LMFDB - Embedded newform 2940.2.f.a.1469.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2940,2,Mod(1469,2940)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2940, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2940.1469"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2940.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1469.24
Character	$\chi$	$=$	2940.1469
Dual form			2940.2.f.a.1469.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.917271 + 1.46922i) q^{3} +(0.536879 + 2.17066i) q^{5} +(-1.31723 + 2.69535i) q^{9} +0.915904i q^{11} -4.31153 q^{13} +(-2.69672 + 2.77988i) q^{15} +0.537062i q^{17} -1.30351i q^{19} +7.98961 q^{23} +(-4.42352 + 2.33076i) q^{25} +(-5.16832 + 0.537062i) q^{27} -3.46154i q^{29} +6.42144i q^{31} +(-1.34567 + 0.840132i) q^{33} +5.04345i q^{37} +(-3.95484 - 6.33460i) q^{39} -9.89809 q^{41} +8.22096i q^{43} +(-6.55788 - 1.41218i) q^{45} +4.34132i q^{47} +(-0.789063 + 0.492631i) q^{51} +1.96985 q^{53} +(-1.98812 + 0.491730i) q^{55} +(1.91514 - 1.19567i) q^{57} -14.3073 q^{59} -9.68095i q^{61} +(-2.31477 - 9.35886i) q^{65} -12.1070i q^{67} +(7.32863 + 11.7385i) q^{69} -0.943900i q^{71} -10.2242 q^{73} +(-7.48198 - 4.36120i) q^{75} -11.4363 q^{79} +(-5.52981 - 7.10079i) q^{81} +9.35240i q^{83} +(-1.16578 + 0.288337i) q^{85} +(5.08577 - 3.17517i) q^{87} +1.74901 q^{89} +(-9.43453 + 5.89020i) q^{93} +(2.82947 - 0.699827i) q^{95} +10.7844 q^{97} +(-2.46868 - 1.20646i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{15} - 12 q^{25} - 48 q^{39} + 20 q^{51} + 56 q^{79} + 40 q^{81} - 4 q^{85} - 28 q^{99}+O(q^{100}) $ 32 * q + 2 * q^15 - 12 * q^25 - 48 * q^39 + 20 * q^51 + 56 * q^79 + 40 * q^81 - 4 * q^85 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$.

$n$	$1081$	$1177$	$1471$	$1961$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.917271	+	1.46922i	0.529586	+	0.848256i
$3$	0.917271	+	1.46922i	0.529586	+	0.848256i
$4$		0			0
$5$	0.536879	+	2.17066i	0.240100	+	0.970748i
$5$	0.536879	+	2.17066i	0.240100	+	0.970748i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.31723	+	2.69535i	−0.439076	+	0.898450i
$10$		0			0
$11$			0.915904i			0.276155i	0.990421	+	0.138078i	$0.0440924\pi$
$11$			0.915904i			0.276155i	−0.990421	+	0.138078i	$0.955908\pi$
$12$		0			0
$13$	−4.31153			−1.19580			−0.597902	−	0.801569i	$-0.703999\pi$
$13$	−4.31153			−1.19580			−0.597902	+	0.801569i	$0.703999\pi$
$14$		0			0
$15$	−2.69672	+	2.77988i	−0.696289	+	0.717761i
$16$		0			0
$17$			0.537062i			0.130257i	0.997877	+	0.0651283i	$0.0207457\pi$
$17$			0.537062i			0.130257i	−0.997877	+	0.0651283i	$0.979254\pi$
$18$		0			0
$19$		−	1.30351i		−	0.299045i	−0.988758	−	0.149523i	$-0.952226\pi$
$19$		−	1.30351i		−	0.299045i	0.988758	−	0.149523i	$-0.0477737\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7.98961			1.66595			0.832974	−	0.553312i	$-0.186636\pi$
$23$	7.98961			1.66595			0.832974	+	0.553312i	$0.186636\pi$
$24$		0			0
$25$	−4.42352	+	2.33076i	−0.884704	+	0.466153i
$26$		0			0
$27$	−5.16832	+	0.537062i	−0.994644	+	0.103358i
$28$		0			0
$29$		−	3.46154i		−	0.642791i	−0.946945	−	0.321396i	$-0.895848\pi$
$29$		−	3.46154i		−	0.642791i	0.946945	−	0.321396i	$-0.104152\pi$
$30$		0			0
$31$			6.42144i			1.15333i	0.816982	+	0.576663i	$0.195645\pi$
$31$			6.42144i			1.15333i	−0.816982	+	0.576663i	$0.804355\pi$
$32$		0			0
$33$	−1.34567	+	0.840132i	−0.234251	+	0.146248i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			5.04345i			0.829137i	0.910018	+	0.414569i	$0.136068\pi$
$37$			5.04345i			0.829137i	−0.910018	+	0.414569i	$0.863932\pi$
$38$		0			0
$39$	−3.95484	−	6.33460i	−0.633281	−	1.01435i
$40$		0			0
$41$	−9.89809			−1.54582			−0.772911	−	0.634515i	$-0.781200\pi$
$41$	−9.89809			−1.54582			−0.772911	+	0.634515i	$0.781200\pi$
$42$		0			0
$43$			8.22096i			1.25369i	0.779146	+	0.626843i	$0.215653\pi$
$43$			8.22096i			1.25369i	−0.779146	+	0.626843i	$0.784347\pi$
$44$		0			0
$45$	−6.55788	−	1.41218i	−0.977591	−	0.210515i
$46$		0			0
$47$			4.34132i			0.633246i	0.948551	+	0.316623i	$0.102549\pi$
$47$			4.34132i			0.633246i	−0.948551	+	0.316623i	$0.897451\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.789063	+	0.492631i	−0.110491	+	0.0689821i
$52$		0			0
$53$	1.96985			0.270580			0.135290	−	0.990806i	$-0.456803\pi$
$53$	1.96985			0.270580			0.135290	+	0.990806i	$0.456803\pi$
$54$		0			0
$55$	−1.98812	+	0.491730i	−0.268077	+	0.0663048i
$56$		0			0
$57$	1.91514	−	1.19567i	0.253667	−	0.158370i
$58$		0			0
$59$	−14.3073			−1.86265			−0.931323	−	0.364195i	$-0.881344\pi$
$59$	−14.3073			−1.86265			−0.931323	+	0.364195i	$0.881344\pi$
$60$		0			0
$61$		−	9.68095i		−	1.23952i	−0.784792	−	0.619759i	$-0.787230\pi$
$61$		−	9.68095i		−	1.23952i	0.784792	−	0.619759i	$-0.212770\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.31477	−	9.35886i	−0.287112	−	1.16082i
$66$		0			0
$67$		−	12.1070i		−	1.47910i	−0.673100	−	0.739551i	$-0.735038\pi$
$67$		−	12.1070i		−	1.47910i	0.673100	−	0.739551i	$-0.264962\pi$
$68$		0			0
$69$	7.32863	+	11.7385i	0.882264	+	1.41315i
$70$		0			0
$71$		−	0.943900i		−	0.112020i	−0.998430	−	0.0560102i	$-0.982162\pi$
$71$		−	0.943900i		−	0.112020i	0.998430	−	0.0560102i	$-0.0178379\pi$
$72$		0			0
$73$	−10.2242			−1.19665			−0.598326	−	0.801253i	$-0.704167\pi$
$73$	−10.2242			−1.19665			−0.598326	+	0.801253i	$0.704167\pi$
$74$		0			0
$75$	−7.48198	−	4.36120i	−0.863944	−	0.503588i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−11.4363			−1.28669			−0.643345	−	0.765577i	$-0.722454\pi$
$79$	−11.4363			−1.28669			−0.643345	+	0.765577i	$0.722454\pi$
$80$		0			0
$81$	−5.52981	−	7.10079i	−0.614424	−	0.788976i
$82$		0			0
$83$			9.35240i			1.02656i	0.858222	+	0.513279i	$0.171570\pi$
$83$			9.35240i			1.02656i	−0.858222	+	0.513279i	$0.828430\pi$
$84$		0			0
$85$	−1.16578	+	0.288337i	−0.126446	+	0.0312746i
$86$		0			0
$87$	5.08577	−	3.17517i	0.545252	−	0.340414i
$88$		0			0
$89$	1.74901			0.185395			0.0926976	−	0.995694i	$-0.470451\pi$
$89$	1.74901			0.185395			0.0926976	+	0.995694i	$0.470451\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−9.43453	+	5.89020i	−0.978315	+	0.610785i
$94$		0			0
$95$	2.82947	−	0.699827i	0.290298	−	0.0718007i
$96$		0			0
$97$	10.7844			1.09499			0.547494	−	0.836809i	$-0.315582\pi$
$97$	10.7844			1.09499			0.547494	+	0.836809i	$0.315582\pi$
$98$		0			0
$99$	−2.46868	−	1.20646i	−0.248112	−	0.121253i
$100$		0			0
$101$	9.84960			0.980072			0.490036	−	0.871702i	$-0.336984\pi$
$101$	9.84960			0.980072			0.490036	+	0.871702i	$0.336984\pi$
$102$		0			0
$103$	2.45793			0.242188			0.121094	−	0.992641i	$-0.461360\pi$
$103$	2.45793			0.242188			0.121094	+	0.992641i	$0.461360\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.49963			0.144975			0.0724873	−	0.997369i	$-0.476906\pi$
$107$	1.49963			0.144975			0.0724873	+	0.997369i	$0.476906\pi$
$108$		0			0
$109$	−3.86452			−0.370154			−0.185077	−	0.982724i	$-0.559253\pi$
$109$	−3.86452			−0.370154			−0.185077	+	0.982724i	$0.559253\pi$
$110$		0			0
$111$	−7.40994	+	4.62620i	−0.703321	+	0.439100i
$112$		0			0
$113$	10.1791			0.957567			0.478783	−	0.877933i	$-0.341078\pi$
$113$	10.1791			0.957567			0.478783	+	0.877933i	$0.341078\pi$
$114$		0			0
$115$	4.28945	+	17.3427i	0.399994	+	1.61722i
$116$		0			0
$117$	5.67927	−	11.6211i	0.525049	−	1.07437i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	10.1611			0.923738
$122$		0			0
$123$	−9.07922	−	14.5425i	−0.818646	−	1.31125i
$124$		0			0
$125$	−7.43419	−	8.35062i	−0.664934	−	0.746902i
$126$		0			0
$127$		−	9.73798i		−	0.864106i	−0.901848	−	0.432053i	$-0.857789\pi$
$127$		−	9.73798i		−	0.864106i	0.901848	−	0.432053i	$-0.142211\pi$
$128$		0			0
$129$	−12.0784	+	7.54085i	−1.06345	+	0.663935i
$130$		0			0
$131$	17.6002			1.53773			0.768867	−	0.639409i	$-0.220821\pi$
$131$	17.6002			1.53773			0.768867	+	0.639409i	$0.220821\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−3.94054	−	10.9303i	−0.339148	−	0.940733i
$136$		0			0
$137$	10.4195			0.890194			0.445097	−	0.895482i	$-0.353169\pi$
$137$	10.4195			0.890194			0.445097	+	0.895482i	$0.353169\pi$
$138$		0			0
$139$			7.09182i			0.601520i	0.953700	+	0.300760i	$0.0972403\pi$
$139$			7.09182i			0.601520i	−0.953700	+	0.300760i	$0.902760\pi$
$140$		0			0
$141$	−6.37836	+	3.98216i	−0.537155	+	0.335359i
$142$		0			0
$143$		−	3.94895i		−	0.330228i
$144$		0			0
$145$	7.51382	−	1.85843i	0.623988	−	0.154334i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			6.26524i			0.513269i	0.966509	+	0.256634i	$0.0826136\pi$
$149$			6.26524i			0.513269i	−0.966509	+	0.256634i	$0.917386\pi$
$150$		0			0
$151$	−17.7116			−1.44135			−0.720673	−	0.693275i	$-0.756167\pi$
$151$	−17.7116			−1.44135			−0.720673	+	0.693275i	$0.756167\pi$
$152$		0			0
$153$	−1.44757	−	0.707433i	−0.117029	−	0.0571926i
$154$		0			0
$155$	−13.9388	+	3.44754i	−1.11959	+	0.276913i
$156$		0			0
$157$	−0.773945			−0.0617676			−0.0308838	−	0.999523i	$-0.509832\pi$
$157$	−0.773945			−0.0617676			−0.0308838	+	0.999523i	$0.509832\pi$
$158$		0			0
$159$	1.80689	+	2.89415i	0.143296	+	0.229521i
$160$		0			0
$161$		0			0
$162$		0			0
$163$		−	6.88703i		−	0.539434i	−0.962940	−	0.269717i	$-0.913070\pi$
$163$		−	6.88703i		−	0.539434i	0.962940	−	0.269717i	$-0.0869302\pi$
$164$		0			0
$165$	−2.54610	−	2.46993i	−0.198214	−	0.192284i
$166$		0			0
$167$		−	9.49709i		−	0.734907i	−0.930042	−	0.367453i	$-0.880230\pi$
$167$		−	9.49709i		−	0.734907i	0.930042	−	0.367453i	$-0.119770\pi$
$168$		0			0
$169$	5.58930			0.429946
$170$		0			0
$171$	3.51341	+	1.71702i	0.268677	+	0.131304i
$172$		0			0
$173$			11.9498i			0.908529i	0.890867	+	0.454264i	$0.150098\pi$
$173$			11.9498i			0.908529i	−0.890867	+	0.454264i	$0.849902\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−13.1236	−	21.0205i	−0.986432	−	1.58000i
$178$		0			0
$179$		−	18.7457i		−	1.40112i	−0.713593	−	0.700561i	$-0.752933\pi$
$179$		−	18.7457i		−	1.40112i	0.713593	−	0.700561i	$-0.247067\pi$
$180$		0			0
$181$			16.1024i			1.19688i	0.801167	+	0.598441i	$0.204213\pi$
$181$			16.1024i			1.19688i	−0.801167	+	0.598441i	$0.795787\pi$
$182$		0			0
$183$	14.2235	−	8.88005i	1.05143	−	0.656432i
$184$		0			0
$185$	−10.9476	+	2.70772i	−0.804884	+	0.199076i
$186$		0			0
$187$	−0.491897			−0.0359711
$188$		0			0
$189$		0			0
$190$		0			0
$191$			17.3181i			1.25309i	0.779385	+	0.626546i	$0.215532\pi$
$191$			17.3181i			1.25309i	−0.779385	+	0.626546i	$0.784468\pi$
$192$		0			0
$193$			15.1303i			1.08911i	0.838727	+	0.544553i	$0.183301\pi$
$193$			15.1303i			1.08911i	−0.838727	+	0.544553i	$0.816699\pi$
$194$		0			0
$195$	11.6270	−	11.9855i	0.832625	−	0.858301i
$196$		0			0
$197$	−18.6287			−1.32724			−0.663619	−	0.748071i	$-0.730980\pi$
$197$	−18.6287			−1.32724			−0.663619	+	0.748071i	$0.730980\pi$
$198$		0			0
$199$			10.0492i			0.712366i	0.934416	+	0.356183i	$0.115922\pi$
$199$			10.0492i			0.712366i	−0.934416	+	0.356183i	$0.884078\pi$
$200$		0			0
$201$	17.7878	−	11.1054i	1.25466	−	0.783313i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−5.31408	−	21.4854i	−0.371151	−	1.50060i
$206$		0			0
$207$	−10.5241	+	21.5348i	−0.731479	+	1.49677i
$208$		0			0
$209$	1.19389			0.0825830
$210$		0			0
$211$	−1.68592			−0.116064			−0.0580319	−	0.998315i	$-0.518483\pi$
$211$	−1.68592			−0.116064			−0.0580319	+	0.998315i	$0.518483\pi$
$212$		0			0
$213$	1.38680	−	0.865812i	0.0950219	−	0.0593244i
$214$		0			0
$215$	−17.8449	+	4.41366i	−1.21701	+	0.301009i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−9.37836	−	15.0216i	−0.633731	−	1.01507i
$220$		0			0
$221$		−	2.31556i		−	0.155761i
$222$		0			0
$223$	−14.2095			−0.951541			−0.475770	−	0.879570i	$-0.657831\pi$
$223$	−14.2095			−0.951541			−0.475770	+	0.879570i	$0.657831\pi$
$224$		0			0
$225$	−0.455428	−	14.9931i	−0.0303619	−	0.999539i
$226$		0			0
$227$		−	0.681753i		−	0.0452496i	−0.999744	−	0.0226248i	$-0.992798\pi$
$227$		−	0.681753i		−	0.0452496i	0.999744	−	0.0226248i	$-0.00720231\pi$
$228$		0			0
$229$		−	2.95734i		−	0.195427i	−0.995215	−	0.0977133i	$-0.968847\pi$
$229$		−	2.95734i		−	0.195427i	0.995215	−	0.0977133i	$-0.0311528\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	26.9371			1.76471			0.882353	−	0.470587i	$-0.155958\pi$
$233$	26.9371			1.76471			0.882353	+	0.470587i	$0.155958\pi$
$234$		0			0
$235$	−9.42352	+	2.33076i	−0.614723	+	0.152042i
$236$		0			0
$237$	−10.4902	−	16.8025i	−0.681413	−	1.09144i
$238$		0			0
$239$		−	17.3461i		−	1.12202i	−0.827808	−	0.561012i	$-0.810412\pi$
$239$		−	17.3461i		−	1.12202i	0.827808	−	0.561012i	$-0.189588\pi$
$240$		0			0
$241$		−	1.52746i		−	0.0983921i	−0.998789	−	0.0491961i	$-0.984334\pi$
$241$		−	1.52746i		−	0.0983921i	0.998789	−	0.0491961i	$-0.0156659\pi$
$242$		0			0
$243$	5.36030	−	14.6379i	0.343863	−	0.939020i
$244$		0			0
$245$		0			0
$246$		0			0
$247$			5.62012i			0.357600i
$248$		0			0
$249$	−13.7408	+	8.57868i	−0.870785	+	0.543652i
$250$		0			0
$251$	6.56268			0.414233			0.207116	−	0.978316i	$-0.433592\pi$
$251$	6.56268			0.414233			0.207116	+	0.978316i	$0.433592\pi$
$252$		0			0
$253$			7.31771i			0.460061i
$254$		0			0
$255$	−1.49296	−	1.44830i	−0.0934931	−	0.0906963i
$256$		0			0
$257$			16.9729i			1.05874i	0.848391	+	0.529370i	$0.177572\pi$
$257$			16.9729i			1.05874i	−0.848391	+	0.529370i	$0.822428\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	9.33005	+	4.55964i	0.577516	+	0.282234i
$262$		0			0
$263$	5.31969			0.328026			0.164013	−	0.986458i	$-0.447556\pi$
$263$	5.31969			0.328026			0.164013	+	0.986458i	$0.447556\pi$
$264$		0			0
$265$	1.05757	+	4.27588i	0.0649662	+	0.262665i
$266$		0			0
$267$	1.60432	+	2.56969i	0.0981828	+	0.157263i
$268$		0			0
$269$	6.55668			0.399768			0.199884	−	0.979820i	$-0.435943\pi$
$269$	6.55668			0.399768			0.199884	+	0.979820i	$0.435943\pi$
$270$		0			0
$271$			5.24431i			0.318569i	0.987233	+	0.159285i	$0.0509187\pi$
$271$			5.24431i			0.318569i	−0.987233	+	0.159285i	$0.949081\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.13476	−	4.05152i	−0.128731	−	0.244316i
$276$		0			0
$277$		−	2.77326i		−	0.166629i	−0.996523	−	0.0833145i	$-0.973449\pi$
$277$		−	2.77326i		−	0.166629i	0.996523	−	0.0833145i	$-0.0265506\pi$
$278$		0			0
$279$	−17.3080	−	8.45851i	−1.03620	−	0.506398i
$280$		0			0
$281$			22.4373i			1.33850i	0.743038	+	0.669250i	$0.233384\pi$
$281$			22.4373i			1.33850i	−0.743038	+	0.669250i	$0.766616\pi$
$282$		0			0
$283$	7.24680			0.430778			0.215389	−	0.976528i	$-0.430898\pi$
$283$	7.24680			0.430778			0.215389	+	0.976528i	$0.430898\pi$
$284$		0			0
$285$	3.62359	+	3.51520i	0.214643	+	0.208222i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	16.7116			0.983033
$290$		0			0
$291$	9.89220	+	15.8447i	0.579891	+	0.928831i
$292$		0			0
$293$			26.1686i			1.52879i	0.644750	+	0.764393i	$0.276961\pi$
$293$			26.1686i			1.52879i	−0.644750	+	0.764393i	$0.723039\pi$
$294$		0			0
$295$	−7.68127	−	31.0562i	−0.447221	−	1.80816i
$296$		0			0
$297$	−0.491897	−	4.73369i	−0.0285428	−	0.274676i
$298$		0			0
$299$	−34.4474			−1.99215
$300$		0			0
$301$		0			0
$302$		0			0
$303$	9.03475	+	14.4712i	0.519033	+	0.831352i
$304$		0			0
$305$	21.0140	−	5.19750i	1.20326	−	0.297608i
$306$		0			0
$307$	22.4144			1.27926			0.639630	−	0.768683i	$-0.279088\pi$
$307$	22.4144			1.27926			0.639630	+	0.768683i	$0.279088\pi$
$308$		0			0
$309$	2.25459	+	3.61125i	0.128259	+	0.205437i
$310$		0			0
$311$	−19.6276			−1.11298			−0.556488	−	0.830855i	$-0.687852\pi$
$311$	−19.6276			−1.11298			−0.556488	+	0.830855i	$0.687852\pi$
$312$		0			0
$313$	−12.8333			−0.725380			−0.362690	−	0.931910i	$-0.618142\pi$
$313$	−12.8333			−0.725380			−0.362690	+	0.931910i	$0.618142\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.9690			0.896908			0.448454	−	0.893806i	$-0.351975\pi$
$317$	15.9690			0.896908			0.448454	+	0.893806i	$0.351975\pi$
$318$		0			0
$319$	3.17044			0.177510
$320$		0			0
$321$	1.37557	+	2.20329i	0.0767766	+	0.122976i
$322$		0			0
$323$	0.700065			0.0389526
$324$		0			0
$325$	19.0722	−	10.0492i	1.05793	−	0.557427i
$326$		0			0
$327$	−3.54481	−	5.67784i	−0.196029	−	0.313985i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−19.6378			−1.07939			−0.539694	−	0.841861i	$-0.681460\pi$
$331$	−19.6378			−1.07939			−0.539694	+	0.841861i	$0.681460\pi$
$332$		0			0
$333$	−13.5938	−	6.64337i	−0.744938	−	0.364055i
$334$		0			0
$335$	26.2801	−	6.49998i	1.43584	−	0.355132i
$336$		0			0
$337$			0.304237i			0.0165729i	0.999966	+	0.00828643i	$0.00263768\pi$
$337$			0.304237i			0.0165729i	−0.999966	+	0.00828643i	$0.997362\pi$
$338$		0			0
$339$	9.33696	+	14.9553i	0.507114	+	0.812262i
$340$		0			0
$341$	−5.88143			−0.318497
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−21.5457	+	22.2101i	−1.15998	+	1.19575i
$346$		0			0
$347$	28.4469			1.52711			0.763556	−	0.645742i	$-0.223452\pi$
$347$	28.4469			1.52711			0.763556	+	0.645742i	$0.223452\pi$
$348$		0			0
$349$		−	13.9719i		−	0.747897i	−0.927450	−	0.373948i	$-0.878004\pi$
$349$		−	13.9719i		−	0.747897i	0.927450	−	0.373948i	$-0.121996\pi$
$350$		0			0
$351$	22.2834	−	2.31556i	1.18940	−	0.123595i
$352$		0			0
$353$			34.6036i			1.84176i	0.389843	+	0.920881i	$0.372529\pi$
$353$			34.6036i			1.84176i	−0.389843	+	0.920881i	$0.627471\pi$
$354$		0			0
$355$	2.04888	−	0.506760i	0.108744	−	0.0268960i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	22.8931i		−	1.20825i	−0.796889	−	0.604126i	$-0.793523\pi$
$359$		−	22.8931i		−	1.20825i	0.796889	−	0.604126i	$-0.206477\pi$
$360$		0			0
$361$	17.3009			0.910572
$362$		0			0
$363$	9.32050	+	14.9289i	0.489199	+	0.783566i
$364$		0			0
$365$	−5.48916	−	22.1933i	−0.287316	−	1.16165i
$366$		0			0
$367$	−28.9997			−1.51377			−0.756887	−	0.653546i	$-0.773281\pi$
$367$	−28.9997			−1.51377			−0.756887	+	0.653546i	$0.773281\pi$
$368$		0			0
$369$	13.0381	−	26.6788i	0.678734	−	1.38884i
$370$		0			0
$371$		0			0
$372$		0			0
$373$			24.0309i			1.24427i	0.782909	+	0.622136i	$0.213735\pi$
$373$			24.0309i			1.24427i	−0.782909	+	0.622136i	$0.786265\pi$
$374$		0			0
$375$	5.44975	−	18.5823i	0.281424	−	0.959583i
$376$		0			0
$377$			14.9245i			0.768652i
$378$		0			0
$379$	−14.0820			−0.723342			−0.361671	−	0.932306i	$-0.617794\pi$
$379$	−14.0820			−0.723342			−0.361671	+	0.932306i	$0.617794\pi$
$380$		0			0
$381$	14.3073	−	8.93236i	0.732983	−	0.457619i
$382$		0			0
$383$			29.4030i			1.50242i	0.660062	+	0.751211i	$0.270530\pi$
$383$			29.4030i			1.50242i	−0.660062	+	0.751211i	$0.729470\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−22.1584	−	10.8289i	−1.12637	−	0.550464i
$388$		0			0
$389$			23.4092i			1.18690i	0.804873	+	0.593448i	$0.202234\pi$
$389$			23.4092i			1.18690i	−0.804873	+	0.593448i	$0.797766\pi$
$390$		0			0
$391$			4.29091i			0.217001i
$392$		0			0
$393$	16.1441	+	25.8586i	0.814363	+	1.30439i
$394$		0			0
$395$	−6.13993	−	24.8244i	−0.308934	−	1.24905i
$396$		0			0
$397$	−11.9378			−0.599140			−0.299570	−	0.954074i	$-0.596843\pi$
$397$	−11.9378			−0.599140			−0.299570	+	0.954074i	$0.596843\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			25.0390i			1.25039i	0.780470	+	0.625193i	$0.214980\pi$
$401$			25.0390i			1.25039i	−0.780470	+	0.625193i	$0.785020\pi$
$402$		0			0
$403$		−	27.6863i		−	1.37915i
$404$		0			0
$405$	12.4445	−	15.8156i	0.618374	−	0.785884i
$406$		0			0
$407$	−4.61931			−0.228971
$408$		0			0
$409$		−	30.1813i		−	1.49237i	−0.665740	−	0.746184i	$-0.731884\pi$
$409$		−	30.1813i		−	1.49237i	0.665740	−	0.746184i	$-0.268116\pi$
$410$		0			0
$411$	9.55746	+	15.3085i	0.471435	+	0.755113i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−20.3009	+	5.02111i	−0.996530	+	0.246476i
$416$		0			0
$417$	−10.4195	+	6.50511i	−0.510243	+	0.318557i
$418$		0			0
$419$	−9.85560			−0.481477			−0.240739	−	0.970590i	$-0.577390\pi$
$419$	−9.85560			−0.481477			−0.240739	+	0.970590i	$0.577390\pi$
$420$		0			0
$421$	−8.16112			−0.397749			−0.198874	−	0.980025i	$-0.563729\pi$
$421$	−8.16112			−0.397749			−0.198874	+	0.980025i	$0.563729\pi$
$422$		0			0
$423$	−11.7014	−	5.71851i	−0.568940	−	0.278044i
$424$		0			0
$425$	−1.25176	−	2.37570i	−0.0607194	−	0.115239i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	5.80188	−	3.62225i	0.280118	−	0.174884i
$430$		0			0
$431$			3.28745i			0.158351i	0.996861	+	0.0791755i	$0.0252288\pi$
$431$			3.28745i			0.158351i	−0.996861	+	0.0791755i	$0.974771\pi$
$432$		0			0
$433$	−31.9717			−1.53646			−0.768231	−	0.640173i	$-0.778863\pi$
$433$	−31.9717			−1.53646			−0.768231	+	0.640173i	$0.778863\pi$
$434$		0			0
$435$	9.62265	+	9.33479i	0.461371	+	0.447569i
$436$		0			0
$437$		−	10.4145i		−	0.498194i
$438$		0			0
$439$			41.7097i			1.99070i	0.0963398	+	0.995349i	$0.469286\pi$
$439$			41.7097i			1.99070i	−0.0963398	+	0.995349i	$0.530714\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	18.9577			0.900708			0.450354	−	0.892850i	$-0.351298\pi$
$443$	18.9577			0.900708			0.450354	+	0.892850i	$0.351298\pi$
$444$		0			0
$445$	0.939010	+	3.79651i	0.0445133	+	0.179972i
$446$		0			0
$447$	−9.20503	+	5.74692i	−0.435383	+	0.271820i
$448$		0			0
$449$			40.0091i			1.88815i	0.329737	+	0.944073i	$0.393040\pi$
$449$			40.0091i			1.88815i	−0.329737	+	0.944073i	$0.606960\pi$
$450$		0			0
$451$		−	9.06570i		−	0.426887i
$452$		0			0
$453$	−16.2463	−	26.0222i	−0.763318	−	1.22263i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			11.3868i			0.532652i	0.963883	+	0.266326i	$0.0858098\pi$
$457$			11.3868i			0.532652i	−0.963883	+	0.266326i	$0.914190\pi$
$458$		0			0
$459$	−0.288435	−	2.77571i	−0.0134630	−	0.129559i
$460$		0			0
$461$	−8.71020			−0.405674			−0.202837	−	0.979212i	$-0.565016\pi$
$461$	−8.71020			−0.405674			−0.202837	+	0.979212i	$0.565016\pi$
$462$		0			0
$463$			16.1154i			0.748944i	0.927238	+	0.374472i	$0.122176\pi$
$463$			16.1154i			0.748944i	−0.927238	+	0.374472i	$0.877824\pi$
$464$		0			0
$465$	−17.8508	−	17.3168i	−0.827812	−	0.803048i
$466$		0			0
$467$		−	9.10472i		−	0.421316i	−0.977560	−	0.210658i	$-0.932439\pi$
$467$		−	9.10472i		−	0.421316i	0.977560	−	0.210658i	$-0.0675607\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.709917	−	1.13710i	−0.0327113	−	0.0523947i
$472$		0			0
$473$	−7.52961			−0.346212
$474$		0			0
$475$	3.03817	+	5.76610i	0.139401	+	0.264567i
$476$		0			0
$477$	−2.59475	+	5.30944i	−0.118805	+	0.243103i
$478$		0			0
$479$	26.4185			1.20709			0.603546	−	0.797328i	$-0.293754\pi$
$479$	26.4185			1.20709			0.603546	+	0.797328i	$0.293754\pi$
$480$		0			0
$481$		−	21.7450i		−	0.991485i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	5.78991	+	23.4092i	0.262906	+	1.06296i
$486$		0			0
$487$			9.16130i			0.415138i	0.978220	+	0.207569i	$0.0665552\pi$
$487$			9.16130i			0.415138i	−0.978220	+	0.207569i	$0.933445\pi$
$488$		0			0
$489$	10.1186	−	6.31727i	0.457578	−	0.285677i
$490$		0			0
$491$		−	33.0800i		−	1.49288i	−0.665453	−	0.746440i	$-0.731761\pi$
$491$		−	33.0800i		−	1.49288i	0.665453	−	0.746440i	$-0.268239\pi$
$492$		0			0
$493$	1.85906			0.0837278
$494$		0			0
$495$	1.29342	−	6.00639i	0.0581349	−	0.269967i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	17.0873			0.764933			0.382466	−	0.923969i	$-0.375075\pi$
$499$	17.0873			0.764933			0.382466	+	0.923969i	$0.375075\pi$
$500$		0			0
$501$	13.9533	−	8.71140i	0.623389	−	0.389197i
$502$		0			0
$503$			21.1753i			0.944158i	0.881556	+	0.472079i	$0.156496\pi$
$503$			21.1753i			0.944158i	−0.881556	+	0.472079i	$0.843504\pi$
$504$		0			0
$505$	5.28804	+	21.3801i	0.235315	+	0.951403i
$506$		0			0
$507$	5.12690	+	8.21192i	0.227694	+	0.364704i
$508$		0			0
$509$	31.1837			1.38219			0.691096	−	0.722763i	$-0.257128\pi$
$509$	31.1837			1.38219			0.691096	+	0.722763i	$0.257128\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	0.700065	+	6.73696i	0.0309086	+	0.297444i
$514$		0			0
$515$	1.31961	+	5.33534i	0.0581491	+	0.235103i
$516$		0			0
$517$	−3.97623			−0.174874
$518$		0			0
$519$	−17.5570	+	10.9612i	−0.770665	+	0.481145i
$520$		0			0
$521$	38.9111			1.70473			0.852363	−	0.522951i	$-0.175169\pi$
$521$	38.9111			1.70473			0.852363	+	0.522951i	$0.175169\pi$
$522$		0			0
$523$	3.76247			0.164521			0.0822606	−	0.996611i	$-0.473786\pi$
$523$	3.76247			0.164521			0.0822606	+	0.996611i	$0.473786\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.44871			−0.150228
$528$		0			0
$529$	40.8338			1.77538
$530$		0			0
$531$	18.8459	−	38.5630i	0.817844	−	1.67349i
$532$		0			0
$533$	42.6759			1.84850
$534$		0			0
$535$	0.805120	+	3.25518i	0.0348084	+	0.140734i
$536$		0			0
$537$	27.5416	−	17.1949i	1.18851	−	0.742015i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	27.2445			1.17133			0.585667	−	0.810552i	$-0.300833\pi$
$541$	27.2445			1.17133			0.585667	+	0.810552i	$0.300833\pi$
$542$		0			0
$543$	−23.6580	+	14.7703i	−1.01526	+	0.633852i
$544$		0			0
$545$	−2.07478	−	8.38856i	−0.0888739	−	0.359326i
$546$		0			0
$547$			13.4516i			0.575148i	0.957758	+	0.287574i	$0.0928487\pi$
$547$			13.4516i			0.575148i	−0.957758	+	0.287574i	$0.907151\pi$
$548$		0			0
$549$	26.0935	+	12.7520i	1.11365	+	0.544243i
$550$		0			0
$551$	−4.51214			−0.192224
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−14.0202	−	13.6007i	−0.595122	−	0.577320i
$556$		0			0
$557$	−37.6174			−1.59390			−0.796950	−	0.604046i	$-0.793554\pi$
$557$	−37.6174			−1.59390			−0.796950	+	0.604046i	$0.793554\pi$
$558$		0			0
$559$		−	35.4449i		−	1.49916i
$560$		0			0
$561$	−0.451203	−	0.722706i	−0.0190498	−	0.0305127i
$562$		0			0
$563$			10.1788i			0.428987i	0.976725	+	0.214494i	$0.0688101\pi$
$563$			10.1788i			0.428987i	−0.976725	+	0.214494i	$0.931190\pi$
$564$		0			0
$565$	5.46493	+	22.0953i	0.229911	+	0.929556i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	0.859912i		−	0.0360494i	−0.999838	−	0.0180247i	$-0.994262\pi$
$569$		−	0.859912i		−	0.0360494i	0.999838	−	0.0180247i	$-0.00573775\pi$
$570$		0			0
$571$	3.43634			0.143806			0.0719032	−	0.997412i	$-0.477093\pi$
$571$	3.43634			0.143806			0.0719032	+	0.997412i	$0.477093\pi$
$572$		0			0
$573$	−25.4441	+	15.8854i	−1.06294	+	0.663620i
$574$		0			0
$575$	−35.3422	+	18.6219i	−1.47387	+	0.776586i
$576$		0			0
$577$	25.6996			1.06989			0.534944	−	0.844888i	$-0.320333\pi$
$577$	25.6996			1.06989			0.534944	+	0.844888i	$0.320333\pi$
$578$		0			0
$579$	−22.2298	+	13.8786i	−0.923840	+	0.576775i
$580$		0			0
$581$		0			0
$582$		0			0
$583$			1.80420i			0.0747222i
$584$		0			0
$585$	28.2745	+	6.08865i	1.16901	+	0.251735i
$586$		0			0
$587$		−	22.5090i		−	0.929048i	−0.885561	−	0.464524i	$-0.846225\pi$
$587$		−	22.5090i		−	0.929048i	0.885561	−	0.464524i	$-0.153775\pi$
$588$		0			0
$589$	8.37041			0.344897
$590$		0			0
$591$	−17.0875	−	27.3697i	−0.702887	−	1.12584i
$592$		0			0
$593$			23.7727i			0.976227i	0.872780	+	0.488114i	$0.162315\pi$
$593$			23.7727i			0.976227i	−0.872780	+	0.488114i	$0.837685\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−14.7644	+	9.21780i	−0.604269	+	0.377259i
$598$		0			0
$599$			43.5310i			1.77863i	0.457296	+	0.889314i	$0.348818\pi$
$599$			43.5310i			1.77863i	−0.457296	+	0.889314i	$0.651182\pi$
$600$		0			0
$601$		−	19.9347i		−	0.813153i	−0.913617	−	0.406577i	$-0.866722\pi$
$601$		−	19.9347i		−	0.813153i	0.913617	−	0.406577i	$-0.133278\pi$
$602$		0			0
$603$	32.6325	+	15.9477i	1.32890	+	0.649439i
$604$		0			0
$605$	5.45529	+	22.0563i	0.221789	+	0.896717i
$606$		0			0
$607$	−10.6333			−0.431590			−0.215795	−	0.976439i	$-0.569234\pi$
$607$	−10.6333			−0.431590			−0.215795	+	0.976439i	$0.569234\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	18.7177i		−	0.757238i
$612$		0			0
$613$		−	15.1344i		−	0.611273i	−0.952148	−	0.305637i	$-0.901131\pi$
$613$		−	15.1344i		−	0.611273i	0.952148	−	0.305637i	$-0.0988693\pi$
$614$		0			0
$615$	26.6923	−	27.5155i	1.07634	−	1.10953i
$616$		0			0
$617$	−7.39865			−0.297858			−0.148929	−	0.988848i	$-0.547583\pi$
$617$	−7.39865			−0.297858			−0.148929	+	0.988848i	$0.547583\pi$
$618$		0			0
$619$		−	18.5279i		−	0.744700i	−0.928092	−	0.372350i	$-0.878552\pi$
$619$		−	18.5279i		−	0.744700i	0.928092	−	0.372350i	$-0.121448\pi$
$620$		0			0
$621$	−41.2929	+	4.29091i	−1.65703	+	0.172188i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	14.1351	−	20.6204i	0.565403	−	0.824814i
$626$		0			0
$627$	1.09512	+	1.75409i	0.0437349	+	0.0700516i
$628$		0			0
$629$	−2.70864			−0.108001
$630$		0			0
$631$	13.1786			0.524632			0.262316	−	0.964982i	$-0.415514\pi$
$631$	13.1786			0.524632			0.262316	+	0.964982i	$0.415514\pi$
$632$		0			0
$633$	−1.54645	−	2.47700i	−0.0614658	−	0.0984518i
$634$		0			0
$635$	21.1378	−	5.22812i	0.838829	−	0.207471i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	2.54414	+	1.24333i	0.100645	+	0.0491855i
$640$		0			0
$641$			14.1322i			0.558189i	0.960264	+	0.279094i	$0.0900343\pi$
$641$			14.1322i			0.558189i	−0.960264	+	0.279094i	$0.909966\pi$
$642$		0			0
$643$	−17.9278			−0.707005			−0.353503	−	0.935434i	$-0.615009\pi$
$643$	−17.9278			−0.707005			−0.353503	+	0.935434i	$0.615009\pi$
$644$		0			0
$645$	−22.8533	−	22.1696i	−0.899846	−	0.872928i
$646$		0			0
$647$			24.0053i			0.943744i	0.881667	+	0.471872i	$0.156422\pi$
$647$			24.0053i			0.943744i	−0.881667	+	0.471872i	$0.843578\pi$
$648$		0			0
$649$		−	13.1041i		−	0.514380i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	28.9489			1.13286			0.566430	−	0.824110i	$-0.308324\pi$
$653$	28.9489			1.13286			0.566430	+	0.824110i	$0.308324\pi$
$654$		0			0
$655$	9.44916	+	38.2040i	0.369209	+	1.49275i
$656$		0			0
$657$	13.4676	−	27.5578i	0.525422	−	1.07513i
$658$		0			0
$659$		−	5.09127i		−	0.198328i	−0.995071	−	0.0991638i	$-0.968383\pi$
$659$		−	5.09127i		−	0.198328i	0.995071	−	0.0991638i	$-0.0316168\pi$
$660$		0			0
$661$		−	29.0717i		−	1.13076i	−0.824832	−	0.565378i	$-0.808730\pi$
$661$		−	29.0717i		−	1.13076i	0.824832	−	0.565378i	$-0.191270\pi$
$662$		0			0
$663$	3.40207	−	2.12399i	0.132125	−	0.0824891i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		−	27.6563i		−	1.07086i
$668$		0			0
$669$	−13.0340	−	20.8770i	−0.503923	−	0.807150i
$670$		0			0
$671$	8.86682			0.342300
$672$		0			0
$673$			8.51862i			0.328369i	0.986430	+	0.164184i	$0.0524992\pi$
$673$			8.51862i			0.328369i	−0.986430	+	0.164184i	$0.947501\pi$
$674$		0			0
$675$	21.6104	−	14.4218i	0.831786	−	0.555097i
$676$		0			0
$677$			18.9765i			0.729325i	0.931140	+	0.364662i	$0.118816\pi$
$677$			18.9765i			0.729325i	−0.931140	+	0.364662i	$0.881184\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.00165	−	0.625352i	0.0383832	−	0.0239636i
$682$		0			0
$683$	−20.9173			−0.800379			−0.400190	−	0.916432i	$-0.631056\pi$
$683$	−20.9173			−0.800379			−0.400190	+	0.916432i	$0.631056\pi$
$684$		0			0
$685$	5.59399	+	22.6171i	0.213735	+	0.864154i
$686$		0			0
$687$	4.34499	−	2.71268i	0.165772	−	0.103495i
$688$		0			0
$689$	−8.49309			−0.323561
$690$		0			0
$691$			34.0523i			1.29541i	0.761891	+	0.647705i	$0.224271\pi$
$691$			34.0523i			1.29541i	−0.761891	+	0.647705i	$0.775729\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−15.3939	+	3.80745i	−0.583924	+	0.144425i
$696$		0			0
$697$		−	5.31588i		−	0.201353i
$698$		0			0
$699$	24.7086	+	39.5766i	0.934565	+	1.49692i
$700$		0			0
$701$		−	18.9758i		−	0.716706i	−0.933586	−	0.358353i	$-0.883338\pi$
$701$		−	18.9758i		−	0.716706i	0.933586	−	0.358353i	$-0.116662\pi$
$702$		0			0
$703$	6.57418			0.247950
$704$		0			0
$705$	−12.0683	−	11.7073i	−0.454520	−	0.440923i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	3.07381			0.115439			0.0577197	−	0.998333i	$-0.481617\pi$
$709$	3.07381			0.115439			0.0577197	+	0.998333i	$0.481617\pi$
$710$		0			0
$711$	15.0643	−	30.8249i	0.564955	−	1.15603i
$712$		0			0
$713$			51.3048i			1.92138i
$714$		0			0
$715$	8.57182	−	2.12011i	0.320568	−	0.0792875i
$716$		0			0
$717$	25.4852	−	15.9110i	0.951764	−	0.594209i
$718$		0			0
$719$	−13.4021			−0.499815			−0.249907	−	0.968270i	$-0.580400\pi$
$719$	−13.4021			−0.499815			−0.249907	+	0.968270i	$0.580400\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	2.24417	−	1.40109i	0.0834617	−	0.0521071i
$724$		0			0
$725$	8.06802	+	15.3122i	0.299639	+	0.568680i
$726$		0			0
$727$	4.88627			0.181222			0.0906109	−	0.995886i	$-0.471118\pi$
$727$	4.88627			0.181222			0.0906109	+	0.995886i	$0.471118\pi$
$728$		0			0
$729$	26.4231	−	5.55142i	0.978634	−	0.205608i
$730$		0			0
$731$	−4.41516			−0.163301
$732$		0			0
$733$	36.9909			1.36629			0.683145	−	0.730283i	$-0.260612\pi$
$733$	36.9909			1.36629			0.683145	+	0.730283i	$0.260612\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	11.0888			0.408462
$738$		0			0
$739$	37.9518			1.39608			0.698040	−	0.716058i	$-0.254056\pi$
$739$	37.9518			1.39608			0.698040	+	0.716058i	$0.254056\pi$
$740$		0			0
$741$	−8.25721	+	5.15517i	−0.303336	+	0.189380i
$742$		0			0
$743$	14.0878			0.516830			0.258415	−	0.966034i	$-0.416800\pi$
$743$	14.0878			0.516830			0.258415	+	0.966034i	$0.416800\pi$
$744$		0			0
$745$	−13.5997	+	3.36368i	−0.498255	+	0.123236i
$746$		0			0
$747$	−25.2080	−	12.3193i	−0.922312	−	0.450738i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−25.7504			−0.939646			−0.469823	−	0.882761i	$-0.655682\pi$
$751$	−25.7504			−0.939646			−0.469823	+	0.882761i	$0.655682\pi$
$752$		0			0
$753$	6.01975	+	9.64204i	0.219372	+	0.351375i
$754$		0			0
$755$	−9.50897	−	38.4458i	−0.346067	−	1.39918i
$756$		0			0
$757$		−	40.3111i		−	1.46513i	−0.680697	−	0.732565i	$-0.738323\pi$
$757$		−	40.3111i		−	1.46513i	0.680697	−	0.732565i	$-0.261677\pi$
$758$		0			0
$759$	−10.7513	+	6.71232i	−0.390249	+	0.243642i
$760$		0			0
$761$	−19.5306			−0.707983			−0.353991	−	0.935249i	$-0.615176\pi$
$761$	−19.5306			−0.707983			−0.353991	+	0.935249i	$0.615176\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.758427	−	3.52198i	0.0274210	−	0.127338i
$766$		0			0
$767$	61.6862			2.22736
$768$		0			0
$769$		−	47.6475i		−	1.71821i	−0.511797	−	0.859107i	$-0.671020\pi$
$769$		−	47.6475i		−	1.71821i	0.511797	−	0.859107i	$-0.328980\pi$
$770$		0			0
$771$	−24.9370	+	15.5687i	−0.898083	+	0.560695i
$772$		0			0
$773$		−	21.1247i		−	0.759803i	−0.925027	−	0.379901i	$-0.875958\pi$
$773$		−	21.1247i		−	0.759803i	0.925027	−	0.379901i	$-0.124042\pi$
$774$		0			0
$775$	−14.9669	−	28.4054i	−0.537626	−	1.02035i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			12.9022i			0.462271i
$780$		0			0
$781$	0.864522			0.0309350
$782$		0			0
$783$	1.85906	+	17.8903i	0.0664373	+	0.639349i
$784$		0			0
$785$	−0.415515	−	1.67997i	−0.0148304	−	0.0599608i
$786$		0			0
$787$	6.54661			0.233361			0.116681	−	0.993169i	$-0.462775\pi$
$787$	6.54661			0.233361			0.116681	+	0.993169i	$0.462775\pi$
$788$		0			0
$789$	4.87959	+	7.81581i	0.173718	+	0.278250i
$790$		0			0
$791$		0			0
$792$		0			0
$793$			41.7397i			1.48222i
$794$		0			0
$795$	−5.31214	+	5.47595i	−0.188402	+	0.194212i
$796$		0			0
$797$		−	6.50728i		−	0.230500i	−0.993337	−	0.115250i	$-0.963233\pi$
$797$		−	6.50728i		−	0.230500i	0.993337	−	0.115250i	$-0.0367669\pi$
$798$		0			0
$799$	−2.33156			−0.0824845
$800$		0			0
$801$	−2.30385	+	4.71421i	−0.0814027	+	0.166568i
$802$		0			0
$803$		−	9.36439i		−	0.330462i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.01425	+	9.63322i	0.211712	+	0.339106i
$808$		0			0
$809$		−	1.63413i		−	0.0574528i	−0.999587	−	0.0287264i	$-0.990855\pi$
$809$		−	1.63413i		−	0.0574528i	0.999587	−	0.0287264i	$-0.00914515\pi$
$810$		0			0
$811$		−	29.4411i		−	1.03382i	−0.856041	−	0.516909i	$-0.827083\pi$
$811$		−	29.4411i		−	1.03382i	0.856041	−	0.516909i	$-0.172917\pi$
$812$		0			0
$813$	−7.70506	+	4.81045i	−0.270228	+	0.168710i
$814$		0			0
$815$	14.9494	−	3.69750i	0.523655	−	0.129518i
$816$		0			0
$817$	10.7161			0.374909
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	22.6734i		−	0.791307i	−0.918400	−	0.395654i	$-0.870518\pi$
$821$		−	22.6734i		−	0.791307i	0.918400	−	0.395654i	$-0.129482\pi$
$822$		0			0
$823$			19.1888i			0.668878i	0.942417	+	0.334439i	$0.108547\pi$
$823$			19.1888i			0.668878i	−0.942417	+	0.334439i	$0.891453\pi$
$824$		0			0
$825$	3.99444	−	6.85277i	0.139068	−	0.238583i
$826$		0			0
$827$	−32.5074			−1.13039			−0.565196	−	0.824957i	$-0.691200\pi$
$827$	−32.5074			−1.13039			−0.565196	+	0.824957i	$0.691200\pi$
$828$		0			0
$829$		−	51.6859i		−	1.79513i	−0.440887	−	0.897563i	$-0.645336\pi$
$829$		−	51.6859i		−	1.79513i	0.440887	−	0.897563i	$-0.354664\pi$
$830$		0			0
$831$	4.07454	−	2.54383i	0.141344	−	0.0882445i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	20.6149	−	5.09879i	0.713409	−	0.176451i
$836$		0			0
$837$	−3.44871	−	33.1881i	−0.119205	−	1.14715i
$838$		0			0
$839$	−2.88841			−0.0997192			−0.0498596	−	0.998756i	$-0.515877\pi$
$839$	−2.88841			−0.0997192			−0.0498596	+	0.998756i	$0.515877\pi$
$840$		0			0
$841$	17.0178			0.586819
$842$		0			0
$843$	−32.9654	+	20.5811i	−1.13539	+	0.708851i
$844$		0			0
$845$	3.00078	+	12.1325i	0.103230	+	0.417369i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	6.64728	+	10.6472i	0.228134	+	0.365410i
$850$		0			0
$851$			40.2952i			1.38130i
$852$		0			0
$853$	49.3673			1.69031			0.845153	−	0.534525i	$-0.179509\pi$
$853$	49.3673			1.69031			0.845153	+	0.534525i	$0.179509\pi$
$854$		0			0
$855$	−1.84079	+	8.54825i	−0.0629536	+	0.292344i
$856$		0			0
$857$		−	17.5037i		−	0.597915i	−0.954266	−	0.298957i	$-0.903361\pi$
$857$		−	17.5037i		−	0.597915i	0.954266	−	0.298957i	$-0.0966389\pi$
$858$		0			0
$859$		−	6.04085i		−	0.206111i	−0.994676	−	0.103056i	$-0.967138\pi$
$859$		−	6.04085i		−	0.206111i	0.994676	−	0.103056i	$-0.0328619\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	34.0169			1.15795			0.578975	−	0.815345i	$-0.303453\pi$
$863$	34.0169			1.15795			0.578975	+	0.815345i	$0.303453\pi$
$864$		0			0
$865$	−25.9390	+	6.41562i	−0.881953	+	0.218137i
$866$		0			0
$867$	15.3290	+	24.5530i	0.520601	+	0.833864i
$868$		0			0
$869$		−	10.4746i		−	0.355326i
$870$		0			0
$871$			52.1996i			1.76872i
$872$		0			0
$873$	−14.2055	+	29.0677i	−0.480784	+	0.983792i
$874$		0			0
$875$		0			0
$876$		0			0
$877$			7.24003i			0.244478i	0.992501	+	0.122239i	$0.0390075\pi$
$877$			7.24003i			0.244478i	−0.992501	+	0.122239i	$0.960992\pi$
$878$		0			0
$879$	−38.4475	+	24.0037i	−1.29680	+	0.809625i
$880$		0			0
$881$	25.9119			0.872993			0.436496	−	0.899706i	$-0.356219\pi$
$881$	25.9119			0.872993			0.436496	+	0.899706i	$0.356219\pi$
$882$		0			0
$883$			17.5664i			0.591155i	0.955319	+	0.295577i	$0.0955120\pi$
$883$			17.5664i			0.591155i	−0.955319	+	0.295577i	$0.904488\pi$
$884$		0			0
$885$	38.5826	−	39.7724i	1.29694	−	1.33693i
$886$		0			0
$887$			14.7678i			0.495855i	0.968779	+	0.247928i	$0.0797496\pi$
$887$			14.7678i			0.495855i	−0.968779	+	0.247928i	$0.920250\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	6.50364	−	5.06478i	0.217880	−	0.169676i
$892$		0			0
$893$	5.65895			0.189369
$894$		0			0
$895$	40.6906	−	10.0642i	1.36014	−	0.336409i
$896$		0			0
$897$	−31.5976	−	50.6110i	−1.05501	−	1.68985i
$898$		0			0
$899$	22.2281			0.741347
$900$		0			0
$901$			1.05793i			0.0352449i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−34.9528	+	8.64504i	−1.16187	+	0.287371i
$906$		0			0
$907$			29.3244i			0.973701i	0.873485	+	0.486851i	$0.161854\pi$
$907$			29.3244i			0.973701i	−0.873485	+	0.486851i	$0.838146\pi$
$908$		0			0
$909$	−12.9742	+	26.5481i	−0.430326	+	0.880545i
$910$		0			0
$911$			30.3043i			1.00403i	0.864860	+	0.502013i	$0.167407\pi$
$911$			30.3043i			1.00403i	−0.864860	+	0.502013i	$0.832593\pi$
$912$		0			0
$913$	−8.56590			−0.283490
$914$		0			0
$915$	26.9118	+	26.1068i	0.889678	+	0.863064i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−7.63775			−0.251946			−0.125973	−	0.992034i	$-0.540205\pi$
$919$	−7.63775			−0.251946			−0.125973	+	0.992034i	$0.540205\pi$
$920$		0			0
$921$	20.5601	+	32.9318i	0.677479	+	1.08514i
$922$		0			0
$923$			4.06965i			0.133954i
$924$		0			0
$925$	−11.7551	−	22.3098i	−0.386505	−	0.733541i
$926$		0			0
$927$	−3.23766	+	6.62499i	−0.106339	+	0.217593i
$928$		0			0
$929$	17.2502			0.565959			0.282980	−	0.959126i	$-0.408677\pi$
$929$	17.2502			0.565959			0.282980	+	0.959126i	$0.408677\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−18.0038	−	28.8372i	−0.589417	−	0.944089i
$934$		0			0
$935$	−0.264089	−	1.06774i	−0.00863664	−	0.0349188i
$936$		0			0
$937$	36.0492			1.17768			0.588839	−	0.808251i	$-0.299585\pi$
$937$	36.0492			1.17768			0.588839	+	0.808251i	$0.299585\pi$
$938$		0			0
$939$	−11.7716	−	18.8549i	−0.384151	−	0.615308i
$940$		0			0
$941$	−31.6307			−1.03113			−0.515565	−	0.856850i	$-0.672418\pi$
$941$	−31.6307			−1.03113			−0.515565	+	0.856850i	$0.672418\pi$
$942$		0			0
$943$	−79.0818			−2.57526
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−40.6174			−1.31989			−0.659944	−	0.751315i	$-0.729420\pi$
$947$	−40.6174			−1.31989			−0.659944	+	0.751315i	$0.729420\pi$
$948$		0			0
$949$	44.0820			1.43096
$950$		0			0
$951$	14.6479	+	23.4620i	0.474990	+	0.760807i
$952$		0			0
$953$	5.31938			0.172312			0.0861558	−	0.996282i	$-0.472542\pi$
$953$	5.31938			0.172312			0.0861558	+	0.996282i	$0.472542\pi$
$954$		0			0
$955$	−37.5916	+	9.29771i	−1.21644	+	0.300867i
$956$		0			0
$957$	2.90815	+	4.65807i	0.0940070	+	0.150574i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−10.2349			−0.330159
$962$		0			0
$963$	−1.97536	+	4.04203i	−0.0636550	+	0.130252i
$964$		0			0
$965$	−32.8428	+	8.12316i	−1.05725	+	0.261494i
$966$		0			0
$967$			6.75930i			0.217364i	0.994077	+	0.108682i	$0.0346631\pi$
$967$			6.75930i			0.217364i	−0.994077	+	0.108682i	$0.965337\pi$
$968$		0			0
$969$	0.642149	+	1.02855i	0.0206288	+	0.0330418i
$970$		0			0
$971$	−43.9702			−1.41107			−0.705535	−	0.708675i	$-0.749293\pi$
$971$	−43.9702			−1.41107			−0.705535	+	0.708675i	$0.749293\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	32.2588	+	18.8034i	1.03311	+	0.602192i
$976$		0			0
$977$	−9.24885			−0.295897			−0.147949	−	0.988995i	$-0.547267\pi$
$977$	−9.24885			−0.295897			−0.147949	+	0.988995i	$0.547267\pi$
$978$		0			0
$979$			1.60193i			0.0511979i
$980$		0			0
$981$	5.09046	−	10.4162i	0.162526	−	0.332565i
$982$		0			0
$983$			13.1389i			0.419067i	0.977801	+	0.209533i	$0.0671945\pi$
$983$			13.1389i			0.419067i	−0.977801	+	0.209533i	$0.932805\pi$
$984$		0			0
$985$	−10.0013	−	40.4365i	−0.318669	−	1.28841i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			65.6823i			2.08857i
$990$		0			0
$991$	−6.37041			−0.202363			−0.101181	−	0.994868i	$-0.532262\pi$
$991$	−6.37041			−0.202363			−0.101181	+	0.994868i	$0.532262\pi$
$992$		0			0
$993$	−18.0131	−	28.8522i	−0.571630	−	0.915598i
$994$		0			0
$995$	−21.8133	+	5.39518i	−0.691528	+	0.171039i
$996$		0			0
$997$	23.5091			0.744542			0.372271	−	0.928124i	$-0.378579\pi$
$997$	23.5091			0.744542			0.372271	+	0.928124i	$0.378579\pi$
$998$		0			0
$999$	−2.70864	−	26.0662i	−0.0856976	−	0.824697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.f.a.1469.24		32
3.2	odd	2	inner	2940.2.f.a.1469.21		32
5.4	even	2	inner	2940.2.f.a.1469.10		32
7.2	even	3		420.2.bn.a.269.1	yes	32
7.3	odd	6		420.2.bn.a.89.6	yes	32
7.6	odd	2	inner	2940.2.f.a.1469.9		32
15.14	odd	2	inner	2940.2.f.a.1469.11		32
21.2	odd	6		420.2.bn.a.269.11	yes	32
21.17	even	6		420.2.bn.a.89.16	yes	32
21.20	even	2	inner	2940.2.f.a.1469.12		32
35.2	odd	12		2100.2.bi.n.101.9		32
35.3	even	12		2100.2.bi.n.1601.3		32
35.9	even	6		420.2.bn.a.269.16	yes	32
35.17	even	12		2100.2.bi.n.1601.14		32
35.23	odd	12		2100.2.bi.n.101.8		32
35.24	odd	6		420.2.bn.a.89.11	yes	32
35.34	odd	2	inner	2940.2.f.a.1469.23		32
105.2	even	12		2100.2.bi.n.101.14		32
105.17	odd	12		2100.2.bi.n.1601.9		32
105.23	even	12		2100.2.bi.n.101.3		32
105.38	odd	12		2100.2.bi.n.1601.8		32
105.44	odd	6		420.2.bn.a.269.6	yes	32
105.59	even	6		420.2.bn.a.89.1	✓	32
105.104	even	2	inner	2940.2.f.a.1469.22		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bn.a.89.1	✓	32	105.59	even	6
420.2.bn.a.89.6	yes	32	7.3	odd	6
420.2.bn.a.89.11	yes	32	35.24	odd	6
420.2.bn.a.89.16	yes	32	21.17	even	6
420.2.bn.a.269.1	yes	32	7.2	even	3
420.2.bn.a.269.6	yes	32	105.44	odd	6
420.2.bn.a.269.11	yes	32	21.2	odd	6
420.2.bn.a.269.16	yes	32	35.9	even	6
2100.2.bi.n.101.3		32	105.23	even	12
2100.2.bi.n.101.8		32	35.23	odd	12
2100.2.bi.n.101.9		32	35.2	odd	12
2100.2.bi.n.101.14		32	105.2	even	12
2100.2.bi.n.1601.3		32	35.3	even	12
2100.2.bi.n.1601.8		32	105.38	odd	12
2100.2.bi.n.1601.9		32	105.17	odd	12
2100.2.bi.n.1601.14		32	35.17	even	12
2940.2.f.a.1469.9		32	7.6	odd	2	inner
2940.2.f.a.1469.10		32	5.4	even	2	inner
2940.2.f.a.1469.11		32	15.14	odd	2	inner
2940.2.f.a.1469.12		32	21.20	even	2	inner
2940.2.f.a.1469.21		32	3.2	odd	2	inner
2940.2.f.a.1469.22		32	105.104	even	2	inner
2940.2.f.a.1469.23		32	35.34	odd	2	inner
2940.2.f.a.1469.24		32	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.917271 + 1.46922i) q^{3} +(0.536879 + 2.17066i) q^{5} +(-1.31723 + 2.69535i) q^{9} +0.915904i q^{11} -4.31153 q^{13} +(-2.69672 + 2.77988i) q^{15} +0.537062i q^{17} -1.30351i q^{19} +7.98961 q^{23} +(-4.42352 + 2.33076i) q^{25} +(-5.16832 + 0.537062i) q^{27} -3.46154i q^{29} +6.42144i q^{31} +(-1.34567 + 0.840132i) q^{33} +5.04345i q^{37} +(-3.95484 - 6.33460i) q^{39} -9.89809 q^{41} +8.22096i q^{43} +(-6.55788 - 1.41218i) q^{45} +4.34132i q^{47} +(-0.789063 + 0.492631i) q^{51} +1.96985 q^{53} +(-1.98812 + 0.491730i) q^{55} +(1.91514 - 1.19567i) q^{57} -14.3073 q^{59} -9.68095i q^{61} +(-2.31477 - 9.35886i) q^{65} -12.1070i q^{67} +(7.32863 + 11.7385i) q^{69} -0.943900i q^{71} -10.2242 q^{73} +(-7.48198 - 4.36120i) q^{75} -11.4363 q^{79} +(-5.52981 - 7.10079i) q^{81} +9.35240i q^{83} +(-1.16578 + 0.288337i) q^{85} +(5.08577 - 3.17517i) q^{87} +1.74901 q^{89} +(-9.43453 + 5.89020i) q^{93} +(2.82947 - 0.699827i) q^{95} +10.7844 q^{97} +(-2.46868 - 1.20646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{15} - 12 q^{25} - 48 q^{39} + 20 q^{51} + 56 q^{79} + 40 q^{81} - 4 q^{85} - 28 q^{99}+O(q^{100}) \) 32 * q + 2 * q^15 - 12 * q^25 - 48 * q^39 + 20 * q^51 + 56 * q^79 + 40 * q^81 - 4 * q^85 - 28 * q^99

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