LMFDB - Embedded newform 575.2.k.g.26.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(26,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("575.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.k (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 115)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			26.7
Character	$\chi$	$=$	575.26
Dual form			575.2.k.g.376.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.152174 + 1.05840i) q^{2} +(1.14653 - 2.51056i) q^{3} +(0.821942 - 0.241344i) q^{4} +(2.83164 + 0.831443i) q^{6} +(2.32389 - 1.49347i) q^{7} +(1.26891 + 2.77851i) q^{8} +(-3.02378 - 3.48962i) q^{9} +O(q^{10})$	\(q+(0.152174 + 1.05840i) q^{2} +(1.14653 - 2.51056i) q^{3} +(0.821942 - 0.241344i) q^{4} +(2.83164 + 0.831443i) q^{6} +(2.32389 - 1.49347i) q^{7} +(1.26891 + 2.77851i) q^{8} +(-3.02378 - 3.48962i) q^{9} +(-0.562328 + 3.91108i) q^{11} +(0.336476 - 2.34024i) q^{12} +(1.80656 + 1.16100i) q^{13} +(1.93432 + 2.23232i) q^{14} +(-1.30637 + 0.839551i) q^{16} +(2.95957 + 0.869007i) q^{17} +(3.23326 - 3.73138i) q^{18} +(-1.44374 + 0.423921i) q^{19} +(-1.08503 - 7.54656i) q^{21} -4.22504 q^{22} +(-3.90785 - 2.78005i) q^{23} +8.43046 q^{24} +(-0.953890 + 2.08873i) q^{26} +(-4.28324 + 1.25767i) q^{27} +(1.54966 - 1.78840i) q^{28} +(-9.09371 - 2.67015i) q^{29} +(-3.11093 - 6.81198i) q^{31} +(2.91323 + 3.36205i) q^{32} +(9.17425 + 5.89593i) q^{33} +(-0.469383 + 3.26463i) q^{34} +(-3.32757 - 2.13850i) q^{36} +(-2.30662 - 2.66198i) q^{37} +(-0.668376 - 1.46354i) q^{38} +(4.98605 - 3.20434i) q^{39} +(-5.83097 + 6.72930i) q^{41} +(7.82213 - 2.29679i) q^{42} +(0.178352 - 0.390536i) q^{43} +(0.481714 + 3.35039i) q^{44} +(2.34772 - 4.55911i) q^{46} -2.52082 q^{47} +(0.609948 + 4.24228i) q^{48} +(0.262086 - 0.573889i) q^{49} +(5.57493 - 6.43382i) q^{51} +(1.76509 + 0.518276i) q^{52} +(5.62428 - 3.61451i) q^{53} +(-1.98292 - 4.34198i) q^{54} +(7.09842 + 4.56188i) q^{56} +(-0.591020 + 4.11064i) q^{57} +(1.44225 - 10.0311i) q^{58} +(0.279035 + 0.179325i) q^{59} +(-0.560667 - 1.22769i) q^{61} +(6.73637 - 4.32920i) q^{62} +(-12.2386 - 3.59357i) q^{63} +(-5.14890 + 5.94215i) q^{64} +(-4.84415 + 10.6072i) q^{66} +(-0.499184 - 3.47190i) q^{67} +2.64232 q^{68} +(-11.4600 + 6.62346i) q^{69} +(1.43100 + 9.95283i) q^{71} +(5.85909 - 12.8296i) q^{72} +(-7.27861 + 2.13719i) q^{73} +(2.46642 - 2.84640i) q^{74} +(-1.08436 + 0.696876i) q^{76} +(4.53429 + 9.92872i) q^{77} +(4.15021 + 4.78959i) q^{78} +(11.8655 + 7.62551i) q^{79} +(0.217970 - 1.51602i) q^{81} +(-8.00959 - 5.14745i) q^{82} +(10.4759 + 12.0898i) q^{83} +(-2.71315 - 5.94097i) q^{84} +(0.440483 + 0.129337i) q^{86} +(-17.1298 + 19.7688i) q^{87} +(-11.5805 + 3.40035i) q^{88} +(-4.41518 + 9.66790i) q^{89} +5.93216 q^{91} +(-3.88298 - 1.34191i) q^{92} -20.6687 q^{93} +(-0.383604 - 2.66802i) q^{94} +(11.7807 - 3.45914i) q^{96} +(-6.01198 + 6.93819i) q^{97} +(0.647284 + 0.190060i) q^{98} +(15.3485 - 9.86391i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	0.152174	+	1.05840i	0.107603	+	0.748399i	0.970165	+	0.242446i	$0.0779498\pi$
$2$	0.152174	+	1.05840i	0.107603	+	0.748399i	−0.862561	+	0.505952i	$0.831141\pi$
$3$	1.14653	−	2.51056i	0.661951	−	1.44947i	−0.218742	−	0.975783i	$-0.570195\pi$
$3$	1.14653	−	2.51056i	0.661951	−	1.44947i	0.880693	−	0.473688i	$-0.157078\pi$
$4$	0.821942	−	0.241344i	0.410971	−	0.120672i
$5$		0			0
$5$		0			0
$6$	2.83164	+	0.831443i	1.15601	+	0.339435i
$7$	2.32389	−	1.49347i	0.878346	−	0.564479i	−0.0219487	−	0.999759i	$-0.506987\pi$
$7$	2.32389	−	1.49347i	0.878346	−	0.564479i	0.900295	+	0.435280i	$0.143351\pi$
$8$	1.26891	+	2.77851i	0.448626	+	0.982353i
$9$	−3.02378	−	3.48962i	−1.00793	−	1.16321i
$10$		0			0
$11$	−0.562328	+	3.91108i	−0.169548	+	1.17923i	0.710272	+	0.703927i	$0.248572\pi$
$11$	−0.562328	+	3.91108i	−0.169548	+	1.17923i	−0.879820	+	0.475307i	$0.842337\pi$
$12$	0.336476	−	2.34024i	0.0971322	−	0.675569i
$13$	1.80656	+	1.16100i	0.501049	+	0.322005i	0.766636	−	0.642082i	$-0.221929\pi$
$13$	1.80656	+	1.16100i	0.501049	+	0.322005i	−0.265587	+	0.964087i	$0.585566\pi$
$14$	1.93432	+	2.23232i	0.516968	+	0.596613i
$15$		0			0
$16$	−1.30637	+	0.839551i	−0.326592	+	0.209888i
$17$	2.95957	+	0.869007i	0.717800	+	0.210765i	0.620181	−	0.784459i	$-0.287059\pi$
$17$	2.95957	+	0.869007i	0.717800	+	0.210765i	0.0976192	+	0.995224i	$0.468877\pi$
$18$	3.23326	−	3.73138i	0.762087	−	0.879495i
$19$	−1.44374	+	0.423921i	−0.331217	+	0.0972541i	−0.443113	−	0.896466i	$-0.646126\pi$
$19$	−1.44374	+	0.423921i	−0.331217	+	0.0972541i	0.111896	+	0.993720i	$0.464308\pi$
$20$		0			0
$21$	−1.08503	−	7.54656i	−0.236773	−	1.64679i
$22$	−4.22504			−0.900781
$23$	−3.90785	−	2.78005i	−0.814843	−	0.579681i
$23$	−3.90785	−	2.78005i	−0.814843	−	0.579681i
$24$	8.43046			1.72086
$25$		0			0
$26$	−0.953890	+	2.08873i	−0.187073	+	0.409633i
$27$	−4.28324	+	1.25767i	−0.824310	+	0.242039i
$28$	1.54966	−	1.78840i	0.292858	−	0.337976i
$29$	−9.09371	−	2.67015i	−1.68866	−	0.495835i	−0.710501	−	0.703697i	$-0.751531\pi$
$29$	−9.09371	−	2.67015i	−1.68866	−	0.495835i	−0.978158	+	0.207862i	$0.933350\pi$
$30$		0			0
$31$	−3.11093	−	6.81198i	−0.558739	−	1.22347i	−0.952580	−	0.304290i	$-0.901581\pi$
$31$	−3.11093	−	6.81198i	−0.558739	−	1.22347i	0.393840	−	0.919179i	$-0.371146\pi$
$32$	2.91323	+	3.36205i	0.514992	+	0.594332i
$33$	9.17425	+	5.89593i	1.59703	+	1.02635i
$34$	−0.469383	+	3.26463i	−0.0804986	+	0.559880i
$35$		0			0
$36$	−3.32757	−	2.13850i	−0.554595	−	0.356416i
$37$	−2.30662	−	2.66198i	−0.379205	−	0.437626i	0.533777	−	0.845625i	$-0.320772\pi$
$37$	−2.30662	−	2.66198i	−0.379205	−	0.437626i	−0.912982	+	0.407999i	$0.866227\pi$
$38$	−0.668376	−	1.46354i	−0.108425	−	0.237418i
$39$	4.98605	−	3.20434i	0.798407	−	0.513105i
$40$		0			0
$41$	−5.83097	+	6.72930i	−0.910645	+	1.05094i	0.0878521	+	0.996134i	$0.472000\pi$
$41$	−5.83097	+	6.72930i	−0.910645	+	1.05094i	−0.998497	+	0.0548066i	$0.982546\pi$
$42$	7.82213	−	2.29679i	1.20698	−	0.354402i
$43$	0.178352	−	0.390536i	0.0271984	−	0.0595563i	−0.895545	−	0.444970i	$-0.853214\pi$
$43$	0.178352	−	0.390536i	0.0271984	−	0.0595563i	0.922744	+	0.385414i	$0.125941\pi$
$44$	0.481714	+	3.35039i	0.0726211	+	0.505091i
$45$		0			0
$46$	2.34772	−	4.55911i	0.346153	−	0.672203i
$47$	−2.52082			−0.367699			−0.183850	−	0.982954i	$-0.558856\pi$
$47$	−2.52082			−0.367699			−0.183850	+	0.982954i	$0.558856\pi$
$48$	0.609948	+	4.24228i	0.0880384	+	0.612321i
$49$	0.262086	−	0.573889i	0.0374409	−	0.0819841i
$50$		0			0
$51$	5.57493	−	6.43382i	0.780647	−	0.900914i
$52$	1.76509	+	0.518276i	0.244774	+	0.0718720i
$53$	5.62428	−	3.61451i	0.772555	−	0.496491i	−0.0940005	−	0.995572i	$-0.529966\pi$
$53$	5.62428	−	3.61451i	0.772555	−	0.496491i	0.866555	+	0.499081i	$0.166329\pi$
$54$	−1.98292	−	4.34198i	−0.269841	−	0.590869i
$55$		0			0
$56$	7.09842	+	4.56188i	0.948566	+	0.609607i
$57$	−0.591020	+	4.11064i	−0.0782825	+	0.544467i
$58$	1.44225	−	10.0311i	0.189377	−	1.31714i
$59$	0.279035	+	0.179325i	0.0363272	+	0.0233461i	0.558678	−	0.829384i	$-0.311309\pi$
$59$	0.279035	+	0.179325i	0.0363272	+	0.0233461i	−0.522351	+	0.852730i	$0.674945\pi$
$60$		0			0
$61$	−0.560667	−	1.22769i	−0.0717860	−	0.157190i	0.870337	−	0.492456i	$-0.163901\pi$
$61$	−0.560667	−	1.22769i	−0.0717860	−	0.157190i	−0.942123	+	0.335267i	$0.891174\pi$
$62$	6.73637	−	4.32920i	0.855520	−	0.549809i
$63$	−12.2386	−	3.59357i	−1.54191	−	0.452747i
$64$	−5.14890	+	5.94215i	−0.643613	+	0.742769i
$65$		0			0
$66$	−4.84415	+	10.6072i	−0.596273	+	1.30566i
$67$	−0.499184	−	3.47190i	−0.0609851	−	0.424161i	−0.997327	−	0.0730705i	$-0.976720\pi$
$67$	−0.499184	−	3.47190i	−0.0609851	−	0.424161i	0.936342	−	0.351090i	$-0.114189\pi$
$68$	2.64232			0.320428
$69$	−11.4600	+	6.62346i	−1.37962	+	0.797371i
$70$		0			0
$71$	1.43100	+	9.95283i	0.169829	+	1.18118i	0.879236	+	0.476386i	$0.158053\pi$
$71$	1.43100	+	9.95283i	0.169829	+	1.18118i	−0.709408	+	0.704798i	$0.751038\pi$
$72$	5.85909	−	12.8296i	0.690500	−	1.51198i
$73$	−7.27861	+	2.13719i	−0.851897	+	0.250140i	−0.678398	−	0.734695i	$-0.737326\pi$
$73$	−7.27861	+	2.13719i	−0.851897	+	0.250140i	−0.173499	+	0.984834i	$0.555507\pi$
$74$	2.46642	−	2.84640i	0.286715	−	0.330887i
$75$		0			0
$76$	−1.08436	+	0.696876i	−0.124385	+	0.0799372i
$77$	4.53429	+	9.92872i	0.516731	+	1.13148i
$78$	4.15021	+	4.78959i	0.469918	+	0.542315i
$79$	11.8655	+	7.62551i	1.33498	+	0.857937i	0.996545	−	0.0830535i	$-0.0264672\pi$
$79$	11.8655	+	7.62551i	1.33498	+	0.857937i	0.338432	+	0.940991i	$0.390104\pi$
$80$		0			0
$81$	0.217970	−	1.51602i	0.0242189	−	0.168446i
$82$	−8.00959	−	5.14745i	−0.884511	−	0.568441i
$83$	10.4759	+	12.0898i	1.14988	+	1.32703i	0.936746	+	0.350009i	$0.113822\pi$
$83$	10.4759	+	12.0898i	1.14988	+	1.32703i	0.213134	+	0.977023i	$0.431633\pi$
$84$	−2.71315	−	5.94097i	−0.296029	−	0.648213i
$85$		0			0
$86$	0.440483	+	0.129337i	0.0474985	+	0.0139468i
$87$	−17.1298	+	19.7688i	−1.83651	+	2.11944i
$88$	−11.5805	+	3.40035i	−1.23449	+	0.362478i
$89$	−4.41518	+	9.66790i	−0.468008	+	1.02480i	0.517580	+	0.855635i	$0.326833\pi$
$89$	−4.41518	+	9.66790i	−0.468008	+	1.02480i	−0.985588	+	0.169161i	$0.945894\pi$
$90$		0			0
$91$	5.93216			0.621860
$92$	−3.88298	−	1.34191i	−0.404828	−	0.139903i
$93$	−20.6687			−2.14324
$94$	−0.383604	−	2.66802i	−0.0395657	−	0.275186i
$95$		0			0
$96$	11.7807	−	3.45914i	1.20237	−	0.353047i
$97$	−6.01198	+	6.93819i	−0.610424	+	0.704466i	−0.973859	−	0.227153i	$-0.927058\pi$
$97$	−6.01198	+	6.93819i	−0.610424	+	0.704466i	0.363435	+	0.931619i	$0.381604\pi$
$98$	0.647284	+	0.190060i	0.0653856	+	0.0191989i
$99$	15.3485	−	9.86391i	1.54259	−	0.991360i
$100$		0			0
$101$	−2.40489	−	2.77539i	−0.239295	−	0.276161i	0.623381	−	0.781918i	$-0.285759\pi$
$101$	−2.40489	−	2.77539i	−0.239295	−	0.276161i	−0.862676	+	0.505757i	$0.831213\pi$
$102$	7.65788	+	4.92142i	0.758243	+	0.487293i
$103$	−0.773249	+	5.37806i	−0.0761905	+	0.529916i	0.915605	+	0.402079i	$0.131712\pi$
$103$	−0.773249	+	5.37806i	−0.0761905	+	0.529916i	−0.991795	+	0.127837i	$0.959197\pi$
$104$	−0.933517	+	6.49275i	−0.0915389	+	0.636667i
$105$		0			0
$106$	4.68145	+	5.40268i	0.454703	+	0.524755i
$107$	−1.53537	−	3.36199i	−0.148430	−	0.325016i	0.820783	−	0.571240i	$-0.193537\pi$
$107$	−1.53537	−	3.36199i	−0.148430	−	0.325016i	−0.969213	+	0.246224i	$0.920810\pi$
$108$	−3.21704	+	2.06747i	−0.309560	+	0.198942i
$109$	11.6867	+	3.43152i	1.11938	+	0.328680i	0.788525	−	0.615002i	$-0.210845\pi$
$109$	11.6867	+	3.43152i	1.11938	+	0.328680i	0.330855	+	0.943682i	$0.392663\pi$
$110$		0			0
$111$	−9.32766	+	2.73885i	−0.885342	+	0.259960i
$112$	−1.78200	+	3.90204i	−0.168383	+	0.368708i
$113$	−2.76330	−	19.2192i	−0.259949	−	1.80799i	−0.533141	−	0.846026i	$-0.678988\pi$
$113$	−2.76330	−	19.2192i	−0.259949	−	1.80799i	0.273192	−	0.961960i	$-0.411921\pi$
$114$	−4.44062			−0.415902
$115$		0			0
$116$	−8.11892			−0.753823
$117$	−1.41116	−	9.81483i	−0.130462	−	0.907381i
$118$	−0.147334	+	0.322618i	−0.0135632	+	0.0296993i
$119$	8.17553	−	2.40055i	0.749450	−	0.220058i
$120$		0			0
$121$	−4.42589	−	1.29956i	−0.402353	−	0.118142i
$122$	1.21406	−	0.780230i	0.109916	−	0.0706387i
$123$	10.2089	+	22.3544i	0.920505	+	2.01562i
$124$	−4.20103	−	4.84825i	−0.377264	−	0.435386i
$125$		0			0
$126$	1.94102	−	13.5001i	0.172920	−	1.20268i
$127$	2.27619	−	15.8312i	0.201979	−	1.40480i	−0.596423	−	0.802671i	$-0.703412\pi$
$127$	2.27619	−	15.8312i	0.201979	−	1.40480i	0.798402	−	0.602125i	$-0.205679\pi$
$128$	0.412177	+	0.264890i	0.0364316	+	0.0234132i
$129$	−0.775978	−	0.895526i	−0.0683210	−	0.0788467i
$130$		0			0
$131$	9.26039	−	5.95129i	0.809084	−	0.519967i	−0.0694847	−	0.997583i	$-0.522136\pi$
$131$	9.26039	−	5.95129i	0.809084	−	0.519967i	0.878568	+	0.477617i	$0.158499\pi$
$132$	8.96365	+	2.63196i	0.780186	+	0.229083i
$133$	−2.72198	+	3.14133i	−0.236025	+	0.272388i
$134$	3.59869	−	1.05667i	0.310879	−	0.0912823i
$135$		0			0
$136$	1.34086	+	9.32589i	0.114978	+	0.799688i
$137$	−2.85541			−0.243954			−0.121977	−	0.992533i	$-0.538923\pi$
$137$	−2.85541			−0.243954			−0.121977	+	0.992533i	$0.538923\pi$
$138$	−8.75415	−	11.1213i	−0.745203	−	0.946704i
$139$	−10.6535			−0.903621			−0.451811	−	0.892114i	$-0.649222\pi$
$139$	−10.6535			−0.903621			−0.451811	+	0.892114i	$0.649222\pi$
$140$		0			0
$141$	−2.89020	+	6.32866i	−0.243399	+	0.532969i
$142$	−10.3163	+	3.02913i	−0.865722	+	0.254199i
$143$	−5.55666	+	6.41272i	−0.464671	+	0.536259i
$144$	6.87988	+	2.02011i	0.573323	+	0.168343i
$145$		0			0
$146$	−3.36961	−	7.37842i	−0.278871	−	0.610643i
$147$	−1.14029	−	1.31597i	−0.0940496	−	0.108539i
$148$	−2.53836	−	1.63130i	−0.208652	−	0.134092i
$149$	1.31308	−	9.13267i	0.107572	−	0.748177i	−0.862622	−	0.505848i	$-0.831180\pi$
$149$	1.31308	−	9.13267i	0.107572	−	0.748177i	0.970194	−	0.242329i	$-0.0779114\pi$
$150$		0			0
$151$	9.28709	+	5.96845i	0.755773	+	0.485706i	0.860913	−	0.508752i	$-0.169893\pi$
$151$	9.28709	+	5.96845i	0.755773	+	0.485706i	−0.105140	+	0.994457i	$0.533529\pi$
$152$	−3.00984	−	3.47354i	−0.244130	−	0.281741i
$153$	−5.91656	−	12.9555i	−0.478325	−	1.04739i
$154$	−9.81851	+	6.30997i	−0.791198	+	0.508472i
$155$		0			0
$156$	3.32489	−	3.83713i	0.266204	−	0.307216i
$157$	−3.91655	+	1.15000i	−0.312575	+	0.0917803i	−0.434257	−	0.900789i	$-0.642989\pi$
$157$	−3.91655	+	1.15000i	−0.312575	+	0.0917803i	0.121683	+	0.992569i	$0.461171\pi$
$158$	−6.26518	+	13.7188i	−0.498431	+	1.09141i
$159$	−2.62600	−	18.2642i	−0.208255	−	1.44845i
$160$		0			0
$161$	−13.2333	−	0.624265i	−1.04293	−	0.0491989i
$162$	1.63771			0.128671
$163$	−0.789697	−	5.49246i	−0.0618538	−	0.430203i	−0.997093	−	0.0761876i	$-0.975725\pi$
$163$	−0.789697	−	5.49246i	−0.0618538	−	0.430203i	0.935240	−	0.354015i	$-0.115184\pi$
$164$	−3.16864	+	6.93836i	−0.247430	+	0.541795i
$165$		0			0
$166$	−11.2017	+	12.9274i	−0.869418	+	1.00336i
$167$	2.07652	+	0.609721i	0.160686	+	0.0471816i	0.361086	−	0.932533i	$-0.382406\pi$
$167$	2.07652	+	0.609721i	0.160686	+	0.0471816i	−0.200400	+	0.979714i	$0.564224\pi$
$168$	19.5914	−	12.5906i	1.51151	−	0.971390i
$169$	−3.48467	−	7.63037i	−0.268052	−	0.586952i
$170$		0			0
$171$	5.84488	+	3.75627i	0.446969	+	0.287249i
$172$	0.0523414	−	0.364042i	0.00399099	−	0.0277580i
$173$	0.0152913	−	0.106353i	0.00116257	−	0.00808589i	−0.989232	−	0.146357i	$-0.953245\pi$
$173$	0.0152913	−	0.106353i	0.00116257	−	0.00808589i	0.990394	+	0.138271i	$0.0441544\pi$
$174$	−23.5300	−	15.1218i	−1.78380	−	1.14638i
$175$		0			0
$176$	−2.54894	−	5.58140i	−0.192134	−	0.420714i
$177$	0.770127	−	0.494931i	0.0578863	−	0.0372013i
$178$	−10.9043	−	3.20180i	−0.817315	−	0.239985i
$179$	−4.68179	+	5.40307i	−0.349933	+	0.403844i	−0.903242	−	0.429132i	$-0.858820\pi$
$179$	−4.68179	+	5.40307i	−0.349933	+	0.403844i	0.553309	+	0.832976i	$0.313365\pi$
$180$		0			0
$181$	7.71430	−	16.8920i	0.573399	−	1.25557i	−0.371568	−	0.928406i	$-0.621180\pi$
$181$	7.71430	−	16.8920i	0.573399	−	1.25557i	0.944968	−	0.327164i	$-0.106093\pi$
$182$	0.902723	+	6.27858i	0.0669143	+	0.465399i
$183$	−3.72501			−0.275360
$184$	2.76573	−	14.3856i	0.203892	−	1.06052i
$185$		0			0
$186$	−3.14524	−	21.8756i	−0.230620	−	1.60400i
$187$	−5.06300	+	11.0864i	−0.370243	+	0.810720i
$188$	−2.07197	+	0.608384i	−0.151114	+	0.0443710i
$189$	−8.07547	+	9.31959i	−0.587404	+	0.677900i
$190$		0			0
$191$	−3.07197	+	1.97423i	−0.222280	+	0.142851i	−0.647042	−	0.762454i	$-0.723994\pi$
$191$	−3.07197	+	1.97423i	−0.222280	+	0.142851i	0.424762	+	0.905305i	$0.360358\pi$
$192$	9.01472	+	19.7395i	0.650582	+	1.42457i
$193$	−0.895226	−	1.03315i	−0.0644398	−	0.0743675i	0.722614	−	0.691251i	$-0.242940\pi$
$193$	−0.895226	−	1.03315i	−0.0644398	−	0.0743675i	−0.787054	+	0.616884i	$0.788395\pi$
$194$	−8.25822	−	5.30723i	−0.592905	−	0.381037i
$195$		0			0
$196$	0.0769151	−	0.534956i	0.00549393	−	0.0382112i
$197$	3.24560	+	2.08582i	0.231239	+	0.148608i	0.651130	−	0.758966i	$-0.274295\pi$
$197$	3.24560	+	2.08582i	0.231239	+	0.148608i	−0.419891	+	0.907575i	$0.637932\pi$
$198$	12.7756	+	14.7438i	0.907920	+	1.04780i
$199$	6.18514	+	13.5436i	0.438453	+	0.960078i	0.991880	+	0.127180i	$0.0405926\pi$
$199$	6.18514	+	13.5436i	0.438453	+	0.960078i	−0.553427	+	0.832898i	$0.686680\pi$
$200$		0			0
$201$	−9.28874	−	2.72742i	−0.655178	−	0.192377i
$202$	2.57149	−	2.96766i	0.180930	−	0.208804i
$203$	−25.1205	+	7.37605i	−1.76312	+	0.517698i
$204$	3.02951	−	6.63370i	0.212108	−	0.464452i
$205$		0			0
$206$	−5.80979			−0.404787
$207$	2.11513	+	22.0432i	0.147012	+	1.53211i
$208$	−3.33475			−0.231223
$209$	−0.846131	−	5.88497i	−0.0585281	−	0.407072i
$210$		0			0
$211$	−17.8711	+	5.24743i	−1.23030	+	0.361248i	−0.831362	−	0.555731i	$-0.812438\pi$
$211$	−17.8711	+	5.24743i	−1.23030	+	0.361248i	−0.398935	+	0.916979i	$0.630620\pi$
$212$	3.75049	−	4.32830i	0.257585	−	0.297269i
$213$	26.6278	+	7.81864i	1.82451	+	0.535724i
$214$	3.32467	−	2.13664i	0.227270	−	0.146058i
$215$		0			0
$216$	−8.92949	−	10.3052i	−0.607575	−	0.701179i
$217$	−17.4029	−	11.1842i	−1.18139	−	0.759233i
$218$	−1.85349	+	12.8913i	−0.125534	+	0.873110i
$219$	−2.97962	+	20.7237i	−0.201344	+	1.40038i
$220$		0			0
$221$	4.33771	+	5.00598i	0.291786	+	0.336739i
$222$	−4.31821	−	9.45557i	−0.289819	−	0.634616i
$223$	6.22890	−	4.00307i	0.417118	−	0.268065i	−0.315204	−	0.949024i	$-0.602073\pi$
$223$	6.22890	−	4.00307i	0.417118	−	0.268065i	0.732322	+	0.680959i	$0.238437\pi$
$224$	11.7912	+	3.46219i	0.787829	+	0.231328i
$225$		0			0
$226$	19.9210	−	5.84932i	1.32512	−	0.389091i
$227$	3.74813	−	8.20725i	0.248772	−	0.544735i	−0.743512	−	0.668723i	$-0.766841\pi$
$227$	3.74813	−	8.20725i	0.248772	−	0.544735i	0.992284	+	0.123988i	$0.0395685\pi$
$228$	0.506292	+	3.52134i	0.0335300	+	0.233207i
$229$	5.62468			0.371689			0.185845	−	0.982579i	$-0.440498\pi$
$229$	5.62468			0.371689			0.185845	+	0.982579i	$0.440498\pi$
$230$		0			0
$231$	30.1253			1.98210
$232$	−4.11999	−	28.6552i	−0.270491	−	1.88130i
$233$	3.17693	−	6.95650i	0.208128	−	0.455736i	−0.776565	−	0.630037i	$-0.783040\pi$
$233$	3.17693	−	6.95650i	0.208128	−	0.455736i	0.984692	+	0.174302i	$0.0557668\pi$
$234$	10.1732	−	2.98713i	0.665045	−	0.195275i
$235$		0			0
$236$	0.272629	+	0.0800511i	0.0177466	+	0.00521088i
$237$	32.7485	−	21.0462i	2.12724	−	1.36710i
$238$	3.78484	+	8.28765i	0.245335	+	0.537208i
$239$	11.8884	+	13.7199i	0.768994	+	0.887467i	0.996264	−	0.0863654i	$-0.0275252\pi$
$239$	11.8884	+	13.7199i	0.768994	+	0.887467i	−0.227269	+	0.973832i	$0.572980\pi$
$240$		0			0
$241$	−0.0930480	+	0.647163i	−0.00599375	+	0.0416874i	−0.992599	−	0.121440i	$-0.961249\pi$
$241$	−0.0930480	+	0.647163i	−0.00599375	+	0.0416874i	0.986605	+	0.163127i	$0.0521580\pi$
$242$	0.701940	−	4.88210i	0.0451224	−	0.313833i
$243$	−14.8224	−	9.52576i	−0.950856	−	0.611078i
$244$	−0.757131	−	0.873776i	−0.0484703	−	0.0559377i
$245$		0			0
$246$	−22.1062	+	14.2068i	−1.40944	+	0.905793i
$247$	−3.10038	−	0.910353i	−0.197272	−	0.0579244i
$248$	14.9797	−	17.2875i	0.951213	−	1.09776i
$249$	42.3632	−	12.4390i	2.68466	−	0.788287i
$250$		0			0
$251$	−1.11018	−	7.72149i	−0.0700741	−	0.487376i	−0.994392	−	0.105753i	$-0.966275\pi$
$251$	−1.11018	−	7.72149i	−0.0700741	−	0.487376i	0.924318	−	0.381622i	$-0.124635\pi$
$252$	−10.9267			−0.688316
$253$	13.0705	−	13.7206i	0.821735	−	0.862607i
$254$	17.1021			1.07308
$255$		0			0
$256$	−6.75011	+	14.7807i	−0.421882	+	0.923793i
$257$	7.82701	−	2.29822i	0.488236	−	0.143359i	−0.0283438	−	0.999598i	$-0.509023\pi$
$257$	7.82701	−	2.29822i	0.488236	−	0.143359i	0.516579	+	0.856239i	$0.327205\pi$
$258$	0.829737	−	0.957567i	0.0516572	−	0.0596155i
$259$	−9.33590	−	2.74127i	−0.580104	−	0.170334i
$260$		0			0
$261$	18.1795	+	39.8076i	1.12528	+	2.46403i
$262$	7.70801	+	8.89552i	0.476202	+	0.549567i
$263$	16.5410	+	10.6302i	1.01996	+	0.655489i	0.939952	−	0.341306i	$-0.110869\pi$
$263$	16.5410	+	10.6302i	1.01996	+	0.655489i	0.0800079	+	0.996794i	$0.474505\pi$
$264$	−4.74068	+	32.9722i	−0.291769	+	2.02930i
$265$		0			0
$266$	−3.73899	−	2.40290i	−0.229252	−	0.147331i
$267$	19.2097	+	22.1691i	1.17561	+	1.35673i
$268$	−1.24822	−	2.73323i	−0.0762474	−	0.166958i
$269$	−22.3941	+	14.3918i	−1.36539	+	0.877484i	−0.998604	−	0.0528210i	$-0.983179\pi$
$269$	−22.3941	+	14.3918i	−1.36539	+	0.877484i	−0.366787	+	0.930305i	$0.619542\pi$
$270$		0			0
$271$	10.4018	−	12.0043i	0.631866	−	0.729212i	−0.346049	−	0.938216i	$-0.612477\pi$
$271$	10.4018	−	12.0043i	0.631866	−	0.729212i	0.977915	+	0.209005i	$0.0670224\pi$
$272$	−4.59586	+	1.34947i	−0.278665	+	0.0818233i
$273$	6.80142	−	14.8930i	0.411641	−	0.901367i
$274$	−0.434521	−	3.02216i	−0.0262503	−	0.182575i
$275$		0			0
$276$	−7.82089	+	8.20989i	−0.470762	+	0.494177i
$277$	−17.7303			−1.06531			−0.532654	−	0.846333i	$-0.678805\pi$
$277$	−17.7303			−1.06531			−0.532654	+	0.846333i	$0.678805\pi$
$278$	−1.62119	−	11.2757i	−0.0972328	−	0.676269i
$279$	−14.3645	+	31.4539i	−0.859981	+	1.88310i
$280$		0			0
$281$	2.78551	−	3.21465i	0.166169	−	0.191770i	−0.666558	−	0.745454i	$-0.732233\pi$
$281$	2.78551	−	3.21465i	0.166169	−	0.191770i	0.832727	+	0.553684i	$0.186778\pi$
$282$	−7.13804	−	2.09592i	−0.425064	−	0.124810i
$283$	10.8911	−	6.99931i	0.647411	−	0.416066i	−0.175308	−	0.984514i	$-0.556092\pi$
$283$	10.8911	−	6.99931i	0.647411	−	0.416066i	0.822719	+	0.568448i	$0.192456\pi$
$284$	3.57825	+	7.83529i	0.212330	+	0.464939i
$285$		0			0
$286$	−7.63278	−	4.90529i	−0.451336	−	0.290056i
$287$	−3.50050	+	24.3465i	−0.206628	+	1.43713i
$288$	2.92333	−	20.3322i	0.172259	−	1.19809i
$289$	−6.29745	−	4.04712i	−0.370438	−	0.238066i
$290$		0			0
$291$	10.5258	+	23.0483i	0.617033	+	1.35111i
$292$	−5.46680	+	3.51330i	−0.319920	+	0.205600i
$293$	19.3518	+	5.68221i	1.13055	+	0.331958i	0.792922	−	0.609323i	$-0.208559\pi$
$293$	19.3518	+	5.68221i	1.13055	+	0.331958i	0.337624	+	0.941281i	$0.390377\pi$
$294$	1.21929	−	1.40713i	0.0711104	−	0.0820657i
$295$		0			0
$296$	4.46946	−	9.78676i	0.259782	−	0.568844i
$297$	−2.51027	−	17.4593i	−0.145661	−	1.01309i
$298$	9.86579			0.571510
$299$	−3.83211	−	9.55936i	−0.221617	−	0.552832i
$300$		0			0
$301$	−0.168785	−	1.17393i	−0.00972861	−	0.0676640i
$302$	−4.90373	+	10.7377i	−0.282178	+	0.617883i
$303$	−9.72505	+	2.85553i	−0.558689	+	0.164046i
$304$	1.53015	−	1.76589i	0.0877603	−	0.101281i
$305$		0			0
$306$	12.8117	−	8.23355i	0.732393	−	0.470681i
$307$	−2.91839	−	6.39037i	−0.166561	−	0.364718i	0.807885	−	0.589341i	$-0.200612\pi$
$307$	−2.91839	−	6.39037i	−0.166561	−	0.364718i	−0.974446	+	0.224623i	$0.927885\pi$
$308$	6.12316	+	7.06650i	0.348899	+	0.402651i
$309$	12.6154	+	8.10741i	0.717664	+	0.461214i
$310$		0			0
$311$	−2.27442	+	15.8189i	−0.128970	+	0.897009i	0.817892	+	0.575371i	$0.195142\pi$
$311$	−2.27442	+	15.8189i	−0.128970	+	0.897009i	−0.946863	+	0.321638i	$0.895767\pi$
$312$	15.2301	+	9.78780i	0.862236	+	0.554125i
$313$	10.1451	+	11.7080i	0.573433	+	0.661777i	0.966180	−	0.257869i	$-0.0830205\pi$
$313$	10.1451	+	11.7080i	0.573433	+	0.661777i	−0.392746	+	0.919647i	$0.628475\pi$
$314$	−1.81316	−	3.97026i	−0.102322	−	0.224055i
$315$		0			0
$316$	11.5931	+	3.40406i	0.652166	+	0.191493i
$317$	2.65336	−	3.06214i	0.149027	−	0.171987i	−0.676328	−	0.736601i	$-0.736430\pi$
$317$	2.65336	−	3.06214i	0.149027	−	0.171987i	0.825355	+	0.564614i	$0.190975\pi$
$318$	18.9312	−	5.55869i	1.06161	−	0.311716i
$319$	15.5568	−	34.0647i	0.871015	−	1.90726i
$320$		0			0
$321$	−10.2008			−0.569355
$322$	−1.35305	−	14.1011i	−0.0754028	−	0.785823i
$323$	−4.64124			−0.258246
$324$	−0.186722	−	1.29868i	−0.0103735	−	0.0721490i
$325$		0			0
$326$	5.69303	−	1.67162i	0.315308	−	0.0925827i
$327$	22.0142	−	25.4057i	1.21739	−	1.40494i
$328$	−26.0964	−	7.66260i	−1.44093	−	0.423096i
$329$	−5.85810	+	3.76477i	−0.322967	+	0.207559i
$330$		0			0
$331$	4.49035	+	5.18215i	0.246812	+	0.284836i	0.865615	−	0.500710i	$-0.166928\pi$
$331$	4.49035	+	5.18215i	0.246812	+	0.284836i	−0.618803	+	0.785546i	$0.712382\pi$
$332$	11.5284	+	7.40885i	0.632703	+	0.406613i
$333$	−2.31461	+	16.0984i	−0.126840	+	0.882189i
$334$	−0.329333	+	2.29056i	−0.0180203	+	0.125334i
$335$		0			0
$336$	7.75317	+	8.94764i	0.422970	+	0.488134i
$337$	4.39906	+	9.63260i	0.239632	+	0.524721i	0.990791	−	0.135400i	$-0.0432321\pi$
$337$	4.39906	+	9.63260i	0.239632	+	0.524721i	−0.751159	+	0.660121i	$0.770505\pi$
$338$	7.54567	−	4.84931i	0.410430	−	0.263768i
$339$	−51.4190	−	15.0980i	−2.79270	−	0.820010i
$340$		0			0
$341$	28.3916	−	8.33651i	1.53749	−	0.451447i
$342$	−3.08618	+	6.75780i	−0.166882	+	0.365420i
$343$	2.50389	+	17.4150i	0.135198	+	0.940320i
$344$	1.31142			0.0707072
$345$		0			0
$346$	0.114891			0.00617656
$347$	1.47041	+	10.2269i	0.0789357	+	0.549010i	0.990464	+	0.137772i	$0.0439942\pi$
$347$	1.47041	+	10.2269i	0.0789357	+	0.549010i	−0.911528	+	0.411237i	$0.865097\pi$
$348$	−9.30861	+	20.3830i	−0.498994	+	1.09264i
$349$	−18.2709	+	5.36483i	−0.978020	+	0.287173i	−0.731407	−	0.681941i	$-0.761136\pi$
$349$	−18.2709	+	5.36483i	−0.978020	+	0.287173i	−0.246613	+	0.969114i	$0.579318\pi$
$350$		0			0
$351$	−9.19809	−	2.70080i	−0.490958	−	0.144158i
$352$	−14.7874	+	9.50331i	−0.788173	+	0.506528i
$353$	−3.56321	−	7.80234i	−0.189650	−	0.415276i	0.790791	−	0.612086i	$-0.209669\pi$
$353$	−3.56321	−	7.80234i	−0.189650	−	0.415276i	−0.980442	+	0.196809i	$0.936942\pi$
$354$	0.641026	+	0.739783i	0.0340701	+	0.0393190i
$355$		0			0
$356$	−1.29573	+	9.01203i	−0.0686738	+	0.477637i
$357$	3.34679	−	23.2775i	0.177131	−	1.23197i
$358$	−6.43103	−	4.13297i	−0.339891	−	0.218434i
$359$	1.44962	+	1.67295i	0.0765081	+	0.0882950i	0.792713	−	0.609595i	$-0.208668\pi$
$359$	1.44962	+	1.67295i	0.0765081	+	0.0882950i	−0.716205	+	0.697890i	$0.754122\pi$
$360$		0			0
$361$	−14.0791	+	9.04811i	−0.741007	+	0.476216i
$362$	19.0523	+	5.59426i	1.00137	+	0.294028i
$363$	−8.33704	+	9.62145i	−0.437581	+	0.504995i
$364$	4.87589	−	1.43169i	0.255566	−	0.0750410i
$365$		0			0
$366$	−0.566850	−	3.94253i	−0.0296297	−	0.206079i
$367$	−16.8275			−0.878391			−0.439195	−	0.898392i	$-0.644736\pi$
$367$	−16.8275			−0.878391			−0.439195	+	0.898392i	$0.644736\pi$
$368$	7.43909	+	0.350929i	0.387789	+	0.0182934i
$369$	41.1143			2.14032
$370$		0			0
$371$	7.67203	−	16.7994i	0.398312	−	0.872182i
$372$	−16.9884	+	4.98825i	−0.880809	+	0.258629i
$373$	4.10424	−	4.73655i	0.212510	−	0.245249i	−0.639480	−	0.768808i	$-0.720850\pi$
$373$	4.10424	−	4.73655i	0.212510	−	0.245249i	0.851990	+	0.523558i	$0.175396\pi$
$374$	−12.5043	−	3.67159i	−0.646581	−	0.189853i
$375$		0			0
$376$	−3.19868	−	7.00413i	−0.164959	−	0.361211i
$377$	−13.3283	−	15.3816i	−0.686440	−	0.792194i
$378$	−11.0927	−	7.12884i	−0.570546	−	0.366668i
$379$	1.09948	−	7.64706i	0.0564766	−	0.392803i	−0.941902	−	0.335887i	$-0.890964\pi$
$379$	1.09948	−	7.64706i	0.0564766	−	0.392803i	0.998379	−	0.0569165i	$-0.0181269\pi$
$380$		0			0
$381$	−37.1355	−	23.8655i	−1.90251	−	1.22267i
$382$	−2.55700	−	2.95093i	−0.130827	−	0.150983i
$383$	−7.28121	−	15.9436i	−0.372052	−	0.814681i	−0.999355	−	0.0359055i	$-0.988568\pi$
$383$	−7.28121	−	15.9436i	−0.372052	−	0.814681i	0.627303	−	0.778775i	$-0.284159\pi$
$384$	1.13760	−	0.731088i	0.0580527	−	0.0373082i
$385$		0			0
$386$	0.957247	−	1.10472i	0.0487226	−	0.0562289i
$387$	−1.90212	+	0.558513i	−0.0966903	+	0.0283908i
$388$	−3.26700	+	7.15374i	−0.165857	+	0.363176i
$389$	−5.18296	−	36.0483i	−0.262786	−	1.82772i	−0.511666	−	0.859184i	$-0.670971\pi$
$389$	−5.18296	−	36.0483i	−0.262786	−	1.82772i	0.248880	−	0.968534i	$-0.419938\pi$
$390$		0			0
$391$	−9.14966	−	11.6237i	−0.462718	−	0.587836i
$392$	1.92712			0.0973343
$393$	−4.32371	−	30.0721i	−0.218102	−	1.51694i
$394$	−1.71372	+	3.75253i	−0.0863362	+	0.189050i
$395$		0			0
$396$	10.2350	−	11.8118i	0.514329	−	0.593567i
$397$	37.4173	+	10.9867i	1.87792	+	0.551407i	0.996932	+	0.0782685i	$0.0249391\pi$
$397$	37.4173	+	10.9867i	1.87792	+	0.551407i	0.880988	+	0.473139i	$0.156879\pi$
$398$	−13.3932	+	8.60731i	−0.671342	+	0.431445i
$399$	4.76565	+	10.4353i	0.238581	+	0.522419i
$400$		0			0
$401$	−20.4391	−	13.1354i	−1.02068	−	0.655950i	−0.0805426	−	0.996751i	$-0.525665\pi$
$401$	−20.4391	−	13.1354i	−1.02068	−	0.655950i	−0.940135	+	0.340801i	$0.889302\pi$
$402$	1.47318	−	10.2462i	0.0734757	−	0.511035i
$403$	2.28867	−	15.9181i	0.114007	−	0.792935i
$404$	−2.64650	−	1.70080i	−0.131668	−	0.0846180i
$405$		0			0
$406$	−11.6295	−	25.4650i	−0.577162	−	1.26381i
$407$	11.7083	−	7.52445i	0.580357	−	0.372973i
$408$	24.9505	+	7.32613i	1.23523	+	0.362698i
$409$	8.33104	−	9.61453i	0.411943	−	0.475408i	−0.511422	−	0.859329i	$-0.670881\pi$
$409$	8.33104	−	9.61453i	0.411943	−	0.475408i	0.923366	+	0.383921i	$0.125427\pi$
$410$		0			0
$411$	−3.27383	+	7.16868i	−0.161486	+	0.353605i
$412$	0.662397	+	4.60707i	0.0326340	+	0.226974i
$413$	0.916261			0.0450862
$414$	−23.0085	+	5.59305i	−1.13081	+	0.274883i
$415$		0			0
$416$	1.35957	+	9.45602i	0.0666584	+	0.463620i
$417$	−12.2146	+	26.7463i	−0.598153	+	1.30977i
$418$	6.09986	−	1.79108i	0.298354	−	0.0876047i
$419$	−8.68118	+	10.0186i	−0.424104	+	0.489442i	−0.927083	−	0.374857i	$-0.877692\pi$
$419$	−8.68118	+	10.0186i	−0.424104	+	0.489442i	0.502979	+	0.864299i	$0.332237\pi$
$420$		0			0
$421$	12.4520	−	8.00239i	0.606871	−	0.390012i	−0.200811	−	0.979630i	$-0.564358\pi$
$421$	12.4520	−	8.00239i	0.606871	−	0.390012i	0.807683	+	0.589617i	$0.200721\pi$
$422$	−8.27338	−	18.1162i	−0.402742	−	0.881882i
$423$	7.62239	+	8.79671i	0.370614	+	0.427711i
$424$	17.1796	+	11.0407i	0.834317	+	0.536183i
$425$		0			0
$426$	−4.22314	+	29.3726i	−0.204612	+	1.42311i
$427$	−3.13644	−	2.01567i	−0.151783	−	0.0975451i
$428$	−2.07338	−	2.39281i	−0.100221	−	0.115661i
$429$	9.72862	+	21.3027i	0.469702	+	1.02850i
$430$		0			0
$431$	−8.49383	−	2.49401i	−0.409133	−	0.120132i	0.0706882	−	0.997498i	$-0.477480\pi$
$431$	−8.49383	−	2.49401i	−0.409133	−	0.120132i	−0.479822	+	0.877366i	$0.659299\pi$
$432$	4.53961	−	5.23898i	0.218412	−	0.252061i
$433$	12.7842	−	3.75377i	0.614368	−	0.180395i	0.0402800	−	0.999188i	$-0.487175\pi$
$433$	12.7842	−	3.75377i	0.614368	−	0.180395i	0.574088	+	0.818794i	$0.305357\pi$
$434$	9.18902	−	20.1211i	0.441087	−	0.965846i
$435$		0			0
$436$	10.4339			0.499695
$437$	6.82045	+	2.35706i	0.326266	+	0.112753i
$438$	−22.3873			−1.06971
$439$	−3.03134	−	21.0835i	−0.144678	−	1.00626i	−0.924752	−	0.380571i	$-0.875727\pi$
$439$	−3.03134	−	21.0835i	−0.144678	−	1.00626i	0.780074	−	0.625688i	$-0.215182\pi$
$440$		0			0
$441$	−2.79515	+	0.820729i	−0.133102	+	0.0390823i
$442$	−4.63822	+	5.35279i	−0.220618	+	0.254606i
$443$	2.52199	+	0.740522i	0.119823	+	0.0351833i	0.341094	−	0.940029i	$-0.389202\pi$
$443$	2.52199	+	0.740522i	0.119823	+	0.0351833i	−0.221271	+	0.975212i	$0.571021\pi$
$444$	−7.00579	+	4.50234i	−0.332480	+	0.213672i
$445$		0			0
$446$	5.18471	+	5.98347i	0.245503	+	0.283326i
$447$	−21.4226	−	13.7675i	−1.01325	−	0.651179i
$448$	−3.09104	+	21.4986i	−0.146038	+	1.01571i
$449$	3.81280	−	26.5186i	0.179937	−	1.25149i	−0.676967	−	0.736013i	$-0.736706\pi$
$449$	3.81280	−	26.5186i	0.179937	−	1.25149i	0.856904	−	0.515476i	$-0.172385\pi$
$450$		0			0
$451$	−23.0399	−	26.5895i	−1.08491	−	1.25205i
$452$	−6.90969	−	15.1301i	−0.325005	−	0.711661i
$453$	25.6321	−	16.4727i	1.20430	−	0.773957i
$454$	9.25689	+	2.71807i	0.434447	+	0.127565i
$455$		0			0
$456$	−12.1714	+	3.57385i	−0.569978	+	0.167361i
$457$	−5.63341	+	12.3354i	−0.263520	+	0.577028i	−0.994424	−	0.105452i	$-0.966371\pi$
$457$	−5.63341	+	12.3354i	−0.263520	+	0.577028i	0.730905	+	0.682479i	$0.239098\pi$
$458$	0.855932	+	5.95314i	0.0399951	+	0.278172i
$459$	−13.7695			−0.642704
$460$		0			0
$461$	−25.0816			−1.16817			−0.584084	−	0.811693i	$-0.698546\pi$
$461$	−25.0816			−1.16817			−0.584084	+	0.811693i	$0.698546\pi$
$462$	4.58430	+	31.8845i	0.213281	+	1.48340i
$463$	−8.91586	+	19.5230i	−0.414355	+	0.907311i	0.581256	+	0.813721i	$0.302562\pi$
$463$	−8.91586	+	19.5230i	−0.414355	+	0.907311i	−0.995611	+	0.0935899i	$0.970166\pi$
$464$	14.1214	−	4.14643i	0.655572	−	0.192493i
$465$		0			0
$466$	7.84618	+	2.30385i	0.363467	+	0.106724i
$467$	10.6077	−	6.81717i	0.490867	−	0.315461i	−0.271687	−	0.962386i	$-0.587582\pi$
$467$	10.6077	−	6.81717i	0.490867	−	0.315461i	0.762554	+	0.646925i	$0.223945\pi$
$468$	−3.52864	−	7.72664i	−0.163111	−	0.357164i
$469$	−6.34524	−	7.32279i	−0.292996	−	0.338135i
$470$		0			0
$471$	−1.60331	+	11.1512i	−0.0738765	+	0.513822i
$472$	−0.144188	+	1.00285i	−0.00663678	+	0.0461598i
$473$	1.42713	+	0.917158i	0.0656193	+	0.0421710i
$474$	27.2587	+	31.4582i	1.25203	+	1.44492i
$475$		0			0
$476$	6.14045	−	3.94623i	0.281447	−	0.180875i
$477$	−29.6198	−	8.69717i	−1.35620	−	0.398216i
$478$	−12.7120	+	14.6704i	−0.581432	+	0.671009i
$479$	−9.62252	+	2.82543i	−0.439664	+	0.129097i	−0.494070	−	0.869422i	$-0.664492\pi$
$479$	−9.62252	+	2.82543i	−0.439664	+	0.129097i	0.0544064	+	0.998519i	$0.482673\pi$
$480$		0			0
$481$	−1.07647	−	7.48701i	−0.0490828	−	0.341378i
$482$	−0.699114			−0.0318438
$483$	−16.7397	+	32.5073i	−0.761683	+	1.47913i
$484$	−3.95146			−0.179612
$485$		0			0
$486$	7.82644	−	17.1375i	0.355015	−	0.777373i
$487$	20.8578	−	6.12440i	0.945156	−	0.277523i	0.227388	−	0.973804i	$-0.426982\pi$
$487$	20.8578	−	6.12440i	0.945156	−	0.277523i	0.717769	+	0.696281i	$0.245163\pi$
$488$	2.69972	−	3.11564i	0.122211	−	0.141039i
$489$	−14.6946	−	4.31471i	−0.664511	−	0.195118i
$490$		0			0
$491$	−13.8165	−	30.2539i	−0.623530	−	1.36534i	−0.912924	−	0.408130i	$-0.866181\pi$
$491$	−13.8165	−	30.2539i	−0.623530	−	1.36534i	0.289394	−	0.957210i	$-0.406546\pi$
$492$	13.7862	+	15.9101i	0.621530	+	0.717284i
$493$	−24.5930	−	15.8050i	−1.10762	−	0.711821i
$494$	0.491716	−	3.41996i	0.0221233	−	0.153871i
$495$		0			0
$496$	9.78302	+	6.28717i	0.439271	+	0.282302i
$497$	18.1898	+	20.9921i	0.815922	+	0.941624i
$498$	19.6119	+	42.9441i	0.878832	+	1.92437i
$499$	−15.1325	+	9.72510i	−0.677426	+	0.435355i	−0.833596	−	0.552375i	$-0.813722\pi$
$499$	−15.1325	+	9.72510i	−0.677426	+	0.435355i	0.156170	+	0.987730i	$0.450085\pi$
$500$		0			0
$501$	3.91153	−	4.51415i	0.174754	−	0.201677i
$502$	8.00345	−	2.35002i	0.357211	−	0.104887i
$503$	−3.41200	+	7.47123i	−0.152133	+	0.333126i	−0.970319	−	0.241829i	$-0.922253\pi$
$503$	−3.41200	+	7.47123i	−0.152133	+	0.333126i	0.818186	+	0.574954i	$0.194980\pi$
$504$	−5.54480	−	38.5649i	−0.246985	−	1.71782i
$505$		0			0
$506$	16.5108	+	11.7458i	0.733996	+	0.522166i
$507$	−23.1518			−1.02821
$508$	−1.94988	−	13.5617i	−0.0865119	−	0.601703i
$509$	1.79392	−	3.92814i	0.0795143	−	0.174112i	−0.865699	−	0.500564i	$-0.833126\pi$
$509$	1.79392	−	3.92814i	0.0795143	−	0.174112i	0.945214	+	0.326452i	$0.105853\pi$
$510$		0			0
$511$	−13.7228	+	15.8370i	−0.607062	+	0.700587i
$512$	−15.7308	−	4.61898i	−0.695209	−	0.204132i
$513$	5.65074	−	3.63151i	0.249486	−	0.160335i
$514$	3.62349	+	7.93434i	0.159825	+	0.349969i
$515$		0			0
$516$	−0.853938	−	0.548793i	−0.0375925	−	0.0241592i
$517$	1.41753	−	9.85912i	0.0623428	−	0.433604i
$518$	1.48066	−	10.2982i	0.0650565	−	0.452478i
$519$	−0.249474	−	0.160327i	−0.0109507	−	0.00703758i
$520$		0			0
$521$	18.8568	+	41.2906i	0.826131	+	1.80897i	0.509672	+	0.860369i	$0.329767\pi$
$521$	18.8568	+	41.2906i	0.826131	+	1.80897i	0.316459	+	0.948606i	$0.397506\pi$
$522$	−39.3657	+	25.2988i	−1.72299	+	1.10730i
$523$	−18.8365	−	5.53090i	−0.823663	−	0.241849i	−0.157370	−	0.987540i	$-0.550302\pi$
$523$	−18.8365	−	5.53090i	−0.823663	−	0.241849i	−0.666293	+	0.745690i	$0.732120\pi$
$524$	6.17519	−	7.12655i	0.269764	−	0.311325i
$525$		0			0
$526$	−8.73389	+	19.1245i	−0.380816	+	0.833870i
$527$	−3.28734	−	22.8639i	−0.143199	−	0.995969i
$528$	−16.9349			−0.736996
$529$	7.54261	+	21.7281i	0.327939	+	0.944699i
$530$		0			0
$531$	−0.217963	−	1.51596i	−0.00945877	−	0.0657872i
$532$	−1.47917	+	3.23892i	−0.0641300	+	0.140425i
$533$	−18.3467	+	5.38709i	−0.794686	+	0.233341i
$534$	−20.5405	+	23.7050i	−0.888874	+	1.02582i
$535$		0			0
$536$	9.01332	−	5.79251i	0.389316	−	0.250198i
$537$	8.19689	+	17.9487i	0.353722	+	0.774543i
$538$	−18.6400	−	21.5117i	−0.803629	−	0.927437i
$539$	2.09715	+	1.34775i	0.0903304	+	0.0580518i
$540$		0			0
$541$	3.82511	−	26.6042i	0.164454	−	1.14380i	−0.725656	−	0.688058i	$-0.758464\pi$
$541$	3.82511	−	26.6042i	0.164454	−	1.14380i	0.890110	−	0.455746i	$-0.150627\pi$
$542$	14.2882	+	9.18249i	0.613732	+	0.394422i
$543$	−33.5635	−	38.7344i	−1.44035	−	1.66225i
$544$	5.70026	+	12.4818i	0.244397	+	0.535154i
$545$		0			0
$546$	16.7977	+	4.93226i	0.718876	+	0.211081i
$547$	27.6569	−	31.9177i	1.18252	−	1.36470i	0.266371	−	0.963870i	$-0.414175\pi$
$547$	27.6569	−	31.9177i	1.18252	−	1.36470i	0.916151	−	0.400833i	$-0.131279\pi$
$548$	−2.34698	+	0.689137i	−0.100258	+	0.0294385i
$549$	−2.58884	+	5.66877i	−0.110489	+	0.241937i
$550$		0			0
$551$	14.2609			0.607535
$552$	−32.9450	−	23.4371i	−1.40223	−	0.997550i
$553$	38.9626			1.65686
$554$	−2.69809	−	18.7656i	−0.114631	−	0.797275i
$555$		0			0
$556$	−8.75659	+	2.57117i	−0.371362	+	0.109042i
$557$	3.68564	−	4.25346i	0.156166	−	0.180225i	−0.672275	−	0.740301i	$-0.734683\pi$
$557$	3.68564	−	4.25346i	0.156166	−	0.180225i	0.828441	+	0.560077i	$0.189228\pi$
$558$	−35.4766	−	10.4169i	−1.50184	−	0.440981i
$559$	0.775618	−	0.498459i	0.0328051	−	0.0210826i
$560$		0			0
$561$	22.0282	+	25.4219i	0.930032	+	1.07331i
$562$	3.82625	+	2.45898i	0.161401	+	0.103726i
$563$	1.87483	−	13.0397i	0.0790148	−	0.549560i	−0.911409	−	0.411501i	$-0.865005\pi$
$563$	1.87483	−	13.0397i	0.0790148	−	0.549560i	0.990424	−	0.138059i	$-0.0440863\pi$
$564$	−0.848195	+	5.89932i	−0.0357154	+	0.248406i
$565$		0			0
$566$	9.06540	+	10.4620i	0.381047	+	0.439752i
$567$	−1.75759	−	3.84858i	−0.0738117	−	0.161625i
$568$	−25.8383	+	16.6053i	−1.08415	+	0.696741i
$569$	12.9615	+	3.80583i	0.543373	+	0.159549i	0.541889	−	0.840450i	$-0.317709\pi$
$569$	12.9615	+	3.80583i	0.543373	+	0.159549i	0.00148425	+	0.999999i	$0.499528\pi$
$570$		0			0
$571$	−10.4053	+	3.05528i	−0.435450	+	0.127860i	−0.492108	−	0.870534i	$-0.663774\pi$
$571$	−10.4053	+	3.05528i	−0.435450	+	0.127860i	0.0566585	+	0.998394i	$0.481955\pi$
$572$	−3.01958	+	6.61195i	−0.126255	+	0.276460i
$573$	1.43431	+	9.97587i	0.0599193	+	0.416748i
$574$	−26.3009			−1.09778
$575$		0			0
$576$	36.3050			1.51271
$577$	−2.35744	−	16.3964i	−0.0981416	−	0.682590i	−0.978191	−	0.207708i	$-0.933400\pi$
$577$	−2.35744	−	16.3964i	−0.0981416	−	0.682590i	0.880049	−	0.474882i	$-0.157509\pi$
$578$	3.32515	−	7.28106i	0.138308	−	0.302852i
$579$	−3.62018	+	1.06298i	−0.150450	+	0.0441760i
$580$		0			0
$581$	42.4006	+	12.4499i	1.75907	+	0.516511i
$582$	−22.7924	+	14.6478i	−0.944777	+	0.607171i
$583$	10.9739	+	24.0295i	0.454493	+	0.995202i
$584$	−15.1741	−	17.5118i	−0.627908	−	0.724645i
$585$		0			0
$586$	−3.06917	+	21.3466i	−0.126786	+	0.881819i
$587$	−5.09808	+	35.4579i	−0.210420	+	1.46350i	0.561337	+	0.827587i	$0.310287\pi$
$587$	−5.09808	+	35.4579i	−0.210420	+	1.46350i	−0.771758	+	0.635917i	$0.780622\pi$
$588$	−1.25485	−	0.806445i	−0.0517492	−	0.0332572i
$589$	7.37912	+	8.51596i	0.304051	+	0.350894i
$590$		0			0
$591$	8.95775	−	5.75679i	0.368472	−	0.236803i
$592$	5.24815	+	1.54100i	0.215698	+	0.0633346i
$593$	−16.7570	+	19.3386i	−0.688128	+	0.794142i	−0.987098	−	0.160120i	$-0.948812\pi$
$593$	−16.7570	+	19.3386i	−0.688128	+	0.794142i	0.298969	+	0.954263i	$0.403357\pi$
$594$	18.0969	−	5.31372i	0.742523	−	0.218025i
$595$		0			0
$596$	−1.12484	−	7.82343i	−0.0460752	−	0.320460i
$597$	41.0934			1.68184
$598$	9.53444	−	5.51058i	0.389892	−	0.225344i
$599$	32.2356			1.31711			0.658555	−	0.752533i	$-0.271168\pi$
$599$	32.2356			1.31711			0.658555	+	0.752533i	$0.271168\pi$
$600$		0			0
$601$	−8.29172	+	18.1563i	−0.338226	+	0.740613i	−0.999958	−	0.00912799i	$-0.997094\pi$
$601$	−8.29172	+	18.1563i	−0.338226	+	0.740613i	0.661732	+	0.749741i	$0.269822\pi$
$602$	1.21679	−	0.357283i	0.0495928	−	0.0145618i
$603$	−10.6062	+	12.2402i	−0.431919	+	0.498461i
$604$	9.07390	+	2.66434i	0.369212	+	0.108410i
$605$		0			0
$606$	−4.50218	−	9.85841i	−0.182889	−	0.400470i
$607$	−20.1905	−	23.3010i	−0.819505	−	0.945760i	0.179774	−	0.983708i	$-0.442463\pi$
$607$	−20.1905	−	23.3010i	−0.819505	−	0.945760i	−0.999280	+	0.0379482i	$0.987918\pi$
$608$	−5.63120	−	3.61895i	−0.228375	−	0.146768i
$609$	−10.2835	+	71.5234i	−0.416709	+	2.89828i
$610$		0			0
$611$	−4.55401	−	2.92668i	−0.184235	−	0.118401i
$612$	−7.98979	−	9.22071i	−0.322968	−	0.372725i
$613$	0.538924	+	1.18008i	0.0217669	+	0.0476629i	0.920203	−	0.391441i	$-0.128023\pi$
$613$	0.538924	+	1.18008i	0.0217669	+	0.0476629i	−0.898436	+	0.439104i	$0.855296\pi$
$614$	6.31944	−	4.06126i	0.255032	−	0.163899i
$615$		0			0
$616$	−21.8335	+	25.1972i	−0.879697	+	1.01522i
$617$	−4.17238	+	1.22512i	−0.167974	+	0.0493215i	−0.364638	−	0.931149i	$-0.618807\pi$
$617$	−4.17238	+	1.22512i	−0.167974	+	0.0493215i	0.196664	+	0.980471i	$0.436989\pi$
$618$	−6.66111	+	14.5858i	−0.267949	+	0.586727i
$619$	−3.69352	−	25.6890i	−0.148455	−	1.03253i	−0.918750	−	0.394840i	$-0.870800\pi$
$619$	−3.69352	−	25.6890i	−0.148455	−	1.03253i	0.770295	−	0.637688i	$-0.220109\pi$
$620$		0			0
$621$	20.2347	+	6.99284i	0.811990	+	0.280613i
$622$	−17.0888			−0.685198
$623$	4.17835	+	29.0611i	0.167402	+	1.16431i
$624$	−3.82340	+	8.37208i	−0.153059	+	0.335152i
$625$		0			0
$626$	−10.8479	+	12.5192i	−0.433570	+	0.500366i
$627$	−15.7447	−	4.62305i	−0.628781	−	0.184627i
$628$	−2.94163	+	1.89047i	−0.117384	+	0.0754380i
$629$	−4.51331	−	9.88276i	−0.179957	−	0.394052i
$630$		0			0
$631$	36.9803	+	23.7658i	1.47216	+	0.946101i	0.997836	+	0.0657520i	$0.0209446\pi$
$631$	36.9803	+	23.7658i	1.47216	+	0.946101i	0.474326	+	0.880349i	$0.342692\pi$
$632$	−6.13137	+	42.6446i	−0.243893	+	1.69631i
$633$	−7.31584	+	50.8828i	−0.290778	+	2.02241i
$634$	3.64473	+	2.34232i	0.144751	+	0.0930256i
$635$		0			0
$636$	−6.56638	−	14.3784i	−0.260374	−	0.570139i
$637$	1.13976	−	0.732481i	0.0451590	−	0.0290219i
$638$	38.4213	+	11.2815i	1.52111	+	0.446639i
$639$	30.4046	−	35.0888i	1.20279	−	1.38809i
$640$		0			0
$641$	15.2745	−	33.4464i	0.603305	−	1.32105i	−0.323755	−	0.946141i	$-0.604945\pi$
$641$	15.2745	−	33.4464i	0.603305	−	1.32105i	0.927060	−	0.374913i	$-0.122327\pi$
$642$	−1.55230	−	10.7965i	−0.0612646	−	0.426104i
$643$	−27.8185			−1.09706			−0.548528	−	0.836132i	$-0.684812\pi$
$643$	−27.8185			−1.09706			−0.548528	+	0.836132i	$0.684812\pi$
$644$	−11.0277	+	2.68067i	−0.434552	+	0.105633i
$645$		0			0
$646$	−0.706278	−	4.91227i	−0.0277881	−	0.193271i
$647$	−2.69254	+	5.89584i	−0.105855	+	0.231789i	−0.955146	−	0.296135i	$-0.904302\pi$
$647$	−2.69254	+	5.89584i	−0.105855	+	0.231789i	0.849291	+	0.527924i	$0.177029\pi$
$648$	4.48886	−	1.31805i	0.176339	−	0.0517778i
$649$	−0.858261	+	0.990486i	−0.0336897	+	0.0388800i
$650$		0			0
$651$	−48.0316	+	30.8680i	−1.88251	+	1.20981i
$652$	−1.97466	−	4.32390i	−0.0773335	−	0.169337i
$653$	−27.6066	−	31.8598i	−1.08033	−	1.24677i	−0.967423	−	0.253164i	$-0.918529\pi$
$653$	−27.6066	−	31.8598i	−1.08033	−	1.24677i	−0.112908	−	0.993605i	$-0.536017\pi$
$654$	30.2393	+	19.4336i	1.18245	+	0.759914i
$655$		0			0
$656$	1.96780	−	13.6863i	0.0768296	−	0.534362i
$657$	29.4669	+	18.9372i	1.14961	+	0.738811i
$658$	−4.87607	−	5.62728i	−0.190089	−	0.219374i
$659$	16.0641	+	35.1755i	0.625770	+	1.37024i	0.911248	+	0.411859i	$0.135120\pi$
$659$	16.0641	+	35.1755i	0.625770	+	1.37024i	−0.285478	+	0.958385i	$0.592152\pi$
$660$		0			0
$661$	10.4385	+	3.06503i	0.406012	+	0.119216i	0.478360	−	0.878164i	$-0.341231\pi$
$661$	10.4385	+	3.06503i	0.406012	+	0.119216i	−0.0723487	+	0.997379i	$0.523049\pi$
$662$	−4.80144	+	5.54116i	−0.186613	+	0.215363i
$663$	17.5411	−	5.15054i	0.681241	−	0.200030i
$664$	−20.2989	+	44.4483i	−0.787749	+	1.72493i
$665$		0			0
$666$	−17.3907			−0.673878
$667$	28.1137	+	35.7155i	1.08857	+	1.38291i
$668$	1.85393			0.0717307
$669$	−2.90830	−	20.2276i	−0.112441	−	0.782046i
$670$		0			0
$671$	5.11687	−	1.50245i	0.197534	−	0.0580013i
$672$	22.2110	−	25.6328i	0.856807	−	0.988808i
$673$	29.9119	+	8.78293i	1.15302	+	0.338557i	0.801716	−	0.597705i	$-0.203920\pi$
$673$	29.9119	+	8.78293i	1.15302	+	0.338557i	0.351303	+	0.936262i	$0.385739\pi$
$674$	−9.52568	+	6.12178i	−0.366915	+	0.235802i
$675$		0			0
$676$	−4.70574	−	5.43072i	−0.180990	−	0.208874i
$677$	−27.7563	−	17.8379i	−1.06676	−	0.685565i	−0.115298	−	0.993331i	$-0.536782\pi$
$677$	−27.7563	−	17.8379i	−1.06676	−	0.685565i	−0.951462	+	0.307766i	$0.900419\pi$
$678$	8.15498	−	56.7192i	0.313190	−	2.17829i
$679$	−3.60916	+	25.1023i	−0.138507	+	0.963337i
$680$		0			0
$681$	−16.3074	−	18.8198i	−0.624902	−	0.721175i
$682$	13.1438	+	28.7809i	0.503302	+	1.10208i
$683$	17.0847	−	10.9797i	0.653728	−	0.420125i	−0.171299	−	0.985219i	$-0.554796\pi$
$683$	17.0847	−	10.9797i	0.653728	−	0.420125i	0.825027	+	0.565094i	$0.191160\pi$
$684$	5.71070	+	1.67681i	0.218354	+	0.0641146i
$685$		0			0
$686$	−18.0509	+	5.30022i	−0.689187	+	0.202363i
$687$	6.44888	−	14.1211i	0.246040	−	0.538753i
$688$	0.0948821	+	0.659920i	0.00361735	+	0.0251592i
$689$	14.3571			0.546960
$690$		0			0
$691$	7.02101			0.267092			0.133546	−	0.991043i	$-0.457364\pi$
$691$	7.02101			0.267092			0.133546	+	0.991043i	$0.457364\pi$
$692$	−0.0130992	−	0.0911066i	−0.000497955	−	0.00346335i
$693$	20.9368	−	45.8452i	0.795323	−	1.74152i
$694$	−10.6004	+	3.11255i	−0.402384	+	0.118151i
$695$		0			0
$696$	−76.6641	−	22.5106i	−2.90595	−	0.853263i
$697$	−23.1050	+	14.8487i	−0.875163	+	0.562433i
$698$	−8.45847	−	18.5215i	−0.320158	−	0.701048i
$699$	−13.8222	−	15.9517i	−0.522805	−	0.603349i
$700$		0			0
$701$	−2.44481	+	17.0041i	−0.0923394	+	0.642234i	0.890116	+	0.455735i	$0.150623\pi$
$701$	−2.44481	+	17.0041i	−0.0923394	+	0.642234i	−0.982455	+	0.186500i	$0.940286\pi$
$702$	1.45881	−	10.1462i	0.0550591	−	0.382944i
$703$	4.45863	+	2.86538i	0.168160	+	0.108070i
$704$	−20.3448	−	23.4792i	−0.766775	−	0.884905i
$705$		0			0
$706$	7.71573	−	4.95860i	0.290385	−	0.186619i
$707$	−9.73364	−	2.85805i	−0.366071	−	0.107488i
$708$	0.513551	−	0.592669i	0.0193004	−	0.0222739i
$709$	−2.99245	+	0.878661i	−0.112384	+	0.0329988i	−0.337441	−	0.941347i	$-0.609561\pi$
$709$	−2.99245	+	0.878661i	−0.112384	+	0.0329988i	0.225057	+	0.974346i	$0.427743\pi$
$710$		0			0
$711$	−9.26854	−	64.4641i	−0.347597	−	2.41759i
$712$	−32.4649			−1.21667
$713$	−6.78063	+	35.2688i	−0.253937	+	1.32083i
$714$	25.1461			0.941067
$715$		0			0
$716$	−2.54416	+	5.57093i	−0.0950797	+	0.208195i
$717$	48.0750	−	14.1161i	1.79539	−	0.527175i
$718$	−1.55005	+	1.78885i	−0.0578474	+	0.0667594i
$719$	28.7542	+	8.44298i	1.07235	+	0.314870i	0.769814	−	0.638268i	$-0.220349\pi$
$719$	28.7542	+	8.44298i	1.07235	+	0.314870i	0.302535	+	0.953138i	$0.402167\pi$
$720$		0			0
$721$	6.23504	+	13.6528i	0.232205	+	0.508458i
$722$	−11.7190	−	13.5244i	−0.436135	−	0.503326i
$723$	1.51806	+	0.975596i	0.0564572	+	0.0362828i
$724$	2.26393	−	15.7460i	0.0841384	−	0.585196i
$725$		0			0
$726$	−11.4520	−	7.35974i	−0.425023	−	0.273146i
$727$	12.9868	+	14.9876i	0.481655	+	0.555859i	0.943617	−	0.331041i	$-0.107400\pi$
$727$	12.9868	+	14.9876i	0.481655	+	0.555859i	−0.461962	+	0.886900i	$0.652854\pi$
$728$	7.52735	+	16.4826i	0.278982	+	0.610886i
$729$	−37.0439	+	23.8067i	−1.37200	+	0.881729i
$730$		0			0
$731$	0.867224	−	1.00083i	0.0320754	−	0.0370170i
$732$	−3.06174	+	0.899008i	−0.113165	+	0.0332283i
$733$	22.0520	−	48.2871i	0.814508	−	1.78352i	0.227836	−	0.973699i	$-0.426835\pi$
$733$	22.0520	−	48.2871i	0.814508	−	1.78352i	0.586672	−	0.809825i	$-0.300438\pi$
$734$	−2.56072	−	17.8102i	−0.0945179	−	0.657387i
$735$		0			0
$736$	−2.03780	−	21.2373i	−0.0751145	−	0.782819i
$737$	13.8596			0.510525
$738$	6.25654	+	43.5152i	0.230306	+	1.60182i
$739$	−10.5599	+	23.1230i	−0.388453	+	0.850592i	0.609859	+	0.792510i	$0.291226\pi$
$739$	−10.5599	+	23.1230i	−0.388453	+	0.850592i	−0.998312	+	0.0580826i	$0.981501\pi$
$740$		0			0
$741$	−5.84018	+	6.73993i	−0.214544	+	0.247597i
$742$	18.9479	+	5.56361i	0.695599	+	0.204246i
$743$	−6.06116	+	3.89527i	−0.222363	+	0.142904i	−0.647080	−	0.762422i	$-0.724010\pi$
$743$	−6.06116	+	3.89527i	−0.222363	+	0.142904i	0.424717	+	0.905326i	$0.360374\pi$
$744$	−26.2266	−	57.4282i	−0.961513	−	2.10542i
$745$		0			0
$746$	5.63770	+	3.62313i	0.206411	+	0.132652i
$747$	10.5122	−	73.1139i	0.384621	−	2.67510i
$748$	−1.48585	+	10.3343i	−0.0543281	+	0.377860i
$749$	−8.58907	−	5.51986i	−0.313838	−	0.201691i
$750$		0			0
$751$	5.69615	+	12.4728i	0.207856	+	0.455140i	0.984633	−	0.174635i	$-0.0558744\pi$
$751$	5.69615	+	12.4728i	0.207856	+	0.455140i	−0.776778	+	0.629775i	$0.783147\pi$
$752$	3.29312	−	2.11636i	0.120088	−	0.0771756i
$753$	−20.6581	−	6.06576i	−0.752823	−	0.221049i
$754$	14.2516	−	16.4473i	0.519014	−	0.598974i
$755$		0			0
$756$	−4.38834	+	9.60912i	−0.159602	+	0.349480i
$757$	−5.07729	−	35.3133i	−0.184537	−	1.28348i	−0.845869	−	0.533391i	$-0.820918\pi$
$757$	−5.07729	−	35.3133i	−0.184537	−	1.28348i	0.661332	−	0.750093i	$-0.269992\pi$
$758$	8.26093			0.300051
$759$	−19.4606	−	48.5453i	−0.706375	−	1.76208i
$760$		0			0
$761$	−6.74583	−	46.9183i	−0.244536	−	1.70079i	−0.628804	−	0.777564i	$-0.716455\pi$
$761$	−6.74583	−	46.9183i	−0.244536	−	1.70079i	0.384267	−	0.923222i	$-0.374454\pi$
$762$	19.6081	−	42.9358i	0.710327	−	1.55540i
$763$	32.2834	−	9.47925i	1.16874	−	0.343172i
$764$	−2.04851	+	2.36411i	−0.0741125	+	0.0855303i
$765$		0			0
$766$	15.7666	−	10.1326i	0.569672	−	0.366106i
$767$	0.295896	+	0.647921i	0.0106842	+	0.0233951i
$768$	29.3685	+	33.8931i	1.05975	+	1.22301i
$769$	0.249050	+	0.160054i	0.00898096	+	0.00577171i	0.545124	−	0.838356i	$-0.316483\pi$
$769$	0.249050	+	0.160054i	0.00898096	+	0.00577171i	−0.536143	+	0.844127i	$0.680119\pi$
$770$		0			0
$771$	3.20412	−	22.2851i	0.115394	−	0.802580i
$772$	−0.985167	−	0.633129i	−0.0354570	−	0.0227868i
$773$	−25.6544	−	29.6068i	−0.922726	−	1.06488i	−0.997706	−	0.0676970i	$-0.978435\pi$
$773$	−25.6544	−	29.6068i	−0.922726	−	1.06488i	0.0749804	−	0.997185i	$-0.476111\pi$
$774$	−0.880582	−	1.92821i	−0.0316519	−	0.0693079i
$775$		0			0
$776$	−26.9065	−	7.90046i	−0.965887	−	0.283610i
$777$	−17.5860	+	20.2954i	−0.630895	+	0.728092i
$778$	37.3646	−	10.9712i	1.33959	−	0.393338i
$779$	5.56573	−	12.1872i	0.199413	−	0.436653i
$780$		0			0
$781$	−39.7310			−1.42169
$782$	10.9101	−	11.4528i	0.390146	−	0.409551i
$783$	42.3087			1.51199
$784$	0.139428	+	0.969744i	0.00497958	+	0.0346337i
$785$		0			0
$786$	31.1702	−	9.15239i	1.11180	−	0.326455i
$787$	−28.0263	+	32.3441i	−0.999031	+	1.15294i	−0.0108051	+	0.999942i	$0.503439\pi$
$787$	−28.0263	+	32.3441i	−0.999031	+	1.15294i	−0.988226	+	0.153002i	$0.951106\pi$
$788$	3.17109	+	0.931116i	0.112965	+	0.0331696i
$789$	45.6526	−	29.3391i	1.62528	−	1.04450i
$790$		0			0
$791$	−35.1248	−	40.5362i	−1.24890	−	1.44130i
$792$	46.8829	+	30.1298i	1.66591	+	1.07062i
$793$	0.412475	−	2.86883i	0.0146474	−	0.101875i
$794$	−5.93433	+	41.2742i	−0.210602	+	1.46477i
$795$		0			0
$796$	8.35248	+	9.63928i	0.296046	+	0.341655i
$797$	−17.6127	−	38.5664i	−0.623873	−	1.36609i	−0.912668	−	0.408701i	$-0.865982\pi$
$797$	−17.6127	−	38.5664i	−0.623873	−	1.36609i	0.288795	−	0.957391i	$-0.406745\pi$
$798$	−10.3195	+	6.63193i	−0.365306	+	0.234768i
$799$	−7.46053	−	2.19061i	−0.263935	−	0.0774982i
$800$		0			0
$801$	47.0879	−	13.8262i	1.66377	−	0.488526i
$802$	10.7921	−	23.6315i	0.381084	−	0.834457i
$803$	−4.26576	−	29.6690i	−0.150535	−	1.04700i
$804$	−8.29305			−0.292473
$805$		0			0
$806$	17.1959			0.605699
$807$	10.4559	+	72.7223i	0.368065	+	2.55995i
$808$	4.65988	−	10.2037i	0.163934	−	0.358965i
$809$	10.3537	−	3.04012i	0.364016	−	0.106885i	−0.0946093	−	0.995514i	$-0.530160\pi$
$809$	10.3537	−	3.04012i	0.364016	−	0.106885i	0.458625	+	0.888630i	$0.348342\pi$
$810$		0			0
$811$	−27.3155	−	8.02057i	−0.959178	−	0.281640i	−0.235575	−	0.971856i	$-0.575697\pi$
$811$	−27.3155	−	8.02057i	−0.959178	−	0.281640i	−0.723603	+	0.690216i	$0.757516\pi$
$812$	−18.8674	+	12.1254i	−0.662118	+	0.425517i
$813$	−18.2116	−	39.8777i	−0.638707	−	1.39857i
$814$	9.74554	+	11.2470i	0.341581	+	0.394206i
$815$		0			0
$816$	−1.88139	+	13.0854i	−0.0658619	+	0.458079i
$817$	−0.0919377	+	0.639441i	−0.00321649	+	0.0223712i
$818$	11.4437	+	7.35445i	0.400121	+	0.257142i
$819$	−17.9375	−	20.7010i	−0.626788	−	0.723352i
$820$		0			0
$821$	−6.77062	+	4.35121i	−0.236296	+	0.151858i	−0.653431	−	0.756986i	$-0.726671\pi$
$821$	−6.77062	+	4.35121i	−0.236296	+	0.151858i	0.417134	+	0.908845i	$0.363034\pi$
$822$	−8.08549	−	2.37411i	−0.282014	−	0.0828067i
$823$	−17.5153	+	20.2137i	−0.610545	+	0.704607i	−0.973883	−	0.227051i	$-0.927092\pi$
$823$	−17.5153	+	20.2137i	−0.610545	+	0.704607i	0.363338	+	0.931658i	$0.381637\pi$
$824$	−15.9242	+	4.67577i	−0.554746	+	0.162888i
$825$		0			0
$826$	0.139431	+	0.969766i	0.00485144	+	0.0337425i
$827$	−15.5652			−0.541257			−0.270628	−	0.962684i	$-0.587231\pi$
$827$	−15.5652			−0.541257			−0.270628	+	0.962684i	$0.587231\pi$
$828$	7.05850	+	17.6077i	0.245300	+	0.611911i
$829$	19.1865			0.666374			0.333187	−	0.942861i	$-0.391876\pi$
$829$	19.1865			0.666374			0.333187	+	0.942861i	$0.391876\pi$
$830$		0			0
$831$	−20.3283	+	44.5128i	−0.705182	+	1.54413i
$832$	−16.2007	+	4.75694i	−0.561657	+	0.164917i
$833$	1.27438	−	1.47071i	0.0441545	−	0.0509570i
$834$	−30.1669	−	8.85781i	−1.04460	−	0.306721i
$835$		0			0
$836$	−2.11577	−	4.63289i	−0.0731755	−	0.160232i
$837$	21.8921	+	25.2649i	0.756702	+	0.873281i
$838$	−11.9247	−	7.66355i	−0.411932	−	0.264733i
$839$	−5.69772	+	39.6285i	−0.196707	+	1.36813i	0.617050	+	0.786924i	$0.288327\pi$
$839$	−5.69772	+	39.6285i	−0.196707	+	1.36813i	−0.813758	+	0.581204i	$0.802582\pi$
$840$		0			0
$841$	51.1694	+	32.8846i	1.76446	+	1.13395i
$842$	10.3646	+	11.9613i	0.357186	+	0.412215i
$843$	−4.87688	−	10.6789i	−0.167969	−	0.367800i
$844$	−13.4226	+	8.62616i	−0.462024	+	0.296925i
$845$		0			0
$846$	−8.15047	+	9.40614i	−0.280219	+	0.323390i
$847$	−12.2261	+	3.58991i	−0.420094	+	0.123351i
$848$	−4.31281	+	9.44374i	−0.148103	+	0.324300i
$849$	−5.08512	−	35.3678i	−0.174521	−	1.21382i
$850$		0			0
$851$	1.61348	+	16.8151i	0.0553092	+	0.576415i
$852$	23.7735			0.814467
$853$	−0.583690	−	4.05965i	−0.0199852	−	0.139000i	0.977386	−	0.211464i	$-0.0678230\pi$
$853$	−0.583690	−	4.05965i	−0.0199852	−	0.139000i	−0.997371	+	0.0724636i	$0.976914\pi$
$854$	1.65609	−	3.62633i	0.0566702	−	0.124091i
$855$		0			0
$856$	7.39311	−	8.53210i	0.252691	−	0.291621i
$857$	−3.55079	−	1.04261i	−0.121293	−	0.0356147i	0.220523	−	0.975382i	$-0.429224\pi$
$857$	−3.55079	−	1.04261i	−0.121293	−	0.0356147i	−0.341816	+	0.939767i	$0.611042\pi$
$858$	−21.0662	+	13.5385i	−0.719190	+	0.462195i
$859$	6.74482	+	14.7691i	0.230130	+	0.503915i	0.989106	−	0.147204i	$-0.0470273\pi$
$859$	6.74482	+	14.7691i	0.230130	+	0.503915i	−0.758976	+	0.651119i	$0.774300\pi$
$860$		0			0
$861$	57.1099	+	36.7023i	1.94630	+	1.25081i
$862$	1.34711	−	9.36936i	0.0458828	−	0.319122i
$863$	−2.43397	+	16.9287i	−0.0828534	+	0.576258i	0.905531	+	0.424281i	$0.139473\pi$
$863$	−2.43397	+	16.9287i	−0.0828534	+	0.576258i	−0.988384	+	0.151977i	$0.951436\pi$
$864$	−16.7065	−	10.7366i	−0.568365	−	0.365266i
$865$		0			0
$866$	5.91840	+	12.9595i	0.201115	+	0.440381i
$867$	−17.3808	+	11.1699i	−0.590282	+	0.379351i
$868$	−17.0034	−	4.99266i	−0.577135	−	0.169462i
$869$	−36.4963	+	42.1190i	−1.23805	+	1.42879i
$870$		0			0
$871$	3.12909	−	6.85175i	0.106025	−	0.232163i
$872$	5.29476	+	36.8258i	0.179303	+	1.24708i
$873$	42.3905			1.43470
$874$	−1.45680	+	7.57742i	−0.0492771	+	0.256310i
$875$		0			0
$876$	2.55247	+	17.7528i	0.0862399	+	0.599812i
$877$	−10.1360	+	22.1948i	−0.342269	+	0.749466i	−0.999993	−	0.00379402i	$-0.998792\pi$
$877$	−10.1360	+	22.1948i	−0.342269	+	0.749466i	0.657723	+	0.753260i	$0.271520\pi$
$878$	21.8534	−	6.41672i	0.737515	−	0.216554i
$879$	36.4530	−	42.0690i	1.22953	−	1.41895i
$880$		0			0
$881$	11.4278	−	7.34422i	0.385013	−	0.247433i	−0.333789	−	0.942648i	$-0.608327\pi$
$881$	11.4278	−	7.34422i	0.385013	−	0.247433i	0.718802	+	0.695215i	$0.244691\pi$
$882$	−1.29401	−	2.83348i	−0.0435714	−	0.0954081i
$883$	25.8171	+	29.7945i	0.868813	+	1.00266i	0.999936	+	0.0112976i	$0.00359622\pi$
$883$	25.8171	+	29.7945i	0.868813	+	1.00266i	−0.131123	+	0.991366i	$0.541858\pi$
$884$	4.77351	+	3.06775i	0.160550	+	0.103179i
$885$		0			0
$886$	−0.399984	+	2.78195i	−0.0134377	+	0.0934614i
$887$	−21.5673	−	13.8605i	−0.724160	−	0.465390i	0.125922	−	0.992040i	$-0.459811\pi$
$887$	−21.5673	−	13.8605i	−0.724160	−	0.465390i	−0.850082	+	0.526651i	$0.823448\pi$
$888$	−19.4458	−	22.4417i	−0.652560	−	0.753094i
$889$	−18.3539	−	40.1894i	−0.615570	−	1.34791i
$890$		0			0
$891$	5.80668	+	1.70500i	0.194531	+	0.0571195i
$892$	4.15367	−	4.79360i	0.139075	−	0.160501i
$893$	3.63941	−	1.06863i	0.121788	−	0.0357603i
$894$	11.3115	−	24.7686i	0.378312	−	0.828387i
$895$		0			0
$896$	1.35346			0.0452158
$897$	−28.3930	−	1.33940i	−0.948013	−	0.0447213i
$898$	28.6474			0.955975
$899$	10.1008	+	70.2528i	0.336882	+	2.34306i
$900$		0			0
$901$	19.7865	−	5.80983i	0.659183	−	0.193554i
$902$	24.6361	−	28.4316i	0.820292	−	0.946667i
$903$	−3.14073	−	0.922200i	−0.104517	−	0.0306889i
$904$	49.8943	−	32.0651i	1.65946	−	1.06647i
$905$		0			0
$906$	21.3352	+	24.6222i	0.708816	+	0.818017i
$907$	42.8681	+	27.5496i	1.42341	+	0.914771i	0.999961	+	0.00885182i	$0.00281766\pi$
$907$	42.8681	+	27.5496i	1.42341	+	0.914771i	0.423451	+	0.905919i	$0.360819\pi$
$908$	1.09997	−	7.65047i	0.0365038	−	0.253890i
$909$	−2.41322	+	16.7843i	−0.0800414	+	0.556700i
$910$		0			0
$911$	6.50069	+	7.50220i	0.215377	+	0.248559i	0.853150	−	0.521666i	$-0.174689\pi$
$911$	6.50069	+	7.50220i	0.215377	+	0.248559i	−0.637772	+	0.770225i	$0.720144\pi$
$912$	−2.67900	−	5.86619i	−0.0887105	−	0.194249i
$913$	−53.1752	+	34.1736i	−1.75984	+	1.13098i
$914$	−13.9130	−	4.08524i	−0.460202	−	0.135128i
$915$		0			0
$916$	4.62316	−	1.35748i	0.152753	−	0.0448525i
$917$	12.6320	−	27.6602i	0.417146	−	0.913421i
$918$	−2.09536	−	14.5735i	−0.0691572	−	0.480999i
$919$	15.5866			0.514154			0.257077	−	0.966391i	$-0.417241\pi$
$919$	15.5866			0.514154			0.257077	+	0.966391i	$0.417241\pi$
$920$		0			0
$921$	−19.3894			−0.638903
$922$	−3.81678	−	26.5463i	−0.125699	−	0.874256i
$923$	−8.97010	+	19.6418i	−0.295254	+	0.646517i
$924$	24.7613	−	7.27056i	0.814586	−	0.239184i
$925$		0			0
$926$	−22.0198	−	6.46560i	−0.723616	−	0.212473i
$927$	21.1055	−	13.5637i	0.693197	−	0.445491i
$928$	−17.5149	−	38.3523i	−0.574955	−	1.25898i
$929$	−16.7811	−	19.3665i	−0.550571	−	0.635393i	0.410445	−	0.911885i	$-0.365373\pi$
$929$	−16.7811	−	19.3665i	−0.550571	−	0.635393i	−0.961016	+	0.276492i	$0.910828\pi$
$930$		0			0
$931$	−0.135101	+	0.939651i	−0.00442777	+	0.0307958i
$932$	0.932341	−	6.48457i	0.0305398	−	0.212409i
$933$	37.1066	+	23.8470i	1.21482	+	0.780715i
$934$	8.82948	+	10.1898i	0.288909	+	0.333419i
$935$		0			0
$936$	25.4800	−	16.3750i	0.832840	−	0.535234i
$937$	35.2967	+	10.3640i	1.15309	+	0.338579i	0.801745	−	0.597667i	$-0.203905\pi$
$937$	35.2967	+	10.3640i	1.15309	+	0.338579i	0.351348	+	0.936245i	$0.385724\pi$
$938$	6.78483	−	7.83011i	0.221533	−	0.255662i
$939$	41.0253	−	12.0461i	1.33881	−	0.393111i
$940$		0			0
$941$	1.87551	+	13.0444i	0.0611397	+	0.425236i	0.997286	+	0.0736253i	$0.0234569\pi$
$941$	1.87551	+	13.0444i	0.0611397	+	0.425236i	−0.936146	+	0.351611i	$0.885634\pi$
$942$	−12.0464			−0.392493
$943$	41.4944	−	10.0867i	1.35124	−	0.328468i
$944$	−0.515074			−0.0167642
$945$		0			0
$946$	−0.753544	+	1.65003i	−0.0244998	+	0.0536472i
$947$	−41.9677	+	12.3228i	−1.36377	+	0.400438i	−0.880089	−	0.474808i	$-0.842517\pi$
$947$	−41.9677	+	12.3228i	−1.36377	+	0.400438i	−0.483677	+	0.875246i	$0.660699\pi$
$948$	21.8380	−	25.2024i	0.709265	−	0.818536i
$949$	−15.6305	−	4.58954i	−0.507388	−	0.148983i
$950$		0			0
$951$	−4.64551	−	10.1722i	−0.150641	−	0.329858i
$952$	17.0439	+	19.6698i	0.552398	+	0.637501i
$953$	8.39740	+	5.39668i	0.272018	+	0.174816i	0.669537	−	0.742778i	$-0.266492\pi$
$953$	8.39740	+	5.39668i	0.272018	+	0.174816i	−0.397519	+	0.917594i	$0.630129\pi$
$954$	4.69767	−	32.6730i	0.152093	−	1.05783i
$955$		0			0
$956$	13.0828	+	8.40778i	0.423126	+	0.271927i
$957$	−67.6849	−	78.1126i	−2.18794	−	2.52502i
$958$	−4.45472	−	9.75447i	−0.143925	−	0.315153i
$959$	−6.63566	+	4.26448i	−0.214277	+	0.137707i
$960$		0			0
$961$	−16.4246	+	18.9550i	−0.529825	+	0.611451i
$962$	7.76041	−	2.27866i	0.250206	−	0.0734670i
$963$	−7.08947	+	15.5238i	−0.228455	+	0.500247i
$964$	0.0797088	+	0.554387i	0.00256725	+	0.0178556i
$965$		0			0
$966$	−36.9529	−	12.7705i	−1.18894	−	0.410883i
$967$	57.9710			1.86422			0.932111	−	0.362172i	$-0.117965\pi$
$967$	57.9710			1.86422			0.932111	+	0.362172i	$0.117965\pi$
$968$	−2.00519	−	13.9464i	−0.0644492	−	0.448254i
$969$	−5.32134	+	11.6521i	−0.170946	+	0.374319i
$970$		0			0
$971$	−37.6100	+	43.4042i	−1.20696	+	1.39291i	−0.310035	+	0.950725i	$0.600341\pi$
$971$	−37.6100	+	43.4042i	−1.20696	+	1.39291i	−0.896925	+	0.442182i	$0.854205\pi$
$972$	−14.4821	−	4.25233i	−0.464514	−	0.136394i
$973$	−24.7576	+	15.9107i	−0.793692	+	0.510075i
$974$	9.65606	+	21.1438i	0.309400	+	0.677491i
$975$		0			0
$976$	1.76314	+	1.13310i	0.0564369	+	0.0362698i
$977$	2.05629	−	14.3018i	0.0657866	−	0.457556i	−0.930127	−	0.367239i	$-0.880303\pi$
$977$	2.05629	−	14.3018i	0.0657866	−	0.457556i	0.995913	−	0.0903165i	$-0.0287879\pi$
$978$	2.33054	−	16.2092i	0.0745223	−	0.518314i
$979$	−35.3291	−	22.7047i	−1.12912	−	0.725644i
$980$		0			0
$981$	−23.3632	−	51.1582i	−0.745929	−	1.63336i
$982$	29.9181	−	19.2272i	0.954724	−	0.613564i
$983$	25.8739	+	7.59725i	0.825248	+	0.242315i	0.666975	−	0.745081i	$-0.267589\pi$
$983$	25.8739	+	7.59725i	0.825248	+	0.242315i	0.158274	+	0.987395i	$0.449407\pi$
$984$	−49.1578	+	56.7311i	−1.56709	+	1.80852i
$985$		0			0
$986$	12.9855	−	28.4343i	0.413543	−	0.905532i
$987$	2.73517	+	19.0235i	0.0870614	+	0.605525i
$988$	−2.76804			−0.0880630
$989$	−1.78269	+	1.03033i	−0.0566861	+	0.0327626i
$990$		0			0
$991$	1.52954	+	10.6382i	0.0485875	+	0.337934i	0.999587	+	0.0287408i	$0.00914974\pi$
$991$	1.52954	+	10.6382i	0.0485875	+	0.337934i	−0.950999	+	0.309193i	$0.899941\pi$
$992$	13.8394	−	30.3040i	0.439401	−	0.962153i
$993$	18.1584	−	5.33179i	0.576240	−	0.169199i
$994$	−19.4499	+	22.4464i	−0.616914	+	0.711957i
$995$		0			0
$996$	31.8180	−	20.4482i	1.00819	−	0.647926i
$997$	−6.68184	−	14.6312i	−0.211616	−	0.463374i	0.773823	−	0.633401i	$-0.218342\pi$
$997$	−6.68184	−	14.6312i	−0.211616	−	0.463374i	−0.985439	+	0.170027i	$0.945615\pi$
$998$	−12.5958	−	14.5363i	−0.398713	−	0.460139i
$999$	13.2277	+	8.50092i	0.418506	+	0.268957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.k.g.26.7		100
5.2	odd	4		115.2.j.a.49.4	✓	100
5.3	odd	4		115.2.j.a.49.7	yes	100
5.4	even	2	inner	575.2.k.g.26.4		100
23.8	even	11	inner	575.2.k.g.376.7		100
115.8	odd	44		115.2.j.a.54.4	yes	100
115.54	even	22	inner	575.2.k.g.376.4		100
115.77	odd	44		115.2.j.a.54.7	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.49.4	✓	100	5.2	odd	4
115.2.j.a.49.7	yes	100	5.3	odd	4
115.2.j.a.54.4	yes	100	115.8	odd	44
115.2.j.a.54.7	yes	100	115.77	odd	44
575.2.k.g.26.4		100	5.4	even	2	inner
575.2.k.g.26.7		100	1.1	even	1	trivial
575.2.k.g.376.4		100	115.54	even	22	inner
575.2.k.g.376.7		100	23.8	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.152174 + 1.05840i) q^{2} +(1.14653 - 2.51056i) q^{3} +(0.821942 - 0.241344i) q^{4} +(2.83164 + 0.831443i) q^{6} +(2.32389 - 1.49347i) q^{7} +(1.26891 + 2.77851i) q^{8} +(-3.02378 - 3.48962i) q^{9} +O(q^{10})\)	\(q+(0.152174 + 1.05840i) q^{2} +(1.14653 - 2.51056i) q^{3} +(0.821942 - 0.241344i) q^{4} +(2.83164 + 0.831443i) q^{6} +(2.32389 - 1.49347i) q^{7} +(1.26891 + 2.77851i) q^{8} +(-3.02378 - 3.48962i) q^{9} +(-0.562328 + 3.91108i) q^{11} +(0.336476 - 2.34024i) q^{12} +(1.80656 + 1.16100i) q^{13} +(1.93432 + 2.23232i) q^{14} +(-1.30637 + 0.839551i) q^{16} +(2.95957 + 0.869007i) q^{17} +(3.23326 - 3.73138i) q^{18} +(-1.44374 + 0.423921i) q^{19} +(-1.08503 - 7.54656i) q^{21} -4.22504 q^{22} +(-3.90785 - 2.78005i) q^{23} +8.43046 q^{24} +(-0.953890 + 2.08873i) q^{26} +(-4.28324 + 1.25767i) q^{27} +(1.54966 - 1.78840i) q^{28} +(-9.09371 - 2.67015i) q^{29} +(-3.11093 - 6.81198i) q^{31} +(2.91323 + 3.36205i) q^{32} +(9.17425 + 5.89593i) q^{33} +(-0.469383 + 3.26463i) q^{34} +(-3.32757 - 2.13850i) q^{36} +(-2.30662 - 2.66198i) q^{37} +(-0.668376 - 1.46354i) q^{38} +(4.98605 - 3.20434i) q^{39} +(-5.83097 + 6.72930i) q^{41} +(7.82213 - 2.29679i) q^{42} +(0.178352 - 0.390536i) q^{43} +(0.481714 + 3.35039i) q^{44} +(2.34772 - 4.55911i) q^{46} -2.52082 q^{47} +(0.609948 + 4.24228i) q^{48} +(0.262086 - 0.573889i) q^{49} +(5.57493 - 6.43382i) q^{51} +(1.76509 + 0.518276i) q^{52} +(5.62428 - 3.61451i) q^{53} +(-1.98292 - 4.34198i) q^{54} +(7.09842 + 4.56188i) q^{56} +(-0.591020 + 4.11064i) q^{57} +(1.44225 - 10.0311i) q^{58} +(0.279035 + 0.179325i) q^{59} +(-0.560667 - 1.22769i) q^{61} +(6.73637 - 4.32920i) q^{62} +(-12.2386 - 3.59357i) q^{63} +(-5.14890 + 5.94215i) q^{64} +(-4.84415 + 10.6072i) q^{66} +(-0.499184 - 3.47190i) q^{67} +2.64232 q^{68} +(-11.4600 + 6.62346i) q^{69} +(1.43100 + 9.95283i) q^{71} +(5.85909 - 12.8296i) q^{72} +(-7.27861 + 2.13719i) q^{73} +(2.46642 - 2.84640i) q^{74} +(-1.08436 + 0.696876i) q^{76} +(4.53429 + 9.92872i) q^{77} +(4.15021 + 4.78959i) q^{78} +(11.8655 + 7.62551i) q^{79} +(0.217970 - 1.51602i) q^{81} +(-8.00959 - 5.14745i) q^{82} +(10.4759 + 12.0898i) q^{83} +(-2.71315 - 5.94097i) q^{84} +(0.440483 + 0.129337i) q^{86} +(-17.1298 + 19.7688i) q^{87} +(-11.5805 + 3.40035i) q^{88} +(-4.41518 + 9.66790i) q^{89} +5.93216 q^{91} +(-3.88298 - 1.34191i) q^{92} -20.6687 q^{93} +(-0.383604 - 2.66802i) q^{94} +(11.7807 - 3.45914i) q^{96} +(-6.01198 + 6.93819i) q^{97} +(0.647284 + 0.190060i) q^{98} +(15.3485 - 9.86391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Introduction

L-functions

Modular forms

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Database

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