LMFDB - Embedded newform 136.4.c.b.69.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(69,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("136.69");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	136.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.02425976078$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			69.15
Character	$\chi$	$=$	136.69
Dual form			136.4.c.b.69.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.804094 - 2.71172i) q^{2} +0.717271i q^{3} +(-6.70687 - 4.36096i) q^{4} +13.2408i q^{5} +(1.94504 + 0.576753i) q^{6} -11.9399 q^{7} +(-17.2187 + 14.6805i) q^{8} +26.4855 q^{9} +O(q^{10})$	\(q+(0.804094 - 2.71172i) q^{2} +0.717271i q^{3} +(-6.70687 - 4.36096i) q^{4} +13.2408i q^{5} +(1.94504 + 0.576753i) q^{6} -11.9399 q^{7} +(-17.2187 + 14.6805i) q^{8} +26.4855 q^{9} +(35.9053 + 10.6468i) q^{10} +20.9559i q^{11} +(3.12799 - 4.81064i) q^{12} +68.3108i q^{13} +(-9.60077 + 32.3776i) q^{14} -9.49723 q^{15} +(25.9641 + 58.4967i) q^{16} +17.0000 q^{17} +(21.2969 - 71.8214i) q^{18} +20.2691i q^{19} +(57.7425 - 88.8042i) q^{20} -8.56411i q^{21} +(56.8266 + 16.8505i) q^{22} -13.6980 q^{23} +(-10.5299 - 12.3504i) q^{24} -50.3184 q^{25} +(185.240 + 54.9283i) q^{26} +38.3636i q^{27} +(80.0790 + 52.0692i) q^{28} -29.1311i q^{29} +(-7.63667 + 25.7538i) q^{30} -151.675 q^{31} +(179.504 - 23.3705i) q^{32} -15.0311 q^{33} +(13.6696 - 46.0993i) q^{34} -158.093i q^{35} +(-177.635 - 115.502i) q^{36} +61.2676i q^{37} +(54.9642 + 16.2983i) q^{38} -48.9974 q^{39} +(-194.382 - 227.989i) q^{40} -145.472 q^{41} +(-23.2235 - 6.88635i) q^{42} +53.1686i q^{43} +(91.3878 - 140.548i) q^{44} +350.689i q^{45} +(-11.0145 + 37.1452i) q^{46} +290.877 q^{47} +(-41.9580 + 18.6233i) q^{48} -200.440 q^{49} +(-40.4607 + 136.449i) q^{50} +12.1936i q^{51} +(297.901 - 458.152i) q^{52} +510.790i q^{53} +(104.031 + 30.8479i) q^{54} -277.473 q^{55} +(205.588 - 175.283i) q^{56} -14.5384 q^{57} +(-78.9953 - 23.4241i) q^{58} -536.284i q^{59} +(63.6966 + 41.4170i) q^{60} +437.639i q^{61} +(-121.961 + 411.300i) q^{62} -316.233 q^{63} +(80.9642 - 505.558i) q^{64} -904.489 q^{65} +(-12.0864 + 40.7600i) q^{66} -723.449i q^{67} +(-114.017 - 74.1363i) q^{68} -9.82519i q^{69} +(-428.704 - 127.122i) q^{70} -1013.19 q^{71} +(-456.045 + 388.821i) q^{72} +366.792 q^{73} +(166.141 + 49.2649i) q^{74} -36.0919i q^{75} +(88.3928 - 135.942i) q^{76} -250.210i q^{77} +(-39.3985 + 132.867i) q^{78} +230.779 q^{79} +(-774.543 + 343.785i) q^{80} +687.592 q^{81} +(-116.973 + 394.479i) q^{82} +155.610i q^{83} +(-37.3477 + 57.4383i) q^{84} +225.093i q^{85} +(144.179 + 42.7526i) q^{86} +20.8949 q^{87} +(-307.644 - 360.832i) q^{88} +1057.96 q^{89} +(950.971 + 281.987i) q^{90} -815.621i q^{91} +(91.8707 + 59.7365i) q^{92} -108.792i q^{93} +(233.892 - 788.776i) q^{94} -268.379 q^{95} +(16.7630 + 128.753i) q^{96} +1486.92 q^{97} +(-161.173 + 543.537i) q^{98} +555.028i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9}+O(q^{10}) $ 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9	$ 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9} - 16 q^{10} - 18 q^{12} + 26 q^{14} - 180 q^{15} - 103 q^{16} + 408 q^{17} - 5 q^{18} - 24 q^{20} + 172 q^{22} + 624 q^{23} - 310 q^{24} - 600 q^{25} - 180 q^{26} - 132 q^{28} - 80 q^{30} - 744 q^{31} - 39 q^{32} - 280 q^{33} + 17 q^{34} + 791 q^{36} - 162 q^{38} + 1236 q^{39} - 1396 q^{40} + 1132 q^{42} + 886 q^{44} - 1246 q^{46} - 956 q^{47} - 2226 q^{48} + 1688 q^{49} + 2505 q^{50} + 2544 q^{52} - 3264 q^{54} + 1684 q^{55} - 1100 q^{56} - 168 q^{57} + 2800 q^{58} + 2520 q^{60} - 1946 q^{62} - 2520 q^{63} - 2143 q^{64} - 72 q^{65} + 3660 q^{66} + 85 q^{68} - 5084 q^{70} + 1532 q^{71} - 2277 q^{72} + 216 q^{73} + 2188 q^{74} + 2094 q^{76} - 4748 q^{78} - 3176 q^{79} + 116 q^{80} + 2040 q^{81} + 3198 q^{82} + 5916 q^{84} - 2066 q^{86} - 236 q^{87} - 3598 q^{88} - 424 q^{89} + 2180 q^{90} + 1940 q^{92} - 2156 q^{94} - 1248 q^{95} - 4674 q^{96} - 1304 q^{97} + 3705 q^{98}+O(q^{100}) $ 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9 - 16 * q^10 - 18 * q^12 + 26 * q^14 - 180 * q^15 - 103 * q^16 + 408 * q^17 - 5 * q^18 - 24 * q^20 + 172 * q^22 + 624 * q^23 - 310 * q^24 - 600 * q^25 - 180 * q^26 - 132 * q^28 - 80 * q^30 - 744 * q^31 - 39 * q^32 - 280 * q^33 + 17 * q^34 + 791 * q^36 - 162 * q^38 + 1236 * q^39 - 1396 * q^40 + 1132 * q^42 + 886 * q^44 - 1246 * q^46 - 956 * q^47 - 2226 * q^48 + 1688 * q^49 + 2505 * q^50 + 2544 * q^52 - 3264 * q^54 + 1684 * q^55 - 1100 * q^56 - 168 * q^57 + 2800 * q^58 + 2520 * q^60 - 1946 * q^62 - 2520 * q^63 - 2143 * q^64 - 72 * q^65 + 3660 * q^66 + 85 * q^68 - 5084 * q^70 + 1532 * q^71 - 2277 * q^72 + 216 * q^73 + 2188 * q^74 + 2094 * q^76 - 4748 * q^78 - 3176 * q^79 + 116 * q^80 + 2040 * q^81 + 3198 * q^82 + 5916 * q^84 - 2066 * q^86 - 236 * q^87 - 3598 * q^88 - 424 * q^89 + 2180 * q^90 + 1940 * q^92 - 2156 * q^94 - 1248 * q^95 - 4674 * q^96 - 1304 * q^97 + 3705 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	0.804094	−	2.71172i	0.284290	−	0.958738i
$2$	0.804094	−	2.71172i	0.284290	−	0.958738i
$3$			0.717271i			0.138039i	0.997615	+	0.0690194i	$0.0219870\pi$
$3$			0.717271i			0.138039i	−0.997615	+	0.0690194i	$0.978013\pi$
$4$	−6.70687	−	4.36096i	−0.838358	−	0.545120i
$5$			13.2408i			1.18429i	0.805831	+	0.592146i	$0.201719\pi$
$5$			13.2408i			1.18429i	−0.805831	+	0.592146i	$0.798281\pi$
$6$	1.94504	+	0.576753i	0.132343	+	0.0392431i
$7$	−11.9399			−0.644692			−0.322346	−	0.946622i	$-0.604471\pi$
$7$	−11.9399			−0.644692			−0.322346	+	0.946622i	$0.604471\pi$
$8$	−17.2187	+	14.6805i	−0.760964	+	0.648794i
$9$	26.4855			0.980945
$10$	35.9053	+	10.6468i	1.13543	+	0.336683i
$11$			20.9559i			0.574404i	0.957870	+	0.287202i	$0.0927251\pi$
$11$			20.9559i			0.574404i	−0.957870	+	0.287202i	$0.907275\pi$
$12$	3.12799	−	4.81064i	0.0752477	−	0.115726i
$13$			68.3108i			1.45739i	0.684841	+	0.728693i	$0.259872\pi$
$13$			68.3108i			1.45739i	−0.684841	+	0.728693i	$0.740128\pi$
$14$	−9.60077	+	32.3776i	−0.183280	+	0.618090i
$15$	−9.49723			−0.163478
$16$	25.9641	+	58.4967i	0.405689	+	0.914011i
$17$	17.0000			0.242536
$17$	17.0000			0.242536
$18$	21.2969	−	71.8214i	0.278873	−	0.940470i
$19$			20.2691i			0.244740i	0.992485	+	0.122370i	$0.0390494\pi$
$19$			20.2691i			0.244740i	−0.992485	+	0.122370i	$0.960951\pi$
$20$	57.7425	−	88.8042i	0.645581	−	0.992861i
$21$		−	8.56411i		−	0.0889925i
$22$	56.8266	+	16.8505i	0.550703	+	0.163297i
$23$	−13.6980			−0.124184			−0.0620920	−	0.998070i	$-0.519777\pi$
$23$	−13.6980			−0.124184			−0.0620920	+	0.998070i	$0.519777\pi$
$24$	−10.5299	−	12.3504i	−0.0895587	−	0.105043i
$25$	−50.3184			−0.402547
$26$	185.240	+	54.9283i	1.39725	+	0.414321i
$27$			38.3636i			0.273447i
$28$	80.0790	+	52.0692i	0.540482	+	0.351434i
$29$		−	29.1311i		−	0.186535i	−0.995641	−	0.0932673i	$-0.970269\pi$
$29$		−	29.1311i		−	0.186535i	0.995641	−	0.0932673i	$-0.0297311\pi$
$30$	−7.63667	+	25.7538i	−0.0464753	+	0.156733i
$31$	−151.675			−0.878761			−0.439381	−	0.898301i	$-0.644802\pi$
$31$	−151.675			−0.878761			−0.439381	+	0.898301i	$0.644802\pi$
$32$	179.504	−	23.3705i	0.991631	−	0.129105i
$33$	−15.0311			−0.0792900
$34$	13.6696	−	46.0993i	0.0689505	−	0.232528i
$35$		−	158.093i		−	0.763503i
$36$	−177.635	−	115.502i	−0.822383	−	0.534733i
$37$			61.2676i			0.272225i	0.990693	+	0.136113i	$0.0434609\pi$
$37$			61.2676i			0.272225i	−0.990693	+	0.136113i	$0.956539\pi$
$38$	54.9642	+	16.2983i	0.234641	+	0.0695771i
$39$	−48.9974			−0.201176
$40$	−194.382	−	227.989i	−0.768361	−	0.901204i
$41$	−145.472			−0.554118			−0.277059	−	0.960853i	$-0.589360\pi$
$41$	−145.472			−0.554118			−0.277059	+	0.960853i	$0.589360\pi$
$42$	−23.2235	−	6.88635i	−0.0853205	−	0.0252997i
$43$			53.1686i			0.188561i	0.995546	+	0.0942807i	$0.0300551\pi$
$43$			53.1686i			0.188561i	−0.995546	+	0.0942807i	$0.969945\pi$
$44$	91.3878	−	140.548i	0.313119	−	0.481556i
$45$			350.689i			1.16173i
$46$	−11.0145	+	37.1452i	−0.0353043	+	0.119060i
$47$	290.877			0.902739			0.451369	−	0.892337i	$-0.350936\pi$
$47$	290.877			0.902739			0.451369	+	0.892337i	$0.350936\pi$
$48$	−41.9580	+	18.6233i	−0.126169	+	0.0560008i
$49$	−200.440			−0.584373
$50$	−40.4607	+	136.449i	−0.114440	+	0.385937i
$51$			12.1936i			0.0334793i
$52$	297.901	−	458.152i	0.794450	−	1.22181i
$53$			510.790i			1.32382i	0.749584	+	0.661910i	$0.230254\pi$
$53$			510.790i			1.32382i	−0.749584	+	0.661910i	$0.769746\pi$
$54$	104.031	+	30.8479i	0.262164	+	0.0777384i
$55$	−277.473			−0.680262
$56$	205.588	−	175.283i	0.490587	−	0.418272i
$57$	−14.5384			−0.0337836
$58$	−78.9953	−	23.4241i	−0.178838	−	0.0530300i
$59$		−	536.284i		−	1.18336i	−0.806173	−	0.591680i	$-0.798465\pi$
$59$		−	536.284i		−	1.18336i	0.806173	−	0.591680i	$-0.201535\pi$
$60$	63.6966	+	41.4170i	0.137053	+	0.0891152i
$61$			437.639i			0.918589i	0.888284	+	0.459295i	$0.151898\pi$
$61$			437.639i			0.918589i	−0.888284	+	0.459295i	$0.848102\pi$
$62$	−121.961	+	411.300i	−0.249823	+	0.842502i
$63$	−316.233			−0.632407
$64$	80.9642	−	505.558i	0.158133	−	0.987418i
$65$	−904.489			−1.72597
$66$	−12.0864	+	40.7600i	−0.0225414	+	0.0760184i
$67$		−	723.449i		−	1.31915i	−0.751637	−	0.659577i	$-0.770735\pi$
$67$		−	723.449i		−	1.31915i	0.751637	−	0.659577i	$-0.229265\pi$
$68$	−114.017	−	74.1363i	−0.203332	−	0.132211i
$69$		−	9.82519i		−	0.0171422i
$70$	−428.704	−	127.122i	−0.732000	−	0.217056i
$71$	−1013.19			−1.69358			−0.846788	−	0.531930i	$-0.821467\pi$
$71$	−1013.19			−1.69358			−0.846788	+	0.531930i	$0.821467\pi$
$72$	−456.045	+	388.821i	−0.746464	+	0.636431i
$73$	366.792			0.588079			0.294039	−	0.955793i	$-0.405000\pi$
$73$	366.792			0.588079			0.294039	+	0.955793i	$0.405000\pi$
$74$	166.141	+	49.2649i	0.260993	+	0.0773910i
$75$		−	36.0919i		−	0.0555671i
$76$	88.3928	−	135.942i	0.133413	−	0.205180i
$77$		−	250.210i		−	0.370313i
$78$	−39.3985	+	132.867i	−0.0571923	+	0.192875i
$79$	230.779			0.328667			0.164333	−	0.986405i	$-0.447453\pi$
$79$	230.779			0.328667			0.164333	+	0.986405i	$0.447453\pi$
$80$	−774.543	+	343.785i	−1.08246	+	0.480454i
$81$	687.592			0.943199
$82$	−116.973	+	394.479i	−0.157530	+	0.531255i
$83$			155.610i			0.205788i	0.994692	+	0.102894i	$0.0328103\pi$
$83$			155.610i			0.205788i	−0.994692	+	0.102894i	$0.967190\pi$
$84$	−37.3477	+	57.4383i	−0.0485116	+	0.0746076i
$85$			225.093i			0.287233i
$86$	144.179	+	42.7526i	0.180781	+	0.0536062i
$87$	20.8949			0.0257490
$88$	−307.644	−	360.832i	−0.372670	−	0.437101i
$89$	1057.96			1.26004			0.630019	−	0.776579i	$-0.283047\pi$
$89$	1057.96			1.26004			0.630019	+	0.776579i	$0.283047\pi$
$90$	950.971	+	281.987i	1.11379	+	0.330267i
$91$		−	815.621i		−	0.939564i
$92$	91.8707	+	59.7365i	0.104111	+	0.0676952i
$93$		−	108.792i		−	0.121303i
$94$	233.892	−	788.776i	0.256640	−	0.865490i
$95$	−268.379			−0.289843
$96$	16.7630	+	128.753i	0.0178215	+	0.136884i
$97$	1486.92			1.55643			0.778215	−	0.627998i	$-0.216125\pi$
$97$	1486.92			1.55643			0.778215	+	0.627998i	$0.216125\pi$
$98$	−161.173	+	543.537i	−0.166131	+	0.560261i
$99$			555.028i			0.563459i
$100$	337.479	+	219.436i	0.337479	+	0.219436i
$101$		−	1218.74i		−	1.20068i	−0.799744	−	0.600341i	$-0.795032\pi$
$101$		−	1218.74i		−	1.20068i	0.799744	−	0.600341i	$-0.204968\pi$
$102$	33.0657	+	9.80480i	0.0320979	+	0.00951785i
$103$	1488.94			1.42437			0.712184	−	0.701993i	$-0.247706\pi$
$103$	1488.94			1.42437			0.712184	+	0.701993i	$0.247706\pi$
$104$	−1002.84	−	1176.22i	−0.945543	−	1.10902i
$105$	113.396			0.105393
$106$	1385.12	+	410.723i	1.26920	+	0.376349i
$107$		−	1301.49i		−	1.17588i	−0.808903	−	0.587942i	$-0.799938\pi$
$107$		−	1301.49i		−	1.17588i	0.808903	−	0.587942i	$-0.200062\pi$
$108$	167.302	−	257.299i	0.149062	−	0.229247i
$109$			761.097i			0.668806i	0.942430	+	0.334403i	$0.108535\pi$
$109$			761.097i			0.668806i	−0.942430	+	0.334403i	$0.891465\pi$
$110$	−223.114	+	752.428i	−0.193392	+	0.652193i
$111$	−43.9455			−0.0375777
$112$	−310.007	−	698.442i	−0.261544	−	0.589255i
$113$	−710.968			−0.591879			−0.295939	−	0.955207i	$-0.595633\pi$
$113$	−710.968			−0.591879			−0.295939	+	0.955207i	$0.595633\pi$
$114$	−11.6903	+	39.4242i	−0.00960434	+	0.0323896i
$115$		−	181.372i		−	0.147070i
$116$	−127.039	+	195.378i	−0.101684	+	0.156383i
$117$			1809.25i			1.42962i
$118$	−1454.25	−	431.223i	−1.13453	−	0.336418i
$119$	−202.978			−0.156361
$120$	163.529	−	139.424i	0.124401	−	0.106064i
$121$	891.850			0.670060
$122$	1186.76	+	351.903i	0.880686	+	0.261146i
$123$		−	104.343i		−	0.0764899i
$124$	1017.26	+	661.448i	0.736717	+	0.479030i
$125$			988.843i			0.707559i
$126$	−254.281	+	857.537i	−0.179787	+	0.606313i
$127$	2476.17			1.73011			0.865057	−	0.501674i	$-0.167282\pi$
$127$	2476.17			1.73011			0.865057	+	0.501674i	$0.167282\pi$
$128$	−1305.83	−	626.068i	−0.901720	−	0.432322i
$129$	−38.1363			−0.0260288
$130$	−727.294	+	2452.72i	−0.490676	+	1.65475i
$131$			2554.42i			1.70367i	0.523812	+	0.851834i	$0.324509\pi$
$131$			2554.42i			1.70367i	−0.523812	+	0.851834i	$0.675491\pi$
$132$	100.811	+	65.5498i	0.0664734	+	0.0432226i
$133$		−	242.010i		−	0.157782i
$134$	−1961.79	−	581.721i	−1.26472	−	0.375023i
$135$	−507.964			−0.323841
$136$	−292.717	+	249.569i	−0.184561	+	0.157356i
$137$	−88.8205			−0.0553901			−0.0276951	−	0.999616i	$-0.508817\pi$
$137$	−88.8205			−0.0553901			−0.0276951	+	0.999616i	$0.508817\pi$
$138$	−26.6432	−	7.90037i	−0.0164349	−	0.00487337i
$139$		−	2351.68i		−	1.43501i	−0.696553	−	0.717505i	$-0.745284\pi$
$139$		−	2351.68i		−	1.43501i	0.696553	−	0.717505i	$-0.254716\pi$
$140$	−689.437	+	1060.31i	−0.416201	+	0.640089i
$141$			208.637i			0.124613i
$142$	−814.703	+	2747.50i	−0.481467	+	1.62370i
$143$	−1431.52			−0.837128
$144$	687.672	+	1549.32i	0.397958	+	0.896595i
$145$	385.718			0.220911
$146$	294.935	−	994.638i	0.167185	−	0.563814i
$147$		−	143.770i		−	0.0806661i
$148$	267.186	−	410.914i	0.148395	−	0.228222i
$149$		−	82.2527i		−	0.0452242i	−0.999744	−	0.0226121i	$-0.992802\pi$
$149$		−	82.2527i		−	0.0452242i	0.999744	−	0.0226121i	$-0.00719827\pi$
$150$	−97.8712	−	29.0213i	−0.0532743	−	0.0157972i
$151$	1629.85			0.878382			0.439191	−	0.898394i	$-0.355265\pi$
$151$	1629.85			0.878382			0.439191	+	0.898394i	$0.355265\pi$
$152$	−297.561	−	349.007i	−0.158786	−	0.186238i
$153$	450.254			0.237914
$154$	−678.501	−	201.193i	−0.355034	−	0.105276i
$155$		−	2008.29i		−	1.04071i
$156$	328.619	+	213.675i	0.168657	+	0.109665i
$157$		−	1770.07i		−	0.899789i	−0.893082	−	0.449894i	$-0.851462\pi$
$157$		−	1770.07i		−	0.899789i	0.893082	−	0.449894i	$-0.148538\pi$
$158$	185.568	−	625.809i	0.0934368	−	0.315106i
$159$	−366.375			−0.182738
$160$	309.443	+	2376.78i	0.152898	+	1.17438i
$161$	163.552			0.0800604
$162$	552.889	−	1864.56i	0.268142	−	0.904281i
$163$		−	761.521i		−	0.365932i	−0.983119	−	0.182966i	$-0.941430\pi$
$163$		−	761.521i		−	0.365932i	0.983119	−	0.182966i	$-0.0585699\pi$
$164$	975.659	+	634.396i	0.464550	+	0.302061i
$165$		−	199.023i		−	0.0939025i
$166$	421.971	+	125.125i	0.197297	+	0.0585036i
$167$	1746.70			0.809364			0.404682	−	0.914458i	$-0.367382\pi$
$167$	1746.70			0.809364			0.404682	+	0.914458i	$0.367382\pi$
$168$	125.726	+	147.462i	0.0577378	+	0.0677201i
$169$	−2469.37			−1.12397
$170$	610.390	+	180.996i	0.275381	+	0.0816575i
$171$			536.838i			0.240076i
$172$	231.866	−	356.595i	0.102789	−	0.158082i
$173$		−	3247.37i		−	1.42713i	−0.700590	−	0.713564i	$-0.747080\pi$
$173$		−	3247.37i		−	1.42713i	0.700590	−	0.713564i	$-0.252920\pi$
$174$	16.8014	−	56.6610i	0.00732019	−	0.0246866i
$175$	600.794			0.259519
$176$	−1225.85	+	544.101i	−0.525012	+	0.233029i
$177$	384.661			0.163350
$178$	850.699	−	2868.89i	0.358217	−	1.20805i
$179$			3866.00i			1.61429i	0.590350	+	0.807147i	$0.298990\pi$
$179$			3866.00i			1.61429i	−0.590350	+	0.807147i	$0.701010\pi$
$180$	1529.34	−	2352.02i	0.633280	−	0.973942i
$181$			2178.63i			0.894675i	0.894365	+	0.447337i	$0.147628\pi$
$181$			2178.63i			0.894675i	−0.894365	+	0.447337i	$0.852372\pi$
$182$	−2211.74	−	655.836i	−0.900796	−	0.267109i
$183$	−313.906			−0.126801
$184$	235.861	−	201.094i	0.0944996	−	0.0805699i
$185$	−811.231			−0.322394
$186$	−295.013	−	87.4789i	−0.116298	−	0.0344853i
$187$			356.250i			0.139313i
$188$	−1950.87	−	1268.50i	−0.756818	−	0.492101i
$189$		−	458.056i		−	0.176289i
$190$	−215.802	+	727.769i	−0.0823996	+	0.277884i
$191$	−5028.57			−1.90500			−0.952499	−	0.304540i	$-0.901497\pi$
$191$	−5028.57			−1.90500			−0.952499	+	0.304540i	$0.901497\pi$
$192$	362.622	+	58.0732i	0.136302	+	0.0218285i
$193$	−5134.84			−1.91510			−0.957549	−	0.288270i	$-0.906920\pi$
$193$	−5134.84			−1.91510			−0.957549	+	0.288270i	$0.906920\pi$
$194$	1195.62	−	4032.11i	0.442478	−	1.49221i
$195$		−	648.764i		−	0.238251i
$196$	1344.32	+	874.110i	0.489914	+	0.318553i
$197$		−	958.059i		−	0.346492i	−0.984879	−	0.173246i	$-0.944574\pi$
$197$		−	958.059i		−	0.346492i	0.984879	−	0.173246i	$-0.0554256\pi$
$198$	1505.08	+	446.295i	0.540209	+	0.160186i
$199$	2888.52			1.02895			0.514477	−	0.857504i	$-0.327986\pi$
$199$	2888.52			1.02895			0.514477	+	0.857504i	$0.327986\pi$
$200$	866.415	−	738.700i	0.306324	−	0.261170i
$201$	518.909			0.182095
$202$	−3304.87	−	979.979i	−1.15114	−	0.341342i
$203$			347.821i			0.120257i
$204$	53.1758	−	81.7808i	0.0182502	−	0.0280677i
$205$		−	1926.16i		−	0.656238i
$206$	1197.25	−	4037.60i	0.404934	−	1.36560i
$207$	−362.799			−0.121818
$208$	−3995.96	+	1773.63i	−1.33207	+	0.591245i
$209$	−424.758			−0.140579
$210$	91.1807	−	307.497i	0.0299622	−	0.101044i
$211$			2382.64i			0.777383i	0.921368	+	0.388692i	$0.127073\pi$
$211$			2382.64i			0.777383i	−0.921368	+	0.388692i	$0.872927\pi$
$212$	2227.53	−	3425.80i	0.721640	−	1.10983i
$213$		−	726.734i		−	0.233779i
$214$	−3529.27	−	1046.52i	−1.12737	−	0.334293i
$215$	−703.995			−0.223312
$216$	−563.198	−	660.570i	−0.177411	−	0.208084i
$217$	1810.98			0.566530
$218$	2063.88	+	611.994i	0.641210	+	0.190135i
$219$			263.089i			0.0811777i
$220$	1860.97	+	1210.05i	0.570303	+	0.370824i
$221$			1161.28i			0.353468i
$222$	−35.3363	+	119.168i	−0.0106830	+	0.0360271i
$223$	−1304.56			−0.391748			−0.195874	−	0.980629i	$-0.562754\pi$
$223$	−1304.56			−0.391748			−0.195874	+	0.980629i	$0.562754\pi$
$224$	−2143.26	+	279.040i	−0.639296	+	0.0832328i
$225$	−1332.71			−0.394877
$226$	−571.686	+	1927.95i	−0.168265	+	0.567457i
$227$		−	66.2489i		−	0.0193705i	−0.999953	−	0.00968523i	$-0.996917\pi$
$227$		−	66.2489i		−	0.0193705i	0.999953	−	0.00968523i	$-0.00308295\pi$
$228$	97.5074	+	63.4016i	0.0283227	+	0.0184161i
$229$		−	2166.41i		−	0.625156i	−0.949892	−	0.312578i	$-0.898807\pi$
$229$		−	2166.41i		−	0.625156i	0.949892	−	0.312578i	$-0.101193\pi$
$230$	−491.832	−	145.841i	−0.141002	−	0.0418106i
$231$	179.469			0.0511176
$232$	427.659	+	501.598i	0.121022	+	0.141946i
$233$	−892.686			−0.250995			−0.125497	−	0.992094i	$-0.540053\pi$
$233$	−892.686			−0.250995			−0.125497	+	0.992094i	$0.540053\pi$
$234$	4906.18	+	1454.81i	1.37063	+	0.406426i
$235$			3851.43i			1.06911i
$236$	−2338.71	+	3596.79i	−0.645073	+	0.992080i
$237$			165.531i			0.0453688i
$238$	−163.213	+	550.419i	−0.0444518	+	0.149909i
$239$	−4786.26			−1.29539			−0.647693	−	0.761901i	$-0.724266\pi$
$239$	−4786.26			−1.29539			−0.647693	+	0.761901i	$0.724266\pi$
$240$	−246.587	−	555.557i	−0.0663213	−	0.149421i
$241$	5357.41			1.43196			0.715978	−	0.698123i	$-0.245981\pi$
$241$	5357.41			1.43196			0.715978	+	0.698123i	$0.245981\pi$
$242$	717.132	−	2418.45i	0.190492	−	0.642412i
$243$			1529.01i			0.403645i
$244$	1908.53	−	2935.19i	0.500741	−	0.770107i
$245$		−	2653.98i		−	0.692068i
$246$	−282.948	−	83.9013i	−0.0733338	−	0.0217453i
$247$	−1384.60			−0.356680
$248$	2611.64	−	2226.67i	0.668706	−	0.570135i
$249$	−111.615			−0.0284068
$250$	2681.47	+	795.123i	0.678363	+	0.201152i
$251$			6876.50i			1.72925i	0.502422	+	0.864623i	$0.332443\pi$
$251$			6876.50i			1.72925i	−0.502422	+	0.864623i	$0.667557\pi$
$252$	2120.93	+	1379.08i	0.530184	+	0.344738i
$253$		−	287.054i		−	0.0713318i
$254$	1991.07	−	6714.68i	0.491854	−	1.65873i
$255$	−161.453			−0.0396493
$256$	−2747.73	+	3037.63i	−0.670833	+	0.741608i
$257$	2536.41			0.615630			0.307815	−	0.951446i	$-0.400402\pi$
$257$	2536.41			0.615630			0.307815	+	0.951446i	$0.400402\pi$
$258$	−30.6652	+	103.415i	−0.00739973	+	0.0249548i
$259$		−	731.526i		−	0.175501i
$260$	6066.29	+	3944.44i	1.44698	+	0.940861i
$261$		−	771.551i		−	0.182980i
$262$	6926.87	+	2053.99i	1.63337	+	0.484336i
$263$	3286.65			0.770583			0.385292	−	0.922795i	$-0.374101\pi$
$263$	3286.65			0.770583			0.385292	+	0.922795i	$0.374101\pi$
$264$	258.815	−	220.664i	0.0603369	−	0.0514429i
$265$	−6763.26			−1.56779
$266$	−656.265	−	194.599i	−0.151271	−	0.0448558i
$267$			758.843i			0.173934i
$268$	−3154.93	+	4852.08i	−0.719097	+	1.10592i
$269$		−	1407.52i		−	0.319025i	−0.987196	−	0.159513i	$-0.949008\pi$
$269$		−	1407.52i		−	0.319025i	0.987196	−	0.159513i	$-0.0509923\pi$
$270$	−408.451	+	1377.46i	−0.0920650	+	0.310479i
$271$	−3383.29			−0.758377			−0.379188	−	0.925320i	$-0.623797\pi$
$271$	−3383.29			−0.758377			−0.379188	+	0.925320i	$0.623797\pi$
$272$	441.389	+	994.444i	0.0983940	+	0.221680i
$273$	585.021			0.129696
$274$	−71.4201	+	240.857i	−0.0157469	+	0.0531047i
$275$		−	1054.47i		−	0.231225i
$276$	−42.8472	+	65.8962i	−0.00934457	+	0.0143713i
$277$			6296.79i			1.36584i	0.730494	+	0.682919i	$0.239290\pi$
$277$			6296.79i			1.36584i	−0.730494	+	0.682919i	$0.760710\pi$
$278$	−6377.09	−	1890.97i	−1.37580	−	0.407960i
$279$	−4017.19			−0.862017
$280$	2320.89	+	2722.15i	0.495356	+	0.580998i
$281$	−5973.56			−1.26816			−0.634079	−	0.773268i	$-0.718621\pi$
$281$	−5973.56			−1.26816			−0.634079	+	0.773268i	$0.718621\pi$
$282$	565.766	+	167.764i	0.119471	+	0.0354262i
$283$			6700.80i			1.40750i	0.710450	+	0.703748i	$0.248492\pi$
$283$			6700.80i			1.40750i	−0.710450	+	0.703748i	$0.751508\pi$
$284$	6795.35	+	4418.49i	1.41982	+	0.923202i
$285$		−	192.500i		−	0.0400096i
$286$	−1151.07	+	3881.87i	−0.237987	+	0.802587i
$287$	1736.91			0.357236
$288$	4754.27	−	618.979i	0.972736	−	0.126645i
$289$	289.000			0.0588235
$290$	310.154	−	1045.96i	0.0628029	−	0.211796i
$291$			1066.52i			0.214848i
$292$	−2460.03	−	1599.57i	−0.493021	−	0.320574i
$293$		−	2657.43i		−	0.529859i	−0.964268	−	0.264930i	$-0.914651\pi$
$293$		−	2657.43i		−	0.529859i	0.964268	−	0.264930i	$-0.0853487\pi$
$294$	−389.863	−	115.604i	−0.0773377	−	0.0229326i
$295$	7100.83			1.40144
$296$	−899.441	−	1054.95i	−0.176618	−	0.207154i
$297$	−803.944			−0.157069
$298$	−223.047	−	66.1390i	−0.0433582	−	0.0128568i
$299$		−	935.723i		−	0.180984i
$300$	−157.395	+	242.064i	−0.0302907	+	0.0465852i
$301$		−	634.826i		−	0.121564i
$302$	1310.56	−	4419.71i	0.249715	−	0.842138i
$303$	874.164			0.165741
$304$	−1185.68	+	526.269i	−0.223695	+	0.0992882i
$305$	−5794.68			−1.08788
$306$	362.047	−	1220.96i	0.0676367	−	0.228097i
$307$		−	1278.11i		−	0.237608i	−0.992918	−	0.118804i	$-0.962094\pi$
$307$		−	1278.11i		−	0.237608i	0.992918	−	0.118804i	$-0.0379059\pi$
$308$	−1091.16	+	1678.13i	−0.201865	+	0.310455i
$309$			1067.98i			0.196618i
$310$	−5445.93	−	1614.86i	−0.997768	−	0.295864i
$311$	9646.21			1.75880			0.879399	−	0.476085i	$-0.157945\pi$
$311$	9646.21			1.75880			0.879399	+	0.476085i	$0.157945\pi$
$312$	843.669	−	719.307i	0.153088	−	0.130522i
$313$	7516.77			1.35742			0.678711	−	0.734406i	$-0.262539\pi$
$313$	7516.77			1.35742			0.678711	+	0.734406i	$0.262539\pi$
$314$	−4799.93	−	1423.30i	−0.862662	−	0.255801i
$315$		−	4187.18i		−	0.748955i
$316$	−1547.80	−	1006.42i	−0.275541	−	0.179163i
$317$			1716.55i			0.304136i	0.988370	+	0.152068i	$0.0485933\pi$
$317$			1716.55i			0.304136i	−0.988370	+	0.152068i	$0.951407\pi$
$318$	−294.600	+	993.507i	−0.0519508	+	0.175198i
$319$	610.468			0.107146
$320$	6693.98	+	1072.03i	1.16939	+	0.187276i
$321$	933.520			0.162318
$322$	131.511	−	443.508i	0.0227604	−	0.0767570i
$323$			344.575i			0.0593581i
$324$	−4611.59	−	2998.56i	−0.790739	−	0.514156i
$325$		−	3437.29i		−	0.586666i
$326$	−2065.03	−	612.335i	−0.350833	−	0.104031i
$327$	−545.913			−0.0923212
$328$	2504.83	−	2135.60i	0.421664	−	0.359509i
$329$	−3473.02			−0.581988
$330$	−539.695	−	160.033i	−0.0900279	−	0.0266956i
$331$			317.197i			0.0526728i	0.999653	+	0.0263364i	$0.00838411\pi$
$331$			317.197i			0.0526728i	−0.999653	+	0.0263364i	$0.991616\pi$
$332$	678.609	−	1043.66i	0.112179	−	0.172524i
$333$			1622.70i			0.267038i
$334$	1404.51	−	4736.56i	0.230094	−	0.775968i
$335$	9579.03			1.56226
$336$	500.972	−	222.359i	0.0813401	−	0.0361032i
$337$	3120.84			0.504461			0.252230	−	0.967667i	$-0.418836\pi$
$337$	3120.84			0.504461			0.252230	+	0.967667i	$0.418836\pi$
$338$	−1985.61	+	6696.24i	−0.319535	+	1.07760i
$339$		−	509.957i		−	0.0817022i
$340$	981.623	−	1509.67i	0.156576	−	0.240804i
$341$		−	3178.48i		−	0.504764i
$342$	1455.76	+	431.669i	0.230170	+	0.0682514i
$343$	6488.59			1.02143
$344$	−780.544	−	915.493i	−0.122337	−	0.143489i
$345$	130.093			0.0203014
$346$	−8805.96	−	2611.19i	−1.36824	−	0.405718i
$347$			5212.61i			0.806419i	0.915108	+	0.403210i	$0.132105\pi$
$347$			5212.61i			0.806419i	−0.915108	+	0.403210i	$0.867895\pi$
$348$	−140.139	−	91.1216i	−0.0215869	−	0.0140363i
$349$		−	2402.53i		−	0.368495i	−0.982880	−	0.184247i	$-0.941015\pi$
$349$		−	2402.53i		−	0.368495i	0.982880	−	0.184247i	$-0.0589848\pi$
$350$	483.095	−	1629.19i	0.0737786	−	0.248811i
$351$	−2620.65			−0.398518
$352$	489.749	+	3761.68i	0.0741583	+	0.569597i
$353$	7969.92			1.20169			0.600844	−	0.799366i	$-0.294831\pi$
$353$	7969.92			1.20169			0.600844	+	0.799366i	$0.294831\pi$
$354$	309.304	−	1043.09i	0.0464387	−	0.156610i
$355$		−	13415.5i		−	2.00569i
$356$	−7095.59	−	4613.72i	−1.05636	−	0.686872i
$357$		−	145.590i		−	0.0215838i
$358$	10483.5	+	3108.63i	1.54769	+	0.458928i
$359$	−5905.55			−0.868198			−0.434099	−	0.900865i	$-0.642933\pi$
$359$	−5905.55			−0.868198			−0.434099	+	0.900865i	$0.642933\pi$
$360$	−5148.30	−	6038.39i	−0.753720	−	0.884032i
$361$	6448.16			0.940102
$362$	5907.83	+	1751.82i	0.857759	+	0.254347i
$363$			639.698i			0.0924943i
$364$	−3556.89	+	5470.26i	−0.512175	+	0.787691i
$365$			4856.62i			0.696457i
$366$	−252.410	+	851.225i	−0.0360483	+	0.121569i
$367$	−9770.96			−1.38976			−0.694878	−	0.719128i	$-0.744541\pi$
$367$	−9770.96			−1.38976			−0.694878	+	0.719128i	$0.744541\pi$
$368$	−355.656	−	801.289i	−0.0503801	−	0.113506i
$369$	−3852.89			−0.543560
$370$	−652.306	+	2199.83i	−0.0916535	+	0.309092i
$371$		−	6098.76i		−	0.853455i
$372$	−474.437	+	729.653i	−0.0661248	+	0.101695i
$373$		−	975.861i		−	0.135464i	−0.997704	−	0.0677321i	$-0.978424\pi$
$373$		−	975.861i		−	0.135464i	0.997704	−	0.0677321i	$-0.0215763\pi$
$374$	966.052	+	286.459i	0.133565	+	0.0396054i
$375$	−709.268			−0.0976706
$376$	−5008.50	+	4270.22i	−0.686952	+	0.585691i
$377$	1989.97			0.271853
$378$	−1242.12	−	368.320i	−0.169015	−	0.0501173i
$379$			1241.04i			0.168200i	0.996457	+	0.0841002i	$0.0268016\pi$
$379$			1241.04i			0.168200i	−0.996457	+	0.0841002i	$0.973198\pi$
$380$	1799.98	+	1170.39i	0.242993	+	0.157999i
$381$			1776.08i			0.238823i
$382$	−4043.45	+	13636.1i	−0.541573	+	1.82640i
$383$	−7652.88			−1.02100			−0.510501	−	0.859877i	$-0.670540\pi$
$383$	−7652.88			−1.02100			−0.510501	+	0.859877i	$0.670540\pi$
$384$	449.061	−	936.633i	0.0596772	−	0.124472i
$385$	3312.98			0.438559
$386$	−4128.90	+	13924.3i	−0.544444	+	1.83608i
$387$			1408.20i			0.184968i
$388$	−9972.56	−	6484.39i	−1.30485	−	0.848441i
$389$		−	5336.04i		−	0.695496i	−0.937588	−	0.347748i	$-0.886947\pi$
$389$		−	5336.04i		−	0.695496i	0.937588	−	0.347748i	$-0.113053\pi$
$390$	−1759.27	−	521.667i	−0.228420	−	0.0677324i
$391$	−232.866			−0.0301191
$392$	3451.30	−	2942.56i	0.444687	−	0.379137i
$393$	−1832.21			−0.235172
$394$	−2597.99	−	770.370i	−0.332195	−	0.0985043i
$395$			3055.70i			0.389238i
$396$	2420.45	−	3722.50i	0.307153	−	0.472380i
$397$		−	11907.2i		−	1.50530i	−0.658419	−	0.752651i	$-0.728775\pi$
$397$		−	11907.2i		−	1.50530i	0.658419	−	0.752651i	$-0.271225\pi$
$398$	2322.64	−	7832.86i	0.292521	−	0.986497i
$399$	173.587			0.0217800
$400$	−1306.47	−	2943.46i	−0.163309	−	0.367933i
$401$	−15520.3			−1.93279			−0.966394	−	0.257067i	$-0.917244\pi$
$401$	−15520.3			−1.93279			−0.966394	+	0.257067i	$0.917244\pi$
$402$	417.252	−	1407.14i	0.0517677	−	0.174581i
$403$		−	10361.0i		−	1.28069i
$404$	−5314.86	+	8173.90i	−0.654515	+	1.00660i
$405$			9104.26i			1.11702i
$406$	943.193	+	279.681i	0.115295	+	0.0341880i
$407$	−1283.92			−0.156367
$408$	−179.009	−	209.957i	−0.0217212	−	0.0254766i
$409$	7336.45			0.886954			0.443477	−	0.896286i	$-0.353745\pi$
$409$	7336.45			0.886954			0.443477	+	0.896286i	$0.353745\pi$
$410$	−5223.21	−	1548.81i	−0.629160	−	0.186562i
$411$		−	63.7084i		−	0.00764599i
$412$	−9986.14	−	6493.22i	−1.19413	−	0.776451i
$413$			6403.16i			0.762903i
$414$	−291.725	+	983.810i	−0.0346316	+	0.116791i
$415$	−2060.40			−0.243713
$416$	1596.46	+	12262.1i	0.188156	+	1.44519i
$417$	1686.79			0.198087
$418$	−341.545	+	1151.82i	−0.0399654	+	0.134779i
$419$		−	3757.76i		−	0.438135i	−0.975710	−	0.219068i	$-0.929698\pi$
$419$		−	3757.76i		−	0.438135i	0.975710	−	0.219068i	$-0.0703016\pi$
$420$	−760.528	−	494.513i	−0.0883571	−	0.0574518i
$421$		−	6238.57i		−	0.722207i	−0.932526	−	0.361104i	$-0.882400\pi$
$421$		−	6238.57i		−	0.722207i	0.932526	−	0.361104i	$-0.117600\pi$
$422$	6461.06	+	1915.87i	0.745307	+	0.221002i
$423$	7704.02			0.885537
$424$	−7498.67	−	8795.12i	−0.858886	−	1.00738i
$425$	−855.413			−0.0976320
$426$	−1970.70	−	584.363i	−0.224133	−	0.0664612i
$427$		−	5225.35i		−	0.592207i
$428$	−5675.74	+	8728.91i	−0.640998	+	0.985813i
$429$		−	1026.78i		−	0.115556i
$430$	−566.078	+	1909.04i	−0.0634854	+	0.214098i
$431$	4178.86			0.467026			0.233513	−	0.972354i	$-0.424978\pi$
$431$	4178.86			0.467026			0.233513	+	0.972354i	$0.424978\pi$
$432$	−2244.14	+	996.076i	−0.249934	+	0.110935i
$433$	14644.0			1.62528			0.812638	−	0.582769i	$-0.198031\pi$
$433$	14644.0			1.62528			0.812638	+	0.582769i	$0.198031\pi$
$434$	1456.19	−	4910.86i	0.161059	−	0.543154i
$435$			276.664i			0.0304943i
$436$	3319.11	−	5104.58i	0.364580	−	0.560699i
$437$		−	277.647i		−	0.0303928i
$438$	713.425	+	211.549i	0.0778282	+	0.0230780i
$439$	−10919.6			−1.18716			−0.593580	−	0.804775i	$-0.702286\pi$
$439$	−10919.6			−1.18716			−0.593580	+	0.804775i	$0.702286\pi$
$440$	4777.70	−	4073.44i	0.517655	−	0.441350i
$441$	−5308.75			−0.573238
$442$	3149.08	+	933.782i	0.338883	+	0.100487i
$443$		−	11761.7i		−	1.26144i	−0.776013	−	0.630718i	$-0.782761\pi$
$443$		−	11761.7i		−	1.26144i	0.776013	−	0.630718i	$-0.217239\pi$
$444$	294.736	+	191.644i	0.0315035	+	0.0204843i
$445$			14008.2i			1.49225i
$446$	−1048.99	+	3537.60i	−0.111370	+	0.375584i
$447$	58.9975			0.00624270
$448$	−966.701	+	6036.29i	−0.101947	+	0.636580i
$449$	−3071.83			−0.322870			−0.161435	−	0.986883i	$-0.551612\pi$
$449$	−3071.83			−0.322870			−0.161435	+	0.986883i	$0.551612\pi$
$450$	−1071.62	+	3613.93i	−0.112260	+	0.378583i
$451$		−	3048.49i		−	0.318288i
$452$	4768.37	+	3100.50i	0.496206	+	0.322645i
$453$			1169.05i			0.121251i
$454$	−179.649	−	53.2704i	−0.0185712	−	0.00550683i
$455$	10799.5			1.11272
$456$	250.333	−	213.432i	0.0257081	−	0.0219186i
$457$	7087.43			0.725462			0.362731	−	0.931894i	$-0.381844\pi$
$457$	7087.43			0.725462			0.362731	+	0.931894i	$0.381844\pi$
$458$	−5874.71	−	1742.00i	−0.599361	−	0.177726i
$459$			652.181i			0.0663207i
$460$	−790.958	+	1216.44i	−0.0801709	+	0.123297i
$461$		−	15566.5i		−	1.57268i	−0.617795	−	0.786339i	$-0.711974\pi$
$461$		−	15566.5i		−	1.57268i	0.617795	−	0.786339i	$-0.288026\pi$
$462$	144.310	−	486.669i	0.0145322	−	0.0490084i
$463$	1524.64			0.153037			0.0765183	−	0.997068i	$-0.475620\pi$
$463$	1524.64			0.153037			0.0765183	+	0.997068i	$0.475620\pi$
$464$	1704.07	−	756.361i	0.170495	−	0.0756750i
$465$	1440.49			0.143658
$466$	−717.804	+	2420.72i	−0.0713554	+	0.240638i
$467$			16440.6i			1.62908i	0.580104	+	0.814542i	$0.303012\pi$
$467$			16440.6i			1.62908i	−0.580104	+	0.814542i	$0.696988\pi$
$468$	7890.06	−	12134.4i	0.779312	−	1.19853i
$469$			8637.88i			0.850448i
$470$	10444.0	+	3096.92i	1.02499	+	0.303936i
$471$	1269.62			0.124206
$472$	7872.94	+	9234.10i	0.767757	+	0.900495i
$473$	−1114.20			−0.108310
$474$	448.874	+	133.103i	0.0434968	+	0.0128979i
$475$		−	1019.91i		−	0.0985193i
$476$	1361.34	+	885.177i	0.131086	+	0.0852353i
$477$			13528.5i			1.29859i
$478$	−3848.60	+	12979.0i	−0.368266	+	1.24194i
$479$	−12554.7			−1.19758			−0.598789	−	0.800907i	$-0.704351\pi$
$479$	−12554.7			−1.19758			−0.598789	+	0.800907i	$0.704351\pi$
$480$	−1704.79	+	221.955i	−0.162110	+	0.0211058i
$481$	−4185.24			−0.396737
$482$	4307.86	−	14527.8i	0.407091	−	1.37287i
$483$			117.311i			0.0110514i
$484$	−5981.52	−	3889.32i	−0.561750	−	0.365263i
$485$			19688.0i			1.84327i
$486$	4146.24	+	1229.47i	0.386990	+	0.114752i
$487$	14109.3			1.31284			0.656422	−	0.754394i	$-0.272069\pi$
$487$	14109.3			1.31284			0.656422	+	0.754394i	$0.272069\pi$
$488$	−6424.77	−	7535.56i	−0.595975	−	0.699013i
$489$	546.217			0.0505128
$490$	−7196.86	−	2134.05i	−0.663512	−	0.196748i
$491$		−	10534.8i		−	0.968287i	−0.874989	−	0.484143i	$-0.839131\pi$
$491$		−	10534.8i		−	0.968287i	0.874989	−	0.484143i	$-0.160869\pi$
$492$	−455.034	+	699.812i	−0.0416961	+	0.0641259i
$493$		−	495.228i		−	0.0452413i
$494$	−1113.35	+	3754.65i	−0.101401	+	0.341963i
$495$	−7349.01			−0.667300
$496$	−3938.10	−	8872.48i	−0.356504	−	0.803198i
$497$	12097.4			1.09183
$498$	−89.7487	+	302.668i	−0.00807577	+	0.0272347i
$499$		−	14193.0i		−	1.27328i	−0.771162	−	0.636639i	$-0.780324\pi$
$499$		−	14193.0i		−	1.27328i	0.771162	−	0.636639i	$-0.219676\pi$
$500$	4312.30	−	6632.04i	0.385704	−	0.593188i
$501$			1252.86i			0.111724i
$502$	18647.1	+	5529.35i	1.65789	+	0.491608i
$503$	−9621.66			−0.852899			−0.426450	−	0.904511i	$-0.640236\pi$
$503$	−9621.66			−0.852899			−0.426450	+	0.904511i	$0.640236\pi$
$504$	5445.11	−	4642.47i	0.481239	−	0.410302i
$505$	16137.0			1.42196
$506$	−778.411	−	230.819i	−0.0683885	−	0.0202789i
$507$		−	1771.21i		−	0.155152i
$508$	−16607.3	−	10798.5i	−1.45045	−	0.943119i
$509$			1592.69i			0.138693i	0.997593	+	0.0693464i	$0.0220914\pi$
$509$			1592.69i			0.138693i	−0.997593	+	0.0693464i	$0.977909\pi$
$510$	−129.823	+	437.815i	−0.0112719	+	0.0380133i
$511$	−4379.44			−0.379130
$512$	6027.76	+	9893.62i	0.520297	+	0.853985i
$513$	−777.597			−0.0669234
$514$	2039.51	−	6878.04i	0.175018	−	0.590228i
$515$			19714.8i			1.68687i
$516$	255.775	+	166.311i	0.0218215	+	0.0141888i
$517$			6095.58i			0.518536i
$518$	−1983.70	−	588.216i	−0.168260	−	0.0498933i
$519$	2329.24			0.196999
$520$	15574.1	−	13278.4i	1.31340	−	1.11980i
$521$	−1241.48			−0.104396			−0.0521980	−	0.998637i	$-0.516623\pi$
$521$	−1241.48			−0.104396			−0.0521980	+	0.998637i	$0.516623\pi$
$522$	−2092.23	−	620.400i	−0.175430	−	0.0520195i
$523$		−	537.856i		−	0.0449690i	−0.999747	−	0.0224845i	$-0.992842\pi$
$523$		−	537.856i		−	0.0449690i	0.999747	−	0.0224845i	$-0.00715764\pi$
$524$	11139.7	−	17132.1i	0.928703	−	1.42828i
$525$			430.932i			0.0358237i
$526$	2642.77	−	8912.47i	0.219069	−	0.738788i
$527$	−2578.47			−0.213131
$528$	−390.268	−	879.267i	−0.0321671	−	0.0724720i
$529$	−11979.4			−0.984578
$530$	−5438.30	+	18340.1i	−0.445707	+	1.50310i
$531$		−	14203.8i		−	1.16081i
$532$	−1055.40	+	1623.13i	−0.0860099	+	0.132278i
$533$		−	9937.29i		−	0.807564i
$534$	2057.77	+	610.181i	0.166757	+	0.0494478i
$535$	17232.7			1.39259
$536$	10620.6	+	12456.8i	0.855860	+	1.00383i
$537$	−2772.97			−0.222835
$538$	−3816.79	−	1131.78i	−0.305862	−	0.0906957i
$539$		−	4200.40i		−	0.335666i
$540$	3406.85	+	2215.21i	0.271495	+	0.176532i
$541$			20520.5i			1.63077i	0.578922	+	0.815383i	$0.303473\pi$
$541$			20520.5i			1.63077i	−0.578922	+	0.815383i	$0.696527\pi$
$542$	−2720.48	+	9174.53i	−0.215599	+	0.727085i
$543$	−1562.67			−0.123500
$544$	3051.57	−	397.298i	0.240506	−	0.0313125i
$545$	−10077.5			−0.792062
$546$	470.412	−	1586.42i	0.0368714	−	0.124345i
$547$		−	6765.61i		−	0.528842i	−0.964407	−	0.264421i	$-0.914819\pi$
$547$		−	6765.61i		−	0.528842i	0.964407	−	0.264421i	$-0.0851808\pi$
$548$	595.707	+	387.343i	0.0464368	+	0.0301943i
$549$			11591.1i			0.901086i
$550$	−2859.42	−	847.891i	−0.221684	−	0.0657349i
$551$	590.461			0.0456524
$552$	144.239	+	169.176i	0.0111218	+	0.0130446i
$553$	−2755.47			−0.211889
$554$	17075.1	+	5063.21i	1.30948	+	0.388294i
$555$		−	581.873i		−	0.0445029i
$556$	−10255.6	+	15772.4i	−0.782253	+	1.20305i
$557$		−	2102.01i		−	0.159901i	−0.996799	−	0.0799505i	$-0.974524\pi$
$557$		−	2102.01i		−	0.159901i	0.996799	−	0.0799505i	$-0.0254762\pi$
$558$	−3230.20	+	10893.5i	−0.245063	+	0.826448i
$559$	−3631.99			−0.274807
$560$	9247.93	−	4104.74i	0.697850	−	0.309745i
$561$	−255.528			−0.0192307
$562$	−4803.30	+	16198.6i	−0.360525	+	1.21583i
$563$			12057.3i			0.902585i	0.892376	+	0.451293i	$0.149037\pi$
$563$			12057.3i			0.902585i	−0.892376	+	0.451293i	$0.850963\pi$
$564$	909.859	−	1399.30i	0.0679290	−	0.104470i
$565$		−	9413.78i		−	0.700957i
$566$	18170.7	+	5388.08i	1.34942	+	0.400137i
$567$	−8209.75			−0.608072
$568$	17445.8	−	14874.2i	1.28875	−	1.09878i
$569$	−4292.24			−0.316239			−0.158119	−	0.987420i	$-0.550543\pi$
$569$	−4292.24			−0.316239			−0.158119	+	0.987420i	$0.550543\pi$
$570$	−522.008	−	154.789i	−0.0383588	−	0.0113743i
$571$			2904.41i			0.212865i	0.994320	+	0.106432i	$0.0339428\pi$
$571$			2904.41i			0.212865i	−0.994320	+	0.106432i	$0.966057\pi$
$572$	9600.98	+	6242.78i	0.701813	+	0.456335i
$573$		−	3606.85i		−	0.262964i
$574$	1396.64	−	4710.02i	0.101559	−	0.342495i
$575$	689.262			0.0499899
$576$	2144.38	−	13390.0i	0.155120	−	0.968603i
$577$	−11739.7			−0.847021			−0.423510	−	0.905891i	$-0.639202\pi$
$577$	−11739.7			−0.847021			−0.423510	+	0.905891i	$0.639202\pi$
$578$	232.383	−	783.687i	0.0167230	−	0.0563964i
$579$		−	3683.07i		−	0.264358i
$580$	−2586.96	−	1682.10i	−0.185203	−	0.120423i
$581$		−	1857.96i		−	0.132670i
$582$	2892.11	+	857.585i	0.205983	+	0.0610791i
$583$	−10704.1			−0.760407
$584$	−6315.67	+	5384.70i	−0.447507	+	0.381542i
$585$	−23955.9			−1.69308
$586$	−7206.21	−	2136.82i	−0.507996	−	0.150634i
$587$			18978.6i			1.33446i	0.744851	+	0.667231i	$0.232521\pi$
$587$			18978.6i			1.33446i	−0.744851	+	0.667231i	$0.767479\pi$
$588$	−626.973	+	964.244i	−0.0439727	+	0.0676271i
$589$		−	3074.32i		−	0.215068i
$590$	5709.73	−	19255.5i	0.398417	−	1.34362i
$591$	687.188			0.0478293
$592$	−3583.95	+	1590.76i	−0.248817	+	0.110439i
$593$	6185.47			0.428342			0.214171	−	0.976796i	$-0.431295\pi$
$593$	6185.47			0.428342			0.214171	+	0.976796i	$0.431295\pi$
$594$	−646.447	+	2180.07i	−0.0446532	+	0.150588i
$595$		−	2687.58i		−	0.185177i
$596$	−358.701	+	551.658i	−0.0246526	+	0.0379141i
$597$			2071.85i			0.142035i
$598$	−2537.42	−	752.409i	−0.173516	−	0.0514520i
$599$	16315.1			1.11289			0.556443	−	0.830886i	$-0.312166\pi$
$599$	16315.1			1.11289			0.556443	+	0.830886i	$0.312166\pi$
$600$	529.848	+	621.454i	0.0360516	+	0.0422846i
$601$	−1119.90			−0.0760095			−0.0380048	−	0.999278i	$-0.512100\pi$
$601$	−1119.90			−0.0760095			−0.0380048	+	0.999278i	$0.512100\pi$
$602$	−1721.47	−	510.460i	−0.116548	−	0.0345594i
$603$		−	19160.9i		−	1.29402i
$604$	−10931.2	−	7107.73i	−0.736399	−	0.478823i
$605$			11808.8i			0.793547i
$606$	702.910	−	2370.49i	0.0471184	−	0.158902i
$607$	−12453.4			−0.832731			−0.416365	−	0.909197i	$-0.636696\pi$
$607$	−12453.4			−0.832731			−0.416365	+	0.909197i	$0.636696\pi$
$608$	473.699	+	3638.40i	0.0315971	+	0.242692i
$609$	−249.482			−0.0166002
$610$	−4659.47	+	15713.6i	−0.309273	+	1.04299i
$611$			19870.0i			1.31564i
$612$	−3019.79	−	1963.54i	−0.199457	−	0.129692i
$613$			14381.9i			0.947599i	0.880633	+	0.473799i	$0.157118\pi$
$613$			14381.9i			0.947599i	−0.880633	+	0.473799i	$0.842882\pi$
$614$	−3465.87	−	1027.72i	−0.227803	−	0.0675495i
$615$	1381.58			0.0905863
$616$	3673.22	+	4308.29i	0.240257	+	0.281795i
$617$	8663.55			0.565286			0.282643	−	0.959225i	$-0.408789\pi$
$617$	8663.55			0.565286			0.282643	+	0.959225i	$0.408789\pi$
$618$	2896.05	+	858.753i	0.188505	+	0.0558966i
$619$			10965.5i			0.712022i	0.934482	+	0.356011i	$0.115864\pi$
$619$			10965.5i			0.712022i	−0.934482	+	0.356011i	$0.884136\pi$
$620$	−8758.08	+	13469.4i	−0.567312	+	0.872487i
$621$		−	525.505i		−	0.0339578i
$622$	7756.46	−	26157.8i	0.500009	−	1.68623i
$623$	−12631.9			−0.812336
$624$	−1272.17	−	2866.19i	−0.0816148	−	0.183877i
$625$	−19382.9			−1.24050
$626$	6044.19	−	20383.4i	0.385902	−	1.30141i
$627$		−	304.666i		−	0.0194054i
$628$	−7719.19	+	11871.6i	−0.490493	+	0.754345i
$629$			1041.55i			0.0660243i
$630$	−11354.5	−	3366.88i	−0.718051	−	0.212920i
$631$	16019.3			1.01065			0.505324	−	0.862930i	$-0.331373\pi$
$631$	16019.3			1.01065			0.505324	+	0.862930i	$0.331373\pi$
$632$	−3973.71	+	3387.96i	−0.250104	+	0.213237i
$633$	−1709.00			−0.107309
$634$	4654.81	+	1380.27i	0.291587	+	0.0864630i
$635$			32786.4i			2.04896i
$636$	2457.23	+	1597.75i	0.153200	+	0.0996144i
$637$		−	13692.2i		−	0.851657i
$638$	490.873	−	1655.42i	0.0304606	−	0.102725i
$639$	−26835.0			−1.66131
$640$	8289.64	−	17290.2i	0.511995	−	1.06790i
$641$	24479.7			1.50841			0.754204	−	0.656641i	$-0.228023\pi$
$641$	24479.7			1.50841			0.754204	+	0.656641i	$0.228023\pi$
$642$	750.638	−	2531.45i	0.0461453	−	0.155620i
$643$		−	18808.8i		−	1.15357i	−0.816895	−	0.576786i	$-0.804307\pi$
$643$		−	18808.8i		−	1.15357i	0.816895	−	0.576786i	$-0.195693\pi$
$644$	−1096.92	−	713.245i	−0.0671193	−	0.0436425i
$645$		−	504.955i		−	0.0308257i
$646$	934.392	+	277.071i	0.0569089	+	0.0168749i
$647$	22730.5			1.38119			0.690594	−	0.723242i	$-0.257349\pi$
$647$	22730.5			1.38119			0.690594	+	0.723242i	$0.257349\pi$
$648$	−11839.4	+	10094.2i	−0.717741	+	0.611942i
$649$	11238.3			0.679727
$650$	−9320.97	−	2763.91i	−0.562460	−	0.166784i
$651$			1298.96i			0.0782031i
$652$	−3320.96	+	5107.42i	−0.199477	+	0.306782i
$653$		−	20813.3i		−	1.24730i	−0.781704	−	0.623649i	$-0.785649\pi$
$653$		−	20813.3i		−	1.24730i	0.781704	−	0.623649i	$-0.214351\pi$
$654$	−438.965	+	1480.36i	−0.0262460	+	0.0885119i
$655$	−33822.5			−2.01764
$656$	−3777.04	−	8509.62i	−0.224800	−	0.506471i
$657$	9714.68			0.576873
$658$	−2792.64	+	9417.88i	−0.165453	+	0.557974i
$659$			22207.7i			1.31273i	0.754442	+	0.656366i	$0.227907\pi$
$659$			22207.7i			1.31273i	−0.754442	+	0.656366i	$0.772093\pi$
$660$	−867.931	+	1334.82i	−0.0511881	+	0.0787239i
$661$		−	13100.4i		−	0.770875i	−0.922734	−	0.385437i	$-0.874051\pi$
$661$		−	13100.4i		−	0.770875i	0.922734	−	0.385437i	$-0.125949\pi$
$662$	860.149	+	255.056i	0.0504994	+	0.0149744i
$663$	−832.955			−0.0487923
$664$	−2284.44	−	2679.40i	−0.133514	−	0.156598i
$665$	3204.41			0.186860
$666$	4400.32	+	1304.81i	0.256020	+	0.0759163i
$667$			399.038i			0.0231646i
$668$	−11714.9	−	7617.29i	−0.678537	−	0.441200i
$669$		−	935.723i		−	0.0540764i
$670$	7702.45	−	25975.7i	0.444136	−	1.49780i
$671$	−9171.12			−0.527641
$672$	−200.147	−	1537.29i	−0.0114894	−	0.0882477i
$673$	17383.0			0.995641			0.497820	−	0.867280i	$-0.334134\pi$
$673$	17383.0			0.995641			0.497820	+	0.867280i	$0.334134\pi$
$674$	2509.45	−	8462.86i	0.143413	−	0.483646i
$675$		−	1930.39i		−	0.110075i
$676$	16561.7	+	10768.8i	0.942292	+	0.612700i
$677$		−	12946.2i		−	0.734950i	−0.930033	−	0.367475i	$-0.880222\pi$
$677$		−	12946.2i		−	0.734950i	0.930033	−	0.367475i	$-0.119778\pi$
$678$	−1382.86	−	410.053i	−0.0783310	−	0.0232271i
$679$	−17753.6			−1.00342
$680$	−3304.49	−	3875.80i	−0.186355	−	0.218574i
$681$	47.5184			0.00267388
$682$	−8619.16	−	2555.80i	−0.483936	−	0.143499i
$683$		−	33515.9i		−	1.87768i	−0.344360	−	0.938838i	$-0.611904\pi$
$683$		−	33515.9i		−	1.87768i	0.344360	−	0.938838i	$-0.388096\pi$
$684$	2341.13	−	3600.50i	0.130870	−	0.201270i
$685$		−	1176.05i		−	0.0655981i
$686$	5217.44	−	17595.3i	0.290383	−	0.979286i
$687$	1553.91			0.0862958
$688$	−3110.19	+	1380.47i	−0.172347	+	0.0764973i
$689$	−34892.5			−1.92932
$690$	104.607	−	352.776i	0.00577149	−	0.0194637i
$691$		−	27392.7i		−	1.50806i	−0.656842	−	0.754028i	$-0.728108\pi$
$691$		−	27392.7i		−	1.50806i	0.656842	−	0.754028i	$-0.271892\pi$
$692$	−14161.6	+	21779.7i	−0.777955	+	1.19644i
$693$		−	6626.95i		−	0.363257i
$694$	14135.1	+	4191.43i	0.773145	+	0.229257i
$695$	31138.0			1.69947
$696$	−359.781	+	306.748i	−0.0195941	+	0.0167058i
$697$	−2473.02			−0.134393
$698$	−6515.00	−	1931.86i	−0.353290	−	0.104759i
$699$		−	640.298i		−	0.0346470i
$700$	−4029.45	−	2620.04i	−0.217570	−	0.141469i
$701$		−	13733.7i		−	0.739961i	−0.929039	−	0.369981i	$-0.879364\pi$
$701$		−	13733.7i		−	0.739961i	0.929039	−	0.369981i	$-0.120636\pi$
$702$	−2107.25	+	7106.47i	−0.113295	+	0.382075i
$703$	−1241.84			−0.0666244
$704$	10594.4	+	1696.68i	0.567177	+	0.0908323i
$705$	−2762.52			−0.147578
$706$	6408.57	−	21612.2i	0.341628	−	1.15210i
$707$			14551.5i			0.774069i
$708$	−2579.87	−	1677.49i	−0.136946	−	0.0890452i
$709$		−	10618.4i		−	0.562460i	−0.959640	−	0.281230i	$-0.909258\pi$
$709$		−	10618.4i		−	0.562460i	0.959640	−	0.281230i	$-0.0907423\pi$
$710$	−36379.0	−	10787.3i	−1.92293	−	0.570198i
$711$	6112.31			0.322404
$712$	−18216.6	+	15531.4i	−0.958845	+	0.817505i
$713$	2077.64			0.109128
$714$	−394.799	−	117.068i	−0.0206933	−	0.00613608i
$715$		−	18954.4i		−	0.991404i
$716$	16859.5	−	25928.8i	0.879984	−	1.35336i
$717$		−	3433.04i		−	0.178814i
$718$	−4748.62	+	16014.2i	−0.246820	+	0.832375i
$719$	−27836.8			−1.44386			−0.721931	−	0.691965i	$-0.756745\pi$
$719$	−27836.8			−1.44386			−0.721931	+	0.691965i	$0.756745\pi$
$720$	−20514.2	+	9105.32i	−1.06183	+	0.471299i
$721$	−17777.8			−0.918278
$722$	5184.93	−	17485.6i	0.267262	−	0.901312i
$723$			3842.71i			0.197665i
$724$	9500.91	−	14611.8i	0.487705	−	0.750058i
$725$			1465.83i			0.0750889i
$726$	1734.68	+	514.377i	0.0886779	+	0.0262952i
$727$	13627.0			0.695180			0.347590	−	0.937647i	$-0.387000\pi$
$727$	13627.0			0.695180			0.347590	+	0.937647i	$0.387000\pi$
$728$	11973.8	+	14043.9i	0.609584	+	0.714975i
$729$	17468.3			0.887480
$730$	13169.8	+	3905.18i	0.667720	+	0.197996i
$731$			903.867i			0.0457329i
$732$	2105.32	+	1368.93i	0.106305	+	0.0691217i
$733$			16188.1i			0.815716i	0.913045	+	0.407858i	$0.133724\pi$
$733$			16188.1i			0.815716i	−0.913045	+	0.407858i	$0.866276\pi$
$734$	−7856.77	+	26496.1i	−0.395094	+	1.33241i
$735$	1903.62			0.0955322
$736$	−2458.85	+	320.129i	−0.123145	+	0.0160328i
$737$	15160.5			0.757728
$738$	−3098.09	+	10448.0i	−0.154529	+	0.521132i
$739$			23705.5i			1.18000i	0.807402	+	0.590002i	$0.200873\pi$
$739$			23705.5i			1.18000i	−0.807402	+	0.590002i	$0.799127\pi$
$740$	5440.82	+	3537.75i	0.270282	+	0.175743i
$741$		−	993.134i		−	0.0492357i
$742$	−16538.1	−	4903.98i	−0.818240	−	0.242629i
$743$	23239.5			1.14747			0.573737	−	0.819040i	$-0.305493\pi$
$743$	23239.5			1.14747			0.573737	+	0.819040i	$0.305493\pi$
$744$	1597.12	+	1873.25i	0.0787007	+	0.0923074i
$745$	1089.09			0.0535587
$746$	−2646.26	−	784.684i	−0.129875	−	0.0385112i
$747$			4121.42i			0.201867i
$748$	1553.59	−	2389.32i	0.0759425	−	0.116795i
$749$			15539.6i			0.758083i
$750$	−570.318	+	1923.34i	−0.0277668	+	0.0936405i
$751$	31155.2			1.51381			0.756903	−	0.653528i	$-0.226712\pi$
$751$	31155.2			1.51381			0.756903	+	0.653528i	$0.226712\pi$
$752$	7552.34	+	17015.3i	0.366231	+	0.825113i
$753$	−4932.31			−0.238703
$754$	1600.12	−	5396.24i	0.0772851	−	0.260636i
$755$			21580.6i			1.04026i
$756$	−1997.56	+	3072.12i	−0.0960987	+	0.147793i
$757$		−	14859.9i		−	0.713464i	−0.934207	−	0.356732i	$-0.883891\pi$
$757$		−	14859.9i		−	0.713464i	0.934207	−	0.356732i	$-0.116109\pi$
$758$	3365.36	+	997.913i	0.161260	+	0.0478177i
$759$	205.896			0.00984656
$760$	4621.13	−	3939.95i	0.220560	−	0.188049i
$761$	−4697.92			−0.223784			−0.111892	−	0.993720i	$-0.535691\pi$
$761$	−4697.92			−0.223784			−0.111892	+	0.993720i	$0.535691\pi$
$762$	4816.24	+	1428.14i	0.228969	+	0.0678950i
$763$		−	9087.39i		−	0.431174i
$764$	33726.0	+	21929.4i	1.59707	+	1.03845i
$765$			5961.71i			0.281760i
$766$	−6153.64	+	20752.5i	−0.290261	+	0.978874i
$767$	36634.0			1.72461
$768$	−2178.80	−	1970.87i	−0.102371	−	0.0926010i
$769$	−18023.5			−0.845183			−0.422591	−	0.906320i	$-0.638879\pi$
$769$	−18023.5			−0.845183			−0.422591	+	0.906320i	$0.638879\pi$
$770$	2663.95	−	8983.88i	0.124678	−	0.420463i
$771$			1819.29i			0.0849809i
$772$	34438.7	+	22392.8i	1.60554	+	1.04396i
$773$		−	32332.7i		−	1.50443i	−0.658917	−	0.752216i	$-0.728985\pi$
$773$		−	32332.7i		−	1.50443i	0.658917	−	0.752216i	$-0.271015\pi$
$774$	3818.64	+	1132.32i	0.177336	+	0.0525847i
$775$	7632.03			0.353743
$776$	−25602.7	+	21828.7i	−1.18439	+	1.00980i
$777$	524.703			0.0242260
$778$	−14469.8	−	4290.68i	−0.666798	−	0.197723i
$779$		−	2948.58i		−	0.135615i
$780$	−2829.23	+	4351.17i	−0.129875	+	0.199740i
$781$		−	21232.4i		−	0.972797i
$782$	−187.246	+	631.468i	−0.00856255	+	0.0288763i
$783$	1117.57			0.0510074
$784$	−5204.24	−	11725.1i	−0.237073	−	0.534123i
$785$	23437.1			1.06561
$786$	−1473.27	+	4968.44i	−0.0668572	+	0.225469i
$787$		−	4378.98i		−	0.198340i	−0.995070	−	0.0991702i	$-0.968381\pi$
$787$		−	4378.98i		−	0.198340i	0.995070	−	0.0991702i	$-0.0316188\pi$
$788$	−4178.06	+	6425.58i	−0.188880	+	0.290484i
$789$			2357.42i			0.106370i
$790$	8286.20	+	2457.07i	0.373177	+	0.110656i
$791$	8488.86			0.381579
$792$	−8148.10	−	9556.84i	−0.365569	−	0.428772i
$793$	−29895.5			−1.33874
$794$	−32289.0	−	9574.51i	−1.44319	−	0.427943i
$795$		−	4851.09i		−	0.216416i
$796$	−19372.9	−	12596.7i	−0.862631	−	0.560903i
$797$		−	950.538i		−	0.0422456i	−0.999777	−	0.0211228i	$-0.993276\pi$
$797$		−	950.538i		−	0.0422456i	0.999777	−	0.0211228i	$-0.00672410\pi$
$798$	139.580	−	470.720i	0.00619184	−	0.0208813i
$799$	4944.90			0.218946
$800$	−9032.37	+	1175.96i	−0.399178	+	0.0519708i
$801$	28020.6			1.23603
$802$	−12479.8	+	42086.8i	−0.549473	+	1.85304i
$803$			7686.46i			0.337795i
$804$	−3480.25	−	2262.94i	−0.152660	−	0.0992634i
$805$			2165.56i			0.0948149i
$806$	−28096.2	−	8331.25i	−1.22785	−	0.364089i
$807$	1009.57			0.0440379
$808$	17891.7	+	20985.0i	0.778995	+	0.913676i
$809$	−13888.5			−0.603577			−0.301789	−	0.953375i	$-0.597584\pi$
$809$	−13888.5			−0.603577			−0.301789	+	0.953375i	$0.597584\pi$
$810$	24688.2	+	7320.68i	1.07093	+	0.317559i
$811$			39890.8i			1.72719i	0.504183	+	0.863597i	$0.331794\pi$
$811$			39890.8i			1.72719i	−0.504183	+	0.863597i	$0.668206\pi$
$812$	1516.83	−	2332.79i	0.0655546	−	0.100819i
$813$		−	2426.73i		−	0.104685i
$814$	−1032.39	+	3481.63i	−0.0444537	+	0.149915i
$815$	10083.1			0.433370
$816$	−713.286	+	316.596i	−0.0306005	+	0.0135822i
$817$	−1077.68			−0.0461485
$818$	5899.20	−	19894.4i	0.252152	−	0.850357i
$819$		−	21602.2i		−	0.921661i
$820$	−8399.90	+	12918.5i	−0.357728	+	0.550162i
$821$		−	24825.4i		−	1.05531i	−0.849457	−	0.527657i	$-0.823071\pi$
$821$		−	24825.4i		−	1.05531i	0.849457	−	0.527657i	$-0.176929\pi$
$822$	−172.759	−	51.2275i	−0.00733050	−	0.00217368i
$823$	13753.3			0.582516			0.291258	−	0.956644i	$-0.405926\pi$
$823$	13753.3			0.582516			0.291258	+	0.956644i	$0.405926\pi$
$824$	−25637.6	+	21858.5i	−1.08389	+	0.924121i
$825$	756.338			0.0319180
$826$	17363.6	+	5148.74i	0.731424	+	0.216886i
$827$			38901.5i			1.63572i	0.575420	+	0.817858i	$0.304839\pi$
$827$			38901.5i			1.63572i	−0.575420	+	0.817858i	$0.695161\pi$
$828$	2433.24	+	1582.15i	0.102127	+	0.0664053i
$829$		−	8741.28i		−	0.366221i	−0.983092	−	0.183111i	$-0.941383\pi$
$829$		−	8741.28i		−	0.366221i	0.983092	−	0.183111i	$-0.0586166\pi$
$830$	−1656.76	+	5587.23i	−0.0692853	+	0.233657i
$831$	−4516.50			−0.188539
$832$	34535.1	+	5530.73i	1.43905	+	0.230461i
$833$	−3407.48			−0.141731
$834$	1356.34	−	4574.10i	0.0563143	−	0.189914i
$835$			23127.7i			0.958523i
$836$	2848.79	+	1852.35i	0.117856	+	0.0766327i
$837$		−	5818.79i		−	0.240295i
$838$	−10190.0	−	3021.60i	−0.420057	−	0.124558i
$839$	4536.38			0.186667			0.0933333	−	0.995635i	$-0.470248\pi$
$839$	4536.38			0.186667			0.0933333	+	0.995635i	$0.470248\pi$
$840$	−1952.52	+	1664.71i	−0.0802003	+	0.0683784i
$841$	23540.4			0.965205
$842$	−16917.3	−	5016.40i	−0.692408	−	0.205316i
$843$		−	4284.66i		−	0.175055i
$844$	10390.6	−	15980.1i	0.423767	−	0.651725i
$845$		−	32696.4i		−	1.33111i
$846$	6194.76	−	20891.2i	0.251750	−	0.848998i
$847$	−10648.6			−0.431982
$848$	−29879.6	+	13262.2i	−1.20999	+	0.537059i
$849$	−4806.29			−0.194289
$850$	−687.832	+	2319.64i	−0.0277558	+	0.0936035i
$851$		−	839.245i		−	0.0338060i
$852$	−3169.26	+	4874.11i	−0.127438	+	0.195991i
$853$			39648.3i			1.59148i	0.605639	+	0.795739i	$0.292917\pi$
$853$			39648.3i			1.59148i	−0.605639	+	0.795739i	$0.707083\pi$
$854$	−14169.7	−	4201.67i	−0.567771	−	0.168359i
$855$	−7108.16			−0.284320
$856$	19106.5	+	22409.9i	0.762907	+	0.894806i
$857$	−15334.5			−0.611219			−0.305610	−	0.952157i	$-0.598860\pi$
$857$	−15334.5			−0.611219			−0.305610	+	0.952157i	$0.598860\pi$
$858$	−2784.35	−	825.631i	−0.110788	−	0.0328515i
$859$			6188.35i			0.245802i	0.992419	+	0.122901i	$0.0392197\pi$
$859$			6188.35i			0.245802i	−0.992419	+	0.122901i	$0.960780\pi$
$860$	4721.60	+	3070.09i	0.187215	+	0.121732i
$861$			1245.84i			0.0493124i
$862$	3360.19	−	11331.9i	0.132771	−	0.447756i
$863$	−585.289			−0.0230863			−0.0115431	−	0.999933i	$-0.503674\pi$
$863$	−585.289			−0.0230863			−0.0115431	+	0.999933i	$0.503674\pi$
$864$	896.576	+	6886.43i	0.0353034	+	0.271159i
$865$	42997.7			1.69013
$866$	11775.1	−	39710.4i	0.462050	−	1.55821i
$867$			207.291i			0.00811993i
$868$	−12146.0	−	7897.59i	−0.474955	−	0.308827i
$869$			4836.19i			0.188788i
$870$	750.237	+	222.464i	0.0292361	+	0.00866924i
$871$	49419.4			1.92252
$872$	−11173.3	−	13105.1i	−0.433917	−	0.508938i
$873$	39381.8			1.52677
$874$	−752.901	−	223.254i	−0.0291387	−	0.00864037i
$875$		−	11806.6i		−	0.456157i
$876$	1147.32	−	1764.50i	0.0442516	−	0.0680560i
$877$			48720.3i			1.87590i	0.346767	+	0.937951i	$0.387279\pi$
$877$			48720.3i			1.87590i	−0.346767	+	0.937951i	$0.612721\pi$
$878$	−8780.38	+	29610.9i	−0.337498	+	1.13818i
$879$	1906.10			0.0731411
$880$	−7204.32	−	16231.2i	−0.275975	−	0.621767i
$881$	5817.64			0.222476			0.111238	−	0.993794i	$-0.464518\pi$
$881$	5817.64			0.222476			0.111238	+	0.993794i	$0.464518\pi$
$882$	−4268.74	+	14395.9i	−0.162966	+	0.549585i
$883$			49741.7i			1.89574i	0.318650	+	0.947872i	$0.396770\pi$
$883$			49741.7i			1.89574i	−0.318650	+	0.947872i	$0.603230\pi$
$884$	5064.31	−	7788.58i	0.192682	−	0.296333i
$885$			5093.22i			0.193454i
$886$	−31894.5	−	9457.52i	−1.20939	−	0.358614i
$887$	−3079.63			−0.116577			−0.0582885	−	0.998300i	$-0.518564\pi$
$887$	−3079.63			−0.116577			−0.0582885	+	0.998300i	$0.518564\pi$
$888$	756.682	−	645.143i	0.0285952	−	0.0243801i
$889$	−29565.1			−1.11539
$890$	37986.4	+	11263.9i	1.43068	+	0.424233i
$891$			14409.1i			0.541777i
$892$	8749.51	+	5689.13i	0.328425	+	0.213550i
$893$			5895.81i			0.220936i
$894$	47.4395	−	159.985i	0.00177474	−	0.00598511i
$895$	−51188.9			−1.91180
$896$	15591.4	+	7475.17i	0.581331	+	0.278714i
$897$	671.167			0.0249828
$898$	−2470.04	+	8329.94i	−0.0917886	+	0.309547i
$899$			4418.45i			0.163919i
$900$	8938.30	+	5811.89i	0.331048	+	0.215255i
$901$			8683.43i			0.321073i
$902$	−8266.65	−	2451.27i	−0.305155	−	0.0904861i
$903$	455.342			0.0167805
$904$	12241.9	−	10437.4i	0.450398	−	0.384007i
$905$	−28846.7			−1.05956
$906$	3170.13	+	940.024i	0.116248	+	0.0344704i
$907$			1879.65i			0.0688124i	0.999408	+	0.0344062i	$0.0109540\pi$
$907$			1879.65i			0.0688124i	−0.999408	+	0.0344062i	$0.989046\pi$
$908$	−288.909	+	444.323i	−0.0105592	+	0.0162394i
$909$		−	32278.9i		−	1.17780i
$910$	8683.79	−	29285.1i	0.316335	−	1.06681i
$911$	−45338.9			−1.64890			−0.824449	−	0.565936i	$-0.808515\pi$
$911$	−45338.9			−1.64890			−0.824449	+	0.565936i	$0.808515\pi$
$912$	−377.477	−	850.452i	−0.0137056	−	0.0308786i
$913$	−3260.95			−0.118206
$914$	5698.96	−	19219.1i	0.206242	−	0.695528i
$915$		−	4156.36i		−	0.150169i
$916$	−9447.64	+	14529.8i	−0.340785	+	0.524104i
$917$		−	30499.4i		−	1.09834i
$918$	1768.53	+	524.415i	0.0635842	+	0.0188543i
$919$	−856.335			−0.0307376			−0.0153688	−	0.999882i	$-0.504892\pi$
$919$	−856.335			−0.0307376			−0.0153688	+	0.999882i	$0.504892\pi$
$920$	2662.64	+	3122.99i	0.0954182	+	0.111915i
$921$	916.750			0.0327991
$922$	−42212.0	−	12516.9i	−1.50779	−	0.447097i
$923$		−	69212.1i		−	2.46819i
$924$	−1203.67	−	782.655i	−0.0428549	−	0.0278652i
$925$		−	3082.89i		−	0.109583i
$926$	1225.95	−	4134.39i	0.0435068	−	0.146722i
$927$	39435.4			1.39723
$928$	−680.807	−	5229.15i	−0.0240825	−	0.184973i
$929$	−4933.34			−0.174228			−0.0871140	−	0.996198i	$-0.527764\pi$
$929$	−4933.34			−0.174228			−0.0871140	+	0.996198i	$0.527764\pi$
$930$	1158.29	−	3906.21i	0.0408407	−	0.137731i
$931$		−	4062.74i		−	0.143019i
$932$	5987.13	+	3892.97i	0.210424	+	0.136822i
$933$			6918.94i			0.242782i
$934$	44582.5	+	13219.8i	1.56187	+	0.463133i
$935$	−4717.03			−0.164988
$936$	−26560.7	−	31152.8i	−0.927526	−	1.08789i
$937$	−9944.43			−0.346713			−0.173357	−	0.984859i	$-0.555461\pi$
$937$	−9944.43			−0.346713			−0.173357	+	0.984859i	$0.555461\pi$
$938$	23423.5	+	6945.67i	0.815357	+	0.241774i
$939$			5391.56i			0.187377i
$940$	16795.9	−	25831.1i	0.582791	−	0.896294i
$941$		−	23940.4i		−	0.829369i	−0.909965	−	0.414684i	$-0.863892\pi$
$941$		−	23940.4i		−	0.829369i	0.909965	−	0.414684i	$-0.136108\pi$
$942$	1020.89	−	3442.85i	0.0353105	−	0.119081i
$943$	1992.67			0.0688127
$944$	31370.9	−	13924.1i	1.08161	−	0.480076i
$945$	6065.02			0.208778
$946$	−895.919	+	3021.39i	−0.0307916	+	0.103841i
$947$		−	18474.6i		−	0.633941i	−0.948435	−	0.316971i	$-0.897334\pi$
$947$		−	18474.6i		−	0.633941i	0.948435	−	0.316971i	$-0.102666\pi$
$948$	721.875	−	1110.20i	0.0247314	−	0.0380353i
$949$			25055.9i			0.857058i
$950$	−2765.71	−	820.103i	−0.0944542	−	0.0280081i
$951$	−1231.23			−0.0419826
$952$	3495.00	−	2979.82i	0.118985	−	0.101446i
$953$	36167.8			1.22937			0.614685	−	0.788773i	$-0.289283\pi$
$953$	36167.8			1.22937			0.614685	+	0.788773i	$0.289283\pi$
$954$	36685.6	+	10878.2i	1.24501	+	0.369178i
$955$		−	66582.3i		−	2.25607i
$956$	32100.8	+	20872.7i	1.08600	+	0.706141i
$957$			437.871i			0.0147903i
$958$	−10095.2	+	34044.9i	−0.340459	+	1.14816i
$959$	1060.50			0.0357096
$960$	−768.935	+	4801.40i	−0.0258513	+	0.161421i
$961$	−6785.75			−0.227779
$962$	−3365.33	+	11349.2i	−0.112789	+	0.380367i
$963$		−	34470.6i		−	1.15348i
$964$	−35931.4	−	23363.5i	−1.20049	−	0.780587i
$965$		−	67989.3i		−	2.26804i
$966$	318.116	+	94.3293i	0.0105954	+	0.00314182i
$967$	−42024.5			−1.39754			−0.698768	−	0.715348i	$-0.746268\pi$
$967$	−42024.5			−1.39754			−0.698768	+	0.715348i	$0.746268\pi$
$968$	−15356.5	+	13092.8i	−0.509892	+	0.434731i
$969$	−247.154			−0.00819372
$970$	53388.3	+	15831.0i	1.76721	+	0.524023i
$971$		−	27900.9i		−	0.922123i	−0.887368	−	0.461062i	$-0.847469\pi$
$971$		−	27900.9i		−	0.922123i	0.887368	−	0.461062i	$-0.152531\pi$
$972$	6667.94	−	10254.8i	0.220035	−	0.338399i
$973$			28078.7i			0.925139i
$974$	11345.2	−	38260.6i	0.373229	−	1.25867i
$975$	2465.47			0.0809827
$976$	−25600.4	+	11362.9i	−0.839601	+	0.372661i
$977$	−21601.6			−0.707365			−0.353682	−	0.935366i	$-0.615071\pi$
$977$	−21601.6			−0.707365			−0.353682	+	0.935366i	$0.615071\pi$
$978$	439.210	−	1481.19i	0.0143603	−	0.0484286i
$979$			22170.5i			0.723771i
$980$	−11573.9	+	17799.9i	−0.377260	+	0.580201i
$981$			20158.1i			0.656062i
$982$	−28567.4	−	8470.97i	−0.928334	−	0.275274i
$983$	−23616.9			−0.766289			−0.383144	−	0.923688i	$-0.625159\pi$
$983$	−23616.9			−0.766289			−0.383144	+	0.923688i	$0.625159\pi$
$984$	1531.80	+	1796.64i	0.0496261	+	0.0582060i
$985$	12685.5			0.410348
$986$	−1342.92	−	398.210i	−0.0433745	−	0.0128617i
$987$		−	2491.10i		−	0.0803369i
$988$	9286.33	+	6038.19i	0.299026	+	0.194434i
$989$		−	728.305i		−	0.0234163i
$990$	−5909.29	+	19928.5i	−0.189707	+	0.639766i
$991$	−34071.5			−1.09215			−0.546073	−	0.837737i	$-0.683878\pi$
$991$	−34071.5			−1.09215			−0.546073	+	0.837737i	$0.683878\pi$
$992$	−27226.3	+	3544.71i	−0.871407	+	0.113452i
$993$	−227.516			−0.00727089
$994$	9727.44	−	32804.7i	0.310398	−	1.04678i
$995$			38246.3i			1.21858i
$996$	748.584	+	486.747i	0.0238151	+	0.0154851i
$997$			33231.7i			1.05562i	0.849361	+	0.527812i	$0.176987\pi$
$997$			33231.7i			1.05562i	−0.849361	+	0.527812i	$0.823013\pi$
$998$	−38487.5	−	11412.5i	−1.22074	−	0.361981i
$999$	−2350.45			−0.0744393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.c.b.69.15	✓	24
4.3	odd	2		544.4.c.a.273.11		24
8.3	odd	2		544.4.c.a.273.14		24
8.5	even	2	inner	136.4.c.b.69.16	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.c.b.69.15	✓	24	1.1	even	1	trivial
136.4.c.b.69.16	yes	24	8.5	even	2	inner
544.4.c.a.273.11		24	4.3	odd	2
544.4.c.a.273.14		24	8.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.804094 - 2.71172i) q^{2} +0.717271i q^{3} +(-6.70687 - 4.36096i) q^{4} +13.2408i q^{5} +(1.94504 + 0.576753i) q^{6} -11.9399 q^{7} +(-17.2187 + 14.6805i) q^{8} +26.4855 q^{9} +O(q^{10})\)	\(q+(0.804094 - 2.71172i) q^{2} +0.717271i q^{3} +(-6.70687 - 4.36096i) q^{4} +13.2408i q^{5} +(1.94504 + 0.576753i) q^{6} -11.9399 q^{7} +(-17.2187 + 14.6805i) q^{8} +26.4855 q^{9} +(35.9053 + 10.6468i) q^{10} +20.9559i q^{11} +(3.12799 - 4.81064i) q^{12} +68.3108i q^{13} +(-9.60077 + 32.3776i) q^{14} -9.49723 q^{15} +(25.9641 + 58.4967i) q^{16} +17.0000 q^{17} +(21.2969 - 71.8214i) q^{18} +20.2691i q^{19} +(57.7425 - 88.8042i) q^{20} -8.56411i q^{21} +(56.8266 + 16.8505i) q^{22} -13.6980 q^{23} +(-10.5299 - 12.3504i) q^{24} -50.3184 q^{25} +(185.240 + 54.9283i) q^{26} +38.3636i q^{27} +(80.0790 + 52.0692i) q^{28} -29.1311i q^{29} +(-7.63667 + 25.7538i) q^{30} -151.675 q^{31} +(179.504 - 23.3705i) q^{32} -15.0311 q^{33} +(13.6696 - 46.0993i) q^{34} -158.093i q^{35} +(-177.635 - 115.502i) q^{36} +61.2676i q^{37} +(54.9642 + 16.2983i) q^{38} -48.9974 q^{39} +(-194.382 - 227.989i) q^{40} -145.472 q^{41} +(-23.2235 - 6.88635i) q^{42} +53.1686i q^{43} +(91.3878 - 140.548i) q^{44} +350.689i q^{45} +(-11.0145 + 37.1452i) q^{46} +290.877 q^{47} +(-41.9580 + 18.6233i) q^{48} -200.440 q^{49} +(-40.4607 + 136.449i) q^{50} +12.1936i q^{51} +(297.901 - 458.152i) q^{52} +510.790i q^{53} +(104.031 + 30.8479i) q^{54} -277.473 q^{55} +(205.588 - 175.283i) q^{56} -14.5384 q^{57} +(-78.9953 - 23.4241i) q^{58} -536.284i q^{59} +(63.6966 + 41.4170i) q^{60} +437.639i q^{61} +(-121.961 + 411.300i) q^{62} -316.233 q^{63} +(80.9642 - 505.558i) q^{64} -904.489 q^{65} +(-12.0864 + 40.7600i) q^{66} -723.449i q^{67} +(-114.017 - 74.1363i) q^{68} -9.82519i q^{69} +(-428.704 - 127.122i) q^{70} -1013.19 q^{71} +(-456.045 + 388.821i) q^{72} +366.792 q^{73} +(166.141 + 49.2649i) q^{74} -36.0919i q^{75} +(88.3928 - 135.942i) q^{76} -250.210i q^{77} +(-39.3985 + 132.867i) q^{78} +230.779 q^{79} +(-774.543 + 343.785i) q^{80} +687.592 q^{81} +(-116.973 + 394.479i) q^{82} +155.610i q^{83} +(-37.3477 + 57.4383i) q^{84} +225.093i q^{85} +(144.179 + 42.7526i) q^{86} +20.8949 q^{87} +(-307.644 - 360.832i) q^{88} +1057.96 q^{89} +(950.971 + 281.987i) q^{90} -815.621i q^{91} +(91.8707 + 59.7365i) q^{92} -108.792i q^{93} +(233.892 - 788.776i) q^{94} -268.379 q^{95} +(16.7630 + 128.753i) q^{96} +1486.92 q^{97} +(-161.173 + 543.537i) q^{98} +555.028i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9}+O(q^{10}) \) 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9	\( 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9} - 16 q^{10} - 18 q^{12} + 26 q^{14} - 180 q^{15} - 103 q^{16} + 408 q^{17} - 5 q^{18} - 24 q^{20} + 172 q^{22} + 624 q^{23} - 310 q^{24} - 600 q^{25} - 180 q^{26} - 132 q^{28} - 80 q^{30} - 744 q^{31} - 39 q^{32} - 280 q^{33} + 17 q^{34} + 791 q^{36} - 162 q^{38} + 1236 q^{39} - 1396 q^{40} + 1132 q^{42} + 886 q^{44} - 1246 q^{46} - 956 q^{47} - 2226 q^{48} + 1688 q^{49} + 2505 q^{50} + 2544 q^{52} - 3264 q^{54} + 1684 q^{55} - 1100 q^{56} - 168 q^{57} + 2800 q^{58} + 2520 q^{60} - 1946 q^{62} - 2520 q^{63} - 2143 q^{64} - 72 q^{65} + 3660 q^{66} + 85 q^{68} - 5084 q^{70} + 1532 q^{71} - 2277 q^{72} + 216 q^{73} + 2188 q^{74} + 2094 q^{76} - 4748 q^{78} - 3176 q^{79} + 116 q^{80} + 2040 q^{81} + 3198 q^{82} + 5916 q^{84} - 2066 q^{86} - 236 q^{87} - 3598 q^{88} - 424 q^{89} + 2180 q^{90} + 1940 q^{92} - 2156 q^{94} - 1248 q^{95} - 4674 q^{96} - 1304 q^{97} + 3705 q^{98}+O(q^{100}) \) 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9 - 16 * q^10 - 18 * q^12 + 26 * q^14 - 180 * q^15 - 103 * q^16 + 408 * q^17 - 5 * q^18 - 24 * q^20 + 172 * q^22 + 624 * q^23 - 310 * q^24 - 600 * q^25 - 180 * q^26 - 132 * q^28 - 80 * q^30 - 744 * q^31 - 39 * q^32 - 280 * q^33 + 17 * q^34 + 791 * q^36 - 162 * q^38 + 1236 * q^39 - 1396 * q^40 + 1132 * q^42 + 886 * q^44 - 1246 * q^46 - 956 * q^47 - 2226 * q^48 + 1688 * q^49 + 2505 * q^50 + 2544 * q^52 - 3264 * q^54 + 1684 * q^55 - 1100 * q^56 - 168 * q^57 + 2800 * q^58 + 2520 * q^60 - 1946 * q^62 - 2520 * q^63 - 2143 * q^64 - 72 * q^65 + 3660 * q^66 + 85 * q^68 - 5084 * q^70 + 1532 * q^71 - 2277 * q^72 + 216 * q^73 + 2188 * q^74 + 2094 * q^76 - 4748 * q^78 - 3176 * q^79 + 116 * q^80 + 2040 * q^81 + 3198 * q^82 + 5916 * q^84 - 2066 * q^86 - 236 * q^87 - 3598 * q^88 - 424 * q^89 + 2180 * q^90 + 1940 * q^92 - 2156 * q^94 - 1248 * q^95 - 4674 * q^96 - 1304 * q^97 + 3705 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more