LMFDB - Embedded newform 2100.2.q.f.1801.2

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			1801.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	2100.1801
Dual form			2100.2.q.f.1201.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(1.62132 - 2.09077i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(1.62132 - 2.09077i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.12132 + 3.67423i) q^{11} +5.00000 q^{13} +(2.12132 + 3.67423i) q^{17} +(-1.62132 + 2.80821i) q^{19} +(-2.62132 - 0.358719i) q^{21} +(-3.00000 + 5.19615i) q^{23} +1.00000 q^{27} -8.48528 q^{29} +(2.00000 + 3.46410i) q^{31} +(2.12132 - 3.67423i) q^{33} +(-2.50000 + 4.33013i) q^{37} +(-2.50000 - 4.33013i) q^{39} -1.75736 q^{41} +4.48528 q^{43} +(-0.878680 + 1.52192i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(2.12132 - 3.67423i) q^{51} +(2.12132 + 3.67423i) q^{53} +3.24264 q^{57} +(-0.878680 - 1.52192i) q^{59} +(0.500000 - 0.866025i) q^{61} +(1.00000 + 2.44949i) q^{63} +(6.86396 + 11.8887i) q^{67} +6.00000 q^{69} +8.48528 q^{71} +(-6.74264 - 11.6786i) q^{73} +(11.1213 + 1.52192i) q^{77} +(-0.378680 + 0.655892i) q^{79} +(-0.500000 - 0.866025i) q^{81} +10.2426 q^{83} +(4.24264 + 7.34847i) q^{87} +(-8.12132 + 14.0665i) q^{89} +(8.10660 - 10.4539i) q^{91} +(2.00000 - 3.46410i) q^{93} +15.9706 q^{97} -4.24264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$8$		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	$0.0542342\pi$
$11$	2.12132	+	3.67423i	0.639602	+	1.10782i	−0.345918	+	0.938265i	$0.612432\pi$
$12$		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	$0.00535420\pi$
$17$	2.12132	+	3.67423i	0.514496	+	0.891133i	−0.485363	+	0.874313i	$0.661312\pi$
$18$		0			0
$19$	−1.62132	+	2.80821i	−0.371956	+	0.644247i	−0.989866	−	0.142001i	$-0.954646\pi$
$19$	−1.62132	+	2.80821i	−0.371956	+	0.644247i	0.617910	+	0.786249i	$0.287980\pi$
$20$		0			0
$21$	−2.62132	−	0.358719i	−0.572019	−	0.0782790i
$22$		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	$-0.788800\pi$
$29$	−8.48528			−1.57568			−0.787839	+	0.615882i	$0.788800\pi$
$30$		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
$41$	−1.75736			−0.274453			−0.137227	−	0.990540i	$-0.543819\pi$
$41$	−1.75736			−0.274453			−0.137227	+	0.990540i	$0.543819\pi$
$42$		0			0
$43$	4.48528			0.683999			0.341999	−	0.939700i	$-0.388896\pi$
$43$	4.48528			0.683999			0.341999	+	0.939700i	$0.388896\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.878680	+	1.52192i	−0.128169	+	0.221995i	−0.922967	−	0.384879i	$-0.874243\pi$
$47$	−0.878680	+	1.52192i	−0.128169	+	0.221995i	0.794798	+	0.606873i	$0.207577\pi$
$48$		0			0
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$		0			0
$51$	2.12132	−	3.67423i	0.297044	−	0.514496i
$52$		0			0
$53$	2.12132	+	3.67423i	0.291386	+	0.504695i	0.974138	−	0.225955i	$-0.0725503\pi$
$53$	2.12132	+	3.67423i	0.291386	+	0.504695i	−0.682752	+	0.730650i	$0.739217\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.24264			0.429498
$58$		0			0
$59$	−0.878680	−	1.52192i	−0.114394	−	0.198137i	0.803143	−	0.595786i	$-0.203159\pi$
$59$	−0.878680	−	1.52192i	−0.114394	−	0.198137i	−0.917537	+	0.397649i	$0.869826\pi$
$60$		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
$67$	6.86396	+	11.8887i	0.838566	+	1.45244i	0.891093	+	0.453820i	$0.149939\pi$
$67$	6.86396	+	11.8887i	0.838566	+	1.45244i	−0.0525271	+	0.998619i	$0.516728\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		0			0
$71$	8.48528			1.00702			0.503509	−	0.863990i	$-0.332042\pi$
$71$	8.48528			1.00702			0.503509	+	0.863990i	$0.332042\pi$
$72$		0			0
$73$	−6.74264	−	11.6786i	−0.789166	−	1.36688i	−0.926478	−	0.376348i	$-0.877180\pi$
$73$	−6.74264	−	11.6786i	−0.789166	−	1.36688i	0.137312	−	0.990528i	$-0.456154\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	11.1213	+	1.52192i	1.26739	+	0.173439i
$78$		0			0
$79$	−0.378680	+	0.655892i	−0.0426048	+	0.0737937i	−0.886541	−	0.462649i	$-0.846899\pi$
$79$	−0.378680	+	0.655892i	−0.0426048	+	0.0737937i	0.843937	+	0.536443i	$0.180232\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	10.2426			1.12428			0.562138	−	0.827043i	$-0.309979\pi$
$83$	10.2426			1.12428			0.562138	+	0.827043i	$0.309979\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.24264	+	7.34847i	0.454859	+	0.787839i
$88$		0			0
$89$	−8.12132	+	14.0665i	−0.860858	+	1.49105i	0.0102435	+	0.999948i	$0.496739\pi$
$89$	−8.12132	+	14.0665i	−0.860858	+	1.49105i	−0.871102	+	0.491103i	$0.836594\pi$
$90$		0			0
$91$	8.10660	−	10.4539i	0.849803	−	1.09586i
$92$		0			0
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	15.9706			1.62156			0.810782	−	0.585348i	$-0.199042\pi$
$97$	15.9706			1.62156			0.810782	+	0.585348i	$0.199042\pi$
$98$		0			0
$99$	−4.24264			−0.426401
$100$		0			0
$101$	9.36396	+	16.2189i	0.931749	+	1.61384i	0.780331	+	0.625367i	$0.215051\pi$
$101$	9.36396	+	16.2189i	0.931749	+	1.61384i	0.151418	+	0.988470i	$0.451616\pi$
$102$		0			0
$103$	−4.62132	+	8.00436i	−0.455352	+	0.788693i	−0.998708	−	0.0508091i	$-0.983820\pi$
$103$	−4.62132	+	8.00436i	−0.455352	+	0.788693i	0.543356	+	0.839502i	$0.317153\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.36396	−	16.2189i	0.905248	−	1.56794i	0.0846647	−	0.996409i	$-0.473018\pi$
$107$	9.36396	−	16.2189i	0.905248	−	1.56794i	0.820584	−	0.571527i	$-0.193649\pi$
$108$		0			0
$109$	−9.74264	−	16.8747i	−0.933176	−	1.61631i	−0.777855	−	0.628444i	$-0.783692\pi$
$109$	−9.74264	−	16.8747i	−0.933176	−	1.61631i	−0.155321	−	0.987864i	$-0.549641\pi$
$110$		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
$119$	11.1213	+	1.52192i	1.01949	+	0.139514i
$120$		0			0
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$		0			0
$123$	0.878680	+	1.52192i	0.0792279	+	0.137227i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	9.24264			0.820152			0.410076	−	0.912051i	$-0.365502\pi$
$127$	9.24264			0.820152			0.410076	+	0.912051i	$0.365502\pi$
$128$		0			0
$129$	−2.24264	−	3.88437i	−0.197454	−	0.341999i
$130$		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
$133$	3.24264	+	7.94282i	0.281173	+	0.688729i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.24264	−	12.5446i	−0.618781	−	1.07176i	−0.989709	−	0.143098i	$-0.954294\pi$
$137$	−7.24264	−	12.5446i	−0.618781	−	1.07176i	0.370928	−	0.928662i	$-0.379040\pi$
$138$		0			0
$139$	−13.7279			−1.16439			−0.582194	−	0.813050i	$-0.697805\pi$
$139$	−13.7279			−1.16439			−0.582194	+	0.813050i	$0.697805\pi$
$140$		0			0
$141$	1.75736			0.147996
$142$		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
$149$	6.87868	−	11.9142i	0.563523	−	0.976051i	−0.433662	−	0.901076i	$-0.642779\pi$
$149$	6.87868	−	11.9142i	0.563523	−	0.976051i	0.997185	−	0.0749755i	$-0.0238879\pi$
$150$		0			0
$151$	−5.86396	−	10.1567i	−0.477202	−	0.826539i	0.522456	−	0.852666i	$-0.325016\pi$
$151$	−5.86396	−	10.1567i	−0.477202	−	0.826539i	−0.999659	+	0.0261273i	$0.991682\pi$
$152$		0			0
$153$	−4.24264			−0.342997
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.742641	−	1.28629i	−0.0592692	−	0.102657i	0.834868	−	0.550450i	$-0.185544\pi$
$157$	−0.742641	−	1.28629i	−0.0592692	−	0.102657i	−0.894138	+	0.447792i	$0.852210\pi$
$158$		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
$163$	4.37868	−	7.58410i	0.342965	−	0.594032i	−0.642017	−	0.766690i	$-0.721902\pi$
$163$	4.37868	−	7.58410i	0.342965	−	0.594032i	0.984982	+	0.172658i	$0.0552356\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.75736			−0.135989			−0.0679943	−	0.997686i	$-0.521660\pi$
$167$	−1.75736			−0.135989			−0.0679943	+	0.997686i	$0.521660\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	−1.62132	−	2.80821i	−0.123985	−	0.214749i
$172$		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
$177$	−0.878680	+	1.52192i	−0.0660456	+	0.114394i
$178$		0			0
$179$	−1.75736	−	3.04384i	−0.131351	−	0.227507i	0.792846	−	0.609421i	$-0.208598\pi$
$179$	−1.75736	−	3.04384i	−0.131351	−	0.227507i	−0.924198	+	0.381914i	$0.875265\pi$
$180$		0			0
$181$	4.48528			0.333388			0.166694	−	0.986009i	$-0.446691\pi$
$181$	4.48528			0.333388			0.166694	+	0.986009i	$0.446691\pi$
$182$		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
$189$	1.62132	−	2.09077i	0.117934	−	0.152081i
$190$		0			0
$191$	−8.12132	+	14.0665i	−0.587638	+	1.01782i	0.406903	+	0.913471i	$0.366609\pi$
$191$	−8.12132	+	14.0665i	−0.587638	+	1.01782i	−0.994541	+	0.104348i	$0.966725\pi$
$192$		0			0
$193$	−2.24264	−	3.88437i	−0.161429	−	0.279603i	0.773953	−	0.633244i	$-0.218277\pi$
$193$	−2.24264	−	3.88437i	−0.161429	−	0.279603i	−0.935381	+	0.353641i	$0.884944\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.48528			0.604551			0.302276	−	0.953221i	$-0.402254\pi$
$197$	8.48528			0.604551			0.302276	+	0.953221i	$0.402254\pi$
$198$		0			0
$199$	8.62132	+	14.9326i	0.611149	+	1.05854i	0.991047	+	0.133513i	$0.0426258\pi$
$199$	8.62132	+	14.9326i	0.611149	+	1.05854i	−0.379898	+	0.925028i	$0.624041\pi$
$200$		0			0
$201$	6.86396	−	11.8887i	0.484146	−	0.838566i
$202$		0			0
$203$	−13.7574	+	17.7408i	−0.965577	+	1.24516i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.00000	−	5.19615i	−0.208514	−	0.361158i
$208$		0			0
$209$	−13.7574			−0.951616
$210$		0			0
$211$	12.7574			0.878253			0.439126	−	0.898425i	$-0.355288\pi$
$211$	12.7574			0.878253			0.439126	+	0.898425i	$0.355288\pi$
$212$		0			0
$213$	−4.24264	−	7.34847i	−0.290701	−	0.503509i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	10.4853	+	1.43488i	0.711787	+	0.0974059i
$218$		0			0
$219$	−6.74264	+	11.6786i	−0.455625	+	0.789166i
$220$		0			0
$221$	10.6066	+	18.3712i	0.713477	+	1.23578i
$222$		0			0
$223$	9.24264			0.618933			0.309466	−	0.950910i	$-0.399850\pi$
$223$	9.24264			0.618933			0.309466	+	0.950910i	$0.399850\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.75736	+	3.04384i	0.116640	+	0.202026i	0.918434	−	0.395574i	$-0.129454\pi$
$227$	1.75736	+	3.04384i	0.116640	+	0.202026i	−0.801794	+	0.597600i	$0.796121\pi$
$228$		0			0
$229$	2.98528	−	5.17066i	0.197273	−	0.341687i	−0.750370	−	0.661018i	$-0.770125\pi$
$229$	2.98528	−	5.17066i	0.197273	−	0.341687i	0.947643	+	0.319331i	$0.103458\pi$
$230$		0			0
$231$	−4.24264	−	10.3923i	−0.279145	−	0.683763i
$232$		0			0
$233$	5.12132	−	8.87039i	0.335509	−	0.581118i	−0.648074	−	0.761578i	$-0.724425\pi$
$233$	5.12132	−	8.87039i	0.335509	−	0.581118i	0.983582	+	0.180459i	$0.0577584\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.757359			0.0491958
$238$		0			0
$239$	28.9706			1.87395			0.936975	−	0.349397i	$-0.113613\pi$
$239$	28.9706			1.87395			0.936975	+	0.349397i	$0.113613\pi$
$240$		0			0
$241$	−13.9853	−	24.2232i	−0.900871	−	1.56035i	−0.826366	−	0.563134i	$-0.809595\pi$
$241$	−13.9853	−	24.2232i	−0.900871	−	1.56035i	−0.0745056	−	0.997221i	$-0.523738\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−8.10660	+	14.0410i	−0.515811	+	0.893410i
$248$		0			0
$249$	−5.12132	−	8.87039i	−0.324550	−	0.562138i
$250$		0			0
$251$	−7.75736			−0.489640			−0.244820	−	0.969569i	$-0.578729\pi$
$251$	−7.75736			−0.489640			−0.244820	+	0.969569i	$0.578729\pi$
$252$		0			0
$253$	−25.4558			−1.60040
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.87868	−	11.9142i	0.429080	−	0.743189i	−0.567712	−	0.823228i	$-0.692171\pi$
$257$	6.87868	−	11.9142i	0.429080	−	0.743189i	0.996792	+	0.0800388i	$0.0255044\pi$
$258$		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
$263$	2.48528	+	4.30463i	0.153249	+	0.265435i	0.932420	−	0.361376i	$-0.117693\pi$
$263$	2.48528	+	4.30463i	0.153249	+	0.265435i	−0.779171	+	0.626811i	$0.784360\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	16.2426			0.994033
$268$		0			0
$269$	−3.36396	−	5.82655i	−0.205104	−	0.355251i	0.745062	−	0.666996i	$-0.232420\pi$
$269$	−3.36396	−	5.82655i	−0.205104	−	0.355251i	−0.950166	+	0.311745i	$0.899087\pi$
$270$		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
$273$	−13.1066	−	1.79360i	−0.793248	−	0.108553i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−15.7426	−	27.2671i	−0.945884	−	1.63832i	−0.753972	−	0.656906i	$-0.771865\pi$
$277$	−15.7426	−	27.2671i	−0.945884	−	1.63832i	−0.191911	−	0.981412i	$-0.561469\pi$
$278$		0			0
$279$	−4.00000			−0.239474
$280$		0			0
$281$	−19.7574			−1.17863			−0.589313	−	0.807905i	$-0.700601\pi$
$281$	−19.7574			−1.17863			−0.589313	+	0.807905i	$0.700601\pi$
$282$		0			0
$283$	5.62132	+	9.73641i	0.334153	+	0.578770i	0.983322	−	0.181875i	$-0.0582165\pi$
$283$	5.62132	+	9.73641i	0.334153	+	0.578770i	−0.649169	+	0.760644i	$0.724883\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.84924	+	3.67423i	−0.168185	+	0.216883i
$288$		0			0
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$		0			0
$291$	−7.98528	−	13.8309i	−0.468105	−	0.810782i
$292$		0			0
$293$	20.4853			1.19676			0.598381	−	0.801211i	$-0.295811\pi$
$293$	20.4853			1.19676			0.598381	+	0.801211i	$0.295811\pi$
$294$		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
$301$	7.27208	−	9.37769i	0.419156	−	0.540521i
$302$		0			0
$303$	9.36396	−	16.2189i	0.537946	−	0.931749i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−12.4853			−0.712573			−0.356286	−	0.934377i	$-0.615957\pi$
$307$	−12.4853			−0.712573			−0.356286	+	0.934377i	$0.615957\pi$
$308$		0			0
$309$	9.24264			0.525795
$310$		0			0
$311$	1.24264	+	2.15232i	0.0704637	+	0.122047i	0.899105	−	0.437734i	$-0.144219\pi$
$311$	1.24264	+	2.15232i	0.0704637	+	0.122047i	−0.828641	+	0.559781i	$0.810885\pi$
$312$		0			0
$313$	16.4853	−	28.5533i	0.931803	−	1.61393i	0.151566	−	0.988447i	$-0.451569\pi$
$313$	16.4853	−	28.5533i	0.931803	−	1.61393i	0.780238	−	0.625483i	$-0.215098\pi$
$314$		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
$321$	−18.7279			−1.04529
$322$		0			0
$323$	−13.7574			−0.765480
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−9.74264	+	16.8747i	−0.538769	+	0.933176i
$328$		0			0
$329$	1.75736	+	4.30463i	0.0968864	+	0.237322i
$330$		0			0
$331$	4.37868	−	7.58410i	0.240674	−	0.416860i	−0.720232	−	0.693733i	$-0.755965\pi$
$331$	4.37868	−	7.58410i	0.240674	−	0.416860i	0.960906	+	0.276873i	$0.0892982\pi$
$332$		0			0
$333$	−2.50000	−	4.33013i	−0.136999	−	0.237289i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−8.97056			−0.488658			−0.244329	−	0.969692i	$-0.578568\pi$
$337$	−8.97056			−0.488658			−0.244329	+	0.969692i	$0.578568\pi$
$338$		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
$347$	−15.3640	−	26.6112i	−0.824781	−	1.42856i	−0.902087	−	0.431555i	$-0.857965\pi$
$347$	−15.3640	−	26.6112i	−0.824781	−	1.42856i	0.0773062	−	0.997007i	$-0.475368\pi$
$348$		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
$353$	−3.36396	−	5.82655i	−0.179046	−	0.310116i	0.762508	−	0.646978i	$-0.223968\pi$
$353$	−3.36396	−	5.82655i	−0.179046	−	0.310116i	−0.941554	+	0.336862i	$0.890634\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−4.24264	−	10.3923i	−0.224544	−	0.550019i
$358$		0			0
$359$	−15.3640	+	26.6112i	−0.810879	+	1.40448i	0.101371	+	0.994849i	$0.467677\pi$
$359$	−15.3640	+	26.6112i	−0.810879	+	1.40448i	−0.912250	+	0.409635i	$0.865656\pi$
$360$		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
$369$	0.878680	−	1.52192i	0.0457422	−	0.0792279i
$370$		0			0
$371$	11.1213	+	1.52192i	0.577390	+	0.0790140i
$372$		0			0
$373$	7.74264	−	13.4106i	0.400899	−	0.694377i	−0.592936	−	0.805250i	$-0.702031\pi$
$373$	7.74264	−	13.4106i	0.400899	−	0.694377i	0.993835	+	0.110873i	$0.0353646\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−42.4264			−2.18507
$378$		0			0
$379$	11.7279			0.602423			0.301211	−	0.953557i	$-0.402609\pi$
$379$	11.7279			0.602423			0.301211	+	0.953557i	$0.402609\pi$
$380$		0			0
$381$	−4.62132	−	8.00436i	−0.236757	−	0.410076i
$382$		0			0
$383$	−9.72792	+	16.8493i	−0.497074	+	0.860957i	−0.999994	−	0.00337583i	$-0.998925\pi$
$383$	−9.72792	+	16.8493i	−0.497074	+	0.860957i	0.502921	+	0.864333i	$0.332259\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.24264	+	3.88437i	−0.114000	+	0.197454i
$388$		0			0
$389$	−2.63604	−	4.56575i	−0.133652	−	0.231493i	0.791429	−	0.611261i	$-0.209337\pi$
$389$	−2.63604	−	4.56575i	−0.133652	−	0.231493i	−0.925082	+	0.379768i	$0.876004\pi$
$390$		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
$399$	5.25736	−	6.77962i	0.263197	−	0.339405i
$400$		0			0
$401$	−7.60660	+	13.1750i	−0.379856	+	0.657929i	−0.991041	−	0.133558i	$-0.957360\pi$
$401$	−7.60660	+	13.1750i	−0.379856	+	0.657929i	0.611185	+	0.791487i	$0.290693\pi$
$402$		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
$411$	−7.24264	+	12.5446i	−0.357253	+	0.618781i
$412$		0			0
$413$	−4.60660	−	0.630399i	−0.226676	−	0.0310199i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	6.86396	+	11.8887i	0.336130	+	0.582194i
$418$		0			0
$419$	12.7279			0.621800			0.310900	−	0.950443i	$-0.399370\pi$
$419$	12.7279			0.621800			0.310900	+	0.950443i	$0.399370\pi$
$420$		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
$423$	−0.878680	−	1.52192i	−0.0427229	−	0.0739982i
$424$		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
$431$	−13.2426	−	22.9369i	−0.637876	−	1.10483i	−0.985898	−	0.167347i	$-0.946480\pi$
$431$	−13.2426	−	22.9369i	−0.637876	−	1.10483i	0.348023	−	0.937486i	$-0.386853\pi$
$432$		0			0
$433$	−8.97056			−0.431098			−0.215549	−	0.976493i	$-0.569154\pi$
$433$	−8.97056			−0.431098			−0.215549	+	0.976493i	$0.569154\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−9.72792	−	16.8493i	−0.465350	−	0.806009i
$438$		0			0
$439$	−17.8640	+	30.9413i	−0.852600	+	1.47675i	0.0262531	+	0.999655i	$0.491642\pi$
$439$	−17.8640	+	30.9413i	−0.852600	+	1.47675i	−0.878853	+	0.477092i	$0.841691\pi$
$440$		0			0
$441$	6.74264	+	1.88064i	0.321078	+	0.0895542i
$442$		0			0
$443$	−15.7279	+	27.2416i	−0.747256	+	1.29429i	0.201877	+	0.979411i	$0.435296\pi$
$443$	−15.7279	+	27.2416i	−0.747256	+	1.29429i	−0.949133	+	0.314875i	$0.898037\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−13.7574			−0.650701
$448$		0			0
$449$	36.7279			1.73330			0.866649	−	0.498919i	$-0.166269\pi$
$449$	36.7279			1.73330			0.866649	+	0.498919i	$0.166269\pi$
$450$		0			0
$451$	−3.72792	−	6.45695i	−0.175541	−	0.304046i
$452$		0			0
$453$	−5.86396	+	10.1567i	−0.275513	+	0.477202i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.74264	+	6.48244i	−0.175073	+	0.303236i	−0.940187	−	0.340660i	$-0.889350\pi$
$457$	−3.74264	+	6.48244i	−0.175073	+	0.303236i	0.765113	+	0.643896i	$0.222683\pi$
$458$		0			0
$459$	2.12132	+	3.67423i	0.0990148	+	0.171499i
$460$		0			0
$461$	−26.4853			−1.23354			−0.616771	−	0.787142i	$-0.711560\pi$
$461$	−26.4853			−1.23354			−0.616771	+	0.787142i	$0.711560\pi$
$462$		0			0
$463$	−2.75736			−0.128145			−0.0640727	−	0.997945i	$-0.520409\pi$
$463$	−2.75736			−0.128145			−0.0640727	+	0.997945i	$0.520409\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	15.7279	−	27.2416i	0.727801	−	1.26059i	−0.230009	−	0.973188i	$-0.573876\pi$
$467$	15.7279	−	27.2416i	0.727801	−	1.26059i	0.957810	−	0.287401i	$-0.0927911\pi$
$468$		0			0
$469$	35.9853	+	4.92447i	1.66165	+	0.227391i
$470$		0			0
$471$	−0.742641	+	1.28629i	−0.0342191	+	0.0592692i
$472$		0			0
$473$	9.51472	+	16.4800i	0.437487	+	0.757750i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−4.24264			−0.194257
$478$		0			0
$479$	13.6066	+	23.5673i	0.621702	+	1.07682i	0.989169	+	0.146782i	$0.0468916\pi$
$479$	13.6066	+	23.5673i	0.621702	+	1.07682i	−0.367467	+	0.930036i	$0.619775\pi$
$480$		0			0
$481$	−12.5000	+	21.6506i	−0.569951	+	0.987184i
$482$		0			0
$483$	9.72792	−	12.5446i	0.442636	−	0.570800i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−5.75736	−	9.97204i	−0.260891	−	0.451876i	0.705588	−	0.708622i	$-0.250683\pi$
$487$	−5.75736	−	9.97204i	−0.260891	−	0.451876i	−0.966479	+	0.256746i	$0.917350\pi$
$488$		0			0
$489$	−8.75736			−0.396021
$490$		0			0
$491$	21.5147			0.970946			0.485473	−	0.874252i	$-0.338647\pi$
$491$	21.5147			0.970946			0.485473	+	0.874252i	$0.338647\pi$
$492$		0			0
$493$	−18.0000	−	31.1769i	−0.810679	−	1.40414i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	13.7574	−	17.7408i	0.617102	−	0.795782i
$498$		0			0
$499$	2.62132	−	4.54026i	0.117346	−	0.203250i	−0.801369	−	0.598170i	$-0.795895\pi$
$499$	2.62132	−	4.54026i	0.117346	−	0.203250i	0.918715	+	0.394921i	$0.129228\pi$
$500$		0			0
$501$	0.878680	+	1.52192i	0.0392565	+	0.0679943i
$502$		0			0
$503$	−25.4558			−1.13502			−0.567510	−	0.823367i	$-0.692093\pi$
$503$	−25.4558			−1.13502			−0.567510	+	0.823367i	$0.692093\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$		0			0
$509$	−22.2426	+	38.5254i	−0.985888	+	1.70761i	−0.347964	+	0.937508i	$0.613127\pi$
$509$	−22.2426	+	38.5254i	−0.985888	+	1.70761i	−0.637923	+	0.770100i	$0.720206\pi$
$510$		0			0
$511$	−35.3492	−	4.83743i	−1.56376	−	0.213995i
$512$		0			0
$513$	−1.62132	+	2.80821i	−0.0715830	+	0.123985i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−7.45584			−0.327908
$518$		0			0
$519$	−6.00000			−0.263371
$520$		0			0
$521$	21.7279	+	37.6339i	0.951918	+	1.64877i	0.741269	+	0.671208i	$0.234224\pi$
$521$	21.7279	+	37.6339i	0.951918	+	1.64877i	0.210648	+	0.977562i	$0.432443\pi$
$522$		0			0
$523$	3.75736	−	6.50794i	0.164298	−	0.284572i	−0.772108	−	0.635492i	$-0.780798\pi$
$523$	3.75736	−	6.50794i	0.164298	−	0.284572i	0.936406	+	0.350919i	$0.114131\pi$
$524$		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
$531$	1.75736			0.0762629
$532$		0			0
$533$	−8.78680			−0.380598
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.75736	+	3.04384i	−0.0758357	+	0.131351i
$538$		0			0
$539$	21.2132	−	20.7846i	0.913717	−	0.895257i
$540$		0			0
$541$	7.74264	−	13.4106i	0.332882	−	0.576569i	−0.650194	−	0.759769i	$-0.725312\pi$
$541$	7.74264	−	13.4106i	0.332882	−	0.576569i	0.983076	+	0.183200i	$0.0586455\pi$
$542$		0			0
$543$	−2.24264	−	3.88437i	−0.0962409	−	0.166694i
$544$		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
$551$	13.7574	−	23.8284i	0.586083	−	1.01513i
$552$		0			0
$553$	0.757359	+	1.85514i	0.0322062	+	0.0788887i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−22.2426	−	38.5254i	−0.942451	−	1.63237i	−0.760776	−	0.649014i	$-0.775182\pi$
$557$	−22.2426	−	38.5254i	−0.942451	−	1.63237i	−0.181675	−	0.983359i	$-0.558152\pi$
$558$		0			0
$559$	22.4264			0.948536
$560$		0			0
$561$	18.0000			0.759961
$562$		0			0
$563$	−14.1213	−	24.4588i	−0.595143	−	1.03082i	−0.993527	−	0.113599i	$-0.963762\pi$
$563$	−14.1213	−	24.4588i	−0.595143	−	1.03082i	0.398384	−	0.917219i	$-0.369571\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.62132	−	0.358719i	−0.110085	−	0.0150648i
$568$		0			0
$569$	−2.63604	+	4.56575i	−0.110509	+	0.191406i	−0.915975	−	0.401234i	$-0.868581\pi$
$569$	−2.63604	+	4.56575i	−0.110509	+	0.191406i	0.805467	+	0.592641i	$0.201915\pi$
$570$		0			0
$571$	−22.6213	−	39.1813i	−0.946673	−	1.63969i	−0.752367	−	0.658744i	$-0.771088\pi$
$571$	−22.6213	−	39.1813i	−0.946673	−	1.63969i	−0.194306	−	0.980941i	$-0.562245\pi$
$572$		0			0
$573$	16.2426			0.678546
$574$		0			0
$575$		0			0
$576$		0			0
$577$	7.48528	+	12.9649i	0.311616	+	0.539735i	0.978712	−	0.205236i	$-0.0657963\pi$
$577$	7.48528	+	12.9649i	0.311616	+	0.539735i	−0.667096	+	0.744972i	$0.732463\pi$
$578$		0			0
$579$	−2.24264	+	3.88437i	−0.0932010	+	0.161429i
$580$		0			0
$581$	16.6066	−	21.4150i	0.688958	−	0.888444i
$582$		0			0
$583$	−9.00000	+	15.5885i	−0.372742	+	0.645608i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	10.9706			0.452804			0.226402	−	0.974034i	$-0.427304\pi$
$587$	10.9706			0.452804			0.226402	+	0.974034i	$0.427304\pi$
$588$		0			0
$589$	−12.9706			−0.534443
$590$		0			0
$591$	−4.24264	−	7.34847i	−0.174519	−	0.302276i
$592$		0			0
$593$	17.4853	−	30.2854i	0.718034	−	1.24367i	−0.243743	−	0.969840i	$-0.578375\pi$
$593$	17.4853	−	30.2854i	0.718034	−	1.24367i	0.961777	−	0.273832i	$-0.0882913\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.62132	−	14.9326i	0.352847	−	0.611149i
$598$		0			0
$599$	−17.8492	−	30.9158i	−0.729300	−	1.26319i	−0.957179	−	0.289496i	$-0.906512\pi$
$599$	−17.8492	−	30.9158i	−0.729300	−	1.26319i	0.227879	−	0.973689i	$-0.426821\pi$
$600$		0			0
$601$	7.48528			0.305331			0.152665	−	0.988278i	$-0.451214\pi$
$601$	7.48528			0.305331			0.152665	+	0.988278i	$0.451214\pi$
$602$		0			0
$603$	−13.7279			−0.559044
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−21.5919	+	37.3982i	−0.876388	+	1.51795i	−0.0211102	+	0.999777i	$0.506720\pi$
$607$	−21.5919	+	37.3982i	−0.876388	+	1.51795i	−0.855277	+	0.518171i	$0.826613\pi$
$608$		0			0
$609$	22.2426	+	3.04384i	0.901317	+	0.123342i
$610$		0			0
$611$	−4.39340	+	7.60959i	−0.177738	+	0.307851i
$612$		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
$617$	−37.4558			−1.50792			−0.753958	−	0.656923i	$-0.771858\pi$
$617$	−37.4558			−1.50792			−0.753958	+	0.656923i	$0.771858\pi$
$618$		0			0
$619$	−8.24264	−	14.2767i	−0.331300	−	0.573828i	0.651467	−	0.758677i	$-0.274154\pi$
$619$	−8.24264	−	14.2767i	−0.331300	−	0.573828i	−0.982767	+	0.184849i	$0.940820\pi$
$620$		0			0
$621$	−3.00000	+	5.19615i	−0.120386	+	0.208514i
$622$		0			0
$623$	16.2426	+	39.7862i	0.650748	+	1.59400i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	6.87868	+	11.9142i	0.274708	+	0.475808i
$628$		0			0
$629$	−21.2132			−0.845826
$630$		0			0
$631$	−16.2132			−0.645437			−0.322719	−	0.946495i	$-0.604597\pi$
$631$	−16.2132			−0.645437			−0.322719	+	0.946495i	$0.604597\pi$
$632$		0			0
$633$	−6.37868	−	11.0482i	−0.253530	−	0.439126i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−8.71320	−	33.8981i	−0.345230	−	1.34309i
$638$		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
$643$	23.7279			0.935738			0.467869	−	0.883798i	$-0.345022\pi$
$643$	23.7279			0.935738			0.467869	+	0.883798i	$0.345022\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	20.1213	+	34.8511i	0.791051	+	1.37014i	0.925317	+	0.379195i	$0.123799\pi$
$647$	20.1213	+	34.8511i	0.791051	+	1.37014i	−0.134266	+	0.990945i	$0.542868\pi$
$648$		0			0
$649$	3.72792	−	6.45695i	0.146334	−	0.253457i
$650$		0			0
$651$	−4.00000	−	9.79796i	−0.156772	−	0.384012i
$652$		0			0
$653$	11.1213	−	19.2627i	0.435211	−	0.753807i	−0.562102	−	0.827068i	$-0.690007\pi$
$653$	11.1213	−	19.2627i	0.435211	−	0.753807i	0.997313	+	0.0732606i	$0.0233405\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	13.4853			0.526111
$658$		0			0
$659$	23.2721			0.906551			0.453276	−	0.891370i	$-0.350255\pi$
$659$	23.2721			0.906551			0.453276	+	0.891370i	$0.350255\pi$
$660$		0			0
$661$	−0.0147186	−	0.0254934i	−0.000572488	−	0.000991579i	0.865739	−	0.500496i	$-0.166849\pi$
$661$	−0.0147186	−	0.0254934i	−0.000572488	−	0.000991579i	−0.866312	+	0.499504i	$0.833516\pi$
$662$		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
$669$	−4.62132	−	8.00436i	−0.178671	−	0.309466i
$670$		0			0
$671$	4.24264			0.163785
$672$		0			0
$673$	−21.4853			−0.828197			−0.414098	−	0.910232i	$-0.635903\pi$
$673$	−21.4853			−0.828197			−0.414098	+	0.910232i	$0.635903\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.72792	+	16.8493i	−0.373874	+	0.647569i	−0.990158	−	0.139955i	$-0.955304\pi$
$677$	−9.72792	+	16.8493i	−0.373874	+	0.647569i	0.616283	+	0.787524i	$0.288638\pi$
$678$		0			0
$679$	25.8934	−	33.3908i	0.993697	−	1.28142i
$680$		0			0
$681$	1.75736	−	3.04384i	0.0673422	−	0.116640i
$682$		0			0
$683$	12.3640	+	21.4150i	0.473094	+	0.819423i	0.999526	−	0.0307948i	$-0.00980383\pi$
$683$	12.3640	+	21.4150i	0.473094	+	0.819423i	−0.526432	+	0.850217i	$0.676470\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−5.97056			−0.227791
$688$		0			0
$689$	10.6066	+	18.3712i	0.404079	+	0.699886i
$690$		0			0
$691$	15.3492	−	26.5857i	0.583913	−	1.01137i	−0.411097	−	0.911591i	$-0.634854\pi$
$691$	15.3492	−	26.5857i	0.583913	−	1.01137i	0.995010	−	0.0997750i	$-0.0318123\pi$
$692$		0			0
$693$	−6.87868	+	8.87039i	−0.261299	+	0.336958i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−3.72792	−	6.45695i	−0.141205	−	0.244574i
$698$		0			0
$699$	−10.2426			−0.387412
$700$		0			0
$701$	−36.7279			−1.38719			−0.693597	−	0.720363i	$-0.743975\pi$
$701$	−36.7279			−1.38719			−0.693597	+	0.720363i	$0.743975\pi$
$702$		0			0
$703$	−8.10660	−	14.0410i	−0.305746	−	0.529568i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	49.0919	+	6.71807i	1.84629	+	0.252659i
$708$		0			0
$709$	4.74264	−	8.21449i	0.178114	−	0.308502i	−0.763121	−	0.646256i	$-0.776334\pi$
$709$	4.74264	−	8.21449i	0.178114	−	0.308502i	0.941234	+	0.337754i	$0.109667\pi$
$710$		0			0
$711$	−0.378680	−	0.655892i	−0.0142016	−	0.0245979i
$712$		0			0
$713$	−24.0000			−0.898807
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−14.4853	−	25.0892i	−0.540963	−	0.936975i
$718$		0			0
$719$	13.0919	−	22.6758i	0.488245	−	0.845665i	−0.511664	−	0.859186i	$-0.670971\pi$
$719$	13.0919	−	22.6758i	0.488245	−	0.845665i	0.999909	+	0.0135209i	$0.00430397\pi$
$720$		0			0
$721$	9.24264	+	22.6398i	0.344214	+	0.843148i
$722$		0			0
$723$	−13.9853	+	24.2232i	−0.520118	+	0.900871i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−47.2426			−1.75213			−0.876066	−	0.482191i	$-0.839841\pi$
$727$	−47.2426			−1.75213			−0.876066	+	0.482191i	$0.839841\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	9.51472	+	16.4800i	0.351915	+	0.609534i
$732$		0			0
$733$	−4.25736	+	7.37396i	−0.157249	+	0.272364i	−0.933876	−	0.357598i	$-0.883596\pi$
$733$	−4.25736	+	7.37396i	−0.157249	+	0.272364i	0.776627	+	0.629961i	$0.216929\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−29.1213	+	50.4396i	−1.07270	+	1.85797i
$738$		0			0
$739$	20.8345	+	36.0865i	0.766410	+	1.32746i	0.939498	+	0.342555i	$0.111292\pi$
$739$	20.8345	+	36.0865i	0.766410	+	1.32746i	−0.173087	+	0.984906i	$0.555374\pi$
$740$		0			0
$741$	16.2132			0.595607
$742$		0			0
$743$	−22.9706			−0.842708			−0.421354	−	0.906896i	$-0.638445\pi$
$743$	−22.9706			−0.842708			−0.421354	+	0.906896i	$0.638445\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−5.12132	+	8.87039i	−0.187379	+	0.324550i
$748$		0			0
$749$	−18.7279	−	45.8739i	−0.684303	−	1.67619i
$750$		0			0
$751$	3.86396	−	6.69258i	0.140998	−	0.244216i	−0.786875	−	0.617113i	$-0.788302\pi$
$751$	3.86396	−	6.69258i	0.140998	−	0.244216i	0.927873	+	0.372897i	$0.121636\pi$
$752$		0			0
$753$	3.87868	+	6.71807i	0.141347	+	0.244820i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	36.4558			1.32501			0.662505	−	0.749057i	$-0.269493\pi$
$757$	36.4558			1.32501			0.662505	+	0.749057i	$0.269493\pi$
$758$		0			0
$759$	12.7279	+	22.0454i	0.461994	+	0.800198i
$760$		0			0
$761$	−15.8787	+	27.5027i	−0.575602	+	0.996971i	0.420374	+	0.907351i	$0.361899\pi$
$761$	−15.8787	+	27.5027i	−0.575602	+	0.996971i	−0.995976	+	0.0896206i	$0.971435\pi$
$762$		0			0
$763$	−51.0772	−	6.98975i	−1.84912	−	0.253046i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.39340	−	7.60959i	−0.158636	−	0.274766i
$768$		0			0
$769$	−48.4853			−1.74842			−0.874212	−	0.485544i	$-0.838621\pi$
$769$	−48.4853			−1.74842			−0.874212	+	0.485544i	$0.838621\pi$
$770$		0			0
$771$	−13.7574			−0.495459
$772$		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
$777$	8.10660	−	10.4539i	0.290823	−	0.375030i
$778$		0			0
$779$	2.84924	−	4.93503i	0.102085	−	0.176816i
$780$		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
$787$	3.86396	+	6.69258i	0.137735	+	0.238565i	0.926639	−	0.375952i	$-0.122684\pi$
$787$	3.86396	+	6.69258i	0.137735	+	0.238565i	−0.788904	+	0.614517i	$0.789351\pi$
$788$		0			0
$789$	2.48528	−	4.30463i	0.0884784	−	0.153249i
$790$		0			0
$791$	−9.72792	+	12.5446i	−0.345885	+	0.446035i
$792$		0			0
$793$	2.50000	−	4.33013i	0.0887776	−	0.153767i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	36.4264			1.29029			0.645145	−	0.764060i	$-0.276797\pi$
$797$	36.4264			1.29029			0.645145	+	0.764060i	$0.276797\pi$
$798$		0			0
$799$	−7.45584			−0.263769
$800$		0			0
$801$	−8.12132	−	14.0665i	−0.286953	−	0.497017i
$802$		0			0
$803$	28.6066	−	49.5481i	1.00951	−	1.74851i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−3.36396	+	5.82655i	−0.118417	+	0.205104i
$808$		0			0
$809$	−2.27208	−	3.93535i	−0.0798820	−	0.138360i	0.823317	−	0.567582i	$-0.192121\pi$
$809$	−2.27208	−	3.93535i	−0.0798820	−	0.138360i	−0.903199	+	0.429222i	$0.858788\pi$
$810$		0			0
$811$	21.2426			0.745930			0.372965	−	0.927845i	$-0.378341\pi$
$811$	21.2426			0.745930			0.372965	+	0.927845i	$0.378341\pi$
$812$		0			0
$813$	2.00000			0.0701431
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−7.27208	+	12.5956i	−0.254418	+	0.440665i
$818$		0			0
$819$	5.00000	+	12.2474i	0.174714	+	0.427960i
$820$		0			0
$821$	0.878680	−	1.52192i	0.0306661	−	0.0531153i	−0.850285	−	0.526322i	$-0.823570\pi$
$821$	0.878680	−	1.52192i	0.0306661	−	0.0531153i	0.880951	+	0.473207i	$0.156904\pi$
$822$		0			0
$823$	15.3492	+	26.5857i	0.535041	+	0.926718i	0.999161	+	0.0409460i	$0.0130372\pi$
$823$	15.3492	+	26.5857i	0.535041	+	0.926718i	−0.464120	+	0.885772i	$0.653630\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	21.9411			0.762968			0.381484	−	0.924376i	$-0.375413\pi$
$827$	21.9411			0.762968			0.381484	+	0.924376i	$0.375413\pi$
$828$		0			0
$829$	22.7426	+	39.3914i	0.789885	+	1.36812i	0.926037	+	0.377432i	$0.123193\pi$
$829$	22.7426	+	39.3914i	0.789885	+	1.36812i	−0.136153	+	0.990688i	$0.543474\pi$
$830$		0			0
$831$	−15.7426	+	27.2671i	−0.546106	+	0.945884i
$832$		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
$839$	46.9706			1.62160			0.810802	−	0.585321i	$-0.199031\pi$
$839$	46.9706			1.62160			0.810802	+	0.585321i	$0.199031\pi$
$840$		0			0
$841$	43.0000			1.48276
$842$		0			0
$843$	9.87868	+	17.1104i	0.340240	+	0.589313i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	7.00000	+	17.1464i	0.240523	+	0.589158i
$848$		0			0
$849$	5.62132	−	9.73641i	0.192923	−	0.334153i
$850$		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
$857$	11.4853	+	19.8931i	0.392330	+	0.679535i	0.992756	−	0.120145i	$-0.0383359\pi$
$857$	11.4853	+	19.8931i	0.392330	+	0.679535i	−0.600427	+	0.799680i	$0.705003\pi$
$858$		0			0
$859$	−23.4558	+	40.6267i	−0.800303	+	1.38617i	0.119114	+	0.992881i	$0.461995\pi$
$859$	−23.4558	+	40.6267i	−0.800303	+	1.38617i	−0.919417	+	0.393285i	$0.871339\pi$
$860$		0			0
$861$	4.60660	+	0.630399i	0.156993	+	0.0214839i
$862$		0			0
$863$	−9.36396	+	16.2189i	−0.318753	+	0.552096i	−0.980228	−	0.197871i	$-0.936597\pi$
$863$	−9.36396	+	16.2189i	−0.318753	+	0.552096i	0.661475	+	0.749967i	$0.269931\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	1.00000			0.0339618
$868$		0			0
$869$	−3.21320			−0.109000
$870$		0			0
$871$	34.3198	+	59.4436i	1.16288	+	2.01417i
$872$		0			0
$873$	−7.98528	+	13.8309i	−0.270261	+	0.468105i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	14.9853	−	25.9553i	0.506017	−	0.876447i	−0.493959	−	0.869485i	$-0.664451\pi$
$877$	14.9853	−	25.9553i	0.506017	−	0.876447i	0.999976	−	0.00696182i	$-0.00221603\pi$
$878$		0			0
$879$	−10.2426	−	17.7408i	−0.345476	−	0.598381i
$880$		0			0
$881$	32.4853			1.09446			0.547228	−	0.836983i	$-0.315683\pi$
$881$	32.4853			1.09446			0.547228	+	0.836983i	$0.315683\pi$
$882$		0			0
$883$	46.6985			1.57153			0.785765	−	0.618526i	$-0.212270\pi$
$883$	46.6985			1.57153			0.785765	+	0.618526i	$0.212270\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.7574	−	18.6323i	0.361197	−	0.625611i	−0.626961	−	0.779050i	$-0.715702\pi$
$887$	10.7574	−	18.6323i	0.361197	−	0.625611i	0.988158	+	0.153439i	$0.0490349\pi$
$888$		0			0
$889$	14.9853	−	19.3242i	0.502590	−	0.648114i
$890$		0			0
$891$	2.12132	−	3.67423i	0.0710669	−	0.123091i
$892$		0			0
$893$	−2.84924	−	4.93503i	−0.0953463	−	0.165145i
$894$		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
$903$	−11.7574	−	1.60896i	−0.391260	−	0.0535428i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−4.10660	−	7.11284i	−0.136357	−	0.236178i	0.789758	−	0.613419i	$-0.210206\pi$
$907$	−4.10660	−	7.11284i	−0.136357	−	0.236178i	−0.926115	+	0.377241i	$0.876873\pi$
$908$		0			0
$909$	−18.7279			−0.621166
$910$		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
$913$	21.7279	+	37.6339i	0.719089	+	1.24550i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.00000	+	14.6969i	0.198137	+	0.485336i
$918$		0			0
$919$	−24.4853	+	42.4098i	−0.807695	+	1.39897i	0.106762	+	0.994285i	$0.465952\pi$
$919$	−24.4853	+	42.4098i	−0.807695	+	1.39897i	−0.914457	+	0.404684i	$0.867382\pi$
$920$		0			0
$921$	6.24264	+	10.8126i	0.205702	+	0.356286i
$922$		0			0
$923$	42.4264			1.39648
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−4.62132	−	8.00436i	−0.151784	−	0.262898i
$928$		0			0
$929$	−16.0919	+	27.8720i	−0.527958	+	0.914449i	0.471511	+	0.881860i	$0.343709\pi$
$929$	−16.0919	+	27.8720i	−0.527958	+	0.914449i	−0.999469	+	0.0325893i	$0.989625\pi$
$930$		0			0
$931$	21.8640	+	6.09823i	0.716562	+	0.199861i
$932$		0			0
$933$	1.24264	−	2.15232i	0.0406822	−	0.0704637i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	21.4558			0.700932			0.350466	−	0.936575i	$-0.386023\pi$
$937$	21.4558			0.700932			0.350466	+	0.936575i	$0.386023\pi$
$938$		0			0
$939$	−32.9706			−1.07595
$940$		0			0
$941$	−28.4558	−	49.2870i	−0.927634	−	1.60671i	−0.787269	−	0.616609i	$-0.788506\pi$
$941$	−28.4558	−	49.2870i	−0.927634	−	1.60671i	−0.140365	−	0.990100i	$-0.544828\pi$
$942$		0			0
$943$	5.27208	−	9.13151i	0.171682	−	0.297363i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.7279	−	27.2416i	0.511089	−	0.885232i	−0.488829	−	0.872380i	$-0.662576\pi$
$947$	15.7279	−	27.2416i	0.511089	−	0.885232i	0.999917	−	0.0128519i	$-0.00409101\pi$
$948$		0			0
$949$	−33.7132	−	58.3930i	−1.09438	−	1.89552i
$950$		0			0
$951$	6.00000			0.194563
$952$		0			0
$953$	10.2426			0.331792			0.165896	−	0.986143i	$-0.446948\pi$
$953$	10.2426			0.331792			0.165896	+	0.986143i	$0.446948\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−18.0000	+	31.1769i	−0.581857	+	1.00781i
$958$		0			0
$959$	−37.9706	−	5.19615i	−1.22613	−	0.167793i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	9.36396	+	16.2189i	0.301749	+	0.522645i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	9.24264			0.297223			0.148612	−	0.988896i	$-0.452520\pi$
$967$	9.24264			0.297223			0.148612	+	0.988896i	$0.452520\pi$
$968$		0			0
$969$	6.87868	+	11.9142i	0.220975	+	0.382740i
$970$		0			0
$971$	24.3640	−	42.1996i	0.781877	−	1.35425i	−0.148971	−	0.988842i	$-0.547596\pi$
$971$	24.3640	−	42.1996i	0.781877	−	1.35425i	0.930847	−	0.365409i	$-0.119071\pi$
$972$		0			0
$973$	−22.2574	+	28.7019i	−0.713538	+	0.920142i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.150758	−	0.261120i	−0.00482316	−	0.00835396i	0.863604	−	0.504171i	$-0.168202\pi$
$977$	−0.150758	−	0.261120i	−0.00482316	−	0.00835396i	−0.868427	+	0.495817i	$0.834869\pi$
$978$		0			0
$979$	−68.9117			−2.20243
$980$		0			0
$981$	19.4853			0.622117
$982$		0			0
$983$	12.8787	+	22.3065i	0.410766	+	0.711468i	0.994974	−	0.100137i	$-0.0319280\pi$
$983$	12.8787	+	22.3065i	0.410766	+	0.711468i	−0.584208	+	0.811604i	$0.698595\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	2.84924	−	3.67423i	0.0906924	−	0.116952i
$988$		0			0
$989$	−13.4558	+	23.3062i	−0.427871	+	0.741094i
$990$		0			0
$991$	7.48528	+	12.9649i	0.237778	+	0.411843i	0.960076	−	0.279738i	$-0.0902477\pi$
$991$	7.48528	+	12.9649i	0.237778	+	0.411843i	−0.722299	+	0.691581i	$0.756914\pi$
$992$		0			0
$993$	−8.75736			−0.277906
$994$		0			0
$995$		0			0
$996$		0			0
$997$	10.2279	+	17.7153i	0.323922	+	0.561049i	0.981294	−	0.192518i	$-0.0616653\pi$
$997$	10.2279	+	17.7153i	0.323922	+	0.561049i	−0.657372	+	0.753566i	$0.728332\pi$
$998$		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.1801.2	yes	4
5.2	odd	4		2100.2.bc.g.1549.2		8
5.3	odd	4		2100.2.bc.g.1549.3		8
5.4	even	2		2100.2.q.j.1801.1	yes	4
7.4	even	3	inner	2100.2.q.f.1201.2	✓	4
35.4	even	6		2100.2.q.j.1201.1	yes	4
35.18	odd	12		2100.2.bc.g.949.2		8
35.32	odd	12		2100.2.bc.g.949.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.q.f.1201.2	✓	4	7.4	even	3	inner
2100.2.q.f.1801.2	yes	4	1.1	even	1	trivial
2100.2.q.j.1201.1	yes	4	35.4	even	6
2100.2.q.j.1801.1	yes	4	5.4	even	2
2100.2.bc.g.949.2		8	35.18	odd	12
2100.2.bc.g.949.3		8	35.32	odd	12
2100.2.bc.g.1549.2		8	5.2	odd	4
2100.2.bc.g.1549.3		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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(1.62132 - 2.09077i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(1.62132 - 2.09077i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.12132 + 3.67423i) q^{11} +5.00000 q^{13} +(2.12132 + 3.67423i) q^{17} +(-1.62132 + 2.80821i) q^{19} +(-2.62132 - 0.358719i) q^{21} +(-3.00000 + 5.19615i) q^{23} +1.00000 q^{27} -8.48528 q^{29} +(2.00000 + 3.46410i) q^{31} +(2.12132 - 3.67423i) q^{33} +(-2.50000 + 4.33013i) q^{37} +(-2.50000 - 4.33013i) q^{39} -1.75736 q^{41} +4.48528 q^{43} +(-0.878680 + 1.52192i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(2.12132 - 3.67423i) q^{51} +(2.12132 + 3.67423i) q^{53} +3.24264 q^{57} +(-0.878680 - 1.52192i) q^{59} +(0.500000 - 0.866025i) q^{61} +(1.00000 + 2.44949i) q^{63} +(6.86396 + 11.8887i) q^{67} +6.00000 q^{69} +8.48528 q^{71} +(-6.74264 - 11.6786i) q^{73} +(11.1213 + 1.52192i) q^{77} +(-0.378680 + 0.655892i) q^{79} +(-0.500000 - 0.866025i) q^{81} +10.2426 q^{83} +(4.24264 + 7.34847i) q^{87} +(-8.12132 + 14.0665i) q^{89} +(8.10660 - 10.4539i) q^{91} +(2.00000 - 3.46410i) q^{93} +15.9706 q^{97} -4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 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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