LMFDB - Embedded newform 136.4.c.b.69.20

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

$q$-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	$-0.842617\pi$
$3$		−	4.93150i		−	0.949067i	0.880237	−	0.474533i	$-0.157383\pi$
$4$	2.33624	+	7.65127i	0.292031	+	0.956409i
$5$			13.0027i			1.16299i	0.813548	+	0.581497i	$0.197533\pi$
$5$			13.0027i			1.16299i	−0.813548	+	0.581497i	$0.802467\pi$
$6$	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	$0.217759\pi$
$11$			46.1131i			1.26397i	−0.774982	+	0.631983i	$0.782241\pi$
$12$	37.7322	−	11.5212i	0.907696	−	0.277157i
$13$		−	58.0707i		−	1.23892i	−0.785029	−	0.619458i	$-0.787352\pi$
$13$		−	58.0707i		−	1.23892i	0.785029	−	0.619458i	$-0.212648\pi$
$14$	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	$0.381033\pi$
$19$			154.204i			1.86193i	−0.365105	+	0.930966i	$0.618967\pi$
$20$	−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	$-0.744734\pi$
$29$		−	224.481i		−	1.43742i	0.695312	−	0.718708i	$-0.255266\pi$
$30$	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	$-0.912057\pi$
$37$		−	122.784i		−	0.545558i	0.962077	−	0.272779i	$-0.0879428\pi$
$38$	−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	$-0.800586\pi$
$43$		−	330.635i		−	1.17259i	0.810098	−	0.586295i	$-0.199414\pi$
$44$	−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	$-0.787884\pi$
$53$		−	477.018i		−	1.23629i	0.786064	−	0.618145i	$-0.212116\pi$
$54$	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	$-0.927255\pi$
$59$		−	205.340i		−	0.453101i	0.973999	−	0.226551i	$-0.0727449\pi$
$60$	149.806	+	490.620i	0.322332	+	1.05565i
$61$			242.561i			0.509126i	0.967056	+	0.254563i	$0.0819317\pi$
$61$			242.561i			0.509126i	−0.967056	+	0.254563i	$0.918068\pi$
$62$	−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	$-0.991079\pi$
$67$		−	30.7354i		−	0.0560437i	0.999607	−	0.0280219i	$-0.00892080\pi$
$68$	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	$0.239099\pi$
$83$			1032.14i			1.36496i	−0.730903	+	0.682481i	$0.760901\pi$
$84$	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	$-0.866340\pi$
$101$		−	827.606i		−	0.815345i	0.913128	−	0.407673i	$-0.133660\pi$
$102$	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	$0.00813276\pi$
$107$			56.5517i			0.0510941i	−0.999674	+	0.0255470i	$0.991867\pi$
$108$	1119.91	−	341.953i	0.997805	−	0.304670i
$109$		−	127.249i		−	0.111818i	−0.998436	−	0.0559092i	$-0.982194\pi$
$109$		−	127.249i		−	0.111818i	0.998436	−	0.0559092i	$-0.0178057\pi$
$110$	−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	$0.0357092\pi$
$131$			335.703i			0.223897i	−0.993714	+	0.111949i	$0.964291\pi$
$132$	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	$0.203737\pi$
$139$			1957.50i			1.19448i	−0.802061	+	0.597242i	$0.796263\pi$
$140$	−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	$-0.841481\pi$
$149$		−	1737.55i		−	0.955341i	0.878539	−	0.477671i	$-0.158519\pi$
$150$	−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	$0.0247149\pi$
$157$			305.177i			0.155132i	−0.996987	+	0.0775661i	$0.975285\pi$
$158$	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	$-0.784986\pi$
$163$		−	2602.46i		−	1.25055i	0.780403	−	0.625277i	$-0.215014\pi$
$164$	−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	$-0.913144\pi$
$173$		−	1226.44i		−	0.538987i	0.963002	−	0.269494i	$-0.0868564\pi$
$174$	−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	$0.0379552\pi$
$179$			569.772i			0.237915i	−0.992899	+	0.118957i	$0.962045\pi$
$180$	−266.659	+	81.4219i	−0.110420	+	0.0337157i
$181$			1255.34i			0.515519i	0.966209	+	0.257760i	$0.0829842\pi$
$181$			1255.34i			0.515519i	−0.966209	+	0.257760i	$0.917016\pi$
$182$	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	$-0.819809\pi$
$197$		−	2965.95i		−	1.07266i	0.844007	−	0.536332i	$-0.180191\pi$
$198$	−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	$0.0817631\pi$
$211$			1557.31i			0.508102i	−0.967191	+	0.254051i	$0.918237\pi$
$212$	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	$-0.839833\pi$
$227$		−	3298.43i		−	0.964426i	0.876054	−	0.482213i	$-0.160167\pi$
$228$	1776.61	+	5818.44i	0.516047	+	1.69007i
$229$			4946.03i			1.42726i	0.700522	+	0.713631i	$0.252951\pi$
$229$			4946.03i			1.42726i	−0.700522	+	0.713631i	$0.747049\pi$
$230$	−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	$0.0671405\pi$
$251$			1665.14i			0.418735i	−0.977837	+	0.209367i	$0.932860\pi$
$252$	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	$0.107215\pi$
$269$			2916.23i			0.660988i	−0.943808	+	0.330494i	$0.892785\pi$
$270$	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	$0.0724827\pi$
$277$			2081.49i			0.451497i	−0.974186	+	0.225748i	$0.927517\pi$
$278$	−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	$-0.928106\pi$
$283$		−	2132.33i		−	0.447893i	0.974601	−	0.223947i	$-0.0718941\pi$
$284$	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	$-0.825769\pi$
$293$		−	5220.34i		−	1.04087i	0.853900	−	0.520436i	$-0.174231\pi$
$294$	−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	$0.188277\pi$
$307$			5998.74i			1.11520i	−0.830110	+	0.557599i	$0.811723\pi$
$308$	−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	$0.320383\pi$
$317$			9538.08i			1.68994i	−0.534811	+	0.844972i	$0.679617\pi$
$318$	−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	$0.235865\pi$
$331$			8129.96i			1.35004i	−0.737799	+	0.675020i	$0.764135\pi$
$332$	−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	$-0.894169\pi$
$347$		−	4219.47i		−	0.652775i	0.945236	−	0.326387i	$-0.105831\pi$
$348$	−2586.29	−	8470.17i	−0.398389	−	1.30474i
$349$		−	7342.58i		−	1.12619i	−0.826393	−	0.563093i	$-0.809611\pi$
$349$		−	7342.58i		−	1.12619i	0.826393	−	0.563093i	$-0.190389\pi$
$350$	−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	$0.00593903\pi$
$373$			268.803i			0.0373139i	−0.999826	+	0.0186569i	$0.994061\pi$
$374$	−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	$0.280464\pi$
$379$			11383.9i			1.54288i	−0.636300	+	0.771442i	$0.719536\pi$
$380$	−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	$-0.877422\pi$
$389$		−	5764.09i		−	0.751288i	0.926764	−	0.375644i	$-0.122578\pi$
$390$	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	$-0.771693\pi$
$397$		−	10398.9i		−	1.31463i	0.753617	−	0.657314i	$-0.228307\pi$
$398$	−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	$-0.839615\pi$
$419$		−	8281.90i		−	0.965626i	0.875723	−	0.482813i	$-0.160385\pi$
$420$	934.820	+	3061.57i	0.108606	+	0.355688i
$421$		−	8008.11i		−	0.927058i	−0.886082	−	0.463529i	$-0.846583\pi$
$421$		−	8008.11i		−	0.927058i	0.886082	−	0.463529i	$-0.153417\pi$
$422$	−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	$0.201110\pi$
$443$			11013.6i			1.18120i	−0.806963	+	0.590602i	$0.798890\pi$
$444$	−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	$0.0271807\pi$
$461$			1688.36i			0.170574i	−0.996356	+	0.0852870i	$0.972819\pi$
$462$	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	$0.0391206\pi$
$467$			2474.38i			0.245183i	−0.992457	+	0.122592i	$0.960879\pi$
$468$	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	$0.0503261\pi$
$491$			3425.98i			0.314893i	−0.987528	+	0.157446i	$0.949674\pi$
$492$	−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	$0.0183125\pi$
$499$			1281.85i			0.114997i	−0.998346	+	0.0574985i	$0.981688\pi$
$500$	−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	$-0.690587\pi$
$509$		−	18971.8i		−	1.65208i	0.563609	−	0.826042i	$-0.309413\pi$
$510$	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	$0.268036\pi$
$523$			17845.6i			1.49203i	−0.665928	+	0.746016i	$0.731964\pi$
$524$	−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	$0.108030\pi$
$541$			8378.16i			0.665814i	−0.942960	+	0.332907i	$0.891970\pi$
$542$	−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	$0.00124584\pi$
$547$			100.144i			0.00782784i	−0.999992	+	0.00391392i	$0.998754\pi$
$548$	−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	$0.278164\pi$
$557$			20160.8i			1.53365i	−0.641857	+	0.766824i	$0.721836\pi$
$558$	−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	$-0.927289\pi$
$563$		−	6050.08i		−	0.452896i	0.974023	−	0.226448i	$-0.0727114\pi$
$564$	−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	$-0.817481\pi$
$571$		−	14803.9i		−	1.08498i	0.840061	−	0.542492i	$-0.182519\pi$
$572$	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	$-0.945863\pi$
$587$		−	4814.34i		−	0.338517i	0.985572	−	0.169258i	$-0.0541372\pi$
$588$	−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	$-0.946588\pi$
$613$		−	5069.53i		−	0.334023i	0.985955	−	0.167012i	$-0.0534118\pi$
$614$	−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	$-0.792603\pi$
$619$		−	18678.6i		−	1.21285i	0.795140	−	0.606426i	$-0.207397\pi$
$620$	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	$-0.952695\pi$
$643$		−	4828.45i		−	0.296136i	0.988977	−	0.148068i	$-0.0473055\pi$
$644$	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	$-0.987113\pi$
$653$		−	1350.75i		−	0.0809480i	0.999181	−	0.0404740i	$-0.0128868\pi$
$654$	−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	$-0.914567\pi$
$659$		−	8972.32i		−	0.530367i	0.964198	−	0.265184i	$-0.0854326\pi$
$660$	−22624.0	+	6908.03i	−1.33430	+	0.407416i
$661$		−	8276.84i		−	0.487038i	−0.969896	−	0.243519i	$-0.921698\pi$
$661$		−	8276.84i		−	0.487038i	0.969896	−	0.243519i	$-0.0783018\pi$
$662$	−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	$-0.880064\pi$
$677$		−	12962.5i		−	0.735878i	0.929850	−	0.367939i	$-0.119936\pi$
$678$	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	$0.172397\pi$
$683$			18403.4i			1.03102i	−0.856884	+	0.515510i	$0.827603\pi$
$684$	−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	$0.151385\pi$
$691$			16633.5i			0.915727i	−0.889022	+	0.457864i	$0.848615\pi$
$692$	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	$0.334824\pi$
$701$			32233.4i			1.73672i	−0.495939	+	0.868358i	$0.665176\pi$
$702$	−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	$0.256094\pi$
$709$			27204.5i			1.44103i	−0.693442	+	0.720513i	$0.743906\pi$
$710$	−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	$0.0670359\pi$
$733$			8297.14i			0.418093i	−0.977906	+	0.209046i	$0.932964\pi$
$734$	−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	$-0.882752\pi$
$739$		−	14467.2i		−	0.720144i	0.932925	−	0.360072i	$-0.117248\pi$
$740$	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	$0.156283\pi$
$757$			19640.1i			0.942977i	−0.881872	+	0.471488i	$0.843717\pi$
$758$	−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	$0.180542\pi$
$773$			23093.3i			1.07453i	−0.843415	+	0.537263i	$0.819458\pi$
$774$	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	$0.136255\pi$
$787$			18329.4i			0.830207i	−0.909774	+	0.415103i	$0.863745\pi$
$788$	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	$0.232306\pi$
$797$			30003.1i			1.33346i	−0.745301	+	0.666728i	$0.767694\pi$
$798$	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	$0.112138\pi$
$811$			15938.4i			0.690101i	−0.938584	+	0.345051i	$0.887862\pi$
$812$	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	$0.0512745\pi$
$821$			7545.99i			0.320776i	−0.987054	+	0.160388i	$0.948726\pi$
$822$	−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	$-0.803284\pi$
$827$		−	27559.6i		−	1.15882i	0.815037	−	0.579408i	$-0.196716\pi$
$828$	1256.94	+	4116.51i	0.0527556	+	0.172776i
$829$			12281.4i			0.514535i	0.966340	+	0.257268i	$0.0828222\pi$
$829$			12281.4i			0.514535i	−0.966340	+	0.257268i	$0.917178\pi$
$830$	−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	$0.0788178\pi$
$853$			12211.8i			0.490182i	−0.969500	+	0.245091i	$0.921182\pi$
$854$	−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	$-0.613425\pi$
$859$		−	47189.3i		−	1.87436i	0.348841	−	0.937182i	$-0.386575\pi$
$860$	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	$-0.873638\pi$
$877$		−	20083.0i		−	0.773268i	0.922233	−	0.386634i	$-0.126362\pi$
$878$	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	$-0.956274\pi$
$883$		−	7186.04i		−	0.273872i	0.990580	−	0.136936i	$-0.0437255\pi$
$884$	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	$0.174097\pi$
$907$			28412.5i			1.04016i	−0.854119	+	0.520078i	$0.825903\pi$
$908$	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	$0.0696981\pi$
$941$			12540.3i			0.434435i	−0.976123	+	0.217217i	$0.930302\pi$
$942$	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	$-0.906992\pi$
$947$		−	16789.1i		−	0.576105i	0.957615	−	0.288053i	$-0.0930078\pi$
$948$	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	$-0.913206\pi$
$971$		−	16296.9i		−	0.538611i	0.963055	−	0.269306i	$-0.0867942\pi$
$972$	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	$-0.930383\pi$
$997$		−	13660.6i		−	0.433938i	0.976179	−	0.216969i	$-0.0696170\pi$
$998$	−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.69.20	yes	24
4.3	odd	2		544.4.c.a.273.19		24
8.3	odd	2		544.4.c.a.273.6		24
8.5	even	2	inner	136.4.c.b.69.19	✓	24

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

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