LMFDB - Embedded newform 350.6.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,6,Mod(1,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("350.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	350.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:	$56.1343369345$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	350.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-4.00000 q^{2} +16.0000 q^{4} +49.0000 q^{7} -64.0000 q^{8} -243.000 q^{9} +384.000 q^{11} -236.000 q^{13} -196.000 q^{14} +256.000 q^{16} +1172.00 q^{17} +972.000 q^{18} -1100.00 q^{19} -1536.00 q^{22} -1400.00 q^{23} +944.000 q^{26} +784.000 q^{28} -3854.00 q^{29} +88.0000 q^{31} -1024.00 q^{32} -4688.00 q^{34} -3888.00 q^{36} +13240.0 q^{37} +4400.00 q^{38} -13338.0 q^{41} +2504.00 q^{43} +6144.00 q^{44} +5600.00 q^{46} +14728.0 q^{47} +2401.00 q^{49} -3776.00 q^{52} -11232.0 q^{53} -3136.00 q^{56} +15416.0 q^{58} +652.000 q^{59} -1494.00 q^{61} -352.000 q^{62} -11907.0 q^{63} +4096.00 q^{64} -18232.0 q^{67} +18752.0 q^{68} -28356.0 q^{71} +15552.0 q^{72} +70892.0 q^{73} -52960.0 q^{74} -17600.0 q^{76} +18816.0 q^{77} -79828.0 q^{79} +59049.0 q^{81} +53352.0 q^{82} -83712.0 q^{83} -10016.0 q^{86} -24576.0 q^{88} -93290.0 q^{89} -11564.0 q^{91} -22400.0 q^{92} -58912.0 q^{94} -91068.0 q^{97} -9604.00 q^{98} -93312.0 q^{99} +O(q^{100})$

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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	16.0000	0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	−64.0000	−0.353553
$9$	−243.000	−1.00000
$10$	0	0
$11$	384.000	0.956862	0.478431	−	0.878125i	$-0.341206\pi$
$11$	384.000	0.956862	0.478431	+	0.878125i	$0.341206\pi$
$12$	0	0
$13$	−236.000	−0.387305	−0.193653	−	0.981070i	$-0.562034\pi$
$13$	−236.000	−0.387305	−0.193653	+	0.981070i	$0.562034\pi$
$14$	−196.000	−0.267261
$15$	0	0
$16$	256.000	0.250000
$17$	1172.00	0.983570	0.491785	−	0.870717i	$-0.336345\pi$
$17$	1172.00	0.983570	0.491785	+	0.870717i	$0.336345\pi$
$18$	972.000	0.707107
$19$	−1100.00	−0.699051	−0.349525	−	0.936927i	$-0.613657\pi$
$19$	−1100.00	−0.699051	−0.349525	+	0.936927i	$0.613657\pi$
$20$	0	0
$21$	0	0
$22$	−1536.00	−0.676604
$23$	−1400.00	−0.551834	−0.275917	−	0.961181i	$-0.588981\pi$
$23$	−1400.00	−0.551834	−0.275917	+	0.961181i	$0.588981\pi$
$24$	0	0
$25$	0	0
$26$	944.000	0.273866
$27$	0	0
$28$	784.000	0.188982
$29$	−3854.00	−0.850975	−0.425487	−	0.904964i	$-0.639897\pi$
$29$	−3854.00	−0.850975	−0.425487	+	0.904964i	$0.639897\pi$
$30$	0	0
$31$	88.0000	0.0164467	0.00822334	−	0.999966i	$-0.497382\pi$
$31$	88.0000	0.0164467	0.00822334	+	0.999966i	$0.497382\pi$
$32$	−1024.00	−0.176777
$33$	0	0
$34$	−4688.00	−0.695489
$35$	0	0
$36$	−3888.00	−0.500000
$37$	13240.0	1.58995	0.794975	−	0.606642i	$-0.207484\pi$
$37$	13240.0	1.58995	0.794975	+	0.606642i	$0.207484\pi$
$38$	4400.00	0.494303
$39$	0	0
$40$	0	0
$41$	−13338.0	−1.23917	−0.619585	−	0.784929i	$-0.712699\pi$
$41$	−13338.0	−1.23917	−0.619585	+	0.784929i	$0.712699\pi$
$42$	0	0
$43$	2504.00	0.206521	0.103260	−	0.994654i	$-0.467073\pi$
$43$	2504.00	0.206521	0.103260	+	0.994654i	$0.467073\pi$
$44$	6144.00	0.478431
$45$	0	0
$46$	5600.00	0.390206
$47$	14728.0	0.972521	0.486261	−	0.873814i	$-0.338361\pi$
$47$	14728.0	0.972521	0.486261	+	0.873814i	$0.338361\pi$
$48$	0	0
$49$	2401.00	0.142857
$50$	0	0
$51$	0	0
$52$	−3776.00	−0.193653
$53$	−11232.0	−0.549247	−0.274623	−	0.961552i	$-0.588553\pi$
$53$	−11232.0	−0.549247	−0.274623	+	0.961552i	$0.588553\pi$
$54$	0	0
$55$	0	0
$56$	−3136.00	−0.133631
$57$	0	0
$58$	15416.0	0.601730
$59$	652.000	0.0243847	0.0121924	−	0.999926i	$-0.496119\pi$
$59$	652.000	0.0243847	0.0121924	+	0.999926i	$0.496119\pi$
$60$	0	0
$61$	−1494.00	−0.0514074	−0.0257037	−	0.999670i	$-0.508183\pi$
$61$	−1494.00	−0.0514074	−0.0257037	+	0.999670i	$0.508183\pi$
$62$	−352.000	−0.0116296
$63$	−11907.0	−0.377964
$64$	4096.00	0.125000
$65$	0	0
$66$	0	0
$67$	−18232.0	−0.496189	−0.248095	−	0.968736i	$-0.579804\pi$
$67$	−18232.0	−0.496189	−0.248095	+	0.968736i	$0.579804\pi$
$68$	18752.0	0.491785
$69$	0	0
$70$	0	0
$71$	−28356.0	−0.667574	−0.333787	−	0.942649i	$-0.608327\pi$
$71$	−28356.0	−0.667574	−0.333787	+	0.942649i	$0.608327\pi$
$72$	15552.0	0.353553
$73$	70892.0	1.55701	0.778503	−	0.627641i	$-0.215980\pi$
$73$	70892.0	1.55701	0.778503	+	0.627641i	$0.215980\pi$
$74$	−52960.0	−1.12426
$75$	0	0
$76$	−17600.0	−0.349525
$77$	18816.0	0.361660
$78$	0	0
$79$	−79828.0	−1.43909	−0.719544	−	0.694447i	$-0.755649\pi$
$79$	−79828.0	−1.43909	−0.719544	+	0.694447i	$0.755649\pi$
$80$	0	0
$81$	59049.0	1.00000
$82$	53352.0	0.876226
$83$	−83712.0	−1.33381	−0.666903	−	0.745145i	$-0.732380\pi$
$83$	−83712.0	−1.33381	−0.666903	+	0.745145i	$0.732380\pi$
$84$	0	0
$85$	0	0
$86$	−10016.0	−0.146032
$87$	0	0
$88$	−24576.0	−0.338302
$89$	−93290.0	−1.24842	−0.624209	−	0.781257i	$-0.714579\pi$
$89$	−93290.0	−1.24842	−0.624209	+	0.781257i	$0.714579\pi$
$90$	0	0
$91$	−11564.0	−0.146388
$92$	−22400.0	−0.275917
$93$	0	0
$94$	−58912.0	−0.687676
$95$	0	0
$96$	0	0
$97$	−91068.0	−0.982735	−0.491368	−	0.870952i	$-0.663503\pi$
$97$	−91068.0	−0.982735	−0.491368	+	0.870952i	$0.663503\pi$
$98$	−9604.00	−0.101015
$99$	−93312.0	−0.956862
$100$	0	0
$101$	−54306.0	−0.529718	−0.264859	−	0.964287i	$-0.585325\pi$
$101$	−54306.0	−0.529718	−0.264859	+	0.964287i	$0.585325\pi$
$102$	0	0
$103$	−135944.	−1.26260	−0.631302	−	0.775537i	$-0.717479\pi$
$103$	−135944.	−1.26260	−0.631302	+	0.775537i	$0.717479\pi$
$104$	15104.0	0.136933
$105$	0	0
$106$	44928.0	0.388376
$107$	77512.0	0.654500	0.327250	−	0.944938i	$-0.393878\pi$
$107$	77512.0	0.654500	0.327250	+	0.944938i	$0.393878\pi$
$108$	0	0
$109$	−151714.	−1.22309	−0.611546	−	0.791209i	$-0.709452\pi$
$109$	−151714.	−1.22309	−0.611546	+	0.791209i	$0.709452\pi$
$110$	0	0
$111$	0	0
$112$	12544.0	0.0944911
$113$	235312.	1.73360	0.866798	−	0.498659i	$-0.166174\pi$
$113$	235312.	1.73360	0.866798	+	0.498659i	$0.166174\pi$
$114$	0	0
$115$	0	0
$116$	−61664.0	−0.425487
$117$	57348.0	0.387305
$118$	−2608.00	−0.0172426
$119$	57428.0	0.371755
$120$	0	0
$121$	−13595.0	−0.0844143
$122$	5976.00	0.0363506
$123$	0	0
$124$	1408.00	0.00822334
$125$	0	0
$126$	47628.0	0.267261
$127$	−341768.	−1.88028	−0.940139	−	0.340791i	$-0.889305\pi$
$127$	−341768.	−1.88028	−0.940139	+	0.340791i	$0.889305\pi$
$128$	−16384.0	−0.0883883
$129$	0	0
$130$	0	0
$131$	−308276.	−1.56950	−0.784750	−	0.619812i	$-0.787209\pi$
$131$	−308276.	−1.56950	−0.784750	+	0.619812i	$0.787209\pi$
$132$	0	0
$133$	−53900.0	−0.264216
$134$	72928.0	0.350859
$135$	0	0
$136$	−75008.0	−0.347745
$137$	−348136.	−1.58470	−0.792351	−	0.610066i	$-0.791143\pi$
$137$	−348136.	−1.58470	−0.792351	+	0.610066i	$0.791143\pi$
$138$	0	0
$139$	−292364.	−1.28347	−0.641737	−	0.766925i	$-0.721786\pi$
$139$	−292364.	−1.28347	−0.641737	+	0.766925i	$0.721786\pi$
$140$	0	0
$141$	0	0
$142$	113424.	0.472046
$143$	−90624.0	−0.370598
$144$	−62208.0	−0.250000
$145$	0	0
$146$	−283568.	−1.10097
$147$	0	0
$148$	211840.	0.794975
$149$	178806.	0.659806	0.329903	−	0.944015i	$-0.392984\pi$
$149$	178806.	0.659806	0.329903	+	0.944015i	$0.392984\pi$
$150$	0	0
$151$	−173892.	−0.620636	−0.310318	−	0.950633i	$-0.600436\pi$
$151$	−173892.	−0.620636	−0.310318	+	0.950633i	$0.600436\pi$
$152$	70400.0	0.247152
$153$	−284796.	−0.983570
$154$	−75264.0	−0.255732
$155$	0	0
$156$	0	0
$157$	−228540.	−0.739968	−0.369984	−	0.929038i	$-0.620637\pi$
$157$	−228540.	−0.739968	−0.369984	+	0.929038i	$0.620637\pi$
$158$	319312.	1.01759
$159$	0	0
$160$	0	0
$161$	−68600.0	−0.208574
$162$	−236196.	−0.707107
$163$	−609624.	−1.79719	−0.898593	−	0.438783i	$-0.855410\pi$
$163$	−609624.	−1.79719	−0.898593	+	0.438783i	$0.855410\pi$
$164$	−213408.	−0.619585
$165$	0	0
$166$	334848.	0.943143
$167$	648600.	1.79964	0.899820	−	0.436261i	$-0.143697\pi$
$167$	648600.	1.79964	0.899820	+	0.436261i	$0.143697\pi$
$168$	0	0
$169$	−315597.	−0.849994
$170$	0	0
$171$	267300.	0.699051
$172$	40064.0	0.103260
$173$	−127812.	−0.324681	−0.162340	−	0.986735i	$-0.551904\pi$
$173$	−127812.	−0.324681	−0.162340	+	0.986735i	$0.551904\pi$
$174$	0	0
$175$	0	0
$176$	98304.0	0.239216
$177$	0	0
$178$	373160.	0.882765
$179$	637208.	1.48644	0.743222	−	0.669045i	$-0.233297\pi$
$179$	637208.	1.48644	0.743222	+	0.669045i	$0.233297\pi$
$180$	0	0
$181$	461246.	1.04649	0.523246	−	0.852181i	$-0.324721\pi$
$181$	461246.	1.04649	0.523246	+	0.852181i	$0.324721\pi$
$182$	46256.0	0.103512
$183$	0	0
$184$	89600.0	0.195103
$185$	0	0
$186$	0	0
$187$	450048.	0.941141
$188$	235648.	0.486261
$189$	0	0
$190$	0	0
$191$	356444.	0.706981	0.353491	−	0.935438i	$-0.384995\pi$
$191$	356444.	0.706981	0.353491	+	0.935438i	$0.384995\pi$
$192$	0	0
$193$	−191248.	−0.369576	−0.184788	−	0.982778i	$-0.559160\pi$
$193$	−191248.	−0.369576	−0.184788	+	0.982778i	$0.559160\pi$
$194$	364272.	0.694899
$195$	0	0
$196$	38416.0	0.0714286
$197$	−624976.	−1.14735	−0.573677	−	0.819081i	$-0.694484\pi$
$197$	−624976.	−1.14735	−0.573677	+	0.819081i	$0.694484\pi$
$198$	373248.	0.676604
$199$	−247416.	−0.442889	−0.221445	−	0.975173i	$-0.571077\pi$
$199$	−247416.	−0.442889	−0.221445	+	0.975173i	$0.571077\pi$
$200$	0	0
$201$	0	0
$202$	217224.	0.374567
$203$	−188846.	−0.321638
$204$	0	0
$205$	0	0
$206$	543776.	0.892795
$207$	340200.	0.551834
$208$	−60416.0	−0.0968264
$209$	−422400.	−0.668895
$210$	0	0
$211$	300984.	0.465412	0.232706	−	0.972547i	$-0.425242\pi$
$211$	300984.	0.465412	0.232706	+	0.972547i	$0.425242\pi$
$212$	−179712.	−0.274623
$213$	0	0
$214$	−310048.	−0.462801
$215$	0	0
$216$	0	0
$217$	4312.00	0.00621626
$218$	606856.	0.864857
$219$	0	0
$220$	0	0
$221$	−276592.	−0.380942
$222$	0	0
$223$	102136.	0.137536	0.0687680	−	0.997633i	$-0.478093\pi$
$223$	102136.	0.137536	0.0687680	+	0.997633i	$0.478093\pi$
$224$	−50176.0	−0.0668153
$225$	0	0
$226$	−941248.	−1.22584
$227$	595968.	0.767641	0.383821	−	0.923408i	$-0.374608\pi$
$227$	595968.	0.767641	0.383821	+	0.923408i	$0.374608\pi$
$228$	0	0
$229$	1.01543e6	1.27956	0.639778	−	0.768559i	$-0.279026\pi$
$229$	1.01543e6	1.27956	0.639778	+	0.768559i	$0.279026\pi$
$230$	0	0
$231$	0	0
$232$	246656.	0.300865
$233$	23384.0	0.0282182	0.0141091	−	0.999900i	$-0.495509\pi$
$233$	23384.0	0.0282182	0.0141091	+	0.999900i	$0.495509\pi$
$234$	−229392.	−0.273866
$235$	0	0
$236$	10432.0	0.0121924
$237$	0	0
$238$	−229712.	−0.262870
$239$	1.15844e6	1.31183	0.655915	−	0.754835i	$-0.272283\pi$
$239$	1.15844e6	1.31183	0.655915	+	0.754835i	$0.272283\pi$
$240$	0	0
$241$	−977490.	−1.08410	−0.542050	−	0.840346i	$-0.682352\pi$
$241$	−977490.	−1.08410	−0.542050	+	0.840346i	$0.682352\pi$
$242$	54380.0	0.0596899
$243$	0	0
$244$	−23904.0	−0.0257037
$245$	0	0
$246$	0	0
$247$	259600.	0.270746
$248$	−5632.00	−0.00581478
$249$	0	0
$250$	0	0
$251$	−835700.	−0.837271	−0.418636	−	0.908154i	$-0.637492\pi$
$251$	−835700.	−0.837271	−0.418636	+	0.908154i	$0.637492\pi$
$252$	−190512.	−0.188982
$253$	−537600.	−0.528029
$254$	1.36707e6	1.32956
$255$	0	0
$256$	65536.0	0.0625000
$257$	−587772.	−0.555106	−0.277553	−	0.960710i	$-0.589523\pi$
$257$	−587772.	−0.555106	−0.277553	+	0.960710i	$0.589523\pi$
$258$	0	0
$259$	648760.	0.600945
$260$	0	0
$261$	936522.	0.850975
$262$	1.23310e6	1.10980
$263$	−149352.	−0.133144	−0.0665720	−	0.997782i	$-0.521206\pi$
$263$	−149352.	−0.133144	−0.0665720	+	0.997782i	$0.521206\pi$
$264$	0	0
$265$	0	0
$266$	215600.	0.186829
$267$	0	0
$268$	−291712.	−0.248095
$269$	2.00973e6	1.69339	0.846697	−	0.532076i	$-0.178588\pi$
$269$	2.00973e6	1.69339	0.846697	+	0.532076i	$0.178588\pi$
$270$	0	0
$271$	499200.	0.412906	0.206453	−	0.978457i	$-0.433808\pi$
$271$	499200.	0.412906	0.206453	+	0.978457i	$0.433808\pi$
$272$	300032.	0.245893
$273$	0	0
$274$	1.39254e6	1.12055
$275$	0	0
$276$	0	0
$277$	−1.03093e6	−0.807289	−0.403644	−	0.914916i	$-0.632257\pi$
$277$	−1.03093e6	−0.807289	−0.403644	+	0.914916i	$0.632257\pi$
$278$	1.16946e6	0.907553
$279$	−21384.0	−0.0164467
$280$	0	0
$281$	1.12849e6	0.852571	0.426285	−	0.904589i	$-0.359822\pi$
$281$	1.12849e6	0.852571	0.426285	+	0.904589i	$0.359822\pi$
$282$	0	0
$283$	49952.0	0.0370755	0.0185377	−	0.999828i	$-0.494099\pi$
$283$	49952.0	0.0370755	0.0185377	+	0.999828i	$0.494099\pi$
$284$	−453696.	−0.333787
$285$	0	0
$286$	362496.	0.262052
$287$	−653562.	−0.468362
$288$	248832.	0.176777
$289$	−46273.0	−0.0325899
$290$	0	0
$291$	0	0
$292$	1.13427e6	0.778503
$293$	−86340.0	−0.0587548	−0.0293774	−	0.999568i	$-0.509352\pi$
$293$	−86340.0	−0.0587548	−0.0293774	+	0.999568i	$0.509352\pi$
$294$	0	0
$295$	0	0
$296$	−847360.	−0.562132
$297$	0	0
$298$	−715224.	−0.466553
$299$	330400.	0.213728
$300$	0	0
$301$	122696.	0.0780574
$302$	695568.	0.438856
$303$	0	0
$304$	−281600.	−0.174763
$305$	0	0
$306$	1.13918e6	0.695489
$307$	−2.86581e6	−1.73541	−0.867703	−	0.497083i	$-0.834405\pi$
$307$	−2.86581e6	−1.73541	−0.867703	+	0.497083i	$0.834405\pi$
$308$	301056.	0.180830
$309$	0	0
$310$	0	0
$311$	−374904.	−0.219796	−0.109898	−	0.993943i	$-0.535052\pi$
$311$	−374904.	−0.219796	−0.109898	+	0.993943i	$0.535052\pi$
$312$	0	0
$313$	1.99147e6	1.14898	0.574490	−	0.818512i	$-0.305200\pi$
$313$	1.99147e6	1.14898	0.574490	+	0.818512i	$0.305200\pi$
$314$	914160.	0.523237
$315$	0	0
$316$	−1.27725e6	−0.719544
$317$	−417808.	−0.233522	−0.116761	−	0.993160i	$-0.537251\pi$
$317$	−417808.	−0.233522	−0.116761	+	0.993160i	$0.537251\pi$
$318$	0	0
$319$	−1.47994e6	−0.814266
$320$	0	0
$321$	0	0
$322$	274400.	0.147484
$323$	−1.28920e6	−0.687565
$324$	944784.	0.500000
$325$	0	0
$326$	2.43850e6	1.27080
$327$	0	0
$328$	853632.	0.438113
$329$	721672.	0.367579
$330$	0	0
$331$	3.22654e6	1.61870	0.809352	−	0.587323i	$-0.199818\pi$
$331$	3.22654e6	1.61870	0.809352	+	0.587323i	$0.199818\pi$
$332$	−1.33939e6	−0.666903
$333$	−3.21732e6	−1.58995
$334$	−2.59440e6	−1.27254
$335$	0	0
$336$	0	0
$337$	2.97302e6	1.42601	0.713005	−	0.701159i	$-0.247334\pi$
$337$	2.97302e6	1.42601	0.713005	+	0.701159i	$0.247334\pi$
$338$	1.26239e6	0.601037
$339$	0	0
$340$	0	0
$341$	33792.0	0.0157372
$342$	−1.06920e6	−0.494303
$343$	117649.	0.0539949
$344$	−160256.	−0.0730160
$345$	0	0
$346$	511248.	0.229584
$347$	584664.	0.260665	0.130332	−	0.991470i	$-0.458396\pi$
$347$	584664.	0.260665	0.130332	+	0.991470i	$0.458396\pi$
$348$	0	0
$349$	−3.62799e6	−1.59442	−0.797210	−	0.603703i	$-0.793691\pi$
$349$	−3.62799e6	−1.59442	−0.797210	+	0.603703i	$0.793691\pi$
$350$	0	0
$351$	0	0
$352$	−393216.	−0.169151
$353$	−1.62880e6	−0.695713	−0.347856	−	0.937548i	$-0.613090\pi$
$353$	−1.62880e6	−0.695713	−0.347856	+	0.937548i	$0.613090\pi$
$354$	0	0
$355$	0	0
$356$	−1.49264e6	−0.624209
$357$	0	0
$358$	−2.54883e6	−1.05107
$359$	−606052.	−0.248184	−0.124092	−	0.992271i	$-0.539602\pi$
$359$	−606052.	−0.248184	−0.124092	+	0.992271i	$0.539602\pi$
$360$	0	0
$361$	−1.26610e6	−0.511328
$362$	−1.84498e6	−0.739982
$363$	0	0
$364$	−185024.	−0.0731939
$365$	0	0
$366$	0	0
$367$	−2.15002e6	−0.833255	−0.416628	−	0.909077i	$-0.636788\pi$
$367$	−2.15002e6	−0.833255	−0.416628	+	0.909077i	$0.636788\pi$
$368$	−358400.	−0.137958
$369$	3.24113e6	1.23917
$370$	0	0
$371$	−550368.	−0.207596
$372$	0	0
$373$	−1.64186e6	−0.611031	−0.305515	−	0.952187i	$-0.598829\pi$
$373$	−1.64186e6	−0.611031	−0.305515	+	0.952187i	$0.598829\pi$
$374$	−1.80019e6	−0.665487
$375$	0	0
$376$	−942592.	−0.343838
$377$	909544.	0.329587
$378$	0	0
$379$	4.00041e6	1.43056	0.715280	−	0.698838i	$-0.246299\pi$
$379$	4.00041e6	1.43056	0.715280	+	0.698838i	$0.246299\pi$
$380$	0	0
$381$	0	0
$382$	−1.42578e6	−0.499911
$383$	5.71586e6	1.99106	0.995531	−	0.0944312i	$-0.0301033\pi$
$383$	5.71586e6	1.99106	0.995531	+	0.0944312i	$0.0301033\pi$
$384$	0	0
$385$	0	0
$386$	764992.	0.261330
$387$	−608472.	−0.206521
$388$	−1.45709e6	−0.491368
$389$	−1.67611e6	−0.561600	−0.280800	−	0.959766i	$-0.590600\pi$
$389$	−1.67611e6	−0.561600	−0.280800	+	0.959766i	$0.590600\pi$
$390$	0	0
$391$	−1.64080e6	−0.542767
$392$	−153664.	−0.0505076
$393$	0	0
$394$	2.49990e6	0.811302
$395$	0	0
$396$	−1.49299e6	−0.478431
$397$	−945140.	−0.300968	−0.150484	−	0.988612i	$-0.548083\pi$
$397$	−945140.	−0.300968	−0.150484	+	0.988612i	$0.548083\pi$
$398$	989664.	0.313170
$399$	0	0
$400$	0	0
$401$	552786.	0.171671	0.0858353	−	0.996309i	$-0.472644\pi$
$401$	552786.	0.171671	0.0858353	+	0.996309i	$0.472644\pi$
$402$	0	0
$403$	−20768.0	−0.00636989
$404$	−868896.	−0.264859
$405$	0	0
$406$	755384.	0.227433
$407$	5.08416e6	1.52136
$408$	0	0
$409$	−1.04783e6	−0.309729	−0.154865	−	0.987936i	$-0.549494\pi$
$409$	−1.04783e6	−0.309729	−0.154865	+	0.987936i	$0.549494\pi$
$410$	0	0
$411$	0	0
$412$	−2.17510e6	−0.631302
$413$	31948.0	0.00921655
$414$	−1.36080e6	−0.390206
$415$	0	0
$416$	241664.	0.0684666
$417$	0	0
$418$	1.68960e6	0.472980
$419$	−6.88344e6	−1.91545	−0.957724	−	0.287690i	$-0.907113\pi$
$419$	−6.88344e6	−1.91545	−0.957724	+	0.287690i	$0.907113\pi$
$420$	0	0
$421$	−4.56311e6	−1.25475	−0.627373	−	0.778719i	$-0.715870\pi$
$421$	−4.56311e6	−1.25475	−0.627373	+	0.778719i	$0.715870\pi$
$422$	−1.20394e6	−0.329096
$423$	−3.57890e6	−0.972521
$424$	718848.	0.194188
$425$	0	0
$426$	0	0
$427$	−73206.0	−0.0194302
$428$	1.24019e6	0.327250
$429$	0	0
$430$	0	0
$431$	−2.49110e6	−0.645949	−0.322974	−	0.946408i	$-0.604683\pi$
$431$	−2.49110e6	−0.645949	−0.322974	+	0.946408i	$0.604683\pi$
$432$	0	0
$433$	4.42817e6	1.13502	0.567512	−	0.823365i	$-0.307906\pi$
$433$	4.42817e6	1.13502	0.567512	+	0.823365i	$0.307906\pi$
$434$	−17248.0	−0.00439556
$435$	0	0
$436$	−2.42742e6	−0.611546
$437$	1.54000e6	0.385760
$438$	0	0
$439$	635432.	0.157365	0.0786824	−	0.996900i	$-0.474929\pi$
$439$	635432.	0.157365	0.0786824	+	0.996900i	$0.474929\pi$
$440$	0	0
$441$	−583443.	−0.142857
$442$	1.10637e6	0.269367
$443$	−1.80612e6	−0.437258	−0.218629	−	0.975808i	$-0.570158\pi$
$443$	−1.80612e6	−0.437258	−0.218629	+	0.975808i	$0.570158\pi$
$444$	0	0
$445$	0	0
$446$	−408544.	−0.0972527
$447$	0	0
$448$	200704.	0.0472456
$449$	−3.90323e6	−0.913710	−0.456855	−	0.889541i	$-0.651024\pi$
$449$	−3.90323e6	−0.913710	−0.456855	+	0.889541i	$0.651024\pi$
$450$	0	0
$451$	−5.12179e6	−1.18572
$452$	3.76499e6	0.866798
$453$	0	0
$454$	−2.38387e6	−0.542804
$455$	0	0
$456$	0	0
$457$	−4.36264e6	−0.977145	−0.488572	−	0.872523i	$-0.662482\pi$
$457$	−4.36264e6	−0.977145	−0.488572	+	0.872523i	$0.662482\pi$
$458$	−4.06170e6	−0.904783
$459$	0	0
$460$	0	0
$461$	846710.	0.185559	0.0927796	−	0.995687i	$-0.470425\pi$
$461$	846710.	0.185559	0.0927796	+	0.995687i	$0.470425\pi$
$462$	0	0
$463$	7.37970e6	1.59988	0.799938	−	0.600082i	$-0.204866\pi$
$463$	7.37970e6	1.59988	0.799938	+	0.600082i	$0.204866\pi$
$464$	−986624.	−0.212744
$465$	0	0
$466$	−93536.0	−0.0199533
$467$	2.88296e6	0.611711	0.305856	−	0.952078i	$-0.401058\pi$
$467$	2.88296e6	0.611711	0.305856	+	0.952078i	$0.401058\pi$
$468$	917568.	0.193653
$469$	−893368.	−0.187542
$470$	0	0
$471$	0	0
$472$	−41728.0	−0.00862130
$473$	961536.	0.197612
$474$	0	0
$475$	0	0
$476$	918848.	0.185877
$477$	2.72938e6	0.549247
$478$	−4.63374e6	−0.927603
$479$	−6.63322e6	−1.32095	−0.660473	−	0.750849i	$-0.729644\pi$
$479$	−6.63322e6	−1.32095	−0.660473	+	0.750849i	$0.729644\pi$
$480$	0	0
$481$	−3.12464e6	−0.615797
$482$	3.90996e6	0.766575
$483$	0	0
$484$	−217520.	−0.0422071
$485$	0	0
$486$	0	0
$487$	2.17919e6	0.416364	0.208182	−	0.978090i	$-0.433245\pi$
$487$	2.17919e6	0.416364	0.208182	+	0.978090i	$0.433245\pi$
$488$	95616.0	0.0181753
$489$	0	0
$490$	0	0
$491$	7.92307e6	1.48317	0.741583	−	0.670861i	$-0.234075\pi$
$491$	7.92307e6	1.48317	0.741583	+	0.670861i	$0.234075\pi$
$492$	0	0
$493$	−4.51689e6	−0.836993
$494$	−1.03840e6	−0.191446
$495$	0	0
$496$	22528.0	0.00411167
$497$	−1.38944e6	−0.252319
$498$	0	0
$499$	−2.68311e6	−0.482378	−0.241189	−	0.970478i	$-0.577537\pi$
$499$	−2.68311e6	−0.482378	−0.241189	+	0.970478i	$0.577537\pi$
$500$	0	0
$501$	0	0
$502$	3.34280e6	0.592040
$503$	5.90502e6	1.04064	0.520321	−	0.853971i	$-0.325812\pi$
$503$	5.90502e6	1.04064	0.520321	+	0.853971i	$0.325812\pi$
$504$	762048.	0.133631
$505$	0	0
$506$	2.15040e6	0.373373
$507$	0	0
$508$	−5.46829e6	−0.940139
$509$	−2.57879e6	−0.441186	−0.220593	−	0.975366i	$-0.570799\pi$
$509$	−2.57879e6	−0.441186	−0.220593	+	0.975366i	$0.570799\pi$
$510$	0	0
$511$	3.47371e6	0.588493
$512$	−262144.	−0.0441942
$513$	0	0
$514$	2.35109e6	0.392519
$515$	0	0
$516$	0	0
$517$	5.65555e6	0.930569
$518$	−2.59504e6	−0.424932
$519$	0	0
$520$	0	0
$521$	1.03587e7	1.67190	0.835950	−	0.548806i	$-0.184917\pi$
$521$	1.03587e7	1.67190	0.835950	+	0.548806i	$0.184917\pi$
$522$	−3.74609e6	−0.601730
$523$	1.02151e7	1.63301	0.816507	−	0.577335i	$-0.195908\pi$
$523$	1.02151e7	1.63301	0.816507	+	0.577335i	$0.195908\pi$
$524$	−4.93242e6	−0.784750
$525$	0	0
$526$	597408.	0.0941470
$527$	103136.	0.0161765
$528$	0	0
$529$	−4.47634e6	−0.695479
$530$	0	0
$531$	−158436.	−0.0243847
$532$	−862400.	−0.132108
$533$	3.14777e6	0.479938
$534$	0	0
$535$	0	0
$536$	1.16685e6	0.175429
$537$	0	0
$538$	−8.03894e6	−1.19741
$539$	921984.	0.136695
$540$	0	0
$541$	−3.21546e6	−0.472335	−0.236167	−	0.971712i	$-0.575891\pi$
$541$	−3.21546e6	−0.472335	−0.236167	+	0.971712i	$0.575891\pi$
$542$	−1.99680e6	−0.291969
$543$	0	0
$544$	−1.20013e6	−0.173872
$545$	0	0
$546$	0	0
$547$	−3.71041e6	−0.530217	−0.265108	−	0.964219i	$-0.585408\pi$
$547$	−3.71041e6	−0.530217	−0.265108	+	0.964219i	$0.585408\pi$
$548$	−5.57018e6	−0.792351
$549$	363042.	0.0514074
$550$	0	0
$551$	4.23940e6	0.594875
$552$	0	0
$553$	−3.91157e6	−0.543924
$554$	4.12371e6	0.570839
$555$	0	0
$556$	−4.67782e6	−0.641737
$557$	−4.69093e6	−0.640650	−0.320325	−	0.947308i	$-0.603792\pi$
$557$	−4.69093e6	−0.640650	−0.320325	+	0.947308i	$0.603792\pi$
$558$	85536.0	0.0116296
$559$	−590944.	−0.0799865
$560$	0	0
$561$	0	0
$562$	−4.51394e6	−0.602858
$563$	1.14387e7	1.52092	0.760459	−	0.649386i	$-0.224974\pi$
$563$	1.14387e7	1.52092	0.760459	+	0.649386i	$0.224974\pi$
$564$	0	0
$565$	0	0
$566$	−199808.	−0.0262163
$567$	2.89340e6	0.377964
$568$	1.81478e6	0.236023
$569$	8.01383e6	1.03767	0.518835	−	0.854874i	$-0.326366\pi$
$569$	8.01383e6	1.03767	0.518835	+	0.854874i	$0.326366\pi$
$570$	0	0
$571$	−8.91239e6	−1.14394	−0.571971	−	0.820274i	$-0.693821\pi$
$571$	−8.91239e6	−1.14394	−0.571971	+	0.820274i	$0.693821\pi$
$572$	−1.44998e6	−0.185299
$573$	0	0
$574$	2.61425e6	0.331182
$575$	0	0
$576$	−995328.	−0.125000
$577$	−9.12994e6	−1.14164	−0.570819	−	0.821076i	$-0.693374\pi$
$577$	−9.12994e6	−1.14164	−0.570819	+	0.821076i	$0.693374\pi$
$578$	185092.	0.0230445
$579$	0	0
$580$	0	0
$581$	−4.10189e6	−0.504131
$582$	0	0
$583$	−4.31309e6	−0.525553
$584$	−4.53709e6	−0.550484
$585$	0	0
$586$	345360.	0.0415459
$587$	1.62764e7	1.94968	0.974842	−	0.222895i	$-0.0715509\pi$
$587$	1.62764e7	1.94968	0.974842	+	0.222895i	$0.0715509\pi$
$588$	0	0
$589$	−96800.0	−0.0114971
$590$	0	0
$591$	0	0
$592$	3.38944e6	0.397488
$593$	1.40344e7	1.63892	0.819461	−	0.573134i	$-0.194273\pi$
$593$	1.40344e7	1.63892	0.819461	+	0.573134i	$0.194273\pi$
$594$	0	0
$595$	0	0
$596$	2.86090e6	0.329903
$597$	0	0
$598$	−1.32160e6	−0.151129
$599$	1.93710e6	0.220590	0.110295	−	0.993899i	$-0.464821\pi$
$599$	1.93710e6	0.220590	0.110295	+	0.993899i	$0.464821\pi$
$600$	0	0
$601$	−3.81246e6	−0.430545	−0.215273	−	0.976554i	$-0.569064\pi$
$601$	−3.81246e6	−0.430545	−0.215273	+	0.976554i	$0.569064\pi$
$602$	−490784.	−0.0551949
$603$	4.43038e6	0.496189
$604$	−2.78227e6	−0.310318
$605$	0	0
$606$	0	0
$607$	1.29742e7	1.42925	0.714624	−	0.699508i	$-0.246598\pi$
$607$	1.29742e7	1.42925	0.714624	+	0.699508i	$0.246598\pi$
$608$	1.12640e6	0.123576
$609$	0	0
$610$	0	0
$611$	−3.47581e6	−0.376663
$612$	−4.55674e6	−0.491785
$613$	−1.28775e7	−1.38414	−0.692069	−	0.721832i	$-0.743300\pi$
$613$	−1.28775e7	−1.38414	−0.692069	+	0.721832i	$0.743300\pi$
$614$	1.14632e7	1.22712
$615$	0	0
$616$	−1.20422e6	−0.127866
$617$	−1.55320e7	−1.64253	−0.821267	−	0.570544i	$-0.806732\pi$
$617$	−1.55320e7	−1.64253	−0.821267	+	0.570544i	$0.806732\pi$
$618$	0	0
$619$	9.95199e6	1.04396	0.521979	−	0.852958i	$-0.325194\pi$
$619$	9.95199e6	1.04396	0.521979	+	0.852958i	$0.325194\pi$
$620$	0	0
$621$	0	0
$622$	1.49962e6	0.155419
$623$	−4.57121e6	−0.471858
$624$	0	0
$625$	0	0
$626$	−7.96587e6	−0.812452
$627$	0	0
$628$	−3.65664e6	−0.369984
$629$	1.55173e7	1.56383
$630$	0	0
$631$	−1.75371e7	−1.75341	−0.876706	−	0.481027i	$-0.840264\pi$
$631$	−1.75371e7	−1.75341	−0.876706	+	0.481027i	$0.840264\pi$
$632$	5.10899e6	0.508795
$633$	0	0
$634$	1.67123e6	0.165125
$635$	0	0
$636$	0	0
$637$	−566636.	−0.0553294
$638$	5.91974e6	0.575773
$639$	6.89051e6	0.667574
$640$	0	0
$641$	1.29073e7	1.24076	0.620382	−	0.784300i	$-0.286978\pi$
$641$	1.29073e7	1.24076	0.620382	+	0.784300i	$0.286978\pi$
$642$	0	0
$643$	−4.99083e6	−0.476042	−0.238021	−	0.971260i	$-0.576499\pi$
$643$	−4.99083e6	−0.476042	−0.238021	+	0.971260i	$0.576499\pi$
$644$	−1.09760e6	−0.104287
$645$	0	0
$646$	5.15680e6	0.486182
$647$	−951144.	−0.0893276	−0.0446638	−	0.999002i	$-0.514222\pi$
$647$	−951144.	−0.0893276	−0.0446638	+	0.999002i	$0.514222\pi$
$648$	−3.77914e6	−0.353553
$649$	250368.	0.0233328
$650$	0	0
$651$	0	0
$652$	−9.75398e6	−0.898593
$653$	−1.62012e7	−1.48684	−0.743419	−	0.668826i	$-0.766797\pi$
$653$	−1.62012e7	−1.48684	−0.743419	+	0.668826i	$0.766797\pi$
$654$	0	0
$655$	0	0
$656$	−3.41453e6	−0.309793
$657$	−1.72268e7	−1.55701
$658$	−2.88669e6	−0.259917
$659$	6.37817e6	0.572114	0.286057	−	0.958213i	$-0.407655\pi$
$659$	6.37817e6	0.572114	0.286057	+	0.958213i	$0.407655\pi$
$660$	0	0
$661$	1.01756e7	0.905850	0.452925	−	0.891549i	$-0.350380\pi$
$661$	1.01756e7	0.905850	0.452925	+	0.891549i	$0.350380\pi$
$662$	−1.29062e7	−1.14460
$663$	0	0
$664$	5.35757e6	0.471571
$665$	0	0
$666$	1.28693e7	1.12426
$667$	5.39560e6	0.469597
$668$	1.03776e7	0.899820
$669$	0	0
$670$	0	0
$671$	−573696.	−0.0491899
$672$	0	0
$673$	1.87501e7	1.59575	0.797875	−	0.602823i	$-0.205957\pi$
$673$	1.87501e7	1.59575	0.797875	+	0.602823i	$0.205957\pi$
$674$	−1.18921e7	−1.00834
$675$	0	0
$676$	−5.04955e6	−0.424997
$677$	9.56143e6	0.801772	0.400886	−	0.916128i	$-0.368702\pi$
$677$	9.56143e6	0.801772	0.400886	+	0.916128i	$0.368702\pi$
$678$	0	0
$679$	−4.46233e6	−0.371439
$680$	0	0
$681$	0	0
$682$	−135168.	−0.0111279
$683$	−1.20383e7	−0.987450	−0.493725	−	0.869618i	$-0.664365\pi$
$683$	−1.20383e7	−0.987450	−0.493725	+	0.869618i	$0.664365\pi$
$684$	4.27680e6	0.349525
$685$	0	0
$686$	−470596.	−0.0381802
$687$	0	0
$688$	641024.	0.0516301
$689$	2.65075e6	0.212726
$690$	0	0
$691$	1.50689e7	1.20057	0.600284	−	0.799787i	$-0.295054\pi$
$691$	1.50689e7	1.20057	0.600284	+	0.799787i	$0.295054\pi$
$692$	−2.04499e6	−0.162340
$693$	−4.57229e6	−0.361660
$694$	−2.33866e6	−0.184318
$695$	0	0
$696$	0	0
$697$	−1.56321e7	−1.21881
$698$	1.45120e7	1.12742
$699$	0	0
$700$	0	0
$701$	5.00312e6	0.384544	0.192272	−	0.981342i	$-0.438414\pi$
$701$	5.00312e6	0.384544	0.192272	+	0.981342i	$0.438414\pi$
$702$	0	0
$703$	−1.45640e7	−1.11146
$704$	1.57286e6	0.119608
$705$	0	0
$706$	6.51518e6	0.491943
$707$	−2.66099e6	−0.200214
$708$	0	0
$709$	6.39854e6	0.478041	0.239021	−	0.971015i	$-0.423174\pi$
$709$	6.39854e6	0.478041	0.239021	+	0.971015i	$0.423174\pi$
$710$	0	0
$711$	1.93982e7	1.43909
$712$	5.97056e6	0.441382
$713$	−123200.	−0.00907584
$714$	0	0
$715$	0	0
$716$	1.01953e7	0.743222
$717$	0	0
$718$	2.42421e6	0.175493
$719$	−4.18314e6	−0.301773	−0.150886	−	0.988551i	$-0.548213\pi$
$719$	−4.18314e6	−0.301773	−0.150886	+	0.988551i	$0.548213\pi$
$720$	0	0
$721$	−6.66126e6	−0.477219
$722$	5.06440e6	0.361564
$723$	0	0
$724$	7.37994e6	0.523246
$725$	0	0
$726$	0	0
$727$	6.29260e6	0.441564	0.220782	−	0.975323i	$-0.429139\pi$
$727$	6.29260e6	0.441564	0.220782	+	0.975323i	$0.429139\pi$
$728$	740096.	0.0517559
$729$	−1.43489e7	−1.00000
$730$	0	0
$731$	2.93469e6	0.203127
$732$	0	0
$733$	6.62340e6	0.455324	0.227662	−	0.973740i	$-0.426892\pi$
$733$	6.62340e6	0.455324	0.227662	+	0.973740i	$0.426892\pi$
$734$	8.60010e6	0.589201
$735$	0	0
$736$	1.43360e6	0.0975514
$737$	−7.00109e6	−0.474785
$738$	−1.29645e7	−0.876226
$739$	3.44169e6	0.231825	0.115913	−	0.993259i	$-0.463021\pi$
$739$	3.44169e6	0.231825	0.115913	+	0.993259i	$0.463021\pi$
$740$	0	0
$741$	0	0
$742$	2.20147e6	0.146792
$743$	1.85406e7	1.23212	0.616060	−	0.787699i	$-0.288728\pi$
$743$	1.85406e7	1.23212	0.616060	+	0.787699i	$0.288728\pi$
$744$	0	0
$745$	0	0
$746$	6.56742e6	0.432064
$747$	2.03420e7	1.33381
$748$	7.20077e6	0.470571
$749$	3.79809e6	0.247378
$750$	0	0
$751$	3.22428e6	0.208609	0.104305	−	0.994545i	$-0.466738\pi$
$751$	3.22428e6	0.208609	0.104305	+	0.994545i	$0.466738\pi$
$752$	3.77037e6	0.243130
$753$	0	0
$754$	−3.63818e6	−0.233053
$755$	0	0
$756$	0	0
$757$	2.34007e6	0.148419	0.0742095	−	0.997243i	$-0.476357\pi$
$757$	2.34007e6	0.148419	0.0742095	+	0.997243i	$0.476357\pi$
$758$	−1.60016e7	−1.01156
$759$	0	0
$760$	0	0
$761$	−8.34242e6	−0.522192	−0.261096	−	0.965313i	$-0.584084\pi$
$761$	−8.34242e6	−0.522192	−0.261096	+	0.965313i	$0.584084\pi$
$762$	0	0
$763$	−7.43399e6	−0.462286
$764$	5.70310e6	0.353491
$765$	0	0
$766$	−2.28635e7	−1.40789
$767$	−153872.	−0.00944433
$768$	0	0
$769$	3.29971e6	0.201215	0.100607	−	0.994926i	$-0.467921\pi$
$769$	3.29971e6	0.201215	0.100607	+	0.994926i	$0.467921\pi$
$770$	0	0
$771$	0	0
$772$	−3.05997e6	−0.184788
$773$	−7.19867e6	−0.433315	−0.216657	−	0.976248i	$-0.569515\pi$
$773$	−7.19867e6	−0.433315	−0.216657	+	0.976248i	$0.569515\pi$
$774$	2.43389e6	0.146032
$775$	0	0
$776$	5.82835e6	0.347449
$777$	0	0
$778$	6.70442e6	0.397112
$779$	1.46718e7	0.866243
$780$	0	0
$781$	−1.08887e7	−0.638776
$782$	6.56320e6	0.383795
$783$	0	0
$784$	614656.	0.0357143
$785$	0	0
$786$	0	0
$787$	1.79424e7	1.03262	0.516312	−	0.856400i	$-0.327304\pi$
$787$	1.79424e7	1.03262	0.516312	+	0.856400i	$0.327304\pi$
$788$	−9.99962e6	−0.573677
$789$	0	0
$790$	0	0
$791$	1.15303e7	0.655238
$792$	5.97197e6	0.338302
$793$	352584.	0.0199104
$794$	3.78056e6	0.212816
$795$	0	0
$796$	−3.95866e6	−0.221445
$797$	−1.53422e7	−0.855543	−0.427771	−	0.903887i	$-0.640701\pi$
$797$	−1.53422e7	−0.855543	−0.427771	+	0.903887i	$0.640701\pi$
$798$	0	0
$799$	1.72612e7	0.956543
$800$	0	0
$801$	2.26695e7	1.24842
$802$	−2.21114e6	−0.121389
$803$	2.72225e7	1.48984
$804$	0	0
$805$	0	0
$806$	83072.0	0.00450419
$807$	0	0
$808$	3.47558e6	0.187283
$809$	9.88141e6	0.530821	0.265410	−	0.964136i	$-0.414493\pi$
$809$	9.88141e6	0.530821	0.265410	+	0.964136i	$0.414493\pi$
$810$	0	0
$811$	−1.22149e7	−0.652137	−0.326069	−	0.945346i	$-0.605724\pi$
$811$	−1.22149e7	−0.652137	−0.326069	+	0.945346i	$0.605724\pi$
$812$	−3.02154e6	−0.160819
$813$	0	0
$814$	−2.03366e7	−1.07577
$815$	0	0
$816$	0	0
$817$	−2.75440e6	−0.144368
$818$	4.19132e6	0.219012
$819$	2.81005e6	0.146388
$820$	0	0
$821$	−2.12593e7	−1.10075	−0.550377	−	0.834916i	$-0.685516\pi$
$821$	−2.12593e7	−1.10075	−0.550377	+	0.834916i	$0.685516\pi$
$822$	0	0
$823$	−1.76882e7	−0.910297	−0.455149	−	0.890415i	$-0.650414\pi$
$823$	−1.76882e7	−0.910297	−0.455149	+	0.890415i	$0.650414\pi$
$824$	8.70042e6	0.446398
$825$	0	0
$826$	−127792.	−0.00651709
$827$	2.48044e7	1.26115	0.630573	−	0.776130i	$-0.282820\pi$
$827$	2.48044e7	1.26115	0.630573	+	0.776130i	$0.282820\pi$
$828$	5.44320e6	0.275917
$829$	−879386.	−0.0444420	−0.0222210	−	0.999753i	$-0.507074\pi$
$829$	−879386.	−0.0444420	−0.0222210	+	0.999753i	$0.507074\pi$
$830$	0	0
$831$	0	0
$832$	−966656.	−0.0484132
$833$	2.81397e6	0.140510
$834$	0	0
$835$	0	0
$836$	−6.75840e6	−0.334448
$837$	0	0
$838$	2.75337e7	1.35443
$839$	2.27773e7	1.11711	0.558556	−	0.829467i	$-0.311356\pi$
$839$	2.27773e7	1.11711	0.558556	+	0.829467i	$0.311356\pi$
$840$	0	0
$841$	−5.65783e6	−0.275842
$842$	1.82524e7	0.887239
$843$	0	0
$844$	4.81574e6	0.232706
$845$	0	0
$846$	1.43156e7	0.687676
$847$	−666155.	−0.0319056
$848$	−2.87539e6	−0.137312
$849$	0	0
$850$	0	0
$851$	−1.85360e7	−0.877389
$852$	0	0
$853$	1.13876e7	0.535869	0.267934	−	0.963437i	$-0.413659\pi$
$853$	1.13876e7	0.535869	0.267934	+	0.963437i	$0.413659\pi$
$854$	292824.	0.0137392
$855$	0	0
$856$	−4.96077e6	−0.231401
$857$	−3.74896e7	−1.74365	−0.871824	−	0.489819i	$-0.837063\pi$
$857$	−3.74896e7	−1.74365	−0.871824	+	0.489819i	$0.837063\pi$
$858$	0	0
$859$	−3.49422e7	−1.61572	−0.807862	−	0.589372i	$-0.799375\pi$
$859$	−3.49422e7	−1.61572	−0.807862	+	0.589372i	$0.799375\pi$
$860$	0	0
$861$	0	0
$862$	9.96440e6	0.456755
$863$	−3.40644e7	−1.55695	−0.778473	−	0.627678i	$-0.784006\pi$
$863$	−3.40644e7	−1.55695	−0.778473	+	0.627678i	$0.784006\pi$
$864$	0	0
$865$	0	0
$866$	−1.77127e7	−0.802583
$867$	0	0
$868$	68992.0	0.00310813
$869$	−3.06540e7	−1.37701
$870$	0	0
$871$	4.30275e6	0.192177
$872$	9.70970e6	0.432429
$873$	2.21295e7	0.982735
$874$	−6.16000e6	−0.272773
$875$	0	0
$876$	0	0
$877$	−9.56406e6	−0.419897	−0.209949	−	0.977712i	$-0.567330\pi$
$877$	−9.56406e6	−0.419897	−0.209949	+	0.977712i	$0.567330\pi$
$878$	−2.54173e6	−0.111274
$879$	0	0
$880$	0	0
$881$	2.43742e6	0.105801	0.0529006	−	0.998600i	$-0.483153\pi$
$881$	2.43742e6	0.105801	0.0529006	+	0.998600i	$0.483153\pi$
$882$	2.33377e6	0.101015
$883$	−1.08423e6	−0.0467973	−0.0233986	−	0.999726i	$-0.507449\pi$
$883$	−1.08423e6	−0.0467973	−0.0233986	+	0.999726i	$0.507449\pi$
$884$	−4.42547e6	−0.190471
$885$	0	0
$886$	7.22448e6	0.309188
$887$	−1.35583e7	−0.578623	−0.289312	−	0.957235i	$-0.593426\pi$
$887$	−1.35583e7	−0.578623	−0.289312	+	0.957235i	$0.593426\pi$
$888$	0	0
$889$	−1.67466e7	−0.710678
$890$	0	0
$891$	2.26748e7	0.956862
$892$	1.63418e6	0.0687680
$893$	−1.62008e7	−0.679842
$894$	0	0
$895$	0	0
$896$	−802816.	−0.0334077
$897$	0	0
$898$	1.56129e7	0.646090
$899$	−339152.	−0.0139957
$900$	0	0
$901$	−1.31639e7	−0.540223
$902$	2.04872e7	0.838428
$903$	0	0
$904$	−1.50600e7	−0.612919
$905$	0	0
$906$	0	0
$907$	−1.12138e7	−0.452619	−0.226309	−	0.974055i	$-0.572666\pi$
$907$	−1.12138e7	−0.452619	−0.226309	+	0.974055i	$0.572666\pi$
$908$	9.53549e6	0.383821
$909$	1.31964e7	0.529718
$910$	0	0
$911$	−4.15211e7	−1.65757	−0.828787	−	0.559564i	$-0.810969\pi$
$911$	−4.15211e7	−1.65757	−0.828787	+	0.559564i	$0.810969\pi$
$912$	0	0
$913$	−3.21454e7	−1.27627
$914$	1.74506e7	0.690946
$915$	0	0
$916$	1.62468e7	0.639778
$917$	−1.51055e7	−0.593215
$918$	0	0
$919$	−4.13539e7	−1.61520	−0.807602	−	0.589728i	$-0.799235\pi$
$919$	−4.13539e7	−1.61520	−0.807602	+	0.589728i	$0.799235\pi$
$920$	0	0
$921$	0	0
$922$	−3.38684e6	−0.131210
$923$	6.69202e6	0.258555
$924$	0	0
$925$	0	0
$926$	−2.95188e7	−1.13128
$927$	3.30344e7	1.26260
$928$	3.94650e6	0.150433
$929$	945378.	0.0359390	0.0179695	−	0.999839i	$-0.494280\pi$
$929$	945378.	0.0359390	0.0179695	+	0.999839i	$0.494280\pi$
$930$	0	0
$931$	−2.64110e6	−0.0998644
$932$	374144.	0.0141091
$933$	0	0
$934$	−1.15318e7	−0.432545
$935$	0	0
$936$	−3.67027e6	−0.136933
$937$	−4.77950e6	−0.177842	−0.0889208	−	0.996039i	$-0.528342\pi$
$937$	−4.77950e6	−0.177842	−0.0889208	+	0.996039i	$0.528342\pi$
$938$	3.57347e6	0.132612
$939$	0	0
$940$	0	0
$941$	2.87439e7	1.05821	0.529104	−	0.848557i	$-0.322528\pi$
$941$	2.87439e7	1.05821	0.529104	+	0.848557i	$0.322528\pi$
$942$	0	0
$943$	1.86732e7	0.683816
$944$	166912.	0.00609618
$945$	0	0
$946$	−3.84614e6	−0.139733
$947$	1.01090e6	0.0366298	0.0183149	−	0.999832i	$-0.494170\pi$
$947$	1.01090e6	0.0366298	0.0183149	+	0.999832i	$0.494170\pi$
$948$	0	0
$949$	−1.67305e7	−0.603037
$950$	0	0
$951$	0	0
$952$	−3.67539e6	−0.131435
$953$	−4.46529e7	−1.59264	−0.796319	−	0.604877i	$-0.793222\pi$
$953$	−4.46529e7	−1.59264	−0.796319	+	0.604877i	$0.793222\pi$
$954$	−1.09175e7	−0.388376
$955$	0	0
$956$	1.85350e7	0.655915
$957$	0	0
$958$	2.65329e7	0.934051
$959$	−1.70587e7	−0.598961
$960$	0	0
$961$	−2.86214e7	−0.999730
$962$	1.24986e7	0.435434
$963$	−1.88354e7	−0.654500
$964$	−1.56398e7	−0.542050
$965$	0	0
$966$	0	0
$967$	1.83956e7	0.632626	0.316313	−	0.948655i	$-0.397555\pi$
$967$	1.83956e7	0.632626	0.316313	+	0.948655i	$0.397555\pi$
$968$	870080.	0.0298449
$969$	0	0
$970$	0	0
$971$	3.72647e7	1.26838	0.634191	−	0.773177i	$-0.281333\pi$
$971$	3.72647e7	1.26838	0.634191	+	0.773177i	$0.281333\pi$
$972$	0	0
$973$	−1.43258e7	−0.485107
$974$	−8.71677e6	−0.294414
$975$	0	0
$976$	−382464.	−0.0128519
$977$	−8.11308e6	−0.271925	−0.135963	−	0.990714i	$-0.543413\pi$
$977$	−8.11308e6	−0.271925	−0.135963	+	0.990714i	$0.543413\pi$
$978$	0	0
$979$	−3.58234e7	−1.19456
$980$	0	0
$981$	3.68665e7	1.22309
$982$	−3.16923e7	−1.04876
$983$	−2.83324e7	−0.935189	−0.467594	−	0.883943i	$-0.654879\pi$
$983$	−2.83324e7	−0.935189	−0.467594	+	0.883943i	$0.654879\pi$
$984$	0	0
$985$	0	0
$986$	1.80676e7	0.591844
$987$	0	0
$988$	4.15360e6	0.135373
$989$	−3.50560e6	−0.113965
$990$	0	0
$991$	−4.96125e7	−1.60475	−0.802374	−	0.596822i	$-0.796430\pi$
$991$	−4.96125e7	−1.60475	−0.802374	+	0.596822i	$0.796430\pi$
$992$	−90112.0	−0.00290739
$993$	0	0
$994$	5.55778e6	0.178417
$995$	0	0
$996$	0	0
$997$	3.47215e7	1.10627	0.553135	−	0.833092i	$-0.313431\pi$
$997$	3.47215e7	1.10627	0.553135	+	0.833092i	$0.313431\pi$
$998$	1.07324e7	0.341093
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.6.a.c.1.1		1
5.2	odd	4		70.6.c.a.29.1	✓	2
5.3	odd	4		70.6.c.a.29.2	yes	2
5.4	even	2		350.6.a.j.1.1		1
15.2	even	4		630.6.g.c.379.2		2
15.8	even	4		630.6.g.c.379.1		2
20.3	even	4		560.6.g.a.449.1		2
20.7	even	4		560.6.g.a.449.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.c.a.29.1	✓	2	5.2	odd	4
70.6.c.a.29.2	yes	2	5.3	odd	4
350.6.a.c.1.1		1	1.1	even	1	trivial
350.6.a.j.1.1		1	5.4	even	2
560.6.g.a.449.1		2	20.3	even	4
560.6.g.a.449.2		2	20.7	even	4
630.6.g.c.379.1		2	15.8	even	4
630.6.g.c.379.2		2	15.2	even	4

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	350.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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