LMFDB - Embedded newform 375.2.i.d.349.3

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			349.3
Character	$\chi$	$=$	375.349
Dual form			375.2.i.d.274.3

$q$-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 $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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	−0.390811	−	0.920471i	$-0.627805\pi$
$2$	−0.234682	+	0.0762527i	−0.165945	+	0.0539188i	0.224866	+	0.974390i	$0.427805\pi$
$3$	−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	$-0.924289\pi$
$7$		−	1.24676i		−	0.471231i	0.971846	−	0.235615i	$-0.0757105\pi$
$8$	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	0.996503	+	0.0835513i	$0.0266262\pi$
$11$	0.794084	+	2.44394i	0.239425	+	0.736876i	−0.757078	+	0.653324i	$0.773374\pi$
$12$	1.84420	+	0.599218i	0.532376	+	0.172979i
$13$	4.45215	+	1.44659i	1.23480	+	0.401212i	0.852452	−	0.522805i	$-0.175115\pi$
$13$	4.45215	+	1.44659i	1.23480	+	0.401212i	0.382351	+	0.924017i	$0.375115\pi$
$14$	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	−0.155046	−	0.987907i	$-0.549553\pi$
$17$	3.43216	−	4.72397i	0.832422	−	1.14573i	0.987467	−	0.157823i	$-0.0504474\pi$
$18$		−	0.246759i		−	0.0581616i
$19$	3.37244	+	2.45022i	0.773692	+	0.562120i	0.903079	−	0.429474i	$-0.141301\pi$
$19$	3.37244	+	2.45022i	0.773692	+	0.562120i	−0.129387	+	0.991594i	$0.541301\pi$
$20$		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	−0.145468	−	0.989363i	$-0.546469\pi$
$23$	1.52689	−	0.496117i	0.318379	−	0.103447i	0.463847	+	0.885915i	$0.346469\pi$
$24$	−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	−0.802525	−	0.596618i	$-0.796511\pi$
$29$	−2.60158	+	1.89016i	−0.483102	+	0.350994i	0.319423	+	0.947612i	$0.396511\pi$
$30$		0			0
$31$	7.43739	+	5.40358i	1.33579	+	0.970512i	0.999587	+	0.0287236i	$0.00914425\pi$
$31$	7.43739	+	5.40358i	1.33579	+	0.970512i	0.336207	+	0.941788i	$0.390856\pi$
$32$			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	0.207415	−	0.978253i	$-0.433495\pi$
$37$	−1.21524	−	0.394857i	−0.199785	−	0.0649141i	−0.407200	+	0.913339i	$0.633495\pi$
$38$	−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	−0.488340	−	0.872654i	$-0.662397\pi$
$41$	2.68719	−	8.27031i	0.419668	−	1.29161i	0.908008	−	0.418953i	$-0.137603\pi$
$42$	0.180832	−	0.248893i	0.0279029	−	0.0384051i
$43$			3.88086i			0.591825i	0.955215	+	0.295913i	$0.0956237\pi$
$43$			3.88086i			0.591825i	−0.955215	+	0.295913i	$0.904376\pi$
$44$	−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	0.924129	−	0.382082i	$-0.124793\pi$
$47$	1.88651	+	2.59656i	0.275176	+	0.378747i	−0.648953	+	0.760829i	$0.724793\pi$
$48$	−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	−0.863219	−	0.504829i	$-0.831556\pi$
$53$	−7.83770	−	10.7877i	−1.07659	−	1.48180i	−0.213371	−	0.976971i	$-0.568444\pi$
$54$	−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	−0.736206	−	0.676758i	$-0.763384\pi$
$59$	1.97548	−	6.07990i	0.257186	−	0.791536i	0.993391	−	0.114778i	$-0.0366157\pi$
$60$		0			0
$61$	1.18258	+	3.63961i	0.151414	+	0.466005i	0.997780	−	0.0665973i	$-0.0212143\pi$
$61$	1.18258	+	3.63961i	0.151414	+	0.466005i	−0.846366	+	0.532602i	$0.821214\pi$
$62$	−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	0.272277	+	0.962219i	$0.412223\pi$
$67$	−5.95063	+	8.19034i	−0.726985	+	1.00061i	−0.999263	+	0.0383907i	$0.987777\pi$
$68$			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	−0.332888	+	0.942966i	$0.608023\pi$
$71$	−11.2284	+	8.15794i	−1.33257	+	0.968169i	−0.999682	+	0.0252028i	$0.991977\pi$
$72$	0.571334	+	0.786373i	0.0673323	+	0.0926750i
$73$	−10.8243	+	3.51704i	−1.26689	+	0.411638i	−0.863946	−	0.503585i	$-0.832014\pi$
$73$	−10.8243	+	3.51704i	−1.26689	+	0.411638i	−0.402947	+	0.915223i	$0.632014\pi$
$74$	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	0.0739188	−	0.997264i	$-0.476449\pi$
$79$	9.29008	−	6.74964i	1.04522	−	0.759394i	0.971297	+	0.237871i	$0.0764494\pi$
$80$		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	−0.707817	−	0.706396i	$-0.750320\pi$
$83$	1.66478	−	2.29137i	0.182733	−	0.251511i	0.890550	+	0.454885i	$0.150320\pi$
$84$	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	0.971121	−	0.238589i	$-0.0766850\pi$
$89$	0.426682	+	1.31319i	0.0452282	+	0.139198i	−0.925892	+	0.377788i	$0.876685\pi$
$90$		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	0.808106	−	0.589038i	$-0.200493\pi$
$97$	−0.0179322	−	0.0246815i	−0.00182074	−	0.00250603i	−0.809926	+	0.586532i	$0.800493\pi$
$98$	−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	0.787628	−	0.616151i	$-0.211309\pi$
$103$	−0.423783	−	0.583288i	−0.0417566	−	0.0574730i	−0.829385	+	0.558678i	$0.811309\pi$
$104$	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	$0.0326244\pi$
$107$			2.11668i			0.204627i	−0.994752	+	0.102313i	$0.967376\pi$
$108$	−1.13978	+	1.56877i	−0.109675	+	0.150955i
$109$	−0.690602	+	2.12545i	−0.0661477	+	0.203582i	−0.978667	−	0.205451i	$-0.934134\pi$
$109$	−0.690602	+	2.12545i	−0.0661477	+	0.203582i	0.912520	+	0.409033i	$0.134134\pi$
$110$		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	0.446493	−	0.894787i	$-0.352673\pi$
$113$	2.99525	+	0.973217i	0.281770	+	0.0915526i	−0.164723	+	0.986340i	$0.552673\pi$
$114$	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	0.438564	−	0.898700i	$-0.355487\pi$
$127$	14.8938	−	4.83929i	1.32161	−	0.429418i	0.883048	+	0.469282i	$0.155487\pi$
$128$	−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	0.973565	−	0.228411i	$-0.0733530\pi$
$131$	12.1000	+	8.79116i	1.05718	+	0.768087i	0.0836161	+	0.996498i	$0.473353\pi$
$132$			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	−0.150139	−	0.988665i	$-0.547972\pi$
$137$	−9.98092	−	3.24300i	−0.852727	−	0.277068i	−0.702588	+	0.711597i	$0.747972\pi$
$138$	0.376774	+	0.122421i	0.0320731	+	0.0104212i
$139$	−3.84749	−	11.8414i	−0.326340	−	1.00437i	−0.970832	−	0.239761i	$-0.922931\pi$
$139$	−3.84749	−	11.8414i	−0.326340	−	1.00437i	0.644492	−	0.764611i	$-0.277069\pi$
$140$		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	$-0.880336\pi$
$157$		−	9.20058i		−	0.734286i	0.930164	−	0.367143i	$-0.119664\pi$
$158$	−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	0.474620	−	0.880191i	$-0.342586\pi$
$163$	4.35656	+	1.41553i	0.341232	+	0.110873i	−0.133388	+	0.991064i	$0.542586\pi$
$164$	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	−0.805763	−	0.592238i	$-0.798245\pi$
$167$	0.0837776	−	0.115310i	0.00648291	−	0.00892296i	0.812246	+	0.583315i	$0.198245\pi$
$168$			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	0.781445	−	0.623974i	$-0.214483\pi$
$173$	23.4176	−	7.60885i	1.78041	−	0.578490i	0.998965	+	0.0454831i	$0.0144827\pi$
$174$	−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	−0.477446	+	0.878661i	$0.658437\pi$
$179$	−19.5420	+	14.1981i	−1.46064	+	1.06122i	−0.983195	+	0.182557i	$0.941563\pi$
$180$		0			0
$181$	−1.59218	−	1.15679i	−0.118346	−	0.0859834i	0.527038	−	0.849842i	$-0.323303\pi$
$181$	−1.59218	−	1.15679i	−0.118346	−	0.0859834i	−0.645384	+	0.763858i	$0.723303\pi$
$182$			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	−0.999572	−	0.0292607i	$-0.990685\pi$
$191$	−2.40061	+	7.38832i	−0.173702	+	0.534600i	0.825870	+	0.563861i	$0.190685\pi$
$192$	3.86498	−	5.31968i	0.278931	−	0.383915i
$193$		−	14.3458i		−	1.03264i	−0.856397	−	0.516318i	$-0.827302\pi$
$193$		−	14.3458i		−	1.03264i	0.856397	−	0.516318i	$-0.172698\pi$
$194$	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	0.805579	−	0.592489i	$-0.201854\pi$
$197$	−0.0961264	−	0.132307i	−0.00684872	−	0.00942645i	−0.812428	+	0.583062i	$0.801854\pi$
$198$	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	0.979960	−	0.199196i	$-0.0638330\pi$
$211$	1.01784	+	3.13260i	0.0700713	+	0.215657i	−0.909888	+	0.414853i	$0.863833\pi$
$212$	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	−0.764685	−	0.644404i	$-0.777105\pi$
$223$	−15.0012	+	4.87419i	−1.00456	+	0.326400i	−0.239872	+	0.970805i	$0.577105\pi$
$224$	3.54307			0.236731
$225$		0			0
$226$	−0.777142			−0.0516947
$227$	−12.8779	+	4.18427i	−0.854734	+	0.277720i	−0.703428	−	0.710767i	$-0.748348\pi$
$227$	−12.8779	+	4.18427i	−0.854734	+	0.277720i	−0.151307	+	0.988487i	$0.548348\pi$
$228$	4.75125	+	6.53954i	0.314660	+	0.433092i
$229$	−11.9596	+	8.68915i	−0.790312	+	0.574195i	−0.908056	−	0.418849i	$-0.862434\pi$
$229$	−11.9596	+	8.68915i	−0.790312	+	0.574195i	0.117744	+	0.993044i	$0.462434\pi$
$230$		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	−0.818892	−	0.573947i	$-0.805411\pi$
$233$	−0.305049	+	0.419864i	−0.0199844	+	0.0275062i	0.798908	+	0.601453i	$0.205411\pi$
$234$	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	0.834487	−	0.551027i	$-0.185764\pi$
$239$	−2.54331	−	7.82750i	−0.164513	−	0.506319i	−0.999000	+	0.0447086i	$0.985764\pi$
$240$		0			0
$241$	−0.395906	+	1.21847i	−0.0255025	+	0.0784888i	−0.962998	−	0.269509i	$-0.913138\pi$
$241$	−0.395906	+	1.21847i	−0.0255025	+	0.0784888i	0.937495	+	0.347998i	$0.113138\pi$
$242$	−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	$-0.806647\pi$
$257$		−	18.3001i		−	1.14153i	0.821113	−	0.570766i	$-0.193353\pi$
$258$	−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	−0.223606	−	0.974680i	$-0.571783\pi$
$263$	−15.8509	−	5.15027i	−0.977409	−	0.317579i	−0.753803	+	0.657100i	$0.771783\pi$
$264$	−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	0.650807	−	0.759244i	$-0.274431\pi$
$269$	2.12942	+	1.54712i	0.129833	+	0.0943294i	−0.520973	+	0.853573i	$0.674431\pi$
$270$		0			0
$271$	−3.69192	+	2.68233i	−0.224268	+	0.162940i	−0.694246	−	0.719738i	$-0.744262\pi$
$271$	−3.69192	+	2.68233i	−0.224268	+	0.162940i	0.469978	+	0.882678i	$0.344262\pi$
$272$	−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	−0.344775	−	0.938685i	$-0.612045\pi$
$277$	−1.19762	+	0.389132i	−0.0719583	+	0.0233807i	0.272817	+	0.962066i	$0.412045\pi$
$278$	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	0.214910	−	0.976634i	$-0.431054\pi$
$281$	−10.8543	−	7.88611i	−0.647513	−	0.470446i	−0.862423	+	0.506188i	$0.831054\pi$
$282$			0.791979i			0.0471617i
$283$	−14.1591	+	19.4884i	−0.841674	+	1.15846i	0.143962	+	0.989583i	$0.454016\pi$
$283$	−14.1591	+	19.4884i	−0.841674	+	1.15846i	−0.985636	+	0.168882i	$0.945984\pi$
$284$	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	$0.388966\pi$
$293$			32.1727i			1.87955i	−0.341792	+	0.939776i	$0.611034\pi$
$294$	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	$0.196628\pi$
$307$			20.2962i			1.15837i	−0.815198	+	0.579183i	$0.803372\pi$
$308$	−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	−0.970037	−	0.242959i	$-0.921882\pi$
$311$	−5.78554	−	17.8061i	−0.328068	−	1.00969i	0.641969	−	0.766731i	$-0.278118\pi$
$312$	−4.32753	−	1.40610i	−0.244998	−	0.0796048i
$313$	−23.6660	−	7.68955i	−1.33768	−	0.434639i	−0.449151	−	0.893456i	$-0.648274\pi$
$313$	−23.6660	−	7.68955i	−1.33768	−	0.434639i	−0.888531	+	0.458817i	$0.848274\pi$
$314$	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	0.156094	+	0.987742i	$0.450110\pi$
$317$	−14.8052	+	20.3775i	−0.831540	+	1.14452i	−0.987634	+	0.156775i	$0.949890\pi$
$318$		−	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	−0.998874	−	0.0474508i	$-0.984890\pi$
$331$	−24.6097	−	17.8800i	−1.35267	−	0.982773i	−0.353797	−	0.935322i	$-0.615110\pi$
$332$			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	0.188111	−	0.982148i	$-0.439763\pi$
$337$	−4.35066	−	1.41361i	−0.236995	−	0.0770045i	−0.425107	+	0.905143i	$0.639763\pi$
$338$	−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	0.987220	−	0.159363i	$-0.0509442\pi$
$347$	9.88377	+	13.6038i	0.530589	+	0.730293i	−0.456631	+	0.889656i	$0.650944\pi$
$348$	−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	−0.997991	−	0.0633526i	$-0.979821\pi$
$353$	−14.0883	−	19.3909i	−0.749847	−	1.03208i	0.248144	−	0.968723i	$-0.420179\pi$
$354$	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	−0.904819	−	0.425797i	$-0.859994\pi$
$359$	1.46789	−	4.51771i	0.0774724	−	0.238435i	0.982291	+	0.187362i	$0.0599937\pi$
$360$		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	−0.987576	−	0.157141i	$-0.949772\pi$
$367$	−10.2098	+	14.0526i	−0.532948	+	0.733540i	0.454628	+	0.890681i	$0.349772\pi$
$368$		−	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	−0.256634	−	0.966509i	$-0.582614\pi$
$373$	2.00556	−	0.651645i	0.103844	−	0.0337409i	0.360478	+	0.932768i	$0.382614\pi$
$374$	−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	−0.299299	−	0.954159i	$-0.596753\pi$
$379$	10.0391	−	7.29380i	0.515671	−	0.374657i	0.814971	+	0.579502i	$0.196753\pi$
$380$		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	−0.0751836	+	0.997170i	$0.523954\pi$
$383$	−19.5766	+	26.9448i	−1.00032	+	1.37682i	−0.925132	+	0.379646i	$0.876046\pi$
$384$	−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	0.991461	+	0.130405i	$0.0416278\pi$
$389$	5.24639	+	16.1467i	0.266002	+	0.818671i	−0.725459	+	0.688266i	$0.758372\pi$
$390$		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	0.821608	−	0.570053i	$-0.193078\pi$
$397$	0.509357	+	0.701070i	0.0255639	+	0.0351857i	−0.796044	+	0.605239i	$0.793078\pi$
$398$	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	−0.961983	−	0.273109i	$-0.911948\pi$
$409$	−0.469043	+	1.44357i	−0.0231927	+	0.0713797i	0.938790	+	0.344489i	$0.111948\pi$
$410$		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	−0.212866	−	0.977081i	$-0.568280\pi$
$419$	−24.7252	−	17.9639i	−1.20790	−	0.877594i	−0.995039	+	0.0994875i	$0.968280\pi$
$420$		0			0
$421$	5.64016	−	4.09782i	0.274885	−	0.199715i	−0.441799	−	0.897114i	$-0.645659\pi$
$421$	5.64016	−	4.09782i	0.274885	−	0.199715i	0.716683	+	0.697399i	$0.245659\pi$
$422$	−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	0.353686	−	0.935364i	$-0.384928\pi$
$431$	−8.85650	−	6.43463i	−0.426603	−	0.309945i	−0.780289	+	0.625419i	$0.784928\pi$
$432$		−	3.63837i		−	0.175051i
$433$	−6.13609	+	8.44561i	−0.294882	+	0.405870i	−0.930592	−	0.366058i	$-0.880707\pi$
$433$	−6.13609	+	8.44561i	−0.294882	+	0.405870i	0.635710	+	0.771928i	$0.280707\pi$
$434$	−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	−0.998015	−	0.0629758i	$-0.979941\pi$
$439$	−4.76917	−	14.6780i	−0.227620	−	0.700543i	0.770395	−	0.637567i	$-0.220059\pi$
$440$		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	$-0.851698\pi$
$443$		−	18.9105i		−	0.898463i	0.893415	−	0.449231i	$-0.148302\pi$
$444$	−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	$-0.707672\pi$
$457$		−	33.9739i		−	1.58923i	0.607112	−	0.794616i	$-0.292328\pi$
$458$	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	−0.955802	−	0.294012i	$-0.905009\pi$
$461$	−7.62985	−	23.4823i	−0.355358	−	1.09368i	0.600444	−	0.799667i	$-0.294991\pi$
$462$	0.751876	+	0.244299i	0.0349804	+	0.0113658i
$463$	12.9643	+	4.21237i	0.602504	+	0.195765i	0.594357	−	0.804202i	$-0.297407\pi$
$463$	12.9643	+	4.21237i	0.602504	+	0.195765i	0.00814689	+	0.999967i	$0.497407\pi$
$464$	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	−0.660548	−	0.750784i	$-0.729676\pi$
$467$	5.56700	−	7.66232i	0.257610	−	0.354570i	0.918158	+	0.396214i	$0.129676\pi$
$468$		−	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	−0.951056	−	0.309018i	$-0.900000\pi$
$479$	−20.8149	+	15.1229i	−0.951055	+	0.690982i	1.08775e−6		1.00000i	$0.500000\pi$
$480$		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	−0.375551	−	0.926802i	$-0.622547\pi$
$487$	−27.0144	−	8.77751i	−1.22414	−	0.397747i	−0.848588	+	0.529055i	$0.822547\pi$
$488$	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	−0.984551	−	0.175101i	$-0.943975\pi$
$491$	−1.88593	+	5.80429i	−0.0851107	+	0.261944i	0.899440	+	0.437045i	$0.143975\pi$
$492$	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	0.956465	−	0.291848i	$-0.0942703\pi$
$503$	8.59734	+	11.8332i	0.383336	+	0.527617i	−0.573128	+	0.819466i	$0.694270\pi$
$504$	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	−0.917228	−	0.398363i	$-0.869578\pi$
$509$	1.33058	−	4.09510i	0.0589768	−	0.181512i	0.976205	+	0.216851i	$0.0695785\pi$
$510$		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	0.411011	−	0.911630i	$-0.365176\pi$
$521$	32.0705	−	23.3006i	1.40503	−	1.02082i	0.994021	−	0.109186i	$-0.0348243\pi$
$522$	0.466414	+	0.641964i	0.0204144	+	0.0280980i
$523$	34.5114	−	11.2134i	1.50908	−	0.490329i	0.566428	−	0.824111i	$-0.308325\pi$
$523$	34.5114	−	11.2134i	1.50908	−	0.490329i	0.942650	+	0.333782i	$0.108325\pi$
$524$	−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	0.274211	+	0.961670i	$0.411583\pi$
$541$	−11.9294	+	36.7150i	−0.512886	+	1.57850i	−0.787096	+	0.616830i	$0.788417\pi$
$542$	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	0.658709	−	0.752398i	$-0.271103\pi$
$547$	−6.09063	−	8.38303i	−0.260416	−	0.358433i	−0.919125	+	0.393965i	$0.871103\pi$
$548$	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	$0.0865936\pi$
$557$			12.6830i			0.537398i	−0.963224	+	0.268699i	$0.913406\pi$
$558$	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	0.0347068	−	0.999398i	$-0.488950\pi$
$563$	−12.4486	−	4.04480i	−0.524646	−	0.170468i	−0.559353	+	0.828930i	$0.688950\pi$
$564$	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	0.543032	−	0.839712i	$-0.317276\pi$
$569$	−2.09376	−	1.52120i	−0.0877748	−	0.0637721i	−0.630807	+	0.775940i	$0.717276\pi$
$570$		0			0
$571$	8.55571	−	6.21609i	0.358045	−	0.260135i	−0.394191	−	0.919029i	$-0.628975\pi$
$571$	8.55571	−	6.21609i	0.358045	−	0.260135i	0.752236	+	0.658893i	$0.228975\pi$
$572$	−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	−0.308734	−	0.951148i	$-0.599905\pi$
$577$	0.0135910	−	0.00441597i	0.000565800	−	0.000183839i	0.309300	+	0.950965i	$0.399905\pi$
$578$	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	−0.171120	−	0.985250i	$-0.554739\pi$
$587$	−21.5309	−	6.99581i	−0.888675	−	0.288748i	−0.717555	+	0.696502i	$0.754739\pi$
$588$	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	$-0.915739\pi$
$593$		−	12.7423i		−	0.523264i	0.965168	−	0.261632i	$-0.0842606\pi$
$594$	−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	$0.190624\pi$
$607$			27.7763i			1.12741i	−0.825977	+	0.563703i	$0.809376\pi$
$608$	−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	0.377660	−	0.925944i	$-0.376729\pi$
$613$	3.43991	+	1.11769i	0.138937	+	0.0451433i	−0.238723	+	0.971088i	$0.576729\pi$
$614$	−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	0.173259	−	0.984876i	$-0.444570\pi$
$617$	26.2402	−	36.1166i	1.05639	−	1.45400i	0.883133	−	0.469122i	$-0.155430\pi$
$618$		−	0.177909i		−	0.00715655i
$619$	16.5917	+	12.0546i	0.666878	+	0.484515i	0.868979	−	0.494850i	$-0.164777\pi$
$619$	16.5917	+	12.0546i	0.666878	+	0.484515i	−0.202101	+	0.979365i	$0.564777\pi$
$620$		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	0.995704	−	0.0925923i	$-0.0295153\pi$
$631$	30.5288	+	22.1805i	1.21533	+	0.882991i	0.219629	+	0.975583i	$0.429515\pi$
$632$		−	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	−0.991335	−	0.131355i	$-0.958067\pi$
$641$	−2.83865	+	8.73646i	−0.112120	+	0.345070i	0.879216	+	0.476424i	$0.158067\pi$
$642$	−0.307005	+	0.422557i	−0.0121165	+	0.0166770i
$643$		−	3.42111i		−	0.134915i	−0.997722	−	0.0674577i	$-0.978511\pi$
$643$		−	3.42111i		−	0.134915i	0.997722	−	0.0674577i	$-0.0214888\pi$
$644$	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	0.769595	−	0.638532i	$-0.220458\pi$
$647$	−1.92050	−	2.64334i	−0.0755027	−	0.103920i	−0.845098	+	0.534611i	$0.820458\pi$
$648$	−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	0.929227	−	0.369509i	$-0.120474\pi$
$653$	7.42740	+	10.2229i	0.290656	+	0.400054i	−0.638571	+	0.769563i	$0.720474\pi$
$654$	−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	−0.880769	−	0.473546i	$-0.842974\pi$
$659$	2.82719	−	8.70118i	0.110131	−	0.338950i	0.990901	+	0.134596i	$0.0429737\pi$
$660$		0			0
$661$	1.97487	+	6.07804i	0.0768137	+	0.236408i	0.982089	−	0.188417i	$-0.0603356\pi$
$661$	1.97487	+	6.07804i	0.0768137	+	0.236408i	−0.905275	+	0.424825i	$0.860336\pi$
$662$	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	−0.852773	−	0.522282i	$-0.825081\pi$
$673$	−32.0566	+	10.4158i	−1.23569	+	0.401500i	−0.382918	+	0.923782i	$0.625081\pi$
$674$	1.12881			0.0434802
$675$		0			0
$676$	−17.2857			−0.664833
$677$	−8.75295	+	2.84401i	−0.336403	+	0.109304i	−0.472347	−	0.881412i	$-0.656593\pi$
$677$	−8.75295	+	2.84401i	−0.336403	+	0.109304i	0.135944	+	0.990716i	$0.456593\pi$
$678$	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	−0.996759	−	0.0804402i	$-0.974367\pi$
$683$	−16.0005	+	22.0227i	−0.612241	+	0.842677i	0.384519	+	0.923117i	$0.374367\pi$
$684$	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	−0.607923	−	0.793996i	$-0.707997\pi$
$691$	9.21607	−	28.3642i	0.350596	−	1.07902i	0.958519	−	0.285028i	$-0.0920028\pi$
$692$	−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	−0.999274	−	0.0381042i	$-0.987868\pi$
$709$	−4.48525	+	13.8042i	−0.168447	+	0.518427i	0.830827	+	0.556531i	$0.187868\pi$
$710$		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	0.971921	−	0.235306i	$-0.0756091\pi$
$719$	28.1139	+	20.4260i	1.04847	+	0.761760i	0.0765512	+	0.997066i	$0.475609\pi$
$720$		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	−0.941066	−	0.338223i	$-0.890174\pi$
$727$	−40.5415	+	13.1727i	−1.50360	+	0.488550i	−0.562536	+	0.826773i	$0.690174\pi$
$728$	−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	−0.829787	−	0.558081i	$-0.811538\pi$
$733$	−1.15341	+	1.58754i	−0.0426023	+	0.0586370i	0.787184	+	0.616718i	$0.211538\pi$
$734$	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	0.855904	−	0.517135i	$-0.173002\pi$
$739$	−3.81947	−	11.7551i	−0.140501	−	0.432419i	−0.996405	+	0.0847164i	$0.973002\pi$
$740$		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	$-0.949354\pi$
$743$		−	8.63742i		−	0.316876i	0.987369	−	0.158438i	$-0.0506458\pi$
$744$	−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	$-0.969971\pi$
$757$		−	5.18352i		−	0.188398i	0.995553	−	0.0941991i	$-0.0300290\pi$
$758$	−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	0.958735	+	0.284302i	$0.0917618\pi$
$761$	9.66099	+	29.7335i	0.350211	+	1.07784i	−0.608524	+	0.793535i	$0.708238\pi$
$762$	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	−0.289380	−	0.957214i	$-0.593449\pi$
$769$	−35.7497	−	25.9737i	−1.28917	−	0.936636i	−0.999788	+	0.0205786i	$0.993449\pi$
$770$		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	−0.654012	−	0.756484i	$-0.726915\pi$
$773$	−20.5315	+	6.67110i	−0.738468	+	0.239943i	−0.0844563	+	0.996427i	$0.526915\pi$
$774$	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	0.543085	−	0.839678i	$-0.317256\pi$
$787$	13.7153	+	4.45638i	0.488899	+	0.158853i	−0.0541857	+	0.998531i	$0.517256\pi$
$788$	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	0.989445	+	0.144907i	$0.0462883\pi$
$797$	23.1921	+	31.9211i	0.821505	+	1.13070i	−0.167941	+	0.985797i	$0.553712\pi$
$798$	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	−0.913431	−	0.406993i	$-0.866577\pi$
$809$	1.84237	−	5.67024i	0.0647744	−	0.199355i	0.978206	+	0.207638i	$0.0665775\pi$
$810$		0			0
$811$	−12.1062	−	37.2590i	−0.425105	−	1.30834i	−0.902893	−	0.429865i	$-0.858561\pi$
$811$	−12.1062	−	37.2590i	−0.425105	−	1.30834i	0.477788	−	0.878475i	$-0.341439\pi$
$812$	−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	−0.839649	−	0.543130i	$-0.817239\pi$
$821$	−16.6923	+	12.1277i	−0.582567	+	0.423260i	0.257082	+	0.966390i	$0.417239\pi$
$822$	−1.52214	−	2.09505i	−0.0530909	−	0.0730733i
$823$	37.1066	−	12.0567i	1.29345	−	0.420269i	0.420155	−	0.907452i	$-0.361976\pi$
$823$	37.1066	−	12.0567i	1.29345	−	0.420269i	0.873300	+	0.487183i	$0.161976\pi$
$824$	−0.700803			−0.0244136
$825$		0			0
$826$	1.96673			0.0684314
$827$	−18.6384	+	6.05598i	−0.648120	+	0.210587i	−0.614585	−	0.788850i	$-0.710677\pi$
$827$	−18.6384	+	6.05598i	−0.648120	+	0.210587i	−0.0335352	+	0.999438i	$0.510677\pi$
$828$	−1.82988	−	2.51861i	−0.0635927	−	0.0875279i
$829$	−7.01831	+	5.09910i	−0.243756	+	0.177099i	−0.702955	−	0.711234i	$-0.748136\pi$
$829$	−7.01831	+	5.09910i	−0.243756	+	0.177099i	0.459199	+	0.888333i	$0.348136\pi$
$830$		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	0.969530	−	0.244974i	$-0.0787793\pi$
$839$	1.19256	+	3.67033i	0.0411718	+	0.126714i	−0.928358	+	0.371687i	$0.878779\pi$
$840$		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	0.396135	−	0.918192i	$-0.370351\pi$
$853$	−17.5100	−	24.1004i	−0.599531	−	0.825183i	−0.995665	+	0.0930093i	$0.970351\pi$
$854$	−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	$0.212200\pi$
$857$			36.2041i			1.23671i	−0.785899	+	0.618354i	$0.787800\pi$
$858$	−1.74477	+	2.40147i	−0.0595656	+	0.0819850i
$859$	11.6355	−	35.8104i	0.396998	−	1.22184i	−0.530396	−	0.847750i	$-0.677957\pi$
$859$	11.6355	−	35.8104i	0.396998	−	1.22184i	0.927394	−	0.374086i	$-0.122043\pi$
$860$		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	0.349191	−	0.937051i	$-0.386456\pi$
$863$	2.37682	+	0.772275i	0.0809078	+	0.0262885i	−0.268283	+	0.963340i	$0.586456\pi$
$864$	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	0.262537	−	0.964922i	$-0.415441\pi$
$877$	30.8609	−	10.0273i	1.04210	−	0.338599i	0.779563	+	0.626323i	$0.215441\pi$
$878$	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	0.940157	−	0.340740i	$-0.110678\pi$
$881$	26.9099	+	19.5512i	0.906619	+	0.658697i	−0.0335388	+	0.999437i	$0.510678\pi$
$882$		−	1.34375i		−	0.0452464i
$883$	6.44974	−	8.87730i	0.217051	−	0.298745i	−0.686582	−	0.727052i	$-0.740890\pi$
$883$	6.44974	−	8.87730i	0.217051	−	0.298745i	0.903633	+	0.428307i	$0.140890\pi$
$884$	−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	−0.137205	−	0.990543i	$-0.543812\pi$
$887$	−24.7324	−	8.03604i	−0.830432	−	0.269824i	−0.693227	+	0.720719i	$0.743812\pi$
$888$	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	$-0.633524\pi$
$907$		−	55.0108i		−	1.82660i	0.407283	−	0.913302i	$-0.366476\pi$
$908$	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	0.869751	−	0.493490i	$-0.164279\pi$
$911$	−3.74142	−	11.5149i	−0.123959	−	0.381506i	−0.993710	+	0.111985i	$0.964279\pi$
$912$	−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	0.664613	−	0.747188i	$-0.268596\pi$
$919$	4.83138	+	3.51020i	0.159372	+	0.115791i	−0.505241	+	0.862978i	$0.668596\pi$
$920$		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	0.246348	−	0.969182i	$-0.420770\pi$
$929$	37.9232	−	27.5528i	1.24422	−	0.903979i	0.997872	+	0.0652030i	$0.0207695\pi$
$930$		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	−0.00886093	−	0.999961i	$-0.502821\pi$
$937$	−18.4823	−	6.00528i	−0.603792	−	0.196184i	−0.594931	+	0.803777i	$0.702821\pi$
$938$	−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	−0.780174	−	0.625563i	$-0.784870\pi$
$941$	6.70867	−	20.6472i	0.218696	−	0.673078i	0.998870	−	0.0475159i	$-0.0151305\pi$
$942$	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	0.865062	−	0.501665i	$-0.167279\pi$
$947$	3.71222	+	5.10943i	0.120631	+	0.166034i	−0.744431	+	0.667699i	$0.767279\pi$
$948$	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	0.964455	−	0.264245i	$-0.0851229\pi$
$953$	12.8147	+	17.6380i	0.415110	+	0.571350i	−0.549345	+	0.835595i	$0.685123\pi$
$954$	−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	−0.870134	−	0.492815i	$-0.835968\pi$
$967$	−4.12195	+	5.67338i	−0.132553	+	0.182444i	0.737581	+	0.675259i	$0.235968\pi$
$968$		−	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	−0.679810	−	0.733388i	$-0.737938\pi$
$971$	−5.99504	+	4.35565i	−0.192390	+	0.139779i	0.487420	+	0.873167i	$0.337938\pi$
$972$	−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	−0.837741	−	0.546068i	$-0.816124\pi$
$977$	−37.3370	+	12.1315i	−1.19452	+	0.388122i	−0.356776	+	0.934190i	$0.616124\pi$
$978$	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	−0.601158	−	0.799131i	$-0.705294\pi$
$983$	10.8051	−	14.8719i	0.344629	−	0.474341i	0.945786	+	0.324790i	$0.105294\pi$
$984$	−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	−0.268233	−	0.963354i	$-0.586440\pi$
$991$	16.2128	−	49.8980i	0.515018	−	1.58506i	0.783250	−	0.621707i	$-0.213560\pi$
$992$	−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	0.999894	−	0.0145444i	$-0.00462980\pi$
$997$	21.3789	+	29.4256i	0.677077	+	0.931917i	−0.322817	+	0.946461i	$0.604630\pi$
$998$	−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.349.3		24
5.2	odd	4		375.2.g.c.151.2		12
5.3	odd	4		75.2.g.c.31.2	✓	12
5.4	even	2	inner	375.2.i.d.349.4		24
15.8	even	4		225.2.h.d.181.2		12
25.2	odd	20		1875.2.a.k.1.3		6
25.3	odd	20		75.2.g.c.46.2	yes	12
25.4	even	10	inner	375.2.i.d.274.3		24
25.11	even	5		1875.2.b.f.1249.8		12
25.14	even	10		1875.2.b.f.1249.5		12
25.21	even	5	inner	375.2.i.d.274.4		24
25.22	odd	20		375.2.g.c.226.2		12
25.23	odd	20		1875.2.a.j.1.4		6
75.2	even	20		5625.2.a.q.1.4		6
75.23	even	20		5625.2.a.p.1.3		6
75.53	even	20		225.2.h.d.46.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.2	✓	12	5.3	odd	4
75.2.g.c.46.2	yes	12	25.3	odd	20
225.2.h.d.46.2		12	75.53	even	20
225.2.h.d.181.2		12	15.8	even	4
375.2.g.c.151.2		12	5.2	odd	4
375.2.g.c.226.2		12	25.22	odd	20
375.2.i.d.274.3		24	25.4	even	10	inner
375.2.i.d.274.4		24	25.21	even	5	inner
375.2.i.d.349.3		24	1.1	even	1	trivial
375.2.i.d.349.4		24	5.4	even	2	inner
1875.2.a.j.1.4		6	25.23	odd	20
1875.2.a.k.1.3		6	25.2	odd	20
1875.2.b.f.1249.5		12	25.14	even	10
1875.2.b.f.1249.8		12	25.11	even	5
5625.2.a.p.1.3		6	75.23	even	20
5625.2.a.q.1.4		6	75.2	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

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