LMFDB - Embedded newform 930.4.a.c.1.1

Newspace parameters

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	930.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$54.8717763053$
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	$\chi$	$=$	930.1

$q$-expansion

$f(q)$

$=$

$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} +26.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} +26.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} -48.0000 q^{11} +12.0000 q^{12} -88.0000 q^{13} +52.0000 q^{14} -15.0000 q^{15} +16.0000 q^{16} -54.0000 q^{17} +18.0000 q^{18} -160.000 q^{19} -20.0000 q^{20} +78.0000 q^{21} -96.0000 q^{22} -48.0000 q^{23} +24.0000 q^{24} +25.0000 q^{25} -176.000 q^{26} +27.0000 q^{27} +104.000 q^{28} -120.000 q^{29} -30.0000 q^{30} +31.0000 q^{31} +32.0000 q^{32} -144.000 q^{33} -108.000 q^{34} -130.000 q^{35} +36.0000 q^{36} -304.000 q^{37} -320.000 q^{38} -264.000 q^{39} -40.0000 q^{40} +162.000 q^{41} +156.000 q^{42} +272.000 q^{43} -192.000 q^{44} -45.0000 q^{45} -96.0000 q^{46} +96.0000 q^{47} +48.0000 q^{48} +333.000 q^{49} +50.0000 q^{50} -162.000 q^{51} -352.000 q^{52} +582.000 q^{53} +54.0000 q^{54} +240.000 q^{55} +208.000 q^{56} -480.000 q^{57} -240.000 q^{58} +30.0000 q^{59} -60.0000 q^{60} -478.000 q^{61} +62.0000 q^{62} +234.000 q^{63} +64.0000 q^{64} +440.000 q^{65} -288.000 q^{66} -334.000 q^{67} -216.000 q^{68} -144.000 q^{69} -260.000 q^{70} +1062.00 q^{71} +72.0000 q^{72} +212.000 q^{73} -608.000 q^{74} +75.0000 q^{75} -640.000 q^{76} -1248.00 q^{77} -528.000 q^{78} -640.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} +324.000 q^{82} +972.000 q^{83} +312.000 q^{84} +270.000 q^{85} +544.000 q^{86} -360.000 q^{87} -384.000 q^{88} +120.000 q^{89} -90.0000 q^{90} -2288.00 q^{91} -192.000 q^{92} +93.0000 q^{93} +192.000 q^{94} +800.000 q^{95} +96.0000 q^{96} +86.0000 q^{97} +666.000 q^{98} -432.000 q^{99} +O(q^{100})\)

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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	6.00000	0.408248
$7$	26.0000	1.40387	0.701934	−	0.712242i	$-0.252320\pi$
$7$	26.0000	1.40387	0.701934	+	0.712242i	$0.252320\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−10.0000	−0.316228
$11$	−48.0000	−1.31569	−0.657843	−	0.753155i	$-0.728531\pi$
$11$	−48.0000	−1.31569	−0.657843	+	0.753155i	$0.728531\pi$
$12$	12.0000	0.288675
$13$	−88.0000	−1.87745	−0.938723	−	0.344671i	$-0.887990\pi$
$13$	−88.0000	−1.87745	−0.938723	+	0.344671i	$0.887990\pi$
$14$	52.0000	0.992685
$15$	−15.0000	−0.258199
$16$	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
$19$	−160.000	−1.93192	−0.965961	−	0.258688i	$-0.916710\pi$
$19$	−160.000	−1.93192	−0.965961	+	0.258688i	$0.916710\pi$
$20$	−20.0000	−0.223607
$21$	78.0000	0.810524
$22$	−96.0000	−0.930330
$23$	−48.0000	−0.435161	−0.217580	−	0.976042i	$-0.569816\pi$
$23$	−48.0000	−0.435161	−0.217580	+	0.976042i	$0.569816\pi$
$24$	24.0000	0.204124
$25$	25.0000	0.200000
$26$	−176.000	−1.32756
$27$	27.0000	0.192450
$28$	104.000	0.701934
$29$	−120.000	−0.768395	−0.384197	−	0.923251i	$-0.625522\pi$
$29$	−120.000	−0.768395	−0.384197	+	0.923251i	$0.625522\pi$
$30$	−30.0000	−0.182574
$31$	31.0000	0.179605
$31$	31.0000	0.179605
$32$	32.0000	0.176777
$33$	−144.000	−0.759612
$34$	−108.000	−0.544760
$35$	−130.000	−0.627829
$36$	36.0000	0.166667
$37$	−304.000	−1.35074	−0.675369	−	0.737480i	$-0.736016\pi$
$37$	−304.000	−1.35074	−0.675369	+	0.737480i	$0.736016\pi$
$38$	−320.000	−1.36608
$39$	−264.000	−1.08394
$40$	−40.0000	−0.158114
$41$	162.000	0.617077	0.308538	−	0.951212i	$-0.400160\pi$
$41$	162.000	0.617077	0.308538	+	0.951212i	$0.400160\pi$
$42$	156.000	0.573127
$43$	272.000	0.964642	0.482321	−	0.875995i	$-0.339794\pi$
$43$	272.000	0.964642	0.482321	+	0.875995i	$0.339794\pi$
$44$	−192.000	−0.657843
$45$	−45.0000	−0.149071
$46$	−96.0000	−0.307705
$47$	96.0000	0.297937	0.148969	−	0.988842i	$-0.452405\pi$
$47$	96.0000	0.297937	0.148969	+	0.988842i	$0.452405\pi$
$48$	48.0000	0.144338
$49$	333.000	0.970845
$50$	50.0000	0.141421
$51$	−162.000	−0.444795
$52$	−352.000	−0.938723
$53$	582.000	1.50837	0.754187	−	0.656659i	$-0.228031\pi$
$53$	582.000	1.50837	0.754187	+	0.656659i	$0.228031\pi$
$54$	54.0000	0.136083
$55$	240.000	0.588393
$56$	208.000	0.496342
$57$	−480.000	−1.11540
$58$	−240.000	−0.543337
$59$	30.0000	0.0661978	0.0330989	−	0.999452i	$-0.489462\pi$
$59$	30.0000	0.0661978	0.0330989	+	0.999452i	$0.489462\pi$
$60$	−60.0000	−0.129099
$61$	−478.000	−1.00331	−0.501653	−	0.865069i	$-0.667274\pi$
$61$	−478.000	−1.00331	−0.501653	+	0.865069i	$0.667274\pi$
$62$	62.0000	0.127000
$63$	234.000	0.467956
$64$	64.0000	0.125000
$65$	440.000	0.839620
$66$	−288.000	−0.537127
$67$	−334.000	−0.609024	−0.304512	−	0.952509i	$-0.598493\pi$
$67$	−334.000	−0.609024	−0.304512	+	0.952509i	$0.598493\pi$
$68$	−216.000	−0.385204
$69$	−144.000	−0.251240
$70$	−260.000	−0.443942
$71$	1062.00	1.77516	0.887579	−	0.460656i	$-0.152386\pi$
$71$	1062.00	1.77516	0.887579	+	0.460656i	$0.152386\pi$
$72$	72.0000	0.117851
$73$	212.000	0.339900	0.169950	−	0.985453i	$-0.445639\pi$
$73$	212.000	0.339900	0.169950	+	0.985453i	$0.445639\pi$
$74$	−608.000	−0.955116
$75$	75.0000	0.115470
$76$	−640.000	−0.965961
$77$	−1248.00	−1.84705
$78$	−528.000	−0.766464
$79$	−640.000	−0.911464	−0.455732	−	0.890117i	$-0.650622\pi$
$79$	−640.000	−0.911464	−0.455732	+	0.890117i	$0.650622\pi$
$80$	−80.0000	−0.111803
$81$	81.0000	0.111111
$82$	324.000	0.436339
$83$	972.000	1.28543	0.642716	−	0.766105i	$-0.277808\pi$
$83$	972.000	1.28543	0.642716	+	0.766105i	$0.277808\pi$
$84$	312.000	0.405262
$85$	270.000	0.344537
$86$	544.000	0.682105
$87$	−360.000	−0.443633
$88$	−384.000	−0.465165
$89$	120.000	0.142921	0.0714605	−	0.997443i	$-0.477234\pi$
$89$	120.000	0.142921	0.0714605	+	0.997443i	$0.477234\pi$
$90$	−90.0000	−0.105409
$91$	−2288.00	−2.63569
$92$	−192.000	−0.217580
$93$	93.0000	0.103695
$94$	192.000	0.210673
$95$	800.000	0.863982
$96$	96.0000	0.102062
$97$	86.0000	0.0900204	0.0450102	−	0.998987i	$-0.485668\pi$
$97$	86.0000	0.0900204	0.0450102	+	0.998987i	$0.485668\pi$
$98$	666.000	0.686491
$99$	−432.000	−0.438562
$100$	100.000	0.100000
$101$	1722.00	1.69649	0.848245	−	0.529605i	$-0.177660\pi$
$101$	1722.00	1.69649	0.848245	+	0.529605i	$0.177660\pi$
$102$	−324.000	−0.314517
$103$	−1258.00	−1.20344	−0.601721	−	0.798707i	$-0.705518\pi$
$103$	−1258.00	−1.20344	−0.601721	+	0.798707i	$0.705518\pi$
$104$	−704.000	−0.663778
$105$	−390.000	−0.362477
$106$	1164.00	1.06658
$107$	−1884.00	−1.70218	−0.851090	−	0.525021i	$-0.824058\pi$
$107$	−1884.00	−1.70218	−0.851090	+	0.525021i	$0.824058\pi$
$108$	108.000	0.0962250
$109$	−70.0000	−0.0615118	−0.0307559	−	0.999527i	$-0.509791\pi$
$109$	−70.0000	−0.0615118	−0.0307559	+	0.999527i	$0.509791\pi$
$110$	480.000	0.416056
$111$	−912.000	−0.779849
$112$	416.000	0.350967
$113$	−2178.00	−1.81318	−0.906589	−	0.422016i	$-0.861323\pi$
$113$	−2178.00	−1.81318	−0.906589	+	0.422016i	$0.861323\pi$
$114$	−960.000	−0.788704
$115$	240.000	0.194610
$116$	−480.000	−0.384197
$117$	−792.000	−0.625816
$118$	60.0000	0.0468089
$119$	−1404.00	−1.08155
$120$	−120.000	−0.0912871
$121$	973.000	0.731029
$122$	−956.000	−0.709444
$123$	486.000	0.356269
$124$	124.000	0.0898027
$125$	−125.000	−0.0894427
$126$	468.000	0.330895
$127$	−2464.00	−1.72161	−0.860806	−	0.508934i	$-0.830040\pi$
$127$	−2464.00	−1.72161	−0.860806	+	0.508934i	$0.830040\pi$
$128$	128.000	0.0883883
$129$	816.000	0.556936
$130$	880.000	0.593701
$131$	−1458.00	−0.972413	−0.486206	−	0.873844i	$-0.661620\pi$
$131$	−1458.00	−0.972413	−0.486206	+	0.873844i	$0.661620\pi$
$132$	−576.000	−0.379806
$133$	−4160.00	−2.71216
$134$	−668.000	−0.430645
$135$	−135.000	−0.0860663
$136$	−432.000	−0.272380
$137$	966.000	0.602416	0.301208	−	0.953559i	$-0.402610\pi$
$137$	966.000	0.602416	0.301208	+	0.953559i	$0.402610\pi$
$138$	−288.000	−0.177654
$139$	980.000	0.598004	0.299002	−	0.954253i	$-0.403346\pi$
$139$	980.000	0.598004	0.299002	+	0.954253i	$0.403346\pi$
$140$	−520.000	−0.313914
$141$	288.000	0.172014
$142$	2124.00	1.25523
$143$	4224.00	2.47013
$144$	144.000	0.0833333
$145$	600.000	0.343636
$146$	424.000	0.240346
$147$	999.000	0.560518
$148$	−1216.00	−0.675369
$149$	−30.0000	−0.0164946	−0.00824730	−	0.999966i	$-0.502625\pi$
$149$	−30.0000	−0.0164946	−0.00824730	+	0.999966i	$0.502625\pi$
$150$	150.000	0.0816497
$151$	1832.00	0.987325	0.493662	−	0.869654i	$-0.335658\pi$
$151$	1832.00	0.987325	0.493662	+	0.869654i	$0.335658\pi$
$152$	−1280.00	−0.683038
$153$	−486.000	−0.256802
$154$	−2496.00	−1.30606
$155$	−155.000	−0.0803219
$156$	−1056.00	−0.541972
$157$	3566.00	1.81272	0.906362	−	0.422501i	$-0.138848\pi$
$157$	3566.00	1.81272	0.906362	+	0.422501i	$0.138848\pi$
$158$	−1280.00	−0.644502
$159$	1746.00	0.870860
$160$	−160.000	−0.0790569
$161$	−1248.00	−0.610908
$162$	162.000	0.0785674
$163$	−1798.00	−0.863989	−0.431995	−	0.901876i	$-0.642190\pi$
$163$	−1798.00	−0.863989	−0.431995	+	0.901876i	$0.642190\pi$
$164$	648.000	0.308538
$165$	720.000	0.339709
$166$	1944.00	0.908938
$167$	−864.000	−0.400349	−0.200175	−	0.979760i	$-0.564151\pi$
$167$	−864.000	−0.400349	−0.200175	+	0.979760i	$0.564151\pi$
$168$	624.000	0.286563
$169$	5547.00	2.52481
$170$	540.000	0.243624
$171$	−1440.00	−0.643974
$172$	1088.00	0.482321
$173$	1482.00	0.651297	0.325648	−	0.945491i	$-0.394417\pi$
$173$	1482.00	0.651297	0.325648	+	0.945491i	$0.394417\pi$
$174$	−720.000	−0.313696
$175$	650.000	0.280774
$176$	−768.000	−0.328921
$177$	90.0000	0.0382193
$178$	240.000	0.101060
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	−180.000	−0.0745356
$181$	−358.000	−0.147016	−0.0735081	−	0.997295i	$-0.523419\pi$
$181$	−358.000	−0.147016	−0.0735081	+	0.997295i	$0.523419\pi$
$182$	−4576.00	−1.86371
$183$	−1434.00	−0.579259
$184$	−384.000	−0.153852
$185$	1520.00	0.604068
$186$	186.000	0.0733236
$187$	2592.00	1.01361
$188$	384.000	0.148969
$189$	702.000	0.270175
$190$	1600.00	0.610927
$191$	1722.00	0.652354	0.326177	−	0.945309i	$-0.394240\pi$
$191$	1722.00	0.652354	0.326177	+	0.945309i	$0.394240\pi$
$192$	192.000	0.0721688
$193$	−418.000	−0.155898	−0.0779490	−	0.996957i	$-0.524837\pi$
$193$	−418.000	−0.155898	−0.0779490	+	0.996957i	$0.524837\pi$
$194$	172.000	0.0636540
$195$	1320.00	0.484755
$196$	1332.00	0.485423
$197$	−54.0000	−0.0195296	−0.00976482	−	0.999952i	$-0.503108\pi$
$197$	−54.0000	−0.0195296	−0.00976482	+	0.999952i	$0.503108\pi$
$198$	−864.000	−0.310110
$199$	−1720.00	−0.612701	−0.306351	−	0.951919i	$-0.599108\pi$
$199$	−1720.00	−0.612701	−0.306351	+	0.951919i	$0.599108\pi$
$200$	200.000	0.0707107
$201$	−1002.00	−0.351620
$202$	3444.00	1.19960
$203$	−3120.00	−1.07872
$204$	−648.000	−0.222397
$205$	−810.000	−0.275965
$206$	−2516.00	−0.850961
$207$	−432.000	−0.145054
$208$	−1408.00	−0.469362
$209$	7680.00	2.54180
$210$	−780.000	−0.256310
$211$	−2488.00	−0.811758	−0.405879	−	0.913927i	$-0.633035\pi$
$211$	−2488.00	−0.811758	−0.405879	+	0.913927i	$0.633035\pi$
$212$	2328.00	0.754187
$213$	3186.00	1.02489
$214$	−3768.00	−1.20362
$215$	−1360.00	−0.431401
$216$	216.000	0.0680414
$217$	806.000	0.252142
$218$	−140.000	−0.0434954
$219$	636.000	0.196242
$220$	960.000	0.294196
$221$	4752.00	1.44640
$222$	−1824.00	−0.551436
$223$	−3148.00	−0.945317	−0.472658	−	0.881246i	$-0.656706\pi$
$223$	−3148.00	−0.945317	−0.472658	+	0.881246i	$0.656706\pi$
$224$	832.000	0.248171
$225$	225.000	0.0666667
$226$	−4356.00	−1.28211
$227$	1536.00	0.449110	0.224555	−	0.974461i	$-0.427907\pi$
$227$	1536.00	0.449110	0.224555	+	0.974461i	$0.427907\pi$
$228$	−1920.00	−0.557698
$229$	−2770.00	−0.799331	−0.399665	−	0.916661i	$-0.630874\pi$
$229$	−2770.00	−0.799331	−0.399665	+	0.916661i	$0.630874\pi$
$230$	480.000	0.137610
$231$	−3744.00	−1.06639
$232$	−960.000	−0.271668
$233$	−2598.00	−0.730475	−0.365237	−	0.930914i	$-0.619012\pi$
$233$	−2598.00	−0.730475	−0.365237	+	0.930914i	$0.619012\pi$
$234$	−1584.00	−0.442518
$235$	−480.000	−0.133241
$236$	120.000	0.0330989
$237$	−1920.00	−0.526234
$238$	−2808.00	−0.764771
$239$	−5340.00	−1.44525	−0.722627	−	0.691238i	$-0.757066\pi$
$239$	−5340.00	−1.44525	−0.722627	+	0.691238i	$0.757066\pi$
$240$	−240.000	−0.0645497
$241$	3002.00	0.802389	0.401195	−	0.915993i	$-0.368595\pi$
$241$	3002.00	0.802389	0.401195	+	0.915993i	$0.368595\pi$
$242$	1946.00	0.516916
$243$	243.000	0.0641500
$244$	−1912.00	−0.501653
$245$	−1665.00	−0.434175
$246$	972.000	0.251921
$247$	14080.0	3.62708
$248$	248.000	0.0635001
$249$	2916.00	0.742145
$250$	−250.000	−0.0632456
$251$	2352.00	0.591462	0.295731	−	0.955271i	$-0.404437\pi$
$251$	2352.00	0.591462	0.295731	+	0.955271i	$0.404437\pi$
$252$	936.000	0.233978
$253$	2304.00	0.572535
$254$	−4928.00	−1.21736
$255$	810.000	0.198918
$256$	256.000	0.0625000
$257$	−294.000	−0.0713588	−0.0356794	−	0.999363i	$-0.511360\pi$
$257$	−294.000	−0.0713588	−0.0356794	+	0.999363i	$0.511360\pi$
$258$	1632.00	0.393813
$259$	−7904.00	−1.89626
$260$	1760.00	0.419810
$261$	−1080.00	−0.256132
$262$	−2916.00	−0.687600
$263$	−2448.00	−0.573955	−0.286977	−	0.957937i	$-0.592650\pi$
$263$	−2448.00	−0.573955	−0.286977	+	0.957937i	$0.592650\pi$
$264$	−1152.00	−0.268563
$265$	−2910.00	−0.674566
$266$	−8320.00	−1.91779
$267$	360.000	0.0825155
$268$	−1336.00	−0.304512
$269$	−8400.00	−1.90393	−0.951965	−	0.306208i	$-0.900940\pi$
$269$	−8400.00	−1.90393	−0.951965	+	0.306208i	$0.900940\pi$
$270$	−270.000	−0.0608581
$271$	−3688.00	−0.826679	−0.413340	−	0.910577i	$-0.635638\pi$
$271$	−3688.00	−0.826679	−0.413340	+	0.910577i	$0.635638\pi$
$272$	−864.000	−0.192602
$273$	−6864.00	−1.52171
$274$	1932.00	0.425972
$275$	−1200.00	−0.263137
$276$	−576.000	−0.125620
$277$	−9124.00	−1.97909	−0.989545	−	0.144223i	$-0.953932\pi$
$277$	−9124.00	−1.97909	−0.989545	+	0.144223i	$0.953932\pi$
$278$	1960.00	0.422852
$279$	279.000	0.0598684
$280$	−1040.00	−0.221971
$281$	6702.00	1.42280	0.711402	−	0.702786i	$-0.248061\pi$
$281$	6702.00	1.42280	0.711402	+	0.702786i	$0.248061\pi$
$282$	576.000	0.121632
$283$	6482.00	1.36154	0.680768	−	0.732499i	$-0.261646\pi$
$283$	6482.00	1.36154	0.680768	+	0.732499i	$0.261646\pi$
$284$	4248.00	0.887579
$285$	2400.00	0.498820
$286$	8448.00	1.74665
$287$	4212.00	0.866294
$288$	288.000	0.0589256
$289$	−1997.00	−0.406473
$290$	1200.00	0.242988
$291$	258.000	0.0519733
$292$	848.000	0.169950
$293$	4062.00	0.809913	0.404957	−	0.914336i	$-0.367287\pi$
$293$	4062.00	0.809913	0.404957	+	0.914336i	$0.367287\pi$
$294$	1998.00	0.396346
$295$	−150.000	−0.0296045
$296$	−2432.00	−0.477558
$297$	−1296.00	−0.253204
$298$	−60.0000	−0.0116634
$299$	4224.00	0.816991
$300$	300.000	0.0577350
$301$	7072.00	1.35423
$302$	3664.00	0.698144
$303$	5166.00	0.979468
$304$	−2560.00	−0.482980
$305$	2390.00	0.448692
$306$	−972.000	−0.181587
$307$	5006.00	0.930643	0.465322	−	0.885142i	$-0.345939\pi$
$307$	5006.00	0.930643	0.465322	+	0.885142i	$0.345939\pi$
$308$	−4992.00	−0.923525
$309$	−3774.00	−0.694807
$310$	−310.000	−0.0567962
$311$	−438.000	−0.0798608	−0.0399304	−	0.999202i	$-0.512714\pi$
$311$	−438.000	−0.0798608	−0.0399304	+	0.999202i	$0.512714\pi$
$312$	−2112.00	−0.383232
$313$	10292.0	1.85859	0.929294	−	0.369340i	$-0.120416\pi$
$313$	10292.0	1.85859	0.929294	+	0.369340i	$0.120416\pi$
$314$	7132.00	1.28179
$315$	−1170.00	−0.209276
$316$	−2560.00	−0.455732
$317$	−8874.00	−1.57228	−0.786141	−	0.618047i	$-0.787924\pi$
$317$	−8874.00	−1.57228	−0.786141	+	0.618047i	$0.787924\pi$
$318$	3492.00	0.615791
$319$	5760.00	1.01097
$320$	−320.000	−0.0559017
$321$	−5652.00	−0.982754
$322$	−2496.00	−0.431977
$323$	8640.00	1.48837
$324$	324.000	0.0555556
$325$	−2200.00	−0.375489
$326$	−3596.00	−0.610933
$327$	−210.000	−0.0355138
$328$	1296.00	0.218170
$329$	2496.00	0.418264
$330$	1440.00	0.240210
$331$	−9508.00	−1.57887	−0.789436	−	0.613832i	$-0.789627\pi$
$331$	−9508.00	−1.57887	−0.789436	+	0.613832i	$0.789627\pi$
$332$	3888.00	0.642716
$333$	−2736.00	−0.450246
$334$	−1728.00	−0.283090
$335$	1670.00	0.272364
$336$	1248.00	0.202631
$337$	−3304.00	−0.534066	−0.267033	−	0.963687i	$-0.586043\pi$
$337$	−3304.00	−0.534066	−0.267033	+	0.963687i	$0.586043\pi$
$338$	11094.0	1.78531
$339$	−6534.00	−1.04684
$340$	1080.00	0.172268
$341$	−1488.00	−0.236304
$342$	−2880.00	−0.455358
$343$	−260.000	−0.0409291
$344$	2176.00	0.341052
$345$	720.000	0.112358
$346$	2964.00	0.460536
$347$	−5724.00	−0.885534	−0.442767	−	0.896637i	$-0.646003\pi$
$347$	−5724.00	−0.885534	−0.442767	+	0.896637i	$0.646003\pi$
$348$	−1440.00	−0.221816
$349$	10010.0	1.53531	0.767655	−	0.640864i	$-0.221424\pi$
$349$	10010.0	1.53531	0.767655	+	0.640864i	$0.221424\pi$
$350$	1300.00	0.198537
$351$	−2376.00	−0.361315
$352$	−1536.00	−0.232583
$353$	−7758.00	−1.16974	−0.584868	−	0.811129i	$-0.698854\pi$
$353$	−7758.00	−1.16974	−0.584868	+	0.811129i	$0.698854\pi$
$354$	180.000	0.0270251
$355$	−5310.00	−0.793875
$356$	480.000	0.0714605
$357$	−4212.00	−0.624433
$358$	0	0
$359$	8730.00	1.28343	0.641716	−	0.766943i	$-0.278223\pi$
$359$	8730.00	1.28343	0.641716	+	0.766943i	$0.278223\pi$
$360$	−360.000	−0.0527046
$361$	18741.0	2.73232
$362$	−716.000	−0.103956
$363$	2919.00	0.422060
$364$	−9152.00	−1.31784
$365$	−1060.00	−0.152008
$366$	−2868.00	−0.409598
$367$	−5404.00	−0.768628	−0.384314	−	0.923202i	$-0.625562\pi$
$367$	−5404.00	−0.768628	−0.384314	+	0.923202i	$0.625562\pi$
$368$	−768.000	−0.108790
$369$	1458.00	0.205692
$370$	3040.00	0.427141
$371$	15132.0	2.11756
$372$	372.000	0.0518476
$373$	−9538.00	−1.32402	−0.662009	−	0.749496i	$-0.730296\pi$
$373$	−9538.00	−1.32402	−0.662009	+	0.749496i	$0.730296\pi$
$374$	5184.00	0.716733
$375$	−375.000	−0.0516398
$376$	768.000	0.105337
$377$	10560.0	1.44262
$378$	1404.00	0.191042
$379$	−5440.00	−0.737293	−0.368646	−	0.929570i	$-0.620179\pi$
$379$	−5440.00	−0.737293	−0.368646	+	0.929570i	$0.620179\pi$
$380$	3200.00	0.431991
$381$	−7392.00	−0.993973
$382$	3444.00	0.461284
$383$	6672.00	0.890139	0.445070	−	0.895496i	$-0.353179\pi$
$383$	6672.00	0.890139	0.445070	+	0.895496i	$0.353179\pi$
$384$	384.000	0.0510310
$385$	6240.00	0.826026
$386$	−836.000	−0.110236
$387$	2448.00	0.321547
$388$	344.000	0.0450102
$389$	−10440.0	−1.36074	−0.680371	−	0.732867i	$-0.738182\pi$
$389$	−10440.0	−1.36074	−0.680371	+	0.732867i	$0.738182\pi$
$390$	2640.00	0.342773
$391$	2592.00	0.335251
$392$	2664.00	0.343246
$393$	−4374.00	−0.561423
$394$	−108.000	−0.0138095
$395$	3200.00	0.407619
$396$	−1728.00	−0.219281
$397$	−6334.00	−0.800741	−0.400371	−	0.916353i	$-0.631119\pi$
$397$	−6334.00	−0.800741	−0.400371	+	0.916353i	$0.631119\pi$
$398$	−3440.00	−0.433245
$399$	−12480.0	−1.56587
$400$	400.000	0.0500000
$401$	10212.0	1.27173	0.635864	−	0.771801i	$-0.280644\pi$
$401$	10212.0	1.27173	0.635864	+	0.771801i	$0.280644\pi$
$402$	−2004.00	−0.248633
$403$	−2728.00	−0.337199
$404$	6888.00	0.848245
$405$	−405.000	−0.0496904
$406$	−6240.00	−0.762773
$407$	14592.0	1.77715
$408$	−1296.00	−0.157259
$409$	8030.00	0.970802	0.485401	−	0.874292i	$-0.338674\pi$
$409$	8030.00	0.970802	0.485401	+	0.874292i	$0.338674\pi$
$410$	−1620.00	−0.195137
$411$	2898.00	0.347805
$412$	−5032.00	−0.601721
$413$	780.000	0.0929329
$414$	−864.000	−0.102568
$415$	−4860.00	−0.574863
$416$	−2816.00	−0.331889
$417$	2940.00	0.345258
$418$	15360.0	1.79733
$419$	7530.00	0.877958	0.438979	−	0.898497i	$-0.355340\pi$
$419$	7530.00	0.877958	0.438979	+	0.898497i	$0.355340\pi$
$420$	−1560.00	−0.181239
$421$	−4078.00	−0.472089	−0.236045	−	0.971742i	$-0.575851\pi$
$421$	−4078.00	−0.472089	−0.236045	+	0.971742i	$0.575851\pi$
$422$	−4976.00	−0.574000
$423$	864.000	0.0993123
$424$	4656.00	0.533291
$425$	−1350.00	−0.154081
$426$	6372.00	0.724705
$427$	−12428.0	−1.40851
$428$	−7536.00	−0.851090
$429$	12672.0	1.42613
$430$	−2720.00	−0.305047
$431$	15882.0	1.77496	0.887481	−	0.460843i	$-0.152453\pi$
$431$	15882.0	1.77496	0.887481	+	0.460843i	$0.152453\pi$
$432$	432.000	0.0481125
$433$	4772.00	0.529625	0.264813	−	0.964300i	$-0.414690\pi$
$433$	4772.00	0.529625	0.264813	+	0.964300i	$0.414690\pi$
$434$	1612.00	0.178291
$435$	1800.00	0.198399
$436$	−280.000	−0.0307559
$437$	7680.00	0.840696
$438$	1272.00	0.138764
$439$	−1960.00	−0.213088	−0.106544	−	0.994308i	$-0.533979\pi$
$439$	−1960.00	−0.213088	−0.106544	+	0.994308i	$0.533979\pi$
$440$	1920.00	0.208028
$441$	2997.00	0.323615
$442$	9504.00	1.02276
$443$	−4128.00	−0.442725	−0.221363	−	0.975192i	$-0.571050\pi$
$443$	−4128.00	−0.442725	−0.221363	+	0.975192i	$0.571050\pi$
$444$	−3648.00	−0.389924
$445$	−600.000	−0.0639162
$446$	−6296.00	−0.668440
$447$	−90.0000	−0.00952316
$448$	1664.00	0.175484
$449$	−14820.0	−1.55768	−0.778841	−	0.627222i	$-0.784192\pi$
$449$	−14820.0	−1.55768	−0.778841	+	0.627222i	$0.784192\pi$
$450$	450.000	0.0471405
$451$	−7776.00	−0.811879
$452$	−8712.00	−0.906589
$453$	5496.00	0.570032
$454$	3072.00	0.317569
$455$	11440.0	1.17872
$456$	−3840.00	−0.394352
$457$	8516.00	0.871689	0.435844	−	0.900022i	$-0.356450\pi$
$457$	8516.00	0.871689	0.435844	+	0.900022i	$0.356450\pi$
$458$	−5540.00	−0.565212
$459$	−1458.00	−0.148265
$460$	960.000	0.0973048
$461$	13692.0	1.38330	0.691649	−	0.722234i	$-0.256885\pi$
$461$	13692.0	1.38330	0.691649	+	0.722234i	$0.256885\pi$
$462$	−7488.00	−0.754055
$463$	−4288.00	−0.430411	−0.215205	−	0.976569i	$-0.569042\pi$
$463$	−4288.00	−0.430411	−0.215205	+	0.976569i	$0.569042\pi$
$464$	−1920.00	−0.192099
$465$	−465.000	−0.0463739
$466$	−5196.00	−0.516524
$467$	−324.000	−0.0321048	−0.0160524	−	0.999871i	$-0.505110\pi$
$467$	−324.000	−0.0321048	−0.0160524	+	0.999871i	$0.505110\pi$
$468$	−3168.00	−0.312908
$469$	−8684.00	−0.854989
$470$	−960.000	−0.0942160
$471$	10698.0	1.04658
$472$	240.000	0.0234044
$473$	−13056.0	−1.26917
$474$	−3840.00	−0.372103
$475$	−4000.00	−0.386384
$476$	−5616.00	−0.540775
$477$	5238.00	0.502791
$478$	−10680.0	−1.02195
$479$	−8970.00	−0.855636	−0.427818	−	0.903865i	$-0.640718\pi$
$479$	−8970.00	−0.855636	−0.427818	+	0.903865i	$0.640718\pi$
$480$	−480.000	−0.0456435
$481$	26752.0	2.53594
$482$	6004.00	0.567375
$483$	−3744.00	−0.352708
$484$	3892.00	0.365515
$485$	−430.000	−0.0402583
$486$	486.000	0.0453609
$487$	14216.0	1.32277	0.661384	−	0.750047i	$-0.269969\pi$
$487$	14216.0	1.32277	0.661384	+	0.750047i	$0.269969\pi$
$488$	−3824.00	−0.354722
$489$	−5394.00	−0.498824
$490$	−3330.00	−0.307008
$491$	−8268.00	−0.759938	−0.379969	−	0.924999i	$-0.624065\pi$
$491$	−8268.00	−0.759938	−0.379969	+	0.924999i	$0.624065\pi$
$492$	1944.00	0.178135
$493$	6480.00	0.591977
$494$	28160.0	2.56473
$495$	2160.00	0.196131
$496$	496.000	0.0449013
$497$	27612.0	2.49209
$498$	5832.00	0.524775
$499$	−11860.0	−1.06398	−0.531990	−	0.846750i	$-0.678556\pi$
$499$	−11860.0	−1.06398	−0.531990	+	0.846750i	$0.678556\pi$
$500$	−500.000	−0.0447214
$501$	−2592.00	−0.231142
$502$	4704.00	0.418227
$503$	−3768.00	−0.334010	−0.167005	−	0.985956i	$-0.553410\pi$
$503$	−3768.00	−0.334010	−0.167005	+	0.985956i	$0.553410\pi$
$504$	1872.00	0.165447
$505$	−8610.00	−0.758693
$506$	4608.00	0.404843
$507$	16641.0	1.45770
$508$	−9856.00	−0.860806
$509$	−3420.00	−0.297817	−0.148908	−	0.988851i	$-0.547576\pi$
$509$	−3420.00	−0.297817	−0.148908	+	0.988851i	$0.547576\pi$
$510$	1620.00	0.140656
$511$	5512.00	0.477175
$512$	512.000	0.0441942
$513$	−4320.00	−0.371799
$514$	−588.000	−0.0504583
$515$	6290.00	0.538195
$516$	3264.00	0.278468
$517$	−4608.00	−0.391992
$518$	−15808.0	−1.34086
$519$	4446.00	0.376026
$520$	3520.00	0.296850
$521$	−15198.0	−1.27800	−0.638999	−	0.769208i	$-0.720651\pi$
$521$	−15198.0	−1.27800	−0.638999	+	0.769208i	$0.720651\pi$
$522$	−2160.00	−0.181112
$523$	−208.000	−0.0173904	−0.00869522	−	0.999962i	$-0.502768\pi$
$523$	−208.000	−0.0173904	−0.00869522	+	0.999962i	$0.502768\pi$
$524$	−5832.00	−0.486206
$525$	1950.00	0.162105
$526$	−4896.00	−0.405847
$527$	−1674.00	−0.138369
$528$	−2304.00	−0.189903
$529$	−9863.00	−0.810635
$530$	−5820.00	−0.476990
$531$	270.000	0.0220659
$532$	−16640.0	−1.35608
$533$	−14256.0	−1.15853
$534$	720.000	0.0583473
$535$	9420.00	0.761238
$536$	−2672.00	−0.215322
$537$	0	0
$538$	−16800.0	−1.34628
$539$	−15984.0	−1.27733
$540$	−540.000	−0.0430331
$541$	−22918.0	−1.82130	−0.910649	−	0.413182i	$-0.864417\pi$
$541$	−22918.0	−1.82130	−0.910649	+	0.413182i	$0.864417\pi$
$542$	−7376.00	−0.584550
$543$	−1074.00	−0.0848798
$544$	−1728.00	−0.136190
$545$	350.000	0.0275089
$546$	−13728.0	−1.07601
$547$	23906.0	1.86864	0.934321	−	0.356434i	$-0.116007\pi$
$547$	23906.0	1.86864	0.934321	+	0.356434i	$0.116007\pi$
$548$	3864.00	0.301208
$549$	−4302.00	−0.334435
$550$	−2400.00	−0.186066
$551$	19200.0	1.48448
$552$	−1152.00	−0.0888268
$553$	−16640.0	−1.27957
$554$	−18248.0	−1.39943
$555$	4560.00	0.348759
$556$	3920.00	0.299002
$557$	18846.0	1.43363	0.716814	−	0.697265i	$-0.245600\pi$
$557$	18846.0	1.43363	0.716814	+	0.697265i	$0.245600\pi$
$558$	558.000	0.0423334
$559$	−23936.0	−1.81106
$560$	−2080.00	−0.156957
$561$	7776.00	0.585210
$562$	13404.0	1.00607
$563$	19452.0	1.45614	0.728068	−	0.685505i	$-0.240419\pi$
$563$	19452.0	1.45614	0.728068	+	0.685505i	$0.240419\pi$
$564$	1152.00	0.0860070
$565$	10890.0	0.810877
$566$	12964.0	0.962752
$567$	2106.00	0.155985
$568$	8496.00	0.627613
$569$	23940.0	1.76383	0.881913	−	0.471412i	$-0.156256\pi$
$569$	23940.0	1.76383	0.881913	+	0.471412i	$0.156256\pi$
$570$	4800.00	0.352719
$571$	−9628.00	−0.705638	−0.352819	−	0.935692i	$-0.614777\pi$
$571$	−9628.00	−0.705638	−0.352819	+	0.935692i	$0.614777\pi$
$572$	16896.0	1.23507
$573$	5166.00	0.376637
$574$	8424.00	0.612563
$575$	−1200.00	−0.0870321
$576$	576.000	0.0416667
$577$	−23374.0	−1.68643	−0.843217	−	0.537573i	$-0.819341\pi$
$577$	−23374.0	−1.68643	−0.843217	+	0.537573i	$0.819341\pi$
$578$	−3994.00	−0.287420
$579$	−1254.00	−0.0900077
$580$	2400.00	0.171818
$581$	25272.0	1.80458
$582$	516.000	0.0367507
$583$	−27936.0	−1.98455
$584$	1696.00	0.120173
$585$	3960.00	0.279873
$586$	8124.00	0.572695
$587$	−11244.0	−0.790613	−0.395306	−	0.918549i	$-0.629362\pi$
$587$	−11244.0	−0.790613	−0.395306	+	0.918549i	$0.629362\pi$
$588$	3996.00	0.280259
$589$	−4960.00	−0.346983
$590$	−300.000	−0.0209336
$591$	−162.000	−0.0112754
$592$	−4864.00	−0.337684
$593$	−5298.00	−0.366885	−0.183442	−	0.983030i	$-0.558724\pi$
$593$	−5298.00	−0.366885	−0.183442	+	0.983030i	$0.558724\pi$
$594$	−2592.00	−0.179042
$595$	7020.00	0.483684
$596$	−120.000	−0.00824730
$597$	−5160.00	−0.353743
$598$	8448.00	0.577700
$599$	−2430.00	−0.165755	−0.0828774	−	0.996560i	$-0.526411\pi$
$599$	−2430.00	−0.165755	−0.0828774	+	0.996560i	$0.526411\pi$
$600$	600.000	0.0408248
$601$	2702.00	0.183389	0.0916946	−	0.995787i	$-0.470772\pi$
$601$	2702.00	0.183389	0.0916946	+	0.995787i	$0.470772\pi$
$602$	14144.0	0.957585
$603$	−3006.00	−0.203008
$604$	7328.00	0.493662
$605$	−4865.00	−0.326926
$606$	10332.0	0.692589
$607$	8366.00	0.559416	0.279708	−	0.960085i	$-0.409762\pi$
$607$	8366.00	0.559416	0.279708	+	0.960085i	$0.409762\pi$
$608$	−5120.00	−0.341519
$609$	−9360.00	−0.622802
$610$	4780.00	0.317273
$611$	−8448.00	−0.559361
$612$	−1944.00	−0.128401
$613$	−6028.00	−0.397176	−0.198588	−	0.980083i	$-0.563635\pi$
$613$	−6028.00	−0.397176	−0.198588	+	0.980083i	$0.563635\pi$
$614$	10012.0	0.658064
$615$	−2430.00	−0.159329
$616$	−9984.00	−0.653031
$617$	−5634.00	−0.367612	−0.183806	−	0.982963i	$-0.558842\pi$
$617$	−5634.00	−0.367612	−0.183806	+	0.982963i	$0.558842\pi$
$618$	−7548.00	−0.491303
$619$	−10420.0	−0.676600	−0.338300	−	0.941038i	$-0.609852\pi$
$619$	−10420.0	−0.676600	−0.338300	+	0.941038i	$0.609852\pi$
$620$	−620.000	−0.0401610
$621$	−1296.00	−0.0837467
$622$	−876.000	−0.0564701
$623$	3120.00	0.200642
$624$	−4224.00	−0.270986
$625$	625.000	0.0400000
$626$	20584.0	1.31422
$627$	23040.0	1.46751
$628$	14264.0	0.906362
$629$	16416.0	1.04062
$630$	−2340.00	−0.147981
$631$	−7408.00	−0.467366	−0.233683	−	0.972313i	$-0.575078\pi$
$631$	−7408.00	−0.467366	−0.233683	+	0.972313i	$0.575078\pi$
$632$	−5120.00	−0.322251
$633$	−7464.00	−0.468669
$634$	−17748.0	−1.11177
$635$	12320.0	0.769928
$636$	6984.00	0.435430
$637$	−29304.0	−1.82271
$638$	11520.0	0.714861
$639$	9558.00	0.591719
$640$	−640.000	−0.0395285
$641$	−13428.0	−0.827417	−0.413708	−	0.910409i	$-0.635767\pi$
$641$	−13428.0	−0.827417	−0.413708	+	0.910409i	$0.635767\pi$
$642$	−11304.0	−0.694912
$643$	−5848.00	−0.358667	−0.179333	−	0.983788i	$-0.557394\pi$
$643$	−5848.00	−0.358667	−0.179333	+	0.983788i	$0.557394\pi$
$644$	−4992.00	−0.305454
$645$	−4080.00	−0.249070
$646$	17280.0	1.05243
$647$	9456.00	0.574581	0.287290	−	0.957844i	$-0.407246\pi$
$647$	9456.00	0.574581	0.287290	+	0.957844i	$0.407246\pi$
$648$	648.000	0.0392837
$649$	−1440.00	−0.0870954
$650$	−4400.00	−0.265511
$651$	2418.00	0.145574
$652$	−7192.00	−0.431995
$653$	−378.000	−0.0226528	−0.0113264	−	0.999936i	$-0.503605\pi$
$653$	−378.000	−0.0226528	−0.0113264	+	0.999936i	$0.503605\pi$
$654$	−420.000	−0.0251121
$655$	7290.00	0.434876
$656$	2592.00	0.154269
$657$	1908.00	0.113300
$658$	4992.00	0.295757
$659$	6330.00	0.374176	0.187088	−	0.982343i	$-0.440095\pi$
$659$	6330.00	0.374176	0.187088	+	0.982343i	$0.440095\pi$
$660$	2880.00	0.169854
$661$	2702.00	0.158995	0.0794974	−	0.996835i	$-0.474668\pi$
$661$	2702.00	0.158995	0.0794974	+	0.996835i	$0.474668\pi$
$662$	−19016.0	−1.11643
$663$	14256.0	0.835079
$664$	7776.00	0.454469
$665$	20800.0	1.21292
$666$	−5472.00	−0.318372
$667$	5760.00	0.334375
$668$	−3456.00	−0.200175
$669$	−9444.00	−0.545779
$670$	3340.00	0.192590
$671$	22944.0	1.32003
$672$	2496.00	0.143282
$673$	2312.00	0.132424	0.0662118	−	0.997806i	$-0.478909\pi$
$673$	2312.00	0.132424	0.0662118	+	0.997806i	$0.478909\pi$
$674$	−6608.00	−0.377642
$675$	675.000	0.0384900
$676$	22188.0	1.26240
$677$	6486.00	0.368209	0.184104	−	0.982907i	$-0.441062\pi$
$677$	6486.00	0.368209	0.184104	+	0.982907i	$0.441062\pi$
$678$	−13068.0	−0.740226
$679$	2236.00	0.126377
$680$	2160.00	0.121812
$681$	4608.00	0.259294
$682$	−2976.00	−0.167092
$683$	9552.00	0.535135	0.267567	−	0.963539i	$-0.413780\pi$
$683$	9552.00	0.535135	0.267567	+	0.963539i	$0.413780\pi$
$684$	−5760.00	−0.321987
$685$	−4830.00	−0.269408
$686$	−520.000	−0.0289412
$687$	−8310.00	−0.461494
$688$	4352.00	0.241161
$689$	−51216.0	−2.83189
$690$	1440.00	0.0794491
$691$	−26548.0	−1.46155	−0.730777	−	0.682617i	$-0.760842\pi$
$691$	−26548.0	−1.46155	−0.730777	+	0.682617i	$0.760842\pi$
$692$	5928.00	0.325648
$693$	−11232.0	−0.615683
$694$	−11448.0	−0.626167
$695$	−4900.00	−0.267435
$696$	−2880.00	−0.156848
$697$	−8748.00	−0.475400
$698$	20020.0	1.08563
$699$	−7794.00	−0.421740
$700$	2600.00	0.140387
$701$	−20658.0	−1.11304	−0.556521	−	0.830834i	$-0.687864\pi$
$701$	−20658.0	−1.11304	−0.556521	+	0.830834i	$0.687864\pi$
$702$	−4752.00	−0.255488
$703$	48640.0	2.60952
$704$	−3072.00	−0.164461
$705$	−1440.00	−0.0769270
$706$	−15516.0	−0.827128
$707$	44772.0	2.38165
$708$	360.000	0.0191096
$709$	−23530.0	−1.24639	−0.623193	−	0.782068i	$-0.714165\pi$
$709$	−23530.0	−1.24639	−0.623193	+	0.782068i	$0.714165\pi$
$710$	−10620.0	−0.561354
$711$	−5760.00	−0.303821
$712$	960.000	0.0505302
$713$	−1488.00	−0.0781571
$714$	−8424.00	−0.441541
$715$	−21120.0	−1.10468
$716$	0	0
$717$	−16020.0	−0.834418
$718$	17460.0	0.907523
$719$	120.000	0.00622426	0.00311213	−	0.999995i	$-0.499009\pi$
$719$	120.000	0.00622426	0.00311213	+	0.999995i	$0.499009\pi$
$720$	−720.000	−0.0372678
$721$	−32708.0	−1.68947
$722$	37482.0	1.93204
$723$	9006.00	0.463260
$724$	−1432.00	−0.0735081
$725$	−3000.00	−0.153679
$726$	5838.00	0.298441
$727$	24626.0	1.25630	0.628148	−	0.778094i	$-0.283813\pi$
$727$	24626.0	1.25630	0.628148	+	0.778094i	$0.283813\pi$
$728$	−18304.0	−0.931856
$729$	729.000	0.0370370
$730$	−2120.00	−0.107486
$731$	−14688.0	−0.743167
$732$	−5736.00	−0.289629
$733$	−26998.0	−1.36043	−0.680214	−	0.733013i	$-0.738113\pi$
$733$	−26998.0	−1.36043	−0.680214	+	0.733013i	$0.738113\pi$
$734$	−10808.0	−0.543502
$735$	−4995.00	−0.250671
$736$	−1536.00	−0.0769262
$737$	16032.0	0.801284
$738$	2916.00	0.145446
$739$	3620.00	0.180195	0.0900973	−	0.995933i	$-0.471282\pi$
$739$	3620.00	0.180195	0.0900973	+	0.995933i	$0.471282\pi$
$740$	6080.00	0.302034
$741$	42240.0	2.09410
$742$	30264.0	1.49734
$743$	20952.0	1.03453	0.517264	−	0.855826i	$-0.326951\pi$
$743$	20952.0	1.03453	0.517264	+	0.855826i	$0.326951\pi$
$744$	744.000	0.0366618
$745$	150.000	0.00737661
$746$	−19076.0	−0.936222
$747$	8748.00	0.428477
$748$	10368.0	0.506807
$749$	−48984.0	−2.38963
$750$	−750.000	−0.0365148
$751$	8672.00	0.421366	0.210683	−	0.977554i	$-0.432431\pi$
$751$	8672.00	0.421366	0.210683	+	0.977554i	$0.432431\pi$
$752$	1536.00	0.0744843
$753$	7056.00	0.341481
$754$	21120.0	1.02009
$755$	−9160.00	−0.441545
$756$	2808.00	0.135087
$757$	21176.0	1.01672	0.508359	−	0.861146i	$-0.330252\pi$
$757$	21176.0	1.01672	0.508359	+	0.861146i	$0.330252\pi$
$758$	−10880.0	−0.521345
$759$	6912.00	0.330553
$760$	6400.00	0.305464
$761$	27132.0	1.29242	0.646212	−	0.763158i	$-0.276352\pi$
$761$	27132.0	1.29242	0.646212	+	0.763158i	$0.276352\pi$
$762$	−14784.0	−0.702845
$763$	−1820.00	−0.0863544
$764$	6888.00	0.326177
$765$	2430.00	0.114846
$766$	13344.0	0.629423
$767$	−2640.00	−0.124283
$768$	768.000	0.0360844
$769$	−6850.00	−0.321219	−0.160609	−	0.987018i	$-0.551346\pi$
$769$	−6850.00	−0.321219	−0.160609	+	0.987018i	$0.551346\pi$
$770$	12480.0	0.584088
$771$	−882.000	−0.0411990
$772$	−1672.00	−0.0779490
$773$	7422.00	0.345344	0.172672	−	0.984979i	$-0.444760\pi$
$773$	7422.00	0.345344	0.172672	+	0.984979i	$0.444760\pi$
$774$	4896.00	0.227368
$775$	775.000	0.0359211
$776$	688.000	0.0318270
$777$	−23712.0	−1.09480
$778$	−20880.0	−0.962191
$779$	−25920.0	−1.19214
$780$	5280.00	0.242377
$781$	−50976.0	−2.33555
$782$	5184.00	0.237058
$783$	−3240.00	−0.147878
$784$	5328.00	0.242711
$785$	−17830.0	−0.810675
$786$	−8748.00	−0.396986
$787$	−1204.00	−0.0545336	−0.0272668	−	0.999628i	$-0.508680\pi$
$787$	−1204.00	−0.0545336	−0.0272668	+	0.999628i	$0.508680\pi$
$788$	−216.000	−0.00976482
$789$	−7344.00	−0.331373
$790$	6400.00	0.288230
$791$	−56628.0	−2.54546
$792$	−3456.00	−0.155055
$793$	42064.0	1.88365
$794$	−12668.0	−0.566210
$795$	−8730.00	−0.389461
$796$	−6880.00	−0.306351
$797$	37266.0	1.65625	0.828124	−	0.560545i	$-0.189408\pi$
$797$	37266.0	1.65625	0.828124	+	0.560545i	$0.189408\pi$
$798$	−24960.0	−1.10724
$799$	−5184.00	−0.229533
$800$	800.000	0.0353553
$801$	1080.00	0.0476404
$802$	20424.0	0.899248
$803$	−10176.0	−0.447202
$804$	−4008.00	−0.175810
$805$	6240.00	0.273206
$806$	−5456.00	−0.238436
$807$	−25200.0	−1.09923
$808$	13776.0	0.599799
$809$	−25860.0	−1.12384	−0.561922	−	0.827190i	$-0.689938\pi$
$809$	−25860.0	−1.12384	−0.561922	+	0.827190i	$0.689938\pi$
$810$	−810.000	−0.0351364
$811$	−5128.00	−0.222033	−0.111016	−	0.993819i	$-0.535411\pi$
$811$	−5128.00	−0.222033	−0.111016	+	0.993819i	$0.535411\pi$
$812$	−12480.0	−0.539362
$813$	−11064.0	−0.477283
$814$	29184.0	1.25663
$815$	8990.00	0.386388
$816$	−2592.00	−0.111199
$817$	−43520.0	−1.86361
$818$	16060.0	0.686461
$819$	−20592.0	−0.878563
$820$	−3240.00	−0.137983
$821$	8592.00	0.365241	0.182621	−	0.983183i	$-0.441542\pi$
$821$	8592.00	0.365241	0.182621	+	0.983183i	$0.441542\pi$
$822$	5796.00	0.245935
$823$	39392.0	1.66843	0.834216	−	0.551438i	$-0.185921\pi$
$823$	39392.0	1.66843	0.834216	+	0.551438i	$0.185921\pi$
$824$	−10064.0	−0.425481
$825$	−3600.00	−0.151922
$826$	1560.00	0.0657135
$827$	−22044.0	−0.926898	−0.463449	−	0.886123i	$-0.653388\pi$
$827$	−22044.0	−0.926898	−0.463449	+	0.886123i	$0.653388\pi$
$828$	−1728.00	−0.0725268
$829$	−21310.0	−0.892795	−0.446397	−	0.894835i	$-0.647293\pi$
$829$	−21310.0	−0.892795	−0.446397	+	0.894835i	$0.647293\pi$
$830$	−9720.00	−0.406489
$831$	−27372.0	−1.14263
$832$	−5632.00	−0.234681
$833$	−17982.0	−0.747946
$834$	5880.00	0.244134
$835$	4320.00	0.179042
$836$	30720.0	1.27090
$837$	837.000	0.0345651
$838$	15060.0	0.620810
$839$	−14070.0	−0.578963	−0.289482	−	0.957184i	$-0.593483\pi$
$839$	−14070.0	−0.578963	−0.289482	+	0.957184i	$0.593483\pi$
$840$	−3120.00	−0.128155
$841$	−9989.00	−0.409570
$842$	−8156.00	−0.333817
$843$	20106.0	0.821456
$844$	−9952.00	−0.405879
$845$	−27735.0	−1.12913
$846$	1728.00	0.0702244
$847$	25298.0	1.02627
$848$	9312.00	0.377094
$849$	19446.0	0.786084
$850$	−2700.00	−0.108952
$851$	14592.0	0.587788
$852$	12744.0	0.512444
$853$	−22918.0	−0.919927	−0.459963	−	0.887938i	$-0.652137\pi$
$853$	−22918.0	−0.919927	−0.459963	+	0.887938i	$0.652137\pi$
$854$	−24856.0	−0.995966
$855$	7200.00	0.287994
$856$	−15072.0	−0.601811
$857$	−25914.0	−1.03291	−0.516456	−	0.856314i	$-0.672749\pi$
$857$	−25914.0	−1.03291	−0.516456	+	0.856314i	$0.672749\pi$
$858$	25344.0	1.00843
$859$	−31900.0	−1.26707	−0.633535	−	0.773714i	$-0.718397\pi$
$859$	−31900.0	−1.26707	−0.633535	+	0.773714i	$0.718397\pi$
$860$	−5440.00	−0.215701
$861$	12636.0	0.500155
$862$	31764.0	1.25509
$863$	7752.00	0.305772	0.152886	−	0.988244i	$-0.451143\pi$
$863$	7752.00	0.305772	0.152886	+	0.988244i	$0.451143\pi$
$864$	864.000	0.0340207
$865$	−7410.00	−0.291269
$866$	9544.00	0.374502
$867$	−5991.00	−0.234677
$868$	3224.00	0.126071
$869$	30720.0	1.19920
$870$	3600.00	0.140289
$871$	29392.0	1.14341
$872$	−560.000	−0.0217477
$873$	774.000	0.0300068
$874$	15360.0	0.594462
$875$	−3250.00	−0.125566
$876$	2544.00	0.0981208
$877$	28706.0	1.10528	0.552641	−	0.833419i	$-0.313620\pi$
$877$	28706.0	1.10528	0.552641	+	0.833419i	$0.313620\pi$
$878$	−3920.00	−0.150676
$879$	12186.0	0.467604
$880$	3840.00	0.147098
$881$	−43608.0	−1.66764	−0.833820	−	0.552036i	$-0.813851\pi$
$881$	−43608.0	−1.66764	−0.833820	+	0.552036i	$0.813851\pi$
$882$	5994.00	0.228830
$883$	−32668.0	−1.24503	−0.622517	−	0.782606i	$-0.713890\pi$
$883$	−32668.0	−1.24503	−0.622517	+	0.782606i	$0.713890\pi$
$884$	19008.0	0.723199
$885$	−450.000	−0.0170922
$886$	−8256.00	−0.313054
$887$	32316.0	1.22330	0.611649	−	0.791129i	$-0.290507\pi$
$887$	32316.0	1.22330	0.611649	+	0.791129i	$0.290507\pi$
$888$	−7296.00	−0.275718
$889$	−64064.0	−2.41692
$890$	−1200.00	−0.0451956
$891$	−3888.00	−0.146187
$892$	−12592.0	−0.472658
$893$	−15360.0	−0.575591
$894$	−180.000	−0.00673389
$895$	0	0
$896$	3328.00	0.124086
$897$	12672.0	0.471690
$898$	−29640.0	−1.10145
$899$	−3720.00	−0.138008
$900$	900.000	0.0333333
$901$	−31428.0	−1.16206
$902$	−15552.0	−0.574085
$903$	21216.0	0.781865
$904$	−17424.0	−0.641055
$905$	1790.00	0.0657476
$906$	10992.0	0.403074
$907$	45206.0	1.65495	0.827476	−	0.561502i	$-0.189776\pi$
$907$	45206.0	1.65495	0.827476	+	0.561502i	$0.189776\pi$
$908$	6144.00	0.224555
$909$	15498.0	0.565496
$910$	22880.0	0.833478
$911$	−1368.00	−0.0497518	−0.0248759	−	0.999691i	$-0.507919\pi$
$911$	−1368.00	−0.0497518	−0.0248759	+	0.999691i	$0.507919\pi$
$912$	−7680.00	−0.278849
$913$	−46656.0	−1.69122
$914$	17032.0	0.616377
$915$	7170.00	0.259052
$916$	−11080.0	−0.399665
$917$	−37908.0	−1.36514
$918$	−2916.00	−0.104839
$919$	−8260.00	−0.296488	−0.148244	−	0.988951i	$-0.547362\pi$
$919$	−8260.00	−0.296488	−0.148244	+	0.988951i	$0.547362\pi$
$920$	1920.00	0.0688049
$921$	15018.0	0.537307
$922$	27384.0	0.978139
$923$	−93456.0	−3.33276
$924$	−14976.0	−0.533197
$925$	−7600.00	−0.270148
$926$	−8576.00	−0.304346
$927$	−11322.0	−0.401147
$928$	−3840.00	−0.135834
$929$	9120.00	0.322086	0.161043	−	0.986947i	$-0.448514\pi$
$929$	9120.00	0.322086	0.161043	+	0.986947i	$0.448514\pi$
$930$	−930.000	−0.0327913
$931$	−53280.0	−1.87560
$932$	−10392.0	−0.365237
$933$	−1314.00	−0.0461076
$934$	−648.000	−0.0227015
$935$	−12960.0	−0.453302
$936$	−6336.00	−0.221259
$937$	−27274.0	−0.950910	−0.475455	−	0.879740i	$-0.657717\pi$
$937$	−27274.0	−0.950910	−0.475455	+	0.879740i	$0.657717\pi$
$938$	−17368.0	−0.604569
$939$	30876.0	1.07306
$940$	−1920.00	−0.0666207
$941$	49392.0	1.71109	0.855544	−	0.517731i	$-0.173223\pi$
$941$	49392.0	1.71109	0.855544	+	0.517731i	$0.173223\pi$
$942$	21396.0	0.740042
$943$	−7776.00	−0.268527
$944$	480.000	0.0165494
$945$	−3510.00	−0.120826
$946$	−26112.0	−0.897436
$947$	−25164.0	−0.863485	−0.431742	−	0.901997i	$-0.642101\pi$
$947$	−25164.0	−0.863485	−0.431742	+	0.901997i	$0.642101\pi$
$948$	−7680.00	−0.263117
$949$	−18656.0	−0.638145
$950$	−8000.00	−0.273215
$951$	−26622.0	−0.907758
$952$	−11232.0	−0.382386
$953$	−21138.0	−0.718496	−0.359248	−	0.933242i	$-0.616967\pi$
$953$	−21138.0	−0.718496	−0.359248	+	0.933242i	$0.616967\pi$
$954$	10476.0	0.355527
$955$	−8610.00	−0.291741
$956$	−21360.0	−0.722627
$957$	17280.0	0.583681
$958$	−17940.0	−0.605026
$959$	25116.0	0.845712
$960$	−960.000	−0.0322749
$961$	961.000	0.0322581
$962$	53504.0	1.79318
$963$	−16956.0	−0.567393
$964$	12008.0	0.401195
$965$	2090.00	0.0697197
$966$	−7488.00	−0.249402
$967$	21356.0	0.710199	0.355100	−	0.934828i	$-0.384447\pi$
$967$	21356.0	0.710199	0.355100	+	0.934828i	$0.384447\pi$
$968$	7784.00	0.258458
$969$	25920.0	0.859309
$970$	−860.000	−0.0284669
$971$	31242.0	1.03255	0.516274	−	0.856424i	$-0.327319\pi$
$971$	31242.0	1.03255	0.516274	+	0.856424i	$0.327319\pi$
$972$	972.000	0.0320750
$973$	25480.0	0.839518
$974$	28432.0	0.935339
$975$	−6600.00	−0.216789
$976$	−7648.00	−0.250826
$977$	7686.00	0.251686	0.125843	−	0.992050i	$-0.459836\pi$
$977$	7686.00	0.251686	0.125843	+	0.992050i	$0.459836\pi$
$978$	−10788.0	−0.352722
$979$	−5760.00	−0.188039
$980$	−6660.00	−0.217088
$981$	−630.000	−0.0205039
$982$	−16536.0	−0.537357
$983$	−35928.0	−1.16574	−0.582871	−	0.812564i	$-0.698071\pi$
$983$	−35928.0	−1.16574	−0.582871	+	0.812564i	$0.698071\pi$
$984$	3888.00	0.125960
$985$	270.000	0.00873392
$986$	12960.0	0.418591
$987$	7488.00	0.241485
$988$	56320.0	1.81354
$989$	−13056.0	−0.419774
$990$	4320.00	0.138685
$991$	−8968.00	−0.287465	−0.143733	−	0.989617i	$-0.545911\pi$
$991$	−8968.00	−0.287465	−0.143733	+	0.989617i	$0.545911\pi$
$992$	992.000	0.0317500
$993$	−28524.0	−0.911563
$994$	55224.0	1.76217
$995$	8600.00	0.274008
$996$	11664.0	0.371072
$997$	34526.0	1.09674	0.548370	−	0.836236i	$-0.315249\pi$
$997$	34526.0	1.09674	0.548370	+	0.836236i	$0.315249\pi$
$998$	−23720.0	−0.752348
$999$	−8208.00	−0.259950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.4.a.c.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.4.a.c.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	930.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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