LMFDB - Embedded newform 85.2.m.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(9,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("85.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.m (of order $8$, degree $4$, 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:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			9.1
Character	$\chi$	$=$	85.9
Dual form			85.2.m.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.48843 - 1.48843i) q^{2} +(-0.690961 + 1.66813i) q^{3} +2.43082i q^{4} +(1.70647 + 1.44498i) q^{5} +(3.51133 - 1.45444i) q^{6} +(2.47912 - 1.02689i) q^{7} +(0.641241 - 0.641241i) q^{8} +(-0.183901 - 0.183901i) q^{9} +(-0.389210 - 4.69069i) q^{10} +(-0.901470 + 0.373401i) q^{11} +(-4.05491 - 1.67960i) q^{12} +2.65240 q^{13} +(-5.21843 - 2.16155i) q^{14} +(-3.58951 + 1.84818i) q^{15} +2.95276 q^{16} +(-3.25539 + 2.53030i) q^{17} +0.547447i q^{18} +(-0.478059 + 0.478059i) q^{19} +(-3.51248 + 4.14812i) q^{20} +4.84503i q^{21} +(1.89755 + 0.785991i) q^{22} +(-1.54397 - 3.72748i) q^{23} +(0.626599 + 1.51274i) q^{24} +(0.824076 + 4.93162i) q^{25} +(-3.94790 - 3.94790i) q^{26} +(-4.57054 + 1.89318i) q^{27} +(2.49617 + 6.02630i) q^{28} +(3.83958 - 9.26957i) q^{29} +(8.09360 + 2.59183i) q^{30} +(-9.10497 - 3.77140i) q^{31} +(-5.67744 - 5.67744i) q^{32} -1.76177i q^{33} +(8.61157 + 1.07924i) q^{34} +(5.71438 + 1.82993i) q^{35} +(0.447031 - 0.447031i) q^{36} +(2.61646 - 6.31669i) q^{37} +1.42311 q^{38} +(-1.83270 + 4.42454i) q^{39} +(2.02084 - 0.167679i) q^{40} +(2.80190 + 6.76439i) q^{41} +(7.21147 - 7.21147i) q^{42} +(6.29628 - 6.29628i) q^{43} +(-0.907670 - 2.19131i) q^{44} +(-0.0480886 - 0.579556i) q^{45} +(-3.24999 + 7.84616i) q^{46} -0.874497 q^{47} +(-2.04024 + 4.92558i) q^{48} +(0.141809 - 0.141809i) q^{49} +(6.11377 - 8.56693i) q^{50} +(-1.97152 - 7.17875i) q^{51} +6.44750i q^{52} +(2.00842 + 2.00842i) q^{53} +(9.62077 + 3.98505i) q^{54} +(-2.07789 - 0.665407i) q^{55} +(0.931234 - 2.24820i) q^{56} +(-0.467144 - 1.12778i) q^{57} +(-19.5120 + 8.08213i) q^{58} +(-7.59005 - 7.59005i) q^{59} +(-4.49260 - 8.72545i) q^{60} +(0.793008 + 1.91449i) q^{61} +(7.93862 + 19.1655i) q^{62} +(-0.644760 - 0.267068i) q^{63} +10.9954i q^{64} +(4.52624 + 3.83266i) q^{65} +(-2.62227 + 2.62227i) q^{66} +5.73990i q^{67} +(-6.15070 - 7.91327i) q^{68} +7.28473 q^{69} +(-5.78171 - 11.2291i) q^{70} +(1.03955 + 0.430595i) q^{71} -0.235850 q^{72} +(-2.77027 - 1.14748i) q^{73} +(-13.2963 + 5.50752i) q^{74} +(-8.79598 - 2.03289i) q^{75} +(-1.16208 - 1.16208i) q^{76} +(-1.85141 + 1.85141i) q^{77} +(9.31343 - 3.85775i) q^{78} +(-0.377872 + 0.156520i) q^{79} +(5.03879 + 4.26667i) q^{80} -9.71259i q^{81} +(5.89786 - 14.2387i) q^{82} +(4.64846 + 4.64846i) q^{83} -11.7774 q^{84} +(-9.21146 - 0.386088i) q^{85} -18.7431 q^{86} +(12.8098 + 12.8098i) q^{87} +(-0.338619 + 0.817499i) q^{88} -5.62649i q^{89} +(-0.791049 + 0.934201i) q^{90} +(6.57562 - 2.72371i) q^{91} +(9.06082 - 3.75312i) q^{92} +(12.5824 - 12.5824i) q^{93} +(1.30162 + 1.30162i) q^{94} +(-1.50658 + 0.125008i) q^{95} +(13.3936 - 5.54781i) q^{96} +(-14.2405 - 5.89862i) q^{97} -0.422145 q^{98} +(0.234451 + 0.0971126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{9} - 16 q^{10} - 24 q^{14} - 16 q^{15} + 8 q^{16} - 24 q^{19} - 8 q^{20} + 32 q^{24} + 16 q^{25} - 16 q^{26} + 24 q^{29} - 24 q^{31} + 8 q^{34} + 8 q^{35} + 8 q^{36} - 24 q^{39} + 16 q^{40}+ \cdots - 80 q^{99}+O(q^{100}) $ 24 * q - 8 * q^9 - 16 * q^10 - 24 * q^14 - 16 * q^15 + 8 * q^16 - 24 * q^19 - 8 * q^20 + 32 * q^24 + 16 * q^25 - 16 * q^26 + 24 * q^29 - 24 * q^31 + 8 * q^34 + 8 * q^35 + 8 * q^36 - 24 * q^39 + 16 * q^40 - 48 * q^41 + 72 * q^44 + 48 * q^45 - 16 * q^46 + 48 * q^49 + 16 * q^50 + 32 * q^54 + 24 * q^56 - 48 * q^59 + 8 * q^60 + 16 * q^61 + 24 * q^65 - 96 * q^66 + 32 * q^69 + 32 * q^70 + 16 * q^71 - 64 * q^74 - 24 * q^76 - 72 * q^79 - 64 * q^80 - 96 * q^84 - 24 * q^85 - 8 * q^91 - 40 * q^94 - 88 * q^95 + 96 * q^96 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$

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 $

$2$	−1.48843	−	1.48843i	−1.05248	−	1.05248i	−0.998545	−	0.0539308i	$-0.982825\pi$
$2$	−1.48843	−	1.48843i	−1.05248	−	1.05248i	−0.0539308	−	0.998545i	$-0.517175\pi$
$3$	−0.690961	+	1.66813i	−0.398926	+	0.963094i	0.588995	+	0.808137i	$0.299524\pi$
$3$	−0.690961	+	1.66813i	−0.398926	+	0.963094i	−0.987921	+	0.154957i	$0.950476\pi$
$4$			2.43082i			1.21541i
$5$	1.70647	+	1.44498i	0.763156	+	0.646214i
$5$	1.70647	+	1.44498i	0.763156	+	0.646214i
$6$	3.51133	−	1.45444i	1.43349	−	0.593772i
$7$	2.47912	−	1.02689i	0.937021	−	0.388127i	0.138683	−	0.990337i	$-0.455713\pi$
$7$	2.47912	−	1.02689i	0.937021	−	0.388127i	0.798338	+	0.602210i	$0.205713\pi$
$8$	0.641241	−	0.641241i	0.226713	−	0.226713i
$9$	−0.183901	−	0.183901i	−0.0613005	−	0.0613005i
$10$	−0.389210	−	4.69069i	−0.123079	−	1.48333i
$11$	−0.901470	+	0.373401i	−0.271803	+	0.112585i	−0.514422	−	0.857537i	$-0.671994\pi$
$11$	−0.901470	+	0.373401i	−0.271803	+	0.112585i	0.242619	+	0.970122i	$0.421994\pi$
$12$	−4.05491	−	1.67960i	−1.17055	−	0.484859i
$13$	2.65240			0.735643			0.367821	−	0.929896i	$-0.380104\pi$
$13$	2.65240			0.735643			0.367821	+	0.929896i	$0.380104\pi$
$14$	−5.21843	−	2.16155i	−1.39468	−	0.577697i
$15$	−3.58951	+	1.84818i	−0.926808	+	0.477199i
$16$	2.95276			0.738190
$17$	−3.25539	+	2.53030i	−0.789548	+	0.613688i
$17$	−3.25539	+	2.53030i	−0.789548	+	0.613688i
$18$			0.547447i			0.129034i
$19$	−0.478059	+	0.478059i	−0.109674	+	0.109674i	−0.759814	−	0.650140i	$-0.774710\pi$
$19$	−0.478059	+	0.478059i	−0.109674	+	0.109674i	0.650140	+	0.759814i	$0.274710\pi$
$20$	−3.51248	+	4.14812i	−0.785414	+	0.927547i
$21$			4.84503i			1.05727i
$22$	1.89755	+	0.785991i	0.404559	+	0.167574i
$23$	−1.54397	−	3.72748i	−0.321940	−	0.777233i	−0.999141	−	0.0414347i	$-0.986807\pi$
$23$	−1.54397	−	3.72748i	−0.321940	−	0.777233i	0.677201	−	0.735798i	$-0.263193\pi$
$24$	0.626599	+	1.51274i	0.127904	+	0.308788i
$25$	0.824076	+	4.93162i	0.164815	+	0.986324i
$26$	−3.94790	−	3.94790i	−0.774246	−	0.774246i
$27$	−4.57054	+	1.89318i	−0.879601	+	0.364343i
$28$	2.49617	+	6.02630i	0.471733	+	1.13886i
$29$	3.83958	−	9.26957i	0.712992	−	1.72132i	0.0206072	−	0.999788i	$-0.493440\pi$
$29$	3.83958	−	9.26957i	0.712992	−	1.72132i	0.692385	−	0.721528i	$-0.256560\pi$
$30$	8.09360	+	2.59183i	1.47768	+	0.473202i
$31$	−9.10497	−	3.77140i	−1.63530	−	0.677364i	−0.639490	−	0.768800i	$-0.720854\pi$
$31$	−9.10497	−	3.77140i	−1.63530	−	0.677364i	−0.995811	+	0.0914357i	$0.970854\pi$
$32$	−5.67744	−	5.67744i	−1.00364	−	1.00364i
$33$		−	1.76177i		−	0.306685i
$34$	8.61157	+	1.07924i	1.47687	+	0.185089i
$35$	5.71438	+	1.82993i	0.965906	+	0.309314i
$36$	0.447031	−	0.447031i	0.0745052	−	0.0745052i
$37$	2.61646	−	6.31669i	0.430143	−	1.03846i	−0.549098	−	0.835758i	$-0.685029\pi$
$37$	2.61646	−	6.31669i	0.430143	−	1.03846i	0.979241	−	0.202699i	$-0.0649714\pi$
$38$	1.42311			0.230859
$39$	−1.83270	+	4.42454i	−0.293467	+	0.708493i
$40$	2.02084	−	0.167679i	0.319522	−	0.0265124i
$41$	2.80190	+	6.76439i	0.437583	+	1.05642i	0.976781	+	0.214240i	$0.0687276\pi$
$41$	2.80190	+	6.76439i	0.437583	+	1.05642i	−0.539198	+	0.842179i	$0.681272\pi$
$42$	7.21147	−	7.21147i	1.11275	−	1.11275i
$43$	6.29628	−	6.29628i	0.960173	−	0.960173i	−0.0390633	−	0.999237i	$-0.512437\pi$
$43$	6.29628	−	6.29628i	0.960173	−	0.960173i	0.999237	+	0.0390633i	$0.0124374\pi$
$44$	−0.907670	−	2.19131i	−0.136836	−	0.330352i
$45$	−0.0480886	−	0.579556i	−0.00716863	−	0.0863951i
$46$	−3.24999	+	7.84616i	−0.479184	+	1.15685i
$47$	−0.874497			−0.127558			−0.0637792	−	0.997964i	$-0.520315\pi$
$47$	−0.874497			−0.127558			−0.0637792	+	0.997964i	$0.520315\pi$
$48$	−2.04024	+	4.92558i	−0.294483	+	0.710946i
$49$	0.141809	−	0.141809i	0.0202585	−	0.0202585i
$50$	6.11377	−	8.56693i	0.864618	−	1.21155i
$51$	−1.97152	−	7.17875i	−0.276067	−	1.00523i
$52$			6.44750i			0.894107i
$53$	2.00842	+	2.00842i	0.275878	+	0.275878i	0.831461	−	0.555583i	$-0.187505\pi$
$53$	2.00842	+	2.00842i	0.275878	+	0.275878i	−0.555583	+	0.831461i	$0.687505\pi$
$54$	9.62077	+	3.98505i	1.30922	+	0.542297i
$55$	−2.07789	−	0.665407i	−0.280182	−	0.0897234i
$56$	0.931234	−	2.24820i	0.124441	−	0.300428i
$57$	−0.467144	−	1.12778i	−0.0618747	−	0.149379i
$58$	−19.5120	+	8.08213i	−2.56205	+	1.06124i
$59$	−7.59005	−	7.59005i	−0.988140	−	0.988140i	0.0117908	−	0.999930i	$-0.496247\pi$
$59$	−7.59005	−	7.59005i	−0.988140	−	0.988140i	−0.999930	+	0.0117908i	$0.996247\pi$
$60$	−4.49260	−	8.72545i	−0.579992	−	1.12645i
$61$	0.793008	+	1.91449i	0.101534	+	0.245125i	0.966481	−	0.256738i	$-0.0826479\pi$
$61$	0.793008	+	1.91449i	0.101534	+	0.245125i	−0.864947	+	0.501864i	$0.832648\pi$
$62$	7.93862	+	19.1655i	1.00821	+	2.43402i
$63$	−0.644760	−	0.267068i	−0.0812321	−	0.0336475i
$64$			10.9954i			1.37442i
$65$	4.52624	+	3.83266i	0.561410	+	0.475383i
$66$	−2.62227	+	2.62227i	−0.322779	+	0.322779i
$67$			5.73990i			0.701240i	0.936518	+	0.350620i	$0.114029\pi$
$67$			5.73990i			0.701240i	−0.936518	+	0.350620i	$0.885971\pi$
$68$	−6.15070	−	7.91327i	−0.745882	−	0.959624i
$69$	7.28473			0.876979
$70$	−5.78171	−	11.2291i	−0.691047	−	1.34214i
$71$	1.03955	+	0.430595i	0.123372	+	0.0511022i	0.443515	−	0.896267i	$-0.353731\pi$
$71$	1.03955	+	0.430595i	0.123372	+	0.0511022i	−0.320144	+	0.947369i	$0.603731\pi$
$72$	−0.235850			−0.0277952
$73$	−2.77027	−	1.14748i	−0.324236	−	0.134303i	0.214628	−	0.976696i	$-0.431146\pi$
$73$	−2.77027	−	1.14748i	−0.324236	−	0.134303i	−0.538864	+	0.842393i	$0.681146\pi$
$74$	−13.2963	+	5.50752i	−1.54567	+	0.640236i
$75$	−8.79598	−	2.03289i	−1.01567	−	0.234738i
$76$	−1.16208	−	1.16208i	−0.133299	−	0.133299i
$77$	−1.85141	+	1.85141i	−0.210988	+	0.210988i
$78$	9.31343	−	3.85775i	1.05454	−	0.436804i
$79$	−0.377872	+	0.156520i	−0.0425139	+	0.0176099i	−0.403839	−	0.914830i	$-0.632324\pi$
$79$	−0.377872	+	0.156520i	−0.0425139	+	0.0176099i	0.361325	+	0.932440i	$0.382324\pi$
$80$	5.03879	+	4.26667i	0.563354	+	0.477028i
$81$		−	9.71259i		−	1.07918i
$82$	5.89786	−	14.2387i	0.651310	−	1.57240i
$83$	4.64846	+	4.64846i	0.510235	+	0.510235i	0.914598	−	0.404363i	$-0.132507\pi$
$83$	4.64846	+	4.64846i	0.510235	+	0.510235i	−0.404363	+	0.914598i	$0.632507\pi$
$84$	−11.7774			−1.28502
$85$	−9.21146	−	0.386088i	−0.999123	−	0.0418771i
$86$	−18.7431			−2.02112
$87$	12.8098	+	12.8098i	1.37336	+	1.37336i
$88$	−0.338619	+	0.817499i	−0.0360969	+	0.0871457i
$89$		−	5.62649i		−	0.596407i	−0.954502	−	0.298204i	$-0.903613\pi$
$89$		−	5.62649i		−	0.596407i	0.954502	−	0.298204i	$-0.0963874\pi$
$90$	−0.791049	+	0.934201i	−0.0833839	+	0.0984735i
$91$	6.57562	−	2.72371i	0.689312	−	0.285523i
$92$	9.06082	−	3.75312i	0.944656	−	0.391289i
$93$	12.5824	−	12.5824i	1.30473	−	1.30473i
$94$	1.30162	+	1.30162i	0.134252	+	0.134252i
$95$	−1.50658	+	0.125008i	−0.154572	+	0.0128256i
$96$	13.3936	−	5.54781i	1.36698	−	0.566221i
$97$	−14.2405	−	5.89862i	−1.44591	−	0.598915i	−0.484685	−	0.874689i	$-0.661066\pi$
$97$	−14.2405	−	5.89862i	−1.44591	−	0.598915i	−0.961222	+	0.275774i	$0.911066\pi$
$98$	−0.422145			−0.0426430
$99$	0.234451	+	0.0971126i	0.0235632	+	0.00976018i
$100$	−11.9879	+	2.00318i	−1.19879	+	0.200318i
$101$	14.6242			1.45516			0.727582	−	0.686021i	$-0.240644\pi$
$101$	14.6242			1.45516			0.727582	+	0.686021i	$0.240644\pi$
$102$	−7.75057	+	13.6195i	−0.767421	+	1.34853i
$103$			1.63280i			0.160884i	0.996759	+	0.0804421i	$0.0256332\pi$
$103$			1.63280i			0.160884i	−0.996759	+	0.0804421i	$0.974367\pi$
$104$	1.70083	−	1.70083i	0.166780	−	0.166780i
$105$	−7.00097	+	8.26790i	−0.683224	+	0.806864i
$106$		−	5.97877i		−	0.580710i
$107$	5.14591	+	2.13151i	0.497474	+	0.206060i	0.617290	−	0.786736i	$-0.288231\pi$
$107$	5.14591	+	2.13151i	0.497474	+	0.206060i	−0.119816	+	0.992796i	$0.538231\pi$
$108$	−4.60198	−	11.1102i	−0.442826	−	1.06908i
$109$	−1.00965	−	2.43750i	−0.0967066	−	0.233470i	0.868122	−	0.496351i	$-0.165327\pi$
$109$	−1.00965	−	2.43750i	−0.0967066	−	0.233470i	−0.964828	+	0.262881i	$0.915327\pi$
$110$	2.10237	+	4.08319i	0.200453	+	0.389317i
$111$	8.72917	+	8.72917i	0.828536	+	0.828536i
$112$	7.32025	−	3.03215i	0.691699	−	0.286511i
$113$	−2.22293	−	5.36662i	−0.209115	−	0.504849i	0.784169	−	0.620547i	$-0.213090\pi$
$113$	−2.22293	−	5.36662i	−0.209115	−	0.504849i	−0.993284	+	0.115698i	$0.963090\pi$
$114$	−0.983314	+	2.37393i	−0.0920958	+	0.222339i
$115$	2.75138	−	8.59183i	0.256568	−	0.801193i
$116$	22.5326	+	9.33332i	2.09210	+	0.866577i
$117$	−0.487780	−	0.487780i	−0.0450952	−	0.0450952i
$118$			22.5944i			2.07999i
$119$	−5.47219	+	9.61585i	−0.501634	+	0.881483i
$120$	−1.11661	+	3.48687i	−0.101932	+	0.318306i
$121$	−7.10496	+	7.10496i	−0.645905	+	0.645905i
$122$	1.66924	−	4.02991i	0.151126	−	0.364851i
$123$	−13.2199			−1.19199
$124$	9.16759	−	22.1325i	0.823274	−	1.98756i
$125$	−5.71983	+	9.60644i	−0.511597	+	0.859226i
$126$	0.562166	+	1.35719i	0.0500817	+	0.120908i
$127$	−7.53018	+	7.53018i	−0.668195	+	0.668195i	−0.957298	−	0.289103i	$-0.906643\pi$
$127$	−7.53018	+	7.53018i	−0.668195	+	0.668195i	0.289103	+	0.957298i	$0.406643\pi$
$128$	5.01091	−	5.01091i	0.442906	−	0.442906i
$129$	6.15251	+	14.8535i	0.541698	+	1.30778i
$130$	−1.03234	−	12.4416i	−0.0905422	−	1.09120i
$131$	−0.619360	+	1.49527i	−0.0541137	+	0.130642i	−0.948624	−	0.316405i	$-0.897524\pi$
$131$	−0.619360	+	1.49527i	−0.0541137	+	0.130642i	0.894511	+	0.447047i	$0.147524\pi$
$132$	4.28255			0.372748
$133$	−0.694256	+	1.67608i	−0.0601996	+	0.145335i
$134$	8.54341	−	8.54341i	0.738038	−	0.738038i
$135$	−10.5351	−	3.37368i	−0.906717	−	0.290360i
$136$	−0.464958	+	3.71002i	−0.0398698	+	0.318132i
$137$		−	4.70326i		−	0.401826i	−0.979609	−	0.200913i	$-0.935609\pi$
$137$		−	4.70326i		−	0.401826i	0.979609	−	0.200913i	$-0.0643909\pi$
$138$	−10.8428	−	10.8428i	−0.922999	−	0.922999i
$139$	0.761078	+	0.315249i	0.0645538	+	0.0267391i	0.414727	−	0.909946i	$-0.363877\pi$
$139$	0.761078	+	0.315249i	0.0645538	+	0.0267391i	−0.350173	+	0.936685i	$0.613877\pi$
$140$	−4.44822	+	13.8906i	−0.375944	+	1.17397i
$141$	0.604243	−	1.45877i	0.0508865	−	0.122851i
$142$	−0.906381	−	2.18820i	−0.0760618	−	0.183629i
$143$	−2.39106	+	0.990408i	−0.199950	+	0.0828221i
$144$	−0.543017	−	0.543017i	−0.0452514	−	0.0452514i
$145$	19.9465	−	10.2701i	1.65646	−	0.852888i
$146$	2.41540	+	5.83129i	0.199900	+	0.482601i
$147$	0.138571	+	0.334540i	0.0114292	+	0.0275924i
$148$	15.3547	+	6.36014i	1.26215	+	0.522800i
$149$		−	9.60320i		−	0.786725i	−0.919383	−	0.393362i	$-0.871312\pi$
$149$		−	9.60320i		−	0.786725i	0.919383	−	0.393362i	$-0.128688\pi$
$150$	10.0663	+	16.1180i	0.821914	+	1.31603i
$151$	−1.00179	+	1.00179i	−0.0815244	+	0.0815244i	−0.746693	−	0.665169i	$-0.768360\pi$
$151$	−1.00179	+	1.00179i	−0.0815244	+	0.0815244i	0.665169	+	0.746693i	$0.268360\pi$
$152$			0.613103i			0.0497292i
$153$	1.06400	+	0.133345i	0.0860191	+	0.0107803i
$154$	5.51138			0.444120
$155$	−10.0878	−	19.5923i	−0.810268	−	1.57369i
$156$	−10.7552	−	4.45497i	−0.861109	−	0.356683i
$157$	4.81882			0.384584			0.192292	−	0.981338i	$-0.438408\pi$
$157$	4.81882			0.384584			0.192292	+	0.981338i	$0.438408\pi$
$158$	0.795403	+	0.329467i	0.0632788	+	0.0262109i
$159$	−4.73804	+	1.96256i	−0.375751	+	0.155641i
$160$	−1.48460	−	17.8922i	−0.117368	−	1.41450i
$161$	−7.65539	−	7.65539i	−0.603330	−	0.603330i
$162$	−14.4565	+	14.4565i	−1.13581	+	1.13581i
$163$	1.49578	−	0.619572i	0.117158	−	0.0485286i	−0.323334	−	0.946285i	$-0.604804\pi$
$163$	1.49578	−	0.619572i	0.117158	−	0.0485286i	0.440493	+	0.897756i	$0.354804\pi$
$164$	−16.4430	+	6.81091i	−1.28398	+	0.531843i
$165$	2.54572	−	3.00641i	0.198184	−	0.234049i
$166$		−	13.8378i		−	1.07402i
$167$	8.47025	−	20.4490i	0.655447	−	1.58239i	−0.149313	−	0.988790i	$-0.547706\pi$
$167$	8.47025	−	20.4490i	0.655447	−	1.58239i	0.804760	−	0.593600i	$-0.202294\pi$
$168$	3.10683	+	3.10683i	0.239697	+	0.239697i
$169$	−5.96479			−0.458830
$170$	13.1359	+	14.2852i	1.00748	+	1.09563i
$171$	0.175832			0.0134462
$172$	15.3051	+	15.3051i	1.16700	+	1.16700i
$173$	−3.97100	+	9.58685i	−0.301910	+	0.728875i	0.698008	+	0.716089i	$0.254070\pi$
$173$	−3.97100	+	9.58685i	−0.301910	+	0.728875i	−0.999918	+	0.0127852i	$0.995930\pi$
$174$		−	38.1329i		−	2.89085i
$175$	7.10720	+	11.3799i	0.537254	+	0.860237i
$176$	−2.66182	+	1.10256i	−0.200642	+	0.0831088i
$177$	17.9056	−	7.41674i	1.34587	−	0.557476i
$178$	−8.37461	+	8.37461i	−0.627704	+	0.627704i
$179$	13.2428	+	13.2428i	0.989813	+	0.989813i	0.999949	−	0.0101361i	$-0.00322646\pi$
$179$	13.2428	+	13.2428i	0.989813	+	0.989813i	−0.0101361	+	0.999949i	$0.503226\pi$
$180$	1.40879	−	0.116895i	0.105005	−	0.00871282i
$181$	−2.26809	+	0.939472i	−0.168585	+	0.0698304i	−0.465380	−	0.885111i	$-0.654082\pi$
$181$	−2.26809	+	0.939472i	−0.168585	+	0.0698304i	0.296795	+	0.954941i	$0.404082\pi$
$182$	−13.8414	−	5.73328i	−1.02599	−	0.424979i
$183$	−3.74155			−0.276584
$184$	−3.38027	−	1.40015i	−0.249197	−	0.103221i
$185$	13.5924	−	6.99851i	0.999332	−	0.514541i
$186$	−37.4558			−2.74639
$187$	1.98982	−	3.49656i	0.145510	−	0.255694i
$188$		−	2.12574i		−	0.155036i
$189$	−9.38686	+	9.38686i	−0.682793	+	0.682793i
$190$	2.42850	+	2.05636i	0.176182	+	0.149184i
$191$			10.9126i			0.789607i	0.918766	+	0.394803i	$0.129187\pi$
$191$			10.9126i			0.789607i	−0.918766	+	0.394803i	$0.870813\pi$
$192$	−18.3417	−	7.59738i	−1.32370	−	0.548293i
$193$	7.03202	+	16.9768i	0.506176	+	1.22202i	0.946069	+	0.323966i	$0.105016\pi$
$193$	7.03202	+	16.9768i	0.506176	+	1.22202i	−0.439893	+	0.898050i	$0.644984\pi$
$194$	12.4163	+	29.9756i	0.891439	+	2.15213i
$195$	−9.52081	+	4.90212i	−0.681800	+	0.351048i
$196$	0.344712	+	0.344712i	0.0246223	+	0.0246223i
$197$	−18.0071	+	7.45879i	−1.28295	+	0.531417i	−0.916878	−	0.399168i	$-0.869299\pi$
$197$	−18.0071	+	7.45879i	−1.28295	+	0.531417i	−0.366076	+	0.930585i	$0.619299\pi$
$198$	−0.204417	−	0.493507i	−0.0145273	−	0.0350720i
$199$	−8.92336	+	21.5429i	−0.632560	+	1.52713i	0.203834	+	0.979005i	$0.434660\pi$
$199$	−8.92336	+	21.5429i	−0.632560	+	1.52713i	−0.836394	+	0.548129i	$0.815340\pi$
$200$	3.69079	+	2.63393i	0.260978	+	0.186247i
$201$	−9.57488	−	3.96605i	−0.675360	−	0.279743i
$202$	−21.7670	−	21.7670i	−1.53152	−	1.53152i
$203$		−	26.9232i		−	1.88964i
$204$	17.4502	−	4.79240i	1.22176	−	0.335535i
$205$	−4.99303	+	15.5919i	−0.348729	+	1.08899i
$206$	2.43029	−	2.43029i	0.169327	−	0.169327i
$207$	−0.401550	+	0.969427i	−0.0279096	+	0.0673798i
$208$	7.83189			0.543044
$209$	0.252448	−	0.609464i	0.0174622	−	0.0421575i
$210$	22.7266	−	1.88574i	1.56828	−	0.130128i
$211$	−8.77140	−	21.1760i	−0.603848	−	1.45782i	−0.869590	−	0.493774i	$-0.835617\pi$
$211$	−8.77140	−	21.1760i	−0.603848	−	1.45782i	0.265742	−	0.964044i	$-0.414383\pi$
$212$	−4.88211	+	4.88211i	−0.335305	+	0.335305i
$213$	−1.43657	+	1.43657i	−0.0984324	+	0.0984324i
$214$	−4.48671	−	10.8319i	−0.306706	−	0.740453i
$215$	19.8424	−	1.64642i	1.35324	−	0.112285i
$216$	−1.71683	+	4.14480i	−0.116816	+	0.282018i
$217$	−26.4451			−1.79521
$218$	−2.12526	+	5.13082i	−0.143940	+	0.347503i
$219$	3.82830	−	3.82830i	0.258692	−	0.258692i
$220$	1.61748	−	5.05097i	0.109051	−	0.340536i
$221$	−8.63459	+	6.71137i	−0.580826	+	0.451455i
$222$		−	25.9854i		−	1.74403i
$223$	9.23194	+	9.23194i	0.618217	+	0.618217i	0.945074	−	0.326857i	$-0.105990\pi$
$223$	9.23194	+	9.23194i	0.618217	+	0.618217i	−0.326857	+	0.945074i	$0.605990\pi$
$224$	−19.9052	−	8.24499i	−1.32997	−	0.550892i
$225$	0.755383	−	1.05848i	0.0503589	−	0.0705654i
$226$	−4.67915	+	11.2965i	−0.311253	+	0.751430i
$227$	4.09453	+	9.88506i	0.271763	+	0.656095i	0.999559	−	0.0296996i	$-0.00945506\pi$
$227$	4.09453	+	9.88506i	0.271763	+	0.656095i	−0.727796	+	0.685794i	$0.759455\pi$
$228$	2.74144	−	1.13554i	0.181556	−	0.0752031i
$229$	13.3171	+	13.3171i	0.880020	+	0.880020i	0.993536	−	0.113516i	$-0.0362113\pi$
$229$	13.3171	+	13.3171i	0.880020	+	0.880020i	−0.113516	+	0.993536i	$0.536211\pi$
$230$	−16.8835	+	8.69307i	−1.11327	+	0.573204i
$231$	−1.80914	−	4.36765i	−0.119033	−	0.287370i
$232$	−3.48193	−	8.40612i	−0.228600	−	0.551889i
$233$	2.07494	+	0.859469i	0.135934	+	0.0563057i	0.449613	−	0.893223i	$-0.351562\pi$
$233$	2.07494	+	0.859469i	0.135934	+	0.0563057i	−0.313679	+	0.949529i	$0.601562\pi$
$234$			1.45205i			0.0949233i
$235$	−1.49230	−	1.26363i	−0.0973471	−	0.0824301i
$236$	18.4500	−	18.4500i	1.20099	−	1.20099i
$237$		−	0.738488i		−	0.0479700i
$238$	22.4574	−	6.16753i	1.45570	−	0.399782i
$239$	16.7293			1.08213			0.541063	−	0.840982i	$-0.318022\pi$
$239$	16.7293			1.08213			0.541063	+	0.840982i	$0.318022\pi$
$240$	−10.5990	+	5.45724i	−0.684160	+	0.352264i
$241$	10.8767	+	4.50526i	0.700627	+	0.290209i	0.704420	−	0.709784i	$-0.251207\pi$
$241$	10.8767	+	4.50526i	0.700627	+	0.290209i	−0.00379273	+	0.999993i	$0.501207\pi$
$242$	21.1504			1.35960
$243$	2.49021	+	1.03148i	0.159747	+	0.0661693i
$244$	−4.65378	+	1.92766i	−0.297928	+	0.123406i
$245$	0.446904	−	0.0370819i	0.0285517	−	0.00236907i
$246$	19.6768	+	19.6768i	1.25455	+	1.25455i
$247$	−1.26800	+	1.26800i	−0.0806812	+	0.0806812i
$248$	−8.25686	+	3.42010i	−0.524311	+	0.217177i
$249$	−10.9661	+	4.54232i	−0.694950	+	0.287858i
$250$	22.8120	−	5.78493i	1.44276	−	0.365871i
$251$			17.7019i			1.11733i	0.829392	+	0.558666i	$0.188687\pi$
$251$			17.7019i			1.11733i	−0.829392	+	0.558666i	$0.811313\pi$
$252$	0.649195	−	1.56729i	0.0408954	−	0.0987303i
$253$	2.78369	+	2.78369i	0.175009	+	0.175009i
$254$	22.4162			1.40652
$255$	7.00880	−	15.0991i	0.438908	−	0.945543i
$256$	7.07403			0.442127
$257$	5.44763	+	5.44763i	0.339814	+	0.339814i	0.856297	−	0.516483i	$-0.172759\pi$
$257$	5.44763	+	5.44763i	0.339814	+	0.339814i	−0.516483	+	0.856297i	$0.672759\pi$
$258$	12.9507	−	31.2658i	0.806278	−	1.94653i
$259$		−	18.3467i		−	1.14001i
$260$	−9.31649	+	11.0025i	−0.577784	+	0.682343i
$261$	−2.41079	+	0.998582i	−0.149224	+	0.0618107i
$262$	3.14746	−	1.30372i	0.194451	−	0.0805442i
$263$	4.45259	−	4.45259i	0.274558	−	0.274558i	−0.556374	−	0.830932i	$-0.687808\pi$
$263$	4.45259	−	4.45259i	0.274558	−	0.274558i	0.830932	+	0.556374i	$0.187808\pi$
$264$	−1.12972	−	1.12972i	−0.0695295	−	0.0695295i
$265$	0.525185	+	6.32944i	0.0322619	+	0.388814i
$266$	3.52807	−	1.46137i	0.216320	−	0.0896026i
$267$	9.38571	+	3.88769i	0.574396	+	0.237923i
$268$	−13.9527			−0.852294
$269$	−8.55428	−	3.54330i	−0.521563	−	0.216039i	0.106340	−	0.994330i	$-0.466087\pi$
$269$	−8.55428	−	3.54330i	−0.521563	−	0.216039i	−0.627904	+	0.778291i	$0.716087\pi$
$270$	10.6592	+	20.7022i	0.648700	+	1.25989i
$271$	16.7791			1.01926			0.509628	−	0.860395i	$-0.329783\pi$
$271$	16.7791			1.01926			0.509628	+	0.860395i	$0.329783\pi$
$272$	−9.61239	+	7.47137i	−0.582837	+	0.453018i
$273$			12.8510i			0.777775i
$274$	−7.00044	+	7.00044i	−0.422912	+	0.422912i
$275$	−2.58435	−	4.13800i	−0.155842	−	0.249531i
$276$			17.7079i			1.06589i
$277$	−11.0923	−	4.59456i	−0.666469	−	0.276061i	0.0236887	−	0.999719i	$-0.492459\pi$
$277$	−11.0923	−	4.59456i	−0.666469	−	0.276061i	−0.690158	+	0.723659i	$0.742459\pi$
$278$	−0.663584	−	1.60203i	−0.0397991	−	0.0960835i
$279$	0.980851	+	2.36798i	0.0587220	+	0.141767i
$280$	4.83772	−	2.49087i	0.289109	−	0.148858i
$281$	−19.9411	−	19.9411i	−1.18959	−	1.18959i	−0.977182	−	0.212403i	$-0.931871\pi$
$281$	−19.9411	−	19.9411i	−1.18959	−	1.18959i	−0.212403	−	0.977182i	$-0.568129\pi$
$282$	−3.07064	+	1.27190i	−0.182854	+	0.0757407i
$283$	−6.53556	−	15.7782i	−0.388499	−	0.937919i	−0.990258	−	0.139242i	$-0.955534\pi$
$283$	−6.53556	−	15.7782i	−0.388499	−	0.937919i	0.601760	−	0.798677i	$-0.294466\pi$
$284$	−1.04670	+	2.52695i	−0.0621101	+	0.149947i
$285$	0.832458	−	2.59954i	0.0493105	−	0.153984i
$286$	5.03306	+	2.08476i	0.297611	+	0.123274i
$287$	13.8925	+	13.8925i	0.820049	+	0.820049i
$288$			2.08818i			0.123047i
$289$	4.19515	−	16.4742i	0.246774	−	0.969073i
$290$	−44.9751	−	14.4025i	−2.64103	−	0.845743i
$291$	19.6793	−	19.6793i	1.15362	−	1.15362i
$292$	2.78933	−	6.73403i	0.163233	−	0.394079i
$293$	−6.82563			−0.398758			−0.199379	−	0.979922i	$-0.563892\pi$
$293$	−6.82563			−0.398758			−0.199379	+	0.979922i	$0.563892\pi$
$294$	0.291685	−	0.704191i	0.0170114	−	0.0410693i
$295$	−1.98473	−	23.9196i	−0.115556	−	1.39265i
$296$	−2.37274	−	5.72830i	−0.137913	−	0.332951i
$297$	3.41329	−	3.41329i	0.198059	−	0.198059i
$298$	−14.2936	+	14.2936i	−0.828009	+	0.828009i
$299$	−4.09523	−	9.88676i	−0.236833	−	0.571766i
$300$	4.94160	−	21.3814i	0.285303	−	1.23446i
$301$	9.14369	−	22.0748i	0.527033	−	1.27237i
$302$	2.98218			0.171605
$303$	−10.1048	+	24.3950i	−0.580503	+	1.40146i
$304$	−1.41159	+	1.41159i	−0.0809605	+	0.0809605i
$305$	−1.41315	+	4.41290i	−0.0809169	+	0.252682i
$306$	−1.38521	−	1.78215i	−0.0791869	−	0.101879i
$307$		−	0.746287i		−	0.0425929i	−0.999773	−	0.0212964i	$-0.993221\pi$
$307$		−	0.746287i		−	0.0425929i	0.999773	−	0.0212964i	$-0.00677938\pi$
$308$	−4.50045	−	4.50045i	−0.256437	−	0.256437i
$309$	−2.72371	−	1.12820i	−0.154947	−	0.0641810i
$310$	−14.1467	+	44.1765i	−0.803481	+	2.50906i
$311$	−6.96494	+	16.8149i	−0.394946	+	0.953483i	0.593900	+	0.804539i	$0.297587\pi$
$311$	−6.96494	+	16.8149i	−0.394946	+	0.953483i	−0.988846	+	0.148944i	$0.952413\pi$
$312$	1.66199	+	4.01240i	0.0940916	+	0.227157i
$313$	−9.16854	+	3.79773i	−0.518236	+	0.214661i	−0.626442	−	0.779468i	$-0.715490\pi$
$313$	−9.16854	+	3.79773i	−0.518236	+	0.214661i	0.108206	+	0.994129i	$0.465490\pi$
$314$	−7.17245	−	7.17245i	−0.404765	−	0.404765i
$315$	−0.714356	−	1.38741i	−0.0402494	−	0.0781716i
$316$	−0.380471	−	0.918539i	−0.0214032	−	0.0516718i
$317$	−9.30367	−	22.4610i	−0.522546	−	1.26154i	−0.936317	−	0.351157i	$-0.885788\pi$
$317$	−9.30367	−	22.4610i	−0.522546	−	1.26154i	0.413770	−	0.910381i	$-0.364212\pi$
$318$	9.97335	+	4.13110i	0.559278	+	0.231660i
$319$			9.78994i			0.548131i
$320$	−15.8881	+	18.7633i	−0.888171	+	1.04890i
$321$	−7.11125	+	7.11125i	−0.396911	+	0.396911i
$322$			22.7890i			1.26998i
$323$	0.346636	−	2.76591i	0.0192874	−	0.153899i
$324$	23.6095			1.31164
$325$	2.18578	+	13.0806i	0.121245	+	0.725582i
$326$	−3.14854	−	1.30417i	−0.174381	−	0.0722312i
$327$	4.76369			0.263433
$328$	6.13429	+	2.54091i	0.338710	+	0.140298i
$329$	−2.16799	+	0.898009i	−0.119525	+	0.0495088i
$330$	−8.26393	+	0.685700i	−0.454915	+	0.0377465i
$331$	−0.346315	−	0.346315i	−0.0190352	−	0.0190352i	0.697525	−	0.716560i	$-0.254285\pi$
$331$	−0.346315	−	0.346315i	−0.0190352	−	0.0190352i	−0.716560	+	0.697525i	$0.754285\pi$
$332$	−11.2996	+	11.2996i	−0.620144	+	0.620144i
$333$	−1.64282	+	0.680478i	−0.0900259	+	0.0372899i
$334$	−43.0441	+	17.8295i	−2.35527	+	0.975584i
$335$	−8.29403	+	9.79496i	−0.453151	+	0.535156i
$336$			14.3062i			0.780468i
$337$	−2.30186	+	5.55719i	−0.125390	+	0.302719i	−0.974092	−	0.226153i	$-0.927385\pi$
$337$	−2.30186	+	5.55719i	−0.125390	+	0.302719i	0.848701	+	0.528872i	$0.177385\pi$
$338$	8.87814	+	8.87814i	0.482907	+	0.482907i
$339$	10.4882			0.569639
$340$	0.938510	−	22.3914i	0.0508979	−	1.21434i
$341$	9.61610			0.520741
$342$	−0.261712	−	0.261712i	−0.0141518	−	0.0141518i
$343$	−6.98227	+	16.8567i	−0.377007	+	0.910175i
$344$		−	8.07486i		−	0.435367i
$345$	12.4312	+	10.5263i	0.669272	+	0.566716i
$346$	20.1798	−	8.35877i	1.08488	−	0.449370i
$347$	7.29831	−	3.02306i	0.391794	−	0.162286i	−0.178085	−	0.984015i	$-0.556990\pi$
$347$	7.29831	−	3.02306i	0.391794	−	0.162286i	0.569879	+	0.821729i	$0.306990\pi$
$348$	−31.1383	+	31.1383i	−1.66919	+	1.66919i
$349$	−13.5417	−	13.5417i	−0.724868	−	0.724868i	0.244725	−	0.969593i	$-0.421302\pi$
$349$	−13.5417	−	13.5417i	−0.724868	−	0.724868i	−0.969593	+	0.244725i	$0.921302\pi$
$350$	6.35954	−	27.5166i	0.339932	−	1.47083i
$351$	−12.1229	+	5.02147i	−0.647072	+	0.268026i
$352$	7.23801	+	2.99808i	0.385787	+	0.159798i
$353$	13.7165			0.730055			0.365027	−	0.930997i	$-0.381060\pi$
$353$	13.7165			0.730055			0.365027	+	0.930997i	$0.381060\pi$
$354$	−37.6904	−	15.6119i	−2.00322	−	0.829761i
$355$	1.15176	+	2.23692i	0.0611289	+	0.118723i
$356$	13.6770			0.724879
$357$	−12.2594	−	15.7725i	−0.648836	−	0.834768i
$358$		−	39.4218i		−	2.08351i
$359$	17.6460	−	17.6460i	0.931322	−	0.931322i	−0.0664662	−	0.997789i	$-0.521172\pi$
$359$	17.6460	−	17.6460i	0.931322	−	0.931322i	0.997789	+	0.0664662i	$0.0211725\pi$
$360$	−0.402471	−	0.340798i	−0.0212121	−	0.0179617i
$361$			18.5429i			0.975943i
$362$	4.77421	+	1.97754i	0.250927	+	0.103937i
$363$	−6.94272	−	16.7612i	−0.364398	−	0.879736i
$364$	6.62085	+	15.9841i	0.347027	+	0.837797i
$365$	−3.06929	−	5.96113i	−0.160654	−	0.312020i
$366$	5.56902	+	5.56902i	0.291097	+	0.291097i
$367$	7.87910	−	3.26363i	0.411286	−	0.170360i	−0.167440	−	0.985882i	$-0.553550\pi$
$367$	7.87910	−	3.26363i	0.411286	−	0.170360i	0.578726	+	0.815522i	$0.303550\pi$
$368$	−4.55898	−	11.0063i	−0.237653	−	0.573745i
$369$	0.728707	−	1.75925i	0.0379350	−	0.0915831i
$370$	−30.6480	−	9.81449i	−1.59331	−	0.510231i
$371$	7.04155	+	2.91670i	0.365579	+	0.151428i
$372$	30.5854	+	30.5854i	1.58578	+	1.58578i
$373$			11.5593i			0.598519i	0.954172	+	0.299260i	$0.0967397\pi$
$373$			11.5593i			0.598519i	−0.954172	+	0.299260i	$0.903260\pi$
$374$	−8.16606	+	2.24266i	−0.422257	+	0.115965i
$375$	−12.0726	−	16.1791i	−0.623425	−	0.835484i
$376$	−0.560763	+	0.560763i	−0.0289192	+	0.0289192i
$377$	10.1841	−	24.5866i	0.524508	−	1.26627i
$378$	27.9433			1.43725
$379$	4.70807	−	11.3663i	0.241837	−	0.583847i	−0.755628	−	0.655001i	$-0.772668\pi$
$379$	4.70807	−	11.3663i	0.241837	−	0.583847i	0.997465	+	0.0711543i	$0.0226683\pi$
$380$	−0.303873	−	3.66222i	−0.0155883	−	0.187868i
$381$	−7.35824	−	17.7644i	−0.376974	−	0.910096i
$382$	16.2426	−	16.2426i	0.831042	−	0.831042i
$383$	−4.00295	+	4.00295i	−0.204541	+	0.204541i	−0.801942	−	0.597401i	$-0.796200\pi$
$383$	−4.00295	+	4.00295i	−0.204541	+	0.204541i	0.597401	+	0.801942i	$0.296200\pi$
$384$	4.89649	+	11.8212i	0.249873	+	0.603247i
$385$	−5.83464	+	0.484129i	−0.297361	+	0.0246735i
$386$	14.8020	−	35.7353i	0.753404	−	1.81888i
$387$	−2.31579			−0.117718
$388$	14.3385	−	34.6162i	0.727926	−	1.75737i
$389$	1.15168	−	1.15168i	0.0583927	−	0.0583927i	−0.677307	−	0.735700i	$-0.736853\pi$
$389$	1.15168	−	1.15168i	0.0583927	−	0.0583927i	0.735700	+	0.677307i	$0.236853\pi$
$390$	21.4675	+	6.87457i	1.08705	+	0.348108i
$391$	14.4579	+	8.22769i	0.731166	+	0.416092i
$392$		−	0.181868i		−	0.00918570i
$393$	−2.06634	−	2.06634i	−0.104233	−	0.104233i
$394$	37.9041	+	15.7004i	1.90958	+	0.790975i
$395$	−0.870995	−	0.278921i	−0.0438245	−	0.0140340i
$396$	−0.236063	+	0.569907i	−0.0118626	+	0.0286389i
$397$	4.91819	+	11.8736i	0.246837	+	0.595917i	0.997932	−	0.0642772i	$-0.0204742\pi$
$397$	4.91819	+	11.8736i	0.246837	+	0.595917i	−0.751095	+	0.660194i	$0.770474\pi$
$398$	45.3467	−	18.7832i	2.27303	−	0.941518i
$399$	−2.31621	−	2.31621i	−0.115956	−	0.115956i
$400$	2.43330	+	14.5619i	0.121665	+	0.728095i
$401$	−11.0222	−	26.6099i	−0.550422	−	1.32884i	−0.917163	−	0.398512i	$-0.869527\pi$
$401$	−11.0222	−	26.6099i	−0.550422	−	1.32884i	0.366741	−	0.930323i	$-0.380473\pi$
$402$	8.34833	+	20.1547i	0.416377	+	1.00522i
$403$	−24.1500	−	10.0033i	−1.20300	−	0.498298i
$404$			35.5488i			1.76862i
$405$	14.0345	−	16.5742i	0.697379	−	0.823580i
$406$	−40.0732	+	40.0732i	−1.98880	+	1.98880i
$407$			6.67129i			0.330684i
$408$	−5.86752	−	3.33909i	−0.290486	−	0.165310i
$409$	−13.6197			−0.673451			−0.336725	−	0.941603i	$-0.609319\pi$
$409$	−13.6197			−0.673451			−0.336725	+	0.941603i	$0.609319\pi$
$410$	30.6391	−	15.7756i	1.51316	−	0.779103i
$411$	7.84563	+	3.24977i	0.386996	+	0.160299i
$412$	−3.96903			−0.195540
$413$	−26.6108	−	11.0225i	−1.30943	−	0.542384i
$414$	2.04060	−	0.845243i	0.100290	−	0.0415414i
$415$	1.21553	+	14.6494i	0.0596682	+	0.719110i
$416$	−15.0588	−	15.0588i	−0.738320	−	0.738320i
$417$	−1.05175	+	1.05175i	−0.0515045	+	0.0515045i
$418$	−1.28289	+	0.531391i	−0.0627483	+	0.0259912i
$419$	13.1802	−	5.45940i	0.643893	−	0.266709i	−0.0367500	−	0.999324i	$-0.511701\pi$
$419$	13.1802	−	5.45940i	0.643893	−	0.266709i	0.680643	+	0.732615i	$0.261701\pi$
$420$	−20.0978	−	17.0181i	−0.980670	−	0.830397i
$421$			28.9349i			1.41020i	0.709107	+	0.705101i	$0.249098\pi$
$421$			28.9349i			1.41020i	−0.709107	+	0.705101i	$0.750902\pi$
$422$	−18.4634	+	44.5745i	−0.898783	+	2.16985i
$423$	0.160821	+	0.160821i	0.00781940	+	0.00781940i
$424$	2.57576			0.125090
$425$	−15.1612	−	13.9692i	−0.735425	−	0.677606i
$426$	4.27646			0.207195
$427$	3.93193	+	3.93193i	0.190279	+	0.190279i
$428$	−5.18130	+	12.5088i	−0.250448	+	0.604634i
$429$		−	4.67292i		−	0.225611i
$430$	−31.9845	−	27.0833i	−1.54243	−	1.30607i
$431$	−18.9908	+	7.86623i	−0.914753	+	0.378903i	−0.789874	−	0.613269i	$-0.789854\pi$
$431$	−18.9908	+	7.86623i	−0.914753	+	0.378903i	−0.124879	+	0.992172i	$0.539854\pi$
$432$	−13.4957	+	5.59011i	−0.649313	+	0.268954i
$433$	17.0995	−	17.0995i	0.821748	−	0.821748i	−0.164611	−	0.986359i	$-0.552637\pi$
$433$	17.0995	−	17.0995i	0.821748	−	0.821748i	0.986359	+	0.164611i	$0.0526368\pi$
$434$	39.3616	+	39.3616i	1.88942	+	1.88942i
$435$	3.34966	+	40.3695i	0.160604	+	1.93557i
$436$	5.92512	−	2.45427i	0.283762	−	0.117538i
$437$	2.52007	+	1.04385i	0.120551	+	0.0499339i
$438$	−11.3963			−0.544535
$439$	−20.3668	−	8.43621i	−0.972055	−	0.402638i	−0.160578	−	0.987023i	$-0.551336\pi$
$439$	−20.3668	−	8.43621i	−0.972055	−	0.402638i	−0.811477	+	0.584385i	$0.801336\pi$
$440$	−1.75911	+	0.905740i	−0.0838624	+	0.0431795i
$441$	−0.0521578			−0.00248371
$442$	22.8413	+	2.86258i	1.08645	+	0.136159i
$443$			32.3324i			1.53616i	0.640356	+	0.768079i	$0.278787\pi$
$443$			32.3324i			1.53616i	−0.640356	+	0.768079i	$0.721213\pi$
$444$	−21.2190	+	21.2190i	−1.00701	+	1.00701i
$445$	8.13016	−	9.60144i	0.385407	−	0.455152i
$446$		−	27.4821i		−	1.30132i
$447$	16.0194	+	6.63544i	0.757690	+	0.313845i
$448$	11.2910	+	27.2589i	0.533450	+	1.28786i
$449$	12.0051	+	28.9829i	0.566556	+	1.36779i	0.904441	+	0.426599i	$0.140288\pi$
$449$	12.0051	+	28.9829i	0.566556	+	1.36779i	−0.337885	+	0.941187i	$0.609712\pi$
$450$	−2.69980	+	0.451138i	−0.127270	+	0.0212668i
$451$	−5.05166	−	5.05166i	−0.237873	−	0.237873i
$452$	13.0453	−	5.40353i	0.613598	−	0.254161i
$453$	−0.978914	−	2.36331i	−0.0459934	−	0.111038i
$454$	8.61878	−	20.8076i	0.404499	−	0.976548i
$455$	15.1568	+	4.85370i	0.710562	+	0.227545i
$456$	−1.02273	−	0.423630i	−0.0478939	−	0.0198383i
$457$	9.01432	+	9.01432i	0.421672	+	0.421672i	0.885779	−	0.464107i	$-0.153625\pi$
$457$	9.01432	+	9.01432i	0.421672	+	0.421672i	−0.464107	+	0.885779i	$0.653625\pi$
$458$		−	39.6431i		−	1.85240i
$459$	10.0886	−	17.7279i	0.470895	−	0.827467i
$460$	20.8852	+	6.68811i	0.973777	+	0.311835i
$461$	−12.3023	+	12.3023i	−0.572974	+	0.572974i	−0.932958	−	0.359984i	$-0.882782\pi$
$461$	−12.3023	+	12.3023i	−0.572974	+	0.572974i	0.359984	+	0.932958i	$0.382782\pi$
$462$	−3.80815	+	9.19369i	−0.177171	+	0.427729i
$463$	−29.5747			−1.37445			−0.687227	−	0.726443i	$-0.741172\pi$
$463$	−29.5747			−1.37445			−0.687227	+	0.726443i	$0.741172\pi$
$464$	11.3374	−	27.3708i	0.526324	−	1.27066i
$465$	39.6526	−	3.29018i	1.83885	−	0.152578i
$466$	−1.80914	−	4.36765i	−0.0838068	−	0.202327i
$467$	−23.2530	+	23.2530i	−1.07602	+	1.07602i	−0.0791599	+	0.996862i	$0.525224\pi$
$467$	−23.2530	+	23.2530i	−1.07602	+	1.07602i	−0.996862	+	0.0791599i	$0.974776\pi$
$468$	1.18570	−	1.18570i	0.0548092	−	0.0548092i
$469$	5.89422	+	14.2299i	0.272170	+	0.657076i
$470$	0.340363	+	4.10200i	0.0156998	+	0.189211i
$471$	−3.32962	+	8.03840i	−0.153421	+	0.370390i
$472$	−9.73409			−0.448048
$473$	−3.32487	+	8.02694i	−0.152878	+	0.369079i
$474$	−1.09918	+	1.09918i	−0.0504872	+	0.0504872i
$475$	−2.75157	−	1.96365i	−0.126251	−	0.0900985i
$476$	−23.3744	−	13.3019i	−1.07136	−	0.609691i
$477$		−	0.738703i		−	0.0338229i
$478$	−24.9003	−	24.9003i	−1.13891	−	1.13891i
$479$	0.548605	+	0.227240i	0.0250664	+	0.0103828i	0.395181	−	0.918603i	$-0.370682\pi$
$479$	0.548605	+	0.227240i	0.0250664	+	0.0103828i	−0.370115	+	0.928986i	$0.620682\pi$
$480$	30.8722	+	9.88628i	1.40912	+	0.451245i
$481$	6.93989	−	16.7544i	0.316432	−	0.763934i
$482$	−9.48335	−	22.8948i	−0.431955	−	1.04283i
$483$	18.0598	−	7.48059i	0.821747	−	0.340379i
$484$	−17.2709	−	17.2709i	−0.785039	−	0.785039i
$485$	−15.7777	−	30.6431i	−0.716427	−	1.39143i
$486$	−2.17121	−	5.24176i	−0.0984881	−	0.237771i
$487$	−0.862103	−	2.08130i	−0.0390656	−	0.0943127i	0.903142	−	0.429341i	$-0.141254\pi$
$487$	−0.862103	−	2.08130i	−0.0390656	−	0.0943127i	−0.942208	+	0.335028i	$0.891254\pi$
$488$	1.73616	+	0.719141i	0.0785922	+	0.0325540i
$489$			2.92325i			0.132194i
$490$	−0.720377	−	0.609990i	−0.0325433	−	0.0275565i
$491$	−5.16155	+	5.16155i	−0.232937	+	0.232937i	−0.813918	−	0.580980i	$-0.802669\pi$
$491$	−5.16155	+	5.16155i	−0.232937	+	0.232937i	0.580980	+	0.813918i	$0.302669\pi$
$492$		−	32.1351i		−	1.44876i
$493$	10.9555	+	39.8914i	0.493409	+	1.79662i
$494$	3.77466			0.169830
$495$	0.259757	+	0.504496i	0.0116752	+	0.0226754i
$496$	−26.8848	−	11.1360i	−1.20716	−	0.500023i
$497$	3.01934			0.135436
$498$	23.0832	+	9.56136i	1.03438	+	0.428455i
$499$	−7.02196	+	2.90859i	−0.314346	+	0.130206i	−0.534278	−	0.845309i	$-0.679416\pi$
$499$	−7.02196	+	2.90859i	−0.314346	+	0.130206i	0.219932	+	0.975515i	$0.429416\pi$
$500$	−23.3515	−	13.9039i	−1.04431	−	0.621799i
$501$	28.2589	+	28.2589i	1.26251	+	1.26251i
$502$	26.3479	−	26.3479i	1.17597	−	1.17597i
$503$	−14.3260	+	5.93402i	−0.638764	+	0.264585i	−0.678472	−	0.734627i	$-0.737357\pi$
$503$	−14.3260	+	5.93402i	−0.638764	+	0.264585i	0.0397075	+	0.999211i	$0.487357\pi$
$504$	−0.584702	+	0.242191i	−0.0260447	+	0.0107881i
$505$	24.9558	+	21.1317i	1.11052	+	0.940347i
$506$		−	8.28662i		−	0.368385i
$507$	4.12143	−	9.95002i	0.183039	−	0.441896i
$508$	−18.3045	−	18.3045i	−0.812131	−	0.812131i
$509$	−29.3375			−1.30036			−0.650182	−	0.759779i	$-0.725307\pi$
$509$	−29.3375			−1.30036			−0.650182	+	0.759779i	$0.725307\pi$
$510$	−32.9060	+	12.0418i	−1.45710	+	0.533221i
$511$	−8.04618			−0.355942
$512$	−20.5510	−	20.5510i	−0.908233	−	0.908233i
$513$	1.27994	−	3.09004i	0.0565107	−	0.136429i
$514$		−	16.2168i		−	0.715292i
$515$	−2.35935	+	2.78632i	−0.103966	+	0.122780i
$516$	−36.1061	+	14.9556i	−1.58948	+	0.658385i
$517$	0.788333	−	0.326538i	0.0346708	−	0.0143611i
$518$	−27.3076	+	27.3076i	−1.19983	+	1.19983i
$519$	−13.2483	−	13.2483i	−0.581535	−	0.581535i
$520$	5.36006	−	0.444751i	0.235054	−	0.0195036i
$521$	−14.0288	+	5.81093i	−0.614614	+	0.254581i	−0.668200	−	0.743982i	$-0.732935\pi$
$521$	−14.0288	+	5.81093i	−0.614614	+	0.254581i	0.0535860	+	0.998563i	$0.482935\pi$
$522$	5.07460	+	2.10197i	0.222109	+	0.0920006i
$523$	35.8569			1.56791			0.783957	−	0.620815i	$-0.213198\pi$
$523$	35.8569			1.56791			0.783957	+	0.620815i	$0.213198\pi$
$524$	−3.63472	−	1.50555i	−0.158784	−	0.0657703i
$525$	−23.8939	+	3.99268i	−1.04281	+	0.174255i
$526$	−13.2547			−0.577932
$527$	39.1830	−	10.7609i	1.70684	−	0.468753i
$528$		−	5.20209i		−	0.226392i
$529$	4.75321	−	4.75321i	0.206661	−	0.206661i
$530$	8.63919	−	10.2026i	0.375263	−	0.443172i
$531$			2.79164i			0.121147i
$532$	−4.07425	−	1.68761i	−0.176641	−	0.0731671i
$533$	7.43175	+	17.9418i	0.321905	+	0.777148i
$534$	−8.18339	−	19.7565i	−0.354130	−	0.854945i
$535$	5.70136	+	11.0731i	0.246491	+	0.478731i
$536$	3.68066	+	3.68066i	0.158980	+	0.158980i
$537$	−31.2409	+	12.9404i	−1.34814	+	0.558420i
$538$	7.45847	+	18.0063i	0.321557	+	0.776308i
$539$	−0.0748850	+	0.180788i	−0.00322553	+	0.00778711i
$540$	8.20080	−	25.6089i	0.352906	−	1.10203i
$541$	24.6831	+	10.2241i	1.06121	+	0.439568i	0.843881	−	0.536531i	$-0.180266\pi$
$541$	24.6831	+	10.2241i	1.06121	+	0.439568i	0.217329	+	0.976098i	$0.430266\pi$
$542$	−24.9744	−	24.9744i	−1.07274	−	1.07274i
$543$		−	4.43259i		−	0.190221i
$544$	32.8479	+	4.11666i	1.40834	+	0.176500i
$545$	1.79921	−	5.61844i	0.0770695	−	0.240667i
$546$	19.1277	−	19.1277i	0.818589	−	0.818589i
$547$	−5.16946	+	12.4802i	−0.221030	+	0.533614i	−0.995030	−	0.0995712i	$-0.968253\pi$
$547$	−5.16946	+	12.4802i	−0.221030	+	0.533614i	0.774000	+	0.633185i	$0.218253\pi$
$548$	11.4328			0.488383
$549$	0.206242	−	0.497913i	0.00880221	−	0.0212504i
$550$	−2.31248	+	10.0057i	−0.0986047	+	0.426645i
$551$	2.59586	+	6.26695i	0.110587	+	0.266981i
$552$	4.67127	−	4.67127i	0.198822	−	0.198822i
$553$	−0.776064	+	0.776064i	−0.0330016	+	0.0330016i
$554$	9.67133	+	23.3487i	0.410895	+	0.991989i
$555$	2.28260	+	27.5095i	0.0968911	+	1.16771i
$556$	−0.766313	+	1.85004i	−0.0324989	+	0.0784593i
$557$	16.9198			0.716915			0.358458	−	0.933546i	$-0.383303\pi$
$557$	16.9198			0.716915			0.358458	+	0.933546i	$0.383303\pi$
$558$	2.06464	−	4.98449i	0.0874033	−	0.211010i
$559$	16.7002	−	16.7002i	0.706345	−	0.706345i
$560$	16.8732	+	5.40334i	0.713022	+	0.228333i
$561$	4.45781	+	5.73526i	0.188209	+	0.242143i
$562$			59.3616i			2.50402i
$563$	26.6224	+	26.6224i	1.12200	+	1.12200i	0.991441	+	0.130558i	$0.0416768\pi$
$563$	26.6224	+	26.6224i	1.12200	+	1.12200i	0.130558	+	0.991441i	$0.458323\pi$
$564$	3.54601	+	1.46881i	0.149314	+	0.0618479i
$565$	3.96129	−	12.3701i	0.166653	−	0.520412i
$566$	−13.7570	+	33.2124i	−0.578251	+	1.39602i
$567$	−9.97373	−	24.0787i	−0.418857	−	1.01121i
$568$	0.942715	−	0.390485i	0.0395555	−	0.0163844i
$569$	−21.0557	−	21.0557i	−0.882701	−	0.882701i	0.111108	−	0.993808i	$-0.464560\pi$
$569$	−21.0557	−	21.0557i	−0.882701	−	0.882701i	−0.993808	+	0.111108i	$0.964560\pi$
$570$	−5.10827	+	2.63017i	−0.213962	+	0.110166i
$571$	−3.82363	−	9.23107i	−0.160014	−	0.386308i	0.823456	−	0.567381i	$-0.192043\pi$
$571$	−3.82363	−	9.23107i	−0.160014	−	0.386308i	−0.983470	+	0.181072i	$0.942043\pi$
$572$	−2.40750	−	5.81222i	−0.100663	−	0.243021i
$573$	−18.2036	−	7.54017i	−0.760465	−	0.314995i
$574$		−	41.3559i		−	1.72616i
$575$	17.1102	−	10.6860i	0.713543	−	0.445638i
$576$	2.02207	−	2.02207i	0.0842527	−	0.0842527i
$577$		−	17.5104i		−	0.728968i	−0.931210	−	0.364484i	$-0.881245\pi$
$577$		−	17.5104i		−	0.728968i	0.931210	−	0.364484i	$-0.118755\pi$
$578$	−30.7648	+	18.2765i	−1.27965	+	0.760203i
$579$	−33.1783			−1.37884
$580$	24.9648	+	48.4862i	1.03661	+	2.01328i
$581$	16.2976	+	6.75067i	0.676137	+	0.280065i
$582$	−58.5824			−2.42832
$583$	−2.56048	−	1.06058i	−0.106044	−	0.0439249i
$584$	−2.51222	+	1.04060i	−0.103957	+	0.0430602i
$585$	−0.127550	−	1.53721i	−0.00527355	−	0.0635559i
$586$	10.1594	+	10.1594i	0.419683	+	0.419683i
$587$	−11.3396	+	11.3396i	−0.468036	+	0.468036i	−0.901278	−	0.433242i	$-0.857370\pi$
$587$	−11.3396	+	11.3396i	−0.468036	+	0.468036i	0.433242	+	0.901278i	$0.357370\pi$
$588$	−0.813207	+	0.336841i	−0.0335361	+	0.0138911i
$589$	6.15567	−	2.54976i	0.253640	−	0.105061i
$590$	−32.6485	+	38.5567i	−1.34412	+	1.58735i
$591$		−	35.1919i		−	1.44760i
$592$	7.72577	−	18.6517i	0.317527	−	0.766579i
$593$	−27.1563	−	27.1563i	−1.11517	−	1.11517i	−0.992439	−	0.122735i	$-0.960833\pi$
$593$	−27.1563	−	27.1563i	−1.11517	−	1.11517i	−0.122735	−	0.992439i	$-0.539167\pi$
$594$	−10.1609			−0.416905
$595$	−23.2328	+	8.50196i	−0.952452	+	0.348546i
$596$	23.3436			0.956193
$597$	−29.7706	−	29.7706i	−1.21843	−	1.21843i
$598$	−8.62025	+	20.8111i	−0.352508	+	0.851031i
$599$			23.5261i			0.961251i	0.876926	+	0.480625i	$0.159590\pi$
$599$			23.5261i			0.961251i	−0.876926	+	0.480625i	$0.840410\pi$
$600$	−6.94392	+	4.33677i	−0.283484	+	0.177048i
$601$	23.1362	−	9.58331i	0.943744	−	0.390911i	0.142868	−	0.989742i	$-0.454368\pi$
$601$	23.1362	−	9.58331i	0.943744	−	0.390911i	0.800876	+	0.598830i	$0.204368\pi$
$602$	−46.4664	+	19.2470i	−1.89383	+	0.784450i
$603$	1.05558	−	1.05558i	0.0429864	−	0.0429864i
$604$	−2.43517	−	2.43517i	−0.0990855	−	0.0990855i
$605$	−22.3909	+	1.85788i	−0.910319	+	0.0755337i
$606$	51.3504	−	21.2700i	2.08597	−	0.864036i
$607$	29.8946	+	12.3827i	1.21338	+	0.502600i	0.895300	−	0.445463i	$-0.146961\pi$
$607$	29.8946	+	12.3827i	1.21338	+	0.502600i	0.318083	+	0.948063i	$0.396961\pi$
$608$	5.42831			0.220147
$609$	44.9114	+	18.6029i	1.81990	+	0.753827i
$610$	8.67164	−	4.46490i	0.351105	−	0.180778i
$611$	−2.31951			−0.0938375
$612$	−0.324138	+	2.58638i	−0.0131025	+	0.104548i
$613$		−	25.0386i		−	1.01130i	−0.862739	−	0.505650i	$-0.831253\pi$
$613$		−	25.0386i		−	1.01130i	0.862739	−	0.505650i	$-0.168747\pi$
$614$	−1.11079	+	1.11079i	−0.0448280	+	0.0448280i
$615$	−22.5593	−	19.1024i	−0.909678	−	0.770284i
$616$			2.37441i			0.0956675i
$617$	9.00101	+	3.72834i	0.362367	+	0.150097i	0.556436	−	0.830891i	$-0.312169\pi$
$617$	9.00101	+	3.72834i	0.362367	+	0.150097i	−0.194069	+	0.980988i	$0.562169\pi$
$618$	2.37480	+	5.73328i	0.0955285	+	0.230626i
$619$	−2.82897	−	6.82973i	−0.113706	−	0.274510i	0.856774	−	0.515692i	$-0.172465\pi$
$619$	−2.82897	−	6.82973i	−0.113706	−	0.274510i	−0.970480	+	0.241182i	$0.922465\pi$
$620$	47.6252	−	24.5215i	1.91268	−	0.984808i
$621$	14.1136	+	14.1136i	0.566358	+	0.566358i
$622$	35.3944	−	14.6609i	1.41919	−	0.587847i
$623$	−5.77777	−	13.9488i	−0.231481	−	0.558846i
$624$	−5.41153	+	13.0646i	−0.216635	+	0.523002i
$625$	−23.6418	+	8.12807i	−0.945672	+	0.325123i
$626$	19.2993	+	7.99404i	0.771356	+	0.319506i
$627$	0.842232	+	0.842232i	0.0336355	+	0.0336355i
$628$			11.7137i			0.467426i
$629$	7.46553	+	27.1837i	0.297670	+	1.08389i
$630$	−1.00179	+	3.12832i	−0.0399122	+	0.124635i
$631$	−6.09529	+	6.09529i	−0.242650	+	0.242650i	−0.817945	−	0.575296i	$-0.804887\pi$
$631$	−6.09529	+	6.09529i	−0.242650	+	0.242650i	0.575296	+	0.817945i	$0.304887\pi$
$632$	−0.141940	+	0.342674i	−0.00564608	+	0.0136308i
$633$	41.3850			1.64491
$634$	−19.5838	+	47.2794i	−0.777771	+	1.87770i
$635$	−23.7310	+	1.96908i	−0.941735	+	0.0781404i
$636$	−4.77063	−	11.5173i	−0.189168	−	0.456692i
$637$	0.376134	−	0.376134i	0.0149030	−	0.0149030i
$638$	14.5716	−	14.5716i	0.576895	−	0.576895i
$639$	−0.111987	−	0.270361i	−0.00443015	−	0.0106953i
$640$	15.7916	−	1.31031i	0.624219	−	0.0517945i
$641$	−14.9873	+	36.1825i	−0.591963	+	1.42912i	0.289641	+	0.957135i	$0.406464\pi$
$641$	−14.9873	+	36.1825i	−0.591963	+	1.42912i	−0.881604	+	0.471989i	$0.843536\pi$
$642$	21.1691			0.835478
$643$	17.4803	−	42.2011i	0.689355	−	1.66425i	−0.0567210	−	0.998390i	$-0.518065\pi$
$643$	17.4803	−	42.2011i	0.689355	−	1.66425i	0.746076	−	0.665861i	$-0.231935\pi$
$644$	18.6089	−	18.6089i	0.733292	−	0.733292i
$645$	−10.9639	+	34.2372i	−0.431702	+	1.34809i
$646$	−4.63279	+	3.60090i	−0.182275	+	0.141676i
$647$		−	9.17577i		−	0.360737i	−0.983599	−	0.180368i	$-0.942271\pi$
$647$		−	9.17577i		−	0.360737i	0.983599	−	0.180368i	$-0.0577290\pi$
$648$	−6.22811	−	6.22811i	−0.244663	−	0.244663i
$649$	9.67633	+	4.00807i	0.379829	+	0.157330i
$650$	16.2162	−	22.7229i	0.636050	−	0.891265i
$651$	18.2726	−	44.1139i	0.716158	−	1.72896i
$652$	1.50607	+	3.63596i	0.0589821	+	0.142395i
$653$	15.3604	−	6.36250i	0.601100	−	0.248984i	−0.0613178	−	0.998118i	$-0.519530\pi$
$653$	15.3604	−	6.36250i	0.601100	−	0.248984i	0.662418	+	0.749134i	$0.269530\pi$
$654$	−7.09039	−	7.09039i	−0.277256	−	0.277256i
$655$	−3.21755	+	1.65667i	−0.125720	+	0.0647313i
$656$	8.27334	+	19.9736i	0.323020	+	0.779838i
$657$	0.298433	+	0.720481i	0.0116430	+	0.0281086i
$658$	4.56350	+	1.89027i	0.177904	+	0.0736902i
$659$			5.95839i			0.232106i	0.993243	+	0.116053i	$0.0370242\pi$
$659$			5.95839i			0.232106i	−0.993243	+	0.116053i	$0.962976\pi$
$660$	7.30804	+	6.18819i	0.284465	+	0.240875i
$661$	30.3724	−	30.3724i	1.18135	−	1.18135i	0.201955	−	0.979395i	$-0.435270\pi$
$661$	30.3724	−	30.3724i	1.18135	−	1.18135i	0.979395	−	0.201955i	$-0.0647296\pi$
$662$			1.03093i			0.0400681i
$663$	−5.22924	−	19.0409i	−0.203087	−	0.739487i
$664$	5.96157			0.231354
$665$	−3.60663	+	1.85700i	−0.139859	+	0.0720113i
$666$	3.45805	+	1.43237i	0.133997	+	0.0555033i
$667$	−40.4803			−1.56740
$668$	49.7078	+	20.5896i	1.92325	+	0.796637i
$669$	−21.7790	+	9.02114i	−0.842024	+	0.348778i
$670$	26.9241	−	2.23403i	1.04017	−	0.0863080i
$671$	−1.42975	−	1.42975i	−0.0551947	−	0.0551947i
$672$	27.5074	−	27.5074i	1.06112	−	1.06112i
$673$	16.0256	−	6.63803i	0.617743	−	0.255877i	−0.0517924	−	0.998658i	$-0.516493\pi$
$673$	16.0256	−	6.63803i	0.617743	−	0.255877i	0.669535	+	0.742781i	$0.266493\pi$
$674$	11.6976	−	4.84531i	0.450575	−	0.186634i
$675$	−13.1029	−	20.9801i	−0.504332	−	0.807523i
$676$		−	14.4993i		−	0.557666i
$677$	−9.79369	+	23.6441i	−0.376402	+	0.908715i	0.616232	+	0.787565i	$0.288658\pi$
$677$	−9.79369	+	23.6441i	−0.376402	+	0.908715i	−0.992634	+	0.121150i	$0.961342\pi$
$678$	−15.6108	−	15.6108i	−0.599531	−	0.599531i
$679$	−41.3613			−1.58730
$680$	−6.15434	+	5.65919i	−0.236008	+	0.217020i
$681$	−19.3187			−0.740294
$682$	−14.3128	−	14.3128i	−0.548067	−	0.548067i
$683$	2.34480	−	5.66085i	0.0897213	−	0.216606i	−0.872649	−	0.488348i	$-0.837600\pi$
$683$	2.34480	−	5.66085i	0.0897213	−	0.216606i	0.962370	+	0.271742i	$0.0875996\pi$
$684$			0.427415i			0.0163426i
$685$	6.79610	−	8.02596i	0.259666	−	0.306656i
$686$	35.4825	−	14.6973i	1.35473	−	0.561146i
$687$	−31.4163	+	13.0130i	−1.19861	+	0.496479i
$688$	18.5914	−	18.5914i	0.708790	−	0.708790i
$689$	5.32713	+	5.32713i	0.202948	+	0.202948i
$690$	−2.83529	−	34.1705i	−0.107938	−	1.30085i
$691$	−6.87633	+	2.84827i	−0.261588	+	0.108353i	−0.509623	−	0.860398i	$-0.670215\pi$
$691$	−6.87633	+	2.84827i	−0.261588	+	0.108353i	0.248035	+	0.968751i	$0.420215\pi$
$692$	−23.3039	−	9.65279i	−0.885881	−	0.366944i
$693$	0.680955			0.0258674
$694$	−15.3626	−	6.36339i	−0.583156	−	0.241551i
$695$	0.843229	+	1.63770i	0.0319855	+	0.0621217i
$696$	16.4284			0.622715
$697$	−26.2372	−	14.9311i	−0.993806	−	0.565555i
$698$			40.3115i			1.52581i
$699$	−2.86741	+	2.86741i	−0.108455	+	0.108455i
$700$	−27.6624	+	17.2763i	−1.04554	+	0.652984i
$701$		−	25.3350i		−	0.956891i	−0.878117	−	0.478445i	$-0.841200\pi$
$701$		−	25.3350i		−	0.956891i	0.878117	−	0.478445i	$-0.158800\pi$
$702$	25.5181	+	10.5699i	0.963119	+	0.398937i
$703$	1.76893	+	4.27058i	0.0667165	+	0.161068i
$704$	−4.10568	−	9.91200i	−0.154739	−	0.373573i
$705$	3.13902	−	1.61623i	0.118222	−	0.0608708i
$706$	−20.4160	−	20.4160i	−0.768365	−	0.768365i
$707$	36.2552	−	15.0174i	1.36352	−	0.564788i
$708$	18.0287	+	43.5252i	0.677562	+	1.63578i
$709$	6.10174	−	14.7309i	0.229156	−	0.553231i	−0.766919	−	0.641744i	$-0.778211\pi$
$709$	6.10174	−	14.7309i	0.229156	−	0.553231i	0.996075	+	0.0885126i	$0.0282113\pi$
$710$	1.61519	−	5.04379i	0.0606168	−	0.189290i
$711$	0.0982755	+	0.0407070i	0.00368562	+	0.00152663i
$712$	−3.60794	−	3.60794i	−0.135213	−	0.135213i
$713$			39.7615i			1.48908i
$714$	−5.22897	+	41.7233i	−0.195689	+	1.56146i
$715$	−5.51138	−	1.76492i	−0.206114	−	0.0660044i
$716$	−32.1908	+	32.1908i	−1.20303	+	1.20303i
$717$	−11.5593	+	27.9066i	−0.431689	+	1.04219i
$718$	−52.5296			−1.96039
$719$	7.42813	−	17.9331i	0.277022	−	0.668791i	−0.722728	−	0.691132i	$-0.757112\pi$
$719$	7.42813	−	17.9331i	0.277022	−	0.668791i	0.999750	+	0.0223415i	$0.00711210\pi$
$720$	−0.141994	−	1.71129i	−0.00529181	−	0.0637759i
$721$	1.67670	+	4.04790i	0.0624434	+	0.150752i
$722$	27.5997	−	27.5997i	1.02716	−	1.02716i
$723$	−15.0307	+	15.0307i	−0.558997	+	0.558997i
$724$	−2.28369	−	5.51330i	−0.0848725	−	0.204900i
$725$	48.8781	+	11.2965i	1.81529	+	0.419543i
$726$	−14.6141	+	35.2815i	−0.542380	+	1.30942i
$727$	−26.1442			−0.969633			−0.484817	−	0.874616i	$-0.661114\pi$
$727$	−26.1442			−0.969633			−0.484817	+	0.874616i	$0.661114\pi$
$728$	2.47000	−	5.96311i	0.0915444	−	0.221008i
$729$	17.1622	−	17.1622i	0.635639	−	0.635639i
$730$	−4.30428	+	13.4411i	−0.159308	+	0.497478i
$731$	−4.56537	+	36.4283i	−0.168856	+	1.34735i
$732$		−	9.09503i		−	0.336162i
$733$	−3.23474	−	3.23474i	−0.119478	−	0.119478i	0.644840	−	0.764318i	$-0.276924\pi$
$733$	−3.23474	−	3.23474i	−0.119478	−	0.119478i	−0.764318	+	0.644840i	$0.776924\pi$
$734$	−16.5851	−	6.86978i	−0.612168	−	0.253568i
$735$	−0.246936	+	0.771115i	−0.00910837	+	0.0284430i
$736$	−12.3967	+	29.9284i	−0.456950	+	1.10317i
$737$	−2.14328	−	5.17435i	−0.0789489	−	0.190599i
$738$	−3.70314	+	1.53389i	−0.136315	+	0.0564633i
$739$	28.5736	+	28.5736i	1.05110	+	1.05110i	0.998622	+	0.0524727i	$0.0167103\pi$
$739$	28.5736	+	28.5736i	1.05110	+	1.05110i	0.0524727	+	0.998622i	$0.483290\pi$
$740$	17.0121	+	33.0406i	0.625378	+	1.21460i
$741$	−1.23905	−	2.99133i	−0.0455177	−	0.109889i
$742$	−6.13952	−	14.8221i	−0.225389	−	0.544137i
$743$	−21.6747	−	8.97795i	−0.795168	−	0.329369i	−0.0521484	−	0.998639i	$-0.516607\pi$
$743$	−21.6747	−	8.97795i	−0.795168	−	0.329369i	−0.743019	+	0.669270i	$0.766607\pi$
$744$		−	16.1366i		−	0.591598i
$745$	13.8764	−	16.3876i	0.508393	−	0.600394i
$746$	17.2052	−	17.2052i	0.629927	−	0.629927i
$747$		−	1.70972i		−	0.0625553i
$748$	8.49949	+	4.83689i	0.310772	+	0.176854i
$749$	14.9462			0.546121
$750$	−6.11220	+	42.0505i	−0.223186	+	1.53547i
$751$	−29.7279	−	12.3137i	−1.08479	−	0.449333i	−0.232600	−	0.972572i	$-0.574723\pi$
$751$	−29.7279	−	12.3137i	−1.08479	−	0.449333i	−0.852186	+	0.523239i	$0.824723\pi$
$752$	−2.58218			−0.0941624
$753$	−29.5290	−	12.2313i	−1.07610	−	0.445734i
$754$	−51.7536	+	21.4370i	−1.88475	+	0.780690i
$755$	−3.15708	+	0.261959i	−0.114898	+	0.00953367i
$756$	−22.8177	−	22.8177i	−0.829873	−	0.829873i
$757$	25.3721	−	25.3721i	0.922165	−	0.922165i	−0.0750172	−	0.997182i	$-0.523901\pi$
$757$	25.3721	−	25.3721i	0.922165	−	0.922165i	0.997182	+	0.0750172i	$0.0239012\pi$
$758$	−23.9255	+	9.91025i	−0.869012	+	0.359957i
$759$	−6.56697	+	2.72013i	−0.238366	+	0.0987343i
$760$	−0.885920	+	1.04624i	−0.0321357	+	0.0379511i
$761$		−	26.9643i		−	0.977453i	−0.872437	−	0.488727i	$-0.837462\pi$
$761$		−	26.9643i		−	0.977453i	0.872437	−	0.488727i	$-0.162538\pi$
$762$	−15.4887	+	37.3931i	−0.561098	+	1.35461i
$763$	−5.00607	−	5.00607i	−0.181232	−	0.181232i
$764$	−26.5265			−0.959695
$765$	1.62300	+	1.76500i	0.0586796	+	0.0638138i
$766$	11.9162			0.430549
$767$	−20.1318	−	20.1318i	−0.726918	−	0.726918i
$768$	−4.88788	+	11.8004i	−0.176376	+	0.425809i
$769$			13.1666i			0.474800i	0.971412	+	0.237400i	$0.0762952\pi$
$769$			13.1666i			0.474800i	−0.971412	+	0.237400i	$0.923705\pi$
$770$	9.40501	+	7.96383i	0.338933	+	0.286996i
$771$	−12.8514	+	5.32324i	−0.462834	+	0.191712i
$772$	−41.2675	+	17.0936i	−1.48525	+	0.615210i
$773$	22.4347	−	22.4347i	0.806920	−	0.806920i	−0.177247	−	0.984166i	$-0.556719\pi$
$773$	22.4347	−	22.4347i	0.806920	−	0.806920i	0.984166	+	0.177247i	$0.0567191\pi$
$774$	3.44688	+	3.44688i	0.123895	+	0.123895i
$775$	11.0959	−	48.0102i	0.398578	−	1.72458i
$776$	−12.9141	+	5.34918i	−0.463587	+	0.192024i
$777$	30.6046	+	12.6768i	1.09793	+	0.454779i
$778$	−3.42839			−0.122914
$779$	−4.57325	−	1.89430i	−0.163854	−	0.0678705i
$780$	−11.9162	−	23.1434i	−0.426667	−	0.828665i
$781$	−1.09791			−0.0392861
$782$	−9.27317	−	33.7658i	−0.331608	−	1.20746i
$783$			49.6360i			1.77385i
$784$	0.418728	−	0.418728i	0.0149546	−	0.0149546i
$785$	8.22317	+	6.96309i	0.293497	+	0.248523i
$786$			6.15119i			0.219406i
$787$	−10.3704	−	4.29554i	−0.369663	−	0.153120i	0.190115	−	0.981762i	$-0.439114\pi$
$787$	−10.3704	−	4.29554i	−0.369663	−	0.153120i	−0.559779	+	0.828642i	$0.689114\pi$
$788$	−18.1310	−	43.7720i	−0.645889	−	1.55931i
$789$	4.35092	+	10.5041i	0.154897	+	0.373954i
$790$	0.881258	+	1.71156i	0.0313538	+	0.0608947i
$791$	−11.0218	−	11.0218i	−0.391891	−	0.391891i
$792$	0.212612	−	0.0880667i	0.00755483	−	0.00312931i
$793$	2.10337	+	5.07799i	0.0746930	+	0.180325i
$794$	10.3525	−	24.9932i	0.367398	−	0.886977i
$795$	−10.9212	−	3.49732i	−0.387335	−	0.124037i
$796$	−52.3668	−	21.6911i	−1.85609	−	0.768819i
$797$	23.8591	+	23.8591i	0.845134	+	0.845134i	0.989521	−	0.144388i	$-0.0461212\pi$
$797$	23.8591	+	23.8591i	0.845134	+	0.845134i	−0.144388	+	0.989521i	$0.546121\pi$
$798$			6.89502i			0.244081i
$799$	2.84683	−	2.21274i	0.100714	−	0.0782811i
$800$	23.3204	−	32.6776i	0.824499	−	1.15533i
$801$	−1.03472	+	1.03472i	−0.0365600	+	0.0365600i
$802$	−23.2012	+	56.0125i	−0.819261	+	1.97787i
$803$	2.92579			0.103249
$804$	9.64074	−	23.2748i	0.340003	−	0.820839i
$805$	−2.00182	−	24.1256i	−0.0705549	−	0.850315i
$806$	21.0564	+	50.8346i	0.741679	+	1.79057i
$807$	11.8213	−	11.8213i	0.416131	−	0.416131i
$808$	9.37764	−	9.37764i	0.329904	−	0.329904i
$809$	−5.44317	−	13.1410i	−0.191372	−	0.462012i	0.798847	−	0.601534i	$-0.205443\pi$
$809$	−5.44317	−	13.1410i	−0.191372	−	0.462012i	−0.990219	+	0.139522i	$0.955443\pi$
$810$	−45.5588	+	3.78024i	−1.60077	+	0.132824i
$811$	−9.42238	+	22.7476i	−0.330865	+	0.798778i	0.667659	+	0.744467i	$0.267296\pi$
$811$	−9.42238	+	22.7476i	−0.330865	+	0.798778i	−0.998524	+	0.0543111i	$0.982704\pi$
$812$	65.4455			2.29669
$813$	−11.5937	+	27.9896i	−0.406608	+	0.981639i
$814$	9.92972	−	9.92972i	0.348037	−	0.348037i
$815$	3.44777	+	1.10409i	0.120770	+	0.0386745i
$816$	−5.82141	−	21.1971i	−0.203790	−	0.742047i
$817$			6.01999i			0.210613i
$818$	20.2719	+	20.2719i	0.708790	+	0.708790i
$819$	−1.71016	−	0.708372i	−0.0597578	−	0.0247525i
$820$	−37.9011	−	12.1372i	−1.32356	−	0.423848i
$821$	9.55514	−	23.0681i	0.333477	−	0.805084i	−0.664835	−	0.746991i	$-0.731498\pi$
$821$	9.55514	−	23.0681i	0.333477	−	0.805084i	0.998311	−	0.0580931i	$-0.0185020\pi$
$822$	−6.84060	−	16.5147i	−0.238593	−	0.576015i
$823$	−26.6778	+	11.0503i	−0.929931	+	0.385190i	−0.795652	−	0.605753i	$-0.792872\pi$
$823$	−26.6778	+	11.0503i	−0.929931	+	0.385190i	−0.134279	+	0.990944i	$0.542872\pi$
$824$	1.04702	+	1.04702i	0.0364745	+	0.0364745i
$825$	8.68839	−	1.45183i	0.302491	−	0.0505464i
$826$	23.2019	+	56.0144i	0.807298	+	1.94899i
$827$	6.20037	+	14.9690i	0.215608	+	0.520524i	0.994267	−	0.106923i	$-0.0340999\pi$
$827$	6.20037	+	14.9690i	0.215608	+	0.520524i	−0.778659	+	0.627447i	$0.784100\pi$
$828$	−2.35650	−	0.976095i	−0.0818941	−	0.0339216i
$829$			22.2311i			0.772117i	0.922474	+	0.386058i	$0.126164\pi$
$829$			22.2311i			0.772117i	−0.922474	+	0.386058i	$0.873836\pi$
$830$	19.9953	−	23.6137i	0.694046	−	0.819645i
$831$	15.3286	−	15.3286i	0.531744	−	0.531744i
$832$			29.1641i			1.01108i
$833$	−0.102824	+	0.820464i	−0.00356266	+	0.0284274i
$834$	3.13090			0.108414
$835$	44.0026	−	22.6562i	1.52277	−	0.784052i
$836$	1.48150	+	0.613656i	0.0512386	+	0.0212237i
$837$	48.7546			1.68521
$838$	−27.7436	−	11.4918i	−0.958386	−	0.396977i
$839$	43.2196	−	17.9021i	1.49211	−	0.618051i	0.520332	−	0.853964i	$-0.325808\pi$
$839$	43.2196	−	17.9021i	1.49211	−	0.618051i	0.971774	+	0.235914i	$0.0758082\pi$
$840$	0.812410	+	9.79102i	0.0280308	+	0.337822i
$841$	−50.6764	−	50.6764i	−1.74746	−	1.74746i
$842$	43.0675	−	43.0675i	1.48420	−	1.48420i
$843$	47.0428	−	19.4858i	1.62024	−	0.671125i
$844$	51.4751	−	21.3217i	1.77185	−	0.733923i
$845$	−10.1787	−	8.61899i	−0.350159	−	0.296502i
$846$		−	0.478741i		−	0.0164594i
$847$	−10.3181	+	24.9100i	−0.354533	+	0.855919i
$848$	5.93039	+	5.93039i	0.203650	+	0.203650i
$849$	30.8359			1.05829
$850$	1.77417	+	43.3584i	0.0608536	+	1.48718i
$851$	−27.5851			−0.945604
$852$	−3.49205	−	3.49205i	−0.119636	−	0.119636i
$853$	14.6828	−	35.4475i	0.502731	−	1.21370i	−0.445259	−	0.895402i	$-0.646889\pi$
$853$	14.6828	−	35.4475i	0.502731	−	1.21370i	0.947990	−	0.318299i	$-0.103111\pi$
$854$		−	11.7048i		−	0.400529i
$855$	0.300051	+	0.254073i	0.0102615	+	0.00868911i
$856$	4.66658	−	1.93296i	0.159500	−	0.0660672i
$857$	−5.10428	+	2.11426i	−0.174359	+	0.0722218i	−0.468155	−	0.883646i	$-0.655081\pi$
$857$	−5.10428	+	2.11426i	−0.174359	+	0.0722218i	0.293796	+	0.955868i	$0.405081\pi$
$858$	−6.95529	+	6.95529i	−0.237450	+	0.237450i
$859$	10.1314	+	10.1314i	0.345680	+	0.345680i	0.858498	−	0.512817i	$-0.171398\pi$
$859$	10.1314	+	10.1314i	0.345680	+	0.345680i	−0.512817	+	0.858498i	$0.671398\pi$
$860$	4.00215	+	48.2332i	0.136472	+	1.64474i
$861$	−32.7737	+	13.5753i	−1.11692	+	0.462645i
$862$	39.9746	+	16.5580i	1.36154	+	0.563969i
$863$	−9.68459			−0.329667			−0.164834	−	0.986321i	$-0.552709\pi$
$863$	−9.68459			−0.329667			−0.164834	+	0.986321i	$0.552709\pi$
$864$	36.6974	+	15.2006i	1.24847	+	0.517134i
$865$	−20.6292	+	10.6217i	−0.701413	+	0.361147i
$866$	−50.9025			−1.72974
$867$	24.5825	+	18.3811i	0.834864	+	0.624255i
$868$		−	64.2833i		−	2.18192i
$869$	0.282196	−	0.282196i	0.00957284	−	0.00957284i
$870$	55.1012	−	65.0727i	1.86811	−	2.20617i
$871$			15.2245i			0.515862i
$872$	−2.21045	−	0.915599i	−0.0748553	−	0.0310061i
$873$	1.53409	+	3.70362i	0.0519211	+	0.125349i
$874$	−2.19724	−	5.30462i	−0.0743229	−	0.179431i
$875$	−4.31543	+	29.6891i	−0.145888	+	1.00368i
$876$	9.30590	+	9.30590i	0.314417	+	0.314417i
$877$	−13.8214	+	5.72500i	−0.466714	+	0.193319i	−0.603632	−	0.797263i	$-0.706280\pi$
$877$	−13.8214	+	5.72500i	−0.466714	+	0.193319i	0.136918	+	0.990582i	$0.456280\pi$
$878$	17.7578	+	42.8711i	0.599297	+	1.44683i
$879$	4.71625	−	11.3860i	0.159075	−	0.384041i
$880$	−6.13550	−	1.96479i	−0.206828	−	0.0662329i
$881$	9.80896	+	4.06301i	0.330472	+	0.136886i	0.541749	−	0.840540i	$-0.317762\pi$
$881$	9.80896	+	4.06301i	0.330472	+	0.136886i	−0.211277	+	0.977426i	$0.567762\pi$
$882$	0.0776330	+	0.0776330i	0.00261404	+	0.00261404i
$883$		−	52.5251i		−	1.76761i	−0.467855	−	0.883805i	$-0.654973\pi$
$883$		−	52.5251i		−	1.76761i	0.467855	−	0.883805i	$-0.345027\pi$
$884$	−16.3141	−	20.9891i	−0.548703	−	0.705941i
$885$	41.2724	+	13.2167i	1.38736	+	0.444276i
$886$	48.1243	−	48.1243i	1.61677	−	1.61677i
$887$	−6.57850	+	15.8819i	−0.220884	+	0.533262i	−0.995011	−	0.0997691i	$-0.968190\pi$
$887$	−6.57850	+	15.8819i	−0.220884	+	0.533262i	0.774126	+	0.633031i	$0.218190\pi$
$888$	11.1950			0.375680
$889$	−10.9356	+	26.4009i	−0.366768	+	0.885457i
$890$	−26.3922	+	2.18989i	−0.884667	+	0.0734052i
$891$	3.62669	+	8.75561i	0.121499	+	0.293324i
$892$	−22.4412	+	22.4412i	−0.751386	+	0.751386i
$893$	0.418062	−	0.418062i	0.0139899	−	0.0139899i
$894$	−13.9673	−	33.7200i	−0.467135	−	1.12776i
$895$	3.46287	+	41.7340i	0.115751	+	1.39501i
$896$	7.27703	−	17.5683i	0.243108	−	0.586916i
$897$	19.3220			0.645143
$898$	25.2701	−	61.0075i	0.843276	−	2.03585i
$899$	−69.9185	+	69.9185i	−2.33191	+	2.33191i
$900$	2.57298	+	1.83620i	0.0857658	+	0.0612067i
$901$	−11.6201	−	1.45629i	−0.387122	−	0.0485160i
$902$			15.0380i			0.500712i
$903$	30.5057	+	30.5057i	1.01517	+	1.01517i
$904$	−4.86673	−	2.01586i	−0.161865	−	0.0670467i
$905$	−5.22794	−	1.67415i	−0.173782	−	0.0556508i
$906$	−2.06057	+	4.97465i	−0.0684577	+	0.165272i
$907$	4.28190	+	10.3374i	0.142178	+	0.343248i	0.978888	−	0.204398i	$-0.0655238\pi$
$907$	4.28190	+	10.3374i	0.142178	+	0.343248i	−0.836710	+	0.547647i	$0.815524\pi$
$908$	−24.0288	+	9.95305i	−0.797423	+	0.330304i
$909$	−2.68941	−	2.68941i	−0.0892022	−	0.0892022i
$910$	−15.3354	−	29.7841i	−0.508363	−	0.987334i
$911$	1.24981	+	3.01730i	0.0414080	+	0.0999677i	0.943230	−	0.332139i	$-0.107770\pi$
$911$	1.24981	+	3.01730i	0.0414080	+	0.0999677i	−0.901822	+	0.432107i	$0.857770\pi$
$912$	−1.37936	−	3.33008i	−0.0456753	−	0.110270i
$913$	−5.92619	−	2.45471i	−0.196128	−	0.0812390i
$914$		−	26.8343i		−	0.887599i
$915$	−6.38484	−	5.40646i	−0.211076	−	0.178732i
$916$	−32.3715	+	32.3715i	−1.06958	+	1.06958i
$917$			4.34296i			0.143417i
$918$	−41.4027	+	11.3705i	−1.36649	+	0.375284i
$919$	32.6905			1.07836			0.539179	−	0.842191i	$-0.318735\pi$
$919$	32.6905			1.07836			0.539179	+	0.842191i	$0.318735\pi$
$920$	−3.74514	−	7.27373i	−0.123473	−	0.239808i
$921$	1.24490	+	0.515655i	0.0410209	+	0.0169914i
$922$	36.6220			1.20608
$923$	2.75729	+	1.14211i	0.0907574	+	0.0375930i
$924$	10.6170	−	4.39769i	0.349272	−	0.144673i
$925$	33.3077	+	7.69795i	1.09515	+	0.253107i
$926$	44.0198	+	44.0198i	1.44658	+	1.44658i
$927$	0.300273	−	0.300273i	0.00986227	−	0.00986227i
$928$	−74.4264	+	30.8284i	−2.44317	+	1.01199i
$929$	−7.83598	+	3.24577i	−0.257090	+	0.106490i	−0.507506	−	0.861648i	$-0.669433\pi$
$929$	−7.83598	+	3.24577i	−0.257090	+	0.106490i	0.250416	+	0.968138i	$0.419433\pi$
$930$	−63.9172	−	54.1228i	−2.09593	−	1.77476i
$931$			0.135586i			0.00444367i
$932$	−2.08921	+	5.04381i	−0.0684344	+	0.165215i
$933$	−23.2368	−	23.2368i	−0.760739	−	0.760739i
$934$	69.2208			2.26497
$935$	8.44802	−	3.09152i	0.276280	−	0.101104i
$936$	−0.625569			−0.0204473
$937$	−22.0610	−	22.0610i	−0.720703	−	0.720703i	0.248045	−	0.968748i	$-0.420212\pi$
$937$	−22.0610	−	22.0610i	−0.720703	−	0.720703i	−0.968748	+	0.248045i	$0.920212\pi$
$938$	12.4071	−	29.9533i	0.405105	−	0.978009i
$939$		−	17.9184i		−	0.584744i
$940$	3.07165	−	3.62752i	0.100186	−	0.118317i
$941$	19.9946	−	8.28202i	0.651804	−	0.269986i	−0.0321810	−	0.999482i	$-0.510245\pi$
$941$	19.9946	−	8.28202i	0.651804	−	0.269986i	0.683985	+	0.729496i	$0.260245\pi$
$942$	16.9204	−	7.00868i	0.551298	−	0.228355i
$943$	20.8880	−	20.8880i	0.680208	−	0.680208i
$944$	−22.4116	−	22.4116i	−0.729435	−	0.729435i
$945$	−29.5822	+	2.45458i	−0.962309	+	0.0798475i
$946$	16.8963	−	6.99868i	0.549347	−	0.227547i
$947$	−3.63370	−	1.50513i	−0.118079	−	0.0489101i	0.322862	−	0.946446i	$-0.395355\pi$
$947$	−3.63370	−	1.50513i	−0.118079	−	0.0489101i	−0.440941	+	0.897536i	$0.645355\pi$
$948$	1.79513			0.0583031
$949$	−7.34786	−	3.04358i	−0.238522	−	0.0987989i
$950$	1.17275	+	7.01825i	0.0380491	+	0.227702i
$951$	43.8964			1.42344
$952$	2.65708	+	9.67506i	0.0861166	+	0.313571i
$953$		−	4.24356i		−	0.137462i	−0.997635	−	0.0687312i	$-0.978105\pi$
$953$		−	4.24356i		−	0.137462i	0.997635	−	0.0687312i	$-0.0218951\pi$
$954$	−1.09950	+	1.09950i	−0.0355978	+	0.0355978i
$955$	−15.7684	+	18.6220i	−0.510255	+	0.602593i
$956$			40.6658i			1.31523i
$957$	−16.3309	−	6.76447i	−0.527902	−	0.218664i
$958$	−0.478328	−	1.15479i	−0.0154541	−	0.0373095i
$959$	−4.82971	−	11.6600i	−0.155959	−	0.376519i
$960$	−20.3215	−	39.4680i	−0.655873	−	1.27383i
$961$	46.7567	+	46.7567i	1.50828	+	1.50828i
$962$	−35.2671	+	14.6081i	−1.13706	+	0.470985i
$963$	−0.554353	−	1.33833i	−0.0178638	−	0.0431270i
$964$	−10.9515	+	26.4392i	−0.352723	+	0.851549i
$965$	−12.5312	+	39.1315i	−0.403393	+	1.25969i
$966$	−38.0149	−	15.7463i	−1.22311	−	0.506628i
$967$	−25.3036	−	25.3036i	−0.813708	−	0.813708i	0.171480	−	0.985188i	$-0.445145\pi$
$967$	−25.3036	−	25.3036i	−0.813708	−	0.813708i	−0.985188	+	0.171480i	$0.945145\pi$
$968$			9.11197i			0.292870i
$969$	4.37437	+	2.48937i	0.140525	+	0.0799700i
$970$	−22.1261	+	69.0938i	−0.710425	+	2.21847i
$971$	−26.0013	+	26.0013i	−0.834423	+	0.834423i	−0.988118	−	0.153695i	$-0.950883\pi$
$971$	−26.0013	+	26.0013i	−0.834423	+	0.834423i	0.153695	+	0.988118i	$0.450883\pi$
$972$	−2.50733	+	6.05324i	−0.0804228	+	0.194158i
$973$	2.21053			0.0708664
$974$	−1.81468	+	4.38103i	−0.0581462	+	0.140377i
$975$	−23.3304	−	5.39204i	−0.747172	−	0.172684i
$976$	2.34156	+	5.65303i	0.0749516	+	0.180949i
$977$	−18.3472	+	18.3472i	−0.586977	+	0.586977i	−0.936812	−	0.349834i	$-0.886238\pi$
$977$	−18.3472	+	18.3472i	−0.586977	+	0.586977i	0.349834	+	0.936812i	$0.386238\pi$
$978$	4.35104	−	4.35104i	0.139131	−	0.139131i
$979$	2.10094	+	5.07211i	0.0671463	+	0.162105i
$980$	0.0901393	+	1.08634i	0.00287939	+	0.0347019i
$981$	−0.262585	+	0.633935i	−0.00838368	+	0.0202400i
$982$	15.3652			0.490322
$983$	−12.6630	+	30.5712i	−0.403888	+	0.975071i	0.582825	+	0.812598i	$0.301947\pi$
$983$	−12.6630	+	30.5712i	−0.403888	+	0.975071i	−0.986713	+	0.162474i	$0.948053\pi$
$984$	−8.47711	+	8.47711i	−0.270241	+	0.270241i
$985$	−41.5064	−	13.2917i	−1.32250	−	0.423509i
$986$	43.0689	−	75.6817i	1.37159	−	2.41020i
$987$		−	4.23697i		−	0.134864i
$988$	−3.08229	−	3.08229i	−0.0980606	−	0.0980606i
$989$	−33.1905	−	13.7480i	−1.05540	−	0.437160i
$990$	0.364275	−	1.13753i	0.0115774	−	0.0361532i
$991$	13.3710	−	32.2804i	0.424744	−	1.02542i	−0.556186	−	0.831058i	$-0.687736\pi$
$991$	13.3710	−	32.2804i	0.424744	−	1.02542i	0.980930	−	0.194364i	$-0.0622643\pi$
$992$	30.2810	+	73.1049i	0.961423	+	2.32108i
$993$	0.816987	−	0.338407i	0.0259263	−	0.0107390i
$994$	−4.49406	−	4.49406i	−0.142543	−	0.142543i
$995$	−46.3564	+	23.8682i	−1.46960	+	0.756674i
$996$	−11.0416	−	26.6567i	−0.349865	−	0.844649i
$997$	−6.29396	−	15.1950i	−0.199332	−	0.481229i	0.792331	−	0.610092i	$-0.208867\pi$
$997$	−6.29396	−	15.1950i	−0.199332	−	0.481229i	−0.991662	+	0.128862i	$0.958867\pi$
$998$	14.7809	+	6.12244i	0.467881	+	0.193802i
$999$			33.8241i			1.07015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.m.a.9.1	✓	24
3.2	odd	2		765.2.bh.b.604.6		24
5.2	odd	4		425.2.m.e.26.6		24
5.3	odd	4		425.2.m.e.26.1		24
5.4	even	2	inner	85.2.m.a.9.6	yes	24
15.14	odd	2		765.2.bh.b.604.1		24
17.2	even	8	inner	85.2.m.a.19.6	yes	24
17.6	odd	16		1445.2.b.i.579.4		24
17.11	odd	16		1445.2.b.i.579.3		24
51.2	odd	8		765.2.bh.b.19.1		24
85.2	odd	8		425.2.m.e.376.6		24
85.19	even	8	inner	85.2.m.a.19.1	yes	24
85.23	even	16		7225.2.a.by.1.3		24
85.28	even	16		7225.2.a.by.1.4		24
85.53	odd	8		425.2.m.e.376.1		24
85.57	even	16		7225.2.a.by.1.22		24
85.62	even	16		7225.2.a.by.1.21		24
85.74	odd	16		1445.2.b.i.579.21		24
85.79	odd	16		1445.2.b.i.579.22		24
255.104	odd	8		765.2.bh.b.19.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.m.a.9.1	✓	24	1.1	even	1	trivial
85.2.m.a.9.6	yes	24	5.4	even	2	inner
85.2.m.a.19.1	yes	24	85.19	even	8	inner
85.2.m.a.19.6	yes	24	17.2	even	8	inner
425.2.m.e.26.1		24	5.3	odd	4
425.2.m.e.26.6		24	5.2	odd	4
425.2.m.e.376.1		24	85.53	odd	8
425.2.m.e.376.6		24	85.2	odd	8
765.2.bh.b.19.1		24	51.2	odd	8
765.2.bh.b.19.6		24	255.104	odd	8
765.2.bh.b.604.1		24	15.14	odd	2
765.2.bh.b.604.6		24	3.2	odd	2
1445.2.b.i.579.3		24	17.11	odd	16
1445.2.b.i.579.4		24	17.6	odd	16
1445.2.b.i.579.21		24	85.74	odd	16
1445.2.b.i.579.22		24	85.79	odd	16
7225.2.a.by.1.3		24	85.23	even	16
7225.2.a.by.1.4		24	85.28	even	16
7225.2.a.by.1.21		24	85.62	even	16
7225.2.a.by.1.22		24	85.57	even	16

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.48843 - 1.48843i) q^{2} +(-0.690961 + 1.66813i) q^{3} +2.43082i q^{4} +(1.70647 + 1.44498i) q^{5} +(3.51133 - 1.45444i) q^{6} +(2.47912 - 1.02689i) q^{7} +(0.641241 - 0.641241i) q^{8} +(-0.183901 - 0.183901i) q^{9} +(-0.389210 - 4.69069i) q^{10} +(-0.901470 + 0.373401i) q^{11} +(-4.05491 - 1.67960i) q^{12} +2.65240 q^{13} +(-5.21843 - 2.16155i) q^{14} +(-3.58951 + 1.84818i) q^{15} +2.95276 q^{16} +(-3.25539 + 2.53030i) q^{17} +0.547447i q^{18} +(-0.478059 + 0.478059i) q^{19} +(-3.51248 + 4.14812i) q^{20} +4.84503i q^{21} +(1.89755 + 0.785991i) q^{22} +(-1.54397 - 3.72748i) q^{23} +(0.626599 + 1.51274i) q^{24} +(0.824076 + 4.93162i) q^{25} +(-3.94790 - 3.94790i) q^{26} +(-4.57054 + 1.89318i) q^{27} +(2.49617 + 6.02630i) q^{28} +(3.83958 - 9.26957i) q^{29} +(8.09360 + 2.59183i) q^{30} +(-9.10497 - 3.77140i) q^{31} +(-5.67744 - 5.67744i) q^{32} -1.76177i q^{33} +(8.61157 + 1.07924i) q^{34} +(5.71438 + 1.82993i) q^{35} +(0.447031 - 0.447031i) q^{36} +(2.61646 - 6.31669i) q^{37} +1.42311 q^{38} +(-1.83270 + 4.42454i) q^{39} +(2.02084 - 0.167679i) q^{40} +(2.80190 + 6.76439i) q^{41} +(7.21147 - 7.21147i) q^{42} +(6.29628 - 6.29628i) q^{43} +(-0.907670 - 2.19131i) q^{44} +(-0.0480886 - 0.579556i) q^{45} +(-3.24999 + 7.84616i) q^{46} -0.874497 q^{47} +(-2.04024 + 4.92558i) q^{48} +(0.141809 - 0.141809i) q^{49} +(6.11377 - 8.56693i) q^{50} +(-1.97152 - 7.17875i) q^{51} +6.44750i q^{52} +(2.00842 + 2.00842i) q^{53} +(9.62077 + 3.98505i) q^{54} +(-2.07789 - 0.665407i) q^{55} +(0.931234 - 2.24820i) q^{56} +(-0.467144 - 1.12778i) q^{57} +(-19.5120 + 8.08213i) q^{58} +(-7.59005 - 7.59005i) q^{59} +(-4.49260 - 8.72545i) q^{60} +(0.793008 + 1.91449i) q^{61} +(7.93862 + 19.1655i) q^{62} +(-0.644760 - 0.267068i) q^{63} +10.9954i q^{64} +(4.52624 + 3.83266i) q^{65} +(-2.62227 + 2.62227i) q^{66} +5.73990i q^{67} +(-6.15070 - 7.91327i) q^{68} +7.28473 q^{69} +(-5.78171 - 11.2291i) q^{70} +(1.03955 + 0.430595i) q^{71} -0.235850 q^{72} +(-2.77027 - 1.14748i) q^{73} +(-13.2963 + 5.50752i) q^{74} +(-8.79598 - 2.03289i) q^{75} +(-1.16208 - 1.16208i) q^{76} +(-1.85141 + 1.85141i) q^{77} +(9.31343 - 3.85775i) q^{78} +(-0.377872 + 0.156520i) q^{79} +(5.03879 + 4.26667i) q^{80} -9.71259i q^{81} +(5.89786 - 14.2387i) q^{82} +(4.64846 + 4.64846i) q^{83} -11.7774 q^{84} +(-9.21146 - 0.386088i) q^{85} -18.7431 q^{86} +(12.8098 + 12.8098i) q^{87} +(-0.338619 + 0.817499i) q^{88} -5.62649i q^{89} +(-0.791049 + 0.934201i) q^{90} +(6.57562 - 2.72371i) q^{91} +(9.06082 - 3.75312i) q^{92} +(12.5824 - 12.5824i) q^{93} +(1.30162 + 1.30162i) q^{94} +(-1.50658 + 0.125008i) q^{95} +(13.3936 - 5.54781i) q^{96} +(-14.2405 - 5.89862i) q^{97} -0.422145 q^{98} +(0.234451 + 0.0971126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{9} - 16 q^{10} - 24 q^{14} - 16 q^{15} + 8 q^{16} - 24 q^{19} - 8 q^{20} + 32 q^{24} + 16 q^{25} - 16 q^{26} + 24 q^{29} - 24 q^{31} + 8 q^{34} + 8 q^{35} + 8 q^{36} - 24 q^{39} + 16 q^{40}+ \cdots - 80 q^{99}+O(q^{100}) \) 24 * q - 8 * q^9 - 16 * q^10 - 24 * q^14 - 16 * q^15 + 8 * q^16 - 24 * q^19 - 8 * q^20 + 32 * q^24 + 16 * q^25 - 16 * q^26 + 24 * q^29 - 24 * q^31 + 8 * q^34 + 8 * q^35 + 8 * q^36 - 24 * q^39 + 16 * q^40 - 48 * q^41 + 72 * q^44 + 48 * q^45 - 16 * q^46 + 48 * q^49 + 16 * q^50 + 32 * q^54 + 24 * q^56 - 48 * q^59 + 8 * q^60 + 16 * q^61 + 24 * q^65 - 96 * q^66 + 32 * q^69 + 32 * q^70 + 16 * q^71 - 64 * q^74 - 24 * q^76 - 72 * q^79 - 64 * q^80 - 96 * q^84 - 24 * q^85 - 8 * q^91 - 40 * q^94 - 88 * q^95 + 96 * q^96 - 80 * q^99

Introduction

L-functions

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