LMFDB - Embedded newform 624.2.cn.f.353.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(305,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))

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

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

chi := DirichletCharacter("624.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.cn (of order $12$, degree $4$, 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:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			353.1
Character	$\chi$	$=$	624.353
Dual form			624.2.cn.f.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72861 - 0.109042i) q^{3} +(-0.190181 - 0.190181i) q^{5} +(-3.71203 + 0.994635i) q^{7} +(2.97622 + 0.376984i) q^{9} +O(q^{10})$	\(q+(-1.72861 - 0.109042i) q^{3} +(-0.190181 - 0.190181i) q^{5} +(-3.71203 + 0.994635i) q^{7} +(2.97622 + 0.376984i) q^{9} +(4.68976 + 1.25662i) q^{11} +(-2.54840 + 2.55062i) q^{13} +(0.308011 + 0.349487i) q^{15} +(3.17983 - 5.50763i) q^{17} +(-1.61853 - 6.04044i) q^{19} +(6.52512 - 1.31457i) q^{21} +(-1.35337 - 2.34410i) q^{23} -4.92766i q^{25} +(-5.10363 - 0.976194i) q^{27} +(-5.15639 + 2.97704i) q^{29} +(3.97821 - 3.97821i) q^{31} +(-7.96976 - 2.68359i) q^{33} +(0.895116 + 0.516795i) q^{35} +(1.57221 - 5.86758i) q^{37} +(4.68332 - 4.13116i) q^{39} +(-0.124469 + 0.464523i) q^{41} +(2.12670 + 1.22785i) q^{43} +(-0.494324 - 0.637714i) q^{45} +(7.04746 - 7.04746i) q^{47} +(6.72767 - 3.88422i) q^{49} +(-6.09727 + 9.17384i) q^{51} -1.92140i q^{53} +(-0.652917 - 1.13089i) q^{55} +(2.13915 + 10.6181i) q^{57} +(0.300361 + 1.12096i) q^{59} +(-2.23834 + 3.87691i) q^{61} +(-11.4228 + 1.56088i) q^{63} +(0.969735 - 0.000422883i) q^{65} +(2.27708 + 0.610143i) q^{67} +(2.08385 + 4.19962i) q^{69} +(11.1344 - 2.98346i) q^{71} +(-11.8134 - 11.8134i) q^{73} +(-0.537323 + 8.51803i) q^{75} -18.6584 q^{77} +4.69572 q^{79} +(8.71577 + 2.24397i) q^{81} +(-3.68981 - 3.68981i) q^{83} +(-1.65219 + 0.442702i) q^{85} +(9.23803 - 4.58390i) q^{87} +(3.42700 + 0.918262i) q^{89} +(6.92279 - 12.0027i) q^{91} +(-7.31059 + 6.44301i) q^{93} +(-0.840962 + 1.45659i) q^{95} +(-1.32581 - 4.94801i) q^{97} +(13.4840 + 5.50793i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{7}+O(q^{10}) $ 56 * q - 4 * q^7	$ 56 q - 4 q^{7} + 8 q^{13} + 8 q^{15} - 4 q^{19} + 16 q^{21} - 24 q^{27} + 36 q^{31} + 28 q^{33} + 20 q^{37} - 16 q^{39} + 84 q^{43} + 12 q^{45} - 12 q^{49} + 24 q^{55} - 36 q^{57} - 24 q^{61} + 12 q^{63} + 32 q^{67} - 36 q^{69} - 20 q^{73} + 60 q^{75} + 32 q^{79} - 88 q^{85} + 16 q^{87} - 28 q^{91} - 88 q^{93} - 36 q^{97} - 44 q^{99}+O(q^{100}) $ 56 * q - 4 * q^7 + 8 * q^13 + 8 * q^15 - 4 * q^19 + 16 * q^21 - 24 * q^27 + 36 * q^31 + 28 * q^33 + 20 * q^37 - 16 * q^39 + 84 * q^43 + 12 * q^45 - 12 * q^49 + 24 * q^55 - 36 * q^57 - 24 * q^61 + 12 * q^63 + 32 * q^67 - 36 * q^69 - 20 * q^73 + 60 * q^75 + 32 * q^79 - 88 * q^85 + 16 * q^87 - 28 * q^91 - 88 * q^93 - 36 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.72861	−	0.109042i	−0.998016	−	0.0629556i
$3$	−1.72861	−	0.109042i	−0.998016	−	0.0629556i
$4$		0			0
$5$	−0.190181	−	0.190181i	−0.0850514	−	0.0850514i	0.663301	−	0.748353i	$-0.269155\pi$
$5$	−0.190181	−	0.190181i	−0.0850514	−	0.0850514i	−0.748353	+	0.663301i	$0.769155\pi$
$6$		0			0
$7$	−3.71203	+	0.994635i	−1.40301	+	0.375937i	−0.879426	−	0.476035i	$-0.842074\pi$
$7$	−3.71203	+	0.994635i	−1.40301	+	0.375937i	−0.523588	+	0.851972i	$0.675407\pi$
$8$		0			0
$9$	2.97622	+	0.376984i	0.992073	+	0.125661i
$10$		0			0
$11$	4.68976	+	1.25662i	1.41402	+	0.378884i	0.883357	−	0.468702i	$-0.155278\pi$
$11$	4.68976	+	1.25662i	1.41402	+	0.378884i	0.530659	+	0.847586i	$0.321945\pi$
$12$		0			0
$13$	−2.54840	+	2.55062i	−0.706798	+	0.707415i
$13$	−2.54840	+	2.55062i	−0.706798	+	0.707415i
$14$		0			0
$15$	0.308011	+	0.349487i	0.0795282	+	0.0902371i
$16$		0			0
$17$	3.17983	−	5.50763i	0.771222	−	1.33580i	−0.165671	−	0.986181i	$-0.552979\pi$
$17$	3.17983	−	5.50763i	0.771222	−	1.33580i	0.936893	−	0.349615i	$-0.113688\pi$
$18$		0			0
$19$	−1.61853	−	6.04044i	−0.371317	−	1.38577i	−0.858653	−	0.512558i	$-0.828698\pi$
$19$	−1.61853	−	6.04044i	−0.371317	−	1.38577i	0.487336	−	0.873214i	$-0.337969\pi$
$20$		0			0
$21$	6.52512	−	1.31457i	1.42390	−	0.286863i
$22$		0			0
$23$	−1.35337	−	2.34410i	−0.282197	−	0.488779i	0.689729	−	0.724068i	$-0.257730\pi$
$23$	−1.35337	−	2.34410i	−0.282197	−	0.488779i	−0.971926	+	0.235289i	$0.924396\pi$
$24$		0			0
$25$		−	4.92766i		−	0.985533i
$26$		0			0
$27$	−5.10363	−	0.976194i	−0.982194	−	0.187869i
$28$		0			0
$29$	−5.15639	+	2.97704i	−0.957517	+	0.552823i	−0.895408	−	0.445246i	$-0.853116\pi$
$29$	−5.15639	+	2.97704i	−0.957517	+	0.552823i	−0.0621093	+	0.998069i	$0.519783\pi$
$30$		0			0
$31$	3.97821	−	3.97821i	0.714508	−	0.714508i	−0.252967	−	0.967475i	$-0.581406\pi$
$31$	3.97821	−	3.97821i	0.714508	−	0.714508i	0.967475	+	0.252967i	$0.0814063\pi$
$32$		0			0
$33$	−7.96976	−	2.68359i	−1.38736	−	0.467153i
$34$		0			0
$35$	0.895116	+	0.516795i	0.151302	+	0.0873544i
$36$		0			0
$37$	1.57221	−	5.86758i	0.258470	−	0.964625i	−0.707656	−	0.706557i	$-0.750247\pi$
$37$	1.57221	−	5.86758i	0.258470	−	0.964625i	0.966127	−	0.258068i	$-0.0830859\pi$
$38$		0			0
$39$	4.68332	−	4.13116i	0.749932	−	0.661515i
$40$		0			0
$41$	−0.124469	+	0.464523i	−0.0194387	+	0.0725463i	−0.974964	−	0.222363i	$-0.928623\pi$
$41$	−0.124469	+	0.464523i	−0.0194387	+	0.0725463i	0.955525	+	0.294910i	$0.0952896\pi$
$42$		0			0
$43$	2.12670	+	1.22785i	0.324319	+	0.187246i	0.653316	−	0.757085i	$-0.273377\pi$
$43$	2.12670	+	1.22785i	0.324319	+	0.187246i	−0.328997	+	0.944331i	$0.606711\pi$
$44$		0			0
$45$	−0.494324	−	0.637714i	−0.0736895	−	0.0950648i
$46$		0			0
$47$	7.04746	−	7.04746i	1.02798	−	1.02798i	0.0283802	−	0.999597i	$-0.490965\pi$
$47$	7.04746	−	7.04746i	1.02798	−	1.02798i	0.999597	−	0.0283802i	$-0.00903490\pi$
$48$		0			0
$49$	6.72767	−	3.88422i	0.961096	−	0.554889i
$50$		0			0
$51$	−6.09727	+	9.17384i	−0.853788	+	1.28459i
$52$		0			0
$53$		−	1.92140i		−	0.263925i	−0.991255	−	0.131963i	$-0.957872\pi$
$53$		−	1.92140i		−	0.263925i	0.991255	−	0.131963i	$-0.0421279\pi$
$54$		0			0
$55$	−0.652917	−	1.13089i	−0.0880393	−	0.152489i
$56$		0			0
$57$	2.13915	+	10.6181i	0.283338	+	1.40640i
$58$		0			0
$59$	0.300361	+	1.12096i	0.0391037	+	0.145937i	0.982718	−	0.185111i	$-0.0592645\pi$
$59$	0.300361	+	1.12096i	0.0391037	+	0.145937i	−0.943614	+	0.331048i	$0.892598\pi$
$60$		0			0
$61$	−2.23834	+	3.87691i	−0.286590	+	0.496388i	−0.972993	−	0.230833i	$-0.925855\pi$
$61$	−2.23834	+	3.87691i	−0.286590	+	0.496388i	0.686404	+	0.727221i	$0.259188\pi$
$62$		0			0
$63$	−11.4228	+	1.56088i	−1.43913	+	0.196652i
$64$		0			0
$65$	0.969735		0.000422883i	0.120281		5.24522e-5i
$66$		0			0
$67$	2.27708	+	0.610143i	0.278190	+	0.0745408i	0.395217	−	0.918588i	$-0.370670\pi$
$67$	2.27708	+	0.610143i	0.278190	+	0.0745408i	−0.117026	+	0.993129i	$0.537336\pi$
$68$		0			0
$69$	2.08385	+	4.19962i	0.250866	+	0.505575i
$70$		0			0
$71$	11.1344	−	2.98346i	1.32141	−	0.354072i	0.471907	−	0.881648i	$-0.343566\pi$
$71$	11.1344	−	2.98346i	1.32141	−	0.354072i	0.849508	+	0.527576i	$0.176899\pi$
$72$		0			0
$73$	−11.8134	−	11.8134i	−1.38265	−	1.38265i	−0.839883	−	0.542767i	$-0.817377\pi$
$73$	−11.8134	−	11.8134i	−1.38265	−	1.38265i	−0.542767	−	0.839883i	$-0.682623\pi$
$74$		0			0
$75$	−0.537323	+	8.51803i	−0.0620447	+	0.983578i
$76$		0			0
$77$	−18.6584			−2.12632
$78$		0			0
$79$	4.69572			0.528310			0.264155	−	0.964480i	$-0.414907\pi$
$79$	4.69572			0.528310			0.264155	+	0.964480i	$0.414907\pi$
$80$		0			0
$81$	8.71577	+	2.24397i	0.968418	+	0.249330i
$82$		0			0
$83$	−3.68981	−	3.68981i	−0.405009	−	0.405009i	0.474985	−	0.879994i	$-0.342453\pi$
$83$	−3.68981	−	3.68981i	−0.405009	−	0.405009i	−0.879994	+	0.474985i	$0.842453\pi$
$84$		0			0
$85$	−1.65219	+	0.442702i	−0.179205	+	0.0480178i
$86$		0			0
$87$	9.23803	−	4.58390i	0.990421	−	0.491445i
$88$		0			0
$89$	3.42700	+	0.918262i	0.363261	+	0.0973355i	0.435833	−	0.900028i	$-0.356454\pi$
$89$	3.42700	+	0.918262i	0.363261	+	0.0973355i	−0.0725716	+	0.997363i	$0.523121\pi$
$90$		0			0
$91$	6.92279	−	12.0027i	0.725705	−	1.25823i
$92$		0			0
$93$	−7.31059	+	6.44301i	−0.758073	+	0.668109i
$94$		0			0
$95$	−0.840962	+	1.45659i	−0.0862808	+	0.149443i
$96$		0			0
$97$	−1.32581	−	4.94801i	−0.134616	−	0.502394i	−0.999999	−	0.00128314i	$-0.999592\pi$
$97$	−1.32581	−	4.94801i	−0.134616	−	0.502394i	0.865383	−	0.501111i	$-0.167075\pi$
$98$		0			0
$99$	13.4840	+	5.50793i	1.35520	+	0.553568i
$100$		0			0
$101$	4.43271	+	7.67768i	0.441071	+	0.763957i	0.997769	−	0.0667574i	$-0.0212654\pi$
$101$	4.43271	+	7.67768i	0.441071	+	0.763957i	−0.556698	+	0.830715i	$0.687932\pi$
$102$		0			0
$103$			2.77277i			0.273209i	0.990626	+	0.136605i	$0.0436189\pi$
$103$			2.77277i			0.273209i	−0.990626	+	0.136605i	$0.956381\pi$
$104$		0			0
$105$	−1.49096	−	0.990946i	−0.145503	−	0.0967064i
$106$		0			0
$107$	−12.3587	+	7.13532i	−1.19476	+	0.689797i	−0.959383	−	0.282106i	$-0.908967\pi$
$107$	−12.3587	+	7.13532i	−1.19476	+	0.689797i	−0.235381	+	0.971903i	$0.575634\pi$
$108$		0			0
$109$	0.169226	−	0.169226i	0.0162089	−	0.0162089i	−0.698956	−	0.715165i	$-0.746352\pi$
$109$	0.169226	−	0.169226i	0.0162089	−	0.0162089i	0.715165	+	0.698956i	$0.246352\pi$
$110$		0			0
$111$	−3.35757	+	9.97136i	−0.318686	+	0.946439i
$112$		0			0
$113$	5.75283	+	3.32140i	0.541180	+	0.312451i	0.745557	−	0.666442i	$-0.232183\pi$
$113$	5.75283	+	3.32140i	0.541180	+	0.312451i	−0.204377	+	0.978892i	$0.565517\pi$
$114$		0			0
$115$	−0.188418	+	0.703187i	−0.0175701	+	0.0655725i
$116$		0			0
$117$	−8.54613	+	6.63050i	−0.790090	+	0.612990i
$118$		0			0
$119$	−6.32554	+	23.6072i	−0.579862	+	2.16407i
$120$		0			0
$121$	10.8885	+	6.28646i	0.989860	+	0.571496i
$122$		0			0
$123$	0.265811	−	0.789409i	0.0239674	−	0.0711787i
$124$		0			0
$125$	−1.88805	+	1.88805i	−0.168872	+	0.168872i
$126$		0			0
$127$	−10.0297	+	5.79068i	−0.889996	+	0.513840i	−0.873941	−	0.486031i	$-0.838444\pi$
$127$	−10.0297	+	5.79068i	−0.889996	+	0.513840i	−0.0160550	+	0.999871i	$0.505111\pi$
$128$		0			0
$129$	−3.54236	−	2.35438i	−0.311888	−	0.207292i
$130$		0			0
$131$		−	12.5788i		−	1.09902i	−0.835489	−	0.549508i	$-0.814815\pi$
$131$		−	12.5788i		−	1.09902i	0.835489	−	0.549508i	$-0.185185\pi$
$132$		0			0
$133$	12.0161	+	20.8124i	1.04192	+	1.80467i
$134$		0			0
$135$	0.784959	+	1.15626i	0.0675585	+	0.0995154i
$136$		0			0
$137$	1.05946	+	3.95398i	0.0905162	+	0.337811i	0.996302	−	0.0859259i	$-0.0273848\pi$
$137$	1.05946	+	3.95398i	0.0905162	+	0.337811i	−0.905785	+	0.423737i	$0.860718\pi$
$138$		0			0
$139$	−4.00168	+	6.93112i	−0.339418	+	0.587890i	−0.984323	−	0.176373i	$-0.943564\pi$
$139$	−4.00168	+	6.93112i	−0.339418	+	0.587890i	0.644905	+	0.764263i	$0.276897\pi$
$140$		0			0
$141$	−12.9508	+	11.4139i	−1.09066	+	0.961221i
$142$		0			0
$143$	−15.1565	+	8.75944i	−1.26745	+	0.732501i
$144$		0			0
$145$	1.54682	+	0.414469i	0.128457	+	0.0344198i
$146$		0			0
$147$	−12.0531	+	5.98073i	−0.994123	+	0.493282i
$148$		0			0
$149$	−1.55217	+	0.415902i	−0.127158	+	0.0340720i	−0.321837	−	0.946795i	$-0.604300\pi$
$149$	−1.55217	+	0.415902i	−0.127158	+	0.0340720i	0.194679	+	0.980867i	$0.437634\pi$
$150$		0			0
$151$	−4.48182	−	4.48182i	−0.364726	−	0.364726i	0.500824	−	0.865549i	$-0.333030\pi$
$151$	−4.48182	−	4.48182i	−0.364726	−	0.364726i	−0.865549	+	0.500824i	$0.833030\pi$
$152$		0			0
$153$	11.5402	−	15.1932i	0.932967	−	1.22830i
$154$		0			0
$155$	−1.51316			−0.121540
$156$		0			0
$157$	11.2835			0.900518			0.450259	−	0.892898i	$-0.351332\pi$
$157$	11.2835			0.900518			0.450259	+	0.892898i	$0.351332\pi$
$158$		0			0
$159$	−0.209514	+	3.32137i	−0.0166156	+	0.263402i
$160$		0			0
$161$	7.35526	+	7.35526i	0.579676	+	0.579676i
$162$		0			0
$163$	0.634518	−	0.170019i	0.0496993	−	0.0133169i	−0.233884	−	0.972265i	$-0.575144\pi$
$163$	0.634518	−	0.170019i	0.0496993	−	0.0133169i	0.283583	+	0.958948i	$0.408477\pi$
$164$		0			0
$165$	1.00533	+	2.02606i	0.0782647	+	0.157729i
$166$		0			0
$167$	−9.56112	−	2.56190i	−0.739862	−	0.198245i	−0.130845	−	0.991403i	$-0.541769\pi$
$167$	−9.56112	−	2.56190i	−0.739862	−	0.198245i	−0.609017	+	0.793157i	$0.708436\pi$
$168$		0			0
$169$	−0.0113381	−	13.0000i	−0.000872163	−	1.00000i
$170$		0			0
$171$	−2.53995	−	18.5878i	−0.194235	−	1.42145i
$172$		0			0
$173$	7.27868	−	12.6070i	0.553388	−	0.958496i	−0.444639	−	0.895710i	$-0.646668\pi$
$173$	7.27868	−	12.6070i	0.553388	−	0.958496i	0.998027	−	0.0627863i	$-0.0199986\pi$
$174$		0			0
$175$	4.90122	+	18.2916i	0.370498	+	1.38272i
$176$		0			0
$177$	−0.396977	−	1.97047i	−0.0298386	−	0.148109i
$178$		0			0
$179$	9.96880	+	17.2665i	0.745103	+	1.29056i	0.950147	+	0.311803i	$0.100933\pi$
$179$	9.96880	+	17.2665i	0.745103	+	1.29056i	−0.205044	+	0.978753i	$0.565734\pi$
$180$		0			0
$181$		−	11.9949i		−	0.891572i	−0.895140	−	0.445786i	$-0.852924\pi$
$181$		−	11.9949i		−	0.891572i	0.895140	−	0.445786i	$-0.147076\pi$
$182$		0			0
$183$	4.29197	−	6.45762i	0.317272	−	0.477361i
$184$		0			0
$185$	−1.41491	+	0.816896i	−0.104026	+	0.0600594i
$186$		0			0
$187$	21.8336	−	21.8336i	1.59663	−	1.59663i
$188$		0			0
$189$	19.9158	−	1.45259i	1.44866	−	0.105660i
$190$		0			0
$191$	−9.28406	−	5.36015i	−0.671771	−	0.387847i	0.124977	−	0.992160i	$-0.460114\pi$
$191$	−9.28406	−	5.36015i	−0.671771	−	0.387847i	−0.796747	+	0.604313i	$0.793448\pi$
$192$		0			0
$193$	−3.97988	+	14.8531i	−0.286478	+	1.06915i	0.661274	+	0.750144i	$0.270016\pi$
$193$	−3.97988	+	14.8531i	−0.286478	+	1.06915i	−0.947752	+	0.319007i	$0.896651\pi$
$194$		0			0
$195$	−1.67634	−	0.105011i	−0.120045	−	0.00751999i
$196$		0			0
$197$	2.17066	−	8.10102i	0.154653	−	0.577174i	−0.844482	−	0.535585i	$-0.820091\pi$
$197$	2.17066	−	8.10102i	0.154653	−	0.577174i	0.999135	−	0.0415890i	$-0.0132420\pi$
$198$		0			0
$199$	−21.0339	−	12.1439i	−1.49106	−	0.860861i	−0.491108	−	0.871099i	$-0.663408\pi$
$199$	−21.0339	−	12.1439i	−1.49106	−	0.860861i	−0.999948	+	0.0102371i	$0.996741\pi$
$200$		0			0
$201$	−3.86967	−	1.30300i	−0.272945	−	0.0919066i
$202$		0			0
$203$	16.1796	−	16.1796i	1.13558	−	1.13558i
$204$		0			0
$205$	0.112015	−	0.0646718i	0.00782346	−	0.00451687i
$206$		0			0
$207$	−3.14423	−	7.48676i	−0.218539	−	0.520366i
$208$		0			0
$209$		−	30.3621i		−	2.10019i
$210$		0			0
$211$	−3.64773	−	6.31805i	−0.251120	−	0.434953i	0.712714	−	0.701454i	$-0.247466\pi$
$211$	−3.64773	−	6.31805i	−0.251120	−	0.434953i	−0.963834	+	0.266502i	$0.914132\pi$
$212$		0			0
$213$	−19.5725	+	3.94314i	−1.34108	+	0.270179i
$214$		0			0
$215$	−0.170944	−	0.637971i	−0.0116583	−	0.0435093i
$216$		0			0
$217$	−10.8104	+	18.7241i	−0.733856	+	1.27108i
$218$		0			0
$219$	19.1326	+	21.7089i	1.29286	+	1.46695i
$220$		0			0
$221$	5.94440	+	22.1462i	0.399864	+	1.48971i
$222$		0			0
$223$	−5.96696	−	1.59884i	−0.399577	−	0.107066i	0.0534335	−	0.998571i	$-0.482983\pi$
$223$	−5.96696	−	1.59884i	−0.399577	−	0.107066i	−0.453011	+	0.891505i	$0.649650\pi$
$224$		0			0
$225$	1.85765	−	14.6658i	0.123843	−	0.977720i
$226$		0			0
$227$	−18.8123	+	5.04075i	−1.24862	+	0.334566i	−0.821803	−	0.569772i	$-0.807031\pi$
$227$	−18.8123	+	5.04075i	−1.24862	+	0.334566i	−0.426816	+	0.904338i	$0.640365\pi$
$228$		0			0
$229$	−9.08070	−	9.08070i	−0.600070	−	0.600070i	0.340261	−	0.940331i	$-0.389484\pi$
$229$	−9.08070	−	9.08070i	−0.600070	−	0.600070i	−0.940331	+	0.340261i	$0.889484\pi$
$230$		0			0
$231$	32.2532	+	2.03455i	2.12210	+	0.133864i
$232$		0			0
$233$	−5.76371			−0.377593			−0.188797	−	0.982016i	$-0.560459\pi$
$233$	−5.76371			−0.377593			−0.188797	+	0.982016i	$0.560459\pi$
$234$		0			0
$235$	−2.68058			−0.174862
$236$		0			0
$237$	−8.11709	−	0.512032i	−0.527262	−	0.0332600i
$238$		0			0
$239$	−7.01060	−	7.01060i	−0.453478	−	0.453478i	0.443029	−	0.896507i	$-0.353904\pi$
$239$	−7.01060	−	7.01060i	−0.453478	−	0.453478i	−0.896507	+	0.443029i	$0.853904\pi$
$240$		0			0
$241$	9.37198	−	2.51121i	0.603702	−	0.161761i	0.0559942	−	0.998431i	$-0.482167\pi$
$241$	9.37198	−	2.51121i	0.603702	−	0.161761i	0.547708	+	0.836670i	$0.315501\pi$
$242$		0			0
$243$	−14.8215	−	4.82935i	−0.950801	−	0.309803i
$244$		0			0
$245$	−2.01818	−	0.540769i	−0.128937	−	0.0345485i
$246$		0			0
$247$	19.5315	+	11.2652i	1.24276	+	0.716787i
$248$		0			0
$249$	5.97591	+	6.78060i	0.378708	+	0.429703i
$250$		0			0
$251$	−1.34842	+	2.33554i	−0.0851118	+	0.147418i	−0.905439	−	0.424477i	$-0.860458\pi$
$251$	−1.34842	+	2.33554i	−0.0851118	+	0.147418i	0.820327	+	0.571895i	$0.193791\pi$
$252$		0			0
$253$	−3.40133	−	12.6939i	−0.213840	−	0.798061i
$254$		0			0
$255$	2.90427	−	0.585103i	0.181872	−	0.0366406i
$256$		0			0
$257$	14.3802	+	24.9072i	0.897011	+	1.55367i	0.831296	+	0.555831i	$0.187600\pi$
$257$	14.3802	+	24.9072i	0.897011	+	1.55367i	0.0657157	+	0.997838i	$0.479067\pi$
$258$		0			0
$259$			23.3444i			1.45055i
$260$		0			0
$261$	−16.4688	+	6.91646i	−1.01940	+	0.428118i
$262$		0			0
$263$	0.824473	−	0.476009i	0.0508392	−	0.0293520i	−0.474365	−	0.880328i	$-0.657322\pi$
$263$	0.824473	−	0.476009i	0.0508392	−	0.0293520i	0.525204	+	0.850976i	$0.323989\pi$
$264$		0			0
$265$	−0.365414	+	0.365414i	−0.0224472	+	0.0224472i
$266$		0			0
$267$	−5.82383	−	1.96101i	−0.356413	−	0.120012i
$268$		0			0
$269$	−13.6806	−	7.89848i	−0.834119	−	0.481579i	0.0211420	−	0.999776i	$-0.493270\pi$
$269$	−13.6806	−	7.89848i	−0.834119	−	0.481579i	−0.855261	+	0.518198i	$0.826603\pi$
$270$		0			0
$271$	−2.70376	+	10.0906i	−0.164242	+	0.612958i	0.833894	+	0.551925i	$0.186106\pi$
$271$	−2.70376	+	10.0906i	−0.164242	+	0.612958i	−0.998136	+	0.0610337i	$0.980560\pi$
$272$		0			0
$273$	−13.2756	+	19.9932i	−0.803478	+	1.21004i
$274$		0			0
$275$	6.19218	−	23.1095i	0.373403	−	1.39356i
$276$		0			0
$277$	7.55958	+	4.36453i	0.454211	+	0.262239i	0.709607	−	0.704598i	$-0.248872\pi$
$277$	7.55958	+	4.36453i	0.454211	+	0.262239i	−0.255396	+	0.966837i	$0.582206\pi$
$278$		0			0
$279$	13.3398	−	10.3403i	0.798630	−	0.619058i
$280$		0			0
$281$	18.3286	−	18.3286i	1.09339	−	1.09339i	0.0982275	−	0.995164i	$-0.468683\pi$
$281$	18.3286	−	18.3286i	1.09339	−	1.09339i	0.995164	−	0.0982275i	$-0.0313173\pi$
$282$		0			0
$283$	23.9350	−	13.8189i	1.42279	−	0.821446i	0.426250	−	0.904605i	$-0.359834\pi$
$283$	23.9350	−	13.8189i	1.42279	−	0.821446i	0.996536	+	0.0831593i	$0.0265010\pi$
$284$		0			0
$285$	1.61253	−	2.42618i	0.0955179	−	0.143714i
$286$		0			0
$287$		−	1.84812i		−	0.109091i
$288$		0			0
$289$	−11.7227	−	20.3042i	−0.689568	−	1.19437i
$290$		0			0
$291$	1.75228	+	8.69777i	0.102721	+	0.509872i
$292$		0			0
$293$	−3.57000	−	13.3234i	−0.208562	−	0.778363i	−0.988334	−	0.152300i	$-0.951332\pi$
$293$	−3.57000	−	13.3234i	−0.208562	−	0.778363i	0.779772	−	0.626063i	$-0.215335\pi$
$294$		0			0
$295$	0.156063	−	0.270309i	0.00908632	−	0.0157380i
$296$		0			0
$297$	−22.7081	−	10.9914i	−1.31766	−	0.637787i
$298$		0			0
$299$	9.42783	+	2.52177i	0.545226	+	0.145838i
$300$		0			0
$301$	−9.11564	−	2.44253i	−0.525417	−	0.140785i
$302$		0			0
$303$	−6.82526	−	13.7551i	−0.392101	−	0.790210i
$304$		0			0
$305$	1.16300	−	0.311626i	0.0665933	−	0.0178436i
$306$		0			0
$307$	−7.94134	−	7.94134i	−0.453236	−	0.453236i	0.443191	−	0.896427i	$-0.353846\pi$
$307$	−7.94134	−	7.94134i	−0.453236	−	0.453236i	−0.896427	+	0.443191i	$0.853846\pi$
$308$		0			0
$309$	0.302349	−	4.79305i	0.0172000	−	0.272667i
$310$		0			0
$311$	33.5390			1.90182			0.950910	−	0.309468i	$-0.100151\pi$
$311$	33.5390			1.90182			0.950910	+	0.309468i	$0.100151\pi$
$312$		0			0
$313$	−22.4809			−1.27070			−0.635349	−	0.772225i	$-0.719144\pi$
$313$	−22.4809			−1.27070			−0.635349	+	0.772225i	$0.719144\pi$
$314$		0			0
$315$	2.46924	+	1.87554i	0.139126	+	0.105675i
$316$		0			0
$317$	23.9753	+	23.9753i	1.34659	+	1.34659i	0.889338	+	0.457251i	$0.151166\pi$
$317$	23.9753	+	23.9753i	1.34659	+	1.34659i	0.457251	+	0.889338i	$0.348834\pi$
$318$		0			0
$319$	−27.9232	+	7.48200i	−1.56340	+	0.418912i
$320$		0			0
$321$	22.1416	−	10.9866i	1.23582	−	0.613212i
$322$		0			0
$323$	−38.4152	−	10.2933i	−2.13748	−	0.572735i
$324$		0			0
$325$	12.5686	+	12.5576i	0.697181	+	0.696573i
$326$		0			0
$327$	−0.310980	+	0.274074i	−0.0171972	+	0.0151563i
$328$		0			0
$329$	−19.1507	+	33.1700i	−1.05581	+	1.82872i
$330$		0			0
$331$	−0.0412994	−	0.154131i	−0.00227002	−	0.00847182i	0.964782	−	0.263052i	$-0.0847292\pi$
$331$	−0.0412994	−	0.154131i	−0.00227002	−	0.00847182i	−0.967052	+	0.254581i	$0.918063\pi$
$332$		0			0
$333$	6.89124	−	16.8705i	0.377638	−	0.924499i
$334$		0			0
$335$	−0.317020	−	0.549095i	−0.0173206	−	0.0300002i
$336$		0			0
$337$			4.43339i			0.241502i	0.992683	+	0.120751i	$0.0385303\pi$
$337$			4.43339i			0.241502i	−0.992683	+	0.120751i	$0.961470\pi$
$338$		0			0
$339$	−9.58225	−	6.36872i	−0.520436	−	0.345901i
$340$		0			0
$341$	23.6559	−	13.6578i	1.28104	−	0.739609i
$342$		0			0
$343$	−2.08817	+	2.08817i	−0.112751	+	0.112751i
$344$		0			0
$345$	0.402380	−	1.19499i	0.0216634	−	0.0643363i
$346$		0			0
$347$	29.4679	+	17.0133i	1.58192	+	0.913322i	0.994579	+	0.103981i	$0.0331582\pi$
$347$	29.4679	+	17.0133i	1.58192	+	0.913322i	0.587340	+	0.809340i	$0.300175\pi$
$348$		0			0
$349$	1.09276	−	4.07825i	0.0584943	−	0.218304i	−0.930492	−	0.366313i	$-0.880620\pi$
$349$	1.09276	−	4.07825i	0.0584943	−	0.218304i	0.988986	+	0.148009i	$0.0472866\pi$
$350$		0			0
$351$	15.4960	−	10.5297i	0.827114	−	0.562034i
$352$		0			0
$353$	2.31619	−	8.64414i	0.123278	−	0.460081i	−0.876494	−	0.481413i	$-0.840124\pi$
$353$	2.31619	−	8.64414i	0.123278	−	0.460081i	0.999772	+	0.0213316i	$0.00679058\pi$
$354$		0			0
$355$	−2.68495	−	1.55016i	−0.142502	−	0.0822738i
$356$		0			0
$357$	13.5086	−	40.1181i	0.714952	−	2.12327i
$358$		0			0
$359$	11.0583	−	11.0583i	0.583637	−	0.583637i	−0.352264	−	0.935901i	$-0.614588\pi$
$359$	11.0583	−	11.0583i	0.583637	−	0.583637i	0.935901	+	0.352264i	$0.114588\pi$
$360$		0			0
$361$	−17.4128	+	10.0533i	−0.916463	+	0.529120i
$362$		0			0
$363$	−18.1365	−	12.0542i	−0.951918	−	0.632680i
$364$		0			0
$365$			4.49335i			0.235193i
$366$		0			0
$367$	8.25548	+	14.2989i	0.430933	+	0.746397i	0.996954	−	0.0779933i	$-0.0248513\pi$
$367$	8.25548	+	14.2989i	0.430933	+	0.746397i	−0.566021	+	0.824391i	$0.691518\pi$
$368$		0			0
$369$	−0.545564	+	1.33560i	−0.0284009	+	0.0695286i
$370$		0			0
$371$	1.91110	+	7.13231i	0.0992192	+	0.370291i
$372$		0			0
$373$	−4.48630	+	7.77050i	−0.232292	+	0.402341i	−0.958482	−	0.285153i	$-0.907956\pi$
$373$	−4.48630	+	7.77050i	−0.232292	+	0.402341i	0.726190	+	0.687494i	$0.241289\pi$
$374$		0			0
$375$	3.46959	−	3.05783i	0.179169	−	0.157906i
$376$		0			0
$377$	5.54722	−	20.7387i	0.285696	−	1.06810i
$378$		0			0
$379$	7.71852	+	2.06817i	0.396474	+	0.106235i	0.451547	−	0.892247i	$-0.350872\pi$
$379$	7.71852	+	2.06817i	0.396474	+	0.106235i	−0.0550728	+	0.998482i	$0.517539\pi$
$380$		0			0
$381$	17.9690	−	8.91619i	0.920580	−	0.456790i
$382$		0			0
$383$	16.4533	−	4.40864i	0.840724	−	0.225271i	0.187337	−	0.982296i	$-0.440014\pi$
$383$	16.4533	−	4.40864i	0.840724	−	0.225271i	0.653387	+	0.757024i	$0.273348\pi$
$384$		0			0
$385$	3.54846	+	3.54846i	0.180846	+	0.180846i
$386$		0			0
$387$	5.86665	+	4.45609i	0.298219	+	0.226516i
$388$		0			0
$389$	−25.1792			−1.27664			−0.638319	−	0.769772i	$-0.720370\pi$
$389$	−25.1792			−1.27664			−0.638319	+	0.769772i	$0.720370\pi$
$390$		0			0
$391$	−17.2139			−0.870546
$392$		0			0
$393$	−1.37162	+	21.7439i	−0.0691891	+	1.09684i
$394$		0			0
$395$	−0.893035	−	0.893035i	−0.0449335	−	0.0449335i
$396$		0			0
$397$	−25.1521	+	6.73949i	−1.26235	+	0.338245i	−0.827095	−	0.562062i	$-0.810008\pi$
$397$	−25.1521	+	6.73949i	−1.26235	+	0.338245i	−0.435254	+	0.900308i	$0.643342\pi$
$398$		0			0
$399$	−18.5017	−	37.2869i	−0.926244	−	1.86668i
$400$		0			0
$401$	−20.6472	−	5.53240i	−1.03107	−	0.276275i	−0.296663	−	0.954982i	$-0.595874\pi$
$401$	−20.6472	−	5.53240i	−1.03107	−	0.276275i	−0.734409	+	0.678707i	$0.762541\pi$
$402$		0			0
$403$	0.00884590	+	20.2850i	0.000440646	+	1.01047i
$404$		0			0
$405$	−1.23081	−	2.08433i	−0.0611594	−	0.103571i
$406$		0			0
$407$	14.7466	−	25.5419i	0.730962	−	1.26606i
$408$		0			0
$409$	2.39464	+	8.93690i	0.118407	+	0.441901i	0.999519	−	0.0310061i	$-0.00987115\pi$
$409$	2.39464	+	8.93690i	0.118407	+	0.441901i	−0.881112	+	0.472907i	$0.843204\pi$
$410$		0			0
$411$	−1.40026	−	6.95043i	−0.0690695	−	0.342839i
$412$		0			0
$413$	−2.22990	−	3.86230i	−0.109726	−	0.190051i
$414$		0			0
$415$			1.40346i			0.0688931i
$416$		0			0
$417$	7.67315	−	11.5449i	0.375756	−	0.565355i
$418$		0			0
$419$	−9.50476	+	5.48758i	−0.464338	+	0.268086i	−0.713867	−	0.700282i	$-0.753058\pi$
$419$	−9.50476	+	5.48758i	−0.464338	+	0.268086i	0.249529	+	0.968367i	$0.419724\pi$
$420$		0			0
$421$	−1.66714	+	1.66714i	−0.0812516	+	0.0812516i	−0.746565	−	0.665313i	$-0.768298\pi$
$421$	−1.66714	+	1.66714i	−0.0812516	+	0.0812516i	0.665313	+	0.746565i	$0.268298\pi$
$422$		0			0
$423$	23.6316	−	18.3180i	1.14901	−	0.890652i
$424$		0			0
$425$	−27.1397	−	15.6691i	−1.31647	−	0.760065i
$426$		0			0
$427$	4.45266	−	16.6175i	0.215479	−	0.804179i
$428$		0			0
$429$	27.1549	−	13.4890i	1.31105	−	0.651255i
$430$		0			0
$431$	−7.18539	+	26.8162i	−0.346108	+	1.29169i	0.545204	+	0.838303i	$0.316452\pi$
$431$	−7.18539	+	26.8162i	−0.346108	+	1.29169i	−0.891312	+	0.453390i	$0.850215\pi$
$432$		0			0
$433$	30.2566	+	17.4687i	1.45404	+	0.839490i	0.998707	−	0.0508321i	$-0.0161873\pi$
$433$	30.2566	+	17.4687i	1.45404	+	0.839490i	0.455332	+	0.890322i	$0.349521\pi$
$434$		0			0
$435$	−2.62866	−	0.885127i	−0.126035	−	0.0424386i
$436$		0			0
$437$	−11.9689	+	11.9689i	−0.572552	+	0.572552i
$438$		0			0
$439$	−21.4262	+	12.3704i	−1.02262	+	0.590408i	−0.914861	−	0.403770i	$-0.867700\pi$
$439$	−21.4262	+	12.3704i	−1.02262	+	0.590408i	−0.107756	+	0.994177i	$0.534366\pi$
$440$		0			0
$441$	21.4873	−	9.02408i	1.02321	−	0.429718i
$442$		0			0
$443$			27.7009i			1.31611i	0.752970	+	0.658055i	$0.228621\pi$
$443$			27.7009i			1.31611i	−0.752970	+	0.658055i	$0.771379\pi$
$444$		0			0
$445$	−0.477113	−	0.826384i	−0.0226173	−	0.0391744i
$446$		0			0
$447$	2.72845	−	0.549682i	0.129051	−	0.0259991i
$448$		0			0
$449$	−5.46509	−	20.3960i	−0.257914	−	0.962547i	−0.966446	−	0.256869i	$-0.917309\pi$
$449$	−5.46509	−	20.3960i	−0.257914	−	0.962547i	0.708533	−	0.705678i	$-0.249358\pi$
$450$		0			0
$451$	−1.16746	+	2.02209i	−0.0549733	+	0.0952166i
$452$		0			0
$453$	7.25864	+	8.23605i	0.341041	+	0.386964i
$454$		0			0
$455$	−3.59926	+	0.966102i	−0.168736	+	0.0452915i
$456$		0			0
$457$	28.1425	+	7.54076i	1.31645	+	0.352742i	0.847647	−	0.530560i	$-0.178018\pi$
$457$	28.1425	+	7.54076i	1.31645	+	0.352742i	0.468804	+	0.883302i	$0.344685\pi$
$458$		0			0
$459$	−21.6052	+	25.0048i	−1.00844	+	1.16712i
$460$		0			0
$461$	23.9455	−	6.41619i	1.11525	−	0.298832i	0.346293	−	0.938126i	$-0.387440\pi$
$461$	23.9455	−	6.41619i	1.11525	−	0.298832i	0.768962	+	0.639295i	$0.220774\pi$
$462$		0			0
$463$	−4.15314	−	4.15314i	−0.193013	−	0.193013i	0.603984	−	0.796997i	$-0.293579\pi$
$463$	−4.15314	−	4.15314i	−0.193013	−	0.193013i	−0.796997	+	0.603984i	$0.793579\pi$
$464$		0			0
$465$	2.61567	+	0.164998i	0.121299	+	0.00765160i
$466$		0			0
$467$	4.58273			0.212064			0.106032	−	0.994363i	$-0.466185\pi$
$467$	4.58273			0.212064			0.106032	+	0.994363i	$0.466185\pi$
$468$		0			0
$469$	−9.05947			−0.418327
$470$		0			0
$471$	−19.5048	−	1.23037i	−0.898732	−	0.0566926i
$472$		0			0
$473$	8.43078	+	8.43078i	0.387648	+	0.387648i
$474$		0			0
$475$	−29.7653	+	7.97558i	−1.36572	+	0.365944i
$476$		0			0
$477$	0.724339	−	5.71852i	0.0331652	−	0.261833i
$478$		0			0
$479$	−25.2853	−	6.77517i	−1.15531	−	0.309566i	−0.370221	−	0.928944i	$-0.620718\pi$
$479$	−25.2853	−	6.77517i	−1.15531	−	0.309566i	−0.785093	+	0.619378i	$0.787385\pi$
$480$		0			0
$481$	10.9594	+	18.9631i	0.499704	+	0.864641i
$482$		0			0
$483$	−11.9124	−	13.5165i	−0.542032	−	0.615020i
$484$		0			0
$485$	−0.688871	+	1.19316i	−0.0312800	+	0.0541786i
$486$		0			0
$487$	−4.05415	−	15.1303i	−0.183711	−	0.685619i	−0.994903	−	0.100839i	$-0.967847\pi$
$487$	−4.05415	−	15.1303i	−0.183711	−	0.685619i	0.811192	−	0.584780i	$-0.198819\pi$
$488$		0			0
$489$	−1.11538	+	0.224707i	−0.0504391	+	0.0101616i
$490$		0			0
$491$	−7.62282	−	13.2031i	−0.344013	−	0.595848i	0.641161	−	0.767406i	$-0.278453\pi$
$491$	−7.62282	−	13.2031i	−0.344013	−	0.595848i	−0.985174	+	0.171558i	$0.945120\pi$
$492$		0			0
$493$			37.8660i			1.70540i
$494$		0			0
$495$	−1.51690	−	3.61190i	−0.0681795	−	0.162343i
$496$		0			0
$497$	−38.3639	+	22.1494i	−1.72086	+	0.993537i
$498$		0			0
$499$	−3.60383	+	3.60383i	−0.161330	+	0.161330i	−0.783155	−	0.621826i	$-0.786391\pi$
$499$	−3.60383	+	3.60383i	−0.161330	+	0.161330i	0.621826	+	0.783155i	$0.286391\pi$
$500$		0			0
$501$	16.2481	+	5.47110i	0.725914	+	0.244431i
$502$		0			0
$503$	−4.82146	−	2.78367i	−0.214978	−	0.124118i	0.388645	−	0.921388i	$-0.372943\pi$
$503$	−4.82146	−	2.78367i	−0.214978	−	0.124118i	−0.603623	+	0.797270i	$0.706277\pi$
$504$		0			0
$505$	0.617130	−	2.30316i	0.0274619	−	0.102489i
$506$		0			0
$507$	−1.39795	+	22.4732i	−0.0620851	+	0.998071i
$508$		0			0
$509$	8.59596	−	32.0805i	0.381009	−	1.42195i	−0.463354	−	0.886173i	$-0.653354\pi$
$509$	8.59596	−	32.0805i	0.381009	−	1.42195i	0.844363	−	0.535772i	$-0.179979\pi$
$510$		0			0
$511$	55.6015	+	32.1016i	2.45967	+	1.42009i
$512$		0			0
$513$	2.36374	+	32.4082i	0.104362	+	1.43086i
$514$		0			0
$515$	0.527327	−	0.527327i	0.0232368	−	0.0232368i
$516$		0			0
$517$	41.9068	−	24.1949i	1.84306	−	1.06409i
$518$		0			0
$519$	−13.9567	+	20.9990i	−0.612633	+	0.921756i
$520$		0			0
$521$			10.7309i			0.470129i	0.971980	+	0.235065i	$0.0755302\pi$
$521$			10.7309i			0.470129i	−0.971980	+	0.235065i	$0.924470\pi$
$522$		0			0
$523$	−8.02011	−	13.8912i	−0.350695	−	0.607421i	0.635677	−	0.771955i	$-0.280721\pi$
$523$	−8.02011	−	13.8912i	−0.350695	−	0.607421i	−0.986371	+	0.164534i	$0.947388\pi$
$524$		0			0
$525$	−6.47777	−	32.1536i	−0.282713	−	1.40330i
$526$		0			0
$527$	−9.26048	−	34.5606i	−0.403393	−	1.50548i
$528$		0			0
$529$	7.83679	−	13.5737i	0.340730	−	0.590162i
$530$		0			0
$531$	0.471356	+	3.44947i	0.0204551	+	0.149694i
$532$		0			0
$533$	−0.867627	−	1.50126i	−0.0375811	−	0.0650269i
$534$		0			0
$535$	3.70739	+	0.993393i	0.160285	+	0.0429481i
$536$		0			0
$537$	−15.3494	−	30.9341i	−0.662377	−	1.33490i
$538$		0			0
$539$	36.4321	−	9.76196i	1.56924	−	0.420477i
$540$		0			0
$541$	−22.6010	−	22.6010i	−0.971694	−	0.971694i	0.0279162	−	0.999610i	$-0.491113\pi$
$541$	−22.6010	−	22.6010i	−0.971694	−	0.971694i	−0.999610	+	0.0279162i	$0.991113\pi$
$542$		0			0
$543$	−1.30795	+	20.7345i	−0.0561294	+	0.889803i
$544$		0			0
$545$	−0.0643671			−0.00275718
$546$		0			0
$547$	15.6610			0.669617			0.334809	−	0.942286i	$-0.391328\pi$
$547$	15.6610			0.669617			0.334809	+	0.942286i	$0.391328\pi$
$548$		0			0
$549$	−8.12332	+	10.6947i	−0.346695	+	0.456440i
$550$		0			0
$551$	26.3284	+	26.3284i	1.12163	+	1.12163i
$552$		0			0
$553$	−17.4306	+	4.67053i	−0.741226	+	0.198611i
$554$		0			0
$555$	2.53490	−	1.25781i	0.107601	−	0.0533912i
$556$		0			0
$557$	21.1593	+	5.66961i	0.896547	+	0.240229i	0.677533	−	0.735493i	$-0.263049\pi$
$557$	21.1593	+	5.66961i	0.896547	+	0.240229i	0.219014	+	0.975722i	$0.429716\pi$
$558$		0			0
$559$	−8.55147	+	2.29536i	−0.361689	+	0.0970832i
$560$		0			0
$561$	−40.1227	+	35.3611i	−1.69398	+	1.49295i
$562$		0			0
$563$	−6.23667	+	10.8022i	−0.262844	+	0.455260i	−0.966997	−	0.254789i	$-0.917994\pi$
$563$	−6.23667	+	10.8022i	−0.262844	+	0.455260i	0.704152	+	0.710049i	$0.251327\pi$
$564$		0			0
$565$	−0.462411	−	1.72574i	−0.0194538	−	0.0726025i
$566$		0			0
$567$	−34.5851	+	0.339310i	−1.45244	+	0.0142497i
$568$		0			0
$569$	11.6128	+	20.1139i	0.486833	+	0.843220i	0.999885	−	0.0151374i	$-0.00481857\pi$
$569$	11.6128	+	20.1139i	0.486833	+	0.843220i	−0.513052	+	0.858357i	$0.671485\pi$
$570$		0			0
$571$		−	19.7820i		−	0.827852i	−0.910310	−	0.413926i	$-0.864157\pi$
$571$		−	19.7820i		−	0.827852i	0.910310	−	0.413926i	$-0.135843\pi$
$572$		0			0
$573$	15.4641	+	10.2780i	0.646021	+	0.429369i
$574$		0			0
$575$	−11.5509	+	6.66894i	−0.481708	+	0.278114i
$576$		0			0
$577$	20.4133	−	20.4133i	0.849815	−	0.849815i	−0.140295	−	0.990110i	$-0.544805\pi$
$577$	20.4133	−	20.4133i	0.849815	−	0.849815i	0.990110	+	0.140295i	$0.0448049\pi$
$578$		0			0
$579$	8.49930	−	25.2414i	0.353219	−	1.04899i
$580$		0			0
$581$	17.3667	+	10.0267i	0.720491	+	0.415976i
$582$		0			0
$583$	2.41447	−	9.01092i	0.0999971	−	0.373194i
$584$		0			0
$585$	2.88630	+	0.364316i	0.119334	+	0.0150626i
$586$		0			0
$587$	−1.00194	+	3.73929i	−0.0413545	+	0.154337i	−0.983516	−	0.180823i	$-0.942124\pi$
$587$	−1.00194	+	3.73929i	−0.0413545	+	0.154337i	0.942161	+	0.335160i	$0.108790\pi$
$588$		0			0
$589$	−30.4690	−	17.5913i	−1.25545	−	0.724837i
$590$		0			0
$591$	−4.63559	+	13.7668i	−0.190683	+	0.566292i
$592$		0			0
$593$	−22.3363	+	22.3363i	−0.917240	+	0.917240i	−0.996828	−	0.0795880i	$-0.974640\pi$
$593$	−22.3363	+	22.3363i	−0.917240	+	0.917240i	0.0795880	+	0.996828i	$0.474640\pi$
$594$		0			0
$595$	5.69264	−	3.28665i	0.233375	−	0.134739i
$596$		0			0
$597$	35.0354	+	23.2858i	1.43390	+	0.953024i
$598$		0			0
$599$			9.88995i			0.404093i	0.979376	+	0.202046i	$0.0647591\pi$
$599$			9.88995i			0.404093i	−0.979376	+	0.202046i	$0.935241\pi$
$600$		0			0
$601$	20.2582	+	35.0883i	0.826350	+	1.43128i	0.900883	+	0.434061i	$0.142920\pi$
$601$	20.2582	+	35.0883i	0.826350	+	1.43128i	−0.0745337	+	0.997218i	$0.523747\pi$
$602$		0			0
$603$	6.54709	+	2.67434i	0.266618	+	0.108908i
$604$		0			0
$605$	−0.875212	−	3.26634i	−0.0355824	−	0.132795i
$606$		0			0
$607$	−17.1166	+	29.6468i	−0.694742	+	1.20333i	0.275526	+	0.961294i	$0.411148\pi$
$607$	−17.1166	+	29.6468i	−0.694742	+	1.20333i	−0.970268	+	0.242034i	$0.922185\pi$
$608$		0			0
$609$	−29.7325	+	26.2040i	−1.20482	+	1.06184i
$610$		0			0
$611$	0.0156706	+	35.9351i	0.000633966	+	1.45378i
$612$		0			0
$613$	8.94967	+	2.39806i	0.361474	+	0.0968566i	0.434985	−	0.900438i	$-0.356754\pi$
$613$	8.94967	+	2.39806i	0.361474	+	0.0968566i	−0.0735111	+	0.997294i	$0.523420\pi$
$614$		0			0
$615$	−0.200682	+	0.0995783i	−0.00809230	+	0.00401538i
$616$		0			0
$617$	−22.9889	+	6.15986i	−0.925499	+	0.247987i	−0.689934	−	0.723872i	$-0.742361\pi$
$617$	−22.9889	+	6.15986i	−0.925499	+	0.247987i	−0.235564	+	0.971859i	$0.575694\pi$
$618$		0			0
$619$	5.26114	+	5.26114i	0.211463	+	0.211463i	0.804889	−	0.593426i	$-0.202225\pi$
$619$	5.26114	+	5.26114i	0.211463	+	0.211463i	−0.593426	+	0.804889i	$0.702225\pi$
$620$		0			0
$621$	4.61879	+	13.2846i	0.185346	+	0.533092i
$622$		0			0
$623$	−13.6345			−0.546253
$624$		0			0
$625$	−23.9202			−0.956807
$626$		0			0
$627$	−3.31075	+	52.4843i	−0.132219	+	2.09602i
$628$		0			0
$629$	−27.3171	−	27.3171i	−1.08920	−	1.08920i
$630$		0			0
$631$	28.4356	−	7.61929i	1.13200	−	0.303319i	0.356271	−	0.934383i	$-0.384048\pi$
$631$	28.4356	−	7.61929i	1.13200	−	0.303319i	0.775731	+	0.631064i	$0.217381\pi$
$632$		0			0
$633$	5.61658	+	11.3192i	0.223239	+	0.449899i
$634$		0			0
$635$	3.00874	+	0.806189i	0.119398	+	0.0319926i
$636$		0			0
$637$	−7.23760	+	27.0583i	−0.286764	+	1.07209i
$638$		0			0
$639$	34.2633	−	4.68194i	1.35543	−	0.185215i
$640$		0			0
$641$	−18.9744	+	32.8645i	−0.749442	+	1.29807i	0.198648	+	0.980071i	$0.436345\pi$
$641$	−18.9744	+	32.8645i	−0.749442	+	1.29807i	−0.948090	+	0.318001i	$0.896989\pi$
$642$		0			0
$643$	−2.40070	−	8.95954i	−0.0946745	−	0.353330i	0.902295	−	0.431118i	$-0.141881\pi$
$643$	−2.40070	−	8.95954i	−0.0946745	−	0.353330i	−0.996970	+	0.0777883i	$0.975214\pi$
$644$		0			0
$645$	0.225930	+	1.12145i	0.00889600	+	0.0441569i
$646$		0			0
$647$	15.5746	+	26.9760i	0.612301	+	1.06054i	0.990852	+	0.134956i	$0.0430894\pi$
$647$	15.5746	+	26.9760i	0.612301	+	1.06054i	−0.378550	+	0.925581i	$0.623577\pi$
$648$		0			0
$649$			5.63449i			0.221173i
$650$		0			0
$651$	20.7287	−	31.1880i	0.812421	−	1.22235i
$652$		0			0
$653$	−30.0917	+	17.3734i	−1.17758	+	0.679875i	−0.955453	−	0.295143i	$-0.904633\pi$
$653$	−30.0917	+	17.3734i	−1.17758	+	0.679875i	−0.222126	+	0.975018i	$0.571300\pi$
$654$		0			0
$655$	−2.39225	+	2.39225i	−0.0934728	+	0.0934728i
$656$		0			0
$657$	−30.7057	−	39.6126i	−1.19794	−	1.54544i
$658$		0			0
$659$	12.9692	+	7.48778i	0.505209	+	0.291683i	0.730862	−	0.682525i	$-0.239118\pi$
$659$	12.9692	+	7.48778i	0.505209	+	0.291683i	−0.225653	+	0.974208i	$0.572452\pi$
$660$		0			0
$661$	8.07852	−	30.1494i	0.314218	−	1.17268i	−0.610497	−	0.792018i	$-0.709030\pi$
$661$	8.07852	−	30.1494i	0.314218	−	1.17268i	0.924715	−	0.380659i	$-0.124303\pi$
$662$		0			0
$663$	−7.86072	−	38.9304i	−0.305285	−	1.51193i
$664$		0			0
$665$	1.67290	−	6.24334i	0.0648722	−	0.242107i
$666$		0			0
$667$	13.9570	+	8.05807i	0.540416	+	0.312010i
$668$		0			0
$669$	10.1402	+	3.41443i	0.392044	+	0.132010i
$670$		0			0
$671$	−15.3691	+	15.3691i	−0.593316	+	0.593316i
$672$		0			0
$673$	−15.1833	+	8.76609i	−0.585274	+	0.337908i	−0.763226	−	0.646131i	$-0.776386\pi$
$673$	−15.1833	+	8.76609i	−0.585274	+	0.337908i	0.177953	+	0.984039i	$0.443053\pi$
$674$		0			0
$675$	−4.81035	+	25.1490i	−0.185151	+	0.967984i
$676$		0			0
$677$			39.0924i			1.50244i	0.660051	+	0.751221i	$0.270535\pi$
$677$			39.0924i			1.50244i	−0.660051	+	0.751221i	$0.729465\pi$
$678$		0			0
$679$	9.84292	+	17.0484i	0.377737	+	0.654259i
$680$		0			0
$681$	33.0689	−	6.66218i	1.26720	−	0.255295i
$682$		0			0
$683$	−8.12422	−	30.3200i	−0.310865	−	1.16016i	−0.927778	−	0.373132i	$-0.878284\pi$
$683$	−8.12422	−	30.3200i	−0.310865	−	1.16016i	0.616914	−	0.787031i	$-0.288383\pi$
$684$		0			0
$685$	0.550480	−	0.953459i	0.0210328	−	0.0364298i
$686$		0			0
$687$	14.7069	+	16.6872i	0.561102	+	0.636657i
$688$		0			0
$689$	4.90078	+	4.89650i	0.186705	+	0.186542i
$690$		0			0
$691$	40.4008	+	10.8253i	1.53692	+	0.411816i	0.925268	−	0.379314i	$-0.123840\pi$
$691$	40.4008	+	10.8253i	1.53692	+	0.411816i	0.611649	+	0.791129i	$0.290507\pi$
$692$		0			0
$693$	−55.5314	−	7.03391i	−2.10947	−	0.267196i
$694$		0			0
$695$	2.07921	−	0.557122i	0.0788688	−	0.0211328i
$696$		0			0
$697$	2.16263	+	2.16263i	0.0819156	+	0.0819156i
$698$		0			0
$699$	9.96324	+	0.628488i	0.376844	+	0.0237716i
$700$		0			0
$701$	−7.92841			−0.299452			−0.149726	−	0.988728i	$-0.547839\pi$
$701$	−7.92841			−0.299452			−0.149726	+	0.988728i	$0.547839\pi$
$702$		0			0
$703$	−37.9875			−1.43272
$704$		0			0
$705$	4.63369	+	0.292296i	0.174515	+	0.0110085i
$706$		0			0
$707$	−24.0908	−	24.0908i	−0.906029	−	0.906029i
$708$		0			0
$709$	−28.1675	+	7.54745i	−1.05785	+	0.283450i	−0.745493	−	0.666514i	$-0.767786\pi$
$709$	−28.1675	+	7.54745i	−1.05785	+	0.283450i	−0.312358	+	0.949964i	$0.601119\pi$
$710$		0			0
$711$	13.9755	+	1.77021i	0.524122	+	0.0663881i
$712$		0			0
$713$	−14.7093	−	3.94135i	−0.550868	−	0.147605i
$714$		0			0
$715$	4.54835	+	1.21660i	0.170099	+	0.0454983i
$716$		0			0
$717$	11.3542	+	12.8831i	0.424029	+	0.481127i
$718$		0			0
$719$	−1.18581	+	2.05388i	−0.0442231	+	0.0765966i	−0.887290	−	0.461213i	$-0.847415\pi$
$719$	−1.18581	+	2.05388i	−0.0442231	+	0.0765966i	0.843067	+	0.537809i	$0.180748\pi$
$720$		0			0
$721$	−2.75789	−	10.2926i	−0.102709	−	0.383316i
$722$		0			0
$723$	−16.4744	+	3.31898i	−0.612688	+	0.123434i
$724$		0			0
$725$	14.6699	+	25.4089i	0.544825	+	0.943665i
$726$		0			0
$727$			4.61125i			0.171022i	0.996337	+	0.0855108i	$0.0272522\pi$
$727$			4.61125i			0.171022i	−0.996337	+	0.0855108i	$0.972748\pi$
$728$		0			0
$729$	25.0941	+	9.96426i	0.929411	+	0.369047i
$730$		0			0
$731$	13.5251	−	7.80873i	0.500244	−	0.288816i
$732$		0			0
$733$	−1.26644	+	1.26644i	−0.0467771	+	0.0467771i	−0.730108	−	0.683331i	$-0.760530\pi$
$733$	−1.26644	+	1.26644i	−0.0467771	+	0.0467771i	0.683331	+	0.730108i	$0.260530\pi$
$734$		0			0
$735$	3.42968	+	1.15485i	0.126506	+	0.0425972i
$736$		0			0
$737$	9.91226	+	5.72284i	0.365123	+	0.210804i
$738$		0			0
$739$	−1.79877	+	6.71310i	−0.0661688	+	0.246945i	−0.991086	−	0.133223i	$-0.957467\pi$
$739$	−1.79877	+	6.71310i	−0.0661688	+	0.246945i	0.924917	+	0.380169i	$0.124134\pi$
$740$		0			0
$741$	−32.5341	−	21.6029i	−1.19517	−	0.793603i
$742$		0			0
$743$	3.31455	−	12.3701i	0.121599	−	0.453814i	−0.878097	−	0.478484i	$-0.841187\pi$
$743$	3.31455	−	12.3701i	0.121599	−	0.453814i	0.999696	+	0.0246694i	$0.00785330\pi$
$744$		0			0
$745$	0.374288	+	0.216096i	0.0137129	+	0.00791713i
$746$		0			0
$747$	−9.59068	−	12.3727i	−0.350904	−	0.452692i
$748$		0			0
$749$	38.7789	−	38.7789i	1.41695	−	1.41695i
$750$		0			0
$751$	17.7987	−	10.2761i	0.649483	−	0.374979i	−0.138775	−	0.990324i	$-0.544317\pi$
$751$	17.7987	−	10.2761i	0.649483	−	0.374979i	0.788258	+	0.615345i	$0.210983\pi$
$752$		0			0
$753$	2.58558	−	3.89021i	0.0942237	−	0.141767i
$754$		0			0
$755$			1.70471i			0.0620408i
$756$		0			0
$757$	−26.2738	−	45.5076i	−0.954939	−	1.65400i	−0.734508	−	0.678600i	$-0.762587\pi$
$757$	−26.2738	−	45.5076i	−0.954939	−	1.65400i	−0.220431	−	0.975403i	$-0.570746\pi$
$758$		0			0
$759$	4.49541	+	22.3138i	0.163173	+	0.809940i
$760$		0			0
$761$	−3.45176	−	12.8821i	−0.125126	−	0.466977i	0.874718	−	0.484632i	$-0.161047\pi$
$761$	−3.45176	−	12.8821i	−0.125126	−	0.466977i	−0.999844	+	0.0176552i	$0.994380\pi$
$762$		0			0
$763$	−0.459854	+	0.796490i	−0.0166478	+	0.0288349i
$764$		0			0
$765$	−5.08416	+	0.694731i	−0.183818	+	0.0251180i
$766$		0			0
$767$	−3.62459	−	2.09055i	−0.130877	−	0.0754855i
$768$		0			0
$769$	3.63254	+	0.973337i	0.130993	+	0.0350994i	0.323720	−	0.946153i	$-0.395066\pi$
$769$	3.63254	+	0.973337i	0.130993	+	0.0350994i	−0.192727	+	0.981252i	$0.561733\pi$
$770$		0			0
$771$	−22.1419	−	44.6230i	−0.797420	−	1.60706i
$772$		0			0
$773$	49.8132	−	13.3474i	1.79166	−	0.480073i	0.799030	−	0.601291i	$-0.205347\pi$
$773$	49.8132	−	13.3474i	1.79166	−	0.480073i	0.992626	+	0.121218i	$0.0386801\pi$
$774$		0			0
$775$	−19.6033	−	19.6033i	−0.704171	−	0.704171i
$776$		0			0
$777$	2.54553	−	40.3535i	0.0913202	−	1.44767i
$778$		0			0
$779$	3.00738			0.107751
$780$		0			0
$781$	55.9669			2.00265
$782$		0			0
$783$	29.2225	−	10.1601i	1.04433	−	0.363092i
$784$		0			0
$785$	−2.14590	−	2.14590i	−0.0765903	−	0.0765903i
$786$		0			0
$787$	18.9776	−	5.08504i	0.676480	−	0.181262i	0.0958080	−	0.995400i	$-0.469457\pi$
$787$	18.9776	−	5.08504i	0.676480	−	0.181262i	0.580672	+	0.814138i	$0.302790\pi$
$788$		0			0
$789$	−1.47710	+	0.732935i	−0.0525862	+	0.0260932i
$790$		0			0
$791$	−24.6582	−	6.60715i	−0.876746	−	0.234923i
$792$		0			0
$793$	−4.18437	−	15.5891i	−0.148591	−	0.553584i
$794$		0			0
$795$	0.671506	−	0.591814i	0.0238158	−	0.0209895i
$796$		0			0
$797$	10.3359	−	17.9022i	0.366115	−	0.634130i	−0.622839	−	0.782350i	$-0.714021\pi$
$797$	10.3359	−	17.9022i	0.366115	−	0.634130i	0.988954	+	0.148220i	$0.0473543\pi$
$798$		0			0
$799$	−16.4051	−	61.2245i	−0.580369	−	2.16597i
$800$		0			0
$801$	9.85333	+	4.02487i	0.348150	+	0.142212i
$802$		0			0
$803$	−40.5570	−	70.2467i	−1.43122	−	2.47895i
$804$		0			0
$805$		−	2.79766i		−	0.0986045i
$806$		0			0
$807$	22.7872	+	15.1452i	0.802146	+	0.533136i
$808$		0			0
$809$	25.9845	−	15.0021i	0.913565	−	0.527447i	0.0319886	−	0.999488i	$-0.489816\pi$
$809$	25.9845	−	15.0021i	0.913565	−	0.527447i	0.881577	+	0.472041i	$0.156483\pi$
$810$		0			0
$811$	−28.5096	+	28.5096i	−1.00111	+	1.00111i	−0.00110746	+	0.999999i	$0.500353\pi$
$811$	−28.5096	+	28.5096i	−1.00111	+	1.00111i	−0.999999	+	0.00110746i	$0.999647\pi$
$812$		0			0
$813$	5.77406	−	17.1479i	0.202505	−	0.601402i
$814$		0			0
$815$	−0.153007	−	0.0883388i	−0.00535961	−	0.00309437i
$816$		0			0
$817$	3.97463	−	14.8335i	0.139055	−	0.518960i
$818$		0			0
$819$	25.1286	−	33.1129i	0.878063	−	1.15706i
$820$		0			0
$821$	6.28752	−	23.4653i	0.219436	−	0.818946i	−0.765122	−	0.643886i	$-0.777321\pi$
$821$	6.28752	−	23.4653i	0.219436	−	0.818946i	0.984558	−	0.175060i	$-0.0560121\pi$
$822$		0			0
$823$	31.4331	+	18.1479i	1.09569	+	0.632597i	0.935086	−	0.354422i	$-0.115322\pi$
$823$	31.4331	+	18.1479i	1.09569	+	0.632597i	0.160605	+	0.987019i	$0.448656\pi$
$824$		0			0
$825$	−13.2238	+	39.2723i	−0.460394	+	1.36729i
$826$		0			0
$827$	15.6835	−	15.6835i	0.545368	−	0.545368i	−0.379729	−	0.925098i	$-0.623983\pi$
$827$	15.6835	−	15.6835i	0.545368	−	0.545368i	0.925098	+	0.379729i	$0.123983\pi$
$828$		0			0
$829$	−18.0583	+	10.4260i	−0.627191	+	0.362109i	−0.779663	−	0.626199i	$-0.784610\pi$
$829$	−18.0583	+	10.4260i	−0.627191	+	0.362109i	0.152472	+	0.988308i	$0.451277\pi$
$830$		0			0
$831$	−12.5917	−	8.36890i	−0.436801	−	0.290314i
$832$		0			0
$833$		−	49.4047i		−	1.71177i
$834$		0			0
$835$	1.33112	+	2.30556i	0.0460652	+	0.0797873i
$836$		0			0
$837$	−24.1868	+	16.4198i	−0.836019	+	0.567552i
$838$		0			0
$839$	3.01362	+	11.2470i	0.104042	+	0.388289i	0.998235	−	0.0593928i	$-0.0189164\pi$
$839$	3.01362	+	11.2470i	0.104042	+	0.388289i	−0.894193	+	0.447682i	$0.852250\pi$
$840$		0			0
$841$	3.22557	−	5.58684i	0.111226	−	0.192650i
$842$		0			0
$843$	−33.6816	+	29.6845i	−1.16006	+	1.02239i
$844$		0			0
$845$	−2.47019	+	2.47450i	−0.0849772	+	0.0851255i
$846$		0			0
$847$	−46.6710	−	12.5055i	−1.60363	−	0.429693i
$848$		0			0
$849$	−42.8812	+	21.2776i	−1.47168	+	0.730244i
$850$		0			0
$851$	−15.8820	+	4.25557i	−0.544428	+	0.145879i
$852$		0			0
$853$	29.7151	+	29.7151i	1.01743	+	1.01743i	0.999845	+	0.0175805i	$0.00559635\pi$
$853$	29.7151	+	29.7151i	1.01743	+	1.01743i	0.0175805	+	0.999845i	$0.494404\pi$
$854$		0			0
$855$	−3.05200	+	4.01810i	−0.104376	+	0.137416i
$856$		0			0
$857$	38.3632			1.31046			0.655230	−	0.755429i	$-0.272572\pi$
$857$	38.3632			1.31046			0.655230	+	0.755429i	$0.272572\pi$
$858$		0			0
$859$	−14.3517			−0.489675			−0.244837	−	0.969564i	$-0.578735\pi$
$859$	−14.3517			−0.489675			−0.244837	+	0.969564i	$0.578735\pi$
$860$		0			0
$861$	−0.201524	+	3.19469i	−0.00686790	+	0.108875i
$862$		0			0
$863$	7.66658	+	7.66658i	0.260974	+	0.260974i	0.825450	−	0.564476i	$-0.190922\pi$
$863$	7.66658	+	7.66658i	0.260974	+	0.260974i	−0.564476	+	0.825450i	$0.690922\pi$
$864$		0			0
$865$	−3.78188	+	1.01335i	−0.128588	+	0.0344550i
$866$		0			0
$867$	18.0499	+	36.3765i	0.613008	+	1.23541i
$868$		0			0
$869$	22.0218	+	5.90072i	0.747038	+	0.200168i
$870$		0			0
$871$	−7.35916	+	4.25309i	−0.249356	+	0.144111i
$872$		0			0
$873$	−2.08060	−	15.2262i	−0.0704175	−	0.515328i
$874$		0			0
$875$	5.13057	−	8.88641i	0.173445	−	0.300415i
$876$		0			0
$877$	9.56536	+	35.6984i	0.322999	+	1.20545i	0.916308	+	0.400475i	$0.131155\pi$
$877$	9.56536	+	35.6984i	0.322999	+	1.20545i	−0.593309	+	0.804975i	$0.702179\pi$
$878$		0			0
$879$	4.71834	+	23.4204i	0.159146	+	0.789949i
$880$		0			0
$881$	9.32375	+	16.1492i	0.314125	+	0.544081i	0.979251	−	0.202650i	$-0.0649555\pi$
$881$	9.32375	+	16.1492i	0.314125	+	0.544081i	−0.665126	+	0.746731i	$0.731622\pi$
$882$		0			0
$883$		−	36.4628i		−	1.22707i	−0.789667	−	0.613536i	$-0.789746\pi$
$883$		−	36.4628i		−	1.22707i	0.789667	−	0.613536i	$-0.210254\pi$
$884$		0			0
$885$	−0.299247	+	0.450242i	−0.0100591	+	0.0151347i
$886$		0			0
$887$	26.5035	−	15.3018i	0.889901	−	0.513785i	0.0159910	−	0.999872i	$-0.494910\pi$
$887$	26.5035	−	15.3018i	0.889901	−	0.513785i	0.873910	+	0.486087i	$0.161576\pi$
$888$		0			0
$889$	31.4711	−	31.4711i	1.05551	−	1.05551i
$890$		0			0
$891$	38.0550	+	21.4761i	1.27489	+	0.719476i
$892$		0			0
$893$	−53.9763	−	31.1632i	−1.80625	−	1.04284i
$894$		0			0
$895$	1.38787	−	5.17962i	0.0463915	−	0.173136i
$896$		0			0
$897$	−16.0221	−	5.38721i	−0.534963	−	0.179874i
$898$		0			0
$899$	−8.66990	+	32.3565i	−0.289158	+	1.07915i
$900$		0			0
$901$	−10.5824	−	6.10974i	−0.352550	−	0.203545i
$902$		0			0
$903$	15.4911	+	5.21618i	0.515511	+	0.173584i
$904$		0			0
$905$	−2.28119	+	2.28119i	−0.0758294	+	0.0758294i
$906$		0			0
$907$	−1.88674	+	1.08931i	−0.0626483	+	0.0361700i	−0.530997	−	0.847374i	$-0.678182\pi$
$907$	−1.88674	+	1.08931i	−0.0626483	+	0.0361700i	0.468349	+	0.883544i	$0.344849\pi$
$908$		0			0
$909$	10.2984	+	24.5215i	0.341575	+	0.813327i
$910$		0			0
$911$			2.38699i			0.0790845i	0.999218	+	0.0395422i	$0.0125900\pi$
$911$			2.38699i			0.0790845i	−0.999218	+	0.0395422i	$0.987410\pi$
$912$		0			0
$913$	−12.6676	−	21.9410i	−0.419237	−	0.726140i
$914$		0			0
$915$	−2.04436	+	0.411864i	−0.0675846	+	0.0136158i
$916$		0			0
$917$	12.5113	+	46.6929i	0.413160	+	1.54194i
$918$		0			0
$919$	17.6103	−	30.5019i	0.580910	−	1.00617i	−0.414462	−	0.910067i	$-0.636030\pi$
$919$	17.6103	−	30.5019i	0.580910	−	1.00617i	0.995372	−	0.0960990i	$-0.0306366\pi$
$920$		0			0
$921$	12.8616	+	14.5935i	0.423803	+	0.480871i
$922$		0			0
$923$	−20.7653	+	36.0028i	−0.683498	+	1.18505i
$924$		0			0
$925$	−28.9135	−	7.74734i	−0.950669	−	0.254731i
$926$		0			0
$927$	−1.04529	+	8.25237i	−0.0343318	+	0.271043i
$928$		0			0
$929$	11.0931	−	2.97238i	0.363952	−	0.0975207i	−0.0722082	−	0.997390i	$-0.523005\pi$
$929$	11.0931	−	2.97238i	0.363952	−	0.0975207i	0.436161	+	0.899869i	$0.356338\pi$
$930$		0			0
$931$	−34.3514	−	34.3514i	−1.12582	−	1.12582i
$932$		0			0
$933$	−57.9760	−	3.65716i	−1.89805	−	0.119730i
$934$		0			0
$935$	−8.30466			−0.271592
$936$		0			0
$937$	−57.9338			−1.89262			−0.946308	−	0.323266i	$-0.895219\pi$
$937$	−57.9338			−1.89262			−0.946308	+	0.323266i	$0.895219\pi$
$938$		0			0
$939$	38.8609	+	2.45137i	1.26818	+	0.0799975i
$940$		0			0
$941$	−9.41367	−	9.41367i	−0.306877	−	0.306877i	0.536820	−	0.843697i	$-0.319625\pi$
$941$	−9.41367	−	9.41367i	−0.306877	−	0.306877i	−0.843697	+	0.536820i	$0.819625\pi$
$942$		0			0
$943$	1.25734	−	0.336904i	0.0409447	−	0.0109711i
$944$		0			0
$945$	−4.06385	−	3.51134i	−0.132197	−	0.114224i
$946$		0			0
$947$	17.9103	+	4.79906i	0.582008	+	0.155949i	0.537798	−	0.843074i	$-0.319256\pi$
$947$	17.9103	+	4.79906i	0.582008	+	0.155949i	0.0442099	+	0.999022i	$0.485923\pi$
$948$		0			0
$949$	60.2366	−	0.0262681i	1.95536	−	0.000852697i
$950$		0			0
$951$	−38.8298	−	44.0584i	−1.25914	−	1.42869i
$952$		0			0
$953$	12.9705	−	22.4656i	0.420156	−	0.727732i	−0.575798	−	0.817592i	$-0.695309\pi$
$953$	12.9705	−	22.4656i	0.420156	−	0.727732i	0.995954	+	0.0898598i	$0.0286419\pi$
$954$		0			0
$955$	0.746251	+	2.78504i	0.0241481	+	0.0901219i
$956$		0			0
$957$	49.0843	−	9.88869i	1.58667	−	0.319656i
$958$		0			0
$959$	−7.86552	−	13.6235i	−0.253991	−	0.439925i
$960$		0			0
$961$		−	0.652357i		−	0.0210438i
$962$		0			0
$963$	−39.4722	+	16.5772i	−1.27197	+	0.534194i
$964$		0			0
$965$	3.58167	−	2.06788i	0.115298	−	0.0665674i
$966$		0			0
$967$	12.4847	−	12.4847i	0.401480	−	0.401480i	−0.477274	−	0.878754i	$-0.658375\pi$
$967$	12.4847	−	12.4847i	0.401480	−	0.401480i	0.878754	+	0.477274i	$0.158375\pi$
$968$		0			0
$969$	65.2826	+	21.9820i	2.09718	+	0.706165i
$970$		0			0
$971$	−19.9485	−	11.5173i	−0.640179	−	0.369607i	0.144505	−	0.989504i	$-0.453841\pi$
$971$	−19.9485	−	11.5173i	−0.640179	−	0.369607i	−0.784683	+	0.619897i	$0.787174\pi$
$972$		0			0
$973$	7.96042	−	29.7087i	0.255200	−	0.952418i
$974$		0			0
$975$	−20.3570	−	23.0778i	−0.651944	−	0.739082i
$976$		0			0
$977$	1.23036	−	4.59176i	0.0393627	−	0.146904i	−0.943448	−	0.331521i	$-0.892438\pi$
$977$	1.23036	−	4.59176i	0.0393627	−	0.146904i	0.982810	+	0.184618i	$0.0591047\pi$
$978$		0			0
$979$	14.9179	+	8.61285i	0.476778	+	0.275268i
$980$		0			0
$981$	0.567450	−	0.439859i	0.0181173	−	0.0140436i
$982$		0			0
$983$	−21.0098	+	21.0098i	−0.670109	+	0.670109i	−0.957741	−	0.287632i	$-0.907132\pi$
$983$	−21.0098	+	21.0098i	−0.670109	+	0.670109i	0.287632	+	0.957741i	$0.407132\pi$
$984$		0			0
$985$	−1.95347	+	1.12784i	−0.0622429	+	0.0359359i
$986$		0			0
$987$	36.7211	−	55.2499i	1.16885	−	1.75862i
$988$		0			0
$989$		−	6.64694i		−	0.211360i
$990$		0			0
$991$	−17.7404	−	30.7272i	−0.563542	−	0.976083i	−0.997184	−	0.0749978i	$-0.976105\pi$
$991$	−17.7404	−	30.7272i	−0.563542	−	0.976083i	0.433642	−	0.901085i	$-0.357228\pi$
$992$		0			0
$993$	0.0545839	+	0.270937i	0.00173217	+	0.00859793i
$994$		0			0
$995$	1.69070	+	6.30979i	0.0535989	+	0.200034i
$996$		0			0
$997$	13.6862	−	23.7052i	0.433446	−	0.750751i	−0.563721	−	0.825965i	$-0.690631\pi$
$997$	13.6862	−	23.7052i	0.433446	−	0.750751i	0.997167	+	0.0752143i	$0.0239641\pi$
$998$		0			0
$999$	−13.7519	+	28.4112i	−0.435091	+	0.898890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cn.f.353.1		56
3.2	odd	2	inner	624.2.cn.f.353.9		56
4.3	odd	2		312.2.bp.a.41.14	yes	56
12.11	even	2		312.2.bp.a.41.6	✓	56
13.7	odd	12	inner	624.2.cn.f.449.9		56
39.20	even	12	inner	624.2.cn.f.449.1		56
52.7	even	12		312.2.bp.a.137.6	yes	56
156.59	odd	12		312.2.bp.a.137.14	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bp.a.41.6	✓	56	12.11	even	2
312.2.bp.a.41.14	yes	56	4.3	odd	2
312.2.bp.a.137.6	yes	56	52.7	even	12
312.2.bp.a.137.14	yes	56	156.59	odd	12
624.2.cn.f.353.1		56	1.1	even	1	trivial
624.2.cn.f.353.9		56	3.2	odd	2	inner
624.2.cn.f.449.1		56	39.20	even	12	inner
624.2.cn.f.449.9		56	13.7	odd	12	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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.72861 - 0.109042i) q^{3} +(-0.190181 - 0.190181i) q^{5} +(-3.71203 + 0.994635i) q^{7} +(2.97622 + 0.376984i) q^{9} +O(q^{10})\)	\(q+(-1.72861 - 0.109042i) q^{3} +(-0.190181 - 0.190181i) q^{5} +(-3.71203 + 0.994635i) q^{7} +(2.97622 + 0.376984i) q^{9} +(4.68976 + 1.25662i) q^{11} +(-2.54840 + 2.55062i) q^{13} +(0.308011 + 0.349487i) q^{15} +(3.17983 - 5.50763i) q^{17} +(-1.61853 - 6.04044i) q^{19} +(6.52512 - 1.31457i) q^{21} +(-1.35337 - 2.34410i) q^{23} -4.92766i q^{25} +(-5.10363 - 0.976194i) q^{27} +(-5.15639 + 2.97704i) q^{29} +(3.97821 - 3.97821i) q^{31} +(-7.96976 - 2.68359i) q^{33} +(0.895116 + 0.516795i) q^{35} +(1.57221 - 5.86758i) q^{37} +(4.68332 - 4.13116i) q^{39} +(-0.124469 + 0.464523i) q^{41} +(2.12670 + 1.22785i) q^{43} +(-0.494324 - 0.637714i) q^{45} +(7.04746 - 7.04746i) q^{47} +(6.72767 - 3.88422i) q^{49} +(-6.09727 + 9.17384i) q^{51} -1.92140i q^{53} +(-0.652917 - 1.13089i) q^{55} +(2.13915 + 10.6181i) q^{57} +(0.300361 + 1.12096i) q^{59} +(-2.23834 + 3.87691i) q^{61} +(-11.4228 + 1.56088i) q^{63} +(0.969735 - 0.000422883i) q^{65} +(2.27708 + 0.610143i) q^{67} +(2.08385 + 4.19962i) q^{69} +(11.1344 - 2.98346i) q^{71} +(-11.8134 - 11.8134i) q^{73} +(-0.537323 + 8.51803i) q^{75} -18.6584 q^{77} +4.69572 q^{79} +(8.71577 + 2.24397i) q^{81} +(-3.68981 - 3.68981i) q^{83} +(-1.65219 + 0.442702i) q^{85} +(9.23803 - 4.58390i) q^{87} +(3.42700 + 0.918262i) q^{89} +(6.92279 - 12.0027i) q^{91} +(-7.31059 + 6.44301i) q^{93} +(-0.840962 + 1.45659i) q^{95} +(-1.32581 - 4.94801i) q^{97} +(13.4840 + 5.50793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{7}+O(q^{10}) \) 56 * q - 4 * q^7	\( 56 q - 4 q^{7} + 8 q^{13} + 8 q^{15} - 4 q^{19} + 16 q^{21} - 24 q^{27} + 36 q^{31} + 28 q^{33} + 20 q^{37} - 16 q^{39} + 84 q^{43} + 12 q^{45} - 12 q^{49} + 24 q^{55} - 36 q^{57} - 24 q^{61} + 12 q^{63} + 32 q^{67} - 36 q^{69} - 20 q^{73} + 60 q^{75} + 32 q^{79} - 88 q^{85} + 16 q^{87} - 28 q^{91} - 88 q^{93} - 36 q^{97} - 44 q^{99}+O(q^{100}) \) 56 * q - 4 * q^7 + 8 * q^13 + 8 * q^15 - 4 * q^19 + 16 * q^21 - 24 * q^27 + 36 * q^31 + 28 * q^33 + 20 * q^37 - 16 * q^39 + 84 * q^43 + 12 * q^45 - 12 * q^49 + 24 * q^55 - 36 * q^57 - 24 * q^61 + 12 * q^63 + 32 * q^67 - 36 * q^69 - 20 * q^73 + 60 * q^75 + 32 * q^79 - 88 * q^85 + 16 * q^87 - 28 * q^91 - 88 * q^93 - 36 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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