LMFDB - Embedded newform 3100.3.d.h.1301.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3100,3,Mod(1301,3100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3100, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("3100.1301");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 3100 = 2^{2} \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	3100.d (of order $2$, degree $1$, 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:	$84.4688819517$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 620)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1301.10
Character	$\chi$	$=$	3100.1301
Dual form			3100.3.d.h.1301.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.48325i q^{3} +3.21821 q^{7} -11.0995 q^{9} +O(q^{10})$	$q+4.48325i q^{3} +3.21821 q^{7} -11.0995 q^{9} +18.8341i q^{11} -13.8796i q^{13} +13.8252i q^{17} +8.23431 q^{19} +14.4280i q^{21} +21.0811i q^{23} -9.41269i q^{27} +22.1028i q^{29} +(30.4139 - 5.99969i) q^{31} -84.4379 q^{33} +6.01059i q^{37} +62.2259 q^{39} +22.3665 q^{41} -5.93085i q^{43} +48.9623 q^{47} -38.6431 q^{49} -61.9820 q^{51} +52.0935i q^{53} +36.9165i q^{57} -63.3369 q^{59} -85.7365i q^{61} -35.7206 q^{63} +62.1709 q^{67} -94.5120 q^{69} +52.1004 q^{71} +62.7559i q^{73} +60.6121i q^{77} +6.84506i q^{79} -57.6963 q^{81} +109.459i q^{83} -99.0926 q^{87} +29.8993i q^{89} -44.6676i q^{91} +(26.8981 + 136.353i) q^{93} +139.038 q^{97} -209.049i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 44 q^{9}+O(q^{10}) $ 24 * q - 44 * q^9	$ 24 q - 44 q^{9} - 8 q^{19} - 24 q^{31} + 280 q^{39} - 248 q^{41} + 644 q^{49} - 100 q^{51} - 152 q^{59} + 288 q^{69} - 352 q^{71} - 368 q^{81}+O(q^{100}) $ 24 * q - 44 * q^9 - 8 * q^19 - 24 * q^31 + 280 * q^39 - 248 * q^41 + 644 * q^49 - 100 * q^51 - 152 * q^59 + 288 * q^69 - 352 * q^71 - 368 * q^81

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3100\mathbb{Z}\right)^\times$.

$n$	$1551$	$1801$	$2977$
$\chi(n)$	$1$	$-1$	$1$

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
$3$			4.48325i			1.49442i	0.664590	+	0.747208i	$0.268606\pi$
$3$			4.48325i			1.49442i	−0.664590	+	0.747208i	$0.731394\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.21821			0.459744			0.229872	−	0.973221i	$-0.426169\pi$
$7$	3.21821			0.459744			0.229872	+	0.973221i	$0.426169\pi$
$8$		0			0
$9$	−11.0995			−1.23328
$10$		0			0
$11$			18.8341i			1.71219i	0.516819	+	0.856095i	$0.327116\pi$
$11$			18.8341i			1.71219i	−0.516819	+	0.856095i	$0.672884\pi$
$12$		0			0
$13$		−	13.8796i		−	1.06766i	−0.845591	−	0.533832i	$-0.820751\pi$
$13$		−	13.8796i		−	1.06766i	0.845591	−	0.533832i	$-0.179249\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			13.8252i			0.813250i	0.913595	+	0.406625i	$0.133294\pi$
$17$			13.8252i			0.813250i	−0.913595	+	0.406625i	$0.866706\pi$
$18$		0			0
$19$	8.23431			0.433385			0.216692	−	0.976240i	$-0.430473\pi$
$19$	8.23431			0.433385			0.216692	+	0.976240i	$0.430473\pi$
$20$		0			0
$21$			14.4280i			0.687049i
$22$		0			0
$23$			21.0811i			0.916571i	0.888805	+	0.458286i	$0.151536\pi$
$23$			21.0811i			0.916571i	−0.888805	+	0.458286i	$0.848464\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	9.41269i		−	0.348618i
$28$		0			0
$29$			22.1028i			0.762167i	0.924541	+	0.381083i	$0.124449\pi$
$29$			22.1028i			0.762167i	−0.924541	+	0.381083i	$0.875551\pi$
$30$		0			0
$31$	30.4139	−	5.99969i	0.981093	−	0.193538i
$31$	30.4139	−	5.99969i	0.981093	−	0.193538i
$32$		0			0
$33$	−84.4379			−2.55872
$34$		0			0
$35$		0			0
$36$		0			0
$37$			6.01059i			0.162448i	0.996696	+	0.0812242i	$0.0258830\pi$
$37$			6.01059i			0.162448i	−0.996696	+	0.0812242i	$0.974117\pi$
$38$		0			0
$39$	62.2259			1.59553
$40$		0			0
$41$	22.3665			0.545523			0.272762	−	0.962082i	$-0.412063\pi$
$41$	22.3665			0.545523			0.272762	+	0.962082i	$0.412063\pi$
$42$		0			0
$43$		−	5.93085i		−	0.137927i	−0.997619	−	0.0689634i	$-0.978031\pi$
$43$		−	5.93085i		−	0.137927i	0.997619	−	0.0689634i	$-0.0219692\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	48.9623			1.04175			0.520876	−	0.853632i	$-0.325605\pi$
$47$	48.9623			1.04175			0.520876	+	0.853632i	$0.325605\pi$
$48$		0			0
$49$	−38.6431			−0.788635
$50$		0			0
$51$	−61.9820			−1.21533
$52$		0			0
$53$			52.0935i			0.982896i	0.870907	+	0.491448i	$0.163532\pi$
$53$			52.0935i			0.982896i	−0.870907	+	0.491448i	$0.836468\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			36.9165i			0.647657i
$58$		0			0
$59$	−63.3369			−1.07351			−0.536754	−	0.843739i	$-0.680350\pi$
$59$	−63.3369			−1.07351			−0.536754	+	0.843739i	$0.680350\pi$
$60$		0			0
$61$		−	85.7365i		−	1.40552i	−0.711428	−	0.702759i	$-0.751951\pi$
$61$		−	85.7365i		−	1.40552i	0.711428	−	0.702759i	$-0.248049\pi$
$62$		0			0
$63$	−35.7206			−0.566994
$64$		0			0
$65$		0			0
$66$		0			0
$67$	62.1709			0.927924			0.463962	−	0.885855i	$-0.346427\pi$
$67$	62.1709			0.927924			0.463962	+	0.885855i	$0.346427\pi$
$68$		0			0
$69$	−94.5120			−1.36974
$70$		0			0
$71$	52.1004			0.733808			0.366904	−	0.930259i	$-0.380418\pi$
$71$	52.1004			0.733808			0.366904	+	0.930259i	$0.380418\pi$
$72$		0			0
$73$			62.7559i			0.859670i	0.902907	+	0.429835i	$0.141428\pi$
$73$			62.7559i			0.859670i	−0.902907	+	0.429835i	$0.858572\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			60.6121i			0.787170i
$78$		0			0
$79$			6.84506i			0.0866463i	0.999061	+	0.0433231i	$0.0137945\pi$
$79$			6.84506i			0.0866463i	−0.999061	+	0.0433231i	$0.986205\pi$
$80$		0			0
$81$	−57.6963			−0.712300
$82$		0			0
$83$			109.459i			1.31878i	0.751799	+	0.659392i	$0.229186\pi$
$83$			109.459i			1.31878i	−0.751799	+	0.659392i	$0.770814\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−99.0926			−1.13899
$88$		0			0
$89$			29.8993i			0.335948i	0.985791	+	0.167974i	$0.0537224\pi$
$89$			29.8993i			0.335948i	−0.985791	+	0.167974i	$0.946278\pi$
$90$		0			0
$91$		−	44.6676i		−	0.490853i
$92$		0			0
$93$	26.8981	+	136.353i	0.289227	+	1.46616i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	139.038			1.43338			0.716689	−	0.697393i	$-0.245657\pi$
$97$	139.038			1.43338			0.716689	+	0.697393i	$0.245657\pi$
$98$		0			0
$99$		−	209.049i		−	2.11161i
$100$		0			0
$101$	76.4000			0.756436			0.378218	−	0.925717i	$-0.376537\pi$
$101$	76.4000			0.756436			0.378218	+	0.925717i	$0.376537\pi$
$102$		0			0
$103$	−93.4551			−0.907331			−0.453665	−	0.891172i	$-0.649884\pi$
$103$	−93.4551			−0.907331			−0.453665	+	0.891172i	$0.649884\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−91.3976			−0.854183			−0.427091	−	0.904208i	$-0.640462\pi$
$107$	−91.3976			−0.854183			−0.427091	+	0.904208i	$0.640462\pi$
$108$		0			0
$109$	−81.1782			−0.744754			−0.372377	−	0.928081i	$-0.621457\pi$
$109$	−81.1782			−0.744754			−0.372377	+	0.928081i	$0.621457\pi$
$110$		0			0
$111$	−26.9470			−0.242765
$112$		0			0
$113$	−197.874			−1.75109			−0.875547	−	0.483132i	$-0.839499\pi$
$113$	−197.874			−1.75109			−0.875547	+	0.483132i	$0.839499\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$			154.057i			1.31673i
$118$		0			0
$119$			44.4925i			0.373887i
$120$		0			0
$121$	−233.723			−1.93159
$122$		0			0
$123$			100.274i			0.815239i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	79.6437i		−	0.627116i	−0.949569	−	0.313558i	$-0.898479\pi$
$127$		−	79.6437i		−	0.627116i	0.949569	−	0.313558i	$-0.101521\pi$
$128$		0			0
$129$	26.5895			0.206120
$130$		0			0
$131$	−208.437			−1.59112			−0.795562	−	0.605872i	$-0.792824\pi$
$131$	−208.437			−1.59112			−0.795562	+	0.605872i	$0.792824\pi$
$132$		0			0
$133$	26.4997			0.199246
$134$		0			0
$135$		0			0
$136$		0			0
$137$			198.811i			1.45117i	0.688130	+	0.725587i	$0.258432\pi$
$137$			198.811i			1.45117i	−0.688130	+	0.725587i	$0.741568\pi$
$138$		0			0
$139$		−	189.281i		−	1.36174i	−0.732405	−	0.680869i	$-0.761602\pi$
$139$		−	189.281i		−	1.36174i	0.732405	−	0.680869i	$-0.238398\pi$
$140$		0			0
$141$			219.510i			1.55681i
$142$		0			0
$143$	261.410			1.82804
$144$		0			0
$145$		0			0
$146$		0			0
$147$		−	173.247i		−	1.17855i
$148$		0			0
$149$	−173.267			−1.16286			−0.581432	−	0.813595i	$-0.697507\pi$
$149$	−173.267			−1.16286			−0.581432	+	0.813595i	$0.697507\pi$
$150$		0			0
$151$		−	113.321i		−	0.750469i	−0.926930	−	0.375234i	$-0.877562\pi$
$151$		−	113.321i		−	0.750469i	0.926930	−	0.375234i	$-0.122438\pi$
$152$		0			0
$153$		−	153.454i		−	1.00297i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−14.6060			−0.0930320			−0.0465160	−	0.998918i	$-0.514812\pi$
$157$	−14.6060			−0.0930320			−0.0465160	+	0.998918i	$0.514812\pi$
$158$		0			0
$159$	−233.548			−1.46886
$160$		0			0
$161$			67.8435i			0.421388i
$162$		0			0
$163$	109.436			0.671385			0.335693	−	0.941972i	$-0.391030\pi$
$163$	109.436			0.671385			0.335693	+	0.941972i	$0.391030\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			116.222i			0.695942i	0.937505	+	0.347971i	$0.113129\pi$
$167$			116.222i			0.695942i	−0.937505	+	0.347971i	$0.886871\pi$
$168$		0			0
$169$	−23.6442			−0.139907
$170$		0			0
$171$	−91.3969			−0.534485
$172$		0			0
$173$	223.727			1.29322			0.646610	−	0.762821i	$-0.276186\pi$
$173$	223.727			1.29322			0.646610	+	0.762821i	$0.276186\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	283.955i		−	1.60427i
$178$		0			0
$179$		−	40.8639i		−	0.228290i	−0.993464	−	0.114145i	$-0.963587\pi$
$179$		−	40.8639i		−	0.228290i	0.993464	−	0.114145i	$-0.0364128\pi$
$180$		0			0
$181$		−	108.105i		−	0.597266i	−0.954368	−	0.298633i	$-0.903469\pi$
$181$		−	108.105i		−	0.597266i	0.954368	−	0.298633i	$-0.0965306\pi$
$182$		0			0
$183$	384.378			2.10043
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−260.386			−1.39244
$188$		0			0
$189$		−	30.2920i		−	0.160275i
$190$		0			0
$191$	152.194			0.796828			0.398414	−	0.917206i	$-0.369561\pi$
$191$	152.194			0.796828			0.398414	+	0.917206i	$0.369561\pi$
$192$		0			0
$193$	−310.542			−1.60903			−0.804513	−	0.593935i	$-0.797573\pi$
$193$	−310.542			−1.60903			−0.804513	+	0.593935i	$0.797573\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			101.199i			0.513703i	0.966451	+	0.256851i	$0.0826851\pi$
$197$			101.199i			0.513703i	−0.966451	+	0.256851i	$0.917315\pi$
$198$		0			0
$199$			341.297i			1.71506i	0.514433	+	0.857531i	$0.328002\pi$
$199$			341.297i			1.71506i	−0.514433	+	0.857531i	$0.671998\pi$
$200$		0			0
$201$			278.728i			1.38671i
$202$		0			0
$203$			71.1316i			0.350402i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	233.991i		−	1.13039i
$208$		0			0
$209$			155.086i			0.742037i
$210$		0			0
$211$	312.408			1.48061			0.740304	−	0.672272i	$-0.234682\pi$
$211$	312.408			1.48061			0.740304	+	0.672272i	$0.234682\pi$
$212$		0			0
$213$			233.579i			1.09661i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	97.8782	−	19.3083i	0.451052	−	0.0889782i
$218$		0			0
$219$	−281.351			−1.28471
$220$		0			0
$221$	191.889			0.868277
$222$		0			0
$223$		−	276.398i		−	1.23945i	−0.784819	−	0.619726i	$-0.787244\pi$
$223$		−	276.398i		−	1.23945i	0.784819	−	0.619726i	$-0.212756\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−145.212			−0.639702			−0.319851	−	0.947468i	$-0.603633\pi$
$227$	−145.212			−0.639702			−0.319851	+	0.947468i	$0.603633\pi$
$228$		0			0
$229$		−	88.1326i		−	0.384859i	−0.981311	−	0.192429i	$-0.938363\pi$
$229$		−	88.1326i		−	0.384859i	0.981311	−	0.192429i	$-0.0616366\pi$
$230$		0			0
$231$	−271.739			−1.17636
$232$		0			0
$233$	19.1793			0.0823145			0.0411572	−	0.999153i	$-0.486896\pi$
$233$	19.1793			0.0823145			0.0411572	+	0.999153i	$0.486896\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−30.6881			−0.129486
$238$		0			0
$239$			419.216i			1.75404i	0.480453	+	0.877020i	$0.340472\pi$
$239$			419.216i			1.75404i	−0.480453	+	0.877020i	$0.659528\pi$
$240$		0			0
$241$		−	133.457i		−	0.553764i	−0.960904	−	0.276882i	$-0.910699\pi$
$241$		−	133.457i		−	0.553764i	0.960904	−	0.276882i	$-0.0893011\pi$
$242$		0			0
$243$		−	343.381i		−	1.41309i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		−	114.289i		−	0.462709i
$248$		0			0
$249$	−490.732			−1.97081
$250$		0			0
$251$		−	231.713i		−	0.923158i	−0.887099	−	0.461579i	$-0.847283\pi$
$251$		−	231.713i		−	0.923158i	0.887099	−	0.461579i	$-0.152717\pi$
$252$		0			0
$253$	−397.044			−1.56934
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−380.130			−1.47910			−0.739552	−	0.673099i	$-0.764963\pi$
$257$	−380.130			−1.47910			−0.739552	+	0.673099i	$0.764963\pi$
$258$		0			0
$259$			19.3433i			0.0746847i
$260$		0			0
$261$		−	245.331i		−	0.939966i
$262$		0			0
$263$		−	118.460i		−	0.450417i	−0.974311	−	0.225208i	$-0.927694\pi$
$263$		−	118.460i		−	0.450417i	0.974311	−	0.225208i	$-0.0723063\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−134.046			−0.502046
$268$		0			0
$269$		−	345.117i		−	1.28296i	−0.767138	−	0.641482i	$-0.778320\pi$
$269$		−	345.117i		−	1.28296i	0.767138	−	0.641482i	$-0.221680\pi$
$270$		0			0
$271$		−	400.614i		−	1.47828i	−0.673552	−	0.739140i	$-0.735232\pi$
$271$		−	400.614i		−	1.47828i	0.673552	−	0.739140i	$-0.264768\pi$
$272$		0			0
$273$	200.256			0.733538
$274$		0			0
$275$		0			0
$276$		0			0
$277$			250.993i			0.906110i	0.891482	+	0.453055i	$0.149666\pi$
$277$			250.993i			0.906110i	−0.891482	+	0.453055i	$0.850334\pi$
$278$		0			0
$279$	−337.580	+	66.5937i	−1.20996	+	0.238687i
$280$		0			0
$281$	−207.256			−0.737565			−0.368783	−	0.929516i	$-0.620225\pi$
$281$	−207.256			−0.737565			−0.368783	+	0.929516i	$0.620225\pi$
$282$		0			0
$283$	366.455			1.29489			0.647447	−	0.762111i	$-0.275837\pi$
$283$	366.455			1.29489			0.647447	+	0.762111i	$0.275837\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	71.9800			0.250801
$288$		0			0
$289$	97.8626			0.338625
$290$		0			0
$291$			623.341i			2.14206i
$292$		0			0
$293$	219.593			0.749466			0.374733	−	0.927133i	$-0.377734\pi$
$293$	219.593			0.749466			0.374733	+	0.927133i	$0.377734\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	177.280			0.596901
$298$		0			0
$299$	292.599			0.978590
$300$		0			0
$301$		−	19.0867i		−	0.0634110i
$302$		0			0
$303$			342.520i			1.13043i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	435.216			1.41764			0.708821	−	0.705389i	$-0.249228\pi$
$307$	435.216			1.41764			0.708821	+	0.705389i	$0.249228\pi$
$308$		0			0
$309$		−	418.982i		−	1.35593i
$310$		0			0
$311$	−378.699			−1.21768			−0.608841	−	0.793292i	$-0.708365\pi$
$311$	−378.699			−1.21768			−0.608841	+	0.793292i	$0.708365\pi$
$312$		0			0
$313$		−	406.120i		−	1.29751i	−0.760998	−	0.648755i	$-0.775290\pi$
$313$		−	406.120i		−	1.29751i	0.760998	−	0.648755i	$-0.224710\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−127.082			−0.400891			−0.200446	−	0.979705i	$-0.564239\pi$
$317$	−127.082			−0.400891			−0.200446	+	0.979705i	$0.564239\pi$
$318$		0			0
$319$	−416.287			−1.30497
$320$		0			0
$321$		−	409.758i		−	1.27651i
$322$		0			0
$323$			113.841i			0.352450i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	363.942i		−	1.11297i
$328$		0			0
$329$	157.571			0.478940
$330$		0			0
$331$		−	84.9621i		−	0.256683i	−0.991730	−	0.128342i	$-0.959035\pi$
$331$		−	84.9621i		−	0.256683i	0.991730	−	0.128342i	$-0.0409654\pi$
$332$		0			0
$333$		−	66.7147i		−	0.200344i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			214.929i			0.637771i	0.947793	+	0.318886i	$0.103309\pi$
$337$			214.929i			0.637771i	−0.947793	+	0.318886i	$0.896691\pi$
$338$		0			0
$339$		−	887.117i		−	2.61687i
$340$		0			0
$341$	112.999	+	572.818i	0.331374	+	1.67982i
$342$		0			0
$343$	−282.054			−0.822315
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	441.126i		−	1.27126i	−0.771996	−	0.635628i	$-0.780741\pi$
$347$		−	441.126i		−	1.27126i	0.771996	−	0.635628i	$-0.219259\pi$
$348$		0			0
$349$	−47.5681			−0.136298			−0.0681492	−	0.997675i	$-0.521709\pi$
$349$	−47.5681			−0.136298			−0.0681492	+	0.997675i	$0.521709\pi$
$350$		0			0
$351$	−130.645			−0.372207
$352$		0			0
$353$			22.7511i			0.0644508i	0.999481	+	0.0322254i	$0.0102594\pi$
$353$			22.7511i			0.0644508i	−0.999481	+	0.0322254i	$0.989741\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−199.471			−0.558743
$358$		0			0
$359$	−207.050			−0.576742			−0.288371	−	0.957519i	$-0.593114\pi$
$359$	−207.050			−0.576742			−0.288371	+	0.957519i	$0.593114\pi$
$360$		0			0
$361$	−293.196			−0.812178
$362$		0			0
$363$		−	1047.84i		−	2.88661i
$364$		0			0
$365$		0			0
$366$		0			0
$367$			187.417i			0.510672i	0.966852	+	0.255336i	$0.0821861\pi$
$367$			187.417i			0.510672i	−0.966852	+	0.255336i	$0.917814\pi$
$368$		0			0
$369$	−248.257			−0.672783
$370$		0			0
$371$			167.648i			0.451881i
$372$		0			0
$373$	−505.440			−1.35507			−0.677534	−	0.735491i	$-0.736951\pi$
$373$	−505.440			−1.35507			−0.677534	+	0.735491i	$0.736951\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	306.779			0.813738
$378$		0			0
$379$	−25.3655			−0.0669274			−0.0334637	−	0.999440i	$-0.510654\pi$
$379$	−25.3655			−0.0669274			−0.0334637	+	0.999440i	$0.510654\pi$
$380$		0			0
$381$	357.063			0.937173
$382$		0			0
$383$		−	98.1948i		−	0.256383i	−0.991749	−	0.128192i	$-0.959083\pi$
$383$		−	98.1948i		−	0.256383i	0.991749	−	0.128192i	$-0.0409173\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			65.8296i			0.170102i
$388$		0			0
$389$		−	513.777i		−	1.32076i	−0.750931	−	0.660381i	$-0.770395\pi$
$389$		−	513.777i		−	1.32076i	0.750931	−	0.660381i	$-0.229605\pi$
$390$		0			0
$391$	−291.452			−0.745401
$392$		0			0
$393$		−	934.476i		−	2.37780i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	290.826			0.732559			0.366280	−	0.930505i	$-0.380631\pi$
$397$	290.826			0.732559			0.366280	+	0.930505i	$0.380631\pi$
$398$		0			0
$399$			118.805i			0.297757i
$400$		0			0
$401$		−	51.0627i		−	0.127338i	−0.997971	−	0.0636692i	$-0.979720\pi$
$401$		−	51.0627i		−	0.127338i	0.997971	−	0.0636692i	$-0.0202803\pi$
$402$		0			0
$403$	−83.2735	−	422.133i	−0.206634	−	1.04748i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−113.204			−0.278142
$408$		0			0
$409$		−	772.380i		−	1.88846i	−0.329286	−	0.944230i	$-0.606808\pi$
$409$		−	772.380i		−	1.88846i	0.329286	−	0.944230i	$-0.393192\pi$
$410$		0			0
$411$	−891.319			−2.16866
$412$		0			0
$413$	−203.832			−0.493539
$414$		0			0
$415$		0			0
$416$		0			0
$417$	848.596			2.03500
$418$		0			0
$419$	−636.613			−1.51936			−0.759682	−	0.650295i	$-0.774645\pi$
$419$	−636.613			−1.51936			−0.759682	+	0.650295i	$0.774645\pi$
$420$		0			0
$421$	612.077			1.45387			0.726933	−	0.686709i	$-0.240945\pi$
$421$	612.077			1.45387			0.726933	+	0.686709i	$0.240945\pi$
$422$		0			0
$423$	−543.459			−1.28477
$424$		0			0
$425$		0			0
$426$		0			0
$427$		−	275.918i		−	0.646179i
$428$		0			0
$429$			1171.97i			2.73186i
$430$		0			0
$431$	−656.847			−1.52401			−0.762003	−	0.647573i	$-0.775784\pi$
$431$	−656.847			−1.52401			−0.762003	+	0.647573i	$0.775784\pi$
$432$		0			0
$433$			594.844i			1.37377i	0.726765	+	0.686887i	$0.241023\pi$
$433$			594.844i			1.37377i	−0.726765	+	0.686887i	$0.758977\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			173.589i			0.397228i
$438$		0			0
$439$	−597.587			−1.36125			−0.680623	−	0.732634i	$-0.738291\pi$
$439$	−597.587			−1.36125			−0.680623	+	0.732634i	$0.738291\pi$
$440$		0			0
$441$	428.920			0.972608
$442$		0			0
$443$	−35.1445			−0.0793330			−0.0396665	−	0.999213i	$-0.512630\pi$
$443$	−35.1445			−0.0793330			−0.0396665	+	0.999213i	$0.512630\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	776.798i		−	1.73780i
$448$		0			0
$449$		−	56.6822i		−	0.126241i	−0.998006	−	0.0631205i	$-0.979895\pi$
$449$		−	56.6822i		−	0.126241i	0.998006	−	0.0631205i	$-0.0201053\pi$
$450$		0			0
$451$			421.252i			0.934040i
$452$		0			0
$453$	508.045			1.12151
$454$		0			0
$455$		0			0
$456$		0			0
$457$			452.100i			0.989279i	0.869098	+	0.494639i	$0.164700\pi$
$457$			452.100i			0.989279i	−0.869098	+	0.494639i	$0.835300\pi$
$458$		0			0
$459$	130.133			0.283514
$460$		0			0
$461$		−	683.943i		−	1.48361i	−0.670617	−	0.741804i	$-0.733971\pi$
$461$		−	683.943i		−	1.48361i	0.670617	−	0.741804i	$-0.266029\pi$
$462$		0			0
$463$			543.501i			1.17387i	0.809634	+	0.586934i	$0.199665\pi$
$463$			543.501i			1.17387i	−0.809634	+	0.586934i	$0.800335\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	32.3448			0.0692608			0.0346304	−	0.999400i	$-0.488975\pi$
$467$	32.3448			0.0692608			0.0346304	+	0.999400i	$0.488975\pi$
$468$		0			0
$469$	200.079			0.426608
$470$		0			0
$471$		−	65.4825i		−	0.139029i
$472$		0			0
$473$	111.702			0.236157
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	578.213i		−	1.21219i
$478$		0			0
$479$	−112.308			−0.234463			−0.117232	−	0.993105i	$-0.537402\pi$
$479$	−112.308			−0.234463			−0.117232	+	0.993105i	$0.537402\pi$
$480$		0			0
$481$	83.4248			0.173440
$482$		0			0
$483$	−304.160			−0.629730
$484$		0			0
$485$		0			0
$486$		0			0
$487$			181.610i			0.372916i	0.982463	+	0.186458i	$0.0597008\pi$
$487$			181.610i			0.372916i	−0.982463	+	0.186458i	$0.940299\pi$
$488$		0			0
$489$			490.628i			1.00333i
$490$		0			0
$491$		−	107.169i		−	0.218267i	−0.994027	−	0.109134i	$-0.965192\pi$
$491$		−	107.169i		−	0.218267i	0.994027	−	0.109134i	$-0.0348076\pi$
$492$		0			0
$493$	−305.577			−0.619832
$494$		0			0
$495$		0			0
$496$		0			0
$497$	167.670			0.337364
$498$		0			0
$499$			654.047i			1.31072i	0.755318	+	0.655358i	$0.227482\pi$
$499$			654.047i			1.31072i	−0.755318	+	0.655358i	$0.772518\pi$
$500$		0			0
$501$	−521.054			−1.04003
$502$		0			0
$503$	393.697			0.782697			0.391349	−	0.920242i	$-0.372009\pi$
$503$	393.697			0.782697			0.391349	+	0.920242i	$0.372009\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	106.003i		−	0.209079i
$508$		0			0
$509$			414.968i			0.815262i	0.913147	+	0.407631i	$0.133645\pi$
$509$			414.968i			0.815262i	−0.913147	+	0.407631i	$0.866355\pi$
$510$		0			0
$511$			201.962i			0.395229i
$512$		0			0
$513$		−	77.5070i		−	0.151086i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			922.161i			1.78368i
$518$		0			0
$519$			1003.02i			1.93261i
$520$		0			0
$521$	795.823			1.52749			0.763746	−	0.645517i	$-0.223358\pi$
$521$	795.823			1.52749			0.763746	+	0.645517i	$0.223358\pi$
$522$		0			0
$523$		−	36.2497i		−	0.0693111i	−0.999399	−	0.0346556i	$-0.988967\pi$
$523$		−	36.2497i		−	0.0693111i	0.999399	−	0.0346556i	$-0.0110334\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	82.9472	+	420.479i	0.157395	+	0.797873i
$528$		0			0
$529$	84.5855			0.159897
$530$		0			0
$531$	703.010			1.32394
$532$		0			0
$533$		−	310.438i		−	0.582436i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	183.203			0.341160
$538$		0			0
$539$		−	727.808i		−	1.35029i
$540$		0			0
$541$	−519.820			−0.960850			−0.480425	−	0.877036i	$-0.659518\pi$
$541$	−519.820			−0.960850			−0.480425	+	0.877036i	$0.659518\pi$
$542$		0			0
$543$	484.662			0.892564
$544$		0			0
$545$		0			0
$546$		0			0
$547$	733.365			1.34070			0.670352	−	0.742043i	$-0.266143\pi$
$547$	733.365			1.34070			0.670352	+	0.742043i	$0.266143\pi$
$548$		0			0
$549$			951.635i			1.73340i
$550$		0			0
$551$			182.002i			0.330312i
$552$		0			0
$553$			22.0288i			0.0398351i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			407.005i			0.730708i	0.930869	+	0.365354i	$0.119052\pi$
$557$			407.005i			0.730708i	−0.930869	+	0.365354i	$0.880948\pi$
$558$		0			0
$559$	−82.3180			−0.147259
$560$		0			0
$561$		−	1167.37i		−	2.08088i
$562$		0			0
$563$	515.750			0.916074			0.458037	−	0.888933i	$-0.348553\pi$
$563$	515.750			0.916074			0.458037	+	0.888933i	$0.348553\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−185.679			−0.327476
$568$		0			0
$569$			722.033i			1.26895i	0.772943	+	0.634476i	$0.218784\pi$
$569$			722.033i			1.26895i	−0.772943	+	0.634476i	$0.781216\pi$
$570$		0			0
$571$		−	191.199i		−	0.334849i	−0.985885	−	0.167424i	$-0.946455\pi$
$571$		−	191.199i		−	0.334849i	0.985885	−	0.167424i	$-0.0535450\pi$
$572$		0			0
$573$			682.325i			1.19079i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	304.057			0.526961			0.263481	−	0.964665i	$-0.415130\pi$
$577$	304.057			0.526961			0.263481	+	0.964665i	$0.415130\pi$
$578$		0			0
$579$		−	1392.24i		−	2.40455i
$580$		0			0
$581$			352.262i			0.606304i
$582$		0			0
$583$	−981.134			−1.68291
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	615.500i		−	1.04855i	−0.851548	−	0.524276i	$-0.824336\pi$
$587$		−	615.500i		−	1.04855i	0.851548	−	0.524276i	$-0.175664\pi$
$588$		0			0
$589$	250.437	−	49.4033i	0.425191	−	0.0838766i
$590$		0			0
$591$	−453.702			−0.767686
$592$		0			0
$593$	−70.1322			−0.118267			−0.0591334	−	0.998250i	$-0.518834\pi$
$593$	−70.1322			−0.118267			−0.0591334	+	0.998250i	$0.518834\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1530.12			−2.56302
$598$		0			0
$599$	1031.52			1.72207			0.861037	−	0.508543i	$-0.169816\pi$
$599$	1031.52			1.72207			0.861037	+	0.508543i	$0.169816\pi$
$600$		0			0
$601$			910.252i			1.51456i	0.653089	+	0.757281i	$0.273473\pi$
$601$			910.252i			1.51456i	−0.653089	+	0.757281i	$0.726527\pi$
$602$		0			0
$603$	−690.068			−1.14439
$604$		0			0
$605$		0			0
$606$		0			0
$607$	971.049			1.59975			0.799875	−	0.600166i	$-0.204899\pi$
$607$	971.049			1.59975			0.799875	+	0.600166i	$0.204899\pi$
$608$		0			0
$609$	−318.901			−0.523646
$610$		0			0
$611$		−	679.579i		−	1.11224i
$612$		0			0
$613$			1069.36i			1.74446i	0.489094	+	0.872231i	$0.337328\pi$
$613$			1069.36i			1.74446i	−0.489094	+	0.872231i	$0.662672\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−893.953			−1.44887			−0.724435	−	0.689343i	$-0.757899\pi$
$617$	−893.953			−1.44887			−0.724435	+	0.689343i	$0.757899\pi$
$618$		0			0
$619$		−	461.336i		−	0.745292i	−0.927973	−	0.372646i	$-0.878450\pi$
$619$		−	461.336i		−	0.745292i	0.927973	−	0.372646i	$-0.121550\pi$
$620$		0			0
$621$	198.430			0.319534
$622$		0			0
$623$			96.2223i			0.154450i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−695.288			−1.10891
$628$		0			0
$629$	−83.0979			−0.132111
$630$		0			0
$631$			452.521i			0.717149i	0.933501	+	0.358574i	$0.116737\pi$
$631$			452.521i			0.717149i	−0.933501	+	0.358574i	$0.883263\pi$
$632$		0			0
$633$			1400.60i			2.21264i
$634$		0			0
$635$		0			0
$636$		0			0
$637$			536.352i			0.841997i
$638$		0			0
$639$	−578.289			−0.904991
$640$		0			0
$641$			755.215i			1.17818i	0.808067	+	0.589091i	$0.200514\pi$
$641$			755.215i			1.17818i	−0.808067	+	0.589091i	$0.799486\pi$
$642$		0			0
$643$			547.824i			0.851981i	0.904728	+	0.425990i	$0.140074\pi$
$643$			547.824i			0.851981i	−0.904728	+	0.425990i	$0.859926\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			1239.70i			1.91607i	0.286645	+	0.958037i	$0.407460\pi$
$647$			1239.70i			1.91607i	−0.286645	+	0.958037i	$0.592540\pi$
$648$		0			0
$649$		−	1192.89i		−	1.83805i
$650$		0			0
$651$	86.5638	+	438.813i	0.132970	+	0.674059i
$652$		0			0
$653$	1138.13			1.74292			0.871459	−	0.490468i	$-0.163174\pi$
$653$	1138.13			1.74292			0.871459	+	0.490468i	$0.163174\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	696.561i		−	1.06021i
$658$		0			0
$659$	−211.476			−0.320905			−0.160453	−	0.987044i	$-0.551295\pi$
$659$	−211.476			−0.320905			−0.160453	+	0.987044i	$0.551295\pi$
$660$		0			0
$661$	354.893			0.536903			0.268452	−	0.963293i	$-0.413488\pi$
$661$	354.893			0.536903			0.268452	+	0.963293i	$0.413488\pi$
$662$		0			0
$663$			860.288i			1.29757i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−465.953			−0.698580
$668$		0			0
$669$	1239.16			1.85226
$670$		0			0
$671$	1614.77			2.40651
$672$		0			0
$673$		−	383.163i		−	0.569336i	−0.958626	−	0.284668i	$-0.908117\pi$
$673$		−	383.163i		−	0.569336i	0.958626	−	0.284668i	$-0.0918834\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	657.100i		−	0.970605i	−0.874346	−	0.485303i	$-0.838709\pi$
$677$		−	657.100i		−	0.970605i	0.874346	−	0.485303i	$-0.161291\pi$
$678$		0			0
$679$	447.453			0.658988
$680$		0			0
$681$		−	651.023i		−	0.955981i
$682$		0			0
$683$	−165.392			−0.242155			−0.121077	−	0.992643i	$-0.538635\pi$
$683$	−165.392			−0.242155			−0.121077	+	0.992643i	$0.538635\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	395.121			0.575139
$688$		0			0
$689$	723.039			1.04940
$690$		0			0
$691$	−1003.97			−1.45292			−0.726461	−	0.687208i	$-0.758836\pi$
$691$	−1003.97			−1.45292			−0.726461	+	0.687208i	$0.758836\pi$
$692$		0			0
$693$		−	672.765i		−	0.970801i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			309.222i			0.443647i
$698$		0			0
$699$			85.9854i			0.123012i
$700$		0			0
$701$	1237.18			1.76488			0.882438	−	0.470428i	$-0.155901\pi$
$701$	1237.18			1.76488			0.882438	+	0.470428i	$0.155901\pi$
$702$		0			0
$703$			49.4930i			0.0704026i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	245.871			0.347767
$708$		0			0
$709$		−	592.687i		−	0.835947i	−0.908459	−	0.417974i	$-0.862740\pi$
$709$		−	592.687i		−	0.835947i	0.908459	−	0.417974i	$-0.137260\pi$
$710$		0			0
$711$		−	75.9769i		−	0.106859i
$712$		0			0
$713$	126.480	+	641.159i	0.177392	+	0.899241i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1879.45			−2.62127
$718$		0			0
$719$		−	1146.24i		−	1.59422i	−0.603835	−	0.797110i	$-0.706361\pi$
$719$		−	1146.24i		−	1.59422i	0.603835	−	0.797110i	$-0.293639\pi$
$720$		0			0
$721$	−300.758			−0.417140
$722$		0			0
$723$	598.322			0.827554
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−704.034			−0.968410			−0.484205	−	0.874954i	$-0.660891\pi$
$727$	−704.034			−0.968410			−0.484205	+	0.874954i	$0.660891\pi$
$728$		0			0
$729$	1020.20			1.39945
$730$		0			0
$731$	81.9955			0.112169
$732$		0			0
$733$	555.219			0.757461			0.378730	−	0.925507i	$-0.376361\pi$
$733$	555.219			0.757461			0.378730	+	0.925507i	$0.376361\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			1170.93i			1.58878i
$738$		0			0
$739$			900.377i			1.21837i	0.793027	+	0.609186i	$0.208504\pi$
$739$			900.377i			1.21837i	−0.793027	+	0.609186i	$0.791496\pi$
$740$		0			0
$741$	512.387			0.691480
$742$		0			0
$743$			102.316i			0.137706i	0.997627	+	0.0688532i	$0.0219340\pi$
$743$			102.316i			0.137706i	−0.997627	+	0.0688532i	$0.978066\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	1214.94i		−	1.62643i
$748$		0			0
$749$	−294.137			−0.392706
$750$		0			0
$751$	546.187			0.727280			0.363640	−	0.931540i	$-0.381534\pi$
$751$	546.187			0.727280			0.363640	+	0.931540i	$0.381534\pi$
$752$		0			0
$753$	1038.83			1.37958
$754$		0			0
$755$		0			0
$756$		0			0
$757$			481.444i			0.635989i	0.948093	+	0.317995i	$0.103009\pi$
$757$			481.444i			0.635989i	−0.948093	+	0.317995i	$0.896991\pi$
$758$		0			0
$759$		−	1780.05i		−	2.34525i
$760$		0			0
$761$			1306.55i			1.71689i	0.512909	+	0.858443i	$0.328568\pi$
$761$			1306.55i			1.71689i	−0.512909	+	0.858443i	$0.671432\pi$
$762$		0			0
$763$	−261.249			−0.342397
$764$		0			0
$765$		0			0
$766$		0			0
$767$			879.094i			1.14615i
$768$		0			0
$769$	−112.257			−0.145977			−0.0729886	−	0.997333i	$-0.523254\pi$
$769$	−112.257			−0.145977			−0.0729886	+	0.997333i	$0.523254\pi$
$770$		0			0
$771$		−	1704.22i		−	2.21040i
$772$		0			0
$773$			1245.77i			1.61161i	0.592184	+	0.805803i	$0.298266\pi$
$773$			1245.77i			1.61161i	−0.592184	+	0.805803i	$0.701734\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−86.7210			−0.111610
$778$		0			0
$779$	184.172			0.236422
$780$		0			0
$781$			981.263i			1.25642i
$782$		0			0
$783$	208.047			0.265705
$784$		0			0
$785$		0			0
$786$		0			0
$787$			426.534i			0.541975i	0.962583	+	0.270987i	$0.0873501\pi$
$787$			426.534i			0.541975i	−0.962583	+	0.270987i	$0.912650\pi$
$788$		0			0
$789$	531.084			0.673110
$790$		0			0
$791$	−636.799			−0.805056
$792$		0			0
$793$	−1189.99			−1.50062
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	1469.49i		−	1.84378i	−0.387449	−	0.921891i	$-0.626644\pi$
$797$		−	1469.49i		−	1.84378i	0.387449	−	0.921891i	$-0.373356\pi$
$798$		0			0
$799$			676.916i			0.847205i
$800$		0			0
$801$		−	331.868i		−	0.414318i
$802$		0			0
$803$	−1181.95			−1.47192
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1547.25			1.91728
$808$		0			0
$809$		−	678.065i		−	0.838152i	−0.907951	−	0.419076i	$-0.862354\pi$
$809$		−	678.065i		−	0.838152i	0.907951	−	0.419076i	$-0.137646\pi$
$810$		0			0
$811$	−1545.06			−1.90513			−0.952565	−	0.304337i	$-0.901565\pi$
$811$	−1545.06			−1.90513			−0.952565	+	0.304337i	$0.901565\pi$
$812$		0			0
$813$	1796.05			2.20917
$814$		0			0
$815$		0			0
$816$		0			0
$817$		−	48.8365i		−	0.0597754i
$818$		0			0
$819$			495.789i			0.605359i
$820$		0			0
$821$			464.590i			0.565883i	0.959137	+	0.282941i	$0.0913102\pi$
$821$			464.590i			0.565883i	−0.959137	+	0.282941i	$0.908690\pi$
$822$		0			0
$823$			890.360i			1.08185i	0.841072	+	0.540924i	$0.181925\pi$
$823$			890.360i			1.08185i	−0.841072	+	0.540924i	$0.818075\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	1517.24i		−	1.83464i	−0.398155	−	0.917318i	$-0.630349\pi$
$827$		−	1517.24i		−	1.83464i	0.398155	−	0.917318i	$-0.369651\pi$
$828$		0			0
$829$			591.726i			0.713783i	0.934146	+	0.356892i	$0.116163\pi$
$829$			591.726i			0.713783i	−0.934146	+	0.356892i	$0.883837\pi$
$830$		0			0
$831$	−1125.26			−1.35411
$832$		0			0
$833$		−	534.251i		−	0.641357i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−56.4732	−	286.277i	−0.0674710	−	0.342027i
$838$		0			0
$839$	805.910			0.960560			0.480280	−	0.877115i	$-0.340535\pi$
$839$	805.910			0.960560			0.480280	+	0.877115i	$0.340535\pi$
$840$		0			0
$841$	352.464			0.419102
$842$		0			0
$843$		−	929.180i		−	1.10223i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−752.169			−0.888040
$848$		0			0
$849$			1642.91i			1.93511i
$850$		0			0
$851$	−126.710			−0.148896
$852$		0			0
$853$	1180.58			1.38403			0.692016	−	0.721882i	$-0.256723\pi$
$853$	1180.58			1.38403			0.692016	+	0.721882i	$0.256723\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−210.998			−0.246205			−0.123102	−	0.992394i	$-0.539284\pi$
$857$	−210.998			−0.246205			−0.123102	+	0.992394i	$0.539284\pi$
$858$		0			0
$859$			1516.76i			1.76573i	0.469629	+	0.882864i	$0.344388\pi$
$859$			1516.76i			1.76573i	−0.469629	+	0.882864i	$0.655612\pi$
$860$		0			0
$861$			322.704i			0.374802i
$862$		0			0
$863$			723.205i			0.838013i	0.907983	+	0.419006i	$0.137622\pi$
$863$			723.205i			0.838013i	−0.907983	+	0.419006i	$0.862378\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			438.743i			0.506047i
$868$		0			0
$869$	−128.920			−0.148355
$870$		0			0
$871$		−	862.910i		−	0.990711i
$872$		0			0
$873$	−1543.25			−1.76776
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−373.676			−0.426085			−0.213042	−	0.977043i	$-0.568337\pi$
$877$	−373.676			−0.426085			−0.213042	+	0.977043i	$0.568337\pi$
$878$		0			0
$879$			984.492i			1.12001i
$880$		0			0
$881$		−	1679.49i		−	1.90634i	−0.302432	−	0.953171i	$-0.597798\pi$
$881$		−	1679.49i		−	1.90634i	0.302432	−	0.953171i	$-0.402202\pi$
$882$		0			0
$883$		−	779.936i		−	0.883280i	−0.897192	−	0.441640i	$-0.854397\pi$
$883$		−	779.936i		−	0.883280i	0.897192	−	0.441640i	$-0.145603\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1197.60			−1.35017			−0.675084	−	0.737741i	$-0.735893\pi$
$887$	−1197.60			−1.35017			−0.675084	+	0.737741i	$0.735893\pi$
$888$		0			0
$889$		−	256.310i		−	0.288313i
$890$		0			0
$891$		−	1086.66i		−	1.21959i
$892$		0			0
$893$	403.171			0.451479
$894$		0			0
$895$		0			0
$896$		0			0
$897$			1311.79i			1.46242i
$898$		0			0
$899$	132.610	+	672.233i	0.147509	+	0.747756i
$900$		0			0
$901$	−720.205			−0.799340
$902$		0			0
$903$	85.5706			0.0947625
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−214.969			−0.237012			−0.118506	−	0.992953i	$-0.537810\pi$
$907$	−214.969			−0.237012			−0.118506	+	0.992953i	$0.537810\pi$
$908$		0			0
$909$	−848.004			−0.932898
$910$		0			0
$911$			137.331i			0.150748i	0.997155	+	0.0753740i	$0.0240151\pi$
$911$			137.331i			0.150748i	−0.997155	+	0.0753740i	$0.975985\pi$
$912$		0			0
$913$	−2061.56			−2.25801
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−670.795			−0.731510
$918$		0			0
$919$	1155.05			1.25686			0.628430	−	0.777866i	$-0.283698\pi$
$919$	1155.05			1.25686			0.628430	+	0.777866i	$0.283698\pi$
$920$		0			0
$921$			1951.18i			2.11855i
$922$		0			0
$923$		−	723.134i		−	0.783460i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1037.31			1.11899
$928$		0			0
$929$			342.449i			0.368621i	0.982868	+	0.184311i	$0.0590052\pi$
$929$			342.449i			0.368621i	−0.982868	+	0.184311i	$0.940995\pi$
$930$		0			0
$931$	−318.199			−0.341782
$932$		0			0
$933$		−	1697.80i		−	1.81972i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	535.787			0.571812			0.285906	−	0.958258i	$-0.407706\pi$
$937$	535.787			0.571812			0.285906	+	0.958258i	$0.407706\pi$
$938$		0			0
$939$	1820.74			1.93902
$940$		0			0
$941$		−	106.745i		−	0.113438i	−0.998390	−	0.0567189i	$-0.981936\pi$
$941$		−	106.745i		−	0.113438i	0.998390	−	0.0567189i	$-0.0180639\pi$
$942$		0			0
$943$			471.511i			0.500011i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			863.638i			0.911973i	0.889987	+	0.455986i	$0.150713\pi$
$947$			863.638i			0.911973i	−0.889987	+	0.455986i	$0.849287\pi$
$948$		0			0
$949$	871.029			0.917839
$950$		0			0
$951$		−	569.742i		−	0.599098i
$952$		0			0
$953$			974.470i			1.02253i	0.859423	+	0.511265i	$0.170823\pi$
$953$			974.470i			1.02253i	−0.859423	+	0.511265i	$0.829177\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	1866.32i		−	1.95018i
$958$		0			0
$959$			639.815i			0.667169i
$960$		0			0
$961$	889.007	−	364.948i	0.925086	−	0.379758i
$962$		0			0
$963$	1014.47			1.05345
$964$		0			0
$965$		0			0
$966$		0			0
$967$			241.654i			0.249900i	0.992163	+	0.124950i	$0.0398771\pi$
$967$			241.654i			0.249900i	−0.992163	+	0.124950i	$0.960123\pi$
$968$		0			0
$969$	−510.379			−0.526707
$970$		0			0
$971$	1713.55			1.76473			0.882364	−	0.470568i	$-0.155951\pi$
$971$	1713.55			1.76473			0.882364	+	0.470568i	$0.155951\pi$
$972$		0			0
$973$		−	609.148i		−	0.626051i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	21.2146			0.0217140			0.0108570	−	0.999941i	$-0.496544\pi$
$977$	21.2146			0.0217140			0.0108570	+	0.999941i	$0.496544\pi$
$978$		0			0
$979$	−563.127			−0.575206
$980$		0			0
$981$	901.040			0.918491
$982$		0			0
$983$			84.5958i			0.0860588i	0.999074	+	0.0430294i	$0.0137009\pi$
$983$			84.5958i			0.0860588i	−0.999074	+	0.0430294i	$0.986299\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			706.431i			0.715735i
$988$		0			0
$989$	125.029			0.126420
$990$		0			0
$991$			1065.20i			1.07487i	0.843304	+	0.537437i	$0.180607\pi$
$991$			1065.20i			1.07487i	−0.843304	+	0.537437i	$0.819393\pi$
$992$		0			0
$993$	380.906			0.383591
$994$		0			0
$995$		0			0
$996$		0			0
$997$	926.931			0.929720			0.464860	−	0.885384i	$-0.346105\pi$
$997$	926.931			0.929720			0.464860	+	0.885384i	$0.346105\pi$
$998$		0			0
$999$	56.5758			0.0566325

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3100.3.d.h.1301.10		24
5.2	odd	4		620.3.f.c.309.22	yes	24
5.3	odd	4		620.3.f.c.309.3	✓	24
5.4	even	2	inner	3100.3.d.h.1301.15		24
31.30	odd	2	inner	3100.3.d.h.1301.9		24
155.92	even	4		620.3.f.c.309.4	yes	24
155.123	even	4		620.3.f.c.309.21	yes	24
155.154	odd	2	inner	3100.3.d.h.1301.16		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
620.3.f.c.309.3	✓	24	5.3	odd	4
620.3.f.c.309.4	yes	24	155.92	even	4
620.3.f.c.309.21	yes	24	155.123	even	4
620.3.f.c.309.22	yes	24	5.2	odd	4
3100.3.d.h.1301.9		24	31.30	odd	2	inner
3100.3.d.h.1301.10		24	1.1	even	1	trivial
3100.3.d.h.1301.15		24	5.4	even	2	inner
3100.3.d.h.1301.16		24	155.154	odd	2	inner

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:	\( N \)	\(=\)	\( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	3100.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.48325i q^{3} +3.21821 q^{7} -11.0995 q^{9} +O(q^{10})\)	\(q+4.48325i q^{3} +3.21821 q^{7} -11.0995 q^{9} +18.8341i q^{11} -13.8796i q^{13} +13.8252i q^{17} +8.23431 q^{19} +14.4280i q^{21} +21.0811i q^{23} -9.41269i q^{27} +22.1028i q^{29} +(30.4139 - 5.99969i) q^{31} -84.4379 q^{33} +6.01059i q^{37} +62.2259 q^{39} +22.3665 q^{41} -5.93085i q^{43} +48.9623 q^{47} -38.6431 q^{49} -61.9820 q^{51} +52.0935i q^{53} +36.9165i q^{57} -63.3369 q^{59} -85.7365i q^{61} -35.7206 q^{63} +62.1709 q^{67} -94.5120 q^{69} +52.1004 q^{71} +62.7559i q^{73} +60.6121i q^{77} +6.84506i q^{79} -57.6963 q^{81} +109.459i q^{83} -99.0926 q^{87} +29.8993i q^{89} -44.6676i q^{91} +(26.8981 + 136.353i) q^{93} +139.038 q^{97} -209.049i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 44 q^{9}+O(q^{10}) \) 24 * q - 44 * q^9	\( 24 q - 44 q^{9} - 8 q^{19} - 24 q^{31} + 280 q^{39} - 248 q^{41} + 644 q^{49} - 100 q^{51} - 152 q^{59} + 288 q^{69} - 352 q^{71} - 368 q^{81}+O(q^{100}) \) 24 * q - 44 * q^9 - 8 * q^19 - 24 * q^31 + 280 * q^39 - 248 * q^41 + 644 * q^49 - 100 * q^51 - 152 * q^59 + 288 * q^69 - 352 * q^71 - 368 * q^81

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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