LMFDB - Embedded newform 2100.2.q.l.1201.1

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.17819046144.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 10x^{6} + 8x^{5} + 38x^{4} - 4x^{3} + 16x^{2} + 4x + 4 $ x^8 - 2x^7 + 10x^6 + 8x^5 + 38x^4 - 4x^3 + 16x^2 + 4*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1201.1
Root			$0.350883 - 0.607748i$ of defining polynomial
Character	$\chi$	$=$	2100.1201
Dual form			2100.2.q.l.1801.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(-2.30641 + 1.29633i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(-2.30641 + 1.29633i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.07409 - 1.86038i) q^{11} +3.20929 q^{13} +(-1.80641 + 3.12880i) q^{17} +(-2.65730 - 4.60257i) q^{19} +(0.0305535 - 2.64557i) q^{21} +(1.10465 + 1.91330i) q^{23} +1.00000 q^{27} -9.12035 q^{29} +(-3.70929 + 6.42468i) q^{31} +(1.07409 + 1.86038i) q^{33} +(1.27586 + 2.20985i) q^{37} +(-1.60465 + 2.77933i) q^{39} +6.14818 q^{41} -5.44455 q^{43} +(-5.27492 - 9.13644i) q^{47} +(3.63907 - 5.97973i) q^{49} +(-1.80641 - 3.12880i) q^{51} +(-2.70177 + 4.67960i) q^{53} +5.31459 q^{57} +(4.43796 - 7.68677i) q^{59} +(-6.90194 - 11.9545i) q^{61} +(2.27586 + 1.34925i) q^{63} +(0.00817856 - 0.0141657i) q^{67} -2.20929 q^{69} -5.63105 q^{71} +(5.72227 - 9.91127i) q^{73} +(-0.0656346 + 5.68318i) q^{77} +(-7.65543 - 13.2596i) q^{79} +(-0.500000 + 0.866025i) q^{81} -14.0314 q^{83} +(4.56017 - 7.89845i) q^{87} +(1.96879 + 3.41005i) q^{89} +(-7.40194 + 4.16029i) q^{91} +(-3.70929 - 6.42468i) q^{93} +5.16454 q^{97} -2.14818 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9	$ 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{17} - 4 q^{19} - 2 q^{21} - 6 q^{23} + 8 q^{27} - 12 q^{29} - 4 q^{33} - 4 q^{37} + 2 q^{39} + 24 q^{41} + 32 q^{43} - 2 q^{47} - 4 q^{49} + 2 q^{51} - 20 q^{53} + 8 q^{57} + 14 q^{59} - 16 q^{61} + 4 q^{63} - 18 q^{67} + 12 q^{69} - 28 q^{71} + 8 q^{73} + 10 q^{77} + 8 q^{79} - 4 q^{81} - 20 q^{83} + 6 q^{87} + 8 q^{89} - 20 q^{91} - 20 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^13 + 2 * q^17 - 4 * q^19 - 2 * q^21 - 6 * q^23 + 8 * q^27 - 12 * q^29 - 4 * q^33 - 4 * q^37 + 2 * q^39 + 24 * q^41 + 32 * q^43 - 2 * q^47 - 4 * q^49 + 2 * q^51 - 20 * q^53 + 8 * q^57 + 14 * q^59 - 16 * q^61 + 4 * q^63 - 18 * q^67 + 12 * q^69 - 28 * q^71 + 8 * q^73 + 10 * q^77 + 8 * q^79 - 4 * q^81 - 20 * q^83 + 6 * q^87 + 8 * q^89 - 20 * q^91 - 20 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$7$	−2.30641	+	1.29633i	−0.871742	+	0.489966i
$7$	−2.30641	+	1.29633i	−0.871742	+	0.489966i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.07409	−	1.86038i	0.323851	−	0.560926i	−0.657428	−	0.753517i	$-0.728356\pi$
$11$	1.07409	−	1.86038i	0.323851	−	0.560926i	0.981279	+	0.192591i	$0.0616891\pi$
$12$		0			0
$13$	3.20929			0.890097			0.445048	−	0.895506i	$-0.353186\pi$
$13$	3.20929			0.890097			0.445048	+	0.895506i	$0.353186\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.80641	+	3.12880i	−0.438119	+	0.758845i	−0.997544	−	0.0700361i	$-0.977689\pi$
$17$	−1.80641	+	3.12880i	−0.438119	+	0.758845i	0.559425	+	0.828881i	$0.311022\pi$
$18$		0			0
$19$	−2.65730	−	4.60257i	−0.609625	−	1.05590i	−0.991302	−	0.131606i	$-0.957987\pi$
$19$	−2.65730	−	4.60257i	−0.609625	−	1.05590i	0.381677	−	0.924296i	$-0.375347\pi$
$20$		0			0
$21$	0.0305535	−	2.64557i	0.00666733	−	0.577312i
$22$		0			0
$23$	1.10465	+	1.91330i	0.230334	+	0.398951i	0.957907	−	0.287080i	$-0.0926847\pi$
$23$	1.10465	+	1.91330i	0.230334	+	0.398951i	−0.727572	+	0.686031i	$0.759351\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−9.12035			−1.69361			−0.846803	−	0.531907i	$-0.821476\pi$
$29$	−9.12035			−1.69361			−0.846803	+	0.531907i	$0.821476\pi$
$30$		0			0
$31$	−3.70929	+	6.42468i	−0.666208	+	1.15391i	0.312748	+	0.949836i	$0.398750\pi$
$31$	−3.70929	+	6.42468i	−0.666208	+	1.15391i	−0.978956	+	0.204070i	$0.934583\pi$
$32$		0			0
$33$	1.07409	+	1.86038i	0.186975	+	0.323851i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.27586	+	2.20985i	0.209750	+	0.363297i	0.951636	−	0.307229i	$-0.0994017\pi$
$37$	1.27586	+	2.20985i	0.209750	+	0.363297i	−0.741886	+	0.670526i	$0.766068\pi$
$38$		0			0
$39$	−1.60465	+	2.77933i	−0.256949	+	0.445048i
$40$		0			0
$41$	6.14818			0.960185			0.480092	−	0.877218i	$-0.340603\pi$
$41$	6.14818			0.960185			0.480092	+	0.877218i	$0.340603\pi$
$42$		0			0
$43$	−5.44455			−0.830286			−0.415143	−	0.909756i	$-0.636268\pi$
$43$	−5.44455			−0.830286			−0.415143	+	0.909756i	$0.636268\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.27492	−	9.13644i	−0.769427	−	1.33269i	−0.937874	−	0.346976i	$-0.887209\pi$
$47$	−5.27492	−	9.13644i	−0.769427	−	1.33269i	0.168447	−	0.985711i	$-0.446125\pi$
$48$		0			0
$49$	3.63907	−	5.97973i	0.519867	−	0.854247i
$50$		0			0
$51$	−1.80641	−	3.12880i	−0.252948	−	0.438119i
$52$		0			0
$53$	−2.70177	+	4.67960i	−0.371116	+	0.642792i	−0.989738	−	0.142897i	$-0.954358\pi$
$53$	−2.70177	+	4.67960i	−0.371116	+	0.642792i	0.618621	+	0.785689i	$0.287692\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	5.31459			0.703935
$58$		0			0
$59$	4.43796	−	7.68677i	0.577773	−	1.00073i	−0.417961	−	0.908465i	$-0.637255\pi$
$59$	4.43796	−	7.68677i	0.577773	−	1.00073i	0.995734	−	0.0922675i	$-0.0294115\pi$
$60$		0			0
$61$	−6.90194	−	11.9545i	−0.883703	−	1.53062i	−0.847192	−	0.531286i	$-0.821709\pi$
$61$	−6.90194	−	11.9545i	−0.883703	−	1.53062i	−0.0365110	−	0.999333i	$-0.511624\pi$
$62$		0			0
$63$	2.27586	+	1.34925i	0.286731	+	0.169989i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	0.00817856	−	0.0141657i	0.000999170	−	0.00173061i	−0.865525	−	0.500865i	$-0.833015\pi$
$67$	0.00817856	−	0.0141657i	0.000999170	−	0.00173061i	0.866525	+	0.499134i	$0.166349\pi$
$68$		0			0
$69$	−2.20929			−0.265967
$70$		0			0
$71$	−5.63105			−0.668282			−0.334141	−	0.942523i	$-0.608446\pi$
$71$	−5.63105			−0.668282			−0.334141	+	0.942523i	$0.608446\pi$
$72$		0			0
$73$	5.72227	−	9.91127i	0.669742	−	1.16003i	−0.308235	−	0.951310i	$-0.599738\pi$
$73$	5.72227	−	9.91127i	0.669742	−	1.16003i	0.977976	−	0.208716i	$-0.0669285\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.0656346	+	5.68318i	−0.00747976	+	0.647658i
$78$		0			0
$79$	−7.65543	−	13.2596i	−0.861303	−	1.49182i	−0.870672	−	0.491864i	$-0.836316\pi$
$79$	−7.65543	−	13.2596i	−0.861303	−	1.49182i	0.00936887	−	0.999956i	$-0.497018\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−14.0314			−1.54015			−0.770073	−	0.637955i	$-0.779780\pi$
$83$	−14.0314			−1.54015			−0.770073	+	0.637955i	$0.779780\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.56017	−	7.89845i	0.488902	−	0.846803i
$88$		0			0
$89$	1.96879	+	3.41005i	0.208691	+	0.361464i	0.951303	−	0.308259i	$-0.0997462\pi$
$89$	1.96879	+	3.41005i	0.208691	+	0.361464i	−0.742611	+	0.669723i	$0.766413\pi$
$90$		0			0
$91$	−7.40194	+	4.16029i	−0.775935	+	0.436117i
$92$		0			0
$93$	−3.70929	−	6.42468i	−0.384635	−	0.666208i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	5.16454			0.524380			0.262190	−	0.965016i	$-0.415555\pi$
$97$	5.16454			0.524380			0.262190	+	0.965016i	$0.415555\pi$
$98$		0			0
$99$	−2.14818			−0.215901
$100$		0			0
$101$	0.815524	−	1.41253i	0.0811477	−	0.140552i	−0.822595	−	0.568627i	$-0.807475\pi$
$101$	0.815524	−	1.41253i	0.0811477	−	0.140552i	0.903743	+	0.428075i	$0.140808\pi$
$102$		0			0
$103$	−1.02237	−	1.77081i	−0.100738	−	0.174483i	0.811251	−	0.584698i	$-0.198787\pi$
$103$	−1.02237	−	1.77081i	−0.100738	−	0.174483i	−0.911989	+	0.410215i	$0.865454\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.02210	−	5.23442i	−0.292157	−	0.506031i	0.682162	−	0.731201i	$-0.261040\pi$
$107$	−3.02210	−	5.23442i	−0.292157	−	0.506031i	−0.974320	+	0.225170i	$0.927706\pi$
$108$		0			0
$109$	1.59619	−	2.76468i	0.152887	−	0.264808i	−0.779401	−	0.626526i	$-0.784476\pi$
$109$	1.59619	−	2.76468i	0.152887	−	0.264808i	0.932288	+	0.361718i	$0.117810\pi$
$110$		0			0
$111$	−2.55172			−0.242198
$112$		0			0
$113$	−1.10343			−0.103802			−0.0519011	−	0.998652i	$-0.516528\pi$
$113$	−1.10343			−0.103802			−0.0519011	+	0.998652i	$0.516528\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.60465	−	2.77933i	−0.148349	−	0.256949i
$118$		0			0
$119$	0.110385	−	9.55800i	0.0101189	−	0.876180i
$120$		0			0
$121$	3.19265	+	5.52984i	0.290241	+	0.502713i
$122$		0			0
$123$	−3.07409	+	5.32448i	−0.277182	+	0.480092i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	19.6798			1.74630			0.873150	−	0.487451i	$-0.162073\pi$
$127$	19.6798			1.74630			0.873150	+	0.487451i	$0.162073\pi$
$128$		0			0
$129$	2.72227	−	4.71512i	0.239683	−	0.415143i
$130$		0			0
$131$	−7.57316	−	13.1171i	−0.661670	−	1.14605i	−0.980177	−	0.198125i	$-0.936515\pi$
$131$	−7.57316	−	13.1171i	−0.661670	−	1.14605i	0.318507	−	0.947921i	$-0.396819\pi$
$132$		0			0
$133$	12.0953	+	7.17070i	1.04879	+	0.621778i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.84608	+	6.66160i	−0.328593	+	0.569139i	−0.982233	−	0.187666i	$-0.939908\pi$
$137$	−3.84608	+	6.66160i	−0.328593	+	0.569139i	0.653640	+	0.756805i	$0.273241\pi$
$138$		0			0
$139$	−4.84034			−0.410552			−0.205276	−	0.978704i	$-0.565809\pi$
$139$	−4.84034			−0.410552			−0.205276	+	0.978704i	$0.565809\pi$
$140$		0			0
$141$	10.5498			0.888458
$142$		0			0
$143$	3.44707	−	5.97050i	0.288259	−	0.499279i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.35906	+	6.14139i	0.277051	+	0.506534i
$148$		0			0
$149$	−4.48608	−	7.77012i	−0.367514	−	0.636553i	0.621662	−	0.783286i	$-0.286458\pi$
$149$	−4.48608	−	7.77012i	−0.367514	−	0.636553i	−0.989176	+	0.146732i	$0.953124\pi$
$150$		0			0
$151$	1.84084	−	3.18842i	0.149805	−	0.259470i	−0.781350	−	0.624093i	$-0.785469\pi$
$151$	1.84084	−	3.18842i	0.149805	−	0.259470i	0.931155	+	0.364623i	$0.118802\pi$
$152$		0			0
$153$	3.61282			0.292079
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−4.53349	+	7.85224i	−0.361812	+	0.626677i	−0.988259	−	0.152787i	$-0.951175\pi$
$157$	−4.53349	+	7.85224i	−0.361812	+	0.626677i	0.626447	+	0.779464i	$0.284508\pi$
$158$		0			0
$159$	−2.70177	−	4.67960i	−0.214264	−	0.371116i
$160$		0			0
$161$	−5.02803	−	2.98088i	−0.396264	−	0.234926i
$162$		0			0
$163$	−2.46464	−	4.26888i	−0.193046	−	0.334365i	0.753213	−	0.657777i	$-0.228503\pi$
$163$	−2.46464	−	4.26888i	−0.193046	−	0.334365i	−0.946258	+	0.323413i	$0.895170\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−17.0920			−1.32262			−0.661308	−	0.750115i	$-0.729998\pi$
$167$	−17.0920			−1.32262			−0.661308	+	0.750115i	$0.729998\pi$
$168$		0			0
$169$	−2.70046			−0.207727
$170$		0			0
$171$	−2.65730	+	4.60257i	−0.203208	+	0.351967i
$172$		0			0
$173$	−2.42684	−	4.20341i	−0.184509	−	0.319580i	0.758902	−	0.651205i	$-0.225736\pi$
$173$	−2.42684	−	4.20341i	−0.184509	−	0.319580i	−0.943411	+	0.331626i	$0.892403\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.43796	+	7.68677i	0.333577	+	0.577773i
$178$		0			0
$179$	−2.89470	+	5.01377i	−0.216360	+	0.374747i	−0.953692	−	0.300784i	$-0.902752\pi$
$179$	−2.89470	+	5.01377i	−0.216360	+	0.374747i	0.737332	+	0.675530i	$0.236085\pi$
$180$		0			0
$181$	18.6817			1.38860			0.694299	−	0.719687i	$-0.255715\pi$
$181$	18.6817			1.38860			0.694299	+	0.719687i	$0.255715\pi$
$182$		0			0
$183$	13.8039			1.02041
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.88050	+	6.72123i	0.283771	+	0.491505i
$188$		0			0
$189$	−2.30641	+	1.29633i	−0.167767	+	0.0942939i
$190$		0			0
$191$	2.35934	+	4.08650i	0.170716	+	0.295689i	0.938670	−	0.344816i	$-0.112059\pi$
$191$	2.35934	+	4.08650i	0.170716	+	0.295689i	−0.767954	+	0.640504i	$0.778725\pi$
$192$		0			0
$193$	−8.87232	+	15.3673i	−0.638644	+	1.10616i	0.347087	+	0.937833i	$0.387171\pi$
$193$	−8.87232	+	15.3673i	−0.638644	+	1.10616i	−0.985731	+	0.168331i	$0.946162\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−24.5813			−1.75134			−0.875671	−	0.482908i	$-0.839580\pi$
$197$	−24.5813			−1.75134			−0.875671	+	0.482908i	$0.839580\pi$
$198$		0			0
$199$	−6.15543	+	10.6615i	−0.436347	+	0.755775i	−0.997404	−	0.0720019i	$-0.977061\pi$
$199$	−6.15543	+	10.6615i	−0.436347	+	0.755775i	0.561058	+	0.827777i	$0.310395\pi$
$200$		0			0
$201$	0.00817856	+	0.0141657i	0.000576871	+	0.000999170i
$202$		0			0
$203$	21.0353	−	11.8230i	1.47639	−	0.829809i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.10465	−	1.91330i	0.0767781	−	0.132984i
$208$		0			0
$209$	−11.4167			−0.789711
$210$		0			0
$211$	−2.99944			−0.206490			−0.103245	−	0.994656i	$-0.532923\pi$
$211$	−2.99944			−0.206490			−0.103245	+	0.994656i	$0.532923\pi$
$212$		0			0
$213$	2.81552	−	4.87663i	0.192917	−	0.334141i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.226664	−	19.6264i	0.0153869	−	1.33233i
$218$		0			0
$219$	5.72227	+	9.91127i	0.386675	+	0.669742i
$220$		0			0
$221$	−5.79730	+	10.0412i	−0.389969	+	0.675445i
$222$		0			0
$223$	6.11848			0.409724			0.204862	−	0.978791i	$-0.434325\pi$
$223$	6.11848			0.409724			0.204862	+	0.978791i	$0.434325\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.05537	+	5.29205i	−0.202792	+	0.351246i	−0.949427	−	0.313988i	$-0.898335\pi$
$227$	−3.05537	+	5.29205i	−0.202792	+	0.351246i	0.746635	+	0.665234i	$0.231668\pi$
$228$		0			0
$229$	9.55737	+	16.5539i	0.631569	+	1.09391i	0.987231	+	0.159295i	$0.0509221\pi$
$229$	9.55737	+	16.5539i	0.631569	+	1.09391i	−0.355662	+	0.934615i	$0.615745\pi$
$230$		0			0
$231$	−4.88896	−	2.89843i	−0.321670	−	0.190703i
$232$		0			0
$233$	−4.45094	−	7.70926i	−0.291591	−	0.505050i	0.682595	−	0.730797i	$-0.260851\pi$
$233$	−4.45094	−	7.70926i	−0.291591	−	0.505050i	−0.974186	+	0.225746i	$0.927518\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	15.3109			0.994547
$238$		0			0
$239$	−20.4276			−1.32135			−0.660677	−	0.750670i	$-0.729731\pi$
$239$	−20.4276			−1.32135			−0.660677	+	0.750670i	$0.729731\pi$
$240$		0			0
$241$	9.12759	−	15.8095i	0.587960	−	1.01838i	−0.406539	−	0.913633i	$-0.633265\pi$
$241$	9.12759	−	15.8095i	0.587960	−	1.01838i	0.994499	−	0.104743i	$-0.0334021\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−8.52803	−	14.7710i	−0.542626	−	0.939855i
$248$		0			0
$249$	7.01570	−	12.1516i	0.444602	−	0.770073i
$250$		0			0
$251$	−14.5630			−0.919210			−0.459605	−	0.888123i	$-0.652009\pi$
$251$	−14.5630			−0.919210			−0.459605	+	0.888123i	$0.652009\pi$
$252$		0			0
$253$	4.74596			0.298376
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.10917	−	14.0455i	−0.505836	−	0.876134i	−0.999977	−	0.00675233i	$-0.997851\pi$
$257$	−8.10917	−	14.0455i	−0.505836	−	0.876134i	0.494141	−	0.869382i	$-0.335483\pi$
$258$		0			0
$259$	−5.80735	−	3.44290i	−0.360851	−	0.213931i
$260$		0			0
$261$	4.56017	+	7.89845i	0.282268	+	0.488902i
$262$		0			0
$263$	−12.8714	+	22.2939i	−0.793684	+	1.37470i	0.129987	+	0.991516i	$0.458506\pi$
$263$	−12.8714	+	22.2939i	−0.793684	+	1.37470i	−0.923671	+	0.383185i	$0.874827\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−3.93758			−0.240976
$268$		0			0
$269$	12.7546	−	22.0916i	0.777662	−	1.34695i	−0.155623	−	0.987816i	$-0.549739\pi$
$269$	12.7546	−	22.0916i	0.777662	−	1.34695i	0.933286	−	0.359134i	$-0.116928\pi$
$270$		0			0
$271$	−2.03508	−	3.52486i	−0.123622	−	0.214120i	0.797571	−	0.603225i	$-0.206118\pi$
$271$	−2.03508	−	3.52486i	−0.123622	−	0.214120i	−0.921194	+	0.389105i	$0.872784\pi$
$272$		0			0
$273$	0.0980552	−	8.49042i	0.00593457	−	0.513863i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	6.54626	−	11.3384i	0.393326	−	0.681261i	−0.599560	−	0.800330i	$-0.704658\pi$
$277$	6.54626	−	11.3384i	0.393326	−	0.681261i	0.992886	+	0.119069i	$0.0379909\pi$
$278$		0			0
$279$	7.41858			0.444139
$280$		0			0
$281$	19.5976			1.16910			0.584548	−	0.811359i	$-0.301272\pi$
$281$	19.5976			1.16910			0.584548	+	0.811359i	$0.301272\pi$
$282$		0			0
$283$	5.23167	−	9.06151i	0.310990	−	0.538651i	−0.667587	−	0.744532i	$-0.732673\pi$
$283$	5.23167	−	9.06151i	0.310990	−	0.538651i	0.978577	+	0.205881i	$0.0660060\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−14.1802	+	7.97006i	−0.837033	+	0.470458i
$288$		0			0
$289$	1.97375	+	3.41864i	0.116103	+	0.201096i
$290$		0			0
$291$	−2.58227	+	4.47262i	−0.151375	+	0.262190i
$292$		0			0
$293$	−24.7240			−1.44439			−0.722196	−	0.691689i	$-0.756867\pi$
$293$	−24.7240			−1.44439			−0.722196	+	0.691689i	$0.756867\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.07409	−	1.86038i	0.0623251	−	0.107950i
$298$		0			0
$299$	3.54513	+	6.14034i	0.205020	+	0.355105i
$300$		0			0
$301$	12.5574	−	7.05792i	0.723795	−	0.406812i
$302$		0			0
$303$	0.815524	+	1.41253i	0.0468506	+	0.0811477i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	3.24574			0.185244			0.0926220	−	0.995701i	$-0.470475\pi$
$307$	3.24574			0.185244			0.0926220	+	0.995701i	$0.470475\pi$
$308$		0			0
$309$	2.04475			0.116322
$310$		0			0
$311$	−6.57653	+	11.3909i	−0.372921	+	0.645918i	−0.990013	−	0.140973i	$-0.954977\pi$
$311$	−6.57653	+	11.3909i	−0.372921	+	0.645918i	0.617093	+	0.786891i	$0.288310\pi$
$312$		0			0
$313$	−8.02237	−	13.8952i	−0.453451	−	0.785401i	0.545146	−	0.838341i	$-0.316474\pi$
$313$	−8.02237	−	13.8952i	−0.453451	−	0.785401i	−0.998598	+	0.0529400i	$0.983141\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.97151	+	17.2712i	0.560056	+	0.970045i	0.997491	+	0.0707950i	$0.0225536\pi$
$317$	9.97151	+	17.2712i	0.560056	+	0.970045i	−0.437435	+	0.899250i	$0.644113\pi$
$318$		0			0
$319$	−9.79609	+	16.9673i	−0.548476	+	0.949988i
$320$		0			0
$321$	6.04419			0.337354
$322$		0			0
$323$	19.2007			1.06835
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.59619	+	2.76468i	0.0882694	+	0.152887i
$328$		0			0
$329$	24.0100	+	14.2344i	1.32371	+	0.784766i
$330$		0			0
$331$	2.41106	+	4.17607i	0.132524	+	0.229538i	0.924649	−	0.380821i	$-0.124359\pi$
$331$	2.41106	+	4.17607i	0.132524	+	0.229538i	−0.792125	+	0.610359i	$0.791025\pi$
$332$		0			0
$333$	1.27586	−	2.20985i	0.0699166	−	0.121099i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	33.7464			1.83828			0.919140	−	0.393930i	$-0.128885\pi$
$337$	33.7464			1.83828			0.919140	+	0.393930i	$0.128885\pi$
$338$		0			0
$339$	0.551717	−	0.955601i	0.0299651	−	0.0519011i
$340$		0			0
$341$	7.96823	+	13.8014i	0.431504	+	0.747387i
$342$		0			0
$343$	−0.641510	+	18.5091i	−0.0346383	+	0.999400i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.27040	+	14.3247i	−0.443978	+	0.768993i	−0.997980	−	0.0635224i	$-0.979767\pi$
$347$	−8.27040	+	14.3247i	−0.443978	+	0.768993i	0.554002	+	0.832515i	$0.313100\pi$
$348$		0			0
$349$	21.0842			1.12861			0.564306	−	0.825566i	$-0.309144\pi$
$349$	21.0842			1.12861			0.564306	+	0.825566i	$0.309144\pi$
$350$		0			0
$351$	3.20929			0.171299
$352$		0			0
$353$	−15.0516	+	26.0702i	−0.801118	+	1.38758i	0.117763	+	0.993042i	$0.462428\pi$
$353$	−15.0516	+	26.0702i	−0.801118	+	1.38758i	−0.918881	+	0.394535i	$0.870906\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	8.22227	+	4.87459i	0.435169	+	0.257991i
$358$		0			0
$359$	14.5305	+	25.1675i	0.766889	+	1.32829i	0.939242	+	0.343255i	$0.111530\pi$
$359$	14.5305	+	25.1675i	0.766889	+	1.32829i	−0.172353	+	0.985035i	$0.555137\pi$
$360$		0			0
$361$	−4.62244	+	8.00629i	−0.243286	+	0.421384i
$362$		0			0
$363$	−6.38531			−0.335142
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.561762	−	0.973001i	0.0293237	−	0.0507902i	−0.850991	−	0.525180i	$-0.823998\pi$
$367$	0.561762	−	0.973001i	0.0293237	−	0.0507902i	0.880315	+	0.474390i	$0.157331\pi$
$368$		0			0
$369$	−3.07409	−	5.32448i	−0.160031	−	0.277182i
$370$		0			0
$371$	0.165097	−	14.2955i	0.00857141	−	0.742183i
$372$		0			0
$373$	12.3045	+	21.3121i	0.637105	+	1.10350i	0.986065	+	0.166361i	$0.0532017\pi$
$373$	12.3045	+	21.3121i	0.637105	+	1.10350i	−0.348960	+	0.937138i	$0.613465\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−29.2698			−1.50747
$378$		0			0
$379$	28.0997			1.44338			0.721692	−	0.692214i	$-0.243365\pi$
$379$	28.0997			1.44338			0.721692	+	0.692214i	$0.243365\pi$
$380$		0			0
$381$	−9.83990	+	17.0432i	−0.504114	+	0.873150i
$382$		0			0
$383$	−14.4017	−	24.9444i	−0.735891	−	1.27460i	−0.954331	−	0.298750i	$-0.903430\pi$
$383$	−14.4017	−	24.9444i	−0.735891	−	1.27460i	0.218441	−	0.975850i	$-0.429903\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.72227	+	4.71512i	0.138381	+	0.239683i
$388$		0			0
$389$	−7.06901	+	12.2439i	−0.358413	+	0.620789i	−0.987696	−	0.156387i	$-0.950015\pi$
$389$	−7.06901	+	12.2439i	−0.358413	+	0.620789i	0.629283	+	0.777176i	$0.283349\pi$
$390$		0			0
$391$	−7.98178			−0.403656
$392$		0			0
$393$	15.1463			0.764031
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−7.05696	−	12.2230i	−0.354178	−	0.613455i	0.632799	−	0.774316i	$-0.281906\pi$
$397$	−7.05696	−	12.2230i	−0.354178	−	0.613455i	−0.986977	+	0.160861i	$0.948573\pi$
$398$		0			0
$399$	−12.2576	+	6.88945i	−0.613649	+	0.344904i
$400$		0			0
$401$	0.727736	+	1.26048i	0.0363414	+	0.0629451i	0.883624	−	0.468197i	$-0.155096\pi$
$401$	0.727736	+	1.26048i	0.0363414	+	0.0629451i	−0.847283	+	0.531142i	$0.821763\pi$
$402$		0			0
$403$	−11.9042	+	20.6187i	−0.592990	+	1.02709i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.48155			0.271711
$408$		0			0
$409$	−18.1980	+	31.5199i	−0.899835	+	1.55856i	−0.0721304	+	0.997395i	$0.522980\pi$
$409$	−18.1980	+	31.5199i	−0.899835	+	1.55856i	−0.827704	+	0.561164i	$0.810354\pi$
$410$		0			0
$411$	−3.84608	−	6.66160i	−0.189713	−	0.328593i
$412$		0			0
$413$	−0.271191	+	23.4819i	−0.0133444	+	1.15547i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2.42017	−	4.19186i	0.118516	−	0.205276i
$418$		0			0
$419$	31.9369			1.56022			0.780109	−	0.625644i	$-0.215164\pi$
$419$	31.9369			1.56022			0.780109	+	0.625644i	$0.215164\pi$
$420$		0			0
$421$	−35.5151			−1.73090			−0.865450	−	0.500995i	$-0.832967\pi$
$421$	−35.5151			−1.73090			−0.865450	+	0.500995i	$0.832967\pi$
$422$		0			0
$423$	−5.27492	+	9.13644i	−0.256476	+	0.444229i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	31.4157	+	18.6249i	1.52031	+	0.901320i
$428$		0			0
$429$	3.44707	+	5.97050i	0.166426	+	0.288259i
$430$		0			0
$431$	−8.29315	+	14.3642i	−0.399467	+	0.691897i	−0.993660	−	0.112425i	$-0.964138\pi$
$431$	−8.29315	+	14.3642i	−0.399467	+	0.691897i	0.594193	+	0.804322i	$0.297471\pi$
$432$		0			0
$433$	−38.2014			−1.83584			−0.917921	−	0.396764i	$-0.870133\pi$
$433$	−38.2014			−1.83584			−0.917921	+	0.396764i	$0.870133\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.87074	−	10.1684i	0.280835	−	0.486421i
$438$		0			0
$439$	−5.97266	−	10.3450i	−0.285060	−	0.493738i	0.687564	−	0.726124i	$-0.258680\pi$
$439$	−5.97266	−	10.3450i	−0.285060	−	0.493738i	−0.972624	+	0.232386i	$0.925347\pi$
$440$		0			0
$441$	−6.99813	−	0.161663i	−0.333244	−	0.00769825i
$442$		0			0
$443$	−17.9047	−	31.0118i	−0.850676	−	1.47341i	−0.880599	−	0.473862i	$-0.842859\pi$
$443$	−17.9047	−	31.0118i	−0.850676	−	1.47341i	0.0299229	−	0.999552i	$-0.490474\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	8.97216			0.424369
$448$		0			0
$449$	25.5848			1.20742			0.603711	−	0.797203i	$-0.293688\pi$
$449$	25.5848			1.20742			0.603711	+	0.797203i	$0.293688\pi$
$450$		0			0
$451$	6.60371	−	11.4380i	0.310957	−	0.538593i
$452$		0			0
$453$	1.84084	+	3.18842i	0.0864901	+	0.149805i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.79889	+	3.11577i	0.0841484	+	0.145749i	0.905028	−	0.425352i	$-0.139850\pi$
$457$	1.79889	+	3.11577i	0.0841484	+	0.145749i	−0.820880	+	0.571101i	$0.806516\pi$
$458$		0			0
$459$	−1.80641	+	3.12880i	−0.0843161	+	0.146040i
$460$		0			0
$461$	32.8037			1.52782			0.763911	−	0.645322i	$-0.223277\pi$
$461$	32.8037			1.52782			0.763911	+	0.645322i	$0.223277\pi$
$462$		0			0
$463$	9.28219			0.431380			0.215690	−	0.976462i	$-0.430800\pi$
$463$	9.28219			0.431380			0.215690	+	0.976462i	$0.430800\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.15005	−	3.72400i	−0.0994925	−	0.172326i	0.811982	−	0.583682i	$-0.198389\pi$
$467$	−2.15005	−	3.72400i	−0.0994925	−	0.172326i	−0.911475	+	0.411356i	$0.865055\pi$
$468$		0			0
$469$	−0.000499768		0.0432740i	−2.30771e−5		0.00199821i
$470$		0			0
$471$	−4.53349	−	7.85224i	−0.208892	−	0.361812i
$472$		0			0
$473$	−5.84794	+	10.1289i	−0.268889	+	0.465729i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	5.40353			0.247411
$478$		0			0
$479$	−9.88588	+	17.1228i	−0.451697	+	0.782363i	−0.998492	−	0.0549041i	$-0.982515\pi$
$479$	−9.88588	+	17.1228i	−0.451697	+	0.782363i	0.546794	+	0.837267i	$0.315848\pi$
$480$		0			0
$481$	4.09460	+	7.09205i	0.186698	+	0.323370i
$482$		0			0
$483$	5.09553	−	2.86396i	0.231855	−	0.130315i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−21.8121	+	37.7796i	−0.988399	+	1.71196i	−0.362669	+	0.931918i	$0.618134\pi$
$487$	−21.8121	+	37.7796i	−0.988399	+	1.71196i	−0.625730	+	0.780039i	$0.715199\pi$
$488$		0			0
$489$	4.92928			0.222910
$490$		0			0
$491$	−3.23582			−0.146030			−0.0730152	−	0.997331i	$-0.523262\pi$
$491$	−3.23582			−0.146030			−0.0730152	+	0.997331i	$0.523262\pi$
$492$		0			0
$493$	16.4751	−	28.5357i	0.742001	−	1.28518i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.9875	−	7.29968i	0.582570	−	0.327435i
$498$		0			0
$499$	13.7353	+	23.7902i	0.614875	+	1.06499i	0.990406	+	0.138185i	$0.0441267\pi$
$499$	13.7353	+	23.7902i	0.614875	+	1.06499i	−0.375532	+	0.926809i	$0.622540\pi$
$500$		0			0
$501$	8.54598	−	14.8021i	0.381806	−	0.661308i
$502$		0			0
$503$	25.2182			1.12442			0.562212	−	0.826993i	$-0.309951\pi$
$503$	25.2182			1.12442			0.562212	+	0.826993i	$0.309951\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.35023	−	2.33866i	0.0599657	−	0.103864i
$508$		0			0
$509$	9.01822	+	15.6200i	0.399726	+	0.692345i	0.993692	−	0.112145i	$-0.0357720\pi$
$509$	9.01822	+	15.6200i	0.399726	+	0.692345i	−0.593966	+	0.804490i	$0.702439\pi$
$510$		0			0
$511$	−0.349671	+	30.2774i	−0.0154686	+	1.33939i
$512$		0			0
$513$	−2.65730	−	4.60257i	−0.117322	−	0.203208i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−22.6630			−0.996718
$518$		0			0
$519$	4.85368			0.213053
$520$		0			0
$521$	−0.419891	+	0.727272i	−0.0183957	+	0.0318624i	−0.875077	−	0.483984i	$-0.839189\pi$
$521$	−0.419891	+	0.727272i	−0.0183957	+	0.0318624i	0.856681	+	0.515847i	$0.172523\pi$
$522$		0			0
$523$	−20.1987	−	34.9852i	−0.883227	−	1.52979i	−0.847732	−	0.530424i	$-0.822033\pi$
$523$	−20.1987	−	34.9852i	−0.883227	−	1.52979i	−0.0354945	−	0.999370i	$-0.511301\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−13.4010	−	23.2112i	−0.583757	−	1.01110i
$528$		0			0
$529$	9.05952	−	15.6915i	0.393892	−	0.682241i
$530$		0			0
$531$	−8.87592			−0.385182
$532$		0			0
$533$	19.7313			0.854658
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−2.89470	−	5.01377i	−0.124916	−	0.216360i
$538$		0			0
$539$	−7.21588	−	13.1928i	−0.310810	−	0.568256i
$540$		0			0
$541$	11.7087	+	20.2801i	0.503398	+	0.871911i	0.999992	+	0.00392786i	$0.00125028\pi$
$541$	11.7087	+	20.2801i	0.503398	+	0.871911i	−0.496595	+	0.867983i	$0.665416\pi$
$542$		0			0
$543$	−9.34084	+	16.1788i	−0.400854	+	0.694299i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	7.66719			0.327825			0.163913	−	0.986475i	$-0.447588\pi$
$547$	7.66719			0.327825			0.163913	+	0.986475i	$0.447588\pi$
$548$		0			0
$549$	−6.90194	+	11.9545i	−0.294568	+	0.510206i
$550$		0			0
$551$	24.2355	+	41.9770i	1.03247	+	1.78828i
$552$		0			0
$553$	34.8453	+	20.6581i	1.48177	+	0.878473i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−12.2731	+	21.2576i	−0.520026	+	0.900712i	0.479703	+	0.877431i	$0.340744\pi$
$557$	−12.2731	+	21.2576i	−0.520026	+	0.900712i	−0.999729	+	0.0232807i	$0.992589\pi$
$558$		0			0
$559$	−17.4731			−0.739035
$560$		0			0
$561$	−7.76101			−0.327670
$562$		0			0
$563$	2.31646	−	4.01222i	0.0976270	−	0.169095i	−0.813075	−	0.582159i	$-0.802208\pi$
$563$	2.31646	−	4.01222i	0.0976270	−	0.169095i	0.910702	+	0.413064i	$0.135541\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.0305535	−	2.64557i	0.00128313	−	0.111104i
$568$		0			0
$569$	−5.47818	−	9.48849i	−0.229657	−	0.397778i	0.728049	−	0.685525i	$-0.240427\pi$
$569$	−5.47818	−	9.48849i	−0.229657	−	0.397778i	−0.957707	+	0.287747i	$0.907094\pi$
$570$		0			0
$571$	4.07044	−	7.05021i	0.170343	−	0.295042i	−0.768197	−	0.640213i	$-0.778846\pi$
$571$	4.07044	−	7.05021i	0.170343	−	0.295042i	0.938540	+	0.345171i	$0.112179\pi$
$572$		0			0
$573$	−4.71868			−0.197126
$574$		0			0
$575$		0			0
$576$		0			0
$577$	0.200555	−	0.347371i	0.00834921	−	0.0144612i	−0.861821	−	0.507213i	$-0.830676\pi$
$577$	0.200555	−	0.347371i	0.00834921	−	0.0144612i	0.870170	+	0.492752i	$0.164009\pi$
$578$		0			0
$579$	−8.87232	−	15.3673i	−0.368721	−	0.638644i
$580$		0			0
$581$	32.3622	−	18.1893i	1.34261	−	0.754619i
$582$		0			0
$583$	5.80389	+	10.0526i	0.240373	+	0.416337i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.46651			0.349450			0.174725	−	0.984617i	$-0.444096\pi$
$587$	8.46651			0.349450			0.174725	+	0.984617i	$0.444096\pi$
$588$		0			0
$589$	39.4267			1.62455
$590$		0			0
$591$	12.2906	−	21.2880i	0.505569	−	0.875671i
$592$		0			0
$593$	−8.10917	−	14.0455i	−0.333004	−	0.576780i	0.650096	−	0.759852i	$-0.274729\pi$
$593$	−8.10917	−	14.0455i	−0.333004	−	0.576780i	−0.983099	+	0.183073i	$0.941396\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−6.15543	−	10.6615i	−0.251925	−	0.436347i
$598$		0			0
$599$	−8.30276	+	14.3808i	−0.339242	+	0.587584i	−0.984290	−	0.176558i	$-0.943504\pi$
$599$	−8.30276	+	14.3808i	−0.339242	+	0.587584i	0.645049	+	0.764141i	$0.276837\pi$
$600$		0			0
$601$	29.7659			1.21418			0.607088	−	0.794635i	$-0.292338\pi$
$601$	29.7659			1.21418			0.607088	+	0.794635i	$0.292338\pi$
$602$		0			0
$603$	−0.0163571			−0.000666114
$604$		0			0
$605$		0			0
$606$		0			0
$607$	5.13945	+	8.90178i	0.208604	+	0.361312i	0.951275	−	0.308344i	$-0.0997748\pi$
$607$	5.13945	+	8.90178i	0.208604	+	0.361312i	−0.742671	+	0.669656i	$0.766441\pi$
$608$		0			0
$609$	−0.278659	+	24.1286i	−0.0112918	+	0.977739i
$610$		0			0
$611$	−16.9288	−	29.3215i	−0.684864	−	1.18622i
$612$		0			0
$613$	14.2967	−	24.7625i	0.577437	−	1.00015i	−0.418336	−	0.908293i	$-0.637386\pi$
$613$	14.2967	−	24.7625i	0.577437	−	1.00015i	0.995772	−	0.0918571i	$-0.0292803\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−31.1625			−1.25456			−0.627278	−	0.778796i	$-0.715831\pi$
$617$	−31.1625			−1.25456			−0.627278	+	0.778796i	$0.715831\pi$
$618$		0			0
$619$	4.48852	−	7.77435i	0.180409	−	0.312477i	−0.761611	−	0.648035i	$-0.775591\pi$
$619$	4.48852	−	7.77435i	0.180409	−	0.312477i	0.942020	+	0.335557i	$0.108925\pi$
$620$		0			0
$621$	1.10465	+	1.91330i	0.0443279	+	0.0767781i
$622$		0			0
$623$	−8.96138	−	5.31277i	−0.359030	−	0.212852i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	5.70836	−	9.88716i	0.227970	−	0.394855i
$628$		0			0
$629$	−9.21890			−0.367582
$630$		0			0
$631$	−23.3961			−0.931383			−0.465691	−	0.884947i	$-0.654194\pi$
$631$	−23.3961			−0.931383			−0.465691	+	0.884947i	$0.654194\pi$
$632$		0			0
$633$	1.49972	−	2.59759i	0.0596086	−	0.103245i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	11.6788	−	19.1907i	0.462732	−	0.760363i
$638$		0			0
$639$	2.81552	+	4.87663i	0.111380	+	0.192917i
$640$		0			0
$641$	5.76625	−	9.98743i	0.227753	−	0.394480i	−0.729389	−	0.684099i	$-0.760195\pi$
$641$	5.76625	−	9.98743i	0.227753	−	0.394480i	0.957142	+	0.289620i	$0.0935288\pi$
$642$		0			0
$643$	34.3755			1.35564			0.677819	−	0.735229i	$-0.262925\pi$
$643$	34.3755			1.35564			0.677819	+	0.735229i	$0.262925\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12.4849	−	21.6244i	0.490831	−	0.850144i	−0.509113	−	0.860699i	$-0.670027\pi$
$647$	12.4849	−	21.6244i	0.490831	−	0.850144i	0.999944	+	0.0105554i	$0.00335995\pi$
$648$		0			0
$649$	−9.53355	−	16.5126i	−0.374225	−	0.648176i
$650$		0			0
$651$	16.8836	+	10.0095i	0.661722	+	0.392303i
$652$		0			0
$653$	13.8916	+	24.0610i	0.543621	+	0.941579i	0.998692	+	0.0511243i	$0.0162805\pi$
$653$	13.8916	+	24.0610i	0.543621	+	0.941579i	−0.455071	+	0.890455i	$0.650386\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−11.4445			−0.446494
$658$		0			0
$659$	−39.1662			−1.52570			−0.762850	−	0.646575i	$-0.776201\pi$
$659$	−39.1662			−1.52570			−0.762850	+	0.646575i	$0.776201\pi$
$660$		0			0
$661$	−7.13885	+	12.3649i	−0.277669	+	0.480937i	−0.970805	−	0.239870i	$-0.922895\pi$
$661$	−7.13885	+	12.3649i	−0.277669	+	0.480937i	0.693136	+	0.720807i	$0.256229\pi$
$662$		0			0
$663$	−5.79730	−	10.0412i	−0.225148	−	0.389969i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−10.0747	−	17.4500i	−0.390096	−	0.675666i
$668$		0			0
$669$	−3.05924	+	5.29876i	−0.118277	+	0.204862i
$670$		0			0
$671$	−29.6533			−1.14475
$672$		0			0
$673$	19.5978			0.755439			0.377719	−	0.925920i	$-0.376708\pi$
$673$	19.5978			0.755439			0.377719	+	0.925920i	$0.376708\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−0.0700638	−	0.121354i	−0.00269277	−	0.00466402i	0.864676	−	0.502330i	$-0.167524\pi$
$677$	−0.0700638	−	0.121354i	−0.00269277	−	0.00466402i	−0.867369	+	0.497666i	$0.834190\pi$
$678$		0			0
$679$	−11.9116	+	6.69493i	−0.457124	+	0.256928i
$680$		0			0
$681$	−3.05537	−	5.29205i	−0.117082	−	0.202792i
$682$		0			0
$683$	−12.1708	+	21.0805i	−0.465704	+	0.806623i	−0.999233	−	0.0391587i	$-0.987532\pi$
$683$	−12.1708	+	21.0805i	−0.465704	+	0.806623i	0.533529	+	0.845782i	$0.320866\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−19.1147			−0.729273
$688$		0			0
$689$	−8.67075	+	15.0182i	−0.330329	+	0.572147i
$690$		0			0
$691$	2.82420	+	4.89166i	0.107438	+	0.186088i	0.914732	−	0.404062i	$-0.132402\pi$
$691$	2.82420	+	4.89166i	0.107438	+	0.186088i	−0.807294	+	0.590150i	$0.799069\pi$
$692$		0			0
$693$	4.95459	−	2.78475i	0.188209	−	0.105784i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−11.1062	+	19.2364i	−0.420675	+	0.728631i
$698$		0			0
$699$	8.90189			0.336700
$700$		0			0
$701$	−13.4269			−0.507126			−0.253563	−	0.967319i	$-0.581603\pi$
$701$	−13.4269			−0.507126			−0.253563	+	0.967319i	$0.581603\pi$
$702$		0			0
$703$	6.78066	−	11.7445i	0.255738	−	0.442951i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.0498343	+	4.31506i	−0.00187421	+	0.162285i
$708$		0			0
$709$	−7.42900	−	12.8674i	−0.279002	−	0.483246i	0.692135	−	0.721768i	$-0.256670\pi$
$709$	−7.42900	−	12.8674i	−0.279002	−	0.483246i	−0.971137	+	0.238522i	$0.923337\pi$
$710$		0			0
$711$	−7.65543	+	13.2596i	−0.287101	+	0.497273i
$712$		0			0
$713$	−16.3898			−0.613803
$714$		0			0
$715$		0			0
$716$		0			0
$717$	10.2138	−	17.6909i	0.381442	−	0.660677i
$718$		0			0
$719$	23.4746	+	40.6592i	0.875455	+	1.51633i	0.856277	+	0.516516i	$0.172771\pi$
$719$	23.4746	+	40.6592i	0.875455	+	1.51633i	0.0191777	+	0.999816i	$0.493895\pi$
$720$		0			0
$721$	4.65356	+	2.75887i	0.173308	+	0.102746i
$722$		0			0
$723$	9.12759	+	15.8095i	0.339459	+	0.587960i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−15.3550			−0.569487			−0.284744	−	0.958604i	$-0.591908\pi$
$727$	−15.3550			−0.569487			−0.284744	+	0.958604i	$0.591908\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	9.83510	−	17.0349i	0.363764	−	0.630058i
$732$		0			0
$733$	−25.0642	−	43.4125i	−0.925769	−	1.60348i	−0.790320	−	0.612694i	$-0.790086\pi$
$733$	−25.0642	−	43.4125i	−0.925769	−	1.60348i	−0.135449	−	0.990784i	$-0.543248\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.0175690	−	0.0304305i	−0.000647164	−	0.00112092i
$738$		0			0
$739$	9.99972	−	17.3200i	0.367846	−	0.637127i	−0.621383	−	0.783507i	$-0.713429\pi$
$739$	9.99972	−	17.3200i	0.367846	−	0.637127i	0.989228	+	0.146380i	$0.0467621\pi$
$740$		0			0
$741$	17.0561			0.626570
$742$		0			0
$743$	28.2183			1.03523			0.517615	−	0.855613i	$-0.326820\pi$
$743$	28.2183			1.03523			0.517615	+	0.855613i	$0.326820\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	7.01570	+	12.1516i	0.256691	+	0.444602i
$748$		0			0
$749$	13.7557	+	8.15511i	0.502623	+	0.297981i
$750$		0			0
$751$	0.455250	+	0.788516i	0.0166123	+	0.0287734i	0.874212	−	0.485544i	$-0.161379\pi$
$751$	0.455250	+	0.788516i	0.0166123	+	0.0287734i	−0.857600	+	0.514318i	$0.828045\pi$
$752$		0			0
$753$	7.28151	−	12.6120i	0.265353	−	0.459605i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−27.3441			−0.993839			−0.496920	−	0.867797i	$-0.665536\pi$
$757$	−27.3441			−0.993839			−0.496920	+	0.867797i	$0.665536\pi$
$758$		0			0
$759$	−2.37298	+	4.11012i	−0.0861337	+	0.149188i
$760$		0			0
$761$	5.94922	+	10.3043i	0.215659	+	0.373532i	0.953476	−	0.301468i	$-0.0974767\pi$
$761$	5.94922	+	10.3043i	0.215659	+	0.373532i	−0.737817	+	0.675001i	$0.764143\pi$
$762$		0			0
$763$	−0.0975384	+	8.44567i	−0.00353113	+	0.305754i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	14.2427	−	24.6691i	0.514274	−	0.890749i
$768$		0			0
$769$	−1.97760			−0.0713140			−0.0356570	−	0.999364i	$-0.511352\pi$
$769$	−1.97760			−0.0713140			−0.0356570	+	0.999364i	$0.511352\pi$
$770$		0			0
$771$	16.2183			0.584089
$772$		0			0
$773$	16.2842	−	28.2051i	0.585703	−	1.01447i	−0.409084	−	0.912497i	$-0.634152\pi$
$773$	16.2842	−	28.2051i	0.585703	−	1.01447i	0.994787	−	0.101971i	$-0.0325149\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	5.88531	−	3.30786i	0.211134	−	0.118669i
$778$		0			0
$779$	−16.3375	−	28.2974i	−0.585353	−	1.01386i
$780$		0			0
$781$	−6.04826	+	10.4759i	−0.216424	+	0.374857i
$782$		0			0
$783$	−9.12035			−0.325935
$784$		0			0
$785$		0			0
$786$		0			0
$787$	9.27040	−	16.0568i	0.330454	−	0.572363i	−0.652147	−	0.758093i	$-0.726131\pi$
$787$	9.27040	−	16.0568i	0.330454	−	0.572363i	0.982601	+	0.185730i	$0.0594648\pi$
$788$		0			0
$789$	−12.8714	−	22.2939i	−0.458234	−	0.793684i
$790$		0			0
$791$	2.54497	−	1.43041i	0.0904888	−	0.0508595i
$792$		0			0
$793$	−22.1503	−	38.3655i	−0.786582	−	1.36240i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	40.8182			1.44586			0.722928	−	0.690924i	$-0.242796\pi$
$797$	40.8182			1.44586			0.722928	+	0.690924i	$0.242796\pi$
$798$		0			0
$799$	38.1147			1.34840
$800$		0			0
$801$	1.96879	−	3.41005i	0.0695638	−	0.120488i
$802$		0			0
$803$	−12.2925	−	21.2912i	−0.433793	−	0.751351i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	12.7546	+	22.0916i	0.448984	+	0.777662i
$808$		0			0
$809$	14.2270	−	24.6419i	0.500195	−	0.866362i	−0.499805	−	0.866138i	$-0.666595\pi$
$809$	14.2270	−	24.6419i	0.500195	−	0.866362i	1.00000		0.000224716i	$-7.15293e-5\pi$
$810$		0			0
$811$	−39.2740			−1.37910			−0.689548	−	0.724240i	$-0.742191\pi$
$811$	−39.2740			−1.37910			−0.689548	+	0.724240i	$0.742191\pi$
$812$		0			0
$813$	4.07016			0.142747
$814$		0			0
$815$		0			0
$816$		0			0
$817$	14.4678	+	25.0589i	0.506163	+	0.876701i
$818$		0			0
$819$	7.30389	+	4.33013i	0.255219	+	0.151307i
$820$		0			0
$821$	−17.5200	−	30.3454i	−0.611451	−	1.05906i	−0.990996	−	0.133890i	$-0.957253\pi$
$821$	−17.5200	−	30.3454i	−0.611451	−	1.05906i	0.379546	−	0.925173i	$-0.376080\pi$
$822$		0			0
$823$	−27.7632	+	48.0872i	−0.967763	+	1.67622i	−0.265763	+	0.964038i	$0.585624\pi$
$823$	−27.7632	+	48.0872i	−0.967763	+	1.67622i	−0.702000	+	0.712177i	$0.747710\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	6.07933			0.211399			0.105700	−	0.994398i	$-0.466292\pi$
$827$	6.07933			0.211399			0.105700	+	0.994398i	$0.466292\pi$
$828$		0			0
$829$	−1.06456	+	1.84388i	−0.0369738	+	0.0640405i	−0.883920	−	0.467638i	$-0.845105\pi$
$829$	−1.06456	+	1.84388i	−0.0369738	+	0.0640405i	0.846946	+	0.531678i	$0.178438\pi$
$830$		0			0
$831$	6.54626	+	11.3384i	0.227087	+	0.393326i
$832$		0			0
$833$	12.1357	+	22.1878i	0.420477	+	0.768761i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−3.70929	+	6.42468i	−0.128212	+	0.222069i
$838$		0			0
$839$	−33.0636			−1.14148			−0.570740	−	0.821131i	$-0.693344\pi$
$839$	−33.0636			−1.14148			−0.570740	+	0.821131i	$0.693344\pi$
$840$		0			0
$841$	54.1807			1.86830
$842$		0			0
$843$	−9.79881	+	16.9720i	−0.337489	+	0.584548i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−14.5321	−	8.61536i	−0.499327	−	0.296027i
$848$		0			0
$849$	5.23167	+	9.06151i	0.179550	+	0.310990i
$850$		0			0
$851$	−2.81874	+	4.88220i	−0.0966252	+	0.167360i
$852$		0			0
$853$	−15.3223			−0.524627			−0.262313	−	0.964983i	$-0.584485\pi$
$853$	−15.3223			−0.524627			−0.262313	+	0.964983i	$0.584485\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.17028	−	2.02698i	0.0399760	−	0.0692404i	−0.845345	−	0.534221i	$-0.820605\pi$
$857$	1.17028	−	2.02698i	0.0399760	−	0.0692404i	0.885321	+	0.464980i	$0.153939\pi$
$858$		0			0
$859$	−27.7053	−	47.9869i	−0.945292	−	1.63729i	−0.755166	−	0.655534i	$-0.772444\pi$
$859$	−27.7053	−	47.9869i	−0.945292	−	1.63729i	−0.190126	−	0.981760i	$-0.560890\pi$
$860$		0			0
$861$	0.187849	−	16.2655i	0.00640187	−	0.554326i
$862$		0			0
$863$	−5.12543	−	8.87751i	−0.174472	−	0.302194i	0.765507	−	0.643428i	$-0.222488\pi$
$863$	−5.12543	−	8.87751i	−0.174472	−	0.302194i	−0.939978	+	0.341234i	$0.889155\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−3.94751			−0.134064
$868$		0			0
$869$	−32.8905			−1.11573
$870$		0			0
$871$	0.0262474	−	0.0454618i	0.000889359	−	0.00154041i
$872$		0			0
$873$	−2.58227	−	4.47262i	−0.0873966	−	0.151375i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	4.15005	+	7.18810i	0.140137	+	0.242725i	0.927548	−	0.373704i	$-0.121912\pi$
$877$	4.15005	+	7.18810i	0.140137	+	0.242725i	−0.787411	+	0.616428i	$0.788579\pi$
$878$		0			0
$879$	12.3620	−	21.4116i	0.416960	−	0.722196i
$880$		0			0
$881$	−58.0463			−1.95563			−0.977815	−	0.209473i	$-0.932825\pi$
$881$	−58.0463			−1.95563			−0.977815	+	0.209473i	$0.932825\pi$
$882$		0			0
$883$	−13.8439			−0.465885			−0.232942	−	0.972491i	$-0.574835\pi$
$883$	−13.8439			−0.465885			−0.232942	+	0.972491i	$0.574835\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	23.8651	+	41.3356i	0.801313	+	1.38791i	0.918752	+	0.394834i	$0.129198\pi$
$887$	23.8651	+	41.3356i	0.801313	+	1.38791i	−0.117439	+	0.993080i	$0.537469\pi$
$888$		0			0
$889$	−45.3897	+	25.5115i	−1.52232	+	0.855627i
$890$		0			0
$891$	1.07409	+	1.86038i	0.0359834	+	0.0623251i
$892$		0			0
$893$	−28.0341	+	48.5564i	−0.938124	+	1.62488i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−7.09025			−0.236737
$898$		0			0
$899$	33.8300	−	58.5953i	1.12829	−	1.95426i
$900$		0			0
$901$	−9.76101	−	16.9066i	−0.325186	−	0.563239i
$902$		0			0
$903$	−0.166350	+	14.4040i	−0.00553579	+	0.479334i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−5.85728	+	10.1451i	−0.194488	+	0.336863i	−0.946732	−	0.322021i	$-0.895638\pi$
$907$	−5.85728	+	10.1451i	−0.194488	+	0.336863i	0.752245	+	0.658884i	$0.228971\pi$
$908$		0			0
$909$	−1.63105			−0.0540984
$910$		0			0
$911$	−28.6551			−0.949387			−0.474694	−	0.880151i	$-0.657441\pi$
$911$	−28.6551			−0.949387			−0.474694	+	0.880151i	$0.657441\pi$
$912$		0			0
$913$	−15.0710	+	26.1038i	−0.498778	+	0.863908i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	34.4709	+	20.4361i	1.13833	+	0.674860i
$918$		0			0
$919$	12.5925	+	21.8109i	0.415389	+	0.719474i	0.995469	−	0.0950849i	$-0.0303123\pi$
$919$	12.5925	+	21.8109i	0.415389	+	0.719474i	−0.580081	+	0.814559i	$0.696979\pi$
$920$		0			0
$921$	−1.62287	+	2.81089i	−0.0534754	+	0.0926220i
$922$		0			0
$923$	−18.0717			−0.594836
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.02237	+	1.77081i	−0.0335792	+	0.0581609i
$928$		0			0
$929$	0.000361436	0	0.000626026i	1.18583e−5	0	2.05392e-5i	0.866031	−	0.499990i	$-0.166663\pi$
$929$	0.000361436	0	0.000626026i	1.18583e−5	0	2.05392e-5i	−0.866019	+	0.500010i	$0.833330\pi$
$930$		0			0
$931$	−37.1922	−	0.859174i	−1.21893	−	0.0281583i
$932$		0			0
$933$	−6.57653	−	11.3909i	−0.215306	−	0.372921i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	1.23395			0.0403114			0.0201557	−	0.999797i	$-0.493584\pi$
$937$	1.23395			0.0403114			0.0201557	+	0.999797i	$0.493584\pi$
$938$		0			0
$939$	16.0447			0.523601
$940$		0			0
$941$	3.04491	−	5.27393i	0.0992611	−	0.171925i	−0.812118	−	0.583493i	$-0.801685\pi$
$941$	3.04491	−	5.27393i	0.0992611	−	0.171925i	0.911379	+	0.411568i	$0.135019\pi$
$942$		0			0
$943$	6.79156	+	11.7633i	0.221164	+	0.383067i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.43293	−	11.1422i	−0.209042	−	0.362072i	0.742371	−	0.669989i	$-0.233701\pi$
$947$	−6.43293	−	11.1422i	−0.209042	−	0.362072i	−0.951413	+	0.307917i	$0.900368\pi$
$948$		0			0
$949$	18.3644	−	31.8081i	0.596135	−	1.03254i
$950$		0			0
$951$	−19.9430			−0.646697
$952$		0			0
$953$	8.72241			0.282547			0.141273	−	0.989971i	$-0.454880\pi$
$953$	8.72241			0.282547			0.141273	+	0.989971i	$0.454880\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−9.79609	−	16.9673i	−0.316663	−	0.548476i
$958$		0			0
$959$	0.235023	−	20.3502i	0.00758927	−	0.657141i
$960$		0			0
$961$	−12.0177	−	20.8152i	−0.387667	−	0.671458i
$962$		0			0
$963$	−3.02210	+	5.23442i	−0.0973857	+	0.168677i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	29.6333			0.952943			0.476471	−	0.879190i	$-0.341916\pi$
$967$	29.6333			0.952943			0.476471	+	0.879190i	$0.341916\pi$
$968$		0			0
$969$	−9.60034	+	16.6283i	−0.308407	+	0.534177i
$970$		0			0
$971$	5.12543	+	8.87751i	0.164483	+	0.284893i	0.936472	−	0.350744i	$-0.114071\pi$
$971$	5.12543	+	8.87751i	0.164483	+	0.284893i	−0.771989	+	0.635636i	$0.780738\pi$
$972$		0			0
$973$	11.1638	−	6.27466i	0.357895	−	0.201156i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11.9163	+	20.6396i	−0.381236	+	0.660319i	−0.991239	−	0.132079i	$-0.957835\pi$
$977$	−11.9163	+	20.6396i	−0.381236	+	0.660319i	0.610004	+	0.792399i	$0.291168\pi$
$978$		0			0
$979$	8.45865			0.270340
$980$		0			0
$981$	−3.19238			−0.101925
$982$		0			0
$983$	23.6317	−	40.9314i	0.753736	−	1.30551i	−0.192265	−	0.981343i	$-0.561583\pi$
$983$	23.6317	−	40.9314i	0.753736	−	1.30551i	0.946000	−	0.324165i	$-0.105083\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−24.3323	+	13.6761i	−0.774506	+	0.435314i
$988$		0			0
$989$	−6.01429	−	10.4171i	−0.191243	−	0.331243i
$990$		0			0
$991$	21.2833	−	36.8638i	0.676086	−	1.17102i	−0.300064	−	0.953919i	$-0.597008\pi$
$991$	21.2833	−	36.8638i	0.676086	−	1.17102i	0.976150	−	0.217097i	$-0.0696587\pi$
$992$		0			0
$993$	−4.82211			−0.153025
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−16.1572	+	27.9851i	−0.511704	+	0.886297i	0.488204	+	0.872730i	$0.337652\pi$
$997$	−16.1572	+	27.9851i	−0.511704	+	0.886297i	−0.999908	+	0.0135678i	$0.995681\pi$
$998$		0			0
$999$	1.27586	+	2.20985i	0.0403664	+	0.0699166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.q.l.1201.1		8
5.2	odd	4		420.2.bb.a.109.7	yes	16
5.3	odd	4		420.2.bb.a.109.1	✓	16
5.4	even	2		2100.2.q.m.1201.4		8
7.2	even	3	inner	2100.2.q.l.1801.1		8
15.2	even	4		1260.2.bm.c.109.4		16
15.8	even	4		1260.2.bm.c.109.8		16
20.3	even	4		1680.2.di.e.529.5		16
20.7	even	4		1680.2.di.e.529.3		16
35.2	odd	12		420.2.bb.a.289.1	yes	16
35.3	even	12		2940.2.k.g.589.1		8
35.9	even	6		2100.2.q.m.1801.4		8
35.12	even	12		2940.2.bb.i.1549.8		16
35.13	even	4		2940.2.bb.i.949.8		16
35.17	even	12		2940.2.k.g.589.5		8
35.18	odd	12		2940.2.k.f.589.8		8
35.23	odd	12		420.2.bb.a.289.7	yes	16
35.27	even	4		2940.2.bb.i.949.2		16
35.32	odd	12		2940.2.k.f.589.4		8
35.33	even	12		2940.2.bb.i.1549.2		16
105.2	even	12		1260.2.bm.c.289.8		16
105.23	even	12		1260.2.bm.c.289.4		16
140.23	even	12		1680.2.di.e.289.3		16
140.107	even	12		1680.2.di.e.289.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bb.a.109.1	✓	16	5.3	odd	4
420.2.bb.a.109.7	yes	16	5.2	odd	4
420.2.bb.a.289.1	yes	16	35.2	odd	12
420.2.bb.a.289.7	yes	16	35.23	odd	12
1260.2.bm.c.109.4		16	15.2	even	4
1260.2.bm.c.109.8		16	15.8	even	4
1260.2.bm.c.289.4		16	105.23	even	12
1260.2.bm.c.289.8		16	105.2	even	12
1680.2.di.e.289.3		16	140.23	even	12
1680.2.di.e.289.5		16	140.107	even	12
1680.2.di.e.529.3		16	20.7	even	4
1680.2.di.e.529.5		16	20.3	even	4
2100.2.q.l.1201.1		8	1.1	even	1	trivial
2100.2.q.l.1801.1		8	7.2	even	3	inner
2100.2.q.m.1201.4		8	5.4	even	2
2100.2.q.m.1801.4		8	35.9	even	6
2940.2.k.f.589.4		8	35.32	odd	12
2940.2.k.f.589.8		8	35.18	odd	12
2940.2.k.g.589.1		8	35.3	even	12
2940.2.k.g.589.5		8	35.17	even	12
2940.2.bb.i.949.2		16	35.27	even	4
2940.2.bb.i.949.8		16	35.13	even	4
2940.2.bb.i.1549.2		16	35.33	even	12
2940.2.bb.i.1549.8		16	35.12	even	12

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-2.30641 + 1.29633i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-2.30641 + 1.29633i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.07409 - 1.86038i) q^{11} +3.20929 q^{13} +(-1.80641 + 3.12880i) q^{17} +(-2.65730 - 4.60257i) q^{19} +(0.0305535 - 2.64557i) q^{21} +(1.10465 + 1.91330i) q^{23} +1.00000 q^{27} -9.12035 q^{29} +(-3.70929 + 6.42468i) q^{31} +(1.07409 + 1.86038i) q^{33} +(1.27586 + 2.20985i) q^{37} +(-1.60465 + 2.77933i) q^{39} +6.14818 q^{41} -5.44455 q^{43} +(-5.27492 - 9.13644i) q^{47} +(3.63907 - 5.97973i) q^{49} +(-1.80641 - 3.12880i) q^{51} +(-2.70177 + 4.67960i) q^{53} +5.31459 q^{57} +(4.43796 - 7.68677i) q^{59} +(-6.90194 - 11.9545i) q^{61} +(2.27586 + 1.34925i) q^{63} +(0.00817856 - 0.0141657i) q^{67} -2.20929 q^{69} -5.63105 q^{71} +(5.72227 - 9.91127i) q^{73} +(-0.0656346 + 5.68318i) q^{77} +(-7.65543 - 13.2596i) q^{79} +(-0.500000 + 0.866025i) q^{81} -14.0314 q^{83} +(4.56017 - 7.89845i) q^{87} +(1.96879 + 3.41005i) q^{89} +(-7.40194 + 4.16029i) q^{91} +(-3.70929 - 6.42468i) q^{93} +5.16454 q^{97} -2.14818 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9	\( 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{17} - 4 q^{19} - 2 q^{21} - 6 q^{23} + 8 q^{27} - 12 q^{29} - 4 q^{33} - 4 q^{37} + 2 q^{39} + 24 q^{41} + 32 q^{43} - 2 q^{47} - 4 q^{49} + 2 q^{51} - 20 q^{53} + 8 q^{57} + 14 q^{59} - 16 q^{61} + 4 q^{63} - 18 q^{67} + 12 q^{69} - 28 q^{71} + 8 q^{73} + 10 q^{77} + 8 q^{79} - 4 q^{81} - 20 q^{83} + 6 q^{87} + 8 q^{89} - 20 q^{91} - 20 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^13 + 2 * q^17 - 4 * q^19 - 2 * q^21 - 6 * q^23 + 8 * q^27 - 12 * q^29 - 4 * q^33 - 4 * q^37 + 2 * q^39 + 24 * q^41 + 32 * q^43 - 2 * q^47 - 4 * q^49 + 2 * q^51 - 20 * q^53 + 8 * q^57 + 14 * q^59 - 16 * q^61 + 4 * q^63 - 18 * q^67 + 12 * q^69 - 28 * q^71 + 8 * q^73 + 10 * q^77 + 8 * q^79 - 4 * q^81 - 20 * q^83 + 6 * q^87 + 8 * q^89 - 20 * q^91 - 20 * q^97 + 8 * q^99

Introduction

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