LMFDB - Embedded newform 1150.4.a.bb.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1150,4,Mod(1,1150)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1150.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1150, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1150.a (trivial)

Newform invariants

comment:select newform

sage:traces = [9,18,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$67.8521965066$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 179x^{7} + 380x^{6} + 10197x^{5} - 8259x^{4} - 205207x^{3} - 105750x^{2} + 525560x + 178000 $ x^9 - 3x^8 - 179x^7 + 380x^6 + 10197x^5 - 8259x^4 - 205207x^3 - 105750x^2 + 525560x + 178000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-5.67028$ of defining polynomial
Character	$\chi$	$=$	1150.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} -5.67028 q^{3} +4.00000 q^{4} -11.3406 q^{6} +11.4356 q^{7} +8.00000 q^{8} +5.15209 q^{9} -64.3703 q^{11} -22.6811 q^{12} -51.4739 q^{13} +22.8712 q^{14} +16.0000 q^{16} +43.4885 q^{17} +10.3042 q^{18} +35.4680 q^{19} -64.8429 q^{21} -128.741 q^{22} -23.0000 q^{23} -45.3623 q^{24} -102.948 q^{26} +123.884 q^{27} +45.7423 q^{28} +186.801 q^{29} -87.1933 q^{31} +32.0000 q^{32} +364.998 q^{33} +86.9770 q^{34} +20.6084 q^{36} -163.974 q^{37} +70.9360 q^{38} +291.871 q^{39} +243.206 q^{41} -129.686 q^{42} +224.521 q^{43} -257.481 q^{44} -46.0000 q^{46} -403.083 q^{47} -90.7245 q^{48} -212.228 q^{49} -246.592 q^{51} -205.896 q^{52} -562.288 q^{53} +247.768 q^{54} +91.4846 q^{56} -201.114 q^{57} +373.602 q^{58} +605.661 q^{59} +574.329 q^{61} -174.387 q^{62} +58.9172 q^{63} +64.0000 q^{64} +729.995 q^{66} +998.199 q^{67} +173.954 q^{68} +130.416 q^{69} +729.542 q^{71} +41.2167 q^{72} -708.601 q^{73} -327.948 q^{74} +141.872 q^{76} -736.111 q^{77} +583.743 q^{78} +397.078 q^{79} -841.562 q^{81} +486.413 q^{82} -639.409 q^{83} -259.372 q^{84} +449.042 q^{86} -1059.21 q^{87} -514.962 q^{88} -199.463 q^{89} -588.633 q^{91} -92.0000 q^{92} +494.411 q^{93} -806.166 q^{94} -181.449 q^{96} +525.976 q^{97} -424.455 q^{98} -331.642 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 18 q^{2} + 3 q^{3} + 36 q^{4} + 6 q^{6} + 44 q^{7} + 72 q^{8} + 124 q^{9} + 81 q^{11} + 12 q^{12} + 59 q^{13} + 88 q^{14} + 144 q^{16} + 110 q^{17} + 248 q^{18} + 221 q^{19} + 142 q^{21} + 162 q^{22}+ \cdots - 1753 q^{99}+O(q^{100}) $ 9 * q + 18 * q^2 + 3 * q^3 + 36 * q^4 + 6 * q^6 + 44 * q^7 + 72 * q^8 + 124 * q^9 + 81 * q^11 + 12 * q^12 + 59 * q^13 + 88 * q^14 + 144 * q^16 + 110 * q^17 + 248 * q^18 + 221 * q^19 + 142 * q^21 + 162 * q^22 - 207 * q^23 + 24 * q^24 + 118 * q^26 + 336 * q^27 + 176 * q^28 + 205 * q^29 + 336 * q^31 + 288 * q^32 + 437 * q^33 + 220 * q^34 + 496 * q^36 - 5 * q^37 + 442 * q^38 - 44 * q^39 + 360 * q^41 + 284 * q^42 + 366 * q^43 + 324 * q^44 - 414 * q^46 - 122 * q^47 + 48 * q^48 + 457 * q^49 + 1025 * q^51 + 236 * q^52 + 631 * q^53 + 672 * q^54 + 352 * q^56 - 384 * q^57 + 410 * q^58 + 797 * q^59 + 211 * q^61 + 672 * q^62 + 2447 * q^63 + 576 * q^64 + 874 * q^66 + 111 * q^67 + 440 * q^68 - 69 * q^69 + 2912 * q^71 + 992 * q^72 + 98 * q^73 - 10 * q^74 + 884 * q^76 + 942 * q^77 - 88 * q^78 + 1184 * q^79 + 2093 * q^81 + 720 * q^82 + 2375 * q^83 + 568 * q^84 + 732 * q^86 - 1534 * q^87 + 648 * q^88 + 2588 * q^89 + 2677 * q^91 - 828 * q^92 + 1402 * q^93 - 244 * q^94 + 96 * q^96 - 593 * q^97 + 914 * q^98 - 1753 * q^99

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
$3$	−5.67028	−1.09125	−0.545623	−	0.838031i	$-0.683707\pi$
$3$	−5.67028	−1.09125	−0.545623	+	0.838031i	$0.683707\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−11.3406	−0.771628
$7$	11.4356	0.617463	0.308732	−	0.951149i	$-0.400096\pi$
$7$	11.4356	0.617463	0.308732	+	0.951149i	$0.400096\pi$
$8$	8.00000	0.353553
$9$	5.15209	0.190818
$10$	0	0
$11$	−64.3703	−1.76440	−0.882199	−	0.470877i	$-0.843937\pi$
$11$	−64.3703	−1.76440	−0.882199	+	0.470877i	$0.843937\pi$
$12$	−22.6811	−0.545623
$13$	−51.4739	−1.09818	−0.549088	−	0.835765i	$-0.685025\pi$
$13$	−51.4739	−1.09818	−0.549088	+	0.835765i	$0.685025\pi$
$14$	22.8712	0.436612
$15$	0	0
$16$	16.0000	0.250000
$17$	43.4885	0.620442	0.310221	−	0.950664i	$-0.399597\pi$
$17$	43.4885	0.620442	0.310221	+	0.950664i	$0.399597\pi$
$18$	10.3042	0.134929
$19$	35.4680	0.428259	0.214129	−	0.976805i	$-0.431309\pi$
$19$	35.4680	0.428259	0.214129	+	0.976805i	$0.431309\pi$
$20$	0	0
$21$	−64.8429	−0.673804
$22$	−128.741	−1.24762
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−45.3623	−0.385814
$25$	0	0
$26$	−102.948	−0.776528
$27$	123.884	0.883016
$28$	45.7423	0.308732
$29$	186.801	1.19614	0.598070	−	0.801444i	$-0.295934\pi$
$29$	186.801	1.19614	0.598070	+	0.801444i	$0.295934\pi$
$30$	0	0
$31$	−87.1933	−0.505174	−0.252587	−	0.967574i	$-0.581281\pi$
$31$	−87.1933	−0.505174	−0.252587	+	0.967574i	$0.581281\pi$
$32$	32.0000	0.176777
$33$	364.998	1.92539
$34$	86.9770	0.438719
$35$	0	0
$36$	20.6084	0.0954091
$37$	−163.974	−0.728572	−0.364286	−	0.931287i	$-0.618687\pi$
$37$	−163.974	−0.728572	−0.364286	+	0.931287i	$0.618687\pi$
$38$	70.9360	0.302825
$39$	291.871	1.19838
$40$	0	0
$41$	243.206	0.926401	0.463200	−	0.886254i	$-0.346701\pi$
$41$	243.206	0.926401	0.463200	+	0.886254i	$0.346701\pi$
$42$	−129.686	−0.476452
$43$	224.521	0.796258	0.398129	−	0.917329i	$-0.369660\pi$
$43$	224.521	0.796258	0.398129	+	0.917329i	$0.369660\pi$
$44$	−257.481	−0.882199
$45$	0	0
$46$	−46.0000	−0.147442
$47$	−403.083	−1.25097	−0.625486	−	0.780235i	$-0.715099\pi$
$47$	−403.083	−1.25097	−0.625486	+	0.780235i	$0.715099\pi$
$48$	−90.7245	−0.272812
$49$	−212.228	−0.618739
$50$	0	0
$51$	−246.592	−0.677055
$52$	−205.896	−0.549088
$53$	−562.288	−1.45729	−0.728644	−	0.684893i	$-0.759849\pi$
$53$	−562.288	−1.45729	−0.728644	+	0.684893i	$0.759849\pi$
$54$	247.768	0.624387
$55$	0	0
$56$	91.4846	0.218306
$57$	−201.114	−0.467336
$58$	373.602	0.845799
$59$	605.661	1.33645	0.668224	−	0.743960i	$-0.267055\pi$
$59$	605.661	1.33645	0.668224	+	0.743960i	$0.267055\pi$
$60$	0	0
$61$	574.329	1.20550	0.602748	−	0.797932i	$-0.294072\pi$
$61$	574.329	1.20550	0.602748	+	0.797932i	$0.294072\pi$
$62$	−174.387	−0.357212
$63$	58.9172	0.117823
$64$	64.0000	0.125000
$65$	0	0
$66$	729.995	1.36146
$67$	998.199	1.82014	0.910071	−	0.414453i	$-0.136027\pi$
$67$	998.199	1.82014	0.910071	+	0.414453i	$0.136027\pi$
$68$	173.954	0.310221
$69$	130.416	0.227541
$70$	0	0
$71$	729.542	1.21945	0.609724	−	0.792614i	$-0.291280\pi$
$71$	729.542	1.21945	0.609724	+	0.792614i	$0.291280\pi$
$72$	41.2167	0.0674644
$73$	−708.601	−1.13610	−0.568051	−	0.822993i	$-0.692302\pi$
$73$	−708.601	−1.13610	−0.568051	+	0.822993i	$0.692302\pi$
$74$	−327.948	−0.515178
$75$	0	0
$76$	141.872	0.214129
$77$	−736.111	−1.08945
$78$	583.743	0.847383
$79$	397.078	0.565503	0.282752	−	0.959193i	$-0.408753\pi$
$79$	397.078	0.565503	0.282752	+	0.959193i	$0.408753\pi$
$80$	0	0
$81$	−841.562	−1.15441
$82$	486.413	0.655064
$83$	−639.409	−0.845594	−0.422797	−	0.906224i	$-0.638952\pi$
$83$	−639.409	−0.845594	−0.422797	+	0.906224i	$0.638952\pi$
$84$	−259.372	−0.336902
$85$	0	0
$86$	449.042	0.563040
$87$	−1059.21	−1.30528
$88$	−514.962	−0.623809
$89$	−199.463	−0.237562	−0.118781	−	0.992920i	$-0.537899\pi$
$89$	−199.463	−0.237562	−0.118781	+	0.992920i	$0.537899\pi$
$90$	0	0
$91$	−588.633	−0.678083
$92$	−92.0000	−0.104257
$93$	494.411	0.551269
$94$	−806.166	−0.884571
$95$	0	0
$96$	−181.449	−0.192907
$97$	525.976	0.550565	0.275282	−	0.961363i	$-0.411229\pi$
$97$	525.976	0.550565	0.275282	+	0.961363i	$0.411229\pi$
$98$	−424.455	−0.437515
$99$	−331.642	−0.336679
$100$	0	0
$101$	1919.39	1.89096	0.945479	−	0.325682i	$-0.105594\pi$
$101$	1919.39	1.89096	0.945479	+	0.325682i	$0.105594\pi$
$102$	−493.184	−0.478750
$103$	527.068	0.504209	0.252104	−	0.967700i	$-0.418877\pi$
$103$	527.068	0.504209	0.252104	+	0.967700i	$0.418877\pi$
$104$	−411.791	−0.388264
$105$	0	0
$106$	−1124.58	−1.03046
$107$	438.630	0.396298	0.198149	−	0.980172i	$-0.436507\pi$
$107$	438.630	0.396298	0.198149	+	0.980172i	$0.436507\pi$
$108$	495.535	0.441508
$109$	676.923	0.594839	0.297419	−	0.954747i	$-0.403874\pi$
$109$	676.923	0.594839	0.297419	+	0.954747i	$0.403874\pi$
$110$	0	0
$111$	929.779	0.795051
$112$	182.969	0.154366
$113$	136.776	0.113866	0.0569328	−	0.998378i	$-0.481868\pi$
$113$	136.776	0.113866	0.0569328	+	0.998378i	$0.481868\pi$
$114$	−402.227	−0.330456
$115$	0	0
$116$	747.204	0.598070
$117$	−265.198	−0.209552
$118$	1211.32	0.945011
$119$	497.316	0.383100
$120$	0	0
$121$	2812.53	2.11310
$122$	1148.66	0.852415
$123$	−1379.05	−1.01093
$124$	−348.773	−0.252587
$125$	0	0
$126$	117.834	0.0833136
$127$	1229.91	0.859343	0.429671	−	0.902985i	$-0.358629\pi$
$127$	1229.91	0.859343	0.429671	+	0.902985i	$0.358629\pi$
$128$	128.000	0.0883883
$129$	−1273.10	−0.868914
$130$	0	0
$131$	−161.656	−0.107816	−0.0539082	−	0.998546i	$-0.517168\pi$
$131$	−161.656	−0.107816	−0.0539082	+	0.998546i	$0.517168\pi$
$132$	1459.99	0.962696
$133$	405.597	0.264434
$134$	1996.40	1.28703
$135$	0	0
$136$	347.908	0.219359
$137$	629.526	0.392584	0.196292	−	0.980545i	$-0.437110\pi$
$137$	629.526	0.392584	0.196292	+	0.980545i	$0.437110\pi$
$138$	260.833	0.160895
$139$	−3178.39	−1.93948	−0.969738	−	0.244147i	$-0.921492\pi$
$139$	−3178.39	−1.93948	−0.969738	+	0.244147i	$0.921492\pi$
$140$	0	0
$141$	2285.60	1.36512
$142$	1459.08	0.862279
$143$	3313.39	1.93762
$144$	82.4335	0.0477046
$145$	0	0
$146$	−1417.20	−0.803345
$147$	1203.39	0.675197
$148$	−655.896	−0.364286
$149$	2746.92	1.51031	0.755157	−	0.655544i	$-0.227561\pi$
$149$	2746.92	1.51031	0.755157	+	0.655544i	$0.227561\pi$
$150$	0	0
$151$	2177.95	1.17377	0.586883	−	0.809671i	$-0.300355\pi$
$151$	2177.95	1.17377	0.586883	+	0.809671i	$0.300355\pi$
$152$	283.744	0.151412
$153$	224.057	0.118392
$154$	−1472.22	−0.770358
$155$	0	0
$156$	1167.49	0.599190
$157$	85.0989	0.0432588	0.0216294	−	0.999766i	$-0.493115\pi$
$157$	85.0989	0.0432588	0.0216294	+	0.999766i	$0.493115\pi$
$158$	794.156	0.399871
$159$	3188.33	1.59026
$160$	0	0
$161$	−263.018	−0.128750
$162$	−1683.12	−0.816289
$163$	2912.82	1.39969	0.699845	−	0.714295i	$-0.253253\pi$
$163$	2912.82	1.39969	0.699845	+	0.714295i	$0.253253\pi$
$164$	972.825	0.463200
$165$	0	0
$166$	−1278.82	−0.597925
$167$	1434.03	0.664482	0.332241	−	0.943194i	$-0.392195\pi$
$167$	1434.03	0.664482	0.332241	+	0.943194i	$0.392195\pi$
$168$	−518.743	−0.238226
$169$	452.560	0.205990
$170$	0	0
$171$	182.734	0.0817196
$172$	898.083	0.398129
$173$	1523.69	0.669617	0.334808	−	0.942286i	$-0.391328\pi$
$173$	1523.69	0.669617	0.334808	+	0.942286i	$0.391328\pi$
$174$	−2118.43	−0.922975
$175$	0	0
$176$	−1029.92	−0.441099
$177$	−3434.27	−1.45839
$178$	−398.926	−0.167982
$179$	4283.26	1.78853	0.894263	−	0.447541i	$-0.147700\pi$
$179$	4283.26	1.78853	0.894263	+	0.447541i	$0.147700\pi$
$180$	0	0
$181$	1132.16	0.464933	0.232466	−	0.972604i	$-0.425320\pi$
$181$	1132.16	0.464933	0.232466	+	0.972604i	$0.425320\pi$
$182$	−1177.27	−0.479477
$183$	−3256.61	−1.31549
$184$	−184.000	−0.0737210
$185$	0	0
$186$	988.821	0.389806
$187$	−2799.37	−1.09471
$188$	−1612.33	−0.625486
$189$	1416.68	0.545230
$190$	0	0
$191$	−1260.02	−0.477341	−0.238671	−	0.971101i	$-0.576712\pi$
$191$	−1260.02	−0.477341	−0.238671	+	0.971101i	$0.576712\pi$
$192$	−362.898	−0.136406
$193$	−2966.93	−1.10655	−0.553276	−	0.832998i	$-0.686622\pi$
$193$	−2966.93	−1.10655	−0.553276	+	0.832998i	$0.686622\pi$
$194$	1051.95	0.389308
$195$	0	0
$196$	−848.910	−0.309370
$197$	−796.234	−0.287966	−0.143983	−	0.989580i	$-0.545991\pi$
$197$	−796.234	−0.287966	−0.143983	+	0.989580i	$0.545991\pi$
$198$	−663.283	−0.238068
$199$	−1873.80	−0.667489	−0.333745	−	0.942663i	$-0.608312\pi$
$199$	−1873.80	−0.667489	−0.333745	+	0.942663i	$0.608312\pi$
$200$	0	0
$201$	−5660.07	−1.98622
$202$	3838.79	1.33711
$203$	2136.18	0.738573
$204$	−986.368	−0.338527
$205$	0	0
$206$	1054.14	0.356530
$207$	−118.498	−0.0397884
$208$	−823.582	−0.274544
$209$	−2283.09	−0.755619
$210$	0	0
$211$	381.450	0.124456	0.0622278	−	0.998062i	$-0.480179\pi$
$211$	381.450	0.124456	0.0622278	+	0.998062i	$0.480179\pi$
$212$	−2249.15	−0.728644
$213$	−4136.71	−1.33072
$214$	877.259	0.280225
$215$	0	0
$216$	991.070	0.312193
$217$	−997.106	−0.311926
$218$	1353.85	0.420615
$219$	4017.97	1.23977
$220$	0	0
$221$	−2238.52	−0.681354
$222$	1859.56	0.562186
$223$	−2299.47	−0.690512	−0.345256	−	0.938509i	$-0.612208\pi$
$223$	−2299.47	−0.690512	−0.345256	+	0.938509i	$0.612208\pi$
$224$	365.938	0.109153
$225$	0	0
$226$	273.552	0.0805151
$227$	629.815	0.184151	0.0920755	−	0.995752i	$-0.470650\pi$
$227$	629.815	0.184151	0.0920755	+	0.995752i	$0.470650\pi$
$228$	−804.454	−0.233668
$229$	745.954	0.215258	0.107629	−	0.994191i	$-0.465674\pi$
$229$	745.954	0.215258	0.107629	+	0.994191i	$0.465674\pi$
$230$	0	0
$231$	4173.96	1.18886
$232$	1494.41	0.422900
$233$	2819.94	0.792877	0.396439	−	0.918061i	$-0.370246\pi$
$233$	2819.94	0.792877	0.396439	+	0.918061i	$0.370246\pi$
$234$	−530.396	−0.148176
$235$	0	0
$236$	2422.65	0.668224
$237$	−2251.54	−0.617103
$238$	994.632	0.270893
$239$	−4234.05	−1.14593	−0.572967	−	0.819579i	$-0.694208\pi$
$239$	−4234.05	−1.14593	−0.572967	+	0.819579i	$0.694208\pi$
$240$	0	0
$241$	2813.96	0.752130	0.376065	−	0.926593i	$-0.377277\pi$
$241$	2813.96	0.752130	0.376065	+	0.926593i	$0.377277\pi$
$242$	5625.07	1.49419
$243$	1427.03	0.376725
$244$	2297.32	0.602748
$245$	0	0
$246$	−2758.10	−0.714837
$247$	−1825.68	−0.470303
$248$	−697.546	−0.178606
$249$	3625.63	0.922751
$250$	0	0
$251$	6095.66	1.53289	0.766444	−	0.642311i	$-0.222024\pi$
$251$	6095.66	1.53289	0.766444	+	0.642311i	$0.222024\pi$
$252$	235.669	0.0589116
$253$	1480.52	0.367902
$254$	2459.81	0.607647
$255$	0	0
$256$	256.000	0.0625000
$257$	−5536.23	−1.34374	−0.671869	−	0.740670i	$-0.734508\pi$
$257$	−5536.23	−1.34374	−0.671869	+	0.740670i	$0.734508\pi$
$258$	−2546.19	−0.614415
$259$	−1875.14	−0.449866
$260$	0	0
$261$	962.416	0.228245
$262$	−323.312	−0.0762377
$263$	−4002.39	−0.938395	−0.469197	−	0.883093i	$-0.655457\pi$
$263$	−4002.39	−0.938395	−0.469197	+	0.883093i	$0.655457\pi$
$264$	2919.98	0.680729
$265$	0	0
$266$	811.194	0.186983
$267$	1131.01	0.259239
$268$	3992.80	0.910071
$269$	3599.40	0.815833	0.407917	−	0.913019i	$-0.366255\pi$
$269$	3599.40	0.815833	0.407917	+	0.913019i	$0.366255\pi$
$270$	0	0
$271$	−346.478	−0.0776644	−0.0388322	−	0.999246i	$-0.512364\pi$
$271$	−346.478	−0.0776644	−0.0388322	+	0.999246i	$0.512364\pi$
$272$	695.816	0.155110
$273$	3337.72	0.739955
$274$	1259.05	0.277599
$275$	0	0
$276$	521.666	0.113770
$277$	652.428	0.141518	0.0707592	−	0.997493i	$-0.477458\pi$
$277$	652.428	0.141518	0.0707592	+	0.997493i	$0.477458\pi$
$278$	−6356.77	−1.37142
$279$	−449.228	−0.0963963
$280$	0	0
$281$	−4987.95	−1.05892	−0.529460	−	0.848335i	$-0.677605\pi$
$281$	−4987.95	−1.05892	−0.529460	+	0.848335i	$0.677605\pi$
$282$	4571.19	0.965285
$283$	−4830.24	−1.01459	−0.507293	−	0.861773i	$-0.669354\pi$
$283$	−4830.24	−1.01459	−0.507293	+	0.861773i	$0.669354\pi$
$284$	2918.17	0.609724
$285$	0	0
$286$	6626.78	1.37010
$287$	2781.20	0.572018
$288$	164.867	0.0337322
$289$	−3021.75	−0.615052
$290$	0	0
$291$	−2982.43	−0.600801
$292$	−2834.40	−0.568051
$293$	1785.52	0.356011	0.178005	−	0.984030i	$-0.443036\pi$
$293$	1785.52	0.356011	0.178005	+	0.984030i	$0.443036\pi$
$294$	2406.78	0.477436
$295$	0	0
$296$	−1311.79	−0.257589
$297$	−7974.43	−1.55799
$298$	5493.85	1.06795
$299$	1183.90	0.228985
$300$	0	0
$301$	2567.52	0.491660
$302$	4355.89	0.829979
$303$	−10883.5	−2.06350
$304$	567.488	0.107065
$305$	0	0
$306$	448.114	0.0837155
$307$	1187.14	0.220697	0.110348	−	0.993893i	$-0.464803\pi$
$307$	1187.14	0.220697	0.110348	+	0.993893i	$0.464803\pi$
$308$	−2944.44	−0.544725
$309$	−2988.62	−0.550216
$310$	0	0
$311$	9523.04	1.73634	0.868171	−	0.496266i	$-0.165296\pi$
$311$	9523.04	1.73634	0.868171	+	0.496266i	$0.165296\pi$
$312$	2334.97	0.423691
$313$	−9041.46	−1.63276	−0.816379	−	0.577516i	$-0.804022\pi$
$313$	−9041.46	−1.63276	−0.816379	+	0.577516i	$0.804022\pi$
$314$	170.198	0.0305886
$315$	0	0
$316$	1588.31	0.282752
$317$	−7514.37	−1.33139	−0.665693	−	0.746226i	$-0.731864\pi$
$317$	−7514.37	−1.33139	−0.665693	+	0.746226i	$0.731864\pi$
$318$	6376.67	1.12448
$319$	−12024.4	−2.11047
$320$	0	0
$321$	−2487.15	−0.432459
$322$	−526.036	−0.0910400
$323$	1542.45	0.265710
$324$	−3366.25	−0.577203
$325$	0	0
$326$	5825.63	0.989730
$327$	−3838.34	−0.649116
$328$	1945.65	0.327532
$329$	−4609.49	−0.772429
$330$	0	0
$331$	10913.5	1.81227	0.906134	−	0.422992i	$-0.139020\pi$
$331$	10913.5	1.81227	0.906134	+	0.422992i	$0.139020\pi$
$332$	−2557.64	−0.422797
$333$	−844.809	−0.139025
$334$	2868.06	0.469860
$335$	0	0
$336$	−1037.49	−0.168451
$337$	−4471.84	−0.722839	−0.361420	−	0.932403i	$-0.617708\pi$
$337$	−4471.84	−0.722839	−0.361420	+	0.932403i	$0.617708\pi$
$338$	905.120	0.145657
$339$	−775.559	−0.124255
$340$	0	0
$341$	5612.66	0.891327
$342$	365.469	0.0577845
$343$	−6349.35	−0.999512
$344$	1796.17	0.281520
$345$	0	0
$346$	3047.37	0.473491
$347$	−3009.43	−0.465575	−0.232788	−	0.972528i	$-0.574785\pi$
$347$	−3009.43	−0.465575	−0.232788	+	0.972528i	$0.574785\pi$
$348$	−4236.86	−0.652642
$349$	−447.884	−0.0686953	−0.0343477	−	0.999410i	$-0.510935\pi$
$349$	−447.884	−0.0686953	−0.0343477	+	0.999410i	$0.510935\pi$
$350$	0	0
$351$	−6376.78	−0.969707
$352$	−2059.85	−0.311904
$353$	11267.8	1.69894	0.849471	−	0.527636i	$-0.176921\pi$
$353$	11267.8	1.69894	0.849471	+	0.527636i	$0.176921\pi$
$354$	−6868.54	−1.03124
$355$	0	0
$356$	−797.853	−0.118781
$357$	−2819.92	−0.418056
$358$	8566.53	1.26468
$359$	3765.74	0.553615	0.276808	−	0.960925i	$-0.410723\pi$
$359$	3765.74	0.553615	0.276808	+	0.960925i	$0.410723\pi$
$360$	0	0
$361$	−5601.02	−0.816594
$362$	2264.32	0.328757
$363$	−15947.9	−2.30591
$364$	−2354.53	−0.339041
$365$	0	0
$366$	−6513.21	−0.930194
$367$	−2447.74	−0.348149	−0.174075	−	0.984732i	$-0.555693\pi$
$367$	−2447.74	−0.348149	−0.174075	+	0.984732i	$0.555693\pi$
$368$	−368.000	−0.0521286
$369$	1253.02	0.176774
$370$	0	0
$371$	−6430.09	−0.899821
$372$	1977.64	0.275634
$373$	3162.93	0.439062	0.219531	−	0.975605i	$-0.429547\pi$
$373$	3162.93	0.439062	0.219531	+	0.975605i	$0.429547\pi$
$374$	−5598.73	−0.774074
$375$	0	0
$376$	−3224.67	−0.442286
$377$	−9615.37	−1.31357
$378$	2833.36	0.385536
$379$	4542.42	0.615643	0.307821	−	0.951444i	$-0.400400\pi$
$379$	4542.42	0.615643	0.307821	+	0.951444i	$0.400400\pi$
$380$	0	0
$381$	−6973.92	−0.937755
$382$	−2520.05	−0.337531
$383$	9696.63	1.29367	0.646834	−	0.762631i	$-0.276093\pi$
$383$	9696.63	1.29367	0.646834	+	0.762631i	$0.276093\pi$
$384$	−725.796	−0.0964534
$385$	0	0
$386$	−5933.87	−0.782450
$387$	1156.75	0.151941
$388$	2103.90	0.275282
$389$	−12507.2	−1.63019	−0.815093	−	0.579330i	$-0.803314\pi$
$389$	−12507.2	−1.63019	−0.815093	+	0.579330i	$0.803314\pi$
$390$	0	0
$391$	−1000.24	−0.129371
$392$	−1697.82	−0.218757
$393$	916.635	0.117654
$394$	−1592.47	−0.203623
$395$	0	0
$396$	−1326.57	−0.168340
$397$	5105.79	0.645471	0.322736	−	0.946489i	$-0.395397\pi$
$397$	5105.79	0.645471	0.322736	+	0.946489i	$0.395397\pi$
$398$	−3747.61	−0.471986
$399$	−2299.85	−0.288563
$400$	0	0
$401$	−9655.85	−1.20247	−0.601235	−	0.799072i	$-0.705324\pi$
$401$	−9655.85	−1.20247	−0.601235	+	0.799072i	$0.705324\pi$
$402$	−11320.1	−1.40447
$403$	4488.18	0.554769
$404$	7677.57	0.945479
$405$	0	0
$406$	4272.35	0.522250
$407$	10555.1	1.28549
$408$	−1972.74	−0.239375
$409$	−5956.20	−0.720086	−0.360043	−	0.932936i	$-0.617238\pi$
$409$	−5956.20	−0.720086	−0.360043	+	0.932936i	$0.617238\pi$
$410$	0	0
$411$	−3569.59	−0.428406
$412$	2108.27	0.252104
$413$	6926.09	0.825207
$414$	−236.996	−0.0281346
$415$	0	0
$416$	−1647.16	−0.194132
$417$	18022.3	2.11645
$418$	−4566.17	−0.534303
$419$	5950.46	0.693793	0.346896	−	0.937903i	$-0.387236\pi$
$419$	5950.46	0.693793	0.346896	+	0.937903i	$0.387236\pi$
$420$	0	0
$421$	−14734.2	−1.70570	−0.852851	−	0.522155i	$-0.825128\pi$
$421$	−14734.2	−1.70570	−0.852851	+	0.522155i	$0.825128\pi$
$422$	762.900	0.0880034
$423$	−2076.72	−0.238708
$424$	−4498.31	−0.515229
$425$	0	0
$426$	−8273.42	−0.940959
$427$	6567.78	0.744349
$428$	1754.52	0.198149
$429$	−18787.8	−2.11442
$430$	0	0
$431$	−2231.59	−0.249402	−0.124701	−	0.992194i	$-0.539797\pi$
$431$	−2231.59	−0.249402	−0.124701	+	0.992194i	$0.539797\pi$
$432$	1982.14	0.220754
$433$	8218.01	0.912084	0.456042	−	0.889958i	$-0.349267\pi$
$433$	8218.01	0.912084	0.456042	+	0.889958i	$0.349267\pi$
$434$	−1994.21	−0.220565
$435$	0	0
$436$	2707.69	0.297419
$437$	−815.764	−0.0892981
$438$	8035.93	0.876648
$439$	5912.38	0.642784	0.321392	−	0.946946i	$-0.395849\pi$
$439$	5912.38	0.642784	0.321392	+	0.946946i	$0.395849\pi$
$440$	0	0
$441$	−1093.42	−0.118067
$442$	−4477.04	−0.481790
$443$	−4530.67	−0.485912	−0.242956	−	0.970037i	$-0.578117\pi$
$443$	−4530.67	−0.485912	−0.242956	+	0.970037i	$0.578117\pi$
$444$	3719.11	0.397526
$445$	0	0
$446$	−4598.95	−0.488265
$447$	−15575.8	−1.64812
$448$	731.877	0.0771829
$449$	8136.30	0.855180	0.427590	−	0.903973i	$-0.359363\pi$
$449$	8136.30	0.855180	0.427590	+	0.903973i	$0.359363\pi$
$450$	0	0
$451$	−15655.3	−1.63454
$452$	547.104	0.0569328
$453$	−12349.6	−1.28087
$454$	1259.63	0.130214
$455$	0	0
$456$	−1608.91	−0.165228
$457$	15790.1	1.61626	0.808128	−	0.589008i	$-0.200481\pi$
$457$	15790.1	1.61626	0.808128	+	0.589008i	$0.200481\pi$
$458$	1491.91	0.152210
$459$	5387.52	0.547860
$460$	0	0
$461$	−5958.29	−0.601964	−0.300982	−	0.953630i	$-0.597314\pi$
$461$	−5958.29	−0.601964	−0.300982	+	0.953630i	$0.597314\pi$
$462$	8347.92	0.840650
$463$	−11861.8	−1.19064	−0.595319	−	0.803489i	$-0.702974\pi$
$463$	−11861.8	−1.19064	−0.595319	+	0.803489i	$0.702974\pi$
$464$	2988.82	0.299035
$465$	0	0
$466$	5639.88	0.560649
$467$	−1738.19	−0.172235	−0.0861175	−	0.996285i	$-0.527446\pi$
$467$	−1738.19	−0.172235	−0.0861175	+	0.996285i	$0.527446\pi$
$468$	−1060.79	−0.104776
$469$	11415.0	1.12387
$470$	0	0
$471$	−482.535	−0.0472060
$472$	4845.29	0.472506
$473$	−14452.5	−1.40492
$474$	−4503.09	−0.436358
$475$	0	0
$476$	1989.26	0.191550
$477$	−2896.96	−0.278077
$478$	−8468.10	−0.810297
$479$	4015.75	0.383057	0.191528	−	0.981487i	$-0.438656\pi$
$479$	4015.75	0.383057	0.191528	+	0.981487i	$0.438656\pi$
$480$	0	0
$481$	8440.38	0.800100
$482$	5627.93	0.531836
$483$	1491.39	0.140498
$484$	11250.1	1.05655
$485$	0	0
$486$	2854.07	0.266385
$487$	−18618.9	−1.73245	−0.866223	−	0.499658i	$-0.833459\pi$
$487$	−18618.9	−1.73245	−0.866223	+	0.499658i	$0.833459\pi$
$488$	4594.63	0.426207
$489$	−16516.5	−1.52741
$490$	0	0
$491$	7671.89	0.705148	0.352574	−	0.935784i	$-0.385307\pi$
$491$	7671.89	0.705148	0.352574	+	0.935784i	$0.385307\pi$
$492$	−5516.19	−0.505466
$493$	8123.70	0.742136
$494$	−3651.35	−0.332555
$495$	0	0
$496$	−1395.09	−0.126293
$497$	8342.74	0.752963
$498$	7251.26	0.652483
$499$	3591.49	0.322198	0.161099	−	0.986938i	$-0.448496\pi$
$499$	3591.49	0.322198	0.161099	+	0.986938i	$0.448496\pi$
$500$	0	0
$501$	−8131.35	−0.725114
$502$	12191.3	1.08392
$503$	17954.4	1.59155	0.795773	−	0.605595i	$-0.207065\pi$
$503$	17954.4	1.59155	0.795773	+	0.605595i	$0.207065\pi$
$504$	471.337	0.0416568
$505$	0	0
$506$	2961.03	0.260146
$507$	−2566.14	−0.224786
$508$	4919.63	0.429671
$509$	19404.4	1.68975	0.844875	−	0.534963i	$-0.179675\pi$
$509$	19404.4	1.68975	0.844875	+	0.534963i	$0.179675\pi$
$510$	0	0
$511$	−8103.26	−0.701501
$512$	512.000	0.0441942
$513$	4393.91	0.378160
$514$	−11072.5	−0.950166
$515$	0	0
$516$	−5092.38	−0.434457
$517$	25946.6	2.20721
$518$	−3750.27	−0.318103
$519$	−8639.73	−0.730717
$520$	0	0
$521$	−3083.93	−0.259327	−0.129664	−	0.991558i	$-0.541390\pi$
$521$	−3083.93	−0.259327	−0.129664	+	0.991558i	$0.541390\pi$
$522$	1924.83	0.161394
$523$	17638.2	1.47469	0.737346	−	0.675515i	$-0.236079\pi$
$523$	17638.2	1.47469	0.737346	+	0.675515i	$0.236079\pi$
$524$	−646.624	−0.0539082
$525$	0	0
$526$	−8004.78	−0.663545
$527$	−3791.91	−0.313431
$528$	5839.96	0.481348
$529$	529.000	0.0434783
$530$	0	0
$531$	3120.42	0.255019
$532$	1622.39	0.132217
$533$	−12518.8	−1.01735
$534$	2262.03	0.183310
$535$	0	0
$536$	7985.59	0.643517
$537$	−24287.3	−1.95172
$538$	7198.80	0.576881
$539$	13661.2	1.09170
$540$	0	0
$541$	−12203.4	−0.969806	−0.484903	−	0.874568i	$-0.661145\pi$
$541$	−12203.4	−0.969806	−0.484903	+	0.874568i	$0.661145\pi$
$542$	−692.957	−0.0549170
$543$	−6419.67	−0.507356
$544$	1391.63	0.109680
$545$	0	0
$546$	6675.43	0.523227
$547$	24347.9	1.90319	0.951593	−	0.307361i	$-0.0994459\pi$
$547$	24347.9	1.90319	0.951593	+	0.307361i	$0.0994459\pi$
$548$	2518.11	0.196292
$549$	2959.00	0.230031
$550$	0	0
$551$	6625.46	0.512258
$552$	1043.33	0.0804477
$553$	4540.82	0.349177
$554$	1304.86	0.100069
$555$	0	0
$556$	−12713.5	−0.969738
$557$	−5181.49	−0.394159	−0.197080	−	0.980387i	$-0.563146\pi$
$557$	−5181.49	−0.394159	−0.197080	+	0.980387i	$0.563146\pi$
$558$	−898.456	−0.0681625
$559$	−11557.0	−0.874431
$560$	0	0
$561$	15873.2	1.19459
$562$	−9975.91	−0.748769
$563$	22634.6	1.69438	0.847189	−	0.531291i	$-0.178293\pi$
$563$	22634.6	1.69438	0.847189	+	0.531291i	$0.178293\pi$
$564$	9142.38	0.682560
$565$	0	0
$566$	−9660.48	−0.717421
$567$	−9623.75	−0.712803
$568$	5836.34	0.431140
$569$	−10824.0	−0.797476	−0.398738	−	0.917065i	$-0.630552\pi$
$569$	−10824.0	−0.797476	−0.398738	+	0.917065i	$0.630552\pi$
$570$	0	0
$571$	−11248.6	−0.824414	−0.412207	−	0.911090i	$-0.635242\pi$
$571$	−11248.6	−0.824414	−0.412207	+	0.911090i	$0.635242\pi$
$572$	13253.6	0.968809
$573$	7144.69	0.520897
$574$	5562.41	0.404478
$575$	0	0
$576$	329.734	0.0238523
$577$	−23424.7	−1.69009	−0.845046	−	0.534694i	$-0.820427\pi$
$577$	−23424.7	−1.69009	−0.845046	+	0.534694i	$0.820427\pi$
$578$	−6043.50	−0.434907
$579$	16823.3	1.20752
$580$	0	0
$581$	−7312.01	−0.522123
$582$	−5964.86	−0.424831
$583$	36194.7	2.57123
$584$	−5668.81	−0.401673
$585$	0	0
$586$	3571.04	0.251738
$587$	1541.57	0.108394	0.0541972	−	0.998530i	$-0.482740\pi$
$587$	1541.57	0.108394	0.0541972	+	0.998530i	$0.482740\pi$
$588$	4813.56	0.337599
$589$	−3092.57	−0.216345
$590$	0	0
$591$	4514.87	0.314242
$592$	−2623.58	−0.182143
$593$	−13814.3	−0.956636	−0.478318	−	0.878187i	$-0.658753\pi$
$593$	−13814.3	−0.956636	−0.478318	+	0.878187i	$0.658753\pi$
$594$	−15948.9	−1.10167
$595$	0	0
$596$	10987.7	0.755157
$597$	10625.0	0.728395
$598$	2367.80	0.161917
$599$	−20947.4	−1.42886	−0.714432	−	0.699705i	$-0.753315\pi$
$599$	−20947.4	−1.42886	−0.714432	+	0.699705i	$0.753315\pi$
$600$	0	0
$601$	5703.62	0.387114	0.193557	−	0.981089i	$-0.437998\pi$
$601$	5703.62	0.387114	0.193557	+	0.981089i	$0.437998\pi$
$602$	5135.05	0.347656
$603$	5142.82	0.347316
$604$	8711.79	0.586883
$605$	0	0
$606$	−21767.0	−1.45912
$607$	14936.3	0.998759	0.499379	−	0.866383i	$-0.333561\pi$
$607$	14936.3	0.998759	0.499379	+	0.866383i	$0.333561\pi$
$608$	1134.98	0.0757062
$609$	−12112.7	−0.805965
$610$	0	0
$611$	20748.3	1.37379
$612$	896.227	0.0591958
$613$	−21142.2	−1.39302	−0.696512	−	0.717545i	$-0.745266\pi$
$613$	−21142.2	−1.39302	−0.696512	+	0.717545i	$0.745266\pi$
$614$	2374.29	0.156056
$615$	0	0
$616$	−5888.89	−0.385179
$617$	−12531.9	−0.817693	−0.408846	−	0.912603i	$-0.634069\pi$
$617$	−12531.9	−0.817693	−0.408846	+	0.912603i	$0.634069\pi$
$618$	−5977.24	−0.389061
$619$	4726.10	0.306879	0.153440	−	0.988158i	$-0.450965\pi$
$619$	4726.10	0.306879	0.153440	+	0.988158i	$0.450965\pi$
$620$	0	0
$621$	−2849.33	−0.184122
$622$	19046.1	1.22778
$623$	−2280.98	−0.146686
$624$	4669.94	0.299595
$625$	0	0
$626$	−18082.9	−1.15453
$627$	12945.7	0.824566
$628$	340.396	0.0216294
$629$	−7130.98	−0.452036
$630$	0	0
$631$	20880.9	1.31736	0.658682	−	0.752421i	$-0.271114\pi$
$631$	20880.9	1.31736	0.658682	+	0.752421i	$0.271114\pi$
$632$	3176.62	0.199936
$633$	−2162.93	−0.135812
$634$	−15028.7	−0.941432
$635$	0	0
$636$	12753.3	0.795130
$637$	10924.2	0.679485
$638$	−24048.9	−1.49233
$639$	3758.67	0.232693
$640$	0	0
$641$	−27696.7	−1.70664	−0.853318	−	0.521390i	$-0.825414\pi$
$641$	−27696.7	−1.70664	−0.853318	+	0.521390i	$0.825414\pi$
$642$	−4974.31	−0.305795
$643$	−13611.0	−0.834785	−0.417392	−	0.908726i	$-0.637056\pi$
$643$	−13611.0	−0.834785	−0.417392	+	0.908726i	$0.637056\pi$
$644$	−1052.07	−0.0643750
$645$	0	0
$646$	3084.90	0.187885
$647$	−10073.0	−0.612073	−0.306036	−	0.952020i	$-0.599003\pi$
$647$	−10073.0	−0.612073	−0.306036	+	0.952020i	$0.599003\pi$
$648$	−6732.50	−0.408144
$649$	−38986.6	−2.35802
$650$	0	0
$651$	5653.87	0.340388
$652$	11651.3	0.699845
$653$	−24859.7	−1.48979	−0.744896	−	0.667181i	$-0.767501\pi$
$653$	−24859.7	−1.48979	−0.744896	+	0.667181i	$0.767501\pi$
$654$	−7676.69	−0.458994
$655$	0	0
$656$	3891.30	0.231600
$657$	−3650.78	−0.216789
$658$	−9218.98	−0.546190
$659$	17125.8	1.01233	0.506165	−	0.862436i	$-0.331063\pi$
$659$	17125.8	1.01233	0.506165	+	0.862436i	$0.331063\pi$
$660$	0	0
$661$	8533.88	0.502162	0.251081	−	0.967966i	$-0.419214\pi$
$661$	8533.88	0.502162	0.251081	+	0.967966i	$0.419214\pi$
$662$	21827.0	1.28147
$663$	12693.0	0.743525
$664$	−5115.27	−0.298963
$665$	0	0
$666$	−1689.62	−0.0983054
$667$	−4296.42	−0.249413
$668$	5736.12	0.332241
$669$	13038.7	0.753518
$670$	0	0
$671$	−36969.7	−2.12697
$672$	−2074.97	−0.119113
$673$	22983.4	1.31641	0.658206	−	0.752838i	$-0.271316\pi$
$673$	22983.4	1.31641	0.658206	+	0.752838i	$0.271316\pi$
$674$	−8943.69	−0.511125
$675$	0	0
$676$	1810.24	0.102995
$677$	−2276.48	−0.129235	−0.0646176	−	0.997910i	$-0.520583\pi$
$677$	−2276.48	−0.129235	−0.0646176	+	0.997910i	$0.520583\pi$
$678$	−1551.12	−0.0878618
$679$	6014.84	0.339953
$680$	0	0
$681$	−3571.23	−0.200954
$682$	11225.3	0.630263
$683$	23249.8	1.30253	0.651264	−	0.758851i	$-0.274239\pi$
$683$	23249.8	1.30253	0.651264	+	0.758851i	$0.274239\pi$
$684$	730.938	0.0408598
$685$	0	0
$686$	−12698.7	−0.706762
$687$	−4229.77	−0.234899
$688$	3592.33	0.199065
$689$	28943.2	1.60036
$690$	0	0
$691$	−15941.7	−0.877641	−0.438820	−	0.898575i	$-0.644604\pi$
$691$	−15941.7	−0.877641	−0.438820	+	0.898575i	$0.644604\pi$
$692$	6094.74	0.334808
$693$	−3792.51	−0.207887
$694$	−6018.86	−0.329211
$695$	0	0
$696$	−8473.71	−0.461488
$697$	10576.7	0.574778
$698$	−895.768	−0.0485749
$699$	−15989.9	−0.865224
$700$	0	0
$701$	18531.5	0.998464	0.499232	−	0.866468i	$-0.333615\pi$
$701$	18531.5	0.998464	0.499232	+	0.866468i	$0.333615\pi$
$702$	−12753.6	−0.685687
$703$	−5815.83	−0.312017
$704$	−4119.70	−0.220550
$705$	0	0
$706$	22535.7	1.20133
$707$	21949.4	1.16760
$708$	−13737.1	−0.729197
$709$	−3100.98	−0.164259	−0.0821295	−	0.996622i	$-0.526172\pi$
$709$	−3100.98	−0.164259	−0.0821295	+	0.996622i	$0.526172\pi$
$710$	0	0
$711$	2045.78	0.107908
$712$	−1595.71	−0.0839910
$713$	2005.45	0.105336
$714$	−5639.84	−0.295610
$715$	0	0
$716$	17133.1	0.894263
$717$	24008.3	1.25050
$718$	7531.47	0.391465
$719$	16969.2	0.880175	0.440087	−	0.897955i	$-0.354947\pi$
$719$	16969.2	0.880175	0.440087	+	0.897955i	$0.354947\pi$
$720$	0	0
$721$	6027.32	0.311330
$722$	−11202.0	−0.577419
$723$	−15956.0	−0.820759
$724$	4528.64	0.232466
$725$	0	0
$726$	−31895.7	−1.63052
$727$	22219.2	1.13351	0.566756	−	0.823886i	$-0.308198\pi$
$727$	22219.2	1.13351	0.566756	+	0.823886i	$0.308198\pi$
$728$	−4709.07	−0.239739
$729$	14630.5	0.743307
$730$	0	0
$731$	9764.07	0.494032
$732$	−13026.4	−0.657747
$733$	−17810.6	−0.897475	−0.448738	−	0.893664i	$-0.648126\pi$
$733$	−17810.6	−0.897475	−0.448738	+	0.893664i	$0.648126\pi$
$734$	−4895.47	−0.246179
$735$	0	0
$736$	−736.000	−0.0368605
$737$	−64254.4	−3.21145
$738$	2506.04	0.124998
$739$	−16545.3	−0.823583	−0.411792	−	0.911278i	$-0.635097\pi$
$739$	−16545.3	−0.823583	−0.411792	+	0.911278i	$0.635097\pi$
$740$	0	0
$741$	10352.1	0.513217
$742$	−12860.2	−0.636270
$743$	8939.79	0.441412	0.220706	−	0.975340i	$-0.429164\pi$
$743$	8939.79	0.441412	0.220706	+	0.975340i	$0.429164\pi$
$744$	3955.28	0.194903
$745$	0	0
$746$	6325.86	0.310464
$747$	−3294.30	−0.161355
$748$	−11197.5	−0.547353
$749$	5015.98	0.244700
$750$	0	0
$751$	−11447.2	−0.556211	−0.278105	−	0.960551i	$-0.589706\pi$
$751$	−11447.2	−0.556211	−0.278105	+	0.960551i	$0.589706\pi$
$752$	−6449.33	−0.312743
$753$	−34564.1	−1.67276
$754$	−19230.7	−0.928836
$755$	0	0
$756$	5666.73	0.272615
$757$	−30177.1	−1.44889	−0.724443	−	0.689335i	$-0.757903\pi$
$757$	−30177.1	−1.44889	−0.724443	+	0.689335i	$0.757903\pi$
$758$	9084.85	0.435325
$759$	−8394.95	−0.401472
$760$	0	0
$761$	27523.2	1.31106	0.655529	−	0.755170i	$-0.272446\pi$
$761$	27523.2	1.31106	0.655529	+	0.755170i	$0.272446\pi$
$762$	−13947.8	−0.663093
$763$	7741.00	0.367291
$764$	−5040.10	−0.238671
$765$	0	0
$766$	19393.3	0.914761
$767$	−31175.7	−1.46765
$768$	−1451.59	−0.0682029
$769$	14478.0	0.678920	0.339460	−	0.940621i	$-0.389756\pi$
$769$	14478.0	0.678920	0.339460	+	0.940621i	$0.389756\pi$
$770$	0	0
$771$	31392.0	1.46635
$772$	−11867.7	−0.553276
$773$	−31511.5	−1.46622	−0.733110	−	0.680110i	$-0.761932\pi$
$773$	−31511.5	−1.46622	−0.733110	+	0.680110i	$0.761932\pi$
$774$	2313.50	0.107438
$775$	0	0
$776$	4207.81	0.194654
$777$	10632.6	0.490915
$778$	−25014.5	−1.15272
$779$	8626.04	0.396739
$780$	0	0
$781$	−46960.8	−2.15159
$782$	−2000.47	−0.0914792
$783$	23141.6	1.05621
$784$	−3395.64	−0.154685
$785$	0	0
$786$	1833.27	0.0831942
$787$	−17117.5	−0.775316	−0.387658	−	0.921803i	$-0.626716\pi$
$787$	−17117.5	−0.775316	−0.387658	+	0.921803i	$0.626716\pi$
$788$	−3184.94	−0.143983
$789$	22694.7	1.02402
$790$	0	0
$791$	1564.11	0.0703078
$792$	−2653.13	−0.119034
$793$	−29562.9	−1.32385
$794$	10211.6	0.456417
$795$	0	0
$796$	−7495.21	−0.333745
$797$	9546.95	0.424304	0.212152	−	0.977237i	$-0.431953\pi$
$797$	9546.95	0.424304	0.212152	+	0.977237i	$0.431953\pi$
$798$	−4599.70	−0.204045
$799$	−17529.5	−0.776156
$800$	0	0
$801$	−1027.65	−0.0453313
$802$	−19311.7	−0.850274
$803$	45612.8	2.00454
$804$	−22640.3	−0.993111
$805$	0	0
$806$	8976.35	0.392281
$807$	−20409.6	−0.890275
$808$	15355.1	0.668555
$809$	−23328.7	−1.01384	−0.506919	−	0.861994i	$-0.669216\pi$
$809$	−23328.7	−1.01384	−0.506919	+	0.861994i	$0.669216\pi$
$810$	0	0
$811$	637.001	0.0275809	0.0137905	−	0.999905i	$-0.495610\pi$
$811$	637.001	0.0275809	0.0137905	+	0.999905i	$0.495610\pi$
$812$	8544.71	0.369286
$813$	1964.63	0.0847510
$814$	21110.1	0.908979
$815$	0	0
$816$	−3945.47	−0.169264
$817$	7963.30	0.341005
$818$	−11912.4	−0.509178
$819$	−3032.69	−0.129391
$820$	0	0
$821$	19467.7	0.827560	0.413780	−	0.910377i	$-0.364208\pi$
$821$	19467.7	0.827560	0.413780	+	0.910377i	$0.364208\pi$
$822$	−7139.18	−0.302929
$823$	−12780.5	−0.541312	−0.270656	−	0.962676i	$-0.587241\pi$
$823$	−12780.5	−0.541312	−0.270656	+	0.962676i	$0.587241\pi$
$824$	4216.54	0.178265
$825$	0	0
$826$	13852.2	0.583509
$827$	−6151.42	−0.258653	−0.129326	−	0.991602i	$-0.541281\pi$
$827$	−6151.42	−0.258653	−0.129326	+	0.991602i	$0.541281\pi$
$828$	−473.993	−0.0198942
$829$	16579.5	0.694609	0.347305	−	0.937752i	$-0.387097\pi$
$829$	16579.5	0.694609	0.347305	+	0.937752i	$0.387097\pi$
$830$	0	0
$831$	−3699.45	−0.154431
$832$	−3294.33	−0.137272
$833$	−9229.46	−0.383892
$834$	36044.7	1.49655
$835$	0	0
$836$	−9132.34	−0.377809
$837$	−10801.8	−0.446077
$838$	11900.9	0.490585
$839$	11380.2	0.468283	0.234142	−	0.972202i	$-0.424772\pi$
$839$	11380.2	0.468283	0.234142	+	0.972202i	$0.424772\pi$
$840$	0	0
$841$	10505.6	0.430752
$842$	−29468.4	−1.20611
$843$	28283.1	1.15554
$844$	1525.80	0.0622278
$845$	0	0
$846$	−4153.44	−0.168792
$847$	32162.9	1.30476
$848$	−8996.61	−0.364322
$849$	27388.8	1.10716
$850$	0	0
$851$	3771.40	0.151918
$852$	−16546.8	−0.665358
$853$	−1675.74	−0.0672642	−0.0336321	−	0.999434i	$-0.510707\pi$
$853$	−1675.74	−0.0672642	−0.0336321	+	0.999434i	$0.510707\pi$
$854$	13135.6	0.526334
$855$	0	0
$856$	3509.04	0.140113
$857$	16486.9	0.657156	0.328578	−	0.944477i	$-0.393431\pi$
$857$	16486.9	0.657156	0.328578	+	0.944477i	$0.393431\pi$
$858$	−37575.7	−1.49512
$859$	−35291.0	−1.40176	−0.700881	−	0.713278i	$-0.747210\pi$
$859$	−35291.0	−1.40176	−0.700881	+	0.713278i	$0.747210\pi$
$860$	0	0
$861$	−15770.2	−0.624213
$862$	−4463.19	−0.176354
$863$	−29794.9	−1.17524	−0.587620	−	0.809137i	$-0.699935\pi$
$863$	−29794.9	−1.17524	−0.587620	+	0.809137i	$0.699935\pi$
$864$	3964.28	0.156097
$865$	0	0
$866$	16436.0	0.644941
$867$	17134.2	0.671173
$868$	−3988.42	−0.155963
$869$	−25560.0	−0.997773
$870$	0	0
$871$	−51381.2	−1.99883
$872$	5415.38	0.210307
$873$	2709.88	0.105058
$874$	−1631.53	−0.0631433
$875$	0	0
$876$	16071.9	0.619884
$877$	33656.3	1.29589	0.647943	−	0.761689i	$-0.275629\pi$
$877$	33656.3	1.29589	0.647943	+	0.761689i	$0.275629\pi$
$878$	11824.8	0.454517
$879$	−10124.4	−0.388495
$880$	0	0
$881$	−38607.8	−1.47642	−0.738212	−	0.674568i	$-0.764330\pi$
$881$	−38607.8	−1.47642	−0.738212	+	0.674568i	$0.764330\pi$
$882$	−2186.83	−0.0834858
$883$	28429.1	1.08348	0.541741	−	0.840546i	$-0.317765\pi$
$883$	28429.1	1.08348	0.541741	+	0.840546i	$0.317765\pi$
$884$	−8954.09	−0.340677
$885$	0	0
$886$	−9061.35	−0.343591
$887$	1500.63	0.0568052	0.0284026	−	0.999597i	$-0.490958\pi$
$887$	1500.63	0.0568052	0.0284026	+	0.999597i	$0.490958\pi$
$888$	7438.23	0.281093
$889$	14064.7	0.530613
$890$	0	0
$891$	54171.6	2.03683
$892$	−9197.89	−0.345256
$893$	−14296.6	−0.535740
$894$	−31151.7	−1.16540
$895$	0	0
$896$	1463.75	0.0545765
$897$	−6713.04	−0.249880
$898$	16272.6	0.604703
$899$	−16287.8	−0.604259
$900$	0	0
$901$	−24453.1	−0.904162
$902$	−31310.5	−1.15579
$903$	−14558.6	−0.536522
$904$	1094.21	0.0402576
$905$	0	0
$906$	−24699.1	−0.905711
$907$	−37704.3	−1.38032	−0.690160	−	0.723657i	$-0.742460\pi$
$907$	−37704.3	−1.38032	−0.690160	+	0.723657i	$0.742460\pi$
$908$	2519.26	0.0920755
$909$	9888.89	0.360829
$910$	0	0
$911$	36184.8	1.31598	0.657989	−	0.753028i	$-0.271407\pi$
$911$	36184.8	1.31598	0.657989	+	0.753028i	$0.271407\pi$
$912$	−3217.82	−0.116834
$913$	41158.9	1.49196
$914$	31580.2	1.14286
$915$	0	0
$916$	2983.82	0.107629
$917$	−1848.63	−0.0665727
$918$	10775.0	0.387396
$919$	−3810.06	−0.136760	−0.0683800	−	0.997659i	$-0.521783\pi$
$919$	−3810.06	−0.136760	−0.0683800	+	0.997659i	$0.521783\pi$
$920$	0	0
$921$	−6731.44	−0.240835
$922$	−11916.6	−0.425653
$923$	−37552.4	−1.33917
$924$	16695.8	0.594429
$925$	0	0
$926$	−23723.6	−0.841908
$927$	2715.50	0.0962123
$928$	5977.63	0.211450
$929$	−2804.57	−0.0990473	−0.0495237	−	0.998773i	$-0.515770\pi$
$929$	−2804.57	−0.0990473	−0.0495237	+	0.998773i	$0.515770\pi$
$930$	0	0
$931$	−7527.29	−0.264981
$932$	11279.8	0.396439
$933$	−53998.3	−1.89478
$934$	−3476.38	−0.121789
$935$	0	0
$936$	−2121.59	−0.0740878
$937$	−3654.12	−0.127401	−0.0637006	−	0.997969i	$-0.520290\pi$
$937$	−3654.12	−0.127401	−0.0637006	+	0.997969i	$0.520290\pi$
$938$	22830.0	0.794696
$939$	51267.6	1.78174
$940$	0	0
$941$	50184.3	1.73854	0.869268	−	0.494341i	$-0.164591\pi$
$941$	50184.3	1.73854	0.869268	+	0.494341i	$0.164591\pi$
$942$	−965.070	−0.0333797
$943$	−5593.74	−0.193168
$944$	9690.58	0.334112
$945$	0	0
$946$	−28904.9	−0.993425
$947$	44661.5	1.53253	0.766263	−	0.642527i	$-0.222114\pi$
$947$	44661.5	1.53253	0.766263	+	0.642527i	$0.222114\pi$
$948$	−9006.18	−0.308552
$949$	36474.4	1.24764
$950$	0	0
$951$	42608.6	1.45287
$952$	3978.53	0.135446
$953$	34444.6	1.17080	0.585398	−	0.810746i	$-0.300938\pi$
$953$	34444.6	1.17080	0.585398	+	0.810746i	$0.300938\pi$
$954$	−5793.92	−0.196630
$955$	0	0
$956$	−16936.2	−0.572967
$957$	68181.9	2.30304
$958$	8031.49	0.270862
$959$	7199.00	0.242406
$960$	0	0
$961$	−22188.3	−0.744800
$962$	16880.8	0.565756
$963$	2259.86	0.0756210
$964$	11255.9	0.376065
$965$	0	0
$966$	2982.77	0.0993470
$967$	−204.900	−0.00681400	−0.00340700	−	0.999994i	$-0.501084\pi$
$967$	−204.900	−0.00681400	−0.00340700	+	0.999994i	$0.501084\pi$
$968$	22500.3	0.747093
$969$	−8746.13	−0.289955
$970$	0	0
$971$	23785.4	0.786107	0.393054	−	0.919516i	$-0.371419\pi$
$971$	23785.4	0.786107	0.393054	+	0.919516i	$0.371419\pi$
$972$	5708.14	0.188363
$973$	−36346.7	−1.19756
$974$	−37237.7	−1.22502
$975$	0	0
$976$	9189.26	0.301374
$977$	−14532.6	−0.475884	−0.237942	−	0.971279i	$-0.576473\pi$
$977$	−14532.6	−0.475884	−0.237942	+	0.971279i	$0.576473\pi$
$978$	−33033.0	−1.08004
$979$	12839.5	0.419155
$980$	0	0
$981$	3487.57	0.113506
$982$	15343.8	0.498615
$983$	22190.9	0.720021	0.360011	−	0.932948i	$-0.382773\pi$
$983$	22190.9	0.720021	0.360011	+	0.932948i	$0.382773\pi$
$984$	−11032.4	−0.357418
$985$	0	0
$986$	16247.4	0.524769
$987$	26137.1	0.842911
$988$	−7302.70	−0.235152
$989$	−5163.98	−0.166031
$990$	0	0
$991$	−18739.3	−0.600679	−0.300340	−	0.953832i	$-0.597100\pi$
$991$	−18739.3	−0.600679	−0.300340	+	0.953832i	$0.597100\pi$
$992$	−2790.19	−0.0893029
$993$	−61882.6	−1.97763
$994$	16685.5	0.532426
$995$	0	0
$996$	14502.5	0.461375
$997$	23656.5	0.751465	0.375732	−	0.926728i	$-0.377391\pi$
$997$	23656.5	0.751465	0.375732	+	0.926728i	$0.377391\pi$
$998$	7182.97	0.227829
$999$	−20313.7	−0.643341

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.a.bb.1.2		9
5.2	odd	4		230.4.b.b.139.17	yes	18
5.3	odd	4		230.4.b.b.139.2	✓	18
5.4	even	2		1150.4.a.ba.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.b.b.139.2	✓	18	5.3	odd	4
230.4.b.b.139.17	yes	18	5.2	odd	4
1150.4.a.ba.1.8		9	5.4	even	2
1150.4.a.bb.1.2		9	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -5.67028 q^{3} +4.00000 q^{4} -11.3406 q^{6} +11.4356 q^{7} +8.00000 q^{8} +5.15209 q^{9} -64.3703 q^{11} -22.6811 q^{12} -51.4739 q^{13} +22.8712 q^{14} +16.0000 q^{16} +43.4885 q^{17} +10.3042 q^{18} +35.4680 q^{19} -64.8429 q^{21} -128.741 q^{22} -23.0000 q^{23} -45.3623 q^{24} -102.948 q^{26} +123.884 q^{27} +45.7423 q^{28} +186.801 q^{29} -87.1933 q^{31} +32.0000 q^{32} +364.998 q^{33} +86.9770 q^{34} +20.6084 q^{36} -163.974 q^{37} +70.9360 q^{38} +291.871 q^{39} +243.206 q^{41} -129.686 q^{42} +224.521 q^{43} -257.481 q^{44} -46.0000 q^{46} -403.083 q^{47} -90.7245 q^{48} -212.228 q^{49} -246.592 q^{51} -205.896 q^{52} -562.288 q^{53} +247.768 q^{54} +91.4846 q^{56} -201.114 q^{57} +373.602 q^{58} +605.661 q^{59} +574.329 q^{61} -174.387 q^{62} +58.9172 q^{63} +64.0000 q^{64} +729.995 q^{66} +998.199 q^{67} +173.954 q^{68} +130.416 q^{69} +729.542 q^{71} +41.2167 q^{72} -708.601 q^{73} -327.948 q^{74} +141.872 q^{76} -736.111 q^{77} +583.743 q^{78} +397.078 q^{79} -841.562 q^{81} +486.413 q^{82} -639.409 q^{83} -259.372 q^{84} +449.042 q^{86} -1059.21 q^{87} -514.962 q^{88} -199.463 q^{89} -588.633 q^{91} -92.0000 q^{92} +494.411 q^{93} -806.166 q^{94} -181.449 q^{96} +525.976 q^{97} -424.455 q^{98} -331.642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 18 q^{2} + 3 q^{3} + 36 q^{4} + 6 q^{6} + 44 q^{7} + 72 q^{8} + 124 q^{9} + 81 q^{11} + 12 q^{12} + 59 q^{13} + 88 q^{14} + 144 q^{16} + 110 q^{17} + 248 q^{18} + 221 q^{19} + 142 q^{21} + 162 q^{22}+ \cdots - 1753 q^{99}+O(q^{100}) \) 9 * q + 18 * q^2 + 3 * q^3 + 36 * q^4 + 6 * q^6 + 44 * q^7 + 72 * q^8 + 124 * q^9 + 81 * q^11 + 12 * q^12 + 59 * q^13 + 88 * q^14 + 144 * q^16 + 110 * q^17 + 248 * q^18 + 221 * q^19 + 142 * q^21 + 162 * q^22 - 207 * q^23 + 24 * q^24 + 118 * q^26 + 336 * q^27 + 176 * q^28 + 205 * q^29 + 336 * q^31 + 288 * q^32 + 437 * q^33 + 220 * q^34 + 496 * q^36 - 5 * q^37 + 442 * q^38 - 44 * q^39 + 360 * q^41 + 284 * q^42 + 366 * q^43 + 324 * q^44 - 414 * q^46 - 122 * q^47 + 48 * q^48 + 457 * q^49 + 1025 * q^51 + 236 * q^52 + 631 * q^53 + 672 * q^54 + 352 * q^56 - 384 * q^57 + 410 * q^58 + 797 * q^59 + 211 * q^61 + 672 * q^62 + 2447 * q^63 + 576 * q^64 + 874 * q^66 + 111 * q^67 + 440 * q^68 - 69 * q^69 + 2912 * q^71 + 992 * q^72 + 98 * q^73 - 10 * q^74 + 884 * q^76 + 942 * q^77 - 88 * q^78 + 1184 * q^79 + 2093 * q^81 + 720 * q^82 + 2375 * q^83 + 568 * q^84 + 732 * q^86 - 1534 * q^87 + 648 * q^88 + 2588 * q^89 + 2677 * q^91 - 828 * q^92 + 1402 * q^93 - 244 * q^94 + 96 * q^96 - 593 * q^97 + 914 * q^98 - 1753 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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