LMFDB - Embedded newform 375.2.i.d.274.3

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			274.3
Character	$\chi$	$=$	375.274
Dual form			375.2.i.d.349.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.234682 - 0.0762527i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-1.56877 - 1.13978i) q^{4} +(0.199632 - 0.145041i) q^{6} +1.24676i q^{7} +(0.571334 + 0.786373i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.234682 - 0.0762527i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-1.56877 - 1.13978i) q^{4} +(0.199632 - 0.145041i) q^{6} +1.24676i q^{7} +(0.571334 + 0.786373i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(0.794084 - 2.44394i) q^{11} +(1.84420 - 0.599218i) q^{12} +(4.45215 - 1.44659i) q^{13} +(0.0950687 - 0.292592i) q^{14} +(1.12432 + 3.46029i) q^{16} +(3.43216 + 4.72397i) q^{17} +0.246759i q^{18} +(3.37244 - 2.45022i) q^{19} +(-1.00865 - 0.732827i) q^{21} +(-0.372714 + 0.512997i) q^{22} +(1.52689 + 0.496117i) q^{23} -0.972011 q^{24} -1.15514 q^{26} +(0.951057 + 0.309017i) q^{27} +(1.42103 - 1.95588i) q^{28} +(-2.60158 - 1.89016i) q^{29} +(7.43739 - 5.40358i) q^{31} -2.84182i q^{32} +(1.51044 + 2.07894i) q^{33} +(-0.445250 - 1.37034i) q^{34} +(-0.599218 + 1.84420i) q^{36} +(-1.21524 + 0.394857i) q^{37} +(-0.978287 + 0.317865i) q^{38} +(-1.44659 + 4.45215i) q^{39} +(2.68719 + 8.27031i) q^{41} +(0.180832 + 0.248893i) q^{42} -3.88086i q^{43} +(-4.03129 + 2.92891i) q^{44} +(-0.320503 - 0.232859i) q^{46} +(1.88651 - 2.59656i) q^{47} +(-3.46029 - 1.12432i) q^{48} +5.44559 q^{49} -5.83914 q^{51} +(-8.63320 - 2.80510i) q^{52} +(-7.83770 + 10.7877i) q^{53} +(-0.199632 - 0.145041i) q^{54} +(-0.980418 + 0.712315i) q^{56} +4.16857i q^{57} +(0.466414 + 0.641964i) q^{58} +(1.97548 + 6.07990i) q^{59} +(1.18258 - 3.63961i) q^{61} +(-2.15746 + 0.701000i) q^{62} +(1.18574 - 0.385270i) q^{63} +(2.03194 - 6.25366i) q^{64} +(-0.195947 - 0.603064i) q^{66} +(-5.95063 - 8.19034i) q^{67} -11.3227i q^{68} +(-1.29885 + 0.943670i) q^{69} +(-11.2284 - 8.15794i) q^{71} +(0.571334 - 0.786373i) q^{72} +(-10.8243 - 3.51704i) q^{73} +0.315305 q^{74} -8.08332 q^{76} +(3.04700 + 0.990032i) q^{77} +(0.678976 - 0.934531i) q^{78} +(9.29008 + 6.74964i) q^{79} +(-0.809017 + 0.587785i) q^{81} -2.14580i q^{82} +(1.66478 + 2.29137i) q^{83} +(0.747080 + 2.29928i) q^{84} +(-0.295926 + 0.910766i) q^{86} +(3.05835 - 0.993717i) q^{87} +(2.37554 - 0.771858i) q^{88} +(0.426682 - 1.31319i) q^{89} +(1.80355 + 5.55075i) q^{91} +(-1.82988 - 2.51861i) q^{92} +9.19312i q^{93} +(-0.640724 + 0.465513i) q^{94} +(2.29908 + 1.67038i) q^{96} +(-0.0179322 + 0.0246815i) q^{97} +(-1.27798 - 0.415241i) q^{98} -2.56971 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 $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.234682	−	0.0762527i	−0.165945	−	0.0539188i	0.224866	−	0.974390i	$-0.427805\pi$
$2$	−0.234682	−	0.0762527i	−0.165945	−	0.0539188i	−0.390811	+	0.920471i	$0.627805\pi$
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$4$	−1.56877	−	1.13978i	−0.784386	−	0.569890i
$5$		0			0
$5$		0			0
$6$	0.199632	−	0.145041i	0.0814995	−	0.0592129i
$7$			1.24676i			0.471231i	0.971846	+	0.235615i	$0.0757105\pi$
$7$			1.24676i			0.471231i	−0.971846	+	0.235615i	$0.924289\pi$
$8$	0.571334	+	0.786373i	0.201997	+	0.278025i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$		0			0
$11$	0.794084	−	2.44394i	0.239425	−	0.736876i	−0.757078	−	0.653324i	$-0.773374\pi$
$11$	0.794084	−	2.44394i	0.239425	−	0.736876i	0.996503	−	0.0835513i	$-0.0266262\pi$
$12$	1.84420	−	0.599218i	0.532376	−	0.172979i
$13$	4.45215	−	1.44659i	1.23480	−	0.401212i	0.382351	−	0.924017i	$-0.375115\pi$
$13$	4.45215	−	1.44659i	1.23480	−	0.401212i	0.852452	+	0.522805i	$0.175115\pi$
$14$	0.0950687	−	0.292592i	0.0254082	−	0.0781984i
$15$		0			0
$16$	1.12432	+	3.46029i	0.281079	+	0.865073i
$17$	3.43216	+	4.72397i	0.832422	+	1.14573i	0.987467	+	0.157823i	$0.0504474\pi$
$17$	3.43216	+	4.72397i	0.832422	+	1.14573i	−0.155046	+	0.987907i	$0.549553\pi$
$18$			0.246759i			0.0581616i
$19$	3.37244	−	2.45022i	0.773692	−	0.562120i	−0.129387	−	0.991594i	$-0.541301\pi$
$19$	3.37244	−	2.45022i	0.773692	−	0.562120i	0.903079	+	0.429474i	$0.141301\pi$
$20$		0			0
$21$	−1.00865	−	0.732827i	−0.220105	−	0.159916i
$22$	−0.372714	+	0.512997i	−0.0794629	+	0.109371i
$23$	1.52689	+	0.496117i	0.318379	+	0.103447i	0.463847	−	0.885915i	$-0.346469\pi$
$23$	1.52689	+	0.496117i	0.318379	+	0.103447i	−0.145468	+	0.989363i	$0.546469\pi$
$24$	−0.972011			−0.198411
$25$		0			0
$26$	−1.15514			−0.226542
$27$	0.951057	+	0.309017i	0.183031	+	0.0594703i
$28$	1.42103	−	1.95588i	0.268550	−	0.369627i
$29$	−2.60158	−	1.89016i	−0.483102	−	0.350994i	0.319423	−	0.947612i	$-0.396511\pi$
$29$	−2.60158	−	1.89016i	−0.483102	−	0.350994i	−0.802525	+	0.596618i	$0.796511\pi$
$30$		0			0
$31$	7.43739	−	5.40358i	1.33579	−	0.970512i	0.336207	−	0.941788i	$-0.390856\pi$
$31$	7.43739	−	5.40358i	1.33579	−	0.970512i	0.999587	−	0.0287236i	$-0.00914425\pi$
$32$		−	2.84182i		−	0.502368i
$33$	1.51044	+	2.07894i	0.262934	+	0.361897i
$34$	−0.445250	−	1.37034i	−0.0763598	−	0.235011i
$35$		0			0
$36$	−0.599218	+	1.84420i	−0.0998697	+	0.307367i
$37$	−1.21524	+	0.394857i	−0.199785	+	0.0649141i	−0.407200	−	0.913339i	$-0.633495\pi$
$37$	−1.21524	+	0.394857i	−0.199785	+	0.0649141i	0.207415	+	0.978253i	$0.433495\pi$
$38$	−0.978287	+	0.317865i	−0.158699	+	0.0515645i
$39$	−1.44659	+	4.45215i	−0.231640	+	0.712914i
$40$		0			0
$41$	2.68719	+	8.27031i	0.419668	+	1.29161i	0.908008	+	0.418953i	$0.137603\pi$
$41$	2.68719	+	8.27031i	0.419668	+	1.29161i	−0.488340	+	0.872654i	$0.662397\pi$
$42$	0.180832	+	0.248893i	0.0279029	+	0.0384051i
$43$		−	3.88086i		−	0.591825i	−0.955215	−	0.295913i	$-0.904376\pi$
$43$		−	3.88086i		−	0.591825i	0.955215	−	0.295913i	$-0.0956237\pi$
$44$	−4.03129	+	2.92891i	−0.607740	+	0.441549i
$45$		0			0
$46$	−0.320503	−	0.232859i	−0.0472556	−	0.0343332i
$47$	1.88651	−	2.59656i	0.275176	−	0.378747i	−0.648953	−	0.760829i	$-0.724793\pi$
$47$	1.88651	−	2.59656i	0.275176	−	0.378747i	0.924129	+	0.382082i	$0.124793\pi$
$48$	−3.46029	−	1.12432i	−0.499450	−	0.162281i
$49$	5.44559			0.777942
$50$		0			0
$51$	−5.83914			−0.817643
$52$	−8.63320	−	2.80510i	−1.19721	−	0.388997i
$53$	−7.83770	+	10.7877i	−1.07659	+	1.48180i	−0.213371	+	0.976971i	$0.568444\pi$
$53$	−7.83770	+	10.7877i	−1.07659	+	1.48180i	−0.863219	+	0.504829i	$0.831556\pi$
$54$	−0.199632	−	0.145041i	−0.0271665	−	0.0197376i
$55$		0			0
$56$	−0.980418	+	0.712315i	−0.131014	+	0.0951871i
$57$			4.16857i			0.552141i
$58$	0.466414	+	0.641964i	0.0612432	+	0.0842940i
$59$	1.97548	+	6.07990i	0.257186	+	0.791536i	0.993391	+	0.114778i	$0.0366157\pi$
$59$	1.97548	+	6.07990i	0.257186	+	0.791536i	−0.736206	+	0.676758i	$0.763384\pi$
$60$		0			0
$61$	1.18258	−	3.63961i	0.151414	−	0.466005i	−0.846366	−	0.532602i	$-0.821214\pi$
$61$	1.18258	−	3.63961i	0.151414	−	0.466005i	0.997780	+	0.0665973i	$0.0212143\pi$
$62$	−2.15746	+	0.701000i	−0.273997	+	0.0890271i
$63$	1.18574	−	0.385270i	0.149389	−	0.0485394i
$64$	2.03194	−	6.25366i	0.253992	−	0.781708i
$65$		0			0
$66$	−0.195947	−	0.603064i	−0.0241195	−	0.0742321i
$67$	−5.95063	−	8.19034i	−0.726985	−	1.00061i	−0.999263	−	0.0383907i	$-0.987777\pi$
$67$	−5.95063	−	8.19034i	−0.726985	−	1.00061i	0.272277	−	0.962219i	$-0.412223\pi$
$68$		−	11.3227i		−	1.37308i
$69$	−1.29885	+	0.943670i	−0.156363	+	0.113605i
$70$		0			0
$71$	−11.2284	−	8.15794i	−1.33257	−	0.968169i	−0.999682	−	0.0252028i	$-0.991977\pi$
$71$	−11.2284	−	8.15794i	−1.33257	−	0.968169i	−0.332888	−	0.942966i	$-0.608023\pi$
$72$	0.571334	−	0.786373i	0.0673323	−	0.0926750i
$73$	−10.8243	−	3.51704i	−1.26689	−	0.411638i	−0.402947	−	0.915223i	$-0.632014\pi$
$73$	−10.8243	−	3.51704i	−1.26689	−	0.411638i	−0.863946	+	0.503585i	$0.832014\pi$
$74$	0.315305			0.0366534
$75$		0			0
$76$	−8.08332			−0.927220
$77$	3.04700	+	0.990032i	0.347238	+	0.112825i
$78$	0.678976	−	0.934531i	0.0768789	−	0.105815i
$79$	9.29008	+	6.74964i	1.04522	+	0.759394i	0.971297	−	0.237871i	$-0.0764494\pi$
$79$	9.29008	+	6.74964i	1.04522	+	0.759394i	0.0739188	+	0.997264i	$0.476449\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		−	2.14580i		−	0.236964i
$83$	1.66478	+	2.29137i	0.182733	+	0.251511i	0.890550	−	0.454885i	$-0.150320\pi$
$83$	1.66478	+	2.29137i	0.182733	+	0.251511i	−0.707817	+	0.706396i	$0.750320\pi$
$84$	0.747080	+	2.29928i	0.0815131	+	0.250872i
$85$		0			0
$86$	−0.295926	+	0.910766i	−0.0319105	+	0.0982105i
$87$	3.05835	−	0.993717i	0.327889	−	0.106538i
$88$	2.37554	−	0.771858i	0.253233	−	0.0822804i
$89$	0.426682	−	1.31319i	0.0452282	−	0.139198i	−0.925892	−	0.377788i	$-0.876685\pi$
$89$	0.426682	−	1.31319i	0.0452282	−	0.139198i	0.971121	+	0.238589i	$0.0766850\pi$
$90$		0			0
$91$	1.80355	+	5.55075i	0.189063	+	0.581877i
$92$	−1.82988	−	2.51861i	−0.190778	−	0.262584i
$93$			9.19312i			0.953282i
$94$	−0.640724	+	0.465513i	−0.0660857	+	0.0480140i
$95$		0			0
$96$	2.29908	+	1.67038i	0.234649	+	0.170483i
$97$	−0.0179322	+	0.0246815i	−0.00182074	+	0.00250603i	−0.809926	−	0.586532i	$-0.800493\pi$
$97$	−0.0179322	+	0.0246815i	−0.00182074	+	0.00250603i	0.808106	+	0.589038i	$0.200493\pi$
$98$	−1.27798	−	0.415241i	−0.129096	−	0.0419457i
$99$	−2.56971			−0.258266
$100$		0			0
$101$	−11.2308			−1.11750			−0.558751	−	0.829336i	$-0.688719\pi$
$101$	−11.2308			−1.11750			−0.558751	+	0.829336i	$0.688719\pi$
$102$	1.37034	+	0.445250i	0.135684	+	0.0440864i
$103$	−0.423783	+	0.583288i	−0.0417566	+	0.0574730i	−0.829385	−	0.558678i	$-0.811309\pi$
$103$	−0.423783	+	0.583288i	−0.0417566	+	0.0574730i	0.787628	+	0.616151i	$0.211309\pi$
$104$	3.68122	+	2.67456i	0.360973	+	0.262262i
$105$		0			0
$106$	2.66195	−	1.93402i	0.258552	−	0.187849i
$107$		−	2.11668i		−	0.204627i	−0.994752	−	0.102313i	$-0.967376\pi$
$107$		−	2.11668i		−	0.204627i	0.994752	−	0.102313i	$-0.0326244\pi$
$108$	−1.13978	−	1.56877i	−0.109675	−	0.150955i
$109$	−0.690602	−	2.12545i	−0.0661477	−	0.203582i	0.912520	−	0.409033i	$-0.134134\pi$
$109$	−0.690602	−	2.12545i	−0.0661477	−	0.203582i	−0.978667	+	0.205451i	$0.934134\pi$
$110$		0			0
$111$	0.394857	−	1.21524i	0.0374782	−	0.115346i
$112$	−4.31415	+	1.40175i	−0.407649	+	0.132453i
$113$	2.99525	−	0.973217i	0.281770	−	0.0915526i	−0.164723	−	0.986340i	$-0.552673\pi$
$113$	2.99525	−	0.973217i	0.281770	−	0.0915526i	0.446493	+	0.894787i	$0.352673\pi$
$114$	0.317865	−	0.978287i	0.0297708	−	0.0916250i
$115$		0			0
$116$	1.92693	+	5.93047i	0.178911	+	0.550630i
$117$	−2.75158	−	3.78722i	−0.254383	−	0.350129i
$118$		−	1.57748i		−	0.145219i
$119$	−5.88965	+	4.27908i	−0.539903	+	0.392262i
$120$		0			0
$121$	3.55691	+	2.58425i	0.323356	+	0.234932i
$122$	−0.555061	+	0.763975i	−0.0502528	+	0.0691671i
$123$	−8.27031	−	2.68719i	−0.745709	−	0.242296i
$124$	−17.8265			−1.60086
$125$		0			0
$126$	−0.307649			−0.0274075
$127$	14.8938	+	4.83929i	1.32161	+	0.429418i	0.883048	−	0.469282i	$-0.155487\pi$
$127$	14.8938	+	4.83929i	1.32161	+	0.429418i	0.438564	+	0.898700i	$0.355487\pi$
$128$	−4.29448	+	5.91084i	−0.379582	+	0.522450i
$129$	3.13968	+	2.28111i	0.276433	+	0.200841i
$130$		0			0
$131$	12.1000	−	8.79116i	1.05718	−	0.768087i	0.0836161	−	0.996498i	$-0.473353\pi$
$131$	12.1000	−	8.79116i	1.05718	−	0.768087i	0.973565	+	0.228411i	$0.0733530\pi$
$132$		−	4.98295i		−	0.433710i
$133$	3.05484	+	4.20463i	0.264888	+	0.364587i
$134$	0.771969	+	2.37588i	0.0666879	+	0.205244i
$135$		0			0
$136$	−1.75389	+	5.39792i	−0.150395	+	0.462868i
$137$	−9.98092	+	3.24300i	−0.852727	+	0.277068i	−0.702588	−	0.711597i	$-0.747972\pi$
$137$	−9.98092	+	3.24300i	−0.852727	+	0.277068i	−0.150139	+	0.988665i	$0.547972\pi$
$138$	0.376774	−	0.122421i	0.0320731	−	0.0104212i
$139$	−3.84749	+	11.8414i	−0.326340	+	1.00437i	0.644492	+	0.764611i	$0.277069\pi$
$139$	−3.84749	+	11.8414i	−0.326340	+	1.00437i	−0.970832	+	0.239761i	$0.922931\pi$
$140$		0			0
$141$	0.991798	+	3.05244i	0.0835244	+	0.257062i
$142$	2.01304	+	2.77072i	0.168931	+	0.232513i
$143$		−	12.0295i		−	1.00596i
$144$	2.94350	−	2.13858i	0.245292	−	0.178215i
$145$		0			0
$146$	2.27209	+	1.65077i	0.188039	+	0.136619i
$147$	−3.20084	+	4.40558i	−0.264001	+	0.363366i
$148$	2.35649	+	0.765671i	0.193703	+	0.0629378i
$149$	17.0680			1.39826			0.699131	−	0.714994i	$-0.253570\pi$
$149$	17.0680			1.39826			0.699131	+	0.714994i	$0.253570\pi$
$150$		0			0
$151$	−1.57516			−0.128185			−0.0640923	−	0.997944i	$-0.520415\pi$
$151$	−1.57516			−0.128185			−0.0640923	+	0.997944i	$0.520415\pi$
$152$	3.85358	+	1.25210i	0.312567	+	0.101559i
$153$	3.43216	−	4.72397i	0.277474	−	0.381910i
$154$	−0.639584	−	0.464685i	−0.0515391	−	0.0374454i
$155$		0			0
$156$	7.34384	−	5.33561i	0.587978	−	0.427191i
$157$			9.20058i			0.734286i	0.930164	+	0.367143i	$0.119664\pi$
$157$			9.20058i			0.734286i	−0.930164	+	0.367143i	$0.880336\pi$
$158$	−1.66553	−	2.29241i	−0.132503	−	0.182374i
$159$	−4.12052	−	12.6817i	−0.326779	−	1.00572i
$160$		0			0
$161$	−0.618538	+	1.90366i	−0.0487476	+	0.150030i
$162$	0.234682	−	0.0762527i	0.0184383	−	0.00599098i
$163$	4.35656	−	1.41553i	0.341232	−	0.110873i	−0.133388	−	0.991064i	$-0.542586\pi$
$163$	4.35656	−	1.41553i	0.341232	−	0.110873i	0.474620	+	0.880191i	$0.342586\pi$
$164$	5.21075	−	16.0370i	0.406891	−	1.25228i
$165$		0			0
$166$	−0.215970	−	0.664687i	−0.0167625	−	0.0515897i
$167$	0.0837776	+	0.115310i	0.00648291	+	0.00892296i	0.812246	−	0.583315i	$-0.198245\pi$
$167$	0.0837776	+	0.115310i	0.00648291	+	0.00892296i	−0.805763	+	0.592238i	$0.798245\pi$
$168$		−	1.21186i		−	0.0934973i
$169$	7.21176	−	5.23965i	0.554751	−	0.403050i
$170$		0			0
$171$	−3.37244	−	2.45022i	−0.257897	−	0.187373i
$172$	−4.42333	+	6.08819i	−0.337275	+	0.464220i
$173$	23.4176	+	7.60885i	1.78041	+	0.578490i	0.998965	−	0.0454831i	$-0.0144827\pi$
$173$	23.4176	+	7.60885i	1.78041	+	0.578490i	0.781445	+	0.623974i	$0.214483\pi$
$174$	−0.793511			−0.0601559
$175$		0			0
$176$	9.34955			0.704749
$177$	−6.07990	−	1.97548i	−0.456993	−	0.148486i
$178$	−0.200269	+	0.275647i	−0.0150108	+	0.0206606i
$179$	−19.5420	−	14.1981i	−1.46064	−	1.06122i	−0.983195	−	0.182557i	$-0.941563\pi$
$179$	−19.5420	−	14.1981i	−1.46064	−	1.06122i	−0.477446	−	0.878661i	$-0.658437\pi$
$180$		0			0
$181$	−1.59218	+	1.15679i	−0.118346	+	0.0859834i	−0.645384	−	0.763858i	$-0.723303\pi$
$181$	−1.59218	+	1.15679i	−0.118346	+	0.0859834i	0.527038	+	0.849842i	$0.323303\pi$
$182$		−	1.44019i		−	0.106754i
$183$	2.24940	+	3.09604i	0.166281	+	0.228866i
$184$	0.482231	+	1.48415i	0.0355505	+	0.109413i
$185$		0			0
$186$	0.701000	−	2.15746i	0.0513998	−	0.158192i
$187$	14.2705	−	4.63677i	1.04356	−	0.339074i
$188$	−5.91901	+	1.92320i	−0.431689	+	0.140264i
$189$	−0.385270	+	1.18574i	−0.0280242	+	0.0862498i
$190$		0			0
$191$	−2.40061	−	7.38832i	−0.173702	−	0.534600i	0.825870	−	0.563861i	$-0.190685\pi$
$191$	−2.40061	−	7.38832i	−0.173702	−	0.534600i	−0.999572	+	0.0292607i	$0.990685\pi$
$192$	3.86498	+	5.31968i	0.278931	+	0.383915i
$193$			14.3458i			1.03264i	0.856397	+	0.516318i	$0.172698\pi$
$193$			14.3458i			1.03264i	−0.856397	+	0.516318i	$0.827302\pi$
$194$	0.00609039	−	0.00442493i	0.000437265	−	0.000317691i
$195$		0			0
$196$	−8.54290	−	6.20678i	−0.610207	−	0.443341i
$197$	−0.0961264	+	0.132307i	−0.00684872	+	0.00942645i	−0.812428	−	0.583062i	$-0.801854\pi$
$197$	−0.0961264	+	0.132307i	−0.00684872	+	0.00942645i	0.805579	+	0.592489i	$0.201854\pi$
$198$	0.603064	+	0.195947i	0.0428579	+	0.0139254i
$199$	−4.96974			−0.352295			−0.176148	−	0.984364i	$-0.556364\pi$
$199$	−4.96974			−0.352295			−0.176148	+	0.984364i	$0.556364\pi$
$200$		0			0
$201$	10.1238			0.714079
$202$	2.63565	+	0.856375i	0.185444	+	0.0602543i
$203$	2.35658	−	3.24355i	0.165399	−	0.227652i
$204$	9.16029	+	6.65534i	0.641348	+	0.465967i
$205$		0			0
$206$	0.143931	−	0.104572i	0.0100282	−	0.00728590i
$207$		−	1.60547i		−	0.111588i
$208$	10.0112	+	13.7793i	0.694155	+	0.955423i
$209$	−3.31020	−	10.1877i	−0.228971	−	0.704701i
$210$		0			0
$211$	1.01784	−	3.13260i	0.0700713	−	0.215657i	−0.909888	−	0.414853i	$-0.863833\pi$
$211$	1.01784	−	3.13260i	0.0700713	−	0.215657i	0.979960	+	0.199196i	$0.0638330\pi$
$212$	24.5911	−	7.99015i	1.68893	−	0.548766i
$213$	13.1998	−	4.28888i	0.904437	−	0.293869i
$214$	−0.161402	+	0.496745i	−0.0110332	+	0.0339568i
$215$		0			0
$216$	0.300368	+	0.924437i	0.0204374	+	0.0629000i
$217$	6.73696	+	9.27263i	0.457335	+	0.629467i
$218$			0.551465i			0.0373500i
$219$	9.20773	−	6.68981i	0.622201	−	0.452055i
$220$		0			0
$221$	22.1141	+	16.0669i	1.48756	+	1.08077i
$222$	−0.185331	+	0.255087i	−0.0124386	+	0.0171203i
$223$	−15.0012	−	4.87419i	−1.00456	−	0.326400i	−0.239872	−	0.970805i	$-0.577105\pi$
$223$	−15.0012	−	4.87419i	−1.00456	−	0.326400i	−0.764685	+	0.644404i	$0.777105\pi$
$224$	3.54307			0.236731
$225$		0			0
$226$	−0.777142			−0.0516947
$227$	−12.8779	−	4.18427i	−0.854734	−	0.277720i	−0.151307	−	0.988487i	$-0.548348\pi$
$227$	−12.8779	−	4.18427i	−0.854734	−	0.277720i	−0.703428	+	0.710767i	$0.748348\pi$
$228$	4.75125	−	6.53954i	0.314660	−	0.433092i
$229$	−11.9596	−	8.68915i	−0.790312	−	0.574195i	0.117744	−	0.993044i	$-0.462434\pi$
$229$	−11.9596	−	8.68915i	−0.790312	−	0.574195i	−0.908056	+	0.418849i	$0.862434\pi$
$230$		0			0
$231$	−2.59194	+	1.88315i	−0.170537	+	0.123902i
$232$		−	3.12573i		−	0.205214i
$233$	−0.305049	−	0.419864i	−0.0199844	−	0.0275062i	0.798908	−	0.601453i	$-0.205411\pi$
$233$	−0.305049	−	0.419864i	−0.0199844	−	0.0275062i	−0.818892	+	0.573947i	$0.805411\pi$
$234$	0.356959	+	1.09861i	0.0233351	+	0.0718182i
$235$		0			0
$236$	3.83067	−	11.7896i	0.249356	−	0.767438i
$237$	−10.9211	+	3.54849i	−0.709405	+	0.230500i
$238$	1.70848	−	0.555120i	0.110745	−	0.0359831i
$239$	−2.54331	+	7.82750i	−0.164513	+	0.506319i	−0.999000	−	0.0447086i	$-0.985764\pi$
$239$	−2.54331	+	7.82750i	−0.164513	+	0.506319i	0.834487	+	0.551027i	$0.185764\pi$
$240$		0			0
$241$	−0.395906	−	1.21847i	−0.0255025	−	0.0784888i	0.937495	−	0.347998i	$-0.113138\pi$
$241$	−0.395906	−	1.21847i	−0.0255025	−	0.0784888i	−0.962998	+	0.269509i	$0.913138\pi$
$242$	−0.637686	−	0.877700i	−0.0409920	−	0.0564207i
$243$		−	1.00000i		−	0.0641500i
$244$	−6.00356	+	4.36184i	−0.384339	+	0.279238i
$245$		0			0
$246$	1.73599	+	1.26127i	0.110682	+	0.0804155i
$247$	11.4701	−	15.7873i	0.729828	−	1.00452i
$248$	8.49846	+	2.76132i	0.539653	+	0.175344i
$249$	−2.83229			−0.179489
$250$		0			0
$251$	4.63494			0.292555			0.146277	−	0.989244i	$-0.453271\pi$
$251$	4.63494			0.292555			0.146277	+	0.989244i	$0.453271\pi$
$252$	−2.29928	−	0.747080i	−0.144841	−	0.0470616i
$253$	2.42496	−	3.33767i	0.152456	−	0.209837i
$254$	−3.12630	−	2.27139i	−0.196161	−	0.142519i
$255$		0			0
$256$	−9.18081	+	6.67025i	−0.573801	+	0.416891i
$257$			18.3001i			1.14153i	0.821113	+	0.570766i	$0.193353\pi$
$257$			18.3001i			1.14153i	−0.821113	+	0.570766i	$0.806647\pi$
$258$	−0.562885	−	0.774744i	−0.0350437	−	0.0482335i
$259$	−0.492291	−	1.51512i	−0.0305895	−	0.0941448i
$260$		0			0
$261$	−0.993717	+	3.05835i	−0.0615095	+	0.189307i
$262$	−3.51000	+	1.14047i	−0.216848	+	0.0704583i
$263$	−15.8509	+	5.15027i	−0.977409	+	0.317579i	−0.753803	−	0.657100i	$-0.771783\pi$
$263$	−15.8509	+	5.15027i	−0.977409	+	0.317579i	−0.223606	+	0.974680i	$0.571783\pi$
$264$	−0.771858	+	2.37554i	−0.0475046	+	0.146204i
$265$		0			0
$266$	−0.396301	−	1.21969i	−0.0242988	−	0.0747839i
$267$	0.811598	+	1.11707i	0.0496690	+	0.0683635i
$268$			19.6312i			1.19917i
$269$	2.12942	−	1.54712i	0.129833	−	0.0943294i	−0.520973	−	0.853573i	$-0.674431\pi$
$269$	2.12942	−	1.54712i	0.129833	−	0.0943294i	0.650807	+	0.759244i	$0.274431\pi$
$270$		0			0
$271$	−3.69192	−	2.68233i	−0.224268	−	0.162940i	0.469978	−	0.882678i	$-0.344262\pi$
$271$	−3.69192	−	2.68233i	−0.224268	−	0.162940i	−0.694246	+	0.719738i	$0.744262\pi$
$272$	−12.4875	+	17.1875i	−0.757164	+	1.04215i
$273$	−5.55075	−	1.80355i	−0.335947	−	0.109156i
$274$	2.58963			0.156445
$275$		0			0
$276$	3.11318			0.187391
$277$	−1.19762	−	0.389132i	−0.0719583	−	0.0233807i	0.272817	−	0.962066i	$-0.412045\pi$
$277$	−1.19762	−	0.389132i	−0.0719583	−	0.0233807i	−0.344775	+	0.938685i	$0.612045\pi$
$278$	1.80587	−	2.48557i	0.108309	−	0.149075i
$279$	−7.43739	−	5.40358i	−0.445265	−	0.323504i
$280$		0			0
$281$	−10.8543	+	7.88611i	−0.647513	+	0.470446i	−0.862423	−	0.506188i	$-0.831054\pi$
$281$	−10.8543	+	7.88611i	−0.647513	+	0.470446i	0.214910	+	0.976634i	$0.431054\pi$
$282$		−	0.791979i		−	0.0471617i
$283$	−14.1591	−	19.4884i	−0.841674	−	1.15846i	−0.985636	−	0.168882i	$-0.945984\pi$
$283$	−14.1591	−	19.4884i	−0.841674	−	1.15846i	0.143962	−	0.989583i	$-0.454016\pi$
$284$	8.31661	+	25.5959i	0.493500	+	1.51884i
$285$		0			0
$286$	−0.917281	+	2.82310i	−0.0542400	+	0.166934i
$287$	−10.3111	+	3.35028i	−0.608644	+	0.197761i
$288$	−2.70273	+	0.878171i	−0.159260	+	0.0517467i
$289$	−5.28283	+	16.2589i	−0.310754	+	0.956404i
$290$		0			0
$291$	−0.00942751	−	0.0290149i	−0.000552651	−	0.00170088i
$292$	12.9723	+	17.8548i	0.759145	+	1.04487i
$293$		−	32.1727i		−	1.87955i	−0.341792	−	0.939776i	$-0.611034\pi$
$293$		−	32.1727i		−	1.87955i	0.341792	−	0.939776i	$-0.388966\pi$
$294$	1.08712	−	0.789836i	0.0634019	−	0.0460641i
$295$		0			0
$296$	−1.00481	−	0.730041i	−0.0584037	−	0.0424328i
$297$	1.51044	−	2.07894i	0.0876445	−	0.120632i
$298$	−4.00554	−	1.30148i	−0.232035	−	0.0753926i
$299$	7.51561			0.434639
$300$		0			0
$301$	4.83849			0.278886
$302$	0.369661	+	0.120110i	0.0212716	+	0.00691156i
$303$	6.60127	−	9.08587i	0.379233	−	0.521970i
$304$	12.2702	+	8.91482i	0.703744	+	0.511300i
$305$		0			0
$306$	−1.16568	+	0.846917i	−0.0666375	+	0.0484150i
$307$		−	20.2962i		−	1.15837i	−0.815198	−	0.579183i	$-0.803372\pi$
$307$		−	20.2962i		−	1.15837i	0.815198	−	0.579183i	$-0.196628\pi$
$308$	−3.65164	−	5.02605i	−0.208071	−	0.286386i
$309$	−0.222796	−	0.685696i	−0.0126744	−	0.0390079i
$310$		0			0
$311$	−5.78554	+	17.8061i	−0.328068	+	1.00969i	0.641969	+	0.766731i	$0.278118\pi$
$311$	−5.78554	+	17.8061i	−0.328068	+	1.00969i	−0.970037	+	0.242959i	$0.921882\pi$
$312$	−4.32753	+	1.40610i	−0.244998	+	0.0796048i
$313$	−23.6660	+	7.68955i	−1.33768	+	0.434639i	−0.888531	−	0.458817i	$-0.848274\pi$
$313$	−23.6660	+	7.68955i	−1.33768	+	0.434639i	−0.449151	+	0.893456i	$0.648274\pi$
$314$	0.701569	−	2.15921i	0.0395919	−	0.121851i
$315$		0			0
$316$	−6.88092	−	21.1773i	−0.387082	−	1.19132i
$317$	−14.8052	−	20.3775i	−0.831540	−	1.14452i	−0.987634	−	0.156775i	$-0.949890\pi$
$317$	−14.8052	−	20.3775i	−0.831540	−	1.14452i	0.156094	−	0.987742i	$-0.450110\pi$
$318$			3.29036i			0.184514i
$319$	−6.68532	+	4.85717i	−0.374306	+	0.271949i
$320$		0			0
$321$	1.71243	+	1.24415i	0.0955783	+	0.0694417i
$322$	0.290319	−	0.399590i	0.0161788	−	0.0222683i
$323$	23.1496	+	7.52174i	1.28808	+	0.418521i
$324$	1.93911			0.107728
$325$		0			0
$326$	−1.13034			−0.0626039
$327$	2.12545	+	0.690602i	0.117538	+	0.0381904i
$328$	−4.96827	+	6.83824i	−0.274327	+	0.377579i
$329$	3.23728	+	2.35202i	0.178477	+	0.129671i
$330$		0			0
$331$	−24.6097	+	17.8800i	−1.35267	+	0.982773i	−0.353797	+	0.935322i	$0.615110\pi$
$331$	−24.6097	+	17.8800i	−1.35267	+	0.982773i	−0.998874	+	0.0474508i	$0.984890\pi$
$332$		−	5.49212i		−	0.301419i
$333$	0.751062	+	1.03375i	0.0411580	+	0.0566491i
$334$	−0.0108684	−	0.0334494i	−0.000594691	−	0.00183027i
$335$		0			0
$336$	1.40175	−	4.31415i	0.0764719	−	0.235356i
$337$	−4.35066	+	1.41361i	−0.236995	+	0.0770045i	−0.425107	−	0.905143i	$-0.639763\pi$
$337$	−4.35066	+	1.41361i	−0.236995	+	0.0770045i	0.188111	+	0.982148i	$0.439763\pi$
$338$	−2.09200	+	0.679734i	−0.113790	+	0.0369726i
$339$	−0.973217	+	2.99525i	−0.0528579	+	0.162680i
$340$		0			0
$341$	−7.30011	−	22.4674i	−0.395323	−	1.21668i
$342$	0.604615	+	0.832181i	0.0326938	+	0.0449992i
$343$			15.5167i			0.837821i
$344$	3.05180	−	2.21726i	0.164542	−	0.119547i
$345$		0			0
$346$	−4.91550	−	3.57132i	−0.264259	−	0.191995i
$347$	9.88377	−	13.6038i	0.530589	−	0.730293i	−0.456631	−	0.889656i	$-0.650944\pi$
$347$	9.88377	−	13.6038i	0.530589	−	0.730293i	0.987220	+	0.159363i	$0.0509442\pi$
$348$	−5.93047	−	1.92693i	−0.317906	−	0.103294i
$349$	−0.373581			−0.0199973			−0.00999866	−	0.999950i	$-0.503183\pi$
$349$	−0.373581			−0.0199973			−0.00999866	+	0.999950i	$0.503183\pi$
$350$		0			0
$351$	4.68126			0.249867
$352$	−6.94524	−	2.25665i	−0.370183	−	0.120280i
$353$	−14.0883	+	19.3909i	−0.749847	+	1.03208i	0.248144	+	0.968723i	$0.420179\pi$
$353$	−14.0883	+	19.3909i	−0.749847	+	1.03208i	−0.997991	+	0.0633526i	$0.979821\pi$
$354$	1.27621	+	0.927218i	0.0678296	+	0.0492811i
$355$		0			0
$356$	−2.16612	+	1.57378i	−0.114804	+	0.0834101i
$357$		−	7.28000i		−	0.385299i
$358$	3.50352	+	4.82218i	0.185167	+	0.254860i
$359$	1.46789	+	4.51771i	0.0774724	+	0.238435i	0.982291	−	0.187362i	$-0.0599937\pi$
$359$	1.46789	+	4.51771i	0.0774724	+	0.238435i	−0.904819	+	0.425797i	$0.859994\pi$
$360$		0			0
$361$	−0.501540	+	1.54358i	−0.0263969	+	0.0812412i
$362$	0.461865	−	0.150069i	0.0242751	−	0.00788744i
$363$	−4.18140	+	1.35862i	−0.219467	+	0.0713090i
$364$	3.49728	−	10.7635i	0.183307	−	0.564162i
$365$		0			0
$366$	−0.291813	−	0.898107i	−0.0152533	−	0.0469448i
$367$	−10.2098	−	14.0526i	−0.532948	−	0.733540i	0.454628	−	0.890681i	$-0.349772\pi$
$367$	−10.2098	−	14.0526i	−0.532948	−	0.733540i	−0.987576	+	0.157141i	$0.949772\pi$
$368$			5.84128i			0.304498i
$369$	7.03515	−	5.11134i	0.366235	−	0.266085i
$370$		0			0
$371$	−13.4496	−	9.77172i	−0.698270	−	0.507323i
$372$	10.4781	−	14.4219i	0.543266	−	0.747742i
$373$	2.00556	+	0.651645i	0.103844	+	0.0337409i	0.360478	−	0.932768i	$-0.382614\pi$
$373$	2.00556	+	0.651645i	0.103844	+	0.0337409i	−0.256634	+	0.966509i	$0.582614\pi$
$374$	−3.70260			−0.191457
$375$		0			0
$376$	3.11969			0.160886
$377$	−14.3169	−	4.65185i	−0.737359	−	0.239582i
$378$	0.180832	−	0.248893i	0.00930097	−	0.0128017i
$379$	10.0391	+	7.29380i	0.515671	+	0.374657i	0.814971	−	0.579502i	$-0.196753\pi$
$379$	10.0391	+	7.29380i	0.515671	+	0.374657i	−0.299299	+	0.954159i	$0.596753\pi$
$380$		0			0
$381$	−12.6694	+	9.20488i	−0.649075	+	0.471580i
$382$			1.91696i			0.0980801i
$383$	−19.5766	−	26.9448i	−1.00032	−	1.37682i	−0.925132	−	0.379646i	$-0.876046\pi$
$383$	−19.5766	−	26.9448i	−1.00032	−	1.37682i	−0.0751836	−	0.997170i	$-0.523954\pi$
$384$	−2.25774	−	6.94861i	−0.115215	−	0.354595i
$385$		0			0
$386$	1.09391	−	3.36671i	0.0556785	−	0.171361i
$387$	−3.69092	+	1.19925i	−0.187620	+	0.0609614i
$388$	0.0562631	−	0.0182810i	0.00285633	−	0.000928076i
$389$	5.24639	−	16.1467i	0.266002	−	0.818671i	−0.725459	−	0.688266i	$-0.758372\pi$
$389$	5.24639	−	16.1467i	0.266002	−	0.818671i	0.991461	−	0.130405i	$-0.0416278\pi$
$390$		0			0
$391$	2.89690	+	8.91573i	0.146502	+	0.450888i
$392$	3.11125	+	4.28227i	0.157142	+	0.216287i
$393$			14.9564i			0.754451i
$394$	0.0326478	−	0.0237200i	0.00164477	−	0.00119500i
$395$		0			0
$396$	4.03129	+	2.92891i	0.202580	+	0.147183i
$397$	0.509357	−	0.701070i	0.0255639	−	0.0351857i	−0.796044	−	0.605239i	$-0.793078\pi$
$397$	0.509357	−	0.701070i	0.0255639	−	0.0351857i	0.821608	+	0.570053i	$0.193078\pi$
$398$	1.16631	+	0.378956i	0.0584617	+	0.0189953i
$399$	−5.19720			−0.260186
$400$		0			0
$401$	9.68680			0.483736			0.241868	−	0.970309i	$-0.422240\pi$
$401$	9.68680			0.483736			0.241868	+	0.970309i	$0.422240\pi$
$402$	−2.37588	−	0.771969i	−0.118498	−	0.0385023i
$403$	25.2956	−	34.8164i	1.26006	−	1.73433i
$404$	17.6185	+	12.8006i	0.876553	+	0.636853i
$405$		0			0
$406$	−0.800374	+	0.581506i	−0.0397219	+	0.0288597i
$407$			3.28353i			0.162759i
$408$	−3.33610	−	4.59174i	−0.165161	−	0.227325i
$409$	−0.469043	−	1.44357i	−0.0231927	−	0.0713797i	0.938790	−	0.344489i	$-0.111948\pi$
$409$	−0.469043	−	1.44357i	−0.0231927	−	0.0713797i	−0.961983	+	0.273109i	$0.911948\pi$
$410$		0			0
$411$	3.24300	−	9.98092i	0.159965	−	0.492322i
$412$	1.32964	−	0.432026i	0.0655066	−	0.0212844i
$413$	−7.58017	+	2.46295i	−0.372996	+	0.121194i
$414$	−0.122421	+	0.376774i	−0.00601667	+	0.0185174i
$415$		0			0
$416$	−4.11095	−	12.6522i	−0.201556	−	0.620325i
$417$	−7.31837	−	10.0729i	−0.358382	−	0.493271i
$418$			2.64329i			0.129287i
$419$	−24.7252	+	17.9639i	−1.20790	+	0.877594i	−0.995039	−	0.0994875i	$-0.968280\pi$
$419$	−24.7252	+	17.9639i	−1.20790	+	0.877594i	−0.212866	+	0.977081i	$0.568280\pi$
$420$		0			0
$421$	5.64016	+	4.09782i	0.274885	+	0.199715i	0.716683	−	0.697399i	$-0.245659\pi$
$421$	5.64016	+	4.09782i	0.274885	+	0.199715i	−0.441799	+	0.897114i	$0.645659\pi$
$422$	−0.477739	+	0.657551i	−0.0232560	+	0.0320091i
$423$	−3.05244	−	0.991798i	−0.148415	−	0.0482228i
$424$	−12.9611			−0.629445
$425$		0			0
$426$	−3.42480			−0.165932
$427$	4.53772	+	1.47439i	0.219596	+	0.0713510i
$428$	−2.41255	+	3.32058i	−0.116615	+	0.160506i
$429$	9.73206	+	7.07076i	0.469868	+	0.341379i
$430$		0			0
$431$	−8.85650	+	6.43463i	−0.426603	+	0.309945i	−0.780289	−	0.625419i	$-0.784928\pi$
$431$	−8.85650	+	6.43463i	−0.426603	+	0.309945i	0.353686	+	0.935364i	$0.384928\pi$
$432$			3.63837i			0.175051i
$433$	−6.13609	−	8.44561i	−0.294882	−	0.405870i	0.635710	−	0.771928i	$-0.280707\pi$
$433$	−6.13609	−	8.44561i	−0.294882	−	0.405870i	−0.930592	+	0.366058i	$0.880707\pi$
$434$	−0.873978	−	2.68983i	−0.0419523	−	0.129116i
$435$		0			0
$436$	−1.33915	+	4.12149i	−0.0641338	+	0.197384i
$437$	6.36495	−	2.06810i	0.304477	−	0.0989305i
$438$	−2.67100	+	0.867861i	−0.127625	+	0.0414680i
$439$	−4.76917	+	14.6780i	−0.227620	+	0.700543i	0.770395	+	0.637567i	$0.220059\pi$
$439$	−4.76917	+	14.6780i	−0.227620	+	0.700543i	−0.998015	+	0.0629758i	$0.979941\pi$
$440$		0			0
$441$	−1.68278	−	5.17907i	−0.0801324	−	0.246622i
$442$	−3.96464	−	5.45686i	−0.188579	−	0.259556i
$443$			18.9105i			0.898463i	0.893415	+	0.449231i	$0.148302\pi$
$443$			18.9105i			0.898463i	−0.893415	+	0.449231i	$0.851698\pi$
$444$	−2.00455	+	1.45639i	−0.0951318	+	0.0691173i
$445$		0			0
$446$	3.14884	+	2.28777i	0.149102	+	0.108329i
$447$	−10.0323	+	13.8083i	−0.474511	+	0.653109i
$448$	7.79681	+	2.53334i	0.368365	+	0.119689i
$449$	11.4152			0.538714			0.269357	−	0.963040i	$-0.413189\pi$
$449$	11.4152			0.538714			0.269357	+	0.963040i	$0.413189\pi$
$450$		0			0
$451$	22.3460			1.05223
$452$	−5.80813	−	1.88717i	−0.273191	−	0.0887652i
$453$	0.925855	−	1.27433i	0.0435005	−	0.0598733i
$454$	2.70314	+	1.96395i	0.126865	+	0.0921725i
$455$		0			0
$456$	−3.27805	+	2.38164i	−0.153509	+	0.111531i
$457$			33.9739i			1.58923i	0.607112	+	0.794616i	$0.292328\pi$
$457$			33.9739i			1.58923i	−0.607112	+	0.794616i	$0.707672\pi$
$458$	2.14413	+	2.95114i	0.100188	+	0.137898i
$459$	1.80439	+	5.55335i	0.0842219	+	0.259208i
$460$		0			0
$461$	−7.62985	+	23.4823i	−0.355358	+	1.09368i	0.600444	+	0.799667i	$0.294991\pi$
$461$	−7.62985	+	23.4823i	−0.355358	+	1.09368i	−0.955802	+	0.294012i	$0.905009\pi$
$462$	0.751876	−	0.244299i	0.0349804	−	0.0113658i
$463$	12.9643	−	4.21237i	0.602504	−	0.195765i	0.00814689	−	0.999967i	$-0.497407\pi$
$463$	12.9643	−	4.21237i	0.602504	−	0.195765i	0.594357	+	0.804202i	$0.297407\pi$
$464$	3.61551	−	11.1274i	0.167846	−	0.516576i
$465$		0			0
$466$	0.0395737	+	0.121795i	0.00183321	+	0.00564205i
$467$	5.56700	+	7.66232i	0.257610	+	0.354570i	0.918158	−	0.396214i	$-0.129676\pi$
$467$	5.56700	+	7.66232i	0.257610	+	0.354570i	−0.660548	+	0.750784i	$0.729676\pi$
$468$			9.07748i			0.419607i
$469$	10.2114	−	7.41900i	0.471518	−	0.342578i
$470$		0			0
$471$	−7.44343	−	5.40797i	−0.342975	−	0.249186i
$472$	−3.65241	+	5.02712i	−0.168116	+	0.231392i
$473$	−9.48459	−	3.08173i	−0.436102	−	0.141698i
$474$	2.83358			0.130150
$475$		0			0
$476$	14.1167			0.647039
$477$	12.6817	+	4.12052i	0.580654	+	0.188666i
$478$	1.19374	−	1.64304i	0.0546002	−	0.0751508i
$479$	−20.8149	−	15.1229i	−0.951055	−	0.690982i	1.08775e−6	−	1.00000i	$-0.500000\pi$
$479$	−20.8149	−	15.1229i	−0.951055	−	0.690982i	−0.951056	+	0.309018i	$0.900000\pi$
$480$		0			0
$481$	−4.83925	+	3.51592i	−0.220651	+	0.160312i
$482$			0.316142i			0.0143999i
$483$	−1.17653	−	1.61935i	−0.0535339	−	0.0736831i
$484$	−2.63451	−	8.10820i	−0.119751	−	0.368554i
$485$		0			0
$486$	−0.0762527	+	0.234682i	−0.00345889	+	0.0106454i
$487$	−27.0144	+	8.77751i	−1.22414	+	0.397747i	−0.848588	−	0.529055i	$-0.822547\pi$
$487$	−27.0144	+	8.77751i	−1.22414	+	0.397747i	−0.375551	+	0.926802i	$0.622547\pi$
$488$	3.53774	−	1.14948i	0.160146	−	0.0520346i
$489$	−1.41553	+	4.35656i	−0.0640126	+	0.197010i
$490$		0			0
$491$	−1.88593	−	5.80429i	−0.0851107	−	0.261944i	0.899440	−	0.437045i	$-0.143975\pi$
$491$	−1.88593	−	5.80429i	−0.0851107	−	0.261944i	−0.984551	+	0.175101i	$0.943975\pi$
$492$	9.91144	+	13.6419i	0.446842	+	0.615026i
$493$		−	18.7771i		−	0.845679i
$494$	−3.89566	+	2.83036i	−0.175274	+	0.127344i
$495$		0			0
$496$	27.0600	+	19.6602i	1.21503	+	0.882770i
$497$	10.1710	−	13.9992i	0.456231	−	0.627948i
$498$	0.664687	+	0.215970i	0.0297853	+	0.00967784i
$499$	20.3163			0.909481			0.454740	−	0.890624i	$-0.349732\pi$
$499$	20.3163			0.909481			0.454740	+	0.890624i	$0.349732\pi$
$500$		0			0
$501$	−0.142531			−0.00636782
$502$	−1.08773	−	0.353426i	−0.0485480	−	0.0157742i
$503$	8.59734	−	11.8332i	0.383336	−	0.527617i	−0.573128	−	0.819466i	$-0.694270\pi$
$503$	8.59734	−	11.8332i	0.383336	−	0.527617i	0.956465	+	0.291848i	$0.0942703\pi$
$504$	0.980418	+	0.712315i	0.0436713	+	0.0317290i
$505$		0			0
$506$	−0.823600	+	0.598380i	−0.0366135	+	0.0266012i
$507$			8.91422i			0.395894i
$508$	−17.8493	−	24.5674i	−0.791934	−	1.09000i
$509$	1.33058	+	4.09510i	0.0589768	+	0.181512i	0.976205	−	0.216851i	$-0.0695785\pi$
$509$	1.33058	+	4.09510i	0.0589768	+	0.181512i	−0.917228	+	0.398363i	$0.869578\pi$
$510$		0			0
$511$	4.38490	−	13.4953i	0.193977	−	0.596999i
$512$	16.5604	−	5.38081i	0.731874	−	0.237800i
$513$	3.96455	−	1.28816i	0.175039	−	0.0568736i
$514$	1.39543	−	4.29471i	0.0615500	−	0.189431i
$515$		0			0
$516$	−2.32548	−	7.15709i	−0.102374	−	0.315073i
$517$	−4.84779	−	6.67241i	−0.213205	−	0.293452i
$518$			0.393109i			0.0172722i
$519$	−19.9202	+	14.4729i	−0.874401	+	0.635290i
$520$		0			0
$521$	32.0705	+	23.3006i	1.40503	+	1.02082i	0.994021	+	0.109186i	$0.0348243\pi$
$521$	32.0705	+	23.3006i	1.40503	+	1.02082i	0.411011	+	0.911630i	$0.365176\pi$
$522$	0.466414	−	0.641964i	0.0204144	−	0.0280980i
$523$	34.5114	+	11.2134i	1.50908	+	0.490329i	0.942650	−	0.333782i	$-0.108325\pi$
$523$	34.5114	+	11.2134i	1.50908	+	0.490329i	0.566428	+	0.824111i	$0.308325\pi$
$524$	−29.0021			−1.26696
$525$		0			0
$526$	4.11264			0.179320
$527$	51.0526	+	16.5880i	2.22389	+	0.722585i
$528$	−5.49553	+	7.56395i	−0.239162	+	0.329179i
$529$	−16.5221	−	12.0040i	−0.718353	−	0.521914i
$530$		0			0
$531$	5.17187	−	3.75759i	0.224440	−	0.163065i
$532$		−	10.0779i		−	0.436934i
$533$	23.9275	+	32.9334i	1.03642	+	1.42650i
$534$	−0.105288	−	0.324042i	−0.00455625	−	0.0140227i
$535$		0			0
$536$	3.04087	−	9.35883i	0.131346	−	0.404240i
$537$	22.9731	−	7.46440i	0.991360	−	0.322113i
$538$	−0.617709	+	0.200706i	−0.0266313	+	0.00865304i
$539$	4.32426	−	13.3087i	0.186259	−	0.573246i
$540$		0			0
$541$	−11.9294	−	36.7150i	−0.512886	−	1.57850i	−0.787096	−	0.616830i	$-0.788417\pi$
$541$	−11.9294	−	36.7150i	−0.512886	−	1.57850i	0.274211	−	0.961670i	$-0.411583\pi$
$542$	0.661890	+	0.911014i	0.0284306	+	0.0391314i
$543$		−	1.96805i		−	0.0844570i
$544$	13.4247	−	9.75359i	0.575578	−	0.418182i
$545$		0			0
$546$	1.16513	+	0.846520i	0.0498632	+	0.0362277i
$547$	−6.09063	+	8.38303i	−0.260416	+	0.358433i	−0.919125	−	0.393965i	$-0.871103\pi$
$547$	−6.09063	+	8.38303i	−0.260416	+	0.358433i	0.658709	+	0.752398i	$0.271103\pi$
$548$	19.3541	+	6.28853i	0.826766	+	0.268633i
$549$	−3.82692			−0.163329
$550$		0			0
$551$	−13.4050			−0.571073
$552$	−1.48415	−	0.482231i	−0.0631698	−	0.0205251i
$553$	−8.41517	+	11.5825i	−0.357850	+	0.492538i
$554$	0.251388	+	0.182644i	0.0106805	+	0.00775981i
$555$		0			0
$556$	19.5324	−	14.1911i	0.828359	−	0.601838i
$557$		−	12.6830i		−	0.537398i	−0.963224	−	0.268699i	$-0.913406\pi$
$557$		−	12.6830i		−	0.537398i	0.963224	−	0.268699i	$-0.0865936\pi$
$558$	1.33338	+	1.83524i	0.0564465	+	0.0776920i
$559$	−5.61401	−	17.2781i	−0.237447	−	0.730788i
$560$		0			0
$561$	−4.63677	+	14.2705i	−0.195765	+	0.602502i
$562$	3.14864	−	1.02306i	0.132817	−	0.0431550i
$563$	−12.4486	+	4.04480i	−0.524646	+	0.170468i	−0.559353	−	0.828930i	$-0.688950\pi$
$563$	−12.4486	+	4.04480i	−0.524646	+	0.170468i	0.0347068	+	0.999398i	$0.488950\pi$
$564$	1.92320	−	5.91901i	0.0809815	−	0.249235i
$565$		0			0
$566$	1.83685	+	5.65324i	0.0772086	+	0.237624i
$567$	−0.732827	−	1.00865i	−0.0307758	−	0.0423593i
$568$		−	13.4906i		−	0.566055i
$569$	−2.09376	+	1.52120i	−0.0877748	+	0.0637721i	−0.630807	−	0.775940i	$-0.717276\pi$
$569$	−2.09376	+	1.52120i	−0.0877748	+	0.0637721i	0.543032	+	0.839712i	$0.317276\pi$
$570$		0			0
$571$	8.55571	+	6.21609i	0.358045	+	0.260135i	0.752236	−	0.658893i	$-0.228975\pi$
$571$	8.55571	+	6.21609i	0.358045	+	0.260135i	−0.394191	+	0.919029i	$0.628975\pi$
$572$	−13.7110	+	18.8715i	−0.573285	+	0.789059i
$573$	7.38832	+	2.40061i	0.308652	+	0.100287i
$574$	2.67529			0.111665
$575$		0			0
$576$	−6.57549			−0.273979
$577$	0.0135910	+	0.00441597i	0.000565800	+	0.000183839i	0.309300	−	0.950965i	$-0.399905\pi$
$577$	0.0135910	+	0.00441597i	0.000565800	+	0.000183839i	−0.308734	+	0.951148i	$0.599905\pi$
$578$	2.47957	−	3.41283i	0.103136	−	0.141955i
$579$	−11.6060	−	8.43227i	−0.482330	−	0.350433i
$580$		0			0
$581$	−2.85679	+	2.07558i	−0.118519	+	0.0861094i
$582$			0.00752814i			0.000312051i
$583$	20.1406	+	27.7212i	0.834139	+	1.14809i
$584$	−3.41860	−	10.5214i	−0.141463	−	0.435377i
$585$		0			0
$586$	−2.45326	+	7.55035i	−0.101343	+	0.311902i
$587$	−21.5309	+	6.99581i	−0.888675	+	0.288748i	−0.717555	−	0.696502i	$-0.754739\pi$
$587$	−21.5309	+	6.99581i	−0.888675	+	0.288748i	−0.171120	+	0.985250i	$0.554739\pi$
$588$	10.0428	−	3.26310i	0.414157	−	0.134568i
$589$	11.8422	−	36.4465i	0.487949	−	1.50175i
$590$		0			0
$591$	−0.0505366	−	0.155536i	−0.00207880	−	0.00639788i
$592$	−2.73264	−	3.76116i	−0.112311	−	0.154583i
$593$			12.7423i			0.523264i	0.965168	+	0.261632i	$0.0842606\pi$
$593$			12.7423i			0.523264i	−0.965168	+	0.261632i	$0.915739\pi$
$594$	−0.512997	+	0.372714i	−0.0210485	+	0.0152926i
$595$		0			0
$596$	−26.7758	−	19.4537i	−1.09678	−	0.796856i
$597$	2.92114	−	4.02060i	0.119554	−	0.164552i
$598$	−1.76378	−	0.573086i	−0.0721262	−	0.0234352i
$599$	6.83599			0.279311			0.139656	−	0.990200i	$-0.455400\pi$
$599$	6.83599			0.279311			0.139656	+	0.990200i	$0.455400\pi$
$600$		0			0
$601$	31.8422			1.29887			0.649435	−	0.760417i	$-0.275005\pi$
$601$	31.8422			1.29887			0.649435	+	0.760417i	$0.275005\pi$
$602$	−1.13551	−	0.368948i	−0.0462798	−	0.0150372i
$603$	−5.95063	+	8.19034i	−0.242328	+	0.333537i
$604$	2.47107	+	1.79534i	0.100546	+	0.0730511i
$605$		0			0
$606$	−2.24202	+	1.62892i	−0.0910758	+	0.0661705i
$607$		−	27.7763i		−	1.12741i	−0.825977	−	0.563703i	$-0.809376\pi$
$607$		−	27.7763i		−	1.12741i	0.825977	−	0.563703i	$-0.190624\pi$
$608$	−6.96310	−	9.58388i	−0.282391	−	0.388678i
$609$	1.23892	+	3.81302i	0.0502038	+	0.154511i
$610$		0			0
$611$	4.64286	−	14.2893i	0.187830	−	0.578082i
$612$	−10.7686	+	3.49892i	−0.435293	+	0.141435i
$613$	3.43991	−	1.11769i	0.138937	−	0.0451433i	−0.238723	−	0.971088i	$-0.576729\pi$
$613$	3.43991	−	1.11769i	0.138937	−	0.0451433i	0.377660	+	0.925944i	$0.376729\pi$
$614$	−1.54764	+	4.76315i	−0.0624577	+	0.192225i
$615$		0			0
$616$	0.962321	+	2.96172i	0.0387730	+	0.119331i
$617$	26.2402	+	36.1166i	1.05639	+	1.45400i	0.883133	+	0.469122i	$0.155430\pi$
$617$	26.2402	+	36.1166i	1.05639	+	1.45400i	0.173259	+	0.984876i	$0.444570\pi$
$618$			0.177909i			0.00715655i
$619$	16.5917	−	12.0546i	0.666878	−	0.484515i	−0.202101	−	0.979365i	$-0.564777\pi$
$619$	16.5917	−	12.0546i	0.666878	−	0.484515i	0.868979	+	0.494850i	$0.164777\pi$
$620$		0			0
$621$	1.29885	+	0.943670i	0.0521211	+	0.0378682i
$622$	2.71552	−	3.73760i	0.108883	−	0.149864i
$623$	1.63724	+	0.531970i	0.0655945	+	0.0213129i
$624$	−17.0322			−0.681832
$625$		0			0
$626$	6.14033			0.245417
$627$	10.1877	+	3.31020i	0.406859	+	0.132197i
$628$	10.4866	−	14.4336i	0.418463	−	0.575964i
$629$	−6.03621	−	4.38556i	−0.240679	−	0.174864i
$630$		0			0
$631$	30.5288	−	22.1805i	1.21533	−	0.882991i	0.219629	−	0.975583i	$-0.429515\pi$
$631$	30.5288	−	22.1805i	1.21533	−	0.882991i	0.995704	+	0.0925923i	$0.0295153\pi$
$632$			11.1618i			0.443991i
$633$	1.93605	+	2.66475i	0.0769512	+	0.105914i
$634$	1.92066	+	5.91117i	0.0762790	+	0.234763i
$635$		0			0
$636$	−7.99015	+	24.5911i	−0.316830	+	0.975102i
$637$	24.2446	−	7.87754i	0.960605	−	0.312119i
$638$	1.93929	−	0.630115i	0.0767774	−	0.0249465i
$639$	−4.28888	+	13.1998i	−0.169666	+	0.522177i
$640$		0			0
$641$	−2.83865	−	8.73646i	−0.112120	−	0.345070i	0.879216	−	0.476424i	$-0.158067\pi$
$641$	−2.83865	−	8.73646i	−0.112120	−	0.345070i	−0.991335	+	0.131355i	$0.958067\pi$
$642$	−0.307005	−	0.422557i	−0.0121165	−	0.0166770i
$643$			3.42111i			0.134915i	0.997722	+	0.0674577i	$0.0214888\pi$
$643$			3.42111i			0.134915i	−0.997722	+	0.0674577i	$0.978511\pi$
$644$	3.14010	−	2.28142i	0.123737	−	0.0899005i
$645$		0			0
$646$	−4.85922	−	3.53043i	−0.191184	−	0.138903i
$647$	−1.92050	+	2.64334i	−0.0755027	+	0.103920i	−0.845098	−	0.534611i	$-0.820458\pi$
$647$	−1.92050	+	2.64334i	−0.0755027	+	0.103920i	0.769595	+	0.638532i	$0.220458\pi$
$648$	−0.924437	−	0.300368i	−0.0363153	−	0.0117996i
$649$	16.4276			0.644840
$650$		0			0
$651$	−11.4616			−0.449216
$652$	−8.44785	−	2.74487i	−0.330843	−	0.107498i
$653$	7.42740	−	10.2229i	0.290656	−	0.400054i	−0.638571	−	0.769563i	$-0.720474\pi$
$653$	7.42740	−	10.2229i	0.290656	−	0.400054i	0.929227	+	0.369509i	$0.120474\pi$
$654$	−0.446145	−	0.324143i	−0.0174456	−	0.0126750i
$655$		0			0
$656$	−25.5965	+	18.5969i	−0.999374	+	0.726088i
$657$			11.3814i			0.444030i
$658$	−0.580383	−	0.798829i	−0.0226257	−	0.0311416i
$659$	2.82719	+	8.70118i	0.110131	+	0.338950i	0.990901	−	0.134596i	$-0.0429737\pi$
$659$	2.82719	+	8.70118i	0.110131	+	0.338950i	−0.880769	+	0.473546i	$0.842974\pi$
$660$		0			0
$661$	1.97487	−	6.07804i	0.0768137	−	0.236408i	−0.905275	−	0.424825i	$-0.860336\pi$
$661$	1.97487	−	6.07804i	0.0768137	−	0.236408i	0.982089	+	0.188417i	$0.0603356\pi$
$662$	7.13884	−	2.31955i	0.277459	−	0.0901519i
$663$	−25.9967	+	8.44684i	−1.00963	+	0.328048i
$664$	−0.850729	+	2.61827i	−0.0330147	+	0.101609i
$665$		0			0
$666$	−0.0974345	−	0.299872i	−0.00377551	−	0.0116198i
$667$	−3.03459	−	4.17676i	−0.117500	−	0.161725i
$668$		−	0.276383i		−	0.0106936i
$669$	12.7608	−	9.27127i	0.493361	−	0.358448i
$670$		0			0
$671$	−7.95593	−	5.78032i	−0.307135	−	0.223147i
$672$	−2.08256	+	2.86640i	−0.0803366	+	0.110574i
$673$	−32.0566	−	10.4158i	−1.23569	−	0.401500i	−0.382918	−	0.923782i	$-0.625081\pi$
$673$	−32.0566	−	10.4158i	−1.23569	−	0.401500i	−0.852773	+	0.522282i	$0.825081\pi$
$674$	1.12881			0.0434802
$675$		0			0
$676$	−17.2857			−0.664833
$677$	−8.75295	−	2.84401i	−0.336403	−	0.109304i	0.135944	−	0.990716i	$-0.456593\pi$
$677$	−8.75295	−	2.84401i	−0.336403	−	0.109304i	−0.472347	+	0.881412i	$0.656593\pi$
$678$	0.456792	−	0.628721i	0.0175430	−	0.0241459i
$679$	−0.0307719	−	0.0223571i	−0.00118092	−	0.000857988i
$680$		0			0
$681$	10.9546	−	7.95896i	0.419780	−	0.304988i
$682$			5.82935i			0.223217i
$683$	−16.0005	−	22.0227i	−0.612241	−	0.842677i	0.384519	−	0.923117i	$-0.374367\pi$
$683$	−16.0005	−	22.0227i	−0.612241	−	0.842677i	−0.996759	+	0.0804402i	$0.974367\pi$
$684$	2.49788	+	7.68769i	0.0955089	+	0.293946i
$685$		0			0
$686$	1.18319	−	3.64147i	0.0451743	−	0.139032i
$687$	14.0593	−	4.56816i	0.536397	−	0.174286i
$688$	13.4289	−	4.36332i	0.511972	−	0.166350i
$689$	−19.2892	+	59.3662i	−0.734862	+	2.26167i
$690$		0			0
$691$	9.21607	+	28.3642i	0.350596	+	1.07902i	0.958519	+	0.285028i	$0.0920028\pi$
$691$	9.21607	+	28.3642i	0.350596	+	1.07902i	−0.607923	+	0.793996i	$0.707997\pi$
$692$	−28.0645	−	38.6275i	−1.06685	−	1.46840i
$693$		−	3.20381i		−	0.121703i
$694$	−3.35687	+	2.43891i	−0.127425	+	0.0925797i
$695$		0			0
$696$	2.52877	+	1.83726i	0.0958527	+	0.0696410i
$697$	−29.8458	+	41.0792i	−1.13049	+	1.55599i
$698$	0.0876726	+	0.0284865i	0.00331846	+	0.00107823i
$699$	0.518980			0.0196296
$700$		0			0
$701$	−19.1081			−0.721704			−0.360852	−	0.932623i	$-0.617514\pi$
$701$	−19.1081			−0.721704			−0.360852	+	0.932623i	$0.617514\pi$
$702$	−1.09861	−	0.356959i	−0.0414642	−	0.0134725i
$703$	−3.13086	+	4.30925i	−0.118082	+	0.162527i
$704$	−13.6700	−	9.93187i	−0.515209	−	0.374322i
$705$		0			0
$706$	4.78489	−	3.47642i	0.180082	−	0.130837i
$707$		−	14.0020i		−	0.526601i
$708$	7.28637	+	10.0288i	0.273839	+	0.376907i
$709$	−4.48525	−	13.8042i	−0.168447	−	0.518427i	0.830827	−	0.556531i	$-0.187868\pi$
$709$	−4.48525	−	13.8042i	−0.168447	−	0.518427i	−0.999274	+	0.0381042i	$0.987868\pi$
$710$		0			0
$711$	3.54849	−	10.9211i	0.133079	−	0.409575i
$712$	1.27644	−	0.414740i	0.0478365	−	0.0155430i
$713$	14.0369	−	4.56086i	0.525685	−	0.170806i
$714$	−0.555120	+	1.70848i	−0.0207748	+	0.0639384i
$715$		0			0
$716$	14.4743	+	44.5473i	0.540930	+	1.66481i
$717$	−4.83766	−	6.65847i	−0.180666	−	0.248665i
$718$		−	1.17215i		−	0.0437444i
$719$	28.1139	−	20.4260i	1.04847	−	0.761760i	0.0765512	−	0.997066i	$-0.475609\pi$
$719$	28.1139	−	20.4260i	1.04847	−	0.761760i	0.971921	+	0.235306i	$0.0756091\pi$
$720$		0			0
$721$	−0.727219	−	0.528356i	−0.0270831	−	0.0196770i
$722$	0.235405	−	0.324007i	0.00876086	−	0.0120583i
$723$	1.21847	+	0.395906i	0.0453155	+	0.0147239i
$724$	3.81626			0.141830
$725$		0			0
$726$	1.08490			0.0402643
$727$	−40.5415	−	13.1727i	−1.50360	−	0.488550i	−0.562536	−	0.826773i	$-0.690174\pi$
$727$	−40.5415	−	13.1727i	−1.50360	−	0.488550i	−0.941066	+	0.338223i	$0.890174\pi$
$728$	−3.33453	+	4.58959i	−0.123586	+	0.170102i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$		0			0
$731$	18.3330	−	13.3197i	0.678072	−	0.492648i
$732$		−	7.42081i		−	0.274281i
$733$	−1.15341	−	1.58754i	−0.0426023	−	0.0586370i	0.787184	−	0.616718i	$-0.211538\pi$
$733$	−1.15341	−	1.58754i	−0.0426023	−	0.0586370i	−0.829787	+	0.558081i	$0.811538\pi$
$734$	1.32451	+	4.07642i	0.0488885	+	0.150463i
$735$		0			0
$736$	1.40987	−	4.33915i	0.0519687	−	0.159943i
$737$	−24.7420	+	8.03917i	−0.911384	+	0.296127i
$738$	−2.04077	+	0.663088i	−0.0751219	+	0.0244086i
$739$	−3.81947	+	11.7551i	−0.140501	+	0.432419i	−0.996405	−	0.0847164i	$-0.973002\pi$
$739$	−3.81947	+	11.7551i	−0.140501	+	0.432419i	0.855904	+	0.517135i	$0.173002\pi$
$740$		0			0
$741$	6.03021	+	18.5591i	0.221525	+	0.681785i
$742$	2.41126	+	3.31881i	0.0885201	+	0.121838i
$743$			8.63742i			0.316876i	0.987369	+	0.158438i	$0.0506458\pi$
$743$			8.63742i			0.316876i	−0.987369	+	0.158438i	$0.949354\pi$
$744$	−7.22922	+	5.25234i	−0.265036	+	0.192560i
$745$		0			0
$746$	−0.420978	−	0.305858i	−0.0154131	−	0.0111983i
$747$	1.66478	−	2.29137i	0.0609110	−	0.0838369i
$748$	−27.6721	−	8.99121i	−1.01179	−	0.328751i
$749$	2.63898			0.0964264
$750$		0			0
$751$	−24.3654			−0.889105			−0.444552	−	0.895753i	$-0.646637\pi$
$751$	−24.3654			−0.889105			−0.444552	+	0.895753i	$0.646637\pi$
$752$	11.1059	+	3.60852i	0.404990	+	0.131589i
$753$	−2.72435	+	3.74974i	−0.0992807	+	0.136648i
$754$	3.00520	+	2.18341i	0.109443	+	0.0795150i
$755$		0			0
$756$	1.95588	−	1.42103i	0.0711347	−	0.0516824i
$757$			5.18352i			0.188398i	0.995553	+	0.0941991i	$0.0300290\pi$
$757$			5.18352i			0.188398i	−0.995553	+	0.0941991i	$0.969971\pi$
$758$	−1.79981	−	2.47723i	−0.0653720	−	0.0899769i
$759$	1.27488	+	3.92367i	0.0462751	+	0.142420i
$760$		0			0
$761$	9.66099	−	29.7335i	0.350211	−	1.07784i	−0.608524	−	0.793535i	$-0.708238\pi$
$761$	9.66099	−	29.7335i	0.350211	−	1.07784i	0.958735	−	0.284302i	$-0.0917618\pi$
$762$	3.67518	−	1.19414i	0.133138	−	0.0432591i
$763$	2.64993	−	0.861014i	0.0959339	−	0.0311708i
$764$	−4.65505	+	14.3268i	−0.168414	+	0.518324i
$765$		0			0
$766$	2.53964	+	7.81622i	0.0917611	+	0.282412i
$767$	17.5903	+	24.2109i	0.635147	+	0.874205i
$768$		−	11.3481i		−	0.409490i
$769$	−35.7497	+	25.9737i	−1.28917	+	0.936636i	−0.999788	−	0.0205786i	$-0.993449\pi$
$769$	−35.7497	+	25.9737i	−1.28917	+	0.936636i	−0.289380	+	0.957214i	$0.593449\pi$
$770$		0			0
$771$	−14.8051	−	10.7566i	−0.533193	−	0.387388i
$772$	16.3511	−	22.5054i	0.588489	−	0.809986i
$773$	−20.5315	−	6.67110i	−0.738468	−	0.239943i	−0.0844563	−	0.996427i	$-0.526915\pi$
$773$	−20.5315	−	6.67110i	−0.738468	−	0.239943i	−0.654012	+	0.756484i	$0.726915\pi$
$774$	0.957636			0.0344215
$775$		0			0
$776$	−0.0296542			−0.00106452
$777$	1.51512	+	0.492291i	0.0543545	+	0.0176609i
$778$	−2.46246	+	3.38929i	−0.0882835	+	0.121512i
$779$	29.3265	+	21.3070i	1.05073	+	0.763401i
$780$		0			0
$781$	−28.8538	+	20.9635i	−1.03247	+	0.750135i
$782$		−	2.31325i		−	0.0827218i
$783$	−1.89016	−	2.60158i	−0.0675488	−	0.0929730i
$784$	6.12257	+	18.8433i	0.218663	+	0.672977i
$785$		0			0
$786$	1.14047	−	3.51000i	0.0406791	−	0.125197i
$787$	13.7153	−	4.45638i	0.488899	−	0.158853i	−0.0541857	−	0.998531i	$-0.517256\pi$
$787$	13.7153	−	4.45638i	0.488899	−	0.158853i	0.543085	+	0.839678i	$0.317256\pi$
$788$	0.301601	−	0.0979961i	0.0107441	−	0.00349097i
$789$	5.15027	−	15.8509i	0.183355	−	0.564307i
$790$		0			0
$791$	1.21337	+	3.73436i	0.0431424	+	0.132779i
$792$	−1.46816	−	2.02075i	−0.0521689	−	0.0718043i
$793$		−	17.9148i		−	0.636173i
$794$	−0.172995	+	0.125688i	−0.00613937	+	0.00446052i
$795$		0			0
$796$	7.79639	+	5.66441i	0.276336	+	0.200770i
$797$	23.1921	−	31.9211i	0.821505	−	1.13070i	−0.167941	−	0.985797i	$-0.553712\pi$
$797$	23.1921	−	31.9211i	0.821505	−	1.13070i	0.989445	−	0.144907i	$-0.0462883\pi$
$798$	1.21969	+	0.396301i	0.0431765	+	0.0140289i
$799$	18.7409			0.663004
$800$		0			0
$801$	−1.38077			−0.0487872
$802$	−2.27332	−	0.738645i	−0.0802736	−	0.0260825i
$803$	−17.1909	+	23.6612i	−0.606653	+	0.834986i
$804$	−15.8820	−	11.5389i	−0.560114	−	0.406947i
$805$		0			0
$806$	−8.59125	+	6.24191i	−0.302614	+	0.219862i
$807$			2.63211i			0.0926547i
$808$	−6.41650	−	8.83156i	−0.225732	−	0.310693i
$809$	1.84237	+	5.67024i	0.0647744	+	0.199355i	0.978206	−	0.207638i	$-0.0665775\pi$
$809$	1.84237	+	5.67024i	0.0647744	+	0.199355i	−0.913431	+	0.406993i	$0.866577\pi$
$810$		0			0
$811$	−12.1062	+	37.2590i	−0.425105	+	1.30834i	0.477788	+	0.878475i	$0.341439\pi$
$811$	−12.1062	+	37.2590i	−0.425105	+	1.30834i	−0.902893	+	0.429865i	$0.858561\pi$
$812$	−7.39386	+	2.40241i	−0.259474	+	0.0843081i
$813$	4.34011	−	1.41019i	0.152214	−	0.0494574i
$814$	0.250378	−	0.770586i	0.00877576	−	0.0270090i
$815$		0			0
$816$	−6.56505	−	20.2051i	−0.229823	−	0.707322i
$817$	−9.50897	−	13.0880i	−0.332677	−	0.457890i
$818$			0.374544i			0.0130956i
$819$	4.72175	−	3.43055i	0.164991	−	0.119873i
$820$		0			0
$821$	−16.6923	−	12.1277i	−0.582567	−	0.423260i	0.257082	−	0.966390i	$-0.417239\pi$
$821$	−16.6923	−	12.1277i	−0.582567	−	0.423260i	−0.839649	+	0.543130i	$0.817239\pi$
$822$	−1.52214	+	2.09505i	−0.0530909	+	0.0730733i
$823$	37.1066	+	12.0567i	1.29345	+	0.420269i	0.873300	−	0.487183i	$-0.161976\pi$
$823$	37.1066	+	12.0567i	1.29345	+	0.420269i	0.420155	+	0.907452i	$0.361976\pi$
$824$	−0.700803			−0.0244136
$825$		0			0
$826$	1.96673			0.0684314
$827$	−18.6384	−	6.05598i	−0.648120	−	0.210587i	−0.0335352	−	0.999438i	$-0.510677\pi$
$827$	−18.6384	−	6.05598i	−0.648120	−	0.210587i	−0.614585	+	0.788850i	$0.710677\pi$
$828$	−1.82988	+	2.51861i	−0.0635927	+	0.0875279i
$829$	−7.01831	−	5.09910i	−0.243756	−	0.177099i	0.459199	−	0.888333i	$-0.348136\pi$
$829$	−7.01831	−	5.09910i	−0.243756	−	0.177099i	−0.702955	+	0.711234i	$0.748136\pi$
$830$		0			0
$831$	1.01876	−	0.740173i	0.0353404	−	0.0256763i
$832$		−	30.7816i		−	1.06716i
$833$	18.6902	+	25.7248i	0.647575	+	0.891311i
$834$	0.949404	+	2.92196i	0.0328752	+	0.101179i
$835$		0			0
$836$	−6.41884	+	19.7551i	−0.222000	+	0.683246i
$837$	8.74318	−	2.84083i	0.302208	−	0.0981935i
$838$	7.17235	−	2.33044i	0.247765	−	0.0805036i
$839$	1.19256	−	3.67033i	0.0411718	−	0.126714i	−0.928358	−	0.371687i	$-0.878779\pi$
$839$	1.19256	−	3.67033i	0.0411718	−	0.126714i	0.969530	+	0.244974i	$0.0787793\pi$
$840$		0			0
$841$	−5.76596	−	17.7458i	−0.198826	−	0.611925i
$842$	−1.01117	−	1.39176i	−0.0348473	−	0.0479632i
$843$		−	13.4167i		−	0.462094i
$844$	−5.16724	+	3.75422i	−0.177864	+	0.129226i
$845$		0			0
$846$	0.640724	+	0.465513i	0.0220286	+	0.0160047i
$847$	−3.22193	+	4.43461i	−0.110707	+	0.152375i
$848$	−46.1406	−	14.9920i	−1.58447	−	0.514827i
$849$	24.0890			0.826732
$850$		0			0
$851$	−2.05144			−0.0703224
$852$	−25.5959	−	8.31661i	−0.876901	−	0.284922i
$853$	−17.5100	+	24.1004i	−0.599531	+	0.825183i	−0.995665	−	0.0930093i	$-0.970351\pi$
$853$	−17.5100	+	24.1004i	−0.599531	+	0.825183i	0.396135	+	0.918192i	$0.370351\pi$
$854$	−0.952493	−	0.692027i	−0.0325936	−	0.0236807i
$855$		0			0
$856$	1.66450	−	1.20933i	0.0568913	−	0.0413340i
$857$		−	36.2041i		−	1.23671i	−0.785899	−	0.618354i	$-0.787800\pi$
$857$		−	36.2041i		−	1.23671i	0.785899	−	0.618354i	$-0.212200\pi$
$858$	−1.74477	−	2.40147i	−0.0595656	−	0.0819850i
$859$	11.6355	+	35.8104i	0.396998	+	1.22184i	0.927394	+	0.374086i	$0.122043\pi$
$859$	11.6355	+	35.8104i	0.396998	+	1.22184i	−0.530396	+	0.847750i	$0.677957\pi$
$860$		0			0
$861$	3.35028	−	10.3111i	0.114177	−	0.351401i
$862$	2.56912	−	0.834757i	0.0875045	−	0.0284319i
$863$	2.37682	−	0.772275i	0.0809078	−	0.0262885i	−0.268283	−	0.963340i	$-0.586456\pi$
$863$	2.37682	−	0.772275i	0.0809078	−	0.0262885i	0.349191	+	0.937051i	$0.386456\pi$
$864$	0.878171	−	2.70273i	0.0298760	−	0.0919488i
$865$		0			0
$866$	0.796028	+	2.44992i	0.0270501	+	0.0832518i
$867$	−10.0485	−	13.8306i	−0.341266	−	0.469712i
$868$		−	22.2253i		−	0.754376i
$869$	23.8728	−	17.3446i	0.809830	−	0.588376i
$870$		0			0
$871$	−38.3411	−	27.8565i	−1.29914	−	0.943881i
$872$	1.27684	−	1.75741i	0.0432391	−	0.0595136i
$873$	0.0290149	+	0.00942751i	0.000982006	+	0.000319073i
$874$	−1.65143			−0.0558606
$875$		0			0
$876$	−22.0697			−0.745668
$877$	30.8609	+	10.0273i	1.04210	+	0.338599i	0.779563	−	0.626323i	$-0.215441\pi$
$877$	30.8609	+	10.0273i	1.04210	+	0.338599i	0.262537	+	0.964922i	$0.415441\pi$
$878$	2.23847	−	3.08100i	0.0755449	−	0.103979i
$879$	26.0283	+	18.9107i	0.877912	+	0.637841i
$880$		0			0
$881$	26.9099	−	19.5512i	0.906619	−	0.658697i	−0.0335388	−	0.999437i	$-0.510678\pi$
$881$	26.9099	−	19.5512i	0.906619	−	0.658697i	0.940157	+	0.340740i	$0.110678\pi$
$882$			1.34375i			0.0452464i
$883$	6.44974	+	8.87730i	0.217051	+	0.298745i	0.903633	−	0.428307i	$-0.140890\pi$
$883$	6.44974	+	8.87730i	0.217051	+	0.298745i	−0.686582	+	0.727052i	$0.740890\pi$
$884$	−16.3794	−	50.4105i	−0.550897	−	1.69549i
$885$		0			0
$886$	1.44197	−	4.43794i	0.0484440	−	0.149095i
$887$	−24.7324	+	8.03604i	−0.830432	+	0.269824i	−0.693227	−	0.720719i	$-0.743812\pi$
$887$	−24.7324	+	8.03604i	−0.830432	+	0.269824i	−0.137205	+	0.990543i	$0.543812\pi$
$888$	1.18123	−	0.383805i	0.0396395	−	0.0128797i
$889$	−6.03343	+	18.5690i	−0.202355	+	0.622784i
$890$		0			0
$891$	0.794084	+	2.44394i	0.0266028	+	0.0818751i
$892$	17.9780	+	24.7446i	0.601948	+	0.828511i
$893$		−	13.3791i		−	0.447715i
$894$	3.40731	−	2.47556i	0.113958	−	0.0827951i
$895$		0			0
$896$	−7.36940	−	5.35418i	−0.246194	−	0.178871i
$897$	−4.41757	+	6.08026i	−0.147498	+	0.203014i
$898$	−2.67893	−	0.870436i	−0.0893970	−	0.0290468i
$899$	−29.5626			−0.985969
$900$		0			0
$901$	−77.8608			−2.59392
$902$	−5.24420	−	1.70394i	−0.174613	−	0.0567351i
$903$	−2.84400	+	3.91442i	−0.0946423	+	0.130264i
$904$	2.47660	+	1.79936i	0.0823705	+	0.0598457i
$905$		0			0
$906$	−0.314452	+	0.228463i	−0.0104470	+	0.00759018i
$907$			55.0108i			1.82660i	0.407283	+	0.913302i	$0.366476\pi$
$907$			55.0108i			1.82660i	−0.407283	+	0.913302i	$0.633524\pi$
$908$	15.4333	+	21.2421i	0.512172	+	0.704944i
$909$	3.47049	+	10.6811i	0.115109	+	0.354269i
$910$		0			0
$911$	−3.74142	+	11.5149i	−0.123959	+	0.381506i	−0.993710	−	0.111985i	$-0.964279\pi$
$911$	−3.74142	+	11.5149i	−0.123959	+	0.381506i	0.869751	+	0.493490i	$0.164279\pi$
$912$	−14.4245	+	4.68680i	−0.477642	+	0.155195i
$913$	6.92195	−	2.24908i	0.229083	−	0.0744336i
$914$	2.59060	−	7.97306i	0.0856895	−	0.263725i
$915$		0			0
$916$	8.85816	+	27.2626i	0.292682	+	0.900782i
$917$	10.9605	+	15.0858i	0.361946	+	0.498176i
$918$		−	1.44086i		−	0.0475555i
$919$	4.83138	−	3.51020i	0.159372	−	0.115791i	−0.505241	−	0.862978i	$-0.668596\pi$
$919$	4.83138	−	3.51020i	0.159372	−	0.115791i	0.664613	+	0.747188i	$0.268596\pi$
$920$		0			0
$921$	16.4200	+	11.9298i	0.541056	+	0.393100i
$922$	3.58117	−	4.92906i	0.117940	−	0.162330i
$923$	−61.7918	−	20.0774i	−2.03390	−	0.660855i
$924$	6.21254			0.204378
$925$		0			0
$926$	−3.36370			−0.110538
$927$	0.685696	+	0.222796i	0.0225212	+	0.00731758i
$928$	−5.37150	+	7.39324i	−0.176328	+	0.242695i
$929$	37.9232	+	27.5528i	1.24422	+	0.903979i	0.997872	−	0.0652030i	$-0.0207695\pi$
$929$	37.9232	+	27.5528i	1.24422	+	0.903979i	0.246348	+	0.969182i	$0.420770\pi$
$930$		0			0
$931$	18.3650	−	13.3429i	0.601887	−	0.437297i
$932$			1.00636i			0.0329644i
$933$	−11.0048	−	15.1468i	−0.360280	−	0.495882i
$934$	−0.722201	−	2.22271i	−0.0236311	−	0.0727291i
$935$		0			0
$936$	1.40610	−	4.32753i	0.0459598	−	0.141450i
$937$	−18.4823	+	6.00528i	−0.603792	+	0.196184i	−0.594931	−	0.803777i	$-0.702821\pi$
$937$	−18.4823	+	6.00528i	−0.603792	+	0.196184i	−0.00886093	+	0.999961i	$0.502821\pi$
$938$	−2.96214	+	0.962459i	−0.0967174	+	0.0314254i
$939$	7.68955	−	23.6660i	0.250939	−	0.772311i
$940$		0			0
$941$	6.70867	+	20.6472i	0.218696	+	0.673078i	0.998870	+	0.0475159i	$0.0151305\pi$
$941$	6.70867	+	20.6472i	0.218696	+	0.673078i	−0.780174	+	0.625563i	$0.784870\pi$
$942$	1.33446	+	1.83673i	0.0434792	+	0.0598440i
$943$			13.9610i			0.454633i
$944$	−18.8172	+	13.6715i	−0.612447	+	0.444969i
$945$		0			0
$946$	1.99087	+	1.44645i	0.0647287	+	0.0470282i
$947$	3.71222	−	5.10943i	0.120631	−	0.166034i	−0.744431	−	0.667699i	$-0.767279\pi$
$947$	3.71222	−	5.10943i	0.120631	−	0.166034i	0.865062	+	0.501665i	$0.167279\pi$
$948$	21.1773	+	6.88092i	0.687807	+	0.223482i
$949$	−53.2792			−1.72952
$950$		0			0
$951$	25.1880			0.816778
$952$	−6.72990	−	2.18668i	−0.218117	−	0.0708707i
$953$	12.8147	−	17.6380i	0.415110	−	0.571350i	−0.549345	−	0.835595i	$-0.685123\pi$
$953$	12.8147	−	17.6380i	0.415110	−	0.571350i	0.964455	+	0.264245i	$0.0851229\pi$
$954$	−2.66195	−	1.93402i	−0.0861839	−	0.0626163i
$955$		0			0
$956$	12.9115	−	9.38076i	0.417588	−	0.303395i
$957$		−	8.26351i		−	0.267121i
$958$	3.73171	+	5.13625i	0.120566	+	0.165945i
$959$	−4.04324	−	12.4438i	−0.130563	−	0.401831i
$960$		0			0
$961$	16.5366	−	50.8943i	0.533437	−	1.64175i
$962$	1.40378	−	0.456116i	0.0452597	−	0.0147058i
$963$	−2.01308	+	0.654089i	−0.0648705	+	0.0210777i
$964$	−0.767705	+	2.36275i	−0.0247261	+	0.0760992i
$965$		0			0
$966$	0.152630	+	0.469746i	0.00491078	+	0.0151138i
$967$	−4.12195	−	5.67338i	−0.132553	−	0.182444i	0.737581	−	0.675259i	$-0.235968\pi$
$967$	−4.12195	−	5.67338i	−0.132553	−	0.182444i	−0.870134	+	0.492815i	$0.835968\pi$
$968$			4.27353i			0.137356i
$969$	−19.6922	+	14.3072i	−0.632604	+	0.459614i
$970$		0			0
$971$	−5.99504	−	4.35565i	−0.192390	−	0.139779i	0.487420	−	0.873167i	$-0.337938\pi$
$971$	−5.99504	−	4.35565i	−0.192390	−	0.139779i	−0.679810	+	0.733388i	$0.737938\pi$
$972$	−1.13978	+	1.56877i	−0.0365585	+	0.0503184i
$973$	−14.7633	−	4.79690i	−0.473291	−	0.153781i
$974$	7.00909			0.224586
$975$		0			0
$976$	13.9237			0.445688
$977$	−37.3370	−	12.1315i	−1.19452	−	0.388122i	−0.356776	−	0.934190i	$-0.616124\pi$
$977$	−37.3370	−	12.1315i	−1.19452	−	0.388122i	−0.837741	+	0.546068i	$0.816124\pi$
$978$	0.664399	−	0.914467i	0.0212451	−	0.0292414i
$979$	−2.87054	−	2.08557i	−0.0917430	−	0.0666552i
$980$		0			0
$981$	−1.80802	+	1.31360i	−0.0577256	+	0.0419401i
$982$			1.50597i			0.0480573i
$983$	10.8051	+	14.8719i	0.344629	+	0.474341i	0.945786	−	0.324790i	$-0.105294\pi$
$983$	10.8051	+	14.8719i	0.344629	+	0.474341i	−0.601158	+	0.799131i	$0.705294\pi$
$984$	−2.61198	−	8.03883i	−0.0832667	−	0.256269i
$985$		0			0
$986$	−1.43181	+	4.40665i	−0.0455980	+	0.140336i
$987$	−3.80566	+	1.23653i	−0.121135	+	0.0393593i
$988$	−35.9881	+	11.6932i	−1.14493	+	0.372012i
$989$	1.92536	−	5.92564i	0.0612228	−	0.188424i
$990$		0			0
$991$	16.2128	+	49.8980i	0.515018	+	1.58506i	0.783250	+	0.621707i	$0.213560\pi$
$991$	16.2128	+	49.8980i	0.515018	+	1.58506i	−0.268233	+	0.963354i	$0.586440\pi$
$992$	−15.3560	−	21.1357i	−0.487554	−	0.671060i
$993$		−	30.4193i		−	0.965326i
$994$	−3.45442	+	2.50978i	−0.109567	+	0.0796054i
$995$		0			0
$996$	4.44322	+	3.22819i	0.140789	+	0.102289i
$997$	21.3789	−	29.4256i	0.677077	−	0.931917i	−0.322817	−	0.946461i	$-0.604630\pi$
$997$	21.3789	−	29.4256i	0.677077	−	0.931917i	0.999894	+	0.0145444i	$0.00462980\pi$
$998$	−4.76785	−	1.54917i	−0.150924	−	0.0490381i
$999$	−1.27778			−0.0404273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.d.274.3		24
5.2	odd	4		75.2.g.c.46.2	yes	12
5.3	odd	4		375.2.g.c.226.2		12
5.4	even	2	inner	375.2.i.d.274.4		24
15.2	even	4		225.2.h.d.46.2		12
25.6	even	5	inner	375.2.i.d.349.4		24
25.8	odd	20		375.2.g.c.151.2		12
25.9	even	10		1875.2.b.f.1249.8		12
25.12	odd	20		1875.2.a.j.1.4		6
25.13	odd	20		1875.2.a.k.1.3		6
25.16	even	5		1875.2.b.f.1249.5		12
25.17	odd	20		75.2.g.c.31.2	✓	12
25.19	even	10	inner	375.2.i.d.349.3		24
75.17	even	20		225.2.h.d.181.2		12
75.38	even	20		5625.2.a.q.1.4		6
75.62	even	20		5625.2.a.p.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.2	✓	12	25.17	odd	20
75.2.g.c.46.2	yes	12	5.2	odd	4
225.2.h.d.46.2		12	15.2	even	4
225.2.h.d.181.2		12	75.17	even	20
375.2.g.c.151.2		12	25.8	odd	20
375.2.g.c.226.2		12	5.3	odd	4
375.2.i.d.274.3		24	1.1	even	1	trivial
375.2.i.d.274.4		24	5.4	even	2	inner
375.2.i.d.349.3		24	25.19	even	10	inner
375.2.i.d.349.4		24	25.6	even	5	inner
1875.2.a.j.1.4		6	25.12	odd	20
1875.2.a.k.1.3		6	25.13	odd	20
1875.2.b.f.1249.5		12	25.16	even	5
1875.2.b.f.1249.8		12	25.9	even	10
5625.2.a.p.1.3		6	75.62	even	20
5625.2.a.q.1.4		6	75.38	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)

\(f(q)\)	\(=\)	\(q+(-0.234682 - 0.0762527i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-1.56877 - 1.13978i) q^{4} +(0.199632 - 0.145041i) q^{6} +1.24676i q^{7} +(0.571334 + 0.786373i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.234682 - 0.0762527i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-1.56877 - 1.13978i) q^{4} +(0.199632 - 0.145041i) q^{6} +1.24676i q^{7} +(0.571334 + 0.786373i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(0.794084 - 2.44394i) q^{11} +(1.84420 - 0.599218i) q^{12} +(4.45215 - 1.44659i) q^{13} +(0.0950687 - 0.292592i) q^{14} +(1.12432 + 3.46029i) q^{16} +(3.43216 + 4.72397i) q^{17} +0.246759i q^{18} +(3.37244 - 2.45022i) q^{19} +(-1.00865 - 0.732827i) q^{21} +(-0.372714 + 0.512997i) q^{22} +(1.52689 + 0.496117i) q^{23} -0.972011 q^{24} -1.15514 q^{26} +(0.951057 + 0.309017i) q^{27} +(1.42103 - 1.95588i) q^{28} +(-2.60158 - 1.89016i) q^{29} +(7.43739 - 5.40358i) q^{31} -2.84182i q^{32} +(1.51044 + 2.07894i) q^{33} +(-0.445250 - 1.37034i) q^{34} +(-0.599218 + 1.84420i) q^{36} +(-1.21524 + 0.394857i) q^{37} +(-0.978287 + 0.317865i) q^{38} +(-1.44659 + 4.45215i) q^{39} +(2.68719 + 8.27031i) q^{41} +(0.180832 + 0.248893i) q^{42} -3.88086i q^{43} +(-4.03129 + 2.92891i) q^{44} +(-0.320503 - 0.232859i) q^{46} +(1.88651 - 2.59656i) q^{47} +(-3.46029 - 1.12432i) q^{48} +5.44559 q^{49} -5.83914 q^{51} +(-8.63320 - 2.80510i) q^{52} +(-7.83770 + 10.7877i) q^{53} +(-0.199632 - 0.145041i) q^{54} +(-0.980418 + 0.712315i) q^{56} +4.16857i q^{57} +(0.466414 + 0.641964i) q^{58} +(1.97548 + 6.07990i) q^{59} +(1.18258 - 3.63961i) q^{61} +(-2.15746 + 0.701000i) q^{62} +(1.18574 - 0.385270i) q^{63} +(2.03194 - 6.25366i) q^{64} +(-0.195947 - 0.603064i) q^{66} +(-5.95063 - 8.19034i) q^{67} -11.3227i q^{68} +(-1.29885 + 0.943670i) q^{69} +(-11.2284 - 8.15794i) q^{71} +(0.571334 - 0.786373i) q^{72} +(-10.8243 - 3.51704i) q^{73} +0.315305 q^{74} -8.08332 q^{76} +(3.04700 + 0.990032i) q^{77} +(0.678976 - 0.934531i) q^{78} +(9.29008 + 6.74964i) q^{79} +(-0.809017 + 0.587785i) q^{81} -2.14580i q^{82} +(1.66478 + 2.29137i) q^{83} +(0.747080 + 2.29928i) q^{84} +(-0.295926 + 0.910766i) q^{86} +(3.05835 - 0.993717i) q^{87} +(2.37554 - 0.771858i) q^{88} +(0.426682 - 1.31319i) q^{89} +(1.80355 + 5.55075i) q^{91} +(-1.82988 - 2.51861i) q^{92} +9.19312i q^{93} +(-0.640724 + 0.465513i) q^{94} +(2.29908 + 1.67038i) q^{96} +(-0.0179322 + 0.0246815i) q^{97} +(-1.27798 - 0.415241i) q^{98} -2.56971 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more