LMFDB - Embedded newform 275.3.bk.c.82.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(82,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.82"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.bk (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			82.16
Character	$\chi$	$=$	275.82
Dual form			275.3.bk.c.218.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.72172 - 3.37907i) q^{2} +(-2.24871 + 0.356160i) q^{3} +(-6.10266 - 8.39959i) q^{4} +(-2.66816 + 8.21175i) q^{6} +(-0.264482 - 0.0418898i) q^{7} +(-23.9070 + 3.78649i) q^{8} +(-3.62968 + 1.17935i) q^{9} +(-8.77765 - 6.62969i) q^{11} +(16.7147 + 16.7147i) q^{12} +(16.3141 + 8.31246i) q^{13} +(-0.596913 + 0.821581i) q^{14} +(-15.5330 + 47.8055i) q^{16} +(-25.9877 + 13.2414i) q^{17} +(-2.26418 + 14.2955i) q^{18} +(12.9667 - 17.8472i) q^{19} +0.609661 q^{21} +(-37.5149 + 18.2458i) q^{22} +(-11.3432 + 11.3432i) q^{23} +(52.4112 - 17.0294i) q^{24} +(56.1768 - 40.8148i) q^{26} +(25.9993 - 13.2473i) q^{27} +(1.26219 + 2.47718i) q^{28} +(-20.5919 - 28.3423i) q^{29} +(-1.29669 - 3.99079i) q^{31} +(66.3328 + 66.3328i) q^{32} +(22.0996 + 11.7820i) q^{33} +110.612i q^{34} +(32.0568 + 23.2906i) q^{36} +(-35.4724 - 5.61828i) q^{37} +(-37.9817 - 74.5433i) q^{38} +(-39.6462 - 12.8818i) q^{39} +(-18.8632 - 13.7049i) q^{41} +(1.04967 - 2.06009i) q^{42} +(28.8549 - 28.8549i) q^{43} +(-2.11969 + 114.187i) q^{44} +(18.7997 + 57.8594i) q^{46} +(6.00418 + 37.9089i) q^{47} +(17.9026 - 113.033i) q^{48} +(-46.5336 - 15.1197i) q^{49} +(53.7226 - 39.0317i) q^{51} +(-29.7383 - 187.760i) q^{52} +(-40.7810 - 20.7790i) q^{53} -110.662i q^{54} +6.48158 q^{56} +(-22.8019 + 44.7512i) q^{57} +(-131.224 + 20.7838i) q^{58} +(-21.5538 - 29.6662i) q^{59} +(12.2697 - 37.7623i) q^{61} +(-15.7177 - 2.48944i) q^{62} +(1.00939 - 0.159871i) q^{63} +(147.128 - 47.8048i) q^{64} +(77.8616 - 54.3908i) q^{66} +(-51.4949 - 51.4949i) q^{67} +(269.816 + 137.478i) q^{68} +(21.4676 - 29.5476i) q^{69} +(-21.8132 + 67.1340i) q^{71} +(82.3091 - 41.9386i) q^{72} +(9.93715 - 62.7407i) q^{73} +(-80.0583 + 110.191i) q^{74} -229.040 q^{76} +(2.04381 + 2.12113i) q^{77} +(-111.789 + 111.789i) q^{78} +(26.1620 - 8.50056i) q^{79} +(-25.9584 + 18.8599i) q^{81} +(-78.7870 + 40.1440i) q^{82} +(47.2836 + 92.7992i) q^{83} +(-3.72056 - 5.12090i) q^{84} +(-47.8226 - 147.183i) q^{86} +(56.3994 + 56.3994i) q^{87} +(234.951 + 125.259i) q^{88} -6.15373i q^{89} +(-3.96658 - 2.88189i) q^{91} +(164.502 + 26.0546i) q^{92} +(4.33723 + 8.51229i) q^{93} +(138.434 + 44.9801i) q^{94} +(-172.788 - 125.538i) q^{96} +(-0.706632 + 1.38684i) q^{97} +(-131.208 + 131.208i) q^{98} +(39.6788 + 13.7117i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 48 q^{6} + 32 q^{11} + 280 q^{16} - 8 q^{21} + 528 q^{26} - 16 q^{31} + 336 q^{36} - 604 q^{41} - 1152 q^{46} - 1024 q^{51} - 992 q^{56} - 320 q^{61} + 1624 q^{66} + 536 q^{71} + 1776 q^{76} + 3680 q^{81}+ \cdots - 6584 q^{96}+O(q^{100}) $ 128 * q - 48 * q^6 + 32 * q^11 + 280 * q^16 - 8 * q^21 + 528 * q^26 - 16 * q^31 + 336 * q^36 - 604 * q^41 - 1152 * q^46 - 1024 * q^51 - 992 * q^56 - 320 * q^61 + 1624 * q^66 + 536 * q^71 + 1776 * q^76 + 3680 * q^81 + 872 * q^86 - 448 * q^91 - 6584 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.72172	−	3.37907i	0.860862	−	1.68954i	0.147130	−	0.989117i	$-0.452996\pi$
$2$	1.72172	−	3.37907i	0.860862	−	1.68954i	0.713732	−	0.700419i	$-0.247004\pi$
$3$	−2.24871	+	0.356160i	−0.749569	+	0.118720i	−0.519519	−	0.854459i	$-0.673889\pi$
$3$	−2.24871	+	0.356160i	−0.749569	+	0.118720i	−0.230050	+	0.973179i	$0.573889\pi$
$4$	−6.10266	−	8.39959i	−1.52566	−	2.09990i
$5$		0			0
$5$		0			0
$6$	−2.66816	+	8.21175i	−0.444693	+	1.36862i
$7$	−0.264482	−	0.0418898i	−0.0377831	−	0.00598426i	0.137514	−	0.990500i	$-0.456089\pi$
$7$	−0.264482	−	0.0418898i	−0.0377831	−	0.00598426i	−0.175297	+	0.984516i	$0.556089\pi$
$8$	−23.9070	+	3.78649i	−2.98837	+	0.473312i
$9$	−3.62968	+	1.17935i	−0.403298	+	0.131039i
$10$		0			0
$11$	−8.77765	−	6.62969i	−0.797968	−	0.602699i
$11$	−8.77765	−	6.62969i	−0.797968	−	0.602699i
$12$	16.7147	+	16.7147i	1.39289	+	1.39289i
$13$	16.3141	+	8.31246i	1.25493	+	0.639420i	0.949790	−	0.312887i	$-0.101296\pi$
$13$	16.3141	+	8.31246i	1.25493	+	0.639420i	0.305142	+	0.952307i	$0.401296\pi$
$14$	−0.596913	+	0.821581i	−0.0426367	+	0.0586843i
$15$		0			0
$16$	−15.5330	+	47.8055i	−0.970809	+	2.98784i
$17$	−25.9877	+	13.2414i	−1.52869	+	0.778905i	−0.997655	−	0.0684472i	$-0.978196\pi$
$17$	−25.9877	+	13.2414i	−1.52869	+	0.778905i	−0.531032	+	0.847352i	$0.678196\pi$
$18$	−2.26418	+	14.2955i	−0.125788	+	0.794193i
$19$	12.9667	−	17.8472i	0.682459	−	0.939324i	−0.317501	−	0.948258i	$-0.602844\pi$
$19$	12.9667	−	17.8472i	0.682459	−	0.939324i	0.999960	+	0.00893392i	$0.00284379\pi$
$20$		0			0
$21$	0.609661			0.0290315
$22$	−37.5149	+	18.2458i	−1.70522	+	0.829356i
$23$	−11.3432	+	11.3432i	−0.493183	+	0.493183i	−0.909308	−	0.416124i	$-0.863388\pi$
$23$	−11.3432	+	11.3432i	−0.493183	+	0.493183i	0.416124	+	0.909308i	$0.363388\pi$
$24$	52.4112	−	17.0294i	2.18380	−	0.709559i
$25$		0			0
$26$	56.1768	−	40.8148i	2.16065	−	1.56980i
$27$	25.9993	−	13.2473i	0.962938	−	0.490641i
$28$	1.26219	+	2.47718i	0.0450780	+	0.0884706i
$29$	−20.5919	−	28.3423i	−0.710064	−	0.977319i	−0.999796	−	0.0202115i	$-0.993566\pi$
$29$	−20.5919	−	28.3423i	−0.710064	−	0.977319i	0.289732	−	0.957108i	$-0.406434\pi$
$30$		0			0
$31$	−1.29669	−	3.99079i	−0.0418286	−	0.128735i	0.927962	−	0.372676i	$-0.121560\pi$
$31$	−1.29669	−	3.99079i	−0.0418286	−	0.128735i	−0.969790	+	0.243941i	$0.921560\pi$
$32$	66.3328	+	66.3328i	2.07290	+	2.07290i
$33$	22.0996	+	11.7820i	0.669685	+	0.357030i
$34$			110.612i			3.25330i
$35$		0			0
$36$	32.0568	+	23.2906i	0.890466	+	0.646962i
$37$	−35.4724	−	5.61828i	−0.958715	−	0.151845i	−0.342582	−	0.939488i	$-0.611301\pi$
$37$	−35.4724	−	5.61828i	−0.958715	−	0.151845i	−0.616133	+	0.787642i	$0.711301\pi$
$38$	−37.9817	−	74.5433i	−0.999519	−	1.96167i
$39$	−39.6462	−	12.8818i	−1.01657	−	0.330304i
$40$		0			0
$41$	−18.8632	−	13.7049i	−0.460078	−	0.334266i	0.333484	−	0.942756i	$-0.391776\pi$
$41$	−18.8632	−	13.7049i	−0.460078	−	0.334266i	−0.793562	+	0.608490i	$0.791776\pi$
$42$	1.04967	−	2.06009i	0.0249921	−	0.0490498i
$43$	28.8549	−	28.8549i	0.671043	−	0.671043i	−0.286913	−	0.957957i	$-0.592629\pi$
$43$	28.8549	−	28.8549i	0.671043	−	0.671043i	0.957957	+	0.286913i	$0.0926291\pi$
$44$	−2.11969	+	114.187i	−0.0481747	+	2.59517i
$45$		0			0
$46$	18.7997	+	57.8594i	0.408689	+	1.25781i
$47$	6.00418	+	37.9089i	0.127748	+	0.806572i	0.965478	+	0.260486i	$0.0838828\pi$
$47$	6.00418	+	37.9089i	0.127748	+	0.806572i	−0.837729	+	0.546086i	$0.816117\pi$
$48$	17.9026	−	113.033i	0.372971	−	2.35485i
$49$	−46.5336	−	15.1197i	−0.949665	−	0.308565i
$50$		0			0
$51$	53.7226	−	39.0317i	1.05338	−	0.765328i
$52$	−29.7383	−	187.760i	−0.571890	−	3.61077i
$53$	−40.7810	−	20.7790i	−0.769454	−	0.392056i	0.0247612	−	0.999693i	$-0.492117\pi$
$53$	−40.7810	−	20.7790i	−0.769454	−	0.392056i	−0.794215	+	0.607637i	$0.792117\pi$
$54$		−	110.662i		−	2.04929i
$55$		0			0
$56$	6.48158			0.115742
$57$	−22.8019	+	44.7512i	−0.400033	+	0.785109i
$58$	−131.224	+	20.7838i	−2.26248	+	0.358342i
$59$	−21.5538	−	29.6662i	−0.365318	−	0.502817i	0.586303	−	0.810092i	$-0.300583\pi$
$59$	−21.5538	−	29.6662i	−0.365318	−	0.502817i	−0.951621	+	0.307275i	$0.900583\pi$
$60$		0			0
$61$	12.2697	−	37.7623i	0.201143	−	0.619055i	−0.798707	−	0.601721i	$-0.794482\pi$
$61$	12.2697	−	37.7623i	0.201143	−	0.619055i	0.999850	−	0.0173342i	$-0.00551792\pi$
$62$	−15.7177	−	2.48944i	−0.253512	−	0.0401523i
$63$	1.00939	−	0.159871i	0.0160220	−	0.00253764i
$64$	147.128	−	47.8048i	2.29887	−	0.746949i
$65$		0			0
$66$	77.8616	−	54.3908i	1.17972	−	0.824103i
$67$	−51.4949	−	51.4949i	−0.768580	−	0.768580i	0.209277	−	0.977856i	$-0.432889\pi$
$67$	−51.4949	−	51.4949i	−0.768580	−	0.768580i	−0.977856	+	0.209277i	$0.932889\pi$
$68$	269.816	+	137.478i	3.96788	+	2.02174i
$69$	21.4676	−	29.5476i	0.311124	−	0.428226i
$70$		0			0
$71$	−21.8132	+	67.1340i	−0.307228	+	0.945550i	0.671609	+	0.740906i	$0.265604\pi$
$71$	−21.8132	+	67.1340i	−0.307228	+	0.945550i	−0.978836	+	0.204644i	$0.934396\pi$
$72$	82.3091	−	41.9386i	1.14318	−	0.582480i
$73$	9.93715	−	62.7407i	0.136125	−	0.859462i	−0.821240	−	0.570583i	$-0.806717\pi$
$73$	9.93715	−	62.7407i	0.136125	−	0.859462i	0.957366	−	0.288879i	$-0.0932825\pi$
$74$	−80.0583	+	110.191i	−1.08187	+	1.48907i
$75$		0			0
$76$	−229.040			−3.01369
$77$	2.04381	+	2.12113i	0.0265430	+	0.0275471i
$78$	−111.789	+	111.789i	−1.43319	+	1.43319i
$79$	26.1620	−	8.50056i	0.331165	−	0.107602i	−0.138715	−	0.990332i	$-0.544297\pi$
$79$	26.1620	−	8.50056i	0.331165	−	0.107602i	0.469880	+	0.882730i	$0.344297\pi$
$80$		0			0
$81$	−25.9584	+	18.8599i	−0.320474	+	0.232838i
$82$	−78.7870	+	40.1440i	−0.960818	+	0.489561i
$83$	47.2836	+	92.7992i	0.569682	+	1.11806i	0.978654	+	0.205516i	$0.0658873\pi$
$83$	47.2836	+	92.7992i	0.569682	+	1.11806i	−0.408972	+	0.912547i	$0.634113\pi$
$84$	−3.72056	−	5.12090i	−0.0442923	−	0.0609632i
$85$		0			0
$86$	−47.8226	−	147.183i	−0.556077	−	1.71143i
$87$	56.3994	+	56.3994i	0.648269	+	0.648269i
$88$	234.951	+	125.259i	2.66989	+	1.42340i
$89$		−	6.15373i		−	0.0691430i	−0.999402	−	0.0345715i	$-0.988993\pi$
$89$		−	6.15373i		−	0.0691430i	0.999402	−	0.0345715i	$-0.0110066\pi$
$90$		0			0
$91$	−3.96658	−	2.88189i	−0.0435888	−	0.0316691i
$92$	164.502	+	26.0546i	1.78807	+	0.283202i
$93$	4.33723	+	8.51229i	0.0466369	+	0.0915300i
$94$	138.434	+	44.9801i	1.47271	+	0.478511i
$95$		0			0
$96$	−172.788	−	125.538i	−1.79987	−	1.30769i
$97$	−0.706632	+	1.38684i	−0.00728486	+	0.0142973i	−0.894620	−	0.446827i	$-0.852554\pi$
$97$	−0.706632	+	1.38684i	−0.00728486	+	0.0142973i	0.887335	+	0.461125i	$0.152554\pi$
$98$	−131.208	+	131.208i	−1.33886	+	1.33886i
$99$	39.6788	+	13.7117i	0.400796	+	0.138502i
$100$		0			0
$101$	−18.0392	−	55.5189i	−0.178606	−	0.549692i	0.821174	−	0.570678i	$-0.193319\pi$
$101$	−18.0392	−	55.5189i	−0.178606	−	0.549692i	−0.999780	+	0.0209859i	$0.993319\pi$
$102$	−39.3957	−	248.734i	−0.386232	−	2.43857i
$103$	14.5617	−	91.9393i	0.141376	−	0.892614i	−0.810413	−	0.585860i	$-0.800757\pi$
$103$	14.5617	−	91.9393i	0.141376	−	0.892614i	0.951789	−	0.306754i	$-0.0992430\pi$
$104$	−421.497	−	136.953i	−4.05285	−	1.31685i
$105$		0			0
$106$	−140.427	+	102.026i	−1.32479	+	0.962514i
$107$	22.5509	+	142.381i	0.210756	+	1.33066i	0.835353	+	0.549713i	$0.185263\pi$
$107$	22.5509	+	142.381i	0.210756	+	1.33066i	−0.624597	+	0.780947i	$0.714737\pi$
$108$	−269.937	−	137.540i	−2.49942	−	1.27352i
$109$		−	197.319i		−	1.81026i	−0.425130	−	0.905132i	$-0.639772\pi$
$109$		−	197.319i		−	1.81026i	0.425130	−	0.905132i	$-0.360228\pi$
$110$		0			0
$111$	81.7681			0.736649
$112$	6.11075	−	11.9930i	0.0545602	−	0.107080i
$113$	133.043	−	21.0719i	1.17737	−	0.186477i	0.463073	−	0.886320i	$-0.346747\pi$
$113$	133.043	−	21.0719i	1.17737	−	0.186477i	0.714297	+	0.699843i	$0.246747\pi$
$114$	111.959	+	154.098i	0.982097	+	1.35174i
$115$		0			0
$116$	−112.398	+	345.926i	−0.968951	+	2.98212i
$117$	−69.0184	−	10.9314i	−0.589901	−	0.0934311i
$118$	−137.354	+	21.7547i	−1.16402	+	0.184362i
$119$	7.42795	−	2.41349i	0.0624197	−	0.0202814i
$120$		0			0
$121$	33.0943	+	116.386i	0.273507	+	0.961870i
$122$	−106.477	−	106.477i	−0.872759	−	0.872759i
$123$	47.2989	+	24.1000i	0.384544	+	0.195935i
$124$	−25.6078	+	35.2461i	−0.206514	+	0.284243i
$125$		0			0
$126$	1.19767	−	3.68605i	0.00950531	−	0.0292543i
$127$	62.5920	−	31.8922i	0.492851	−	0.251120i	−0.189857	−	0.981812i	$-0.560802\pi$
$127$	62.5920	−	31.8922i	0.492851	−	0.251120i	0.682707	+	0.730692i	$0.260802\pi$
$128$	33.0782	−	208.847i	0.258423	−	1.63162i
$129$	−54.6092	+	75.1631i	−0.423327	+	0.582659i
$130$		0			0
$131$	−16.9883			−0.129682			−0.0648408	−	0.997896i	$-0.520654\pi$
$131$	−16.9883			−0.129682			−0.0648408	+	0.997896i	$0.520654\pi$
$132$	−35.9024	−	257.529i	−0.271988	−	1.95098i
$133$	−4.17707	+	4.17707i	−0.0314066	+	0.0314066i
$134$	−262.665	+	85.3450i	−1.96018	+	0.636903i
$135$		0			0
$136$	571.149	−	414.964i	4.19962	−	3.05120i
$137$	72.5736	−	36.9781i	0.529734	−	0.269913i	−0.168600	−	0.985684i	$-0.553925\pi$
$137$	72.5736	−	36.9781i	0.529734	−	0.269913i	0.698335	+	0.715771i	$0.253925\pi$
$138$	−62.8822	−	123.413i	−0.455668	−	0.894298i
$139$	71.6463	+	98.6127i	0.515441	+	0.709444i	0.984825	−	0.173550i	$-0.0555240\pi$
$139$	71.6463	+	98.6127i	0.515441	+	0.709444i	−0.469384	+	0.882994i	$0.655524\pi$
$140$		0			0
$141$	−27.0033	−	83.1075i	−0.191512	−	0.589415i
$142$	189.295	+	189.295i	1.33306	+	1.33306i
$143$	−88.0906	−	181.122i	−0.616018	−	1.26658i
$144$		−	191.838i		−	1.33221i
$145$		0			0
$146$	−194.896	−	141.600i	−1.33491	−	0.969866i
$147$	110.025	+	17.4263i	0.748472	+	0.118546i
$148$	169.285	+	332.240i	1.14382	+	2.24487i
$149$	223.209	+	72.5250i	1.49805	+	0.486745i	0.939448	−	0.342693i	$-0.111339\pi$
$149$	223.209	+	72.5250i	1.49805	+	0.486745i	0.558599	+	0.829438i	$0.311339\pi$
$150$		0			0
$151$	−92.9400	−	67.5249i	−0.615497	−	0.447185i	0.235849	−	0.971790i	$-0.424213\pi$
$151$	−92.9400	−	67.5249i	−0.615497	−	0.447185i	−0.851346	+	0.524605i	$0.824213\pi$
$152$	−242.417	+	475.770i	−1.59485	+	3.13007i
$153$	78.7106	−	78.7106i	0.514449	−	0.514449i
$154$	10.6863	−	3.25420i	0.0693917	−	0.0211311i
$155$		0			0
$156$	133.745	+	411.626i	0.857341	+	2.63863i
$157$	−10.1236	−	63.9179i	−0.0644815	−	0.407120i	−0.998725	−	0.0504840i	$-0.983924\pi$
$157$	−10.1236	−	63.9179i	−0.0644815	−	0.407120i	0.934243	−	0.356636i	$-0.116076\pi$
$158$	16.3198	−	103.039i	0.103290	−	0.652146i
$159$	99.1052	+	32.2012i	0.623303	+	0.202523i
$160$		0			0
$161$	3.47524	−	2.52491i	0.0215853	−	0.0156827i
$162$	19.0357	+	120.187i	0.117504	+	0.741893i
$163$	72.7852	+	37.0859i	0.446535	+	0.227521i	0.662774	−	0.748820i	$-0.269379\pi$
$163$	72.7852	+	37.0859i	0.446535	+	0.227521i	−0.216239	+	0.976340i	$0.569379\pi$
$164$			242.079i			1.47609i
$165$		0			0
$166$	394.985			2.37942
$167$	24.5061	−	48.0959i	0.146743	−	0.288000i	−0.805922	−	0.592022i	$-0.798330\pi$
$167$	24.5061	−	48.0959i	0.146743	−	0.288000i	0.952665	+	0.304022i	$0.0983298\pi$
$168$	−14.5752	+	2.30848i	−0.0867569	+	0.0137410i
$169$	97.7179	+	134.497i	0.578212	+	0.795841i
$170$		0			0
$171$	−26.0169	+	80.0718i	−0.152146	+	0.468256i
$172$	−418.460	−	66.2776i	−2.43291	−	0.385335i
$173$	−26.9852	+	4.27403i	−0.155984	+	0.0247054i	−0.233938	−	0.972252i	$-0.575161\pi$
$173$	−26.9852	+	4.27403i	−0.155984	+	0.0247054i	0.0779542	+	0.996957i	$0.475161\pi$
$174$	287.682	−	93.4735i	1.65334	−	0.537204i
$175$		0			0
$176$	453.279	−	316.641i	2.57545	−	1.79910i
$177$	59.0340	+	59.0340i	0.333525	+	0.333525i
$178$	−20.7939	−	10.5950i	−0.116820	−	0.0595225i
$179$	142.222	−	195.751i	0.794535	−	1.09358i	−0.198994	−	0.980001i	$-0.563767\pi$
$179$	142.222	−	195.751i	0.794535	−	1.09358i	0.993529	−	0.113582i	$-0.0362326\pi$
$180$		0			0
$181$	−24.9142	+	76.6781i	−0.137648	+	0.423636i	−0.995992	−	0.0894373i	$-0.971493\pi$
$181$	−24.9142	+	76.6781i	−0.137648	+	0.423636i	0.858345	+	0.513073i	$0.171493\pi$
$182$	−16.5675	+	8.44155i	−0.0910301	+	0.0463821i
$183$	−14.1416	+	89.2864i	−0.0772764	+	0.487904i
$184$	228.231	−	314.133i	1.24039	−	1.70725i
$185$		0			0
$186$	36.2312			0.194791
$187$	315.897	+	56.0621i	1.68929	+	0.299797i
$188$	281.778	−	281.778i	1.49882	−	1.49882i
$189$	−7.43128	+	2.41457i	−0.0393189	+	0.0127755i
$190$		0			0
$191$	44.5047	−	32.3346i	0.233009	−	0.169291i	−0.465154	−	0.885230i	$-0.654001\pi$
$191$	44.5047	−	32.3346i	0.233009	−	0.169291i	0.698163	+	0.715939i	$0.254001\pi$
$192$	−313.821	+	159.900i	−1.63449	+	0.832812i
$193$	51.4223	+	100.922i	0.266437	+	0.522911i	0.985001	−	0.172549i	$-0.0552004\pi$
$193$	51.4223	+	100.922i	0.266437	+	0.522911i	−0.718564	+	0.695461i	$0.755200\pi$
$194$	3.46962	+	4.77552i	0.0178846	+	0.0246161i
$195$		0			0
$196$	156.979	+	483.133i	0.800916	+	2.46496i
$197$	−191.948	−	191.948i	−0.974353	−	0.974353i	0.0253260	−	0.999679i	$-0.491938\pi$
$197$	−191.948	−	191.948i	−0.974353	−	0.974353i	−0.999679	+	0.0253260i	$0.991938\pi$
$198$	114.649	−	110.470i	0.579034	−	0.557929i
$199$			33.5384i			0.168534i	0.996443	+	0.0842672i	$0.0268549\pi$
$199$			33.5384i			0.168534i	−0.996443	+	0.0842672i	$0.973145\pi$
$200$		0			0
$201$	134.137	+	97.4564i	0.667349	+	0.484858i
$202$	−218.661	−	34.6325i	−1.08248	−	0.171448i
$203$	4.25892	+	8.35860i	0.0209799	+	0.0411754i
$204$	−655.701	−	213.050i	−3.21422	−	1.04436i
$205$		0			0
$206$	−285.598	−	207.499i	−1.38640	−	1.00728i
$207$	27.7946	−	54.5499i	0.134273	−	0.263526i
$208$	−650.788	+	650.788i	−3.12879	+	3.12879i
$209$	−232.138	+	70.6907i	−1.11071	+	0.338233i
$210$		0			0
$211$	52.4776	+	161.510i	0.248709	+	0.765448i	0.995004	+	0.0998327i	$0.0318308\pi$
$211$	52.4776	+	161.510i	0.248709	+	0.765448i	−0.746295	+	0.665615i	$0.768169\pi$
$212$	74.3379	+	469.351i	0.350650	+	2.21392i
$213$	25.1409	−	158.734i	0.118033	−	0.745229i
$214$	519.941	+	168.939i	2.42963	+	0.789435i
$215$		0			0
$216$	−571.405	+	415.150i	−2.64539	+	1.92199i
$217$	0.175777	+	1.10981i	0.000810031	+	0.00511433i
$218$	−666.755	−	339.728i	−3.05851	−	1.55839i
$219$			144.625i			0.660386i
$220$		0			0
$221$	−534.034			−2.41645
$222$	140.782	−	276.300i	0.634153	−	1.24460i
$223$	−155.796	+	24.6757i	−0.698638	+	0.110653i	−0.495643	−	0.868526i	$-0.665068\pi$
$223$	−155.796	+	24.6757i	−0.698638	+	0.110653i	−0.202995	+	0.979180i	$0.565068\pi$
$224$	−14.7651	−	20.3225i	−0.0659158	−	0.0907254i
$225$		0			0
$226$	157.859	−	485.841i	0.698493	−	2.14974i
$227$	61.1052	+	9.67811i	0.269186	+	0.0426349i	0.289568	−	0.957157i	$-0.406488\pi$
$227$	61.1052	+	9.67811i	0.269186	+	0.0426349i	−0.0203822	+	0.999792i	$0.506488\pi$
$228$	515.044	−	81.5750i	2.25897	−	0.357785i
$229$	−431.134	+	140.084i	−1.88268	+	0.611720i	−0.897279	+	0.441463i	$0.854460\pi$
$229$	−431.134	+	140.084i	−1.88268	+	0.611720i	−0.985400	+	0.170257i	$0.945540\pi$
$230$		0			0
$231$	−5.35140	−	4.04187i	−0.0231662	−	0.0174973i
$232$	599.607	+	599.607i	2.58451	+	2.58451i
$233$	−303.971	−	154.881i	−1.30460	−	0.664725i	−0.343037	−	0.939322i	$-0.611456\pi$
$233$	−303.971	−	154.881i	−1.30460	−	0.664725i	−0.961560	+	0.274596i	$0.911456\pi$
$234$	−155.769	+	214.397i	−0.665678	+	0.916227i
$235$		0			0
$236$	−117.649	+	362.085i	−0.498511	+	1.53426i
$237$	−55.8032	+	28.4331i	−0.235456	+	0.119971i
$238$	4.63352	−	29.2549i	0.0194686	−	0.122920i
$239$	99.8447	−	137.424i	0.417760	−	0.574998i	−0.547329	−	0.836917i	$-0.684356\pi$
$239$	99.8447	−	137.424i	0.417760	−	0.574998i	0.965090	+	0.261920i	$0.0843555\pi$
$240$		0			0
$241$	−209.522			−0.869384			−0.434692	−	0.900579i	$-0.643143\pi$
$241$	−209.522			−0.869384			−0.434692	+	0.900579i	$0.643143\pi$
$242$	450.257	+	88.5568i	1.86057	+	0.365937i
$243$	−134.043	+	134.043i	−0.551617	+	0.551617i
$244$	−392.066	+	127.390i	−1.60683	+	0.522090i
$245$		0			0
$246$	162.871	−	118.333i	0.662078	−	0.481028i
$247$	359.894	−	183.375i	1.45706	−	0.742410i
$248$	46.1110	+	90.4979i	0.185931	+	0.364911i
$249$	−139.378	−	191.838i	−0.559752	−	0.770432i
$250$		0			0
$251$	18.0637	+	55.5944i	0.0719670	+	0.221492i	0.980570	−	0.196169i	$-0.0628501\pi$
$251$	18.0637	+	55.5944i	0.0719670	+	0.221492i	−0.908603	+	0.417661i	$0.862850\pi$
$252$	−7.50280	−	7.50280i	−0.0297730	−	0.0297730i
$253$	174.769	−	24.3648i	0.690786	−	0.0963034i
$254$		−	266.413i		−	1.04887i
$255$		0			0
$256$	−148.141	−	107.631i	−0.578677	−	0.420433i
$257$	−164.934	−	26.1230i	−0.641767	−	0.101646i	−0.172935	−	0.984933i	$-0.555325\pi$
$257$	−164.934	−	26.1230i	−0.641767	−	0.101646i	−0.468832	+	0.883287i	$0.655325\pi$
$258$	159.960	+	313.938i	0.619998	+	1.21682i
$259$	9.14647	+	2.97187i	0.0353145	+	0.0114744i
$260$		0			0
$261$	108.167	+	78.5882i	0.414435	+	0.301104i
$262$	−29.2492	+	57.4047i	−0.111638	+	0.219102i
$263$	−229.419	+	229.419i	−0.872315	+	0.872315i	−0.992724	−	0.120409i	$-0.961579\pi$
$263$	−229.419	+	229.419i	−0.872315	+	0.872315i	0.120409	+	0.992724i	$0.461579\pi$
$264$	−572.947	−	197.992i	−2.17025	−	0.749969i
$265$		0			0
$266$	6.92287	+	21.3064i	0.0260258	+	0.0800993i
$267$	2.19171	+	13.8379i	0.00820866	+	0.0518274i
$268$	−118.280	+	746.791i	−0.441344	+	2.78653i
$269$	447.195	+	145.302i	1.66243	+	0.540157i	0.981380	−	0.192076i	$-0.0615220\pi$
$269$	447.195	+	145.302i	1.66243	+	0.540157i	0.681054	+	0.732233i	$0.261522\pi$
$270$		0			0
$271$	393.019	−	285.545i	1.45026	−	1.05367i	0.464485	−	0.885581i	$-0.346240\pi$
$271$	393.019	−	285.545i	1.45026	−	1.05367i	0.985771	−	0.168092i	$-0.0537605\pi$
$272$	−229.346	−	1448.03i	−0.843183	−	5.32365i
$273$	9.94609	+	5.06779i	0.0364326	+	0.0185633i
$274$		−	308.897i		−	1.12736i
$275$		0			0
$276$	−379.197			−1.37390
$277$	−73.3475	+	143.953i	−0.264792	+	0.519685i	−0.984672	−	0.174414i	$-0.944197\pi$
$277$	−73.3475	+	143.953i	−0.264792	+	0.519685i	0.719880	+	0.694099i	$0.244197\pi$
$278$	456.575	−	72.3143i	1.64235	−	0.260123i
$279$	9.41312	+	12.9560i	0.0337388	+	0.0464374i
$280$		0			0
$281$	−65.0399	+	200.172i	−0.231459	+	0.712357i	0.766113	+	0.642706i	$0.222188\pi$
$281$	−65.0399	+	200.172i	−0.231459	+	0.712357i	−0.997571	+	0.0696507i	$0.977812\pi$
$282$	−327.318	−	51.8421i	−1.16070	−	0.183837i
$283$	183.921	−	29.1302i	0.649897	−	0.102934i	0.177223	−	0.984171i	$-0.443289\pi$
$283$	183.921	−	29.1302i	0.649897	−	0.102934i	0.472674	+	0.881237i	$0.343289\pi$
$284$	697.017	−	226.474i	2.45428	−	0.797445i
$285$		0			0
$286$	−763.690	−	14.1766i	−2.67025	−	0.0495684i
$287$	4.41487	+	4.41487i	0.0153828	+	0.0153828i
$288$	−318.997	−	162.537i	−1.10763	−	0.564364i
$289$	330.155	−	454.419i	1.14240	−	1.57239i
$290$		0			0
$291$	1.09507	−	3.37028i	0.00376312	−	0.0115817i
$292$	−587.639	+	299.417i	−2.01246	+	1.02540i
$293$	−17.6153	+	111.219i	−0.0601205	+	0.379586i	0.939221	+	0.343312i	$0.111549\pi$
$293$	−17.6153	+	111.219i	−0.0601205	+	0.379586i	−0.999342	+	0.0362737i	$0.988451\pi$
$294$	248.318	−	341.780i	0.844619	−	1.16252i
$295$		0			0
$296$	869.313			2.93687
$297$	−316.039	−	56.0872i	−1.06410	−	0.188846i
$298$	629.371	−	629.371i	2.11198	−	2.11198i
$299$	−279.345	+	90.7646i	−0.934263	+	0.303561i
$300$		0			0
$301$	−8.84031	+	6.42286i	−0.0293698	+	0.0213384i
$302$	−388.189	+	197.792i	−1.28539	+	0.654940i
$303$	60.3384	+	118.421i	0.199137	+	0.390828i
$304$	651.781	+	897.099i	2.14402	+	2.95098i
$305$		0			0
$306$	−130.451	−	401.487i	−0.426311	−	1.31205i
$307$	−140.701	−	140.701i	−0.458308	−	0.458308i	0.439792	−	0.898100i	$-0.355052\pi$
$307$	−140.701	−	140.701i	−0.458308	−	0.458308i	−0.898100	+	0.439792i	$0.855052\pi$
$308$	5.34391	−	30.1117i	0.0173504	−	0.0977653i
$309$			211.931i			0.685860i
$310$		0			0
$311$	−184.187	−	133.820i	−0.592241	−	0.430288i	0.250875	−	0.968019i	$-0.419282\pi$
$311$	−184.187	−	133.820i	−0.592241	−	0.430288i	−0.843116	+	0.537731i	$0.819282\pi$
$312$	996.599	+	157.846i	3.19423	+	0.505916i
$313$	−119.867	−	235.253i	−0.382962	−	0.751606i	0.616396	−	0.787437i	$-0.288592\pi$
$313$	−119.867	−	235.253i	−0.382962	−	0.751606i	−0.999358	+	0.0358309i	$0.988592\pi$
$314$	−233.413	−	75.8405i	−0.743354	−	0.241530i
$315$		0			0
$316$	−231.059	−	167.874i	−0.731200	−	0.531248i
$317$	−66.3921	+	130.302i	−0.209439	+	0.411047i	−0.971698	−	0.236225i	$-0.924090\pi$
$317$	−66.3921	+	130.302i	−0.209439	+	0.411047i	0.762260	+	0.647271i	$0.224090\pi$
$318$	279.442	−	279.442i	0.878749	−	0.878749i
$319$	−7.15234	+	385.296i	−0.0224211	+	1.20783i
$320$		0			0
$321$	−101.421	−	312.141i	−0.315952	−	0.972400i
$322$	−2.54845	−	16.0903i	−0.00791444	−	0.0499698i
$323$	−100.654	+	635.503i	−0.311622	+	1.96750i
$324$	316.830	+	102.944i	0.977871	+	0.317729i
$325$		0			0
$326$	250.632	−	182.095i	0.768810	−	0.558573i
$327$	70.2771	+	443.712i	0.214915	+	1.35692i
$328$	502.855	+	256.218i	1.53310	+	0.781151i
$329$		−	10.2777i		−	0.0312393i
$330$		0			0
$331$	544.980			1.64647			0.823233	−	0.567704i	$-0.192168\pi$
$331$	544.980			1.64647			0.823233	+	0.567704i	$0.192168\pi$
$332$	490.920	−	963.485i	1.47867	−	2.90206i
$333$	135.380	−	21.4420i	0.406545	−	0.0643904i
$334$	−120.327	−	165.616i	−0.360260	−	0.495856i
$335$		0			0
$336$	−9.46984	+	29.1452i	−0.0281840	+	0.0867416i
$337$	−298.986	−	47.3547i	−0.887198	−	0.140518i	−0.303830	−	0.952726i	$-0.598265\pi$
$337$	−298.986	−	47.3547i	−0.887198	−	0.140518i	−0.583368	+	0.812208i	$0.698265\pi$
$338$	622.719	−	98.6289i	1.84236	−	0.291802i
$339$	−291.669	+	94.7690i	−0.860381	+	0.279555i
$340$		0			0
$341$	−15.0759	+	43.6264i	−0.0442107	+	0.127937i
$342$	225.775	+	225.775i	0.660159	+	0.660159i
$343$	23.3650	+	11.9050i	0.0681194	+	0.0347086i
$344$	−580.574	+	799.092i	−1.68772	+	2.32294i
$345$		0			0
$346$	−32.0187	+	98.5435i	−0.0925397	+	0.284808i
$347$	−236.217	+	120.359i	−0.680741	+	0.346855i	−0.759930	−	0.650005i	$-0.774767\pi$
$347$	−236.217	+	120.359i	−0.680741	+	0.346855i	0.0791889	+	0.996860i	$0.474767\pi$
$348$	129.546	−	817.918i	0.372257	−	2.35034i
$349$	−321.631	+	442.687i	−0.921579	+	1.26844i	0.0414756	+	0.999140i	$0.486794\pi$
$349$	−321.631	+	442.687i	−0.921579	+	1.26844i	−0.963055	+	0.269305i	$0.913206\pi$
$350$		0			0
$351$	534.274			1.52215
$352$	−142.480	−	1022.01i	−0.404773	−	2.90344i
$353$	−190.687	+	190.687i	−0.540190	+	0.540190i	−0.923585	−	0.383395i	$-0.874755\pi$
$353$	−190.687	+	190.687i	−0.540190	+	0.540190i	0.383395	+	0.923585i	$0.374755\pi$
$354$	301.120	−	97.8399i	0.850622	−	0.276384i
$355$		0			0
$356$	−51.6888	+	37.5541i	−0.145193	+	0.105489i
$357$	−15.8437	+	8.07276i	−0.0443801	+	0.0226128i
$358$	−416.592	−	817.607i	−1.16366	−	2.28382i
$359$	−390.631	−	537.658i	−1.08811	−	1.49765i	−0.850268	−	0.526350i	$-0.823560\pi$
$359$	−390.631	−	537.658i	−1.08811	−	1.49765i	−0.237841	−	0.971304i	$-0.576440\pi$
$360$		0			0
$361$	−38.8300	−	119.507i	−0.107562	−	0.331043i
$362$	216.206	+	216.206i	0.597253	+	0.597253i
$363$	−115.872	−	249.932i	−0.319205	−	0.688517i
$364$			50.9048i			0.139848i
$365$		0			0
$366$	277.357	+	201.512i	0.757807	+	0.550579i
$367$	−255.996	−	40.5459i	−0.697538	−	0.110479i	−0.202412	−	0.979300i	$-0.564878\pi$
$367$	−255.996	−	40.5459i	−0.697538	−	0.110479i	−0.495126	+	0.868821i	$0.664878\pi$
$368$	−366.075	−	718.462i	−0.994768	−	1.95234i
$369$	84.6303	+	27.4980i	0.229350	+	0.0745204i
$370$		0			0
$371$	9.91542	+	7.20397i	0.0267262	+	0.0194177i
$372$	45.0311	−	88.3786i	0.121051	−	0.237577i
$373$	−214.214	+	214.214i	−0.574301	+	0.574301i	−0.933327	−	0.359027i	$-0.883109\pi$
$373$	−214.214	+	214.214i	−0.574301	+	0.574301i	0.359027	+	0.933327i	$0.383109\pi$
$374$	733.325	−	970.916i	1.96076	−	2.59603i
$375$		0			0
$376$	−287.084	−	883.552i	−0.763520	−	2.34987i
$377$	−100.344	−	633.548i	−0.266165	−	1.68050i
$378$	−4.63560	+	29.2680i	−0.0122635	+	0.0774287i
$379$	−271.298	−	88.1499i	−0.715825	−	0.232586i	−0.0716127	−	0.997433i	$-0.522815\pi$
$379$	−271.298	−	88.1499i	−0.715825	−	0.232586i	−0.644212	+	0.764847i	$0.722815\pi$
$380$		0			0
$381$	−129.392	+	94.0091i	−0.339613	+	0.246743i
$382$	−32.6360	−	206.056i	−0.0854346	−	0.539413i
$383$	55.1978	+	28.1247i	0.144119	+	0.0734325i	0.524563	−	0.851372i	$-0.324229\pi$
$383$	55.1978	+	28.1247i	0.144119	+	0.0734325i	−0.380444	+	0.924804i	$0.624229\pi$
$384$			481.418i			1.25369i
$385$		0			0
$386$	429.557			1.11284
$387$	−70.7038	+	138.764i	−0.182697	+	0.358563i
$388$	15.9612	−	2.52801i	0.0411372	−	0.00651550i
$389$	33.9161	+	46.6815i	0.0871879	+	0.120004i	0.850383	−	0.526165i	$-0.176370\pi$
$389$	33.9161	+	46.6815i	0.0871879	+	0.120004i	−0.763195	+	0.646168i	$0.776370\pi$
$390$		0			0
$391$	144.584	−	444.984i	0.369780	−	1.13807i
$392$	1169.73	+	185.267i	2.98400	+	0.472619i
$393$	38.2017	−	6.05055i	0.0972053	−	0.0153958i
$394$	−979.086	+	318.124i	−2.48499	+	0.807422i
$395$		0			0
$396$	−126.974	−	416.964i	−0.320641	−	1.05294i
$397$	−327.770	−	327.770i	−0.825617	−	0.825617i	0.161290	−	0.986907i	$-0.448434\pi$
$397$	−327.770	−	327.770i	−0.825617	−	0.825617i	−0.986907	+	0.161290i	$0.948434\pi$
$398$	113.329	+	57.7438i	0.284745	+	0.145085i
$399$	7.90531	−	10.8807i	0.0198128	−	0.0272700i
$400$		0			0
$401$	−117.251	+	360.860i	−0.292395	+	0.899900i	0.691689	+	0.722196i	$0.256867\pi$
$401$	−117.251	+	360.860i	−0.292395	+	0.899900i	−0.984084	+	0.177704i	$0.943133\pi$
$402$	560.259	−	285.466i	1.39368	−	0.710115i
$403$	12.0190	−	75.8849i	0.0298238	−	0.188300i
$404$	−356.249	+	490.335i	−0.881804	+	1.21370i
$405$		0			0
$406$	35.5770			0.0876281
$407$	274.117	+	284.487i	0.673507	+	0.698985i
$408$	−1136.55	+	1136.55i	−2.78567	+	2.78567i
$409$	54.3872	−	17.6715i	0.132976	−	0.0432065i	−0.241773	−	0.970333i	$-0.577729\pi$
$409$	54.3872	−	17.6715i	0.132976	−	0.0432065i	0.374749	+	0.927126i	$0.377729\pi$
$410$		0			0
$411$	−150.027	+	109.001i	−0.365028	+	0.265208i
$412$	−861.117	+	438.761i	−2.09009	+	1.06495i
$413$	4.45786	+	8.74905i	0.0107939	+	0.0211841i
$414$	−136.474	−	187.840i	−0.329646	−	0.453719i
$415$		0			0
$416$	530.772	+	1633.55i	1.27590	+	3.92680i
$417$	−196.233	−	196.233i	−0.470584	−	0.470584i
$418$	−160.809	+	906.123i	−0.384711	+	2.16776i
$419$		−	759.616i		−	1.81293i	−0.422285	−	0.906463i	$-0.638772\pi$
$419$		−	759.616i		−	1.81293i	0.422285	−	0.906463i	$-0.361228\pi$
$420$		0			0
$421$	205.163	+	149.060i	0.487323	+	0.354061i	0.804154	−	0.594421i	$-0.202619\pi$
$421$	205.163	+	149.060i	0.487323	+	0.354061i	−0.316831	+	0.948482i	$0.602619\pi$
$422$	636.104	+	100.749i	1.50736	+	0.238742i
$423$	−66.5012	−	130.516i	−0.157213	−	0.308549i
$424$	1053.63	+	342.346i	2.48498	+	0.807419i
$425$		0			0
$426$	−493.087	−	358.249i	−1.15748	−	0.840959i
$427$	−4.82698	+	9.47348i	−0.0113044	+	0.0221861i
$428$	1058.32	−	1058.32i	2.47271	−	2.47271i
$429$	262.598	+	375.915i	0.612117	+	0.876258i
$430$		0			0
$431$	−205.208	−	631.566i	−0.476121	−	1.46535i	−0.844440	−	0.535651i	$-0.820066\pi$
$431$	−205.208	−	631.566i	−0.476121	−	1.46535i	0.368318	−	0.929700i	$-0.379934\pi$
$432$	229.449	+	1448.68i	0.531131	+	3.35343i
$433$	102.418	−	646.644i	0.236532	−	1.49340i	−0.528236	−	0.849097i	$-0.677146\pi$
$433$	102.418	−	646.644i	0.236532	−	1.49340i	0.764768	−	0.644306i	$-0.222854\pi$
$434$	4.05277	+	1.31682i	0.00933818	+	0.00303416i
$435$		0			0
$436$	−1657.40	+	1204.17i	−3.80137	+	2.76186i
$437$	55.3599	+	349.528i	0.126682	+	0.799836i
$438$	488.697	+	249.004i	1.11575	+	0.568501i
$439$			230.999i			0.526194i	0.964769	+	0.263097i	$0.0847440\pi$
$439$			230.999i			0.526194i	−0.964769	+	0.263097i	$0.915256\pi$
$440$		0			0
$441$	186.733			0.423432
$442$	−919.460	+	1804.54i	−2.08023	+	4.08267i
$443$	−469.772	+	74.4046i	−1.06043	+	0.167956i	−0.662199	−	0.749328i	$-0.730377\pi$
$443$	−469.772	+	74.4046i	−1.06043	+	0.167956i	−0.398234	+	0.917284i	$0.630377\pi$
$444$	−499.003	−	686.818i	−1.12388	−	1.54689i
$445$		0			0
$446$	−184.857	+	568.932i	−0.414478	+	1.27563i
$447$	−527.762	−	83.5893i	−1.18068	−	0.187001i
$448$	−40.9152	+	6.48033i	−0.0913286	+	0.0144650i
$449$	−132.723	+	43.1244i	−0.295597	+	0.0960453i	−0.453061	−	0.891479i	$-0.649668\pi$
$449$	−132.723	+	43.1244i	−0.295597	+	0.0960453i	0.157464	+	0.987525i	$0.449668\pi$
$450$		0			0
$451$	74.7151	+	245.354i	0.165665	+	0.544022i
$452$	−988.910	−	988.910i	−2.18785	−	2.18785i
$453$	233.044	+	118.742i	0.514447	+	0.262124i
$454$	137.909	−	189.816i	0.303765	−	0.418097i
$455$		0			0
$456$	375.674	−	1156.21i	0.823847	−	2.53554i
$457$	299.602	−	152.655i	0.655584	−	0.334037i	−0.0943600	−	0.995538i	$-0.530080\pi$
$457$	299.602	−	152.655i	0.655584	−	0.334037i	0.749944	+	0.661501i	$0.230080\pi$
$458$	−268.939	+	1698.02i	−0.587204	+	3.70746i
$459$	−500.249	+	688.534i	−1.08987	+	1.50007i
$460$		0			0
$461$	288.038			0.624812			0.312406	−	0.949949i	$-0.398865\pi$
$461$	288.038			0.624812			0.312406	+	0.949949i	$0.398865\pi$
$462$	−22.8714	+	11.1238i	−0.0495052	+	0.0240774i
$463$	−8.59030	+	8.59030i	−0.0185536	+	0.0185536i	−0.716323	−	0.697769i	$-0.754176\pi$
$463$	−8.59030	+	8.59030i	−0.0185536	+	0.0185536i	0.697769	+	0.716323i	$0.254176\pi$
$464$	1674.77	−	544.165i	3.60942	−	1.17277i
$465$		0			0
$466$	−1046.71	+	760.478i	−2.24616	+	1.63193i
$467$	368.828	−	187.927i	0.789781	−	0.402414i	−0.0120776	−	0.999927i	$-0.503845\pi$
$467$	368.828	−	187.927i	0.789781	−	0.402414i	0.801859	+	0.597513i	$0.203845\pi$
$468$	329.376	+	646.437i	0.703795	+	1.38128i
$469$	11.4623	+	15.7766i	0.0244400	+	0.0336387i
$470$		0			0
$471$	45.5300	+	140.127i	0.0966666	+	0.297509i
$472$	627.616	+	627.616i	1.32970	+	1.32970i
$473$	−444.577	+	61.9791i	−0.939909	+	0.131034i
$474$			237.517i			0.501091i
$475$		0			0
$476$	−65.6025	−	47.6630i	−0.137820	−	0.100132i
$477$	172.528	+	27.3257i	0.361694	+	0.0572867i
$478$	−292.462	−	573.989i	−0.611846	−	1.20081i
$479$	−36.1149	−	11.7344i	−0.0753965	−	0.0244978i	0.271076	−	0.962558i	$-0.412621\pi$
$479$	−36.1149	−	11.7344i	−0.0753965	−	0.0244978i	−0.346472	+	0.938060i	$0.612621\pi$
$480$		0			0
$481$	−532.000	−	386.521i	−1.10603	−	0.803577i
$482$	−360.738	+	707.989i	−0.748420	+	1.46886i
$483$	−6.91552	+	6.91552i	−0.0143179	+	0.0143179i
$484$	775.633	−	988.245i	1.60255	−	2.04183i
$485$		0			0
$486$	222.156	+	683.726i	0.457111	+	1.40684i
$487$	7.23241	+	45.6636i	0.0148509	+	0.0937652i	0.994000	−	0.109376i	$-0.0348851\pi$
$487$	7.23241	+	45.6636i	0.0148509	+	0.0937652i	−0.979150	+	0.203141i	$0.934885\pi$
$488$	−150.345	+	949.243i	−0.308085	+	1.94517i
$489$	−176.881	−	57.4721i	−0.361720	−	0.117530i
$490$		0			0
$491$	749.160	−	544.296i	1.52578	−	1.10855i	0.567258	−	0.823540i	$-0.308004\pi$
$491$	749.160	−	544.296i	1.52578	−	1.10855i	0.958526	−	0.285007i	$-0.0919958\pi$
$492$	−86.2190	−	544.365i	−0.175242	−	1.10643i
$493$	910.425	+	463.885i	1.84670	+	0.940943i
$494$		−	1531.83i		−	3.10087i
$495$		0			0
$496$	210.923			0.425249
$497$	8.58142	−	16.8420i	0.0172664	−	0.0338873i
$498$	−888.204	+	140.678i	−1.78354	+	0.282485i
$499$	−326.862	−	449.887i	−0.655035	−	0.901578i	0.344270	−	0.938871i	$-0.388127\pi$
$499$	−326.862	−	449.887i	−0.655035	−	0.901578i	−0.999304	+	0.0372930i	$0.988127\pi$
$500$		0			0
$501$	−37.9772	+	116.882i	−0.0758028	+	0.233297i
$502$	218.958	+	34.6796i	0.436172	+	0.0690828i
$503$	−634.447	+	100.487i	−1.26133	+	0.199775i	−0.751056	−	0.660239i	$-0.770455\pi$
$503$	−634.447	+	100.487i	−1.26133	+	0.199775i	−0.510271	+	0.860013i	$0.670455\pi$
$504$	−23.5261	+	7.64408i	−0.0466787	+	0.0151668i
$505$		0			0
$506$	218.573	−	632.506i	0.431963	−	1.25001i
$507$	−267.641	−	267.641i	−0.527892	−	0.527892i
$508$	−649.860	−	331.120i	−1.27925	−	0.651811i
$509$	159.366	−	219.349i	0.313097	−	0.430941i	−0.623247	−	0.782025i	$-0.714187\pi$
$509$	159.366	−	219.349i	0.313097	−	0.430941i	0.936344	+	0.351084i	$0.114187\pi$
$510$		0			0
$511$	−5.25639	+	16.1775i	−0.0102865	+	0.0316585i
$512$	134.865	−	68.7172i	0.263409	−	0.134213i
$513$	100.699	−	635.788i	0.196294	−	1.23935i
$514$	−372.243	+	512.348i	−0.724207	+	0.996786i
$515$		0			0
$516$	964.600			1.86938
$517$	198.622	−	372.557i	0.384181	−	0.720613i
$518$	25.7898	−	25.7898i	0.0497873	−	0.0497873i
$519$	59.1595	−	19.2221i	0.113987	−	0.0370367i
$520$		0			0
$521$	−380.890	+	276.733i	−0.731076	+	0.531158i	−0.889904	−	0.456149i	$-0.849228\pi$
$521$	−380.890	+	276.733i	−0.731076	+	0.531158i	0.158828	+	0.987306i	$0.449228\pi$
$522$	451.790	−	230.198i	0.865498	−	0.440993i
$523$	249.695	+	490.055i	0.477429	+	0.937007i	0.996604	+	0.0823394i	$0.0262391\pi$
$523$	249.695	+	490.055i	0.477429	+	0.937007i	−0.519175	+	0.854668i	$0.673761\pi$
$524$	103.674	+	142.695i	0.197851	+	0.272318i
$525$		0			0
$526$	380.227	+	1170.22i	0.722865	+	2.22475i
$527$	86.5415	+	86.5415i	0.164215	+	0.164215i
$528$	−906.515	+	873.473i	−1.71689	+	1.65431i
$529$			271.663i			0.513540i
$530$		0			0
$531$	113.220	+	82.2593i	0.213221	+	0.154914i
$532$	60.5770	+	9.59445i	0.113866	+	0.0180347i
$533$	−193.815	−	380.383i	−0.363630	−	0.713664i
$534$	50.5329	+	16.4191i	0.0946308	+	0.0307474i
$535$		0			0
$536$	1426.07	+	1036.10i	2.66058	+	1.93303i
$537$	−250.096	+	490.841i	−0.465728	+	0.914043i
$538$	1260.93	−	1260.93i	2.34374	−	2.34374i
$539$	308.217	+	441.219i	0.571831	+	0.818587i
$540$		0			0
$541$	68.1056	+	209.607i	0.125888	+	0.387444i	0.994062	−	0.108816i	$-0.0347060\pi$
$541$	68.1056	+	209.607i	0.125888	+	0.387444i	−0.868174	+	0.496261i	$0.834706\pi$
$542$	−288.208	−	1819.67i	−0.531748	−	3.35733i
$543$	28.7151	−	181.300i	0.0528823	−	0.333886i
$544$	−2602.17	−	845.497i	−4.78340	−	1.55422i
$545$		0			0
$546$	34.2488	−	24.8832i	0.0627268	−	0.0455737i
$547$	20.5594	+	129.807i	0.0375857	+	0.237307i	0.999328	−	0.0366482i	$-0.0116681\pi$
$547$	20.5594	+	129.807i	0.0375857	+	0.237307i	−0.961743	+	0.273955i	$0.911668\pi$
$548$	−753.492	−	383.924i	−1.37499	−	0.700590i
$549$			151.536i			0.276021i
$550$		0			0
$551$	−772.838			−1.40261
$552$	−401.343	+	787.680i	−0.727071	+	1.42696i
$553$	−7.27547	+	1.15232i	−0.0131564	+	0.00208376i
$554$	360.142	+	495.693i	0.650076	+	0.894753i
$555$		0			0
$556$	391.073	−	1203.60i	0.703369	−	2.16475i
$557$	−333.457	−	52.8144i	−0.598666	−	0.0948193i	−0.150256	−	0.988647i	$-0.548010\pi$
$557$	−333.457	−	52.8144i	−0.598666	−	0.0948193i	−0.448410	+	0.893828i	$0.648010\pi$
$558$	59.9862	−	9.50088i	0.107502	−	0.0170267i
$559$	710.597	−	230.887i	1.27119	−	0.413036i
$560$		0			0
$561$	−730.327	−	13.5572i	−1.30183	−	0.0241662i
$562$	564.416	+	564.416i	1.00430	+	1.00430i
$563$	125.749	+	64.0726i	0.223356	+	0.113806i	0.562088	−	0.827077i	$-0.309998\pi$
$563$	125.749	+	64.0726i	0.223356	+	0.113806i	−0.338732	+	0.940883i	$0.609998\pi$
$564$	−533.277	+	733.993i	−0.945527	+	1.30141i
$565$		0			0
$566$	218.228	−	671.636i	0.385562	−	1.18664i
$567$	7.65555	−	3.90070i	0.0135019	−	0.00687954i
$568$	267.285	−	1687.57i	0.470571	−	2.97107i
$569$	−183.146	+	252.079i	−0.321874	+	0.443022i	−0.939038	−	0.343813i	$-0.888281\pi$
$569$	−183.146	+	252.079i	−0.321874	+	0.443022i	0.617164	+	0.786834i	$0.288281\pi$
$570$		0			0
$571$	81.2513			0.142296			0.0711482	−	0.997466i	$-0.477334\pi$
$571$	81.2513			0.142296			0.0711482	+	0.997466i	$0.477334\pi$
$572$	−983.759	+	1845.25i	−1.71986	+	3.22596i
$573$	−88.5617	+	88.5617i	−0.154558	+	0.154558i
$574$	22.5194	−	7.31699i	0.0392323	−	0.0127474i
$575$		0			0
$576$	−477.649	+	347.032i	−0.829251	+	0.602486i
$577$	988.752	−	503.794i	1.71361	−	0.873127i	0.732225	−	0.681063i	$-0.238482\pi$
$577$	988.752	−	503.794i	1.71361	−	0.873127i	0.981382	−	0.192064i	$-0.0615181\pi$
$578$	−967.080	−	1898.00i	−1.67315	−	3.28374i
$579$	−151.578	−	208.629i	−0.261793	−	0.360327i
$580$		0			0
$581$	−8.61830	−	26.5244i	−0.0148336	−	0.0456530i
$582$	−9.50300	−	9.50300i	−0.0163282	−	0.0163282i
$583$	220.203	+	452.756i	0.377708	+	0.776598i
$584$			1537.57i			2.63282i
$585$		0			0
$586$	345.487	+	251.011i	0.589568	+	0.428346i
$587$	872.285	+	138.156i	1.48601	+	0.235360i	0.846071	−	0.533070i	$-0.178962\pi$
$587$	872.285	+	138.156i	1.48601	+	0.235360i	0.639934	+	0.768430i	$0.278962\pi$
$588$	−525.073	−	1030.51i	−0.892982	−	1.75258i
$589$	−88.0381	−	28.6053i	−0.149470	−	0.0485659i
$590$		0			0
$591$	499.998	+	363.270i	0.846020	+	0.614669i
$592$	819.576	−	1608.51i	1.38442	−	2.71708i
$593$	203.778	−	203.778i	0.343640	−	0.343640i	−0.514094	−	0.857734i	$-0.671872\pi$
$593$	203.778	−	203.778i	0.343640	−	0.343640i	0.857734	+	0.514094i	$0.171872\pi$
$594$	−733.654	+	971.351i	−1.23511	+	1.63527i
$595$		0			0
$596$	−752.988	−	2317.46i	−1.26340	−	3.88835i
$597$	−11.9450	−	75.4179i	−0.0200084	−	0.126328i
$598$	−174.254	+	1100.20i	−0.291395	+	1.83980i
$599$	1046.83	+	340.135i	1.74763	+	0.567839i	0.995803	−	0.0915235i	$-0.0291737\pi$
$599$	1046.83	+	340.135i	1.74763	+	0.567839i	0.751825	+	0.659362i	$0.229174\pi$
$600$		0			0
$601$	−7.40130	+	5.37736i	−0.0123150	+	0.00894735i	−0.593926	−	0.804520i	$-0.702423\pi$
$601$	−7.40130	+	5.37736i	−0.0123150	+	0.00894735i	0.581611	+	0.813467i	$0.302423\pi$
$602$	6.48275	+	40.9305i	0.0107687	+	0.0679908i
$603$	247.641	+	126.179i	0.410681	+	0.209252i
$604$			1192.74i			1.97473i
$605$		0			0
$606$	504.039			0.831747
$607$	−107.816	+	211.600i	−0.177621	+	0.348600i	−0.962602	−	0.270919i	$-0.912672\pi$
$607$	−107.816	+	211.600i	−0.177621	+	0.348600i	0.784981	+	0.619519i	$0.212672\pi$
$608$	2043.97	−	323.733i	3.36179	−	0.532456i
$609$	−12.5541	−	17.2792i	−0.0206142	−	0.0283730i
$610$		0			0
$611$	−217.163	+	668.360i	−0.355423	+	1.09388i
$612$	−1141.48	−	180.793i	−1.86517	−	0.295413i
$613$	−308.840	+	48.9154i	−0.503817	+	0.0797967i	−0.403169	−	0.915125i	$-0.632091\pi$
$613$	−308.840	+	48.9154i	−0.503817	+	0.0797967i	−0.100647	+	0.994922i	$0.532091\pi$
$614$	−717.685	+	233.190i	−1.16887	+	0.379788i
$615$		0			0
$616$	−56.8930	−	42.9709i	−0.0923588	−	0.0697579i
$617$	468.934	+	468.934i	0.760022	+	0.760022i	0.976326	−	0.216304i	$-0.0694002\pi$
$617$	468.934	+	468.934i	0.760022	+	0.760022i	−0.216304	+	0.976326i	$0.569400\pi$
$618$	716.129	+	364.886i	1.15878	+	0.590430i
$619$	280.219	−	385.688i	0.452696	−	0.623083i	−0.520278	−	0.853997i	$-0.674172\pi$
$619$	280.219	−	385.688i	0.452696	−	0.623083i	0.972974	+	0.230914i	$0.0741716\pi$
$620$		0			0
$621$	−144.649	+	445.183i	−0.232929	+	0.716881i
$622$	−769.305	+	391.981i	−1.23683	+	0.630194i
$623$	−0.257778	+	1.62755i	−0.000413769	+	0.00261244i
$624$	1231.65	−	1695.22i	1.97379	−	2.71669i
$625$		0			0
$626$	−1001.31			−1.59954
$627$	496.834	−	241.641i	0.792399	−	0.385393i
$628$	−475.103	+	475.103i	−0.756533	+	0.756533i
$629$	996.240	−	323.698i	1.58385	−	0.514623i
$630$		0			0
$631$	554.825	−	403.104i	0.879279	−	0.638833i	−0.0537820	−	0.998553i	$-0.517128\pi$
$631$	554.825	−	403.104i	0.879279	−	0.638833i	0.933061	+	0.359719i	$0.117128\pi$
$632$	−593.268	+	302.285i	−0.938716	+	0.478300i
$633$	−175.530	−	344.497i	−0.277299	−	0.544229i
$634$	325.990	+	448.687i	0.514180	+	0.707709i
$635$		0			0
$636$	−334.328	−	1028.96i	−0.525673	−	1.61786i
$637$	−633.473	−	633.473i	−0.994463	−	0.994463i
$638$	1289.63	+	687.542i	2.02136	+	1.07765i
$639$		−	269.401i		−	0.421597i
$640$		0			0
$641$	133.478	+	96.9773i	0.208234	+	0.151291i	0.687014	−	0.726644i	$-0.258921\pi$
$641$	133.478	+	96.9773i	0.208234	+	0.151291i	−0.478781	+	0.877935i	$0.658921\pi$
$642$	−1229.36	−	194.712i	−1.91490	−	0.303290i
$643$	−50.5582	−	99.2260i	−0.0786286	−	0.154317i	0.848345	−	0.529444i	$-0.177599\pi$
$643$	−50.5582	−	99.2260i	−0.0786286	−	0.154317i	−0.926974	+	0.375126i	$0.877599\pi$
$644$	−42.4164	−	13.7819i	−0.0658640	−	0.0214005i
$645$		0			0
$646$	1974.11	+	1434.28i	3.05590	+	2.22024i
$647$	−356.766	+	700.193i	−0.551416	+	1.08221i	0.432173	+	0.901791i	$0.357747\pi$
$647$	−356.766	+	700.193i	−0.551416	+	1.08221i	−0.983589	+	0.180424i	$0.942253\pi$
$648$	549.174	−	549.174i	0.847490	−	0.847490i
$649$	−7.48645	+	403.294i	−0.0115354	+	0.621409i
$650$		0			0
$651$	−0.790540	−	2.43303i	−0.00121435	−	0.00373738i
$652$	−132.677	−	837.688i	−0.203492	−	1.28480i
$653$	−11.7418	+	74.1348i	−0.0179813	+	0.113530i	−0.995046	−	0.0994111i	$-0.968304\pi$
$653$	−11.7418	+	74.1348i	−0.0179813	+	0.113530i	0.977065	+	0.212941i	$0.0683041\pi$
$654$	1620.33	+	526.478i	2.47757	+	0.805012i
$655$		0			0
$656$	948.171	−	688.886i	1.44538	−	1.05013i
$657$	37.9248	+	239.448i	0.0577243	+	0.364457i
$658$	−34.7292	−	17.6954i	−0.0527799	−	0.0268927i
$659$		−	8.82858i		−	0.0133969i	−0.999978	−	0.00669847i	$-0.997868\pi$
$659$		−	8.82858i		−	0.0133969i	0.999978	−	0.00669847i	$-0.00213220\pi$
$660$		0			0
$661$	−18.3998			−0.0278363			−0.0139181	−	0.999903i	$-0.504430\pi$
$661$	−18.3998			−0.0278363			−0.0139181	+	0.999903i	$0.504430\pi$
$662$	938.305	−	1841.53i	1.41738	−	2.78176i
$663$	1200.89	−	190.202i	1.81129	−	0.286880i
$664$	−1481.79	−	2039.51i	−2.23161	−	3.07155i
$665$		0			0
$666$	160.632	−	494.375i	0.241189	−	0.742304i
$667$	555.070	+	87.9145i	0.832190	+	0.131806i
$668$	−553.539	+	87.6719i	−0.828651	+	0.131245i
$669$	341.551	−	110.977i	0.510540	−	0.165885i
$670$		0			0
$671$	−358.052	+	250.120i	−0.533610	+	0.372757i
$672$	40.4405	+	40.4405i	0.0601794	+	0.0601794i
$673$	57.8341	+	29.4680i	0.0859348	+	0.0437860i	0.496430	−	0.868077i	$-0.334644\pi$
$673$	57.8341	+	29.4680i	0.0859348	+	0.0437860i	−0.410495	+	0.911863i	$0.634644\pi$
$674$	−674.786	+	928.763i	−1.00117	+	1.37799i
$675$		0			0
$676$	533.382	−	1641.58i	0.789026	−	2.42837i
$677$	−1067.27	+	543.802i	−1.57647	+	0.803252i	−0.999905	−	0.0137987i	$-0.995608\pi$
$677$	−1067.27	+	543.802i	−1.57647	+	0.803252i	−0.576566	+	0.817051i	$0.695608\pi$
$678$	−181.942	+	1148.74i	−0.268351	+	1.69430i
$679$	0.244986	−	0.337194i	0.000360804	−	0.000496604i
$680$		0			0
$681$	−140.855			−0.206835
$682$	121.460	+	126.055i	0.178094	+	0.184832i
$683$	403.111	−	403.111i	0.590207	−	0.590207i	−0.347480	−	0.937687i	$-0.612963\pi$
$683$	403.111	−	403.111i	0.590207	−	0.590207i	0.937687	+	0.347480i	$0.112963\pi$
$684$	831.343	−	270.120i	1.21541	−	0.394912i
$685$		0			0
$686$	80.4560	−	58.4547i	0.117283	−	0.0852109i
$687$	919.600	−	468.560i	1.33857	−	0.682038i
$688$	931.220	+	1827.62i	1.35352	+	2.65643i
$689$	−492.582	−	677.981i	−0.714924	−	0.984008i
$690$		0			0
$691$	−229.306	−	705.732i	−0.331847	−	1.02132i	−0.968255	−	0.249966i	$-0.919580\pi$
$691$	−229.306	−	705.732i	−0.331847	−	1.02132i	0.636408	−	0.771353i	$-0.280420\pi$
$692$	200.581	+	200.581i	0.289857	+	0.289857i
$693$	−9.91995	−	5.28863i	−0.0143145	−	0.00763151i
$694$			1005.42i			1.44873i
$695$		0			0
$696$	−1561.90	−	1134.78i	−2.24410	−	1.63044i
$697$	671.682	+	106.384i	0.963676	+	0.152631i
$698$	942.113	+	1849.00i	1.34973	+	2.64900i
$699$	738.704	+	240.020i	1.05680	+	0.343376i
$700$		0			0
$701$	−710.832	−	516.450i	−1.01403	−	0.736733i	−0.0489764	−	0.998800i	$-0.515596\pi$
$701$	−710.832	−	516.450i	−1.01403	−	0.736733i	−0.965050	+	0.262067i	$0.915596\pi$
$702$	919.872	−	1805.35i	1.31036	−	2.57172i
$703$	−560.231	+	560.231i	−0.796915	+	0.796915i
$704$	−1608.37	−	555.800i	−2.28461	−	0.789488i
$705$		0			0
$706$	316.035	+	972.656i	0.447642	+	1.37770i
$707$	2.44536	+	15.4394i	0.00345878	+	0.0218379i
$708$	135.597	−	856.125i	0.191521	−	1.20922i
$709$	341.238	+	110.875i	0.481295	+	0.156382i	0.539608	−	0.841916i	$-0.318572\pi$
$709$	341.238	+	110.875i	0.481295	+	0.156382i	−0.0583137	+	0.998298i	$0.518572\pi$
$710$		0			0
$711$	−84.9347	+	61.7087i	−0.119458	+	0.0867914i
$712$	23.3010	+	147.117i	0.0327262	+	0.206625i
$713$	59.9770	+	30.5598i	0.0841193	+	0.0428609i
$714$			67.4360i			0.0944482i
$715$		0			0
$716$	−2512.16			−3.50861
$717$	−175.576	+	344.588i	−0.244876	+	0.480597i
$718$	−2489.34	+	394.273i	−3.46705	+	0.549127i
$719$	−113.787	−	156.615i	−0.158258	−	0.217823i	0.722524	−	0.691346i	$-0.242982\pi$
$719$	−113.787	−	156.615i	−0.158258	−	0.217823i	−0.880781	+	0.473523i	$0.842982\pi$
$720$		0			0
$721$	−7.70264	+	23.7063i	−0.0106833	+	0.0328797i
$722$	−470.676	−	74.5477i	−0.651906	−	0.103252i
$723$	471.153	−	74.6232i	0.651663	−	0.103213i
$724$	796.108	−	258.671i	1.09960	−	0.357281i
$725$		0			0
$726$	−1044.04	−	38.7747i	−1.43807	−	0.0534087i
$727$	783.477	+	783.477i	1.07768	+	1.07768i	0.996717	+	0.0809678i	$0.0258011\pi$
$727$	783.477	+	783.477i	1.07768	+	1.07768i	0.0809678	+	0.996717i	$0.474199\pi$
$728$	105.741	+	53.8779i	0.145249	+	0.0740081i
$729$	423.421	−	582.789i	0.580825	−	0.799437i
$730$		0			0
$731$	−367.793	+	1131.95i	−0.503136	+	1.54849i
$732$	836.270	−	426.101i	1.14245	−	0.582105i
$733$	94.7661	−	598.330i	0.129285	−	0.816275i	−0.834775	−	0.550591i	$-0.814402\pi$
$733$	94.7661	−	598.330i	0.129285	−	0.816275i	0.964060	−	0.265684i	$-0.0855977\pi$
$734$	−577.763	+	795.222i	−0.787142	+	1.08341i
$735$		0			0
$736$	−1504.85			−2.04464
$737$	110.609	+	793.399i	0.150080	+	1.07653i
$738$	238.628	−	238.628i	0.323344	−	0.323344i
$739$	−709.511	+	230.534i	−0.960096	+	0.311954i	−0.746811	−	0.665036i	$-0.768416\pi$
$739$	−709.511	+	230.534i	−0.960096	+	0.311954i	−0.213285	+	0.976990i	$0.568416\pi$
$740$		0			0
$741$	−743.986	+	540.537i	−1.00403	+	0.729470i
$742$	41.4143	−	21.1017i	0.0558145	−	0.0284389i
$743$	−200.657	−	393.811i	−0.270063	−	0.530028i	0.715651	−	0.698458i	$-0.246130\pi$
$743$	−200.657	−	393.811i	−0.270063	−	0.530028i	−0.985714	+	0.168430i	$0.946130\pi$
$744$	−135.922	−	187.080i	−0.182691	−	0.251452i
$745$		0			0
$746$	355.028	+	1092.66i	0.475908	+	1.46470i
$747$	−281.067	−	281.067i	−0.376262	−	0.376262i
$748$	−1456.91	−	2995.53i	−1.94774	−	4.00472i
$749$		−	38.6018i		−	0.0515377i
$750$		0			0
$751$	659.513	+	479.164i	0.878180	+	0.638035i	0.932769	−	0.360474i	$-0.117385\pi$
$751$	659.513	+	479.164i	0.878180	+	0.638035i	−0.0545897	+	0.998509i	$0.517385\pi$
$752$	−1905.52	−	301.804i	−2.53393	−	0.401335i
$753$	−60.4205	−	118.582i	−0.0802397	−	0.157479i
$754$	−2313.57	−	751.724i	−3.06840	−	0.996982i
$755$		0			0
$756$	65.6319	+	47.6844i	0.0868147	+	0.0630746i
$757$	73.1375	−	143.540i	0.0966150	−	0.189618i	−0.837641	−	0.546222i	$-0.816066\pi$
$757$	73.1375	−	143.540i	0.0966150	−	0.189618i	0.934256	+	0.356604i	$0.116066\pi$
$758$	−764.964	+	764.964i	−1.00919	+	1.00919i
$759$	−384.326	+	117.035i	−0.506358	+	0.154196i
$760$		0			0
$761$	114.014	+	350.898i	0.149821	+	0.461101i	0.997599	−	0.0692494i	$-0.0220604\pi$
$761$	114.014	+	350.898i	0.149821	+	0.461101i	−0.847779	+	0.530350i	$0.822060\pi$
$762$	94.8856	+	599.084i	0.124522	+	0.786199i
$763$	−8.26565	+	52.1872i	−0.0108331	+	0.0683974i
$764$	−543.194	−	176.494i	−0.710987	−	0.231014i
$765$		0			0
$766$	190.071	−	138.094i	0.248134	−	0.180280i
$767$	−105.031	−	663.143i	−0.136938	−	0.864593i
$768$	371.460	+	189.268i	0.483672	+	0.246443i
$769$			574.792i			0.747454i	0.927539	+	0.373727i	$0.121920\pi$
$769$			574.792i			0.747454i	−0.927539	+	0.373727i	$0.878080\pi$
$770$		0			0
$771$	380.193			0.493116
$772$	533.890	−	1047.82i	0.691567	−	1.35728i
$773$	−352.990	+	55.9081i	−0.456649	+	0.0723262i	−0.380522	−	0.924772i	$-0.624256\pi$
$773$	−352.990	+	55.9081i	−0.456649	+	0.0723262i	−0.0761275	+	0.997098i	$0.524256\pi$
$774$	347.161	+	477.827i	0.448529	+	0.617347i
$775$		0			0
$776$	11.6422	−	35.8309i	0.0150028	−	0.0461738i
$777$	−21.6262	−	3.42525i	−0.0278329	−	0.00440830i
$778$	216.134	−	34.2323i	0.277807	−	0.0440004i
$779$	−489.187	+	158.947i	−0.627968	+	0.204039i
$780$		0			0
$781$	636.547	−	444.665i	0.815040	−	0.569353i
$782$	−1254.70	−	1254.70i	−1.60447	−	1.60447i
$783$	−910.833	−	464.093i	−1.16326	−	0.592711i
$784$	1445.61	−	1989.71i	1.84389	−	2.53789i
$785$		0			0
$786$	45.3275	−	139.504i	0.0576686	−	0.177486i
$787$	1169.61	−	595.947i	1.48617	−	0.757239i	0.492575	−	0.870270i	$-0.336056\pi$
$787$	1169.61	−	595.947i	1.48617	−	0.757239i	0.993591	+	0.113031i	$0.0360559\pi$
$788$	−440.890	+	2783.67i	−0.559505	+	3.53258i
$789$	434.186	−	597.606i	0.550299	−	0.757421i
$790$		0			0
$791$	−36.0701			−0.0456006
$792$	−1000.52	−	177.562i	−1.26328	−	0.224194i
$793$	514.068	−	514.068i	0.648257	−	0.648257i
$794$	−1671.89	+	543.229i	−2.10565	+	0.684167i
$795$		0			0
$796$	281.708	−	204.673i	0.353905	−	0.257127i
$797$	392.129	−	199.800i	0.492007	−	0.250690i	−0.190341	−	0.981718i	$-0.560959\pi$
$797$	392.129	−	199.800i	0.492007	−	0.250690i	0.682347	+	0.731028i	$0.260959\pi$
$798$	−23.1560	−	45.4462i	−0.0290175	−	0.0569501i
$799$	−658.000	−	905.660i	−0.823530	−	1.13349i
$800$		0			0
$801$	7.25742	+	22.3361i	0.00906045	+	0.0278852i
$802$	1017.50	+	1017.50i	1.26870	+	1.26870i
$803$	−503.176	+	484.836i	−0.626621	+	0.603780i
$804$		−	1721.44i		−	2.14110i
$805$		0			0
$806$	−235.727	−	171.266i	−0.292466	−	0.212489i
$807$	−1057.36	−	167.469i	−1.31024	−	0.207521i
$808$	641.484	+	1258.98i	0.793916	+	1.55815i
$809$	−516.346	−	167.771i	−0.638252	−	0.207381i	−0.0280248	−	0.999607i	$-0.508922\pi$
$809$	−516.346	−	167.771i	−0.638252	−	0.207381i	−0.610227	+	0.792227i	$0.708922\pi$
$810$		0			0
$811$	−962.374	−	699.206i	−1.18665	−	0.862152i	−0.193745	−	0.981052i	$-0.562063\pi$
$811$	−962.374	−	699.206i	−1.18665	−	0.862152i	−0.992906	+	0.118900i	$0.962063\pi$
$812$	44.2181	−	86.7829i	0.0544558	−	0.106875i
$813$	−782.085	+	782.085i	−0.961975	+	0.961975i
$814$	1433.26	−	436.455i	1.76076	−	0.536185i
$815$		0			0
$816$	1031.46	+	3174.51i	1.26405	+	3.89033i
$817$	−140.824	−	889.130i	−0.172368	−	1.08829i
$818$	33.9265	−	214.204i	0.0414749	−	0.261862i
$819$	17.7962	+	5.78233i	0.0217292	+	0.00706024i
$820$		0			0
$821$	−107.913	+	78.4034i	−0.131441	+	0.0954975i	−0.651563	−	0.758594i	$-0.725886\pi$
$821$	−107.913	+	78.4034i	−0.131441	+	0.0954975i	0.520122	+	0.854092i	$0.325886\pi$
$822$	110.017	+	694.619i	0.133841	+	0.845036i
$823$	42.8055	+	21.8105i	0.0520115	+	0.0265012i	0.479803	−	0.877376i	$-0.340708\pi$
$823$	42.8055	+	21.8105i	0.0520115	+	0.0265012i	−0.427791	+	0.903878i	$0.640708\pi$
$824$			2253.13i			2.73438i
$825$		0			0
$826$	37.2389			0.0450834
$827$	−191.334	+	375.514i	−0.231359	+	0.454068i	−0.977276	−	0.211971i	$-0.932012\pi$
$827$	−191.334	+	375.514i	−0.231359	+	0.454068i	0.745917	+	0.666039i	$0.232012\pi$
$828$	−627.818	+	99.4366i	−0.758234	+	0.120092i
$829$	364.741	+	502.023i	0.439977	+	0.605576i	0.970207	−	0.242278i	$-0.0778944\pi$
$829$	364.741	+	502.023i	0.439977	+	0.605576i	−0.530230	+	0.847854i	$0.677894\pi$
$830$		0			0
$831$	113.667	−	349.831i	0.136783	−	0.420975i
$832$	2797.64	+	443.102i	3.36255	+	0.532575i
$833$	1409.50	−	223.244i	1.69208	−	0.268000i
$834$	−1000.95	+	325.227i	−1.20018	+	0.389961i
$835$		0			0
$836$	2010.44	+	1518.47i	2.40483	+	1.81635i
$837$	−86.5803	−	86.5803i	−0.103441	−	0.103441i
$838$	−2566.80	−	1307.85i	−3.06300	−	1.56068i
$839$	189.672	−	261.061i	0.226069	−	0.311157i	−0.680882	−	0.732393i	$-0.738404\pi$
$839$	189.672	−	261.061i	0.226069	−	0.311157i	0.906951	+	0.421236i	$0.138404\pi$
$840$		0			0
$841$	−119.376	+	367.401i	−0.141945	+	0.436862i
$842$	856.918	−	436.621i	1.01772	−	0.518553i
$843$	74.9623	−	473.293i	0.0889232	−	0.561439i
$844$	1036.36	−	1426.43i	1.22792	−	1.69008i
$845$		0			0
$846$	−555.520			−0.656643
$847$	−3.87745	−	32.1684i	−0.00457786	−	0.0379792i
$848$	1626.80	−	1626.80i	1.91840	−	1.91840i
$849$	−403.209	+	131.011i	−0.474922	+	0.154312i
$850$		0			0
$851$	466.101	−	338.642i	0.547710	−	0.397934i
$852$	−1486.72	+	757.524i	−1.74498	+	0.889113i
$853$	539.096	+	1058.03i	0.632000	+	1.24037i	0.955737	+	0.294222i	$0.0950606\pi$
$853$	539.096	+	1058.03i	0.632000	+	1.24037i	−0.323737	+	0.946147i	$0.604939\pi$
$854$	23.7008	+	32.6214i	0.0277527	+	0.0381984i
$855$		0			0
$856$	−1078.25	−	3318.50i	−1.25963	−	3.87676i
$857$	−352.891	−	352.891i	−0.411775	−	0.411775i	0.470582	−	0.882356i	$-0.344044\pi$
$857$	−352.891	−	352.891i	−0.411775	−	0.411775i	−0.882356	+	0.470582i	$0.844044\pi$
$858$	1722.36	−	240.117i	2.00742	−	0.279857i
$859$		−	479.820i		−	0.558580i	−0.960207	−	0.279290i	$-0.909901\pi$
$859$		−	479.820i		−	0.558580i	0.960207	−	0.279290i	$-0.0900990\pi$
$860$		0			0
$861$	−11.5002	−	8.35535i	−0.0133567	−	0.00970424i
$862$	−2487.42	−	393.969i	−2.88564	−	0.457040i
$863$	−414.755	−	814.002i	−0.480597	−	0.943224i	−0.996258	−	0.0864314i	$-0.972454\pi$
$863$	−414.755	−	814.002i	−0.480597	−	0.943224i	0.515661	−	0.856793i	$-0.327546\pi$
$864$	2603.34	+	845.876i	3.01312	+	0.979023i
$865$		0			0
$866$	−2008.72	−	1459.42i	−2.31954	−	1.68524i
$867$	−580.575	+	1139.44i	−0.669637	+	1.31424i
$868$	8.24925	−	8.24925i	0.00950374	−	0.00950374i
$869$	−285.997	−	98.8313i	−0.329111	−	0.113730i
$870$		0			0
$871$	−412.044	−	1268.14i	−0.473071	−	1.45596i
$872$	747.147	+	4717.30i	0.856820	+	5.40975i
$873$	0.929268	−	5.86717i	0.00106445	−	0.00672069i
$874$	1276.40	+	414.726i	1.46041	+	0.474515i
$875$		0			0
$876$	1214.79	−	882.595i	1.38674	−	1.00753i
$877$	186.351	+	1176.57i	0.212487	+	1.34159i	0.831201	+	0.555972i	$0.187654\pi$
$877$	186.351	+	1176.57i	0.212487	+	1.34159i	−0.618715	+	0.785616i	$0.712346\pi$
$878$	780.563	+	397.717i	0.889024	+	0.452981i
$879$		−	256.372i		−	0.291663i
$880$		0			0
$881$	720.309			0.817604			0.408802	−	0.912623i	$-0.365947\pi$
$881$	720.309			0.817604			0.408802	+	0.912623i	$0.365947\pi$
$882$	321.503	−	630.986i	0.364516	−	0.715403i
$883$	1507.09	−	238.699i	1.70678	−	0.270328i	0.774635	−	0.632408i	$-0.217933\pi$
$883$	1507.09	−	238.699i	1.70678	−	0.270328i	0.932147	+	0.362080i	$0.117933\pi$
$884$	3259.03	+	4485.67i	3.68669	+	5.07429i
$885$		0			0
$886$	−557.399	+	1715.50i	−0.629118	+	1.93623i
$887$	648.602	+	102.728i	0.731231	+	0.115816i	0.510937	−	0.859618i	$-0.329298\pi$
$887$	648.602	+	102.728i	0.731231	+	0.115816i	0.220294	+	0.975434i	$0.429298\pi$
$888$	−1954.83	+	309.614i	−2.20138	+	0.348665i
$889$	−17.8904	+	5.81295i	−0.0201242	+	0.00653875i
$890$		0			0
$891$	352.889	+	6.55075i	0.396059	+	0.00735214i
$892$	1158.04	+	1158.04i	1.29825	+	1.29825i
$893$	754.420	+	384.396i	0.844815	+	0.430455i
$894$	−1191.11	+	1639.43i	−1.33234	+	1.83381i
$895$		0			0
$896$	−17.4972	+	53.8507i	−0.0195281	+	0.0601012i
$897$	595.837	−	303.594i	0.664256	−	0.338455i
$898$	−82.7922	+	522.729i	−0.0921962	+	0.582104i
$899$	−86.4069	+	118.929i	−0.0961145	+	0.132290i
$900$		0			0
$901$	1334.95			1.48163
$902$	957.708	+	169.964i	1.06176	+	0.188430i
$903$	17.5917	−	17.5917i	0.0194814	−	0.0194814i
$904$	−3100.86	+	1007.53i	−3.43016	+	1.11453i
$905$		0			0
$906$	802.476	−	583.033i	0.885735	−	0.643524i
$907$	−1457.77	+	742.773i	−1.60725	+	0.818934i	−0.607552	+	0.794280i	$0.707848\pi$
$907$	−1457.77	+	742.773i	−1.60725	+	0.818934i	−0.999696	+	0.0246539i	$0.992152\pi$
$908$	−291.612	−	572.321i	−0.321159	−	0.630309i
$909$	130.953	+	180.241i	0.144063	+	0.198285i
$910$		0			0
$911$	−3.10080	−	9.54327i	−0.00340373	−	0.0104756i	0.949340	−	0.314250i	$-0.101753\pi$
$911$	−3.10080	−	9.54327i	−0.00340373	−	0.0104756i	−0.952744	+	0.303775i	$0.901753\pi$
$912$	−1785.17	−	1785.17i	−1.95743	−	1.95743i
$913$	200.192	−	1128.03i	0.219268	−	1.23553i
$914$		−	1275.21i		−	1.39519i
$915$		0			0
$916$	3807.71	+	2766.46i	4.15689	+	3.02015i
$917$	4.49310	+	0.711637i	0.00489978	+	0.000776049i
$918$	1465.32	+	2875.84i	1.59620	+	3.13273i
$919$	912.133	+	296.370i	0.992528	+	0.322492i	0.759876	−	0.650068i	$-0.225260\pi$
$919$	912.133	+	296.370i	0.992528	+	0.322492i	0.232652	+	0.972560i	$0.425260\pi$
$920$		0			0
$921$	366.506	+	266.282i	0.397944	+	0.289123i
$922$	495.922	−	973.302i	0.537876	−	1.05564i
$923$	−913.912	+	913.912i	−0.990154	+	0.990154i
$924$	−1.29229	+	69.6157i	−0.00139858	+	0.0753416i
$925$		0			0
$926$	14.2371	+	43.8174i	0.0153749	+	0.0473190i
$927$	55.5745	+	350.884i	0.0599509	+	0.378515i
$928$	514.106	−	3245.94i	0.553993	−	3.49778i
$929$	−1566.61	−	509.024i	−1.68634	−	0.547926i	−0.700218	−	0.713929i	$-0.746914\pi$
$929$	−1566.61	−	509.024i	−1.68634	−	0.547926i	−0.986125	+	0.166002i	$0.946914\pi$
$930$		0			0
$931$	−873.231	+	634.439i	−0.937949	+	0.681460i
$932$	554.095	+	3498.42i	0.594523	+	3.75367i
$933$	461.844	+	235.321i	0.495009	+	0.252220i
$934$		−	1569.85i		−	1.68079i
$935$		0			0
$936$	1691.41			1.80707
$937$	−110.409	+	216.690i	−0.117833	+	0.231259i	−0.942388	−	0.334522i	$-0.891425\pi$
$937$	−110.409	+	216.690i	−0.117833	+	0.231259i	0.824556	+	0.565781i	$0.191425\pi$
$938$	73.0451	−	11.5692i	0.0778733	−	0.0123339i
$939$	353.334	+	486.322i	0.376287	+	0.517915i
$940$		0			0
$941$	489.886	−	1507.72i	0.520602	−	1.60225i	−0.252251	−	0.967662i	$-0.581171\pi$
$941$	489.886	−	1507.72i	0.520602	−	1.60225i	0.772852	−	0.634586i	$-0.218829\pi$
$942$	551.889	+	87.4106i	0.585869	+	0.0927926i
$943$	369.427	−	58.5115i	0.391757	−	0.0620482i
$944$	1753.00	−	569.584i	1.85699	−	0.603373i
$945$		0			0
$946$	−556.007	+	1608.97i	−0.587745	+	1.70081i
$947$	−945.689	−	945.689i	−0.998615	−	0.998615i	0.00138355	−	0.999999i	$-0.499560\pi$
$947$	−945.689	−	945.689i	−0.998615	−	0.998615i	−0.999999	+	0.00138355i	$0.999560\pi$
$948$	579.375	+	295.206i	0.611155	+	0.311399i
$949$	683.645	−	940.957i	0.720385	−	0.991525i
$950$		0			0
$951$	102.888	−	316.657i	0.108189	−	0.332972i
$952$	−168.441	+	85.8251i	−0.176934	+	0.0901524i
$953$	47.1815	−	297.893i	0.0495084	−	0.312584i	−0.950490	−	0.310755i	$-0.899418\pi$
$953$	47.1815	−	297.893i	0.0495084	−	0.312584i	0.999998	−	0.00182850i	$-0.000582028\pi$
$954$	389.381	−	535.937i	0.408156	−	0.561779i
$955$		0			0
$956$	−1763.63			−1.84480
$957$	−121.144	−	868.965i	−0.126587	−	0.908010i
$958$	−101.831	+	101.831i	−0.106296	+	0.106296i
$959$	−20.7434	+	6.73994i	−0.0216302	+	0.00702809i
$960$		0			0
$961$	763.220	−	554.512i	0.794194	−	0.577016i
$962$	−2222.04	+	1132.18i	−2.30981	+	1.17691i
$963$	−249.770	−	490.201i	−0.259366	−	0.509035i
$964$	1278.64	+	1759.90i	1.32639	+	1.82562i
$965$		0			0
$966$	11.4614	+	35.2747i	0.0118648	+	0.0365162i
$967$	−695.911	−	695.911i	−0.719660	−	0.719660i	0.248876	−	0.968535i	$-0.419939\pi$
$967$	−695.911	−	695.911i	−0.719660	−	0.719660i	−0.968535	+	0.248876i	$0.919939\pi$
$968$	−1231.88	−	2657.13i	−1.27261	−	2.74497i
$969$		−	1464.91i		−	1.51177i
$970$		0			0
$971$	−740.809	−	538.229i	−0.762934	−	0.554304i	0.136875	−	0.990588i	$-0.456294\pi$
$971$	−740.809	−	538.229i	−0.762934	−	0.554304i	−0.899809	+	0.436284i	$0.856294\pi$
$972$	1943.93	+	307.888i	1.99992	+	0.316757i
$973$	−14.8183	−	29.0825i	−0.0152295	−	0.0298895i
$974$	166.753	+	54.1813i	0.171204	+	0.0556277i
$975$		0			0
$976$	1614.66	+	1173.12i	1.65437	+	1.20197i
$977$	−90.6052	+	177.823i	−0.0927381	+	0.182009i	−0.932716	−	0.360612i	$-0.882568\pi$
$977$	−90.6052	+	177.823i	−0.0927381	+	0.182009i	0.839978	+	0.542621i	$0.182568\pi$
$978$	−498.743	+	498.743i	−0.509962	+	0.509962i
$979$	−40.7973	+	54.0153i	−0.0416724	+	0.0551739i
$980$		0			0
$981$	232.709	+	716.204i	0.237216	+	0.730076i
$982$	−549.371	−	3468.59i	−0.559441	−	3.53217i
$983$	255.639	−	1614.04i	0.260060	−	1.64196i	−0.419080	−	0.907949i	$-0.637647\pi$
$983$	255.639	−	1614.04i	0.260060	−	1.64196i	0.679141	−	0.734008i	$-0.262353\pi$
$984$	−1222.03	−	397.061i	−1.24190	−	0.403517i
$985$		0			0
$986$	3135.00	−	2277.71i	3.17951	−	2.31005i
$987$	3.66051	+	23.1116i	0.00370873	+	0.0234160i
$988$	−3736.59	−	1903.89i	−3.78197	−	1.92701i
$989$			654.614i			0.661895i
$990$		0			0
$991$	−935.782			−0.944281			−0.472141	−	0.881523i	$-0.656519\pi$
$991$	−935.782			−0.944281			−0.472141	+	0.881523i	$0.656519\pi$
$992$	178.708	−	350.733i	0.180149	−	0.353562i
$993$	−1225.50	+	194.100i	−1.23414	+	0.195468i
$994$	−42.1355	−	57.9945i	−0.0423898	−	0.0583445i
$995$		0			0
$996$	−760.780	+	2341.44i	−0.763835	+	2.35084i
$997$	−1426.04	−	225.862i	−1.43033	−	0.226542i	−0.607269	−	0.794496i	$-0.707735\pi$
$997$	−1426.04	−	225.862i	−1.43033	−	0.226542i	−0.823060	+	0.567955i	$0.807735\pi$
$998$	−2082.97	+	329.910i	−2.08714	+	0.330571i
$999$	−996.687	+	323.843i	−0.997684	+	0.324167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.bk.c.82.16	yes	128
5.2	odd	4	inner	275.3.bk.c.93.16	yes	128
5.3	odd	4	inner	275.3.bk.c.93.1	yes	128
5.4	even	2	inner	275.3.bk.c.82.1	✓	128
11.9	even	5	inner	275.3.bk.c.207.1	yes	128
55.9	even	10	inner	275.3.bk.c.207.16	yes	128
55.42	odd	20	inner	275.3.bk.c.218.1	yes	128
55.53	odd	20	inner	275.3.bk.c.218.16	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.bk.c.82.1	✓	128	5.4	even	2	inner
275.3.bk.c.82.16	yes	128	1.1	even	1	trivial
275.3.bk.c.93.1	yes	128	5.3	odd	4	inner
275.3.bk.c.93.16	yes	128	5.2	odd	4	inner
275.3.bk.c.207.1	yes	128	11.9	even	5	inner
275.3.bk.c.207.16	yes	128	55.9	even	10	inner
275.3.bk.c.218.1	yes	128	55.42	odd	20	inner
275.3.bk.c.218.16	yes	128	55.53	odd	20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72172 - 3.37907i) q^{2} +(-2.24871 + 0.356160i) q^{3} +(-6.10266 - 8.39959i) q^{4} +(-2.66816 + 8.21175i) q^{6} +(-0.264482 - 0.0418898i) q^{7} +(-23.9070 + 3.78649i) q^{8} +(-3.62968 + 1.17935i) q^{9} +(-8.77765 - 6.62969i) q^{11} +(16.7147 + 16.7147i) q^{12} +(16.3141 + 8.31246i) q^{13} +(-0.596913 + 0.821581i) q^{14} +(-15.5330 + 47.8055i) q^{16} +(-25.9877 + 13.2414i) q^{17} +(-2.26418 + 14.2955i) q^{18} +(12.9667 - 17.8472i) q^{19} +0.609661 q^{21} +(-37.5149 + 18.2458i) q^{22} +(-11.3432 + 11.3432i) q^{23} +(52.4112 - 17.0294i) q^{24} +(56.1768 - 40.8148i) q^{26} +(25.9993 - 13.2473i) q^{27} +(1.26219 + 2.47718i) q^{28} +(-20.5919 - 28.3423i) q^{29} +(-1.29669 - 3.99079i) q^{31} +(66.3328 + 66.3328i) q^{32} +(22.0996 + 11.7820i) q^{33} +110.612i q^{34} +(32.0568 + 23.2906i) q^{36} +(-35.4724 - 5.61828i) q^{37} +(-37.9817 - 74.5433i) q^{38} +(-39.6462 - 12.8818i) q^{39} +(-18.8632 - 13.7049i) q^{41} +(1.04967 - 2.06009i) q^{42} +(28.8549 - 28.8549i) q^{43} +(-2.11969 + 114.187i) q^{44} +(18.7997 + 57.8594i) q^{46} +(6.00418 + 37.9089i) q^{47} +(17.9026 - 113.033i) q^{48} +(-46.5336 - 15.1197i) q^{49} +(53.7226 - 39.0317i) q^{51} +(-29.7383 - 187.760i) q^{52} +(-40.7810 - 20.7790i) q^{53} -110.662i q^{54} +6.48158 q^{56} +(-22.8019 + 44.7512i) q^{57} +(-131.224 + 20.7838i) q^{58} +(-21.5538 - 29.6662i) q^{59} +(12.2697 - 37.7623i) q^{61} +(-15.7177 - 2.48944i) q^{62} +(1.00939 - 0.159871i) q^{63} +(147.128 - 47.8048i) q^{64} +(77.8616 - 54.3908i) q^{66} +(-51.4949 - 51.4949i) q^{67} +(269.816 + 137.478i) q^{68} +(21.4676 - 29.5476i) q^{69} +(-21.8132 + 67.1340i) q^{71} +(82.3091 - 41.9386i) q^{72} +(9.93715 - 62.7407i) q^{73} +(-80.0583 + 110.191i) q^{74} -229.040 q^{76} +(2.04381 + 2.12113i) q^{77} +(-111.789 + 111.789i) q^{78} +(26.1620 - 8.50056i) q^{79} +(-25.9584 + 18.8599i) q^{81} +(-78.7870 + 40.1440i) q^{82} +(47.2836 + 92.7992i) q^{83} +(-3.72056 - 5.12090i) q^{84} +(-47.8226 - 147.183i) q^{86} +(56.3994 + 56.3994i) q^{87} +(234.951 + 125.259i) q^{88} -6.15373i q^{89} +(-3.96658 - 2.88189i) q^{91} +(164.502 + 26.0546i) q^{92} +(4.33723 + 8.51229i) q^{93} +(138.434 + 44.9801i) q^{94} +(-172.788 - 125.538i) q^{96} +(-0.706632 + 1.38684i) q^{97} +(-131.208 + 131.208i) q^{98} +(39.6788 + 13.7117i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 48 q^{6} + 32 q^{11} + 280 q^{16} - 8 q^{21} + 528 q^{26} - 16 q^{31} + 336 q^{36} - 604 q^{41} - 1152 q^{46} - 1024 q^{51} - 992 q^{56} - 320 q^{61} + 1624 q^{66} + 536 q^{71} + 1776 q^{76} + 3680 q^{81}+ \cdots - 6584 q^{96}+O(q^{100}) \) 128 * q - 48 * q^6 + 32 * q^11 + 280 * q^16 - 8 * q^21 + 528 * q^26 - 16 * q^31 + 336 * q^36 - 604 * q^41 - 1152 * q^46 - 1024 * q^51 - 992 * q^56 - 320 * q^61 + 1624 * q^66 + 536 * q^71 + 1776 * q^76 + 3680 * q^81 + 872 * q^86 - 448 * q^91 - 6584 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

Properties

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