LMFDB - Embedded newform 124.4.d.c.123.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,4,Mod(123,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("124.123");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	124.d (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:	$7.31623684071$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			123.8
Character	$\chi$	$=$	124.123
Dual form			124.4.d.c.123.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59794 + 1.11835i) q^{2} +8.21784 q^{3} +(5.49858 - 5.81081i) q^{4} +6.37189 q^{5} +(-21.3495 + 9.19042i) q^{6} +24.3788i q^{7} +(-7.78647 + 21.2455i) q^{8} +40.5329 q^{9} +O(q^{10})$	\(q+(-2.59794 + 1.11835i) q^{2} +8.21784 q^{3} +(5.49858 - 5.81081i) q^{4} +6.37189 q^{5} +(-21.3495 + 9.19042i) q^{6} +24.3788i q^{7} +(-7.78647 + 21.2455i) q^{8} +40.5329 q^{9} +(-16.5538 + 7.12601i) q^{10} +4.11924 q^{11} +(45.1865 - 47.7523i) q^{12} -3.21970i q^{13} +(-27.2640 - 63.3346i) q^{14} +52.3632 q^{15} +(-3.53113 - 63.9025i) q^{16} +7.66134i q^{17} +(-105.302 + 45.3300i) q^{18} -53.5148i q^{19} +(35.0364 - 37.0259i) q^{20} +200.341i q^{21} +(-10.7015 + 4.60675i) q^{22} +134.680 q^{23} +(-63.9879 + 174.592i) q^{24} -84.3990 q^{25} +(3.60075 + 8.36459i) q^{26} +111.211 q^{27} +(141.661 + 134.049i) q^{28} +191.200i q^{29} +(-136.036 + 58.5604i) q^{30} +(172.600 - 0.266751i) q^{31} +(80.6391 + 162.066i) q^{32} +33.8512 q^{33} +(-8.56806 - 19.9037i) q^{34} +155.339i q^{35} +(222.874 - 235.529i) q^{36} -342.585i q^{37} +(59.8483 + 139.028i) q^{38} -26.4590i q^{39} +(-49.6145 + 135.374i) q^{40} -368.673 q^{41} +(-224.051 - 520.474i) q^{42} +0.524399 q^{43} +(22.6500 - 23.9361i) q^{44} +258.271 q^{45} +(-349.890 + 150.619i) q^{46} -521.551i q^{47} +(-29.0182 - 525.141i) q^{48} -251.326 q^{49} +(219.264 - 94.3877i) q^{50} +62.9596i q^{51} +(-18.7091 - 17.7038i) q^{52} +679.302i q^{53} +(-288.920 + 124.373i) q^{54} +26.2473 q^{55} +(-517.939 - 189.825i) q^{56} -439.776i q^{57} +(-213.829 - 496.727i) q^{58} +151.118i q^{59} +(287.923 - 304.273i) q^{60} -622.927i q^{61} +(-448.107 + 193.721i) q^{62} +988.143i q^{63} +(-390.742 - 330.855i) q^{64} -20.5156i q^{65} +(-87.9435 + 37.8575i) q^{66} -639.069i q^{67} +(44.5186 + 42.1265i) q^{68} +1106.78 q^{69} +(-173.723 - 403.561i) q^{70} -406.107i q^{71} +(-315.608 + 861.141i) q^{72} -424.285i q^{73} +(383.130 + 890.016i) q^{74} -693.578 q^{75} +(-310.965 - 294.256i) q^{76} +100.422i q^{77} +(29.5904 + 68.7388i) q^{78} -985.028 q^{79} +(-22.4999 - 407.180i) q^{80} -180.473 q^{81} +(957.789 - 412.305i) q^{82} +811.239 q^{83} +(1164.14 + 1101.59i) q^{84} +48.8172i q^{85} +(-1.36236 + 0.586462i) q^{86} +1571.25i q^{87} +(-32.0743 + 87.5152i) q^{88} +729.206i q^{89} +(-670.973 + 288.838i) q^{90} +78.4924 q^{91} +(740.549 - 782.600i) q^{92} +(1418.40 - 2.19212i) q^{93} +(583.277 + 1354.96i) q^{94} -340.991i q^{95} +(662.679 + 1331.83i) q^{96} -453.812 q^{97} +(652.929 - 281.070i) q^{98} +166.965 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9	$ 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9} + 228 q^{10} - 104 q^{14} - 78 q^{16} + 114 q^{18} - 44 q^{20} + 28 q^{25} + 48 q^{28} - 602 q^{32} - 136 q^{33} - 482 q^{36} + 420 q^{38} - 516 q^{40} - 4 q^{41} - 1596 q^{45} + 1876 q^{49} - 662 q^{50} + 1576 q^{56} - 838 q^{62} - 302 q^{64} - 3900 q^{66} - 872 q^{69} - 912 q^{70} - 2166 q^{72} + 3220 q^{76} - 476 q^{78} + 572 q^{80} - 2056 q^{81} + 3096 q^{82} - 6220 q^{90} - 2904 q^{93} + 6408 q^{94} - 1836 q^{97} - 1358 q^{98}+O(q^{100}) $ 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9 + 228 * q^10 - 104 * q^14 - 78 * q^16 + 114 * q^18 - 44 * q^20 + 28 * q^25 + 48 * q^28 - 602 * q^32 - 136 * q^33 - 482 * q^36 + 420 * q^38 - 516 * q^40 - 4 * q^41 - 1596 * q^45 + 1876 * q^49 - 662 * q^50 + 1576 * q^56 - 838 * q^62 - 302 * q^64 - 3900 * q^66 - 872 * q^69 - 912 * q^70 - 2166 * q^72 + 3220 * q^76 - 476 * q^78 + 572 * q^80 - 2056 * q^81 + 3096 * q^82 - 6220 * q^90 - 2904 * q^93 + 6408 * q^94 - 1836 * q^97 - 1358 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.59794	+	1.11835i	−0.918511	+	0.395397i
$2$	−2.59794	+	1.11835i	−0.918511	+	0.395397i
$3$	8.21784			1.58152			0.790762	−	0.612124i	$-0.209685\pi$
$3$	8.21784			1.58152			0.790762	+	0.612124i	$0.209685\pi$
$4$	5.49858	−	5.81081i	0.687323	−	0.726352i
$5$	6.37189			0.569919			0.284960	−	0.958540i	$-0.408020\pi$
$5$	6.37189			0.569919			0.284960	+	0.958540i	$0.408020\pi$
$6$	−21.3495	+	9.19042i	−1.45265	+	0.625329i
$7$			24.3788i			1.31633i	0.752873	+	0.658166i	$0.228667\pi$
$7$			24.3788i			1.31633i	−0.752873	+	0.658166i	$0.771333\pi$
$8$	−7.78647	+	21.2455i	−0.344117	+	0.938927i
$9$	40.5329			1.50122
$10$	−16.5538	+	7.12601i	−0.523477	+	0.225344i
$11$	4.11924			0.112909			0.0564544	−	0.998405i	$-0.482020\pi$
$11$	4.11924			0.112909			0.0564544	+	0.998405i	$0.482020\pi$
$12$	45.1865	−	47.7523i	1.08702	−	1.14874i
$13$		−	3.21970i		−	0.0686911i	−0.999410	−	0.0343455i	$-0.989065\pi$
$13$		−	3.21970i		−	0.0686911i	0.999410	−	0.0343455i	$-0.0109347\pi$
$14$	−27.2640	−	63.3346i	−0.520473	−	1.20906i
$15$	52.3632			0.901341
$16$	−3.53113	−	63.9025i	−0.0551738	−	0.998477i
$17$			7.66134i			0.109303i	0.998505	+	0.0546514i	$0.0174047\pi$
$17$			7.66134i			0.109303i	−0.998505	+	0.0546514i	$0.982595\pi$
$18$	−105.302	+	45.3300i	−1.37888	+	0.593576i
$19$		−	53.5148i		−	0.646166i	−0.946371	−	0.323083i	$-0.895281\pi$
$19$		−	53.5148i		−	0.646166i	0.946371	−	0.323083i	$-0.104719\pi$
$20$	35.0364	−	37.0259i	0.391719	−	0.413962i
$21$			200.341i			2.08181i
$22$	−10.7015	+	4.60675i	−0.103708	+	0.0446437i
$23$	134.680			1.22099			0.610493	−	0.792021i	$-0.290971\pi$
$23$	134.680			1.22099			0.610493	+	0.792021i	$0.290971\pi$
$24$	−63.9879	+	174.592i	−0.544228	+	1.48494i
$25$	−84.3990			−0.675192
$26$	3.60075	+	8.36459i	0.0271602	+	0.0630935i
$27$	111.211			0.792688
$28$	141.661	+	134.049i	0.956119	+	0.904745i
$29$			191.200i			1.22431i	0.790738	+	0.612155i	$0.209697\pi$
$29$			191.200i			1.22431i	−0.790738	+	0.612155i	$0.790303\pi$
$30$	−136.036	+	58.5604i	−0.827891	+	0.356387i
$31$	172.600	−	0.266751i	0.999999	−	0.00154548i
$31$	172.600	−	0.266751i	0.999999	−	0.00154548i
$32$	80.6391	+	162.066i	0.445472	+	0.895296i
$33$	33.8512			0.178568
$34$	−8.56806	−	19.9037i	−0.0432179	−	0.100396i
$35$			155.339i			0.750202i
$36$	222.874	−	235.529i	1.03182	−	1.09041i
$37$		−	342.585i		−	1.52218i	−0.648646	−	0.761090i	$-0.724665\pi$
$37$		−	342.585i		−	1.52218i	0.648646	−	0.761090i	$-0.275335\pi$
$38$	59.8483	+	139.028i	0.255492	+	0.593510i
$39$		−	26.4590i		−	0.108637i
$40$	−49.6145	+	135.374i	−0.196119	+	0.535112i
$41$	−368.673			−1.40432			−0.702158	−	0.712021i	$-0.747780\pi$
$41$	−368.673			−1.40432			−0.702158	+	0.712021i	$0.747780\pi$
$42$	−224.051	−	520.474i	−0.823140	−	1.91216i
$43$	0.524399			0.00185977			0.000929886	−	1.00000i	$-0.499704\pi$
$43$	0.524399			0.00185977			0.000929886		1.00000i	$0.499704\pi$
$44$	22.6500	−	23.9361i	0.0776048	−	0.0820115i
$45$	258.271			0.855573
$46$	−349.890	+	150.619i	−1.12149	+	0.482774i
$47$		−	521.551i		−	1.61864i	−0.587368	−	0.809320i	$-0.699836\pi$
$47$		−	521.551i		−	1.61864i	0.587368	−	0.809320i	$-0.300164\pi$
$48$	−29.0182	−	525.141i	−0.0872588	−	1.57911i
$49$	−251.326			−0.732727
$50$	219.264	−	94.3877i	0.620171	−	0.266969i
$51$			62.9596i			0.172865i
$52$	−18.7091	−	17.7038i	−0.0498939	−	0.0472130i
$53$			679.302i			1.76055i	0.474461	+	0.880276i	$0.342643\pi$
$53$			679.302i			1.76055i	−0.474461	+	0.880276i	$0.657357\pi$
$54$	−288.920	+	124.373i	−0.728092	+	0.313426i
$55$	26.2473			0.0643489
$56$	−517.939	−	189.825i	−1.23594	−	0.452971i
$57$		−	439.776i		−	1.02193i
$58$	−213.829	−	496.727i	−0.484088	−	1.12454i
$59$			151.118i			0.333455i	0.986003	+	0.166728i	$0.0533201\pi$
$59$			151.118i			0.333455i	−0.986003	+	0.166728i	$0.946680\pi$
$60$	287.923	−	304.273i	0.619512	−	0.654691i
$61$		−	622.927i		−	1.30750i	−0.756710	−	0.653751i	$-0.773194\pi$
$61$		−	622.927i		−	1.30750i	0.756710	−	0.653751i	$-0.226806\pi$
$62$	−448.107	+	193.721i	−0.917898	+	0.396816i
$63$			988.143i			1.97610i
$64$	−390.742	−	330.855i	−0.763168	−	0.646201i
$65$		−	20.5156i		−	0.0391484i
$66$	−87.9435	+	37.8575i	−0.164017	+	0.0706052i
$67$		−	639.069i		−	1.16529i	−0.812726	−	0.582647i	$-0.802017\pi$
$67$		−	639.069i		−	1.16529i	0.812726	−	0.582647i	$-0.197983\pi$
$68$	44.5186	+	42.1265i	0.0793923	+	0.0751263i
$69$	1106.78			1.93102
$70$	−173.723	−	403.561i	−0.296627	−	0.689069i
$71$		−	406.107i		−	0.678817i	−0.940639	−	0.339409i	$-0.889773\pi$
$71$		−	406.107i		−	0.678817i	0.940639	−	0.339409i	$-0.110227\pi$
$72$	−315.608	+	861.141i	−0.516594	+	1.40953i
$73$		−	424.285i		−	0.680257i	−0.940379	−	0.340128i	$-0.889529\pi$
$73$		−	424.285i		−	0.680257i	0.940379	−	0.340128i	$-0.110471\pi$
$74$	383.130	+	890.016i	0.601865	+	1.39814i
$75$	−693.578			−1.06783
$76$	−310.965	−	294.256i	−0.469343	−	0.444125i
$77$			100.422i			0.148625i
$78$	29.5904	+	68.7388i	0.0429545	+	0.0997838i
$79$	−985.028			−1.40284			−0.701419	−	0.712749i	$-0.747450\pi$
$79$	−985.028			−1.40284			−0.701419	+	0.712749i	$0.747450\pi$
$80$	−22.4999	−	407.180i	−0.0314446	−	0.569051i
$81$	−180.473			−0.247563
$82$	957.789	−	412.305i	1.28988	−	0.555262i
$83$	811.239			1.07283			0.536416	−	0.843954i	$-0.319778\pi$
$83$	811.239			1.07283			0.536416	+	0.843954i	$0.319778\pi$
$84$	1164.14	+	1101.59i	1.51213	+	1.43088i
$85$			48.8172i			0.0622938i
$86$	−1.36236	+	0.586462i	−0.00170822	+	0.000735347i
$87$			1571.25i			1.93628i
$88$	−32.0743	+	87.5152i	−0.0388538	+	0.106013i
$89$			729.206i			0.868491i	0.900794	+	0.434246i	$0.142985\pi$
$89$			729.206i			0.868491i	−0.900794	+	0.434246i	$0.857015\pi$
$90$	−670.973	+	288.838i	−0.785853	+	0.338291i
$91$	78.4924			0.0904202
$92$	740.549	−	782.600i	0.839213	−	0.886866i
$93$	1418.40	−	2.19212i	1.58152	−	0.00244421i
$94$	583.277	+	1354.96i	0.640004	+	1.48674i
$95$		−	340.991i		−	0.368262i
$96$	662.679	+	1331.83i	0.704525	+	1.41593i
$97$	−453.812			−0.475027			−0.237513	−	0.971384i	$-0.576332\pi$
$97$	−453.812			−0.475027			−0.237513	+	0.971384i	$0.576332\pi$
$98$	652.929	−	281.070i	0.673018	−	0.289718i
$99$	166.965			0.169501
$100$	−464.075	+	490.427i	−0.464075	+	0.490427i
$101$	−91.5450			−0.0901888			−0.0450944	−	0.998983i	$-0.514359\pi$
$101$	−91.5450			−0.0901888			−0.0450944	+	0.998983i	$0.514359\pi$
$102$	−70.4109	−	163.565i	−0.0683502	−	0.158778i
$103$		−	150.428i		−	0.143904i	−0.997408	−	0.0719519i	$-0.977077\pi$
$103$		−	150.428i		−	0.143904i	0.997408	−	0.0719519i	$-0.0229228\pi$
$104$	68.4041	+	25.0701i	0.0644959	+	0.0236377i
$105$			1276.55i			1.18646i
$106$	−759.697	−	1764.79i	−0.696116	−	1.61709i
$107$			822.621i			0.743232i	0.928387	+	0.371616i	$0.121196\pi$
$107$			822.621i			0.743232i	−0.928387	+	0.371616i	$0.878804\pi$
$108$	611.503	−	646.227i	0.544833	−	0.575770i
$109$	−1101.11			−0.967588			−0.483794	−	0.875182i	$-0.660742\pi$
$109$	−1101.11			−0.967588			−0.483794	+	0.875182i	$0.660742\pi$
$110$	−68.1890	+	29.3537i	−0.0591051	+	0.0254433i
$111$		−	2815.31i		−	2.40736i
$112$	1557.87	−	86.0846i	1.31433	−	0.0726271i
$113$	−1626.67			−1.35420			−0.677100	−	0.735891i	$-0.736763\pi$
$113$	−1626.67			−1.35420			−0.677100	+	0.735891i	$0.736763\pi$
$114$	491.824	+	1142.51i	0.404066	+	0.938650i
$115$	858.166			0.695864
$116$	1111.03	+	1051.33i	0.889280	+	0.841497i
$117$		−	130.504i		−	0.103120i
$118$	−169.003	−	392.595i	−0.131847	−	0.306282i
$119$	−186.774			−0.143879
$120$	−407.724	+	1112.48i	−0.310166	+	0.846293i
$121$	−1314.03			−0.987252
$122$	696.651	+	1618.33i	0.516982	+	1.20095i
$123$	−3029.69			−2.22096
$124$	947.508	−	1004.42i	0.686200	−	0.727413i
$125$	−1334.27			−0.954724
$126$	−1105.09	−	2567.14i	−0.781343	−	1.81507i
$127$	8.22941			0.00574994			0.00287497	−	0.999996i	$-0.499085\pi$
$127$	8.22941			0.00574994			0.00287497	+	0.999996i	$0.499085\pi$
$128$	1385.14	+	422.554i	0.956483	+	0.291788i
$129$	4.30943			0.00294127
$130$	22.9436	+	53.2982i	0.0154791	+	0.0359582i
$131$		−	897.000i		−	0.598254i	−0.954213	−	0.299127i	$-0.903305\pi$
$131$		−	897.000i		−	0.598254i	0.954213	−	0.299127i	$-0.0966954\pi$
$132$	186.134	−	196.703i	0.122734	−	0.129703i
$133$	1304.63			0.850568
$134$	714.703	+	1660.26i	0.460753	+	1.07033i
$135$	708.625			0.451768
$136$	−162.769	−	59.6548i	−0.102627	−	0.0376129i
$137$		−	3027.12i		−	1.88777i	−0.330280	−	0.943883i	$-0.607143\pi$
$137$		−	3027.12i		−	1.88777i	0.330280	−	0.943883i	$-0.392857\pi$
$138$	−2875.34	+	1237.77i	−1.77366	+	0.763519i
$139$	−1864.92			−1.13799			−0.568994	−	0.822342i	$-0.692667\pi$
$139$	−1864.92			−1.13799			−0.568994	+	0.822342i	$0.692667\pi$
$140$	902.646	+	854.145i	0.544911	+	0.515631i
$141$		−	4286.02i		−	2.55992i
$142$	454.170	+	1055.04i	0.268402	+	0.623501i
$143$		−	13.2627i		−	0.00775583i
$144$	−143.127	−	2590.15i	−0.0828280	−	1.49893i
$145$			1218.31i			0.697758i
$146$	474.499	+	1102.27i	0.268971	+	0.624823i
$147$	−2065.35			−1.15883
$148$	−1990.70	−	1883.73i	−1.10564	−	1.04623i
$149$	2717.97			1.49440			0.747199	−	0.664601i	$-0.231398\pi$
$149$	2717.97			1.49440			0.747199	+	0.664601i	$0.231398\pi$
$150$	1801.87	−	775.663i	0.980815	−	0.422217i
$151$	843.042			0.454343			0.227172	−	0.973855i	$-0.427052\pi$
$151$	843.042			0.454343			0.227172	+	0.973855i	$0.427052\pi$
$152$	1136.95	+	416.692i	0.606702	+	0.222356i
$153$			310.536i			0.164087i
$154$	−112.307	−	260.890i	−0.0587660	−	0.136514i
$155$	1099.79	−	1.69971i	0.569918	−	0.000880799i
$156$	−153.748	−	145.487i	−0.0789084	−	0.0746684i
$157$	674.043			0.342640			0.171320	−	0.985215i	$-0.445197\pi$
$157$	674.043			0.342640			0.171320	+	0.985215i	$0.445197\pi$
$158$	2559.04	−	1101.61i	1.28852	−	0.554678i
$159$			5582.39i			2.78436i
$160$	513.823	+	1032.67i	0.253883	+	0.510246i
$161$			3283.33i			1.60722i
$162$	468.859	−	201.832i	0.227389	−	0.0978855i
$163$			2780.43i			1.33608i	0.744127	+	0.668038i	$0.232866\pi$
$163$			2780.43i			1.33608i	−0.744127	+	0.668038i	$0.767134\pi$
$164$	−2027.18	+	2142.29i	−0.965219	+	1.02003i
$165$	215.696			0.101769
$166$	−2107.55	+	907.249i	−0.985407	+	0.424194i
$167$	2616.11			1.21222			0.606110	−	0.795381i	$-0.292729\pi$
$167$	2616.11			1.21222			0.606110	+	0.795381i	$0.292729\pi$
$168$	−4256.34	−	1559.95i	−1.95467	−	0.716385i
$169$	2186.63			0.995282
$170$	−54.5947	−	126.824i	−0.0246307	−	0.0572175i
$171$		−	2169.11i		−	0.970035i
$172$	2.88345	−	3.04719i	0.00127826	−	0.00135085i
$173$	597.428			0.262553			0.131276	−	0.991346i	$-0.458092\pi$
$173$	597.428			0.262553			0.131276	+	0.991346i	$0.458092\pi$
$174$	−1757.21	−	4082.02i	−0.765597	−	1.77849i
$175$		−	2057.55i		−	0.888776i
$176$	−14.5455	−	263.230i	−0.00622961	−	0.112737i
$177$			1241.86i			0.527367i
$178$	−815.508	−	1894.43i	−0.343399	−	0.797718i
$179$	−1741.04			−0.726991			−0.363496	−	0.931596i	$-0.618417\pi$
$179$	−1741.04			−0.726991			−0.363496	+	0.931596i	$0.618417\pi$
$180$	1420.13	−	1500.77i	0.588055	−	0.621447i
$181$			2109.76i			0.866395i	0.901299	+	0.433197i	$0.142615\pi$
$181$			2109.76i			0.866395i	−0.901299	+	0.433197i	$0.857385\pi$
$182$	−203.918	+	87.7820i	−0.0830519	+	0.0357518i
$183$		−	5119.12i		−	2.06785i
$184$	−1048.68	+	2861.34i	−0.420162	+	1.14642i
$185$		−	2182.91i		−	0.867519i
$186$	−3682.47	+	1591.97i	−1.45168	+	0.627573i
$187$			31.5589i			0.0123412i
$188$	−3030.64	−	2867.79i	−1.17570	−	1.11253i
$189$			2711.19i			1.04344i
$190$	381.347	+	885.873i	0.145610	+	0.338253i
$191$			3518.47i			1.33292i	0.745541	+	0.666460i	$0.232191\pi$
$191$			3518.47i			1.33292i	−0.745541	+	0.666460i	$0.767809\pi$
$192$	−3211.05	−	2718.91i	−1.20697	−	1.02198i
$193$	−208.681			−0.0778301			−0.0389150	−	0.999243i	$-0.512390\pi$
$193$	−208.681			−0.0778301			−0.0389150	+	0.999243i	$0.512390\pi$
$194$	1178.98	−	507.521i	0.436317	−	0.187824i
$195$		−	168.594i		−	0.0619141i
$196$	−1381.93	+	1460.41i	−0.503621	+	0.532218i
$197$			1942.13i			0.702392i	0.936302	+	0.351196i	$0.114225\pi$
$197$			1942.13i			0.702392i	−0.936302	+	0.351196i	$0.885775\pi$
$198$	−433.764	+	186.725i	−0.155688	+	0.0670200i
$199$	3686.68			1.31328			0.656638	−	0.754206i	$-0.271978\pi$
$199$	3686.68			1.31328			0.656638	+	0.754206i	$0.271978\pi$
$200$	657.170	−	1793.10i	0.232345	−	0.633956i
$201$		−	5251.76i		−	1.84294i
$202$	237.828	−	102.379i	0.0828393	−	0.0356603i
$203$	−4661.23			−1.61160
$204$	365.847	+	346.189i	0.125561	+	0.118814i
$205$	−2349.14			−0.800347
$206$	168.231	+	390.802i	0.0568991	+	0.132177i
$207$	5458.96			1.83297
$208$	−205.747	+	11.3692i	−0.0685864	+	0.00378995i
$209$		−	220.440i		−	0.0729578i
$210$	−1427.63	−	3316.40i	−0.469123	−	1.08978i
$211$			2817.07i			0.919123i	0.888146	+	0.459562i	$0.151993\pi$
$211$			2817.07i			0.919123i	−0.888146	+	0.459562i	$0.848007\pi$
$212$	3947.30	+	3735.20i	1.27878	+	1.21007i
$213$		−	3337.32i		−	1.07357i
$214$	−919.979	−	2137.12i	−0.293871	−	0.682666i
$215$	3.34142			0.00105992
$216$	−865.941	+	2362.73i	−0.272777	+	0.744276i
$217$	6.50307	+	4207.79i	0.00203436	+	1.31633i
$218$	2860.62	−	1231.43i	0.888740	−	0.382581i
$219$		−	3486.70i		−	1.07584i
$220$	144.323	−	152.518i	0.0442285	−	0.0467399i
$221$	24.6672			0.00750813
$222$	3148.50	+	7314.01i	0.951863	+	2.21119i
$223$	6236.78			1.87285			0.936425	−	0.350868i	$-0.114113\pi$
$223$	6236.78			1.87285			0.936425	+	0.350868i	$0.114113\pi$
$224$	−3950.97	+	1965.88i	−1.17851	+	0.586389i
$225$	−3420.94			−1.01361
$226$	4226.00	−	1819.19i	1.24385	−	0.535446i
$227$		−	492.860i		−	0.144107i	−0.997401	−	0.0720534i	$-0.977045\pi$
$227$		−	492.860i		−	0.144107i	0.997401	−	0.0720534i	$-0.0229552\pi$
$228$	−2555.46	−	2418.15i	−0.742278	−	0.702394i
$229$			495.691i			0.143040i	0.997439	+	0.0715201i	$0.0227850\pi$
$229$			495.691i			0.143040i	−0.997439	+	0.0715201i	$0.977215\pi$
$230$	−2229.46	+	959.730i	−0.639158	+	0.275142i
$231$			825.252i			0.235055i
$232$	−4062.14	−	1488.77i	−1.14954	−	0.421305i
$233$	3120.86			0.877486			0.438743	−	0.898612i	$-0.355424\pi$
$233$	3120.86			0.877486			0.438743	+	0.898612i	$0.355424\pi$
$234$	145.949	+	339.041i	0.0407734	+	0.0947170i
$235$		−	3323.27i		−	0.922494i
$236$	878.117	+	830.934i	0.242206	+	0.229191i
$237$	−8094.80			−2.21862
$238$	485.228	−	208.879i	0.132154	−	0.0568891i
$239$	4611.23			1.24802			0.624008	−	0.781418i	$-0.285503\pi$
$239$	4611.23			1.24802			0.624008	+	0.781418i	$0.285503\pi$
$240$	−184.901	−	3346.14i	−0.0497304	−	0.899968i
$241$		−	3920.07i		−	1.04778i	−0.851787	−	0.523888i	$-0.824481\pi$
$241$		−	3920.07i		−	1.04778i	0.851787	−	0.523888i	$-0.175519\pi$
$242$	3413.78	−	1469.55i	0.906801	−	0.390356i
$243$	−4485.80			−1.18421
$244$	−3619.71	−	3425.22i	−0.949707	−	0.898677i
$245$	−1601.42			−0.417595
$246$	7870.96	−	3388.26i	2.03998	−	0.878160i
$247$	−172.302			−0.0443858
$248$	−1338.28	+	3669.06i	−0.342665	+	0.939458i
$249$	6666.63			1.69671
$250$	3466.35	−	1492.18i	0.876924	−	0.377495i
$251$	−932.359			−0.234462			−0.117231	−	0.993105i	$-0.537402\pi$
$251$	−932.359			−0.234462			−0.117231	+	0.993105i	$0.537402\pi$
$252$	5741.91	+	5433.39i	1.43534	+	1.35822i
$253$	554.778			0.137860
$254$	−21.3795	+	9.20336i	−0.00528138	+	0.00227351i
$255$			401.172i			0.0985191i
$256$	−4071.06	+	451.296i	−0.993912	+	0.110180i
$257$	−2870.10			−0.696621			−0.348311	−	0.937379i	$-0.613245\pi$
$257$	−2870.10			−0.696621			−0.348311	+	0.937379i	$0.613245\pi$
$258$	−11.1956	+	4.81945i	−0.00270159	+	0.00116297i
$259$	8351.81			2.00369
$260$	−119.212	−	112.807i	−0.0284355	−	0.0269076i
$261$			7749.90i			1.83796i
$262$	1003.16	+	2330.35i	0.236548	+	0.549503i
$263$	−7122.00			−1.66982			−0.834908	−	0.550390i	$-0.814479\pi$
$263$	−7122.00			−1.66982			−0.834908	+	0.550390i	$0.814479\pi$
$264$	−263.582	+	719.186i	−0.0614482	+	0.167662i
$265$			4328.44i			1.00337i
$266$	−3389.34	+	1459.03i	−0.781255	+	0.336312i
$267$			5992.50i			1.37354i
$268$	−3713.51	−	3513.97i	−0.846413	−	0.800933i
$269$			8156.73i			1.84879i	0.381435	+	0.924396i	$0.375430\pi$
$269$			8156.73i			1.84879i	−0.381435	+	0.924396i	$0.624570\pi$
$270$	−1840.96	+	792.491i	−0.414954	+	0.178628i
$271$	−156.738			−0.0351334			−0.0175667	−	0.999846i	$-0.505592\pi$
$271$	−156.738			−0.0351334			−0.0175667	+	0.999846i	$0.505592\pi$
$272$	489.579	−	27.0532i	0.109136	−	0.00603066i
$273$	645.038			0.143002
$274$	3385.38	+	7864.27i	0.746416	+	1.73393i
$275$	−347.660			−0.0762351
$276$	6085.71	−	6431.28i	1.32723	−	1.40260i
$277$		−	2551.02i		−	0.553343i	−0.960965	−	0.276671i	$-0.910769\pi$
$277$		−	2551.02i		−	0.553343i	0.960965	−	0.276671i	$-0.0892314\pi$
$278$	4844.95	−	2085.63i	1.04525	−	0.449957i
$279$	6996.00	−	10.8122i	1.50122	−	0.00232010i
$280$	−3300.25	−	1209.54i	−0.704385	−	0.258157i
$281$	1291.63			0.274207			0.137104	−	0.990557i	$-0.456221\pi$
$281$	1291.63			0.274207			0.137104	+	0.990557i	$0.456221\pi$
$282$	4793.28	+	11134.8i	1.01218	+	2.35131i
$283$			3764.73i			0.790778i	0.918514	+	0.395389i	$0.129390\pi$
$283$			3764.73i			0.790778i	−0.918514	+	0.395389i	$0.870610\pi$
$284$	−2359.81	−	2233.01i	−0.493060	−	0.466567i
$285$		−	2802.21i		−	0.582415i
$286$	14.8324	+	34.4557i	0.00306663	+	0.00712381i
$287$		−	8987.79i		−	1.84855i
$288$	3268.53	+	6569.00i	0.668751	+	1.34403i
$289$	4854.30			0.988053
$290$	−1362.49	−	3165.09i	−0.275891	−	0.640898i
$291$	−3729.35			−0.751266
$292$	−2465.44	−	2332.96i	−0.494106	−	0.467556i
$293$	−3704.15			−0.738562			−0.369281	−	0.929318i	$-0.620396\pi$
$293$	−3704.15			−0.738562			−0.369281	+	0.929318i	$0.620396\pi$
$294$	5365.66	−	2309.79i	1.06439	−	0.458196i
$295$			962.906i			0.190043i
$296$	7278.39	+	2667.53i	1.42922	+	0.523807i
$297$	458.105			0.0895015
$298$	−7061.13	+	3039.65i	−1.37262	+	0.590879i
$299$		−	433.629i		−	0.0838709i
$300$	−3813.70	+	4030.25i	−0.733946	+	0.775622i
$301$			12.7842i			0.00244807i
$302$	−2190.17	+	942.817i	−0.417319	+	0.179646i
$303$	−752.302			−0.142636
$304$	−3419.73	+	188.968i	−0.645181	+	0.0356514i
$305$		−	3969.22i		−	0.745171i
$306$	−347.288	−	806.754i	−0.0648796	−	0.150716i
$307$		−	8943.10i		−	1.66257i	−0.555845	−	0.831286i	$-0.687605\pi$
$307$		−	8943.10i		−	1.66257i	0.555845	−	0.831286i	$-0.312395\pi$
$308$	583.534	+	552.179i	0.107954	+	0.102154i
$309$		−	1236.19i		−	0.227587i
$310$	−2855.29	+	1234.37i	−0.523128	+	0.226153i
$311$			6079.45i			1.10847i	0.832360	+	0.554235i	$0.186989\pi$
$311$			6079.45i			1.10847i	−0.832360	+	0.554235i	$0.813011\pi$
$312$	562.134	+	206.022i	0.102002	+	0.0373836i
$313$		−	5292.00i		−	0.955660i	−0.878452	−	0.477830i	$-0.841423\pi$
$313$		−	5292.00i		−	0.955660i	0.878452	−	0.477830i	$-0.158577\pi$
$314$	−1751.12	+	753.816i	−0.314718	+	0.135479i
$315$			6296.34i			1.12622i
$316$	−5416.26	+	5723.81i	−0.964204	+	1.01895i
$317$	−2198.06			−0.389450			−0.194725	−	0.980858i	$-0.562381\pi$
$317$	−2198.06			−0.389450			−0.194725	+	0.980858i	$0.562381\pi$
$318$	−6243.07	−	14502.7i	−1.10092	−	2.55746i
$319$			787.599i			0.138235i
$320$	−2489.76	−	2108.17i	−0.434944	−	0.368282i
$321$			6760.17i			1.17544i
$322$	−3671.92	−	8529.90i	−0.635490	−	1.47625i
$323$	409.995			0.0706277
$324$	−992.347	+	1048.70i	−0.170156	+	0.179818i
$325$			271.739i			0.0463797i
$326$	−3109.50	−	7223.40i	−0.528280	−	1.22720i
$327$	−9048.74			−1.53026
$328$	2870.66	−	7832.63i	0.483249	−	1.31855i
$329$	12714.8			2.13067
$330$	−560.366	+	241.224i	−0.0934762	+	0.0402392i
$331$	5474.89			0.909145			0.454572	−	0.890710i	$-0.349792\pi$
$331$	5474.89			0.909145			0.454572	+	0.890710i	$0.349792\pi$
$332$	4460.67	−	4713.96i	0.737382	−	0.779253i
$333$		−	13886.0i		−	2.28512i
$334$	−6796.49	+	2925.73i	−1.11344	+	0.479307i
$335$		−	4072.08i		−	0.664123i
$336$	12802.3	−	707.429i	2.07864	−	0.114861i
$337$			6373.90i			1.03029i	0.857102	+	0.515146i	$0.172262\pi$
$337$			6373.90i			1.03029i	−0.857102	+	0.515146i	$0.827738\pi$
$338$	−5680.74	+	2445.42i	−0.914177	+	0.393531i
$339$	−13367.7			−2.14170
$340$	283.668	+	268.426i	0.0452472	+	0.0428159i
$341$	710.982	−	1.09881i	0.112909	−	0.000174498i
$342$	2425.83	+	5635.22i	0.383549	+	0.890988i
$343$			2234.91i			0.351819i
$344$	−4.08322	+	11.1411i	−0.000639978	+	0.00174619i
$345$	7052.27			1.10053
$346$	−1552.08	+	668.134i	−0.241158	+	0.103812i
$347$	5249.23			0.812085			0.406043	−	0.913854i	$-0.366908\pi$
$347$	5249.23			0.812085			0.406043	+	0.913854i	$0.366908\pi$
$348$	9130.26	+	8639.67i	1.40642	+	1.33085i
$349$	−6385.22			−0.979350			−0.489675	−	0.871905i	$-0.662884\pi$
$349$	−6385.22			−0.979350			−0.489675	+	0.871905i	$0.662884\pi$
$350$	2301.06	+	5345.38i	0.351419	+	0.816350i
$351$		−	358.066i		−	0.0544506i
$352$	332.171	+	667.588i	0.0502977	+	0.101087i
$353$		−	11832.1i		−	1.78403i	−0.452008	−	0.892014i	$-0.649292\pi$
$353$		−	11832.1i		−	1.78403i	0.452008	−	0.892014i	$-0.350708\pi$
$354$	−1388.84	−	3226.28i	−0.208519	−	0.484392i
$355$		−	2587.67i		−	0.386871i
$356$	4237.28	+	4009.60i	0.630830	+	0.596934i
$357$	−1534.88			−0.227548
$358$	4523.12	−	1947.09i	0.667749	−	0.287450i
$359$			7973.37i			1.17220i	0.810240	+	0.586098i	$0.199337\pi$
$359$			7973.37i			1.17220i	−0.810240	+	0.586098i	$0.800663\pi$
$360$	−2011.02	+	5487.10i	−0.294417	+	0.803320i
$361$	3995.16			0.582470
$362$	−2359.45	−	5481.04i	−0.342569	−	0.795793i
$363$	−10798.5			−1.56136
$364$	431.597	−	456.105i	0.0621479	−	0.0656769i
$365$		−	2703.49i		−	0.387691i
$366$	5724.96	+	13299.2i	0.817619	+	1.89934i
$367$	−7390.19			−1.05113			−0.525565	−	0.850753i	$-0.676146\pi$
$367$	−7390.19			−1.05113			−0.525565	+	0.850753i	$0.676146\pi$
$368$	−475.572	−	8606.38i	−0.0673666	−	1.21913i
$369$	−14943.4			−2.10819
$370$	2441.26	+	5671.08i	0.343014	+	0.796826i
$371$	−16560.6			−2.31747
$372$	7786.47	−	8254.13i	1.08524	−	1.15042i
$373$	10312.0			1.43147			0.715734	−	0.698373i	$-0.246092\pi$
$373$	10312.0			1.43147			0.715734	+	0.698373i	$0.246092\pi$
$374$	−35.2939	−	81.9880i	−0.00487969	−	0.0113356i
$375$	−10964.8			−1.50992
$376$	11080.6	+	4061.04i	1.51978	+	0.557001i
$377$	615.607			0.0840992
$378$	−3032.06	−	7043.51i	−0.412573	−	0.958411i
$379$			6741.72i			0.913718i	0.889539	+	0.456859i	$0.151026\pi$
$379$			6741.72i			0.913718i	−0.889539	+	0.456859i	$0.848974\pi$
$380$	−1981.43	−	1874.97i	−0.267488	−	0.253115i
$381$	67.6280			0.00909366
$382$	−3934.89	−	9140.78i	−0.527032	−	1.22430i
$383$	4966.24			0.662567			0.331284	−	0.943531i	$-0.392518\pi$
$383$	4966.24			0.662567			0.331284	+	0.943531i	$0.392518\pi$
$384$	11382.8	+	3472.48i	1.51270	+	0.461470i
$385$			639.878i			0.0847044i
$386$	542.141	−	233.379i	0.0714877	−	0.0307737i
$387$	21.2554			0.00279192
$388$	−2495.32	+	2637.02i	−0.326497	+	0.345037i
$389$		−	7562.25i		−	0.985659i	−0.870126	−	0.492829i	$-0.835963\pi$
$389$		−	7562.25i		−	0.985659i	0.870126	−	0.492829i	$-0.164037\pi$
$390$	188.547	+	437.996i	0.0244806	+	0.0568687i
$391$			1031.83i			0.133457i
$392$	1956.94	−	5339.53i	0.252144	−	0.687978i
$393$		−	7371.41i		−	0.946153i
$394$	−2171.99	−	5045.55i	−0.277723	−	0.645155i
$395$	−6276.49			−0.799505
$396$	918.069	−	970.200i	0.116502	−	0.123117i
$397$	−15118.7			−1.91130			−0.955652	−	0.294500i	$-0.904847\pi$
$397$	−15118.7			−1.91130			−0.955652	+	0.294500i	$0.904847\pi$
$398$	−9577.78	+	4123.00i	−1.20626	+	0.519265i
$399$	10721.2			1.34519
$400$	298.024	+	5393.31i	0.0372529	+	0.674164i
$401$			2660.11i			0.331271i	0.986187	+	0.165635i	$0.0529675\pi$
$401$			2660.11i			0.331271i	−0.986187	+	0.165635i	$0.947032\pi$
$402$	5873.31	+	13643.8i	0.728692	+	1.69276i
$403$	−0.858858	−	555.722i	−0.000106161	−	0.0686910i
$404$	−503.368	+	531.951i	−0.0619888	+	0.0655088i
$405$	−1149.96			−0.141091
$406$	12109.6	−	5212.89i	1.48027	−	0.637220i
$407$		−	1411.19i		−	0.171867i
$408$	−1337.61	−	490.233i	−0.162308	−	0.0594857i
$409$			10763.0i			1.30121i	0.759417	+	0.650604i	$0.225484\pi$
$409$			10763.0i			1.30121i	−0.759417	+	0.650604i	$0.774516\pi$
$410$	6102.93	−	2627.16i	0.735127	−	0.316454i
$411$		−	24876.4i		−	2.98555i
$412$	−874.108	−	827.140i	−0.104525	−	0.0989084i
$413$	−3684.07			−0.438937
$414$	−14182.1	+	6105.04i	−1.68360	+	0.724749i
$415$	5169.13			0.611427
$416$	521.803	−	259.633i	0.0614988	−	0.0306000i
$417$	−15325.6			−1.79976
$418$	246.529	+	572.691i	0.0288473	+	0.0670125i
$419$		−	6632.28i		−	0.773289i	−0.922229	−	0.386645i	$-0.873634\pi$
$419$		−	6632.28i		−	0.773289i	0.922229	−	0.386645i	$-0.126366\pi$
$420$	7417.80	+	7019.22i	0.861789	+	0.815483i
$421$	6926.28			0.801820			0.400910	−	0.916117i	$-0.368694\pi$
$421$	6926.28			0.801820			0.400910	+	0.916117i	$0.368694\pi$
$422$	−3150.47	−	7318.58i	−0.363418	−	0.844224i
$423$		−	21140.0i		−	2.42993i
$424$	−14432.1	−	5289.36i	−1.65303	−	0.605835i
$425$		−	646.609i		−	0.0738004i
$426$	3732.29	+	8670.16i	0.424484	+	0.986081i
$427$	15186.2			1.72111
$428$	4780.10	+	4523.25i	0.539848	+	0.510840i
$429$		−	108.991i		−	0.0122660i
$430$	−8.68080	+	3.73687i	−0.000973547	+	0.000419088i
$431$			13596.8i			1.51957i	0.650173	+	0.759786i	$0.274696\pi$
$431$			13596.8i			1.51957i	−0.650173	+	0.759786i	$0.725304\pi$
$432$	−392.700	−	7106.67i	−0.0437357	−	0.791481i
$433$		−	4322.71i		−	0.479760i	−0.970803	−	0.239880i	$-0.922892\pi$
$433$		−	4322.71i		−	0.479760i	0.970803	−	0.239880i	$-0.0771081\pi$
$434$	−4722.68	−	10924.3i	−0.522341	−	1.20826i
$435$			10011.9i			1.10352i
$436$	−6054.54	+	6398.34i	−0.665046	+	0.702810i
$437$		−	7207.37i		−	0.788960i
$438$	3899.35	+	9058.24i	0.425384	+	0.988173i
$439$			3573.81i			0.388539i	0.980948	+	0.194269i	$0.0622336\pi$
$439$			3573.81i			0.388539i	−0.980948	+	0.194269i	$0.937766\pi$
$440$	−204.374	+	557.637i	−0.0221435	+	0.0604189i
$441$	−10186.9			−1.09998
$442$	−64.0839	+	27.5866i	−0.00689629	+	0.00296869i
$443$			9881.07i			1.05974i	0.848080	+	0.529869i	$0.177759\pi$
$443$			9881.07i			1.05974i	−0.848080	+	0.529869i	$0.822241\pi$
$444$	−16359.2	−	15480.2i	−1.74859	−	1.65464i
$445$			4646.42i			0.494970i
$446$	−16202.8	+	6974.90i	−1.72023	+	0.740519i
$447$	22335.9			2.36342
$448$	8065.84	−	9525.81i	0.850614	−	1.00458i
$449$		−	3376.75i		−	0.354920i	−0.984128	−	0.177460i	$-0.943212\pi$
$449$		−	3376.75i		−	0.354920i	0.984128	−	0.177460i	$-0.0567880\pi$
$450$	8887.39	−	3825.80i	0.931012	−	0.400778i
$451$	−1518.65			−0.158560
$452$	−8944.40	+	9452.29i	−0.930772	+	0.983625i
$453$	6927.99			0.718555
$454$	551.190	+	1280.42i	0.0569794	+	0.132364i
$455$	500.145			0.0515322
$456$	9343.26	+	3424.30i	0.959514	+	0.351662i
$457$			18986.2i			1.94341i	0.236199	+	0.971705i	$0.424098\pi$
$457$			18986.2i			1.94341i	−0.236199	+	0.971705i	$0.575902\pi$
$458$	−554.357	−	1287.78i	−0.0565576	−	0.131384i
$459$			852.025i			0.0866430i
$460$	4718.70	−	4986.64i	0.478283	−	0.505442i
$461$			4730.38i			0.477908i	0.971031	+	0.238954i	$0.0768045\pi$
$461$			4730.38i			0.477908i	−0.971031	+	0.238954i	$0.923195\pi$
$462$	−922.921	−	2143.96i	−0.0929398	−	0.215900i
$463$	5068.16			0.508720			0.254360	−	0.967110i	$-0.418135\pi$
$463$	5068.16			0.508720			0.254360	+	0.967110i	$0.418135\pi$
$464$	12218.2	−	675.152i	1.22245	−	0.0675499i
$465$	9037.91	−	13.9679i	0.901340	−	0.00139300i
$466$	−8107.81	+	3490.21i	−0.805980	+	0.346955i
$467$		−	3333.36i		−	0.330298i	−0.986269	−	0.165149i	$-0.947189\pi$
$467$		−	3333.36i		−	0.330298i	0.986269	−	0.165149i	$-0.0528106\pi$
$468$	−758.333	−	717.586i	−0.0749016	−	0.0708769i
$469$	15579.7			1.53391
$470$	3716.58	+	8633.65i	0.364751	+	0.847320i
$471$	5539.18			0.541893
$472$	−3210.57	−	1176.67i	−0.313090	−	0.114747i
$473$	2.16013			0.000209985
$474$	21029.8	−	9052.82i	2.03783	−	0.877236i
$475$			4516.60i			0.436286i
$476$	−1026.99	+	1085.31i	−0.0988911	+	0.104507i
$477$			27534.1i			2.64297i
$478$	−11979.7	+	5156.98i	−1.14632	+	0.493461i
$479$		−	12341.2i		−	1.17721i	−0.808422	−	0.588604i	$-0.799678\pi$
$479$		−	12341.2i		−	1.17721i	0.808422	−	0.588604i	$-0.200322\pi$
$480$	4222.52	+	8486.28i	0.401522	+	0.806967i
$481$	−1103.02			−0.104560
$482$	4384.02	+	10184.1i	0.414287	+	0.962394i
$483$			26981.9i			2.54186i
$484$	−7225.32	+	7635.60i	−0.678561	+	0.717092i
$485$	−2891.64			−0.270727
$486$	11653.8	−	5016.69i	1.08771	−	0.468234i
$487$	1383.56			0.128737			0.0643687	−	0.997926i	$-0.479497\pi$
$487$	1383.56			0.128737			0.0643687	+	0.997926i	$0.479497\pi$
$488$	13234.4	+	4850.40i	1.22765	+	0.449933i
$489$			22849.2i			2.11304i
$490$	4160.39	−	1790.95i	0.383566	−	0.165116i
$491$	−11694.5			−1.07488			−0.537440	−	0.843302i	$-0.680609\pi$
$491$	−11694.5			−1.07488			−0.537440	+	0.843302i	$0.680609\pi$
$492$	−16659.0	+	17605.0i	−1.52652	+	1.61320i
$493$	−1464.85			−0.133821
$494$	447.629	−	192.694i	0.0407688	−	0.0175500i
$495$	1063.88			0.0966017
$496$	−626.520	−	11028.7i	−0.0567169	−	0.998390i
$497$	9900.39			0.893548
$498$	−17319.5	+	7455.63i	−1.55845	+	0.670873i
$499$	−12374.0			−1.11009			−0.555045	−	0.831821i	$-0.687299\pi$
$499$	−12374.0			−1.11009			−0.555045	+	0.831821i	$0.687299\pi$
$500$	−7336.58	+	7753.18i	−0.656204	+	0.693466i
$501$	21498.8			1.91715
$502$	2422.21	−	1042.70i	0.215356	−	0.0927055i
$503$		−	2691.77i		−	0.238608i	−0.992858	−	0.119304i	$-0.961934\pi$
$503$		−	2691.77i		−	0.238608i	0.992858	−	0.119304i	$-0.0380663\pi$
$504$	−20993.6	−	7694.14i	−1.85541	−	0.680009i
$505$	−583.315			−0.0514003
$506$	−1441.28	+	620.437i	−0.126626	+	0.0545094i
$507$	17969.4			1.57406
$508$	45.2501	−	47.8196i	0.00395206	−	0.00417648i
$509$			448.742i			0.0390769i	0.999809	+	0.0195385i	$0.00621968\pi$
$509$			448.742i			0.0390769i	−0.999809	+	0.0195385i	$0.993780\pi$
$510$	−448.651	−	1042.22i	−0.0389541	−	0.0904908i
$511$	10343.5			0.895443
$512$	10071.7	−	5725.31i	0.869354	−	0.494190i
$513$		−	5951.44i		−	0.512208i
$514$	7456.34	−	3209.77i	0.639854	−	0.275442i
$515$		−	958.510i		−	0.0820135i
$516$	23.6958	−	25.0413i	0.00202160	−	0.00213640i
$517$		−	2148.39i		−	0.182759i
$518$	−21697.5	+	9340.25i	−1.84041	+	0.792253i
$519$	4909.57			0.415234
$520$	435.863	+	159.744i	0.0367574	+	0.0134716i
$521$	11857.0			0.997057			0.498528	−	0.866873i	$-0.333874\pi$
$521$	11857.0			0.997057			0.498528	+	0.866873i	$0.333874\pi$
$522$	−8667.10	−	20133.8i	−0.726722	−	1.68818i
$523$	7735.42			0.646743			0.323371	−	0.946272i	$-0.395184\pi$
$523$	7735.42			0.646743			0.323371	+	0.946272i	$0.395184\pi$
$524$	−5212.30	−	4932.23i	−0.434543	−	0.411194i
$525$		−	16908.6i		−	1.40562i
$526$	18502.5	−	7964.89i	1.53374	−	0.660239i
$527$	2.04367	+	1322.35i	0.000168925	+	0.109303i
$528$	−119.533	−	2163.18i	−0.00985228	−	0.178296i
$529$	5971.68			0.490809
$530$	−4840.71	−	11245.0i	−0.396730	−	0.921608i
$531$			6125.24i			0.500589i
$532$	7173.60	−	7580.95i	0.584615	−	0.617811i
$533$			1187.02i			0.0964640i
$534$	−6701.72	−	15568.2i	−0.543093	−	1.26161i
$535$			5241.65i			0.423582i
$536$	13577.3	+	4976.09i	1.09413	+	0.400997i
$537$	−14307.6			−1.14975
$538$	−9122.09	−	21190.7i	−0.731006	−	1.69813i
$539$	−1035.27			−0.0827314
$540$	3896.43	−	4117.69i	0.310511	−	0.328143i
$541$	−12026.7			−0.955766			−0.477883	−	0.878423i	$-0.658596\pi$
$541$	−12026.7			−0.955766			−0.477883	+	0.878423i	$0.658596\pi$
$542$	407.196	−	175.288i	0.0322704	−	0.0138916i
$543$			17337.7i			1.37022i
$544$	−1241.64	+	617.803i	−0.0978583	+	0.0486913i
$545$	−7016.15			−0.551447
$546$	−1675.77	+	721.378i	−0.131349	+	0.0565424i
$547$		−	23953.9i		−	1.87238i	−0.351488	−	0.936192i	$-0.614324\pi$
$547$		−	23953.9i		−	1.87238i	0.351488	−	0.936192i	$-0.385676\pi$
$548$	−17590.0	−	16644.9i	−1.37118	−	1.29751i
$549$		−	25249.0i		−	1.96285i
$550$	903.199	−	388.805i	0.0700228	−	0.0301431i
$551$	10232.1			0.791107
$552$	−8617.89	+	23514.0i	−0.664496	+	1.81309i
$553$		−	24013.8i		−	1.84660i
$554$	2852.94	+	6627.40i	0.218790	+	0.508251i
$555$		−	17938.8i		−	1.37200i
$556$	−10254.4	+	10836.7i	−0.782165	+	0.826580i
$557$			3287.46i			0.250079i	0.992152	+	0.125040i	$0.0399058\pi$
$557$			3287.46i			0.250079i	−0.992152	+	0.125040i	$0.960094\pi$
$558$	−18163.1	+	7852.06i	−1.37797	+	0.595707i
$559$		−	1.68841i		−	0.000127750i
$560$	9926.55	−	548.522i	0.749060	−	0.0413915i
$561$			259.346i			0.0195180i
$562$	−3355.58	+	1444.50i	−0.251862	+	0.108421i
$563$			1480.42i			0.110821i	0.998464	+	0.0554104i	$0.0176467\pi$
$563$			1480.42i			0.110821i	−0.998464	+	0.0554104i	$0.982353\pi$
$564$	−24905.3	−	23567.1i	−1.85940	−	1.75949i
$565$	−10365.0			−0.771784
$566$	−4210.29	−	9780.55i	−0.312671	−	0.726338i
$567$		−	4399.72i		−	0.325875i
$568$	8627.94	+	3162.14i	0.637360	+	0.233592i
$569$		−	14217.7i		−	1.04752i	−0.851866	−	0.523760i	$-0.824529\pi$
$569$		−	14217.7i		−	1.04752i	0.851866	−	0.523760i	$-0.175471\pi$
$570$	3133.85	+	7279.96i	0.230285	+	0.534955i
$571$	13527.4			0.991426			0.495713	−	0.868486i	$-0.334907\pi$
$571$	13527.4			0.991426			0.495713	+	0.868486i	$0.334907\pi$
$572$	−77.0671	−	72.9261i	−0.00563346	−	0.00533076i
$573$			28914.2i			2.10805i
$574$	10051.5	+	23349.7i	0.730909	+	1.69791i
$575$	−11366.9			−0.824401
$576$	−15837.9	−	13410.5i	−1.14568	−	0.970088i
$577$	−5347.07			−0.385791			−0.192895	−	0.981219i	$-0.561788\pi$
$577$	−5347.07			−0.385791			−0.192895	+	0.981219i	$0.561788\pi$
$578$	−12611.2	+	5428.81i	−0.907537	+	0.390673i
$579$	−1714.91			−0.123090
$580$	7079.36	+	6698.96i	0.506818	+	0.479585i
$581$			19777.0i			1.41220i
$582$	9688.63	−	4170.72i	0.690046	−	0.297048i
$583$			2798.21i			0.198782i
$584$	9014.13	+	3303.68i	0.638711	+	0.234088i
$585$		−	831.555i		−	0.0587702i
$586$	9623.16	−	4142.54i	0.678377	−	0.292025i
$587$	−617.638			−0.0434287			−0.0217144	−	0.999764i	$-0.506912\pi$
$587$	−617.638			−0.0434287			−0.0217144	+	0.999764i	$0.506912\pi$
$588$	−11356.5	+	12001.4i	−0.796488	+	0.841715i
$589$	−14.2751	−	9236.69i	−0.000998636	−	0.646165i
$590$	−1076.87	−	2501.57i	−0.0751422	−	0.174556i
$591$			15960.1i			1.11085i
$592$	−21892.1	+	1209.71i	−1.51986	+	0.0839845i
$593$	−14345.5			−0.993419			−0.496710	−	0.867917i	$-0.665459\pi$
$593$	−14345.5			−0.993419			−0.496710	+	0.867917i	$0.665459\pi$
$594$	−1190.13	+	512.322i	−0.0822080	+	0.0353886i
$595$	−1190.10			−0.0819992
$596$	14945.0	−	15793.6i	1.02713	−	1.08546i
$597$	30296.6			2.07698
$598$	484.949	+	1126.54i	0.0331623	+	0.0770363i
$599$		−	4714.45i		−	0.321581i	−0.986989	−	0.160791i	$-0.948596\pi$
$599$		−	4714.45i		−	0.321581i	0.986989	−	0.160791i	$-0.0514044\pi$
$600$	5400.52	−	14735.4i	0.367459	−	1.00262i
$601$		−	17139.6i		−	1.16329i	−0.813443	−	0.581645i	$-0.802409\pi$
$601$		−	17139.6i		−	1.16329i	0.813443	−	0.581645i	$-0.197591\pi$
$602$	−14.2972	−	33.2126i	−0.000967960	−	0.00224858i
$603$		−	25903.3i		−	1.74936i
$604$	4635.54	−	4898.76i	0.312281	−	0.330013i
$605$	−8372.87			−0.562654
$606$	1954.44	−	841.337i	0.131012	−	0.0563977i
$607$		−	5484.88i		−	0.366762i	−0.983042	−	0.183381i	$-0.941296\pi$
$607$		−	5484.88i		−	0.366762i	0.983042	−	0.183381i	$-0.0587041\pi$
$608$	8672.93	−	4315.39i	0.578509	−	0.287849i
$609$	−38305.3			−2.54878
$610$	4438.98	+	10311.8i	0.294638	+	0.684447i
$611$	−1679.24			−0.111186
$612$	1804.47	+	1707.51i	0.119185	+	0.112781i
$613$			17217.3i			1.13442i	0.823572	+	0.567212i	$0.191978\pi$
$613$			17217.3i			1.13442i	−0.823572	+	0.567212i	$0.808022\pi$
$614$	10001.5	+	23233.6i	0.657375	+	1.52709i
$615$	−19304.9			−1.26577
$616$	−2133.52	−	781.933i	−0.139548	−	0.0511444i
$617$	−24689.5			−1.61096			−0.805480	−	0.592623i	$-0.798092\pi$
$617$	−24689.5			−1.61096			−0.805480	+	0.592623i	$0.798092\pi$
$618$	1382.50	+	3211.55i	0.0899872	+	0.209041i
$619$	−1617.84			−0.105051			−0.0525255	−	0.998620i	$-0.516727\pi$
$619$	−1617.84			−0.105051			−0.0525255	+	0.998620i	$0.516727\pi$
$620$	6037.42	−	6400.03i	0.391078	−	0.414567i
$621$	14977.9			0.967862
$622$	−6798.96	−	15794.1i	−0.438285	−	1.01814i
$623$	−17777.2			−1.14322
$624$	−1690.79	+	93.4300i	−0.108471	+	0.00599390i
$625$	2048.07			0.131077
$626$	5918.31	+	13748.3i	0.377865	+	0.877784i
$627$		−	1811.54i		−	0.115384i
$628$	3706.28	−	3916.74i	0.235504	−	0.248877i
$629$	2624.66			0.166378
$630$	−7041.51	−	16357.5i	−0.445302	−	1.03444i
$631$	−15779.9			−0.995542			−0.497771	−	0.867309i	$-0.665848\pi$
$631$	−15779.9			−0.995542			−0.497771	+	0.867309i	$0.665848\pi$
$632$	7669.89	−	20927.4i	0.482740	−	1.31716i
$633$			23150.2i			1.45362i
$634$	5710.44	−	2458.21i	0.357714	−	0.153987i
$635$	52.4369			0.00327700
$636$	32438.3	+	30695.3i	2.02242	+	1.91375i
$637$			809.193i			0.0503318i
$638$	−880.812	−	2046.14i	−0.0546578	−	0.126971i
$639$		−	16460.7i		−	1.01905i
$640$	8825.93	+	2692.47i	0.545118	+	0.166296i
$641$		−	7025.46i		−	0.432900i	−0.976294	−	0.216450i	$-0.930552\pi$
$641$		−	7025.46i		−	0.432900i	0.976294	−	0.216450i	$-0.0694478\pi$
$642$	−7560.24	−	17562.5i	−0.464765	−	1.07965i
$643$	9969.78			0.611461			0.305731	−	0.952118i	$-0.401099\pi$
$643$	9969.78			0.611461			0.305731	+	0.952118i	$0.401099\pi$
$644$	19078.8	+	18053.7i	1.16741	+	1.10468i
$645$	27.4592			0.00167629
$646$	−1065.14	+	458.518i	−0.0648723	+	0.0279259i
$647$	5450.08			0.331167			0.165583	−	0.986196i	$-0.447049\pi$
$647$	5450.08			0.331167			0.165583	+	0.986196i	$0.447049\pi$
$648$	1405.25	−	3834.24i	0.0851904	−	0.232443i
$649$			622.490i			0.0376500i
$650$	−303.900	−	705.963i	−0.0183384	−	0.0426002i
$651$	53.4411	+	34579.0i	0.00321739	+	2.08181i
$652$	16156.6	+	15288.5i	0.970461	+	0.918316i
$653$	10249.9			0.614255			0.307127	−	0.951668i	$-0.400632\pi$
$653$	10249.9			0.614255			0.307127	+	0.951668i	$0.400632\pi$
$654$	23508.1	−	10119.7i	1.40556	−	0.605061i
$655$		−	5715.59i		−	0.340956i
$656$	1301.83	+	23559.1i	0.0774816	+	1.40218i
$657$		−	17197.5i		−	1.02121i
$658$	−33032.3	+	14219.6i	−1.95704	+	0.842458i
$659$			15288.1i			0.903701i	0.892094	+	0.451850i	$0.149236\pi$
$659$			15288.1i			0.903701i	−0.892094	+	0.451850i	$0.850764\pi$
$660$	1186.02	−	1253.37i	0.0699484	−	0.0739203i
$661$	−18036.6			−1.06133			−0.530667	−	0.847581i	$-0.678058\pi$
$661$	−18036.6			−1.06133			−0.530667	+	0.847581i	$0.678058\pi$
$662$	−14223.4	+	6122.84i	−0.835059	+	0.359473i
$663$	202.711			0.0118743
$664$	−6316.69	+	17235.2i	−0.369179	+	1.00731i
$665$	8312.94			0.484755
$666$	15529.4	+	36074.9i	0.903530	+	2.09891i
$667$			25750.8i			1.49487i
$668$	14384.9	−	15201.7i	0.833186	−	0.880498i
$669$	51252.8			2.96196
$670$	4554.01	+	10579.0i	0.262592	+	0.610004i
$671$		−	2565.98i		−	0.147629i
$672$	−32468.4	+	16155.3i	−1.86384	+	0.927388i
$673$			28021.3i			1.60497i	0.596675	+	0.802483i	$0.296488\pi$
$673$			28021.3i			1.60497i	−0.596675	+	0.802483i	$0.703512\pi$
$674$	−7128.25	−	16559.0i	−0.407374	−	0.946334i
$675$	−9386.10			−0.535217
$676$	12023.4	−	12706.1i	0.684080	−	0.722925i
$677$		−	15621.1i		−	0.886808i	−0.896322	−	0.443404i	$-0.853771\pi$
$677$		−	15621.1i		−	0.886808i	0.896322	−	0.443404i	$-0.146229\pi$
$678$	34728.6	−	14949.8i	1.96717	−	0.846820i
$679$		−	11063.4i		−	0.625293i
$680$	−1037.15	−	380.114i	−0.0584893	−	0.0214363i
$681$		−	4050.24i		−	0.227908i
$682$	−1845.86	+	797.982i	−0.103639	+	0.0448040i
$683$		−	11709.8i		−	0.656023i	−0.944674	−	0.328012i	$-0.893621\pi$
$683$		−	11709.8i		−	0.656023i	0.944674	−	0.328012i	$-0.106379\pi$
$684$	−12604.3	−	11927.0i	−0.704587	−	0.666728i
$685$		−	19288.5i		−	1.07587i
$686$	−2499.42	−	5806.17i	−0.139108	−	0.323150i
$687$			4073.51i			0.226222i
$688$	−1.85172	−	33.5104i	−0.000102611	−	0.00185694i
$689$	2187.15			0.120934
$690$	−18321.4	+	7886.90i	−1.01084	+	0.435144i
$691$			14082.3i			0.775277i	0.921811	+	0.387639i	$0.126709\pi$
$691$			14082.3i			0.775277i	−0.921811	+	0.387639i	$0.873291\pi$
$692$	3285.01	−	3471.55i	0.180459	−	0.190706i
$693$			4070.39i			0.223119i
$694$	−13637.2	+	5870.48i	−0.745909	+	0.321096i
$695$	−11883.1			−0.648561
$696$	−33382.0	−	12234.5i	−1.81802	−	0.666305i
$697$		−	2824.53i		−	0.153496i
$698$	16588.4	−	7140.91i	0.899543	−	0.387231i
$699$	25646.7			1.38777
$700$	−11956.0	−	11313.6i	−0.645564	−	0.610877i
$701$	−23267.1			−1.25362			−0.626810	−	0.779172i	$-0.715640\pi$
$701$	−23267.1			−1.25362			−0.626810	+	0.779172i	$0.715640\pi$
$702$	400.443	+	930.234i	0.0215296	+	0.0500134i
$703$	−18333.4			−0.983580
$704$	−1609.56	−	1362.87i	−0.0861683	−	0.0729617i
$705$		−	27310.1i		−	1.45895i
$706$	13232.5	+	30739.2i	0.705398	+	1.63865i
$707$		−	2231.76i		−	0.118718i
$708$	7216.23	+	6828.48i	0.383054	+	0.362472i
$709$			2172.74i			0.115090i	0.998343	+	0.0575451i	$0.0183273\pi$
$709$			2172.74i			0.115090i	−0.998343	+	0.0575451i	$0.981673\pi$
$710$	2893.92	+	6722.61i	0.152967	+	0.355345i
$711$	−39926.0			−2.10597
$712$	−15492.4	−	5677.94i	−0.815450	−	0.298862i
$713$	23245.8	−	35.9260i	1.22099	−	0.00188701i
$714$	3987.53	−	1716.53i	0.209005	−	0.0899715i
$715$		−	84.5085i		−	0.00442019i
$716$	−9573.26	+	10116.9i	−0.499678	+	0.528051i
$717$	37894.4			1.97377
$718$	−8917.02	−	20714.3i	−0.463482	−	1.07667i
$719$	−756.839			−0.0392564			−0.0196282	−	0.999807i	$-0.506248\pi$
$719$	−756.839			−0.0392564			−0.0196282	+	0.999807i	$0.506248\pi$
$720$	−911.988	−	16504.2i	−0.0472052	−	0.854270i
$721$	3667.25			0.189425
$722$	−10379.2	+	4467.99i	−0.535005	+	0.230307i
$723$		−	32214.5i		−	1.65708i
$724$	12259.4	+	11600.7i	0.629307	+	0.595493i
$725$		−	16137.1i		−	0.826645i
$726$	28053.9	−	12076.5i	1.43413	−	0.617357i
$727$			19408.3i			0.990113i	0.868861	+	0.495057i	$0.164853\pi$
$727$			19408.3i			0.990113i	−0.868861	+	0.495057i	$0.835147\pi$
$728$	−611.178	+	1667.61i	−0.0311151	+	0.0848980i
$729$	−31990.8			−1.62530
$730$	3023.45	+	7023.52i	0.153292	+	0.356099i
$731$			4.01760i			0.000203278i
$732$	−29746.2	−	28147.9i	−1.50198	−	1.42128i
$733$	−20136.0			−1.01465			−0.507325	−	0.861755i	$-0.669366\pi$
$733$	−20136.0			−1.01465			−0.507325	+	0.861755i	$0.669366\pi$
$734$	19199.3	−	8264.82i	0.965474	−	0.415613i
$735$	−13160.2			−0.660437
$736$	10860.5	+	21827.0i	0.543916	+	1.09314i
$737$		−	2632.48i		−	0.131572i
$738$	38822.0	−	16711.9i	1.93639	−	0.833569i
$739$	−4767.83			−0.237331			−0.118665	−	0.992934i	$-0.537862\pi$
$739$	−4767.83			−0.237331			−0.118665	+	0.992934i	$0.537862\pi$
$740$	−12684.5	−	12002.9i	−0.630124	−	0.596266i
$741$	−1415.95			−0.0701972
$742$	43023.3	−	18520.5i	2.12862	−	0.916320i
$743$	12976.0			0.640707			0.320353	−	0.947298i	$-0.396198\pi$
$743$	12976.0			0.640707			0.320353	+	0.947298i	$0.396198\pi$
$744$	−10997.8	+	30151.7i	−0.541933	+	1.48577i
$745$	17318.6			0.851686
$746$	−26790.1	+	11532.5i	−1.31482	+	0.565997i
$747$	32881.9			1.61055
$748$	183.383	+	173.529i	0.00896409	+	0.00848242i
$749$	−20054.5			−0.978339
$750$	28485.9	−	12262.5i	1.38688	−	0.597017i
$751$		−	17680.1i		−	0.859061i	−0.903052	−	0.429530i	$-0.858679\pi$
$751$		−	17680.1i		−	0.859061i	0.903052	−	0.429530i	$-0.141321\pi$
$752$	−33328.4	+	1841.66i	−1.61617	+	0.0893066i
$753$	−7661.98			−0.370807
$754$	−1599.31	+	688.465i	−0.0772460	+	0.0332525i
$755$	5371.77			0.258939
$756$	15754.2	+	14907.7i	0.757904	+	0.717180i
$757$		−	6029.84i		−	0.289509i	−0.989468	−	0.144754i	$-0.953761\pi$
$757$		−	6029.84i		−	0.289509i	0.989468	−	0.144754i	$-0.0462392\pi$
$758$	−7539.61	−	17514.6i	−0.361281	−	0.839259i
$759$	4559.08			0.218029
$760$	7244.51	+	2655.11i	0.345771	+	0.126725i
$761$			31328.1i			1.49230i	0.665777	+	0.746151i	$0.268100\pi$
$761$			31328.1i			1.49230i	−0.665777	+	0.746151i	$0.731900\pi$
$762$	−175.693	+	75.6318i	−0.00835263	+	0.00359560i
$763$		−	26843.7i		−	1.27367i
$764$	20445.2	+	19346.6i	0.968169	+	0.916147i
$765$			1978.70i			0.0935165i
$766$	−12902.0	+	5554.00i	−0.608575	+	0.261977i
$767$	486.554			0.0229054
$768$	−33455.3	+	3708.68i	−1.57190	+	0.174252i
$769$	15877.3			0.744539			0.372269	−	0.928125i	$-0.378580\pi$
$769$	15877.3			0.744539			0.372269	+	0.928125i	$0.378580\pi$
$770$	−715.608	−	1662.37i	−0.0334918	−	0.0778019i
$771$	−23586.0			−1.10172
$772$	−1147.45	+	1212.61i	−0.0534944	+	0.0565320i
$773$			7719.60i			0.359191i	0.983741	+	0.179596i	$0.0574789\pi$
$773$			7719.60i			0.359191i	−0.983741	+	0.179596i	$0.942521\pi$
$774$	−55.2203	+	23.7710i	−0.00256441	+	0.00110392i
$775$	−14567.3	+	22.5135i	−0.675191	+	0.00104350i
$776$	3533.59	−	9641.46i	0.163465	−	0.446016i
$777$	68633.9			3.16889
$778$	8457.24	+	19646.3i	0.389726	+	0.905338i
$779$			19729.5i			0.907421i
$780$	−979.666	−	927.027i	−0.0449714	−	0.0425550i
$781$		−	1672.85i		−	0.0766444i
$782$	−1153.95	−	2680.63i	−0.0527685	−	0.122582i
$783$			21263.6i			0.970496i
$784$	887.462	+	16060.3i	0.0404274	+	0.731611i
$785$	4294.93			0.195277
$786$	8243.81	+	19150.5i	0.374106	+	0.869052i
$787$	−8739.04			−0.395824			−0.197912	−	0.980220i	$-0.563416\pi$
$787$	−8739.04			−0.395824			−0.197912	+	0.980220i	$0.563416\pi$
$788$	11285.4	+	10679.0i	0.510184	+	0.482770i
$789$	−58527.5			−2.64085
$790$	16305.9	−	7019.31i	0.734354	−	0.316121i
$791$		−	39656.3i		−	1.78257i
$792$	−1300.06	+	3547.24i	−0.0583280	+	0.159149i
$793$	−2005.64			−0.0898137
$794$	39277.6	−	16908.0i	1.75555	−	0.755723i
$795$			35570.4i			1.58686i
$796$	20271.5	−	21422.6i	0.902646	−	0.953901i
$797$			22427.4i			0.996762i	0.866958	+	0.498381i	$0.166072\pi$
$797$			22427.4i			0.996762i	−0.866958	+	0.498381i	$0.833928\pi$
$798$	−27853.1	+	11990.1i	−1.23557	+	0.531885i
$799$	3995.78			0.176922
$800$	−6805.86	−	13678.2i	−0.300779	−	0.604497i
$801$			29556.8i			1.30379i
$802$	−2974.94	−	6910.81i	−0.130983	−	0.304276i
$803$		−	1747.73i		−	0.0768070i
$804$	−30517.0	−	28877.3i	−1.33862	−	1.26669i
$805$			20921.0i			0.915987i
$806$	623.723	+	1442.77i	0.0272577	+	0.0630514i
$807$			67030.7i			2.92391i
$808$	712.812	−	1944.92i	0.0310354	−	0.0846807i
$809$		−	1481.51i		−	0.0643847i	−0.999482	−	0.0321924i	$-0.989751\pi$
$809$		−	1481.51i		−	0.0643847i	0.999482	−	0.0321924i	$-0.0102489\pi$
$810$	2987.52	−	1286.05i	0.129593	−	0.0557868i
$811$		−	15631.4i		−	0.676808i	−0.941001	−	0.338404i	$-0.890113\pi$
$811$		−	15631.4i		−	0.676808i	0.941001	−	0.338404i	$-0.109887\pi$
$812$	−25630.2	+	27085.5i	−1.10769	+	1.17059i
$813$	−1288.05			−0.0555643
$814$	1578.20	+	3666.19i	0.0679558	+	0.157862i
$815$			17716.6i			0.761456i
$816$	4023.28	−	222.318i	0.172602	−	0.00953763i
$817$		−	28.0631i		−	0.00120172i
$818$	−12036.8	−	27961.5i	−0.514494	−	1.19517i
$819$	3181.52			0.135740
$820$	−12917.0	+	13650.4i	−0.550097	+	0.581334i
$821$		−	29286.0i		−	1.24493i	−0.782647	−	0.622466i	$-0.786131\pi$
$821$		−	29286.0i		−	1.24493i	0.782647	−	0.622466i	$-0.213869\pi$
$822$	27820.5	+	64627.3i	1.18048	+	2.74226i
$823$	−3469.07			−0.146931			−0.0734654	−	0.997298i	$-0.523406\pi$
$823$	−3469.07			−0.146931			−0.0734654	+	0.997298i	$0.523406\pi$
$824$	3195.91	+	1171.30i	0.135115	+	0.0495197i
$825$	−2857.01			−0.120568
$826$	9570.99	−	4120.08i	0.403169	−	0.173554i
$827$	11410.0			0.479764			0.239882	−	0.970802i	$-0.422891\pi$
$827$	11410.0			0.479764			0.239882	+	0.970802i	$0.422891\pi$
$828$	30016.6	−	31721.0i	1.25984	−	1.33138i
$829$		−	12401.3i		−	0.519559i	−0.965668	−	0.259779i	$-0.916350\pi$
$829$		−	12401.3i		−	0.519559i	0.965668	−	0.259779i	$-0.0836498\pi$
$830$	−13429.1	+	5780.89i	−0.561603	+	0.241756i
$831$		−	20963.9i		−	0.875125i
$832$	−1065.25	+	1258.07i	−0.0443882	+	0.0524228i
$833$		−	1925.49i		−	0.0800892i
$834$	39815.0	−	17139.4i	1.65309	−	0.711617i
$835$	16669.6			0.690867
$836$	−1280.94	−	1212.11i	−0.0529930	−	0.0501456i
$837$	19195.1	−	29.6657i	0.792687	−	0.00122508i
$838$	7417.22	+	17230.3i	0.305756	+	0.710274i
$839$			16120.0i			0.663320i	0.943399	+	0.331660i	$0.107609\pi$
$839$			16120.0i			0.663320i	−0.943399	+	0.331660i	$0.892391\pi$
$840$	−27120.9	−	9939.82i	−1.11400	−	0.408281i
$841$	−12168.5			−0.498935
$842$	−17994.1	+	7746.01i	−0.736480	+	0.317037i
$843$	10614.4			0.433665
$844$	16369.5	+	15489.9i	0.667607	+	0.631735i
$845$	13933.0			0.567230
$846$	23641.9	+	54920.4i	0.960786	+	2.23192i
$847$		−	32034.5i		−	1.29955i
$848$	43409.1	−	2398.70i	1.75787	−	0.0971365i
$849$			30938.0i			1.25063i
$850$	723.136	+	1679.85i	0.0291804	+	0.0677864i
$851$		−	46139.3i		−	1.85856i
$852$	−19392.6	−	18350.5i	−0.779786	−	0.737886i
$853$	−41657.7			−1.67214			−0.836068	−	0.548625i	$-0.815151\pi$
$853$	−41657.7			−1.67214			−0.836068	+	0.548625i	$0.815151\pi$
$854$	−39452.9	+	16983.5i	−1.58085	+	0.680519i
$855$		−	13821.3i		−	0.552842i
$856$	−17477.0	−	6405.31i	−0.697840	−	0.255758i
$857$	−21081.2			−0.840280			−0.420140	−	0.907459i	$-0.638019\pi$
$857$	−21081.2			−0.840280			−0.420140	+	0.907459i	$0.638019\pi$
$858$	121.890	+	283.152i	0.00484994	+	0.0112665i
$859$	3810.49			0.151353			0.0756765	−	0.997132i	$-0.475888\pi$
$859$	3810.49			0.151353			0.0756765	+	0.997132i	$0.475888\pi$
$860$	18.3731	−	19.4163i	0.000728507	−	0.000769874i
$861$		−	73860.2i		−	2.92352i
$862$	−15206.0	−	35323.7i	−0.600834	−	1.39574i
$863$	30169.9			1.19003			0.595014	−	0.803715i	$-0.297146\pi$
$863$	30169.9			1.19003			0.595014	+	0.803715i	$0.297146\pi$
$864$	8967.95	+	18023.5i	0.353120	+	0.709690i
$865$	3806.75			0.149634
$866$	4834.30	+	11230.1i	0.189695	+	0.440665i
$867$	39891.9			1.56263
$868$	24486.5	+	23099.1i	0.957517	+	0.903266i
$869$	−4057.56			−0.158393
$870$	−11196.8	−	26010.2i	−0.436328	−	1.01360i
$871$	−2057.61			−0.0800453
$872$	8573.75	−	23393.6i	0.332963	−	0.908495i
$873$	−18394.3			−0.713119
$874$	8060.37	+	18724.3i	0.311952	+	0.724668i
$875$		−	32527.8i		−	1.25673i
$876$	−20260.6	−	19171.9i	−0.781440	−	0.739451i
$877$	−5489.99			−0.211384			−0.105692	−	0.994399i	$-0.533706\pi$
$877$	−5489.99			−0.211384			−0.105692	+	0.994399i	$0.533706\pi$
$878$	−3996.77	−	9284.54i	−0.153627	−	0.356877i
$879$	−30440.1			−1.16805
$880$	−92.6826	−	1677.27i	−0.00355038	−	0.0642509i
$881$		−	261.977i		−	0.0100184i	−0.999987	−	0.00500921i	$-0.998406\pi$
$881$		−	261.977i		−	0.0100184i	0.999987	−	0.00500921i	$-0.00159449\pi$
$882$	26465.1	−	11392.6i	1.01035	−	0.434930i
$883$	−25733.9			−0.980765			−0.490383	−	0.871507i	$-0.663143\pi$
$883$	−25733.9			−0.980765			−0.490383	+	0.871507i	$0.663143\pi$
$884$	135.635	−	143.337i	0.00516051	−	0.00545354i
$885$			7913.00i			0.300557i
$886$	−11050.5	−	25670.4i	−0.419016	−	0.973380i
$887$			14312.8i			0.541800i	0.962608	+	0.270900i	$0.0873212\pi$
$887$			14312.8i			0.541800i	−0.962608	+	0.270900i	$0.912679\pi$
$888$	59812.6	+	21921.3i	2.26034	+	0.828414i
$889$			200.623i			0.00756882i
$890$	−5196.33	−	12071.1i	−0.195709	−	0.454635i
$891$	−743.412			−0.0279520
$892$	34293.5	−	36240.8i	1.28725	−	1.36035i
$893$	−27910.7			−1.04591
$894$	−58027.3	+	24979.3i	−2.17083	+	0.934490i
$895$	−11093.7			−0.414326
$896$	−10301.4	+	33767.9i	−0.384090	+	1.25905i
$897$		−	3563.49i		−	0.132644i
$898$	3776.39	+	8772.60i	0.140334	+	0.325997i
$899$	51.0028	+	33001.3i	0.00189215	+	1.22431i
$900$	−18810.3	+	19878.4i	−0.696678	+	0.736238i
$901$	−5204.36			−0.192433
$902$	3945.36	−	1698.38i	0.145639	−	0.0626940i
$903$			105.059i			0.00387169i
$904$	12666.0	−	34559.5i	0.466002	−	1.27149i
$905$			13443.2i			0.493775i
$906$	−17998.5	+	7747.92i	−0.660000	+	0.284114i
$907$			45682.4i			1.67239i	0.548430	+	0.836196i	$0.315226\pi$
$907$			45682.4i			1.67239i	−0.548430	+	0.836196i	$0.684774\pi$
$908$	−2863.92	−	2710.03i	−0.104672	−	0.0990480i
$909$	−3710.58			−0.135393
$910$	−1299.35	+	559.337i	−0.0473329	+	0.0203757i
$911$	−7089.18			−0.257821			−0.128911	−	0.991656i	$-0.541148\pi$
$911$	−7089.18			−0.257821			−0.128911	+	0.991656i	$0.541148\pi$
$912$	−28102.8	+	1552.91i	−1.02037	+	0.0563836i
$913$	3341.69			0.121132
$914$	−21233.2	−	49325.1i	−0.768417	−	1.78504i
$915$		−	32618.4i		−	1.17851i
$916$	2880.37	+	2725.60i	0.103898	+	0.0983148i
$917$	21867.8			0.787500
$918$	−952.863	−	2213.51i	−0.0342584	−	0.0795825i
$919$		−	18233.4i		−	0.654478i	−0.944942	−	0.327239i	$-0.893882\pi$
$919$		−	18233.4i		−	0.654478i	0.944942	−	0.327239i	$-0.106118\pi$
$920$	−6682.08	+	18232.1i	−0.239458	+	0.653365i
$921$		−	73492.9i		−	2.62940i
$922$	−5290.22	−	12289.2i	−0.188963	−	0.438964i
$923$	−1307.54			−0.0466287
$924$	4795.39	+	4537.72i	0.170732	+	0.161558i
$925$			28913.8i			1.02776i
$926$	−13166.8	+	5667.97i	−0.467264	+	0.201146i
$927$		−	6097.27i		−	0.216031i
$928$	−30987.0	+	15418.2i	−1.09612	+	0.545396i
$929$			2119.94i			0.0748686i	0.999299	+	0.0374343i	$0.0119185\pi$
$929$			2119.94i			0.0748686i	−0.999299	+	0.0374343i	$0.988082\pi$
$930$	−23464.3	+	10143.8i	−0.827339	+	0.357666i
$931$			13449.6i			0.473463i
$932$	17160.3	−	18134.7i	0.603117	−	0.637364i
$933$			49960.0i			1.75307i
$934$	3727.86	+	8659.86i	0.130599	+	0.303383i
$935$			201.090i			0.00703351i
$936$	2772.62	+	1016.16i	0.0968224	+	0.0354854i
$937$	21580.4			0.752402			0.376201	−	0.926538i	$-0.377230\pi$
$937$	21580.4			0.752402			0.376201	+	0.926538i	$0.377230\pi$
$938$	−40475.2	+	17423.6i	−1.40891	+	0.606504i
$939$		−	43488.8i		−	1.51140i
$940$	−19310.9	−	18273.3i	−0.670055	−	0.634051i
$941$			27530.2i			0.953727i	0.878977	+	0.476864i	$0.158226\pi$
$941$			27530.2i			0.953727i	−0.878977	+	0.476864i	$0.841774\pi$
$942$	−14390.4	+	6194.74i	−0.497735	+	0.214263i
$943$	−49652.8			−1.71465
$944$	9656.80	−	533.616i	0.332947	−	0.0183980i
$945$			17275.4i			0.594676i
$946$	−5.61188	+	2.41578i	−0.000192873	+	8.30272e-5i
$947$	34068.2			1.16903			0.584513	−	0.811384i	$-0.301286\pi$
$947$	34068.2			1.16903			0.584513	+	0.811384i	$0.301286\pi$
$948$	−44509.9	+	47037.4i	−1.52491	+	1.61150i
$949$	−1366.07			−0.0467276
$950$	−5051.14	−	11733.9i	−0.172506	−	0.400733i
$951$	−18063.3			−0.615924
$952$	1454.31	−	3968.11i	0.0495110	−	0.135092i
$953$		−	8468.47i		−	0.287850i	−0.989589	−	0.143925i	$-0.954028\pi$
$953$		−	8468.47i		−	0.287850i	0.989589	−	0.143925i	$-0.0459724\pi$
$954$	−30792.7	−	71531.8i	−1.04502	−	2.42760i
$955$			22419.3i			0.759657i
$956$	25355.3	−	26795.0i	0.857791	−	0.906499i
$957$			6472.36i			0.218623i
$958$	13801.8	+	32061.6i	0.465464	+	1.08128i
$959$	73797.4			2.48493
$960$	−20460.5	−	17324.6i	−0.687874	−	0.582447i
$961$	29790.9	−	92.0827i	0.999995	−	0.00309096i
$962$	2865.58	−	1233.56i	0.0960396	−	0.0413427i
$963$			33343.2i			1.11575i
$964$	−22778.8	−	21554.9i	−0.761055	−	0.720161i
$965$	−1329.69			−0.0443568
$966$	−30175.2	−	70097.4i	−1.00504	−	2.33473i
$967$	−41759.5			−1.38872			−0.694361	−	0.719627i	$-0.744313\pi$
$967$	−41759.5			−1.38872			−0.694361	+	0.719627i	$0.744313\pi$
$968$	10231.7	−	27917.3i	0.339730	−	0.926957i
$969$	3369.27			0.111699
$970$	7512.30	−	3233.87i	0.248666	−	0.107045i
$971$			7146.50i			0.236192i	0.993002	+	0.118096i	$0.0376790\pi$
$971$			7146.50i			0.236192i	−0.993002	+	0.118096i	$0.962321\pi$
$972$	−24665.5	+	26066.1i	−0.813938	+	0.860156i
$973$		−	45464.5i		−	1.49797i
$974$	−3594.41	+	1547.30i	−0.118247	+	0.0509023i
$975$			2233.11i			0.0733506i
$976$	−39806.6	+	2199.63i	−1.30551	+	0.0721399i
$977$	47479.2			1.55475			0.777377	−	0.629035i	$-0.216550\pi$
$977$	47479.2			1.55475			0.777377	+	0.629035i	$0.216550\pi$
$978$	−25553.4	−	59360.8i	−0.835487	−	1.94085i
$979$			3003.77i			0.0980603i
$980$	−8805.54	+	9305.55i	−0.287023	+	0.303321i
$981$	−44631.1			−1.45256
$982$	30381.7	−	13078.6i	0.987289	−	0.425004i
$983$	39884.1			1.29411			0.647053	−	0.762445i	$-0.276001\pi$
$983$	39884.1			1.29411			0.647053	+	0.762445i	$0.276001\pi$
$984$	23590.6	−	64367.3i	0.764269	−	2.08532i
$985$			12375.1i			0.400307i
$986$	3805.59	−	1638.22i	0.122916	−	0.0529122i
$987$	104488.			3.36970
$988$	−947.415	+	1001.21i	−0.0305074	+	0.0322397i
$989$	70.6261			0.00227076
$990$	−2763.90	+	1189.79i	−0.0887297	+	0.0381960i
$991$	−33296.6			−1.06731			−0.533654	−	0.845703i	$-0.679182\pi$
$991$	−33296.6			−1.06731			−0.533654	+	0.845703i	$0.679182\pi$
$992$	13961.6	+	27951.1i	0.446855	+	0.894606i
$993$	44991.7			1.43783
$994$	−25720.6	+	11072.1i	−0.820733	+	0.353306i
$995$	23491.1			0.748462
$996$	36657.0	−	38738.6i	1.16619	−	1.23241i
$997$	35975.1			1.14277			0.571385	−	0.820682i	$-0.306406\pi$
$997$	35975.1			1.14277			0.571385	+	0.820682i	$0.306406\pi$
$998$	32146.8	−	13838.4i	1.01963	−	0.438926i
$999$		−	38099.3i		−	1.20661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.4.d.c.123.8	yes	40
4.3	odd	2	inner	124.4.d.c.123.5	✓	40
31.30	odd	2	inner	124.4.d.c.123.7	yes	40
124.123	even	2	inner	124.4.d.c.123.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.4.d.c.123.5	✓	40	4.3	odd	2	inner
124.4.d.c.123.6	yes	40	124.123	even	2	inner
124.4.d.c.123.7	yes	40	31.30	odd	2	inner
124.4.d.c.123.8	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	124.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.59794 + 1.11835i) q^{2} +8.21784 q^{3} +(5.49858 - 5.81081i) q^{4} +6.37189 q^{5} +(-21.3495 + 9.19042i) q^{6} +24.3788i q^{7} +(-7.78647 + 21.2455i) q^{8} +40.5329 q^{9} +O(q^{10})\)	\(q+(-2.59794 + 1.11835i) q^{2} +8.21784 q^{3} +(5.49858 - 5.81081i) q^{4} +6.37189 q^{5} +(-21.3495 + 9.19042i) q^{6} +24.3788i q^{7} +(-7.78647 + 21.2455i) q^{8} +40.5329 q^{9} +(-16.5538 + 7.12601i) q^{10} +4.11924 q^{11} +(45.1865 - 47.7523i) q^{12} -3.21970i q^{13} +(-27.2640 - 63.3346i) q^{14} +52.3632 q^{15} +(-3.53113 - 63.9025i) q^{16} +7.66134i q^{17} +(-105.302 + 45.3300i) q^{18} -53.5148i q^{19} +(35.0364 - 37.0259i) q^{20} +200.341i q^{21} +(-10.7015 + 4.60675i) q^{22} +134.680 q^{23} +(-63.9879 + 174.592i) q^{24} -84.3990 q^{25} +(3.60075 + 8.36459i) q^{26} +111.211 q^{27} +(141.661 + 134.049i) q^{28} +191.200i q^{29} +(-136.036 + 58.5604i) q^{30} +(172.600 - 0.266751i) q^{31} +(80.6391 + 162.066i) q^{32} +33.8512 q^{33} +(-8.56806 - 19.9037i) q^{34} +155.339i q^{35} +(222.874 - 235.529i) q^{36} -342.585i q^{37} +(59.8483 + 139.028i) q^{38} -26.4590i q^{39} +(-49.6145 + 135.374i) q^{40} -368.673 q^{41} +(-224.051 - 520.474i) q^{42} +0.524399 q^{43} +(22.6500 - 23.9361i) q^{44} +258.271 q^{45} +(-349.890 + 150.619i) q^{46} -521.551i q^{47} +(-29.0182 - 525.141i) q^{48} -251.326 q^{49} +(219.264 - 94.3877i) q^{50} +62.9596i q^{51} +(-18.7091 - 17.7038i) q^{52} +679.302i q^{53} +(-288.920 + 124.373i) q^{54} +26.2473 q^{55} +(-517.939 - 189.825i) q^{56} -439.776i q^{57} +(-213.829 - 496.727i) q^{58} +151.118i q^{59} +(287.923 - 304.273i) q^{60} -622.927i q^{61} +(-448.107 + 193.721i) q^{62} +988.143i q^{63} +(-390.742 - 330.855i) q^{64} -20.5156i q^{65} +(-87.9435 + 37.8575i) q^{66} -639.069i q^{67} +(44.5186 + 42.1265i) q^{68} +1106.78 q^{69} +(-173.723 - 403.561i) q^{70} -406.107i q^{71} +(-315.608 + 861.141i) q^{72} -424.285i q^{73} +(383.130 + 890.016i) q^{74} -693.578 q^{75} +(-310.965 - 294.256i) q^{76} +100.422i q^{77} +(29.5904 + 68.7388i) q^{78} -985.028 q^{79} +(-22.4999 - 407.180i) q^{80} -180.473 q^{81} +(957.789 - 412.305i) q^{82} +811.239 q^{83} +(1164.14 + 1101.59i) q^{84} +48.8172i q^{85} +(-1.36236 + 0.586462i) q^{86} +1571.25i q^{87} +(-32.0743 + 87.5152i) q^{88} +729.206i q^{89} +(-670.973 + 288.838i) q^{90} +78.4924 q^{91} +(740.549 - 782.600i) q^{92} +(1418.40 - 2.19212i) q^{93} +(583.277 + 1354.96i) q^{94} -340.991i q^{95} +(662.679 + 1331.83i) q^{96} -453.812 q^{97} +(652.929 - 281.070i) q^{98} +166.965 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9	\( 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9} + 228 q^{10} - 104 q^{14} - 78 q^{16} + 114 q^{18} - 44 q^{20} + 28 q^{25} + 48 q^{28} - 602 q^{32} - 136 q^{33} - 482 q^{36} + 420 q^{38} - 516 q^{40} - 4 q^{41} - 1596 q^{45} + 1876 q^{49} - 662 q^{50} + 1576 q^{56} - 838 q^{62} - 302 q^{64} - 3900 q^{66} - 872 q^{69} - 912 q^{70} - 2166 q^{72} + 3220 q^{76} - 476 q^{78} + 572 q^{80} - 2056 q^{81} + 3096 q^{82} - 6220 q^{90} - 2904 q^{93} + 6408 q^{94} - 1836 q^{97} - 1358 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9 + 228 * q^10 - 104 * q^14 - 78 * q^16 + 114 * q^18 - 44 * q^20 + 28 * q^25 + 48 * q^28 - 602 * q^32 - 136 * q^33 - 482 * q^36 + 420 * q^38 - 516 * q^40 - 4 * q^41 - 1596 * q^45 + 1876 * q^49 - 662 * q^50 + 1576 * q^56 - 838 * q^62 - 302 * q^64 - 3900 * q^66 - 872 * q^69 - 912 * q^70 - 2166 * q^72 + 3220 * q^76 - 476 * q^78 + 572 * q^80 - 2056 * q^81 + 3096 * q^82 - 6220 * q^90 - 2904 * q^93 + 6408 * q^94 - 1836 * q^97 - 1358 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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