LMFDB - Embedded newform 136.4.c.b.69.19

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			69.19
Character	$\chi$	$=$	136.69
Dual form			136.4.c.b.69.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.27335 - 1.68282i) q^{2} +4.93150i q^{3} +(2.33624 - 7.65127i) q^{4} -13.0027i q^{5} +(8.29881 + 11.2110i) q^{6} +6.24020 q^{7} +(-7.56460 - 21.3255i) q^{8} +2.68034 q^{9} +O(q^{10})$	\(q+(2.27335 - 1.68282i) q^{2} +4.93150i q^{3} +(2.33624 - 7.65127i) q^{4} -13.0027i q^{5} +(8.29881 + 11.2110i) q^{6} +6.24020 q^{7} +(-7.56460 - 21.3255i) q^{8} +2.68034 q^{9} +(-21.8811 - 29.5596i) q^{10} -46.1131i q^{11} +(37.7322 + 11.5212i) q^{12} +58.0707i q^{13} +(14.1862 - 10.5011i) q^{14} +64.1227 q^{15} +(-53.0839 - 35.7505i) q^{16} +17.0000 q^{17} +(6.09335 - 4.51053i) q^{18} -154.204i q^{19} +(-99.4870 - 30.3774i) q^{20} +30.7735i q^{21} +(-77.6000 - 104.831i) q^{22} +200.727 q^{23} +(105.167 - 37.3048i) q^{24} -44.0696 q^{25} +(97.7225 + 132.015i) q^{26} +146.368i q^{27} +(14.5786 - 47.7454i) q^{28} +224.481i q^{29} +(145.773 - 107.907i) q^{30} -230.196 q^{31} +(-180.840 + 8.05723i) q^{32} +227.407 q^{33} +(38.6470 - 28.6079i) q^{34} -81.1393i q^{35} +(6.26193 - 20.5080i) q^{36} +122.784i q^{37} +(-259.497 - 350.559i) q^{38} -286.376 q^{39} +(-277.289 + 98.3600i) q^{40} -110.794 q^{41} +(51.7862 + 69.9590i) q^{42} +330.635i q^{43} +(-352.824 - 107.731i) q^{44} -34.8516i q^{45} +(456.323 - 337.787i) q^{46} -100.218 q^{47} +(176.303 - 261.783i) q^{48} -304.060 q^{49} +(-100.186 + 74.1612i) q^{50} +83.8354i q^{51} +(444.315 + 135.667i) q^{52} +477.018i q^{53} +(246.312 + 332.747i) q^{54} -599.594 q^{55} +(-47.2046 - 133.075i) q^{56} +760.454 q^{57} +(377.761 + 510.324i) q^{58} +205.340i q^{59} +(149.806 - 490.620i) q^{60} -242.561i q^{61} +(-523.317 + 387.379i) q^{62} +16.7259 q^{63} +(-397.554 + 322.638i) q^{64} +755.075 q^{65} +(516.975 - 382.684i) q^{66} +30.7354i q^{67} +(39.7162 - 130.072i) q^{68} +989.884i q^{69} +(-136.543 - 184.458i) q^{70} +696.651 q^{71} +(-20.2757 - 57.1596i) q^{72} +841.141 q^{73} +(206.624 + 279.132i) q^{74} -217.329i q^{75} +(-1179.85 - 360.257i) q^{76} -287.755i q^{77} +(-651.032 + 481.918i) q^{78} +752.937 q^{79} +(-464.852 + 690.233i) q^{80} -649.447 q^{81} +(-251.875 + 186.447i) q^{82} -1032.14i q^{83} +(235.457 + 71.8944i) q^{84} -221.046i q^{85} +(556.399 + 751.649i) q^{86} -1107.03 q^{87} +(-983.385 + 348.827i) q^{88} -302.246 q^{89} +(-58.6489 - 79.2299i) q^{90} +362.373i q^{91} +(468.947 - 1535.82i) q^{92} -1135.21i q^{93} +(-227.831 + 168.649i) q^{94} -2005.06 q^{95} +(-39.7342 - 891.812i) q^{96} -104.306 q^{97} +(-691.235 + 511.678i) q^{98} -123.599i 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 $

$2$	2.27335	−	1.68282i	0.803751	−	0.594966i
$2$	2.27335	−	1.68282i	0.803751	−	0.594966i
$3$			4.93150i			0.949067i	0.880237	+	0.474533i	$0.157383\pi$
$3$			4.93150i			0.949067i	−0.880237	+	0.474533i	$0.842617\pi$
$4$	2.33624	−	7.65127i	0.292031	−	0.956409i
$5$		−	13.0027i		−	1.16299i	−0.813548	−	0.581497i	$-0.802467\pi$
$5$		−	13.0027i		−	1.16299i	0.813548	−	0.581497i	$-0.197533\pi$
$6$	8.29881	+	11.2110i	0.564663	+	0.762813i
$7$	6.24020			0.336939			0.168469	−	0.985707i	$-0.446118\pi$
$7$	6.24020			0.336939			0.168469	+	0.985707i	$0.446118\pi$
$8$	−7.56460	−	21.3255i	−0.334311	−	0.942463i
$9$	2.68034			0.0992719
$10$	−21.8811	−	29.5596i	−0.691943	−	0.934758i
$11$		−	46.1131i		−	1.26397i	−0.774982	−	0.631983i	$-0.782241\pi$
$11$		−	46.1131i		−	1.26397i	0.774982	−	0.631983i	$-0.217759\pi$
$12$	37.7322	+	11.5212i	0.907696	+	0.277157i
$13$			58.0707i			1.23892i	0.785029	+	0.619458i	$0.212648\pi$
$13$			58.0707i			1.23892i	−0.785029	+	0.619458i	$0.787352\pi$
$14$	14.1862	−	10.5011i	0.270815	−	0.200467i
$15$	64.1227			1.10376
$16$	−53.0839	−	35.7505i	−0.829436	−	0.558601i
$17$	17.0000			0.242536
$17$	17.0000			0.242536
$18$	6.09335	−	4.51053i	0.0797898	−	0.0590634i
$19$		−	154.204i		−	1.86193i	−0.365105	−	0.930966i	$-0.618967\pi$
$19$		−	154.204i		−	1.86193i	0.365105	−	0.930966i	$-0.381033\pi$
$20$	−99.4870	−	30.3774i	−1.11230	−	0.339630i
$21$			30.7735i			0.319778i
$22$	−77.6000	−	104.831i	−0.752017	−	1.01591i
$23$	200.727			1.81976			0.909880	−	0.414872i	$-0.136174\pi$
$23$	200.727			1.81976			0.909880	+	0.414872i	$0.136174\pi$
$24$	105.167	−	37.3048i	0.894460	−	0.317284i
$25$	−44.0696			−0.352557
$26$	97.7225	+	132.015i	0.737114	+	0.995780i
$27$			146.368i			1.04328i
$28$	14.5786	−	47.7454i	0.0983965	−	0.322251i
$29$			224.481i			1.43742i	0.695312	+	0.718708i	$0.255266\pi$
$29$			224.481i			1.43742i	−0.695312	+	0.718708i	$0.744734\pi$
$30$	145.773	−	107.907i	0.887148	−	0.656700i
$31$	−230.196			−1.33369			−0.666847	−	0.745195i	$-0.732356\pi$
$31$	−230.196			−1.33369			−0.666847	+	0.745195i	$0.732356\pi$
$32$	−180.840	+	8.05723i	−0.999009	+	0.0445103i
$33$	227.407			1.19959
$34$	38.6470	−	28.6079i	0.194938	−	0.144300i
$35$		−	81.1393i		−	0.391858i
$36$	6.26193	−	20.5080i	0.0289904	−	0.0949445i
$37$			122.784i			0.545558i	0.962077	+	0.272779i	$0.0879428\pi$
$37$			122.784i			0.545558i	−0.962077	+	0.272779i	$0.912057\pi$
$38$	−259.497	−	350.559i	−1.10779	−	1.49653i
$39$	−286.376			−1.17582
$40$	−277.289	+	98.3600i	−1.09608	+	0.388802i
$41$	−110.794			−0.422029			−0.211015	−	0.977483i	$-0.567677\pi$
$41$	−110.794			−0.422029			−0.211015	+	0.977483i	$0.567677\pi$
$42$	51.7862	+	69.9590i	0.190257	+	0.257022i
$43$			330.635i			1.17259i	0.810098	+	0.586295i	$0.199414\pi$
$43$			330.635i			1.17259i	−0.810098	+	0.586295i	$0.800586\pi$
$44$	−352.824	−	107.731i	−1.20887	−	0.369117i
$45$		−	34.8516i		−	0.115453i
$46$	456.323	−	337.787i	1.46263	−	1.08270i
$47$	−100.218			−0.311027			−0.155514	−	0.987834i	$-0.549703\pi$
$47$	−100.218			−0.311027			−0.155514	+	0.987834i	$0.549703\pi$
$48$	176.303	−	261.783i	0.530150	−	0.787191i
$49$	−304.060			−0.886472
$50$	−100.186	+	74.1612i	−0.283368	+	0.209760i
$51$			83.8354i			0.230183i
$52$	444.315	+	135.667i	1.18491	+	0.361802i
$53$			477.018i			1.23629i	0.786064	+	0.618145i	$0.212116\pi$
$53$			477.018i			1.23629i	−0.786064	+	0.618145i	$0.787884\pi$
$54$	246.312	+	332.747i	0.620718	+	0.838539i
$55$	−599.594			−1.46999
$56$	−47.2046	−	133.075i	−0.112642	−	0.317552i
$57$	760.454			1.76710
$58$	377.761	+	510.324i	0.855214	+	1.15532i
$59$			205.340i			0.453101i	0.973999	+	0.226551i	$0.0727449\pi$
$59$			205.340i			0.453101i	−0.973999	+	0.226551i	$0.927255\pi$
$60$	149.806	−	490.620i	0.322332	−	1.05565i
$61$		−	242.561i		−	0.509126i	−0.967056	−	0.254563i	$-0.918068\pi$
$61$		−	242.561i		−	0.509126i	0.967056	−	0.254563i	$-0.0819317\pi$
$62$	−523.317	+	387.379i	−1.07196	+	0.793503i
$63$	16.7259			0.0334486
$64$	−397.554	+	322.638i	−0.776472	+	0.630152i
$65$	755.075			1.44085
$66$	516.975	−	382.684i	0.964170	−	0.713714i
$67$			30.7354i			0.0560437i	0.999607	+	0.0280219i	$0.00892080\pi$
$67$			30.7354i			0.0560437i	−0.999607	+	0.0280219i	$0.991079\pi$
$68$	39.7162	−	130.072i	0.0708278	−	0.231963i
$69$			989.884i			1.72707i
$70$	−136.543	−	184.458i	−0.233142	−	0.314956i
$71$	696.651			1.16447			0.582234	−	0.813021i	$-0.302179\pi$
$71$	696.651			1.16447			0.582234	+	0.813021i	$0.302179\pi$
$72$	−20.2757	−	57.1596i	−0.0331877	−	0.0935600i
$73$	841.141			1.34860			0.674302	−	0.738456i	$-0.264445\pi$
$73$	841.141			1.34860			0.674302	+	0.738456i	$0.264445\pi$
$74$	206.624	+	279.132i	0.324588	+	0.438493i
$75$		−	217.329i		−	0.334600i
$76$	−1179.85	−	360.257i	−1.78077	−	0.543741i
$77$		−	287.755i		−	0.425879i
$78$	−651.032	+	481.918i	−0.945062	+	0.699570i
$79$	752.937			1.07230			0.536152	−	0.844122i	$-0.319877\pi$
$79$	752.937			1.07230			0.536152	+	0.844122i	$0.319877\pi$
$80$	−464.852	+	690.233i	−0.649650	+	0.964630i
$81$	−649.447			−0.890873
$82$	−251.875	+	186.447i	−0.339206	+	0.251093i
$83$		−	1032.14i		−	1.36496i	−0.730903	−	0.682481i	$-0.760901\pi$
$83$		−	1032.14i		−	1.36496i	0.730903	−	0.682481i	$-0.239099\pi$
$84$	235.457	+	71.8944i	0.305838	+	0.0933848i
$85$		−	221.046i		−	0.282068i
$86$	556.399	+	751.649i	0.697651	+	0.942470i
$87$	−1107.03			−1.36420
$88$	−983.385	+	348.827i	−1.19124	+	0.422558i
$89$	−302.246			−0.359978			−0.179989	−	0.983669i	$-0.557606\pi$
$89$	−302.246			−0.359978			−0.179989	+	0.983669i	$0.557606\pi$
$90$	−58.6489	−	79.2299i	−0.0686904	−	0.0927952i
$91$			362.373i			0.417439i
$92$	468.947	−	1535.82i	0.531425	−	1.74043i
$93$		−	1135.21i		−	1.26576i
$94$	−227.831	+	168.649i	−0.249989	+	0.185051i
$95$	−2005.06			−2.16542
$96$	−39.7342	−	891.812i	−0.0422433	−	0.948126i
$97$	−104.306			−0.109182			−0.0545910	−	0.998509i	$-0.517386\pi$
$97$	−104.306			−0.109182			−0.0545910	+	0.998509i	$0.517386\pi$
$98$	−691.235	+	511.678i	−0.712503	+	0.527421i
$99$		−	123.599i		−	0.125476i
$100$	−102.957	+	337.189i	−0.102957	+	0.337189i
$101$			827.606i			0.815345i	0.913128	+	0.407673i	$0.133660\pi$
$101$			827.606i			0.815345i	−0.913128	+	0.407673i	$0.866340\pi$
$102$	141.080	+	190.587i	0.136951	+	0.185009i
$103$	−315.597			−0.301909			−0.150955	−	0.988541i	$-0.548235\pi$
$103$	−315.597			−0.301909			−0.150955	+	0.988541i	$0.548235\pi$
$104$	1238.39	−	439.282i	1.16763	−	0.414184i
$105$	400.138			0.371900
$106$	802.734	+	1084.43i	0.735551	+	0.993670i
$107$		−	56.5517i		−	0.0510941i	−0.999674	−	0.0255470i	$-0.991867\pi$
$107$		−	56.5517i		−	0.0510941i	0.999674	−	0.0255470i	$-0.00813276\pi$
$108$	1119.91	+	341.953i	0.997805	+	0.304670i
$109$			127.249i			0.111818i	0.998436	+	0.0559092i	$0.0178057\pi$
$109$			127.249i			0.111818i	−0.998436	+	0.0559092i	$0.982194\pi$
$110$	−1363.09	+	1009.01i	−1.18150	+	0.874592i
$111$	−605.511			−0.517771
$112$	−331.254	−	223.090i	−0.279469	−	0.188215i
$113$	2262.56			1.88357			0.941786	−	0.336212i	$-0.109146\pi$
$113$	2262.56			1.88357			0.941786	+	0.336212i	$0.109146\pi$
$114$	1728.78	−	1279.71i	1.42031	−	1.05136i
$115$		−	2609.99i		−	2.11637i
$116$	1717.56	+	524.442i	1.37476	+	0.419769i
$117$			155.649i			0.122990i
$118$	345.550	+	466.810i	0.269580	+	0.364181i
$119$	106.083			0.0817197
$120$	−485.062	−	1367.45i	−0.368999	−	1.04025i
$121$	−795.418			−0.597609
$122$	−408.186	−	551.425i	−0.302913	−	0.409211i
$123$		−	546.383i		−	0.400534i
$124$	−537.795	+	1761.30i	−0.389479	+	1.27556i
$125$		−	1052.31i		−	0.752973i
$126$	38.0237	−	28.1466i	0.0268843	−	0.0199008i
$127$	−963.686			−0.673333			−0.336667	−	0.941624i	$-0.609300\pi$
$127$	−963.686			−0.673333			−0.336667	+	0.941624i	$0.609300\pi$
$128$	−360.838	+	1402.48i	−0.249171	+	0.968459i
$129$	−1630.53			−1.11287
$130$	1716.55	−	1270.65i	1.15809	−	0.857259i
$131$		−	335.703i		−	0.223897i	−0.993714	−	0.111949i	$-0.964291\pi$
$131$		−	335.703i		−	0.223897i	0.993714	−	0.111949i	$-0.0357092\pi$
$132$	531.277	−	1739.95i	0.350316	−	1.14730i
$133$		−	962.261i		−	0.627358i
$134$	51.7221	+	69.8724i	0.0333441	+	0.0450452i
$135$	1903.18			1.21333
$136$	−128.598	−	362.533i	−0.0810824	−	0.228581i
$137$	−2802.43			−1.74765			−0.873823	−	0.486245i	$-0.838366\pi$
$137$	−2802.43			−1.74765			−0.873823	+	0.486245i	$0.838366\pi$
$138$	1665.80	+	2250.35i	1.02755	+	1.38814i
$139$		−	1957.50i		−	1.19448i	−0.802061	−	0.597242i	$-0.796263\pi$
$139$		−	1957.50i		−	1.19448i	0.802061	−	0.597242i	$-0.203737\pi$
$140$	−620.819	−	189.561i	−0.374777	−	0.114435i
$141$		−	494.224i		−	0.295186i
$142$	1583.73	−	1172.34i	0.935942	−	0.692819i
$143$	2677.82			1.56595
$144$	−142.283	−	95.8235i	−0.0823397	−	0.0554534i
$145$	2918.85			1.67171
$146$	1912.21	−	1415.49i	1.08394	−	0.802374i
$147$		−	1499.47i		−	0.841321i
$148$	939.457	+	286.854i	0.521776	+	0.159320i
$149$			1737.55i			0.955341i	0.878539	+	0.477671i	$0.158519\pi$
$149$			1737.55i			0.955341i	−0.878539	+	0.477671i	$0.841481\pi$
$150$	−365.726	−	494.066i	−0.199076	−	0.268935i
$151$	−49.4392			−0.0266444			−0.0133222	−	0.999911i	$-0.504241\pi$
$151$	−49.4392			−0.0266444			−0.0133222	+	0.999911i	$0.504241\pi$
$152$	−3288.47	+	1166.49i	−1.75480	+	0.622465i
$153$	45.5658			0.0240770
$154$	−484.239	−	654.168i	−0.253384	−	0.342301i
$155$			2993.17i			1.55108i
$156$	−669.043	+	2191.14i	−0.343374	+	1.12456i
$157$		−	305.177i		−	0.155132i	−0.996987	−	0.0775661i	$-0.975285\pi$
$157$		−	305.177i		−	0.155132i	0.996987	−	0.0775661i	$-0.0247149\pi$
$158$	1711.69	−	1267.06i	0.861865	−	0.637984i
$159$	−2352.41			−1.17332
$160$	104.766	+	2351.40i	0.0517653	+	1.16184i
$161$	1252.58			0.613148
$162$	−1476.42	+	1092.90i	−0.716040	+	0.530039i
$163$			2602.46i			1.25055i	0.780403	+	0.625277i	$0.215014\pi$
$163$			2602.46i			1.25055i	−0.780403	+	0.625277i	$0.784986\pi$
$164$	−258.843	+	847.719i	−0.123245	+	0.403632i
$165$		−	2956.89i		−	1.39511i
$166$	−1736.90	−	2346.41i	−0.812107	−	1.09709i
$167$	−758.471			−0.351451			−0.175725	−	0.984439i	$-0.556227\pi$
$167$	−758.471			−0.351451			−0.175725	+	0.984439i	$0.556227\pi$
$168$	656.260	−	232.789i	0.301379	−	0.106905i
$169$	−1175.21			−0.534915
$170$	−371.979	−	502.514i	−0.167821	−	0.226712i
$171$		−	413.318i		−	0.184838i
$172$	2529.78	+	772.444i	1.12148	+	0.342432i
$173$			1226.44i			0.538987i	0.963002	+	0.269494i	$0.0868564\pi$
$173$			1226.44i			0.538987i	−0.963002	+	0.269494i	$0.913144\pi$
$174$	−2516.66	+	1862.93i	−1.09648	+	0.811655i
$175$	−275.003			−0.118790
$176$	−1648.57	+	2447.86i	−0.706053	+	1.04838i
$177$	−1012.63			−0.430023
$178$	−687.112	+	508.626i	−0.289333	+	0.214175i
$179$		−	569.772i		−	0.237915i	−0.992899	−	0.118957i	$-0.962045\pi$
$179$		−	569.772i		−	0.237915i	0.992899	−	0.118957i	$-0.0379552\pi$
$180$	−266.659	−	81.4219i	−0.110420	−	0.0337157i
$181$		−	1255.34i		−	0.515519i	−0.966209	−	0.257760i	$-0.917016\pi$
$181$		−	1255.34i		−	0.515519i	0.966209	−	0.257760i	$-0.0829842\pi$
$182$	609.807	+	823.800i	0.248362	+	0.335517i
$183$	1196.19			0.483195
$184$	−1518.42	−	4280.60i	−0.608366	−	1.71506i
$185$	1596.53			0.634481
$186$	−1910.36	−	2580.74i	−0.753087	−	1.01736i
$187$		−	783.923i		−	0.306557i
$188$	−234.134	+	766.795i	−0.0908295	+	0.297469i
$189$			913.368i			0.351523i
$190$	−4558.20	+	3374.15i	−1.74046	+	1.28835i
$191$	3455.05			1.30889			0.654446	−	0.756109i	$-0.272902\pi$
$191$	3455.05			1.30889			0.654446	+	0.756109i	$0.272902\pi$
$192$	−1591.09	−	1960.53i	−0.598056	−	0.736924i
$193$	−1169.12			−0.436038			−0.218019	−	0.975945i	$-0.569959\pi$
$193$	−1169.12			−0.436038			−0.218019	+	0.975945i	$0.569959\pi$
$194$	−237.124	+	175.528i	−0.0877551	+	0.0649596i
$195$			3723.65i			1.36747i
$196$	−710.358	+	2326.45i	−0.258877	+	0.847830i
$197$			2965.95i			1.07266i	0.844007	+	0.536332i	$0.180191\pi$
$197$			2965.95i			1.07266i	−0.844007	+	0.536332i	$0.819809\pi$
$198$	−207.994	−	280.983i	−0.0746541	−	0.100852i
$199$	−1658.44			−0.590773			−0.295386	−	0.955378i	$-0.595448\pi$
$199$	−1658.44			−0.590773			−0.295386	+	0.955378i	$0.595448\pi$
$200$	333.369	+	939.807i	0.117864	+	0.332272i
$201$	−151.572			−0.0531892
$202$	1392.71	+	1881.44i	0.485103	+	0.655334i
$203$			1400.81i			0.484322i
$204$	641.448	+	195.860i	0.220149	+	0.0672203i
$205$			1440.63i			0.490818i
$206$	−717.462	+	531.092i	−0.242660	+	0.179626i
$207$	538.017			0.180651
$208$	2076.06	−	3082.62i	0.692061	−	1.02760i
$209$	−7110.80			−2.35342
$210$	909.654	−	673.360i	0.298915	−	0.221268i
$211$		−	1557.31i		−	0.508102i	−0.967191	−	0.254051i	$-0.918237\pi$
$211$		−	1557.31i		−	0.508102i	0.967191	−	0.254051i	$-0.0817631\pi$
$212$	3649.79	+	1114.43i	1.18240	+	0.361035i
$213$			3435.53i			1.10516i
$214$	−95.1663	−	128.562i	−0.0303992	−	0.0410669i
$215$	4299.14			1.36372
$216$	3121.38	−	1107.22i	0.983255	−	0.348781i
$217$	−1436.47			−0.449373
$218$	214.136	+	289.281i	0.0665282	+	0.0898741i
$219$			4148.08i			1.27992i
$220$	−1400.80	+	4587.65i	−0.429281	+	1.40591i
$221$			987.202i			0.300481i
$222$	−1376.54	+	1018.97i	−0.416159	+	0.308056i
$223$	−987.634			−0.296578			−0.148289	−	0.988944i	$-0.547377\pi$
$223$	−987.634			−0.296578			−0.148289	+	0.988944i	$0.547377\pi$
$224$	−1128.48	+	50.2787i	−0.336605	+	0.0149973i
$225$	−118.122			−0.0349990
$226$	5143.59	−	3807.48i	1.51392	−	1.12066i
$227$			3298.43i			0.964426i	0.876054	+	0.482213i	$0.160167\pi$
$227$			3298.43i			0.964426i	−0.876054	+	0.482213i	$0.839833\pi$
$228$	1776.61	−	5818.44i	0.516047	−	1.69007i
$229$		−	4946.03i		−	1.42726i	−0.700522	−	0.713631i	$-0.747049\pi$
$229$		−	4946.03i		−	1.42726i	0.700522	−	0.713631i	$-0.252951\pi$
$230$	−4392.14	−	5933.42i	−1.25917	−	1.70103i
$231$	1419.06			0.404188
$232$	4787.17	−	1698.11i	1.35471	−	0.480544i
$233$	−240.751			−0.0676916			−0.0338458	−	0.999427i	$-0.510776\pi$
$233$	−240.751			−0.0676916			−0.0338458	+	0.999427i	$0.510776\pi$
$234$	261.929	+	353.845i	0.0731746	+	0.0988530i
$235$			1303.10i			0.361723i
$236$	1571.11	+	479.724i	0.433350	+	0.132319i
$237$			3713.10i			1.01769i
$238$	241.165	−	178.519i	0.0656823	−	0.0486205i
$239$	−2969.72			−0.803745			−0.401872	−	0.915696i	$-0.631640\pi$
$239$	−2969.72			−0.803745			−0.401872	+	0.915696i	$0.631640\pi$
$240$	−3403.88	−	2292.42i	−0.915499	−	0.616562i
$241$	3418.36			0.913677			0.456839	−	0.889550i	$-0.348982\pi$
$241$	3418.36			0.913677			0.456839	+	0.889550i	$0.348982\pi$
$242$	−1808.26	+	1338.54i	−0.480329	+	0.355557i
$243$			749.206i			0.197784i
$244$	−1855.90	−	566.681i	−0.486933	−	0.148680i
$245$			3953.59i			1.03096i
$246$	−919.463	−	1242.12i	−0.238304	−	0.321929i
$247$	8954.71			2.30678
$248$	1741.34	+	4909.05i	0.445869	+	1.25696i
$249$	5089.99			1.29544
$250$	−1770.85	−	2392.27i	−0.447993	−	0.605202i
$251$		−	1665.14i		−	0.418735i	−0.977837	−	0.209367i	$-0.932860\pi$
$251$		−	1665.14i		−	0.418735i	0.977837	−	0.209367i	$-0.0671405\pi$
$252$	39.0757	−	127.974i	0.00976800	−	0.0319905i
$253$		−	9256.14i		−	2.30011i
$254$	−2190.80	+	1621.71i	−0.541192	+	0.400610i
$255$	1090.09			0.267701
$256$	1539.81	+	3795.55i	0.375929	+	0.926648i
$257$	−5377.01			−1.30509			−0.652547	−	0.757749i	$-0.726299\pi$
$257$	−5377.01			−1.30509			−0.652547	+	0.757749i	$0.726299\pi$
$258$	−3706.76	+	2743.88i	−0.894467	+	0.662118i
$259$			766.199i			0.183820i
$260$	1764.04	−	5777.28i	0.420773	−	1.37805i
$261$			601.685i			0.142695i
$262$	−564.927	−	763.171i	−0.133211	−	0.179957i
$263$	−1553.07			−0.364132			−0.182066	−	0.983286i	$-0.558278\pi$
$263$	−1553.07			−0.364132			−0.182066	+	0.983286i	$0.558278\pi$
$264$	−1720.24	−	4849.56i	−0.401036	−	1.13057i
$265$	6202.51			1.43780
$266$	−1619.31	−	2187.56i	−0.373257	−	0.504239i
$267$		−	1490.53i		−	0.341643i
$268$	235.165	+	71.8054i	0.0536007	+	0.0163665i
$269$		−	2916.23i		−	0.660988i	−0.943808	−	0.330494i	$-0.892785\pi$
$269$		−	2916.23i		−	0.660988i	0.943808	−	0.330494i	$-0.107215\pi$
$270$	4326.60	−	3202.71i	0.975217	−	0.721892i
$271$	−3894.77			−0.873027			−0.436513	−	0.899698i	$-0.643787\pi$
$271$	−3894.77			−0.873027			−0.436513	+	0.899698i	$0.643787\pi$
$272$	−902.427	−	607.758i	−0.201168	−	0.135481i
$273$	−1787.04			−0.396178
$274$	−6370.90	+	4715.97i	−1.40467	+	1.03979i
$275$			2032.19i			0.445620i
$276$	7573.88	+	2312.61i	1.65179	+	0.504358i
$277$		−	2081.49i		−	0.451497i	−0.974186	−	0.225748i	$-0.927517\pi$
$277$		−	2081.49i		−	0.451497i	0.974186	−	0.225748i	$-0.0724827\pi$
$278$	−3294.12	−	4450.09i	−0.710677	−	0.960067i
$279$	−617.005			−0.132398
$280$	−1730.34	+	613.786i	−0.369312	+	0.131003i
$281$	−8815.02			−1.87139			−0.935694	−	0.352813i	$-0.885225\pi$
$281$	−8815.02			−1.87139			−0.935694	+	0.352813i	$0.885225\pi$
$282$	−831.690	−	1123.55i	−0.175626	−	0.237256i
$283$			2132.33i			0.447893i	0.974601	+	0.223947i	$0.0718941\pi$
$283$			2132.33i			0.447893i	−0.974601	+	0.223947i	$0.928106\pi$
$284$	1627.55	−	5330.26i	0.340060	−	1.11371i
$285$		−	9887.94i		−	2.05513i
$286$	6087.62	−	4506.29i	1.25863	−	0.931686i
$287$	−691.380			−0.142198
$288$	−484.713	+	21.5961i	−0.0991735	+	0.00441862i
$289$	289.000			0.0588235
$290$	6635.58	−	4911.90i	1.34364	−	0.994610i
$291$		−	514.384i		−	0.103621i
$292$	1965.11	−	6435.80i	0.393834	−	1.28982i
$293$			5220.34i			1.04087i	0.853900	+	0.520436i	$0.174231\pi$
$293$			5220.34i			1.04087i	−0.853900	+	0.520436i	$0.825769\pi$
$294$	−2523.34	−	3408.82i	−0.500558	−	0.676213i
$295$	2669.97			0.526955
$296$	2618.44	−	928.815i	0.514168	−	0.182386i
$297$	6749.50			1.31867
$298$	2923.99	+	3950.07i	0.568396	+	0.767856i
$299$			11656.4i			2.25453i
$300$	−1662.85	−	507.734i	−0.320015	−	0.0977135i
$301$			2063.23i			0.395091i
$302$	−112.393	+	83.1973i	−0.0214155	+	0.0158525i
$303$	−4081.34			−0.773817
$304$	−5512.85	+	8185.73i	−1.04008	+	1.54435i
$305$	−3153.94			−0.592112
$306$	103.587	−	76.6789i	0.0193519	−	0.0143250i
$307$		−	5998.74i		−	1.11520i	−0.830110	−	0.557599i	$-0.811723\pi$
$307$		−	5998.74i		−	1.11520i	0.830110	−	0.557599i	$-0.188277\pi$
$308$	−2201.69	−	672.266i	−0.407315	−	0.124370i
$309$		−	1556.36i		−	0.286532i
$310$	5036.96	+	6804.53i	0.922840	+	1.24668i
$311$	2266.33			0.413222			0.206611	−	0.978423i	$-0.433757\pi$
$311$	2266.33			0.413222			0.206611	+	0.978423i	$0.433757\pi$
$312$	2166.32	+	6107.10i	0.393088	+	1.10816i
$313$	−3880.48			−0.700759			−0.350379	−	0.936608i	$-0.613947\pi$
$313$	−3880.48			−0.700759			−0.350379	+	0.936608i	$0.613947\pi$
$314$	−513.557	−	693.774i	−0.0922984	−	0.124688i
$315$		−	217.481i		−	0.0389005i
$316$	1759.04	−	5760.92i	0.313145	−	1.02556i
$317$		−	9538.08i		−	1.68994i	−0.534811	−	0.844972i	$-0.679617\pi$
$317$		−	9538.08i		−	1.68994i	0.534811	−	0.844972i	$-0.320383\pi$
$318$	−5347.85	+	3958.68i	−0.943059	+	0.698087i
$319$	10351.5			1.81684
$320$	4195.15	+	5169.26i	0.732863	+	0.903033i
$321$	278.885			0.0484917
$322$	2847.54	−	2107.86i	0.492818	−	0.364802i
$323$		−	2621.46i		−	0.451585i
$324$	−1517.27	+	4969.09i	−0.260162	+	0.852039i
$325$		−	2559.16i		−	0.436789i
$326$	4379.47	+	5916.30i	0.744037	+	1.00513i
$327$	−627.526			−0.106123
$328$	838.116	+	2362.75i	0.141089	+	0.397747i
$329$	−625.380			−0.104797
$330$	−4975.92	−	6722.06i	−0.830046	−	1.12132i
$331$		−	8129.96i		−	1.35004i	−0.737799	−	0.675020i	$-0.764135\pi$
$331$		−	8129.96i		−	1.35004i	0.737799	−	0.675020i	$-0.235865\pi$
$332$	−7897.17	−	2411.33i	−1.30546	−	0.398611i
$333$			329.104i			0.0541585i
$334$	−1724.27	+	1276.37i	−0.282479	+	0.209101i
$335$	399.643			0.0651786
$336$	1100.17	−	1633.58i	0.178628	−	0.265235i
$337$	−9.52682			−0.00153994			−0.000769969	−	1.00000i	$-0.500245\pi$
$337$	−9.52682			−0.00153994			−0.000769969		1.00000i	$0.500245\pi$
$338$	−2671.66	+	1977.66i	−0.429938	+	0.318256i
$339$			11157.8i			1.78764i
$340$	−1691.28	−	516.416i	−0.269772	−	0.0823724i
$341$			10615.1i			1.68574i
$342$	−695.539	−	939.617i	−0.109972	−	0.148563i
$343$	−4037.78			−0.635626
$344$	7050.96	−	2501.12i	1.10512	−	0.392010i
$345$	12871.1			2.00858
$346$	2063.88	+	2788.14i	0.320679	+	0.433212i
$347$			4219.47i			0.652775i	0.945236	+	0.326387i	$0.105831\pi$
$347$			4219.47i			0.652775i	−0.945236	+	0.326387i	$0.894169\pi$
$348$	−2586.29	+	8470.17i	−0.398389	+	1.30474i
$349$			7342.58i			1.12619i	0.826393	+	0.563093i	$0.190389\pi$
$349$			7342.58i			1.12619i	−0.826393	+	0.563093i	$0.809611\pi$
$350$	−625.179	+	462.781i	−0.0954777	+	0.0706762i
$351$	−8499.72			−1.29254
$352$	371.544	+	8339.09i	0.0562595	+	1.26271i
$353$	7798.26			1.17581			0.587903	−	0.808931i	$-0.299954\pi$
$353$	7798.26			1.17581			0.587903	+	0.808931i	$0.299954\pi$
$354$	−2302.07	+	1704.08i	−0.345632	+	0.255849i
$355$		−	9058.32i		−	1.35427i
$356$	−706.121	+	2312.57i	−0.105125	+	0.344286i
$357$			523.150i			0.0775575i
$358$	−958.823	−	1295.29i	−0.141551	−	0.191224i
$359$	1414.01			0.207879			0.103939	−	0.994584i	$-0.466855\pi$
$359$	1414.01			0.207879			0.103939	+	0.994584i	$0.466855\pi$
$360$	−743.228	+	263.638i	−0.108810	+	0.0385971i
$361$	−16919.7			−2.46679
$362$	−2112.52	−	2853.84i	−0.306716	−	0.414349i
$363$		−	3922.60i		−	0.567171i
$364$	2772.61	+	846.591i	0.399243	+	0.121905i
$365$		−	10937.1i		−	1.56842i
$366$	2719.35	−	2012.97i	0.388368	−	0.287485i
$367$	−10162.5			−1.44544			−0.722720	−	0.691141i	$-0.757108\pi$
$367$	−10162.5			−1.44544			−0.722720	+	0.691141i	$0.757108\pi$
$368$	−10655.4	−	7176.09i	−1.50937	−	1.01652i
$369$	−296.967			−0.0418956
$370$	3629.46	−	2686.66i	0.509965	−	0.377495i
$371$			2976.68i			0.416555i
$372$	−8685.82	−	2652.14i	−1.21059	−	0.369642i
$373$		−	268.803i		−	0.0373139i	−0.999826	−	0.0186569i	$-0.994061\pi$
$373$		−	268.803i		−	0.0373139i	0.999826	−	0.0186569i	$-0.00593903\pi$
$374$	−1319.20	−	1782.13i	−0.182391	−	0.246395i
$375$	5189.47			0.714622
$376$	758.109	+	2137.20i	0.103980	+	0.293132i
$377$	−13035.8			−1.78084
$378$	1537.03	+	2076.41i	0.209144	+	0.282537i
$379$		−	11383.9i		−	1.54288i	−0.636300	−	0.771442i	$-0.719536\pi$
$379$		−	11383.9i		−	1.54288i	0.636300	−	0.771442i	$-0.280464\pi$
$380$	−4684.31	+	15341.3i	−0.632368	+	2.07103i
$381$		−	4752.41i		−	0.639038i
$382$	7854.53	−	5814.22i	1.05202	−	0.778747i
$383$	2397.46			0.319854			0.159927	−	0.987129i	$-0.448874\pi$
$383$	2397.46			0.319854			0.159927	+	0.987129i	$0.448874\pi$
$384$	−6916.32	−	1779.47i	−0.919133	−	0.236480i
$385$	−3741.58			−0.495295
$386$	−2657.82	+	1967.42i	−0.350466	+	0.259428i
$387$			886.214i			0.116405i
$388$	−243.684	+	798.073i	−0.0318845	+	0.104423i
$389$			5764.09i			0.751288i	0.926764	+	0.375644i	$0.122578\pi$
$389$			5764.09i			0.751288i	−0.926764	+	0.375644i	$0.877422\pi$
$390$	6266.23	+	8465.16i	0.813597	+	1.09910i
$391$	3412.36			0.441357
$392$	2300.09	+	6484.23i	0.296358	+	0.835467i
$393$	1655.52			0.212493
$394$	4991.15	+	6742.63i	0.638199	+	0.862155i
$395$		−	9790.19i		−	1.24708i
$396$	−945.688	−	288.757i	−0.120007	−	0.0366429i
$397$			10398.9i			1.31463i	0.753617	+	0.657314i	$0.228307\pi$
$397$			10398.9i			1.31463i	−0.753617	+	0.657314i	$0.771693\pi$
$398$	−3770.22	+	2790.86i	−0.474834	+	0.351490i
$399$	4745.38			0.595404
$400$	2339.39	+	1575.51i	0.292424	+	0.196939i
$401$	14598.4			1.81797			0.908987	−	0.416824i	$-0.136857\pi$
$401$	14598.4			1.81797			0.908987	+	0.416824i	$0.136857\pi$
$402$	−344.575	+	255.067i	−0.0427509	+	0.0316458i
$403$		−	13367.7i		−	1.65234i
$404$	6332.24	+	1933.49i	0.779803	+	0.238106i
$405$			8444.55i			1.03608i
$406$	2357.30	+	3184.52i	0.288155	+	0.389274i
$407$	5661.97			0.689566
$408$	1787.83	−	634.182i	0.216938	−	0.0769526i
$409$	2444.59			0.295543			0.147771	−	0.989022i	$-0.452790\pi$
$409$	2444.59			0.295543			0.147771	+	0.989022i	$0.452790\pi$
$410$	2424.31	+	3275.05i	0.292020	+	0.394495i
$411$		−	13820.2i		−	1.65863i
$412$	−737.311	+	2414.72i	−0.0881668	+	0.288749i
$413$			1281.36i			0.152667i
$414$	1223.10	−	905.384i	0.145198	−	0.107481i
$415$	−13420.6			−1.58744
$416$	−467.889	−	10501.5i	−0.0551446	−	1.23769i
$417$	9653.42			1.13365
$418$	−16165.3	+	11966.2i	−1.89156	+	1.40020i
$419$			8281.90i			0.965626i	0.875723	+	0.482813i	$0.160385\pi$
$419$			8281.90i			0.965626i	−0.875723	+	0.482813i	$0.839615\pi$
$420$	934.820	−	3061.57i	0.108606	−	0.355688i
$421$			8008.11i			0.927058i	0.886082	+	0.463529i	$0.153417\pi$
$421$			8008.11i			0.927058i	−0.886082	+	0.463529i	$0.846583\pi$
$422$	−2620.67	−	3540.31i	−0.302304	−	0.408387i
$423$	−268.618			−0.0308763
$424$	10172.6	−	3608.45i	1.16516	−	0.413306i
$425$	−749.184			−0.0855077
$426$	5781.37	+	7810.16i	0.657532	+	0.888272i
$427$		−	1513.63i		−	0.171545i
$428$	−432.693	−	132.119i	−0.0488668	−	0.0149210i
$429$			13205.7i			1.48619i
$430$	9773.45	−	7234.67i	1.09609	−	0.811365i
$431$	3597.98			0.402108			0.201054	−	0.979580i	$-0.435563\pi$
$431$	3597.98			0.402108			0.201054	+	0.979580i	$0.435563\pi$
$432$	5232.74	−	7769.81i	0.582779	−	0.865336i
$433$	−12957.7			−1.43812			−0.719061	−	0.694947i	$-0.755428\pi$
$433$	−12957.7			−1.43812			−0.719061	+	0.694947i	$0.755428\pi$
$434$	−3265.60	+	2417.32i	−0.361184	+	0.267362i
$435$			14394.3i			1.58656i
$436$	973.614	+	297.284i	0.106944	+	0.0326544i
$437$		−	30952.8i		−	3.38827i
$438$	6980.47	+	9430.05i	0.761507	+	1.02873i
$439$	1834.22			0.199414			0.0997070	−	0.995017i	$-0.468209\pi$
$439$	1834.22			0.199414			0.0997070	+	0.995017i	$0.468209\pi$
$440$	4535.69	+	12786.6i	0.491433	+	1.38541i
$441$	−814.984			−0.0880017
$442$	1661.28	+	2244.26i	0.178776	+	0.241512i
$443$		−	11013.6i		−	1.18120i	−0.806963	−	0.590602i	$-0.798890\pi$
$443$		−	11013.6i		−	1.18120i	0.806963	−	0.590602i	$-0.201110\pi$
$444$	−1414.62	+	4632.93i	−0.151205	+	0.495201i
$445$			3930.01i			0.418653i
$446$	−2245.24	+	1662.01i	−0.238375	+	0.176454i
$447$	−8568.74			−0.906683
$448$	−2480.81	+	2013.32i	−0.261624	+	0.212323i
$449$	2249.91			0.236481			0.118240	−	0.992985i	$-0.462275\pi$
$449$	2249.91			0.236481			0.118240	+	0.992985i	$0.462275\pi$
$450$	−268.532	+	198.777i	−0.0281305	+	0.0208232i
$451$			5109.08i			0.533430i
$452$	5285.89	−	17311.5i	0.550061	−	1.80147i
$453$		−	243.809i		−	0.0252873i
$454$	5550.66	+	7498.50i	0.573801	+	0.775158i
$455$	4711.82			0.485480
$456$	−5752.53	−	16217.1i	−0.590761	−	1.66542i
$457$	8498.43			0.869890			0.434945	−	0.900457i	$-0.356768\pi$
$457$	8498.43			0.869890			0.434945	+	0.900457i	$0.356768\pi$
$458$	−8323.28	−	11244.1i	−0.849173	−	1.14716i
$459$			2488.26i			0.253033i
$460$	−19969.7	−	6097.57i	−2.02412	−	0.618045i
$461$		−	1688.36i		−	0.170574i	−0.996356	−	0.0852870i	$-0.972819\pi$
$461$		−	1688.36i		−	0.170574i	0.996356	−	0.0852870i	$-0.0271807\pi$
$462$	3226.03	−	2388.02i	0.324866	−	0.240478i
$463$	−14714.8			−1.47701			−0.738505	−	0.674248i	$-0.764468\pi$
$463$	−14714.8			−1.47701			−0.738505	+	0.674248i	$0.764468\pi$
$464$	8025.30	−	11916.3i	0.802943	−	1.19225i
$465$	−14760.8			−1.47208
$466$	−547.312	+	405.141i	−0.0544072	+	0.0402742i
$467$		−	2474.38i		−	0.245183i	−0.992457	−	0.122592i	$-0.960879\pi$
$467$		−	2474.38i		−	0.245183i	0.992457	−	0.122592i	$-0.0391206\pi$
$468$	1190.91	+	363.635i	0.117628	+	0.0359167i
$469$			191.795i			0.0188833i
$470$	2192.88	+	2962.41i	0.215213	+	0.290735i
$471$	1504.98			0.147231
$472$	4378.98	−	1553.31i	0.427031	−	0.151477i
$473$	15246.6			1.48211
$474$	6248.48	+	8441.19i	0.605490	+	0.817968i
$475$			6795.70i			0.656438i
$476$	247.837	−	811.673i	0.0238647	−	0.0781575i
$477$			1278.57i			0.122729i
$478$	−6751.21	+	4997.50i	−0.646011	+	0.478201i
$479$	−12091.7			−1.15341			−0.576704	−	0.816953i	$-0.695662\pi$
$479$	−12091.7			−1.15341			−0.576704	+	0.816953i	$0.695662\pi$
$480$	−11595.9	+	516.651i	−1.10267	+	0.0491287i
$481$	−7130.18			−0.675901
$482$	7771.14	−	5752.49i	0.734369	−	0.543607i
$483$			6177.07i			0.581918i
$484$	−1858.29	+	6085.96i	−0.174520	+	0.571559i
$485$			1356.26i			0.126978i
$486$	1260.78	+	1703.21i	0.117675	+	0.158969i
$487$	−18153.1			−1.68911			−0.844554	−	0.535471i	$-0.820134\pi$
$487$	−18153.1			−1.68911			−0.844554	+	0.535471i	$0.820134\pi$
$488$	−5172.73	+	1834.87i	−0.479833	+	0.170207i
$489$	−12834.0			−1.18686
$490$	6653.18	+	8987.90i	0.613388	+	0.828637i
$491$		−	3425.98i		−	0.314893i	−0.987528	−	0.157446i	$-0.949674\pi$
$491$		−	3425.98i		−	0.314893i	0.987528	−	0.157446i	$-0.0503261\pi$
$492$	−4180.52	−	1276.48i	−0.383074	−	0.116968i
$493$			3816.18i			0.348625i
$494$	20357.2	−	15069.2i	1.85408	−	1.37246i
$495$	−1607.12			−0.145928
$496$	12219.7	+	8229.63i	1.10621	+	0.745003i
$497$	4347.24			0.392355
$498$	11571.3	−	8565.52i	1.04121	−	0.770744i
$499$		−	1281.85i		−	0.114997i	−0.998346	−	0.0574985i	$-0.981688\pi$
$499$		−	1281.85i		−	0.114997i	0.998346	−	0.0574985i	$-0.0183125\pi$
$500$	−8051.52	−	2458.46i	−0.720150	−	0.219891i
$501$		−	3740.40i		−	0.333550i
$502$	−2802.12	−	3785.44i	−0.249133	−	0.336558i
$503$	1615.27			0.143183			0.0715917	−	0.997434i	$-0.477192\pi$
$503$	1615.27			0.143183			0.0715917	+	0.997434i	$0.477192\pi$
$504$	−126.524	−	356.687i	−0.0111822	−	0.0315240i
$505$	10761.1			0.948242
$506$	−15576.4	−	21042.5i	−1.36849	−	1.84872i
$507$		−	5795.53i		−	0.507670i
$508$	−2251.41	+	7373.42i	−0.196634	+	0.643982i
$509$			18971.8i			1.65208i	0.563609	+	0.826042i	$0.309413\pi$
$509$			18971.8i			1.65208i	−0.563609	+	0.826042i	$0.690587\pi$
$510$	2478.15	−	1834.42i	0.215165	−	0.159273i
$511$	5248.89			0.454397
$512$	9887.74	+	6037.41i	0.853478	+	0.521129i
$513$	22570.5			1.94252
$514$	−12223.8	+	9048.54i	−1.04897	+	0.776486i
$515$			4103.60i			0.351119i
$516$	−3809.31	+	12475.6i	−0.324991	+	1.06436i
$517$			4621.36i			0.393128i
$518$	1289.37	+	1741.84i	0.109366	+	0.147745i
$519$	−6048.21			−0.511535
$520$	−5711.84	−	16102.3i	−0.481694	−	1.35795i
$521$	−2228.67			−0.187408			−0.0937042	−	0.995600i	$-0.529871\pi$
$521$	−2228.67			−0.187408			−0.0937042	+	0.995600i	$0.529871\pi$
$522$	1012.53	+	1367.84i	0.0848987	+	0.114691i
$523$		−	17845.6i		−	1.49203i	−0.665928	−	0.746016i	$-0.731964\pi$
$523$		−	17845.6i		−	1.49203i	0.665928	−	0.746016i	$-0.268036\pi$
$524$	−2568.56	−	784.285i	−0.214137	−	0.0653848i
$525$		−	1356.18i		−	0.112740i
$526$	−3530.68	+	2613.54i	−0.292671	+	0.216646i
$527$	−3913.34			−0.323468
$528$	−12071.6	−	8129.90i	−0.994982	−	0.670091i
$529$	28124.3			2.31152
$530$	14100.5	−	10437.7i	1.15563	−	0.855442i
$531$			550.381i			0.0449802i
$532$	−7362.52	−	2248.08i	−0.600011	−	0.183208i
$533$		−	6433.92i		−	0.522859i
$534$	−2508.29	−	3388.49i	−0.203266	−	0.274596i
$535$	−735.324			−0.0594221
$536$	655.448	−	232.501i	0.0528191	−	0.0187360i
$537$	2809.83			0.225797
$538$	−4907.49	−	6629.62i	−0.393266	−	0.531270i
$539$			14021.1i			1.12047i
$540$	4446.30	−	14561.8i	0.354330	−	1.16044i
$541$		−	8378.16i		−	0.665814i	−0.942960	−	0.332907i	$-0.891970\pi$
$541$		−	8378.16i		−	0.665814i	0.942960	−	0.332907i	$-0.108030\pi$
$542$	−8854.17	+	6554.19i	−0.701696	+	0.519421i
$543$	6190.72			0.489262
$544$	−3074.28	+	136.973i	−0.242295	+	0.0107953i
$545$	1654.57			0.130044
$546$	−4062.57	+	3007.26i	−0.318428	+	0.235712i
$547$		−	100.144i		−	0.00782784i	−0.999992	−	0.00391392i	$-0.998754\pi$
$547$		−	100.144i		−	0.00782784i	0.999992	−	0.00391392i	$-0.00124584\pi$
$548$	−6547.15	+	21442.1i	−0.510366	+	1.67146i
$549$		−	650.145i		−	0.0505419i
$550$	3419.80	+	4619.87i	0.265129	+	0.358167i
$551$	34615.8			2.67637
$552$	21109.8	−	7488.08i	1.62770	−	0.577380i
$553$	4698.47			0.361301
$554$	−3502.77	−	4731.96i	−0.268625	−	0.362891i
$555$			7873.27i			0.602165i
$556$	−14977.4	−	4573.21i	−1.14241	−	0.348826i
$557$		−	20160.8i		−	1.53365i	−0.641857	−	0.766824i	$-0.721836\pi$
$557$		−	20160.8i		−	1.53365i	0.641857	−	0.766824i	$-0.278164\pi$
$558$	−1402.67	+	1038.31i	−0.106415	+	0.0787725i
$559$	−19200.2			−1.45274
$560$	−2900.77	+	4307.19i	−0.218893	+	0.325022i
$561$	3865.91			0.290943
$562$	−20039.6	+	14834.1i	−1.50413	+	1.11341i
$563$			6050.08i			0.452896i	0.974023	+	0.226448i	$0.0727114\pi$
$563$			6050.08i			0.452896i	−0.974023	+	0.226448i	$0.927289\pi$
$564$	−3781.45	−	1154.63i	−0.282318	−	0.0862033i
$565$		−	29419.3i		−	2.19059i
$566$	3588.32	+	4847.53i	0.266481	+	0.359994i
$567$	−4052.67			−0.300170
$568$	−5269.88	−	14856.4i	−0.389295	−	1.09747i
$569$	11431.5			0.842240			0.421120	−	0.907005i	$-0.361637\pi$
$569$	11431.5			0.842240			0.421120	+	0.907005i	$0.361637\pi$
$570$	−16639.6	−	22478.8i	−1.22273	−	1.65181i
$571$			14803.9i			1.08498i	0.840061	+	0.542492i	$0.182519\pi$
$571$			14803.9i			1.08498i	−0.840061	+	0.542492i	$0.817481\pi$
$572$	6256.04	−	20488.7i	0.457305	−	1.49769i
$573$			17038.6i			1.24223i
$574$	−1571.75	+	1163.47i	−0.114292	+	0.0846030i
$575$	−8845.97			−0.641569
$576$	−1065.58	+	864.779i	−0.0770818	+	0.0625563i
$577$	10387.3			0.749445			0.374722	−	0.927137i	$-0.377738\pi$
$577$	10387.3			0.749445			0.374722	+	0.927137i	$0.377738\pi$
$578$	656.998	−	486.335i	0.0472795	−	0.0349980i
$579$		−	5765.52i		−	0.413829i
$580$	6819.16	−	22332.9i	0.488190	−	1.59884i
$581$		−	6440.75i		−	0.459909i
$582$	−865.615	−	1169.38i	−0.0616510	−	0.0832855i
$583$	21996.8			1.56263
$584$	−6362.89	−	17937.7i	−0.450853	−	1.27101i
$585$	2023.86			0.143036
$586$	8784.89	+	11867.7i	0.619284	+	0.836602i
$587$			4814.34i			0.338517i	0.985572	+	0.169258i	$0.0541372\pi$
$587$			4814.34i			0.338517i	−0.985572	+	0.169258i	$0.945863\pi$
$588$	−11472.9	−	3503.13i	−0.804647	−	0.245692i
$589$			35497.1i			2.48325i
$590$	6069.77	−	4493.07i	0.423540	−	0.313520i
$591$	−14626.5			−1.01803
$592$	4389.60	−	6517.88i	0.304749	−	0.452505i
$593$	−17341.2			−1.20087			−0.600437	−	0.799672i	$-0.705007\pi$
$593$	−17341.2			−1.20087			−0.600437	+	0.799672i	$0.705007\pi$
$594$	15344.0	−	11358.2i	1.05988	−	0.784566i
$595$		−	1379.37i		−	0.0950396i
$596$	13294.5	+	4059.35i	0.913697	+	0.278989i
$597$		−	8178.60i		−	0.560683i
$598$	19615.5	+	26499.0i	1.34137	+	1.81208i
$599$	13117.9			0.894798			0.447399	−	0.894334i	$-0.352350\pi$
$599$	13117.9			0.894798			0.447399	+	0.894334i	$0.352350\pi$
$600$	−4634.66	+	1644.01i	−0.315348	+	0.111861i
$601$	−17403.3			−1.18119			−0.590595	−	0.806968i	$-0.701107\pi$
$601$	−17403.3			−1.18119			−0.590595	+	0.806968i	$0.701107\pi$
$602$	3472.04	+	4690.44i	0.235066	+	0.317555i
$603$			82.3814i			0.00556356i
$604$	−115.502	+	378.273i	−0.00778099	+	0.0254830i
$605$			10342.6i			0.695016i
$606$	−9278.31	+	6868.15i	−0.621956	+	0.460395i
$607$	−1099.59			−0.0735269			−0.0367634	−	0.999324i	$-0.511705\pi$
$607$	−1099.59			−0.0735269			−0.0367634	+	0.999324i	$0.511705\pi$
$608$	1242.45	+	27886.2i	0.0828752	+	1.86009i
$609$	−6908.07			−0.459654
$610$	−7170.01	+	5307.51i	−0.475910	+	0.352286i
$611$		−	5819.73i		−	0.385337i
$612$	106.453	−	348.636i	0.00703121	−	0.0230274i
$613$			5069.53i			0.334023i	0.985955	+	0.167012i	$0.0534118\pi$
$613$			5069.53i			0.334023i	−0.985955	+	0.167012i	$0.946588\pi$
$614$	−10094.8	−	13637.2i	−0.663505	−	0.896342i
$615$	−7104.44			−0.465819
$616$	−6136.51	+	2176.75i	−0.401375	+	0.142376i
$617$	19958.8			1.30229			0.651144	−	0.758954i	$-0.274289\pi$
$617$	19958.8			1.30229			0.651144	+	0.758954i	$0.274289\pi$
$618$	−2619.08	−	3538.16i	−0.170477	−	0.230301i
$619$			18678.6i			1.21285i	0.795140	+	0.606426i	$0.207397\pi$
$619$			18678.6i			1.21285i	−0.795140	+	0.606426i	$0.792603\pi$
$620$	22901.6	+	6992.78i	1.48347	+	0.452962i
$621$			29380.1i			1.89852i
$622$	5152.17	−	3813.83i	0.332127	−	0.245853i
$623$	−1886.08			−0.121291
$624$	15201.9	+	10238.1i	0.975264	+	0.656812i
$625$	−19191.6			−1.22826
$626$	−8821.68	+	6530.14i	−0.563236	+	0.416928i
$627$		−	35066.9i		−	2.23355i
$628$	−2334.99	−	712.968i	−0.148370	−	0.0453034i
$629$			2087.34i			0.132317i
$630$	−365.981	−	494.410i	−0.0231445	−	0.0312663i
$631$	8009.39			0.505307			0.252654	−	0.967557i	$-0.418697\pi$
$631$	8009.39			0.505307			0.252654	+	0.967557i	$0.418697\pi$
$632$	−5695.66	−	16056.7i	−0.358483	−	1.01061i
$633$	7679.86			0.482223
$634$	−16050.9	−	21683.4i	−1.00546	−	1.35829i
$635$			12530.5i			0.783083i
$636$	−5495.81	+	17998.9i	−0.342646	+	1.12218i
$637$		−	17657.0i		−	1.09827i
$638$	23532.6	−	17419.7i	1.46029	−	1.08096i
$639$	1867.26			0.115599
$640$	18236.0	+	4691.86i	1.12631	+	0.289785i
$641$	−18242.7			−1.12409			−0.562046	−	0.827106i	$-0.689986\pi$
$641$	−18242.7			−1.12409			−0.562046	+	0.827106i	$0.689986\pi$
$642$	634.003	−	469.312i	0.0389752	−	0.0288509i
$643$			4828.45i			0.296136i	0.988977	+	0.148068i	$0.0473055\pi$
$643$			4828.45i			0.296136i	−0.988977	+	0.148068i	$0.952695\pi$
$644$	2926.32	−	9583.80i	0.179058	−	0.586420i
$645$			21201.2i			1.29426i
$646$	−4411.44	−	5959.50i	−0.268678	−	0.362962i
$647$	14596.0			0.886904			0.443452	−	0.896298i	$-0.353754\pi$
$647$	14596.0			0.886904			0.443452	+	0.896298i	$0.353754\pi$
$648$	4912.80	+	13849.8i	0.297829	+	0.839615i
$649$	9468.86			0.572704
$650$	−4306.59	−	5817.86i	−0.259875	−	0.351069i
$651$		−	7083.95i		−	0.426485i
$652$	19912.1	+	6079.98i	1.19604	+	0.365200i
$653$			1350.75i			0.0809480i	0.999181	+	0.0404740i	$0.0128868\pi$
$653$			1350.75i			0.0809480i	−0.999181	+	0.0404740i	$0.987113\pi$
$654$	−1426.59	+	1056.01i	−0.0852966	+	0.0631397i
$655$	−4365.04			−0.260391
$656$	5881.41	+	3960.96i	0.350046	+	0.235746i
$657$	2254.54			0.133878
$658$	−1421.71	+	1052.40i	−0.0842309	+	0.0623508i
$659$			8972.32i			0.530367i	0.964198	+	0.265184i	$0.0854326\pi$
$659$			8972.32i			0.530367i	−0.964198	+	0.265184i	$0.914567\pi$
$660$	−22624.0	−	6908.03i	−1.33430	−	0.407416i
$661$			8276.84i			0.487038i	0.969896	+	0.243519i	$0.0783018\pi$
$661$			8276.84i			0.487038i	−0.969896	+	0.243519i	$0.921698\pi$
$662$	−13681.3	−	18482.3i	−0.803228	−	1.08510i
$663$	−4868.38			−0.285177
$664$	−22010.9	+	7807.71i	−1.28643	+	0.456322i
$665$	−12512.0			−0.729614
$666$	553.822	+	748.169i	0.0322225	+	0.0435300i
$667$			45059.4i			2.61575i
$668$	−1771.97	+	5803.27i	−0.102634	+	0.336130i
$669$		−	4870.51i		−	0.281472i
$670$	908.528	−	672.526i	0.0523873	−	0.0387790i
$671$	−11185.2			−0.643518
$672$	−247.949	−	5565.08i	−0.0142334	−	0.319461i
$673$	−10941.6			−0.626700			−0.313350	−	0.949638i	$-0.601451\pi$
$673$	−10941.6			−0.626700			−0.313350	+	0.949638i	$0.601451\pi$
$674$	−21.6578	+	16.0319i	−0.00123773	+	0.000916211i
$675$		−	6450.41i		−	0.367817i
$676$	−2745.57	+	8991.84i	−0.156211	+	0.511597i
$677$			12962.5i			0.735878i	0.929850	+	0.367939i	$0.119936\pi$
$677$			12962.5i			0.735878i	−0.929850	+	0.367939i	$0.880064\pi$
$678$	18776.6	+	25365.6i	1.06358	+	1.43681i
$679$	−650.889			−0.0367877
$680$	−4713.91	+	1672.12i	−0.265838	+	0.0942984i
$681$	−16266.2			−0.915305
$682$	17863.2	+	24131.8i	1.00296	+	1.35492i
$683$		−	18403.4i		−	1.03102i	−0.856884	−	0.515510i	$-0.827603\pi$
$683$		−	18403.4i		−	1.03102i	0.856884	−	0.515510i	$-0.172397\pi$
$684$	−3162.41	−	965.612i	−0.176780	−	0.0539782i
$685$			36439.0i			2.03250i
$686$	−9179.29	+	6794.85i	−0.510885	+	0.378176i
$687$	24391.3			1.35457
$688$	11820.4	−	17551.4i	0.655010	−	0.972589i
$689$	−27700.8			−1.53166
$690$	29260.6	−	21659.8i	1.61440	−	1.19504i
$691$		−	16633.5i		−	0.915727i	−0.889022	−	0.457864i	$-0.848615\pi$
$691$		−	16633.5i		−	0.915727i	0.889022	−	0.457864i	$-0.151385\pi$
$692$	9383.86	+	2865.27i	0.515492	+	0.157401i
$693$		−	771.281i		−	0.0422778i
$694$	7100.60	+	9592.33i	0.388379	+	0.524668i
$695$	−25452.8			−1.38918
$696$	8374.22	+	23607.9i	0.456069	+	1.28571i
$697$	−1883.51			−0.102357
$698$	12356.2	+	16692.2i	0.670043	+	0.905173i
$699$		−	1187.27i		−	0.0642439i
$700$	−642.475	+	2104.12i	−0.0346904	+	0.113612i
$701$		−	32233.4i		−	1.73672i	−0.495939	−	0.868358i	$-0.665176\pi$
$701$		−	32233.4i		−	1.73672i	0.495939	−	0.868358i	$-0.334824\pi$
$702$	−19322.8	+	14303.5i	−1.03888	+	0.769018i
$703$	18933.8			1.01579
$704$	14877.8	+	18332.4i	0.796490	+	0.981434i
$705$	−6426.24			−0.343300
$706$	17728.2	−	13123.1i	0.945055	−	0.699565i
$707$			5164.42i			0.274722i
$708$	−2365.76	+	7747.93i	−0.125580	+	0.411278i
$709$		−	27204.5i		−	1.44103i	−0.693442	−	0.720513i	$-0.743906\pi$
$709$		−	27204.5i		−	1.44103i	0.693442	−	0.720513i	$-0.256094\pi$
$710$	−15243.5	−	20592.7i	−0.805745	−	1.08850i
$711$	2018.13			0.106450
$712$	2286.37	+	6445.55i	0.120345	+	0.339266i
$713$	−46206.6			−2.42700
$714$	880.366	+	1189.30i	0.0461441	+	0.0623369i
$715$		−	34818.8i		−	1.82119i
$716$	−4359.48	−	1331.13i	−0.227544	−	0.0694784i
$717$		−	14645.2i		−	0.762808i
$718$	3214.53	−	2379.52i	0.167083	−	0.123681i
$719$	12763.2			0.662014			0.331007	−	0.943628i	$-0.392612\pi$
$719$	12763.2			0.662014			0.331007	+	0.943628i	$0.392612\pi$
$720$	−1245.96	+	1850.06i	−0.0644920	+	0.0957606i
$721$	−1969.39			−0.101725
$722$	−38464.5	+	28472.8i	−1.98269	+	1.46766i
$723$			16857.7i			0.867141i
$724$	−9604.98	−	2932.79i	−0.493047	−	0.150547i
$725$		−	9892.80i		−	0.506771i
$726$	−6601.02	−	8917.44i	−0.337448	−	0.455864i
$727$	29845.7			1.52258			0.761290	−	0.648412i	$-0.224566\pi$
$727$	29845.7			1.52258			0.761290	+	0.648412i	$0.224566\pi$
$728$	7727.78	−	2741.20i	0.393421	−	0.139555i
$729$	−21229.8			−1.07858
$730$	−18405.1	−	24863.8i	−0.933157	−	1.26062i
$731$			5620.80i			0.284395i
$732$	2794.59	−	9152.35i	0.141108	−	0.462132i
$733$		−	8297.14i		−	0.418093i	−0.977906	−	0.209046i	$-0.932964\pi$
$733$		−	8297.14i		−	0.418093i	0.977906	−	0.209046i	$-0.0670359\pi$
$734$	−23102.8	+	17101.6i	−1.16177	+	0.859987i
$735$	−19497.1			−0.978453
$736$	−36299.5	+	1617.30i	−1.81796	+	0.0809981i
$737$	1417.31			0.0708373
$738$	−675.110	+	499.741i	−0.0336736	+	0.0249265i
$739$			14467.2i			0.720144i	0.932925	+	0.360072i	$0.117248\pi$
$739$			14467.2i			0.720144i	−0.932925	+	0.360072i	$0.882752\pi$
$740$	3729.88	−	12215.5i	0.185288	−	0.606823i
$741$			44160.1i			2.18929i
$742$	5009.22	+	6767.05i	0.247836	+	0.334806i
$743$	13574.5			0.670257			0.335129	−	0.942172i	$-0.391220\pi$
$743$	13574.5			0.670257			0.335129	+	0.942172i	$0.391220\pi$
$744$	−24209.0	+	8587.43i	−1.19294	+	0.423159i
$745$	22592.8			1.11106
$746$	−452.346	−	611.083i	−0.0222005	−	0.0299910i
$747$		−	2766.48i		−	0.135502i
$748$	−5998.01	−	1831.43i	−0.293194	−	0.0895239i
$749$		−	352.894i		−	0.0172156i
$750$	11797.5	−	8732.94i	0.574378	−	0.425176i
$751$	−29177.8			−1.41773			−0.708864	−	0.705345i	$-0.750792\pi$
$751$	−29177.8			−1.41773			−0.708864	+	0.705345i	$0.750792\pi$
$752$	5319.96	+	3582.84i	0.257977	+	0.173740i
$753$	8211.61			0.397407
$754$	−29634.9	+	21936.8i	−1.43135	+	1.05954i
$755$			642.843i			0.0309873i
$756$	6988.43	+	2133.85i	0.336199	+	0.102655i
$757$		−	19640.1i		−	0.942977i	−0.881872	−	0.471488i	$-0.843717\pi$
$757$		−	19640.1i		−	0.942977i	0.881872	−	0.471488i	$-0.156283\pi$
$758$	−19157.1	−	25879.7i	−0.917964	−	1.24009i
$759$	45646.6			2.18296
$760$	15167.5	+	42758.9i	0.723924	+	2.04083i
$761$	−12966.0			−0.617629			−0.308815	−	0.951122i	$-0.599932\pi$
$761$	−12966.0			−0.617629			−0.308815	+	0.951122i	$0.599932\pi$
$762$	−7997.45	−	10803.9i	−0.380206	−	0.513627i
$763$			794.056i			0.0376760i
$764$	8071.84	−	26435.5i	0.382237	−	1.25184i
$765$		−	592.477i		−	0.0280014i
$766$	5450.26	−	4034.48i	0.257083	−	0.190303i
$767$	−11924.2			−0.561355
$768$	−18717.8	+	7593.55i	−0.879451	+	0.356782i
$769$	42371.2			1.98692			0.993461	−	0.114170i	$-0.0364207\pi$
$769$	42371.2			1.98692			0.993461	+	0.114170i	$0.0364207\pi$
$770$	−8505.93	+	6296.41i	−0.398094	+	0.294684i
$771$		−	26516.7i		−	1.23862i
$772$	−2731.36	+	8945.27i	−0.127336	+	0.417030i
$773$		−	23093.3i		−	1.07453i	−0.843415	−	0.537263i	$-0.819458\pi$
$773$		−	23093.3i		−	1.07453i	0.843415	−	0.537263i	$-0.180542\pi$
$774$	1491.34	+	2014.68i	0.0692571	+	0.0935608i
$775$	10144.7			0.470203
$776$	789.032	+	2224.37i	0.0365008	+	0.102900i
$777$	−3778.51			−0.174457
$778$	9699.91	+	13103.8i	0.446991	+	0.603848i
$779$			17084.9i			0.785790i
$780$	28490.7	+	8699.35i	1.30786	+	0.399342i
$781$		−	32124.7i		−	1.47185i
$782$	7757.49	−	5742.38i	0.354741	−	0.262592i
$783$	−32856.9			−1.49963
$784$	16140.7	+	10870.3i	0.735272	+	0.495184i
$785$	−3968.12			−0.180418
$786$	3763.57	−	2785.94i	0.170792	−	0.126426i
$787$		−	18329.4i		−	0.830207i	−0.909774	−	0.415103i	$-0.863745\pi$
$787$		−	18329.4i		−	0.830207i	0.909774	−	0.415103i	$-0.136255\pi$
$788$	22693.3	+	6929.17i	1.02591	+	0.313251i
$789$		−	7658.98i		−	0.345585i
$790$	−16475.1	−	22256.5i	−0.741973	−	1.00234i
$791$	14118.8			0.634649
$792$	−2635.81	+	934.975i	−0.118257	+	0.0419481i
$793$	14085.7			0.630765
$794$	17499.5	+	23640.4i	0.782159	+	1.05663i
$795$			30587.6i			1.36457i
$796$	−3874.52	+	12689.2i	−0.172524	+	0.565020i
$797$		−	30003.1i		−	1.33346i	−0.745301	−	0.666728i	$-0.767694\pi$
$797$		−	30003.1i		−	1.33346i	0.745301	−	0.666728i	$-0.232306\pi$
$798$	10787.9	−	7985.62i	0.478557	−	0.354245i
$799$	−1703.71			−0.0754352
$800$	7969.55	−	355.079i	0.352208	−	0.0156924i
$801$	−810.123			−0.0357357
$802$	33187.2	−	24566.4i	1.46120	−	1.08163i
$803$		−	38787.6i		−	1.70459i
$804$	−354.108	+	1159.72i	−0.0155329	+	0.0508707i
$805$		−	16286.8i		−	0.713088i
$806$	−22495.4	−	30389.4i	−0.983084	−	1.32807i
$807$	14381.4			0.627322
$808$	17649.1	−	6260.51i	0.768432	−	0.272579i
$809$	24423.2			1.06140			0.530700	−	0.847560i	$-0.321929\pi$
$809$	24423.2			1.06140			0.530700	+	0.847560i	$0.321929\pi$
$810$	14210.6	+	19197.4i	0.616433	+	0.832751i
$811$		−	15938.4i		−	0.690101i	−0.938584	−	0.345051i	$-0.887862\pi$
$811$		−	15938.4i		−	0.690101i	0.938584	−	0.345051i	$-0.112138\pi$
$812$	10717.9	+	3272.62i	0.463209	+	0.141437i
$813$		−	19207.0i		−	0.828561i
$814$	12871.6	−	9528.07i	0.554239	−	0.410269i
$815$	33838.9			1.45439
$816$	2997.16	−	4450.31i	0.128580	−	0.190922i
$817$	50985.1			2.18328
$818$	5557.40	−	4113.80i	0.237543	−	0.175838i
$819$			971.282i			0.0414400i
$820$	11022.6	+	3365.65i	0.469422	+	0.143334i
$821$		−	7545.99i		−	0.320776i	−0.987054	−	0.160388i	$-0.948726\pi$
$821$		−	7545.99i		−	0.320776i	0.987054	−	0.160388i	$-0.0512745\pi$
$822$	−23256.8	−	31418.1i	−0.986830	−	1.33313i
$823$	−37736.8			−1.59832			−0.799162	−	0.601115i	$-0.794723\pi$
$823$	−37736.8			−1.59832			−0.799162	+	0.601115i	$0.794723\pi$
$824$	2387.36	+	6730.26i	0.100932	+	0.284538i
$825$	−10021.7			−0.422923
$826$	2156.30	+	2912.98i	0.0908320	+	0.122707i
$827$			27559.6i			1.15882i	0.815037	+	0.579408i	$0.196716\pi$
$827$			27559.6i			1.15882i	−0.815037	+	0.579408i	$0.803284\pi$
$828$	1256.94	−	4116.51i	0.0527556	−	0.172776i
$829$		−	12281.4i		−	0.514535i	−0.966340	−	0.257268i	$-0.917178\pi$
$829$		−	12281.4i		−	0.514535i	0.966340	−	0.257268i	$-0.0828222\pi$
$830$	−30509.6	+	22584.4i	−1.27591	+	0.944476i
$831$	10264.9			0.428501
$832$	−18735.8	−	23086.2i	−0.780706	−	0.961984i
$833$	−5169.02			−0.215001
$834$	21945.6	−	16245.0i	0.911168	−	0.674480i
$835$			9862.15i			0.408735i
$836$	−16612.6	+	54406.7i	−0.687270	+	2.25083i
$837$		−	33693.5i		−	1.39142i
$838$	13936.9	+	18827.7i	0.574515	+	0.776123i
$839$	36922.3			1.51931			0.759653	−	0.650328i	$-0.225369\pi$
$839$	36922.3			1.51931			0.759653	+	0.650328i	$0.225369\pi$
$840$	−3026.88	−	8533.14i	−0.124330	−	0.350502i
$841$	−26002.7			−1.06617
$842$	13476.2	+	18205.2i	0.551568	+	0.745124i
$843$		−	43471.2i		−	1.77607i
$844$	−11915.4	−	3638.25i	−0.485953	−	0.148381i
$845$			15280.9i			0.622103i
$846$	−610.663	+	452.036i	−0.0248168	+	0.0183703i
$847$	−4963.56			−0.201358
$848$	17053.6	−	25322.0i	0.690594	−	1.02542i
$849$	−10515.6			−0.425081
$850$	−1703.16	+	1260.74i	−0.0687269	+	0.0508742i
$851$			24646.2i			0.992784i
$852$	26286.2	+	8026.24i	1.05698	+	0.322740i
$853$		−	12211.8i		−	0.490182i	−0.969500	−	0.245091i	$-0.921182\pi$
$853$		−	12211.8i		−	0.490182i	0.969500	−	0.245091i	$-0.0788178\pi$
$854$	−2547.16	−	3441.00i	−0.102063	−	0.137879i
$855$	−5374.24			−0.214965
$856$	−1205.99	+	427.791i	−0.0481542	+	0.0170813i
$857$	−4453.87			−0.177528			−0.0887638	−	0.996053i	$-0.528292\pi$
$857$	−4453.87			−0.177528			−0.0887638	+	0.996053i	$0.528292\pi$
$858$	22222.7	+	30021.1i	0.884233	+	1.19453i
$859$			47189.3i			1.87436i	0.348841	+	0.937182i	$0.386575\pi$
$859$			47189.3i			1.87436i	−0.348841	+	0.937182i	$0.613425\pi$
$860$	10043.8	−	32893.9i	0.398247	−	1.30427i
$861$		−	3409.54i		−	0.134955i
$862$	8179.47	−	6054.75i	0.323195	−	0.239241i
$863$	−980.872			−0.0386898			−0.0193449	−	0.999813i	$-0.506158\pi$
$863$	−980.872			−0.0386898			−0.0193449	+	0.999813i	$0.506158\pi$
$864$	−1179.32	−	26469.3i	−0.0464368	−	1.04225i
$865$	15947.1			0.626840
$866$	−29457.4	+	21805.5i	−1.15589	+	0.855634i
$867$			1425.20i			0.0558275i
$868$	−3355.95	+	10990.8i	−0.131231	+	0.429785i
$869$		−	34720.2i		−	1.35536i
$870$	24223.0	+	32723.3i	0.943951	+	1.27520i
$871$	−1784.83			−0.0694335
$872$	2713.64	−	962.585i	0.105385	−	0.0373821i
$873$	−279.575			−0.0108387
$874$	−52088.0	−	70366.6i	−2.01591	−	2.72332i
$875$		−	6566.63i		−	0.253706i
$876$	31738.1	+	9690.94i	1.22412	+	0.373774i
$877$			20083.0i			0.773268i	0.922233	+	0.386634i	$0.126362\pi$
$877$			20083.0i			0.773268i	−0.922233	+	0.386634i	$0.873638\pi$
$878$	4169.83	−	3086.67i	0.160279	−	0.118645i
$879$	−25744.1			−0.987858
$880$	31828.8	+	21435.8i	1.21926	+	0.821136i
$881$	−5596.18			−0.214007			−0.107004	−	0.994259i	$-0.534126\pi$
$881$	−5596.18			−0.214007			−0.107004	+	0.994259i	$0.534126\pi$
$882$	−1852.74	+	1371.47i	−0.0707315	+	0.0523581i
$883$			7186.04i			0.273872i	0.990580	+	0.136936i	$0.0437255\pi$
$883$			7186.04i			0.273872i	−0.990580	+	0.136936i	$0.956274\pi$
$884$	7553.35	+	2306.35i	0.287383	+	0.0877498i
$885$			13166.9i			0.500115i
$886$	−18533.9	−	25037.8i	−0.702776	−	0.949393i
$887$	−3387.47			−0.128230			−0.0641151	−	0.997943i	$-0.520422\pi$
$887$	−3387.47			−0.128230			−0.0641151	+	0.997943i	$0.520422\pi$
$888$	4580.45	+	12912.8i	0.173097	+	0.487980i
$889$	−6013.59			−0.226872
$890$	6613.49	+	8934.29i	0.249084	+	0.336492i
$891$			29948.0i			1.12603i
$892$	−2307.35	+	7556.65i	−0.0866098	+	0.283650i
$893$			15454.0i			0.579112i
$894$	−19479.7	+	14419.6i	−0.728747	+	0.539446i
$895$	−7408.57			−0.276694
$896$	−2251.70	+	8751.75i	−0.0839554	+	0.326312i
$897$	−57483.3			−2.13970
$898$	5114.83	−	3786.19i	0.190071	−	0.140698i
$899$		−	51674.7i		−	1.91707i
$900$	−275.961	+	903.781i	−0.0102208	+	0.0334734i
$901$			8109.30i			0.299845i
$902$	8597.65	+	11614.7i	0.317373	+	0.428745i
$903$	−10174.8			−0.374968
$904$	−17115.4	−	48250.2i	−0.629699	−	1.77520i
$905$	−16322.8			−0.599546
$906$	−410.287	−	554.264i	−0.0150451	−	0.0203247i
$907$		−	28412.5i		−	1.04016i	−0.854119	−	0.520078i	$-0.825903\pi$
$907$		−	28412.5i		−	1.04016i	0.854119	−	0.520078i	$-0.174097\pi$
$908$	25237.2	+	7705.95i	0.922386	+	0.281642i
$909$			2218.27i			0.0809408i
$910$	10711.6	−	7929.13i	0.390205	−	0.288844i
$911$	7556.66			0.274823			0.137411	−	0.990514i	$-0.456122\pi$
$911$	7556.66			0.274823			0.137411	+	0.990514i	$0.456122\pi$
$912$	−40367.9	−	27186.6i	−1.46570	−	0.987104i
$913$	−47595.1			−1.72527
$914$	19319.9	−	14301.3i	0.699175	−	0.517555i
$915$		−	15553.6i		−	0.561953i
$916$	−37843.4	−	11555.1i	−1.36505	−	0.416804i
$917$		−	2094.85i		−	0.0754397i
$918$	4187.30	+	5656.70i	0.150546	+	0.203376i
$919$	−35062.1			−1.25853			−0.629266	−	0.777190i	$-0.716644\pi$
$919$	−35062.1			−1.25853			−0.629266	+	0.777190i	$0.716644\pi$
$920$	−55659.3	+	19743.5i	−1.99460	+	0.707527i
$921$	29582.7			1.05840
$922$	−2841.20	−	3838.23i	−0.101486	−	0.137099i
$923$			40455.0i			1.44268i
$924$	3315.28	−	10857.6i	0.118035	−	0.386569i
$925$		−	5411.07i		−	0.192340i
$926$	−33451.9	+	24762.4i	−1.18715	+	0.878771i
$927$	−845.907			−0.0299711
$928$	−1808.69	−	40595.1i	−0.0639799	−	1.43599i
$929$	−9636.63			−0.340331			−0.170166	−	0.985415i	$-0.554430\pi$
$929$	−9636.63			−0.340331			−0.170166	+	0.985415i	$0.554430\pi$
$930$	−33556.5	+	24839.8i	−1.18318	+	0.875837i
$931$			46887.1i			1.65055i
$932$	−562.454	+	1842.05i	−0.0197680	+	0.0647409i
$933$			11176.4i			0.392175i
$934$	−4163.93	−	5625.13i	−0.145876	−	0.197066i
$935$	−10193.1			−0.356524
$936$	3319.30	−	1177.42i	0.115913	−	0.0411168i
$937$	−43940.8			−1.53200			−0.766000	−	0.642841i	$-0.777756\pi$
$937$	−43940.8			−1.53200			−0.766000	+	0.642841i	$0.777756\pi$
$938$	322.756	+	436.017i	0.0112349	+	0.0151775i
$939$		−	19136.6i		−	0.665067i
$940$	9970.39	+	3044.36i	0.345955	+	0.105634i
$941$		−	12540.3i		−	0.434435i	−0.976123	−	0.217217i	$-0.930302\pi$
$941$		−	12540.3i		−	0.434435i	0.976123	−	0.217217i	$-0.0696981\pi$
$942$	3421.34	−	2532.61i	0.118337	−	0.0875974i
$943$	−22239.4			−0.767992
$944$	7341.00	−	10900.2i	0.253103	−	0.375819i
$945$	11876.2			0.408819
$946$	34660.9	−	25657.3i	1.19125	−	0.881807i
$947$			16789.1i			0.576105i	0.957615	+	0.288053i	$0.0930078\pi$
$947$			16789.1i			0.576105i	−0.957615	+	0.288053i	$0.906992\pi$
$948$	28410.0	+	8674.72i	0.973326	+	0.297196i
$949$			48845.7i			1.67081i
$950$	11435.9	+	15449.0i	0.390558	+	0.527612i
$951$	47037.0			1.60387
$952$	−802.478	−	2262.28i	−0.0273198	−	0.0770178i
$953$	35725.2			1.21432			0.607162	−	0.794578i	$-0.292308\pi$
$953$	35725.2			1.21432			0.607162	+	0.794578i	$0.292308\pi$
$954$	2151.60	+	2906.64i	0.0730195	+	0.0986434i
$955$		−	44924.9i		−	1.52224i
$956$	−6937.99	+	22722.1i	−0.234718	+	0.768709i
$957$			51048.5i			1.72431i
$958$	−27488.6	+	20348.1i	−0.927053	+	0.686239i
$959$	−17487.7			−0.588850
$960$	−25492.2	+	20688.4i	−0.857039	+	0.695536i
$961$	23199.4			0.778739
$962$	−16209.4	+	11998.8i	−0.543256	+	0.402138i
$963$		−	151.578i		−	0.00507220i
$964$	7986.14	−	26154.8i	0.266822	−	0.873849i
$965$			15201.7i			0.507109i
$966$	10394.9	+	14042.7i	0.346222	+	0.467717i
$967$	42242.7			1.40479			0.702396	−	0.711786i	$-0.252113\pi$
$967$	42242.7			1.40479			0.702396	+	0.711786i	$0.252113\pi$
$968$	6017.02	+	16962.7i	0.199787	+	0.563224i
$969$	12927.7			0.428584
$970$	2282.33	+	3083.24i	0.0755477	+	0.102059i
$971$			16296.9i			0.538611i	0.963055	+	0.269306i	$0.0867942\pi$
$971$			16296.9i			0.538611i	−0.963055	+	0.269306i	$0.913206\pi$
$972$	5732.38	+	1750.33i	0.189163	+	0.0577590i
$973$		−	12215.2i		−	0.402468i
$974$	−41268.4	+	30548.4i	−1.35762	+	1.00496i
$975$	12620.5			0.414542
$976$	−8671.66	+	12876.1i	−0.284399	+	0.422288i
$977$	−48093.1			−1.57486			−0.787428	−	0.616407i	$-0.788588\pi$
$977$	−48093.1			−1.57486			−0.787428	+	0.616407i	$0.788588\pi$
$978$	−29176.2	+	21597.3i	−0.953939	+	0.706141i
$979$			13937.5i			0.455000i
$980$	30250.0	+	9236.56i	0.986022	+	0.301073i
$981$			341.070i			0.0111004i
$982$	−5765.30	−	7788.45i	−0.187350	−	0.253095i
$983$	−9648.19			−0.313051			−0.156526	−	0.987674i	$-0.550029\pi$
$983$	−9648.19			−0.313051			−0.156526	+	0.987674i	$0.550029\pi$
$984$	−11651.9	+	4133.17i	−0.377488	+	0.133903i
$985$	38565.2			1.24750
$986$	6421.93	+	8675.51i	0.207420	+	0.280207i
$987$		−	3084.06i		−	0.0994596i
$988$	20920.4	−	68514.9i	0.673650	−	2.20622i
$989$			66367.4i			2.13383i
$990$	−3653.54	+	2704.48i	−0.117290	+	0.0868223i
$991$	999.925			0.0320521			0.0160261	−	0.999872i	$-0.494899\pi$
$991$	999.925			0.0320521			0.0160261	+	0.999872i	$0.494899\pi$
$992$	41628.7	−	1854.75i	1.33237	−	0.0593631i
$993$	40092.9			1.28128
$994$	9882.79	−	7315.61i	0.315355	−	0.233438i
$995$			21564.2i			0.687066i
$996$	11891.5	−	38944.9i	0.378308	−	1.23897i
$997$			13660.6i			0.433938i	0.976179	+	0.216969i	$0.0696170\pi$
$997$			13660.6i			0.433938i	−0.976179	+	0.216969i	$0.930383\pi$
$998$	−2157.12	−	2914.10i	−0.0684194	−	0.0924290i
$999$	−17971.8			−0.569171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.c.b.69.19	✓	24
4.3	odd	2		544.4.c.a.273.6		24
8.3	odd	2		544.4.c.a.273.19		24
8.5	even	2	inner	136.4.c.b.69.20	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.c.b.69.19	✓	24	1.1	even	1	trivial
136.4.c.b.69.20	yes	24	8.5	even	2	inner
544.4.c.a.273.6		24	4.3	odd	2
544.4.c.a.273.19		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)

\(f(q)\)	\(=\)	\(q+(2.27335 - 1.68282i) q^{2} +4.93150i q^{3} +(2.33624 - 7.65127i) q^{4} -13.0027i q^{5} +(8.29881 + 11.2110i) q^{6} +6.24020 q^{7} +(-7.56460 - 21.3255i) q^{8} +2.68034 q^{9} +O(q^{10})\)	\(q+(2.27335 - 1.68282i) q^{2} +4.93150i q^{3} +(2.33624 - 7.65127i) q^{4} -13.0027i q^{5} +(8.29881 + 11.2110i) q^{6} +6.24020 q^{7} +(-7.56460 - 21.3255i) q^{8} +2.68034 q^{9} +(-21.8811 - 29.5596i) q^{10} -46.1131i q^{11} +(37.7322 + 11.5212i) q^{12} +58.0707i q^{13} +(14.1862 - 10.5011i) q^{14} +64.1227 q^{15} +(-53.0839 - 35.7505i) q^{16} +17.0000 q^{17} +(6.09335 - 4.51053i) q^{18} -154.204i q^{19} +(-99.4870 - 30.3774i) q^{20} +30.7735i q^{21} +(-77.6000 - 104.831i) q^{22} +200.727 q^{23} +(105.167 - 37.3048i) q^{24} -44.0696 q^{25} +(97.7225 + 132.015i) q^{26} +146.368i q^{27} +(14.5786 - 47.7454i) q^{28} +224.481i q^{29} +(145.773 - 107.907i) q^{30} -230.196 q^{31} +(-180.840 + 8.05723i) q^{32} +227.407 q^{33} +(38.6470 - 28.6079i) q^{34} -81.1393i q^{35} +(6.26193 - 20.5080i) q^{36} +122.784i q^{37} +(-259.497 - 350.559i) q^{38} -286.376 q^{39} +(-277.289 + 98.3600i) q^{40} -110.794 q^{41} +(51.7862 + 69.9590i) q^{42} +330.635i q^{43} +(-352.824 - 107.731i) q^{44} -34.8516i q^{45} +(456.323 - 337.787i) q^{46} -100.218 q^{47} +(176.303 - 261.783i) q^{48} -304.060 q^{49} +(-100.186 + 74.1612i) q^{50} +83.8354i q^{51} +(444.315 + 135.667i) q^{52} +477.018i q^{53} +(246.312 + 332.747i) q^{54} -599.594 q^{55} +(-47.2046 - 133.075i) q^{56} +760.454 q^{57} +(377.761 + 510.324i) q^{58} +205.340i q^{59} +(149.806 - 490.620i) q^{60} -242.561i q^{61} +(-523.317 + 387.379i) q^{62} +16.7259 q^{63} +(-397.554 + 322.638i) q^{64} +755.075 q^{65} +(516.975 - 382.684i) q^{66} +30.7354i q^{67} +(39.7162 - 130.072i) q^{68} +989.884i q^{69} +(-136.543 - 184.458i) q^{70} +696.651 q^{71} +(-20.2757 - 57.1596i) q^{72} +841.141 q^{73} +(206.624 + 279.132i) q^{74} -217.329i q^{75} +(-1179.85 - 360.257i) q^{76} -287.755i q^{77} +(-651.032 + 481.918i) q^{78} +752.937 q^{79} +(-464.852 + 690.233i) q^{80} -649.447 q^{81} +(-251.875 + 186.447i) q^{82} -1032.14i q^{83} +(235.457 + 71.8944i) q^{84} -221.046i q^{85} +(556.399 + 751.649i) q^{86} -1107.03 q^{87} +(-983.385 + 348.827i) q^{88} -302.246 q^{89} +(-58.6489 - 79.2299i) q^{90} +362.373i q^{91} +(468.947 - 1535.82i) q^{92} -1135.21i q^{93} +(-227.831 + 168.649i) q^{94} -2005.06 q^{95} +(-39.7342 - 891.812i) q^{96} -104.306 q^{97} +(-691.235 + 511.678i) q^{98} -123.599i 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

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