LMFDB - Embedded newform 275.3.bk.c.82.1

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			82.1
Character	$\chi$	$=$	275.82
Dual form			275.3.bk.c.218.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.72172 + 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	$0.547004\pi$
$2$	−1.72172	+	3.37907i	−0.860862	+	1.68954i	−0.713732	+	0.700419i	$0.752996\pi$
$3$	2.24871	−	0.356160i	0.749569	−	0.118720i	0.230050	−	0.973179i	$-0.426111\pi$
$3$	2.24871	−	0.356160i	0.749569	−	0.118720i	0.519519	+	0.854459i	$0.326111\pi$
$4$	−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	0.175297	−	0.984516i	$-0.443911\pi$
$7$	0.264482	+	0.0418898i	0.0377831	+	0.00598426i	−0.137514	+	0.990500i	$0.543911\pi$
$8$	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	−0.305142	−	0.952307i	$-0.598704\pi$
$13$	−16.3141	−	8.31246i	−1.25493	−	0.639420i	−0.949790	+	0.312887i	$0.898704\pi$
$14$	−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	0.531032	−	0.847352i	$-0.321804\pi$
$17$	25.9877	−	13.2414i	1.52869	−	0.778905i	0.997655	+	0.0684472i	$0.0218045\pi$
$18$	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	−0.416124	−	0.909308i	$-0.636612\pi$
$23$	11.3432	−	11.3432i	0.493183	−	0.493183i	0.909308	+	0.416124i	$0.136612\pi$
$24$	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	0.616133	−	0.787642i	$-0.288699\pi$
$37$	35.4724	+	5.61828i	0.958715	+	0.151845i	0.342582	+	0.939488i	$0.388699\pi$
$38$	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	−0.957957	−	0.286913i	$-0.907371\pi$
$43$	−28.8549	+	28.8549i	−0.671043	+	0.671043i	0.286913	+	0.957957i	$0.407371\pi$
$44$	−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	$-0.916117\pi$
$47$	−6.00418	−	37.9089i	−0.127748	−	0.806572i	0.837729	−	0.546086i	$-0.183883\pi$
$48$	−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	0.794215	−	0.607637i	$-0.207883\pi$
$53$	40.7810	+	20.7790i	0.769454	+	0.392056i	−0.0247612	+	0.999693i	$0.507883\pi$
$54$		−	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	0.977856	−	0.209277i	$-0.0671109\pi$
$67$	51.4949	+	51.4949i	0.768580	+	0.768580i	−0.209277	+	0.977856i	$0.567111\pi$
$68$	−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	$0.193283\pi$
$73$	−9.93715	+	62.7407i	−0.136125	+	0.859462i	−0.957366	+	0.288879i	$0.906717\pi$
$74$	−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	$-0.934113\pi$
$83$	−47.2836	−	92.7992i	−0.569682	−	1.11806i	0.408972	−	0.912547i	$-0.365887\pi$
$84$	−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	−0.887335	−	0.461125i	$-0.847446\pi$
$97$	0.706632	−	1.38684i	0.00728486	−	0.0142973i	0.894620	+	0.446827i	$0.147446\pi$
$98$	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	$0.199243\pi$
$103$	−14.5617	+	91.9393i	−0.141376	+	0.892614i	−0.951789	+	0.306754i	$0.900757\pi$
$104$	−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	$-0.814737\pi$
$107$	−22.5509	−	142.381i	−0.210756	−	1.33066i	0.624597	−	0.780947i	$-0.285263\pi$
$108$	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	−0.714297	−	0.699843i	$-0.753253\pi$
$113$	−133.043	+	21.0719i	−1.17737	+	0.186477i	−0.463073	+	0.886320i	$0.653253\pi$
$114$	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	−0.682707	−	0.730692i	$-0.739198\pi$
$127$	−62.5920	+	31.8922i	−0.492851	+	0.251120i	0.189857	+	0.981812i	$0.439198\pi$
$128$	−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	−0.698335	−	0.715771i	$-0.746075\pi$
$137$	−72.5736	+	36.9781i	−0.529734	+	0.269913i	0.168600	+	0.985684i	$0.446075\pi$
$138$	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	$0.0160764\pi$
$157$	10.1236	+	63.9179i	0.0644815	+	0.407120i	−0.934243	+	0.356636i	$0.883924\pi$
$158$	−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	0.216239	−	0.976340i	$-0.430621\pi$
$163$	−72.7852	−	37.0859i	−0.446535	−	0.227521i	−0.662774	+	0.748820i	$0.730621\pi$
$164$			242.079i			1.47609i
$165$		0			0
$166$	394.985			2.37942
$167$	−24.5061	+	48.0959i	−0.146743	+	0.288000i	−0.952665	−	0.304022i	$-0.901670\pi$
$167$	−24.5061	+	48.0959i	−0.146743	+	0.288000i	0.805922	+	0.592022i	$0.201670\pi$
$168$	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	−0.0779542	−	0.996957i	$-0.524839\pi$
$173$	26.9852	−	4.27403i	0.155984	−	0.0247054i	0.233938	+	0.972252i	$0.424839\pi$
$174$	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	0.718564	−	0.695461i	$-0.244800\pi$
$193$	−51.4223	−	100.922i	−0.266437	−	0.522911i	−0.985001	+	0.172549i	$0.944800\pi$
$194$	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	0.999679	−	0.0253260i	$-0.00806237\pi$
$197$	191.948	+	191.948i	0.974353	+	0.974353i	−0.0253260	+	0.999679i	$0.508062\pi$
$198$	−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	0.202995	−	0.979180i	$-0.434932\pi$
$223$	155.796	−	24.6757i	0.698638	−	0.110653i	0.495643	+	0.868526i	$0.334932\pi$
$224$	−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	0.0203822	−	0.999792i	$-0.493512\pi$
$227$	−61.1052	−	9.67811i	−0.269186	−	0.0426349i	−0.289568	+	0.957157i	$0.593512\pi$
$228$	−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	0.961560	−	0.274596i	$-0.0885442\pi$
$233$	303.971	+	154.881i	1.30460	+	0.664725i	0.343037	+	0.939322i	$0.388544\pi$
$234$	−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	0.468832	−	0.883287i	$-0.344675\pi$
$257$	164.934	+	26.1230i	0.641767	+	0.101646i	0.172935	+	0.984933i	$0.444675\pi$
$258$	−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	−0.120409	−	0.992724i	$-0.538421\pi$
$263$	229.419	−	229.419i	0.872315	−	0.872315i	0.992724	+	0.120409i	$0.0384206\pi$
$264$	−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	−0.719880	−	0.694099i	$-0.755803\pi$
$277$	73.3475	−	143.953i	0.264792	−	0.519685i	0.984672	+	0.174414i	$0.0558031\pi$
$278$	−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	−0.472674	−	0.881237i	$-0.656711\pi$
$283$	−183.921	+	29.1302i	−0.649897	+	0.102934i	−0.177223	+	0.984171i	$0.556711\pi$
$284$	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	$-0.888451\pi$
$293$	17.6153	−	111.219i	0.0601205	−	0.379586i	0.999342	−	0.0362737i	$-0.0115488\pi$
$294$	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	0.898100	−	0.439792i	$-0.144948\pi$
$307$	140.701	+	140.701i	0.458308	+	0.458308i	−0.439792	+	0.898100i	$0.644948\pi$
$308$	−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	0.999358	−	0.0358309i	$-0.0114078\pi$
$313$	119.867	+	235.253i	0.382962	+	0.751606i	−0.616396	+	0.787437i	$0.711408\pi$
$314$	−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	−0.762260	−	0.647271i	$-0.775910\pi$
$317$	66.3921	−	130.302i	0.209439	−	0.411047i	0.971698	+	0.236225i	$0.0759101\pi$
$318$	−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	0.583368	−	0.812208i	$-0.301735\pi$
$337$	298.986	+	47.3547i	0.887198	+	0.140518i	0.303830	+	0.952726i	$0.401735\pi$
$338$	−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	−0.0791889	−	0.996860i	$-0.525233\pi$
$347$	236.217	−	120.359i	0.680741	−	0.346855i	0.759930	+	0.650005i	$0.225233\pi$
$348$	−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	−0.383395	−	0.923585i	$-0.625245\pi$
$353$	190.687	−	190.687i	0.540190	−	0.540190i	0.923585	+	0.383395i	$0.125245\pi$
$354$	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	0.495126	−	0.868821i	$-0.335122\pi$
$367$	255.996	+	40.5459i	0.697538	+	0.110479i	0.202412	+	0.979300i	$0.435122\pi$
$368$	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	−0.359027	−	0.933327i	$-0.616891\pi$
$373$	214.214	−	214.214i	0.574301	−	0.574301i	0.933327	+	0.359027i	$0.116891\pi$
$374$	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	0.380444	−	0.924804i	$-0.375771\pi$
$383$	−55.1978	−	28.1247i	−0.144119	−	0.0734325i	−0.524563	+	0.851372i	$0.675771\pi$
$384$			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	0.986907	−	0.161290i	$-0.0515656\pi$
$397$	327.770	+	327.770i	0.825617	+	0.825617i	−0.161290	+	0.986907i	$0.551566\pi$
$398$	−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	$0.322854\pi$
$433$	−102.418	+	646.644i	−0.236532	+	1.49340i	−0.764768	+	0.644306i	$0.777146\pi$
$434$	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	0.398234	−	0.917284i	$-0.369623\pi$
$443$	469.772	−	74.4046i	1.06043	−	0.167956i	0.662199	+	0.749328i	$0.269623\pi$
$444$	−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	−0.749944	−	0.661501i	$-0.769920\pi$
$457$	−299.602	+	152.655i	−0.655584	+	0.334037i	0.0943600	+	0.995538i	$0.469920\pi$
$458$	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	−0.697769	−	0.716323i	$-0.745824\pi$
$463$	8.59030	−	8.59030i	0.0185536	−	0.0185536i	0.716323	+	0.697769i	$0.245824\pi$
$464$	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	−0.801859	−	0.597513i	$-0.796155\pi$
$467$	−368.828	+	187.927i	−0.789781	+	0.402414i	0.0120776	+	0.999927i	$0.496155\pi$
$468$	−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	0.979150	−	0.203141i	$-0.0651149\pi$
$487$	−7.23241	−	45.6636i	−0.0148509	−	0.0937652i	−0.994000	+	0.109376i	$0.965115\pi$
$488$	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	0.510271	−	0.860013i	$-0.329545\pi$
$503$	634.447	−	100.487i	1.26133	−	0.199775i	0.751056	+	0.660239i	$0.229545\pi$
$504$	−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	$-0.973761\pi$
$523$	−249.695	−	490.055i	−0.477429	−	0.937007i	0.519175	−	0.854668i	$-0.326239\pi$
$524$	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	0.961743	−	0.273955i	$-0.0883319\pi$
$547$	−20.5594	−	129.807i	−0.0375857	−	0.237307i	−0.999328	+	0.0366482i	$0.988332\pi$
$548$	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	0.448410	−	0.893828i	$-0.351990\pi$
$557$	333.457	+	52.8144i	0.598666	+	0.0948193i	0.150256	+	0.988647i	$0.451990\pi$
$558$	−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	0.338732	−	0.940883i	$-0.390002\pi$
$563$	−125.749	−	64.0726i	−0.223356	−	0.113806i	−0.562088	+	0.827077i	$0.690002\pi$
$564$	−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	$0.761518\pi$
$577$	−988.752	+	503.794i	−1.71361	+	0.873127i	−0.981382	+	0.192064i	$0.938482\pi$
$578$	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	−0.639934	−	0.768430i	$-0.721038\pi$
$587$	−872.285	−	138.156i	−1.48601	−	0.235360i	−0.846071	+	0.533070i	$0.821038\pi$
$588$	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	−0.857734	−	0.514094i	$-0.828128\pi$
$593$	−203.778	+	203.778i	−0.343640	+	0.343640i	0.514094	+	0.857734i	$0.328128\pi$
$594$	−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	−0.784981	−	0.619519i	$-0.787328\pi$
$607$	107.816	−	211.600i	0.177621	−	0.348600i	0.962602	+	0.270919i	$0.0873276\pi$
$608$	−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	0.100647	−	0.994922i	$-0.467909\pi$
$613$	308.840	−	48.9154i	0.503817	−	0.0797967i	0.403169	+	0.915125i	$0.367909\pi$
$614$	−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	0.216304	−	0.976326i	$-0.430600\pi$
$617$	−468.934	−	468.934i	−0.760022	−	0.760022i	−0.976326	+	0.216304i	$0.930600\pi$
$618$	−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	0.926974	−	0.375126i	$-0.122401\pi$
$643$	50.5582	+	99.2260i	0.0786286	+	0.154317i	−0.848345	+	0.529444i	$0.822401\pi$
$644$	−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	$-0.642253\pi$
$647$	356.766	−	700.193i	0.551416	−	1.08221i	0.983589	−	0.180424i	$-0.0577469\pi$
$648$	−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	−0.977065	−	0.212941i	$-0.931696\pi$
$653$	11.7418	−	74.1348i	0.0179813	−	0.113530i	0.995046	+	0.0994111i	$0.0316959\pi$
$654$	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	0.410495	−	0.911863i	$-0.365356\pi$
$673$	−57.8341	−	29.4680i	−0.0859348	−	0.0437860i	−0.496430	+	0.868077i	$0.665356\pi$
$674$	−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	0.576566	−	0.817051i	$-0.304392\pi$
$677$	1067.27	−	543.802i	1.57647	−	0.803252i	0.999905	+	0.0137987i	$0.00439240\pi$
$678$	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	−0.937687	−	0.347480i	$-0.887037\pi$
$683$	−403.111	+	403.111i	−0.590207	+	0.590207i	0.347480	+	0.937687i	$0.387037\pi$
$684$	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	$-0.974199\pi$
$727$	−783.477	−	783.477i	−1.07768	−	1.07768i	−0.0809678	−	0.996717i	$-0.525801\pi$
$728$	−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	$0.185598\pi$
$733$	−94.7661	+	598.330i	−0.129285	+	0.816275i	−0.964060	+	0.265684i	$0.914402\pi$
$734$	−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	0.985714	−	0.168430i	$-0.0538698\pi$
$743$	200.657	+	393.811i	0.270063	+	0.530028i	−0.715651	+	0.698458i	$0.753870\pi$
$744$	−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	−0.934256	−	0.356604i	$-0.883934\pi$
$757$	−73.1375	+	143.540i	−0.0966150	+	0.189618i	0.837641	+	0.546222i	$0.183934\pi$
$758$	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	0.0761275	−	0.997098i	$-0.475744\pi$
$773$	352.990	−	55.9081i	0.456649	−	0.0723262i	0.380522	+	0.924772i	$0.375744\pi$
$774$	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	−0.993591	−	0.113031i	$-0.963944\pi$
$787$	−1169.61	+	595.947i	−1.48617	+	0.757239i	−0.492575	+	0.870270i	$0.663944\pi$
$788$	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	−0.682347	−	0.731028i	$-0.739041\pi$
$797$	−392.129	+	199.800i	−0.492007	+	0.250690i	0.190341	+	0.981718i	$0.439041\pi$
$798$	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	0.427791	−	0.903878i	$-0.359292\pi$
$823$	−42.8055	−	21.8105i	−0.0520115	−	0.0265012i	−0.479803	+	0.877376i	$0.659292\pi$
$824$			2253.13i			2.73438i
$825$		0			0
$826$	37.2389			0.0450834
$827$	191.334	−	375.514i	0.231359	−	0.454068i	−0.745917	−	0.666039i	$-0.767988\pi$
$827$	191.334	−	375.514i	0.231359	−	0.454068i	0.977276	+	0.211971i	$0.0679883\pi$
$828$	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	$-0.904939\pi$
$853$	−539.096	−	1058.03i	−0.632000	−	1.24037i	0.323737	−	0.946147i	$-0.395061\pi$
$854$	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	0.882356	−	0.470582i	$-0.155956\pi$
$857$	352.891	+	352.891i	0.411775	+	0.411775i	−0.470582	+	0.882356i	$0.655956\pi$
$858$	−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	$0.0275463\pi$
$863$	414.755	+	814.002i	0.480597	+	0.943224i	−0.515661	+	0.856793i	$0.672454\pi$
$864$	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	$-0.812346\pi$
$877$	−186.351	−	1176.57i	−0.212487	−	1.34159i	0.618715	−	0.785616i	$-0.287654\pi$
$878$	−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	−0.932147	−	0.362080i	$-0.882067\pi$
$883$	−1507.09	+	238.699i	−1.70678	+	0.270328i	−0.774635	+	0.632408i	$0.782067\pi$
$884$	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	−0.220294	−	0.975434i	$-0.570702\pi$
$887$	−648.602	−	102.728i	−0.731231	−	0.115816i	−0.510937	+	0.859618i	$0.670702\pi$
$888$	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	$-0.292152\pi$
$907$	1457.77	−	742.773i	1.60725	−	0.818934i	0.999696	−	0.0246539i	$-0.00784839\pi$
$908$	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	−0.824556	−	0.565781i	$-0.808575\pi$
$937$	110.409	−	216.690i	0.117833	−	0.231259i	0.942388	+	0.334522i	$0.108575\pi$
$938$	−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	0.999999	−	0.00138355i	$-0.000440398\pi$
$947$	945.689	+	945.689i	0.998615	+	0.998615i	−0.00138355	+	0.999999i	$0.500440\pi$
$948$	−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	$0.100582\pi$
$953$	−47.1815	+	297.893i	−0.0495084	+	0.312584i	−0.999998	+	0.00182850i	$0.999418\pi$
$954$	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	0.968535	−	0.248876i	$-0.0800611\pi$
$967$	695.911	+	695.911i	0.719660	+	0.719660i	−0.248876	+	0.968535i	$0.580061\pi$
$968$	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	−0.839978	−	0.542621i	$-0.817432\pi$
$977$	90.6052	−	177.823i	0.0927381	−	0.182009i	0.932716	+	0.360612i	$0.117432\pi$
$978$	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	$0.362353\pi$
$983$	−255.639	+	1614.04i	−0.260060	+	1.64196i	−0.679141	+	0.734008i	$0.737647\pi$
$984$	−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	0.823060	−	0.567955i	$-0.192265\pi$
$997$	1426.04	+	225.862i	1.43033	+	0.226542i	0.607269	+	0.794496i	$0.292265\pi$
$998$	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.82.1	✓	128
5.2	odd	4	inner	275.3.bk.c.93.1	yes	128
5.3	odd	4	inner	275.3.bk.c.93.16	yes	128
5.4	even	2	inner	275.3.bk.c.82.16	yes	128
11.9	even	5	inner	275.3.bk.c.207.16	yes	128
55.9	even	10	inner	275.3.bk.c.207.1	yes	128
55.42	odd	20	inner	275.3.bk.c.218.16	yes	128
55.53	odd	20	inner	275.3.bk.c.218.1	yes	128

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

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Database

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