LMFDB - Embedded newform 700.6.a.n.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,6,Mod(1,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, 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("700.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	700.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:	$112.268673869$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 393x^{2} - 1002x + 16596 $ x^4 - 2x^3 - 393x^2 - 1002*x + 16596
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-14.8527$ of defining polynomial
Character	$\chi$	$=$	700.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+20.8527 q^{3} +49.0000 q^{7} +191.833 q^{9} -675.135 q^{11} +79.5620 q^{13} -1797.57 q^{17} +1956.46 q^{19} +1021.78 q^{21} +4124.37 q^{23} -1066.97 q^{27} -3120.39 q^{29} +2579.22 q^{31} -14078.4 q^{33} -8800.84 q^{37} +1659.08 q^{39} -13036.6 q^{41} -8688.18 q^{43} +5672.55 q^{47} +2401.00 q^{49} -37484.1 q^{51} -27344.8 q^{53} +40797.3 q^{57} -19904.8 q^{59} +46440.9 q^{61} +9399.82 q^{63} -27926.4 q^{67} +86004.0 q^{69} -23386.9 q^{71} -85638.7 q^{73} -33081.6 q^{77} +16596.9 q^{79} -68864.5 q^{81} -107606. q^{83} -65068.5 q^{87} +69441.9 q^{89} +3898.54 q^{91} +53783.5 q^{93} -39228.8 q^{97} -129513. q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 22 q^{3} + 196 q^{7} - 62 q^{9} + 48 q^{11} - 430 q^{13} - 1286 q^{17} - 384 q^{19} + 1078 q^{21} + 1256 q^{23} - 1196 q^{27} - 4994 q^{29} + 4618 q^{31} - 15268 q^{33} - 16922 q^{37} + 3200 q^{39}+ \cdots - 170416 q^{99}+O(q^{100}) $ 4 * q + 22 * q^3 + 196 * q^7 - 62 * q^9 + 48 * q^11 - 430 * q^13 - 1286 * q^17 - 384 * q^19 + 1078 * q^21 + 1256 * q^23 - 1196 * q^27 - 4994 * q^29 + 4618 * q^31 - 15268 * q^33 - 16922 * q^37 + 3200 * q^39 - 9192 * q^41 - 12368 * q^43 + 4476 * q^47 + 9604 * q^49 - 30396 * q^51 - 16736 * q^53 + 29946 * q^57 - 14614 * q^59 - 7122 * q^61 - 3038 * q^63 + 21408 * q^67 + 11822 * q^69 - 39748 * q^71 - 89364 * q^73 + 2352 * q^77 - 37640 * q^79 - 125192 * q^81 - 83842 * q^83 + 90982 * q^87 - 12444 * q^89 - 21070 * q^91 - 137840 * q^93 + 57034 * q^97 - 170416 * q^99

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
$3$	20.8527	1.33770	0.668849	−	0.743398i	$-0.266787\pi$
$3$	20.8527	1.33770	0.668849	+	0.743398i	$0.266787\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	0	0
$9$	191.833	0.789436
$10$	0	0
$11$	−675.135	−1.68232	−0.841161	−	0.540785i	$-0.818127\pi$
$11$	−675.135	−1.68232	−0.841161	+	0.540785i	$0.818127\pi$
$12$	0	0
$13$	79.5620	0.130571	0.0652856	−	0.997867i	$-0.479204\pi$
$13$	79.5620	0.130571	0.0652856	+	0.997867i	$0.479204\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−1797.57	−1.50856	−0.754282	−	0.656551i	$-0.772015\pi$
$17$	−1797.57	−1.50856	−0.754282	+	0.656551i	$0.772015\pi$
$18$	0	0
$19$	1956.46	1.24333	0.621664	−	0.783284i	$-0.286457\pi$
$19$	1956.46	1.24333	0.621664	+	0.783284i	$0.286457\pi$
$20$	0	0
$21$	1021.78	0.505602
$22$	0	0
$23$	4124.37	1.62569	0.812845	−	0.582480i	$-0.197918\pi$
$23$	4124.37	1.62569	0.812845	+	0.582480i	$0.197918\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−1066.97	−0.281671
$28$	0	0
$29$	−3120.39	−0.688993	−0.344496	−	0.938788i	$-0.611950\pi$
$29$	−3120.39	−0.688993	−0.344496	+	0.938788i	$0.611950\pi$
$30$	0	0
$31$	2579.22	0.482041	0.241020	−	0.970520i	$-0.422518\pi$
$31$	2579.22	0.482041	0.241020	+	0.970520i	$0.422518\pi$
$32$	0	0
$33$	−14078.4	−2.25044
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−8800.84	−1.05687	−0.528433	−	0.848975i	$-0.677220\pi$
$37$	−8800.84	−1.05687	−0.528433	+	0.848975i	$0.677220\pi$
$38$	0	0
$39$	1659.08	0.174665
$40$	0	0
$41$	−13036.6	−1.21117	−0.605586	−	0.795780i	$-0.707061\pi$
$41$	−13036.6	−1.21117	−0.605586	+	0.795780i	$0.707061\pi$
$42$	0	0
$43$	−8688.18	−0.716569	−0.358284	−	0.933613i	$-0.616638\pi$
$43$	−8688.18	−0.716569	−0.358284	+	0.933613i	$0.616638\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	5672.55	0.374571	0.187285	−	0.982306i	$-0.440031\pi$
$47$	5672.55	0.374571	0.187285	+	0.982306i	$0.440031\pi$
$48$	0	0
$49$	2401.00	0.142857
$50$	0	0
$51$	−37484.1	−2.01800
$52$	0	0
$53$	−27344.8	−1.33717	−0.668583	−	0.743638i	$-0.733099\pi$
$53$	−27344.8	−1.33717	−0.668583	+	0.743638i	$0.733099\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	40797.3	1.66320
$58$	0	0
$59$	−19904.8	−0.744436	−0.372218	−	0.928145i	$-0.621403\pi$
$59$	−19904.8	−0.744436	−0.372218	+	0.928145i	$0.621403\pi$
$60$	0	0
$61$	46440.9	1.59800	0.798998	−	0.601333i	$-0.205364\pi$
$61$	46440.9	1.59800	0.798998	+	0.601333i	$0.205364\pi$
$62$	0	0
$63$	9399.82	0.298379
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−27926.4	−0.760026	−0.380013	−	0.924981i	$-0.624080\pi$
$67$	−27926.4	−0.760026	−0.380013	+	0.924981i	$0.624080\pi$
$68$	0	0
$69$	86004.0	2.17468
$70$	0	0
$71$	−23386.9	−0.550588	−0.275294	−	0.961360i	$-0.588775\pi$
$71$	−23386.9	−0.550588	−0.275294	+	0.961360i	$0.588775\pi$
$72$	0	0
$73$	−85638.7	−1.88089	−0.940444	−	0.339949i	$-0.889590\pi$
$73$	−85638.7	−1.88089	−0.940444	+	0.339949i	$0.889590\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−33081.6	−0.635858
$78$	0	0
$79$	16596.9	0.299198	0.149599	−	0.988747i	$-0.452202\pi$
$79$	16596.9	0.299198	0.149599	+	0.988747i	$0.452202\pi$
$80$	0	0
$81$	−68864.5	−1.16623
$82$	0	0
$83$	−107606.	−1.71452	−0.857258	−	0.514887i	$-0.827834\pi$
$83$	−107606.	−1.71452	−0.857258	+	0.514887i	$0.827834\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−65068.5	−0.921664
$88$	0	0
$89$	69441.9	0.929281	0.464640	−	0.885500i	$-0.346184\pi$
$89$	69441.9	0.929281	0.464640	+	0.885500i	$0.346184\pi$
$90$	0	0
$91$	3898.54	0.0493513
$92$	0	0
$93$	53783.5	0.644825
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−39228.8	−0.423326	−0.211663	−	0.977343i	$-0.567888\pi$
$97$	−39228.8	−0.423326	−0.211663	+	0.977343i	$0.567888\pi$
$98$	0	0
$99$	−129513.	−1.32809
$100$	0	0
$101$	−119236.	−1.16307	−0.581534	−	0.813522i	$-0.697547\pi$
$101$	−119236.	−1.16307	−0.581534	+	0.813522i	$0.697547\pi$
$102$	0	0
$103$	102923.	0.955915	0.477957	−	0.878383i	$-0.341377\pi$
$103$	102923.	0.955915	0.477957	+	0.878383i	$0.341377\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	171298.	1.44641	0.723206	−	0.690632i	$-0.242668\pi$
$107$	171298.	1.44641	0.723206	+	0.690632i	$0.242668\pi$
$108$	0	0
$109$	−135653.	−1.09361	−0.546805	−	0.837260i	$-0.684156\pi$
$109$	−135653.	−1.09361	−0.546805	+	0.837260i	$0.684156\pi$
$110$	0	0
$111$	−183521.	−1.41377
$112$	0	0
$113$	−102107.	−0.752244	−0.376122	−	0.926570i	$-0.622743\pi$
$113$	−102107.	−0.752244	−0.376122	+	0.926570i	$0.622743\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	15262.6	0.103078
$118$	0	0
$119$	−88080.9	−0.570183
$120$	0	0
$121$	294756.	1.83021
$122$	0	0
$123$	−271848.	−1.62018
$124$	0	0
$125$	0	0
$126$	0	0
$127$	278332.	1.53128	0.765639	−	0.643270i	$-0.222423\pi$
$127$	278332.	1.53128	0.765639	+	0.643270i	$0.222423\pi$
$128$	0	0
$129$	−181172.	−0.958553
$130$	0	0
$131$	−275429.	−1.40227	−0.701134	−	0.713029i	$-0.747323\pi$
$131$	−275429.	−1.40227	−0.701134	+	0.713029i	$0.747323\pi$
$132$	0	0
$133$	95866.3	0.469934
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−77939.7	−0.354778	−0.177389	−	0.984141i	$-0.556765\pi$
$137$	−77939.7	−0.354778	−0.177389	+	0.984141i	$0.556765\pi$
$138$	0	0
$139$	44711.5	0.196283	0.0981414	−	0.995172i	$-0.468710\pi$
$139$	44711.5	0.196283	0.0981414	+	0.995172i	$0.468710\pi$
$140$	0	0
$141$	118288.	0.501063
$142$	0	0
$143$	−53715.1	−0.219663
$144$	0	0
$145$	0	0
$146$	0	0
$147$	50067.2	0.191100
$148$	0	0
$149$	−479386.	−1.76897	−0.884484	−	0.466570i	$-0.845490\pi$
$149$	−479386.	−1.76897	−0.884484	+	0.466570i	$0.845490\pi$
$150$	0	0
$151$	251338.	0.897049	0.448525	−	0.893770i	$-0.351950\pi$
$151$	251338.	0.897049	0.448525	+	0.893770i	$0.351950\pi$
$152$	0	0
$153$	−344833.	−1.19091
$154$	0	0
$155$	0	0
$156$	0	0
$157$	421795.	1.36569	0.682845	−	0.730563i	$-0.260742\pi$
$157$	421795.	1.36569	0.682845	+	0.730563i	$0.260742\pi$
$158$	0	0
$159$	−570212.	−1.78872
$160$	0	0
$161$	202094.	0.614453
$162$	0	0
$163$	104613.	0.308401	0.154200	−	0.988040i	$-0.450720\pi$
$163$	104613.	0.308401	0.154200	+	0.988040i	$0.450720\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−11879.3	−0.0329608	−0.0164804	−	0.999864i	$-0.505246\pi$
$167$	−11879.3	−0.0329608	−0.0164804	+	0.999864i	$0.505246\pi$
$168$	0	0
$169$	−364963.	−0.982951
$170$	0	0
$171$	375313.	0.981529
$172$	0	0
$173$	534748.	1.35842	0.679210	−	0.733944i	$-0.262322\pi$
$173$	534748.	1.35842	0.679210	+	0.733944i	$0.262322\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−415067.	−0.995831
$178$	0	0
$179$	333077.	0.776984	0.388492	−	0.921452i	$-0.372996\pi$
$179$	333077.	0.776984	0.388492	+	0.921452i	$0.372996\pi$
$180$	0	0
$181$	−458322.	−1.03986	−0.519929	−	0.854209i	$-0.674042\pi$
$181$	−458322.	−1.03986	−0.519929	+	0.854209i	$0.674042\pi$
$182$	0	0
$183$	968415.	2.13764
$184$	0	0
$185$	0	0
$186$	0	0
$187$	1.21360e6	2.53789
$188$	0	0
$189$	−52281.4	−0.106461
$190$	0	0
$191$	−191262.	−0.379354	−0.189677	−	0.981847i	$-0.560744\pi$
$191$	−191262.	−0.379354	−0.189677	+	0.981847i	$0.560744\pi$
$192$	0	0
$193$	−335390.	−0.648122	−0.324061	−	0.946036i	$-0.605048\pi$
$193$	−335390.	−0.648122	−0.324061	+	0.946036i	$0.605048\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	133555.	0.245185	0.122592	−	0.992457i	$-0.460879\pi$
$197$	133555.	0.245185	0.122592	+	0.992457i	$0.460879\pi$
$198$	0	0
$199$	133576.	0.239109	0.119555	−	0.992828i	$-0.461853\pi$
$199$	133576.	0.239109	0.119555	+	0.992828i	$0.461853\pi$
$200$	0	0
$201$	−582340.	−1.01669
$202$	0	0
$203$	−152899.	−0.260415
$204$	0	0
$205$	0	0
$206$	0	0
$207$	791190.	1.28338
$208$	0	0
$209$	−1.32087e6	−2.09168
$210$	0	0
$211$	413079.	0.638745	0.319372	−	0.947629i	$-0.396528\pi$
$211$	413079.	0.638745	0.319372	+	0.947629i	$0.396528\pi$
$212$	0	0
$213$	−487679.	−0.736520
$214$	0	0
$215$	0	0
$216$	0	0
$217$	126382.	0.182194
$218$	0	0
$219$	−1.78579e6	−2.51606
$220$	0	0
$221$	−143018.	−0.196975
$222$	0	0
$223$	−125631.	−0.169174	−0.0845869	−	0.996416i	$-0.526957\pi$
$223$	−125631.	−0.169174	−0.0845869	+	0.996416i	$0.526957\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−82682.0	−0.106499	−0.0532496	−	0.998581i	$-0.516958\pi$
$227$	−82682.0	−0.106499	−0.0532496	+	0.998581i	$0.516958\pi$
$228$	0	0
$229$	−399678.	−0.503642	−0.251821	−	0.967774i	$-0.581029\pi$
$229$	−399678.	−0.503642	−0.251821	+	0.967774i	$0.581029\pi$
$230$	0	0
$231$	−689840.	−0.850586
$232$	0	0
$233$	−213322.	−0.257422	−0.128711	−	0.991682i	$-0.541084\pi$
$233$	−213322.	−0.257422	−0.128711	+	0.991682i	$0.541084\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	346089.	0.400237
$238$	0	0
$239$	1.04735e6	1.18603	0.593017	−	0.805190i	$-0.297937\pi$
$239$	1.04735e6	1.18603	0.593017	+	0.805190i	$0.297937\pi$
$240$	0	0
$241$	445975.	0.494615	0.247308	−	0.968937i	$-0.420454\pi$
$241$	445975.	0.494615	0.247308	+	0.968937i	$0.420454\pi$
$242$	0	0
$243$	−1.17673e6	−1.27839
$244$	0	0
$245$	0	0
$246$	0	0
$247$	155660.	0.162343
$248$	0	0
$249$	−2.24387e6	−2.29351
$250$	0	0
$251$	−1.23552e6	−1.23784	−0.618921	−	0.785453i	$-0.712430\pi$
$251$	−1.23552e6	−1.23784	−0.618921	+	0.785453i	$0.712430\pi$
$252$	0	0
$253$	−2.78450e6	−2.73493
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−440385.	−0.415910	−0.207955	−	0.978138i	$-0.566681\pi$
$257$	−440385.	−0.415910	−0.207955	+	0.978138i	$0.566681\pi$
$258$	0	0
$259$	−431241.	−0.399458
$260$	0	0
$261$	−598595.	−0.543916
$262$	0	0
$263$	509080.	0.453834	0.226917	−	0.973914i	$-0.427135\pi$
$263$	509080.	0.453834	0.226917	+	0.973914i	$0.427135\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	1.44805e6	1.24310
$268$	0	0
$269$	−622366.	−0.524403	−0.262201	−	0.965013i	$-0.584448\pi$
$269$	−622366.	−0.524403	−0.262201	+	0.965013i	$0.584448\pi$
$270$	0	0
$271$	−709244.	−0.586641	−0.293321	−	0.956014i	$-0.594760\pi$
$271$	−709244.	−0.586641	−0.293321	+	0.956014i	$0.594760\pi$
$272$	0	0
$273$	81294.9	0.0660171
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−1.20740e6	−0.945478	−0.472739	−	0.881203i	$-0.656735\pi$
$277$	−1.20740e6	−0.945478	−0.472739	+	0.881203i	$0.656735\pi$
$278$	0	0
$279$	494779.	0.380541
$280$	0	0
$281$	1.64668e6	1.24406	0.622032	−	0.782992i	$-0.286307\pi$
$281$	1.64668e6	1.24406	0.622032	+	0.782992i	$0.286307\pi$
$282$	0	0
$283$	296298.	0.219919	0.109959	−	0.993936i	$-0.464928\pi$
$283$	296298.	0.219919	0.109959	+	0.993936i	$0.464928\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−638795.	−0.457780
$288$	0	0
$289$	1.81140e6	1.27576
$290$	0	0
$291$	−818023.	−0.566283
$292$	0	0
$293$	389254.	0.264889	0.132445	−	0.991190i	$-0.457717\pi$
$293$	389254.	0.264889	0.132445	+	0.991190i	$0.457717\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	720347.	0.473861
$298$	0	0
$299$	328143.	0.212268
$300$	0	0
$301$	−425721.	−0.270838
$302$	0	0
$303$	−2.48639e6	−1.55583
$304$	0	0
$305$	0	0
$306$	0	0
$307$	403571.	0.244385	0.122192	−	0.992506i	$-0.461007\pi$
$307$	403571.	0.244385	0.122192	+	0.992506i	$0.461007\pi$
$308$	0	0
$309$	2.14622e6	1.27873
$310$	0	0
$311$	−1.47942e6	−0.867344	−0.433672	−	0.901071i	$-0.642782\pi$
$311$	−1.47942e6	−0.867344	−0.433672	+	0.901071i	$0.642782\pi$
$312$	0	0
$313$	−612825.	−0.353570	−0.176785	−	0.984249i	$-0.556570\pi$
$313$	−612825.	−0.353570	−0.176785	+	0.984249i	$0.556570\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	705848.	0.394515	0.197257	−	0.980352i	$-0.436797\pi$
$317$	705848.	0.394515	0.197257	+	0.980352i	$0.436797\pi$
$318$	0	0
$319$	2.10669e6	1.15911
$320$	0	0
$321$	3.57201e6	1.93486
$322$	0	0
$323$	−3.51687e6	−1.87564
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−2.82872e6	−1.46292
$328$	0	0
$329$	277955.	0.141574
$330$	0	0
$331$	−3.85632e6	−1.93466	−0.967328	−	0.253530i	$-0.918408\pi$
$331$	−3.85632e6	−1.93466	−0.967328	+	0.253530i	$0.918408\pi$
$332$	0	0
$333$	−1.68829e6	−0.834328
$334$	0	0
$335$	0	0
$336$	0	0
$337$	28307.7	0.0135778	0.00678891	−	0.999977i	$-0.497839\pi$
$337$	28307.7	0.0135778	0.00678891	+	0.999977i	$0.497839\pi$
$338$	0	0
$339$	−2.12920e6	−1.00627
$340$	0	0
$341$	−1.74132e6	−0.810948
$342$	0	0
$343$	117649.	0.0539949
$344$	0	0
$345$	0	0
$346$	0	0
$347$	2.31337e6	1.03139	0.515693	−	0.856774i	$-0.327535\pi$
$347$	2.31337e6	1.03139	0.515693	+	0.856774i	$0.327535\pi$
$348$	0	0
$349$	−3.44482e6	−1.51392	−0.756961	−	0.653460i	$-0.773317\pi$
$349$	−3.44482e6	−1.51392	−0.756961	+	0.653460i	$0.773317\pi$
$350$	0	0
$351$	−84890.1	−0.0367781
$352$	0	0
$353$	−2.02337e6	−0.864250	−0.432125	−	0.901814i	$-0.642236\pi$
$353$	−2.02337e6	−0.864250	−0.432125	+	0.901814i	$0.642236\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−1.83672e6	−0.762733
$358$	0	0
$359$	2.92497e6	1.19780	0.598901	−	0.800823i	$-0.295604\pi$
$359$	2.92497e6	1.19780	0.598901	+	0.800823i	$0.295604\pi$
$360$	0	0
$361$	1.35162e6	0.545866
$362$	0	0
$363$	6.14645e6	2.44826
$364$	0	0
$365$	0	0
$366$	0	0
$367$	1.31035e6	0.507836	0.253918	−	0.967226i	$-0.418281\pi$
$367$	1.31035e6	0.507836	0.253918	+	0.967226i	$0.418281\pi$
$368$	0	0
$369$	−2.50086e6	−0.956143
$370$	0	0
$371$	−1.33990e6	−0.505401
$372$	0	0
$373$	3.84239e6	1.42998	0.714989	−	0.699136i	$-0.246432\pi$
$373$	3.84239e6	1.42998	0.714989	+	0.699136i	$0.246432\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−248265.	−0.0899626
$378$	0	0
$379$	−4.63179e6	−1.65635	−0.828173	−	0.560472i	$-0.810620\pi$
$379$	−4.63179e6	−1.65635	−0.828173	+	0.560472i	$0.810620\pi$
$380$	0	0
$381$	5.80396e6	2.04839
$382$	0	0
$383$	2.68186e6	0.934199	0.467100	−	0.884205i	$-0.345299\pi$
$383$	2.68186e6	0.934199	0.467100	+	0.884205i	$0.345299\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−1.66668e6	−0.565685
$388$	0	0
$389$	−169277.	−0.0567183	−0.0283592	−	0.999598i	$-0.509028\pi$
$389$	−169277.	−0.0567183	−0.0283592	+	0.999598i	$0.509028\pi$
$390$	0	0
$391$	−7.41384e6	−2.45246
$392$	0	0
$393$	−5.74342e6	−1.87581
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−5.27555e6	−1.67993	−0.839965	−	0.542641i	$-0.817425\pi$
$397$	−5.27555e6	−1.67993	−0.839965	+	0.542641i	$0.817425\pi$
$398$	0	0
$399$	1.99907e6	0.628630
$400$	0	0
$401$	−3.04252e6	−0.944870	−0.472435	−	0.881365i	$-0.656625\pi$
$401$	−3.04252e6	−0.944870	−0.472435	+	0.881365i	$0.656625\pi$
$402$	0	0
$403$	205208.	0.0629407
$404$	0	0
$405$	0	0
$406$	0	0
$407$	5.94175e6	1.77799
$408$	0	0
$409$	6.16440e6	1.82214	0.911071	−	0.412249i	$-0.135256\pi$
$409$	6.16440e6	1.82214	0.911071	+	0.412249i	$0.135256\pi$
$410$	0	0
$411$	−1.62525e6	−0.474586
$412$	0	0
$413$	−975334.	−0.281370
$414$	0	0
$415$	0	0
$416$	0	0
$417$	932353.	0.262567
$418$	0	0
$419$	1.70863e6	0.475460	0.237730	−	0.971331i	$-0.423597\pi$
$419$	1.70863e6	0.475460	0.237730	+	0.971331i	$0.423597\pi$
$420$	0	0
$421$	5.96013e6	1.63889	0.819446	−	0.573156i	$-0.194281\pi$
$421$	5.96013e6	1.63889	0.819446	+	0.573156i	$0.194281\pi$
$422$	0	0
$423$	1.08818e6	0.295700
$424$	0	0
$425$	0	0
$426$	0	0
$427$	2.27560e6	0.603986
$428$	0	0
$429$	−1.12010e6	−0.293843
$430$	0	0
$431$	6.36452e6	1.65034	0.825169	−	0.564886i	$-0.191080\pi$
$431$	6.36452e6	1.65034	0.825169	+	0.564886i	$0.191080\pi$
$432$	0	0
$433$	3.83046e6	0.981820	0.490910	−	0.871210i	$-0.336664\pi$
$433$	3.83046e6	0.981820	0.490910	+	0.871210i	$0.336664\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	8.06914e6	2.02127
$438$	0	0
$439$	2.03749e6	0.504584	0.252292	−	0.967651i	$-0.418816\pi$
$439$	2.03749e6	0.504584	0.252292	+	0.967651i	$0.418816\pi$
$440$	0	0
$441$	460591.	0.112777
$442$	0	0
$443$	5.75256e6	1.39268	0.696340	−	0.717712i	$-0.254810\pi$
$443$	5.75256e6	1.39268	0.696340	+	0.717712i	$0.254810\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−9.99648e6	−2.36635
$448$	0	0
$449$	6.69118e6	1.56634	0.783171	−	0.621806i	$-0.213601\pi$
$449$	6.69118e6	1.56634	0.783171	+	0.621806i	$0.213601\pi$
$450$	0	0
$451$	8.80149e6	2.03758
$452$	0	0
$453$	5.24107e6	1.19998
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−1.52836e6	−0.342322	−0.171161	−	0.985243i	$-0.554752\pi$
$457$	−1.52836e6	−0.342322	−0.171161	+	0.985243i	$0.554752\pi$
$458$	0	0
$459$	1.91795e6	0.424918
$460$	0	0
$461$	465889.	0.102101	0.0510505	−	0.998696i	$-0.483743\pi$
$461$	465889.	0.102101	0.0510505	+	0.998696i	$0.483743\pi$
$462$	0	0
$463$	3.62236e6	0.785307	0.392653	−	0.919687i	$-0.371557\pi$
$463$	3.62236e6	0.785307	0.392653	+	0.919687i	$0.371557\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−6.38448e6	−1.35467	−0.677335	−	0.735675i	$-0.736865\pi$
$467$	−6.38448e6	−1.35467	−0.677335	+	0.735675i	$0.736865\pi$
$468$	0	0
$469$	−1.36840e6	−0.287263
$470$	0	0
$471$	8.79554e6	1.82688
$472$	0	0
$473$	5.86570e6	1.20550
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−5.24564e6	−1.05561
$478$	0	0
$479$	−4.72262e6	−0.940469	−0.470235	−	0.882541i	$-0.655831\pi$
$479$	−4.72262e6	−0.940469	−0.470235	+	0.882541i	$0.655831\pi$
$480$	0	0
$481$	−700212.	−0.137996
$482$	0	0
$483$	4.21419e6	0.821953
$484$	0	0
$485$	0	0
$486$	0	0
$487$	7.89067e6	1.50762	0.753809	−	0.657093i	$-0.228214\pi$
$487$	7.89067e6	1.50762	0.753809	+	0.657093i	$0.228214\pi$
$488$	0	0
$489$	2.18145e6	0.412547
$490$	0	0
$491$	8.17244e6	1.52985	0.764923	−	0.644121i	$-0.222777\pi$
$491$	8.17244e6	1.52985	0.764923	+	0.644121i	$0.222777\pi$
$492$	0	0
$493$	5.60913e6	1.03939
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−1.14596e6	−0.208103
$498$	0	0
$499$	−5.29079e6	−0.951195	−0.475597	−	0.879663i	$-0.657768\pi$
$499$	−5.29079e6	−0.951195	−0.475597	+	0.879663i	$0.657768\pi$
$500$	0	0
$501$	−247714.	−0.0440916
$502$	0	0
$503$	−4.59481e6	−0.809743	−0.404872	−	0.914374i	$-0.632684\pi$
$503$	−4.59481e6	−0.809743	−0.404872	+	0.914374i	$0.632684\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−7.61044e6	−1.31489
$508$	0	0
$509$	−3.70680e6	−0.634168	−0.317084	−	0.948397i	$-0.602704\pi$
$509$	−3.70680e6	−0.634168	−0.317084	+	0.948397i	$0.602704\pi$
$510$	0	0
$511$	−4.19630e6	−0.710909
$512$	0	0
$513$	−2.08747e6	−0.350209
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−3.82974e6	−0.630149
$518$	0	0
$519$	1.11509e7	1.81716
$520$	0	0
$521$	−4.58202e6	−0.739542	−0.369771	−	0.929123i	$-0.620564\pi$
$521$	−4.58202e6	−0.739542	−0.369771	+	0.929123i	$0.620564\pi$
$522$	0	0
$523$	9.45246e6	1.51109	0.755545	−	0.655096i	$-0.227372\pi$
$523$	9.45246e6	1.51109	0.755545	+	0.655096i	$0.227372\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−4.63632e6	−0.727189
$528$	0	0
$529$	1.05741e7	1.64287
$530$	0	0
$531$	−3.81839e6	−0.587685
$532$	0	0
$533$	−1.03722e6	−0.158144
$534$	0	0
$535$	0	0
$536$	0	0
$537$	6.94554e6	1.03937
$538$	0	0
$539$	−1.62100e6	−0.240332
$540$	0	0
$541$	−3.11444e6	−0.457496	−0.228748	−	0.973486i	$-0.573463\pi$
$541$	−3.11444e6	−0.457496	−0.228748	+	0.973486i	$0.573463\pi$
$542$	0	0
$543$	−9.55723e6	−1.39102
$544$	0	0
$545$	0	0
$546$	0	0
$547$	6.73813e6	0.962878	0.481439	−	0.876480i	$-0.340114\pi$
$547$	6.73813e6	0.962878	0.481439	+	0.876480i	$0.340114\pi$
$548$	0	0
$549$	8.90889e6	1.26152
$550$	0	0
$551$	−6.10491e6	−0.856644
$552$	0	0
$553$	813248.	0.113086
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−9.55922e6	−1.30552	−0.652761	−	0.757564i	$-0.726390\pi$
$557$	−9.55922e6	−1.30552	−0.652761	+	0.757564i	$0.726390\pi$
$558$	0	0
$559$	−691250.	−0.0935633
$560$	0	0
$561$	2.53068e7	3.39493
$562$	0	0
$563$	854448.	0.113610	0.0568048	−	0.998385i	$-0.481909\pi$
$563$	854448.	0.113610	0.0568048	+	0.998385i	$0.481909\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−3.37436e6	−0.440792
$568$	0	0
$569$	−1.99627e6	−0.258487	−0.129243	−	0.991613i	$-0.541255\pi$
$569$	−1.99627e6	−0.258487	−0.129243	+	0.991613i	$0.541255\pi$
$570$	0	0
$571$	−1.44997e7	−1.86110	−0.930548	−	0.366170i	$-0.880669\pi$
$571$	−1.44997e7	−1.86110	−0.930548	+	0.366170i	$0.880669\pi$
$572$	0	0
$573$	−3.98831e6	−0.507461
$574$	0	0
$575$	0	0
$576$	0	0
$577$	8.16304e6	1.02073	0.510367	−	0.859957i	$-0.329510\pi$
$577$	8.16304e6	1.02073	0.510367	+	0.859957i	$0.329510\pi$
$578$	0	0
$579$	−6.99377e6	−0.866991
$580$	0	0
$581$	−5.27270e6	−0.648026
$582$	0	0
$583$	1.84614e7	2.24954
$584$	0	0
$585$	0	0
$586$	0	0
$587$	3.08241e6	0.369229	0.184614	−	0.982811i	$-0.440896\pi$
$587$	3.08241e6	0.369229	0.184614	+	0.982811i	$0.440896\pi$
$588$	0	0
$589$	5.04613e6	0.599335
$590$	0	0
$591$	2.78497e6	0.327983
$592$	0	0
$593$	4.02090e6	0.469555	0.234777	−	0.972049i	$-0.424564\pi$
$593$	4.02090e6	0.469555	0.234777	+	0.972049i	$0.424564\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	2.78542e6	0.319856
$598$	0	0
$599$	1.01764e7	1.15885	0.579424	−	0.815026i	$-0.303278\pi$
$599$	1.01764e7	1.15885	0.579424	+	0.815026i	$0.303278\pi$
$600$	0	0
$601$	−7.83641e6	−0.884974	−0.442487	−	0.896775i	$-0.645904\pi$
$601$	−7.83641e6	−0.884974	−0.442487	+	0.896775i	$0.645904\pi$
$602$	0	0
$603$	−5.35721e6	−0.599992
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−5.52135e6	−0.608238	−0.304119	−	0.952634i	$-0.598362\pi$
$607$	−5.52135e6	−0.608238	−0.304119	+	0.952634i	$0.598362\pi$
$608$	0	0
$609$	−3.18836e6	−0.348356
$610$	0	0
$611$	451320.	0.0489082
$612$	0	0
$613$	−1.57387e7	−1.69168	−0.845840	−	0.533437i	$-0.820900\pi$
$613$	−1.57387e7	−1.69168	−0.845840	+	0.533437i	$0.820900\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	7.24585e6	0.766260	0.383130	−	0.923694i	$-0.374846\pi$
$617$	7.24585e6	0.766260	0.383130	+	0.923694i	$0.374846\pi$
$618$	0	0
$619$	1.24709e7	1.30819	0.654095	−	0.756412i	$-0.273050\pi$
$619$	1.24709e7	1.30819	0.654095	+	0.756412i	$0.273050\pi$
$620$	0	0
$621$	−4.40056e6	−0.457909
$622$	0	0
$623$	3.40266e6	0.351235
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−2.75437e7	−2.79803
$628$	0	0
$629$	1.58201e7	1.59435
$630$	0	0
$631$	1.10646e6	0.110627	0.0553135	−	0.998469i	$-0.482384\pi$
$631$	1.10646e6	0.110627	0.0553135	+	0.998469i	$0.482384\pi$
$632$	0	0
$633$	8.61380e6	0.854447
$634$	0	0
$635$	0	0
$636$	0	0
$637$	191028.	0.0186530
$638$	0	0
$639$	−4.48638e6	−0.434654
$640$	0	0
$641$	1.11794e7	1.07467	0.537334	−	0.843369i	$-0.319431\pi$
$641$	1.11794e7	1.07467	0.537334	+	0.843369i	$0.319431\pi$
$642$	0	0
$643$	−1.62540e7	−1.55036	−0.775179	−	0.631742i	$-0.782340\pi$
$643$	−1.62540e7	−1.55036	−0.775179	+	0.631742i	$0.782340\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−1.52553e7	−1.43272	−0.716360	−	0.697731i	$-0.754193\pi$
$647$	−1.52553e7	−1.43272	−0.716360	+	0.697731i	$0.754193\pi$
$648$	0	0
$649$	1.34384e7	1.25238
$650$	0	0
$651$	2.63539e6	0.243721
$652$	0	0
$653$	−626612.	−0.0575064	−0.0287532	−	0.999587i	$-0.509154\pi$
$653$	−626612.	−0.0575064	−0.0287532	+	0.999587i	$0.509154\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−1.64283e7	−1.48484
$658$	0	0
$659$	1.89918e7	1.70354	0.851770	−	0.523916i	$-0.175529\pi$
$659$	1.89918e7	1.70354	0.851770	+	0.523916i	$0.175529\pi$
$660$	0	0
$661$	1.86619e7	1.66132	0.830659	−	0.556781i	$-0.187964\pi$
$661$	1.86619e7	1.66132	0.830659	+	0.556781i	$0.187964\pi$
$662$	0	0
$663$	−2.98231e6	−0.263493
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−1.28697e7	−1.12009
$668$	0	0
$669$	−2.61973e6	−0.226304
$670$	0	0
$671$	−3.13539e7	−2.68834
$672$	0	0
$673$	−1.77800e7	−1.51319	−0.756597	−	0.653882i	$-0.773139\pi$
$673$	−1.77800e7	−1.51319	−0.756597	+	0.653882i	$0.773139\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	1.74689e7	1.46485	0.732427	−	0.680845i	$-0.238387\pi$
$677$	1.74689e7	1.46485	0.732427	+	0.680845i	$0.238387\pi$
$678$	0	0
$679$	−1.92221e6	−0.160002
$680$	0	0
$681$	−1.72414e6	−0.142464
$682$	0	0
$683$	1.47841e7	1.21267	0.606336	−	0.795208i	$-0.292639\pi$
$683$	1.47841e7	1.21267	0.606336	+	0.795208i	$0.292639\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−8.33435e6	−0.673721
$688$	0	0
$689$	−2.17561e6	−0.174595
$690$	0	0
$691$	1.04037e7	0.828885	0.414443	−	0.910075i	$-0.363977\pi$
$691$	1.04037e7	0.828885	0.414443	+	0.910075i	$0.363977\pi$
$692$	0	0
$693$	−6.34615e6	−0.501969
$694$	0	0
$695$	0	0
$696$	0	0
$697$	2.34343e7	1.82713
$698$	0	0
$699$	−4.44832e6	−0.344353
$700$	0	0
$701$	−1.41605e7	−1.08839	−0.544195	−	0.838959i	$-0.683165\pi$
$701$	−1.41605e7	−1.08839	−0.544195	+	0.838959i	$0.683165\pi$
$702$	0	0
$703$	−1.72184e7	−1.31403
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−5.84258e6	−0.439598
$708$	0	0
$709$	1.14282e7	0.853815	0.426908	−	0.904295i	$-0.359603\pi$
$709$	1.14282e7	0.853815	0.426908	+	0.904295i	$0.359603\pi$
$710$	0	0
$711$	3.18383e6	0.236198
$712$	0	0
$713$	1.06376e7	0.783649
$714$	0	0
$715$	0	0
$716$	0	0
$717$	2.18400e7	1.58656
$718$	0	0
$719$	−8.64651e6	−0.623761	−0.311881	−	0.950121i	$-0.600959\pi$
$719$	−8.64651e6	−0.623761	−0.311881	+	0.950121i	$0.600959\pi$
$720$	0	0
$721$	5.04323e6	0.361302
$722$	0	0
$723$	9.29975e6	0.661646
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−1.86324e6	−0.130747	−0.0653736	−	0.997861i	$-0.520824\pi$
$727$	−1.86324e6	−0.130747	−0.0653736	+	0.997861i	$0.520824\pi$
$728$	0	0
$729$	−7.80396e6	−0.543871
$730$	0	0
$731$	1.56176e7	1.08099
$732$	0	0
$733$	−9.79301e6	−0.673219	−0.336609	−	0.941644i	$-0.609280\pi$
$733$	−9.79301e6	−0.673219	−0.336609	+	0.941644i	$0.609280\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	1.88541e7	1.27861
$738$	0	0
$739$	−36632.6	−0.00246750	−0.00123375	−	0.999999i	$-0.500393\pi$
$739$	−36632.6	−0.00246750	−0.00123375	+	0.999999i	$0.500393\pi$
$740$	0	0
$741$	3.24591e6	0.217166
$742$	0	0
$743$	−3.64775e6	−0.242412	−0.121206	−	0.992627i	$-0.538676\pi$
$743$	−3.64775e6	−0.242412	−0.121206	+	0.992627i	$0.538676\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−2.06424e7	−1.35350
$748$	0	0
$749$	8.39359e6	0.546693
$750$	0	0
$751$	−2.62357e7	−1.69743	−0.848717	−	0.528847i	$-0.822624\pi$
$751$	−2.62357e7	−1.69743	−0.848717	+	0.528847i	$0.822624\pi$
$752$	0	0
$753$	−2.57638e7	−1.65586
$754$	0	0
$755$	0	0
$756$	0	0
$757$	2.76939e7	1.75648	0.878241	−	0.478218i	$-0.158717\pi$
$757$	2.76939e7	1.75648	0.878241	+	0.478218i	$0.158717\pi$
$758$	0	0
$759$	−5.80643e7	−3.65851
$760$	0	0
$761$	−2.55677e7	−1.60040	−0.800202	−	0.599730i	$-0.795275\pi$
$761$	−2.55677e7	−1.60040	−0.800202	+	0.599730i	$0.795275\pi$
$762$	0	0
$763$	−6.64699e6	−0.413346
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−1.58367e6	−0.0972019
$768$	0	0
$769$	2.88320e6	0.175816	0.0879080	−	0.996129i	$-0.471982\pi$
$769$	2.88320e6	0.175816	0.0879080	+	0.996129i	$0.471982\pi$
$770$	0	0
$771$	−9.18320e6	−0.556363
$772$	0	0
$773$	1.45234e6	0.0874219	0.0437109	−	0.999044i	$-0.486082\pi$
$773$	1.45234e6	0.0874219	0.0437109	+	0.999044i	$0.486082\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−8.99252e6	−0.534354
$778$	0	0
$779$	−2.55056e7	−1.50588
$780$	0	0
$781$	1.57893e7	0.926266
$782$	0	0
$783$	3.32936e6	0.194069
$784$	0	0
$785$	0	0
$786$	0	0
$787$	1.08394e7	0.623834	0.311917	−	0.950109i	$-0.399029\pi$
$787$	1.08394e7	0.623834	0.311917	+	0.950109i	$0.399029\pi$
$788$	0	0
$789$	1.06157e7	0.607093
$790$	0	0
$791$	−5.00323e6	−0.284321
$792$	0	0
$793$	3.69493e6	0.208652
$794$	0	0
$795$	0	0
$796$	0	0
$797$	8.99837e6	0.501785	0.250893	−	0.968015i	$-0.419276\pi$
$797$	8.99837e6	0.501785	0.250893	+	0.968015i	$0.419276\pi$
$798$	0	0
$799$	−1.01968e7	−0.565064
$800$	0	0
$801$	1.33213e7	0.733608
$802$	0	0
$803$	5.78177e7	3.16426
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−1.29780e7	−0.701493
$808$	0	0
$809$	−2.79190e7	−1.49978	−0.749892	−	0.661560i	$-0.769895\pi$
$809$	−2.79190e7	−1.49978	−0.749892	+	0.661560i	$0.769895\pi$
$810$	0	0
$811$	1.82994e7	0.976978	0.488489	−	0.872570i	$-0.337548\pi$
$811$	1.82994e7	0.976978	0.488489	+	0.872570i	$0.337548\pi$
$812$	0	0
$813$	−1.47896e7	−0.784749
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−1.69980e7	−0.890930
$818$	0	0
$819$	747869.	0.0389597
$820$	0	0
$821$	2.96361e7	1.53449	0.767243	−	0.641357i	$-0.221628\pi$
$821$	2.96361e7	1.53449	0.767243	+	0.641357i	$0.221628\pi$
$822$	0	0
$823$	−2.18772e7	−1.12588	−0.562940	−	0.826498i	$-0.690330\pi$
$823$	−2.18772e7	−1.12588	−0.562940	+	0.826498i	$0.690330\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−4.39376e6	−0.223395	−0.111697	−	0.993742i	$-0.535629\pi$
$827$	−4.39376e6	−0.223395	−0.111697	+	0.993742i	$0.535629\pi$
$828$	0	0
$829$	−1.89255e6	−0.0956449	−0.0478225	−	0.998856i	$-0.515228\pi$
$829$	−1.89255e6	−0.0956449	−0.0478225	+	0.998856i	$0.515228\pi$
$830$	0	0
$831$	−2.51775e7	−1.26476
$832$	0	0
$833$	−4.31597e6	−0.215509
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−2.75194e6	−0.135777
$838$	0	0
$839$	−8.64925e6	−0.424203	−0.212101	−	0.977248i	$-0.568031\pi$
$839$	−8.64925e6	−0.424203	−0.212101	+	0.977248i	$0.568031\pi$
$840$	0	0
$841$	−1.07743e7	−0.525289
$842$	0	0
$843$	3.43376e7	1.66418
$844$	0	0
$845$	0	0
$846$	0	0
$847$	1.44431e7	0.691753
$848$	0	0
$849$	6.17860e6	0.294185
$850$	0	0
$851$	−3.62979e7	−1.71814
$852$	0	0
$853$	3.92341e7	1.84625	0.923127	−	0.384495i	$-0.125624\pi$
$853$	3.92341e7	1.84625	0.923127	+	0.384495i	$0.125624\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−1.34282e6	−0.0624548	−0.0312274	−	0.999512i	$-0.509942\pi$
$857$	−1.34282e6	−0.0624548	−0.0312274	+	0.999512i	$0.509942\pi$
$858$	0	0
$859$	−2.85020e7	−1.31793	−0.658966	−	0.752173i	$-0.729006\pi$
$859$	−2.85020e7	−1.31793	−0.658966	+	0.752173i	$0.729006\pi$
$860$	0	0
$861$	−1.33206e7	−0.612371
$862$	0	0
$863$	−2.25694e7	−1.03156	−0.515778	−	0.856722i	$-0.672497\pi$
$863$	−2.25694e7	−1.03156	−0.515778	+	0.856722i	$0.672497\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	3.77725e7	1.70658
$868$	0	0
$869$	−1.12051e7	−0.503348
$870$	0	0
$871$	−2.22188e6	−0.0992375
$872$	0	0
$873$	−7.52537e6	−0.334189
$874$	0	0
$875$	0	0
$876$	0	0
$877$	2.01167e7	0.883199	0.441599	−	0.897212i	$-0.354411\pi$
$877$	2.01167e7	0.883199	0.441599	+	0.897212i	$0.354411\pi$
$878$	0	0
$879$	8.11698e6	0.354342
$880$	0	0
$881$	2.49283e7	1.08207	0.541033	−	0.841002i	$-0.318034\pi$
$881$	2.49283e7	1.08207	0.541033	+	0.841002i	$0.318034\pi$
$882$	0	0
$883$	−2.56878e7	−1.10873	−0.554364	−	0.832274i	$-0.687038\pi$
$883$	−2.56878e7	−1.10873	−0.554364	+	0.832274i	$0.687038\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	3.29320e7	1.40543	0.702716	−	0.711471i	$-0.251971\pi$
$887$	3.29320e7	1.40543	0.702716	+	0.711471i	$0.251971\pi$
$888$	0	0
$889$	1.36383e7	0.578769
$890$	0	0
$891$	4.64929e7	1.96197
$892$	0	0
$893$	1.10981e7	0.465715
$894$	0	0
$895$	0	0
$896$	0	0
$897$	6.84265e6	0.283951
$898$	0	0
$899$	−8.04818e6	−0.332123
$900$	0	0
$901$	4.91542e7	2.01720
$902$	0	0
$903$	−8.87741e6	−0.362299
$904$	0	0
$905$	0	0
$906$	0	0
$907$	1.54386e7	0.623144	0.311572	−	0.950223i	$-0.399145\pi$
$907$	1.54386e7	0.623144	0.311572	+	0.950223i	$0.399145\pi$
$908$	0	0
$909$	−2.28734e7	−0.918167
$910$	0	0
$911$	−3.32850e7	−1.32878	−0.664389	−	0.747387i	$-0.731308\pi$
$911$	−3.32850e7	−1.32878	−0.664389	+	0.747387i	$0.731308\pi$
$912$	0	0
$913$	7.26486e7	2.88437
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−1.34960e7	−0.530008
$918$	0	0
$919$	2.02686e6	0.0791653	0.0395827	−	0.999216i	$-0.487397\pi$
$919$	2.02686e6	0.0791653	0.0395827	+	0.999216i	$0.487397\pi$
$920$	0	0
$921$	8.41553e6	0.326913
$922$	0	0
$923$	−1.86071e6	−0.0718909
$924$	0	0
$925$	0	0
$926$	0	0
$927$	1.97440e7	0.754634
$928$	0	0
$929$	−696504.	−0.0264779	−0.0132390	−	0.999912i	$-0.504214\pi$
$929$	−696504.	−0.0264779	−0.0132390	+	0.999912i	$0.504214\pi$
$930$	0	0
$931$	4.69745e6	0.177618
$932$	0	0
$933$	−3.08499e7	−1.16024
$934$	0	0
$935$	0	0
$936$	0	0
$937$	4.24032e6	0.157779	0.0788896	−	0.996883i	$-0.474863\pi$
$937$	4.24032e6	0.157779	0.0788896	+	0.996883i	$0.474863\pi$
$938$	0	0
$939$	−1.27790e7	−0.472970
$940$	0	0
$941$	−9.27150e6	−0.341331	−0.170666	−	0.985329i	$-0.554592\pi$
$941$	−9.27150e6	−0.341331	−0.170666	+	0.985329i	$0.554592\pi$
$942$	0	0
$943$	−5.37679e7	−1.96899
$944$	0	0
$945$	0	0
$946$	0	0
$947$	1.47822e7	0.535629	0.267814	−	0.963471i	$-0.413699\pi$
$947$	1.47822e7	0.535629	0.267814	+	0.963471i	$0.413699\pi$
$948$	0	0
$949$	−6.81359e6	−0.245590
$950$	0	0
$951$	1.47188e7	0.527742
$952$	0	0
$953$	−2.87437e7	−1.02520	−0.512602	−	0.858626i	$-0.671318\pi$
$953$	−2.87437e7	−1.02520	−0.512602	+	0.858626i	$0.671318\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	4.39300e7	1.55054
$958$	0	0
$959$	−3.81904e6	−0.134094
$960$	0	0
$961$	−2.19768e7	−0.767637
$962$	0	0
$963$	3.28606e7	1.14185
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−4.49093e7	−1.54444	−0.772218	−	0.635358i	$-0.780853\pi$
$967$	−4.49093e7	−1.54444	−0.772218	+	0.635358i	$0.780853\pi$
$968$	0	0
$969$	−7.33360e7	−2.50904
$970$	0	0
$971$	−9.27531e6	−0.315704	−0.157852	−	0.987463i	$-0.550457\pi$
$971$	−9.27531e6	−0.315704	−0.157852	+	0.987463i	$0.550457\pi$
$972$	0	0
$973$	2.19086e6	0.0741879
$974$	0	0
$975$	0	0
$976$	0	0
$977$	2.75871e7	0.924632	0.462316	−	0.886715i	$-0.347019\pi$
$977$	2.75871e7	0.924632	0.462316	+	0.886715i	$0.347019\pi$
$978$	0	0
$979$	−4.68827e7	−1.56335
$980$	0	0
$981$	−2.60227e7	−0.863336
$982$	0	0
$983$	1.78897e7	0.590499	0.295249	−	0.955420i	$-0.404597\pi$
$983$	1.78897e7	0.590499	0.295249	+	0.955420i	$0.404597\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	5.79610e6	0.189384
$988$	0	0
$989$	−3.58333e7	−1.16492
$990$	0	0
$991$	−4.35413e7	−1.40837	−0.704186	−	0.710015i	$-0.748688\pi$
$991$	−4.35413e7	−1.40837	−0.704186	+	0.710015i	$0.748688\pi$
$992$	0	0
$993$	−8.04146e7	−2.58798
$994$	0	0
$995$	0	0
$996$	0	0
$997$	4.55376e7	1.45088	0.725442	−	0.688284i	$-0.241636\pi$
$997$	4.55376e7	1.45088	0.725442	+	0.688284i	$0.241636\pi$
$998$	0	0
$999$	9.39020e6	0.297688

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.6.a.n.1.4	yes	4
5.2	odd	4		700.6.e.j.449.1		8
5.3	odd	4		700.6.e.j.449.8		8
5.4	even	2		700.6.a.k.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.6.a.k.1.1	✓	4	5.4	even	2
700.6.a.n.1.4	yes	4	1.1	even	1	trivial
700.6.e.j.449.1		8	5.2	odd	4
700.6.e.j.449.8		8	5.3	odd	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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	700.a (trivial)

\(f(q)\)	\(=\)	\(q+20.8527 q^{3} +49.0000 q^{7} +191.833 q^{9} -675.135 q^{11} +79.5620 q^{13} -1797.57 q^{17} +1956.46 q^{19} +1021.78 q^{21} +4124.37 q^{23} -1066.97 q^{27} -3120.39 q^{29} +2579.22 q^{31} -14078.4 q^{33} -8800.84 q^{37} +1659.08 q^{39} -13036.6 q^{41} -8688.18 q^{43} +5672.55 q^{47} +2401.00 q^{49} -37484.1 q^{51} -27344.8 q^{53} +40797.3 q^{57} -19904.8 q^{59} +46440.9 q^{61} +9399.82 q^{63} -27926.4 q^{67} +86004.0 q^{69} -23386.9 q^{71} -85638.7 q^{73} -33081.6 q^{77} +16596.9 q^{79} -68864.5 q^{81} -107606. q^{83} -65068.5 q^{87} +69441.9 q^{89} +3898.54 q^{91} +53783.5 q^{93} -39228.8 q^{97} -129513. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 22 q^{3} + 196 q^{7} - 62 q^{9} + 48 q^{11} - 430 q^{13} - 1286 q^{17} - 384 q^{19} + 1078 q^{21} + 1256 q^{23} - 1196 q^{27} - 4994 q^{29} + 4618 q^{31} - 15268 q^{33} - 16922 q^{37} + 3200 q^{39}+ \cdots - 170416 q^{99}+O(q^{100}) \) 4 * q + 22 * q^3 + 196 * q^7 - 62 * q^9 + 48 * q^11 - 430 * q^13 - 1286 * q^17 - 384 * q^19 + 1078 * q^21 + 1256 * q^23 - 1196 * q^27 - 4994 * q^29 + 4618 * q^31 - 15268 * q^33 - 16922 * q^37 + 3200 * q^39 - 9192 * q^41 - 12368 * q^43 + 4476 * q^47 + 9604 * q^49 - 30396 * q^51 - 16736 * q^53 + 29946 * q^57 - 14614 * q^59 - 7122 * q^61 - 3038 * q^63 + 21408 * q^67 + 11822 * q^69 - 39748 * q^71 - 89364 * q^73 + 2352 * q^77 - 37640 * q^79 - 125192 * q^81 - 83842 * q^83 + 90982 * q^87 - 12444 * q^89 - 21070 * q^91 - 137840 * q^93 + 57034 * q^97 - 170416 * q^99

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