LMFDB - Embedded newform 375.2.i.d.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(49,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("375.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (of order $10$, degree $4$, not 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:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	375.49
Dual form			375.2.i.d.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18666 + 1.63330i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.641469 - 1.97424i) q^{4} +(0.623865 - 1.92006i) q^{6} +1.01887i q^{7} +(0.145612 + 0.0473123i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.18666 + 1.63330i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.641469 - 1.97424i) q^{4} +(0.623865 - 1.92006i) q^{6} +1.01887i q^{7} +(0.145612 + 0.0473123i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-3.85061 - 2.79763i) q^{11} +(1.22015 + 1.67939i) q^{12} +(-0.0610339 - 0.0840060i) q^{13} +(-1.66412 - 1.20905i) q^{14} +(3.10871 - 2.25861i) q^{16} +(-5.55204 - 1.80397i) q^{17} +2.01887i q^{18} +(0.223853 - 0.688949i) q^{19} +(-0.314848 - 0.969003i) q^{21} +(9.13874 - 2.96936i) q^{22} +(5.33210 - 7.33901i) q^{23} -0.153106 q^{24} +0.209634 q^{26} +(-0.587785 + 0.809017i) q^{27} +(2.01149 - 0.653574i) q^{28} +(1.23251 + 3.79326i) q^{29} +(0.329605 - 1.01442i) q^{31} +8.06387i q^{32} +(4.52666 + 1.47080i) q^{33} +(9.53482 - 6.92745i) q^{34} +(-1.67939 - 1.22015i) q^{36} +(-2.36655 - 3.25727i) q^{37} +(0.859623 + 1.18317i) q^{38} +(0.0840060 + 0.0610339i) q^{39} +(-5.83282 + 4.23780i) q^{41} +(1.95629 + 0.635638i) q^{42} -8.62791i q^{43} +(-3.05314 + 9.39661i) q^{44} +(5.65940 + 17.4179i) q^{46} +(7.79673 - 2.53331i) q^{47} +(-2.25861 + 3.10871i) q^{48} +5.96190 q^{49} +5.83776 q^{51} +(-0.126697 + 0.174383i) q^{52} +(-4.15345 + 1.34954i) q^{53} +(-0.623865 - 1.92006i) q^{54} +(-0.0482051 + 0.148360i) q^{56} +0.724404i q^{57} +(-7.65810 - 2.48827i) q^{58} +(-3.97458 + 2.88770i) q^{59} +(-5.63428 - 4.09354i) q^{61} +(1.26572 + 1.74212i) q^{62} +(0.598877 + 0.824283i) q^{63} +(-6.95331 - 5.05187i) q^{64} +(-7.77388 + 5.64805i) q^{66} +(-9.43446 - 3.06544i) q^{67} +12.1183i q^{68} +(-2.80325 + 8.62753i) q^{69} +(-3.33323 - 10.2586i) q^{71} +(0.145612 - 0.0473123i) q^{72} +(-5.07326 + 6.98275i) q^{73} +8.12840 q^{74} -1.50375 q^{76} +(2.85042 - 3.92327i) q^{77} +(-0.199374 + 0.0647804i) q^{78} +(-0.767263 - 2.36139i) q^{79} +(0.309017 - 0.951057i) q^{81} -14.5556i q^{82} +(-4.03614 - 1.31142i) q^{83} +(-1.71108 + 1.24317i) q^{84} +(14.0920 + 10.2384i) q^{86} +(-2.34436 - 3.22674i) q^{87} +(-0.428333 - 0.589550i) q^{88} +(-14.8659 - 10.8007i) q^{89} +(0.0855912 - 0.0621857i) q^{91} +(-17.9093 - 5.81910i) q^{92} +1.06662i q^{93} +(-5.11443 + 15.7406i) q^{94} +(-2.49187 - 7.66920i) q^{96} +(-6.37090 + 2.07003i) q^{97} +(-7.07477 + 9.73758i) q^{98} -4.75961 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{4} + 6 q^{9}+O(q^{10}) $ 24 * q + 20 * q^4 + 6 * q^9	$ 24 q + 20 q^{4} + 6 q^{9} - 8 q^{11} - 12 q^{14} + 32 q^{16} - 14 q^{19} - 6 q^{21} - 12 q^{24} - 112 q^{26} + 2 q^{29} + 26 q^{31} + 50 q^{34} - 4 q^{39} + 16 q^{41} - 66 q^{44} - 44 q^{46} + 56 q^{49} + 52 q^{51} + 90 q^{56} + 44 q^{59} - 16 q^{61} - 98 q^{64} - 6 q^{66} - 12 q^{69} - 42 q^{71} + 88 q^{74} - 104 q^{76} - 20 q^{79} - 6 q^{81} + 12 q^{84} + 112 q^{86} - 114 q^{89} - 14 q^{91} + 46 q^{94} - 46 q^{96} - 12 q^{99}+O(q^{100}) $ 24 * q + 20 * q^4 + 6 * q^9 - 8 * q^11 - 12 * q^14 + 32 * q^16 - 14 * q^19 - 6 * q^21 - 12 * q^24 - 112 * q^26 + 2 * q^29 + 26 * q^31 + 50 * q^34 - 4 * q^39 + 16 * q^41 - 66 * q^44 - 44 * q^46 + 56 * q^49 + 52 * q^51 + 90 * q^56 + 44 * q^59 - 16 * q^61 - 98 * q^64 - 6 * q^66 - 12 * q^69 - 42 * q^71 + 88 * q^74 - 104 * q^76 - 20 * q^79 - 6 * q^81 + 12 * q^84 + 112 * q^86 - 114 * q^89 - 14 * q^91 + 46 * q^94 - 46 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	−1.18666	+	1.63330i	−0.839097	+	1.15492i	0.147064	+	0.989127i	$0.453018\pi$
$2$	−1.18666	+	1.63330i	−0.839097	+	1.15492i	−0.986161	+	0.165791i	$0.946982\pi$
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	−0.641469	−	1.97424i	−0.320735	−	0.987119i
$5$		0			0
$5$		0			0
$6$	0.623865	−	1.92006i	0.254692	−	0.783861i
$7$			1.01887i			0.385097i	0.981287	+	0.192548i	$0.0616752\pi$
$7$			1.01887i			0.385097i	−0.981287	+	0.192548i	$0.938325\pi$
$8$	0.145612	+	0.0473123i	0.0514817	+	0.0167274i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$		0			0
$11$	−3.85061	−	2.79763i	−1.16100	−	0.843517i	−0.171097	−	0.985254i	$-0.554731\pi$
$11$	−3.85061	−	2.79763i	−1.16100	−	0.843517i	−0.989904	+	0.141737i	$0.954731\pi$
$12$	1.22015	+	1.67939i	0.352226	+	0.484797i
$13$	−0.0610339	−	0.0840060i	−0.0169278	−	0.0232991i	0.800469	−	0.599374i	$-0.204584\pi$
$13$	−0.0610339	−	0.0840060i	−0.0169278	−	0.0232991i	−0.817397	+	0.576075i	$0.804584\pi$
$14$	−1.66412	−	1.20905i	−0.444755	−	0.323134i
$15$		0			0
$16$	3.10871	−	2.25861i	0.777177	−	0.564652i
$17$	−5.55204	−	1.80397i	−1.34657	−	0.437527i	−0.455032	−	0.890475i	$-0.650372\pi$
$17$	−5.55204	−	1.80397i	−1.34657	−	0.437527i	−0.891537	+	0.452949i	$0.850372\pi$
$18$			2.01887i			0.475852i
$19$	0.223853	−	0.688949i	0.0513554	−	0.158056i	−0.922090	−	0.386976i	$-0.873520\pi$
$19$	0.223853	−	0.688949i	0.0513554	−	0.158056i	0.973445	+	0.228920i	$0.0735196\pi$
$20$		0			0
$21$	−0.314848	−	0.969003i	−0.0687055	−	0.211454i
$22$	9.13874	−	2.96936i	1.94839	−	0.633069i
$23$	5.33210	−	7.33901i	1.11182	−	1.53029i	0.293114	−	0.956077i	$-0.405308\pi$
$23$	5.33210	−	7.33901i	1.11182	−	1.53029i	0.818707	−	0.574212i	$-0.194692\pi$
$24$	−0.153106			−0.0312526
$25$		0			0
$26$	0.209634			0.0411126
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	2.01149	−	0.653574i	0.380136	−	0.123514i
$29$	1.23251	+	3.79326i	0.228871	+	0.704391i	0.997876	+	0.0651484i	$0.0207521\pi$
$29$	1.23251	+	3.79326i	0.228871	+	0.704391i	−0.769005	+	0.639243i	$0.779248\pi$
$30$		0			0
$31$	0.329605	−	1.01442i	0.0591988	−	0.182195i	−0.917084	−	0.398694i	$-0.869464\pi$
$31$	0.329605	−	1.01442i	0.0591988	−	0.182195i	0.976283	+	0.216498i	$0.0694636\pi$
$32$			8.06387i			1.42550i
$33$	4.52666	+	1.47080i	0.787990	+	0.256034i
$34$	9.53482	−	6.92745i	1.63521	−	1.18805i
$35$		0			0
$36$	−1.67939	−	1.22015i	−0.279898	−	0.203358i
$37$	−2.36655	−	3.25727i	−0.389058	−	0.535493i	0.568898	−	0.822408i	$-0.307370\pi$
$37$	−2.36655	−	3.25727i	−0.389058	−	0.535493i	−0.957956	+	0.286916i	$0.907370\pi$
$38$	0.859623	+	1.18317i	0.139449	+	0.191935i
$39$	0.0840060	+	0.0610339i	0.0134517	+	0.00977325i
$40$		0			0
$41$	−5.83282	+	4.23780i	−0.910934	+	0.661832i	−0.941251	−	0.337708i	$-0.890348\pi$
$41$	−5.83282	+	4.23780i	−0.910934	+	0.661832i	0.0303167	+	0.999540i	$0.490348\pi$
$42$	1.95629	+	0.635638i	0.301862	+	0.0980810i
$43$		−	8.62791i		−	1.31574i	−0.753130	−	0.657872i	$-0.771457\pi$
$43$		−	8.62791i		−	1.31574i	0.753130	−	0.657872i	$-0.228543\pi$
$44$	−3.05314	+	9.39661i	−0.460279	+	1.41659i
$45$		0			0
$46$	5.65940	+	17.4179i	0.834434	+	2.56812i
$47$	7.79673	−	2.53331i	1.13727	−	0.369522i	0.320936	−	0.947101i	$-0.396003\pi$
$47$	7.79673	−	2.53331i	1.13727	−	0.369522i	0.816335	+	0.577579i	$0.196003\pi$
$48$	−2.25861	+	3.10871i	−0.326002	+	0.448703i
$49$	5.96190			0.851700
$50$		0			0
$51$	5.83776			0.817451
$52$	−0.126697	+	0.174383i	−0.0175696	+	0.0241825i
$53$	−4.15345	+	1.34954i	−0.570520	+	0.185373i	−0.580049	−	0.814581i	$-0.696967\pi$
$53$	−4.15345	+	1.34954i	−0.570520	+	0.185373i	0.00952922	+	0.999955i	$0.496967\pi$
$54$	−0.623865	−	1.92006i	−0.0848973	−	0.261287i
$55$		0			0
$56$	−0.0482051	+	0.148360i	−0.00644168	+	0.0198254i
$57$			0.724404i			0.0959497i
$58$	−7.65810	−	2.48827i	−1.00556	−	0.326726i
$59$	−3.97458	+	2.88770i	−0.517446	+	0.375947i	−0.815641	−	0.578558i	$-0.803616\pi$
$59$	−3.97458	+	2.88770i	−0.517446	+	0.375947i	0.298195	+	0.954505i	$0.403616\pi$
$60$		0			0
$61$	−5.63428	−	4.09354i	−0.721396	−	0.524125i	0.165434	−	0.986221i	$-0.447097\pi$
$61$	−5.63428	−	4.09354i	−0.721396	−	0.524125i	−0.886830	+	0.462096i	$0.847097\pi$
$62$	1.26572	+	1.74212i	0.160747	+	0.221249i
$63$	0.598877	+	0.824283i	0.0754514	+	0.103850i
$64$	−6.95331	−	5.05187i	−0.869163	−	0.631484i
$65$		0			0
$66$	−7.77388	+	5.64805i	−0.956898	+	0.695227i
$67$	−9.43446	−	3.06544i	−1.15260	−	0.374503i	−0.330480	−	0.943813i	$-0.607210\pi$
$67$	−9.43446	−	3.06544i	−1.15260	−	0.374503i	−0.822123	+	0.569310i	$0.807210\pi$
$68$			12.1183i			1.46955i
$69$	−2.80325	+	8.62753i	−0.337472	+	1.03863i
$70$		0			0
$71$	−3.33323	−	10.2586i	−0.395582	−	1.21748i	−0.928507	−	0.371314i	$-0.878907\pi$
$71$	−3.33323	−	10.2586i	−0.395582	−	1.21748i	0.532925	−	0.846162i	$-0.321093\pi$
$72$	0.145612	−	0.0473123i	0.0171606	−	0.00557581i
$73$	−5.07326	+	6.98275i	−0.593781	+	0.817269i	−0.995121	−	0.0986599i	$-0.968544\pi$
$73$	−5.07326	+	6.98275i	−0.593781	+	0.817269i	0.401341	+	0.915929i	$0.368544\pi$
$74$	8.12840			0.944907
$75$		0			0
$76$	−1.50375			−0.172491
$77$	2.85042	−	3.92327i	0.324836	−	0.447098i
$78$	−0.199374	+	0.0647804i	−0.0225746	+	0.00733493i
$79$	−0.767263	−	2.36139i	−0.0863238	−	0.265677i	0.898572	−	0.438826i	$-0.144606\pi$
$79$	−0.767263	−	2.36139i	−0.0863238	−	0.265677i	−0.984896	+	0.173149i	$0.944606\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		−	14.5556i		−	1.60740i
$83$	−4.03614	−	1.31142i	−0.443024	−	0.143947i	0.0790064	−	0.996874i	$-0.474825\pi$
$83$	−4.03614	−	1.31142i	−0.443024	−	0.143947i	−0.522030	+	0.852927i	$0.674825\pi$
$84$	−1.71108	+	1.24317i	−0.186694	+	0.135641i
$85$		0			0
$86$	14.0920	+	10.2384i	1.51958	+	1.10404i
$87$	−2.34436	−	3.22674i	−0.251342	−	0.345943i
$88$	−0.428333	−	0.589550i	−0.0456605	−	0.0628463i
$89$	−14.8659	−	10.8007i	−1.57578	−	1.14487i	−0.921344	−	0.388749i	$-0.872907\pi$
$89$	−14.8659	−	10.8007i	−1.57578	−	1.14487i	−0.654434	−	0.756120i	$-0.727093\pi$
$90$		0			0
$91$	0.0855912	−	0.0621857i	0.00897240	−	0.00651883i
$92$	−17.9093	−	5.81910i	−1.86718	−	0.606683i
$93$			1.06662i			0.110604i
$94$	−5.11443	+	15.7406i	−0.527513	+	1.62352i
$95$		0			0
$96$	−2.49187	−	7.66920i	−0.254326	−	0.782734i
$97$	−6.37090	+	2.07003i	−0.646867	+	0.210180i	−0.614032	−	0.789281i	$-0.710454\pi$
$97$	−6.37090	+	2.07003i	−0.646867	+	0.210180i	−0.0328349	+	0.999461i	$0.510454\pi$
$98$	−7.07477	+	9.73758i	−0.714659	+	0.983644i
$99$	−4.75961			−0.478359
$100$		0			0
$101$	5.66147			0.563337			0.281669	−	0.959512i	$-0.409112\pi$
$101$	5.66147			0.563337			0.281669	+	0.959512i	$0.409112\pi$
$102$	−6.92745	+	9.53482i	−0.685920	+	0.944088i
$103$	0.565393	−	0.183707i	0.0557098	−	0.0181012i	−0.281030	−	0.959699i	$-0.590676\pi$
$103$	0.565393	−	0.183707i	0.0557098	−	0.0181012i	0.336739	+	0.941598i	$0.390676\pi$
$104$	−0.00491278	−	0.0151200i	−0.000481737	−	0.00148263i
$105$		0			0
$106$	2.72454	−	8.38527i	0.264631	−	0.814450i
$107$			1.38651i			0.134039i	0.997752	+	0.0670193i	$0.0213489\pi$
$107$			1.38651i			0.134039i	−0.997752	+	0.0670193i	$0.978651\pi$
$108$	1.97424	+	0.641469i	0.189971	+	0.0617254i
$109$	−7.16528	+	5.20588i	−0.686309	+	0.498633i	−0.875445	−	0.483318i	$-0.839431\pi$
$109$	−7.16528	+	5.20588i	−0.686309	+	0.498633i	0.189136	+	0.981951i	$0.439431\pi$
$110$		0			0
$111$	3.25727	+	2.36655i	0.309167	+	0.224623i
$112$	2.30123	+	3.16737i	0.217446	+	0.299288i
$113$	3.87373	+	5.33173i	0.364410	+	0.501567i	0.951371	−	0.308048i	$-0.0996757\pi$
$113$	3.87373	+	5.33173i	0.364410	+	0.501567i	−0.586961	+	0.809615i	$0.699676\pi$
$114$	−1.18317	−	0.859623i	−0.110814	−	0.0805111i
$115$		0			0
$116$	6.69819	−	4.86652i	0.621911	−	0.451845i
$117$	−0.0987550	−	0.0320874i	−0.00912990	−	0.00296649i
$118$		−	9.91841i		−	0.913064i
$119$	1.83801	−	5.65681i	0.168490	−	0.518559i
$120$		0			0
$121$	3.60125	+	11.0835i	0.327387	+	1.00759i
$122$	13.3720	−	4.34482i	1.21064	−	0.393361i
$123$	4.23780	−	5.83282i	0.382109	−	0.525928i
$124$	−2.21414			−0.198836
$125$		0			0
$126$	−2.05697			−0.183249
$127$	−4.28580	+	5.89890i	−0.380303	+	0.523443i	−0.955665	−	0.294457i	$-0.904861\pi$
$127$	−4.28580	+	5.89890i	−0.380303	+	0.523443i	0.575362	+	0.817899i	$0.304861\pi$
$128$	1.16406	−	0.378226i	0.102889	−	0.0334308i
$129$	2.66617	+	8.20563i	0.234743	+	0.722465i
$130$		0			0
$131$	−2.95230	+	9.08626i	−0.257944	+	0.793870i	0.735291	+	0.677751i	$0.237045\pi$
$131$	−2.95230	+	9.08626i	−0.257944	+	0.793870i	−0.993235	+	0.116119i	$0.962955\pi$
$132$		−	9.88018i		−	0.859959i
$133$	0.701950	+	0.228077i	0.0608668	+	0.0197768i
$134$	16.2023	−	11.7717i	1.39967	−	1.01692i
$135$		0			0
$136$	−0.723096	−	0.525360i	−0.0620050	−	0.0450493i
$137$	3.64418	+	5.01578i	0.311343	+	0.428527i	0.935799	−	0.352533i	$-0.114680\pi$
$137$	3.64418	+	5.01578i	0.311343	+	0.428527i	−0.624457	+	0.781060i	$0.714680\pi$
$138$	−10.7648	−	14.8165i	−0.916363	−	1.26127i
$139$	−0.733399	−	0.532846i	−0.0622061	−	0.0451954i	0.556248	−	0.831017i	$-0.312241\pi$
$139$	−0.733399	−	0.532846i	−0.0622061	−	0.0451954i	−0.618454	+	0.785821i	$0.712241\pi$
$140$		0			0
$141$	−6.63230	+	4.81865i	−0.558540	+	0.405803i
$142$	20.7109	+	6.72937i	1.73802	+	0.564716i
$143$			0.494225i			0.0413291i
$144$	1.18742	−	3.65450i	0.0989517	−	0.304542i
$145$		0			0
$146$	−5.38468	−	16.5723i	−0.445639	−	1.37154i
$147$	−5.67011	+	1.84233i	−0.467663	+	0.151953i
$148$	−4.91257	+	6.76157i	−0.403811	+	0.555798i
$149$	4.89808			0.401267			0.200633	−	0.979666i	$-0.435700\pi$
$149$	4.89808			0.401267			0.200633	+	0.979666i	$0.435700\pi$
$150$		0			0
$151$	−10.2626			−0.835161			−0.417581	−	0.908640i	$-0.637122\pi$
$151$	−10.2626			−0.835161			−0.417581	+	0.908640i	$0.637122\pi$
$152$	0.0651916	−	0.0897285i	0.00528773	−	0.00727794i
$153$	−5.55204	+	1.80397i	−0.448856	+	0.145842i
$154$	3.02539	+	9.31119i	0.243793	+	0.750317i
$155$		0			0
$156$	0.0666083	−	0.204999i	0.00533293	−	0.0164131i
$157$		−	8.89537i		−	0.709928i	−0.934880	−	0.354964i	$-0.884493\pi$
$157$		−	8.89537i		−	0.709928i	0.934880	−	0.354964i	$-0.115507\pi$
$158$	4.76734	+	1.54900i	0.379269	+	0.123232i
$159$	3.53313	−	2.56697i	0.280196	−	0.203574i
$160$		0			0
$161$	7.47750	+	5.43272i	0.589310	+	0.428159i
$162$	1.18666	+	1.63330i	0.0932330	+	0.128324i
$163$	6.92356	+	9.52946i	0.542295	+	0.746405i	0.988942	−	0.148305i	$-0.0473819\pi$
$163$	6.92356	+	9.52946i	0.542295	+	0.746405i	−0.446647	+	0.894710i	$0.647382\pi$
$164$	12.1080	+	8.79697i	0.945476	+	0.686928i
$165$		0			0
$166$	6.93148	−	5.03602i	0.537987	−	0.390871i
$167$	16.5258	+	5.36954i	1.27880	+	0.415508i	0.868158	−	0.496288i	$-0.165304\pi$
$167$	16.5258	+	5.36954i	1.27880	+	0.415508i	0.410644	+	0.911796i	$0.365304\pi$
$168$		−	0.155995i		−	0.0120353i
$169$	4.01389	−	12.3535i	0.308761	−	0.950268i
$170$		0			0
$171$	−0.223853	−	0.688949i	−0.0171185	−	0.0526853i
$172$	−17.0336	+	5.53454i	−1.29880	+	0.422004i
$173$	7.61744	−	10.4845i	0.579144	−	0.797123i	−0.414458	−	0.910069i	$-0.636029\pi$
$173$	7.61744	−	10.4845i	0.579144	−	0.797123i	0.993601	+	0.112946i	$0.0360287\pi$
$174$	8.05221			0.610436
$175$		0			0
$176$	−18.2892			−1.37860
$177$	2.88770	−	3.97458i	0.217053	−	0.298748i
$178$	35.2815	−	11.4636i	2.64446	−	0.859237i
$179$	−0.339600	−	1.04518i	−0.0253829	−	0.0781206i	0.937563	−	0.347817i	$-0.113077\pi$
$179$	−0.339600	−	1.04518i	−0.0253829	−	0.0781206i	−0.962946	+	0.269696i	$0.913077\pi$
$180$		0			0
$181$	−4.62898	+	14.2465i	−0.344069	+	1.05894i	0.618011	+	0.786170i	$0.287939\pi$
$181$	−4.62898	+	14.2465i	−0.344069	+	1.05894i	−0.962080	+	0.272767i	$0.912061\pi$
$182$			0.213590i			0.0158323i
$183$	6.62349	+	2.15210i	0.489623	+	0.159088i
$184$	1.12365	−	0.816376i	0.0828363	−	0.0601841i
$185$		0			0
$186$	−1.74212	−	1.26572i	−0.127738	−	0.0928073i
$187$	16.3319	+	22.4789i	1.19431	+	1.64382i
$188$	−10.0027	−	13.7676i	−0.729524	−	1.00410i
$189$	−0.824283	−	0.598877i	−0.0599578	−	0.0435619i
$190$		0			0
$191$	10.3072	−	7.48861i	0.745802	−	0.541857i	−0.148721	−	0.988879i	$-0.547516\pi$
$191$	10.3072	−	7.48861i	0.745802	−	0.541857i	0.894523	+	0.447022i	$0.147516\pi$
$192$	8.17410	+	2.65593i	0.589915	+	0.191675i
$193$			4.38386i			0.315557i	0.987475	+	0.157779i	$0.0504332\pi$
$193$			4.38386i			0.315557i	−0.987475	+	0.157779i	$0.949567\pi$
$194$	4.17913	−	12.8620i	0.300044	−	0.923440i
$195$		0			0
$196$	−3.82438	−	11.7702i	−0.273170	−	0.840730i
$197$	−3.06397	+	0.995545i	−0.218299	+	0.0709296i	−0.416125	−	0.909308i	$-0.636612\pi$
$197$	−3.06397	+	0.995545i	−0.218299	+	0.0709296i	0.197826	+	0.980237i	$0.436612\pi$
$198$	5.64805	−	7.77388i	0.401390	−	0.552465i
$199$	2.70518			0.191765			0.0958825	−	0.995393i	$-0.469433\pi$
$199$	2.70518			0.191765			0.0958825	+	0.995393i	$0.469433\pi$
$200$		0			0
$201$	9.91998			0.699701
$202$	−6.71825	+	9.24688i	−0.472694	+	0.650608i
$203$	−3.86484	+	1.25576i	−0.271259	+	0.0881373i
$204$	−3.74475	−	11.5251i	−0.262185	−	0.806921i
$205$		0			0
$206$	−0.370881	+	1.14145i	−0.0258405	+	0.0795289i
$207$		−	9.07152i		−	0.630514i
$208$	−0.379473	−	0.123298i	−0.0263117	−	0.00854920i
$209$	−2.78940	+	2.02661i	−0.192947	+	0.140184i
$210$		0			0
$211$	−21.3932	−	15.5431i	−1.47277	−	1.07003i	−0.979799	−	0.199983i	$-0.935911\pi$
$211$	−21.3932	−	15.5431i	−1.47277	−	1.07003i	−0.492970	−	0.870046i	$-0.664089\pi$
$212$	5.32862	+	7.33421i	0.365971	+	0.503716i
$213$	6.34019	+	8.72652i	0.434423	+	0.597931i
$214$	−2.26458	−	1.64531i	−0.154804	−	0.112471i
$215$		0			0
$216$	−0.123865	+	0.0899934i	−0.00842796	+	0.00612327i
$217$	1.03356	+	0.335825i	0.0701628	+	0.0227973i
$218$		−	17.8807i		−	1.21103i
$219$	2.66717	−	8.20871i	0.180231	−	0.554694i
$220$		0			0
$221$	0.187319	+	0.576508i	0.0126004	+	0.0387802i
$222$	−7.73057	+	2.51181i	−0.518842	+	0.168582i
$223$	4.72136	−	6.49839i	0.316165	−	0.435164i	−0.621126	−	0.783711i	$-0.713325\pi$
$223$	4.72136	−	6.49839i	0.316165	−	0.435164i	0.937292	+	0.348546i	$0.113325\pi$
$224$	−8.21604			−0.548957
$225$		0			0
$226$	−13.3051			−0.885044
$227$	9.67356	−	13.3145i	0.642056	−	0.883715i	−0.356667	−	0.934232i	$-0.616087\pi$
$227$	9.67356	−	13.3145i	0.642056	−	0.883715i	0.998723	+	0.0505168i	$0.0160868\pi$
$228$	1.43015	−	0.464683i	0.0947138	−	0.0307744i
$229$	−0.126476	−	0.389253i	−0.00835776	−	0.0257226i	0.946791	−	0.321850i	$-0.104305\pi$
$229$	−0.126476	−	0.389253i	−0.00835776	−	0.0257226i	−0.955148	+	0.296127i	$0.904305\pi$
$230$		0			0
$231$	−1.49856	+	4.61208i	−0.0985977	+	0.303453i
$232$			0.610658i			0.0400917i
$233$	17.5604	+	5.70571i	1.15042	+	0.373794i	0.821301	−	0.570495i	$-0.193249\pi$
$233$	17.5604	+	5.70571i	1.15042	+	0.373794i	0.329118	+	0.944289i	$0.393249\pi$
$234$	0.169597	−	0.123220i	0.0110869	−	0.00805512i
$235$		0			0
$236$	8.25058	+	5.99440i	0.537067	+	0.390202i
$237$	1.45942	+	2.00872i	0.0947995	+	0.130480i
$238$	7.05818	+	9.71475i	0.457514	+	0.629714i
$239$	−3.73509	−	2.71370i	−0.241603	−	0.175535i	0.460394	−	0.887715i	$-0.347708\pi$
$239$	−3.73509	−	2.71370i	−0.241603	−	0.175535i	−0.701997	+	0.712180i	$0.747708\pi$
$240$		0			0
$241$	23.6251	−	17.1646i	1.52183	−	1.10567i	0.561253	−	0.827644i	$-0.310319\pi$
$241$	23.6251	−	17.1646i	1.52183	−	1.10567i	0.960573	−	0.278028i	$-0.0896807\pi$
$242$	−22.3762	−	7.27047i	−1.43840	−	0.467363i
$243$			1.00000i			0.0641500i
$244$	−4.46742	+	13.7493i	−0.285997	+	0.880208i
$245$		0			0
$246$	4.49792	+	13.8432i	0.286777	+	0.882609i
$247$	−0.0715385	+	0.0232443i	−0.00455189	+	0.00147900i
$248$	0.0959892	−	0.132118i	0.00609532	−	0.00838949i
$249$	4.24385			0.268943
$250$		0			0
$251$	0.389664			0.0245954			0.0122977	−	0.999924i	$-0.496085\pi$
$251$	0.389664			0.0245954			0.0122977	+	0.999924i	$0.496085\pi$
$252$	1.24317	−	1.71108i	0.0783124	−	0.107788i
$253$	−41.0637	+	13.3424i	−2.58165	+	0.838829i
$254$	−4.54888	−	14.0000i	−0.285422	−	0.878438i
$255$		0			0
$256$	4.54826	−	13.9981i	0.284266	−	0.874882i
$257$			8.03324i			0.501100i	0.968104	+	0.250550i	$0.0806114\pi$
$257$			8.03324i			0.501100i	−0.968104	+	0.250550i	$0.919389\pi$
$258$	−16.5661	−	5.38265i	−1.03136	−	0.335109i
$259$	3.31874	−	2.41121i	0.206216	−	0.149825i
$260$		0			0
$261$	3.22674	+	2.34436i	0.199730	+	0.145113i
$262$	−11.3372	−	15.6043i	−0.700415	−	0.964038i
$263$	−14.2321	−	19.5888i	−0.877590	−	1.20790i	−0.977083	−	0.212860i	$-0.931722\pi$
$263$	−14.2321	−	19.5888i	−0.877590	−	1.20790i	0.0994928	−	0.995038i	$-0.468278\pi$
$264$	0.589550	+	0.428333i	0.0362843	+	0.0263621i
$265$		0			0
$266$	−1.20550	+	0.875844i	−0.0739137	+	0.0537015i
$267$	17.4759	+	5.67825i	1.06950	+	0.347503i
$268$			20.5923i			1.25787i
$269$	−8.15998	+	25.1138i	−0.497523	+	1.53122i	0.315465	+	0.948937i	$0.397839\pi$
$269$	−8.15998	+	25.1138i	−0.497523	+	1.53122i	−0.812988	+	0.582281i	$0.802161\pi$
$270$		0			0
$271$	−3.21648	−	9.89932i	−0.195387	−	0.601341i	−0.999972	−	0.00750242i	$-0.997612\pi$
$271$	−3.21648	−	9.89932i	−0.195387	−	0.601341i	0.804584	−	0.593838i	$-0.202388\pi$
$272$	−21.3341	+	6.93188i	−1.29357	+	0.420307i
$273$	−0.0621857	+	0.0855912i	−0.00376365	+	0.00518022i
$274$	−12.5167			−0.756160
$275$		0			0
$276$	18.8310			1.13349
$277$	−14.4129	+	19.8376i	−0.865987	+	1.19193i	0.114122	+	0.993467i	$0.463595\pi$
$277$	−14.4129	+	19.8376i	−0.865987	+	1.19193i	−0.980109	+	0.198462i	$0.936405\pi$
$278$	1.74059	−	0.565553i	0.104394	−	0.0339196i
$279$	−0.329605	−	1.01442i	−0.0197329	−	0.0607318i
$280$		0			0
$281$	−4.45690	+	13.7169i	−0.265876	+	0.818283i	0.725614	+	0.688102i	$0.241556\pi$
$281$	−4.45690	+	13.7169i	−0.265876	+	0.818283i	−0.991490	+	0.130181i	$0.958444\pi$
$282$		−	16.5506i		−	0.985576i
$283$	−2.04406	−	0.664155i	−0.121507	−	0.0394799i	0.247633	−	0.968854i	$-0.420347\pi$
$283$	−2.04406	−	0.664155i	−0.121507	−	0.0394799i	−0.369139	+	0.929374i	$0.620347\pi$
$284$	−18.1148	+	13.1612i	−1.07492	+	0.780974i
$285$		0			0
$286$	−0.807217	−	0.586478i	−0.0477317	−	0.0346791i
$287$	−4.31776	−	5.94289i	−0.254870	−	0.350798i
$288$	4.73982	+	6.52381i	0.279297	+	0.384419i
$289$	13.8176	+	10.0391i	0.812800	+	0.590534i
$290$		0			0
$291$	5.41941	−	3.93743i	0.317692	−	0.230816i
$292$	17.0400	+	5.53662i	0.997188	+	0.324006i
$293$			9.02970i			0.527521i	0.964588	+	0.263760i	$0.0849628\pi$
$293$			9.02970i			0.527521i	−0.964588	+	0.263760i	$0.915037\pi$
$294$	3.71942	−	11.4472i	0.216921	−	0.667615i
$295$		0			0
$296$	−0.190489	−	0.586266i	−0.0110720	−	0.0340760i
$297$	4.52666	−	1.47080i	0.262663	−	0.0853445i
$298$	−5.81237	+	8.00004i	−0.336702	+	0.463430i
$299$	−0.941960			−0.0544750
$300$		0			0
$301$	8.79072			0.506689
$302$	12.1783	−	16.7620i	0.700781	−	0.964543i
$303$	−5.38438	+	1.74949i	−0.309324	+	0.100506i
$304$	−0.860173	−	2.64734i	−0.0493343	−	0.151835i
$305$		0			0
$306$	3.64198	−	11.2089i	0.208198	−	0.640768i
$307$			5.03454i			0.287336i	0.989626	+	0.143668i	$0.0458898\pi$
$307$			5.03454i			0.287336i	−0.989626	+	0.143668i	$0.954110\pi$
$308$	−9.57393	−	3.11076i	−0.545525	−	0.177252i
$309$	−0.480952	+	0.349432i	−0.0273604	+	0.0198785i
$310$		0			0
$311$	3.95737	+	2.87520i	0.224402	+	0.163038i	0.694306	−	0.719680i	$-0.255711\pi$
$311$	3.95737	+	2.87520i	0.224402	+	0.163038i	−0.469904	+	0.882718i	$0.655711\pi$
$312$	0.00934465	+	0.0128618i	0.000529037	+	0.000728157i
$313$	−1.86494	−	2.56686i	−0.105412	−	0.145088i	0.753052	−	0.657961i	$-0.228581\pi$
$313$	−1.86494	−	2.56686i	−0.105412	−	0.145088i	−0.858464	+	0.512874i	$0.828581\pi$
$314$	14.5288	+	10.5558i	0.819908	+	0.595698i
$315$		0			0
$316$	−4.16978	+	3.02952i	−0.234568	+	0.170424i
$317$	−19.0166	−	6.17888i	−1.06808	−	0.347041i	−0.278341	−	0.960482i	$-0.589785\pi$
$317$	−19.0166	−	6.17888i	−1.06808	−	0.347041i	−0.789740	+	0.613442i	$0.789785\pi$
$318$			8.81680i			0.494422i
$319$	5.86625	−	18.0545i	0.328447	−	1.01086i
$320$		0			0
$321$	−0.428454	−	1.31865i	−0.0239140	−	0.0735996i
$322$	−17.7465	+	5.76620i	−0.988976	+	0.321338i
$323$	−2.48569	+	3.42125i	−0.138307	+	0.190364i
$324$	−2.07584			−0.115324
$325$		0			0
$326$	−23.7804			−1.31707
$327$	5.20588	−	7.16528i	0.287886	−	0.396241i
$328$	−1.04983	+	0.341111i	−0.0579672	+	0.0188347i
$329$	2.58112	+	7.94386i	0.142302	+	0.437959i
$330$		0			0
$331$	1.85943	−	5.72274i	0.102204	−	0.314550i	−0.886860	−	0.462037i	$-0.847119\pi$
$331$	1.85943	−	5.72274i	0.102204	−	0.314550i	0.989064	+	0.147487i	$0.0471186\pi$
$332$			8.80954i			0.483486i
$333$	−3.82916	−	1.24417i	−0.209836	−	0.0681800i
$334$	−28.3806	+	20.6197i	−1.55292	+	1.12826i
$335$		0			0
$336$	−3.16737	−	2.30123i	−0.172794	−	0.125542i
$337$	−13.4095	−	18.4566i	−0.730463	−	1.00540i	−0.999111	−	0.0421575i	$-0.986577\pi$
$337$	−13.4095	−	18.4566i	−0.730463	−	1.00540i	0.268648	−	0.963238i	$-0.413423\pi$
$338$	15.4138	+	21.2153i	0.838401	+	1.15396i
$339$	−5.33173	−	3.87373i	−0.289580	−	0.210392i
$340$		0			0
$341$	−4.10715	+	2.98402i	−0.222415	+	0.161594i
$342$	1.39090	+	0.451931i	0.0752112	+	0.0244376i
$343$			13.2065i			0.713084i
$344$	0.408206	−	1.25633i	0.0220090	−	0.0677368i
$345$		0			0
$346$	8.08502	+	24.8831i	0.434654	+	1.33773i
$347$	−9.31149	+	3.02549i	−0.499867	+	0.162417i	−0.548089	−	0.836420i	$-0.684644\pi$
$347$	−9.31149	+	3.02549i	−0.499867	+	0.162417i	0.0482222	+	0.998837i	$0.484644\pi$
$348$	−4.86652	+	6.69819i	−0.260873	+	0.359061i
$349$	1.28648			0.0688639			0.0344320	−	0.999407i	$-0.489038\pi$
$349$	1.28648			0.0688639			0.0344320	+	0.999407i	$0.489038\pi$
$350$		0			0
$351$	0.103837			0.00554242
$352$	22.5597	−	31.0508i	1.20244	−	1.65501i
$353$	1.10724	−	0.359765i	0.0589326	−	0.0191484i	−0.279402	−	0.960174i	$-0.590136\pi$
$353$	1.10724	−	0.359765i	0.0589326	−	0.0191484i	0.338335	+	0.941026i	$0.390136\pi$
$354$	3.06496	+	9.43297i	0.162901	+	0.501357i
$355$		0			0
$356$	−11.7871	+	36.2770i	−0.624716	+	1.92268i
$357$			5.94793i			0.314798i
$358$	2.11009	+	0.685609i	0.111522	+	0.0362356i
$359$	15.4121	−	11.1975i	0.813418	−	0.590983i	−0.101402	−	0.994846i	$-0.532333\pi$
$359$	15.4121	−	11.1975i	0.813418	−	0.590983i	0.914820	+	0.403863i	$0.132333\pi$
$360$		0			0
$361$	14.9468	+	10.8595i	0.786673	+	0.571551i
$362$	−17.7758	−	24.4663i	−0.934277	−	1.28592i
$363$	−6.84999	−	9.42821i	−0.359531	−	0.494853i
$364$	−0.177673	−	0.129087i	−0.00931262	−	0.00676602i
$365$		0			0
$366$	−11.3749	+	8.26433i	−0.594575	+	0.431984i
$367$	15.9487	+	5.18204i	0.832514	+	0.270500i	0.694104	−	0.719875i	$-0.255801\pi$
$367$	15.9487	+	5.18204i	0.832514	+	0.270500i	0.138410	+	0.990375i	$0.455801\pi$
$368$		−	34.8580i		−	1.81710i
$369$	−2.22794	+	6.85690i	−0.115982	+	0.356956i
$370$		0			0
$371$	−1.37500	−	4.23183i	−0.0713866	−	0.219705i
$372$	2.10577	−	0.684207i	0.109179	−	0.0354745i
$373$	10.0229	−	13.7954i	0.518967	−	0.714297i	−0.466432	−	0.884557i	$-0.654461\pi$
$373$	10.0229	−	13.7954i	0.518967	−	0.714297i	0.985399	+	0.170260i	$0.0544607\pi$
$374$	−56.0953			−2.90062
$375$		0			0
$376$	1.25516			0.0647298
$377$	0.243432	−	0.335056i	0.0125374	−	0.0172562i
$378$	1.95629	−	0.635638i	0.100621	−	0.0326937i
$379$	−0.514857	−	1.58457i	−0.0264464	−	0.0813938i	0.936962	−	0.349431i	$-0.113625\pi$
$379$	−0.514857	−	1.58457i	−0.0264464	−	0.0813938i	−0.963409	+	0.268037i	$0.913625\pi$
$380$		0			0
$381$	2.25318	−	6.93457i	0.115434	−	0.355269i
$382$			25.7212i			1.31601i
$383$	−2.90416	−	0.943618i	−0.148396	−	0.0482166i	0.233877	−	0.972266i	$-0.424859\pi$
$383$	−2.90416	−	0.943618i	−0.148396	−	0.0482166i	−0.382273	+	0.924049i	$0.624859\pi$
$384$	−0.990210	+	0.719429i	−0.0505314	+	0.0367132i
$385$		0			0
$386$	−7.16016	−	5.20216i	−0.364443	−	0.264783i
$387$	−5.07136	−	6.98013i	−0.257792	−	0.354820i
$388$	8.17347	+	11.2498i	0.414945	+	0.571123i
$389$	22.8730	+	16.6182i	1.15971	+	0.842575i	0.989741	−	0.142875i	$-0.0456347\pi$
$389$	22.8730	+	16.6182i	1.15971	+	0.842575i	0.169965	+	0.985450i	$0.445635\pi$
$390$		0			0
$391$	−42.8434	+	31.1276i	−2.16669	+	1.57419i
$392$	0.868127	+	0.282071i	0.0438470	+	0.0142468i
$393$		−	9.55386i		−	0.481928i
$394$	2.00988	−	6.18576i	0.101256	−	0.311634i
$395$		0			0
$396$	3.05314	+	9.39661i	0.153426	+	0.472197i
$397$	19.4760	−	6.32814i	0.977472	−	0.317600i	0.223644	−	0.974671i	$-0.428205\pi$
$397$	19.4760	−	6.32814i	0.977472	−	0.317600i	0.753829	+	0.657071i	$0.228205\pi$
$398$	−3.21013	+	4.41837i	−0.160909	+	0.221473i
$399$	−0.738074			−0.0369499
$400$		0			0
$401$	25.5952			1.27816			0.639081	−	0.769139i	$-0.279315\pi$
$401$	25.5952			1.27816			0.639081	+	0.769139i	$0.279315\pi$
$402$	−11.7717	+	16.2023i	−0.587117	+	0.808097i
$403$	−0.105335	+	0.0342253i	−0.00524709	+	0.00170488i
$404$	−3.63166	−	11.1771i	−0.180682	−	0.556081i
$405$		0			0
$406$	2.53522	−	7.80262i	0.125821	−	0.387237i
$407$			19.1632i			0.949885i
$408$	0.850050	+	0.276198i	0.0420838	+	0.0136738i
$409$	−9.74072	+	7.07705i	−0.481648	+	0.349938i	−0.801963	−	0.597373i	$-0.796211\pi$
$409$	−9.74072	+	7.07705i	−0.481648	+	0.349938i	0.320316	+	0.947311i	$0.396211\pi$
$410$		0			0
$411$	−5.01578	−	3.64418i	−0.247410	−	0.179754i
$412$	−0.725364	−	0.998377i	−0.0357361	−	0.0491865i
$413$	−2.94219	−	4.04958i	−0.144776	−	0.199267i
$414$	14.8165	+	10.7648i	0.728192	+	0.529062i
$415$		0			0
$416$	0.677414	−	0.492170i	0.0332129	−	0.0241306i
$417$	0.862162	+	0.280134i	0.0422203	+	0.0137182i
$418$		−	6.96083i		−	0.340465i
$419$	10.6934	−	32.9108i	0.522405	−	1.60780i	−0.246985	−	0.969019i	$-0.579440\pi$
$419$	10.6934	−	32.9108i	0.522405	−	1.60780i	0.769390	−	0.638779i	$-0.220560\pi$
$420$		0			0
$421$	−4.62056	−	14.2206i	−0.225193	−	0.693071i	−0.998272	−	0.0587622i	$-0.981285\pi$
$421$	−4.62056	−	14.2206i	−0.225193	−	0.693071i	0.773079	−	0.634309i	$-0.218715\pi$
$422$	50.7730	−	16.4972i	2.47159	−	0.803069i
$423$	4.81865	−	6.63230i	0.234291	−	0.322473i
$424$	−0.668643			−0.0324722
$425$		0			0
$426$	−21.7767			−1.05508
$427$	4.17079	−	5.74060i	0.201839	−	0.277807i
$428$	2.73729	−	0.889401i	0.132312	−	0.0429908i
$429$	−0.152724	−	0.470035i	−0.00737357	−	0.0226935i
$430$		0			0
$431$	1.48670	−	4.57560i	0.0716119	−	0.220399i	−0.908845	−	0.417135i	$-0.863034\pi$
$431$	1.48670	−	4.57560i	0.0716119	−	0.220399i	0.980456	+	0.196736i	$0.0630342\pi$
$432$			3.84257i			0.184876i
$433$	−9.83725	−	3.19632i	−0.472748	−	0.153605i	0.0629466	−	0.998017i	$-0.479950\pi$
$433$	−9.83725	−	3.19632i	−0.472748	−	0.153605i	−0.535695	+	0.844412i	$0.679950\pi$
$434$	−1.77499	+	1.28961i	−0.0852024	+	0.0619032i
$435$		0			0
$436$	14.8739	+	10.8066i	0.712333	+	0.517540i
$437$	−3.86260	−	5.31641i	−0.184773	−	0.254318i
$438$	10.2423	+	14.0973i	0.489394	+	0.673593i
$439$	24.8886	+	18.0826i	1.18787	+	0.863037i	0.993037	−	0.117800i	$-0.0375840\pi$
$439$	24.8886	+	18.0826i	1.18787	+	0.863037i	0.194831	+	0.980837i	$0.437584\pi$
$440$		0			0
$441$	4.82328	−	3.50432i	0.229680	−	0.166872i
$442$	−1.16390	−	0.378173i	−0.0553609	−	0.0179878i
$443$			17.7545i			0.843543i	0.906702	+	0.421772i	$0.138592\pi$
$443$			17.7545i			0.843543i	−0.906702	+	0.421772i	$0.861408\pi$
$444$	2.58269	−	7.94870i	0.122569	−	0.377229i
$445$		0			0
$446$	5.01117	+	15.4228i	0.237286	+	0.730290i
$447$	−4.65836	+	1.51359i	−0.220333	+	0.0715904i
$448$	5.14720	−	7.08452i	0.243183	−	0.334712i
$449$	37.2184			1.75645			0.878223	−	0.478251i	$-0.158729\pi$
$449$	37.2184			1.75645			0.878223	+	0.478251i	$0.158729\pi$
$450$		0			0
$451$	34.3157			1.61586
$452$	8.04124	−	11.0678i	0.378228	−	0.520586i
$453$	9.76034	−	3.17133i	0.458581	−	0.149002i
$454$	10.2673	+	31.5996i	0.481870	+	1.48304i
$455$		0			0
$456$	−0.0342732	+	0.105482i	−0.00160499	+	0.00493966i
$457$		−	27.6987i		−	1.29569i	−0.761772	−	0.647846i	$-0.775670\pi$
$457$		−	27.6987i		−	1.29569i	0.761772	−	0.647846i	$-0.224330\pi$
$458$	0.785851	+	0.255338i	0.0367204	+	0.0119312i
$459$	4.72285	−	3.43135i	0.220444	−	0.160162i
$460$		0			0
$461$	−7.94246	−	5.77053i	−0.369917	−	0.268760i	0.387259	−	0.921971i	$-0.373422\pi$
$461$	−7.94246	−	5.77053i	−0.369917	−	0.268760i	−0.757177	+	0.653210i	$0.773422\pi$
$462$	−5.75463	−	7.92057i	−0.267730	−	0.368498i
$463$	−2.19086	−	3.01546i	−0.101818	−	0.140140i	0.755068	−	0.655647i	$-0.227604\pi$
$463$	−2.19086	−	3.01546i	−0.101818	−	0.140140i	−0.856886	+	0.515506i	$0.827604\pi$
$464$	12.3990	+	9.00840i	0.575609	+	0.418204i
$465$		0			0
$466$	−30.1574	+	21.9106i	−1.39701	+	1.01499i
$467$	−6.75179	−	2.19379i	−0.312436	−	0.101516i	0.148602	−	0.988897i	$-0.452523\pi$
$467$	−6.75179	−	2.19379i	−0.312436	−	0.101516i	−0.461038	+	0.887381i	$0.652523\pi$
$468$			0.215549i			0.00996376i
$469$	3.12329	−	9.61249i	0.144220	−	0.443864i
$470$		0			0
$471$	2.74882	+	8.46000i	0.126659	+	0.389816i
$472$	−0.715372	+	0.232438i	−0.0329277	+	0.0106988i
$473$	−24.1377	+	33.2227i	−1.10985	+	1.52758i
$474$	−5.01268			−0.230240
$475$		0			0
$476$	−12.3469			−0.565920
$477$	−2.56697	+	3.53313i	−0.117534	+	0.161771i
$478$	8.86457	−	2.88027i	0.405456	−	0.131741i
$479$	8.79003	+	27.0529i	0.401627	+	1.23608i	0.923679	+	0.383166i	$0.125166\pi$
$479$	8.79003	+	27.0529i	0.401627	+	1.23608i	−0.522053	+	0.852913i	$0.674834\pi$
$480$		0			0
$481$	−0.129191	+	0.397609i	−0.00589060	+	0.0181294i
$482$			58.9555i			2.68535i
$483$	−8.79033	−	2.85615i	−0.399974	−	0.129959i
$484$	19.5714	−	14.2195i	0.889610	−	0.646340i
$485$		0			0
$486$	−1.63330	−	1.18666i	−0.0740880	−	0.0538281i
$487$	8.66301	+	11.9236i	0.392558	+	0.540310i	0.958857	−	0.283890i	$-0.0916250\pi$
$487$	8.66301	+	11.9236i	0.392558	+	0.540310i	−0.566298	+	0.824200i	$0.691625\pi$
$488$	−0.626746	−	0.862641i	−0.0283714	−	0.0390499i
$489$	−9.52946	−	6.92356i	−0.430937	−	0.313094i
$490$		0			0
$491$	22.9772	−	16.6939i	1.03695	−	0.753387i	0.0672603	−	0.997735i	$-0.478574\pi$
$491$	22.9772	−	16.6939i	1.03695	−	0.753387i	0.969687	+	0.244349i	$0.0785742\pi$
$492$	−14.2338	−	4.62484i	−0.641709	−	0.208504i
$493$		−	23.2838i		−	1.04865i
$494$	0.0469272	−	0.144427i	0.00211135	−	0.00649808i
$495$		0			0
$496$	−1.26653	−	3.89799i	−0.0568690	−	0.175025i
$497$	10.4522	−	3.39613i	0.468846	−	0.152337i
$498$	−5.03602	+	6.93148i	−0.225669	+	0.310607i
$499$	−26.3842			−1.18112			−0.590559	−	0.806995i	$-0.701093\pi$
$499$	−26.3842			−1.18112			−0.590559	+	0.806995i	$0.701093\pi$
$500$		0			0
$501$	−17.3762			−0.776312
$502$	−0.462400	+	0.636439i	−0.0206379	+	0.0284057i
$503$	15.8438	−	5.14796i	0.706440	−	0.229536i	0.0663060	−	0.997799i	$-0.478879\pi$
$503$	15.8438	−	5.14796i	0.706440	−	0.229536i	0.640134	+	0.768263i	$0.278879\pi$
$504$	0.0482051	+	0.148360i	0.00214723	+	0.00660848i
$505$		0			0
$506$	26.9366	−	82.9022i	1.19748	−	3.68545i
$507$			12.9892i			0.576871i
$508$	14.3950	+	4.67723i	0.638677	+	0.207519i
$509$	−25.7073	+	18.6774i	−1.13946	+	0.827863i	−0.987043	−	0.160454i	$-0.948704\pi$
$509$	−25.7073	+	18.6774i	−1.13946	+	0.827863i	−0.152413	+	0.988317i	$0.548704\pi$
$510$		0			0
$511$	−7.11452	−	5.16900i	−0.314728	−	0.228663i
$512$	18.9047	+	26.0201i	0.835479	+	1.14994i
$513$	0.425794	+	0.586055i	0.0187993	+	0.0258750i
$514$	−13.1207	−	9.53274i	−0.578729	−	0.420471i
$515$		0			0
$516$	14.4896	−	10.5273i	0.637869	−	0.463439i
$517$	−37.1094	−	12.0576i	−1.63207	−	0.530292i
$518$			8.28179i			0.363881i
$519$	−4.00473	+	12.3253i	−0.175788	+	0.541020i
$520$		0			0
$521$	−0.183050	−	0.563371i	−0.00801958	−	0.0246817i	0.946967	−	0.321332i	$-0.104130\pi$
$521$	−0.183050	−	0.563371i	−0.00801958	−	0.0246817i	−0.954986	+	0.296650i	$0.904130\pi$
$522$	−7.65810	+	2.48827i	−0.335186	+	0.108909i
$523$	10.1274	−	13.9392i	0.442840	−	0.609518i	−0.528000	−	0.849244i	$-0.677058\pi$
$523$	10.1274	−	13.9392i	0.442840	−	0.609518i	0.970840	+	0.239727i	$0.0770579\pi$
$524$	19.8323			0.866376
$525$		0			0
$526$	48.8832			2.13141
$527$	−3.65997	+	5.03751i	−0.159431	+	0.219437i
$528$	17.3940	−	5.65166i	0.756978	−	0.245957i
$529$	−18.3224	−	56.3904i	−0.796625	−	2.45176i
$530$		0			0
$531$	−1.51815	+	4.67240i	−0.0658823	+	0.202765i
$532$		−	1.53212i		−	0.0664259i
$533$	0.712001	+	0.231343i	0.0308402	+	0.0100206i
$534$	−30.0122	+	21.8052i	−1.29876	+	0.943601i
$535$		0			0
$536$	−1.22874	−	0.892732i	−0.0530735	−	0.0385602i
$537$	0.645959	+	0.889086i	0.0278752	+	0.0383669i
$538$	−31.3353	−	43.1293i	−1.35096	−	1.85944i
$539$	−22.9569	−	16.6792i	−0.988826	−	0.718424i
$540$		0			0
$541$	−11.9726	+	8.69863i	−0.514744	+	0.373983i	−0.814620	−	0.579995i	$-0.803055\pi$
$541$	−11.9726	+	8.69863i	−0.514744	+	0.373983i	0.299876	+	0.953978i	$0.403055\pi$
$542$	19.9854	+	6.49366i	0.858448	+	0.278927i
$543$		−	14.9797i		−	0.642840i
$544$	14.5470	−	44.7710i	0.623696	−	1.91954i
$545$		0			0
$546$	−0.0660028	−	0.203136i	−0.00282466	−	0.00869341i
$547$	−6.18953	+	2.01110i	−0.264645	+	0.0859884i	−0.438334	−	0.898812i	$-0.644431\pi$
$547$	−6.18953	+	2.01110i	−0.264645	+	0.0859884i	0.173689	+	0.984801i	$0.444431\pi$
$548$	7.56472	−	10.4119i	0.323149	−	0.444776i
$549$	−6.96435			−0.297231
$550$		0			0
$551$	2.88927			0.123087
$552$	−0.816376	+	1.12365i	−0.0347473	+	0.0478255i
$553$	2.40595	−	0.781741i	0.102311	−	0.0332430i
$554$	−15.2976	−	47.0812i	−0.649933	−	2.00029i
$555$		0			0
$556$	−0.581512	+	1.78971i	−0.0246616	+	0.0759006i
$557$		−	6.67224i		−	0.282712i	−0.989959	−	0.141356i	$-0.954854\pi$
$557$		−	6.67224i		−	0.282712i	0.989959	−	0.141356i	$-0.0451462\pi$
$558$	2.04798	+	0.665430i	0.0866981	+	0.0281699i
$559$	−0.724796	+	0.526595i	−0.0306556	+	0.0222726i
$560$		0			0
$561$	−22.4789	−	16.3319i	−0.949061	−	0.689534i
$562$	−17.1150	−	23.5568i	−0.721953	−	0.993684i
$563$	11.7947	+	16.2340i	0.497087	+	0.684181i	0.981675	−	0.190561i	$-0.0610308\pi$
$563$	11.7947	+	16.2340i	0.497087	+	0.684181i	−0.484589	+	0.874742i	$0.661031\pi$
$564$	13.7676	+	10.0027i	0.579719	+	0.421191i
$565$		0			0
$566$	3.51037	−	2.55043i	0.147552	−	0.107203i
$567$	0.969003	+	0.314848i	0.0406943	+	0.0132224i
$568$		−	1.65149i		−	0.0692949i
$569$	6.67287	−	20.5370i	0.279741	−	0.860955i	−0.708185	−	0.706027i	$-0.750486\pi$
$569$	6.67287	−	20.5370i	0.279741	−	0.860955i	0.987926	−	0.154927i	$-0.0495144\pi$
$570$		0			0
$571$	−8.13758	−	25.0449i	−0.340547	−	1.04810i	−0.963925	−	0.266176i	$-0.914240\pi$
$571$	−8.13758	−	25.0449i	−0.340547	−	1.04810i	0.623377	−	0.781921i	$-0.285760\pi$
$572$	0.975717	−	0.317030i	0.0407968	−	0.0132557i
$573$	−7.48861	+	10.3072i	−0.312841	+	0.430589i
$574$	14.8303			0.619003
$575$		0			0
$576$	−8.59476			−0.358115
$577$	−5.39728	+	7.42872i	−0.224692	+	0.309262i	−0.906448	−	0.422318i	$-0.861217\pi$
$577$	−5.39728	+	7.42872i	−0.224692	+	0.309262i	0.681756	+	0.731580i	$0.261217\pi$
$578$	−32.7937	+	10.6553i	−1.36404	+	0.443202i
$579$	−1.35469	−	4.16930i	−0.0562989	−	0.173270i
$580$		0			0
$581$	1.33617	−	4.11230i	0.0554336	−	0.170607i
$582$			13.5239i			0.560585i
$583$	19.7688	+	6.42327i	0.818740	+	0.266025i
$584$	−1.06910	+	0.776746i	−0.0442397	+	0.0321420i
$585$		0			0
$586$	−14.7482	−	10.7152i	−0.609243	−	0.442641i
$587$	−23.4980	−	32.3422i	−0.969865	−	1.33491i	−0.942115	−	0.335290i	$-0.891166\pi$
$587$	−23.4980	−	32.3422i	−0.969865	−	1.33491i	−0.0277503	−	0.999615i	$-0.508834\pi$
$588$	7.27440	+	10.0123i	0.299991	+	0.412902i
$589$	−0.625101	−	0.454163i	−0.0257568	−	0.0187134i
$590$		0			0
$591$	2.60637	−	1.89364i	0.107212	−	0.0778939i
$592$	−14.7138	−	4.78081i	−0.604734	−	0.196490i
$593$			41.6331i			1.70967i	0.518902	+	0.854834i	$0.326341\pi$
$593$			41.6331i			1.70967i	−0.518902	+	0.854834i	$0.673659\pi$
$594$	−2.96936	+	9.13874i	−0.121834	+	0.374967i
$595$		0			0
$596$	−3.14197	−	9.66999i	−0.128700	−	0.396098i
$597$	−2.57278	+	0.835946i	−0.105297	+	0.0342130i
$598$	1.11779	−	1.53850i	0.0457098	−	0.0629141i
$599$	−39.0726			−1.59646			−0.798232	−	0.602350i	$-0.794231\pi$
$599$	−39.0726			−1.59646			−0.798232	+	0.602350i	$0.794231\pi$
$600$		0			0
$601$	5.46965			0.223112			0.111556	−	0.993758i	$-0.464417\pi$
$601$	5.46965			0.223112			0.111556	+	0.993758i	$0.464417\pi$
$602$	−10.4316	+	14.3579i	−0.425161	+	0.585184i
$603$	−9.43446	+	3.06544i	−0.384201	+	0.124834i
$604$	6.58316	+	20.2609i	0.267865	+	0.824404i
$605$		0			0
$606$	3.53199	−	10.8704i	0.143477	−	0.441578i
$607$			42.3108i			1.71734i	0.512527	+	0.858671i	$0.328709\pi$
$607$			42.3108i			1.71734i	−0.512527	+	0.858671i	$0.671291\pi$
$608$	5.55560	+	1.80512i	0.225309	+	0.0732074i
$609$	3.28763	−	2.38860i	0.133222	−	0.0967911i
$610$		0			0
$611$	−0.688679	−	0.500355i	−0.0278610	−	0.0202422i
$612$	7.12293	+	9.80387i	0.287927	+	0.396298i
$613$	−19.9885	−	27.5118i	−0.807327	−	1.11119i	−0.991730	−	0.128340i	$-0.959035\pi$
$613$	−19.9885	−	27.5118i	−0.807327	−	1.11119i	0.184403	−	0.982851i	$-0.440965\pi$
$614$	−8.22292	−	5.97430i	−0.331850	−	0.241103i
$615$		0			0
$616$	0.600675	−	0.436416i	0.0242019	−	0.0175837i
$617$	22.1760	+	7.20543i	0.892773	+	0.290080i	0.719251	−	0.694750i	$-0.244485\pi$
$617$	22.1760	+	7.20543i	0.892773	+	0.290080i	0.173522	+	0.984830i	$0.444485\pi$
$618$		−	1.20020i		−	0.0482790i
$619$	−10.9082	+	33.5721i	−0.438439	+	1.34938i	0.451083	+	0.892482i	$0.351038\pi$
$619$	−10.9082	+	33.5721i	−0.438439	+	1.34938i	−0.889521	+	0.456893i	$0.848962\pi$
$620$		0			0
$621$	2.80325	+	8.62753i	0.112491	+	0.346211i
$622$	−9.39213	+	3.05169i	−0.376590	+	0.122362i
$623$	11.0045	−	15.1464i	0.440885	−	0.606827i
$624$	0.399002			0.0159729
$625$		0			0
$626$	6.40551			0.256016
$627$	2.02661	−	2.78940i	0.0809352	−	0.111398i
$628$	−17.5616	+	5.70610i	−0.700783	+	0.227698i
$629$	7.26316	+	22.3537i	0.289601	+	0.891301i
$630$		0			0
$631$	−1.08290	+	3.33282i	−0.0431095	+	0.132677i	−0.970295	−	0.241926i	$-0.922221\pi$
$631$	−1.08290	+	3.33282i	−0.0431095	+	0.132677i	0.927185	+	0.374603i	$0.122221\pi$
$632$		−	0.380149i		−	0.0151215i
$633$	25.1492	+	8.17148i	0.999592	+	0.324787i
$634$	32.6583	−	23.7276i	1.29703	−	0.942345i
$635$		0			0
$636$	−7.33421	−	5.32862i	−0.290820	−	0.211293i
$637$	−0.363878	−	0.500836i	−0.0144174	−	0.0198438i
$638$	22.5271	+	31.0059i	0.891856	+	1.22753i
$639$	−8.72652	−	6.34019i	−0.345216	−	0.250814i
$640$		0			0
$641$	7.51448	−	5.45959i	0.296804	−	0.215641i	−0.429409	−	0.903110i	$-0.641278\pi$
$641$	7.51448	−	5.45959i	0.296804	−	0.215641i	0.726214	+	0.687469i	$0.241278\pi$
$642$	2.66218	+	0.864993i	0.105068	+	0.0341386i
$643$			0.0291680i			0.00115028i	1.00000		0.000575138i	$0.000183072\pi$
$643$			0.0291680i			0.00115028i	−1.00000		0.000575138i	$0.999817\pi$
$644$	5.92891	−	18.2473i	0.233632	−	0.719044i
$645$		0			0
$646$	−2.63826	−	8.11974i	−0.103801	−	0.319467i
$647$	0.802787	−	0.260841i	0.0315608	−	0.0102547i	−0.293194	−	0.956053i	$-0.594718\pi$
$647$	0.802787	−	0.260841i	0.0315608	−	0.0102547i	0.324755	+	0.945798i	$0.394718\pi$
$648$	0.0899934	−	0.123865i	0.00353527	−	0.00486589i
$649$	23.3833			0.917874
$650$		0			0
$651$	−1.08675			−0.0425932
$652$	14.3722	−	19.7816i	0.562858	−	0.774708i
$653$	36.2077	−	11.7646i	1.41692	−	0.460385i	0.502297	−	0.864695i	$-0.332489\pi$
$653$	36.2077	−	11.7646i	1.41692	−	0.460385i	0.914622	+	0.404311i	$0.132489\pi$
$654$	5.52543	+	17.0055i	0.216061	+	0.664969i
$655$		0			0
$656$	−8.56103	+	26.3481i	−0.334252	+	1.02872i
$657$			8.63115i			0.336733i
$658$	−16.0376	−	5.21094i	−0.625212	−	0.203144i
$659$	30.6086	−	22.2385i	1.19234	−	0.866287i	0.198832	−	0.980034i	$-0.436285\pi$
$659$	30.6086	−	22.2385i	1.19234	−	0.866287i	0.993510	+	0.113746i	$0.0362851\pi$
$660$		0			0
$661$	15.0165	+	10.9101i	0.584074	+	0.424355i	0.840191	−	0.542291i	$-0.182443\pi$
$661$	15.0165	+	10.9101i	0.584074	+	0.424355i	−0.256116	+	0.966646i	$0.582443\pi$
$662$	7.14044	+	9.82797i	0.277521	+	0.381975i
$663$	−0.356302	−	0.490407i	−0.0138376	−	0.0190458i
$664$	−0.525665	−	0.381918i	−0.0203998	−	0.0148213i
$665$		0			0
$666$	6.57601	−	4.77775i	0.254815	−	0.185134i
$667$	34.4106	+	11.1807i	1.33239	+	0.432918i
$668$		−	36.0702i		−	1.39560i
$669$	−2.48216	+	7.63932i	−0.0959660	+	0.295353i
$670$		0			0
$671$	10.2432	+	31.5253i	0.395433	+	1.21702i
$672$	7.81392	−	2.53890i	0.301428	−	0.0979400i
$673$	−10.6746	+	14.6923i	−0.411475	+	0.566347i	−0.963578	−	0.267429i	$-0.913826\pi$
$673$	−10.6746	+	14.6923i	−0.411475	+	0.566347i	0.552102	+	0.833776i	$0.313826\pi$
$674$	46.0578			1.77408
$675$		0			0
$676$	−26.9635			−1.03706
$677$	−3.31695	+	4.56538i	−0.127481	+	0.175462i	−0.867986	−	0.496588i	$-0.834586\pi$
$677$	−3.31695	+	4.56538i	−0.127481	+	0.175462i	0.740506	+	0.672050i	$0.234586\pi$
$678$	12.6539	−	4.11151i	0.485971	−	0.157902i
$679$	−2.10909	−	6.49112i	−0.0809396	−	0.249106i
$680$		0			0
$681$	−5.08569	+	15.6521i	−0.194884	+	0.599791i
$682$		−	10.2492i		−	0.392464i
$683$	−28.9567	−	9.40859i	−1.10800	−	0.360010i	−0.302821	−	0.953047i	$-0.597929\pi$
$683$	−28.9567	−	9.40859i	−1.10800	−	0.360010i	−0.805175	+	0.593038i	$0.797929\pi$
$684$	−1.21656	+	0.883879i	−0.0465162	+	0.0337960i
$685$		0			0
$686$	−21.5702	−	15.6717i	−0.823553	−	0.598346i
$687$	0.240572	+	0.331118i	0.00917838	+	0.0126330i
$688$	−19.4871	−	26.8216i	−0.742937	−	1.02257i
$689$	0.366871	+	0.266547i	0.0139767	+	0.0101546i
$690$		0			0
$691$	7.46294	−	5.42214i	0.283904	−	0.206268i	−0.436715	−	0.899600i	$-0.643858\pi$
$691$	7.46294	−	5.42214i	0.283904	−	0.206268i	0.720618	+	0.693332i	$0.243858\pi$
$692$	−25.5853	−	8.31316i	−0.972607	−	0.316019i
$693$		−	4.84943i		−	0.184215i
$694$	6.10806	−	18.7987i	0.231859	−	0.713588i
$695$		0			0
$696$	−0.188704	−	0.580771i	−0.00715280	−	0.0220141i
$697$	40.0290	−	13.0062i	1.51620	−	0.492645i
$698$	−1.52662	+	2.10121i	−0.0577835	+	0.0795322i
$699$	−18.4641			−0.698375
$700$		0			0
$701$	−19.9822			−0.754717			−0.377358	−	0.926067i	$-0.623168\pi$
$701$	−19.9822			−0.754717			−0.377358	+	0.926067i	$0.623168\pi$
$702$	−0.123220	+	0.169597i	−0.00465062	+	0.00640104i
$703$	−2.77386	+	0.901281i	−0.104618	+	0.0339924i
$704$	12.6412	+	38.9056i	0.476432	+	1.46631i
$705$		0			0
$706$	−0.726319	+	2.23538i	−0.0273354	+	0.0841296i
$707$			5.76830i			0.216939i
$708$	−9.69914	−	3.15144i	−0.364516	−	0.118438i
$709$	−21.7026	+	15.7679i	−0.815059	+	0.592175i	−0.915293	−	0.402789i	$-0.868041\pi$
$709$	−21.7026	+	15.7679i	−0.815059	+	0.592175i	0.100234	+	0.994964i	$0.468041\pi$
$710$		0			0
$711$	−2.00872	−	1.45942i	−0.0753329	−	0.0547325i
$712$	−1.65365	−	2.27605i	−0.0619730	−	0.0852985i
$713$	−5.68735	−	7.82797i	−0.212993	−	0.293160i
$714$	−9.71475	−	7.05818i	−0.363565	−	0.264146i
$715$		0			0
$716$	−1.84560	+	1.34090i	−0.0689732	+	0.0501120i
$717$	4.39086	+	1.42668i	0.163980	+	0.0532802i
$718$			38.4602i			1.43532i
$719$	−11.9968	+	36.9223i	−0.447404	+	1.37697i	0.432421	+	0.901672i	$0.357659\pi$
$719$	−11.9968	+	36.9223i	−0.447404	+	1.37697i	−0.879825	+	0.475297i	$0.842341\pi$
$720$		0			0
$721$	0.187174	+	0.576062i	0.00697072	+	0.0214537i
$722$	−35.4736	+	11.5261i	−1.32019	+	0.428956i
$723$	−17.1646	+	23.6251i	−0.638360	+	0.878627i
$724$	31.0954			1.15565
$725$		0			0
$726$	23.5277			0.873196
$727$	17.3846	−	23.9278i	0.644759	−	0.887434i	−0.354099	−	0.935208i	$-0.615213\pi$
$727$	17.3846	−	23.9278i	0.644759	−	0.887434i	0.998858	+	0.0477734i	$0.0152125\pi$
$728$	0.0154053	−	0.00500548i	0.000570958	−	0.000185515i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$		0			0
$731$	−15.5645	+	47.9025i	−0.575673	+	1.77174i
$732$		−	14.4569i		−	0.534341i
$733$	46.4859	+	15.1042i	1.71700	+	0.557886i	0.991473	−	0.130311i	$-0.0415976\pi$
$733$	46.4859	+	15.1042i	1.71700	+	0.557886i	0.725524	+	0.688197i	$0.241598\pi$
$734$	−27.3895	+	19.8997i	−1.01097	+	0.734510i
$735$		0			0
$736$	59.1808	+	42.9974i	2.18143	+	1.58490i
$737$	27.7524	+	38.1979i	1.02227	+	1.40704i
$738$	−8.55556	−	11.7757i	−0.314934	−	0.433470i
$739$	17.6045	+	12.7904i	0.647590	+	0.470502i	0.862450	−	0.506143i	$-0.168929\pi$
$739$	17.6045	+	12.7904i	0.647590	+	0.470502i	−0.214859	+	0.976645i	$0.568929\pi$
$740$		0			0
$741$	0.0608543	−	0.0442132i	0.00223554	−	0.00162421i
$742$	8.54351	+	2.77595i	0.313642	+	0.101908i
$743$			9.75724i			0.357959i	0.983853	+	0.178979i	$0.0572795\pi$
$743$			9.75724i			0.357959i	−0.983853	+	0.178979i	$0.942720\pi$
$744$	−0.0504645	+	0.155314i	−0.00185012	+	0.00569408i
$745$		0			0
$746$	10.6382	+	32.7409i	0.389491	+	1.19873i
$747$	−4.03614	+	1.31142i	−0.147675	+	0.0479824i
$748$	33.9024	−	46.6626i	1.23959	−	1.70615i
$749$	−1.41267			−0.0516178
$750$		0			0
$751$	−17.6413			−0.643741			−0.321871	−	0.946784i	$-0.604312\pi$
$751$	−17.6413			−0.643741			−0.321871	+	0.946784i	$0.604312\pi$
$752$	18.5160	−	25.4851i	0.675209	−	0.929346i
$753$	−0.370593	+	0.120413i	−0.0135052	+	0.00438809i
$754$	0.258375	+	0.795196i	0.00940945	+	0.0289593i
$755$		0			0
$756$	−0.653574	+	2.01149i	−0.0237702	+	0.0731573i
$757$		−	44.2551i		−	1.60848i	−0.594305	−	0.804240i	$-0.702573\pi$
$757$		−	44.2551i		−	1.60848i	0.594305	−	0.804240i	$-0.297427\pi$
$758$	3.19904	+	1.03943i	0.116194	+	0.0377538i
$759$	34.9308	−	25.3787i	1.26791	−	0.921190i
$760$		0			0
$761$	−32.2600	−	23.4382i	−1.16942	−	0.849636i	−0.178483	−	0.983943i	$-0.557119\pi$
$761$	−32.2600	−	23.4382i	−1.16942	−	0.849636i	−0.990940	+	0.134307i	$0.957119\pi$
$762$	8.65248	+	11.9091i	0.313446	+	0.431422i
$763$	−5.30412	−	7.30049i	−0.192022	−	0.264295i
$764$	−21.3960	−	15.5451i	−0.774082	−	0.562403i
$765$		0			0
$766$	4.98747	−	3.62361i	0.180205	−	0.130926i
$767$	0.485169	+	0.157641i	0.0175184	+	0.00569208i
$768$			14.7185i			0.531108i
$769$	−10.8980	+	33.5407i	−0.392993	+	1.20951i	0.537521	+	0.843250i	$0.319361\pi$
$769$	−10.8980	+	33.5407i	−0.392993	+	1.20951i	−0.930514	+	0.366257i	$0.880639\pi$
$770$		0			0
$771$	−2.48241	−	7.64007i	−0.0894018	−	0.275150i
$772$	8.65479	−	2.81211i	0.311493	−	0.101210i
$773$	13.6611	−	18.8029i	0.491357	−	0.676295i	−0.489281	−	0.872126i	$-0.662741\pi$
$773$	13.6611	−	18.8029i	0.491357	−	0.676295i	0.980638	+	0.195832i	$0.0627406\pi$
$774$	17.4186			0.626100
$775$		0			0
$776$	−1.02562			−0.0368176
$777$	−2.41121	+	3.31874i	−0.0865015	+	0.119059i
$778$	−54.2850	+	17.6383i	−1.94621	+	0.632362i
$779$	1.61393	+	4.96717i	0.0578250	+	0.177967i
$780$		0			0
$781$	−15.8649	+	48.8272i	−0.567691	+	1.74717i
$782$		−	106.914i		−	3.82324i
$783$	−3.79326	−	1.23251i	−0.135560	−	0.0440462i
$784$	18.5338	−	13.4656i	0.661922	−	0.480914i
$785$		0			0
$786$	15.6043	+	11.3372i	0.556588	+	0.404385i
$787$	−4.01513	−	5.52636i	−0.143124	−	0.196993i	0.731437	−	0.681909i	$-0.238850\pi$
$787$	−4.01513	−	5.52636i	−0.143124	−	0.196993i	−0.874561	+	0.484916i	$0.838850\pi$
$788$	3.93089	+	5.41040i	0.140032	+	0.192738i
$789$	19.5888	+	14.2321i	0.697381	+	0.506677i
$790$		0			0
$791$	−5.43235	+	3.94683i	−0.193152	+	0.140333i
$792$	−0.693058	−	0.225188i	−0.0246267	−	0.00800172i
$793$			0.723159i			0.0256801i
$794$	−12.7757	+	39.3195i	−0.453392	+	1.39540i
$795$		0			0
$796$	−1.73529	−	5.34067i	−0.0615056	−	0.189295i
$797$	−51.2892	+	16.6649i	−1.81676	+	0.590301i	−0.816849	+	0.576852i	$0.804281\pi$
$797$	−51.2892	+	16.6649i	−1.81676	+	0.590301i	−0.999910	+	0.0134488i	$0.995719\pi$
$798$	0.875844	−	1.20550i	0.0310046	−	0.0426741i
$799$	−47.8578			−1.69309
$800$		0			0
$801$	−18.3752			−0.649256
$802$	−30.3728	+	41.8046i	−1.07250	+	1.47617i
$803$	39.0703	−	12.6947i	1.37876	−	0.447987i
$804$	−6.36336	−	19.5844i	−0.224418	−	0.690689i
$805$		0			0
$806$	0.0690964	−	0.212657i	0.00243382	−	0.00749052i
$807$		−	26.4063i		−	0.929544i
$808$	0.824380	+	0.267857i	0.0290016	+	0.00942318i
$809$	−14.8943	+	10.8214i	−0.523656	+	0.380459i	−0.817980	−	0.575247i	$-0.804906\pi$
$809$	−14.8943	+	10.8214i	−0.523656	+	0.380459i	0.294323	+	0.955706i	$0.404906\pi$
$810$		0			0
$811$	9.53916	+	6.93060i	0.334965	+	0.243366i	0.742534	−	0.669808i	$-0.233624\pi$
$811$	9.53916	+	6.93060i	0.334965	+	0.243366i	−0.407569	+	0.913174i	$0.633624\pi$
$812$	4.95835	+	6.82459i	0.174004	+	0.239496i
$813$	6.11811	+	8.42086i	0.214572	+	0.295333i
$814$	−31.2993	−	22.7403i	−1.09704	−	0.797046i
$815$		0			0
$816$	18.1479	−	13.1852i	0.635304	−	0.461575i
$817$	−5.94419	−	1.93139i	−0.207961	−	0.0675706i
$818$		−	24.3076i		−	0.849895i
$819$	0.0326929	−	0.100619i	0.00114238	−	0.00351590i
$820$		0			0
$821$	−3.80899	−	11.7229i	−0.132935	−	0.409130i	0.862329	−	0.506349i	$-0.169005\pi$
$821$	−3.80899	−	11.7229i	−0.132935	−	0.409130i	−0.995263	+	0.0972189i	$0.969005\pi$
$822$	11.9041	−	3.86787i	0.415202	−	0.134907i
$823$	−1.65668	+	2.28023i	−0.0577484	+	0.0794839i	−0.836914	−	0.547334i	$-0.815643\pi$
$823$	−1.65668	+	2.28023i	−0.0577484	+	0.0794839i	0.779166	+	0.626818i	$0.215643\pi$
$824$	0.0910197			0.00317082
$825$		0			0
$826$	10.1056			0.351618
$827$	−21.9979	+	30.2776i	−0.764943	+	1.05285i	0.231844	+	0.972753i	$0.425524\pi$
$827$	−21.9979	+	30.2776i	−0.764943	+	1.05285i	−0.996787	+	0.0801008i	$0.974476\pi$
$828$	−17.9093	+	5.81910i	−0.622393	+	0.202228i
$829$	−9.56205	−	29.4289i	−0.332104	−	1.02211i	−0.968131	−	0.250443i	$-0.919424\pi$
$829$	−9.56205	−	29.4289i	−0.332104	−	1.02211i	0.636028	−	0.771666i	$-0.280576\pi$
$830$		0			0
$831$	7.57731	−	23.3206i	0.262854	−	0.808981i
$832$			0.892455i			0.0309403i
$833$	−33.1008	−	10.7551i	−1.14687	−	0.372642i
$834$	−1.48064	+	1.07575i	−0.0512703	+	0.0372501i
$835$		0			0
$836$	5.79033	+	4.20692i	0.200263	+	0.145499i
$837$	0.626946	+	0.862918i	0.0216704	+	0.0298268i
$838$	41.0638	+	56.5195i	1.41853	+	1.95243i
$839$	−21.5988	−	15.6924i	−0.745672	−	0.541762i	0.148810	−	0.988866i	$-0.452456\pi$
$839$	−21.5988	−	15.6924i	−0.745672	−	0.541762i	−0.894482	+	0.447103i	$0.852456\pi$
$840$		0			0
$841$	10.5917	−	7.69534i	0.365232	−	0.265356i
$842$	28.7096	+	9.32832i	0.989399	+	0.321475i
$843$		−	14.4228i		−	0.496748i
$844$	−16.9627	+	52.2057i	−0.583879	+	1.79699i
$845$		0			0
$846$	5.11443	+	15.7406i	0.175838	+	0.541173i
$847$	−11.2927	+	3.66921i	−0.388021	+	0.126076i
$848$	−9.86378	+	13.5763i	−0.338724	+	0.466213i
$849$	2.14925			0.0737620
$850$		0			0
$851$	−36.5239			−1.25202
$852$	13.1612	−	18.1148i	0.450895	−	0.620604i
$853$	27.8279	−	9.04183i	0.952808	−	0.309586i	0.208952	−	0.977926i	$-0.432995\pi$
$853$	27.8279	−	9.04183i	0.952808	−	0.309586i	0.743856	+	0.668340i	$0.232995\pi$
$854$	4.42681	+	13.6243i	0.151482	+	0.466214i
$855$		0			0
$856$	−0.0655988	+	0.201892i	−0.00224212	+	0.00690054i
$857$		−	33.5284i		−	1.14531i	−0.819797	−	0.572654i	$-0.805914\pi$
$857$		−	33.5284i		−	1.14531i	0.819797	−	0.572654i	$-0.194086\pi$
$858$	0.948941	+	0.308329i	0.0323963	+	0.0105262i
$859$	−20.8923	+	15.1792i	−0.712837	+	0.517906i	−0.884088	−	0.467321i	$-0.845219\pi$
$859$	−20.8923	+	15.1792i	−0.712837	+	0.517906i	0.171251	+	0.985227i	$0.445219\pi$
$860$		0			0
$861$	5.94289	+	4.31776i	0.202533	+	0.147149i
$862$	5.70911	+	7.85792i	0.194453	+	0.267642i
$863$	−16.9803	−	23.3713i	−0.578015	−	0.795569i	0.415461	−	0.909611i	$-0.363620\pi$
$863$	−16.9803	−	23.3713i	−0.578015	−	0.795569i	−0.993476	+	0.114042i	$0.963620\pi$
$864$	−6.52381	−	4.73982i	−0.221944	−	0.161252i
$865$		0			0
$866$	16.8940	−	12.2742i	0.574083	−	0.417096i
$867$	−16.2436	−	5.27785i	−0.551660	−	0.179245i
$868$		−	2.25592i		−	0.0765710i
$869$	−3.65187	+	11.2393i	−0.123881	+	0.381267i
$870$		0			0
$871$	0.318307	+	0.979647i	0.0107854	+	0.0331941i
$872$	−1.28965	+	0.419034i	−0.0436732	+	0.0141903i
$873$	−3.93743	+	5.41941i	−0.133262	+	0.183419i
$874$	13.2669			0.448759
$875$		0			0
$876$	−17.9169			−0.605355
$877$	−8.87581	+	12.2165i	−0.299715	+	0.412522i	−0.932139	−	0.362100i	$-0.882060\pi$
$877$	−8.87581	+	12.2165i	−0.299715	+	0.412522i	0.632425	+	0.774622i	$0.282060\pi$
$878$	−59.0688	+	19.1926i	−1.99347	+	0.647719i
$879$	−2.79033	−	8.58775i	−0.0941155	−	0.289658i
$880$		0			0
$881$	11.3167	−	34.8292i	0.381269	−	1.17342i	−0.557882	−	0.829920i	$-0.688386\pi$
$881$	11.3167	−	34.8292i	0.381269	−	1.17342i	0.939151	−	0.343505i	$-0.111614\pi$
$882$			12.0363i			0.405284i
$883$	32.8551	+	10.6753i	1.10566	+	0.359251i	0.804279	−	0.594252i	$-0.202552\pi$
$883$	32.8551	+	10.6753i	1.10566	+	0.359251i	0.301383	+	0.953503i	$0.402552\pi$
$884$	1.01801	−	0.739625i	0.0342392	−	0.0248763i
$885$		0			0
$886$	−28.9985	−	21.0686i	−0.974223	−	0.707814i
$887$	−19.4181	−	26.7267i	−0.651995	−	0.897394i	0.347189	−	0.937795i	$-0.387136\pi$
$887$	−19.4181	−	26.7267i	−0.651995	−	0.897394i	−0.999184	+	0.0404016i	$0.987136\pi$
$888$	0.362332	+	0.498708i	0.0121591	+	0.0167355i
$889$	−6.01021	−	4.36668i	−0.201576	−	0.146454i
$890$		0			0
$891$	−3.85061	+	2.79763i	−0.129000	+	0.0937241i
$892$	−15.8580	−	5.15257i	−0.530964	−	0.172521i
$893$		−	5.93864i		−	0.198729i
$894$	3.05574	−	9.40461i	0.102199	−	0.314537i
$895$		0			0
$896$	0.385364	+	1.18603i	0.0128741	+	0.0396224i
$897$	0.895858	−	0.291082i	0.0299118	−	0.00971894i
$898$	−44.1657	+	60.7889i	−1.47383	+	2.02855i
$899$	4.25420			0.141886
$900$		0			0
$901$	25.4947			0.849350
$902$	−40.7211	+	56.0478i	−1.35587	+	1.86619i
$903$	−8.36047	+	2.71648i	−0.278219	+	0.0903989i
$904$	0.311806	+	0.959641i	0.0103705	+	0.0319172i
$905$		0			0
$906$	−6.40250	+	19.7049i	−0.212709	+	0.654650i
$907$		−	44.2708i		−	1.46999i	−0.678074	−	0.734994i	$-0.737185\pi$
$907$		−	44.2708i		−	1.46999i	0.678074	−	0.734994i	$-0.262815\pi$
$908$	−32.4913	−	10.5571i	−1.07826	−	0.350348i
$909$	4.58022	−	3.32773i	0.151916	−	0.110374i
$910$		0			0
$911$	31.4581	+	22.8556i	1.04225	+	0.757241i	0.970724	−	0.240197i	$-0.0772121\pi$
$911$	31.4581	+	22.8556i	1.04225	+	0.757241i	0.0715293	+	0.997439i	$0.477212\pi$
$912$	1.63615	+	2.25196i	0.0541782	+	0.0745699i
$913$	11.8727	+	16.3414i	0.392930	+	0.540821i
$914$	45.2403	+	32.8690i	1.49642	+	1.08721i
$915$		0			0
$916$	−0.687348	+	0.499387i	−0.0227106	+	0.0165002i
$917$	−9.25772	−	3.00802i	−0.305717	−	0.0993334i
$918$			11.7857i			0.388986i
$919$	8.81634	−	27.1339i	0.290824	−	0.895065i	−0.693768	−	0.720198i	$-0.744051\pi$
$919$	8.81634	−	27.1339i	0.290824	−	0.895065i	0.984592	−	0.174866i	$-0.0559493\pi$
$920$		0			0
$921$	−1.55576	−	4.78813i	−0.0512640	−	0.157774i
$922$	18.8500	−	6.12474i	0.620793	−	0.201708i
$923$	−0.658347	+	0.906137i	−0.0216698	+	0.0298259i
$924$	10.0666			0.331168
$925$		0			0
$926$	7.52497			0.247286
$927$	0.349432	−	0.480952i	0.0114768	−	0.0157965i
$928$	−30.5884	+	9.93877i	−1.00411	+	0.326256i
$929$	−11.2447	−	34.6076i	−0.368926	−	1.13544i	−0.947486	−	0.319798i	$-0.896385\pi$
$929$	−11.2447	−	34.6076i	−0.368926	−	1.13544i	0.578559	−	0.815640i	$-0.303615\pi$
$930$		0			0
$931$	1.33459	−	4.10745i	0.0437395	−	0.134616i
$932$		−	38.3284i		−	1.25549i
$933$	−4.65217	−	1.51158i	−0.152305	−	0.0494870i
$934$	11.5952	−	8.42441i	0.379407	−	0.275655i
$935$		0			0
$936$	−0.0128618	−	0.00934465i	−0.000420402	−	0.000305440i
$937$	27.8230	+	38.2951i	0.908939	+	1.25105i	0.967528	+	0.252765i	$0.0813398\pi$
$937$	27.8230	+	38.2951i	0.908939	+	1.25105i	−0.0585890	+	0.998282i	$0.518660\pi$
$938$	11.9938	+	16.5080i	0.391611	+	0.539007i
$939$	2.56686	+	1.86494i	0.0837664	+	0.0608599i
$940$		0			0
$941$	−42.8175	+	31.1087i	−1.39581	+	1.01412i	−0.400611	+	0.916248i	$0.631202\pi$
$941$	−42.8175	+	31.1087i	−1.39581	+	1.01412i	−0.995199	+	0.0978679i	$0.968798\pi$
$942$	−17.0796	−	5.54951i	−0.556485	−	0.180813i
$943$			65.4035i			2.12983i
$944$	−5.83362	+	17.9540i	−0.189868	+	0.584354i
$945$		0			0
$946$	−25.6193	−	78.8482i	−0.832957	−	2.56358i
$947$	−18.0063	+	5.85061i	−0.585127	+	0.190119i	−0.586596	−	0.809880i	$-0.699532\pi$
$947$	−18.0063	+	5.85061i	−0.585127	+	0.190119i	0.00146915	+	0.999999i	$0.499532\pi$
$948$	3.02952	−	4.16978i	0.0983942	−	0.135428i
$949$	0.896234			0.0290930
$950$		0			0
$951$	19.9953			0.648392
$952$	0.535274	−	0.736741i	0.0173483	−	0.0238779i
$953$	−10.8895	+	3.53822i	−0.352746	+	0.114614i	−0.480030	−	0.877252i	$-0.659374\pi$
$953$	−10.8895	+	3.53822i	−0.352746	+	0.114614i	0.127284	+	0.991866i	$0.459374\pi$
$954$	−2.72454	−	8.38527i	−0.0882103	−	0.271483i
$955$		0			0
$956$	−2.96155	+	9.11471i	−0.0957833	+	0.294791i
$957$			18.9836i			0.613652i
$958$	−54.6163	−	17.7459i	−1.76457	−	0.573345i
$959$	−5.11043	+	3.71294i	−0.165024	+	0.119897i
$960$		0			0
$961$	24.1591	+	17.5526i	0.779326	+	0.566214i
$962$	−0.496108	−	0.682835i	−0.0159952	−	0.0220155i
$963$	0.814968	+	1.12171i	0.0262620	+	0.0361465i
$964$	−49.0419	−	35.6310i	−1.57953	−	1.14760i
$965$		0			0
$966$	15.0961	−	10.9680i	0.485709	−	0.352888i
$967$	−35.1821	−	11.4313i	−1.13138	−	0.367607i	−0.317279	−	0.948332i	$-0.602769\pi$
$967$	−35.1821	−	11.4313i	−1.13138	−	0.367607i	−0.814100	+	0.580725i	$0.802769\pi$
$968$			1.78428i			0.0573490i
$969$	1.30680	−	4.02192i	0.0419805	−	0.129203i
$970$		0			0
$971$	−9.36004	−	28.8072i	−0.300378	−	0.924468i	−0.981362	−	0.192170i	$-0.938448\pi$
$971$	−9.36004	−	28.8072i	−0.300378	−	0.924468i	0.680984	−	0.732298i	$-0.261552\pi$
$972$	1.97424	−	0.641469i	0.0633237	−	0.0205751i
$973$	0.542901	−	0.747239i	0.0174046	−	0.0239554i
$974$	−29.7549			−0.953408
$975$		0			0
$976$	−26.7610			−0.856600
$977$	9.78136	−	13.4629i	0.312934	−	0.430716i	−0.623360	−	0.781935i	$-0.714233\pi$
$977$	9.78136	−	13.4629i	0.312934	−	0.430716i	0.936293	+	0.351219i	$0.114233\pi$
$978$	22.6165	−	7.34855i	0.723196	−	0.234981i
$979$	27.0263	+	83.1783i	0.863763	+	2.65839i
$980$		0			0
$981$	−2.73689	+	8.42329i	−0.0873822	+	0.268935i
$982$			57.3388i			1.82975i
$983$	−24.9078	−	8.09305i	−0.794437	−	0.258128i	−0.116445	−	0.993197i	$-0.537150\pi$
$983$	−24.9078	−	8.09305i	−0.794437	−	0.258128i	−0.677992	+	0.735069i	$0.737150\pi$
$984$	0.893040	−	0.648831i	0.0284691	−	0.0206840i
$985$		0			0
$986$	38.0294	+	27.6300i	1.21110	+	0.879917i
$987$	−4.90958	−	6.75745i	−0.156274	−	0.215092i
$988$	0.0917795	+	0.126324i	0.00291990	+	0.00401889i
$989$	−63.3203	−	46.0049i	−2.01347	−	1.46287i
$990$		0			0
$991$	20.0938	−	14.5990i	0.638300	−	0.463752i	−0.220966	−	0.975282i	$-0.570921\pi$
$991$	20.0938	−	14.5990i	0.638300	−	0.463752i	0.859266	+	0.511530i	$0.170921\pi$
$992$	8.18016	+	2.65789i	0.259720	+	0.0843882i
$993$			6.01724i			0.190951i
$994$	−6.85635	+	21.1017i	−0.217470	+	0.669305i
$995$		0			0
$996$	−2.72230	−	8.37837i	−0.0862593	−	0.265479i
$997$	−23.8585	+	7.75208i	−0.755605	+	0.245511i	−0.661391	−	0.750041i	$-0.730034\pi$
$997$	−23.8585	+	7.75208i	−0.755605	+	0.245511i	−0.0942136	+	0.995552i	$0.530034\pi$
$998$	31.3091	−	43.0933i	0.991072	−	1.36409i
$999$	4.02621			0.127384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.d.49.2		24
5.2	odd	4		375.2.g.c.76.1		12
5.3	odd	4		75.2.g.c.16.3	✓	12
5.4	even	2	inner	375.2.i.d.49.5		24
15.8	even	4		225.2.h.d.91.1		12
25.2	odd	20		375.2.g.c.301.1		12
25.6	even	5		1875.2.b.f.1249.4		12
25.8	odd	20		1875.2.a.j.1.2		6
25.11	even	5	inner	375.2.i.d.199.5		24
25.14	even	10	inner	375.2.i.d.199.2		24
25.17	odd	20		1875.2.a.k.1.5		6
25.19	even	10		1875.2.b.f.1249.9		12
25.23	odd	20		75.2.g.c.61.3	yes	12
75.8	even	20		5625.2.a.p.1.5		6
75.17	even	20		5625.2.a.q.1.2		6
75.23	even	20		225.2.h.d.136.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.3	✓	12	5.3	odd	4
75.2.g.c.61.3	yes	12	25.23	odd	20
225.2.h.d.91.1		12	15.8	even	4
225.2.h.d.136.1		12	75.23	even	20
375.2.g.c.76.1		12	5.2	odd	4
375.2.g.c.301.1		12	25.2	odd	20
375.2.i.d.49.2		24	1.1	even	1	trivial
375.2.i.d.49.5		24	5.4	even	2	inner
375.2.i.d.199.2		24	25.14	even	10	inner
375.2.i.d.199.5		24	25.11	even	5	inner
1875.2.a.j.1.2		6	25.8	odd	20
1875.2.a.k.1.5		6	25.17	odd	20
1875.2.b.f.1249.4		12	25.6	even	5
1875.2.b.f.1249.9		12	25.19	even	10
5625.2.a.p.1.5		6	75.8	even	20
5625.2.a.q.1.2		6	75.17	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.18666 + 1.63330i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.641469 - 1.97424i) q^{4} +(0.623865 - 1.92006i) q^{6} +1.01887i q^{7} +(0.145612 + 0.0473123i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.18666 + 1.63330i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.641469 - 1.97424i) q^{4} +(0.623865 - 1.92006i) q^{6} +1.01887i q^{7} +(0.145612 + 0.0473123i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-3.85061 - 2.79763i) q^{11} +(1.22015 + 1.67939i) q^{12} +(-0.0610339 - 0.0840060i) q^{13} +(-1.66412 - 1.20905i) q^{14} +(3.10871 - 2.25861i) q^{16} +(-5.55204 - 1.80397i) q^{17} +2.01887i q^{18} +(0.223853 - 0.688949i) q^{19} +(-0.314848 - 0.969003i) q^{21} +(9.13874 - 2.96936i) q^{22} +(5.33210 - 7.33901i) q^{23} -0.153106 q^{24} +0.209634 q^{26} +(-0.587785 + 0.809017i) q^{27} +(2.01149 - 0.653574i) q^{28} +(1.23251 + 3.79326i) q^{29} +(0.329605 - 1.01442i) q^{31} +8.06387i q^{32} +(4.52666 + 1.47080i) q^{33} +(9.53482 - 6.92745i) q^{34} +(-1.67939 - 1.22015i) q^{36} +(-2.36655 - 3.25727i) q^{37} +(0.859623 + 1.18317i) q^{38} +(0.0840060 + 0.0610339i) q^{39} +(-5.83282 + 4.23780i) q^{41} +(1.95629 + 0.635638i) q^{42} -8.62791i q^{43} +(-3.05314 + 9.39661i) q^{44} +(5.65940 + 17.4179i) q^{46} +(7.79673 - 2.53331i) q^{47} +(-2.25861 + 3.10871i) q^{48} +5.96190 q^{49} +5.83776 q^{51} +(-0.126697 + 0.174383i) q^{52} +(-4.15345 + 1.34954i) q^{53} +(-0.623865 - 1.92006i) q^{54} +(-0.0482051 + 0.148360i) q^{56} +0.724404i q^{57} +(-7.65810 - 2.48827i) q^{58} +(-3.97458 + 2.88770i) q^{59} +(-5.63428 - 4.09354i) q^{61} +(1.26572 + 1.74212i) q^{62} +(0.598877 + 0.824283i) q^{63} +(-6.95331 - 5.05187i) q^{64} +(-7.77388 + 5.64805i) q^{66} +(-9.43446 - 3.06544i) q^{67} +12.1183i q^{68} +(-2.80325 + 8.62753i) q^{69} +(-3.33323 - 10.2586i) q^{71} +(0.145612 - 0.0473123i) q^{72} +(-5.07326 + 6.98275i) q^{73} +8.12840 q^{74} -1.50375 q^{76} +(2.85042 - 3.92327i) q^{77} +(-0.199374 + 0.0647804i) q^{78} +(-0.767263 - 2.36139i) q^{79} +(0.309017 - 0.951057i) q^{81} -14.5556i q^{82} +(-4.03614 - 1.31142i) q^{83} +(-1.71108 + 1.24317i) q^{84} +(14.0920 + 10.2384i) q^{86} +(-2.34436 - 3.22674i) q^{87} +(-0.428333 - 0.589550i) q^{88} +(-14.8659 - 10.8007i) q^{89} +(0.0855912 - 0.0621857i) q^{91} +(-17.9093 - 5.81910i) q^{92} +1.06662i q^{93} +(-5.11443 + 15.7406i) q^{94} +(-2.49187 - 7.66920i) q^{96} +(-6.37090 + 2.07003i) q^{97} +(-7.07477 + 9.73758i) q^{98} -4.75961 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{4} + 6 q^{9}+O(q^{10}) \) 24 * q + 20 * q^4 + 6 * q^9	\( 24 q + 20 q^{4} + 6 q^{9} - 8 q^{11} - 12 q^{14} + 32 q^{16} - 14 q^{19} - 6 q^{21} - 12 q^{24} - 112 q^{26} + 2 q^{29} + 26 q^{31} + 50 q^{34} - 4 q^{39} + 16 q^{41} - 66 q^{44} - 44 q^{46} + 56 q^{49} + 52 q^{51} + 90 q^{56} + 44 q^{59} - 16 q^{61} - 98 q^{64} - 6 q^{66} - 12 q^{69} - 42 q^{71} + 88 q^{74} - 104 q^{76} - 20 q^{79} - 6 q^{81} + 12 q^{84} + 112 q^{86} - 114 q^{89} - 14 q^{91} + 46 q^{94} - 46 q^{96} - 12 q^{99}+O(q^{100}) \) 24 * q + 20 * q^4 + 6 * q^9 - 8 * q^11 - 12 * q^14 + 32 * q^16 - 14 * q^19 - 6 * q^21 - 12 * q^24 - 112 * q^26 + 2 * q^29 + 26 * q^31 + 50 * q^34 - 4 * q^39 + 16 * q^41 - 66 * q^44 - 44 * q^46 + 56 * q^49 + 52 * q^51 + 90 * q^56 + 44 * q^59 - 16 * q^61 - 98 * q^64 - 6 * q^66 - 12 * q^69 - 42 * q^71 + 88 * q^74 - 104 * q^76 - 20 * q^79 - 6 * q^81 + 12 * q^84 + 112 * q^86 - 114 * q^89 - 14 * q^91 + 46 * q^94 - 46 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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