LMFDB - Embedded newform 475.2.p.g.468.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(107,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("475.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.p (of order $12$, degree $4$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.11007531417600000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 $ x^16 - 7x^12 + 48x^8 - 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			468.4
Root			$-0.418778 - 1.56290i$ of defining polynomial
Character	$\chi$	$=$	475.468
Dual form			475.2.p.g.407.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.578737 - 2.15988i) q^{2} +(2.52883 + 0.677597i) q^{3} +(-2.59808 - 1.50000i) q^{4} +(2.92705 - 5.06980i) q^{6} +(-1.22474 + 1.22474i) q^{7} +(-1.58114 + 1.58114i) q^{8} +(3.33775 + 1.92705i) q^{9} +O(q^{10})$	\(q+(0.578737 - 2.15988i) q^{2} +(2.52883 + 0.677597i) q^{3} +(-2.59808 - 1.50000i) q^{4} +(2.92705 - 5.06980i) q^{6} +(-1.22474 + 1.22474i) q^{7} +(-1.58114 + 1.58114i) q^{8} +(3.33775 + 1.92705i) q^{9} +4.85410 q^{11} +(-5.55369 - 5.55369i) q^{12} +(-1.25633 - 4.68870i) q^{13} +(1.93649 + 3.35410i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.38006 + 1.17363i) q^{17} +(6.09387 - 6.09387i) q^{18} +(-4.33013 - 0.500000i) q^{19} +(-3.92705 + 2.26728i) q^{21} +(2.80925 - 10.4843i) q^{22} +(-5.01910 + 1.34486i) q^{23} +(-5.06980 + 2.92705i) q^{24} -10.8541 q^{26} +(1.58114 + 1.58114i) q^{27} +(5.01910 - 1.34486i) q^{28} +(-2.26728 + 3.92705i) q^{29} +10.1396i q^{31} +(-6.47963 + 1.73621i) q^{32} +(12.2752 + 3.28913i) q^{33} +(5.06980 - 8.78115i) q^{34} +(-5.78115 - 10.0133i) q^{36} +(2.62210 + 2.62210i) q^{37} +(-3.58594 + 9.06317i) q^{38} -12.7082i q^{39} +(0.572949 - 0.330792i) q^{41} +(2.62432 + 9.79410i) q^{42} +(2.17603 - 8.12107i) q^{43} +(-12.6113 - 7.28115i) q^{44} +11.6190i q^{46} +(-1.00240 - 3.74101i) q^{47} +(-0.677597 - 2.52883i) q^{48} +4.00000i q^{49} +(10.2812 + 5.93583i) q^{51} +(-3.76900 + 14.0661i) q^{52} +(1.17190 + 4.37358i) q^{53} +(4.33013 - 2.50000i) q^{54} -3.87298i q^{56} +(-10.6113 - 4.19849i) q^{57} +(7.16978 + 7.16978i) q^{58} +(3.25966 + 5.64590i) q^{59} +(-5.28115 + 9.14723i) q^{61} +(21.9003 + 5.86816i) q^{62} +(-6.44804 + 1.72775i) q^{63} +13.0000i q^{64} +(14.2082 - 24.6093i) q^{66} +(-5.79555 + 1.55291i) q^{67} +(-9.61927 - 9.61927i) q^{68} -13.6037 q^{69} +(-3.35410 + 1.93649i) q^{71} +(-8.32438 + 2.23051i) q^{72} +(-0.0654043 + 0.244092i) q^{73} +(7.18091 - 4.14590i) q^{74} +(10.5000 + 7.79423i) q^{76} +(-5.94504 + 5.94504i) q^{77} +(-27.4481 - 7.35471i) q^{78} +(-0.992377 - 1.71885i) q^{79} +(-2.85410 - 4.94345i) q^{81} +(-0.382883 - 1.42894i) q^{82} +(-7.81628 - 7.81628i) q^{83} +13.6037 q^{84} +(-16.2812 - 9.39993i) q^{86} +(-8.39453 + 8.39453i) q^{87} +(-7.67501 + 7.67501i) q^{88} +(6.47106 - 11.2082i) q^{89} +(7.28115 + 4.20378i) q^{91} +(15.0573 + 4.03459i) q^{92} +(-6.87056 + 25.6413i) q^{93} -8.66025 q^{94} -17.5623 q^{96} +(2.99254 - 11.1683i) q^{97} +(8.63950 + 2.31495i) q^{98} +(16.2018 + 9.35410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 20 q^{6}+O(q^{10}) $ 16 * q + 20 * q^6	$ 16 q + 20 q^{6} + 24 q^{11} - 8 q^{16} - 36 q^{21} - 120 q^{26} - 12 q^{36} + 36 q^{41} + 84 q^{51} - 4 q^{61} + 120 q^{66} + 168 q^{76} + 8 q^{81} - 180 q^{86} + 36 q^{91} - 120 q^{96}+O(q^{100}) $ 16 * q + 20 * q^6 + 24 * q^11 - 8 * q^16 - 36 * q^21 - 120 * q^26 - 12 * q^36 + 36 * q^41 + 84 * q^51 - 4 * q^61 + 120 * q^66 + 168 * q^76 + 8 * q^81 - 180 * q^86 + 36 * q^91 - 120 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.578737	−	2.15988i	0.409229	−	1.52726i	−0.386892	−	0.922125i	$-0.626451\pi$
$2$	0.578737	−	2.15988i	0.409229	−	1.52726i	0.796121	−	0.605138i	$-0.206882\pi$
$3$	2.52883	+	0.677597i	1.46002	+	0.391211i	0.899496	−	0.436928i	$-0.143934\pi$
$3$	2.52883	+	0.677597i	1.46002	+	0.391211i	0.560522	+	0.828139i	$0.310600\pi$
$4$	−2.59808	−	1.50000i	−1.29904	−	0.750000i
$5$		0			0
$5$		0			0
$6$	2.92705	−	5.06980i	1.19496	−	2.06974i
$7$	−1.22474	+	1.22474i	−0.462910	+	0.462910i	−0.899608	−	0.436698i	$-0.856148\pi$
$7$	−1.22474	+	1.22474i	−0.462910	+	0.462910i	0.436698	+	0.899608i	$0.356148\pi$
$8$	−1.58114	+	1.58114i	−0.559017	+	0.559017i
$9$	3.33775	+	1.92705i	1.11258	+	0.642350i
$10$		0			0
$11$	4.85410			1.46357			0.731783	−	0.681537i	$-0.238688\pi$
$11$	4.85410			1.46357			0.731783	+	0.681537i	$0.238688\pi$
$12$	−5.55369	−	5.55369i	−1.60321	−	1.60321i
$13$	−1.25633	−	4.68870i	−0.348444	−	1.30041i	−0.888536	−	0.458806i	$-0.848277\pi$
$13$	−1.25633	−	4.68870i	−0.348444	−	1.30041i	0.540092	−	0.841606i	$-0.318389\pi$
$14$	1.93649	+	3.35410i	0.517549	+	0.896421i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.38006	+	1.17363i	1.06232	+	0.284648i	0.747334	−	0.664449i	$-0.231334\pi$
$17$	4.38006	+	1.17363i	1.06232	+	0.284648i	0.314986	+	0.949096i	$0.398000\pi$
$18$	6.09387	−	6.09387i	1.43634	−	1.43634i
$19$	−4.33013	−	0.500000i	−0.993399	−	0.114708i
$19$	−4.33013	−	0.500000i	−0.993399	−	0.114708i
$20$		0			0
$21$	−3.92705	+	2.26728i	−0.856953	+	0.494762i
$22$	2.80925	−	10.4843i	0.598934	−	2.23525i
$23$	−5.01910	+	1.34486i	−1.04655	+	0.280423i	−0.740827	−	0.671696i	$-0.765566\pi$
$23$	−5.01910	+	1.34486i	−1.04655	+	0.280423i	−0.305727	+	0.952119i	$0.598900\pi$
$24$	−5.06980	+	2.92705i	−1.03487	+	0.597482i
$25$		0			0
$26$	−10.8541			−2.12866
$27$	1.58114	+	1.58114i	0.304290	+	0.304290i
$28$	5.01910	−	1.34486i	0.948520	−	0.254155i
$29$	−2.26728	+	3.92705i	−0.421024	+	0.729235i	−0.996040	−	0.0889072i	$-0.971663\pi$
$29$	−2.26728	+	3.92705i	−0.421024	+	0.729235i	0.575016	+	0.818142i	$0.304996\pi$
$30$		0			0
$31$			10.1396i			1.82113i	0.413370	+	0.910563i	$0.364352\pi$
$31$			10.1396i			1.82113i	−0.413370	+	0.910563i	$0.635648\pi$
$32$	−6.47963	+	1.73621i	−1.14545	+	0.306922i
$33$	12.2752	+	3.28913i	2.13683	+	0.572563i
$34$	5.06980	−	8.78115i	0.869464	−	1.50596i
$35$		0			0
$36$	−5.78115	−	10.0133i	−0.963525	−	1.66888i
$37$	2.62210	+	2.62210i	0.431070	+	0.431070i	0.888992	−	0.457922i	$-0.151406\pi$
$37$	2.62210	+	2.62210i	0.431070	+	0.431070i	−0.457922	+	0.888992i	$0.651406\pi$
$38$	−3.58594	+	9.06317i	−0.581717	+	1.47024i
$39$		−	12.7082i		−	2.03494i
$40$		0			0
$41$	0.572949	−	0.330792i	0.0894796	−	0.0516611i	−0.454593	−	0.890700i	$-0.650215\pi$
$41$	0.572949	−	0.330792i	0.0894796	−	0.0516611i	0.544072	+	0.839038i	$0.316882\pi$
$42$	2.62432	+	9.79410i	0.404942	+	1.51126i
$43$	2.17603	−	8.12107i	0.331842	−	1.23845i	−0.575410	−	0.817865i	$-0.695158\pi$
$43$	2.17603	−	8.12107i	0.331842	−	1.23845i	0.907252	−	0.420587i	$-0.138176\pi$
$44$	−12.6113	−	7.28115i	−1.90123	−	1.09768i
$45$		0			0
$46$			11.6190i			1.71312i
$47$	−1.00240	−	3.74101i	−0.146215	−	0.545683i	−0.999698	−	0.0245623i	$-0.992181\pi$
$47$	−1.00240	−	3.74101i	−0.146215	−	0.545683i	0.853483	−	0.521121i	$-0.174486\pi$
$48$	−0.677597	−	2.52883i	−0.0978027	−	0.365005i
$49$			4.00000i			0.571429i
$50$		0			0
$51$	10.2812	+	5.93583i	1.43965	+	0.831182i
$52$	−3.76900	+	14.0661i	−0.522667	+	1.95062i
$53$	1.17190	+	4.37358i	0.160972	+	0.600758i	0.998520	+	0.0543925i	$0.0173222\pi$
$53$	1.17190	+	4.37358i	0.160972	+	0.600758i	−0.837547	+	0.546365i	$0.816011\pi$
$54$	4.33013	−	2.50000i	0.589256	−	0.340207i
$55$		0			0
$56$		−	3.87298i		−	0.517549i
$57$	−10.6113	−	4.19849i	−1.40551	−	0.556104i
$58$	7.16978	+	7.16978i	0.941438	+	0.941438i
$59$	3.25966	+	5.64590i	0.424372	+	0.735033i	0.996362	−	0.0852274i	$-0.0271617\pi$
$59$	3.25966	+	5.64590i	0.424372	+	0.735033i	−0.571990	+	0.820261i	$0.693828\pi$
$60$		0			0
$61$	−5.28115	+	9.14723i	−0.676182	+	1.17118i	0.299939	+	0.953958i	$0.403034\pi$
$61$	−5.28115	+	9.14723i	−0.676182	+	1.17118i	−0.976122	+	0.217224i	$0.930300\pi$
$62$	21.9003	+	5.86816i	2.78134	+	0.745257i
$63$	−6.44804	+	1.72775i	−0.812376	+	0.217676i
$64$			13.0000i			1.62500i
$65$		0			0
$66$	14.2082	−	24.6093i	1.74891	−	3.02920i
$67$	−5.79555	+	1.55291i	−0.708040	+	0.189719i	−0.594829	−	0.803852i	$-0.702780\pi$
$67$	−5.79555	+	1.55291i	−0.708040	+	0.189719i	−0.113211	+	0.993571i	$0.536114\pi$
$68$	−9.61927	−	9.61927i	−1.16651	−	1.16651i
$69$	−13.6037			−1.63769
$70$		0			0
$71$	−3.35410	+	1.93649i	−0.398059	+	0.229819i	−0.685646	−	0.727935i	$-0.740480\pi$
$71$	−3.35410	+	1.93649i	−0.398059	+	0.229819i	0.287587	+	0.957754i	$0.407147\pi$
$72$	−8.32438	+	2.23051i	−0.981038	+	0.262868i
$73$	−0.0654043	+	0.244092i	−0.00765499	+	0.0285688i	−0.969648	−	0.244506i	$-0.921374\pi$
$73$	−0.0654043	+	0.244092i	−0.00765499	+	0.0285688i	0.961993	+	0.273075i	$0.0880408\pi$
$74$	7.18091	−	4.14590i	0.834763	−	0.481951i
$75$		0			0
$76$	10.5000	+	7.79423i	1.20443	+	0.894059i
$77$	−5.94504	+	5.94504i	−0.677500	+	0.677500i
$78$	−27.4481	−	7.35471i	−3.10789	−	0.832757i
$79$	−0.992377	−	1.71885i	−0.111651	−	0.193385i	0.804785	−	0.593566i	$-0.202281\pi$
$79$	−0.992377	−	1.71885i	−0.111651	−	0.193385i	−0.916436	+	0.400181i	$0.868947\pi$
$80$		0			0
$81$	−2.85410	−	4.94345i	−0.317122	−	0.549272i
$82$	−0.382883	−	1.42894i	−0.0422824	−	0.157800i
$83$	−7.81628	−	7.81628i	−0.857948	−	0.857948i	0.133148	−	0.991096i	$-0.457491\pi$
$83$	−7.81628	−	7.81628i	−0.857948	−	0.857948i	−0.991096	+	0.133148i	$0.957491\pi$
$84$	13.6037			1.48429
$85$		0			0
$86$	−16.2812	−	9.39993i	−1.75564	−	1.01362i
$87$	−8.39453	+	8.39453i	−0.899988	+	0.899988i
$88$	−7.67501	+	7.67501i	−0.818159	+	0.818159i
$89$	6.47106	−	11.2082i	0.685931	−	1.18807i	−0.287212	−	0.957867i	$-0.592729\pi$
$89$	6.47106	−	11.2082i	0.685931	−	1.18807i	0.973143	−	0.230200i	$-0.0739381\pi$
$90$		0			0
$91$	7.28115	+	4.20378i	0.763272	+	0.440675i
$92$	15.0573	+	4.03459i	1.56983	+	0.420635i
$93$	−6.87056	+	25.6413i	−0.712444	+	2.65888i
$94$	−8.66025			−0.893237
$95$		0			0
$96$	−17.5623			−1.79245
$97$	2.99254	−	11.1683i	0.303847	−	1.13397i	−0.630086	−	0.776525i	$-0.716981\pi$
$97$	2.99254	−	11.1683i	0.303847	−	1.13397i	0.933933	−	0.357447i	$-0.116353\pi$
$98$	8.63950	+	2.31495i	0.872722	+	0.233845i
$99$	16.2018	+	9.35410i	1.62834	+	0.940123i
$100$		0			0
$101$	−1.14590	+	1.98475i	−0.114021	+	0.197490i	−0.917388	−	0.397994i	$-0.869706\pi$
$101$	−1.14590	+	1.98475i	−0.114021	+	0.197490i	0.803367	+	0.595484i	$0.203040\pi$
$102$	18.7707	−	18.7707i	1.85858	−	1.85858i
$103$	2.62210	−	2.62210i	0.258363	−	0.258363i	−0.566025	−	0.824388i	$-0.691520\pi$
$103$	2.62210	−	2.62210i	0.258363	−	0.258363i	0.824388	+	0.566025i	$0.191520\pi$
$104$	9.39993	+	5.42705i	0.921739	+	0.532166i
$105$		0			0
$106$	10.1246			0.983389
$107$	−7.13483	−	7.13483i	−0.689750	−	0.689750i	0.272427	−	0.962177i	$-0.412174\pi$
$107$	−7.13483	−	7.13483i	−0.689750	−	0.689750i	−0.962177	+	0.272427i	$0.912174\pi$
$108$	−1.73621	−	6.47963i	−0.167067	−	0.623502i
$109$	4.07742	+	7.06231i	0.390546	+	0.676446i	0.992522	−	0.122069i	$-0.0389528\pi$
$109$	4.07742	+	7.06231i	0.390546	+	0.676446i	−0.601975	+	0.798515i	$0.705619\pi$
$110$		0			0
$111$	4.85410	+	8.40755i	0.460731	+	0.798009i
$112$	1.67303	+	0.448288i	0.158087	+	0.0423592i
$113$	−2.35201	+	2.35201i	−0.221258	+	0.221258i	−0.809028	−	0.587770i	$-0.800006\pi$
$113$	−2.35201	+	2.35201i	−0.221258	+	0.221258i	0.587770	+	0.809028i	$0.300006\pi$
$114$	−15.2094	+	20.4894i	−1.42449	+	1.91900i
$115$		0			0
$116$	11.7812	−	6.80185i	1.09385	−	0.631536i
$117$	4.84204	−	18.0707i	0.447647	−	1.67064i
$118$	14.0809	−	3.77297i	1.29625	−	0.347330i
$119$	−6.80185	+	3.92705i	−0.623525	+	0.359992i
$120$		0			0
$121$	12.5623			1.14203
$122$	16.7005	+	16.7005i	1.51199	+	1.51199i
$123$	1.67303	−	0.448288i	0.150852	−	0.0404207i
$124$	15.2094	−	26.3435i	1.36584	−	2.36571i
$125$		0			0
$126$			14.9269i			1.32979i
$127$	8.27055	−	2.21609i	0.733893	−	0.196646i	0.127531	−	0.991835i	$-0.459295\pi$
$127$	8.27055	−	2.21609i	0.733893	−	0.196646i	0.606362	+	0.795189i	$0.292628\pi$
$128$	15.1191	+	4.05116i	1.33635	+	0.358075i
$129$	11.0056	−	19.0623i	0.968991	−	1.67834i
$130$		0			0
$131$	−7.63525	−	13.2246i	−0.667095	−	1.15544i	−0.978713	−	0.205235i	$-0.934204\pi$
$131$	−7.63525	−	13.2246i	−0.667095	−	1.15544i	0.311617	−	0.950208i	$-0.399129\pi$
$132$	−26.9582	−	26.9582i	−2.34641	−	2.34641i
$133$	5.91567	−	4.69093i	0.512954	−	0.406755i
$134$			13.4164i			1.15900i
$135$		0			0
$136$	−8.78115	+	5.06980i	−0.752978	+	0.434732i
$137$	1.00240	+	3.74101i	0.0856410	+	0.319616i	0.995435	−	0.0954440i	$-0.0304271\pi$
$137$	1.00240	+	3.74101i	0.0856410	+	0.319616i	−0.909794	+	0.415060i	$0.863760\pi$
$138$	−7.87297	+	29.3823i	−0.670191	+	2.50119i
$139$	19.5395	+	11.2812i	1.65732	+	0.956855i	0.973944	+	0.226790i	$0.0728230\pi$
$139$	19.5395	+	11.2812i	1.65732	+	0.956855i	0.683378	+	0.730065i	$0.260510\pi$
$140$		0			0
$141$		−	10.1396i		−	0.853909i
$142$	2.24144	+	8.36516i	0.188097	+	0.701989i
$143$	−6.09837	−	22.7594i	−0.509972	−	1.90324i
$144$		−	3.85410i		−	0.321175i
$145$		0			0
$146$	0.489357	+	0.282530i	0.0404995	+	0.0233824i
$147$	−2.71039	+	10.1153i	−0.223549	+	0.834296i
$148$	−2.87926	−	10.7455i	−0.236674	−	0.883279i
$149$	−3.21140	+	1.85410i	−0.263088	+	0.151894i	−0.625742	−	0.780030i	$-0.715204\pi$
$149$	−3.21140	+	1.85410i	−0.263088	+	0.151894i	0.362654	+	0.931924i	$0.381871\pi$
$150$		0			0
$151$		−	18.5472i		−	1.50935i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$		−	18.5472i		−	1.50935i	0.656101	−	0.754673i	$-0.272204\pi$
$152$	7.63710	−	6.05596i	0.619451	−	0.491203i
$153$	12.3579	+	12.3579i	0.999076	+	0.999076i
$154$	9.39993	+	16.2812i	0.757468	+	1.31197i
$155$		0			0
$156$	−19.0623	+	33.0169i	−1.52621	+	2.64347i
$157$	−9.79410	−	2.62432i	−0.781655	−	0.209444i	−0.154140	−	0.988049i	$-0.549261\pi$
$157$	−9.79410	−	2.62432i	−0.781655	−	0.209444i	−0.627514	+	0.778605i	$0.715928\pi$
$158$	−4.28682	+	1.14865i	−0.341041	+	0.0913817i
$159$			11.8541i			0.940091i
$160$		0			0
$161$	4.50000	−	7.79423i	0.354650	−	0.614271i
$162$	−12.3290	+	3.30355i	−0.968659	+	0.259551i
$163$	1.22474	+	1.22474i	0.0959294	+	0.0959294i	0.753443	−	0.657513i	$-0.228392\pi$
$163$	1.22474	+	1.22474i	0.0959294	+	0.0959294i	−0.657513	+	0.753443i	$0.728392\pi$
$164$	−1.98475			−0.154983
$165$		0			0
$166$	−21.4058	+	12.3586i	−1.66141	+	0.959215i
$167$	−3.26673	+	0.875317i	−0.252787	+	0.0677341i	−0.382987	−	0.923754i	$-0.625105\pi$
$167$	−3.26673	+	0.875317i	−0.252787	+	0.0677341i	0.130200	+	0.991488i	$0.458438\pi$
$168$	2.62432	−	9.79410i	0.202471	−	0.755631i
$169$	−9.14723	+	5.28115i	−0.703633	+	0.406243i
$170$		0			0
$171$	−13.4894	−	10.0133i	−1.03156	−	0.765732i
$172$	−17.8351	+	17.8351i	−1.35991	+	1.35991i
$173$	13.0131	+	3.48685i	0.989366	+	0.265100i	0.716984	−	0.697089i	$-0.245522\pi$
$173$	13.0131	+	3.48685i	0.989366	+	0.265100i	0.272382	+	0.962189i	$0.412189\pi$
$174$	13.2729	+	22.9894i	1.00622	+	1.74282i
$175$		0			0
$176$	−2.42705	−	4.20378i	−0.182946	−	0.316872i
$177$	4.41747	+	16.4862i	0.332038	+	1.23918i
$178$	−20.4633	−	20.4633i	−1.53379	−	1.53379i
$179$	−1.32317			−0.0988983			−0.0494492	−	0.998777i	$-0.515747\pi$
$179$	−1.32317			−0.0988983			−0.0494492	+	0.998777i	$0.515747\pi$
$180$		0			0
$181$	3.21885	+	1.85840i	0.239255	+	0.138134i	0.614834	−	0.788656i	$-0.289223\pi$
$181$	3.21885	+	1.85840i	0.239255	+	0.138134i	−0.375579	+	0.926790i	$0.622556\pi$
$182$	13.2935	−	13.2935i	0.985380	−	0.985380i
$183$	−19.5533	+	19.5533i	−1.44542	+	1.44542i
$184$	5.80948	−	10.0623i	0.428280	−	0.741803i
$185$		0			0
$186$	51.4058	+	29.6791i	3.76925	+	2.17618i
$187$	21.2612	+	5.69693i	1.55478	+	0.416601i
$188$	−3.00721	+	11.2230i	−0.219323	+	0.818525i
$189$	−3.87298			−0.281718
$190$		0			0
$191$	13.8541			1.00245			0.501224	−	0.865318i	$-0.332883\pi$
$191$	13.8541			1.00245			0.501224	+	0.865318i	$0.332883\pi$
$192$	−8.80876	+	32.8747i	−0.635718	+	2.37253i
$193$	20.9685	+	5.61850i	1.50935	+	0.404428i	0.916218	−	0.400680i	$-0.131226\pi$
$193$	20.9685	+	5.61850i	1.50935	+	0.404428i	0.593128	+	0.805108i	$0.297893\pi$
$194$	−22.3903	−	12.9271i	−1.60753	−	0.928108i
$195$		0			0
$196$	6.00000	−	10.3923i	0.428571	−	0.742307i
$197$	−12.3579	+	12.3579i	−0.880463	+	0.880463i	−0.993581	−	0.113119i	$-0.963916\pi$
$197$	−12.3579	+	12.3579i	−0.880463	+	0.880463i	0.113119	+	0.993581i	$0.463916\pi$
$198$	29.5803	−	29.5803i	2.10218	−	2.10218i
$199$	−16.5624	−	9.56231i	−1.17408	−	0.677854i	−0.219440	−	0.975626i	$-0.570423\pi$
$199$	−16.5624	−	9.56231i	−1.17408	−	0.677854i	−0.954637	+	0.297772i	$0.903756\pi$
$200$		0			0
$201$	−15.7082			−1.10797
$202$	3.62365	+	3.62365i	0.254959	+	0.254959i
$203$	−2.03279	−	7.58648i	−0.142674	−	0.532467i
$204$	−17.8075	−	30.8435i	−1.24677	−	2.15947i
$205$		0			0
$206$	−4.14590	−	7.18091i	−0.288858	−	0.500317i
$207$	−19.3441	−	5.18324i	−1.34451	−	0.360260i
$208$	−3.43237	+	3.43237i	−0.237992	+	0.237992i
$209$	−21.0189	−	2.42705i	−1.45391	−	0.167883i
$210$		0			0
$211$	14.3435	−	8.28120i	0.987444	−	0.570101i	0.0829350	−	0.996555i	$-0.473571\pi$
$211$	14.3435	−	8.28120i	0.987444	−	0.570101i	0.904509	+	0.426454i	$0.140237\pi$
$212$	3.51569	−	13.1207i	0.241459	−	0.901136i
$213$	−9.79410	+	2.62432i	−0.671081	+	0.179816i
$214$	−19.5395	+	11.2812i	−1.33569	+	0.771164i
$215$		0			0
$216$	−5.00000			−0.340207
$217$	−12.4184	−	12.4184i	−0.843018	−	0.843018i
$218$	17.6135	−	4.71951i	1.19293	−	0.319646i
$219$	−0.330792	+	0.572949i	−0.0223529	+	0.0387163i
$220$		0			0
$221$		−	22.0113i		−	1.48064i
$222$	20.9685	−	5.61850i	1.40731	−	0.377089i
$223$	−9.80018	−	2.62595i	−0.656269	−	0.175847i	−0.0847073	−	0.996406i	$-0.526996\pi$
$223$	−9.80018	−	2.62595i	−0.656269	−	0.175847i	−0.571562	+	0.820559i	$0.693662\pi$
$224$	5.80948	−	10.0623i	0.388162	−	0.672316i
$225$		0			0
$226$	3.71885	+	6.44123i	0.247374	+	0.428464i
$227$	−3.20168	−	3.20168i	−0.212503	−	0.212503i	0.592827	−	0.805330i	$-0.298012\pi$
$227$	−3.20168	−	3.20168i	−0.212503	−	0.212503i	−0.805330	+	0.592827i	$0.798012\pi$
$228$	21.2713	+	26.8250i	1.40873	+	1.77653i
$229$		−	11.0000i		−	0.726900i	−0.931614	−	0.363450i	$-0.881599\pi$
$229$		−	11.0000i		−	0.726900i	0.931614	−	0.363450i	$-0.118401\pi$
$230$		0			0
$231$	−19.0623	+	11.0056i	−1.25421	+	0.724117i
$232$	−2.62432	−	9.79410i	−0.172295	−	0.643014i
$233$	0.342461	−	1.27808i	0.0224354	−	0.0837300i	−0.953800	−	0.300441i	$-0.902866\pi$
$233$	0.342461	−	1.27808i	0.0224354	−	0.0837300i	0.976236	+	0.216711i	$0.0695329\pi$
$234$	−36.2283	−	20.9164i	−2.36832	−	1.36735i
$235$		0			0
$236$		−	19.5580i		−	1.27312i
$237$	−1.34486	−	5.01910i	−0.0873583	−	0.326025i
$238$	4.54546	+	16.9639i	0.294638	+	1.09961i
$239$		−	29.8328i		−	1.92972i	−0.262756	−	0.964862i	$-0.584632\pi$
$239$		−	29.8328i		−	1.92972i	0.262756	−	0.964862i	$-0.415368\pi$
$240$		0			0
$241$	−3.21885	−	1.85840i	−0.207344	−	0.119710i	0.392732	−	0.919653i	$-0.371530\pi$
$241$	−3.21885	−	1.85840i	−0.207344	−	0.119710i	−0.600077	+	0.799943i	$0.704863\pi$
$242$	7.27027	−	27.1330i	0.467351	−	1.74418i
$243$	−5.60407	−	20.9147i	−0.359501	−	1.34168i
$244$	27.4417	−	15.8435i	1.75677	−	1.01427i
$245$		0			0
$246$		−	3.87298i		−	0.246932i
$247$	3.09573	+	20.9308i	0.196977	+	1.33180i
$248$	−16.0321	−	16.0321i	−1.01804	−	1.01804i
$249$	−14.4697	−	25.0623i	−0.916982	−	1.58826i
$250$		0			0
$251$	−13.6353	+	23.6170i	−0.860650	+	1.49069i	0.0106532	+	0.999943i	$0.496609\pi$
$251$	−13.6353	+	23.6170i	−0.860650	+	1.49069i	−0.871303	+	0.490746i	$0.836724\pi$
$252$	19.3441	+	5.18324i	1.21856	+	0.326513i
$253$	−24.3632	+	6.52810i	−1.53170	+	0.410418i
$254$		−	19.1459i		−	1.20132i
$255$		0			0
$256$	4.50000	−	7.79423i	0.281250	−	0.487139i
$257$	1.16068	−	0.311004i	0.0724013	−	0.0193999i	−0.222437	−	0.974947i	$-0.571401\pi$
$257$	1.16068	−	0.311004i	0.0724013	−	0.0193999i	0.294838	+	0.955547i	$0.404734\pi$
$258$	−34.8028	−	34.8028i	−2.16673	−	2.16673i
$259$	−6.42280			−0.399093
$260$		0			0
$261$	−15.1353	+	8.73834i	−0.936849	+	0.540890i
$262$	−32.9824	+	8.83761i	−2.03766	+	0.545989i
$263$	−0.659940	+	2.46293i	−0.0406937	+	0.151871i	−0.983283	−	0.182083i	$-0.941716\pi$
$263$	−0.659940	+	2.46293i	−0.0406937	+	0.151871i	0.942590	+	0.333953i	$0.108383\pi$
$264$	−24.6093	+	14.2082i	−1.51460	+	0.874455i
$265$		0			0
$266$	−6.70820	−	15.4919i	−0.411306	−	0.949871i
$267$	23.9588	−	23.9588i	1.46626	−	1.46626i
$268$	17.3867	+	4.65874i	1.06206	+	0.284578i
$269$	10.0133	+	17.3435i	0.610519	+	1.05745i	0.991153	+	0.132724i	$0.0423723\pi$
$269$	10.0133	+	17.3435i	0.610519	+	1.05745i	−0.380634	+	0.924726i	$0.624294\pi$
$270$		0			0
$271$	9.78115	+	16.9415i	0.594163	+	1.02912i	0.993664	+	0.112388i	$0.0358498\pi$
$271$	9.78115	+	16.9415i	0.594163	+	1.02912i	−0.399502	+	0.916732i	$0.630817\pi$
$272$	−1.17363	−	4.38006i	−0.0711619	−	0.265580i
$273$	15.5643	+	15.5643i	0.941995	+	0.941995i
$274$	8.66025			0.523185
$275$		0			0
$276$	35.3435	+	20.4056i	2.12743	+	1.22827i
$277$	19.5959	−	19.5959i	1.17740	−	1.17740i	0.197001	−	0.980403i	$-0.436880\pi$
$277$	19.5959	−	19.5959i	1.17740	−	1.17740i	0.980403	−	0.197001i	$-0.0631203\pi$
$278$	35.6741	−	35.6741i	2.13959	−	2.13959i
$279$	−19.5395	+	33.8435i	−1.16980	+	2.02615i
$280$		0			0
$281$	−4.50000	−	2.59808i	−0.268447	−	0.154988i	0.359734	−	0.933055i	$-0.382867\pi$
$281$	−4.50000	−	2.59808i	−0.268447	−	0.154988i	−0.628182	+	0.778067i	$0.716201\pi$
$282$	−21.9003	−	5.86816i	−1.30414	−	0.349444i
$283$	−6.84558	+	25.5481i	−0.406928	+	1.51867i	0.393545	+	0.919305i	$0.371249\pi$
$283$	−6.84558	+	25.5481i	−0.406928	+	1.51867i	−0.800473	+	0.599369i	$0.795418\pi$
$284$	11.6190			0.689458
$285$		0			0
$286$	−52.6869			−3.11544
$287$	−0.296580	+	1.10685i	−0.0175066	+	0.0653354i
$288$	−24.9731	−	6.69153i	−1.47156	−	0.394302i
$289$	3.08505	+	1.78115i	0.181473	+	0.104774i
$290$		0			0
$291$	15.1353	−	26.2150i	0.887244	−	1.53675i
$292$	0.536064	−	0.536064i	0.0313707	−	0.0313707i
$293$	15.0799	−	15.0799i	0.880979	−	0.880979i	−0.112655	−	0.993634i	$-0.535936\pi$
$293$	15.0799	−	15.0799i	0.880979	−	0.880979i	0.993634	+	0.112655i	$0.0359356\pi$
$294$	20.2792	+	11.7082i	1.18271	+	0.682836i
$295$		0			0
$296$	−8.29180			−0.481951
$297$	7.67501	+	7.67501i	0.445349	+	0.445349i
$298$	2.14607	+	8.00926i	0.124319	+	0.463964i
$299$	12.6113	+	21.8435i	0.729332	+	1.26324i
$300$		0			0
$301$	7.28115	+	12.6113i	0.419679	+	0.726905i
$302$	−40.0595	−	10.7339i	−2.30517	−	0.617668i
$303$	−4.24264	+	4.24264i	−0.243733	+	0.243733i
$304$	1.73205	+	4.00000i	0.0993399	+	0.229416i
$305$		0			0
$306$	33.8435	−	19.5395i	1.93470	−	1.11700i
$307$	−1.36962	+	5.11148i	−0.0781682	+	0.291728i	−0.993933	−	0.109987i	$-0.964919\pi$
$307$	−1.36962	+	5.11148i	−0.0781682	+	0.291728i	0.915765	+	0.401715i	$0.131586\pi$
$308$	24.3632	−	6.52810i	1.38822	−	0.371973i
$309$	8.40755	−	4.85410i	0.478289	−	0.276140i
$310$		0			0
$311$	−9.00000			−0.510343			−0.255172	−	0.966896i	$-0.582132\pi$
$311$	−9.00000			−0.510343			−0.255172	+	0.966896i	$0.582132\pi$
$312$	20.0934	+	20.0934i	1.13757	+	1.13757i
$313$	−11.2230	+	3.00721i	−0.634364	+	0.169977i	−0.561649	−	0.827375i	$-0.689833\pi$
$313$	−11.2230	+	3.00721i	−0.634364	+	0.169977i	−0.0727147	+	0.997353i	$0.523166\pi$
$314$	−11.3364	+	19.6353i	−0.639751	+	1.10808i
$315$		0			0
$316$			5.95426i			0.334953i
$317$	17.2790	−	4.62990i	0.970486	−	0.260041i	0.261453	−	0.965216i	$-0.415798\pi$
$317$	17.2790	−	4.62990i	0.970486	−	0.260041i	0.709033	+	0.705175i	$0.249132\pi$
$318$	25.6034	+	6.86041i	1.43577	+	0.384713i
$319$	−11.0056	+	19.0623i	−0.616197	+	1.06728i
$320$		0			0
$321$	−13.2082	−	22.8773i	−0.737210	−	1.27689i
$322$	−14.2302	−	14.2302i	−0.793021	−	0.793021i
$323$	−18.3794	−	7.27201i	−1.02266	−	0.404625i
$324$			17.1246i			0.951367i
$325$		0			0
$326$	3.35410	−	1.93649i	0.185767	−	0.107252i
$327$	5.52570	+	20.6222i	0.305572	+	1.14041i
$328$	−0.382883	+	1.42894i	−0.0211412	+	0.0789000i
$329$	5.80948	+	3.35410i	0.320287	+	0.184918i
$330$		0			0
$331$		−	10.3923i		−	0.571213i	−0.958347	−	0.285606i	$-0.907805\pi$
$331$		−	10.3923i		−	0.571213i	0.958347	−	0.285606i	$-0.0921950\pi$
$332$	8.58287	+	32.0317i	0.471046	+	1.75797i
$333$	3.69899	+	13.8048i	0.202703	+	0.756499i
$334$			7.56231i			0.413791i
$335$		0			0
$336$	3.92705	+	2.26728i	0.214238	+	0.123690i
$337$	5.20863	−	19.4389i	0.283732	−	1.05890i	−0.666028	−	0.745926i	$-0.732007\pi$
$337$	5.20863	−	19.4389i	0.283732	−	1.05890i	0.949761	−	0.312977i	$-0.101326\pi$
$338$	6.11280	+	22.8133i	0.332492	+	1.24088i
$339$	−7.54153	+	4.35410i	−0.409599	+	0.236482i
$340$		0			0
$341$			49.2187i			2.66534i
$342$	−29.4342	+	23.3403i	−1.59162	+	1.26210i
$343$	−13.4722	−	13.4722i	−0.727430	−	0.727430i
$344$	9.39993	+	16.2812i	0.506810	+	0.877821i
$345$		0			0
$346$	15.0623	−	26.0887i	0.809755	−	1.40254i
$347$	−26.8261	−	7.18804i	−1.44010	−	0.385874i	−0.547533	−	0.836784i	$-0.684433\pi$
$347$	−26.8261	−	7.18804i	−1.44010	−	0.385874i	−0.892570	+	0.450910i	$0.851100\pi$
$348$	34.4014	−	9.21783i	1.84411	−	0.494128i
$349$		−	11.0000i		−	0.588817i	−0.955680	−	0.294408i	$-0.904877\pi$
$349$		−	11.0000i		−	0.588817i	0.955680	−	0.294408i	$-0.0951225\pi$
$350$		0			0
$351$	5.42705	−	9.39993i	0.289675	−	0.501731i
$352$	−31.4528	+	8.42774i	−1.67644	+	0.449200i
$353$	−0.867369	−	0.867369i	−0.0461654	−	0.0461654i	0.683647	−	0.729813i	$-0.260393\pi$
$353$	−0.867369	−	0.867369i	−0.0461654	−	0.0461654i	−0.729813	+	0.683647i	$0.760393\pi$
$354$	38.1648			2.02843
$355$		0			0
$356$	−33.6246	+	19.4132i	−1.78210	+	1.02890i
$357$	−19.8617	+	5.32192i	−1.05119	+	0.281666i
$358$	−0.765767	+	2.85788i	−0.0404720	+	0.151044i
$359$	13.8380	−	7.98936i	0.730340	−	0.421662i	−0.0882064	−	0.996102i	$-0.528114\pi$
$359$	13.8380	−	7.98936i	0.730340	−	0.421662i	0.818547	+	0.574440i	$0.194780\pi$
$360$		0			0
$361$	18.5000	+	4.33013i	0.973684	+	0.227901i
$362$	5.87678	−	5.87678i	0.308877	−	0.308877i
$363$	31.7679	+	8.51218i	1.66738	+	0.446774i
$364$	−12.6113	−	21.8435i	−0.661013	−	1.14491i
$365$		0			0
$366$	30.9164	+	53.5488i	1.61603	+	2.79904i
$367$	1.85856	+	6.93622i	0.0970158	+	0.362068i	0.997317	−	0.0731988i	$-0.0233208\pi$
$367$	1.85856	+	6.93622i	0.0970158	+	0.362068i	−0.900302	+	0.435267i	$0.856654\pi$
$368$	3.67423	+	3.67423i	0.191533	+	0.191533i
$369$	2.54981			0.132738
$370$		0			0
$371$	−6.79180	−	3.92125i	−0.352612	−	0.203581i
$372$	56.3122	−	56.3122i	2.91965	−	2.91965i
$373$	12.9192	−	12.9192i	0.668931	−	0.668931i	−0.288538	−	0.957469i	$-0.593169\pi$
$373$	12.9192	−	12.9192i	0.668931	−	0.668931i	0.957469	+	0.288538i	$0.0931690\pi$
$374$	24.6093	−	42.6246i	1.27252	−	2.20407i
$375$		0			0
$376$	7.50000	+	4.33013i	0.386783	+	0.223309i
$377$	21.2612	+	5.69693i	1.09501	+	0.293407i
$378$	−2.24144	+	8.36516i	−0.115287	+	0.430258i
$379$	3.96951			0.203900			0.101950	−	0.994790i	$-0.467492\pi$
$379$	3.96951			0.203900			0.101950	+	0.994790i	$0.467492\pi$
$380$		0			0
$381$	22.4164			1.14843
$382$	8.01788	−	29.9231i	0.410230	−	1.53100i
$383$	−0.0538292	−	0.0144235i	−0.00275054	−	0.000737006i	0.257444	−	0.966293i	$-0.417120\pi$
$383$	−0.0538292	−	0.0144235i	−0.00275054	−	0.000737006i	−0.260194	+	0.965556i	$0.583787\pi$
$384$	35.4886	+	20.4894i	1.81102	+	1.04559i
$385$		0			0
$386$	24.2705	−	42.0378i	1.23534	−	2.13967i
$387$	22.9128	−	22.9128i	1.16472	−	1.16472i
$388$	−24.5274	+	24.5274i	−1.24519	+	1.24519i
$389$	4.20378	+	2.42705i	0.213140	+	0.123056i	0.602770	−	0.797915i	$-0.294064\pi$
$389$	4.20378	+	2.42705i	0.213140	+	0.123056i	−0.389630	+	0.920972i	$0.627397\pi$
$390$		0			0
$391$	−23.5623			−1.19160
$392$	−6.32456	−	6.32456i	−0.319438	−	0.319438i
$393$	−10.3473	−	38.6165i	−0.521950	−	1.94794i
$394$	19.5395	+	33.8435i	0.984387	+	1.70501i
$395$		0			0
$396$	−28.0623	−	48.6053i	−1.41018	−	2.44251i
$397$	1.18485	+	0.317479i	0.0594658	+	0.0159338i	0.288429	−	0.957501i	$-0.406867\pi$
$397$	1.18485	+	0.317479i	0.0594658	+	0.0159338i	−0.228963	+	0.973435i	$0.573534\pi$
$398$	−30.2387	+	30.2387i	−1.51573	+	1.51573i
$399$	18.1383	−	7.85410i	0.908049	−	0.393197i
$400$		0			0
$401$	3.43769	−	1.98475i	0.171670	−	0.0991139i	−0.411703	−	0.911318i	$-0.635066\pi$
$401$	3.43769	−	1.98475i	0.171670	−	0.0991139i	0.583373	+	0.812204i	$0.301733\pi$
$402$	−9.09092	+	33.9278i	−0.453414	+	1.69216i
$403$	47.5416	−	12.7387i	2.36821	−	0.634561i
$404$	5.95426	−	3.43769i	0.296236	−	0.171032i
$405$		0			0
$406$	−17.5623			−0.871603
$407$	12.7279	+	12.7279i	0.630900	+	0.630900i
$408$	−25.6413	+	6.87056i	−1.26943	+	0.340144i
$409$	−11.6190	+	20.1246i	−0.574520	+	0.995098i	0.421573	+	0.906794i	$0.361478\pi$
$409$	−11.6190	+	20.1246i	−0.574520	+	0.995098i	−0.996094	+	0.0883038i	$0.971855\pi$
$410$		0			0
$411$			10.1396i			0.500150i
$412$	−10.7455	+	2.87926i	−0.529395	+	0.141851i
$413$	−10.9070	−	2.92253i	−0.536700	−	0.143808i
$414$	−22.3903	+	38.7812i	−1.10042	+	1.90599i
$415$		0			0
$416$	16.2812	+	28.1998i	0.798249	+	1.38261i
$417$	41.7680	+	41.7680i	2.04539	+	2.04539i
$418$	−17.4065	+	43.9935i	−0.851381	+	2.15179i
$419$			4.58359i			0.223923i	0.993713	+	0.111962i	$0.0357134\pi$
$419$			4.58359i			0.223923i	−0.993713	+	0.111962i	$0.964287\pi$
$420$		0			0
$421$	11.1246	−	6.42280i	0.542180	−	0.313028i	−0.203782	−	0.979016i	$-0.565323\pi$
$421$	11.1246	−	6.42280i	0.542180	−	0.313028i	0.745962	+	0.665988i	$0.231990\pi$
$422$	−9.58527	−	35.7727i	−0.466604	−	1.74139i
$423$	3.86336	−	14.4183i	0.187843	−	0.701039i
$424$	−8.76817	−	5.06231i	−0.425820	−	0.245847i
$425$		0			0
$426$			22.6728i			1.09850i
$427$	−4.73495	−	17.6711i	−0.229140	−	0.855164i
$428$	7.83458	+	29.2391i	0.378699	+	1.41332i
$429$		−	61.6869i		−	2.97827i
$430$		0			0
$431$	−18.5729	−	10.7231i	−0.894627	−	0.516513i	−0.0191742	−	0.999816i	$-0.506104\pi$
$431$	−18.5729	−	10.7231i	−0.894627	−	0.516513i	−0.875453	+	0.483303i	$0.839437\pi$
$432$	0.578737	−	2.15988i	0.0278445	−	0.103917i
$433$	6.76155	+	25.2344i	0.324939	+	1.21269i	0.914373	+	0.404873i	$0.132684\pi$
$433$	6.76155	+	25.2344i	0.324939	+	1.21269i	−0.589434	+	0.807817i	$0.700649\pi$
$434$	−34.0093	+	19.6353i	−1.63250	+	0.942522i
$435$		0			0
$436$		−	24.4645i		−	1.17164i
$437$	22.4058	−	3.31388i	1.07181	−	0.158524i
$438$	1.04606	+	1.04606i	0.0499825	+	0.0499825i
$439$	−1.11873	−	1.93769i	−0.0533940	−	0.0924811i	0.838093	−	0.545527i	$-0.183671\pi$
$439$	−1.11873	−	1.93769i	−0.0533940	−	0.0924811i	−0.891487	+	0.453046i	$0.850337\pi$
$440$		0			0
$441$	−7.70820	+	13.3510i	−0.367057	+	0.635762i
$442$	−47.5416	−	12.7387i	−2.26132	−	0.605919i
$443$	−38.8747	+	10.4164i	−1.84699	+	0.494900i	−0.999363	−	0.0356880i	$-0.988638\pi$
$443$	−38.8747	+	10.4164i	−1.84699	+	0.494900i	−0.847630	+	0.530588i	$0.821971\pi$
$444$		−	29.1246i		−	1.38219i
$445$		0			0
$446$	−11.3435	+	19.6474i	−0.537128	+	0.930334i
$447$	−9.37740	+	2.51267i	−0.443536	+	0.118845i
$448$	−15.9217	−	15.9217i	−0.752229	−	0.752229i
$449$	6.51932			0.307666			0.153833	−	0.988097i	$-0.450838\pi$
$449$	6.51932			0.307666			0.153833	+	0.988097i	$0.450838\pi$
$450$		0			0
$451$	2.78115	−	1.60570i	0.130959	−	0.0756094i
$452$	9.63870	−	2.58268i	0.453366	−	0.121479i
$453$	12.5675	−	46.9025i	0.590472	−	2.20367i
$454$	−8.76817	+	5.06231i	−0.411511	+	0.237586i
$455$		0			0
$456$	23.4164	−	10.1396i	1.09657	−	0.474830i
$457$	7.70584	−	7.70584i	0.360464	−	0.360464i	−0.503520	−	0.863984i	$-0.667962\pi$
$457$	7.70584	−	7.70584i	0.360464	−	0.360464i	0.863984	+	0.503520i	$0.167962\pi$
$458$	−23.7586	−	6.36611i	−1.11017	−	0.297469i
$459$	5.06980	+	8.78115i	0.236638	+	0.409869i
$460$		0			0
$461$	−11.7812	−	20.4056i	−0.548703	−	0.950381i	−0.998364	−	0.0571821i	$-0.981788\pi$
$461$	−11.7812	−	20.4056i	−0.548703	−	0.950381i	0.449661	−	0.893199i	$-0.351545\pi$
$462$	12.7387	+	47.5416i	0.592659	+	2.21183i
$463$	−6.81241	−	6.81241i	−0.316599	−	0.316599i	0.530860	−	0.847459i	$-0.321869\pi$
$463$	−6.81241	−	6.81241i	−0.316599	−	0.316599i	−0.847459	+	0.530860i	$0.821869\pi$
$464$	4.53457			0.210512
$465$		0			0
$466$	−2.56231	−	1.47935i	−0.118697	−	0.0685295i
$467$	−18.3029	+	18.3029i	−0.846958	+	0.846958i	−0.989752	−	0.142794i	$-0.954391\pi$
$467$	−18.3029	+	18.3029i	−0.846958	+	0.846958i	0.142794	+	0.989752i	$0.454391\pi$
$468$	−39.6861	+	39.6861i	−1.83449	+	1.83449i
$469$	5.19615	−	9.00000i	0.239936	−	0.415581i
$470$		0			0
$471$	−22.9894	−	13.2729i	−1.05929	−	0.611583i
$472$	−14.0809	−	3.77297i	−0.648127	−	0.173665i
$473$	10.5627	−	39.4205i	0.485673	−	1.81256i
$474$	−11.6190			−0.533676
$475$		0			0
$476$	23.5623			1.07998
$477$	−4.51661	+	16.8562i	−0.206801	+	0.771794i
$478$	−64.4352	−	17.2654i	−2.94720	−	0.789699i
$479$	−12.2323	−	7.06231i	−0.558907	−	0.322685i	0.193800	−	0.981041i	$-0.437919\pi$
$479$	−12.2323	−	7.06231i	−0.558907	−	0.322685i	−0.752707	+	0.658356i	$0.771252\pi$
$480$		0			0
$481$	9.00000	−	15.5885i	0.410365	−	0.710772i
$482$	−5.87678	+	5.87678i	−0.267680	+	0.267680i
$483$	16.6611	−	16.6611i	0.758105	−	0.758105i
$484$	−32.6378	−	18.8435i	−1.48354	−	0.856521i
$485$		0			0
$486$	−48.4164			−2.19621
$487$	9.98761	+	9.98761i	0.452582	+	0.452582i	0.896211	−	0.443629i	$-0.146309\pi$
$487$	9.98761	+	9.98761i	0.452582	+	0.452582i	−0.443629	+	0.896211i	$0.646309\pi$
$488$	−6.11280	−	22.8133i	−0.276713	−	1.03271i
$489$	2.26728	+	3.92705i	0.102530	+	0.177587i
$490$		0			0
$491$	16.0623	+	27.8207i	0.724882	+	1.25553i	0.959023	+	0.283329i	$0.0914389\pi$
$491$	16.0623	+	27.8207i	0.724882	+	1.25553i	−0.234141	+	0.972203i	$0.575228\pi$
$492$	−5.01910	−	1.34486i	−0.226278	−	0.0606311i
$493$	−14.5397	+	14.5397i	−0.654837	+	0.654837i
$494$	46.9996	+	5.42705i	2.11461	+	0.244175i
$495$		0			0
$496$	8.78115	−	5.06980i	0.394285	−	0.227641i
$497$	1.73621	−	6.47963i	0.0778797	−	0.290651i
$498$	−62.5056	+	16.7483i	−2.80094	+	0.750511i
$499$	8.76817	−	5.06231i	0.392517	−	0.226620i	−0.290733	−	0.956804i	$-0.593899\pi$
$499$	8.76817	−	5.06231i	0.392517	−	0.226620i	0.683250	+	0.730184i	$0.260566\pi$
$500$		0			0
$501$	−8.85410			−0.395572
$502$	43.1185	+	43.1185i	1.92447	+	1.92447i
$503$	8.66688	−	2.32228i	0.386437	−	0.103545i	−0.0603695	−	0.998176i	$-0.519228\pi$
$503$	8.66688	−	2.32228i	0.386437	−	0.103545i	0.446807	+	0.894631i	$0.352561\pi$
$504$	7.46344	−	12.9271i	0.332448	−	0.575817i
$505$		0			0
$506$			56.3996i			2.50727i
$507$	−26.7102	+	7.15699i	−1.18624	+	0.317853i
$508$	−24.8117	−	6.64826i	−1.10084	−	0.294969i
$509$	10.9574	−	18.9787i	0.485677	−	0.841217i	−0.514188	−	0.857678i	$-0.671907\pi$
$509$	10.9574	−	18.9787i	0.485677	−	0.841217i	0.999865	+	0.0164609i	$0.00523991\pi$
$510$		0			0
$511$	−0.218847	−	0.379054i	−0.00968122	−	0.0167684i
$512$	7.90569	+	7.90569i	0.349386	+	0.349386i
$513$	−6.05596	−	7.63710i	−0.267377	−	0.337186i
$514$		−	2.68692i		−	0.118515i
$515$		0			0
$516$	−57.1869	+	33.0169i	−2.51751	+	1.45349i
$517$	−4.86576	−	18.1593i	−0.213996	−	0.798644i
$518$	−3.71711	+	13.8724i	−0.163320	+	0.609520i
$519$	30.5452	+	17.6353i	1.34078	+	0.774102i
$520$		0			0
$521$		−	13.0386i		−	0.571233i	−0.958344	−	0.285617i	$-0.907802\pi$
$521$		−	13.0386i		−	0.571233i	0.958344	−	0.285617i	$-0.0921984\pi$
$522$	10.1144	+	37.7475i	0.442695	+	1.65216i
$523$	7.35471	+	27.4481i	0.321599	+	1.20022i	0.917687	+	0.397304i	$0.130054\pi$
$523$	7.35471	+	27.4481i	0.321599	+	1.20022i	−0.596088	+	0.802919i	$0.703279\pi$
$524$			45.8115i			2.00129i
$525$		0			0
$526$	4.93769	+	2.85078i	0.215294	+	0.124300i
$527$	−11.9002	+	44.4120i	−0.518379	+	1.93462i
$528$	−3.28913	−	12.2752i	−0.143141	−	0.534209i
$529$	3.46410	−	2.00000i	0.150613	−	0.0869565i
$530$		0			0
$531$			25.1261i			1.09038i
$532$	−22.4058	+	3.31388i	−0.971413	+	0.143675i
$533$	−2.27080	−	2.27080i	−0.0983593	−	0.0983593i
$534$	−37.8822	−	65.6140i	−1.63932	−	2.83939i
$535$		0			0
$536$	6.70820	−	11.6190i	0.289750	−	0.501862i
$537$	−3.34607	−	0.896575i	−0.144393	−	0.0386901i
$538$	43.2548	−	11.5901i	1.86484	−	0.499684i
$539$			19.4164i			0.836324i
$540$		0			0
$541$	−2.21885	+	3.84316i	−0.0953957	+	0.165230i	−0.909774	−	0.415105i	$-0.863745\pi$
$541$	−2.21885	+	3.84316i	−0.0953957	+	0.165230i	0.814378	+	0.580335i	$0.197078\pi$
$542$	42.2522	−	11.3214i	1.81489	−	0.486297i
$543$	6.88066	+	6.88066i	0.295277	+	0.295277i
$544$	−30.4188			−1.30420
$545$		0			0
$546$	42.6246	−	24.6093i	1.82416	−	1.05318i
$547$	24.5504	−	6.57825i	1.04970	−	0.281266i	0.307571	−	0.951525i	$-0.400484\pi$
$547$	24.5504	−	6.57825i	1.04970	−	0.281266i	0.742127	+	0.670259i	$0.233817\pi$
$548$	3.00721	−	11.2230i	0.128461	−	0.479425i
$549$	−35.2543	+	20.3541i	−1.50462	+	0.868692i
$550$		0			0
$551$	11.7812	−	15.8710i	0.501894	−	0.676127i
$552$	21.5093	−	21.5093i	0.915498	−	0.915498i
$553$	3.32056	+	0.889741i	0.141204	+	0.0378356i
$554$	−30.9839	−	53.6656i	−1.31638	−	2.28003i
$555$		0			0
$556$	−33.8435	−	58.6186i	−1.43528	−	2.48598i
$557$	−7.87297	−	29.3823i	−0.333588	−	1.24497i	−0.905392	−	0.424578i	$-0.860423\pi$
$557$	−7.87297	−	29.3823i	−0.333588	−	1.24497i	0.571803	−	0.820391i	$-0.306244\pi$
$558$	61.7894	+	61.7894i	2.61575	+	2.61575i
$559$	−40.8111			−1.72613
$560$		0			0
$561$	49.9058	+	28.8131i	2.10702	+	1.21649i
$562$	−8.21584	+	8.21584i	−0.346564	+	0.346564i
$563$	−15.1193	+	15.1193i	−0.637204	+	0.637204i	−0.949865	−	0.312661i	$-0.898780\pi$
$563$	−15.1193	+	15.1193i	−0.637204	+	0.637204i	0.312661	+	0.949865i	$0.398780\pi$
$564$	−15.2094	+	26.3435i	−0.640431	+	1.10926i
$565$		0			0
$566$	51.2188	+	29.5712i	2.15289	+	1.24297i
$567$	9.55001	+	2.55892i	0.401063	+	0.107464i
$568$	2.24144	−	8.36516i	0.0940487	−	0.350994i
$569$	32.5001			1.36247			0.681237	−	0.732063i	$-0.261442\pi$
$569$	32.5001			1.36247			0.681237	+	0.732063i	$0.261442\pi$
$570$		0			0
$571$	−19.1246			−0.800340			−0.400170	−	0.916441i	$-0.631049\pi$
$571$	−19.1246			−0.800340			−0.400170	+	0.916441i	$0.631049\pi$
$572$	−18.2951	+	68.2783i	−0.764957	+	2.85486i
$573$	35.0346	+	9.38750i	1.46359	+	0.392168i
$574$	2.21902	+	1.28115i	0.0926202	+	0.0534743i
$575$		0			0
$576$	−25.0517	+	43.3908i	−1.04382	+	1.80795i
$577$	16.4317	−	16.4317i	0.684060	−	0.684060i	−0.276853	−	0.960912i	$-0.589291\pi$
$577$	16.4317	−	16.4317i	0.684060	−	0.684060i	0.960912	+	0.276853i	$0.0892914\pi$
$578$	5.63250	−	5.63250i	0.234281	−	0.234281i
$579$	49.2187	+	28.4164i	2.04546	+	1.18095i
$580$		0			0
$581$	19.1459			0.794306
$582$	−47.8619	−	47.8619i	−1.98394	−	1.98394i
$583$	5.68851	+	21.2298i	0.235594	+	0.879249i
$584$	−0.282530	−	0.489357i	−0.0116912	−	0.0202497i
$585$		0			0
$586$	−23.8435	−	41.2981i	−0.984964	−	1.70601i
$587$	−11.3163	−	3.03219i	−0.467073	−	0.125152i	0.0176041	−	0.999845i	$-0.494396\pi$
$587$	−11.3163	−	3.03219i	−0.467073	−	0.125152i	−0.484677	+	0.874693i	$0.661063\pi$
$588$	22.2148	−	22.2148i	0.916121	−	0.916121i
$589$	5.06980	−	43.9058i	0.208898	−	1.80911i
$590$		0			0
$591$	−39.6246	+	22.8773i	−1.62994	+	0.941046i
$592$	0.959754	−	3.58185i	0.0394456	−	0.147213i
$593$	−2.46293	+	0.659940i	−0.101140	+	0.0271005i	−0.309034	−	0.951051i	$-0.600006\pi$
$593$	−2.46293	+	0.659940i	−0.101140	+	0.0271005i	0.207894	+	0.978151i	$0.433339\pi$
$594$	21.0189	−	12.1353i	0.862415	−	0.497916i
$595$		0			0
$596$	11.1246			0.455682
$597$	−35.4040	−	35.4040i	−1.44899	−	1.44899i
$598$	54.4778	−	14.5973i	2.22776	−	0.596927i
$599$	20.4056	−	35.3435i	0.833748	−	1.44409i	−0.0612970	−	0.998120i	$-0.519524\pi$
$599$	20.4056	−	35.3435i	0.833748	−	1.44409i	0.895045	−	0.445975i	$-0.147143\pi$
$600$		0			0
$601$		−	31.1769i		−	1.27173i	−0.771799	−	0.635866i	$-0.780643\pi$
$601$		−	31.1769i		−	1.27173i	0.771799	−	0.635866i	$-0.219357\pi$
$602$	31.4528	−	8.42774i	1.28192	−	0.343489i
$603$	−22.3367	−	5.98509i	−0.909619	−	0.243732i
$604$	−27.8207	+	48.1869i	−1.13201	+	1.96070i
$605$		0			0
$606$	6.70820	+	11.6190i	0.272502	+	0.471988i
$607$	25.6471	+	25.6471i	1.04098	+	1.04098i	0.999123	+	0.0418612i	$0.0133287\pi$
$607$	25.6471	+	25.6471i	1.04098	+	1.04098i	0.0418612	+	0.999123i	$0.486671\pi$
$608$	28.9257	−	4.27820i	1.17309	−	0.173504i
$609$		−	20.5623i		−	0.833227i
$610$		0			0
$611$	−16.2812	+	9.39993i	−0.658665	+	0.380280i
$612$	−13.5699	−	50.6435i	−0.548531	−	2.04714i
$613$	1.21405	−	4.53091i	0.0490352	−	0.183002i	−0.937065	−	0.349156i	$-0.886468\pi$
$613$	1.21405	−	4.53091i	0.0490352	−	0.183002i	0.986100	+	0.166154i	$0.0531350\pi$
$614$	10.2475	+	5.91641i	0.413556	+	0.238767i
$615$		0			0
$616$		−	18.7999i		−	0.757468i
$617$	11.4188	+	42.6157i	0.459705	+	1.71564i	0.673873	+	0.738847i	$0.264629\pi$
$617$	11.4188	+	42.6157i	0.459705	+	1.71564i	−0.214168	+	0.976797i	$0.568704\pi$
$618$	−5.61850	−	20.9685i	−0.226009	−	0.843477i
$619$			7.56231i			0.303955i	0.988384	+	0.151977i	$0.0485641\pi$
$619$			7.56231i			0.303955i	−0.988384	+	0.151977i	$0.951436\pi$
$620$		0			0
$621$	−10.0623	−	5.80948i	−0.403786	−	0.233126i
$622$	−5.20863	+	19.4389i	−0.208847	+	0.779428i
$623$	5.80179	+	21.6526i	0.232444	+	0.867493i
$624$	−11.0056	+	6.35410i	−0.440578	+	0.254368i
$625$		0			0
$626$			25.9808i			1.03840i
$627$	−51.5085	−	20.3799i	−2.05705	−	0.813896i
$628$	21.5093	+	21.5093i	0.858316	+	0.858316i
$629$	8.40755	+	14.5623i	0.335231	+	0.580637i
$630$		0			0
$631$	3.28115	−	5.68312i	0.130621	−	0.226242i	−0.793295	−	0.608837i	$-0.791636\pi$
$631$	3.28115	−	5.68312i	0.130621	−	0.226242i	0.923916	+	0.382595i	$0.124970\pi$
$632$	4.28682	+	1.14865i	0.170521	+	0.0456909i
$633$	41.8834	−	11.2226i	1.66472	−	0.446060i
$634$		−	40.0000i		−	1.58860i
$635$		0			0
$636$	17.7812	−	30.7979i	0.705069	−	1.22121i
$637$	18.7548	−	5.02534i	0.743093	−	0.199111i
$638$	34.8028	+	34.8028i	1.37786	+	1.37786i
$639$	−14.9269			−0.590498
$640$		0			0
$641$	18.4058	−	10.6266i	0.726984	−	0.419724i	−0.0903338	−	0.995912i	$-0.528793\pi$
$641$	18.4058	−	10.6266i	0.726984	−	0.419724i	0.817318	+	0.576187i	$0.195460\pi$
$642$	−57.0562	+	15.2882i	−2.25183	+	0.603375i
$643$	1.92396	−	7.18031i	0.0758736	−	0.283164i	−0.917556	−	0.397606i	$-0.869841\pi$
$643$	1.92396	−	7.18031i	0.0758736	−	0.283164i	0.993430	+	0.114442i	$0.0365079\pi$
$644$	−23.3827	+	13.5000i	−0.921407	+	0.531975i
$645$		0			0
$646$	−26.3435	+	35.4886i	−1.03647	+	1.39628i
$647$	−25.2518	+	25.2518i	−0.992752	+	0.992752i	−0.999974	−	0.00722199i	$-0.997701\pi$
$647$	−25.2518	+	25.2518i	−0.992752	+	0.992752i	0.00722199	+	0.999974i	$0.497701\pi$
$648$	12.3290	+	3.30355i	0.484329	+	0.129776i
$649$	15.8227	+	27.4058i	0.621096	+	1.07577i
$650$		0			0
$651$	−22.9894	−	39.8187i	−0.901024	−	1.56062i
$652$	−1.34486	−	5.01910i	−0.0526689	−	0.196563i
$653$	−22.9128	−	22.9128i	−0.896646	−	0.896646i	0.0984916	−	0.995138i	$-0.468598\pi$
$653$	−22.9128	−	22.9128i	−0.896646	−	0.896646i	−0.995138	+	0.0984916i	$0.968598\pi$
$654$	47.7393			1.86675
$655$		0			0
$656$	−0.572949	−	0.330792i	−0.0223699	−	0.0129153i
$657$	−0.688681	+	0.688681i	−0.0268680	+	0.0268680i
$658$	10.6066	−	10.6066i	0.413488	−	0.413488i
$659$	−16.2018	+	28.0623i	−0.631132	+	1.09315i	0.356189	+	0.934414i	$0.384076\pi$
$659$	−16.2018	+	28.0623i	−0.631132	+	1.09315i	−0.987321	+	0.158738i	$0.949257\pi$
$660$		0			0
$661$	19.2812	+	11.1320i	0.749950	+	0.432984i	0.825676	−	0.564145i	$-0.190794\pi$
$661$	19.2812	+	11.1320i	0.749950	+	0.432984i	−0.0757259	+	0.997129i	$0.524127\pi$
$662$	−22.4461	−	6.01441i	−0.872392	−	0.233757i
$663$	14.9148	−	55.6626i	0.579241	−	2.16176i
$664$	24.7172			0.959215
$665$		0			0
$666$	31.9574			1.23833
$667$	6.09837	−	22.7594i	0.236130	−	0.881249i
$668$	9.80018	+	2.62595i	0.379181	+	0.101601i
$669$	−23.0036	−	13.2812i	−0.889372	−	0.513479i
$670$		0			0
$671$	−25.6353	+	44.4016i	−0.989638	+	1.71410i
$672$	21.5093	−	21.5093i	0.829741	−	0.829741i
$673$	−15.0405	+	15.0405i	−0.579770	+	0.579770i	−0.934840	−	0.355070i	$-0.884457\pi$
$673$	−15.0405	+	15.0405i	−0.579770	+	0.579770i	0.355070	+	0.934840i	$0.384457\pi$
$674$	−38.9711	−	22.5000i	−1.50111	−	0.866668i
$675$		0			0
$676$	31.6869			1.21873
$677$	−1.58114	−	1.58114i	−0.0607681	−	0.0607681i	0.676070	−	0.736838i	$-0.263682\pi$
$677$	−1.58114	−	1.58114i	−0.0607681	−	0.0607681i	−0.736838	+	0.676070i	$0.763682\pi$
$678$	5.03976	+	18.8086i	0.193551	+	0.722341i
$679$	10.0133	+	17.3435i	0.384273	+	0.665581i
$680$		0			0
$681$	−5.92705	−	10.2660i	−0.227125	−	0.393392i
$682$	106.306	+	28.4847i	4.07067	+	1.09073i
$683$	−22.2542	+	22.2542i	−0.851532	+	0.851532i	−0.990322	−	0.138790i	$-0.955679\pi$
$683$	−22.2542	+	22.2542i	−0.851532	+	0.851532i	0.138790	+	0.990322i	$0.455679\pi$
$684$	20.0265	+	46.2492i	0.765732	+	1.76838i
$685$		0			0
$686$	−36.8951	+	21.3014i	−1.40866	+	0.813292i
$687$	7.45357	−	27.8171i	0.284371	−	1.06129i
$688$	−8.12107	+	2.17603i	−0.309613	+	0.0829605i
$689$	19.0341	−	10.9894i	0.725142	−	0.418661i
$690$		0			0
$691$	10.5623			0.401809			0.200905	−	0.979611i	$-0.435612\pi$
$691$	10.5623			0.401809			0.200905	+	0.979611i	$0.435612\pi$
$692$	−28.5787	−	28.5787i	−1.08640	−	1.08640i
$693$	−31.2994	+	8.38666i	−1.18897	+	0.318583i
$694$	−31.0506	+	53.7812i	−1.17866	+	2.04150i
$695$		0			0
$696$		−	26.5458i		−	1.00622i
$697$	2.89778	−	0.776457i	0.109761	−	0.0294104i
$698$	−23.7586	−	6.36611i	−0.899278	−	0.240961i
$699$	1.73205	−	3.00000i	0.0655122	−	0.113470i
$700$		0			0
$701$	5.42705	+	9.39993i	0.204977	+	0.355030i	0.950125	−	0.311868i	$-0.100955\pi$
$701$	5.42705	+	9.39993i	0.204977	+	0.355030i	−0.745148	+	0.666899i	$0.767621\pi$
$702$	−17.1618	−	17.1618i	−0.647732	−	0.647732i
$703$	−10.0430	−	12.6651i	−0.378777	−	0.477672i
$704$			63.1033i			2.37830i
$705$		0			0
$706$	−2.37539	+	1.37143i	−0.0893989	+	0.0516145i
$707$	−1.02738	−	3.83425i	−0.0386388	−	0.144202i
$708$	13.2524	−	49.4587i	0.498056	−	1.85877i
$709$	26.9547	+	15.5623i	1.01231	+	0.584455i	0.911866	−	0.410489i	$-0.134642\pi$
$709$	26.9547	+	15.5623i	1.01231	+	0.584455i	0.100439	+	0.994943i	$0.467975\pi$
$710$		0			0
$711$		−	7.64944i		−	0.286877i
$712$	7.49008	+	27.9534i	0.280703	+	1.04760i
$713$	−13.6364	−	50.8917i	−0.510686	−	1.90591i
$714$			45.9787i			1.72071i
$715$		0			0
$716$	3.43769	+	1.98475i	0.128473	+	0.0741737i
$717$	20.2146	−	75.4420i	0.754929	−	2.81743i
$718$	−9.24747	−	34.5120i	−0.345113	−	1.28798i
$719$	−1.83997	+	1.06231i	−0.0686192	+	0.0396173i	−0.533917	−	0.845537i	$-0.679281\pi$
$719$	−1.83997	+	1.06231i	−0.0686192	+	0.0396173i	0.465298	+	0.885154i	$0.345947\pi$
$720$		0			0
$721$			6.42280i			0.239197i
$722$	20.0592	−	37.4517i	0.746525	−	1.39381i
$723$	−6.88066	−	6.88066i	−0.255894	−	0.255894i
$724$	−5.57521	−	9.65654i	−0.207201	−	0.358883i
$725$		0			0
$726$	36.7705	−	63.6884i	1.36468	−	2.36370i
$727$	−20.7731	−	5.56612i	−0.770430	−	0.206436i	−0.147869	−	0.989007i	$-0.547241\pi$
$727$	−20.7731	−	5.56612i	−0.770430	−	0.206436i	−0.622561	+	0.782571i	$0.713908\pi$
$728$	−18.1593	+	4.86576i	−0.673027	+	0.180337i
$729$		−	39.5623i		−	1.46527i
$730$		0			0
$731$	19.0623	−	33.0169i	0.705045	−	1.22117i
$732$	80.1307	−	21.4710i	2.96172	−	0.793590i
$733$	13.9822	+	13.9822i	0.516444	+	0.516444i	0.916493	−	0.400050i	$-0.131007\pi$
$733$	13.9822	+	13.9822i	0.516444	+	0.516444i	−0.400050	+	0.916493i	$0.631007\pi$
$734$	16.0570			0.592674
$735$		0			0
$736$	30.1869	−	17.4284i	1.11270	−	0.642420i
$737$	−28.1322	+	7.53800i	−1.03626	+	0.277666i
$738$	1.47567	−	5.50728i	0.0543202	−	0.202726i
$739$	−11.2583	+	6.50000i	−0.414144	+	0.239106i	−0.692569	−	0.721352i	$-0.743521\pi$
$739$	−11.2583	+	6.50000i	−0.414144	+	0.239106i	0.278425	+	0.960458i	$0.410188\pi$
$740$		0			0
$741$	−6.35410	+	55.0281i	−0.233424	+	2.02151i
$742$	−12.4001	+	12.4001i	−0.455221	+	0.455221i
$743$	17.3328	+	4.64432i	0.635880	+	0.170384i	0.562337	−	0.826908i	$-0.309903\pi$
$743$	17.3328	+	4.64432i	0.635880	+	0.170384i	0.0735435	+	0.997292i	$0.476569\pi$
$744$	−29.6791	−	51.4058i	−1.08809	−	1.88463i
$745$		0			0
$746$	−20.4271	−	35.3807i	−0.747887	−	1.29538i
$747$	−11.0264	−	41.1512i	−0.403436	−	1.50564i
$748$	−46.6929	−	46.6929i	−1.70726	−	1.70726i
$749$	17.4767			0.638584
$750$		0			0
$751$	−37.6869	−	21.7586i	−1.37522	−	0.793981i	−0.383636	−	0.923484i	$-0.625328\pi$
$751$	−37.6869	−	21.7586i	−1.37522	−	0.793981i	−0.991579	+	0.129503i	$0.958662\pi$
$752$	−2.73861	+	2.73861i	−0.0998669	+	0.0998669i
$753$	−50.4840	+	50.4840i	−1.83974	+	1.83974i
$754$	24.6093	−	42.6246i	0.896219	−	1.55230i
$755$		0			0
$756$	10.0623	+	5.80948i	0.365963	+	0.211289i
$757$	−18.4034	−	4.93117i	−0.668881	−	0.179226i	−0.0916305	−	0.995793i	$-0.529208\pi$
$757$	−18.4034	−	4.93117i	−0.668881	−	0.179226i	−0.577251	+	0.816567i	$0.695875\pi$
$758$	2.29730	−	8.57364i	0.0834417	−	0.311409i
$759$	−66.0338			−2.39687
$760$		0			0
$761$	−12.0000			−0.435000			−0.217500	−	0.976060i	$-0.569790\pi$
$761$	−12.0000			−0.435000			−0.217500	+	0.976060i	$0.569790\pi$
$762$	12.9732	−	48.4167i	0.469970	−	1.75395i
$763$	−13.6433	−	3.65572i	−0.493922	−	0.132346i
$764$	−35.9940	−	20.7812i	−1.30222	−	0.751836i
$765$		0			0
$766$	−0.0623059	+	0.107917i	−0.00225120	+	0.00389920i
$767$	22.3767	−	22.3767i	0.807976	−	0.807976i
$768$	16.6611	−	16.6611i	0.601204	−	0.601204i
$769$	−32.1509	−	18.5623i	−1.15939	−	0.669374i	−0.208232	−	0.978079i	$-0.566771\pi$
$769$	−32.1509	−	18.5623i	−1.15939	−	0.669374i	−0.951158	+	0.308706i	$0.900104\pi$
$770$		0			0
$771$	3.14590			0.113297
$772$	−46.0501	−	46.0501i	−1.65738	−	1.65738i
$773$	13.3110	+	49.6771i	0.478762	+	1.78676i	0.606644	+	0.794973i	$0.292515\pi$
$773$	13.3110	+	49.6771i	0.478762	+	1.78676i	−0.127883	+	0.991789i	$0.540818\pi$
$774$	−36.2283	−	62.7492i	−1.30220	−	2.25547i
$775$		0			0
$776$	12.9271	+	22.3903i	0.464054	+	0.803765i
$777$	−16.2421	−	4.35207i	−0.582684	−	0.156130i
$778$	7.67501	−	7.67501i	0.275162	−	0.275162i
$779$	−2.64634	+	1.14590i	−0.0948149	+	0.0410561i
$780$		0			0
$781$	−16.2812	+	9.39993i	−0.582585	+	0.336356i
$782$	−13.6364	+	50.8917i	−0.487636	+	1.81988i
$783$	−9.79410	+	2.62432i	−0.350013	+	0.0937856i
$784$	3.46410	−	2.00000i	0.123718	−	0.0714286i
$785$		0			0
$786$	−89.3951			−3.18862
$787$	9.98761	+	9.98761i	0.356020	+	0.356020i	0.862344	−	0.506324i	$-0.168996\pi$
$787$	9.98761	+	9.98761i	0.356020	+	0.356020i	−0.506324	+	0.862344i	$0.668996\pi$
$788$	50.6435	−	13.5699i	1.80410	−	0.483408i
$789$	−3.33775	+	5.78115i	−0.118827	+	0.205814i
$790$		0			0
$791$		−	5.76121i		−	0.204845i
$792$	−40.4074	+	10.8271i	−1.43581	+	0.384725i
$793$	49.5235	+	13.2698i	1.75863	+	0.471224i
$794$	1.37143	−	2.37539i	0.0486703	−	0.0842994i
$795$		0			0
$796$	28.6869	+	49.6872i	1.01678	+	1.76112i
$797$	−29.4284	−	29.4284i	−1.04241	−	1.04241i	−0.999060	−	0.0433471i	$-0.986198\pi$
$797$	−29.4284	−	29.4284i	−1.04241	−	1.04241i	−0.0433471	−	0.999060i	$-0.513802\pi$
$798$	−6.46660	−	43.7219i	−0.228915	−	1.54774i
$799$		−	17.5623i		−	0.621310i
$800$		0			0
$801$	43.1976	−	24.9401i	1.52631	−	0.881216i
$802$	−2.29730	−	8.57364i	−0.0811205	−	0.302746i
$803$	−0.317479	+	1.18485i	−0.0112036	+	0.0418124i
$804$	40.8111	+	23.5623i	1.43930	+	0.830978i
$805$		0			0
$806$		−	110.056i		−	3.87657i
$807$	13.5699	+	50.6435i	0.477683	+	1.78274i
$808$	−1.32635	−	4.94999i	−0.0466607	−	0.174140i
$809$			15.4377i			0.542760i	0.962472	+	0.271380i	$0.0874801\pi$
$809$			15.4377i			0.542760i	−0.962472	+	0.271380i	$0.912520\pi$
$810$		0			0
$811$	26.7812	+	15.4621i	0.940413	+	0.542948i	0.890090	−	0.455785i	$-0.150641\pi$
$811$	26.7812	+	15.4621i	0.940413	+	0.542948i	0.0503236	+	0.998733i	$0.483975\pi$
$812$	−6.09837	+	22.7594i	−0.214011	+	0.798700i
$813$	13.2554	+	49.4697i	0.464886	+	1.73498i
$814$	34.8569	−	20.1246i	1.22173	−	0.705367i
$815$		0			0
$816$		−	11.8717i		−	0.415591i
$817$	−13.4830	+	34.0773i	−0.471712	+	1.19221i
$818$	36.7423	+	36.7423i	1.28467	+	1.28467i
$819$	16.2018	+	28.0623i	0.566136	+	0.980576i
$820$		0			0
$821$	2.56231	−	4.43804i	0.0894251	−	0.154889i	−0.817843	−	0.575441i	$-0.804830\pi$
$821$	2.56231	−	4.43804i	0.0894251	−	0.154889i	0.907268	+	0.420552i	$0.138164\pi$
$822$	21.9003	+	5.86816i	0.763860	+	0.204676i
$823$	35.8303	−	9.60071i	1.24897	−	0.334660i	0.427030	−	0.904237i	$-0.359560\pi$
$823$	35.8303	−	9.60071i	1.24897	−	0.334660i	0.821938	+	0.569578i	$0.192893\pi$
$824$			8.29180i			0.288858i
$825$		0			0
$826$	−12.6246	+	21.8665i	−0.439266	+	0.760832i
$827$	34.7195	−	9.30306i	1.20732	−	0.323499i	0.401607	−	0.915812i	$-0.368452\pi$
$827$	34.7195	−	9.30306i	1.20732	−	0.323499i	0.805708	+	0.592313i	$0.201785\pi$
$828$	42.4826	+	42.4826i	1.47637	+	1.47637i
$829$	−29.4080			−1.02138			−0.510691	−	0.859764i	$-0.670610\pi$
$829$	−29.4080			−1.02138			−0.510691	+	0.859764i	$0.670610\pi$
$830$		0			0
$831$	62.8328	−	36.2765i	2.17965	−	1.25842i
$832$	60.9531	−	16.3323i	2.11317	−	0.566222i
$833$	−4.69453	+	17.5202i	−0.162656	+	0.607040i
$834$	114.386	−	66.0410i	3.96088	−	2.28681i
$835$		0			0
$836$	50.9681	+	37.8340i	1.76277	+	1.30852i
$837$	−16.0321	+	16.0321i	−0.554151	+	0.554151i
$838$	9.89999	+	2.65269i	0.341989	+	0.0916358i
$839$	−17.8557	−	30.9271i	−0.616449	−	1.06772i	−0.990128	−	0.140163i	$-0.955237\pi$
$839$	−17.8557	−	30.9271i	−0.616449	−	1.06772i	0.373680	−	0.927558i	$-0.378096\pi$
$840$		0			0
$841$	4.21885	+	7.30726i	0.145477	+	0.251974i
$842$	−7.43422	−	27.7449i	−0.256200	−	0.956152i
$843$	−9.61927	−	9.61927i	−0.331305	−	0.331305i
$844$	−49.6872			−1.71030
$845$		0			0
$846$	−28.9058	−	16.6888i	−0.993801	−	0.573771i
$847$	−15.3856	+	15.3856i	−0.528656	+	0.528656i
$848$	3.20168	−	3.20168i	0.109946	−	0.109946i
$849$	−34.6226	+	59.9681i	−1.18824	+	2.05810i
$850$		0			0
$851$	−16.6869	−	9.63420i	−0.572020	−	0.330256i
$852$	29.3823	+	7.87297i	1.00662	+	0.269723i
$853$	−0.644501	+	2.40531i	−0.0220673	+	0.0823562i	−0.976081	−	0.217406i	$-0.930241\pi$
$853$	−0.644501	+	2.40531i	−0.0220673	+	0.0823562i	0.954014	+	0.299762i	$0.0969072\pi$
$854$	−40.9076			−1.39983
$855$		0			0
$856$	22.5623			0.771164
$857$	−9.89622	+	36.9332i	−0.338049	+	1.26161i	0.562478	+	0.826812i	$0.309848\pi$
$857$	−9.89622	+	36.9332i	−0.338049	+	1.26161i	−0.900526	+	0.434802i	$0.856818\pi$
$858$	−133.236	−	35.7005i	−4.54860	−	1.21879i
$859$	17.6996	+	10.2188i	0.603901	+	0.348663i	0.770575	−	0.637350i	$-0.219969\pi$
$859$	17.6996	+	10.2188i	0.603901	+	0.348663i	−0.166674	+	0.986012i	$0.553303\pi$
$860$		0			0
$861$	−1.50000	+	2.59808i	−0.0511199	+	0.0885422i
$862$	−33.9094	+	33.9094i	−1.15496	+	1.15496i
$863$	−14.1908	+	14.1908i	−0.483062	+	0.483062i	−0.906108	−	0.423046i	$-0.860961\pi$
$863$	−14.1908	+	14.1908i	−0.483062	+	0.483062i	0.423046	+	0.906108i	$0.360961\pi$
$864$	−12.9904	−	7.50000i	−0.441942	−	0.255155i
$865$		0			0
$866$	58.4164			1.98507
$867$	6.59465	+	6.59465i	0.223966	+	0.223966i
$868$	13.6364	+	50.8917i	0.462849	+	1.72738i
$869$	−4.81710	−	8.34346i	−0.163409	−	0.283032i
$870$		0			0
$871$	14.5623	+	25.2227i	0.493425	+	0.854637i
$872$	−17.6135	−	4.71951i	−0.596467	−	0.159823i
$873$	31.5103	−	31.5103i	1.06646	−	1.06646i
$874$	5.80948	−	50.3115i	0.196508	−	1.70181i
$875$		0			0
$876$	1.71885	−	0.992377i	0.0580745	−	0.0335293i
$877$	9.86738	−	36.8255i	0.333198	−	1.24351i	−0.572612	−	0.819826i	$-0.694070\pi$
$877$	9.86738	−	36.8255i	0.333198	−	1.24351i	0.905810	−	0.423684i	$-0.139263\pi$
$878$	−4.83263	+	1.29490i	−0.163093	+	0.0437007i
$879$	48.3526	−	27.9164i	1.63089	−	0.941597i
$880$		0			0
$881$	24.4377			0.823327			0.411663	−	0.911336i	$-0.364948\pi$
$881$	24.4377			0.823327			0.411663	+	0.911336i	$0.364948\pi$
$882$	24.3755	+	24.3755i	0.820765	+	0.820765i
$883$	−16.7303	+	4.48288i	−0.563020	+	0.150861i	−0.529094	−	0.848563i	$-0.677468\pi$
$883$	−16.7303	+	4.48288i	−0.563020	+	0.150861i	−0.0339267	+	0.999424i	$0.510801\pi$
$884$	−33.0169	+	57.1869i	−1.11048	+	1.92340i
$885$		0			0
$886$			89.9929i			3.02337i
$887$	−42.3060	+	11.3359i	−1.42050	+	0.380621i	−0.885660	−	0.464335i	$-0.846293\pi$
$887$	−42.3060	+	11.3359i	−1.42050	+	0.380621i	−0.534836	+	0.844956i	$0.679627\pi$
$888$	−20.9685	−	5.61850i	−0.703657	−	0.188544i
$889$	−7.41517	+	12.8435i	−0.248697	+	0.430756i
$890$		0			0
$891$	−13.8541	−	23.9960i	−0.464130	−	0.803897i
$892$	21.5227	+	21.5227i	0.720633	+	0.720633i
$893$	2.47002	+	16.7003i	0.0826561	+	0.558853i
$894$			21.7082i			0.726031i
$895$		0			0
$896$	−23.4787	+	13.5554i	−0.784369	+	0.452856i
$897$	17.0908	+	63.7837i	0.570645	+	2.12968i
$898$	3.77297	−	14.0809i	0.125906	−	0.469887i
$899$	−39.8187	−	22.9894i	−1.32803	−	0.766738i
$900$		0			0
$901$			20.5319i			0.684017i
$902$	−1.85856	−	6.93622i	−0.0618831	−	0.230951i
$903$	9.86738	+	36.8255i	0.328366	+	1.22548i
$904$		−	7.43769i		−	0.247374i
$905$		0			0
$906$	−94.0304	−	54.2885i	−3.12395	−	1.80361i
$907$	−4.17887	+	15.5957i	−0.138757	+	0.517848i	0.861197	+	0.508271i	$0.169715\pi$
$907$	−4.17887	+	15.5957i	−0.138757	+	0.517848i	−0.999954	+	0.00957703i	$0.996951\pi$
$908$	3.51569	+	13.1207i	0.116672	+	0.435427i
$909$	−7.64944	+	4.41641i	−0.253716	+	0.146483i
$910$		0			0
$911$			28.5306i			0.945260i	0.881261	+	0.472630i	$0.156695\pi$
$911$			28.5306i			0.945260i	−0.881261	+	0.472630i	$0.843305\pi$
$912$	1.66967	+	11.2889i	0.0552882	+	0.373814i
$913$	−37.9410	−	37.9410i	−1.25566	−	1.25566i
$914$	−12.1840	−	21.1033i	−0.403011	−	0.698036i
$915$		0			0
$916$	−16.5000	+	28.5788i	−0.545175	+	0.944271i
$917$	25.5481	+	6.84558i	0.843671	+	0.226061i
$918$	21.9003	−	5.86816i	0.722817	−	0.193678i
$919$			26.4377i			0.872099i	0.899923	+	0.436050i	$0.143623\pi$
$919$			26.4377i			0.872099i	−0.899923	+	0.436050i	$0.856377\pi$
$920$		0			0
$921$	−6.92705	+	11.9980i	−0.228254	+	0.395348i
$922$	−50.8917	+	13.6364i	−1.67603	+	0.449090i
$923$	13.2935	+	13.2935i	0.437561	+	0.437561i
$924$	66.0338			2.17235
$925$		0			0
$926$	−18.6565	+	10.7714i	−0.613092	+	0.353969i
$927$	13.8048	−	3.69899i	0.453410	−	0.121491i
$928$	7.87297	−	29.3823i	0.258443	−	0.964522i
$929$	−15.9675	+	9.21885i	−0.523877	+	0.302461i	−0.738519	−	0.674232i	$-0.764475\pi$
$929$	−15.9675	+	9.21885i	−0.523877	+	0.302461i	0.214642	+	0.976693i	$0.431141\pi$
$930$		0			0
$931$	2.00000	−	17.3205i	0.0655474	−	0.567657i
$932$	−2.80687	+	2.80687i	−0.0919419	+	0.0919419i
$933$	−22.7594	−	6.09837i	−0.745111	−	0.199652i
$934$	28.9395	+	50.1246i	0.946928	+	1.64013i
$935$		0			0
$936$	20.9164	+	36.2283i	0.683674	+	1.18416i
$937$	11.1418	+	41.5817i	0.363986	+	1.35842i	0.868790	+	0.495181i	$0.164898\pi$
$937$	11.1418	+	41.5817i	0.363986	+	1.35842i	−0.504803	+	0.863234i	$0.668435\pi$
$938$	−16.4317	−	16.4317i	−0.536513	−	0.536513i
$939$	−30.4188			−0.992680
$940$		0			0
$941$	−33.6246	−	19.4132i	−1.09613	−	0.632852i	−0.160929	−	0.986966i	$-0.551449\pi$
$941$	−33.6246	−	19.4132i	−1.09613	−	0.632852i	−0.935202	+	0.354114i	$0.884782\pi$
$942$	−41.9726	+	41.9726i	−1.36754	+	1.36754i
$943$	−2.43082	+	2.43082i	−0.0791583	+	0.0791583i
$944$	3.25966	−	5.64590i	0.106093	−	0.183758i
$945$		0			0
$946$	−79.0304	−	45.6282i	−2.56950	−	1.48350i
$947$	49.9113	+	13.3737i	1.62190	+	0.434586i	0.951559	−	0.307468i	$-0.0994816\pi$
$947$	49.9113	+	13.3737i	1.62190	+	0.434586i	0.670340	+	0.742054i	$0.266148\pi$
$948$	−4.03459	+	15.0573i	−0.131037	+	0.489038i
$949$	1.22665			0.0398186
$950$		0			0
$951$	46.8328			1.51866
$952$	4.54546	−	16.9639i	0.147319	−	0.549803i
$953$	25.0270	+	6.70596i	0.810703	+	0.217227i	0.640278	−	0.768143i	$-0.278819\pi$
$953$	25.0270	+	6.70596i	0.810703	+	0.217227i	0.170425	+	0.985371i	$0.445486\pi$
$954$	33.7934	+	19.5106i	1.09410	+	0.631680i
$955$		0			0
$956$	−44.7492	+	77.5079i	−1.44729	+	2.50679i
$957$	−40.7479	+	40.7479i	−1.31719	+	1.31719i
$958$	−22.3330	+	22.3330i	−0.721546	+	0.721546i
$959$	−5.80948	−	3.35410i	−0.187598	−	0.108310i
$960$		0			0
$961$	−71.8115			−2.31650
$962$	−28.4605	−	28.4605i	−0.917603	−	0.917603i
$963$	−10.0651	−	37.5634i	−0.324343	−	1.21047i
$964$	5.57521	+	9.65654i	0.179565	+	0.311016i
$965$		0			0
$966$	−26.3435	−	45.6282i	−0.847587	−	1.46806i
$967$	3.34607	+	0.896575i	0.107602	+	0.0288319i	0.312218	−	0.950010i	$-0.398928\pi$
$967$	3.34607	+	0.896575i	0.107602	+	0.0288319i	−0.204616	+	0.978842i	$0.565595\pi$
$968$	−19.8627	+	19.8627i	−0.638413	+	0.638413i
$969$	−41.5508	−	30.8435i	−1.33480	−	0.990835i
$970$		0			0
$971$	−12.3541	+	7.13264i	−0.396462	+	0.228897i	−0.684956	−	0.728584i	$-0.740179\pi$
$971$	−12.3541	+	7.13264i	−0.396462	+	0.228897i	0.288494	+	0.957482i	$0.406845\pi$
$972$	−16.8122	+	62.7441i	−0.539252	+	2.01252i
$973$	−37.7475	+	10.1144i	−1.21013	+	0.324253i
$974$	27.3522	−	15.7918i	0.876421	−	0.506002i
$975$		0			0
$976$	10.5623			0.338091
$977$	−24.4485	−	24.4485i	−0.782178	−	0.782178i	0.198020	−	0.980198i	$-0.436549\pi$
$977$	−24.4485	−	24.4485i	−0.782178	−	0.782178i	−0.980198	+	0.198020i	$0.936549\pi$
$978$	9.79410	−	2.62432i	0.313181	−	0.0839166i
$979$	31.4112	−	54.4058i	1.00391	−	1.73882i
$980$		0			0
$981$			31.4296i			1.00347i
$982$	69.3852	−	18.5917i	2.21417	−	0.593285i
$983$	−15.0653	−	4.03674i	−0.480508	−	0.128752i	0.0104309	−	0.999946i	$-0.496680\pi$
$983$	−15.0653	−	4.03674i	−0.480508	−	0.128752i	−0.490939	+	0.871194i	$0.663346\pi$
$984$	−1.93649	+	3.35410i	−0.0617331	+	0.106925i
$985$		0			0
$986$	22.9894	+	39.8187i	0.732130	+	1.26809i
$987$	12.4184	+	12.4184i	0.395283	+	0.395283i
$988$	23.3533	−	59.0235i	0.742968	−	1.87779i
$989$			43.6869i			1.38916i
$990$		0			0
$991$	18.8435	−	10.8793i	0.598582	−	0.345592i	−0.169901	−	0.985461i	$-0.554345\pi$
$991$	18.8435	−	10.8793i	0.598582	−	0.345592i	0.768484	+	0.639869i	$0.221012\pi$
$992$	−17.6045	−	65.7008i	−0.558943	−	2.08600i
$993$	7.04180	−	26.2803i	0.223465	−	0.833981i
$994$	−12.9904	−	7.50000i	−0.412030	−	0.237886i
$995$		0			0
$996$			86.8184i			2.75095i
$997$	3.64216	+	13.5927i	0.115348	+	0.430486i	0.999313	−	0.0370681i	$-0.0118018\pi$
$997$	3.64216	+	13.5927i	0.115348	+	0.430486i	−0.883964	+	0.467554i	$0.845135\pi$
$998$	−5.85949	−	21.8679i	−0.185479	−	0.692216i
$999$			8.29180i			0.262341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.p.g.468.4	yes	16
5.2	odd	4	inner	475.2.p.g.107.4	yes	16
5.3	odd	4	inner	475.2.p.g.107.1	✓	16
5.4	even	2	inner	475.2.p.g.468.1	yes	16
19.8	odd	6	inner	475.2.p.g.293.4	yes	16
95.8	even	12	inner	475.2.p.g.407.1	yes	16
95.27	even	12	inner	475.2.p.g.407.4	yes	16
95.84	odd	6	inner	475.2.p.g.293.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.p.g.107.1	✓	16	5.3	odd	4	inner
475.2.p.g.107.4	yes	16	5.2	odd	4	inner
475.2.p.g.293.1	yes	16	95.84	odd	6	inner
475.2.p.g.293.4	yes	16	19.8	odd	6	inner
475.2.p.g.407.1	yes	16	95.8	even	12	inner
475.2.p.g.407.4	yes	16	95.27	even	12	inner
475.2.p.g.468.1	yes	16	5.4	even	2	inner
475.2.p.g.468.4	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.578737 - 2.15988i) q^{2} +(2.52883 + 0.677597i) q^{3} +(-2.59808 - 1.50000i) q^{4} +(2.92705 - 5.06980i) q^{6} +(-1.22474 + 1.22474i) q^{7} +(-1.58114 + 1.58114i) q^{8} +(3.33775 + 1.92705i) q^{9} +O(q^{10})\)	\(q+(0.578737 - 2.15988i) q^{2} +(2.52883 + 0.677597i) q^{3} +(-2.59808 - 1.50000i) q^{4} +(2.92705 - 5.06980i) q^{6} +(-1.22474 + 1.22474i) q^{7} +(-1.58114 + 1.58114i) q^{8} +(3.33775 + 1.92705i) q^{9} +4.85410 q^{11} +(-5.55369 - 5.55369i) q^{12} +(-1.25633 - 4.68870i) q^{13} +(1.93649 + 3.35410i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.38006 + 1.17363i) q^{17} +(6.09387 - 6.09387i) q^{18} +(-4.33013 - 0.500000i) q^{19} +(-3.92705 + 2.26728i) q^{21} +(2.80925 - 10.4843i) q^{22} +(-5.01910 + 1.34486i) q^{23} +(-5.06980 + 2.92705i) q^{24} -10.8541 q^{26} +(1.58114 + 1.58114i) q^{27} +(5.01910 - 1.34486i) q^{28} +(-2.26728 + 3.92705i) q^{29} +10.1396i q^{31} +(-6.47963 + 1.73621i) q^{32} +(12.2752 + 3.28913i) q^{33} +(5.06980 - 8.78115i) q^{34} +(-5.78115 - 10.0133i) q^{36} +(2.62210 + 2.62210i) q^{37} +(-3.58594 + 9.06317i) q^{38} -12.7082i q^{39} +(0.572949 - 0.330792i) q^{41} +(2.62432 + 9.79410i) q^{42} +(2.17603 - 8.12107i) q^{43} +(-12.6113 - 7.28115i) q^{44} +11.6190i q^{46} +(-1.00240 - 3.74101i) q^{47} +(-0.677597 - 2.52883i) q^{48} +4.00000i q^{49} +(10.2812 + 5.93583i) q^{51} +(-3.76900 + 14.0661i) q^{52} +(1.17190 + 4.37358i) q^{53} +(4.33013 - 2.50000i) q^{54} -3.87298i q^{56} +(-10.6113 - 4.19849i) q^{57} +(7.16978 + 7.16978i) q^{58} +(3.25966 + 5.64590i) q^{59} +(-5.28115 + 9.14723i) q^{61} +(21.9003 + 5.86816i) q^{62} +(-6.44804 + 1.72775i) q^{63} +13.0000i q^{64} +(14.2082 - 24.6093i) q^{66} +(-5.79555 + 1.55291i) q^{67} +(-9.61927 - 9.61927i) q^{68} -13.6037 q^{69} +(-3.35410 + 1.93649i) q^{71} +(-8.32438 + 2.23051i) q^{72} +(-0.0654043 + 0.244092i) q^{73} +(7.18091 - 4.14590i) q^{74} +(10.5000 + 7.79423i) q^{76} +(-5.94504 + 5.94504i) q^{77} +(-27.4481 - 7.35471i) q^{78} +(-0.992377 - 1.71885i) q^{79} +(-2.85410 - 4.94345i) q^{81} +(-0.382883 - 1.42894i) q^{82} +(-7.81628 - 7.81628i) q^{83} +13.6037 q^{84} +(-16.2812 - 9.39993i) q^{86} +(-8.39453 + 8.39453i) q^{87} +(-7.67501 + 7.67501i) q^{88} +(6.47106 - 11.2082i) q^{89} +(7.28115 + 4.20378i) q^{91} +(15.0573 + 4.03459i) q^{92} +(-6.87056 + 25.6413i) q^{93} -8.66025 q^{94} -17.5623 q^{96} +(2.99254 - 11.1683i) q^{97} +(8.63950 + 2.31495i) q^{98} +(16.2018 + 9.35410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 20 q^{6}+O(q^{10}) \) 16 * q + 20 * q^6	\( 16 q + 20 q^{6} + 24 q^{11} - 8 q^{16} - 36 q^{21} - 120 q^{26} - 12 q^{36} + 36 q^{41} + 84 q^{51} - 4 q^{61} + 120 q^{66} + 168 q^{76} + 8 q^{81} - 180 q^{86} + 36 q^{91} - 120 q^{96}+O(q^{100}) \) 16 * q + 20 * q^6 + 24 * q^11 - 8 * q^16 - 36 * q^21 - 120 * q^26 - 12 * q^36 + 36 * q^41 + 84 * q^51 - 4 * q^61 + 120 * q^66 + 168 * q^76 + 8 * q^81 - 180 * q^86 + 36 * q^91 - 120 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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