LMFDB - Embedded newform 1520.2.d.k.609.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1520,2,Mod(609,1520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1520, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1520.609");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1520.d (of order $2$, degree $1$, not 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:	$12.1372611072$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 9 x^{10} - 8 x^{9} - 11 x^{8} + 60 x^{7} - 126 x^{6} + 180 x^{5} - 99 x^{4} + \cdots + 729 $ x^12 - 4x^11 + 9x^10 - 8x^9 - 11x^8 + 60x^7 - 126x^6 + 180x^5 - 99x^4 - 216x^3 + 729x^2 - 972*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 760)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			609.7
Root			$-1.72675 + 0.135465i$ of defining polynomial
Character	$\chi$	$=$	1520.609
Dual form			1520.2.d.k.609.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.366738i q^{3} +(2.20191 - 0.389375i) q^{5} +3.08675i q^{7} +2.86550 q^{9} +4.94567 q^{11} -3.79016i q^{13} +(0.142799 + 0.807521i) q^{15} -3.97713i q^{17} +1.00000 q^{19} -1.13203 q^{21} -6.56426i q^{23} +(4.69677 - 1.71473i) q^{25} +2.15110i q^{27} -5.14084 q^{29} -4.25626 q^{31} +1.81376i q^{33} +(1.20191 + 6.79674i) q^{35} +7.75503i q^{37} +1.39000 q^{39} -2.25626 q^{41} +10.2276i q^{43} +(6.30957 - 1.11576i) q^{45} +0.935652i q^{47} -2.52804 q^{49} +1.45856 q^{51} -7.52117i q^{53} +(10.8899 - 1.92572i) q^{55} +0.366738i q^{57} -10.4356 q^{59} +10.9163 q^{61} +8.84510i q^{63} +(-1.47580 - 8.34558i) q^{65} -6.80924i q^{67} +2.40736 q^{69} +2.98093 q^{71} -2.19638i q^{73} +(0.628858 + 1.72248i) q^{75} +15.2661i q^{77} -3.26652 q^{79} +7.80762 q^{81} +4.09936i q^{83} +(-1.54860 - 8.75726i) q^{85} -1.88534i q^{87} +12.4134 q^{89} +11.6993 q^{91} -1.56093i q^{93} +(2.20191 - 0.389375i) q^{95} +10.6172i q^{97} +14.1718 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} - 16 q^{9} + 4 q^{11} + 12 q^{15} + 12 q^{19} + 36 q^{21} + 18 q^{25} + 4 q^{29} - 16 q^{31} - 6 q^{35} - 36 q^{39} + 8 q^{41} - 2 q^{45} - 4 q^{49} + 68 q^{51} + 18 q^{55} - 4 q^{59} + 20 q^{61}+ \cdots - 44 q^{99}+O(q^{100}) $ 12 * q + 6 * q^5 - 16 * q^9 + 4 * q^11 + 12 * q^15 + 12 * q^19 + 36 * q^21 + 18 * q^25 + 4 * q^29 - 16 * q^31 - 6 * q^35 - 36 * q^39 + 8 * q^41 - 2 * q^45 - 4 * q^49 + 68 * q^51 + 18 * q^55 - 4 * q^59 + 20 * q^61 + 20 * q^65 - 36 * q^69 + 16 * q^71 + 16 * q^75 - 40 * q^79 + 12 * q^81 + 6 * q^85 - 64 * q^89 - 20 * q^91 + 6 * q^95 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$.

$n$	$191$	$401$	$1141$	$1217$
$\chi(n)$	$1$	$1$	$1$	$-1$

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
$3$			0.366738i			0.211736i	0.994380	+	0.105868i	$0.0337621\pi$
$3$			0.366738i			0.211736i	−0.994380	+	0.105868i	$0.966238\pi$
$4$		0			0
$5$	2.20191	−	0.389375i	0.984722	−	0.174134i
$5$	2.20191	−	0.389375i	0.984722	−	0.174134i
$6$		0			0
$7$			3.08675i			1.16668i	0.812227	+	0.583341i	$0.198255\pi$
$7$			3.08675i			1.16668i	−0.812227	+	0.583341i	$0.801745\pi$
$8$		0			0
$9$	2.86550			0.955168
$10$		0			0
$11$	4.94567			1.49118			0.745588	−	0.666407i	$-0.232169\pi$
$11$	4.94567			1.49118			0.745588	+	0.666407i	$0.232169\pi$
$12$		0			0
$13$		−	3.79016i		−	1.05120i	−0.850731	−	0.525601i	$-0.823840\pi$
$13$		−	3.79016i		−	1.05120i	0.850731	−	0.525601i	$-0.176160\pi$
$14$		0			0
$15$	0.142799	+	0.807521i	0.0368704	+	0.208501i
$16$		0			0
$17$		−	3.97713i		−	0.964596i	−0.876007	−	0.482298i	$-0.839802\pi$
$17$		−	3.97713i		−	0.964596i	0.876007	−	0.482298i	$-0.160198\pi$
$18$		0			0
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$		0			0
$21$	−1.13203			−0.247029
$22$		0			0
$23$		−	6.56426i		−	1.36874i	−0.729133	−	0.684372i	$-0.760077\pi$
$23$		−	6.56426i		−	1.36874i	0.729133	−	0.684372i	$-0.239923\pi$
$24$		0			0
$25$	4.69677	−	1.71473i	0.939355	−	0.342947i
$26$		0			0
$27$			2.15110i			0.413980i
$28$		0			0
$29$	−5.14084			−0.954630			−0.477315	−	0.878732i	$-0.658390\pi$
$29$	−5.14084			−0.954630			−0.477315	+	0.878732i	$0.658390\pi$
$30$		0			0
$31$	−4.25626			−0.764447			−0.382224	−	0.924070i	$-0.624842\pi$
$31$	−4.25626			−0.764447			−0.382224	+	0.924070i	$0.624842\pi$
$32$		0			0
$33$			1.81376i			0.315736i
$34$		0			0
$35$	1.20191	+	6.79674i	0.203159	+	1.14886i
$36$		0			0
$37$			7.75503i			1.27492i	0.770484	+	0.637459i	$0.220015\pi$
$37$			7.75503i			1.27492i	−0.770484	+	0.637459i	$0.779985\pi$
$38$		0			0
$39$	1.39000			0.222577
$40$		0			0
$41$	−2.25626			−0.352369			−0.176184	−	0.984357i	$-0.556376\pi$
$41$	−2.25626			−0.352369			−0.176184	+	0.984357i	$0.556376\pi$
$42$		0			0
$43$			10.2276i			1.55969i	0.625971	+	0.779846i	$0.284703\pi$
$43$			10.2276i			1.55969i	−0.625971	+	0.779846i	$0.715297\pi$
$44$		0			0
$45$	6.30957	−	1.11576i	0.940575	−	0.166327i
$46$		0			0
$47$			0.935652i			0.136479i	0.997669	+	0.0682395i	$0.0217382\pi$
$47$			0.935652i			0.136479i	−0.997669	+	0.0682395i	$0.978262\pi$
$48$		0			0
$49$	−2.52804			−0.361149
$50$		0			0
$51$	1.45856			0.204240
$52$		0			0
$53$		−	7.52117i		−	1.03311i	−0.856253	−	0.516556i	$-0.827214\pi$
$53$		−	7.52117i		−	1.03311i	0.856253	−	0.516556i	$-0.172786\pi$
$54$		0			0
$55$	10.8899	−	1.92572i	1.46839	−	0.259664i
$56$		0			0
$57$			0.366738i			0.0485756i
$58$		0			0
$59$	−10.4356			−1.35860			−0.679298	−	0.733863i	$-0.737715\pi$
$59$	−10.4356			−1.35860			−0.679298	+	0.733863i	$0.737715\pi$
$60$		0			0
$61$	10.9163			1.39769			0.698847	−	0.715271i	$-0.253697\pi$
$61$	10.9163			1.39769			0.698847	+	0.715271i	$0.253697\pi$
$62$		0			0
$63$			8.84510i			1.11438i
$64$		0			0
$65$	−1.47580	−	8.34558i	−0.183050	−	1.03514i
$66$		0			0
$67$		−	6.80924i		−	0.831881i	−0.909392	−	0.415940i	$-0.863453\pi$
$67$		−	6.80924i		−	0.831881i	0.909392	−	0.415940i	$-0.136547\pi$
$68$		0			0
$69$	2.40736			0.289812
$70$		0			0
$71$	2.98093			0.353771			0.176886	−	0.984231i	$-0.443398\pi$
$71$	2.98093			0.353771			0.176886	+	0.984231i	$0.443398\pi$
$72$		0			0
$73$		−	2.19638i		−	0.257066i	−0.991705	−	0.128533i	$-0.958973\pi$
$73$		−	2.19638i		−	0.257066i	0.991705	−	0.128533i	$-0.0410269\pi$
$74$		0			0
$75$	0.628858	+	1.72248i	0.0726142	+	0.198895i
$76$		0			0
$77$			15.2661i			1.73973i
$78$		0			0
$79$	−3.26652			−0.367513			−0.183756	−	0.982972i	$-0.558826\pi$
$79$	−3.26652			−0.367513			−0.183756	+	0.982972i	$0.558826\pi$
$80$		0			0
$81$	7.80762			0.867513
$82$		0			0
$83$			4.09936i			0.449963i	0.974363	+	0.224982i	$0.0722322\pi$
$83$			4.09936i			0.449963i	−0.974363	+	0.224982i	$0.927768\pi$
$84$		0			0
$85$	−1.54860	−	8.75726i	−0.167969	−	0.949859i
$86$		0			0
$87$		−	1.88534i		−	0.202129i
$88$		0			0
$89$	12.4134			1.31581			0.657907	−	0.753099i	$-0.271442\pi$
$89$	12.4134			1.31581			0.657907	+	0.753099i	$0.271442\pi$
$90$		0			0
$91$	11.6993			1.22642
$92$		0			0
$93$		−	1.56093i		−	0.161861i
$94$		0			0
$95$	2.20191	−	0.389375i	0.225911	−	0.0399491i
$96$		0			0
$97$			10.6172i			1.07801i	0.842302	+	0.539007i	$0.181200\pi$
$97$			10.6172i			1.07801i	−0.842302	+	0.539007i	$0.818800\pi$
$98$		0			0
$99$	14.1718			1.42432
$100$		0			0
$101$	−13.1119			−1.30469			−0.652343	−	0.757924i	$-0.726214\pi$
$101$	−13.1119			−1.30469			−0.652343	+	0.757924i	$0.726214\pi$
$102$		0			0
$103$			4.95691i			0.488419i	0.969723	+	0.244209i	$0.0785284\pi$
$103$			4.95691i			0.488419i	−0.969723	+	0.244209i	$0.921472\pi$
$104$		0			0
$105$	−2.49262	+	0.440784i	−0.243255	+	0.0430161i
$106$		0			0
$107$		−	18.9142i		−	1.82850i	−0.405148	−	0.914251i	$-0.632780\pi$
$107$		−	18.9142i		−	1.82850i	0.405148	−	0.914251i	$-0.367220\pi$
$108$		0			0
$109$	−8.90118			−0.852578			−0.426289	−	0.904587i	$-0.640179\pi$
$109$	−8.90118			−0.852578			−0.426289	+	0.904587i	$0.640179\pi$
$110$		0			0
$111$	−2.84406			−0.269946
$112$		0			0
$113$			9.85071i			0.926677i	0.886181	+	0.463339i	$0.153349\pi$
$113$			9.85071i			0.926677i	−0.886181	+	0.463339i	$0.846651\pi$
$114$		0			0
$115$	−2.55596	−	14.4539i	−0.238345	−	1.34783i
$116$		0			0
$117$		−	10.8607i		−	1.00407i
$118$		0			0
$119$	12.2764			1.12538
$120$		0			0
$121$	13.4596			1.22360
$122$		0			0
$123$		−	0.827456i		−	0.0746092i
$124$		0			0
$125$	9.67418	−	5.60449i	0.865285	−	0.501281i
$126$		0			0
$127$			3.76384i			0.333987i	0.985958	+	0.166993i	$0.0534058\pi$
$127$			3.76384i			0.333987i	−0.985958	+	0.166993i	$0.946594\pi$
$128$		0			0
$129$	−3.75084			−0.330243
$130$		0			0
$131$	−10.0488			−0.877966			−0.438983	−	0.898495i	$-0.644661\pi$
$131$	−10.0488			−0.877966			−0.438983	+	0.898495i	$0.644661\pi$
$132$		0			0
$133$			3.08675i			0.267655i
$134$		0			0
$135$	0.837585	+	4.73652i	0.0720879	+	0.407655i
$136$		0			0
$137$			14.6244i			1.24945i	0.780845	+	0.624724i	$0.214789\pi$
$137$			14.6244i			1.24945i	−0.780845	+	0.624724i	$0.785211\pi$
$138$		0			0
$139$	−12.0773			−1.02438			−0.512191	−	0.858872i	$-0.671166\pi$
$139$	−12.0773			−1.02438			−0.512191	+	0.858872i	$0.671166\pi$
$140$		0			0
$141$	−0.343139			−0.0288975
$142$		0			0
$143$		−	18.7449i		−	1.56753i
$144$		0			0
$145$	−11.3196	+	2.00172i	−0.940045	+	0.166233i
$146$		0			0
$147$		−	0.927129i		−	0.0764683i
$148$		0			0
$149$	−12.5739			−1.03009			−0.515046	−	0.857162i	$-0.672225\pi$
$149$	−12.5739			−1.03009			−0.515046	+	0.857162i	$0.672225\pi$
$150$		0			0
$151$	0.390336			0.0317651			0.0158826	−	0.999874i	$-0.494944\pi$
$151$	0.390336			0.0317651			0.0158826	+	0.999874i	$0.494944\pi$
$152$		0			0
$153$		−	11.3965i		−	0.921351i
$154$		0			0
$155$	−9.37189	+	1.65728i	−0.752768	+	0.133116i
$156$		0			0
$157$			17.6517i			1.40876i	0.709824	+	0.704379i	$0.248774\pi$
$157$			17.6517i			1.40876i	−0.709824	+	0.704379i	$0.751226\pi$
$158$		0			0
$159$	2.75830			0.218747
$160$		0			0
$161$	20.2623			1.59689
$162$		0			0
$163$			5.72733i			0.448599i	0.974520	+	0.224300i	$0.0720094\pi$
$163$			5.72733i			0.448599i	−0.974520	+	0.224300i	$0.927991\pi$
$164$		0			0
$165$	0.706234	+	3.99373i	0.0549803	+	0.310912i
$166$		0			0
$167$		−	8.22343i		−	0.636348i	−0.948032	−	0.318174i	$-0.896930\pi$
$167$		−	8.22343i		−	0.636348i	0.948032	−	0.318174i	$-0.103070\pi$
$168$		0			0
$169$	−1.36534			−0.105027
$170$		0			0
$171$	2.86550			0.219131
$172$		0			0
$173$			15.1427i			1.15127i	0.817705	+	0.575637i	$0.195246\pi$
$173$			15.1427i			1.15127i	−0.817705	+	0.575637i	$0.804754\pi$
$174$		0			0
$175$	5.29296	+	14.4978i	0.400110	+	1.09593i
$176$		0			0
$177$		−	3.82712i		−	0.287664i
$178$		0			0
$179$	4.07415			0.304516			0.152258	−	0.988341i	$-0.451346\pi$
$179$	4.07415			0.304516			0.152258	+	0.988341i	$0.451346\pi$
$180$		0			0
$181$	2.92981			0.217771			0.108885	−	0.994054i	$-0.465272\pi$
$181$	2.92981			0.217771			0.108885	+	0.994054i	$0.465272\pi$
$182$		0			0
$183$			4.00343i			0.295942i
$184$		0			0
$185$	3.01962	+	17.0758i	0.222007	+	1.25544i
$186$		0			0
$187$		−	19.6696i		−	1.43838i
$188$		0			0
$189$	−6.63992			−0.482983
$190$		0			0
$191$	5.41644			0.391920			0.195960	−	0.980612i	$-0.437218\pi$
$191$	5.41644			0.391920			0.195960	+	0.980612i	$0.437218\pi$
$192$		0			0
$193$			24.6275i			1.77273i	0.462991	+	0.886363i	$0.346776\pi$
$193$			24.6275i			1.77273i	−0.462991	+	0.886363i	$0.653224\pi$
$194$		0			0
$195$	3.06064	−	0.541230i	0.219177	−	0.0387583i
$196$		0			0
$197$		−	3.93923i		−	0.280658i	−0.990105	−	0.140329i	$-0.955184\pi$
$197$		−	3.93923i		−	0.280658i	0.990105	−	0.140329i	$-0.0448161\pi$
$198$		0			0
$199$	−20.8079			−1.47504			−0.737518	−	0.675328i	$-0.764002\pi$
$199$	−20.8079			−1.47504			−0.737518	+	0.675328i	$0.764002\pi$
$200$		0			0
$201$	2.49720			0.176139
$202$		0			0
$203$		−	15.8685i		−	1.11375i
$204$		0			0
$205$	−4.96807	+	0.878533i	−0.346985	+	0.0613594i
$206$		0			0
$207$		−	18.8099i		−	1.30738i
$208$		0			0
$209$	4.94567			0.342099
$210$		0			0
$211$	22.9069			1.57698			0.788488	−	0.615050i	$-0.210864\pi$
$211$	22.9069			1.57698			0.788488	+	0.615050i	$0.210864\pi$
$212$		0			0
$213$			1.09322i			0.0749061i
$214$		0			0
$215$	3.98237	+	22.5202i	0.271595	+	1.53586i
$216$		0			0
$217$		−	13.1380i		−	0.891868i
$218$		0			0
$219$	0.805494			0.0544302
$220$		0			0
$221$	−15.0740			−1.01399
$222$		0			0
$223$			16.6488i			1.11489i	0.830214	+	0.557444i	$0.188218\pi$
$223$			16.6488i			1.11489i	−0.830214	+	0.557444i	$0.811782\pi$
$224$		0			0
$225$	13.4586	−	4.91358i	0.897241	−	0.327572i
$226$		0			0
$227$			11.8343i			0.785469i	0.919652	+	0.392735i	$0.128471\pi$
$227$			11.8343i			0.785469i	−0.919652	+	0.392735i	$0.871529\pi$
$228$		0			0
$229$	−4.84288			−0.320026			−0.160013	−	0.987115i	$-0.551154\pi$
$229$	−4.84288			−0.320026			−0.160013	+	0.987115i	$0.551154\pi$
$230$		0			0
$231$	−5.59864			−0.368363
$232$		0			0
$233$		−	9.60851i		−	0.629474i	−0.949179	−	0.314737i	$-0.898084\pi$
$233$		−	9.60851i		−	0.629474i	0.949179	−	0.314737i	$-0.101916\pi$
$234$		0			0
$235$	0.364320	+	2.06022i	0.0237656	+	0.134394i
$236$		0			0
$237$		−	1.19796i		−	0.0778157i
$238$		0			0
$239$	−9.49984			−0.614493			−0.307247	−	0.951630i	$-0.599408\pi$
$239$	−9.49984			−0.614493			−0.307247	+	0.951630i	$0.599408\pi$
$240$		0			0
$241$	−21.8687			−1.40868			−0.704342	−	0.709860i	$-0.748758\pi$
$241$	−21.8687			−1.40868			−0.704342	+	0.709860i	$0.748758\pi$
$242$		0			0
$243$			9.31665i			0.597663i
$244$		0			0
$245$	−5.56651	+	0.984358i	−0.355632	+	0.0628883i
$246$		0			0
$247$		−	3.79016i		−	0.241162i
$248$		0			0
$249$	−1.50339			−0.0952734
$250$		0			0
$251$	−2.03109			−0.128201			−0.0641007	−	0.997943i	$-0.520418\pi$
$251$	−2.03109			−0.128201			−0.0641007	+	0.997943i	$0.520418\pi$
$252$		0			0
$253$		−	32.4647i		−	2.04104i
$254$		0			0
$255$	3.21162	−	0.567928i	0.201119	−	0.0355651i
$256$		0			0
$257$			7.62917i			0.475894i	0.971278	+	0.237947i	$0.0764745\pi$
$257$			7.62917i			0.475894i	−0.971278	+	0.237947i	$0.923525\pi$
$258$		0			0
$259$	−23.9379			−1.48743
$260$		0			0
$261$	−14.7311			−0.911831
$262$		0			0
$263$		−	30.3299i		−	1.87022i	−0.354352	−	0.935112i	$-0.615298\pi$
$263$		−	30.3299i		−	1.87022i	0.354352	−	0.935112i	$-0.384702\pi$
$264$		0			0
$265$	−2.92856	−	16.5609i	−0.179900	−	1.01733i
$266$		0			0
$267$			4.55245i			0.278605i
$268$		0			0
$269$	−24.3382			−1.48393			−0.741963	−	0.670441i	$-0.766105\pi$
$269$	−24.3382			−1.48393			−0.741963	+	0.670441i	$0.766105\pi$
$270$		0			0
$271$	−3.62084			−0.219951			−0.109975	−	0.993934i	$-0.535077\pi$
$271$	−3.62084			−0.219951			−0.109975	+	0.993934i	$0.535077\pi$
$272$		0			0
$273$			4.29057i			0.259677i
$274$		0			0
$275$	23.2287	−	8.48051i	1.40074	−	0.511394i
$276$		0			0
$277$		−	29.6842i		−	1.78355i	−0.452477	−	0.891776i	$-0.649459\pi$
$277$		−	29.6842i		−	1.78355i	0.452477	−	0.891776i	$-0.350541\pi$
$278$		0			0
$279$	−12.1963			−0.730175
$280$		0			0
$281$	29.1363			1.73813			0.869064	−	0.494700i	$-0.164722\pi$
$281$	29.1363			1.73813			0.869064	+	0.494700i	$0.164722\pi$
$282$		0			0
$283$			24.2081i			1.43902i	0.694481	+	0.719511i	$0.255634\pi$
$283$			24.2081i			1.43902i	−0.694481	+	0.719511i	$0.744366\pi$
$284$		0			0
$285$	0.142799	+	0.807521i	0.00845866	+	0.0478334i
$286$		0			0
$287$		−	6.96452i		−	0.411103i
$288$		0			0
$289$	1.18244			0.0695551
$290$		0			0
$291$	−3.89373			−0.228254
$292$		0			0
$293$			15.9338i			0.930865i	0.885083	+	0.465433i	$0.154101\pi$
$293$			15.9338i			0.930865i	−0.885083	+	0.465433i	$0.845899\pi$
$294$		0			0
$295$	−22.9781	+	4.06335i	−1.33784	+	0.236578i
$296$		0			0
$297$			10.6386i			0.617316i
$298$		0			0
$299$	−24.8796			−1.43883
$300$		0			0
$301$	−31.5700			−1.81967
$302$		0			0
$303$		−	4.80864i		−	0.276249i
$304$		0			0
$305$	24.0367	−	4.25055i	1.37634	−	0.243386i
$306$		0			0
$307$		−	25.9373i		−	1.48032i	−0.672429	−	0.740161i	$-0.734749\pi$
$307$		−	25.9373i		−	1.48032i	0.672429	−	0.740161i	$-0.265251\pi$
$308$		0			0
$309$	−1.81788			−0.103416
$310$		0			0
$311$	2.58526			0.146597			0.0732983	−	0.997310i	$-0.476647\pi$
$311$	2.58526			0.146597			0.0732983	+	0.997310i	$0.476647\pi$
$312$		0			0
$313$		−	17.1027i		−	0.966701i	−0.875427	−	0.483351i	$-0.839420\pi$
$313$		−	17.1027i		−	0.966701i	0.875427	−	0.483351i	$-0.160580\pi$
$314$		0			0
$315$	3.44406	+	19.4761i	0.194051	+	1.09735i
$316$		0			0
$317$			24.5591i			1.37938i	0.724105	+	0.689690i	$0.242253\pi$
$317$			24.5591i			1.37938i	−0.724105	+	0.689690i	$0.757747\pi$
$318$		0			0
$319$	−25.4249			−1.42352
$320$		0			0
$321$	6.93654			0.387160
$322$		0			0
$323$		−	3.97713i		−	0.221293i
$324$		0			0
$325$	−6.49913	−	17.8015i	−0.360507	−	0.987452i
$326$		0			0
$327$		−	3.26440i		−	0.180522i
$328$		0			0
$329$	−2.88813			−0.159228
$330$		0			0
$331$	−16.4328			−0.903227			−0.451614	−	0.892214i	$-0.649151\pi$
$331$	−16.4328			−0.903227			−0.451614	+	0.892214i	$0.649151\pi$
$332$		0			0
$333$			22.2221i			1.21776i
$334$		0			0
$335$	−2.65135	−	14.9933i	−0.144859	−	0.819171i
$336$		0			0
$337$		−	12.0174i		−	0.654627i	−0.944916	−	0.327314i	$-0.893857\pi$
$337$		−	12.0174i		−	0.654627i	0.944916	−	0.327314i	$-0.106143\pi$
$338$		0			0
$339$	−3.61263			−0.196211
$340$		0			0
$341$	−21.0501			−1.13992
$342$		0			0
$343$			13.8038i			0.745336i
$344$		0			0
$345$	5.30078	−	0.937367i	0.285385	−	0.0504662i
$346$		0			0
$347$		−	28.3681i		−	1.52288i	−0.648236	−	0.761439i	$-0.724493\pi$
$347$		−	28.3681i		−	1.52288i	0.648236	−	0.761439i	$-0.275507\pi$
$348$		0			0
$349$	−33.9733			−1.81855			−0.909275	−	0.416195i	$-0.863363\pi$
$349$	−33.9733			−1.81855			−0.909275	+	0.416195i	$0.863363\pi$
$350$		0			0
$351$	8.15302			0.435176
$352$		0			0
$353$		−	26.6181i		−	1.41674i	−0.705842	−	0.708369i	$-0.749431\pi$
$353$		−	26.6181i		−	1.41674i	0.705842	−	0.708369i	$-0.250569\pi$
$354$		0			0
$355$	6.56372	−	1.16070i	0.348366	−	0.0616035i
$356$		0			0
$357$			4.50222i			0.238283i
$358$		0			0
$359$	5.84964			0.308732			0.154366	−	0.988014i	$-0.450666\pi$
$359$	5.84964			0.308732			0.154366	+	0.988014i	$0.450666\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$		0			0
$363$			4.93616i			0.259081i
$364$		0			0
$365$	−0.855215	−	4.83621i	−0.0447640	−	0.253139i
$366$		0			0
$367$		−	2.41146i		−	0.125877i	−0.998017	−	0.0629385i	$-0.979953\pi$
$367$		−	2.41146i		−	0.125877i	0.998017	−	0.0629385i	$-0.0200472\pi$
$368$		0			0
$369$	−6.46533			−0.336571
$370$		0			0
$371$	23.2160			1.20531
$372$		0			0
$373$		−	27.2074i		−	1.40874i	−0.709831	−	0.704372i	$-0.751229\pi$
$373$		−	27.2074i		−	1.40874i	0.709831	−	0.704372i	$-0.248771\pi$
$374$		0			0
$375$	2.05538	+	3.54788i	0.106139	+	0.183212i
$376$		0			0
$377$			19.4846i			1.00351i
$378$		0			0
$379$	−37.0749			−1.90441			−0.952204	−	0.305461i	$-0.901189\pi$
$379$	−37.0749			−1.90441			−0.952204	+	0.305461i	$0.901189\pi$
$380$		0			0
$381$	−1.38034			−0.0707170
$382$		0			0
$383$		−	0.238749i		−	0.0121995i	−0.999981	−	0.00609975i	$-0.998058\pi$
$383$		−	0.238749i		−	0.0121995i	0.999981	−	0.00609975i	$-0.00194162\pi$
$384$		0			0
$385$	5.94423	+	33.6144i	0.302946	+	1.71315i
$386$		0			0
$387$			29.3072i			1.48977i
$388$		0			0
$389$	−21.3399			−1.08197			−0.540987	−	0.841031i	$-0.681949\pi$
$389$	−21.3399			−1.08197			−0.540987	+	0.841031i	$0.681949\pi$
$390$		0			0
$391$	−26.1069			−1.32028
$392$		0			0
$393$		−	3.68527i		−	0.185897i
$394$		0			0
$395$	−7.19258	+	1.27190i	−0.361898	+	0.0639964i
$396$		0			0
$397$		−	17.7416i		−	0.890424i	−0.895425	−	0.445212i	$-0.853128\pi$
$397$		−	17.7416i		−	0.890424i	0.895425	−	0.445212i	$-0.146872\pi$
$398$		0			0
$399$	−1.13203			−0.0566723
$400$		0			0
$401$	36.4310			1.81928			0.909638	−	0.415401i	$-0.136359\pi$
$401$	36.4310			1.81928			0.909638	+	0.415401i	$0.136359\pi$
$402$		0			0
$403$			16.1319i			0.803589i
$404$		0			0
$405$	17.1916	−	3.04009i	0.854260	−	0.151064i
$406$		0			0
$407$			38.3538i			1.90113i
$408$		0			0
$409$	0.530833			0.0262480			0.0131240	−	0.999914i	$-0.495822\pi$
$409$	0.530833			0.0262480			0.0131240	+	0.999914i	$0.495822\pi$
$410$		0			0
$411$	−5.36332			−0.264553
$412$		0			0
$413$		−	32.2120i		−	1.58505i
$414$		0			0
$415$	1.59619	+	9.02640i	0.0783539	+	0.443089i
$416$		0			0
$417$		−	4.42919i		−	0.216898i
$418$		0			0
$419$	29.3816			1.43538			0.717692	−	0.696361i	$-0.245199\pi$
$419$	29.3816			1.43538			0.717692	+	0.696361i	$0.245199\pi$
$420$		0			0
$421$	2.95912			0.144219			0.0721093	−	0.997397i	$-0.477027\pi$
$421$	2.95912			0.144219			0.0721093	+	0.997397i	$0.477027\pi$
$422$		0			0
$423$			2.68112i			0.130360i
$424$		0			0
$425$	−6.81972	−	18.6797i	−0.330805	−	0.906098i
$426$		0			0
$427$			33.6960i			1.63067i
$428$		0			0
$429$	6.87446			0.331902
$430$		0			0
$431$	32.4518			1.56315			0.781573	−	0.623814i	$-0.214418\pi$
$431$	32.4518			1.56315			0.781573	+	0.623814i	$0.214418\pi$
$432$		0			0
$433$		−	27.7821i		−	1.33512i	−0.744554	−	0.667562i	$-0.767338\pi$
$433$		−	27.7821i		−	1.33512i	0.744554	−	0.667562i	$-0.232662\pi$
$434$		0			0
$435$	−0.734104	−	4.15134i	−0.0351976	−	0.199041i
$436$		0			0
$437$		−	6.56426i		−	0.314011i
$438$		0			0
$439$	−0.0388357			−0.00185352			−0.000926762	−	1.00000i	$-0.500295\pi$
$439$	−0.0388357			−0.00185352			−0.000926762		1.00000i	$0.500295\pi$
$440$		0			0
$441$	−7.24412			−0.344958
$442$		0			0
$443$			3.98842i			0.189496i	0.995501	+	0.0947479i	$0.0302045\pi$
$443$			3.98842i			0.189496i	−0.995501	+	0.0947479i	$0.969796\pi$
$444$		0			0
$445$	27.3330	−	4.83346i	1.29571	−	0.229128i
$446$		0			0
$447$		−	4.61132i		−	0.218108i
$448$		0			0
$449$	−23.1695			−1.09343			−0.546717	−	0.837317i	$-0.684123\pi$
$449$	−23.1695			−1.09343			−0.546717	+	0.837317i	$0.684123\pi$
$450$		0			0
$451$	−11.1587			−0.525444
$452$		0			0
$453$			0.143151i			0.00672582i
$454$		0			0
$455$	25.7608	−	4.55542i	1.20768	−	0.213561i
$456$		0			0
$457$			11.5398i			0.539811i	0.962887	+	0.269905i	$0.0869925\pi$
$457$			11.5398i			0.539811i	−0.962887	+	0.269905i	$0.913008\pi$
$458$		0			0
$459$	8.55521			0.399323
$460$		0			0
$461$	8.96090			0.417351			0.208675	−	0.977985i	$-0.433085\pi$
$461$	8.96090			0.417351			0.208675	+	0.977985i	$0.433085\pi$
$462$		0			0
$463$		−	4.43012i		−	0.205885i	−0.994687	−	0.102943i	$-0.967174\pi$
$463$		−	4.43012i		−	0.205885i	0.994687	−	0.102943i	$-0.0328258\pi$
$464$		0			0
$465$	−0.607788	−	3.43702i	−0.0281855	−	0.159388i
$466$		0			0
$467$			30.6874i			1.42004i	0.704180	+	0.710021i	$0.251315\pi$
$467$			30.6874i			1.42004i	−0.704180	+	0.710021i	$0.748685\pi$
$468$		0			0
$469$	21.0184			0.970541
$470$		0			0
$471$	−6.47354			−0.298285
$472$		0			0
$473$			50.5823i			2.32578i
$474$		0			0
$475$	4.69677	−	1.71473i	0.215503	−	0.0786774i
$476$		0			0
$477$		−	21.5519i		−	0.986796i
$478$		0			0
$479$	−18.0047			−0.822657			−0.411328	−	0.911487i	$-0.634935\pi$
$479$	−18.0047			−0.822657			−0.411328	+	0.911487i	$0.634935\pi$
$480$		0			0
$481$	29.3928			1.34020
$482$		0			0
$483$			7.43093i			0.338119i
$484$		0			0
$485$	4.13407	+	23.3781i	0.187719	+	1.06154i
$486$		0			0
$487$			14.7434i			0.668087i	0.942558	+	0.334043i	$0.108413\pi$
$487$			14.7434i			0.668087i	−0.942558	+	0.334043i	$0.891587\pi$
$488$		0			0
$489$	−2.10043			−0.0949847
$490$		0			0
$491$	−40.0805			−1.80881			−0.904404	−	0.426677i	$-0.859684\pi$
$491$	−40.0805			−1.80881			−0.904404	+	0.426677i	$0.859684\pi$
$492$		0			0
$493$			20.4458i			0.920832i
$494$		0			0
$495$	31.2050	−	5.51816i	1.40256	−	0.248023i
$496$		0			0
$497$			9.20139i			0.412739i
$498$		0			0
$499$	12.7838			0.572282			0.286141	−	0.958188i	$-0.407627\pi$
$499$	12.7838			0.572282			0.286141	+	0.958188i	$0.407627\pi$
$500$		0			0
$501$	3.01584			0.134738
$502$		0			0
$503$		−	11.9101i		−	0.531046i	−0.964105	−	0.265523i	$-0.914455\pi$
$503$		−	11.9101i		−	0.531046i	0.964105	−	0.265523i	$-0.0855446\pi$
$504$		0			0
$505$	−28.8712	+	5.10546i	−1.28475	+	0.227190i
$506$		0			0
$507$		−	0.500723i		−	0.0222379i
$508$		0			0
$509$	−15.7374			−0.697549			−0.348775	−	0.937207i	$-0.613402\pi$
$509$	−15.7374			−0.697549			−0.348775	+	0.937207i	$0.613402\pi$
$510$		0			0
$511$	6.77967			0.299915
$512$		0			0
$513$			2.15110i			0.0949734i
$514$		0			0
$515$	1.93010	+	10.9146i	0.0850502	+	0.480956i
$516$		0			0
$517$			4.62743i			0.203514i
$518$		0			0
$519$	−5.55338			−0.243766
$520$		0			0
$521$	5.67909			0.248806			0.124403	−	0.992232i	$-0.460299\pi$
$521$	5.67909			0.248806			0.124403	+	0.992232i	$0.460299\pi$
$522$		0			0
$523$		−	36.8094i		−	1.60956i	−0.593572	−	0.804781i	$-0.702283\pi$
$523$		−	36.8094i		−	1.60956i	0.593572	−	0.804781i	$-0.297717\pi$
$524$		0			0
$525$	−5.31688	+	1.94113i	−0.232048	+	0.0847178i
$526$		0			0
$527$			16.9277i			0.737382i
$528$		0			0
$529$	−20.0896			−0.873459
$530$		0			0
$531$	−29.9032			−1.29769
$532$		0			0
$533$			8.55160i			0.370411i
$534$		0			0
$535$	−7.36471	−	41.6472i	−0.318404	−	1.80057i
$536$		0			0
$537$			1.49414i			0.0644770i
$538$		0			0
$539$	−12.5029			−0.538537
$540$		0			0
$541$	−24.9051			−1.07076			−0.535378	−	0.844613i	$-0.679831\pi$
$541$	−24.9051			−1.07076			−0.535378	+	0.844613i	$0.679831\pi$
$542$		0			0
$543$			1.07447i			0.0461100i
$544$		0			0
$545$	−19.5996	+	3.46590i	−0.839553	+	0.148463i
$546$		0			0
$547$		−	9.17066i		−	0.392109i	−0.980593	−	0.196055i	$-0.937187\pi$
$547$		−	9.17066i		−	0.392109i	0.980593	−	0.196055i	$-0.0628130\pi$
$548$		0			0
$549$	31.2808			1.33503
$550$		0			0
$551$	−5.14084			−0.219007
$552$		0			0
$553$		−	10.0830i		−	0.428771i
$554$		0			0
$555$	−6.26235	+	1.10741i	−0.265822	+	0.0470068i
$556$		0			0
$557$		−	16.3168i		−	0.691364i	−0.938352	−	0.345682i	$-0.887648\pi$
$557$		−	16.3168i		−	0.691364i	0.938352	−	0.345682i	$-0.112352\pi$
$558$		0			0
$559$	38.7642			1.63955
$560$		0			0
$561$	7.21357			0.304557
$562$		0			0
$563$			23.4254i			0.987264i	0.869671	+	0.493632i	$0.164331\pi$
$563$			23.4254i			0.987264i	−0.869671	+	0.493632i	$0.835669\pi$
$564$		0			0
$565$	3.83562	+	21.6903i	0.161366	+	0.912519i
$566$		0			0
$567$			24.1002i			1.01211i
$568$		0			0
$569$	21.5994			0.905495			0.452748	−	0.891639i	$-0.350444\pi$
$569$	21.5994			0.905495			0.452748	+	0.891639i	$0.350444\pi$
$570$		0			0
$571$	13.9099			0.582111			0.291055	−	0.956706i	$-0.405994\pi$
$571$	13.9099			0.582111			0.291055	+	0.956706i	$0.405994\pi$
$572$		0			0
$573$			1.98641i			0.0829836i
$574$		0			0
$575$	−11.2560	−	30.8309i	−0.469407	−	1.28574i
$576$		0			0
$577$		−	27.0208i		−	1.12489i	−0.826834	−	0.562445i	$-0.809861\pi$
$577$		−	27.0208i		−	1.12489i	0.826834	−	0.562445i	$-0.190139\pi$
$578$		0			0
$579$	−9.03183			−0.375350
$580$		0			0
$581$	−12.6537			−0.524964
$582$		0			0
$583$		−	37.1972i		−	1.54055i
$584$		0			0
$585$	−4.22890	−	23.9143i	−0.174843	−	0.988734i
$586$		0			0
$587$		−	2.29463i		−	0.0947096i	−0.998878	−	0.0473548i	$-0.984921\pi$
$587$		−	2.29463i		−	0.0947096i	0.998878	−	0.0473548i	$-0.0150791\pi$
$588$		0			0
$589$	−4.25626			−0.175376
$590$		0			0
$591$	1.44466			0.0594255
$592$		0			0
$593$			22.6929i			0.931888i	0.884814	+	0.465944i	$0.154285\pi$
$593$			22.6929i			0.931888i	−0.884814	+	0.465944i	$0.845715\pi$
$594$		0			0
$595$	27.0315	−	4.78013i	1.10818	−	0.195966i
$596$		0			0
$597$		−	7.63105i		−	0.312318i
$598$		0			0
$599$	−4.95675			−0.202527			−0.101264	−	0.994860i	$-0.532289\pi$
$599$	−4.95675			−0.202527			−0.101264	+	0.994860i	$0.532289\pi$
$600$		0			0
$601$	−33.5372			−1.36801			−0.684005	−	0.729477i	$-0.739763\pi$
$601$	−33.5372			−1.36801			−0.684005	+	0.729477i	$0.739763\pi$
$602$		0			0
$603$		−	19.5119i		−	0.794586i
$604$		0			0
$605$	29.6369	−	5.24085i	1.20491	−	0.213071i
$606$		0			0
$607$		−	32.9103i		−	1.33579i	−0.744257	−	0.667893i	$-0.767196\pi$
$607$		−	32.9103i		−	1.33579i	0.744257	−	0.667893i	$-0.232804\pi$
$608$		0			0
$609$	5.81957			0.235821
$610$		0			0
$611$	3.54628			0.143467
$612$		0			0
$613$			44.4090i			1.79366i	0.442374	+	0.896831i	$0.354137\pi$
$613$			44.4090i			1.79366i	−0.442374	+	0.896831i	$0.645863\pi$
$614$		0			0
$615$	−0.322191	−	1.82198i	−0.0129920	−	0.0734693i
$616$		0			0
$617$			18.2962i			0.736579i	0.929711	+	0.368290i	$0.120056\pi$
$617$			18.2962i			0.736579i	−0.929711	+	0.368290i	$0.879944\pi$
$618$		0			0
$619$	2.76770			0.111243			0.0556216	−	0.998452i	$-0.482286\pi$
$619$	2.76770			0.111243			0.0556216	+	0.998452i	$0.482286\pi$
$620$		0			0
$621$	14.1204			0.566632
$622$		0			0
$623$			38.3170i			1.53514i
$624$		0			0
$625$	19.1194	−	16.1074i	0.764775	−	0.644298i
$626$		0			0
$627$			1.81376i			0.0724347i
$628$		0			0
$629$	30.8428			1.22978
$630$		0			0
$631$	5.74488			0.228700			0.114350	−	0.993441i	$-0.463521\pi$
$631$	5.74488			0.228700			0.114350	+	0.993441i	$0.463521\pi$
$632$		0			0
$633$			8.40083i			0.333903i
$634$		0			0
$635$	1.46555	+	8.28761i	0.0581584	+	0.328884i
$636$		0			0
$637$			9.58170i			0.379641i
$638$		0			0
$639$	8.54186			0.337911
$640$		0			0
$641$	19.3436			0.764028			0.382014	−	0.924157i	$-0.375231\pi$
$641$	19.3436			0.764028			0.382014	+	0.924157i	$0.375231\pi$
$642$		0			0
$643$		−	11.0400i		−	0.435375i	−0.976019	−	0.217687i	$-0.930149\pi$
$643$		−	11.0400i		−	0.435375i	0.976019	−	0.217687i	$-0.0698513\pi$
$644$		0			0
$645$	−8.25900	+	1.46049i	−0.325198	+	0.0575065i
$646$		0			0
$647$		−	3.35938i		−	0.132071i	−0.997817	−	0.0660353i	$-0.978965\pi$
$647$		−	3.35938i		−	0.132071i	0.997817	−	0.0660353i	$-0.0210350\pi$
$648$		0			0
$649$	−51.6109			−2.02590
$650$		0			0
$651$	4.81821			0.188841
$652$		0			0
$653$		−	44.1434i		−	1.72747i	−0.503950	−	0.863733i	$-0.668121\pi$
$653$		−	44.1434i		−	1.72747i	0.503950	−	0.863733i	$-0.331879\pi$
$654$		0			0
$655$	−22.1265	+	3.91275i	−0.864553	+	0.152884i
$656$		0			0
$657$		−	6.29372i		−	0.245542i
$658$		0			0
$659$	35.1874			1.37071			0.685354	−	0.728210i	$-0.259648\pi$
$659$	35.1874			1.37071			0.685354	+	0.728210i	$0.259648\pi$
$660$		0			0
$661$	10.3574			0.402855			0.201428	−	0.979503i	$-0.435442\pi$
$661$	10.3574			0.402855			0.201428	+	0.979503i	$0.435442\pi$
$662$		0			0
$663$		−	5.52819i		−	0.214697i
$664$		0			0
$665$	1.20191	+	6.79674i	0.0466079	+	0.263566i
$666$		0			0
$667$			33.7458i			1.30664i
$668$		0			0
$669$	−6.10575			−0.236062
$670$		0			0
$671$	53.9886			2.08421
$672$		0			0
$673$		−	36.0384i		−	1.38918i	−0.719407	−	0.694589i	$-0.755586\pi$
$673$		−	36.0384i		−	1.38918i	0.719407	−	0.694589i	$-0.244414\pi$
$674$		0			0
$675$	3.68857	+	10.1032i	0.141973	+	0.388874i
$676$		0			0
$677$			11.4531i			0.440177i	0.975480	+	0.220089i	$0.0706347\pi$
$677$			11.4531i			0.440177i	−0.975480	+	0.220089i	$0.929365\pi$
$678$		0			0
$679$	−32.7727			−1.25770
$680$		0			0
$681$	−4.34008			−0.166312
$682$		0			0
$683$		−	42.9554i		−	1.64364i	−0.569745	−	0.821821i	$-0.692958\pi$
$683$		−	42.9554i		−	1.64364i	0.569745	−	0.821821i	$-0.307042\pi$
$684$		0			0
$685$	5.69439	+	32.2016i	0.217571	+	1.23036i
$686$		0			0
$687$		−	1.77607i		−	0.0677611i
$688$		0			0
$689$	−28.5065			−1.08601
$690$		0			0
$691$	−5.23235			−0.199048			−0.0995241	−	0.995035i	$-0.531732\pi$
$691$	−5.23235			−0.199048			−0.0995241	+	0.995035i	$0.531732\pi$
$692$		0			0
$693$			43.7449i			1.66173i
$694$		0			0
$695$	−26.5930	+	4.70259i	−1.00873	+	0.178380i
$696$		0			0
$697$			8.97345i			0.339894i
$698$		0			0
$699$	3.52380			0.133282
$700$		0			0
$701$	−17.3930			−0.656925			−0.328463	−	0.944517i	$-0.606531\pi$
$701$	−17.3930			−0.656925			−0.328463	+	0.944517i	$0.606531\pi$
$702$		0			0
$703$			7.75503i			0.292486i
$704$		0			0
$705$	−0.755559	+	0.133610i	−0.0284560	+	0.00503204i
$706$		0			0
$707$		−	40.4733i		−	1.52215i
$708$		0			0
$709$	21.5383			0.808888			0.404444	−	0.914563i	$-0.367465\pi$
$709$	21.5383			0.808888			0.404444	+	0.914563i	$0.367465\pi$
$710$		0			0
$711$	−9.36024			−0.351036
$712$		0			0
$713$			27.9392i			1.04633i
$714$		0			0
$715$	−7.29880	−	41.2745i	−0.272960	−	1.54358i
$716$		0			0
$717$		−	3.48395i		−	0.130110i
$718$		0			0
$719$	30.8923			1.15209			0.576044	−	0.817418i	$-0.304596\pi$
$719$	30.8923			1.15209			0.576044	+	0.817418i	$0.304596\pi$
$720$		0			0
$721$	−15.3007			−0.569830
$722$		0			0
$723$		−	8.02006i		−	0.298269i
$724$		0			0
$725$	−24.1454	+	8.81517i	−0.896736	+	0.327387i
$726$		0			0
$727$		−	20.9947i		−	0.778649i	−0.921101	−	0.389325i	$-0.872708\pi$
$727$		−	20.9947i		−	0.778649i	0.921101	−	0.389325i	$-0.127292\pi$
$728$		0			0
$729$	20.0061			0.740967
$730$		0			0
$731$	40.6765			1.50447
$732$		0			0
$733$			22.0911i			0.815955i	0.912992	+	0.407978i	$0.133766\pi$
$733$			22.0911i			0.815955i	−0.912992	+	0.407978i	$0.866234\pi$
$734$		0			0
$735$	−0.361001	−	2.04145i	−0.0133157	−	0.0753000i
$736$		0			0
$737$		−	33.6762i		−	1.24048i
$738$		0			0
$739$	−7.81209			−0.287372			−0.143686	−	0.989623i	$-0.545896\pi$
$739$	−7.81209			−0.287372			−0.143686	+	0.989623i	$0.545896\pi$
$740$		0			0
$741$	1.39000			0.0510628
$742$		0			0
$743$		−	17.9012i		−	0.656731i	−0.944551	−	0.328365i	$-0.893502\pi$
$743$		−	17.9012i		−	0.656731i	0.944551	−	0.328365i	$-0.106498\pi$
$744$		0			0
$745$	−27.6865	+	4.89596i	−1.01436	+	0.179374i
$746$		0			0
$747$			11.7467i			0.429790i
$748$		0			0
$749$	58.3834			2.13328
$750$		0			0
$751$	48.8802			1.78366			0.891832	−	0.452367i	$-0.149420\pi$
$751$	48.8802			1.78366			0.891832	+	0.452367i	$0.149420\pi$
$752$		0			0
$753$		−	0.744878i		−	0.0271449i
$754$		0			0
$755$	0.859484	−	0.151987i	0.0312798	−	0.00553138i
$756$		0			0
$757$		−	6.75011i		−	0.245337i	−0.992448	−	0.122668i	$-0.960855\pi$
$757$		−	6.75011i		−	0.245337i	0.992448	−	0.122668i	$-0.0391452\pi$
$758$		0			0
$759$	11.9060			0.432161
$760$		0			0
$761$	47.5563			1.72392			0.861958	−	0.506980i	$-0.169238\pi$
$761$	47.5563			1.72392			0.861958	+	0.506980i	$0.169238\pi$
$762$		0			0
$763$		−	27.4757i		−	0.994689i
$764$		0			0
$765$	−4.43751	−	25.0940i	−0.160438	−	0.907274i
$766$		0			0
$767$			39.5525i			1.42816i
$768$		0			0
$769$	0.849714			0.0306415			0.0153207	−	0.999883i	$-0.495123\pi$
$769$	0.849714			0.0306415			0.0153207	+	0.999883i	$0.495123\pi$
$770$		0			0
$771$	−2.79790			−0.100764
$772$		0			0
$773$		−	4.74109i		−	0.170525i	−0.996359	−	0.0852627i	$-0.972827\pi$
$773$		−	4.74109i		−	0.170525i	0.996359	−	0.0852627i	$-0.0271729\pi$
$774$		0			0
$775$	−19.9907	+	7.29836i	−0.718087	+	0.262165i
$776$		0			0
$777$		−	8.77891i		−	0.314942i
$778$		0			0
$779$	−2.25626			−0.0808390
$780$		0			0
$781$	14.7427			0.527535
$782$		0			0
$783$		−	11.0585i		−	0.395197i
$784$		0			0
$785$	6.87313	+	38.8673i	0.245312	+	1.38723i
$786$		0			0
$787$		−	19.0208i		−	0.678018i	−0.940783	−	0.339009i	$-0.889908\pi$
$787$		−	19.0208i		−	0.678018i	0.940783	−	0.339009i	$-0.110092\pi$
$788$		0			0
$789$	11.1231			0.395994
$790$		0			0
$791$	−30.4067			−1.08114
$792$		0			0
$793$		−	41.3747i		−	1.46926i
$794$		0			0
$795$	6.07351	−	1.07401i	0.215405	−	0.0380913i
$796$		0			0

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:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.366738i q^{3} +(2.20191 - 0.389375i) q^{5} +3.08675i q^{7} +2.86550 q^{9} +4.94567 q^{11} -3.79016i q^{13} +(0.142799 + 0.807521i) q^{15} -3.97713i q^{17} +1.00000 q^{19} -1.13203 q^{21} -6.56426i q^{23} +(4.69677 - 1.71473i) q^{25} +2.15110i q^{27} -5.14084 q^{29} -4.25626 q^{31} +1.81376i q^{33} +(1.20191 + 6.79674i) q^{35} +7.75503i q^{37} +1.39000 q^{39} -2.25626 q^{41} +10.2276i q^{43} +(6.30957 - 1.11576i) q^{45} +0.935652i q^{47} -2.52804 q^{49} +1.45856 q^{51} -7.52117i q^{53} +(10.8899 - 1.92572i) q^{55} +0.366738i q^{57} -10.4356 q^{59} +10.9163 q^{61} +8.84510i q^{63} +(-1.47580 - 8.34558i) q^{65} -6.80924i q^{67} +2.40736 q^{69} +2.98093 q^{71} -2.19638i q^{73} +(0.628858 + 1.72248i) q^{75} +15.2661i q^{77} -3.26652 q^{79} +7.80762 q^{81} +4.09936i q^{83} +(-1.54860 - 8.75726i) q^{85} -1.88534i q^{87} +12.4134 q^{89} +11.6993 q^{91} -1.56093i q^{93} +(2.20191 - 0.389375i) q^{95} +10.6172i q^{97} +14.1718 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} - 16 q^{9} + 4 q^{11} + 12 q^{15} + 12 q^{19} + 36 q^{21} + 18 q^{25} + 4 q^{29} - 16 q^{31} - 6 q^{35} - 36 q^{39} + 8 q^{41} - 2 q^{45} - 4 q^{49} + 68 q^{51} + 18 q^{55} - 4 q^{59} + 20 q^{61}+ \cdots - 44 q^{99}+O(q^{100}) \) 12 * q + 6 * q^5 - 16 * q^9 + 4 * q^11 + 12 * q^15 + 12 * q^19 + 36 * q^21 + 18 * q^25 + 4 * q^29 - 16 * q^31 - 6 * q^35 - 36 * q^39 + 8 * q^41 - 2 * q^45 - 4 * q^49 + 68 * q^51 + 18 * q^55 - 4 * q^59 + 20 * q^61 + 20 * q^65 - 36 * q^69 + 16 * q^71 + 16 * q^75 - 40 * q^79 + 12 * q^81 + 6 * q^85 - 64 * q^89 - 20 * q^91 + 6 * q^95 - 44 * q^99

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