LMFDB - Embedded newform 375.2.i.d.199.1

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			199.1
Character	$\chi$	$=$	375.199
Dual form			375.2.i.d.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26995 - 1.74793i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.824463 + 2.53744i) q^{4} +(-0.667650 - 2.05481i) q^{6} -3.16056i q^{7} +(1.37265 - 0.446002i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.26995 - 1.74793i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.824463 + 2.53744i) q^{4} +(-0.667650 - 2.05481i) q^{6} -3.16056i q^{7} +(1.37265 - 0.446002i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.24455 + 0.904220i) q^{11} +(-1.56822 + 2.15847i) q^{12} +(3.08084 - 4.24041i) q^{13} +(-5.52444 + 4.01374i) q^{14} +(1.79417 + 1.30354i) q^{16} +(-1.22751 + 0.398843i) q^{17} -2.16056i q^{18} +(-1.68287 - 5.17933i) q^{19} +(0.976667 - 3.00587i) q^{21} +(3.16103 + 1.02708i) q^{22} +(-3.78677 - 5.21204i) q^{23} +1.44329 q^{24} -11.3244 q^{26} +(0.587785 + 0.809017i) q^{27} +(8.01972 + 2.60577i) q^{28} +(0.730396 - 2.24793i) q^{29} +(-1.37989 - 4.24687i) q^{31} -7.67809i q^{32} +(-1.46306 + 0.475377i) q^{33} +(2.25602 + 1.63910i) q^{34} +(-2.15847 + 1.56822i) q^{36} +(-3.50174 + 4.81973i) q^{37} +(-6.91596 + 9.51901i) q^{38} +(4.24041 - 3.08084i) q^{39} +(6.90269 + 5.01510i) q^{41} +(-6.49436 + 2.11015i) q^{42} +8.48426i q^{43} +(-1.26831 - 3.90347i) q^{44} +(-4.30129 + 13.2380i) q^{46} +(0.716212 + 0.232712i) q^{47} +(1.30354 + 1.79417i) q^{48} -2.98914 q^{49} -1.29068 q^{51} +(8.21974 + 11.3135i) q^{52} +(-9.27271 - 3.01289i) q^{53} +(0.667650 - 2.05481i) q^{54} +(-1.40962 - 4.33836i) q^{56} -5.44587i q^{57} +(-4.85678 + 1.57806i) q^{58} +(3.32724 + 2.41738i) q^{59} +(8.65159 - 6.28574i) q^{61} +(-5.67084 + 7.80525i) q^{62} +(1.85773 - 2.55695i) q^{63} +(-9.83243 + 7.14368i) q^{64} +(2.68893 + 1.95362i) q^{66} +(1.80572 - 0.586713i) q^{67} -3.44357i q^{68} +(-1.99082 - 6.12712i) q^{69} +(-0.0219023 + 0.0674084i) q^{71} +(1.37265 + 0.446002i) q^{72} +(2.35774 + 3.24515i) q^{73} +12.8716 q^{74} +14.5297 q^{76} +(2.85784 + 3.93348i) q^{77} +(-10.7702 - 3.49944i) q^{78} +(-0.500141 + 1.53928i) q^{79} +(0.309017 + 0.951057i) q^{81} -18.4343i q^{82} +(12.5053 - 4.06322i) q^{83} +(6.82198 + 4.95646i) q^{84} +(14.8299 - 10.7745i) q^{86} +(1.38930 - 1.91220i) q^{87} +(-1.30506 + 1.79626i) q^{88} +(5.88638 - 4.27671i) q^{89} +(-13.4021 - 9.73718i) q^{91} +(16.3473 - 5.31155i) q^{92} -4.46542i q^{93} +(-0.502787 - 1.54742i) q^{94} +(2.37266 - 7.30230i) q^{96} +(9.69499 + 3.15009i) q^{97} +(3.79604 + 5.22480i) q^{98} -1.53835 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 $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.26995	−	1.74793i	−0.897987	−	1.23597i	−0.971106	−	0.238650i	$-0.923295\pi$
$2$	−1.26995	−	1.74793i	−0.897987	−	1.23597i	0.0731189	−	0.997323i	$-0.476705\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−0.824463	+	2.53744i	−0.412232	+	1.26872i
$5$		0			0
$5$		0			0
$6$	−0.667650	−	2.05481i	−0.272567	−	0.838875i
$7$		−	3.16056i		−	1.19458i	−0.802026	−	0.597290i	$-0.796244\pi$
$7$		−	3.16056i		−	1.19458i	0.802026	−	0.597290i	$-0.203756\pi$
$8$	1.37265	−	0.446002i	0.485307	−	0.157686i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$		0			0
$11$	−1.24455	+	0.904220i	−0.375247	+	0.272633i	−0.759383	−	0.650644i	$-0.774499\pi$
$11$	−1.24455	+	0.904220i	−0.375247	+	0.272633i	0.384137	+	0.923276i	$0.374499\pi$
$12$	−1.56822	+	2.15847i	−0.452707	+	0.623097i
$13$	3.08084	−	4.24041i	0.854471	−	1.17608i	−0.128389	−	0.991724i	$-0.540981\pi$
$13$	3.08084	−	4.24041i	0.854471	−	1.17608i	0.982860	−	0.184355i	$-0.0590195\pi$
$14$	−5.52444	+	4.01374i	−1.47647	+	1.07272i
$15$		0			0
$16$	1.79417	+	1.30354i	0.448542	+	0.325885i
$17$	−1.22751	+	0.398843i	−0.297716	+	0.0967337i	−0.454066	−	0.890968i	$-0.650027\pi$
$17$	−1.22751	+	0.398843i	−0.297716	+	0.0967337i	0.156351	+	0.987702i	$0.450027\pi$
$18$		−	2.16056i		−	0.509249i
$19$	−1.68287	−	5.17933i	−0.386076	−	1.18822i	−0.935696	−	0.352806i	$-0.885228\pi$
$19$	−1.68287	−	5.17933i	−0.386076	−	1.18822i	0.549620	−	0.835415i	$-0.314772\pi$
$20$		0			0
$21$	0.976667	−	3.00587i	0.213126	−	0.655935i
$22$	3.16103	+	1.02708i	0.673933	+	0.218974i
$23$	−3.78677	−	5.21204i	−0.789596	−	1.08679i	−0.994158	−	0.107932i	$-0.965577\pi$
$23$	−3.78677	−	5.21204i	−0.789596	−	1.08679i	0.204562	−	0.978854i	$-0.434423\pi$
$24$	1.44329			0.294611
$25$		0			0
$26$	−11.3244			−2.22090
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	8.01972	+	2.60577i	1.51558	+	0.492443i
$29$	0.730396	−	2.24793i	0.135631	−	0.417430i	−0.860056	−	0.510199i	$-0.829572\pi$
$29$	0.730396	−	2.24793i	0.135631	−	0.417430i	0.995688	+	0.0927690i	$0.0295718\pi$
$30$		0			0
$31$	−1.37989	−	4.24687i	−0.247836	−	0.762760i	−0.995157	−	0.0982974i	$-0.968660\pi$
$31$	−1.37989	−	4.24687i	−0.247836	−	0.762760i	0.747321	−	0.664463i	$-0.231340\pi$
$32$		−	7.67809i		−	1.35731i
$33$	−1.46306	+	0.475377i	−0.254686	+	0.0827525i
$34$	2.25602	+	1.63910i	0.386905	+	0.281103i
$35$		0			0
$36$	−2.15847	+	1.56822i	−0.359745	+	0.261370i
$37$	−3.50174	+	4.81973i	−0.575682	+	0.792358i	−0.993214	−	0.116304i	$-0.962895\pi$
$37$	−3.50174	+	4.81973i	−0.575682	+	0.792358i	0.417532	+	0.908662i	$0.362895\pi$
$38$	−6.91596	+	9.51901i	−1.12192	+	1.54419i
$39$	4.24041	−	3.08084i	0.679009	−	0.493329i
$40$		0			0
$41$	6.90269	+	5.01510i	1.07802	+	0.783227i	0.977336	−	0.211692i	$-0.0678974\pi$
$41$	6.90269	+	5.01510i	1.07802	+	0.783227i	0.100683	+	0.994919i	$0.467897\pi$
$42$	−6.49436	+	2.11015i	−1.00210	+	0.325603i
$43$			8.48426i			1.29384i	0.762559	+	0.646919i	$0.223943\pi$
$43$			8.48426i			1.29384i	−0.762559	+	0.646919i	$0.776057\pi$
$44$	−1.26831	−	3.90347i	−0.191206	−	0.588470i
$45$		0			0
$46$	−4.30129	+	13.2380i	−0.634191	+	1.95184i
$47$	0.716212	+	0.232712i	0.104470	+	0.0339445i	0.360786	−	0.932649i	$-0.382509\pi$
$47$	0.716212	+	0.232712i	0.104470	+	0.0339445i	−0.256315	+	0.966593i	$0.582509\pi$
$48$	1.30354	+	1.79417i	0.188150	+	0.258966i
$49$	−2.98914			−0.427020
$50$		0			0
$51$	−1.29068			−0.180732
$52$	8.21974	+	11.3135i	1.13987	+	1.56890i
$53$	−9.27271	−	3.01289i	−1.27371	−	0.413852i	−0.407346	−	0.913274i	$-0.633546\pi$
$53$	−9.27271	−	3.01289i	−1.27371	−	0.413852i	−0.866359	+	0.499422i	$0.833546\pi$
$54$	0.667650	−	2.05481i	0.0908556	−	0.279625i
$55$		0			0
$56$	−1.40962	−	4.33836i	−0.188368	−	0.579737i
$57$		−	5.44587i		−	0.721324i
$58$	−4.85678	+	1.57806i	−0.637727	+	0.207210i
$59$	3.32724	+	2.41738i	0.433170	+	0.314717i	0.782915	−	0.622128i	$-0.213732\pi$
$59$	3.32724	+	2.41738i	0.433170	+	0.314717i	−0.349745	+	0.936845i	$0.613732\pi$
$60$		0			0
$61$	8.65159	−	6.28574i	1.10772	−	0.804807i	0.125419	−	0.992104i	$-0.459973\pi$
$61$	8.65159	−	6.28574i	1.10772	−	0.804807i	0.982303	+	0.187297i	$0.0599726\pi$
$62$	−5.67084	+	7.80525i	−0.720198	+	0.991267i
$63$	1.85773	−	2.55695i	0.234052	−	0.322145i
$64$	−9.83243	+	7.14368i	−1.22905	+	0.892960i
$65$		0			0
$66$	2.68893	+	1.95362i	0.330984	+	0.240474i
$67$	1.80572	−	0.586713i	0.220604	−	0.0716785i	−0.196630	−	0.980478i	$-0.563000\pi$
$67$	1.80572	−	0.586713i	0.220604	−	0.0716785i	0.417233	+	0.908799i	$0.363000\pi$
$68$		−	3.44357i		−	0.417594i
$69$	−1.99082	−	6.12712i	−0.239667	−	0.737619i
$70$		0			0
$71$	−0.0219023	+	0.0674084i	−0.00259933	+	0.00799990i	−0.952348	−	0.305014i	$-0.901339\pi$
$71$	−0.0219023	+	0.0674084i	−0.00259933	+	0.00799990i	0.949748	+	0.313014i	$0.101339\pi$
$72$	1.37265	+	0.446002i	0.161769	+	0.0525619i
$73$	2.35774	+	3.24515i	0.275952	+	0.379816i	0.924388	−	0.381454i	$-0.124576\pi$
$73$	2.35774	+	3.24515i	0.275952	+	0.379816i	−0.648436	+	0.761270i	$0.724576\pi$
$74$	12.8716			1.49629
$75$		0			0
$76$	14.5297			1.66667
$77$	2.85784	+	3.93348i	0.325681	+	0.448262i
$78$	−10.7702	−	3.49944i	−1.21948	−	0.396234i
$79$	−0.500141	+	1.53928i	−0.0562703	+	0.173182i	−0.975242	−	0.221143i	$-0.929021\pi$
$79$	−0.500141	+	1.53928i	−0.0562703	+	0.173182i	0.918971	+	0.394325i	$0.129021\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	18.4343i		−	2.03573i
$83$	12.5053	−	4.06322i	1.37263	−	0.445996i	0.472393	−	0.881388i	$-0.343390\pi$
$83$	12.5053	−	4.06322i	1.37263	−	0.445996i	0.900241	+	0.435392i	$0.143390\pi$
$84$	6.82198	+	4.95646i	0.744339	+	0.540794i
$85$		0			0
$86$	14.8299	−	10.7745i	1.59915	−	1.16185i
$87$	1.38930	−	1.91220i	0.148948	−	0.205010i
$88$	−1.30506	+	1.79626i	−0.139119	+	0.191481i
$89$	5.88638	−	4.27671i	0.623955	−	0.453330i	−0.230345	−	0.973109i	$-0.573986\pi$
$89$	5.88638	−	4.27671i	0.623955	−	0.453330i	0.854301	+	0.519779i	$0.173986\pi$
$90$		0			0
$91$	−13.4021	−	9.73718i	−1.40492	−	1.02073i
$92$	16.3473	−	5.31155i	1.70432	−	0.553768i
$93$		−	4.46542i		−	0.463043i
$94$	−0.502787	−	1.54742i	−0.0518585	−	0.159604i
$95$		0			0
$96$	2.37266	−	7.30230i	0.242159	−	0.745288i
$97$	9.69499	+	3.15009i	0.984377	+	0.319843i	0.756606	−	0.653871i	$-0.226856\pi$
$97$	9.69499	+	3.15009i	0.984377	+	0.319843i	0.227771	+	0.973715i	$0.426856\pi$
$98$	3.79604	+	5.22480i	0.383458	+	0.527785i
$99$	−1.53835			−0.154610
$100$		0			0
$101$	1.08759			0.108219			0.0541096	−	0.998535i	$-0.482768\pi$
$101$	1.08759			0.108219			0.0541096	+	0.998535i	$0.482768\pi$
$102$	1.63910	+	2.25602i	0.162295	+	0.223380i
$103$	4.69590	+	1.52579i	0.462701	+	0.150341i	0.531085	−	0.847319i	$-0.321784\pi$
$103$	4.69590	+	1.52579i	0.462701	+	0.150341i	−0.0683845	+	0.997659i	$0.521784\pi$
$104$	2.33769	−	7.19468i	0.229230	−	0.705497i
$105$		0			0
$106$	6.50952	+	20.0343i	0.632261	+	1.94590i
$107$			15.3059i			1.47967i	0.672786	+	0.739837i	$0.265098\pi$
$107$			15.3059i			1.47967i	−0.672786	+	0.739837i	$0.734902\pi$
$108$	−2.53744	+	0.824463i	−0.244165	+	0.0793340i
$109$	5.38724	+	3.91406i	0.516004	+	0.374899i	0.815097	−	0.579325i	$-0.196684\pi$
$109$	5.38724	+	3.91406i	0.516004	+	0.374899i	−0.299092	+	0.954224i	$0.596684\pi$
$110$		0			0
$111$	−4.81973	+	3.50174i	−0.457468	+	0.332370i
$112$	4.11991	−	5.67058i	0.389295	−	0.535819i
$113$	5.27328	−	7.25804i	0.496068	−	0.682779i	−0.485425	−	0.874278i	$-0.661335\pi$
$113$	5.27328	−	7.25804i	0.496068	−	0.682779i	0.981493	+	0.191499i	$0.0613350\pi$
$114$	−9.51901	+	6.91596i	−0.891537	+	0.647739i
$115$		0			0
$116$	5.10179	+	3.70667i	0.473689	+	0.344155i
$117$	4.98490	−	1.61969i	0.460854	−	0.149741i
$118$		−	8.88573i		−	0.817998i
$119$	1.26057	+	3.87963i	0.115556	+	0.355645i
$120$		0			0
$121$	−2.66789	+	8.21092i	−0.242536	+	0.746448i
$122$	−21.9741	−	7.13981i	−1.98944	−	0.646408i
$123$	5.01510	+	6.90269i	0.452196	+	0.622395i
$124$	11.9138			1.06989
$125$		0			0
$126$	−6.82858			−0.608338
$127$	−5.88870	−	8.10511i	−0.522538	−	0.719212i	0.463432	−	0.886132i	$-0.346618\pi$
$127$	−5.88870	−	8.10511i	−0.522538	−	0.719212i	−0.985970	+	0.166920i	$0.946618\pi$
$128$	10.3687	+	3.36899i	0.916471	+	0.297780i
$129$	−2.62178	+	8.06901i	−0.230835	+	0.710437i
$130$		0			0
$131$	−1.97111	−	6.06645i	−0.172217	−	0.530029i	0.827279	−	0.561792i	$-0.189888\pi$
$131$	−1.97111	−	6.06645i	−0.172217	−	0.530029i	−0.999495	+	0.0317631i	$0.989888\pi$
$132$		−	4.10435i		−	0.357238i
$133$	−16.3696	+	5.31880i	−1.41942	+	0.461199i
$134$	−3.31870	−	2.41117i	−0.286692	−	0.208294i
$135$		0			0
$136$	−1.50707	+	1.09495i	−0.129230	+	0.0938910i
$137$	−5.39429	+	7.42461i	−0.460866	+	0.634327i	−0.974688	−	0.223570i	$-0.928229\pi$
$137$	−5.39429	+	7.42461i	−0.460866	+	0.634327i	0.513822	+	0.857897i	$0.328229\pi$
$138$	−8.18154	+	11.2609i	−0.696459	+	0.958594i
$139$	−7.49586	+	5.44606i	−0.635790	+	0.461929i	−0.858401	−	0.512979i	$-0.828542\pi$
$139$	−7.49586	+	5.44606i	−0.635790	+	0.461929i	0.222611	+	0.974907i	$0.428542\pi$
$140$		0			0
$141$	0.609247	+	0.442644i	0.0513078	+	0.0372773i
$142$	0.145640	−	0.0473213i	0.0122218	−	0.00397111i
$143$			8.06317i			0.674276i
$144$	0.685311	+	2.10917i	0.0571093	+	0.175764i
$145$		0			0
$146$	2.67809	−	8.24232i	0.221641	−	0.682140i
$147$	−2.84284	−	0.923695i	−0.234473	−	0.0761850i
$148$	−9.34270	−	12.8591i	−0.767965	−	1.05701i
$149$	10.0817			0.825928			0.412964	−	0.910747i	$-0.364494\pi$
$149$	10.0817			0.825928			0.412964	+	0.910747i	$0.364494\pi$
$150$		0			0
$151$	10.7375			0.873804			0.436902	−	0.899509i	$-0.356076\pi$
$151$	10.7375			0.873804			0.436902	+	0.899509i	$0.356076\pi$
$152$	−4.61999	−	6.35887i	−0.374731	−	0.515773i
$153$	−1.22751	−	0.398843i	−0.0992385	−	0.0322446i
$154$	3.24615	−	9.99061i	0.261582	−	0.805067i
$155$		0			0
$156$	4.32137	+	13.2998i	0.345987	+	1.06484i
$157$			17.4417i			1.39200i	0.718041	+	0.696001i	$0.245039\pi$
$157$			17.4417i			1.39200i	−0.718041	+	0.696001i	$0.754961\pi$
$158$	3.32570	−	1.08058i	0.264578	−	0.0859667i
$159$	−7.88784	−	5.73085i	−0.625546	−	0.454486i
$160$		0			0
$161$	−16.4730	+	11.9683i	−1.29825	+	0.943235i
$162$	1.26995	−	1.74793i	0.0997763	−	0.137330i
$163$	9.55586	−	13.1525i	0.748473	−	1.03018i	−0.249613	−	0.968346i	$-0.580303\pi$
$163$	9.55586	−	13.1525i	0.748473	−	1.03018i	0.998086	−	0.0618392i	$-0.0196966\pi$
$164$	−18.4165	+	13.3804i	−1.43809	+	1.04483i
$165$		0			0
$166$	−22.9832	−	16.6983i	−1.78385	−	1.29604i
$167$	10.8331	−	3.51989i	0.838290	−	0.272377i	0.141757	−	0.989902i	$-0.454725\pi$
$167$	10.8331	−	3.51989i	0.838290	−	0.272377i	0.696533	+	0.717525i	$0.254725\pi$
$168$		−	4.56162i		−	0.351936i
$169$	−4.47230	−	13.7643i	−0.344023	−	1.05879i
$170$		0			0
$171$	1.68287	−	5.17933i	0.128692	−	0.396074i
$172$	−21.5283	−	6.99496i	−1.64152	−	0.533361i
$173$	5.55954	+	7.65205i	0.422684	+	0.581775i	0.966255	−	0.257589i	$-0.0829280\pi$
$173$	5.55954	+	7.65205i	0.422684	+	0.581775i	−0.543571	+	0.839363i	$0.682928\pi$
$174$	−5.10672			−0.387140
$175$		0			0
$176$	−3.41162			−0.257161
$177$	2.41738	+	3.32724i	0.181702	+	0.250091i
$178$	−14.9508	−	4.85780i	−1.12061	−	0.364107i
$179$	−1.26001	+	3.87790i	−0.0941773	+	0.289848i	−0.987038	−	0.160484i	$-0.948694\pi$
$179$	−1.26001	+	3.87790i	−0.0941773	+	0.289848i	0.892861	+	0.450332i	$0.148694\pi$
$180$		0			0
$181$	−3.43633	−	10.5759i	−0.255421	−	0.786104i	−0.993747	−	0.111660i	$-0.964383\pi$
$181$	−3.43633	−	10.5759i	−0.255421	−	0.786104i	0.738326	−	0.674444i	$-0.235617\pi$
$182$			35.7916i			2.65305i
$183$	10.1705	−	3.30461i	0.751829	−	0.244284i
$184$	−7.52251	−	5.46542i	−0.554567	−	0.402916i
$185$		0			0
$186$	−7.80525	+	5.67084i	−0.572308	+	0.415806i
$187$	1.16706	−	1.60632i	0.0853440	−	0.117466i
$188$	−1.18098	+	1.62548i	−0.0861319	+	0.118550i
$189$	2.55695	−	1.85773i	0.185990	−	0.135130i
$190$		0			0
$191$	−2.92164	−	2.12270i	−0.211403	−	0.153593i	0.477046	−	0.878879i	$-0.341708\pi$
$191$	−2.92164	−	2.12270i	−0.211403	−	0.153593i	−0.688448	+	0.725286i	$0.741708\pi$
$192$	−11.5587	+	3.75565i	−0.834178	+	0.271041i
$193$			17.0562i			1.22774i	0.789409	+	0.613868i	$0.210387\pi$
$193$			17.0562i			1.22774i	−0.789409	+	0.613868i	$0.789613\pi$
$194$	−6.80596	−	20.9466i	−0.488640	−	1.50388i
$195$		0			0
$196$	2.46443	−	7.58475i	0.176031	−	0.541768i
$197$	−4.18963	−	1.36129i	−0.298498	−	0.0969880i	0.155939	−	0.987767i	$-0.450160\pi$
$197$	−4.18963	−	1.36129i	−0.298498	−	0.0969880i	−0.454437	+	0.890779i	$0.650160\pi$
$198$	1.95362	+	2.68893i	0.138838	+	0.191094i
$199$	−16.5956			−1.17643			−0.588214	−	0.808705i	$-0.700169\pi$
$199$	−16.5956			−1.17643			−0.588214	+	0.808705i	$0.700169\pi$
$200$		0			0
$201$	1.89864			0.133920
$202$	−1.38118	−	1.90103i	−0.0971795	−	0.133756i
$203$	−7.10471	−	2.30846i	−0.498653	−	0.162022i
$204$	1.06412	−	3.27503i	0.0745034	−	0.229298i
$205$		0			0
$206$	−3.29656	−	10.1458i	−0.229682	−	0.706889i
$207$		−	6.44244i		−	0.447780i
$208$	11.0551	−	3.59202i	0.766532	−	0.249061i
$209$	6.77768	+	4.92427i	0.468822	+	0.340619i
$210$		0			0
$211$	−15.0035	+	10.9007i	−1.03288	+	0.750434i	−0.968884	−	0.247516i	$-0.920386\pi$
$211$	−15.0035	+	10.9007i	−1.03288	+	0.750434i	−0.0640001	+	0.997950i	$0.520386\pi$
$212$	15.2900	−	21.0449i	1.05012	−	1.44537i
$213$	−0.0416607	+	0.0573410i	−0.00285454	+	0.00392894i
$214$	26.7536	−	19.4376i	1.82884	−	1.32873i
$215$		0			0
$216$	1.16765	+	0.848347i	0.0794485	+	0.0577227i
$217$	−13.4225	+	4.36123i	−0.911178	+	0.296060i
$218$		−	14.3872i		−	0.974422i
$219$	1.23954	+	3.81490i	0.0837601	+	0.257787i
$220$		0			0
$221$	−2.09051	+	6.43393i	−0.140623	+	0.432793i
$222$	12.2416	+	3.97753i	0.821601	+	0.266954i
$223$	−0.453510	−	0.624203i	−0.0303693	−	0.0417997i	0.793562	−	0.608489i	$-0.208224\pi$
$223$	−0.453510	−	0.624203i	−0.0303693	−	0.0417997i	−0.823932	+	0.566689i	$0.808224\pi$
$224$	−24.2671			−1.62141
$225$		0			0
$226$	−19.3833			−1.28936
$227$	−6.71919	−	9.24817i	−0.445968	−	0.613823i	0.525557	−	0.850758i	$-0.323857\pi$
$227$	−6.71919	−	9.24817i	−0.445968	−	0.613823i	−0.971525	+	0.236936i	$0.923857\pi$
$228$	13.8186	+	4.48992i	0.915157	+	0.297352i
$229$	−3.15962	+	9.72432i	−0.208794	+	0.642601i	0.790743	+	0.612149i	$0.209695\pi$
$229$	−3.15962	+	9.72432i	−0.208794	+	0.642601i	−0.999536	+	0.0304520i	$0.990305\pi$
$230$		0			0
$231$	1.50246	+	4.62409i	0.0988544	+	0.304242i
$232$		−	3.41139i		−	0.223969i
$233$	−21.4206	+	6.95997i	−1.40331	+	0.455963i	−0.910260	−	0.414038i	$-0.864118\pi$
$233$	−21.4206	+	6.95997i	−1.40331	+	0.455963i	−0.493050	+	0.870001i	$0.664118\pi$
$234$	−9.16166	−	6.65634i	−0.598917	−	0.435138i
$235$		0			0
$236$	−8.87715	+	6.44963i	−0.577853	+	0.419835i
$237$	−0.951325	+	1.30939i	−0.0617952	+	0.0850538i
$238$	5.18047	−	7.13030i	0.335800	−	0.462189i
$239$	−0.476571	+	0.346249i	−0.0308268	+	0.0223970i	−0.603092	−	0.797672i	$-0.706065\pi$
$239$	−0.476571	+	0.346249i	−0.0308268	+	0.0223970i	0.572265	+	0.820069i	$0.306065\pi$
$240$		0			0
$241$	−1.22110	−	0.887185i	−0.0786583	−	0.0571486i	0.547761	−	0.836635i	$-0.315480\pi$
$241$	−1.22110	−	0.887185i	−0.0786583	−	0.0571486i	−0.626419	+	0.779486i	$0.715480\pi$
$242$	17.7402	−	5.76414i	1.14038	−	0.370533i
$243$			1.00000i			0.0641500i
$244$	8.81677	+	27.1352i	0.564436	+	1.73715i
$245$		0			0
$246$	5.69652	−	17.5321i	0.363197	−	1.11780i
$247$	−27.1472	−	8.82065i	−1.72733	−	0.561244i
$248$	−3.78823	−	5.21405i	−0.240553	−	0.331093i
$249$	13.1488			0.833274
$250$		0			0
$251$	11.8953			0.750823			0.375412	−	0.926858i	$-0.377501\pi$
$251$	11.8953			0.750823			0.375412	+	0.926858i	$0.377501\pi$
$252$	4.95646	+	6.82198i	0.312228	+	0.429744i
$253$	9.42567	+	3.06258i	0.592587	+	0.192543i
$254$	−6.68882	+	20.5861i	−0.419694	+	1.29169i
$255$		0			0
$256$	0.232398	+	0.715248i	0.0145249	+	0.0447030i
$257$		−	18.0492i		−	1.12588i	−0.826498	−	0.562939i	$-0.809671\pi$
$257$		−	18.0492i		−	1.12588i	0.826498	−	0.562939i	$-0.190329\pi$
$258$	17.4336	−	5.66451i	1.08537	−	0.352657i
$259$	15.2330	+	11.0674i	0.946534	+	0.687698i
$260$		0			0
$261$	1.91220	−	1.38930i	0.118362	−	0.0859953i
$262$	−8.10053	+	11.1494i	−0.500453	+	0.688814i
$263$	11.2306	−	15.4576i	0.692509	−	0.953157i	−0.307490	−	0.951551i	$-0.599489\pi$
$263$	11.2306	−	15.4576i	0.692509	−	0.953157i	0.999999	−	0.00160518i	$-0.000510946\pi$
$264$	−1.79626	+	1.30506i	−0.110552	+	0.0803206i
$265$		0			0
$266$	30.0854	+	21.8583i	1.84465	+	1.34022i
$267$	6.91986	−	2.24840i	0.423489	−	0.137600i
$268$			5.06562i			0.309432i
$269$	6.86791	+	21.1372i	0.418744	+	1.28876i	0.908859	+	0.417103i	$0.136955\pi$
$269$	6.86791	+	21.1372i	0.418744	+	1.28876i	−0.490115	+	0.871658i	$0.663045\pi$
$270$		0			0
$271$	6.24546	−	19.2216i	0.379385	−	1.16763i	−0.561088	−	0.827756i	$-0.689617\pi$
$271$	6.24546	−	19.2216i	0.379385	−	1.16763i	0.940472	−	0.339870i	$-0.110383\pi$
$272$	−2.72227	−	0.884520i	−0.165062	−	0.0536319i
$273$	−9.73718	−	13.4021i	−0.589321	−	0.811130i
$274$	19.8281			1.19786
$275$		0			0
$276$	17.1885			1.03463
$277$	9.42882	+	12.9777i	0.566523	+	0.779752i	0.992137	−	0.125153i	$-0.0399421\pi$
$277$	9.42882	+	12.9777i	0.566523	+	0.779752i	−0.425615	+	0.904904i	$0.639942\pi$
$278$	19.0387	+	6.18604i	1.14186	+	0.371014i
$279$	1.37989	−	4.24687i	0.0826120	−	0.254253i
$280$		0			0
$281$	2.58742	+	7.96327i	0.154353	+	0.475049i	0.998095	−	0.0617001i	$-0.0196522\pi$
$281$	2.58742	+	7.96327i	0.154353	+	0.475049i	−0.843742	+	0.536749i	$0.819652\pi$
$282$		−	1.62705i		−	0.0968896i
$283$	−1.07465	+	0.349174i	−0.0638811	+	0.0207562i	−0.340783	−	0.940142i	$-0.610692\pi$
$283$	−1.07465	+	0.349174i	−0.0638811	+	0.0207562i	0.276902	+	0.960898i	$0.410692\pi$
$284$	−0.152987	−	0.111151i	−0.00907810	−	0.00659563i
$285$		0			0
$286$	14.0939	−	10.2398i	0.833387	−	0.605491i
$287$	15.8505	−	21.8164i	0.935626	−	1.28778i
$288$	4.51307	−	6.21171i	0.265935	−	0.366028i
$289$	−12.4056	+	9.01318i	−0.729740	+	0.530187i
$290$		0			0
$291$	8.24705	+	5.99183i	0.483451	+	0.351247i
$292$	−10.1782	+	3.30711i	−0.595636	+	0.193534i
$293$			2.37857i			0.138958i	0.997583	+	0.0694789i	$0.0221337\pi$
$293$			2.37857i			0.138958i	−0.997583	+	0.0694789i	$0.977866\pi$
$294$	1.99570	+	6.14212i	0.116391	+	0.358216i
$295$		0			0
$296$	−2.65706	+	8.17760i	−0.154439	+	0.475313i
$297$	−1.46306	−	0.475377i	−0.0848953	−	0.0275842i
$298$	−12.8032	−	17.6222i	−0.741672	−	1.02082i
$299$	−33.7676			−1.95283
$300$		0			0
$301$	26.8150			1.54559
$302$	−13.6360	−	18.7684i	−0.784665	−	1.08000i
$303$	1.03436	+	0.336084i	0.0594224	+	0.0193075i
$304$	3.73212	−	11.4863i	0.214052	−	0.658783i
$305$		0			0
$306$	0.861724	+	2.65212i	0.0492615	+	0.151611i
$307$			2.89366i			0.165150i	0.996585	+	0.0825748i	$0.0263143\pi$
$307$			2.89366i			0.165150i	−0.996585	+	0.0825748i	$0.973686\pi$
$308$	−12.3371	+	4.00858i	−0.702974	+	0.228410i
$309$	3.99457	+	2.90222i	0.227243	+	0.165102i
$310$		0			0
$311$	5.78079	−	4.19999i	0.327799	−	0.238160i	−0.411697	−	0.911321i	$-0.635064\pi$
$311$	5.78079	−	4.19999i	0.327799	−	0.238160i	0.739496	+	0.673161i	$0.235064\pi$
$312$	4.44656	−	6.12016i	0.251737	−	0.346486i
$313$	−13.5378	+	18.6331i	−0.765200	+	1.05321i	0.231563	+	0.972820i	$0.425616\pi$
$313$	−13.5378	+	18.6331i	−0.765200	+	1.05321i	−0.996764	+	0.0803879i	$0.974384\pi$
$314$	30.4869	−	22.1500i	1.72048	−	1.25000i
$315$		0			0
$316$	−3.49347	−	2.53815i	−0.196523	−	0.142782i
$317$	19.7582	−	6.41981i	1.10973	−	0.360573i	0.303890	−	0.952707i	$-0.401715\pi$
$317$	19.7582	−	6.41981i	1.10973	−	0.360573i	0.805839	+	0.592135i	$0.201715\pi$
$318$			21.0653i			1.18128i
$319$	1.12361	+	3.45810i	0.0629098	+	0.193617i
$320$		0			0
$321$	−4.72978	+	14.5568i	−0.263990	+	0.812479i
$322$	41.8395	+	13.5945i	2.33163	+	0.757591i
$323$	4.13148	+	5.68650i	0.229882	+	0.316405i
$324$	−2.66802			−0.148223
$325$		0			0
$326$	−35.1251			−1.94540
$327$	3.91406	+	5.38724i	0.216448	+	0.297915i
$328$	11.7118	+	3.80538i	0.646673	+	0.210117i
$329$	0.735499	−	2.26363i	0.0405494	−	0.124798i
$330$		0			0
$331$	−5.94869	−	18.3082i	−0.326969	−	1.00631i	−0.970544	−	0.240925i	$-0.922549\pi$
$331$	−5.94869	−	18.3082i	−0.326969	−	1.00631i	0.643574	−	0.765383i	$-0.277451\pi$
$332$			35.0814i			1.92534i
$333$	−5.66593	+	1.84097i	−0.310491	+	0.100885i
$334$	−19.9099	−	14.4654i	−1.08942	−	0.791513i
$335$		0			0
$336$	5.67058	−	4.11991i	0.309355	−	0.224760i
$337$	12.7587	−	17.5609i	0.695012	−	0.956602i	−0.304979	−	0.952359i	$-0.598649\pi$
$337$	12.7587	−	17.5609i	0.695012	−	0.956602i	0.999991	−	0.00424305i	$-0.00135061\pi$
$338$	−18.3795	+	25.2972i	−0.999712	+	1.37599i
$339$	7.25804	−	5.27328i	0.394203	−	0.286405i
$340$		0			0
$341$	5.55745	+	4.03773i	0.300953	+	0.218655i
$342$	−11.1903	+	3.63594i	−0.605100	+	0.196609i
$343$		−	12.6766i		−	0.684470i
$344$	3.78400	+	11.6460i	0.204020	+	0.627908i
$345$		0			0
$346$	6.31493	−	19.4354i	0.339493	−	1.04485i
$347$	−1.63100	−	0.529944i	−0.0875567	−	0.0284489i	0.264911	−	0.964273i	$-0.414657\pi$
$347$	−1.63100	−	0.529944i	−0.0875567	−	0.0284489i	−0.352468	+	0.935824i	$0.614657\pi$
$348$	3.70667	+	5.10179i	0.198698	+	0.273485i
$349$	15.5553			0.832654			0.416327	−	0.909215i	$-0.363317\pi$
$349$	15.5553			0.832654			0.416327	+	0.909215i	$0.363317\pi$
$350$		0			0
$351$	5.24144			0.279767
$352$	6.94268	+	9.55579i	0.370046	+	0.509325i
$353$	−14.7923	−	4.80632i	−0.787316	−	0.255814i	−0.112355	−	0.993668i	$-0.535839\pi$
$353$	−14.7923	−	4.80632i	−0.787316	−	0.255814i	−0.674961	+	0.737854i	$0.735839\pi$
$354$	2.74584	−	8.45083i	0.145940	−	0.449157i
$355$		0			0
$356$	5.99877	+	18.4623i	0.317934	+	0.978501i
$357$			4.07928i			0.215899i
$358$	8.37844	−	2.72232i	0.442814	−	0.143879i
$359$	−19.8509	−	14.4225i	−1.04769	−	0.761191i	−0.0759181	−	0.997114i	$-0.524189\pi$
$359$	−19.8509	−	14.4225i	−1.04769	−	0.761191i	−0.971772	+	0.235923i	$0.924189\pi$
$360$		0			0
$361$	−8.62214	+	6.26435i	−0.453797	+	0.329703i
$362$	−14.1221	+	19.4373i	−0.742239	+	1.02160i
$363$	−5.07463	+	6.98463i	−0.266349	+	0.366598i
$364$	35.7570	−	25.9790i	1.87418	−	1.36167i
$365$		0			0
$366$	−18.6923	−	13.5807i	−0.977060	−	0.709876i
$367$	−26.7311	+	8.68548i	−1.39535	+	0.453378i	−0.907686	−	0.419651i	$-0.862153\pi$
$367$	−26.7311	+	8.68548i	−1.39535	+	0.453378i	−0.487669	+	0.873029i	$0.662153\pi$
$368$		−	14.2875i		−	0.744786i
$369$	2.63659	+	8.11460i	0.137256	+	0.422429i
$370$		0			0
$371$	−9.52241	+	29.3070i	−0.494379	+	1.52154i
$372$	11.3307	+	3.68158i	0.587471	+	0.190881i
$373$	−5.70637	−	7.85414i	−0.295464	−	0.406672i	0.635315	−	0.772253i	$-0.280870\pi$
$373$	−5.70637	−	7.85414i	−0.295464	−	0.406672i	−0.930779	+	0.365581i	$0.880870\pi$
$374$	−4.28984			−0.221823
$375$		0			0
$376$	1.08690			0.0560527
$377$	−7.28191	−	10.0227i	−0.375037	−	0.516195i
$378$	−6.49436	−	2.11015i	−0.334034	−	0.108534i
$379$	6.88071	−	21.1767i	0.353438	−	1.08777i	−0.603471	−	0.797385i	$-0.706216\pi$
$379$	6.88071	−	21.1767i	0.353438	−	1.08777i	0.956909	−	0.290387i	$-0.0937839\pi$
$380$		0			0
$381$	−3.09587	−	9.52812i	−0.158606	−	0.488141i
$382$			7.80253i			0.399212i
$383$	−12.9628	+	4.21189i	−0.662371	+	0.215217i	−0.620861	−	0.783921i	$-0.713217\pi$
$383$	−12.9628	+	4.21189i	−0.662371	+	0.215217i	−0.0415099	+	0.999138i	$0.513217\pi$
$384$	8.82014	+	6.40820i	0.450101	+	0.327017i
$385$		0			0
$386$	29.8131	−	21.6605i	1.51745	−	1.10249i
$387$	−4.98692	+	6.86391i	−0.253500	+	0.348912i
$388$	−15.9863	+	22.0033i	−0.811582	+	1.11705i
$389$	15.5577	−	11.3034i	0.788808	−	0.573103i	−0.118801	−	0.992918i	$-0.537905\pi$
$389$	15.5577	−	11.3034i	0.788808	−	0.573103i	0.907610	+	0.419815i	$0.137905\pi$
$390$		0			0
$391$	6.72710	+	4.88752i	0.340204	+	0.247173i
$392$	−4.10305	+	1.33316i	−0.207236	+	0.0673349i
$393$		−	6.37865i		−	0.321760i
$394$	2.94115	+	9.05194i	0.148173	+	0.456030i
$395$		0			0
$396$	1.26831	−	3.90347i	0.0637352	−	0.196157i
$397$	21.1402	+	6.86887i	1.06100	+	0.344739i	0.786975	−	0.616984i	$-0.211646\pi$
$397$	21.1402	+	6.86887i	1.06100	+	0.344739i	0.274022	+	0.961723i	$0.411646\pi$
$398$	21.0755	+	29.0079i	1.05642	+	1.45403i
$399$	−17.2120			−0.861678
$400$		0			0
$401$	4.71728			0.235570			0.117785	−	0.993039i	$-0.462421\pi$
$401$	4.71728			0.235570			0.117785	+	0.993039i	$0.462421\pi$
$402$	−2.41117	−	3.31870i	−0.120258	−	0.165522i
$403$	−22.2597	−	7.23261i	−1.10883	−	0.360282i
$404$	−0.896678	+	2.75969i	−0.0446114	+	0.137300i
$405$		0			0
$406$	4.98757	+	15.3502i	0.247529	+	0.761815i
$407$		−	9.16474i		−	0.454279i
$408$	−1.77166	+	0.575648i	−0.0877104	+	0.0284988i
$409$	−10.0971	−	7.33597i	−0.499269	−	0.362740i	0.309469	−	0.950910i	$-0.399849\pi$
$409$	−10.0971	−	7.33597i	−0.499269	−	0.362740i	−0.808738	+	0.588169i	$0.799849\pi$
$410$		0			0
$411$	−7.42461	+	5.39429i	−0.366229	+	0.266081i
$412$	−7.74319	+	10.6576i	−0.381480	+	0.525062i
$413$	7.64029	−	10.5160i	0.375954	−	0.517456i
$414$	−11.2609	+	8.18154i	−0.553444	+	0.402101i
$415$		0			0
$416$	−32.5583	−	23.6550i	−1.59630	−	1.15978i
$417$	−8.81191	+	2.86316i	−0.431521	+	0.140210i
$418$		−	18.1005i		−	0.885322i
$419$	−10.7996	−	33.2379i	−0.527597	−	1.62378i	−0.759123	−	0.650947i	$-0.774372\pi$
$419$	−10.7996	−	33.2379i	−0.527597	−	1.62378i	0.231527	−	0.972829i	$-0.425628\pi$
$420$		0			0
$421$	−12.2247	+	37.6239i	−0.595797	+	1.83368i	−0.0450804	+	0.998983i	$0.514354\pi$
$421$	−12.2247	+	37.6239i	−0.595797	+	1.83368i	−0.550717	+	0.834692i	$0.685646\pi$
$422$	38.1073	+	12.3818i	1.85503	+	0.602737i
$423$	0.442644	+	0.609247i	0.0215221	+	0.0296226i
$424$	−14.0720			−0.683396
$425$		0			0
$426$	0.153135			0.00741940
$427$	−19.8665	−	27.3439i	−0.961406	−	1.32326i
$428$	−38.8377	−	12.6191i	−1.87729	−	0.609969i
$429$	−2.49166	+	7.66853i	−0.120298	+	0.370240i
$430$		0			0
$431$	−4.34429	−	13.3703i	−0.209257	−	0.644027i	−0.999512	−	0.0312481i	$-0.990052\pi$
$431$	−4.34429	−	13.3703i	−0.209257	−	0.644027i	0.790255	−	0.612778i	$-0.209948\pi$
$432$			2.21771i			0.106700i
$433$	−0.522775	+	0.169860i	−0.0251230	+	0.00816294i	−0.321552	−	0.946892i	$-0.604204\pi$
$433$	−0.522775	+	0.169860i	−0.0251230	+	0.00816294i	0.296429	+	0.955055i	$0.404204\pi$
$434$	24.6689	+	17.9230i	1.18415	+	0.860333i
$435$		0			0
$436$	−14.3733	+	10.4428i	−0.688355	+	0.500119i
$437$	−20.6223	+	28.3841i	−0.986497	+	1.35780i
$438$	5.09404	−	7.01134i	0.243402	−	0.335015i
$439$	−2.40583	+	1.74794i	−0.114824	+	0.0834245i	−0.643715	−	0.765265i	$-0.722608\pi$
$439$	−2.40583	+	1.74794i	−0.114824	+	0.0834245i	0.528891	+	0.848690i	$0.322608\pi$
$440$		0			0
$441$	−2.41826	−	1.75697i	−0.115155	−	0.0836653i
$442$	13.9009	−	4.51667i	0.661198	−	0.214836i
$443$			36.6893i			1.74316i	0.490253	+	0.871580i	$0.336905\pi$
$443$			36.6893i			1.74316i	−0.490253	+	0.871580i	$0.663095\pi$
$444$	−4.91175	−	15.1168i	−0.233101	−	0.717412i
$445$		0			0
$446$	−0.515130	+	1.58541i	−0.0243921	+	0.0750712i
$447$	9.58830	+	3.11543i	0.453511	+	0.147355i
$448$	22.5780	+	31.0760i	1.06671	+	1.46820i
$449$	17.8432			0.842071			0.421036	−	0.907044i	$-0.361667\pi$
$449$	17.8432			0.842071			0.421036	+	0.907044i	$0.361667\pi$
$450$		0			0
$451$	−13.1255			−0.618056
$452$	14.0692	+	19.3646i	0.661759	+	0.910834i
$453$	10.2120	+	3.31807i	0.479800	+	0.155896i
$454$	−7.63215	+	23.4893i	−0.358195	+	1.10241i
$455$		0			0
$456$	−2.42887	−	7.47530i	−0.113742	−	0.350063i
$457$		−	24.1784i		−	1.13102i	−0.824742	−	0.565509i	$-0.808680\pi$
$457$		−	24.1784i		−	1.13102i	0.824742	−	0.565509i	$-0.191320\pi$
$458$	21.0100	−	6.82655i	0.981731	−	0.318984i
$459$	−1.04418	−	0.758645i	−0.0487384	−	0.0354105i
$460$		0			0
$461$	30.2470	−	21.9757i	1.40874	−	1.02351i	0.415240	−	0.909712i	$-0.363698\pi$
$461$	30.2470	−	21.9757i	1.40874	−	1.02351i	0.993504	−	0.113800i	$-0.0363024\pi$
$462$	6.17454	−	8.49852i	0.287266	−	0.395387i
$463$	−12.0093	+	16.5294i	−0.558120	+	0.768186i	−0.991086	−	0.133224i	$-0.957467\pi$
$463$	−12.0093	+	16.5294i	−0.558120	+	0.768186i	0.432966	+	0.901410i	$0.357467\pi$
$464$	4.24072	−	3.08106i	0.196870	−	0.143035i
$465$		0			0
$466$	39.3685	+	28.6029i	1.82371	+	1.32500i
$467$	−29.6848	+	9.64517i	−1.37365	+	0.446325i	−0.900576	−	0.434699i	$-0.856855\pi$
$467$	−29.6848	+	9.64517i	−1.37365	+	0.446325i	−0.473072	+	0.881024i	$0.656855\pi$
$468$			13.9843i			0.646422i
$469$	−1.85434	−	5.70708i	−0.0856256	−	0.263529i
$470$		0			0
$471$	−5.38979	+	16.5881i	−0.248348	+	0.764338i
$472$	5.64532	+	1.83427i	0.259847	+	0.0844293i
$473$	−7.67164	−	10.5591i	−0.352742	−	0.485508i
$474$	3.49684			0.160615
$475$		0			0
$476$	−10.8836			−0.498849
$477$	−5.73085	−	7.88784i	−0.262398	−	0.361159i
$478$	1.21044	+	0.393295i	0.0553641	+	0.0179889i
$479$	−3.42915	+	10.5538i	−0.156682	+	0.482217i	−0.998327	−	0.0578133i	$-0.981587\pi$
$479$	−3.42915	+	10.5538i	−0.156682	+	0.482217i	0.841646	+	0.540030i	$0.181587\pi$
$480$		0			0
$481$	9.64933	+	29.6976i	0.439972	+	1.35409i
$482$			3.26108i			0.148538i
$483$	−19.3651	+	6.29211i	−0.881144	+	0.286301i
$484$	−18.6351	−	13.5392i	−0.847051	−	0.615418i
$485$		0			0
$486$	1.74793	−	1.26995i	0.0792877	−	0.0576059i
$487$	4.19504	−	5.77397i	0.190095	−	0.261644i	−0.703322	−	0.710871i	$-0.748301\pi$
$487$	4.19504	−	5.77397i	0.190095	−	0.261644i	0.893417	+	0.449228i	$0.148301\pi$
$488$	9.07218	−	12.4868i	0.410678	−	0.565250i
$489$	13.1525	−	9.55586i	0.594777	−	0.432131i
$490$		0			0
$491$	−5.85201	−	4.25173i	−0.264097	−	0.191878i	0.447854	−	0.894107i	$-0.352188\pi$
$491$	−5.85201	−	4.25173i	−0.264097	−	0.191878i	−0.711951	+	0.702229i	$0.752188\pi$
$492$	−21.6499	+	7.03448i	−0.976053	+	0.317139i
$493$			3.05067i			0.137395i
$494$	19.0575	+	58.6531i	0.857439	+	2.63893i
$495$		0			0
$496$	3.06020	−	9.41834i	0.137407	−	0.422896i
$497$	0.213048	+	0.0692236i	0.00955652	+	0.00310510i
$498$	−16.6983	−	22.9832i	−0.748269	−	1.02990i
$499$	−16.0169			−0.717014			−0.358507	−	0.933527i	$-0.616714\pi$
$499$	−16.0169			−0.717014			−0.358507	+	0.933527i	$0.616714\pi$
$500$		0			0
$501$	11.3906			0.508894
$502$	−15.1063	−	20.7921i	−0.674229	−	0.927997i
$503$	32.1422	+	10.4436i	1.43315	+	0.465659i	0.919755	−	0.392492i	$-0.128387\pi$
$503$	32.1422	+	10.4436i	1.43315	+	0.465659i	0.513396	+	0.858152i	$0.328387\pi$
$504$	1.40962	−	4.33836i	0.0627894	−	0.193246i
$505$		0			0
$506$	−6.61690	−	20.3647i	−0.294157	−	0.905322i
$507$		−	14.4727i		−	0.642753i
$508$	25.4212	−	8.25985i	1.12788	−	0.366472i
$509$	−29.4701	−	21.4113i	−1.30624	−	0.949038i	−0.306243	−	0.951953i	$-0.599072\pi$
$509$	−29.4701	−	21.4113i	−1.30624	−	0.949038i	−0.999996	+	0.00291563i	$0.999072\pi$
$510$		0			0
$511$	10.2565	−	7.45178i	0.453720	−	0.329647i
$512$	13.7715	−	18.9548i	0.608619	−	0.837692i
$513$	3.20100	−	4.40581i	0.141328	−	0.194521i
$514$	−31.5487	+	22.9215i	−1.39156	+	1.01102i
$515$		0			0
$516$	−18.3130	−	13.3052i	−0.806187	−	0.585729i
$517$	−1.10179	+	0.357992i	−0.0484565	+	0.0157445i
$518$		−	40.6813i		−	1.78743i
$519$	2.92282	+	8.99552i	0.128298	+	0.394860i
$520$		0			0
$521$	7.87972	−	24.2513i	0.345217	−	1.06247i	−0.616251	−	0.787550i	$-0.711349\pi$
$521$	7.87972	−	24.2513i	0.345217	−	1.06247i	0.961468	−	0.274918i	$-0.0886507\pi$
$522$	−4.85678	−	1.57806i	−0.212576	−	0.0690700i
$523$	−4.13315	−	5.68880i	−0.180730	−	0.248754i	0.709034	−	0.705174i	$-0.249131\pi$
$523$	−4.13315	−	5.68880i	−0.180730	−	0.248754i	−0.889764	+	0.456420i	$0.849131\pi$
$524$	17.0184			0.743450
$525$		0			0
$526$	−41.2811			−1.79994
$527$	3.38767	+	4.66273i	0.147569	+	0.203112i
$528$	−3.24465	−	1.05425i	−0.141205	−	0.0458803i
$529$	−5.71836	+	17.5993i	−0.248624	+	0.765187i
$530$		0			0
$531$	1.27089	+	3.91141i	0.0551521	+	0.169741i
$532$		−	45.9220i		−	1.99097i
$533$	42.5322	−	13.8195i	1.84227	−	0.598590i
$534$	−12.7179	−	9.24008i	−0.550357	−	0.399858i
$535$		0			0
$536$	2.21695	−	1.61071i	0.0957577	−	0.0695721i
$537$	−2.39667	+	3.29874i	−0.103424	+	0.142351i
$538$	28.2246	−	38.8478i	1.21685	−	1.67485i
$539$	3.72014	−	2.70284i	0.160238	−	0.116420i
$540$		0			0
$541$	21.9629	+	15.9570i	0.944258	+	0.686044i	0.949442	−	0.313943i	$-0.101650\pi$
$541$	21.9629	+	15.9570i	0.944258	+	0.686044i	−0.00518365	+	0.999987i	$0.501650\pi$
$542$	−41.5293	+	13.4937i	−1.78384	+	0.579604i
$543$		−	11.1202i		−	0.477214i
$544$	3.06235	+	9.42496i	0.131297	+	0.404092i
$545$		0			0
$546$	−11.0602	+	34.0398i	−0.473333	+	1.45677i
$547$	41.9196	+	13.6205i	1.79235	+	0.582371i	0.999630	−	0.0272113i	$-0.00866269\pi$
$547$	41.9196	+	13.6205i	1.79235	+	0.582371i	0.792723	+	0.609582i	$0.208663\pi$
$548$	−14.3921	−	19.8090i	−0.614799	−	0.846198i
$549$	10.6939			0.456407
$550$		0			0
$551$	−12.8719			−0.548363
$552$	−5.46542	−	7.52251i	−0.232624	−	0.320179i
$553$	4.86497	+	1.58073i	0.206880	+	0.0672193i
$554$	10.7099	−	32.9618i	0.455022	−	1.40041i
$555$		0			0
$556$	−7.63897	−	23.5103i	−0.323965	−	0.997061i
$557$		−	9.85667i		−	0.417641i	−0.977954	−	0.208820i	$-0.933038\pi$
$557$		−	9.85667i		−	0.417641i	0.977954	−	0.208820i	$-0.0669624\pi$
$558$	−9.17562	+	2.98134i	−0.388435	+	0.126210i
$559$	35.9768	+	26.1386i	1.52165	+	1.10555i
$560$		0			0
$561$	1.60632	−	1.16706i	0.0678190	−	0.0492734i
$562$	10.6334	−	14.6356i	0.448541	−	0.617363i
$563$	7.28367	−	10.0251i	0.306970	−	0.422508i	−0.627463	−	0.778646i	$-0.715907\pi$
$563$	7.28367	−	10.0251i	0.306970	−	0.422508i	0.934433	+	0.356138i	$0.115907\pi$
$564$	−1.62548	+	1.18098i	−0.0684451	+	0.0497283i
$565$		0			0
$566$	1.97507	+	1.43497i	0.0830185	+	0.0603165i
$567$	3.00587	−	0.976667i	0.126235	−	0.0410161i
$568$			0.102297i			0.00429228i
$569$	3.62037	+	11.1424i	0.151774	+	0.467112i	0.997820	−	0.0659983i	$-0.0210232\pi$
$569$	3.62037	+	11.1424i	0.151774	+	0.467112i	−0.846046	+	0.533110i	$0.821023\pi$
$570$		0			0
$571$	8.95523	−	27.5614i	0.374765	−	1.15341i	−0.568872	−	0.822426i	$-0.692620\pi$
$571$	8.95523	−	27.5614i	0.374765	−	1.15341i	0.943637	−	0.330982i	$-0.107380\pi$
$572$	−20.4598	−	6.64779i	−0.855467	−	0.277958i
$573$	−2.12270	−	2.92164i	−0.0886769	−	0.122053i
$574$	−58.2628			−2.43184
$575$		0			0
$576$	−12.1535			−0.506398
$577$	19.2808	+	26.5377i	0.802668	+	1.10478i	0.992414	+	0.122945i	$0.0392338\pi$
$577$	19.2808	+	26.5377i	0.802668	+	1.10478i	−0.189745	+	0.981833i	$0.560766\pi$
$578$	31.5088	+	10.2378i	1.31059	+	0.425838i
$579$	−5.27067	+	16.2215i	−0.219042	+	0.674141i
$580$		0			0
$581$	−12.8420	−	39.5237i	−0.532777	−	1.63972i
$582$		−	22.0246i		−	0.912947i
$583$	14.2647	−	4.63488i	0.590783	−	0.191957i
$584$	4.68371	+	3.40291i	0.193813	+	0.140813i
$585$		0			0
$586$	4.15758	−	3.02066i	0.171748	−	0.124782i
$587$	10.9560	−	15.0797i	0.452203	−	0.622405i	−0.520666	−	0.853761i	$-0.674316\pi$
$587$	10.9560	−	15.0797i	0.452203	−	0.622405i	0.972869	+	0.231356i	$0.0743162\pi$
$588$	4.68763	−	6.45197i	0.193315	−	0.266075i
$589$	−19.6738	+	14.2938i	−0.810644	+	0.588967i
$590$		0			0
$591$	−3.56391	−	2.58933i	−0.146600	−	0.106511i
$592$	−12.5654	+	4.08275i	−0.516435	+	0.167800i
$593$		−	1.55882i		−	0.0640129i	−0.999488	−	0.0320064i	$-0.989810\pi$
$593$		−	1.55882i		−	0.0640129i	0.999488	−	0.0320064i	$-0.0101897\pi$
$594$	1.02708	+	3.16103i	0.0421416	+	0.129698i
$595$		0			0
$596$	−8.31202	+	25.5818i	−0.340474	+	1.04787i
$597$	−15.7833	−	5.12831i	−0.645969	−	0.209888i
$598$	42.8830	+	59.0234i	1.75362	+	2.41365i
$599$	31.5470			1.28898			0.644489	−	0.764614i	$-0.277070\pi$
$599$	31.5470			1.28898			0.644489	+	0.764614i	$0.277070\pi$
$600$		0			0
$601$	−32.3999			−1.32162			−0.660809	−	0.750554i	$-0.729787\pi$
$601$	−32.3999			−1.32162			−0.660809	+	0.750554i	$0.729787\pi$
$602$	−34.0536	−	46.8707i	−1.38792	−	1.91031i
$603$	1.80572	+	0.586713i	0.0735345	+	0.0238928i
$604$	−8.85266	+	27.2457i	−0.360210	+	1.10861i
$605$		0			0
$606$	−0.726129	−	2.23480i	−0.0294970	−	0.0907824i
$607$			24.8410i			1.00827i	0.863626	+	0.504133i	$0.168188\pi$
$607$			24.8410i			1.00827i	−0.863626	+	0.504133i	$0.831812\pi$
$608$	−39.7674	+	12.9212i	−1.61278	+	0.524024i
$609$	−6.04363	−	4.39095i	−0.244900	−	0.177930i
$610$		0			0
$611$	3.19333	−	2.32009i	0.129188	−	0.0938607i
$612$	2.02408	−	2.78590i	0.0818185	−	0.112614i
$613$	2.31915	−	3.19204i	0.0936697	−	0.128925i	−0.759610	−	0.650379i	$-0.774610\pi$
$613$	2.31915	−	3.19204i	0.0936697	−	0.128925i	0.853280	+	0.521454i	$0.174610\pi$
$614$	5.05791	−	3.67478i	0.204120	−	0.148302i
$615$		0			0
$616$	5.67717	+	4.12471i	0.228740	+	0.166189i
$617$	16.6264	−	5.40225i	0.669354	−	0.217486i	0.0454257	−	0.998968i	$-0.485536\pi$
$617$	16.6264	−	5.40225i	0.669354	−	0.217486i	0.623929	+	0.781481i	$0.285536\pi$
$618$		−	10.6679i		−	0.429126i
$619$	4.44581	+	13.6828i	0.178692	+	0.549958i	0.999783	−	0.0208398i	$-0.00663400\pi$
$619$	4.44581	+	13.6828i	0.178692	+	0.549958i	−0.821091	+	0.570798i	$0.806634\pi$
$620$		0			0
$621$	1.99082	−	6.12712i	0.0798890	−	0.245873i
$622$	−14.6826	−	4.77066i	−0.588718	−	0.191286i
$623$	−13.5168	−	18.6043i	−0.541539	−	0.745364i
$624$	11.6240			0.465333
$625$		0			0
$626$	49.7617			1.98888
$627$	4.92427	+	6.77768i	0.196656	+	0.270674i
$628$	−44.2573	−	14.3801i	−1.76606	−	0.573827i
$629$	2.37611	−	7.31292i	0.0947418	−	0.291585i
$630$		0			0
$631$	−5.46214	−	16.8107i	−0.217444	−	0.669225i	−0.998971	−	0.0453529i	$-0.985559\pi$
$631$	−5.46214	−	16.8107i	−0.217444	−	0.669225i	0.781527	−	0.623872i	$-0.214441\pi$
$632$			2.33596i			0.0929194i
$633$	−17.6377	+	5.73083i	−0.701035	+	0.227780i
$634$	−36.3132	−	26.3831i	−1.44218	−	1.04781i
$635$		0			0
$636$	21.0449	−	15.2900i	0.834485	−	0.606289i
$637$	−9.20905	+	12.6752i	−0.364876	+	0.502209i
$638$	4.61760	−	6.35559i	0.182813	−	0.251620i
$639$	−0.0573410	+	0.0416607i	−0.00226837	+	0.00164807i
$640$		0			0
$641$	2.21774	+	1.61128i	0.0875954	+	0.0636417i	0.630721	−	0.776010i	$-0.282759\pi$
$641$	2.21774	+	1.61128i	0.0875954	+	0.0636417i	−0.543126	+	0.839651i	$0.682759\pi$
$642$	31.4507	−	10.2190i	1.24126	−	0.403310i
$643$		−	20.9276i		−	0.825303i	−0.910889	−	0.412651i	$-0.864603\pi$
$643$		−	20.9276i		−	0.825303i	0.910889	−	0.412651i	$-0.135397\pi$
$644$	−16.7875	−	51.6665i	−0.661519	−	2.03595i
$645$		0			0
$646$	4.69284	−	14.4431i	0.184637	−	0.568256i
$647$	−1.75629	−	0.570653i	−0.0690469	−	0.0224347i	0.274290	−	0.961647i	$-0.411557\pi$
$647$	−1.75629	−	0.570653i	−0.0690469	−	0.0224347i	−0.343337	+	0.939212i	$0.611557\pi$
$648$	0.848347	+	1.16765i	0.0333262	+	0.0458696i
$649$	−6.32678			−0.248348
$650$		0			0
$651$	−14.1132			−0.553141
$652$	25.4952	+	35.0912i	0.998470	+	1.37428i
$653$	17.5121	+	5.69002i	0.685300	+	0.222667i	0.630914	−	0.775853i	$-0.282680\pi$
$653$	17.5121	+	5.69002i	0.685300	+	0.222667i	0.0543858	+	0.998520i	$0.482680\pi$
$654$	4.44588	−	13.6830i	0.173848	−	0.535048i
$655$		0			0
$656$	5.84721	+	17.9959i	0.228295	+	0.702620i
$657$			4.01123i			0.156493i
$658$	−4.89071	+	1.58909i	−0.190660	+	0.0619491i
$659$	−10.8246	−	7.86455i	−0.421668	−	0.306360i	0.356641	−	0.934242i	$-0.383922\pi$
$659$	−10.8246	−	7.86455i	−0.421668	−	0.306360i	−0.778308	+	0.627882i	$0.783922\pi$
$660$		0			0
$661$	−31.7001	+	23.0315i	−1.23299	+	0.895820i	−0.997111	−	0.0759628i	$-0.975797\pi$
$661$	−31.7001	+	23.0315i	−1.23299	+	0.895820i	−0.235879	+	0.971782i	$0.575797\pi$
$662$	−24.4469	+	33.6483i	−0.950155	+	1.30778i
$663$	−3.97639	+	5.47303i	−0.154430	+	0.212555i
$664$	15.3532	−	11.1548i	0.595821	−	0.432890i
$665$		0			0
$666$	10.4133	+	7.56571i	0.403507	+	0.293165i
$667$	−14.4821	+	4.70553i	−0.560751	+	0.182199i
$668$			30.3903i			1.17584i
$669$	−0.238424	−	0.733794i	−0.00921801	−	0.0283701i
$670$		0			0
$671$	−5.08365	+	15.6459i	−0.196252	+	0.604002i
$672$	−23.0794	−	7.49894i	−0.890305	−	0.289278i
$673$	11.3978	+	15.6877i	0.439353	+	0.604718i	0.970068	−	0.242832i	$-0.0780765\pi$
$673$	11.3978	+	15.6877i	0.439353	+	0.604718i	−0.530715	+	0.847550i	$0.678077\pi$
$674$	−46.8981			−1.80645
$675$		0			0
$676$	38.6133			1.48513
$677$	26.8522	+	36.9588i	1.03201	+	1.42044i	0.903425	+	0.428746i	$0.141044\pi$
$677$	26.8522	+	36.9588i	1.03201	+	1.42044i	0.128587	+	0.991698i	$0.458956\pi$
$678$	−18.4346	−	5.98977i	−0.707978	−	0.230036i
$679$	9.95606	−	30.6416i	0.382078	−	1.17592i
$680$		0			0
$681$	−3.53249	−	10.8719i	−0.135365	−	0.416611i
$682$		−	14.8417i		−	0.568319i
$683$	11.0220	−	3.58128i	0.421747	−	0.137034i	−0.0904520	−	0.995901i	$-0.528831\pi$
$683$	11.0220	−	3.58128i	0.421747	−	0.137034i	0.512199	+	0.858867i	$0.328831\pi$
$684$	11.7548	+	8.54034i	0.449455	+	0.326548i
$685$		0			0
$686$	−22.1577	+	16.0985i	−0.845987	+	0.614645i
$687$	−6.00996	+	8.27200i	−0.229294	+	0.315596i
$688$	−11.0596	+	15.2222i	−0.421642	+	0.580340i
$689$	−41.3436	+	30.0379i	−1.57507	+	1.14435i
$690$		0			0
$691$	17.5091	+	12.7211i	0.666077	+	0.483934i	0.868710	−	0.495321i	$-0.164950\pi$
$691$	17.5091	+	12.7211i	0.666077	+	0.483934i	−0.202632	+	0.979255i	$0.564950\pi$
$692$	−24.0002	+	7.79815i	−0.912352	+	0.296441i
$693$			4.86205i			0.184694i
$694$	1.14498	+	3.52388i	0.0434627	+	0.133764i
$695$		0			0
$696$	1.05418	−	3.24442i	0.0399585	−	0.122980i
$697$	−10.4734	−	3.40301i	−0.396707	−	0.128898i
$698$	−19.7543	−	27.1895i	−0.747713	−	1.02914i
$699$	−22.5229			−0.851896
$700$		0			0
$701$	−8.61904			−0.325537			−0.162768	−	0.986664i	$-0.552042\pi$
$701$	−8.61904			−0.325537			−0.162768	+	0.986664i	$0.552042\pi$
$702$	−6.65634	−	9.16166i	−0.251227	−	0.345785i
$703$	30.8559	+	10.0257i	1.16375	+	0.378126i
$704$	5.77751	−	17.7814i	0.217748	−	0.670160i
$705$		0			0
$706$	10.3843	+	31.9597i	0.390820	+	1.20282i
$707$		−	3.43739i		−	0.129276i
$708$	−10.4357	+	3.39077i	−0.392198	+	0.127433i
$709$	12.9443	+	9.40460i	0.486134	+	0.353197i	0.803696	−	0.595041i	$-0.202864\pi$
$709$	12.9443	+	9.40460i	0.486134	+	0.353197i	−0.317562	+	0.948238i	$0.602864\pi$
$710$		0			0
$711$	−1.30939	+	0.951325i	−0.0491058	+	0.0356775i
$712$	6.17255	−	8.49579i	0.231326	−	0.318393i
$713$	−16.9095	+	23.2740i	−0.633267	+	0.871617i
$714$	7.13030	−	5.18047i	0.266845	−	0.193874i
$715$		0			0
$716$	−8.80110	−	6.39437i	−0.328913	−	0.238969i
$717$	−0.560243	+	0.182034i	−0.0209226	+	0.00679818i
$718$			53.0138i			1.97846i
$719$	15.0132	+	46.2060i	0.559899	+	1.72319i	0.682642	+	0.730753i	$0.260831\pi$
$719$	15.0132	+	46.2060i	0.559899	+	1.72319i	−0.122743	+	0.992438i	$0.539169\pi$
$720$		0			0
$721$	4.82235	−	14.8417i	0.179594	−	0.552733i
$722$	21.8993	+	7.11551i	0.815007	+	0.264812i
$723$	−0.887185	−	1.22110i	−0.0329948	−	0.0454134i
$724$	29.6689			1.10264
$725$		0			0
$726$	18.6531			0.692283
$727$	−14.9490	−	20.5756i	−0.554429	−	0.763106i	0.436176	−	0.899861i	$-0.356333\pi$
$727$	−14.9490	−	20.5756i	−0.554429	−	0.763106i	−0.990605	+	0.136755i	$0.956333\pi$
$728$	−22.7392	−	7.38842i	−0.842772	−	0.273833i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	−3.38389	−	10.4145i	−0.125158	−	0.385196i
$732$			28.5317i			1.05456i
$733$	−17.7077	+	5.75358i	−0.654049	+	0.212513i	−0.617199	−	0.786807i	$-0.711733\pi$
$733$	−17.7077	+	5.75358i	−0.654049	+	0.212513i	−0.0368505	+	0.999321i	$0.511733\pi$
$734$	49.1287	+	35.6941i	1.81337	+	1.31749i
$735$		0			0
$736$	−40.0185	+	29.0752i	−1.47510	+	1.07172i
$737$	−1.71679	+	2.36296i	−0.0632389	+	0.0870408i
$738$	10.8354	−	14.9137i	0.398857	−	0.548980i
$739$	37.9326	−	27.5596i	1.39537	−	1.01380i	0.400121	−	0.916462i	$-0.368968\pi$
$739$	37.9326	−	27.5596i	1.39537	−	1.01380i	0.995252	−	0.0973351i	$-0.0310319\pi$
$740$		0			0
$741$	−23.0927	−	16.7779i	−0.848333	−	0.616350i
$742$	63.3194	−	20.5737i	2.32453	−	0.755286i
$743$			42.7061i			1.56674i	0.621558	+	0.783368i	$0.286500\pi$
$743$			42.7061i			1.56674i	−0.621558	+	0.783368i	$0.713500\pi$
$744$	−1.99159	−	6.12948i	−0.0730152	−	0.224718i
$745$		0			0
$746$	−6.48171	+	19.9487i	−0.237312	+	0.730372i
$747$	12.5053	+	4.06322i	0.457545	+	0.148665i
$748$	3.11374	+	4.28570i	0.113850	+	0.156701i
$749$	48.3751			1.76759
$750$		0			0
$751$	−2.64893			−0.0966608			−0.0483304	−	0.998831i	$-0.515390\pi$
$751$	−2.64893			−0.0966608			−0.0483304	+	0.998831i	$0.515390\pi$
$752$	0.981657	+	1.35113i	0.0357973	+	0.0492708i
$753$	11.3131	+	3.67584i	0.412272	+	0.133955i
$754$	−8.27133	+	25.4565i	−0.301224	+	0.927072i
$755$		0			0
$756$	2.60577	+	8.01972i	0.0947708	+	0.291674i
$757$			52.9153i			1.92324i	0.274383	+	0.961620i	$0.411526\pi$
$757$			52.9153i			1.92324i	−0.274383	+	0.961620i	$0.588474\pi$
$758$	−45.7534	+	14.8662i	−1.66184	+	0.539964i
$759$	8.01795	+	5.82538i	0.291033	+	0.211448i
$760$		0			0
$761$	−41.0808	+	29.8470i	−1.48918	+	1.08195i	−0.514728	+	0.857354i	$0.672107\pi$
$761$	−41.0808	+	29.8470i	−1.48918	+	1.08195i	−0.974451	+	0.224598i	$0.927893\pi$
$762$	−12.7229	+	17.5116i	−0.460902	+	0.634377i
$763$	12.3706	−	17.0267i	0.447847	−	0.616408i
$764$	7.79499	−	5.66339i	0.282013	−	0.204894i
$765$		0			0
$766$	23.8242	+	17.3093i	0.860803	+	0.625410i
$767$	20.5014	−	6.66131i	0.740263	−	0.240526i
$768$			0.752056i			0.0271375i
$769$	−7.59580	−	23.3775i	−0.273912	−	0.843013i	−0.989505	−	0.144496i	$-0.953844\pi$
$769$	−7.59580	−	23.3775i	−0.273912	−	0.843013i	0.715594	−	0.698517i	$-0.246156\pi$
$770$		0			0
$771$	5.57751	−	17.1658i	0.200869	−	0.618212i
$772$	−43.2791	−	14.0622i	−1.55765	−	0.506111i
$773$	−11.7623	−	16.1894i	−0.423061	−	0.582293i	0.543282	−	0.839550i	$-0.317181\pi$
$773$	−11.7623	−	16.1894i	−0.423061	−	0.582293i	−0.966343	+	0.257257i	$0.917181\pi$
$774$	18.3308			0.658885
$775$		0			0
$776$	14.7128			0.528159
$777$	11.0674	+	15.2330i	0.397042	+	0.546482i
$778$	−39.5149	−	12.8392i	−1.41668	−	0.460307i
$779$	14.3586	−	44.1911i	0.514449	−	1.58331i
$780$		0			0
$781$	−0.0336934	−	0.103698i	−0.00120565	−	0.00371060i
$782$		−	17.9654i		−	0.642441i
$783$	2.24793	−	0.730396i	0.0803344	−	0.0261022i
$784$	−5.36302	−	3.89646i	−0.191536	−	0.139159i
$785$		0			0
$786$	−11.1494	+	8.10053i	−0.397687	+	0.288936i
$787$	5.28579	−	7.27526i	0.188418	−	0.259335i	−0.704349	−	0.709854i	$-0.748761\pi$
$787$	5.28579	−	7.27526i	0.188418	−	0.259335i	0.892767	+	0.450519i	$0.148761\pi$
$788$	6.90838	−	9.50857i	0.246101	−	0.338729i
$789$	15.4576	−	11.2306i	0.550305	−	0.399820i
$790$		0			0
$791$	−22.9395	−	16.6665i	−0.815634	−	0.592593i
$792$	−2.11162	+	0.686108i	−0.0750333	+	0.0243798i
$793$		−	56.0517i		−	1.99045i
$794$	−14.8406	−	45.6747i	−0.526674	−	1.62093i
$795$		0			0
$796$	13.6824	−	42.1102i	0.484961	−	1.49256i
$797$	−35.9084	−	11.6674i	−1.27194	−	0.413279i	−0.406207	−	0.913781i	$-0.633149\pi$
$797$	−35.9084	−	11.6674i	−1.27194	−	0.413279i	−0.865735	+	0.500502i	$0.833149\pi$
$798$	21.8583	+	30.0854i	0.773776	+	1.06501i
$799$	−0.971976			−0.0343860
$800$		0			0
$801$	7.27597			0.257084
$802$	−5.99069	−	8.24547i	−0.211538	−	0.291158i
$803$	−5.86866	−	1.90684i	−0.207100	−	0.0672910i
$804$	−1.56536	+	4.81769i	−0.0552061	+	0.169907i
$805$		0			0
$806$	15.6265	+	48.0934i	0.550420	+	1.69402i
$807$			22.2250i			0.782358i
$808$	1.49289	−	0.485068i	0.0525195	−	0.0170646i
$809$	−39.5610	−	28.7428i	−1.39089	−	1.01054i	−0.995767	−	0.0919140i	$-0.970702\pi$
$809$	−39.5610	−	28.7428i	−1.39089	−	1.01054i	−0.395124	−	0.918628i	$-0.629298\pi$
$810$		0			0
$811$	14.6069	−	10.6125i	0.512916	−	0.372655i	−0.301013	−	0.953620i	$-0.597325\pi$
$811$	14.6069	−	10.6125i	0.512916	−	0.372655i	0.813929	+	0.580965i	$0.197325\pi$
$812$	11.7151	−	16.1245i	0.411121	−	0.565860i
$813$	11.8796	−	16.3508i	0.416635	−	0.573449i
$814$	−16.0193	+	11.6387i	−0.561477	+	0.407937i
$815$		0			0
$816$	−2.31570	−	1.68246i	−0.0810658	−	0.0588978i
$817$	43.9428	−	14.2779i	1.53736	−	0.499520i
$818$			26.9653i			0.942819i
$819$	−5.11914	−	15.7551i	−0.178877	−	0.550527i
$820$		0			0
$821$	15.6393	−	48.1327i	0.545814	−	1.67984i	−0.173232	−	0.984881i	$-0.555421\pi$
$821$	15.6393	−	48.1327i	0.545814	−	1.67984i	0.719046	−	0.694962i	$-0.244579\pi$
$822$	18.8577	+	6.12723i	0.657737	+	0.213712i
$823$	−15.7568	−	21.6873i	−0.549246	−	0.755972i	0.440664	−	0.897672i	$-0.354743\pi$
$823$	−15.7568	−	21.6873i	−0.549246	−	0.755972i	−0.989910	+	0.141700i	$0.954743\pi$
$824$	7.12635			0.248258
$825$		0			0
$826$	−28.0839			−0.977163
$827$	12.5580	+	17.2845i	0.436683	+	0.601042i	0.969471	−	0.245206i	$-0.0788557\pi$
$827$	12.5580	+	17.2845i	0.436683	+	0.601042i	−0.532788	+	0.846249i	$0.678856\pi$
$828$	16.3473	+	5.31155i	0.568107	+	0.184589i
$829$	14.8675	−	45.7575i	0.516370	−	1.58922i	−0.264405	−	0.964412i	$-0.585176\pi$
$829$	14.8675	−	45.7575i	0.516370	−	1.58922i	0.780775	−	0.624812i	$-0.214824\pi$
$830$		0			0
$831$	4.95702	+	15.2561i	0.171957	+	0.529230i
$832$			63.7021i			2.20847i
$833$	3.66921	−	1.19220i	0.127130	−	0.0413072i
$834$	16.1953	+	11.7665i	0.560796	+	0.407442i
$835$		0			0
$836$	−18.0830	+	13.1380i	−0.625412	+	0.454389i
$837$	2.62471	−	3.61260i	0.0907232	−	0.124870i
$838$	−44.3825	+	61.0873i	−1.53317	+	2.11022i
$839$	−33.8606	+	24.6012i	−1.16900	+	0.849327i	−0.990889	−	0.134684i	$-0.956998\pi$
$839$	−33.8606	+	24.6012i	−1.16900	+	0.849327i	−0.178110	+	0.984011i	$0.556998\pi$
$840$		0			0
$841$	18.9418	+	13.7620i	0.653165	+	0.474552i
$842$	81.2886	−	26.4123i	2.80139	−	0.910227i
$843$			8.37308i			0.288384i
$844$	−15.2900	−	47.0577i	−0.526302	−	1.61979i
$845$		0			0
$846$	0.502787	−	1.54742i	0.0172862	−	0.0532014i
$847$	25.9511	+	8.43203i	0.891691	+	0.289728i
$848$	−12.7094	−	17.4930i	−0.436442	−	0.600711i
$849$	−1.12995			−0.0387798
$850$		0			0
$851$	38.3809			1.31568
$852$	−0.111151	−	0.152987i	−0.00380799	−	0.00524124i
$853$	55.3537	+	17.9855i	1.89527	+	0.615812i	0.973819	+	0.227327i	$0.0729985\pi$
$853$	55.3537	+	17.9855i	1.89527	+	0.615812i	0.921455	+	0.388485i	$0.127002\pi$
$854$	−22.5658	+	69.4504i	−0.772186	+	2.37654i
$855$		0			0
$856$	6.82646	+	21.0097i	0.233324	+	0.718096i
$857$		−	3.22045i		−	0.110008i	−0.998486	−	0.0550042i	$-0.982483\pi$
$857$		−	3.22045i		−	0.110008i	0.998486	−	0.0550042i	$-0.0175172\pi$
$858$	16.5683	−	5.38337i	0.565633	−	0.183785i
$859$	40.0003	+	29.0619i	1.36479	+	0.991580i	0.998124	+	0.0612288i	$0.0195019\pi$
$859$	40.0003	+	29.0619i	1.36479	+	0.991580i	0.366669	+	0.930351i	$0.380498\pi$
$860$		0			0
$861$	21.8164	−	15.8505i	0.743500	−	0.540184i
$862$	−17.8534	+	24.5731i	−0.608089	+	0.836963i
$863$	−12.6329	+	17.3878i	−0.430030	+	0.591886i	−0.967960	−	0.251104i	$-0.919207\pi$
$863$	−12.6329	+	17.3878i	−0.430030	+	0.591886i	0.537930	+	0.842990i	$0.319207\pi$
$864$	6.21171	−	4.51307i	0.211327	−	0.153538i
$865$		0			0
$866$	0.960798	+	0.698061i	0.0326493	+	0.0237211i
$867$	−14.5836	+	4.73851i	−0.495286	+	0.160928i
$868$		−	37.6544i		−	1.27807i
$869$	−0.769392	−	2.36795i	−0.0260999	−	0.0803271i
$870$		0			0
$871$	3.07522	−	9.46456i	0.104200	−	0.320694i
$872$	9.14051	+	2.96993i	0.309537	+	0.100575i
$873$	5.99183	+	8.24705i	0.202793	+	0.279120i
$874$	75.8026			2.56406
$875$		0			0
$876$	−10.7020			−0.361588
$877$	−9.03971	−	12.4421i	−0.305249	−	0.420140i	0.628643	−	0.777694i	$-0.283611\pi$
$877$	−9.03971	−	12.4421i	−0.305249	−	0.420140i	−0.933892	+	0.357554i	$0.883611\pi$
$878$	6.11054	+	1.98544i	0.206221	+	0.0670052i
$879$	−0.735020	+	2.26216i	−0.0247916	+	0.0763007i
$880$		0			0
$881$	5.84891	+	18.0011i	0.197055	+	0.606472i	0.999946	+	0.0103472i	$0.00329367\pi$
$881$	5.84891	+	18.0011i	0.197055	+	0.606472i	−0.802892	+	0.596125i	$0.796706\pi$
$882$			6.45821i			0.217459i
$883$	6.00790	−	1.95208i	0.202182	−	0.0656928i	−0.206175	−	0.978515i	$-0.566102\pi$
$883$	6.00790	−	1.95208i	0.202182	−	0.0656928i	0.408357	+	0.912822i	$0.366102\pi$
$884$	−14.6021	−	10.6091i	−0.491123	−	0.356822i
$885$		0			0
$886$	64.1303	−	46.5934i	2.15450	−	1.56534i
$887$	0.0424138	−	0.0583776i	0.00142412	−	0.00196013i	−0.808304	−	0.588765i	$-0.799614\pi$
$887$	0.0424138	−	0.0583776i	0.00142412	−	0.00196013i	0.809728	+	0.586805i	$0.199614\pi$
$888$	−5.05404	+	6.95628i	−0.169602	+	0.233438i
$889$	−25.6167	+	18.6116i	−0.859156	+	0.624213i
$890$		0			0
$891$	−1.24455	−	0.904220i	−0.0416941	−	0.0302925i
$892$	1.95778	−	0.636120i	0.0655512	−	0.0212989i
$893$		−	4.10113i		−	0.137239i
$894$	−6.73107	−	20.7161i	−0.225121	−	0.692850i
$895$		0			0
$896$	10.6479	−	32.7709i	0.355721	−	1.09480i
$897$	−32.1149	−	10.4348i	−1.07229	−	0.348407i
$898$	−22.6599	−	31.1886i	−0.756169	−	1.04078i
$899$	−10.5545			−0.352013
$900$		0			0
$901$	12.5840			0.419235
$902$	16.6687	+	22.9425i	0.555006	+	0.763901i
$903$	25.5026	+	8.28629i	0.848673	+	0.275751i
$904$	4.00128	−	12.3147i	0.133081	−	0.409580i
$905$		0			0
$906$	−7.16888	−	22.0635i	−0.238170	−	0.733012i
$907$		−	25.4951i		−	0.846550i	−0.906001	−	0.423275i	$-0.860880\pi$
$907$		−	25.4951i		−	0.846550i	0.906001	−	0.423275i	$-0.139120\pi$
$908$	29.0064	−	9.42474i	0.962610	−	0.312771i
$909$	0.879879	+	0.639269i	0.0291837	+	0.0212032i
$910$		0			0
$911$	−2.87851	+	2.09136i	−0.0953692	+	0.0692898i	−0.634448	−	0.772966i	$-0.718773\pi$
$911$	−2.87851	+	2.09136i	−0.0953692	+	0.0692898i	0.539079	+	0.842255i	$0.318773\pi$
$912$	7.09891	−	9.77081i	0.235068	−	0.323544i
$913$	−11.8894	+	16.3644i	−0.393483	+	0.541583i
$914$	−42.2621	+	30.7052i	−1.39791	+	1.01564i
$915$		0			0
$916$	−22.0698	−	16.0347i	−0.729208	−	0.529801i
$917$	−19.1734	+	6.22981i	−0.633161	+	0.205727i
$918$			2.78860i			0.0920375i
$919$	−2.46277	−	7.57962i	−0.0812392	−	0.250029i	0.902185	−	0.431350i	$-0.141963\pi$
$919$	−2.46277	−	7.57962i	−0.0812392	−	0.250029i	−0.983424	+	0.181321i	$0.941963\pi$
$920$		0			0
$921$	−0.894189	+	2.75203i	−0.0294645	+	0.0906825i
$922$	−76.8241	−	24.9617i	−2.53007	−	0.822068i
$923$	0.218362	+	0.300549i	0.00718747	+	0.00989270i
$924$	−12.9720			−0.426749
$925$		0			0
$926$	44.1434			1.45064
$927$	2.90222	+	3.99457i	0.0953216	+	0.131199i
$928$	−17.2598	−	5.60805i	−0.566581	−	0.184093i
$929$	−15.0004	+	46.1666i	−0.492149	+	1.51468i	0.329205	+	0.944258i	$0.393219\pi$
$929$	−15.0004	+	46.1666i	−0.492149	+	1.51468i	−0.821354	+	0.570419i	$0.806781\pi$
$930$		0			0
$931$	5.03032	+	15.4817i	0.164862	+	0.507394i
$932$		−	60.0916i		−	1.96837i
$933$	6.79573	−	2.20807i	0.222482	−	0.0722888i
$934$	54.5571	+	39.6381i	1.78516	+	1.29700i
$935$		0			0
$936$	6.12016	−	4.44656i	0.200044	−	0.145340i
$937$	18.6502	−	25.6698i	0.609274	−	0.838594i	−0.387243	−	0.921978i	$-0.626573\pi$
$937$	18.6502	−	25.6698i	0.609274	−	0.838594i	0.996518	+	0.0833833i	$0.0265726\pi$
$938$	−7.62066	+	10.4889i	−0.248823	+	0.342476i
$939$	−18.6331	+	13.5378i	−0.608070	+	0.441789i
$940$		0			0
$941$	−33.1752	−	24.1032i	−1.08148	−	0.785742i	−0.103541	−	0.994625i	$-0.533017\pi$
$941$	−33.1752	−	24.1032i	−1.08148	−	0.785742i	−0.977941	+	0.208883i	$0.933017\pi$
$942$	35.8395	−	11.6450i	1.16771	−	0.379414i
$943$		−	54.9681i		−	1.79001i
$944$	2.81848	+	8.67439i	0.0917337	+	0.282327i
$945$		0			0
$946$	−8.71401	+	26.8190i	−0.283317	+	0.871960i
$947$	−9.33737	−	3.03389i	−0.303424	−	0.0985883i	0.153348	−	0.988172i	$-0.450994\pi$
$947$	−9.33737	−	3.03389i	−0.303424	−	0.0985883i	−0.456772	+	0.889584i	$0.650994\pi$
$948$	−2.53815	−	3.49347i	−0.0824353	−	0.113463i
$949$	21.0246			0.682487
$950$		0			0
$951$	20.7750			0.673674
$952$	3.46065	+	4.76317i	0.112160	+	0.154375i
$953$	−50.5123	−	16.4125i	−1.63626	−	0.531652i	−0.660558	−	0.750775i	$-0.729680\pi$
$953$	−50.5123	−	16.4125i	−1.63626	−	0.531652i	−0.975697	+	0.219123i	$0.929680\pi$
$954$	−6.50952	+	20.0343i	−0.210754	+	0.648633i
$955$		0			0
$956$	−0.485670	−	1.49474i	−0.0157077	−	0.0483433i
$957$			3.63606i			0.117537i
$958$	22.8022	−	7.40888i	0.736705	−	0.239370i
$959$	23.4659	+	17.0490i	0.757754	+	0.550540i
$960$		0			0
$961$	8.94773	−	6.50090i	0.288636	−	0.209707i
$962$	39.6552	−	54.5807i	1.27853	−	1.75975i
$963$	−8.99657	+	12.3827i	−0.289910	+	0.399027i
$964$	3.25793	−	2.36703i	0.104931	−	0.0762368i
$965$		0			0
$966$	35.5908	+	25.8583i	1.14512	+	0.831976i
$967$	2.32754	−	0.756262i	0.0748485	−	0.0243198i	−0.271353	−	0.962480i	$-0.587471\pi$
$967$	2.32754	−	0.756262i	0.0748485	−	0.0243198i	0.346202	+	0.938160i	$0.387471\pi$
$968$			12.4606i			0.400500i
$969$	2.17205	+	6.68488i	0.0697763	+	0.214749i
$970$		0			0
$971$	−14.8230	+	45.6205i	−0.475693	+	1.46403i	0.369328	+	0.929299i	$0.379588\pi$
$971$	−14.8230	+	45.6205i	−0.475693	+	1.46403i	−0.845021	+	0.534734i	$0.820412\pi$
$972$	−2.53744	−	0.824463i	−0.0813883	−	0.0264447i
$973$	17.2126	+	23.6911i	0.551811	+	0.759502i
$974$	−15.4200			−0.494088
$975$		0			0
$976$	23.7161			0.759134
$977$	−13.9276	−	19.1696i	−0.445582	−	0.613291i	0.525859	−	0.850572i	$-0.323744\pi$
$977$	−13.9276	−	19.1696i	−0.445582	−	0.613291i	−0.971441	+	0.237280i	$0.923744\pi$
$978$	−33.4060	−	10.8543i	−1.06820	−	0.347081i
$979$	−3.45883	+	10.6452i	−0.110545	+	0.340221i
$980$		0			0
$981$	2.05774	+	6.33308i	0.0656987	+	0.202200i
$982$			15.6284i			0.498721i
$983$	12.3167	−	4.00193i	0.392841	−	0.127642i	−0.105934	−	0.994373i	$-0.533783\pi$
$983$	12.3167	−	4.00193i	0.392841	−	0.127642i	0.498775	+	0.866731i	$0.333783\pi$
$984$	9.96261	+	7.23826i	0.317597	+	0.230747i
$985$		0			0
$986$	5.33236	−	3.87419i	0.169817	−	0.123379i
$987$	1.39900	−	1.92556i	0.0445307	−	0.0612913i
$988$	44.7637	−	61.6119i	1.42412	−	1.96014i
$989$	44.2203	−	32.1279i	1.40612	−	1.02161i
$990$		0			0
$991$	−35.9986	−	26.1545i	−1.14353	−	0.830826i	−0.155926	−	0.987769i	$-0.549836\pi$
$991$	−35.9986	−	26.1545i	−1.14353	−	0.830826i	−0.987608	+	0.156943i	$0.949836\pi$
$992$	−32.6079	+	10.5949i	−1.03530	+	0.336389i
$993$		−	19.2504i		−	0.610891i
$994$	−0.149562	−	0.460303i	−0.00474381	−	0.0145999i
$995$		0			0
$996$	−10.8407	+	33.3644i	−0.343502	+	1.05719i
$997$	−52.8324	−	17.1663i	−1.67322	−	0.543662i	−0.689642	−	0.724150i	$-0.742232\pi$
$997$	−52.8324	−	17.1663i	−1.67322	−	0.543662i	−0.983577	+	0.180488i	$0.942232\pi$
$998$	20.3406	+	27.9964i	0.643869	+	0.886209i
$999$	−5.95751			−0.188487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.d.199.1		24
5.2	odd	4		375.2.g.c.301.3		12
5.3	odd	4		75.2.g.c.61.1	yes	12
5.4	even	2	inner	375.2.i.d.199.6		24
15.8	even	4		225.2.h.d.136.3		12
25.3	odd	20		1875.2.a.j.1.5		6
25.4	even	10		1875.2.b.f.1249.3		12
25.9	even	10	inner	375.2.i.d.49.1		24
25.12	odd	20		375.2.g.c.76.3		12
25.13	odd	20		75.2.g.c.16.1	✓	12
25.16	even	5	inner	375.2.i.d.49.6		24
25.21	even	5		1875.2.b.f.1249.10		12
25.22	odd	20		1875.2.a.k.1.2		6
75.38	even	20		225.2.h.d.91.3		12
75.47	even	20		5625.2.a.q.1.5		6
75.53	even	20		5625.2.a.p.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.1	✓	12	25.13	odd	20
75.2.g.c.61.1	yes	12	5.3	odd	4
225.2.h.d.91.3		12	75.38	even	20
225.2.h.d.136.3		12	15.8	even	4
375.2.g.c.76.3		12	25.12	odd	20
375.2.g.c.301.3		12	5.2	odd	4
375.2.i.d.49.1		24	25.9	even	10	inner
375.2.i.d.49.6		24	25.16	even	5	inner
375.2.i.d.199.1		24	1.1	even	1	trivial
375.2.i.d.199.6		24	5.4	even	2	inner
1875.2.a.j.1.5		6	25.3	odd	20
1875.2.a.k.1.2		6	25.22	odd	20
1875.2.b.f.1249.3		12	25.4	even	10
1875.2.b.f.1249.10		12	25.21	even	5
5625.2.a.p.1.2		6	75.53	even	20
5625.2.a.q.1.5		6	75.47	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.26995 - 1.74793i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.824463 + 2.53744i) q^{4} +(-0.667650 - 2.05481i) q^{6} -3.16056i q^{7} +(1.37265 - 0.446002i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.26995 - 1.74793i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.824463 + 2.53744i) q^{4} +(-0.667650 - 2.05481i) q^{6} -3.16056i q^{7} +(1.37265 - 0.446002i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.24455 + 0.904220i) q^{11} +(-1.56822 + 2.15847i) q^{12} +(3.08084 - 4.24041i) q^{13} +(-5.52444 + 4.01374i) q^{14} +(1.79417 + 1.30354i) q^{16} +(-1.22751 + 0.398843i) q^{17} -2.16056i q^{18} +(-1.68287 - 5.17933i) q^{19} +(0.976667 - 3.00587i) q^{21} +(3.16103 + 1.02708i) q^{22} +(-3.78677 - 5.21204i) q^{23} +1.44329 q^{24} -11.3244 q^{26} +(0.587785 + 0.809017i) q^{27} +(8.01972 + 2.60577i) q^{28} +(0.730396 - 2.24793i) q^{29} +(-1.37989 - 4.24687i) q^{31} -7.67809i q^{32} +(-1.46306 + 0.475377i) q^{33} +(2.25602 + 1.63910i) q^{34} +(-2.15847 + 1.56822i) q^{36} +(-3.50174 + 4.81973i) q^{37} +(-6.91596 + 9.51901i) q^{38} +(4.24041 - 3.08084i) q^{39} +(6.90269 + 5.01510i) q^{41} +(-6.49436 + 2.11015i) q^{42} +8.48426i q^{43} +(-1.26831 - 3.90347i) q^{44} +(-4.30129 + 13.2380i) q^{46} +(0.716212 + 0.232712i) q^{47} +(1.30354 + 1.79417i) q^{48} -2.98914 q^{49} -1.29068 q^{51} +(8.21974 + 11.3135i) q^{52} +(-9.27271 - 3.01289i) q^{53} +(0.667650 - 2.05481i) q^{54} +(-1.40962 - 4.33836i) q^{56} -5.44587i q^{57} +(-4.85678 + 1.57806i) q^{58} +(3.32724 + 2.41738i) q^{59} +(8.65159 - 6.28574i) q^{61} +(-5.67084 + 7.80525i) q^{62} +(1.85773 - 2.55695i) q^{63} +(-9.83243 + 7.14368i) q^{64} +(2.68893 + 1.95362i) q^{66} +(1.80572 - 0.586713i) q^{67} -3.44357i q^{68} +(-1.99082 - 6.12712i) q^{69} +(-0.0219023 + 0.0674084i) q^{71} +(1.37265 + 0.446002i) q^{72} +(2.35774 + 3.24515i) q^{73} +12.8716 q^{74} +14.5297 q^{76} +(2.85784 + 3.93348i) q^{77} +(-10.7702 - 3.49944i) q^{78} +(-0.500141 + 1.53928i) q^{79} +(0.309017 + 0.951057i) q^{81} -18.4343i q^{82} +(12.5053 - 4.06322i) q^{83} +(6.82198 + 4.95646i) q^{84} +(14.8299 - 10.7745i) q^{86} +(1.38930 - 1.91220i) q^{87} +(-1.30506 + 1.79626i) q^{88} +(5.88638 - 4.27671i) q^{89} +(-13.4021 - 9.73718i) q^{91} +(16.3473 - 5.31155i) q^{92} -4.46542i q^{93} +(-0.502787 - 1.54742i) q^{94} +(2.37266 - 7.30230i) q^{96} +(9.69499 + 3.15009i) q^{97} +(3.79604 + 5.22480i) q^{98} -1.53835 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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