LMFDB - Embedded newform 1078.2.i.d.901.4

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			901.4
Character	$\chi$	$=$	1078.901
Dual form			1078.2.i.d.1011.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.60021 - 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.80322 - 1.61844i) q^{5} -1.84776 q^{6} -1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +O(q^{10})$	\(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} +(-1.23604 - 3.07769i) 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} +(-4.82134 - 3.78300i) 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} +(2.04734 - 2.60929i) 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} +(2.28390 + 5.68684i) 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} +(-3.07769 + 1.23604i) 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	0.0390089	−	0.999239i	$-0.487580\pi$
$3$	1.60021	−	0.923880i	0.923880	−	0.533402i	0.884871	+	0.465837i	$0.154247\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.80322	−	1.61844i	−1.25364	−	0.723789i	−0.281809	−	0.959471i	$-0.590934\pi$
$5$	−2.80322	−	1.61844i	−1.25364	−	0.723789i	−0.971830	+	0.235682i	$0.924268\pi$
$6$	−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
$11$	−1.23604	−	3.07769i	−0.372680	−	0.927960i
$11$	−1.23604	−	3.07769i	−0.372680	−	0.927960i
$12$	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	$0.0392545\pi$
$29$			1.32485i			0.246019i	−0.992406	+	0.123009i	$0.960745\pi$
$30$	5.17968	+	2.99049i	0.945676	+	0.545986i
$31$	2.03928	−	1.17738i	0.366266	−	0.211464i	−0.305560	−	0.952173i	$-0.598844\pi$
$31$	2.03928	−	1.17738i	0.366266	−	0.211464i	0.671826	+	0.740709i	$0.265510\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−4.82134	−	3.78300i	−0.839287	−	0.658535i
$34$		−	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	$-0.907991\pi$
$43$		−	3.73834i		−	0.570091i	0.958514	−	0.285045i	$-0.0920087\pi$
$44$	2.04734	−	2.60929i	0.308648	−	0.393365i
$45$	−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	0.388351	−	0.921511i	$-0.373045\pi$
$47$	−1.47757	−	0.853074i	−0.215525	−	0.124434i	−0.603877	+	0.797078i	$0.706378\pi$
$48$			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	−0.913833	−	0.406090i	$-0.866892\pi$
$59$	−7.82759	+	4.51926i	−1.01907	+	0.588358i	−0.105233	+	0.994448i	$0.533559\pi$
$60$	−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
$66$	2.28390	+	5.68684i	0.281129	+	0.700001i
$67$	−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	0.0259772	−	0.999663i	$-0.491730\pi$
$79$	−7.34847	−	4.24264i	−0.826767	−	0.477334i	−0.852745	+	0.522328i	$0.825064\pi$
$80$	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
$88$	−3.07769	+	1.23604i	−0.328083	+	0.131762i
$89$	4.03668	+	2.33058i	0.427887	+	0.247041i	0.698446	−	0.715663i	$-0.253875\pi$
$89$	4.03668	+	2.33058i	0.427887	+	0.247041i	−0.270559	+	0.962703i	$0.587209\pi$
$90$	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	$0.0622364\pi$
$97$			3.82683i			0.388556i	−0.980946	+	0.194278i	$0.937764\pi$
$98$		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	−0.273628	−	0.961836i	$-0.588224\pi$
$103$	−12.6193	−	7.28575i	−1.24342	−	0.717887i	−0.969788	+	0.243949i	$0.921557\pi$
$104$			6.10838i			0.598975i
$105$		0			0
$106$		−	3.98098i		−	0.386667i
$107$	−6.81876	−	3.93681i	−0.659194	−	0.380586i	0.132776	−	0.991146i	$-0.457611\pi$
$107$	−6.81876	−	3.93681i	−0.659194	−	0.380586i	−0.791970	+	0.610560i	$0.790944\pi$
$108$	−4.13779	+	2.38896i	−0.398159	+	0.229877i
$109$	5.19615	−	3.00000i	0.497701	−	0.287348i	−0.230063	−	0.973176i	$-0.573893\pi$
$109$	5.19615	−	3.00000i	0.497701	−	0.287348i	0.727764	+	0.685828i	$0.240560\pi$
$110$	6.62700	−	8.44596i	0.631860	−	0.805291i
$111$			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
$121$	−7.94441	+	7.60831i	−0.722219	+	0.691664i
$122$	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	$0.125181\pi$
$127$			8.63710i			0.766419i	−0.923661	+	0.383209i	$0.874819\pi$
$128$	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
$143$	7.55019	+	18.7997i	0.631379	+	1.57211i
$144$	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	$-0.997204\pi$
$149$	−18.4020	−	10.6244i	−1.50755	−	0.870383i	−0.507586	−	0.861601i	$-0.669462\pi$
$150$	−5.06046	−	8.76497i	−0.413185	−	0.715657i
$151$	−14.4411	+	8.33757i	−1.17520	+	0.678502i	−0.954899	−	0.296930i	$-0.904037\pi$
$151$	−14.4411	+	8.33757i	−1.17520	+	0.678502i	−0.220301	+	0.975432i	$0.570704\pi$
$152$	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	−0.865553	−	0.500817i	$-0.833033\pi$
$157$	−10.8335	+	6.25474i	−0.864610	+	0.499183i	0.000943620		1.00000i	$0.499700\pi$
$158$	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
$165$	7.39272	+	18.4076i	0.575523	+	1.43303i
$166$	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	$-0.835778\pi$
$181$		−	13.2743i		−	0.986670i	0.869839	−	0.493335i	$-0.164222\pi$
$182$		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
$187$	16.6481	−	21.2176i	1.21743	−	1.55158i
$188$		−	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	−0.649442	−	0.760411i	$-0.724998\pi$
$193$	−4.38485	+	2.53159i	−0.315628	+	0.182228i	0.333814	+	0.942639i	$0.391664\pi$
$194$	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	$0.253854\pi$
$197$			20.0883i			1.43123i	−0.698493	+	0.715617i	$0.746146\pi$
$198$	1.08080	+	0.848037i	0.0768093	+	0.0602674i
$199$	12.8341	−	7.40979i	0.909788	−	0.525266i	0.0294248	−	0.999567i	$-0.490632\pi$
$199$	12.8341	−	7.40979i	0.909788	−	0.525266i	0.880363	+	0.474301i	$0.157299\pi$
$200$	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	$0.102550\pi$
$211$			9.19848i			0.633249i	−0.948551	+	0.316625i	$0.897450\pi$
$212$	−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
$220$	−9.96213	+	4.00091i	−0.671647	+	0.269742i
$221$	−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	$-0.881358\pi$
$223$		−	10.8760i		−	0.728310i	0.931338	−	0.364155i	$-0.118642\pi$
$224$		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	−0.325018	−	0.945708i	$-0.605370\pi$
$229$	−19.7715	−	11.4151i	−1.30653	−	0.754328i	−0.981516	+	0.191380i	$0.938704\pi$
$230$	17.1743			1.13244
$231$		0			0
$232$	1.32485			0.0869808
$233$	−12.7383	−	7.35445i	−0.834512	−	0.481806i	0.0208827	−	0.999782i	$-0.493352\pi$
$233$	−12.7383	−	7.35445i	−0.834512	−	0.481806i	−0.855395	+	0.517976i	$0.826686\pi$
$234$	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	$-0.741760\pi$
$239$		−	22.4218i		−	1.45035i	0.688567	−	0.725173i	$-0.258240\pi$
$240$	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	$0.667322\pi$
$242$	10.6842	−	2.61678i	0.686807	−	0.168213i
$243$	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	$0.0491590\pi$
$251$			4.87408i			0.307649i	−0.988098	+	0.153825i	$0.950841\pi$
$252$		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	−0.140532	−	0.990076i	$-0.544881\pi$
$257$	−17.1250	−	9.88713i	−1.06823	−	0.616742i	−0.927697	+	0.373334i	$0.878214\pi$
$258$			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	−0.256023	−	0.966671i	$-0.582412\pi$
$263$	7.34847	−	4.24264i	0.453126	−	0.261612i	0.709150	+	0.705058i	$0.249079\pi$
$264$	−3.78300	+	4.82134i	−0.232827	+	0.296733i
$265$		−	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	−0.291759	−	0.956492i	$-0.594240\pi$
$269$	6.40809	−	3.69971i	0.390708	−	0.225575i	0.682467	+	0.730916i	$0.260907\pi$
$270$	−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
$275$	11.2141	−	14.2921i	0.676237	−	0.861848i
$276$	8.49042	−	4.90195i	0.511063	−	0.295063i
$277$	1.89648	−	1.09493i	0.113948	−	0.0657882i	−0.441943	−	0.897043i	$-0.645711\pi$
$277$	1.89648	−	1.09493i	0.113948	−	0.0657882i	0.555891	+	0.831255i	$0.312377\pi$
$278$	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	$-0.721959\pi$
$281$		−	25.7003i		−	1.53315i	0.642154	−	0.766575i	$-0.278041\pi$
$282$	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
$297$	14.7050	−	5.90569i	0.853268	−	0.342683i
$298$	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	0.0498046	−	0.998759i	$-0.484140\pi$
$311$	16.5710	−	9.56730i	0.939658	−	0.542512i	0.889853	+	0.456247i	$0.150807\pi$
$312$	5.64340	+	9.77466i	0.319495	+	0.553381i
$313$	−1.02066	−	0.589279i	−0.0576912	−	0.0333080i	0.470877	−	0.882199i	$-0.343938\pi$
$313$	−1.02066	−	0.589279i	−0.0576912	−	0.0333080i	−0.528568	+	0.848891i	$0.677271\pi$
$314$	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
$319$	4.07749	−	1.63757i	0.228296	−	0.0916863i
$320$	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	$0.186698\pi$
$337$			20.3209i			1.10695i	−0.832867	+	0.553474i	$0.813302\pi$
$338$	−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
$341$	−6.14424	−	4.82100i	−0.332729	−	0.261072i
$342$		−	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	0.190679	−	0.981652i	$-0.438931\pi$
$347$	21.1642	−	12.2192i	1.13615	−	0.655959i	0.945475	+	0.325693i	$0.105598\pi$
$348$	−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
$352$	−2.60929	−	2.04734i	−0.139076	−	0.109124i
$353$	−29.2196	+	16.8700i	−1.55520	+	0.897897i	−0.557499	+	0.830178i	$0.688239\pi$
$353$	−29.2196	+	16.8700i	−1.55520	+	0.897897i	−0.997704	+	0.0677191i	$0.978428\pi$
$354$	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	−0.376083	−	0.926586i	$-0.622729\pi$
$359$	−25.8928	−	14.9492i	−1.36657	−	0.788990i	−0.990488	+	0.137596i	$0.956063\pi$
$360$	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	−0.578202	−	0.815893i	$-0.696246\pi$
$367$	−3.07894	+	1.77763i	−0.160719	+	0.0927914i	0.417483	+	0.908685i	$0.362912\pi$
$368$	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	0.891839	−	0.452353i	$-0.149415\pi$
$373$	18.2705	+	10.5485i	0.946010	+	0.546179i	0.0541707	+	0.998532i	$0.482748\pi$
$374$	−25.0264	+	10.0509i	−1.29409	+	0.519720i
$375$	−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	$0.00548369\pi$
$383$	29.6432	+	17.1145i	1.51470	+	0.874510i	0.514845	+	0.857284i	$0.327850\pi$
$384$	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
$396$	−0.511984	−	1.27482i	−0.0257282	−	0.0640623i
$397$	10.9477	+	6.32068i	0.549451	+	0.317226i	0.748901	−	0.662682i	$-0.230582\pi$
$397$	10.9477	+	6.32068i	0.549451	+	0.317226i	−0.199450	+	0.979908i	$0.563915\pi$
$398$	−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
$418$	−17.2614	−	13.5439i	−0.844284	−	0.662456i
$419$		−	20.3391i		−	0.993631i	−0.867856	−	0.496816i	$-0.834503\pi$
$419$		−	20.3391i		−	0.993631i	0.867856	−	0.496816i	$-0.165497\pi$
$420$		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
$429$	29.4505	+	23.1080i	1.42189	+	1.11566i
$430$	10.4794	−	6.05028i	0.505361	−	0.291770i
$431$	−1.87844	+	1.08452i	−0.0904814	+	0.0522394i	−0.544558	−	0.838723i	$-0.683303\pi$
$431$	−1.87844	+	1.08452i	−0.0904814	+	0.0522394i	0.454077	+	0.890963i	$0.349969\pi$
$432$	−4.13779	−	2.38896i	−0.199080	−	0.114939i
$433$			38.4356i			1.84710i	0.383479	+	0.923550i	$0.374726\pi$
$433$			38.4356i			1.84710i	−0.383479	+	0.923550i	$0.625274\pi$
$434$		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
$451$	−1.51292	−	3.76711i	−0.0712405	−	0.177386i
$452$	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	0.950013	−	0.312211i	$-0.101070\pi$
$457$	24.6833	+	14.2509i	1.15464	+	0.666629i	0.204623	+	0.978841i	$0.434403\pi$
$458$	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	0.918817	−	0.394685i	$-0.129146\pi$
$467$	22.3972	+	12.9310i	1.03642	+	0.598376i	0.117601	+	0.993061i	$0.462479\pi$
$468$	−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
$473$	−11.5055	+	4.62073i	−0.529022	+	0.212461i
$474$	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	$0.179362\pi$
$491$			23.6712i			1.06826i	−0.845401	+	0.534132i	$0.820638\pi$
$492$	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
$495$	3.49843	+	2.74500i	0.157243	+	0.123378i
$496$			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
$506$	13.8444	+	10.8628i	0.615461	+	0.482912i
$507$	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	0.482528	−	0.875880i	$-0.339719\pi$
$509$	−0.783816	−	0.452537i	−0.0347421	−	0.0200583i	−0.517270	+	0.855822i	$0.673052\pi$
$510$			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	−0.339070	−	0.940761i	$-0.610112\pi$
$521$	6.98727	−	4.03410i	0.306118	−	0.176737i	0.645188	+	0.764024i	$0.276779\pi$
$522$	−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
$528$	5.68684	−	2.28390i	0.247488	−	0.0993941i
$529$	−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	0.527239	−	0.849717i	$-0.323227\pi$
$541$	1.27884	+	0.738336i	0.0549815	+	0.0317436i	−0.472257	+	0.881461i	$0.656561\pi$
$542$	−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	$0.113570\pi$
$547$			16.3374i			0.698536i	−0.937023	+	0.349268i	$0.886430\pi$
$548$	−4.51257	+	7.81600i	−0.192767	+	0.333883i
$549$	1.77208	+	3.06934i	0.0756307	+	0.130996i
$550$	−16.8578	+	6.77029i	−0.718818	+	0.288686i
$551$	−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	−0.783320	−	0.621619i	$-0.786475\pi$
$557$	−15.0253	+	8.67485i	−0.636641	+	0.367565i	0.146678	+	0.989184i	$0.453142\pi$
$558$	−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	0.664972	−	0.746868i	$-0.268443\pi$
$569$	8.36434	+	4.82916i	0.350652	+	0.202449i	−0.314321	+	0.949317i	$0.601777\pi$
$570$	−34.2655	+	19.7832i	−1.43522	+	0.828627i
$571$	−10.3301	+	5.96410i	−0.432302	+	0.249590i	−0.700327	−	0.713822i	$-0.746962\pi$
$571$	−10.3301	+	5.96410i	−0.432302	+	0.249590i	0.268025	+	0.963412i	$0.413629\pi$
$572$	−12.5059	+	15.9385i	−0.522899	+	0.666423i
$573$		−	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	−0.988766	−	0.149471i	$-0.952243\pi$
$577$	−32.5171	+	18.7737i	−1.35370	+	0.781561i	−0.364938	+	0.931032i	$0.618910\pi$
$578$	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
$583$	8.15042	−	10.3875i	0.337556	−	0.430207i
$584$	−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	$-0.794200\pi$
$587$		−	29.1914i		−	1.20486i	0.798173	−	0.602429i	$-0.205800\pi$
$588$		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
$605$	34.5835	−	8.47020i	1.40602	−	0.344363i
$606$	−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	−0.900609	−	0.434629i	$-0.856879\pi$
$613$	−24.1278	+	13.9302i	−0.974514	+	0.562636i	−0.0739045	+	0.997265i	$0.523546\pi$
$614$	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	−0.109729	−	0.993962i	$-0.534998\pi$
$619$	17.3213	−	10.0005i	0.696203	−	0.401953i	0.805932	+	0.592009i	$0.201665\pi$
$620$	−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
$627$	37.6206	−	15.1089i	1.50242	−	0.603390i
$628$	−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	$0.0474760\pi$
$643$			7.53612i			0.297196i	−0.988898	+	0.148598i	$0.952524\pi$
$644$		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	0.0842084	−	0.996448i	$-0.473164\pi$
$647$	25.1631	−	14.5279i	0.989262	−	0.571151i	0.905054	+	0.425297i	$0.139831\pi$
$648$	8.72180	−	5.03553i	0.342625	−	0.197814i
$649$	23.5841	+	18.5050i	0.925758	+	0.726383i
$650$			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	$-0.966476\pi$
$659$		−	5.39725i		−	0.210247i	0.994459	−	0.105124i	$-0.0335238\pi$
$660$	−12.2451	+	15.6061i	−0.476640	+	0.607467i
$661$	−25.5047	+	14.7252i	−0.992018	+	0.572742i	−0.905877	−	0.423541i	$-0.860787\pi$
$661$	−25.5047	+	14.7252i	−0.992018	+	0.572742i	−0.0861414	+	0.996283i	$0.527454\pi$
$662$	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	$-0.967952\pi$
$673$		−	5.21501i		−	0.201024i	0.994936	−	0.100512i	$-0.0320481\pi$
$674$	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
$682$	2.91057	+	7.24723i	0.111452	+	0.277511i
$683$	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	$0.00925328\pi$
$691$	40.0753	+	23.1375i	1.52454	+	0.880192i	0.524961	+	0.851127i	$0.324080\pi$
$692$	−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	$-0.817038\pi$
$701$		−	28.7883i		−	1.08732i	0.839306	−	0.543660i	$-0.182962\pi$
$702$	−14.5926	+	25.2752i	−0.550764	+	0.953950i
$703$	−17.4871	−	30.2885i	−0.659538	−	1.14235i
$704$	1.23604	+	3.07769i	0.0465850	+	0.115995i
$705$	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	0.534094	−	0.845425i	$-0.320653\pi$
$719$	1.84966	+	1.06790i	0.0689807	+	0.0398260i	−0.465113	+	0.885251i	$0.653986\pi$
$720$		−	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
$726$	14.6794	−	14.0583i	0.544802	−	0.521753i
$727$			35.5296i			1.31772i	0.752266	+	0.658859i	$0.228961\pi$
$727$			35.5296i			1.31772i	−0.752266	+	0.658859i	$0.771039\pi$
$728$		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
$737$	−4.81335	+	6.13450i	−0.177302	+	0.225967i
$738$	−0.439074	+	0.253499i	−0.0161625	+	0.00933144i
$739$	11.8757	−	6.85645i	0.436855	−	0.252218i	−0.265408	−	0.964136i	$-0.585507\pi$
$739$	11.8757	−	6.85645i	0.436855	−	0.252218i	0.702263	+	0.711918i	$0.252173\pi$
$740$	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	$0.301144\pi$
$743$			44.2193i			1.62225i	−0.584873	+	0.811125i	$0.698856\pi$
$744$	−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
$759$	−30.1734	+	12.1180i	−1.09522	+	0.439856i
$760$	−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	−0.600988	−	0.799258i	$-0.705226\pi$
$773$	−5.81924	+	3.35974i	−0.209303	+	0.120841i	0.391684	+	0.920100i	$0.371893\pi$
$774$	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
$781$	8.87409	+	22.0962i	0.317540	+	0.790663i
$782$	−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	$-0.998003\pi$
$797$		−	0.354303i		−	0.0125501i	0.999980	−	0.00627504i	$-0.00199742\pi$
$798$		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
$803$	−22.5059	+	28.6833i	−0.794217	+	1.01221i
$804$		−	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	0.391843	−	0.920032i	$-0.371838\pi$
$809$	39.3802	−	22.7362i	1.38454	−	0.799362i	0.992693	+	0.120670i	$0.0385044\pi$
$810$	−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
$814$	−13.7948	−	10.8239i	−0.483508	−	0.379378i
$815$	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	0.839302	−	0.543665i	$-0.182964\pi$
$821$	22.5822	+	13.0379i	0.788126	+	0.455025i	−0.0511765	+	0.998690i	$0.516297\pi$
$822$	−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	$0.349775\pi$
$827$			51.2279i			1.78137i	−0.454621	+	0.890685i	$0.650225\pi$
$828$	1.09887	−	1.90330i	0.0381885	−	0.0661444i
$829$	−3.72964	+	2.15331i	−0.129536	+	0.0747875i	−0.563368	−	0.826206i	$-0.690495\pi$
$829$	−3.72964	+	2.15331i	−0.129536	+	0.0747875i	0.433832	+	0.900994i	$0.357161\pi$
$830$	−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
$836$	8.17686	+	20.3601i	0.282803	+	0.704169i
$837$	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	$0.186862\pi$
$839$			32.0881i			1.10781i	−0.832581	+	0.553903i	$0.813138\pi$
$840$		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	$-0.425352\pi$
$858$	−13.9509	−	34.7373i	−0.476277	−	1.18591i
$859$	−20.3138	−	11.7282i	−0.693097	−	0.400160i	0.111674	−	0.993745i	$-0.464379\pi$
$859$	−20.3138	−	11.7282i	−0.693097	−	0.400160i	−0.804771	+	0.593585i	$0.797712\pi$
$860$	−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	0.262389	−	0.964962i	$-0.415490\pi$
$877$	−13.0924	−	7.55888i	−0.442098	−	0.255245i	−0.704487	+	0.709717i	$0.748823\pi$
$878$	4.95574	−	2.86120i	0.167248	−	0.0965608i
$879$	4.98386	−	2.87744i	0.168102	−	0.0970535i
$880$	−8.44596	−	6.62700i	−0.284713	−	0.223396i
$881$			4.23924i			0.142824i	0.997447	+	0.0714118i	$0.0227504\pi$
$881$			4.23924i			0.142824i	−0.997447	+	0.0714118i	$0.977250\pi$
$882$		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
$891$	20.6189	−	26.2783i	0.690760	−	0.880357i
$892$	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
$913$	6.92352	+	17.2393i	0.229135	+	0.570539i
$914$	−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	0.261259	−	0.965269i	$-0.415862\pi$
$919$	−13.4617	−	7.77209i	−0.444059	−	0.256378i	−0.705318	+	0.708891i	$0.749196\pi$
$920$	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	0.0605732	−	0.998164i	$-0.480707\pi$
$929$	−23.5782	−	13.6129i	−0.773575	−	0.446624i	−0.834149	+	0.551540i	$0.814040\pi$
$930$	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
$935$	−81.0076	+	32.5336i	−2.64923	+	1.06396i
$936$	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	$0.00563181\pi$
$953$			1.09232i			0.0353838i	−0.999843	+	0.0176919i	$0.994368\pi$
$954$	−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
$957$	5.01191	−	6.38756i	0.162012	−	0.206480i
$958$			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	$-0.770652\pi$
$967$		−	41.0334i		−	1.31955i	0.751465	−	0.659773i	$-0.229348\pi$
$968$	7.60831	+	7.94441i	0.244540	+	0.255343i
$969$	−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	0.608029	−	0.793915i	$-0.291961\pi$
$971$	6.99539	+	4.03879i	0.224493	+	0.129611i	−0.383536	+	0.923526i	$0.625294\pi$
$972$			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	−0.930180	−	0.367103i	$-0.880350\pi$
$983$	−33.7780	+	19.5017i	−1.07735	+	0.622008i	−0.147169	+	0.989111i	$0.547016\pi$
$984$	−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
$990$	−1.65723	−	4.12645i	−0.0526703	−	0.131147i
$991$	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.901.4		32
7.2	even	3		1078.2.c.c.1077.16	yes	16
7.3	odd	6	inner	1078.2.i.d.1011.16		32
7.4	even	3	inner	1078.2.i.d.1011.15		32
7.5	odd	6		1078.2.c.c.1077.9	yes	16
7.6	odd	2	inner	1078.2.i.d.901.3		32
11.10	odd	2	inner	1078.2.i.d.901.16		32
77.10	even	6	inner	1078.2.i.d.1011.4		32
77.32	odd	6	inner	1078.2.i.d.1011.3		32
77.54	even	6		1078.2.c.c.1077.1	✓	16
77.65	odd	6		1078.2.c.c.1077.8	yes	16
77.76	even	2	inner	1078.2.i.d.901.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.c.c.1077.1	✓	16	77.54	even	6
1078.2.c.c.1077.8	yes	16	77.65	odd	6
1078.2.c.c.1077.9	yes	16	7.5	odd	6
1078.2.c.c.1077.16	yes	16	7.2	even	3
1078.2.i.d.901.3		32	7.6	odd	2	inner
1078.2.i.d.901.4		32	1.1	even	1	trivial
1078.2.i.d.901.15		32	77.76	even	2	inner
1078.2.i.d.901.16		32	11.10	odd	2	inner
1078.2.i.d.1011.3		32	77.32	odd	6	inner
1078.2.i.d.1011.4		32	77.10	even	6	inner
1078.2.i.d.1011.15		32	7.4	even	3	inner
1078.2.i.d.1011.16		32	7.3	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} +(-1.23604 - 3.07769i) 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} +(-4.82134 - 3.78300i) 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} +(2.04734 - 2.60929i) 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} +(2.28390 + 5.68684i) 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} +(-3.07769 + 1.23604i) 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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