LMFDB - Embedded newform 416.2.bi.a.395.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(99,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 2]))

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

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

chi := DirichletCharacter("416.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bi (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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			395.1
Character	$\chi$	$=$	416.395
Dual form			416.2.bi.a.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41416 + 0.0124808i) q^{2} +(0.185333 + 0.447434i) q^{3} +(1.99969 - 0.0352996i) q^{4} +(-0.172454 - 0.416340i) q^{5} +(-0.267675 - 0.630429i) q^{6} -2.63339 q^{7} +(-2.82744 + 0.0748769i) q^{8} +(1.95547 - 1.95547i) q^{9} +(0.249073 + 0.586618i) q^{10} +(-3.87756 + 1.60614i) q^{11} +(0.386403 + 0.888186i) q^{12} +(-3.51680 - 0.795059i) q^{13} +(3.72404 - 0.0328668i) q^{14} +(0.154323 - 0.154323i) q^{15} +(3.99751 - 0.141176i) q^{16} -3.57510 q^{17} +(-2.74094 + 2.78975i) q^{18} +(-0.249856 + 0.603205i) q^{19} +(-0.359550 - 0.826462i) q^{20} +(-0.488055 - 1.17827i) q^{21} +(5.46344 - 2.31973i) q^{22} +(-2.69830 + 2.69830i) q^{23} +(-0.557520 - 1.25121i) q^{24} +(3.39194 - 3.39194i) q^{25} +(4.98324 + 1.08045i) q^{26} +(2.57966 + 1.06853i) q^{27} +(-5.26597 + 0.0929578i) q^{28} +(-1.95294 + 0.808934i) q^{29} +(-0.216311 + 0.220163i) q^{30} +(-3.43007 - 3.43007i) q^{31} +(-5.65135 + 0.249538i) q^{32} +(-1.43728 - 1.43728i) q^{33} +(5.05576 - 0.0446200i) q^{34} +(0.454138 + 1.09639i) q^{35} +(3.84131 - 3.97936i) q^{36} +(-2.19017 + 0.907197i) q^{37} +(0.345807 - 0.856146i) q^{38} +(-0.296044 - 1.72089i) q^{39} +(0.518775 + 1.16426i) q^{40} +0.550727i q^{41} +(0.704893 + 1.66017i) q^{42} +(-4.93862 - 2.04564i) q^{43} +(-7.69721 + 3.34865i) q^{44} +(-1.15137 - 0.476912i) q^{45} +(3.78215 - 3.84950i) q^{46} +(-2.63314 - 2.63314i) q^{47} +(0.804038 + 1.76246i) q^{48} -0.0652357 q^{49} +(-4.75440 + 4.83907i) q^{50} +(-0.662585 - 1.59962i) q^{51} +(-7.06057 - 1.46573i) q^{52} +(-11.0699 - 4.58531i) q^{53} +(-3.66138 - 1.47887i) q^{54} +(1.33740 + 1.33740i) q^{55} +(7.44575 - 0.197180i) q^{56} -0.316201 q^{57} +(2.75167 - 1.16834i) q^{58} +(-0.722775 - 1.74493i) q^{59} +(0.303151 - 0.314046i) q^{60} +(2.34981 - 0.973321i) q^{61} +(4.89347 + 4.80785i) q^{62} +(-5.14953 + 5.14953i) q^{63} +(7.98879 - 0.423419i) q^{64} +(0.275470 + 1.60129i) q^{65} +(2.05048 + 2.01460i) q^{66} +(10.2284 + 4.23674i) q^{67} +(-7.14909 + 0.126200i) q^{68} +(-1.70740 - 0.707226i) q^{69} +(-0.655907 - 1.54480i) q^{70} +0.852067i q^{71} +(-5.38255 + 5.67539i) q^{72} +6.22970 q^{73} +(3.08592 - 1.31026i) q^{74} +(2.14631 + 0.889029i) q^{75} +(-0.478341 + 1.21504i) q^{76} +(10.2111 - 4.22959i) q^{77} +(0.440130 + 2.42991i) q^{78} -1.67033 q^{79} +(-0.748162 - 1.63997i) q^{80} -6.94410i q^{81} +(-0.00687351 - 0.778816i) q^{82} +(-3.20382 + 7.73471i) q^{83} +(-1.01755 - 2.33894i) q^{84} +(0.616538 + 1.48846i) q^{85} +(7.00953 + 2.83123i) q^{86} +(-0.723890 - 0.723890i) q^{87} +(10.8433 - 4.83159i) q^{88} +3.24654i q^{89} +(1.63417 + 0.660060i) q^{90} +(9.26112 + 2.09370i) q^{91} +(-5.30051 + 5.49101i) q^{92} +(0.899024 - 2.17044i) q^{93} +(3.75654 + 3.69081i) q^{94} +0.294227 q^{95} +(-1.15903 - 2.48236i) q^{96} +(13.6088 - 13.6088i) q^{97} +(0.0922536 - 0.000814192i) q^{98} +(-4.44170 + 10.7232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 4 q^{11} + 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} - 4 q^{19} - 20 q^{20} - 16 q^{21} - 24 q^{22}+ \cdots - 116 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 4 * q^11 + 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 - 4 * q^19 - 20 * q^20 - 16 * q^21 - 24 * q^22 + 28 * q^24 - 4 * q^26 - 8 * q^27 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 4 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 + 20 * q^39 - 8 * q^40 - 48 * q^42 + 32 * q^43 - 20 * q^44 + 4 * q^45 - 24 * q^46 - 8 * q^47 - 8 * q^48 + 168 * q^49 + 20 * q^50 - 4 * q^52 - 8 * q^53 + 20 * q^54 - 40 * q^55 - 56 * q^56 - 8 * q^57 + 32 * q^58 + 4 * q^59 - 36 * q^60 - 8 * q^61 - 72 * q^62 - 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 - 4 * q^70 + 56 * q^72 - 8 * q^73 - 8 * q^74 - 4 * q^76 - 56 * q^77 - 136 * q^78 - 16 * q^79 + 28 * q^80 + 88 * q^82 - 44 * q^83 + 44 * q^84 - 24 * q^85 + 64 * q^86 - 8 * q^87 - 64 * q^88 + 64 * q^90 + 16 * q^91 - 8 * q^92 + 56 * q^93 - 56 * q^94 - 28 * q^96 - 8 * q^97 - 76 * q^98 - 116 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.41416	+	0.0124808i	−0.999961	+	0.00882524i
$2$	−1.41416	+	0.0124808i	−0.999961	+	0.00882524i
$3$	0.185333	+	0.447434i	0.107002	+	0.258326i	0.968307	−	0.249762i	$-0.0803524\pi$
$3$	0.185333	+	0.447434i	0.107002	+	0.258326i	−0.861305	+	0.508088i	$0.830352\pi$
$4$	1.99969	−	0.0352996i	0.999844	−	0.0176498i
$5$	−0.172454	−	0.416340i	−0.0771236	−	0.186193i	0.880615	−	0.473832i	$-0.157130\pi$
$5$	−0.172454	−	0.416340i	−0.0771236	−	0.186193i	−0.957739	+	0.287639i	$0.907130\pi$
$6$	−0.267675	−	0.630429i	−0.109278	−	0.257372i
$7$	−2.63339			−0.995329			−0.497665	−	0.867369i	$-0.665809\pi$
$7$	−2.63339			−0.995329			−0.497665	+	0.867369i	$0.665809\pi$
$8$	−2.82744	+	0.0748769i	−0.999650	+	0.0264730i
$9$	1.95547	−	1.95547i	0.651824	−	0.651824i
$10$	0.249073	+	0.586618i	0.0787637	+	0.185505i
$11$	−3.87756	+	1.60614i	−1.16913	+	0.484269i	−0.880904	−	0.473294i	$-0.843065\pi$
$11$	−3.87756	+	1.60614i	−1.16913	+	0.484269i	−0.288224	+	0.957563i	$0.593065\pi$
$12$	0.386403	+	0.888186i	0.111545	+	0.256397i
$13$	−3.51680	−	0.795059i	−0.975385	−	0.220510i
$13$	−3.51680	−	0.795059i	−0.975385	−	0.220510i
$14$	3.72404	−	0.0328668i	0.995291	−	0.00878402i
$15$	0.154323	−	0.154323i	0.0398461	−	0.0398461i
$16$	3.99751	−	0.141176i	0.999377	−	0.0352941i
$17$	−3.57510			−0.867089			−0.433545	−	0.901132i	$-0.642737\pi$
$17$	−3.57510			−0.867089			−0.433545	+	0.901132i	$0.642737\pi$
$18$	−2.74094	+	2.78975i	−0.646046	+	0.657551i
$19$	−0.249856	+	0.603205i	−0.0573208	+	0.138385i	−0.949945	−	0.312416i	$-0.898862\pi$
$19$	−0.249856	+	0.603205i	−0.0573208	+	0.138385i	0.892624	+	0.450801i	$0.148862\pi$
$20$	−0.359550	−	0.826462i	−0.0803978	−	0.184803i
$21$	−0.488055	−	1.17827i	−0.106502	−	0.257120i
$22$	5.46344	−	2.31973i	1.16481	−	0.494568i
$23$	−2.69830	+	2.69830i	−0.562634	+	0.562634i	−0.930055	−	0.367421i	$-0.880241\pi$
$23$	−2.69830	+	2.69830i	−0.562634	+	0.562634i	0.367421	+	0.930055i	$0.380241\pi$
$24$	−0.557520	−	1.25121i	−0.113803	−	0.255403i
$25$	3.39194	−	3.39194i	0.678387	−	0.678387i
$26$	4.98324	+	1.08045i	0.977293	+	0.211893i
$27$	2.57966	+	1.06853i	0.496456	+	0.205639i
$28$	−5.26597	+	0.0929578i	−0.995174	+	0.0175674i
$29$	−1.95294	+	0.808934i	−0.362652	+	0.150215i	−0.556566	−	0.830803i	$-0.687882\pi$
$29$	−1.95294	+	0.808934i	−0.362652	+	0.150215i	0.193915	+	0.981018i	$0.437882\pi$
$30$	−0.216311	+	0.220163i	−0.0394929	+	0.0401962i
$31$	−3.43007	−	3.43007i	−0.616059	−	0.616059i	0.328459	−	0.944518i	$-0.393471\pi$
$31$	−3.43007	−	3.43007i	−0.616059	−	0.616059i	−0.944518	+	0.328459i	$0.893471\pi$
$32$	−5.65135	+	0.249538i	−0.999027	+	0.0441125i
$33$	−1.43728	−	1.43728i	−0.250198	−	0.250198i
$34$	5.05576	−	0.0446200i	0.867055	−	0.00765227i
$35$	0.454138	+	1.09639i	0.0767633	+	0.185323i
$36$	3.84131	−	3.97936i	0.640218	−	0.663227i
$37$	−2.19017	+	0.907197i	−0.360061	+	0.149142i	−0.555378	−	0.831598i	$-0.687426\pi$
$37$	−2.19017	+	0.907197i	−0.360061	+	0.149142i	0.195317	+	0.980740i	$0.437426\pi$
$38$	0.345807	−	0.856146i	0.0560973	−	0.138885i
$39$	−0.296044	−	1.72089i	−0.0474049	−	0.275562i
$40$	0.518775	+	1.16426i	0.0820256	+	0.184086i
$41$			0.550727i			0.0860092i	0.999075	+	0.0430046i	$0.0136930\pi$
$41$			0.550727i			0.0860092i	−0.999075	+	0.0430046i	$0.986307\pi$
$42$	0.704893	+	1.66017i	0.108767	+	0.256170i
$43$	−4.93862	−	2.04564i	−0.753133	−	0.311958i	−0.0271138	−	0.999632i	$-0.508632\pi$
$43$	−4.93862	−	2.04564i	−0.753133	−	0.311958i	−0.726019	+	0.687674i	$0.758632\pi$
$44$	−7.69721	+	3.34865i	−1.16040	+	0.504828i
$45$	−1.15137	−	0.476912i	−0.171636	−	0.0710939i
$46$	3.78215	−	3.84950i	0.557647	−	0.567578i
$47$	−2.63314	−	2.63314i	−0.384083	−	0.384083i	0.488488	−	0.872571i	$-0.337549\pi$
$47$	−2.63314	−	2.63314i	−0.384083	−	0.384083i	−0.872571	+	0.488488i	$0.837549\pi$
$48$	0.804038	+	1.76246i	0.116053	+	0.254389i
$49$	−0.0652357			−0.00931938
$50$	−4.75440	+	4.83907i	−0.672374	+	0.684348i
$51$	−0.662585	−	1.59962i	−0.0927804	−	0.223992i
$52$	−7.06057	−	1.46573i	−0.979125	−	0.203260i
$53$	−11.0699	−	4.58531i	−1.52057	−	0.629841i	−0.542864	−	0.839820i	$-0.682660\pi$
$53$	−11.0699	−	4.58531i	−1.52057	−	0.629841i	−0.977706	+	0.209980i	$0.932660\pi$
$54$	−3.66138	−	1.47887i	−0.498251	−	0.201249i
$55$	1.33740	+	1.33740i	0.180335	+	0.180335i
$56$	7.44575	−	0.197180i	0.994981	−	0.0263493i
$57$	−0.316201			−0.0418818
$58$	2.75167	−	1.16834i	0.361312	−	0.153410i
$59$	−0.722775	−	1.74493i	−0.0940973	−	0.227171i	0.869822	−	0.493366i	$-0.164234\pi$
$59$	−0.722775	−	1.74493i	−0.0940973	−	0.227171i	−0.963919	+	0.266195i	$0.914234\pi$
$60$	0.303151	−	0.314046i	0.0391366	−	0.0405431i
$61$	2.34981	−	0.973321i	0.300862	−	0.124621i	−0.227146	−	0.973861i	$-0.572939\pi$
$61$	2.34981	−	0.973321i	0.300862	−	0.124621i	0.528007	+	0.849240i	$0.322939\pi$
$62$	4.89347	+	4.80785i	0.621472	+	0.610598i
$63$	−5.14953	+	5.14953i	−0.648779	+	0.648779i
$64$	7.98879	−	0.423419i	0.998598	−	0.0529274i
$65$	0.275470	+	1.60129i	0.0341678	+	0.198616i
$66$	2.05048	+	2.01460i	0.252397	+	0.247981i
$67$	10.2284	+	4.23674i	1.24960	+	0.517600i	0.906701	−	0.421774i	$-0.138592\pi$
$67$	10.2284	+	4.23674i	1.24960	+	0.517600i	0.342896	+	0.939373i	$0.388592\pi$
$68$	−7.14909	+	0.126200i	−0.866954	+	0.0153039i
$69$	−1.70740	−	0.707226i	−0.205546	−	0.0851400i
$70$	−0.655907	−	1.54480i	−0.0783959	−	0.184638i
$71$			0.852067i			0.101122i	0.998721	+	0.0505609i	$0.0161009\pi$
$71$			0.852067i			0.101122i	−0.998721	+	0.0505609i	$0.983899\pi$
$72$	−5.38255	+	5.67539i	−0.634340	+	0.668851i
$73$	6.22970			0.729131			0.364566	−	0.931178i	$-0.381218\pi$
$73$	6.22970			0.729131			0.364566	+	0.931178i	$0.381218\pi$
$74$	3.08592	−	1.31026i	0.358731	−	0.152314i
$75$	2.14631	+	0.889029i	0.247834	+	0.102656i
$76$	−0.478341	+	1.21504i	−0.0548694	+	0.139375i
$77$	10.2111	−	4.22959i	1.16367	−	0.482007i
$78$	0.440130	+	2.42991i	0.0498350	+	0.275133i
$79$	−1.67033			−0.187926			−0.0939632	−	0.995576i	$-0.529954\pi$
$79$	−1.67033			−0.187926			−0.0939632	+	0.995576i	$0.529954\pi$
$80$	−0.748162	−	1.63997i	−0.0836470	−	0.183355i
$81$		−	6.94410i		−	0.771567i
$82$	−0.00687351	−	0.778816i	−0.000759052	−	0.0860058i
$83$	−3.20382	+	7.73471i	−0.351665	+	0.848994i	0.644750	+	0.764394i	$0.276961\pi$
$83$	−3.20382	+	7.73471i	−0.351665	+	0.848994i	−0.996415	+	0.0846007i	$0.973039\pi$
$84$	−1.01755	−	2.33894i	−0.111024	−	0.255200i
$85$	0.616538	+	1.48846i	0.0668730	+	0.161446i
$86$	7.00953	+	2.83123i	0.755857	+	0.305299i
$87$	−0.723890	−	0.723890i	−0.0776091	−	0.0776091i
$88$	10.8433	−	4.83159i	1.15590	−	0.515049i
$89$			3.24654i			0.344132i	0.985085	+	0.172066i	$0.0550442\pi$
$89$			3.24654i			0.344132i	−0.985085	+	0.172066i	$0.944956\pi$
$90$	1.63417	+	0.660060i	0.172257	+	0.0695764i
$91$	9.26112	+	2.09370i	0.970829	+	0.219480i
$92$	−5.30051	+	5.49101i	−0.552616	+	0.572477i
$93$	0.899024	−	2.17044i	0.0932244	−	0.225064i
$94$	3.75654	+	3.69081i	0.387457	+	0.380678i
$95$	0.294227			0.0301870
$96$	−1.15903	−	2.48236i	−0.118293	−	0.253355i
$97$	13.6088	−	13.6088i	1.38177	−	1.38177i	0.540285	−	0.841482i	$-0.318317\pi$
$97$	13.6088	−	13.6088i	1.38177	−	1.38177i	0.841482	−	0.540285i	$-0.181683\pi$
$98$	0.0922536		0.000814192i	0.00931902		8.22458e-5i
$99$	−4.44170	+	10.7232i	−0.446408	+	1.07772i
$100$	6.66308	−	6.90255i	0.666308	−	0.690255i
$101$	13.9387	+	5.77360i	1.38695	+	0.574495i	0.946331	−	0.323199i	$-0.104758\pi$
$101$	13.9387	+	5.77360i	1.38695	+	0.574495i	0.440621	+	0.897693i	$0.354758\pi$
$102$	0.956964	+	2.25385i	0.0947536	+	0.223164i
$103$	10.6797	+	10.6797i	1.05230	+	1.05230i	0.998555	+	0.0537430i	$0.0171152\pi$
$103$	10.6797	+	10.6797i	1.05230	+	1.05230i	0.0537430	+	0.998555i	$0.482885\pi$
$104$	10.0031	+	1.98465i	0.980880	+	0.194611i
$105$	−0.406394	+	0.406394i	−0.0396600	+	0.0396600i
$106$	15.7118	+	6.34619i	1.52607	+	0.616397i
$107$	−4.68149	+	11.3021i	−0.452577	+	1.09262i	0.518762	+	0.854918i	$0.326393\pi$
$107$	−4.68149	+	11.3021i	−0.452577	+	1.09262i	−0.971339	+	0.237698i	$0.923607\pi$
$108$	5.19624	+	2.04567i	0.500008	+	0.196844i
$109$	6.36372	+	2.63594i	0.609533	+	0.252477i	0.666029	−	0.745926i	$-0.267993\pi$
$109$	6.36372	+	2.63594i	0.609533	+	0.252477i	−0.0564956	+	0.998403i	$0.517993\pi$
$110$	−1.90798	−	1.87460i	−0.181919	−	0.178736i
$111$	−0.811822	−	0.811822i	−0.0770547	−	0.0770547i
$112$	−10.5270	+	0.371773i	−0.994709	+	0.0351293i
$113$		−	11.4759i		−	1.07956i	−0.841807	−	0.539779i	$-0.818508\pi$
$113$		−	11.4759i		−	1.07956i	0.841807	−	0.539779i	$-0.181492\pi$
$114$	0.447158	−	0.00394643i	0.0418802	−	0.000369617i
$115$	1.58874	+	0.658078i	0.148151	+	0.0613661i
$116$	−3.87672	+	1.68655i	−0.359944	+	0.156593i
$117$	−8.43172	+	5.32229i	−0.779513	+	0.492046i
$118$	1.04390	+	2.45859i	0.0960985	+	0.226332i
$119$	9.41465			0.863039
$120$	−0.424783	+	0.447894i	−0.0387772	+	0.0408869i
$121$	4.67761	−	4.67761i	0.425237	−	0.425237i
$122$	−3.31085	+	1.40576i	−0.299750	+	0.127271i
$123$	−0.246414	+	0.102068i	−0.0222184	+	0.00920317i
$124$	−6.98015	−	6.73799i	−0.626836	−	0.605089i
$125$	−4.07885	−	1.68951i	−0.364823	−	0.151115i
$126$	7.21798	−	7.34652i	0.643029	−	0.654480i
$127$	−14.4199			−1.27956			−0.639779	−	0.768559i	$-0.720974\pi$
$127$	−14.4199			−1.27956			−0.639779	+	0.768559i	$0.720974\pi$
$128$	−11.2921	+	0.698488i	−0.998092	+	0.0617382i
$129$		−	2.58883i		−	0.227934i
$130$	−0.409544	−	2.26104i	−0.0359194	−	0.198307i
$131$	0.209230	+	0.505126i	0.0182805	+	0.0441331i	0.932756	−	0.360508i	$-0.117397\pi$
$131$	0.209230	+	0.505126i	0.0182805	+	0.0441331i	−0.914476	+	0.404641i	$0.867397\pi$
$132$	−2.92485	−	2.82338i	−0.254575	−	0.245744i
$133$	0.657968	−	1.58848i	0.0570531	−	0.137738i
$134$	−14.5174	−	5.86376i	−1.25412	−	0.506552i
$135$		−	1.25829i		−	0.108296i
$136$	10.1084	−	0.267692i	0.866785	−	0.0229544i
$137$	−0.754536			−0.0644643			−0.0322322	−	0.999480i	$-0.510262\pi$
$137$	−0.754536			−0.0644643			−0.0322322	+	0.999480i	$0.510262\pi$
$138$	2.42335	+	0.978820i	0.206290	+	0.0833227i
$139$	0.706301	−	1.70516i	0.0599077	−	0.144630i	−0.891091	−	0.453824i	$-0.850059\pi$
$139$	0.706301	−	1.70516i	0.0599077	−	0.144630i	0.950999	+	0.309194i	$0.100059\pi$
$140$	0.946837	+	2.17640i	0.0800223	+	0.183939i
$141$	0.690147	−	1.66616i	0.0581209	−	0.140316i
$142$	−0.0106345	−	1.20496i	−0.000892424	−	0.101118i
$143$	14.9136	−	2.56558i	1.24714	−	0.214544i
$144$	7.54095	−	8.09308i	0.628412	−	0.674423i
$145$	0.673583	+	0.673583i	0.0559380	+	0.0559380i
$146$	−8.80978	+	0.0777515i	−0.729103	+	0.00643476i
$147$	−0.0120903	−	0.0291887i	−0.000997194	−	0.00240744i
$148$	−4.34763	+	1.89142i	−0.357373	+	0.155474i
$149$	−15.8300	+	6.55699i	−1.29684	+	0.537170i	−0.921018	−	0.389521i	$-0.872641\pi$
$149$	−15.8300	+	6.55699i	−1.29684	+	0.537170i	−0.375825	+	0.926691i	$0.622641\pi$
$150$	−3.04631	−	1.23044i	−0.248730	−	0.100465i
$151$		−	20.0815i		−	1.63421i	−0.576491	−	0.817103i	$-0.695579\pi$
$151$		−	20.0815i		−	1.63421i	0.576491	−	0.817103i	$-0.304421\pi$
$152$	0.661285	−	1.72423i	0.0536373	−	0.139854i
$153$	−6.99101	+	6.99101i	−0.565189	+	0.565189i
$154$	−14.3874	+	6.10876i	−1.15937	+	0.492258i
$155$	−0.836546	+	2.01960i	−0.0671930	+	0.162218i
$156$	−0.652741	−	3.43079i	−0.0522611	−	0.274683i
$157$	−16.4982	+	6.83380i	−1.31670	+	0.545396i	−0.926833	−	0.375473i	$-0.877480\pi$
$157$	−16.4982	+	6.83380i	−1.31670	+	0.545396i	−0.389870	+	0.920870i	$0.627480\pi$
$158$	2.36211	−	0.0208470i	0.187919	−	0.00165850i
$159$		−	5.80287i		−	0.460197i
$160$	1.07849	+	2.30985i	0.0852619	+	0.182609i
$161$	7.10569	−	7.10569i	0.560006	−	0.560006i
$162$	0.0866678	+	9.82006i	0.00680927	+	0.771537i
$163$	−0.318089	+	0.767936i	−0.0249147	+	0.0601494i	−0.935847	−	0.352406i	$-0.885364\pi$
$163$	−0.318089	+	0.767936i	−0.0249147	+	0.0601494i	0.910933	+	0.412555i	$0.135364\pi$
$164$	0.0194405	+	1.10128i	0.00151804	+	0.0859958i
$165$	−0.350533	+	0.846261i	−0.0272889	+	0.0658813i
$166$	4.43417	−	10.9781i	0.344159	−	0.852065i
$167$	5.30089			0.410195			0.205097	−	0.978742i	$-0.434249\pi$
$167$	5.30089			0.410195			0.205097	+	0.978742i	$0.434249\pi$
$168$	1.46817	+	3.29494i	0.113272	+	0.254210i
$169$	11.7358	+	5.59213i	0.902751	+	0.430164i
$170$	−0.890460	−	2.09722i	−0.0682952	−	0.160849i
$171$	0.690964	+	1.66814i	0.0528394	+	0.127566i
$172$	−9.94792	−	3.91632i	−0.758522	−	0.298617i
$173$	13.9930	−	5.79607i	1.06387	−	0.440667i	0.219043	−	0.975715i	$-0.429706\pi$
$173$	13.9930	−	5.79607i	1.06387	−	0.440667i	0.844822	+	0.535048i	$0.179706\pi$
$174$	1.03273	+	1.01466i	0.0782910	+	0.0769212i
$175$	−8.93230	+	8.93230i	−0.675219	+	0.675219i
$176$	−15.2738	+	6.96797i	−1.15131	+	0.525230i
$177$	0.646789	−	0.646789i	0.0486156	−	0.0486156i
$178$	−0.0405193	−	4.59112i	−0.00303705	−	0.344119i
$179$	8.24999	+	19.9172i	0.616633	+	1.48868i	0.855590	+	0.517654i	$0.173194\pi$
$179$	8.24999	+	19.9172i	0.616633	+	1.48868i	−0.238957	+	0.971030i	$0.576806\pi$
$180$	−2.31921	−	0.913033i	−0.172864	−	0.0680535i
$181$	−9.45598	+	22.8288i	−0.702858	+	1.69685i	0.0142622	+	0.999898i	$0.495460\pi$
$181$	−9.45598	+	22.8288i	−0.702858	+	1.69685i	−0.717120	+	0.696950i	$0.754540\pi$
$182$	−13.1228	−	2.84524i	−0.972728	−	0.210903i
$183$	0.870994	+	0.870994i	0.0643857	+	0.0643857i
$184$	7.42723	−	7.83131i	0.547542	−	0.577332i
$185$	0.755404	+	0.755404i	0.0555384	+	0.0555384i
$186$	−1.24427	+	3.08056i	−0.0912346	+	0.225878i
$187$	13.8627	−	5.74210i	1.01374	−	0.419904i
$188$	−5.35840	−	5.17251i	−0.390802	−	0.377244i
$189$	−6.79326	−	2.81386i	−0.494137	−	0.204678i
$190$	−0.416083	+	0.00367218i	−0.0301858	+	0.000266408i
$191$		−	26.0148i		−	1.88237i	−0.337897	−	0.941183i	$-0.609715\pi$
$191$		−	26.0148i		−	1.88237i	0.337897	−	0.941183i	$-0.390285\pi$
$192$	1.67004	+	3.49598i	0.120525	+	0.252301i
$193$	8.75087	+	8.75087i	0.629901	+	0.629901i	0.948043	−	0.318142i	$-0.103059\pi$
$193$	8.75087	+	8.75087i	0.629901	+	0.629901i	−0.318142	+	0.948043i	$0.603059\pi$
$194$	−19.0752	+	19.4149i	−1.36952	+	1.39391i
$195$	−0.665419	+	0.420028i	−0.0476517	+	0.0300788i
$196$	−0.130451	+	0.00230279i	−0.00931793	+	0.000164485i
$197$	−5.36139	−	12.9435i	−0.381983	−	0.922189i	−0.991582	−	0.129479i	$-0.958669\pi$
$197$	−5.36139	−	12.9435i	−0.381983	−	0.922189i	0.609599	−	0.792710i	$-0.291331\pi$
$198$	6.14743	−	15.2198i	0.436879	−	1.08162i
$199$	−3.95138	−	3.95138i	−0.280106	−	0.280106i	0.553045	−	0.833151i	$-0.313466\pi$
$199$	−3.95138	−	3.95138i	−0.280106	−	0.280106i	−0.833151	+	0.553045i	$0.813466\pi$
$200$	−9.33650	+	9.84446i	−0.660190	+	0.696108i
$201$			5.36174i			0.378188i
$202$	−19.7836	−	7.99082i	−1.39197	−	0.562232i
$203$	5.14286	−	2.13024i	0.360958	−	0.149514i
$204$	−1.38143	−	3.17535i	−0.0967194	−	0.222319i
$205$	0.229290	−	0.0949749i	0.0160143	−	0.00663333i
$206$	−15.2360	−	14.9694i	−1.06154	−	1.04297i
$207$			10.5529i			0.733477i
$208$	−14.1707	−	2.68176i	−0.982560	−	0.185947i
$209$		−	2.74027i		−	0.189548i
$210$	0.569633	−	0.579777i	0.0393084	−	0.0400084i
$211$	−18.1612	+	7.52260i	−1.25027	+	0.517877i	−0.906908	−	0.421328i	$-0.861564\pi$
$211$	−18.1612	+	7.52260i	−1.25027	+	0.517877i	−0.343357	+	0.939205i	$0.611564\pi$
$212$	−22.2982	−	8.77843i	−1.53145	−	0.602905i
$213$	−0.381244	+	0.157916i	−0.0261224	+	0.0108203i
$214$	6.47931	−	16.0414i	0.442916	−	1.09657i
$215$			2.40892i			0.164287i
$216$	−7.37383	−	2.82804i	−0.501726	−	0.192424i
$217$	9.03273	+	9.03273i	0.613181	+	0.613181i
$218$	−9.03220	−	3.64821i	−0.611738	−	0.247088i
$219$	1.15457	+	2.78738i	0.0780186	+	0.188354i
$220$	2.72159	+	2.62717i	0.183489	+	0.177124i
$221$	12.5729	+	2.84241i	0.845745	+	0.191201i
$222$	1.15818	+	1.13791i	0.0777317	+	0.0763717i
$223$	−19.3144	−	19.3144i	−1.29339	−	1.29339i	−0.932678	−	0.360709i	$-0.882535\pi$
$223$	−19.3144	−	19.3144i	−1.29339	−	1.29339i	−0.360709	−	0.932678i	$-0.617465\pi$
$224$	14.8822	−	0.657131i	0.994361	−	0.0439064i
$225$		−	13.2657i		−	0.884378i
$226$	0.143228	+	16.2287i	0.00952736	+	1.07952i
$227$	−7.77973	−	3.22247i	−0.516359	−	0.213883i	0.109258	−	0.994013i	$-0.465153\pi$
$227$	−7.77973	−	3.22247i	−0.516359	−	0.213883i	−0.625617	+	0.780131i	$0.715153\pi$
$228$	−0.632303	+	0.0111618i	−0.0418753	+	0.000739206i
$229$	−3.90938	+	1.61932i	−0.258339	+	0.107008i	−0.508094	−	0.861301i	$-0.669650\pi$
$229$	−3.90938	+	1.61932i	−0.258339	+	0.107008i	0.249755	+	0.968309i	$0.419650\pi$
$230$	−2.25494	−	0.910797i	−0.148687	−	0.0600562i
$231$	3.78493	+	3.78493i	0.249030	+	0.249030i
$232$	5.46124	−	2.43344i	0.358548	−	0.159763i
$233$	−1.42378	−	1.42378i	−0.0932749	−	0.0932749i	0.658930	−	0.752205i	$-0.271009\pi$
$233$	−1.42378	−	1.42378i	−0.0932749	−	0.0932749i	−0.752205	+	0.658930i	$0.771009\pi$
$234$	11.8574	−	7.63179i	0.775140	−	0.498906i
$235$	−0.642186	+	1.55037i	−0.0418916	+	0.101135i
$236$	−1.50692	−	3.46381i	−0.0980922	−	0.225475i
$237$	−0.309567	−	0.747361i	−0.0201085	−	0.0485463i
$238$	−13.3138	+	0.117502i	−0.863006	+	0.00761653i
$239$	−1.21682	+	1.21682i	−0.0787098	+	0.0787098i	−0.745366	−	0.666656i	$-0.767725\pi$
$239$	−1.21682	+	1.21682i	−0.0787098	+	0.0787098i	0.666656	+	0.745366i	$0.267725\pi$
$240$	0.595121	−	0.638695i	0.0384149	−	0.0412276i
$241$	−9.65310	+	9.65310i	−0.621811	+	0.621811i	−0.945994	−	0.324184i	$-0.894910\pi$
$241$	−9.65310	+	9.65310i	−0.621811	+	0.621811i	0.324184	+	0.945994i	$0.394910\pi$
$242$	−6.55650	+	6.67326i	−0.421468	+	0.428974i
$243$	10.8460	−	4.49256i	0.695772	−	0.288198i
$244$	4.66452	−	2.02929i	0.298615	−	0.129912i
$245$	0.0112501	+	0.0271602i	0.000718744	+	0.00173520i
$246$	0.347195	−	0.147416i	0.0221363	−	0.00939890i
$247$	1.35828	−	1.92270i	0.0864250	−	0.122339i
$248$	9.95514	+	9.44147i	0.632152	+	0.599534i
$249$	−4.05454			−0.256946
$250$	5.78922	+	2.33833i	0.366142	+	0.147889i
$251$	9.25371	−	22.3404i	0.584089	−	1.41012i	−0.304987	−	0.952357i	$-0.598652\pi$
$251$	9.25371	−	22.3404i	0.584089	−	1.41012i	0.889076	−	0.457759i	$-0.151348\pi$
$252$	−10.1157	+	10.4792i	−0.637228	+	0.660129i
$253$	6.12897	−	14.7967i	0.385325	−	0.930258i
$254$	20.3920	−	0.179971i	1.27951	−	0.0112924i
$255$	−0.551721	+	0.551721i	−0.0345501	+	0.0345501i
$256$	15.9601	−	1.12871i	0.997509	−	0.0705442i
$257$			23.5781i			1.47076i	0.677653	+	0.735382i	$0.262997\pi$
$257$			23.5781i			1.47076i	−0.677653	+	0.735382i	$0.737003\pi$
$258$	0.0323107	+	3.66102i	0.00201157	+	0.227925i
$259$	5.76757	−	2.38901i	0.358380	−	0.148446i
$260$	0.607379	+	3.19236i	0.0376681	+	0.197982i
$261$	−2.23707	+	5.40077i	−0.138471	+	0.334299i
$262$	−0.302189	−	0.711717i	−0.0186693	−	0.0439700i
$263$	−1.40524	+	1.40524i	−0.0866506	+	0.0866506i	−0.749104	−	0.662453i	$-0.769515\pi$
$263$	−1.40524	+	1.40524i	−0.0866506	+	0.0866506i	0.662453	+	0.749104i	$0.269515\pi$
$264$	4.17144	+	3.95620i	0.256734	+	0.243487i
$265$			5.39960i			0.331695i
$266$	−0.910646	+	2.25457i	−0.0558353	+	0.138237i
$267$	−1.45261	+	0.601691i	−0.0888983	+	0.0368229i
$268$	20.6032	+	8.11110i	1.25854	+	0.495464i
$269$	−1.03371	−	2.49561i	−0.0630267	−	0.152160i	0.889228	−	0.457464i	$-0.151242\pi$
$269$	−1.03371	−	2.49561i	−0.0630267	−	0.152160i	−0.952255	+	0.305304i	$0.901242\pi$
$270$	0.0157044	+	1.77942i	0.000955739	+	0.108292i
$271$	1.46108	+	1.46108i	0.0887544	+	0.0887544i	0.750090	−	0.661336i	$-0.230010\pi$
$271$	1.46108	+	1.46108i	0.0887544	+	0.0887544i	−0.661336	+	0.750090i	$0.730010\pi$
$272$	−14.2915	+	0.504720i	−0.866549	+	0.0306031i
$273$	0.779599	+	4.53177i	0.0471835	+	0.274275i
$274$	1.06703	−	0.00941719i	0.0644618	−	0.000568914i
$275$	−7.70451	+	18.6003i	−0.464600	+	1.12164i
$276$	−3.43922	−	1.35396i	−0.207017	−	0.0814989i
$277$	4.60313	−	11.1129i	0.276576	−	0.667712i	−0.723161	−	0.690680i	$-0.757311\pi$
$277$	4.60313	−	11.1129i	0.276576	−	0.667712i	0.999736	+	0.0229675i	$0.00731142\pi$
$278$	−0.977540	+	2.42019i	−0.0586290	+	0.145153i
$279$	−13.4148			−0.803124
$280$	−1.36614	−	3.06596i	−0.0816425	−	0.183226i
$281$		−	26.0042i		−	1.55128i	−0.631175	−	0.775640i	$-0.717427\pi$
$281$		−	26.0042i		−	1.55128i	0.631175	−	0.775640i	$-0.282573\pi$
$282$	−0.955183	+	2.36483i	−0.0568803	+	0.140824i
$283$	9.06166	−	21.8768i	0.538660	−	1.30044i	−0.386999	−	0.922080i	$-0.626488\pi$
$283$	9.06166	−	21.8768i	0.538660	−	1.30044i	0.925659	−	0.378359i	$-0.123512\pi$
$284$	0.0300776	+	1.70387i	0.00178478	+	0.101106i
$285$	0.0545300	+	0.131647i	0.00323008	+	0.00779809i
$286$	−21.0581	+	3.81426i	−1.24519	+	0.225542i
$287$		−	1.45028i		−	0.0856075i
$288$	−10.5631	+	11.5390i	−0.622436	+	0.679943i
$289$	−4.21866			−0.248157
$290$	−0.960960	−	0.944146i	−0.0564295	−	0.0554422i
$291$	8.61122	+	3.56688i	0.504799	+	0.209094i
$292$	12.4575	−	0.219906i	0.729017	−	0.0128690i
$293$	−9.92567	+	4.11135i	−0.579864	+	0.240188i	−0.653283	−	0.757114i	$-0.726609\pi$
$293$	−9.92567	+	4.11135i	−0.579864	+	0.240188i	0.0734192	+	0.997301i	$0.476609\pi$
$294$	0.0174619	+	0.0411265i	0.00101840	+	0.00239855i
$295$	−0.601840	+	0.601840i	−0.0350405	+	0.0350405i
$296$	6.12463	−	2.72903i	0.355987	−	0.158622i
$297$	−11.7190			−0.680005
$298$	22.3043	−	9.47020i	1.29205	−	0.548594i
$299$	11.6347	−	7.34407i	0.672851	−	0.424719i
$300$	4.32332	+	1.70202i	0.249607	+	0.0982660i
$301$	13.0053	+	5.38699i	0.749615	+	0.310501i
$302$	0.250632	+	28.3984i	0.0144223	+	1.63414i
$303$			7.30669i			0.419758i
$304$	−0.913642	+	2.44659i	−0.0524009	+	0.140322i
$305$	−0.810464	−	0.810464i	−0.0464070	−	0.0464070i
$306$	9.79914	−	9.97364i	0.560179	−	0.570155i
$307$	−19.9281	−	8.25449i	−1.13736	−	0.471109i	−0.267081	−	0.963674i	$-0.586059\pi$
$307$	−19.9281	−	8.25449i	−1.13736	−	0.471109i	−0.870275	+	0.492565i	$0.836059\pi$
$308$	20.2698	−	8.81832i	1.15498	−	0.502470i
$309$	−2.79915	+	6.75774i	−0.159238	+	0.384434i
$310$	1.15780	−	2.86648i	0.0657588	−	0.162805i
$311$	4.52724	−	4.52724i	0.256716	−	0.256716i	−0.567001	−	0.823717i	$-0.691896\pi$
$311$	4.52724	−	4.52724i	0.256716	−	0.256716i	0.823717	+	0.567001i	$0.191896\pi$
$312$	0.965899	+	4.84353i	0.0546832	+	0.274211i
$313$	18.9534	+	18.9534i	1.07131	+	1.07131i	0.997254	+	0.0740542i	$0.0235938\pi$
$313$	18.9534	+	18.9534i	1.07131	+	1.07131i	0.0740542	+	0.997254i	$0.476406\pi$
$314$	23.2458	−	9.86998i	1.31184	−	0.556995i
$315$	3.03201	+	1.25590i	0.170834	+	0.0707618i
$316$	−3.34013	+	0.0589618i	−0.187897	+	0.00331686i
$317$	0.613714	−	1.48164i	0.0344696	−	0.0832171i	−0.905707	−	0.423904i	$-0.860660\pi$
$317$	0.613714	−	1.48164i	0.0344696	−	0.0832171i	0.940177	+	0.340687i	$0.110660\pi$
$318$	0.0724243	+	8.20617i	0.00406135	+	0.460179i
$319$	6.27338	−	6.27338i	0.351242	−	0.351242i
$320$	−1.55398	−	3.25303i	−0.0868701	−	0.181850i
$321$	−5.92459			−0.330678
$322$	−9.95988	+	10.1372i	−0.555042	+	0.564927i
$323$	0.893259	−	2.15652i	0.0497023	−	0.119992i
$324$	−0.245124	−	13.8860i	−0.0136180	−	0.771447i
$325$	−14.6255	+	9.23197i	−0.811279	+	0.512098i
$326$	0.440245	−	1.08995i	0.0243829	−	0.0603669i
$327$			3.33587i			0.184474i
$328$	−0.0412368	−	1.55715i	−0.00227692	−	0.0859790i
$329$	6.93409	+	6.93409i	0.382289	+	0.382289i
$330$	0.485147	−	1.20112i	0.0267065	−	0.0661196i
$331$	−9.40568	−	22.7073i	−0.516983	−	1.24811i	−0.939748	−	0.341868i	$-0.888940\pi$
$331$	−9.40568	−	22.7073i	−0.516983	−	1.24811i	0.422765	−	0.906239i	$-0.361060\pi$
$332$	−6.13361	+	15.5801i	−0.336626	+	0.855069i
$333$	−2.50881	+	6.05681i	−0.137482	+	0.331911i
$334$	−7.49629	+	0.0661592i	−0.410179	+	0.00362007i
$335$		−	4.98912i		−	0.272585i
$336$	−2.11735	−	4.64124i	−0.115511	−	0.253200i
$337$	−29.6958			−1.61763			−0.808816	−	0.588062i	$-0.799891\pi$
$337$	−29.6958			−1.61763			−0.808816	+	0.588062i	$0.799891\pi$
$338$	−16.6660	−	7.76168i	−0.906512	−	0.422180i
$339$	5.13469	−	2.12686i	0.278878	−	0.115515i
$340$	1.28543	+	2.95468i	0.0697121	+	0.160240i
$341$	18.8095	+	7.79113i	1.01859	+	0.421914i
$342$	−0.997953	−	2.35038i	−0.0539631	−	0.127094i
$343$	18.6055			1.00461
$344$	14.1168	+	5.41414i	0.761128	+	0.291911i
$345$			0.832820i			0.0448375i
$346$	−19.7159	+	8.37121i	−1.05993	+	0.450039i
$347$	14.7882	+	6.12549i	0.793875	+	0.328834i	0.742500	−	0.669846i	$-0.233640\pi$
$347$	14.7882	+	6.12549i	0.793875	+	0.328834i	0.0513744	+	0.998679i	$0.483640\pi$
$348$	−1.47311	−	1.42200i	−0.0789668	−	0.0762272i
$349$	0.510261	+	0.211357i	0.0273137	+	0.0113137i	0.396298	−	0.918122i	$-0.370295\pi$
$349$	0.510261	+	0.211357i	0.0273137	+	0.0113137i	−0.368985	+	0.929435i	$0.620295\pi$
$350$	12.5202	−	12.7432i	0.669233	−	0.681151i
$351$	−8.22260	−	5.80879i	−0.438890	−	0.310050i
$352$	21.5126	−	10.0444i	1.14663	−	0.535370i
$353$	12.5620	−	12.5620i	0.668609	−	0.668609i	−0.288785	−	0.957394i	$-0.593251\pi$
$353$	12.5620	−	12.5620i	0.668609	−	0.668609i	0.957394	+	0.288785i	$0.0932512\pi$
$354$	−0.906589	+	0.922734i	−0.0481847	+	0.0490428i
$355$	0.354749	−	0.146942i	0.0188281	−	0.00779887i
$356$	0.114601	+	6.49206i	0.00607386	+	0.344078i
$357$	1.74485	+	4.21243i	0.0923471	+	0.222946i
$358$	−11.9154	−	28.0632i	−0.629747	−	1.48318i
$359$	−6.04880			−0.319243			−0.159622	−	0.987178i	$-0.551027\pi$
$359$	−6.04880			−0.319243			−0.159622	+	0.987178i	$0.551027\pi$
$360$	3.29113	+	1.26223i	0.173458	+	0.0665253i
$361$	13.1336	+	13.1336i	0.691242	+	0.691242i
$362$	13.0873	−	32.4015i	0.687855	−	1.70299i
$363$	2.95984	+	1.22601i	0.155351	+	0.0643486i
$364$	18.5933	+	3.85984i	0.974552	+	0.202311i
$365$	−1.07433	−	2.59367i	−0.0562332	−	0.135759i
$366$	−1.24259	−	1.22085i	−0.0649514	−	0.0638150i
$367$	−27.6654			−1.44412			−0.722060	−	0.691830i	$-0.756805\pi$
$367$	−27.6654			−1.44412			−0.722060	+	0.691830i	$0.756805\pi$
$368$	−10.4055	+	11.1674i	−0.542426	+	0.582141i
$369$	1.07693	+	1.07693i	0.0560628	+	0.0560628i
$370$	−1.07769	−	1.05883i	−0.0560264	−	0.0550461i
$371$	29.1515	+	12.0749i	1.51347	+	0.626899i
$372$	1.72115	−	4.37193i	0.0892376	−	0.226674i
$373$	6.47746	+	2.68305i	0.335390	+	0.138923i	0.544022	−	0.839071i	$-0.316901\pi$
$373$	6.47746	+	2.68305i	0.335390	+	0.138923i	−0.208631	+	0.977994i	$0.566901\pi$
$374$	−19.5323	+	8.29326i	−1.00999	+	0.428834i
$375$		−	2.13814i		−	0.110413i
$376$	7.64219	+	7.24787i	0.394116	+	0.373780i
$377$	7.51125	−	1.29216i	0.386849	−	0.0665495i
$378$	9.64187	+	3.89446i	0.495924	+	0.200309i
$379$	−16.9050	+	7.00227i	−0.868351	+	0.359683i	−0.771968	−	0.635662i	$-0.780727\pi$
$379$	−16.9050	+	7.00227i	−0.868351	+	0.359683i	−0.0963829	+	0.995344i	$0.530727\pi$
$380$	0.588362	−	0.0103861i	0.0301823	−	0.000532795i
$381$	−2.67248	−	6.45195i	−0.136916	−	0.330543i
$382$	0.324685	+	36.7891i	0.0166123	+	1.88229i
$383$	23.4869	+	23.4869i	1.20013	+	1.20013i	0.974128	+	0.225999i	$0.0725645\pi$
$383$	23.4869	+	23.4869i	1.20013	+	1.20013i	0.225999	+	0.974128i	$0.427435\pi$
$384$	−2.40533	−	4.92303i	−0.122747	−	0.251227i
$385$	−3.52189	−	3.52189i	−0.179492	−	0.179492i
$386$	−12.4843	−	12.2659i	−0.635436	−	0.624318i
$387$	−13.6575	+	5.65714i	−0.694252	+	0.287568i
$388$	26.7330	−	27.6938i	1.35716	−	1.40594i
$389$	−6.59087	−	2.73003i	−0.334170	−	0.138418i	0.209288	−	0.977854i	$-0.432885\pi$
$389$	−6.59087	−	2.73003i	−0.334170	−	0.138418i	−0.543458	+	0.839436i	$0.682885\pi$
$390$	0.935766	−	0.602290i	0.0473844	−	0.0304982i
$391$	9.64669	−	9.64669i	0.487854	−	0.487854i
$392$	0.184450	−	0.00488464i	0.00931611	−	0.000246712i
$393$	−0.187233	+	0.187233i	−0.00944468	+	0.00944468i
$394$	7.74340	+	18.2373i	0.390107	+	0.918782i
$395$	0.288054	+	0.695423i	0.0144935	+	0.0349905i
$396$	−8.50349	+	21.5999i	−0.427316	+	1.08543i
$397$	−12.6356	+	30.5051i	−0.634165	+	1.53101i	0.200176	+	0.979760i	$0.435849\pi$
$397$	−12.6356	+	30.5051i	−0.634165	+	1.53101i	−0.834341	+	0.551249i	$0.814151\pi$
$398$	5.63720	+	5.53856i	0.282567	+	0.277623i
$399$	0.832682			0.0416862
$400$	13.0804	−	14.0382i	0.654021	−	0.701908i
$401$	3.29915	−	3.29915i	0.164752	−	0.164752i	−0.619916	−	0.784668i	$-0.712833\pi$
$401$	3.29915	−	3.29915i	0.164752	−	0.164752i	0.784668	+	0.619916i	$0.212833\pi$
$402$	−0.0669187	−	7.58235i	−0.00333760	−	0.378173i
$403$	9.33576	+	14.7900i	0.465047	+	0.736741i
$404$	28.0769	+	11.0534i	1.39688	+	0.549926i
$405$	−2.89110	+	1.19753i	−0.143660	+	0.0595060i
$406$	−7.24623	+	3.07669i	−0.359625	+	0.152693i
$407$	7.03542	−	7.03542i	0.348733	−	0.348733i
$408$	1.99319	+	4.47321i	0.0986776	+	0.221457i
$409$	−17.9804			−0.889076			−0.444538	−	0.895760i	$-0.646632\pi$
$409$	−17.9804			−0.889076			−0.444538	+	0.895760i	$0.646632\pi$
$410$	−0.323067	+	0.137171i	−0.0159551	+	0.00677440i
$411$	−0.139841	−	0.337605i	−0.00689783	−	0.0166528i
$412$	21.7330	+	20.9790i	1.07071	+	1.03356i
$413$	1.90335	+	4.59510i	0.0936579	+	0.226110i
$414$	−0.131708	−	14.9235i	−0.00647311	−	0.733448i
$415$	3.77277			0.185198
$416$	20.0731	+	3.61558i	0.984163	+	0.177268i
$417$	0.893849			0.0437720
$418$	0.0342006	+	3.87517i	0.00167281	+	0.189541i
$419$	−9.34590	−	22.5630i	−0.456577	−	1.10227i	−0.969774	−	0.244004i	$-0.921539\pi$
$419$	−9.34590	−	22.5630i	−0.456577	−	1.10227i	0.513197	−	0.858271i	$-0.328461\pi$
$420$	−0.798315	+	0.827006i	−0.0389538	+	0.0403538i
$421$	3.30850	+	7.98743i	0.161246	+	0.389283i	0.983767	−	0.179453i	$-0.0574326\pi$
$421$	3.30850	+	7.98743i	0.161246	+	0.389283i	−0.822520	+	0.568736i	$0.807433\pi$
$422$	25.5889	−	10.8648i	1.24565	−	0.528891i
$423$	−10.2981			−0.500708
$424$	31.6428	+	12.1358i	1.53671	+	0.589366i
$425$	−12.1265	+	12.1265i	−0.588222	+	0.588222i
$426$	0.537168	−	0.228077i	0.0260259	−	0.0110504i
$427$	−6.18796	+	2.56314i	−0.299457	+	0.124039i
$428$	−8.96256	+	22.7660i	−0.433222	+	1.10043i
$429$	3.91191	+	6.19735i	0.188869	+	0.299211i
$430$	−0.0300652	−	3.40660i	−0.00144987	−	0.164281i
$431$	12.3761	−	12.3761i	0.596135	−	0.596135i	−0.343147	−	0.939282i	$-0.611493\pi$
$431$	12.3761	−	12.3761i	0.596135	−	0.596135i	0.939282	+	0.343147i	$0.111493\pi$
$432$	10.4631	+	3.90727i	0.503404	+	0.187989i
$433$	−35.6420			−1.71285			−0.856424	−	0.516274i	$-0.827319\pi$
$433$	−35.6420			−1.71285			−0.856424	+	0.516274i	$0.827319\pi$
$434$	−12.8864	−	12.6610i	−0.618569	−	0.607746i
$435$	−0.176547	+	0.426221i	−0.00846476	+	0.0204357i
$436$	12.8185	+	5.04642i	0.613895	+	0.241680i
$437$	−0.953442	−	2.30181i	−0.0456093	−	0.110111i
$438$	−1.66753	−	3.92739i	−0.0796778	−	0.187658i
$439$	12.0227	−	12.0227i	0.573811	−	0.573811i	−0.359380	−	0.933191i	$-0.617012\pi$
$439$	12.0227	−	12.0227i	0.573811	−	0.573811i	0.933191	+	0.359380i	$0.117012\pi$
$440$	−3.88154	−	3.68126i	−0.185045	−	0.175497i
$441$	−0.127566	+	0.127566i	−0.00607459	+	0.00607459i
$442$	−17.8156	−	3.86271i	−0.847400	−	0.183730i
$443$	−32.4987	−	13.4614i	−1.54406	−	0.639570i	−0.561828	−	0.827254i	$-0.689902\pi$
$443$	−32.4987	−	13.4614i	−1.54406	−	0.639570i	−0.982229	+	0.187684i	$0.939902\pi$
$444$	−1.65205	−	1.59473i	−0.0784027	−	0.0756827i
$445$	1.35166	−	0.559876i	0.0640749	−	0.0265407i
$446$	27.5547	+	27.0726i	1.30475	+	1.28192i
$447$	−5.86764	−	5.86764i	−0.277530	−	0.277530i
$448$	−21.0376	+	1.11503i	−0.993934	+	0.0526802i
$449$	−22.9559	−	22.9559i	−1.08336	−	1.08336i	−0.996194	−	0.0871624i	$-0.972220\pi$
$449$	−22.9559	−	22.9559i	−1.08336	−	1.08336i	−0.0871624	−	0.996194i	$-0.527780\pi$
$450$	0.165566	+	18.7598i	0.00780485	+	0.884343i
$451$	−0.884544	−	2.13548i	−0.0416515	−	0.100556i
$452$	−0.405093	−	22.9481i	−0.0190540	−	1.07939i
$453$	8.98513	−	3.72176i	0.422158	−	0.174864i
$454$	11.0420	+	4.45998i	0.518226	+	0.209317i
$455$	−0.725421	−	4.21684i	−0.0340083	−	0.197688i
$456$	0.894038	−	0.0236761i	0.0418672	−	0.00110874i
$457$		−	18.5351i		−	0.867035i	−0.901145	−	0.433518i	$-0.857272\pi$
$457$		−	18.5351i		−	0.867035i	0.901145	−	0.433518i	$-0.142728\pi$
$458$	5.50828	−	2.33877i	0.257385	−	0.109283i
$459$	−9.22254	−	3.82010i	−0.430471	−	0.178307i
$460$	3.20021	+	1.25987i	0.149211	+	0.0587417i
$461$	12.0552	+	4.99345i	0.561469	+	0.232568i	0.645323	−	0.763910i	$-0.276723\pi$
$461$	12.0552	+	4.99345i	0.561469	+	0.232568i	−0.0838539	+	0.996478i	$0.526723\pi$
$462$	−5.39973	−	5.30525i	−0.251218	−	0.246822i
$463$	−21.6017	−	21.6017i	−1.00392	−	1.00392i	−0.999992	−	0.00392297i	$-0.998751\pi$
$463$	−21.6017	−	21.6017i	−1.00392	−	1.00392i	−0.00392297	−	0.999992i	$-0.501249\pi$
$464$	−7.69269	+	3.50943i	−0.357124	+	0.162921i
$465$	−1.05868			−0.0490950
$466$	2.03122	+	1.99568i	0.0940945	+	0.0924481i
$467$	−6.82331	−	16.4729i	−0.315745	−	0.762276i	−0.999471	−	0.0325366i	$-0.989641\pi$
$467$	−6.82331	−	16.4729i	−0.315745	−	0.762276i	0.683726	−	0.729739i	$-0.260359\pi$
$468$	−16.6729	+	10.9406i	−0.770707	+	0.505727i
$469$	−26.9354	−	11.1570i	−1.24376	−	0.515182i
$470$	0.888802	−	2.20049i	0.0409974	−	0.101501i
$471$	−6.11535	−	6.11535i	−0.281780	−	0.281780i
$472$	2.17426	+	4.87957i	0.100078	+	0.224600i
$473$	22.4354			1.03158
$474$	0.447104	+	1.05302i	0.0205362	+	0.0483669i
$475$	1.19854	+	2.89353i	0.0549927	+	0.132764i
$476$	18.8264	−	0.332333i	0.862905	−	0.0152325i
$477$	−30.6134	+	12.6805i	−1.40169	+	0.580599i
$478$	1.70559	−	1.73597i	0.0780121	−	0.0794013i
$479$	−6.94012	+	6.94012i	−0.317102	+	0.317102i	−0.847653	−	0.530551i	$-0.821985\pi$
$479$	−6.94012	+	6.94012i	−0.317102	+	0.317102i	0.530551	+	0.847653i	$0.321985\pi$
$480$	−0.833624	+	0.910643i	−0.0380496	+	0.0415650i
$481$	8.42366	−	1.44912i	0.384086	−	0.0660741i
$482$	13.5305	−	13.7715i	0.616299	−	0.627274i
$483$	4.49624	+	1.86241i	0.204586	+	0.0847424i
$484$	9.18864	−	9.51888i	0.417666	−	0.432676i
$485$	−8.01278	−	3.31900i	−0.363842	−	0.150708i
$486$	−15.2819	+	6.48856i	−0.693201	+	0.294327i
$487$			13.5241i			0.612835i	0.951897	+	0.306418i	$0.0991304\pi$
$487$			13.5241i			0.612835i	−0.951897	+	0.306418i	$0.900870\pi$
$488$	−6.57104	+	2.92795i	−0.297457	+	0.132542i
$489$	−0.402553			−0.0182041
$490$	−0.0162484	−	0.0382684i	−0.000734029	−	0.00172879i
$491$	−23.3693	−	9.67989i	−1.05464	−	0.436847i	−0.213096	−	0.977031i	$-0.568355\pi$
$491$	−23.3693	−	9.67989i	−1.05464	−	0.436847i	−0.841547	+	0.540184i	$0.818355\pi$
$492$	−0.489149	+	0.212803i	−0.0220525	+	0.00959389i
$493$	6.98196	−	2.89202i	0.314452	−	0.130250i
$494$	−1.89682	+	2.73596i	−0.0853420	+	0.123097i
$495$	5.23048			0.235093
$496$	−14.1960	−	13.2275i	−0.637418	−	0.593932i
$497$		−	2.24383i		−	0.100649i
$498$	5.73377	−	0.0506039i	0.256936	−	0.00226761i
$499$	−5.04911	+	12.1896i	−0.226029	+	0.545683i	−0.995687	−	0.0927736i	$-0.970427\pi$
$499$	−5.04911	+	12.1896i	−0.226029	+	0.545683i	0.769658	+	0.638456i	$0.220427\pi$
$500$	−8.21606	−	3.23452i	−0.367433	−	0.144652i
$501$	0.982430	+	2.37180i	0.0438917	+	0.105964i
$502$	−12.8074	+	31.7084i	−0.571622	+	1.41522i
$503$	23.6144	+	23.6144i	1.05292	+	1.05292i	0.998519	+	0.0543969i	$0.0173236\pi$
$503$	23.6144	+	23.6144i	1.05292	+	1.05292i	0.0543969	+	0.998519i	$0.482676\pi$
$504$	14.1744	−	14.9455i	0.631377	−	0.665727i
$505$		−	6.79891i		−	0.302548i
$506$	−8.48267	+	21.0013i	−0.377101	+	0.933622i
$507$	−0.327080	+	6.28739i	−0.0145261	+	0.279233i
$508$	−28.8353	+	0.509016i	−1.27936	+	0.0225839i
$509$	10.8299	−	26.1458i	0.480028	−	1.15889i	−0.479567	−	0.877505i	$-0.659206\pi$
$509$	10.8299	−	26.1458i	0.480028	−	1.15889i	0.959595	−	0.281385i	$-0.0907938\pi$
$510$	0.773334	−	0.787106i	0.0342438	−	0.0348536i
$511$	−16.4053			−0.725726
$512$	−22.5561	+	1.79537i	−0.996847	+	0.0793447i
$513$	−1.28909	+	1.28909i	−0.0569145	+	0.0569145i
$514$	−0.294273	−	33.3432i	−0.0129798	−	1.47071i
$515$	2.60462	−	6.28811i	0.114773	−	0.277087i
$516$	−0.0913848	−	5.17686i	−0.00402299	−	0.227899i
$517$	14.4393	+	5.98097i	0.635041	+	0.263043i
$518$	−8.12645	+	3.45042i	−0.357056	+	0.151603i
$519$	5.18672	+	5.18672i	0.227672	+	0.227672i
$520$	−0.898774	−	4.50693i	−0.0394138	−	0.197642i
$521$	−23.2085	+	23.2085i	−1.01678	+	1.01678i	−0.0169272	+	0.999857i	$0.505388\pi$
$521$	−23.2085	+	23.2085i	−1.01678	+	1.01678i	−0.999857	+	0.0169272i	$0.994612\pi$
$522$	3.09617	−	7.66546i	0.135516	−	0.335508i
$523$	5.67701	−	13.7055i	0.248238	−	0.599300i	−0.749816	−	0.661646i	$-0.769858\pi$
$523$	5.67701	−	13.7055i	0.248238	−	0.599300i	0.998055	+	0.0623460i	$0.0198582\pi$
$524$	0.436226	+	1.00271i	0.0190566	+	0.0438036i
$525$	−5.65207	−	2.34116i	−0.246676	−	0.102177i
$526$	1.96969	−	2.00477i	0.0858825	−	0.0874120i
$527$	12.2628	+	12.2628i	0.534178	+	0.534178i
$528$	−5.94845	−	5.54263i	−0.258873	−	0.241212i
$529$			8.43836i			0.366885i
$530$	−0.0673912	−	7.63589i	−0.00292729	−	0.331682i
$531$	−4.82554	−	1.99880i	−0.209410	−	0.0867406i
$532$	1.25966	−	3.19968i	0.0546132	−	0.138724i
$533$	0.437861	−	1.93680i	0.0189659	−	0.0838920i
$534$	2.04671	−	0.869016i	0.0885699	−	0.0376060i
$535$	5.51286			0.238342
$536$	−29.2374	−	11.2132i	−1.26286	−	0.484338i
$537$	−7.38265	+	7.38265i	−0.318585	+	0.318585i
$538$	1.49298	+	3.51628i	0.0643670	+	0.151598i
$539$	0.252955	−	0.104777i	0.0108955	−	0.00451308i
$540$	−0.0444170	−	2.51618i	−0.00191140	−	0.108279i
$541$	21.1844	+	8.77487i	0.910789	+	0.377261i	0.788358	−	0.615216i	$-0.210931\pi$
$541$	21.1844	+	8.77487i	0.910789	+	0.377261i	0.122430	+	0.992477i	$0.460931\pi$
$542$	−2.08444	−	2.04797i	−0.0895342	−	0.0879676i
$543$	−11.9669			−0.513548
$544$	20.2041	−	0.892123i	0.866245	−	0.0382494i
$545$		−	3.10404i		−	0.132963i
$546$	−1.15904	−	6.39891i	−0.0496022	−	0.273848i
$547$	−15.5375	−	37.5109i	−0.664337	−	1.60385i	−0.790937	−	0.611897i	$-0.790407\pi$
$547$	−15.5375	−	37.5109i	−0.664337	−	1.60385i	0.126600	−	0.991954i	$-0.459593\pi$
$548$	−1.50884	+	0.0266348i	−0.0644543	+	0.00113778i
$549$	2.69168	−	6.49828i	0.114878	−	0.277340i
$550$	10.6633	−	26.4000i	0.454683	−	1.12570i
$551$		−	1.38014i		−	0.0587960i
$552$	4.88051	+	1.87179i	0.207728	+	0.0796688i
$553$	4.39863			0.187049
$554$	−6.37086	+	15.7729i	−0.270672	+	0.670127i
$555$	−0.197992	+	0.477995i	−0.00840429	+	0.0202898i
$556$	1.35219	−	3.43473i	0.0573457	−	0.145665i
$557$	0.690403	−	1.66678i	0.0292533	−	0.0706237i	−0.908578	−	0.417716i	$-0.862831\pi$
$557$	0.690403	−	1.66678i	0.0292533	−	0.0706237i	0.937831	+	0.347092i	$0.112831\pi$
$558$	18.9707	−	0.167427i	0.803092	−	0.00708776i
$559$	15.7417	+	11.1206i	0.665805	+	0.470352i
$560$	1.97020	+	4.31870i	0.0832563	+	0.182498i
$561$	5.13842	+	5.13842i	0.216944	+	0.216944i
$562$	0.324553	+	36.7741i	0.0136904	+	1.55122i
$563$	−7.89974	−	19.0717i	−0.332934	−	0.803774i	−0.998357	−	0.0573073i	$-0.981749\pi$
$563$	−7.89974	−	19.0717i	−0.332934	−	0.803774i	0.665422	−	0.746467i	$-0.268251\pi$
$564$	1.32126	−	3.35617i	0.0556353	−	0.141320i
$565$	−4.77785	+	1.97905i	−0.201006	+	0.0832593i
$566$	−12.5416	+	31.0503i	−0.527162	+	1.30514i
$567$			18.2866i			0.767963i
$568$	−0.0638002	−	2.40917i	−0.00267700	−	0.101086i
$569$	−19.9627	+	19.9627i	−0.836878	+	0.836878i	−0.988447	−	0.151569i	$-0.951567\pi$
$569$	−19.9627	+	19.9627i	−0.836878	+	0.836878i	0.151569	+	0.988447i	$0.451567\pi$
$570$	−0.0787571	−	0.185489i	−0.00329877	−	0.00776928i
$571$	−8.00981	+	19.3374i	−0.335200	+	0.809245i	0.662962	+	0.748653i	$0.269299\pi$
$571$	−8.00981	+	19.3374i	−0.335200	+	0.809245i	−0.998163	+	0.0605921i	$0.980701\pi$
$572$	29.7319	−	5.65680i	1.24315	−	0.236523i
$573$	11.6399	−	4.82141i	0.486264	−	0.201417i
$574$	0.0181007	+	2.05093i	0.000755507	+	0.0856041i
$575$			18.3049i			0.763368i
$576$	14.7939	−	16.4498i	0.616411	−	0.685410i
$577$	8.77453	−	8.77453i	0.365288	−	0.365288i	−0.500467	−	0.865755i	$-0.666838\pi$
$577$	8.77453	−	8.77453i	0.365288	−	0.365288i	0.865755	+	0.500467i	$0.166838\pi$
$578$	5.96586	−	0.0526522i	0.248147	−	0.00219004i
$579$	−2.29361	+	5.53726i	−0.0953191	+	0.230121i
$580$	1.37073	+	1.32318i	0.0569166	+	0.0549420i
$581$	8.43692	−	20.3685i	0.350022	−	0.845029i
$582$	−12.2221	−	4.93666i	−0.506624	−	0.204631i
$583$	50.2889			2.08275
$584$	−17.6141	+	0.466460i	−0.728876	+	0.0193023i
$585$	3.66996	+	2.59261i	0.151734	+	0.107191i
$586$	13.9852	−	5.93798i	0.577722	−	0.245296i
$587$	−2.14549	−	5.17967i	−0.0885538	−	0.213788i	0.873398	−	0.487007i	$-0.161911\pi$
$587$	−2.14549	−	5.17967i	−0.0885538	−	0.213788i	−0.961952	+	0.273219i	$0.911911\pi$
$588$	−0.0252073	−	0.0579414i	−0.00103953	−	0.00238946i
$589$	2.92606	−	1.21201i	0.120566	−	0.0499401i
$590$	0.843586	−	0.858609i	0.0347299	−	0.0353484i
$591$	4.79774	−	4.79774i	0.197353	−	0.197353i
$592$	−8.62714	+	3.93573i	−0.354573	+	0.161757i
$593$	−7.38567	+	7.38567i	−0.303293	+	0.303293i	−0.842301	−	0.539008i	$-0.818799\pi$
$593$	−7.38567	+	7.38567i	−0.303293	+	0.303293i	0.539008	+	0.842301i	$0.318799\pi$
$594$	16.5725	−	0.146262i	0.679978	−	0.00600121i
$595$	−1.62359	−	3.91969i	−0.0665606	−	0.160692i
$596$	−31.4236	+	13.6707i	−1.28716	+	0.559975i
$597$	1.03566	−	2.50030i	0.0423867	−	0.102331i
$598$	−16.3616	+	10.5309i	−0.669077	+	0.430640i
$599$	−15.6822	−	15.6822i	−0.640757	−	0.640757i	0.309984	−	0.950742i	$-0.399676\pi$
$599$	−15.6822	−	15.6822i	−0.640757	−	0.640757i	−0.950742	+	0.309984i	$0.899676\pi$
$600$	−6.13511	−	2.35296i	−0.250465	−	0.0960593i
$601$	−0.967007	−	0.967007i	−0.0394450	−	0.0394450i	0.687109	−	0.726554i	$-0.258879\pi$
$601$	−0.967007	−	0.967007i	−0.0394450	−	0.0394450i	−0.726554	+	0.687109i	$0.758879\pi$
$602$	−18.4588	−	7.45574i	−0.752326	−	0.303873i
$603$	28.2862	−	11.7165i	1.15190	−	0.477133i
$604$	−0.708868	−	40.1567i	−0.0288434	−	1.63395i
$605$	−2.75414	−	1.14080i	−0.111972	−	0.0463803i
$606$	−0.0911932	−	10.3328i	−0.00370447	−	0.419742i
$607$			10.4569i			0.424432i	0.977223	+	0.212216i	$0.0680680\pi$
$607$			10.4569i			0.424432i	−0.977223	+	0.212216i	$0.931932\pi$
$608$	1.26150	−	3.47127i	0.0511605	−	0.140779i
$609$	1.90629	+	1.90629i	0.0772466	+	0.0772466i
$610$	1.15624	+	1.13601i	0.0468148	+	0.0459957i
$611$	7.16672	+	11.3537i	0.289934	+	0.459322i
$612$	−13.7331	+	14.2266i	−0.555126	+	0.575077i
$613$	−7.21348	−	17.4149i	−0.291350	−	0.703380i	0.708648	−	0.705562i	$-0.249305\pi$
$613$	−7.21348	−	17.4149i	−0.291350	−	0.703380i	−0.999998	+	0.00218189i	$0.999305\pi$
$614$	28.2845	+	11.4244i	1.14147	+	0.461053i
$615$	0.0849900	+	0.0849900i	0.00342713	+	0.00342713i
$616$	−28.5546	+	12.7235i	−1.15050	+	0.512644i
$617$			45.7307i			1.84105i	0.390684	+	0.920525i	$0.372239\pi$
$617$			45.7307i			1.84105i	−0.390684	+	0.920525i	$0.627761\pi$
$618$	3.87409	−	9.59145i	0.155839	−	0.385825i
$619$	−6.89667	+	2.85670i	−0.277201	+	0.114820i	−0.516953	−	0.856014i	$-0.672934\pi$
$619$	−6.89667	+	2.85670i	−0.277201	+	0.114820i	0.239752	+	0.970834i	$0.422934\pi$
$620$	−1.60154	+	4.06810i	−0.0643194	+	0.163379i
$621$	−9.84391	+	4.07748i	−0.395022	+	0.163624i
$622$	−6.34574	+	6.45874i	−0.254441	+	0.258972i
$623$		−	8.54941i		−	0.342525i
$624$	−1.42638	−	6.83746i	−0.0571011	−	0.273718i
$625$		−	21.9951i		−	0.879802i
$626$	−27.0396	−	26.5665i	−1.08072	−	1.06181i
$627$	1.22609	−	0.507862i	0.0489652	−	0.0202821i
$628$	−32.7501	+	14.2478i	−1.30687	+	0.568551i
$629$	7.83007	−	3.24332i	0.312205	−	0.129320i
$630$	−4.30341	−	1.73820i	−0.171452	−	0.0692514i
$631$			4.57858i			0.182270i	0.995839	+	0.0911351i	$0.0290495\pi$
$631$			4.57858i			0.182270i	−0.995839	+	0.0911351i	$0.970950\pi$
$632$	4.72274	−	0.125069i	0.187861	−	0.00497497i
$633$	−6.73173	−	6.73173i	−0.267562	−	0.267562i
$634$	−0.849397	+	2.10293i	−0.0337339	+	0.0835180i
$635$	2.48676	+	6.00357i	0.0986841	+	0.238244i
$636$	−0.204839	−	11.6039i	−0.00812239	−	0.460126i
$637$	0.229421	+	0.0518662i	0.00908998	+	0.00205501i
$638$	−8.79326	+	8.94985i	−0.348128	+	0.354328i
$639$	1.66619	+	1.66619i	0.0659136	+	0.0659136i
$640$	2.23817	+	4.58090i	0.0884716	+	0.181076i
$641$		−	0.228751i		−	0.00903512i	−0.999990	−	0.00451756i	$-0.998562\pi$
$641$		−	0.228751i		−	0.00903512i	0.999990	−	0.00451756i	$-0.00143799\pi$
$642$	8.37830	−	0.0739434i	0.330665	−	0.00291831i
$643$	5.94814	+	2.46380i	0.234572	+	0.0971628i	0.496873	−	0.867823i	$-0.334481\pi$
$643$	5.94814	+	2.46380i	0.234572	+	0.0971628i	−0.262301	+	0.964986i	$0.584481\pi$
$644$	13.9583	−	14.4600i	0.550035	−	0.569803i
$645$	−1.07783	+	0.446453i	−0.0424397	+	0.0175791i
$646$	−1.23629	+	3.06081i	−0.0486414	+	0.120426i
$647$	−10.9157	−	10.9157i	−0.429140	−	0.429140i	0.459196	−	0.888335i	$-0.348138\pi$
$647$	−10.9157	−	10.9157i	−0.429140	−	0.429140i	−0.888335	+	0.459196i	$0.848138\pi$
$648$	0.519953	+	19.6340i	0.0204257	+	0.771296i
$649$	5.60521	+	5.60521i	0.220024	+	0.220024i
$650$	20.5676	−	13.2380i	0.806728	−	0.519237i
$651$	−2.36748	+	5.71561i	−0.0927890	+	0.224013i
$652$	−0.608972	+	1.54686i	−0.0238492	+	0.0605798i
$653$	−5.69002	−	13.7369i	−0.222668	−	0.537567i	0.772583	−	0.634914i	$-0.218964\pi$
$653$	−5.69002	−	13.7369i	−0.222668	−	0.537567i	−0.995251	+	0.0973467i	$0.968964\pi$
$654$	−0.0416343	−	4.71745i	−0.00162803	−	0.184467i
$655$	0.174222	−	0.174222i	0.00680740	−	0.00680740i
$656$	0.0777497	+	2.20154i	0.00303562	+	0.0859556i
$657$	12.1820	−	12.1820i	0.475265	−	0.475265i
$658$	−9.89244	−	9.71936i	−0.385648	−	0.378900i
$659$	5.08050	−	2.10441i	0.197908	−	0.0819763i	−0.281528	−	0.959553i	$-0.590841\pi$
$659$	5.08050	−	2.10441i	0.197908	−	0.0819763i	0.479436	+	0.877577i	$0.340841\pi$
$660$	−0.671084	+	1.70463i	−0.0261219	+	0.0663527i
$661$	11.2446	+	27.1469i	0.437364	+	1.05589i	0.976856	+	0.213900i	$0.0686165\pi$
$661$	11.2446	+	27.1469i	0.437364	+	1.05589i	−0.539491	+	0.841991i	$0.681383\pi$
$662$	13.5845	+	31.9944i	0.527978	+	1.24350i
$663$	1.05839	+	6.15234i	0.0411043	+	0.238937i
$664$	8.47944	−	22.1093i	0.329066	−	0.858006i
$665$	−0.774815			−0.0300460
$666$	3.47226	−	8.59660i	0.134548	−	0.333111i
$667$	3.08687	−	7.45236i	0.119524	−	0.288557i
$668$	10.6001	−	0.187119i	0.410131	−	0.00723986i
$669$	5.06232	−	12.2215i	0.195721	−	0.472511i
$670$	0.0622682	+	7.05541i	0.00240563	+	0.272574i
$671$	−7.54822	+	7.54822i	−0.291396	+	0.291396i
$672$	3.05219	+	6.53703i	0.117741	+	0.252171i
$673$			25.1989i			0.971345i	0.874141	+	0.485672i	$0.161425\pi$
$673$			25.1989i			0.971345i	−0.874141	+	0.485672i	$0.838575\pi$
$674$	41.9945	−	0.370626i	1.61757	−	0.0142760i
$675$	12.3744	−	5.12566i	0.476292	−	0.197287i
$676$	23.6653	+	10.7682i	0.910203	+	0.414163i
$677$	9.76167	−	23.5668i	0.375171	−	0.905744i	−0.617685	−	0.786426i	$-0.711929\pi$
$677$	9.76167	−	23.5668i	0.375171	−	0.905744i	0.992856	−	0.119318i	$-0.0380709\pi$
$678$	−7.23471	+	3.07180i	−0.277848	+	0.117972i
$679$	−35.8374	+	35.8374i	−1.37531	+	1.37531i
$680$	−1.85467	−	4.16235i	−0.0711235	−	0.159619i
$681$		−	4.07815i		−	0.156275i
$682$	−26.6968	−	10.7831i	−1.02227	−	0.412908i
$683$	39.6130	−	16.4083i	1.51575	−	0.627845i	0.539016	−	0.842295i	$-0.318796\pi$
$683$	39.6130	−	16.4083i	1.51575	−	0.627845i	0.976735	+	0.214451i	$0.0687961\pi$
$684$	1.44060	+	3.31136i	0.0550827	+	0.126613i
$685$	0.130122	+	0.314143i	0.00497172	+	0.0120028i
$686$	−26.3112	+	0.232212i	−1.00457	+	0.00886589i
$687$	−1.44908	−	1.44908i	−0.0552857	−	0.0552857i
$688$	−20.0310	−	7.48026i	−0.763674	−	0.285182i
$689$	35.2851	+	24.9269i	1.34426	+	0.949638i
$690$	−0.0103942	−	1.17774i	−0.000395702	−	0.0448358i
$691$	−7.75145	+	18.7136i	−0.294879	+	0.711901i	0.705117	+	0.709091i	$0.250894\pi$
$691$	−7.75145	+	18.7136i	−0.294879	+	0.711901i	−0.999996	+	0.00280983i	$0.999106\pi$
$692$	27.7770	−	12.0843i	1.05592	−	0.459376i
$693$	11.6967	−	28.2384i	0.444323	−	1.07269i
$694$	−20.9894	−	8.47785i	−0.796746	−	0.321815i
$695$	−0.831731			−0.0315493
$696$	2.10095	+	1.99255i	0.0796364	+	0.0755274i
$697$		−	1.96891i		−	0.0745776i
$698$	−0.724228	−	0.292524i	−0.0274124	−	0.0110722i
$699$	0.373174	−	0.900921i	0.0141147	−	0.0340760i
$700$	−17.5465	+	18.1771i	−0.663196	+	0.687031i
$701$	−10.3561	−	25.0019i	−0.391146	−	0.944310i	−0.989691	−	0.143221i	$-0.954254\pi$
$701$	−10.3561	−	25.0019i	−0.391146	−	0.944310i	0.598545	−	0.801089i	$-0.295746\pi$
$702$	11.7006	+	8.11192i	0.441609	+	0.306165i
$703$		−	1.54779i		−	0.0583759i
$704$	−30.2969	+	14.4729i	−1.14186	+	0.545469i
$705$	−0.812708			−0.0306084
$706$	−17.6079	+	17.9215i	−0.662682	+	0.674484i
$707$	−36.7061	−	15.2042i	−1.38047	−	0.571811i
$708$	1.27054	−	1.31621i	0.0477500	−	0.0494661i
$709$	−13.4622	+	5.57622i	−0.505583	+	0.209419i	−0.620871	−	0.783913i	$-0.713221\pi$
$709$	−13.4622	+	5.57622i	−0.505583	+	0.209419i	0.115288	+	0.993332i	$0.463221\pi$
$710$	−0.499838	+	0.212227i	−0.0187586	+	0.00796473i
$711$	−3.26628	+	3.26628i	−0.122495	+	0.122495i
$712$	−0.243091	−	9.17937i	−0.00911020	−	0.344011i
$713$	18.5107			0.693231
$714$	−2.52006	−	5.93527i	−0.0943110	−	0.222122i
$715$	−3.64005	−	5.76667i	−0.136130	−	0.215661i
$716$	17.2005	+	39.5370i	0.642812	+	1.47757i
$717$	−0.769966	−	0.318930i	−0.0287549	−	0.0119107i
$718$	8.55396	−	0.0754937i	0.319231	−	0.00281740i
$719$			16.2008i			0.604189i	0.953278	+	0.302095i	$0.0976858\pi$
$719$			16.2008i			0.604189i	−0.953278	+	0.302095i	$0.902314\pi$
$720$	−4.66993	−	1.74391i	−0.174038	−	0.0649919i
$721$	−28.1237	−	28.1237i	−1.04738	−	1.04738i
$722$	−18.7369	−	18.4091i	−0.697316	−	0.685115i
$723$	−6.10816	−	2.53008i	−0.227165	−	0.0940948i
$724$	−18.1032	+	45.9842i	−0.672799	+	1.70899i
$725$	−3.88039	+	9.36810i	−0.144114	+	0.347923i
$726$	−4.20098	−	1.69682i	−0.155913	−	0.0629751i
$727$	2.58250	−	2.58250i	0.0957795	−	0.0957795i	−0.657593	−	0.753373i	$-0.728426\pi$
$727$	2.58250	−	2.58250i	0.0957795	−	0.0957795i	0.753373	+	0.657593i	$0.228426\pi$
$728$	−26.3420	−	5.22637i	−0.976299	−	0.193702i
$729$	−10.7104	−	10.7104i	−0.396682	−	0.396682i
$730$	1.55165	+	3.65445i	0.0574291	+	0.135257i
$731$	17.6561	+	7.31338i	0.653033	+	0.270495i
$732$	1.77246	+	1.71097i	0.0655121	+	0.0632393i
$733$	16.6302	−	40.1489i	0.614251	−	1.48293i	−0.244038	−	0.969766i	$-0.578472\pi$
$733$	16.6302	−	40.1489i	0.614251	−	1.48293i	0.858289	−	0.513167i	$-0.171528\pi$
$734$	39.1232	−	0.345285i	1.44406	−	0.0127447i
$735$	−0.0100674	+	0.0100674i	−0.000371341	+	0.000371341i
$736$	14.5757	−	15.9224i	0.537267	−	0.586906i
$737$	−46.4660			−1.71160
$738$	−1.53639	−	1.50951i	−0.0565554	−	0.0555659i
$739$	−3.57267	+	8.62519i	−0.131423	+	0.317283i	−0.975869	−	0.218358i	$-0.929930\pi$
$739$	−3.57267	+	8.62519i	−0.131423	+	0.317283i	0.844446	+	0.535641i	$0.179930\pi$
$740$	1.53724	+	1.48391i	0.0565100	+	0.0545495i
$741$	1.11202	+	0.251398i	0.0408509	+	0.00923535i
$742$	−41.3755	−	16.7120i	−1.51894	−	0.613518i
$743$			44.3683i			1.62772i	0.581064	+	0.813858i	$0.302637\pi$
$743$			44.3683i			1.62772i	−0.581064	+	0.813858i	$0.697363\pi$
$744$	−2.37942	+	6.20408i	−0.0872337	+	0.227453i
$745$	5.45987	+	5.45987i	0.200034	+	0.200034i
$746$	−9.19364	−	3.71342i	−0.336603	−	0.135958i
$747$	8.86002	+	21.3900i	0.324171	+	0.782618i
$748$	27.5183	−	11.9718i	1.00617	−	0.437731i
$749$	12.3282	−	29.7629i	0.450463	−	1.08751i
$750$	0.0266856	+	3.02367i	0.000974421	+	0.110409i
$751$			11.0170i			0.402016i	0.979590	+	0.201008i	$0.0644217\pi$
$751$			11.0170i			0.402016i	−0.979590	+	0.201008i	$0.935578\pi$
$752$	−10.8977	−	10.1543i	−0.397399	−	0.370287i
$753$	11.7109			0.426769
$754$	−10.6060	+	1.92106i	−0.386247	+	0.0699610i
$755$	−8.36071	+	3.46312i	−0.304277	+	0.126036i
$756$	−13.6837	−	5.38705i	−0.497673	−	0.195925i
$757$	13.5167	+	5.59880i	0.491272	+	0.203492i	0.614546	−	0.788881i	$-0.289339\pi$
$757$	13.5167	+	5.59880i	0.491272	+	0.203492i	−0.123274	+	0.992373i	$0.539339\pi$
$758$	23.8189	−	10.1133i	0.865143	−	0.367332i
$759$	7.75643			0.281541
$760$	−0.831907	+	0.0220308i	−0.0301764	+	0.000799140i
$761$		−	42.6686i		−	1.54674i	−0.633957	−	0.773369i	$-0.718570\pi$
$761$		−	42.6686i		−	1.54674i	0.633957	−	0.773369i	$-0.281430\pi$
$762$	3.85984	+	9.09072i	0.139827	+	0.329322i
$763$	−16.7582	−	6.94146i	−0.606687	−	0.251298i
$764$	−0.918313	−	52.0215i	−0.0332234	−	1.88207i
$765$	4.11626	+	1.70501i	0.148824	+	0.0616447i
$766$	−33.5074	−	32.9211i	−1.21067	−	1.18949i
$767$	1.15453	+	6.71123i	0.0416877	+	0.242329i
$768$	3.46297	+	6.93192i	0.124959	+	0.250134i
$769$	−15.7175	+	15.7175i	−0.566787	+	0.566787i	−0.931227	−	0.364440i	$-0.881261\pi$
$769$	−15.7175	+	15.7175i	−0.566787	+	0.566787i	0.364440	+	0.931227i	$0.381261\pi$
$770$	5.02447	+	4.93656i	0.181069	+	0.177901i
$771$	−10.5497	+	4.36981i	−0.379937	+	0.157375i
$772$	17.8079	+	17.1901i	0.640921	+	0.618685i
$773$	0.800644	+	1.93293i	0.0287972	+	0.0695225i	0.937624	−	0.347651i	$-0.113021\pi$
$773$	0.800644	+	1.93293i	0.0287972	+	0.0695225i	−0.908827	+	0.417174i	$0.863021\pi$
$774$	19.2433	−	8.17055i	0.691687	−	0.293684i
$775$	−23.2692			−0.835853
$776$	−37.4591	+	39.4971i	−1.34470	+	1.41786i
$777$	2.13785	+	2.13785i	0.0766948	+	0.0766948i
$778$	9.35460	+	3.77843i	0.335379	+	0.135463i
$779$	−0.332202	−	0.137602i	−0.0119024	−	0.00493012i
$780$	−1.31580	+	0.863413i	−0.0471134	+	0.0309152i
$781$	−1.36854	−	3.30394i	−0.0489701	−	0.118224i
$782$	−13.5215	+	13.7623i	−0.483530	+	0.492140i
$783$	−5.90229			−0.210931
$784$	−0.260780	+	0.00920974i	−0.00931357	+	0.000328919i
$785$	5.69036	+	5.69036i	0.203098	+	0.203098i
$786$	0.262441	−	0.267115i	0.00936096	−	0.00952766i
$787$	40.0529	+	16.5905i	1.42773	+	0.591386i	0.956791	−	0.290778i	$-0.0939140\pi$
$787$	40.0529	+	16.5905i	1.42773	+	0.591386i	0.470942	+	0.882164i	$0.343914\pi$
$788$	−11.1780	−	25.6938i	−0.398200	−	0.915304i
$789$	−0.889188	−	0.368314i	−0.0316559	−	0.0131123i
$790$	−0.416033	−	0.979843i	−0.0148018	−	0.0348613i
$791$			30.2204i			1.07452i
$792$	11.7557	−	30.6518i	0.417721	−	1.08916i
$793$	−9.03764	+	1.55474i	−0.320936	+	0.0552105i
$794$	17.4881	−	43.2968i	0.620628	−	1.53655i
$795$	−2.41596	+	1.00072i	−0.0856854	+	0.0354921i
$796$	−8.04101	−	7.76205i	−0.285006	−	0.275119i
$797$	14.2206	+	34.3316i	0.503721	+	1.21609i	0.947443	+	0.319925i	$0.103658\pi$
$797$	14.2206	+	34.3316i	0.503721	+	1.21609i	−0.443722	+	0.896164i	$0.646342\pi$
$798$	−1.17754	+	0.0103925i	−0.0416846	+	0.000367891i
$799$	9.41373	+	9.41373i	0.333034	+	0.333034i
$800$	−18.3226	+	20.0154i	−0.647801	+	0.707652i
$801$	6.34851	+	6.34851i	0.224314	+	0.224314i
$802$	−4.62434	+	4.70669i	−0.163291	+	0.166199i
$803$	−24.1560	+	10.0058i	−0.852447	+	0.353095i
$804$	0.189267	+	10.7218i	0.00667494	+	0.378129i
$805$	−4.18378	−	1.73298i	−0.147459	−	0.0610794i
$806$	−13.3868	−	20.7989i	−0.471531	−	0.732608i
$807$	0.925038	−	0.925038i	0.0325629	−	0.0325629i
$808$	−39.8431	−	15.2808i	−1.40167	−	0.537576i
$809$	23.9002	−	23.9002i	0.840286	−	0.840286i	−0.148610	−	0.988896i	$-0.547480\pi$
$809$	23.9002	−	23.9002i	0.840286	−	0.840286i	0.988896	+	0.148610i	$0.0474799\pi$
$810$	4.07353	−	1.72959i	0.143129	−	0.0607715i
$811$	5.05027	+	12.1924i	0.177339	+	0.428134i	0.987407	−	0.158202i	$-0.0505698\pi$
$811$	5.05027	+	12.1924i	0.177339	+	0.428134i	−0.810068	+	0.586336i	$0.800570\pi$
$812$	10.2089	−	4.44136i	0.358263	−	0.155861i
$813$	−0.382951	+	0.924524i	−0.0134307	+	0.0324245i
$814$	−9.86139	+	10.0370i	−0.345642	+	0.351797i
$815$	0.374578			0.0131209
$816$	−2.87452	−	6.30096i	−0.100628	−	0.220578i
$817$	2.46789	−	2.46789i	0.0863404	−	0.0863404i
$818$	25.4272	−	0.224410i	0.889041	−	0.00784631i
$819$	22.2040	−	14.0157i	0.775872	−	0.489747i
$820$	0.455155	−	0.198014i	0.0158947	−	0.00691495i
$821$	23.0340	−	9.54101i	0.803893	−	0.332983i	0.0573786	−	0.998352i	$-0.481726\pi$
$821$	23.0340	−	9.54101i	0.803893	−	0.332983i	0.746515	+	0.665369i	$0.231726\pi$
$822$	0.201970	+	0.475682i	0.00704452	+	0.0165913i
$823$	11.7697	−	11.7697i	0.410266	−	0.410266i	−0.471565	−	0.881831i	$-0.656311\pi$
$823$	11.7697	−	11.7697i	0.410266	−	0.410266i	0.881831	+	0.471565i	$0.156311\pi$
$824$	−30.9957	−	29.3964i	−1.07979	−	1.02407i
$825$	−9.75033			−0.339463
$826$	−2.74899	−	6.47444i	−0.0956497	−	0.225275i
$827$	−12.2912	−	29.6736i	−0.427407	−	1.03185i	−0.980107	−	0.198471i	$-0.936402\pi$
$827$	−12.2912	−	29.6736i	−0.427407	−	1.03185i	0.552700	−	0.833380i	$-0.313598\pi$
$828$	0.372513	+	21.1025i	0.0129457	+	0.733363i
$829$	17.6245	+	42.5493i	0.612124	+	1.47780i	0.860663	+	0.509176i	$0.170050\pi$
$829$	17.6245	+	42.5493i	0.612124	+	1.47780i	−0.248539	+	0.968622i	$0.579950\pi$
$830$	−5.33530	+	0.0470872i	−0.185191	+	0.00163442i
$831$	5.82542			0.202082
$832$	−28.4316	−	4.86247i	−0.985689	−	0.168576i
$833$	0.233224			0.00808073
$834$	−1.26404	+	0.0111559i	−0.0437703	+	0.000386298i
$835$	−0.914156	−	2.20697i	−0.0316357	−	0.0763753i
$836$	−0.0967303	−	5.47968i	−0.00334549	−	0.189519i
$837$	−5.18328	−	12.5135i	−0.179160	−	0.432531i
$838$	13.4982	+	31.7910i	0.466287	+	1.09820i
$839$	23.6791			0.817492			0.408746	−	0.912648i	$-0.365966\pi$
$839$	23.6791			0.817492			0.408746	+	0.912648i	$0.365966\pi$
$840$	1.11862	−	1.17948i	0.0385961	−	0.0406960i
$841$	−17.3465	+	17.3465i	−0.598155	+	0.598155i
$842$	−4.77843	−	11.2542i	−0.164676	−	0.387845i
$843$	11.6352	−	4.81944i	0.400736	−	0.165990i
$844$	−36.0511	+	15.6839i	−1.24093	+	0.539863i
$845$	0.304350	−	5.85044i	0.0104700	−	0.201261i
$846$	14.5631	−	0.128528i	0.500689	−	0.00441887i
$847$	−12.3180	+	12.3180i	−0.423251	+	0.423251i
$848$	−44.8994	−	16.7670i	−1.54185	−	0.575781i
$849$	11.4678			0.393575
$850$	16.9975	−	17.3002i	0.583008	−	0.593390i
$851$	3.46184	−	8.35762i	0.118670	−	0.286495i
$852$	−0.756795	+	0.329241i	−0.0259274	+	0.0112796i
$853$	8.41225	+	20.3090i	0.288030	+	0.695366i	0.999976	−	0.00686787i	$-0.00218613\pi$
$853$	8.41225	+	20.3090i	0.288030	+	0.695366i	−0.711946	+	0.702234i	$0.752186\pi$
$854$	8.71877	−	3.70191i	0.298350	−	0.126677i
$855$	0.575352	−	0.575352i	0.0196766	−	0.0196766i
$856$	12.3903	−	32.3065i	0.423493	−	1.10421i
$857$	−7.24346	+	7.24346i	−0.247432	+	0.247432i	−0.819916	−	0.572484i	$-0.805980\pi$
$857$	−7.24346	+	7.24346i	−0.247432	+	0.247432i	0.572484	+	0.819916i	$0.305980\pi$
$858$	−5.60940	−	8.71521i	−0.191502	−	0.297533i
$859$	−10.9818	−	4.54881i	−0.374694	−	0.155204i	0.187385	−	0.982286i	$-0.439999\pi$
$859$	−10.9818	−	4.54881i	−0.374694	−	0.155204i	−0.562080	+	0.827083i	$0.689999\pi$
$860$	0.0850340	+	4.81710i	0.00289964	+	0.164262i
$861$	0.648906	−	0.268786i	0.0221146	−	0.00916019i
$862$	−17.3473	+	17.6562i	−0.590851	+	0.601373i
$863$	29.2868	+	29.2868i	0.996936	+	0.996936i	0.999995	−	0.00305937i	$-0.000973828\pi$
$863$	29.2868	+	29.2868i	0.996936	+	0.996936i	−0.00305937	+	0.999995i	$0.500974\pi$
$864$	−14.8452	−	5.39491i	−0.505044	−	0.183539i
$865$	−4.82627	−	4.82627i	−0.164098	−	0.164098i
$866$	50.4035	−	0.444840i	1.71278	−	0.0151163i
$867$	−0.781858	−	1.88757i	−0.0265533	−	0.0641053i
$868$	18.3815	+	17.7438i	0.623908	+	0.602263i
$869$	6.47679	−	2.68277i	0.219710	−	0.0910069i
$870$	0.244345	−	0.604948i	0.00828408	−	0.0205096i
$871$	−32.6027	−	23.0319i	−1.10470	−	0.780407i
$872$	−18.1904	−	6.97645i	−0.616004	−	0.236252i
$873$		−	53.2233i		−	1.80134i
$874$	1.37705	+	3.24323i	0.0465793	+	0.109704i
$875$	10.7412	+	4.44915i	0.363119	+	0.150409i
$876$	2.40717	+	5.53313i	0.0813309	+	0.186947i
$877$	33.4217	+	13.8437i	1.12857	+	0.467469i	0.867294	−	0.497796i	$-0.165857\pi$
$877$	33.4217	+	13.8437i	1.12857	+	0.467469i	0.261275	+	0.965264i	$0.415857\pi$
$878$	−16.8519	+	17.1520i	−0.568725	+	0.578853i
$879$	−3.67911	−	3.67911i	−0.124093	−	0.124093i
$880$	5.53506	+	5.15745i	0.186587	+	0.173857i
$881$	39.1508			1.31902			0.659512	−	0.751694i	$-0.270763\pi$
$881$	39.1508			1.31902			0.659512	+	0.751694i	$0.270763\pi$
$882$	0.178807	−	0.181991i	0.00602075	−	0.00612797i
$883$	3.66168	+	8.84008i	0.123225	+	0.297492i	0.973439	−	0.228945i	$-0.0735275\pi$
$883$	3.66168	+	8.84008i	0.123225	+	0.297492i	−0.850214	+	0.526437i	$0.823528\pi$
$884$	25.2422	+	5.24013i	0.848988	+	0.176244i
$885$	−0.380825	−	0.157743i	−0.0128013	−	0.00530246i
$886$	46.1263	+	18.6309i	1.54964	+	0.625918i
$887$	26.6197	+	26.6197i	0.893802	+	0.893802i	0.994879	−	0.101076i	$-0.0322286\pi$
$887$	26.6197	+	26.6197i	0.893802	+	0.893802i	−0.101076	+	0.994879i	$0.532229\pi$
$888$	2.35616	+	2.23459i	0.0790676	+	0.0749878i
$889$	37.9733			1.27358
$890$	−1.90448	+	0.808624i	−0.0638382	+	0.0271051i
$891$	11.1532	+	26.9262i	0.373646	+	0.902060i
$892$	−39.3046	−	37.9410i	−1.31601	−	1.27036i
$893$	2.24623	−	0.930417i	0.0751671	−	0.0311352i
$894$	8.37101	+	8.22454i	0.279968	+	0.275070i
$895$	6.86959	−	6.86959i	0.229625	−	0.229625i
$896$	29.7366	−	1.83939i	0.993431	−	0.0614499i
$897$	5.44228	+	3.84465i	0.181712	+	0.128369i
$898$	32.7498	+	32.1768i	1.09288	+	1.07375i
$899$	9.47342	+	3.92402i	0.315956	+	0.130873i
$900$	−0.468273	−	26.5272i	−0.0156091	−	0.884240i
$901$	39.5761	+	16.3929i	1.31847	+	0.546128i
$902$	1.27754	+	3.00886i	0.0425374	+	0.100184i
$903$			6.81742i			0.226870i
$904$	0.859276	+	32.4472i	0.0285791	+	1.07918i
$905$	11.1352			0.370148
$906$	−12.6599	+	5.37530i	−0.420599	+	0.178583i
$907$	−44.8203	−	18.5652i	−1.48823	−	0.616447i	−0.517303	−	0.855802i	$-0.673064\pi$
$907$	−44.8203	−	18.5652i	−1.48823	−	0.616447i	−0.970932	+	0.239355i	$0.923064\pi$
$908$	−15.6708	−	6.16931i	−0.520053	−	0.204736i
$909$	38.5468	−	15.9666i	1.27852	−	0.529579i
$910$	1.07849	+	5.95422i	0.0357516	+	0.197381i
$911$	44.7981			1.48423			0.742114	−	0.670273i	$-0.233823\pi$
$911$	44.7981			1.48423			0.742114	+	0.670273i	$0.233823\pi$
$912$	−1.26402	+	0.0446401i	−0.0418557	+	0.00147818i
$913$		−	35.1376i		−	1.16288i
$914$	0.231332	+	26.2116i	0.00765180	+	0.867001i
$915$	0.212423	−	0.512835i	0.00702250	−	0.0169538i
$916$	−7.76039	+	3.37613i	−0.256410	+	0.111551i
$917$	−0.550986	−	1.33020i	−0.0181951	−	0.0439270i
$918$	13.0898	+	5.28713i	0.432028	+	0.174501i
$919$	−7.77642	−	7.77642i	−0.256520	−	0.256520i	0.567117	−	0.823637i	$-0.308059\pi$
$919$	−7.77642	−	7.77642i	−0.256520	−	0.256520i	−0.823637	+	0.567117i	$0.808059\pi$
$920$	−4.54133	−	1.74171i	−0.149723	−	0.0574226i
$921$		−	10.4463i		−	0.344219i
$922$	−17.1104	−	6.91107i	−0.563500	−	0.227604i
$923$	0.677444	−	2.99655i	0.0222983	−	0.0986327i
$924$	7.70228	+	7.43507i	0.253386	+	0.244596i
$925$	−4.35175	+	10.5061i	−0.143085	+	0.345437i
$926$	30.8178	+	30.2786i	1.01274	+	0.995016i
$927$	41.7675			1.37183
$928$	10.8349	−	5.05890i	0.355673	−	0.166067i
$929$	−30.6347	+	30.6347i	−1.00509	+	1.00509i	−0.00510357	+	0.999987i	$0.501625\pi$
$929$	−30.6347	+	30.6347i	−1.00509	+	1.00509i	−0.999987	+	0.00510357i	$0.998375\pi$
$930$	1.49714	−	0.0132131i	0.0490931	−	0.000433276i
$931$	0.0162995	−	0.0393505i	0.000534195	−	0.00128966i
$932$	−2.89737	−	2.79686i	−0.0949067	−	0.0916141i
$933$	2.86469	+	1.18659i	0.0937858	+	0.0388473i
$934$	9.85483	+	23.2102i	0.322460	+	0.759460i
$935$	−4.78133	−	4.78133i	−0.156366	−	0.156366i
$936$	23.4416	−	15.6798i	0.766213	−	0.512509i
$937$	−31.7291	+	31.7291i	−1.03654	+	1.03654i	−0.0372383	+	0.999306i	$0.511856\pi$
$937$	−31.7291	+	31.7291i	−1.03654	+	1.03654i	−0.999306	+	0.0372383i	$0.988144\pi$
$938$	38.2302	+	15.4416i	1.24826	+	0.504186i
$939$	−4.96770	+	11.9931i	−0.162115	+	0.391379i
$940$	−1.22944	+	3.12293i	−0.0401000	+	0.101859i
$941$	−40.3547	−	16.7155i	−1.31552	−	0.544908i	−0.389033	−	0.921224i	$-0.627191\pi$
$941$	−40.3547	−	16.7155i	−1.31552	−	0.544908i	−0.926492	+	0.376315i	$0.877191\pi$
$942$	8.72439	+	8.57175i	0.284256	+	0.279283i
$943$	−1.48603	−	1.48603i	−0.0483917	−	0.0483917i
$944$	−3.13564	−	6.87335i	−0.102057	−	0.223708i
$945$			3.31356i			0.107790i
$946$	−31.7272	+	0.280011i	−1.03154	+	0.00910395i
$947$	−42.1560	−	17.4616i	−1.36988	−	0.567425i	−0.428128	−	0.903718i	$-0.640827\pi$
$947$	−42.1560	−	17.4616i	−1.36988	−	0.567425i	−0.941757	+	0.336293i	$0.890827\pi$
$948$	−0.645419	−	1.48356i	−0.0209622	−	0.0481838i
$949$	−21.9086	−	4.95298i	−0.711183	−	0.160780i
$950$	−1.73104	−	4.07695i	−0.0561622	−	0.132274i
$951$	0.776677			0.0251855
$952$	−26.6193	+	0.704940i	−0.862737	+	0.0228472i
$953$	−14.1067	+	14.1067i	−0.456960	+	0.456960i	−0.897656	−	0.440696i	$-0.854732\pi$
$953$	−14.1067	+	14.1067i	−0.456960	+	0.456960i	0.440696	+	0.897656i	$0.354732\pi$
$954$	43.1339	−	18.3143i	1.39651	−	0.592946i
$955$	−10.8310	+	4.48635i	−0.350483	+	0.145175i
$956$	−2.39031	+	2.47622i	−0.0773083	+	0.0800867i
$957$	3.96959	+	1.64426i	0.128319	+	0.0531513i
$958$	9.72781	−	9.90105i	0.314291	−	0.319888i
$959$	1.98699			0.0641633
$960$	1.16751	−	1.29820i	0.0376813	−	0.0418992i
$961$		−	7.46924i		−	0.240943i
$962$	−11.8943	+	2.15442i	−0.383488	+	0.0694612i
$963$	12.9464	+	31.2555i	0.417193	+	1.00719i
$964$	−18.9624	+	19.6439i	−0.610739	+	0.632689i
$965$	2.13421	−	5.15245i	0.0687028	−	0.165863i
$966$	−6.38165	−	2.57762i	−0.205326	−	0.0829336i
$967$		−	36.8303i		−	1.18438i	−0.805798	−	0.592191i	$-0.798263\pi$
$967$		−	36.8303i		−	1.18438i	0.805798	−	0.592191i	$-0.201737\pi$
$968$	−12.8754	+	13.5759i	−0.413831	+	0.436346i
$969$	1.13045			0.0363153
$970$	11.3728	+	4.59359i	0.365158	+	0.147491i
$971$	18.6616	−	45.0532i	0.598881	−	1.44583i	−0.275842	−	0.961203i	$-0.588957\pi$
$971$	18.6616	−	45.0532i	0.598881	−	1.44583i	0.874723	−	0.484623i	$-0.161043\pi$
$972$	21.5301	−	9.36659i	0.690577	−	0.300433i
$973$	−1.85997	+	4.49036i	−0.0596279	+	0.143954i
$974$	−0.168791	−	19.1252i	−0.00540842	−	0.612811i
$975$	−6.84130	−	4.83298i	−0.219097	−	0.154779i
$976$	9.25595	−	4.22260i	0.296276	−	0.135162i
$977$	26.2643	+	26.2643i	0.840269	+	0.840269i	0.988894	−	0.148625i	$-0.0474846\pi$
$977$	26.2643	+	26.2643i	0.840269	+	0.840269i	−0.148625	+	0.988894i	$0.547485\pi$
$978$	0.569274	−	0.00502418i	0.0182034	−	0.000160655i
$979$	−5.21438	−	12.5886i	−0.166652	−	0.402334i
$980$	0.0234555	+	0.0539148i	0.000749258	+	0.00172224i
$981$	17.5986	−	7.28957i	0.561879	−	0.232738i
$982$	33.1687	+	13.3972i	1.05846	+	0.427523i
$983$			22.5795i			0.720175i	0.932919	+	0.360087i	$0.117253\pi$
$983$			22.5795i			0.720175i	−0.932919	+	0.360087i	$0.882747\pi$
$984$	0.689078	−	0.307042i	0.0219670	−	0.00978813i
$985$	−4.46432	+	4.46432i	−0.142245	+	0.142245i
$986$	−9.83750	+	4.17692i	−0.313290	+	0.133020i
$987$	−1.81743	+	4.38766i	−0.0578494	+	0.139661i
$988$	2.64826	−	3.89275i	0.0842523	−	0.123845i
$989$	18.8456	−	7.80612i	0.599257	−	0.248220i
$990$	−7.39673	+	0.0652805i	−0.235084	+	0.00207475i
$991$			38.7016i			1.22940i	0.788762	+	0.614699i	$0.210722\pi$
$991$			38.7016i			1.22940i	−0.788762	+	0.614699i	$0.789278\pi$
$992$	20.2404	+	18.5286i	0.642635	+	0.588283i
$993$	8.41685	−	8.41685i	0.267101	−	0.267101i
$994$	0.0280047	+	3.17313i	0.000888256	+	0.100646i
$995$	−0.963687	+	2.32655i	−0.0305509	+	0.0737565i
$996$	−8.10783	+	0.143124i	−0.256906	+	0.00453505i
$997$	−1.17773	+	2.84328i	−0.0372989	+	0.0900476i	−0.941431	−	0.337205i	$-0.890518\pi$
$997$	−1.17773	+	2.84328i	−0.0372989	+	0.0900476i	0.904132	+	0.427253i	$0.140518\pi$
$998$	6.98810	−	17.3011i	0.221205	−	0.547656i
$999$	−6.61926			−0.209424

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bi.a.395.1	yes	216
13.8	odd	4		416.2.bd.a.203.28	✓	216
32.3	odd	8		416.2.bd.a.291.28	yes	216
416.99	even	8	inner	416.2.bi.a.99.1	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bd.a.203.28	✓	216	13.8	odd	4
416.2.bd.a.291.28	yes	216	32.3	odd	8
416.2.bi.a.99.1	yes	216	416.99	even	8	inner
416.2.bi.a.395.1	yes	216	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bi (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41416 + 0.0124808i) q^{2} +(0.185333 + 0.447434i) q^{3} +(1.99969 - 0.0352996i) q^{4} +(-0.172454 - 0.416340i) q^{5} +(-0.267675 - 0.630429i) q^{6} -2.63339 q^{7} +(-2.82744 + 0.0748769i) q^{8} +(1.95547 - 1.95547i) q^{9} +(0.249073 + 0.586618i) q^{10} +(-3.87756 + 1.60614i) q^{11} +(0.386403 + 0.888186i) q^{12} +(-3.51680 - 0.795059i) q^{13} +(3.72404 - 0.0328668i) q^{14} +(0.154323 - 0.154323i) q^{15} +(3.99751 - 0.141176i) q^{16} -3.57510 q^{17} +(-2.74094 + 2.78975i) q^{18} +(-0.249856 + 0.603205i) q^{19} +(-0.359550 - 0.826462i) q^{20} +(-0.488055 - 1.17827i) q^{21} +(5.46344 - 2.31973i) q^{22} +(-2.69830 + 2.69830i) q^{23} +(-0.557520 - 1.25121i) q^{24} +(3.39194 - 3.39194i) q^{25} +(4.98324 + 1.08045i) q^{26} +(2.57966 + 1.06853i) q^{27} +(-5.26597 + 0.0929578i) q^{28} +(-1.95294 + 0.808934i) q^{29} +(-0.216311 + 0.220163i) q^{30} +(-3.43007 - 3.43007i) q^{31} +(-5.65135 + 0.249538i) q^{32} +(-1.43728 - 1.43728i) q^{33} +(5.05576 - 0.0446200i) q^{34} +(0.454138 + 1.09639i) q^{35} +(3.84131 - 3.97936i) q^{36} +(-2.19017 + 0.907197i) q^{37} +(0.345807 - 0.856146i) q^{38} +(-0.296044 - 1.72089i) q^{39} +(0.518775 + 1.16426i) q^{40} +0.550727i q^{41} +(0.704893 + 1.66017i) q^{42} +(-4.93862 - 2.04564i) q^{43} +(-7.69721 + 3.34865i) q^{44} +(-1.15137 - 0.476912i) q^{45} +(3.78215 - 3.84950i) q^{46} +(-2.63314 - 2.63314i) q^{47} +(0.804038 + 1.76246i) q^{48} -0.0652357 q^{49} +(-4.75440 + 4.83907i) q^{50} +(-0.662585 - 1.59962i) q^{51} +(-7.06057 - 1.46573i) q^{52} +(-11.0699 - 4.58531i) q^{53} +(-3.66138 - 1.47887i) q^{54} +(1.33740 + 1.33740i) q^{55} +(7.44575 - 0.197180i) q^{56} -0.316201 q^{57} +(2.75167 - 1.16834i) q^{58} +(-0.722775 - 1.74493i) q^{59} +(0.303151 - 0.314046i) q^{60} +(2.34981 - 0.973321i) q^{61} +(4.89347 + 4.80785i) q^{62} +(-5.14953 + 5.14953i) q^{63} +(7.98879 - 0.423419i) q^{64} +(0.275470 + 1.60129i) q^{65} +(2.05048 + 2.01460i) q^{66} +(10.2284 + 4.23674i) q^{67} +(-7.14909 + 0.126200i) q^{68} +(-1.70740 - 0.707226i) q^{69} +(-0.655907 - 1.54480i) q^{70} +0.852067i q^{71} +(-5.38255 + 5.67539i) q^{72} +6.22970 q^{73} +(3.08592 - 1.31026i) q^{74} +(2.14631 + 0.889029i) q^{75} +(-0.478341 + 1.21504i) q^{76} +(10.2111 - 4.22959i) q^{77} +(0.440130 + 2.42991i) q^{78} -1.67033 q^{79} +(-0.748162 - 1.63997i) q^{80} -6.94410i q^{81} +(-0.00687351 - 0.778816i) q^{82} +(-3.20382 + 7.73471i) q^{83} +(-1.01755 - 2.33894i) q^{84} +(0.616538 + 1.48846i) q^{85} +(7.00953 + 2.83123i) q^{86} +(-0.723890 - 0.723890i) q^{87} +(10.8433 - 4.83159i) q^{88} +3.24654i q^{89} +(1.63417 + 0.660060i) q^{90} +(9.26112 + 2.09370i) q^{91} +(-5.30051 + 5.49101i) q^{92} +(0.899024 - 2.17044i) q^{93} +(3.75654 + 3.69081i) q^{94} +0.294227 q^{95} +(-1.15903 - 2.48236i) q^{96} +(13.6088 - 13.6088i) q^{97} +(0.0922536 - 0.000814192i) q^{98} +(-4.44170 + 10.7232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 4 q^{11} + 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} - 4 q^{19} - 20 q^{20} - 16 q^{21} - 24 q^{22}+ \cdots - 116 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 4 * q^11 + 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 - 4 * q^19 - 20 * q^20 - 16 * q^21 - 24 * q^22 + 28 * q^24 - 4 * q^26 - 8 * q^27 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 4 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 + 20 * q^39 - 8 * q^40 - 48 * q^42 + 32 * q^43 - 20 * q^44 + 4 * q^45 - 24 * q^46 - 8 * q^47 - 8 * q^48 + 168 * q^49 + 20 * q^50 - 4 * q^52 - 8 * q^53 + 20 * q^54 - 40 * q^55 - 56 * q^56 - 8 * q^57 + 32 * q^58 + 4 * q^59 - 36 * q^60 - 8 * q^61 - 72 * q^62 - 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 - 4 * q^70 + 56 * q^72 - 8 * q^73 - 8 * q^74 - 4 * q^76 - 56 * q^77 - 136 * q^78 - 16 * q^79 + 28 * q^80 + 88 * q^82 - 44 * q^83 + 44 * q^84 - 24 * q^85 + 64 * q^86 - 8 * q^87 - 64 * q^88 + 64 * q^90 + 16 * q^91 - 8 * q^92 + 56 * q^93 - 56 * q^94 - 28 * q^96 - 8 * q^97 - 76 * q^98 - 116 * q^99

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