LMFDB - Embedded newform 1050.4.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,4,Mod(1,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1050.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1050.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:	$61.9520055060$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1050.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +3.00000 q^{11} -12.0000 q^{12} -4.00000 q^{13} +14.0000 q^{14} +16.0000 q^{16} -54.0000 q^{17} +18.0000 q^{18} -148.000 q^{19} -21.0000 q^{21} +6.00000 q^{22} -15.0000 q^{23} -24.0000 q^{24} -8.00000 q^{26} -27.0000 q^{27} +28.0000 q^{28} -69.0000 q^{29} +146.000 q^{31} +32.0000 q^{32} -9.00000 q^{33} -108.000 q^{34} +36.0000 q^{36} -19.0000 q^{37} -296.000 q^{38} +12.0000 q^{39} -24.0000 q^{41} -42.0000 q^{42} +29.0000 q^{43} +12.0000 q^{44} -30.0000 q^{46} +228.000 q^{47} -48.0000 q^{48} +49.0000 q^{49} +162.000 q^{51} -16.0000 q^{52} +174.000 q^{53} -54.0000 q^{54} +56.0000 q^{56} +444.000 q^{57} -138.000 q^{58} -732.000 q^{59} -220.000 q^{61} +292.000 q^{62} +63.0000 q^{63} +64.0000 q^{64} -18.0000 q^{66} +11.0000 q^{67} -216.000 q^{68} +45.0000 q^{69} -429.000 q^{71} +72.0000 q^{72} -910.000 q^{73} -38.0000 q^{74} -592.000 q^{76} +21.0000 q^{77} +24.0000 q^{78} -889.000 q^{79} +81.0000 q^{81} -48.0000 q^{82} +78.0000 q^{83} -84.0000 q^{84} +58.0000 q^{86} +207.000 q^{87} +24.0000 q^{88} -960.000 q^{89} -28.0000 q^{91} -60.0000 q^{92} -438.000 q^{93} +456.000 q^{94} -96.0000 q^{96} -550.000 q^{97} +98.0000 q^{98} +27.0000 q^{99} +O(q^{100})\)

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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	0	0
$11$	3.00000	0.0822304	0.0411152	−	0.999154i	$-0.486909\pi$
$11$	3.00000	0.0822304	0.0411152	+	0.999154i	$0.486909\pi$
$12$	−12.0000	−0.288675
$13$	−4.00000	−0.0853385	−0.0426692	−	0.999089i	$-0.513586\pi$
$13$	−4.00000	−0.0853385	−0.0426692	+	0.999089i	$0.513586\pi$
$14$	14.0000	0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	−54.0000	−0.770407	−0.385204	−	0.922832i	$-0.625869\pi$
$17$	−54.0000	−0.770407	−0.385204	+	0.922832i	$0.625869\pi$
$18$	18.0000	0.235702
$19$	−148.000	−1.78703	−0.893514	−	0.449036i	$-0.851768\pi$
$19$	−148.000	−1.78703	−0.893514	+	0.449036i	$0.851768\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	6.00000	0.0581456
$23$	−15.0000	−0.135988	−0.0679938	−	0.997686i	$-0.521660\pi$
$23$	−15.0000	−0.135988	−0.0679938	+	0.997686i	$0.521660\pi$
$24$	−24.0000	−0.204124
$25$	0	0
$26$	−8.00000	−0.0603434
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	−69.0000	−0.441827	−0.220913	−	0.975293i	$-0.570904\pi$
$29$	−69.0000	−0.441827	−0.220913	+	0.975293i	$0.570904\pi$
$30$	0	0
$31$	146.000	0.845883	0.422942	−	0.906157i	$-0.360998\pi$
$31$	146.000	0.845883	0.422942	+	0.906157i	$0.360998\pi$
$32$	32.0000	0.176777
$33$	−9.00000	−0.0474757
$34$	−108.000	−0.544760
$35$	0	0
$36$	36.0000	0.166667
$37$	−19.0000	−0.0844211	−0.0422106	−	0.999109i	$-0.513440\pi$
$37$	−19.0000	−0.0844211	−0.0422106	+	0.999109i	$0.513440\pi$
$38$	−296.000	−1.26362
$39$	12.0000	0.0492702
$40$	0	0
$41$	−24.0000	−0.0914188	−0.0457094	−	0.998955i	$-0.514555\pi$
$41$	−24.0000	−0.0914188	−0.0457094	+	0.998955i	$0.514555\pi$
$42$	−42.0000	−0.154303
$43$	29.0000	0.102848	0.0514239	−	0.998677i	$-0.483624\pi$
$43$	29.0000	0.102848	0.0514239	+	0.998677i	$0.483624\pi$
$44$	12.0000	0.0411152
$45$	0	0
$46$	−30.0000	−0.0961578
$47$	228.000	0.707600	0.353800	−	0.935321i	$-0.384889\pi$
$47$	228.000	0.707600	0.353800	+	0.935321i	$0.384889\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	0	0
$51$	162.000	0.444795
$52$	−16.0000	−0.0426692
$53$	174.000	0.450957	0.225479	−	0.974248i	$-0.427605\pi$
$53$	174.000	0.450957	0.225479	+	0.974248i	$0.427605\pi$
$54$	−54.0000	−0.136083
$55$	0	0
$56$	56.0000	0.133631
$57$	444.000	1.03174
$58$	−138.000	−0.312419
$59$	−732.000	−1.61523	−0.807613	−	0.589713i	$-0.799241\pi$
$59$	−732.000	−1.61523	−0.807613	+	0.589713i	$0.799241\pi$
$60$	0	0
$61$	−220.000	−0.461772	−0.230886	−	0.972981i	$-0.574163\pi$
$61$	−220.000	−0.461772	−0.230886	+	0.972981i	$0.574163\pi$
$62$	292.000	0.598130
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	0	0
$66$	−18.0000	−0.0335704
$67$	11.0000	0.0200577	0.0100288	−	0.999950i	$-0.496808\pi$
$67$	11.0000	0.0200577	0.0100288	+	0.999950i	$0.496808\pi$
$68$	−216.000	−0.385204
$69$	45.0000	0.0785125
$70$	0	0
$71$	−429.000	−0.717084	−0.358542	−	0.933514i	$-0.616726\pi$
$71$	−429.000	−0.717084	−0.358542	+	0.933514i	$0.616726\pi$
$72$	72.0000	0.117851
$73$	−910.000	−1.45901	−0.729503	−	0.683978i	$-0.760249\pi$
$73$	−910.000	−1.45901	−0.729503	+	0.683978i	$0.760249\pi$
$74$	−38.0000	−0.0596947
$75$	0	0
$76$	−592.000	−0.893514
$77$	21.0000	0.0310802
$78$	24.0000	0.0348393
$79$	−889.000	−1.26608	−0.633040	−	0.774119i	$-0.718193\pi$
$79$	−889.000	−1.26608	−0.633040	+	0.774119i	$0.718193\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−48.0000	−0.0646428
$83$	78.0000	0.103152	0.0515760	−	0.998669i	$-0.483576\pi$
$83$	78.0000	0.103152	0.0515760	+	0.998669i	$0.483576\pi$
$84$	−84.0000	−0.109109
$85$	0	0
$86$	58.0000	0.0727244
$87$	207.000	0.255089
$88$	24.0000	0.0290728
$89$	−960.000	−1.14337	−0.571684	−	0.820474i	$-0.693710\pi$
$89$	−960.000	−1.14337	−0.571684	+	0.820474i	$0.693710\pi$
$90$	0	0
$91$	−28.0000	−0.0322549
$92$	−60.0000	−0.0679938
$93$	−438.000	−0.488371
$94$	456.000	0.500349
$95$	0	0
$96$	−96.0000	−0.102062
$97$	−550.000	−0.575712	−0.287856	−	0.957674i	$-0.592942\pi$
$97$	−550.000	−0.575712	−0.287856	+	0.957674i	$0.592942\pi$
$98$	98.0000	0.101015
$99$	27.0000	0.0274101
$100$	0	0
$101$	−330.000	−0.325111	−0.162556	−	0.986699i	$-0.551974\pi$
$101$	−330.000	−0.325111	−0.162556	+	0.986699i	$0.551974\pi$
$102$	324.000	0.314517
$103$	−1300.00	−1.24362	−0.621810	−	0.783168i	$-0.713602\pi$
$103$	−1300.00	−1.24362	−0.621810	+	0.783168i	$0.713602\pi$
$104$	−32.0000	−0.0301717
$105$	0	0
$106$	348.000	0.318875
$107$	1356.00	1.22514	0.612568	−	0.790418i	$-0.290137\pi$
$107$	1356.00	1.22514	0.612568	+	0.790418i	$0.290137\pi$
$108$	−108.000	−0.0962250
$109$	341.000	0.299650	0.149825	−	0.988713i	$-0.452129\pi$
$109$	341.000	0.299650	0.149825	+	0.988713i	$0.452129\pi$
$110$	0	0
$111$	57.0000	0.0487405
$112$	112.000	0.0944911
$113$	−1467.00	−1.22127	−0.610636	−	0.791911i	$-0.709086\pi$
$113$	−1467.00	−1.22127	−0.610636	+	0.791911i	$0.709086\pi$
$114$	888.000	0.729551
$115$	0	0
$116$	−276.000	−0.220913
$117$	−36.0000	−0.0284462
$118$	−1464.00	−1.14214
$119$	−378.000	−0.291187
$120$	0	0
$121$	−1322.00	−0.993238
$122$	−440.000	−0.326522
$123$	72.0000	0.0527807
$124$	584.000	0.422942
$125$	0	0
$126$	126.000	0.0890871
$127$	719.000	0.502370	0.251185	−	0.967939i	$-0.419180\pi$
$127$	719.000	0.502370	0.251185	+	0.967939i	$0.419180\pi$
$128$	128.000	0.0883883
$129$	−87.0000	−0.0593792
$130$	0	0
$131$	−1170.00	−0.780331	−0.390166	−	0.920745i	$-0.627582\pi$
$131$	−1170.00	−0.780331	−0.390166	+	0.920745i	$0.627582\pi$
$132$	−36.0000	−0.0237379
$133$	−1036.00	−0.675433
$134$	22.0000	0.0141829
$135$	0	0
$136$	−432.000	−0.272380
$137$	−18.0000	−0.0112251	−0.00561257	−	0.999984i	$-0.501787\pi$
$137$	−18.0000	−0.0112251	−0.00561257	+	0.999984i	$0.501787\pi$
$138$	90.0000	0.0555167
$139$	−838.000	−0.511354	−0.255677	−	0.966762i	$-0.582298\pi$
$139$	−838.000	−0.511354	−0.255677	+	0.966762i	$0.582298\pi$
$140$	0	0
$141$	−684.000	−0.408533
$142$	−858.000	−0.507055
$143$	−12.0000	−0.00701742
$144$	144.000	0.0833333
$145$	0	0
$146$	−1820.00	−1.03167
$147$	−147.000	−0.0824786
$148$	−76.0000	−0.0422106
$149$	513.000	0.282058	0.141029	−	0.990005i	$-0.454959\pi$
$149$	513.000	0.282058	0.141029	+	0.990005i	$0.454959\pi$
$150$	0	0
$151$	293.000	0.157907	0.0789536	−	0.996878i	$-0.474842\pi$
$151$	293.000	0.157907	0.0789536	+	0.996878i	$0.474842\pi$
$152$	−1184.00	−0.631810
$153$	−486.000	−0.256802
$154$	42.0000	0.0219770
$155$	0	0
$156$	48.0000	0.0246351
$157$	2660.00	1.35217	0.676086	−	0.736822i	$-0.263675\pi$
$157$	2660.00	1.35217	0.676086	+	0.736822i	$0.263675\pi$
$158$	−1778.00	−0.895254
$159$	−522.000	−0.260360
$160$	0	0
$161$	−105.000	−0.0513985
$162$	162.000	0.0785674
$163$	1220.00	0.586244	0.293122	−	0.956075i	$-0.405306\pi$
$163$	1220.00	0.586244	0.293122	+	0.956075i	$0.405306\pi$
$164$	−96.0000	−0.0457094
$165$	0	0
$166$	156.000	0.0729394
$167$	−1176.00	−0.544920	−0.272460	−	0.962167i	$-0.587837\pi$
$167$	−1176.00	−0.544920	−0.272460	+	0.962167i	$0.587837\pi$
$168$	−168.000	−0.0771517
$169$	−2181.00	−0.992717
$170$	0	0
$171$	−1332.00	−0.595676
$172$	116.000	0.0514239
$173$	4272.00	1.87742	0.938711	−	0.344704i	$-0.112021\pi$
$173$	4272.00	1.87742	0.938711	+	0.344704i	$0.112021\pi$
$174$	414.000	0.180375
$175$	0	0
$176$	48.0000	0.0205576
$177$	2196.00	0.932551
$178$	−1920.00	−0.808484
$179$	12.0000	0.00501074	0.00250537	−	0.999997i	$-0.499203\pi$
$179$	12.0000	0.00501074	0.00250537	+	0.999997i	$0.499203\pi$
$180$	0	0
$181$	−1258.00	−0.516610	−0.258305	−	0.966063i	$-0.583164\pi$
$181$	−1258.00	−0.516610	−0.258305	+	0.966063i	$0.583164\pi$
$182$	−56.0000	−0.0228077
$183$	660.000	0.266604
$184$	−120.000	−0.0480789
$185$	0	0
$186$	−876.000	−0.345330
$187$	−162.000	−0.0633509
$188$	912.000	0.353800
$189$	−189.000	−0.0727393
$190$	0	0
$191$	−2196.00	−0.831921	−0.415961	−	0.909383i	$-0.636555\pi$
$191$	−2196.00	−0.831921	−0.415961	+	0.909383i	$0.636555\pi$
$192$	−192.000	−0.0721688
$193$	−4705.00	−1.75478	−0.877392	−	0.479774i	$-0.840719\pi$
$193$	−4705.00	−1.75478	−0.877392	+	0.479774i	$0.840719\pi$
$194$	−1100.00	−0.407090
$195$	0	0
$196$	196.000	0.0714286
$197$	2373.00	0.858220	0.429110	−	0.903252i	$-0.358827\pi$
$197$	2373.00	0.858220	0.429110	+	0.903252i	$0.358827\pi$
$198$	54.0000	0.0193819
$199$	2456.00	0.874881	0.437440	−	0.899247i	$-0.355885\pi$
$199$	2456.00	0.874881	0.437440	+	0.899247i	$0.355885\pi$
$200$	0	0
$201$	−33.0000	−0.0115803
$202$	−660.000	−0.229888
$203$	−483.000	−0.166995
$204$	648.000	0.222397
$205$	0	0
$206$	−2600.00	−0.879372
$207$	−135.000	−0.0453292
$208$	−64.0000	−0.0213346
$209$	−444.000	−0.146948
$210$	0	0
$211$	−748.000	−0.244049	−0.122025	−	0.992527i	$-0.538939\pi$
$211$	−748.000	−0.244049	−0.122025	+	0.992527i	$0.538939\pi$
$212$	696.000	0.225479
$213$	1287.00	0.414008
$214$	2712.00	0.866301
$215$	0	0
$216$	−216.000	−0.0680414
$217$	1022.00	0.319714
$218$	682.000	0.211885
$219$	2730.00	0.842358
$220$	0	0
$221$	216.000	0.0657454
$222$	114.000	0.0344648
$223$	−178.000	−0.0534518	−0.0267259	−	0.999643i	$-0.508508\pi$
$223$	−178.000	−0.0534518	−0.0267259	+	0.999643i	$0.508508\pi$
$224$	224.000	0.0668153
$225$	0	0
$226$	−2934.00	−0.863570
$227$	3624.00	1.05962	0.529809	−	0.848117i	$-0.322264\pi$
$227$	3624.00	1.05962	0.529809	+	0.848117i	$0.322264\pi$
$228$	1776.00	0.515870
$229$	−1906.00	−0.550009	−0.275004	−	0.961443i	$-0.588679\pi$
$229$	−1906.00	−0.550009	−0.275004	+	0.961443i	$0.588679\pi$
$230$	0	0
$231$	−63.0000	−0.0179441
$232$	−552.000	−0.156209
$233$	3603.00	1.01305	0.506524	−	0.862226i	$-0.330930\pi$
$233$	3603.00	1.01305	0.506524	+	0.862226i	$0.330930\pi$
$234$	−72.0000	−0.0201145
$235$	0	0
$236$	−2928.00	−0.807613
$237$	2667.00	0.730972
$238$	−756.000	−0.205900
$239$	−4848.00	−1.31210	−0.656048	−	0.754719i	$-0.727773\pi$
$239$	−4848.00	−1.31210	−0.656048	+	0.754719i	$0.727773\pi$
$240$	0	0
$241$	−760.000	−0.203137	−0.101568	−	0.994829i	$-0.532386\pi$
$241$	−760.000	−0.203137	−0.101568	+	0.994829i	$0.532386\pi$
$242$	−2644.00	−0.702325
$243$	−243.000	−0.0641500
$244$	−880.000	−0.230886
$245$	0	0
$246$	144.000	0.0373216
$247$	592.000	0.152502
$248$	1168.00	0.299065
$249$	−234.000	−0.0595548
$250$	0	0
$251$	−5310.00	−1.33532	−0.667658	−	0.744468i	$-0.732703\pi$
$251$	−5310.00	−1.33532	−0.667658	+	0.744468i	$0.732703\pi$
$252$	252.000	0.0629941
$253$	−45.0000	−0.0111823
$254$	1438.00	0.355229
$255$	0	0
$256$	256.000	0.0625000
$257$	−1590.00	−0.385920	−0.192960	−	0.981207i	$-0.561809\pi$
$257$	−1590.00	−0.385920	−0.192960	+	0.981207i	$0.561809\pi$
$258$	−174.000	−0.0419875
$259$	−133.000	−0.0319082
$260$	0	0
$261$	−621.000	−0.147276
$262$	−2340.00	−0.551777
$263$	6183.00	1.44966	0.724829	−	0.688929i	$-0.241919\pi$
$263$	6183.00	1.44966	0.724829	+	0.688929i	$0.241919\pi$
$264$	−72.0000	−0.0167852
$265$	0	0
$266$	−2072.00	−0.477603
$267$	2880.00	0.660124
$268$	44.0000	0.0100288
$269$	−5334.00	−1.20900	−0.604498	−	0.796607i	$-0.706626\pi$
$269$	−5334.00	−1.20900	−0.604498	+	0.796607i	$0.706626\pi$
$270$	0	0
$271$	5312.00	1.19070	0.595352	−	0.803465i	$-0.297012\pi$
$271$	5312.00	1.19070	0.595352	+	0.803465i	$0.297012\pi$
$272$	−864.000	−0.192602
$273$	84.0000	0.0186224
$274$	−36.0000	−0.00793737
$275$	0	0
$276$	180.000	0.0392563
$277$	3674.00	0.796929	0.398464	−	0.917184i	$-0.369543\pi$
$277$	3674.00	0.796929	0.398464	+	0.917184i	$0.369543\pi$
$278$	−1676.00	−0.361582
$279$	1314.00	0.281961
$280$	0	0
$281$	867.000	0.184060	0.0920300	−	0.995756i	$-0.470664\pi$
$281$	867.000	0.184060	0.0920300	+	0.995756i	$0.470664\pi$
$282$	−1368.00	−0.288877
$283$	−4498.00	−0.944800	−0.472400	−	0.881384i	$-0.656612\pi$
$283$	−4498.00	−0.944800	−0.472400	+	0.881384i	$0.656612\pi$
$284$	−1716.00	−0.358542
$285$	0	0
$286$	−24.0000	−0.00496206
$287$	−168.000	−0.0345531
$288$	288.000	0.0589256
$289$	−1997.00	−0.406473
$290$	0	0
$291$	1650.00	0.332387
$292$	−3640.00	−0.729503
$293$	192.000	0.0382825	0.0191412	−	0.999817i	$-0.493907\pi$
$293$	192.000	0.0382825	0.0191412	+	0.999817i	$0.493907\pi$
$294$	−294.000	−0.0583212
$295$	0	0
$296$	−152.000	−0.0298474
$297$	−81.0000	−0.0158252
$298$	1026.00	0.199445
$299$	60.0000	0.0116050
$300$	0	0
$301$	203.000	0.0388728
$302$	586.000	0.111657
$303$	990.000	0.187703
$304$	−2368.00	−0.446757
$305$	0	0
$306$	−972.000	−0.181587
$307$	3926.00	0.729865	0.364933	−	0.931034i	$-0.381092\pi$
$307$	3926.00	0.729865	0.364933	+	0.931034i	$0.381092\pi$
$308$	84.0000	0.0155401
$309$	3900.00	0.718004
$310$	0	0
$311$	6342.00	1.15634	0.578170	−	0.815916i	$-0.303767\pi$
$311$	6342.00	1.15634	0.578170	+	0.815916i	$0.303767\pi$
$312$	96.0000	0.0174196
$313$	−2500.00	−0.451464	−0.225732	−	0.974189i	$-0.572477\pi$
$313$	−2500.00	−0.451464	−0.225732	+	0.974189i	$0.572477\pi$
$314$	5320.00	0.956130
$315$	0	0
$316$	−3556.00	−0.633040
$317$	381.000	0.0675050	0.0337525	−	0.999430i	$-0.489254\pi$
$317$	381.000	0.0675050	0.0337525	+	0.999430i	$0.489254\pi$
$318$	−1044.00	−0.184103
$319$	−207.000	−0.0363316
$320$	0	0
$321$	−4068.00	−0.707332
$322$	−210.000	−0.0363442
$323$	7992.00	1.37674
$324$	324.000	0.0555556
$325$	0	0
$326$	2440.00	0.414537
$327$	−1023.00	−0.173003
$328$	−192.000	−0.0323214
$329$	1596.00	0.267448
$330$	0	0
$331$	11315.0	1.87894	0.939469	−	0.342633i	$-0.111319\pi$
$331$	11315.0	1.87894	0.939469	+	0.342633i	$0.111319\pi$
$332$	312.000	0.0515760
$333$	−171.000	−0.0281404
$334$	−2352.00	−0.385317
$335$	0	0
$336$	−336.000	−0.0545545
$337$	7274.00	1.17579	0.587893	−	0.808939i	$-0.299958\pi$
$337$	7274.00	1.17579	0.587893	+	0.808939i	$0.299958\pi$
$338$	−4362.00	−0.701957
$339$	4401.00	0.705102
$340$	0	0
$341$	438.000	0.0695573
$342$	−2664.00	−0.421206
$343$	343.000	0.0539949
$344$	232.000	0.0363622
$345$	0	0
$346$	8544.00	1.32754
$347$	303.000	0.0468758	0.0234379	−	0.999725i	$-0.492539\pi$
$347$	303.000	0.0468758	0.0234379	+	0.999725i	$0.492539\pi$
$348$	828.000	0.127544
$349$	812.000	0.124543	0.0622713	−	0.998059i	$-0.480166\pi$
$349$	812.000	0.124543	0.0622713	+	0.998059i	$0.480166\pi$
$350$	0	0
$351$	108.000	0.0164234
$352$	96.0000	0.0145364
$353$	−2670.00	−0.402577	−0.201289	−	0.979532i	$-0.564513\pi$
$353$	−2670.00	−0.402577	−0.201289	+	0.979532i	$0.564513\pi$
$354$	4392.00	0.659413
$355$	0	0
$356$	−3840.00	−0.571684
$357$	1134.00	0.168117
$358$	24.0000	0.00354313
$359$	8811.00	1.29534	0.647670	−	0.761921i	$-0.275744\pi$
$359$	8811.00	1.29534	0.647670	+	0.761921i	$0.275744\pi$
$360$	0	0
$361$	15045.0	2.19347
$362$	−2516.00	−0.365298
$363$	3966.00	0.573446
$364$	−112.000	−0.0161275
$365$	0	0
$366$	1320.00	0.188518
$367$	3836.00	0.545606	0.272803	−	0.962070i	$-0.412049\pi$
$367$	3836.00	0.545606	0.272803	+	0.962070i	$0.412049\pi$
$368$	−240.000	−0.0339969
$369$	−216.000	−0.0304729
$370$	0	0
$371$	1218.00	0.170446
$372$	−1752.00	−0.244185
$373$	−2497.00	−0.346621	−0.173311	−	0.984867i	$-0.555446\pi$
$373$	−2497.00	−0.346621	−0.173311	+	0.984867i	$0.555446\pi$
$374$	−324.000	−0.0447958
$375$	0	0
$376$	1824.00	0.250175
$377$	276.000	0.0377048
$378$	−378.000	−0.0514344
$379$	−11917.0	−1.61513	−0.807566	−	0.589777i	$-0.799216\pi$
$379$	−11917.0	−1.61513	−0.807566	+	0.589777i	$0.799216\pi$
$380$	0	0
$381$	−2157.00	−0.290043
$382$	−4392.00	−0.588257
$383$	5460.00	0.728441	0.364221	−	0.931313i	$-0.381335\pi$
$383$	5460.00	0.728441	0.364221	+	0.931313i	$0.381335\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	−9410.00	−1.24082
$387$	261.000	0.0342826
$388$	−2200.00	−0.287856
$389$	6279.00	0.818401	0.409200	−	0.912445i	$-0.365808\pi$
$389$	6279.00	0.818401	0.409200	+	0.912445i	$0.365808\pi$
$390$	0	0
$391$	810.000	0.104766
$392$	392.000	0.0505076
$393$	3510.00	0.450524
$394$	4746.00	0.606853
$395$	0	0
$396$	108.000	0.0137051
$397$	−12526.0	−1.58353	−0.791766	−	0.610825i	$-0.790838\pi$
$397$	−12526.0	−1.58353	−0.791766	+	0.610825i	$0.790838\pi$
$398$	4912.00	0.618634
$399$	3108.00	0.389961
$400$	0	0
$401$	4503.00	0.560771	0.280385	−	0.959888i	$-0.409538\pi$
$401$	4503.00	0.560771	0.280385	+	0.959888i	$0.409538\pi$
$402$	−66.0000	−0.00818851
$403$	−584.000	−0.0721864
$404$	−1320.00	−0.162556
$405$	0	0
$406$	−966.000	−0.118083
$407$	−57.0000	−0.00694198
$408$	1296.00	0.157259
$409$	−10720.0	−1.29601	−0.648007	−	0.761634i	$-0.724397\pi$
$409$	−10720.0	−1.29601	−0.648007	+	0.761634i	$0.724397\pi$
$410$	0	0
$411$	54.0000	0.00648084
$412$	−5200.00	−0.621810
$413$	−5124.00	−0.610498
$414$	−270.000	−0.0320526
$415$	0	0
$416$	−128.000	−0.0150859
$417$	2514.00	0.295230
$418$	−888.000	−0.103908
$419$	−5142.00	−0.599530	−0.299765	−	0.954013i	$-0.596908\pi$
$419$	−5142.00	−0.599530	−0.299765	+	0.954013i	$0.596908\pi$
$420$	0	0
$421$	9635.00	1.11539	0.557697	−	0.830044i	$-0.311685\pi$
$421$	9635.00	1.11539	0.557697	+	0.830044i	$0.311685\pi$
$422$	−1496.00	−0.172569
$423$	2052.00	0.235867
$424$	1392.00	0.159437
$425$	0	0
$426$	2574.00	0.292748
$427$	−1540.00	−0.174534
$428$	5424.00	0.612568
$429$	36.0000	0.00405151
$430$	0	0
$431$	15624.0	1.74613	0.873064	−	0.487605i	$-0.162129\pi$
$431$	15624.0	1.74613	0.873064	+	0.487605i	$0.162129\pi$
$432$	−432.000	−0.0481125
$433$	−13552.0	−1.50408	−0.752041	−	0.659116i	$-0.770931\pi$
$433$	−13552.0	−1.50408	−0.752041	+	0.659116i	$0.770931\pi$
$434$	2044.00	0.226072
$435$	0	0
$436$	1364.00	0.149825
$437$	2220.00	0.243014
$438$	5460.00	0.595637
$439$	−7516.00	−0.817128	−0.408564	−	0.912730i	$-0.633970\pi$
$439$	−7516.00	−0.817128	−0.408564	+	0.912730i	$0.633970\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	432.000	0.0464890
$443$	8268.00	0.886737	0.443369	−	0.896339i	$-0.353783\pi$
$443$	8268.00	0.886737	0.443369	+	0.896339i	$0.353783\pi$
$444$	228.000	0.0243703
$445$	0	0
$446$	−356.000	−0.0377962
$447$	−1539.00	−0.162846
$448$	448.000	0.0472456
$449$	165.000	0.0173426	0.00867130	−	0.999962i	$-0.497240\pi$
$449$	165.000	0.0173426	0.00867130	+	0.999962i	$0.497240\pi$
$450$	0	0
$451$	−72.0000	−0.00751740
$452$	−5868.00	−0.610636
$453$	−879.000	−0.0911678
$454$	7248.00	0.749263
$455$	0	0
$456$	3552.00	0.364776
$457$	−13261.0	−1.35738	−0.678691	−	0.734424i	$-0.737452\pi$
$457$	−13261.0	−1.35738	−0.678691	+	0.734424i	$0.737452\pi$
$458$	−3812.00	−0.388915
$459$	1458.00	0.148265
$460$	0	0
$461$	3648.00	0.368556	0.184278	−	0.982874i	$-0.441005\pi$
$461$	3648.00	0.368556	0.184278	+	0.982874i	$0.441005\pi$
$462$	−126.000	−0.0126884
$463$	−3436.00	−0.344891	−0.172445	−	0.985019i	$-0.555167\pi$
$463$	−3436.00	−0.344891	−0.172445	+	0.985019i	$0.555167\pi$
$464$	−1104.00	−0.110457
$465$	0	0
$466$	7206.00	0.716334
$467$	−5058.00	−0.501191	−0.250596	−	0.968092i	$-0.580626\pi$
$467$	−5058.00	−0.501191	−0.250596	+	0.968092i	$0.580626\pi$
$468$	−144.000	−0.0142231
$469$	77.0000	0.00758109
$470$	0	0
$471$	−7980.00	−0.780677
$472$	−5856.00	−0.571068
$473$	87.0000	0.00845722
$474$	5334.00	0.516875
$475$	0	0
$476$	−1512.00	−0.145593
$477$	1566.00	0.150319
$478$	−9696.00	−0.927792
$479$	11172.0	1.06568	0.532841	−	0.846215i	$-0.321124\pi$
$479$	11172.0	1.06568	0.532841	+	0.846215i	$0.321124\pi$
$480$	0	0
$481$	76.0000	0.00720437
$482$	−1520.00	−0.143639
$483$	315.000	0.0296749
$484$	−5288.00	−0.496619
$485$	0	0
$486$	−486.000	−0.0453609
$487$	−6883.00	−0.640449	−0.320224	−	0.947342i	$-0.603758\pi$
$487$	−6883.00	−0.640449	−0.320224	+	0.947342i	$0.603758\pi$
$488$	−1760.00	−0.163261
$489$	−3660.00	−0.338468
$490$	0	0
$491$	7863.00	0.722713	0.361357	−	0.932428i	$-0.382314\pi$
$491$	7863.00	0.722713	0.361357	+	0.932428i	$0.382314\pi$
$492$	288.000	0.0263903
$493$	3726.00	0.340387
$494$	1184.00	0.107835
$495$	0	0
$496$	2336.00	0.211471
$497$	−3003.00	−0.271032
$498$	−468.000	−0.0421116
$499$	16988.0	1.52402	0.762011	−	0.647564i	$-0.224212\pi$
$499$	16988.0	1.52402	0.762011	+	0.647564i	$0.224212\pi$
$500$	0	0
$501$	3528.00	0.314610
$502$	−10620.0	−0.944211
$503$	3342.00	0.296247	0.148124	−	0.988969i	$-0.452677\pi$
$503$	3342.00	0.296247	0.148124	+	0.988969i	$0.452677\pi$
$504$	504.000	0.0445435
$505$	0	0
$506$	−90.0000	−0.00790709
$507$	6543.00	0.573146
$508$	2876.00	0.251185
$509$	12588.0	1.09618	0.548088	−	0.836421i	$-0.315356\pi$
$509$	12588.0	1.09618	0.548088	+	0.836421i	$0.315356\pi$
$510$	0	0
$511$	−6370.00	−0.551452
$512$	512.000	0.0441942
$513$	3996.00	0.343914
$514$	−3180.00	−0.272887
$515$	0	0
$516$	−348.000	−0.0296896
$517$	684.000	0.0581862
$518$	−266.000	−0.0225625
$519$	−12816.0	−1.08393
$520$	0	0
$521$	−4746.00	−0.399090	−0.199545	−	0.979889i	$-0.563946\pi$
$521$	−4746.00	−0.399090	−0.199545	+	0.979889i	$0.563946\pi$
$522$	−1242.00	−0.104140
$523$	−376.000	−0.0314366	−0.0157183	−	0.999876i	$-0.505003\pi$
$523$	−376.000	−0.0314366	−0.0157183	+	0.999876i	$0.505003\pi$
$524$	−4680.00	−0.390166
$525$	0	0
$526$	12366.0	1.02506
$527$	−7884.00	−0.651674
$528$	−144.000	−0.0118689
$529$	−11942.0	−0.981507
$530$	0	0
$531$	−6588.00	−0.538408
$532$	−4144.00	−0.337717
$533$	96.0000	0.00780154
$534$	5760.00	0.466778
$535$	0	0
$536$	88.0000	0.00709146
$537$	−36.0000	−0.00289295
$538$	−10668.0	−0.854889
$539$	147.000	0.0117472
$540$	0	0
$541$	−637.000	−0.0506225	−0.0253112	−	0.999680i	$-0.508058\pi$
$541$	−637.000	−0.0506225	−0.0253112	+	0.999680i	$0.508058\pi$
$542$	10624.0	0.841955
$543$	3774.00	0.298265
$544$	−1728.00	−0.136190
$545$	0	0
$546$	168.000	0.0131680
$547$	−3625.00	−0.283352	−0.141676	−	0.989913i	$-0.545249\pi$
$547$	−3625.00	−0.283352	−0.141676	+	0.989913i	$0.545249\pi$
$548$	−72.0000	−0.00561257
$549$	−1980.00	−0.153924
$550$	0	0
$551$	10212.0	0.789557
$552$	360.000	0.0277584
$553$	−6223.00	−0.478533
$554$	7348.00	0.563514
$555$	0	0
$556$	−3352.00	−0.255677
$557$	−9843.00	−0.748764	−0.374382	−	0.927275i	$-0.622145\pi$
$557$	−9843.00	−0.748764	−0.374382	+	0.927275i	$0.622145\pi$
$558$	2628.00	0.199377
$559$	−116.000	−0.00877688
$560$	0	0
$561$	486.000	0.0365756
$562$	1734.00	0.130150
$563$	16806.0	1.25806	0.629031	−	0.777381i	$-0.283452\pi$
$563$	16806.0	1.25806	0.629031	+	0.777381i	$0.283452\pi$
$564$	−2736.00	−0.204267
$565$	0	0
$566$	−8996.00	−0.668074
$567$	567.000	0.0419961
$568$	−3432.00	−0.253527
$569$	−11853.0	−0.873293	−0.436646	−	0.899633i	$-0.643834\pi$
$569$	−11853.0	−0.873293	−0.436646	+	0.899633i	$0.643834\pi$
$570$	0	0
$571$	13331.0	0.977032	0.488516	−	0.872555i	$-0.337538\pi$
$571$	13331.0	0.977032	0.488516	+	0.872555i	$0.337538\pi$
$572$	−48.0000	−0.00350871
$573$	6588.00	0.480310
$574$	−336.000	−0.0244327
$575$	0	0
$576$	576.000	0.0416667
$577$	1856.00	0.133910	0.0669552	−	0.997756i	$-0.478672\pi$
$577$	1856.00	0.133910	0.0669552	+	0.997756i	$0.478672\pi$
$578$	−3994.00	−0.287420
$579$	14115.0	1.01313
$580$	0	0
$581$	546.000	0.0389878
$582$	3300.00	0.235033
$583$	522.000	0.0370824
$584$	−7280.00	−0.515837
$585$	0	0
$586$	384.000	0.0270698
$587$	−18882.0	−1.32767	−0.663836	−	0.747878i	$-0.731073\pi$
$587$	−18882.0	−1.32767	−0.663836	+	0.747878i	$0.731073\pi$
$588$	−588.000	−0.0412393
$589$	−21608.0	−1.51162
$590$	0	0
$591$	−7119.00	−0.495493
$592$	−304.000	−0.0211053
$593$	15684.0	1.08611	0.543056	−	0.839696i	$-0.317267\pi$
$593$	15684.0	1.08611	0.543056	+	0.839696i	$0.317267\pi$
$594$	−162.000	−0.0111901
$595$	0	0
$596$	2052.00	0.141029
$597$	−7368.00	−0.505113
$598$	120.000	0.00820596
$599$	12741.0	0.869087	0.434544	−	0.900651i	$-0.356910\pi$
$599$	12741.0	0.869087	0.434544	+	0.900651i	$0.356910\pi$
$600$	0	0
$601$	3788.00	0.257098	0.128549	−	0.991703i	$-0.458968\pi$
$601$	3788.00	0.257098	0.128549	+	0.991703i	$0.458968\pi$
$602$	406.000	0.0274873
$603$	99.0000	0.00668589
$604$	1172.00	0.0789536
$605$	0	0
$606$	1980.00	0.132726
$607$	−18472.0	−1.23518	−0.617591	−	0.786500i	$-0.711891\pi$
$607$	−18472.0	−1.23518	−0.617591	+	0.786500i	$0.711891\pi$
$608$	−4736.00	−0.315905
$609$	1449.00	0.0964145
$610$	0	0
$611$	−912.000	−0.0603855
$612$	−1944.00	−0.128401
$613$	−1879.00	−0.123804	−0.0619022	−	0.998082i	$-0.519717\pi$
$613$	−1879.00	−0.123804	−0.0619022	+	0.998082i	$0.519717\pi$
$614$	7852.00	0.516093
$615$	0	0
$616$	168.000	0.0109885
$617$	15519.0	1.01260	0.506298	−	0.862359i	$-0.331014\pi$
$617$	15519.0	1.01260	0.506298	+	0.862359i	$0.331014\pi$
$618$	7800.00	0.507706
$619$	5528.00	0.358948	0.179474	−	0.983763i	$-0.442560\pi$
$619$	5528.00	0.358948	0.179474	+	0.983763i	$0.442560\pi$
$620$	0	0
$621$	405.000	0.0261708
$622$	12684.0	0.817656
$623$	−6720.00	−0.432153
$624$	192.000	0.0123176
$625$	0	0
$626$	−5000.00	−0.319234
$627$	1332.00	0.0848404
$628$	10640.0	0.676086
$629$	1026.00	0.0650386
$630$	0	0
$631$	6107.00	0.385287	0.192643	−	0.981269i	$-0.438294\pi$
$631$	6107.00	0.385287	0.192643	+	0.981269i	$0.438294\pi$
$632$	−7112.00	−0.447627
$633$	2244.00	0.140902
$634$	762.000	0.0477333
$635$	0	0
$636$	−2088.00	−0.130180
$637$	−196.000	−0.0121912
$638$	−414.000	−0.0256903
$639$	−3861.00	−0.239028
$640$	0	0
$641$	18135.0	1.11746	0.558728	−	0.829351i	$-0.311290\pi$
$641$	18135.0	1.11746	0.558728	+	0.829351i	$0.311290\pi$
$642$	−8136.00	−0.500159
$643$	−11500.0	−0.705312	−0.352656	−	0.935753i	$-0.614721\pi$
$643$	−11500.0	−0.705312	−0.352656	+	0.935753i	$0.614721\pi$
$644$	−420.000	−0.0256993
$645$	0	0
$646$	15984.0	0.973502
$647$	28482.0	1.73067	0.865335	−	0.501195i	$-0.167106\pi$
$647$	28482.0	1.73067	0.865335	+	0.501195i	$0.167106\pi$
$648$	648.000	0.0392837
$649$	−2196.00	−0.132821
$650$	0	0
$651$	−3066.00	−0.184587
$652$	4880.00	0.293122
$653$	−10782.0	−0.646144	−0.323072	−	0.946374i	$-0.604716\pi$
$653$	−10782.0	−0.646144	−0.323072	+	0.946374i	$0.604716\pi$
$654$	−2046.00	−0.122332
$655$	0	0
$656$	−384.000	−0.0228547
$657$	−8190.00	−0.486335
$658$	3192.00	0.189114
$659$	−324.000	−0.0191521	−0.00957606	−	0.999954i	$-0.503048\pi$
$659$	−324.000	−0.0191521	−0.00957606	+	0.999954i	$0.503048\pi$
$660$	0	0
$661$	13400.0	0.788502	0.394251	−	0.919003i	$-0.371004\pi$
$661$	13400.0	0.788502	0.394251	+	0.919003i	$0.371004\pi$
$662$	22630.0	1.32861
$663$	−648.000	−0.0379581
$664$	624.000	0.0364697
$665$	0	0
$666$	−342.000	−0.0198982
$667$	1035.00	0.0600830
$668$	−4704.00	−0.272460
$669$	534.000	0.0308604
$670$	0	0
$671$	−660.000	−0.0379717
$672$	−672.000	−0.0385758
$673$	−7054.00	−0.404029	−0.202015	−	0.979383i	$-0.564749\pi$
$673$	−7054.00	−0.404029	−0.202015	+	0.979383i	$0.564749\pi$
$674$	14548.0	0.831407
$675$	0	0
$676$	−8724.00	−0.496359
$677$	−14790.0	−0.839625	−0.419812	−	0.907611i	$-0.637904\pi$
$677$	−14790.0	−0.839625	−0.419812	+	0.907611i	$0.637904\pi$
$678$	8802.00	0.498582
$679$	−3850.00	−0.217599
$680$	0	0
$681$	−10872.0	−0.611771
$682$	876.000	0.0491844
$683$	26679.0	1.49465	0.747323	−	0.664461i	$-0.231339\pi$
$683$	26679.0	1.49465	0.747323	+	0.664461i	$0.231339\pi$
$684$	−5328.00	−0.297838
$685$	0	0
$686$	686.000	0.0381802
$687$	5718.00	0.317548
$688$	464.000	0.0257120
$689$	−696.000	−0.0384840
$690$	0	0
$691$	−16924.0	−0.931721	−0.465861	−	0.884858i	$-0.654255\pi$
$691$	−16924.0	−0.931721	−0.465861	+	0.884858i	$0.654255\pi$
$692$	17088.0	0.938711
$693$	189.000	0.0103601
$694$	606.000	0.0331462
$695$	0	0
$696$	1656.00	0.0901875
$697$	1296.00	0.0704297
$698$	1624.00	0.0880649
$699$	−10809.0	−0.584884
$700$	0	0
$701$	10410.0	0.560885	0.280442	−	0.959871i	$-0.409519\pi$
$701$	10410.0	0.560885	0.280442	+	0.959871i	$0.409519\pi$
$702$	216.000	0.0116131
$703$	2812.00	0.150863
$704$	192.000	0.0102788
$705$	0	0
$706$	−5340.00	−0.284665
$707$	−2310.00	−0.122880
$708$	8784.00	0.466275
$709$	−13042.0	−0.690836	−0.345418	−	0.938449i	$-0.612263\pi$
$709$	−13042.0	−0.690836	−0.345418	+	0.938449i	$0.612263\pi$
$710$	0	0
$711$	−8001.00	−0.422027
$712$	−7680.00	−0.404242
$713$	−2190.00	−0.115030
$714$	2268.00	0.118876
$715$	0	0
$716$	48.0000	0.00250537
$717$	14544.0	0.757539
$718$	17622.0	0.915943
$719$	34680.0	1.79881	0.899406	−	0.437114i	$-0.143999\pi$
$719$	34680.0	1.79881	0.899406	+	0.437114i	$0.143999\pi$
$720$	0	0
$721$	−9100.00	−0.470044
$722$	30090.0	1.55102
$723$	2280.00	0.117281
$724$	−5032.00	−0.258305
$725$	0	0
$726$	7932.00	0.405488
$727$	−10678.0	−0.544739	−0.272369	−	0.962193i	$-0.587807\pi$
$727$	−10678.0	−0.544739	−0.272369	+	0.962193i	$0.587807\pi$
$728$	−224.000	−0.0114038
$729$	729.000	0.0370370
$730$	0	0
$731$	−1566.00	−0.0792348
$732$	2640.00	0.133302
$733$	−18100.0	−0.912058	−0.456029	−	0.889965i	$-0.650729\pi$
$733$	−18100.0	−0.912058	−0.456029	+	0.889965i	$0.650729\pi$
$734$	7672.00	0.385802
$735$	0	0
$736$	−480.000	−0.0240394
$737$	33.0000	0.00164935
$738$	−432.000	−0.0215476
$739$	17765.0	0.884298	0.442149	−	0.896942i	$-0.354216\pi$
$739$	17765.0	0.884298	0.442149	+	0.896942i	$0.354216\pi$
$740$	0	0
$741$	−1776.00	−0.0880472
$742$	2436.00	0.120523
$743$	30648.0	1.51328	0.756639	−	0.653832i	$-0.226840\pi$
$743$	30648.0	1.51328	0.756639	+	0.653832i	$0.226840\pi$
$744$	−3504.00	−0.172665
$745$	0	0
$746$	−4994.00	−0.245098
$747$	702.000	0.0343840
$748$	−648.000	−0.0316754
$749$	9492.00	0.463058
$750$	0	0
$751$	−33016.0	−1.60422	−0.802111	−	0.597175i	$-0.796290\pi$
$751$	−33016.0	−1.60422	−0.802111	+	0.597175i	$0.796290\pi$
$752$	3648.00	0.176900
$753$	15930.0	0.770945
$754$	552.000	0.0266613
$755$	0	0
$756$	−756.000	−0.0363696
$757$	20597.0	0.988918	0.494459	−	0.869201i	$-0.335366\pi$
$757$	20597.0	0.988918	0.494459	+	0.869201i	$0.335366\pi$
$758$	−23834.0	−1.14207
$759$	135.000	0.00645611
$760$	0	0
$761$	−29844.0	−1.42161	−0.710804	−	0.703390i	$-0.751669\pi$
$761$	−29844.0	−1.42161	−0.710804	+	0.703390i	$0.751669\pi$
$762$	−4314.00	−0.205092
$763$	2387.00	0.113257
$764$	−8784.00	−0.415961
$765$	0	0
$766$	10920.0	0.515086
$767$	2928.00	0.137841
$768$	−768.000	−0.0360844
$769$	6392.00	0.299742	0.149871	−	0.988706i	$-0.452114\pi$
$769$	6392.00	0.299742	0.149871	+	0.988706i	$0.452114\pi$
$770$	0	0
$771$	4770.00	0.222811
$772$	−18820.0	−0.877392
$773$	−7986.00	−0.371587	−0.185793	−	0.982589i	$-0.559485\pi$
$773$	−7986.00	−0.371587	−0.185793	+	0.982589i	$0.559485\pi$
$774$	522.000	0.0242415
$775$	0	0
$776$	−4400.00	−0.203545
$777$	399.000	0.0184222
$778$	12558.0	0.578697
$779$	3552.00	0.163368
$780$	0	0
$781$	−1287.00	−0.0589660
$782$	1620.00	0.0740807
$783$	1863.00	0.0850296
$784$	784.000	0.0357143
$785$	0	0
$786$	7020.00	0.318569
$787$	15782.0	0.714825	0.357413	−	0.933947i	$-0.383659\pi$
$787$	15782.0	0.714825	0.357413	+	0.933947i	$0.383659\pi$
$788$	9492.00	0.429110
$789$	−18549.0	−0.836961
$790$	0	0
$791$	−10269.0	−0.461597
$792$	216.000	0.00969094
$793$	880.000	0.0394070
$794$	−25052.0	−1.11973
$795$	0	0
$796$	9824.00	0.437440
$797$	−7830.00	−0.347996	−0.173998	−	0.984746i	$-0.555669\pi$
$797$	−7830.00	−0.347996	−0.173998	+	0.984746i	$0.555669\pi$
$798$	6216.00	0.275744
$799$	−12312.0	−0.545140
$800$	0	0
$801$	−8640.00	−0.381123
$802$	9006.00	0.396525
$803$	−2730.00	−0.119975
$804$	−132.000	−0.00579015
$805$	0	0
$806$	−1168.00	−0.0510435
$807$	16002.0	0.698014
$808$	−2640.00	−0.114944
$809$	1929.00	0.0838319	0.0419160	−	0.999121i	$-0.486654\pi$
$809$	1929.00	0.0838319	0.0419160	+	0.999121i	$0.486654\pi$
$810$	0	0
$811$	−35026.0	−1.51656	−0.758279	−	0.651930i	$-0.773960\pi$
$811$	−35026.0	−1.51656	−0.758279	+	0.651930i	$0.773960\pi$
$812$	−1932.00	−0.0834974
$813$	−15936.0	−0.687454
$814$	−114.000	−0.00490872
$815$	0	0
$816$	2592.00	0.111199
$817$	−4292.00	−0.183792
$818$	−21440.0	−0.916421
$819$	−252.000	−0.0107516
$820$	0	0
$821$	13554.0	0.576173	0.288086	−	0.957604i	$-0.406981\pi$
$821$	13554.0	0.576173	0.288086	+	0.957604i	$0.406981\pi$
$822$	108.000	0.00458264
$823$	2843.00	0.120414	0.0602070	−	0.998186i	$-0.480824\pi$
$823$	2843.00	0.120414	0.0602070	+	0.998186i	$0.480824\pi$
$824$	−10400.0	−0.439686
$825$	0	0
$826$	−10248.0	−0.431687
$827$	46083.0	1.93768	0.968841	−	0.247684i	$-0.0796694\pi$
$827$	46083.0	1.93768	0.968841	+	0.247684i	$0.0796694\pi$
$828$	−540.000	−0.0226646
$829$	974.000	0.0408063	0.0204031	−	0.999792i	$-0.493505\pi$
$829$	974.000	0.0408063	0.0204031	+	0.999792i	$0.493505\pi$
$830$	0	0
$831$	−11022.0	−0.460107
$832$	−256.000	−0.0106673
$833$	−2646.00	−0.110058
$834$	5028.00	0.208759
$835$	0	0
$836$	−1776.00	−0.0734740
$837$	−3942.00	−0.162790
$838$	−10284.0	−0.423932
$839$	19986.0	0.822400	0.411200	−	0.911545i	$-0.365110\pi$
$839$	19986.0	0.822400	0.411200	+	0.911545i	$0.365110\pi$
$840$	0	0
$841$	−19628.0	−0.804789
$842$	19270.0	0.788703
$843$	−2601.00	−0.106267
$844$	−2992.00	−0.122025
$845$	0	0
$846$	4104.00	0.166783
$847$	−9254.00	−0.375409
$848$	2784.00	0.112739
$849$	13494.0	0.545480
$850$	0	0
$851$	285.000	0.0114802
$852$	5148.00	0.207004
$853$	−38500.0	−1.54539	−0.772693	−	0.634779i	$-0.781091\pi$
$853$	−38500.0	−1.54539	−0.772693	+	0.634779i	$0.781091\pi$
$854$	−3080.00	−0.123414
$855$	0	0
$856$	10848.0	0.433151
$857$	4140.00	0.165017	0.0825086	−	0.996590i	$-0.473707\pi$
$857$	4140.00	0.165017	0.0825086	+	0.996590i	$0.473707\pi$
$858$	72.0000	0.00286485
$859$	22106.0	0.878052	0.439026	−	0.898474i	$-0.355324\pi$
$859$	22106.0	0.878052	0.439026	+	0.898474i	$0.355324\pi$
$860$	0	0
$861$	504.000	0.0199492
$862$	31248.0	1.23470
$863$	−18081.0	−0.713192	−0.356596	−	0.934259i	$-0.616063\pi$
$863$	−18081.0	−0.713192	−0.356596	+	0.934259i	$0.616063\pi$
$864$	−864.000	−0.0340207
$865$	0	0
$866$	−27104.0	−1.06355
$867$	5991.00	0.234677
$868$	4088.00	0.159857
$869$	−2667.00	−0.104110
$870$	0	0
$871$	−44.0000	−0.00171169
$872$	2728.00	0.105942
$873$	−4950.00	−0.191904
$874$	4440.00	0.171837
$875$	0	0
$876$	10920.0	0.421179
$877$	−49066.0	−1.88921	−0.944607	−	0.328203i	$-0.893557\pi$
$877$	−49066.0	−1.88921	−0.944607	+	0.328203i	$0.893557\pi$
$878$	−15032.0	−0.577797
$879$	−576.000	−0.0221024
$880$	0	0
$881$	−40326.0	−1.54213	−0.771066	−	0.636756i	$-0.780276\pi$
$881$	−40326.0	−1.54213	−0.771066	+	0.636756i	$0.780276\pi$
$882$	882.000	0.0336718
$883$	−11389.0	−0.434055	−0.217027	−	0.976166i	$-0.569636\pi$
$883$	−11389.0	−0.434055	−0.217027	+	0.976166i	$0.569636\pi$
$884$	864.000	0.0328727
$885$	0	0
$886$	16536.0	0.627018
$887$	16092.0	0.609150	0.304575	−	0.952488i	$-0.401485\pi$
$887$	16092.0	0.609150	0.304575	+	0.952488i	$0.401485\pi$
$888$	456.000	0.0172324
$889$	5033.00	0.189878
$890$	0	0
$891$	243.000	0.00913671
$892$	−712.000	−0.0267259
$893$	−33744.0	−1.26450
$894$	−3078.00	−0.115150
$895$	0	0
$896$	896.000	0.0334077
$897$	−180.000	−0.00670014
$898$	330.000	0.0122631
$899$	−10074.0	−0.373734
$900$	0	0
$901$	−9396.00	−0.347421
$902$	−144.000	−0.00531560
$903$	−609.000	−0.0224432
$904$	−11736.0	−0.431785
$905$	0	0
$906$	−1758.00	−0.0644654
$907$	28712.0	1.05112	0.525560	−	0.850756i	$-0.323856\pi$
$907$	28712.0	1.05112	0.525560	+	0.850756i	$0.323856\pi$
$908$	14496.0	0.529809
$909$	−2970.00	−0.108370
$910$	0	0
$911$	5481.00	0.199334	0.0996672	−	0.995021i	$-0.468222\pi$
$911$	5481.00	0.199334	0.0996672	+	0.995021i	$0.468222\pi$
$912$	7104.00	0.257935
$913$	234.000	0.00848222
$914$	−26522.0	−0.959814
$915$	0	0
$916$	−7624.00	−0.275004
$917$	−8190.00	−0.294937
$918$	2916.00	0.104839
$919$	−47221.0	−1.69497	−0.847485	−	0.530820i	$-0.821884\pi$
$919$	−47221.0	−1.69497	−0.847485	+	0.530820i	$0.821884\pi$
$920$	0	0
$921$	−11778.0	−0.421388
$922$	7296.00	0.260608
$923$	1716.00	0.0611948
$924$	−252.000	−0.00897207
$925$	0	0
$926$	−6872.00	−0.243875
$927$	−11700.0	−0.414540
$928$	−2208.00	−0.0781047
$929$	45678.0	1.61318	0.806591	−	0.591110i	$-0.201310\pi$
$929$	45678.0	1.61318	0.806591	+	0.591110i	$0.201310\pi$
$930$	0	0
$931$	−7252.00	−0.255290
$932$	14412.0	0.506524
$933$	−19026.0	−0.667613
$934$	−10116.0	−0.354396
$935$	0	0
$936$	−288.000	−0.0100572
$937$	−25612.0	−0.892964	−0.446482	−	0.894793i	$-0.647323\pi$
$937$	−25612.0	−0.892964	−0.446482	+	0.894793i	$0.647323\pi$
$938$	154.000	0.00536064
$939$	7500.00	0.260653
$940$	0	0
$941$	16974.0	0.588030	0.294015	−	0.955801i	$-0.405008\pi$
$941$	16974.0	0.588030	0.294015	+	0.955801i	$0.405008\pi$
$942$	−15960.0	−0.552022
$943$	360.000	0.0124318
$944$	−11712.0	−0.403806
$945$	0	0
$946$	174.000	0.00598016
$947$	−57636.0	−1.97774	−0.988869	−	0.148787i	$-0.952463\pi$
$947$	−57636.0	−1.97774	−0.988869	+	0.148787i	$0.952463\pi$
$948$	10668.0	0.365486
$949$	3640.00	0.124509
$950$	0	0
$951$	−1143.00	−0.0389740
$952$	−3024.00	−0.102950
$953$	−19419.0	−0.660066	−0.330033	−	0.943969i	$-0.607060\pi$
$953$	−19419.0	−0.660066	−0.330033	+	0.943969i	$0.607060\pi$
$954$	3132.00	0.106292
$955$	0	0
$956$	−19392.0	−0.656048
$957$	621.000	0.0209760
$958$	22344.0	0.753551
$959$	−126.000	−0.00424270
$960$	0	0
$961$	−8475.00	−0.284482
$962$	152.000	0.00509426
$963$	12204.0	0.408378
$964$	−3040.00	−0.101568
$965$	0	0
$966$	630.000	0.0209834
$967$	47912.0	1.59333	0.796663	−	0.604424i	$-0.206597\pi$
$967$	47912.0	1.59333	0.796663	+	0.604424i	$0.206597\pi$
$968$	−10576.0	−0.351163
$969$	−23976.0	−0.794861
$970$	0	0
$971$	−10656.0	−0.352181	−0.176090	−	0.984374i	$-0.556345\pi$
$971$	−10656.0	−0.352181	−0.176090	+	0.984374i	$0.556345\pi$
$972$	−972.000	−0.0320750
$973$	−5866.00	−0.193274
$974$	−13766.0	−0.452866
$975$	0	0
$976$	−3520.00	−0.115443
$977$	−23481.0	−0.768909	−0.384454	−	0.923144i	$-0.625610\pi$
$977$	−23481.0	−0.768909	−0.384454	+	0.923144i	$0.625610\pi$
$978$	−7320.00	−0.239333
$979$	−2880.00	−0.0940196
$980$	0	0
$981$	3069.00	0.0998834
$982$	15726.0	0.511035
$983$	6906.00	0.224076	0.112038	−	0.993704i	$-0.464262\pi$
$983$	6906.00	0.224076	0.112038	+	0.993704i	$0.464262\pi$
$984$	576.000	0.0186608
$985$	0	0
$986$	7452.00	0.240690
$987$	−4788.00	−0.154411
$988$	2368.00	0.0762511
$989$	−435.000	−0.0139860
$990$	0	0
$991$	−49165.0	−1.57596	−0.787981	−	0.615700i	$-0.788873\pi$
$991$	−49165.0	−1.57596	−0.787981	+	0.615700i	$0.788873\pi$
$992$	4672.00	0.149532
$993$	−33945.0	−1.08481
$994$	−6006.00	−0.191649
$995$	0	0
$996$	−936.000	−0.0297774
$997$	21404.0	0.679911	0.339956	−	0.940441i	$-0.389588\pi$
$997$	21404.0	0.679911	0.339956	+	0.940441i	$0.389588\pi$
$998$	33976.0	1.07765
$999$	513.000	0.0162468

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.4.a.o.1.1	yes	1
5.2	odd	4		1050.4.g.e.799.2		2
5.3	odd	4		1050.4.g.e.799.1		2
5.4	even	2		1050.4.a.h.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.4.a.h.1.1	✓	1	5.4	even	2
1050.4.a.o.1.1	yes	1	1.1	even	1	trivial
1050.4.g.e.799.1		2	5.3	odd	4
1050.4.g.e.799.2		2	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1050.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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