LMFDB - Embedded newform 275.2.z.c.174.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(49,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.z (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			174.8
Character	$\chi$	$=$	275.174
Dual form			275.2.z.c.49.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.63006 + 0.854560i) q^{2} +(-0.964848 - 1.32800i) q^{3} +(4.56893 + 3.31953i) q^{4} +(-1.40276 - 4.31724i) q^{6} +(-1.11557 + 1.53545i) q^{7} +(5.92892 + 8.16046i) q^{8} +(0.0944009 - 0.290536i) q^{9} +(0.102720 - 3.31503i) q^{11} -9.27038i q^{12} +(-1.96439 - 0.638270i) q^{13} +(-4.24616 + 3.08501i) q^{14} +(5.12949 + 15.7870i) q^{16} +(-3.44822 + 1.12040i) q^{17} +(0.496561 - 0.683457i) q^{18} +(-1.03575 + 0.752517i) q^{19} +3.11543 q^{21} +(3.10305 - 8.63097i) q^{22} -3.36725i q^{23} +(5.11658 - 15.7472i) q^{24} +(-4.62104 - 3.35738i) q^{26} +(-5.16038 + 1.67671i) q^{27} +(-10.1939 + 3.31221i) q^{28} +(0.910336 + 0.661398i) q^{29} +(1.42251 - 4.37805i) q^{31} +25.7304i q^{32} +(-4.50147 + 3.06209i) q^{33} -10.0265 q^{34} +(1.39575 - 1.01407i) q^{36} +(-1.05926 + 1.45794i) q^{37} +(-3.36716 + 1.09406i) q^{38} +(1.04772 + 3.22455i) q^{39} +(-3.73360 + 2.71262i) q^{41} +(8.19379 + 2.66232i) q^{42} +0.0110430i q^{43} +(11.4737 - 14.8052i) q^{44} +(2.87752 - 8.85610i) q^{46} +(-5.42297 - 7.46408i) q^{47} +(16.0159 - 22.0440i) q^{48} +(1.05001 + 3.23159i) q^{49} +(4.81489 + 3.49822i) q^{51} +(-6.85643 - 9.43707i) q^{52} +(6.22368 + 2.02220i) q^{53} -15.0050 q^{54} -19.1441 q^{56} +(1.99868 + 0.649412i) q^{57} +(1.82904 + 2.51746i) q^{58} +(4.43142 + 3.21961i) q^{59} +(2.27166 + 6.99144i) q^{61} +(7.48261 - 10.2989i) q^{62} +(0.340793 + 0.469061i) q^{63} +(-11.7292 + 36.0987i) q^{64} +(-14.4559 + 4.20672i) q^{66} +7.01002i q^{67} +(-19.4739 - 6.32745i) q^{68} +(-4.47171 + 3.24889i) q^{69} +(-3.68735 - 11.3485i) q^{71} +(2.93060 - 0.952211i) q^{72} +(1.77865 - 2.44810i) q^{73} +(-4.03181 + 2.92928i) q^{74} -7.23028 q^{76} +(4.97548 + 3.85587i) q^{77} +9.37610i q^{78} +(1.89180 - 5.82235i) q^{79} +(6.46422 + 4.69653i) q^{81} +(-12.1377 + 3.94377i) q^{82} +(13.9332 - 4.52716i) q^{83} +(14.2342 + 10.3418i) q^{84} +(-0.00943687 + 0.0290437i) q^{86} -1.84707i q^{87} +(27.6612 - 18.8163i) q^{88} +13.8156 q^{89} +(3.17145 - 2.30419i) q^{91} +(11.1777 - 15.3848i) q^{92} +(-7.18656 + 2.33505i) q^{93} +(-7.88426 - 24.2653i) q^{94} +(34.1699 - 24.8259i) q^{96} +(16.4571 + 5.34722i) q^{97} +9.39658i q^{98} +(-0.953440 - 0.342786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{4} - 6 q^{6} - 16 q^{9} - 10 q^{11} - 6 q^{14} - 8 q^{16} + 26 q^{19} + 20 q^{21} + 86 q^{24} - 68 q^{26} + 22 q^{29} - 20 q^{31} - 40 q^{34} + 6 q^{36} - 6 q^{39} + 50 q^{41} + 2 q^{44} + 80 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) $ 32 * q + 4 * q^4 - 6 * q^6 - 16 * q^9 - 10 * q^11 - 6 * q^14 - 8 * q^16 + 26 * q^19 + 20 * q^21 + 86 * q^24 - 68 * q^26 + 22 * q^29 - 20 * q^31 - 40 * q^34 + 6 * q^36 - 6 * q^39 + 50 * q^41 + 2 * q^44 + 80 * q^46 - 32 * q^49 + 70 * q^51 - 120 * q^54 - 40 * q^56 - 28 * q^59 + 32 * q^61 - 80 * q^64 - 110 * q^66 - 70 * q^69 - 92 * q^71 + 14 * q^74 - 124 * q^76 + 78 * q^79 - 86 * q^81 + 108 * q^84 + 4 * q^86 + 44 * q^89 - 68 * q^91 + 80 * q^94 + 216 * q^96 + 20 * q^99

Character values

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

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.63006	+	0.854560i	1.85974	+	0.604265i	0.994733	+	0.102499i	$0.0326840\pi$
$2$	2.63006	+	0.854560i	1.85974	+	0.604265i	0.865004	+	0.501766i	$0.167316\pi$
$3$	−0.964848	−	1.32800i	−0.557055	−	0.766721i	0.433893	−	0.900964i	$-0.357139\pi$
$3$	−0.964848	−	1.32800i	−0.557055	−	0.766721i	−0.990948	+	0.134244i	$0.957139\pi$
$4$	4.56893	+	3.31953i	2.28447	+	1.65976i
$5$		0			0
$5$		0			0
$6$	−1.40276	−	4.31724i	−0.572673	−	1.76251i
$7$	−1.11557	+	1.53545i	−0.421646	+	0.580346i	−0.966010	−	0.258503i	$-0.916771\pi$
$7$	−1.11557	+	1.53545i	−0.421646	+	0.580346i	0.544365	+	0.838849i	$0.316771\pi$
$8$	5.92892	+	8.16046i	2.09619	+	2.88516i
$9$	0.0944009	−	0.290536i	0.0314670	−	0.0968453i
$10$		0			0
$11$	0.102720	−	3.31503i	0.0309712	−	0.999520i
$11$	0.102720	−	3.31503i	0.0309712	−	0.999520i
$12$		−	9.27038i		−	2.67613i
$13$	−1.96439	−	0.638270i	−0.544825	−	0.177024i	0.0236571	−	0.999720i	$-0.492469\pi$
$13$	−1.96439	−	0.638270i	−0.544825	−	0.177024i	−0.568482	+	0.822696i	$0.692469\pi$
$14$	−4.24616	+	3.08501i	−1.13483	+	0.824504i
$15$		0			0
$16$	5.12949	+	15.7870i	1.28237	+	3.94674i
$17$	−3.44822	+	1.12040i	−0.836317	+	0.271736i	−0.695704	−	0.718329i	$-0.744907\pi$
$17$	−3.44822	+	1.12040i	−0.836317	+	0.271736i	−0.140613	+	0.990065i	$0.544907\pi$
$18$	0.496561	−	0.683457i	0.117040	−	0.161092i
$19$	−1.03575	+	0.752517i	−0.237618	+	0.172639i	−0.700221	−	0.713926i	$-0.746915\pi$
$19$	−1.03575	+	0.752517i	−0.237618	+	0.172639i	0.462604	+	0.886565i	$0.346915\pi$
$20$		0			0
$21$	3.11543			0.679843
$22$	3.10305	−	8.63097i	0.661573	−	1.84013i
$23$		−	3.36725i		−	0.702121i	−0.936353	−	0.351061i	$-0.885821\pi$
$23$		−	3.36725i		−	0.702121i	0.936353	−	0.351061i	$-0.114179\pi$
$24$	5.11658	−	15.7472i	1.04442	−	3.21438i
$25$		0			0
$26$	−4.62104	−	3.35738i	−0.906261	−	0.658437i
$27$	−5.16038	+	1.67671i	−0.993116	+	0.322683i
$28$	−10.1939	+	3.31221i	−1.92647	+	0.625949i
$29$	0.910336	+	0.661398i	0.169045	+	0.122819i	0.669091	−	0.743180i	$-0.266684\pi$
$29$	0.910336	+	0.661398i	0.169045	+	0.122819i	−0.500046	+	0.865999i	$0.666684\pi$
$30$		0			0
$31$	1.42251	−	4.37805i	0.255491	−	0.786321i	−0.738241	−	0.674537i	$-0.764343\pi$
$31$	1.42251	−	4.37805i	0.255491	−	0.786321i	0.993732	−	0.111784i	$-0.0356566\pi$
$32$			25.7304i			4.54853i
$33$	−4.50147	+	3.06209i	−0.783605	+	0.533042i
$34$	−10.0265			−1.71953
$35$		0			0
$36$	1.39575	−	1.01407i	0.232625	−	0.169012i
$37$	−1.05926	+	1.45794i	−0.174141	+	0.239684i	−0.887162	−	0.461459i	$-0.847326\pi$
$37$	−1.05926	+	1.45794i	−0.174141	+	0.239684i	0.713021	+	0.701142i	$0.247326\pi$
$38$	−3.36716	+	1.09406i	−0.546226	+	0.177480i
$39$	1.04772	+	3.22455i	0.167769	+	0.516341i
$40$		0			0
$41$	−3.73360	+	2.71262i	−0.583090	+	0.423639i	−0.839837	−	0.542839i	$-0.817349\pi$
$41$	−3.73360	+	2.71262i	−0.583090	+	0.423639i	0.256747	+	0.966479i	$0.417349\pi$
$42$	8.19379	+	2.66232i	1.26433	+	0.410805i
$43$			0.0110430i			0.00168404i	1.00000		0.000842018i	$0.000268023\pi$
$43$			0.0110430i			0.00168404i	−1.00000		0.000842018i	$0.999732\pi$
$44$	11.4737	−	14.8052i	1.72972	−	2.23197i
$45$		0			0
$46$	2.87752	−	8.85610i	0.424267	−	1.30576i
$47$	−5.42297	−	7.46408i	−0.791022	−	1.08875i	−0.993980	−	0.109561i	$-0.965056\pi$
$47$	−5.42297	−	7.46408i	−0.791022	−	1.08875i	0.202958	−	0.979187i	$-0.434944\pi$
$48$	16.0159	−	22.0440i	2.31169	−	3.18177i
$49$	1.05001	+	3.23159i	0.150001	+	0.461656i
$50$		0			0
$51$	4.81489	+	3.49822i	0.674220	+	0.489849i
$52$	−6.85643	−	9.43707i	−0.950816	−	1.30869i
$53$	6.22368	+	2.02220i	0.854888	+	0.277770i	0.703492	−	0.710703i	$-0.251623\pi$
$53$	6.22368	+	2.02220i	0.854888	+	0.277770i	0.151396	+	0.988473i	$0.451623\pi$
$54$	−15.0050			−2.04192
$55$		0			0
$56$	−19.1441			−2.55824
$57$	1.99868	+	0.649412i	0.264732	+	0.0860167i
$58$	1.82904	+	2.51746i	0.240165	+	0.330558i
$59$	4.43142	+	3.21961i	0.576921	+	0.419158i	0.837613	−	0.546264i	$-0.183951\pi$
$59$	4.43142	+	3.21961i	0.576921	+	0.419158i	−0.260692	+	0.965422i	$0.583951\pi$
$60$		0			0
$61$	2.27166	+	6.99144i	0.290856	+	0.895162i	0.984582	+	0.174923i	$0.0559678\pi$
$61$	2.27166	+	6.99144i	0.290856	+	0.895162i	−0.693726	+	0.720239i	$0.744032\pi$
$62$	7.48261	−	10.2989i	0.950293	−	1.30797i
$63$	0.340793	+	0.469061i	0.0429359	+	0.0590962i
$64$	−11.7292	+	36.0987i	−1.46615	+	4.51234i
$65$		0			0
$66$	−14.4559	+	4.20672i	−1.77940	+	0.517812i
$67$			7.01002i			0.856410i	0.903682	+	0.428205i	$0.140854\pi$
$67$			7.01002i			0.856410i	−0.903682	+	0.428205i	$0.859146\pi$
$68$	−19.4739	−	6.32745i	−2.36155	−	0.767316i
$69$	−4.47171	+	3.24889i	−0.538331	+	0.391120i
$70$		0			0
$71$	−3.68735	−	11.3485i	−0.437607	−	1.34682i	−0.890391	−	0.455197i	$-0.849569\pi$
$71$	−3.68735	−	11.3485i	−0.437607	−	1.34682i	0.452783	−	0.891621i	$-0.350431\pi$
$72$	2.93060	−	0.952211i	0.345375	−	0.112219i
$73$	1.77865	−	2.44810i	0.208175	−	0.286529i	−0.692143	−	0.721760i	$-0.743333\pi$
$73$	1.77865	−	2.44810i	0.208175	−	0.286529i	0.900319	+	0.435231i	$0.143333\pi$
$74$	−4.03181	+	2.92928i	−0.468688	+	0.340522i
$75$		0			0
$76$	−7.23028			−0.829370
$77$	4.97548	+	3.85587i	0.567009	+	0.439418i
$78$			9.37610i			1.06163i
$79$	1.89180	−	5.82235i	0.212844	−	0.655066i	−0.786456	−	0.617646i	$-0.788086\pi$
$79$	1.89180	−	5.82235i	0.212844	−	0.655066i	0.999300	−	0.0374192i	$-0.0119137\pi$
$80$		0			0
$81$	6.46422	+	4.69653i	0.718247	+	0.521837i
$82$	−12.1377	+	3.94377i	−1.34038	+	0.435517i
$83$	13.9332	−	4.52716i	1.52936	−	0.496921i	0.580946	−	0.813942i	$-0.302683\pi$
$83$	13.9332	−	4.52716i	1.52936	−	0.496921i	0.948418	+	0.317021i	$0.102683\pi$
$84$	14.2342	+	10.3418i	1.55308	+	1.12838i
$85$		0			0
$86$	−0.00943687	+	0.0290437i	−0.00101760	+	0.00313186i
$87$		−	1.84707i		−	0.198027i
$88$	27.6612	−	18.8163i	2.94870	−	2.00583i
$89$	13.8156			1.46445			0.732227	−	0.681060i	$-0.238481\pi$
$89$	13.8156			1.46445			0.732227	+	0.681060i	$0.238481\pi$
$90$		0			0
$91$	3.17145	−	2.30419i	0.332458	−	0.241545i
$92$	11.1777	−	15.3848i	1.16535	−	1.60397i
$93$	−7.18656	+	2.33505i	−0.745211	+	0.242134i
$94$	−7.88426	−	24.2653i	−0.813200	−	2.50277i
$95$		0			0
$96$	34.1699	−	24.8259i	3.48745	−	2.53378i
$97$	16.4571	+	5.34722i	1.67096	+	0.542928i	0.983124	−	0.182938i	$-0.0585609\pi$
$97$	16.4571	+	5.34722i	1.67096	+	0.542928i	0.687836	+	0.725866i	$0.258561\pi$
$98$			9.39658i			0.949198i
$99$	−0.953440	−	0.342786i	−0.0958243	−	0.0344513i
$100$		0			0
$101$	−4.60266	+	14.1655i	−0.457982	+	1.40952i	0.409617	+	0.912258i	$0.365662\pi$
$101$	−4.60266	+	14.1655i	−0.457982	+	1.40952i	−0.867599	+	0.497265i	$0.834338\pi$
$102$	9.67404	+	13.3152i	0.957873	+	1.31840i
$103$	0.249996	−	0.344090i	0.0246329	−	0.0339042i	−0.796523	−	0.604608i	$-0.793330\pi$
$103$	0.249996	−	0.344090i	0.0246329	−	0.0339042i	0.821156	+	0.570704i	$0.193330\pi$
$104$	−6.43816	−	19.8146i	−0.631313	−	1.94298i
$105$		0			0
$106$	14.6406	+	10.6370i	1.42202	+	1.03316i
$107$	4.96085	+	6.82802i	0.479583	+	0.660090i	0.978425	−	0.206603i	$-0.0662410\pi$
$107$	4.96085	+	6.82802i	0.479583	+	0.660090i	−0.498841	+	0.866693i	$0.666241\pi$
$108$	−29.1433	−	9.46924i	−2.80432	−	0.911178i
$109$	−0.922589			−0.0883680			−0.0441840	−	0.999023i	$-0.514069\pi$
$109$	−0.922589			−0.0883680			−0.0441840	+	0.999023i	$0.514069\pi$
$110$		0			0
$111$	2.95816			0.280776
$112$	−29.9624	−	9.73537i	−2.83118	−	0.919906i
$113$	−1.59417	−	2.19418i	−0.149967	−	0.206411i	0.727424	−	0.686189i	$-0.240718\pi$
$113$	−1.59417	−	2.19418i	−0.149967	−	0.206411i	−0.877390	+	0.479777i	$0.840718\pi$
$114$	4.70171	+	3.41599i	0.440355	+	0.319937i
$115$		0			0
$116$	1.96374	+	6.04377i	0.182329	+	0.561150i
$117$	−0.370881	+	0.510474i	−0.0342880	+	0.0471933i
$118$	8.90356	+	12.2547i	0.819639	+	1.12814i
$119$	2.12642	−	6.54445i	0.194929	−	0.599929i
$120$		0			0
$121$	−10.9789	−	0.681040i	−0.998082	−	0.0619127i
$122$			20.3292i			1.84052i
$123$	7.20470	+	2.34095i	0.649626	+	0.211076i
$124$	21.0324	−	15.2809i	1.88877	−	1.37227i
$125$		0			0
$126$	0.495467	+	1.52489i	0.0441397	+	0.135848i
$127$	−7.73903	+	2.51456i	−0.686728	+	0.223131i	−0.631539	−	0.775345i	$-0.717576\pi$
$127$	−7.73903	+	2.51456i	−0.686728	+	0.223131i	−0.0551893	+	0.998476i	$0.517576\pi$
$128$	−31.4491	+	43.2860i	−2.77973	+	3.82598i
$129$	0.0146650	−	0.0106548i	0.00129118	−	0.000938101i
$130$		0			0
$131$	2.69256			0.235250			0.117625	−	0.993058i	$-0.462472\pi$
$131$	2.69256			0.235250			0.117625	+	0.993058i	$0.462472\pi$
$132$	−30.7316	−	0.952252i	−2.67484	−	0.0828829i
$133$		−	2.42983i		−	0.210693i
$134$	−5.99048	+	18.4368i	−0.517498	+	1.59270i
$135$		0			0
$136$	−29.5872	−	21.4963i	−2.53708	−	1.84330i
$137$	8.07211	−	2.62279i	0.689647	−	0.224080i	0.0568330	−	0.998384i	$-0.481900\pi$
$137$	8.07211	−	2.62279i	0.689647	−	0.224080i	0.632814	+	0.774304i	$0.281900\pi$
$138$	−14.5373	+	4.72344i	−1.23749	+	0.402086i
$139$	−17.8961	−	13.0023i	−1.51793	−	1.10284i	−0.962502	−	0.271275i	$-0.912555\pi$
$139$	−17.8961	−	13.0023i	−1.51793	−	1.10284i	−0.555427	−	0.831565i	$-0.687445\pi$
$140$		0			0
$141$	−4.67995	+	14.4034i	−0.394123	+	1.21299i
$142$		−	32.9983i		−	2.76916i
$143$	−2.31767	+	6.44647i	−0.193813	+	0.539081i
$144$	5.07091			0.422575
$145$		0			0
$146$	6.77002	−	4.91871i	0.560291	−	0.407075i
$147$	3.27845	−	4.51240i	0.270402	−	0.372176i
$148$	−9.67934	+	3.14501i	−0.795637	+	0.258518i
$149$	4.96839	+	15.2911i	0.407026	+	1.25270i	0.919191	+	0.393811i	$0.128844\pi$
$149$	4.96839	+	15.2911i	0.407026	+	1.25270i	−0.512165	+	0.858887i	$0.671156\pi$
$150$		0			0
$151$	−18.7865	+	13.6492i	−1.52882	+	1.11075i	−0.571933	+	0.820300i	$0.693806\pi$
$151$	−18.7865	+	13.6492i	−1.52882	+	1.11075i	−0.956889	+	0.290454i	$0.906194\pi$
$152$	−12.2818	−	3.99059i	−0.996183	−	0.323680i
$153$			1.10760i			0.0895441i
$154$	9.79076	+	14.3930i	0.788962	+	1.15982i
$155$		0			0
$156$	−5.91700	+	18.2107i	−0.473740	+	1.45802i
$157$	−9.54418	−	13.1364i	−0.761709	−	1.04840i	−0.997070	−	0.0764941i	$-0.975627\pi$
$157$	−9.54418	−	13.1364i	−0.761709	−	1.04840i	0.235361	−	0.971908i	$-0.424373\pi$
$158$	9.95109	−	13.6965i	0.791666	−	1.08964i
$159$	−3.31943	−	10.2162i	−0.263248	−	0.810194i
$160$		0			0
$161$	5.17025	+	3.75641i	0.407473	+	0.296047i
$162$	12.9878	+	17.8762i	1.02042	+	1.40449i
$163$	11.6599	+	3.78855i	0.913277	+	0.296742i	0.727706	−	0.685889i	$-0.240586\pi$
$163$	11.6599	+	3.78855i	0.913277	+	0.296742i	0.185571	+	0.982631i	$0.440586\pi$
$164$	−26.0631			−2.03519
$165$		0			0
$166$	40.5139			3.14449
$167$	−6.02648	−	1.95812i	−0.466343	−	0.151524i	0.0664141	−	0.997792i	$-0.478844\pi$
$167$	−6.02648	−	1.95812i	−0.466343	−	0.151524i	−0.532757	+	0.846268i	$0.678844\pi$
$168$	18.4712	+	25.4234i	1.42508	+	1.96146i
$169$	−7.06577	−	5.13358i	−0.543521	−	0.394891i
$170$		0			0
$171$	0.120858	+	0.371961i	0.00924221	+	0.0284446i
$172$	−0.0366574	+	0.0504546i	−0.00279510	+	0.00384712i
$173$	1.23853	+	1.70469i	0.0941637	+	0.129605i	0.853499	−	0.521094i	$-0.174476\pi$
$173$	1.23853	+	1.70469i	0.0941637	+	0.129605i	−0.759336	+	0.650699i	$0.774476\pi$
$174$	1.57844	−	4.85792i	0.119661	−	0.368278i
$175$		0			0
$176$	52.8612	−	15.3828i	3.98456	−	1.15952i
$177$		−	8.99135i		−	0.675831i
$178$	36.3360	+	11.8063i	2.72350	+	0.884919i
$179$	−7.90157	+	5.74083i	−0.590591	+	0.429090i	−0.842527	−	0.538654i	$-0.818933\pi$
$179$	−7.90157	+	5.74083i	−0.590591	+	0.429090i	0.251936	+	0.967744i	$0.418933\pi$
$180$		0			0
$181$	−5.97245	−	18.3813i	−0.443928	−	1.36627i	−0.883655	−	0.468139i	$-0.844924\pi$
$181$	−5.97245	−	18.3813i	−0.443928	−	1.36627i	0.439726	−	0.898132i	$-0.355076\pi$
$182$	10.3102	−	3.34999i	0.764242	−	0.248317i
$183$	7.09282	−	9.76243i	0.524317	−	0.721660i
$184$	27.4784	−	19.9642i	2.02573	−	1.47178i
$185$		0			0
$186$	−20.8965			−1.53221
$187$	3.35995	+	11.5461i	0.245704	+	0.844331i
$188$		−	52.1046i		−	3.80012i
$189$	3.18226	−	9.79400i	0.231476	−	0.712409i
$190$		0			0
$191$	−11.7719	−	8.55279i	−0.851785	−	0.618858i	0.0738525	−	0.997269i	$-0.476471\pi$
$191$	−11.7719	−	8.55279i	−0.851785	−	0.618858i	−0.925638	+	0.378411i	$0.876471\pi$
$192$	59.2559	−	19.2534i	4.27643	−	1.38950i
$193$	−21.1376	+	6.86801i	−1.52151	+	0.494370i	−0.946206	−	0.323566i	$-0.895118\pi$
$193$	−21.1376	+	6.86801i	−1.52151	+	0.494370i	−0.575309	+	0.817936i	$0.695118\pi$
$194$	38.7136	+	28.1271i	2.77947	+	2.01941i
$195$		0			0
$196$	−5.92993	+	18.2504i	−0.423566	+	1.30360i
$197$		−	9.00781i		−	0.641780i	−0.947116	−	0.320890i	$-0.896018\pi$
$197$		−	9.00781i		−	0.641780i	0.947116	−	0.320890i	$-0.103982\pi$
$198$	−2.21468	−	1.71632i	−0.157390	−	0.121974i
$199$	−0.459925			−0.0326032			−0.0163016	−	0.999867i	$-0.505189\pi$
$199$	−0.459925			−0.0326032			−0.0163016	+	0.999867i	$0.505189\pi$
$200$		0			0
$201$	9.30929	−	6.76360i	0.656627	−	0.477067i
$202$	−24.2106	+	33.3230i	−1.70345	+	2.34460i
$203$	−2.03109	+	0.659941i	−0.142554	+	0.0463187i
$204$	10.3865	+	31.9663i	0.727199	+	2.23809i
$205$		0			0
$206$	0.951553	−	0.691343i	0.0662978	−	0.0481682i
$207$	−0.978309	−	0.317872i	−0.0679972	−	0.0220936i
$208$		−	34.2858i		−	2.37729i
$209$	2.38823	+	3.51085i	0.165197	+	0.242850i
$210$		0			0
$211$	0.242564	−	0.746536i	0.0166988	−	0.0513936i	−0.942360	−	0.334601i	$-0.891398\pi$
$211$	0.242564	−	0.746536i	0.0166988	−	0.0513936i	0.959059	+	0.283207i	$0.0913985\pi$
$212$	21.7229	+	29.8989i	1.49193	+	2.05347i
$213$	−11.5130	+	15.8463i	−0.788861	+	1.08577i
$214$	7.21240	+	22.1975i	0.493029	+	1.51739i
$215$		0			0
$216$	−44.2782	−	32.1700i	−3.01275	−	2.18889i
$217$	5.13536	+	7.06822i	0.348611	+	0.479822i
$218$	−2.42647	−	0.788407i	−0.164341	−	0.0533977i
$219$	−4.96721			−0.335653
$220$		0			0
$221$	7.48878			0.503750
$222$	7.78016	+	2.52793i	0.522170	+	0.169663i
$223$	−7.84950	−	10.8039i	−0.525641	−	0.723483i	0.460817	−	0.887495i	$-0.347556\pi$
$223$	−7.84950	−	10.8039i	−0.525641	−	0.723483i	−0.986458	+	0.164012i	$0.947556\pi$
$224$	−39.5077	−	28.7041i	−2.63972	−	1.91787i
$225$		0			0
$226$	−2.31770	−	7.13316i	−0.154171	−	0.474491i
$227$	10.1561	−	13.9787i	0.674087	−	0.927801i	−0.325757	−	0.945453i	$-0.605619\pi$
$227$	10.1561	−	13.9787i	0.674087	−	0.927801i	0.999844	+	0.0176523i	$0.00561919\pi$
$228$	6.97612	+	9.60180i	0.462005	+	0.635895i
$229$	−3.64367	+	11.2141i	−0.240780	+	0.741045i	0.755522	+	0.655124i	$0.227384\pi$
$229$	−3.64367	+	11.2141i	−0.240780	+	0.741045i	−0.996302	+	0.0859217i	$0.972616\pi$
$230$		0			0
$231$	0.320017	−	10.3278i	0.0210556	−	0.679517i
$232$			11.3501i			0.745173i
$233$	−2.40272	−	0.780690i	−0.157407	−	0.0511447i	0.229254	−	0.973367i	$-0.426372\pi$
$233$	−2.40272	−	0.780690i	−0.157407	−	0.0511447i	−0.386661	+	0.922222i	$0.626372\pi$
$234$	−1.41167	+	1.02564i	−0.0922838	+	0.0670481i
$235$		0			0
$236$	9.55927	+	29.4204i	0.622255	+	1.91510i
$237$	−9.55737	+	3.10538i	−0.620818	+	0.201716i
$238$	11.1853	−	15.3952i	0.725032	−	0.997922i
$239$	20.0190	−	14.5446i	1.29492	−	0.940815i	0.295028	−	0.955489i	$-0.404671\pi$
$239$	20.0190	−	14.5446i	1.29492	−	0.940815i	0.999892	+	0.0146739i	$0.00467102\pi$
$240$		0			0
$241$	18.8935			1.21704			0.608520	−	0.793539i	$-0.291764\pi$
$241$	18.8935			1.21704			0.608520	+	0.793539i	$0.291764\pi$
$242$	−28.2932	−	11.1733i	−1.81876	−	0.718247i
$243$			3.16193i			0.202838i
$244$	−12.8292	+	39.4843i	−0.821306	+	2.52772i
$245$		0			0
$246$	16.9484	+	12.3137i	1.08059	+	0.785093i
$247$	2.51493	−	0.817151i	0.160021	−	0.0519941i
$248$	44.1609	−	14.3487i	2.80422	−	0.911146i
$249$	−19.4555	−	14.1352i	−1.23294	−	0.895783i
$250$		0			0
$251$	1.11446	−	3.42996i	0.0703443	−	0.216497i	−0.909704	−	0.415258i	$-0.863691\pi$
$251$	1.11446	−	3.42996i	0.0703443	−	0.216497i	0.980048	+	0.198760i	$0.0636915\pi$
$252$			3.27438i			0.206267i
$253$	−11.1626	−	0.345884i	−0.701784	−	0.0217455i
$254$	−22.5030			−1.41196
$255$		0			0
$256$	−58.2889	+	42.3493i	−3.64305	+	2.64683i
$257$	7.72911	−	10.6382i	0.482129	−	0.663593i	−0.496784	−	0.867874i	$-0.665486\pi$
$257$	7.72911	−	10.6382i	0.482129	−	0.663593i	0.978912	+	0.204281i	$0.0654857\pi$
$258$	0.0476752	−	0.0154906i	0.00296813	−	0.000964402i
$259$	−1.05692	−	3.25287i	−0.0656739	−	0.202123i
$260$		0			0
$261$	0.278096	−	0.202049i	0.0172137	−	0.0125065i
$262$	7.08162	+	2.30096i	0.437504	+	0.142154i
$263$		−	6.24673i		−	0.385190i	−0.981278	−	0.192595i	$-0.938310\pi$
$263$		−	6.24673i		−	0.385190i	0.981278	−	0.192595i	$-0.0616904\pi$
$264$	−51.6769	−	18.5792i	−3.18050	−	1.14347i
$265$		0			0
$266$	2.07644	−	6.39061i	0.127314	−	0.391834i
$267$	−13.3300	−	18.3472i	−0.815782	−	1.12283i
$268$	−23.2699	+	32.0283i	−1.42144	+	1.95644i
$269$	6.92064	+	21.2995i	0.421959	+	1.29866i	0.905876	+	0.423542i	$0.139213\pi$
$269$	6.92064	+	21.2995i	0.421959	+	1.29866i	−0.483918	+	0.875114i	$0.660787\pi$
$270$		0			0
$271$	7.00497	+	5.08941i	0.425521	+	0.309159i	0.779856	−	0.625959i	$-0.215292\pi$
$271$	7.00497	+	5.08941i	0.425521	+	0.309159i	−0.354334	+	0.935119i	$0.615292\pi$
$272$	−35.3752	−	48.6899i	−2.14494	−	2.95226i
$273$	−6.11994	−	1.98849i	−0.370395	−	0.120349i
$274$	23.4715			1.41797
$275$		0			0
$276$	−31.2157			−1.87897
$277$	−2.47505	−	0.804194i	−0.148712	−	0.0483193i	0.233715	−	0.972305i	$-0.424912\pi$
$277$	−2.47505	−	0.804194i	−0.148712	−	0.0483193i	−0.382427	+	0.923986i	$0.624912\pi$
$278$	−35.9567	−	49.4902i	−2.15654	−	2.96822i
$279$	−1.13769	−	0.826583i	−0.0681120	−	0.0494862i
$280$		0			0
$281$	−6.39755	−	19.6896i	−0.381646	−	1.17459i	−0.938884	−	0.344233i	$-0.888139\pi$
$281$	−6.39755	−	19.6896i	−0.381646	−	1.17459i	0.557238	−	0.830353i	$-0.311861\pi$
$282$	−24.6171	+	33.8826i	−1.46593	+	2.01768i
$283$	6.35430	+	8.74594i	0.377724	+	0.519892i	0.954980	−	0.296671i	$-0.0958765\pi$
$283$	6.35430	+	8.74594i	0.377724	+	0.519892i	−0.577256	+	0.816563i	$0.695877\pi$
$284$	20.8243	−	64.0907i	1.23570	−	3.80308i
$285$		0			0
$286$	−11.6045	+	14.9740i	−0.686189	+	0.885434i
$287$		−	8.75886i		−	0.517019i
$288$	7.47560	+	2.42897i	0.440504	+	0.143128i
$289$	−3.11834	+	2.26561i	−0.183432	+	0.133271i
$290$		0			0
$291$	−8.77745	−	27.0142i	−0.514543	−	1.58360i
$292$	16.2531	−	5.28095i	0.951140	−	0.309044i
$293$	−0.307457	+	0.423178i	−0.0179618	+	0.0247223i	−0.817903	−	0.575355i	$-0.804864\pi$
$293$	−0.307457	+	0.423178i	−0.0179618	+	0.0247223i	0.799942	+	0.600078i	$0.204864\pi$
$294$	12.4787	−	9.06627i	0.727770	−	0.528756i
$295$		0			0
$296$	−18.1777			−1.05656
$297$	5.02828	+	17.2791i	0.291770	+	1.00263i
$298$			44.4624i			2.57564i
$299$	−2.14922	+	6.61461i	−0.124292	+	0.382533i
$300$		0			0
$301$	−0.0169559	−	0.0123192i	−0.000977323	−	0.000710067i
$302$	−61.0737	+	19.8440i	−3.51440	+	1.14190i
$303$	23.2527	−	7.55525i	1.33583	−	0.434038i
$304$	−17.1928	−	12.4913i	−0.986076	−	0.716426i
$305$		0			0
$306$	−0.946510	+	2.91306i	−0.0541083	+	0.166528i
$307$			20.0401i			1.14375i	0.820342	+	0.571873i	$0.193783\pi$
$307$			20.0401i			1.14375i	−0.820342	+	0.571873i	$0.806217\pi$
$308$	9.93297	+	34.1335i	0.565983	+	1.94493i
$309$	−0.698160			−0.0397169
$310$		0			0
$311$	12.3892	−	9.00127i	0.702527	−	0.510415i	−0.178227	−	0.983989i	$-0.557036\pi$
$311$	12.3892	−	9.00127i	0.702527	−	0.510415i	0.880754	+	0.473574i	$0.157036\pi$
$312$	−20.1019	+	27.6679i	−1.13805	+	1.56639i
$313$	−27.0333	+	8.78365i	−1.52801	+	0.496481i	−0.948039	−	0.318154i	$-0.896937\pi$
$313$	−27.0333	+	8.78365i	−1.52801	+	0.496481i	−0.579974	+	0.814635i	$0.696937\pi$
$314$	−13.8759	−	42.7058i	−0.783065	−	2.41003i
$315$		0			0
$316$	27.9709	−	20.3221i	1.57349	−	1.14321i
$317$	−17.9251	−	5.82421i	−1.00677	−	0.327120i	−0.241204	−	0.970474i	$-0.577542\pi$
$317$	−17.9251	−	5.82421i	−1.00677	−	0.327120i	−0.765569	+	0.643354i	$0.777542\pi$
$318$		−	29.7058i		−	1.66582i
$319$	2.28607	−	2.94986i	0.127995	−	0.165160i
$320$		0			0
$321$	4.28114	−	13.1760i	0.238950	−	0.735413i
$322$	10.3880	+	14.2979i	0.578902	+	0.796790i
$323$	2.72838	−	3.75530i	0.151811	−	0.208950i
$324$	13.9443	+	42.9163i	0.774686	+	2.38424i
$325$		0			0
$326$	27.4289	+	19.9282i	1.51914	+	1.10372i
$327$	0.890158	+	1.22520i	0.0492258	+	0.0677535i
$328$	−44.2724	−	14.3850i	−2.44453	−	0.794277i
$329$	17.5104			0.965381
$330$		0			0
$331$	−12.0888			−0.664461			−0.332230	−	0.943198i	$-0.607801\pi$
$331$	−12.0888			−0.664461			−0.332230	+	0.943198i	$0.607801\pi$
$332$	78.6878	+	25.5672i	4.31855	+	1.40318i
$333$	0.323589	+	0.445383i	0.0177326	+	0.0244068i
$334$	−14.1767	−	10.3000i	−0.775715	−	0.563590i
$335$		0			0
$336$	15.9806	+	49.1832i	0.871812	+	2.68316i
$337$	13.7159	−	18.8783i	0.747151	−	1.02837i	−0.251024	−	0.967981i	$-0.580767\pi$
$337$	13.7159	−	18.8783i	0.747151	−	1.02837i	0.998175	−	0.0603846i	$-0.0192327\pi$
$338$	−14.1965	−	19.5398i	−0.772186	−	1.06282i
$339$	−1.37574	+	4.23411i	−0.0747202	+	0.229965i
$340$		0			0
$341$	−14.3673	−	5.16540i	−0.778031	−	0.279722i
$342$			1.08156i			0.0584842i
$343$	−18.7685	−	6.09826i	−1.01340	−	0.329275i
$344$	−0.0901157	+	0.0654729i	−0.00485871	+	0.00353006i
$345$		0			0
$346$	1.80065	+	5.54185i	0.0968038	+	0.297931i
$347$	19.6295	−	6.37801i	1.05377	−	0.342389i	0.269621	−	0.962967i	$-0.413102\pi$
$347$	19.6295	−	6.37801i	1.05377	−	0.342389i	0.784145	+	0.620577i	$0.213102\pi$
$348$	6.13141	−	8.43916i	0.328678	−	0.452387i
$349$	−20.6326	+	14.9904i	−1.10444	+	0.802419i	−0.981778	−	0.190030i	$-0.939141\pi$
$349$	−20.6326	+	14.9904i	−1.10444	+	0.802419i	−0.122657	+	0.992449i	$0.539141\pi$
$350$		0			0
$351$	11.2072			0.598197
$352$	85.2971	+	2.64302i	4.54635	+	0.140874i
$353$		−	3.41010i		−	0.181501i	−0.995874	−	0.0907506i	$-0.971073\pi$
$353$		−	3.41010i		−	0.181501i	0.995874	−	0.0907506i	$-0.0289266\pi$
$354$	7.68365	−	23.6478i	0.408381	−	1.25687i
$355$		0			0
$356$	63.1227	+	45.8614i	3.34550	+	2.43065i
$357$	−10.7427	+	3.49052i	−0.568564	+	0.184738i
$358$	−25.6875	+	8.34638i	−1.35763	+	0.441120i
$359$	3.86662	+	2.80926i	0.204072	+	0.148267i	0.685128	−	0.728423i	$-0.259746\pi$
$359$	3.86662	+	2.80926i	0.204072	+	0.148267i	−0.481055	+	0.876690i	$0.659746\pi$
$360$		0			0
$361$	−5.36482	+	16.5112i	−0.282359	+	0.869012i
$362$		−	53.4478i		−	2.80916i
$363$	9.68854	+	15.2371i	0.508517	+	0.799738i
$364$	22.1390			1.16040
$365$		0			0
$366$	26.9972	−	19.6146i	1.41116	−	1.02527i
$367$	−7.71953	+	10.6250i	−0.402956	+	0.554622i	−0.961483	−	0.274865i	$-0.911367\pi$
$367$	−7.71953	+	10.6250i	−0.402956	+	0.554622i	0.558526	+	0.829487i	$0.311367\pi$
$368$	53.1587	−	17.2723i	2.77109	−	0.900381i
$369$	0.435658	+	1.34082i	0.0226794	+	0.0698001i
$370$		0			0
$371$	−10.0479	+	7.30025i	−0.521663	+	0.379010i
$372$	−40.5862	−	13.1872i	−2.10429	−	0.683727i
$373$		−	24.9476i		−	1.29174i	−0.763448	−	0.645869i	$-0.776495\pi$
$373$		−	24.9476i		−	1.29174i	0.763448	−	0.645869i	$-0.223505\pi$
$374$	−1.02992	+	33.2382i	−0.0532559	+	1.71870i
$375$		0			0
$376$	28.7580	−	88.5079i	1.48308	−	4.56445i
$377$	−1.36611	−	1.88029i	−0.0703582	−	0.0968397i
$378$	16.7391	−	23.0394i	0.860968	−	1.18502i
$379$	0.630173	+	1.93947i	0.0323698	+	0.0996240i	0.965936	−	0.258781i	$-0.0833207\pi$
$379$	0.630173	+	1.93947i	0.0323698	+	0.0996240i	−0.933566	+	0.358405i	$0.883321\pi$
$380$		0			0
$381$	10.8063	+	7.85125i	0.553625	+	0.402232i
$382$	−23.6520	−	32.5542i	−1.21014	−	1.66562i
$383$	30.6224	+	9.94983i	1.56473	+	0.508413i	0.958067	−	0.286544i	$-0.0925066\pi$
$383$	30.6224	+	9.94983i	1.56473	+	0.508413i	0.606666	+	0.794957i	$0.292507\pi$
$384$	87.8273			4.48192
$385$		0			0
$386$	−61.4623			−3.12835
$387$	0.00320838	+	0.00104247i	0.000163091	+	5.29915e-5i
$388$	57.4410	+	79.0607i	2.91612	+	4.01370i
$389$	2.25775	+	1.64035i	0.114473	+	0.0831692i	0.643549	−	0.765405i	$-0.277461\pi$
$389$	2.25775	+	1.64035i	0.114473	+	0.0831692i	−0.529076	+	0.848574i	$0.677461\pi$
$390$		0			0
$391$	3.77266	+	11.6110i	0.190791	+	0.587196i
$392$	−20.1458	+	27.7284i	−1.01752	+	1.40049i
$393$	−2.59791	−	3.57572i	−0.131047	−	0.180371i
$394$	7.69772	−	23.6911i	0.387805	−	1.19354i
$395$		0			0
$396$	−3.21832	−	4.73113i	−0.161727	−	0.237748i
$397$		−	26.6387i		−	1.33696i	−0.743730	−	0.668480i	$-0.766945\pi$
$397$		−	26.6387i		−	1.33696i	0.743730	−	0.668480i	$-0.233055\pi$
$398$	−1.20963	−	0.393033i	−0.0606333	−	0.0197010i
$399$	−3.22681	+	2.34442i	−0.161543	+	0.117368i
$400$		0			0
$401$	−5.62283	−	17.3053i	−0.280791	−	0.864186i	−0.987629	−	0.156810i	$-0.949879\pi$
$401$	−5.62283	−	17.3053i	−0.280791	−	0.864186i	0.706838	−	0.707376i	$-0.250121\pi$
$402$	30.2639	−	9.83335i	1.50943	−	0.490443i
$403$	−5.58876	+	7.69226i	−0.278396	+	0.383179i
$404$	−68.0521	+	49.4427i	−3.38572	+	2.45987i
$405$		0			0
$406$	−5.90585			−0.293103
$407$	4.72431	+	3.66123i	0.234176	+	0.181480i
$408$			60.0324i			2.97205i
$409$	−2.34693	+	7.22312i	−0.116048	+	0.357160i	−0.992164	−	0.124940i	$-0.960126\pi$
$409$	−2.34693	+	7.22312i	−0.116048	+	0.357160i	0.876116	+	0.482101i	$0.160126\pi$
$410$		0			0
$411$	−11.2714	−	8.18916i	−0.555978	−	0.403942i
$412$	2.28443	−	0.742258i	0.112546	−	0.0365684i
$413$	−9.88711	+	3.21252i	−0.486513	+	0.158078i
$414$	−2.30137	−	1.67205i	−0.113106	−	0.0821766i
$415$		0			0
$416$	16.4229	−	50.5446i	0.805201	−	2.47815i
$417$			36.3113i			1.77817i
$418$	3.28096	+	11.2746i	0.160477	+	0.551461i
$419$	−29.8323			−1.45740			−0.728701	−	0.684832i	$-0.759875\pi$
$419$	−29.8323			−1.45740			−0.728701	+	0.684832i	$0.759875\pi$
$420$		0			0
$421$	−20.4942	+	14.8899i	−0.998828	+	0.725691i	−0.961837	−	0.273624i	$-0.911778\pi$
$421$	−20.4942	+	14.8899i	−0.998828	+	0.725691i	−0.0369918	+	0.999316i	$0.511778\pi$
$422$	1.27592	−	1.75615i	0.0621108	−	0.0854881i
$423$	−2.68052	+	0.870953i	−0.130331	+	0.0423472i
$424$	20.3977	+	62.7775i	0.990598	+	3.04875i
$425$		0			0
$426$	−43.8217	+	31.8383i	−2.12317	+	1.54257i
$427$	−13.2692	−	4.31143i	−0.642142	−	0.208645i
$428$			47.6644i			2.30395i
$429$	10.7971	−	3.14200i	0.521289	−	0.151697i
$430$		0			0
$431$	−6.34030	+	19.5134i	−0.305401	+	0.939929i	0.674126	+	0.738617i	$0.264521\pi$
$431$	−6.34030	+	19.5134i	−0.305401	+	0.939929i	−0.979527	+	0.201312i	$0.935479\pi$
$432$	−52.9403	−	72.8660i	−2.54709	−	3.50577i
$433$	8.08542	−	11.1286i	0.388560	−	0.534807i	−0.569267	−	0.822153i	$-0.692773\pi$
$433$	8.08542	−	11.1286i	0.388560	−	0.534807i	0.957827	+	0.287346i	$0.0927728\pi$
$434$	7.46612	+	22.9784i	0.358385	+	1.10300i
$435$		0			0
$436$	−4.21525	−	3.06256i	−0.201874	−	0.146670i
$437$	2.53392	+	3.48764i	0.121214	+	0.166836i
$438$	−13.0641	−	4.24478i	−0.624226	−	0.202823i
$439$	24.1841			1.15425			0.577123	−	0.816657i	$-0.304175\pi$
$439$	24.1841			1.15425			0.577123	+	0.816657i	$0.304175\pi$
$440$		0			0
$441$	1.03801			0.0494293
$442$	19.6960	+	6.39961i	0.936842	+	0.304398i
$443$	−0.997848	−	1.37342i	−0.0474092	−	0.0652532i	0.784654	−	0.619934i	$-0.212840\pi$
$443$	−0.997848	−	1.37342i	−0.0474092	−	0.0652532i	−0.832063	+	0.554680i	$0.812840\pi$
$444$	13.5157	+	9.81970i	0.641425	+	0.466022i
$445$		0			0
$446$	−11.4121	−	35.1228i	−0.540379	−	1.66311i
$447$	15.5129	−	21.3516i	0.733733	−	1.00990i
$448$	−42.3430	−	58.2802i	−2.00052	−	2.75348i
$449$	−0.804184	+	2.47502i	−0.0379518	+	0.116804i	−0.968238	−	0.250032i	$-0.919559\pi$
$449$	−0.804184	+	2.47502i	−0.0379518	+	0.116804i	0.930286	+	0.366836i	$0.119559\pi$
$450$		0			0
$451$	8.60890	+	12.6556i	0.405377	+	0.595931i
$452$		−	15.3170i		−	0.720449i
$453$	36.2522	+	11.7790i	1.70328	+	0.553428i
$454$	38.6570	−	28.0859i	1.81426	−	1.31814i
$455$		0			0
$456$	6.55054	+	20.1605i	0.306757	+	0.944102i
$457$	−13.2778	+	4.31421i	−0.621108	+	0.201810i	−0.602632	−	0.798019i	$-0.705881\pi$
$457$	−13.2778	+	4.31421i	−0.621108	+	0.201810i	−0.0184756	+	0.999829i	$0.505881\pi$
$458$	−19.1662	+	26.3800i	−0.895576	+	1.23265i
$459$	15.9156	−	11.5633i	0.742875	−	0.539730i
$460$		0			0
$461$	26.5365			1.23593			0.617963	−	0.786207i	$-0.287958\pi$
$461$	26.5365			1.23593			0.617963	+	0.786207i	$0.287958\pi$
$462$	9.66736	−	26.8892i	0.449766	−	1.25100i
$463$		−	23.6363i		−	1.09847i	−0.835667	−	0.549237i	$-0.814919\pi$
$463$		−	23.6363i		−	1.09847i	0.835667	−	0.549237i	$-0.185081\pi$
$464$	−5.77190	+	17.7641i	−0.267954	+	0.824676i
$465$		0			0
$466$	−5.65215	−	4.10653i	−0.261831	−	0.190231i
$467$	−9.62866	+	3.12854i	−0.445561	+	0.144772i	−0.523200	−	0.852210i	$-0.675262\pi$
$467$	−9.62866	+	3.12854i	−0.445561	+	0.144772i	0.0776386	+	0.996982i	$0.475262\pi$
$468$	−3.38906	+	1.10117i	−0.156659	+	0.0509017i
$469$	−10.7635	−	7.82016i	−0.497014	−	0.361102i
$470$		0			0
$471$	−8.23650	+	25.3493i	−0.379518	+	1.16804i
$472$			55.2512i			2.54314i
$473$	0.0366078	+	0.00113433i	0.00168323	+	5.21566e-5i
$474$	−27.7902			−1.27645
$475$		0			0
$476$	31.4400	−	22.8425i	1.44105	−	1.04698i
$477$	1.17504	−	1.61731i	0.0538015	−	0.0740513i
$478$	65.0805	−	21.1459i	2.97671	−	0.967192i
$479$	−0.210601	−	0.648162i	−0.00962259	−	0.0296153i	0.946130	−	0.323787i	$-0.104956\pi$
$479$	−0.210601	−	0.648162i	−0.00962259	−	0.0296153i	−0.955753	+	0.294172i	$0.904956\pi$
$480$		0			0
$481$	3.01135	−	2.18788i	0.137306	−	0.0997586i
$482$	49.6912	+	16.1457i	2.26337	+	0.735414i
$483$		−	10.4905i		−	0.477332i
$484$	−47.9011	−	39.5564i	−2.17732	−	1.79802i
$485$		0			0
$486$	−2.70206	+	8.31608i	−0.122568	+	0.377225i
$487$	6.24493	+	8.59541i	0.282985	+	0.389495i	0.926720	−	0.375754i	$-0.122616\pi$
$487$	6.24493	+	8.59541i	0.282985	+	0.389495i	−0.643735	+	0.765249i	$0.722616\pi$
$488$	−43.5849	+	59.9895i	−1.97300	+	2.71560i
$489$	−6.21889	−	19.1398i	−0.281228	−	0.865530i
$490$		0			0
$491$	9.34180	+	6.78722i	0.421590	+	0.306303i	0.778277	−	0.627921i	$-0.216094\pi$
$491$	9.34180	+	6.78722i	0.421590	+	0.306303i	−0.356687	+	0.934224i	$0.616094\pi$
$492$	25.1470	+	34.6118i	1.13371	+	1.56042i
$493$	−3.88007	−	1.26071i	−0.174750	−	0.0567796i
$494$	7.31274			0.329016
$495$		0			0
$496$	76.4128			3.43104
$497$	21.5385	+	6.99829i	0.966135	+	0.313916i
$498$	−39.0897	−	53.8024i	−1.75165	−	2.41094i
$499$	−7.47146	−	5.42833i	−0.334469	−	0.243006i	0.407856	−	0.913046i	$-0.366277\pi$
$499$	−7.47146	−	5.42833i	−0.334469	−	0.243006i	−0.742324	+	0.670041i	$0.766277\pi$
$500$		0			0
$501$	3.21425	+	9.89246i	0.143602	+	0.441962i
$502$	5.86222	−	8.06865i	0.261644	−	0.360122i
$503$	11.3426	+	15.6117i	0.505740	+	0.696092i	0.983194	−	0.182565i	$-0.0584401\pi$
$503$	11.3426	+	15.6117i	0.505740	+	0.696092i	−0.477453	+	0.878657i	$0.658440\pi$
$504$	−1.80722	+	5.56205i	−0.0805000	+	0.247754i
$505$		0			0
$506$	−29.0627	−	10.4488i	−1.29199	−	0.464505i
$507$			14.3365i			0.636704i
$508$	−43.7063	−	14.2010i	−1.93915	−	0.630069i
$509$	2.62203	−	1.90502i	0.116219	−	0.0844384i	−0.528157	−	0.849147i	$-0.677117\pi$
$509$	2.62203	−	1.90502i	0.116219	−	0.0844384i	0.644377	+	0.764708i	$0.277117\pi$
$510$		0			0
$511$	1.77473	+	5.46206i	0.0785095	+	0.241627i
$512$	−87.7221	+	28.5026i	−3.87681	+	1.25965i
$513$	4.08312	−	5.61993i	0.180274	−	0.248126i
$514$	29.4190	−	21.3742i	1.29762	−	0.942775i
$515$		0			0
$516$	0.102372			0.00450669
$517$	−25.3007	+	17.2106i	−1.11272	+	0.756922i
$518$		−	9.45846i		−	0.415581i
$519$	1.06883	−	3.28953i	0.0469166	−	0.144395i
$520$		0			0
$521$	9.45689	+	6.87083i	0.414314	+	0.301017i	0.775346	−	0.631537i	$-0.217576\pi$
$521$	9.45689	+	6.87083i	0.414314	+	0.301017i	−0.361032	+	0.932553i	$0.617576\pi$
$522$	0.904075	−	0.293752i	0.0395703	−	0.0128572i
$523$	10.4551	−	3.39708i	0.457171	−	0.148544i	−0.0713730	−	0.997450i	$-0.522738\pi$
$523$	10.4551	−	3.39708i	0.457171	−	0.148544i	0.528544	+	0.848906i	$0.322738\pi$
$524$	12.3021	+	8.93803i	0.537422	+	0.390460i
$525$		0			0
$526$	5.33821	−	16.4293i	0.232757	−	0.716352i
$527$			16.6903i			0.727039i
$528$	−71.4313	−	55.3575i	−3.10865	−	2.40913i
$529$	11.6616			0.507026
$530$		0			0
$531$	1.35374	−	0.983552i	0.0587474	−	0.0426825i
$532$	8.06588	−	11.1017i	0.349700	−	0.481321i
$533$	9.06563	−	2.94560i	0.392676	−	0.127588i
$534$	−19.3800	−	59.6455i	−0.838654	−	2.58111i
$535$		0			0
$536$	−57.2050	+	41.5618i	−2.47088	+	1.79520i
$537$	15.2476	+	4.95425i	0.657984	+	0.213792i
$538$			61.9333i			2.67013i
$539$	10.8207	−	3.14886i	0.466080	−	0.135631i
$540$		0			0
$541$	−6.93398	+	21.3406i	−0.298115	+	0.917504i	0.684042	+	0.729442i	$0.260220\pi$
$541$	−6.93398	+	21.3406i	−0.298115	+	0.917504i	−0.982157	+	0.188061i	$0.939780\pi$
$542$	14.0743	+	19.3716i	0.604544	+	0.832083i
$543$	−18.6478	+	25.6666i	−0.800256	+	1.10146i
$544$	−28.8282	−	88.7241i	−1.23600	−	3.80401i
$545$		0			0
$546$	−14.3965	−	10.4597i	−0.616115	−	0.447634i
$547$	15.7458	+	21.6722i	0.673242	+	0.926638i	0.999828	−	0.0185290i	$-0.00589830\pi$
$547$	15.7458	+	21.6722i	0.673242	+	0.926638i	−0.326586	+	0.945167i	$0.605898\pi$
$548$	45.5874	+	14.8122i	1.94740	+	0.632747i
$549$	2.24571			0.0958446
$550$		0			0
$551$	−1.44060			−0.0613714
$552$	−53.0248	−	17.2288i	−2.25689	−	0.733307i
$553$	6.82950	+	9.40000i	0.290420	+	0.399729i
$554$	−5.82232	−	4.23016i	−0.247367	−	0.179722i
$555$		0			0
$556$	−38.6048	−	118.813i	−1.63721	−	5.03880i
$557$	−3.63214	+	4.99921i	−0.153899	+	0.211824i	−0.879004	−	0.476815i	$-0.841791\pi$
$557$	−3.63214	+	4.99921i	−0.153899	+	0.211824i	0.725105	+	0.688638i	$0.241791\pi$
$558$	−2.28584	−	3.14620i	−0.0967675	−	0.133189i
$559$	0.00704839	−	0.0216927i	0.000298115	−	0.000917504i
$560$		0			0
$561$	12.0913	−	15.6022i	0.510496	−	0.658725i
$562$		−	57.2521i		−	2.41503i
$563$	−28.0133	−	9.10209i	−1.18062	−	0.383607i	−0.348024	−	0.937486i	$-0.613147\pi$
$563$	−28.0133	−	9.10209i	−1.18062	−	0.383607i	−0.832598	+	0.553878i	$0.813147\pi$
$564$	−69.1948	+	50.2730i	−2.91363	+	2.11687i
$565$		0			0
$566$	9.23828	+	28.4325i	0.388314	+	1.19511i
$567$	−14.4226	+	4.68618i	−0.605691	+	0.196801i
$568$	70.7469	−	97.3747i	2.96847	−	4.08575i
$569$	31.0867	−	22.5858i	1.30322	−	0.946845i	0.303239	−	0.952915i	$-0.401932\pi$
$569$	31.0867	−	22.5858i	1.30322	−	0.946845i	0.999982	+	0.00606937i	$0.00193195\pi$
$570$		0			0
$571$	23.3745			0.978193			0.489096	−	0.872230i	$-0.337327\pi$
$571$	23.3745			0.978193			0.489096	+	0.872230i	$0.337327\pi$
$572$	−31.9885	+	21.7599i	−1.33751	+	0.909828i
$573$			23.8852i			0.997819i
$574$	7.48497	−	23.0364i	0.312417	−	0.961520i
$575$		0			0
$576$	9.38073	+	6.81550i	0.390864	+	0.283979i
$577$	17.7618	−	5.77115i	0.739432	−	0.240256i	0.0850044	−	0.996381i	$-0.472910\pi$
$577$	17.7618	−	5.77115i	0.739432	−	0.240256i	0.654428	+	0.756124i	$0.272910\pi$
$578$	−10.1375	+	3.29388i	−0.421666	+	0.137007i
$579$	29.5152	+	21.4441i	1.22661	+	0.891185i
$580$		0			0
$581$	−8.59220	+	26.4441i	−0.356464	+	1.09708i
$582$		−	78.5499i		−	3.25600i
$583$	7.34294	−	20.4240i	0.304114	−	0.845875i
$584$	30.5231			1.26306
$585$		0			0
$586$	−1.17026	+	0.850245i	−0.0483431	+	0.0351233i
$587$	−10.9774	+	15.1091i	−0.453087	+	0.623621i	−0.973057	−	0.230563i	$-0.925943\pi$
$587$	−10.9774	+	15.1091i	−0.453087	+	0.623621i	0.519970	+	0.854184i	$0.325943\pi$
$588$	29.9581	−	9.73396i	1.23545	−	0.401422i
$589$	1.82119	+	5.60504i	0.0750407	+	0.230951i
$590$		0			0
$591$	−11.9624	+	8.69117i	−0.492066	+	0.357507i
$592$	−28.4499	−	9.24392i	−1.16928	−	0.379923i
$593$		−	10.2335i		−	0.420240i	−0.977676	−	0.210120i	$-0.932615\pi$
$593$		−	10.2335i		−	0.420240i	0.977676	−	0.210120i	$-0.0673854\pi$
$594$	−1.54131	+	49.7421i	−0.0632408	+	2.04094i
$595$		0			0
$596$	−28.0590	+	86.3569i	−1.14934	+	3.53731i
$597$	0.443757	+	0.610779i	0.0181618	+	0.0249975i
$598$	−11.3052	+	15.5602i	−0.462303	+	0.636305i
$599$	−6.79277	−	20.9060i	−0.277545	−	0.854196i	−0.988535	−	0.150994i	$-0.951753\pi$
$599$	−6.79277	−	20.9060i	−0.277545	−	0.854196i	0.710990	−	0.703203i	$-0.248247\pi$
$600$		0			0
$601$	−15.0923	−	10.9652i	−0.615627	−	0.447279i	0.235764	−	0.971810i	$-0.424241\pi$
$601$	−15.0923	−	10.9652i	−0.615627	−	0.447279i	−0.851391	+	0.524531i	$0.824241\pi$
$602$	−0.0340677	−	0.0468901i	−0.00138850	−	0.00191110i
$603$	2.03666	+	0.661752i	0.0829393	+	0.0269486i
$604$	−131.143			−5.33613
$605$		0			0
$606$	67.6124			2.74657
$607$	−3.15306	−	1.02449i	−0.127979	−	0.0415829i	0.244327	−	0.969693i	$-0.421433\pi$
$607$	−3.15306	−	1.02449i	−0.127979	−	0.0415829i	−0.372306	+	0.928110i	$0.621433\pi$
$608$	−19.3626	−	26.6503i	−0.785256	−	1.08081i
$609$	2.83609	+	2.06054i	0.114924	+	0.0834973i
$610$		0			0
$611$	5.88875	+	18.1237i	0.238233	+	0.733207i
$612$	−3.67670	+	5.06055i	−0.148622	+	0.204560i
$613$	13.1489	+	18.0980i	0.531081	+	0.730970i	0.987295	−	0.158900i	$-0.0507948\pi$
$613$	13.1489	+	18.0980i	0.531081	+	0.730970i	−0.456214	+	0.889870i	$0.650795\pi$
$614$	−17.1254	+	52.7066i	−0.691126	+	2.12707i
$615$		0			0
$616$	−1.96648	+	63.4634i	−0.0792318	+	2.55701i
$617$			11.3963i			0.458798i	0.973332	+	0.229399i	$0.0736761\pi$
$617$			11.3963i			0.458798i	−0.973332	+	0.229399i	$0.926324\pi$
$618$	−1.83621	−	0.596620i	−0.0738631	−	0.0239996i
$619$	−16.5704	+	12.0391i	−0.666019	+	0.483891i	−0.868690	−	0.495356i	$-0.835038\pi$
$619$	−16.5704	+	12.0391i	−0.666019	+	0.483891i	0.202671	+	0.979247i	$0.435038\pi$
$620$		0			0
$621$	5.64591	+	17.3763i	0.226563	+	0.697288i
$622$	40.2765	−	13.0866i	1.61494	−	0.524726i
$623$	−15.4123	+	21.2132i	−0.617481	+	0.849890i
$624$	−45.5315	+	33.0806i	−1.82272	+	1.32428i
$625$		0			0
$626$	−78.6055			−3.14171
$627$	2.35813	−	6.55900i	0.0941745	−	0.261941i
$628$		−	91.7017i		−	3.65930i
$629$	2.01908	−	6.21409i	0.0805060	−	0.247772i
$630$		0			0
$631$	−14.1408	−	10.2739i	−0.562937	−	0.408998i	0.269596	−	0.962974i	$-0.413110\pi$
$631$	−14.1408	−	10.2739i	−0.562937	−	0.408998i	−0.832533	+	0.553976i	$0.813110\pi$
$632$	58.7294	−	19.0823i	2.33613	−	0.759054i
$633$	−1.22544	+	0.398168i	−0.0487067	+	0.0158258i
$634$	−42.1670	−	30.6361i	−1.67467	−	1.21672i
$635$		0			0
$636$	18.7465	−	57.6959i	0.743348	−	2.28779i
$637$		−	7.01830i		−	0.278075i
$638$	8.53333	−	5.80473i	0.337838	−	0.229812i
$639$	−3.64523			−0.144203
$640$		0			0
$641$	−4.17247	+	3.03148i	−0.164803	+	0.119736i	−0.667130	−	0.744942i	$-0.732477\pi$
$641$	−4.17247	+	3.03148i	−0.164803	+	0.119736i	0.502327	+	0.864678i	$0.332477\pi$
$642$	22.5194	−	30.9953i	0.888769	−	1.22328i
$643$	−17.9324	+	5.82659i	−0.707185	+	0.229778i	−0.640458	−	0.767993i	$-0.721256\pi$
$643$	−17.9324	+	5.82659i	−0.707185	+	0.229778i	−0.0667267	+	0.997771i	$0.521256\pi$
$644$	11.1531	+	34.3256i	0.439492	+	1.35262i
$645$		0			0
$646$	10.3849	−	7.54511i	0.408590	−	0.296858i
$647$	−23.3851	−	7.59827i	−0.919362	−	0.298719i	−0.189157	−	0.981947i	$-0.560575\pi$
$647$	−23.3851	−	7.59827i	−0.919362	−	0.298719i	−0.730205	+	0.683228i	$0.760575\pi$
$648$			80.5964i			3.16612i
$649$	11.1283	−	14.3596i	0.436825	−	0.563663i
$650$		0			0
$651$	4.43175	−	13.6395i	0.173694	−	0.534575i
$652$	40.6974	+	56.0151i	1.59383	+	2.19372i
$653$	24.2736	−	33.4097i	0.949898	−	1.30742i	−0.00167469	−	0.999999i	$-0.500533\pi$
$653$	24.2736	−	33.4097i	0.949898	−	1.30742i	0.951573	−	0.307424i	$-0.0994669\pi$
$654$	1.29417	+	3.98304i	0.0506060	+	0.155749i
$655$		0			0
$656$	−61.9754	−	45.0277i	−2.41973	−	1.75804i
$657$	−0.543356	−	0.747865i	−0.0211983	−	0.0291770i
$658$	46.0536	+	14.9637i	1.79536	+	0.583346i
$659$	4.73658			0.184511			0.0922555	−	0.995735i	$-0.470592\pi$
$659$	4.73658			0.184511			0.0922555	+	0.995735i	$0.470592\pi$
$660$		0			0
$661$	10.7556			0.418344			0.209172	−	0.977879i	$-0.432923\pi$
$661$	10.7556			0.418344			0.209172	+	0.977879i	$0.432923\pi$
$662$	−31.7943	−	10.3306i	−1.23572	−	0.401511i
$663$	−7.22553	−	9.94509i	−0.280616	−	0.386235i
$664$	119.552	+	86.8599i	4.63953	+	3.37082i
$665$		0			0
$666$	0.470455	+	1.44791i	0.0182298	+	0.0561054i
$667$	2.22710	−	3.06533i	0.0862335	−	0.118690i
$668$	−21.0346	−	28.9516i	−0.813852	−	1.12017i
$669$	−6.77401	+	20.8482i	−0.261898	+	0.806040i
$670$		0			0
$671$	23.4102	−	6.81246i	0.903741	−	0.262992i
$672$			80.1613i			3.09229i
$673$	35.8921	+	11.6621i	1.38354	+	0.449539i	0.903831	−	0.427889i	$-0.140743\pi$
$673$	35.8921	+	11.6621i	1.38354	+	0.449539i	0.479708	+	0.877428i	$0.340743\pi$
$674$	52.2063	−	37.9301i	2.01091	−	1.46101i
$675$		0			0
$676$	−15.2420	−	46.9100i	−0.586230	−	1.80423i
$677$	−22.1331	+	7.19149i	−0.850646	+	0.276392i	−0.701716	−	0.712456i	$-0.747583\pi$
$677$	−22.1331	+	7.19149i	−0.850646	+	0.276392i	−0.148929	+	0.988848i	$0.547583\pi$
$678$	−7.23659	+	9.96032i	−0.277920	+	0.382524i
$679$	−26.5694	+	19.3038i	−1.01964	+	0.740811i
$680$		0			0
$681$	−28.3629			−1.08687
$682$	−33.3727	−	25.8630i	−1.27791	−	0.990346i
$683$			12.6153i			0.482712i	0.970437	+	0.241356i	$0.0775922\pi$
$683$			12.6153i			0.482712i	−0.970437	+	0.241356i	$0.922408\pi$
$684$	−0.682545	+	2.10066i	−0.0260977	+	0.0803206i
$685$		0			0
$686$	−44.1511	−	32.0776i	−1.68570	−	1.22473i
$687$	18.4078	−	5.98107i	0.702303	−	0.228192i
$688$	−0.174335	+	0.0566448i	−0.00664645	+	0.00215956i
$689$	−10.9350	−	7.94478i	−0.416592	−	0.302672i
$690$		0			0
$691$	2.26469	−	6.97000i	0.0861529	−	0.265151i	−0.898694	−	0.438576i	$-0.855483\pi$
$691$	2.26469	−	6.97000i	0.0861529	−	0.265151i	0.984847	+	0.173424i	$0.0554831\pi$
$692$			11.9000i			0.452368i
$693$	1.58996	−	1.08156i	0.0603976	−	0.0410850i
$694$	57.0772			2.16662
$695$		0			0
$696$	15.0730	−	10.9512i	0.571340	−	0.415103i
$697$	9.83506	−	13.5368i	0.372530	−	0.512743i
$698$	−67.0752	+	21.7940i	−2.53883	+	0.824917i
$699$	1.28150	+	3.94405i	0.0484708	+	0.149178i
$700$		0			0
$701$	29.7236	−	21.5954i	1.12264	−	0.815649i	0.138036	−	0.990427i	$-0.455921\pi$
$701$	29.7236	−	21.5954i	1.12264	−	0.815649i	0.984608	+	0.174778i	$0.0559209\pi$
$702$	29.4757	+	9.57724i	1.11249	+	0.361470i
$703$		−	2.30717i		−	0.0870166i
$704$	118.464	+	42.5907i	4.46476	+	1.60520i
$705$		0			0
$706$	2.91413	−	8.96878i	0.109675	−	0.337545i
$707$	−16.6159	−	22.8698i	−0.624904	−	0.860107i
$708$	29.8470	−	41.0809i	1.12172	−	1.54391i
$709$	8.01840	+	24.6781i	0.301137	+	0.926806i	0.981090	+	0.193550i	$0.0620002\pi$
$709$	8.01840	+	24.6781i	0.301137	+	0.926806i	−0.679953	+	0.733256i	$0.738000\pi$
$710$		0			0
$711$	−1.51302	−	1.09927i	−0.0567425	−	0.0412258i
$712$	81.9118	+	112.742i	3.06978	+	4.22518i
$713$	−14.7420	−	4.78997i	−0.552093	−	0.179386i
$714$	−31.2369			−1.16901
$715$		0			0
$716$	−55.1586			−2.06137
$717$	−38.6305	−	12.5518i	−1.44268	−	0.468756i
$718$	7.76877	+	10.6928i	0.289928	+	0.399052i
$719$	−2.19677	−	1.59605i	−0.0819259	−	0.0595226i	0.546068	−	0.837741i	$-0.316124\pi$
$719$	−2.19677	−	1.59605i	−0.0819259	−	0.0595226i	−0.627994	+	0.778218i	$0.716124\pi$
$720$		0			0
$721$	0.249445	+	0.767714i	0.00928983	+	0.0285912i
$722$	−28.2197	+	38.8410i	−1.05023	+	1.44551i
$723$	−18.2294	−	25.0906i	−0.677958	−	0.933129i
$724$	33.7295	−	103.809i	1.25355	−	3.85802i
$725$		0			0
$726$	12.4605	+	48.3539i	0.462453	+	1.79458i
$727$			18.6564i			0.691926i	0.938248	+	0.345963i	$0.112448\pi$
$727$			18.6564i			0.691926i	−0.938248	+	0.345963i	$0.887552\pi$
$728$	37.6066	+	12.2191i	1.39379	+	0.452871i
$729$	23.5917	−	17.1404i	0.873767	−	0.634829i
$730$		0			0
$731$	−0.0123725	−	0.0380786i	−0.000457613	−	0.00140839i
$732$	64.8133	−	21.0591i	2.39557	−	0.778367i
$733$	19.7188	−	27.1407i	0.728332	−	1.00246i	−0.270874	−	0.962615i	$-0.587313\pi$
$733$	19.7188	−	27.1407i	0.728332	−	1.00246i	0.999206	−	0.0398480i	$-0.0126874\pi$
$734$	−29.3826	+	21.3477i	−1.08453	+	0.787958i
$735$		0			0
$736$	86.6408			3.19362
$737$	23.2384	+	0.720068i	0.855999	+	0.0265240i
$738$			3.89873i			0.143514i
$739$	−13.7840	+	42.4228i	−0.507053	+	1.56055i	0.290238	+	0.956955i	$0.406266\pi$
$739$	−13.7840	+	42.4228i	−0.507053	+	1.56055i	−0.797291	+	0.603595i	$0.793734\pi$
$740$		0			0
$741$	−3.51170	−	2.55140i	−0.129006	−	0.0937280i
$742$	−32.6652	+	10.6136i	−1.19918	+	0.389637i
$743$	−12.8523	+	4.17597i	−0.471506	+	0.153202i	−0.535125	−	0.844773i	$-0.679736\pi$
$743$	−12.8523	+	4.17597i	−0.471506	+	0.153202i	0.0636194	+	0.997974i	$0.479736\pi$
$744$	−61.6636	−	44.8013i	−2.26070	−	1.64249i
$745$		0			0
$746$	21.3192	−	65.6139i	0.780553	−	2.40229i
$747$		−	4.47546i		−	0.163748i
$748$	−22.9761	+	63.9066i	−0.840088	+	2.33666i
$749$	−16.0183			−0.585295
$750$		0			0
$751$	20.4965	−	14.8915i	0.747926	−	0.543400i	−0.147257	−	0.989098i	$-0.547045\pi$
$751$	20.4965	−	14.8915i	0.747926	−	0.543400i	0.895183	+	0.445698i	$0.147045\pi$
$752$	90.0180	−	123.899i	3.28262	−	4.51814i
$753$	−5.63028	+	1.82939i	−0.205179	+	0.0666666i
$754$	−1.98614	−	6.11270i	−0.0723308	−	0.222611i
$755$		0			0
$756$	47.0510	−	34.1845i	1.71123	−	1.24328i
$757$	−16.8676	−	5.48060i	−0.613062	−	0.199196i	−0.0140044	−	0.999902i	$-0.504458\pi$
$757$	−16.8676	−	5.48060i	−0.613062	−	0.199196i	−0.599057	+	0.800706i	$0.704458\pi$
$758$			5.63946i			0.204834i
$759$	10.3108	+	15.1576i	0.374260	+	0.550186i
$760$		0			0
$761$	7.43998	−	22.8979i	0.269699	−	0.830048i	−0.720875	−	0.693066i	$-0.756260\pi$
$761$	7.43998	−	22.8979i	0.269699	−	0.830048i	0.990573	−	0.136982i	$-0.0437404\pi$
$762$	21.7120	+	29.8840i	0.786541	+	1.08258i
$763$	1.02921	−	1.41659i	0.0372600	−	0.0512840i
$764$	−25.3939	−	78.1543i	−0.918718	−	2.82752i
$765$		0			0
$766$	72.0362	+	52.3374i	2.60278	+	1.89103i
$767$	−6.65006	−	9.15303i	−0.240120	−	0.330497i
$768$	112.480	+	36.5469i	4.05876	+	1.31877i
$769$	−25.1389			−0.906532			−0.453266	−	0.891375i	$-0.649741\pi$
$769$	−25.1389			−0.906532			−0.453266	+	0.891375i	$0.649741\pi$
$770$		0			0
$771$	−21.5849			−0.777363
$772$	−119.375	−	38.7872i	−4.29639	−	1.39598i
$773$	27.2173	+	37.4614i	0.978937	+	1.34739i	0.937400	+	0.348255i	$0.113226\pi$
$773$	27.2173	+	37.4614i	0.978937	+	1.34739i	0.0415374	+	0.999137i	$0.486774\pi$
$774$	0.00754739	+	0.00548350i	0.000271285	+	0.000197100i
$775$		0			0
$776$	53.9368	+	166.000i	1.93622	+	5.95907i
$777$	−3.30004	+	4.54211i	−0.118388	+	0.162947i
$778$	4.53625	+	6.24362i	0.162633	+	0.223845i
$779$	1.82579	−	5.61919i	0.0654155	−	0.201328i
$780$		0			0
$781$	−37.9994	+	11.0580i	−1.35972	+	0.395685i
$782$			33.7618i			1.20732i
$783$	−5.80666	−	1.88670i	−0.207513	−	0.0674251i
$784$	−45.6309	+	33.1528i	−1.62968	+	1.18403i
$785$		0			0
$786$	−3.77701	−	11.6245i	−0.134722	−	0.414630i
$787$	−18.0319	+	5.85893i	−0.642769	+	0.208848i	−0.612223	−	0.790685i	$-0.709724\pi$
$787$	−18.0319	+	5.85893i	−0.642769	+	0.208848i	−0.0305456	+	0.999533i	$0.509724\pi$
$788$	29.9017	−	41.1561i	1.06520	−	1.46613i
$789$	−8.29565	+	6.02714i	−0.295333	+	0.214572i
$790$		0			0
$791$	5.14747			0.183023
$792$	−2.85558	−	9.81286i	−0.101469	−	0.348685i
$793$		−	15.1839i		−	0.539195i
$794$	22.7644	−	70.0616i	0.807878	−	2.48639i
$795$		0			0
$796$	−2.10137	−	1.52673i	−0.0744809	−	0.0541136i
$797$	11.2888	−	3.66796i	0.399871	−	0.129926i	−0.102176	−	0.994766i	$-0.532581\pi$
$797$	11.2888	−	3.66796i	0.399871	−	0.129926i	0.502047	+	0.864841i	$0.332581\pi$
$798$	−10.4902	+	3.40846i	−0.371348	+	0.120658i
$799$	27.0623	+	19.6619i	0.957396	+	0.695589i
$800$		0			0
$801$	1.30421	−	4.01394i	0.0460819	−	0.141826i
$802$		−	50.3191i		−	1.77683i
$803$	−7.93284	−	6.14776i	−0.279944	−	0.216950i
$804$	64.9855			2.29186
$805$		0			0
$806$	−21.2723	+	15.4552i	−0.749285	+	0.544387i
$807$	21.6084	−	29.7414i	0.760652	−	1.04695i
$808$	−142.886	+	46.4265i	−5.02671	+	1.63328i
$809$	2.17500	+	6.69397i	0.0764690	+	0.235347i	0.981983	−	0.188969i	$-0.0605145\pi$
$809$	2.17500	+	6.69397i	0.0764690	+	0.235347i	−0.905514	+	0.424316i	$0.860514\pi$
$810$		0			0
$811$	28.5326	−	20.7302i	1.00192	−	0.727935i	0.0394182	−	0.999223i	$-0.487450\pi$
$811$	28.5326	−	20.7302i	1.00192	−	0.727935i	0.962498	+	0.271288i	$0.0874496\pi$
$812$	−11.4706	−	3.72702i	−0.402539	−	0.130793i
$813$		−	14.2131i		−	0.498475i
$814$	9.29651	+	13.6665i	0.325843	+	0.479010i
$815$		0			0
$816$	−30.5283	+	93.9566i	−1.06871	+	3.28914i
$817$	−0.00831002	−	0.0114378i	−0.000290731	−	0.000400157i
$818$	−12.3452	+	16.9917i	−0.431639	+	0.594100i
$819$	−0.370064	−	1.13894i	−0.0129311	−	0.0397977i
$820$		0			0
$821$	−41.5952	−	30.2207i	−1.45168	−	1.05471i	−0.985435	−	0.170053i	$-0.945606\pi$
$821$	−41.5952	−	30.2207i	−1.45168	−	1.05471i	−0.466246	−	0.884655i	$-0.654394\pi$
$822$	−22.6464	−	31.1701i	−0.789885	−	1.08718i
$823$	−36.7186	−	11.9306i	−1.27993	−	0.415875i	−0.411376	−	0.911466i	$-0.634952\pi$
$823$	−36.7186	−	11.9306i	−1.27993	−	0.415875i	−0.868556	+	0.495591i	$0.834952\pi$
$824$	4.29015			0.149454
$825$		0			0
$826$	−28.7490			−1.00031
$827$	−16.7851	−	5.45382i	−0.583677	−	0.189648i	0.00227034	−	0.999997i	$-0.499277\pi$
$827$	−16.7851	−	5.45382i	−0.583677	−	0.189648i	−0.585947	+	0.810349i	$0.699277\pi$
$828$	−3.41464	−	4.69986i	−0.118667	−	0.163331i
$829$	−20.5573	−	14.9357i	−0.713984	−	0.518740i	0.170472	−	0.985362i	$-0.445471\pi$
$829$	−20.5573	−	14.9357i	−0.713984	−	0.518740i	−0.884457	+	0.466623i	$0.845471\pi$
$830$		0			0
$831$	1.32008	+	4.06279i	0.0457931	+	0.140937i
$832$	46.0814	−	63.4257i	1.59759	−	2.19889i
$833$	−7.24131	−	9.96681i	−0.250897	−	0.345330i
$834$	−31.0301	+	95.5010i	−1.07449	+	3.30693i
$835$		0			0
$836$	−0.742693	+	23.9686i	−0.0256866	+	0.828972i
$837$			24.9776i			0.863351i
$838$	−78.4608	−	25.4935i	−2.71038	−	0.880657i
$839$	−44.0635	+	32.0140i	−1.52124	+	1.10525i	−0.560372	+	0.828241i	$0.689342\pi$
$839$	−44.0635	+	32.0140i	−1.52124	+	1.10525i	−0.960868	+	0.277005i	$0.910658\pi$
$840$		0			0
$841$	−8.57023	−	26.3764i	−0.295525	−	0.909533i
$842$	−66.6255	+	21.6480i	−2.29607	+	0.746038i
$843$	−19.9752	+	27.4934i	−0.687981	+	0.946924i
$844$	3.58640	−	2.60567i	0.123449	−	0.0896910i
$845$		0			0
$846$	−7.79421			−0.267971
$847$	13.2934	−	16.0978i	0.456768	−	0.553127i
$848$			108.626i			3.73022i
$849$	5.48367	−	16.8770i	0.188199	−	0.579217i
$850$		0			0
$851$	4.90926	+	3.56678i	0.168287	+	0.122268i
$852$	−105.205	+	34.1831i	−3.60425	+	1.17109i
$853$	−1.61978	+	0.526298i	−0.0554601	+	0.0180201i	−0.336616	−	0.941642i	$-0.609282\pi$
$853$	−1.61978	+	0.526298i	−0.0554601	+	0.0180201i	0.281156	+	0.959662i	$0.409282\pi$
$854$	−31.2145	−	22.6787i	−1.06814	−	0.776048i
$855$		0			0
$856$	−26.3073	+	80.9656i	−0.899166	+	2.76735i
$857$			34.5112i			1.17888i	0.807812	+	0.589440i	$0.200652\pi$
$857$			34.5112i			1.17888i	−0.807812	+	0.589440i	$0.799348\pi$
$858$	31.0821	+	0.963112i	1.06113	+	0.0328801i
$859$	41.1808			1.40507			0.702535	−	0.711650i	$-0.252052\pi$
$859$	41.1808			1.40507			0.702535	+	0.711650i	$0.252052\pi$
$860$		0			0
$861$	−11.6318	+	8.45097i	−0.396409	+	0.288008i
$862$	−33.3508	+	45.9034i	−1.13593	+	1.56348i
$863$	−17.3860	+	5.64904i	−0.591825	+	0.192296i	−0.589591	−	0.807702i	$-0.700711\pi$
$863$	−17.3860	+	5.64904i	−0.591825	+	0.192296i	−0.00223395	+	0.999998i	$0.500711\pi$
$864$	−43.1424	−	132.779i	−1.46773	−	4.51722i
$865$		0			0
$866$	30.7752	−	22.3595i	1.04579	−	0.759808i
$867$	6.01744	+	1.95519i	0.204363	+	0.0664016i
$868$			49.3412i			1.67475i
$869$	−19.1070	−	6.86944i	−0.648159	−	0.233030i
$870$		0			0
$871$	4.47428	−	13.7704i	0.151605	−	0.466593i
$872$	−5.46996	−	7.52875i	−0.185236	−	0.254956i
$873$	3.10712	−	4.27658i	0.105160	−	0.144740i
$874$	3.68397	+	11.3381i	0.124612	+	0.383517i
$875$		0			0
$876$	−22.6948	−	16.4888i	−0.766788	−	0.557104i
$877$	−24.3907	−	33.5709i	−0.823614	−	1.13361i	−0.989078	−	0.147392i	$-0.952912\pi$
$877$	−24.3907	−	33.5709i	−0.823614	−	1.13361i	0.165464	−	0.986216i	$-0.447088\pi$
$878$	63.6059	+	20.6668i	2.14659	+	0.697471i
$879$	0.858629			0.0289608
$880$		0			0
$881$	49.7389			1.67575			0.837873	−	0.545866i	$-0.183799\pi$
$881$	49.7389			1.67575			0.837873	+	0.545866i	$0.183799\pi$
$882$	2.73005	+	0.887046i	0.0919254	+	0.0298684i
$883$	−11.1785	−	15.3859i	−0.376186	−	0.517776i	0.578383	−	0.815765i	$-0.303684\pi$
$883$	−11.1785	−	15.3859i	−0.376186	−	0.517776i	−0.954569	+	0.297990i	$0.903684\pi$
$884$	34.2157	+	24.8592i	1.15080	+	0.836105i
$885$		0			0
$886$	−1.45074	−	4.46491i	−0.0487384	−	0.150001i
$887$	1.98443	−	2.73133i	0.0666305	−	0.0917090i	−0.774401	−	0.632695i	$-0.781949\pi$
$887$	1.98443	−	2.73133i	0.0666305	−	0.0917090i	0.841032	+	0.540986i	$0.181949\pi$
$888$	17.5387	+	24.1400i	0.588561	+	0.810085i
$889$	4.77244	−	14.6881i	0.160063	−	0.492622i
$890$		0			0
$891$	16.2332	−	20.9467i	0.543831	−	0.701740i
$892$		−	75.4189i		−	2.52521i
$893$	11.2337	+	3.65005i	0.375921	+	0.122144i
$894$	59.0461	−	42.8995i	1.97480	−	1.43477i
$895$		0			0
$896$	−31.3798	−	96.5771i	−1.04833	−	3.22641i
$897$	10.8579	−	3.52794i	0.362534	−	0.117794i
$898$	−4.23011	+	5.82225i	−0.141161	+	0.194291i
$899$	4.19060	−	3.04465i	0.139764	−	0.101545i
$900$		0			0
$901$	−23.7263			−0.790437
$902$	11.8270	+	40.6420i	0.393795	+	1.35323i
$903$			0.0344036i			0.00114488i
$904$	8.45385	−	26.0183i	0.281171	−	0.865355i
$905$		0			0
$906$	85.2797	+	61.9593i	2.83323	+	2.05846i
$907$	31.9372	−	10.3770i	1.06046	−	0.344563i	0.273692	−	0.961817i	$-0.411755\pi$
$907$	31.9372	−	10.3770i	1.06046	−	0.344563i	0.786764	+	0.617254i	$0.211755\pi$
$908$	92.8055	−	30.1543i	3.07986	−	1.00071i
$909$	3.68110	+	2.67448i	0.122094	+	0.0887068i
$910$		0			0
$911$	14.7638	−	45.4384i	0.489147	−	1.50544i	−0.336736	−	0.941599i	$-0.609323\pi$
$911$	14.7638	−	45.4384i	0.489147	−	1.50544i	0.825883	−	0.563841i	$-0.190677\pi$
$912$			34.8843i			1.15513i
$913$	−13.5765	−	46.6540i	−0.449316	−	1.54402i
$914$	−38.6081			−1.27704
$915$		0			0
$916$	−53.8730	+	39.1410i	−1.78001	+	1.29326i
$917$	−3.00374	+	4.13430i	−0.0991923	+	0.136527i
$918$	51.7405	−	16.8115i	1.70769	−	0.554863i
$919$	−3.79764	−	11.6879i	−0.125273	−	0.385550i	0.868678	−	0.495377i	$-0.164970\pi$
$919$	−3.79764	−	11.6879i	−0.125273	−	0.385550i	−0.993951	+	0.109827i	$0.964970\pi$
$920$		0			0
$921$	26.6132	−	19.3356i	0.876934	−	0.637130i
$922$	69.7926	+	22.6770i	2.29850	+	0.746827i
$923$			24.6464i			0.811246i
$924$	35.7454	−	46.1246i	1.17594	−	1.51739i
$925$		0			0
$926$	20.1987	−	62.1651i	0.663769	−	2.04287i
$927$	−0.0763708	−	0.105115i	−0.00250835	−	0.00345244i
$928$	−17.0180	+	23.4233i	−0.558644	+	0.768908i
$929$	−16.3005	−	50.1679i	−0.534804	−	1.64596i	−0.744073	−	0.668098i	$-0.767109\pi$
$929$	−16.3005	−	50.1679i	−0.534804	−	1.64596i	0.209269	−	0.977858i	$-0.432891\pi$
$930$		0			0
$931$	−3.51937	−	2.55697i	−0.115343	−	0.0838014i
$932$	−8.38633	−	11.5428i	−0.274703	−	0.378097i
$933$	−23.9074	−	7.76797i	−0.782692	−	0.254312i
$934$	−27.9975			−0.916107
$935$		0			0
$936$	−6.36462			−0.208034
$937$	38.5181	+	12.5153i	1.25833	+	0.408857i	0.860900	−	0.508775i	$-0.169901\pi$
$937$	38.5181	+	12.5153i	1.25833	+	0.408857i	0.397432	+	0.917632i	$0.369901\pi$
$938$	−21.6260	−	29.7656i	−0.706114	−	0.971882i
$939$	37.7477	+	27.4253i	1.23185	+	0.894991i
$940$		0			0
$941$	2.10825	+	6.48852i	0.0687269	+	0.211520i	0.979521	−	0.201341i	$-0.0645298\pi$
$941$	2.10825	+	6.48852i	0.0687269	+	0.211520i	−0.910794	+	0.412860i	$0.864530\pi$
$942$	−43.3250	+	59.6318i	−1.41161	+	1.94291i
$943$	9.13407	+	12.5720i	0.297446	+	0.409400i
$944$	−28.0969	+	86.4735i	−0.914478	+	2.81447i
$945$		0			0
$946$	0.0953115	+	0.0342669i	0.00309884	+	0.00111411i
$947$			31.5841i			1.02634i	0.858286	+	0.513172i	$0.171530\pi$
$947$			31.5841i			1.02634i	−0.858286	+	0.513172i	$0.828470\pi$
$948$	−53.9754	−	17.5377i	−1.75304	−	0.569597i
$949$	−5.05652	+	3.67378i	−0.164142	+	0.119256i
$950$		0			0
$951$	9.56043	+	29.4240i	0.310018	+	0.954138i
$952$	66.0132	−	21.4490i	2.13950	−	0.695165i
$953$	12.7347	−	17.5279i	0.412519	−	0.567784i	−0.551312	−	0.834299i	$-0.685872\pi$
$953$	12.7347	−	17.5279i	0.412519	−	0.567784i	0.963831	+	0.266516i	$0.0858724\pi$
$954$	4.47252	−	3.24948i	0.144803	−	0.105206i
$955$		0			0
$956$	139.747			4.51973
$957$	−6.12311	−	0.189731i	−0.197932	−	0.00613314i
$958$		−	1.88468i		−	0.0608912i
$959$	−4.97785	+	15.3202i	−0.160743	+	0.494716i
$960$		0			0
$961$	7.93576	+	5.76566i	0.255992	+	0.185989i
$962$	9.78973	−	3.18088i	0.315634	−	0.102556i
$963$	2.45209	−	0.796734i	0.0790176	−	0.0256744i
$964$	86.3233	+	62.7175i	2.78029	+	2.02000i
$965$		0			0
$966$	8.96472	−	27.5906i	0.288435	−	0.887712i
$967$		−	9.03757i		−	0.290629i	−0.989386	−	0.145314i	$-0.953581\pi$
$967$		−	9.03757i		−	0.290629i	0.989386	−	0.145314i	$-0.0464193\pi$
$968$	−59.5354	−	93.6307i	−1.91354	−	3.00940i
$969$	−7.61950			−0.244774
$970$		0			0
$971$	−27.7379	+	20.1528i	−0.890151	+	0.646733i	−0.935917	−	0.352220i	$-0.885427\pi$
$971$	−27.7379	+	20.1528i	−0.890151	+	0.646733i	0.0457664	+	0.998952i	$0.485427\pi$
$972$	−10.4961	+	14.4467i	−0.336663	+	0.463377i
$973$	39.9288	−	12.9736i	1.28006	−	0.415916i
$974$	9.07928	+	27.9431i	0.290919	+	0.895356i
$975$		0			0
$976$	−98.7211	+	71.7251i	−3.15998	+	2.29586i
$977$	16.3381	+	5.30858i	0.522703	+	0.169837i	0.558472	−	0.829523i	$-0.311388\pi$
$977$	16.3381	+	5.30858i	0.522703	+	0.169837i	−0.0357684	+	0.999360i	$0.511388\pi$
$978$		−	55.6532i		−	1.77959i
$979$	1.41914	−	45.7993i	0.0453559	−	1.46375i
$980$		0			0
$981$	−0.0870932	+	0.268045i	−0.00278067	+	0.00855802i
$982$	18.7695	+	25.8340i	0.598958	+	0.824395i
$983$	2.26844	−	3.12224i	0.0723519	−	0.0995839i	−0.771307	−	0.636463i	$-0.780397\pi$
$983$	2.26844	−	3.12224i	0.0723519	−	0.0995839i	0.843659	+	0.536879i	$0.180397\pi$
$984$	23.6129	+	72.6730i	0.752751	+	2.31673i
$985$		0			0
$986$	−9.12748	−	6.63150i	−0.290678	−	0.211190i
$987$	−16.8949	−	23.2538i	−0.537771	−	0.740178i
$988$	14.2031	+	4.61487i	0.451861	+	0.146819i
$989$	0.0371845			0.00118240
$990$		0			0
$991$	−31.5631			−1.00263			−0.501317	−	0.865264i	$-0.667151\pi$
$991$	−31.5631			−1.00263			−0.501317	+	0.865264i	$0.667151\pi$
$992$	112.649	+	36.6019i	3.57661	+	1.16211i
$993$	11.6639	+	16.0539i	0.370141	+	0.509456i
$994$	50.6673	+	36.8119i	1.60707	+	1.16760i
$995$		0			0
$996$	−41.9685	−	129.166i	−1.32982	−	4.09277i
$997$	−5.44564	+	7.49529i	−0.172465	+	0.237378i	−0.886496	−	0.462736i	$-0.846868\pi$
$997$	−5.44564	+	7.49529i	−0.172465	+	0.237378i	0.714031	+	0.700114i	$0.246868\pi$
$998$	−15.0116	−	20.6617i	−0.475184	−	0.654034i
$999$	3.02162	−	9.29959i	0.0955999	−	0.294226i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.z.c.174.8		32
5.2	odd	4		275.2.h.c.251.1	yes	16
5.3	odd	4		275.2.h.e.251.4	yes	16
5.4	even	2	inner	275.2.z.c.174.1		32
11.5	even	5	inner	275.2.z.c.49.1		32
55.7	even	20		3025.2.a.bm.1.8		8
55.18	even	20		3025.2.a.bj.1.1		8
55.27	odd	20		275.2.h.c.126.1	✓	16
55.37	odd	20		3025.2.a.bi.1.1		8
55.38	odd	20		275.2.h.e.126.4	yes	16
55.48	odd	20		3025.2.a.bn.1.8		8
55.49	even	10	inner	275.2.z.c.49.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.h.c.126.1	✓	16	55.27	odd	20
275.2.h.c.251.1	yes	16	5.2	odd	4
275.2.h.e.126.4	yes	16	55.38	odd	20
275.2.h.e.251.4	yes	16	5.3	odd	4
275.2.z.c.49.1		32	11.5	even	5	inner
275.2.z.c.49.8		32	55.49	even	10	inner
275.2.z.c.174.1		32	5.4	even	2	inner
275.2.z.c.174.8		32	1.1	even	1	trivial
3025.2.a.bi.1.1		8	55.37	odd	20
3025.2.a.bj.1.1		8	55.18	even	20
3025.2.a.bm.1.8		8	55.7	even	20
3025.2.a.bn.1.8		8	55.48	odd	20

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.z (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.63006 + 0.854560i) q^{2} +(-0.964848 - 1.32800i) q^{3} +(4.56893 + 3.31953i) q^{4} +(-1.40276 - 4.31724i) q^{6} +(-1.11557 + 1.53545i) q^{7} +(5.92892 + 8.16046i) q^{8} +(0.0944009 - 0.290536i) q^{9} +(0.102720 - 3.31503i) q^{11} -9.27038i q^{12} +(-1.96439 - 0.638270i) q^{13} +(-4.24616 + 3.08501i) q^{14} +(5.12949 + 15.7870i) q^{16} +(-3.44822 + 1.12040i) q^{17} +(0.496561 - 0.683457i) q^{18} +(-1.03575 + 0.752517i) q^{19} +3.11543 q^{21} +(3.10305 - 8.63097i) q^{22} -3.36725i q^{23} +(5.11658 - 15.7472i) q^{24} +(-4.62104 - 3.35738i) q^{26} +(-5.16038 + 1.67671i) q^{27} +(-10.1939 + 3.31221i) q^{28} +(0.910336 + 0.661398i) q^{29} +(1.42251 - 4.37805i) q^{31} +25.7304i q^{32} +(-4.50147 + 3.06209i) q^{33} -10.0265 q^{34} +(1.39575 - 1.01407i) q^{36} +(-1.05926 + 1.45794i) q^{37} +(-3.36716 + 1.09406i) q^{38} +(1.04772 + 3.22455i) q^{39} +(-3.73360 + 2.71262i) q^{41} +(8.19379 + 2.66232i) q^{42} +0.0110430i q^{43} +(11.4737 - 14.8052i) q^{44} +(2.87752 - 8.85610i) q^{46} +(-5.42297 - 7.46408i) q^{47} +(16.0159 - 22.0440i) q^{48} +(1.05001 + 3.23159i) q^{49} +(4.81489 + 3.49822i) q^{51} +(-6.85643 - 9.43707i) q^{52} +(6.22368 + 2.02220i) q^{53} -15.0050 q^{54} -19.1441 q^{56} +(1.99868 + 0.649412i) q^{57} +(1.82904 + 2.51746i) q^{58} +(4.43142 + 3.21961i) q^{59} +(2.27166 + 6.99144i) q^{61} +(7.48261 - 10.2989i) q^{62} +(0.340793 + 0.469061i) q^{63} +(-11.7292 + 36.0987i) q^{64} +(-14.4559 + 4.20672i) q^{66} +7.01002i q^{67} +(-19.4739 - 6.32745i) q^{68} +(-4.47171 + 3.24889i) q^{69} +(-3.68735 - 11.3485i) q^{71} +(2.93060 - 0.952211i) q^{72} +(1.77865 - 2.44810i) q^{73} +(-4.03181 + 2.92928i) q^{74} -7.23028 q^{76} +(4.97548 + 3.85587i) q^{77} +9.37610i q^{78} +(1.89180 - 5.82235i) q^{79} +(6.46422 + 4.69653i) q^{81} +(-12.1377 + 3.94377i) q^{82} +(13.9332 - 4.52716i) q^{83} +(14.2342 + 10.3418i) q^{84} +(-0.00943687 + 0.0290437i) q^{86} -1.84707i q^{87} +(27.6612 - 18.8163i) q^{88} +13.8156 q^{89} +(3.17145 - 2.30419i) q^{91} +(11.1777 - 15.3848i) q^{92} +(-7.18656 + 2.33505i) q^{93} +(-7.88426 - 24.2653i) q^{94} +(34.1699 - 24.8259i) q^{96} +(16.4571 + 5.34722i) q^{97} +9.39658i q^{98} +(-0.953440 - 0.342786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4} - 6 q^{6} - 16 q^{9} - 10 q^{11} - 6 q^{14} - 8 q^{16} + 26 q^{19} + 20 q^{21} + 86 q^{24} - 68 q^{26} + 22 q^{29} - 20 q^{31} - 40 q^{34} + 6 q^{36} - 6 q^{39} + 50 q^{41} + 2 q^{44} + 80 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) \) 32 * q + 4 * q^4 - 6 * q^6 - 16 * q^9 - 10 * q^11 - 6 * q^14 - 8 * q^16 + 26 * q^19 + 20 * q^21 + 86 * q^24 - 68 * q^26 + 22 * q^29 - 20 * q^31 - 40 * q^34 + 6 * q^36 - 6 * q^39 + 50 * q^41 + 2 * q^44 + 80 * q^46 - 32 * q^49 + 70 * q^51 - 120 * q^54 - 40 * q^56 - 28 * q^59 + 32 * q^61 - 80 * q^64 - 110 * q^66 - 70 * q^69 - 92 * q^71 + 14 * q^74 - 124 * q^76 + 78 * q^79 - 86 * q^81 + 108 * q^84 + 4 * q^86 + 44 * q^89 - 68 * q^91 + 80 * q^94 + 216 * q^96 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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