LMFDB - Embedded newform 1900.3.g.d.949.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,3,Mod(949,1900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1900, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1900.949");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1900.g (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$51.7712502285$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			949.10
Character	$\chi$	$=$	1900.949
Dual form			1900.3.g.d.949.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.16913 q^{3} -8.18099i q^{7} -4.29489 q^{9} +O(q^{10})$	$q-2.16913 q^{3} -8.18099i q^{7} -4.29489 q^{9} +3.30255 q^{11} +8.86162 q^{13} -10.2495i q^{17} +(-18.5676 + 4.03031i) q^{19} +17.7456i q^{21} +0.896508i q^{23} +28.8383 q^{27} -17.9058i q^{29} -40.8943i q^{31} -7.16364 q^{33} -7.68123 q^{37} -19.2220 q^{39} -69.9101i q^{41} +25.9969i q^{43} +12.4912i q^{47} -17.9286 q^{49} +22.2324i q^{51} +55.9407 q^{53} +(40.2755 - 8.74226i) q^{57} +105.529i q^{59} -48.2803 q^{61} +35.1365i q^{63} -14.6303 q^{67} -1.94464i q^{69} -2.89388i q^{71} +75.9531i q^{73} -27.0181i q^{77} -86.1594i q^{79} -23.8998 q^{81} +52.0562i q^{83} +38.8400i q^{87} -39.5469i q^{89} -72.4968i q^{91} +88.7050i q^{93} +172.660 q^{97} -14.1841 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 104 q^{9}+O(q^{10}) $ 28 * q + 104 * q^9	$ 28 q + 104 q^{9} + 8 q^{11} + 58 q^{19} + 112 q^{39} - 276 q^{49} - 100 q^{61} + 132 q^{81} - 184 q^{99}+O(q^{100}) $ 28 * q + 104 * q^9 + 8 * q^11 + 58 * q^19 + 112 * q^39 - 276 * q^49 - 100 * q^61 + 132 * q^81 - 184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

$n$	$77$	$401$	$951$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.16913			−0.723042			−0.361521	−	0.932364i	$-0.617742\pi$
$3$	−2.16913			−0.723042			−0.361521	+	0.932364i	$0.617742\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	8.18099i		−	1.16871i	−0.811497	−	0.584356i	$-0.801347\pi$
$7$		−	8.18099i		−	1.16871i	0.811497	−	0.584356i	$-0.198653\pi$
$8$		0			0
$9$	−4.29489			−0.477211
$10$		0			0
$11$	3.30255			0.300232			0.150116	−	0.988668i	$-0.452035\pi$
$11$	3.30255			0.300232			0.150116	+	0.988668i	$0.452035\pi$
$12$		0			0
$13$	8.86162			0.681663			0.340832	−	0.940124i	$-0.389291\pi$
$13$	8.86162			0.681663			0.340832	+	0.940124i	$0.389291\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	10.2495i		−	0.602910i	−0.953480	−	0.301455i	$-0.902528\pi$
$17$		−	10.2495i		−	0.602910i	0.953480	−	0.301455i	$-0.0974724\pi$
$18$		0			0
$19$	−18.5676	+	4.03031i	−0.977243	+	0.212122i
$19$	−18.5676	+	4.03031i	−0.977243	+	0.212122i
$20$		0			0
$21$			17.7456i			0.845028i
$22$		0			0
$23$			0.896508i			0.0389786i	0.999810	+	0.0194893i	$0.00620403\pi$
$23$			0.896508i			0.0389786i	−0.999810	+	0.0194893i	$0.993796\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	28.8383			1.06808
$28$		0			0
$29$		−	17.9058i		−	0.617442i	−0.951153	−	0.308721i	$-0.900099\pi$
$29$		−	17.9058i		−	0.617442i	0.951153	−	0.308721i	$-0.0999010\pi$
$30$		0			0
$31$		−	40.8943i		−	1.31917i	−0.751629	−	0.659586i	$-0.770732\pi$
$31$		−	40.8943i		−	1.31917i	0.751629	−	0.659586i	$-0.229268\pi$
$32$		0			0
$33$	−7.16364			−0.217080
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−7.68123			−0.207601			−0.103800	−	0.994598i	$-0.533100\pi$
$37$	−7.68123			−0.207601			−0.103800	+	0.994598i	$0.533100\pi$
$38$		0			0
$39$	−19.2220			−0.492871
$40$		0			0
$41$		−	69.9101i		−	1.70512i	−0.522626	−	0.852562i	$-0.675048\pi$
$41$		−	69.9101i		−	1.70512i	0.522626	−	0.852562i	$-0.324952\pi$
$42$		0			0
$43$			25.9969i			0.604579i	0.953216	+	0.302290i	$0.0977510\pi$
$43$			25.9969i			0.604579i	−0.953216	+	0.302290i	$0.902249\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			12.4912i			0.265770i	0.991131	+	0.132885i	$0.0424241\pi$
$47$			12.4912i			0.265770i	−0.991131	+	0.132885i	$0.957576\pi$
$48$		0			0
$49$	−17.9286			−0.365889
$50$		0			0
$51$			22.2324i			0.435929i
$52$		0			0
$53$	55.9407			1.05549			0.527743	−	0.849404i	$-0.323038\pi$
$53$	55.9407			1.05549			0.527743	+	0.849404i	$0.323038\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	40.2755	−	8.74226i	0.706588	−	0.153373i
$58$		0			0
$59$			105.529i			1.78862i	0.447444	+	0.894312i	$0.352334\pi$
$59$			105.529i			1.78862i	−0.447444	+	0.894312i	$0.647666\pi$
$60$		0			0
$61$	−48.2803			−0.791480			−0.395740	−	0.918363i	$-0.629512\pi$
$61$	−48.2803			−0.791480			−0.395740	+	0.918363i	$0.629512\pi$
$62$		0			0
$63$			35.1365i			0.557722i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−14.6303			−0.218363			−0.109181	−	0.994022i	$-0.534823\pi$
$67$	−14.6303			−0.218363			−0.109181	+	0.994022i	$0.534823\pi$
$68$		0			0
$69$		−	1.94464i		−	0.0281832i
$70$		0			0
$71$		−	2.89388i		−	0.0407588i	−0.999792	−	0.0203794i	$-0.993513\pi$
$71$		−	2.89388i		−	0.0407588i	0.999792	−	0.0203794i	$-0.00648742\pi$
$72$		0			0
$73$			75.9531i			1.04045i	0.854028	+	0.520227i	$0.174153\pi$
$73$			75.9531i			1.04045i	−0.854028	+	0.520227i	$0.825847\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	27.0181i		−	0.350885i
$78$		0			0
$79$		−	86.1594i		−	1.09063i	−0.838233	−	0.545313i	$-0.816411\pi$
$79$		−	86.1594i		−	1.09063i	0.838233	−	0.545313i	$-0.183589\pi$
$80$		0			0
$81$	−23.8998			−0.295060
$82$		0			0
$83$			52.0562i			0.627183i	0.949558	+	0.313591i	$0.101532\pi$
$83$			52.0562i			0.627183i	−0.949558	+	0.313591i	$0.898468\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			38.8400i			0.446437i
$88$		0			0
$89$		−	39.5469i		−	0.444347i	−0.975007	−	0.222174i	$-0.928685\pi$
$89$		−	39.5469i		−	0.444347i	0.975007	−	0.222174i	$-0.0713151\pi$
$90$		0			0
$91$		−	72.4968i		−	0.796668i
$92$		0			0
$93$			88.7050i			0.953817i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	172.660			1.78000			0.889999	−	0.455962i	$-0.150705\pi$
$97$	172.660			1.78000			0.889999	+	0.455962i	$0.150705\pi$
$98$		0			0
$99$	−14.1841			−0.143274
$100$		0			0
$101$	−143.421			−1.42001			−0.710007	−	0.704194i	$-0.751308\pi$
$101$	−143.421			−1.42001			−0.710007	+	0.704194i	$0.751308\pi$
$102$		0			0
$103$	−101.659			−0.986979			−0.493490	−	0.869752i	$-0.664279\pi$
$103$	−101.659			−0.986979			−0.493490	+	0.869752i	$0.664279\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−155.201			−1.45048			−0.725239	−	0.688497i	$-0.758271\pi$
$107$	−155.201			−1.45048			−0.725239	+	0.688497i	$0.758271\pi$
$108$		0			0
$109$			52.7937i			0.484345i	0.970233	+	0.242173i	$0.0778601\pi$
$109$			52.7937i			0.484345i	−0.970233	+	0.242173i	$0.922140\pi$
$110$		0			0
$111$	16.6616			0.150104
$112$		0			0
$113$	−90.0032			−0.796488			−0.398244	−	0.917279i	$-0.630380\pi$
$113$	−90.0032			−0.796488			−0.398244	+	0.917279i	$0.630380\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−38.0597			−0.325297
$118$		0			0
$119$	−83.8508			−0.704629
$120$		0			0
$121$	−110.093			−0.909861
$122$		0			0
$123$			151.644i			1.23288i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−74.1001			−0.583466			−0.291733	−	0.956500i	$-0.594232\pi$
$127$	−74.1001			−0.583466			−0.291733	+	0.956500i	$0.594232\pi$
$128$		0			0
$129$		−	56.3906i		−	0.437136i
$130$		0			0
$131$	−59.3187			−0.452814			−0.226407	−	0.974033i	$-0.572698\pi$
$131$	−59.3187			−0.452814			−0.226407	+	0.974033i	$0.572698\pi$
$132$		0			0
$133$	32.9720	+	151.902i	0.247909	+	1.14212i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	153.881i		−	1.12322i	−0.827402	−	0.561610i	$-0.810182\pi$
$137$		−	153.881i		−	1.12322i	0.827402	−	0.561610i	$-0.189818\pi$
$138$		0			0
$139$	−42.6118			−0.306560			−0.153280	−	0.988183i	$-0.548984\pi$
$139$	−42.6118			−0.306560			−0.153280	+	0.988183i	$0.548984\pi$
$140$		0			0
$141$		−	27.0950i		−	0.192163i
$142$		0			0
$143$	29.2659			0.204657
$144$		0			0
$145$		0			0
$146$		0			0
$147$	38.8893			0.264553
$148$		0			0
$149$	−43.1276			−0.289447			−0.144723	−	0.989472i	$-0.546229\pi$
$149$	−43.1276			−0.289447			−0.144723	+	0.989472i	$0.546229\pi$
$150$		0			0
$151$			88.7161i			0.587524i	0.955879	+	0.293762i	$0.0949073\pi$
$151$			88.7161i			0.587524i	−0.955879	+	0.293762i	$0.905093\pi$
$152$		0			0
$153$			44.0204i			0.287715i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	86.8111i		−	0.552937i	−0.961023	−	0.276469i	$-0.910836\pi$
$157$		−	86.8111i		−	0.552937i	0.961023	−	0.276469i	$-0.0891642\pi$
$158$		0			0
$159$	−121.342			−0.763160
$160$		0			0
$161$	7.33432			0.0455548
$162$		0			0
$163$			116.020i			0.711781i	0.934528	+	0.355890i	$0.115822\pi$
$163$			116.020i			0.711781i	−0.934528	+	0.355890i	$0.884178\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	184.203			1.10301			0.551505	−	0.834172i	$-0.314054\pi$
$167$	184.203			1.10301			0.551505	+	0.834172i	$0.314054\pi$
$168$		0			0
$169$	−90.4717			−0.535335
$170$		0			0
$171$	79.7460	−	17.3098i	0.466351	−	0.101227i
$172$		0			0
$173$	−180.352			−1.04250			−0.521249	−	0.853404i	$-0.674534\pi$
$173$	−180.352			−1.04250			−0.521249	+	0.853404i	$0.674534\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	228.905i		−	1.29325i
$178$		0			0
$179$			62.4477i			0.348870i	0.984669	+	0.174435i	$0.0558099\pi$
$179$			62.4477i			0.348870i	−0.984669	+	0.174435i	$0.944190\pi$
$180$		0			0
$181$			229.533i			1.26814i	0.773277	+	0.634069i	$0.218616\pi$
$181$			229.533i			1.26814i	−0.773277	+	0.634069i	$0.781384\pi$
$182$		0			0
$183$	104.726			0.572273
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	33.8494i		−	0.181013i
$188$		0			0
$189$		−	235.926i		−	1.24828i
$190$		0			0
$191$	−250.559			−1.31182			−0.655912	−	0.754837i	$-0.727716\pi$
$191$	−250.559			−1.31182			−0.655912	+	0.754837i	$0.727716\pi$
$192$		0			0
$193$	144.603			0.749239			0.374619	−	0.927179i	$-0.377773\pi$
$193$	144.603			0.749239			0.374619	+	0.927179i	$0.377773\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	172.063i		−	0.873414i	−0.899604	−	0.436707i	$-0.856145\pi$
$197$		−	172.063i		−	0.873414i	0.899604	−	0.436707i	$-0.143855\pi$
$198$		0			0
$199$	−334.796			−1.68239			−0.841196	−	0.540731i	$-0.818148\pi$
$199$	−334.796			−1.68239			−0.841196	+	0.540731i	$0.818148\pi$
$200$		0			0
$201$	31.7350			0.157885
$202$		0			0
$203$	−146.487			−0.721613
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	3.85041i		−	0.0186010i
$208$		0			0
$209$	−61.3205	+	13.3103i	−0.293399	+	0.0636857i
$210$		0			0
$211$		−	47.6699i		−	0.225924i	−0.993599	−	0.112962i	$-0.963966\pi$
$211$		−	47.6699i		−	0.225924i	0.993599	−	0.112962i	$-0.0360338\pi$
$212$		0			0
$213$			6.27718i			0.0294703i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−334.556			−1.54173
$218$		0			0
$219$		−	164.752i		−	0.752292i
$220$		0			0
$221$		−	90.8270i		−	0.410982i
$222$		0			0
$223$	−289.875			−1.29989			−0.649945	−	0.759981i	$-0.725208\pi$
$223$	−289.875			−1.29989			−0.649945	+	0.759981i	$0.725208\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	39.5372			0.174172			0.0870862	−	0.996201i	$-0.472244\pi$
$227$	39.5372			0.174172			0.0870862	+	0.996201i	$0.472244\pi$
$228$		0			0
$229$	−2.51216			−0.0109701			−0.00548507	−	0.999985i	$-0.501746\pi$
$229$	−2.51216			−0.0109701			−0.00548507	+	0.999985i	$0.501746\pi$
$230$		0			0
$231$			58.6057i			0.253704i
$232$		0			0
$233$			161.184i			0.691775i	0.938276	+	0.345887i	$0.112422\pi$
$233$			161.184i			0.691775i	−0.938276	+	0.345887i	$0.887578\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			186.891i			0.788568i
$238$		0			0
$239$	−140.111			−0.586240			−0.293120	−	0.956076i	$-0.594694\pi$
$239$	−140.111			−0.586240			−0.293120	+	0.956076i	$0.594694\pi$
$240$		0			0
$241$		−	12.3672i		−	0.0513163i	−0.999671	−	0.0256582i	$-0.991832\pi$
$241$		−	12.3672i		−	0.0513163i	0.999671	−	0.0256582i	$-0.00816814\pi$
$242$		0			0
$243$	−207.703			−0.854745
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−164.539	+	35.7151i	−0.666151	+	0.144596i
$248$		0			0
$249$		−	112.916i		−	0.453479i
$250$		0			0
$251$	−463.827			−1.84792			−0.923958	−	0.382494i	$-0.875065\pi$
$251$	−463.827			−1.84792			−0.923958	+	0.382494i	$0.875065\pi$
$252$		0			0
$253$			2.96076i			0.0117026i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	244.454			0.951185			0.475592	−	0.879666i	$-0.342234\pi$
$257$	244.454			0.951185			0.475592	+	0.879666i	$0.342234\pi$
$258$		0			0
$259$			62.8401i			0.242626i
$260$		0			0
$261$			76.9037i			0.294650i
$262$		0			0
$263$		−	67.3381i		−	0.256038i	−0.991772	−	0.128019i	$-0.959138\pi$
$263$		−	67.3381i		−	0.256038i	0.991772	−	0.128019i	$-0.0408619\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			85.7822i			0.321281i
$268$		0			0
$269$		−	11.2184i		−	0.0417040i	−0.999783	−	0.0208520i	$-0.993362\pi$
$269$		−	11.2184i		−	0.0417040i	0.999783	−	0.0208520i	$-0.00663788\pi$
$270$		0			0
$271$	96.9961			0.357919			0.178960	−	0.983856i	$-0.442727\pi$
$271$	96.9961			0.357919			0.178960	+	0.983856i	$0.442727\pi$
$272$		0			0
$273$			157.255i			0.576025i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			34.6288i			0.125014i	0.998045	+	0.0625069i	$0.0199096\pi$
$277$			34.6288i			0.125014i	−0.998045	+	0.0625069i	$0.980090\pi$
$278$		0			0
$279$			175.637i			0.629523i
$280$		0			0
$281$			334.616i			1.19080i	0.803428	+	0.595402i	$0.203007\pi$
$281$			334.616i			1.19080i	−0.803428	+	0.595402i	$0.796993\pi$
$282$		0			0
$283$			219.370i			0.775158i	0.921836	+	0.387579i	$0.126689\pi$
$283$			219.370i			0.775158i	−0.921836	+	0.387579i	$0.873311\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−571.934			−1.99280
$288$		0			0
$289$	183.948			0.636499
$290$		0			0
$291$	−374.521			−1.28701
$292$		0			0
$293$	7.91053			0.0269984			0.0134992	−	0.999909i	$-0.495703\pi$
$293$	7.91053			0.0269984			0.0134992	+	0.999909i	$0.495703\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	95.2399			0.320673
$298$		0			0
$299$			7.94451i			0.0265703i
$300$		0			0
$301$	212.680			0.706580
$302$		0			0
$303$	311.099			1.02673
$304$		0			0
$305$		0			0
$306$		0			0
$307$	245.743			0.800466			0.400233	−	0.916413i	$-0.368929\pi$
$307$	245.743			0.800466			0.400233	+	0.916413i	$0.368929\pi$
$308$		0			0
$309$	220.511			0.713627
$310$		0			0
$311$	−512.022			−1.64637			−0.823187	−	0.567771i	$-0.807806\pi$
$311$	−512.022			−1.64637			−0.823187	+	0.567771i	$0.807806\pi$
$312$		0			0
$313$			502.653i			1.60592i	0.596033	+	0.802960i	$0.296743\pi$
$313$			502.653i			1.60592i	−0.596033	+	0.802960i	$0.703257\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	173.029			0.545834			0.272917	−	0.962038i	$-0.412012\pi$
$317$	173.029			0.545834			0.272917	+	0.962038i	$0.412012\pi$
$318$		0			0
$319$		−	59.1349i		−	0.185376i
$320$		0			0
$321$	336.651			1.04876
$322$		0			0
$323$	41.3086	+	190.308i	0.127890	+	0.589190i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	114.516i		−	0.350202i
$328$		0			0
$329$	102.190			0.310609
$330$		0			0
$331$		−	287.986i		−	0.870049i	−0.900419	−	0.435025i	$-0.856740\pi$
$331$		−	287.986i		−	0.870049i	0.900419	−	0.435025i	$-0.143260\pi$
$332$		0			0
$333$	32.9901			0.0990694
$334$		0			0
$335$		0			0
$336$		0			0
$337$	135.116			0.400939			0.200469	−	0.979700i	$-0.435753\pi$
$337$	135.116			0.400939			0.200469	+	0.979700i	$0.435753\pi$
$338$		0			0
$339$	195.228			0.575894
$340$		0			0
$341$		−	135.056i		−	0.396057i
$342$		0			0
$343$		−	254.195i		−	0.741093i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			302.548i			0.871896i	0.899972	+	0.435948i	$0.143587\pi$
$347$			302.548i			0.871896i	−0.899972	+	0.435948i	$0.856413\pi$
$348$		0			0
$349$	241.844			0.692964			0.346482	−	0.938057i	$-0.387376\pi$
$349$	241.844			0.692964			0.346482	+	0.938057i	$0.387376\pi$
$350$		0			0
$351$	255.554			0.728074
$352$		0			0
$353$		−	182.840i		−	0.517960i	−0.965883	−	0.258980i	$-0.916614\pi$
$353$		−	182.840i		−	0.517960i	0.965883	−	0.258980i	$-0.0833864\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	181.883			0.509476
$358$		0			0
$359$	−187.980			−0.523622			−0.261811	−	0.965119i	$-0.584320\pi$
$359$	−187.980			−0.523622			−0.261811	+	0.965119i	$0.584320\pi$
$360$		0			0
$361$	328.513	−	149.667i	0.910009	−	0.414589i
$362$		0			0
$363$	238.806			0.657867
$364$		0			0
$365$		0			0
$366$		0			0
$367$		−	168.184i		−	0.458268i	−0.973395	−	0.229134i	$-0.926411\pi$
$367$		−	168.184i		−	0.458268i	0.973395	−	0.229134i	$-0.0735894\pi$
$368$		0			0
$369$			300.256i			0.813703i
$370$		0			0
$371$		−	457.651i		−	1.23356i
$372$		0			0
$373$	−677.168			−1.81546			−0.907732	−	0.419550i	$-0.862188\pi$
$373$	−677.168			−1.81546			−0.907732	+	0.419550i	$0.862188\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	158.675i		−	0.420888i
$378$		0			0
$379$			410.871i			1.08409i	0.840349	+	0.542046i	$0.182350\pi$
$379$			410.871i			1.08409i	−0.840349	+	0.542046i	$0.817650\pi$
$380$		0			0
$381$	160.732			0.421870
$382$		0			0
$383$	−253.500			−0.661880			−0.330940	−	0.943652i	$-0.607366\pi$
$383$	−253.500			−0.661880			−0.330940	+	0.943652i	$0.607366\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	111.654i		−	0.288512i
$388$		0			0
$389$	−105.069			−0.270101			−0.135051	−	0.990839i	$-0.543120\pi$
$389$	−105.069			−0.270101			−0.135051	+	0.990839i	$0.543120\pi$
$390$		0			0
$391$	9.18873			0.0235006
$392$		0			0
$393$	128.670			0.327404
$394$		0			0
$395$		0			0
$396$		0			0
$397$			38.8390i			0.0978313i	0.998803	+	0.0489156i	$0.0155765\pi$
$397$			38.8390i			0.0978313i	−0.998803	+	0.0489156i	$0.984423\pi$
$398$		0			0
$399$	−71.5203	−	329.493i	−0.179249	−	0.825798i
$400$		0			0
$401$		−	386.689i		−	0.964311i	−0.876086	−	0.482155i	$-0.839854\pi$
$401$		−	386.689i		−	0.964311i	0.876086	−	0.482155i	$-0.160146\pi$
$402$		0			0
$403$		−	362.390i		−	0.899231i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−25.3677			−0.0623284
$408$		0			0
$409$		−	299.046i		−	0.731165i	−0.930779	−	0.365582i	$-0.880870\pi$
$409$		−	299.046i		−	0.731165i	0.930779	−	0.365582i	$-0.119130\pi$
$410$		0			0
$411$			333.787i			0.812134i
$412$		0			0
$413$	863.330			2.09039
$414$		0			0
$415$		0			0
$416$		0			0
$417$	92.4304			0.221656
$418$		0			0
$419$	228.600			0.545585			0.272793	−	0.962073i	$-0.412053\pi$
$419$	228.600			0.545585			0.272793	+	0.962073i	$0.412053\pi$
$420$		0			0
$421$			373.332i			0.886775i	0.896330	+	0.443387i	$0.146223\pi$
$421$			373.332i			0.886775i	−0.896330	+	0.443387i	$0.853777\pi$
$422$		0			0
$423$		−	53.6484i		−	0.126828i
$424$		0			0
$425$		0			0
$426$		0			0
$427$			394.980i			0.925012i
$428$		0			0
$429$	−63.4815			−0.147976
$430$		0			0
$431$		−	216.245i		−	0.501729i	−0.968022	−	0.250865i	$-0.919285\pi$
$431$		−	216.245i		−	0.501729i	0.968022	−	0.250865i	$-0.0807149\pi$
$432$		0			0
$433$	652.519			1.50697			0.753486	−	0.657464i	$-0.228371\pi$
$433$	652.519			1.50697			0.753486	+	0.657464i	$0.228371\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.61321	−	16.6460i	−0.00826821	−	0.0380916i
$438$		0			0
$439$			607.514i			1.38386i	0.721965	+	0.691929i	$0.243239\pi$
$439$			607.514i			1.38386i	−0.721965	+	0.691929i	$0.756761\pi$
$440$		0			0
$441$	77.0014			0.174606
$442$		0			0
$443$		−	513.684i		−	1.15956i	−0.814774	−	0.579779i	$-0.803139\pi$
$443$		−	513.684i		−	1.15956i	0.814774	−	0.579779i	$-0.196861\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	93.5491			0.209282
$448$		0			0
$449$			223.870i			0.498596i	0.968427	+	0.249298i	$0.0801998\pi$
$449$			223.870i			0.498596i	−0.968427	+	0.249298i	$0.919800\pi$
$450$		0			0
$451$		−	230.881i		−	0.511932i
$452$		0			0
$453$		−	192.436i		−	0.424804i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	438.522i		−	0.959567i	−0.877387	−	0.479784i	$-0.840715\pi$
$457$		−	438.522i		−	0.959567i	0.877387	−	0.479784i	$-0.159285\pi$
$458$		0			0
$459$		−	295.577i		−	0.643959i
$460$		0			0
$461$	703.015			1.52498			0.762489	−	0.647001i	$-0.223977\pi$
$461$	703.015			1.52498			0.762489	+	0.647001i	$0.223977\pi$
$462$		0			0
$463$		−	642.827i		−	1.38839i	−0.719785	−	0.694197i	$-0.755760\pi$
$463$		−	642.827i		−	1.38839i	0.719785	−	0.694197i	$-0.244240\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			927.468i			1.98601i	0.118061	+	0.993006i	$0.462332\pi$
$467$			927.468i			1.98601i	−0.118061	+	0.993006i	$0.537668\pi$
$468$		0			0
$469$			119.690i			0.255203i
$470$		0			0
$471$			188.304i			0.399797i
$472$		0			0
$473$			85.8561i			0.181514i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−240.260			−0.503689
$478$		0			0
$479$	−257.644			−0.537880			−0.268940	−	0.963157i	$-0.586673\pi$
$479$	−257.644			−0.537880			−0.268940	+	0.963157i	$0.586673\pi$
$480$		0			0
$481$	−68.0682			−0.141514
$482$		0			0
$483$	−15.9091			−0.0329380
$484$		0			0
$485$		0			0
$486$		0			0
$487$	609.090			1.25070			0.625349	−	0.780345i	$-0.284957\pi$
$487$	609.090			1.25070			0.625349	+	0.780345i	$0.284957\pi$
$488$		0			0
$489$		−	251.663i		−	0.514647i
$490$		0			0
$491$	138.936			0.282966			0.141483	−	0.989941i	$-0.454813\pi$
$491$	138.936			0.282966			0.141483	+	0.989941i	$0.454813\pi$
$492$		0			0
$493$	−183.525			−0.372262
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−23.6748			−0.0476354
$498$		0			0
$499$	−228.666			−0.458248			−0.229124	−	0.973397i	$-0.573586\pi$
$499$	−228.666			−0.458248			−0.229124	+	0.973397i	$0.573586\pi$
$500$		0			0
$501$	−399.558			−0.797522
$502$		0			0
$503$		−	465.208i		−	0.924868i	−0.886654	−	0.462434i	$-0.846976\pi$
$503$		−	465.208i		−	0.924868i	0.886654	−	0.462434i	$-0.153024\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	196.244			0.387070
$508$		0			0
$509$		−	395.633i		−	0.777276i	−0.921391	−	0.388638i	$-0.872946\pi$
$509$		−	395.633i		−	0.777276i	0.921391	−	0.388638i	$-0.127054\pi$
$510$		0			0
$511$	621.372			1.21599
$512$		0			0
$513$	−535.459	+	116.227i	−1.04378	+	0.226564i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			41.2528i			0.0797926i
$518$		0			0
$519$	391.207			0.753770
$520$		0			0
$521$			204.842i			0.393172i	0.980487	+	0.196586i	$0.0629854\pi$
$521$			204.842i			0.393172i	−0.980487	+	0.196586i	$0.937015\pi$
$522$		0			0
$523$	755.700			1.44493			0.722466	−	0.691406i	$-0.243008\pi$
$523$	755.700			1.44493			0.722466	+	0.691406i	$0.243008\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−419.146			−0.795343
$528$		0			0
$529$	528.196			0.998481
$530$		0			0
$531$		−	453.235i		−	0.853550i
$532$		0			0
$533$		−	619.517i		−	1.16232i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		−	135.457i		−	0.252248i
$538$		0			0
$539$	−59.2100			−0.109852
$540$		0			0
$541$	458.741			0.847951			0.423975	−	0.905674i	$-0.360634\pi$
$541$	458.741			0.847951			0.423975	+	0.905674i	$0.360634\pi$
$542$		0			0
$543$		−	497.886i		−	0.916916i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−731.948			−1.33811			−0.669057	−	0.743211i	$-0.733302\pi$
$547$	−731.948			−1.33811			−0.669057	+	0.743211i	$0.733302\pi$
$548$		0			0
$549$	207.359			0.377702
$550$		0			0
$551$	72.1661	+	332.469i	0.130973	+	0.603391i
$552$		0			0
$553$	−704.869			−1.27463
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	534.752i		−	0.960057i	−0.877253	−	0.480028i	$-0.840626\pi$
$557$		−	534.752i		−	0.960057i	0.877253	−	0.480028i	$-0.159374\pi$
$558$		0			0
$559$			230.375i			0.412120i
$560$		0			0
$561$			73.4236i			0.130880i
$562$		0			0
$563$	408.400			0.725401			0.362700	−	0.931906i	$-0.381855\pi$
$563$	408.400			0.725401			0.362700	+	0.931906i	$0.381855\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			195.524i			0.344840i
$568$		0			0
$569$			465.410i			0.817944i	0.912547	+	0.408972i	$0.134113\pi$
$569$			465.410i			0.817944i	−0.912547	+	0.408972i	$0.865887\pi$
$570$		0			0
$571$	−60.8428			−0.106555			−0.0532774	−	0.998580i	$-0.516967\pi$
$571$	−60.8428			−0.106555			−0.0532774	+	0.998580i	$0.516967\pi$
$572$		0			0
$573$	543.493			0.948504
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	657.921i		−	1.14024i	−0.821560	−	0.570122i	$-0.806896\pi$
$577$		−	657.921i		−	1.14024i	0.821560	−	0.570122i	$-0.193104\pi$
$578$		0			0
$579$	−313.662			−0.541731
$580$		0			0
$581$	425.871			0.732996
$582$		0			0
$583$	184.747			0.316890
$584$		0			0
$585$		0			0
$586$		0			0
$587$			1050.70i			1.78996i	0.446110	+	0.894978i	$0.352809\pi$
$587$			1050.70i			1.78996i	−0.446110	+	0.894978i	$0.647191\pi$
$588$		0			0
$589$	164.817	+	759.311i	0.279825	+	1.28915i
$590$		0			0
$591$			373.225i			0.631515i
$592$		0			0
$593$		−	520.953i		−	0.878505i	−0.898364	−	0.439252i	$-0.855243\pi$
$593$		−	520.953i		−	0.878505i	0.898364	−	0.439252i	$-0.144757\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	726.214			1.21644
$598$		0			0
$599$		−	518.236i		−	0.865169i	−0.901593	−	0.432584i	$-0.857602\pi$
$599$		−	518.236i		−	0.865169i	0.901593	−	0.432584i	$-0.142398\pi$
$600$		0			0
$601$		−	312.656i		−	0.520226i	−0.965578	−	0.260113i	$-0.916240\pi$
$601$		−	312.656i		−	0.520226i	0.965578	−	0.260113i	$-0.0837598\pi$
$602$		0			0
$603$	62.8356			0.104205
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−40.6637			−0.0669913			−0.0334956	−	0.999439i	$-0.510664\pi$
$607$	−40.6637			−0.0669913			−0.0334956	+	0.999439i	$0.510664\pi$
$608$		0			0
$609$	317.750			0.521756
$610$		0			0
$611$			110.692i			0.181166i
$612$		0			0
$613$		−	23.2110i		−	0.0378646i	−0.999821	−	0.0189323i	$-0.993973\pi$
$613$		−	23.2110i		−	0.0378646i	0.999821	−	0.0189323i	$-0.00602671\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			782.983i			1.26902i	0.772916	+	0.634508i	$0.218797\pi$
$617$			782.983i			1.26902i	−0.772916	+	0.634508i	$0.781203\pi$
$618$		0			0
$619$	669.801			1.08207			0.541034	−	0.841000i	$-0.318033\pi$
$619$	669.801			1.08207			0.541034	+	0.841000i	$0.318033\pi$
$620$		0			0
$621$			25.8538i			0.0416325i
$622$		0			0
$623$	−323.533			−0.519314
$624$		0			0
$625$		0			0
$626$		0			0
$627$	133.012	−	28.8717i	0.212140	−	0.0460474i
$628$		0			0
$629$			78.7286i			0.125165i
$630$		0			0
$631$	−190.219			−0.301457			−0.150728	−	0.988575i	$-0.548162\pi$
$631$	−190.219			−0.301457			−0.150728	+	0.988575i	$0.548162\pi$
$632$		0			0
$633$			103.402i			0.163352i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−158.876			−0.249413
$638$		0			0
$639$			12.4289i			0.0194505i
$640$		0			0
$641$			519.869i			0.811029i	0.914089	+	0.405514i	$0.132908\pi$
$641$			519.869i			0.811029i	−0.914089	+	0.405514i	$0.867092\pi$
$642$		0			0
$643$		−	594.211i		−	0.924123i	−0.886848	−	0.462062i	$-0.847110\pi$
$643$		−	594.211i		−	0.924123i	0.886848	−	0.462062i	$-0.152890\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			830.788i			1.28406i	0.766679	+	0.642031i	$0.221908\pi$
$647$			830.788i			1.28406i	−0.766679	+	0.642031i	$0.778092\pi$
$648$		0			0
$649$			348.514i			0.537002i
$650$		0			0
$651$	725.694			1.11474
$652$		0			0
$653$		−	726.157i		−	1.11203i	−0.831172	−	0.556016i	$-0.812329\pi$
$653$		−	726.157i		−	1.11203i	0.831172	−	0.556016i	$-0.187671\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	326.211i		−	0.496516i
$658$		0			0
$659$		−	30.7289i		−	0.0466295i	−0.999728	−	0.0233148i	$-0.992578\pi$
$659$		−	30.7289i		−	0.0466295i	0.999728	−	0.0233148i	$-0.00742199\pi$
$660$		0			0
$661$		−	721.605i		−	1.09169i	−0.837887	−	0.545844i	$-0.816209\pi$
$661$		−	721.605i		−	1.09169i	0.837887	−	0.545844i	$-0.183791\pi$
$662$		0			0
$663$			197.015i			0.297157i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	16.0527			0.0240670
$668$		0			0
$669$	628.776			0.939875
$670$		0			0
$671$	−159.448			−0.237627
$672$		0			0
$673$	−435.074			−0.646469			−0.323235	−	0.946319i	$-0.604770\pi$
$673$	−435.074			−0.646469			−0.323235	+	0.946319i	$0.604770\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−607.496			−0.897335			−0.448667	−	0.893699i	$-0.648101\pi$
$677$	−607.496			−0.897335			−0.448667	+	0.893699i	$0.648101\pi$
$678$		0			0
$679$		−	1412.53i		−	2.08031i
$680$		0			0
$681$	−85.7611			−0.125934
$682$		0			0
$683$	−291.254			−0.426434			−0.213217	−	0.977005i	$-0.568394\pi$
$683$	−291.254			−0.426434			−0.213217	+	0.977005i	$0.568394\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	5.44920			0.00793188
$688$		0			0
$689$	495.726			0.719486
$690$		0			0
$691$	−444.232			−0.642883			−0.321441	−	0.946929i	$-0.604167\pi$
$691$	−444.232			−0.642883			−0.321441	+	0.946929i	$0.604167\pi$
$692$		0			0
$693$			116.040i			0.167446i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−716.542			−1.02804
$698$		0			0
$699$		−	349.627i		−	0.500182i
$700$		0			0
$701$	481.762			0.687250			0.343625	−	0.939107i	$-0.388345\pi$
$701$	481.762			0.687250			0.343625	+	0.939107i	$0.388345\pi$
$702$		0			0
$703$	142.622	−	30.9578i	0.202877	−	0.0440367i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			1173.33i			1.65959i
$708$		0			0
$709$	1135.31			1.60128			0.800642	−	0.599143i	$-0.204492\pi$
$709$	1135.31			1.60128			0.800642	+	0.599143i	$0.204492\pi$
$710$		0			0
$711$			370.046i			0.520458i
$712$		0			0
$713$	36.6621			0.0514195
$714$		0			0
$715$		0			0
$716$		0			0
$717$	303.919			0.423876
$718$		0			0
$719$	−12.5461			−0.0174493			−0.00872467	−	0.999962i	$-0.502777\pi$
$719$	−12.5461			−0.0174493			−0.00872467	+	0.999962i	$0.502777\pi$
$720$		0			0
$721$			831.670i			1.15350i
$722$		0			0
$723$			26.8261i			0.0371038i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	387.455i		−	0.532951i	−0.963842	−	0.266475i	$-0.914141\pi$
$727$		−	387.455i		−	0.532951i	0.963842	−	0.266475i	$-0.0858591\pi$
$728$		0			0
$729$	665.632			0.913076
$730$		0			0
$731$	266.455			0.364507
$732$		0			0
$733$		−	550.259i		−	0.750694i	−0.926884	−	0.375347i	$-0.877523\pi$
$733$		−	550.259i		−	0.750694i	0.926884	−	0.375347i	$-0.122477\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−48.3173			−0.0655595
$738$		0			0
$739$	72.2829			0.0978118			0.0489059	−	0.998803i	$-0.484427\pi$
$739$	72.2829			0.0978118			0.0489059	+	0.998803i	$0.484427\pi$
$740$		0			0
$741$	356.906	−	77.4706i	0.481655	−	0.104549i
$742$		0			0
$743$	−330.742			−0.445144			−0.222572	−	0.974916i	$-0.571445\pi$
$743$	−330.742			−0.445144			−0.222572	+	0.974916i	$0.571445\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	223.576i		−	0.299298i
$748$		0			0
$749$			1269.70i			1.69519i
$750$		0			0
$751$			964.716i			1.28458i	0.766464	+	0.642288i	$0.222015\pi$
$751$			964.716i			1.28458i	−0.766464	+	0.642288i	$0.777985\pi$
$752$		0			0
$753$	1006.10			1.33612
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	865.952i		−	1.14393i	−0.820279	−	0.571963i	$-0.806182\pi$
$757$		−	865.952i		−	1.14393i	0.820279	−	0.571963i	$-0.193818\pi$
$758$		0			0
$759$		−	6.42226i		−	0.00846148i
$760$		0			0
$761$	280.071			0.368030			0.184015	−	0.982923i	$-0.441091\pi$
$761$	280.071			0.368030			0.184015	+	0.982923i	$0.441091\pi$
$762$		0			0
$763$	431.904			0.566061
$764$		0			0
$765$		0			0
$766$		0			0
$767$			935.156i			1.21924i
$768$		0			0
$769$	627.438			0.815915			0.407957	−	0.913001i	$-0.366241\pi$
$769$	627.438			0.815915			0.407957	+	0.913001i	$0.366241\pi$
$770$		0			0
$771$	−530.252			−0.687746
$772$		0			0
$773$	−684.186			−0.885105			−0.442552	−	0.896743i	$-0.645927\pi$
$773$	−684.186			−0.885105			−0.442552	+	0.896743i	$0.645927\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		−	136.308i		−	0.175429i
$778$		0			0
$779$	281.760	+	1298.06i	0.361694	+	1.66632i
$780$		0			0
$781$		−	9.55717i		−	0.0122371i
$782$		0			0
$783$		−	516.374i		−	0.659481i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−918.570			−1.16718			−0.583589	−	0.812049i	$-0.698352\pi$
$787$	−918.570			−1.16718			−0.583589	+	0.812049i	$0.698352\pi$
$788$		0			0
$789$			146.065i			0.185126i
$790$		0			0
$791$			736.315i			0.930866i
$792$		0			0
$793$	−427.841			−0.539522
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1245.67			−1.56295			−0.781474	−	0.623938i	$-0.785532\pi$
$797$	−1245.67			−1.56295			−0.781474	+	0.623938i	$0.785532\pi$
$798$		0			0
$799$	128.028			0.160236
$800$		0			0
$801$			169.850i			0.212047i
$802$		0			0
$803$			250.839i			0.312377i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			24.3341i			0.0301537i
$808$		0			0
$809$	−1198.51			−1.48148			−0.740738	−	0.671794i	$-0.765524\pi$
$809$	−1198.51			−1.48148			−0.740738	+	0.671794i	$0.765524\pi$
$810$		0			0
$811$			295.291i			0.364107i	0.983289	+	0.182054i	$0.0582744\pi$
$811$			295.291i			0.364107i	−0.983289	+	0.182054i	$0.941726\pi$
$812$		0			0
$813$	−210.397			−0.258791
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−104.776	−	482.701i	−0.128244	−	0.590821i
$818$		0			0
$819$			311.366i			0.380179i
$820$		0			0
$821$	−271.018			−0.330107			−0.165054	−	0.986285i	$-0.552780\pi$
$821$	−271.018			−0.330107			−0.165054	+	0.986285i	$0.552780\pi$
$822$		0			0
$823$			146.642i			0.178180i	0.996024	+	0.0890900i	$0.0283959\pi$
$823$			146.642i			0.178180i	−0.996024	+	0.0890900i	$0.971604\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1037.94			1.25506			0.627532	−	0.778591i	$-0.284065\pi$
$827$	1037.94			1.25506			0.627532	+	0.778591i	$0.284065\pi$
$828$		0			0
$829$		−	1008.15i		−	1.21610i	−0.793898	−	0.608050i	$-0.791952\pi$
$829$		−	1008.15i		−	1.21610i	0.793898	−	0.608050i	$-0.208048\pi$
$830$		0			0
$831$		−	75.1143i		−	0.0903903i
$832$		0			0
$833$			183.759i			0.220599i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	1179.32i		−	1.40899i
$838$		0			0
$839$		−	1596.51i		−	1.90287i	−0.307850	−	0.951435i	$-0.599610\pi$
$839$		−	1596.51i		−	1.90287i	0.307850	−	0.951435i	$-0.400390\pi$
$840$		0			0
$841$	520.381			0.618765
$842$		0			0
$843$		−	725.824i		−	0.861002i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			900.671i			1.06337i
$848$		0			0
$849$		−	475.841i		−	0.560472i
$850$		0			0
$851$		−	6.88629i		−	0.00809199i
$852$		0			0
$853$		−	733.131i		−	0.859474i	−0.902954	−	0.429737i	$-0.858606\pi$
$853$		−	733.131i		−	0.859474i	0.902954	−	0.429737i	$-0.141394\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	473.032			0.551963			0.275981	−	0.961163i	$-0.410997\pi$
$857$	473.032			0.551963			0.275981	+	0.961163i	$0.410997\pi$
$858$		0			0
$859$	−694.138			−0.808077			−0.404038	−	0.914742i	$-0.632394\pi$
$859$	−694.138			−0.808077			−0.404038	+	0.914742i	$0.632394\pi$
$860$		0			0
$861$	1240.60			1.44088
$862$		0			0
$863$	−301.961			−0.349897			−0.174948	−	0.984578i	$-0.555976\pi$
$863$	−301.961			−0.349897			−0.174948	+	0.984578i	$0.555976\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−399.007			−0.460216
$868$		0			0
$869$		−	284.546i		−	0.327440i
$870$		0			0
$871$	−129.648			−0.148850
$872$		0			0
$873$	−741.556			−0.849434
$874$		0			0
$875$		0			0
$876$		0			0
$877$	954.932			1.08886			0.544431	−	0.838806i	$-0.316746\pi$
$877$	954.932			1.08886			0.544431	+	0.838806i	$0.316746\pi$
$878$		0			0
$879$	−17.1589			−0.0195210
$880$		0			0
$881$	−355.458			−0.403471			−0.201736	−	0.979440i	$-0.564658\pi$
$881$	−355.458			−0.403471			−0.201736	+	0.979440i	$0.564658\pi$
$882$		0			0
$883$		−	378.377i		−	0.428514i	−0.976777	−	0.214257i	$-0.931267\pi$
$883$		−	378.377i		−	0.428514i	0.976777	−	0.214257i	$-0.0687329\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1001.77			−1.12939			−0.564693	−	0.825301i	$-0.691006\pi$
$887$	−1001.77			−1.12939			−0.564693	+	0.825301i	$0.691006\pi$
$888$		0			0
$889$			606.212i			0.681904i
$890$		0			0
$891$	−78.9303			−0.0885863
$892$		0			0
$893$	−50.3434	−	231.932i	−0.0563756	−	0.259722i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	17.2326i		−	0.0192114i
$898$		0			0
$899$	−732.247			−0.814513
$900$		0			0
$901$		−	573.363i		−	0.636363i
$902$		0			0
$903$	−461.331			−0.510887
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1687.59			1.86063			0.930314	−	0.366765i	$-0.119535\pi$
$907$	1687.59			1.86063			0.930314	+	0.366765i	$0.119535\pi$
$908$		0			0
$909$	615.980			0.677646
$910$		0			0
$911$		−	932.015i		−	1.02307i	−0.859263	−	0.511534i	$-0.829077\pi$
$911$		−	932.015i		−	1.02307i	0.859263	−	0.511534i	$-0.170923\pi$
$912$		0			0
$913$			171.918i			0.188300i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			485.286i			0.529210i
$918$		0			0
$919$	−702.329			−0.764232			−0.382116	−	0.924114i	$-0.624805\pi$
$919$	−702.329			−0.764232			−0.382116	+	0.924114i	$0.624805\pi$
$920$		0			0
$921$	−533.047			−0.578770
$922$		0			0
$923$		−	25.6444i		−	0.0277838i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	436.614			0.470997
$928$		0			0
$929$	−1337.11			−1.43930			−0.719650	−	0.694337i	$-0.755698\pi$
$929$	−1337.11			−1.43930			−0.719650	+	0.694337i	$0.755698\pi$
$930$		0			0
$931$	332.891	−	72.2578i	0.357563	−	0.0776131i
$932$		0			0
$933$	1110.64			1.19040
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	1370.84i		−	1.46301i	−0.681834	−	0.731507i	$-0.738817\pi$
$937$		−	1370.84i		−	1.46301i	0.681834	−	0.731507i	$-0.261183\pi$
$938$		0			0
$939$		−	1090.32i		−	1.16115i
$940$		0			0
$941$			879.481i			0.934624i	0.884093	+	0.467312i	$0.154777\pi$
$941$			879.481i			0.934624i	−0.884093	+	0.467312i	$0.845223\pi$
$942$		0			0
$943$	62.6749			0.0664633
$944$		0			0
$945$		0			0
$946$		0			0
$947$			235.757i			0.248951i	0.992223	+	0.124476i	$0.0397249\pi$
$947$			235.757i			0.248951i	−0.992223	+	0.124476i	$0.960275\pi$
$948$		0			0
$949$			673.068i			0.709239i
$950$		0			0
$951$	−375.322			−0.394661
$952$		0			0
$953$	−518.106			−0.543657			−0.271829	−	0.962346i	$-0.587628\pi$
$953$	−518.106			−0.543657			−0.271829	+	0.962346i	$0.587628\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			128.271i			0.134034i
$958$		0			0
$959$	−1258.90			−1.31272
$960$		0			0
$961$	−711.348			−0.740216
$962$		0			0
$963$	666.573			0.692184
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	54.2136i		−	0.0560637i	−0.999607	−	0.0280319i	$-0.991076\pi$
$967$		−	54.2136i		−	0.0560637i	0.999607	−	0.0280319i	$-0.00892398\pi$
$968$		0			0
$969$	−89.6035	−	412.803i	−0.0924701	−	0.426009i
$970$		0			0
$971$		−	1229.47i		−	1.26619i	−0.774075	−	0.633093i	$-0.781785\pi$
$971$		−	1229.47i		−	1.26619i	0.774075	−	0.633093i	$-0.218215\pi$
$972$		0			0
$973$			348.607i			0.358280i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−957.658			−0.980202			−0.490101	−	0.871666i	$-0.663040\pi$
$977$	−957.658			−0.980202			−0.490101	+	0.871666i	$0.663040\pi$
$978$		0			0
$979$		−	130.606i		−	0.133407i
$980$		0			0
$981$		−	226.743i		−	0.231135i
$982$		0			0
$983$	1624.35			1.65244			0.826220	−	0.563348i	$-0.190487\pi$
$983$	1624.35			1.65244			0.826220	+	0.563348i	$0.190487\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−221.664			−0.224583
$988$		0			0
$989$	−23.3064			−0.0235657
$990$		0			0
$991$		−	496.019i		−	0.500524i	−0.968178	−	0.250262i	$-0.919483\pi$
$991$		−	496.019i		−	0.500524i	0.968178	−	0.250262i	$-0.0805167\pi$
$992$		0			0
$993$			624.678i			0.629082i
$994$		0			0
$995$		0			0
$996$		0			0
$997$			231.271i			0.231967i	0.993251	+	0.115983i	$0.0370019\pi$
$997$			231.271i			0.231967i	−0.993251	+	0.115983i	$0.962998\pi$
$998$		0			0
$999$	−221.514			−0.221735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.3.g.d.949.10		28
5.2	odd	4		1900.3.e.g.1101.10	yes	14
5.3	odd	4		1900.3.e.h.1101.5	yes	14
5.4	even	2	inner	1900.3.g.d.949.19		28
19.18	odd	2	inner	1900.3.g.d.949.20		28
95.18	even	4		1900.3.e.h.1101.10	yes	14
95.37	even	4		1900.3.e.g.1101.5	✓	14
95.94	odd	2	inner	1900.3.g.d.949.9		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1900.3.e.g.1101.5	✓	14	95.37	even	4
1900.3.e.g.1101.10	yes	14	5.2	odd	4
1900.3.e.h.1101.5	yes	14	5.3	odd	4
1900.3.e.h.1101.10	yes	14	95.18	even	4
1900.3.g.d.949.9		28	95.94	odd	2	inner
1900.3.g.d.949.10		28	1.1	even	1	trivial
1900.3.g.d.949.19		28	5.4	even	2	inner
1900.3.g.d.949.20		28	19.18	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1900.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.16913 q^{3} -8.18099i q^{7} -4.29489 q^{9} +O(q^{10})\)	\(q-2.16913 q^{3} -8.18099i q^{7} -4.29489 q^{9} +3.30255 q^{11} +8.86162 q^{13} -10.2495i q^{17} +(-18.5676 + 4.03031i) q^{19} +17.7456i q^{21} +0.896508i q^{23} +28.8383 q^{27} -17.9058i q^{29} -40.8943i q^{31} -7.16364 q^{33} -7.68123 q^{37} -19.2220 q^{39} -69.9101i q^{41} +25.9969i q^{43} +12.4912i q^{47} -17.9286 q^{49} +22.2324i q^{51} +55.9407 q^{53} +(40.2755 - 8.74226i) q^{57} +105.529i q^{59} -48.2803 q^{61} +35.1365i q^{63} -14.6303 q^{67} -1.94464i q^{69} -2.89388i q^{71} +75.9531i q^{73} -27.0181i q^{77} -86.1594i q^{79} -23.8998 q^{81} +52.0562i q^{83} +38.8400i q^{87} -39.5469i q^{89} -72.4968i q^{91} +88.7050i q^{93} +172.660 q^{97} -14.1841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 104 q^{9}+O(q^{10}) \) 28 * q + 104 * q^9	\( 28 q + 104 q^{9} + 8 q^{11} + 58 q^{19} + 112 q^{39} - 276 q^{49} - 100 q^{61} + 132 q^{81} - 184 q^{99}+O(q^{100}) \) 28 * q + 104 * q^9 + 8 * q^11 + 58 * q^19 + 112 * q^39 - 276 * q^49 - 100 * q^61 + 132 * q^81 - 184 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more