LMFDB - Embedded newform 450.4.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,4,Mod(1,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("450.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	450.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:	$26.5508595026$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +4.00000 q^{4} +2.00000 q^{7} +8.00000 q^{8} +O(q^{10})$

$q+2.00000 q^{2} +4.00000 q^{4} +2.00000 q^{7} +8.00000 q^{8} -70.0000 q^{11} -54.0000 q^{13} +4.00000 q^{14} +16.0000 q^{16} -22.0000 q^{17} +24.0000 q^{19} -140.000 q^{22} -100.000 q^{23} -108.000 q^{26} +8.00000 q^{28} -216.000 q^{29} +208.000 q^{31} +32.0000 q^{32} -44.0000 q^{34} +254.000 q^{37} +48.0000 q^{38} +206.000 q^{41} -292.000 q^{43} -280.000 q^{44} -200.000 q^{46} -320.000 q^{47} -339.000 q^{49} -216.000 q^{52} -402.000 q^{53} +16.0000 q^{56} -432.000 q^{58} +370.000 q^{59} -550.000 q^{61} +416.000 q^{62} +64.0000 q^{64} -728.000 q^{67} -88.0000 q^{68} +540.000 q^{71} -604.000 q^{73} +508.000 q^{74} +96.0000 q^{76} -140.000 q^{77} +792.000 q^{79} +412.000 q^{82} +404.000 q^{83} -584.000 q^{86} -560.000 q^{88} +938.000 q^{89} -108.000 q^{91} -400.000 q^{92} -640.000 q^{94} -56.0000 q^{97} -678.000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	0	0
$3$	0	0
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	2.00000	0.107990	0.0539949	−	0.998541i	$-0.482805\pi$
$7$	2.00000	0.107990	0.0539949	+	0.998541i	$0.482805\pi$
$8$	8.00000	0.353553
$9$	0	0
$10$	0	0
$11$	−70.0000	−1.91871	−0.959354	−	0.282204i	$-0.908934\pi$
$11$	−70.0000	−1.91871	−0.959354	+	0.282204i	$0.908934\pi$
$12$	0	0
$13$	−54.0000	−1.15207	−0.576035	−	0.817425i	$-0.695401\pi$
$13$	−54.0000	−1.15207	−0.576035	+	0.817425i	$0.695401\pi$
$14$	4.00000	0.0763604
$15$	0	0
$16$	16.0000	0.250000
$17$	−22.0000	−0.313870	−0.156935	−	0.987609i	$-0.550161\pi$
$17$	−22.0000	−0.313870	−0.156935	+	0.987609i	$0.550161\pi$
$18$	0	0
$19$	24.0000	0.289788	0.144894	−	0.989447i	$-0.453716\pi$
$19$	24.0000	0.289788	0.144894	+	0.989447i	$0.453716\pi$
$20$	0	0
$21$	0	0
$22$	−140.000	−1.35673
$23$	−100.000	−0.906584	−0.453292	−	0.891362i	$-0.649751\pi$
$23$	−100.000	−0.906584	−0.453292	+	0.891362i	$0.649751\pi$
$24$	0	0
$25$	0	0
$26$	−108.000	−0.814636
$27$	0	0
$28$	8.00000	0.0539949
$29$	−216.000	−1.38311	−0.691555	−	0.722324i	$-0.743074\pi$
$29$	−216.000	−1.38311	−0.691555	+	0.722324i	$0.743074\pi$
$30$	0	0
$31$	208.000	1.20509	0.602547	−	0.798084i	$-0.294153\pi$
$31$	208.000	1.20509	0.602547	+	0.798084i	$0.294153\pi$
$32$	32.0000	0.176777
$33$	0	0
$34$	−44.0000	−0.221939
$35$	0	0
$36$	0	0
$37$	254.000	1.12858	0.564288	−	0.825578i	$-0.309151\pi$
$37$	254.000	1.12858	0.564288	+	0.825578i	$0.309151\pi$
$38$	48.0000	0.204911
$39$	0	0
$40$	0	0
$41$	206.000	0.784678	0.392339	−	0.919821i	$-0.371666\pi$
$41$	206.000	0.784678	0.392339	+	0.919821i	$0.371666\pi$
$42$	0	0
$43$	−292.000	−1.03557	−0.517786	−	0.855510i	$-0.673244\pi$
$43$	−292.000	−1.03557	−0.517786	+	0.855510i	$0.673244\pi$
$44$	−280.000	−0.959354
$45$	0	0
$46$	−200.000	−0.641052
$47$	−320.000	−0.993123	−0.496562	−	0.868001i	$-0.665404\pi$
$47$	−320.000	−0.993123	−0.496562	+	0.868001i	$0.665404\pi$
$48$	0	0
$49$	−339.000	−0.988338
$50$	0	0
$51$	0	0
$52$	−216.000	−0.576035
$53$	−402.000	−1.04187	−0.520933	−	0.853597i	$-0.674416\pi$
$53$	−402.000	−1.04187	−0.520933	+	0.853597i	$0.674416\pi$
$54$	0	0
$55$	0	0
$56$	16.0000	0.0381802
$57$	0	0
$58$	−432.000	−0.978007
$59$	370.000	0.816439	0.408219	−	0.912884i	$-0.366150\pi$
$59$	370.000	0.816439	0.408219	+	0.912884i	$0.366150\pi$
$60$	0	0
$61$	−550.000	−1.15443	−0.577215	−	0.816592i	$-0.695861\pi$
$61$	−550.000	−1.15443	−0.577215	+	0.816592i	$0.695861\pi$
$62$	416.000	0.852130
$63$	0	0
$64$	64.0000	0.125000
$65$	0	0
$66$	0	0
$67$	−728.000	−1.32745	−0.663727	−	0.747975i	$-0.731026\pi$
$67$	−728.000	−1.32745	−0.663727	+	0.747975i	$0.731026\pi$
$68$	−88.0000	−0.156935
$69$	0	0
$70$	0	0
$71$	540.000	0.902623	0.451311	−	0.892367i	$-0.350956\pi$
$71$	540.000	0.902623	0.451311	+	0.892367i	$0.350956\pi$
$72$	0	0
$73$	−604.000	−0.968395	−0.484198	−	0.874959i	$-0.660888\pi$
$73$	−604.000	−0.968395	−0.484198	+	0.874959i	$0.660888\pi$
$74$	508.000	0.798024
$75$	0	0
$76$	96.0000	0.144894
$77$	−140.000	−0.207201
$78$	0	0
$79$	792.000	1.12794	0.563968	−	0.825797i	$-0.309274\pi$
$79$	792.000	1.12794	0.563968	+	0.825797i	$0.309274\pi$
$80$	0	0
$81$	0	0
$82$	412.000	0.554851
$83$	404.000	0.534274	0.267137	−	0.963659i	$-0.413922\pi$
$83$	404.000	0.534274	0.267137	+	0.963659i	$0.413922\pi$
$84$	0	0
$85$	0	0
$86$	−584.000	−0.732260
$87$	0	0
$88$	−560.000	−0.678366
$89$	938.000	1.11717	0.558583	−	0.829449i	$-0.311345\pi$
$89$	938.000	1.11717	0.558583	+	0.829449i	$0.311345\pi$
$90$	0	0
$91$	−108.000	−0.124412
$92$	−400.000	−0.453292
$93$	0	0
$94$	−640.000	−0.702244
$95$	0	0
$96$	0	0
$97$	−56.0000	−0.0586179	−0.0293090	−	0.999570i	$-0.509331\pi$
$97$	−56.0000	−0.0586179	−0.0293090	+	0.999570i	$0.509331\pi$
$98$	−678.000	−0.698861
$99$	0	0
$100$	0	0
$101$	592.000	0.583230	0.291615	−	0.956536i	$-0.405807\pi$
$101$	592.000	0.583230	0.291615	+	0.956536i	$0.405807\pi$
$102$	0	0
$103$	−62.0000	−0.0593111	−0.0296555	−	0.999560i	$-0.509441\pi$
$103$	−62.0000	−0.0593111	−0.0296555	+	0.999560i	$0.509441\pi$
$104$	−432.000	−0.407318
$105$	0	0
$106$	−804.000	−0.736711
$107$	84.0000	0.0758933	0.0379467	−	0.999280i	$-0.487918\pi$
$107$	84.0000	0.0758933	0.0379467	+	0.999280i	$0.487918\pi$
$108$	0	0
$109$	370.000	0.325134	0.162567	−	0.986698i	$-0.448023\pi$
$109$	370.000	0.325134	0.162567	+	0.986698i	$0.448023\pi$
$110$	0	0
$111$	0	0
$112$	32.0000	0.0269975
$113$	−1746.00	−1.45354	−0.726769	−	0.686882i	$-0.758979\pi$
$113$	−1746.00	−1.45354	−0.726769	+	0.686882i	$0.758979\pi$
$114$	0	0
$115$	0	0
$116$	−864.000	−0.691555
$117$	0	0
$118$	740.000	0.577310
$119$	−44.0000	−0.0338947
$120$	0	0
$121$	3569.00	2.68144
$122$	−1100.00	−0.816306
$123$	0	0
$124$	832.000	0.602547
$125$	0	0
$126$	0	0
$127$	−1630.00	−1.13889	−0.569445	−	0.822029i	$-0.692842\pi$
$127$	−1630.00	−1.13889	−0.569445	+	0.822029i	$0.692842\pi$
$128$	128.000	0.0883883
$129$	0	0
$130$	0	0
$131$	870.000	0.580246	0.290123	−	0.956989i	$-0.406304\pi$
$131$	870.000	0.580246	0.290123	+	0.956989i	$0.406304\pi$
$132$	0	0
$133$	48.0000	0.0312942
$134$	−1456.00	−0.938651
$135$	0	0
$136$	−176.000	−0.110970
$137$	918.000	0.572482	0.286241	−	0.958158i	$-0.407594\pi$
$137$	918.000	0.572482	0.286241	+	0.958158i	$0.407594\pi$
$138$	0	0
$139$	−596.000	−0.363684	−0.181842	−	0.983328i	$-0.558206\pi$
$139$	−596.000	−0.363684	−0.181842	+	0.983328i	$0.558206\pi$
$140$	0	0
$141$	0	0
$142$	1080.00	0.638251
$143$	3780.00	2.21049
$144$	0	0
$145$	0	0
$146$	−1208.00	−0.684759
$147$	0	0
$148$	1016.00	0.564288
$149$	−1076.00	−0.591606	−0.295803	−	0.955249i	$-0.595587\pi$
$149$	−1076.00	−0.591606	−0.295803	+	0.955249i	$0.595587\pi$
$150$	0	0
$151$	−32.0000	−0.0172458	−0.00862292	−	0.999963i	$-0.502745\pi$
$151$	−32.0000	−0.0172458	−0.00862292	+	0.999963i	$0.502745\pi$
$152$	192.000	0.102456
$153$	0	0
$154$	−280.000	−0.146513
$155$	0	0
$156$	0	0
$157$	2554.00	1.29829	0.649145	−	0.760665i	$-0.275127\pi$
$157$	2554.00	1.29829	0.649145	+	0.760665i	$0.275127\pi$
$158$	1584.00	0.797571
$159$	0	0
$160$	0	0
$161$	−200.000	−0.0979019
$162$	0	0
$163$	−752.000	−0.361357	−0.180678	−	0.983542i	$-0.557829\pi$
$163$	−752.000	−0.361357	−0.180678	+	0.983542i	$0.557829\pi$
$164$	824.000	0.392339
$165$	0	0
$166$	808.000	0.377789
$167$	2700.00	1.25109	0.625546	−	0.780188i	$-0.284876\pi$
$167$	2700.00	1.25109	0.625546	+	0.780188i	$0.284876\pi$
$168$	0	0
$169$	719.000	0.327264
$170$	0	0
$171$	0	0
$172$	−1168.00	−0.517786
$173$	−1334.00	−0.586255	−0.293128	−	0.956073i	$-0.594696\pi$
$173$	−1334.00	−0.586255	−0.293128	+	0.956073i	$0.594696\pi$
$174$	0	0
$175$	0	0
$176$	−1120.00	−0.479677
$177$	0	0
$178$	1876.00	0.789956
$179$	1714.00	0.715700	0.357850	−	0.933779i	$-0.383510\pi$
$179$	1714.00	0.715700	0.357850	+	0.933779i	$0.383510\pi$
$180$	0	0
$181$	−4006.00	−1.64510	−0.822551	−	0.568691i	$-0.807450\pi$
$181$	−4006.00	−1.64510	−0.822551	+	0.568691i	$0.807450\pi$
$182$	−216.000	−0.0879724
$183$	0	0
$184$	−800.000	−0.320526
$185$	0	0
$186$	0	0
$187$	1540.00	0.602224
$188$	−1280.00	−0.496562
$189$	0	0
$190$	0	0
$191$	684.000	0.259123	0.129562	−	0.991571i	$-0.458643\pi$
$191$	684.000	0.259123	0.129562	+	0.991571i	$0.458643\pi$
$192$	0	0
$193$	4484.00	1.67236	0.836180	−	0.548455i	$-0.184784\pi$
$193$	4484.00	1.67236	0.836180	+	0.548455i	$0.184784\pi$
$194$	−112.000	−0.0414491
$195$	0	0
$196$	−1356.00	−0.494169
$197$	−1058.00	−0.382636	−0.191318	−	0.981528i	$-0.561276\pi$
$197$	−1058.00	−0.382636	−0.191318	+	0.981528i	$0.561276\pi$
$198$	0	0
$199$	−1128.00	−0.401818	−0.200909	−	0.979610i	$-0.564390\pi$
$199$	−1128.00	−0.401818	−0.200909	+	0.979610i	$0.564390\pi$
$200$	0	0
$201$	0	0
$202$	1184.00	0.412406
$203$	−432.000	−0.149362
$204$	0	0
$205$	0	0
$206$	−124.000	−0.0419393
$207$	0	0
$208$	−864.000	−0.288017
$209$	−1680.00	−0.556019
$210$	0	0
$211$	780.000	0.254490	0.127245	−	0.991871i	$-0.459387\pi$
$211$	780.000	0.254490	0.127245	+	0.991871i	$0.459387\pi$
$212$	−1608.00	−0.520933
$213$	0	0
$214$	168.000	0.0536647
$215$	0	0
$216$	0	0
$217$	416.000	0.130138
$218$	740.000	0.229904
$219$	0	0
$220$	0	0
$221$	1188.00	0.361600
$222$	0	0
$223$	2570.00	0.771749	0.385874	−	0.922551i	$-0.373900\pi$
$223$	2570.00	0.771749	0.385874	+	0.922551i	$0.373900\pi$
$224$	64.0000	0.0190901
$225$	0	0
$226$	−3492.00	−1.02781
$227$	−2836.00	−0.829216	−0.414608	−	0.910000i	$-0.636081\pi$
$227$	−2836.00	−0.829216	−0.414608	+	0.910000i	$0.636081\pi$
$228$	0	0
$229$	−610.000	−0.176026	−0.0880130	−	0.996119i	$-0.528052\pi$
$229$	−610.000	−0.176026	−0.0880130	+	0.996119i	$0.528052\pi$
$230$	0	0
$231$	0	0
$232$	−1728.00	−0.489003
$233$	3514.00	0.988025	0.494012	−	0.869455i	$-0.335530\pi$
$233$	3514.00	0.988025	0.494012	+	0.869455i	$0.335530\pi$
$234$	0	0
$235$	0	0
$236$	1480.00	0.408219
$237$	0	0
$238$	−88.0000	−0.0239672
$239$	1844.00	0.499073	0.249536	−	0.968365i	$-0.419722\pi$
$239$	1844.00	0.499073	0.249536	+	0.968365i	$0.419722\pi$
$240$	0	0
$241$	982.000	0.262474	0.131237	−	0.991351i	$-0.458105\pi$
$241$	982.000	0.262474	0.131237	+	0.991351i	$0.458105\pi$
$242$	7138.00	1.89607
$243$	0	0
$244$	−2200.00	−0.577215
$245$	0	0
$246$	0	0
$247$	−1296.00	−0.333856
$248$	1664.00	0.426065
$249$	0	0
$250$	0	0
$251$	3174.00	0.798172	0.399086	−	0.916914i	$-0.369328\pi$
$251$	3174.00	0.798172	0.399086	+	0.916914i	$0.369328\pi$
$252$	0	0
$253$	7000.00	1.73947
$254$	−3260.00	−0.805317
$255$	0	0
$256$	256.000	0.0625000
$257$	−1194.00	−0.289804	−0.144902	−	0.989446i	$-0.546287\pi$
$257$	−1194.00	−0.289804	−0.144902	+	0.989446i	$0.546287\pi$
$258$	0	0
$259$	508.000	0.121875
$260$	0	0
$261$	0	0
$262$	1740.00	0.410296
$263$	140.000	0.0328242	0.0164121	−	0.999865i	$-0.494776\pi$
$263$	140.000	0.0328242	0.0164121	+	0.999865i	$0.494776\pi$
$264$	0	0
$265$	0	0
$266$	96.0000	0.0221283
$267$	0	0
$268$	−2912.00	−0.663727
$269$	−5256.00	−1.19132	−0.595658	−	0.803238i	$-0.703109\pi$
$269$	−5256.00	−1.19132	−0.595658	+	0.803238i	$0.703109\pi$
$270$	0	0
$271$	544.000	0.121940	0.0609698	−	0.998140i	$-0.480581\pi$
$271$	544.000	0.121940	0.0609698	+	0.998140i	$0.480581\pi$
$272$	−352.000	−0.0784674
$273$	0	0
$274$	1836.00	0.404806
$275$	0	0
$276$	0	0
$277$	−946.000	−0.205197	−0.102599	−	0.994723i	$-0.532716\pi$
$277$	−946.000	−0.205197	−0.102599	+	0.994723i	$0.532716\pi$
$278$	−1192.00	−0.257163
$279$	0	0
$280$	0	0
$281$	−1278.00	−0.271313	−0.135657	−	0.990756i	$-0.543314\pi$
$281$	−1278.00	−0.271313	−0.135657	+	0.990756i	$0.543314\pi$
$282$	0	0
$283$	−7424.00	−1.55940	−0.779701	−	0.626152i	$-0.784629\pi$
$283$	−7424.00	−1.55940	−0.779701	+	0.626152i	$0.784629\pi$
$284$	2160.00	0.451311
$285$	0	0
$286$	7560.00	1.56305
$287$	412.000	0.0847373
$288$	0	0
$289$	−4429.00	−0.901486
$290$	0	0
$291$	0	0
$292$	−2416.00	−0.484198
$293$	−1362.00	−0.271566	−0.135783	−	0.990739i	$-0.543355\pi$
$293$	−1362.00	−0.271566	−0.135783	+	0.990739i	$0.543355\pi$
$294$	0	0
$295$	0	0
$296$	2032.00	0.399012
$297$	0	0
$298$	−2152.00	−0.418329
$299$	5400.00	1.04445
$300$	0	0
$301$	−584.000	−0.111831
$302$	−64.0000	−0.0121947
$303$	0	0
$304$	384.000	0.0724471
$305$	0	0
$306$	0	0
$307$	7740.00	1.43891	0.719455	−	0.694539i	$-0.244392\pi$
$307$	7740.00	1.43891	0.719455	+	0.694539i	$0.244392\pi$
$308$	−560.000	−0.103601
$309$	0	0
$310$	0	0
$311$	−4980.00	−0.908006	−0.454003	−	0.891000i	$-0.650004\pi$
$311$	−4980.00	−0.908006	−0.454003	+	0.891000i	$0.650004\pi$
$312$	0	0
$313$	−604.000	−0.109074	−0.0545369	−	0.998512i	$-0.517368\pi$
$313$	−604.000	−0.109074	−0.0545369	+	0.998512i	$0.517368\pi$
$314$	5108.00	0.918029
$315$	0	0
$316$	3168.00	0.563968
$317$	−8566.00	−1.51771	−0.758856	−	0.651259i	$-0.774241\pi$
$317$	−8566.00	−1.51771	−0.758856	+	0.651259i	$0.774241\pi$
$318$	0	0
$319$	15120.0	2.65379
$320$	0	0
$321$	0	0
$322$	−400.000	−0.0692271
$323$	−528.000	−0.0909557
$324$	0	0
$325$	0	0
$326$	−1504.00	−0.255518
$327$	0	0
$328$	1648.00	0.277426
$329$	−640.000	−0.107247
$330$	0	0
$331$	3472.00	0.576551	0.288275	−	0.957548i	$-0.406918\pi$
$331$	3472.00	0.576551	0.288275	+	0.957548i	$0.406918\pi$
$332$	1616.00	0.267137
$333$	0	0
$334$	5400.00	0.884655
$335$	0	0
$336$	0	0
$337$	−5668.00	−0.916189	−0.458094	−	0.888904i	$-0.651468\pi$
$337$	−5668.00	−0.916189	−0.458094	+	0.888904i	$0.651468\pi$
$338$	1438.00	0.231411
$339$	0	0
$340$	0	0
$341$	−14560.0	−2.31222
$342$	0	0
$343$	−1364.00	−0.214720
$344$	−2336.00	−0.366130
$345$	0	0
$346$	−2668.00	−0.414545
$347$	10836.0	1.67639	0.838194	−	0.545371i	$-0.183611\pi$
$347$	10836.0	1.67639	0.838194	+	0.545371i	$0.183611\pi$
$348$	0	0
$349$	−8990.00	−1.37886	−0.689432	−	0.724350i	$-0.742140\pi$
$349$	−8990.00	−1.37886	−0.689432	+	0.724350i	$0.742140\pi$
$350$	0	0
$351$	0	0
$352$	−2240.00	−0.339183
$353$	−5078.00	−0.765651	−0.382825	−	0.923821i	$-0.625049\pi$
$353$	−5078.00	−0.765651	−0.382825	+	0.923821i	$0.625049\pi$
$354$	0	0
$355$	0	0
$356$	3752.00	0.558583
$357$	0	0
$358$	3428.00	0.506077
$359$	3696.00	0.543363	0.271682	−	0.962387i	$-0.412420\pi$
$359$	3696.00	0.543363	0.271682	+	0.962387i	$0.412420\pi$
$360$	0	0
$361$	−6283.00	−0.916023
$362$	−8012.00	−1.16326
$363$	0	0
$364$	−432.000	−0.0622059
$365$	0	0
$366$	0	0
$367$	−286.000	−0.0406787	−0.0203393	−	0.999793i	$-0.506475\pi$
$367$	−286.000	−0.0406787	−0.0203393	+	0.999793i	$0.506475\pi$
$368$	−1600.00	−0.226646
$369$	0	0
$370$	0	0
$371$	−804.000	−0.112511
$372$	0	0
$373$	−8262.00	−1.14689	−0.573445	−	0.819244i	$-0.694393\pi$
$373$	−8262.00	−1.14689	−0.573445	+	0.819244i	$0.694393\pi$
$374$	3080.00	0.425837
$375$	0	0
$376$	−2560.00	−0.351122
$377$	11664.0	1.59344
$378$	0	0
$379$	−2956.00	−0.400632	−0.200316	−	0.979731i	$-0.564197\pi$
$379$	−2956.00	−0.400632	−0.200316	+	0.979731i	$0.564197\pi$
$380$	0	0
$381$	0	0
$382$	1368.00	0.183228
$383$	−5240.00	−0.699090	−0.349545	−	0.936920i	$-0.613664\pi$
$383$	−5240.00	−0.699090	−0.349545	+	0.936920i	$0.613664\pi$
$384$	0	0
$385$	0	0
$386$	8968.00	1.18254
$387$	0	0
$388$	−224.000	−0.0293090
$389$	884.000	0.115220	0.0576100	−	0.998339i	$-0.481652\pi$
$389$	884.000	0.115220	0.0576100	+	0.998339i	$0.481652\pi$
$390$	0	0
$391$	2200.00	0.284549
$392$	−2712.00	−0.349430
$393$	0	0
$394$	−2116.00	−0.270565
$395$	0	0
$396$	0	0
$397$	−3394.00	−0.429068	−0.214534	−	0.976717i	$-0.568823\pi$
$397$	−3394.00	−0.429068	−0.214534	+	0.976717i	$0.568823\pi$
$398$	−2256.00	−0.284128
$399$	0	0
$400$	0	0
$401$	6826.00	0.850060	0.425030	−	0.905179i	$-0.360263\pi$
$401$	6826.00	0.850060	0.425030	+	0.905179i	$0.360263\pi$
$402$	0	0
$403$	−11232.0	−1.38835
$404$	2368.00	0.291615
$405$	0	0
$406$	−864.000	−0.105615
$407$	−17780.0	−2.16541
$408$	0	0
$409$	7814.00	0.944688	0.472344	−	0.881414i	$-0.343408\pi$
$409$	7814.00	0.944688	0.472344	+	0.881414i	$0.343408\pi$
$410$	0	0
$411$	0	0
$412$	−248.000	−0.0296555
$413$	740.000	0.0881671
$414$	0	0
$415$	0	0
$416$	−1728.00	−0.203659
$417$	0	0
$418$	−3360.00	−0.393165
$419$	−8290.00	−0.966570	−0.483285	−	0.875463i	$-0.660557\pi$
$419$	−8290.00	−0.966570	−0.483285	+	0.875463i	$0.660557\pi$
$420$	0	0
$421$	2110.00	0.244264	0.122132	−	0.992514i	$-0.461027\pi$
$421$	2110.00	0.244264	0.122132	+	0.992514i	$0.461027\pi$
$422$	1560.00	0.179952
$423$	0	0
$424$	−3216.00	−0.368356
$425$	0	0
$426$	0	0
$427$	−1100.00	−0.124667
$428$	336.000	0.0379467
$429$	0	0
$430$	0	0
$431$	12080.0	1.35005	0.675027	−	0.737793i	$-0.264132\pi$
$431$	12080.0	1.35005	0.675027	+	0.737793i	$0.264132\pi$
$432$	0	0
$433$	−16492.0	−1.83038	−0.915190	−	0.403022i	$-0.867960\pi$
$433$	−16492.0	−1.83038	−0.915190	+	0.403022i	$0.867960\pi$
$434$	832.000	0.0920214
$435$	0	0
$436$	1480.00	0.162567
$437$	−2400.00	−0.262718
$438$	0	0
$439$	−15048.0	−1.63600	−0.817998	−	0.575222i	$-0.804916\pi$
$439$	−15048.0	−1.63600	−0.817998	+	0.575222i	$0.804916\pi$
$440$	0	0
$441$	0	0
$442$	2376.00	0.255690
$443$	−9876.00	−1.05919	−0.529597	−	0.848249i	$-0.677657\pi$
$443$	−9876.00	−1.05919	−0.529597	+	0.848249i	$0.677657\pi$
$444$	0	0
$445$	0	0
$446$	5140.00	0.545709
$447$	0	0
$448$	128.000	0.0134987
$449$	−17166.0	−1.80426	−0.902131	−	0.431462i	$-0.857998\pi$
$449$	−17166.0	−1.80426	−0.902131	+	0.431462i	$0.857998\pi$
$450$	0	0
$451$	−14420.0	−1.50557
$452$	−6984.00	−0.726769
$453$	0	0
$454$	−5672.00	−0.586344
$455$	0	0
$456$	0	0
$457$	−14848.0	−1.51983	−0.759913	−	0.650025i	$-0.774758\pi$
$457$	−14848.0	−1.51983	−0.759913	+	0.650025i	$0.774758\pi$
$458$	−1220.00	−0.124469
$459$	0	0
$460$	0	0
$461$	1260.00	0.127297	0.0636486	−	0.997972i	$-0.479726\pi$
$461$	1260.00	0.127297	0.0636486	+	0.997972i	$0.479726\pi$
$462$	0	0
$463$	11238.0	1.12802	0.564011	−	0.825767i	$-0.309258\pi$
$463$	11238.0	1.12802	0.564011	+	0.825767i	$0.309258\pi$
$464$	−3456.00	−0.345778
$465$	0	0
$466$	7028.00	0.698639
$467$	14772.0	1.46374	0.731870	−	0.681444i	$-0.238648\pi$
$467$	14772.0	1.46374	0.731870	+	0.681444i	$0.238648\pi$
$468$	0	0
$469$	−1456.00	−0.143351
$470$	0	0
$471$	0	0
$472$	2960.00	0.288655
$473$	20440.0	1.98696
$474$	0	0
$475$	0	0
$476$	−176.000	−0.0169474
$477$	0	0
$478$	3688.00	0.352898
$479$	6116.00	0.583397	0.291699	−	0.956510i	$-0.405780\pi$
$479$	6116.00	0.583397	0.291699	+	0.956510i	$0.405780\pi$
$480$	0	0
$481$	−13716.0	−1.30020
$482$	1964.00	0.185597
$483$	0	0
$484$	14276.0	1.34072
$485$	0	0
$486$	0	0
$487$	−15906.0	−1.48002	−0.740010	−	0.672596i	$-0.765179\pi$
$487$	−15906.0	−1.48002	−0.740010	+	0.672596i	$0.765179\pi$
$488$	−4400.00	−0.408153
$489$	0	0
$490$	0	0
$491$	−18714.0	−1.72006	−0.860032	−	0.510241i	$-0.829556\pi$
$491$	−18714.0	−1.72006	−0.860032	+	0.510241i	$0.829556\pi$
$492$	0	0
$493$	4752.00	0.434116
$494$	−2592.00	−0.236072
$495$	0	0
$496$	3328.00	0.301273
$497$	1080.00	0.0974741
$498$	0	0
$499$	−4056.00	−0.363871	−0.181935	−	0.983310i	$-0.558236\pi$
$499$	−4056.00	−0.363871	−0.181935	+	0.983310i	$0.558236\pi$
$500$	0	0
$501$	0	0
$502$	6348.00	0.564393
$503$	6288.00	0.557392	0.278696	−	0.960379i	$-0.410098\pi$
$503$	6288.00	0.557392	0.278696	+	0.960379i	$0.410098\pi$
$504$	0	0
$505$	0	0
$506$	14000.0	1.22999
$507$	0	0
$508$	−6520.00	−0.569445
$509$	−2856.00	−0.248703	−0.124352	−	0.992238i	$-0.539685\pi$
$509$	−2856.00	−0.248703	−0.124352	+	0.992238i	$0.539685\pi$
$510$	0	0
$511$	−1208.00	−0.104577
$512$	512.000	0.0441942
$513$	0	0
$514$	−2388.00	−0.204922
$515$	0	0
$516$	0	0
$517$	22400.0	1.90551
$518$	1016.00	0.0861785
$519$	0	0
$520$	0	0
$521$	−17078.0	−1.43609	−0.718043	−	0.695999i	$-0.754962\pi$
$521$	−17078.0	−1.43609	−0.718043	+	0.695999i	$0.754962\pi$
$522$	0	0
$523$	8560.00	0.715684	0.357842	−	0.933782i	$-0.383513\pi$
$523$	8560.00	0.715684	0.357842	+	0.933782i	$0.383513\pi$
$524$	3480.00	0.290123
$525$	0	0
$526$	280.000	0.0232102
$527$	−4576.00	−0.378242
$528$	0	0
$529$	−2167.00	−0.178105
$530$	0	0
$531$	0	0
$532$	192.000	0.0156471
$533$	−11124.0	−0.904004
$534$	0	0
$535$	0	0
$536$	−5824.00	−0.469326
$537$	0	0
$538$	−10512.0	−0.842388
$539$	23730.0	1.89633
$540$	0	0
$541$	15970.0	1.26914	0.634569	−	0.772866i	$-0.281178\pi$
$541$	15970.0	1.26914	0.634569	+	0.772866i	$0.281178\pi$
$542$	1088.00	0.0862244
$543$	0	0
$544$	−704.000	−0.0554848
$545$	0	0
$546$	0	0
$547$	15524.0	1.21345	0.606726	−	0.794911i	$-0.292482\pi$
$547$	15524.0	1.21345	0.606726	+	0.794911i	$0.292482\pi$
$548$	3672.00	0.286241
$549$	0	0
$550$	0	0
$551$	−5184.00	−0.400809
$552$	0	0
$553$	1584.00	0.121806
$554$	−1892.00	−0.145096
$555$	0	0
$556$	−2384.00	−0.181842
$557$	6774.00	0.515303	0.257651	−	0.966238i	$-0.417051\pi$
$557$	6774.00	0.515303	0.257651	+	0.966238i	$0.417051\pi$
$558$	0	0
$559$	15768.0	1.19305
$560$	0	0
$561$	0	0
$562$	−2556.00	−0.191848
$563$	−10484.0	−0.784810	−0.392405	−	0.919793i	$-0.628357\pi$
$563$	−10484.0	−0.784810	−0.392405	+	0.919793i	$0.628357\pi$
$564$	0	0
$565$	0	0
$566$	−14848.0	−1.10266
$567$	0	0
$568$	4320.00	0.319125
$569$	−23302.0	−1.71682	−0.858410	−	0.512964i	$-0.828547\pi$
$569$	−23302.0	−1.71682	−0.858410	+	0.512964i	$0.828547\pi$
$570$	0	0
$571$	21520.0	1.57720	0.788602	−	0.614903i	$-0.210805\pi$
$571$	21520.0	1.57720	0.788602	+	0.614903i	$0.210805\pi$
$572$	15120.0	1.10524
$573$	0	0
$574$	824.000	0.0599183
$575$	0	0
$576$	0	0
$577$	−3856.00	−0.278210	−0.139105	−	0.990278i	$-0.544423\pi$
$577$	−3856.00	−0.278210	−0.139105	+	0.990278i	$0.544423\pi$
$578$	−8858.00	−0.637447
$579$	0	0
$580$	0	0
$581$	808.000	0.0576962
$582$	0	0
$583$	28140.0	1.99904
$584$	−4832.00	−0.342379
$585$	0	0
$586$	−2724.00	−0.192026
$587$	−26796.0	−1.88414	−0.942069	−	0.335418i	$-0.891122\pi$
$587$	−26796.0	−1.88414	−0.942069	+	0.335418i	$0.891122\pi$
$588$	0	0
$589$	4992.00	0.349222
$590$	0	0
$591$	0	0
$592$	4064.00	0.282144
$593$	9870.00	0.683495	0.341747	−	0.939792i	$-0.388981\pi$
$593$	9870.00	0.683495	0.341747	+	0.939792i	$0.388981\pi$
$594$	0	0
$595$	0	0
$596$	−4304.00	−0.295803
$597$	0	0
$598$	10800.0	0.738537
$599$	13296.0	0.906945	0.453472	−	0.891270i	$-0.350185\pi$
$599$	13296.0	0.906945	0.453472	+	0.891270i	$0.350185\pi$
$600$	0	0
$601$	−9262.00	−0.628627	−0.314314	−	0.949319i	$-0.601774\pi$
$601$	−9262.00	−0.628627	−0.314314	+	0.949319i	$0.601774\pi$
$602$	−1168.00	−0.0790766
$603$	0	0
$604$	−128.000	−0.00862292
$605$	0	0
$606$	0	0
$607$	−5498.00	−0.367639	−0.183820	−	0.982960i	$-0.558846\pi$
$607$	−5498.00	−0.367639	−0.183820	+	0.982960i	$0.558846\pi$
$608$	768.000	0.0512278
$609$	0	0
$610$	0	0
$611$	17280.0	1.14415
$612$	0	0
$613$	−394.000	−0.0259600	−0.0129800	−	0.999916i	$-0.504132\pi$
$613$	−394.000	−0.0259600	−0.0129800	+	0.999916i	$0.504132\pi$
$614$	15480.0	1.01746
$615$	0	0
$616$	−1120.00	−0.0732566
$617$	7370.00	0.480883	0.240442	−	0.970664i	$-0.422708\pi$
$617$	7370.00	0.480883	0.240442	+	0.970664i	$0.422708\pi$
$618$	0	0
$619$	25316.0	1.64384	0.821919	−	0.569604i	$-0.192903\pi$
$619$	25316.0	1.64384	0.821919	+	0.569604i	$0.192903\pi$
$620$	0	0
$621$	0	0
$622$	−9960.00	−0.642057
$623$	1876.00	0.120643
$624$	0	0
$625$	0	0
$626$	−1208.00	−0.0771268
$627$	0	0
$628$	10216.0	0.649145
$629$	−5588.00	−0.354226
$630$	0	0
$631$	2552.00	0.161004	0.0805020	−	0.996754i	$-0.474348\pi$
$631$	2552.00	0.161004	0.0805020	+	0.996754i	$0.474348\pi$
$632$	6336.00	0.398786
$633$	0	0
$634$	−17132.0	−1.07318
$635$	0	0
$636$	0	0
$637$	18306.0	1.13863
$638$	30240.0	1.87651
$639$	0	0
$640$	0	0
$641$	−8050.00	−0.496031	−0.248016	−	0.968756i	$-0.579778\pi$
$641$	−8050.00	−0.496031	−0.248016	+	0.968756i	$0.579778\pi$
$642$	0	0
$643$	19368.0	1.18787	0.593934	−	0.804514i	$-0.297574\pi$
$643$	19368.0	1.18787	0.593934	+	0.804514i	$0.297574\pi$
$644$	−800.000	−0.0489510
$645$	0	0
$646$	−1056.00	−0.0643154
$647$	9912.00	0.602289	0.301144	−	0.953579i	$-0.402631\pi$
$647$	9912.00	0.602289	0.301144	+	0.953579i	$0.402631\pi$
$648$	0	0
$649$	−25900.0	−1.56651
$650$	0	0
$651$	0	0
$652$	−3008.00	−0.180678
$653$	27986.0	1.67715	0.838573	−	0.544789i	$-0.183390\pi$
$653$	27986.0	1.67715	0.838573	+	0.544789i	$0.183390\pi$
$654$	0	0
$655$	0	0
$656$	3296.00	0.196169
$657$	0	0
$658$	−1280.00	−0.0758353
$659$	−7562.00	−0.447001	−0.223501	−	0.974704i	$-0.571748\pi$
$659$	−7562.00	−0.447001	−0.223501	+	0.974704i	$0.571748\pi$
$660$	0	0
$661$	20234.0	1.19064	0.595319	−	0.803490i	$-0.297026\pi$
$661$	20234.0	1.19064	0.595319	+	0.803490i	$0.297026\pi$
$662$	6944.00	0.407683
$663$	0	0
$664$	3232.00	0.188894
$665$	0	0
$666$	0	0
$667$	21600.0	1.25391
$668$	10800.0	0.625546
$669$	0	0
$670$	0	0
$671$	38500.0	2.21502
$672$	0	0
$673$	−25332.0	−1.45093	−0.725466	−	0.688258i	$-0.758376\pi$
$673$	−25332.0	−1.45093	−0.725466	+	0.688258i	$0.758376\pi$
$674$	−11336.0	−0.647843
$675$	0	0
$676$	2876.00	0.163632
$677$	−18358.0	−1.04218	−0.521090	−	0.853502i	$-0.674474\pi$
$677$	−18358.0	−1.04218	−0.521090	+	0.853502i	$0.674474\pi$
$678$	0	0
$679$	−112.000	−0.00633014
$680$	0	0
$681$	0	0
$682$	−29120.0	−1.63499
$683$	−124.000	−0.00694689	−0.00347345	−	0.999994i	$-0.501106\pi$
$683$	−124.000	−0.00694689	−0.00347345	+	0.999994i	$0.501106\pi$
$684$	0	0
$685$	0	0
$686$	−2728.00	−0.151830
$687$	0	0
$688$	−4672.00	−0.258893
$689$	21708.0	1.20030
$690$	0	0
$691$	−17456.0	−0.961009	−0.480505	−	0.876992i	$-0.659547\pi$
$691$	−17456.0	−0.961009	−0.480505	+	0.876992i	$0.659547\pi$
$692$	−5336.00	−0.293128
$693$	0	0
$694$	21672.0	1.18539
$695$	0	0
$696$	0	0
$697$	−4532.00	−0.246287
$698$	−17980.0	−0.975004
$699$	0	0
$700$	0	0
$701$	17816.0	0.959916	0.479958	−	0.877291i	$-0.340652\pi$
$701$	17816.0	0.959916	0.479958	+	0.877291i	$0.340652\pi$
$702$	0	0
$703$	6096.00	0.327048
$704$	−4480.00	−0.239839
$705$	0	0
$706$	−10156.0	−0.541397
$707$	1184.00	0.0629829
$708$	0	0
$709$	−14298.0	−0.757366	−0.378683	−	0.925526i	$-0.623623\pi$
$709$	−14298.0	−0.757366	−0.378683	+	0.925526i	$0.623623\pi$
$710$	0	0
$711$	0	0
$712$	7504.00	0.394978
$713$	−20800.0	−1.09252
$714$	0	0
$715$	0	0
$716$	6856.00	0.357850
$717$	0	0
$718$	7392.00	0.384216
$719$	18440.0	0.956462	0.478231	−	0.878234i	$-0.341278\pi$
$719$	18440.0	0.956462	0.478231	+	0.878234i	$0.341278\pi$
$720$	0	0
$721$	−124.000	−0.00640499
$722$	−12566.0	−0.647726
$723$	0	0
$724$	−16024.0	−0.822551
$725$	0	0
$726$	0	0
$727$	−9666.00	−0.493112	−0.246556	−	0.969129i	$-0.579299\pi$
$727$	−9666.00	−0.493112	−0.246556	+	0.969129i	$0.579299\pi$
$728$	−864.000	−0.0439862
$729$	0	0
$730$	0	0
$731$	6424.00	0.325035
$732$	0	0
$733$	6094.00	0.307076	0.153538	−	0.988143i	$-0.450933\pi$
$733$	6094.00	0.307076	0.153538	+	0.988143i	$0.450933\pi$
$734$	−572.000	−0.0287642
$735$	0	0
$736$	−3200.00	−0.160263
$737$	50960.0	2.54700
$738$	0	0
$739$	9952.00	0.495386	0.247693	−	0.968839i	$-0.420328\pi$
$739$	9952.00	0.495386	0.247693	+	0.968839i	$0.420328\pi$
$740$	0	0
$741$	0	0
$742$	−1608.00	−0.0795573
$743$	−2208.00	−0.109022	−0.0545112	−	0.998513i	$-0.517360\pi$
$743$	−2208.00	−0.109022	−0.0545112	+	0.998513i	$0.517360\pi$
$744$	0	0
$745$	0	0
$746$	−16524.0	−0.810974
$747$	0	0
$748$	6160.00	0.301112
$749$	168.000	0.00819571
$750$	0	0
$751$	−9400.00	−0.456739	−0.228369	−	0.973575i	$-0.573339\pi$
$751$	−9400.00	−0.456739	−0.228369	+	0.973575i	$0.573339\pi$
$752$	−5120.00	−0.248281
$753$	0	0
$754$	23328.0	1.12673
$755$	0	0
$756$	0	0
$757$	22574.0	1.08384	0.541919	−	0.840430i	$-0.317698\pi$
$757$	22574.0	1.08384	0.541919	+	0.840430i	$0.317698\pi$
$758$	−5912.00	−0.283290
$759$	0	0
$760$	0	0
$761$	−7278.00	−0.346685	−0.173343	−	0.984862i	$-0.555457\pi$
$761$	−7278.00	−0.346685	−0.173343	+	0.984862i	$0.555457\pi$
$762$	0	0
$763$	740.000	0.0351111
$764$	2736.00	0.129562
$765$	0	0
$766$	−10480.0	−0.494331
$767$	−19980.0	−0.940595
$768$	0	0
$769$	−16542.0	−0.775708	−0.387854	−	0.921721i	$-0.626784\pi$
$769$	−16542.0	−0.775708	−0.387854	+	0.921721i	$0.626784\pi$
$770$	0	0
$771$	0	0
$772$	17936.0	0.836180
$773$	−28926.0	−1.34592	−0.672960	−	0.739679i	$-0.734977\pi$
$773$	−28926.0	−1.34592	−0.672960	+	0.739679i	$0.734977\pi$
$774$	0	0
$775$	0	0
$776$	−448.000	−0.0207246
$777$	0	0
$778$	1768.00	0.0814728
$779$	4944.00	0.227390
$780$	0	0
$781$	−37800.0	−1.73187
$782$	4400.00	0.201207
$783$	0	0
$784$	−5424.00	−0.247085
$785$	0	0
$786$	0	0
$787$	−20608.0	−0.933413	−0.466706	−	0.884412i	$-0.654560\pi$
$787$	−20608.0	−0.933413	−0.466706	+	0.884412i	$0.654560\pi$
$788$	−4232.00	−0.191318
$789$	0	0
$790$	0	0
$791$	−3492.00	−0.156967
$792$	0	0
$793$	29700.0	1.32998
$794$	−6788.00	−0.303397
$795$	0	0
$796$	−4512.00	−0.200909
$797$	−41350.0	−1.83776	−0.918878	−	0.394541i	$-0.870904\pi$
$797$	−41350.0	−1.83776	−0.918878	+	0.394541i	$0.870904\pi$
$798$	0	0
$799$	7040.00	0.311711
$800$	0	0
$801$	0	0
$802$	13652.0	0.601083
$803$	42280.0	1.85807
$804$	0	0
$805$	0	0
$806$	−22464.0	−0.981713
$807$	0	0
$808$	4736.00	0.206203
$809$	−1794.00	−0.0779650	−0.0389825	−	0.999240i	$-0.512412\pi$
$809$	−1794.00	−0.0779650	−0.0389825	+	0.999240i	$0.512412\pi$
$810$	0	0
$811$	22756.0	0.985291	0.492646	−	0.870230i	$-0.336030\pi$
$811$	22756.0	0.985291	0.492646	+	0.870230i	$0.336030\pi$
$812$	−1728.00	−0.0746809
$813$	0	0
$814$	−35560.0	−1.53118
$815$	0	0
$816$	0	0
$817$	−7008.00	−0.300097
$818$	15628.0	0.667995
$819$	0	0
$820$	0	0
$821$	23632.0	1.00458	0.502291	−	0.864698i	$-0.332490\pi$
$821$	23632.0	1.00458	0.502291	+	0.864698i	$0.332490\pi$
$822$	0	0
$823$	−33210.0	−1.40660	−0.703298	−	0.710896i	$-0.748290\pi$
$823$	−33210.0	−1.40660	−0.703298	+	0.710896i	$0.748290\pi$
$824$	−496.000	−0.0209696
$825$	0	0
$826$	1480.00	0.0623436
$827$	30476.0	1.28144	0.640722	−	0.767773i	$-0.278635\pi$
$827$	30476.0	1.28144	0.640722	+	0.767773i	$0.278635\pi$
$828$	0	0
$829$	29802.0	1.24857	0.624286	−	0.781196i	$-0.285390\pi$
$829$	29802.0	1.24857	0.624286	+	0.781196i	$0.285390\pi$
$830$	0	0
$831$	0	0
$832$	−3456.00	−0.144009
$833$	7458.00	0.310209
$834$	0	0
$835$	0	0
$836$	−6720.00	−0.278010
$837$	0	0
$838$	−16580.0	−0.683468
$839$	28024.0	1.15315	0.576577	−	0.817043i	$-0.304388\pi$
$839$	28024.0	1.15315	0.576577	+	0.817043i	$0.304388\pi$
$840$	0	0
$841$	22267.0	0.912994
$842$	4220.00	0.172721
$843$	0	0
$844$	3120.00	0.127245
$845$	0	0
$846$	0	0
$847$	7138.00	0.289569
$848$	−6432.00	−0.260467
$849$	0	0
$850$	0	0
$851$	−25400.0	−1.02315
$852$	0	0
$853$	−3938.00	−0.158071	−0.0790355	−	0.996872i	$-0.525184\pi$
$853$	−3938.00	−0.158071	−0.0790355	+	0.996872i	$0.525184\pi$
$854$	−2200.00	−0.0881528
$855$	0	0
$856$	672.000	0.0268323
$857$	−8094.00	−0.322621	−0.161310	−	0.986904i	$-0.551572\pi$
$857$	−8094.00	−0.322621	−0.161310	+	0.986904i	$0.551572\pi$
$858$	0	0
$859$	9044.00	0.359229	0.179614	−	0.983737i	$-0.442515\pi$
$859$	9044.00	0.359229	0.179614	+	0.983737i	$0.442515\pi$
$860$	0	0
$861$	0	0
$862$	24160.0	0.954632
$863$	−6252.00	−0.246606	−0.123303	−	0.992369i	$-0.539349\pi$
$863$	−6252.00	−0.246606	−0.123303	+	0.992369i	$0.539349\pi$
$864$	0	0
$865$	0	0
$866$	−32984.0	−1.29427
$867$	0	0
$868$	1664.00	0.0650689
$869$	−55440.0	−2.16418
$870$	0	0
$871$	39312.0	1.52932
$872$	2960.00	0.114952
$873$	0	0
$874$	−4800.00	−0.185769
$875$	0	0
$876$	0	0
$877$	−40166.0	−1.54653	−0.773267	−	0.634081i	$-0.781379\pi$
$877$	−40166.0	−1.54653	−0.773267	+	0.634081i	$0.781379\pi$
$878$	−30096.0	−1.15682
$879$	0	0
$880$	0	0
$881$	12834.0	0.490793	0.245396	−	0.969423i	$-0.421082\pi$
$881$	12834.0	0.490793	0.245396	+	0.969423i	$0.421082\pi$
$882$	0	0
$883$	−27192.0	−1.03633	−0.518167	−	0.855279i	$-0.673386\pi$
$883$	−27192.0	−1.03633	−0.518167	+	0.855279i	$0.673386\pi$
$884$	4752.00	0.180800
$885$	0	0
$886$	−19752.0	−0.748963
$887$	42060.0	1.59215	0.796075	−	0.605198i	$-0.206906\pi$
$887$	42060.0	1.59215	0.796075	+	0.605198i	$0.206906\pi$
$888$	0	0
$889$	−3260.00	−0.122989
$890$	0	0
$891$	0	0
$892$	10280.0	0.385874
$893$	−7680.00	−0.287796
$894$	0	0
$895$	0	0
$896$	256.000	0.00954504
$897$	0	0
$898$	−34332.0	−1.27581
$899$	−44928.0	−1.66678
$900$	0	0
$901$	8844.00	0.327010
$902$	−28840.0	−1.06460
$903$	0	0
$904$	−13968.0	−0.513904
$905$	0	0
$906$	0	0
$907$	−41172.0	−1.50727	−0.753635	−	0.657293i	$-0.771701\pi$
$907$	−41172.0	−1.50727	−0.753635	+	0.657293i	$0.771701\pi$
$908$	−11344.0	−0.414608
$909$	0	0
$910$	0	0
$911$	48.0000	0.00174568	0.000872838	−	1.00000i	$-0.499722\pi$
$911$	48.0000	0.00174568	0.000872838		1.00000i	$0.499722\pi$
$912$	0	0
$913$	−28280.0	−1.02512
$914$	−29696.0	−1.07468
$915$	0	0
$916$	−2440.00	−0.0880130
$917$	1740.00	0.0626607
$918$	0	0
$919$	−34584.0	−1.24137	−0.620686	−	0.784059i	$-0.713146\pi$
$919$	−34584.0	−1.24137	−0.620686	+	0.784059i	$0.713146\pi$
$920$	0	0
$921$	0	0
$922$	2520.00	0.0900128
$923$	−29160.0	−1.03988
$924$	0	0
$925$	0	0
$926$	22476.0	0.797632
$927$	0	0
$928$	−6912.00	−0.244502
$929$	3474.00	0.122689	0.0613446	−	0.998117i	$-0.480461\pi$
$929$	3474.00	0.122689	0.0613446	+	0.998117i	$0.480461\pi$
$930$	0	0
$931$	−8136.00	−0.286409
$932$	14056.0	0.494012
$933$	0	0
$934$	29544.0	1.03502
$935$	0	0
$936$	0	0
$937$	−44408.0	−1.54829	−0.774144	−	0.633009i	$-0.781819\pi$
$937$	−44408.0	−1.54829	−0.774144	+	0.633009i	$0.781819\pi$
$938$	−2912.00	−0.101365
$939$	0	0
$940$	0	0
$941$	−20188.0	−0.699373	−0.349686	−	0.936867i	$-0.613712\pi$
$941$	−20188.0	−0.699373	−0.349686	+	0.936867i	$0.613712\pi$
$942$	0	0
$943$	−20600.0	−0.711377
$944$	5920.00	0.204110
$945$	0	0
$946$	40880.0	1.40499
$947$	−31212.0	−1.07102	−0.535509	−	0.844530i	$-0.679880\pi$
$947$	−31212.0	−1.07102	−0.535509	+	0.844530i	$0.679880\pi$
$948$	0	0
$949$	32616.0	1.11566
$950$	0	0
$951$	0	0
$952$	−352.000	−0.0119836
$953$	20182.0	0.686001	0.343001	−	0.939335i	$-0.388557\pi$
$953$	20182.0	0.686001	0.343001	+	0.939335i	$0.388557\pi$
$954$	0	0
$955$	0	0
$956$	7376.00	0.249536
$957$	0	0
$958$	12232.0	0.412524
$959$	1836.00	0.0618222
$960$	0	0
$961$	13473.0	0.452251
$962$	−27432.0	−0.919380
$963$	0	0
$964$	3928.00	0.131237
$965$	0	0
$966$	0	0
$967$	53722.0	1.78654	0.893269	−	0.449522i	$-0.148406\pi$
$967$	53722.0	1.78654	0.893269	+	0.449522i	$0.148406\pi$
$968$	28552.0	0.948033
$969$	0	0
$970$	0	0
$971$	−22554.0	−0.745409	−0.372705	−	0.927950i	$-0.621570\pi$
$971$	−22554.0	−0.745409	−0.372705	+	0.927950i	$0.621570\pi$
$972$	0	0
$973$	−1192.00	−0.0392742
$974$	−31812.0	−1.04653
$975$	0	0
$976$	−8800.00	−0.288608
$977$	−18126.0	−0.593554	−0.296777	−	0.954947i	$-0.595912\pi$
$977$	−18126.0	−0.593554	−0.296777	+	0.954947i	$0.595912\pi$
$978$	0	0
$979$	−65660.0	−2.14352
$980$	0	0
$981$	0	0
$982$	−37428.0	−1.21627
$983$	6232.00	0.202207	0.101104	−	0.994876i	$-0.467763\pi$
$983$	6232.00	0.202207	0.101104	+	0.994876i	$0.467763\pi$
$984$	0	0
$985$	0	0
$986$	9504.00	0.306967
$987$	0	0
$988$	−5184.00	−0.166928
$989$	29200.0	0.938833
$990$	0	0
$991$	15184.0	0.486716	0.243358	−	0.969937i	$-0.421751\pi$
$991$	15184.0	0.486716	0.243358	+	0.969937i	$0.421751\pi$
$992$	6656.00	0.213032
$993$	0	0
$994$	2160.00	0.0689246
$995$	0	0
$996$	0	0
$997$	29922.0	0.950491	0.475245	−	0.879853i	$-0.342359\pi$
$997$	29922.0	0.950491	0.475245	+	0.879853i	$0.342359\pi$
$998$	−8112.00	−0.257295
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.4.a.p.1.1		1
3.2	odd	2		150.4.a.d.1.1		1
5.2	odd	4		90.4.c.a.19.2		2
5.3	odd	4		90.4.c.a.19.1		2
5.4	even	2		450.4.a.e.1.1		1
12.11	even	2		1200.4.a.h.1.1		1
15.2	even	4		30.4.c.a.19.1	✓	2
15.8	even	4		30.4.c.a.19.2	yes	2
15.14	odd	2		150.4.a.f.1.1		1
20.3	even	4		720.4.f.c.289.1		2
20.7	even	4		720.4.f.c.289.2		2
60.23	odd	4		240.4.f.d.49.1		2
60.47	odd	4		240.4.f.d.49.2		2
60.59	even	2		1200.4.a.bc.1.1		1
120.53	even	4		960.4.f.c.769.1		2
120.77	even	4		960.4.f.c.769.2		2
120.83	odd	4		960.4.f.d.769.2		2
120.107	odd	4		960.4.f.d.769.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.4.c.a.19.1	✓	2	15.2	even	4
30.4.c.a.19.2	yes	2	15.8	even	4
90.4.c.a.19.1		2	5.3	odd	4
90.4.c.a.19.2		2	5.2	odd	4
150.4.a.d.1.1		1	3.2	odd	2
150.4.a.f.1.1		1	15.14	odd	2
240.4.f.d.49.1		2	60.23	odd	4
240.4.f.d.49.2		2	60.47	odd	4
450.4.a.e.1.1		1	5.4	even	2
450.4.a.p.1.1		1	1.1	even	1	trivial
720.4.f.c.289.1		2	20.3	even	4
720.4.f.c.289.2		2	20.7	even	4
960.4.f.c.769.1		2	120.53	even	4
960.4.f.c.769.2		2	120.77	even	4
960.4.f.d.769.1		2	120.107	odd	4
960.4.f.d.769.2		2	120.83	odd	4
1200.4.a.h.1.1		1	12.11	even	2
1200.4.a.bc.1.1		1	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	450.a (trivial)

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