LMFDB - Embedded newform 336.2.s.c.155.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.11
Character	$\chi$	$=$	336.155
Dual form			336.2.s.c.323.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.153777 - 1.40583i) q^{2} +(1.26429 + 1.18388i) q^{3} +(-1.95271 - 0.432367i) q^{4} +(-2.84277 + 2.84277i) q^{5} +(1.85875 - 1.59532i) q^{6} -1.00000 q^{7} +(-0.908115 + 2.67868i) q^{8} +(0.196841 + 2.99354i) q^{9} +O(q^{10})$	\(q+(0.153777 - 1.40583i) q^{2} +(1.26429 + 1.18388i) q^{3} +(-1.95271 - 0.432367i) q^{4} +(-2.84277 + 2.84277i) q^{5} +(1.85875 - 1.59532i) q^{6} -1.00000 q^{7} +(-0.908115 + 2.67868i) q^{8} +(0.196841 + 2.99354i) q^{9} +(3.55929 + 4.43360i) q^{10} +(-3.31805 - 3.31805i) q^{11} +(-1.95691 - 2.85841i) q^{12} +(-2.31290 + 2.31290i) q^{13} +(-0.153777 + 1.40583i) q^{14} +(-6.95958 + 0.228568i) q^{15} +(3.62612 + 1.68857i) q^{16} +0.814979i q^{17} +(4.23867 + 0.183612i) q^{18} +(4.39281 + 4.39281i) q^{19} +(6.78021 - 4.32197i) q^{20} +(-1.26429 - 1.18388i) q^{21} +(-5.17485 + 4.15437i) q^{22} +3.30328i q^{23} +(-4.31936 + 2.31152i) q^{24} -11.1627i q^{25} +(2.89588 + 3.60722i) q^{26} +(-3.29513 + 4.01772i) q^{27} +(1.95271 + 0.432367i) q^{28} +(3.25705 + 3.25705i) q^{29} +(-0.748894 + 9.81913i) q^{30} -3.89472i q^{31} +(2.93145 - 4.83803i) q^{32} +(-0.266782 - 8.12315i) q^{33} +(1.14572 + 0.125325i) q^{34} +(2.84277 - 2.84277i) q^{35} +(0.909934 - 5.93060i) q^{36} +(-3.65469 - 3.65469i) q^{37} +(6.85105 - 5.50002i) q^{38} +(-5.66238 + 0.185965i) q^{39} +(-5.03331 - 10.1964i) q^{40} +3.20387 q^{41} +(-1.85875 + 1.59532i) q^{42} +(1.63867 - 1.63867i) q^{43} +(5.04456 + 7.91380i) q^{44} +(-9.06950 - 7.95036i) q^{45} +(4.64384 + 0.507968i) q^{46} +6.70608 q^{47} +(2.58538 + 6.42774i) q^{48} +1.00000 q^{49} +(-15.6928 - 1.71656i) q^{50} +(-0.964840 + 1.03037i) q^{51} +(5.51645 - 3.51640i) q^{52} +(-7.69839 + 7.69839i) q^{53} +(5.14151 + 5.25022i) q^{54} +18.8649 q^{55} +(0.908115 - 2.67868i) q^{56} +(0.353196 + 10.7543i) q^{57} +(5.07970 - 4.07799i) q^{58} +(7.31843 + 7.31843i) q^{59} +(13.6888 + 2.56277i) q^{60} +(-5.54897 + 5.54897i) q^{61} +(-5.47531 - 0.598917i) q^{62} +(-0.196841 - 2.99354i) q^{63} +(-6.35066 - 4.86510i) q^{64} -13.1501i q^{65} +(-11.4608 - 0.874102i) q^{66} +(-0.0553126 - 0.0553126i) q^{67} +(0.352370 - 1.59141i) q^{68} +(-3.91070 + 4.17629i) q^{69} +(-3.55929 - 4.43360i) q^{70} -6.50772i q^{71} +(-8.19748 - 2.19120i) q^{72} -6.05260i q^{73} +(-5.69987 + 4.57585i) q^{74} +(13.2153 - 14.1128i) q^{75} +(-6.67855 - 10.4772i) q^{76} +(3.31805 + 3.31805i) q^{77} +(-0.609308 + 7.98893i) q^{78} +15.1804i q^{79} +(-15.1084 + 5.50799i) q^{80} +(-8.92251 + 1.17850i) q^{81} +(0.492680 - 4.50409i) q^{82} +(-4.25907 + 4.25907i) q^{83} +(1.95691 + 2.85841i) q^{84} +(-2.31680 - 2.31680i) q^{85} +(-2.05170 - 2.55567i) q^{86} +(0.261877 + 7.97380i) q^{87} +(11.9012 - 5.87483i) q^{88} +2.31624 q^{89} +(-12.5715 + 11.5276i) q^{90} +(2.31290 - 2.31290i) q^{91} +(1.42823 - 6.45033i) q^{92} +(4.61089 - 4.92404i) q^{93} +(1.03124 - 9.42759i) q^{94} -24.9755 q^{95} +(9.43387 - 2.64616i) q^{96} -15.2402 q^{97} +(0.153777 - 1.40583i) q^{98} +(9.27958 - 10.5858i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

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 $

$2$	0.153777	−	1.40583i	0.108737	−	0.994071i
$2$	0.153777	−	1.40583i	0.108737	−	0.994071i
$3$	1.26429	+	1.18388i	0.729936	+	0.683515i
$3$	1.26429	+	1.18388i	0.729936	+	0.683515i
$4$	−1.95271	−	0.432367i	−0.976353	−	0.216184i
$5$	−2.84277	+	2.84277i	−1.27133	+	1.27133i	−0.325932	+	0.945393i	$0.605678\pi$
$5$	−2.84277	+	2.84277i	−1.27133	+	1.27133i	−0.945393	+	0.325932i	$0.894322\pi$
$6$	1.85875	−	1.59532i	0.758833	−	0.651285i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−0.908115	+	2.67868i	−0.321067	+	0.947056i
$9$	0.196841	+	2.99354i	0.0656136	+	0.997845i
$10$	3.55929	+	4.43360i	1.12555	+	1.40203i
$11$	−3.31805	−	3.31805i	−1.00043	−	1.00043i	−1.00000		0.000430454i	$-0.999863\pi$
$11$	−3.31805	−	3.31805i	−1.00043	−	1.00043i	−0.000430454	−	1.00000i	$-0.500137\pi$
$12$	−1.95691	−	2.85841i	−0.564910	−	0.825152i
$13$	−2.31290	+	2.31290i	−0.641484	+	0.641484i	−0.950920	−	0.309436i	$-0.899860\pi$
$13$	−2.31290	+	2.31290i	−0.641484	+	0.641484i	0.309436	+	0.950920i	$0.399860\pi$
$14$	−0.153777	+	1.40583i	−0.0410986	+	0.375723i
$15$	−6.95958	+	0.228568i	−1.79696	+	0.0590160i
$16$	3.62612	+	1.68857i	0.906529	+	0.422143i
$17$			0.814979i			0.197661i	0.995104	+	0.0988307i	$0.0315102\pi$
$17$			0.814979i			0.197661i	−0.995104	+	0.0988307i	$0.968490\pi$
$18$	4.23867	+	0.183612i	0.999063	+	0.0432777i
$19$	4.39281	+	4.39281i	1.00778	+	1.00778i	0.999970	+	0.00780997i	$0.00248601\pi$
$19$	4.39281	+	4.39281i	1.00778	+	1.00778i	0.00780997	+	0.999970i	$0.497514\pi$
$20$	6.78021	−	4.32197i	1.51610	−	0.966422i
$21$	−1.26429	−	1.18388i	−0.275890	−	0.258345i
$22$	−5.17485	+	4.15437i	−1.10328	+	0.885715i
$23$			3.30328i			0.688782i	0.938826	+	0.344391i	$0.111915\pi$
$23$			3.30328i			0.688782i	−0.938826	+	0.344391i	$0.888085\pi$
$24$	−4.31936	+	2.31152i	−0.881686	+	0.471837i
$25$		−	11.1627i		−	2.23254i
$26$	2.89588	+	3.60722i	0.567928	+	0.707433i
$27$	−3.29513	+	4.01772i	−0.634149	+	0.773211i
$28$	1.95271	+	0.432367i	0.369027	+	0.0817097i
$29$	3.25705	+	3.25705i	0.604818	+	0.604818i	0.941587	−	0.336769i	$-0.109334\pi$
$29$	3.25705	+	3.25705i	0.604818	+	0.604818i	−0.336769	+	0.941587i	$0.609334\pi$
$30$	−0.748894	+	9.81913i	−0.136729	+	1.79272i
$31$		−	3.89472i		−	0.699513i	−0.936841	−	0.349756i	$-0.886264\pi$
$31$		−	3.89472i		−	0.699513i	0.936841	−	0.349756i	$-0.113736\pi$
$32$	2.93145	−	4.83803i	0.518213	−	0.855252i
$33$	−0.266782	−	8.12315i	−0.0464408	−	1.41406i
$34$	1.14572	+	0.125325i	0.196489	+	0.0214930i
$35$	2.84277	−	2.84277i	0.480516	−	0.480516i
$36$	0.909934	−	5.93060i	0.151656	−	0.988433i
$37$	−3.65469	−	3.65469i	−0.600827	−	0.600827i	0.339705	−	0.940532i	$-0.389673\pi$
$37$	−3.65469	−	3.65469i	−0.600827	−	0.600827i	−0.940532	+	0.339705i	$0.889673\pi$
$38$	6.85105	−	5.50002i	1.11139	−	0.892221i
$39$	−5.66238	+	0.185965i	−0.906707	+	0.0297783i
$40$	−5.03331	−	10.1964i	−0.795836	−	1.61220i
$41$	3.20387			0.500360			0.250180	−	0.968199i	$-0.419510\pi$
$41$	3.20387			0.500360			0.250180	+	0.968199i	$0.419510\pi$
$42$	−1.85875	+	1.59532i	−0.286812	+	0.246163i
$43$	1.63867	−	1.63867i	0.249895	−	0.249895i	−0.571033	−	0.820927i	$-0.693457\pi$
$43$	1.63867	−	1.63867i	0.249895	−	0.249895i	0.820927	+	0.571033i	$0.193457\pi$
$44$	5.04456	+	7.91380i	0.760496	+	1.19305i
$45$	−9.06950	−	7.95036i	−1.35200	−	1.18517i
$46$	4.64384	+	0.507968i	0.684697	+	0.0748957i
$47$	6.70608			0.978182			0.489091	−	0.872233i	$-0.337329\pi$
$47$	6.70608			0.978182			0.489091	+	0.872233i	$0.337329\pi$
$48$	2.58538	+	6.42774i	0.373167	+	0.927764i
$49$	1.00000			0.142857
$50$	−15.6928	−	1.71656i	−2.21930	−	0.242758i
$51$	−0.964840	+	1.03037i	−0.135105	+	0.144280i
$52$	5.51645	−	3.51640i	0.764993	−	0.487636i
$53$	−7.69839	+	7.69839i	−1.05746	+	1.05746i	−0.0592097	+	0.998246i	$0.518858\pi$
$53$	−7.69839	+	7.69839i	−1.05746	+	1.05746i	−0.998246	+	0.0592097i	$0.981142\pi$
$54$	5.14151	+	5.25022i	0.699671	+	0.714465i
$55$	18.8649			2.54374
$56$	0.908115	−	2.67868i	0.121352	−	0.357954i
$57$	0.353196	+	10.7543i	0.0467820	+	1.42445i
$58$	5.07970	−	4.07799i	0.666998	−	0.535466i
$59$	7.31843	+	7.31843i	0.952778	+	0.952778i	0.998934	−	0.0461561i	$-0.0146972\pi$
$59$	7.31843	+	7.31843i	0.952778	+	0.952778i	−0.0461561	+	0.998934i	$0.514697\pi$
$60$	13.6888	+	2.56277i	1.76722	+	0.330852i
$61$	−5.54897	+	5.54897i	−0.710473	+	0.710473i	−0.966634	−	0.256161i	$-0.917542\pi$
$61$	−5.54897	+	5.54897i	−0.710473	+	0.710473i	0.256161	+	0.966634i	$0.417542\pi$
$62$	−5.47531	−	0.598917i	−0.695365	−	0.0760626i
$63$	−0.196841	−	2.99354i	−0.0247996	−	0.377150i
$64$	−6.35066	−	4.86510i	−0.793832	−	0.608137i
$65$		−	13.1501i		−	1.63107i
$66$	−11.4608	−	0.874102i	−1.41073	−	0.107595i
$67$	−0.0553126	−	0.0553126i	−0.00675751	−	0.00675751i	0.703720	−	0.710477i	$-0.251521\pi$
$67$	−0.0553126	−	0.0553126i	−0.00675751	−	0.00675751i	−0.710477	+	0.703720i	$0.751521\pi$
$68$	0.352370	−	1.59141i	0.0427312	−	0.192987i
$69$	−3.91070	+	4.17629i	−0.470793	+	0.502767i
$70$	−3.55929	−	4.43360i	−0.425417	−	0.529916i
$71$		−	6.50772i		−	0.772325i	−0.922431	−	0.386162i	$-0.873800\pi$
$71$		−	6.50772i		−	0.772325i	0.922431	−	0.386162i	$-0.126200\pi$
$72$	−8.19748	−	2.19120i	−0.966082	−	0.258235i
$73$		−	6.05260i		−	0.708403i	−0.935169	−	0.354201i	$-0.884753\pi$
$73$		−	6.05260i		−	0.708403i	0.935169	−	0.354201i	$-0.115247\pi$
$74$	−5.69987	+	4.57585i	−0.662596	+	0.531932i
$75$	13.2153	−	14.1128i	1.52597	−	1.62961i
$76$	−6.67855	−	10.4772i	−0.766083	−	1.20181i
$77$	3.31805	+	3.31805i	0.378127	+	0.378127i
$78$	−0.609308	+	7.98893i	−0.0689905	+	0.904569i
$79$			15.1804i			1.70792i	0.520335	+	0.853962i	$0.325807\pi$
$79$			15.1804i			1.70792i	−0.520335	+	0.853962i	$0.674193\pi$
$80$	−15.1084	+	5.50799i	−1.68917	+	0.615813i
$81$	−8.92251	+	1.17850i	−0.991390	+	0.130944i
$82$	0.492680	−	4.50409i	0.0544074	−	0.497393i
$83$	−4.25907	+	4.25907i	−0.467494	+	0.467494i	−0.901102	−	0.433608i	$-0.857240\pi$
$83$	−4.25907	+	4.25907i	−0.467494	+	0.467494i	0.433608	+	0.901102i	$0.357240\pi$
$84$	1.95691	+	2.85841i	0.213516	+	0.311878i
$85$	−2.31680	−	2.31680i	−0.251292	−	0.251292i
$86$	−2.05170	−	2.55567i	−0.221240	−	0.275585i
$87$	0.261877	+	7.97380i	0.0280762	+	0.854881i
$88$	11.9012	−	5.87483i	1.26867	−	0.626259i
$89$	2.31624			0.245521			0.122761	−	0.992436i	$-0.460825\pi$
$89$	2.31624			0.245521			0.122761	+	0.992436i	$0.460825\pi$
$90$	−12.5715	+	11.5276i	−1.32515	+	1.21511i
$91$	2.31290	−	2.31290i	0.242458	−	0.242458i
$92$	1.42823	−	6.45033i	0.148903	−	0.672494i
$93$	4.61089	−	4.92404i	0.478128	−	0.510599i
$94$	1.03124	−	9.42759i	0.106364	−	0.972382i
$95$	−24.9755			−2.56243
$96$	9.43387	−	2.64616i	0.962840	−	0.270073i
$97$	−15.2402			−1.54741			−0.773703	−	0.633549i	$-0.781598\pi$
$97$	−15.2402			−1.54741			−0.773703	+	0.633549i	$0.781598\pi$
$98$	0.153777	−	1.40583i	0.0155338	−	0.142010i
$99$	9.27958	−	10.5858i	0.932633	−	1.06392i
$100$	−4.82638	+	21.7974i	−0.482638	+	2.17974i
$101$	−1.01023	+	1.01023i	−0.100522	+	0.100522i	−0.755579	−	0.655058i	$-0.772644\pi$
$101$	−1.01023	+	1.01023i	−0.100522	+	0.100522i	0.655058	+	0.755579i	$0.272644\pi$
$102$	1.30015	+	1.51485i	0.128734	+	0.149992i
$103$	5.54554			0.546418			0.273209	−	0.961955i	$-0.411915\pi$
$103$	5.54554			0.546418			0.273209	+	0.961955i	$0.411915\pi$
$104$	−4.09515	−	8.29591i	−0.401562	−	0.813481i
$105$	6.95958	−	0.228568i	0.679186	−	0.0223060i
$106$	9.63878	+	12.0064i	0.936201	+	1.16617i
$107$	6.92329	+	6.92329i	0.669300	+	0.669300i	0.957554	−	0.288254i	$-0.0930748\pi$
$107$	6.92329	+	6.92329i	0.669300	+	0.669300i	−0.288254	+	0.957554i	$0.593075\pi$
$108$	8.17156	−	6.42072i	0.786308	−	0.617834i
$109$	1.69753	−	1.69753i	0.162594	−	0.162594i	−0.621121	−	0.783715i	$-0.713322\pi$
$109$	1.69753	−	1.69753i	0.162594	−	0.162594i	0.783715	+	0.621121i	$0.213322\pi$
$110$	2.90098	−	26.5208i	0.276598	−	2.52866i
$111$	−0.293849	−	8.94729i	−0.0278909	−	0.849239i
$112$	−3.62612	−	1.68857i	−0.342636	−	0.159555i
$113$		−	3.05425i		−	0.287320i	−0.989627	−	0.143660i	$-0.954113\pi$
$113$		−	3.05425i		−	0.287320i	0.989627	−	0.143660i	$-0.0458871\pi$
$114$	15.1731	+	1.15723i	1.42109	+	0.108385i
$115$	−9.39046	−	9.39046i	−0.875665	−	0.875665i
$116$	−4.95181	−	7.76829i	−0.459764	−	0.721268i
$117$	−7.37904	−	6.46849i	−0.682192	−	0.598012i
$118$	11.4139	−	9.16305i	1.05073	−	0.843527i
$119$		−	0.814979i		−	0.0747090i
$120$	5.70784	−	18.8501i	0.521052	−	1.72077i
$121$			11.0189i			1.00172i
$122$	6.94760	+	8.65420i	0.629006	+	0.783515i
$123$	4.05061	+	3.79301i	0.365231	+	0.342004i
$124$	−1.68395	+	7.60524i	−0.151223	+	0.682971i
$125$	17.5191	+	17.5191i	1.56695	+	1.56695i
$126$	−4.23867	−	0.183612i	−0.377610	−	0.0163574i
$127$			1.00904i			0.0895376i	0.998997	+	0.0447688i	$0.0142551\pi$
$127$			1.00904i			0.0895376i	−0.998997	+	0.0447688i	$0.985745\pi$
$128$	−7.81607	+	8.17979i	−0.690850	+	0.722998i
$129$	4.01174	−	0.131754i	0.353214	−	0.0116003i
$130$	−18.4868	−	2.02218i	−1.62140	−	0.177357i
$131$	−1.25508	+	1.25508i	−0.109657	+	0.109657i	−0.759806	−	0.650150i	$-0.774706\pi$
$131$	−1.25508	+	1.25508i	−0.109657	+	0.109657i	0.650150	+	0.759806i	$0.274706\pi$
$132$	−2.99124	+	15.9775i	−0.260354	+	1.39066i
$133$	−4.39281	−	4.39281i	−0.380905	−	0.380905i
$134$	−0.0862659	+	0.0692543i	−0.00745224	+	0.00598266i
$135$	−2.05416	−	20.7888i	−0.176794	−	1.78921i
$136$	−2.18307	−	0.740094i	−0.187197	−	0.0634626i
$137$	−5.70652			−0.487540			−0.243770	−	0.969833i	$-0.578384\pi$
$137$	−5.70652			−0.487540			−0.243770	+	0.969833i	$0.578384\pi$
$138$	5.26978	+	6.13999i	0.448593	+	0.522670i
$139$	−6.78446	+	6.78446i	−0.575450	+	0.575450i	−0.933646	−	0.358196i	$-0.883392\pi$
$139$	−6.78446	+	6.78446i	−0.575450	+	0.575450i	0.358196	+	0.933646i	$0.383392\pi$
$140$	−6.78021	+	4.32197i	−0.573033	+	0.365273i
$141$	8.47840	+	7.93921i	0.714010	+	0.668602i
$142$	−9.14874	−	1.00074i	−0.767745	−	0.0839799i
$143$	15.3487			1.28352
$144$	−4.34103	+	11.1873i	−0.361753	+	0.932274i
$145$	−18.5181			−1.53784
$146$	−8.50891	−	0.930749i	−0.704203	−	0.0770293i
$147$	1.26429	+	1.18388i	0.104277	+	0.0976450i
$148$	5.55636	+	8.71669i	0.456730	+	0.716508i
$149$	4.36672	−	4.36672i	0.357736	−	0.357736i	−0.505242	−	0.862978i	$-0.668597\pi$
$149$	4.36672	−	4.36672i	0.357736	−	0.357736i	0.862978	+	0.505242i	$0.168597\pi$
$150$	−17.8080	−	20.7487i	−1.45402	−	1.69412i
$151$	7.01244			0.570664			0.285332	−	0.958429i	$-0.407896\pi$
$151$	7.01244			0.570664			0.285332	+	0.958429i	$0.407896\pi$
$152$	−15.7561	+	7.77776i	−1.27799	+	0.630859i
$153$	−2.43967	+	0.160421i	−0.197235	+	0.0129693i
$154$	5.17485	−	4.15437i	0.417001	−	0.334769i
$155$	11.0718	+	11.0718i	0.889308	+	0.889308i
$156$	11.1374	+	2.08509i	0.891703	+	0.166941i
$157$	10.3514	−	10.3514i	0.826129	−	0.826129i	−0.160850	−	0.986979i	$-0.551423\pi$
$157$	10.3514	−	10.3514i	0.826129	−	0.826129i	0.986979	+	0.160850i	$0.0514235\pi$
$158$	21.3410	+	2.33439i	1.69780	+	0.185714i
$159$	−18.8470	+	0.618976i	−1.49466	+	0.0490880i
$160$	5.41997	+	22.0869i	0.428486	+	1.74612i
$161$		−	3.30328i		−	0.260335i
$162$	0.284695	+	12.7247i	0.0223678	+	0.999750i
$163$	11.2691	+	11.2691i	0.882661	+	0.882661i	0.993804	−	0.111143i	$-0.0354512\pi$
$163$	11.2691	+	11.2691i	0.882661	+	0.882661i	−0.111143	+	0.993804i	$0.535451\pi$
$164$	−6.25621	−	1.38525i	−0.488528	−	0.108170i
$165$	23.8507	+	22.3339i	1.85677	+	1.73869i
$166$	5.33258	+	6.64247i	0.413888	+	0.515556i
$167$		−	4.10358i		−	0.317545i	−0.987315	−	0.158772i	$-0.949246\pi$
$167$		−	4.10358i		−	0.317545i	0.987315	−	0.158772i	$-0.0507536\pi$
$168$	4.31936	−	2.31152i	0.333246	−	0.178337i
$169$			2.30095i			0.176996i
$170$	−3.61329	+	2.90075i	−0.277127	+	0.222477i
$171$	−12.2853	+	14.0147i	−0.939484	+	1.07173i
$172$	−3.90834	+	2.49133i	−0.298008	+	0.189962i
$173$	−0.181676	−	0.181676i	−0.0138126	−	0.0138126i	0.700167	−	0.713979i	$-0.253109\pi$
$173$	−0.181676	−	0.181676i	−0.0138126	−	0.0138126i	−0.713979	+	0.700167i	$0.753109\pi$
$174$	11.2501	+	0.858031i	0.852865	+	0.0650471i
$175$			11.1627i			0.843819i
$176$	−6.42888	−	17.6344i	−0.484595	−	1.32924i
$177$	0.588426	+	17.9168i	0.0442288	+	1.34671i
$178$	0.356184	−	3.25624i	0.0266971	−	0.244065i
$179$	8.19489	−	8.19489i	0.612515	−	0.612515i	−0.331086	−	0.943601i	$-0.607415\pi$
$179$	8.19489	−	8.19489i	0.612515	−	0.612515i	0.943601	+	0.331086i	$0.107415\pi$
$180$	14.2726	+	19.4461i	1.06382	+	1.44942i
$181$	14.1393	+	14.1393i	1.05097	+	1.05097i	0.998630	+	0.0523357i	$0.0166666\pi$
$181$	14.1393	+	14.1393i	1.05097	+	1.05097i	0.0523357	+	0.998630i	$0.483333\pi$
$182$	−2.89588	−	3.60722i	−0.214657	−	0.267385i
$183$	−13.5848	+	0.446156i	−1.00422	+	0.0329808i
$184$	−8.84843	−	2.99976i	−0.652315	−	0.221145i
$185$	20.7789			1.52769
$186$	−6.21331	−	7.23933i	−0.455582	−	0.530813i
$187$	2.70414	−	2.70414i	0.197746	−	0.197746i
$188$	−13.0950	−	2.89949i	−0.955050	−	0.211467i
$189$	3.29513	−	4.01772i	0.239686	−	0.292246i
$190$	−3.84065	+	35.1112i	−0.278630	+	2.54724i
$191$	8.99690			0.650993			0.325497	−	0.945543i	$-0.394469\pi$
$191$	8.99690			0.650993			0.325497	+	0.945543i	$0.394469\pi$
$192$	−2.26934	−	13.6693i	−0.163776	−	0.986498i
$193$	24.9613			1.79676			0.898378	−	0.439222i	$-0.144746\pi$
$193$	24.9613			1.79676			0.898378	+	0.439222i	$0.144746\pi$
$194$	−2.34359	+	21.4251i	−0.168260	+	1.53823i
$195$	15.5682	−	16.6255i	1.11486	−	1.19058i
$196$	−1.95271	−	0.432367i	−0.139479	−	0.0308834i
$197$	2.68965	−	2.68965i	0.191630	−	0.191630i	−0.604770	−	0.796400i	$-0.706735\pi$
$197$	2.68965	−	2.68965i	0.191630	−	0.191630i	0.796400	+	0.604770i	$0.206735\pi$
$198$	−13.4549	−	14.6733i	−0.956197	−	1.04279i
$199$	−5.82077			−0.412624			−0.206312	−	0.978486i	$-0.566146\pi$
$199$	−5.82077			−0.412624			−0.206312	+	0.978486i	$0.566146\pi$
$200$	29.9012	+	10.1370i	2.11434	+	0.716794i
$201$	−0.00444732	−	0.135415i	−0.000313690	−	0.00955142i
$202$	1.26486	+	1.57556i	0.0889951	+	0.110856i
$203$	−3.25705	−	3.25705i	−0.228600	−	0.228600i
$204$	2.32955	−	1.59484i	0.163101	−	0.111661i
$205$	−9.10786	+	9.10786i	−0.636120	+	0.636120i
$206$	0.852775	−	7.79608i	0.0594156	−	0.543178i
$207$	−9.88849	+	0.650221i	−0.687297	+	0.0451935i
$208$	−12.2924	+	4.48136i	−0.852322	+	0.310726i
$209$		−	29.1511i		−	2.01643i
$210$	0.748894	−	9.81913i	0.0516786	−	0.677584i
$211$	−5.04692	−	5.04692i	−0.347444	−	0.347444i	0.511712	−	0.859157i	$-0.329011\pi$
$211$	−5.04692	−	5.04692i	−0.347444	−	0.347444i	−0.859157	+	0.511712i	$0.829011\pi$
$212$	18.3612	−	11.7042i	1.26105	−	0.803845i
$213$	7.70439	−	8.22763i	0.527896	−	0.563748i
$214$	10.7976	−	8.66832i	0.738109	−	0.592554i
$215$			9.31671i			0.635394i
$216$	−7.76984	−	12.4752i	−0.528670	−	0.848827i
$217$			3.89472i			0.264391i
$218$	−2.12540	−	2.64748i	−0.143950	−	0.179310i
$219$	7.16557	−	7.65222i	0.484204	−	0.517089i
$220$	−36.8376	−	8.15657i	−2.48359	−	0.549916i
$221$	−1.88497	−	1.88497i	−0.126797	−	0.126797i
$222$	−12.6235	−	0.962784i	−0.847237	−	0.0646179i
$223$			2.61492i			0.175108i	0.996160	+	0.0875539i	$0.0279050\pi$
$223$			2.61492i			0.175108i	−0.996160	+	0.0875539i	$0.972095\pi$
$224$	−2.93145	+	4.83803i	−0.195866	+	0.323255i
$225$	33.4159	−	2.19727i	2.22772	−	0.146485i
$226$	−4.29375	−	0.469672i	−0.285616	−	0.0312421i
$227$	−1.46915	+	1.46915i	−0.0975109	+	0.0975109i	−0.754179	−	0.656668i	$-0.771965\pi$
$227$	−1.46915	+	1.46915i	−0.0975109	+	0.0975109i	0.656668	+	0.754179i	$0.271965\pi$
$228$	3.96014	−	21.1528i	0.262266	−	1.40088i
$229$	−14.8529	−	14.8529i	−0.981505	−	0.981505i	0.0183274	−	0.999832i	$-0.494166\pi$
$229$	−14.8529	−	14.8529i	−0.981505	−	0.981505i	−0.999832	+	0.0183274i	$0.994166\pi$
$230$	−14.6454	+	11.7573i	−0.965690	+	0.775256i
$231$	0.266782	+	8.12315i	0.0175530	+	0.534464i
$232$	−11.6824	+	5.76681i	−0.766984	+	0.378610i
$233$	−29.3923			−1.92556			−0.962778	−	0.270295i	$-0.912879\pi$
$233$	−29.3923			−1.92556			−0.962778	+	0.270295i	$0.912879\pi$
$234$	−10.2283	+	9.37895i	−0.668645	+	0.613121i
$235$	−19.0638	+	19.0638i	−1.24359	+	1.24359i
$236$	−11.1265	−	17.4550i	−0.724272	−	1.13622i
$237$	−17.9718	+	19.1923i	−1.16739	+	1.24668i
$238$	−1.14572	−	0.125325i	−0.0742660	−	0.00812360i
$239$	0.818139			0.0529210			0.0264605	−	0.999650i	$-0.491576\pi$
$239$	0.818139			0.0529210			0.0264605	+	0.999650i	$0.491576\pi$
$240$	−25.6222	−	10.9229i	−1.65391	−	0.705073i
$241$	8.11229			0.522558			0.261279	−	0.965263i	$-0.415856\pi$
$241$	8.11229			0.522558			0.261279	+	0.965263i	$0.415856\pi$
$242$	15.4907	+	1.69446i	0.995782	+	0.108924i
$243$	−12.6758	−	9.07324i	−0.813154	−	0.582049i
$244$	13.2347	−	8.43631i	0.847265	−	0.540080i
$245$	−2.84277	+	2.84277i	−0.181618	+	0.181618i
$246$	5.95520	−	5.11118i	0.379690	−	0.325877i
$247$	−20.3203			−1.29295
$248$	10.4327	+	3.53685i	0.662478	+	0.224590i
$249$	−10.4269	+	0.342443i	−0.660780	+	0.0217015i
$250$	27.3228	−	21.9348i	1.72805	−	1.38728i
$251$	17.1026	+	17.1026i	1.07951	+	1.07951i	0.996553	+	0.0829549i	$0.0264358\pi$
$251$	17.1026	+	17.1026i	1.07951	+	1.07951i	0.0829549	+	0.996553i	$0.473564\pi$
$252$	−0.909934	+	5.93060i	−0.0573205	+	0.373593i
$253$	10.9605	−	10.9605i	0.689078	−	0.689078i
$254$	1.41853	+	0.155166i	0.0890067	+	0.00973601i
$255$	−0.186278	−	5.67191i	−0.0116652	−	0.355189i
$256$	10.2975	+	12.2459i	0.643591	+	0.765370i
$257$			17.1523i			1.06993i	0.844874	+	0.534966i	$0.179675\pi$
$257$			17.1523i			1.06993i	−0.844874	+	0.534966i	$0.820325\pi$
$258$	0.431688	−	5.66007i	0.0268757	−	0.352381i
$259$	3.65469	+	3.65469i	0.227091	+	0.227091i
$260$	−5.68568	+	25.6783i	−0.352611	+	1.59250i
$261$	−9.10896	+	10.3912i	−0.563831	+	0.643199i
$262$	1.57142	+	1.95742i	0.0970827	+	0.120930i
$263$		−	5.92938i		−	0.365621i	−0.983148	−	0.182811i	$-0.941480\pi$
$263$		−	5.92938i		−	0.365621i	0.983148	−	0.182811i	$-0.0585196\pi$
$264$	22.0016	+	6.66213i	1.35411	+	0.410026i
$265$		−	43.7695i		−	2.68874i
$266$	−6.85105	+	5.50002i	−0.420065	+	0.337228i
$267$	2.92839	+	2.74216i	0.179215	+	0.167818i
$268$	0.0840939	+	0.131925i	0.00513685	+	0.00805858i
$269$	−4.43027	−	4.43027i	−0.270119	−	0.270119i	0.559029	−	0.829148i	$-0.311174\pi$
$269$	−4.43027	−	4.43027i	−0.270119	−	0.270119i	−0.829148	+	0.559029i	$0.811174\pi$
$270$	−29.5413	−	0.309036i	−1.79783	−	0.0188073i
$271$		−	16.4128i		−	0.997006i	−0.866888	−	0.498503i	$-0.833883\pi$
$271$		−	16.4128i		−	0.997006i	0.866888	−	0.498503i	$-0.166117\pi$
$272$	−1.37615	+	2.95521i	−0.0834414	+	0.179186i
$273$	5.66238	−	0.185965i	0.342703	−	0.0112551i
$274$	−0.877529	+	8.02238i	−0.0530135	+	0.484650i
$275$	−37.0383	+	37.0383i	−2.23350	+	2.23350i
$276$	9.44213	−	6.46421i	0.568350	−	0.389100i
$277$	−20.2225	−	20.2225i	−1.21505	−	1.21505i	−0.969344	−	0.245709i	$-0.920979\pi$
$277$	−20.2225	−	20.2225i	−1.21505	−	1.21505i	−0.245709	−	0.969344i	$-0.579021\pi$
$278$	8.49449	+	10.5811i	0.509466	+	0.634611i
$279$	11.6590	−	0.766640i	0.698005	−	0.0458976i
$280$	5.03331	+	10.1964i	0.300798	+	0.609353i
$281$	−3.30930			−0.197416			−0.0987082	−	0.995116i	$-0.531471\pi$
$281$	−3.30930			−0.197416			−0.0987082	+	0.995116i	$0.531471\pi$
$282$	12.4649	−	10.6983i	0.742277	−	0.637075i
$283$	2.67402	−	2.67402i	0.158954	−	0.158954i	−0.623149	−	0.782103i	$-0.714147\pi$
$283$	2.67402	−	2.67402i	0.158954	−	0.158954i	0.782103	+	0.623149i	$0.214147\pi$
$284$	−2.81373	+	12.7077i	−0.166964	+	0.754061i
$285$	−31.5762	−	29.5681i	−1.87041	−	1.75146i
$286$	2.36027	−	21.5776i	0.139566	−	1.27591i
$287$	−3.20387			−0.189118
$288$	15.0599	+	7.82309i	0.887411	+	0.460980i
$289$	16.3358			0.960930
$290$	−2.84765	+	26.0332i	−0.167220	+	1.52872i
$291$	−19.2680	−	18.0426i	−1.12951	−	1.05768i
$292$	−2.61695	+	11.8189i	−0.153145	+	0.691651i
$293$	4.59716	−	4.59716i	0.268569	−	0.268569i	−0.559954	−	0.828523i	$-0.689181\pi$
$293$	4.59716	−	4.59716i	0.268569	−	0.268569i	0.828523	+	0.559954i	$0.189181\pi$
$294$	1.85875	−	1.59532i	0.108405	−	0.0930407i
$295$	−41.6092			−2.42258
$296$	13.1086	−	6.47086i	0.761922	−	0.376111i
$297$	24.2644	−	2.39759i	1.40797	−	0.139122i
$298$	−5.46736	−	6.81036i	−0.316716	−	0.394513i
$299$	−7.64017	−	7.64017i	−0.441842	−	0.441842i
$300$	−31.9075	+	21.8443i	−1.84218	+	1.26118i
$301$	−1.63867	+	1.63867i	−0.0944513	+	0.0944513i
$302$	1.07835	−	9.85829i	0.0620521	−	0.567281i
$303$	−2.47321	+	0.0812257i	−0.142082	+	0.00466630i
$304$	8.51127	+	23.3464i	0.488155	+	1.33901i
$305$		−	31.5489i		−	1.80648i
$306$	−0.149640	+	3.45442i	−0.00855432	+	0.197476i
$307$	10.2535	+	10.2535i	0.585198	+	0.585198i	0.936327	−	0.351129i	$-0.114202\pi$
$307$	10.2535	+	10.2535i	0.585198	+	0.585198i	−0.351129	+	0.936327i	$0.614202\pi$
$308$	−5.04456	−	7.91380i	−0.287441	−	0.450930i
$309$	7.01115	+	6.56527i	0.398850	+	0.373485i
$310$	17.2676	−	13.8625i	0.980735	−	0.787335i
$311$		−	28.4542i		−	1.61349i	−0.590901	−	0.806744i	$-0.701228\pi$
$311$		−	28.4542i		−	1.61349i	0.590901	−	0.806744i	$-0.298772\pi$
$312$	4.64395	−	15.3366i	0.262912	−	0.868263i
$313$			23.6568i			1.33716i	0.743641	+	0.668579i	$0.233097\pi$
$313$			23.6568i			1.33716i	−0.743641	+	0.668579i	$0.766903\pi$
$314$	−12.9604	−	16.1440i	−0.731400	−	0.911061i
$315$	9.06950	+	7.95036i	0.511009	+	0.447952i
$316$	6.56349	−	29.6428i	0.369225	−	1.66754i
$317$	5.31748	+	5.31748i	0.298660	+	0.298660i	0.840489	−	0.541829i	$-0.182268\pi$
$317$	5.31748	+	5.31748i	0.298660	+	0.298660i	−0.541829	+	0.840489i	$0.682268\pi$
$318$	−2.02805	+	26.5908i	−0.113727	+	1.49114i
$319$		−	21.6141i		−	1.21016i
$320$	31.8838	−	4.22310i	1.78236	−	0.236078i
$321$	0.556655	+	16.9494i	0.0310695	+	0.946023i
$322$	−4.64384	−	0.507968i	−0.258791	−	0.0283079i
$323$	−3.58005	+	3.58005i	−0.199199	+	0.199199i
$324$	17.9326	+	1.55654i	0.996254	+	0.0864742i
$325$	25.8182	+	25.8182i	1.43214	+	1.43214i
$326$	17.5753	−	14.1095i	0.973405	−	0.781450i
$327$	4.15585	−	0.136487i	0.229819	−	0.00754776i
$328$	−2.90948	+	8.58214i	−0.160649	+	0.473869i
$329$	−6.70608			−0.369718
$330$	35.0652	−	30.0955i	1.93028	−	1.65670i
$331$	6.17926	−	6.17926i	0.339643	−	0.339643i	−0.516590	−	0.856233i	$-0.672799\pi$
$331$	6.17926	−	6.17926i	0.339643	−	0.339643i	0.856233	+	0.516590i	$0.172799\pi$
$332$	10.1582	−	6.47523i	0.557504	−	0.355374i
$333$	10.2210	−	11.6598i	0.560110	−	0.638954i
$334$	−5.76893	−	0.631035i	−0.315662	−	0.0345287i
$335$	0.314482			0.0171820
$336$	−2.58538	−	6.42774i	−0.141044	−	0.350662i
$337$	−0.191549			−0.0104343			−0.00521717	−	0.999986i	$-0.501661\pi$
$337$	−0.191549			−0.0104343			−0.00521717	+	0.999986i	$0.501661\pi$
$338$	3.23474	+	0.353832i	0.175946	+	0.0192459i
$339$	3.61587	−	3.86145i	0.196387	−	0.209725i
$340$	3.52232	+	5.52573i	0.191024	+	0.299675i
$341$	−12.9229	+	12.9229i	−0.699814	+	0.699814i
$342$	17.8131	+	19.4262i	0.963221	+	1.05045i
$343$	−1.00000			−0.0539949
$344$	2.90137	+	5.87757i	0.156431	+	0.316897i
$345$	−0.755024	−	22.9895i	−0.0406491	−	1.23771i
$346$	−0.283343	+	0.227468i	−0.0152326	+	0.0122288i
$347$	−17.6420	−	17.6420i	−0.947073	−	0.947073i	0.0515951	−	0.998668i	$-0.483569\pi$
$347$	−17.6420	−	17.6420i	−0.947073	−	0.947073i	−0.998668	+	0.0515951i	$0.983569\pi$
$348$	2.93624	−	15.6837i	0.157399	−	0.840735i
$349$	9.44916	−	9.44916i	0.505802	−	0.505802i	−0.407433	−	0.913235i	$-0.633576\pi$
$349$	9.44916	−	9.44916i	0.505802	−	0.505802i	0.913235	+	0.407433i	$0.133576\pi$
$350$	15.6928	+	1.71656i	0.838816	+	0.0917540i
$351$	−1.67128	−	16.9139i	−0.0892064	−	0.902799i
$352$	−25.7796	+	6.32613i	−1.37406	+	0.337184i
$353$			37.3053i			1.98556i	0.119950	+	0.992780i	$0.461726\pi$
$353$			37.3053i			1.98556i	−0.119950	+	0.992780i	$0.538274\pi$
$354$	25.2784	+	1.92795i	1.34353	+	0.102470i
$355$	18.5000	+	18.5000i	0.981876	+	0.981876i
$356$	−4.52294	−	1.00147i	−0.239715	−	0.0530777i
$357$	0.964840	−	1.03037i	0.0510647	−	0.0545328i
$358$	−10.2604	−	12.7808i	−0.542280	−	0.675486i
$359$		−	29.6103i		−	1.56277i	−0.624049	−	0.781385i	$-0.714514\pi$
$359$		−	29.6103i		−	1.56277i	0.624049	−	0.781385i	$-0.285486\pi$
$360$	29.5326	−	17.0745i	1.55651	−	0.899903i
$361$			19.5935i			1.03124i
$362$	22.0517	−	17.7031i	1.15901	−	0.930455i
$363$	−13.0451	+	13.9311i	−0.684692	+	0.731193i
$364$	−5.51645	+	3.51640i	−0.289140	+	0.184309i
$365$	17.2061	+	17.2061i	0.900611	+	0.900611i
$366$	−1.46181	+	19.1665i	−0.0764101	+	1.00185i
$367$			22.1073i			1.15399i	0.816746	+	0.576997i	$0.195776\pi$
$367$			22.1073i			1.15399i	−0.816746	+	0.576997i	$0.804224\pi$
$368$	−5.57783	+	11.9781i	−0.290764	+	0.624401i
$369$	0.630652	+	9.59089i	0.0328304	+	0.499282i
$370$	3.19531	−	29.2115i	0.166116	−	1.51863i
$371$	7.69839	−	7.69839i	0.399681	−	0.399681i
$372$	−11.1327	+	7.62161i	−0.577204	+	0.395162i
$373$	−13.9397	−	13.9397i	−0.721771	−	0.721771i	0.247195	−	0.968966i	$-0.420491\pi$
$373$	−13.9397	−	13.9397i	−0.721771	−	0.721771i	−0.968966	+	0.247195i	$0.920491\pi$
$374$	−3.38573	−	4.21739i	−0.175072	−	0.218076i
$375$	1.40859	+	42.8897i	0.0727393	+	2.21481i
$376$	−6.08989	+	17.9634i	−0.314062	+	0.926393i
$377$	−15.0665			−0.775963
$378$	−5.14151	−	5.25022i	−0.264451	−	0.270042i
$379$	−6.03251	+	6.03251i	−0.309869	+	0.309869i	−0.844859	−	0.534989i	$-0.820316\pi$
$379$	−6.03251	+	6.03251i	−0.309869	+	0.309869i	0.534989	+	0.844859i	$0.320316\pi$
$380$	48.7698	+	10.7986i	2.50184	+	0.553956i
$381$	−1.19458	+	1.27571i	−0.0612003	+	0.0653567i
$382$	1.38351	−	12.6481i	0.0707867	−	0.647133i
$383$	−9.07832			−0.463880			−0.231940	−	0.972730i	$-0.574507\pi$
$383$	−9.07832			−0.463880			−0.231940	+	0.972730i	$0.574507\pi$
$384$	−19.5657	+	1.08828i	−0.998457	+	0.0555361i
$385$	−18.8649			−0.961445
$386$	3.83847	−	35.0914i	0.195373	−	1.78610i
$387$	5.22797	+	4.58285i	0.265753	+	0.232960i
$388$	29.7596	+	6.58936i	1.51081	+	0.334524i
$389$	−19.6351	+	19.6351i	−0.995538	+	0.995538i	−0.999990	−	0.00445242i	$-0.998583\pi$
$389$	−19.6351	+	19.6351i	−0.995538	+	0.995538i	0.00445242	+	0.999990i	$0.498583\pi$
$390$	−20.9786	−	24.4428i	−1.06229	−	1.23771i
$391$	−2.69210			−0.136146
$392$	−0.908115	+	2.67868i	−0.0458667	+	0.135294i
$393$	−3.07264	+	0.100912i	−0.154994	+	0.00509035i
$394$	−3.36758	−	4.19479i	−0.169656	−	0.211330i
$395$	−43.1543	−	43.1543i	−2.17133	−	2.17133i
$396$	−22.6973	+	16.6588i	−1.14058	+	0.837138i
$397$	2.09474	−	2.09474i	0.105132	−	0.105132i	−0.652584	−	0.757716i	$-0.726315\pi$
$397$	2.09474	−	2.09474i	0.105132	−	0.105132i	0.757716	+	0.652584i	$0.226315\pi$
$398$	−0.895099	+	8.18300i	−0.0448673	+	0.410177i
$399$	−0.353196	−	10.7543i	−0.0176819	−	0.538391i
$400$	18.8490	−	40.4772i	0.942449	−	2.02386i
$401$		−	3.50963i		−	0.175263i	−0.996153	−	0.0876313i	$-0.972070\pi$
$401$		−	3.50963i		−	0.175263i	0.996153	−	0.0876313i	$-0.0279297\pi$
$402$	−0.191054	−	0.0145715i	−0.00952889	−	0.000726759i
$403$	9.00812	+	9.00812i	0.448726	+	0.448726i
$404$	2.40947	−	1.53589i	0.119876	−	0.0764133i
$405$	22.0144	−	28.7148i	1.09391	−	1.42685i
$406$	−5.07970	+	4.07799i	−0.252102	+	0.202387i
$407$			24.2529i			1.20217i
$408$	−1.88384	−	3.52019i	−0.0932639	−	0.174275i
$409$			19.5923i			0.968778i	0.874853	+	0.484389i	$0.160958\pi$
$409$			19.5923i			0.968778i	−0.874853	+	0.484389i	$0.839042\pi$
$410$	11.4035	+	14.2047i	0.563179	+	0.701518i
$411$	−7.21467	−	6.75585i	−0.355873	−	0.333241i
$412$	−10.8288	−	2.39771i	−0.533497	−	0.118127i
$413$	−7.31843	−	7.31843i	−0.360116	−	0.360116i
$414$	−0.606520	+	14.0015i	−0.0298088	+	0.688136i
$415$		−	24.2151i		−	1.18867i
$416$	4.40974	+	17.9701i	0.216205	+	0.881056i
$417$	−16.6095	+	0.545493i	−0.813371	+	0.0267129i
$418$	−40.9815	−	4.48277i	−2.00447	−	0.219259i
$419$	−3.04462	+	3.04462i	−0.148739	+	0.148739i	−0.777555	−	0.628815i	$-0.783540\pi$
$419$	−3.04462	+	3.04462i	−0.148739	+	0.148739i	0.628815	+	0.777555i	$0.283540\pi$
$420$	−13.6888	−	2.56277i	−0.667947	−	0.125050i
$421$	25.3941	+	25.3941i	1.23763	+	1.23763i	0.960965	+	0.276668i	$0.0892303\pi$
$421$	25.3941	+	25.3941i	1.23763	+	1.23763i	0.276668	+	0.960965i	$0.410770\pi$
$422$	−7.87120	+	6.31900i	−0.383164	+	0.307604i
$423$	1.32003	+	20.0749i	0.0641821	+	0.976074i
$424$	−13.6305	−	27.6125i	−0.661956	−	1.34098i
$425$	9.09735			0.441286
$426$	−10.3819	−	12.0963i	−0.503004	−	0.586066i
$427$	5.54897	−	5.54897i	0.268534	−	0.268534i
$428$	−10.5257	−	16.5126i	−0.508781	−	0.798164i
$429$	19.4051	+	18.1710i	0.936888	+	0.877306i
$430$	13.0977	+	1.43269i	0.631627	+	0.0690906i
$431$	33.5588			1.61647			0.808235	−	0.588860i	$-0.200423\pi$
$431$	33.5588			1.61647			0.808235	+	0.588860i	$0.200423\pi$
$432$	−18.7328	+	9.00467i	−0.901280	+	0.433237i
$433$	−23.2355			−1.11663			−0.558313	−	0.829631i	$-0.688551\pi$
$433$	−23.2355			−1.11663			−0.558313	+	0.829631i	$0.688551\pi$
$434$	5.47531	+	0.598917i	0.262823	+	0.0287490i
$435$	−23.4121	−	21.9232i	−1.12253	−	1.05114i
$436$	−4.04874	+	2.58082i	−0.193899	+	0.123599i
$437$	−14.5107	+	14.5107i	−0.694140	+	0.694140i
$438$	−9.65581	−	11.2503i	−0.461372	−	0.537560i
$439$	27.6659			1.32042			0.660211	−	0.751080i	$-0.270467\pi$
$439$	27.6659			1.32042			0.660211	+	0.751080i	$0.270467\pi$
$440$	−17.1315	+	50.5331i	−0.816713	+	2.40907i
$441$	0.196841	+	2.99354i	0.00937338	+	0.142549i
$442$	−2.93981	+	2.36008i	−0.139832	+	0.112257i
$443$	−20.5742	−	20.5742i	−0.977507	−	0.977507i	0.0222452	−	0.999753i	$-0.492919\pi$
$443$	−20.5742	−	20.5742i	−0.977507	−	0.977507i	−0.999753	+	0.0222452i	$0.992919\pi$
$444$	−3.29472	+	17.5985i	−0.156360	+	0.835187i
$445$	−6.58455	+	6.58455i	−0.312137	+	0.312137i
$446$	3.67612	+	0.402113i	0.174070	+	0.0190406i
$447$	10.6905	−	0.351099i	0.505642	−	0.0166064i
$448$	6.35066	+	4.86510i	0.300040	+	0.229854i
$449$		−	36.3315i		−	1.71459i	−0.514826	−	0.857294i	$-0.672144\pi$
$449$		−	36.3315i		−	1.71459i	0.514826	−	0.857294i	$-0.327856\pi$
$450$	2.04960	−	47.3149i	0.0966189	−	2.23044i
$451$	−10.6306	−	10.6306i	−0.500575	−	0.500575i
$452$	−1.32056	+	5.96405i	−0.0621138	+	0.280525i
$453$	8.86573	+	8.30191i	0.416549	+	0.390058i
$454$	1.83945	+	2.29129i	0.0863297	+	0.107536i
$455$			13.1501i			0.616487i
$456$	−29.1282	−	8.82008i	−1.36405	−	0.413038i
$457$			3.28562i			0.153695i	0.997043	+	0.0768474i	$0.0244854\pi$
$457$			3.28562i			0.153695i	−0.997043	+	0.0768474i	$0.975515\pi$
$458$	−23.1646	+	18.5965i	−1.08241	+	0.868960i
$459$	−3.27436	−	2.68546i	−0.152834	−	0.125347i
$460$	14.2767	+	22.3969i	0.665654	+	1.04426i
$461$	−15.0027	−	15.0027i	−0.698744	−	0.698744i	0.265396	−	0.964140i	$-0.414497\pi$
$461$	−15.0027	−	15.0027i	−0.698744	−	0.698744i	−0.964140	+	0.265396i	$0.914497\pi$
$462$	11.4608	+	0.874102i	0.533204	+	0.0406669i
$463$			25.8407i			1.20092i	0.799656	+	0.600458i	$0.205015\pi$
$463$			25.8407i			1.20092i	−0.799656	+	0.600458i	$0.794985\pi$
$464$	6.31067	+	17.3102i	0.292966	+	0.803605i
$465$	0.890209	+	27.1056i	0.0412824	+	1.25699i
$466$	−4.51986	+	41.3206i	−0.209378	+	1.91414i
$467$	22.0389	−	22.0389i	1.01984	−	1.01984i	0.0200376	−	0.999799i	$-0.493621\pi$
$467$	22.0389	−	22.0389i	1.01984	−	1.01984i	0.999799	−	0.0200376i	$-0.00637859\pi$
$468$	11.6123	+	15.8215i	0.536780	+	0.731349i
$469$	0.0553126	+	0.0553126i	0.00255410	+	0.00255410i
$470$	23.8689	+	29.7320i	1.10099	+	1.37144i
$471$	25.3419	−	0.832284i	1.16769	−	0.0383496i
$472$	−26.2497	+	12.9578i	−1.20824	+	0.596429i
$473$	−10.8744			−0.500004
$474$	24.2175	+	28.2166i	1.11235	+	1.29603i
$475$	49.0355	−	49.0355i	2.24990	−	2.24990i
$476$	−0.352370	+	1.59141i	−0.0161509	+	0.0729423i
$477$	−24.5608	−	21.5300i	−1.12456	−	0.985793i
$478$	0.125811	−	1.15016i	0.00575445	−	0.0526073i
$479$	19.7108			0.900608			0.450304	−	0.892875i	$-0.351316\pi$
$479$	19.7108			0.900608			0.450304	+	0.892875i	$0.351316\pi$
$480$	−19.2959	+	34.3407i	−0.880732	+	1.56743i
$481$	16.9059			0.770842
$482$	1.24748	−	11.4045i	0.0568212	−	0.519460i
$483$	3.91070	−	4.17629i	0.177943	−	0.190028i
$484$	4.76423	−	21.5167i	0.216556	−	0.978034i
$485$	43.3243	−	43.3243i	1.96726	−	1.96726i
$486$	−14.7047	+	16.4248i	−0.667017	+	0.745042i
$487$	3.69188			0.167295			0.0836475	−	0.996495i	$-0.473343\pi$
$487$	3.69188			0.167295			0.0836475	+	0.996495i	$0.473343\pi$
$488$	−9.82482	−	19.9030i	−0.444749	−	0.900967i
$489$	0.906070	+	27.5886i	0.0409739	+	1.24760i
$490$	3.55929	+	4.43360i	0.160793	+	0.200290i
$491$	−10.5801	−	10.5801i	−0.477475	−	0.477475i	0.426848	−	0.904323i	$-0.359624\pi$
$491$	−10.5801	−	10.5801i	−0.477475	−	0.477475i	−0.904323	+	0.426848i	$0.859624\pi$
$492$	−6.26967	−	9.15797i	−0.282659	−	0.412873i
$493$	−2.65442	+	2.65442i	−0.119549	+	0.119549i
$494$	−3.12479	+	28.5668i	−0.140591	+	1.28528i
$495$	3.71339	+	56.4728i	0.166904	+	2.53826i
$496$	6.57652	−	14.1227i	0.295294	−	0.634129i
$497$			6.50772i			0.291911i
$498$	−1.12200	+	14.7111i	−0.0502781	+	0.659222i
$499$	−29.1727	−	29.1727i	−1.30595	−	1.30595i	−0.924313	−	0.381636i	$-0.875361\pi$
$499$	−29.1727	−	29.1727i	−1.30595	−	1.30595i	−0.381636	−	0.924313i	$-0.624639\pi$
$500$	−26.6349	−	41.7843i	−1.19115	−	1.86865i
$501$	4.85816	−	5.18810i	0.217047	−	0.231787i
$502$	26.6733	−	21.4134i	1.19049	−	0.955725i
$503$		−	15.0826i		−	0.672498i	−0.941773	−	0.336249i	$-0.890842\pi$
$503$		−	15.0826i		−	0.672498i	0.941773	−	0.336249i	$-0.109158\pi$
$504$	8.19748	+	2.19120i	0.365145	+	0.0976038i
$505$		−	5.74369i		−	0.255591i
$506$	−13.7231	−	17.0940i	−0.610064	−	0.759920i
$507$	−2.72405	+	2.90906i	−0.120979	+	0.129196i
$508$	0.436275	−	1.97035i	0.0193566	−	0.0874202i
$509$	16.5998	+	16.5998i	0.735773	+	0.735773i	0.971757	−	0.235984i	$-0.0758312\pi$
$509$	16.5998	+	16.5998i	0.735773	+	0.735773i	−0.235984	+	0.971757i	$0.575831\pi$
$510$	−8.00238	−	0.610333i	−0.354351	−	0.0270260i
$511$			6.05260i			0.267751i
$512$	18.7992	−	12.5933i	0.830814	−	0.556551i
$513$	−32.1240	+	3.17420i	−1.41831	+	0.140144i
$514$	24.1132	+	2.63762i	1.06359	+	0.116341i
$515$	−15.7647	+	15.7647i	−0.694675	+	0.694675i
$516$	−7.89071	−	1.47727i	−0.347369	−	0.0650330i
$517$	−22.2511	−	22.2511i	−0.978603	−	0.978603i
$518$	5.69987	−	4.57585i	0.250438	−	0.201052i
$519$	−0.0146074	−	0.444774i	−0.000641193	−	0.0195234i
$520$	35.2249	+	11.9418i	1.54472	+	0.523683i
$521$	21.5578			0.944465			0.472232	−	0.881474i	$-0.343448\pi$
$521$	21.5578			0.944465			0.472232	+	0.881474i	$0.343448\pi$
$522$	13.2075	+	14.4036i	0.578076	+	0.630427i
$523$	−25.5106	+	25.5106i	−1.11550	+	1.11550i	−0.123109	+	0.992393i	$0.539287\pi$
$523$	−25.5106	+	25.5106i	−1.11550	+	1.11550i	−0.992393	+	0.123109i	$0.960713\pi$
$524$	2.99345	−	1.90814i	0.130769	−	0.0833575i
$525$	−13.2153	+	14.1128i	−0.576763	+	0.615934i
$526$	−8.33569	−	0.911801i	−0.363454	−	0.0397564i
$527$	3.17412			0.138267
$528$	12.7491	−	29.9060i	0.554835	−	1.30149i
$529$	12.0883			0.525580
$530$	−61.5324	−	6.73073i	−2.67280	−	0.292364i
$531$	−20.4674	+	23.3485i	−0.888210	+	1.01324i
$532$	6.67855	+	10.4772i	0.289552	+	0.454243i
$533$	−7.41024	+	7.41024i	−0.320973	+	0.320973i
$534$	4.30533	−	3.69514i	0.186310	−	0.159904i
$535$	−39.3626			−1.70180
$536$	0.198395	−	0.0979347i	0.00856936	−	0.00423013i
$537$	20.0625	−	0.658896i	0.865760	−	0.0284335i
$538$	−6.90948	+	5.54693i	−0.297889	+	0.239145i
$539$	−3.31805	−	3.31805i	−0.142919	−	0.142919i
$540$	−4.97722	+	41.4825i	−0.214185	+	1.78512i
$541$	7.33890	−	7.33890i	0.315524	−	0.315524i	−0.531521	−	0.847045i	$-0.678379\pi$
$541$	7.33890	−	7.33890i	0.315524	−	0.315524i	0.847045	+	0.531521i	$0.178379\pi$
$542$	−23.0736	−	2.52390i	−0.991094	−	0.108411i
$543$	1.13685	+	34.6154i	0.0487867	+	1.48549i
$544$	3.94290	+	2.38907i	0.169050	+	0.102431i
$545$			9.65138i			0.413420i
$546$	0.609308	−	7.98893i	0.0260760	−	0.341895i
$547$	−5.52913	−	5.52913i	−0.236408	−	0.236408i	0.578953	−	0.815361i	$-0.303462\pi$
$547$	−5.52913	−	5.52913i	−0.236408	−	0.236408i	−0.815361	+	0.578953i	$0.803462\pi$
$548$	11.1431	+	2.46731i	0.476011	+	0.105398i
$549$	−17.7033	−	15.5188i	−0.755559	−	0.662325i
$550$	46.3739	+	57.7652i	1.97739	+	2.46312i
$551$			28.6152i			1.21905i
$552$	−7.63559	−	14.2681i	−0.324992	−	0.607289i
$553$		−	15.1804i		−	0.645535i
$554$	−31.5391	+	25.3196i	−1.33997	+	1.07573i
$555$	26.2704	+	24.5997i	1.11512	+	1.04420i
$556$	16.1814	−	10.3147i	0.686246	−	0.437440i
$557$	−27.8816	−	27.8816i	−1.18138	−	1.18138i	−0.979386	−	0.201995i	$-0.935257\pi$
$557$	−27.8816	−	27.8816i	−1.18138	−	1.18138i	−0.201995	−	0.979386i	$-0.564743\pi$
$558$	0.715116	−	16.5084i	0.0302733	−	0.698857i
$559$			7.58017i			0.320607i
$560$	15.1084	−	5.50799i	0.638448	−	0.232755i
$561$	6.62020	−	0.217422i	0.279505	−	0.00917956i
$562$	−0.508894	+	4.65231i	−0.0214664	+	0.196246i
$563$	1.04328	−	1.04328i	0.0439691	−	0.0439691i	−0.684780	−	0.728749i	$-0.740102\pi$
$563$	1.04328	−	1.04328i	0.0439691	−	0.0439691i	0.728749	+	0.684780i	$0.240102\pi$
$564$	−13.1232	−	19.1687i	−0.552585	−	0.807149i
$565$	8.68253	+	8.68253i	0.365277	+	0.365277i
$566$	−3.34802	−	4.17042i	−0.140728	−	0.175296i
$567$	8.92251	−	1.17850i	0.374710	−	0.0494924i
$568$	17.4321	+	5.90976i	0.731435	+	0.247968i
$569$	−22.1966			−0.930530			−0.465265	−	0.885171i	$-0.654041\pi$
$569$	−22.1966			−0.930530			−0.465265	+	0.885171i	$0.654041\pi$
$570$	−46.4233	+	39.8438i	−1.94446	+	1.66887i
$571$	4.44290	−	4.44290i	0.185930	−	0.185930i	−0.608004	−	0.793934i	$-0.708030\pi$
$571$	4.44290	−	4.44290i	0.185930	−	0.185930i	0.793934	+	0.608004i	$0.208030\pi$
$572$	−29.9714	−	6.63626i	−1.25317	−	0.277476i
$573$	11.3747	+	10.6513i	0.475183	+	0.444964i
$574$	−0.492680	+	4.50409i	−0.0205641	+	0.187997i
$575$	36.8735			1.53773
$576$	13.3138	−	19.9686i	0.554741	−	0.832023i
$577$	−2.94900			−0.122768			−0.0613842	−	0.998114i	$-0.519551\pi$
$577$	−2.94900			−0.122768			−0.0613842	+	0.998114i	$0.519551\pi$
$578$	2.51207	−	22.9653i	0.104488	−	0.955232i
$579$	31.5583	+	29.5513i	1.31152	+	1.22811i
$580$	36.1603	+	8.00660i	1.50148	+	0.332456i
$581$	4.25907	−	4.25907i	0.176696	−	0.176696i
$582$	−28.3278	+	24.3129i	−1.17422	+	1.00780i
$583$	51.0873			2.11582
$584$	16.2130	+	5.49645i	0.670898	+	0.227445i
$585$	39.3653	−	2.58848i	1.62756	−	0.107020i
$586$	−5.75588	−	7.16975i	−0.237773	−	0.296180i
$587$	13.8692	+	13.8692i	0.572443	+	0.572443i	0.932811	−	0.360367i	$-0.117349\pi$
$587$	13.8692	+	13.8692i	0.572443	+	0.572443i	−0.360367	+	0.932811i	$0.617349\pi$
$588$	−1.95691	−	2.85841i	−0.0807015	−	0.117879i
$589$	17.1088	−	17.1088i	0.704954	−	0.704954i
$590$	−6.39853	+	58.4954i	−0.263423	+	2.40822i
$591$	6.58472	−	0.216257i	0.270859	−	0.00889561i
$592$	−7.08112	−	19.4235i	−0.291032	−	0.798302i
$593$			22.9708i			0.943296i	0.881787	+	0.471648i	$0.156341\pi$
$593$			22.9708i			0.943296i	−0.881787	+	0.471648i	$0.843659\pi$
$594$	0.360704	−	34.4803i	0.0147999	−	1.41474i
$595$	2.31680	+	2.31680i	0.0949794	+	0.0949794i
$596$	−10.4149	+	6.63889i	−0.426613	+	0.271940i
$597$	−7.35912	−	6.89111i	−0.301189	−	0.282035i
$598$	−11.9156	+	9.56589i	−0.487267	+	0.391178i
$599$		−	6.85784i		−	0.280204i	−0.990137	−	0.140102i	$-0.955257\pi$
$599$		−	6.85784i		−	0.280204i	0.990137	−	0.140102i	$-0.0447430\pi$
$600$	25.8027	+	48.2156i	1.05339	+	1.96840i
$601$			28.1867i			1.14976i	0.818237	+	0.574881i	$0.194952\pi$
$601$			28.1867i			1.14976i	−0.818237	+	0.574881i	$0.805048\pi$
$602$	2.05170	+	2.55567i	0.0836209	+	0.104162i
$603$	0.154693	−	0.176468i	0.00629957	−	0.00718634i
$604$	−13.6932	−	3.03195i	−0.557170	−	0.123368i
$605$	−31.3243	−	31.3243i	−1.27351	−	1.27351i
$606$	−0.266133	+	3.48940i	−0.0108109	+	0.141747i
$607$		−	3.92533i		−	0.159324i	−0.996822	−	0.0796620i	$-0.974616\pi$
$607$		−	3.92533i		−	0.159324i	0.996822	−	0.0796620i	$-0.0253841\pi$
$608$	34.1299	−	8.37524i	1.38415	−	0.339661i
$609$	−0.261877	−	7.97380i	−0.0106118	−	0.323115i
$610$	−44.3523	−	4.85149i	−1.79577	−	0.196431i
$611$	−15.5105	+	15.5105i	−0.627488	+	0.627488i
$612$	4.83331	+	0.741577i	0.195375	+	0.0299765i
$613$	−11.4345	−	11.4345i	−0.461835	−	0.461835i	0.437421	−	0.899257i	$-0.355892\pi$
$613$	−11.4345	−	11.4345i	−0.461835	−	0.461835i	−0.899257	+	0.437421i	$0.855892\pi$
$614$	15.9914	−	12.8379i	0.645361	−	0.518096i
$615$	−22.2976	+	0.732302i	−0.899125	+	0.0295293i
$616$	−11.9012	+	5.87483i	−0.479512	+	0.236704i
$617$	−43.5345			−1.75263			−0.876316	−	0.481738i	$-0.840006\pi$
$617$	−43.5345			−1.75263			−0.876316	+	0.481738i	$0.840006\pi$
$618$	10.3078	−	8.84689i	0.414640	−	0.355874i
$619$	23.4517	−	23.4517i	0.942603	−	0.942603i	−0.0558372	−	0.998440i	$-0.517783\pi$
$619$	23.4517	−	23.4517i	0.942603	−	0.942603i	0.998440	+	0.0558372i	$0.0177828\pi$
$620$	−16.8329	−	26.4070i	−0.676024	−	1.06053i
$621$	−13.2717	−	10.8847i	−0.532574	−	0.436790i
$622$	−40.0017	−	4.37559i	−1.60392	−	0.175445i
$623$	−2.31624			−0.0927983
$624$	−20.8465	−	8.88701i	−0.834527	−	0.355765i
$625$	−43.7920			−1.75168
$626$	33.2573	+	3.63786i	1.32923	+	0.145398i
$627$	34.5115	−	36.8554i	1.37826	−	1.47186i
$628$	−24.6888	+	15.7376i	−0.985189	+	0.627998i
$629$	2.97849	−	2.97849i	0.118760	−	0.118760i
$630$	12.5715	−	11.5276i	0.500861	−	0.459270i
$631$	25.1262			1.00026			0.500129	−	0.865951i	$-0.333286\pi$
$631$	25.1262			1.00026			0.500129	+	0.865951i	$0.333286\pi$
$632$	−40.6634	−	13.7855i	−1.61750	−	0.548358i
$633$	−0.405789	−	12.3557i	−0.0161287	−	0.491096i
$634$	8.29317	−	6.65776i	0.329364	−	0.264414i
$635$	−2.86846	−	2.86846i	−0.113831	−	0.113831i
$636$	37.0702	+	6.94013i	1.46993	+	0.275194i
$637$	−2.31290	+	2.31290i	−0.0916406	+	0.0916406i
$638$	−30.3857	−	3.32374i	−1.20298	−	0.131588i
$639$	19.4811	−	1.28099i	0.770661	−	0.0506750i
$640$	−1.03396	−	45.4726i	−0.0408710	−	1.79746i
$641$			33.0405i			1.30502i	0.757779	+	0.652511i	$0.226284\pi$
$641$			33.0405i			1.30502i	−0.757779	+	0.652511i	$0.773716\pi$
$642$	23.9135	+	1.82386i	0.943792	+	0.0719820i
$643$	−2.66006	−	2.66006i	−0.104902	−	0.104902i	0.652708	−	0.757610i	$-0.273633\pi$
$643$	−2.66006	−	2.66006i	−0.104902	−	0.104902i	−0.757610	+	0.652708i	$0.773633\pi$
$644$	−1.42823	+	6.45033i	−0.0562802	+	0.254179i
$645$	−11.0299	+	11.7790i	−0.434302	+	0.463797i
$646$	4.48240	+	5.58346i	0.176358	+	0.219678i
$647$			36.7484i			1.44473i	0.691512	+	0.722365i	$0.256945\pi$
$647$			36.7484i			1.44473i	−0.691512	+	0.722365i	$0.743055\pi$
$648$	4.94583	−	24.9708i	0.194291	−	0.980944i
$649$		−	48.5658i		−	1.90638i
$650$	40.2662	−	32.3257i	1.57937	−	1.26792i
$651$	−4.61089	+	4.92404i	−0.180715	+	0.192988i
$652$	−17.1328	−	26.8775i	−0.670972	−	1.05261i
$653$	21.7533	+	21.7533i	0.851271	+	0.851271i	0.990290	−	0.139019i	$-0.0443949\pi$
$653$	21.7533	+	21.7533i	0.851271	+	0.851271i	−0.139019	+	0.990290i	$0.544395\pi$
$654$	0.447195	−	5.86339i	0.0174867	−	0.229277i
$655$		−	7.13579i		−	0.278818i
$656$	11.6176	+	5.40996i	0.453591	+	0.211223i
$657$	18.1187	−	1.19140i	0.706876	−	0.0464809i
$658$	−1.03124	+	9.42759i	−0.0402019	+	0.367526i
$659$	−11.3925	+	11.3925i	−0.443790	+	0.443790i	−0.893283	−	0.449494i	$-0.851604\pi$
$659$	−11.3925	+	11.3925i	−0.443790	+	0.443790i	0.449494	+	0.893283i	$0.351604\pi$
$660$	−36.9169	−	53.9237i	−1.43699	−	2.09898i
$661$	13.7678	+	13.7678i	0.535506	+	0.535506i	0.922206	−	0.386700i	$-0.126385\pi$
$661$	13.7678	+	13.7678i	0.535506	+	0.535506i	−0.386700	+	0.922206i	$0.626385\pi$
$662$	−7.73675	−	9.63720i	−0.300697	−	0.374561i
$663$	−0.151558	−	4.61472i	−0.00588601	−	0.179221i
$664$	−7.54097	−	15.2764i	−0.292646	−	0.592840i
$665$	24.9755			0.968508
$666$	−14.8199	−	16.1620i	−0.574261	−	0.626266i
$667$	−10.7589	+	10.7589i	−0.416588	+	0.416588i
$668$	−1.77425	+	8.01309i	−0.0686480	+	0.310036i
$669$	−3.09576	+	3.30600i	−0.119689	+	0.127818i
$670$	0.0483600	−	0.442108i	0.00186831	−	0.0170801i
$671$	36.8236			1.42156
$672$	−9.43387	+	2.64616i	−0.363919	+	0.102078i
$673$	23.8933			0.921019			0.460509	−	0.887655i	$-0.347667\pi$
$673$	23.8933			0.921019			0.460509	+	0.887655i	$0.347667\pi$
$674$	−0.0294558	+	0.269285i	−0.00113459	+	0.0103725i
$675$	44.8486	+	36.7825i	1.72622	+	1.41576i
$676$	0.994854	−	4.49307i	0.0382636	−	0.172810i
$677$	30.9999	−	30.9999i	1.19142	−	1.19142i	0.214755	−	0.976668i	$-0.431105\pi$
$677$	30.9999	−	30.9999i	1.19142	−	1.19142i	0.976668	−	0.214755i	$-0.0688951\pi$
$678$	−4.87249	−	5.67710i	−0.187127	−	0.218028i
$679$	15.2402			0.584864
$680$	8.30988	−	4.10204i	0.318669	−	0.157306i
$681$	−3.59673	+	0.118125i	−0.137827	+	0.00452654i
$682$	16.1801	+	20.1546i	0.619569	+	0.771759i
$683$	22.6478	+	22.6478i	0.866595	+	0.866595i	0.992094	−	0.125498i	$-0.0400530\pi$
$683$	22.6478	+	22.6478i	0.866595	+	0.866595i	−0.125498	+	0.992094i	$0.540053\pi$
$684$	30.0492	−	22.0548i	1.14896	−	0.843287i
$685$	16.2223	−	16.2223i	0.619823	−	0.619823i
$686$	−0.153777	+	1.40583i	−0.00587122	+	0.0536748i
$687$	−1.19422	−	36.3623i	−0.0455623	−	1.38731i
$688$	8.70901	−	3.17499i	0.332028	−	0.121045i
$689$		−	35.6113i		−	1.35668i
$690$	−32.4353	−	2.47381i	−1.23479	−	0.0941763i
$691$	−14.7567	−	14.7567i	−0.561372	−	0.561372i	0.368325	−	0.929697i	$-0.379931\pi$
$691$	−14.7567	−	14.7567i	−0.561372	−	0.561372i	−0.929697	+	0.368325i	$0.879931\pi$
$692$	0.276209	+	0.433311i	0.0104999	+	0.0164720i
$693$	−9.27958	+	10.5858i	−0.352502	+	0.402123i
$694$	−27.5146	+	22.0887i	−1.04444	+	0.838476i
$695$		−	38.5733i		−	1.46317i
$696$	−21.5971	−	6.53964i	−0.818635	−	0.247884i
$697$			2.61108i			0.0989019i
$698$	−11.8308	−	14.7370i	−0.447804	−	0.557802i
$699$	−37.1603	−	34.7971i	−1.40553	−	1.31615i
$700$	4.82638	−	21.7974i	0.182420	−	0.823865i
$701$	21.8411	+	21.8411i	0.824928	+	0.824928i	0.986810	−	0.161882i	$-0.0517564\pi$
$701$	21.8411	+	21.8411i	0.824928	+	0.824928i	−0.161882	+	0.986810i	$0.551756\pi$
$702$	−24.0351	−	0.251435i	−0.907146	−	0.00948979i
$703$		−	32.1087i		−	1.21100i
$704$	4.92916	+	37.2145i	0.185775	+	1.40257i
$705$	−46.6715	+	1.53279i	−1.75775	+	0.0577284i
$706$	52.4448	+	5.73668i	1.97379	+	0.215903i
$707$	1.01023	−	1.01023i	0.0379936	−	0.0379936i
$708$	6.59760	−	35.2406i	0.247953	−	1.32442i
$709$	2.48004	+	2.48004i	0.0931400	+	0.0931400i	0.752142	−	0.659002i	$-0.229021\pi$
$709$	2.48004	+	2.48004i	0.0931400	+	0.0931400i	−0.659002	+	0.752142i	$0.729021\pi$
$710$	28.8526	−	23.1629i	1.08282	−	0.869288i
$711$	−45.4430	+	2.98812i	−1.70424	+	0.112063i
$712$	−2.10341	+	6.20447i	−0.0788288	+	0.232523i
$713$	12.8654			0.481811
$714$	−1.30015	−	1.51485i	−0.0486568	−	0.0566917i
$715$	−43.6327	+	43.6327i	−1.63177	+	1.63177i
$716$	−19.5454	+	12.4590i	−0.730446	+	0.465615i
$717$	1.03436	+	0.968582i	0.0386290	+	0.0361723i
$718$	−41.6269	−	4.55337i	−1.55350	−	0.169930i
$719$	35.4163			1.32080			0.660402	−	0.750912i	$-0.270386\pi$
$719$	35.4163			1.32080			0.660402	+	0.750912i	$0.270386\pi$
$720$	−19.4623	−	44.1434i	−0.725318	−	1.64513i
$721$	−5.54554			−0.206527
$722$	27.5451	+	3.01303i	1.02512	+	0.112133i
$723$	10.2563	+	9.60400i	0.381434	+	0.357177i
$724$	−21.4965	−	33.7232i	−0.798911	−	1.25331i
$725$	36.3574	−	36.3574i	1.35028	−	1.35028i
$726$	17.5787	+	20.4815i	0.652406	+	0.760140i
$727$	10.1700			0.377184			0.188592	−	0.982056i	$-0.439608\pi$
$727$	10.1700			0.377184			0.188592	+	0.982056i	$0.439608\pi$
$728$	4.09515	+	8.29591i	0.151776	+	0.307467i
$729$	−5.28420	−	26.4779i	−0.195711	−	0.980662i
$730$	26.8348	−	21.5430i	0.993200	−	0.797341i
$731$	1.33548	+	1.33548i	0.0493945	+	0.0493945i
$732$	26.7201	+	5.00242i	0.987602	+	0.184895i
$733$	−14.9007	+	14.9007i	−0.550371	+	0.550371i	−0.926548	−	0.376177i	$-0.877239\pi$
$733$	−14.9007	+	14.9007i	−0.550371	+	0.550371i	0.376177	+	0.926548i	$0.377239\pi$
$734$	31.0791	+	3.39959i	1.14715	+	0.125481i
$735$	−6.95958	+	0.228568i	−0.256708	+	0.00843086i
$736$	15.9814	+	9.68341i	0.589082	+	0.356935i
$737$			0.367060i			0.0135208i
$738$	13.5801	+	0.588267i	0.499891	+	0.0216544i
$739$	30.2894	+	30.2894i	1.11421	+	1.11421i	0.992574	+	0.121640i	$0.0388154\pi$
$739$	30.2894	+	30.2894i	1.11421	+	1.11421i	0.121640	+	0.992574i	$0.461185\pi$
$740$	−40.5750	−	8.98410i	−1.49157	−	0.330262i
$741$	−25.6907	−	24.0569i	−0.943770	−	0.883751i
$742$	−9.63878	−	12.0064i	−0.353851	−	0.440771i
$743$		−	0.334889i		−	0.0122859i	−0.999981	−	0.00614294i	$-0.998045\pi$
$743$		−	0.334889i		−	0.0122859i	0.999981	−	0.00614294i	$-0.00195537\pi$
$744$	9.00272	+	16.8227i	0.330056	+	0.616750i
$745$			24.8272i			0.909597i
$746$	−21.7404	+	17.4532i	−0.795974	+	0.639008i
$747$	−13.5880	−	11.9113i	−0.497161	−	0.435813i
$748$	−6.44958	+	4.11121i	−0.235820	+	0.150321i
$749$	−6.92329	−	6.92329i	−0.252972	−	0.252972i
$750$	60.5121	+	4.61520i	2.20959	+	0.168523i
$751$		−	22.8597i		−	0.834164i	−0.908869	−	0.417082i	$-0.863053\pi$
$751$		−	22.8597i		−	0.834164i	0.908869	−	0.417082i	$-0.136947\pi$
$752$	24.3170	+	11.3237i	0.886750	+	0.412933i
$753$	1.37511	+	41.8701i	0.0501117	+	1.52583i
$754$	−2.31687	+	21.1809i	−0.0843755	+	0.771362i
$755$	−19.9348	+	19.9348i	−0.725500	+	0.725500i
$756$	−8.17156	+	6.42072i	−0.297197	+	0.233519i
$757$	5.43514	+	5.43514i	0.197544	+	0.197544i	0.798946	−	0.601403i	$-0.205391\pi$
$757$	5.43514	+	5.43514i	0.197544	+	0.197544i	−0.601403	+	0.798946i	$0.705391\pi$
$758$	7.55301	+	9.40833i	0.274338	+	0.341726i
$759$	26.8331	−	0.881257i	0.973978	−	0.0319876i
$760$	22.6806	−	66.9013i	0.822712	−	2.42677i
$761$	23.2552			0.843000			0.421500	−	0.906828i	$-0.361504\pi$
$761$	23.2552			0.843000			0.421500	+	0.906828i	$0.361504\pi$
$762$	1.60973	+	1.87555i	0.0583145	+	0.0679441i
$763$	−1.69753	+	1.69753i	−0.0614548	+	0.0614548i
$764$	−17.5683	−	3.88997i	−0.635599	−	0.140734i
$765$	6.47937	−	7.39146i	0.234262	−	0.267239i
$766$	−1.39603	+	12.7626i	−0.0504408	+	0.461130i
$767$	−33.8536			−1.22238
$768$	−1.47881	+	27.6733i	−0.0533620	+	0.998575i
$769$	13.2676			0.478443			0.239221	−	0.970965i	$-0.423108\pi$
$769$	13.2676			0.478443			0.239221	+	0.970965i	$0.423108\pi$
$770$	−2.90098	+	26.5208i	−0.104544	+	0.955744i
$771$	−20.3063	+	21.6854i	−0.731314	+	0.780981i
$772$	−48.7422	−	10.7925i	−1.75427	−	0.388429i
$773$	−3.63940	+	3.63940i	−0.130900	+	0.130900i	−0.769521	−	0.638621i	$-0.779505\pi$
$773$	−3.63940	+	3.63940i	−0.130900	+	0.130900i	0.638621	+	0.769521i	$0.279505\pi$
$774$	7.24664	−	6.64489i	0.260475	−	0.238846i
$775$	−43.4755			−1.56169
$776$	13.8398	−	40.8236i	0.496821	−	1.46548i
$777$	0.293849	+	8.94729i	0.0105418	+	0.320982i
$778$	24.5841	+	30.6230i	0.881383	+	1.09789i
$779$	14.0740	+	14.0740i	0.504253	+	0.504253i
$780$	−37.5884	+	25.7335i	−1.34588	+	0.921408i
$781$	−21.5930	+	21.5930i	−0.772657	+	0.772657i
$782$	−0.413983	+	3.78464i	−0.0148040	+	0.135338i
$783$	−23.8183	+	2.35351i	−0.851197	+	0.0841076i
$784$	3.62612	+	1.68857i	0.129504	+	0.0603061i
$785$			58.8531i			2.10056i
$786$	−0.330635	+	4.33512i	−0.0117934	+	0.154629i
$787$	−28.7316	−	28.7316i	−1.02417	−	1.02417i	−0.999701	−	0.0244694i	$-0.992210\pi$
$787$	−28.7316	−	28.7316i	−1.02417	−	1.02417i	−0.0244694	−	0.999701i	$-0.507790\pi$
$788$	−6.41501	+	4.08918i	−0.228525	+	0.145671i
$789$	7.01970	−	7.49644i	0.249908	−	0.266880i
$790$	−67.3036	+	54.0314i	−2.39456	+	1.92235i
$791$			3.05425i			0.108597i
$792$	19.9291	+	34.4702i	0.708151	+	1.22484i
$793$		−	25.6685i		−	0.911514i
$794$	−2.62273	−	3.26697i	−0.0930770	−	0.115940i
$795$	51.8180	−	55.3372i	1.83779	−	1.96261i
$796$	11.3663	+	2.51671i	0.402866	+	0.0892025i
$797$	28.8804	+	28.8804i	1.02300	+	1.02300i	0.999729	+	0.0232677i	$0.00740700\pi$
$797$	28.8804	+	28.8804i	1.02300	+	1.02300i	0.0232677	+	0.999729i	$0.492593\pi$
$798$	−15.1731	−	1.15723i	−0.537121	−	0.0409656i
$799$			5.46531i			0.193349i
$800$	−54.0054	−	32.7229i	−1.90938	−	1.15693i
$801$	0.455931	+	6.93376i	0.0161095	+	0.244992i
$802$	−4.93394	−	0.539699i	−0.174223	−	0.0190574i
$803$	−20.0828	+	20.0828i	−0.708708	+	0.708708i
$804$	−0.0498646	+	0.266348i	−0.00175859	+	0.00939337i
$805$	9.39046	+	9.39046i	0.330970	+	0.330970i
$806$	14.0491	−	11.2786i	0.494859	−	0.397273i
$807$	−0.356209	−	10.8461i	−0.0125391	−	0.381799i
$808$	−1.78868	−	3.62348i	−0.0629254	−	0.127474i
$809$	23.8315			0.837870			0.418935	−	0.908016i	$-0.362403\pi$
$809$	23.8315			0.837870			0.418935	+	0.908016i	$0.362403\pi$
$810$	−36.9828	−	35.3642i	−1.29944	−	1.24257i
$811$	0.597878	−	0.597878i	0.0209943	−	0.0209943i	−0.696532	−	0.717526i	$-0.745274\pi$
$811$	0.597878	−	0.597878i	0.0209943	−	0.0209943i	0.717526	+	0.696532i	$0.245274\pi$
$812$	4.95181	+	7.76829i	0.173775	+	0.272614i
$813$	19.4308	−	20.7505i	0.681469	−	0.727750i
$814$	34.0954	+	3.72953i	1.19504	+	0.130720i
$815$	−64.0707			−2.24430
$816$	−5.23847	+	2.10703i	−0.183383	+	0.0737608i
$817$	14.3967			0.503677
$818$	27.5434	+	3.01284i	0.963034	+	0.105342i
$819$	7.37904	+	6.46849i	0.257844	+	0.226027i
$820$	21.7229	−	13.8470i	0.758597	−	0.483559i
$821$	−9.64131	+	9.64131i	−0.336484	+	0.336484i	−0.855042	−	0.518558i	$-0.826469\pi$
$821$	−9.64131	+	9.64131i	−0.336484	+	0.336484i	0.518558	+	0.855042i	$0.326469\pi$
$822$	−10.6070	+	9.10369i	−0.369962	+	0.317528i
$823$	11.2582			0.392436			0.196218	−	0.980560i	$-0.437134\pi$
$823$	11.2582			0.392436			0.196218	+	0.980560i	$0.437134\pi$
$824$	−5.03599	+	14.8547i	−0.175437	+	0.517489i
$825$	−90.6762	+	2.97801i	−3.15694	+	0.103681i
$826$	−11.4139	+	9.16305i	−0.397139	+	0.318823i
$827$	−19.4759	−	19.4759i	−0.677245	−	0.677245i	0.282131	−	0.959376i	$-0.408959\pi$
$827$	−19.4759	−	19.4759i	−0.677245	−	0.677245i	−0.959376	+	0.282131i	$0.908959\pi$
$828$	19.5904	+	3.00577i	0.680815	+	0.104458i
$829$	−31.7146	+	31.7146i	−1.10149	+	1.10149i	−0.107263	+	0.994231i	$0.534209\pi$
$829$	−31.7146	+	31.7146i	−1.10149	+	1.10149i	−0.994231	+	0.107263i	$0.965791\pi$
$830$	−34.0423	−	3.72372i	−1.18163	−	0.129252i
$831$	−1.62596	−	49.5081i	−0.0564038	−	1.71742i
$832$	25.9410	−	3.43595i	0.899341	−	0.119120i
$833$			0.814979i			0.0282373i
$834$	−1.78729	+	23.4340i	−0.0618887	+	0.811453i
$835$	11.6655	+	11.6655i	0.403703	+	0.403703i
$836$	−12.6040	+	56.9236i	−0.435918	+	1.96874i
$837$	15.6479	+	12.8336i	0.540871	+	0.443595i
$838$	3.81202	+	4.74840i	0.131684	+	0.164031i
$839$		−	26.3441i		−	0.909498i	−0.890620	−	0.454749i	$-0.849729\pi$
$839$		−	26.3441i		−	0.909498i	0.890620	−	0.454749i	$-0.150271\pi$
$840$	−5.70784	+	18.8501i	−0.196939	+	0.650389i
$841$		−	7.78330i		−	0.268390i
$842$	39.6048	−	31.7947i	1.36487	−	1.09572i
$843$	−4.18391	−	3.91783i	−0.144101	−	0.134937i
$844$	7.67302	+	12.0373i	0.264116	+	0.414340i
$845$	−6.54106	−	6.54106i	−0.225019	−	0.225019i
$846$	28.4248	+	1.23131i	0.977265	+	0.0423334i
$847$		−	11.0189i		−	0.378615i
$848$	−40.9146	+	14.9160i	−1.40501	+	0.512217i
$849$	6.54647	−	0.215000i	0.224674	−	0.00737879i
$850$	1.39896	−	12.7893i	0.0479839	−	0.438670i
$851$	12.0725	−	12.0725i	0.413838	−	0.413838i
$852$	−18.6018	+	12.7350i	−0.637286	+	0.436294i
$853$	−33.6622	−	33.6622i	−1.15257	−	1.15257i	−0.986035	−	0.166538i	$-0.946741\pi$
$853$	−33.6622	−	33.6622i	−1.15257	−	1.15257i	−0.166538	−	0.986035i	$-0.553259\pi$
$854$	−6.94760	−	8.65420i	−0.237742	−	0.296141i
$855$	−4.91620	−	74.7650i	−0.168130	−	2.55691i
$856$	−24.8324	+	12.2581i	−0.848755	+	0.418975i
$857$	−25.7318			−0.878982			−0.439491	−	0.898247i	$-0.644841\pi$
$857$	−25.7318			−0.878982			−0.439491	+	0.898247i	$0.644841\pi$
$858$	28.5294	−	24.4860i	0.973978	−	0.835938i
$859$	19.5545	−	19.5545i	0.667189	−	0.667189i	−0.289875	−	0.957064i	$-0.593614\pi$
$859$	19.5545	−	19.5545i	0.667189	−	0.667189i	0.957064	+	0.289875i	$0.0936138\pi$
$860$	4.02824	−	18.1928i	0.137362	−	0.620369i
$861$	−4.05061	−	3.79301i	−0.138044	−	0.129265i
$862$	5.16056	−	47.1779i	0.175769	−	1.60688i
$863$	44.8475			1.52663			0.763314	−	0.646028i	$-0.223571\pi$
$863$	44.8475			1.52663			0.763314	+	0.646028i	$0.223571\pi$
$864$	9.77835	+	27.7197i	0.332666	+	0.943045i
$865$	1.03293			0.0351206
$866$	−3.57307	+	32.6651i	−0.121418	+	1.11000i
$867$	20.6531	+	19.3397i	0.701418	+	0.656810i
$868$	1.68395	−	7.60524i	0.0571570	−	0.258139i
$869$	50.3693	−	50.3693i	1.70866	−	1.70866i
$870$	−34.4205	+	29.5422i	−1.16697	+	1.00157i
$871$	0.255866			0.00866968
$872$	3.00559	+	6.08870i	0.101782	+	0.206189i
$873$	−2.99989	−	45.6220i	−0.101531	−	1.54407i
$874$	18.1681	+	22.6309i	0.614546	+	0.765502i
$875$	−17.5191	−	17.5191i	−0.592253	−	0.592253i
$876$	−17.3008	+	11.8444i	−0.584540	+	0.400184i
$877$	−37.7902	+	37.7902i	−1.27608	+	1.27608i	−0.333244	+	0.942841i	$0.608143\pi$
$877$	−37.7902	+	37.7902i	−1.27608	+	1.27608i	−0.942841	+	0.333244i	$0.891857\pi$
$878$	4.25437	−	38.8935i	0.143578	−	1.31259i
$879$	11.2546	−	0.369627i	0.379609	−	0.0124672i
$880$	68.4064	+	31.8548i	2.30598	+	1.07382i
$881$		−	1.93495i		−	0.0651903i	−0.999469	−	0.0325951i	$-0.989623\pi$
$881$		−	1.93495i		−	0.0651903i	0.999469	−	0.0325951i	$-0.0103772\pi$
$882$	4.23867	+	0.183612i	0.142723	+	0.00618252i
$883$	3.35788	+	3.35788i	0.113002	+	0.113002i	0.761347	−	0.648345i	$-0.224539\pi$
$883$	3.35788	+	3.35788i	0.113002	+	0.113002i	−0.648345	+	0.761347i	$0.724539\pi$
$884$	2.86579	+	4.49579i	0.0963869	+	0.151210i
$885$	−52.6060	−	49.2604i	−1.76833	−	1.65587i
$886$	−32.0875	+	25.7599i	−1.07800	+	0.865421i
$887$			17.6612i			0.593005i	0.955032	+	0.296502i	$0.0958202\pi$
$887$			17.6612i			0.593005i	−0.955032	+	0.296502i	$0.904180\pi$
$888$	24.2338	+	7.33804i	0.813232	+	0.246249i
$889$		−	1.00904i		−	0.0338420i
$890$	8.24419	+	10.2693i	0.276346	+	0.344227i
$891$	33.5157	+	25.6950i	1.12282	+	0.860816i
$892$	1.13060	−	5.10616i	0.0378554	−	0.170967i
$893$	29.4585	+	29.4585i	0.985791	+	0.985791i
$894$	1.15036	−	15.0830i	0.0384738	−	0.504450i
$895$			46.5924i			1.55741i
$896$	7.81607	−	8.17979i	0.261117	−	0.273268i
$897$	−0.614295	−	18.7044i	−0.0205107	−	0.624523i
$898$	−51.0758	−	5.58694i	−1.70442	−	0.186438i
$899$	12.6853	−	12.6853i	0.423078	−	0.423078i
$900$	−66.2014	−	10.1573i	−2.20671	−	0.338577i
$901$	−6.27403	−	6.27403i	−0.209018	−	0.209018i
$902$	−16.5795	+	13.3101i	−0.552038	+	0.443176i
$903$	−4.01174	+	0.131754i	−0.133502	+	0.00438451i
$904$	8.18136	+	2.77361i	0.272108	+	0.0922489i
$905$	−80.3895			−2.67224
$906$	13.0344	−	11.1871i	0.433039	−	0.371665i
$907$	6.00083	−	6.00083i	0.199254	−	0.199254i	−0.600426	−	0.799680i	$-0.705002\pi$
$907$	6.00083	−	6.00083i	0.199254	−	0.199254i	0.799680	+	0.600426i	$0.205002\pi$
$908$	3.50403	−	2.23361i	0.116285	−	0.0741248i
$909$	−3.22301	−	2.82530i	−0.106900	−	0.0937093i
$910$	18.4868	+	2.02218i	0.612831	+	0.0670346i
$911$	−21.4940			−0.712127			−0.356064	−	0.934462i	$-0.615881\pi$
$911$	−21.4940			−0.712127			−0.356064	+	0.934462i	$0.615881\pi$
$912$	−16.8787	+	39.5929i	−0.558911	+	1.31105i
$913$	28.2636			0.935390
$914$	4.61902	+	0.505252i	0.152784	+	0.0167123i
$915$	37.3502	−	39.8868i	1.23476	−	1.31862i
$916$	22.5814	+	35.4252i	0.746110	+	1.17048i
$917$	1.25508	−	1.25508i	0.0414463	−	0.0414463i
$918$	−4.27882	+	4.19023i	−0.141222	+	0.138298i
$919$	29.2110			0.963582			0.481791	−	0.876286i	$-0.339986\pi$
$919$	29.2110			0.963582			0.481791	+	0.876286i	$0.339986\pi$
$920$	33.6817	−	16.6264i	1.11045	−	0.548157i
$921$	0.824416	+	25.1023i	0.0271654	+	0.827150i
$922$	−23.3982	+	18.7841i	−0.770580	+	0.618622i
$923$	15.0517	+	15.0517i	0.495434	+	0.495434i
$924$	2.99124	−	15.9775i	0.0984045	−	0.525620i
$925$	−40.7961	+	40.7961i	−1.34137	+	1.34137i
$926$	36.3275	+	3.97369i	1.19380	+	0.130584i
$927$	1.09159	+	16.6008i	0.0358525	+	0.545241i
$928$	25.3056	−	6.20982i	0.830696	−	0.203847i
$929$		−	37.2301i		−	1.22148i	−0.791831	−	0.610741i	$-0.790872\pi$
$929$		−	37.2301i		−	1.22148i	0.791831	−	0.610741i	$-0.209128\pi$
$930$	38.2428	+	2.91673i	1.25403	+	0.0956435i
$931$	4.39281	+	4.39281i	0.143968	+	0.143968i
$932$	57.3946	+	12.7083i	1.88002	+	0.416274i
$933$	33.6864	−	35.9742i	1.10284	−	1.17774i
$934$	−27.5938	−	34.3719i	−0.902896	−	1.12468i
$935$			15.3745i			0.502800i
$936$	24.0280	−	13.8919i	0.785380	−	0.454073i
$937$			28.8582i			0.942755i	0.881931	+	0.471378i	$0.156243\pi$
$937$			28.8582i			0.942755i	−0.881931	+	0.471378i	$0.843757\pi$
$938$	0.0862659	−	0.0692543i	0.00281668	−	0.00226123i
$939$	−28.0068	+	29.9089i	−0.913969	+	0.976041i
$940$	45.4686	−	28.9835i	1.48302	−	0.945336i
$941$	−36.5463	−	36.5463i	−1.19138	−	1.19138i	−0.976681	−	0.214696i	$-0.931124\pi$
$941$	−36.5463	−	36.5463i	−1.19138	−	1.19138i	−0.214696	−	0.976681i	$-0.568876\pi$
$942$	2.72695	−	35.7544i	0.0888487	−	1.16494i
$943$			10.5833i			0.344639i
$944$	14.1798	+	38.8952i	0.461513	+	1.26593i
$945$	2.05416	+	20.7888i	0.0668217	+	0.676259i
$946$	−1.67223	+	15.2875i	−0.0543687	+	0.497039i
$947$	11.9514	−	11.9514i	0.388367	−	0.388367i	−0.485738	−	0.874105i	$-0.661449\pi$
$947$	11.9514	−	11.9514i	0.388367	−	0.388367i	0.874105	+	0.485738i	$0.161449\pi$
$948$	43.3917	−	29.7066i	1.40930	−	0.964824i
$949$	13.9991	+	13.9991i	0.454429	+	0.454429i
$950$	−61.3950	−	76.4760i	−1.99192	−	2.48121i
$951$	0.427543	+	13.0181i	0.0138640	+	0.422141i
$952$	2.18307	+	0.740094i	0.0707536	+	0.0239866i
$953$	51.5749			1.67068			0.835338	−	0.549737i	$-0.185272\pi$
$953$	51.5749			1.67068			0.835338	+	0.549737i	$0.185272\pi$
$954$	−34.0444	+	31.2174i	−1.10223	+	1.01070i
$955$	−25.5761	+	25.5761i	−0.827624	+	0.827624i
$956$	−1.59759	−	0.353737i	−0.0516696	−	0.0114407i
$957$	25.5886	−	27.3264i	0.827161	−	0.883337i
$958$	3.03106	−	27.7099i	0.0979290	−	0.895268i
$959$	5.70652			0.184273
$960$	45.3099	+	32.4075i	1.46237	+	1.04595i
$961$	15.8311			0.510682
$962$	2.59973	−	23.7668i	0.0838187	−	0.766271i
$963$	−19.3623	+	22.0879i	−0.623942	+	0.711773i
$964$	−15.8409	−	3.50749i	−0.510201	−	0.112969i
$965$	−70.9594	+	70.9594i	−2.28426	+	2.28426i
$966$	−5.26978	−	6.13999i	−0.169552	−	0.197551i
$967$	2.76614			0.0889531			0.0444766	−	0.999010i	$-0.485838\pi$
$967$	2.76614			0.0889531			0.0444766	+	0.999010i	$0.485838\pi$
$968$	−29.5162	−	10.0065i	−0.948687	−	0.321620i
$969$	−8.76456	+	0.287848i	−0.281558	+	0.00924700i
$970$	−54.2443	−	67.5688i	−1.74168	−	2.16950i
$971$	26.6491	+	26.6491i	0.855210	+	0.855210i	0.990769	−	0.135559i	$-0.0432830\pi$
$971$	26.6491	+	26.6491i	0.855210	+	0.855210i	−0.135559	+	0.990769i	$0.543283\pi$
$972$	20.8292	+	23.1980i	0.668095	+	0.744076i
$973$	6.78446	−	6.78446i	0.217500	−	0.217500i
$974$	0.567725	−	5.19015i	0.0181911	−	0.166303i
$975$	2.07587	+	63.2074i	0.0664810	+	2.02426i
$976$	−29.4911	+	10.7514i	−0.943986	+	0.344143i
$977$		−	15.9054i		−	0.508859i	−0.967091	−	0.254429i	$-0.918112\pi$
$977$		−	15.9054i		−	0.508859i	0.967091	−	0.254429i	$-0.0818877\pi$
$978$	38.9241	+	2.96870i	1.24466	+	0.0949287i
$979$	−7.68542	−	7.68542i	−0.245627	−	0.245627i
$980$	6.78021	−	4.32197i	0.216586	−	0.138060i
$981$	5.41576	+	4.74748i	0.172912	+	0.151575i
$982$	−16.5008	+	13.2469i	−0.526563	+	0.422725i
$983$			58.2649i			1.85836i	0.369625	+	0.929181i	$0.379486\pi$
$983$			58.2649i			1.85836i	−0.369625	+	0.929181i	$0.620514\pi$
$984$	−13.8387	+	7.40580i	−0.441160	+	0.236088i
$985$			15.2921i			0.487247i
$986$	3.32348	+	4.13985i	0.105841	+	0.131840i
$987$	−8.47840	−	7.93921i	−0.269870	−	0.252708i
$988$	39.6795	+	8.78583i	1.26237	+	0.279514i
$989$	5.41298	+	5.41298i	0.172123	+	0.172123i
$990$	79.9621	+	3.46382i	2.54136	+	0.110087i
$991$		−	5.20415i		−	0.165315i	−0.996578	−	0.0826576i	$-0.973659\pi$
$991$		−	5.20415i		−	0.165315i	0.996578	−	0.0826576i	$-0.0263408\pi$
$992$	−18.8428	−	11.4172i	−0.598259	−	0.362496i
$993$	15.1279	−	0.496833i	0.480069	−	0.0157665i
$994$	9.14874	+	1.00074i	0.290180	+	0.0317414i
$995$	16.5471	−	16.5471i	0.524579	−	0.524579i
$996$	20.5088	+	3.83957i	0.649846	+	0.121662i
$997$	23.8283	+	23.8283i	0.754650	+	0.754650i	0.975343	−	0.220693i	$-0.0708319\pi$
$997$	23.8283	+	23.8283i	0.754650	+	0.754650i	−0.220693	+	0.975343i	$0.570832\pi$
$998$	−45.4978	+	36.5257i	−1.44021	+	1.15620i
$999$	26.7262	−	2.64084i	0.845579	−	0.0835525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.c.155.11	yes	40
3.2	odd	2	inner	336.2.s.c.155.10	✓	40
4.3	odd	2		1344.2.s.c.911.5		40
12.11	even	2		1344.2.s.c.911.6		40
16.3	odd	4	inner	336.2.s.c.323.10	yes	40
16.13	even	4		1344.2.s.c.239.6		40
48.29	odd	4		1344.2.s.c.239.5		40
48.35	even	4	inner	336.2.s.c.323.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.10	✓	40	3.2	odd	2	inner
336.2.s.c.155.11	yes	40	1.1	even	1	trivial
336.2.s.c.323.10	yes	40	16.3	odd	4	inner
336.2.s.c.323.11	yes	40	48.35	even	4	inner
1344.2.s.c.239.5		40	48.29	odd	4
1344.2.s.c.239.6		40	16.13	even	4
1344.2.s.c.911.5		40	4.3	odd	2
1344.2.s.c.911.6		40	12.11	even	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.153777 - 1.40583i) q^{2} +(1.26429 + 1.18388i) q^{3} +(-1.95271 - 0.432367i) q^{4} +(-2.84277 + 2.84277i) q^{5} +(1.85875 - 1.59532i) q^{6} -1.00000 q^{7} +(-0.908115 + 2.67868i) q^{8} +(0.196841 + 2.99354i) q^{9} +O(q^{10})\)	\(q+(0.153777 - 1.40583i) q^{2} +(1.26429 + 1.18388i) q^{3} +(-1.95271 - 0.432367i) q^{4} +(-2.84277 + 2.84277i) q^{5} +(1.85875 - 1.59532i) q^{6} -1.00000 q^{7} +(-0.908115 + 2.67868i) q^{8} +(0.196841 + 2.99354i) q^{9} +(3.55929 + 4.43360i) q^{10} +(-3.31805 - 3.31805i) q^{11} +(-1.95691 - 2.85841i) q^{12} +(-2.31290 + 2.31290i) q^{13} +(-0.153777 + 1.40583i) q^{14} +(-6.95958 + 0.228568i) q^{15} +(3.62612 + 1.68857i) q^{16} +0.814979i q^{17} +(4.23867 + 0.183612i) q^{18} +(4.39281 + 4.39281i) q^{19} +(6.78021 - 4.32197i) q^{20} +(-1.26429 - 1.18388i) q^{21} +(-5.17485 + 4.15437i) q^{22} +3.30328i q^{23} +(-4.31936 + 2.31152i) q^{24} -11.1627i q^{25} +(2.89588 + 3.60722i) q^{26} +(-3.29513 + 4.01772i) q^{27} +(1.95271 + 0.432367i) q^{28} +(3.25705 + 3.25705i) q^{29} +(-0.748894 + 9.81913i) q^{30} -3.89472i q^{31} +(2.93145 - 4.83803i) q^{32} +(-0.266782 - 8.12315i) q^{33} +(1.14572 + 0.125325i) q^{34} +(2.84277 - 2.84277i) q^{35} +(0.909934 - 5.93060i) q^{36} +(-3.65469 - 3.65469i) q^{37} +(6.85105 - 5.50002i) q^{38} +(-5.66238 + 0.185965i) q^{39} +(-5.03331 - 10.1964i) q^{40} +3.20387 q^{41} +(-1.85875 + 1.59532i) q^{42} +(1.63867 - 1.63867i) q^{43} +(5.04456 + 7.91380i) q^{44} +(-9.06950 - 7.95036i) q^{45} +(4.64384 + 0.507968i) q^{46} +6.70608 q^{47} +(2.58538 + 6.42774i) q^{48} +1.00000 q^{49} +(-15.6928 - 1.71656i) q^{50} +(-0.964840 + 1.03037i) q^{51} +(5.51645 - 3.51640i) q^{52} +(-7.69839 + 7.69839i) q^{53} +(5.14151 + 5.25022i) q^{54} +18.8649 q^{55} +(0.908115 - 2.67868i) q^{56} +(0.353196 + 10.7543i) q^{57} +(5.07970 - 4.07799i) q^{58} +(7.31843 + 7.31843i) q^{59} +(13.6888 + 2.56277i) q^{60} +(-5.54897 + 5.54897i) q^{61} +(-5.47531 - 0.598917i) q^{62} +(-0.196841 - 2.99354i) q^{63} +(-6.35066 - 4.86510i) q^{64} -13.1501i q^{65} +(-11.4608 - 0.874102i) q^{66} +(-0.0553126 - 0.0553126i) q^{67} +(0.352370 - 1.59141i) q^{68} +(-3.91070 + 4.17629i) q^{69} +(-3.55929 - 4.43360i) q^{70} -6.50772i q^{71} +(-8.19748 - 2.19120i) q^{72} -6.05260i q^{73} +(-5.69987 + 4.57585i) q^{74} +(13.2153 - 14.1128i) q^{75} +(-6.67855 - 10.4772i) q^{76} +(3.31805 + 3.31805i) q^{77} +(-0.609308 + 7.98893i) q^{78} +15.1804i q^{79} +(-15.1084 + 5.50799i) q^{80} +(-8.92251 + 1.17850i) q^{81} +(0.492680 - 4.50409i) q^{82} +(-4.25907 + 4.25907i) q^{83} +(1.95691 + 2.85841i) q^{84} +(-2.31680 - 2.31680i) q^{85} +(-2.05170 - 2.55567i) q^{86} +(0.261877 + 7.97380i) q^{87} +(11.9012 - 5.87483i) q^{88} +2.31624 q^{89} +(-12.5715 + 11.5276i) q^{90} +(2.31290 - 2.31290i) q^{91} +(1.42823 - 6.45033i) q^{92} +(4.61089 - 4.92404i) q^{93} +(1.03124 - 9.42759i) q^{94} -24.9755 q^{95} +(9.43387 - 2.64616i) q^{96} -15.2402 q^{97} +(0.153777 - 1.40583i) q^{98} +(9.27958 - 10.5858i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

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