LMFDB - Embedded newform 75.3.c.c.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(26,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("75.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.c (of order $2$, degree $1$, 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:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-11}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 3 $ x^2 - x + 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.1
Root			$0.500000 + 1.65831i$ of defining polynomial
Character	$\chi$	$=$	75.26
Dual form			75.3.c.c.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.31662i q^{2} +(-2.50000 - 1.65831i) q^{3} -7.00000 q^{4} +(-5.50000 + 8.29156i) q^{6} +9.94987i q^{8} +(3.50000 + 8.29156i) q^{9} +O(q^{10})$	\(q-3.31662i q^{2} +(-2.50000 - 1.65831i) q^{3} -7.00000 q^{4} +(-5.50000 + 8.29156i) q^{6} +9.94987i q^{8} +(3.50000 + 8.29156i) q^{9} -16.5831i q^{11} +(17.5000 + 11.6082i) q^{12} -10.0000 q^{13} +5.00000 q^{16} -3.31662i q^{17} +(27.5000 - 11.6082i) q^{18} +7.00000 q^{19} -55.0000 q^{22} -19.8997i q^{23} +(16.5000 - 24.8747i) q^{24} +33.1662i q^{26} +(5.00000 - 26.5330i) q^{27} -33.1662i q^{29} +42.0000 q^{31} +23.2164i q^{32} +(-27.5000 + 41.4578i) q^{33} -11.0000 q^{34} +(-24.5000 - 58.0409i) q^{36} +40.0000 q^{37} -23.2164i q^{38} +(25.0000 + 16.5831i) q^{39} +16.5831i q^{41} +50.0000 q^{43} +116.082i q^{44} -66.0000 q^{46} +46.4327i q^{47} +(-12.5000 - 8.29156i) q^{48} -49.0000 q^{49} +(-5.50000 + 8.29156i) q^{51} +70.0000 q^{52} +46.4327i q^{53} +(-88.0000 - 16.5831i) q^{54} +(-17.5000 - 11.6082i) q^{57} -110.000 q^{58} -66.3325i q^{59} -8.00000 q^{61} -139.298i q^{62} +97.0000 q^{64} +(137.500 + 91.2072i) q^{66} -45.0000 q^{67} +23.2164i q^{68} +(-33.0000 + 49.7494i) q^{69} -33.1662i q^{71} +(-82.5000 + 34.8246i) q^{72} +35.0000 q^{73} -132.665i q^{74} -49.0000 q^{76} +(55.0000 - 82.9156i) q^{78} +12.0000 q^{79} +(-56.5000 + 58.0409i) q^{81} +55.0000 q^{82} -69.6491i q^{83} -165.831i q^{86} +(-55.0000 + 82.9156i) q^{87} +165.000 q^{88} +149.248i q^{89} +139.298i q^{92} +(-105.000 - 69.6491i) q^{93} +154.000 q^{94} +(38.5000 - 58.0409i) q^{96} +70.0000 q^{97} +162.515i q^{98} +(137.500 - 58.0409i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 5 q^{3} - 14 q^{4} - 11 q^{6} + 7 q^{9}+O(q^{10}) $ 2 * q - 5 * q^3 - 14 * q^4 - 11 * q^6 + 7 * q^9	$ 2 q - 5 q^{3} - 14 q^{4} - 11 q^{6} + 7 q^{9} + 35 q^{12} - 20 q^{13} + 10 q^{16} + 55 q^{18} + 14 q^{19} - 110 q^{22} + 33 q^{24} + 10 q^{27} + 84 q^{31} - 55 q^{33} - 22 q^{34} - 49 q^{36} + 80 q^{37} + 50 q^{39} + 100 q^{43} - 132 q^{46} - 25 q^{48} - 98 q^{49} - 11 q^{51} + 140 q^{52} - 176 q^{54} - 35 q^{57} - 220 q^{58} - 16 q^{61} + 194 q^{64} + 275 q^{66} - 90 q^{67} - 66 q^{69} - 165 q^{72} + 70 q^{73} - 98 q^{76} + 110 q^{78} + 24 q^{79} - 113 q^{81} + 110 q^{82} - 110 q^{87} + 330 q^{88} - 210 q^{93} + 308 q^{94} + 77 q^{96} + 140 q^{97} + 275 q^{99}+O(q^{100}) $ 2 * q - 5 * q^3 - 14 * q^4 - 11 * q^6 + 7 * q^9 + 35 * q^12 - 20 * q^13 + 10 * q^16 + 55 * q^18 + 14 * q^19 - 110 * q^22 + 33 * q^24 + 10 * q^27 + 84 * q^31 - 55 * q^33 - 22 * q^34 - 49 * q^36 + 80 * q^37 + 50 * q^39 + 100 * q^43 - 132 * q^46 - 25 * q^48 - 98 * q^49 - 11 * q^51 + 140 * q^52 - 176 * q^54 - 35 * q^57 - 220 * q^58 - 16 * q^61 + 194 * q^64 + 275 * q^66 - 90 * q^67 - 66 * q^69 - 165 * q^72 + 70 * q^73 - 98 * q^76 + 110 * q^78 + 24 * q^79 - 113 * q^81 + 110 * q^82 - 110 * q^87 + 330 * q^88 - 210 * q^93 + 308 * q^94 + 77 * q^96 + 140 * q^97 + 275 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	3.31662i		−	1.65831i	−0.559017	−	0.829156i	$-0.688821\pi$
$2$		−	3.31662i		−	1.65831i	0.559017	−	0.829156i	$-0.311179\pi$
$3$	−2.50000	−	1.65831i	−0.833333	−	0.552771i
$3$	−2.50000	−	1.65831i	−0.833333	−	0.552771i
$4$	−7.00000			−1.75000
$5$		0			0
$5$		0			0
$6$	−5.50000	+	8.29156i	−0.916667	+	1.38193i
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$			9.94987i			1.24373i
$9$	3.50000	+	8.29156i	0.388889	+	0.921285i
$10$		0			0
$11$		−	16.5831i		−	1.50756i	−0.657129	−	0.753778i	$-0.728229\pi$
$11$		−	16.5831i		−	1.50756i	0.657129	−	0.753778i	$-0.271771\pi$
$12$	17.5000	+	11.6082i	1.45833	+	0.967349i
$13$	−10.0000			−0.769231			−0.384615	−	0.923077i	$-0.625666\pi$
$13$	−10.0000			−0.769231			−0.384615	+	0.923077i	$0.625666\pi$
$14$		0			0
$15$		0			0
$16$	5.00000			0.312500
$17$		−	3.31662i		−	0.195096i	−0.995231	−	0.0975478i	$-0.968900\pi$
$17$		−	3.31662i		−	0.195096i	0.995231	−	0.0975478i	$-0.0310999\pi$
$18$	27.5000	−	11.6082i	1.52778	−	0.644899i
$19$	7.00000			0.368421			0.184211	−	0.982887i	$-0.441027\pi$
$19$	7.00000			0.368421			0.184211	+	0.982887i	$0.441027\pi$
$20$		0			0
$21$		0			0
$22$	−55.0000			−2.50000
$23$		−	19.8997i		−	0.865206i	−0.901584	−	0.432603i	$-0.857595\pi$
$23$		−	19.8997i		−	0.865206i	0.901584	−	0.432603i	$-0.142405\pi$
$24$	16.5000	−	24.8747i	0.687500	−	1.03645i
$25$		0			0
$26$			33.1662i			1.27562i
$27$	5.00000	−	26.5330i	0.185185	−	0.982704i
$28$		0			0
$29$		−	33.1662i		−	1.14366i	−0.820371	−	0.571832i	$-0.806233\pi$
$29$		−	33.1662i		−	1.14366i	0.820371	−	0.571832i	$-0.193767\pi$
$30$		0			0
$31$	42.0000			1.35484			0.677419	−	0.735597i	$-0.263098\pi$
$31$	42.0000			1.35484			0.677419	+	0.735597i	$0.263098\pi$
$32$			23.2164i			0.725512i
$33$	−27.5000	+	41.4578i	−0.833333	+	1.25630i
$34$	−11.0000			−0.323529
$35$		0			0
$36$	−24.5000	−	58.0409i	−0.680556	−	1.61225i
$37$	40.0000			1.08108			0.540541	−	0.841318i	$-0.318220\pi$
$37$	40.0000			1.08108			0.540541	+	0.841318i	$0.318220\pi$
$38$		−	23.2164i		−	0.610957i
$39$	25.0000	+	16.5831i	0.641026	+	0.425208i
$40$		0			0
$41$			16.5831i			0.404466i	0.979337	+	0.202233i	$0.0648199\pi$
$41$			16.5831i			0.404466i	−0.979337	+	0.202233i	$0.935180\pi$
$42$		0			0
$43$	50.0000			1.16279			0.581395	−	0.813621i	$-0.302507\pi$
$43$	50.0000			1.16279			0.581395	+	0.813621i	$0.302507\pi$
$44$			116.082i			2.63822i
$45$		0			0
$46$	−66.0000			−1.43478
$47$			46.4327i			0.987931i	0.869482	+	0.493965i	$0.164453\pi$
$47$			46.4327i			0.987931i	−0.869482	+	0.493965i	$0.835547\pi$
$48$	−12.5000	−	8.29156i	−0.260417	−	0.172741i
$49$	−49.0000			−1.00000
$50$		0			0
$51$	−5.50000	+	8.29156i	−0.107843	+	0.162580i
$52$	70.0000			1.34615
$53$			46.4327i			0.876090i	0.898953	+	0.438045i	$0.144329\pi$
$53$			46.4327i			0.876090i	−0.898953	+	0.438045i	$0.855671\pi$
$54$	−88.0000	−	16.5831i	−1.62963	−	0.307095i
$55$		0			0
$56$		0			0
$57$	−17.5000	−	11.6082i	−0.307018	−	0.203652i
$58$	−110.000			−1.89655
$59$		−	66.3325i		−	1.12428i	−0.827042	−	0.562140i	$-0.809978\pi$
$59$		−	66.3325i		−	1.12428i	0.827042	−	0.562140i	$-0.190022\pi$
$60$		0			0
$61$	−8.00000			−0.131148			−0.0655738	−	0.997848i	$-0.520888\pi$
$61$	−8.00000			−0.131148			−0.0655738	+	0.997848i	$0.520888\pi$
$62$		−	139.298i		−	2.24675i
$63$		0			0
$64$	97.0000			1.51562
$65$		0			0
$66$	137.500	+	91.2072i	2.08333	+	1.38193i
$67$	−45.0000			−0.671642			−0.335821	−	0.941926i	$-0.609014\pi$
$67$	−45.0000			−0.671642			−0.335821	+	0.941926i	$0.609014\pi$
$68$			23.2164i			0.341417i
$69$	−33.0000	+	49.7494i	−0.478261	+	0.721005i
$70$		0			0
$71$		−	33.1662i		−	0.467130i	−0.972341	−	0.233565i	$-0.924961\pi$
$71$		−	33.1662i		−	0.467130i	0.972341	−	0.233565i	$-0.0750392\pi$
$72$	−82.5000	+	34.8246i	−1.14583	+	0.483674i
$73$	35.0000			0.479452			0.239726	−	0.970841i	$-0.422942\pi$
$73$	35.0000			0.479452			0.239726	+	0.970841i	$0.422942\pi$
$74$		−	132.665i		−	1.79277i
$75$		0			0
$76$	−49.0000			−0.644737
$77$		0			0
$78$	55.0000	−	82.9156i	0.705128	−	1.06302i
$79$	12.0000			0.151899			0.0759494	−	0.997112i	$-0.475801\pi$
$79$	12.0000			0.151899			0.0759494	+	0.997112i	$0.475801\pi$
$80$		0			0
$81$	−56.5000	+	58.0409i	−0.697531	+	0.716555i
$82$	55.0000			0.670732
$83$		−	69.6491i		−	0.839146i	−0.907722	−	0.419573i	$-0.862180\pi$
$83$		−	69.6491i		−	0.839146i	0.907722	−	0.419573i	$-0.137820\pi$
$84$		0			0
$85$		0			0
$86$		−	165.831i		−	1.92827i
$87$	−55.0000	+	82.9156i	−0.632184	+	0.953053i
$88$	165.000			1.87500
$89$			149.248i			1.67695i	0.544944	+	0.838473i	$0.316551\pi$
$89$			149.248i			1.67695i	−0.544944	+	0.838473i	$0.683449\pi$
$90$		0			0
$91$		0			0
$92$			139.298i			1.51411i
$93$	−105.000	−	69.6491i	−1.12903	−	0.748915i
$94$	154.000			1.63830
$95$		0			0
$96$	38.5000	−	58.0409i	0.401042	−	0.604593i
$97$	70.0000			0.721649			0.360825	−	0.932634i	$-0.382495\pi$
$97$	70.0000			0.721649			0.360825	+	0.932634i	$0.382495\pi$
$98$			162.515i			1.65831i
$99$	137.500	−	58.0409i	1.38889	−	0.586272i
$100$		0			0
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$	27.5000	+	18.2414i	0.269608	+	0.178838i
$103$	70.0000			0.679612			0.339806	−	0.940496i	$-0.389639\pi$
$103$	70.0000			0.679612			0.339806	+	0.940496i	$0.389639\pi$
$104$		−	99.4987i		−	0.956719i
$105$		0			0
$106$	154.000			1.45283
$107$		−	69.6491i		−	0.650926i	−0.945555	−	0.325463i	$-0.894480\pi$
$107$		−	69.6491i		−	0.650926i	0.945555	−	0.325463i	$-0.105520\pi$
$108$	−35.0000	+	185.731i	−0.324074	+	1.71973i
$109$	−88.0000			−0.807339			−0.403670	−	0.914905i	$-0.632266\pi$
$109$	−88.0000			−0.807339			−0.403670	+	0.914905i	$0.632266\pi$
$110$		0			0
$111$	−100.000	−	66.3325i	−0.900901	−	0.597590i
$112$		0			0
$113$		−	102.815i		−	0.909871i	−0.890525	−	0.454935i	$-0.849662\pi$
$113$		−	102.815i		−	0.909871i	0.890525	−	0.454935i	$-0.150338\pi$
$114$	−38.5000	+	58.0409i	−0.337719	+	0.509131i
$115$		0			0
$116$			232.164i			2.00141i
$117$	−35.0000	−	82.9156i	−0.299145	−	0.708681i
$118$	−220.000			−1.86441
$119$		0			0
$120$		0			0
$121$	−154.000			−1.27273
$122$			26.5330i			0.217484i
$123$	27.5000	−	41.4578i	0.223577	−	0.337055i
$124$	−294.000			−2.37097
$125$		0			0
$126$		0			0
$127$	−190.000			−1.49606			−0.748031	−	0.663663i	$-0.769001\pi$
$127$	−190.000			−1.49606			−0.748031	+	0.663663i	$0.769001\pi$
$128$		−	228.847i		−	1.78787i
$129$	−125.000	−	82.9156i	−0.968992	−	0.642757i
$130$		0			0
$131$			198.997i			1.51906i	0.650469	+	0.759532i	$0.274572\pi$
$131$			198.997i			1.51906i	−0.650469	+	0.759532i	$0.725428\pi$
$132$	192.500	−	290.205i	1.45833	−	2.19852i
$133$		0			0
$134$			149.248i			1.11379i
$135$		0			0
$136$	33.0000			0.242647
$137$		−	69.6491i		−	0.508388i	−0.967153	−	0.254194i	$-0.918190\pi$
$137$		−	69.6491i		−	0.508388i	0.967153	−	0.254194i	$-0.0818101\pi$
$138$	165.000	+	109.449i	1.19565	+	0.793106i
$139$	77.0000			0.553957			0.276978	−	0.960876i	$-0.410667\pi$
$139$	77.0000			0.553957			0.276978	+	0.960876i	$0.410667\pi$
$140$		0			0
$141$	77.0000	−	116.082i	0.546099	−	0.823276i
$142$	−110.000			−0.774648
$143$			165.831i			1.15966i
$144$	17.5000	+	41.4578i	0.121528	+	0.287901i
$145$		0			0
$146$		−	116.082i		−	0.795081i
$147$	122.500	+	81.2573i	0.833333	+	0.552771i
$148$	−280.000			−1.89189
$149$			165.831i			1.11296i	0.830861	+	0.556481i	$0.187849\pi$
$149$			165.831i			1.11296i	−0.830861	+	0.556481i	$0.812151\pi$
$150$		0			0
$151$	172.000			1.13907			0.569536	−	0.821966i	$-0.307123\pi$
$151$	172.000			1.13907			0.569536	+	0.821966i	$0.307123\pi$
$152$			69.6491i			0.458218i
$153$	27.5000	−	11.6082i	0.179739	−	0.0758705i
$154$		0			0
$155$		0			0
$156$	−175.000	−	116.082i	−1.12179	−	0.744115i
$157$	250.000			1.59236			0.796178	−	0.605062i	$-0.206852\pi$
$157$	250.000			1.59236			0.796178	+	0.605062i	$0.206852\pi$
$158$		−	39.7995i		−	0.251896i
$159$	77.0000	−	116.082i	0.484277	−	0.730075i
$160$		0			0
$161$		0			0
$162$	192.500	+	187.389i	1.18827	+	1.15672i
$163$	−35.0000			−0.214724			−0.107362	−	0.994220i	$-0.534240\pi$
$163$	−35.0000			−0.214724			−0.107362	+	0.994220i	$0.534240\pi$
$164$		−	116.082i		−	0.707816i
$165$		0			0
$166$	−231.000			−1.39157
$167$			179.098i			1.07244i	0.844078	+	0.536221i	$0.180149\pi$
$167$			179.098i			1.07244i	−0.844078	+	0.536221i	$0.819851\pi$
$168$		0			0
$169$	−69.0000			−0.408284
$170$		0			0
$171$	24.5000	+	58.0409i	0.143275	+	0.339421i
$172$	−350.000			−2.03488
$173$			278.596i			1.61038i	0.593014	+	0.805192i	$0.297938\pi$
$173$			278.596i			1.61038i	−0.593014	+	0.805192i	$0.702062\pi$
$174$	275.000	+	182.414i	1.58046	+	1.04836i
$175$		0			0
$176$		−	82.9156i		−	0.471111i
$177$	−110.000	+	165.831i	−0.621469	+	0.936900i
$178$	495.000			2.78090
$179$		−	116.082i		−	0.648502i	−0.945971	−	0.324251i	$-0.894888\pi$
$179$		−	116.082i		−	0.648502i	0.945971	−	0.324251i	$-0.105112\pi$
$180$		0			0
$181$	182.000			1.00552			0.502762	−	0.864425i	$-0.332317\pi$
$181$	182.000			1.00552			0.502762	+	0.864425i	$0.332317\pi$
$182$		0			0
$183$	20.0000	+	13.2665i	0.109290	+	0.0724945i
$184$	198.000			1.07609
$185$		0			0
$186$	−231.000	+	348.246i	−1.24194	+	1.87229i
$187$	−55.0000			−0.294118
$188$		−	325.029i		−	1.72888i
$189$		0			0
$190$		0			0
$191$		−	232.164i		−	1.21552i	−0.794122	−	0.607758i	$-0.792069\pi$
$191$		−	232.164i		−	1.21552i	0.794122	−	0.607758i	$-0.207931\pi$
$192$	−242.500	−	160.856i	−1.26302	−	0.837793i
$193$	25.0000			0.129534			0.0647668	−	0.997900i	$-0.479370\pi$
$193$	25.0000			0.129534			0.0647668	+	0.997900i	$0.479370\pi$
$194$		−	232.164i		−	1.19672i
$195$		0			0
$196$	343.000			1.75000
$197$		−	218.897i		−	1.11115i	−0.831465	−	0.555577i	$-0.812498\pi$
$197$		−	218.897i		−	1.11115i	0.831465	−	0.555577i	$-0.187502\pi$
$198$	−192.500	−	456.036i	−0.972222	−	2.30321i
$199$	−68.0000			−0.341709			−0.170854	−	0.985296i	$-0.554653\pi$
$199$	−68.0000			−0.341709			−0.170854	+	0.985296i	$0.554653\pi$
$200$		0			0
$201$	112.500	+	74.6241i	0.559701	+	0.371264i
$202$		0			0
$203$		0			0
$204$	38.5000	−	58.0409i	0.188725	−	0.284514i
$205$		0			0
$206$		−	232.164i		−	1.12701i
$207$	165.000	−	69.6491i	0.797101	−	0.336469i
$208$	−50.0000			−0.240385
$209$		−	116.082i		−	0.555416i
$210$		0			0
$211$	77.0000			0.364929			0.182464	−	0.983212i	$-0.441593\pi$
$211$	77.0000			0.364929			0.182464	+	0.983212i	$0.441593\pi$
$212$		−	325.029i		−	1.53316i
$213$	−55.0000	+	82.9156i	−0.258216	+	0.389275i
$214$	−231.000			−1.07944
$215$		0			0
$216$	264.000	+	49.7494i	1.22222	+	0.230321i
$217$		0			0
$218$			291.863i			1.33882i
$219$	−87.5000	−	58.0409i	−0.399543	−	0.265027i
$220$		0			0
$221$			33.1662i			0.150074i
$222$	−220.000	+	331.662i	−0.990991	+	1.49398i
$223$	−140.000			−0.627803			−0.313901	−	0.949456i	$-0.601636\pi$
$223$	−140.000			−0.627803			−0.313901	+	0.949456i	$0.601636\pi$
$224$		0			0
$225$		0			0
$226$	−341.000			−1.50885
$227$		−	185.731i		−	0.818198i	−0.912490	−	0.409099i	$-0.865843\pi$
$227$		−	185.731i		−	0.818198i	0.912490	−	0.409099i	$-0.134157\pi$
$228$	122.500	+	81.2573i	0.537281	+	0.356392i
$229$	372.000			1.62445			0.812227	−	0.583341i	$-0.198255\pi$
$229$	372.000			1.62445			0.812227	+	0.583341i	$0.198255\pi$
$230$		0			0
$231$		0			0
$232$	330.000			1.42241
$233$		−	119.398i		−	0.512440i	−0.966619	−	0.256220i	$-0.917523\pi$
$233$		−	119.398i		−	0.512440i	0.966619	−	0.256220i	$-0.0824771\pi$
$234$	−275.000	+	116.082i	−1.17521	+	0.496076i
$235$		0			0
$236$			464.327i			1.96749i
$237$	−30.0000	−	19.8997i	−0.126582	−	0.0839652i
$238$		0			0
$239$			232.164i			0.971396i	0.874127	+	0.485698i	$0.161435\pi$
$239$			232.164i			0.971396i	−0.874127	+	0.485698i	$0.838565\pi$
$240$		0			0
$241$	−413.000			−1.71369			−0.856846	−	0.515572i	$-0.827580\pi$
$241$	−413.000			−1.71369			−0.856846	+	0.515572i	$0.827580\pi$
$242$			510.760i			2.11058i
$243$	237.500	−	51.4077i	0.977366	−	0.211554i
$244$	56.0000			0.229508
$245$		0			0
$246$	−137.500	−	91.2072i	−0.558943	−	0.370761i
$247$	−70.0000			−0.283401
$248$			417.895i			1.68506i
$249$	−115.500	+	174.123i	−0.463855	+	0.699288i
$250$		0			0
$251$		−	248.747i		−	0.991023i	−0.868601	−	0.495512i	$-0.834981\pi$
$251$		−	248.747i		−	0.991023i	0.868601	−	0.495512i	$-0.165019\pi$
$252$		0			0
$253$	−330.000			−1.30435
$254$			630.159i			2.48094i
$255$		0			0
$256$	−371.000			−1.44922
$257$			278.596i			1.08403i	0.840368	+	0.542017i	$0.182339\pi$
$257$			278.596i			1.08403i	−0.840368	+	0.542017i	$0.817661\pi$
$258$	−275.000	+	414.578i	−1.06589	+	1.60689i
$259$		0			0
$260$		0			0
$261$	275.000	−	116.082i	1.05364	−	0.444758i
$262$	660.000			2.51908
$263$		−	285.230i		−	1.08452i	−0.840210	−	0.542262i	$-0.817568\pi$
$263$		−	285.230i		−	1.08452i	0.840210	−	0.542262i	$-0.182432\pi$
$264$	−412.500	−	273.622i	−1.56250	−	1.03645i
$265$		0			0
$266$		0			0
$267$	247.500	−	373.120i	0.926966	−	1.39745i
$268$	315.000			1.17537
$269$		−	464.327i		−	1.72612i	−0.505098	−	0.863062i	$-0.668544\pi$
$269$		−	464.327i		−	1.72612i	0.505098	−	0.863062i	$-0.331456\pi$
$270$		0			0
$271$	22.0000			0.0811808			0.0405904	−	0.999176i	$-0.487076\pi$
$271$	22.0000			0.0811808			0.0405904	+	0.999176i	$0.487076\pi$
$272$		−	16.5831i		−	0.0609674i
$273$		0			0
$274$	−231.000			−0.843066
$275$		0			0
$276$	231.000	−	348.246i	0.836957	−	1.26176i
$277$	210.000			0.758123			0.379061	−	0.925372i	$-0.376247\pi$
$277$	210.000			0.758123			0.379061	+	0.925372i	$0.376247\pi$
$278$		−	255.380i		−	0.918633i
$279$	147.000	+	348.246i	0.526882	+	1.24819i
$280$		0			0
$281$			198.997i			0.708176i	0.935212	+	0.354088i	$0.115209\pi$
$281$			198.997i			0.708176i	−0.935212	+	0.354088i	$0.884791\pi$
$282$	−385.000	−	255.380i	−1.36525	−	0.905603i
$283$	−345.000			−1.21908			−0.609541	−	0.792755i	$-0.708646\pi$
$283$	−345.000			−1.21908			−0.609541	+	0.792755i	$0.708646\pi$
$284$			232.164i			0.817478i
$285$		0			0
$286$	550.000			1.92308
$287$		0			0
$288$	−192.500	+	81.2573i	−0.668403	+	0.282143i
$289$	278.000			0.961938
$290$		0			0
$291$	−175.000	−	116.082i	−0.601375	−	0.398907i
$292$	−245.000			−0.839041
$293$		−	318.396i		−	1.08668i	−0.839514	−	0.543338i	$-0.817160\pi$
$293$		−	318.396i		−	1.08668i	0.839514	−	0.543338i	$-0.182840\pi$
$294$	269.500	−	406.287i	0.916667	−	1.38193i
$295$		0			0
$296$			397.995i			1.34458i
$297$	−440.000	−	82.9156i	−1.48148	−	0.279177i
$298$	550.000			1.84564
$299$			198.997i			0.665543i
$300$		0			0
$301$		0			0
$302$		−	570.459i		−	1.88894i
$303$		0			0
$304$	35.0000			0.115132
$305$		0			0
$306$	−38.5000	−	91.2072i	−0.125817	−	0.298063i
$307$	−325.000			−1.05863			−0.529316	−	0.848425i	$-0.677551\pi$
$307$	−325.000			−1.05863			−0.529316	+	0.848425i	$0.677551\pi$
$308$		0			0
$309$	−175.000	−	116.082i	−0.566343	−	0.375669i
$310$		0			0
$311$			397.995i			1.27973i	0.768489	+	0.639863i	$0.221009\pi$
$311$			397.995i			1.27973i	−0.768489	+	0.639863i	$0.778991\pi$
$312$	−165.000	+	248.747i	−0.528846	+	0.797266i
$313$	490.000			1.56550			0.782748	−	0.622339i	$-0.213818\pi$
$313$	490.000			1.56550			0.782748	+	0.622339i	$0.213818\pi$
$314$		−	829.156i		−	2.64062i
$315$		0			0
$316$	−84.0000			−0.265823
$317$			212.264i			0.669602i	0.942289	+	0.334801i	$0.108669\pi$
$317$			212.264i			0.669602i	−0.942289	+	0.334801i	$0.891331\pi$
$318$	−385.000	−	255.380i	−1.21069	−	0.803082i
$319$	−550.000			−1.72414
$320$		0			0
$321$	−115.500	+	174.123i	−0.359813	+	0.542439i
$322$		0			0
$323$		−	23.2164i		−	0.0718773i
$324$	395.500	−	406.287i	1.22068	−	1.25397i
$325$		0			0
$326$			116.082i			0.356079i
$327$	220.000	+	145.931i	0.672783	+	0.446274i
$328$	−165.000			−0.503049
$329$		0			0
$330$		0			0
$331$	−243.000			−0.734139			−0.367069	−	0.930194i	$-0.619639\pi$
$331$	−243.000			−0.734139			−0.367069	+	0.930194i	$0.619639\pi$
$332$			487.544i			1.46851i
$333$	140.000	+	331.662i	0.420420	+	0.995983i
$334$	594.000			1.77844
$335$		0			0
$336$		0			0
$337$	−385.000			−1.14243			−0.571217	−	0.820799i	$-0.693528\pi$
$337$	−385.000			−1.14243			−0.571217	+	0.820799i	$0.693528\pi$
$338$			228.847i			0.677062i
$339$	−170.500	+	257.038i	−0.502950	+	0.758225i
$340$		0			0
$341$		−	696.491i		−	2.04250i
$342$	192.500	−	81.2573i	0.562865	−	0.237594i
$343$		0			0
$344$			497.494i			1.44620i
$345$		0			0
$346$	924.000			2.67052
$347$			295.180i			0.850662i	0.905038	+	0.425331i	$0.139842\pi$
$347$			295.180i			0.850662i	−0.905038	+	0.425331i	$0.860158\pi$
$348$	385.000	−	580.409i	1.10632	−	1.66784i
$349$	532.000			1.52436			0.762178	−	0.647368i	$-0.224130\pi$
$349$	532.000			1.52436			0.762178	+	0.647368i	$0.224130\pi$
$350$		0			0
$351$	−50.0000	+	265.330i	−0.142450	+	0.755926i
$352$	385.000			1.09375
$353$			278.596i			0.789225i	0.918848	+	0.394613i	$0.129121\pi$
$353$			278.596i			0.789225i	−0.918848	+	0.394613i	$0.870879\pi$
$354$	550.000	+	364.829i	1.55367	+	1.03059i
$355$		0			0
$356$		−	1044.74i		−	2.93465i
$357$		0			0
$358$	−385.000			−1.07542
$359$		−	397.995i		−	1.10862i	−0.832310	−	0.554311i	$-0.812982\pi$
$359$		−	397.995i		−	1.10862i	0.832310	−	0.554311i	$-0.187018\pi$
$360$		0			0
$361$	−312.000			−0.864266
$362$		−	603.626i		−	1.66747i
$363$	385.000	+	255.380i	1.06061	+	0.703526i
$364$		0			0
$365$		0			0
$366$	44.0000	−	66.3325i	0.120219	−	0.181236i
$367$	180.000			0.490463			0.245232	−	0.969465i	$-0.421136\pi$
$367$	180.000			0.490463			0.245232	+	0.969465i	$0.421136\pi$
$368$		−	99.4987i		−	0.270377i
$369$	−137.500	+	58.0409i	−0.372629	+	0.157293i
$370$		0			0
$371$		0			0
$372$	735.000	+	487.544i	1.97581	+	1.31060i
$373$	110.000			0.294906			0.147453	−	0.989069i	$-0.452892\pi$
$373$	110.000			0.294906			0.147453	+	0.989069i	$0.452892\pi$
$374$			182.414i			0.487739i
$375$		0			0
$376$	−462.000			−1.22872
$377$			331.662i			0.879741i
$378$		0			0
$379$	−533.000			−1.40633			−0.703166	−	0.711025i	$-0.748231\pi$
$379$	−533.000			−1.40633			−0.703166	+	0.711025i	$0.748231\pi$
$380$		0			0
$381$	475.000	+	315.079i	1.24672	+	0.826980i
$382$	−770.000			−2.01571
$383$			79.5990i			0.207830i	0.994586	+	0.103915i	$0.0331370\pi$
$383$			79.5990i			0.207830i	−0.994586	+	0.103915i	$0.966863\pi$
$384$	−379.500	+	572.118i	−0.988281	+	1.48989i
$385$		0			0
$386$		−	82.9156i		−	0.214807i
$387$	175.000	+	414.578i	0.452196	+	1.07126i
$388$	−490.000			−1.26289
$389$		−	99.4987i		−	0.255781i	−0.991788	−	0.127890i	$-0.959179\pi$
$389$		−	99.4987i		−	0.255781i	0.991788	−	0.127890i	$-0.0408206\pi$
$390$		0			0
$391$	−66.0000			−0.168798
$392$		−	487.544i		−	1.24373i
$393$	330.000	−	497.494i	0.839695	−	1.26589i
$394$	−726.000			−1.84264
$395$		0			0
$396$	−962.500	+	406.287i	−2.43056	+	1.02598i
$397$	20.0000			0.0503778			0.0251889	−	0.999683i	$-0.491981\pi$
$397$	20.0000			0.0503778			0.0251889	+	0.999683i	$0.491981\pi$
$398$			225.530i			0.566660i
$399$		0			0
$400$		0			0
$401$			746.241i			1.86095i	0.366357	+	0.930475i	$0.380605\pi$
$401$			746.241i			1.86095i	−0.366357	+	0.930475i	$0.619395\pi$
$402$	247.500	−	373.120i	0.615672	−	0.928160i
$403$	−420.000			−1.04218
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	663.325i		−	1.62979i
$408$	−82.5000	−	54.7243i	−0.202206	−	0.134128i
$409$	77.0000			0.188264			0.0941320	−	0.995560i	$-0.469992\pi$
$409$	77.0000			0.188264			0.0941320	+	0.995560i	$0.469992\pi$
$410$		0			0
$411$	−115.500	+	174.123i	−0.281022	+	0.423656i
$412$	−490.000			−1.18932
$413$		0			0
$414$	−231.000	−	547.243i	−0.557971	−	1.32184i
$415$		0			0
$416$		−	232.164i		−	0.558086i
$417$	−192.500	−	127.690i	−0.461631	−	0.306211i
$418$	−385.000			−0.921053
$419$			116.082i			0.277045i	0.990359	+	0.138523i	$0.0442353\pi$
$419$			116.082i			0.277045i	−0.990359	+	0.138523i	$0.955765\pi$
$420$		0			0
$421$	412.000			0.978622			0.489311	−	0.872109i	$-0.337248\pi$
$421$	412.000			0.978622			0.489311	+	0.872109i	$0.337248\pi$
$422$		−	255.380i		−	0.605166i
$423$	−385.000	+	162.515i	−0.910165	+	0.384195i
$424$	−462.000			−1.08962
$425$		0			0
$426$	275.000	+	182.414i	0.645540	+	0.428203i
$427$		0			0
$428$			487.544i			1.13912i
$429$	275.000	−	414.578i	0.641026	−	0.966383i
$430$		0			0
$431$			198.997i			0.461711i	0.972988	+	0.230856i	$0.0741525\pi$
$431$			198.997i			0.461711i	−0.972988	+	0.230856i	$0.925848\pi$
$432$	25.0000	−	132.665i	0.0578704	−	0.307095i
$433$	455.000			1.05081			0.525404	−	0.850853i	$-0.323914\pi$
$433$	455.000			1.05081			0.525404	+	0.850853i	$0.323914\pi$
$434$		0			0
$435$		0			0
$436$	616.000			1.41284
$437$		−	139.298i		−	0.318760i
$438$	−192.500	+	290.205i	−0.439498	+	0.662568i
$439$	22.0000			0.0501139			0.0250569	−	0.999686i	$-0.492023\pi$
$439$	22.0000			0.0501139			0.0250569	+	0.999686i	$0.492023\pi$
$440$		0			0
$441$	−171.500	−	406.287i	−0.388889	−	0.921285i
$442$	110.000			0.248869
$443$			527.343i			1.19039i	0.803581	+	0.595196i	$0.202925\pi$
$443$			527.343i			1.19039i	−0.803581	+	0.595196i	$0.797075\pi$
$444$	700.000	+	464.327i	1.57658	+	1.04578i
$445$		0			0
$446$			464.327i			1.04109i
$447$	275.000	−	414.578i	0.615213	−	0.927468i
$448$		0			0
$449$			82.9156i			0.184667i	0.995728	+	0.0923337i	$0.0294326\pi$
$449$			82.9156i			0.184667i	−0.995728	+	0.0923337i	$0.970567\pi$
$450$		0			0
$451$	275.000			0.609756
$452$			719.708i			1.59227i
$453$	−430.000	−	285.230i	−0.949227	−	0.629646i
$454$	−616.000			−1.35683
$455$		0			0
$456$	115.500	−	174.123i	0.253289	−	0.381848i
$457$	275.000			0.601751			0.300875	−	0.953663i	$-0.402721\pi$
$457$	275.000			0.601751			0.300875	+	0.953663i	$0.402721\pi$
$458$		−	1233.78i		−	2.69385i
$459$	−88.0000	−	16.5831i	−0.191721	−	0.0361288i
$460$		0			0
$461$		−	596.992i		−	1.29499i	−0.762068	−	0.647497i	$-0.775816\pi$
$461$		−	596.992i		−	1.29499i	0.762068	−	0.647497i	$-0.224184\pi$
$462$		0			0
$463$	240.000			0.518359			0.259179	−	0.965829i	$-0.416548\pi$
$463$	240.000			0.518359			0.259179	+	0.965829i	$0.416548\pi$
$464$		−	165.831i		−	0.357395i
$465$		0			0
$466$	−396.000			−0.849785
$467$			13.2665i			0.0284079i	0.999899	+	0.0142040i	$0.00452141\pi$
$467$			13.2665i			0.0284079i	−0.999899	+	0.0142040i	$0.995479\pi$
$468$	245.000	+	580.409i	0.523504	+	1.24019i
$469$		0			0
$470$		0			0
$471$	−625.000	−	414.578i	−1.32696	−	0.880208i
$472$	660.000			1.39831
$473$		−	829.156i		−	1.75297i
$474$	−66.0000	+	99.4987i	−0.139241	+	0.209913i
$475$		0			0
$476$		0			0
$477$	−385.000	+	162.515i	−0.807128	+	0.340701i
$478$	770.000			1.61088
$479$			298.496i			0.623165i	0.950219	+	0.311583i	$0.100859\pi$
$479$			298.496i			0.623165i	−0.950219	+	0.311583i	$0.899141\pi$
$480$		0			0
$481$	−400.000			−0.831601
$482$			1369.77i			2.84184i
$483$		0			0
$484$	1078.00			2.22727
$485$		0			0
$486$	−170.500	−	787.698i	−0.350823	−	1.62078i
$487$	−410.000			−0.841889			−0.420945	−	0.907086i	$-0.638301\pi$
$487$	−410.000			−0.841889			−0.420945	+	0.907086i	$0.638301\pi$
$488$		−	79.5990i		−	0.163113i
$489$	87.5000	+	58.0409i	0.178937	+	0.118693i
$490$		0			0
$491$			265.330i			0.540387i	0.962806	+	0.270193i	$0.0870877\pi$
$491$			265.330i			0.540387i	−0.962806	+	0.270193i	$0.912912\pi$
$492$	−192.500	+	290.205i	−0.391260	+	0.589847i
$493$	−110.000			−0.223124
$494$			232.164i			0.469967i
$495$		0			0
$496$	210.000			0.423387
$497$		0			0
$498$	577.500	+	383.070i	1.15964	+	0.769217i
$499$	322.000			0.645291			0.322645	−	0.946520i	$-0.395428\pi$
$499$	322.000			0.645291			0.322645	+	0.946520i	$0.395428\pi$
$500$		0			0
$501$	297.000	−	447.744i	0.592814	−	0.893701i
$502$	−825.000			−1.64343
$503$			411.261i			0.817617i	0.912620	+	0.408809i	$0.134056\pi$
$503$			411.261i			0.817617i	−0.912620	+	0.408809i	$0.865944\pi$
$504$		0			0
$505$		0			0
$506$			1094.49i			2.16302i
$507$	172.500	+	114.424i	0.340237	+	0.225687i
$508$	1330.00			2.61811
$509$			431.161i			0.847075i	0.905879	+	0.423538i	$0.139212\pi$
$509$			431.161i			0.847075i	−0.905879	+	0.423538i	$0.860788\pi$
$510$		0			0
$511$		0			0
$512$			315.079i			0.615389i
$513$	35.0000	−	185.731i	0.0682261	−	0.362049i
$514$	924.000			1.79767
$515$		0			0
$516$	875.000	+	580.409i	1.69574	+	1.12482i
$517$	770.000			1.48936
$518$		0			0
$519$	462.000	−	696.491i	0.890173	−	1.34199i
$520$		0			0
$521$		−	281.913i		−	0.541100i	−0.962706	−	0.270550i	$-0.912794\pi$
$521$		−	281.913i		−	0.541100i	0.962706	−	0.270550i	$-0.0872055\pi$
$522$	−385.000	−	912.072i	−0.737548	−	1.74726i
$523$	−1015.00			−1.94073			−0.970363	−	0.241651i	$-0.922311\pi$
$523$	−1015.00			−1.94073			−0.970363	+	0.241651i	$0.922311\pi$
$524$		−	1392.98i		−	2.65836i
$525$		0			0
$526$	−946.000			−1.79848
$527$		−	139.298i		−	0.264323i
$528$	−137.500	+	207.289i	−0.260417	+	0.392593i
$529$	133.000			0.251418
$530$		0			0
$531$	550.000	−	232.164i	1.03578	−	0.437220i
$532$		0			0
$533$		−	165.831i		−	0.311128i
$534$	−1237.50	−	820.865i	−2.31742	−	1.53720i
$535$		0			0
$536$		−	447.744i		−	0.835344i
$537$	−192.500	+	290.205i	−0.358473	+	0.540418i
$538$	−1540.00			−2.86245
$539$			812.573i			1.50756i
$540$		0			0
$541$	912.000			1.68577			0.842884	−	0.538096i	$-0.180856\pi$
$541$	912.000			1.68577			0.842884	+	0.538096i	$0.180856\pi$
$542$		−	72.9657i		−	0.134623i
$543$	−455.000	−	301.813i	−0.837937	−	0.555825i
$544$	77.0000			0.141544
$545$		0			0
$546$		0			0
$547$	−55.0000			−0.100548			−0.0502742	−	0.998735i	$-0.516010\pi$
$547$	−55.0000			−0.100548			−0.0502742	+	0.998735i	$0.516010\pi$
$548$			487.544i			0.889679i
$549$	−28.0000	−	66.3325i	−0.0510018	−	0.120824i
$550$		0			0
$551$		−	232.164i		−	0.421350i
$552$	−495.000	−	328.346i	−0.896739	−	0.594829i
$553$		0			0
$554$		−	696.491i		−	1.25720i
$555$		0			0
$556$	−539.000			−0.969424
$557$		−	1014.89i		−	1.82206i	−0.412341	−	0.911030i	$-0.635289\pi$
$557$		−	1014.89i		−	1.82206i	0.412341	−	0.911030i	$-0.364711\pi$
$558$	1155.00	−	487.544i	2.06989	−	0.873734i
$559$	−500.000			−0.894454
$560$		0			0
$561$	137.500	+	91.2072i	0.245098	+	0.162580i
$562$	660.000			1.17438
$563$		−	119.398i		−	0.212075i	−0.994362	−	0.106038i	$-0.966184\pi$
$563$		−	119.398i		−	0.212075i	0.994362	−	0.106038i	$-0.0338164\pi$
$564$	−539.000	+	812.573i	−0.955674	+	1.44073i
$565$		0			0
$566$			1144.24i			2.02162i
$567$		0			0
$568$	330.000			0.580986
$569$		−	49.7494i		−	0.0874330i	−0.999044	−	0.0437165i	$-0.986080\pi$
$569$		−	49.7494i		−	0.0874330i	0.999044	−	0.0437165i	$-0.0139198\pi$
$570$		0			0
$571$	242.000			0.423818			0.211909	−	0.977289i	$-0.432032\pi$
$571$	242.000			0.423818			0.211909	+	0.977289i	$0.432032\pi$
$572$		−	1160.82i		−	2.02940i
$573$	−385.000	+	580.409i	−0.671902	+	1.01293i
$574$		0			0
$575$		0			0
$576$	339.500	+	804.282i	0.589410	+	1.39632i
$577$	−665.000			−1.15251			−0.576256	−	0.817269i	$-0.695487\pi$
$577$	−665.000			−1.15251			−0.576256	+	0.817269i	$0.695487\pi$
$578$		−	922.022i		−	1.59519i
$579$	−62.5000	−	41.4578i	−0.107945	−	0.0716024i
$580$		0			0
$581$		0			0
$582$	−385.000	+	580.409i	−0.661512	+	0.997267i
$583$	770.000			1.32075
$584$			348.246i			0.596311i
$585$		0			0
$586$	−1056.00			−1.80205
$587$			626.842i			1.06787i	0.845524	+	0.533937i	$0.179288\pi$
$587$			626.842i			1.06787i	−0.845524	+	0.533937i	$0.820712\pi$
$588$	−857.500	−	568.801i	−1.45833	−	0.967349i
$589$	294.000			0.499151
$590$		0			0
$591$	−363.000	+	547.243i	−0.614213	+	0.925961i
$592$	200.000			0.337838
$593$			859.006i			1.44858i	0.689497	+	0.724288i	$0.257831\pi$
$593$			859.006i			1.44858i	−0.689497	+	0.724288i	$0.742169\pi$
$594$	−275.000	+	1459.31i	−0.462963	+	2.45676i
$595$		0			0
$596$		−	1160.82i		−	1.94768i
$597$	170.000	+	112.765i	0.284757	+	0.188887i
$598$	660.000			1.10368
$599$		−	331.662i		−	0.553694i	−0.960914	−	0.276847i	$-0.910711\pi$
$599$		−	331.662i		−	0.553694i	0.960914	−	0.276847i	$-0.0892895\pi$
$600$		0			0
$601$	−343.000			−0.570715			−0.285358	−	0.958421i	$-0.592112\pi$
$601$	−343.000			−0.570715			−0.285358	+	0.958421i	$0.592112\pi$
$602$		0			0
$603$	−157.500	−	373.120i	−0.261194	−	0.618773i
$604$	−1204.00			−1.99338
$605$		0			0
$606$		0			0
$607$	1100.00			1.81219			0.906096	−	0.423073i	$-0.139049\pi$
$607$	1100.00			1.81219			0.906096	+	0.423073i	$0.139049\pi$
$608$			162.515i			0.267294i
$609$		0			0
$610$		0			0
$611$		−	464.327i		−	0.759947i
$612$	−192.500	+	81.2573i	−0.314542	+	0.132773i
$613$	290.000			0.473083			0.236542	−	0.971621i	$-0.423986\pi$
$613$	290.000			0.473083			0.236542	+	0.971621i	$0.423986\pi$
$614$			1077.90i			1.75554i
$615$		0			0
$616$		0			0
$617$			79.5990i			0.129010i	0.997917	+	0.0645049i	$0.0205468\pi$
$617$			79.5990i			0.129010i	−0.997917	+	0.0645049i	$0.979453\pi$
$618$	−385.000	+	580.409i	−0.622977	+	0.939174i
$619$	−58.0000			−0.0936995			−0.0468498	−	0.998902i	$-0.514918\pi$
$619$	−58.0000			−0.0936995			−0.0468498	+	0.998902i	$0.514918\pi$
$620$		0			0
$621$	−528.000	−	99.4987i	−0.850242	−	0.160223i
$622$	1320.00			2.12219
$623$		0			0
$624$	125.000	+	82.9156i	0.200321	+	0.132878i
$625$		0			0
$626$		−	1625.15i		−	2.59608i
$627$	−192.500	+	290.205i	−0.307018	+	0.462846i
$628$	−1750.00			−2.78662
$629$		−	132.665i		−	0.210914i
$630$		0			0
$631$	862.000			1.36609			0.683043	−	0.730378i	$-0.260656\pi$
$631$	862.000			1.36609			0.683043	+	0.730378i	$0.260656\pi$
$632$			119.398i			0.188922i
$633$	−192.500	−	127.690i	−0.304107	−	0.201722i
$634$	704.000			1.11041
$635$		0			0
$636$	−539.000	+	812.573i	−0.847484	+	1.27763i
$637$	490.000			0.769231
$638$			1824.14i			2.85916i
$639$	275.000	−	116.082i	0.430360	−	0.181662i
$640$		0			0
$641$			596.992i			0.931345i	0.884957	+	0.465673i	$0.154188\pi$
$641$			596.992i			0.931345i	−0.884957	+	0.465673i	$0.845812\pi$
$642$	577.500	+	383.070i	0.899533	+	0.596682i
$643$	1050.00			1.63297			0.816485	−	0.577366i	$-0.195920\pi$
$643$	1050.00			1.63297			0.816485	+	0.577366i	$0.195920\pi$
$644$		0			0
$645$		0			0
$646$	−77.0000			−0.119195
$647$		−	252.063i		−	0.389588i	−0.980844	−	0.194794i	$-0.937596\pi$
$647$		−	252.063i		−	0.389588i	0.980844	−	0.194794i	$-0.0624038\pi$
$648$	−577.500	−	562.168i	−0.891204	−	0.867543i
$649$	−1100.00			−1.69492
$650$		0			0
$651$		0			0
$652$	245.000			0.375767
$653$			1207.25i			1.84878i	0.381452	+	0.924389i	$0.375424\pi$
$653$			1207.25i			1.84878i	−0.381452	+	0.924389i	$0.624576\pi$
$654$	484.000	−	729.657i	0.740061	−	1.11568i
$655$		0			0
$656$			82.9156i			0.126396i
$657$	122.500	+	290.205i	0.186454	+	0.441712i
$658$		0			0
$659$		−	812.573i		−	1.23304i	−0.787339	−	0.616520i	$-0.788542\pi$
$659$		−	812.573i		−	1.23304i	0.787339	−	0.616520i	$-0.211458\pi$
$660$		0			0
$661$	−98.0000			−0.148260			−0.0741301	−	0.997249i	$-0.523618\pi$
$661$	−98.0000			−0.148260			−0.0741301	+	0.997249i	$0.523618\pi$
$662$			805.940i			1.21743i
$663$	55.0000	−	82.9156i	0.0829563	−	0.125061i
$664$	693.000			1.04367
$665$		0			0
$666$	1100.00	−	464.327i	1.65165	−	0.697188i
$667$	−660.000			−0.989505
$668$		−	1253.68i		−	1.87677i
$669$	350.000	+	232.164i	0.523169	+	0.347031i
$670$		0			0
$671$			132.665i			0.197712i
$672$		0			0
$673$	210.000			0.312036			0.156018	−	0.987754i	$-0.450134\pi$
$673$	210.000			0.312036			0.156018	+	0.987754i	$0.450134\pi$
$674$			1276.90i			1.89451i
$675$		0			0
$676$	483.000			0.714497
$677$			79.5990i			0.117576i	0.998270	+	0.0587880i	$0.0187236\pi$
$677$			79.5990i			0.117576i	−0.998270	+	0.0587880i	$0.981276\pi$
$678$	852.500	+	565.485i	1.25737	+	0.834048i
$679$		0			0
$680$		0			0
$681$	−308.000	+	464.327i	−0.452276	+	0.681832i
$682$	−2310.00			−3.38710
$683$		−	169.148i		−	0.247654i	−0.992304	−	0.123827i	$-0.960483\pi$
$683$		−	169.148i		−	0.247654i	0.992304	−	0.123827i	$-0.0395168\pi$
$684$	−171.500	−	406.287i	−0.250731	−	0.593986i
$685$		0			0
$686$		0			0
$687$	−930.000	−	616.892i	−1.35371	−	0.897951i
$688$	250.000			0.363372
$689$		−	464.327i		−	0.673915i
$690$		0			0
$691$	−713.000			−1.03184			−0.515919	−	0.856637i	$-0.672549\pi$
$691$	−713.000			−1.03184			−0.515919	+	0.856637i	$0.672549\pi$
$692$		−	1950.18i		−	2.81817i
$693$		0			0
$694$	979.000			1.41066
$695$		0			0
$696$	−825.000	−	547.243i	−1.18534	−	0.786269i
$697$	55.0000			0.0789096
$698$		−	1764.44i		−	2.52786i
$699$	−198.000	+	298.496i	−0.283262	+	0.427033i
$700$		0			0
$701$			1160.82i			1.65595i	0.560767	+	0.827973i	$0.310506\pi$
$701$			1160.82i			1.65595i	−0.560767	+	0.827973i	$0.689494\pi$
$702$	880.000	+	165.831i	1.25356	+	0.236227i
$703$	280.000			0.398293
$704$		−	1608.56i		−	2.28489i
$705$		0			0
$706$	924.000			1.30878
$707$		0			0
$708$	770.000	−	1160.82i	1.08757	−	1.63957i
$709$	−248.000			−0.349788			−0.174894	−	0.984587i	$-0.555958\pi$
$709$	−248.000			−0.349788			−0.174894	+	0.984587i	$0.555958\pi$
$710$		0			0
$711$	42.0000	+	99.4987i	0.0590717	+	0.139942i
$712$	−1485.00			−2.08567
$713$		−	835.789i		−	1.17222i
$714$		0			0
$715$		0			0
$716$			812.573i			1.13488i
$717$	385.000	−	580.409i	0.536960	−	0.809497i
$718$	−1320.00			−1.83844
$719$			198.997i			0.276770i	0.990379	+	0.138385i	$0.0441911\pi$
$719$			198.997i			0.276770i	−0.990379	+	0.138385i	$0.955809\pi$
$720$		0			0
$721$		0			0
$722$			1034.79i			1.43322i
$723$	1032.50	+	684.883i	1.42808	+	0.947279i
$724$	−1274.00			−1.75967
$725$		0			0
$726$	847.000	−	1276.90i	1.16667	−	1.75882i
$727$	10.0000			0.0137552			0.00687758	−	0.999976i	$-0.497811\pi$
$727$	10.0000			0.0137552			0.00687758	+	0.999976i	$0.497811\pi$
$728$		0			0
$729$	−679.000	−	265.330i	−0.931413	−	0.363964i
$730$		0			0
$731$		−	165.831i		−	0.226855i
$732$	−140.000	−	92.8655i	−0.191257	−	0.126865i
$733$	−770.000			−1.05048			−0.525239	−	0.850955i	$-0.676024\pi$
$733$	−770.000			−1.05048			−0.525239	+	0.850955i	$0.676024\pi$
$734$		−	596.992i		−	0.813341i
$735$		0			0
$736$	462.000			0.627717
$737$			746.241i			1.01254i
$738$	192.500	+	456.036i	0.260840	+	0.617935i
$739$	802.000			1.08525			0.542625	−	0.839975i	$-0.317430\pi$
$739$	802.000			1.08525			0.542625	+	0.839975i	$0.317430\pi$
$740$		0			0
$741$	175.000	+	116.082i	0.236167	+	0.156656i
$742$		0			0
$743$		−	1346.55i		−	1.81231i	−0.422941	−	0.906157i	$-0.639002\pi$
$743$		−	1346.55i		−	1.81231i	0.422941	−	0.906157i	$-0.360998\pi$
$744$	693.000	−	1044.74i	0.931452	−	1.40422i
$745$		0			0
$746$		−	364.829i		−	0.489047i
$747$	577.500	−	243.772i	0.773092	−	0.326335i
$748$	385.000			0.514706
$749$		0			0
$750$		0			0
$751$	322.000			0.428762			0.214381	−	0.976750i	$-0.431227\pi$
$751$	322.000			0.428762			0.214381	+	0.976750i	$0.431227\pi$
$752$			232.164i			0.308728i
$753$	−412.500	+	621.867i	−0.547809	+	0.825853i
$754$	1100.00			1.45889
$755$		0			0
$756$		0			0
$757$	−400.000			−0.528402			−0.264201	−	0.964468i	$-0.585108\pi$
$757$	−400.000			−0.528402			−0.264201	+	0.964468i	$0.585108\pi$
$758$			1767.76i			2.33214i
$759$	825.000	+	547.243i	1.08696	+	0.721005i
$760$		0			0
$761$		−	348.246i		−	0.457616i	−0.973472	−	0.228808i	$-0.926517\pi$
$761$		−	348.246i		−	0.457616i	0.973472	−	0.228808i	$-0.0734828\pi$
$762$	1045.00	−	1575.40i	1.37139	−	2.06745i
$763$		0			0
$764$			1625.15i			2.12715i
$765$		0			0
$766$	264.000			0.344648
$767$			663.325i			0.864830i
$768$	927.500	+	615.234i	1.20768	+	0.801086i
$769$	−193.000			−0.250975			−0.125488	−	0.992095i	$-0.540050\pi$
$769$	−193.000			−0.250975			−0.125488	+	0.992095i	$0.540050\pi$
$770$		0			0
$771$	462.000	−	696.491i	0.599222	−	0.903361i
$772$	−175.000			−0.226684
$773$		−	417.895i		−	0.540614i	−0.962774	−	0.270307i	$-0.912875\pi$
$773$		−	417.895i		−	0.540614i	0.962774	−	0.270307i	$-0.0871252\pi$
$774$	1375.00	−	580.409i	1.77649	−	0.749883i
$775$		0			0
$776$			696.491i			0.897540i
$777$		0			0
$778$	−330.000			−0.424165
$779$			116.082i			0.149014i
$780$		0			0
$781$	−550.000			−0.704225
$782$			218.897i			0.279920i
$783$	−880.000	−	165.831i	−1.12388	−	0.211790i
$784$	−245.000			−0.312500
$785$		0			0
$786$	−1650.00	−	1094.49i	−2.09924	−	1.39248i
$787$	−910.000			−1.15629			−0.578145	−	0.815934i	$-0.696223\pi$
$787$	−910.000			−1.15629			−0.578145	+	0.815934i	$0.696223\pi$
$788$			1532.28i			1.94452i
$789$	−473.000	+	713.074i	−0.599493	+	0.903770i
$790$		0			0
$791$		0			0
$792$	577.500	+	1368.11i	0.729167	+	1.72741i
$793$	80.0000			0.100883
$794$		−	66.3325i		−	0.0835422i
$795$		0			0
$796$	476.000			0.597990
$797$			1107.75i			1.38990i	0.719057	+	0.694951i	$0.244574\pi$
$797$			1107.75i			1.38990i	−0.719057	+	0.694951i	$0.755426\pi$
$798$		0			0
$799$	154.000			0.192741
$800$		0			0
$801$	−1237.50	+	522.368i	−1.54494	+	0.652145i
$802$	2475.00			3.08603
$803$		−	580.409i		−	0.722801i
$804$	−787.500	−	522.368i	−0.979478	−	0.649712i
$805$		0			0
$806$			1392.98i			1.72827i
$807$	−770.000	+	1160.82i	−0.954151	+	1.43844i
$808$		0			0
$809$			1260.32i			1.55787i	0.627104	+	0.778935i	$0.284240\pi$
$809$			1260.32i			1.55787i	−0.627104	+	0.778935i	$0.715760\pi$
$810$		0			0
$811$	−858.000			−1.05795			−0.528977	−	0.848636i	$-0.677424\pi$
$811$	−858.000			−1.05795			−0.528977	+	0.848636i	$0.677424\pi$
$812$		0			0
$813$	−55.0000	−	36.4829i	−0.0676507	−	0.0448744i
$814$	−2200.00			−2.70270
$815$		0			0
$816$	−27.5000	+	41.4578i	−0.0337010	+	0.0508061i
$817$	350.000			0.428397
$818$		−	255.380i		−	0.312201i
$819$		0			0
$820$		0			0
$821$		−	696.491i		−	0.848345i	−0.905581	−	0.424172i	$-0.860565\pi$
$821$		−	696.491i		−	0.848345i	0.905581	−	0.424172i	$-0.139435\pi$
$822$	577.500	+	383.070i	0.702555	+	0.466022i
$823$	1060.00			1.28797			0.643985	−	0.765038i	$-0.277280\pi$
$823$	1060.00			1.28797			0.643985	+	0.765038i	$0.277280\pi$
$824$			696.491i			0.845256i
$825$		0			0
$826$		0			0
$827$		−	500.810i		−	0.605575i	−0.953058	−	0.302787i	$-0.902083\pi$
$827$		−	500.810i		−	0.605575i	0.953058	−	0.302787i	$-0.0979172\pi$
$828$	−1155.00	+	487.544i	−1.39493	+	0.588821i
$829$	−1038.00			−1.25211			−0.626055	−	0.779779i	$-0.715332\pi$
$829$	−1038.00			−1.25211			−0.626055	+	0.779779i	$0.715332\pi$
$830$		0			0
$831$	−525.000	−	348.246i	−0.631769	−	0.419068i
$832$	−970.000			−1.16587
$833$			162.515i			0.195096i
$834$	−423.500	+	638.450i	−0.507794	+	0.765528i
$835$		0			0
$836$			812.573i			0.971977i
$837$	210.000	−	1114.39i	0.250896	−	1.33140i
$838$	385.000			0.459427
$839$		−	928.655i		−	1.10686i	−0.832896	−	0.553430i	$-0.813319\pi$
$839$		−	928.655i		−	1.10686i	0.832896	−	0.553430i	$-0.186681\pi$
$840$		0			0
$841$	−259.000			−0.307967
$842$		−	1366.45i		−	1.62286i
$843$	330.000	−	497.494i	0.391459	−	0.590147i
$844$	−539.000			−0.638626
$845$		0			0
$846$	539.000	+	1276.90i	0.637116	+	1.50934i
$847$		0			0
$848$			232.164i			0.273778i
$849$	862.500	+	572.118i	1.01590	+	0.673873i
$850$		0			0
$851$		−	795.990i		−	0.935358i
$852$	385.000	−	580.409i	0.451878	−	0.681232i
$853$	−630.000			−0.738570			−0.369285	−	0.929316i	$-0.620397\pi$
$853$	−630.000			−0.738570			−0.369285	+	0.929316i	$0.620397\pi$
$854$		0			0
$855$		0			0
$856$	693.000			0.809579
$857$		−	1296.80i		−	1.51319i	−0.653886	−	0.756593i	$-0.726862\pi$
$857$		−	1296.80i		−	1.51319i	0.653886	−	0.756593i	$-0.273138\pi$
$858$	−1375.00	−	912.072i	−1.60256	−	1.06302i
$859$	307.000			0.357392			0.178696	−	0.983904i	$-0.442812\pi$
$859$	307.000			0.357392			0.178696	+	0.983904i	$0.442812\pi$
$860$		0			0
$861$		0			0
$862$	660.000			0.765661
$863$		−	484.227i		−	0.561098i	−0.959840	−	0.280549i	$-0.909484\pi$
$863$		−	484.227i		−	0.561098i	0.959840	−	0.280549i	$-0.0905165\pi$
$864$	616.000	+	116.082i	0.712963	+	0.134354i
$865$		0			0
$866$		−	1509.06i		−	1.74257i
$867$	−695.000	−	461.011i	−0.801615	−	0.531731i
$868$		0			0
$869$		−	198.997i		−	0.228996i
$870$		0			0
$871$	450.000			0.516648
$872$		−	875.589i		−	1.00412i
$873$	245.000	+	580.409i	0.280641	+	0.664845i
$874$	−462.000			−0.528604
$875$		0			0
$876$	612.500	+	406.287i	0.699201	+	0.463797i
$877$	−840.000			−0.957811			−0.478905	−	0.877867i	$-0.658966\pi$
$877$	−840.000			−0.957811			−0.478905	+	0.877867i	$0.658966\pi$
$878$		−	72.9657i		−	0.0831045i
$879$	−528.000	+	795.990i	−0.600683	+	0.905563i
$880$		0			0
$881$		−	464.327i		−	0.527046i	−0.964653	−	0.263523i	$-0.915116\pi$
$881$		−	464.327i		−	0.527046i	0.964653	−	0.263523i	$-0.0848845\pi$
$882$	−1347.50	+	568.801i	−1.52778	+	0.644899i
$883$	−995.000			−1.12684			−0.563420	−	0.826171i	$-0.690515\pi$
$883$	−995.000			−1.12684			−0.563420	+	0.826171i	$0.690515\pi$
$884$		−	232.164i		−	0.262629i
$885$		0			0
$886$	1749.00			1.97404
$887$			477.594i			0.538437i	0.963079	+	0.269219i	$0.0867654\pi$
$887$			477.594i			0.538437i	−0.963079	+	0.269219i	$0.913235\pi$
$888$	660.000	−	994.987i	0.743243	−	1.12048i
$889$		0			0
$890$		0			0
$891$	962.500	+	936.947i	1.08025	+	1.05157i
$892$	980.000			1.09865
$893$			325.029i			0.363975i
$894$	−1375.00	−	912.072i	−1.53803	−	1.02021i
$895$		0			0
$896$		0			0
$897$	330.000	−	497.494i	0.367893	−	0.554620i
$898$	275.000			0.306236
$899$		−	1392.98i		−	1.54948i
$900$		0			0
$901$	154.000			0.170921
$902$		−	912.072i		−	1.01117i
$903$		0			0
$904$	1023.00			1.13164
$905$		0			0
$906$	−946.000	+	1426.15i	−1.04415	+	1.57412i
$907$	1050.00			1.15766			0.578831	−	0.815447i	$-0.303509\pi$
$907$	1050.00			1.15766			0.578831	+	0.815447i	$0.303509\pi$
$908$			1300.12i			1.43185i
$909$		0			0
$910$		0			0
$911$			729.657i			0.800941i	0.916310	+	0.400471i	$0.131153\pi$
$911$			729.657i			0.800941i	−0.916310	+	0.400471i	$0.868847\pi$
$912$	−87.5000	−	58.0409i	−0.0959430	−	0.0636414i
$913$	−1155.00			−1.26506
$914$		−	912.072i		−	0.997890i
$915$		0			0
$916$	−2604.00			−2.84279
$917$		0			0
$918$	−55.0000	+	291.863i	−0.0599129	+	0.317934i
$919$	1342.00			1.46028			0.730141	−	0.683296i	$-0.239454\pi$
$919$	1342.00			1.46028			0.730141	+	0.683296i	$0.239454\pi$
$920$		0			0
$921$	812.500	+	538.952i	0.882193	+	0.585181i
$922$	−1980.00			−2.14751
$923$			331.662i			0.359331i
$924$		0			0
$925$		0			0
$926$		−	795.990i		−	0.859600i
$927$	245.000	+	580.409i	0.264293	+	0.626116i
$928$	770.000			0.829741
$929$			464.327i			0.499814i	0.968270	+	0.249907i	$0.0804001\pi$
$929$			464.327i			0.499814i	−0.968270	+	0.249907i	$0.919600\pi$
$930$		0			0
$931$	−343.000			−0.368421
$932$			835.789i			0.896770i
$933$	660.000	−	994.987i	0.707395	−	1.06644i
$934$	44.0000			0.0471092
$935$		0			0
$936$	825.000	−	348.246i	0.881410	−	0.372057i
$937$	165.000			0.176094			0.0880470	−	0.996116i	$-0.471937\pi$
$937$	165.000			0.176094			0.0880470	+	0.996116i	$0.471937\pi$
$938$		0			0
$939$	−1225.00	−	812.573i	−1.30458	−	0.865360i
$940$		0			0
$941$		−	232.164i		−	0.246720i	−0.992362	−	0.123360i	$-0.960633\pi$
$941$		−	232.164i		−	0.246720i	0.992362	−	0.123360i	$-0.0393670\pi$
$942$	−1375.00	+	2072.89i	−1.45966	+	2.20052i
$943$	330.000			0.349947
$944$		−	331.662i		−	0.351337i
$945$		0			0
$946$	−2750.00			−2.90698
$947$			278.596i			0.294188i	0.989122	+	0.147094i	$0.0469921\pi$
$947$			278.596i			0.294188i	−0.989122	+	0.147094i	$0.953008\pi$
$948$	210.000	+	139.298i	0.221519	+	0.146939i
$949$	−350.000			−0.368809
$950$		0			0
$951$	352.000	−	530.660i	0.370137	−	0.558002i
$952$		0			0
$953$			195.681i			0.205331i	0.994716	+	0.102666i	$0.0327372\pi$
$953$			195.681i			0.205331i	−0.994716	+	0.102666i	$0.967263\pi$
$954$	539.000	+	1276.90i	0.564990	+	1.33847i
$955$		0			0
$956$		−	1625.15i		−	1.69994i
$957$	1375.00	+	912.072i	1.43678	+	0.953053i
$958$	990.000			1.03340
$959$		0			0
$960$		0			0
$961$	803.000			0.835588
$962$			1326.65i			1.37905i
$963$	577.500	−	243.772i	0.599688	−	0.253138i
$964$	2891.00			2.99896
$965$		0			0
$966$		0			0
$967$	280.000			0.289555			0.144778	−	0.989464i	$-0.453753\pi$
$967$	280.000			0.289555			0.144778	+	0.989464i	$0.453753\pi$
$968$		−	1532.28i		−	1.58293i
$969$	−38.5000	+	58.0409i	−0.0397317	+	0.0598978i
$970$		0			0
$971$			1044.74i			1.07594i	0.842964	+	0.537970i	$0.180808\pi$
$971$			1044.74i			1.07594i	−0.842964	+	0.537970i	$0.819192\pi$
$972$	−1662.50	+	359.854i	−1.71039	+	0.370220i
$973$		0			0
$974$			1359.82i			1.39612i
$975$		0			0
$976$	−40.0000			−0.0409836
$977$		−	1097.80i		−	1.12365i	−0.827257	−	0.561823i	$-0.810100\pi$
$977$		−	1097.80i		−	1.12365i	0.827257	−	0.561823i	$-0.189900\pi$
$978$	192.500	−	290.205i	0.196830	−	0.296733i
$979$	2475.00			2.52809
$980$		0			0
$981$	−308.000	−	729.657i	−0.313965	−	0.743789i
$982$	880.000			0.896130
$983$			1671.58i			1.70049i	0.526389	+	0.850244i	$0.323545\pi$
$983$			1671.58i			1.70049i	−0.526389	+	0.850244i	$0.676455\pi$
$984$	412.500	+	273.622i	0.419207	+	0.278071i
$985$		0			0
$986$			364.829i			0.370009i
$987$		0			0
$988$	490.000			0.495951
$989$		−	994.987i		−	1.00605i
$990$		0			0
$991$	452.000			0.456105			0.228052	−	0.973649i	$-0.426764\pi$
$991$	452.000			0.456105			0.228052	+	0.973649i	$0.426764\pi$
$992$			975.088i			0.982951i
$993$	607.500	+	402.970i	0.611782	+	0.405811i
$994$		0			0
$995$		0			0
$996$	808.500	−	1218.86i	0.811747	−	1.22375i
$997$	420.000			0.421264			0.210632	−	0.977565i	$-0.432448\pi$
$997$	420.000			0.421264			0.210632	+	0.977565i	$0.432448\pi$
$998$		−	1067.95i		−	1.07009i
$999$	200.000	−	1061.32i	0.200200	−	1.06238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.c.c.26.1	✓	2
3.2	odd	2	inner	75.3.c.c.26.2	yes	2
4.3	odd	2		1200.3.l.s.401.2		2
5.2	odd	4		75.3.d.c.74.4		4
5.3	odd	4		75.3.d.c.74.1		4
5.4	even	2		75.3.c.f.26.2	yes	2
12.11	even	2		1200.3.l.s.401.1		2
15.2	even	4		75.3.d.c.74.2		4
15.8	even	4		75.3.d.c.74.3		4
15.14	odd	2		75.3.c.f.26.1	yes	2
20.3	even	4		1200.3.c.d.449.2		4
20.7	even	4		1200.3.c.d.449.3		4
20.19	odd	2		1200.3.l.f.401.1		2
60.23	odd	4		1200.3.c.d.449.4		4
60.47	odd	4		1200.3.c.d.449.1		4
60.59	even	2		1200.3.l.f.401.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.c.c.26.1	✓	2	1.1	even	1	trivial
75.3.c.c.26.2	yes	2	3.2	odd	2	inner
75.3.c.f.26.1	yes	2	15.14	odd	2
75.3.c.f.26.2	yes	2	5.4	even	2
75.3.d.c.74.1		4	5.3	odd	4
75.3.d.c.74.2		4	15.2	even	4
75.3.d.c.74.3		4	15.8	even	4
75.3.d.c.74.4		4	5.2	odd	4
1200.3.c.d.449.1		4	60.47	odd	4
1200.3.c.d.449.2		4	20.3	even	4
1200.3.c.d.449.3		4	20.7	even	4
1200.3.c.d.449.4		4	60.23	odd	4
1200.3.l.f.401.1		2	20.19	odd	2
1200.3.l.f.401.2		2	60.59	even	2
1200.3.l.s.401.1		2	12.11	even	2
1200.3.l.s.401.2		2	4.3	odd	2

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.31662i q^{2} +(-2.50000 - 1.65831i) q^{3} -7.00000 q^{4} +(-5.50000 + 8.29156i) q^{6} +9.94987i q^{8} +(3.50000 + 8.29156i) q^{9} +O(q^{10})\)	\(q-3.31662i q^{2} +(-2.50000 - 1.65831i) q^{3} -7.00000 q^{4} +(-5.50000 + 8.29156i) q^{6} +9.94987i q^{8} +(3.50000 + 8.29156i) q^{9} -16.5831i q^{11} +(17.5000 + 11.6082i) q^{12} -10.0000 q^{13} +5.00000 q^{16} -3.31662i q^{17} +(27.5000 - 11.6082i) q^{18} +7.00000 q^{19} -55.0000 q^{22} -19.8997i q^{23} +(16.5000 - 24.8747i) q^{24} +33.1662i q^{26} +(5.00000 - 26.5330i) q^{27} -33.1662i q^{29} +42.0000 q^{31} +23.2164i q^{32} +(-27.5000 + 41.4578i) q^{33} -11.0000 q^{34} +(-24.5000 - 58.0409i) q^{36} +40.0000 q^{37} -23.2164i q^{38} +(25.0000 + 16.5831i) q^{39} +16.5831i q^{41} +50.0000 q^{43} +116.082i q^{44} -66.0000 q^{46} +46.4327i q^{47} +(-12.5000 - 8.29156i) q^{48} -49.0000 q^{49} +(-5.50000 + 8.29156i) q^{51} +70.0000 q^{52} +46.4327i q^{53} +(-88.0000 - 16.5831i) q^{54} +(-17.5000 - 11.6082i) q^{57} -110.000 q^{58} -66.3325i q^{59} -8.00000 q^{61} -139.298i q^{62} +97.0000 q^{64} +(137.500 + 91.2072i) q^{66} -45.0000 q^{67} +23.2164i q^{68} +(-33.0000 + 49.7494i) q^{69} -33.1662i q^{71} +(-82.5000 + 34.8246i) q^{72} +35.0000 q^{73} -132.665i q^{74} -49.0000 q^{76} +(55.0000 - 82.9156i) q^{78} +12.0000 q^{79} +(-56.5000 + 58.0409i) q^{81} +55.0000 q^{82} -69.6491i q^{83} -165.831i q^{86} +(-55.0000 + 82.9156i) q^{87} +165.000 q^{88} +149.248i q^{89} +139.298i q^{92} +(-105.000 - 69.6491i) q^{93} +154.000 q^{94} +(38.5000 - 58.0409i) q^{96} +70.0000 q^{97} +162.515i q^{98} +(137.500 - 58.0409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 5 q^{3} - 14 q^{4} - 11 q^{6} + 7 q^{9}+O(q^{10}) \) 2 * q - 5 * q^3 - 14 * q^4 - 11 * q^6 + 7 * q^9	\( 2 q - 5 q^{3} - 14 q^{4} - 11 q^{6} + 7 q^{9} + 35 q^{12} - 20 q^{13} + 10 q^{16} + 55 q^{18} + 14 q^{19} - 110 q^{22} + 33 q^{24} + 10 q^{27} + 84 q^{31} - 55 q^{33} - 22 q^{34} - 49 q^{36} + 80 q^{37} + 50 q^{39} + 100 q^{43} - 132 q^{46} - 25 q^{48} - 98 q^{49} - 11 q^{51} + 140 q^{52} - 176 q^{54} - 35 q^{57} - 220 q^{58} - 16 q^{61} + 194 q^{64} + 275 q^{66} - 90 q^{67} - 66 q^{69} - 165 q^{72} + 70 q^{73} - 98 q^{76} + 110 q^{78} + 24 q^{79} - 113 q^{81} + 110 q^{82} - 110 q^{87} + 330 q^{88} - 210 q^{93} + 308 q^{94} + 77 q^{96} + 140 q^{97} + 275 q^{99}+O(q^{100}) \) 2 * q - 5 * q^3 - 14 * q^4 - 11 * q^6 + 7 * q^9 + 35 * q^12 - 20 * q^13 + 10 * q^16 + 55 * q^18 + 14 * q^19 - 110 * q^22 + 33 * q^24 + 10 * q^27 + 84 * q^31 - 55 * q^33 - 22 * q^34 - 49 * q^36 + 80 * q^37 + 50 * q^39 + 100 * q^43 - 132 * q^46 - 25 * q^48 - 98 * q^49 - 11 * q^51 + 140 * q^52 - 176 * q^54 - 35 * q^57 - 220 * q^58 - 16 * q^61 + 194 * q^64 + 275 * q^66 - 90 * q^67 - 66 * q^69 - 165 * q^72 + 70 * q^73 - 98 * q^76 + 110 * q^78 + 24 * q^79 - 113 * q^81 + 110 * q^82 - 110 * q^87 + 330 * q^88 - 210 * q^93 + 308 * q^94 + 77 * q^96 + 140 * q^97 + 275 * q^99

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