.60265i	0.772605	+	0.634887i	$0.218953\pi$
$173$	6.84915	+	21.0795i	0.520731	+	1.60265i	−0.251874	+	0.967760i	$0.581047\pi$
$174$	12.1008	−	3.26388i	0.917359	−	0.247434i
$175$			1.34708i			0.101830i
$176$		0			0
$177$	1.61803	−	4.23607i	0.121619	−	0.318402i
$178$	−10.5902	−	14.5761i	−0.793767	−	1.09253i
$179$	−3.75123	+	1.21885i	−0.280380	+	0.0911009i	−0.445831	−	0.895117i	$-0.647092\pi$
$179$	−3.75123	+	1.21885i	−0.280380	+	0.0911009i	0.165452	+	0.986218i	$0.447092\pi$
$180$	−6.39050	−	10.9845i	−0.476320	−	0.818739i
$181$	−9.89919	−	7.19218i	−0.735801	−	0.534591i	0.155592	−	0.987821i	$-0.450271\pi$
$181$	−9.89919	−	7.19218i	−0.735801	−	0.534591i	−0.891393	+	0.453231i	$0.850271\pi$
$182$	−3.44095	−	2.50000i	−0.255061	−	0.185312i
$183$	−5.73279	−	4.62663i	−0.423780	−	0.342010i
$184$	−1.21885	+	0.396027i	−0.0898546	+	0.0291955i
$185$	4.61653	+	6.35410i	0.339414	+	0.467163i
$186$	−2.62866	−	1.00406i	−0.192742	−	0.0736210i
$187$		0			0
$188$		−	11.8541i		−	0.864549i
$189$	−1.69719	+	3.37222i	−0.123453	+	0.245293i
$190$	6.54508	+	20.1437i	0.474830	+	1.46138i
$191$	18.7966	+	6.10739i	1.36008	+	0.441915i	0.896068	−	0.443916i	$-0.146411\pi$
$191$	18.7966	+	6.10739i	1.36008	+	0.441915i	0.464007	+	0.885831i	$0.346411\pi$
$192$	4.45276	+	6.83187i	0.321351	+	0.493048i
$193$	−11.8713	+	16.3395i	−0.854517	+	1.17614i	0.128333	+	0.991731i	$0.459037\pi$
$193$	−11.8713	+	16.3395i	−0.854517	+	1.17614i	−0.982849	+	0.184410i	$0.940963\pi$
$194$	−3.88998	+	11.9721i	−0.279284	+	0.859549i
$195$	−0.707328	+	13.9380i	−0.0506528	+	0.998123i
$196$	−8.47214	+	6.15537i	−0.605153	+	0.439669i
$197$	−15.8374			−1.12837			−0.564186	−	0.825648i	$-0.690810\pi$
$197$	−15.8374			−1.12837			−0.564186	+	0.825648i	$0.690810\pi$
$198$		0			0
$199$	−2.23607			−0.158511			−0.0792553	−	0.996854i	$-0.525254\pi$
$199$	−2.23607			−0.158511			−0.0792553	+	0.996854i	$0.525254\pi$
$200$	−1.08981	+	0.791796i	−0.0770615	+	0.0559884i
$201$	0.730921	−	14.4029i	0.0515552	−	1.01590i
$202$	7.33688	−	22.5806i	0.516221	−	1.58877i
$203$	1.62460	−	2.23607i	0.114024	−	0.156941i
$204$	4.02250	+	6.17171i	0.281631	+	0.432106i
$205$	7.66312	+	2.48990i	0.535215	+	0.173902i
$206$	−3.97574	−	12.2361i	−0.277003	−	0.852527i
$207$	−0.535717	+	5.26461i	−0.0372349	+	0.365916i
$208$		−	14.2128i		−	0.985484i
$209$		0			0
$210$	−5.85410	−	2.23607i	−0.403971	−	0.154303i
$211$	3.98278	+	5.48183i	0.274186	+	0.377384i	0.923797	−	0.382882i	$-0.125068\pi$
$211$	3.98278	+	5.48183i	0.274186	+	0.377384i	−0.649611	+	0.760266i	$0.725068\pi$
$212$	−7.46969	+	2.42705i	−0.513021	+	0.166691i
$213$	−13.9183	−	11.2327i	−0.953667	−	0.769654i
$214$	0.263932	+	0.191758i	0.0180420	+	0.0131083i
$215$	−3.44095	−	2.50000i	−0.234671	−	0.170499i
$216$	−3.72577	+	0.609085i	−0.253506	+	0.0414430i
$217$	−0.590170	+	0.191758i	−0.0400633	+	0.0130174i
$218$	−8.50651	−	11.7082i	−0.576133	−	0.792980i
$219$	9.40456	−	24.6215i	0.635502	−	1.66376i
$220$		0			0
$221$		−	8.09017i		−	0.544204i
$222$	−9.54264	+	2.57388i	−0.640460	+	0.172748i
$223$	1.92705	+	5.93085i	0.129045	+	0.397159i	0.994616	−	0.103626i	$-0.0330446\pi$
$223$	1.92705	+	5.93085i	0.129045	+	0.397159i	−0.865571	+	0.500785i	$0.833045\pi$
$224$	5.06555	+	1.64590i	0.338457	+	0.109971i
$225$	1.17447	+	5.43690i	0.0782983	+	0.362460i
$226$	22.2984	−	30.6911i	1.48327	−	2.04154i
$227$	−1.95511	+	6.01722i	−0.129765	+	0.399377i	−0.994739	−	0.102440i	$-0.967335\pi$
$227$	−1.95511	+	6.01722i	−0.129765	+	0.399377i	0.864974	+	0.501817i	$0.167335\pi$
$228$	−11.9045	−	0.604130i	−0.788395	−	0.0400095i
$229$	−20.3262	+	14.7679i	−1.34320	+	0.975889i	−0.343876	+	0.939015i	$0.611740\pi$
$229$	−20.3262	+	14.7679i	−1.34320	+	0.975889i	−0.999320	+	0.0368735i	$0.988260\pi$
$230$	−8.78402			−0.579201
$231$		0			0
$232$	2.76393			0.181461
$233$	−5.79210	+	4.20820i	−0.379453	+	0.275689i	−0.761120	−	0.648611i	$-0.775350\pi$
$233$	−5.79210	+	4.20820i	−0.379453	+	0.275689i	0.381667	+	0.924300i	$0.375350\pi$
$234$	−16.0675	−	7.09008i	−1.05037	−	0.463493i
$235$	−5.92705	+	18.2416i	−0.386638	+	1.18995i
$236$	−2.48990	+	3.42705i	−0.162079	+	0.223082i
$237$	−15.5062	+	10.1064i	−1.00724	+	0.656479i
$238$	3.45492	+	1.12257i	0.223949	+	0.0727654i
$239$	−7.97172	−	24.5344i	−0.515648	−	1.58700i	−0.782100	−	0.623153i	$-0.785851\pi$
$239$	−7.97172	−	24.5344i	−0.515648	−	1.58700i	0.266452	−	0.963848i	$-0.414149\pi$
$240$	−5.45335	−	20.2182i	−0.352012	−	1.30508i
$241$			19.5762i			1.26101i	0.776185	+	0.630506i	$0.217152\pi$
$241$			19.5762i			1.26101i	−0.776185	+	0.630506i	$0.782848\pi$
$242$		0			0
$243$	−3.90983	+	15.0902i	−0.250816	+	0.968035i
$244$	4.04508	+	5.56758i	0.258960	+	0.356428i
$245$	16.1150	−	5.23607i	1.02955	−	0.334520i
$246$	−6.36801	+	7.89050i	−0.406009	+	0.503080i
$247$	10.5902	+	7.69421i	0.673836	+	0.489571i
$248$	−0.502029	−	0.364745i	−0.0318788	−	0.0231613i
$249$	15.7624	−	19.5310i	0.998902	−	1.23772i
$250$	14.8992	−	4.84104i	0.942307	−	0.306174i
$251$	2.74717	+	3.78115i	0.173400	+	0.238664i	0.886868	−	0.462024i	$-0.152877\pi$
$251$	2.74717	+	3.78115i	0.173400	+	0.238664i	−0.713468	+	0.700688i	$0.752877\pi$
$252$	2.35114	−	2.62866i	0.148108	−	0.165590i
$253$		0			0
$254$			25.1246i			1.57646i
$255$	−3.10413	−	11.5085i	−0.194388	−	0.720693i
$256$	6.26393	+	19.2784i	0.391496	+	1.20490i
$257$	10.7189	+	3.48278i	0.668626	+	0.217250i	0.623609	−	0.781736i	$-0.285666\pi$
$257$	10.7189	+	3.48278i	0.668626	+	0.217250i	0.0450171	+	0.998986i	$0.485666\pi$
$258$	4.48401	−	2.92252i	0.279162	−	0.181948i
$259$	−1.28115	+	1.76336i	−0.0796070	+	0.109570i
$260$	4.02874	−	12.3992i	0.249852	−	0.768965i
$261$	4.60741	−	10.4413i	0.285192	−	0.646301i
$262$	6.28115	−	4.56352i	0.388051	−	0.281936i
$263$	23.2744			1.43516			0.717580	−	0.696476i	$-0.245250\pi$
$263$	23.2744			1.43516			0.717580	+	0.696476i	$0.245250\pi$
$264$		0			0
$265$	12.7082			0.780659
$266$	−4.75528	+	3.45492i	−0.291565	+	0.211834i
$267$	−16.3851	−	0.831514i	−1.00275	−	0.0508878i
$268$	−4.16312	+	12.8128i	−0.254303	+	0.782664i
$269$	−13.6578	+	18.7984i	−0.832732	+	1.14616i	0.154677	+	0.987965i	$0.450566\pi$
$269$	−13.6578	+	18.7984i	−0.832732	+	1.14616i	−0.987408	+	0.158192i	$0.949434\pi$
$270$	−25.5770	−	3.92090i	−1.55657	−	0.238618i
$271$	22.4615	+	7.29818i	1.36444	+	0.443333i	0.897522	−	0.440969i	$-0.145365\pi$
$271$	22.4615	+	7.29818i	1.36444	+	0.443333i	0.466916	+	0.884302i	$0.345365\pi$
$272$	3.75123	+	11.5451i	0.227451	+	0.700024i
$273$	−3.73935	+	1.00859i	−0.226316	+	0.0610428i
$274$			16.5640i			1.00067i
$275$		0			0
$276$	1.76393	−	4.61803i	0.106176	−	0.277973i
$277$	12.0729	+	16.6170i	0.725393	+	0.998418i	0.999327	+	0.0366697i	$0.0116749\pi$
$277$	12.0729	+	16.6170i	0.725393	+	0.998418i	−0.273934	+	0.961748i	$0.588325\pi$
$278$	−3.13068	+	1.01722i	−0.187766	+	0.0610089i
$279$	−2.21477	+	1.28849i	−0.132595	+	0.0771400i
$280$	−1.11803	−	0.812299i	−0.0668153	−	0.0485442i
$281$	13.3148	+	9.67376i	0.794294	+	0.577088i	0.909235	−	0.416284i	$-0.136668\pi$
$281$	13.3148	+	9.67376i	0.794294	+	0.577088i	−0.114941	+	0.993372i	$0.536668\pi$
$282$	−18.7829	−	15.1586i	−1.11850	−	0.902684i
$283$	7.56231	−	2.45714i	0.449532	−	0.146062i	−0.0754970	−	0.997146i	$-0.524054\pi$
$283$	7.56231	−	2.45714i	0.449532	−	0.146062i	0.525029	+	0.851084i	$0.324054\pi$
$284$	9.82084	+	13.5172i	0.582759	+	0.802099i
$285$	18.0171	+	6.88191i	1.06724	+	0.407649i
$286$		0			0
$287$			2.23607i			0.131991i
$288$	21.8798	+	2.22645i	1.28928	+	0.131195i
$289$	−3.11803	−	9.59632i	−0.183414	−	0.564490i
$290$	18.0171	+	5.85410i	1.05800	+	0.343765i
$291$	6.25898	+	9.60314i	0.366908	+	0.562946i
$292$	−14.4721	+	19.9192i	−0.846918	+	1.16568i
$293$	3.02468	−	9.30902i	0.176704	−	0.543839i	−0.823003	−	0.568037i	$-0.807703\pi$
$293$	3.02468	−	9.30902i	0.176704	−	0.543839i	0.999707	+	0.0241980i	$0.00770321\pi$
$294$	−1.08070	+	21.2954i	−0.0630278	+	1.24197i
$295$	5.54508	−	4.02874i	0.322847	−	0.234562i
$296$	−2.17963			−0.126688
$297$		0			0
$298$	0.326238			0.0188985
$299$	−4.39201	+	3.19098i	−0.253997	+	0.184539i
$300$	0.263356	−	5.18947i	0.0152049	−	0.299614i
$301$	0.364745	−	1.12257i	0.0210236	−	0.0647039i
$302$	−19.6417	+	27.0344i	−1.13025	+	1.55566i
$303$	−11.8050	−	18.1124i	−0.678181	−	1.04053i
$304$	−18.6803	−	6.06961i	−1.07139	−	0.348116i
$305$	−3.44095	−	10.5902i	−0.197028	−	0.606391i
$306$	14.9229	+	1.51853i	0.853088	+	0.0868086i
$307$		−	5.87785i		−	0.335467i	−0.985832	−	0.167733i	$-0.946355\pi$
$307$		−	5.87785i		−	0.335467i	0.985832	−	0.167733i	$-0.0536448\pi$
$308$		0			0
$309$	−10.9443	−	4.18034i	−0.622598	−	0.237811i
$310$	−2.50000	−	3.44095i	−0.141990	−	0.195433i
$311$	−4.75528	+	1.54508i	−0.269647	+	0.0876137i	−0.440720	−	0.897645i	$-0.645277\pi$
$311$	−4.75528	+	1.54508i	−0.269647	+	0.0876137i	0.171072	+	0.985258i	$0.445277\pi$
$312$	−3.01390	−	2.43236i	−0.170629	−	0.137705i
$313$	−8.89919	−	6.46564i	−0.503012	−	0.365459i	0.307154	−	0.951660i	$-0.400623\pi$
$313$	−8.89919	−	6.46564i	−0.503012	−	0.365459i	−0.810166	+	0.586200i	$0.800623\pi$
$314$	5.70634	+	4.14590i	0.322027	+	0.233967i
$315$	−4.93236	+	2.86951i	−0.277907	+	0.161679i
$316$	16.4443	−	5.34307i	0.925063	−	0.300571i
$317$	0.138757	+	0.190983i	0.00779339	+	0.0107267i	0.812896	−	0.582409i	$-0.197890\pi$
$317$	0.138757	+	0.190983i	0.00779339	+	0.0107267i	−0.805103	+	0.593136i	$0.797890\pi$
$318$	−5.70634	+	14.9394i	−0.319996	+	0.837759i
$319$		0			0
$320$			12.3262i			0.689058i
$321$	0.286820	−	0.0773622i	0.0160087	−	0.00431794i
$322$	−0.753289	−	2.31838i	−0.0419791	−	0.129199i
$323$	−10.6331	−	3.45492i	−0.591643	−	0.192237i
$324$	7.19749	−	12.6593i	0.399861	−	0.703292i
$325$	−3.35410	+	4.61653i	−0.186052	+	0.256079i
$326$	−7.27794	+	22.3992i	−0.403088	+	1.24058i
$327$	−13.1613	−	0.667910i	−0.727821	−	0.0369355i
$328$	−1.80902	+	1.31433i	−0.0998863	+	0.0725716i
$329$	−5.32282			−0.293457
$330$		0			0
$331$	−22.8885			−1.25807			−0.629034	−	0.777378i	$-0.716549\pi$
$331$	−22.8885			−1.25807			−0.629034	+	0.777378i	$0.716549\pi$
$332$	−18.9681	+	13.7812i	−1.04101	+	0.756339i
$333$	−3.63339	+	8.23398i	−0.199109	+	0.451219i
$334$	0.0623059	−	0.191758i	0.00340923	−	0.0104925i
$335$	12.8128	−	17.6353i	0.700036	−	0.963517i
$336$	4.86858	−	3.17316i	0.265603	−	0.173110i
$337$	−9.79837	−	3.18368i	−0.533751	−	0.173426i	0.0297256	−	0.999558i	$-0.490537\pi$
$337$	−9.79837	−	3.18368i	−0.533751	−	0.173426i	−0.563477	+	0.826132i	$0.690537\pi$
$338$	2.07363	+	6.38197i	0.112790	+	0.347133i
$339$	−8.99599	−	33.3526i	−0.488595	−	1.81146i
$340$			11.1352i			0.603889i
$341$		0			0
$342$	−16.1803	+	18.0902i	−0.874933	+	0.978204i
$343$	5.75329	+	7.91872i	0.310648	+	0.427571i
$344$	1.12257	−	0.364745i	0.0605249	−	0.0196657i
$345$	−5.02343	+	6.22446i	−0.270452	+	0.335114i
$346$	−34.1074	−	24.7805i	−1.83362	−	1.33221i
$347$	24.8990	+	18.0902i	1.33665	+	0.971131i	0.999560	+	0.0296578i	$0.00944176\pi$
$347$	24.8990	+	18.0902i	1.33665	+	0.971131i	0.337087	+	0.941473i	$0.390558\pi$
$348$	−6.69572	+	8.29657i	−0.358928	+	0.444743i
$349$	−15.4894	+	5.03280i	−0.829126	+	0.269399i	−0.692677	−	0.721248i	$-0.743569\pi$
$349$	−15.4894	+	5.03280i	−0.829126	+	0.269399i	−0.136449	+	0.990647i	$0.543569\pi$
$350$	−1.50609	−	2.07295i	−0.0805037	−	0.110804i
$351$	−14.2128	+	7.33094i	−0.758626	+	0.391297i
$352$		0			0
$353$		−	15.5967i		−	0.830131i	−0.909792	−	0.415066i	$-0.863759\pi$
$353$		−	15.5967i		−	0.830131i	0.909792	−	0.415066i	$-0.136241\pi$
$354$	2.24617	+	8.32766i	0.119383	+	0.442610i
$355$	−8.35410	−	25.7113i	−0.443390	−	1.36461i
$356$	14.5761	+	4.73607i	0.772533	+	0.251011i
$357$	2.77127	−	1.80621i	0.146671	−	0.0955950i
$358$	4.40983	−	6.06961i	0.233067	−	0.320789i
$359$	−7.71445	+	23.7426i	−0.407153	+	1.25309i	0.511931	+	0.859027i	$0.328931\pi$
$359$	−7.71445	+	23.7426i	−0.407153	+	1.25309i	−0.919084	+	0.394062i	$0.871069\pi$
$360$	−5.22066	−	2.30371i	−0.275153	−	0.121416i
$361$	−0.736068	+	0.534785i	−0.0387404	+	0.0281466i
$362$	23.2744			1.22327
$363$		0			0
$364$	3.61803			0.189637
$365$	32.2299	−	23.4164i	1.68699	−	1.22567i
$366$	13.9946	+	0.710198i	0.731508	+	0.0371226i
$367$	−7.10081	+	21.8541i	−0.370659	+	1.14077i	0.575701	+	0.817660i	$0.304729\pi$
$367$	−7.10081	+	21.8541i	−0.370659	+	1.14077i	−0.946361	+	0.323112i	$0.895271\pi$
$368$	4.78804	−	6.59017i	0.249594	−	0.343536i
$369$	1.94955	+	9.02488i	0.101489	+	0.469817i
$370$	−14.2082	−	4.61653i	−0.738649	−	0.240002i
$371$	1.08981	+	3.35410i	0.0565803	+	0.174136i
$372$	2.31105	−	0.623345i	0.119822	−	0.0323189i
$373$			19.5357i			1.01152i	0.862675	+	0.505759i	$0.168788\pi$
$373$			19.5357i			1.01152i	−0.862675	+	0.505759i	$0.831212\pi$
$374$		0			0
$375$	5.09017	−	13.3262i	0.262855	−	0.688164i
$376$	−3.12868	−	4.30625i	−0.161349	−	0.222078i
$377$	11.1352	−	3.61803i	0.573490	−	0.186338i
$378$	−1.15855	−	7.08683i	−0.0595893	−	0.364507i
$379$	26.6074	+	19.3314i	1.36673	+	0.992987i	0.997985	+	0.0634569i	$0.0202125\pi$
$379$	26.6074	+	19.3314i	1.36673	+	0.992987i	0.368745	+	0.929530i	$0.379787\pi$
$380$	−14.5761	−	10.5902i	−0.747739	−	0.543264i
$381$	17.8036	+	14.3683i	0.912105	+	0.736112i
$382$	−35.7533	+	11.6169i	−1.82930	+	0.594375i
$383$	−8.47375	−	11.6631i	−0.432988	−	0.595958i	0.535647	−	0.844442i	$-0.320068\pi$
$383$	−8.47375	−	11.6631i	−0.432988	−	0.595958i	−0.968636	+	0.248484i	$0.920068\pi$
$384$	9.23305	+	3.52671i	0.471172	+	0.179972i
$385$		0			0
$386$		−	38.4164i		−	1.95534i
$387$	0.493401	−	4.84876i	0.0250810	−	0.246476i
$388$	−3.30902	−	10.1841i	−0.167990	−	0.517020i
$389$	−9.14729	−	2.97214i	−0.463786	−	0.150693i	0.0677974	−	0.997699i	$-0.478403\pi$
$389$	−9.14729	−	2.97214i	−0.463786	−	0.150693i	−0.531584	+	0.847006i	$0.678403\pi$
$390$	−14.4947	−	22.2392i	−0.733969	−	1.12613i
$391$	2.72542	−	3.75123i	0.137831	−	0.189708i
$392$	−1.45309	+	4.47214i	−0.0733919	+	0.225877i
$393$	0.358317	−	7.06070i	0.0180747	−	0.356165i
$394$	24.3713	−	17.7068i	1.22781	−	0.892056i
$395$	−27.9767			−1.40766
$396$		0			0
$397$	−23.0000			−1.15434			−0.577168	−	0.816625i	$-0.695842\pi$
$397$	−23.0000			−1.15434			−0.577168	+	0.816625i	$0.695842\pi$
$398$	3.44095	−	2.50000i	0.172479	−	0.125314i
$399$	−0.271271	+	5.34545i	−0.0135806	+	0.267607i
$400$	2.64590	−	8.14324i	0.132295	−	0.407162i
$401$	12.4292	−	17.1074i	0.620687	−	0.854302i	−0.376716	−	0.926329i	$-0.622947\pi$
$401$	12.4292	−	17.1074i	0.620687	−	0.854302i	0.997403	+	0.0720266i	$0.0229466\pi$
$402$	14.9782	+	22.9810i	0.747045	+	1.14619i
$403$	−2.50000	−	0.812299i	−0.124534	−	0.0404635i
$404$	6.24112	+	19.2082i	0.310508	+	0.955644i
$405$	−17.4054	+	15.8819i	−0.864883	+	0.789176i
$406$			5.25731i			0.260916i
$407$		0			0
$408$	3.09017	+	1.18034i	0.152986	+	0.0584355i
$409$	−20.1246	−	27.6992i	−0.995098	−	1.36963i	−0.928285	−	0.371869i	$-0.878717\pi$
$409$	−20.1246	−	27.6992i	−0.995098	−	1.36963i	−0.0668129	−	0.997766i	$-0.521283\pi$
$410$	−14.5761	+	4.73607i	−0.719863	+	0.233898i
$411$	11.7374	+	9.47266i	0.578965	+	0.467252i
$412$	8.85410	+	6.43288i	0.436210	+	0.316925i
$413$	1.53884	+	1.11803i	0.0757215	+	0.0550149i
$414$	−5.06163	−	8.70035i	−0.248765	−	0.427599i
$415$	36.0795	−	11.7229i	1.77107	−	0.575457i
$416$	13.2618	+	18.2533i	0.650213	+	0.894941i
$417$	−1.06957	+	2.80017i	−0.0523770	+	0.137125i
$418$		0			0
$419$			5.85410i			0.285992i	0.989723	+	0.142996i	$0.0456735\pi$
$419$			5.85410i			0.285992i	−0.989723	+	0.142996i	$0.954326\pi$
$420$	5.14677	−	1.38821i	0.251137	−	0.0677377i
$421$	7.98936	+	24.5887i	0.389377	+	1.19838i	0.933255	+	0.359216i	$0.116956\pi$
$421$	7.98936	+	24.5887i	0.389377	+	1.19838i	−0.543877	+	0.839165i	$0.683044\pi$
$422$	−12.2577	−	3.98278i	−0.596697	−	0.193879i
$423$	−21.4832	+	4.64078i	−1.04455	+	0.225642i
$424$	−2.07295	+	2.85317i	−0.100671	+	0.138562i
$425$	1.50609	−	4.63525i	0.0730559	−	0.224843i
$426$	33.9767	+	1.72425i	1.64617	+	0.0835401i
$427$	2.50000	−	1.81636i	0.120983	−	0.0878996i
$428$	−0.277515			−0.0134142
$429$		0			0
$430$	8.09017			0.390143
$431$	18.2416	−	13.2533i	0.878666	−	0.638388i	−0.0542320	−	0.998528i	$-0.517271\pi$
$431$	18.2416	−	13.2533i	0.878666	−	0.638388i	0.932898	+	0.360140i	$0.117271\pi$
$432$	16.8833	−	17.0518i	0.812297	−	0.820405i
$433$	−1.85410	+	5.70634i	−0.0891025	+	0.274229i	−0.985672	−	0.168674i	$-0.946051\pi$
$433$	−1.85410	+	5.70634i	−0.0891025	+	0.274229i	0.896569	+	0.442903i	$0.146051\pi$
$434$	0.693786	−	0.954915i	0.0333028	−	0.0458374i
$435$	14.4519	−	9.41924i	0.692917	−	0.451618i
$436$	11.7082	+	3.80423i	0.560721	+	0.182189i
$437$	2.31838	+	7.13525i	0.110903	+	0.341326i
$438$	13.0555	+	48.4032i	0.623816	+	2.31279i
$439$		−	25.3480i		−	1.20979i	−0.796304	−	0.604897i	$-0.793214\pi$
$439$		−	25.3480i		−	1.20979i	0.796304	−	0.604897i	$-0.206786\pi$
$440$		0			0
$441$	14.4721	+	12.9443i	0.689149	+	0.616394i
$442$	9.04508	+	12.4495i	0.430231	+	0.592162i
$443$	9.95959	−	3.23607i	0.473195	−	0.153750i	−0.0627048	−	0.998032i	$-0.519973\pi$
$443$	9.95959	−	3.23607i	0.473195	−	0.153750i	0.535899	+	0.844282i	$0.319973\pi$
$444$	5.28022	−	6.54264i	0.250588	−	0.310500i
$445$	−20.0623	−	14.5761i	−0.951045	−	0.690974i
$446$	−9.59632	−	6.97214i	−0.454399	−	0.330140i
$447$	0.186570	−	0.231176i	0.00882445	−	0.0109342i
$448$	−3.25329	+	1.05706i	−0.153703	+	0.0499413i
$449$	4.63677	+	6.38197i	0.218823	+	0.301184i	0.904289	−	0.426921i	$-0.140402\pi$
$449$	4.63677	+	6.38197i	0.218823	+	0.301184i	−0.685466	+	0.728104i	$0.740402\pi$
$450$	−7.88597	−	7.05342i	−0.371748	−	0.332502i
$451$		0			0
$452$			32.2705i			1.51788i
$453$	7.92418	+	29.3788i	0.372311	+	1.38034i
$454$	−3.71885	−	11.4454i	−0.174534	−	0.537161i
$455$	−5.56758	−	1.80902i	−0.261012	−	0.0848080i
$456$	−4.48401	+	2.92252i	−0.209983	+	0.136859i
$457$	6.34346	−	8.73102i	0.296734	−	0.408420i	−0.634453	−	0.772962i	$-0.718774\pi$
$457$	6.34346	−	8.73102i	0.296734	−	0.408420i	0.931187	+	0.364542i	$0.118774\pi$
$458$	14.7679	−	45.4508i	0.690058	−	2.12378i
$459$	9.61022	−	9.70614i	0.448566	−	0.453044i
$460$	6.04508	−	4.39201i	0.281854	−	0.204779i
$461$	26.8666			1.25130			0.625651	−	0.780103i	$-0.284833\pi$
$461$	26.8666			1.25130			0.625651	+	0.780103i	$0.284833\pi$
$462$		0			0
$463$	−0.270510			−0.0125717			−0.00628583	−	0.999980i	$-0.502001\pi$
$463$	−0.270510			−0.0125717			−0.00628583	+	0.999980i	$0.502001\pi$
$464$	−14.2128	+	10.3262i	−0.659815	+	0.479384i
$465$	−3.86801	−	0.196294i	−0.179374	−	0.00910291i
$466$	4.20820	−	12.9515i	0.194941	−	0.599968i
$467$	13.9026	−	19.1353i	0.643335	−	0.885474i	−0.355453	−	0.934694i	$-0.615674\pi$
$467$	13.9026	−	19.1353i	0.643335	−	0.885474i	0.998788	+	0.0492200i	$0.0156735\pi$
$468$	14.6026	−	3.15443i	0.675004	−	0.145814i
$469$	5.75329	+	1.86936i	0.265662	+	0.0863189i
$470$	−11.2739	−	34.6976i	−0.520027	−	1.60048i
$471$	6.20119	−	1.67261i	0.285736	−	0.0770698i
$472$			1.90211i			0.0875518i
$473$		0			0
$474$	12.5623	−	32.8885i	0.577006	−	1.51062i
$475$	4.63525	+	6.37988i	0.212680	+	0.292729i
$476$	−2.93893	+	0.954915i	−0.134705	+	0.0437685i
$477$	7.32286	+	12.5872i	0.335291	+	0.576326i
$478$	39.6976	+	28.8420i	1.81572	+	1.31920i
$479$	−18.5191	−	13.4549i	−0.846159	−	0.614771i	0.0779250	−	0.996959i	$-0.475171\pi$
$479$	−18.5191	−	13.4549i	−0.846159	−	0.614771i	−0.924084	+	0.382188i	$0.875171\pi$
$480$	25.8690	+	20.8775i	1.18075	+	0.952922i
$481$	−8.78115	+	2.85317i	−0.400386	+	0.130093i
$482$	−21.8868	−	30.1246i	−0.996917	−	1.37214i
$483$	−2.07363	−	0.792055i	−0.0943533	−	0.0360397i
$484$		0			0
$485$			17.3262i			0.786744i
$486$	−10.8547	−	27.5927i	−0.492380	−	1.25163i
$487$	−2.30902	−	7.10642i	−0.104632	−	0.322023i	0.885012	−	0.465568i	$-0.154150\pi$
$487$	−2.30902	−	7.10642i	−0.104632	−	0.322023i	−0.989644	+	0.143545i	$0.954150\pi$
$488$	2.93893	+	0.954915i	0.133039	+	0.0432270i
$489$	11.7102	+	17.9669i	0.529553	+	0.812493i
$490$	−18.9443	+	26.0746i	−0.855815	+	1.17793i
$491$	8.24924	−	25.3885i	0.372283	−	1.14577i	−0.573011	−	0.819548i	$-0.694225\pi$
$491$	8.24924	−	25.3885i	0.372283	−	1.14577i	0.945294	−	0.326221i	$-0.105775\pi$
$492$	0.437153	−	8.61418i	0.0197084	−	0.388357i
$493$	−8.09017	+	5.87785i	−0.364363	+	0.264725i
$494$	−24.8990			−1.12026
$495$		0			0
$496$	3.94427			0.177103
$497$	6.06961	−	4.40983i	0.272259	−	0.197808i
$498$	−2.41956	+	47.6780i	−0.108423	+	2.13650i
$499$	3.39261	−	10.4414i	0.151874	−	0.467420i	−0.845957	−	0.533252i	$-0.820970\pi$
$499$	3.39261	−	10.4414i	0.151874	−	0.467420i	0.997831	+	0.0658313i	$0.0209699\pi$
$500$	−7.83297	+	10.7812i	−0.350301	+	0.482148i
$501$	−0.100250	−	0.153814i	−0.00447884	−	0.00687189i
$502$	−8.45492	−	2.74717i	−0.377361	−	0.122612i
$503$	1.62460	+	5.00000i	0.0724373	+	0.222939i	0.980720	−	0.195418i	$-0.0626062\pi$
$503$	1.62460	+	5.00000i	0.0724373	+	0.222939i	−0.908283	+	0.418357i	$0.862606\pi$
$504$	0.160316	−	1.57546i	0.00714102	−	0.0701764i
$505$		−	32.6789i		−	1.45419i
$506$		0			0
$507$	5.70820	+	2.18034i	0.253510	+	0.0968323i
$508$	−12.5623	−	17.2905i	−0.557362	−	0.767143i
$509$	−0.257270	+	0.0835921i	−0.0114033	+	0.00370516i	−0.314713	−	0.949187i	$-0.601908\pi$
$509$	−0.257270	+	0.0835921i	−0.0114033	+	0.00370516i	0.303310	+	0.952892i	$0.401908\pi$
$510$	17.6437	+	14.2393i	0.781276	+	0.630527i
$511$	8.94427	+	6.49839i	0.395671	+	0.287472i
$512$	−21.9601	−	15.9549i	−0.970507	−	0.705114i
$513$	3.56564	+	21.8110i	0.157427	+	0.962980i
$514$	−20.3885	+	6.62464i	−0.899300	+	0.292200i
$515$	−10.4086	−	14.3262i	−0.458659	−	0.631289i
$516$	−1.62460	+	4.25325i	−0.0715190	+	0.187239i
$517$		0			0
$518$		−	4.14590i		−	0.182160i
$519$	−37.0651	+	9.99736i	−1.62698	+	0.438836i
$520$	−1.80902	−	5.56758i	−0.0793306	−	0.244155i
$521$	−19.2986	−	6.27051i	−0.845489	−	0.274716i	−0.145934	−	0.989294i	$-0.546619\pi$
$521$	−19.2986	−	6.27051i	−0.845489	−	0.274716i	−0.699555	+	0.714578i	$0.746619\pi$
$522$	4.58366	+	21.2188i	0.200621	+	0.928720i
$523$	−1.87132	+	2.57565i	−0.0818272	+	0.112626i	−0.847968	−	0.530047i	$-0.822174\pi$
$523$	−1.87132	+	2.57565i	−0.0818272	+	0.112626i	0.766141	+	0.642672i	$0.222174\pi$
$524$	−2.04087	+	6.28115i	−0.0891558	+	0.274393i
$525$	−2.33022	−	0.118254i	−0.101699	−	0.00516103i
$526$	−35.8156	+	26.0216i	−1.56163	+	1.13459i
$527$	2.24514			0.0977998
$528$		0			0
$529$	19.8885			0.864719
$530$	−19.5559	+	14.2082i	−0.849455	+	0.617165i
$531$	7.18562	+	3.17078i	0.311829	+	0.137600i
$532$	1.54508	−	4.75528i	0.0669879	−	0.206168i
$533$	−5.56758	+	7.66312i	−0.241159	+	0.331927i
$534$	26.1438	−	17.0396i	1.13135	−	0.737374i
$535$	0.427051	+	0.138757i	0.0184630	+	0.00599900i
$536$	1.86936	+	5.75329i	0.0807439	+	0.248504i
$537$	−1.77909	−	6.59596i	−0.0767734	−	0.284637i
$538$		−	44.1976i		−	1.90550i
$539$		0			0
$540$	19.5623	−	10.0902i	0.841828	−	0.434212i
$541$	14.5344	+	20.0049i	0.624884	+	0.860080i	0.997697	−	0.0678270i	$-0.0216066\pi$
$541$	14.5344	+	20.0049i	0.624884	+	0.860080i	−0.372813	+	0.927907i	$0.621607\pi$
$542$	−42.7243	+	13.8820i	−1.83517	+	0.596281i
$543$	13.3102	−	16.4925i	0.571196	−	0.707761i
$544$	−15.5902	−	11.3269i	−0.668423	−	0.485638i
$545$	−16.1150	−	11.7082i	−0.690289	−	0.501524i
$546$	4.62663	−	5.73279i	0.198001	−	0.245341i
$547$	−29.2082	+	9.49032i	−1.24885	+	0.405777i	−0.857510	−	0.514468i	$-0.827989\pi$
$547$	−29.2082	+	9.49032i	−1.24885	+	0.405777i	−0.391343	+	0.920245i	$0.627989\pi$
$548$	−8.28199	−	11.3992i	−0.353789	−	0.486949i
$549$	8.50651	−	9.51057i	0.363049	−	0.405901i
$550$		0			0
$551$		−	16.1803i		−	0.689306i
$552$	−0.578061	−	2.14316i	−0.0246039	−	0.0912188i
$553$	−2.39919	−	7.38394i	−0.102024	−	0.313997i
$554$	−37.1567	−	12.0729i	−1.57864	−	0.512930i
$555$	−11.3967	+	7.42798i	−0.483765	+	0.315300i
$556$	1.64590	−	2.26538i	0.0698016	−	0.0960737i
$557$	−2.48990	+	7.66312i	−0.105500	+	0.324697i	−0.989848	−	0.142133i	$-0.954604\pi$
$557$	−2.48990	+	7.66312i	−0.105500	+	0.324697i	0.884347	+	0.466830i	$0.154604\pi$
$558$	1.96760	−	4.45897i	0.0832952	−	0.188763i
$559$	4.04508	−	2.93893i	0.171089	−	0.124303i
$560$	8.78402			0.371193
$561$		0			0
$562$	−31.3050			−1.32052
$563$	−18.6049	+	13.5172i	−0.784101	+	0.569683i	−0.906207	−	0.422834i	$-0.861035\pi$
$563$	−18.6049	+	13.5172i	−0.784101	+	0.569683i	0.122106	+	0.992517i	$0.461035\pi$
$564$	20.5055	+	1.04062i	0.863438	+	0.0438178i
$565$	16.1353	−	49.6592i	0.678815	−	2.08918i
$566$	−8.89002	+	12.2361i	−0.373676	+	0.514320i
$567$	−5.68436	−	3.23187i	−0.238721	−	0.135726i
$568$	7.13525	+	2.31838i	0.299389	+	0.0972773i
$569$	2.52265	+	7.76393i	0.105755	+	0.325481i	0.989907	−	0.141719i	$-0.0452629\pi$
$569$	2.52265	+	7.76393i	0.105755	+	0.325481i	−0.884152	+	0.467200i	$0.845263\pi$
$570$	−35.4196	+	9.55353i	−1.48357	+	0.400153i
$571$			6.04937i			0.253158i	0.991957	+	0.126579i	$0.0403997\pi$
$571$			6.04937i			0.253158i	−0.991957	+	0.126579i	$0.959600\pi$
$572$		0			0
$573$	−12.2148	+	31.9787i	−0.510280	+	1.33593i
$574$	−2.50000	−	3.44095i	−0.104348	−	0.143623i
$575$	−3.11044	+	1.01064i	−0.129714	+	0.0421467i
$576$	−12.2088	+	7.10276i	−0.508701	+	0.295948i
$577$	6.47214	+	4.70228i	0.269439	+	0.195759i	0.714298	−	0.699842i	$-0.246746\pi$
$577$	6.47214	+	4.70228i	0.269439	+	0.195759i	−0.444859	+	0.895601i	$0.646746\pi$
$578$	15.5272	+	11.2812i	0.645845	+	0.469234i
$579$	−27.2223	−	21.9697i	−1.13132	−	0.913028i
$580$	−15.3262	+	4.97980i	−0.636387	+	0.206775i
$581$	6.18812	+	8.51722i	0.256727	+	0.353354i
$582$	−20.3682	−	7.77997i	−0.844290	−	0.322490i
$583$		0			0
$584$			11.0557i			0.457489i
$585$	−24.0483	−	2.44711i	−0.994273	−	0.101175i
$586$	5.75329	+	17.7068i	0.237666	+	0.731461i
$587$	−5.65334	−	1.83688i	−0.233338	−	0.0758162i	0.190014	−	0.981781i	$-0.439147\pi$
$587$	−5.65334	−	1.83688i	−0.233338	−	0.0758162i	−0.423352	+	0.905965i	$0.639147\pi$
$588$	−9.90398	−	15.1957i	−0.408433	−	0.626659i
$589$	−2.13525	+	2.93893i	−0.0879816	+	0.121096i
$590$	−4.02874	+	12.3992i	−0.165861	+	0.510466i
$591$	1.39029	−	27.3960i	0.0571891	−	1.12692i
$592$	11.2082	−	8.14324i	0.460654	−	0.334685i
$593$	3.35520			0.137781			0.0688907	−	0.997624i	$-0.478054\pi$
$593$	3.35520			0.137781			0.0688907	+	0.997624i	$0.478054\pi$
$594$		0			0
$595$	5.00000			0.204980
$596$	−0.224514	+	0.163119i	−0.00919645	+	0.00668161i
$597$	0.196294	−	3.86801i	0.00803377	−	0.158307i
$598$	3.19098	−	9.82084i	0.130489	−	0.401604i
$599$	−4.87380	+	6.70820i	−0.199138	+	0.274090i	−0.896894	−	0.442246i	$-0.854182\pi$
$599$	−4.87380	+	6.70820i	−0.199138	+	0.274090i	0.697756	+	0.716335i	$0.254182\pi$
$600$	−1.27400	−	1.95469i	−0.0520108	−	0.0798001i
$601$	−16.5451	−	5.37582i	−0.674888	−	0.219284i	−0.0485321	−	0.998822i	$-0.515454\pi$
$601$	−16.5451	−	5.37582i	−0.674888	−	0.219284i	−0.626356	+	0.779537i	$0.715454\pi$
$602$	0.693786	+	2.13525i	0.0282766	+	0.0870265i
$603$	24.8504	+	2.52873i	1.01199	+	0.102978i
$604$		−	28.4257i		−	1.15663i
$605$		0			0
$606$	38.4164	+	14.6738i	1.56056	+	0.596081i
$607$	−7.27458	−	10.0126i	−0.295266	−	0.406399i	0.635450	−	0.772142i	$-0.280815\pi$
$607$	−7.27458	−	10.0126i	−0.295266	−	0.406399i	−0.930716	+	0.365744i	$0.880815\pi$
$608$	29.6543	−	9.63525i	1.20264	−	0.390761i
$609$	3.72539	+	3.00656i	0.150960	+	0.121832i
$610$	17.1353	+	12.4495i	0.693786	+	0.504065i
$611$	−18.2416	−	13.2533i	−0.737976	−	0.536171i
$612$	−11.0291	+	6.41643i	−0.445825	+	0.259369i
$613$	−22.3607	+	7.26543i	−0.903139	+	0.293448i	−0.723532	−	0.690291i	$-0.757483\pi$
$613$	−22.3607	+	7.26543i	−0.903139	+	0.293448i	−0.179607	+	0.983738i	$0.557483\pi$
$614$	6.57164	+	9.04508i	0.265210	+	0.365030i
$615$	−4.97980	+	13.0373i	−0.200805	+	0.525714i
$616$		0			0
$617$		−	20.2361i		−	0.814673i	−0.913278	−	0.407337i	$-0.866458\pi$
$617$		−	20.2361i		−	0.814673i	0.913278	−	0.407337i	$-0.133542\pi$
$618$	21.5153	−	5.80319i	0.865471	−	0.233438i
$619$	3.83688	+	11.8087i	0.154217	+	0.474632i	0.998081	−	0.0619260i	$-0.0197243\pi$
$619$	3.83688	+	11.8087i	0.154217	+	0.474632i	−0.843863	+	0.536558i	$0.819724\pi$
$620$	3.44095	+	1.11803i	0.138192	+	0.0449013i
$621$	−9.05982	−	1.38885i	−0.363558	−	0.0557327i
$622$	5.59017	−	7.69421i	0.224145	−	0.308510i
$623$	2.12663	−	6.54508i	0.0852015	−	0.262223i
$624$	24.5857	+	1.24768i	0.984217	+	0.0499471i
$625$	24.9443	−	18.1231i	0.997771	−	0.724923i
$626$	20.9232			0.836261
$627$		0			0
$628$	−6.00000			−0.239426
$629$	6.37988	−	4.63525i	0.254383	−	0.184820i
$630$	4.38191	−	9.93028i	0.174579	−	0.395632i
$631$	−3.84752	+	11.8415i	−0.153168	+	0.471401i	−0.997971	−	0.0636762i	$-0.979718\pi$
$631$	−3.84752	+	11.8415i	−0.153168	+	0.471401i	0.844803	+	0.535077i	$0.179718\pi$
$632$	4.56352	−	6.28115i	0.181527	−	0.249851i
$633$	−9.83223	+	6.40829i	−0.390796	+	0.254707i
$634$	−0.427051	−	0.138757i	−0.0169604	−	0.00551076i
$635$	10.6861	+	32.8885i	0.424066	+	1.30514i
$636$	−3.54264	−	13.1343i	−0.140475	−	0.520810i
$637$			19.9192i			0.789227i
$638$		0			0
$639$	20.6525	−	23.0902i	0.816999	−	0.913433i
$640$	8.78115	+	12.0862i	0.347106	+	0.477750i
$641$	−16.9803	+	5.51722i	−0.670680	+	0.217917i	−0.624510	−	0.781016i	$-0.714701\pi$
$641$	−16.9803	+	5.51722i	−0.670680	+	0.217917i	−0.0461695	+	0.998934i	$0.514701\pi$
$642$	−0.354877	+	0.439723i	−0.0140059	+	0.0173545i
$643$	−6.39919	−	4.64928i	−0.252359	−	0.183350i	0.454412	−	0.890791i	$-0.349849\pi$
$643$	−6.39919	−	4.64928i	−0.252359	−	0.183350i	−0.706772	+	0.707442i	$0.749849\pi$
$644$	1.67760	+	1.21885i	0.0661067	+	0.0480293i
$645$	4.62663	−	5.73279i	0.182173	−	0.225728i
$646$	20.2254	−	6.57164i	0.795759	−	0.258558i
$647$	25.9560	+	35.7254i	1.02044	+	1.40451i	0.911897	+	0.410419i	$0.134618\pi$
$647$	25.9560	+	35.7254i	1.02044	+	1.40451i	0.108540	+	0.994092i	$0.465382\pi$
$648$	−0.726543	−	6.49839i	−0.0285413	−	0.255281i
$649$		0			0
$650$		−	10.8541i		−	0.425733i
$651$	−0.279899	−	1.03772i	−0.0109701	−	0.0406716i
$652$	−6.19098	−	19.0539i	−0.242458	−	0.746208i
$653$	33.4257	+	10.8607i	1.30805	+	0.425011i	0.878375	−	0.477972i	$-0.158628\pi$
$653$	33.4257	+	10.8607i	1.30805	+	0.425011i	0.429675	+	0.902984i	$0.358628\pi$
$654$	20.9999	−	13.6870i	0.821161	−	0.535203i
$655$	6.28115	−	8.64527i	0.245425	−	0.337798i
$656$	4.39201	−	13.5172i	0.171479	−	0.527759i
$657$	41.7652	+	18.4296i	1.62942	+	0.719009i
$658$	8.19098	−	5.95110i	0.319318	−	0.231998i
$659$	−39.8384			−1.55188			−0.775941	−	0.630805i	$-0.782725\pi$
$659$	−39.8384			−1.55188			−0.775941	+	0.630805i	$0.782725\pi$
$660$		0			0
$661$	32.4508			1.26219			0.631096	−	0.775705i	$-0.282605\pi$
$661$	32.4508			1.26219			0.631096	+	0.775705i	$0.282605\pi$
$662$	35.2218	−	25.5902i	1.36894	−	0.994590i
$663$	13.9946	+	0.710198i	0.543504	+	0.0275818i
$664$	−3.25329	+	10.0126i	−0.126252	+	0.388564i
$665$	−4.75528	+	6.54508i	−0.184402	+	0.253808i
$666$	−3.61466	−	16.7331i	−0.140065	−	0.648393i
$667$	6.38197	+	2.07363i	0.247111	+	0.0802911i
$668$	0.0530006	+	0.163119i	0.00205065	+	0.00631126i
$669$	−10.4285	+	2.81282i	−0.403189	+	0.108750i
$670$			41.4630i			1.60185i
$671$		0			0
$672$	−3.29180	+	8.61803i	−0.126984	+	0.332448i
$673$	−17.6631	−	24.3112i	−0.680863	−	0.937128i	0.319081	−	0.947728i	$-0.396626\pi$
$673$	−17.6631	−	24.3112i	−0.680863	−	0.937128i	−0.999944	+	0.0105998i	$0.996626\pi$
$674$	18.6376	−	6.05573i	0.717894	−	0.233258i
$675$	−9.50798	+	1.55436i	−0.365962	+	0.0598272i
$676$	−4.61803	−	3.35520i	−0.177617	−	0.129046i
$677$	31.9524	+	23.2148i	1.22803	+	0.892217i	0.996741	−	0.0806684i	$-0.0257055\pi$
$677$	31.9524	+	23.2148i	1.22803	+	0.892217i	0.231290	+	0.972885i	$0.425705\pi$
$678$	51.1327	+	41.2665i	1.96374	+	1.58483i
$679$	−4.57295	+	1.48584i	−0.175494	+	0.0570214i
$680$	2.93893	+	4.04508i	0.112703	+	0.155122i
$681$	−10.2371	−	3.91023i	−0.392287	−	0.149840i
$682$		0			0
$683$		−	9.00000i		−	0.344375i	−0.985064	−	0.172188i	$-0.944916\pi$
$683$		−	9.00000i		−	0.344375i	0.985064	−	0.172188i	$-0.0550836\pi$
$684$	2.09008	−	20.5397i	0.0799162	−	0.785354i
$685$	7.04508	+	21.6825i	0.269179	+	0.828447i
$686$	−17.7068	−	5.75329i	−0.676049	−	0.219662i
$687$	−23.7615	−	36.4572i	−0.906558	−	1.39093i
$688$	−4.40983	+	6.06961i	−0.168123	+	0.231402i
$689$	−4.61653	+	14.2082i	−0.175876	+	0.541289i
$690$	0.771108	−	15.1948i	0.0293556	−	0.578457i
$691$	−27.7984	+	20.1967i	−1.05750	+	0.768319i	−0.973624	−	0.228158i	$-0.926730\pi$
$691$	−27.7984	+	20.1967i	−1.05750	+	0.768319i	−0.0838757	+	0.996476i	$0.526730\pi$
$692$	35.8626			1.36329
$693$		0			0
$694$	−58.5410			−2.22219
$695$	−3.66547	+	2.66312i	−0.139039	+	0.101018i
$696$	−0.242632	+	4.78112i	−0.00919696	+	0.181228i
$697$	2.50000	−	7.69421i	0.0946943	−	0.291439i
$698$	18.2088	−	25.0623i	0.689214	−	0.948622i
$699$	−6.77099	−	10.3887i	−0.256103	−	0.392938i
$700$	2.07295	+	0.673542i	0.0783501	+	0.0254575i
$701$	−5.39607	−	16.6074i	−0.203807	−	0.627252i	−0.999760	−	0.0218948i	$-0.993030\pi$
$701$	−5.39607	−	16.6074i	−0.203807	−	0.627252i	0.795954	−	0.605358i	$-0.206970\pi$
$702$	13.6751	−	27.1716i	0.516133	−	1.02553i
$703$			12.7598i			0.481244i
$704$		0			0
$705$	−31.0344	−	11.8541i	−1.16882	−	0.446451i
$706$	17.4377	+	24.0009i	0.656276	+	0.903287i
$707$	8.62502	−	2.80244i	0.324377	−	0.105397i
$708$	−5.70962	−	4.60793i	−0.214581	−	0.173177i
$709$	−14.1631	−	10.2901i	−0.531907	−	0.386453i	0.289164	−	0.957280i	$-0.406623\pi$
$709$	−14.1631	−	10.2901i	−0.531907	−	0.386453i	−0.821071	+	0.570827i	$0.806623\pi$
$710$	41.6017	+	30.2254i	1.56129	+	1.13434i
$711$	−16.1210	−	27.7102i	−0.604586	−	1.03921i
$712$	6.54508	−	2.12663i	0.245287	−	0.0796987i
$713$	−0.885544	−	1.21885i	−0.0331639	−	0.0456462i
$714$	−2.24514	+	5.87785i	−0.0840222	+	0.219973i
$715$		0			0
$716$			6.38197i			0.238505i
$717$	43.1401	−	11.6359i	1.61110	−	0.434551i
$718$	−14.6738	−	45.1612i	−0.547620	−	1.68540i
$719$	9.62908	+	3.12868i	0.359104	+	0.116680i	0.483012	−	0.875614i	$-0.339543\pi$
$719$	9.62908	+	3.12868i	0.359104	+	0.116680i	−0.123908	+	0.992294i	$0.539543\pi$
$720$	35.4528	−	7.65848i	1.32125	−	0.285415i
$721$	2.88854	−	3.97574i	0.107575	−	0.148064i
$722$	0.534785	−	1.64590i	0.0199026	−	0.0612540i
$723$	−33.8633	−	1.71850i	−1.25939	−	0.0639116i
$724$	−16.0172	+	11.6372i	−0.595275	+	0.432493i
$725$	7.05342			0.261958
$726$		0			0
$727$	−21.1459			−0.784258			−0.392129	−	0.919910i	$-0.628261\pi$
$727$	−21.1459			−0.784258			−0.392129	+	0.919910i	$0.628261\pi$
$728$	1.31433	−	0.954915i	0.0487122	−	0.0353915i
$729$	−25.7601	−	8.08802i	−0.954079	−	0.299556i
$730$	−23.4164	+	72.0683i	−0.866680	+	2.66737i
$731$	−2.51014	+	3.45492i	−0.0928410	+	0.127785i
$732$	−9.98604	+	6.50854i	−0.369095	+	0.240562i
$733$	−32.6869	−	10.6206i	−1.20732	−	0.392282i	−0.364870	−	0.931058i	$-0.618887\pi$
$733$	−32.6869	−	10.6206i	−1.20732	−	0.392282i	−0.842449	+	0.538777i	$0.818887\pi$
$734$	−13.5065	−	41.5689i	−0.498536	−	1.53434i
$735$	7.64282	+	28.3357i	0.281910	+	1.04518i
$736$			12.9313i			0.476653i
$737$		0			0
$738$	−13.0902	−	11.7082i	−0.481856	−	0.430985i
$739$	−9.57295	−	13.1760i	−0.352147	−	0.484688i	0.595793	−	0.803138i	$-0.296838\pi$
$739$	−9.57295	−	13.1760i	−0.352147	−	0.484688i	−0.947940	+	0.318450i	$0.896838\pi$
$740$	12.0862	−	3.92705i	0.444298	−	0.144361i
$741$	−14.2393	+	17.6437i	−0.523094	+	0.648158i
$742$	−5.42705	−	3.94298i	−0.199233	−	0.144751i
$743$	33.8218	+	24.5729i	1.24080	+	0.901494i	0.997651	−	0.0684950i	$-0.0218197\pi$
$743$	33.8218	+	24.5729i	1.24080	+	0.901494i	0.243149	+	0.969989i	$0.421820\pi$
$744$	0.675016	−	0.836402i	0.0247473	−	0.0306640i
$745$	0.427051	−	0.138757i	0.0156459	−	0.00508367i
$746$	−21.8415	−	30.0623i	−0.799676	−	1.10066i
$747$	32.4014	+	28.9807i	1.18551	+	1.06035i
$748$		0			0
$749$			0.124612i			0.00455322i
$750$	7.06622	+	26.1980i	0.258022	+	0.956614i
$751$	1.71885	+	5.29007i	0.0627216	+	0.193037i	0.977507	−	0.210903i	$-0.0676404\pi$
$751$	1.71885	+	5.29007i	0.0627216	+	0.193037i	−0.914785	+	0.403940i	$0.867640\pi$
$752$	32.1769	+	10.4549i	1.17337	+	0.381252i
$753$	−6.78189	+	4.42019i	−0.247146	+	0.161081i
$754$	−13.0902	+	18.0171i	−0.476716	+	0.656143i
$755$	−14.2128	+	43.7426i	−0.517258	+	1.59196i
$756$	4.34072	+	4.29782i	0.157870	+	0.156310i
$757$	20.1353	−	14.6291i	0.731828	−	0.531704i	−0.158313	−	0.987389i	$-0.550606\pi$
$757$	20.1353	−	14.6291i	0.731828	−	0.531704i	0.890141	+	0.455685i	$0.150606\pi$
$758$	−62.5577			−2.27220
$759$		0			0
$760$	−8.09017			−0.293461
$761$	−35.7239	+	25.9549i	−1.29499	+	0.940865i	−0.999893	−	0.0146026i	$-0.995352\pi$
$761$	−35.7239	+	25.9549i	−1.29499	+	0.940865i	−0.295096	+	0.955468i	$0.595352\pi$
$762$	−43.4612	−	2.20557i	−1.57443	−	0.0798994i
$763$	1.70820	−	5.25731i	0.0618411	−	0.190327i
$764$	18.7966	−	25.8713i	0.680038	−	0.935992i
$765$	20.1802	−	4.35932i	0.729618	−	0.157612i
$766$	26.0795	+	8.47375i	0.942292	+	0.306169i
$767$	2.48990	+	7.66312i	0.0899050	+	0.276699i
$768$	−33.8981	+	9.14315i	−1.22319	+	0.329925i
$769$		−	26.8666i		−	0.968835i	−0.874837	−	0.484417i	$-0.839032\pi$
$769$		−	26.8666i		−	0.968835i	0.874837	−	0.484417i	$-0.160968\pi$
$770$		0			0
$771$	−6.96556	+	18.2361i	−0.250858	+	0.656756i
$772$	19.2082	+	26.4378i	0.691318	+	0.951518i
$773$	7.44945	−	2.42047i	0.267938	−	0.0870584i	−0.171967	−	0.985103i	$-0.555012\pi$
$773$	7.44945	−	2.42047i	0.267938	−	0.0870584i	0.439905	+	0.898044i	$0.355012\pi$
$774$	4.66181	+	8.01311i	0.167565	+	0.288025i
$775$	−1.28115	−	0.930812i	−0.0460204	−	0.0334358i
$776$	−3.88998	−	2.82624i	−0.139642	−	0.101456i
$777$	−2.93783	−	2.37097i	−0.105394	−	0.0850580i
$778$	17.3992	−	5.65334i	0.623791	−	0.202682i
$779$	7.69421	+	10.5902i	0.275674	+	0.379432i
$780$	21.0948	+	8.05748i	0.755313	+	0.288504i
$781$		0			0
$782$			8.81966i			0.315390i
$783$	17.6572	+	8.88661i	0.631016	+	0.317582i
$784$	−9.23607	−	28.4257i	−0.329860	−	1.01520i
$785$	9.23305	+	3.00000i	0.329542	+	0.107075i
$786$	7.34271	+	11.2659i	0.261906	+	0.401841i
$787$	−32.0344	+	44.0916i	−1.14190	+	1.57170i	−0.378726	+	0.925509i	$0.623638\pi$
$787$	−32.0344	+	44.0916i	−1.14190	+	1.57170i	−0.763178	+	0.646188i	$0.776362\pi$
$788$	−7.91872	+	24.3713i	−0.282093	+	0.868192i
$789$	−2.04315	+	40.2606i	−0.0727380	+	1.43332i
$790$	43.0517	−	31.2789i	1.53171	−	1.11285i
$791$	14.4904			0.515218
$792$		0			0
$793$	13.0902			0.464846
$794$	35.3934	−	25.7148i	1.25606	−	0.912583i
$795$	−1.11559	+	21.9830i	−0.0395660	+	0.779655i
$796$	−1.11803	+	3.44095i	−0.0396277	+	0.121961i
$797$	12.9718	−	17.8541i	0.459483	−	0.632425i	−0.514918	−	0.857239i	$-0.672178\pi$
$797$	12.9718	−	17.8541i	0.459483	−	0.632425i	0.974402	+	0.224815i	$0.0721777\pi$
$798$	−5.55895	−	8.52910i	−0.196785	−	0.301927i
$799$	18.3156	+	5.95110i	0.647959	+	0.210535i
$800$	4.20025	+	12.9271i	0.148501	+	0.457040i
$801$	2.87675	−	28.2704i	0.101645	−	0.998886i
$802$			40.2219i			1.42028i
$803$		0			0
$804$	−21.7984	−	8.32624i	−0.768769	−	0.293644i
$805$	−1.97214	−	2.71441i	−0.0695087	−	0.0956705i
$806$	4.75528	−	1.54508i	0.167498	−	0.0544233i
$807$	−31.3189	−	25.2759i	−1.10248	−	0.889752i
$808$	7.33688	+	5.33056i	0.258111	+	0.187528i
$809$	−21.1805	−	15.3885i	−0.744667	−	0.541032i	0.149502	−	0.988761i	$-0.452233\pi$
$809$	−21.1805	−	15.3885i	−0.744667	−	0.541032i	−0.894169	+	0.447729i	$0.852233\pi$
$810$	9.02775	−	43.8995i	0.317203	−	1.54247i
$811$	12.2984	−	3.99598i	0.431854	−	0.140318i	−0.0850200	−	0.996379i	$-0.527095\pi$
$811$	12.2984	−	3.99598i	0.431854	−	0.140318i	0.516874	+	0.856061i	$0.327095\pi$
$812$	−2.62866	−	3.61803i	−0.0922477	−	0.126968i
$813$	−14.5964	+	38.2138i	−0.511917	+	1.34022i
$814$		0			0
$815$			32.4164i			1.13550i
$816$	−20.3003	+	5.47547i	−0.710652	+	0.191680i
$817$	−2.13525	−	6.57164i	−0.0747031	−	0.229913i
$818$	61.9372	+	20.1246i	2.16558	+	0.703641i
$819$	−1.41643	−	6.55696i	−0.0494940	−	0.229119i
$820$	7.66312	−	10.5474i	0.267608	−	0.368330i
$821$	11.4252	−	35.1631i	0.398742	−	1.22720i	−0.527267	−	0.849700i	$-0.676783\pi$
$821$	11.4252	−	35.1631i	0.398742	−	1.22720i	0.926009	−	0.377502i	$-0.123217\pi$
$822$	−28.6528	−	1.45407i	−0.999381	−	0.0507167i
$823$	11.4271	−	8.30224i	0.398322	−	0.289398i	−0.370535	−	0.928818i	$-0.620826\pi$
$823$	11.4271	−	8.30224i	0.398322	−	0.289398i	0.768857	+	0.639421i	$0.220826\pi$
$824$	4.91428			0.171197
$825$		0			0
$826$	−3.61803			−0.125888
$827$	−0.277515	+	0.201626i	−0.00965013	+	0.00701123i	−0.592600	−	0.805497i	$-0.701898\pi$
$827$	−0.277515	+	0.201626i	−0.00965013	+	0.00701123i	0.582950	+	0.812508i	$0.301898\pi$
$828$	7.83354	+	3.45669i	0.272234	+	0.120128i
$829$	8.73607	−	26.8869i	0.303416	−	0.933819i	−0.676847	−	0.736123i	$-0.736654\pi$
$829$	8.73607	−	26.8869i	0.303416	−	0.933819i	0.980263	−	0.197696i	$-0.0633457\pi$
$830$	−42.4140	+	58.3779i	−1.47221	+	2.02633i
$831$	−29.8043	+	19.4254i	−1.03390	+	0.673858i
$832$	−13.7812	−	4.47777i	−0.477776	−	0.155239i
$833$	−5.25731	−	16.1803i	−0.182155	−	0.560616i
$834$	−1.48479	−	5.50483i	−0.0514139	−	0.190617i
$835$		−	0.277515i		−	0.00960379i
$836$		0			0
$837$	−2.03444	−	3.94427i	−0.0703206	−	0.136334i
$838$	−6.54508	−	9.00854i	−0.226096	−	0.311195i
$839$	−28.2012	+	9.16312i	−0.973613	+	0.316346i	−0.752274	−	0.658851i	$-0.771043\pi$
$839$	−28.2012	+	9.16312i	−0.973613	+	0.316346i	−0.221339	+	0.975197i	$0.571043\pi$
$840$	1.50328	−	1.86269i	0.0518682	−	0.0642691i
$841$	11.7533	+	8.53926i	0.405286	+	0.294457i
$842$	−39.7854	−	28.9058i	−1.37109	−	0.996158i
$843$	−17.9028	+	22.1830i	−0.616604	+	0.764025i
$844$	10.4271	−	3.38795i	0.358914	−	0.116618i
$845$	5.42882	+	7.47214i	0.186757	+	0.257049i
$846$	27.8707	−	31.1604i	0.958213	−	1.07131i
$847$		0			0
$848$		−	22.4164i		−	0.769783i
$849$	3.58657	+	13.2972i	0.123091	+	0.456358i
$850$	2.86475	+	8.81678i	0.0982599	+	0.302413i
$851$	−5.03280	−	1.63525i	−0.172522	−	0.0560558i
$852$	−24.2445	+	15.8017i	−0.830605	+	0.541358i
$853$	26.6074	−	36.6219i	0.911020	−	1.25391i	−0.0557975	−	0.998442i	$-0.517770\pi$
$853$	26.6074	−	36.6219i	0.911020	−	1.25391i	0.966817	−	0.255469i	$-0.0822299\pi$
$854$	−1.81636	+	5.59017i	−0.0621544	+	0.191292i
$855$	−13.4861	+	30.5622i	−0.461216	+	1.04521i
$856$	−0.100813	+	0.0732450i	−0.00344572	+	0.00250346i
$857$	−24.2380			−0.827953			−0.413976	−	0.910288i	$-0.635860\pi$
$857$	−24.2380			−0.827953			−0.413976	+	0.910288i	$0.635860\pi$
$858$		0			0
$859$	34.5279			1.17808			0.589038	−	0.808106i	$-0.299507\pi$
$859$	34.5279			1.17808			0.589038	+	0.808106i	$0.299507\pi$
$860$	−5.56758	+	4.04508i	−0.189853	+	0.137936i
$861$	−3.86801	−	0.196294i	−0.131821	−	0.00668967i
$862$	−13.2533	+	40.7894i	−0.451409	+	1.38929i
$863$	−22.9969	+	31.6525i	−0.782823	+	1.07746i	0.212142	+	0.977239i	$0.431956\pi$
$863$	−22.9969	+	31.6525i	−0.782823	+	1.07746i	−0.994965	+	0.100224i	$0.968044\pi$
$864$	−5.77210	+	37.6528i	−0.196371	+	1.28097i
$865$	−55.1869	−	17.9313i	−1.87641	−	0.609683i
$866$	−3.52671	−	10.8541i	−0.119843	−	0.368837i
$867$	16.8737	−	4.55124i	0.573060	−	0.154568i
$868$			1.00406i			0.0340799i
$869$		0			0
$870$	−11.7082	+	30.6525i	−0.396945	+	1.03922i
$871$	15.0623	+	20.7315i	0.510367	+	0.702460i
$872$	5.25731	−	1.70820i	0.178035	−	0.0578471i
$873$	−17.1612	+	9.98392i	−0.580819	+	0.337904i
$874$	−11.5451	−	8.38800i	−0.390518	−	0.283728i
$875$	4.84104	+	3.51722i	0.163657	+	0.118904i
$876$	−33.1863	−	26.7829i	−1.12126	−	0.904909i
$877$	7.72542	−	2.51014i	0.260869	−	0.0847615i	−0.175662	−	0.984450i	$-0.556207\pi$
$877$	7.72542	−	2.51014i	0.260869	−	0.0847615i	0.436532	+	0.899689i	$0.356207\pi$
$878$	28.3399	+	39.0066i	0.956427	+	1.31641i
$879$	15.8374	+	6.04937i	0.534184	+	0.204040i
$880$		0			0
$881$			34.9230i			1.17659i	0.808648	+	0.588293i	$0.200200\pi$
$881$			34.9230i			1.17659i	−0.808648	+	0.588293i	$0.799800\pi$
$882$	−36.7425	−	3.73885i	−1.23718	−	0.125894i
$883$	−5.50658	−	16.9475i	−0.185311	−	0.570329i	0.814642	−	0.579963i	$-0.196933\pi$
$883$	−5.50658	−	16.9475i	−0.185311	−	0.570329i	−0.999954	+	0.00963455i	$0.996933\pi$
$884$	−12.4495	−	4.04508i	−0.418722	−	0.136051i
$885$	6.48224	+	9.94569i	0.217898	+	0.334321i
$886$	−11.7082	+	16.1150i	−0.393345	+	0.541393i
$887$	−3.02468	+	9.30902i	−0.101559	+	0.312566i	−0.988907	−	0.148533i	$-0.952545\pi$
$887$	−3.02468	+	9.30902i	−0.101559	+	0.312566i	0.887349	+	0.461099i	$0.152545\pi$
$888$	0.191339	−	3.77037i	0.00642092	−	0.126525i
$889$	−7.76393	+	5.64083i	−0.260394	+	0.189187i
$890$	47.1693			1.58112
$891$		0			0
$892$	10.0902			0.337844
$893$	−25.2093	+	18.3156i	−0.843596	+	0.612908i
$894$	−0.0286389	+	0.564334i	−0.000957827	+	0.0188742i
$895$	3.19098	−	9.82084i	0.106663	−	0.328274i
$896$	−2.43690	+	3.35410i	−0.0814110	+	0.112053i
$897$	−5.13429	−	7.87753i	−0.171429	−	0.263023i
$898$	−14.2705	−	4.63677i	−0.476213	−	0.154731i
$899$	1.00406	+	3.09017i	0.0334872	+	0.103063i
$900$	8.95376	+	0.911119i	0.298459	+	0.0303706i
$901$		−	12.7598i		−	0.425089i
$902$		0			0
$903$	1.90983	+	0.729490i	0.0635552	+	0.0242759i
$904$	8.51722	+	11.7229i	0.283279	+	0.389899i
$905$	30.4666	−	9.89919i	1.01274	−	0.329060i
$906$	−45.0406	−	36.3499i	−1.49637	−	1.20764i
$907$	−34.2984	−	24.9192i	−1.13886	−	0.827429i	−0.151899	−	0.988396i	$-0.548539\pi$
$907$	−34.2984	−	24.9192i	−1.13886	−	0.827429i	−0.986960	+	0.160967i	$0.948539\pi$
$908$	8.28199	+	6.01722i	0.274848	+	0.199688i
$909$	32.3677	−	18.8306i	1.07357	−	0.624573i
$910$	10.5902	−	3.44095i	0.351061	−	0.114067i
$911$	−33.9278	−	46.6976i	−1.12408	−	1.54716i	−0.798857	−	0.601521i	$-0.794562\pi$
$911$	−33.9278	−	46.6976i	−1.12408	−	1.54716i	−0.325220	−	0.945638i	$-0.605438\pi$
$912$	12.1392	−	31.7809i	0.401970	−	1.05237i
$913$		0			0
$914$			20.5279i			0.679001i
$915$	18.6212	−	5.02259i	0.615598	−	0.166042i
$916$	12.5623	+	38.6628i	0.415070	+	1.27745i
$917$	2.82041	+	0.916408i	0.0931383	+	0.0302625i
$918$	−3.93681	+	25.6808i	−0.129934	+	0.847591i
$919$	18.3926	−	25.3153i	0.606716	−	0.835073i	−0.389586	−	0.920990i	$-0.627382\pi$
$919$	18.3926	−	25.3153i	0.606716	−	0.835073i	0.996302	+	0.0859168i	$0.0273819\pi$
$920$	1.03681	−	3.19098i	0.0341827	−	0.105204i
$921$	10.1677	+	0.515989i	0.335036	+	0.0170024i
$922$	−41.3435	+	30.0378i	−1.36157	+	0.989242i
$923$	31.7809			1.04608
$924$		0			0
$925$	−5.56231			−0.182887
$926$	0.416272	−	0.302439i	0.0136795	−	0.00993877i
$927$	8.19200	−	18.5647i	0.269061	−	0.609745i
$928$	8.61803	−	26.5236i	0.282901	−	0.870679i
$929$	−17.8128	+	24.5172i	−0.584419	+	0.804384i	−0.994171	−	0.107813i	$-0.965615\pi$
$929$	−17.8128	+	24.5172i	−0.584419	+	0.804384i	0.409752	+	0.912197i	$0.365615\pi$
$930$	6.17171	−	4.02250i	0.202378	−	0.131903i
$931$	26.1803	+	8.50651i	0.858026	+	0.278790i
$932$	3.57971	+	11.0172i	0.117257	+	0.360881i
$933$	−2.25528	−	8.36144i	−0.0738346	−	0.273741i
$934$			44.9897i			1.47211i
$935$		0			0
$936$	4.47214	−	5.00000i	0.146176	−	0.163430i
$937$	−22.2599	−	30.6381i	−0.727198	−	1.00090i	−0.999254	−	0.0386209i	$-0.987704\pi$
$937$	−22.2599	−	30.6381i	−0.727198	−	1.00090i	0.272056	−	0.962281i	$-0.412296\pi$
$938$	−10.9434	+	3.55573i	−0.357315	+	0.116099i
$939$	11.9656	−	14.8264i	0.390484	−	0.483843i
$940$	25.1074	+	18.2416i	0.818913	+	0.594975i
$941$	−39.1648	−	28.4549i	−1.27674	−	0.927604i	−0.277288	−	0.960787i	$-0.589436\pi$
$941$	−39.1648	−	28.4549i	−1.27674	−	0.927604i	−0.999449	+	0.0331832i	$0.989436\pi$
$942$	−7.67261	+	9.50702i	−0.249987	+	0.309755i
$943$	−5.16312	+	1.67760i	−0.168134	+	0.0546301i
$944$	−7.10642	−	9.78115i	−0.231294	−	0.318349i
$945$	−4.53077	−	8.78402i	−0.147386	−	0.285744i
$946$		0			0
$947$		−	23.8541i		−	0.775154i	−0.921837	−	0.387577i	$-0.873312\pi$
$947$		−	23.8541i		−	0.775154i	0.921837	−	0.387577i	$-0.126688\pi$
$948$	7.79901	+	28.9148i	0.253300	+	0.939107i
$949$	14.4721	+	44.5407i	0.469785	+	1.44585i
$950$	−14.2658	−	4.63525i	−0.462845	−	0.150388i
$951$	−0.342548	+	0.223260i	−0.0111079	+	0.00723971i
$952$	−0.815595	+	1.12257i	−0.0264336	+	0.0363827i
$953$	−13.7638	+	42.3607i	−0.445854	+	1.37220i	0.435691	+	0.900096i	$0.356504\pi$
$953$	−13.7638	+	42.3607i	−0.445854	+	1.37220i	−0.881545	+	0.472101i	$0.843496\pi$
$954$	−25.3416	−	11.1824i	−0.820464	−	0.362044i
$955$	−41.8607	+	30.4136i	−1.35458	+	0.984160i
$956$	−41.7405			−1.34998
$957$		0			0
$958$	43.5410			1.40675
$959$	−5.11855	+	3.71885i	−0.165287	+	0.120088i
$960$	−21.3222	−	1.08206i	−0.688172	−	0.0349234i
$961$	−9.35410	+	28.7890i	−0.301745	+	0.928676i
$962$	10.3229	−	14.2082i	0.332823	−	0.458091i
$963$	0.108645	+	0.502939i	0.00350102	+	0.0162070i
$964$	30.1246	+	9.78808i	0.970248	+	0.315253i
$965$	−16.3395	−	50.2877i	−0.525986	−	1.61882i
$966$	4.07653	−	1.09954i	0.131160	−	0.0353770i
$967$		−	20.9232i		−	0.672846i	−0.941711	−	0.336423i	$-0.890783\pi$
$967$		−	20.9232i		−	0.672846i	0.941711	−	0.336423i	$-0.109217\pi$
$968$		0			0
$969$	6.90983	−	18.0902i	0.221976	−	0.581140i
$970$	−19.3713	−	26.6623i	−0.621976	−	0.856076i
$971$	−13.4863	+	4.38197i	−0.432796	+	0.140624i	−0.517310	−	0.855798i	$-0.673066\pi$
$971$	−13.4863	+	4.38197i	−0.432796	+	0.140624i	0.0845134	+	0.996422i	$0.473066\pi$
$972$	21.2665	+	13.5617i	0.682122	+	0.434992i
$973$	−1.01722	−	0.739054i	−0.0326106	−	0.0236930i
$974$	11.4984	+	8.35410i	0.368434	+	0.267683i
$975$	−7.69134	−	6.20727i	−0.246320	−	0.198792i
$976$	−18.6803	+	6.06961i	−0.597943	+	0.194283i
$977$	−30.5321	−	42.0238i	−0.976808	−	1.34446i	−0.938532	−	0.345193i	$-0.887813\pi$
$977$	−30.5321	−	42.0238i	−0.976808	−	1.34446i	−0.0382760	−	0.999267i	$-0.512187\pi$
$978$	−38.1078	−	14.5559i	−1.21855	−	0.465446i
$979$		0			0
$980$		−	27.4164i		−	0.875785i
$981$	2.31073	−	22.7081i	0.0737761	−	0.725014i
$982$	15.6910	+	48.2919i	0.500719	+	1.54106i
$983$	5.04531	+	1.63932i	0.160920	+	0.0522862i	0.388369	−	0.921504i	$-0.373038\pi$
$983$	5.04531	+	1.63932i	0.160920	+	0.0522862i	−0.227449	+	0.973790i	$0.573038\pi$
$984$	−2.11475	−	3.24466i	−0.0674158	−	0.103436i
$985$	24.3713	−	33.5442i	0.776535	−	1.06881i
$986$	5.87785	−	18.0902i	0.187189	−	0.576108i
$987$	0.467265	−	9.20755i	0.0148732	−	0.293080i
$988$	17.1353	−	12.4495i	0.545145	−	0.396071i
$989$	2.86568			0.0911234
$990$		0			0
$991$	7.56231			0.240225			0.120112	−	0.992760i	$-0.461675\pi$
$991$	7.56231			0.240225			0.120112	+	0.992760i	$0.461675\pi$
$992$	−5.06555	+	3.68034i	−0.160831	+	0.116851i
$993$	2.00928	−	39.5932i	0.0637625	−	1.25645i
$994$	−4.40983	+	13.5721i	−0.139871	+	0.430480i
$995$	3.44095	−	4.73607i	0.109086	−	0.150143i
$996$	−22.1739	−	34.0213i	−0.702606	−	1.07801i
$997$	38.8435	+	12.6210i	1.23018	+	0.399711i	0.850781	−	0.525520i	$-0.176129\pi$
$997$	38.8435	+	12.6210i	1.23018	+	0.399711i	0.379403	+	0.925231i	$0.376129\pi$
$998$	6.45313	+	19.8607i	0.204270	+	0.628679i
$999$	−13.9244	−	7.00795i	−0.440548	−	0.221722i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.f.e.239.1		8
3.2	odd	2	inner	363.2.f.e.239.2		8
11.2	odd	10		363.2.d.f.362.2		8
11.3	even	5		33.2.f.a.17.2	yes	8
11.4	even	5		363.2.f.d.161.1		8
11.5	even	5		363.2.f.b.233.2		8
11.6	odd	10		33.2.f.a.2.1	✓	8
11.7	odd	10	inner	363.2.f.e.161.2		8
11.8	odd	10		363.2.f.b.215.1		8
11.9	even	5		363.2.d.f.362.8		8
11.10	odd	2		363.2.f.d.239.2		8
33.2	even	10		363.2.d.f.362.7		8
33.5	odd	10		363.2.f.b.233.1		8
33.8	even	10		363.2.f.b.215.2		8
33.14	odd	10		33.2.f.a.17.1	yes	8
33.17	even	10		33.2.f.a.2.2	yes	8
33.20	odd	10		363.2.d.f.362.1		8
33.26	odd	10		363.2.f.d.161.2		8
33.29	even	10	inner	363.2.f.e.161.1		8
33.32	even	2		363.2.f.d.239.1		8
44.3	odd	10		528.2.bn.c.17.1		8
44.39	even	10		528.2.bn.c.497.2		8
55.3	odd	20		825.2.bs.d.149.2		8
55.14	even	10		825.2.bi.b.776.1		8
55.17	even	20		825.2.bs.a.299.2		8
55.28	even	20		825.2.bs.d.299.1		8
55.39	odd	10		825.2.bi.b.101.2		8
55.47	odd	20		825.2.bs.a.149.1		8
99.14	odd	30		891.2.u.a.512.2		16
99.25	even	15		891.2.u.a.215.2		16
99.47	odd	30		891.2.u.a.215.1		16
99.50	even	30		891.2.u.a.431.2		16
99.58	even	15		891.2.u.a.512.1		16
99.61	odd	30		891.2.u.a.134.2		16
99.83	even	30		891.2.u.a.134.1		16
99.94	odd	30		891.2.u.a.431.1		16
132.47	even	10		528.2.bn.c.17.2		8
132.83	odd	10		528.2.bn.c.497.1		8
165.14	odd	10		825.2.bi.b.776.2		8
165.17	odd	20		825.2.bs.d.299.2		8
165.47	even	20		825.2.bs.d.149.1		8
165.83	odd	20		825.2.bs.a.299.1		8
165.113	even	20		825.2.bs.a.149.2		8
165.149	even	10		825.2.bi.b.101.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.f.a.2.1	✓	8	11.6	odd	10
33.2.f.a.2.2	yes	8	33.17	even	10
33.2.f.a.17.1	yes	8	33.14	odd	10
33.2.f.a.17.2	yes	8	11.3	even	5
363.2.d.f.362.1		8	33.20	odd	10
363.2.d.f.362.2		8	11.2	odd	10
363.2.d.f.362.7		8	33.2	even	10
363.2.d.f.362.8		8	11.9	even	5
363.2.f.b.215.1		8	11.8	odd	10
363.2.f.b.215.2		8	33.8	even	10
363.2.f.b.233.1		8	33.5	odd	10
363.2.f.b.233.2		8	11.5	even	5
363.2.f.d.161.1		8	11.4	even	5
363.2.f.d.161.2		8	33.26	odd	10
363.2.f.d.239.1		8	33.32	even	2
363.2.f.d.239.2		8	11.10	odd	2
363.2.f.e.161.1		8	33.29	even	10	inner
363.2.f.e.161.2		8	11.7	odd	10	inner
363.2.f.e.239.1		8	1.1	even	1	trivial
363.2.f.e.239.2		8	3.2	odd	2	inner
528.2.bn.c.17.1		8	44.3	odd	10
528.2.bn.c.17.2		8	132.47	even	10
528.2.bn.c.497.1		8	132.83	odd	10
528.2.bn.c.497.2		8	44.39	even	10
825.2.bi.b.101.1		8	165.149	even	10
825.2.bi.b.101.2		8	55.39	odd	10
825.2.bi.b.776.1		8	55.14	even	10
825.2.bi.b.776.2		8	165.14	odd	10
825.2.bs.a.149.1		8	55.47	odd	20
825.2.bs.a.149.2		8	165.113	even	20
825.2.bs.a.299.1		8	165.83	odd	20
825.2.bs.a.299.2		8	55.17	even	20
825.2.bs.d.149.1		8	165.47	even	20
825.2.bs.d.149.2		8	55.3	odd	20
825.2.bs.d.299.1		8	55.28	even	20
825.2.bs.d.299.2		8	165.17	odd	20
891.2.u.a.134.1		16	99.83	even	30
891.2.u.a.134.2		16	99.61	odd	30
891.2.u.a.215.1		16	99.47	odd	30
891.2.u.a.215.2		16	99.25	even	15
891.2.u.a.431.1		16	99.94	odd	30
891.2.u.a.431.2		16	99.50	even	30
891.2.u.a.512.1		16	99.58	even	15
891.2.u.a.512.2		16	99.14	odd	30

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.f (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.53884 + 1.11803i) q^{2} +(-0.0877853 + 1.72982i) q^{3} +(0.500000 - 1.53884i) q^{4} +(-1.53884 + 2.11803i) q^{5} +(-1.79892 - 2.76007i) q^{6} +(-0.690983 - 0.224514i) q^{7} +(-0.224514 - 0.690983i) q^{8} +(-2.98459 - 0.303706i) q^{9} +O(q^{10})\)	\(q+(-1.53884 + 1.11803i) q^{2} +(-0.0877853 + 1.72982i) q^{3} +(0.500000 - 1.53884i) q^{4} +(-1.53884 + 2.11803i) q^{5} +(-1.79892 - 2.76007i) q^{6} +(-0.690983 - 0.224514i) q^{7} +(-0.224514 - 0.690983i) q^{8} +(-2.98459 - 0.303706i) q^{9} -4.97980i q^{10} +(2.61803 + 1.00000i) q^{12} +(-1.80902 - 2.48990i) q^{13} +(1.31433 - 0.427051i) q^{14} +(-3.52874 - 2.84786i) q^{15} +(3.73607 + 2.71441i) q^{16} +(2.12663 + 1.54508i) q^{17} +(4.93236 - 2.86951i) q^{18} +(-4.04508 + 1.31433i) q^{19} +(2.48990 + 3.42705i) q^{20} +(0.449028 - 1.17557i) q^{21} -1.76393i q^{23} +(1.21499 - 0.327712i) q^{24} +(-0.572949 - 1.76336i) q^{25} +(5.56758 + 1.80902i) q^{26} +(0.787361 - 5.13615i) q^{27} +(-0.690983 + 0.951057i) q^{28} +(-1.17557 + 3.61803i) q^{29} +(8.61418 + 0.437153i) q^{30} +(0.690983 - 0.502029i) q^{31} -7.33094 q^{32} -5.00000 q^{34} +(1.53884 - 1.11803i) q^{35} +(-1.95965 + 4.44095i) q^{36} +(0.927051 - 2.85317i) q^{37} +(4.75528 - 6.54508i) q^{38} +(4.46589 - 2.91071i) q^{39} +(1.80902 + 0.587785i) q^{40} +(-0.951057 - 2.92705i) q^{41} +(0.623345 + 2.31105i) q^{42} +1.62460i q^{43} +(5.23607 - 5.85410i) q^{45} +(1.97214 + 2.71441i) q^{46} +(6.96767 - 2.26393i) q^{47} +(-5.02343 + 6.22446i) q^{48} +(-5.23607 - 3.80423i) q^{49} +(2.85317 + 2.07295i) q^{50} +(-2.85941 + 3.54306i) q^{51} +(-4.73607 + 1.53884i) q^{52} +(-2.85317 - 3.92705i) q^{53} +(4.53077 + 8.78402i) q^{54} +0.527864i q^{56} +(-1.91846 - 7.11267i) q^{57} +(-2.23607 - 6.88191i) q^{58} +(-2.48990 - 0.809017i) q^{59} +(-6.14677 + 4.00624i) q^{60} +(-2.50000 + 3.44095i) q^{61} +(-0.502029 + 1.54508i) q^{62} +(1.99411 + 0.879937i) q^{63} +(3.80902 - 2.76741i) q^{64} +8.05748 q^{65} -8.32624 q^{67} +(3.44095 - 2.50000i) q^{68} +(3.05129 + 0.154847i) q^{69} +(-1.11803 + 3.44095i) q^{70} +(-6.06961 + 8.35410i) q^{71} +(0.460226 + 2.13049i) q^{72} +(-14.4721 - 4.70228i) q^{73} +(1.76336 + 5.42705i) q^{74} +(3.10059 - 0.836305i) q^{75} +6.88191i q^{76} +(-3.61803 + 9.47214i) q^{78} +(6.28115 + 8.64527i) q^{79} +(-11.4984 + 3.73607i) q^{80} +(8.81553 + 1.81288i) q^{81} +(4.73607 + 3.44095i) q^{82} +(-11.7229 - 8.51722i) q^{83} +(-1.58450 - 1.27877i) q^{84} +(-6.54508 + 2.12663i) q^{85} +(-1.81636 - 2.50000i) q^{86} +(-6.15537 - 2.35114i) q^{87} +9.47214i q^{89} +(-1.51240 + 14.8626i) q^{90} +(0.690983 + 2.12663i) q^{91} +(-2.71441 - 0.881966i) q^{92} +(0.807763 + 1.23935i) q^{93} +(-8.19098 + 11.2739i) q^{94} +(3.44095 - 10.5902i) q^{95} +(0.643548 - 12.6812i) q^{96} +(5.35410 - 3.88998i) q^{97} +12.3107 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{4} + 10 q^{6} - 10 q^{7} - 10 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^4 + 10 * q^6 - 10 * q^7 - 10 * q^9	\( 8 q + 4 q^{3} + 4 q^{4} + 10 q^{6} - 10 q^{7} - 10 q^{9} + 12 q^{12} - 10 q^{13} + 4 q^{15} + 12 q^{16} + 20 q^{18} - 10 q^{19} + 20 q^{24} - 18 q^{25} - 2 q^{27} - 10 q^{28} + 30 q^{30} + 10 q^{31} - 40 q^{34} - 6 q^{37} + 10 q^{39} + 10 q^{40} - 10 q^{42} + 24 q^{45} - 20 q^{46} - 14 q^{48} - 24 q^{49} + 10 q^{51} - 20 q^{52} - 10 q^{57} - 8 q^{60} - 20 q^{61} - 10 q^{63} + 26 q^{64} - 4 q^{67} + 34 q^{69} + 20 q^{72} - 80 q^{73} + 6 q^{75} - 20 q^{78} + 10 q^{79} - 2 q^{81} + 20 q^{82} - 10 q^{84} - 30 q^{85} + 30 q^{90} + 10 q^{91} - 70 q^{94} + 30 q^{96} + 16 q^{97}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^4 + 10 * q^6 - 10 * q^7 - 10 * q^9 + 12 * q^12 - 10 * q^13 + 4 * q^15 + 12 * q^16 + 20 * q^18 - 10 * q^19 + 20 * q^24 - 18 * q^25 - 2 * q^27 - 10 * q^28 + 30 * q^30 + 10 * q^31 - 40 * q^34 - 6 * q^37 + 10 * q^39 + 10 * q^40 - 10 * q^42 + 24 * q^45 - 20 * q^46 - 14 * q^48 - 24 * q^49 + 10 * q^51 - 20 * q^52 - 10 * q^57 - 8 * q^60 - 20 * q^61 - 10 * q^63 + 26 * q^64 - 4 * q^67 + 34 * q^69 + 20 * q^72 - 80 * q^73 + 6 * q^75 - 20 * q^78 + 10 * q^79 - 2 * q^81 + 20 * q^82 - 10 * q^84 - 30 * q^85 + 30 * q^90 + 10 * q^91 - 70 * q^94 + 30 * q^96 + 16 * q^97

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