LMFDB - Embedded newform 592.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,6,Mod(1,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("592.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	592.a (trivial)

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:	yes
Analytic conductor:	$94.9472213293$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	592.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-7.00000 q^{3} -84.0000 q^{5} +139.000 q^{7} -194.000 q^{9} +O(q^{10})$

$q-7.00000 q^{3} -84.0000 q^{5} +139.000 q^{7} -194.000 q^{9} +147.000 q^{11} -280.000 q^{13} +588.000 q^{15} +978.000 q^{17} -1154.00 q^{19} -973.000 q^{21} +1158.00 q^{23} +3931.00 q^{25} +3059.00 q^{27} -3198.00 q^{29} +5932.00 q^{31} -1029.00 q^{33} -11676.0 q^{35} +1369.00 q^{37} +1960.00 q^{39} +10023.0 q^{41} +4036.00 q^{43} +16296.0 q^{45} +11631.0 q^{47} +2514.00 q^{49} -6846.00 q^{51} +11193.0 q^{53} -12348.0 q^{55} +8078.00 q^{57} -24660.0 q^{59} -13360.0 q^{61} -26966.0 q^{63} +23520.0 q^{65} +32860.0 q^{67} -8106.00 q^{69} -60123.0 q^{71} +41915.0 q^{73} -27517.0 q^{75} +20433.0 q^{77} +60898.0 q^{79} +25729.0 q^{81} +80169.0 q^{83} -82152.0 q^{85} +22386.0 q^{87} -131358. q^{89} -38920.0 q^{91} -41524.0 q^{93} +96936.0 q^{95} -122872. q^{97} -28518.0 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

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
$3$	−7.00000	−0.449050	−0.224525	−	0.974468i	$-0.572083\pi$
$3$	−7.00000	−0.449050	−0.224525	+	0.974468i	$0.572083\pi$
$4$	0	0
$5$	−84.0000	−1.50264	−0.751319	−	0.659939i	$-0.770582\pi$
$5$	−84.0000	−1.50264	−0.751319	+	0.659939i	$0.770582\pi$
$6$	0	0
$7$	139.000	1.07218	0.536092	−	0.844159i	$-0.319900\pi$
$7$	139.000	1.07218	0.536092	+	0.844159i	$0.319900\pi$
$8$	0	0
$9$	−194.000	−0.798354
$10$	0	0
$11$	147.000	0.366299	0.183149	−	0.983085i	$-0.441371\pi$
$11$	147.000	0.366299	0.183149	+	0.983085i	$0.441371\pi$
$12$	0	0
$13$	−280.000	−0.459515	−0.229757	−	0.973248i	$-0.573793\pi$
$13$	−280.000	−0.459515	−0.229757	+	0.973248i	$0.573793\pi$
$14$	0	0
$15$	588.000	0.674760
$16$	0	0
$17$	978.000	0.820761	0.410380	−	0.911914i	$-0.365396\pi$
$17$	978.000	0.820761	0.410380	+	0.911914i	$0.365396\pi$
$18$	0	0
$19$	−1154.00	−0.733368	−0.366684	−	0.930346i	$-0.619507\pi$
$19$	−1154.00	−0.733368	−0.366684	+	0.930346i	$0.619507\pi$
$20$	0	0
$21$	−973.000	−0.481465
$22$	0	0
$23$	1158.00	0.456446	0.228223	−	0.973609i	$-0.426709\pi$
$23$	1158.00	0.456446	0.228223	+	0.973609i	$0.426709\pi$
$24$	0	0
$25$	3931.00	1.25792
$26$	0	0
$27$	3059.00	0.807551
$28$	0	0
$29$	−3198.00	−0.706128	−0.353064	−	0.935599i	$-0.614860\pi$
$29$	−3198.00	−0.706128	−0.353064	+	0.935599i	$0.614860\pi$
$30$	0	0
$31$	5932.00	1.10866	0.554328	−	0.832298i	$-0.312975\pi$
$31$	5932.00	1.10866	0.554328	+	0.832298i	$0.312975\pi$
$32$	0	0
$33$	−1029.00	−0.164487
$34$	0	0
$35$	−11676.0	−1.61111
$36$	0	0
$37$	1369.00	0.164399
$37$	1369.00	0.164399
$38$	0	0
$39$	1960.00	0.206345
$40$	0	0
$41$	10023.0	0.931190	0.465595	−	0.884998i	$-0.345840\pi$
$41$	10023.0	0.931190	0.465595	+	0.884998i	$0.345840\pi$
$42$	0	0
$43$	4036.00	0.332874	0.166437	−	0.986052i	$-0.446774\pi$
$43$	4036.00	0.332874	0.166437	+	0.986052i	$0.446774\pi$
$44$	0	0
$45$	16296.0	1.19964
$46$	0	0
$47$	11631.0	0.768020	0.384010	−	0.923329i	$-0.374543\pi$
$47$	11631.0	0.768020	0.384010	+	0.923329i	$0.374543\pi$
$48$	0	0
$49$	2514.00	0.149581
$50$	0	0
$51$	−6846.00	−0.368563
$52$	0	0
$53$	11193.0	0.547340	0.273670	−	0.961824i	$-0.411762\pi$
$53$	11193.0	0.547340	0.273670	+	0.961824i	$0.411762\pi$
$54$	0	0
$55$	−12348.0	−0.550415
$56$	0	0
$57$	8078.00	0.329319
$58$	0	0
$59$	−24660.0	−0.922281	−0.461140	−	0.887327i	$-0.652560\pi$
$59$	−24660.0	−0.922281	−0.461140	+	0.887327i	$0.652560\pi$
$60$	0	0
$61$	−13360.0	−0.459708	−0.229854	−	0.973225i	$-0.573825\pi$
$61$	−13360.0	−0.459708	−0.229854	+	0.973225i	$0.573825\pi$
$62$	0	0
$63$	−26966.0	−0.855983
$64$	0	0
$65$	23520.0	0.690484
$66$	0	0
$67$	32860.0	0.894294	0.447147	−	0.894460i	$-0.352440\pi$
$67$	32860.0	0.894294	0.447147	+	0.894460i	$0.352440\pi$
$68$	0	0
$69$	−8106.00	−0.204967
$70$	0	0
$71$	−60123.0	−1.41545	−0.707725	−	0.706488i	$-0.750279\pi$
$71$	−60123.0	−1.41545	−0.707725	+	0.706488i	$0.750279\pi$
$72$	0	0
$73$	41915.0	0.920582	0.460291	−	0.887768i	$-0.347745\pi$
$73$	41915.0	0.920582	0.460291	+	0.887768i	$0.347745\pi$
$74$	0	0
$75$	−27517.0	−0.564869
$76$	0	0
$77$	20433.0	0.392740
$78$	0	0
$79$	60898.0	1.09783	0.548915	−	0.835878i	$-0.315041\pi$
$79$	60898.0	1.09783	0.548915	+	0.835878i	$0.315041\pi$
$80$	0	0
$81$	25729.0	0.435723
$82$	0	0
$83$	80169.0	1.27735	0.638677	−	0.769475i	$-0.279482\pi$
$83$	80169.0	1.27735	0.638677	+	0.769475i	$0.279482\pi$
$84$	0	0
$85$	−82152.0	−1.23331
$86$	0	0
$87$	22386.0	0.317087
$88$	0	0
$89$	−131358.	−1.75785	−0.878924	−	0.476961i	$-0.841738\pi$
$89$	−131358.	−1.75785	−0.878924	+	0.476961i	$0.841738\pi$
$90$	0	0
$91$	−38920.0	−0.492685
$92$	0	0
$93$	−41524.0	−0.497842
$94$	0	0
$95$	96936.0	1.10199
$96$	0	0
$97$	−122872.	−1.32594	−0.662970	−	0.748646i	$-0.730704\pi$
$97$	−122872.	−1.32594	−0.662970	+	0.748646i	$0.730704\pi$
$98$	0	0
$99$	−28518.0	−0.292436
$100$	0	0
$101$	−188265.	−1.83640	−0.918198	−	0.396123i	$-0.870356\pi$
$101$	−188265.	−1.83640	−0.918198	+	0.396123i	$0.870356\pi$
$102$	0	0
$103$	−165248.	−1.53477	−0.767385	−	0.641187i	$-0.778442\pi$
$103$	−165248.	−1.53477	−0.767385	+	0.641187i	$0.778442\pi$
$104$	0	0
$105$	81732.0	0.723467
$106$	0	0
$107$	−100812.	−0.851241	−0.425621	−	0.904902i	$-0.639944\pi$
$107$	−100812.	−0.851241	−0.425621	+	0.904902i	$0.639944\pi$
$108$	0	0
$109$	−66058.0	−0.532549	−0.266274	−	0.963897i	$-0.585793\pi$
$109$	−66058.0	−0.532549	−0.266274	+	0.963897i	$0.585793\pi$
$110$	0	0
$111$	−9583.00	−0.0738234
$112$	0	0
$113$	−122742.	−0.904268	−0.452134	−	0.891950i	$-0.649337\pi$
$113$	−122742.	−0.904268	−0.452134	+	0.891950i	$0.649337\pi$
$114$	0	0
$115$	−97272.0	−0.685872
$116$	0	0
$117$	54320.0	0.366856
$118$	0	0
$119$	135942.	0.880007
$120$	0	0
$121$	−139442.	−0.865825
$122$	0	0
$123$	−70161.0	−0.418151
$124$	0	0
$125$	−67704.0	−0.387560
$126$	0	0
$127$	159469.	0.877338	0.438669	−	0.898649i	$-0.355450\pi$
$127$	159469.	0.877338	0.438669	+	0.898649i	$0.355450\pi$
$128$	0	0
$129$	−28252.0	−0.149477
$130$	0	0
$131$	−1818.00	−0.00925584	−0.00462792	−	0.999989i	$-0.501473\pi$
$131$	−1818.00	−0.00925584	−0.00462792	+	0.999989i	$0.501473\pi$
$132$	0	0
$133$	−160406.	−0.786306
$134$	0	0
$135$	−256956.	−1.21346
$136$	0	0
$137$	368178.	1.67593	0.837966	−	0.545722i	$-0.183745\pi$
$137$	368178.	1.67593	0.837966	+	0.545722i	$0.183745\pi$
$138$	0	0
$139$	−138788.	−0.609277	−0.304639	−	0.952468i	$-0.598536\pi$
$139$	−138788.	−0.609277	−0.304639	+	0.952468i	$0.598536\pi$
$140$	0	0
$141$	−81417.0	−0.344879
$142$	0	0
$143$	−41160.0	−0.168320
$144$	0	0
$145$	268632.	1.06105
$146$	0	0
$147$	−17598.0	−0.0671692
$148$	0	0
$149$	495363.	1.82792	0.913961	−	0.405801i	$-0.133007\pi$
$149$	495363.	1.82792	0.913961	+	0.405801i	$0.133007\pi$
$150$	0	0
$151$	129784.	0.463211	0.231605	−	0.972810i	$-0.425602\pi$
$151$	129784.	0.463211	0.231605	+	0.972810i	$0.425602\pi$
$152$	0	0
$153$	−189732.	−0.655258
$154$	0	0
$155$	−498288.	−1.66591
$156$	0	0
$157$	−277993.	−0.900087	−0.450044	−	0.893007i	$-0.648592\pi$
$157$	−277993.	−0.900087	−0.450044	+	0.893007i	$0.648592\pi$
$158$	0	0
$159$	−78351.0	−0.245783
$160$	0	0
$161$	160962.	0.489394
$162$	0	0
$163$	−255620.	−0.753574	−0.376787	−	0.926300i	$-0.622971\pi$
$163$	−255620.	−0.753574	−0.376787	+	0.926300i	$0.622971\pi$
$164$	0	0
$165$	86436.0	0.247164
$166$	0	0
$167$	308478.	0.855920	0.427960	−	0.903798i	$-0.359232\pi$
$167$	308478.	0.855920	0.427960	+	0.903798i	$0.359232\pi$
$168$	0	0
$169$	−292893.	−0.788846
$170$	0	0
$171$	223876.	0.585487
$172$	0	0
$173$	−314691.	−0.799409	−0.399705	−	0.916644i	$-0.630887\pi$
$173$	−314691.	−0.799409	−0.399705	+	0.916644i	$0.630887\pi$
$174$	0	0
$175$	546409.	1.34872
$176$	0	0
$177$	172620.	0.414150
$178$	0	0
$179$	−717894.	−1.67466	−0.837332	−	0.546695i	$-0.815886\pi$
$179$	−717894.	−1.67466	−0.837332	+	0.546695i	$0.815886\pi$
$180$	0	0
$181$	−493603.	−1.11991	−0.559953	−	0.828525i	$-0.689181\pi$
$181$	−493603.	−1.11991	−0.559953	+	0.828525i	$0.689181\pi$
$182$	0	0
$183$	93520.0	0.206432
$184$	0	0
$185$	−114996.	−0.247032
$186$	0	0
$187$	143766.	0.300644
$188$	0	0
$189$	425201.	0.865844
$190$	0	0
$191$	−890376.	−1.76600	−0.882999	−	0.469376i	$-0.844479\pi$
$191$	−890376.	−1.76600	−0.882999	+	0.469376i	$0.844479\pi$
$192$	0	0
$193$	643760.	1.24403	0.622015	−	0.783005i	$-0.286314\pi$
$193$	643760.	1.24403	0.622015	+	0.783005i	$0.286314\pi$
$194$	0	0
$195$	−164640.	−0.310062
$196$	0	0
$197$	−767253.	−1.40855	−0.704276	−	0.709926i	$-0.748728\pi$
$197$	−767253.	−1.40855	−0.704276	+	0.709926i	$0.748728\pi$
$198$	0	0
$199$	652642.	1.16827	0.584134	−	0.811657i	$-0.301434\pi$
$199$	652642.	1.16827	0.584134	+	0.811657i	$0.301434\pi$
$200$	0	0
$201$	−230020.	−0.401583
$202$	0	0
$203$	−444522.	−0.757100
$204$	0	0
$205$	−841932.	−1.39924
$206$	0	0
$207$	−224652.	−0.364405
$208$	0	0
$209$	−169638.	−0.268632
$210$	0	0
$211$	554923.	0.858078	0.429039	−	0.903286i	$-0.358852\pi$
$211$	554923.	0.858078	0.429039	+	0.903286i	$0.358852\pi$
$212$	0	0
$213$	420861.	0.635608
$214$	0	0
$215$	−339024.	−0.500189
$216$	0	0
$217$	824548.	1.18868
$218$	0	0
$219$	−293405.	−0.413387
$220$	0	0
$221$	−273840.	−0.377152
$222$	0	0
$223$	1.22263e6	1.64639	0.823193	−	0.567761i	$-0.192190\pi$
$223$	1.22263e6	1.64639	0.823193	+	0.567761i	$0.192190\pi$
$224$	0	0
$225$	−762614.	−1.00427
$226$	0	0
$227$	−385128.	−0.496067	−0.248034	−	0.968751i	$-0.579784\pi$
$227$	−385128.	−0.496067	−0.248034	+	0.968751i	$0.579784\pi$
$228$	0	0
$229$	834299.	1.05132	0.525658	−	0.850696i	$-0.323819\pi$
$229$	834299.	1.05132	0.525658	+	0.850696i	$0.323819\pi$
$230$	0	0
$231$	−143031.	−0.176360
$232$	0	0
$233$	−1.32475e6	−1.59861	−0.799306	−	0.600925i	$-0.794799\pi$
$233$	−1.32475e6	−1.59861	−0.799306	+	0.600925i	$0.794799\pi$
$234$	0	0
$235$	−977004.	−1.15406
$236$	0	0
$237$	−426286.	−0.492981
$238$	0	0
$239$	−1.64021e6	−1.85740	−0.928701	−	0.370830i	$-0.879073\pi$
$239$	−1.64021e6	−1.85740	−0.928701	+	0.370830i	$0.879073\pi$
$240$	0	0
$241$	−1.03175e6	−1.14427	−0.572137	−	0.820158i	$-0.693886\pi$
$241$	−1.03175e6	−1.14427	−0.572137	+	0.820158i	$0.693886\pi$
$242$	0	0
$243$	−923440.	−1.00321
$244$	0	0
$245$	−211176.	−0.224765
$246$	0	0
$247$	323120.	0.336993
$248$	0	0
$249$	−561183.	−0.573596
$250$	0	0
$251$	−1.50124e6	−1.50406	−0.752029	−	0.659130i	$-0.770925\pi$
$251$	−1.50124e6	−1.50406	−0.752029	+	0.659130i	$0.770925\pi$
$252$	0	0
$253$	170226.	0.167196
$254$	0	0
$255$	575064.	0.553816
$256$	0	0
$257$	126288.	0.119269	0.0596347	−	0.998220i	$-0.481006\pi$
$257$	126288.	0.119269	0.0596347	+	0.998220i	$0.481006\pi$
$258$	0	0
$259$	190291.	0.176266
$260$	0	0
$261$	620412.	0.563740
$262$	0	0
$263$	−1.06975e6	−0.953658	−0.476829	−	0.878996i	$-0.658214\pi$
$263$	−1.06975e6	−0.953658	−0.476829	+	0.878996i	$0.658214\pi$
$264$	0	0
$265$	−940212.	−0.822453
$266$	0	0
$267$	919506.	0.789362
$268$	0	0
$269$	−680130.	−0.573075	−0.286537	−	0.958069i	$-0.592504\pi$
$269$	−680130.	−0.573075	−0.286537	+	0.958069i	$0.592504\pi$
$270$	0	0
$271$	−984575.	−0.814377	−0.407189	−	0.913344i	$-0.633491\pi$
$271$	−984575.	−0.814377	−0.407189	+	0.913344i	$0.633491\pi$
$272$	0	0
$273$	272440.	0.221240
$274$	0	0
$275$	577857.	0.460775
$276$	0	0
$277$	1.76000e6	1.37820	0.689102	−	0.724665i	$-0.258005\pi$
$277$	1.76000e6	1.37820	0.689102	+	0.724665i	$0.258005\pi$
$278$	0	0
$279$	−1.15081e6	−0.885100
$280$	0	0
$281$	−102264.	−0.0772604	−0.0386302	−	0.999254i	$-0.512299\pi$
$281$	−102264.	−0.0772604	−0.0386302	+	0.999254i	$0.512299\pi$
$282$	0	0
$283$	188740.	0.140087	0.0700435	−	0.997544i	$-0.477686\pi$
$283$	188740.	0.140087	0.0700435	+	0.997544i	$0.477686\pi$
$284$	0	0
$285$	−678552.	−0.494847
$286$	0	0
$287$	1.39320e6	0.998407
$288$	0	0
$289$	−463373.	−0.326352
$290$	0	0
$291$	860104.	0.595413
$292$	0	0
$293$	252798.	0.172030	0.0860151	−	0.996294i	$-0.472587\pi$
$293$	252798.	0.172030	0.0860151	+	0.996294i	$0.472587\pi$
$294$	0	0
$295$	2.07144e6	1.38585
$296$	0	0
$297$	449673.	0.295805
$298$	0	0
$299$	−324240.	−0.209744
$300$	0	0
$301$	561004.	0.356903
$302$	0	0
$303$	1.31786e6	0.824634
$304$	0	0
$305$	1.12224e6	0.690774
$306$	0	0
$307$	1.72815e6	1.04649	0.523246	−	0.852182i	$-0.324721\pi$
$307$	1.72815e6	1.04649	0.523246	+	0.852182i	$0.324721\pi$
$308$	0	0
$309$	1.15674e6	0.689189
$310$	0	0
$311$	1.09755e6	0.643463	0.321731	−	0.946831i	$-0.395735\pi$
$311$	1.09755e6	0.643463	0.321731	+	0.946831i	$0.395735\pi$
$312$	0	0
$313$	1.45314e6	0.838389	0.419194	−	0.907897i	$-0.362313\pi$
$313$	1.45314e6	0.838389	0.419194	+	0.907897i	$0.362313\pi$
$314$	0	0
$315$	2.26514e6	1.28623
$316$	0	0
$317$	42726.0	0.0238805	0.0119403	−	0.999929i	$-0.496199\pi$
$317$	42726.0	0.0238805	0.0119403	+	0.999929i	$0.496199\pi$
$318$	0	0
$319$	−470106.	−0.258654
$320$	0	0
$321$	705684.	0.382250
$322$	0	0
$323$	−1.12861e6	−0.601919
$324$	0	0
$325$	−1.10068e6	−0.578033
$326$	0	0
$327$	462406.	0.239141
$328$	0	0
$329$	1.61671e6	0.823459
$330$	0	0
$331$	2.39863e6	1.20335	0.601677	−	0.798740i	$-0.294500\pi$
$331$	2.39863e6	1.20335	0.601677	+	0.798740i	$0.294500\pi$
$332$	0	0
$333$	−265586.	−0.131249
$334$	0	0
$335$	−2.76024e6	−1.34380
$336$	0	0
$337$	−787393.	−0.377674	−0.188837	−	0.982008i	$-0.560472\pi$
$337$	−787393.	−0.377674	−0.188837	+	0.982008i	$0.560472\pi$
$338$	0	0
$339$	859194.	0.406062
$340$	0	0
$341$	872004.	0.406100
$342$	0	0
$343$	−1.98673e6	−0.911807
$344$	0	0
$345$	680904.	0.307991
$346$	0	0
$347$	275118.	0.122658	0.0613289	−	0.998118i	$-0.480466\pi$
$347$	275118.	0.122658	0.0613289	+	0.998118i	$0.480466\pi$
$348$	0	0
$349$	−952402.	−0.418559	−0.209280	−	0.977856i	$-0.567112\pi$
$349$	−952402.	−0.418559	−0.209280	+	0.977856i	$0.567112\pi$
$350$	0	0
$351$	−856520.	−0.371082
$352$	0	0
$353$	3.27239e6	1.39775	0.698874	−	0.715245i	$-0.253685\pi$
$353$	3.27239e6	1.39775	0.698874	+	0.715245i	$0.253685\pi$
$354$	0	0
$355$	5.05033e6	2.12691
$356$	0	0
$357$	−951594.	−0.395167
$358$	0	0
$359$	−747351.	−0.306047	−0.153024	−	0.988223i	$-0.548901\pi$
$359$	−747351.	−0.306047	−0.153024	+	0.988223i	$0.548901\pi$
$360$	0	0
$361$	−1.14438e6	−0.462172
$362$	0	0
$363$	976094.	0.388799
$364$	0	0
$365$	−3.52086e6	−1.38330
$366$	0	0
$367$	4.08359e6	1.58262	0.791311	−	0.611414i	$-0.209399\pi$
$367$	4.08359e6	1.58262	0.791311	+	0.611414i	$0.209399\pi$
$368$	0	0
$369$	−1.94446e6	−0.743419
$370$	0	0
$371$	1.55583e6	0.586849
$372$	0	0
$373$	1.57898e6	0.587630	0.293815	−	0.955862i	$-0.405075\pi$
$373$	1.57898e6	0.587630	0.293815	+	0.955862i	$0.405075\pi$
$374$	0	0
$375$	473928.	0.174034
$376$	0	0
$377$	895440.	0.324476
$378$	0	0
$379$	−2.69866e6	−0.965051	−0.482526	−	0.875882i	$-0.660280\pi$
$379$	−2.69866e6	−0.965051	−0.482526	+	0.875882i	$0.660280\pi$
$380$	0	0
$381$	−1.11628e6	−0.393969
$382$	0	0
$383$	−2.39651e6	−0.834799	−0.417400	−	0.908723i	$-0.637058\pi$
$383$	−2.39651e6	−0.834799	−0.417400	+	0.908723i	$0.637058\pi$
$384$	0	0
$385$	−1.71637e6	−0.590146
$386$	0	0
$387$	−782984.	−0.265751
$388$	0	0
$389$	2.49714e6	0.836698	0.418349	−	0.908286i	$-0.362609\pi$
$389$	2.49714e6	0.836698	0.418349	+	0.908286i	$0.362609\pi$
$390$	0	0
$391$	1.13252e6	0.374633
$392$	0	0
$393$	12726.0	0.00415633
$394$	0	0
$395$	−5.11543e6	−1.64964
$396$	0	0
$397$	4.78574e6	1.52396	0.761979	−	0.647602i	$-0.224228\pi$
$397$	4.78574e6	1.52396	0.761979	+	0.647602i	$0.224228\pi$
$398$	0	0
$399$	1.12284e6	0.353091
$400$	0	0
$401$	−1.46224e6	−0.454105	−0.227053	−	0.973882i	$-0.572909\pi$
$401$	−1.46224e6	−0.454105	−0.227053	+	0.973882i	$0.572909\pi$
$402$	0	0
$403$	−1.66096e6	−0.509444
$404$	0	0
$405$	−2.16124e6	−0.654734
$406$	0	0
$407$	201243.	0.0602192
$408$	0	0
$409$	−76780.0	−0.0226955	−0.0113478	−	0.999936i	$-0.503612\pi$
$409$	−76780.0	−0.0226955	−0.0113478	+	0.999936i	$0.503612\pi$
$410$	0	0
$411$	−2.57725e6	−0.752578
$412$	0	0
$413$	−3.42774e6	−0.988855
$414$	0	0
$415$	−6.73420e6	−1.91940
$416$	0	0
$417$	971516.	0.273596
$418$	0	0
$419$	−286677.	−0.0797733	−0.0398867	−	0.999204i	$-0.512700\pi$
$419$	−286677.	−0.0797733	−0.0398867	+	0.999204i	$0.512700\pi$
$420$	0	0
$421$	−3.45581e6	−0.950264	−0.475132	−	0.879915i	$-0.657600\pi$
$421$	−3.45581e6	−0.950264	−0.475132	+	0.879915i	$0.657600\pi$
$422$	0	0
$423$	−2.25641e6	−0.613152
$424$	0	0
$425$	3.84452e6	1.03245
$426$	0	0
$427$	−1.85704e6	−0.492892
$428$	0	0
$429$	288120.	0.0755841
$430$	0	0
$431$	5.92498e6	1.53636	0.768181	−	0.640233i	$-0.221162\pi$
$431$	5.92498e6	1.53636	0.768181	+	0.640233i	$0.221162\pi$
$432$	0	0
$433$	889733.	0.228055	0.114028	−	0.993478i	$-0.463625\pi$
$433$	889733.	0.228055	0.114028	+	0.993478i	$0.463625\pi$
$434$	0	0
$435$	−1.88042e6	−0.476467
$436$	0	0
$437$	−1.33633e6	−0.334742
$438$	0	0
$439$	2.88771e6	0.715141	0.357571	−	0.933886i	$-0.383605\pi$
$439$	2.88771e6	0.715141	0.357571	+	0.933886i	$0.383605\pi$
$440$	0	0
$441$	−487716.	−0.119418
$442$	0	0
$443$	1.20829e6	0.292524	0.146262	−	0.989246i	$-0.453276\pi$
$443$	1.20829e6	0.292524	0.146262	+	0.989246i	$0.453276\pi$
$444$	0	0
$445$	1.10341e7	2.64141
$446$	0	0
$447$	−3.46754e6	−0.820829
$448$	0	0
$449$	4.58427e6	1.07313	0.536567	−	0.843857i	$-0.319721\pi$
$449$	4.58427e6	1.07313	0.536567	+	0.843857i	$0.319721\pi$
$450$	0	0
$451$	1.47338e6	0.341094
$452$	0	0
$453$	−908488.	−0.208005
$454$	0	0
$455$	3.26928e6	0.740327
$456$	0	0
$457$	2.16838e6	0.485675	0.242837	−	0.970067i	$-0.421922\pi$
$457$	2.16838e6	0.485675	0.242837	+	0.970067i	$0.421922\pi$
$458$	0	0
$459$	2.99170e6	0.662806
$460$	0	0
$461$	−2.19754e6	−0.481597	−0.240798	−	0.970575i	$-0.577409\pi$
$461$	−2.19754e6	−0.481597	−0.240798	+	0.970575i	$0.577409\pi$
$462$	0	0
$463$	−1.59900e6	−0.346654	−0.173327	−	0.984864i	$-0.555452\pi$
$463$	−1.59900e6	−0.346654	−0.173327	+	0.984864i	$0.555452\pi$
$464$	0	0
$465$	3.48802e6	0.748077
$466$	0	0
$467$	−2.98676e6	−0.633735	−0.316868	−	0.948470i	$-0.602631\pi$
$467$	−2.98676e6	−0.633735	−0.316868	+	0.948470i	$0.602631\pi$
$468$	0	0
$469$	4.56754e6	0.958849
$470$	0	0
$471$	1.94595e6	0.404184
$472$	0	0
$473$	593292.	0.121931
$474$	0	0
$475$	−4.53637e6	−0.922518
$476$	0	0
$477$	−2.17144e6	−0.436971
$478$	0	0
$479$	2.17790e6	0.433709	0.216855	−	0.976204i	$-0.430420\pi$
$479$	2.17790e6	0.433709	0.216855	+	0.976204i	$0.430420\pi$
$480$	0	0
$481$	−383320.	−0.0755438
$482$	0	0
$483$	−1.12673e6	−0.219762
$484$	0	0
$485$	1.03212e7	1.99241
$486$	0	0
$487$	7.87061e6	1.50379	0.751893	−	0.659286i	$-0.229141\pi$
$487$	7.87061e6	1.50379	0.751893	+	0.659286i	$0.229141\pi$
$488$	0	0
$489$	1.78934e6	0.338392
$490$	0	0
$491$	−2.03394e6	−0.380745	−0.190373	−	0.981712i	$-0.560970\pi$
$491$	−2.03394e6	−0.380745	−0.190373	+	0.981712i	$0.560970\pi$
$492$	0	0
$493$	−3.12764e6	−0.579562
$494$	0	0
$495$	2.39551e6	0.439426
$496$	0	0
$497$	−8.35710e6	−1.51762
$498$	0	0
$499$	−2.50273e6	−0.449948	−0.224974	−	0.974365i	$-0.572230\pi$
$499$	−2.50273e6	−0.449948	−0.224974	+	0.974365i	$0.572230\pi$
$500$	0	0
$501$	−2.15935e6	−0.384351
$502$	0	0
$503$	3.53321e6	0.622659	0.311329	−	0.950302i	$-0.399226\pi$
$503$	3.53321e6	0.622659	0.311329	+	0.950302i	$0.399226\pi$
$504$	0	0
$505$	1.58143e7	2.75944
$506$	0	0
$507$	2.05025e6	0.354231
$508$	0	0
$509$	−8.39836e6	−1.43681	−0.718406	−	0.695624i	$-0.755128\pi$
$509$	−8.39836e6	−1.43681	−0.718406	+	0.695624i	$0.755128\pi$
$510$	0	0
$511$	5.82618e6	0.987034
$512$	0	0
$513$	−3.53009e6	−0.592232
$514$	0	0
$515$	1.38808e7	2.30620
$516$	0	0
$517$	1.70976e6	0.281325
$518$	0	0
$519$	2.20284e6	0.358975
$520$	0	0
$521$	−1.00759e7	−1.62626	−0.813129	−	0.582084i	$-0.802237\pi$
$521$	−1.00759e7	−1.62626	−0.813129	+	0.582084i	$0.802237\pi$
$522$	0	0
$523$	−6.17640e6	−0.987372	−0.493686	−	0.869640i	$-0.664351\pi$
$523$	−6.17640e6	−0.987372	−0.493686	+	0.869640i	$0.664351\pi$
$524$	0	0
$525$	−3.82486e6	−0.605644
$526$	0	0
$527$	5.80150e6	0.909941
$528$	0	0
$529$	−5.09538e6	−0.791657
$530$	0	0
$531$	4.78404e6	0.736306
$532$	0	0
$533$	−2.80644e6	−0.427896
$534$	0	0
$535$	8.46821e6	1.27911
$536$	0	0
$537$	5.02526e6	0.752008
$538$	0	0
$539$	369558.	0.0547912
$540$	0	0
$541$	−7.89089e6	−1.15913	−0.579566	−	0.814925i	$-0.696778\pi$
$541$	−7.89089e6	−1.15913	−0.579566	+	0.814925i	$0.696778\pi$
$542$	0	0
$543$	3.45522e6	0.502894
$544$	0	0
$545$	5.54887e6	0.800227
$546$	0	0
$547$	30892.0	0.00441446	0.00220723	−	0.999998i	$-0.499297\pi$
$547$	30892.0	0.00441446	0.00220723	+	0.999998i	$0.499297\pi$
$548$	0	0
$549$	2.59184e6	0.367010
$550$	0	0
$551$	3.69049e6	0.517852
$552$	0	0
$553$	8.46482e6	1.17708
$554$	0	0
$555$	804972.	0.110930
$556$	0	0
$557$	1.66821e6	0.227831	0.113915	−	0.993490i	$-0.463661\pi$
$557$	1.66821e6	0.227831	0.113915	+	0.993490i	$0.463661\pi$
$558$	0	0
$559$	−1.13008e6	−0.152961
$560$	0	0
$561$	−1.00636e6	−0.135004
$562$	0	0
$563$	−3.53330e6	−0.469797	−0.234898	−	0.972020i	$-0.575476\pi$
$563$	−3.53330e6	−0.469797	−0.234898	+	0.972020i	$0.575476\pi$
$564$	0	0
$565$	1.03103e7	1.35879
$566$	0	0
$567$	3.57633e6	0.467176
$568$	0	0
$569$	2.92326e6	0.378518	0.189259	−	0.981927i	$-0.439391\pi$
$569$	2.92326e6	0.378518	0.189259	+	0.981927i	$0.439391\pi$
$570$	0	0
$571$	−3.16341e6	−0.406036	−0.203018	−	0.979175i	$-0.565075\pi$
$571$	−3.16341e6	−0.406036	−0.203018	+	0.979175i	$0.565075\pi$
$572$	0	0
$573$	6.23263e6	0.793021
$574$	0	0
$575$	4.55210e6	0.574172
$576$	0	0
$577$	−8.92771e6	−1.11635	−0.558175	−	0.829723i	$-0.688498\pi$
$577$	−8.92771e6	−1.11635	−0.558175	+	0.829723i	$0.688498\pi$
$578$	0	0
$579$	−4.50632e6	−0.558632
$580$	0	0
$581$	1.11435e7	1.36956
$582$	0	0
$583$	1.64537e6	0.200490
$584$	0	0
$585$	−4.56288e6	−0.551251
$586$	0	0
$587$	−4.59495e6	−0.550409	−0.275205	−	0.961386i	$-0.588746\pi$
$587$	−4.59495e6	−0.550409	−0.275205	+	0.961386i	$0.588746\pi$
$588$	0	0
$589$	−6.84553e6	−0.813053
$590$	0	0
$591$	5.37077e6	0.632511
$592$	0	0
$593$	−1.41159e7	−1.64844	−0.824219	−	0.566271i	$-0.808386\pi$
$593$	−1.41159e7	−1.64844	−0.824219	+	0.566271i	$0.808386\pi$
$594$	0	0
$595$	−1.14191e7	−1.32233
$596$	0	0
$597$	−4.56849e6	−0.524611
$598$	0	0
$599$	−2.44585e6	−0.278525	−0.139262	−	0.990256i	$-0.544473\pi$
$599$	−2.44585e6	−0.278525	−0.139262	+	0.990256i	$0.544473\pi$
$600$	0	0
$601$	−1.43970e7	−1.62587	−0.812937	−	0.582352i	$-0.802133\pi$
$601$	−1.43970e7	−1.62587	−0.812937	+	0.582352i	$0.802133\pi$
$602$	0	0
$603$	−6.37484e6	−0.713963
$604$	0	0
$605$	1.17131e7	1.30102
$606$	0	0
$607$	9.28038e6	1.02234	0.511168	−	0.859481i	$-0.329213\pi$
$607$	9.28038e6	1.02234	0.511168	+	0.859481i	$0.329213\pi$
$608$	0	0
$609$	3.11165e6	0.339976
$610$	0	0
$611$	−3.25668e6	−0.352917
$612$	0	0
$613$	6.78601e6	0.729396	0.364698	−	0.931126i	$-0.381172\pi$
$613$	6.78601e6	0.729396	0.364698	+	0.931126i	$0.381172\pi$
$614$	0	0
$615$	5.89352e6	0.628329
$616$	0	0
$617$	1.31689e7	1.39263	0.696315	−	0.717736i	$-0.254822\pi$
$617$	1.31689e7	1.39263	0.696315	+	0.717736i	$0.254822\pi$
$618$	0	0
$619$	−5.84201e6	−0.612824	−0.306412	−	0.951899i	$-0.599129\pi$
$619$	−5.84201e6	−0.612824	−0.306412	+	0.951899i	$0.599129\pi$
$620$	0	0
$621$	3.54232e6	0.368603
$622$	0	0
$623$	−1.82588e7	−1.88474
$624$	0	0
$625$	−6.59724e6	−0.675557
$626$	0	0
$627$	1.18747e6	0.120629
$628$	0	0
$629$	1.33888e6	0.134932
$630$	0	0
$631$	9.40619e6	0.940460	0.470230	−	0.882544i	$-0.344171\pi$
$631$	9.40619e6	0.940460	0.470230	+	0.882544i	$0.344171\pi$
$632$	0	0
$633$	−3.88446e6	−0.385320
$634$	0	0
$635$	−1.33954e7	−1.31832
$636$	0	0
$637$	−703920.	−0.0687345
$638$	0	0
$639$	1.16639e7	1.13003
$640$	0	0
$641$	−1.36098e7	−1.30830	−0.654151	−	0.756364i	$-0.726974\pi$
$641$	−1.36098e7	−1.30830	−0.654151	+	0.756364i	$0.726974\pi$
$642$	0	0
$643$	−2.03645e7	−1.94243	−0.971217	−	0.238195i	$-0.923444\pi$
$643$	−2.03645e7	−1.94243	−0.971217	+	0.238195i	$0.923444\pi$
$644$	0	0
$645$	2.37317e6	0.224610
$646$	0	0
$647$	8.69847e6	0.816925	0.408462	−	0.912775i	$-0.366065\pi$
$647$	8.69847e6	0.816925	0.408462	+	0.912775i	$0.366065\pi$
$648$	0	0
$649$	−3.62502e6	−0.337830
$650$	0	0
$651$	−5.77184e6	−0.533779
$652$	0	0
$653$	1.08785e7	0.998361	0.499181	−	0.866498i	$-0.333634\pi$
$653$	1.08785e7	0.998361	0.499181	+	0.866498i	$0.333634\pi$
$654$	0	0
$655$	152712.	0.0139082
$656$	0	0
$657$	−8.13151e6	−0.734950
$658$	0	0
$659$	1.04726e7	0.939378	0.469689	−	0.882832i	$-0.344366\pi$
$659$	1.04726e7	0.939378	0.469689	+	0.882832i	$0.344366\pi$
$660$	0	0
$661$	1.43929e7	1.28128	0.640639	−	0.767842i	$-0.278669\pi$
$661$	1.43929e7	1.28128	0.640639	+	0.767842i	$0.278669\pi$
$662$	0	0
$663$	1.91688e6	0.169360
$664$	0	0
$665$	1.34741e7	1.18153
$666$	0	0
$667$	−3.70328e6	−0.322309
$668$	0	0
$669$	−8.55839e6	−0.739310
$670$	0	0
$671$	−1.96392e6	−0.168390
$672$	0	0
$673$	2.28451e6	0.194427	0.0972133	−	0.995264i	$-0.469007\pi$
$673$	2.28451e6	0.194427	0.0972133	+	0.995264i	$0.469007\pi$
$674$	0	0
$675$	1.20249e7	1.01583
$676$	0	0
$677$	3.91453e6	0.328252	0.164126	−	0.986439i	$-0.447520\pi$
$677$	3.91453e6	0.328252	0.164126	+	0.986439i	$0.447520\pi$
$678$	0	0
$679$	−1.70792e7	−1.42165
$680$	0	0
$681$	2.69590e6	0.222759
$682$	0	0
$683$	−2.22302e7	−1.82344	−0.911720	−	0.410811i	$-0.865246\pi$
$683$	−2.22302e7	−1.82344	−0.911720	+	0.410811i	$0.865246\pi$
$684$	0	0
$685$	−3.09270e7	−2.51832
$686$	0	0
$687$	−5.84009e6	−0.472093
$688$	0	0
$689$	−3.13404e6	−0.251511
$690$	0	0
$691$	−8.01410e6	−0.638498	−0.319249	−	0.947671i	$-0.603431\pi$
$691$	−8.01410e6	−0.638498	−0.319249	+	0.947671i	$0.603431\pi$
$692$	0	0
$693$	−3.96400e6	−0.313546
$694$	0	0
$695$	1.16582e7	0.915523
$696$	0	0
$697$	9.80249e6	0.764284
$698$	0	0
$699$	9.27322e6	0.717857
$700$	0	0
$701$	−1.72312e7	−1.32441	−0.662203	−	0.749324i	$-0.730378\pi$
$701$	−1.72312e7	−1.32441	−0.662203	+	0.749324i	$0.730378\pi$
$702$	0	0
$703$	−1.57983e6	−0.120565
$704$	0	0
$705$	6.83903e6	0.518229
$706$	0	0
$707$	−2.61688e7	−1.96896
$708$	0	0
$709$	3.37761e6	0.252344	0.126172	−	0.992008i	$-0.459731\pi$
$709$	3.37761e6	0.252344	0.126172	+	0.992008i	$0.459731\pi$
$710$	0	0
$711$	−1.18142e7	−0.876457
$712$	0	0
$713$	6.86926e6	0.506041
$714$	0	0
$715$	3.45744e6	0.252924
$716$	0	0
$717$	1.14815e7	0.834066
$718$	0	0
$719$	7.43292e6	0.536213	0.268107	−	0.963389i	$-0.413602\pi$
$719$	7.43292e6	0.536213	0.268107	+	0.963389i	$0.413602\pi$
$720$	0	0
$721$	−2.29695e7	−1.64556
$722$	0	0
$723$	7.22222e6	0.513837
$724$	0	0
$725$	−1.25713e7	−0.888253
$726$	0	0
$727$	−1.28188e7	−0.899523	−0.449761	−	0.893149i	$-0.648491\pi$
$727$	−1.28188e7	−0.899523	−0.449761	+	0.893149i	$0.648491\pi$
$728$	0	0
$729$	211933.	0.0147700
$730$	0	0
$731$	3.94721e6	0.273210
$732$	0	0
$733$	8.75160e6	0.601627	0.300814	−	0.953683i	$-0.402742\pi$
$733$	8.75160e6	0.601627	0.300814	+	0.953683i	$0.402742\pi$
$734$	0	0
$735$	1.47823e6	0.100931
$736$	0	0
$737$	4.83042e6	0.327579
$738$	0	0
$739$	−1.15693e7	−0.779283	−0.389641	−	0.920967i	$-0.627401\pi$
$739$	−1.15693e7	−0.779283	−0.389641	+	0.920967i	$0.627401\pi$
$740$	0	0
$741$	−2.26184e6	−0.151327
$742$	0	0
$743$	−2.21079e7	−1.46918	−0.734591	−	0.678510i	$-0.762626\pi$
$743$	−2.21079e7	−1.46918	−0.734591	+	0.678510i	$0.762626\pi$
$744$	0	0
$745$	−4.16105e7	−2.74671
$746$	0	0
$747$	−1.55528e7	−1.01978
$748$	0	0
$749$	−1.40129e7	−0.912688
$750$	0	0
$751$	1.65053e7	1.06788	0.533942	−	0.845521i	$-0.320710\pi$
$751$	1.65053e7	1.06788	0.533942	+	0.845521i	$0.320710\pi$
$752$	0	0
$753$	1.05087e7	0.675398
$754$	0	0
$755$	−1.09019e7	−0.696038
$756$	0	0
$757$	1.35366e7	0.858562	0.429281	−	0.903171i	$-0.358767\pi$
$757$	1.35366e7	0.858562	0.429281	+	0.903171i	$0.358767\pi$
$758$	0	0
$759$	−1.19158e6	−0.0750792
$760$	0	0
$761$	−7.40555e6	−0.463549	−0.231775	−	0.972770i	$-0.574453\pi$
$761$	−7.40555e6	−0.463549	−0.231775	+	0.972770i	$0.574453\pi$
$762$	0	0
$763$	−9.18206e6	−0.570990
$764$	0	0
$765$	1.59375e7	0.984615
$766$	0	0
$767$	6.90480e6	0.423802
$768$	0	0
$769$	−2.61625e7	−1.59538	−0.797690	−	0.603068i	$-0.793945\pi$
$769$	−2.61625e7	−1.59538	−0.797690	+	0.603068i	$0.793945\pi$
$770$	0	0
$771$	−884016.	−0.0535580
$772$	0	0
$773$	−5.90612e6	−0.355511	−0.177756	−	0.984075i	$-0.556884\pi$
$773$	−5.90612e6	−0.355511	−0.177756	+	0.984075i	$0.556884\pi$
$774$	0	0
$775$	2.33187e7	1.39460
$776$	0	0
$777$	−1.33204e6	−0.0791523
$778$	0	0
$779$	−1.15665e7	−0.682904
$780$	0	0
$781$	−8.83808e6	−0.518478
$782$	0	0
$783$	−9.78268e6	−0.570235
$784$	0	0
$785$	2.33514e7	1.35251
$786$	0	0
$787$	1.46812e7	0.844939	0.422469	−	0.906377i	$-0.361163\pi$
$787$	1.46812e7	0.844939	0.422469	+	0.906377i	$0.361163\pi$
$788$	0	0
$789$	7.48824e6	0.428240
$790$	0	0
$791$	−1.70611e7	−0.969542
$792$	0	0
$793$	3.74080e6	0.211243
$794$	0	0
$795$	6.58148e6	0.369323
$796$	0	0
$797$	−2.81229e7	−1.56825	−0.784123	−	0.620606i	$-0.786887\pi$
$797$	−2.81229e7	−1.56825	−0.784123	+	0.620606i	$0.786887\pi$
$798$	0	0
$799$	1.13751e7	0.630360
$800$	0	0
$801$	2.54835e7	1.40339
$802$	0	0
$803$	6.16151e6	0.337208
$804$	0	0
$805$	−1.35208e7	−0.735382
$806$	0	0
$807$	4.76091e6	0.257339
$808$	0	0
$809$	−2.44219e7	−1.31192	−0.655960	−	0.754795i	$-0.727736\pi$
$809$	−2.44219e7	−1.31192	−0.655960	+	0.754795i	$0.727736\pi$
$810$	0	0
$811$	5.68689e6	0.303615	0.151807	−	0.988410i	$-0.451491\pi$
$811$	5.68689e6	0.303615	0.151807	+	0.988410i	$0.451491\pi$
$812$	0	0
$813$	6.89202e6	0.365696
$814$	0	0
$815$	2.14721e7	1.13235
$816$	0	0
$817$	−4.65754e6	−0.244119
$818$	0	0
$819$	7.55048e6	0.393337
$820$	0	0
$821$	−2.83725e7	−1.46906	−0.734531	−	0.678575i	$-0.762598\pi$
$821$	−2.83725e7	−1.46906	−0.734531	+	0.678575i	$0.762598\pi$
$822$	0	0
$823$	2.12488e7	1.09354	0.546770	−	0.837283i	$-0.315857\pi$
$823$	2.12488e7	1.09354	0.546770	+	0.837283i	$0.315857\pi$
$824$	0	0
$825$	−4.04500e6	−0.206911
$826$	0	0
$827$	3.27949e7	1.66741	0.833706	−	0.552209i	$-0.186215\pi$
$827$	3.27949e7	1.66741	0.833706	+	0.552209i	$0.186215\pi$
$828$	0	0
$829$	−3.55433e7	−1.79627	−0.898134	−	0.439721i	$-0.855077\pi$
$829$	−3.55433e7	−1.79627	−0.898134	+	0.439721i	$0.855077\pi$
$830$	0	0
$831$	−1.23200e7	−0.618882
$832$	0	0
$833$	2.45869e6	0.122770
$834$	0	0
$835$	−2.59122e7	−1.28614
$836$	0	0
$837$	1.81460e7	0.895297
$838$	0	0
$839$	4.54394e6	0.222858	0.111429	−	0.993772i	$-0.464457\pi$
$839$	4.54394e6	0.222858	0.111429	+	0.993772i	$0.464457\pi$
$840$	0	0
$841$	−1.02839e7	−0.501383
$842$	0	0
$843$	715848.	0.0346938
$844$	0	0
$845$	2.46030e7	1.18535
$846$	0	0
$847$	−1.93824e7	−0.928325
$848$	0	0
$849$	−1.32118e6	−0.0629061
$850$	0	0
$851$	1.58530e6	0.0750392
$852$	0	0
$853$	1.82388e6	0.0858270	0.0429135	−	0.999079i	$-0.486336\pi$
$853$	1.82388e6	0.0858270	0.0429135	+	0.999079i	$0.486336\pi$
$854$	0	0
$855$	−1.88056e7	−0.879775
$856$	0	0
$857$	−3.78424e6	−0.176006	−0.0880029	−	0.996120i	$-0.528048\pi$
$857$	−3.78424e6	−0.176006	−0.0880029	+	0.996120i	$0.528048\pi$
$858$	0	0
$859$	−2.13312e7	−0.986354	−0.493177	−	0.869929i	$-0.664164\pi$
$859$	−2.13312e7	−0.986354	−0.493177	+	0.869929i	$0.664164\pi$
$860$	0	0
$861$	−9.75238e6	−0.448335
$862$	0	0
$863$	−4.09733e6	−0.187272	−0.0936362	−	0.995606i	$-0.529849\pi$
$863$	−4.09733e6	−0.187272	−0.0936362	+	0.995606i	$0.529849\pi$
$864$	0	0
$865$	2.64340e7	1.20122
$866$	0	0
$867$	3.24361e6	0.146548
$868$	0	0
$869$	8.95201e6	0.402134
$870$	0	0
$871$	−9.20080e6	−0.410942
$872$	0	0
$873$	2.38372e7	1.05857
$874$	0	0
$875$	−9.41086e6	−0.415536
$876$	0	0
$877$	1.82256e7	0.800171	0.400086	−	0.916478i	$-0.368980\pi$
$877$	1.82256e7	0.800171	0.400086	+	0.916478i	$0.368980\pi$
$878$	0	0
$879$	−1.76959e6	−0.0772502
$880$	0	0
$881$	1.11601e7	0.484425	0.242213	−	0.970223i	$-0.422127\pi$
$881$	1.11601e7	0.484425	0.242213	+	0.970223i	$0.422127\pi$
$882$	0	0
$883$	−2.59857e7	−1.12159	−0.560793	−	0.827956i	$-0.689504\pi$
$883$	−2.59857e7	−1.12159	−0.560793	+	0.827956i	$0.689504\pi$
$884$	0	0
$885$	−1.45001e7	−0.622318
$886$	0	0
$887$	−8.83725e6	−0.377145	−0.188572	−	0.982059i	$-0.560386\pi$
$887$	−8.83725e6	−0.377145	−0.188572	+	0.982059i	$0.560386\pi$
$888$	0	0
$889$	2.21662e7	0.940669
$890$	0	0
$891$	3.78216e6	0.159605
$892$	0	0
$893$	−1.34222e7	−0.563241
$894$	0	0
$895$	6.03031e7	2.51641
$896$	0	0
$897$	2.26968e6	0.0941854
$898$	0	0
$899$	−1.89705e7	−0.782853
$900$	0	0
$901$	1.09468e7	0.449235
$902$	0	0
$903$	−3.92703e6	−0.160267
$904$	0	0
$905$	4.14627e7	1.68281
$906$	0	0
$907$	−6.35281e6	−0.256417	−0.128209	−	0.991747i	$-0.540923\pi$
$907$	−6.35281e6	−0.256417	−0.128209	+	0.991747i	$0.540923\pi$
$908$	0	0
$909$	3.65234e7	1.46609
$910$	0	0
$911$	−1.75069e7	−0.698896	−0.349448	−	0.936956i	$-0.613631\pi$
$911$	−1.75069e7	−0.698896	−0.349448	+	0.936956i	$0.613631\pi$
$912$	0	0
$913$	1.17848e7	0.467893
$914$	0	0
$915$	−7.85568e6	−0.310192
$916$	0	0
$917$	−252702.	−0.00992397
$918$	0	0
$919$	−3.34259e7	−1.30555	−0.652776	−	0.757551i	$-0.726396\pi$
$919$	−3.34259e7	−1.30555	−0.652776	+	0.757551i	$0.726396\pi$
$920$	0	0
$921$	−1.20971e7	−0.469927
$922$	0	0
$923$	1.68344e7	0.650421
$924$	0	0
$925$	5.38154e6	0.206801
$926$	0	0
$927$	3.20581e7	1.22529
$928$	0	0
$929$	−4.53366e7	−1.72349	−0.861747	−	0.507338i	$-0.830630\pi$
$929$	−4.53366e7	−1.72349	−0.861747	+	0.507338i	$0.830630\pi$
$930$	0	0
$931$	−2.90116e6	−0.109698
$932$	0	0
$933$	−7.68285e6	−0.288947
$934$	0	0
$935$	−1.20763e7	−0.451759
$936$	0	0
$937$	−3.12117e7	−1.16136	−0.580682	−	0.814130i	$-0.697214\pi$
$937$	−3.12117e7	−1.16136	−0.580682	+	0.814130i	$0.697214\pi$
$938$	0	0
$939$	−1.01720e7	−0.376479
$940$	0	0
$941$	−9.86035e6	−0.363010	−0.181505	−	0.983390i	$-0.558097\pi$
$941$	−9.86035e6	−0.363010	−0.181505	+	0.983390i	$0.558097\pi$
$942$	0	0
$943$	1.16066e7	0.425037
$944$	0	0
$945$	−3.57169e7	−1.30105
$946$	0	0
$947$	1.11578e7	0.404302	0.202151	−	0.979354i	$-0.435207\pi$
$947$	1.11578e7	0.404302	0.202151	+	0.979354i	$0.435207\pi$
$948$	0	0
$949$	−1.17362e7	−0.423021
$950$	0	0
$951$	−299082.	−0.0107236
$952$	0	0
$953$	240981.	0.00859509	0.00429755	−	0.999991i	$-0.498632\pi$
$953$	240981.	0.00859509	0.00429755	+	0.999991i	$0.498632\pi$
$954$	0	0
$955$	7.47916e7	2.65365
$956$	0	0
$957$	3.29074e6	0.116149
$958$	0	0
$959$	5.11767e7	1.79691
$960$	0	0
$961$	6.55947e6	0.229119
$962$	0	0
$963$	1.95575e7	0.679592
$964$	0	0
$965$	−5.40758e7	−1.86933
$966$	0	0
$967$	−4.32780e7	−1.48834	−0.744169	−	0.667992i	$-0.767154\pi$
$967$	−4.32780e7	−1.48834	−0.744169	+	0.667992i	$0.767154\pi$
$968$	0	0
$969$	7.90028e6	0.270292
$970$	0	0
$971$	4.51121e7	1.53548	0.767742	−	0.640759i	$-0.221380\pi$
$971$	4.51121e7	1.53548	0.767742	+	0.640759i	$0.221380\pi$
$972$	0	0
$973$	−1.92915e7	−0.653258
$974$	0	0
$975$	7.70476e6	0.259566
$976$	0	0
$977$	−2.08737e7	−0.699621	−0.349811	−	0.936820i	$-0.613754\pi$
$977$	−2.08737e7	−0.699621	−0.349811	+	0.936820i	$0.613754\pi$
$978$	0	0
$979$	−1.93096e7	−0.643898
$980$	0	0
$981$	1.28153e7	0.425162
$982$	0	0
$983$	−2.40935e7	−0.795274	−0.397637	−	0.917543i	$-0.630170\pi$
$983$	−2.40935e7	−0.795274	−0.397637	+	0.917543i	$0.630170\pi$
$984$	0	0
$985$	6.44493e7	2.11654
$986$	0	0
$987$	−1.13170e7	−0.369775
$988$	0	0
$989$	4.67369e6	0.151939
$990$	0	0
$991$	5.18446e7	1.67695	0.838473	−	0.544943i	$-0.183449\pi$
$991$	5.18446e7	1.67695	0.838473	+	0.544943i	$0.183449\pi$
$992$	0	0
$993$	−1.67904e7	−0.540366
$994$	0	0
$995$	−5.48219e7	−1.75548
$996$	0	0
$997$	−3.10444e7	−0.989113	−0.494557	−	0.869145i	$-0.664670\pi$
$997$	−3.10444e7	−0.989113	−0.494557	+	0.869145i	$0.664670\pi$
$998$	0	0
$999$	4.18777e6	0.132761

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.6.a.a.1.1		1
4.3	odd	2		74.6.a.b.1.1	✓	1
12.11	even	2		666.6.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.a.b.1.1	✓	1	4.3	odd	2
592.6.a.a.1.1		1	1.1	even	1	trivial
666.6.a.b.1.1		1	12.11	even	2

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	592.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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