LMFDB - Embedded newform 136.4.h.a.101.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(101,136)]

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, 1]))

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

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

chi := DirichletCharacter("136.101");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	136.h (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:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.20
Character	$\chi$	$=$	136.101
Dual form			136.4.h.a.101.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64670 + 2.29965i) q^{2} +3.96792 q^{3} +(-2.57674 - 7.57367i) q^{4} -5.58507 q^{5} +(-6.53398 + 9.12481i) q^{6} +3.60918i q^{7} +(21.6599 + 6.54599i) q^{8} -11.2556 q^{9} +O(q^{10})$	\(q+(-1.64670 + 2.29965i) q^{2} +3.96792 q^{3} +(-2.57674 - 7.57367i) q^{4} -5.58507 q^{5} +(-6.53398 + 9.12481i) q^{6} +3.60918i q^{7} +(21.6599 + 6.54599i) q^{8} -11.2556 q^{9} +(9.19694 - 12.8437i) q^{10} -50.2528 q^{11} +(-10.2243 - 30.0517i) q^{12} +45.3934i q^{13} +(-8.29983 - 5.94324i) q^{14} -22.1611 q^{15} +(-50.7208 + 39.0307i) q^{16} +(-59.0292 + 37.7962i) q^{17} +(18.5347 - 25.8839i) q^{18} +85.4733i q^{19} +(14.3913 + 42.2994i) q^{20} +14.3209i q^{21} +(82.7515 - 115.564i) q^{22} -176.742i q^{23} +(85.9446 + 25.9740i) q^{24} -93.8070 q^{25} +(-104.389 - 74.7494i) q^{26} -151.795 q^{27} +(27.3347 - 9.29991i) q^{28} +211.680 q^{29} +(36.4927 - 50.9627i) q^{30} -3.22438i q^{31} +(-6.23469 - 180.912i) q^{32} -199.399 q^{33} +(10.2856 - 197.985i) q^{34} -20.1575i q^{35} +(29.0028 + 85.2463i) q^{36} -355.514 q^{37} +(-196.558 - 140.749i) q^{38} +180.117i q^{39} +(-120.972 - 36.5598i) q^{40} -412.291i q^{41} +(-32.9331 - 23.5823i) q^{42} +464.709i q^{43} +(129.488 + 380.598i) q^{44} +62.8633 q^{45} +(406.443 + 291.041i) q^{46} +180.837 q^{47} +(-201.256 + 154.871i) q^{48} +329.974 q^{49} +(154.472 - 215.723i) q^{50} +(-234.223 + 149.972i) q^{51} +(343.794 - 116.967i) q^{52} +81.8134i q^{53} +(249.962 - 349.075i) q^{54} +280.665 q^{55} +(-23.6257 + 78.1743i) q^{56} +339.151i q^{57} +(-348.574 + 486.789i) q^{58} +297.123i q^{59} +(57.1033 + 167.841i) q^{60} +303.899 q^{61} +(7.41493 + 5.30959i) q^{62} -40.6235i q^{63} +(426.300 + 283.571i) q^{64} -253.525i q^{65} +(328.351 - 458.547i) q^{66} +3.06619i q^{67} +(438.359 + 349.676i) q^{68} -701.297i q^{69} +(46.3551 + 33.1934i) q^{70} +680.135i q^{71} +(-243.795 - 73.6791i) q^{72} +186.773i q^{73} +(585.427 - 817.557i) q^{74} -372.219 q^{75} +(647.346 - 220.242i) q^{76} -181.371i q^{77} +(-414.206 - 296.600i) q^{78} +808.517i q^{79} +(283.279 - 217.989i) q^{80} -298.410 q^{81} +(948.122 + 678.920i) q^{82} +282.350i q^{83} +(108.462 - 36.9013i) q^{84} +(329.682 - 211.094i) q^{85} +(-1068.67 - 765.237i) q^{86} +839.930 q^{87} +(-1088.47 - 328.955i) q^{88} -1117.41 q^{89} +(-103.517 + 144.563i) q^{90} -163.833 q^{91} +(-1338.58 + 455.417i) q^{92} -12.7941i q^{93} +(-297.786 + 415.862i) q^{94} -477.374i q^{95} +(-24.7387 - 717.844i) q^{96} -954.348i q^{97} +(-543.369 + 758.823i) q^{98} +565.626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9}+O(q^{10}) $ 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9	$ 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9} - 232 q^{15} - 78 q^{16} - 28 q^{17} - 2 q^{18} + 1052 q^{25} + 448 q^{26} - 368 q^{30} + 958 q^{32} - 344 q^{33} - 198 q^{34} + 138 q^{36} - 524 q^{38} + 936 q^{47} - 1964 q^{49} - 1038 q^{50} - 1424 q^{52} - 1384 q^{55} + 2320 q^{60} - 2078 q^{64} - 1888 q^{66} - 874 q^{68} + 2472 q^{70} - 4010 q^{72} + 436 q^{76} + 1884 q^{81} - 2264 q^{84} - 1420 q^{86} + 1976 q^{87} - 224 q^{89} + 80 q^{94} + 5746 q^{98}+O(q^{100}) $ 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9 - 232 * q^15 - 78 * q^16 - 28 * q^17 - 2 * q^18 + 1052 * q^25 + 448 * q^26 - 368 * q^30 + 958 * q^32 - 344 * q^33 - 198 * q^34 + 138 * q^36 - 524 * q^38 + 936 * q^47 - 1964 * q^49 - 1038 * q^50 - 1424 * q^52 - 1384 * q^55 + 2320 * q^60 - 2078 * q^64 - 1888 * q^66 - 874 * q^68 + 2472 * q^70 - 4010 * q^72 + 436 * q^76 + 1884 * q^81 - 2264 * q^84 - 1420 * q^86 + 1976 * q^87 - 224 * q^89 + 80 * q^94 + 5746 * 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 $

$2$	−1.64670	+	2.29965i	−0.582197	+	0.813047i
$2$	−1.64670	+	2.29965i	−0.582197	+	0.813047i
$3$	3.96792			0.763627			0.381813	−	0.924239i	$-0.375300\pi$
$3$	3.96792			0.763627			0.381813	+	0.924239i	$0.375300\pi$
$4$	−2.57674	−	7.57367i	−0.322092	−	0.946708i
$5$	−5.58507			−0.499543			−0.249772	−	0.968305i	$-0.580356\pi$
$5$	−5.58507			−0.499543			−0.249772	+	0.968305i	$0.580356\pi$
$6$	−6.53398	+	9.12481i	−0.444581	+	0.620865i
$7$			3.60918i			0.194877i	0.995242	+	0.0974387i	$0.0310650\pi$
$7$			3.60918i			0.194877i	−0.995242	+	0.0974387i	$0.968935\pi$
$8$	21.6599	+	6.54599i	0.957240	+	0.289295i
$9$	−11.2556			−0.416875
$10$	9.19694	−	12.8437i	0.290833	−	0.406153i
$11$	−50.2528			−1.37744			−0.688718	−	0.725029i	$-0.741826\pi$
$11$	−50.2528			−1.37744			−0.688718	+	0.725029i	$0.741826\pi$
$12$	−10.2243	−	30.0517i	−0.245958	−	0.722932i
$13$			45.3934i			0.968450i	0.874943	+	0.484225i	$0.160898\pi$
$13$			45.3934i			0.968450i	−0.874943	+	0.484225i	$0.839102\pi$
$14$	−8.29983	−	5.94324i	−0.158445	−	0.113457i
$15$	−22.1611			−0.381465
$16$	−50.7208	+	39.0307i	−0.792513	+	0.609855i
$17$	−59.0292	+	37.7962i	−0.842158	+	0.539231i
$17$	−59.0292	+	37.7962i	−0.842158	+	0.539231i
$18$	18.5347	−	25.8839i	0.242703	−	0.338939i
$19$			85.4733i			1.03205i	0.856574	+	0.516024i	$0.172588\pi$
$19$			85.4733i			1.03205i	−0.856574	+	0.516024i	$0.827412\pi$
$20$	14.3913	+	42.2994i	0.160899	+	0.472922i
$21$			14.3209i			0.148813i
$22$	82.7515	−	115.564i	0.801940	−	1.11992i
$23$		−	176.742i		−	1.60231i	−0.598455	−	0.801156i	$-0.704218\pi$
$23$		−	176.742i		−	1.60231i	0.598455	−	0.801156i	$-0.295782\pi$
$24$	85.9446	+	25.9740i	0.730974	+	0.220913i
$25$	−93.8070			−0.750456
$26$	−104.389	−	74.7494i	−0.787396	−	0.563829i
$27$	−151.795			−1.08196
$28$	27.3347	−	9.29991i	0.184492	−	0.0627685i
$29$	211.680			1.35545			0.677724	−	0.735316i	$-0.262966\pi$
$29$	211.680			1.35545			0.677724	+	0.735316i	$0.262966\pi$
$30$	36.4927	−	50.9627i	0.222088	−	0.310149i
$31$		−	3.22438i		−	0.0186811i	−0.999956	−	0.00934057i	$-0.997027\pi$
$31$		−	3.22438i		−	0.0186811i	0.999956	−	0.00934057i	$-0.00297324\pi$
$32$	−6.23469	−	180.912i	−0.0344421	−	0.999407i
$33$	−199.399			−1.05185
$34$	10.2856	−	197.985i	0.0518816	−	0.998653i
$35$		−	20.1575i		−	0.0973497i
$36$	29.0028	+	85.2463i	0.134272	+	0.394659i
$37$	−355.514			−1.57963			−0.789814	−	0.613347i	$-0.789823\pi$
$37$	−355.514			−1.57963			−0.789814	+	0.613347i	$0.789823\pi$
$38$	−196.558	−	140.749i	−0.839104	−	0.600856i
$39$			180.117i			0.739534i
$40$	−120.972	−	36.5598i	−0.478183	−	0.144515i
$41$		−	412.291i		−	1.57046i	−0.619203	−	0.785231i	$-0.712544\pi$
$41$		−	412.291i		−	1.57046i	0.619203	−	0.785231i	$-0.287456\pi$
$42$	−32.9331	−	23.5823i	−0.120992	−	0.0866388i
$43$			464.709i			1.64808i	0.566532	+	0.824040i	$0.308285\pi$
$43$			464.709i			1.64808i	−0.566532	+	0.824040i	$0.691715\pi$
$44$	129.488	+	380.598i	0.443662	+	1.30403i
$45$	62.8633			0.208247
$46$	406.443	+	291.041i	1.30276	+	0.932862i
$47$	180.837			0.561231			0.280615	−	0.959820i	$-0.409461\pi$
$47$	180.837			0.561231			0.280615	+	0.959820i	$0.409461\pi$
$48$	−201.256	+	154.871i	−0.605184	+	0.465701i
$49$	329.974			0.962023
$50$	154.472	−	215.723i	0.436914	−	0.610157i
$51$	−234.223	+	149.972i	−0.643094	+	0.411771i
$52$	343.794	−	116.967i	0.916840	−	0.311930i
$53$			81.8134i			0.212037i	0.994364	+	0.106018i	$0.0338102\pi$
$53$			81.8134i			0.212037i	−0.994364	+	0.106018i	$0.966190\pi$
$54$	249.962	−	349.075i	0.629916	−	0.879687i
$55$	280.665			0.688089
$56$	−23.6257	+	78.1743i	−0.0563770	+	0.186544i
$57$			339.151i			0.788099i
$58$	−348.574	+	486.789i	−0.789139	+	1.10204i
$59$			297.123i			0.655629i	0.944742	+	0.327815i	$0.106312\pi$
$59$			297.123i			0.655629i	−0.944742	+	0.327815i	$0.893688\pi$
$60$	57.1033	+	167.841i	0.122867	+	0.361136i
$61$	303.899			0.637874			0.318937	−	0.947776i	$-0.396674\pi$
$61$	303.899			0.637874			0.318937	+	0.947776i	$0.396674\pi$
$62$	7.41493	+	5.30959i	0.0151887	+	0.0108761i
$63$		−	40.6235i		−	0.0812394i
$64$	426.300	+	283.571i	0.832617	+	0.553849i
$65$		−	253.525i		−	0.483783i
$66$	328.351	−	458.547i	0.612382	−	0.855201i
$67$			3.06619i			0.00559097i	0.999996	+	0.00279549i	$0.000889832\pi$
$67$			3.06619i			0.00559097i	−0.999996	+	0.00279549i	$0.999110\pi$
$68$	438.359	+	349.676i	0.781747	+	0.623596i
$69$		−	701.297i		−	1.22357i
$70$	46.3551	+	33.1934i	0.0791499	+	0.0566767i
$71$			680.135i			1.13686i	0.822731	+	0.568431i	$0.192449\pi$
$71$			680.135i			1.13686i	−0.822731	+	0.568431i	$0.807551\pi$
$72$	−243.795	−	73.6791i	−0.399049	−	0.120600i
$73$			186.773i			0.299453i	0.988727	+	0.149727i	$0.0478393\pi$
$73$			186.773i			0.299453i	−0.988727	+	0.149727i	$0.952161\pi$
$74$	585.427	−	817.557i	0.919655	−	1.28431i
$75$	−372.219			−0.573068
$76$	647.346	−	220.242i	0.977048	−	0.332415i
$77$		−	181.371i		−	0.268431i
$78$	−414.206	−	296.600i	−0.601276	−	0.430555i
$79$			808.517i			1.15146i	0.817640	+	0.575730i	$0.195282\pi$
$79$			808.517i			1.15146i	−0.817640	+	0.575730i	$0.804718\pi$
$80$	283.279	−	217.989i	0.395895	−	0.304649i
$81$	−298.410			−0.409341
$82$	948.122	+	678.920i	1.27686	+	0.914319i
$83$			282.350i			0.373397i	0.982417	+	0.186699i	$0.0597788\pi$
$83$			282.350i			0.373397i	−0.982417	+	0.186699i	$0.940221\pi$
$84$	108.462	−	36.9013i	0.140883	−	0.0479317i
$85$	329.682	−	211.094i	0.420694	−	0.269369i
$86$	−1068.67	−	765.237i	−1.33997	−	0.959508i
$87$	839.930			1.03506
$88$	−1088.47	−	328.955i	−1.31854	−	0.398485i
$89$	−1117.41			−1.33084			−0.665422	−	0.746468i	$-0.731748\pi$
$89$	−1117.41			−1.33084			−0.665422	+	0.746468i	$0.731748\pi$
$90$	−103.517	+	144.563i	−0.121241	+	0.169315i
$91$	−163.833			−0.188729
$92$	−1338.58	+	455.417i	−1.51692	+	0.516093i
$93$		−	12.7941i		−	0.0142654i
$94$	−297.786	+	415.862i	−0.326747	+	0.456307i
$95$		−	477.374i		−	0.515553i
$96$	−24.7387	−	717.844i	−0.0263009	−	0.763173i
$97$		−	954.348i		−	0.998963i	−0.866325	−	0.499481i	$-0.833524\pi$
$97$		−	954.348i		−	0.998963i	0.866325	−	0.499481i	$-0.166476\pi$
$98$	−543.369	+	758.823i	−0.560087	+	0.782170i
$99$	565.626			0.574218
$100$	241.716	+	710.463i	0.241716	+	0.710463i
$101$		−	1602.71i		−	1.57897i	−0.613771	−	0.789484i	$-0.710348\pi$
$101$		−	1602.71i		−	1.57897i	0.613771	−	0.789484i	$-0.289652\pi$
$102$	40.8126	−	785.590i	0.0396181	−	0.762598i
$103$	−292.616			−0.279926			−0.139963	−	0.990157i	$-0.544698\pi$
$103$	−292.616			−0.279926			−0.139963	+	0.990157i	$0.544698\pi$
$104$	−297.145	+	983.214i	−0.280168	+	0.927039i
$105$		−	79.9833i		−	0.0743388i
$106$	−188.142	−	134.722i	−0.172396	−	0.123447i
$107$	−191.142			−0.172695			−0.0863476	−	0.996265i	$-0.527520\pi$
$107$	−191.142			−0.172695			−0.0863476	+	0.996265i	$0.527520\pi$
$108$	391.137	+	1149.65i	0.348492	+	1.02430i
$109$	458.741			0.403114			0.201557	−	0.979477i	$-0.435400\pi$
$109$	458.741			0.403114			0.201557	+	0.979477i	$0.435400\pi$
$110$	−462.172	+	645.431i	−0.400604	+	0.559449i
$111$	−1410.65			−1.20625
$112$	−140.869	−	183.061i	−0.118847	−	0.154443i
$113$		−	1139.90i		−	0.948963i	−0.880265	−	0.474482i	$-0.842636\pi$
$113$		−	1139.90i		−	0.948963i	0.880265	−	0.474482i	$-0.157364\pi$
$114$	−779.927	−	558.481i	−0.640762	−	0.458829i
$115$			987.114i			0.800425i
$116$	−545.445	−	1603.19i	−0.436580	−	1.28321i
$117$		−	510.930i		−	0.403722i
$118$	−683.278	−	489.273i	−0.533058	−	0.381706i
$119$	−136.413	−	213.047i	−0.105084	−	0.164117i
$120$	−480.006	−	145.066i	−0.365153	−	0.110356i
$121$	1194.35			0.897331
$122$	−500.432	+	698.861i	−0.371369	+	0.518622i
$123$		−	1635.94i		−	1.19925i
$124$	−24.4204	+	8.30838i	−0.0176856	+	0.00601706i
$125$	1222.05			0.874429
$126$	93.4197	+	66.8949i	0.0660515	+	0.0472974i
$127$	1900.13			1.32763			0.663815	−	0.747897i	$-0.268936\pi$
$127$	1900.13			1.32763			0.663815	+	0.747897i	$0.268936\pi$
$128$	−1354.10	+	513.382i	−0.935053	+	0.354508i
$129$			1843.93i			1.25852i
$130$	583.017	+	417.480i	0.393339	+	0.281657i
$131$	851.725			0.568058			0.284029	−	0.958816i	$-0.408329\pi$
$131$	851.725			0.568058			0.284029	+	0.958816i	$0.408329\pi$
$132$	513.800	+	1510.18i	0.338792	+	0.995792i
$133$	−308.488			−0.201123
$134$	−7.05116	−	5.04911i	−0.00454573	−	0.00325505i
$135$	847.786			0.540487
$136$	−1525.98	+	432.257i	−0.962144	+	0.272542i
$137$	−1042.37			−0.650043			−0.325022	−	0.945707i	$-0.605372\pi$
$137$	−1042.37			−0.650043			−0.325022	+	0.945707i	$0.605372\pi$
$138$	1612.73	+	1154.83i	0.994819	+	0.712358i
$139$	−669.165			−0.408330			−0.204165	−	0.978936i	$-0.565448\pi$
$139$	−669.165			−0.408330			−0.204165	+	0.978936i	$0.565448\pi$
$140$	−152.666	+	51.9406i	−0.0921617	+	0.0313556i
$141$	717.549			0.428571
$142$	−1564.07	−	1119.98i	−0.924322	−	0.661878i
$143$		−	2281.14i		−	1.33398i
$144$	570.894	−	439.315i	0.330378	−	0.254233i
$145$	−1182.25			−0.677106
$146$	−429.511	−	307.559i	−0.243470	−	0.174341i
$147$	1309.31			0.734626
$148$	916.068	+	2692.55i	0.508786	+	1.49545i
$149$			1322.92i			0.727367i	0.931523	+	0.363684i	$0.118481\pi$
$149$			1322.92i			0.727367i	−0.931523	+	0.363684i	$0.881519\pi$
$150$	612.934	−	855.971i	0.333639	−	0.465932i
$151$	266.561			0.143658			0.0718292	−	0.997417i	$-0.477116\pi$
$151$	266.561			0.143658			0.0718292	+	0.997417i	$0.477116\pi$
$152$	−559.507	+	1851.34i	−0.298566	+	0.987918i
$153$	664.410	−	425.420i	0.351074	−	0.224792i
$154$	417.090	+	298.665i	0.218247	+	0.156280i
$155$			18.0084i			0.00933204i
$156$	1364.15	−	464.115i	0.700123	−	0.238198i
$157$		−	422.085i		−	0.214561i	−0.994229	−	0.107280i	$-0.965786\pi$
$157$		−	422.085i		−	0.214561i	0.994229	−	0.107280i	$-0.0342142\pi$
$158$	−1859.30	−	1331.39i	−0.936191	−	0.670377i
$159$			324.629i			0.161917i
$160$	34.8211	+	1010.40i	0.0172053	+	0.499247i
$161$	637.892			0.312254
$162$	491.392	−	686.236i	0.238317	−	0.332814i
$163$	−3335.56			−1.60283			−0.801415	−	0.598108i	$-0.795919\pi$
$163$	−3335.56			−1.60283			−0.801415	+	0.598108i	$0.795919\pi$
$164$	−3122.55	+	1062.37i	−1.48677	+	0.505834i
$165$	1113.66			0.525443
$166$	−649.306	−	464.947i	−0.303590	−	0.217391i
$167$			3909.11i			1.81135i	0.423968	+	0.905677i	$0.360637\pi$
$167$			3909.11i			1.81135i	−0.423968	+	0.905677i	$0.639363\pi$
$168$	−93.7447	+	310.190i	−0.0430509	+	0.142450i
$169$	136.443			0.0621041
$170$	−57.4460	+	1105.76i	−0.0259171	+	0.498871i
$171$		−	962.054i		−	0.430235i
$172$	3519.55	−	1197.43i	1.56025	−	0.530834i
$173$	−1124.10			−0.494008			−0.247004	−	0.969014i	$-0.579446\pi$
$173$	−1124.10			−0.494008			−0.247004	+	0.969014i	$0.579446\pi$
$174$	−1383.11	+	1931.54i	−0.602607	+	0.841550i
$175$		−	338.566i		−	0.146247i
$176$	2548.87	−	1961.40i	1.09164	−	0.840036i
$177$			1178.96i			0.500656i
$178$	1840.04	−	2569.64i	0.774814	−	1.08204i
$179$		−	103.033i		−	0.0430226i	−0.999769	−	0.0215113i	$-0.993152\pi$
$179$		−	103.033i		−	0.0430226i	0.999769	−	0.0215113i	$-0.00684778\pi$
$180$	−161.982	−	476.106i	−0.0670748	−	0.197149i
$181$	−2314.03			−0.950278			−0.475139	−	0.879911i	$-0.657602\pi$
$181$	−2314.03			−0.950278			−0.475139	+	0.879911i	$0.657602\pi$
$182$	269.784	−	376.757i	0.109878	−	0.153446i
$183$	1205.85			0.487098
$184$	1156.95	−	3828.20i	0.463541	−	1.53380i
$185$	1985.57			0.789092
$186$	29.4218	+	21.0680i	0.0115985	+	0.00830529i
$187$	2966.38	−	1899.37i	1.16002	−	0.742756i
$188$	−465.971	−	1369.60i	−0.180768	−	0.531322i
$189$		−	547.856i		−	0.210850i
$190$	1097.79	+	786.093i	0.419169	+	0.300154i
$191$	−4926.83			−1.86646			−0.933228	−	0.359284i	$-0.883021\pi$
$191$	−4926.83			−1.86646			−0.933228	+	0.359284i	$0.883021\pi$
$192$	1691.52	+	1125.19i	0.635809	+	0.422934i
$193$			4824.36i			1.79930i	0.436611	+	0.899651i	$0.356179\pi$
$193$			4824.36i			1.79930i	−0.436611	+	0.899651i	$0.643821\pi$
$194$	2194.66	+	1571.53i	0.812204	+	0.581594i
$195$		−	1005.97i		−	0.369429i
$196$	−850.256	−	2499.11i	−0.309860	−	0.910755i
$197$	−43.7756			−0.0158319			−0.00791595	−	0.999969i	$-0.502520\pi$
$197$	−43.7756			−0.0158319			−0.00791595	+	0.999969i	$0.502520\pi$
$198$	−931.419	+	1300.74i	−0.334308	+	0.466867i
$199$		−	3511.51i		−	1.25088i	−0.780274	−	0.625438i	$-0.784920\pi$
$199$		−	3511.51i		−	1.25088i	0.780274	−	0.625438i	$-0.215080\pi$
$200$	−2031.85	−	614.060i	−0.718367	−	0.217103i
$201$			12.1664i			0.00426941i
$202$	3685.67	+	2639.19i	1.28378	+	0.919271i
$203$			763.991i			0.264146i
$204$	1739.37	+	1387.49i	0.596963	+	0.476194i
$205$			2302.67i			0.784514i
$206$	481.852	−	672.914i	0.162972	−	0.227593i
$207$			1989.34i			0.667964i
$208$	−1771.74	−	2302.39i	−0.590614	−	0.767509i
$209$		−	4295.27i		−	1.42158i
$210$	183.933	+	131.709i	0.0604410	+	0.0432799i
$211$	2959.42			0.965569			0.482785	−	0.875739i	$-0.339625\pi$
$211$	2959.42			0.965569			0.482785	+	0.875739i	$0.339625\pi$
$212$	619.627	−	210.812i	0.200737	−	0.0682954i
$213$			2698.72i			0.868138i
$214$	314.754	−	439.558i	0.100543	−	0.140409i
$215$		−	2595.43i		−	0.823287i
$216$	−3287.86	−	993.650i	−1.03570	−	0.313006i
$217$	11.6374			0.00364053
$218$	−755.411	+	1054.94i	−0.234692	+	0.327751i
$219$			741.098i			0.228670i
$220$	−723.201	−	2125.67i	−0.221628	−	0.651420i
$221$	−1715.70	−	2679.53i	−0.522219	−	0.815588i
$222$	2322.93	−	3244.00i	0.702273	−	0.980735i
$223$	1816.62			0.545515			0.272757	−	0.962083i	$-0.412064\pi$
$223$	1816.62			0.545515			0.272757	+	0.962083i	$0.412064\pi$
$224$	652.943	−	22.5021i	0.194762	−	0.00671198i
$225$	1055.86			0.312846
$226$	2621.37	+	1877.08i	0.771552	+	0.552484i
$227$	−3744.84			−1.09495			−0.547475	−	0.836822i	$-0.684411\pi$
$227$	−3744.84			−1.09495			−0.547475	+	0.836822i	$0.684411\pi$
$228$	2568.62	−	873.904i	0.746100	−	0.253841i
$229$			3032.89i			0.875193i	0.899171	+	0.437596i	$0.144170\pi$
$229$			3032.89i			0.875193i	−0.899171	+	0.437596i	$0.855830\pi$
$230$	−2270.01	−	1625.48i	−0.650783	−	0.466005i
$231$		−	719.667i		−	0.204981i
$232$	4584.96	+	1385.66i	1.29749	+	0.392124i
$233$			2090.43i			0.587761i	0.955842	+	0.293881i	$0.0949468\pi$
$233$			2090.43i			0.587761i	−0.955842	+	0.293881i	$0.905053\pi$
$234$	1174.96	+	841.350i	0.328245	+	0.235046i
$235$	−1009.99			−0.280359
$236$	2250.31	−	765.608i	0.620690	−	0.211173i
$237$			3208.13i			0.879285i
$238$	714.565	+	37.1227i	0.194615	+	0.0101105i
$239$	−102.308			−0.0276894			−0.0138447	−	0.999904i	$-0.504407\pi$
$239$	−102.308			−0.0276894			−0.0138447	+	0.999904i	$0.504407\pi$
$240$	1124.03	−	864.963i	0.302316	−	0.232638i
$241$		−	970.078i		−	0.259287i	−0.991561	−	0.129644i	$-0.958617\pi$
$241$		−	970.078i		−	0.259287i	0.991561	−	0.129644i	$-0.0413833\pi$
$242$	−1966.73	+	2746.57i	−0.522424	+	0.729572i
$243$	2914.41			0.769379
$244$	−783.070	−	2301.63i	−0.205454	−	0.603881i
$245$	−1842.93			−0.480572
$246$	3762.07	+	2693.90i	0.975045	+	0.698198i
$247$	−3879.92			−0.999487
$248$	21.1068	−	69.8396i	0.00540436	−	0.0178823i
$249$			1120.34i			0.285136i
$250$	−2012.36	+	2810.29i	−0.509090	+	0.710952i
$251$			2165.36i			0.544528i	0.962223	+	0.272264i	$0.0877724\pi$
$251$			2165.36i			0.544528i	−0.962223	+	0.272264i	$0.912228\pi$
$252$	−307.669	+	104.676i	−0.0769100	+	0.0261666i
$253$			8881.77i			2.20708i
$254$	−3128.95	+	4369.62i	−0.772943	+	1.07943i
$255$	1308.15	−	837.605i	0.321253	−	0.205698i
$256$	1049.21	−	3959.34i	0.256154	−	0.966636i
$257$	4668.83			1.13320			0.566602	−	0.823991i	$-0.308258\pi$
$257$	4668.83			1.13320			0.566602	+	0.823991i	$0.308258\pi$
$258$	−4240.38	−	3036.40i	−1.02323	−	0.732705i
$259$		−	1283.11i		−	0.307834i
$260$	−1920.11	+	653.267i	−0.458001	+	0.155823i
$261$	−2382.59			−0.565052
$262$	−1402.54	+	1958.67i	−0.330722	+	0.461858i
$263$	−1721.64			−0.403654			−0.201827	−	0.979421i	$-0.564688\pi$
$263$	−1721.64			−0.403654			−0.201827	+	0.979421i	$0.564688\pi$
$264$	−4318.96	−	1305.27i	−1.00687	−	0.304294i
$265$		−	456.933i		−	0.105921i
$266$	507.989	−	709.414i	0.117093	−	0.163522i
$267$	−4433.79			−1.01627
$268$	23.2223	−	7.90078i	0.00529302	−	0.00180081i
$269$	−1654.44			−0.374992			−0.187496	−	0.982265i	$-0.560037\pi$
$269$	−1654.44			−0.374992			−0.187496	+	0.982265i	$0.560037\pi$
$270$	−1396.05	+	1949.61i	−0.314670	+	0.439442i
$271$	−6057.17			−1.35774			−0.678869	−	0.734259i	$-0.737530\pi$
$271$	−6057.17			−1.35774			−0.678869	+	0.734259i	$0.737530\pi$
$272$	1518.80	−	4221.01i	0.338568	−	0.940942i
$273$	−650.075			−0.144118
$274$	1716.48	−	2397.09i	0.378453	−	0.528516i
$275$	4714.07			1.03371
$276$	−5311.39	+	1807.06i	−1.15836	+	0.394102i
$277$	−6390.39			−1.38614			−0.693071	−	0.720869i	$-0.743743\pi$
$277$	−6390.39			−1.38614			−0.693071	+	0.720869i	$0.743743\pi$
$278$	1101.92	−	1538.84i	0.237729	−	0.331992i
$279$			36.2924i			0.00778770i
$280$	131.951	−	436.609i	0.0281627	−	0.0931870i
$281$	−7615.33			−1.61670			−0.808349	−	0.588703i	$-0.799639\pi$
$281$	−7615.33			−1.61670			−0.808349	+	0.588703i	$0.799639\pi$
$282$	−1181.59	+	1650.11i	−0.249513	+	0.348448i
$283$	−1672.36			−0.351278			−0.175639	−	0.984455i	$-0.556199\pi$
$283$	−1672.36			−0.351278			−0.175639	+	0.984455i	$0.556199\pi$
$284$	5151.12	−	1752.53i	1.07628	−	0.366174i
$285$		−	1894.18i		−	0.393690i
$286$	5245.82	+	3756.37i	1.08459	+	0.776639i
$287$	1488.03			0.306048
$288$	70.1752	+	2036.27i	0.0143580	+	0.416627i
$289$	2055.89	−	4462.16i	0.418460	−	0.908235i
$290$	1946.81	−	2718.75i	0.394209	−	0.550519i
$291$		−	3786.78i		−	0.762834i
$292$	1414.55	−	481.264i	0.283495	−	0.0964515i
$293$		−	1783.03i		−	0.355514i	−0.984074	−	0.177757i	$-0.943116\pi$
$293$		−	1783.03i		−	0.355514i	0.984074	−	0.177757i	$-0.0568841\pi$
$294$	−2156.04	+	3010.95i	−0.427697	+	0.597286i
$295$		−	1659.45i		−	0.327515i
$296$	−7700.40	−	2327.19i	−1.51208	−	0.456978i
$297$	7628.14			1.49033
$298$	−3042.24	−	2178.45i	−0.591384	−	0.423471i
$299$	8022.90			1.55176
$300$	959.111	+	2819.06i	0.184581	+	0.542529i
$301$	−1677.22			−0.321173
$302$	−438.947	+	612.996i	−0.0836375	+	0.116801i
$303$		−	6359.43i		−	1.20574i
$304$	−3336.08	−	4335.28i	−0.629400	−	0.817912i
$305$	−1697.30			−0.318646
$306$	−115.771	+	2228.45i	−0.0216281	+	0.416313i
$307$			7946.57i			1.47731i	0.674082	+	0.738656i	$0.264539\pi$
$307$			7946.57i			1.47731i	−0.674082	+	0.738656i	$0.735461\pi$
$308$	−1373.65	+	467.347i	−0.254126	+	0.0864596i
$309$	−1161.08			−0.213759
$310$	−41.4129	−	29.6544i	−0.00758739	−	0.00543309i
$311$			9967.26i			1.81734i	0.417520	+	0.908668i	$0.362899\pi$
$311$			9967.26i			1.81734i	−0.417520	+	0.908668i	$0.637101\pi$
$312$	−1179.05	+	3901.32i	−0.213943	+	0.707912i
$313$		−	8854.42i		−	1.59898i	−0.600678	−	0.799491i	$-0.705103\pi$
$313$		−	8854.42i		−	1.59898i	0.600678	−	0.799491i	$-0.294897\pi$
$314$	970.645	+	695.048i	0.174448	+	0.124917i
$315$			226.885i			0.0405826i
$316$	6123.44	−	2083.34i	1.09010	−	0.370876i
$317$	8924.75			1.58127			0.790637	−	0.612285i	$-0.209750\pi$
$317$	8924.75			1.58127			0.790637	+	0.612285i	$0.209750\pi$
$318$	−746.532	−	534.568i	−0.131646	−	0.0942675i
$319$	−10637.5			−1.86704
$320$	−2380.91	−	1583.76i	−0.415928	−	0.276672i
$321$	−758.435			−0.131875
$322$	−1050.42	+	1466.93i	−0.181794	+	0.253878i
$323$	−3230.57	−	5045.42i	−0.556512	−	0.869147i
$324$	768.924	+	2260.05i	0.131846	+	0.387527i
$325$		−	4258.22i		−	0.726780i
$326$	5492.68	−	7670.61i	0.933164	−	1.30318i
$327$	1820.25			0.307829
$328$	2698.85	−	8930.16i	0.454326	−	1.50331i
$329$			652.675i			0.109371i
$330$	−1833.86	+	2561.02i	−0.305912	+	0.427210i
$331$		−	203.773i		−	0.0338380i	−0.999857	−	0.0169190i	$-0.994614\pi$
$331$		−	203.773i		−	0.0338380i	0.999857	−	0.0169190i	$-0.00538574\pi$
$332$	2138.43	−	727.543i	0.353498	−	0.120268i
$333$	4001.53			0.658506
$334$	−8989.57	−	6437.14i	−1.47272	−	1.05457i
$335$		−	17.1249i		−	0.00279293i
$336$	−558.956	−	726.370i	−0.0907547	−	0.117937i
$337$			8219.48i			1.32862i	0.747459	+	0.664308i	$0.231274\pi$
$337$			8219.48i			1.32862i	−0.747459	+	0.664308i	$0.768726\pi$
$338$	−224.680	+	313.770i	−0.0361568	+	0.0504935i
$339$		−	4523.03i		−	0.724653i
$340$	−2448.26	−	1952.97i	−0.390517	−	0.311513i
$341$			162.034i			0.0257321i
$342$	2212.38	+	1584.22i	0.349801	+	0.250481i
$343$			2428.88i			0.382354i
$344$	−3041.98	+	10065.5i	−0.476781	+	1.57761i
$345$			3916.79i			0.611226i
$346$	1851.05	−	2585.02i	0.287610	−	0.401652i
$347$	−3076.83			−0.476002			−0.238001	−	0.971265i	$-0.576492\pi$
$347$	−3076.83			−0.476002			−0.238001	+	0.971265i	$0.576492\pi$
$348$	−2164.28	−	6361.35i	−0.333384	−	0.979897i
$349$			6679.79i			1.02453i	0.858827	+	0.512265i	$0.171194\pi$
$349$			6679.79i			1.02453i	−0.858827	+	0.512265i	$0.828806\pi$
$350$	778.583	+	557.518i	0.118906	+	0.0851446i
$351$		−	6890.49i		−	1.04783i
$352$	313.311	+	9091.34i	0.0474418	+	1.37662i
$353$	−5558.14			−0.838045			−0.419022	−	0.907976i	$-0.637627\pi$
$353$	−5558.14			−0.838045			−0.419022	+	0.907976i	$0.637627\pi$
$354$	−2711.19	−	1941.40i	−0.407057	−	0.291481i
$355$		−	3798.60i		−	0.567912i
$356$	2879.27	+	8462.88i	0.428655	+	1.25992i
$357$	−541.277	−	845.353i	−0.0802449	−	0.125324i
$358$	236.939	+	169.665i	0.0349794	+	0.0250476i
$359$	13509.2			1.98604			0.993018	−	0.117963i	$-0.0376365\pi$
$359$	13509.2			1.98604			0.993018	+	0.117963i	$0.0376365\pi$
$360$	1361.61	+	411.503i	0.199342	+	0.0602447i
$361$	−446.681			−0.0651233
$362$	3810.52	−	5321.45i	0.553250	−	0.772621i
$363$	4739.07			0.685225
$364$	422.154	+	1240.81i	0.0607882	+	0.178671i
$365$		−	1043.14i		−	0.149590i
$366$	−1985.67	+	2773.02i	−0.283587	+	0.396034i
$367$		−	2183.01i		−	0.310497i	−0.987875	−	0.155248i	$-0.950382\pi$
$367$		−	2183.01i		−	0.310497i	0.987875	−	0.155248i	$-0.0496178\pi$
$368$	6898.36	+	8964.49i	0.977179	+	1.26985i
$369$			4640.58i			0.654686i
$370$	−3269.65	+	4566.11i	−0.459408	+	0.641570i
$371$	−295.279			−0.0413211
$372$	−96.8981	+	32.9670i	−0.0135052	+	0.00459478i
$373$		−	10025.2i		−	1.39165i	−0.718209	−	0.695827i	$-0.755038\pi$
$373$		−	10025.2i		−	1.39165i	0.718209	−	0.695827i	$-0.244962\pi$
$374$	−516.883	+	9949.33i	−0.0714636	+	1.37558i
$375$	4849.00			0.667737
$376$	3916.92	+	1183.76i	0.537233	+	0.162361i
$377$			9608.87i			1.31268i
$378$	1259.87	+	902.156i	0.171431	+	0.122756i
$379$	2116.32			0.286829			0.143415	−	0.989663i	$-0.454192\pi$
$379$	2116.32			0.286829			0.143415	+	0.989663i	$0.454192\pi$
$380$	−3615.47	+	1230.07i	−0.488078	+	0.166056i
$381$	7539.55			1.01381
$382$	8113.03	−	11330.0i	1.08665	−	1.51752i
$383$	−5242.21			−0.699385			−0.349693	−	0.936864i	$-0.613714\pi$
$383$	−5242.21			−0.699385			−0.349693	+	0.936864i	$0.613714\pi$
$384$	−5372.97	+	2037.06i	−0.714031	+	0.270712i
$385$			1012.97i			0.134093i
$386$	−11094.3	−	7944.29i	−1.46292	−	1.04755i
$387$		−	5230.58i		−	0.687042i
$388$	−7227.92	+	2459.11i	−0.945726	+	0.321758i
$389$		−	6794.48i		−	0.885588i	−0.896623	−	0.442794i	$-0.853987\pi$
$389$		−	6794.48i		−	0.885588i	0.896623	−	0.442794i	$-0.146013\pi$
$390$	2313.37	+	1656.53i	0.300364	+	0.215081i
$391$	6680.17	+	10432.9i	0.864017	+	1.34940i
$392$	7147.19	+	2160.01i	0.920887	+	0.278308i
$393$	3379.58			0.433784
$394$	72.0855	−	100.668i	0.00921729	−	0.0128721i
$395$		−	4515.62i		−	0.575204i
$396$	−1457.47	−	4283.87i	−0.184951	−	0.543617i
$397$	−1568.70			−0.198315			−0.0991574	−	0.995072i	$-0.531615\pi$
$397$	−1568.70			−0.198315			−0.0991574	+	0.995072i	$0.531615\pi$
$398$	8075.22	+	5782.41i	1.01702	+	0.728256i
$399$	−1224.06			−0.153583
$400$	4757.97	−	3661.36i	0.594746	−	0.457670i
$401$		−	5584.03i		−	0.695394i	−0.937607	−	0.347697i	$-0.886964\pi$
$401$		−	5584.03i		−	0.695394i	0.937607	−	0.347697i	$-0.113036\pi$
$402$	−27.9784	−	20.0345i	−0.00347124	−	0.00248564i
$403$	146.365			0.0180918
$404$	−12138.4	+	4129.77i	−1.49482	+	0.508573i
$405$	1666.64			0.204484
$406$	−1756.91	−	1258.07i	−0.214763	−	0.153785i
$407$	17865.6			2.17584
$408$	−6054.96	+	1715.16i	−0.734719	+	0.208120i
$409$	3024.68			0.365674			0.182837	−	0.983143i	$-0.441472\pi$
$409$	3024.68			0.365674			0.182837	+	0.983143i	$0.441472\pi$
$410$	−5295.32	−	3791.81i	−0.637847	−	0.456742i
$411$	−4136.05			−0.496390
$412$	753.996	+	2216.18i	0.0901620	+	0.265008i
$413$	−1072.37			−0.127767
$414$	−4574.77	−	3275.85i	−0.543086	−	0.388887i
$415$		−	1576.94i		−	0.186528i
$416$	8212.20	−	283.013i	0.967876	−	0.0333555i
$417$	−2655.19			−0.311812
$418$	9877.61	+	7073.04i	1.15581	+	0.827640i
$419$	−7564.25			−0.881952			−0.440976	−	0.897519i	$-0.645368\pi$
$419$	−7564.25			−0.881952			−0.440976	+	0.897519i	$0.645368\pi$
$420$	−605.767	+	206.096i	−0.0703772	+	0.0239440i
$421$			2210.99i			0.255955i	0.991777	+	0.127977i	$0.0408485\pi$
$421$			2210.99i			0.255955i	−0.991777	+	0.127977i	$0.959151\pi$
$422$	−4873.29	+	6805.63i	−0.562152	+	0.785054i
$423$	−2035.44			−0.233963
$424$	−535.550	+	1772.07i	−0.0613410	+	0.202970i
$425$	5537.35	−	3545.55i	0.632003	−	0.404669i
$426$	−6206.10	−	4443.99i	−0.705837	−	0.505427i
$427$			1096.83i			0.124307i
$428$	492.523	+	1447.64i	0.0556238	+	0.163492i
$429$		−	9051.40i		−	1.01866i
$430$	5968.57	+	4273.90i	0.669372	+	0.479316i
$431$		−	1387.02i		−	0.155013i	−0.996992	−	0.0775064i	$-0.975304\pi$
$431$		−	1387.02i		−	0.155013i	0.996992	−	0.0775064i	$-0.0246958\pi$
$432$	7699.18	−	5924.68i	0.857470	−	0.659841i
$433$	3801.82			0.421949			0.210974	−	0.977492i	$-0.432336\pi$
$433$	3801.82			0.421949			0.210974	+	0.977492i	$0.432336\pi$
$434$	−19.1633	+	26.7618i	−0.00211951	+	0.00295993i
$435$	−4691.06			−0.517056
$436$	−1182.06	−	3474.35i	−0.129840	−	0.381632i
$437$	15106.7			1.65366
$438$	−1704.26	−	1220.37i	−0.185920	−	0.133131i
$439$			4754.35i			0.516886i	0.966027	+	0.258443i	$0.0832094\pi$
$439$			4754.35i			0.516886i	−0.966027	+	0.258443i	$0.916791\pi$
$440$	6079.17	+	1837.23i	0.658667	+	0.199061i
$441$	−3714.06			−0.401043
$442$	8987.22	+	466.900i	0.967146	+	0.0502447i
$443$			12346.2i			1.32412i	0.749452	+	0.662059i	$0.230317\pi$
$443$			12346.2i			1.32412i	−0.749452	+	0.662059i	$0.769683\pi$
$444$	3634.88	+	10683.8i	0.388522	+	1.14196i
$445$	6240.80			0.664814
$446$	−2991.43	+	4177.58i	−0.317597	+	0.443530i
$447$			5249.24i			0.555437i
$448$	−1023.46	+	1538.59i	−0.107933	+	0.162258i
$449$			9274.67i			0.974830i	0.873170	+	0.487415i	$0.162060\pi$
$449$			9274.67i			0.974830i	−0.873170	+	0.487415i	$0.837940\pi$
$450$	−1738.68	+	2428.09i	−0.182138	+	0.254359i
$451$			20718.8i			2.16321i
$452$	−8633.23	+	2937.23i	−0.898391	+	0.305654i
$453$	1057.69			0.109701
$454$	6166.64	−	8611.80i	0.637477	−	0.890247i
$455$	915.017			0.0942783
$456$	−2220.08	+	7345.97i	−0.227993	+	0.754400i
$457$	−6107.91			−0.625199			−0.312600	−	0.949885i	$-0.601200\pi$
$457$	−6107.91			−0.625199			−0.312600	+	0.949885i	$0.601200\pi$
$458$	−6974.58	−	4994.27i	−0.711573	−	0.509535i
$459$	8960.35	−	5737.28i	0.911184	−	0.583428i
$460$	7476.07	−	2543.54i	0.757769	−	0.257811i
$461$		−	19516.5i		−	1.97175i	−0.167487	−	0.985874i	$-0.553565\pi$
$461$		−	19516.5i		−	1.97175i	0.167487	−	0.985874i	$-0.446435\pi$
$462$	1654.98	+	1185.08i	0.166659	+	0.119339i
$463$	564.749			0.0566871			0.0283435	−	0.999598i	$-0.490977\pi$
$463$	564.749			0.0566871			0.0283435	+	0.999598i	$0.490977\pi$
$464$	−10736.6	+	8262.03i	−1.07421	+	0.826627i
$465$			71.4558i			0.00712620i
$466$	−4807.24	−	3442.31i	−0.477878	−	0.342193i
$467$			4243.88i			0.420521i	0.977645	+	0.210261i	$0.0674313\pi$
$467$			4243.88i			0.420521i	−0.977645	+	0.210261i	$0.932569\pi$
$468$	−3869.61	+	1316.53i	−0.382207	+	0.130036i
$469$	−11.0664			−0.00108955
$470$	1663.15	−	2322.62i	0.163224	−	0.227945i
$471$		−	1674.80i		−	0.163844i
$472$	−1944.96	+	6435.65i	−0.189670	+	0.627595i
$473$		−	23352.9i		−	2.27012i
$474$	−7377.56	−	5282.84i	−0.714900	−	0.511917i
$475$		−	8018.00i		−	0.774507i
$476$	−1262.04	+	1582.12i	−0.121525	+	0.152345i
$477$		−	920.860i		−	0.0883926i
$478$	168.471	−	235.273i	0.0161207	−	0.0225128i
$479$		−	8871.92i		−	0.846280i	−0.906064	−	0.423140i	$-0.860928\pi$
$479$		−	8871.92i		−	0.846280i	0.906064	−	0.423140i	$-0.139072\pi$
$480$	138.167	+	4009.21i	0.0131384	+	0.381238i
$481$		−	16138.0i		−	1.52979i
$482$	2230.84	+	1597.43i	0.210813	+	0.150956i
$483$	2531.11			0.238446
$484$	−3077.52	−	9045.59i	−0.289023	−	0.849510i
$485$			5330.10i			0.499025i
$486$	−4799.16	+	6702.10i	−0.447931	+	0.625542i
$487$		−	636.492i		−	0.0592242i	−0.999561	−	0.0296121i	$-0.990573\pi$
$487$		−	636.492i		−	0.0592242i	0.999561	−	0.0296121i	$-0.00942720\pi$
$488$	6582.42	+	1989.32i	0.610599	+	0.184534i
$489$	−13235.2			−1.22396
$490$	3034.75	−	4238.07i	0.279788	−	0.390728i
$491$			3844.10i			0.353323i	0.984272	+	0.176662i	$0.0565298\pi$
$491$			3844.10i			0.353323i	−0.984272	+	0.176662i	$0.943470\pi$
$492$	−12390.0	+	4215.38i	−1.13534	+	0.386268i
$493$	−12495.3	+	8000.71i	−1.14150	+	0.730900i
$494$	6389.07	−	8922.44i	0.581899	−	0.812631i
$495$	−3159.06			−0.286847
$496$	125.850	+	163.543i	0.0113928	+	0.0148051i
$497$	−2454.73			−0.221549
$498$	−2576.39	−	1844.87i	−0.231829	−	0.166005i
$499$	−9286.78			−0.833133			−0.416567	−	0.909105i	$-0.636767\pi$
$499$	−9286.78			−0.833133			−0.416567	+	0.909105i	$0.636767\pi$
$500$	−3148.91	−	9255.41i	−0.281647	−	0.827829i
$501$			15511.0i			1.38320i
$502$	−4979.57	−	3565.71i	−0.442727	−	0.317023i
$503$			3479.75i			0.308458i	0.988035	+	0.154229i	$0.0492894\pi$
$503$			3479.75i			0.308458i	−0.988035	+	0.154229i	$0.950711\pi$
$504$	265.921	−	879.900i	0.0235021	−	0.0777656i
$505$			8951.25i			0.788763i
$506$	−20424.9	−	14625.6i	−1.79446	−	1.28496i
$507$	541.393			0.0474243
$508$	−4896.13	−	14390.9i	−0.427620	−	1.25688i
$509$		−	13024.0i		−	1.13414i	−0.823670	−	0.567070i	$-0.808077\pi$
$509$		−	13024.0i		−	1.13414i	0.823670	−	0.567070i	$-0.191923\pi$
$510$	−227.941	+	4387.57i	−0.0197910	+	0.380951i
$511$	−674.095			−0.0583566
$512$	7377.35	+	8932.66i	0.636789	+	0.771038i
$513$		−	12974.4i		−	1.11664i
$514$	−7688.18	+	10736.7i	−0.659749	+	0.921349i
$515$	1634.28			0.139835
$516$	13965.3	−	4751.32i	1.19145	−	0.405359i
$517$	−9087.59			−0.773060
$518$	2950.71	+	2112.91i	0.250283	+	0.179220i
$519$	−4460.32			−0.377238
$520$	1659.57	−	5491.32i	0.139956	−	0.463096i
$521$			8878.51i			0.746592i	0.927712	+	0.373296i	$0.121772\pi$
$521$			8878.51i			0.746592i	−0.927712	+	0.373296i	$0.878228\pi$
$522$	3923.42	−	5479.11i	0.328972	−	0.459414i
$523$			13119.8i			1.09692i	0.836177	+	0.548459i	$0.184785\pi$
$523$			13119.8i			1.09692i	−0.836177	+	0.548459i	$0.815215\pi$
$524$	−2194.67	−	6450.68i	−0.182967	−	0.537785i
$525$		−	1343.40i		−	0.111678i
$526$	2835.04	−	3959.17i	0.235006	−	0.328190i
$527$	121.869	+	190.333i	0.0100735	+	0.0157325i
$528$	10113.7	−	7782.69i	0.833602	−	0.641474i
$529$	−19070.6			−1.56741
$530$	1050.78	+	752.433i	0.0861192	+	0.0616672i
$531$		−	3344.30i		−	0.273315i
$532$	794.894	+	2336.39i	0.0647801	+	0.190405i
$533$	18715.3			1.52091
$534$	7301.13	−	10196.1i	0.591668	−	0.826274i
$535$	1067.54			0.0862687
$536$	−20.0713	+	66.4134i	−0.00161744	+	0.00535190i
$537$		−	408.826i		−	0.0328532i
$538$	2724.36	−	3804.62i	0.218319	−	0.304886i
$539$	−16582.1			−1.32513
$540$	−2184.52	−	6420.85i	−0.174087	−	0.511684i
$541$	−10188.3			−0.809664			−0.404832	−	0.914391i	$-0.632670\pi$
$541$	−10188.3			−0.809664			−0.404832	+	0.914391i	$0.632670\pi$
$542$	9974.36	−	13929.4i	0.790472	−	1.10391i
$543$	−9181.88			−0.725658
$544$	7205.82	+	10443.4i	0.567917	+	0.823086i
$545$	−2562.10			−0.201373
$546$	1070.48	−	1494.94i	0.0839054	−	0.117175i
$547$	−4399.60			−0.343900			−0.171950	−	0.985106i	$-0.555007\pi$
$547$	−4399.60			−0.343900			−0.171950	+	0.985106i	$0.555007\pi$
$548$	2685.92	+	7894.58i	0.209374	+	0.615401i
$549$	−3420.57			−0.265914
$550$	−7762.67	+	10840.7i	−0.601821	+	0.840452i
$551$			18093.0i			1.39889i
$552$	4590.68	−	15190.0i	0.353972	−	1.17125i
$553$	−2918.08			−0.224393
$554$	10523.1	−	14695.6i	0.807009	−	1.12700i
$555$	7878.59			0.602572
$556$	1724.26	+	5068.03i	0.131520	+	0.386569i
$557$		−	11164.3i		−	0.849273i	−0.905364	−	0.424637i	$-0.860402\pi$
$557$		−	11164.3i		−	0.849273i	0.905364	−	0.424637i	$-0.139598\pi$
$558$	−83.4596	−	59.7627i	−0.00633177	−	0.00453398i
$559$	−21094.7			−1.59608
$560$	786.762	+	1022.40i	0.0593692	+	0.0771509i
$561$	11770.4	−	7536.54i	0.885821	−	0.567189i
$562$	12540.2	−	17512.6i	0.941238	−	1.31445i
$563$			7510.92i			0.562252i	0.959671	+	0.281126i	$0.0907078\pi$
$563$			7510.92i			0.562252i	−0.959671	+	0.281126i	$0.909292\pi$
$564$	−1848.94	−	5434.47i	−0.138039	−	0.405732i
$565$			6366.42i			0.474048i
$566$	2753.88	−	3845.84i	0.204513	−	0.285605i
$567$		−	1077.01i		−	0.0797713i
$568$	−4452.16	+	14731.6i	−0.328888	+	1.08825i
$569$	−7281.16			−0.536454			−0.268227	−	0.963356i	$-0.586438\pi$
$569$	−7281.16			−0.536454			−0.268227	+	0.963356i	$0.586438\pi$
$570$	4355.94	+	3119.15i	0.320089	+	0.229205i
$571$	−6333.20			−0.464161			−0.232081	−	0.972697i	$-0.574553\pi$
$571$	−6333.20			−0.464161			−0.232081	+	0.972697i	$0.574553\pi$
$572$	−17276.6	+	5877.92i	−1.26289	+	0.429664i
$573$	−19549.3			−1.42528
$574$	−2450.34	+	3421.94i	−0.178180	+	0.248831i
$575$			16579.6i			1.20247i
$576$	−4798.27	−	3191.76i	−0.347097	−	0.230886i
$577$	7726.62			0.557476			0.278738	−	0.960367i	$-0.410084\pi$
$577$	7726.62			0.557476			0.278738	+	0.960367i	$0.410084\pi$
$578$	6875.94	+	12075.7i	0.494812	+	0.869000i
$579$			19142.7i			1.37399i
$580$	3046.34	+	8953.95i	0.218091	+	0.641021i
$581$	−1019.05			−0.0727667
$582$	8708.25	+	6235.70i	0.620221	+	0.444120i
$583$		−	4111.36i		−	0.292067i
$584$	−1222.61	+	4045.47i	−0.0866302	+	0.286648i
$585$			2853.58i			0.201677i
$586$	4100.33	+	2936.12i	0.289050	+	0.206979i
$587$			18469.0i			1.29864i	0.760517	+	0.649318i	$0.224945\pi$
$587$			18469.0i			1.29864i	−0.760517	+	0.649318i	$0.775055\pi$
$588$	−3373.75	−	9916.27i	−0.236617	−	0.695477i
$589$	275.598			0.0192798
$590$	3816.15	+	2732.62i	0.266285	+	0.190679i
$591$	−173.698			−0.0120897
$592$	18032.0	−	13876.0i	1.25188	−	0.963344i
$593$	4888.22			0.338508			0.169254	−	0.985572i	$-0.445864\pi$
$593$	4888.22			0.338508			0.169254	+	0.985572i	$0.445864\pi$
$594$	−12561.3	+	17542.0i	−0.867669	+	1.21171i
$595$	761.877	+	1189.88i	0.0524940	+	0.0819838i
$596$	10019.3	−	3408.82i	0.688605	−	0.234279i
$597$		−	13933.4i		−	0.955202i
$598$	−13211.3	+	18449.8i	−0.903431	+	1.26165i
$599$	13200.8			0.900453			0.450227	−	0.892914i	$-0.351343\pi$
$599$	13200.8			0.900453			0.450227	+	0.892914i	$0.351343\pi$
$600$	−8062.21	−	2436.54i	−0.548564	−	0.165786i
$601$		−	407.078i		−	0.0276291i	−0.999905	−	0.0138145i	$-0.995603\pi$
$601$		−	407.078i		−	0.0276291i	0.999905	−	0.0138145i	$-0.00439744\pi$
$602$	2761.88	−	3857.00i	0.186986	−	0.261129i
$603$		−	34.5119i		−	0.00233073i
$604$	−686.858	−	2018.84i	−0.0462713	−	0.136003i
$605$	−6670.51			−0.448256
$606$	14624.4	+	10472.1i	0.980325	+	0.701980i
$607$		−	21194.5i		−	1.41723i	−0.705595	−	0.708615i	$-0.749320\pi$
$607$		−	21194.5i		−	1.41723i	0.705595	−	0.708615i	$-0.250680\pi$
$608$	15463.1	−	532.899i	1.03144	−	0.0355459i
$609$			3031.46i			0.201709i
$610$	2794.95	−	3903.18i	0.185515	−	0.259074i
$611$			8208.82i			0.543524i
$612$	−4934.00	−	3935.82i	−0.325891	−	0.259961i
$613$			25367.0i			1.67139i	0.549191	+	0.835697i	$0.314936\pi$
$613$			25367.0i			1.67139i	−0.549191	+	0.835697i	$0.685064\pi$
$614$	−18274.3	−	13085.6i	−1.20113	−	0.860087i
$615$			9136.81i			0.599076i
$616$	1187.26	−	3928.48i	0.0776557	−	0.256953i
$617$			2919.48i			0.190492i	0.995454	+	0.0952461i	$0.0303638\pi$
$617$			2919.48i			0.190492i	−0.995454	+	0.0952461i	$0.969636\pi$
$618$	1911.95	−	2670.07i	0.124450	−	0.173796i
$619$	−596.827			−0.0387537			−0.0193768	−	0.999812i	$-0.506168\pi$
$619$	−596.827			−0.0387537			−0.0193768	+	0.999812i	$0.506168\pi$
$620$	136.389	−	46.4029i	0.00883472	−	0.00300578i
$621$			26828.5i			1.73364i
$622$	−22921.2	−	16413.1i	−1.47758	−	1.05805i
$623$		−	4032.93i		−	0.259351i
$624$	−7030.11	−	9135.70i	−0.451009	−	0.586091i
$625$	4900.64			0.313641
$626$	20362.0	+	14580.6i	1.30005	+	0.930923i
$627$		−	17043.3i		−	1.08556i
$628$	−3196.73	+	1087.60i	−0.203126	+	0.0691084i
$629$	20985.7	−	13437.1i	1.33030	−	0.851784i
$630$	−521.755	−	373.612i	−0.0329956	−	0.0236271i
$631$	21069.5			1.32926			0.664632	−	0.747171i	$-0.268588\pi$
$631$	21069.5			1.32926			0.664632	+	0.747171i	$0.268588\pi$
$632$	−5292.55	+	17512.4i	−0.333111	+	1.10222i
$633$	11742.8			0.737334
$634$	−14696.4	+	20523.8i	−0.920613	+	1.28565i
$635$	−10612.3			−0.663209
$636$	2458.63	−	836.484i	0.153288	−	0.0521521i
$637$			14978.6i			0.931671i
$638$	17516.8	−	24462.5i	1.08699	−	1.51800i
$639$		−	7655.34i		−	0.473929i
$640$	7562.74	−	2867.27i	0.467100	−	0.177092i
$641$			5527.94i			0.340625i	0.985390	+	0.170312i	$0.0544776\pi$
$641$			5527.94i			0.340625i	−0.985390	+	0.170312i	$0.945522\pi$
$642$	1248.92	−	1744.13i	0.0767770	−	0.107220i
$643$	11206.4			0.687307			0.343653	−	0.939097i	$-0.388335\pi$
$643$	11206.4			0.687307			0.343653	+	0.939097i	$0.388335\pi$
$644$	−1643.68	−	4831.18i	−0.100575	−	0.295614i
$645$		−	10298.5i		−	0.628684i
$646$	16922.5	+	879.148i	1.03066	+	0.0535443i
$647$	26877.0			1.63315			0.816573	−	0.577242i	$-0.195871\pi$
$647$	26877.0			1.63315			0.816573	+	0.577242i	$0.195871\pi$
$648$	−6463.51	−	1953.39i	−0.391838	−	0.118420i
$649$		−	14931.3i		−	0.903087i
$650$	9792.39	+	7012.02i	0.590906	+	0.423129i
$651$	46.1761			0.00278001
$652$	8594.87	+	25262.4i	0.516260	+	1.51741i
$653$	−12384.8			−0.742195			−0.371097	−	0.928594i	$-0.621018\pi$
$653$	−12384.8			−0.742195			−0.371097	+	0.928594i	$0.621018\pi$
$654$	−2997.41	+	4185.93i	−0.179217	+	0.250279i
$655$	−4756.94			−0.283769
$656$	16092.0	+	20911.7i	0.957754	+	1.24461i
$657$		−	2102.24i		−	0.124834i
$658$	−1500.92	−	1074.76i	−0.0889240	−	0.0636756i
$659$		−	22390.6i		−	1.32354i	−0.749705	−	0.661772i	$-0.769805\pi$
$659$		−	22390.6i		−	1.32354i	0.749705	−	0.661772i	$-0.230195\pi$
$660$	−2869.60	−	8434.47i	−0.169241	−	0.497441i
$661$			16036.4i			0.943636i	0.881696	+	0.471818i	$0.156402\pi$
$661$			16036.4i			0.943636i	−0.881696	+	0.471818i	$0.843598\pi$
$662$	468.605	+	335.553i	0.0275119	+	0.0197004i
$663$	−6807.75	−	10632.2i	−0.398780	−	0.622805i
$664$	−1848.26	+	6115.67i	−0.108022	+	0.357431i
$665$	1722.93			0.100470
$666$	−6589.34	+	9202.11i	−0.383381	+	0.535397i
$667$		−	37412.7i		−	2.17185i
$668$	29606.3	−	10072.8i	1.71482	−	0.583423i
$669$	7208.20			0.416570
$670$	39.3812	+	28.1996i	0.00227079	+	0.00162604i
$671$	−15271.8			−0.878631
$672$	2590.83	−	89.2865i	0.148725	−	0.00512545i
$673$			29521.8i			1.69091i	0.534048	+	0.845454i	$0.320670\pi$
$673$			29521.8i			1.69091i	−0.534048	+	0.845454i	$0.679330\pi$
$674$	−18901.9	−	13535.0i	−1.08023	−	0.773517i
$675$	14239.5			0.811966
$676$	−351.577	−	1033.37i	−0.0200032	−	0.0587944i
$677$	12136.9			0.689008			0.344504	−	0.938785i	$-0.388047\pi$
$677$	12136.9			0.689008			0.344504	+	0.938785i	$0.388047\pi$
$678$	10401.4	+	7448.09i	0.589178	+	0.421891i
$679$	3444.41			0.194675
$680$	8522.69	−	2414.18i	0.480633	−	0.136147i
$681$	−14859.2			−0.836133
$682$	−372.621	−	266.822i	−0.0209214	−	0.0149812i
$683$	4710.94			0.263923			0.131961	−	0.991255i	$-0.457873\pi$
$683$	4710.94			0.263923			0.131961	+	0.991255i	$0.457873\pi$
$684$	−7286.28	+	2478.96i	−0.407307	+	0.138575i
$685$	5821.72			0.324725
$686$	−5585.57	−	3999.65i	−0.310872	−	0.222605i
$687$			12034.3i			0.668320i
$688$	−18137.9	−	23570.4i	−1.00509	−	1.30612i
$689$	−3713.79			−0.205347
$690$	−9007.23	−	6449.79i	−0.496955	−	0.355854i
$691$	−7822.50			−0.430654			−0.215327	−	0.976542i	$-0.569082\pi$
$691$	−7822.50			−0.430654			−0.215327	+	0.976542i	$0.569082\pi$
$692$	2896.50	+	8513.52i	0.159116	+	0.467681i
$693$			2041.45i			0.111902i
$694$	5066.62	−	7075.61i	0.277127	−	0.387012i
$695$	3737.33			0.203979
$696$	18192.8	+	5498.17i	0.990798	+	0.299436i
$697$	15583.0	+	24337.2i	0.846842	+	1.32258i
$698$	−15361.2	−	10999.6i	−0.832992	−	0.596479i
$699$			8294.64i			0.448830i
$700$	−2564.19	+	872.397i	−0.138453	+	0.0471050i
$701$		−	19853.3i		−	1.06969i	−0.844951	−	0.534843i	$-0.820371\pi$
$701$		−	19853.3i		−	1.06969i	0.844951	−	0.534843i	$-0.179629\pi$
$702$	15845.7	+	11346.6i	0.851933	+	0.610042i
$703$		−	30387.0i		−	1.63025i
$704$	−21422.8	−	14250.2i	−1.14688	−	0.762892i
$705$	−4007.56			−0.214090
$706$	9152.60	−	12781.7i	0.487907	−	0.681370i
$707$	5784.47			0.307705
$708$	8929.05	−	3037.87i	0.473975	−	0.161257i
$709$	20864.8			1.10521			0.552605	−	0.833443i	$-0.313634\pi$
$709$	20864.8			1.10521			0.552605	+	0.833443i	$0.313634\pi$
$710$	8735.43	+	6255.16i	0.461739	+	0.330637i
$711$		−	9100.35i		−	0.480014i
$712$	−24202.9	−	7314.55i	−1.27394	−	0.385006i
$713$	−569.882			−0.0299330
$714$	2835.33	+	147.300i	0.148613	+	0.00772068i
$715$			12740.3i			0.666380i
$716$	−780.337	+	265.489i	−0.0407298	+	0.0138572i
$717$	−405.951			−0.0211444
$718$	−22245.6	+	31066.3i	−1.15626	+	1.61474i
$719$		−	25691.2i		−	1.33257i	−0.745697	−	0.666286i	$-0.767883\pi$
$719$		−	25691.2i		−	1.33257i	0.745697	−	0.666286i	$-0.232117\pi$
$720$	−3188.48	+	2453.60i	−0.165038	+	0.127000i
$721$		−	1056.10i		−	0.0545512i
$722$	735.550	−	1027.21i	0.0379146	−	0.0529483i
$723$		−	3849.19i		−	0.197999i
$724$	5962.65	+	17525.7i	0.306077	+	0.899636i
$725$	−19857.1			−1.01721
$726$	−7803.85	+	10898.2i	−0.398936	+	0.557121i
$727$	−4195.31			−0.214024			−0.107012	−	0.994258i	$-0.534128\pi$
$727$	−4195.31			−0.214024			−0.107012	+	0.994258i	$0.534128\pi$
$728$	−3548.60	−	1072.45i	−0.180659	−	0.0545983i
$729$	19621.2			0.996859
$730$	2398.84	+	1717.74i	0.121624	+	0.0870908i
$731$	−17564.2	−	27431.4i	−0.888696	−	1.38794i
$732$	−3107.16	−	9132.70i	−0.156890	−	0.461140i
$733$			434.712i			0.0219051i	0.999940	+	0.0109526i	$0.00348638\pi$
$733$			434.712i			0.0219051i	−0.999940	+	0.0109526i	$0.996514\pi$
$734$	5020.16	+	3594.77i	0.252449	+	0.180770i
$735$	−7312.58			−0.366978
$736$	−31974.7	+	1101.93i	−1.60136	+	0.0551870i
$737$		−	154.085i		−	0.00770121i
$738$	−10671.7	−	7641.66i	−0.532291	−	0.381156i
$739$		−	32433.4i		−	1.61445i	−0.590241	−	0.807227i	$-0.700967\pi$
$739$		−	32433.4i		−	1.61445i	0.590241	−	0.807227i	$-0.299033\pi$
$740$	−5116.30	−	15038.1i	−0.254161	−	0.747040i
$741$	−15395.2			−0.763235
$742$	486.237	−	679.038i	0.0240570	−	0.0335960i
$743$			26343.4i			1.30073i	0.759621	+	0.650366i	$0.225385\pi$
$743$			26343.4i			1.30073i	−0.759621	+	0.650366i	$0.774615\pi$
$744$	83.7499	−	277.118i	0.00412691	−	0.0136554i
$745$		−	7388.59i		−	0.363352i
$746$	23054.5	+	16508.6i	1.13148	+	0.810217i
$747$		−	3178.03i		−	0.155660i
$748$	−22028.8	−	17572.2i	−1.07681	−	0.858963i
$749$		−	689.865i		−	0.0336544i
$750$	−7984.87	+	11151.0i	−0.388755	+	0.542902i
$751$		−	7794.47i		−	0.378727i	−0.981907	−	0.189364i	$-0.939357\pi$
$751$		−	7794.47i		−	0.378727i	0.981907	−	0.189364i	$-0.0606425\pi$
$752$	−9172.23	+	7058.22i	−0.444783	+	0.342270i
$753$			8591.99i			0.415816i
$754$	−22097.0	−	15823.0i	−1.06728	−	0.764242i
$755$	−1488.76			−0.0717636
$756$	−4149.28	+	1411.68i	−0.199613	+	0.0679132i
$757$		−	8502.18i		−	0.408213i	−0.978949	−	0.204106i	$-0.934571\pi$
$757$		−	8502.18i		−	0.408213i	0.978949	−	0.204106i	$-0.0654288\pi$
$758$	−3484.96	+	4866.79i	−0.166991	+	0.233206i
$759$			35242.2i			1.68539i
$760$	3124.88	−	10339.9i	0.149147	−	0.493508i
$761$	−7693.97			−0.366500			−0.183250	−	0.983066i	$-0.558662\pi$
$761$	−7693.97			−0.366500			−0.183250	+	0.983066i	$0.558662\pi$
$762$	−12415.4	+	17338.3i	−0.590240	+	0.824279i
$763$			1655.68i			0.0785578i
$764$	12695.2	+	37314.2i	0.601171	+	1.76699i
$765$	−3710.77	+	2376.00i	−0.175377	+	0.112293i
$766$	8632.37	−	12055.2i	0.407180	−	0.568634i
$767$	−13487.4			−0.634944
$768$	4163.16	−	15710.3i	0.195606	−	0.738149i
$769$	32455.6			1.52195			0.760974	−	0.648783i	$-0.224722\pi$
$769$	32455.6			1.52195			0.760974	+	0.648783i	$0.224722\pi$
$770$	−2329.47	−	1668.06i	−0.109024	−	0.0780686i
$771$	18525.5			0.865345
$772$	36538.1	−	12431.1i	1.70341	−	0.579541i
$773$			38959.3i			1.81277i	0.422458	+	0.906383i	$0.361167\pi$
$773$			38959.3i			1.81277i	−0.422458	+	0.906383i	$0.638833\pi$
$774$	12028.5	+	8613.21i	0.558598	+	0.399994i
$775$			302.469i			0.0140194i
$776$	6247.16	−	20671.1i	0.288995	−	0.956247i
$777$		−	5091.30i		−	0.235070i
$778$	15624.9	+	11188.5i	0.720025	+	0.515587i
$779$	35239.8			1.62079
$780$	−7618.85	+	2592.11i	−0.349742	+	0.118990i
$781$		−	34178.7i		−	1.56595i
$782$	−34992.3	−	1817.90i	−1.60016	−	0.0831305i
$783$	−32132.0			−1.46655
$784$	−16736.5	+	12879.1i	−0.762416	+	0.586694i
$785$			2357.37i			0.107182i
$786$	−5565.16	+	7771.83i	−0.252548	+	0.352687i
$787$	17362.0			0.786390			0.393195	−	0.919455i	$-0.371370\pi$
$787$	17362.0			0.786390			0.393195	+	0.919455i	$0.371370\pi$
$788$	112.798	+	331.542i	0.00509933	+	0.0149882i
$789$	−6831.34			−0.308241
$790$	10384.3	+	7435.88i	0.467668	+	0.334882i
$791$	4114.11			0.184931
$792$	12251.4	+	3702.59i	0.549665	+	0.166118i
$793$			13795.0i			0.617750i
$794$	2583.19	−	3607.46i	0.115458	−	0.161239i
$795$		−	1813.07i		−	0.0808844i
$796$	−26595.0	+	9048.24i	−1.18421	+	0.402897i
$797$			30076.1i			1.33670i	0.743847	+	0.668350i	$0.232999\pi$
$797$			30076.1i			1.33670i	−0.743847	+	0.668350i	$0.767001\pi$
$798$	2015.66	−	2814.90i	0.0894154	−	0.124870i
$799$	−10674.7	+	6834.97i	−0.472645	+	0.302633i
$800$	584.858	+	16970.8i	0.0258473	+	0.750011i
$801$	12577.1			0.554795
$802$	12841.3	+	9195.23i	0.565388	+	0.404856i
$803$		−	9385.85i		−	0.412477i
$804$	92.1443	−	31.3497i	0.00404189	−	0.00137515i
$805$	−3562.67			−0.155985
$806$	−241.020	+	336.589i	−0.0105330	+	0.0147095i
$807$	−6564.67			−0.286354
$808$	10491.3	−	34714.5i	0.456787	−	1.51145i
$809$		−	9812.44i		−	0.426436i	−0.977005	−	0.213218i	$-0.931606\pi$
$809$		−	9812.44i		−	0.426436i	0.977005	−	0.213218i	$-0.0683945\pi$
$810$	−2744.46	+	3832.67i	−0.119050	+	0.166255i
$811$	25891.9			1.12107			0.560535	−	0.828131i	$-0.310596\pi$
$811$	25891.9			1.12107			0.560535	+	0.828131i	$0.310596\pi$
$812$	5786.22	−	1968.61i	0.250069	−	0.0850795i
$813$	−24034.4			−1.03680
$814$	−29419.3	+	41084.6i	−1.26677	+	1.76906i
$815$	18629.3			0.800683
$816$	6026.46	−	16748.6i	0.258540	−	0.718528i
$817$	−39720.2			−1.70090
$818$	−4980.75	+	6955.69i	−0.212895	+	0.297310i
$819$	1844.04			0.0786763
$820$	17439.6	−	5933.38i	0.742706	−	0.252686i
$821$	23472.8			0.997813			0.498907	−	0.866656i	$-0.333735\pi$
$821$	23472.8			0.997813			0.498907	+	0.866656i	$0.333735\pi$
$822$	6810.85	−	9511.45i	0.288997	−	0.403589i
$823$		−	11678.8i		−	0.494649i	−0.968933	−	0.247324i	$-0.920449\pi$
$823$		−	11678.8i		−	0.494649i	0.968933	−	0.247324i	$-0.0795513\pi$
$824$	−6338.03	−	1915.46i	−0.267956	−	0.0809810i
$825$	18705.1			0.789365
$826$	1765.87	−	2466.07i	0.0743858	−	0.103881i
$827$	−3225.66			−0.135631			−0.0678157	−	0.997698i	$-0.521603\pi$
$827$	−3225.66			−0.135631			−0.0678157	+	0.997698i	$0.521603\pi$
$828$	15066.6	−	5126.00i	0.632367	−	0.215146i
$829$		−	2726.47i		−	0.114227i	−0.998368	−	0.0571134i	$-0.981810\pi$
$829$		−	2726.47i		−	0.114227i	0.998368	−	0.0571134i	$-0.0181897\pi$
$830$	3626.41	+	2596.76i	0.151656	+	0.108596i
$831$	−25356.6			−1.05850
$832$	−12872.2	+	19351.2i	−0.536375	+	0.806348i
$833$	−19478.1	+	12471.8i	−0.810175	+	0.518753i
$834$	4372.32	−	6106.01i	0.181536	−	0.253518i
$835$		−	21832.6i		−	0.904850i
$836$	−32531.0	+	11067.8i	−1.34582	+	0.457880i
$837$			489.445i			0.0202123i
$838$	12456.1	−	17395.1i	0.513470	−	0.717069i
$839$		−	734.014i		−	0.0302038i	−0.999886	−	0.0151019i	$-0.995193\pi$
$839$		−	734.014i		−	0.0302038i	0.999886	−	0.0151019i	$-0.00480727\pi$
$840$	523.570	−	1732.43i	0.0215058	−	0.0711601i
$841$	20419.5			0.837242
$842$	−5084.49	−	3640.84i	−0.208103	−	0.149016i
$843$	−30217.0			−1.23455
$844$	−7625.66	−	22413.7i	−0.311003	−	0.914113i
$845$	−762.041			−0.0310237
$846$	3351.76	−	4680.78i	0.136213	−	0.190223i
$847$			4310.61i			0.174869i
$848$	−3193.24	−	4149.64i	−0.129312	−	0.168042i
$849$	−6635.80			−0.268245
$850$	−964.866	+	18572.4i	−0.0389349	+	0.749446i
$851$			62834.2i			2.53106i
$852$	20439.2	−	6953.90i	0.821873	−	0.279621i
$853$	−44819.1			−1.79904			−0.899518	−	0.436883i	$-0.856082\pi$
$853$	−44819.1			−1.79904			−0.899518	+	0.436883i	$0.856082\pi$
$854$	−2522.31	−	1806.15i	−0.101068	−	0.0723714i
$855$			5373.13i			0.214921i
$856$	−4140.11	−	1251.21i	−0.165311	−	0.0499598i
$857$		−	24869.7i		−	0.991288i	−0.868526	−	0.495644i	$-0.834932\pi$
$857$		−	24869.7i		−	0.991288i	0.868526	−	0.495644i	$-0.165068\pi$
$858$	20815.0	+	14905.0i	0.828220	+	0.593062i
$859$		−	32702.9i		−	1.29896i	−0.760378	−	0.649481i	$-0.774986\pi$
$859$		−	32702.9i		−	1.29896i	0.760378	−	0.649481i	$-0.225014\pi$
$860$	−19656.9	+	6687.74i	−0.779413	+	0.265175i
$861$	5904.38			0.233706
$862$	3189.66	+	2284.01i	0.126033	+	0.0902480i
$863$	28968.1			1.14263			0.571313	−	0.820733i	$-0.306434\pi$
$863$	28968.1			1.14263			0.571313	+	0.820733i	$0.306434\pi$
$864$	946.395	+	27461.6i	0.0372651	+	1.08132i
$865$	6278.15			0.246778
$866$	−6260.47	+	8742.84i	−0.245657	+	0.343064i
$867$	8157.61	−	17705.5i	0.319547	−	0.693553i
$868$	−29.9864	−	88.1375i	−0.00117259	−	0.00344652i
$869$		−	40630.3i		−	1.58606i
$870$	7724.79	−	10787.8i	0.301029	−	0.420391i
$871$	−139.185			−0.00541458
$872$	9936.28	+	3002.92i	0.385877	+	0.116619i
$873$			10741.8i			0.416442i
$874$	−24876.2	+	34740.0i	−0.962759	+	1.34451i
$875$			4410.60i			0.170406i
$876$	5612.83	−	1909.62i	0.216484	−	0.0736530i
$877$	43317.7			1.66789			0.833943	−	0.551851i	$-0.186078\pi$
$877$	43317.7			1.66789			0.833943	+	0.551851i	$0.186078\pi$
$878$	−10933.3	−	7829.01i	−0.420253	−	0.300930i
$879$		−	7074.91i		−	0.271480i
$880$	−14235.6	+	10954.6i	−0.545320	+	0.419635i
$881$		−	38749.8i		−	1.48185i	−0.671585	−	0.740927i	$-0.734386\pi$
$881$		−	38749.8i		−	1.48185i	0.671585	−	0.740927i	$-0.265614\pi$
$882$	6115.95	−	8541.02i	0.233486	−	0.326067i
$883$		−	15267.3i		−	0.581865i	−0.956744	−	0.290932i	$-0.906035\pi$
$883$		−	15267.3i		−	0.581865i	0.956744	−	0.290932i	$-0.0939654\pi$
$884$	−15873.0	+	19898.6i	−0.603921	+	0.757083i
$885$		−	6584.57i		−	0.250099i
$886$	−28391.8	−	20330.5i	−1.07657	−	0.770898i
$887$		−	23837.0i		−	0.902330i	−0.892440	−	0.451165i	$-0.851009\pi$
$887$		−	23837.0i		−	0.902330i	0.892440	−	0.451165i	$-0.148991\pi$
$888$	−30554.6	−	9234.12i	−1.15467	−	0.348960i
$889$			6857.90i			0.258725i
$890$	−10276.7	+	14351.6i	−0.387053	+	0.540525i
$891$	14995.9			0.563841
$892$	−4680.95	−	13758.5i	−0.175706	−	0.516443i
$893$			15456.8i			0.579217i
$894$	−12071.4	−	8643.93i	−0.451597	−	0.323374i
$895$			575.445i			0.0214916i
$896$	−1852.89	−	4887.19i	−0.0690856	−	0.182221i
$897$	31834.2			1.18497
$898$	−21328.5	−	15272.6i	−0.792583	−	0.567544i
$899$		−	682.537i		−	0.0253213i
$900$	−2720.67	−	7996.70i	−0.100765	−	0.296174i
$901$	−3092.24	−	4829.38i	−0.114337	−	0.178568i
$902$	−47645.8	−	34117.7i	−1.75879	−	1.25942i
$903$	−6655.06			−0.245256
$904$	7461.78	−	24690.1i	0.274530	−	0.908386i
$905$	12924.0			0.474705
$906$	−1741.70	+	2432.32i	−0.0638678	+	0.0891924i
$907$	8219.18			0.300897			0.150448	−	0.988618i	$-0.451928\pi$
$907$	8219.18			0.300897			0.150448	+	0.988618i	$0.451928\pi$
$908$	9649.47	+	28362.2i	0.352675	+	1.03660i
$909$			18039.5i			0.658231i
$910$	−1506.76	+	2104.21i	−0.0548886	+	0.0766528i
$911$		−	2137.80i		−	0.0777480i	−0.999244	−	0.0388740i	$-0.987623\pi$
$911$		−	2137.80i		−	0.0777480i	0.999244	−	0.0388740i	$-0.0123771\pi$
$912$	−13237.3	−	17202.0i	−0.480626	−	0.624579i
$913$		−	14188.9i		−	0.514331i
$914$	10057.9	−	14046.0i	0.363989	−	0.508317i
$915$	−6734.74			−0.243327
$916$	22970.1	−	7814.97i	0.828552	−	0.281893i
$917$			3074.03i			0.110702i
$918$	−1561.31	+	30053.2i	−0.0561339	+	1.08051i
$919$	4777.02			0.171468			0.0857341	−	0.996318i	$-0.472676\pi$
$919$	4777.02			0.171468			0.0857341	+	0.996318i	$0.472676\pi$
$920$	−6461.64	+	21380.8i	−0.231559	+	0.766199i
$921$			31531.4i			1.12811i
$922$	44881.1	+	32138.0i	1.60313	+	1.14795i
$923$	−30873.6			−1.10099
$924$	−5450.52	+	1854.39i	−0.194057	+	0.0660228i
$925$	33349.8			1.18544
$926$	−929.974	+	1298.72i	−0.0330031	+	0.0460893i
$927$	3293.58			0.116694
$928$	−1319.76	−	38295.5i	−0.0466845	−	1.35464i
$929$			2478.09i			0.0875173i	0.999042	+	0.0437586i	$0.0139333\pi$
$929$			2478.09i			0.0875173i	−0.999042	+	0.0437586i	$0.986067\pi$
$930$	−164.323	−	117.666i	−0.00579394	−	0.00414885i
$931$			28203.9i			0.992854i
$932$	15832.2	−	5386.48i	0.556439	−	0.189313i
$933$			39549.3i			1.38777i
$934$	−9759.43	−	6988.42i	−0.341904	−	0.244827i
$935$	−16567.4	+	10608.1i	−0.579480	+	0.371039i
$936$	3344.54	−	11066.7i	0.116795	−	0.386459i
$937$	−43983.1			−1.53348			−0.766738	−	0.641960i	$-0.778121\pi$
$937$	−43983.1			−1.53348			−0.766738	+	0.641960i	$0.778121\pi$
$938$	18.2231	−	25.4489i	0.000634335	−	0.000885859i
$939$		−	35133.6i		−	1.22102i
$940$	2602.48	+	7649.32i	0.0903016	+	0.265418i
$941$	−44283.1			−1.53410			−0.767051	−	0.641587i	$-0.778277\pi$
$941$	−44283.1			−1.53410			−0.767051	+	0.641587i	$0.778277\pi$
$942$	3851.44	+	2757.90i	0.133213	+	0.0953897i
$943$	−72868.9			−2.51637
$944$	−11596.9	−	15070.3i	−0.399839	−	0.519595i
$945$			3059.81i			0.105329i
$946$	53703.5	+	38455.3i	1.84572	+	1.32166i
$947$	−38659.4			−1.32657			−0.663285	−	0.748367i	$-0.730838\pi$
$947$	−38659.4			−1.32657			−0.663285	+	0.748367i	$0.730838\pi$
$948$	24297.3	−	8266.52i	0.832426	−	0.283211i
$949$	−8478.23			−0.290005
$950$	18438.5	+	13203.3i	0.629711	+	0.450916i
$951$	35412.7			1.20750
$952$	−1560.09	−	5507.53i	−0.0531122	−	0.187500i
$953$	−21138.8			−0.718524			−0.359262	−	0.933237i	$-0.616972\pi$
$953$	−21138.8			−0.718524			−0.359262	+	0.933237i	$0.616972\pi$
$954$	2117.65	+	1516.38i	0.0718674	+	0.0514620i
$955$	27516.7			0.932376
$956$	263.622	+	774.849i	0.00891856	+	0.0262138i
$957$	−42208.9			−1.42572
$958$	20402.3	+	14609.4i	0.688066	+	0.492702i
$959$		−	3762.11i		−	0.126679i
$960$	−9447.27	−	6284.23i	−0.317614	−	0.211274i
$961$	29780.6			0.999651
$962$	37111.7	+	26574.5i	1.24379	+	0.890640i
$963$	2151.42			0.0719922
$964$	−7347.05	+	2499.64i	−0.245469	+	0.0835144i
$965$		−	26944.4i		−	0.898829i
$966$	−4167.98	+	5820.65i	−0.138823	+	0.193868i
$967$	15325.8			0.509662			0.254831	−	0.966986i	$-0.417980\pi$
$967$	15325.8			0.509662			0.254831	+	0.966986i	$0.417980\pi$
$968$	25869.4	+	7818.18i	0.858961	+	0.259593i
$969$	−12818.6	−	20019.8i	−0.424968	−	0.663704i
$970$	−12257.3	−	8777.09i	−0.405731	−	0.290531i
$971$			40479.0i			1.33783i	0.743338	+	0.668915i	$0.233241\pi$
$971$			40479.0i			1.33783i	−0.743338	+	0.668915i	$0.766759\pi$
$972$	−7509.66	−	22072.7i	−0.247811	−	0.728378i
$973$		−	2415.14i		−	0.0795743i
$974$	1463.71	+	1048.11i	0.0481521	+	0.0344802i
$975$		−	16896.3i		−	0.554988i
$976$	−15414.0	+	11861.4i	−0.505524	+	0.389011i
$977$	11827.3			0.387296			0.193648	−	0.981071i	$-0.437968\pi$
$977$	11827.3			0.387296			0.193648	+	0.981071i	$0.437968\pi$
$978$	21794.5	−	30436.4i	0.712589	−	0.995141i
$979$	56152.9			1.83315
$980$	4748.74	+	13957.7i	0.154789	+	0.454962i
$981$	−5163.42			−0.168048
$982$	−8840.06	−	6330.08i	−0.287268	−	0.205704i
$983$			20465.6i			0.664040i	0.943272	+	0.332020i	$0.107730\pi$
$983$			20465.6i			0.664040i	−0.943272	+	0.332020i	$0.892270\pi$
$984$	10708.8	−	35434.2i	0.346936	−	1.14797i
$985$	244.490			0.00790872
$986$	2177.27	−	41909.6i	0.0703228	−	1.35362i
$987$			2589.76i			0.0835187i
$988$	9997.54	+	29385.2i	0.321927	+	0.946223i
$989$	82133.4			2.64074
$990$	5202.03	−	7264.72i	0.167002	−	0.233220i
$991$			25049.8i			0.802961i	0.915868	+	0.401480i	$0.131504\pi$
$991$			25049.8i			0.802961i	−0.915868	+	0.401480i	$0.868496\pi$
$992$	−583.329	+	20.1030i	−0.0186701	+	0.000643418i
$993$		−	808.554i		−	0.0258396i
$994$	4042.21	−	5645.01i	0.128985	−	0.180129i
$995$			19612.0i			0.624867i
$996$	8485.11	−	2886.83i	0.269941	−	0.0918401i
$997$	9705.23			0.308292			0.154146	−	0.988048i	$-0.450737\pi$
$997$	9705.23			0.308292			0.154146	+	0.988048i	$0.450737\pi$
$998$	15292.6	−	21356.3i	0.485048	−	0.677377i
$999$	53965.4			1.70910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.h.a.101.20	yes	52
4.3	odd	2		544.4.h.a.305.15		52
8.3	odd	2		544.4.h.a.305.37		52
8.5	even	2	inner	136.4.h.a.101.17	✓	52
17.16	even	2	inner	136.4.h.a.101.19	yes	52
68.67	odd	2		544.4.h.a.305.38		52
136.67	odd	2		544.4.h.a.305.16		52
136.101	even	2	inner	136.4.h.a.101.18	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.h.a.101.17	✓	52	8.5	even	2	inner
136.4.h.a.101.18	yes	52	136.101	even	2	inner
136.4.h.a.101.19	yes	52	17.16	even	2	inner
136.4.h.a.101.20	yes	52	1.1	even	1	trivial
544.4.h.a.305.15		52	4.3	odd	2
544.4.h.a.305.16		52	136.67	odd	2
544.4.h.a.305.37		52	8.3	odd	2
544.4.h.a.305.38		52	68.67	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.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64670 + 2.29965i) q^{2} +3.96792 q^{3} +(-2.57674 - 7.57367i) q^{4} -5.58507 q^{5} +(-6.53398 + 9.12481i) q^{6} +3.60918i q^{7} +(21.6599 + 6.54599i) q^{8} -11.2556 q^{9} +O(q^{10})\)	\(q+(-1.64670 + 2.29965i) q^{2} +3.96792 q^{3} +(-2.57674 - 7.57367i) q^{4} -5.58507 q^{5} +(-6.53398 + 9.12481i) q^{6} +3.60918i q^{7} +(21.6599 + 6.54599i) q^{8} -11.2556 q^{9} +(9.19694 - 12.8437i) q^{10} -50.2528 q^{11} +(-10.2243 - 30.0517i) q^{12} +45.3934i q^{13} +(-8.29983 - 5.94324i) q^{14} -22.1611 q^{15} +(-50.7208 + 39.0307i) q^{16} +(-59.0292 + 37.7962i) q^{17} +(18.5347 - 25.8839i) q^{18} +85.4733i q^{19} +(14.3913 + 42.2994i) q^{20} +14.3209i q^{21} +(82.7515 - 115.564i) q^{22} -176.742i q^{23} +(85.9446 + 25.9740i) q^{24} -93.8070 q^{25} +(-104.389 - 74.7494i) q^{26} -151.795 q^{27} +(27.3347 - 9.29991i) q^{28} +211.680 q^{29} +(36.4927 - 50.9627i) q^{30} -3.22438i q^{31} +(-6.23469 - 180.912i) q^{32} -199.399 q^{33} +(10.2856 - 197.985i) q^{34} -20.1575i q^{35} +(29.0028 + 85.2463i) q^{36} -355.514 q^{37} +(-196.558 - 140.749i) q^{38} +180.117i q^{39} +(-120.972 - 36.5598i) q^{40} -412.291i q^{41} +(-32.9331 - 23.5823i) q^{42} +464.709i q^{43} +(129.488 + 380.598i) q^{44} +62.8633 q^{45} +(406.443 + 291.041i) q^{46} +180.837 q^{47} +(-201.256 + 154.871i) q^{48} +329.974 q^{49} +(154.472 - 215.723i) q^{50} +(-234.223 + 149.972i) q^{51} +(343.794 - 116.967i) q^{52} +81.8134i q^{53} +(249.962 - 349.075i) q^{54} +280.665 q^{55} +(-23.6257 + 78.1743i) q^{56} +339.151i q^{57} +(-348.574 + 486.789i) q^{58} +297.123i q^{59} +(57.1033 + 167.841i) q^{60} +303.899 q^{61} +(7.41493 + 5.30959i) q^{62} -40.6235i q^{63} +(426.300 + 283.571i) q^{64} -253.525i q^{65} +(328.351 - 458.547i) q^{66} +3.06619i q^{67} +(438.359 + 349.676i) q^{68} -701.297i q^{69} +(46.3551 + 33.1934i) q^{70} +680.135i q^{71} +(-243.795 - 73.6791i) q^{72} +186.773i q^{73} +(585.427 - 817.557i) q^{74} -372.219 q^{75} +(647.346 - 220.242i) q^{76} -181.371i q^{77} +(-414.206 - 296.600i) q^{78} +808.517i q^{79} +(283.279 - 217.989i) q^{80} -298.410 q^{81} +(948.122 + 678.920i) q^{82} +282.350i q^{83} +(108.462 - 36.9013i) q^{84} +(329.682 - 211.094i) q^{85} +(-1068.67 - 765.237i) q^{86} +839.930 q^{87} +(-1088.47 - 328.955i) q^{88} -1117.41 q^{89} +(-103.517 + 144.563i) q^{90} -163.833 q^{91} +(-1338.58 + 455.417i) q^{92} -12.7941i q^{93} +(-297.786 + 415.862i) q^{94} -477.374i q^{95} +(-24.7387 - 717.844i) q^{96} -954.348i q^{97} +(-543.369 + 758.823i) q^{98} +565.626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9}+O(q^{10}) \) 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9	\( 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9} - 232 q^{15} - 78 q^{16} - 28 q^{17} - 2 q^{18} + 1052 q^{25} + 448 q^{26} - 368 q^{30} + 958 q^{32} - 344 q^{33} - 198 q^{34} + 138 q^{36} - 524 q^{38} + 936 q^{47} - 1964 q^{49} - 1038 q^{50} - 1424 q^{52} - 1384 q^{55} + 2320 q^{60} - 2078 q^{64} - 1888 q^{66} - 874 q^{68} + 2472 q^{70} - 4010 q^{72} + 436 q^{76} + 1884 q^{81} - 2264 q^{84} - 1420 q^{86} + 1976 q^{87} - 224 q^{89} + 80 q^{94} + 5746 q^{98}+O(q^{100}) \) 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9 - 232 * q^15 - 78 * q^16 - 28 * q^17 - 2 * q^18 + 1052 * q^25 + 448 * q^26 - 368 * q^30 + 958 * q^32 - 344 * q^33 - 198 * q^34 + 138 * q^36 - 524 * q^38 + 936 * q^47 - 1964 * q^49 - 1038 * q^50 - 1424 * q^52 - 1384 * q^55 + 2320 * q^60 - 2078 * q^64 - 1888 * q^66 - 874 * q^68 + 2472 * q^70 - 4010 * q^72 + 436 * q^76 + 1884 * q^81 - 2264 * q^84 - 1420 * q^86 + 1976 * q^87 - 224 * q^89 + 80 * q^94 + 5746 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more