LMFDB - Embedded newform 2100.2.q.f.1801.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1201,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("2100.1201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.q (of order $3$, degree $2$, 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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1801.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	2100.1801
Dual form			2100.2.q.f.1201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(-2.62132 + 0.358719i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(-2.62132 + 0.358719i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-2.12132 - 3.67423i) q^{11} +5.00000 q^{13} +(-2.12132 - 3.67423i) q^{17} +(2.62132 - 4.54026i) q^{19} +(1.62132 + 2.09077i) q^{21} +(-3.00000 + 5.19615i) q^{23} +1.00000 q^{27} +8.48528 q^{29} +(2.00000 + 3.46410i) q^{31} +(-2.12132 + 3.67423i) q^{33} +(-2.50000 + 4.33013i) q^{37} +(-2.50000 - 4.33013i) q^{39} -10.2426 q^{41} -12.4853 q^{43} +(-5.12132 + 8.87039i) q^{47} +(6.74264 - 1.88064i) q^{49} +(-2.12132 + 3.67423i) q^{51} +(-2.12132 - 3.67423i) q^{53} -5.24264 q^{57} +(-5.12132 - 8.87039i) q^{59} +(0.500000 - 0.866025i) q^{61} +(1.00000 - 2.44949i) q^{63} +(-5.86396 - 10.1567i) q^{67} +6.00000 q^{69} -8.48528 q^{71} +(1.74264 + 3.01834i) q^{73} +(6.87868 + 8.87039i) q^{77} +(-4.62132 + 8.00436i) q^{79} +(-0.500000 - 0.866025i) q^{81} +1.75736 q^{83} +(-4.24264 - 7.34847i) q^{87} +(-3.87868 + 6.71807i) q^{89} +(-13.1066 + 1.79360i) q^{91} +(2.00000 - 3.46410i) q^{93} -17.9706 q^{97} +4.24264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} - 2 q^{7} - 2 q^{9} + 20 q^{13} + 2 q^{19} - 2 q^{21} - 12 q^{23} + 4 q^{27} + 8 q^{31} - 10 q^{37} - 10 q^{39} - 24 q^{41} - 16 q^{43} - 12 q^{47} + 10 q^{49} - 4 q^{57} - 12 q^{59} + 2 q^{61} + 4 q^{63} + 2 q^{67} + 24 q^{69} - 10 q^{73} + 36 q^{77} - 10 q^{79} - 2 q^{81} + 24 q^{83} - 24 q^{89} - 10 q^{91} + 8 q^{93} - 4 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^7 - 2 * q^9 + 20 * q^13 + 2 * q^19 - 2 * q^21 - 12 * q^23 + 4 * q^27 + 8 * q^31 - 10 * q^37 - 10 * q^39 - 24 * q^41 - 16 * q^43 - 12 * q^47 + 10 * q^49 - 4 * q^57 - 12 * q^59 + 2 * q^61 + 4 * q^63 + 2 * q^67 + 24 * q^69 - 10 * q^73 + 36 * q^77 - 10 * q^79 - 2 * q^81 + 24 * q^83 - 24 * q^89 - 10 * q^91 + 8 * q^93 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.12132	−	3.67423i	−0.639602	−	1.10782i	−0.985520	−	0.169559i	$-0.945766\pi$
$11$	−2.12132	−	3.67423i	−0.639602	−	1.10782i	0.345918	−	0.938265i	$-0.387568\pi$
$12$		0			0
$13$	5.00000			1.38675			0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000			1.38675			0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.12132	−	3.67423i	−0.514496	−	0.891133i	−0.999859	−	0.0168199i	$-0.994646\pi$
$17$	−2.12132	−	3.67423i	−0.514496	−	0.891133i	0.485363	−	0.874313i	$-0.338688\pi$
$18$		0			0
$19$	2.62132	−	4.54026i	0.601372	−	1.04161i	−0.391241	−	0.920288i	$-0.627954\pi$
$19$	2.62132	−	4.54026i	0.601372	−	1.04161i	0.992614	−	0.121319i	$-0.0387124\pi$
$20$		0			0
$21$	1.62132	+	2.09077i	0.353801	+	0.456243i
$22$		0			0
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	8.48528			1.57568			0.787839	−	0.615882i	$-0.211200\pi$
$29$	8.48528			1.57568			0.787839	+	0.615882i	$0.211200\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$		0			0
$33$	−2.12132	+	3.67423i	−0.369274	+	0.639602i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.50000	+	4.33013i	−0.410997	+	0.711868i	−0.994999	−	0.0998840i	$-0.968153\pi$
$37$	−2.50000	+	4.33013i	−0.410997	+	0.711868i	0.584002	+	0.811752i	$0.301486\pi$
$38$		0			0
$39$	−2.50000	−	4.33013i	−0.400320	−	0.693375i
$40$		0			0
$41$	−10.2426			−1.59963			−0.799816	−	0.600245i	$-0.795070\pi$
$41$	−10.2426			−1.59963			−0.799816	+	0.600245i	$0.795070\pi$
$42$		0			0
$43$	−12.4853			−1.90399			−0.951994	−	0.306117i	$-0.900970\pi$
$43$	−12.4853			−1.90399			−0.951994	+	0.306117i	$0.900970\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.12132	+	8.87039i	−0.747021	+	1.29388i	0.202223	+	0.979339i	$0.435183\pi$
$47$	−5.12132	+	8.87039i	−0.747021	+	1.29388i	−0.949244	+	0.314539i	$0.898150\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$		0			0
$51$	−2.12132	+	3.67423i	−0.297044	+	0.514496i
$52$		0			0
$53$	−2.12132	−	3.67423i	−0.291386	−	0.504695i	0.682752	−	0.730650i	$-0.260783\pi$
$53$	−2.12132	−	3.67423i	−0.291386	−	0.504695i	−0.974138	+	0.225955i	$0.927450\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−5.24264			−0.694405
$58$		0			0
$59$	−5.12132	−	8.87039i	−0.666739	−	1.15483i	−0.978811	−	0.204767i	$-0.934356\pi$
$59$	−5.12132	−	8.87039i	−0.666739	−	1.15483i	0.312072	−	0.950059i	$-0.398977\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$		0			0
$63$	1.00000	−	2.44949i	0.125988	−	0.308607i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.86396	−	10.1567i	−0.716397	−	1.24084i	−0.962418	−	0.271571i	$-0.912457\pi$
$67$	−5.86396	−	10.1567i	−0.716397	−	1.24084i	0.246021	−	0.969264i	$-0.420877\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		0			0
$71$	−8.48528			−1.00702			−0.503509	−	0.863990i	$-0.667958\pi$
$71$	−8.48528			−1.00702			−0.503509	+	0.863990i	$0.667958\pi$
$72$		0			0
$73$	1.74264	+	3.01834i	0.203961	+	0.353270i	0.949801	−	0.312854i	$-0.101285\pi$
$73$	1.74264	+	3.01834i	0.203961	+	0.353270i	−0.745840	+	0.666125i	$0.767952\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.87868	+	8.87039i	0.783898	+	1.01087i
$78$		0			0
$79$	−4.62132	+	8.00436i	−0.519939	+	0.900561i	0.479792	+	0.877382i	$0.340712\pi$
$79$	−4.62132	+	8.00436i	−0.519939	+	0.900561i	−0.999731	+	0.0231789i	$0.992621\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	1.75736			0.192895			0.0964476	−	0.995338i	$-0.469252\pi$
$83$	1.75736			0.192895			0.0964476	+	0.995338i	$0.469252\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−4.24264	−	7.34847i	−0.454859	−	0.787839i
$88$		0			0
$89$	−3.87868	+	6.71807i	−0.411139	+	0.712114i	−0.995015	−	0.0997293i	$-0.968202\pi$
$89$	−3.87868	+	6.71807i	−0.411139	+	0.712114i	0.583875	+	0.811843i	$0.301536\pi$
$90$		0			0
$91$	−13.1066	+	1.79360i	−1.37395	+	0.188020i
$92$		0			0
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−17.9706			−1.82463			−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−17.9706			−1.82463			−0.912317	+	0.409484i	$0.865709\pi$
$98$		0			0
$99$	4.24264			0.426401
$100$		0			0
$101$	−3.36396	−	5.82655i	−0.334727	−	0.579764i	0.648706	−	0.761039i	$-0.275311\pi$
$101$	−3.36396	−	5.82655i	−0.334727	−	0.579764i	−0.983432	+	0.181276i	$0.941977\pi$
$102$		0			0
$103$	−0.378680	+	0.655892i	−0.0373124	+	0.0646270i	−0.884079	−	0.467338i	$-0.845213\pi$
$103$	−0.378680	+	0.655892i	−0.0373124	+	0.0646270i	0.846766	+	0.531965i	$0.178546\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.36396	+	5.82655i	−0.325206	+	0.563274i	−0.981554	−	0.191185i	$-0.938767\pi$
$107$	−3.36396	+	5.82655i	−0.325206	+	0.563274i	0.656348	+	0.754459i	$0.272100\pi$
$108$		0			0
$109$	−1.25736	−	2.17781i	−0.120433	−	0.208596i	0.799505	−	0.600659i	$-0.205095\pi$
$109$	−1.25736	−	2.17781i	−0.120433	−	0.208596i	−0.919939	+	0.392063i	$0.871762\pi$
$110$		0			0
$111$	5.00000			0.474579
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.50000	+	4.33013i	−0.231125	+	0.400320i
$118$		0			0
$119$	6.87868	+	8.87039i	0.630568	+	0.813147i
$120$		0			0
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$		0			0
$123$	5.12132	+	8.87039i	0.461774	+	0.799816i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.757359			0.0672048			0.0336024	−	0.999435i	$-0.489302\pi$
$127$	0.757359			0.0672048			0.0336024	+	0.999435i	$0.489302\pi$
$128$		0			0
$129$	6.24264	+	10.8126i	0.549634	+	0.951994i
$130$		0			0
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	−0.966803	−	0.255524i	$-0.917752\pi$
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	0.704692	+	0.709514i	$0.251085\pi$
$132$		0			0
$133$	−5.24264	+	12.8418i	−0.454595	+	1.11352i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.24264	+	2.15232i	0.106166	+	0.183885i	0.914214	−	0.405232i	$-0.132809\pi$
$137$	1.24264	+	2.15232i	0.106166	+	0.183885i	−0.808048	+	0.589117i	$0.799476\pi$
$138$		0			0
$139$	11.7279			0.994749			0.497375	−	0.867536i	$-0.334297\pi$
$139$	11.7279			0.994749			0.497375	+	0.867536i	$0.334297\pi$
$140$		0			0
$141$	10.2426			0.862586
$142$		0			0
$143$	−10.6066	−	18.3712i	−0.886969	−	1.53627i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.00000	−	4.89898i	−0.412393	−	0.404061i
$148$		0			0
$149$	11.1213	−	19.2627i	0.911094	−	1.57806i	0.0985727	−	0.995130i	$-0.468572\pi$
$149$	11.1213	−	19.2627i	0.911094	−	1.57806i	0.812521	−	0.582931i	$-0.198094\pi$
$150$		0			0
$151$	6.86396	+	11.8887i	0.558581	+	0.967491i	0.997615	+	0.0690206i	$0.0219874\pi$
$151$	6.86396	+	11.8887i	0.558581	+	0.967491i	−0.439034	+	0.898470i	$0.644679\pi$
$152$		0			0
$153$	4.24264			0.342997
$154$		0			0
$155$		0			0
$156$		0			0
$157$	7.74264	+	13.4106i	0.617930	+	1.07029i	0.989863	+	0.142027i	$0.0453618\pi$
$157$	7.74264	+	13.4106i	0.617930	+	1.07029i	−0.371933	+	0.928260i	$0.621305\pi$
$158$		0			0
$159$	−2.12132	+	3.67423i	−0.168232	+	0.291386i
$160$		0			0
$161$	6.00000	−	14.6969i	0.472866	−	1.15828i
$162$		0			0
$163$	8.62132	−	14.9326i	0.675274	−	1.16961i	−0.301115	−	0.953588i	$-0.597359\pi$
$163$	8.62132	−	14.9326i	0.675274	−	1.16961i	0.976389	−	0.216021i	$-0.0693079\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.2426			−0.792599			−0.396300	−	0.918121i	$-0.629706\pi$
$167$	−10.2426			−0.792599			−0.396300	+	0.918121i	$0.629706\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	2.62132	+	4.54026i	0.200457	+	0.347202i
$172$		0			0
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.12132	+	8.87039i	−0.384942	+	0.666739i
$178$		0			0
$179$	−10.2426	−	17.7408i	−0.765571	−	1.32601i	−0.939944	−	0.341328i	$-0.889123\pi$
$179$	−10.2426	−	17.7408i	−0.765571	−	1.32601i	0.174373	−	0.984680i	$-0.444210\pi$
$180$		0			0
$181$	−12.4853			−0.928024			−0.464012	−	0.885829i	$-0.653590\pi$
$181$	−12.4853			−0.928024			−0.464012	+	0.885829i	$0.653590\pi$
$182$		0			0
$183$	−1.00000			−0.0739221
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−9.00000	+	15.5885i	−0.658145	+	1.13994i
$188$		0			0
$189$	−2.62132	+	0.358719i	−0.190673	+	0.0260930i
$190$		0			0
$191$	−3.87868	+	6.71807i	−0.280651	+	0.486103i	−0.971545	−	0.236854i	$-0.923884\pi$
$191$	−3.87868	+	6.71807i	−0.280651	+	0.486103i	0.690894	+	0.722956i	$0.257217\pi$
$192$		0			0
$193$	6.24264	+	10.8126i	0.449355	+	0.778306i	0.998344	−	0.0575237i	$-0.0183205\pi$
$193$	6.24264	+	10.8126i	0.449355	+	0.778306i	−0.548989	+	0.835830i	$0.684987\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.48528			−0.604551			−0.302276	−	0.953221i	$-0.597746\pi$
$197$	−8.48528			−0.604551			−0.302276	+	0.953221i	$0.597746\pi$
$198$		0			0
$199$	4.37868	+	7.58410i	0.310396	+	0.537622i	0.978448	−	0.206492i	$-0.0662049\pi$
$199$	4.37868	+	7.58410i	0.310396	+	0.537622i	−0.668052	+	0.744115i	$0.732872\pi$
$200$		0			0
$201$	−5.86396	+	10.1567i	−0.413612	+	0.716397i
$202$		0			0
$203$	−22.2426	+	3.04384i	−1.56113	+	0.213635i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.00000	−	5.19615i	−0.208514	−	0.361158i
$208$		0			0
$209$	−22.2426			−1.53856
$210$		0			0
$211$	21.2426			1.46240			0.731202	−	0.682161i	$-0.238960\pi$
$211$	21.2426			1.46240			0.731202	+	0.682161i	$0.238960\pi$
$212$		0			0
$213$	4.24264	+	7.34847i	0.290701	+	0.503509i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−6.48528	−	8.36308i	−0.440250	−	0.567723i
$218$		0			0
$219$	1.74264	−	3.01834i	0.117757	−	0.203961i
$220$		0			0
$221$	−10.6066	−	18.3712i	−0.713477	−	1.23578i
$222$		0			0
$223$	0.757359			0.0507165			0.0253583	−	0.999678i	$-0.491927\pi$
$223$	0.757359			0.0507165			0.0253583	+	0.999678i	$0.491927\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.2426	+	17.7408i	0.679828	+	1.17750i	0.975032	+	0.222062i	$0.0712789\pi$
$227$	10.2426	+	17.7408i	0.679828	+	1.17750i	−0.295205	+	0.955434i	$0.595388\pi$
$228$		0			0
$229$	−13.9853	+	24.2232i	−0.924173	+	1.60072i	−0.131288	+	0.991344i	$0.541911\pi$
$229$	−13.9853	+	24.2232i	−0.924173	+	1.60072i	−0.792885	+	0.609371i	$0.791422\pi$
$230$		0			0
$231$	4.24264	−	10.3923i	0.279145	−	0.683763i
$232$		0			0
$233$	0.878680	−	1.52192i	0.0575642	−	0.0997042i	−0.835807	−	0.549023i	$-0.815000\pi$
$233$	0.878680	−	1.52192i	0.0575642	−	0.0997042i	0.893371	+	0.449319i	$0.148333\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	9.24264			0.600374
$238$		0			0
$239$	−4.97056			−0.321519			−0.160759	−	0.986994i	$-0.551394\pi$
$239$	−4.97056			−0.321519			−0.160759	+	0.986994i	$0.551394\pi$
$240$		0			0
$241$	2.98528	+	5.17066i	0.192299	+	0.333071i	0.946012	−	0.324132i	$-0.105072\pi$
$241$	2.98528	+	5.17066i	0.192299	+	0.333071i	−0.753713	+	0.657204i	$0.771739\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	13.1066	−	22.7013i	0.833953	−	1.44445i
$248$		0			0
$249$	−0.878680	−	1.52192i	−0.0556841	−	0.0964476i
$250$		0			0
$251$	−16.2426			−1.02523			−0.512613	−	0.858620i	$-0.671323\pi$
$251$	−16.2426			−1.02523			−0.512613	+	0.858620i	$0.671323\pi$
$252$		0			0
$253$	25.4558			1.60040
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.1213	−	19.2627i	0.693729	−	1.20157i	−0.276878	−	0.960905i	$-0.589300\pi$
$257$	11.1213	−	19.2627i	0.693729	−	1.20157i	0.970607	−	0.240669i	$-0.0773667\pi$
$258$		0			0
$259$	5.00000	−	12.2474i	0.310685	−	0.761019i
$260$		0			0
$261$	−4.24264	+	7.34847i	−0.262613	+	0.454859i
$262$		0			0
$263$	−14.4853	−	25.0892i	−0.893201	−	1.54707i	−0.836016	−	0.548705i	$-0.815121\pi$
$263$	−14.4853	−	25.0892i	−0.893201	−	1.54707i	−0.0571849	−	0.998364i	$-0.518212\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	7.75736			0.474743
$268$		0			0
$269$	9.36396	+	16.2189i	0.570931	+	0.988881i	0.996471	+	0.0839415i	$0.0267509\pi$
$269$	9.36396	+	16.2189i	0.570931	+	0.988881i	−0.425540	+	0.904940i	$0.639916\pi$
$270$		0			0
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	−0.894799	−	0.446469i	$-0.852681\pi$
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	0.834053	+	0.551684i	$0.186015\pi$
$272$		0			0
$273$	8.10660	+	10.4539i	0.490634	+	0.632696i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−7.25736	−	12.5701i	−0.436052	−	0.755265i	0.561328	−	0.827593i	$-0.310290\pi$
$277$	−7.25736	−	12.5701i	−0.436052	−	0.755265i	−0.997381	+	0.0723281i	$0.976957\pi$
$278$		0			0
$279$	−4.00000			−0.239474
$280$		0			0
$281$	−28.2426			−1.68481			−0.842407	−	0.538841i	$-0.818862\pi$
$281$	−28.2426			−1.68481			−0.842407	+	0.538841i	$0.818862\pi$
$282$		0			0
$283$	1.37868	+	2.38794i	0.0819540	+	0.141948i	0.904089	−	0.427344i	$-0.140551\pi$
$283$	1.37868	+	2.38794i	0.0819540	+	0.141948i	−0.822135	+	0.569292i	$0.807217\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	26.8492	−	3.67423i	1.58486	−	0.216883i
$288$		0			0
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$		0			0
$291$	8.98528	+	15.5630i	0.526727	+	0.912317i
$292$		0			0
$293$	3.51472			0.205332			0.102666	−	0.994716i	$-0.467263\pi$
$293$	3.51472			0.205332			0.102666	+	0.994716i	$0.467263\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.12132	−	3.67423i	−0.123091	−	0.213201i
$298$		0			0
$299$	−15.0000	+	25.9808i	−0.867472	+	1.50251i
$300$		0			0
$301$	32.7279	−	4.47871i	1.88641	−	0.258149i
$302$		0			0
$303$	−3.36396	+	5.82655i	−0.193255	+	0.334727i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	4.48528			0.255989			0.127994	−	0.991775i	$-0.459146\pi$
$307$	4.48528			0.255989			0.127994	+	0.991775i	$0.459146\pi$
$308$		0			0
$309$	0.757359			0.0430847
$310$		0			0
$311$	−7.24264	−	12.5446i	−0.410692	−	0.711340i	0.584273	−	0.811557i	$-0.301380\pi$
$311$	−7.24264	−	12.5446i	−0.410692	−	0.711340i	−0.994966	+	0.100217i	$0.968046\pi$
$312$		0			0
$313$	−0.485281	+	0.840532i	−0.0274297	+	0.0475097i	−0.879414	−	0.476057i	$-0.842066\pi$
$313$	−0.485281	+	0.840532i	−0.0274297	+	0.0475097i	0.851985	+	0.523567i	$0.175399\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$		0			0
$319$	−18.0000	−	31.1769i	−1.00781	−	1.74557i
$320$		0			0
$321$	6.72792			0.375516
$322$		0			0
$323$	−22.2426			−1.23761
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−1.25736	+	2.17781i	−0.0695321	+	0.120433i
$328$		0			0
$329$	10.2426	−	25.0892i	0.564695	−	1.38321i
$330$		0			0
$331$	8.62132	−	14.9326i	0.473871	−	0.820768i	−0.525682	−	0.850681i	$-0.676190\pi$
$331$	8.62132	−	14.9326i	0.473871	−	0.820768i	0.999552	+	0.0299132i	$0.00952310\pi$
$332$		0			0
$333$	−2.50000	−	4.33013i	−0.136999	−	0.237289i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	24.9706			1.36023			0.680117	−	0.733104i	$-0.261929\pi$
$337$	24.9706			1.36023			0.680117	+	0.733104i	$0.261929\pi$
$338$		0			0
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$		0			0
$341$	8.48528	−	14.6969i	0.459504	−	0.795884i
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.63604	−	4.56575i	−0.141510	−	0.245102i	0.786555	−	0.617520i	$-0.211862\pi$
$347$	−2.63604	−	4.56575i	−0.141510	−	0.245102i	−0.928065	+	0.372417i	$0.878529\pi$
$348$		0			0
$349$	8.00000			0.428230			0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000			0.428230			0.214115	+	0.976808i	$0.431313\pi$
$350$		0			0
$351$	5.00000			0.266880
$352$		0			0
$353$	9.36396	+	16.2189i	0.498393	+	0.863243i	0.999998	−	0.00185420i	$-0.000590210\pi$
$353$	9.36396	+	16.2189i	0.498393	+	0.863243i	−0.501605	+	0.865097i	$0.667257\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	4.24264	−	10.3923i	0.224544	−	0.550019i
$358$		0			0
$359$	−2.63604	+	4.56575i	−0.139125	+	0.240971i	−0.927166	−	0.374652i	$-0.877762\pi$
$359$	−2.63604	+	4.56575i	−0.139125	+	0.240971i	0.788041	+	0.615623i	$0.211096\pi$
$360$		0			0
$361$	−4.24264	−	7.34847i	−0.223297	−	0.386762i
$362$		0			0
$363$	7.00000			0.367405
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.00000	−	12.1244i	−0.365397	−	0.632886i	0.623443	−	0.781869i	$-0.285733\pi$
$367$	−7.00000	−	12.1244i	−0.365397	−	0.632886i	−0.988840	+	0.148983i	$0.952400\pi$
$368$		0			0
$369$	5.12132	−	8.87039i	0.266605	−	0.461774i
$370$		0			0
$371$	6.87868	+	8.87039i	0.357123	+	0.460528i
$372$		0			0
$373$	−0.742641	+	1.28629i	−0.0384525	+	0.0666016i	−0.884611	−	0.466329i	$-0.845576\pi$
$373$	−0.742641	+	1.28629i	−0.0384525	+	0.0666016i	0.846159	+	0.532931i	$0.178909\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	42.4264			2.18507
$378$		0			0
$379$	−13.7279			−0.705156			−0.352578	−	0.935782i	$-0.614695\pi$
$379$	−13.7279			−0.705156			−0.352578	+	0.935782i	$0.614695\pi$
$380$		0			0
$381$	−0.378680	−	0.655892i	−0.0194003	−	0.0336024i
$382$		0			0
$383$	15.7279	−	27.2416i	0.803659	−	1.39198i	−0.113533	−	0.993534i	$-0.536217\pi$
$383$	15.7279	−	27.2416i	0.803659	−	1.39198i	0.917192	−	0.398444i	$-0.130450\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.24264	−	10.8126i	0.317331	−	0.549634i
$388$		0			0
$389$	−15.3640	−	26.6112i	−0.778984	−	1.34924i	−0.932528	−	0.361098i	$-0.882402\pi$
$389$	−15.3640	−	26.6112i	−0.778984	−	1.34924i	0.153544	−	0.988142i	$-0.450931\pi$
$390$		0			0
$391$	25.4558			1.28736
$392$		0			0
$393$	6.00000			0.302660
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−10.0000	+	17.3205i	−0.501886	+	0.869291i	0.498112	+	0.867113i	$0.334027\pi$
$397$	−10.0000	+	17.3205i	−0.501886	+	0.869291i	−0.999998	+	0.00217869i	$0.999307\pi$
$398$		0			0
$399$	13.7426	−	1.88064i	0.687993	−	0.0941496i
$400$		0			0
$401$	13.6066	−	23.5673i	0.679481	−	1.17690i	−0.295656	−	0.955294i	$-0.595538\pi$
$401$	13.6066	−	23.5673i	0.679481	−	1.17690i	0.975137	−	0.221602i	$-0.0711284\pi$
$402$		0			0
$403$	10.0000	+	17.3205i	0.498135	+	0.862796i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	21.2132			1.05150
$408$		0			0
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	0.939490	−	0.342578i	$-0.111300\pi$
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	−0.766426	+	0.642333i	$0.777967\pi$
$410$		0			0
$411$	1.24264	−	2.15232i	0.0612949	−	0.106166i
$412$		0			0
$413$	16.6066	+	21.4150i	0.817157	+	1.05376i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−5.86396	−	10.1567i	−0.287159	−	0.497375i
$418$		0			0
$419$	−12.7279			−0.621800			−0.310900	−	0.950443i	$-0.600630\pi$
$419$	−12.7279			−0.621800			−0.310900	+	0.950443i	$0.600630\pi$
$420$		0			0
$421$	−1.00000			−0.0487370			−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000			−0.0487370			−0.0243685	+	0.999703i	$0.507758\pi$
$422$		0			0
$423$	−5.12132	−	8.87039i	−0.249007	−	0.431293i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.00000	+	2.44949i	−0.0483934	+	0.118539i
$428$		0			0
$429$	−10.6066	+	18.3712i	−0.512092	+	0.886969i
$430$		0			0
$431$	−4.75736	−	8.23999i	−0.229154	−	0.396906i	0.728404	−	0.685148i	$-0.240263\pi$
$431$	−4.75736	−	8.23999i	−0.229154	−	0.396906i	−0.957558	+	0.288242i	$0.906929\pi$
$432$		0			0
$433$	24.9706			1.20001			0.600004	−	0.799997i	$-0.295166\pi$
$433$	24.9706			1.20001			0.600004	+	0.799997i	$0.295166\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15.7279	+	27.2416i	0.752369	+	1.30314i
$438$		0			0
$439$	−5.13604	+	8.89588i	−0.245130	+	0.424577i	−0.962168	−	0.272457i	$-0.912164\pi$
$439$	−5.13604	+	8.89588i	−0.245130	+	0.424577i	0.717038	+	0.697034i	$0.245497\pi$
$440$		0			0
$441$	−1.74264	+	6.77962i	−0.0829829	+	0.322839i
$442$		0			0
$443$	9.72792	−	16.8493i	0.462188	−	0.800532i	−0.536882	−	0.843657i	$-0.680398\pi$
$443$	9.72792	−	16.8493i	0.462188	−	0.800532i	0.999070	+	0.0431250i	$0.0137314\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−22.2426			−1.05204
$448$		0			0
$449$	11.2721			0.531962			0.265981	−	0.963978i	$-0.414304\pi$
$449$	11.2721			0.531962			0.265981	+	0.963978i	$0.414304\pi$
$450$		0			0
$451$	21.7279	+	37.6339i	1.02313	+	1.77211i
$452$		0			0
$453$	6.86396	−	11.8887i	0.322497	−	0.558581i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.74264	−	8.21449i	0.221851	−	0.384258i	−0.733519	−	0.679669i	$-0.762123\pi$
$457$	4.74264	−	8.21449i	0.221851	−	0.384258i	0.955370	+	0.295411i	$0.0954567\pi$
$458$		0			0
$459$	−2.12132	−	3.67423i	−0.0990148	−	0.171499i
$460$		0			0
$461$	−9.51472			−0.443145			−0.221572	−	0.975144i	$-0.571119\pi$
$461$	−9.51472			−0.443145			−0.221572	+	0.975144i	$0.571119\pi$
$462$		0			0
$463$	−11.2426			−0.522490			−0.261245	−	0.965273i	$-0.584133\pi$
$463$	−11.2426			−0.522490			−0.261245	+	0.965273i	$0.584133\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.72792	+	16.8493i	−0.450155	+	0.779691i	−0.998395	−	0.0566301i	$-0.981964\pi$
$467$	−9.72792	+	16.8493i	−0.450155	+	0.779691i	0.548241	+	0.836321i	$0.315298\pi$
$468$		0			0
$469$	19.0147	+	24.5204i	0.878018	+	1.13225i
$470$		0			0
$471$	7.74264	−	13.4106i	0.356762	−	0.617930i
$472$		0			0
$473$	26.4853	+	45.8739i	1.21779	+	2.10928i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	4.24264			0.194257
$478$		0			0
$479$	−7.60660	−	13.1750i	−0.347555	−	0.601982i	0.638260	−	0.769821i	$-0.279655\pi$
$479$	−7.60660	−	13.1750i	−0.347555	−	0.601982i	−0.985814	+	0.167839i	$0.946321\pi$
$480$		0			0
$481$	−12.5000	+	21.6506i	−0.569951	+	0.987184i
$482$		0			0
$483$	−15.7279	+	2.15232i	−0.715645	+	0.0979338i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−14.2426	−	24.6690i	−0.645396	−	1.11786i	−0.984210	−	0.177005i	$-0.943359\pi$
$487$	−14.2426	−	24.6690i	−0.645396	−	1.11786i	0.338814	−	0.940853i	$-0.389974\pi$
$488$		0			0
$489$	−17.2426			−0.779739
$490$		0			0
$491$	38.4853			1.73682			0.868408	−	0.495850i	$-0.165143\pi$
$491$	38.4853			1.73682			0.868408	+	0.495850i	$0.165143\pi$
$492$		0			0
$493$	−18.0000	−	31.1769i	−0.810679	−	1.40414i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	22.2426	−	3.04384i	0.997719	−	0.136535i
$498$		0			0
$499$	−1.62132	+	2.80821i	−0.0725803	+	0.125713i	−0.900031	−	0.435825i	$-0.856457\pi$
$499$	−1.62132	+	2.80821i	−0.0725803	+	0.125713i	0.827451	+	0.561538i	$0.189790\pi$
$500$		0			0
$501$	5.12132	+	8.87039i	0.228804	+	0.396300i
$502$		0			0
$503$	25.4558			1.13502			0.567510	−	0.823367i	$-0.307907\pi$
$503$	25.4558			1.13502			0.567510	+	0.823367i	$0.307907\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$		0			0
$509$	−13.7574	+	23.8284i	−0.609784	+	1.05618i	0.381491	+	0.924372i	$0.375411\pi$
$509$	−13.7574	+	23.8284i	−0.609784	+	1.05618i	−0.991276	+	0.131805i	$0.957923\pi$
$510$		0			0
$511$	−5.65076	−	7.28692i	−0.249975	−	0.322354i
$512$		0			0
$513$	2.62132	−	4.54026i	0.115734	−	0.200457i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	43.4558			1.91119
$518$		0			0
$519$	−6.00000			−0.263371
$520$		0			0
$521$	−3.72792	−	6.45695i	−0.163323	−	0.282884i	0.772735	−	0.634728i	$-0.218888\pi$
$521$	−3.72792	−	6.45695i	−0.163323	−	0.282884i	−0.936059	+	0.351844i	$0.885555\pi$
$522$		0			0
$523$	12.2426	−	21.2049i	0.535333	−	0.927224i	−0.463814	−	0.885933i	$-0.653519\pi$
$523$	12.2426	−	21.2049i	0.535333	−	0.927224i	0.999147	−	0.0412918i	$-0.0131473\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.48528	−	14.6969i	0.369625	−	0.640209i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	10.2426			0.444493
$532$		0			0
$533$	−51.2132			−2.21829
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−10.2426	+	17.7408i	−0.442003	+	0.765571i
$538$		0			0
$539$	−21.2132	−	20.7846i	−0.913717	−	0.895257i
$540$		0			0
$541$	−0.742641	+	1.28629i	−0.0319286	+	0.0553020i	−0.881548	−	0.472094i	$-0.843498\pi$
$541$	−0.742641	+	1.28629i	−0.0319286	+	0.0553020i	0.849620	+	0.527396i	$0.176832\pi$
$542$		0			0
$543$	6.24264	+	10.8126i	0.267897	+	0.464012i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	26.0000			1.11168			0.555840	−	0.831289i	$-0.312397\pi$
$547$	26.0000			1.11168			0.555840	+	0.831289i	$0.312397\pi$
$548$		0			0
$549$	0.500000	+	0.866025i	0.0213395	+	0.0369611i
$550$		0			0
$551$	22.2426	−	38.5254i	0.947568	−	1.64124i
$552$		0			0
$553$	9.24264	−	22.6398i	0.393037	−	0.962740i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−13.7574	−	23.8284i	−0.582918	−	1.00964i	−0.995131	−	0.0985563i	$-0.968578\pi$
$557$	−13.7574	−	23.8284i	−0.582918	−	1.00964i	0.412213	−	0.911087i	$-0.364756\pi$
$558$		0			0
$559$	−62.4264			−2.64036
$560$		0			0
$561$	18.0000			0.759961
$562$		0			0
$563$	−9.87868	−	17.1104i	−0.416337	−	0.721116i	0.579231	−	0.815163i	$-0.303353\pi$
$563$	−9.87868	−	17.1104i	−0.416337	−	0.721116i	−0.995568	+	0.0940471i	$0.970020\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.62132	+	2.09077i	0.0680891	+	0.0878041i
$568$		0			0
$569$	−15.3640	+	26.6112i	−0.644091	+	1.11560i	0.340420	+	0.940273i	$0.389431\pi$
$569$	−15.3640	+	26.6112i	−0.644091	+	1.11560i	−0.984511	+	0.175324i	$0.943903\pi$
$570$		0			0
$571$	−18.3787	−	31.8328i	−0.769124	−	1.33216i	−0.938039	−	0.346531i	$-0.887360\pi$
$571$	−18.3787	−	31.8328i	−0.769124	−	1.33216i	0.168915	−	0.985631i	$-0.445974\pi$
$572$		0			0
$573$	7.75736			0.324068
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−9.48528	−	16.4290i	−0.394877	−	0.683948i	0.598208	−	0.801341i	$-0.295880\pi$
$577$	−9.48528	−	16.4290i	−0.394877	−	0.683948i	−0.993086	+	0.117393i	$0.962546\pi$
$578$		0			0
$579$	6.24264	−	10.8126i	0.259435	−	0.449355i
$580$		0			0
$581$	−4.60660	+	0.630399i	−0.191114	+	0.0261534i
$582$		0			0
$583$	−9.00000	+	15.5885i	−0.372742	+	0.645608i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−22.9706			−0.948097			−0.474048	−	0.880499i	$-0.657208\pi$
$587$	−22.9706			−0.948097			−0.474048	+	0.880499i	$0.657208\pi$
$588$		0			0
$589$	20.9706			0.864077
$590$		0			0
$591$	4.24264	+	7.34847i	0.174519	+	0.302276i
$592$		0			0
$593$	0.514719	−	0.891519i	0.0211370	−	0.0366103i	−0.855263	−	0.518193i	$-0.826605\pi$
$593$	0.514719	−	0.891519i	0.0211370	−	0.0366103i	0.876400	+	0.481583i	$0.159938\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	4.37868	−	7.58410i	0.179207	−	0.310396i
$598$		0			0
$599$	11.8492	+	20.5235i	0.484147	+	0.838567i	0.999834	−	0.0182098i	$-0.00579669\pi$
$599$	11.8492	+	20.5235i	0.484147	+	0.838567i	−0.515687	+	0.856777i	$0.672463\pi$
$600$		0			0
$601$	−9.48528			−0.386913			−0.193456	−	0.981109i	$-0.561970\pi$
$601$	−9.48528			−0.386913			−0.193456	+	0.981109i	$0.561970\pi$
$602$		0			0
$603$	11.7279			0.477598
$604$		0			0
$605$		0			0
$606$		0			0
$607$	16.5919	−	28.7380i	0.673444	−	1.16644i	−0.303477	−	0.952839i	$-0.598148\pi$
$607$	16.5919	−	28.7380i	0.673444	−	1.16644i	0.976921	−	0.213600i	$-0.0685190\pi$
$608$		0			0
$609$	13.7574	+	17.7408i	0.557476	+	0.718892i
$610$		0			0
$611$	−25.6066	+	44.3519i	−1.03593	+	1.79429i
$612$		0			0
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.4558			0.541712			0.270856	−	0.962620i	$-0.412693\pi$
$617$	13.4558			0.541712			0.270856	+	0.962620i	$0.412693\pi$
$618$		0			0
$619$	0.242641	+	0.420266i	0.00975255	+	0.0168919i	0.870860	−	0.491530i	$-0.163562\pi$
$619$	0.242641	+	0.420266i	0.00975255	+	0.0168919i	−0.861108	+	0.508422i	$0.830229\pi$
$620$		0			0
$621$	−3.00000	+	5.19615i	−0.120386	+	0.208514i
$622$		0			0
$623$	7.75736	−	19.0016i	0.310792	−	0.761282i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	11.1213	+	19.2627i	0.444143	+	0.769278i
$628$		0			0
$629$	21.2132			0.845826
$630$		0			0
$631$	26.2132			1.04353			0.521766	−	0.853089i	$-0.325274\pi$
$631$	26.2132			1.04353			0.521766	+	0.853089i	$0.325274\pi$
$632$		0			0
$633$	−10.6213	−	18.3967i	−0.422160	−	0.731202i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	33.7132	−	9.40319i	1.33577	−	0.372568i
$638$		0			0
$639$	4.24264	−	7.34847i	0.167836	−	0.290701i
$640$		0			0
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	0.525584	−	0.850741i	$-0.323847\pi$
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	−0.999556	+	0.0297987i	$0.990513\pi$
$642$		0			0
$643$	−1.72792			−0.0681426			−0.0340713	−	0.999419i	$-0.510847\pi$
$643$	−1.72792			−0.0681426			−0.0340713	+	0.999419i	$0.510847\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	15.8787	+	27.5027i	0.624255	+	1.08124i	0.988684	+	0.150011i	$0.0479308\pi$
$647$	15.8787	+	27.5027i	0.624255	+	1.08124i	−0.364429	+	0.931231i	$0.618736\pi$
$648$		0			0
$649$	−21.7279	+	37.6339i	−0.852896	+	1.47726i
$650$		0			0
$651$	−4.00000	+	9.79796i	−0.156772	+	0.384012i
$652$		0			0
$653$	6.87868	−	11.9142i	0.269184	−	0.466240i	−0.699468	−	0.714664i	$-0.746580\pi$
$653$	6.87868	−	11.9142i	0.269184	−	0.466240i	0.968651	+	0.248425i	$0.0799128\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−3.48528			−0.135974
$658$		0			0
$659$	48.7279			1.89817			0.949085	−	0.315020i	$-0.102011\pi$
$659$	48.7279			1.89817			0.949085	+	0.315020i	$0.102011\pi$
$660$		0			0
$661$	−16.9853	−	29.4194i	−0.660651	−	1.14428i	−0.980445	−	0.196794i	$-0.936947\pi$
$661$	−16.9853	−	29.4194i	−0.660651	−	1.14428i	0.319794	−	0.947487i	$-0.396386\pi$
$662$		0			0
$663$	−10.6066	+	18.3712i	−0.411926	+	0.713477i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−25.4558	+	44.0908i	−0.985654	+	1.70720i
$668$		0			0
$669$	−0.378680	−	0.655892i	−0.0146406	−	0.0253583i
$670$		0			0
$671$	−4.24264			−0.163785
$672$		0			0
$673$	−4.51472			−0.174030			−0.0870148	−	0.996207i	$-0.527733\pi$
$673$	−4.51472			−0.174030			−0.0870148	+	0.996207i	$0.527733\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	15.7279	−	27.2416i	0.604473	−	1.04698i	−0.387661	−	0.921802i	$-0.626717\pi$
$677$	15.7279	−	27.2416i	0.604473	−	1.04698i	0.992135	−	0.125176i	$-0.0399497\pi$
$678$		0			0
$679$	47.1066	−	6.44639i	1.80779	−	0.247390i
$680$		0			0
$681$	10.2426	−	17.7408i	0.392499	−	0.679828i
$682$		0			0
$683$	−0.363961	−	0.630399i	−0.0139266	−	0.0241215i	0.858978	−	0.512012i	$-0.171100\pi$
$683$	−0.363961	−	0.630399i	−0.0139266	−	0.0241215i	−0.872905	+	0.487891i	$0.837766\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	27.9706			1.06714
$688$		0			0
$689$	−10.6066	−	18.3712i	−0.404079	−	0.699886i
$690$		0			0
$691$	−14.3492	+	24.8536i	−0.545871	+	0.945476i	0.452681	+	0.891673i	$0.350468\pi$
$691$	−14.3492	+	24.8536i	−0.545871	+	0.945476i	−0.998552	+	0.0538034i	$0.982866\pi$
$692$		0			0
$693$	−11.1213	+	1.52192i	−0.422464	+	0.0578129i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	21.7279	+	37.6339i	0.823004	+	1.42548i
$698$		0			0
$699$	−1.75736			−0.0664694
$700$		0			0
$701$	−11.2721			−0.425741			−0.212870	−	0.977080i	$-0.568281\pi$
$701$	−11.2721			−0.425741			−0.212870	+	0.977080i	$0.568281\pi$
$702$		0			0
$703$	13.1066	+	22.7013i	0.494325	+	0.856196i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	10.9081	+	14.0665i	0.410242	+	0.529027i
$708$		0			0
$709$	−3.74264	+	6.48244i	−0.140558	+	0.243453i	−0.927707	−	0.373310i	$-0.878223\pi$
$709$	−3.74264	+	6.48244i	−0.140558	+	0.243453i	0.787149	+	0.616763i	$0.211556\pi$
$710$		0			0
$711$	−4.62132	−	8.00436i	−0.173313	−	0.300187i
$712$		0			0
$713$	−24.0000			−0.898807
$714$		0			0
$715$		0			0
$716$		0			0
$717$	2.48528	+	4.30463i	0.0928145	+	0.160759i
$718$		0			0
$719$	−25.0919	+	43.4604i	−0.935769	+	1.62080i	−0.162513	+	0.986706i	$0.551960\pi$
$719$	−25.0919	+	43.4604i	−0.935769	+	1.62080i	−0.773256	+	0.634094i	$0.781373\pi$
$720$		0			0
$721$	0.757359	−	1.85514i	0.0282055	−	0.0690892i
$722$		0			0
$723$	2.98528	−	5.17066i	0.111024	−	0.192299i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−38.7574			−1.43743			−0.718715	−	0.695304i	$-0.755270\pi$
$727$	−38.7574			−1.43743			−0.718715	+	0.695304i	$0.755270\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	26.4853	+	45.8739i	0.979594	+	1.69671i
$732$		0			0
$733$	−12.7426	+	22.0709i	−0.470660	+	0.815207i	−0.999437	−	0.0335536i	$-0.989318\pi$
$733$	−12.7426	+	22.0709i	−0.470660	+	0.815207i	0.528777	+	0.848761i	$0.322651\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−24.8787	+	43.0911i	−0.916418	+	1.58728i
$738$		0			0
$739$	−25.8345	−	44.7467i	−0.950338	−	1.64603i	−0.744692	−	0.667408i	$-0.767404\pi$
$739$	−25.8345	−	44.7467i	−0.950338	−	1.64603i	−0.205646	−	0.978626i	$-0.565929\pi$
$740$		0			0
$741$	−26.2132			−0.962966
$742$		0			0
$743$	10.9706			0.402471			0.201235	−	0.979543i	$-0.435504\pi$
$743$	10.9706			0.402471			0.201235	+	0.979543i	$0.435504\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.878680	+	1.52192i	−0.0321492	+	0.0556841i
$748$		0			0
$749$	6.72792	−	16.4800i	0.245833	−	0.602165i
$750$		0			0
$751$	−8.86396	+	15.3528i	−0.323451	+	0.560233i	−0.981198	−	0.193006i	$-0.938176\pi$
$751$	−8.86396	+	15.3528i	−0.323451	+	0.560233i	0.657747	+	0.753239i	$0.271510\pi$
$752$		0			0
$753$	8.12132	+	14.0665i	0.295957	+	0.512613i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−14.4558			−0.525407			−0.262703	−	0.964877i	$-0.584614\pi$
$757$	−14.4558			−0.525407			−0.262703	+	0.964877i	$0.584614\pi$
$758$		0			0
$759$	−12.7279	−	22.0454i	−0.461994	−	0.800198i
$760$		0			0
$761$	−20.1213	+	34.8511i	−0.729397	+	1.26335i	0.227741	+	0.973722i	$0.426866\pi$
$761$	−20.1213	+	34.8511i	−0.729397	+	1.26335i	−0.957138	+	0.289631i	$0.906467\pi$
$762$		0			0
$763$	4.07716	+	5.25770i	0.147603	+	0.190341i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−25.6066	−	44.3519i	−0.924601	−	1.60146i
$768$		0			0
$769$	−31.5147			−1.13645			−0.568225	−	0.822873i	$-0.692370\pi$
$769$	−31.5147			−1.13645			−0.568225	+	0.822873i	$0.692370\pi$
$770$		0			0
$771$	−22.2426			−0.801049
$772$		0			0
$773$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$773$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−13.1066	+	1.79360i	−0.470197	+	0.0643449i
$778$		0			0
$779$	−26.8492	+	46.5043i	−0.961974	+	1.66619i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$		0			0
$783$	8.48528			0.303239
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−8.86396	−	15.3528i	−0.315966	−	0.547269i	0.663676	−	0.748020i	$-0.268995\pi$
$787$	−8.86396	−	15.3528i	−0.315966	−	0.547269i	−0.979642	+	0.200751i	$0.935662\pi$
$788$		0			0
$789$	−14.4853	+	25.0892i	−0.515690	+	0.893201i
$790$		0			0
$791$	15.7279	−	2.15232i	0.559221	−	0.0765276i
$792$		0			0
$793$	2.50000	−	4.33013i	0.0887776	−	0.153767i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−48.4264			−1.71535			−0.857676	−	0.514191i	$-0.828092\pi$
$797$	−48.4264			−1.71535			−0.857676	+	0.514191i	$0.828092\pi$
$798$		0			0
$799$	43.4558			1.53736
$800$		0			0
$801$	−3.87868	−	6.71807i	−0.137046	−	0.237371i
$802$		0			0
$803$	7.39340	−	12.8057i	0.260907	−	0.451905i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	9.36396	−	16.2189i	0.329627	−	0.570931i
$808$		0			0
$809$	−27.7279	−	48.0262i	−0.974862	−	1.68851i	−0.680390	−	0.732850i	$-0.738190\pi$
$809$	−27.7279	−	48.0262i	−0.974862	−	1.68851i	−0.294472	−	0.955660i	$-0.595144\pi$
$810$		0			0
$811$	12.7574			0.447971			0.223986	−	0.974592i	$-0.428093\pi$
$811$	12.7574			0.447971			0.223986	+	0.974592i	$0.428093\pi$
$812$		0			0
$813$	2.00000			0.0701431
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−32.7279	+	56.6864i	−1.14501	+	1.98321i
$818$		0			0
$819$	5.00000	−	12.2474i	0.174714	−	0.427960i
$820$		0			0
$821$	5.12132	−	8.87039i	0.178735	−	0.309579i	−0.762712	−	0.646738i	$-0.776133\pi$
$821$	5.12132	−	8.87039i	0.178735	−	0.309579i	0.941448	+	0.337159i	$0.109466\pi$
$822$		0			0
$823$	−14.3492	−	24.8536i	−0.500183	−	0.866343i	−1.00000		0.000211493i	$-0.999933\pi$
$823$	−14.3492	−	24.8536i	−0.500183	−	0.866343i	0.499817	−	0.866131i	$-0.333401\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−45.9411			−1.59753			−0.798765	−	0.601644i	$-0.794513\pi$
$827$	−45.9411			−1.59753			−0.798765	+	0.601644i	$0.794513\pi$
$828$		0			0
$829$	14.2574	+	24.6945i	0.495179	+	0.857674i	0.999985	−	0.00555840i	$-0.00176930\pi$
$829$	14.2574	+	24.6945i	0.495179	+	0.857674i	−0.504806	+	0.863233i	$0.668436\pi$
$830$		0			0
$831$	−7.25736	+	12.5701i	−0.251755	+	0.436052i
$832$		0			0
$833$	−21.2132	−	20.7846i	−0.734994	−	0.720144i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.00000	+	3.46410i	0.0691301	+	0.119737i
$838$		0			0
$839$	13.0294			0.449826			0.224913	−	0.974379i	$-0.427790\pi$
$839$	13.0294			0.449826			0.224913	+	0.974379i	$0.427790\pi$
$840$		0			0
$841$	43.0000			1.48276
$842$		0			0
$843$	14.1213	+	24.4588i	0.486364	+	0.842407i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	7.00000	−	17.1464i	0.240523	−	0.589158i
$848$		0			0
$849$	1.37868	−	2.38794i	0.0473162	−	0.0819540i
$850$		0			0
$851$	−15.0000	−	25.9808i	−0.514193	−	0.890609i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.48528	−	9.50079i	−0.187374	−	0.324541i	0.757000	−	0.653415i	$-0.226664\pi$
$857$	−5.48528	−	9.50079i	−0.187374	−	0.324541i	−0.944374	+	0.328874i	$0.893331\pi$
$858$		0			0
$859$	27.4558	−	47.5549i	0.936781	−	1.62255i	0.165355	−	0.986234i	$-0.447123\pi$
$859$	27.4558	−	47.5549i	0.936781	−	1.62255i	0.771426	−	0.636319i	$-0.219544\pi$
$860$		0			0
$861$	−16.6066	−	21.4150i	−0.565951	−	0.729822i
$862$		0			0
$863$	3.36396	−	5.82655i	0.114511	−	0.198338i	−0.803073	−	0.595880i	$-0.796803\pi$
$863$	3.36396	−	5.82655i	0.114511	−	0.198338i	0.917584	+	0.397542i	$0.130137\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	1.00000			0.0339618
$868$		0			0
$869$	39.2132			1.33022
$870$		0			0
$871$	−29.3198	−	50.7834i	−0.993464	−	1.72073i
$872$		0			0
$873$	8.98528	−	15.5630i	0.304106	−	0.526727i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.98528	+	3.43861i	−0.0670382	+	0.116114i	−0.897596	−	0.440818i	$-0.854688\pi$
$877$	−1.98528	+	3.43861i	−0.0670382	+	0.116114i	0.830558	+	0.556932i	$0.188022\pi$
$878$		0			0
$879$	−1.75736	−	3.04384i	−0.0592743	−	0.102666i
$880$		0			0
$881$	15.5147			0.522704			0.261352	−	0.965244i	$-0.415832\pi$
$881$	15.5147			0.522704			0.261352	+	0.965244i	$0.415832\pi$
$882$		0			0
$883$	−12.6985			−0.427338			−0.213669	−	0.976906i	$-0.568541\pi$
$883$	−12.6985			−0.427338			−0.213669	+	0.976906i	$0.568541\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.2426	−	33.3292i	0.646105	−	1.11909i	−0.337941	−	0.941167i	$-0.609730\pi$
$887$	19.2426	−	33.3292i	0.646105	−	1.11909i	0.984045	−	0.177919i	$-0.0569364\pi$
$888$		0			0
$889$	−1.98528	+	0.271680i	−0.0665842	+	0.00911184i
$890$		0			0
$891$	−2.12132	+	3.67423i	−0.0710669	+	0.123091i
$892$		0			0
$893$	26.8492	+	46.5043i	0.898476	+	1.55621i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	30.0000			1.00167
$898$		0			0
$899$	16.9706	+	29.3939i	0.566000	+	0.980341i
$900$		0			0
$901$	−9.00000	+	15.5885i	−0.299833	+	0.519327i
$902$		0			0
$903$	−20.2426	−	26.1039i	−0.673633	−	0.868682i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	17.1066	+	29.6295i	0.568015	+	0.983832i	0.996762	+	0.0804068i	$0.0256219\pi$
$907$	17.1066	+	29.6295i	0.568015	+	0.983832i	−0.428747	+	0.903425i	$0.641045\pi$
$908$		0			0
$909$	6.72792			0.223151
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$		0			0
$913$	−3.72792	−	6.45695i	−0.123376	−	0.213694i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.00000	−	14.6969i	0.198137	−	0.485336i
$918$		0			0
$919$	−7.51472	+	13.0159i	−0.247888	+	0.429354i	−0.962940	−	0.269717i	$-0.913070\pi$
$919$	−7.51472	+	13.0159i	−0.247888	+	0.429354i	0.715052	+	0.699071i	$0.246403\pi$
$920$		0			0
$921$	−2.24264	−	3.88437i	−0.0738975	−	0.127994i
$922$		0			0
$923$	−42.4264			−1.39648
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.378680	−	0.655892i	−0.0124375	−	0.0215423i
$928$		0			0
$929$	22.0919	−	38.2643i	0.724811	−	1.25541i	−0.234241	−	0.972179i	$-0.575260\pi$
$929$	22.0919	−	38.2643i	0.724811	−	1.25541i	0.959052	−	0.283231i	$-0.0914063\pi$
$930$		0			0
$931$	9.13604	−	35.5431i	0.299422	−	1.16488i
$932$		0			0
$933$	−7.24264	+	12.5446i	−0.237113	+	0.410692i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−29.4558			−0.962280			−0.481140	−	0.876644i	$-0.659777\pi$
$937$	−29.4558			−0.962280			−0.481140	+	0.876644i	$0.659777\pi$
$938$		0			0
$939$	0.970563			0.0316731
$940$		0			0
$941$	22.4558	+	38.8947i	0.732040	+	1.26793i	0.956010	+	0.293334i	$0.0947647\pi$
$941$	22.4558	+	38.8947i	0.732040	+	1.26793i	−0.223970	+	0.974596i	$0.571902\pi$
$942$		0			0
$943$	30.7279	−	53.2223i	1.00064	−	1.73316i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.72792	+	16.8493i	−0.316115	+	0.547527i	−0.979674	−	0.200597i	$-0.935712\pi$
$947$	−9.72792	+	16.8493i	−0.316115	+	0.547527i	0.663559	+	0.748124i	$0.269045\pi$
$948$		0			0
$949$	8.71320	+	15.0917i	0.282843	+	0.489898i
$950$		0			0
$951$	6.00000			0.194563
$952$		0			0
$953$	1.75736			0.0569265			0.0284632	−	0.999595i	$-0.490939\pi$
$953$	1.75736			0.0569265			0.0284632	+	0.999595i	$0.490939\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−18.0000	+	31.1769i	−0.581857	+	1.00781i
$958$		0			0
$959$	−4.02944	−	5.19615i	−0.130117	−	0.167793i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	−3.36396	−	5.82655i	−0.108402	−	0.187758i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.757359			0.0243550			0.0121775	−	0.999926i	$-0.496124\pi$
$967$	0.757359			0.0243550			0.0121775	+	0.999926i	$0.496124\pi$
$968$		0			0
$969$	11.1213	+	19.2627i	0.357268	+	0.618807i
$970$		0			0
$971$	11.6360	−	20.1542i	0.373418	−	0.646779i	−0.616671	−	0.787221i	$-0.711519\pi$
$971$	11.6360	−	20.1542i	0.373418	−	0.646779i	0.990089	+	0.140442i	$0.0448523\pi$
$972$		0			0
$973$	−30.7426	+	4.20703i	−0.985564	+	0.134871i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−29.8492	−	51.7004i	−0.954962	−	1.65404i	−0.734455	−	0.678657i	$-0.762562\pi$
$977$	−29.8492	−	51.7004i	−0.954962	−	1.65404i	−0.220506	−	0.975386i	$-0.570771\pi$
$978$		0			0
$979$	32.9117			1.05186
$980$		0			0
$981$	2.51472			0.0802888
$982$		0			0
$983$	17.1213	+	29.6550i	0.546085	+	0.945848i	0.998538	+	0.0540590i	$0.0172159\pi$
$983$	17.1213	+	29.6550i	0.546085	+	0.945848i	−0.452452	+	0.891789i	$0.649451\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−26.8492	+	3.67423i	−0.854621	+	0.116952i
$988$		0			0
$989$	37.4558	−	64.8754i	1.19103	−	2.06292i
$990$		0			0
$991$	−9.48528	−	16.4290i	−0.301310	−	0.521884i	0.675123	−	0.737705i	$-0.264091\pi$
$991$	−9.48528	−	16.4290i	−0.301310	−	0.521884i	−0.976433	+	0.215821i	$0.930757\pi$
$992$		0			0
$993$	−17.2426			−0.547179
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−15.2279	−	26.3755i	−0.482273	−	0.835322i	0.517520	−	0.855671i	$-0.326855\pi$
$997$	−15.2279	−	26.3755i	−0.482273	−	0.835322i	−0.999793	+	0.0203497i	$0.993522\pi$
$998$		0			0
$999$	−2.50000	+	4.33013i	−0.0790965	+	0.136999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.q.f.1801.1	yes	4
5.2	odd	4		2100.2.bc.g.1549.1		8
5.3	odd	4		2100.2.bc.g.1549.4		8
5.4	even	2		2100.2.q.j.1801.2	yes	4
7.4	even	3	inner	2100.2.q.f.1201.1	✓	4
35.4	even	6		2100.2.q.j.1201.2	yes	4
35.18	odd	12		2100.2.bc.g.949.1		8
35.32	odd	12		2100.2.bc.g.949.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.q.f.1201.1	✓	4	7.4	even	3	inner
2100.2.q.f.1801.1	yes	4	1.1	even	1	trivial
2100.2.q.j.1201.2	yes	4	35.4	even	6
2100.2.q.j.1801.2	yes	4	5.4	even	2
2100.2.bc.g.949.1		8	35.18	odd	12
2100.2.bc.g.949.4		8	35.32	odd	12
2100.2.bc.g.1549.1		8	5.2	odd	4
2100.2.bc.g.1549.4		8	5.3	odd	4

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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-2.62132 + 0.358719i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-2.62132 + 0.358719i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-2.12132 - 3.67423i) q^{11} +5.00000 q^{13} +(-2.12132 - 3.67423i) q^{17} +(2.62132 - 4.54026i) q^{19} +(1.62132 + 2.09077i) q^{21} +(-3.00000 + 5.19615i) q^{23} +1.00000 q^{27} +8.48528 q^{29} +(2.00000 + 3.46410i) q^{31} +(-2.12132 + 3.67423i) q^{33} +(-2.50000 + 4.33013i) q^{37} +(-2.50000 - 4.33013i) q^{39} -10.2426 q^{41} -12.4853 q^{43} +(-5.12132 + 8.87039i) q^{47} +(6.74264 - 1.88064i) q^{49} +(-2.12132 + 3.67423i) q^{51} +(-2.12132 - 3.67423i) q^{53} -5.24264 q^{57} +(-5.12132 - 8.87039i) q^{59} +(0.500000 - 0.866025i) q^{61} +(1.00000 - 2.44949i) q^{63} +(-5.86396 - 10.1567i) q^{67} +6.00000 q^{69} -8.48528 q^{71} +(1.74264 + 3.01834i) q^{73} +(6.87868 + 8.87039i) q^{77} +(-4.62132 + 8.00436i) q^{79} +(-0.500000 - 0.866025i) q^{81} +1.75736 q^{83} +(-4.24264 - 7.34847i) q^{87} +(-3.87868 + 6.71807i) q^{89} +(-13.1066 + 1.79360i) q^{91} +(2.00000 - 3.46410i) q^{93} -17.9706 q^{97} +4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} - 2 q^{7} - 2 q^{9} + 20 q^{13} + 2 q^{19} - 2 q^{21} - 12 q^{23} + 4 q^{27} + 8 q^{31} - 10 q^{37} - 10 q^{39} - 24 q^{41} - 16 q^{43} - 12 q^{47} + 10 q^{49} - 4 q^{57} - 12 q^{59} + 2 q^{61} + 4 q^{63} + 2 q^{67} + 24 q^{69} - 10 q^{73} + 36 q^{77} - 10 q^{79} - 2 q^{81} + 24 q^{83} - 24 q^{89} - 10 q^{91} + 8 q^{93} - 4 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^7 - 2 * q^9 + 20 * q^13 + 2 * q^19 - 2 * q^21 - 12 * q^23 + 4 * q^27 + 8 * q^31 - 10 * q^37 - 10 * q^39 - 24 * q^41 - 16 * q^43 - 12 * q^47 + 10 * q^49 - 4 * q^57 - 12 * q^59 + 2 * q^61 + 4 * q^63 + 2 * q^67 + 24 * q^69 - 10 * q^73 + 36 * q^77 - 10 * q^79 - 2 * q^81 + 24 * q^83 - 24 * q^89 - 10 * q^91 + 8 * q^93 - 4 * q^97

Introduction

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