LMFDB - Embedded newform 2070.2.j.h.323.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(323,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.j (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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 24 x^{14} - 48 x^{13} + 160 x^{12} - 292 x^{11} + 436 x^{10} - 176 x^{9} - 914 x^{8} + \cdots + 81 $ x^16 - 4x^15 + 24x^14 - 48x^13 + 160x^12 - 292x^11 + 436x^10 - 176x^9 - 914x^8 + 820x^7 + 1624x^6 - 768x^5 - 568x^4 - 636x^3 + 540x^2 + 432*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.6
Root			$0.889432 - 0.368415i$ of defining polynomial
Character	$\chi$	$=$	2070.323
Dual form			2070.2.j.h.737.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.25785 + 1.84873i) q^{5} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.25785 + 1.84873i) q^{5} +(-0.707107 + 0.707107i) q^{8} +(-2.19669 + 0.417821i) q^{10} +6.26456i q^{11} +(-4.39337 - 4.39337i) q^{13} -1.00000 q^{16} +(-2.28326 - 2.28326i) q^{17} +0.722087i q^{19} +(-1.84873 - 1.25785i) q^{20} +(-4.42972 + 4.42972i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(-1.83564 - 4.65085i) q^{25} -6.21316i q^{26} +5.95183 q^{29} -6.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} -3.22901i q^{34} +(1.05678 - 1.05678i) q^{37} +(-0.510593 + 0.510593i) q^{38} +(-0.417821 - 2.19669i) q^{40} -6.80974i q^{41} +(1.20070 + 1.20070i) q^{43} -6.26456 q^{44} -1.00000 q^{46} +(-8.78026 - 8.78026i) q^{47} +7.00000i q^{49} +(1.99065 - 4.58664i) q^{50} +(4.39337 - 4.39337i) q^{52} +(-2.23754 + 2.23754i) q^{53} +(-11.5815 - 7.87986i) q^{55} +(4.20858 + 4.20858i) q^{58} +12.7905 q^{59} +4.90833 q^{61} +(-4.24264 - 4.24264i) q^{62} -1.00000i q^{64} +(13.6484 - 2.59599i) q^{65} +(-7.15180 + 7.15180i) q^{67} +(2.28326 - 2.28326i) q^{68} +3.68633i q^{71} +(-11.6020 - 11.6020i) q^{73} +1.49451 q^{74} -0.722087 q^{76} +0.442271i q^{79} +(1.25785 - 1.84873i) q^{80} +(4.81521 - 4.81521i) q^{82} +(-11.9671 + 11.9671i) q^{83} +(7.09312 - 1.34915i) q^{85} +1.69805i q^{86} +(-4.42972 - 4.42972i) q^{88} -5.95183 q^{89} +(-0.707107 - 0.707107i) q^{92} -12.4172i q^{94} +(-1.33495 - 0.908275i) q^{95} +(6.97957 - 6.97957i) q^{97} +(-4.94975 + 4.94975i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{10} - 16 q^{13} - 16 q^{16} + 8 q^{22} - 16 q^{25} - 96 q^{31} + 24 q^{37} + 8 q^{43} - 16 q^{46} + 16 q^{52} - 32 q^{58} + 16 q^{61} - 8 q^{67} - 32 q^{73} + 16 q^{76} + 32 q^{82} + 96 q^{85} + 8 q^{88} + 80 q^{97}+O(q^{100}) $ 16 * q - 8 * q^10 - 16 * q^13 - 16 * q^16 + 8 * q^22 - 16 * q^25 - 96 * q^31 + 24 * q^37 + 8 * q^43 - 16 * q^46 + 16 * q^52 - 32 * q^58 + 16 * q^61 - 8 * q^67 - 32 * q^73 + 16 * q^76 + 32 * q^82 + 96 * q^85 + 8 * q^88 + 80 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−1.25785	+	1.84873i	−0.562526	+	0.826779i
$5$	−1.25785	+	1.84873i	−0.562526	+	0.826779i
$6$		0			0
$7$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$7$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−2.19669	+	0.417821i	−0.694653	+	0.132127i
$11$			6.26456i			1.88884i	0.328745	+	0.944419i	$0.393374\pi$
$11$			6.26456i			1.88884i	−0.328745	+	0.944419i	$0.606626\pi$
$12$		0			0
$13$	−4.39337	−	4.39337i	−1.21850	−	1.21850i	−0.968157	−	0.250345i	$-0.919456\pi$
$13$	−4.39337	−	4.39337i	−1.21850	−	1.21850i	−0.250345	−	0.968157i	$-0.580544\pi$
$14$		0			0
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.28326	−	2.28326i	−0.553771	−	0.553771i	0.373756	−	0.927527i	$-0.378070\pi$
$17$	−2.28326	−	2.28326i	−0.553771	−	0.553771i	−0.927527	+	0.373756i	$0.878070\pi$
$18$		0			0
$19$			0.722087i			0.165658i	0.996564	+	0.0828291i	$0.0263955\pi$
$19$			0.722087i			0.165658i	−0.996564	+	0.0828291i	$0.973604\pi$
$20$	−1.84873	−	1.25785i	−0.413390	−	0.281263i
$21$		0			0
$22$	−4.42972	+	4.42972i	−0.944419	+	0.944419i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$24$		0			0
$25$	−1.83564	−	4.65085i	−0.367128	−	0.930170i
$26$		−	6.21316i		−	1.21850i
$27$		0			0
$28$		0			0
$29$	5.95183			1.10523			0.552614	−	0.833438i	$-0.313631\pi$
$29$	5.95183			1.10523			0.552614	+	0.833438i	$0.313631\pi$
$30$		0			0
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$		−	3.22901i		−	0.553771i
$35$		0			0
$36$		0			0
$37$	1.05678	−	1.05678i	0.173733	−	0.173733i	−0.614884	−	0.788617i	$-0.710797\pi$
$37$	1.05678	−	1.05678i	0.173733	−	0.173733i	0.788617	+	0.614884i	$0.210797\pi$
$38$	−0.510593	+	0.510593i	−0.0828291	+	0.0828291i
$39$		0			0
$40$	−0.417821	−	2.19669i	−0.0660633	−	0.347326i
$41$		−	6.80974i		−	1.06350i	−0.846901	−	0.531751i	$-0.821534\pi$
$41$		−	6.80974i		−	1.06350i	0.846901	−	0.531751i	$-0.178466\pi$
$42$		0			0
$43$	1.20070	+	1.20070i	0.183106	+	0.183106i	0.792708	−	0.609602i	$-0.208671\pi$
$43$	1.20070	+	1.20070i	0.183106	+	0.183106i	−0.609602	+	0.792708i	$0.708671\pi$
$44$	−6.26456			−0.944419
$45$		0			0
$46$	−1.00000			−0.147442
$47$	−8.78026	−	8.78026i	−1.28073	−	1.28073i	−0.940251	−	0.340481i	$-0.889410\pi$
$47$	−8.78026	−	8.78026i	−1.28073	−	1.28073i	−0.340481	−	0.940251i	$-0.610590\pi$
$48$		0			0
$49$			7.00000i			1.00000i
$50$	1.99065	−	4.58664i	0.281521	−	0.648649i
$51$		0			0
$52$	4.39337	−	4.39337i	0.609251	−	0.609251i
$53$	−2.23754	+	2.23754i	−0.307350	+	0.307350i	−0.843881	−	0.536531i	$-0.819734\pi$
$53$	−2.23754	+	2.23754i	−0.307350	+	0.307350i	0.536531	+	0.843881i	$0.319734\pi$
$54$		0			0
$55$	−11.5815	−	7.87986i	−1.56165	−	1.06252i
$56$		0			0
$57$		0			0
$58$	4.20858	+	4.20858i	0.552614	+	0.552614i
$59$	12.7905			1.66518			0.832588	−	0.553893i	$-0.186858\pi$
$59$	12.7905			1.66518			0.832588	+	0.553893i	$0.186858\pi$
$60$		0			0
$61$	4.90833			0.628448			0.314224	−	0.949349i	$-0.398256\pi$
$61$	4.90833			0.628448			0.314224	+	0.949349i	$0.398256\pi$
$62$	−4.24264	−	4.24264i	−0.538816	−	0.538816i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	13.6484	−	2.59599i	1.69287	−	0.321993i
$66$		0			0
$67$	−7.15180	+	7.15180i	−0.873732	+	0.873732i	−0.992877	−	0.119145i	$-0.961985\pi$
$67$	−7.15180	+	7.15180i	−0.873732	+	0.873732i	0.119145	+	0.992877i	$0.461985\pi$
$68$	2.28326	−	2.28326i	0.276885	−	0.276885i
$69$		0			0
$70$		0			0
$71$			3.68633i			0.437487i	0.975782	+	0.218744i	$0.0701958\pi$
$71$			3.68633i			0.437487i	−0.975782	+	0.218744i	$0.929804\pi$
$72$		0			0
$73$	−11.6020	−	11.6020i	−1.35791	−	1.35791i	−0.876495	−	0.481410i	$-0.840125\pi$
$73$	−11.6020	−	11.6020i	−1.35791	−	1.35791i	−0.481410	−	0.876495i	$-0.659875\pi$
$74$	1.49451			0.173733
$75$		0			0
$76$	−0.722087			−0.0828291
$77$		0			0
$78$		0			0
$79$			0.442271i			0.0497594i	0.999690	+	0.0248797i	$0.00792027\pi$
$79$			0.442271i			0.0497594i	−0.999690	+	0.0248797i	$0.992080\pi$
$80$	1.25785	−	1.84873i	0.140632	−	0.206695i
$81$		0			0
$82$	4.81521	−	4.81521i	0.531751	−	0.531751i
$83$	−11.9671	+	11.9671i	−1.31356	+	1.31356i	−0.394794	+	0.918770i	$0.629184\pi$
$83$	−11.9671	+	11.9671i	−1.31356	+	1.31356i	−0.918770	+	0.394794i	$0.870816\pi$
$84$		0			0
$85$	7.09312	−	1.34915i	0.769357	−	0.146336i
$86$			1.69805i			0.183106i
$87$		0			0
$88$	−4.42972	−	4.42972i	−0.472209	−	0.472209i
$89$	−5.95183			−0.630893			−0.315446	−	0.948943i	$-0.602154\pi$
$89$	−5.95183			−0.630893			−0.315446	+	0.948943i	$0.602154\pi$
$90$		0			0
$91$		0			0
$92$	−0.707107	−	0.707107i	−0.0737210	−	0.0737210i
$93$		0			0
$94$		−	12.4172i		−	1.28073i
$95$	−1.33495	−	0.908275i	−0.136963	−	0.0931870i
$96$		0			0
$97$	6.97957	−	6.97957i	0.708668	−	0.708668i	−0.257587	−	0.966255i	$-0.582927\pi$
$97$	6.97957	−	6.97957i	0.708668	−	0.708668i	0.966255	+	0.257587i	$0.0829275\pi$
$98$	−4.94975	+	4.94975i	−0.500000	+	0.500000i
$99$		0			0
$100$	4.65085	−	1.83564i	0.465085	−	0.183564i
$101$		−	9.40572i		−	0.935905i	−0.883754	−	0.467952i	$-0.844992\pi$
$101$		−	9.40572i		−	0.935905i	0.883754	−	0.467952i	$-0.155008\pi$
$102$		0			0
$103$	−6.00000	−	6.00000i	−0.591198	−	0.591198i	0.346757	−	0.937955i	$-0.387283\pi$
$103$	−6.00000	−	6.00000i	−0.591198	−	0.591198i	−0.937955	+	0.346757i	$0.887283\pi$
$104$	6.21316			0.609251
$105$		0			0
$106$	−3.16436			−0.307350
$107$	0.0457171	+	0.0457171i	0.00441964	+	0.00441964i	0.709313	−	0.704894i	$-0.249005\pi$
$107$	0.0457171	+	0.0457171i	0.00441964	+	0.00441964i	−0.704894	+	0.709313i	$0.749005\pi$
$108$		0			0
$109$		−	5.25280i		−	0.503127i	−0.967841	−	0.251564i	$-0.919055\pi$
$109$		−	5.25280i		−	0.503127i	0.967841	−	0.251564i	$-0.0809448\pi$
$110$	−2.61747	−	13.7613i	−0.249566	−	1.31209i
$111$		0			0
$112$		0			0
$113$	−5.47582	+	5.47582i	−0.515122	+	0.515122i	−0.916091	−	0.400970i	$-0.868673\pi$
$113$	−5.47582	+	5.47582i	−0.515122	+	0.515122i	0.400970	+	0.916091i	$0.368673\pi$
$114$		0			0
$115$	−0.417821	−	2.19669i	−0.0389620	−	0.204842i
$116$			5.95183i			0.552614i
$117$		0			0
$118$	9.04422	+	9.04422i	0.832588	+	0.832588i
$119$		0			0
$120$		0			0
$121$	−28.2448			−2.56771
$122$	3.47072	+	3.47072i	0.314224	+	0.314224i
$123$		0			0
$124$		−	6.00000i		−	0.538816i
$125$	10.9071	+	2.45644i	0.975565	+	0.219711i
$126$		0			0
$127$	−6.95110	+	6.95110i	−0.616810	+	0.616810i	−0.944712	−	0.327902i	$-0.893659\pi$
$127$	−6.95110	+	6.95110i	−0.616810	+	0.616810i	0.327902	+	0.944712i	$0.393659\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	11.4865	+	7.81521i	1.00743	+	0.685439i
$131$		−	3.19256i		−	0.278935i	−0.990227	−	0.139468i	$-0.955461\pi$
$131$		−	3.19256i		−	0.278935i	0.990227	−	0.139468i	$-0.0445391\pi$
$132$		0			0
$133$		0			0
$134$	−10.1142			−0.873732
$135$		0			0
$136$	3.22901			0.276885
$137$	13.8919	+	13.8919i	1.18687	+	1.18687i	0.977928	+	0.208940i	$0.0670014\pi$
$137$	13.8919	+	13.8919i	1.18687	+	1.18687i	0.208940	+	0.977928i	$0.432999\pi$
$138$		0			0
$139$			13.0746i			1.10897i	0.832193	+	0.554486i	$0.187085\pi$
$139$			13.0746i			1.10897i	−0.832193	+	0.554486i	$0.812915\pi$
$140$		0			0
$141$		0			0
$142$	−2.60663	+	2.60663i	−0.218744	+	0.218744i
$143$	27.5226	−	27.5226i	2.30155	−	2.30155i
$144$		0			0
$145$	−7.48649	+	11.0034i	−0.621719	+	0.913779i
$146$		−	16.4076i		−	1.35791i
$147$		0			0
$148$	1.05678	+	1.05678i	0.0868666	+	0.0868666i
$149$	−21.8835			−1.79276			−0.896381	−	0.443284i	$-0.853813\pi$
$149$	−21.8835			−1.79276			−0.896381	+	0.443284i	$0.853813\pi$
$150$		0			0
$151$	−5.30170			−0.431446			−0.215723	−	0.976455i	$-0.569211\pi$
$151$	−5.30170			−0.431446			−0.215723	+	0.976455i	$0.569211\pi$
$152$	−0.510593	−	0.510593i	−0.0414145	−	0.0414145i
$153$		0			0
$154$		0			0
$155$	7.54708	−	11.0924i	0.606196	−	0.890964i
$156$		0			0
$157$	10.2858	−	10.2858i	0.820895	−	0.820895i	−0.165341	−	0.986236i	$-0.552872\pi$
$157$	10.2858	−	10.2858i	0.820895	−	0.820895i	0.986236	+	0.165341i	$0.0528725\pi$
$158$	−0.312733	+	0.312733i	−0.0248797	+	0.0248797i
$159$		0			0
$160$	2.19669	−	0.417821i	0.173663	−	0.0330316i
$161$		0			0
$162$		0			0
$163$	−12.9730	−	12.9730i	−1.01612	−	1.01612i	−0.999868	−	0.0162548i	$-0.994826\pi$
$163$	−12.9730	−	12.9730i	−1.01612	−	1.01612i	−0.0162548	−	0.999868i	$-0.505174\pi$
$164$	6.80974			0.531751
$165$		0			0
$166$	−16.9241			−1.31356
$167$	−1.15288	−	1.15288i	−0.0892126	−	0.0892126i	0.661092	−	0.750305i	$-0.270093\pi$
$167$	−1.15288	−	1.15288i	−0.0892126	−	0.0892126i	−0.750305	+	0.661092i	$0.770093\pi$
$168$		0			0
$169$			25.6034i			1.96949i
$170$	5.96959	+	4.06160i	0.457846	+	0.311511i
$171$		0			0
$172$	−1.20070	+	1.20070i	−0.0915528	+	0.0915528i
$173$	−12.4666	+	12.4666i	−0.947817	+	0.947817i	−0.998704	−	0.0508872i	$-0.983795\pi$
$173$	−12.4666	+	12.4666i	−0.947817	+	0.947817i	0.0508872	+	0.998704i	$0.483795\pi$
$174$		0			0
$175$		0			0
$176$		−	6.26456i		−	0.472209i
$177$		0			0
$178$	−4.20858	−	4.20858i	−0.315446	−	0.315446i
$179$	12.9511			0.968007			0.484004	−	0.875066i	$-0.339182\pi$
$179$	12.9511			0.968007			0.484004	+	0.875066i	$0.339182\pi$
$180$		0			0
$181$	−7.09167			−0.527119			−0.263560	−	0.964643i	$-0.584897\pi$
$181$	−7.09167			−0.527119			−0.263560	+	0.964643i	$0.584897\pi$
$182$		0			0
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	0.624437	+	3.28297i	0.0459095	+	0.241368i
$186$		0			0
$187$	14.3036	−	14.3036i	1.04598	−	1.04598i
$188$	8.78026	−	8.78026i	0.640366	−	0.640366i
$189$		0			0
$190$	−0.301703	−	1.58620i	−0.0218878	−	0.115075i
$191$		−	2.30576i		−	0.166839i	−0.996515	−	0.0834195i	$-0.973416\pi$
$191$		−	2.30576i		−	0.166839i	0.996515	−	0.0834195i	$-0.0265842\pi$
$192$		0			0
$193$	4.44417	+	4.44417i	0.319899	+	0.319899i	0.848728	−	0.528829i	$-0.177369\pi$
$193$	4.44417	+	4.44417i	0.319899	+	0.319899i	−0.528829	+	0.848728i	$0.677369\pi$
$194$	9.87060			0.708668
$195$		0			0
$196$	−7.00000			−0.500000
$197$	3.35584	+	3.35584i	0.239094	+	0.239094i	0.816475	−	0.577381i	$-0.195925\pi$
$197$	3.35584	+	3.35584i	0.239094	+	0.239094i	−0.577381	+	0.816475i	$0.695925\pi$
$198$		0			0
$199$			11.0903i			0.786174i	0.919501	+	0.393087i	$0.128593\pi$
$199$			11.0903i			0.786174i	−0.919501	+	0.393087i	$0.871407\pi$
$200$	4.58664	+	1.99065i	0.324325	+	0.140760i
$201$		0			0
$202$	6.65085	−	6.65085i	0.467952	−	0.467952i
$203$		0			0
$204$		0			0
$205$	12.5894	+	8.56561i	0.879281	+	0.598248i
$206$		−	8.48528i		−	0.591198i
$207$		0			0
$208$	4.39337	+	4.39337i	0.304625	+	0.304625i
$209$	−4.52356			−0.312901
$210$		0			0
$211$	−8.12931			−0.559645			−0.279822	−	0.960052i	$-0.590276\pi$
$211$	−8.12931			−0.559645			−0.279822	+	0.960052i	$0.590276\pi$
$212$	−2.23754	−	2.23754i	−0.153675	−	0.153675i
$213$		0			0
$214$			0.0646537i			0.00441964i
$215$	−3.73008	+	0.709481i	−0.254390	+	0.0483862i
$216$		0			0
$217$		0			0
$218$	3.71429	−	3.71429i	0.251564	−	0.251564i
$219$		0			0
$220$	7.87986	−	11.5815i	0.531260	−	0.780826i
$221$			20.0624i			1.34954i
$222$		0			0
$223$	11.7644	+	11.7644i	0.787803	+	0.787803i	0.981134	−	0.193331i	$-0.0619290\pi$
$223$	11.7644	+	11.7644i	0.787803	+	0.787803i	−0.193331	+	0.981134i	$0.561929\pi$
$224$		0			0
$225$		0			0
$226$	−7.74397			−0.515122
$227$	4.61223	+	4.61223i	0.306124	+	0.306124i	0.843404	−	0.537280i	$-0.180548\pi$
$227$	4.61223	+	4.61223i	0.306124	+	0.306124i	−0.537280	+	0.843404i	$0.680548\pi$
$228$		0			0
$229$		−	0.0237900i		−	0.00157209i	−1.00000		0.000786044i	$-0.999750\pi$
$229$		−	0.0237900i		−	0.00157209i	1.00000		0.000786044i	$-0.000250205\pi$
$230$	1.25785	−	1.84873i	0.0829400	−	0.121902i
$231$		0			0
$232$	−4.20858	+	4.20858i	−0.276307	+	0.276307i
$233$	1.18178	−	1.18178i	0.0774207	−	0.0774207i	−0.667336	−	0.744757i	$-0.732566\pi$
$233$	1.18178	−	1.18178i	0.0774207	−	0.0774207i	0.744757	+	0.667336i	$0.232566\pi$
$234$		0			0
$235$	27.2766	−	5.18815i	1.77933	−	0.338437i
$236$			12.7905i			0.832588i
$237$		0			0
$238$		0			0
$239$	26.7224			1.72853			0.864265	−	0.503036i	$-0.167784\pi$
$239$	26.7224			1.72853			0.864265	+	0.503036i	$0.167784\pi$
$240$		0			0
$241$	−22.7050			−1.46256			−0.731279	−	0.682078i	$-0.761076\pi$
$241$	−22.7050			−1.46256			−0.731279	+	0.682078i	$0.761076\pi$
$242$	−19.9721	−	19.9721i	−1.28385	−	1.28385i
$243$		0			0
$244$			4.90833i			0.314224i
$245$	−12.9411	−	8.80493i	−0.826779	−	0.562526i
$246$		0			0
$247$	3.17240	−	3.17240i	0.201855	−	0.201855i
$248$	4.24264	−	4.24264i	0.269408	−	0.269408i
$249$		0			0
$250$	5.97555	+	9.44949i	0.377927	+	0.597638i
$251$			14.3878i			0.908148i	0.890964	+	0.454074i	$0.150030\pi$
$251$			14.3878i			0.908148i	−0.890964	+	0.454074i	$0.849970\pi$
$252$		0			0
$253$	−4.42972	−	4.42972i	−0.278494	−	0.278494i
$254$	−9.83034			−0.616810
$255$		0			0
$256$	1.00000			0.0625000
$257$	12.1650	+	12.1650i	0.758832	+	0.758832i	0.976110	−	0.217278i	$-0.0697179\pi$
$257$	12.1650	+	12.1650i	0.758832	+	0.758832i	−0.217278	+	0.976110i	$0.569718\pi$
$258$		0			0
$259$		0			0
$260$	2.59599	+	13.6484i	0.160996	+	0.846436i
$261$		0			0
$262$	2.25748	−	2.25748i	0.139468	−	0.139468i
$263$	−12.2342	+	12.2342i	−0.754390	+	0.754390i	−0.975295	−	0.220905i	$-0.929099\pi$
$263$	−12.2342	+	12.2342i	−0.754390	+	0.754390i	0.220905	+	0.975295i	$0.429099\pi$
$264$		0			0
$265$	−1.32213	−	6.95110i	−0.0812181	−	0.427003i
$266$		0			0
$267$		0			0
$268$	−7.15180	−	7.15180i	−0.436866	−	0.436866i
$269$	−23.0475			−1.40523			−0.702615	−	0.711571i	$-0.747984\pi$
$269$	−23.0475			−1.40523			−0.702615	+	0.711571i	$0.747984\pi$
$270$		0			0
$271$	−11.4879			−0.697843			−0.348922	−	0.937152i	$-0.613452\pi$
$271$	−11.4879			−0.697843			−0.348922	+	0.937152i	$0.613452\pi$
$272$	2.28326	+	2.28326i	0.138443	+	0.138443i
$273$		0			0
$274$			19.6462i			1.18687i
$275$	29.1356	−	11.4995i	1.75694	−	0.693446i
$276$		0			0
$277$	−5.58152	+	5.58152i	−0.335361	+	0.335361i	−0.854618	−	0.519257i	$-0.826209\pi$
$277$	−5.58152	+	5.58152i	−0.335361	+	0.335361i	0.519257	+	0.854618i	$0.326209\pi$
$278$	−9.24513	+	9.24513i	−0.554486	+	0.554486i
$279$		0			0
$280$		0			0
$281$			24.1378i			1.43994i	0.694005	+	0.719971i	$0.255845\pi$
$281$			24.1378i			1.43994i	−0.694005	+	0.719971i	$0.744155\pi$
$282$		0			0
$283$	−0.920888	−	0.920888i	−0.0547411	−	0.0547411i	0.679206	−	0.733947i	$-0.262324\pi$
$283$	−0.920888	−	0.920888i	−0.0547411	−	0.0547411i	−0.733947	+	0.679206i	$0.762324\pi$
$284$	−3.68633			−0.218744
$285$		0			0
$286$	38.9228			2.30155
$287$		0			0
$288$		0			0
$289$		−	6.57348i		−	0.386675i
$290$	−13.0743	+	2.48680i	−0.767749	+	0.146030i
$291$		0			0
$292$	11.6020	−	11.6020i	0.678953	−	0.678953i
$293$	−12.1482	+	12.1482i	−0.709704	+	0.709704i	−0.966473	−	0.256769i	$-0.917342\pi$
$293$	−12.1482	+	12.1482i	−0.709704	+	0.709704i	0.256769	+	0.966473i	$0.417342\pi$
$294$		0			0
$295$	−16.0884	+	23.6462i	−0.936705	+	1.37673i
$296$			1.49451i			0.0868666i
$297$		0			0
$298$	−15.4739	−	15.4739i	−0.896381	−	0.896381i
$299$	6.21316			0.359317
$300$		0			0
$301$		0			0
$302$	−3.74887	−	3.74887i	−0.215723	−	0.215723i
$303$		0			0
$304$		−	0.722087i		−	0.0414145i
$305$	−6.17393	+	9.07421i	−0.353518	+	0.519588i
$306$		0			0
$307$	−2.45802	+	2.45802i	−0.140287	+	0.140287i	−0.773763	−	0.633476i	$-0.781628\pi$
$307$	−2.45802	+	2.45802i	−0.140287	+	0.140287i	0.633476	+	0.773763i	$0.281628\pi$
$308$		0			0
$309$		0			0
$310$	13.1801	−	2.50693i	0.748580	−	0.142384i
$311$			24.3589i			1.38127i	0.723206	+	0.690633i	$0.242668\pi$
$311$			24.3589i			1.38127i	−0.723206	+	0.690633i	$0.757332\pi$
$312$		0			0
$313$	16.8120	+	16.8120i	0.950270	+	0.950270i	0.998821	−	0.0485511i	$-0.0154604\pi$
$313$	16.8120	+	16.8120i	0.950270	+	0.950270i	−0.0485511	+	0.998821i	$0.515460\pi$
$314$	14.5463			0.820895
$315$		0			0
$316$	−0.442271			−0.0248797
$317$	−7.88871	−	7.88871i	−0.443074	−	0.443074i	0.449970	−	0.893044i	$-0.351435\pi$
$317$	−7.88871	−	7.88871i	−0.443074	−	0.443074i	−0.893044	+	0.449970i	$0.851435\pi$
$318$		0			0
$319$			37.2856i			2.08759i
$320$	1.84873	+	1.25785i	0.103347	+	0.0703158i
$321$		0			0
$322$		0			0
$323$	1.64871	−	1.64871i	0.0917367	−	0.0917367i
$324$		0			0
$325$	−12.3683	+	28.4976i	−0.686068	+	1.58076i
$326$		−	18.3466i		−	1.01612i
$327$		0			0
$328$	4.81521	+	4.81521i	0.265875	+	0.265875i
$329$		0			0
$330$		0			0
$331$	0.271778			0.0149383			0.00746915	−	0.999972i	$-0.497622\pi$
$331$	0.271778			0.0149383			0.00746915	+	0.999972i	$0.497622\pi$
$332$	−11.9671	−	11.9671i	−0.656782	−	0.656782i
$333$		0			0
$334$		−	1.63042i		−	0.0892126i
$335$	−4.22591	−	22.2177i	−0.230886	−	1.21388i
$336$		0			0
$337$	−6.83710	+	6.83710i	−0.372440	+	0.372440i	−0.868365	−	0.495925i	$-0.834829\pi$
$337$	−6.83710	+	6.83710i	−0.372440	+	0.372440i	0.495925	+	0.868365i	$0.334829\pi$
$338$	−18.1043	+	18.1043i	−0.984746	+	0.984746i
$339$		0			0
$340$	1.34915	+	7.09312i	0.0731679	+	0.384679i
$341$		−	37.5874i		−	2.03547i
$342$		0			0
$343$		0			0
$344$	−1.69805			−0.0915528
$345$		0			0
$346$	−17.6304			−0.947817
$347$	0.759852	+	0.759852i	0.0407910	+	0.0407910i	0.727208	−	0.686417i	$-0.240818\pi$
$347$	0.759852	+	0.759852i	0.0407910	+	0.0407910i	−0.686417	+	0.727208i	$0.740818\pi$
$348$		0			0
$349$		−	24.2338i		−	1.29721i	−0.761126	−	0.648603i	$-0.775353\pi$
$349$		−	24.2338i		−	1.29721i	0.761126	−	0.648603i	$-0.224647\pi$
$350$		0			0
$351$		0			0
$352$	4.42972	−	4.42972i	0.236105	−	0.236105i
$353$	−18.3156	+	18.3156i	−0.974842	+	0.974842i	−0.999691	−	0.0248491i	$-0.992089\pi$
$353$	−18.3156	+	18.3156i	−0.974842	+	0.974842i	0.0248491	+	0.999691i	$0.492089\pi$
$354$		0			0
$355$	−6.81505	−	4.63684i	−0.361705	−	0.246098i
$356$		−	5.95183i		−	0.315446i
$357$		0			0
$358$	9.15778	+	9.15778i	0.484004	+	0.484004i
$359$	24.1694			1.27561			0.637806	−	0.770197i	$-0.279842\pi$
$359$	24.1694			1.27561			0.637806	+	0.770197i	$0.279842\pi$
$360$		0			0
$361$	18.4786			0.972557
$362$	−5.01457	−	5.01457i	−0.263560	−	0.263560i
$363$		0			0
$364$		0			0
$365$	36.0424	−	6.85545i	1.88655	−	0.358831i
$366$		0			0
$367$	20.3445	−	20.3445i	1.06197	−	1.06197i	0.0640243	−	0.997948i	$-0.479606\pi$
$367$	20.3445	−	20.3445i	1.06197	−	1.06197i	0.997948	−	0.0640243i	$-0.0203935\pi$
$368$	0.707107	−	0.707107i	0.0368605	−	0.0368605i
$369$		0			0
$370$	−1.87986	+	2.76295i	−0.0977295	+	0.143639i
$371$		0			0
$372$		0			0
$373$	11.5148	+	11.5148i	0.596214	+	0.596214i	0.939303	−	0.343089i	$-0.111473\pi$
$373$	11.5148	+	11.5148i	0.596214	+	0.596214i	−0.343089	+	0.939303i	$0.611473\pi$
$374$	20.2284			1.04598
$375$		0			0
$376$	12.4172			0.640366
$377$	−26.1486	−	26.1486i	−1.34672	−	1.34672i
$378$		0			0
$379$		−	21.4837i		−	1.10354i	−0.833995	−	0.551772i	$-0.813952\pi$
$379$		−	21.4837i		−	1.10354i	0.833995	−	0.551772i	$-0.186048\pi$
$380$	0.908275	−	1.33495i	0.0465935	−	0.0684814i
$381$		0			0
$382$	1.63042	−	1.63042i	0.0834195	−	0.0834195i
$383$	−0.455567	+	0.455567i	−0.0232784	+	0.0232784i	−0.718650	−	0.695372i	$-0.755240\pi$
$383$	−0.455567	+	0.455567i	−0.0232784	+	0.0232784i	0.695372	+	0.718650i	$0.255240\pi$
$384$		0			0
$385$		0			0
$386$			6.28501i			0.319899i
$387$		0			0
$388$	6.97957	+	6.97957i	0.354334	+	0.354334i
$389$	−15.0448			−0.762803			−0.381401	−	0.924410i	$-0.624558\pi$
$389$	−15.0448			−0.762803			−0.381401	+	0.924410i	$0.624558\pi$
$390$		0			0
$391$	3.22901			0.163298
$392$	−4.94975	−	4.94975i	−0.250000	−	0.250000i
$393$		0			0
$394$			4.74588i			0.239094i
$395$	−0.817642	−	0.556310i	−0.0411401	−	0.0279910i
$396$		0			0
$397$	24.1531	−	24.1531i	1.21221	−	1.21221i	0.241911	−	0.970299i	$-0.422226\pi$
$397$	24.1531	−	24.1531i	1.21221	−	1.21221i	0.970299	−	0.241911i	$-0.0777741\pi$
$398$	−7.84206	+	7.84206i	−0.393087	+	0.393087i
$399$		0			0
$400$	1.83564	+	4.65085i	0.0917821	+	0.232543i
$401$			0.714842i			0.0356975i	0.999841	+	0.0178488i	$0.00568174\pi$
$401$			0.714842i			0.0356975i	−0.999841	+	0.0178488i	$0.994318\pi$
$402$		0			0
$403$	26.3602	+	26.3602i	1.31310	+	1.31310i
$404$	9.40572			0.467952
$405$		0			0
$406$		0			0
$407$	6.62025	+	6.62025i	0.328154	+	0.328154i
$408$		0			0
$409$			4.88835i			0.241713i	0.992670	+	0.120857i	$0.0385641\pi$
$409$			4.88835i			0.241713i	−0.992670	+	0.120857i	$0.961436\pi$
$410$	2.84525	+	14.9588i	0.140517	+	0.738765i
$411$		0			0
$412$	6.00000	−	6.00000i	0.295599	−	0.295599i
$413$		0			0
$414$		0			0
$415$	−7.07124	−	37.1769i	−0.347113	−	1.82494i
$416$			6.21316i			0.304625i
$417$		0			0
$418$	−3.19864	−	3.19864i	−0.156451	−	0.156451i
$419$	15.2034			0.742732			0.371366	−	0.928486i	$-0.378889\pi$
$419$	15.2034			0.742732			0.371366	+	0.928486i	$0.378889\pi$
$420$		0			0
$421$	21.3821			1.04210			0.521050	−	0.853526i	$-0.325540\pi$
$421$	21.3821			1.04210			0.521050	+	0.853526i	$0.325540\pi$
$422$	−5.74829	−	5.74829i	−0.279822	−	0.279822i
$423$		0			0
$424$		−	3.16436i		−	0.153675i
$425$	−6.42785	+	14.8103i	−0.311796	+	0.718406i
$426$		0			0
$427$		0			0
$428$	−0.0457171	+	0.0457171i	−0.00220982	+	0.00220982i
$429$		0			0
$430$	−3.13925	−	2.13589i	−0.151388	−	0.103002i
$431$		−	25.6387i		−	1.23497i	−0.786581	−	0.617487i	$-0.788151\pi$
$431$		−	25.6387i		−	1.23497i	0.786581	−	0.617487i	$-0.211849\pi$
$432$		0			0
$433$	−13.4376	−	13.4376i	−0.645769	−	0.645769i	0.306198	−	0.951968i	$-0.400943\pi$
$433$	−13.4376	−	13.4376i	−0.645769	−	0.645769i	−0.951968	+	0.306198i	$0.900943\pi$
$434$		0			0
$435$		0			0
$436$	5.25280			0.251564
$437$	−0.510593	−	0.510593i	−0.0244250	−	0.0244250i
$438$		0			0
$439$			28.7327i			1.37134i	0.727914	+	0.685669i	$0.240490\pi$
$439$			28.7327i			1.37134i	−0.727914	+	0.685669i	$0.759510\pi$
$440$	13.7613	−	2.61747i	0.656043	−	0.124783i
$441$		0			0
$442$	−14.1862	+	14.1862i	−0.674771	+	0.674771i
$443$	8.41612	−	8.41612i	0.399862	−	0.399862i	−0.478322	−	0.878184i	$-0.658755\pi$
$443$	8.41612	−	8.41612i	0.399862	−	0.399862i	0.878184	+	0.478322i	$0.158755\pi$
$444$		0			0
$445$	7.48649	−	11.0034i	0.354894	−	0.521609i
$446$			16.6374i			0.787803i
$447$		0			0
$448$		0			0
$449$	−12.6495			−0.596965			−0.298482	−	0.954415i	$-0.596480\pi$
$449$	−12.6495			−0.596965			−0.298482	+	0.954415i	$0.596480\pi$
$450$		0			0
$451$	42.6600			2.00878
$452$	−5.47582	−	5.47582i	−0.257561	−	0.257561i
$453$		0			0
$454$			6.52268i			0.306124i
$455$		0			0
$456$		0			0
$457$	−2.29702	+	2.29702i	−0.107450	+	0.107450i	−0.758788	−	0.651338i	$-0.774208\pi$
$457$	−2.29702	+	2.29702i	−0.107450	+	0.107450i	0.651338	+	0.758788i	$0.274208\pi$
$458$	0.0168221	−	0.0168221i	0.000786044	−	0.000786044i
$459$		0			0
$460$	2.19669	−	0.417821i	0.102421	−	0.0194810i
$461$			42.5253i			1.98060i	0.138946	+	0.990300i	$0.455628\pi$
$461$			42.5253i			1.98060i	−0.138946	+	0.990300i	$0.544372\pi$
$462$		0			0
$463$	4.29367	+	4.29367i	0.199544	+	0.199544i	0.799804	−	0.600261i	$-0.204937\pi$
$463$	4.29367	+	4.29367i	0.199544	+	0.199544i	−0.600261	+	0.799804i	$0.704937\pi$
$464$	−5.95183			−0.276307
$465$		0			0
$466$	1.67128			0.0774207
$467$	−26.5050	−	26.5050i	−1.22650	−	1.22650i	−0.965277	−	0.261227i	$-0.915873\pi$
$467$	−26.5050	−	26.5050i	−1.22650	−	1.22650i	−0.261227	−	0.965277i	$-0.584127\pi$
$468$		0			0
$469$		0			0
$470$	22.9560	+	15.6189i	1.05888	+	0.720446i
$471$		0			0
$472$	−9.04422	+	9.04422i	−0.416294	+	0.416294i
$473$	−7.52189	+	7.52189i	−0.345857	+	0.345857i
$474$		0			0
$475$	3.35832	−	1.32549i	0.154090	−	0.0608178i
$476$		0			0
$477$		0			0
$478$	18.8956	+	18.8956i	0.864265	+	0.864265i
$479$	−25.4781			−1.16413			−0.582063	−	0.813144i	$-0.697754\pi$
$479$	−25.4781			−1.16413			−0.582063	+	0.813144i	$0.697754\pi$
$480$		0			0
$481$	−9.28563			−0.423388
$482$	−16.0549	−	16.0549i	−0.731279	−	0.731279i
$483$		0			0
$484$		−	28.2448i		−	1.28385i
$485$	4.12414	+	21.6826i	0.187268	+	0.984556i
$486$		0			0
$487$	1.74720	−	1.74720i	0.0791731	−	0.0791731i	−0.666411	−	0.745584i	$-0.732170\pi$
$487$	1.74720	−	1.74720i	0.0791731	−	0.0791731i	0.745584	+	0.666411i	$0.232170\pi$
$488$	−3.47072	+	3.47072i	−0.157112	+	0.157112i
$489$		0			0
$490$	−2.92475	−	15.3768i	−0.132127	−	0.694653i
$491$			36.6333i			1.65324i	0.562762	+	0.826619i	$0.309739\pi$
$491$			36.6333i			1.65324i	−0.562762	+	0.826619i	$0.690261\pi$
$492$		0			0
$493$	−13.5896	−	13.5896i	−0.612043	−	0.612043i
$494$	4.48644			0.201855
$495$		0			0
$496$	6.00000			0.269408
$497$		0			0
$498$		0			0
$499$		−	13.7189i		−	0.614141i	−0.951687	−	0.307070i	$-0.900651\pi$
$499$		−	13.7189i		−	0.614141i	0.951687	−	0.307070i	$-0.0993487\pi$
$500$	−2.45644	+	10.9071i	−0.109856	+	0.487782i
$501$		0			0
$502$	−10.1737	+	10.1737i	−0.454074	+	0.454074i
$503$	−21.7313	+	21.7313i	−0.968951	+	0.968951i	−0.999532	−	0.0305811i	$-0.990264\pi$
$503$	−21.7313	+	21.7313i	−0.968951	+	0.968951i	0.0305811	+	0.999532i	$0.490264\pi$
$504$		0			0
$505$	17.3887	+	11.8310i	0.773787	+	0.526471i
$506$		−	6.26456i		−	0.278494i
$507$		0			0
$508$	−6.95110	−	6.95110i	−0.308405	−	0.308405i
$509$	10.1563			0.450169			0.225084	−	0.974339i	$-0.427734\pi$
$509$	10.1563			0.450169			0.225084	+	0.974339i	$0.427734\pi$
$510$		0			0
$511$		0			0
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$			17.2039i			0.758832i
$515$	18.6395	−	3.54533i	0.821354	−	0.156226i
$516$		0			0
$517$	55.0045	−	55.0045i	2.41909	−	2.41909i
$518$		0			0
$519$		0			0
$520$	−7.81521	+	11.4865i	−0.342720	+	0.503716i
$521$			33.5528i			1.46998i	0.678080	+	0.734988i	$0.262812\pi$
$521$			33.5528i			1.46998i	−0.678080	+	0.734988i	$0.737188\pi$
$522$		0			0
$523$	11.8041	+	11.8041i	0.516158	+	0.516158i	0.916407	−	0.400249i	$-0.131076\pi$
$523$	11.8041	+	11.8041i	0.516158	+	0.516158i	−0.400249	+	0.916407i	$0.631076\pi$
$524$	3.19256			0.139468
$525$		0			0
$526$	−17.3017			−0.754390
$527$	13.6995	+	13.6995i	0.596761	+	0.596761i
$528$		0			0
$529$		−	1.00000i		−	0.0434783i
$530$	3.98028	−	5.85006i	0.172892	−	0.254110i
$531$		0			0
$532$		0			0
$533$	−29.9177	+	29.9177i	−1.29588	+	1.29588i
$534$		0			0
$535$	−0.142024	+	0.0270137i	−0.00614022	+	0.00116790i
$536$		−	10.1142i		−	0.436866i
$537$		0			0
$538$	−16.2970	−	16.2970i	−0.702615	−	0.702615i
$539$	−43.8519			−1.88884
$540$		0			0
$541$	−21.5195			−0.925194			−0.462597	−	0.886569i	$-0.653082\pi$
$541$	−21.5195			−0.925194			−0.462597	+	0.886569i	$0.653082\pi$
$542$	−8.12321	−	8.12321i	−0.348922	−	0.348922i
$543$		0			0
$544$			3.22901i			0.138443i
$545$	9.71104	+	6.60722i	0.415975	+	0.283022i
$546$		0			0
$547$	−3.74397	+	3.74397i	−0.160081	+	0.160081i	−0.782603	−	0.622522i	$-0.786108\pi$
$547$	−3.74397	+	3.74397i	−0.160081	+	0.160081i	0.622522	+	0.782603i	$0.286108\pi$
$548$	−13.8919	+	13.8919i	−0.593434	+	0.593434i
$549$		0			0
$550$	28.7333	+	12.4706i	1.22519	+	0.531747i
$551$			4.29774i			0.183090i
$552$		0			0
$553$		0			0
$554$	−7.89346			−0.335361
$555$		0			0
$556$	−13.0746			−0.554486
$557$	−24.2124	−	24.2124i	−1.02591	−	1.02591i	−0.999655	−	0.0262582i	$-0.991641\pi$
$557$	−24.2124	−	24.2124i	−1.02591	−	1.02591i	−0.0262582	−	0.999655i	$-0.508359\pi$
$558$		0			0
$559$		−	10.5503i		−	0.446229i
$560$		0			0
$561$		0			0
$562$	−17.0680	+	17.0680i	−0.719971	+	0.719971i
$563$	11.5714	−	11.5714i	0.487677	−	0.487677i	−0.419895	−	0.907572i	$-0.637933\pi$
$563$	11.5714	−	11.5714i	0.487677	−	0.487677i	0.907572	+	0.419895i	$0.137933\pi$
$564$		0			0
$565$	−3.23559	−	17.0111i	−0.136122	−	0.715661i
$566$		−	1.30233i		−	0.0547411i
$567$		0			0
$568$	−2.60663	−	2.60663i	−0.109372	−	0.109372i
$569$	−25.4874			−1.06849			−0.534244	−	0.845330i	$-0.679404\pi$
$569$	−25.4874			−1.06849			−0.534244	+	0.845330i	$0.679404\pi$
$570$		0			0
$571$	15.3004			0.640301			0.320151	−	0.947367i	$-0.396267\pi$
$571$	15.3004			0.640301			0.320151	+	0.947367i	$0.396267\pi$
$572$	27.5226	+	27.5226i	1.15078	+	1.15078i
$573$		0			0
$574$		0			0
$575$	4.58664	+	1.99065i	0.191276	+	0.0830160i
$576$		0			0
$577$	5.27323	−	5.27323i	0.219528	−	0.219528i	−0.588772	−	0.808299i	$-0.700388\pi$
$577$	5.27323	−	5.27323i	0.219528	−	0.219528i	0.808299	+	0.588772i	$0.200388\pi$
$578$	4.64815	−	4.64815i	0.193338	−	0.193338i
$579$		0			0
$580$	−11.0034	−	7.48649i	−0.456890	−	0.310860i
$581$		0			0
$582$		0			0
$583$	−14.0172	−	14.0172i	−0.580533	−	0.580533i
$584$	16.4076			0.678953
$585$		0			0
$586$	−17.1801			−0.709704
$587$	−4.20238	−	4.20238i	−0.173451	−	0.173451i	0.615043	−	0.788494i	$-0.289139\pi$
$587$	−4.20238	−	4.20238i	−0.173451	−	0.173451i	−0.788494	+	0.615043i	$0.789139\pi$
$588$		0			0
$589$		−	4.33252i		−	0.178518i
$590$	−28.0966	+	5.34412i	−1.15672	+	0.220014i
$591$		0			0
$592$	−1.05678	+	1.05678i	−0.0434333	+	0.0434333i
$593$	15.0512	−	15.0512i	0.618079	−	0.618079i	−0.326959	−	0.945038i	$-0.606024\pi$
$593$	15.0512	−	15.0512i	0.618079	−	0.618079i	0.945038	+	0.326959i	$0.106024\pi$
$594$		0			0
$595$		0			0
$596$		−	21.8835i		−	0.896381i
$597$		0			0
$598$	4.39337	+	4.39337i	0.179658	+	0.179658i
$599$	13.5906			0.555296			0.277648	−	0.960683i	$-0.410445\pi$
$599$	13.5906			0.555296			0.277648	+	0.960683i	$0.410445\pi$
$600$		0			0
$601$	−2.41335			−0.0984428			−0.0492214	−	0.998788i	$-0.515674\pi$
$601$	−2.41335			−0.0984428			−0.0492214	+	0.998788i	$0.515674\pi$
$602$		0			0
$603$		0			0
$604$		−	5.30170i		−	0.215723i
$605$	35.5276	−	52.2171i	1.44440	−	2.12293i
$606$		0			0
$607$	−26.9683	+	26.9683i	−1.09461	+	1.09461i	−0.0995803	+	0.995030i	$0.531750\pi$
$607$	−26.9683	+	26.9683i	−1.09461	+	1.09461i	−0.995030	+	0.0995803i	$0.968250\pi$
$608$	0.510593	−	0.510593i	0.0207073	−	0.0207073i
$609$		0			0
$610$	−10.7821	+	2.05080i	−0.436553	+	0.0830346i
$611$			77.1499i			3.12115i
$612$		0			0
$613$	−28.2526	−	28.2526i	−1.14111	−	1.14111i	−0.988247	−	0.152867i	$-0.951150\pi$
$613$	−28.2526	−	28.2526i	−1.14111	−	1.14111i	−0.152867	−	0.988247i	$-0.548850\pi$
$614$	−3.47617			−0.140287
$615$		0			0
$616$		0			0
$617$	2.21410	+	2.21410i	0.0891363	+	0.0891363i	0.750269	−	0.661133i	$-0.229924\pi$
$617$	2.21410	+	2.21410i	0.0891363	+	0.0891363i	−0.661133	+	0.750269i	$0.729924\pi$
$618$		0			0
$619$			16.1940i			0.650890i	0.945561	+	0.325445i	$0.105514\pi$
$619$			16.1940i			0.650890i	−0.945561	+	0.325445i	$0.894486\pi$
$620$	11.0924	+	7.54708i	0.445482	+	0.303098i
$621$		0			0
$622$	−17.2243	+	17.2243i	−0.690633	+	0.690633i
$623$		0			0
$624$		0			0
$625$	−18.2608	+	17.0746i	−0.730434	+	0.682984i
$626$			23.7757i			0.950270i
$627$		0			0
$628$	10.2858	+	10.2858i	0.410448	+	0.410448i
$629$	−4.82579			−0.192417
$630$		0			0
$631$	38.9479			1.55049			0.775245	−	0.631660i	$-0.217626\pi$
$631$	38.9479			1.55049			0.775245	+	0.631660i	$0.217626\pi$
$632$	−0.312733	−	0.312733i	−0.0124399	−	0.0124399i
$633$		0			0
$634$		−	11.1563i		−	0.443074i
$635$	−4.10732	−	21.5942i	−0.162994	−	0.856938i
$636$		0			0
$637$	30.7536	−	30.7536i	1.21850	−	1.21850i
$638$	−26.3649	+	26.3649i	−1.04380	+	1.04380i
$639$		0			0
$640$	0.417821	+	2.19669i	0.0165158	+	0.0868316i
$641$		−	15.2454i		−	0.602159i	−0.953599	−	0.301079i	$-0.902653\pi$
$641$		−	15.2454i		−	0.602159i	0.953599	−	0.301079i	$-0.0973469\pi$
$642$		0			0
$643$	20.1405	+	20.1405i	0.794265	+	0.794265i	0.982185	−	0.187919i	$-0.0601743\pi$
$643$	20.1405	+	20.1405i	0.794265	+	0.794265i	−0.187919	+	0.982185i	$0.560174\pi$
$644$		0			0
$645$		0			0
$646$	2.33163			0.0917367
$647$	7.52664	+	7.52664i	0.295903	+	0.295903i	0.839407	−	0.543504i	$-0.182903\pi$
$647$	7.52664	+	7.52664i	0.295903	+	0.295903i	−0.543504	+	0.839407i	$0.682903\pi$
$648$		0			0
$649$			80.1267i			3.14525i
$650$	−28.8965	+	11.4051i	−1.13341	+	0.447346i
$651$		0			0
$652$	12.9730	−	12.9730i	0.508061	−	0.508061i
$653$	13.7605	−	13.7605i	0.538489	−	0.538489i	−0.384596	−	0.923085i	$-0.625659\pi$
$653$	13.7605	−	13.7605i	0.538489	−	0.538489i	0.923085	+	0.384596i	$0.125659\pi$
$654$		0			0
$655$	5.90220	+	4.01575i	0.230618	+	0.156908i
$656$			6.80974i			0.265875i
$657$		0			0
$658$		0			0
$659$	−10.7974			−0.420608			−0.210304	−	0.977636i	$-0.567445\pi$
$659$	−10.7974			−0.420608			−0.210304	+	0.977636i	$0.567445\pi$
$660$		0			0
$661$	12.5954			0.489903			0.244952	−	0.969535i	$-0.421228\pi$
$661$	12.5954			0.489903			0.244952	+	0.969535i	$0.421228\pi$
$662$	0.192176	+	0.192176i	0.00746915	+	0.00746915i
$663$		0			0
$664$		−	16.9241i		−	0.656782i
$665$		0			0
$666$		0			0
$667$	−4.20858	+	4.20858i	−0.162957	+	0.162957i
$668$	1.15288	−	1.15288i	0.0446063	−	0.0446063i
$669$		0			0
$670$	12.7221	−	18.6984i	0.491497	−	0.722383i
$671$			30.7486i			1.18704i
$672$		0			0
$673$	−2.30025	−	2.30025i	−0.0886680	−	0.0886680i	0.661382	−	0.750050i	$-0.269970\pi$
$673$	−2.30025	−	2.30025i	−0.0886680	−	0.0886680i	−0.750050	+	0.661382i	$0.769970\pi$
$674$	−9.66912			−0.372440
$675$		0			0
$676$	−25.6034			−0.984746
$677$	24.8493	+	24.8493i	0.955035	+	0.955035i	0.999032	−	0.0439971i	$-0.0140092\pi$
$677$	24.8493	+	24.8493i	0.955035	+	0.955035i	−0.0439971	+	0.999032i	$0.514009\pi$
$678$		0			0
$679$		0			0
$680$	−4.06160	+	5.96959i	−0.155755	+	0.228923i
$681$		0			0
$682$	26.5783	−	26.5783i	1.01774	−	1.01774i
$683$	−32.6923	+	32.6923i	−1.25093	+	1.25093i	−0.295632	+	0.955302i	$0.595530\pi$
$683$	−32.6923	+	32.6923i	−1.25093	+	1.25093i	−0.955302	+	0.295632i	$0.904470\pi$
$684$		0			0
$685$	−43.1565	+	8.20858i	−1.64892	+	0.313634i
$686$		0			0
$687$		0			0
$688$	−1.20070	−	1.20070i	−0.0457764	−	0.0457764i
$689$	19.6607			0.749012
$690$		0			0
$691$	−36.3223			−1.38176			−0.690882	−	0.722967i	$-0.742778\pi$
$691$	−36.3223			−1.38176			−0.690882	+	0.722967i	$0.742778\pi$
$692$	−12.4666	−	12.4666i	−0.473909	−	0.473909i
$693$		0			0
$694$			1.07459i			0.0407910i
$695$	−24.1715	−	16.4458i	−0.916876	−	0.623826i
$696$		0			0
$697$	−15.5484	+	15.5484i	−0.588937	+	0.588937i
$698$	17.1359	−	17.1359i	0.648603	−	0.648603i
$699$		0			0
$700$		0			0
$701$		−	29.9039i		−	1.12945i	−0.825278	−	0.564727i	$-0.808982\pi$
$701$		−	29.9039i		−	1.12945i	0.825278	−	0.564727i	$-0.191018\pi$
$702$		0			0
$703$	0.763085	+	0.763085i	0.0287803	+	0.0287803i
$704$	6.26456			0.236105
$705$		0			0
$706$	−25.9022			−0.974842
$707$		0			0
$708$		0			0
$709$		−	40.4278i		−	1.51830i	−0.650917	−	0.759149i	$-0.725616\pi$
$709$		−	40.4278i		−	1.51830i	0.650917	−	0.759149i	$-0.274384\pi$
$710$	−1.54023	−	8.09771i	−0.0578036	−	0.303902i
$711$		0			0
$712$	4.20858	−	4.20858i	0.157723	−	0.157723i
$713$	4.24264	−	4.24264i	0.158888	−	0.158888i
$714$		0			0
$715$	16.2627	+	85.5011i	0.608192	+	3.19756i
$716$			12.9511i			0.484004i
$717$		0			0
$718$	17.0903	+	17.0903i	0.637806	+	0.637806i
$719$	−1.60639			−0.0599082			−0.0299541	−	0.999551i	$-0.509536\pi$
$719$	−1.60639			−0.0599082			−0.0299541	+	0.999551i	$0.509536\pi$
$720$		0			0
$721$		0			0
$722$	13.0663	+	13.0663i	0.486279	+	0.486279i
$723$		0			0
$724$		−	7.09167i		−	0.263560i
$725$	−10.9254	−	27.6811i	−0.405760	−	1.02805i
$726$		0			0
$727$	12.6034	−	12.6034i	0.467434	−	0.467434i	−0.433648	−	0.901082i	$-0.642774\pi$
$727$	12.6034	−	12.6034i	0.467434	−	0.467434i	0.901082	+	0.433648i	$0.142774\pi$
$728$		0			0
$729$		0			0
$730$	30.3334	+	20.6383i	1.12269	+	0.763858i
$731$		−	5.48303i		−	0.202797i
$732$		0			0
$733$	−9.52284	−	9.52284i	−0.351734	−	0.351734i	0.509020	−	0.860754i	$-0.330008\pi$
$733$	−9.52284	−	9.52284i	−0.351734	−	0.351734i	−0.860754	+	0.509020i	$0.830008\pi$
$734$	28.7714			1.06197
$735$		0			0
$736$	1.00000			0.0368605
$737$	−44.8029	−	44.8029i	−1.65034	−	1.65034i
$738$		0			0
$739$			29.4757i			1.08428i	0.840288	+	0.542140i	$0.182386\pi$
$739$			29.4757i			1.08428i	−0.840288	+	0.542140i	$0.817614\pi$
$740$	−3.28297	+	0.624437i	−0.120684	+	0.0229548i
$741$		0			0
$742$		0			0
$743$	8.67746	−	8.67746i	0.318345	−	0.318345i	−0.529786	−	0.848131i	$-0.677728\pi$
$743$	8.67746	−	8.67746i	0.318345	−	0.318345i	0.848131	+	0.529786i	$0.177728\pi$
$744$		0			0
$745$	27.5260	−	40.4567i	1.00848	−	1.48222i
$746$			16.2844i			0.596214i
$747$		0			0
$748$	14.3036	+	14.3036i	0.522992	+	0.522992i
$749$		0			0
$750$		0			0
$751$	−5.87328			−0.214319			−0.107160	−	0.994242i	$-0.534176\pi$
$751$	−5.87328			−0.214319			−0.107160	+	0.994242i	$0.534176\pi$
$752$	8.78026	+	8.78026i	0.320183	+	0.320183i
$753$		0			0
$754$		−	36.9797i		−	1.34672i
$755$	6.66873	−	9.80144i	0.242700	−	0.356711i
$756$		0			0
$757$	−0.00597368	+	0.00597368i	−0.000217117	+	0.000217117i	−0.707215	−	0.706998i	$-0.750049\pi$
$757$	−0.00597368	+	0.00597368i	−0.000217117	+	0.000217117i	0.706998	+	0.707215i	$0.250049\pi$
$758$	15.1913	−	15.1913i	0.551772	−	0.551772i
$759$		0			0
$760$	1.58620	−	0.301703i	0.0575374	−	0.0109439i
$761$		−	43.3852i		−	1.57271i	−0.617772	−	0.786357i	$-0.711965\pi$
$761$		−	43.3852i		−	1.57271i	0.617772	−	0.786357i	$-0.288035\pi$
$762$		0			0
$763$		0			0
$764$	2.30576			0.0834195
$765$		0			0
$766$	−0.644270			−0.0232784
$767$	−56.1932	−	56.1932i	−2.02902	−	2.02902i
$768$		0			0
$769$		−	11.2856i		−	0.406970i	−0.979078	−	0.203485i	$-0.934773\pi$
$769$		−	11.2856i		−	0.406970i	0.979078	−	0.203485i	$-0.0652268\pi$
$770$		0			0
$771$		0			0
$772$	−4.44417	+	4.44417i	−0.159949	+	0.159949i
$773$	−12.8566	+	12.8566i	−0.462421	+	0.462421i	−0.899448	−	0.437027i	$-0.856031\pi$
$773$	−12.8566	+	12.8566i	−0.462421	+	0.462421i	0.437027	+	0.899448i	$0.356031\pi$
$774$		0			0
$775$	11.0139	+	27.9051i	0.395629	+	1.00238i
$776$			9.87060i			0.354334i
$777$		0			0
$778$	−10.6383	−	10.6383i	−0.381401	−	0.381401i
$779$	4.91722			0.176178
$780$		0			0
$781$	−23.0933			−0.826342
$782$	2.28326	+	2.28326i	0.0816491	+	0.0816491i
$783$		0			0
$784$		−	7.00000i		−	0.250000i
$785$	6.07775	+	31.9536i	0.216924	+	1.14047i
$786$		0			0
$787$	30.0521	−	30.0521i	1.07124	−	1.07124i	0.0739820	−	0.997260i	$-0.476429\pi$
$787$	30.0521	−	30.0521i	1.07124	−	1.07124i	0.997260	−	0.0739820i	$-0.0235707\pi$
$788$	−3.35584	+	3.35584i	−0.119547	+	0.119547i
$789$		0			0
$790$	−0.184790	−	0.971531i	−0.00657454	−	0.0345655i
$791$		0			0
$792$		0			0
$793$	−21.5641	−	21.5641i	−0.765764	−	0.765764i
$794$	34.1576			1.21221
$795$		0			0
$796$	−11.0903			−0.393087
$797$	13.3907	+	13.3907i	0.474321	+	0.474321i	0.903310	−	0.428989i	$-0.141130\pi$
$797$	13.3907	+	13.3907i	0.474321	+	0.474321i	−0.428989	+	0.903310i	$0.641130\pi$
$798$		0			0
$799$			40.0952i			1.41846i
$800$	−1.99065	+	4.58664i	−0.0703802	+	0.162162i
$801$		0			0
$802$	−0.505470	+	0.505470i	−0.0178488	+	0.0178488i
$803$	72.6812	−	72.6812i	2.56486	−	2.56486i
$804$		0			0
$805$		0			0
$806$			37.2790i			1.31310i
$807$		0			0
$808$	6.65085	+	6.65085i	0.233976	+	0.233976i
$809$	−41.5216			−1.45982			−0.729911	−	0.683542i	$-0.760439\pi$
$809$	−41.5216			−1.45982			−0.729911	+	0.683542i	$0.760439\pi$
$810$		0			0
$811$	−52.2691			−1.83542			−0.917709	−	0.397254i	$-0.869963\pi$
$811$	−52.2691			−1.83542			−0.917709	+	0.397254i	$0.869963\pi$
$812$		0			0
$813$		0			0
$814$			9.36245i			0.328154i
$815$	40.3016	−	7.66558i	1.41171	−	0.268514i
$816$		0			0
$817$	−0.867013	+	0.867013i	−0.0303329	+	0.0303329i
$818$	−3.45658	+	3.45658i	−0.120857	+	0.120857i
$819$		0			0
$820$	−8.56561	+	12.5894i	−0.299124	+	0.439641i
$821$			9.66500i			0.337311i	0.985675	+	0.168655i	$0.0539425\pi$
$821$			9.66500i			0.337311i	−0.985675	+	0.168655i	$0.946058\pi$
$822$		0			0
$823$	−25.8528	−	25.8528i	−0.901174	−	0.901174i	0.0943641	−	0.995538i	$-0.469918\pi$
$823$	−25.8528	−	25.8528i	−0.901174	−	0.901174i	−0.995538	+	0.0943641i	$0.969918\pi$
$824$	8.48528			0.295599
$825$		0			0
$826$		0			0
$827$	30.1240	+	30.1240i	1.04751	+	1.04751i	0.998813	+	0.0487005i	$0.0155080\pi$
$827$	30.1240	+	30.1240i	1.04751	+	1.04751i	0.0487005	+	0.998813i	$0.484492\pi$
$828$		0			0
$829$		−	22.0315i		−	0.765186i	−0.923917	−	0.382593i	$-0.875031\pi$
$829$		−	22.0315i		−	0.765186i	0.923917	−	0.382593i	$-0.124969\pi$
$830$	21.2879	−	31.2881i	0.738914	−	1.08603i
$831$		0			0
$832$	−4.39337	+	4.39337i	−0.152313	+	0.152313i
$833$	15.9828	−	15.9828i	0.553771	−	0.553771i
$834$		0			0
$835$	3.58152	−	0.681223i	0.123944	−	0.0235747i
$836$		−	4.52356i		−	0.156451i
$837$		0			0
$838$	10.7504	+	10.7504i	0.371366	+	0.371366i
$839$	16.2687			0.561658			0.280829	−	0.959758i	$-0.409391\pi$
$839$	16.2687			0.561658			0.280829	+	0.959758i	$0.409391\pi$
$840$		0			0
$841$	6.42429			0.221527
$842$	15.1194	+	15.1194i	0.521050	+	0.521050i
$843$		0			0
$844$		−	8.12931i		−	0.279822i
$845$	−47.3339	−	32.2052i	−1.62834	−	1.10789i
$846$		0			0
$847$		0			0
$848$	2.23754	−	2.23754i	0.0768374	−	0.0768374i
$849$		0			0
$850$	−15.0177	+	5.92731i	−0.515101	+	0.203305i
$851$			1.49451i			0.0512311i
$852$		0			0
$853$	9.96685	+	9.96685i	0.341259	+	0.341259i	0.856840	−	0.515582i	$-0.172424\pi$
$853$	9.96685	+	9.96685i	0.341259	+	0.341259i	−0.515582	+	0.856840i	$0.672424\pi$
$854$		0			0
$855$		0			0
$856$	−0.0646537			−0.00220982
$857$	1.50565	+	1.50565i	0.0514319	+	0.0514319i	0.732355	−	0.680923i	$-0.238421\pi$
$857$	1.50565	+	1.50565i	0.0514319	+	0.0514319i	−0.680923	+	0.732355i	$0.738421\pi$
$858$		0			0
$859$		−	17.4471i		−	0.595287i	−0.954677	−	0.297643i	$-0.903799\pi$
$859$		−	17.4471i		−	0.595287i	0.954677	−	0.297643i	$-0.0962006\pi$
$860$	−0.709481	−	3.73008i	−0.0241931	−	0.127195i
$861$		0			0
$862$	18.1293	−	18.1293i	0.617487	−	0.617487i
$863$	33.7330	−	33.7330i	1.14829	−	1.14829i	0.161396	−	0.986890i	$-0.448400\pi$
$863$	33.7330	−	33.7330i	1.14829	−	1.14829i	0.986890	−	0.161396i	$-0.0515995\pi$
$864$		0			0
$865$	−7.36636	−	38.7285i	−0.250464	−	1.31681i
$866$		−	19.0036i		−	0.645769i
$867$		0			0
$868$		0			0
$869$	−2.77064			−0.0939874
$870$		0			0
$871$	62.8410			2.12929
$872$	3.71429	+	3.71429i	0.125782	+	0.125782i
$873$		0			0
$874$		−	0.722087i		−	0.0244250i
$875$		0			0
$876$		0			0
$877$	3.12349	−	3.12349i	0.105473	−	0.105473i	−0.652401	−	0.757874i	$-0.726238\pi$
$877$	3.12349	−	3.12349i	0.105473	−	0.105473i	0.757874	+	0.652401i	$0.226238\pi$
$878$	−20.3171	+	20.3171i	−0.685669	+	0.685669i
$879$		0			0
$880$	11.5815	+	7.87986i	0.390413	+	0.265630i
$881$			16.8416i			0.567407i	0.958912	+	0.283703i	$0.0915631\pi$
$881$			16.8416i			0.567407i	−0.958912	+	0.283703i	$0.908437\pi$
$882$		0			0
$883$	21.3583	+	21.3583i	0.718765	+	0.718765i	0.968352	−	0.249588i	$-0.0802950\pi$
$883$	21.3583	+	21.3583i	0.718765	+	0.718765i	−0.249588	+	0.968352i	$0.580295\pi$
$884$	−20.0624			−0.674771
$885$		0			0
$886$	11.9022			0.399862
$887$	−15.8540	−	15.8540i	−0.532326	−	0.532326i	0.388938	−	0.921264i	$-0.372842\pi$
$887$	−15.8540	−	15.8540i	−0.532326	−	0.532326i	−0.921264	+	0.388938i	$0.872842\pi$
$888$		0			0
$889$		0			0
$890$	13.0743	−	2.48680i	0.438252	−	0.0833577i
$891$		0			0
$892$	−11.7644	+	11.7644i	−0.393901	+	0.393901i
$893$	6.34011	−	6.34011i	0.212164	−	0.212164i
$894$		0			0
$895$	−16.2904	+	23.9431i	−0.544529	+	0.800328i
$896$		0			0
$897$		0			0
$898$	−8.94452	−	8.94452i	−0.298482	−	0.298482i
$899$	−35.7110			−1.19103
$900$		0			0
$901$	10.2178			0.340403
$902$	30.1652	+	30.1652i	1.00439	+	1.00439i
$903$		0			0
$904$		−	7.74397i		−	0.257561i
$905$	8.92023	−	13.1106i	0.296519	−	0.435812i
$906$		0			0
$907$	−17.0302	+	17.0302i	−0.565479	+	0.565479i	−0.930859	−	0.365380i	$-0.880939\pi$
$907$	−17.0302	+	17.0302i	−0.565479	+	0.565479i	0.365380	+	0.930859i	$0.380939\pi$
$908$	−4.61223	+	4.61223i	−0.153062	+	0.153062i
$909$		0			0
$910$		0			0
$911$		−	32.6902i		−	1.08307i	−0.840677	−	0.541537i	$-0.817843\pi$
$911$		−	32.6902i		−	1.08307i	0.840677	−	0.541537i	$-0.182157\pi$
$912$		0			0
$913$	−74.9689	−	74.9689i	−2.48111	−	2.48111i
$914$	−3.24848			−0.107450
$915$		0			0
$916$	0.0237900			0.000786044
$917$		0			0
$918$		0			0
$919$		−	13.3715i		−	0.441085i	−0.975377	−	0.220542i	$-0.929217\pi$
$919$		−	13.3715i		−	0.441085i	0.975377	−	0.220542i	$-0.0707827\pi$
$920$	1.84873	+	1.25785i	0.0609510	+	0.0414700i
$921$		0			0
$922$	−30.0699	+	30.0699i	−0.990300	+	0.990300i
$923$	16.1954	−	16.1954i	0.533079	−	0.533079i
$924$		0			0
$925$	−6.85478	−	2.97505i	−0.225384	−	0.0978190i
$926$			6.07216i			0.199544i
$927$		0			0
$928$	−4.20858	−	4.20858i	−0.138153	−	0.138153i
$929$	0.280920			0.00921668			0.00460834	−	0.999989i	$-0.498533\pi$
$929$	0.280920			0.00921668			0.00460834	+	0.999989i	$0.498533\pi$
$930$		0			0
$931$	−5.05461			−0.165658
$932$	1.18178	+	1.18178i	0.0387104	+	0.0387104i
$933$		0			0
$934$		−	37.4837i		−	1.22650i
$935$	8.45183	+	44.4353i	0.276404	+	1.45319i
$936$		0			0
$937$	−38.5530	+	38.5530i	−1.25947	+	1.25947i	−0.308128	+	0.951345i	$0.599703\pi$
$937$	−38.5530	+	38.5530i	−1.25947	+	1.25947i	−0.951345	+	0.308128i	$0.900297\pi$
$938$		0			0
$939$		0			0
$940$	5.18815	+	27.2766i	0.169219	+	0.889664i
$941$		−	52.6281i		−	1.71563i	−0.513961	−	0.857813i	$-0.671823\pi$
$941$		−	52.6281i		−	1.71563i	0.513961	−	0.857813i	$-0.328177\pi$
$942$		0			0
$943$	4.81521	+	4.81521i	0.156805	+	0.156805i
$944$	−12.7905			−0.416294
$945$		0			0
$946$	−10.6376			−0.345857
$947$	−28.3086	−	28.3086i	−0.919906	−	0.919906i	0.0771160	−	0.997022i	$-0.475429\pi$
$947$	−28.3086	−	28.3086i	−0.919906	−	0.919906i	−0.997022	+	0.0771160i	$0.975429\pi$
$948$		0			0
$949$			101.943i			3.30922i
$950$	3.31196	+	1.43743i	0.107454	+	0.0466362i
$951$		0			0
$952$		0			0
$953$	0.897938	−	0.897938i	0.0290871	−	0.0290871i	−0.692414	−	0.721501i	$-0.743453\pi$
$953$	0.897938	−	0.897938i	0.0290871	−	0.0290871i	0.721501	+	0.692414i	$0.243453\pi$
$954$		0			0
$955$	4.26274	+	2.90030i	0.137939	+	0.0938514i
$956$			26.7224i			0.864265i
$957$		0			0
$958$	−18.0158	−	18.0158i	−0.582063	−	0.582063i
$959$		0			0
$960$		0			0
$961$	5.00000			0.161290
$962$	−6.56593	−	6.56593i	−0.211694	−	0.211694i
$963$		0			0
$964$		−	22.7050i		−	0.731279i
$965$	−13.8062	+	2.62601i	−0.444437	+	0.0845342i
$966$		0			0
$967$	22.2291	−	22.2291i	0.714841	−	0.714841i	−0.252703	−	0.967544i	$-0.581319\pi$
$967$	22.2291	−	22.2291i	0.714841	−	0.714841i	0.967544	+	0.252703i	$0.0813195\pi$
$968$	19.9721	−	19.9721i	0.641926	−	0.641926i
$969$		0			0
$970$	−12.4157	+	18.2481i	−0.398644	+	0.585912i
$971$		−	31.3301i		−	1.00543i	−0.864452	−	0.502715i	$-0.832335\pi$
$971$		−	31.3301i		−	1.00543i	0.864452	−	0.502715i	$-0.167665\pi$
$972$		0			0
$973$		0			0
$974$	2.47091			0.0791731
$975$		0			0
$976$	−4.90833			−0.157112
$977$	−3.63699	−	3.63699i	−0.116358	−	0.116358i	0.646531	−	0.762888i	$-0.276219\pi$
$977$	−3.63699	−	3.63699i	−0.116358	−	0.116358i	−0.762888	+	0.646531i	$0.776219\pi$
$978$		0			0
$979$		−	37.2856i		−	1.19165i
$980$	8.80493	−	12.9411i	0.281263	−	0.413390i
$981$		0			0
$982$	−25.9037	+	25.9037i	−0.826619	+	0.826619i
$983$	−25.6239	+	25.6239i	−0.817275	+	0.817275i	−0.985712	−	0.168438i	$-0.946128\pi$
$983$	−25.6239	+	25.6239i	−0.817275	+	0.817275i	0.168438	+	0.985712i	$0.446128\pi$
$984$		0			0
$985$	−10.4252	+	1.98293i	−0.332174	+	0.0631813i
$986$		−	19.2185i		−	0.612043i
$987$		0			0
$988$	3.17240	+	3.17240i	0.100927	+	0.100927i
$989$	−1.69805			−0.0539949
$990$		0			0
$991$	34.8437			1.10685			0.553423	−	0.832900i	$-0.313321\pi$
$991$	34.8437			1.10685			0.553423	+	0.832900i	$0.313321\pi$
$992$	4.24264	+	4.24264i	0.134704	+	0.134704i
$993$		0			0
$994$		0			0
$995$	−20.5031	−	13.9500i	−0.649992	−	0.442243i
$996$		0			0
$997$	−3.76776	+	3.76776i	−0.119326	+	0.119326i	−0.764248	−	0.644922i	$-0.776890\pi$
$997$	−3.76776	+	3.76776i	−0.119326	+	0.119326i	0.644922	+	0.764248i	$0.276890\pi$
$998$	9.70070	−	9.70070i	0.307070	−	0.307070i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.h.323.6	yes	16
3.2	odd	2	inner	2070.2.j.h.323.3	✓	16
5.2	odd	4	inner	2070.2.j.h.737.3	yes	16
15.2	even	4	inner	2070.2.j.h.737.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.h.323.3	✓	16	3.2	odd	2	inner
2070.2.j.h.323.6	yes	16	1.1	even	1	trivial
2070.2.j.h.737.3	yes	16	5.2	odd	4	inner
2070.2.j.h.737.6	yes	16	15.2	even	4	inner

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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.25785 + 1.84873i) q^{5} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.25785 + 1.84873i) q^{5} +(-0.707107 + 0.707107i) q^{8} +(-2.19669 + 0.417821i) q^{10} +6.26456i q^{11} +(-4.39337 - 4.39337i) q^{13} -1.00000 q^{16} +(-2.28326 - 2.28326i) q^{17} +0.722087i q^{19} +(-1.84873 - 1.25785i) q^{20} +(-4.42972 + 4.42972i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(-1.83564 - 4.65085i) q^{25} -6.21316i q^{26} +5.95183 q^{29} -6.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} -3.22901i q^{34} +(1.05678 - 1.05678i) q^{37} +(-0.510593 + 0.510593i) q^{38} +(-0.417821 - 2.19669i) q^{40} -6.80974i q^{41} +(1.20070 + 1.20070i) q^{43} -6.26456 q^{44} -1.00000 q^{46} +(-8.78026 - 8.78026i) q^{47} +7.00000i q^{49} +(1.99065 - 4.58664i) q^{50} +(4.39337 - 4.39337i) q^{52} +(-2.23754 + 2.23754i) q^{53} +(-11.5815 - 7.87986i) q^{55} +(4.20858 + 4.20858i) q^{58} +12.7905 q^{59} +4.90833 q^{61} +(-4.24264 - 4.24264i) q^{62} -1.00000i q^{64} +(13.6484 - 2.59599i) q^{65} +(-7.15180 + 7.15180i) q^{67} +(2.28326 - 2.28326i) q^{68} +3.68633i q^{71} +(-11.6020 - 11.6020i) q^{73} +1.49451 q^{74} -0.722087 q^{76} +0.442271i q^{79} +(1.25785 - 1.84873i) q^{80} +(4.81521 - 4.81521i) q^{82} +(-11.9671 + 11.9671i) q^{83} +(7.09312 - 1.34915i) q^{85} +1.69805i q^{86} +(-4.42972 - 4.42972i) q^{88} -5.95183 q^{89} +(-0.707107 - 0.707107i) q^{92} -12.4172i q^{94} +(-1.33495 - 0.908275i) q^{95} +(6.97957 - 6.97957i) q^{97} +(-4.94975 + 4.94975i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{10} - 16 q^{13} - 16 q^{16} + 8 q^{22} - 16 q^{25} - 96 q^{31} + 24 q^{37} + 8 q^{43} - 16 q^{46} + 16 q^{52} - 32 q^{58} + 16 q^{61} - 8 q^{67} - 32 q^{73} + 16 q^{76} + 32 q^{82} + 96 q^{85} + 8 q^{88} + 80 q^{97}+O(q^{100}) \) 16 * q - 8 * q^10 - 16 * q^13 - 16 * q^16 + 8 * q^22 - 16 * q^25 - 96 * q^31 + 24 * q^37 + 8 * q^43 - 16 * q^46 + 16 * q^52 - 32 * q^58 + 16 * q^61 - 8 * q^67 - 32 * q^73 + 16 * q^76 + 32 * q^82 + 96 * q^85 + 8 * q^88 + 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more