LMFDB - Embedded newform 425.2.r.a.69.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(69,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([9, 0]))

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

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

chi := DirichletCharacter("425.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.4
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.42763 + 0.788786i) q^{2} +(-0.379903 - 0.522892i) q^{3} +(3.65319 - 2.65420i) q^{4} +(-1.95346 - 1.08812i) q^{5} +(1.33472 + 0.969728i) q^{6} +1.82616i q^{7} +(-3.77429 + 5.19486i) q^{8} +(0.797961 - 2.45587i) q^{9} +(5.60057 + 1.10071i) q^{10} +(-0.252384 - 0.776759i) q^{11} +(-2.77572 - 0.901885i) q^{12} +(4.44485 + 1.44422i) q^{13} +(-1.44045 - 4.43324i) q^{14} +(0.173153 + 1.43483i) q^{15} +(2.27417 - 6.99917i) q^{16} +(0.587785 - 0.809017i) q^{17} +6.59138i q^{18} +(-3.75697 - 2.72960i) q^{19} +(-10.0244 + 1.20974i) q^{20} +(0.954883 - 0.693763i) q^{21} +(1.22539 + 1.68661i) q^{22} +(-4.28238 + 1.39143i) q^{23} +4.15022 q^{24} +(2.63198 + 4.25120i) q^{25} -11.9297 q^{26} +(-3.43139 + 1.11493i) q^{27} +(4.84698 + 6.67129i) q^{28} +(0.424962 - 0.308753i) q^{29} +(-1.55213 - 3.34666i) q^{30} +(-2.99586 - 2.17662i) q^{31} +5.94285i q^{32} +(-0.310280 + 0.427063i) q^{33} +(-0.788786 + 2.42763i) q^{34} +(1.98708 - 3.56732i) q^{35} +(-3.60327 - 11.0897i) q^{36} +(-9.79608 - 3.18294i) q^{37} +(11.2736 + 3.66302i) q^{38} +(-0.933443 - 2.87284i) q^{39} +(13.0256 - 6.04104i) q^{40} +(-0.341185 + 1.05006i) q^{41} +(-1.77088 + 2.43740i) q^{42} -6.28773i q^{43} +(-2.98368 - 2.16777i) q^{44} +(-4.23107 + 3.92916i) q^{45} +(9.29850 - 6.75576i) q^{46} +(-7.48548 - 10.3029i) q^{47} +(-4.52378 + 1.46986i) q^{48} +3.66515 q^{49} +(-9.74276 - 8.24429i) q^{50} -0.646330 q^{51} +(20.0711 - 6.52150i) q^{52} +(-4.22499 - 5.81519i) q^{53} +(7.45073 - 5.41327i) q^{54} +(-0.352188 + 1.79199i) q^{55} +(-9.48663 - 6.89244i) q^{56} +3.00147i q^{57} +(-0.788113 + 1.08474i) q^{58} +(0.823691 - 2.53506i) q^{59} +(4.44088 + 4.78211i) q^{60} +(-0.591581 - 1.82070i) q^{61} +(8.98974 + 2.92094i) q^{62} +(4.48481 + 1.45720i) q^{63} +(-0.139298 - 0.428714i) q^{64} +(-7.11133 - 7.65777i) q^{65} +(0.416384 - 1.28150i) q^{66} +(-1.11507 + 1.53476i) q^{67} -4.51559i q^{68} +(2.35446 + 1.71061i) q^{69} +(-2.01006 + 10.2275i) q^{70} +(-5.97436 + 4.34062i) q^{71} +(9.74618 + 13.4145i) q^{72} +(-10.7608 + 3.49641i) q^{73} +26.2920 q^{74} +(1.22302 - 2.99129i) q^{75} -20.9698 q^{76} +(1.41848 - 0.460893i) q^{77} +(4.53212 + 6.23792i) q^{78} +(0.707508 - 0.514035i) q^{79} +(-12.0584 + 11.1980i) q^{80} +(-4.38068 - 3.18275i) q^{81} -2.81828i q^{82} +(1.74374 - 2.40005i) q^{83} +(1.64698 - 5.06889i) q^{84} +(-2.02852 + 0.940796i) q^{85} +(4.95967 + 15.2643i) q^{86} +(-0.322889 - 0.104913i) q^{87} +(4.98773 + 1.62061i) q^{88} +(4.28955 + 13.2019i) q^{89} +(7.17223 - 12.8760i) q^{90} +(-2.63737 + 8.11700i) q^{91} +(-11.9512 + 16.4494i) q^{92} +2.39342i q^{93} +(26.2988 + 19.1072i) q^{94} +(4.36893 + 9.42018i) q^{95} +(3.10747 - 2.25771i) q^{96} +(2.75135 + 3.78691i) q^{97} +(-8.89765 + 2.89102i) q^{98} -2.10901 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.42763	+	0.788786i	−1.71660	+	0.557756i	−0.991409	−	0.130796i	$-0.958247\pi$
$2$	−2.42763	+	0.788786i	−1.71660	+	0.557756i	−0.725187	+	0.688552i	$0.758247\pi$
$3$	−0.379903	−	0.522892i	−0.219337	−	0.301892i	0.685142	−	0.728410i	$-0.259740\pi$
$3$	−0.379903	−	0.522892i	−0.219337	−	0.301892i	−0.904479	+	0.426518i	$0.859740\pi$
$4$	3.65319	−	2.65420i	1.82659	−	1.32710i
$5$	−1.95346	−	1.08812i	−0.873612	−	0.486623i
$5$	−1.95346	−	1.08812i	−0.873612	−	0.486623i
$6$	1.33472	+	0.969728i	0.544896	+	0.395890i
$7$			1.82616i			0.690222i	0.938562	+	0.345111i	$0.112159\pi$
$7$			1.82616i			0.690222i	−0.938562	+	0.345111i	$0.887841\pi$
$8$	−3.77429	+	5.19486i	−1.33441	+	1.83666i
$9$	0.797961	−	2.45587i	0.265987	−	0.818624i
$10$	5.60057	+	1.10071i	1.77106	+	0.348074i
$11$	−0.252384	−	0.776759i	−0.0760968	−	0.234202i	0.905771	−	0.423767i	$-0.139292\pi$
$11$	−0.252384	−	0.776759i	−0.0760968	−	0.234202i	−0.981868	+	0.189565i	$0.939292\pi$
$12$	−2.77572	−	0.901885i	−0.801280	−	0.260352i
$13$	4.44485	+	1.44422i	1.23278	+	0.400555i	0.851721	−	0.523996i	$-0.175559\pi$
$13$	4.44485	+	1.44422i	1.23278	+	0.400555i	0.381059	+	0.924551i	$0.375559\pi$
$14$	−1.44045	−	4.43324i	−0.384976	−	1.18483i
$15$	0.173153	+	1.43483i	0.0447080	+	0.370471i
$16$	2.27417	−	6.99917i	0.568542	−	1.74979i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$18$			6.59138i			1.55360i
$19$	−3.75697	−	2.72960i	−0.861907	−	0.626212i	0.0664961	−	0.997787i	$-0.478818\pi$
$19$	−3.75697	−	2.72960i	−0.861907	−	0.626212i	−0.928403	+	0.371575i	$0.878818\pi$
$20$	−10.0244	+	1.20974i	−2.24153	+	0.270506i
$21$	0.954883	−	0.693763i	0.208373	−	0.151392i
$22$	1.22539	+	1.68661i	0.261255	+	0.359586i
$23$	−4.28238	+	1.39143i	−0.892937	+	0.290133i	−0.719319	−	0.694680i	$-0.755546\pi$
$23$	−4.28238	+	1.39143i	−0.892937	+	0.290133i	−0.173618	+	0.984813i	$0.555546\pi$
$24$	4.15022			0.847160
$25$	2.63198	+	4.25120i	0.526395	+	0.850240i
$26$	−11.9297			−2.33960
$27$	−3.43139	+	1.11493i	−0.660372	+	0.214568i
$28$	4.84698	+	6.67129i	0.915993	+	1.26076i
$29$	0.424962	−	0.308753i	0.0789135	−	0.0573340i	−0.547629	−	0.836721i	$-0.684469\pi$
$29$	0.424962	−	0.308753i	0.0789135	−	0.0573340i	0.626543	+	0.779387i	$0.284469\pi$
$30$	−1.55213	−	3.34666i	−0.283378	−	0.611013i
$31$	−2.99586	−	2.17662i	−0.538072	−	0.390933i	0.285296	−	0.958439i	$-0.407908\pi$
$31$	−2.99586	−	2.17662i	−0.538072	−	0.390933i	−0.823369	+	0.567507i	$0.807908\pi$
$32$			5.94285i			1.05056i
$33$	−0.310280	+	0.427063i	−0.0540128	+	0.0743422i
$34$	−0.788786	+	2.42763i	−0.135276	+	0.416336i
$35$	1.98708	−	3.56732i	0.335878	−	0.602986i
$36$	−3.60327	−	11.0897i	−0.600544	−	1.84829i
$37$	−9.79608	−	3.18294i	−1.61047	−	0.523272i	−0.640801	−	0.767707i	$-0.721397\pi$
$37$	−9.79608	−	3.18294i	−1.61047	−	0.523272i	−0.969666	+	0.244435i	$0.921397\pi$
$38$	11.2736	+	3.66302i	1.82882	+	0.594220i
$39$	−0.933443	−	2.87284i	−0.149471	−	0.460023i
$40$	13.0256	−	6.04104i	2.05952	−	0.955173i
$41$	−0.341185	+	1.05006i	−0.0532841	+	0.163992i	−0.974157	−	0.225871i	$-0.927477\pi$
$41$	−0.341185	+	1.05006i	−0.0532841	+	0.163992i	0.920873	+	0.389862i	$0.127477\pi$
$42$	−1.77088	+	2.43740i	−0.273252	+	0.376099i
$43$		−	6.28773i		−	0.958870i	−0.877577	−	0.479435i	$-0.840842\pi$
$43$		−	6.28773i		−	0.958870i	0.877577	−	0.479435i	$-0.159158\pi$
$44$	−2.98368	−	2.16777i	−0.449807	−	0.326804i
$45$	−4.23107	+	3.92916i	−0.630731	+	0.585724i
$46$	9.29850	−	6.75576i	1.37099	−	0.996082i
$47$	−7.48548	−	10.3029i	−1.09187	−	1.50283i	−0.845741	−	0.533593i	$-0.820841\pi$
$47$	−7.48548	−	10.3029i	−1.09187	−	1.50283i	−0.246129	−	0.969237i	$-0.579159\pi$
$48$	−4.52378	+	1.46986i	−0.652951	+	0.212157i
$49$	3.66515			0.523593
$50$	−9.74276	−	8.24429i	−1.37783	−	1.16592i
$51$	−0.646330			−0.0905043
$52$	20.0711	−	6.52150i	2.78336	−	0.904370i
$53$	−4.22499	−	5.81519i	−0.580346	−	0.798778i	0.413387	−	0.910555i	$-0.364346\pi$
$53$	−4.22499	−	5.81519i	−0.580346	−	0.798778i	−0.993733	+	0.111777i	$0.964346\pi$
$54$	7.45073	−	5.41327i	1.01392	−	0.736653i
$55$	−0.352188	+	1.79199i	−0.0474890	+	0.241632i
$56$	−9.48663	−	6.89244i	−1.26770	−	0.921041i
$57$			3.00147i			0.397554i
$58$	−0.788113	+	1.08474i	−0.103484	+	0.142434i
$59$	0.823691	−	2.53506i	0.107235	−	0.330037i	−0.883013	−	0.469348i	$-0.844489\pi$
$59$	0.823691	−	2.53506i	0.107235	−	0.330037i	0.990249	+	0.139312i	$0.0444889\pi$
$60$	4.44088	+	4.78211i	0.573315	+	0.617368i
$61$	−0.591581	−	1.82070i	−0.0757442	−	0.233117i	0.906015	−	0.423246i	$-0.139109\pi$
$61$	−0.591581	−	1.82070i	−0.0757442	−	0.233117i	−0.981759	+	0.190129i	$0.939109\pi$
$62$	8.98974	+	2.92094i	1.14170	+	0.370960i
$63$	4.48481	+	1.45720i	0.565033	+	0.183590i
$64$	−0.139298	−	0.428714i	−0.0174122	−	0.0535892i
$65$	−7.11133	−	7.65777i	−0.882052	−	0.949829i
$66$	0.416384	−	1.28150i	0.0512533	−	0.157741i
$67$	−1.11507	+	1.53476i	−0.136228	+	0.187501i	−0.871680	−	0.490075i	$-0.836969\pi$
$67$	−1.11507	+	1.53476i	−0.136228	+	0.187501i	0.735453	+	0.677576i	$0.236969\pi$
$68$		−	4.51559i		−	0.547596i
$69$	2.35446	+	1.71061i	0.283443	+	0.205934i
$70$	−2.01006	+	10.2275i	−0.240248	+	1.22242i
$71$	−5.97436	+	4.34062i	−0.709026	+	0.515137i	−0.882859	−	0.469638i	$-0.844385\pi$
$71$	−5.97436	+	4.34062i	−0.709026	+	0.515137i	0.173834	+	0.984775i	$0.444385\pi$
$72$	9.74618	+	13.4145i	1.14860	+	1.58091i
$73$	−10.7608	+	3.49641i	−1.25946	+	0.409223i	−0.861302	−	0.508094i	$-0.830350\pi$
$73$	−10.7608	+	3.49641i	−1.25946	+	0.409223i	−0.398158	+	0.917317i	$0.630350\pi$
$74$	26.2920			3.05638
$75$	1.22302	−	2.99129i	0.141222	−	0.345404i
$76$	−20.9698			−2.40540
$77$	1.41848	−	0.460893i	0.161651	−	0.0525237i
$78$	4.53212	+	6.23792i	0.513161	+	0.706306i
$79$	0.707508	−	0.514035i	0.0796009	−	0.0578334i	−0.547273	−	0.836954i	$-0.684334\pi$
$79$	0.707508	−	0.514035i	0.0796009	−	0.0578334i	0.626874	+	0.779121i	$0.284334\pi$
$80$	−12.0584	+	11.1980i	−1.34818	+	1.25197i
$81$	−4.38068	−	3.18275i	−0.486743	−	0.353639i
$82$		−	2.81828i		−	0.311227i
$83$	1.74374	−	2.40005i	0.191401	−	0.263440i	−0.702522	−	0.711662i	$-0.747943\pi$
$83$	1.74374	−	2.40005i	0.191401	−	0.263440i	0.893922	+	0.448222i	$0.147943\pi$
$84$	1.64698	−	5.06889i	0.179701	−	0.553062i
$85$	−2.02852	+	0.940796i	−0.220024	+	0.102044i
$86$	4.95967	+	15.2643i	0.534815	+	1.64599i
$87$	−0.322889	−	0.104913i	−0.0346174	−	0.0112479i
$88$	4.98773	+	1.62061i	0.531694	+	0.172758i
$89$	4.28955	+	13.2019i	0.454692	+	1.39940i	0.871497	+	0.490402i	$0.163150\pi$
$89$	4.28955	+	13.2019i	0.454692	+	1.39940i	−0.416805	+	0.908996i	$0.636850\pi$
$90$	7.17223	−	12.8760i	0.756020	−	1.35725i
$91$	−2.63737	+	8.11700i	−0.276472	+	0.850892i
$92$	−11.9512	+	16.4494i	−1.24600	+	1.71497i
$93$			2.39342i			0.248186i
$94$	26.2988	+	19.1072i	2.71251	+	1.97076i
$95$	4.36893	+	9.42018i	0.448243	+	0.966490i
$96$	3.10747	−	2.25771i	0.317155	−	0.230426i
$97$	2.75135	+	3.78691i	0.279358	+	0.384503i	0.925521	−	0.378696i	$-0.123628\pi$
$97$	2.75135	+	3.78691i	0.279358	+	0.384503i	−0.646163	+	0.763199i	$0.723628\pi$
$98$	−8.89765	+	2.89102i	−0.898798	+	0.292037i
$99$	−2.10901			−0.211964
$100$	20.8986	+	8.54465i	2.08986	+	0.854465i
$101$	−17.4925			−1.74057			−0.870285	−	0.492549i	$-0.836065\pi$
$101$	−17.4925			−1.74057			−0.870285	+	0.492549i	$0.836065\pi$
$102$	1.56905	−	0.509816i	0.155359	−	0.0504793i
$103$	−8.60124	−	11.8386i	−0.847505	−	1.16649i	−0.984407	−	0.175906i	$-0.943715\pi$
$103$	−8.60124	−	11.8386i	−0.847505	−	1.16649i	0.136902	−	0.990585i	$-0.456285\pi$
$104$	−24.2787	+	17.6395i	−2.38072	+	1.72969i
$105$	−2.62022	+	0.316205i	−0.255707	+	0.0308585i
$106$	14.8437	+	10.7846i	1.44174	+	1.04749i
$107$			10.0640i			0.972920i	0.873703	+	0.486460i	$0.161712\pi$
$107$			10.0640i			0.972920i	−0.873703	+	0.486460i	$0.838288\pi$
$108$	−9.57629	+	13.1806i	−0.921479	+	1.26831i
$109$	2.82444	−	8.69272i	0.270532	−	0.832612i	−0.719835	−	0.694145i	$-0.755783\pi$
$109$	2.82444	−	8.69272i	0.270532	−	0.832612i	0.990367	−	0.138467i	$-0.0442174\pi$
$110$	−0.558514	−	4.62810i	−0.0532522	−	0.441272i
$111$	2.05723	+	6.33150i	0.195264	+	0.600960i
$112$	12.7816	+	4.15299i	1.20775	+	0.392420i
$113$	17.2760	+	5.61333i	1.62519	+	0.528057i	0.973159	−	0.230132i	$-0.0739158\pi$
$113$	17.2760	+	5.61333i	1.62519	+	0.528057i	0.652034	+	0.758190i	$0.273916\pi$
$114$	−2.36752	−	7.28647i	−0.221738	−	0.682440i
$115$	9.87948	+	1.94166i	0.921266	+	0.181061i
$116$	0.732976	−	2.25587i	0.0680551	−	0.209452i
$117$	7.09364	−	9.76356i	0.655807	−	0.902641i
$118$			6.80391i			0.626351i
$119$	1.47739	+	1.07339i	0.135432	+	0.0983973i
$120$	−8.10727	−	4.51595i	−0.740089	−	0.412248i
$121$	8.35953	−	6.07355i	0.759957	−	0.552141i
$122$	2.87229	+	3.95336i	0.260045	+	0.357921i
$123$	0.678685	−	0.220518i	0.0611950	−	0.0198835i
$124$	−16.7216			−1.50165
$125$	−0.515623	−	11.1684i	−0.0461188	−	0.998936i
$126$	−12.0369			−1.07233
$127$	−5.94030	+	1.93012i	−0.527117	+	0.171271i	−0.560473	−	0.828173i	$-0.689380\pi$
$127$	−5.94030	+	1.93012i	−0.527117	+	0.171271i	0.0333561	+	0.999444i	$0.489380\pi$
$128$	−6.30991	−	8.68484i	−0.557722	−	0.767639i
$129$	−3.28780	+	2.38873i	−0.289475	+	0.210316i
$130$	23.3040	+	12.9809i	2.04390	+	1.13850i
$131$	6.89651	+	5.01061i	0.602551	+	0.437779i	0.846783	−	0.531938i	$-0.178536\pi$
$131$	6.89651	+	5.01061i	0.602551	+	0.437779i	−0.244233	+	0.969717i	$0.578536\pi$
$132$			2.38369i			0.207473i
$133$	4.98467	−	6.86081i	0.432226	−	0.594907i
$134$	1.49638	−	4.60539i	0.129268	−	0.397845i
$135$	7.91625	+	1.55582i	0.681323	+	0.133903i
$136$	1.98426	+	6.10693i	0.170149	+	0.523665i
$137$	3.44977	+	1.12090i	0.294734	+	0.0957649i	0.452652	−	0.891687i	$-0.350478\pi$
$137$	3.44977	+	1.12090i	0.294734	+	0.0957649i	−0.157918	+	0.987452i	$0.550478\pi$
$138$	−7.06506	−	2.29558i	−0.601418	−	0.195413i
$139$	−5.55232	−	17.0883i	−0.470941	−	1.44941i	−0.851354	−	0.524592i	$-0.824218\pi$
$139$	−5.55232	−	17.0883i	−0.470941	−	1.44941i	0.380412	−	0.924817i	$-0.375782\pi$
$140$	−2.20917	−	18.3062i	−0.186709	−	1.54715i
$141$	−2.54354	+	7.82820i	−0.214204	+	0.659254i
$142$	11.0797	−	15.2499i	0.929790	−	1.27975i
$143$		−	3.81708i		−	0.319200i
$144$	−15.3744	−	11.1701i	−1.28120	−	0.930845i
$145$	−1.16611	+	0.140724i	−0.0968399	+	0.0116865i
$146$	23.3654	−	16.9760i	1.93374	−	1.40494i
$147$	−1.39240	−	1.91648i	−0.114844	−	0.158069i
$148$	−44.2351	+	14.3728i	−3.63610	+	1.18144i
$149$	8.97259			0.735064			0.367532	−	0.930011i	$-0.380203\pi$
$149$	8.97259			0.735064			0.367532	+	0.930011i	$0.380203\pi$
$150$	−0.609565	+	8.22645i	−0.0497707	+	0.671687i
$151$	0.791360			0.0644000			0.0322000	−	0.999481i	$-0.489749\pi$
$151$	0.791360			0.0644000			0.0322000	+	0.999481i	$0.489749\pi$
$152$	28.3597	−	9.21464i	2.30028	−	0.747406i
$153$	−1.51781	−	2.08909i	−0.122708	−	0.168893i
$154$	−3.08001	+	2.23776i	−0.248195	+	0.180324i
$155$	3.48385	+	7.51179i	0.279830	+	0.603362i
$156$	−11.0351	−	8.01749i	−0.883518	−	0.641913i
$157$			19.9771i			1.59435i	0.603749	+	0.797175i	$0.293673\pi$
$157$			19.9771i			1.59435i	−0.603749	+	0.797175i	$0.706327\pi$
$158$	−1.31211	+	1.80596i	−0.104386	+	0.143675i
$159$	−1.43563	+	4.41842i	−0.113853	+	0.350404i
$160$	6.46655	−	11.6091i	0.511225	−	0.917779i
$161$	−2.54097	−	7.82029i	−0.200256	−	0.616325i
$162$	13.1452	+	4.27114i	1.03279	+	0.335572i
$163$	−8.34491	−	2.71142i	−0.653623	−	0.212375i	−0.0366123	−	0.999330i	$-0.511657\pi$
$163$	−8.34491	−	2.71142i	−0.653623	−	0.212375i	−0.617011	+	0.786954i	$0.711657\pi$
$164$	1.54065	+	4.74164i	0.120305	+	0.370260i
$165$	1.07081	−	0.496627i	0.0833628	−	0.0386623i
$166$	−2.34004	+	7.20189i	−0.181622	+	0.558975i
$167$	−9.90015	+	13.6264i	−0.766096	+	1.05444i	0.230586	+	0.973052i	$0.425936\pi$
$167$	−9.90015	+	13.6264i	−0.766096	+	1.05444i	−0.996682	+	0.0813892i	$0.974064\pi$
$168$			7.57895i			0.584729i
$169$	7.15372	+	5.19748i	0.550286	+	0.399806i
$170$	4.18242	−	3.88398i	0.320777	−	0.297888i
$171$	−9.70145	+	7.04852i	−0.741888	+	0.539014i
$172$	−16.6889	−	22.9703i	−1.27251	−	1.75147i
$173$	21.8571	−	7.10182i	1.66177	−	0.539941i	0.680526	−	0.732724i	$-0.261751\pi$
$173$	21.8571	−	7.10182i	1.66177	−	0.539941i	0.981242	+	0.192782i	$0.0617512\pi$
$174$	0.866611			0.0656976
$175$	−7.76336	+	4.80640i	−0.586855	+	0.363330i
$176$	−6.01064			−0.453069
$177$	−1.63849	+	0.532376i	−0.123156	+	0.0400158i
$178$	−20.8269	−	28.6658i	−1.56104	−	2.14859i
$179$	−5.58351	+	4.05666i	−0.417331	+	0.303209i	−0.776563	−	0.630039i	$-0.783039\pi$
$179$	−5.58351	+	4.05666i	−0.417331	+	0.303209i	0.359232	+	0.933248i	$0.383039\pi$
$180$	−5.02815	+	25.5841i	−0.374776	+	1.90692i
$181$	1.43968	+	1.04599i	0.107011	+	0.0777477i	0.640004	−	0.768372i	$-0.278933\pi$
$181$	1.43968	+	1.04599i	0.107011	+	0.0777477i	−0.532993	+	0.846120i	$0.678933\pi$
$182$		−	21.7854i		−	1.61484i
$183$	−0.727286	+	1.00102i	−0.0537625	+	0.0739978i
$184$	8.93464	−	27.4980i	0.658671	−	2.02718i
$185$	15.6728	+	16.8771i	1.15229	+	1.24083i
$186$	−1.88789	−	5.81034i	−0.138427	−	0.426035i
$187$	−0.776759	−	0.252384i	−0.0568023	−	0.0184562i
$188$	−54.6918	−	17.7704i	−3.98881	−	1.29604i
$189$	−2.03603	−	6.26626i	−0.148100	−	0.455804i
$190$	−18.0367	−	19.4226i	−1.30852	−	1.40906i
$191$	5.31971	−	16.3724i	0.384921	−	1.18466i	−0.551617	−	0.834097i	$-0.685989\pi$
$191$	5.31971	−	16.3724i	0.384921	−	1.18466i	0.936538	−	0.350566i	$-0.114011\pi$
$192$	−0.171251	+	0.235707i	−0.0123590	+	0.0170107i
$193$		−	14.4071i		−	1.03705i	−0.855063	−	0.518524i	$-0.826482\pi$
$193$		−	14.4071i		−	1.03705i	0.855063	−	0.518524i	$-0.173518\pi$
$194$	−9.66634	−	7.02301i	−0.694003	−	0.504223i
$195$	−1.30257	+	6.62767i	−0.0932787	+	0.474617i
$196$	13.3895	−	9.72803i	0.956392	−	0.694860i
$197$	−12.5184	−	17.2302i	−0.891902	−	1.22760i	−0.972980	−	0.230890i	$-0.925836\pi$
$197$	−12.5184	−	17.2302i	−0.891902	−	1.22760i	0.0810778	−	0.996708i	$-0.474164\pi$
$198$	5.11992	−	1.66356i	0.363857	−	0.118224i
$199$	−16.8459			−1.19417			−0.597086	−	0.802177i	$-0.703675\pi$
$199$	−16.8459			−1.19417			−0.597086	+	0.802177i	$0.703675\pi$
$200$	−32.0182	−	2.37249i	−2.26403	−	0.167761i
$201$	1.22613			0.0864849
$202$	42.4654	−	13.7978i	2.98785	−	0.970813i
$203$	0.563832	+	0.776048i	0.0395732	+	0.0544679i
$204$	−2.36117	+	1.71549i	−0.165315	+	0.120108i
$205$	1.80908	−	1.67999i	0.126352	−	0.117336i
$206$	30.2188	+	21.9552i	2.10544	+	1.52969i
$207$			11.6273i			0.808151i
$208$	20.2167	−	27.8259i	1.40177	−	1.92938i
$209$	−1.17204	+	3.60716i	−0.0810716	+	0.249513i
$210$	6.11152	−	2.83442i	0.421735	−	0.195594i
$211$	2.56003	+	7.87897i	0.176240	+	0.542411i	0.999688	−	0.0249810i	$-0.00795252\pi$
$211$	2.56003	+	7.87897i	0.176240	+	0.542411i	−0.823448	+	0.567392i	$0.807953\pi$
$212$	−30.8693	−	10.0301i	−2.12011	−	0.688867i
$213$	4.53936	+	1.47493i	0.311032	+	0.101060i
$214$	−7.93831	−	24.4316i	−0.542652	−	1.67011i
$215$	−6.84182	+	12.2828i	−0.466608	+	0.837680i
$216$	7.15918	−	22.0337i	0.487120	−	1.49920i
$217$	3.97485	−	5.47091i	0.269830	−	0.371390i
$218$			23.3306i			1.58015i
$219$	5.91632	+	4.29846i	0.399788	+	0.290463i
$220$	3.46968	+	7.48125i	0.233926	+	0.504386i
$221$	3.78102	−	2.74707i	0.254339	−	0.184788i
$222$	−9.98840	−	13.7479i	−0.670378	−	0.922696i
$223$	16.9980	−	5.52300i	1.13827	−	0.369847i	0.321559	−	0.946890i	$-0.395793\pi$
$223$	16.9980	−	5.52300i	1.13827	−	0.369847i	0.816714	+	0.577042i	$0.195793\pi$
$224$	−10.8526			−0.725118
$225$	12.5406	−	3.07151i	0.836041	−	0.204767i
$226$	−46.3676			−3.08433
$227$	12.9157	−	4.19657i	0.857246	−	0.278536i	0.152768	−	0.988262i	$-0.451181\pi$
$227$	12.9157	−	4.19657i	0.857246	−	0.278536i	0.704478	+	0.709726i	$0.251181\pi$
$228$	7.96649	+	10.9649i	0.527594	+	0.726171i
$229$	8.51792	−	6.18863i	0.562880	−	0.408956i	−0.269632	−	0.962963i	$-0.586902\pi$
$229$	8.51792	−	6.18863i	0.562880	−	0.408956i	0.832512	+	0.554007i	$0.186902\pi$
$230$	−25.5153	+	3.07916i	−1.68243	+	0.203034i
$231$	−0.779884	−	0.566619i	−0.0513126	−	0.0372808i
$232$			3.37294i			0.221445i
$233$	11.1384	−	15.3307i	0.729699	−	1.00434i	−0.269447	−	0.963015i	$-0.586841\pi$
$233$	11.1384	−	15.3307i	0.729699	−	1.00434i	0.999146	−	0.0413292i	$-0.0131592\pi$
$234$	−9.51940	+	29.2977i	−0.622303	+	1.91525i
$235$	3.41176	+	28.2714i	0.222558	+	1.84422i
$236$	−3.71945	−	11.4473i	−0.242115	−	0.745155i
$237$	−0.537570	−	0.174667i	−0.0349189	−	0.0113458i
$238$	−4.43324	−	1.44045i	−0.287364	−	0.0933703i
$239$	5.13676	+	15.8093i	0.332269	+	1.02262i	0.968052	+	0.250751i	$0.0806775\pi$
$239$	5.13676	+	15.8093i	0.332269	+	1.02262i	−0.635783	+	0.771868i	$0.719323\pi$
$240$	10.4364	+	2.05111i	0.673666	+	0.132399i
$241$	−1.90160	+	5.85251i	−0.122493	+	0.376993i	−0.993436	−	0.114390i	$-0.963509\pi$
$241$	−1.90160	+	5.85251i	−0.122493	+	0.376993i	0.870943	+	0.491383i	$0.163509\pi$
$242$	−15.5031	+	21.3382i	−0.996580	+	1.37167i
$243$			14.3237i			0.918866i
$244$	−6.99365	−	5.08119i	−0.447723	−	0.325290i
$245$	−7.15971	−	3.98814i	−0.457417	−	0.254793i
$246$	−1.47366	+	1.07067i	−0.0939570	+	0.0682637i
$247$	−12.7570	−	17.5585i	−0.811710	−	1.11722i
$248$	22.6145	−	7.34789i	1.43602	−	0.466592i
$249$	−1.91742			−0.121512
$250$	10.0613	+	26.7062i	0.636330	+	1.68905i
$251$	11.6749			0.736914			0.368457	−	0.929645i	$-0.379886\pi$
$251$	11.6749			0.736914			0.368457	+	0.929645i	$0.379886\pi$
$252$	20.2515	−	6.58013i	1.27573	−	0.414509i
$253$	2.16161	+	2.97520i	0.135899	+	0.187049i
$254$	12.8984	−	9.37125i	0.809319	−	0.588005i
$255$	1.26258	+	0.703287i	0.0790657	+	0.0440415i
$256$	22.8980	+	16.6364i	1.43113	+	1.03977i
$257$		−	6.42976i		−	0.401077i	−0.979686	−	0.200539i	$-0.935731\pi$
$257$		−	6.42976i		−	0.401077i	0.979686	−	0.200539i	$-0.0642692\pi$
$258$	6.09739	−	8.39234i	0.379607	−	0.522484i
$259$	5.81255	−	17.8892i	0.361174	−	1.11158i
$260$	−46.3042	−	9.10038i	−2.87167	−	0.564382i
$261$	−0.419155	−	1.29003i	−0.0259450	−	0.0798506i
$262$	−20.6945	−	6.72405i	−1.27851	−	0.415413i
$263$	13.6985	+	4.45090i	0.844684	+	0.274454i	0.699218	−	0.714909i	$-0.253532\pi$
$263$	13.6985	+	4.45090i	0.844684	+	0.274454i	0.145466	+	0.989363i	$0.453532\pi$
$264$	−1.04745	−	3.22372i	−0.0644661	−	0.198406i
$265$	1.92568	+	15.9570i	0.118293	+	0.980232i
$266$	−6.68924	+	20.5874i	−0.410144	+	1.26229i
$267$	5.27355	−	7.25842i	0.322736	−	0.444208i
$268$			8.56639i			0.523276i
$269$	8.31107	+	6.03835i	0.506735	+	0.368165i	0.811584	−	0.584236i	$-0.198606\pi$
$269$	8.31107	+	6.03835i	0.506735	+	0.368165i	−0.304849	+	0.952401i	$0.598606\pi$
$270$	−20.4450	+	2.46728i	−1.24424	+	0.150154i
$271$	−19.0030	+	13.8065i	−1.15435	+	0.838683i	−0.989053	−	0.147561i	$-0.952858\pi$
$271$	−19.0030	+	13.8065i	−1.15435	+	0.838683i	−0.165295	+	0.986244i	$0.552858\pi$
$272$	−4.32573	−	5.95385i	−0.262286	−	0.361005i
$273$	5.24626	−	1.70461i	0.317518	−	0.103168i
$274$	−9.25893			−0.559353
$275$	2.63789	−	3.11735i	0.159071	−	0.187983i
$276$	13.1416			0.791030
$277$	9.37235	−	3.04526i	0.563130	−	0.182972i	−0.0135991	−	0.999908i	$-0.504329\pi$
$277$	9.37235	−	3.04526i	0.563130	−	0.182972i	0.576729	+	0.816936i	$0.304329\pi$
$278$	26.9580	+	37.1045i	1.61683	+	2.22538i
$279$	−7.73608	+	5.62059i	−0.463147	+	0.336496i
$280$	11.0319	+	23.7867i	0.659282	+	1.42153i
$281$	5.29966	+	3.85043i	0.316151	+	0.229697i	0.734531	−	0.678575i	$-0.237402\pi$
$281$	5.29966	+	3.85043i	0.316151	+	0.229697i	−0.418380	+	0.908272i	$0.637402\pi$
$282$		−	21.0103i		−	1.25115i
$283$	13.6451	−	18.7809i	0.811119	−	1.11641i	−0.180030	−	0.983661i	$-0.557620\pi$
$283$	13.6451	−	18.7809i	0.811119	−	1.11641i	0.991150	−	0.132749i	$-0.0423804\pi$
$284$	−10.3046	+	31.7142i	−0.611464	+	1.88189i
$285$	3.26597	−	5.86324i	0.193459	−	0.347308i
$286$	3.01086	+	9.26647i	0.178036	+	0.547938i
$287$	−1.91757	−	0.623057i	−0.113191	−	0.0367779i
$288$	14.5949	+	4.74216i	0.860011	+	0.279435i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	2.71988	−	1.26144i	0.159717	−	0.0740741i
$291$	0.934899	−	2.87732i	0.0548047	−	0.168672i
$292$	−30.0312	+	41.3344i	−1.75744	+	2.41891i
$293$		−	29.8333i		−	1.74288i	−0.490501	−	0.871441i	$-0.663186\pi$
$293$		−	29.8333i		−	1.74288i	0.490501	−	0.871441i	$-0.336814\pi$
$294$	4.89194	+	3.55420i	0.285304	+	0.207285i
$295$	−4.36750	+	4.05585i	−0.254286	+	0.236141i
$296$	53.5082	−	38.8760i	3.11010	−	2.25962i
$297$	1.73206	+	2.38398i	0.100504	+	0.138332i
$298$	−21.7822	+	7.07746i	−1.26181	+	0.409986i
$299$	−21.0441			−1.21701
$300$	−3.47153	−	14.1739i	−0.200429	−	0.818329i
$301$	11.4824			0.661833
$302$	−1.92113	+	0.624214i	−0.110549	+	0.0359195i
$303$	6.64546	+	9.14669i	0.381772	+	0.525464i
$304$	−27.6489	+	20.0881i	−1.58577	+	1.15213i
$305$	−0.825518	+	4.20037i	−0.0472690	+	0.240512i
$306$	5.33254	+	3.87432i	0.304841	+	0.221480i
$307$		−	21.6746i		−	1.23704i	−0.785770	−	0.618518i	$-0.787733\pi$
$307$		−	21.6746i		−	1.23704i	0.785770	−	0.618518i	$-0.212267\pi$
$308$	3.95869	−	5.44867i	0.225567	−	0.310467i
$309$	−2.92266	+	8.99504i	−0.166265	+	0.511710i
$310$	−14.3827	−	15.4879i	−0.816883	−	0.879652i
$311$	−1.15750	−	3.56241i	−0.0656356	−	0.202006i	0.912860	−	0.408272i	$-0.133869\pi$
$311$	−1.15750	−	3.56241i	−0.0656356	−	0.202006i	−0.978496	+	0.206267i	$0.933869\pi$
$312$	18.4471	+	5.99383i	1.04436	+	0.339334i
$313$	2.77947	+	0.903103i	0.157105	+	0.0510464i	0.386513	−	0.922284i	$-0.373679\pi$
$313$	2.77947	+	0.903103i	0.157105	+	0.0510464i	−0.229409	+	0.973330i	$0.573679\pi$
$314$	−15.7577	−	48.4972i	−0.889258	−	2.73685i
$315$	−7.17526	−	7.72660i	−0.404280	−	0.435345i
$316$	1.22031	−	3.75573i	0.0686479	−	0.211276i
$317$	−9.96365	+	13.7138i	−0.559614	+	0.770243i	−0.991277	−	0.131792i	$-0.957927\pi$
$317$	−9.96365	+	13.7138i	−0.559614	+	0.770243i	0.431663	+	0.902035i	$0.357927\pi$
$318$		−	11.8587i		−	0.665004i
$319$	−0.347081	−	0.252169i	−0.0194328	−	0.0141187i
$320$	−0.194382	+	0.989046i	−0.0108663	+	0.0552894i
$321$	5.26237	−	3.82333i	0.293717	−	0.213398i
$322$	12.3371	+	16.9805i	0.687518	+	0.946287i
$323$	−4.41658	+	1.43503i	−0.245745	+	0.0798474i
$324$	−24.4511			−1.35840
$325$	5.55908	+	22.6971i	0.308362	+	1.25901i
$326$	22.3971			1.24046
$327$	−5.61837	+	1.82552i	−0.310697	+	0.100951i
$328$	−4.16718	−	5.73564i	−0.230094	−	0.316698i
$329$	18.8147	−	13.6697i	1.03729	−	0.753633i
$330$	−2.20781	+	2.05027i	−0.121536	+	0.112864i
$331$	−21.4026	−	15.5499i	−1.17639	−	0.854700i	−0.184633	−	0.982807i	$-0.559110\pi$
$331$	−21.4026	−	15.5499i	−1.17639	−	0.854700i	−0.991760	+	0.128107i	$0.959110\pi$
$332$		−	13.3961i		−	0.735206i
$333$	−15.6338	+	21.5181i	−0.856727	+	1.17918i
$334$	13.2856	−	40.8890i	0.726957	−	2.23734i
$335$	3.84825	−	1.78476i	0.210252	−	0.0975117i
$336$	−2.68420	−	8.26112i	−0.146435	−	0.450681i
$337$	−11.0942	−	3.60473i	−0.604340	−	0.196362i	−0.00916488	−	0.999958i	$-0.502917\pi$
$337$	−11.0942	−	3.60473i	−0.604340	−	0.196362i	−0.595175	+	0.803596i	$0.702917\pi$
$338$	−21.4663	−	6.97483i	−1.16761	−	0.379381i
$339$	−3.62806	−	11.1660i	−0.197049	−	0.606456i
$340$	−4.91352	+	8.82100i	−0.266473	+	0.478386i
$341$	−0.934601	+	2.87641i	−0.0506115	+	0.155766i
$342$	17.9918	−	24.7636i	0.972885	−	1.33906i
$343$			19.4762i			1.05162i
$344$	32.6639	+	23.7317i	1.76112	+	1.27953i
$345$	−2.73797	−	5.90354i	−0.147407	−	0.317836i
$346$	−47.4593	+	34.4812i	−2.55143	+	1.85372i
$347$	3.59763	+	4.95171i	0.193131	+	0.265822i	0.894590	−	0.446888i	$-0.147468\pi$
$347$	3.59763	+	4.95171i	0.193131	+	0.265822i	−0.701459	+	0.712710i	$0.747468\pi$
$348$	−1.45803	+	0.473744i	−0.0781589	+	0.0253954i
$349$	−20.0847			−1.07511			−0.537555	−	0.843229i	$-0.680652\pi$
$349$	−20.0847			−1.07511			−0.537555	+	0.843229i	$0.680652\pi$
$350$	15.0554	−	17.7918i	0.804743	−	0.951012i
$351$	−16.8622			−0.900040
$352$	4.61616	−	1.49988i	0.246042	−	0.0799440i
$353$	−16.1304	−	22.2015i	−0.858533	−	1.18167i	−0.981917	−	0.189310i	$-0.939375\pi$
$353$	−16.1304	−	22.2015i	−0.858533	−	1.18167i	0.123384	−	0.992359i	$-0.460625\pi$
$354$	3.55771	−	2.58483i	0.189090	−	0.137382i
$355$	16.3938	−	1.97838i	0.870091	−	0.105002i
$356$	50.7110	+	36.8437i	2.68768	+	1.95271i
$357$		−	1.18030i		−	0.0624681i
$358$	10.3549	−	14.2523i	0.547273	−	0.753256i
$359$	−9.53832	+	29.3559i	−0.503413	+	1.54935i	0.300008	+	0.953937i	$0.403011\pi$
$359$	−9.53832	+	29.3559i	−0.503413	+	1.54935i	−0.803422	+	0.595410i	$0.796989\pi$
$360$	−4.44214	−	36.8096i	−0.234122	−	1.94004i
$361$	0.792776	+	2.43991i	0.0417251	+	0.128417i
$362$	−4.32007	−	1.40368i	−0.227058	−	0.0737756i
$363$	−6.35163	−	2.06377i	−0.333374	−	0.108320i
$364$	11.9093	+	36.6530i	0.624216	+	1.92114i
$365$	24.8253	+	4.87903i	1.29942	+	0.255380i
$366$	0.975991	−	3.00379i	0.0510159	−	0.157011i
$367$	−19.8116	+	27.2683i	−1.03416	+	1.42339i	−0.132376	+	0.991200i	$0.542261\pi$
$367$	−19.8116	+	27.2683i	−1.03416	+	1.42339i	−0.901780	+	0.432195i	$0.857739\pi$
$368$			33.1374i			1.72741i
$369$	2.30656	+	1.67581i	0.120075	+	0.0872394i
$370$	−51.3602	−	28.6089i	−2.67009	−	1.48730i
$371$	10.6195	−	7.71549i	0.551335	−	0.400568i
$372$	6.35260	+	8.74360i	0.329367	+	0.453335i
$373$	14.6915	−	4.77355i	0.760696	−	0.247165i	0.0971189	−	0.995273i	$-0.469037\pi$
$373$	14.6915	−	4.77355i	0.760696	−	0.247165i	0.663577	+	0.748108i	$0.269037\pi$
$374$	2.08476			0.107801
$375$	−5.64400	+	4.51254i	−0.291455	+	0.233027i
$376$	81.7745			4.21720
$377$	2.33480	−	0.758623i	0.120248	−	0.0390711i
$378$	9.88548	+	13.6062i	0.508454	+	0.699827i
$379$	24.9097	−	18.0980i	1.27953	−	0.929631i	0.279989	−	0.960003i	$-0.409669\pi$
$379$	24.9097	−	18.0980i	1.27953	−	0.929631i	0.999539	+	0.0303725i	$0.00966934\pi$
$380$	40.9635	+	22.8177i	2.10139	+	1.17052i
$381$	3.26599	+	2.37288i	0.167322	+	0.121566i
$382$			43.9422i			2.24828i
$383$	−15.8665	+	21.8384i	−0.810741	+	1.11589i	0.180468	+	0.983581i	$0.442239\pi$
$383$	−15.8665	+	21.8384i	−0.810741	+	1.11589i	−0.991209	+	0.132308i	$0.957761\pi$
$384$	−2.14408	+	6.59880i	−0.109415	+	0.336744i
$385$	−3.27245	−	0.643150i	−0.166780	−	0.0327780i
$386$	11.3641	+	34.9753i	0.578420	+	1.78019i
$387$	−15.4419	−	5.01737i	−0.784954	−	0.255047i
$388$	20.1024	+	6.53167i	1.02055	+	0.331595i
$389$	−0.314048	−	0.966540i	−0.0159229	−	0.0490055i	0.942779	−	0.333417i	$-0.108202\pi$
$389$	−0.314048	−	0.966540i	−0.0159229	−	0.0490055i	−0.958702	+	0.284412i	$0.908202\pi$
$390$	−2.06566	−	17.1170i	−0.104599	−	0.866753i
$391$	−1.39143	+	4.28238i	−0.0703676	+	0.216569i
$392$	−13.8333	+	19.0400i	−0.698689	+	0.961663i
$393$		−	5.50968i		−	0.277926i
$394$	43.9811	+	31.9541i	2.21574	+	1.60983i
$395$	−1.94142	+	0.234288i	−0.0976834	+	0.0117883i
$396$	−7.70463	+	5.59774i	−0.387172	+	0.281297i
$397$	10.1423	+	13.9597i	0.509030	+	0.700619i	0.983755	−	0.179515i	$-0.0574528\pi$
$397$	10.1423	+	13.9597i	0.509030	+	0.700619i	−0.474726	+	0.880134i	$0.657453\pi$
$398$	40.8956	−	13.2878i	2.04991	−	0.666057i
$399$	−5.48115			−0.274401
$400$	35.7404	−	8.75371i	1.78702	−	0.437686i
$401$	4.44548			0.221997			0.110998	−	0.993821i	$-0.464595\pi$
$401$	4.44548			0.221997			0.110998	+	0.993821i	$0.464595\pi$
$402$	−2.97661	+	0.967158i	−0.148460	+	0.0482374i
$403$	−10.1726	−	14.0014i	−0.506735	−	0.697461i
$404$	−63.9034	+	46.4285i	−3.17931	+	2.30991i
$405$	5.09425	+	10.9841i	0.253135	+	0.545804i
$406$	−1.98091	−	1.43922i	−0.0983110	−	0.0714271i
$407$			8.41252i			0.416993i
$408$	2.43944	−	3.35760i	0.120770	−	0.166226i
$409$	−2.54968	+	7.84710i	−0.126074	+	0.388014i	−0.994095	−	0.108512i	$-0.965391\pi$
$409$	−2.54968	+	7.84710i	−0.126074	+	0.388014i	0.868022	+	0.496526i	$0.165391\pi$
$410$	−3.06664	+	5.50539i	−0.151450	+	0.271892i
$411$	−0.724471	−	2.22969i	−0.0357355	−	0.109983i
$412$	−62.8439	−	20.4192i	−3.09609	−	1.00598i
$413$	4.62942	+	1.50419i	0.227799	+	0.0740163i
$414$	−9.17143	−	28.2268i	−0.450751	−	1.38727i
$415$	−6.01788	+	2.79099i	−0.295406	+	0.137005i
$416$	−8.58278	+	26.4151i	−0.420805	+	1.29511i
$417$	−6.82598	+	9.39516i	−0.334270	+	0.460083i
$418$		−	9.68136i		−	0.473531i
$419$	−29.5237	−	21.4502i	−1.44232	−	1.04791i	−0.987550	−	0.157304i	$-0.949720\pi$
$419$	−29.5237	−	21.4502i	−1.44232	−	1.04791i	−0.454775	−	0.890607i	$-0.650280\pi$
$420$	−8.73289	+	8.10974i	−0.426121	+	0.395715i
$421$	11.3906	−	8.27577i	0.555145	−	0.403336i	−0.274534	−	0.961577i	$-0.588524\pi$
$421$	11.3906	−	8.27577i	0.555145	−	0.403336i	0.829679	+	0.558241i	$0.188524\pi$
$422$	−12.4296	−	17.1079i	−0.605066	−	0.832801i
$423$	−31.2757	+	10.1621i	−1.52068	+	0.494098i
$424$	46.1555			2.24151
$425$	4.98633	+	0.369478i	0.241873	+	0.0179223i
$426$	−12.1833			−0.590283
$427$	3.32488	−	1.08032i	0.160902	−	0.0522804i
$428$	26.7117	+	36.7655i	1.29116	+	1.77713i
$429$	−1.99592	+	1.45012i	−0.0963640	+	0.0700125i
$430$	6.92094	−	35.2149i	0.333757	−	1.69821i
$431$	9.15967	+	6.65489i	0.441206	+	0.320555i	0.786114	−	0.618082i	$-0.212090\pi$
$431$	9.15967	+	6.65489i	0.441206	+	0.320555i	−0.344908	+	0.938637i	$0.612090\pi$
$432$			26.5524i			1.27751i
$433$	−4.00537	+	5.51292i	−0.192486	+	0.264934i	−0.894341	−	0.447385i	$-0.852355\pi$
$433$	−4.00537	+	5.51292i	−0.192486	+	0.264934i	0.701855	+	0.712319i	$0.252355\pi$
$434$	−5.33410	+	16.4167i	−0.256045	+	0.788025i
$435$	0.516591	+	0.556286i	0.0247687	+	0.0266719i
$436$	−12.7540	−	39.2528i	−0.610806	−	1.87987i
$437$	19.8868	+	6.46160i	0.951313	+	0.309100i
$438$	−17.7532	−	5.76837i	−0.848281	−	0.275623i
$439$	−0.847907	−	2.60959i	−0.0404684	−	0.124549i	0.928781	−	0.370628i	$-0.120858\pi$
$439$	−0.847907	−	2.60959i	−0.0404684	−	0.124549i	−0.969250	+	0.246079i	$0.920858\pi$
$440$	−7.97988	−	8.59306i	−0.380426	−	0.409658i
$441$	2.92465	−	9.00115i	0.139269	−	0.428626i
$442$	−7.01207	+	9.65129i	−0.333530	+	0.459065i
$443$		−	16.9668i		−	0.806116i	−0.915174	−	0.403058i	$-0.867947\pi$
$443$		−	16.9668i		−	0.806116i	0.915174	−	0.403058i	$-0.132053\pi$
$444$	24.3205	+	17.6699i	1.15420	+	0.838576i
$445$	5.98583	−	30.4569i	0.283755	−	1.44379i
$446$	−36.9086	+	26.8156i	−1.74767	+	1.26976i
$447$	−3.40872	−	4.69170i	−0.161227	−	0.221910i
$448$	0.782898	−	0.254379i	0.0369885	−	0.0120183i
$449$	35.6600			1.68290			0.841449	−	0.540337i	$-0.181703\pi$
$449$	35.6600			1.68290			0.841449	+	0.540337i	$0.181703\pi$
$450$	−28.0213	+	17.3484i	−1.32094	+	0.817810i
$451$	0.901753			0.0424619
$452$	78.0115	−	25.3475i	3.66935	−	1.19225i
$453$	−0.300640	−	0.413796i	−0.0141253	−	0.0194418i
$454$	−28.0444	+	20.3755i	−1.31619	+	0.956269i
$455$	13.9843	−	12.9864i	0.655593	−	0.608812i
$456$	−15.5922	−	11.3284i	−0.730173	−	0.530502i
$457$			1.71463i			0.0802070i	0.999196	+	0.0401035i	$0.0127688\pi$
$457$			1.71463i			0.0802070i	−0.999196	+	0.0401035i	$0.987231\pi$
$458$	−15.7969	+	21.7425i	−0.738140	+	1.01596i
$459$	−1.11493	+	3.43139i	−0.0520404	+	0.160164i
$460$	41.2451	−	19.1288i	1.92306	−	0.891886i
$461$	−12.4540	−	38.3294i	−0.580040	−	1.78518i	−0.618339	−	0.785912i	$-0.712194\pi$
$461$	−12.4540	−	38.3294i	−0.580040	−	1.78518i	0.0382990	−	0.999266i	$-0.487806\pi$
$462$	2.34022	+	0.760382i	0.108877	+	0.0353762i
$463$	31.1667	+	10.1267i	1.44844	+	0.470626i	0.924517	−	0.381140i	$-0.124468\pi$
$463$	31.1667	+	10.1267i	1.44844	+	0.470626i	0.523922	+	0.851766i	$0.324468\pi$
$464$	−1.19458	−	3.67654i	−0.0554570	−	0.170679i
$465$	2.60433	−	4.67543i	0.120773	−	0.216818i
$466$	−14.9473	+	46.0030i	−0.692419	+	2.13105i
$467$	11.0798	−	15.2500i	0.512712	−	0.705688i	−0.471662	−	0.881780i	$-0.656346\pi$
$467$	11.0798	−	15.2500i	0.512712	−	0.705688i	0.984374	+	0.176092i	$0.0563456\pi$
$468$		−	54.4960i		−	2.51908i
$469$	−2.80272	−	2.03629i	−0.129417	−	0.0940273i
$470$	−30.5825	−	65.9414i	−1.41067	−	3.04165i
$471$	10.4459	−	7.58938i	0.481321	−	0.349700i
$472$	10.0604	+	13.8470i	0.463069	+	0.637360i
$473$	−4.88405	+	1.58692i	−0.224569	+	0.0729669i
$474$	1.44280			0.0662698
$475$	1.71581	−	23.1558i	0.0787266	−	1.06246i
$476$	8.24617			0.377963
$477$	−17.6528	+	5.73573i	−0.808264	+	0.262621i
$478$	−24.9403	−	34.3274i	−1.14074	−	1.57010i
$479$	14.3400	−	10.4186i	0.655213	−	0.476040i	−0.209830	−	0.977738i	$-0.567291\pi$
$479$	14.3400	−	10.4186i	0.655213	−	0.476040i	0.865043	+	0.501698i	$0.167291\pi$
$480$	−8.52696	+	1.02902i	−0.389201	+	0.0469683i
$481$	−38.9453	−	28.2954i	−1.77575	−	1.29016i
$482$		−	15.7077i		−	0.715466i
$483$	−3.12385	+	4.29961i	−0.142140	+	0.195639i
$484$	14.4185	−	44.3757i	0.655388	−	2.01708i
$485$	−1.25402	−	10.3914i	−0.0569421	−	0.471848i
$486$	−11.2983	−	34.7727i	−0.512503	−	1.57732i
$487$	10.8280	+	3.51823i	0.490664	+	0.159426i	0.543891	−	0.839156i	$-0.316951\pi$
$487$	10.8280	+	3.51823i	0.490664	+	0.159426i	−0.0532268	+	0.998582i	$0.516951\pi$
$488$	11.6911	+	3.79866i	0.529231	+	0.171957i
$489$	1.75248	+	5.39356i	0.0792497	+	0.243905i
$490$	20.5269	+	4.03425i	0.927313	+	0.182249i
$491$	2.36251	−	7.27107i	0.106619	−	0.328139i	−0.883488	−	0.468453i	$-0.844811\pi$
$491$	2.36251	−	7.27107i	0.106619	−	0.328139i	0.990107	+	0.140315i	$0.0448114\pi$
$492$	1.89407	−	2.60696i	0.0853911	−	0.117531i
$493$		−	0.525282i		−	0.0236575i
$494$	44.8193	+	32.5631i	2.01652	+	1.46508i
$495$	4.11987	+	2.29487i	0.185174	+	0.103147i
$496$	−22.0476	+	16.0185i	−0.989968	+	0.719254i
$497$	−7.92666	−	10.9101i	−0.355559	−	0.489385i
$498$	4.65480	−	1.51244i	0.208587	−	0.0677739i
$499$	−17.1205			−0.766419			−0.383210	−	0.923661i	$-0.625181\pi$
$499$	−17.1205			−0.766419			−0.383210	+	0.923661i	$0.625181\pi$
$500$	−31.5269	−	39.4319i	−1.40993	−	1.76345i
$501$	10.8862			0.486361
$502$	−28.3424	+	9.20900i	−1.26498	+	0.411018i
$503$	−2.45705	−	3.38184i	−0.109555	−	0.150789i	0.750719	−	0.660622i	$-0.229707\pi$
$503$	−2.45705	−	3.38184i	−0.109555	−	0.150789i	−0.860273	+	0.509833i	$0.829707\pi$
$504$	−24.4969	+	17.7981i	−1.09118	+	0.792789i
$505$	34.1708	+	19.0340i	1.52058	+	0.847002i
$506$	−7.59439	−	5.51765i	−0.337612	−	0.245289i
$507$		−	5.71516i		−	0.253819i
$508$	−16.5781	+	22.8178i	−0.735535	+	1.01238i
$509$	−3.81293	+	11.7350i	−0.169005	+	0.520144i	−0.999309	−	0.0371668i	$-0.988167\pi$
$509$	−3.81293	+	11.7350i	−0.169005	+	0.520144i	0.830304	+	0.557311i	$0.188167\pi$
$510$	−3.61982	−	0.711419i	−0.160288	−	0.0315022i
$511$	−6.38498	−	19.6510i	−0.282455	−	0.869307i
$512$	−48.2912	−	15.6908i	−2.13419	−	0.693440i
$513$	15.9349	+	5.17757i	0.703544	+	0.228595i
$514$	5.07170	+	15.6091i	0.223703	+	0.688488i
$515$	3.92030	+	32.4853i	0.172749	+	1.43148i
$516$	−5.67081	+	17.4530i	−0.249643	+	0.768324i
$517$	−6.11364	+	8.41471i	−0.268878	+	0.370078i
$518$			48.0132i			2.10958i
$519$	−12.0171	−	8.73093i	−0.527492	−	0.383245i
$520$	66.6213	−	8.03978i	2.92154	−	0.352568i
$521$	−12.0467	+	8.75242i	−0.527775	+	0.383451i	−0.819525	−	0.573044i	$-0.805762\pi$
$521$	−12.0467	+	8.75242i	−0.527775	+	0.383451i	0.291750	+	0.956495i	$0.405762\pi$
$522$	2.03511	+	2.80109i	0.0890743	+	0.122600i
$523$	34.6364	−	11.2540i	1.51454	−	0.492105i	0.570323	−	0.821420i	$-0.306818\pi$
$523$	34.6364	−	11.2540i	1.51454	−	0.492105i	0.944220	+	0.329316i	$0.106818\pi$
$524$	38.4934			1.68159
$525$	5.46256	+	2.23343i	0.238405	+	0.0974748i
$526$	−36.7657			−1.60306
$527$	−3.52185	+	1.14432i	−0.153414	+	0.0498472i
$528$	2.28346	+	3.14291i	0.0993749	+	0.136778i
$529$	−2.20472	+	1.60182i	−0.0958574	+	0.0696445i
$530$	−17.2615	−	37.2189i	−0.749792	−	1.61668i
$531$	−5.56851	−	4.04576i	−0.241653	−	0.175571i
$532$		−	38.2941i		−	1.66026i
$533$	−3.03303	+	4.17461i	−0.131375	+	0.180823i
$534$	−7.07691	+	21.7805i	−0.306248	+	0.942534i
$535$	10.9508	−	19.6595i	0.473446	−	0.849954i
$536$	−3.76428	−	11.5853i	−0.162592	−	0.500408i
$537$	4.24239	+	1.37844i	0.183073	+	0.0594839i
$538$	−24.9392	−	8.10324i	−1.07521	−	0.349355i
$539$	−0.925027	−	2.84694i	−0.0398437	−	0.122626i
$540$	33.0490	−	15.3276i	1.42220	−	0.659595i
$541$	−8.21469	+	25.2822i	−0.353177	+	1.08697i	0.603882	+	0.797074i	$0.293620\pi$
$541$	−8.21469	+	25.2822i	−0.353177	+	1.08697i	−0.957059	+	0.289893i	$0.906380\pi$
$542$	35.2419	−	48.5063i	1.51377	−	2.08352i
$543$		−	1.15017i		−	0.0493586i
$544$	4.80786	+	3.49312i	0.206135	+	0.149766i
$545$	−14.9762	+	13.9075i	−0.641508	+	0.595733i
$546$	−11.3914	+	8.27635i	−0.487508	+	0.354195i
$547$	15.0944	+	20.7756i	0.645389	+	0.888301i	0.998889	−	0.0471334i	$-0.0150086\pi$
$547$	15.0944	+	20.7756i	0.645389	+	0.888301i	−0.353500	+	0.935434i	$0.615009\pi$
$548$	15.5778	−	5.06152i	0.665449	−	0.216217i
$549$	−4.94347			−0.210982
$550$	−3.94491	+	9.64851i	−0.168211	+	0.411414i
$551$	−2.43934			−0.103919
$552$	−17.7728	+	5.77473i	−0.756460	+	0.245789i
$553$	0.938708	+	1.29202i	0.0399179	+	0.0549423i
$554$	−20.3506	+	14.7856i	−0.864613	+	0.628178i
$555$	2.87075	−	14.6068i	0.121856	−	0.620026i
$556$	−65.6393	−	47.6897i	−2.78373	−	2.02250i
$557$			2.47593i			0.104909i	0.998623	+	0.0524543i	$0.0167044\pi$
$557$			2.47593i			0.104909i	−0.998623	+	0.0524543i	$0.983296\pi$
$558$	14.3469	−	19.7469i	0.607354	−	0.835951i
$559$	9.08087	−	27.9480i	0.384080	−	1.18208i
$560$	−20.4493	−	22.0206i	−0.864140	−	0.930541i
$561$	0.163124	+	0.502043i	0.00688709	+	0.0211963i
$562$	−15.9028	−	5.16713i	−0.670819	−	0.217962i
$563$	−5.76190	−	1.87215i	−0.242835	−	0.0789019i	0.185071	−	0.982725i	$-0.440749\pi$
$563$	−5.76190	−	1.87215i	−0.242835	−	0.0789019i	−0.427906	+	0.903823i	$0.640749\pi$
$564$	11.4856	+	35.3489i	0.483630	+	1.48846i
$565$	−27.6400	−	29.7638i	−1.16282	−	1.25217i
$566$	−18.3113	+	56.3563i	−0.769680	+	2.36883i
$567$	5.81221	−	7.99982i	0.244090	−	0.335961i
$568$		−	47.4187i		−	1.98965i
$569$	20.0854	+	14.5929i	0.842023	+	0.611766i	0.922935	−	0.384956i	$-0.125783\pi$
$569$	20.0854	+	14.5929i	0.842023	+	0.611766i	−0.0809120	+	0.996721i	$0.525783\pi$
$570$	−3.30373	+	16.8099i	−0.138378	+	0.704091i
$571$	−37.9340	+	27.5607i	−1.58749	+	1.15338i	−0.680074	+	0.733144i	$0.738052\pi$
$571$	−37.9340	+	27.5607i	−1.58749	+	1.15338i	−0.907415	+	0.420235i	$0.861948\pi$
$572$	−10.1313	−	13.9445i	−0.423610	−	0.583049i
$573$	−10.5820	+	3.43829i	−0.442068	+	0.143637i
$574$	5.14662			0.214816
$575$	−17.1864	−	14.5430i	−0.716721	−	0.606486i
$576$	−1.16402			−0.0485009
$577$	−6.36681	+	2.06870i	−0.265054	+	0.0861213i	−0.438529	−	0.898717i	$-0.644500\pi$
$577$	−6.36681	+	2.06870i	−0.265054	+	0.0861213i	0.173475	+	0.984838i	$0.444500\pi$
$578$	1.50036	+	2.06507i	0.0624068	+	0.0858955i
$579$	−7.53338	+	5.47332i	−0.313077	+	0.227463i
$580$	−3.88650	+	3.60917i	−0.161378	+	0.149863i
$581$	4.38288	+	3.18435i	0.181832	+	0.132109i
$582$			7.72252i			0.320109i
$583$	−3.45069	+	4.74946i	−0.142913	+	0.196703i
$584$	22.4511	−	69.0975i	0.929034	−	2.85927i
$585$	−24.4811	+	11.3539i	−1.01217	+	0.469427i
$586$	23.5321	+	72.4244i	0.972103	+	2.99182i
$587$	33.0033	+	10.7234i	1.36219	+	0.442603i	0.896774	−	0.442488i	$-0.145904\pi$
$587$	33.0033	+	10.7234i	1.36219	+	0.442603i	0.465418	+	0.885091i	$0.345904\pi$
$588$	−10.1734	−	3.30555i	−0.419545	−	0.136318i
$589$	5.31405	+	16.3550i	0.218962	+	0.673895i
$590$	7.40349	−	13.2911i	0.304797	−	0.547187i
$591$	−4.25372	+	13.0916i	−0.174974	+	0.538516i
$592$	−44.5559	+	61.3259i	−1.83124	+	2.52048i
$593$		−	1.59726i		−	0.0655915i	−0.999462	−	0.0327957i	$-0.989559\pi$
$593$		−	1.59726i		−	0.0655915i	0.999462	−	0.0327957i	$-0.0104411\pi$
$594$	−6.08526	−	4.42120i	−0.249681	−	0.181404i
$595$	−1.71804	−	3.70440i	−0.0704328	−	0.151866i
$596$	32.7786	−	23.8150i	1.34266	−	0.975502i
$597$	6.39981	+	8.80858i	0.261927	+	0.360511i
$598$	51.0873	−	16.5993i	2.08911	−	0.678794i
$599$	15.9980			0.653659			0.326830	−	0.945083i	$-0.394020\pi$
$599$	15.9980			0.653659			0.326830	+	0.945083i	$0.394020\pi$
$600$	10.9233	+	17.6434i	0.445941	+	0.720289i
$601$	14.3489			0.585302			0.292651	−	0.956219i	$-0.405463\pi$
$601$	14.3489			0.585302			0.292651	+	0.956219i	$0.405463\pi$
$602$	−27.8750	+	9.05714i	−1.13610	+	0.369141i
$603$	2.87940	+	3.96315i	0.117258	+	0.161392i
$604$	2.89099	−	2.10042i	0.117633	−	0.0854651i
$605$	−22.9387	+	2.76822i	−0.932593	+	0.112544i
$606$	−23.3475	−	16.9630i	−0.948429	−	0.689074i
$607$		−	2.47490i		−	0.100453i	−0.998738	−	0.0502266i	$-0.984006\pi$
$607$		−	2.47490i		−	0.100453i	0.998738	−	0.0502266i	$-0.0159943\pi$
$608$	16.2216	−	22.3271i	0.657871	−	0.905482i
$609$	0.191588	−	0.589646i	0.00776353	−	0.0238937i
$610$	−1.30914	−	10.8481i	−0.0530055	−	0.439227i
$611$	−18.3922	−	56.6055i	−0.744070	−	2.29001i
$612$	−11.0897	−	3.60327i	−0.448275	−	0.145653i
$613$	27.3383	+	8.88277i	1.10419	+	0.358772i	0.803712	−	0.595019i	$-0.202855\pi$
$613$	27.3383	+	8.88277i	1.10419	+	0.358772i	0.300473	+	0.953790i	$0.402855\pi$
$614$	17.0966	+	52.6181i	0.689964	+	2.12349i
$615$	−1.56573	−	0.307720i	−0.0631364	−	0.0124085i
$616$	−2.95949	+	9.10838i	−0.119241	+	0.366987i
$617$	−25.8192	+	35.5371i	−1.03944	+	1.43067i	−0.141826	+	0.989892i	$0.545297\pi$
$617$	−25.8192	+	35.5371i	−1.03944	+	1.43067i	−0.897616	+	0.440777i	$0.854703\pi$
$618$		−	24.1420i		−	0.971134i
$619$	12.1994	+	8.86340i	0.490336	+	0.356250i	0.805314	−	0.592849i	$-0.201997\pi$
$619$	12.1994	+	8.86340i	0.490336	+	0.356250i	−0.314977	+	0.949099i	$0.601997\pi$
$620$	32.6649	+	18.1952i	1.31186	+	0.730736i
$621$	13.1432	−	9.54908i	0.527418	−	0.383191i
$622$	5.61995	+	7.73520i	0.225340	+	0.310153i
$623$	−24.1087	+	7.83340i	−0.965896	+	0.313838i
$624$	−22.2303			−0.889925
$625$	−11.1454	+	22.3781i	−0.445816	+	0.895125i
$626$	−7.45988			−0.298157
$627$	2.33142	−	0.757524i	0.0931079	−	0.0302526i
$628$	53.0233	+	72.9803i	2.11586	+	2.91223i
$629$	−8.33305	+	6.05431i	−0.332260	+	0.241401i
$630$	23.5135	+	13.0976i	0.936802	+	0.521822i
$631$	30.3216	+	22.0299i	1.20708	+	0.876997i	0.994963	−	0.100246i	$-0.0319630\pi$
$631$	30.3216	+	22.0299i	1.20708	+	0.876997i	0.212121	+	0.977243i	$0.431963\pi$
$632$			5.61552i			0.223374i
$633$	3.14729	−	4.33187i	0.125093	−	0.172176i
$634$	13.3709	−	41.1513i	0.531024	−	1.63432i
$635$	13.7043	+	2.69337i	0.543839	+	0.106883i
$636$	6.48273	+	19.9518i	0.257057	+	0.791140i
$637$	16.2911	+	5.29329i	0.645475	+	0.209728i
$638$	1.04149	+	0.338401i	0.0412331	+	0.0133974i
$639$	5.89271	+	18.1359i	0.233112	+	0.717445i
$640$	2.87595	+	23.8314i	0.113682	+	0.942019i
$641$	7.60402	−	23.4028i	0.300341	−	0.924353i	−0.681034	−	0.732251i	$-0.738470\pi$
$641$	7.60402	−	23.4028i	0.300341	−	0.924353i	0.981375	−	0.192102i	$-0.0615304\pi$
$642$	−9.75931	+	13.4325i	−0.385169	+	0.530140i
$643$		−	16.4935i		−	0.650438i	−0.945639	−	0.325219i	$-0.894562\pi$
$643$		−	16.4935i		−	0.650438i	0.945639	−	0.325219i	$-0.105438\pi$
$644$	−30.0392	−	21.8248i	−1.18371	−	0.860016i
$645$	9.02181	−	1.08874i	0.355233	−	0.0428692i
$646$	9.58990	−	6.96747i	0.377310	−	0.274131i
$647$	8.58270	+	11.8131i	0.337421	+	0.464420i	0.943686	−	0.330843i	$-0.107333\pi$
$647$	8.58270	+	11.8131i	0.337421	+	0.464420i	−0.606265	+	0.795263i	$0.707333\pi$
$648$	33.0679	−	10.7444i	1.29903	−	0.422081i
$649$	−2.17702			−0.0854554
$650$	−31.3986	−	50.7153i	−1.23155	−	1.98922i
$651$	−4.37075			−0.171303
$652$	−37.6822	+	12.2437i	−1.47575	+	0.479499i
$653$	−21.5765	−	29.6975i	−0.844353	−	1.16215i	−0.985079	−	0.172104i	$-0.944944\pi$
$653$	−21.5765	−	29.6975i	−0.844353	−	1.16215i	0.140726	−	0.990049i	$-0.455056\pi$
$654$	12.1994	−	8.86338i	0.477034	−	0.346586i
$655$	−8.01987	−	17.2922i	−0.313362	−	0.675664i
$656$	6.57363	+	4.77602i	0.256657	+	0.186472i
$657$			29.2172i			1.13987i
$658$	−34.8927	+	48.0257i	−1.36026	+	1.87224i
$659$	−6.27071	+	19.2993i	−0.244272	+	0.751792i	0.751483	+	0.659752i	$0.229339\pi$
$659$	−6.27071	+	19.2993i	−0.244272	+	0.751792i	−0.995755	+	0.0920402i	$0.970661\pi$
$660$	2.59374	−	4.65642i	0.100961	−	0.181251i
$661$	2.43119	+	7.48245i	0.0945625	+	0.291033i	0.987139	−	0.159862i	$-0.0511048\pi$
$661$	2.43119	+	7.48245i	0.0945625	+	0.291033i	−0.892577	+	0.450895i	$0.851105\pi$
$662$	64.2232	+	20.8674i	2.49611	+	0.811034i
$663$	−2.87284	−	0.933443i	−0.111572	−	0.0362519i
$664$	5.88657	+	18.1170i	0.228443	+	0.703076i
$665$	−17.2027	+	7.97835i	−0.667093	+	0.309387i
$666$	20.9800	−	64.5697i	0.812957	−	2.50203i
$667$	−1.39024	+	1.91350i	−0.0538303	+	0.0740911i
$668$			76.0567i			2.94272i
$669$	−9.34555	−	6.78994i	−0.361320	−	0.262514i
$670$	−7.93435	+	7.36818i	−0.306531	+	0.284658i
$671$	−1.26494	+	0.919033i	−0.0488325	+	0.0354789i
$672$	4.12293	+	5.67472i	0.159045	+	0.218907i
$673$	−11.7227	+	3.80895i	−0.451878	+	0.146824i	−0.526109	−	0.850417i	$-0.676350\pi$
$673$	−11.7227	+	3.80895i	−0.451878	+	0.146824i	0.0742311	+	0.997241i	$0.476350\pi$
$674$	29.7760			1.14693
$675$	−13.7711	−	11.6531i	−0.530051	−	0.448527i
$676$	39.9290			1.53573
$677$	−27.5322	+	8.94574i	−1.05815	+	0.343813i	−0.785861	−	0.618403i	$-0.787780\pi$
$677$	−27.5322	+	8.94574i	−1.05815	+	0.343813i	−0.272286	+	0.962216i	$0.587780\pi$
$678$	17.6152	+	24.2453i	0.676508	+	0.931134i
$679$	−6.91550	+	5.02440i	−0.265392	+	0.192819i
$680$	2.76892	−	14.0887i	0.106183	−	0.540278i
$681$	−7.10108	−	5.15924i	−0.272114	−	0.197702i
$682$		−	7.72006i		−	0.295617i
$683$	−25.8518	+	35.5820i	−0.989192	+	1.36151i	−0.0574647	+	0.998348i	$0.518302\pi$
$683$	−25.8518	+	35.5820i	−0.989192	+	1.36151i	−0.931727	+	0.363159i	$0.881698\pi$
$684$	−16.7331	+	51.4991i	−0.639805	+	1.96912i
$685$	−5.51930	−	5.94340i	−0.210882	−	0.227086i
$686$	−15.3626	−	47.2812i	−0.586546	−	1.80520i
$687$	−6.47197	−	2.10287i	−0.246921	−	0.0802295i
$688$	−44.0089	−	14.2994i	−1.67782	−	0.545158i
$689$	−10.3810	−	31.9495i	−0.395485	−	1.21718i
$690$	11.3034	+	12.1720i	0.430314	+	0.463379i
$691$	0.865113	−	2.66254i	0.0329104	−	0.101288i	−0.933252	−	0.359223i	$-0.883042\pi$
$691$	0.865113	−	2.66254i	0.0329104	−	0.101288i	0.966162	+	0.257935i	$0.0830419\pi$
$692$	60.9986	−	83.9574i	2.31882	−	3.19158i
$693$		−	3.85139i		−	0.146302i
$694$	−12.6396	−	9.18317i	−0.479791	−	0.348588i
$695$	−7.74794	+	39.4228i	−0.293896	+	1.49539i
$696$	1.76369	−	1.28139i	0.0668524	−	0.0485711i
$697$	0.648972	+	0.893234i	0.0245816	+	0.0338336i
$698$	48.7583	−	15.8425i	1.84553	−	0.599649i
$699$	−12.2478			−0.463254
$700$	−15.6039	+	38.1642i	−0.589771	+	1.44247i
$701$	38.5311			1.45530			0.727649	−	0.685949i	$-0.240613\pi$
$701$	38.5311			1.45530			0.727649	+	0.685949i	$0.240613\pi$
$702$	40.9353	−	13.3007i	1.54501	−	0.502003i
$703$	28.1154	+	38.6975i	1.06039	+	1.45951i
$704$	−0.297851	+	0.216401i	−0.0112257	+	0.00815593i
$705$	13.4867	−	12.5244i	0.507940	−	0.471695i
$706$	56.6709	+	41.1738i	2.13284	+	1.54960i
$707$		−	31.9441i		−	1.20138i
$708$	−4.57266	+	6.29373i	−0.171851	+	0.236533i
$709$	2.37238	−	7.30144i	0.0890966	−	0.274211i	−0.896574	−	0.442895i	$-0.853952\pi$
$709$	2.37238	−	7.30144i	0.0890966	−	0.274211i	0.985670	+	0.168683i	$0.0539516\pi$
$710$	−38.2376	+	17.7340i	−1.43503	+	0.665544i
$711$	−0.697840	−	2.14773i	−0.0261710	−	0.0805462i
$712$	−84.7720	−	27.5441i	−3.17697	−	1.03226i
$713$	15.8580	+	5.15258i	0.593887	+	0.192966i
$714$	0.931004	+	2.86534i	0.0348420	+	0.107233i
$715$	−4.15345	+	7.45649i	−0.155330	+	0.278857i
$716$	−9.63045	+	29.6395i	−0.359907	+	1.10768i
$717$	6.31509	−	8.69198i	0.235841	−	0.324608i
$718$		−	78.7891i		−	2.94038i
$719$	−9.26989	−	6.73497i	−0.345708	−	0.251172i	0.401358	−	0.915921i	$-0.368538\pi$
$719$	−9.26989	−	6.73497i	−0.345708	−	0.251172i	−0.747066	+	0.664749i	$0.768538\pi$
$720$	17.8787	+	38.5496i	0.666299	+	1.43666i
$721$	21.6191	−	15.7072i	0.805138	−	0.584967i
$722$	−3.84914	−	5.29789i	−0.143250	−	0.197167i
$723$	3.78266	−	1.22906i	0.140678	−	0.0457092i
$724$	8.03568			0.298644
$725$	2.43106	+	0.993968i	0.0902874	+	0.0369150i
$726$	17.0473			0.632685
$727$	3.13499	−	1.01862i	0.116270	−	0.0377786i	−0.250304	−	0.968167i	$-0.580531\pi$
$727$	3.13499	−	1.01862i	0.116270	−	0.0377786i	0.366574	+	0.930389i	$0.380531\pi$
$728$	−32.2125	−	44.3367i	−1.19387	−	1.64323i
$729$	−5.65230	+	4.10664i	−0.209344	+	0.152098i
$730$	−64.1153	+	7.73736i	−2.37301	+	0.286373i
$731$	−5.08688	−	3.69583i	−0.188145	−	0.136695i
$732$			5.58729i			0.206512i
$733$	−24.6416	+	33.9162i	−0.910157	+	1.25272i	0.0569559	+	0.998377i	$0.481861\pi$
$733$	−24.6416	+	33.9162i	−0.910157	+	1.25272i	−0.967113	+	0.254347i	$0.918139\pi$
$734$	26.5864	−	81.8246i	0.981323	−	3.02020i
$735$	0.634634	+	5.25886i	0.0234088	+	0.193976i
$736$	−8.26904	−	25.4495i	−0.304801	−	0.938081i
$737$	1.47357	+	0.478791i	0.0542796	+	0.0176365i
$738$	−6.92134	−	2.24888i	−0.254778	−	0.0827824i
$739$	−9.48541	−	29.1931i	−0.348926	−	1.07389i	−0.959448	−	0.281886i	$-0.909040\pi$
$739$	−9.48541	−	29.1931i	−0.348926	−	1.07389i	0.610522	−	0.792000i	$-0.290960\pi$
$740$	102.051	+	20.0565i	3.75146	+	0.737291i
$741$	−4.33478	+	13.3411i	−0.159242	+	0.490097i
$742$	−19.6943	+	27.1069i	−0.723000	+	0.995124i
$743$			9.48227i			0.347871i	0.984757	+	0.173935i	$0.0556484\pi$
$743$			9.48227i			0.347871i	−0.984757	+	0.173935i	$0.944352\pi$
$744$	−12.4335	−	9.03345i	−0.455833	−	0.331182i
$745$	−17.5276	−	9.76329i	−0.642160	−	0.357699i
$746$	−31.9002	+	23.1769i	−1.16795	+	0.848566i
$747$	−4.50279	−	6.19756i	−0.164748	−	0.226757i
$748$	−3.50753	+	1.13966i	−0.128248	+	0.0416702i
$749$	−18.3784			−0.671531
$750$	10.1421	−	15.4067i	0.370339	−	0.562574i
$751$	27.7097			1.01114			0.505570	−	0.862785i	$-0.331282\pi$
$751$	27.7097			1.01114			0.505570	+	0.862785i	$0.331282\pi$
$752$	−89.1349	+	28.9617i	−3.25042	+	1.05612i
$753$	−4.43534	−	6.10472i	−0.161633	−	0.222468i
$754$	−5.06965	+	3.68332i	−0.184626	+	0.134139i
$755$	−1.54589	−	0.861097i	−0.0562606	−	0.0313385i
$756$	−24.0699	−	17.4878i	−0.875414	−	0.636025i
$757$		−	0.735992i		−	0.0267501i	−0.999911	−	0.0133750i	$-0.995742\pi$
$757$		−	0.735992i		−	0.0267501i	0.999911	−	0.0133750i	$-0.00425754\pi$
$758$	−46.1963	+	63.5837i	−1.67792	+	2.30946i
$759$	0.734506	−	2.26058i	0.0266609	−	0.0820538i
$760$	−65.4262	−	12.8585i	−2.37326	−	0.466427i
$761$	8.51964	+	26.2207i	0.308837	+	0.950501i	0.978218	+	0.207582i	$0.0665594\pi$
$761$	8.51964	+	26.2207i	0.308837	+	0.950501i	−0.669381	+	0.742919i	$0.733441\pi$
$762$	−9.80031	−	3.18431i	−0.355028	−	0.115356i
$763$	15.8743	+	5.15786i	0.574687	+	0.186727i
$764$	−24.0216	−	73.9309i	−0.869071	−	2.67473i
$765$	0.691793	+	5.73251i	0.0250118	+	0.207259i
$766$	21.2923	−	65.5309i	0.769321	−	2.36773i
$767$	7.32237	−	10.0784i	0.264395	−	0.363909i
$768$		−	18.2934i		−	0.660106i
$769$	−8.13283	−	5.90884i	−0.293277	−	0.213078i	0.431411	−	0.902156i	$-0.358016\pi$
$769$	−8.13283	−	5.90884i	−0.293277	−	0.213078i	−0.724688	+	0.689077i	$0.758016\pi$
$770$	8.45163	−	1.01993i	0.304576	−	0.0367558i
$771$	−3.36207	+	2.44269i	−0.121082	+	0.0879712i

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.42763 + 0.788786i) q^{2} +(-0.379903 - 0.522892i) q^{3} +(3.65319 - 2.65420i) q^{4} +(-1.95346 - 1.08812i) q^{5} +(1.33472 + 0.969728i) q^{6} +1.82616i q^{7} +(-3.77429 + 5.19486i) q^{8} +(0.797961 - 2.45587i) q^{9} +(5.60057 + 1.10071i) q^{10} +(-0.252384 - 0.776759i) q^{11} +(-2.77572 - 0.901885i) q^{12} +(4.44485 + 1.44422i) q^{13} +(-1.44045 - 4.43324i) q^{14} +(0.173153 + 1.43483i) q^{15} +(2.27417 - 6.99917i) q^{16} +(0.587785 - 0.809017i) q^{17} +6.59138i q^{18} +(-3.75697 - 2.72960i) q^{19} +(-10.0244 + 1.20974i) q^{20} +(0.954883 - 0.693763i) q^{21} +(1.22539 + 1.68661i) q^{22} +(-4.28238 + 1.39143i) q^{23} +4.15022 q^{24} +(2.63198 + 4.25120i) q^{25} -11.9297 q^{26} +(-3.43139 + 1.11493i) q^{27} +(4.84698 + 6.67129i) q^{28} +(0.424962 - 0.308753i) q^{29} +(-1.55213 - 3.34666i) q^{30} +(-2.99586 - 2.17662i) q^{31} +5.94285i q^{32} +(-0.310280 + 0.427063i) q^{33} +(-0.788786 + 2.42763i) q^{34} +(1.98708 - 3.56732i) q^{35} +(-3.60327 - 11.0897i) q^{36} +(-9.79608 - 3.18294i) q^{37} +(11.2736 + 3.66302i) q^{38} +(-0.933443 - 2.87284i) q^{39} +(13.0256 - 6.04104i) q^{40} +(-0.341185 + 1.05006i) q^{41} +(-1.77088 + 2.43740i) q^{42} -6.28773i q^{43} +(-2.98368 - 2.16777i) q^{44} +(-4.23107 + 3.92916i) q^{45} +(9.29850 - 6.75576i) q^{46} +(-7.48548 - 10.3029i) q^{47} +(-4.52378 + 1.46986i) q^{48} +3.66515 q^{49} +(-9.74276 - 8.24429i) q^{50} -0.646330 q^{51} +(20.0711 - 6.52150i) q^{52} +(-4.22499 - 5.81519i) q^{53} +(7.45073 - 5.41327i) q^{54} +(-0.352188 + 1.79199i) q^{55} +(-9.48663 - 6.89244i) q^{56} +3.00147i q^{57} +(-0.788113 + 1.08474i) q^{58} +(0.823691 - 2.53506i) q^{59} +(4.44088 + 4.78211i) q^{60} +(-0.591581 - 1.82070i) q^{61} +(8.98974 + 2.92094i) q^{62} +(4.48481 + 1.45720i) q^{63} +(-0.139298 - 0.428714i) q^{64} +(-7.11133 - 7.65777i) q^{65} +(0.416384 - 1.28150i) q^{66} +(-1.11507 + 1.53476i) q^{67} -4.51559i q^{68} +(2.35446 + 1.71061i) q^{69} +(-2.01006 + 10.2275i) q^{70} +(-5.97436 + 4.34062i) q^{71} +(9.74618 + 13.4145i) q^{72} +(-10.7608 + 3.49641i) q^{73} +26.2920 q^{74} +(1.22302 - 2.99129i) q^{75} -20.9698 q^{76} +(1.41848 - 0.460893i) q^{77} +(4.53212 + 6.23792i) q^{78} +(0.707508 - 0.514035i) q^{79} +(-12.0584 + 11.1980i) q^{80} +(-4.38068 - 3.18275i) q^{81} -2.81828i q^{82} +(1.74374 - 2.40005i) q^{83} +(1.64698 - 5.06889i) q^{84} +(-2.02852 + 0.940796i) q^{85} +(4.95967 + 15.2643i) q^{86} +(-0.322889 - 0.104913i) q^{87} +(4.98773 + 1.62061i) q^{88} +(4.28955 + 13.2019i) q^{89} +(7.17223 - 12.8760i) q^{90} +(-2.63737 + 8.11700i) q^{91} +(-11.9512 + 16.4494i) q^{92} +2.39342i q^{93} +(26.2988 + 19.1072i) q^{94} +(4.36893 + 9.42018i) q^{95} +(3.10747 - 2.25771i) q^{96} +(2.75135 + 3.78691i) q^{97} +(-8.89765 + 2.89102i) q^{98} -2.10901 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

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Database

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