LMFDB - Embedded newform 1520.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1520,4,Mod(1,1520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1520, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("1520.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1520.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:	$89.6829032087$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1520.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-4.00000 q^{3} +5.00000 q^{5} +32.0000 q^{7} -11.0000 q^{9} +O(q^{10})$

$q-4.00000 q^{3} +5.00000 q^{5} +32.0000 q^{7} -11.0000 q^{9} +12.0000 q^{11} -42.0000 q^{13} -20.0000 q^{15} +114.000 q^{17} -19.0000 q^{19} -128.000 q^{21} -160.000 q^{23} +25.0000 q^{25} +152.000 q^{27} +214.000 q^{29} +144.000 q^{31} -48.0000 q^{33} +160.000 q^{35} +94.0000 q^{37} +168.000 q^{39} -6.00000 q^{41} +308.000 q^{43} -55.0000 q^{45} -184.000 q^{47} +681.000 q^{49} -456.000 q^{51} -274.000 q^{53} +60.0000 q^{55} +76.0000 q^{57} -276.000 q^{59} -826.000 q^{61} -352.000 q^{63} -210.000 q^{65} -52.0000 q^{67} +640.000 q^{69} +344.000 q^{71} -166.000 q^{73} -100.000 q^{75} +384.000 q^{77} +688.000 q^{79} -311.000 q^{81} -996.000 q^{83} +570.000 q^{85} -856.000 q^{87} +1578.00 q^{89} -1344.00 q^{91} -576.000 q^{93} -95.0000 q^{95} +786.000 q^{97} -132.000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	−4.00000	−0.769800	−0.384900	−	0.922958i	$-0.625764\pi$
$3$	−4.00000	−0.769800	−0.384900	+	0.922958i	$0.625764\pi$
$4$	0	0
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0	0
$7$	32.0000	1.72784	0.863919	−	0.503631i	$-0.168003\pi$
$7$	32.0000	1.72784	0.863919	+	0.503631i	$0.168003\pi$
$8$	0	0
$9$	−11.0000	−0.407407
$10$	0	0
$11$	12.0000	0.328921	0.164461	−	0.986384i	$-0.447412\pi$
$11$	12.0000	0.328921	0.164461	+	0.986384i	$0.447412\pi$
$12$	0	0
$13$	−42.0000	−0.896054	−0.448027	−	0.894020i	$-0.647873\pi$
$13$	−42.0000	−0.896054	−0.448027	+	0.894020i	$0.647873\pi$
$14$	0	0
$15$	−20.0000	−0.344265
$16$	0	0
$17$	114.000	1.62642	0.813208	−	0.581974i	$-0.197719\pi$
$17$	114.000	1.62642	0.813208	+	0.581974i	$0.197719\pi$
$18$	0	0
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	0	0
$21$	−128.000	−1.33009
$22$	0	0
$23$	−160.000	−1.45054	−0.725268	−	0.688467i	$-0.758284\pi$
$23$	−160.000	−1.45054	−0.725268	+	0.688467i	$0.758284\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	0	0
$27$	152.000	1.08342
$28$	0	0
$29$	214.000	1.37030	0.685152	−	0.728400i	$-0.259736\pi$
$29$	214.000	1.37030	0.685152	+	0.728400i	$0.259736\pi$
$30$	0	0
$31$	144.000	0.834296	0.417148	−	0.908839i	$-0.363030\pi$
$31$	144.000	0.834296	0.417148	+	0.908839i	$0.363030\pi$
$32$	0	0
$33$	−48.0000	−0.253204
$34$	0	0
$35$	160.000	0.772712
$36$	0	0
$37$	94.0000	0.417662	0.208831	−	0.977952i	$-0.433034\pi$
$37$	94.0000	0.417662	0.208831	+	0.977952i	$0.433034\pi$
$38$	0	0
$39$	168.000	0.689783
$40$	0	0
$41$	−6.00000	−0.0228547	−0.0114273	−	0.999935i	$-0.503638\pi$
$41$	−6.00000	−0.0228547	−0.0114273	+	0.999935i	$0.503638\pi$
$42$	0	0
$43$	308.000	1.09232	0.546158	−	0.837682i	$-0.316090\pi$
$43$	308.000	1.09232	0.546158	+	0.837682i	$0.316090\pi$
$44$	0	0
$45$	−55.0000	−0.182198
$46$	0	0
$47$	−184.000	−0.571046	−0.285523	−	0.958372i	$-0.592167\pi$
$47$	−184.000	−0.571046	−0.285523	+	0.958372i	$0.592167\pi$
$48$	0	0
$49$	681.000	1.98542
$50$	0	0
$51$	−456.000	−1.25202
$52$	0	0
$53$	−274.000	−0.710128	−0.355064	−	0.934842i	$-0.615541\pi$
$53$	−274.000	−0.710128	−0.355064	+	0.934842i	$0.615541\pi$
$54$	0	0
$55$	60.0000	0.147098
$56$	0	0
$57$	76.0000	0.176604
$58$	0	0
$59$	−276.000	−0.609019	−0.304510	−	0.952509i	$-0.598493\pi$
$59$	−276.000	−0.609019	−0.304510	+	0.952509i	$0.598493\pi$
$60$	0	0
$61$	−826.000	−1.73375	−0.866873	−	0.498530i	$-0.833873\pi$
$61$	−826.000	−1.73375	−0.866873	+	0.498530i	$0.833873\pi$
$62$	0	0
$63$	−352.000	−0.703934
$64$	0	0
$65$	−210.000	−0.400728
$66$	0	0
$67$	−52.0000	−0.0948181	−0.0474090	−	0.998876i	$-0.515096\pi$
$67$	−52.0000	−0.0948181	−0.0474090	+	0.998876i	$0.515096\pi$
$68$	0	0
$69$	640.000	1.11662
$70$	0	0
$71$	344.000	0.575004	0.287502	−	0.957780i	$-0.407175\pi$
$71$	344.000	0.575004	0.287502	+	0.957780i	$0.407175\pi$
$72$	0	0
$73$	−166.000	−0.266148	−0.133074	−	0.991106i	$-0.542485\pi$
$73$	−166.000	−0.266148	−0.133074	+	0.991106i	$0.542485\pi$
$74$	0	0
$75$	−100.000	−0.153960
$76$	0	0
$77$	384.000	0.568323
$78$	0	0
$79$	688.000	0.979823	0.489912	−	0.871772i	$-0.337029\pi$
$79$	688.000	0.979823	0.489912	+	0.871772i	$0.337029\pi$
$80$	0	0
$81$	−311.000	−0.426612
$82$	0	0
$83$	−996.000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−996.000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	570.000	0.727355
$86$	0	0
$87$	−856.000	−1.05486
$88$	0	0
$89$	1578.00	1.87941	0.939706	−	0.341983i	$-0.111099\pi$
$89$	1578.00	1.87941	0.939706	+	0.341983i	$0.111099\pi$
$90$	0	0
$91$	−1344.00	−1.54824
$92$	0	0
$93$	−576.000	−0.642241
$94$	0	0
$95$	−95.0000	−0.102598
$96$	0	0
$97$	786.000	0.822744	0.411372	−	0.911467i	$-0.365050\pi$
$97$	786.000	0.822744	0.411372	+	0.911467i	$0.365050\pi$
$98$	0	0
$99$	−132.000	−0.134005
$100$	0	0
$101$	126.000	0.124133	0.0620667	−	0.998072i	$-0.480231\pi$
$101$	126.000	0.124133	0.0620667	+	0.998072i	$0.480231\pi$
$102$	0	0
$103$	368.000	0.352040	0.176020	−	0.984387i	$-0.443678\pi$
$103$	368.000	0.352040	0.176020	+	0.984387i	$0.443678\pi$
$104$	0	0
$105$	−640.000	−0.594834
$106$	0	0
$107$	−204.000	−0.184312	−0.0921562	−	0.995745i	$-0.529376\pi$
$107$	−204.000	−0.184312	−0.0921562	+	0.995745i	$0.529376\pi$
$108$	0	0
$109$	−1434.00	−1.26011	−0.630056	−	0.776549i	$-0.716968\pi$
$109$	−1434.00	−1.26011	−0.630056	+	0.776549i	$0.716968\pi$
$110$	0	0
$111$	−376.000	−0.321517
$112$	0	0
$113$	1218.00	1.01398	0.506990	−	0.861952i	$-0.330758\pi$
$113$	1218.00	1.01398	0.506990	+	0.861952i	$0.330758\pi$
$114$	0	0
$115$	−800.000	−0.648699
$116$	0	0
$117$	462.000	0.365059
$118$	0	0
$119$	3648.00	2.81018
$120$	0	0
$121$	−1187.00	−0.891811
$122$	0	0
$123$	24.0000	0.0175936
$124$	0	0
$125$	125.000	0.0894427
$126$	0	0
$127$	−904.000	−0.631630	−0.315815	−	0.948821i	$-0.602278\pi$
$127$	−904.000	−0.631630	−0.315815	+	0.948821i	$0.602278\pi$
$128$	0	0
$129$	−1232.00	−0.840865
$130$	0	0
$131$	2180.00	1.45395	0.726975	−	0.686664i	$-0.240926\pi$
$131$	2180.00	1.45395	0.726975	+	0.686664i	$0.240926\pi$
$132$	0	0
$133$	−608.000	−0.396393
$134$	0	0
$135$	760.000	0.484521
$136$	0	0
$137$	−2566.00	−1.60021	−0.800103	−	0.599863i	$-0.795222\pi$
$137$	−2566.00	−1.60021	−0.800103	+	0.599863i	$0.795222\pi$
$138$	0	0
$139$	−1988.00	−1.21309	−0.606547	−	0.795048i	$-0.707446\pi$
$139$	−1988.00	−1.21309	−0.606547	+	0.795048i	$0.707446\pi$
$140$	0	0
$141$	736.000	0.439591
$142$	0	0
$143$	−504.000	−0.294731
$144$	0	0
$145$	1070.00	0.612818
$146$	0	0
$147$	−2724.00	−1.52838
$148$	0	0
$149$	1134.00	0.623496	0.311748	−	0.950165i	$-0.399086\pi$
$149$	1134.00	0.623496	0.311748	+	0.950165i	$0.399086\pi$
$150$	0	0
$151$	2440.00	1.31500	0.657498	−	0.753456i	$-0.271615\pi$
$151$	2440.00	1.31500	0.657498	+	0.753456i	$0.271615\pi$
$152$	0	0
$153$	−1254.00	−0.662614
$154$	0	0
$155$	720.000	0.373108
$156$	0	0
$157$	3238.00	1.64599	0.822995	−	0.568048i	$-0.192301\pi$
$157$	3238.00	1.64599	0.822995	+	0.568048i	$0.192301\pi$
$158$	0	0
$159$	1096.00	0.546657
$160$	0	0
$161$	−5120.00	−2.50629
$162$	0	0
$163$	1420.00	0.682350	0.341175	−	0.940000i	$-0.389175\pi$
$163$	1420.00	0.682350	0.341175	+	0.940000i	$0.389175\pi$
$164$	0	0
$165$	−240.000	−0.113236
$166$	0	0
$167$	2336.00	1.08243	0.541213	−	0.840886i	$-0.317965\pi$
$167$	2336.00	1.08243	0.541213	+	0.840886i	$0.317965\pi$
$168$	0	0
$169$	−433.000	−0.197087
$170$	0	0
$171$	209.000	0.0934657
$172$	0	0
$173$	1206.00	0.530003	0.265001	−	0.964248i	$-0.414628\pi$
$173$	1206.00	0.530003	0.265001	+	0.964248i	$0.414628\pi$
$174$	0	0
$175$	800.000	0.345568
$176$	0	0
$177$	1104.00	0.468823
$178$	0	0
$179$	1412.00	0.589597	0.294798	−	0.955559i	$-0.404747\pi$
$179$	1412.00	0.589597	0.294798	+	0.955559i	$0.404747\pi$
$180$	0	0
$181$	3742.00	1.53669	0.768344	−	0.640037i	$-0.221081\pi$
$181$	3742.00	1.53669	0.768344	+	0.640037i	$0.221081\pi$
$182$	0	0
$183$	3304.00	1.33464
$184$	0	0
$185$	470.000	0.186784
$186$	0	0
$187$	1368.00	0.534963
$188$	0	0
$189$	4864.00	1.87198
$190$	0	0
$191$	1472.00	0.557645	0.278822	−	0.960343i	$-0.410056\pi$
$191$	1472.00	0.557645	0.278822	+	0.960343i	$0.410056\pi$
$192$	0	0
$193$	1458.00	0.543778	0.271889	−	0.962329i	$-0.412352\pi$
$193$	1458.00	0.543778	0.271889	+	0.962329i	$0.412352\pi$
$194$	0	0
$195$	840.000	0.308480
$196$	0	0
$197$	2046.00	0.739957	0.369978	−	0.929040i	$-0.379365\pi$
$197$	2046.00	0.739957	0.369978	+	0.929040i	$0.379365\pi$
$198$	0	0
$199$	1496.00	0.532908	0.266454	−	0.963848i	$-0.414148\pi$
$199$	1496.00	0.532908	0.266454	+	0.963848i	$0.414148\pi$
$200$	0	0
$201$	208.000	0.0729910
$202$	0	0
$203$	6848.00	2.36766
$204$	0	0
$205$	−30.0000	−0.0102209
$206$	0	0
$207$	1760.00	0.590959
$208$	0	0
$209$	−228.000	−0.0754598
$210$	0	0
$211$	−844.000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−844.000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	0	0
$213$	−1376.00	−0.442638
$214$	0	0
$215$	1540.00	0.488498
$216$	0	0
$217$	4608.00	1.44153
$218$	0	0
$219$	664.000	0.204881
$220$	0	0
$221$	−4788.00	−1.45736
$222$	0	0
$223$	3400.00	1.02099	0.510495	−	0.859881i	$-0.329462\pi$
$223$	3400.00	1.02099	0.510495	+	0.859881i	$0.329462\pi$
$224$	0	0
$225$	−275.000	−0.0814815
$226$	0	0
$227$	−1844.00	−0.539166	−0.269583	−	0.962977i	$-0.586886\pi$
$227$	−1844.00	−0.539166	−0.269583	+	0.962977i	$0.586886\pi$
$228$	0	0
$229$	−1090.00	−0.314538	−0.157269	−	0.987556i	$-0.550269\pi$
$229$	−1090.00	−0.314538	−0.157269	+	0.987556i	$0.550269\pi$
$230$	0	0
$231$	−1536.00	−0.437495
$232$	0	0
$233$	2842.00	0.799080	0.399540	−	0.916716i	$-0.369170\pi$
$233$	2842.00	0.799080	0.399540	+	0.916716i	$0.369170\pi$
$234$	0	0
$235$	−920.000	−0.255380
$236$	0	0
$237$	−2752.00	−0.754268
$238$	0	0
$239$	2400.00	0.649553	0.324776	−	0.945791i	$-0.394711\pi$
$239$	2400.00	0.649553	0.324776	+	0.945791i	$0.394711\pi$
$240$	0	0
$241$	2130.00	0.569317	0.284658	−	0.958629i	$-0.408120\pi$
$241$	2130.00	0.569317	0.284658	+	0.958629i	$0.408120\pi$
$242$	0	0
$243$	−2860.00	−0.755017
$244$	0	0
$245$	3405.00	0.887908
$246$	0	0
$247$	798.000	0.205569
$248$	0	0
$249$	3984.00	1.01396
$250$	0	0
$251$	2364.00	0.594480	0.297240	−	0.954803i	$-0.403934\pi$
$251$	2364.00	0.594480	0.297240	+	0.954803i	$0.403934\pi$
$252$	0	0
$253$	−1920.00	−0.477112
$254$	0	0
$255$	−2280.00	−0.559918
$256$	0	0
$257$	6290.00	1.52669	0.763345	−	0.645991i	$-0.223556\pi$
$257$	6290.00	1.52669	0.763345	+	0.645991i	$0.223556\pi$
$258$	0	0
$259$	3008.00	0.721653
$260$	0	0
$261$	−2354.00	−0.558272
$262$	0	0
$263$	−8112.00	−1.90193	−0.950965	−	0.309300i	$-0.899905\pi$
$263$	−8112.00	−1.90193	−0.950965	+	0.309300i	$0.899905\pi$
$264$	0	0
$265$	−1370.00	−0.317579
$266$	0	0
$267$	−6312.00	−1.44677
$268$	0	0
$269$	−4794.00	−1.08660	−0.543300	−	0.839539i	$-0.682825\pi$
$269$	−4794.00	−1.08660	−0.543300	+	0.839539i	$0.682825\pi$
$270$	0	0
$271$	−304.000	−0.0681427	−0.0340714	−	0.999419i	$-0.510847\pi$
$271$	−304.000	−0.0681427	−0.0340714	+	0.999419i	$0.510847\pi$
$272$	0	0
$273$	5376.00	1.19183
$274$	0	0
$275$	300.000	0.0657843
$276$	0	0
$277$	2062.00	0.447269	0.223635	−	0.974673i	$-0.428208\pi$
$277$	2062.00	0.447269	0.223635	+	0.974673i	$0.428208\pi$
$278$	0	0
$279$	−1584.00	−0.339898
$280$	0	0
$281$	−4054.00	−0.860645	−0.430323	−	0.902675i	$-0.641600\pi$
$281$	−4054.00	−0.860645	−0.430323	+	0.902675i	$0.641600\pi$
$282$	0	0
$283$	−7996.00	−1.67955	−0.839775	−	0.542934i	$-0.817313\pi$
$283$	−7996.00	−1.67955	−0.839775	+	0.542934i	$0.817313\pi$
$284$	0	0
$285$	380.000	0.0789799
$286$	0	0
$287$	−192.000	−0.0394892
$288$	0	0
$289$	8083.00	1.64523
$290$	0	0
$291$	−3144.00	−0.633349
$292$	0	0
$293$	−3906.00	−0.778809	−0.389404	−	0.921067i	$-0.627319\pi$
$293$	−3906.00	−0.778809	−0.389404	+	0.921067i	$0.627319\pi$
$294$	0	0
$295$	−1380.00	−0.272362
$296$	0	0
$297$	1824.00	0.356361
$298$	0	0
$299$	6720.00	1.29976
$300$	0	0
$301$	9856.00	1.88734
$302$	0	0
$303$	−504.000	−0.0955579
$304$	0	0
$305$	−4130.00	−0.775354
$306$	0	0
$307$	1820.00	0.338348	0.169174	−	0.985586i	$-0.445890\pi$
$307$	1820.00	0.338348	0.169174	+	0.985586i	$0.445890\pi$
$308$	0	0
$309$	−1472.00	−0.271000
$310$	0	0
$311$	−712.000	−0.129819	−0.0649097	−	0.997891i	$-0.520676\pi$
$311$	−712.000	−0.129819	−0.0649097	+	0.997891i	$0.520676\pi$
$312$	0	0
$313$	9130.00	1.64875	0.824374	−	0.566046i	$-0.191527\pi$
$313$	9130.00	1.64875	0.824374	+	0.566046i	$0.191527\pi$
$314$	0	0
$315$	−1760.00	−0.314809
$316$	0	0
$317$	6342.00	1.12367	0.561833	−	0.827251i	$-0.310096\pi$
$317$	6342.00	1.12367	0.561833	+	0.827251i	$0.310096\pi$
$318$	0	0
$319$	2568.00	0.450722
$320$	0	0
$321$	816.000	0.141884
$322$	0	0
$323$	−2166.00	−0.373125
$324$	0	0
$325$	−1050.00	−0.179211
$326$	0	0
$327$	5736.00	0.970035
$328$	0	0
$329$	−5888.00	−0.986675
$330$	0	0
$331$	4748.00	0.788440	0.394220	−	0.919016i	$-0.371015\pi$
$331$	4748.00	0.788440	0.394220	+	0.919016i	$0.371015\pi$
$332$	0	0
$333$	−1034.00	−0.170159
$334$	0	0
$335$	−260.000	−0.0424039
$336$	0	0
$337$	5154.00	0.833105	0.416552	−	0.909112i	$-0.363238\pi$
$337$	5154.00	0.833105	0.416552	+	0.909112i	$0.363238\pi$
$338$	0	0
$339$	−4872.00	−0.780563
$340$	0	0
$341$	1728.00	0.274418
$342$	0	0
$343$	10816.0	1.70265
$344$	0	0
$345$	3200.00	0.499369
$346$	0	0
$347$	12148.0	1.87936	0.939681	−	0.342051i	$-0.111122\pi$
$347$	12148.0	1.87936	0.939681	+	0.342051i	$0.111122\pi$
$348$	0	0
$349$	−602.000	−0.0923333	−0.0461666	−	0.998934i	$-0.514701\pi$
$349$	−602.000	−0.0923333	−0.0461666	+	0.998934i	$0.514701\pi$
$350$	0	0
$351$	−6384.00	−0.970805
$352$	0	0
$353$	2.00000	0.000301556 0	0.000150778	−	1.00000i	$-0.499952\pi$
$353$	2.00000	0.000301556 0	0.000150778		1.00000i	$0.499952\pi$
$354$	0	0
$355$	1720.00	0.257150
$356$	0	0
$357$	−14592.0	−2.16328
$358$	0	0
$359$	−1960.00	−0.288147	−0.144074	−	0.989567i	$-0.546020\pi$
$359$	−1960.00	−0.288147	−0.144074	+	0.989567i	$0.546020\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	0	0
$363$	4748.00	0.686516
$364$	0	0
$365$	−830.000	−0.119025
$366$	0	0
$367$	5864.00	0.834055	0.417028	−	0.908894i	$-0.363072\pi$
$367$	5864.00	0.834055	0.417028	+	0.908894i	$0.363072\pi$
$368$	0	0
$369$	66.0000	0.00931117
$370$	0	0
$371$	−8768.00	−1.22699
$372$	0	0
$373$	558.000	0.0774588	0.0387294	−	0.999250i	$-0.487669\pi$
$373$	558.000	0.0774588	0.0387294	+	0.999250i	$0.487669\pi$
$374$	0	0
$375$	−500.000	−0.0688530
$376$	0	0
$377$	−8988.00	−1.22787
$378$	0	0
$379$	4876.00	0.660853	0.330427	−	0.943832i	$-0.392807\pi$
$379$	4876.00	0.660853	0.330427	+	0.943832i	$0.392807\pi$
$380$	0	0
$381$	3616.00	0.486229
$382$	0	0
$383$	424.000	0.0565676	0.0282838	−	0.999600i	$-0.490996\pi$
$383$	424.000	0.0565676	0.0282838	+	0.999600i	$0.490996\pi$
$384$	0	0
$385$	1920.00	0.254162
$386$	0	0
$387$	−3388.00	−0.445017
$388$	0	0
$389$	−9890.00	−1.28906	−0.644528	−	0.764581i	$-0.722946\pi$
$389$	−9890.00	−1.28906	−0.644528	+	0.764581i	$0.722946\pi$
$390$	0	0
$391$	−18240.0	−2.35917
$392$	0	0
$393$	−8720.00	−1.11925
$394$	0	0
$395$	3440.00	0.438190
$396$	0	0
$397$	−234.000	−0.0295822	−0.0147911	−	0.999891i	$-0.504708\pi$
$397$	−234.000	−0.0295822	−0.0147911	+	0.999891i	$0.504708\pi$
$398$	0	0
$399$	2432.00	0.305144
$400$	0	0
$401$	11602.0	1.44483	0.722414	−	0.691461i	$-0.243032\pi$
$401$	11602.0	1.44483	0.722414	+	0.691461i	$0.243032\pi$
$402$	0	0
$403$	−6048.00	−0.747574
$404$	0	0
$405$	−1555.00	−0.190787
$406$	0	0
$407$	1128.00	0.137378
$408$	0	0
$409$	−14806.0	−1.79000	−0.894999	−	0.446067i	$-0.852824\pi$
$409$	−14806.0	−1.79000	−0.894999	+	0.446067i	$0.852824\pi$
$410$	0	0
$411$	10264.0	1.23184
$412$	0	0
$413$	−8832.00	−1.05229
$414$	0	0
$415$	−4980.00	−0.589057
$416$	0	0
$417$	7952.00	0.933840
$418$	0	0
$419$	−6252.00	−0.728950	−0.364475	−	0.931213i	$-0.618752\pi$
$419$	−6252.00	−0.728950	−0.364475	+	0.931213i	$0.618752\pi$
$420$	0	0
$421$	−10482.0	−1.21345	−0.606724	−	0.794913i	$-0.707517\pi$
$421$	−10482.0	−1.21345	−0.606724	+	0.794913i	$0.707517\pi$
$422$	0	0
$423$	2024.00	0.232648
$424$	0	0
$425$	2850.00	0.325283
$426$	0	0
$427$	−26432.0	−2.99563
$428$	0	0
$429$	2016.00	0.226884
$430$	0	0
$431$	−3936.00	−0.439885	−0.219943	−	0.975513i	$-0.570587\pi$
$431$	−3936.00	−0.439885	−0.219943	+	0.975513i	$0.570587\pi$
$432$	0	0
$433$	10946.0	1.21485	0.607426	−	0.794376i	$-0.292202\pi$
$433$	10946.0	1.21485	0.607426	+	0.794376i	$0.292202\pi$
$434$	0	0
$435$	−4280.00	−0.471748
$436$	0	0
$437$	3040.00	0.332776
$438$	0	0
$439$	7800.00	0.848004	0.424002	−	0.905661i	$-0.360625\pi$
$439$	7800.00	0.848004	0.424002	+	0.905661i	$0.360625\pi$
$440$	0	0
$441$	−7491.00	−0.808876
$442$	0	0
$443$	11364.0	1.21878	0.609390	−	0.792870i	$-0.291414\pi$
$443$	11364.0	1.21878	0.609390	+	0.792870i	$0.291414\pi$
$444$	0	0
$445$	7890.00	0.840499
$446$	0	0
$447$	−4536.00	−0.479967
$448$	0	0
$449$	7330.00	0.770432	0.385216	−	0.922826i	$-0.374127\pi$
$449$	7330.00	0.770432	0.385216	+	0.922826i	$0.374127\pi$
$450$	0	0
$451$	−72.0000	−0.00751740
$452$	0	0
$453$	−9760.00	−1.01228
$454$	0	0
$455$	−6720.00	−0.692392
$456$	0	0
$457$	−12774.0	−1.30753	−0.653766	−	0.756696i	$-0.726812\pi$
$457$	−12774.0	−1.30753	−0.653766	+	0.756696i	$0.726812\pi$
$458$	0	0
$459$	17328.0	1.76210
$460$	0	0
$461$	−3786.00	−0.382498	−0.191249	−	0.981542i	$-0.561254\pi$
$461$	−3786.00	−0.382498	−0.191249	+	0.981542i	$0.561254\pi$
$462$	0	0
$463$	19448.0	1.95211	0.976053	−	0.217532i	$-0.0698007\pi$
$463$	19448.0	1.95211	0.976053	+	0.217532i	$0.0698007\pi$
$464$	0	0
$465$	−2880.00	−0.287219
$466$	0	0
$467$	−4596.00	−0.455412	−0.227706	−	0.973730i	$-0.573123\pi$
$467$	−4596.00	−0.455412	−0.227706	+	0.973730i	$0.573123\pi$
$468$	0	0
$469$	−1664.00	−0.163830
$470$	0	0
$471$	−12952.0	−1.26708
$472$	0	0
$473$	3696.00	0.359286
$474$	0	0
$475$	−475.000	−0.0458831
$476$	0	0
$477$	3014.00	0.289311
$478$	0	0
$479$	−12432.0	−1.18587	−0.592936	−	0.805250i	$-0.702031\pi$
$479$	−12432.0	−1.18587	−0.592936	+	0.805250i	$0.702031\pi$
$480$	0	0
$481$	−3948.00	−0.374248
$482$	0	0
$483$	20480.0	1.92934
$484$	0	0
$485$	3930.00	0.367942
$486$	0	0
$487$	18016.0	1.67635	0.838175	−	0.545401i	$-0.183622\pi$
$487$	18016.0	1.67635	0.838175	+	0.545401i	$0.183622\pi$
$488$	0	0
$489$	−5680.00	−0.525273
$490$	0	0
$491$	−1972.00	−0.181253	−0.0906264	−	0.995885i	$-0.528887\pi$
$491$	−1972.00	−0.181253	−0.0906264	+	0.995885i	$0.528887\pi$
$492$	0	0
$493$	24396.0	2.22868
$494$	0	0
$495$	−660.000	−0.0599289
$496$	0	0
$497$	11008.0	0.993514
$498$	0	0
$499$	−18780.0	−1.68479	−0.842393	−	0.538864i	$-0.818854\pi$
$499$	−18780.0	−1.68479	−0.842393	+	0.538864i	$0.818854\pi$
$500$	0	0
$501$	−9344.00	−0.833252
$502$	0	0
$503$	−8256.00	−0.731843	−0.365921	−	0.930646i	$-0.619246\pi$
$503$	−8256.00	−0.731843	−0.365921	+	0.930646i	$0.619246\pi$
$504$	0	0
$505$	630.000	0.0555141
$506$	0	0
$507$	1732.00	0.151718
$508$	0	0
$509$	−13290.0	−1.15731	−0.578653	−	0.815574i	$-0.696421\pi$
$509$	−13290.0	−1.15731	−0.578653	+	0.815574i	$0.696421\pi$
$510$	0	0
$511$	−5312.00	−0.459861
$512$	0	0
$513$	−2888.00	−0.248554
$514$	0	0
$515$	1840.00	0.157437
$516$	0	0
$517$	−2208.00	−0.187829
$518$	0	0
$519$	−4824.00	−0.407996
$520$	0	0
$521$	7610.00	0.639924	0.319962	−	0.947430i	$-0.396330\pi$
$521$	7610.00	0.639924	0.319962	+	0.947430i	$0.396330\pi$
$522$	0	0
$523$	13636.0	1.14008	0.570039	−	0.821618i	$-0.306928\pi$
$523$	13636.0	1.14008	0.570039	+	0.821618i	$0.306928\pi$
$524$	0	0
$525$	−3200.00	−0.266018
$526$	0	0
$527$	16416.0	1.35691
$528$	0	0
$529$	13433.0	1.10405
$530$	0	0
$531$	3036.00	0.248119
$532$	0	0
$533$	252.000	0.0204790
$534$	0	0
$535$	−1020.00	−0.0824270
$536$	0	0
$537$	−5648.00	−0.453872
$538$	0	0
$539$	8172.00	0.653048
$540$	0	0
$541$	1350.00	0.107285	0.0536424	−	0.998560i	$-0.482917\pi$
$541$	1350.00	0.107285	0.0536424	+	0.998560i	$0.482917\pi$
$542$	0	0
$543$	−14968.0	−1.18294
$544$	0	0
$545$	−7170.00	−0.563540
$546$	0	0
$547$	20396.0	1.59428	0.797139	−	0.603796i	$-0.206346\pi$
$547$	20396.0	1.59428	0.797139	+	0.603796i	$0.206346\pi$
$548$	0	0
$549$	9086.00	0.706341
$550$	0	0
$551$	−4066.00	−0.314369
$552$	0	0
$553$	22016.0	1.69298
$554$	0	0
$555$	−1880.00	−0.143787
$556$	0	0
$557$	−4458.00	−0.339123	−0.169562	−	0.985520i	$-0.554235\pi$
$557$	−4458.00	−0.339123	−0.169562	+	0.985520i	$0.554235\pi$
$558$	0	0
$559$	−12936.0	−0.978774
$560$	0	0
$561$	−5472.00	−0.411815
$562$	0	0
$563$	−18228.0	−1.36451	−0.682255	−	0.731115i	$-0.739000\pi$
$563$	−18228.0	−1.36451	−0.682255	+	0.731115i	$0.739000\pi$
$564$	0	0
$565$	6090.00	0.453466
$566$	0	0
$567$	−9952.00	−0.737116
$568$	0	0
$569$	−8246.00	−0.607540	−0.303770	−	0.952745i	$-0.598245\pi$
$569$	−8246.00	−0.607540	−0.303770	+	0.952745i	$0.598245\pi$
$570$	0	0
$571$	924.000	0.0677201	0.0338601	−	0.999427i	$-0.489220\pi$
$571$	924.000	0.0677201	0.0338601	+	0.999427i	$0.489220\pi$
$572$	0	0
$573$	−5888.00	−0.429275
$574$	0	0
$575$	−4000.00	−0.290107
$576$	0	0
$577$	16322.0	1.17763	0.588816	−	0.808267i	$-0.299594\pi$
$577$	16322.0	1.17763	0.588816	+	0.808267i	$0.299594\pi$
$578$	0	0
$579$	−5832.00	−0.418600
$580$	0	0
$581$	−31872.0	−2.27586
$582$	0	0
$583$	−3288.00	−0.233576
$584$	0	0
$585$	2310.00	0.163259
$586$	0	0
$587$	−17500.0	−1.23050	−0.615249	−	0.788333i	$-0.710945\pi$
$587$	−17500.0	−1.23050	−0.615249	+	0.788333i	$0.710945\pi$
$588$	0	0
$589$	−2736.00	−0.191401
$590$	0	0
$591$	−8184.00	−0.569619
$592$	0	0
$593$	−1486.00	−0.102905	−0.0514525	−	0.998675i	$-0.516385\pi$
$593$	−1486.00	−0.102905	−0.0514525	+	0.998675i	$0.516385\pi$
$594$	0	0
$595$	18240.0	1.25675
$596$	0	0
$597$	−5984.00	−0.410233
$598$	0	0
$599$	−24616.0	−1.67910	−0.839551	−	0.543280i	$-0.817182\pi$
$599$	−24616.0	−1.67910	−0.839551	+	0.543280i	$0.817182\pi$
$600$	0	0
$601$	−13334.0	−0.905000	−0.452500	−	0.891764i	$-0.649468\pi$
$601$	−13334.0	−0.905000	−0.452500	+	0.891764i	$0.649468\pi$
$602$	0	0
$603$	572.000	0.0386296
$604$	0	0
$605$	−5935.00	−0.398830
$606$	0	0
$607$	12056.0	0.806158	0.403079	−	0.915165i	$-0.367940\pi$
$607$	12056.0	0.806158	0.403079	+	0.915165i	$0.367940\pi$
$608$	0	0
$609$	−27392.0	−1.82263
$610$	0	0
$611$	7728.00	0.511688
$612$	0	0
$613$	−98.0000	−0.00645707	−0.00322853	−	0.999995i	$-0.501028\pi$
$613$	−98.0000	−0.00645707	−0.00322853	+	0.999995i	$0.501028\pi$
$614$	0	0
$615$	120.000	0.00786808
$616$	0	0
$617$	2938.00	0.191701	0.0958504	−	0.995396i	$-0.469443\pi$
$617$	2938.00	0.191701	0.0958504	+	0.995396i	$0.469443\pi$
$618$	0	0
$619$	−25316.0	−1.64384	−0.821919	−	0.569604i	$-0.807097\pi$
$619$	−25316.0	−1.64384	−0.821919	+	0.569604i	$0.807097\pi$
$620$	0	0
$621$	−24320.0	−1.57154
$622$	0	0
$623$	50496.0	3.24732
$624$	0	0
$625$	625.000	0.0400000
$626$	0	0
$627$	912.000	0.0580890
$628$	0	0
$629$	10716.0	0.679292
$630$	0	0
$631$	−1256.00	−0.0792402	−0.0396201	−	0.999215i	$-0.512615\pi$
$631$	−1256.00	−0.0792402	−0.0396201	+	0.999215i	$0.512615\pi$
$632$	0	0
$633$	3376.00	0.211981
$634$	0	0
$635$	−4520.00	−0.282474
$636$	0	0
$637$	−28602.0	−1.77905
$638$	0	0
$639$	−3784.00	−0.234261
$640$	0	0
$641$	20290.0	1.25024	0.625122	−	0.780527i	$-0.285049\pi$
$641$	20290.0	1.25024	0.625122	+	0.780527i	$0.285049\pi$
$642$	0	0
$643$	−10676.0	−0.654775	−0.327388	−	0.944890i	$-0.606168\pi$
$643$	−10676.0	−0.654775	−0.327388	+	0.944890i	$0.606168\pi$
$644$	0	0
$645$	−6160.00	−0.376046
$646$	0	0
$647$	−11264.0	−0.684441	−0.342221	−	0.939620i	$-0.611179\pi$
$647$	−11264.0	−0.684441	−0.342221	+	0.939620i	$0.611179\pi$
$648$	0	0
$649$	−3312.00	−0.200320
$650$	0	0
$651$	−18432.0	−1.10969
$652$	0	0
$653$	25878.0	1.55082	0.775409	−	0.631459i	$-0.217544\pi$
$653$	25878.0	1.55082	0.775409	+	0.631459i	$0.217544\pi$
$654$	0	0
$655$	10900.0	0.650226
$656$	0	0
$657$	1826.00	0.108431
$658$	0	0
$659$	−1500.00	−0.0886672	−0.0443336	−	0.999017i	$-0.514116\pi$
$659$	−1500.00	−0.0886672	−0.0443336	+	0.999017i	$0.514116\pi$
$660$	0	0
$661$	−7618.00	−0.448269	−0.224135	−	0.974558i	$-0.571956\pi$
$661$	−7618.00	−0.448269	−0.224135	+	0.974558i	$0.571956\pi$
$662$	0	0
$663$	19152.0	1.12187
$664$	0	0
$665$	−3040.00	−0.177272
$666$	0	0
$667$	−34240.0	−1.98767
$668$	0	0
$669$	−13600.0	−0.785959
$670$	0	0
$671$	−9912.00	−0.570266
$672$	0	0
$673$	−4110.00	−0.235407	−0.117703	−	0.993049i	$-0.537553\pi$
$673$	−4110.00	−0.235407	−0.117703	+	0.993049i	$0.537553\pi$
$674$	0	0
$675$	3800.00	0.216685
$676$	0	0
$677$	−21474.0	−1.21907	−0.609537	−	0.792758i	$-0.708645\pi$
$677$	−21474.0	−1.21907	−0.609537	+	0.792758i	$0.708645\pi$
$678$	0	0
$679$	25152.0	1.42157
$680$	0	0
$681$	7376.00	0.415050
$682$	0	0
$683$	−4668.00	−0.261517	−0.130758	−	0.991414i	$-0.541741\pi$
$683$	−4668.00	−0.261517	−0.130758	+	0.991414i	$0.541741\pi$
$684$	0	0
$685$	−12830.0	−0.715634
$686$	0	0
$687$	4360.00	0.242132
$688$	0	0
$689$	11508.0	0.636313
$690$	0	0
$691$	−13292.0	−0.731768	−0.365884	−	0.930661i	$-0.619233\pi$
$691$	−13292.0	−0.731768	−0.365884	+	0.930661i	$0.619233\pi$
$692$	0	0
$693$	−4224.00	−0.231539
$694$	0	0
$695$	−9940.00	−0.542512
$696$	0	0
$697$	−684.000	−0.0371712
$698$	0	0
$699$	−11368.0	−0.615132
$700$	0	0
$701$	7206.00	0.388255	0.194128	−	0.980976i	$-0.437812\pi$
$701$	7206.00	0.388255	0.194128	+	0.980976i	$0.437812\pi$
$702$	0	0
$703$	−1786.00	−0.0958183
$704$	0	0
$705$	3680.00	0.196591
$706$	0	0
$707$	4032.00	0.214482
$708$	0	0
$709$	−5666.00	−0.300128	−0.150064	−	0.988676i	$-0.547948\pi$
$709$	−5666.00	−0.300128	−0.150064	+	0.988676i	$0.547948\pi$
$710$	0	0
$711$	−7568.00	−0.399187
$712$	0	0
$713$	−23040.0	−1.21018
$714$	0	0
$715$	−2520.00	−0.131808
$716$	0	0
$717$	−9600.00	−0.500026
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	11776.0	0.608268
$722$	0	0
$723$	−8520.00	−0.438260
$724$	0	0
$725$	5350.00	0.274061
$726$	0	0
$727$	4048.00	0.206509	0.103254	−	0.994655i	$-0.467074\pi$
$727$	4048.00	0.206509	0.103254	+	0.994655i	$0.467074\pi$
$728$	0	0
$729$	19837.0	1.00782
$730$	0	0
$731$	35112.0	1.77656
$732$	0	0
$733$	12134.0	0.611432	0.305716	−	0.952123i	$-0.401104\pi$
$733$	12134.0	0.611432	0.305716	+	0.952123i	$0.401104\pi$
$734$	0	0
$735$	−13620.0	−0.683512
$736$	0	0
$737$	−624.000	−0.0311877
$738$	0	0
$739$	13556.0	0.674784	0.337392	−	0.941364i	$-0.390455\pi$
$739$	13556.0	0.674784	0.337392	+	0.941364i	$0.390455\pi$
$740$	0	0
$741$	−3192.00	−0.158247
$742$	0	0
$743$	−4368.00	−0.215675	−0.107837	−	0.994169i	$-0.534393\pi$
$743$	−4368.00	−0.215675	−0.107837	+	0.994169i	$0.534393\pi$
$744$	0	0
$745$	5670.00	0.278836
$746$	0	0
$747$	10956.0	0.536625
$748$	0	0
$749$	−6528.00	−0.318462
$750$	0	0
$751$	−3872.00	−0.188138	−0.0940688	−	0.995566i	$-0.529987\pi$
$751$	−3872.00	−0.188138	−0.0940688	+	0.995566i	$0.529987\pi$
$752$	0	0
$753$	−9456.00	−0.457631
$754$	0	0
$755$	12200.0	0.588084
$756$	0	0
$757$	6190.00	0.297199	0.148599	−	0.988897i	$-0.452524\pi$
$757$	6190.00	0.297199	0.148599	+	0.988897i	$0.452524\pi$
$758$	0	0
$759$	7680.00	0.367281
$760$	0	0
$761$	−7062.00	−0.336396	−0.168198	−	0.985753i	$-0.553795\pi$
$761$	−7062.00	−0.336396	−0.168198	+	0.985753i	$0.553795\pi$
$762$	0	0
$763$	−45888.0	−2.17727
$764$	0	0
$765$	−6270.00	−0.296330
$766$	0	0
$767$	11592.0	0.545714
$768$	0	0
$769$	−5438.00	−0.255006	−0.127503	−	0.991838i	$-0.540696\pi$
$769$	−5438.00	−0.255006	−0.127503	+	0.991838i	$0.540696\pi$
$770$	0	0
$771$	−25160.0	−1.17525
$772$	0	0
$773$	1182.00	0.0549982	0.0274991	−	0.999622i	$-0.491246\pi$
$773$	1182.00	0.0549982	0.0274991	+	0.999622i	$0.491246\pi$
$774$	0	0
$775$	3600.00	0.166859
$776$	0	0
$777$	−12032.0	−0.555528
$778$	0	0
$779$	114.000	0.00524323
$780$	0	0
$781$	4128.00	0.189131
$782$	0	0
$783$	32528.0	1.48462
$784$	0	0
$785$	16190.0	0.736109
$786$	0	0
$787$	−12452.0	−0.563997	−0.281999	−	0.959415i	$-0.590997\pi$
$787$	−12452.0	−0.563997	−0.281999	+	0.959415i	$0.590997\pi$
$788$	0	0
$789$	32448.0	1.46411
$790$	0	0
$791$	38976.0	1.75199
$792$	0	0
$793$	34692.0	1.55353
$794$	0	0
$795$	5480.00	0.244472
$796$	0	0
$797$	15526.0	0.690037	0.345018	−	0.938596i	$-0.387873\pi$
$797$	15526.0	0.690037	0.345018	+	0.938596i	$0.387873\pi$
$798$	0	0
$799$	−20976.0	−0.928758
$800$	0	0
$801$	−17358.0	−0.765686
$802$	0	0
$803$	−1992.00	−0.0875419
$804$	0	0
$805$	−25600.0	−1.12085
$806$	0	0
$807$	19176.0	0.836465
$808$	0	0
$809$	31034.0	1.34870	0.674349	−	0.738412i	$-0.264424\pi$
$809$	31034.0	1.34870	0.674349	+	0.738412i	$0.264424\pi$
$810$	0	0
$811$	34636.0	1.49967	0.749836	−	0.661623i	$-0.230132\pi$
$811$	34636.0	1.49967	0.749836	+	0.661623i	$0.230132\pi$
$812$	0	0
$813$	1216.00	0.0524563
$814$	0	0
$815$	7100.00	0.305156
$816$	0	0
$817$	−5852.00	−0.250594
$818$	0	0
$819$	14784.0	0.630763
$820$	0	0
$821$	−20082.0	−0.853674	−0.426837	−	0.904328i	$-0.640372\pi$
$821$	−20082.0	−0.853674	−0.426837	+	0.904328i	$0.640372\pi$
$822$	0	0
$823$	−33568.0	−1.42176	−0.710879	−	0.703314i	$-0.751703\pi$
$823$	−33568.0	−1.42176	−0.710879	+	0.703314i	$0.751703\pi$
$824$	0	0
$825$	−1200.00	−0.0506408
$826$	0	0
$827$	−19644.0	−0.825984	−0.412992	−	0.910735i	$-0.635516\pi$
$827$	−19644.0	−0.825984	−0.412992	+	0.910735i	$0.635516\pi$
$828$	0	0
$829$	726.000	0.0304162	0.0152081	−	0.999884i	$-0.495159\pi$
$829$	726.000	0.0304162	0.0152081	+	0.999884i	$0.495159\pi$
$830$	0	0
$831$	−8248.00	−0.344308
$832$	0	0
$833$	77634.0	3.22912
$834$	0	0
$835$	11680.0	0.484076
$836$	0	0
$837$	21888.0	0.903895
$838$	0	0
$839$	−3512.00	−0.144515	−0.0722573	−	0.997386i	$-0.523020\pi$
$839$	−3512.00	−0.144515	−0.0722573	+	0.997386i	$0.523020\pi$
$840$	0	0
$841$	21407.0	0.877732
$842$	0	0
$843$	16216.0	0.662525
$844$	0	0
$845$	−2165.00	−0.0881400
$846$	0	0
$847$	−37984.0	−1.54090
$848$	0	0
$849$	31984.0	1.29292
$850$	0	0
$851$	−15040.0	−0.605834
$852$	0	0
$853$	−39442.0	−1.58320	−0.791599	−	0.611041i	$-0.790751\pi$
$853$	−39442.0	−1.58320	−0.791599	+	0.611041i	$0.790751\pi$
$854$	0	0
$855$	1045.00	0.0417991
$856$	0	0
$857$	−40454.0	−1.61246	−0.806232	−	0.591599i	$-0.798497\pi$
$857$	−40454.0	−1.61246	−0.806232	+	0.591599i	$0.798497\pi$
$858$	0	0
$859$	3436.00	0.136478	0.0682391	−	0.997669i	$-0.478262\pi$
$859$	3436.00	0.136478	0.0682391	+	0.997669i	$0.478262\pi$
$860$	0	0
$861$	768.000	0.0303988
$862$	0	0
$863$	10056.0	0.396651	0.198326	−	0.980136i	$-0.436450\pi$
$863$	10056.0	0.396651	0.198326	+	0.980136i	$0.436450\pi$
$864$	0	0
$865$	6030.00	0.237024
$866$	0	0
$867$	−32332.0	−1.26650
$868$	0	0
$869$	8256.00	0.322285
$870$	0	0
$871$	2184.00	0.0849621
$872$	0	0
$873$	−8646.00	−0.335192
$874$	0	0
$875$	4000.00	0.154542
$876$	0	0
$877$	−44394.0	−1.70933	−0.854663	−	0.519183i	$-0.826236\pi$
$877$	−44394.0	−1.70933	−0.854663	+	0.519183i	$0.826236\pi$
$878$	0	0
$879$	15624.0	0.599527
$880$	0	0
$881$	−18222.0	−0.696839	−0.348419	−	0.937339i	$-0.613281\pi$
$881$	−18222.0	−0.696839	−0.348419	+	0.937339i	$0.613281\pi$
$882$	0	0
$883$	29404.0	1.12064	0.560319	−	0.828277i	$-0.310679\pi$
$883$	29404.0	1.12064	0.560319	+	0.828277i	$0.310679\pi$
$884$	0	0
$885$	5520.00	0.209664
$886$	0	0
$887$	−18576.0	−0.703180	−0.351590	−	0.936154i	$-0.614359\pi$
$887$	−18576.0	−0.703180	−0.351590	+	0.936154i	$0.614359\pi$
$888$	0	0
$889$	−28928.0	−1.09135
$890$	0	0
$891$	−3732.00	−0.140322
$892$	0	0
$893$	3496.00	0.131007
$894$	0	0
$895$	7060.00	0.263676
$896$	0	0
$897$	−26880.0	−1.00055
$898$	0	0
$899$	30816.0	1.14324
$900$	0	0
$901$	−31236.0	−1.15496
$902$	0	0
$903$	−39424.0	−1.45288
$904$	0	0
$905$	18710.0	0.687228
$906$	0	0
$907$	2644.00	0.0967945	0.0483972	−	0.998828i	$-0.484589\pi$
$907$	2644.00	0.0967945	0.0483972	+	0.998828i	$0.484589\pi$
$908$	0	0
$909$	−1386.00	−0.0505728
$910$	0	0
$911$	−39744.0	−1.44542	−0.722710	−	0.691151i	$-0.757104\pi$
$911$	−39744.0	−1.44542	−0.722710	+	0.691151i	$0.757104\pi$
$912$	0	0
$913$	−11952.0	−0.433246
$914$	0	0
$915$	16520.0	0.596868
$916$	0	0
$917$	69760.0	2.51219
$918$	0	0
$919$	19720.0	0.707838	0.353919	−	0.935276i	$-0.384849\pi$
$919$	19720.0	0.707838	0.353919	+	0.935276i	$0.384849\pi$
$920$	0	0
$921$	−7280.00	−0.260461
$922$	0	0
$923$	−14448.0	−0.515235
$924$	0	0
$925$	2350.00	0.0835325
$926$	0	0
$927$	−4048.00	−0.143424
$928$	0	0
$929$	36258.0	1.28050	0.640251	−	0.768166i	$-0.278830\pi$
$929$	36258.0	1.28050	0.640251	+	0.768166i	$0.278830\pi$
$930$	0	0
$931$	−12939.0	−0.455487
$932$	0	0
$933$	2848.00	0.0999350
$934$	0	0
$935$	6840.00	0.239243
$936$	0	0
$937$	14586.0	0.508542	0.254271	−	0.967133i	$-0.418164\pi$
$937$	14586.0	0.508542	0.254271	+	0.967133i	$0.418164\pi$
$938$	0	0
$939$	−36520.0	−1.26921
$940$	0	0
$941$	30182.0	1.04560	0.522798	−	0.852457i	$-0.324888\pi$
$941$	30182.0	1.04560	0.522798	+	0.852457i	$0.324888\pi$
$942$	0	0
$943$	960.000	0.0331515
$944$	0	0
$945$	24320.0	0.837174
$946$	0	0
$947$	−15828.0	−0.543127	−0.271563	−	0.962421i	$-0.587541\pi$
$947$	−15828.0	−0.543127	−0.271563	+	0.962421i	$0.587541\pi$
$948$	0	0
$949$	6972.00	0.238483
$950$	0	0
$951$	−25368.0	−0.864999
$952$	0	0
$953$	22746.0	0.773153	0.386577	−	0.922257i	$-0.373657\pi$
$953$	22746.0	0.773153	0.386577	+	0.922257i	$0.373657\pi$
$954$	0	0
$955$	7360.00	0.249386
$956$	0	0
$957$	−10272.0	−0.346966
$958$	0	0
$959$	−82112.0	−2.76490
$960$	0	0
$961$	−9055.00	−0.303951
$962$	0	0
$963$	2244.00	0.0750902
$964$	0	0
$965$	7290.00	0.243185
$966$	0	0
$967$	−16480.0	−0.548047	−0.274023	−	0.961723i	$-0.588355\pi$
$967$	−16480.0	−0.548047	−0.274023	+	0.961723i	$0.588355\pi$
$968$	0	0
$969$	8664.00	0.287232
$970$	0	0
$971$	16940.0	0.559867	0.279933	−	0.960019i	$-0.409688\pi$
$971$	16940.0	0.559867	0.279933	+	0.960019i	$0.409688\pi$
$972$	0	0
$973$	−63616.0	−2.09603
$974$	0	0
$975$	4200.00	0.137957
$976$	0	0
$977$	−40062.0	−1.31187	−0.655935	−	0.754817i	$-0.727725\pi$
$977$	−40062.0	−1.31187	−0.655935	+	0.754817i	$0.727725\pi$
$978$	0	0
$979$	18936.0	0.618179
$980$	0	0
$981$	15774.0	0.513379
$982$	0	0
$983$	−4832.00	−0.156782	−0.0783911	−	0.996923i	$-0.524978\pi$
$983$	−4832.00	−0.156782	−0.0783911	+	0.996923i	$0.524978\pi$
$984$	0	0
$985$	10230.0	0.330919
$986$	0	0
$987$	23552.0	0.759542
$988$	0	0
$989$	−49280.0	−1.58444
$990$	0	0
$991$	4144.00	0.132834	0.0664170	−	0.997792i	$-0.478843\pi$
$991$	4144.00	0.132834	0.0664170	+	0.997792i	$0.478843\pi$
$992$	0	0
$993$	−18992.0	−0.606941
$994$	0	0
$995$	7480.00	0.238324
$996$	0	0
$997$	35294.0	1.12114	0.560568	−	0.828109i	$-0.310583\pi$
$997$	35294.0	1.12114	0.560568	+	0.828109i	$0.310583\pi$
$998$	0	0
$999$	14288.0	0.452505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1520.4.a.c.1.1		1
4.3	odd	2		95.4.a.d.1.1	✓	1
12.11	even	2		855.4.a.a.1.1		1
20.3	even	4		475.4.b.a.324.1		2
20.7	even	4		475.4.b.a.324.2		2
20.19	odd	2		475.4.a.a.1.1		1
76.75	even	2		1805.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.4.a.d.1.1	✓	1	4.3	odd	2
475.4.a.a.1.1		1	20.19	odd	2
475.4.b.a.324.1		2	20.3	even	4
475.4.b.a.324.2		2	20.7	even	4
855.4.a.a.1.1		1	12.11	even	2
1520.4.a.c.1.1		1	1.1	even	1	trivial
1805.4.a.a.1.1		1	76.75	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:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1520.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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