LMFDB - Embedded newform 1078.2.i.d.901.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(901,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("1078.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.i (of order $6$, degree $2$, not 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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.15
Character	$\chi$	$=$	1078.901
Dual form			1078.2.i.d.1011.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.60021 + 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.80322 + 1.61844i) q^{5} -1.84776 q^{6} +1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.60021 + 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.80322 + 1.61844i) q^{5} -1.84776 q^{6} +1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +(1.61844 + 2.80322i) q^{10} +(-2.04734 - 2.60929i) q^{11} +(-1.60021 - 0.923880i) q^{12} -6.10838 q^{13} -5.98098 q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.06577 + 7.04213i) q^{17} +(0.358719 - 0.207107i) q^{18} +(-3.30769 + 5.72908i) q^{19} +3.23688i q^{20} +(-0.468406 - 3.28338i) q^{22} +(2.65291 - 4.59498i) q^{23} +(-0.923880 - 1.60021i) q^{24} +(2.73870 + 4.74357i) q^{25} +(-5.29001 - 3.05419i) q^{26} -4.77791i q^{27} -1.32485i q^{29} +(-5.17968 - 2.99049i) q^{30} +(-2.03928 + 1.17738i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(5.68684 + 2.28390i) q^{33} +8.13155i q^{34} +0.414214 q^{36} +(-2.64340 + 4.57851i) q^{37} +(-5.72908 + 3.30769i) q^{38} +(9.77466 - 5.64340i) q^{39} +(-1.61844 + 2.80322i) q^{40} +1.22400 q^{41} +3.73834i q^{43} +(1.23604 - 3.07769i) q^{44} +(1.16113 - 0.670380i) q^{45} +(4.59498 - 2.65291i) q^{46} +(1.47757 + 0.853074i) q^{47} -1.84776i q^{48} +5.47740i q^{50} +(-13.0122 - 7.51257i) q^{51} +(-3.05419 - 5.29001i) q^{52} +(1.99049 + 3.44763i) q^{53} +(2.38896 - 4.13779i) q^{54} +(-1.51617 - 10.6279i) q^{55} -12.2236i q^{57} +(0.662426 - 1.14736i) q^{58} +(7.82759 - 4.51926i) q^{59} +(-2.99049 - 5.17968i) q^{60} +(-4.27819 + 7.41004i) q^{61} -2.35476 q^{62} -1.00000 q^{64} +(-17.1231 - 9.88604i) q^{65} +(3.78300 + 4.82134i) q^{66} +(-1.17551 - 2.03605i) q^{67} +(-4.06577 + 7.04213i) q^{68} +9.80389i q^{69} -7.17945 q^{71} +(0.358719 + 0.207107i) q^{72} +(-5.49637 - 9.52000i) q^{73} +(-4.57851 + 2.64340i) q^{74} +(-8.76497 - 5.06046i) q^{75} -6.61537 q^{76} +11.2868 q^{78} +(7.34847 + 4.24264i) q^{79} +(-2.80322 + 1.61844i) q^{80} +(5.03553 + 8.72180i) q^{81} +(1.06002 + 0.612002i) q^{82} -5.60138 q^{83} +26.3209i q^{85} +(-1.86917 + 3.23749i) q^{86} +(1.22400 + 2.12004i) q^{87} +(2.60929 - 2.04734i) q^{88} +(-4.03668 - 2.33058i) q^{89} +1.34076 q^{90} +5.30583 q^{92} +(2.17551 - 3.76810i) q^{93} +(0.853074 + 1.47757i) q^{94} +(-18.5444 + 10.7066i) q^{95} +(0.923880 - 1.60021i) q^{96} -3.82683i q^{97} +(-1.36002 + 0.194020i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 - 16 * q^9	$ 32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^9 - 16 * q^11 - 16 * q^16 - 16 * q^22 + 16 * q^23 + 64 * q^25 - 32 * q^36 + 80 * q^37 + 16 * q^44 - 32 * q^53 + 48 * q^58 - 32 * q^64 - 16 * q^67 - 96 * q^71 + 32 * q^78 + 48 * q^81 - 32 * q^86 - 8 * q^88 + 32 * q^92 + 48 * q^93 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−1.60021	+	0.923880i	−0.923880	+	0.533402i	−0.884871	−	0.465837i	$-0.845753\pi$
$3$	−1.60021	+	0.923880i	−0.923880	+	0.533402i	−0.0390089	+	0.999239i	$0.512420\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.80322	+	1.61844i	1.25364	+	0.723789i	0.971830	−	0.235682i	$-0.0757324\pi$
$5$	2.80322	+	1.61844i	1.25364	+	0.723789i	0.281809	+	0.959471i	$0.409066\pi$
$6$	−1.84776			−0.754344
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	0.207107	−	0.358719i	0.0690356	−	0.119573i
$10$	1.61844	+	2.80322i	0.511796	+	0.886457i
$11$	−2.04734	−	2.60929i	−0.617297	−	0.786730i
$11$	−2.04734	−	2.60929i	−0.617297	−	0.786730i
$12$	−1.60021	−	0.923880i	−0.461940	−	0.266701i
$13$	−6.10838			−1.69416			−0.847079	−	0.531467i	$-0.821641\pi$
$13$	−6.10838			−1.69416			−0.847079	+	0.531467i	$0.821641\pi$
$14$		0			0
$15$	−5.98098			−1.54428
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.06577	+	7.04213i	0.986095	+	1.70797i	0.636965	+	0.770892i	$0.280189\pi$
$17$	4.06577	+	7.04213i	0.986095	+	1.70797i	0.349130	+	0.937074i	$0.386477\pi$
$18$	0.358719	−	0.207107i	0.0845510	−	0.0488155i
$19$	−3.30769	+	5.72908i	−0.758835	+	1.31434i	0.184609	+	0.982812i	$0.440898\pi$
$19$	−3.30769	+	5.72908i	−0.758835	+	1.31434i	−0.943445	+	0.331530i	$0.892435\pi$
$20$			3.23688i			0.723789i
$21$		0			0
$22$	−0.468406	−	3.28338i	−0.0998645	−	0.700019i
$23$	2.65291	−	4.59498i	0.553171	−	0.958120i	−0.444872	−	0.895594i	$-0.646751\pi$
$23$	2.65291	−	4.59498i	0.553171	−	0.958120i	0.998043	−	0.0625262i	$-0.0199157\pi$
$24$	−0.923880	−	1.60021i	−0.188586	−	0.326641i
$25$	2.73870	+	4.74357i	0.547740	+	0.948714i
$26$	−5.29001	−	3.05419i	−1.03746	−	0.598975i
$27$		−	4.77791i		−	0.919509i
$28$		0			0
$29$		−	1.32485i		−	0.246019i	−0.992406	−	0.123009i	$-0.960745\pi$
$29$		−	1.32485i		−	0.246019i	0.992406	−	0.123009i	$-0.0392545\pi$
$30$	−5.17968	−	2.99049i	−0.945676	−	0.545986i
$31$	−2.03928	+	1.17738i	−0.366266	+	0.211464i	−0.671826	−	0.740709i	$-0.734490\pi$
$31$	−2.03928	+	1.17738i	−0.366266	+	0.211464i	0.305560	+	0.952173i	$0.401156\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	5.68684	+	2.28390i	0.989952	+	0.397577i
$34$			8.13155i			1.39455i
$35$		0			0
$36$	0.414214			0.0690356
$37$	−2.64340	+	4.57851i	−0.434573	+	0.752702i	−0.997261	−	0.0739673i	$-0.976434\pi$
$37$	−2.64340	+	4.57851i	−0.434573	+	0.752702i	0.562688	+	0.826669i	$0.309767\pi$
$38$	−5.72908	+	3.30769i	−0.929380	+	0.536578i
$39$	9.77466	−	5.64340i	1.56520	−	0.903668i
$40$	−1.61844	+	2.80322i	−0.255898	+	0.443228i
$41$	1.22400			0.191157			0.0955786	−	0.995422i	$-0.469530\pi$
$41$	1.22400			0.191157			0.0955786	+	0.995422i	$0.469530\pi$
$42$		0			0
$43$			3.73834i			0.570091i	0.958514	+	0.285045i	$0.0920087\pi$
$43$			3.73834i			0.570091i	−0.958514	+	0.285045i	$0.907991\pi$
$44$	1.23604	−	3.07769i	0.186340	−	0.463980i
$45$	1.16113	−	0.670380i	0.173091	−	0.0999344i
$46$	4.59498	−	2.65291i	0.677493	−	0.391151i
$47$	1.47757	+	0.853074i	0.215525	+	0.124434i	0.603877	−	0.797078i	$-0.293622\pi$
$47$	1.47757	+	0.853074i	0.215525	+	0.124434i	−0.388351	+	0.921511i	$0.626955\pi$
$48$		−	1.84776i		−	0.266701i
$49$		0			0
$50$			5.47740i			0.774622i
$51$	−13.0122	−	7.51257i	−1.82207	−	1.05197i
$52$	−3.05419	−	5.29001i	−0.423540	−	0.733592i
$53$	1.99049	+	3.44763i	0.273415	+	0.473568i	0.969734	−	0.244164i	$-0.0785136\pi$
$53$	1.99049	+	3.44763i	0.273415	+	0.473568i	−0.696319	+	0.717732i	$0.745180\pi$
$54$	2.38896	−	4.13779i	0.325096	−	0.563082i
$55$	−1.51617	−	10.6279i	−0.204441	−	1.43307i
$56$		0			0
$57$		−	12.2236i		−	1.61906i
$58$	0.662426	−	1.14736i	0.0869808	−	0.150655i
$59$	7.82759	−	4.51926i	1.01907	−	0.588358i	0.105233	−	0.994448i	$-0.466441\pi$
$59$	7.82759	−	4.51926i	1.01907	−	0.588358i	0.913833	+	0.406090i	$0.133108\pi$
$60$	−2.99049	−	5.17968i	−0.386070	−	0.668694i
$61$	−4.27819	+	7.41004i	−0.547766	+	0.948759i	0.450661	+	0.892695i	$0.351188\pi$
$61$	−4.27819	+	7.41004i	−0.547766	+	0.948759i	−0.998427	+	0.0560638i	$0.982145\pi$
$62$	−2.35476			−0.299055
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−17.1231	−	9.88604i	−2.12386	−	1.22621i
$66$	3.78300	+	4.82134i	0.465655	+	0.593466i
$67$	−1.17551	−	2.03605i	−0.143612	−	0.248743i	0.785242	−	0.619188i	$-0.212538\pi$
$67$	−1.17551	−	2.03605i	−0.143612	−	0.248743i	−0.928854	+	0.370446i	$0.879205\pi$
$68$	−4.06577	+	7.04213i	−0.493048	+	0.853983i
$69$			9.80389i			1.18025i
$70$		0			0
$71$	−7.17945			−0.852044			−0.426022	−	0.904713i	$-0.640085\pi$
$71$	−7.17945			−0.852044			−0.426022	+	0.904713i	$0.640085\pi$
$72$	0.358719	+	0.207107i	0.0422755	+	0.0244078i
$73$	−5.49637	−	9.52000i	−0.643302	−	1.11423i	−0.984691	−	0.174309i	$-0.944231\pi$
$73$	−5.49637	−	9.52000i	−0.643302	−	1.11423i	0.341389	−	0.939922i	$-0.389103\pi$
$74$	−4.57851	+	2.64340i	−0.532241	+	0.307289i
$75$	−8.76497	−	5.06046i	−1.01209	−	0.584332i
$76$	−6.61537			−0.758835
$77$		0			0
$78$	11.2868			1.27798
$79$	7.34847	+	4.24264i	0.826767	+	0.477334i	0.852745	−	0.522328i	$-0.174936\pi$
$79$	7.34847	+	4.24264i	0.826767	+	0.477334i	−0.0259772	+	0.999663i	$0.508270\pi$
$80$	−2.80322	+	1.61844i	−0.313410	+	0.180947i
$81$	5.03553	+	8.72180i	0.559504	+	0.969089i
$82$	1.06002	+	0.612002i	0.117059	+	0.0675843i
$83$	−5.60138			−0.614831			−0.307415	−	0.951575i	$-0.599464\pi$
$83$	−5.60138			−0.614831			−0.307415	+	0.951575i	$0.599464\pi$
$84$		0			0
$85$			26.3209i			2.85490i
$86$	−1.86917	+	3.23749i	−0.201558	+	0.349108i
$87$	1.22400	+	2.12004i	0.131227	+	0.227292i
$88$	2.60929	−	2.04734i	0.278151	−	0.218247i
$89$	−4.03668	−	2.33058i	−0.427887	−	0.247041i	0.270559	−	0.962703i	$-0.412791\pi$
$89$	−4.03668	−	2.33058i	−0.427887	−	0.247041i	−0.698446	+	0.715663i	$0.746125\pi$
$90$	1.34076			0.141329
$91$		0			0
$92$	5.30583			0.553171
$93$	2.17551	−	3.76810i	0.225590	−	0.390734i
$94$	0.853074	+	1.47757i	0.0879879	+	0.152399i
$95$	−18.5444	+	10.7066i	−1.90261	+	1.09847i
$96$	0.923880	−	1.60021i	0.0942931	−	0.163320i
$97$		−	3.82683i		−	0.388556i	−0.980946	−	0.194278i	$-0.937764\pi$
$97$		−	3.82683i		−	0.388556i	0.980946	−	0.194278i	$-0.0622364\pi$
$98$		0			0
$99$	−1.36002	+	0.194020i	−0.136687	+	0.0194997i
$100$	−2.73870	+	4.74357i	−0.273870	+	0.474357i
$101$	1.83018	+	3.16997i	0.182110	+	0.315424i	0.942599	−	0.333927i	$-0.108374\pi$
$101$	1.83018	+	3.16997i	0.182110	+	0.315424i	−0.760489	+	0.649351i	$0.775041\pi$
$102$	−7.51257	−	13.0122i	−0.743855	−	1.28840i
$103$	12.6193	+	7.28575i	1.24342	+	0.717887i	0.969788	−	0.243949i	$-0.0784429\pi$
$103$	12.6193	+	7.28575i	1.24342	+	0.717887i	0.273628	+	0.961836i	$0.411776\pi$
$104$		−	6.10838i		−	0.598975i
$105$		0			0
$106$			3.98098i			0.386667i
$107$	6.81876	+	3.93681i	0.659194	+	0.380586i	0.791970	−	0.610560i	$-0.209056\pi$
$107$	6.81876	+	3.93681i	0.659194	+	0.380586i	−0.132776	+	0.991146i	$0.542389\pi$
$108$	4.13779	−	2.38896i	0.398159	−	0.229877i
$109$	−5.19615	+	3.00000i	−0.497701	+	0.287348i	−0.727764	−	0.685828i	$-0.759440\pi$
$109$	−5.19615	+	3.00000i	−0.497701	+	0.287348i	0.230063	+	0.973176i	$0.426107\pi$
$110$	4.00091	−	9.96213i	0.381472	−	0.949852i
$111$		−	9.76874i		−	0.927208i
$112$		0			0
$113$	13.5216			1.27200			0.636001	−	0.771688i	$-0.280587\pi$
$113$	13.5216			1.27200			0.636001	+	0.771688i	$0.280587\pi$
$114$	6.11181	−	10.5860i	0.572423	−	0.991466i
$115$	14.8734	−	8.58717i	1.38695	−	0.800758i
$116$	1.14736	−	0.662426i	0.106529	−	0.0615047i
$117$	−1.26509	+	2.19119i	−0.116957	+	0.202576i
$118$	9.03853			0.832064
$119$		0			0
$120$		−	5.98098i		−	0.545986i
$121$	−2.61678	+	10.6842i	−0.237889	+	0.971292i
$122$	−7.41004	+	4.27819i	−0.670874	+	0.387329i
$123$	−1.95866	+	1.13083i	−0.176606	+	0.101964i
$124$	−2.03928	−	1.17738i	−0.183133	−	0.105732i
$125$			1.54529i			0.138215i
$126$		0			0
$127$		−	8.63710i		−	0.766419i	−0.923661	−	0.383209i	$-0.874819\pi$
$127$		−	8.63710i		−	0.766419i	0.923661	−	0.383209i	$-0.125181\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−3.45377	−	5.98211i	−0.304088	−	0.526695i
$130$	−9.88604	−	17.1231i	−0.867063	−	1.50180i
$131$	3.10109	−	5.37125i	0.270944	−	0.469288i	−0.698160	−	0.715942i	$-0.745998\pi$
$131$	3.10109	−	5.37125i	0.270944	−	0.469288i	0.969104	+	0.246654i	$0.0793310\pi$
$132$	0.865501	+	6.06690i	0.0753322	+	0.528056i
$133$		0			0
$134$		−	2.35103i		−	0.203098i
$135$	7.73276	−	13.3935i	0.665530	−	1.15273i
$136$	−7.04213	+	4.06577i	−0.603857	+	0.348637i
$137$	4.51257	+	7.81600i	0.385535	+	0.667766i	0.991843	−	0.127464i	$-0.0406836\pi$
$137$	4.51257	+	7.81600i	0.385535	+	0.667766i	−0.606308	+	0.795230i	$0.707350\pi$
$138$	−4.90195	+	8.49042i	−0.417281	+	0.722753i
$139$	−8.34638			−0.707930			−0.353965	−	0.935259i	$-0.615167\pi$
$139$	−8.34638			−0.707930			−0.353965	+	0.935259i	$0.615167\pi$
$140$		0			0
$141$	−3.15255			−0.265493
$142$	−6.21759	−	3.58973i	−0.521768	−	0.301243i
$143$	12.5059	+	15.9385i	1.04580	+	1.33285i
$144$	0.207107	+	0.358719i	0.0172589	+	0.0298933i
$145$	2.14419	−	3.71385i	0.178066	−	0.308419i
$146$		−	10.9927i		−	0.909766i
$147$		0			0
$148$	−5.28681			−0.434573
$149$	18.4020	+	10.6244i	1.50755	+	0.870383i	0.999961	+	0.00878227i	$0.00279552\pi$
$149$	18.4020	+	10.6244i	1.50755	+	0.870383i	0.507586	+	0.861601i	$0.330538\pi$
$150$	−5.06046	−	8.76497i	−0.413185	−	0.715657i
$151$	14.4411	−	8.33757i	1.17520	−	0.678502i	0.220301	−	0.975432i	$-0.429296\pi$
$151$	14.4411	−	8.33757i	1.17520	−	0.678502i	0.954899	+	0.296930i	$0.0959627\pi$
$152$	−5.72908	−	3.30769i	−0.464690	−	0.268289i
$153$	3.36820			0.272303
$154$		0			0
$155$	−7.62207			−0.612220
$156$	9.77466	+	5.64340i	0.782599	+	0.451834i
$157$	10.8335	−	6.25474i	0.864610	−	0.499183i	−0.000943620	−	1.00000i	$-0.500300\pi$
$157$	10.8335	−	6.25474i	0.864610	−	0.499183i	0.865553	+	0.500817i	$0.166967\pi$
$158$	4.24264	+	7.34847i	0.337526	+	0.584613i
$159$	−6.37038	−	3.67794i	−0.505204	−	0.291680i
$160$	−3.23688			−0.255898
$161$		0			0
$162$			10.0711i			0.791258i
$163$	−4.19796	+	7.27108i	−0.328810	+	0.569515i	−0.982276	−	0.187441i	$-0.939981\pi$
$163$	−4.19796	+	7.27108i	−0.328810	+	0.569515i	0.653466	+	0.756956i	$0.273314\pi$
$164$	0.612002	+	1.06002i	0.0477893	+	0.0827735i
$165$	12.2451	+	15.6061i	0.953280	+	1.21493i
$166$	−4.85093	−	2.80069i	−0.376506	−	0.217376i
$167$	4.04635			0.313116			0.156558	−	0.987669i	$-0.449960\pi$
$167$	4.04635			0.313116			0.156558	+	0.987669i	$0.449960\pi$
$168$		0			0
$169$	24.3123			1.87017
$170$	−13.1604	+	22.7945i	−1.00936	+	1.74826i
$171$	1.37009	+	2.37306i	0.104773	+	0.181473i
$172$	−3.23749	+	1.86917i	−0.246857	+	0.142523i
$173$	−1.53801	+	2.66392i	−0.116933	+	0.202534i	−0.918551	−	0.395303i	$-0.870640\pi$
$173$	−1.53801	+	2.66392i	−0.116933	+	0.202534i	0.801618	+	0.597837i	$0.203973\pi$
$174$			2.44801i			0.185583i
$175$		0			0
$176$	3.28338	−	0.468406i	0.247494	−	0.0353074i
$177$	−8.35051	+	14.4635i	−0.627663	+	1.08714i
$178$	−2.33058	−	4.03668i	−0.174684	−	0.302562i
$179$	5.73276	+	9.92944i	0.428487	+	0.742161i	0.996739	−	0.0806934i	$-0.0257135\pi$
$179$	5.73276	+	9.92944i	0.428487	+	0.742161i	−0.568252	+	0.822855i	$0.692380\pi$
$180$	1.16113	+	0.670380i	0.0865457	+	0.0499672i
$181$			13.2743i			0.986670i	0.869839	+	0.493335i	$0.164222\pi$
$181$			13.2743i			0.986670i	−0.869839	+	0.493335i	$0.835778\pi$
$182$		0			0
$183$		−	15.8101i		−	1.16872i
$184$	4.59498	+	2.65291i	0.338747	+	0.195575i
$185$	−14.8201	+	8.55638i	−1.08959	+	0.629078i
$186$	3.76810	−	2.17551i	0.276290	−	0.159516i
$187$	10.0509	−	25.0264i	0.734996	−	1.83011i
$188$			1.70615i			0.124434i
$189$		0			0
$190$	−21.4132			−1.55348
$191$	6.10735	−	10.5782i	0.441913	−	0.765415i	−0.555919	−	0.831237i	$-0.687633\pi$
$191$	6.10735	−	10.5782i	0.441913	−	0.765415i	0.997831	+	0.0658215i	$0.0209668\pi$
$192$	1.60021	−	0.923880i	0.115485	−	0.0666753i
$193$	4.38485	−	2.53159i	0.315628	−	0.182228i	−0.333814	−	0.942639i	$-0.608336\pi$
$193$	4.38485	−	2.53159i	0.315628	−	0.182228i	0.649442	+	0.760411i	$0.275002\pi$
$194$	1.91342	−	3.31414i	0.137375	−	0.237941i
$195$	36.5341			2.61626
$196$		0			0
$197$		−	20.0883i		−	1.43123i	−0.698493	−	0.715617i	$-0.746146\pi$
$197$		−	20.0883i		−	1.43123i	0.698493	−	0.715617i	$-0.253854\pi$
$198$	−1.27482	−	0.511984i	−0.0905977	−	0.0363851i
$199$	−12.8341	+	7.40979i	−0.909788	+	0.525266i	−0.880363	−	0.474301i	$-0.842701\pi$
$199$	−12.8341	+	7.40979i	−0.909788	+	0.525266i	−0.0294248	+	0.999567i	$0.509368\pi$
$200$	−4.74357	+	2.73870i	−0.335421	+	0.193655i
$201$	3.76213	+	2.17206i	0.265360	+	0.153206i
$202$			3.66037i			0.257543i
$203$		0			0
$204$		−	15.0251i		−	1.05197i
$205$	3.43115	+	1.98098i	0.239642	+	0.138357i
$206$	7.28575	+	12.6193i	0.507623	+	0.879228i
$207$	−1.09887	−	1.90330i	−0.0763770	−	0.132289i
$208$	3.05419	−	5.29001i	0.211770	−	0.366796i
$209$	21.7208	−	3.09868i	1.50246	−	0.214340i
$210$		0			0
$211$		−	9.19848i		−	0.633249i	−0.948551	−	0.316625i	$-0.897450\pi$
$211$		−	9.19848i		−	0.633249i	0.948551	−	0.316625i	$-0.102550\pi$
$212$	−1.99049	+	3.44763i	−0.136707	+	0.236784i
$213$	11.4886	−	6.63295i	0.787186	−	0.454482i
$214$	3.93681	+	6.81876i	0.269115	+	0.466121i
$215$	−6.05028	+	10.4794i	−0.412625	+	0.714688i
$216$	4.77791			0.325096
$217$		0			0
$218$	−6.00000			−0.406371
$219$	17.5907	+	10.1560i	1.18867	+	0.686277i
$220$	8.44596	−	6.62700i	0.569426	−	0.446793i
$221$	−24.8353	−	43.0160i	−1.67060	−	2.89357i
$222$	4.88437	−	8.45998i	0.327818	−	0.567797i
$223$			10.8760i			0.728310i	0.931338	+	0.364155i	$0.118642\pi$
$223$			10.8760i			0.728310i	−0.931338	+	0.364155i	$0.881358\pi$
$224$		0			0
$225$	2.26881			0.151254
$226$	11.7100	+	6.76078i	0.778939	+	0.449721i
$227$	−11.7396	−	20.3337i	−0.779187	−	1.34959i	−0.932411	−	0.361400i	$-0.882299\pi$
$227$	−11.7396	−	20.3337i	−0.779187	−	1.34959i	0.153224	−	0.988192i	$-0.451035\pi$
$228$	10.5860	−	6.11181i	0.701073	−	0.404764i
$229$	19.7715	+	11.4151i	1.30653	+	0.754328i	0.981516	−	0.191380i	$-0.0612962\pi$
$229$	19.7715	+	11.4151i	1.30653	+	0.754328i	0.325018	+	0.945708i	$0.394630\pi$
$230$	17.1743			1.13244
$231$		0			0
$232$	1.32485			0.0869808
$233$	12.7383	+	7.35445i	0.834512	+	0.481806i	0.855395	−	0.517976i	$-0.173314\pi$
$233$	12.7383	+	7.35445i	0.834512	+	0.481806i	−0.0208827	+	0.999782i	$0.506648\pi$
$234$	−2.19119	+	1.26509i	−0.143243	+	0.0827013i
$235$	2.76130	+	4.78271i	0.180127	+	0.311990i
$236$	7.82759	+	4.51926i	0.509533	+	0.294179i
$237$	−15.6788			−1.01844
$238$		0			0
$239$			22.4218i			1.45035i	0.688567	+	0.725173i	$0.258240\pi$
$239$			22.4218i			1.45035i	−0.688567	+	0.725173i	$0.741760\pi$
$240$	2.99049	−	5.17968i	0.193035	−	0.334347i
$241$	7.73437	+	13.3963i	0.498215	+	0.862933i	0.999998	−	0.00206005i	$-0.000655735\pi$
$241$	7.73437	+	13.3963i	0.498215	+	0.862933i	−0.501783	+	0.864994i	$0.667322\pi$
$242$	−7.60831	+	7.94441i	−0.489080	+	0.510686i
$243$	−3.70241	−	2.13759i	−0.237510	−	0.137126i
$244$	−8.55638			−0.547766
$245$		0			0
$246$	−2.26166			−0.144198
$247$	20.2046	−	34.9954i	1.28559	−	2.22670i
$248$	−1.17738	−	2.03928i	−0.0747636	−	0.129494i
$249$	8.96336	−	5.17500i	0.568030	−	0.327952i
$250$	−0.772647	+	1.33826i	−0.0488665	+	0.0846392i
$251$		−	4.87408i		−	0.307649i	−0.988098	−	0.153825i	$-0.950841\pi$
$251$		−	4.87408i		−	0.307649i	0.988098	−	0.153825i	$-0.0491590\pi$
$252$		0			0
$253$	−17.4211	+	2.48528i	−1.09525	+	0.156248i
$254$	4.31855	−	7.47995i	0.270970	−	0.469334i
$255$	−24.3173	−	42.1188i	−1.52281	−	2.63758i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	17.1250	+	9.88713i	1.06823	+	0.616742i	0.927697	−	0.373334i	$-0.121786\pi$
$257$	17.1250	+	9.88713i	1.06823	+	0.616742i	0.140532	+	0.990076i	$0.455119\pi$
$258$		−	6.90755i		−	0.430045i
$259$		0			0
$260$		−	19.7721i		−	1.22621i
$261$	−0.475250	−	0.274386i	−0.0294172	−	0.0169841i
$262$	5.37125	−	3.10109i	0.331837	−	0.191586i
$263$	−7.34847	+	4.24264i	−0.453126	+	0.261612i	−0.709150	−	0.705058i	$-0.750921\pi$
$263$	−7.34847	+	4.24264i	−0.453126	+	0.261612i	0.256023	+	0.966671i	$0.417588\pi$
$264$	−2.28390	+	5.68684i	−0.140565	+	0.350001i
$265$			12.8860i			0.791578i
$266$		0			0
$267$	8.61269			0.527088
$268$	1.17551	−	2.03605i	0.0718059	−	0.124371i
$269$	−6.40809	+	3.69971i	−0.390708	+	0.225575i	−0.682467	−	0.730916i	$-0.739093\pi$
$269$	−6.40809	+	3.69971i	−0.390708	+	0.225575i	0.291759	+	0.956492i	$0.405760\pi$
$270$	13.3935	−	7.73276i	0.815105	−	0.470601i
$271$	7.18047	−	12.4369i	0.436183	−	0.755491i	−0.561209	−	0.827674i	$-0.689663\pi$
$271$	7.18047	−	12.4369i	0.436183	−	0.755491i	0.997391	+	0.0721838i	$0.0229968\pi$
$272$	−8.13155			−0.493048
$273$		0			0
$274$			9.02514i			0.545229i
$275$	6.77029	−	16.8578i	0.408264	−	1.01656i
$276$	−8.49042	+	4.90195i	−0.511063	+	0.295063i
$277$	−1.89648	+	1.09493i	−0.113948	+	0.0657882i	−0.555891	−	0.831255i	$-0.687623\pi$
$277$	−1.89648	+	1.09493i	−0.113948	+	0.0657882i	0.441943	+	0.897043i	$0.354289\pi$
$278$	−7.22817	−	4.17319i	−0.433517	−	0.250291i
$279$			0.975373i			0.0583940i
$280$		0			0
$281$			25.7003i			1.53315i	0.642154	+	0.766575i	$0.278041\pi$
$281$			25.7003i			1.53315i	−0.642154	+	0.766575i	$0.721959\pi$
$282$	−2.73019	−	1.57628i	−0.162580	−	0.0938658i
$283$	7.77887	+	13.4734i	0.462406	+	0.800910i	0.999080	−	0.0428792i	$-0.0136531\pi$
$283$	7.77887	+	13.4734i	0.462406	+	0.800910i	−0.536675	+	0.843789i	$0.680320\pi$
$284$	−3.58973	−	6.21759i	−0.213011	−	0.368946i
$285$	19.7832	−	34.2655i	1.17186	−	2.02971i
$286$	2.86120	+	20.0561i	0.169186	+	1.18594i
$287$		0			0
$288$			0.414214i			0.0244078i
$289$	−24.5610	+	42.5410i	−1.44477	+	2.50241i
$290$	3.71385	−	2.14419i	0.218085	−	0.125911i
$291$	3.53553	+	6.12372i	0.207257	+	0.358979i
$292$	5.49637	−	9.52000i	0.321651	−	0.557116i
$293$	3.11451			0.181952			0.0909759	−	0.995853i	$-0.471001\pi$
$293$	3.11451			0.181952			0.0909759	+	0.995853i	$0.471001\pi$
$294$		0			0
$295$	29.2566			1.70339
$296$	−4.57851	−	2.64340i	−0.266120	−	0.153645i
$297$	−12.4669	+	9.78202i	−0.723406	+	0.567610i
$298$	10.6244	+	18.4020i	0.615454	+	1.06600i
$299$	−16.2050	+	28.0679i	−0.937159	+	1.62321i
$300$		−	10.1209i		−	0.584332i
$301$		0			0
$302$	16.6751			0.959547
$303$	−5.85734	−	3.38174i	−0.336496	−	0.194276i
$304$	−3.30769	−	5.72908i	−0.189709	−	0.328585i
$305$	−23.9854	+	13.8480i	−1.37340	+	0.792934i
$306$	2.91694	+	1.68410i	0.166751	+	0.0962735i
$307$	−8.93072			−0.509703			−0.254852	−	0.966980i	$-0.582027\pi$
$307$	−8.93072			−0.509703			−0.254852	+	0.966980i	$0.582027\pi$
$308$		0			0
$309$	−26.9246			−1.53169
$310$	−6.60091	−	3.81104i	−0.374906	−	0.216452i
$311$	−16.5710	+	9.56730i	−0.939658	+	0.542512i	−0.889853	−	0.456247i	$-0.849193\pi$
$311$	−16.5710	+	9.56730i	−0.939658	+	0.542512i	−0.0498046	+	0.998759i	$0.515860\pi$
$312$	5.64340	+	9.77466i	0.319495	+	0.553381i
$313$	1.02066	+	0.589279i	0.0576912	+	0.0333080i	0.528568	−	0.848891i	$-0.322729\pi$
$313$	1.02066	+	0.589279i	0.0576912	+	0.0333080i	−0.470877	+	0.882199i	$0.656062\pi$
$314$	12.5095			0.705951
$315$		0			0
$316$			8.48528i			0.477334i
$317$	4.54847	−	7.87818i	0.255468	−	0.442483i	−0.709555	−	0.704650i	$-0.751104\pi$
$317$	4.54847	−	7.87818i	0.255468	−	0.442483i	0.965022	+	0.262167i	$0.0844373\pi$
$318$	−3.67794	−	6.37038i	−0.206249	−	0.357233i
$319$	−3.45692	+	2.71243i	−0.193550	+	0.151867i
$320$	−2.80322	−	1.61844i	−0.156705	−	0.0904736i
$321$	−14.5486			−0.812021
$322$		0			0
$323$	−53.7932			−2.99314
$324$	−5.03553	+	8.72180i	−0.279752	+	0.484544i
$325$	−16.7290	−	28.9755i	−0.927959	−	1.60727i
$326$	−7.27108	+	4.19796i	−0.402708	+	0.232503i
$327$	5.54328	−	9.60124i	0.306544	−	0.530950i
$328$			1.22400i			0.0675843i
$329$		0			0
$330$	2.80152	+	19.6378i	0.154219	+	1.08103i
$331$	−1.36486	+	2.36401i	−0.0750197	+	0.129938i	−0.901095	−	0.433622i	$-0.857235\pi$
$331$	−1.36486	+	2.36401i	−0.0750197	+	0.129938i	0.826075	+	0.563560i	$0.190569\pi$
$332$	−2.80069	−	4.85093i	−0.153708	−	0.266230i
$333$	1.09493	+	1.89648i	0.0600020	+	0.103926i
$334$	3.50424	+	2.02317i	0.191743	+	0.110703i
$335$		−	7.60999i		−	0.415778i
$336$		0			0
$337$		−	20.3209i		−	1.10695i	−0.832867	−	0.553474i	$-0.813302\pi$
$337$		−	20.3209i		−	1.10695i	0.832867	−	0.553474i	$-0.186698\pi$
$338$	21.0550	+	12.1561i	1.14524	+	0.661206i
$339$	−21.6373	+	12.4923i	−1.17518	+	0.678489i
$340$	−22.7945	+	13.1604i	−1.23621	+	0.713725i
$341$	7.24723	+	2.91057i	0.392459	+	0.157616i
$342$			2.74018i			0.148172i
$343$		0			0
$344$	−3.73834			−0.201558
$345$	−15.8670	+	27.4825i	−0.854252	+	1.47961i
$346$	−2.66392	+	1.53801i	−0.143213	+	0.0826841i
$347$	−21.1642	+	12.2192i	−1.13615	+	0.655959i	−0.945475	−	0.325693i	$-0.894402\pi$
$347$	−21.1642	+	12.2192i	−1.13615	+	0.655959i	−0.190679	+	0.981652i	$0.561069\pi$
$348$	−1.22400	+	2.12004i	−0.0656135	+	0.113646i
$349$	3.07603			0.164656			0.0823280	−	0.996605i	$-0.473764\pi$
$349$	3.07603			0.164656			0.0823280	+	0.996605i	$0.473764\pi$
$350$		0			0
$351$			29.1853i			1.55779i
$352$	3.07769	+	1.23604i	0.164042	+	0.0658811i
$353$	29.2196	−	16.8700i	1.55520	−	0.897897i	0.557499	−	0.830178i	$-0.311761\pi$
$353$	29.2196	−	16.8700i	1.55520	−	0.897897i	0.997704	−	0.0677191i	$-0.0215722\pi$
$354$	−14.4635	+	8.35051i	−0.768727	+	0.443825i
$355$	−20.1256	−	11.6195i	−1.06816	−	0.616700i
$356$		−	4.66115i		−	0.247041i
$357$		0			0
$358$			11.4655i			0.605972i
$359$	25.8928	+	14.9492i	1.36657	+	0.788990i	0.990488	−	0.137596i	$-0.0439375\pi$
$359$	25.8928	+	14.9492i	1.36657	+	0.788990i	0.376083	+	0.926586i	$0.377271\pi$
$360$	0.670380	+	1.16113i	0.0353321	+	0.0611971i
$361$	−12.3816	−	21.4455i	−0.651663	−	1.12871i
$362$	−6.63714	+	11.4959i	−0.348841	+	0.604210i
$363$	−5.68354	−	19.5145i	−0.298309	−	1.02425i
$364$		0			0
$365$		−	35.5822i		−	1.86246i
$366$	7.90507	−	13.6920i	0.413204	−	0.715691i
$367$	3.07894	−	1.77763i	0.160719	−	0.0927914i	−0.417483	−	0.908685i	$-0.637088\pi$
$367$	3.07894	−	1.77763i	0.160719	−	0.0927914i	0.578202	+	0.815893i	$0.303754\pi$
$368$	2.65291	+	4.59498i	0.138293	+	0.239530i
$369$	0.253499	−	0.439074i	0.0131967	−	0.0228573i
$370$	−17.1128			−0.889650
$371$		0			0
$372$	4.35103			0.225590
$373$	−18.2705	−	10.5485i	−0.946010	−	0.546179i	−0.0541707	−	0.998532i	$-0.517252\pi$
$373$	−18.2705	−	10.5485i	−0.946010	−	0.546179i	−0.891839	+	0.452353i	$0.850585\pi$
$374$	21.2176	−	16.6481i	1.09713	−	0.860851i
$375$	−1.42766	−	2.47279i	−0.0737243	−	0.127694i
$376$	−0.853074	+	1.47757i	−0.0439939	+	0.0761997i
$377$			8.09269i			0.416795i
$378$		0			0
$379$	8.61063			0.442298			0.221149	−	0.975240i	$-0.429019\pi$
$379$	8.61063			0.442298			0.221149	+	0.975240i	$0.429019\pi$
$380$	−18.5444	−	10.7066i	−0.951306	−	0.549237i
$381$	7.97964	+	13.8211i	0.408809	+	0.708079i
$382$	10.5782	−	6.10735i	0.541230	−	0.312479i
$383$	−29.6432	−	17.1145i	−1.51470	−	0.874510i	−0.999852	−	0.0172267i	$-0.994516\pi$
$383$	−29.6432	−	17.1145i	−1.51470	−	0.874510i	−0.514845	−	0.857284i	$-0.672150\pi$
$384$	1.84776			0.0942931
$385$		0			0
$386$	5.06319			0.257709
$387$	1.34101	+	0.774235i	0.0681676	+	0.0393566i
$388$	3.31414	−	1.91342i	0.168250	−	0.0971390i
$389$	−11.4126	−	19.7672i	−0.578641	−	1.00224i	−0.995636	−	0.0933265i	$-0.970250\pi$
$389$	−11.4126	−	19.7672i	−0.578641	−	1.00224i	0.416995	−	0.908909i	$-0.363083\pi$
$390$	31.6394	+	18.2670i	1.60212	+	0.924987i
$391$	43.1446			2.18192
$392$		0			0
$393$			11.4601i			0.578088i
$394$	10.0442	−	17.3970i	0.506018	−	0.876448i
$395$	13.7329	+	23.7861i	0.690978	+	1.19681i
$396$	−0.848037	−	1.08080i	−0.0426155	−	0.0543124i
$397$	−10.9477	−	6.32068i	−0.549451	−	0.317226i	0.199450	−	0.979908i	$-0.436085\pi$
$397$	−10.9477	−	6.32068i	−0.549451	−	0.317226i	−0.748901	+	0.662682i	$0.769418\pi$
$398$	−14.8196			−0.742839
$399$		0			0
$400$	−5.47740			−0.273870
$401$	2.60875	−	4.51849i	0.130275	−	0.225642i	−0.793508	−	0.608560i	$-0.791747\pi$
$401$	2.60875	−	4.51849i	0.130275	−	0.225642i	0.923782	+	0.382918i	$0.125081\pi$
$402$	2.17206	+	3.76213i	0.108333	+	0.187638i
$403$	12.4567	−	7.19187i	0.620512	−	0.358253i
$404$	−1.83018	+	3.16997i	−0.0910551	+	0.157712i
$405$			32.5989i			1.61985i
$406$		0			0
$407$	17.3586	−	2.47637i	0.860434	−	0.122749i
$408$	7.51257	−	13.0122i	0.371928	−	0.644198i
$409$	−10.1741	−	17.6221i	−0.503079	−	0.871359i	−0.999994	−	0.00355936i	$-0.998867\pi$
$409$	−10.1741	−	17.6221i	−0.503079	−	0.871359i	0.496914	−	0.867800i	$-0.334466\pi$
$410$	1.98098	+	3.43115i	0.0978335	+	0.169453i
$411$	−14.4421	−	8.33814i	−0.712376	−	0.411290i
$412$			14.5715i			0.717887i
$413$		0			0
$414$		−	2.19775i		−	0.108013i
$415$	−15.7019	−	9.06550i	−0.770776	−	0.445008i
$416$	5.29001	−	3.05419i	0.259364	−	0.149744i
$417$	13.3559	−	7.71105i	0.654042	−	0.377612i
$418$	20.3601	+	8.17686i	0.995845	+	0.399943i
$419$			20.3391i			0.993631i	0.867856	+	0.496816i	$0.165497\pi$
$419$			20.3391i			0.993631i	−0.867856	+	0.496816i	$0.834503\pi$
$420$		0			0
$421$	−15.3327			−0.747272			−0.373636	−	0.927575i	$-0.621889\pi$
$421$	−15.3327			−0.747272			−0.373636	+	0.927575i	$0.621889\pi$
$422$	4.59924	−	7.96611i	0.223887	−	0.387784i
$423$	0.612028	−	0.353355i	0.0297578	−	0.0171807i
$424$	−3.44763	+	1.99049i	−0.167432	+	0.0966667i
$425$	−22.2699	+	38.5726i	−1.08025	+	1.87104i
$426$	13.2659			0.642735
$427$		0			0
$428$			7.87362i			0.380586i
$429$	−34.7373	−	13.9509i	−1.67713	−	0.673558i
$430$	−10.4794	+	6.05028i	−0.505361	+	0.291770i
$431$	1.87844	−	1.08452i	0.0904814	−	0.0522394i	−0.454077	−	0.890963i	$-0.650031\pi$
$431$	1.87844	−	1.08452i	0.0904814	−	0.0522394i	0.544558	+	0.838723i	$0.316697\pi$
$432$	4.13779	+	2.38896i	0.199080	+	0.114939i
$433$		−	38.4356i		−	1.84710i	−0.383479	−	0.923550i	$-0.625274\pi$
$433$		−	38.4356i		−	1.84710i	0.383479	−	0.923550i	$-0.374726\pi$
$434$		0			0
$435$			7.92391i			0.379922i
$436$	−5.19615	−	3.00000i	−0.248851	−	0.143674i
$437$	17.5500	+	30.3975i	0.839531	+	1.45411i
$438$	10.1560	+	17.5907i	0.485271	+	0.840514i
$439$	−2.86120	+	4.95574i	−0.136558	+	0.236525i	−0.926191	−	0.377054i	$-0.876937\pi$
$439$	−2.86120	+	4.95574i	−0.136558	+	0.236525i	0.789634	+	0.613578i	$0.210271\pi$
$440$	10.6279	−	1.51617i	0.506666	−	0.0722808i
$441$		0			0
$442$		−	49.6706i		−	2.36259i
$443$	−3.59367	+	6.22441i	−0.170740	+	0.295731i	−0.938679	−	0.344793i	$-0.887949\pi$
$443$	−3.59367	+	6.22441i	−0.170740	+	0.295731i	0.767939	+	0.640523i	$0.221283\pi$
$444$	8.45998	−	4.88437i	0.401493	−	0.231802i
$445$	−7.54380	−	13.0662i	−0.357610	−	0.619399i
$446$	−5.43800	+	9.41888i	−0.257497	+	0.445997i
$447$	−39.2626			−1.85706
$448$		0			0
$449$	8.63068			0.407307			0.203654	−	0.979043i	$-0.434718\pi$
$449$	8.63068			0.407307			0.203654	+	0.979043i	$0.434718\pi$
$450$	1.96485	+	1.13441i	0.0926239	+	0.0534765i
$451$	−2.50595	−	3.19378i	−0.118001	−	0.150389i
$452$	6.76078	+	11.7100i	0.318001	+	0.550793i
$453$	−15.4058	+	26.6837i	−0.723829	+	1.25371i
$454$		−	23.4793i		−	1.10194i
$455$		0			0
$456$	12.2236			0.572423
$457$	−24.6833	−	14.2509i	−1.15464	−	0.666629i	−0.204623	−	0.978841i	$-0.565597\pi$
$457$	−24.6833	−	14.2509i	−1.15464	−	0.666629i	−0.950013	+	0.312211i	$0.898930\pi$
$458$	11.4151	+	19.7715i	0.533390	+	0.923859i
$459$	33.6467	−	19.4259i	1.57049	−	0.906724i
$460$	14.8734	+	8.58717i	0.693477	+	0.400379i
$461$	35.6022			1.65816			0.829080	−	0.559129i	$-0.188865\pi$
$461$	35.6022			1.65816			0.829080	+	0.559129i	$0.188865\pi$
$462$		0			0
$463$	32.2369			1.49818			0.749088	−	0.662471i	$-0.230492\pi$
$463$	32.2369			1.49818			0.749088	+	0.662471i	$0.230492\pi$
$464$	1.14736	+	0.662426i	0.0532646	+	0.0307524i
$465$	12.1969	−	7.04188i	0.565617	−	0.326559i
$466$	7.35445	+	12.7383i	0.340688	+	0.590089i
$467$	−22.3972	−	12.9310i	−1.03642	−	0.598376i	−0.117601	−	0.993061i	$-0.537521\pi$
$467$	−22.3972	−	12.9310i	−1.03642	−	0.598376i	−0.918817	+	0.394685i	$0.870854\pi$
$468$	−2.53017			−0.116957
$469$		0			0
$470$			5.52260i			0.254738i
$471$	−11.5573	+	20.0177i	−0.532530	+	0.922369i
$472$	4.51926	+	7.82759i	0.208016	+	0.360294i
$473$	9.75440	−	7.65365i	0.448508	−	0.351915i
$474$	−13.5782	−	7.83938i	−0.623667	−	0.360075i
$475$	−36.2351			−1.66258
$476$		0			0
$477$	1.64897			0.0755014
$478$	−11.2109	+	19.4178i	−0.512774	+	0.888151i
$479$	−6.26028	−	10.8431i	−0.286040	−	0.495435i	0.686821	−	0.726826i	$-0.259006\pi$
$479$	−6.26028	−	10.8431i	−0.286040	−	0.495435i	−0.972861	+	0.231391i	$0.925672\pi$
$480$	5.17968	−	2.99049i	0.236419	−	0.136497i
$481$	16.1469	−	27.9672i	0.736235	−	1.27520i
$482$			15.4687i			0.704582i
$483$		0			0
$484$	−10.5612	+	3.07591i	−0.480054	+	0.139814i
$485$	6.19350	−	10.7275i	0.281233	−	0.487109i
$486$	−2.13759	−	3.70241i	−0.0969630	−	0.167945i
$487$	−10.3542	−	17.9341i	−0.469195	−	0.812670i	0.530185	−	0.847882i	$-0.322123\pi$
$487$	−10.3542	−	17.9341i	−0.469195	−	0.812670i	−0.999380	+	0.0352123i	$0.988789\pi$
$488$	−7.41004	−	4.27819i	−0.335437	−	0.193665i
$489$		−	15.5136i		−	0.701551i
$490$		0			0
$491$		−	23.6712i		−	1.06826i	−0.845401	−	0.534132i	$-0.820638\pi$
$491$		−	23.6712i		−	1.06826i	0.845401	−	0.534132i	$-0.179362\pi$
$492$	−1.95866	−	1.13083i	−0.0883031	−	0.0509818i
$493$	9.32978	−	5.38655i	0.420192	−	0.242598i
$494$	34.9954	−	20.2046i	1.57452	−	0.909048i
$495$	−4.12645	−	1.65723i	−0.185470	−	0.0744871i
$496$		−	2.35476i		−	0.105732i
$497$		0			0
$498$	10.3500			0.463794
$499$	−5.80619	+	10.0566i	−0.259921	+	0.450196i	−0.966220	−	0.257717i	$-0.917030\pi$
$499$	−5.80619	+	10.0566i	−0.259921	+	0.450196i	0.706300	+	0.707913i	$0.250363\pi$
$500$	−1.33826	+	0.772647i	−0.0598489	+	0.0345538i
$501$	−6.47499	+	3.73834i	−0.289281	+	0.167017i
$502$	2.43704	−	4.22107i	0.108770	−	0.188396i
$503$	−11.7871			−0.525561			−0.262780	−	0.964856i	$-0.584639\pi$
$503$	−11.7871			−0.525561			−0.262780	+	0.964856i	$0.584639\pi$
$504$		0			0
$505$			11.8482i			0.527237i
$506$	−16.3297	−	6.55821i	−0.725945	−	0.291548i
$507$	−38.9046	+	22.4616i	−1.72781	+	0.997554i
$508$	7.47995	−	4.31855i	0.331869	−	0.191605i
$509$	0.783816	+	0.452537i	0.0347421	+	0.0200583i	0.517270	−	0.855822i	$-0.326948\pi$
$509$	0.783816	+	0.452537i	0.0347421	+	0.0200583i	−0.482528	+	0.875880i	$0.660281\pi$
$510$		−	48.6346i		−	2.15358i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	27.3730	+	15.8038i	1.20855	+	0.697756i
$514$	9.88713	+	17.1250i	0.436102	+	0.755352i
$515$	23.5831	+	40.8472i	1.03920	+	1.79994i
$516$	3.45377	−	5.98211i	0.152044	−	0.263348i
$517$	−0.799170	−	5.60193i	−0.0351474	−	0.246373i
$518$		0			0
$519$		−	5.68376i		−	0.249489i
$520$	9.88604	−	17.1231i	0.433532	−	0.750899i
$521$	−6.98727	+	4.03410i	−0.306118	+	0.176737i	−0.645188	−	0.764024i	$-0.723221\pi$
$521$	−6.98727	+	4.03410i	−0.306118	+	0.176737i	0.339070	+	0.940761i	$0.389888\pi$
$522$	−0.274386	−	0.475250i	−0.0120095	−	0.0208011i
$523$	8.91730	−	15.4452i	0.389926	−	0.675372i	−0.602513	−	0.798109i	$-0.705834\pi$
$523$	8.91730	−	15.4452i	0.389926	−	0.675372i	0.992439	+	0.122737i	$0.0391672\pi$
$524$	6.20218			0.270944
$525$		0			0
$526$	−8.48528			−0.369976
$527$	−16.5825	−	9.57391i	−0.722345	−	0.417046i
$528$	−4.82134	+	3.78300i	−0.209822	+	0.164634i
$529$	−2.57591	−	4.46161i	−0.111996	−	0.193983i
$530$	−6.44298	+	11.1596i	−0.279865	+	0.484740i
$531$		−	3.74388i		−	0.162471i
$532$		0			0
$533$	−7.47667			−0.323851
$534$	7.45881	+	4.30634i	0.322774	+	0.186354i
$535$	12.7430	+	22.0715i	0.550928	+	0.954235i
$536$	2.03605	−	1.17551i	0.0879439	−	0.0507744i
$537$	−18.3472	−	10.5928i	−0.791741	−	0.457112i
$538$	−7.39943			−0.319012
$539$		0			0
$540$	15.4655			0.665530
$541$	−1.27884	−	0.738336i	−0.0549815	−	0.0317436i	0.472257	−	0.881461i	$-0.343439\pi$
$541$	−1.27884	−	0.738336i	−0.0549815	−	0.0317436i	−0.527239	+	0.849717i	$0.676773\pi$
$542$	12.4369	−	7.18047i	0.534212	−	0.308428i
$543$	−12.2638	−	21.2416i	−0.526292	−	0.911564i
$544$	−7.04213	−	4.06577i	−0.301929	−	0.174319i
$545$	−19.4213			−0.831917
$546$		0			0
$547$		−	16.3374i		−	0.698536i	−0.937023	−	0.349268i	$-0.886430\pi$
$547$		−	16.3374i		−	0.698536i	0.937023	−	0.349268i	$-0.113570\pi$
$548$	−4.51257	+	7.81600i	−0.192767	+	0.333883i
$549$	1.77208	+	3.06934i	0.0756307	+	0.130996i
$550$	14.2921	−	11.2141i	0.609418	−	0.478172i
$551$	7.59019	+	4.38220i	0.323353	+	0.186688i
$552$	−9.80389			−0.417281
$553$		0			0
$554$	−2.18987			−0.0930385
$555$	15.8101	−	27.3840i	0.671103	−	1.16238i
$556$	−4.17319	−	7.22817i	−0.176983	−	0.306543i
$557$	15.0253	−	8.67485i	0.636641	−	0.367565i	−0.146678	−	0.989184i	$-0.546858\pi$
$557$	15.0253	−	8.67485i	0.636641	−	0.367565i	0.783320	+	0.621619i	$0.213525\pi$
$558$	−0.487686	+	0.844698i	−0.0206454	+	0.0357589i
$559$		−	22.8352i		−	0.965824i
$560$		0			0
$561$	7.03786	+	49.3333i	0.297139	+	2.08285i
$562$	−12.8501	+	22.2571i	−0.542051	+	0.938859i
$563$	4.46536	+	7.73423i	0.188192	+	0.325959i	0.944648	−	0.328087i	$-0.106404\pi$
$563$	4.46536	+	7.73423i	0.188192	+	0.325959i	−0.756455	+	0.654046i	$0.773070\pi$
$564$	−1.57628	−	2.73019i	−0.0663732	−	0.114962i
$565$	37.9039	+	21.8839i	1.59463	+	0.920661i
$566$			15.5577i			0.653940i
$567$		0			0
$568$		−	7.17945i		−	0.301243i
$569$	−8.36434	−	4.82916i	−0.350652	−	0.202449i	0.314321	−	0.949317i	$-0.398223\pi$
$569$	−8.36434	−	4.82916i	−0.350652	−	0.202449i	−0.664972	+	0.746868i	$0.731557\pi$
$570$	34.2655	−	19.7832i	1.43522	−	0.828627i
$571$	10.3301	−	5.96410i	0.432302	−	0.249590i	−0.268025	−	0.963412i	$-0.586371\pi$
$571$	10.3301	−	5.96410i	0.432302	−	0.249590i	0.700327	+	0.713822i	$0.253038\pi$
$572$	−7.55019	+	18.7997i	−0.315689	+	0.786056i
$573$			22.5698i			0.942868i
$574$		0			0
$575$	29.0622			1.21198
$576$	−0.207107	+	0.358719i	−0.00862945	+	0.0149466i
$577$	32.5171	−	18.7737i	1.35370	−	0.781561i	0.364938	−	0.931032i	$-0.381090\pi$
$577$	32.5171	−	18.7737i	1.35370	−	0.781561i	0.988766	+	0.149471i	$0.0477569\pi$
$578$	−42.5410	+	24.5610i	−1.76947	+	1.02160i
$579$	−4.67778	+	8.10215i	−0.194402	+	0.336714i
$580$	4.28839			0.178066
$581$		0			0
$582$			7.07107i			0.293105i
$583$	4.92065	−	12.2522i	0.203792	−	0.507436i
$584$	9.52000	−	5.49637i	0.393940	−	0.227442i
$585$	−7.09263	+	4.09493i	−0.293244	+	0.169305i
$586$	2.69725	+	1.55726i	0.111422	+	0.0643297i
$587$			29.1914i			1.20486i	0.798173	+	0.602429i	$0.205800\pi$
$587$			29.1914i			1.20486i	−0.798173	+	0.602429i	$0.794200\pi$
$588$		0			0
$589$		−	15.5776i		−	0.641864i
$590$	25.3370	+	14.6283i	1.04311	+	0.602238i
$591$	18.5592	+	32.1455i	0.763423	+	1.32229i
$592$	−2.64340	−	4.57851i	−0.108643	−	0.188176i
$593$	−14.3449	+	24.8461i	−0.589076	+	1.02031i	0.405278	+	0.914193i	$0.367175\pi$
$593$	−14.3449	+	24.8461i	−0.589076	+	1.02031i	−0.994354	+	0.106115i	$0.966159\pi$
$594$	−15.6877	+	2.23800i	−0.643674	+	0.0918263i
$595$		0			0
$596$			21.2488i			0.870383i
$597$	13.6915	−	23.7144i	0.560356	−	0.970565i
$598$	−28.0679	+	16.2050i	−1.14778	+	0.662672i
$599$	5.32806	+	9.22848i	0.217699	+	0.377065i	0.954104	−	0.299475i	$-0.0968116\pi$
$599$	5.32806	+	9.22848i	0.217699	+	0.377065i	−0.736405	+	0.676541i	$0.763478\pi$
$600$	5.06046	−	8.76497i	0.206592	−	0.357829i
$601$	−43.5354			−1.77585			−0.887923	−	0.459992i	$-0.847852\pi$
$601$	−43.5354			−1.77585			−0.887923	+	0.459992i	$0.847852\pi$
$602$		0			0
$603$	−0.973827			−0.0396573
$604$	14.4411	+	8.33757i	0.587600	+	0.339251i
$605$	−24.6272	+	25.7151i	−1.00124	+	1.04547i
$606$	−3.38174	−	5.85734i	−0.137374	−	0.237938i
$607$	−13.6748	+	23.6855i	−0.555044	+	0.961365i	0.442856	+	0.896593i	$0.353965\pi$
$607$	−13.6748	+	23.6855i	−0.555044	+	0.961365i	−0.997900	+	0.0647718i	$0.979368\pi$
$608$		−	6.61537i		−	0.268289i
$609$		0			0
$610$	−27.6960			−1.12138
$611$	−9.02554	−	5.21090i	−0.365134	−	0.210810i
$612$	1.68410	+	2.91694i	0.0680757	+	0.117911i
$613$	24.1278	−	13.9302i	0.974514	−	0.562636i	0.0739045	−	0.997265i	$-0.476454\pi$
$613$	24.1278	−	13.9302i	0.974514	−	0.562636i	0.900609	+	0.434629i	$0.143121\pi$
$614$	−7.73423	−	4.46536i	−0.312128	−	0.180207i
$615$	−7.32074			−0.295201
$616$		0			0
$617$	32.0263			1.28933			0.644665	−	0.764465i	$-0.276997\pi$
$617$	32.0263			1.28933			0.644665	+	0.764465i	$0.276997\pi$
$618$	−23.3174	−	13.4623i	−0.937964	−	0.541534i
$619$	−17.3213	+	10.0005i	−0.696203	+	0.401953i	−0.805932	−	0.592009i	$-0.798335\pi$
$619$	−17.3213	+	10.0005i	−0.696203	+	0.401953i	0.109729	+	0.993962i	$0.465002\pi$
$620$	−3.81104	−	6.60091i	−0.153055	−	0.265099i
$621$	−21.9544	−	12.6754i	−0.881000	−	0.508646i
$622$	−19.1346			−0.767227
$623$		0			0
$624$			11.2868i			0.451834i
$625$	11.1925	−	19.3860i	0.447702	−	0.775442i
$626$	0.589279	+	1.02066i	0.0235523	+	0.0407938i
$627$	−31.8950	+	25.0259i	−1.27376	+	0.999439i
$628$	10.8335	+	6.25474i	0.432305	+	0.249591i
$629$	−42.9899			−1.71412
$630$		0			0
$631$	25.3751			1.01017			0.505084	−	0.863070i	$-0.331461\pi$
$631$	25.3751			1.01017			0.505084	+	0.863070i	$0.331461\pi$
$632$	−4.24264	+	7.34847i	−0.168763	+	0.292306i
$633$	8.49828	+	14.7195i	0.337776	+	0.585046i
$634$	7.87818	−	4.54847i	0.312883	−	0.180643i
$635$	13.9786	−	24.2117i	0.554725	−	0.960812i
$636$		−	7.35589i		−	0.291680i
$637$		0			0
$638$	−4.34999	+	0.620568i	−0.172218	+	0.0245685i
$639$	−1.48691	+	2.57541i	−0.0588214	+	0.101882i
$640$	−1.61844	−	2.80322i	−0.0639745	−	0.110807i
$641$	−14.6685	−	25.4067i	−0.579373	−	1.00350i	−0.995551	−	0.0942201i	$-0.969964\pi$
$641$	−14.6685	−	25.4067i	−0.579373	−	1.00350i	0.416179	−	0.909283i	$-0.363369\pi$
$642$	−12.5994	−	7.27428i	−0.497260	−	0.287093i
$643$		−	7.53612i		−	0.297196i	−0.988898	−	0.148598i	$-0.952524\pi$
$643$		−	7.53612i		−	0.297196i	0.988898	−	0.148598i	$-0.0474760\pi$
$644$		0			0
$645$		−	22.3589i		−	0.880381i
$646$	−46.5863	−	26.8966i	−1.83291	−	1.05823i
$647$	−25.1631	+	14.5279i	−0.989262	+	0.571151i	−0.905054	−	0.425297i	$-0.860169\pi$
$647$	−25.1631	+	14.5279i	−0.989262	+	0.571151i	−0.0842084	+	0.996448i	$0.526836\pi$
$648$	−8.72180	+	5.03553i	−0.342625	+	0.197814i
$649$	−27.8178	−	11.1720i	−1.09195	−	0.438538i
$650$		−	33.4580i		−	1.31233i
$651$		0			0
$652$	−8.39592			−0.328810
$653$	−14.7920	+	25.6205i	−0.578856	+	1.00261i	0.416755	+	0.909019i	$0.363167\pi$
$653$	−14.7920	+	25.6205i	−0.578856	+	1.00261i	−0.995611	+	0.0935894i	$0.970166\pi$
$654$	9.60124	−	5.54328i	0.375438	−	0.216759i
$655$	17.3861	−	10.0379i	0.679331	−	0.392212i
$656$	−0.612002	+	1.06002i	−0.0238947	+	0.0413868i
$657$	−4.55335			−0.177643
$658$		0			0
$659$			5.39725i			0.210247i	0.994459	+	0.105124i	$0.0335238\pi$
$659$			5.39725i			0.210247i	−0.994459	+	0.105124i	$0.966476\pi$
$660$	−7.39272	+	18.4076i	−0.287761	+	0.716516i
$661$	25.5047	−	14.7252i	0.992018	−	0.572742i	0.0861414	−	0.996283i	$-0.472546\pi$
$661$	25.5047	−	14.7252i	0.992018	−	0.572742i	0.905877	+	0.423541i	$0.139213\pi$
$662$	−2.36401	+	1.36486i	−0.0918800	+	0.0530469i
$663$	79.4831	+	45.8896i	3.08687	+	1.78220i
$664$		−	5.60138i		−	0.217376i
$665$		0			0
$666$			2.18987i			0.0848556i
$667$	−6.08767	−	3.51472i	−0.235716	−	0.136090i
$668$	2.02317	+	3.50424i	0.0782789	+	0.135583i
$669$	−10.0481	−	17.4038i	−0.388482	−	0.672871i
$670$	3.80500	−	6.59044i	0.147000	−	0.254611i
$671$	28.0939	−	4.00786i	1.08455	−	0.154722i
$672$		0			0
$673$			5.21501i			0.201024i	0.994936	+	0.100512i	$0.0320481\pi$
$673$			5.21501i			0.201024i	−0.994936	+	0.100512i	$0.967952\pi$
$674$	10.1604	−	17.5984i	0.391365	−	0.677864i
$675$	22.6643	−	13.0853i	0.872351	−	0.503652i
$676$	12.1561	+	21.0550i	0.467543	+	0.809809i
$677$	−4.86736	+	8.43051i	−0.187068	+	0.324011i	−0.944271	−	0.329168i	$-0.893232\pi$
$677$	−4.86736	+	8.43051i	−0.187068	+	0.324011i	0.757204	+	0.653179i	$0.226565\pi$
$678$	−24.9846			−0.959528
$679$		0			0
$680$	−26.3209			−1.00936
$681$	37.5717	+	21.6920i	1.43975	+	0.831240i
$682$	4.82100	+	6.14424i	0.184605	+	0.235275i
$683$	8.75076	+	15.1568i	0.334838	+	0.579957i	0.983454	−	0.181159i	$-0.0579849\pi$
$683$	8.75076	+	15.1568i	0.334838	+	0.579957i	−0.648615	+	0.761116i	$0.724652\pi$
$684$	−1.37009	+	2.37306i	−0.0523867	+	0.0907364i
$685$			29.2133i			1.11618i
$686$		0			0
$687$	−42.1845			−1.60944
$688$	−3.23749	−	1.86917i	−0.123428	−	0.0712614i
$689$	−12.1587	−	21.0594i	−0.463208	−	0.802299i
$690$	−27.4825	+	15.8670i	−1.04624	+	0.604047i
$691$	−40.0753	−	23.1375i	−1.52454	−	0.880192i	−0.999577	−	0.0290659i	$-0.990747\pi$
$691$	−40.0753	−	23.1375i	−1.52454	−	0.880192i	−0.524961	−	0.851127i	$-0.675920\pi$
$692$	−3.07603			−0.116933
$693$		0			0
$694$	−24.4383			−0.927666
$695$	−23.3967	−	13.5081i	−0.887489	−	0.512392i
$696$	−2.12004	+	1.22400i	−0.0803598	+	0.0463957i
$697$	4.97652	+	8.61959i	0.188499	+	0.326490i
$698$	2.66392	+	1.53801i	0.100831	+	0.0582147i
$699$	−27.1785			−1.02799
$700$		0			0
$701$			28.7883i			1.08732i	0.839306	+	0.543660i	$0.182962\pi$
$701$			28.7883i			1.08732i	−0.839306	+	0.543660i	$0.817038\pi$
$702$	−14.5926	+	25.2752i	−0.550764	+	0.953950i
$703$	−17.4871	−	30.2885i	−0.659538	−	1.14235i
$704$	2.04734	+	2.60929i	0.0771621	+	0.0983413i
$705$	−8.83730	−	5.10222i	−0.332832	−	0.192161i
$706$	33.7399			1.26982
$707$		0			0
$708$	−16.7010			−0.627663
$709$	−1.25142	+	2.16753i	−0.0469982	+	0.0814032i	−0.888568	−	0.458746i	$-0.848299\pi$
$709$	−1.25142	+	2.16753i	−0.0469982	+	0.0814032i	0.841569	+	0.540149i	$0.181632\pi$
$710$	−11.6195	−	20.1256i	−0.436073	−	0.755300i
$711$	3.04384	−	1.75736i	0.114153	−	0.0659061i
$712$	2.33058	−	4.03668i	0.0873421	−	0.151281i
$713$			12.4939i			0.467902i
$714$		0			0
$715$	9.26136	+	64.9193i	0.346355	+	2.42784i
$716$	−5.73276	+	9.92944i	−0.214243	+	0.371081i
$717$	−20.7150	−	35.8795i	−0.773617	−	1.33994i
$718$	14.9492	+	25.8928i	0.557900	+	0.966312i
$719$	−1.84966	−	1.06790i	−0.0689807	−	0.0398260i	0.465113	−	0.885251i	$-0.346014\pi$
$719$	−1.84966	−	1.06790i	−0.0689807	−	0.0398260i	−0.534094	+	0.845425i	$0.679347\pi$
$720$			1.34076i			0.0499672i
$721$		0			0
$722$		−	24.7632i		−	0.921590i
$723$	−24.7532	−	14.2913i	−0.920581	−	0.531498i
$724$	−11.4959	+	6.63714i	−0.427241	+	0.246668i
$725$	6.28453	−	3.62837i	0.233401	−	0.134754i
$726$	4.83518	−	19.7419i	0.179450	−	0.732689i
$727$		−	35.5296i		−	1.31772i	−0.752266	−	0.658859i	$-0.771039\pi$
$727$		−	35.5296i		−	1.31772i	0.752266	−	0.658859i	$-0.228961\pi$
$728$		0			0
$729$	−22.3137			−0.826434
$730$	17.7911	−	30.8151i	0.658479	−	1.14052i
$731$	−26.3258	+	15.1992i	−0.973696	+	0.562164i
$732$	13.6920	−	7.90507i	0.506070	−	0.292180i
$733$	1.17128	−	2.02871i	0.0432622	−	0.0749323i	−0.843584	−	0.536998i	$-0.819558\pi$
$733$	1.17128	−	2.02871i	0.0432622	−	0.0749323i	0.886846	+	0.462066i	$0.152892\pi$
$734$	3.55525			0.131227
$735$		0			0
$736$			5.30583i			0.195575i
$737$	−2.90596	+	7.23574i	−0.107042	+	0.266532i
$738$	0.439074	−	0.253499i	0.0161625	−	0.00933144i
$739$	−11.8757	+	6.85645i	−0.436855	+	0.252218i	−0.702263	−	0.711918i	$-0.747827\pi$
$739$	−11.8757	+	6.85645i	−0.436855	+	0.252218i	0.265408	+	0.964136i	$0.414493\pi$
$740$	−14.8201	−	8.55638i	−0.544797	−	0.314539i
$741$			74.6664i			2.74294i
$742$		0			0
$743$		−	44.2193i		−	1.62225i	−0.584873	−	0.811125i	$-0.698856\pi$
$743$		−	44.2193i		−	1.62225i	0.584873	−	0.811125i	$-0.301144\pi$
$744$	3.76810	+	2.17551i	0.138145	+	0.0797582i
$745$	34.3899	+	59.5650i	1.25995	+	2.18229i
$746$	−10.5485	−	18.2705i	−0.386207	−	0.668930i
$747$	−1.16008	+	2.00932i	−0.0424452	+	0.0735173i
$748$	26.6990	−	3.80886i	0.976211	−	0.139266i
$749$		0			0
$750$		−	2.85533i		−	0.104262i
$751$	−4.83164	+	8.36864i	−0.176309	+	0.305376i	−0.940613	−	0.339479i	$-0.889749\pi$
$751$	−4.83164	+	8.36864i	−0.176309	+	0.305376i	0.764305	+	0.644855i	$0.223082\pi$
$752$	−1.47757	+	0.853074i	−0.0538813	+	0.0311084i
$753$	4.50306	+	7.79953i	0.164101	+	0.284231i
$754$	−4.04635	+	7.00848i	−0.147359	+	0.255234i
$755$	53.9755			1.96437
$756$		0			0
$757$	−29.0384			−1.05542			−0.527710	−	0.849425i	$-0.676949\pi$
$757$	−29.0384			−1.05542			−0.527710	+	0.849425i	$0.676949\pi$
$758$	7.45702	+	4.30531i	0.270851	+	0.156376i
$759$	25.5812	−	20.0719i	0.928538	−	0.728565i
$760$	−10.7066	−	18.5444i	−0.388369	−	0.672675i
$761$	10.6811	−	18.5003i	0.387191	−	0.670635i	−0.604879	−	0.796317i	$-0.706779\pi$
$761$	10.6811	−	18.5003i	0.387191	−	0.670635i	0.992071	+	0.125682i	$0.0401120\pi$
$762$			15.9593i			0.578144i
$763$		0			0
$764$	12.2147			0.441913
$765$	9.44180	+	5.45123i	0.341369	+	0.197090i
$766$	−17.1145	−	29.6432i	−0.618372	−	1.07105i
$767$	−47.8139	+	27.6054i	−1.72646	+	0.996772i
$768$	1.60021	+	0.923880i	0.0577425	+	0.0333376i
$769$	15.7726			0.568773			0.284387	−	0.958710i	$-0.408210\pi$
$769$	15.7726			0.568773			0.284387	+	0.958710i	$0.408210\pi$
$770$		0			0
$771$	−36.5381			−1.31589
$772$	4.38485	+	2.53159i	0.157814	+	0.0911141i
$773$	5.81924	−	3.35974i	0.209303	−	0.120841i	−0.391684	−	0.920100i	$-0.628107\pi$
$773$	5.81924	−	3.35974i	0.209303	−	0.120841i	0.600988	+	0.799258i	$0.294774\pi$
$774$	0.774235	+	1.34101i	0.0278293	+	0.0482018i
$775$	−11.1700	−	6.44898i	−0.401237	−	0.231654i
$776$	3.82683			0.137375
$777$		0			0
$778$		−	22.8252i		−	0.818322i
$779$	−4.04862	+	7.01242i	−0.145057	+	0.251246i
$780$	18.2670	+	31.6394i	0.654064	+	1.13287i
$781$	14.6988	+	18.7333i	0.525964	+	0.670329i
$782$	37.3643	+	21.5723i	1.33615	+	0.771424i
$783$	−6.33002			−0.226217
$784$		0			0
$785$	40.4917			1.44521
$786$	−5.73007	+	9.92477i	−0.204385	+	0.354005i
$787$	−23.5398	−	40.7721i	−0.839103	−	1.45337i	−0.890646	−	0.454698i	$-0.849747\pi$
$787$	−23.5398	−	40.7721i	−0.839103	−	1.45337i	0.0515429	−	0.998671i	$-0.483586\pi$
$788$	17.3970	−	10.0442i	0.619743	−	0.357809i
$789$	7.83938	−	13.5782i	0.279089	−	0.483397i
$790$			27.4659i			0.977191i
$791$		0			0
$792$	−0.194020	−	1.36002i	−0.00689420	−	0.0483263i
$793$	26.1328	−	45.2633i	0.928003	−	1.60735i
$794$	−6.32068	−	10.9477i	−0.224312	−	0.388521i
$795$	−11.9051	−	20.6202i	−0.422229	−	0.731322i
$796$	−12.8341	−	7.40979i	−0.454894	−	0.262633i
$797$			0.354303i			0.0125501i	0.999980	+	0.00627504i	$0.00199742\pi$
$797$			0.354303i			0.0125501i	−0.999980	+	0.00627504i	$0.998003\pi$
$798$		0			0
$799$			13.8736i			0.490814i
$800$	−4.74357	−	2.73870i	−0.167710	−	0.0968277i
$801$	−1.67205	+	0.965357i	−0.0590789	+	0.0341092i
$802$	4.51849	−	2.60875i	0.159553	−	0.0921181i
$803$	−13.5875	+	33.8323i	−0.479491	+	1.19392i
$804$			4.34413i			0.153206i
$805$		0			0
$806$	14.3837			0.506646
$807$	6.83618	−	11.8406i	0.240645	−	0.416809i
$808$	−3.16997	+	1.83018i	−0.111519	+	0.0643857i
$809$	−39.3802	+	22.7362i	−1.38454	+	0.799362i	−0.992693	−	0.120670i	$-0.961496\pi$
$809$	−39.3802	+	22.7362i	−1.38454	+	0.799362i	−0.391843	+	0.920032i	$0.628162\pi$
$810$	−16.2994	+	28.2314i	−0.572703	+	0.991952i
$811$	18.9483			0.665366			0.332683	−	0.943039i	$-0.392046\pi$
$811$	18.9483			0.665366			0.332683	+	0.943039i	$0.392046\pi$
$812$		0			0
$813$			26.5356i			0.930643i
$814$	16.2712	+	6.53470i	0.570304	+	0.229041i
$815$	−23.5356	+	13.5883i	−0.824417	+	0.475977i
$816$	13.0122	−	7.51257i	0.455517	−	0.262993i
$817$	−21.4172	−	12.3652i	−0.749294	−	0.432605i
$818$		−	20.3483i		−	0.711462i
$819$		0			0
$820$			3.96195i			0.138357i
$821$	−22.5822	−	13.0379i	−0.788126	−	0.455025i	0.0511765	−	0.998690i	$-0.483703\pi$
$821$	−22.5822	−	13.0379i	−0.788126	−	0.455025i	−0.839302	+	0.543665i	$0.817036\pi$
$822$	−8.33814	−	14.4421i	−0.290826	−	0.503726i
$823$	20.7848	+	36.0003i	0.724513	+	1.25489i	0.959174	+	0.282816i	$0.0912686\pi$
$823$	20.7848	+	36.0003i	0.724513	+	1.25489i	−0.234661	+	0.972077i	$0.575398\pi$
$824$	−7.28575	+	12.6193i	−0.253811	+	0.439614i
$825$	4.74070	+	33.2308i	0.165050	+	1.15695i
$826$		0			0
$827$		−	51.2279i		−	1.78137i	−0.454621	−	0.890685i	$-0.650225\pi$
$827$		−	51.2279i		−	1.78137i	0.454621	−	0.890685i	$-0.349775\pi$
$828$	1.09887	−	1.90330i	0.0381885	−	0.0661444i
$829$	3.72964	−	2.15331i	0.129536	−	0.0747875i	−0.433832	−	0.900994i	$-0.642839\pi$
$829$	3.72964	−	2.15331i	0.129536	−	0.0747875i	0.563368	+	0.826206i	$0.309505\pi$
$830$	−9.06550	−	15.7019i	−0.314668	−	0.545021i
$831$	2.02317	−	3.50424i	0.0701831	−	0.121561i
$832$	6.10838			0.211770
$833$		0			0
$834$	15.4221			0.534023
$835$	11.3428	+	6.54877i	0.392534	+	0.226630i
$836$	13.5439	+	17.2614i	0.468427	+	0.596999i
$837$	5.62541	+	9.74350i	0.194443	+	0.336785i
$838$	−10.1696	+	17.6142i	−0.351302	+	0.608472i
$839$		−	32.0881i		−	1.10781i	−0.832581	−	0.553903i	$-0.813138\pi$
$839$		−	32.0881i		−	1.10781i	0.832581	−	0.553903i	$-0.186862\pi$
$840$		0			0
$841$	27.2448			0.939475
$842$	−13.2785	−	7.66637i	−0.457609	−	0.264200i
$843$	−23.7440	−	41.1258i	−0.817786	−	1.41645i
$844$	7.96611	−	4.59924i	0.274205	−	0.158312i
$845$	68.1526	+	39.3479i	2.34452	+	1.35361i
$846$	0.706710			0.0242972
$847$		0			0
$848$	−3.98098			−0.136707
$849$	−24.8956	−	14.3735i	−0.854414	−	0.493296i
$850$	−38.5726	+	22.2699i	−1.32303	+	0.763851i
$851$	14.0254	+	24.2928i	0.480786	+	0.832746i
$852$	11.4886	+	6.63295i	0.393593	+	0.227241i
$853$	46.8146			1.60290			0.801451	−	0.598060i	$-0.204062\pi$
$853$	46.8146			1.60290			0.801451	+	0.598060i	$0.204062\pi$
$854$		0			0
$855$			8.86963i			0.303335i
$856$	−3.93681	+	6.81876i	−0.134557	+	0.233060i
$857$	−21.2573	−	36.8187i	−0.726135	−	1.25770i	−0.958505	−	0.285076i	$-0.907981\pi$
$857$	−21.2573	−	36.8187i	−0.726135	−	1.25770i	0.232370	−	0.972628i	$-0.425352\pi$
$858$	−23.1080	−	29.4505i	−0.788893	−	1.00542i
$859$	20.3138	+	11.7282i	0.693097	+	0.400160i	0.804771	−	0.593585i	$-0.202288\pi$
$859$	20.3138	+	11.7282i	0.693097	+	0.400160i	−0.111674	+	0.993745i	$0.535621\pi$
$860$	−12.1006			−0.412625
$861$		0			0
$862$	2.16904			0.0738777
$863$	−6.82055	+	11.8135i	−0.232174	+	0.402137i	−0.958448	−	0.285268i	$-0.907917\pi$
$863$	−6.82055	+	11.8135i	−0.232174	+	0.402137i	0.726274	+	0.687406i	$0.241251\pi$
$864$	2.38896	+	4.13779i	0.0812739	+	0.140771i
$865$	−8.62279	+	4.97837i	−0.293183	+	0.169270i
$866$	19.2178	−	33.2862i	0.653048	−	1.13111i
$867$		−	90.7658i		−	3.08257i
$868$		0			0
$869$	−3.97456	−	27.8604i	−0.134828	−	0.945100i
$870$	−3.96195	+	6.86231i	−0.134323	+	0.232654i
$871$	7.18047	+	12.4369i	0.243301	+	0.421410i
$872$	−3.00000	−	5.19615i	−0.101593	−	0.175964i
$873$	−1.37276	−	0.792563i	−0.0464609	−	0.0268242i
$874$			35.1000i			1.18728i
$875$		0			0
$876$			20.3119i			0.686277i
$877$	13.0924	+	7.55888i	0.442098	+	0.255245i	0.704487	−	0.709717i	$-0.251177\pi$
$877$	13.0924	+	7.55888i	0.442098	+	0.255245i	−0.262389	+	0.964962i	$0.584510\pi$
$878$	−4.95574	+	2.86120i	−0.167248	+	0.0965608i
$879$	−4.98386	+	2.87744i	−0.168102	+	0.0970535i
$880$	9.96213	+	4.00091i	0.335823	+	0.134871i
$881$		−	4.23924i		−	0.142824i	−0.997447	−	0.0714118i	$-0.977250\pi$
$881$		−	4.23924i		−	0.142824i	0.997447	−	0.0714118i	$-0.0227504\pi$
$882$		0			0
$883$	12.9457			0.435658			0.217829	−	0.975987i	$-0.430102\pi$
$883$	12.9457			0.435658			0.217829	+	0.975987i	$0.430102\pi$
$884$	24.8353	−	43.0160i	0.835301	−	1.44678i
$885$	−46.8167	+	27.0296i	−1.57372	+	0.908590i
$886$	−6.22441	+	3.59367i	−0.209113	+	0.120732i
$887$	−11.3206	+	19.6079i	−0.380109	+	0.658369i	−0.991078	−	0.133286i	$-0.957447\pi$
$887$	−11.3206	+	19.6079i	−0.380109	+	0.658369i	0.610968	+	0.791655i	$0.290780\pi$
$888$	9.76874			0.327818
$889$		0			0
$890$		−	15.0876i		−	0.505738i
$891$	12.4482	−	30.9957i	0.417032	−	1.03839i
$892$	−9.41888	+	5.43800i	−0.315368	+	0.182078i
$893$	−9.77466	+	5.64340i	−0.327097	+	0.188849i
$894$	−34.0024	−	19.6313i	−1.13721	−	0.656569i
$895$			37.1126i			1.24054i
$896$		0			0
$897$		−	59.8859i		−	1.99953i
$898$	7.47439	+	4.31534i	0.249424	+	0.144005i
$899$	1.55985	+	2.70174i	0.0520240	+	0.0901082i
$900$	1.13441	+	1.96485i	0.0378136	+	0.0654950i
$901$	−16.1858	+	28.0345i	−0.539226	+	0.933966i
$902$	−0.573330	−	4.01887i	−0.0190898	−	0.133814i
$903$		0			0
$904$			13.5216i			0.449721i
$905$	−21.4836	+	37.2108i	−0.714141	+	1.23693i
$906$	−26.6837	+	15.4058i	−0.886506	+	0.511824i
$907$	−24.4560	−	42.3591i	−0.812049	−	1.40651i	−0.911428	−	0.411460i	$-0.865019\pi$
$907$	−24.4560	−	42.3591i	−0.812049	−	1.40651i	0.0993790	−	0.995050i	$-0.468314\pi$
$908$	11.7396	−	20.3337i	0.389594	−	0.674796i
$909$	1.51617			0.0502883
$910$		0			0
$911$	−52.4028			−1.73618			−0.868091	−	0.496406i	$-0.834653\pi$
$911$	−52.4028			−1.73618			−0.868091	+	0.496406i	$0.834653\pi$
$912$	10.5860	+	6.11181i	0.350536	+	0.202382i
$913$	11.4679	+	14.6156i	0.379533	+	0.483706i
$914$	−14.2509	−	24.6833i	−0.471378	−	0.816451i
$915$	25.5878	−	44.3193i	0.845905	−	1.46515i
$916$			22.8301i			0.754328i
$917$		0			0
$918$	38.8518			1.28230
$919$	13.4617	+	7.77209i	0.444059	+	0.256378i	0.705318	−	0.708891i	$-0.250804\pi$
$919$	13.4617	+	7.77209i	0.444059	+	0.256378i	−0.261259	+	0.965269i	$0.584138\pi$
$920$	8.58717	+	14.8734i	0.283111	+	0.490362i
$921$	14.2910	−	8.25091i	0.470904	−	0.271877i
$922$	30.8324	+	17.8011i	1.01541	+	0.586248i
$923$	43.8548			1.44350
$924$		0			0
$925$	−28.9580			−0.952132
$926$	27.9180	+	16.1184i	0.917441	+	0.529685i
$927$	5.22708	−	3.01786i	0.171680	−	0.0991195i
$928$	0.662426	+	1.14736i	0.0217452	+	0.0376638i
$929$	23.5782	+	13.6129i	0.773575	+	0.446624i	0.834149	−	0.551540i	$-0.185960\pi$
$929$	23.5782	+	13.6129i	0.773575	+	0.446624i	−0.0605732	+	0.998164i	$0.519293\pi$
$930$	14.0838			0.461824
$931$		0			0
$932$			14.7089i			0.481806i
$933$	17.6781	−	30.6193i	0.578754	−	1.00243i
$934$	−12.9310	−	22.3972i	−0.423116	−	0.732858i
$935$	68.6787	−	53.8878i	2.24603	−	1.76232i
$936$	−2.19119	−	1.26509i	−0.0716214	−	0.0413506i
$937$	28.7613			0.939590			0.469795	−	0.882776i	$-0.344328\pi$
$937$	28.7613			0.939590			0.469795	+	0.882776i	$0.344328\pi$
$938$		0			0
$939$	−2.17769			−0.0710663
$940$	−2.76130	+	4.78271i	−0.0900636	+	0.155995i
$941$	17.6492	+	30.5693i	0.575348	+	0.996531i	0.996004	+	0.0893112i	$0.0284666\pi$
$941$	17.6492	+	30.5693i	0.575348	+	0.996531i	−0.420656	+	0.907220i	$0.638200\pi$
$942$	−20.0177	+	11.5573i	−0.652213	+	0.376556i
$943$	3.24718	−	5.62427i	0.105743	−	0.183152i
$944$			9.03853i			0.294179i
$945$		0			0
$946$	12.2744	−	1.75106i	0.399075	−	0.0569318i
$947$	−20.5123	+	35.5283i	−0.666559	+	1.15451i	0.312301	+	0.949983i	$0.398900\pi$
$947$	−20.5123	+	35.5283i	−0.666559	+	1.15451i	−0.978860	+	0.204531i	$0.934433\pi$
$948$	−7.83938	−	13.5782i	−0.254611	−	0.440999i
$949$	33.5739	+	58.1517i	1.08986	+	1.88768i
$950$	−31.3805	−	18.1175i	−1.01812	−	0.587810i
$951$			16.8090i			0.545068i
$952$		0			0
$953$		−	1.09232i		−	0.0353838i	−0.999843	−	0.0176919i	$-0.994368\pi$
$953$		−	1.09232i		−	0.0353838i	0.999843	−	0.0176919i	$-0.00563181\pi$
$954$	1.42805	+	0.824487i	0.0462350	+	0.0266938i
$955$	34.2405	−	19.7688i	1.10800	−	0.639703i
$956$	−19.4178	+	11.2109i	−0.628018	+	0.362586i
$957$	3.02583	−	7.53422i	0.0978113	−	0.243547i
$958$		−	12.5206i		−	0.404521i
$959$		0			0
$960$	5.98098			0.193035
$961$	−12.7276	+	22.0448i	−0.410566	+	0.711122i
$962$	27.9672	−	16.1469i	0.901700	−	0.520597i
$963$	2.82442	−	1.63068i	0.0910157	−	0.0525480i
$964$	−7.73437	+	13.3963i	−0.249107	+	0.431467i
$965$	16.3889			0.527579
$966$		0			0
$967$			41.0334i			1.31955i	0.751465	+	0.659773i	$0.229348\pi$
$967$			41.0334i			1.31955i	−0.751465	+	0.659773i	$0.770652\pi$
$968$	−10.6842	−	2.61678i	−0.343404	−	0.0841065i
$969$	86.0803	−	49.6985i	2.76530	−	1.59654i
$970$	10.7275	−	6.19350i	0.344438	−	0.198861i
$971$	−6.99539	−	4.03879i	−0.224493	−	0.129611i	0.383536	−	0.923526i	$-0.374706\pi$
$971$	−6.99539	−	4.03879i	−0.224493	−	0.129611i	−0.608029	+	0.793915i	$0.708039\pi$
$972$		−	4.27518i		−	0.137126i
$973$		0			0
$974$		−	20.7085i		−	0.663542i
$975$	53.5397	+	30.9112i	1.71464	+	0.989950i
$976$	−4.27819	−	7.41004i	−0.136942	−	0.237190i
$977$	−17.8216	−	30.8679i	−0.570164	−	0.987553i	−0.996549	−	0.0830109i	$-0.973546\pi$
$977$	−17.8216	−	30.8679i	−0.570164	−	0.987553i	0.426385	−	0.904542i	$-0.359787\pi$
$978$	7.75682	−	13.4352i	0.248036	−	0.429610i
$979$	2.18331	+	15.3043i	0.0697789	+	0.489129i
$980$		0			0
$981$			2.48528i			0.0793489i
$982$	11.8356	−	20.4998i	0.377688	−	0.654176i
$983$	33.7780	−	19.5017i	1.07735	−	0.622008i	0.147169	−	0.989111i	$-0.452984\pi$
$983$	33.7780	−	19.5017i	1.07735	−	0.622008i	0.930180	+	0.367103i	$0.119650\pi$
$984$	−1.13083	−	1.95866i	−0.0360496	−	0.0624397i
$985$	32.5118	−	56.3120i	1.03591	−	1.79425i
$986$	10.7731			0.343085
$987$		0			0
$988$	40.4092			1.28559
$989$	17.1776	+	9.91749i	0.546216	+	0.315358i
$990$	−2.74500	−	3.49843i	−0.0872417	−	0.111187i
$991$	8.30189	+	14.3793i	0.263718	+	0.456773i	0.967227	−	0.253913i	$-0.0817178\pi$
$991$	8.30189	+	14.3793i	0.263718	+	0.456773i	−0.703509	+	0.710687i	$0.748384\pi$
$992$	1.17738	−	2.03928i	0.0373818	−	0.0647472i
$993$		−	5.04388i		−	0.160063i
$994$		0			0
$995$	−47.9692			−1.52073
$996$	8.96336	+	5.17500i	0.284015	+	0.163976i
$997$	−21.1693	−	36.6663i	−0.670439	−	1.16123i	−0.977780	−	0.209635i	$-0.932773\pi$
$997$	−21.1693	−	36.6663i	−0.670439	−	1.16123i	0.307341	−	0.951599i	$-0.400561\pi$
$998$	−10.0566	+	5.80619i	−0.318337	+	0.183792i
$999$	21.8757	+	12.6299i	0.692117	+	0.399594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.i.d.901.15		32
7.2	even	3		1078.2.c.c.1077.1	✓	16
7.3	odd	6	inner	1078.2.i.d.1011.3		32
7.4	even	3	inner	1078.2.i.d.1011.4		32
7.5	odd	6		1078.2.c.c.1077.8	yes	16
7.6	odd	2	inner	1078.2.i.d.901.16		32
11.10	odd	2	inner	1078.2.i.d.901.3		32
77.10	even	6	inner	1078.2.i.d.1011.15		32
77.32	odd	6	inner	1078.2.i.d.1011.16		32
77.54	even	6		1078.2.c.c.1077.16	yes	16
77.65	odd	6		1078.2.c.c.1077.9	yes	16
77.76	even	2	inner	1078.2.i.d.901.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.c.c.1077.1	✓	16	7.2	even	3
1078.2.c.c.1077.8	yes	16	7.5	odd	6
1078.2.c.c.1077.9	yes	16	77.65	odd	6
1078.2.c.c.1077.16	yes	16	77.54	even	6
1078.2.i.d.901.3		32	11.10	odd	2	inner
1078.2.i.d.901.4		32	77.76	even	2	inner
1078.2.i.d.901.15		32	1.1	even	1	trivial
1078.2.i.d.901.16		32	7.6	odd	2	inner
1078.2.i.d.1011.3		32	7.3	odd	6	inner
1078.2.i.d.1011.4		32	7.4	even	3	inner
1078.2.i.d.1011.15		32	77.10	even	6	inner
1078.2.i.d.1011.16		32	77.32	odd	6	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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.60021 + 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.80322 + 1.61844i) q^{5} -1.84776 q^{6} +1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.60021 + 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.80322 + 1.61844i) q^{5} -1.84776 q^{6} +1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +(1.61844 + 2.80322i) q^{10} +(-2.04734 - 2.60929i) q^{11} +(-1.60021 - 0.923880i) q^{12} -6.10838 q^{13} -5.98098 q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.06577 + 7.04213i) q^{17} +(0.358719 - 0.207107i) q^{18} +(-3.30769 + 5.72908i) q^{19} +3.23688i q^{20} +(-0.468406 - 3.28338i) q^{22} +(2.65291 - 4.59498i) q^{23} +(-0.923880 - 1.60021i) q^{24} +(2.73870 + 4.74357i) q^{25} +(-5.29001 - 3.05419i) q^{26} -4.77791i q^{27} -1.32485i q^{29} +(-5.17968 - 2.99049i) q^{30} +(-2.03928 + 1.17738i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(5.68684 + 2.28390i) q^{33} +8.13155i q^{34} +0.414214 q^{36} +(-2.64340 + 4.57851i) q^{37} +(-5.72908 + 3.30769i) q^{38} +(9.77466 - 5.64340i) q^{39} +(-1.61844 + 2.80322i) q^{40} +1.22400 q^{41} +3.73834i q^{43} +(1.23604 - 3.07769i) q^{44} +(1.16113 - 0.670380i) q^{45} +(4.59498 - 2.65291i) q^{46} +(1.47757 + 0.853074i) q^{47} -1.84776i q^{48} +5.47740i q^{50} +(-13.0122 - 7.51257i) q^{51} +(-3.05419 - 5.29001i) q^{52} +(1.99049 + 3.44763i) q^{53} +(2.38896 - 4.13779i) q^{54} +(-1.51617 - 10.6279i) q^{55} -12.2236i q^{57} +(0.662426 - 1.14736i) q^{58} +(7.82759 - 4.51926i) q^{59} +(-2.99049 - 5.17968i) q^{60} +(-4.27819 + 7.41004i) q^{61} -2.35476 q^{62} -1.00000 q^{64} +(-17.1231 - 9.88604i) q^{65} +(3.78300 + 4.82134i) q^{66} +(-1.17551 - 2.03605i) q^{67} +(-4.06577 + 7.04213i) q^{68} +9.80389i q^{69} -7.17945 q^{71} +(0.358719 + 0.207107i) q^{72} +(-5.49637 - 9.52000i) q^{73} +(-4.57851 + 2.64340i) q^{74} +(-8.76497 - 5.06046i) q^{75} -6.61537 q^{76} +11.2868 q^{78} +(7.34847 + 4.24264i) q^{79} +(-2.80322 + 1.61844i) q^{80} +(5.03553 + 8.72180i) q^{81} +(1.06002 + 0.612002i) q^{82} -5.60138 q^{83} +26.3209i q^{85} +(-1.86917 + 3.23749i) q^{86} +(1.22400 + 2.12004i) q^{87} +(2.60929 - 2.04734i) q^{88} +(-4.03668 - 2.33058i) q^{89} +1.34076 q^{90} +5.30583 q^{92} +(2.17551 - 3.76810i) q^{93} +(0.853074 + 1.47757i) q^{94} +(-18.5444 + 10.7066i) q^{95} +(0.923880 - 1.60021i) q^{96} -3.82683i q^{97} +(-1.36002 + 0.194020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 - 16 * q^9	\( 32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^9 - 16 * q^11 - 16 * q^16 - 16 * q^22 + 16 * q^23 + 64 * q^25 - 32 * q^36 + 80 * q^37 + 16 * q^44 - 32 * q^53 + 48 * q^58 - 32 * q^64 - 16 * q^67 - 96 * q^71 + 32 * q^78 + 48 * q^81 - 32 * q^86 - 8 * q^88 + 32 * q^92 + 48 * q^93 + 48 * q^99

Introduction

L-functions

Modular forms

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