LMFDB - Embedded newform 312.4.m.a.181.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (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:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.19
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.23230 - 1.73690i) q^{2} +3.00000i q^{3} +(1.96633 + 7.75458i) q^{4} -12.2791 q^{5} +(5.21071 - 6.69690i) q^{6} +32.4044i q^{7} +(9.07951 - 20.7259i) q^{8} -9.00000 q^{9} +(27.4107 + 21.3277i) q^{10} -68.1675 q^{11} +(-23.2637 + 5.89900i) q^{12} +(-8.22964 + 46.1440i) q^{13} +(56.2833 - 72.3363i) q^{14} -36.8374i q^{15} +(-56.2671 + 30.4962i) q^{16} +86.0275 q^{17} +(20.0907 + 15.6321i) q^{18} +16.5885 q^{19} +(-24.1449 - 95.2195i) q^{20} -97.2131 q^{21} +(152.170 + 118.400i) q^{22} -41.2086 q^{23} +(62.1777 + 27.2385i) q^{24} +25.7771 q^{25} +(98.5188 - 88.7133i) q^{26} -27.0000i q^{27} +(-251.282 + 63.7178i) q^{28} +21.6289i q^{29} +(-63.9830 + 82.2322i) q^{30} -111.539i q^{31} +(178.574 + 29.6538i) q^{32} -204.503i q^{33} +(-192.039 - 149.421i) q^{34} -397.898i q^{35} +(-17.6970 - 69.7912i) q^{36} +410.686 q^{37} +(-37.0305 - 28.8126i) q^{38} +(-138.432 - 24.6889i) q^{39} +(-111.489 + 254.496i) q^{40} +253.880i q^{41} +(217.009 + 168.850i) q^{42} -341.204i q^{43} +(-134.040 - 528.611i) q^{44} +110.512 q^{45} +(91.9900 + 71.5753i) q^{46} -360.180i q^{47} +(-91.4886 - 168.801i) q^{48} -707.044 q^{49} +(-57.5423 - 44.7724i) q^{50} +258.082i q^{51} +(-374.010 + 26.9172i) q^{52} +226.059i q^{53} +(-46.8964 + 60.2721i) q^{54} +837.038 q^{55} +(671.610 + 294.216i) q^{56} +49.7655i q^{57} +(37.5673 - 48.2822i) q^{58} -725.135 q^{59} +(285.659 - 72.4346i) q^{60} -118.535i q^{61} +(-193.733 + 248.989i) q^{62} -291.639i q^{63} +(-347.125 - 376.362i) q^{64} +(101.053 - 566.609i) q^{65} +(-355.201 + 456.511i) q^{66} -685.284 q^{67} +(169.159 + 667.107i) q^{68} -123.626i q^{69} +(-691.110 + 888.227i) q^{70} +312.909i q^{71} +(-81.7156 + 186.533i) q^{72} -736.026i q^{73} +(-916.774 - 713.322i) q^{74} +77.3314i q^{75} +(32.6185 + 128.637i) q^{76} -2208.93i q^{77} +(266.140 + 295.556i) q^{78} -354.167 q^{79} +(690.911 - 374.467i) q^{80} +81.0000 q^{81} +(440.965 - 566.736i) q^{82} +798.760 q^{83} +(-191.153 - 753.847i) q^{84} -1056.34 q^{85} +(-592.639 + 761.671i) q^{86} -64.8867 q^{87} +(-618.928 + 1412.83i) q^{88} -509.714i q^{89} +(-246.696 - 191.949i) q^{90} +(-1495.27 - 266.676i) q^{91} +(-81.0298 - 319.555i) q^{92} +334.617 q^{93} +(-625.597 + 804.029i) q^{94} -203.692 q^{95} +(-88.9614 + 535.722i) q^{96} +1799.10i q^{97} +(1578.33 + 1228.07i) q^{98} +613.508 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.23230	−	1.73690i	−0.789238	−	0.614088i
$2$	−2.23230	−	1.73690i	−0.789238	−	0.614088i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	1.96633	+	7.75458i	0.245792	+	0.969323i
$5$	−12.2791			−1.09828			−0.549140	−	0.835731i	$-0.685044\pi$
$5$	−12.2791			−1.09828			−0.549140	+	0.835731i	$0.685044\pi$
$6$	5.21071	−	6.69690i	0.354544	−	0.455666i
$7$			32.4044i			1.74967i	0.484419	+	0.874836i	$0.339031\pi$
$7$			32.4044i			1.74967i	−0.484419	+	0.874836i	$0.660969\pi$
$8$	9.07951	−	20.7259i	0.401261	−	0.915964i
$9$	−9.00000			−0.333333
$10$	27.4107	+	21.3277i	0.866803	+	0.674440i
$11$	−68.1675			−1.86848			−0.934240	−	0.356644i	$-0.883921\pi$
$11$	−68.1675			−1.86848			−0.934240	+	0.356644i	$0.883921\pi$
$12$	−23.2637	+	5.89900i	−0.559639	+	0.141908i
$13$	−8.22964	+	46.1440i	−0.175576	+	0.984466i
$13$	−8.22964	+	46.1440i	−0.175576	+	0.984466i
$14$	56.2833	−	72.3363i	1.07445	−	1.38091i
$15$		−	36.8374i		−	0.634092i
$16$	−56.2671	+	30.4962i	−0.879173	+	0.476503i
$17$	86.0275			1.22734			0.613668	−	0.789564i	$-0.289693\pi$
$17$	86.0275			1.22734			0.613668	+	0.789564i	$0.289693\pi$
$18$	20.0907	+	15.6321i	0.263079	+	0.204696i
$19$	16.5885			0.200298			0.100149	−	0.994972i	$-0.468068\pi$
$19$	16.5885			0.200298			0.100149	+	0.994972i	$0.468068\pi$
$20$	−24.1449	−	95.2195i	−0.269948	−	1.06459i
$21$	−97.2131			−1.01017
$22$	152.170	+	118.400i	1.47467	+	1.14741i
$23$	−41.2086			−0.373591			−0.186795	−	0.982399i	$-0.559810\pi$
$23$	−41.2086			−0.373591			−0.186795	+	0.982399i	$0.559810\pi$
$24$	62.1777	+	27.2385i	0.528832	+	0.231668i
$25$	25.7771			0.206217
$26$	98.5188	−	88.7133i	0.743120	−	0.669158i
$27$		−	27.0000i		−	0.192450i
$28$	−251.282	+	63.7178i	−1.69600	+	0.430055i
$29$			21.6289i			0.138496i	0.997599	+	0.0692481i	$0.0220600\pi$
$29$			21.6289i			0.138496i	−0.997599	+	0.0692481i	$0.977940\pi$
$30$	−63.9830	+	82.2322i	−0.389388	+	0.500449i
$31$		−	111.539i		−	0.646226i	−0.946360	−	0.323113i	$-0.895271\pi$
$31$		−	111.539i		−	0.646226i	0.946360	−	0.323113i	$-0.104729\pi$
$32$	178.574	+	29.6538i	0.986491	+	0.163816i
$33$		−	204.503i		−	1.07877i
$34$	−192.039	−	149.421i	−0.968660	−	0.753693i
$35$		−	397.898i		−	1.92163i
$36$	−17.6970	−	69.7912i	−0.0819306	−	0.323108i
$37$	410.686			1.82477			0.912383	−	0.409338i	$-0.134240\pi$
$37$	410.686			1.82477			0.912383	+	0.409338i	$0.134240\pi$
$38$	−37.0305	−	28.8126i	−0.158083	−	0.123001i
$39$	−138.432	−	24.6889i	−0.568382	−	0.101369i
$40$	−111.489	+	254.496i	−0.440697	+	1.00598i
$41$			253.880i			0.967058i	0.875328	+	0.483529i	$0.160645\pi$
$41$			253.880i			0.967058i	−0.875328	+	0.483529i	$0.839355\pi$
$42$	217.009	+	168.850i	0.797267	+	0.620336i
$43$		−	341.204i		−	1.21007i	−0.796197	−	0.605037i	$-0.793158\pi$
$43$		−	341.204i		−	1.21007i	0.796197	−	0.605037i	$-0.206842\pi$
$44$	−134.040	−	528.611i	−0.459257	−	1.81116i
$45$	110.512			0.366093
$46$	91.9900	+	71.5753i	0.294852	+	0.229418i
$47$		−	360.180i		−	1.11782i	−0.829228	−	0.558910i	$-0.811220\pi$
$47$		−	360.180i		−	1.11782i	0.829228	−	0.558910i	$-0.188780\pi$
$48$	−91.4886	−	168.801i	−0.275109	−	0.507591i
$49$	−707.044			−2.06135
$50$	−57.5423	−	44.7724i	−0.162754	−	0.126635i
$51$			258.082i			0.708603i
$52$	−374.010	+	26.9172i	−0.997420	+	0.0717834i
$53$			226.059i			0.585880i	0.956131	+	0.292940i	$0.0946336\pi$
$53$			226.059i			0.585880i	−0.956131	+	0.292940i	$0.905366\pi$
$54$	−46.8964	+	60.2721i	−0.118181	+	0.151889i
$55$	837.038			2.05211
$56$	671.610	+	294.216i	1.60264	+	0.702076i
$57$			49.7655i			0.115642i
$58$	37.5673	−	48.2822i	0.0850488	−	0.109306i
$59$	−725.135			−1.60008			−0.800038	−	0.599949i	$-0.795188\pi$
$59$	−725.135			−1.60008			−0.800038	+	0.599949i	$0.795188\pi$
$60$	285.659	−	72.4346i	0.614640	−	0.155854i
$61$		−	118.535i		−	0.248801i	−0.992232	−	0.124401i	$-0.960299\pi$
$61$		−	118.535i		−	0.248801i	0.992232	−	0.124401i	$-0.0397008\pi$
$62$	−193.733	+	248.989i	−0.396840	+	0.510026i
$63$		−	291.639i		−	0.583224i
$64$	−347.125	−	376.362i	−0.677978	−	0.735082i
$65$	101.053	−	566.609i	0.192832	−	1.08122i
$66$	−355.201	+	456.511i	−0.662458	+	0.851404i
$67$	−685.284			−1.24956			−0.624782	−	0.780800i	$-0.714812\pi$
$67$	−685.284			−1.24956			−0.624782	+	0.780800i	$0.714812\pi$
$68$	169.159	+	667.107i	0.301669	+	1.18969i
$69$		−	123.626i		−	0.215693i
$70$	−691.110	+	888.227i	−1.18005	+	1.51662i
$71$			312.909i			0.523034i	0.965199	+	0.261517i	$0.0842228\pi$
$71$			312.909i			0.523034i	−0.965199	+	0.261517i	$0.915777\pi$
$72$	−81.7156	+	186.533i	−0.133754	+	0.305321i
$73$		−	736.026i		−	1.18007i	−0.807376	−	0.590037i	$-0.799113\pi$
$73$		−	736.026i		−	1.18007i	0.807376	−	0.590037i	$-0.200887\pi$
$74$	−916.774	−	713.322i	−1.44017	−	1.12057i
$75$			77.3314i			0.119059i
$76$	32.6185	+	128.637i	0.0492316	+	0.194153i
$77$		−	2208.93i		−	3.26923i
$78$	266.140	+	295.556i	0.386339	+	0.429041i
$79$	−354.167			−0.504391			−0.252196	−	0.967676i	$-0.581153\pi$
$79$	−354.167			−0.504391			−0.252196	+	0.967676i	$0.581153\pi$
$80$	690.911	−	374.467i	0.965577	−	0.523333i
$81$	81.0000			0.111111
$82$	440.965	−	566.736i	0.593858	−	0.763238i
$83$	798.760			1.05633			0.528164	−	0.849142i	$-0.322881\pi$
$83$	798.760			1.05633			0.528164	+	0.849142i	$0.322881\pi$
$84$	−191.153	−	753.847i	−0.248292	−	0.979184i
$85$	−1056.34			−1.34796
$86$	−592.639	+	761.671i	−0.743092	+	0.955036i
$87$	−64.8867			−0.0799608
$88$	−618.928	+	1412.83i	−0.749749	+	1.71146i
$89$		−	509.714i		−	0.607074i	−0.952820	−	0.303537i	$-0.901832\pi$
$89$		−	509.714i		−	0.607074i	0.952820	−	0.303537i	$-0.0981676\pi$
$90$	−246.696	−	191.949i	−0.288934	−	0.224813i
$91$	−1495.27	−	266.676i	−1.72249	−	0.307201i
$92$	−81.0298	−	319.555i	−0.0918255	−	0.362130i
$93$	334.617			0.373099
$94$	−625.597	+	804.029i	−0.686440	+	0.882226i
$95$	−203.692			−0.219983
$96$	−88.9614	+	535.722i	−0.0945790	+	0.569551i
$97$			1799.10i			1.88320i	0.336733	+	0.941600i	$0.390678\pi$
$97$			1799.10i			1.88320i	−0.336733	+	0.941600i	$0.609322\pi$
$98$	1578.33	+	1228.07i	1.62690	+	1.26585i
$99$	613.508			0.622827
$100$	50.6864	+	199.891i	0.0506864	+	0.199891i
$101$		−	1155.41i		−	1.13829i	−0.822236	−	0.569147i	$-0.807274\pi$
$101$		−	1155.41i		−	1.13829i	0.822236	−	0.569147i	$-0.192726\pi$
$102$	448.264	−	576.117i	0.435145	−	0.559256i
$103$	−88.7363			−0.0848878			−0.0424439	−	0.999099i	$-0.513514\pi$
$103$	−88.7363			−0.0848878			−0.0424439	+	0.999099i	$0.513514\pi$
$104$	881.655	+	589.532i	0.831283	+	0.555850i
$105$	1193.69			1.10945
$106$	392.643	−	504.632i	0.359782	−	0.462398i
$107$			1278.51i			1.15512i	0.816347	+	0.577562i	$0.195996\pi$
$107$			1278.51i			1.15512i	−0.816347	+	0.577562i	$0.804004\pi$
$108$	209.374	−	53.0910i	0.186546	−	0.0473026i
$109$	1258.78			1.10614			0.553070	−	0.833135i	$-0.313456\pi$
$109$	1258.78			1.10614			0.553070	+	0.833135i	$0.313456\pi$
$110$	−1868.52	−	1453.85i	−1.61960	−	1.26018i
$111$			1232.06i			1.05353i
$112$	−988.210	−	1823.30i	−0.833724	−	1.53826i
$113$	−1111.76			−0.925537			−0.462769	−	0.886479i	$-0.653144\pi$
$113$	−1111.76			−0.925537			−0.462769	+	0.886479i	$0.653144\pi$
$114$	86.4379	−	111.092i	0.0710145	−	0.0912691i
$115$	506.006			0.410307
$116$	−167.723	+	42.5296i	−0.134247	+	0.0340412i
$117$	74.0668	−	415.296i	0.0585254	−	0.328155i
$118$	1618.72	+	1259.49i	1.26284	+	0.982588i
$119$			2787.67i			2.14744i
$120$	−763.488	−	334.466i	−0.580805	−	0.254437i
$121$	3315.81			2.49122
$122$	−205.884	+	264.606i	−0.152786	+	0.196363i
$123$	−761.639			−0.558331
$124$	864.939	−	219.323i	0.626402	−	0.158837i
$125$	1218.37			0.871795
$126$	−506.549	+	651.027i	−0.358151	+	0.460302i
$127$	1070.88			0.748230			0.374115	−	0.927382i	$-0.377947\pi$
$127$	1070.88			0.748230			0.374115	+	0.927382i	$0.377947\pi$
$128$	121.183	+	1443.08i	0.0836811	+	0.996493i
$129$	1023.61			0.698636
$130$	−1209.73	+	1089.32i	−0.816153	+	0.734922i
$131$		−	1246.30i		−	0.831220i	−0.909543	−	0.415610i	$-0.863568\pi$
$131$		−	1246.30i		−	0.831220i	0.909543	−	0.415610i	$-0.136432\pi$
$132$	1585.83	−	402.120i	1.04567	−	0.265152i
$133$			537.540i			0.350456i
$134$	1529.76	+	1190.27i	0.986202	+	0.767342i
$135$			331.537i			0.211364i
$136$	781.087	−	1783.00i	0.492483	−	1.12420i
$137$		−	408.168i		−	0.254541i	−0.991868	−	0.127271i	$-0.959378\pi$
$137$		−	408.168i		−	0.254541i	0.991868	−	0.127271i	$-0.0406217\pi$
$138$	−214.726	+	275.970i	−0.132454	+	0.170233i
$139$		−	1117.40i		−	0.681847i	−0.940091	−	0.340923i	$-0.889260\pi$
$139$		−	1117.40i		−	0.681847i	0.940091	−	0.340923i	$-0.110740\pi$
$140$	3085.53	−	782.400i	1.86268	−	0.472320i
$141$	1080.54			0.645374
$142$	543.492	−	698.506i	0.321189	−	0.412798i
$143$	560.995	−	3145.53i	0.328061	−	1.83946i
$144$	506.404	−	274.466i	0.293058	−	0.158834i
$145$		−	265.584i		−	0.152107i
$146$	−1278.41	+	1643.03i	−0.724669	+	0.931358i
$147$		−	2121.13i		−	1.19012i
$148$	807.545	+	3184.70i	0.448512	+	1.76879i
$149$	2219.67			1.22042			0.610209	−	0.792241i	$-0.291086\pi$
$149$	2219.67			1.22042			0.610209	+	0.792241i	$0.291086\pi$
$150$	134.317	−	172.627i	0.0731130	−	0.0939662i
$151$			2664.08i			1.43576i	0.696166	+	0.717881i	$0.254888\pi$
$151$			2664.08i			1.43576i	−0.696166	+	0.717881i	$0.745112\pi$
$152$	150.615	−	343.811i	0.0803719	−	0.183466i
$153$	−774.247			−0.409112
$154$	−3836.69	+	4930.99i	−2.00759	+	2.58020i
$155$			1369.60i			0.709737i
$156$	−80.7515	−	1122.03i	−0.0414442	−	0.575861i
$157$			1240.93i			0.630808i	0.948958	+	0.315404i	$0.102140\pi$
$157$			1240.93i			0.630808i	−0.948958	+	0.315404i	$0.897860\pi$
$158$	790.607	+	615.154i	0.398084	+	0.309741i
$159$	−678.178			−0.338258
$160$	−2192.73	−	364.123i	−1.08344	−	0.179915i
$161$		−	1335.34i		−	0.653661i
$162$	−180.816	−	140.689i	−0.0876931	−	0.0682320i
$163$	−1339.78			−0.643799			−0.321900	−	0.946774i	$-0.604321\pi$
$163$	−1339.78			−0.643799			−0.321900	+	0.946774i	$0.604321\pi$
$164$	−1968.73	+	499.212i	−0.937391	+	0.237695i
$165$			2511.12i			1.18479i
$166$	−1783.07	−	1387.37i	−0.833694	−	0.648679i
$167$			1721.59i			0.797730i	0.917010	+	0.398865i	$0.130596\pi$
$167$			1721.59i			0.797730i	−0.917010	+	0.398865i	$0.869404\pi$
$168$	−882.648	+	2014.83i	−0.405344	+	0.925282i
$169$	−2061.55	−	759.498i	−0.938346	−	0.345698i
$170$	2358.07	+	1834.77i	1.06386	+	0.827765i
$171$	−149.297			−0.0667660
$172$	2645.90	−	670.922i	1.17295	−	0.297426i
$173$		−	1620.78i		−	0.712288i	−0.934431	−	0.356144i	$-0.884091\pi$
$173$		−	1620.78i		−	0.712288i	0.934431	−	0.356144i	$-0.115909\pi$
$174$	144.847	+	112.702i	0.0631080	+	0.0491030i
$175$			835.292i			0.360812i
$176$	3835.59	−	2078.85i	1.64272	−	0.890336i
$177$		−	2175.40i		−	0.923805i
$178$	−885.324	+	1137.84i	−0.372797	+	0.479126i
$179$			141.093i			0.0589149i	0.999566	+	0.0294574i	$0.00937795\pi$
$179$			141.093i			0.0589149i	−0.999566	+	0.0294574i	$0.990622\pi$
$180$	217.304	+	856.976i	0.0899826	+	0.354862i
$181$			810.805i			0.332965i	0.986044	+	0.166483i	$0.0532409\pi$
$181$			810.805i			0.332965i	−0.986044	+	0.166483i	$0.946759\pi$
$182$	2874.70	+	3192.44i	1.17081	+	1.30022i
$183$	355.606			0.143645
$184$	−374.154	+	854.085i	−0.149908	+	0.342195i
$185$	−5042.87			−2.00410
$186$	−746.967	−	581.198i	−0.294464	−	0.229116i
$187$	−5864.28			−2.29325
$188$	2793.04	−	708.233i	1.08353	−	0.274751i
$189$	874.918			0.336725
$190$	454.703	+	353.794i	0.173619	+	0.135089i
$191$	−702.992			−0.266318			−0.133159	−	0.991095i	$-0.542512\pi$
$191$	−702.992			−0.266318			−0.133159	+	0.991095i	$0.542512\pi$
$192$	1129.09	−	1041.37i	0.424400	−	0.391431i
$193$		−	1153.51i		−	0.430216i	−0.976590	−	0.215108i	$-0.930990\pi$
$193$		−	1153.51i		−	0.430216i	0.976590	−	0.215108i	$-0.0690104\pi$
$194$	3124.85	−	4016.12i	1.15645	−	1.48629i
$195$	1699.83	+	303.159i	0.624242	+	0.111332i
$196$	−1390.28	−	5482.83i	−0.506663	−	1.99812i
$197$	−1846.76			−0.667898			−0.333949	−	0.942591i	$-0.608381\pi$
$197$	−1846.76			−0.667898			−0.333949	+	0.942591i	$0.608381\pi$
$198$	−1369.53	−	1065.60i	−0.491558	−	0.382471i
$199$	−2201.10			−0.784079			−0.392040	−	0.919948i	$-0.628230\pi$
$199$	−2201.10			−0.784079			−0.392040	+	0.919948i	$0.628230\pi$
$200$	234.044	−	534.254i	0.0827469	−	0.188887i
$201$		−	2055.85i		−	0.721436i
$202$	−2006.84	+	2579.22i	−0.699012	+	0.898384i
$203$	−700.871			−0.242323
$204$	−2001.32	+	507.476i	−0.686865	+	0.174169i
$205$		−	3117.42i		−	1.06210i
$206$	198.086	+	154.126i	0.0669967	+	0.0521286i
$207$	370.877			0.124530
$208$	−944.160	−	2847.36i	−0.314739	−	0.949178i
$209$	−1130.80			−0.374253
$210$	−2664.68	−	2073.33i	−0.875622	−	0.681302i
$211$		−	3082.53i		−	1.00573i	−0.864364	−	0.502867i	$-0.832278\pi$
$211$		−	3082.53i		−	1.00573i	0.864364	−	0.502867i	$-0.167722\pi$
$212$	−1752.99	+	444.508i	−0.567906	+	0.144004i
$213$	−938.726			−0.301974
$214$	2220.65	−	2854.02i	0.709348	−	0.911668i
$215$			4189.69i			1.32900i
$216$	−559.599	−	245.147i	−0.176277	−	0.0772228i
$217$	3614.36			1.13068
$218$	−2809.98	−	2186.38i	−0.873007	−	0.679267i
$219$	2208.08			0.681316
$220$	1645.90	+	6490.88i	0.504392	+	1.98916i
$221$	−707.975	+	3969.65i	−0.215491	+	1.20827i
$222$	2139.96	−	2750.32i	0.646960	−	0.831485i
$223$		−	397.116i		−	0.119251i	−0.998221	−	0.0596253i	$-0.981009\pi$
$223$		−	397.116i		−	0.119251i	0.998221	−	0.0596253i	$-0.0189906\pi$
$224$	−960.913	+	5786.58i	−0.286624	+	1.72604i
$225$	−231.994			−0.0687390
$226$	2481.79	+	1931.02i	0.730469	+	0.568361i
$227$	−497.923			−0.145587			−0.0727936	−	0.997347i	$-0.523191\pi$
$227$	−497.923			−0.145587			−0.0727936	+	0.997347i	$0.523191\pi$
$228$	−385.911	+	97.8556i	−0.112095	+	0.0284239i
$229$	−1061.31			−0.306259			−0.153129	−	0.988206i	$-0.548935\pi$
$229$	−1061.31			−0.306259			−0.153129	+	0.988206i	$0.548935\pi$
$230$	−1129.56	−	878.883i	−0.323830	−	0.251965i
$231$	6626.78			1.88749
$232$	448.278	+	196.380i	0.126857	+	0.0555732i
$233$	−1895.98			−0.533090			−0.266545	−	0.963822i	$-0.585882\pi$
$233$	−1895.98			−0.533090			−0.266545	+	0.963822i	$0.585882\pi$
$234$	−886.669	+	798.420i	−0.247707	+	0.223053i
$235$			4422.69i			1.22768i
$236$	−1425.86	−	5623.12i	−0.393286	−	1.55099i
$237$		−	1062.50i		−	0.291210i
$238$	4841.91	−	6222.91i	1.31872	−	1.69484i
$239$			3083.31i			0.834489i	0.908794	+	0.417244i	$0.137004\pi$
$239$			3083.31i			0.834489i	−0.908794	+	0.417244i	$0.862996\pi$
$240$	1123.40	+	2072.73i	0.302147	+	0.557476i
$241$			769.489i			0.205673i	0.994698	+	0.102836i	$0.0327918\pi$
$241$			769.489i			0.205673i	−0.994698	+	0.102836i	$0.967208\pi$
$242$	−7401.89	−	5759.25i	−1.96616	−	1.52983i
$243$			243.000i			0.0641500i
$244$	919.191	−	233.080i	0.241169	−	0.0611533i
$245$	8681.89			2.26394
$246$	1700.21	+	1322.89i	0.440656	+	0.342864i
$247$	−136.517	+	765.461i	−0.0351676	+	0.197187i
$248$	−2311.75	−	1012.72i	−0.591920	−	0.259306i
$249$			2396.28i			0.609872i
$250$	−2719.77	−	2116.19i	−0.688054	−	0.535359i
$251$		−	231.523i		−	0.0582214i	−0.999576	−	0.0291107i	$-0.990732\pi$
$251$		−	231.523i		−	0.0582214i	0.999576	−	0.0291107i	$-0.00926754\pi$
$252$	2261.54	−	573.460i	0.565332	−	0.143352i
$253$	2809.09			0.698047
$254$	−2390.53	−	1860.01i	−0.590531	−	0.459479i
$255$		−	3169.03i		−	0.778244i
$256$	2235.97	−	3431.86i	0.545890	−	0.837857i
$257$	−6738.02			−1.63543			−0.817716	−	0.575622i	$-0.804760\pi$
$257$	−6738.02			−1.63543			−0.817716	+	0.575622i	$0.804760\pi$
$258$	−2285.01	−	1777.92i	−0.551390	−	0.429024i
$259$			13308.0i			3.19274i
$260$	4592.52	−	330.519i	1.09545	−	0.0788382i
$261$		−	194.660i		−	0.0461654i
$262$	−2164.70	+	2782.12i	−0.510442	+	0.656030i
$263$	−4363.07			−1.02296			−0.511479	−	0.859296i	$-0.670902\pi$
$263$	−4363.07			−1.02296			−0.511479	+	0.859296i	$0.670902\pi$
$264$	−4238.50	−	1856.78i	−0.988112	−	0.432868i
$265$		−	2775.81i		−	0.643459i
$266$	933.655	−	1199.95i	0.215211	−	0.276593i
$267$	1529.14			0.350494
$268$	−1347.50	−	5314.09i	−0.307132	−	1.21123i
$269$			6945.92i			1.57435i	0.616729	+	0.787175i	$0.288457\pi$
$269$			6945.92i			1.57435i	−0.616729	+	0.787175i	$0.711543\pi$
$270$	575.847	−	740.089i	0.129796	−	0.166816i
$271$		−	5815.95i		−	1.30367i	−0.758362	−	0.651833i	$-0.774000\pi$
$271$		−	5815.95i		−	1.30367i	0.758362	−	0.651833i	$-0.226000\pi$
$272$	−4840.51	+	2623.51i	−1.07904	+	0.584830i
$273$	800.029	−	4485.81i	0.177363	−	0.994481i
$274$	−708.949	+	911.155i	−0.156311	+	0.200894i
$275$	−1757.16			−0.385313
$276$	958.666	−	243.089i	0.209076	−	0.0530155i
$277$		−	4616.88i		−	1.00145i	−0.865606	−	0.500725i	$-0.833067\pi$
$277$		−	4616.88i		−	1.00145i	0.865606	−	0.500725i	$-0.166933\pi$
$278$	−1940.82	+	2494.37i	−0.418714	+	0.538139i
$279$			1003.85i			0.215409i
$280$	−8246.78	−	3612.72i	−1.76014	−	0.771075i
$281$		−	1619.89i		−	0.343895i	−0.985106	−	0.171948i	$-0.944994\pi$
$281$		−	1619.89i		−	0.343895i	0.985106	−	0.171948i	$-0.0550060\pi$
$282$	−2412.09	−	1876.79i	−0.509354	−	0.396317i
$283$			2242.90i			0.471119i	0.971860	+	0.235559i	$0.0756922\pi$
$283$			2242.90i			0.471119i	−0.971860	+	0.235559i	$0.924308\pi$
$284$	−2426.48	+	615.283i	−0.506989	+	0.128557i
$285$		−	611.077i		−	0.127007i
$286$	−6715.78	+	6047.37i	−1.38851	+	1.25031i
$287$	−8226.82			−1.69203
$288$	−1607.17	−	266.884i	−0.328830	−	0.0546052i
$289$	2487.72			0.506355
$290$	−461.294	+	592.864i	−0.0934073	+	0.120049i
$291$	−5397.29			−1.08727
$292$	5707.58	−	1447.27i	1.14387	−	0.290052i
$293$	−9531.90			−1.90054			−0.950272	−	0.311420i	$-0.899196\pi$
$293$	−9531.90			−1.90054			−0.950272	+	0.311420i	$0.899196\pi$
$294$	−3684.20	+	4735.00i	−0.730840	+	0.939289i
$295$	8904.03			1.75733
$296$	3728.83	−	8511.83i	0.732208	−	1.67142i
$297$			1840.52i			0.359589i
$298$	−4954.97	−	3855.35i	−0.963199	−	0.749444i
$299$	339.132	−	1901.53i	0.0655937	−	0.367787i
$300$	−599.673	+	152.059i	−0.115407	+	0.0292638i
$301$	11056.5			2.11723
$302$	4627.26	−	5947.04i	0.881684	−	1.13316i
$303$	3466.23			0.657194
$304$	−933.386	+	505.886i	−0.176097	+	0.0954426i
$305$			1455.51i			0.273253i
$306$	1728.35	+	1344.79i	0.322887	+	0.251231i
$307$	−4725.75			−0.878544			−0.439272	−	0.898354i	$-0.644764\pi$
$307$	−4725.75			−0.878544			−0.439272	+	0.898354i	$0.644764\pi$
$308$	17129.3	−	4343.49i	3.16894	−	0.803549i
$309$		−	266.209i		−	0.0490100i
$310$	2378.87	−	3057.37i	0.435841	−	0.560151i
$311$	−4068.93			−0.741890			−0.370945	−	0.928655i	$-0.620966\pi$
$311$	−4068.93			−0.741890			−0.370945	+	0.928655i	$0.620966\pi$
$312$	−1768.60	+	2644.97i	−0.320920	+	0.479941i
$313$	−3049.57			−0.550709			−0.275355	−	0.961343i	$-0.588795\pi$
$313$	−3049.57			−0.550709			−0.275355	+	0.961343i	$0.588795\pi$
$314$	2155.37	−	2770.12i	0.387372	−	0.497857i
$315$			3581.08i			0.640543i
$316$	−696.410	−	2746.42i	−0.123975	−	0.488918i
$317$	−2469.66			−0.437570			−0.218785	−	0.975773i	$-0.570209\pi$
$317$	−2469.66			−0.437570			−0.218785	+	0.975773i	$0.570209\pi$
$318$	1513.90	+	1177.93i	0.266966	+	0.207720i
$319$		−	1474.39i		−	0.258777i
$320$	4262.39	+	4621.40i	0.744610	+	0.807325i
$321$	−3835.53			−0.666912
$322$	−2319.35	+	2980.88i	−0.401405	+	0.515894i
$323$	1427.07			0.245833
$324$	159.273	+	628.121i	0.0273102	+	0.107703i
$325$	−212.137	+	1189.46i	−0.0362068	+	0.203014i
$326$	2990.78	+	2327.06i	0.508111	+	0.395350i
$327$			3776.34i			0.638630i
$328$	5261.88	+	2305.10i	0.885789	+	0.388043i
$329$	11671.4			1.95582
$330$	4361.56	−	5605.56i	0.727564	−	0.935079i
$331$	2231.98			0.370636			0.185318	−	0.982679i	$-0.440668\pi$
$331$	2231.98			0.370636			0.185318	+	0.982679i	$0.440668\pi$
$332$	1570.63	+	6194.05i	0.259637	+	1.02392i
$333$	−3696.17			−0.608255
$334$	2990.24	−	3843.12i	0.489877	−	0.629599i
$335$	8414.69			1.37237
$336$	5469.90	−	2964.63i	0.888117	−	0.481351i
$337$	10028.0			1.62095			0.810476	−	0.585772i	$-0.199209\pi$
$337$	10028.0			1.62095			0.810476	+	0.585772i	$0.199209\pi$
$338$	3282.82	+	5276.13i	0.528289	+	0.849065i
$339$		−	3335.28i		−	0.534359i
$340$	−2077.12	−	8191.50i	−0.331317	−	1.30661i
$341$			7603.35i			1.20746i
$342$	333.275	+	259.314i	0.0526942	+	0.0410002i
$343$		−	11796.6i		−	1.85702i
$344$	−7071.76	−	3097.97i	−1.10838	−	0.485556i
$345$			1518.02i			0.236891i
$346$	−2815.14	+	3618.07i	−0.437408	+	0.562164i
$347$		−	5462.03i		−	0.845006i	−0.906361	−	0.422503i	$-0.861152\pi$
$347$		−	5462.03i		−	0.845006i	0.906361	−	0.422503i	$-0.138848\pi$
$348$	−127.589	−	503.169i	−0.0196537	−	0.0775078i
$349$	4873.75			0.747524			0.373762	−	0.927525i	$-0.378068\pi$
$349$	4873.75			0.747524			0.373762	+	0.927525i	$0.378068\pi$
$350$	1450.82	−	1864.62i	0.221570	−	0.284767i
$351$	1245.89	+	222.200i	0.189461	+	0.0337897i
$352$	−12172.9	−	2021.43i	−1.84324	−	0.306086i
$353$		−	9847.90i		−	1.48485i	−0.669931	−	0.742423i	$-0.733676\pi$
$353$		−	9847.90i		−	1.48485i	0.669931	−	0.742423i	$-0.266324\pi$
$354$	−3778.47	+	4856.16i	−0.567297	+	0.729101i
$355$		−	3842.25i		−	0.574437i
$356$	3952.62	−	1002.27i	0.588451	−	0.149214i
$357$	−8363.00			−1.23982
$358$	245.064	−	314.961i	0.0361789	−	0.0464978i
$359$		−	438.907i		−	0.0645254i	−0.999479	−	0.0322627i	$-0.989729\pi$
$359$		−	438.907i		−	0.0645254i	0.999479	−	0.0322627i	$-0.0102713\pi$
$360$	1003.40	−	2290.46i	0.146899	−	0.335328i
$361$	−6583.82			−0.959881
$362$	1408.29	−	1809.96i	0.204470	−	0.262789i
$363$			9947.44i			1.43831i
$364$	−872.234	−	12119.6i	−0.125597	−	1.74516i
$365$			9037.77i			1.29605i
$366$	−793.819	−	617.652i	−0.113370	−	0.0882110i
$367$	−4343.24			−0.617753			−0.308877	−	0.951102i	$-0.599953\pi$
$367$	−4343.24			−0.617753			−0.308877	+	0.951102i	$0.599953\pi$
$368$	2318.69	−	1256.70i	0.328451	−	0.178017i
$369$		−	2284.92i		−	0.322353i
$370$	11257.2	+	8758.97i	1.58171	+	1.23070i
$371$	−7325.31			−1.02510
$372$	657.969	+	2594.82i	0.0917046	+	0.361653i
$373$			6760.28i			0.938430i	0.883084	+	0.469215i	$0.155463\pi$
$373$			6760.28i			0.938430i	−0.883084	+	0.469215i	$0.844537\pi$
$374$	13090.8	+	10185.7i	1.80992	+	1.40826i
$375$			3655.11i			0.503331i
$376$	−7465.04	−	3270.25i	−1.02388	−	0.448538i
$377$	−998.045	−	177.998i	−0.136345	−	0.0243166i
$378$	−1953.08	−	1519.65i	−0.265756	−	0.206779i
$379$	7560.67			1.02471			0.512355	−	0.858773i	$-0.328773\pi$
$379$	7560.67			1.02471			0.512355	+	0.858773i	$0.328773\pi$
$380$	−400.527	−	1579.55i	−0.0540700	−	0.213235i
$381$			3212.64i			0.431991i
$382$	1569.29	+	1221.03i	0.210188	+	0.163543i
$383$		−	1033.71i		−	0.137912i	−0.997620	−	0.0689561i	$-0.978033\pi$
$383$		−	1033.71i		−	0.137912i	0.997620	−	0.0689561i	$-0.0219668\pi$
$384$	−4329.23	+	363.550i	−0.575325	+	0.0483133i
$385$			27123.7i			3.59053i
$386$	−2003.54	+	2574.99i	−0.264191	+	0.339543i
$387$			3070.84i			0.403358i
$388$	−13951.2	+	3537.62i	−1.82543	+	0.462875i
$389$		−	3396.43i		−	0.442688i	−0.975196	−	0.221344i	$-0.928956\pi$
$389$		−	3396.43i		−	0.442688i	0.975196	−	0.221344i	$-0.0710444\pi$
$390$	−3267.97	−	3629.18i	−0.424308	−	0.471206i
$391$	−3545.07			−0.458521
$392$	−6419.61	+	14654.1i	−0.827141	+	1.88812i
$393$	3738.90			0.479905
$394$	4122.51	+	3207.64i	0.527130	+	0.410148i
$395$	4348.86			0.553962
$396$	1206.36	+	4757.50i	0.153086	+	0.603720i
$397$	14322.9			1.81070			0.905350	−	0.424665i	$-0.139608\pi$
$397$	14322.9			1.81070			0.905350	+	0.424665i	$0.139608\pi$
$398$	4913.51	+	3823.10i	0.618825	+	0.481494i
$399$	−1612.62			−0.202336
$400$	−1450.40	+	786.104i	−0.181300	+	0.0982630i
$401$		−	6038.23i		−	0.751957i	−0.926628	−	0.375979i	$-0.877307\pi$
$401$		−	6038.23i		−	0.751957i	0.926628	−	0.375979i	$-0.122693\pi$
$402$	−3570.81	+	4589.28i	−0.443025	+	0.569384i
$403$	5146.87	+	917.927i	0.636188	+	0.113462i
$404$	8959.72	−	2271.92i	1.10337	−	0.279783i
$405$	−994.610			−0.122031
$406$	1564.56	+	1217.35i	0.191250	+	0.148808i
$407$	−27995.4			−3.40954
$408$	5348.99	+	2343.26i	0.649055	+	0.284335i
$409$		−	6379.88i		−	0.771307i	−0.922644	−	0.385654i	$-0.873976\pi$
$409$		−	6379.88i		−	0.771307i	0.922644	−	0.385654i	$-0.126024\pi$
$410$	−5414.66	+	6959.03i	−0.652222	+	0.838248i
$411$	1224.51			0.146960
$412$	−174.485	−	688.113i	−0.0208647	−	0.0822837i
$413$		−	23497.5i		−	2.79961i
$414$	−827.910	−	644.178i	−0.0982839	−	0.0764725i
$415$	−9808.08			−1.16014
$416$	−2837.95	+	7996.08i	−0.334475	+	0.942405i
$417$	3352.20			0.393664
$418$	2524.28	+	1964.09i	0.295375	+	0.229824i
$419$		−	12520.8i		−	1.45986i	−0.683522	−	0.729930i	$-0.739553\pi$
$419$		−	12520.8i		−	1.45986i	0.683522	−	0.729930i	$-0.260447\pi$
$420$	2347.20	+	9256.59i	0.272694	+	1.07542i
$421$	−8797.22			−1.01841			−0.509205	−	0.860646i	$-0.670060\pi$
$421$	−8797.22			−1.01841			−0.509205	+	0.860646i	$0.670060\pi$
$422$	−5354.06	+	6881.13i	−0.617610	+	0.793764i
$423$			3241.62i			0.372607i
$424$	4685.28	+	2052.51i	0.536644	+	0.235091i
$425$	2217.54			0.253098
$426$	2095.52	+	1630.48i	0.238329	+	0.185439i
$427$	3841.06			0.435321
$428$	−9914.32	+	2513.98i	−1.11969	+	0.283920i
$429$	9436.58	+	1682.98i	1.06201	+	0.189406i
$430$	7277.09	−	9352.66i	0.816122	−	1.04890i
$431$			542.587i			0.0606392i	0.999540	+	0.0303196i	$0.00965251\pi$
$431$			542.587i			0.0606392i	−0.999540	+	0.0303196i	$0.990347\pi$
$432$	823.397	+	1519.21i	0.0917030	+	0.169197i
$433$	−608.491			−0.0675340			−0.0337670	−	0.999430i	$-0.510750\pi$
$433$	−608.491			−0.0675340			−0.0337670	+	0.999430i	$0.510750\pi$
$434$	−8068.33	−	6277.79i	−0.892378	−	0.694340i
$435$	796.753			0.0878192
$436$	2475.18	+	9761.31i	0.271880	+	1.07221i
$437$	−683.589			−0.0748295
$438$	−4929.10	−	3835.22i	−0.537720	−	0.418388i
$439$	6350.28			0.690393			0.345197	−	0.938530i	$-0.387812\pi$
$439$	6350.28			0.690393			0.345197	+	0.938530i	$0.387812\pi$
$440$	7599.90	−	17348.4i	0.823434	−	1.87966i
$441$	6363.40			0.687118
$442$	8475.32	−	7631.78i	0.912059	−	0.821282i
$443$			12566.8i			1.34778i	0.738834	+	0.673888i	$0.235377\pi$
$443$			12566.8i			1.34778i	−0.738834	+	0.673888i	$0.764623\pi$
$444$	−9554.09	+	2422.64i	−1.02121	+	0.258949i
$445$			6258.85i			0.666737i
$446$	−689.752	+	886.483i	−0.0732303	+	0.0941170i
$447$			6659.00i			0.704609i
$448$	12195.8	−	11248.4i	1.28615	−	1.18624i
$449$			6925.73i			0.727941i	0.931410	+	0.363971i	$0.118579\pi$
$449$			6925.73i			0.727941i	−0.931410	+	0.363971i	$0.881421\pi$
$450$	517.881	+	402.951i	0.0542514	+	0.0422118i
$451$		−	17306.4i		−	1.80693i
$452$	−2186.09	−	8621.24i	−0.227489	−	0.897144i
$453$	−7992.25			−0.828937
$454$	1111.51	+	864.844i	0.114903	+	0.0894034i
$455$	18360.6	+	3274.56i	1.89178	+	0.337392i
$456$	1031.43	+	451.846i	0.105924	+	0.0464027i
$457$		−	2587.54i		−	0.264858i	−0.991192	−	0.132429i	$-0.957722\pi$
$457$		−	2587.54i		−	0.264858i	0.991192	−	0.132429i	$-0.0422777\pi$
$458$	2369.16	+	1843.39i	0.241711	+	0.188070i
$459$		−	2322.74i		−	0.236201i
$460$	994.976	+	3923.86i	0.100850	+	0.397720i
$461$	−1934.54			−0.195446			−0.0977231	−	0.995214i	$-0.531156\pi$
$461$	−1934.54			−0.195446			−0.0977231	+	0.995214i	$0.531156\pi$
$462$	−14793.0	−	11510.1i	−1.48968	−	1.15909i
$463$			14.8325i			0.00148882i	1.00000		0.000744411i	$0.000236953\pi$
$463$			14.8325i			0.00148882i	−1.00000		0.000744411i	$0.999763\pi$
$464$	−659.599	−	1217.00i	−0.0659938	−	0.121762i
$465$	−4108.81			−0.409767
$466$	4232.41	+	3293.14i	0.420735	+	0.327364i
$467$		−	6870.30i		−	0.680770i	−0.940286	−	0.340385i	$-0.889443\pi$
$467$		−	6870.30i		−	0.680770i	0.940286	−	0.340385i	$-0.110557\pi$
$468$	3366.09	−	242.254i	0.332473	−	0.0239278i
$469$		−	22206.2i		−	2.18633i
$470$	7681.79	−	9872.78i	0.753903	−	0.968931i
$471$	−3722.78			−0.364197
$472$	−6583.87	+	15029.1i	−0.642049	+	1.46561i
$473$			23259.1i			2.26100i
$474$	−1845.46	+	2371.82i	−0.178829	+	0.229834i
$475$	427.604			0.0413049
$476$	−21617.2	+	5481.48i	−2.08156	+	0.527822i
$477$		−	2034.53i		−	0.195293i
$478$	5355.41	−	6882.88i	0.512450	−	0.658610i
$479$			10988.5i			1.04818i	0.851663	+	0.524089i	$0.175594\pi$
$479$			10988.5i			1.04818i	−0.851663	+	0.524089i	$0.824406\pi$
$480$	1092.37	−	6578.20i	0.103874	−	0.625526i
$481$	−3379.80	+	18950.7i	−0.320386	+	1.79642i
$482$	1336.53	−	1717.73i	0.126301	−	0.162325i
$483$	4006.02			0.377391
$484$	6520.00	+	25712.7i	0.612321	+	2.41480i
$485$		−	22091.3i		−	2.06828i
$486$	422.068	−	542.449i	0.0393938	−	0.0506296i
$487$		−	15324.2i		−	1.42588i	−0.701224	−	0.712941i	$-0.747363\pi$
$487$		−	15324.2i		−	1.42588i	0.701224	−	0.712941i	$-0.252637\pi$
$488$	−2456.75	−	1076.24i	−0.227893	−	0.0998343i
$489$		−	4019.33i		−	0.371698i
$490$	−19380.6	−	15079.6i	−1.78679	−	1.39026i
$491$			2957.73i			0.271854i	0.990719	+	0.135927i	$0.0434013\pi$
$491$			2957.73i			0.271854i	−0.990719	+	0.135927i	$0.956599\pi$
$492$	−1497.64	−	5906.19i	−0.137233	−	0.541203i
$493$			1860.68i			0.169981i
$494$	1634.28	−	1471.62i	0.148846	−	0.134031i
$495$	−7533.35			−0.684038
$496$	3401.52	+	6275.98i	0.307929	+	0.568145i
$497$	−10139.6			−0.915138
$498$	4162.11	−	5349.22i	0.374515	−	0.481334i
$499$	−19909.4			−1.78611			−0.893054	−	0.449949i	$-0.851442\pi$
$499$	−19909.4			−1.78611			−0.893054	+	0.449949i	$0.851442\pi$
$500$	2395.72	+	9447.96i	0.214280	+	0.845051i
$501$	−5164.78			−0.460570
$502$	−402.132	+	516.828i	−0.0357531	+	0.0459505i
$503$	11860.2			1.05133			0.525667	−	0.850690i	$-0.323816\pi$
$503$	11860.2			1.05133			0.525667	+	0.850690i	$0.323816\pi$
$504$	−6044.49	−	2647.94i	−0.534212	−	0.234025i
$505$			14187.4i			1.25016i
$506$	−6270.73	−	4879.11i	−0.550925	−	0.428662i
$507$	2278.49	−	6184.64i	0.199589	−	0.541754i
$508$	2105.71	+	8304.22i	0.183909	+	0.725276i
$509$	−9315.87			−0.811235			−0.405617	−	0.914043i	$-0.632943\pi$
$509$	−9315.87			−0.811235			−0.405617	+	0.914043i	$0.632943\pi$
$510$	−5504.30	+	7074.22i	−0.477910	+	0.614219i
$511$	23850.5			2.06474
$512$	−10952.2	+	3777.29i	−0.945355	+	0.326044i
$513$		−	447.890i		−	0.0385474i
$514$	15041.3	+	11703.3i	1.29074	+	1.00430i
$515$	1089.60			0.0932305
$516$	2012.76	+	7937.69i	0.171719	+	0.677204i
$517$			24552.6i			2.08863i
$518$	23114.7	−	29707.5i	1.96062	−	2.51983i
$519$	4862.35			0.411240
$520$	−10826.0	−	7238.94i	−0.912981	−	0.610478i
$521$	−6666.57			−0.560591			−0.280295	−	0.959914i	$-0.590432\pi$
$521$	−6666.57			−0.560591			−0.280295	+	0.959914i	$0.590432\pi$
$522$	−338.106	+	434.540i	−0.0283496	+	0.0364354i
$523$			743.792i			0.0621869i	0.999516	+	0.0310935i	$0.00989895\pi$
$523$			743.792i			0.0621869i	−0.999516	+	0.0310935i	$0.990101\pi$
$524$	9664.54	−	2450.64i	0.805720	−	0.204307i
$525$	−2505.88			−0.208315
$526$	9739.68	+	7578.22i	0.807357	+	0.628187i
$527$		−	9595.43i		−	0.793137i
$528$	6236.55	+	11506.8i	0.514036	+	0.948423i
$529$	−10468.9			−0.860430
$530$	−4821.32	+	6196.45i	−0.395141	+	0.507842i
$531$	6526.21			0.533359
$532$	−4168.40	+	1056.98i	−0.339705	+	0.0861392i
$533$	−11715.0	−	2089.34i	−0.952035	−	0.169792i
$534$	−3413.51	−	2655.97i	−0.276623	−	0.215234i
$535$		−	15699.0i		−	1.26865i
$536$	−6222.04	+	14203.1i	−0.501401	+	1.14455i
$537$	−423.278			−0.0340145
$538$	12064.4	−	15505.4i	0.966790	−	1.24254i
$539$	48197.4			3.85160
$540$	−2570.93	+	651.912i	−0.204880	+	0.0519515i
$541$	−18892.4			−1.50138			−0.750692	−	0.660652i	$-0.770280\pi$
$541$	−18892.4			−1.50138			−0.750692	+	0.660652i	$0.770280\pi$
$542$	−10101.7	+	12982.9i	−0.800566	+	1.02890i
$543$	−2432.42			−0.192238
$544$	15362.3	+	2551.04i	1.21076	+	0.201057i
$545$	−15456.7			−1.21485
$546$	−9577.32	+	8624.10i	−0.750680	+	0.675966i
$547$			20234.2i			1.58163i	0.612056	+	0.790814i	$0.290343\pi$
$547$			20234.2i			1.58163i	−0.612056	+	0.790814i	$0.709657\pi$
$548$	3165.18	−	802.595i	0.246733	−	0.0625642i
$549$			1066.82i			0.0829337i
$550$	3922.52	+	3052.02i	0.304103	+	0.236616i
$551$			358.791i			0.0277405i
$552$	−2562.25	−	1122.46i	−0.197567	−	0.0865491i
$553$		−	11476.6i		−	0.882519i
$554$	−8019.08	+	10306.3i	−0.614979	+	0.790382i
$555$		−	15128.6i		−	1.15707i
$556$	8664.97	−	2197.18i	0.660929	−	0.167592i
$557$	−11090.0			−0.843627			−0.421813	−	0.906683i	$-0.638606\pi$
$557$	−11090.0			−0.843627			−0.421813	+	0.906683i	$0.638606\pi$
$558$	1743.59	−	2240.90i	0.132280	−	0.170009i
$559$	15744.5	+	2807.99i	1.19128	+	0.212460i
$560$	12134.4	+	22388.5i	0.915662	+	1.68944i
$561$		−	17592.8i		−	1.32401i
$562$	−2813.59	+	3616.08i	−0.211182	+	0.271415i
$563$			4094.03i			0.306470i	0.988190	+	0.153235i	$0.0489692\pi$
$563$			4094.03i			0.306470i	−0.988190	+	0.153235i	$0.951031\pi$
$564$	2124.70	+	8379.12i	0.158628	+	0.625576i
$565$	13651.5			1.01650
$566$	3895.70	−	5006.83i	0.289308	−	0.371825i
$567$			2624.75i			0.194408i
$568$	6485.31	+	2841.06i	0.479080	+	0.209873i
$569$	17754.7			1.30811			0.654057	−	0.756445i	$-0.273066\pi$
$569$	17754.7			1.30811			0.654057	+	0.756445i	$0.273066\pi$
$570$	−1061.38	+	1364.11i	−0.0779937	+	0.100239i
$571$		−	22379.2i		−	1.64017i	−0.572240	−	0.820086i	$-0.693925\pi$
$571$		−	22379.2i		−	1.64017i	0.572240	−	0.820086i	$-0.306075\pi$
$572$	25495.3	−	1834.88i	1.86366	−	0.134126i
$573$		−	2108.98i		−	0.153759i
$574$	18364.7	+	14289.2i	1.33542	+	1.03906i
$575$	−1062.24			−0.0770407
$576$	3124.12	+	3387.26i	0.225993	+	0.245027i
$577$		−	5263.77i		−	0.379781i	−0.981805	−	0.189891i	$-0.939187\pi$
$577$		−	5263.77i		−	0.379781i	0.981805	−	0.189891i	$-0.0608133\pi$
$578$	−5553.35	−	4320.94i	−0.399635	−	0.310947i
$579$	3460.54			0.248386
$580$	2059.49	−	522.227i	0.147441	−	0.0373867i
$581$			25883.3i			1.84823i
$582$	12048.4	+	9374.56i	0.858111	+	0.667677i
$583$		−	15409.9i		−	1.09470i
$584$	−15254.8	−	6682.76i	−1.08090	−	0.473518i
$585$	−909.476	+	5099.48i	−0.0642773	+	0.360406i
$586$	21278.1	+	16556.0i	1.49998	+	1.16710i
$587$	−17373.1			−1.22158			−0.610788	−	0.791794i	$-0.709147\pi$
$587$	−17373.1			−1.22158			−0.610788	+	0.791794i	$0.709147\pi$
$588$	16448.5	−	4170.85i	1.15361	−	0.292522i
$589$		−	1850.27i		−	0.129438i
$590$	−19876.5	−	15465.4i	−1.38695	−	1.07916i
$591$		−	5540.27i		−	0.385611i
$592$	−23108.1	+	12524.4i	−1.60428	+	0.869506i
$593$		−	1386.85i		−	0.0960391i	−0.998846	−	0.0480195i	$-0.984709\pi$
$593$		−	1386.85i		−	0.0960391i	0.998846	−	0.0480195i	$-0.0152910\pi$
$594$	3196.81	−	4108.60i	0.220819	−	0.283801i
$595$		−	34230.1i		−	2.35848i
$596$	4364.61	+	17212.6i	0.299969	+	1.18298i
$597$		−	6603.30i		−	0.452688i
$598$	−4059.82	+	3655.75i	−0.277623	+	0.249991i
$599$	24658.1			1.68198			0.840988	−	0.541054i	$-0.181975\pi$
$599$	24658.1			1.68198			0.840988	+	0.541054i	$0.181975\pi$
$600$	1602.76	+	702.131i	0.109054	+	0.0477740i
$601$	12778.0			0.867262			0.433631	−	0.901091i	$-0.357232\pi$
$601$	12778.0			0.867262			0.433631	+	0.901091i	$0.357232\pi$
$602$	−24681.5	−	19204.1i	−1.67100	−	1.30017i
$603$	6167.55			0.416521
$604$	−20658.9	+	5238.48i	−1.39172	+	0.352898i
$605$	−40715.3			−2.73605
$606$	−7737.67	−	6020.51i	−0.518682	−	0.403575i
$607$	−21279.4			−1.42291			−0.711453	−	0.702733i	$-0.751963\pi$
$607$	−21279.4			−1.42291			−0.711453	+	0.702733i	$0.751963\pi$
$608$	2962.27	+	491.912i	0.197592	+	0.0328119i
$609$		−	2102.61i		−	0.139905i
$610$	2528.08	−	3249.13i	0.167802	−	0.215662i
$611$	16620.1	+	2964.15i	1.10046	+	0.196263i
$612$	−1522.43	−	6003.96i	−0.100556	−	0.396562i
$613$	−1231.53			−0.0811436			−0.0405718	−	0.999177i	$-0.512918\pi$
$613$	−1231.53			−0.0811436			−0.0405718	+	0.999177i	$0.512918\pi$
$614$	10549.3	+	8208.17i	0.693380	+	0.539503i
$615$	9352.27			0.613203
$616$	−45782.0	−	20056.0i	−2.99449	−	1.31182i
$617$		−	23252.0i		−	1.51716i	−0.651578	−	0.758582i	$-0.725893\pi$
$617$		−	23252.0i		−	1.51716i	0.651578	−	0.758582i	$-0.274107\pi$
$618$	−462.379	+	594.258i	−0.0300965	+	0.0386805i
$619$	−13316.4			−0.864673			−0.432337	−	0.901712i	$-0.642311\pi$
$619$	−13316.4			−0.864673			−0.432337	+	0.901712i	$0.642311\pi$
$620$	−10620.7	+	2693.10i	−0.687964	+	0.174447i
$621$			1112.63i			0.0718976i
$622$	9083.07	+	7067.34i	0.585527	+	0.455586i
$623$	16517.0			1.06218
$624$	8542.09	−	2832.48i	0.548008	−	0.181715i
$625$	−18182.7			−1.16369
$626$	6807.56	+	5296.81i	0.434640	+	0.338184i
$627$		−	3392.39i		−	0.216075i
$628$	−9622.88	+	2440.08i	−0.611456	+	0.155047i
$629$	35330.3			2.23960
$630$	6219.99	−	7994.05i	0.393350	−	0.505540i
$631$		−	27537.3i		−	1.73731i	−0.495417	−	0.868655i	$-0.664985\pi$
$631$		−	27537.3i		−	1.73731i	0.495417	−	0.868655i	$-0.335015\pi$
$632$	−3215.66	+	7340.42i	−0.202393	+	0.462004i
$633$	9247.59			0.580661
$634$	5513.02	+	4289.56i	0.345347	+	0.268707i
$635$	−13149.5			−0.821765
$636$	−1333.52	−	5258.98i	−0.0831410	−	0.327881i
$637$	5818.72	−	32625.9i	0.361925	−	2.02933i
$638$	−2560.87	+	3291.28i	−0.158912	+	0.204237i
$639$		−	2816.18i		−	0.174345i
$640$	−1488.03	−	17719.7i	−0.0919053	−	1.09443i
$641$	19752.9			1.21715			0.608573	−	0.793498i	$-0.291742\pi$
$641$	19752.9			1.21715			0.608573	+	0.793498i	$0.291742\pi$
$642$	8562.06	+	6661.95i	0.526352	+	0.409542i
$643$	17495.7			1.07304			0.536518	−	0.843889i	$-0.319739\pi$
$643$	17495.7			1.07304			0.536518	+	0.843889i	$0.319739\pi$
$644$	10355.0	−	2625.72i	0.633609	−	0.160664i
$645$	−12569.1			−0.767298
$646$	−3185.64	−	2478.68i	−0.194021	−	0.150963i
$647$	−25309.6			−1.53790			−0.768952	−	0.639306i	$-0.779222\pi$
$647$	−25309.6			−1.53790			−0.768952	+	0.639306i	$0.779222\pi$
$648$	735.440	−	1678.80i	0.0445846	−	0.101774i
$649$	49430.7			2.98971
$650$	2539.53	−	2286.77i	0.153244	−	0.137992i
$651$			10843.1i			0.652801i
$652$	−2634.45	−	10389.4i	−0.158241	−	0.624049i
$653$		−	3090.76i		−	0.185223i	−0.995702	−	0.0926116i	$-0.970479\pi$
$653$		−	3090.76i		−	0.185223i	0.995702	−	0.0926116i	$-0.0295215\pi$
$654$	6559.14	−	8429.93i	0.392175	−	0.504031i
$655$			15303.5i			0.912911i
$656$	−7742.37	−	14285.1i	−0.460806	−	0.850211i
$657$			6624.24i			0.393358i
$658$	−26054.1	−	20272.1i	−1.54361	−	1.20105i
$659$			14959.9i			0.884302i	0.896941	+	0.442151i	$0.145784\pi$
$659$			14959.9i			0.884302i	−0.896941	+	0.442151i	$0.854216\pi$
$660$	−19472.6	+	4937.69i	−1.14844	+	0.291211i
$661$	5061.91			0.297860			0.148930	−	0.988848i	$-0.452417\pi$
$661$	5061.91			0.297860			0.148930	+	0.988848i	$0.452417\pi$
$662$	−4982.45	−	3876.73i	−0.292520	−	0.227603i
$663$	−11909.0	−	2123.93i	−0.697596	−	0.124414i
$664$	7252.35	−	16555.0i	0.423864	−	0.967559i
$665$		−	6600.53i		−	0.384898i
$666$	8250.97	+	6419.89i	0.480058	+	0.373522i
$667$		−	891.297i		−	0.0517409i
$668$	−13350.2	+	3385.23i	−0.773258	+	0.196076i
$669$	1191.35			0.0688493
$670$	−18784.1	−	14615.5i	−1.08313	−	0.842755i
$671$			8080.25i			0.464880i
$672$	−17359.7	−	2882.74i	−0.996527	−	0.165482i
$673$	2117.72			0.121296			0.0606480	−	0.998159i	$-0.480683\pi$
$673$	2117.72			0.121296			0.0606480	+	0.998159i	$0.480683\pi$
$674$	−22385.5	−	17417.7i	−1.27932	−	0.995407i
$675$		−	695.982i		−	0.0396865i
$676$	1835.90	−	17479.9i	0.104455	−	0.994530i
$677$		−	11921.9i		−	0.676801i	−0.941002	−	0.338400i	$-0.890114\pi$
$677$		−	11921.9i		−	0.676801i	0.941002	−	0.338400i	$-0.109886\pi$
$678$	−5793.07	+	7445.36i	−0.328144	+	0.421736i
$679$	−58298.6			−3.29498
$680$	−9591.07	+	21893.6i	−0.540884	+	1.23468i
$681$		−	1493.77i		−	0.0840548i
$682$	13206.3	−	16973.0i	0.741488	−	0.952974i
$683$	−15712.2			−0.880248			−0.440124	−	0.897937i	$-0.645066\pi$
$683$	−15712.2			−0.880248			−0.440124	+	0.897937i	$0.645066\pi$
$684$	−293.567	−	1157.73i	−0.0164105	−	0.0647178i
$685$			5011.96i			0.279558i
$686$	−20489.6	+	26333.6i	−1.14037	+	1.46563i
$687$		−	3183.93i		−	0.176819i
$688$	10405.4	+	19198.6i	0.576604	+	1.06386i
$689$	−10431.3	−	1860.39i	−0.576779	−	0.102867i
$690$	2636.65	−	3388.67i	0.145472	−	0.186963i
$691$	5345.61			0.294293			0.147147	−	0.989115i	$-0.452991\pi$
$691$	5345.61			0.294293			0.147147	+	0.989115i	$0.452991\pi$
$692$	12568.5	−	3187.00i	0.690437	−	0.175074i
$693$			19880.3i			1.08974i
$694$	−9487.02	+	12192.9i	−0.518908	+	0.666911i
$695$			13720.7i			0.748858i
$696$	−589.140	+	1344.84i	−0.0320852	+	0.0732412i
$697$			21840.6i			1.18691i
$698$	−10879.7	−	8465.23i	−0.589974	−	0.459046i
$699$		−	5687.95i		−	0.307780i
$700$	−6477.34	+	1642.46i	−0.349743	+	0.0886846i
$701$			25908.7i			1.39595i	0.716125	+	0.697973i	$0.245914\pi$
$701$			25908.7i			1.39595i	−0.716125	+	0.697973i	$0.754086\pi$
$702$	−2395.26	−	2660.01i	−0.128780	−	0.143014i
$703$	6812.66			0.365497
$704$	23662.7	+	25655.7i	1.26679	+	1.37349i
$705$	−13268.1			−0.708801
$706$	−17104.9	+	21983.5i	−0.911827	+	1.17190i
$707$	37440.4			1.99164
$708$	16869.4	−	4277.57i	0.895465	−	0.227064i
$709$	−22006.2			−1.16567			−0.582835	−	0.812591i	$-0.698057\pi$
$709$	−22006.2			−1.16567			−0.582835	+	0.812591i	$0.698057\pi$
$710$	−6673.61	+	8577.05i	−0.352755	+	0.453368i
$711$	3187.50			0.168130
$712$	−10564.3	−	4627.95i	−0.556058	−	0.243595i
$713$			4596.37i			0.241424i
$714$	18668.7	+	14525.7i	0.978515	+	0.761361i
$715$	−6888.53	+	38624.3i	−0.360303	+	2.02024i
$716$	−1094.12	+	277.435i	−0.0571075	+	0.0144808i
$717$	−9249.93			−0.481792
$718$	−762.339	+	979.772i	−0.0396243	+	0.0509259i
$719$	−6330.11			−0.328336			−0.164168	−	0.986432i	$-0.552494\pi$
$719$	−6330.11			−0.328336			−0.164168	+	0.986432i	$0.552494\pi$
$720$	−6218.20	+	3370.20i	−0.321859	+	0.174444i
$721$		−	2875.44i		−	0.148526i
$722$	14697.1	+	11435.5i	0.757574	+	0.589451i
$723$	−2308.47			−0.118745
$724$	−6287.46	+	1594.31i	−0.322751	+	0.0818401i
$725$			557.531i			0.0285603i
$726$	17277.7	−	22205.7i	0.883247	−	1.13517i
$727$	4693.46			0.239437			0.119719	−	0.992808i	$-0.461801\pi$
$727$	4693.46			0.239437			0.119719	+	0.992808i	$0.461801\pi$
$728$	−19103.4	+	28569.5i	−0.972555	+	1.45447i
$729$	−729.000			−0.0370370
$730$	15697.7	−	20175.0i	0.795889	−	1.02289i
$731$		−	29352.9i		−	1.48517i
$732$	699.239	+	2757.57i	0.0353069	+	0.139239i
$733$	10858.5			0.547161			0.273581	−	0.961849i	$-0.411792\pi$
$733$	10858.5			0.547161			0.273581	+	0.961849i	$0.411792\pi$
$734$	9695.42	+	7543.79i	0.487554	+	0.379355i
$735$			26045.7i			1.30709i
$736$	−7358.78	−	1221.99i	−0.368544	−	0.0612000i
$737$	46714.1			2.33478
$738$	−3968.68	+	5100.62i	−0.197953	+	0.254413i
$739$	−30692.5			−1.52780			−0.763899	−	0.645336i	$-0.776717\pi$
$739$	−30692.5			−1.52780			−0.763899	+	0.645336i	$0.776717\pi$
$740$	−9915.96	−	39105.3i	−0.492592	−	1.94262i
$741$	−2296.38	−	409.552i	−0.113846	−	0.0203040i
$742$	16352.3	+	12723.4i	0.809045	+	0.629500i
$743$		−	12764.0i		−	0.630236i	−0.949053	−	0.315118i	$-0.897956\pi$
$743$		−	12764.0i		−	0.630236i	0.949053	−	0.315118i	$-0.102044\pi$
$744$	3038.16	−	6935.24i	0.149710	−	0.341745i
$745$	−27255.6			−1.34036
$746$	11742.0	−	15091.0i	0.576278	−	0.740644i
$747$	−7188.84			−0.352110
$748$	−11531.1	−	45475.0i	−0.563663	−	2.22290i
$749$	−41429.4			−2.02109
$750$	6348.58	−	8159.31i	0.309090	−	0.397248i
$751$	−36902.3			−1.79306			−0.896528	−	0.442987i	$-0.853919\pi$
$751$	−36902.3			−1.79306			−0.896528	+	0.442987i	$0.853919\pi$
$752$	10984.1	+	20266.2i	0.532645	+	0.982758i
$753$	694.568			0.0336142
$754$	1918.77	+	2130.85i	0.0926758	+	0.102919i
$755$		−	32712.6i		−	1.57687i
$756$	1720.38	+	6784.63i	0.0827641	+	0.326395i
$757$		−	20098.2i		−	0.964971i	−0.875904	−	0.482486i	$-0.839734\pi$
$757$		−	20098.2i		−	0.964971i	0.875904	−	0.482486i	$-0.160266\pi$
$758$	−16877.7	−	13132.1i	−0.808740	−	0.629263i
$759$			8427.26i			0.403018i
$760$	−1849.43	+	4221.71i	−0.0882708	+	0.201497i
$761$		−	7163.25i		−	0.341219i	−0.985339	−	0.170609i	$-0.945426\pi$
$761$		−	7163.25i		−	0.341219i	0.985339	−	0.170609i	$-0.0545736\pi$
$762$	5580.04	−	7171.58i	0.265280	−	0.340943i
$763$			40790.0i			1.93538i
$764$	−1382.32	−	5451.41i	−0.0654588	−	0.258148i
$765$	9507.08			0.449319
$766$	−1795.46	+	2307.56i	−0.0846902	+	0.108845i
$767$	5967.60	−	33460.7i	0.280936	−	1.57522i
$768$	10295.6	+	6707.90i	0.483737	+	0.315170i
$769$			39460.5i			1.85043i	0.379441	+	0.925216i	$0.376116\pi$
$769$			39460.5i			1.85043i	−0.379441	+	0.925216i	$0.623884\pi$
$770$	47111.3	−	60548.3i	2.20490	−	2.83378i
$771$		−	20214.0i		−	0.944217i
$772$	8945.02	−	2268.19i	0.417018	−	0.105744i
$773$	17510.7			0.814768			0.407384	−	0.913257i	$-0.366441\pi$
$773$	17510.7			0.814768			0.407384	+	0.913257i	$0.366441\pi$
$774$	5333.75	−	6855.04i	0.247697	−

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.23230 - 1.73690i) q^{2} +3.00000i q^{3} +(1.96633 + 7.75458i) q^{4} -12.2791 q^{5} +(5.21071 - 6.69690i) q^{6} +32.4044i q^{7} +(9.07951 - 20.7259i) q^{8} -9.00000 q^{9} +(27.4107 + 21.3277i) q^{10} -68.1675 q^{11} +(-23.2637 + 5.89900i) q^{12} +(-8.22964 + 46.1440i) q^{13} +(56.2833 - 72.3363i) q^{14} -36.8374i q^{15} +(-56.2671 + 30.4962i) q^{16} +86.0275 q^{17} +(20.0907 + 15.6321i) q^{18} +16.5885 q^{19} +(-24.1449 - 95.2195i) q^{20} -97.2131 q^{21} +(152.170 + 118.400i) q^{22} -41.2086 q^{23} +(62.1777 + 27.2385i) q^{24} +25.7771 q^{25} +(98.5188 - 88.7133i) q^{26} -27.0000i q^{27} +(-251.282 + 63.7178i) q^{28} +21.6289i q^{29} +(-63.9830 + 82.2322i) q^{30} -111.539i q^{31} +(178.574 + 29.6538i) q^{32} -204.503i q^{33} +(-192.039 - 149.421i) q^{34} -397.898i q^{35} +(-17.6970 - 69.7912i) q^{36} +410.686 q^{37} +(-37.0305 - 28.8126i) q^{38} +(-138.432 - 24.6889i) q^{39} +(-111.489 + 254.496i) q^{40} +253.880i q^{41} +(217.009 + 168.850i) q^{42} -341.204i q^{43} +(-134.040 - 528.611i) q^{44} +110.512 q^{45} +(91.9900 + 71.5753i) q^{46} -360.180i q^{47} +(-91.4886 - 168.801i) q^{48} -707.044 q^{49} +(-57.5423 - 44.7724i) q^{50} +258.082i q^{51} +(-374.010 + 26.9172i) q^{52} +226.059i q^{53} +(-46.8964 + 60.2721i) q^{54} +837.038 q^{55} +(671.610 + 294.216i) q^{56} +49.7655i q^{57} +(37.5673 - 48.2822i) q^{58} -725.135 q^{59} +(285.659 - 72.4346i) q^{60} -118.535i q^{61} +(-193.733 + 248.989i) q^{62} -291.639i q^{63} +(-347.125 - 376.362i) q^{64} +(101.053 - 566.609i) q^{65} +(-355.201 + 456.511i) q^{66} -685.284 q^{67} +(169.159 + 667.107i) q^{68} -123.626i q^{69} +(-691.110 + 888.227i) q^{70} +312.909i q^{71} +(-81.7156 + 186.533i) q^{72} -736.026i q^{73} +(-916.774 - 713.322i) q^{74} +77.3314i q^{75} +(32.6185 + 128.637i) q^{76} -2208.93i q^{77} +(266.140 + 295.556i) q^{78} -354.167 q^{79} +(690.911 - 374.467i) q^{80} +81.0000 q^{81} +(440.965 - 566.736i) q^{82} +798.760 q^{83} +(-191.153 - 753.847i) q^{84} -1056.34 q^{85} +(-592.639 + 761.671i) q^{86} -64.8867 q^{87} +(-618.928 + 1412.83i) q^{88} -509.714i q^{89} +(-246.696 - 191.949i) q^{90} +(-1495.27 - 266.676i) q^{91} +(-81.0298 - 319.555i) q^{92} +334.617 q^{93} +(-625.597 + 804.029i) q^{94} -203.692 q^{95} +(-88.9614 + 535.722i) q^{96} +1799.10i q^{97} +(1578.33 + 1228.07i) q^{98} +613.508 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

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