LMFDB - Embedded newform 529.4.a.m.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [529,4,Mod(1,529)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(529, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("529.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	529.a (trivial)

Newform invariants

comment:select newform

sage:traces = [25,0,-1,80,-51] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$31.2120103930$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	529.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.66204 q^{2} +2.67124 q^{3} +5.41053 q^{4} +4.26056 q^{5} -9.78218 q^{6} +14.5832 q^{7} +9.48276 q^{8} -19.8645 q^{9} -15.6023 q^{10} +14.0673 q^{11} +14.4528 q^{12} -38.2348 q^{13} -53.4043 q^{14} +11.3810 q^{15} -78.0104 q^{16} +45.6230 q^{17} +72.7445 q^{18} -103.879 q^{19} +23.0518 q^{20} +38.9552 q^{21} -51.5150 q^{22} +25.3307 q^{24} -106.848 q^{25} +140.017 q^{26} -125.186 q^{27} +78.9028 q^{28} -149.252 q^{29} -41.6775 q^{30} +237.837 q^{31} +209.815 q^{32} +37.5771 q^{33} -167.073 q^{34} +62.1326 q^{35} -107.477 q^{36} -300.565 q^{37} +380.408 q^{38} -102.134 q^{39} +40.4018 q^{40} +335.440 q^{41} -142.655 q^{42} +386.390 q^{43} +76.1114 q^{44} -84.6338 q^{45} -417.787 q^{47} -208.384 q^{48} -130.330 q^{49} +391.280 q^{50} +121.870 q^{51} -206.870 q^{52} -405.962 q^{53} +458.437 q^{54} +59.9345 q^{55} +138.289 q^{56} -277.485 q^{57} +546.565 q^{58} +37.7222 q^{59} +61.5770 q^{60} -40.1827 q^{61} -870.967 q^{62} -289.688 q^{63} -144.268 q^{64} -162.902 q^{65} -137.609 q^{66} +395.664 q^{67} +246.845 q^{68} -227.532 q^{70} -264.160 q^{71} -188.370 q^{72} +462.739 q^{73} +1100.68 q^{74} -285.415 q^{75} -562.039 q^{76} +205.146 q^{77} +374.020 q^{78} +467.988 q^{79} -332.368 q^{80} +201.939 q^{81} -1228.40 q^{82} -359.161 q^{83} +210.768 q^{84} +194.380 q^{85} -1414.97 q^{86} -398.686 q^{87} +133.397 q^{88} -907.444 q^{89} +309.932 q^{90} -557.586 q^{91} +635.318 q^{93} +1529.95 q^{94} -442.581 q^{95} +560.466 q^{96} -63.4707 q^{97} +477.274 q^{98} -279.440 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) $ 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * 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 $

$2$	−3.66204	−1.29473	−0.647363	−	0.762182i	$-0.724128\pi$
$2$	−3.66204	−1.29473	−0.647363	+	0.762182i	$0.724128\pi$
$3$	2.67124	0.514080	0.257040	−	0.966401i	$-0.417253\pi$
$3$	2.67124	0.514080	0.257040	+	0.966401i	$0.417253\pi$
$4$	5.41053	0.676316
$5$	4.26056	0.381076	0.190538	−	0.981680i	$-0.438977\pi$
$5$	4.26056	0.381076	0.190538	+	0.981680i	$0.438977\pi$
$6$	−9.78218	−0.665593
$7$	14.5832	0.787419	0.393710	−	0.919235i	$-0.371192\pi$
$7$	14.5832	0.787419	0.393710	+	0.919235i	$0.371192\pi$
$8$	9.48276	0.419083
$9$	−19.8645	−0.735722
$10$	−15.6023	−0.493389
$11$	14.0673	0.385586	0.192793	−	0.981239i	$-0.438245\pi$
$11$	14.0673	0.385586	0.192793	+	0.981239i	$0.438245\pi$
$12$	14.4528	0.347680
$13$	−38.2348	−0.815725	−0.407863	−	0.913043i	$-0.633726\pi$
$13$	−38.2348	−0.815725	−0.407863	+	0.913043i	$0.633726\pi$
$14$	−53.4043	−1.01949
$15$	11.3810	0.195903
$16$	−78.0104	−1.21891
$17$	45.6230	0.650895	0.325447	−	0.945560i	$-0.394485\pi$
$17$	45.6230	0.650895	0.325447	+	0.945560i	$0.394485\pi$
$18$	72.7445	0.952558
$19$	−103.879	−1.25429	−0.627143	−	0.778904i	$-0.715776\pi$
$19$	−103.879	−1.25429	−0.627143	+	0.778904i	$0.715776\pi$
$20$	23.0518	0.257727
$21$	38.9552	0.404796
$22$	−51.5150	−0.499229
$23$	0	0
$23$	0	0
$24$	25.3307	0.215442
$25$	−106.848	−0.854781
$26$	140.017	1.05614
$27$	−125.186	−0.892300
$28$	78.9028	0.532544
$29$	−149.252	−0.955701	−0.477850	−	0.878441i	$-0.658584\pi$
$29$	−149.252	−0.955701	−0.477850	+	0.878441i	$0.658584\pi$
$30$	−41.6775	−0.253641
$31$	237.837	1.37796	0.688979	−	0.724781i	$-0.258059\pi$
$31$	237.837	1.37796	0.688979	+	0.724781i	$0.258059\pi$
$32$	209.815	1.15908
$33$	37.5771	0.198222
$34$	−167.073	−0.842731
$35$	62.1326	0.300066
$36$	−107.477	−0.497580
$37$	−300.565	−1.33547	−0.667737	−	0.744397i	$-0.732737\pi$
$37$	−300.565	−1.33547	−0.667737	+	0.744397i	$0.732737\pi$
$38$	380.408	1.62396
$39$	−102.134	−0.419348
$40$	40.4018	0.159702
$41$	335.440	1.27773	0.638865	−	0.769318i	$-0.279404\pi$
$41$	335.440	1.27773	0.638865	+	0.769318i	$0.279404\pi$
$42$	−142.655	−0.524100
$43$	386.390	1.37032	0.685161	−	0.728392i	$-0.259732\pi$
$43$	386.390	1.37032	0.685161	+	0.728392i	$0.259732\pi$
$44$	76.1114	0.260778
$45$	−84.6338	−0.280366
$46$	0	0
$47$	−417.787	−1.29661	−0.648303	−	0.761383i	$-0.724521\pi$
$47$	−417.787	−1.29661	−0.648303	+	0.761383i	$0.724521\pi$
$48$	−208.384	−0.626619
$49$	−130.330	−0.379971
$50$	391.280	1.10671
$51$	121.870	0.334612
$52$	−206.870	−0.551688
$53$	−405.962	−1.05213	−0.526067	−	0.850443i	$-0.676334\pi$
$53$	−405.962	−1.05213	−0.526067	+	0.850443i	$0.676334\pi$
$54$	458.437	1.15528
$55$	59.9345	0.146938
$56$	138.289	0.329994
$57$	−277.485	−0.644803
$58$	546.565	1.23737
$59$	37.7222	0.0832375	0.0416187	−	0.999134i	$-0.486749\pi$
$59$	37.7222	0.0832375	0.0416187	+	0.999134i	$0.486749\pi$
$60$	61.5770	0.132493
$61$	−40.1827	−0.0843420	−0.0421710	−	0.999110i	$-0.513427\pi$
$61$	−40.1827	−0.0843420	−0.0421710	+	0.999110i	$0.513427\pi$
$62$	−870.967	−1.78408
$63$	−289.688	−0.579321
$64$	−144.268	−0.281773
$65$	−162.902	−0.310853
$66$	−137.609	−0.256643
$67$	395.664	0.721464	0.360732	−	0.932670i	$-0.382527\pi$
$67$	395.664	0.721464	0.360732	+	0.932670i	$0.382527\pi$
$68$	246.845	0.440210
$69$	0	0
$70$	−227.532	−0.388504
$71$	−264.160	−0.441550	−0.220775	−	0.975325i	$-0.570859\pi$
$71$	−264.160	−0.441550	−0.220775	+	0.975325i	$0.570859\pi$
$72$	−188.370	−0.308328
$73$	462.739	0.741911	0.370955	−	0.928651i	$-0.379030\pi$
$73$	462.739	0.741911	0.370955	+	0.928651i	$0.379030\pi$
$74$	1100.68	1.72907
$75$	−285.415	−0.439426
$76$	−562.039	−0.848293
$77$	205.146	0.303618
$78$	374.020	0.542941
$79$	467.988	0.666491	0.333246	−	0.942840i	$-0.391856\pi$
$79$	467.988	0.666491	0.333246	+	0.942840i	$0.391856\pi$
$80$	−332.368	−0.464498
$81$	201.939	0.277008
$82$	−1228.40	−1.65431
$83$	−359.161	−0.474976	−0.237488	−	0.971390i	$-0.576324\pi$
$83$	−359.161	−0.474976	−0.237488	+	0.971390i	$0.576324\pi$
$84$	210.768	0.273770
$85$	194.380	0.248040
$86$	−1414.97	−1.77419
$87$	−398.686	−0.491306
$88$	133.397	0.161592
$89$	−907.444	−1.08077	−0.540387	−	0.841417i	$-0.681722\pi$
$89$	−907.444	−1.08077	−0.540387	+	0.841417i	$0.681722\pi$
$90$	309.932	0.362997
$91$	−557.586	−0.642318
$92$	0	0
$93$	635.318	0.708381
$94$	1529.95	1.67875
$95$	−442.581	−0.477978
$96$	560.466	0.595858
$97$	−63.4707	−0.0664379	−0.0332190	−	0.999448i	$-0.510576\pi$
$97$	−63.4707	−0.0664379	−0.0332190	+	0.999448i	$0.510576\pi$
$98$	477.274	0.491959
$99$	−279.440	−0.283684
$100$	−578.102	−0.578102
$101$	−329.736	−0.324851	−0.162425	−	0.986721i	$-0.551932\pi$
$101$	−329.736	−0.324851	−0.162425	+	0.986721i	$0.551932\pi$
$102$	−446.293	−0.433231
$103$	−1529.93	−1.46358	−0.731788	−	0.681532i	$-0.761314\pi$
$103$	−1529.93	−1.46358	−0.731788	+	0.681532i	$0.761314\pi$
$104$	−362.571	−0.341856
$105$	165.971	0.154258
$106$	1486.65	1.36223
$107$	−1511.12	−1.36528	−0.682642	−	0.730753i	$-0.739169\pi$
$107$	−1511.12	−1.36528	−0.682642	+	0.730753i	$0.739169\pi$
$108$	−677.323	−0.603476
$109$	−2061.41	−1.81144	−0.905719	−	0.423878i	$-0.860669\pi$
$109$	−2061.41	−1.81144	−0.905719	+	0.423878i	$0.860669\pi$
$110$	−219.482	−0.190244
$111$	−802.880	−0.686541
$112$	−1137.64	−0.959795
$113$	−2204.26	−1.83504	−0.917520	−	0.397690i	$-0.869812\pi$
$113$	−2204.26	−1.83504	−0.917520	+	0.397690i	$0.869812\pi$
$114$	1016.16	0.834843
$115$	0	0
$116$	−807.529	−0.646355
$117$	759.515	0.600147
$118$	−138.140	−0.107770
$119$	665.330	0.512527
$120$	107.923	0.0820997
$121$	−1133.11	−0.851323
$122$	147.150	0.109200
$123$	896.041	0.656856
$124$	1286.82	0.931935
$125$	−987.800	−0.706812
$126$	1060.85	0.750062
$127$	−571.347	−0.399203	−0.199602	−	0.979877i	$-0.563965\pi$
$127$	−571.347	−0.399203	−0.199602	+	0.979877i	$0.563965\pi$
$128$	−1150.21	−0.794257
$129$	1032.14	0.704455
$130$	596.552	0.402470
$131$	2359.78	1.57385	0.786926	−	0.617047i	$-0.211671\pi$
$131$	2359.78	1.57385	0.786926	+	0.617047i	$0.211671\pi$
$132$	203.312	0.134061
$133$	−1514.89	−0.987648
$134$	−1448.94	−0.934098
$135$	−533.363	−0.340034
$136$	432.632	0.272779
$137$	−2161.67	−1.34806	−0.674028	−	0.738706i	$-0.735437\pi$
$137$	−2161.67	−1.34806	−0.674028	+	0.738706i	$0.735437\pi$
$138$	0	0
$139$	854.209	0.521245	0.260622	−	0.965441i	$-0.416072\pi$
$139$	854.209	0.521245	0.260622	+	0.965441i	$0.416072\pi$
$140$	336.170	0.202940
$141$	−1116.01	−0.666559
$142$	967.365	0.571687
$143$	−537.860	−0.314532
$144$	1549.64	0.896781
$145$	−635.895	−0.364194
$146$	−1694.57	−0.960571
$147$	−348.143	−0.195336
$148$	−1626.21	−0.903202
$149$	−1264.18	−0.695070	−0.347535	−	0.937667i	$-0.612981\pi$
$149$	−1264.18	−0.695070	−0.347535	+	0.937667i	$0.612981\pi$
$150$	1045.20	0.568936
$151$	−93.2143	−0.0502362	−0.0251181	−	0.999684i	$-0.507996\pi$
$151$	−93.2143	−0.0502362	−0.0251181	+	0.999684i	$0.507996\pi$
$152$	−985.057	−0.525649
$153$	−906.279	−0.478878
$154$	−751.253	−0.393102
$155$	1013.32	0.525107
$156$	−552.600	−0.283612
$157$	3109.34	1.58059	0.790294	−	0.612728i	$-0.209928\pi$
$157$	3109.34	1.58059	0.790294	+	0.612728i	$0.209928\pi$
$158$	−1713.79	−0.862923
$159$	−1084.42	−0.540881
$160$	893.929	0.441696
$161$	0	0
$162$	−739.509	−0.358650
$163$	−575.568	−0.276576	−0.138288	−	0.990392i	$-0.544160\pi$
$163$	−575.568	−0.276576	−0.138288	+	0.990392i	$0.544160\pi$
$164$	1814.91	0.864149
$165$	160.099	0.0755376
$166$	1315.26	0.614964
$167$	−5.53768	−0.00256598	−0.00128299	−	0.999999i	$-0.500408\pi$
$167$	−5.53768	−0.00256598	−0.00128299	+	0.999999i	$0.500408\pi$
$168$	369.403	0.169643
$169$	−735.099	−0.334592
$170$	−711.825	−0.321144
$171$	2063.50	0.922805
$172$	2090.57	0.926770
$173$	−2604.44	−1.14458	−0.572289	−	0.820052i	$-0.693944\pi$
$173$	−2604.44	−1.14458	−0.572289	+	0.820052i	$0.693944\pi$
$174$	1460.00	0.636107
$175$	−1558.18	−0.673071
$176$	−1097.40	−0.469996
$177$	100.765	0.0427907
$178$	3323.10	1.39931
$179$	2695.23	1.12543	0.562713	−	0.826652i	$-0.309758\pi$
$179$	2695.23	1.12543	0.562713	+	0.826652i	$0.309758\pi$
$180$	−457.913	−0.189616
$181$	4089.19	1.67927	0.839633	−	0.543155i	$-0.182770\pi$
$181$	4089.19	1.67927	0.839633	+	0.543155i	$0.182770\pi$
$182$	2041.90	0.831625
$183$	−107.337	−0.0433585
$184$	0	0
$185$	−1280.57	−0.508917
$186$	−2326.56	−0.917159
$187$	641.793	0.250976
$188$	−2260.45	−0.876915
$189$	−1825.62	−0.702614
$190$	1620.75	0.618850
$191$	40.9753	0.0155229	0.00776143	−	0.999970i	$-0.497529\pi$
$191$	40.9753	0.0155229	0.00776143	+	0.999970i	$0.497529\pi$
$192$	−385.373	−0.144854
$193$	−251.434	−0.0937754	−0.0468877	−	0.998900i	$-0.514930\pi$
$193$	−251.434	−0.0937754	−0.0468877	+	0.998900i	$0.514930\pi$
$194$	232.432	0.0860189
$195$	−435.149	−0.159803
$196$	−705.155	−0.256981
$197$	2547.43	0.921304	0.460652	−	0.887581i	$-0.347616\pi$
$197$	2547.43	0.921304	0.460652	+	0.887581i	$0.347616\pi$
$198$	1023.32	0.367293
$199$	2392.89	0.852401	0.426200	−	0.904629i	$-0.359852\pi$
$199$	2392.89	0.852401	0.426200	+	0.904629i	$0.359852\pi$
$200$	−1013.21	−0.358224
$201$	1056.91	0.370890
$202$	1207.50	0.420593
$203$	−2176.57	−0.752537
$204$	659.381	0.226303
$205$	1429.16	0.486912
$206$	5602.66	1.89493
$207$	0	0
$208$	2982.71	0.994298
$209$	−1461.29	−0.483635
$210$	−607.792	−0.199722
$211$	−3462.41	−1.12968	−0.564839	−	0.825201i	$-0.691062\pi$
$211$	−3462.41	−1.12968	−0.564839	+	0.825201i	$0.691062\pi$
$212$	−2196.47	−0.711575
$213$	−705.635	−0.226992
$214$	5533.78	1.76767
$215$	1646.23	0.522197
$216$	−1187.11	−0.373947
$217$	3468.42	1.08503
$218$	7548.95	2.34532
$219$	1236.09	0.381401
$220$	324.277	0.0993762
$221$	−1744.39	−0.530952
$222$	2940.18	0.888882
$223$	4138.91	1.24288	0.621440	−	0.783462i	$-0.286548\pi$
$223$	4138.91	1.24288	0.621440	+	0.783462i	$0.286548\pi$
$224$	3059.78	0.912678
$225$	2122.47	0.628881
$226$	8072.09	2.37587
$227$	5304.16	1.55088	0.775439	−	0.631422i	$-0.217529\pi$
$227$	5304.16	1.55088	0.775439	+	0.631422i	$0.217529\pi$
$228$	−1501.34	−0.436090
$229$	−3957.23	−1.14193	−0.570963	−	0.820976i	$-0.693430\pi$
$229$	−3957.23	−1.14193	−0.570963	+	0.820976i	$0.693430\pi$
$230$	0	0
$231$	547.994	0.156084
$232$	−1415.32	−0.400517
$233$	1233.34	0.346775	0.173387	−	0.984854i	$-0.444529\pi$
$233$	1233.34	0.346775	0.173387	+	0.984854i	$0.444529\pi$
$234$	−2781.37	−0.777026
$235$	−1780.00	−0.494105
$236$	204.097	0.0562948
$237$	1250.11	0.342630
$238$	−2436.46	−0.663582
$239$	1302.39	0.352489	0.176244	−	0.984346i	$-0.443605\pi$
$239$	1302.39	0.352489	0.176244	+	0.984346i	$0.443605\pi$
$240$	−887.833	−0.238789
$241$	−2144.78	−0.573267	−0.286634	−	0.958040i	$-0.592536\pi$
$241$	−2144.78	−0.573267	−0.286634	+	0.958040i	$0.592536\pi$
$242$	4149.50	1.10223
$243$	3919.45	1.03470
$244$	−217.409	−0.0570418
$245$	−555.279	−0.144798
$246$	−3281.34	−0.850448
$247$	3971.79	1.02315
$248$	2255.35	0.577479
$249$	−959.403	−0.244176
$250$	3617.36	0.915128
$251$	−797.294	−0.200497	−0.100249	−	0.994962i	$-0.531964\pi$
$251$	−797.294	−0.200497	−0.100249	+	0.994962i	$0.531964\pi$
$252$	−1567.36	−0.391804
$253$	0	0
$254$	2092.29	0.516859
$255$	519.234	0.127513
$256$	5366.24	1.31012
$257$	−7247.23	−1.75903	−0.879514	−	0.475874i	$-0.842132\pi$
$257$	−7247.23	−1.75903	−0.879514	+	0.475874i	$0.842132\pi$
$258$	−3779.73	−0.912076
$259$	−4383.20	−1.05158
$260$	−881.383	−0.210235
$261$	2964.81	0.703130
$262$	−8641.59	−2.03771
$263$	−1999.08	−0.468703	−0.234351	−	0.972152i	$-0.575297\pi$
$263$	−1999.08	−0.468703	−0.234351	+	0.972152i	$0.575297\pi$
$264$	356.334	0.0830714
$265$	−1729.62	−0.400943
$266$	5547.57	1.27873
$267$	−2424.00	−0.555604
$268$	2140.75	0.487937
$269$	2361.47	0.535246	0.267623	−	0.963524i	$-0.413762\pi$
$269$	2361.47	0.535246	0.267623	+	0.963524i	$0.413762\pi$
$270$	1953.20	0.440251
$271$	−7756.45	−1.73864	−0.869318	−	0.494253i	$-0.835442\pi$
$271$	−7756.45	−1.73864	−0.869318	+	0.494253i	$0.835442\pi$
$272$	−3559.07	−0.793384
$273$	−1489.45	−0.330203
$274$	7916.10	1.74536
$275$	−1503.06	−0.329592
$276$	0	0
$277$	1424.32	0.308949	0.154475	−	0.987997i	$-0.450632\pi$
$277$	1424.32	0.308949	0.154475	+	0.987997i	$0.450632\pi$
$278$	−3128.15	−0.674869
$279$	−4724.50	−1.01379
$280$	589.188	0.125753
$281$	−4790.26	−1.01695	−0.508475	−	0.861077i	$-0.669791\pi$
$281$	−4790.26	−1.01695	−0.508475	+	0.861077i	$0.669791\pi$
$282$	4086.86	0.863011
$283$	2991.24	0.628307	0.314154	−	0.949372i	$-0.398279\pi$
$283$	2991.24	0.628307	0.314154	+	0.949372i	$0.398279\pi$
$284$	−1429.25	−0.298627
$285$	−1182.24	−0.245719
$286$	1969.67	0.407233
$287$	4891.79	1.00611
$288$	−4167.87	−0.852757
$289$	−2831.54	−0.576336
$290$	2328.67	0.471532
$291$	−169.545	−0.0341544
$292$	2503.66	0.501766
$293$	1997.77	0.398331	0.199166	−	0.979966i	$-0.436177\pi$
$293$	1997.77	0.398331	0.199166	+	0.979966i	$0.436177\pi$
$294$	1274.91	0.252906
$295$	160.718	0.0317198
$296$	−2850.18	−0.559674
$297$	−1761.03	−0.344058
$298$	4629.47	0.899926
$299$	0	0
$300$	−1544.25	−0.297191
$301$	5634.80	1.07902
$302$	341.354	0.0650421
$303$	−880.803	−0.166999
$304$	8103.63	1.52886
$305$	−171.200	−0.0321407
$306$	3318.83	0.620015
$307$	972.558	0.180804	0.0904020	−	0.995905i	$-0.471185\pi$
$307$	972.558	0.180804	0.0904020	+	0.995905i	$0.471185\pi$
$308$	1109.95	0.205342
$309$	−4086.80	−0.752395
$310$	−3710.80	−0.679869
$311$	−372.641	−0.0679437	−0.0339719	−	0.999423i	$-0.510816\pi$
$311$	−372.641	−0.0679437	−0.0339719	+	0.999423i	$0.510816\pi$
$312$	−968.514	−0.175741
$313$	1698.01	0.306636	0.153318	−	0.988177i	$-0.451004\pi$
$313$	1698.01	0.306636	0.153318	+	0.988177i	$0.451004\pi$
$314$	−11386.5	−2.04643
$315$	−1234.23	−0.220765
$316$	2532.06	0.450758
$317$	1656.38	0.293474	0.146737	−	0.989176i	$-0.453123\pi$
$317$	1656.38	0.293474	0.146737	+	0.989176i	$0.453123\pi$
$318$	3971.19	0.700293
$319$	−2099.57	−0.368505
$320$	−614.660	−0.107377
$321$	−4036.56	−0.701865
$322$	0	0
$323$	−4739.27	−0.816408
$324$	1092.60	0.187345
$325$	4085.30	0.697267
$326$	2107.75	0.358091
$327$	−5506.50	−0.931224
$328$	3180.90	0.535475
$329$	−6092.67	−1.02097
$330$	−586.290	−0.0978006
$331$	3610.02	0.599471	0.299736	−	0.954022i	$-0.403102\pi$
$331$	3610.02	0.599471	0.299736	+	0.954022i	$0.403102\pi$
$332$	−1943.25	−0.321234
$333$	5970.57	0.982538
$334$	20.2792	0.00332224
$335$	1685.75	0.274932
$336$	−3038.91	−0.493411
$337$	7485.75	1.21001	0.605007	−	0.796220i	$-0.293170\pi$
$337$	7485.75	1.21001	0.605007	+	0.796220i	$0.293170\pi$
$338$	2691.96	0.433205
$339$	−5888.11	−0.943357
$340$	1051.70	0.167754
$341$	3345.72	0.531322
$342$	−7556.61	−1.19478
$343$	−6902.67	−1.08662
$344$	3664.04	0.574278
$345$	0	0
$346$	9537.56	1.48191
$347$	−2515.40	−0.389146	−0.194573	−	0.980888i	$-0.562332\pi$
$347$	−2515.40	−0.389146	−0.194573	+	0.980888i	$0.562332\pi$
$348$	−2157.10	−0.332278
$349$	11639.5	1.78523	0.892617	−	0.450816i	$-0.148867\pi$
$349$	11639.5	1.78523	0.892617	+	0.450816i	$0.148867\pi$
$350$	5706.12	0.871443
$351$	4786.47	0.727872
$352$	2951.53	0.446924
$353$	−7474.21	−1.12695	−0.563473	−	0.826134i	$-0.690535\pi$
$353$	−7474.21	−1.12695	−0.563473	+	0.826134i	$0.690535\pi$
$354$	−369.005	−0.0554023
$355$	−1125.47	−0.168264
$356$	−4909.75	−0.730944
$357$	1777.26	0.263480
$358$	−9870.05	−1.45712
$359$	11817.3	1.73731	0.868656	−	0.495416i	$-0.164984\pi$
$359$	11817.3	1.73731	0.868656	+	0.495416i	$0.164984\pi$
$360$	−802.561	−0.117496
$361$	3931.80	0.573233
$362$	−14974.8	−2.17419
$363$	−3026.81	−0.437648
$364$	−3016.83	−0.434409
$365$	1971.52	0.282724
$366$	393.074	0.0561374
$367$	1777.53	0.252823	0.126412	−	0.991978i	$-0.459654\pi$
$367$	1777.53	0.252823	0.126412	+	0.991978i	$0.459654\pi$
$368$	0	0
$369$	−6663.35	−0.940055
$370$	4689.51	0.658908
$371$	−5920.22	−0.828471
$372$	3437.41	0.479089
$373$	4579.51	0.635705	0.317853	−	0.948140i	$-0.397038\pi$
$373$	4579.51	0.635705	0.317853	+	0.948140i	$0.397038\pi$
$374$	−2350.27	−0.324945
$375$	−2638.65	−0.363358
$376$	−3961.77	−0.543385
$377$	5706.61	0.779589
$378$	6685.48	0.909692
$379$	−8278.99	−1.12207	−0.561033	−	0.827793i	$-0.689596\pi$
$379$	−8278.99	−1.12207	−0.561033	+	0.827793i	$0.689596\pi$
$380$	−2394.60	−0.323264
$381$	−1526.20	−0.205222
$382$	−150.053	−0.0200978
$383$	−11024.4	−1.47081	−0.735404	−	0.677629i	$-0.763008\pi$
$383$	−11024.4	−1.47081	−0.735404	+	0.677629i	$0.763008\pi$
$384$	−3072.48	−0.408312
$385$	874.037	0.115701
$386$	920.762	0.121413
$387$	−7675.43	−1.00818
$388$	−343.410	−0.0449330
$389$	−7709.12	−1.00480	−0.502401	−	0.864635i	$-0.667550\pi$
$389$	−7709.12	−1.00480	−0.502401	+	0.864635i	$0.667550\pi$
$390$	1593.53	0.206902
$391$	0	0
$392$	−1235.89	−0.159239
$393$	6303.52	0.809086
$394$	−9328.78	−1.19284
$395$	1993.89	0.253984
$396$	−1511.91	−0.191860
$397$	−1800.91	−0.227671	−0.113835	−	0.993500i	$-0.536314\pi$
$397$	−1800.91	−0.227671	−0.113835	+	0.993500i	$0.536314\pi$
$398$	−8762.87	−1.10363
$399$	−4046.62	−0.507730
$400$	8335.23	1.04190
$401$	−635.696	−0.0791650	−0.0395825	−	0.999216i	$-0.512603\pi$
$401$	−635.696	−0.0791650	−0.0395825	+	0.999216i	$0.512603\pi$
$402$	−3870.46	−0.480201
$403$	−9093.64	−1.12404
$404$	−1784.04	−0.219702
$405$	860.373	0.105561
$406$	7970.67	0.974329
$407$	−4228.13	−0.514941
$408$	1155.66	0.140230
$409$	−14420.0	−1.74333	−0.871665	−	0.490102i	$-0.836960\pi$
$409$	−14420.0	−1.74333	−0.871665	+	0.490102i	$0.836960\pi$
$410$	−5233.65	−0.630418
$411$	−5774.32	−0.693008
$412$	−8277.72	−0.989839
$413$	550.110	0.0655428
$414$	0	0
$415$	−1530.22	−0.181002
$416$	−8022.24	−0.945487
$417$	2281.80	0.267962
$418$	5351.31	0.626175
$419$	3719.67	0.433694	0.216847	−	0.976206i	$-0.430423\pi$
$419$	3719.67	0.433694	0.216847	+	0.976206i	$0.430423\pi$
$420$	897.989	0.104327
$421$	−5136.00	−0.594568	−0.297284	−	0.954789i	$-0.596081\pi$
$421$	−5136.00	−0.594568	−0.297284	+	0.954789i	$0.596081\pi$
$422$	12679.5	1.46262
$423$	8299.12	0.953941
$424$	−3849.64	−0.440931
$425$	−4874.72	−0.556373
$426$	2584.06	0.293893
$427$	−585.992	−0.0664125
$428$	−8175.95	−0.923363
$429$	−1436.75	−0.161695
$430$	−6028.57	−0.676102
$431$	−7349.58	−0.821385	−0.410693	−	0.911774i	$-0.634713\pi$
$431$	−7349.58	−0.821385	−0.410693	+	0.911774i	$0.634713\pi$
$432$	9765.83	1.08764
$433$	8531.96	0.946928	0.473464	−	0.880813i	$-0.343003\pi$
$433$	8531.96	0.946928	0.473464	+	0.880813i	$0.343003\pi$
$434$	−12701.5	−1.40482
$435$	−1698.63	−0.187225
$436$	−11153.3	−1.22510
$437$	0	0
$438$	−4526.59	−0.493810
$439$	10738.0	1.16742	0.583710	−	0.811962i	$-0.301600\pi$
$439$	10738.0	1.16742	0.583710	+	0.811962i	$0.301600\pi$
$440$	568.344	0.0615790
$441$	2588.94	0.279553
$442$	6388.02	0.687437
$443$	−6308.26	−0.676557	−0.338278	−	0.941046i	$-0.609845\pi$
$443$	−6308.26	−0.676557	−0.338278	+	0.941046i	$0.609845\pi$
$444$	−4344.00	−0.464318
$445$	−3866.22	−0.411857
$446$	−15156.9	−1.60919
$447$	−3376.92	−0.357322
$448$	−2103.88	−0.221873
$449$	13873.5	1.45820	0.729098	−	0.684409i	$-0.239940\pi$
$449$	13873.5	1.45820	0.729098	+	0.684409i	$0.239940\pi$
$450$	−7772.58	−0.814229
$451$	4718.74	0.492675
$452$	−11926.2	−1.24107
$453$	−248.997	−0.0258254
$454$	−19424.0	−2.00796
$455$	−2375.63	−0.244772
$456$	−2631.32	−0.270226
$457$	11793.4	1.20716	0.603579	−	0.797303i	$-0.293741\pi$
$457$	11793.4	1.20716	0.603579	+	0.797303i	$0.293741\pi$
$458$	14491.5	1.47848
$459$	−5711.38	−0.580793
$460$	0	0
$461$	984.189	0.0994322	0.0497161	−	0.998763i	$-0.484168\pi$
$461$	984.189	0.0994322	0.0497161	+	0.998763i	$0.484168\pi$
$462$	−2006.78	−0.202086
$463$	14604.9	1.46598	0.732989	−	0.680240i	$-0.238125\pi$
$463$	14604.9	1.46598	0.732989	+	0.680240i	$0.238125\pi$
$464$	11643.2	1.16492
$465$	2706.81	0.269947
$466$	−4516.52	−0.448978
$467$	−7928.35	−0.785611	−0.392806	−	0.919622i	$-0.628495\pi$
$467$	−7928.35	−0.785611	−0.392806	+	0.919622i	$0.628495\pi$
$468$	4109.38	0.405889
$469$	5770.05	0.568094
$470$	6518.44	0.639731
$471$	8305.78	0.812549
$472$	357.710	0.0348834
$473$	5435.45	0.528377
$474$	−4577.94	−0.443612
$475$	11099.2	1.07214
$476$	3599.79	0.346630
$477$	8064.23	0.774079
$478$	−4769.41	−0.456376
$479$	−10757.2	−1.02612	−0.513058	−	0.858354i	$-0.671487\pi$
$479$	−10757.2	−1.02612	−0.513058	+	0.858354i	$0.671487\pi$
$480$	2387.90	0.227067
$481$	11492.0	1.08938
$482$	7854.26	0.742224
$483$	0	0
$484$	−6130.73	−0.575763
$485$	−270.421	−0.0253179
$486$	−14353.2	−1.33966
$487$	−6314.51	−0.587552	−0.293776	−	0.955874i	$-0.594912\pi$
$487$	−6314.51	−0.587552	−0.293776	+	0.955874i	$0.594912\pi$
$488$	−381.042	−0.0353463
$489$	−1537.48	−0.142182
$490$	2033.45	0.187474
$491$	7706.00	0.708283	0.354142	−	0.935192i	$-0.384773\pi$
$491$	7706.00	0.708283	0.354142	+	0.935192i	$0.384773\pi$
$492$	4848.05	0.444242
$493$	−6809.31	−0.622061
$494$	−14544.8	−1.32470
$495$	−1190.57	−0.108105
$496$	−18553.7	−1.67961
$497$	−3852.30	−0.347685
$498$	3513.37	0.316140
$499$	−9724.80	−0.872428	−0.436214	−	0.899843i	$-0.643681\pi$
$499$	−9724.80	−0.872428	−0.436214	+	0.899843i	$0.643681\pi$
$500$	−5344.52	−0.478028
$501$	−14.7925	−0.00131912
$502$	2919.72	0.259589
$503$	−2647.59	−0.234693	−0.117346	−	0.993091i	$-0.537439\pi$
$503$	−2647.59	−0.234693	−0.117346	+	0.993091i	$0.537439\pi$
$504$	−2747.04	−0.242783
$505$	−1404.86	−0.123793
$506$	0	0
$507$	−1963.62	−0.172007
$508$	−3091.28	−0.269987
$509$	6869.56	0.598208	0.299104	−	0.954220i	$-0.403312\pi$
$509$	6869.56	0.598208	0.299104	+	0.954220i	$0.403312\pi$
$510$	−1901.45	−0.165094
$511$	6748.21	0.584194
$512$	−10449.7	−0.901987
$513$	13004.2	1.11920
$514$	26539.6	2.27746
$515$	−6518.35	−0.557733
$516$	5584.41	0.476434
$517$	−5877.13	−0.499953
$518$	16051.4	1.36151
$519$	−6957.08	−0.588404
$520$	−1544.76	−0.130273
$521$	10400.1	0.874543	0.437272	−	0.899330i	$-0.355945\pi$
$521$	10400.1	0.874543	0.437272	+	0.899330i	$0.355945\pi$
$522$	−10857.2	−0.910360
$523$	12959.0	1.08348	0.541739	−	0.840547i	$-0.317766\pi$
$523$	12959.0	1.08348	0.541739	+	0.840547i	$0.317766\pi$
$524$	12767.6	1.06442
$525$	−4162.27	−0.346012
$526$	7320.73	0.606842
$527$	10850.8	0.896906
$528$	−2931.40	−0.241615
$529$	0	0
$530$	6333.95	0.519112
$531$	−749.332	−0.0612396
$532$	−8196.33	−0.667962
$533$	−12825.5	−1.04228
$534$	8876.78	0.719355
$535$	−6438.21	−0.520277
$536$	3751.99	0.302353
$537$	7199.61	0.578559
$538$	−8647.78	−0.692997
$539$	−1833.39	−0.146512
$540$	−2885.77	−0.229970
$541$	5526.65	0.439204	0.219602	−	0.975590i	$-0.429524\pi$
$541$	5526.65	0.439204	0.219602	+	0.975590i	$0.429524\pi$
$542$	28404.4	2.25106
$543$	10923.2	0.863277
$544$	9572.40	0.754437
$545$	−8782.73	−0.690295
$546$	5454.41	0.427522
$547$	18131.0	1.41723	0.708616	−	0.705594i	$-0.249320\pi$
$547$	18131.0	1.41723	0.708616	+	0.705594i	$0.249320\pi$
$548$	−11695.7	−0.911711
$549$	798.208	0.0620522
$550$	5504.25	0.426731
$551$	15504.1	1.19872
$552$	0	0
$553$	6824.77	0.524808
$554$	−5215.90	−0.400005
$555$	−3420.72	−0.261624
$556$	4621.72	0.352526
$557$	−5663.69	−0.430841	−0.215420	−	0.976521i	$-0.569112\pi$
$557$	−5663.69	−0.430841	−0.215420	+	0.976521i	$0.569112\pi$
$558$	17301.3	1.31259
$559$	−14773.5	−1.11781
$560$	−4846.99	−0.365755
$561$	1714.38	0.129022
$562$	17542.1	1.31667
$563$	17856.0	1.33666	0.668331	−	0.743864i	$-0.267009\pi$
$563$	17856.0	1.33666	0.668331	+	0.743864i	$0.267009\pi$
$564$	−6038.19	−0.450804
$565$	−9391.38	−0.699289
$566$	−10954.0	−0.813486
$567$	2944.92	0.218122
$568$	−2504.97	−0.185046
$569$	−24468.7	−1.80278	−0.901391	−	0.433007i	$-0.857453\pi$
$569$	−24468.7	−1.80278	−0.901391	+	0.433007i	$0.857453\pi$
$570$	4329.41	0.318139
$571$	6365.27	0.466512	0.233256	−	0.972415i	$-0.425062\pi$
$571$	6365.27	0.466512	0.233256	+	0.972415i	$0.425062\pi$
$572$	−2910.11	−0.212723
$573$	109.455	0.00797999
$574$	−17913.9	−1.30264
$575$	0	0
$576$	2865.80	0.207306
$577$	−15281.7	−1.10257	−0.551286	−	0.834316i	$-0.685863\pi$
$577$	−15281.7	−1.10257	−0.551286	+	0.834316i	$0.685863\pi$
$578$	10369.2	0.746197
$579$	−671.641	−0.0482080
$580$	−3440.52	−0.246310
$581$	−5237.71	−0.374005
$582$	620.882	0.0442206
$583$	−5710.78	−0.405689
$584$	4388.04	0.310922
$585$	3235.96	0.228701
$586$	−7315.91	−0.515730
$587$	10436.6	0.733839	0.366920	−	0.930253i	$-0.380412\pi$
$587$	10436.6	0.733839	0.366920	+	0.930253i	$0.380412\pi$
$588$	−1883.64	−0.132109
$589$	−24706.2	−1.72835
$590$	−588.554	−0.0410684
$591$	6804.79	0.473624
$592$	23447.2	1.62783
$593$	−8293.70	−0.574336	−0.287168	−	0.957880i	$-0.592714\pi$
$593$	−8293.70	−0.574336	−0.287168	+	0.957880i	$0.592714\pi$
$594$	6448.96	0.445461
$595$	2834.68	0.195312
$596$	−6839.86	−0.470087
$597$	6391.99	0.438202
$598$	0	0
$599$	−18225.4	−1.24319	−0.621595	−	0.783339i	$-0.713515\pi$
$599$	−18225.4	−1.24319	−0.621595	+	0.783339i	$0.713515\pi$
$600$	−2706.53	−0.184156
$601$	13078.9	0.887689	0.443844	−	0.896104i	$-0.353614\pi$
$601$	13078.9	0.887689	0.443844	+	0.896104i	$0.353614\pi$
$602$	−20634.8	−1.39703
$603$	−7859.67	−0.530797
$604$	−504.338	−0.0339755
$605$	−4827.68	−0.324419
$606$	3225.53	0.216218
$607$	14543.0	0.972461	0.486230	−	0.873831i	$-0.338372\pi$
$607$	14543.0	0.972461	0.486230	+	0.873831i	$0.338372\pi$
$608$	−21795.3	−1.45381
$609$	−5814.12	−0.386864
$610$	626.943	0.0416134
$611$	15974.0	1.05767
$612$	−4903.44	−0.323872
$613$	12455.1	0.820650	0.410325	−	0.911939i	$-0.365415\pi$
$613$	12455.1	0.820650	0.410325	+	0.911939i	$0.365415\pi$
$614$	−3561.55	−0.234092
$615$	3817.63	0.250312
$616$	1945.35	0.127241
$617$	6465.47	0.421864	0.210932	−	0.977501i	$-0.432350\pi$
$617$	6465.47	0.421864	0.210932	+	0.977501i	$0.432350\pi$
$618$	14966.0	0.974146
$619$	−5203.61	−0.337885	−0.168942	−	0.985626i	$-0.554035\pi$
$619$	−5203.61	−0.337885	−0.168942	+	0.985626i	$0.554035\pi$
$620$	5482.57	0.355138
$621$	0	0
$622$	1364.62	0.0879685
$623$	−13233.4	−0.851022
$624$	7967.54	0.511149
$625$	9147.38	0.585432
$626$	−6218.17	−0.397009
$627$	−3903.46	−0.248627
$628$	16823.2	1.06898
$629$	−13712.7	−0.869254
$630$	4519.80	0.285831
$631$	2632.91	0.166108	0.0830542	−	0.996545i	$-0.473533\pi$
$631$	2632.91	0.166108	0.0830542	+	0.996545i	$0.473533\pi$
$632$	4437.82	0.279315
$633$	−9248.92	−0.580745
$634$	−6065.71	−0.379969
$635$	−2434.25	−0.152127
$636$	−5867.29	−0.365807
$637$	4983.15	0.309952
$638$	7688.69	0.477113
$639$	5247.41	0.324858
$640$	−4900.52	−0.302672
$641$	26639.5	1.64150	0.820748	−	0.571291i	$-0.193557\pi$
$641$	26639.5	1.64150	0.820748	+	0.571291i	$0.193557\pi$
$642$	14782.0	0.908723
$643$	3377.07	0.207121	0.103561	−	0.994623i	$-0.466976\pi$
$643$	3377.07	0.207121	0.103561	+	0.994623i	$0.466976\pi$
$644$	0	0
$645$	4397.48	0.268451
$646$	17355.4	1.05703
$647$	−7954.78	−0.483361	−0.241681	−	0.970356i	$-0.577699\pi$
$647$	−7954.78	−0.483361	−0.241681	+	0.970356i	$0.577699\pi$
$648$	1914.94	0.116089
$649$	530.649	0.0320952
$650$	−14960.5	−0.902769
$651$	9264.98	0.557793
$652$	−3114.12	−0.187053
$653$	−14035.4	−0.841115	−0.420557	−	0.907266i	$-0.638165\pi$
$653$	−14035.4	−0.841115	−0.420557	+	0.907266i	$0.638165\pi$
$654$	20165.0	1.20568
$655$	10054.0	0.599757
$656$	−26167.8	−1.55744
$657$	−9192.07	−0.545840
$658$	22311.6	1.32188
$659$	−16714.4	−0.988011	−0.494005	−	0.869459i	$-0.664468\pi$
$659$	−16714.4	−0.988011	−0.494005	+	0.869459i	$0.664468\pi$
$660$	866.221	0.0510873
$661$	18855.3	1.10951	0.554754	−	0.832014i	$-0.312812\pi$
$661$	18855.3	1.10951	0.554754	+	0.832014i	$0.312812\pi$
$662$	−13220.0	−0.776151
$663$	−4659.68	−0.272952
$664$	−3405.83	−0.199054
$665$	−6454.26	−0.376369
$666$	−21864.4	−1.27212
$667$	0	0
$668$	−29.9617	−0.00173541
$669$	11056.0	0.638940
$670$	−6173.28	−0.355962
$671$	−565.261	−0.0325211
$672$	8173.39	0.469190
$673$	22147.8	1.26855	0.634276	−	0.773106i	$-0.281298\pi$
$673$	22147.8	1.26855	0.634276	+	0.773106i	$0.281298\pi$
$674$	−27413.1	−1.56664
$675$	13375.9	0.762721
$676$	−3977.27	−0.226290
$677$	−3446.04	−0.195631	−0.0978155	−	0.995205i	$-0.531186\pi$
$677$	−3446.04	−0.195631	−0.0978155	+	0.995205i	$0.531186\pi$
$678$	21562.5	1.22139
$679$	−925.607	−0.0523145
$680$	1843.25	0.103949
$681$	14168.7	0.797275
$682$	−12252.1	−0.687916
$683$	9564.98	0.535862	0.267931	−	0.963438i	$-0.413660\pi$
$683$	9564.98	0.535862	0.267931	+	0.963438i	$0.413660\pi$
$684$	11164.6	0.624108
$685$	−9209.90	−0.513711
$686$	25277.8	1.40687
$687$	−10570.7	−0.587041
$688$	−30142.4	−1.67030
$689$	15521.9	0.858253
$690$	0	0
$691$	6743.85	0.371271	0.185636	−	0.982619i	$-0.440566\pi$
$691$	6743.85	0.371271	0.185636	+	0.982619i	$0.440566\pi$
$692$	−14091.4	−0.774095
$693$	−4075.12	−0.223378
$694$	9211.49	0.503838
$695$	3639.41	0.198634
$696$	−3780.65	−0.205898
$697$	15303.8	0.831669
$698$	−42624.2	−2.31139
$699$	3294.53	0.178270
$700$	−8430.58	−0.455208
$701$	−9873.30	−0.531968	−0.265984	−	0.963977i	$-0.585697\pi$
$701$	−9873.30	−0.531968	−0.265984	+	0.963977i	$0.585697\pi$
$702$	−17528.2	−0.942394
$703$	31222.3	1.67507
$704$	−2029.45	−0.108648
$705$	−4754.81	−0.254009
$706$	27370.8	1.45909
$707$	−4808.60	−0.255794
$708$	545.191	0.0289400
$709$	−7772.24	−0.411696	−0.205848	−	0.978584i	$-0.565995\pi$
$709$	−7772.24	−0.411696	−0.205848	+	0.978584i	$0.565995\pi$
$710$	4121.51	0.217856
$711$	−9296.35	−0.490352
$712$	−8605.07	−0.452934
$713$	0	0
$714$	−6508.38	−0.341134
$715$	−2291.58	−0.119861
$716$	14582.6	0.761143
$717$	3479.00	0.181207
$718$	−43275.5	−2.24934
$719$	15754.5	0.817167	0.408584	−	0.912721i	$-0.366023\pi$
$719$	15754.5	0.817167	0.408584	+	0.912721i	$0.366023\pi$
$720$	6602.32	0.341741
$721$	−22311.3	−1.15245
$722$	−14398.4	−0.742180
$723$	−5729.21	−0.294705
$724$	22124.7	1.13571
$725$	15947.2	0.816915
$726$	11084.3	0.566635
$727$	−6008.39	−0.306518	−0.153259	−	0.988186i	$-0.548977\pi$
$727$	−6008.39	−0.306518	−0.153259	+	0.988186i	$0.548977\pi$
$728$	−5287.45	−0.269184
$729$	5017.44	0.254912
$730$	−7219.80	−0.366050
$731$	17628.3	0.891936
$732$	−580.752	−0.0293241
$733$	−32667.1	−1.64609	−0.823047	−	0.567973i	$-0.807728\pi$
$733$	−32667.1	−1.64609	−0.823047	+	0.567973i	$0.807728\pi$
$734$	−6509.37	−0.327337
$735$	−1483.28	−0.0744377
$736$	0	0
$737$	5565.93	0.278187
$738$	24401.4	1.21711
$739$	−29263.2	−1.45665	−0.728325	−	0.685231i	$-0.759701\pi$
$739$	−29263.2	−1.45665	−0.728325	+	0.685231i	$0.759701\pi$
$740$	−6928.58	−0.344188
$741$	10609.6	0.525982
$742$	21680.1	1.07264
$743$	11886.5	0.586909	0.293454	−	0.955973i	$-0.405195\pi$
$743$	11886.5	0.586909	0.293454	+	0.955973i	$0.405195\pi$
$744$	6024.57	0.296870
$745$	−5386.10	−0.264874
$746$	−16770.3	−0.823064
$747$	7134.54	0.349450
$748$	3472.44	0.169739
$749$	−22037.0	−1.07505
$750$	9662.83	0.470449
$751$	−25780.5	−1.25265	−0.626327	−	0.779561i	$-0.715442\pi$
$751$	−25780.5	−1.25265	−0.626327	+	0.779561i	$0.715442\pi$
$752$	32591.7	1.58045
$753$	−2129.76	−0.103072
$754$	−20897.8	−1.00935
$755$	−397.145	−0.0191438
$756$	−9877.54	−0.475189
$757$	13359.3	0.641416	0.320708	−	0.947178i	$-0.396079\pi$
$757$	13359.3	0.641416	0.320708	+	0.947178i	$0.396079\pi$
$758$	30318.0	1.45277
$759$	0	0
$760$	−4196.89	−0.200312
$761$	96.8213	0.00461205	0.00230603	−	0.999997i	$-0.499266\pi$
$761$	96.8213	0.00461205	0.00230603	+	0.999997i	$0.499266\pi$
$762$	5589.01	0.265707
$763$	−30061.9	−1.42636
$764$	221.698	0.0104984
$765$	−3861.25	−0.182489
$766$	40371.7	1.90429
$767$	−1442.30	−0.0678989
$768$	14334.5	0.673505
$769$	−1788.06	−0.0838477	−0.0419239	−	0.999121i	$-0.513349\pi$
$769$	−1788.06	−0.0838477	−0.0419239	+	0.999121i	$0.513349\pi$
$770$	−3200.76	−0.149802
$771$	−19359.1	−0.904281
$772$	−1360.39	−0.0634217
$773$	20117.0	0.936037	0.468018	−	0.883719i	$-0.344968\pi$
$773$	20117.0	0.936037	0.468018	+	0.883719i	$0.344968\pi$
$774$	28107.7	1.30531
$775$	−25412.3	−1.17785
$776$	−601.878	−0.0278430
$777$	−11708.6	−0.540595
$778$	28231.1	1.30094
$779$	−34845.1	−1.60264
$780$	−2354.38	−0.108078
$781$	−3716.02	−0.170256
$782$	0	0
$783$	18684.2	0.852771
$784$	10167.1	0.463152
$785$	13247.5	0.602324
$786$	−23083.7	−1.04754
$787$	−17474.8	−0.791501	−0.395750	−	0.918358i	$-0.629515\pi$
$787$	−17474.8	−0.791501	−0.395750	+	0.918358i	$0.629515\pi$
$788$	13782.9	0.623092
$789$	−5340.03	−0.240951
$790$	−7301.70	−0.328839
$791$	−32145.2	−1.44494
$792$	−2649.86	−0.118887
$793$	1536.38	0.0687999
$794$	6595.01	0.294771
$795$	−4620.24	−0.206117
$796$	12946.8	0.576492
$797$	−9096.85	−0.404300	−0.202150	−	0.979355i	$-0.564793\pi$
$797$	−9096.85	−0.404300	−0.202150	+	0.979355i	$0.564793\pi$
$798$	14818.9	0.657372
$799$	−19060.7	−0.843954
$800$	−22418.3	−0.990756
$801$	18025.9	0.795149
$802$	2327.94	0.102497
$803$	6509.48	0.286070
$804$	5718.46	0.250839
$805$	0	0
$806$	33301.3	1.45532
$807$	6308.04	0.275159
$808$	−3126.80	−0.136139
$809$	32640.3	1.41851	0.709253	−	0.704954i	$-0.249032\pi$
$809$	32640.3	1.41851	0.709253	+	0.704954i	$0.249032\pi$
$810$	−3150.72	−0.136673
$811$	34031.0	1.47348	0.736738	−	0.676178i	$-0.236365\pi$
$811$	34031.0	1.47348	0.736738	+	0.676178i	$0.236365\pi$
$812$	−11776.4	−0.508952
$813$	−20719.3	−0.893798
$814$	15483.6	0.666707
$815$	−2452.24	−0.105397
$816$	−9507.13	−0.407863
$817$	−40137.7	−1.71878
$818$	52806.5	2.25714
$819$	11076.2	0.472567
$820$	7732.52	0.329306
$821$	30188.5	1.28330	0.641648	−	0.767000i	$-0.278251\pi$
$821$	30188.5	1.28330	0.641648	+	0.767000i	$0.278251\pi$
$822$	21145.8	0.897256
$823$	14632.0	0.619733	0.309867	−	0.950780i	$-0.399716\pi$
$823$	14632.0	0.619733	0.309867	+	0.950780i	$0.399716\pi$
$824$	−14507.9	−0.613359
$825$	−4015.02	−0.169437
$826$	−2014.53	−0.0848599
$827$	−16334.2	−0.686816	−0.343408	−	0.939186i	$-0.611581\pi$
$827$	−16334.2	−0.686816	−0.343408	+	0.939186i	$0.611581\pi$
$828$	0	0
$829$	25548.5	1.07037	0.535185	−	0.844735i	$-0.320242\pi$
$829$	25548.5	1.07037	0.535185	+	0.844735i	$0.320242\pi$
$830$	5603.74	0.234348
$831$	3804.69	0.158825
$832$	5516.05	0.229849
$833$	−5946.06	−0.247321
$834$	−8356.02	−0.346937
$835$	−23.5936	−0.000977832 0
$836$	−7906.36	−0.327090
$837$	−29773.9	−1.22955
$838$	−13621.6	−0.561516
$839$	−16241.4	−0.668314	−0.334157	−	0.942517i	$-0.608452\pi$
$839$	−16241.4	−0.668314	−0.334157	+	0.942517i	$0.608452\pi$
$840$	1573.86	0.0646469
$841$	−2112.98	−0.0866365
$842$	18808.2	0.769803
$843$	−12795.9	−0.522793
$844$	−18733.5	−0.764019
$845$	−3131.93	−0.127505
$846$	−30391.7	−1.23509
$847$	−16524.4	−0.670348
$848$	31669.3	1.28246
$849$	7990.32	0.323000
$850$	17851.4	0.720350
$851$	0	0
$852$	−3817.86	−0.153518
$853$	21888.3	0.878594	0.439297	−	0.898342i	$-0.355228\pi$
$853$	21888.3	0.878594	0.439297	+	0.898342i	$0.355228\pi$
$854$	2145.92	0.0859860
$855$	8791.65	0.351659
$856$	−14329.6	−0.572167
$857$	−22310.5	−0.889280	−0.444640	−	0.895709i	$-0.646668\pi$
$857$	−22310.5	−0.889280	−0.444640	+	0.895709i	$0.646668\pi$
$858$	5261.44	0.209351
$859$	36284.0	1.44120	0.720602	−	0.693349i	$-0.243866\pi$
$859$	36284.0	1.44120	0.720602	+	0.693349i	$0.243866\pi$
$860$	8906.99	0.353170
$861$	13067.1	0.517221
$862$	26914.5	1.06347
$863$	15966.6	0.629792	0.314896	−	0.949126i	$-0.398030\pi$
$863$	15966.6	0.629792	0.314896	+	0.949126i	$0.398030\pi$
$864$	−26266.0	−1.03424
$865$	−11096.4	−0.436171
$866$	−31244.4	−1.22601
$867$	−7563.71	−0.296283
$868$	18766.0	0.733823
$869$	6583.33	0.256990
$870$	6220.43	0.242405
$871$	−15128.2	−0.588516
$872$	−19547.8	−0.759142
$873$	1260.81	0.0488798
$874$	0	0
$875$	−14405.3	−0.556557
$876$	6687.87	0.257948
$877$	−24553.1	−0.945382	−0.472691	−	0.881228i	$-0.656717\pi$
$877$	−24553.1	−0.945382	−0.472691	+	0.881228i	$0.656717\pi$
$878$	−39323.0	−1.51149
$879$	5336.52	0.204774
$880$	−4675.51	−0.179104
$881$	4322.25	0.165290	0.0826450	−	0.996579i	$-0.473663\pi$
$881$	4322.25	0.165290	0.0826450	+	0.996579i	$0.473663\pi$
$882$	−9480.81	−0.361945
$883$	−23333.7	−0.889289	−0.444644	−	0.895707i	$-0.646670\pi$
$883$	−23333.7	−0.889289	−0.444644	+	0.895707i	$0.646670\pi$
$884$	−9438.06	−0.359091
$885$	429.315	0.0163065
$886$	23101.1	0.875956
$887$	7978.16	0.302007	0.151004	−	0.988533i	$-0.451749\pi$
$887$	7978.16	0.302007	0.151004	+	0.988533i	$0.451749\pi$
$888$	−7613.52	−0.287717
$889$	−8332.06	−0.314340
$890$	14158.2	0.533242
$891$	2840.74	0.106811
$892$	22393.7	0.840579
$893$	43399.2	1.62631
$894$	12366.4	0.462634
$895$	11483.2	0.428872
$896$	−16773.7	−0.625413
$897$	0	0
$898$	−50805.3	−1.88797
$899$	−35497.5	−1.31692
$900$	11483.7	0.425322
$901$	−18521.2	−0.684829
$902$	−17280.2	−0.637880
$903$	15051.9	0.554701
$904$	−20902.5	−0.769033
$905$	17422.2	0.639927
$906$	911.838	0.0334369
$907$	45500.6	1.66574	0.832868	−	0.553472i	$-0.186698\pi$
$907$	45500.6	1.66574	0.832868	+	0.553472i	$0.186698\pi$
$908$	28698.3	1.04888
$909$	6550.03	0.239000
$910$	8699.64	0.316912
$911$	−54365.5	−1.97718	−0.988590	−	0.150634i	$-0.951868\pi$
$911$	−54365.5	−1.97718	−0.988590	+	0.150634i	$0.951868\pi$
$912$	21646.7	0.785959
$913$	−5052.42	−0.183144
$914$	−43187.9	−1.56294
$915$	−457.317	−0.0165229
$916$	−21410.7	−0.772302
$917$	34413.1	1.23928
$918$	20915.3	0.751968
$919$	−3342.64	−0.119982	−0.0599910	−	0.998199i	$-0.519107\pi$
$919$	−3342.64	−0.119982	−0.0599910	+	0.998199i	$0.519107\pi$
$920$	0	0
$921$	2597.93	0.0929477
$922$	−3604.14	−0.128737
$923$	10100.1	0.360184
$924$	2964.94	0.105562
$925$	32114.7	1.14154
$926$	−53483.8	−1.89804
$927$	30391.2	1.07678
$928$	−31315.2	−1.10773
$929$	19662.1	0.694393	0.347197	−	0.937792i	$-0.387134\pi$
$929$	19662.1	0.694393	0.347197	+	0.937792i	$0.387134\pi$
$930$	−9912.44	−0.349507
$931$	13538.5	0.476593
$932$	6672.99	0.234529
$933$	−995.411	−0.0349285
$934$	29033.9	1.01715
$935$	2734.39	0.0956409
$936$	7202.30	0.251511
$937$	12008.4	0.418674	0.209337	−	0.977844i	$-0.432869\pi$
$937$	12008.4	0.418674	0.209337	+	0.977844i	$0.432869\pi$
$938$	−21130.2	−0.735527
$939$	4535.78	0.157635
$940$	−9630.76	−0.334171
$941$	904.922	0.0313492	0.0156746	−	0.999877i	$-0.495010\pi$
$941$	904.922	0.0313492	0.0156746	+	0.999877i	$0.495010\pi$
$942$	−30416.1	−1.05203
$943$	0	0
$944$	−2942.72	−0.101459
$945$	−7778.14	−0.267749
$946$	−19904.8	−0.684104
$947$	35613.4	1.22205	0.611025	−	0.791612i	$-0.290758\pi$
$947$	35613.4	1.22205	0.611025	+	0.791612i	$0.290758\pi$
$948$	6763.74	0.231726
$949$	−17692.7	−0.605195
$950$	−40645.7	−1.38813
$951$	4424.57	0.150869
$952$	6309.16	0.214791
$953$	11832.5	0.402194	0.201097	−	0.979571i	$-0.435549\pi$
$953$	11832.5	0.402194	0.201097	+	0.979571i	$0.435549\pi$
$954$	−29531.5	−1.00222
$955$	174.577	0.00591538
$956$	7046.63	0.238394
$957$	−5608.44	−0.189441
$958$	39393.3	1.32854
$959$	−31524.0	−1.06148
$960$	−1641.90	−0.0552002
$961$	26775.3	0.898770
$962$	−42084.3	−1.41045
$963$	30017.6	1.00447
$964$	−11604.4	−0.387710
$965$	−1071.25	−0.0357355
$966$	0	0
$967$	−28058.1	−0.933078	−0.466539	−	0.884501i	$-0.654499\pi$
$967$	−28058.1	−0.933078	−0.466539	+	0.884501i	$0.654499\pi$
$968$	−10745.0	−0.356775
$969$	−12659.7	−0.419699
$970$	990.291	0.0327797
$971$	3658.17	0.120902	0.0604512	−	0.998171i	$-0.480746\pi$
$971$	3658.17	0.120902	0.0604512	+	0.998171i	$0.480746\pi$
$972$	21206.3	0.699787
$973$	12457.1	0.410438
$974$	23124.0	0.760719
$975$	10912.8	0.358451
$976$	3134.67	0.102806
$977$	−15310.6	−0.501360	−0.250680	−	0.968070i	$-0.580654\pi$
$977$	−15310.6	−0.501360	−0.250680	+	0.968070i	$0.580654\pi$
$978$	5630.30	0.184087
$979$	−12765.3	−0.416732
$980$	−3004.35	−0.0979291
$981$	40948.8	1.33272
$982$	−28219.7	−0.917033
$983$	58178.9	1.88771	0.943856	−	0.330358i	$-0.107170\pi$
$983$	58178.9	1.88771	0.943856	+	0.330358i	$0.107170\pi$
$984$	8496.94	0.275277
$985$	10853.5	0.351086
$986$	24936.0	0.805398
$987$	−16275.0	−0.524861
$988$	21489.5	0.691974
$989$	0	0
$990$	4359.91	0.139967
$991$	−47516.8	−1.52313	−0.761564	−	0.648090i	$-0.775568\pi$
$991$	−47516.8	−1.52313	−0.761564	+	0.648090i	$0.775568\pi$
$992$	49901.7	1.59716
$993$	9643.23	0.308176
$994$	14107.3	0.450157
$995$	10195.1	0.324829
$996$	−5190.88	−0.165140
$997$	45782.9	1.45432	0.727161	−	0.686467i	$-0.240839\pi$
$997$	45782.9	1.45432	0.727161	+	0.686467i	$0.240839\pi$
$998$	35612.6	1.12956
$999$	37626.6	1.19164

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.6		25
23.15	odd	22		23.4.c.a.18.5	yes	50
23.20	odd	22		23.4.c.a.9.5	✓	50
23.22	odd	2		529.4.a.n.1.6		25
69.20	even	22		207.4.i.a.55.1		50
69.38	even	22		207.4.i.a.64.1		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.9.5	✓	50	23.20	odd	22
23.4.c.a.18.5	yes	50	23.15	odd	22
207.4.i.a.55.1		50	69.20	even	22
207.4.i.a.64.1		50	69.38	even	22
529.4.a.m.1.6		25	1.1	even	1	trivial
529.4.a.n.1.6		25	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q-3.66204 q^{2} +2.67124 q^{3} +5.41053 q^{4} +4.26056 q^{5} -9.78218 q^{6} +14.5832 q^{7} +9.48276 q^{8} -19.8645 q^{9} -15.6023 q^{10} +14.0673 q^{11} +14.4528 q^{12} -38.2348 q^{13} -53.4043 q^{14} +11.3810 q^{15} -78.0104 q^{16} +45.6230 q^{17} +72.7445 q^{18} -103.879 q^{19} +23.0518 q^{20} +38.9552 q^{21} -51.5150 q^{22} +25.3307 q^{24} -106.848 q^{25} +140.017 q^{26} -125.186 q^{27} +78.9028 q^{28} -149.252 q^{29} -41.6775 q^{30} +237.837 q^{31} +209.815 q^{32} +37.5771 q^{33} -167.073 q^{34} +62.1326 q^{35} -107.477 q^{36} -300.565 q^{37} +380.408 q^{38} -102.134 q^{39} +40.4018 q^{40} +335.440 q^{41} -142.655 q^{42} +386.390 q^{43} +76.1114 q^{44} -84.6338 q^{45} -417.787 q^{47} -208.384 q^{48} -130.330 q^{49} +391.280 q^{50} +121.870 q^{51} -206.870 q^{52} -405.962 q^{53} +458.437 q^{54} +59.9345 q^{55} +138.289 q^{56} -277.485 q^{57} +546.565 q^{58} +37.7222 q^{59} +61.5770 q^{60} -40.1827 q^{61} -870.967 q^{62} -289.688 q^{63} -144.268 q^{64} -162.902 q^{65} -137.609 q^{66} +395.664 q^{67} +246.845 q^{68} -227.532 q^{70} -264.160 q^{71} -188.370 q^{72} +462.739 q^{73} +1100.68 q^{74} -285.415 q^{75} -562.039 q^{76} +205.146 q^{77} +374.020 q^{78} +467.988 q^{79} -332.368 q^{80} +201.939 q^{81} -1228.40 q^{82} -359.161 q^{83} +210.768 q^{84} +194.380 q^{85} -1414.97 q^{86} -398.686 q^{87} +133.397 q^{88} -907.444 q^{89} +309.932 q^{90} -557.586 q^{91} +635.318 q^{93} +1529.95 q^{94} -442.581 q^{95} +560.466 q^{96} -63.4707 q^{97} +477.274 q^{98} -279.440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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