LMFDB - Embedded newform 136.4.c.b.69.5

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			69.5
Character	$\chi$	$=$	136.69
Dual form			136.4.c.b.69.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.13166 - 1.85904i) q^{2} -3.55140i q^{3} +(1.08798 + 7.92567i) q^{4} +10.8958i q^{5} +(-6.60218 + 7.57039i) q^{6} -8.16814 q^{7} +(12.4149 - 18.9175i) q^{8} +14.3876 q^{9} +O(q^{10})$	\(q+(-2.13166 - 1.85904i) q^{2} -3.55140i q^{3} +(1.08798 + 7.92567i) q^{4} +10.8958i q^{5} +(-6.60218 + 7.57039i) q^{6} -8.16814 q^{7} +(12.4149 - 18.9175i) q^{8} +14.3876 q^{9} +(20.2557 - 23.2263i) q^{10} -62.6144i q^{11} +(28.1472 - 3.86383i) q^{12} -14.7826i q^{13} +(17.4117 + 15.1849i) q^{14} +38.6955 q^{15} +(-61.6326 + 17.2459i) q^{16} +17.0000 q^{17} +(-30.6694 - 26.7470i) q^{18} -64.7762i q^{19} +(-86.3568 + 11.8544i) q^{20} +29.0083i q^{21} +(-116.402 + 133.473i) q^{22} -62.3580 q^{23} +(-67.1834 - 44.0903i) q^{24} +6.28076 q^{25} +(-27.4814 + 31.5115i) q^{26} -146.984i q^{27} +(-8.88673 - 64.7380i) q^{28} -152.875i q^{29} +(-82.4857 - 71.9362i) q^{30} -97.7896 q^{31} +(163.441 + 77.8148i) q^{32} -222.369 q^{33} +(-36.2383 - 31.6036i) q^{34} -88.9987i q^{35} +(15.6533 + 114.031i) q^{36} -146.380i q^{37} +(-120.421 + 138.081i) q^{38} -52.4989 q^{39} +(206.121 + 135.271i) q^{40} +172.887 q^{41} +(53.9275 - 61.8360i) q^{42} -271.920i q^{43} +(496.261 - 68.1229i) q^{44} +156.764i q^{45} +(132.926 + 115.926i) q^{46} +331.783 q^{47} +(61.2470 + 218.882i) q^{48} -276.282 q^{49} +(-13.3885 - 11.6761i) q^{50} -60.3738i q^{51} +(117.162 - 16.0831i) q^{52} +465.834i q^{53} +(-273.248 + 313.320i) q^{54} +682.236 q^{55} +(-101.407 + 154.520i) q^{56} -230.046 q^{57} +(-284.199 + 325.877i) q^{58} -252.139i q^{59} +(42.0997 + 306.688i) q^{60} -490.851i q^{61} +(208.455 + 181.794i) q^{62} -117.520 q^{63} +(-203.740 - 469.717i) q^{64} +161.069 q^{65} +(474.015 + 413.391i) q^{66} +527.722i q^{67} +(18.4956 + 134.736i) q^{68} +221.458i q^{69} +(-165.452 + 189.715i) q^{70} +743.115 q^{71} +(178.620 - 272.176i) q^{72} -804.814 q^{73} +(-272.126 + 312.034i) q^{74} -22.3055i q^{75} +(513.395 - 70.4749i) q^{76} +511.443i q^{77} +(111.910 + 97.5973i) q^{78} +1003.28 q^{79} +(-187.908 - 671.539i) q^{80} -133.534 q^{81} +(-368.536 - 321.403i) q^{82} +133.183i q^{83} +(-229.911 + 31.5603i) q^{84} +185.229i q^{85} +(-505.509 + 579.641i) q^{86} -542.919 q^{87} +(-1184.50 - 777.352i) q^{88} +1441.82 q^{89} +(291.431 - 334.169i) q^{90} +120.746i q^{91} +(-67.8440 - 494.229i) q^{92} +347.290i q^{93} +(-707.249 - 616.796i) q^{94} +705.791 q^{95} +(276.352 - 580.443i) q^{96} -1551.80 q^{97} +(588.939 + 513.617i) q^{98} -900.868i 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 $

$2$	−2.13166	−	1.85904i	−0.753657	−	0.657268i
$2$	−2.13166	−	1.85904i	−0.753657	−	0.657268i
$3$		−	3.55140i		−	0.683467i	−0.939797	−	0.341734i	$-0.888986\pi$
$3$		−	3.55140i		−	0.683467i	0.939797	−	0.341734i	$-0.111014\pi$
$4$	1.08798	+	7.92567i	0.135997	+	0.990709i
$5$			10.8958i			0.974553i	0.873248	+	0.487277i	$0.162010\pi$
$5$			10.8958i			0.974553i	−0.873248	+	0.487277i	$0.837990\pi$
$6$	−6.60218	+	7.57039i	−0.449221	+	0.515100i
$7$	−8.16814			−0.441038			−0.220519	−	0.975383i	$-0.570775\pi$
$7$	−8.16814			−0.441038			−0.220519	+	0.975383i	$0.570775\pi$
$8$	12.4149	−	18.9175i	0.548667	−	0.836041i
$9$	14.3876			0.532873
$10$	20.2557	−	23.2263i	0.640543	−	0.734479i
$11$		−	62.6144i		−	1.71627i	−0.513426	−	0.858134i	$-0.671624\pi$
$11$		−	62.6144i		−	1.71627i	0.513426	−	0.858134i	$-0.328376\pi$
$12$	28.1472	−	3.86383i	0.677117	−	0.0929494i
$13$		−	14.7826i		−	0.315381i	−0.987489	−	0.157690i	$-0.949595\pi$
$13$		−	14.7826i		−	0.315381i	0.987489	−	0.157690i	$-0.0504048\pi$
$14$	17.4117	+	15.1849i	0.332391	+	0.289880i
$15$	38.6955			0.666075
$16$	−61.6326	+	17.2459i	−0.963010	+	0.269467i
$17$	17.0000			0.242536
$17$	17.0000			0.242536
$18$	−30.6694	−	26.7470i	−0.401603	−	0.350240i
$19$		−	64.7762i		−	0.782142i	−0.920361	−	0.391071i	$-0.872105\pi$
$19$		−	64.7762i		−	0.782142i	0.920361	−	0.391071i	$-0.127895\pi$
$20$	−86.3568	+	11.8544i	−0.965499	+	0.132536i
$21$			29.0083i			0.301435i
$22$	−116.402	+	133.473i	−1.12805	+	1.29348i
$23$	−62.3580			−0.565328			−0.282664	−	0.959219i	$-0.591218\pi$
$23$	−62.3580			−0.565328			−0.282664	+	0.959219i	$0.591218\pi$
$24$	−67.1834	−	44.0903i	−0.571407	−	0.374996i
$25$	6.28076			0.0502460
$26$	−27.4814	+	31.5115i	−0.207290	+	0.237689i
$27$		−	146.984i		−	1.04767i
$28$	−8.88673	−	64.7380i	−0.0599798	−	0.436940i
$29$		−	152.875i		−	0.978900i	−0.872031	−	0.489450i	$-0.837198\pi$
$29$		−	152.875i		−	0.978900i	0.872031	−	0.489450i	$-0.162802\pi$
$30$	−82.4857	−	71.9362i	−0.501992	−	0.437790i
$31$	−97.7896			−0.566566			−0.283283	−	0.959036i	$-0.591424\pi$
$31$	−97.7896			−0.566566			−0.283283	+	0.959036i	$0.591424\pi$
$32$	163.441	+	77.8148i	0.902891	+	0.429870i
$33$	−222.369			−1.17301
$34$	−36.2383	−	31.6036i	−0.182789	−	0.159411i
$35$		−	88.9987i		−	0.429815i
$36$	15.6533	+	114.031i	0.0724690	+	0.527922i
$37$		−	146.380i		−	0.650400i	−0.945645	−	0.325200i	$-0.894568\pi$
$37$		−	146.380i		−	0.650400i	0.945645	−	0.325200i	$-0.105432\pi$
$38$	−120.421	+	138.081i	−0.514077	+	0.589466i
$39$	−52.4989			−0.215553
$40$	206.121	+	135.271i	0.814767	+	0.534705i
$41$	172.887			0.658546			0.329273	−	0.944235i	$-0.393196\pi$
$41$	172.887			0.658546			0.329273	+	0.944235i	$0.393196\pi$
$42$	53.9275	−	61.8360i	0.198124	−	0.227179i
$43$		−	271.920i		−	0.964358i	−0.876073	−	0.482179i	$-0.839846\pi$
$43$		−	271.920i		−	0.964358i	0.876073	−	0.482179i	$-0.160154\pi$
$44$	496.261	−	68.1229i	1.70032	−	0.233407i
$45$			156.764i			0.519313i
$46$	132.926	+	115.926i	0.426063	+	0.371572i
$47$	331.783			1.02969			0.514846	−	0.857283i	$-0.327849\pi$
$47$	331.783			1.02969			0.514846	+	0.857283i	$0.327849\pi$
$48$	61.2470	+	218.882i	0.184172	+	0.658186i
$49$	−276.282			−0.805485
$50$	−13.3885	−	11.6761i	−0.0378683	−	0.0330251i
$51$		−	60.3738i		−	0.165765i
$52$	117.162	−	16.0831i	0.312451	−	0.0428908i
$53$			465.834i			1.20731i	0.797247	+	0.603653i	$0.206289\pi$
$53$			465.834i			1.20731i	−0.797247	+	0.603653i	$0.793711\pi$
$54$	−273.248	+	313.320i	−0.688599	+	0.789582i
$55$	682.236			1.67259
$56$	−101.407	+	154.520i	−0.241983	+	0.368726i
$57$	−230.046			−0.534568
$58$	−284.199	+	325.877i	−0.643400	+	0.737754i
$59$		−	252.139i		−	0.556369i	−0.960528	−	0.278184i	$-0.910267\pi$
$59$		−	252.139i		−	0.556369i	0.960528	−	0.278184i	$-0.0897326\pi$
$60$	42.0997	+	306.688i	0.0905841	+	0.659887i
$61$		−	490.851i		−	1.03028i	−0.857107	−	0.515139i	$-0.827740\pi$
$61$		−	490.851i		−	1.03028i	0.857107	−	0.515139i	$-0.172260\pi$
$62$	208.455	+	181.794i	0.426996	+	0.372386i
$63$	−117.520			−0.235017
$64$	−203.740	−	469.717i	−0.397930	−	0.917416i
$65$	161.069			0.307356
$66$	474.015	+	413.391i	0.884049	+	0.770984i
$67$			527.722i			0.962262i	0.876649	+	0.481131i	$0.159774\pi$
$67$			527.722i			0.962262i	−0.876649	+	0.481131i	$0.840226\pi$
$68$	18.4956	+	134.736i	0.0329841	+	0.240282i
$69$			221.458i			0.386383i
$70$	−165.452	+	189.715i	−0.282504	+	0.323933i
$71$	743.115			1.24213			0.621067	−	0.783757i	$-0.286699\pi$
$71$	743.115			1.24213			0.621067	+	0.783757i	$0.286699\pi$
$72$	178.620	−	272.176i	0.292369	−	0.445503i
$73$	−804.814			−1.29036			−0.645181	−	0.764030i	$-0.723218\pi$
$73$	−804.814			−1.29036			−0.645181	+	0.764030i	$0.723218\pi$
$74$	−272.126	+	312.034i	−0.427487	+	0.490178i
$75$		−	22.3055i		−	0.0343415i
$76$	513.395	−	70.4749i	0.774875	−	0.106369i
$77$			511.443i			0.756939i
$78$	111.910	+	97.5973i	0.162453	+	0.141676i
$79$	1003.28			1.42883			0.714416	−	0.699722i	$-0.246693\pi$
$79$	1003.28			1.42883			0.714416	+	0.699722i	$0.246693\pi$
$80$	−187.908	−	671.539i	−0.262610	−	0.938504i
$81$	−133.534			−0.183174
$82$	−368.536	−	321.403i	−0.496318	−	0.432841i
$83$			133.183i			0.176130i	0.996115	+	0.0880649i	$0.0280683\pi$
$83$			133.183i			0.176130i	−0.996115	+	0.0880649i	$0.971932\pi$
$84$	−229.911	+	31.5603i	−0.298634	+	0.0409942i
$85$			185.229i			0.236364i
$86$	−505.509	+	579.641i	−0.633842	+	0.726795i
$87$	−542.919			−0.669046
$88$	−1184.50	−	777.352i	−1.43487	−	0.941659i
$89$	1441.82			1.71722			0.858612	−	0.512626i	$-0.171327\pi$
$89$	1441.82			1.71722			0.858612	+	0.512626i	$0.171327\pi$
$90$	291.431	−	334.169i	0.341328	−	0.391383i
$91$			120.746i			0.139095i
$92$	−67.8440	−	494.229i	−0.0768829	−	0.560076i
$93$			347.290i			0.387229i
$94$	−707.249	−	616.796i	−0.776034	−	0.676783i
$95$	705.791			0.762239
$96$	276.352	−	580.443i	0.293802	−	0.617096i
$97$	−1551.80			−1.62434			−0.812172	−	0.583418i	$-0.801715\pi$
$97$	−1551.80			−1.62434			−0.812172	+	0.583418i	$0.801715\pi$
$98$	588.939	+	513.617i	0.607060	+	0.529420i
$99$		−	900.868i		−	0.914552i
$100$	6.83331	+	49.7792i	0.00683331	+	0.0497792i
$101$			543.224i			0.535176i	0.963533	+	0.267588i	$0.0862267\pi$
$101$			543.224i			0.535176i	−0.963533	+	0.267588i	$0.913773\pi$
$102$	−112.237	+	128.697i	−0.108952	+	0.124930i
$103$	−1488.80			−1.42423			−0.712114	−	0.702064i	$-0.752262\pi$
$103$	−1488.80			−1.42423			−0.712114	+	0.702064i	$0.752262\pi$
$104$	−279.649	−	183.525i	−0.263671	−	0.173039i
$105$	−316.070			−0.293764
$106$	866.002	−	993.002i	0.793524	−	0.909895i
$107$		−	908.313i		−	0.820654i	−0.911939	−	0.410327i	$-0.865415\pi$
$107$		−	908.313i		−	0.820654i	0.911939	−	0.410327i	$-0.134585\pi$
$108$	1164.95	−	159.915i	1.03793	−	0.142480i
$109$			305.670i			0.268605i	0.990940	+	0.134302i	$0.0428793\pi$
$109$			305.670i			0.268605i	−0.990940	+	0.134302i	$0.957121\pi$
$110$	−1454.30	−	1268.30i	−1.26056	−	1.09934i
$111$	−519.855			−0.444527
$112$	503.424	−	140.867i	0.424724	−	0.118845i
$113$	725.219			0.603742			0.301871	−	0.953349i	$-0.402389\pi$
$113$	725.219			0.603742			0.301871	+	0.953349i	$0.402389\pi$
$114$	490.381	+	427.664i	0.402881	+	0.351355i
$115$		−	679.443i		−	0.550942i
$116$	1211.63	−	166.324i	0.969805	−	0.133127i
$117$		−	212.685i		−	0.168058i
$118$	−468.736	+	537.476i	−0.365683	+	0.419311i
$119$	−138.858			−0.106967
$120$	480.401	−	732.020i	0.365453	−	0.556866i
$121$	−2589.56			−1.94558
$122$	−912.509	+	1046.33i	−0.677169	+	0.776476i
$123$		−	613.990i		−	0.450095i
$124$	−106.393	−	775.049i	−0.0770512	−	0.561302i
$125$			1430.41i			1.02352i
$126$	250.512	+	218.473i	0.177122	+	0.154469i
$127$	−1291.13			−0.902122			−0.451061	−	0.892493i	$-0.648954\pi$
$127$	−1291.13			−0.902122			−0.451061	+	0.892493i	$0.648954\pi$
$128$	−438.916	+	1380.04i	−0.303086	+	0.952963i
$129$	−965.696			−0.659107
$130$	−343.344	−	299.432i	−0.231641	−	0.202015i
$131$			2814.64i			1.87722i	0.344976	+	0.938611i	$0.387887\pi$
$131$			2814.64i			1.87722i	−0.344976	+	0.938611i	$0.612113\pi$
$132$	−241.932	−	1762.42i	−0.159526	−	1.16211i
$133$			529.101i			0.344954i
$134$	981.054	−	1124.93i	0.632464	−	0.725215i
$135$	1601.51			1.02101
$136$	211.054	−	321.597i	0.133071	−	0.202770i
$137$	−306.014			−0.190836			−0.0954181	−	0.995437i	$-0.530419\pi$
$137$	−306.014			−0.190836			−0.0954181	+	0.995437i	$0.530419\pi$
$138$	411.699	−	472.074i	0.253957	−	0.291200i
$139$			696.538i			0.425033i	0.977157	+	0.212516i	$0.0681659\pi$
$139$			696.538i			0.425033i	−0.977157	+	0.212516i	$0.931834\pi$
$140$	705.375	−	96.8284i	0.425822	−	0.0584535i
$141$		−	1178.29i		−	0.703760i
$142$	−1584.07	−	1381.48i	−0.936143	−	0.816416i
$143$	−925.603			−0.541278
$144$	−886.743	+	248.126i	−0.513161	+	0.143591i
$145$	1665.70			0.953990
$146$	1715.59	+	1496.18i	0.972489	+	0.848113i
$147$			981.186i			0.550523i
$148$	1160.16	−	159.258i	0.644357	−	0.0884523i
$149$		−	997.878i		−	0.548654i	−0.961637	−	0.274327i	$-0.911545\pi$
$149$		−	997.878i		−	0.548654i	0.961637	−	0.274327i	$-0.0884550\pi$
$150$	−41.4667	+	47.5478i	−0.0225716	+	0.0258817i
$151$	2915.88			1.57146			0.785732	−	0.618567i	$-0.212287\pi$
$151$	2915.88			1.57146			0.785732	+	0.618567i	$0.212287\pi$
$152$	−1225.40	−	804.191i	−0.653903	−	0.429135i
$153$	244.588			0.129241
$154$	950.790	−	1090.22i	0.497512	−	0.570472i
$155$		−	1065.50i		−	0.552148i
$156$	−57.1175	−	416.089i	−0.0293145	−	0.213550i
$157$			2928.25i			1.48853i	0.667884	+	0.744266i	$0.267200\pi$
$157$			2928.25i			1.48853i	−0.667884	+	0.744266i	$0.732800\pi$
$158$	−2138.65	−	1865.13i	−1.07685	−	0.939125i
$159$	1654.36			0.825155
$160$	−847.858	+	1780.82i	−0.418931	+	0.879915i
$161$	509.349			0.249331
$162$	284.650	+	248.245i	0.138051	+	0.120395i
$163$			1964.51i			0.944001i	0.881598	+	0.472000i	$0.156468\pi$
$163$			1964.51i			0.944001i	−0.881598	+	0.472000i	$0.843532\pi$
$164$	188.097	+	1370.24i	0.0895602	+	0.652428i
$165$		−	2422.89i		−	1.14316i
$166$	247.593	−	283.902i	0.115765	−	0.132741i
$167$	−925.453			−0.428825			−0.214412	−	0.976743i	$-0.568784\pi$
$167$	−925.453			−0.428825			−0.214412	+	0.976743i	$0.568784\pi$
$168$	548.764	+	360.136i	0.252012	+	0.165387i
$169$	1978.48			0.900535
$170$	344.348	−	394.846i	0.155354	−	0.178137i
$171$		−	931.972i		−	0.416782i
$172$	2155.15	−	295.842i	0.955398	−	0.131150i
$173$			1838.45i			0.807947i	0.914771	+	0.403974i	$0.132371\pi$
$173$			1838.45i			0.807947i	−0.914771	+	0.403974i	$0.867629\pi$
$174$	1157.32	+	1009.31i	0.504231	+	0.439743i
$175$	−51.3021			−0.0221604
$176$	1079.84	+	3859.09i	0.462477	+	1.65278i
$177$	−895.448			−0.380260
$178$	−3073.48	−	2680.40i	−1.29420	−	1.12868i
$179$		−	276.597i		−	0.115496i	−0.998331	−	0.0577481i	$-0.981608\pi$
$179$		−	276.597i		−	0.115496i	0.998331	−	0.0577481i	$-0.0183920\pi$
$180$	−1242.46	+	170.556i	−0.514488	+	0.0706249i
$181$		−	855.586i		−	0.351355i	−0.984448	−	0.175677i	$-0.943788\pi$
$181$		−	855.586i		−	0.351355i	0.984448	−	0.175677i	$-0.0562115\pi$
$182$	224.472	−	257.390i	0.0914227	−	0.104830i
$183$	−1743.21			−0.704162
$184$	−774.169	+	1179.65i	−0.310177	+	0.472638i
$185$	1594.94			0.633849
$186$	645.624	−	740.305i	0.254513	−	0.291838i
$187$		−	1064.44i		−	0.416256i
$188$	360.971	+	2629.60i	0.140035	+	1.02012i
$189$			1200.58i			0.462061i
$190$	−1504.51	−	1312.09i	−0.574466	−	0.500995i
$191$	−3467.50			−1.31361			−0.656805	−	0.754061i	$-0.728092\pi$
$191$	−3467.50			−1.31361			−0.656805	+	0.754061i	$0.728092\pi$
$192$	−1668.15	+	723.562i	−0.627024	+	0.271972i
$193$	3613.66			1.34776			0.673879	−	0.738842i	$-0.264627\pi$
$193$	3613.66			1.34776			0.673879	+	0.738842i	$0.264627\pi$
$194$	3307.91	+	2884.85i	1.22420	+	1.06763i
$195$		−	572.019i		−	0.210067i
$196$	−300.587	−	2189.72i	−0.109544	−	0.798002i
$197$		−	2374.00i		−	0.858580i	−0.903167	−	0.429290i	$-0.858764\pi$
$197$		−	2374.00i		−	0.858580i	0.903167	−	0.429290i	$-0.141236\pi$
$198$	−1674.75	+	1920.35i	−0.601106	+	0.689258i
$199$	−694.972			−0.247564			−0.123782	−	0.992309i	$-0.539502\pi$
$199$	−694.972			−0.247564			−0.123782	+	0.992309i	$0.539502\pi$
$200$	77.9750	−	118.816i	0.0275683	−	0.0420078i
$201$	1874.15			0.657674
$202$	1009.87	−	1157.97i	0.351754	−	0.403339i
$203$			1248.70i			0.431732i
$204$	478.503	−	65.6852i	0.164225	−	0.0225435i
$205$			1883.75i			0.641788i
$206$	3173.61	+	2767.73i	1.07338	+	0.936100i
$207$	−897.180			−0.301248
$208$	254.939	+	911.090i	0.0849847	+	0.303715i
$209$	−4055.92			−1.34236
$210$	673.755	+	587.585i	0.221398	+	0.193082i
$211$		−	2722.73i		−	0.888343i	−0.895942	−	0.444171i	$-0.853498\pi$
$211$		−	2722.73i		−	0.888343i	0.895942	−	0.444171i	$-0.146502\pi$
$212$	−3692.05	+	506.816i	−1.19609	+	0.164190i
$213$		−	2639.10i		−	0.848958i
$214$	−1688.59	+	1936.22i	−0.539390	+	0.618491i
$215$	2962.79			0.939818
$216$	−2780.56	−	1824.79i	−0.875894	−	0.574821i
$217$	798.759			0.249877
$218$	568.252	−	651.586i	0.176545	−	0.202436i
$219$			2858.22i			0.881920i
$220$	742.256	+	5407.18i	0.227468	+	1.65705i
$221$		−	251.304i		−	0.0764911i
$222$	1108.16	+	966.429i	0.335021	+	0.292173i
$223$	−3688.64			−1.10767			−0.553834	−	0.832627i	$-0.686836\pi$
$223$	−3688.64			−1.10767			−0.553834	+	0.832627i	$0.686836\pi$
$224$	−1335.01	−	635.602i	−0.398209	−	0.189589i
$225$	90.3647			0.0267747
$226$	−1545.92	−	1348.21i	−0.455014	−	0.396820i
$227$			2572.44i			0.752153i	0.926589	+	0.376077i	$0.122727\pi$
$227$			2572.44i			0.752153i	−0.926589	+	0.376077i	$0.877273\pi$
$228$	−250.285	−	1823.27i	−0.0726996	−	0.529602i
$229$		−	2963.31i		−	0.855115i	−0.903988	−	0.427557i	$-0.859374\pi$
$229$		−	2963.31i		−	0.855115i	0.903988	−	0.427557i	$-0.140626\pi$
$230$	−1263.11	+	1448.34i	−0.362117	+	0.415221i
$231$	1816.34			0.517343
$232$	−2892.00	−	1897.92i	−0.818401	−	0.537090i
$233$	1152.67			0.324093			0.162047	−	0.986783i	$-0.448190\pi$
$233$	1152.67			0.324093			0.162047	+	0.986783i	$0.448190\pi$
$234$	−395.390	+	453.374i	−0.110459	+	0.126658i
$235$			3615.05i			1.00349i
$236$	1998.37	−	274.321i	0.551200	−	0.0756644i
$237$		−	3563.04i		−	0.976559i
$238$	295.999	+	258.143i	0.0806167	+	0.0703063i
$239$	−4065.47			−1.10031			−0.550154	−	0.835063i	$-0.685431\pi$
$239$	−4065.47			−1.10031			−0.550154	+	0.835063i	$0.685431\pi$
$240$	−2384.90	+	667.337i	−0.641437	+	0.179485i
$241$	3377.66			0.902797			0.451398	−	0.892323i	$-0.350925\pi$
$241$	3377.66			0.902797			0.451398	+	0.892323i	$0.350925\pi$
$242$	5520.07	+	4814.08i	1.46630	+	1.27876i
$243$		−	3494.33i		−	0.922475i
$244$	3890.32	−	534.033i	1.02071	−	0.140115i
$245$		−	3010.32i		−	0.784988i
$246$	−1141.43	+	1308.82i	−0.295833	+	0.339217i
$247$	−957.561			−0.246673
$248$	−1214.05	+	1849.93i	−0.310856	+	0.473672i
$249$	472.987			0.120379
$250$	2659.19	−	3049.16i	0.672728	−	0.771383i
$251$		−	1268.26i		−	0.318933i	−0.987203	−	0.159466i	$-0.949023\pi$
$251$		−	1268.26i		−	0.318933i	0.987203	−	0.159466i	$-0.0509773\pi$
$252$	−127.858	−	931.422i	−0.0319616	−	0.232834i
$253$			3904.51i			0.970254i
$254$	2752.26	+	2400.26i	0.679890	+	0.592936i
$255$	657.823			0.161547
$256$	3501.16	−	2125.82i	0.854775	−	0.518998i
$257$	2731.82			0.663059			0.331529	−	0.943445i	$-0.392435\pi$
$257$	2731.82			0.663059			0.331529	+	0.943445i	$0.392435\pi$
$258$	2058.54	+	1795.26i	0.496740	+	0.433210i
$259$			1195.66i			0.286851i
$260$	175.239	+	1276.58i	0.0417994	+	0.304500i
$261$		−	2199.49i		−	0.521629i
$262$	5232.51	−	5999.86i	1.23384	−	1.41478i
$263$	3061.53			0.717802			0.358901	−	0.933376i	$-0.383152\pi$
$263$	3061.53			0.717802			0.358901	+	0.933376i	$0.383152\pi$
$264$	−2760.69	+	4206.65i	−0.643593	+	0.980687i
$265$	−5075.65			−1.17658
$266$	983.618	−	1127.87i	0.226727	−	0.259977i
$267$		−	5120.49i		−	1.17367i
$268$	−4182.56	+	574.149i	−0.953322	+	0.130865i
$269$		−	7702.94i		−	1.74594i	−0.487778	−	0.872968i	$-0.662192\pi$
$269$		−	7702.94i		−	1.74594i	0.487778	−	0.872968i	$-0.337808\pi$
$270$	−3413.88	−	2977.27i	−0.769490	−	0.671076i
$271$	1948.45			0.436752			0.218376	−	0.975865i	$-0.429924\pi$
$271$	1948.45			0.436752			0.218376	+	0.975865i	$0.429924\pi$
$272$	−1047.75	+	293.180i	−0.233564	+	0.0653553i
$273$	428.818			0.0950669
$274$	652.319	+	568.891i	0.143825	+	0.125431i
$275$		−	393.266i		−	0.0862357i
$276$	−1755.21	+	240.941i	−0.382793	+	0.0525469i
$277$		−	6832.34i		−	1.48201i	−0.671502	−	0.741003i	$-0.734350\pi$
$277$		−	6832.34i		−	1.48201i	0.671502	−	0.741003i	$-0.265650\pi$
$278$	1294.89	−	1484.78i	0.279361	−	0.320329i
$279$	−1406.95			−0.301907
$280$	−1683.63	−	1104.91i	−0.359343	−	0.235825i
$281$	4671.00			0.991632			0.495816	−	0.868427i	$-0.334869\pi$
$281$	4671.00			0.991632			0.495816	+	0.868427i	$0.334869\pi$
$282$	−2190.49	+	2511.72i	−0.462559	+	0.530394i
$283$		−	644.053i		−	0.135283i	−0.997710	−	0.0676413i	$-0.978453\pi$
$283$		−	644.053i		−	0.135283i	0.997710	−	0.0676413i	$-0.0215473\pi$
$284$	808.491	+	5889.69i	0.168926	+	1.23059i
$285$		−	2506.55i		−	0.520965i
$286$	1973.07	+	1720.73i	0.407938	+	0.355765i
$287$	−1412.16			−0.290444
$288$	2351.51	+	1119.57i	0.481126	+	0.229066i
$289$	289.000			0.0588235
$290$	−3550.70	−	3096.59i	−0.718981	−	0.627027i
$291$			5511.06i			1.11019i
$292$	−875.618	−	6378.69i	−0.175485	−	1.27837i
$293$			3630.67i			0.723912i	0.932195	+	0.361956i	$0.117891\pi$
$293$			3630.67i			0.723912i	−0.932195	+	0.361956i	$0.882109\pi$
$294$	1824.06	−	2091.56i	0.361841	−	0.414905i
$295$	2747.27			0.542211
$296$	−2769.14	−	1817.30i	−0.543761	−	0.356853i
$297$	−9203.30			−1.79808
$298$	−1855.09	+	2127.14i	−0.360613	+	0.413496i
$299$			921.813i			0.178294i
$300$	176.786	−	24.2678i	0.0340225	−	0.00467034i
$301$			2221.08i			0.425318i
$302$	−6215.67	−	5420.72i	−1.18434	−	1.03287i
$303$	1929.21			0.365775
$304$	1117.12	+	3992.33i	0.210761	+	0.753210i
$305$	5348.23			1.00406
$306$	−521.380	−	454.699i	−0.0974030	−	0.0849457i
$307$		−	2681.36i		−	0.498480i	−0.968442	−	0.249240i	$-0.919819\pi$
$307$		−	2681.36i		−	0.498480i	0.968442	−	0.249240i	$-0.0801808\pi$
$308$	−4053.53	+	556.437i	−0.749907	+	0.102941i
$309$			5287.31i			0.973414i
$310$	−1980.80	+	2271.29i	−0.362910	+	0.416130i
$311$	−9120.00			−1.66285			−0.831427	−	0.555634i	$-0.812476\pi$
$311$	−9120.00			−1.66285			−0.831427	+	0.555634i	$0.812476\pi$
$312$	−651.769	+	993.145i	−0.118267	+	0.180211i
$313$	5442.81			0.982895			0.491447	−	0.870907i	$-0.336468\pi$
$313$	5442.81			0.982895			0.491447	+	0.870907i	$0.336468\pi$
$314$	5443.71	−	6242.03i	0.978364	−	1.12184i
$315$		−	1280.47i		−	0.229037i
$316$	1091.54	+	7951.66i	0.194317	+	1.41556i
$317$		−	6144.16i		−	1.08861i	−0.838886	−	0.544307i	$-0.816793\pi$
$317$		−	6144.16i		−	1.08861i	0.838886	−	0.544307i	$-0.183207\pi$
$318$	−3526.55	−	3075.52i	−0.621883	−	0.542348i
$319$	−9572.15			−1.68005
$320$	5117.96	−	2219.92i	0.894071	−	0.387803i
$321$	−3225.78			−0.560890
$322$	−1085.76	−	946.898i	−0.187910	−	0.163877i
$323$		−	1101.20i		−	0.189697i
$324$	−145.282	−	1058.35i	−0.0249111	−	0.181472i
$325$		−	92.8458i		−	0.0158466i
$326$	3652.09	−	4187.67i	0.620462	−	0.711453i
$327$	1085.56			0.183583
$328$	2146.37	−	3270.58i	0.361322	−	0.550571i
$329$	−2710.05			−0.454133
$330$	−4504.24	+	5164.79i	−0.751365	+	0.861553i
$331$			11144.8i			1.85068i	0.379136	+	0.925341i	$0.376221\pi$
$331$			11144.8i			1.85068i	−0.379136	+	0.925341i	$0.623779\pi$
$332$	−1055.57	+	144.900i	−0.174493	+	0.0239531i
$333$		−	2106.06i		−	0.346580i
$334$	1972.75	+	1720.45i	0.323187	+	0.281853i
$335$	−5749.98			−0.937775
$336$	−500.274	−	1787.86i	−0.0812267	−	0.290285i
$337$	−9184.27			−1.48457			−0.742283	−	0.670086i	$-0.766257\pi$
$337$	−9184.27			−1.48457			−0.742283	+	0.670086i	$0.766257\pi$
$338$	−4217.44	−	3678.06i	−0.678694	−	0.591893i
$339$		−	2575.54i		−	0.412638i
$340$	−1468.07	+	201.525i	−0.234168	+	0.0321447i
$341$			6123.04i			0.972378i
$342$	−1732.57	+	1986.65i	−0.273937	+	0.314110i
$343$	5058.38			0.796288
$344$	−5144.03	−	3375.86i	−0.806243	−	0.529111i
$345$	−2412.97			−0.376551
$346$	3417.75	−	3918.96i	0.531038	−	0.608915i
$347$		−	4093.64i		−	0.633309i	−0.948541	−	0.316654i	$-0.897441\pi$
$347$		−	4093.64i		−	0.633309i	0.948541	−	0.316654i	$-0.102559\pi$
$348$	−590.682	−	4303.00i	−0.0909882	−	0.662830i
$349$			4922.14i			0.754946i	0.926021	+	0.377473i	$0.123207\pi$
$349$			4922.14i			0.754946i	−0.926021	+	0.377473i	$0.876793\pi$
$350$	109.359	+	95.3724i	0.0167013	+	0.0145653i
$351$	−2172.80			−0.330415
$352$	4872.33	−	10233.7i	0.737773	−	1.54960i
$353$	4771.76			0.719476			0.359738	−	0.933053i	$-0.382866\pi$
$353$	4771.76			0.719476			0.359738	+	0.933053i	$0.382866\pi$
$354$	1908.79	+	1664.67i	0.286585	+	0.249933i
$355$			8096.86i			1.21053i
$356$	1568.67	+	11427.4i	0.233537	+	1.70127i
$357$			493.142i			0.0731087i
$358$	−514.204	+	589.612i	−0.0759120	+	0.0870445i
$359$	13204.6			1.94126			0.970631	−	0.240573i	$-0.0773355\pi$
$359$	13204.6			1.94126			0.970631	+	0.240573i	$0.0773355\pi$
$360$	2965.58	+	1946.22i	0.434167	+	0.284930i
$361$	2663.04			0.388255
$362$	−1590.56	+	1823.82i	−0.230934	+	0.264801i
$363$			9196.57i			1.32974i
$364$	−956.995	+	131.369i	−0.137803	+	0.0189165i
$365$		−	8769.12i		−	1.25753i
$366$	3715.93	+	3240.68i	0.530696	+	0.462823i
$367$	3524.61			0.501317			0.250658	−	0.968076i	$-0.419353\pi$
$367$	3524.61			0.501317			0.250658	+	0.968076i	$0.419353\pi$
$368$	3843.29	−	1075.42i	0.544416	−	0.152337i
$369$	2487.42			0.350921
$370$	−3399.87	−	2965.04i	−0.477705	−	0.416609i
$371$		−	3805.00i		−	0.532468i
$372$	−2752.51	+	377.843i	−0.383631	+	0.0526619i
$373$			12367.5i			1.71680i	0.512980	+	0.858401i	$0.328542\pi$
$373$			12367.5i			1.71680i	−0.512980	+	0.858401i	$0.671458\pi$
$374$	−1978.84	+	2269.04i	−0.273592	+	0.313714i
$375$	5079.97			0.699543
$376$	4119.05	−	6276.48i	0.564957	−	0.860864i
$377$	−2259.88			−0.308726
$378$	2231.93	−	2559.24i	0.303698	−	0.348236i
$379$		−	8198.03i		−	1.11109i	−0.831485	−	0.555547i	$-0.812509\pi$
$379$		−	8198.03i		−	1.11109i	0.831485	−	0.555547i	$-0.187491\pi$
$380$	767.883	+	5593.87i	0.103662	+	0.755157i
$381$			4585.33i			0.616571i
$382$	7391.54	+	6446.20i	0.990011	+	0.863394i
$383$	7613.13			1.01570			0.507849	−	0.861446i	$-0.330441\pi$
$383$	7613.13			1.01570			0.507849	+	0.861446i	$0.330441\pi$
$384$	4901.07	+	1558.76i	0.651319	+	0.207149i
$385$	−5572.60			−0.737678
$386$	−7703.11	−	6717.93i	−1.01575	−	0.885838i
$387$		−	3912.26i		−	0.513880i
$388$	−1688.32	−	12299.1i	−0.220906	−	1.60925i
$389$			9953.39i			1.29732i	0.761079	+	0.648659i	$0.224670\pi$
$389$			9953.39i			1.29732i	−0.761079	+	0.648659i	$0.775330\pi$
$390$	−1063.40	+	1219.35i	−0.138071	+	0.158319i
$391$	−1060.09			−0.137112
$392$	−3430.01	+	5226.54i	−0.441943	+	0.673419i
$393$	9995.91			1.28302
$394$	−4413.34	+	5060.56i	−0.564317	+	0.647074i
$395$			10931.6i			1.39247i
$396$	7139.99	−	980.122i	0.906055	−	0.124376i
$397$			6307.36i			0.797374i	0.917087	+	0.398687i	$0.130534\pi$
$397$			6307.36i			0.797374i	−0.917087	+	0.398687i	$0.869466\pi$
$398$	1481.45	+	1291.98i	0.186578	+	0.162716i
$399$	1879.05			0.235765
$400$	−387.099	+	108.317i	−0.0483874	+	0.0135396i
$401$	9352.81			1.16473			0.582365	−	0.812927i	$-0.302127\pi$
$401$	9352.81			1.16473			0.582365	+	0.812927i	$0.302127\pi$
$402$	−3995.06	−	3484.12i	−0.495661	−	0.432269i
$403$			1445.58i			0.178684i
$404$	−4305.42	+	591.014i	−0.530204	+	0.0727823i
$405$		−	1454.97i		−	0.178513i
$406$	2321.38	−	2661.81i	0.283764	−	0.325378i
$407$	−9165.52			−1.11626
$408$	−1142.12	−	749.535i	−0.138586	−	0.0909498i
$409$	5388.82			0.651492			0.325746	−	0.945457i	$-0.394385\pi$
$409$	5388.82			0.651492			0.325746	+	0.945457i	$0.394385\pi$
$410$	3501.95	−	4015.51i	0.421827	−	0.483688i
$411$			1086.78i			0.130430i
$412$	−1619.77	−	11799.7i	−0.193691	−	1.41100i
$413$			2059.51i			0.245380i
$414$	1912.48	+	1667.89i	0.227037	+	0.198001i
$415$	−1451.14			−0.171648
$416$	1150.30	−	2416.08i	0.135573	−	0.284755i
$417$	2473.68			0.290496
$418$	8645.86	+	7540.11i	1.01168	+	0.882293i
$419$		−	8630.30i		−	1.00625i	−0.864214	−	0.503124i	$-0.832184\pi$
$419$		−	8630.30i		−	1.00625i	0.864214	−	0.503124i	$-0.167816\pi$
$420$	−343.876	−	2505.07i	−0.0399511	−	0.291035i
$421$			13664.5i			1.58187i	0.611902	+	0.790933i	$0.290404\pi$
$421$			13664.5i			1.58187i	−0.611902	+	0.790933i	$0.709596\pi$
$422$	−5061.65	+	5803.94i	−0.583879	+	0.669505i
$423$	4773.54			0.548694
$424$	8812.40	+	5783.29i	1.00936	+	0.662409i
$425$	106.773			0.0121865
$426$	−4906.18	+	5625.67i	−0.557993	+	0.639823i
$427$			4009.34i			0.454392i
$428$	7198.99	−	988.222i	0.813029	−	0.111606i
$429$			3287.19i			0.369946i
$430$	−6315.68	−	5507.94i	−0.708300	−	0.617713i
$431$	−13628.8			−1.52315			−0.761575	−	0.648076i	$-0.775574\pi$
$431$	−13628.8			−1.52315			−0.761575	+	0.648076i	$0.775574\pi$
$432$	2534.86	+	9059.00i	0.282312	+	1.00891i
$433$	−5448.76			−0.604736			−0.302368	−	0.953191i	$-0.597777\pi$
$433$	−5448.76			−0.604736			−0.302368	+	0.953191i	$0.597777\pi$
$434$	−1702.69	−	1484.92i	−0.188321	−	0.164236i
$435$		−	5915.55i		−	0.652021i
$436$	−2422.64	+	332.562i	−0.266109	+	0.0365294i
$437$			4039.32i			0.442167i
$438$	5313.53	−	6092.76i	0.579658	−	0.664665i
$439$	6254.85			0.680017			0.340009	−	0.940422i	$-0.389570\pi$
$439$	6254.85			0.680017			0.340009	+	0.940422i	$0.389570\pi$
$440$	8469.90	−	12906.2i	0.917697	−	1.39836i
$441$	−3975.02			−0.429221
$442$	−467.183	+	535.695i	−0.0502752	+	0.0576480i
$443$		−	557.355i		−	0.0597759i	−0.999553	−	0.0298880i	$-0.990485\pi$
$443$		−	557.355i		−	0.0597759i	0.999553	−	0.0298880i	$-0.00951505\pi$
$444$	−565.590	−	4120.20i	−0.0604543	−	0.440397i
$445$			15709.9i			1.67353i
$446$	7862.95	+	6857.32i	0.834801	+	0.728035i
$447$	−3543.87			−0.374987
$448$	1664.18	+	3836.71i	0.175502	+	0.404615i
$449$	−3343.54			−0.351429			−0.175714	−	0.984441i	$-0.556224\pi$
$449$	−3343.54			−0.351429			−0.175714	+	0.984441i	$0.556224\pi$
$450$	−192.627	−	167.991i	−0.0201790	−	0.0175982i
$451$		−	10825.2i		−	1.13024i
$452$	789.020	+	5747.85i	0.0821070	+	0.598133i
$453$		−	10355.5i		−	1.07404i
$454$	4782.26	−	5483.57i	0.494366	−	0.566865i
$455$	−1315.63			−0.135555
$456$	−2856.01	+	4351.89i	−0.293300	+	0.446921i
$457$	−10730.8			−1.09839			−0.549197	−	0.835693i	$-0.685066\pi$
$457$	−10730.8			−1.09839			−0.549197	+	0.835693i	$0.685066\pi$
$458$	−5508.91	+	6316.79i	−0.562040	+	0.644463i
$459$		−	2498.72i		−	0.254097i
$460$	5385.04	−	739.217i	0.545824	−	0.0749264i
$461$		−	1708.56i		−	0.172615i	−0.996269	−	0.0863075i	$-0.972493\pi$
$461$		−	1708.56i		−	0.172615i	0.996269	−	0.0863075i	$-0.0275067\pi$
$462$	−3871.82	−	3376.64i	−0.389899	−	0.340033i
$463$	−4187.54			−0.420328			−0.210164	−	0.977666i	$-0.567400\pi$
$463$	−4187.54			−0.420328			−0.210164	+	0.977666i	$0.567400\pi$
$464$	2636.46	+	9422.06i	0.263781	+	0.942690i
$465$	−3784.02			−0.377375
$466$	−2457.10	−	2142.85i	−0.244255	−	0.213016i
$467$			6587.33i			0.652731i	0.945244	+	0.326365i	$0.105824\pi$
$467$			6587.33i			0.652731i	−0.945244	+	0.326365i	$0.894176\pi$
$468$	1685.67	−	231.396i	0.166496	−	0.0228553i
$469$		−	4310.51i		−	0.424394i
$470$	6720.51	−	7706.07i	0.659561	−	0.756286i
$471$	10399.4			1.01736
$472$	−4769.83	−	3130.29i	−0.465147	−	0.305261i
$473$	−17026.1			−1.65510
$474$	−6623.82	+	7595.21i	−0.641861	+	0.735990i
$475$		−	406.844i		−	0.0392995i
$476$	−151.074	−	1100.55i	−0.0145472	−	0.105974i
$477$			6702.22i			0.643341i
$478$	8666.21	+	7557.85i	0.829254	+	0.723197i
$479$	−3409.47			−0.325224			−0.162612	−	0.986690i	$-0.551992\pi$
$479$	−3409.47			−0.325224			−0.162612	+	0.986690i	$0.551992\pi$
$480$	6324.41	+	3011.08i	0.601393	+	0.286326i
$481$	−2163.88			−0.205124
$482$	−7200.03	−	6279.18i	−0.680399	−	0.593380i
$483$		−	1808.90i		−	0.170410i
$484$	−2817.38	−	20524.0i	−0.264592	−	1.92750i
$485$		−	16908.2i		−	1.58301i
$486$	−6496.08	+	7448.73i	−0.606313	+	0.695229i
$487$	−894.451			−0.0832268			−0.0416134	−	0.999134i	$-0.513250\pi$
$487$	−894.451			−0.0832268			−0.0416134	+	0.999134i	$0.513250\pi$
$488$	−9285.64	−	6093.87i	−0.861355	−	0.565280i
$489$	6976.75			0.645194
$490$	−5596.29	+	6416.98i	−0.515948	+	0.591612i
$491$		−	7512.03i		−	0.690455i	−0.938519	−	0.345227i	$-0.887802\pi$
$491$		−	7512.03i		−	0.690455i	0.938519	−	0.345227i	$-0.112198\pi$
$492$	4866.29	−	668.006i	0.445913	−	0.0612115i
$493$		−	2598.87i		−	0.237418i
$494$	2041.20	+	1780.14i	0.185906	+	0.162130i
$495$	9815.71			0.891280
$496$	6027.03	−	1686.47i	0.545608	−	0.152671i
$497$	−6069.87			−0.547829
$498$	−1008.25	−	879.300i	−0.0907244	−	0.0791213i
$499$			6479.68i			0.581303i	0.956829	+	0.290652i	$0.0938721\pi$
$499$			6479.68i			0.581303i	−0.956829	+	0.290652i	$0.906128\pi$
$500$	−11337.0	+	1556.25i	−1.01401	+	0.139196i
$501$			3286.65i			0.293088i
$502$	−2357.75	+	2703.51i	−0.209624	+	0.240366i
$503$	17759.8			1.57430			0.787149	−	0.616763i	$-0.211556\pi$
$503$	17759.8			1.57430			0.787149	+	0.616763i	$0.211556\pi$
$504$	−1459.00	+	2223.17i	−0.128946	+	0.196484i
$505$	−5918.88			−0.521558
$506$	7258.62	−	8323.10i	0.637717	−	0.731239i
$507$		−	7026.36i		−	0.615486i
$508$	−1404.72	−	10233.1i	−0.122686	−	0.893740i
$509$		−	5606.99i		−	0.488262i	−0.969742	−	0.244131i	$-0.921497\pi$
$509$		−	5606.99i		−	0.488262i	0.969742	−	0.244131i	$-0.0785027\pi$
$510$	−1402.26	−	1222.92i	−0.121751	−	0.106180i
$511$	6573.83			0.569098
$512$	−11415.3	−	1977.26i	−0.985328	−	0.170670i
$513$	−9521.06			−0.819425
$514$	−5823.31	−	5078.54i	−0.499719	−	0.435807i
$515$		−	16221.7i		−	1.38799i
$516$	−1050.65	−	7653.79i	−0.0896365	−	0.652983i
$517$		−	20774.4i		−	1.76723i
$518$	2222.77	−	2548.73i	0.188538	−	0.216187i
$519$	6529.08			0.552205
$520$	1999.65	−	3047.01i	0.168636	−	0.256962i
$521$	−10440.6			−0.877952			−0.438976	−	0.898499i	$-0.644659\pi$
$521$	−10440.6			−0.877952			−0.438976	+	0.898499i	$0.644659\pi$
$522$	−4088.93	+	4688.58i	−0.342850	+	0.393129i
$523$		−	1098.83i		−	0.0918712i	−0.998944	−	0.0459356i	$-0.985373\pi$
$523$		−	1098.83i		−	0.0918712i	0.998944	−	0.0459356i	$-0.0146269\pi$
$524$	−22307.9	+	3062.26i	−1.85978	+	0.255296i
$525$			182.194i			0.0151459i
$526$	−6526.14	−	5691.49i	−0.540976	−	0.471788i
$527$	−1662.42			−0.137412
$528$	13705.2	−	3834.94i	1.12962	−	0.316088i
$529$	−8278.48			−0.680404
$530$	10819.6	+	9435.82i	0.886741	+	0.773332i
$531$		−	3627.67i		−	0.296474i
$532$	−4193.48	+	575.649i	−0.341749	+	0.0469127i
$533$		−	2555.71i		−	0.207693i
$534$	−9519.17	+	10915.2i	−0.771414	+	0.884541i
$535$	9896.83			0.799771
$536$	9983.16	+	6551.63i	0.804490	+	0.527961i
$537$	−982.307			−0.0789379
$538$	−14320.0	+	16420.1i	−1.14755	+	1.31584i
$539$			17299.2i			1.38243i
$540$	1742.40	+	12693.1i	0.138854	+	1.01152i
$541$			3257.62i			0.258884i	0.991587	+	0.129442i	$0.0413186\pi$
$541$			3257.62i			0.258884i	−0.991587	+	0.129442i	$0.958681\pi$
$542$	−4153.44	−	3622.24i	−0.329161	−	0.287063i
$543$	−3038.53			−0.240139
$544$	2778.49	+	1322.85i	0.218983	+	0.104259i
$545$	−3330.54			−0.261770
$546$	−914.096	−	797.188i	−0.0716478	−	0.0624844i
$547$		−	2889.22i		−	0.225840i	−0.993604	−	0.112920i	$-0.963980\pi$
$547$		−	2889.22i		−	0.225840i	0.993604	−	0.112920i	$-0.0360203\pi$
$548$	−332.936	−	2425.37i	−0.0259531	−	0.189063i
$549$		−	7062.14i		−	0.549007i
$550$	−731.095	+	838.310i	−0.0566800	+	0.0649921i
$551$	−9902.64			−0.765638
$552$	4189.43	+	2749.38i	0.323032	+	0.211996i
$553$	−8194.92			−0.630169
$554$	−12701.6	+	14564.3i	−0.974076	+	1.11692i
$555$		−	5664.26i		−	0.433215i
$556$	−5520.53	+	757.816i	−0.421084	+	0.0578032i
$557$		−	25031.9i		−	1.90419i	−0.305798	−	0.952096i	$-0.598923\pi$
$557$		−	25031.9i		−	1.90419i	0.305798	−	0.952096i	$-0.401077\pi$
$558$	2999.15	+	2615.58i	0.227534	+	0.198434i
$559$	−4019.68			−0.304140
$560$	1534.86	+	5485.22i	0.115821	+	0.413916i
$561$	−3780.27			−0.284497
$562$	−9957.01	−	8683.56i	−0.747350	−	0.651769i
$563$			18498.5i			1.38476i	0.721533	+	0.692380i	$0.243438\pi$
$563$			18498.5i			1.38476i	−0.721533	+	0.692380i	$0.756562\pi$
$564$	9338.77	−	1281.95i	0.697222	−	0.0957092i
$565$			7901.87i			0.588379i
$566$	−1197.32	+	1372.90i	−0.0889169	+	0.101957i
$567$	1090.72			0.0807868
$568$	9225.71	−	14057.8i	0.681518	−	1.03848i
$569$	20011.7			1.47440			0.737200	−	0.675675i	$-0.236148\pi$
$569$	20011.7			1.47440			0.737200	+	0.675675i	$0.236148\pi$
$570$	−4659.76	+	5343.11i	−0.342414	+	0.392629i
$571$		−	17149.0i		−	1.25685i	−0.777870	−	0.628426i	$-0.783700\pi$
$571$		−	17149.0i		−	1.25685i	0.777870	−	0.628426i	$-0.216300\pi$
$572$	−1007.03	−	7336.02i	−0.0736121	−	0.536249i
$573$			12314.5i			0.897809i
$574$	3010.26	+	2625.26i	0.218895	+	0.190899i
$575$	−391.655			−0.0284055
$576$	−2931.32	−	6758.08i	−0.212046	−	0.488866i
$577$	18141.8			1.30893			0.654467	−	0.756091i	$-0.272893\pi$
$577$	18141.8			1.30893			0.654467	+	0.756091i	$0.272893\pi$
$578$	−616.051	−	537.261i	−0.0443327	−	0.0386628i
$579$		−	12833.6i		−	0.921148i
$580$	1812.24	+	13201.8i	0.129740	+	0.945127i
$581$		−	1087.86i		−	0.0776799i
$582$	10245.3	−	11747.7i	0.729690	−	0.836699i
$583$	29167.9			2.07206
$584$	−9991.70	+	15225.0i	−0.707978	+	1.07880i
$585$	2317.38			0.163781
$586$	6749.55	−	7739.37i	0.475804	−	0.545581i
$587$		−	11305.4i		−	0.794929i	−0.917618	−	0.397464i	$-0.869890\pi$
$587$		−	11305.4i		−	0.794929i	0.917618	−	0.397464i	$-0.130110\pi$
$588$	−7776.56	+	1067.51i	−0.545408	+	0.0748694i
$589$			6334.44i			0.443134i
$590$	−5856.25	−	5107.27i	−0.408641	−	0.356378i
$591$	−8431.01			−0.586811
$592$	2524.46	+	9021.81i	0.175261	+	0.626341i
$593$	14549.2			1.00753			0.503764	−	0.863841i	$-0.331948\pi$
$593$	14549.2			1.00753			0.503764	+	0.863841i	$0.331948\pi$
$594$	19618.3	+	17109.3i	1.35513	+	1.18182i
$595$		−	1512.98i		−	0.104245i
$596$	7908.86	−	1085.67i	0.543556	−	0.0746152i
$597$			2468.12i			0.169202i
$598$	1713.68	−	1964.99i	0.117187	−	0.134372i
$599$	11416.9			0.778765			0.389383	−	0.921076i	$-0.372688\pi$
$599$	11416.9			0.778765			0.389383	+	0.921076i	$0.372688\pi$
$600$	−421.963	−	276.921i	−0.0287109	−	0.0188421i
$601$	22910.6			1.55498			0.777491	−	0.628894i	$-0.216492\pi$
$601$	22910.6			1.55498			0.777491	+	0.628894i	$0.216492\pi$
$602$	4129.06	−	4734.59i	0.279548	−	0.320544i
$603$			7592.64i			0.512763i
$604$	3172.40	+	23110.3i	0.213714	+	1.55686i
$605$		−	28215.4i		−	1.89607i
$606$	−4112.42	−	3586.46i	−0.275669	−	0.240413i
$607$	−8585.05			−0.574064			−0.287032	−	0.957921i	$-0.592669\pi$
$607$	−8585.05			−0.574064			−0.287032	+	0.957921i	$0.592669\pi$
$608$	5040.55	−	10587.1i	0.336219	−	0.706188i
$609$	4434.64			0.295075
$610$	−11400.6	−	9942.55i	−0.756717	−	0.659938i
$611$		−	4904.61i		−	0.324745i
$612$	266.106	+	1938.53i	0.0175763	+	0.128040i
$613$			24711.6i			1.62821i	0.580717	+	0.814106i	$0.302772\pi$
$613$			24711.6i			1.62821i	−0.580717	+	0.814106i	$0.697228\pi$
$614$	−4984.75	+	5715.76i	−0.327635	+	0.375683i
$615$	6689.94			0.438641
$616$	9675.20	+	6349.52i	0.632832	+	0.415307i
$617$	25625.0			1.67200			0.836000	−	0.548729i	$-0.184888\pi$
$617$	25625.0			1.67200			0.836000	+	0.548729i	$0.184888\pi$
$618$	9829.30	−	11270.8i	0.639794	−	0.733620i
$619$		−	4931.80i		−	0.320236i	−0.987098	−	0.160118i	$-0.948813\pi$
$619$		−	4931.80i		−	0.320236i	0.987098	−	0.160118i	$-0.0511874\pi$
$620$	8444.80	−	1159.24i	0.547018	−	0.0750904i
$621$			9165.62i			0.592276i
$622$	19440.8	+	16954.4i	1.25322	+	1.09294i
$623$	−11777.0			−0.757361
$624$	3235.64	−	905.389i	0.207579	−	0.0580842i
$625$	−14800.5			−0.947229
$626$	−11602.2	−	10118.4i	−0.740765	−	0.646025i
$627$			14404.2i			0.917462i
$628$	−23208.3	+	3185.86i	−1.47470	+	0.202436i
$629$		−	2488.47i		−	0.157745i
$630$	−2380.45	+	2729.54i	−0.150538	+	0.172615i
$631$	−25392.4			−1.60199			−0.800994	−	0.598672i	$-0.795695\pi$
$631$	−25392.4			−1.60199			−0.800994	+	0.598672i	$0.795695\pi$
$632$	12455.6	−	18979.5i	0.783952	−	1.19456i
$633$	−9669.49			−0.607153
$634$	−11422.2	+	13097.3i	−0.715511	+	0.820441i
$635$		−	14068.0i		−	0.879166i
$636$	1799.91	+	13111.9i	0.112218	+	0.817488i
$637$			4084.16i			0.254035i
$638$	20404.6	+	17795.0i	1.26618	+	1.10425i
$639$	10691.6			0.661899
$640$	−15036.7	−	4782.35i	−0.928713	−	0.295374i
$641$	−8756.93			−0.539591			−0.269796	−	0.962918i	$-0.586956\pi$
$641$	−8756.93			−0.539591			−0.269796	+	0.962918i	$0.586956\pi$
$642$	6876.28	+	5996.85i	0.422718	+	0.368655i
$643$		−	8506.91i		−	0.521742i	−0.965374	−	0.260871i	$-0.915990\pi$
$643$		−	8506.91i		−	0.521742i	0.965374	−	0.260871i	$-0.0840097\pi$
$644$	554.159	+	4036.93i	0.0339083	+	0.247015i
$645$		−	10522.1i		−	0.642335i
$646$	−2047.16	+	2347.38i	−0.124682	+	0.142967i
$647$	14886.9			0.904581			0.452291	−	0.891871i	$-0.350607\pi$
$647$	14886.9			0.904581			0.452291	+	0.891871i	$0.350607\pi$
$648$	−1657.81	+	2526.12i	−0.100502	+	0.153141i
$649$	−15787.6			−0.954878
$650$	−172.604	+	197.916i	−0.0104155	+	0.0119429i
$651$		−	2836.71i		−	0.170783i
$652$	−15570.0	+	2137.34i	−0.935230	+	0.128381i
$653$		−	23734.1i		−	1.42234i	−0.703021	−	0.711169i	$-0.748166\pi$
$653$		−	23734.1i		−	1.42234i	0.703021	−	0.711169i	$-0.251834\pi$
$654$	−2314.04	−	2018.09i	−0.138358	−	0.120663i
$655$	−30667.8			−1.82945
$656$	−10655.5	+	2981.58i	−0.634186	+	0.177456i
$657$	−11579.3			−0.687598
$658$	5776.91	+	5038.07i	0.342260	+	0.298487i
$659$			22807.5i			1.34818i	0.738647	+	0.674092i	$0.235465\pi$
$659$			22807.5i			1.34818i	−0.738647	+	0.674092i	$0.764535\pi$
$660$	19203.1	−	2636.05i	1.13254	−	0.155467i
$661$			28985.2i			1.70559i	0.522246	+	0.852795i	$0.325094\pi$
$661$			28985.2i			1.70559i	−0.522246	+	0.852795i	$0.674906\pi$
$662$	20718.7	−	23757.0i	1.21639	−	1.39478i
$663$	−892.481			−0.0522792
$664$	2519.49	+	1653.46i	0.147252	+	0.0966366i
$665$	−5765.00			−0.336176
$666$	−3915.23	+	4489.40i	−0.227796	+	0.261202i
$667$			9532.96i			0.553400i
$668$	−1006.87	−	7334.84i	−0.0583188	−	0.424840i
$669$			13099.8i			0.757054i
$670$	12257.0	+	10689.4i	0.706761	+	0.616370i
$671$	−30734.3			−1.76823
$672$	−2257.28	+	4741.14i	−0.129578	+	0.272163i
$673$	−8638.63			−0.494792			−0.247396	−	0.968914i	$-0.579575\pi$
$673$	−8638.63			−0.494792			−0.247396	+	0.968914i	$0.579575\pi$
$674$	19577.8	+	17073.9i	1.11885	+	0.975759i
$675$		−	923.169i		−	0.0526412i
$676$	2152.53	+	15680.7i	0.122470	+	0.892168i
$677$			14353.8i			0.814860i	0.913237	+	0.407430i	$0.133575\pi$
$677$			14353.8i			0.814860i	−0.913237	+	0.407430i	$0.866425\pi$
$678$	−4788.02	+	5490.19i	−0.271214	+	0.310987i
$679$	12675.3			0.716398
$680$	3504.06	+	2299.60i	0.197610	+	0.129685i
$681$	9135.76			0.514072
$682$	11382.9	−	13052.3i	0.639113	−	0.732839i
$683$			22323.3i			1.25062i	0.780375	+	0.625312i	$0.215028\pi$
$683$			22323.3i			1.25062i	−0.780375	+	0.625312i	$0.784972\pi$
$684$	7386.51	−	1013.96i	0.412910	−	0.0566810i
$685$		−	3334.28i		−	0.185980i
$686$	−10782.8	−	9403.70i	−0.600128	−	0.523375i
$687$	−10523.9			−0.584443
$688$	4689.49	+	16759.1i	0.259862	+	0.928686i
$689$	6886.24			0.380762
$690$	5143.65	+	4485.80i	0.283790	+	0.247495i
$691$			12988.9i			0.715082i	0.933897	+	0.357541i	$0.116385\pi$
$691$			12988.9i			0.715082i	−0.933897	+	0.357541i	$0.883615\pi$
$692$	−14571.0	+	2000.19i	−0.800441	+	0.109878i
$693$			7358.42i			0.403352i
$694$	−7610.22	+	8726.26i	−0.416254	+	0.477297i
$695$	−7589.36			−0.414217
$696$	−6740.29	+	10270.6i	−0.367083	+	0.559350i
$697$	2939.08			0.159721
$698$	9150.43	−	10492.3i	0.496202	−	0.568970i
$699$		−	4093.58i		−	0.221507i
$700$	−55.8154	−	406.604i	−0.00301375	−	0.0219545i
$701$		−	23328.1i		−	1.25690i	−0.777849	−	0.628451i	$-0.783689\pi$
$701$		−	23328.1i		−	1.25690i	0.777849	−	0.628451i	$-0.216311\pi$
$702$	4631.68	+	4039.31i	0.249019	+	0.217171i
$703$	−9481.97			−0.508705
$704$	−29411.0	+	12757.0i	−1.57453	+	0.682954i
$705$	12838.5			0.685852
$706$	−10171.8	−	8870.86i	−0.542238	−	0.472888i
$707$		−	4437.13i		−	0.236033i
$708$	−974.225	−	7097.03i	−0.0517141	−	0.376727i
$709$		−	19123.4i		−	1.01297i	−0.862250	−	0.506483i	$-0.830945\pi$
$709$		−	19123.4i		−	1.01297i	0.862250	−	0.506483i	$-0.169055\pi$
$710$	15052.4	−	17259.8i	0.795641	−	0.912321i
$711$	14434.7			0.761385
$712$	17900.1	−	27275.6i	0.942184	−	1.43567i
$713$	6097.97			0.320295
$714$	916.768	−	1051.21i	0.0480520	−	0.0550989i
$715$		−	10085.2i		−	0.527504i
$716$	2192.22	−	300.931i	0.114423	−	0.0157071i
$717$			14438.1i			0.752024i
$718$	−28147.8	−	24547.8i	−1.46305	−	1.27593i
$719$	−9531.82			−0.494405			−0.247202	−	0.968964i	$-0.579511\pi$
$719$	−9531.82			−0.494405			−0.247202	+	0.968964i	$0.579511\pi$
$720$	−2703.54	−	9661.81i	−0.139937	−	0.500103i
$721$	12160.7			0.628139
$722$	−5676.70	−	4950.68i	−0.292611	−	0.255187i
$723$		−	11995.4i		−	0.617032i
$724$	6781.09	−	930.856i	0.348090	−	0.0477831i
$725$		−	960.168i		−	0.0491858i
$726$	17096.7	−	19604.0i	0.873994	−	1.00217i
$727$	6515.69			0.332398			0.166199	−	0.986092i	$-0.446851\pi$
$727$	6515.69			0.332398			0.166199	+	0.986092i	$0.446851\pi$
$728$	2284.21	+	1499.05i	0.116289	+	0.0763168i
$729$	−16015.2			−0.813655
$730$	−16302.1	+	18692.8i	−0.826532	+	0.947743i
$731$		−	4622.64i		−	0.233891i
$732$	−1896.57	−	13816.1i	−0.0957638	−	0.697619i
$733$			19670.7i			0.991205i	0.868549	+	0.495603i	$0.165053\pi$
$733$			19670.7i			0.991205i	−0.868549	+	0.495603i	$0.834947\pi$
$734$	−7513.29	−	6552.38i	−0.377821	−	0.329500i
$735$	−10690.8			−0.536514
$736$	−10191.8	−	4852.38i	−0.510429	−	0.243018i
$737$	33043.0			1.65150
$738$	−5302.34	−	4624.20i	−0.264474	−	0.230649i
$739$			7682.52i			0.382417i	0.981549	+	0.191208i	$0.0612406\pi$
$739$			7682.52i			0.382417i	−0.981549	+	0.191208i	$0.938759\pi$
$740$	1735.25	+	12640.9i	0.0862015	+	0.627960i
$741$			3400.68i			0.168593i
$742$	−7073.63	+	8110.98i	−0.349974	+	0.401298i
$743$	−11831.5			−0.584192			−0.292096	−	0.956389i	$-0.594353\pi$
$743$	−11831.5			−0.584192			−0.292096	+	0.956389i	$0.594353\pi$
$744$	6569.84	+	4311.58i	0.323739	+	0.212460i
$745$	10872.7			0.534692
$746$	22991.7	−	26363.4i	1.12840	−	1.29388i
$747$			1916.18i			0.0938547i
$748$	8436.44	−	1158.09i	0.412389	−	0.0566095i
$749$			7419.23i			0.361940i
$750$	−10828.8	−	9443.85i	−0.527215	−	0.459787i
$751$	32087.0			1.55908			0.779541	−	0.626351i	$-0.215452\pi$
$751$	32087.0			1.55908			0.779541	+	0.626351i	$0.215452\pi$
$752$	−20448.6	+	5721.88i	−0.991602	+	0.277468i
$753$	−4504.11			−0.217980
$754$	4817.31	+	4201.20i	0.232674	+	0.202916i
$755$			31771.0i			1.53147i
$756$	−9515.44	+	1306.21i	−0.457769	+	0.0628389i
$757$		−	29111.1i		−	1.39770i	−0.715268	−	0.698851i	$-0.753695\pi$
$757$		−	29111.1i		−	1.39770i	0.715268	−	0.698851i	$-0.246305\pi$
$758$	−15240.4	+	17475.4i	−0.730286	+	0.837383i
$759$	13866.5			0.663137
$760$	8762.34	−	13351.8i	0.418215	−	0.637263i
$761$	26414.1			1.25823			0.629113	−	0.777314i	$-0.283418\pi$
$761$	26414.1			1.25823			0.629113	+	0.777314i	$0.283418\pi$
$762$	8524.29	−	9774.37i	0.405252	−	0.464683i
$763$		−	2496.76i		−	0.118465i
$764$	−3772.55	−	27482.3i	−0.178647	−	1.30141i
$765$			2665.00i			0.125952i
$766$	−16228.6	−	14153.1i	−0.765488	−	0.667586i
$767$	−3727.27			−0.175468
$768$	−7549.62	−	12434.0i	−0.354718	−	0.584211i
$769$	26242.0			1.23057			0.615287	−	0.788303i	$-0.289040\pi$
$769$	26242.0			1.23057			0.615287	+	0.788303i	$0.289040\pi$
$770$	11878.9	+	10359.7i	0.555956	+	0.484852i
$771$		−	9701.78i		−	0.453179i
$772$	3931.57	+	28640.7i	0.183291	+	1.33524i
$773$			37601.7i			1.74960i	0.484487	+	0.874798i	$0.339006\pi$
$773$			37601.7i			1.74960i	−0.484487	+	0.874798i	$0.660994\pi$
$774$	−7273.03	+	8339.63i	−0.337757	+	0.387289i
$775$	−614.193			−0.0284677
$776$	−19265.5	+	29356.1i	−0.891224	+	1.35802i
$777$	4246.25			0.196053
$778$	18503.7	−	21217.3i	0.852687	−	0.977733i
$779$		−	11199.0i		−	0.515076i
$780$	4533.64	−	622.343i	0.208116	−	0.0285685i
$781$		−	46529.7i		−	2.13184i
$782$	2259.75	+	1970.74i	0.103336	+	0.0901195i
$783$	−22470.1			−1.02556
$784$	17028.0	−	4764.72i	0.775690	−	0.217052i
$785$	−31905.7			−1.45065
$786$	−21307.9	−	18582.8i	−0.966957	−	0.843288i
$787$			19358.8i			0.876831i	0.898772	+	0.438415i	$0.144460\pi$
$787$			19358.8i			0.876831i	−0.898772	+	0.438415i	$0.855540\pi$
$788$	18815.5	−	2582.85i	0.850603	−	0.116764i
$789$		−	10872.7i		−	0.490594i
$790$	20322.2	−	23302.4i	0.915228	−	1.04945i
$791$	−5923.69			−0.266273
$792$	−17042.1	−	11184.2i	−0.764603	−	0.501784i
$793$	−7256.04			−0.324930
$794$	11725.6	−	13445.2i	0.524088	−	0.600946i
$795$			18025.7i			0.804157i
$796$	−756.112	−	5508.12i	−0.0336680	−	0.245264i
$797$			9691.27i			0.430718i	0.976535	+	0.215359i	$0.0690922\pi$
$797$			9691.27i			0.430718i	−0.976535	+	0.215359i	$0.930908\pi$
$798$	−4005.50	−	3493.22i	−0.177686	−	0.154961i
$799$	5640.31			0.249737
$800$	1026.53	+	488.736i	0.0453667	+	0.0215993i
$801$	20744.3			0.915061
$802$	−19937.0	−	17387.2i	−0.877807	−	0.765541i
$803$			50392.9i			2.21461i
$804$	2039.03	+	14853.9i	0.0894417	+	0.651564i
$805$			5549.78i			0.242986i
$806$	2687.39	−	3081.50i	0.117443	−	0.134666i
$807$	−27356.2			−1.19329
$808$	10276.4	+	6744.08i	0.447429	+	0.293633i
$809$	−15463.1			−0.672008			−0.336004	−	0.941861i	$-0.609076\pi$
$809$	−15463.1			−0.672008			−0.336004	+	0.941861i	$0.609076\pi$
$810$	−2704.83	+	3101.50i	−0.117331	+	0.134538i
$811$			40767.5i			1.76515i	0.470167	+	0.882577i	$0.344194\pi$
$811$			40767.5i			1.76515i	−0.470167	+	0.882577i	$0.655806\pi$
$812$	−9896.79	+	1358.56i	−0.427721	+	0.0587142i
$813$		−	6919.72i		−	0.298506i
$814$	19537.8	+	17039.0i	0.841277	+	0.733682i
$815$	−21405.0			−0.919979
$816$	1041.20	+	3721.00i	0.0446682	+	0.159633i
$817$	−17613.9			−0.754264
$818$	−11487.2	−	10018.0i	−0.491001	−	0.428205i
$819$			1737.24i			0.0741199i
$820$	−14930.0	+	2049.47i	−0.635825	+	0.0872812i
$821$			16244.1i			0.690529i	0.938505	+	0.345264i	$0.112211\pi$
$821$			16244.1i			0.690529i	−0.938505	+	0.345264i	$0.887789\pi$
$822$	2020.36	−	2316.65i	0.0857277	−	0.0982997i
$823$	41478.1			1.75679			0.878393	−	0.477938i	$-0.158616\pi$
$823$	41478.1			1.75679			0.878393	+	0.477938i	$0.158616\pi$
$824$	−18483.3	+	28164.2i	−0.781427	+	1.19071i
$825$	−1396.64			−0.0589393
$826$	3828.70	−	4390.18i	0.161280	−	0.184932i
$827$		−	8352.28i		−	0.351194i	−0.984462	−	0.175597i	$-0.943814\pi$
$827$		−	8352.28i		−	0.351194i	0.984462	−	0.175597i	$-0.0561856\pi$
$828$	−976.109	−	7110.75i	−0.0409688	−	0.298449i
$829$		−	45864.5i		−	1.92152i	−0.277383	−	0.960759i	$-0.589467\pi$
$829$		−	45864.5i		−	1.92152i	0.277383	−	0.960759i	$-0.410533\pi$
$830$	3093.35	+	2697.73i	0.129364	+	0.112819i
$831$	−24264.4			−1.01290
$832$	−6943.63	+	3011.80i	−0.289336	+	0.125499i
$833$	−4696.79			−0.195359
$834$	−5273.06	−	4598.67i	−0.218934	−	0.190934i
$835$		−	10083.6i		−	0.417912i
$836$	−4412.74	−	32145.9i	−0.182557	−	1.32989i
$837$			14373.5i			0.593573i
$838$	−16044.0	+	18396.9i	−0.661375	+	0.758365i
$839$	−44459.8			−1.82947			−0.914733	−	0.404058i	$-0.867599\pi$
$839$	−44459.8			−1.82947			−0.914733	+	0.404058i	$0.867599\pi$
$840$	−3923.98	+	5979.24i	−0.161179	+	0.245599i
$841$	1018.36			0.0417550
$842$	25402.7	−	29128.1i	1.03971	−	1.19218i
$843$		−	16588.6i		−	0.677748i
$844$	21579.5	−	2962.26i	0.880089	−	0.120812i
$845$			21557.1i			0.877619i
$846$	−10175.6	−	8874.19i	−0.413527	−	0.360639i
$847$	21151.9			0.858073
$848$	−8033.72	−	28710.6i	−0.325329	−	1.16265i
$849$	−2287.29			−0.0924612
$850$	−227.604	−	198.494i	−0.00918440	−	0.00800977i
$851$			9127.99i			0.367689i
$852$	20916.6	−	2871.27i	0.841071	−	0.115456i
$853$			19647.1i			0.788635i	0.918974	+	0.394317i	$0.129019\pi$
$853$			19647.1i			0.788635i	−0.918974	+	0.394317i	$0.870981\pi$
$854$	7453.50	−	8546.55i	0.298657	−	0.342456i
$855$	10154.6			0.406176
$856$	−17183.0	−	11276.6i	−0.686100	−	0.450265i
$857$	1698.85			0.0677146			0.0338573	−	0.999427i	$-0.489221\pi$
$857$	1698.85			0.0677146			0.0338573	+	0.999427i	$0.489221\pi$
$858$	6110.99	−	7007.17i	0.243154	−	0.278812i
$859$			6422.27i			0.255093i	0.991833	+	0.127547i	$0.0407102\pi$
$859$			6422.27i			0.255093i	−0.991833	+	0.127547i	$0.959290\pi$
$860$	3223.45	+	23482.1i	0.127812	+	0.931086i
$861$			5015.16i			0.198509i
$862$	29052.1	+	25336.5i	1.14793	+	1.00112i
$863$	−7961.57			−0.314038			−0.157019	−	0.987596i	$-0.550188\pi$
$863$	−7961.57			−0.314038			−0.157019	+	0.987596i	$0.550188\pi$
$864$	11437.5	−	24023.1i	0.450361	−	0.945930i
$865$	−20031.5			−0.787388
$866$	11614.9	+	10129.4i	0.455764	+	0.397474i
$867$		−	1026.35i		−	0.0402040i
$868$	869.030	+	6330.70i	0.0339825	+	0.247555i
$869$		−	62819.7i		−	2.45226i
$870$	−10997.2	+	12610.0i	−0.428553	+	0.491400i
$871$	7801.10			0.303479
$872$	5782.51	+	3794.87i	0.224565	+	0.147375i
$873$	−22326.6			−0.865568
$874$	7509.24	−	8610.47i	0.290622	−	0.333242i
$875$		−	11683.8i		−	0.451412i
$876$	−22653.3	+	3109.67i	−0.873726	+	0.119938i
$877$		−	39811.5i		−	1.53288i	−0.642315	−	0.766441i	$-0.722026\pi$
$877$		−	39811.5i		−	1.53288i	0.642315	−	0.766441i	$-0.277974\pi$
$878$	−13333.2	−	11628.0i	−0.512500	−	0.446954i
$879$	12894.0			0.494770
$880$	−42048.0	+	11765.8i	−1.61072	+	0.450709i
$881$	27386.1			1.04729			0.523643	−	0.851938i	$-0.324572\pi$
$881$	27386.1			1.04729			0.523643	+	0.851938i	$0.324572\pi$
$882$	8473.40	+	7389.70i	0.323485	+	0.282113i
$883$		−	225.723i		−	0.00860271i	−0.999991	−	0.00430135i	$-0.998631\pi$
$883$		−	225.723i		−	0.00860271i	0.999991	−	0.00430135i	$-0.00136917\pi$
$884$	1991.75	−	273.412i	0.0757805	−	0.0104026i
$885$		−	9756.65i		−	0.370583i
$886$	−1036.14	+	1188.09i	−0.0392888	+	0.0450505i
$887$	25202.8			0.954034			0.477017	−	0.878894i	$-0.341718\pi$
$887$	25202.8			0.954034			0.477017	+	0.878894i	$0.341718\pi$
$888$	−6453.96	+	9834.34i	−0.243897	+	0.371643i
$889$	10546.1			0.397870
$890$	29205.2	−	33488.1i	1.09996	−	1.26126i
$891$			8361.15i			0.314376i
$892$	−4013.15	−	29235.0i	−0.150639	−	1.09738i
$893$		−	21491.6i		−	0.805364i
$894$	7554.33	+	6588.17i	0.282611	+	0.246467i
$895$	3013.76			0.112557
$896$	3585.12	−	11272.3i	0.133673	−	0.420293i
$897$	3273.73			0.121858
$898$	7127.31	+	6215.77i	0.264857	+	0.230983i
$899$			14949.5i			0.554611i
$900$	98.3146	+	716.201i	0.00364128	+	0.0265260i
$901$			7919.18i			0.292815i
$902$	−20124.4	+	23075.7i	−0.742872	+	0.851814i
$903$	7887.94			0.290691
$904$	9003.53	−	13719.3i	0.331253	−	0.504753i
$905$	9322.32			0.342414
$906$	−19251.2	+	22074.3i	−0.705935	+	0.809460i
$907$			10454.1i			0.382716i	0.981520	+	0.191358i	$0.0612892\pi$
$907$			10454.1i			0.382716i	−0.981520	+	0.191358i	$0.938711\pi$
$908$	−20388.3	+	2798.75i	−0.745165	+	0.102290i
$909$			7815.67i			0.285181i
$910$	2804.48	+	2445.80i	0.102162	+	0.0890963i
$911$	−36271.9			−1.31915			−0.659573	−	0.751641i	$-0.729263\pi$
$911$	−36271.9			−1.31915			−0.659573	+	0.751641i	$0.729263\pi$
$912$	14178.4	−	3967.35i	0.514794	−	0.144048i
$913$	8339.19			0.302286
$914$	22874.5	+	19948.9i	0.827812	+	0.721939i
$915$		−	18993.7i		−	0.686243i
$916$	23486.3	−	3224.01i	0.847170	−	0.116293i
$917$		−	22990.4i		−	0.827927i
$918$	−4645.22	+	5326.44i	−0.167010	+	0.191502i
$919$	25103.5			0.901076			0.450538	−	0.892757i	$-0.351232\pi$
$919$	25103.5			0.901076			0.450538	+	0.892757i	$0.351232\pi$
$920$	−12853.3	−	8435.22i	−0.460610	−	0.302284i
$921$	−9522.59			−0.340695
$922$	−3176.27	+	3642.07i	−0.113454	+	0.130092i
$923$		−	10985.2i		−	0.391746i
$924$	1976.13	+	14395.7i	0.0703571	+	0.512537i
$925$		−	919.379i		−	0.0326800i
$926$	8926.43	+	7784.79i	0.316783	+	0.276268i
$927$	−21420.2			−0.758932
$928$	11895.9	−	24985.9i	0.420800	−	0.883840i
$929$	42800.4			1.51156			0.755778	−	0.654828i	$-0.227259\pi$
$929$	42800.4			1.51156			0.755778	+	0.654828i	$0.227259\pi$
$930$	8066.25	+	7034.62i	0.284411	+	0.248037i
$931$			17896.5i			0.630004i
$932$	1254.07	+	9135.66i	0.0440757	+	0.321082i
$933$			32388.8i			1.13651i
$934$	12246.1	−	14042.0i	0.429019	−	0.491935i
$935$	11598.0			0.405664
$936$	−4023.46	−	2640.47i	−0.140503	−	0.0922078i
$937$	−37669.7			−1.31336			−0.656679	−	0.754171i	$-0.728039\pi$
$937$	−37669.7			−1.31336			−0.656679	+	0.754171i	$0.728039\pi$
$938$	−8013.39	+	9188.55i	−0.278941	+	0.319847i
$939$		−	19329.6i		−	0.671776i
$940$	−28651.7	+	3933.08i	−0.994166	+	0.136471i
$941$			2436.59i			0.0844108i	0.999109	+	0.0422054i	$0.0134384\pi$
$941$			2436.59i			0.0844108i	−0.999109	+	0.0422054i	$0.986562\pi$
$942$	−22168.0	−	19332.8i	−0.766742	−	0.668680i
$943$	−10780.9			−0.372294
$944$	4348.36	+	15540.0i	0.149923	+	0.535788i
$945$	−13081.4			−0.450304
$946$	36293.9	+	31652.1i	1.24737	+	1.08784i
$947$			18066.6i			0.619943i	0.950746	+	0.309972i	$0.100320\pi$
$947$			18066.6i			0.619943i	−0.950746	+	0.309972i	$0.899680\pi$
$948$	28239.5	−	3876.50i	0.967486	−	0.132809i
$949$			11897.2i			0.406955i
$950$	−756.337	+	867.254i	−0.0258303	+	0.0296183i
$951$	−21820.4			−0.744032
$952$	−1723.91	+	2626.85i	−0.0586895	+	0.0894292i
$953$	−57382.7			−1.95048			−0.975240	−	0.221149i	$-0.929019\pi$
$953$	−57382.7			−1.95048			−0.975240	+	0.221149i	$0.929019\pi$
$954$	12459.7	−	14286.9i	0.422847	−	0.484858i
$955$		−	37781.3i		−	1.28018i
$956$	−4423.13	−	32221.6i	−0.149638	−	1.09008i
$957$			33994.5i			1.14826i
$958$	7267.83	+	6338.32i	0.245108	+	0.213760i
$959$	2499.57			0.0841660
$960$	−7883.81	−	18175.9i	−0.265051	−	0.611068i
$961$	−20228.2			−0.679003
$962$	4612.67	+	4022.73i	0.154593	+	0.134821i
$963$		−	13068.4i		−	0.437304i
$964$	3674.81	+	26770.2i	0.122778	+	0.894409i
$965$			39373.9i			1.31346i
$966$	−3362.81	+	3855.97i	−0.112005	+	0.128430i
$967$	28797.2			0.957659			0.478829	−	0.877908i	$-0.341061\pi$
$967$	28797.2			0.957659			0.478829	+	0.877908i	$0.341061\pi$
$968$	−32149.2	+	48987.9i	−1.06747	+	1.62658i
$969$	−3910.79			−0.129652
$970$	−31432.9	+	36042.5i	−1.04046	+	1.19305i
$971$			24933.8i			0.824061i	0.911170	+	0.412030i	$0.135180\pi$
$971$			24933.8i			0.824061i	−0.911170	+	0.412030i	$0.864820\pi$
$972$	27694.9	−	3801.74i	0.913904	−	0.125454i
$973$		−	5689.42i		−	0.187456i
$974$	1906.67	+	1662.82i	0.0627245	+	0.0547023i
$975$	−329.733			−0.0108307
$976$	8465.15	+	30252.4i	0.277626	+	0.992168i
$977$	14908.0			0.488176			0.244088	−	0.969753i	$-0.421511\pi$
$977$	14908.0			0.488176			0.244088	+	0.969753i	$0.421511\pi$
$978$	−14872.1	−	12970.0i	−0.486254	−	0.424065i
$979$		−	90278.9i		−	2.94722i
$980$	23858.8	−	3275.15i	0.777695	−	0.106756i
$981$			4397.85i			0.143132i
$982$	−13965.1	+	16013.1i	−0.453814	+	0.520366i
$983$	−25874.4			−0.839538			−0.419769	−	0.907631i	$-0.637889\pi$
$983$	−25874.4			−0.839538			−0.419769	+	0.907631i	$0.637889\pi$
$984$	−11615.1	−	7622.63i	−0.376298	−	0.246952i
$985$	25866.7			0.836731
$986$	−4831.39	+	5539.91i	−0.156047	+	0.178932i
$987$			9624.46i			0.310385i
$988$	−1041.80	−	7589.31i	−0.0335467	−	0.244381i
$989$			16956.4i			0.545179i
$990$	−20923.8	−	18247.8i	−0.671719	−	0.585810i
$991$	−145.917			−0.00467729			−0.00233865	−	0.999997i	$-0.500744\pi$
$991$	−145.917			−0.00467729			−0.00233865	+	0.999997i	$0.500744\pi$
$992$	−15982.8	−	7609.48i	−0.511547	−	0.243550i
$993$	39579.8			1.26488
$994$	12938.9	+	11284.1i	0.412875	+	0.360070i
$995$		−	7572.30i		−	0.241264i
$996$	514.598	+	3748.74i	0.0163712	+	0.119261i
$997$		−	18028.5i		−	0.572686i	−0.958127	−	0.286343i	$-0.907560\pi$
$997$		−	18028.5i		−	0.572686i	0.958127	−	0.286343i	$-0.0924397\pi$
$998$	12046.0	−	13812.5i	0.382072	−	0.438103i
$999$	−21515.5			−0.681403

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.c.b.69.5	✓	24
4.3	odd	2		544.4.c.a.273.16		24
8.3	odd	2		544.4.c.a.273.9		24
8.5	even	2	inner	136.4.c.b.69.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.c.b.69.5	✓	24	1.1	even	1	trivial
136.4.c.b.69.6	yes	24	8.5	even	2	inner
544.4.c.a.273.9		24	8.3	odd	2
544.4.c.a.273.16		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)

\(f(q)\)	\(=\)	\(q+(-2.13166 - 1.85904i) q^{2} -3.55140i q^{3} +(1.08798 + 7.92567i) q^{4} +10.8958i q^{5} +(-6.60218 + 7.57039i) q^{6} -8.16814 q^{7} +(12.4149 - 18.9175i) q^{8} +14.3876 q^{9} +O(q^{10})\)	\(q+(-2.13166 - 1.85904i) q^{2} -3.55140i q^{3} +(1.08798 + 7.92567i) q^{4} +10.8958i q^{5} +(-6.60218 + 7.57039i) q^{6} -8.16814 q^{7} +(12.4149 - 18.9175i) q^{8} +14.3876 q^{9} +(20.2557 - 23.2263i) q^{10} -62.6144i q^{11} +(28.1472 - 3.86383i) q^{12} -14.7826i q^{13} +(17.4117 + 15.1849i) q^{14} +38.6955 q^{15} +(-61.6326 + 17.2459i) q^{16} +17.0000 q^{17} +(-30.6694 - 26.7470i) q^{18} -64.7762i q^{19} +(-86.3568 + 11.8544i) q^{20} +29.0083i q^{21} +(-116.402 + 133.473i) q^{22} -62.3580 q^{23} +(-67.1834 - 44.0903i) q^{24} +6.28076 q^{25} +(-27.4814 + 31.5115i) q^{26} -146.984i q^{27} +(-8.88673 - 64.7380i) q^{28} -152.875i q^{29} +(-82.4857 - 71.9362i) q^{30} -97.7896 q^{31} +(163.441 + 77.8148i) q^{32} -222.369 q^{33} +(-36.2383 - 31.6036i) q^{34} -88.9987i q^{35} +(15.6533 + 114.031i) q^{36} -146.380i q^{37} +(-120.421 + 138.081i) q^{38} -52.4989 q^{39} +(206.121 + 135.271i) q^{40} +172.887 q^{41} +(53.9275 - 61.8360i) q^{42} -271.920i q^{43} +(496.261 - 68.1229i) q^{44} +156.764i q^{45} +(132.926 + 115.926i) q^{46} +331.783 q^{47} +(61.2470 + 218.882i) q^{48} -276.282 q^{49} +(-13.3885 - 11.6761i) q^{50} -60.3738i q^{51} +(117.162 - 16.0831i) q^{52} +465.834i q^{53} +(-273.248 + 313.320i) q^{54} +682.236 q^{55} +(-101.407 + 154.520i) q^{56} -230.046 q^{57} +(-284.199 + 325.877i) q^{58} -252.139i q^{59} +(42.0997 + 306.688i) q^{60} -490.851i q^{61} +(208.455 + 181.794i) q^{62} -117.520 q^{63} +(-203.740 - 469.717i) q^{64} +161.069 q^{65} +(474.015 + 413.391i) q^{66} +527.722i q^{67} +(18.4956 + 134.736i) q^{68} +221.458i q^{69} +(-165.452 + 189.715i) q^{70} +743.115 q^{71} +(178.620 - 272.176i) q^{72} -804.814 q^{73} +(-272.126 + 312.034i) q^{74} -22.3055i q^{75} +(513.395 - 70.4749i) q^{76} +511.443i q^{77} +(111.910 + 97.5973i) q^{78} +1003.28 q^{79} +(-187.908 - 671.539i) q^{80} -133.534 q^{81} +(-368.536 - 321.403i) q^{82} +133.183i q^{83} +(-229.911 + 31.5603i) q^{84} +185.229i q^{85} +(-505.509 + 579.641i) q^{86} -542.919 q^{87} +(-1184.50 - 777.352i) q^{88} +1441.82 q^{89} +(291.431 - 334.169i) q^{90} +120.746i q^{91} +(-67.8440 - 494.229i) q^{92} +347.290i q^{93} +(-707.249 - 616.796i) q^{94} +705.791 q^{95} +(276.352 - 580.443i) q^{96} -1551.80 q^{97} +(588.939 + 513.617i) q^{98} -900.868i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9}+O(q^{10}) \) 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9	\( 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9} - 16 q^{10} - 18 q^{12} + 26 q^{14} - 180 q^{15} - 103 q^{16} + 408 q^{17} - 5 q^{18} - 24 q^{20} + 172 q^{22} + 624 q^{23} - 310 q^{24} - 600 q^{25} - 180 q^{26} - 132 q^{28} - 80 q^{30} - 744 q^{31} - 39 q^{32} - 280 q^{33} + 17 q^{34} + 791 q^{36} - 162 q^{38} + 1236 q^{39} - 1396 q^{40} + 1132 q^{42} + 886 q^{44} - 1246 q^{46} - 956 q^{47} - 2226 q^{48} + 1688 q^{49} + 2505 q^{50} + 2544 q^{52} - 3264 q^{54} + 1684 q^{55} - 1100 q^{56} - 168 q^{57} + 2800 q^{58} + 2520 q^{60} - 1946 q^{62} - 2520 q^{63} - 2143 q^{64} - 72 q^{65} + 3660 q^{66} + 85 q^{68} - 5084 q^{70} + 1532 q^{71} - 2277 q^{72} + 216 q^{73} + 2188 q^{74} + 2094 q^{76} - 4748 q^{78} - 3176 q^{79} + 116 q^{80} + 2040 q^{81} + 3198 q^{82} + 5916 q^{84} - 2066 q^{86} - 236 q^{87} - 3598 q^{88} - 424 q^{89} + 2180 q^{90} + 1940 q^{92} - 2156 q^{94} - 1248 q^{95} - 4674 q^{96} - 1304 q^{97} + 3705 q^{98}+O(q^{100}) \) 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9 - 16 * q^10 - 18 * q^12 + 26 * q^14 - 180 * q^15 - 103 * q^16 + 408 * q^17 - 5 * q^18 - 24 * q^20 + 172 * q^22 + 624 * q^23 - 310 * q^24 - 600 * q^25 - 180 * q^26 - 132 * q^28 - 80 * q^30 - 744 * q^31 - 39 * q^32 - 280 * q^33 + 17 * q^34 + 791 * q^36 - 162 * q^38 + 1236 * q^39 - 1396 * q^40 + 1132 * q^42 + 886 * q^44 - 1246 * q^46 - 956 * q^47 - 2226 * q^48 + 1688 * q^49 + 2505 * q^50 + 2544 * q^52 - 3264 * q^54 + 1684 * q^55 - 1100 * q^56 - 168 * q^57 + 2800 * q^58 + 2520 * q^60 - 1946 * q^62 - 2520 * q^63 - 2143 * q^64 - 72 * q^65 + 3660 * q^66 + 85 * q^68 - 5084 * q^70 + 1532 * q^71 - 2277 * q^72 + 216 * q^73 + 2188 * q^74 + 2094 * q^76 - 4748 * q^78 - 3176 * q^79 + 116 * q^80 + 2040 * q^81 + 3198 * q^82 + 5916 * q^84 - 2066 * q^86 - 236 * q^87 - 3598 * q^88 - 424 * q^89 + 2180 * q^90 + 1940 * q^92 - 2156 * q^94 - 1248 * q^95 - 4674 * q^96 - 1304 * q^97 + 3705 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more