LMFDB - Embedded newform 390.2.bd.b.223.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(7,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 11]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("390.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bd (of order $12$, degree $4$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			223.3
Root			$0.277956 - 0.213283i$ of defining polynomial
Character	$\chi$	$=$	390.223
Dual form			390.2.bd.b.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.860320 - 2.06394i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.259847 - 0.450069i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.860320 - 2.06394i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.259847 - 0.450069i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.77703 - 1.35727i) q^{10} +(0.222514 - 0.830435i) q^{11} +(-0.707107 - 0.707107i) q^{12} +(-3.14490 + 1.76341i) q^{13} -0.519695i q^{14} +(-2.21628 + 0.296818i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.08479 - 1.09452i) q^{17} -1.00000 q^{18} +(-0.0538940 + 0.0144409i) q^{19} +(-2.21758 - 0.286912i) q^{20} +(-0.367480 - 0.367480i) q^{21} +(-0.222514 - 0.830435i) q^{22} +(0.177222 + 0.0474866i) q^{23} +(-0.965926 - 0.258819i) q^{24} +(-3.51970 + 3.55130i) q^{25} +(-1.84186 + 3.09961i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.259847 - 0.450069i) q^{28} +(6.27365 - 3.62210i) q^{29} +(-1.77095 + 1.36519i) q^{30} +(3.09986 - 3.09986i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.744548 - 0.429865i) q^{33} +(2.99027 - 2.99027i) q^{34} +(-1.15247 - 0.149107i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(0.112851 + 0.195463i) q^{37} +(-0.0394531 + 0.0394531i) q^{38} +(0.889363 + 3.49414i) q^{39} +(-2.06394 + 0.860320i) q^{40} +(-0.0280536 - 0.00751694i) q^{41} +(-0.501987 - 0.134507i) q^{42} +(1.24134 + 4.63274i) q^{43} +(-0.607921 - 0.607921i) q^{44} +(-0.286912 + 2.21758i) q^{45} +(0.177222 - 0.0474866i) q^{46} +5.53738 q^{47} +(-0.965926 + 0.258819i) q^{48} +(3.36496 + 5.82828i) q^{49} +(-1.27250 + 4.83536i) q^{50} -4.22888i q^{51} +(-0.0452920 + 3.60527i) q^{52} +(2.49867 + 2.49867i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(-1.90540 + 0.255183i) q^{55} +(-0.450069 - 0.259847i) q^{56} +0.0557952i q^{57} +(3.62210 - 6.27365i) q^{58} +(1.31167 + 4.89521i) q^{59} +(-0.851088 + 2.06776i) q^{60} +(7.21773 - 12.5015i) q^{61} +(1.13463 - 4.23449i) q^{62} +(-0.450069 + 0.259847i) q^{63} -1.00000 q^{64} +(6.34519 + 4.97379i) q^{65} -0.859730 q^{66} +(-11.8766 + 6.85698i) q^{67} +(1.09452 - 4.08479i) q^{68} +(0.0917371 - 0.158893i) q^{69} +(-1.07262 + 0.447104i) q^{70} +(-1.78083 - 6.64614i) q^{71} +(-0.500000 + 0.866025i) q^{72} +2.40525i q^{73} +(0.195463 + 0.112851i) q^{74} +(2.51932 + 4.31891i) q^{75} +(-0.0144409 + 0.0538940i) q^{76} +(-0.315933 - 0.315933i) q^{77} +(2.51728 + 2.58133i) q^{78} +16.0201i q^{79} +(-1.35727 + 1.77703i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.0280536 + 0.00751694i) q^{82} -4.83100 q^{83} +(-0.501987 + 0.134507i) q^{84} +(-5.77324 - 7.48913i) q^{85} +(3.39140 + 3.39140i) q^{86} +(-1.87494 - 6.99735i) q^{87} +(-0.830435 - 0.222514i) q^{88} +(14.9100 + 3.99511i) q^{89} +(0.860320 + 2.06394i) q^{90} +(-0.0235380 + 1.87364i) q^{91} +(0.129736 - 0.129736i) q^{92} +(-2.19193 - 3.79654i) q^{93} +(4.79551 - 2.76869i) q^{94} +(0.0761711 + 0.0988102i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(-5.45027 - 3.14672i) q^{97} +(5.82828 + 3.36496i) q^{98} +(-0.607921 + 0.607921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7	$ 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7} + 12 q^{11} - 8 q^{13} + 12 q^{15} - 8 q^{16} + 16 q^{17} - 16 q^{18} + 4 q^{19} - 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{25} + 4 q^{26} - 4 q^{28} + 48 q^{29} - 8 q^{30} + 16 q^{31} + 20 q^{34} + 12 q^{35} + 20 q^{37} - 4 q^{38} - 4 q^{39} - 12 q^{41} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 64 q^{47} + 4 q^{49} + 16 q^{50} - 16 q^{52} + 32 q^{53} - 44 q^{55} - 24 q^{56} - 12 q^{58} - 4 q^{59} + 12 q^{60} + 4 q^{61} - 20 q^{62} - 24 q^{63} - 16 q^{64} - 8 q^{65} + 32 q^{66} - 36 q^{67} - 4 q^{68} - 4 q^{69} - 36 q^{71} - 8 q^{72} - 12 q^{74} + 8 q^{76} - 4 q^{77} - 12 q^{78} - 8 q^{80} + 8 q^{81} - 12 q^{82} + 24 q^{83} - 52 q^{85} + 16 q^{86} - 12 q^{87} + 24 q^{89} - 4 q^{90} - 8 q^{92} - 36 q^{94} - 44 q^{95} + 60 q^{97} + 12 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7 + 12 * q^11 - 8 * q^13 + 12 * q^15 - 8 * q^16 + 16 * q^17 - 16 * q^18 + 4 * q^19 - 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^25 + 4 * q^26 - 4 * q^28 + 48 * q^29 - 8 * q^30 + 16 * q^31 + 20 * q^34 + 12 * q^35 + 20 * q^37 - 4 * q^38 - 4 * q^39 - 12 * q^41 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 64 * q^47 + 4 * q^49 + 16 * q^50 - 16 * q^52 + 32 * q^53 - 44 * q^55 - 24 * q^56 - 12 * q^58 - 4 * q^59 + 12 * q^60 + 4 * q^61 - 20 * q^62 - 24 * q^63 - 16 * q^64 - 8 * q^65 + 32 * q^66 - 36 * q^67 - 4 * q^68 - 4 * q^69 - 36 * q^71 - 8 * q^72 - 12 * q^74 + 8 * q^76 - 4 * q^77 - 12 * q^78 - 8 * q^80 + 8 * q^81 - 12 * q^82 + 24 * q^83 - 52 * q^85 + 16 * q^86 - 12 * q^87 + 24 * q^89 - 4 * q^90 - 8 * q^92 - 36 * q^94 - 44 * q^95 + 60 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.860320	−	2.06394i	−0.384747	−	0.923022i
$5$	−0.860320	−	2.06394i	−0.384747	−	0.923022i
$6$	−0.258819	−	0.965926i	−0.105662	−	0.394338i
$7$	0.259847	−	0.450069i	0.0982131	−	0.170110i	−0.812732	−	0.582638i	$-0.802021\pi$
$7$	0.259847	−	0.450069i	0.0982131	−	0.170110i	0.910945	+	0.412528i	$0.135354\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−1.77703	−	1.35727i	−0.561946	−	0.429205i
$11$	0.222514	−	0.830435i	0.0670906	−	0.250386i	−0.924233	−	0.381829i	$-0.875294\pi$
$11$	0.222514	−	0.830435i	0.0670906	−	0.250386i	0.991324	+	0.131443i	$0.0419611\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	−3.14490	+	1.76341i	−0.872238	+	0.489082i
$13$	−3.14490	+	1.76341i	−0.872238	+	0.489082i
$14$		−	0.519695i		−	0.138894i
$15$	−2.21628	+	0.296818i	−0.572241	+	0.0766380i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.08479	−	1.09452i	0.990707	−	0.265459i	0.273159	−	0.961969i	$-0.411931\pi$
$17$	4.08479	−	1.09452i	0.990707	−	0.265459i	0.717547	+	0.696510i	$0.245265\pi$
$18$	−1.00000			−0.235702
$19$	−0.0538940	+	0.0144409i	−0.0123641	+	0.00331296i	−0.264996	−	0.964250i	$-0.585371\pi$
$19$	−0.0538940	+	0.0144409i	−0.0123641	+	0.00331296i	0.252632	+	0.967563i	$0.418704\pi$
$20$	−2.21758	−	0.286912i	−0.495867	−	0.0641554i
$21$	−0.367480	−	0.367480i	−0.0801907	−	0.0801907i
$22$	−0.222514	−	0.830435i	−0.0474402	−	0.177049i
$23$	0.177222	+	0.0474866i	0.0369534	+	0.00990164i	0.277248	−	0.960798i	$-0.410578\pi$
$23$	0.177222	+	0.0474866i	0.0369534	+	0.00990164i	−0.240295	+	0.970700i	$0.577244\pi$
$24$	−0.965926	−	0.258819i	−0.197169	−	0.0528312i
$25$	−3.51970	+	3.55130i	−0.703940	+	0.710259i
$26$	−1.84186	+	3.09961i	−0.361218	+	0.607883i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−0.259847	−	0.450069i	−0.0491066	−	0.0850550i
$29$	6.27365	−	3.62210i	1.16499	−	0.672606i	0.212494	−	0.977162i	$-0.431841\pi$
$29$	6.27365	−	3.62210i	1.16499	−	0.672606i	0.952494	+	0.304556i	$0.0985081\pi$
$30$	−1.77095	+	1.36519i	−0.323329	+	0.249249i
$31$	3.09986	−	3.09986i	0.556752	−	0.556752i	−0.371629	−	0.928381i	$-0.621201\pi$
$31$	3.09986	−	3.09986i	0.556752	−	0.556752i	0.928381	+	0.371629i	$0.121201\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−0.744548	−	0.429865i	−0.129609	−	0.0748299i
$34$	2.99027	−	2.99027i	0.512828	−	0.512828i
$35$	−1.15247	−	0.149107i	−0.194803	−	0.0252036i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	0.112851	+	0.195463i	0.0185525	+	0.0321339i	0.875153	−	0.483847i	$-0.160761\pi$
$37$	0.112851	+	0.195463i	0.0185525	+	0.0321339i	−0.856600	+	0.515981i	$0.827428\pi$
$38$	−0.0394531	+	0.0394531i	−0.00640014	+	0.00640014i
$39$	0.889363	+	3.49414i	0.142412	+	0.559511i
$40$	−2.06394	+	0.860320i	−0.326338	+	0.136028i
$41$	−0.0280536	−	0.00751694i	−0.00438124	−	0.00117395i	0.256628	−	0.966510i	$-0.417389\pi$
$41$	−0.0280536	−	0.00751694i	−0.00438124	−	0.00117395i	−0.261009	+	0.965336i	$0.584055\pi$
$42$	−0.501987	−	0.134507i	−0.0774582	−	0.0207549i
$43$	1.24134	+	4.63274i	0.189303	+	0.706487i	0.993668	+	0.112352i	$0.0358385\pi$
$43$	1.24134	+	4.63274i	0.189303	+	0.706487i	−0.804366	+	0.594134i	$0.797495\pi$
$44$	−0.607921	−	0.607921i	−0.0916475	−	0.0916475i
$45$	−0.286912	+	2.21758i	−0.0427703	+	0.330578i
$46$	0.177222	−	0.0474866i	0.0261300	−	0.00700152i
$47$	5.53738			0.807710			0.403855	−	0.914823i	$-0.367670\pi$
$47$	5.53738			0.807710			0.403855	+	0.914823i	$0.367670\pi$
$48$	−0.965926	+	0.258819i	−0.139419	+	0.0373573i
$49$	3.36496	+	5.82828i	0.480708	+	0.832611i
$50$	−1.27250	+	4.83536i	−0.179959	+	0.683824i
$51$		−	4.22888i		−	0.592162i
$52$	−0.0452920	+	3.60527i	−0.00628087	+	0.499961i
$53$	2.49867	+	2.49867i	0.343219	+	0.343219i	0.857576	−	0.514357i	$-0.171969\pi$
$53$	2.49867	+	2.49867i	0.343219	+	0.343219i	−0.514357	+	0.857576i	$0.671969\pi$
$54$	−0.258819	+	0.965926i	−0.0352208	+	0.131446i
$55$	−1.90540	+	0.255183i	−0.256924	+	0.0344089i
$56$	−0.450069	−	0.259847i	−0.0601430	−	0.0347236i
$57$			0.0557952i			0.00739025i
$58$	3.62210	−	6.27365i	0.475605	−	0.823771i
$59$	1.31167	+	4.89521i	0.170765	+	0.637302i	0.997234	+	0.0743209i	$0.0236789\pi$
$59$	1.31167	+	4.89521i	0.170765	+	0.637302i	−0.826470	+	0.562981i	$0.809654\pi$
$60$	−0.851088	+	2.06776i	−0.109875	+	0.266947i
$61$	7.21773	−	12.5015i	0.924135	−	1.60065i	0.131189	−	0.991357i	$-0.458120\pi$
$61$	7.21773	−	12.5015i	0.924135	−	1.60065i	0.792946	−	0.609292i	$-0.208546\pi$
$62$	1.13463	−	4.23449i	0.144098	−	0.537781i
$63$	−0.450069	+	0.259847i	−0.0567034	+	0.0327377i
$64$	−1.00000			−0.125000
$65$	6.34519	+	4.97379i	0.787024	+	0.616922i
$66$	−0.859730			−0.105825
$67$	−11.8766	+	6.85698i	−1.45096	+	0.837713i	−0.998536	−	0.0540887i	$-0.982775\pi$
$67$	−11.8766	+	6.85698i	−1.45096	+	0.837713i	−0.452426	+	0.891802i	$0.649441\pi$
$68$	1.09452	−	4.08479i	0.132730	−	0.495353i
$69$	0.0917371	−	0.158893i	0.0110438	−	0.0191285i
$70$	−1.07262	+	0.447104i	−0.128203	+	0.0534391i
$71$	−1.78083	−	6.64614i	−0.211345	−	0.788752i	−0.987421	−	0.158112i	$-0.949459\pi$
$71$	−1.78083	−	6.64614i	−0.211345	−	0.788752i	0.776076	−	0.630640i	$-0.217207\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$			2.40525i			0.281513i	0.990044	+	0.140756i	$0.0449534\pi$
$73$			2.40525i			0.281513i	−0.990044	+	0.140756i	$0.955047\pi$
$74$	0.195463	+	0.112851i	0.0227221	+	0.0131186i
$75$	2.51932	+	4.31891i	0.290906	+	0.498705i
$76$	−0.0144409	+	0.0538940i	−0.00165648	+	0.00618206i
$77$	−0.315933	−	0.315933i	−0.0360039	−	0.0360039i
$78$	2.51728	+	2.58133i	0.285026	+	0.292279i
$79$			16.0201i			1.80240i	0.433402	+	0.901201i	$0.357313\pi$
$79$			16.0201i			1.80240i	−0.433402	+	0.901201i	$0.642687\pi$
$80$	−1.35727	+	1.77703i	−0.151747	+	0.198678i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−0.0280536	+	0.00751694i	−0.00309800	+	0.000830108i
$83$	−4.83100			−0.530271			−0.265136	−	0.964211i	$-0.585417\pi$
$83$	−4.83100			−0.530271			−0.265136	+	0.964211i	$0.585417\pi$
$84$	−0.501987	+	0.134507i	−0.0547712	+	0.0146759i
$85$	−5.77324	−	7.48913i	−0.626196	−	0.812310i
$86$	3.39140	+	3.39140i	0.365704	+	0.365704i
$87$	−1.87494	−	6.99735i	−0.201014	−	0.750195i
$88$	−0.830435	−	0.222514i	−0.0885247	−	0.0237201i
$89$	14.9100	+	3.99511i	1.58045	+	0.423481i	0.939066	−	0.343737i	$-0.111693\pi$
$89$	14.9100	+	3.99511i	1.58045	+	0.423481i	0.641386	+	0.767218i	$0.278360\pi$
$90$	0.860320	+	2.06394i	0.0906856	+	0.217558i
$91$	−0.0235380	+	1.87364i	−0.00246745	+	0.196411i
$92$	0.129736	−	0.129736i	0.0135259	−	0.0135259i
$93$	−2.19193	−	3.79654i	−0.227293	−	0.393683i
$94$	4.79551	−	2.76869i	0.494619	−	0.285569i
$95$	0.0761711	+	0.0988102i	0.00781499	+	0.0101377i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	−5.45027	−	3.14672i	−0.553392	−	0.319501i	0.197097	−	0.980384i	$-0.436849\pi$
$97$	−5.45027	−	3.14672i	−0.553392	−	0.319501i	−0.750489	+	0.660883i	$0.770182\pi$
$98$	5.82828	+	3.36496i	0.588745	+	0.339912i
$99$	−0.607921	+	0.607921i	−0.0610983	+	0.0610983i
$100$	1.31566	+	4.82380i	0.131566	+	0.482380i
$101$	4.39076	−	2.53501i	0.436897	−	0.252243i	−0.265384	−	0.964143i	$-0.585499\pi$
$101$	4.39076	−	2.53501i	0.436897	−	0.252243i	0.702281	+	0.711900i	$0.252165\pi$
$102$	−2.11444	−	3.66232i	−0.209361	−	0.362624i
$103$	−5.95248	+	5.95248i	−0.586515	+	0.586515i	−0.936686	−	0.350171i	$-0.886124\pi$
$103$	−5.95248	+	5.95248i	−0.586515	+	0.586515i	0.350171	+	0.936686i	$0.386124\pi$
$104$	1.76341	+	3.14490i	0.172917	+	0.308383i
$105$	−0.442306	+	1.07461i	−0.0431647	+	0.104871i
$106$	3.41325	+	0.914577i	0.331524	+	0.0888315i
$107$	6.77519	+	1.81541i	0.654982	+	0.175502i	0.570980	−	0.820964i	$-0.306563\pi$
$107$	6.77519	+	1.81541i	0.654982	+	0.175502i	0.0840016	+	0.996466i	$0.473230\pi$
$108$	0.258819	+	0.965926i	0.0249049	+	0.0929463i
$109$	−6.23531	−	6.23531i	−0.597235	−	0.597235i	0.342341	−	0.939576i	$-0.388780\pi$
$109$	−6.23531	−	6.23531i	−0.597235	−	0.597235i	−0.939576	+	0.342341i	$0.888780\pi$
$110$	−1.52254	+	1.17370i	−0.145168	+	0.111908i
$111$	0.218011	−	0.0584158i	0.0206927	−	0.00554458i
$112$	−0.519695			−0.0491066
$113$	−5.64837	+	1.51348i	−0.531354	+	0.142376i	−0.514513	−	0.857482i	$-0.672027\pi$
$113$	−5.64837	+	1.51348i	−0.531354	+	0.142376i	−0.0168406	+	0.999858i	$0.505361\pi$
$114$	0.0278976	+	0.0483200i	0.00261285	+	0.00452559i
$115$	−0.0544584	−	0.406630i	−0.00507827	−	0.0379185i
$116$		−	7.24419i		−	0.672606i
$117$	3.60527	+	0.0452920i	0.333307	+	0.00418725i
$118$	3.58354	+	3.58354i	0.329892	+	0.329892i
$119$	0.568814	−	2.12284i	0.0521431	−	0.194601i
$120$	0.296818	+	2.21628i	0.0270956	+	0.202318i
$121$	8.88617	+	5.13043i	0.807834	+	0.466403i
$122$		−	14.4355i		−	1.30692i
$123$	−0.0145216	+	0.0251522i	−0.00130937	+	0.00226790i
$124$	−1.13463	−	4.23449i	−0.101893	−	0.380268i
$125$	10.3577	+	4.20920i	0.926424	+	0.376482i
$126$	−0.259847	+	0.450069i	−0.0231491	+	0.0400953i
$127$	−2.69043	+	10.0408i	−0.238737	+	0.890979i	0.737691	+	0.675138i	$0.235916\pi$
$127$	−2.69043	+	10.0408i	−0.238737	+	0.890979i	−0.976429	+	0.215841i	$0.930751\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	4.79617			0.422279
$130$	7.98199	+	1.13483i	0.700067	+	0.0995313i
$131$	−17.3948			−1.51979			−0.759894	−	0.650047i	$-0.774749\pi$
$131$	−17.3948			−1.51979			−0.759894	+	0.650047i	$0.774749\pi$
$132$	−0.744548	+	0.429865i	−0.0648046	+	0.0374149i
$133$	−0.00750484	+	0.0280084i	−0.000650752	+	0.00242864i
$134$	−6.85698	+	11.8766i	−0.592353	+	1.02599i
$135$	2.06776	+	0.851088i	0.177965	+	0.0732500i
$136$	−1.09452	−	4.08479i	−0.0938540	−	0.350268i
$137$	4.54350	−	7.86958i	0.388178	−	0.672343i	−0.604027	−	0.796964i	$-0.706438\pi$
$137$	4.54350	−	7.86958i	0.388178	−	0.672343i	0.992204	+	0.124621i	$0.0397714\pi$
$138$		−	0.183474i		−	0.0156184i
$139$	−2.33716	−	1.34936i	−0.198236	−	0.114451i	0.397597	−	0.917560i	$-0.369844\pi$
$139$	−2.33716	−	1.34936i	−0.198236	−	0.114451i	−0.595832	+	0.803109i	$0.703178\pi$
$140$	−0.705364	+	0.923513i	−0.0596141	+	0.0780511i
$141$	1.43318	−	5.34870i	0.120695	−	0.450442i
$142$	−4.86531	−	4.86531i	−0.408288	−	0.408288i
$143$	0.764612	+	3.00402i	0.0639401	+	0.251209i
$144$			1.00000i			0.0833333i
$145$	−12.8731	−	9.83229i	−1.06906	−	0.816527i
$146$	1.20262	+	2.08300i	0.0995298	+	0.172391i
$147$	6.50060	−	1.74183i	0.536161	−	0.143664i
$148$	0.225701			0.0185525
$149$	−4.01632	+	1.07617i	−0.329029	+	0.0881632i	−0.419552	−	0.907731i	$-0.637813\pi$
$149$	−4.01632	+	1.07617i	−0.329029	+	0.0881632i	0.0905228	+	0.995894i	$0.471146\pi$
$150$	4.34125	+	2.48063i	0.354462	+	0.202542i
$151$	2.79391	+	2.79391i	0.227365	+	0.227365i	0.811591	−	0.584226i	$-0.198602\pi$
$151$	2.79391	+	2.79391i	0.227365	+	0.227365i	−0.584226	+	0.811591i	$0.698602\pi$
$152$	0.0144409	+	0.0538940i	0.00117131	+	0.00437138i
$153$	−4.08479	−	1.09452i	−0.330236	−	0.0884864i
$154$	−0.431573	−	0.115640i	−0.0347771	−	0.00931851i
$155$	−9.06480	−	3.73106i	−0.728102	−	0.299686i
$156$	3.47070	+	0.976860i	0.277878	+	0.0782114i
$157$	−9.39011	+	9.39011i	−0.749413	+	0.749413i	−0.974369	−	0.224956i	$-0.927776\pi$
$157$	−9.39011	+	9.39011i	−0.749413	+	0.749413i	0.224956	+	0.974369i	$0.427776\pi$
$158$	8.01005	+	13.8738i	0.637245	+	1.10374i
$159$	3.06023	−	1.76683i	0.242692	−	0.140118i
$160$	−0.286912	+	2.21758i	−0.0226824	+	0.175315i
$161$	0.0674231	−	0.0674231i	0.00531368	−	0.00531368i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	−19.7602	−	11.4085i	−1.54773	−	0.893585i	−0.998314	−	0.0580388i	$-0.981515\pi$
$163$	−19.7602	−	11.4085i	−1.54773	−	0.893585i	−0.549420	−	0.835546i	$-0.685151\pi$
$164$	−0.0205367	+	0.0205367i	−0.00160364	+	0.00160364i
$165$	−0.246666	+	1.90652i	−0.0192030	+	0.148423i
$166$	−4.18377	+	2.41550i	−0.324723	+	0.187479i
$167$	−6.65800	−	11.5320i	−0.515211	−	0.892372i	−0.999844	−	0.0176545i	$-0.994380\pi$
$167$	−6.65800	−	11.5320i	−0.515211	−	0.892372i	0.484633	−	0.874718i	$-0.338953\pi$
$168$	−0.367480	+	0.367480i	−0.0283517	+	0.0283517i
$169$	6.78077	−	11.0915i	0.521598	−	0.853191i
$170$	−8.74434	−	3.59915i	−0.670660	−	0.276043i
$171$	0.0538940	+	0.0144409i	0.00412138	+	0.00110432i
$172$	4.63274	+	1.24134i	0.353243	+	0.0946513i
$173$	−4.99132	−	18.6279i	−0.379483	−	1.41625i	−0.846682	−	0.532099i	$-0.821403\pi$
$173$	−4.99132	−	18.6279i	−0.379483	−	1.41625i	0.467199	−	0.884152i	$-0.345263\pi$
$174$	−5.12242	−	5.12242i	−0.388329	−	0.388329i
$175$	0.683743	+	2.50690i	0.0516861	+	0.189504i
$176$	−0.830435	+	0.222514i	−0.0625964	+	0.0167727i
$177$	5.06789			0.380926
$178$	14.9100	−	3.99511i	1.11755	−	0.299446i
$179$	10.1381	+	17.5596i	0.757754	+	1.31247i	0.943994	+	0.329964i	$0.107037\pi$
$179$	10.1381	+	17.5596i	0.757754	+	1.31247i	−0.186240	+	0.982504i	$0.559630\pi$
$180$	1.77703	+	1.35727i	0.132452	+	0.101165i
$181$		−	14.3123i		−	1.06382i	−0.846799	−	0.531912i	$-0.821474\pi$
$181$		−	14.3123i		−	1.06382i	0.846799	−	0.531912i	$-0.178526\pi$
$182$	0.916435	+	1.63439i	0.0679307	+	0.121149i
$183$	−10.2074	−	10.2074i	−0.754553	−	0.754553i
$184$	0.0474866	−	0.177222i	0.00350076	−	0.0130650i
$185$	0.306336	−	0.401078i	0.0225223	−	0.0294878i
$186$	−3.79654	−	2.19193i	−0.278376	−	0.160720i
$187$		−	3.63570i		−	0.265869i
$188$	2.76869	−	4.79551i	0.201927	−	0.349749i
$189$	0.134507	+	0.501987i	0.00978394	+	0.0365142i
$190$	0.115371	+	0.0474866i	0.00836991	+	0.00344504i
$191$	−6.39485	+	11.0762i	−0.462715	+	0.801446i	−0.999095	−	0.0425302i	$-0.986458\pi$
$191$	−6.39485	+	11.0762i	−0.462715	+	0.801446i	0.536380	+	0.843977i	$0.319791\pi$
$192$	−0.258819	+	0.965926i	−0.0186787	+	0.0697097i
$193$	−1.91307	+	1.10451i	−0.137706	+	0.0795045i	−0.567270	−	0.823532i	$-0.692000\pi$
$193$	−1.91307	+	1.10451i	−0.137706	+	0.0795045i	0.429564	+	0.903036i	$0.358667\pi$
$194$	−6.29344			−0.451842
$195$	6.44657	−	4.84167i	0.461648	−	0.346719i
$196$	6.72992			0.480708
$197$	−10.5133	+	6.06986i	−0.749042	+	0.432460i	−0.825348	−	0.564625i	$-0.809021\pi$
$197$	−10.5133	+	6.06986i	−0.749042	+	0.432460i	0.0763056	+	0.997084i	$0.475688\pi$
$198$	−0.222514	+	0.830435i	−0.0158134	+	0.0590165i
$199$	2.03805	−	3.53001i	0.144474	−	0.250236i	−0.784703	−	0.619872i	$-0.787184\pi$
$199$	2.03805	−	3.53001i	0.144474	−	0.250236i	0.929176	+	0.369636i	$0.120518\pi$
$200$	3.55130	+	3.51970i	0.251115	+	0.248880i
$201$	3.54943	+	13.2467i	0.250358	+	0.934348i
$202$	2.53501	−	4.39076i	0.178362	−	0.308933i
$203$		−	3.76477i		−	0.264235i
$204$	−3.66232	−	2.11444i	−0.256414	−	0.148041i
$205$	0.00862055	+	0.0643680i	0.000602085	+	0.00449565i
$206$	−2.17876	+	8.13124i	−0.151801	+	0.566530i
$207$	−0.129736	−	0.129736i	−0.00901727	−	0.00901727i
$208$	3.09961	+	1.84186i	0.214919	+	0.127710i
$209$			0.0479688i			0.00331807i
$210$	0.154255	+	1.15179i	0.0106446	+	0.0794810i
$211$	7.38509	+	12.7914i	0.508411	+	0.880593i	0.999953	+	0.00973918i	$0.00310013\pi$
$211$	7.38509	+	12.7914i	0.508411	+	0.880593i	−0.491542	+	0.870854i	$0.663567\pi$
$212$	3.41325	−	0.914577i	0.234423	−	0.0628134i
$213$	−6.88059			−0.471450
$214$	6.77519	−	1.81541i	0.463142	−	0.124099i
$215$	8.49376	−	6.54769i	0.579269	−	0.446549i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−0.589661	−	2.20064i	−0.0400288	−	0.149389i
$218$	−8.51759	−	2.28228i	−0.576884	−	0.154576i
$219$	2.32329	+	0.622524i	0.156993	+	0.0420662i
$220$	−0.731706	+	1.77772i	−0.0493316	+	0.119854i
$221$	−10.9162	+	10.6453i	−0.734301	+	0.716080i
$222$	0.159595	−	0.159595i	0.0107113	−	0.0107113i
$223$	1.58981	+	2.75364i	0.106462	+	0.184397i	0.914334	−	0.404960i	$-0.132714\pi$
$223$	1.58981	+	2.75364i	0.106462	+	0.184397i	−0.807873	+	0.589357i	$0.799381\pi$
$224$	−0.450069	+	0.259847i	−0.0300715	+	0.0173618i
$225$	4.82380	−	1.31566i	0.321587	−	0.0877109i
$226$	−4.13489	+	4.13489i	−0.275049	+	0.275049i
$227$	−25.0852	−	14.4830i	−1.66496	−	0.961267i	−0.970291	−	0.241942i	$-0.922216\pi$
$227$	−25.0852	−	14.4830i	−1.66496	−	0.961267i	−0.694673	−	0.719326i	$-0.744451\pi$
$228$	0.0483200	+	0.0278976i	0.00320007	+	0.00184756i
$229$	8.53343	−	8.53343i	0.563905	−	0.563905i	−0.366509	−	0.930414i	$-0.619447\pi$
$229$	8.53343	−	8.53343i	0.563905	−	0.563905i	0.930414	+	0.366509i	$0.119447\pi$
$230$	−0.250478	−	0.324923i	−0.0165160	−	0.0214248i
$231$	−0.386938	+	0.223399i	−0.0254586	+	0.0146985i
$232$	−3.62210	−	6.27365i	−0.237802	−	0.411886i
$233$	−7.11568	+	7.11568i	−0.466164	+	0.466164i	−0.900669	−	0.434505i	$-0.856923\pi$
$233$	−7.11568	+	7.11568i	−0.466164	+	0.466164i	0.434505	+	0.900669i	$0.356923\pi$
$234$	3.14490	−	1.76341i	0.205588	−	0.115278i
$235$	−4.76392	−	11.4288i	−0.310764	−	0.745534i
$236$	4.89521	+	1.31167i	0.318651	+	0.0853823i
$237$	15.4742	+	4.14631i	1.00516	+	0.269331i
$238$	−0.568814	−	2.12284i	−0.0368708	−	0.137604i
$239$	−15.7046	−	15.7046i	−1.01584	−	1.01584i	−0.999872	−	0.0159718i	$-0.994916\pi$
$239$	−15.7046	−	15.7046i	−1.01584	−	1.01584i	−0.0159718	−	0.999872i	$-0.505084\pi$
$240$	1.36519	+	1.77095i	0.0881228	+	0.114314i
$241$	24.1684	−	6.47591i	1.55682	−	0.417150i	0.625168	−	0.780490i	$-0.285031\pi$
$241$	24.1684	−	6.47591i	1.55682	−	0.417150i	0.931656	+	0.363341i	$0.118364\pi$
$242$	10.2609			0.659593
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−7.21773	−	12.5015i	−0.462068	−	0.800325i
$245$	9.13428	−	11.9593i	0.583568	−	0.764049i
$246$			0.0290432i			0.00185173i
$247$	0.144026	−	0.140452i	0.00916415	−	0.00893676i
$248$	−3.09986	−	3.09986i	−0.196841	−	0.196841i
$249$	−1.25035	+	4.66639i	−0.0792380	+	0.295720i
$250$	11.0747	−	1.53359i	0.700423	−	0.0969928i
$251$	−23.7056	−	13.6864i	−1.49628	−	0.863878i	−0.496290	−	0.868157i	$-0.665305\pi$
$251$	−23.7056	−	13.6864i	−1.49628	−	0.863878i	−0.999991	+	0.00427828i	$0.998638\pi$
$252$			0.519695i			0.0327377i
$253$	0.0788691	−	0.136605i	0.00495846	−	0.00858830i
$254$	2.69043	+	10.0408i	0.168813	+	0.630017i
$255$	−8.72817	+	3.63819i	−0.546579	+	0.227832i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.0669693	+	0.249933i	−0.00417743	+	0.0155904i	−0.967983	−	0.251015i	$-0.919236\pi$
$257$	−0.0669693	+	0.249933i	−0.00417743	+	0.0155904i	0.963806	+	0.266606i	$0.0859022\pi$
$258$	4.15360	−	2.39808i	0.258592	−	0.149298i
$259$	0.117296			0.00728840
$260$	7.48002	−	3.00820i	0.463891	−	0.186561i
$261$	−7.24419			−0.448404
$262$	−15.0643	+	8.69738i	−0.930676	+	0.537326i
$263$	−1.60883	+	6.00425i	−0.0992050	+	0.370238i	−0.997623	−	0.0689024i	$-0.978050\pi$
$263$	−1.60883	+	6.00425i	−0.0992050	+	0.370238i	0.898418	+	0.439140i	$0.144717\pi$
$264$	−0.429865	+	0.744548i	−0.0264564	+	0.0458238i
$265$	3.00745	−	7.30676i	0.184746	−	0.448851i
$266$	0.00750484	+	0.0280084i	0.000460151	+	0.00171731i
$267$	7.71796	−	13.3679i	0.472332	−	0.818102i
$268$			13.7140i			0.837713i
$269$	−0.338208	−	0.195264i	−0.0206209	−	0.0119055i	0.489654	−	0.871917i	$-0.337123\pi$
$269$	−0.338208	−	0.195264i	−0.0206209	−	0.0119055i	−0.510275	+	0.860011i	$0.670456\pi$
$270$	2.21628	−	0.296818i	0.134879	−	0.0180638i
$271$	−4.36922	+	16.3061i	−0.265411	+	0.990528i	0.696587	+	0.717472i	$0.254701\pi$
$271$	−4.36922	+	16.3061i	−0.265411	+	0.990528i	−0.961998	+	0.273056i	$0.911966\pi$
$272$	−2.99027	−	2.99027i	−0.181312	−	0.181312i
$273$	1.80370	+	0.507669i	0.109165	+	0.0307255i
$274$		−	9.08700i		−	0.548966i
$275$	2.16594	+	3.71310i	0.130611	+	0.223908i
$276$	−0.0917371	−	0.158893i	−0.00552192	−	0.00956425i
$277$	−1.02095	+	0.273563i	−0.0613430	+	0.0164368i	−0.289360	−	0.957220i	$-0.593442\pi$
$277$	−1.02095	+	0.273563i	−0.0613430	+	0.0164368i	0.228017	+	0.973657i	$0.426776\pi$
$278$	−2.69872			−0.161859
$279$	−4.23449	+	1.13463i	−0.253512	+	0.0679284i
$280$	−0.149107	+	1.15247i	−0.00891082	+	0.0688731i
$281$	9.59800	+	9.59800i	0.572568	+	0.572568i	0.932845	−	0.360277i	$-0.117318\pi$
$281$	9.59800	+	9.59800i	0.572568	+	0.572568i	−0.360277	+	0.932845i	$0.617318\pi$
$282$	−1.43318	−	5.34870i	−0.0853446	−	0.318510i
$283$	9.27878	+	2.48624i	0.551566	+	0.147792i	0.523829	−	0.851823i	$-0.324503\pi$
$283$	9.27878	+	2.48624i	0.551566	+	0.147792i	0.0277374	+	0.999615i	$0.491170\pi$
$284$	−6.64614	−	1.78083i	−0.394376	−	0.105673i
$285$	0.115158	−	0.0480017i	0.00682136	−	0.00284337i
$286$	2.16418	+	2.21925i	0.127971	+	0.131227i
$287$	−0.0106728	+	0.0106728i	−0.000629996	+	0.000629996i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	0.765102	−	0.441732i	0.0450060	−	0.0259842i
$290$	−16.0646	−	2.07844i	−0.943346	−	0.122050i
$291$	−4.45013	+	4.45013i	−0.260871	+	0.260871i
$292$	2.08300	+	1.20262i	0.121899	+	0.0703782i
$293$	−5.04648	−	2.91359i	−0.294819	−	0.170214i	0.345294	−	0.938494i	$-0.387779\pi$
$293$	−5.04648	−	2.91359i	−0.294819	−	0.170214i	−0.640113	+	0.768281i	$0.721112\pi$
$294$	4.75877	−	4.75877i	0.277537	−	0.277537i
$295$	8.97497	−	6.91865i	0.522543	−	0.402819i
$296$	0.195463	−	0.112851i	0.0113611	−	0.00655931i
$297$	0.429865	+	0.744548i	0.0249433	+	0.0432031i
$298$	−2.94015	+	2.94015i	−0.170318	+	0.170318i
$299$	−0.641085	+	0.163175i	−0.0370749	+	0.00943666i
$300$	4.99995	−	0.0223420i	0.288672	−	0.00128991i
$301$	2.40761	+	0.645118i	0.138772	+	0.0371840i
$302$	3.81656	+	1.02264i	0.219618	+	0.0588465i
$303$	−1.31222	−	4.89726i	−0.0753848	−	0.281340i
$304$	0.0394531	+	0.0394531i	0.00226279	+	0.00226279i
$305$	−32.0118	−	4.14170i	−1.83299	−	0.237153i
$306$	−4.08479	+	1.09452i	−0.233512	+	0.0625693i
$307$	4.52688			0.258363			0.129181	−	0.991621i	$-0.458765\pi$
$307$	4.52688			0.258363			0.129181	+	0.991621i	$0.458765\pi$
$308$	−0.431573	+	0.115640i	−0.0245912	+	0.00658918i
$309$	4.20904	+	7.29027i	0.239444	+	0.414729i
$310$	−9.71588	+	1.30121i	−0.551825	+	0.0739037i
$311$		−	27.6370i		−	1.56715i	−0.621297	−	0.783575i	$-0.713394\pi$
$311$		−	27.6370i		−	1.56715i	0.621297	−	0.783575i	$-0.286606\pi$
$312$	3.49414	−	0.889363i	0.197817	−	0.0503503i
$313$	22.4963	+	22.4963i	1.27157	+	1.27157i	0.945266	+	0.326301i	$0.105802\pi$
$313$	22.4963	+	22.4963i	1.27157	+	1.27157i	0.326301	+	0.945266i	$0.394198\pi$
$314$	−3.43702	+	12.8271i	−0.193962	+	0.723877i
$315$	0.923513	+	0.705364i	0.0520341	+	0.0397427i
$316$	13.8738	+	8.01005i	0.780463	+	0.450600i
$317$			1.80472i			0.101363i	0.998715	+	0.0506817i	$0.0161394\pi$
$317$			1.80472i			0.101363i	−0.998715	+	0.0506817i	$0.983861\pi$
$318$	1.76683	−	3.06023i	0.0990787	−	0.171609i
$319$	−1.61194	−	6.01583i	−0.0902512	−	0.336822i
$320$	0.860320	+	2.06394i	0.0480933	+	0.115378i
$321$	3.50709	−	6.07447i	0.195747	−	0.339044i
$322$	0.0246786	−	0.0921016i	0.00137528	−	0.00513262i
$323$	−0.204340	+	0.117976i	−0.0113698	+	0.00656434i
$324$	1.00000			0.0555556
$325$	4.80671	−	17.3751i	0.266628	−	0.963799i
$326$	−22.8171			−1.26372
$327$	−7.63667	+	4.40903i	−0.422309	+	0.243820i
$328$	−0.00751694	+	0.0280536i	−0.000415054	+	0.00154900i
$329$	1.43887	−	2.49220i	0.0793277	−	0.137400i
$330$	0.739642	+	1.77443i	0.0407160	+	0.0976792i
$331$	5.25635	+	19.6170i	0.288915	+	1.07825i	0.945930	+	0.324369i	$0.105152\pi$
$331$	5.25635	+	19.6170i	0.288915	+	1.07825i	−0.657015	+	0.753877i	$0.728181\pi$
$332$	−2.41550	+	4.18377i	−0.132568	+	0.229614i
$333$		−	0.225701i		−	0.0123684i
$334$	−11.5320	−	6.65800i	−0.631002	−	0.364309i
$335$	24.3701	+	18.6135i	1.33148	+	1.01696i
$336$	−0.134507	+	0.501987i	−0.00733796	+	0.0273856i
$337$	16.0244	+	16.0244i	0.872903	+	0.872903i	0.992788	−	0.119885i	$-0.0382525\pi$
$337$	16.0244	+	16.0244i	0.872903	+	0.872903i	−0.119885	+	0.992788i	$0.538253\pi$
$338$	0.326579	−	12.9959i	0.0177636	−	0.706884i
$339$			5.84762i			0.317599i
$340$	−9.37239	+	1.25521i	−0.508289	+	0.0680732i
$341$	−1.88447	−	3.26400i	−0.102050	−	0.176755i
$342$	0.0538940	−	0.0144409i	0.00291425	−	0.000780872i
$343$	7.13537			0.385274
$344$	4.63274	−	1.24134i	0.249781	−	0.0669285i
$345$	−0.406870	−	0.0526409i	−0.0219051	−	0.00283409i
$346$	−13.6366	−	13.6366i	−0.733106	−	0.733106i
$347$	9.33516	+	34.8393i	0.501138	+	1.87027i	0.492507	+	0.870309i	$0.336081\pi$
$347$	9.33516	+	34.8393i	0.501138	+	1.87027i	0.00863072	+	0.999963i	$0.497253\pi$
$348$	−6.99735	−	1.87494i	−0.375097	−	0.100507i
$349$	3.51575	+	0.942042i	0.188194	+	0.0504264i	0.351685	−	0.936118i	$-0.385609\pi$
$349$	3.51575	+	0.942042i	0.188194	+	0.0504264i	−0.163491	+	0.986545i	$0.552276\pi$
$350$	1.84559	+	1.82917i	0.0986510	+	0.0977733i
$351$	0.976860	−	3.47070i	0.0521410	−	0.185252i
$352$	−0.607921	+	0.607921i	−0.0324023	+	0.0324023i
$353$	14.1482	+	24.5055i	0.753034	+	1.30429i	0.946346	+	0.323156i	$0.104744\pi$
$353$	14.1482	+	24.5055i	0.753034	+	1.30429i	−0.193311	+	0.981137i	$0.561923\pi$
$354$	4.38892	−	2.53395i	0.233269	−	0.134678i
$355$	−12.1852	+	9.39333i	−0.646721	+	0.498546i
$356$	10.9148	−	10.9148i	0.578486	−	0.578486i
$357$	−1.90329	−	1.09886i	−0.100733	−	0.0581581i
$358$	17.5596	+	10.1381i	0.928055	+	0.535813i
$359$	−4.76749	+	4.76749i	−0.251619	+	0.251619i	−0.821634	−	0.570015i	$-0.806937\pi$
$359$	−4.76749	+	4.76749i	−0.251619	+	0.251619i	0.570015	+	0.821634i	$0.306937\pi$
$360$	2.21758	+	0.286912i	0.116877	+	0.0151216i
$361$	−16.4518	+	9.49844i	−0.865884	+	0.499918i
$362$	−7.15615	−	12.3948i	−0.376119	−	0.651457i
$363$	7.25553	−	7.25553i	0.380816	−	0.380816i
$364$	1.61085	+	0.957204i	0.0844315	+	0.0501711i
$365$	4.96429	−	2.06928i	0.259843	−	0.108311i
$366$	−13.9436	−	3.73617i	−0.728843	−	0.195293i
$367$	30.0541	+	8.05298i	1.56881	+	0.420362i	0.935440	−	0.353485i	$-0.115003\pi$
$367$	30.0541	+	8.05298i	1.56881	+	0.420362i	0.633373	+	0.773847i	$0.281670\pi$
$368$	−0.0474866	−	0.177222i	−0.00247541	−	0.00923836i
$369$	0.0205367	+	0.0205367i	0.00106910	+	0.00106910i
$370$	0.0647563	−	0.500512i	0.00336652	−	0.0260204i
$371$	1.77385	−	0.475301i	0.0920935	−	0.0246764i
$372$	−4.38387			−0.227293
$373$	21.8000	−	5.84130i	1.12876	−	0.302451i	0.354338	−	0.935117i	$-0.384706\pi$
$373$	21.8000	−	5.84130i	1.12876	−	0.302451i	0.774425	+	0.632666i	$0.218039\pi$
$374$	−1.81785	−	3.14861i	−0.0939987	−	0.162811i
$375$	6.74656	−	8.91538i	0.348391	−	0.460388i
$376$		−	5.53738i		−	0.285569i
$377$	−13.3428	+	22.4541i	−0.687188	+	1.15645i
$378$	0.367480	+	0.367480i	0.0189011	+	0.0189011i
$379$	3.85119	−	14.3728i	0.197822	−	0.738283i	−0.793696	−	0.608315i	$-0.791846\pi$
$379$	3.85119	−	14.3728i	0.197822	−	0.738283i	0.991518	−	0.129968i	$-0.0414875\pi$
$380$	0.123658	−	0.0165610i	0.00634351	−	0.000849561i
$381$	9.00236	+	5.19751i	0.461205	+	0.266277i
$382$			12.7897i			0.654378i
$383$	5.68179	−	9.84116i	0.290326	−	0.502860i	−0.683561	−	0.729894i	$-0.739570\pi$
$383$	5.68179	−	9.84116i	0.290326	−	0.502860i	0.973887	+	0.227034i	$0.0729029\pi$
$384$	0.258819	+	0.965926i	0.0132078	+	0.0492922i
$385$	−0.380264	+	0.923871i	−0.0193800	+	0.0470848i
$386$	−1.10451	+	1.91307i	−0.0562182	+	0.0973727i
$387$	1.24134	−	4.63274i	0.0631008	−	0.235496i
$388$	−5.45027	+	3.14672i	−0.276696	+	0.159750i
$389$	−0.783134			−0.0397065			−0.0198532	−	0.999803i	$-0.506320\pi$
$389$	−0.783134			−0.0397065			−0.0198532	+	0.999803i	$0.506320\pi$
$390$	3.16205	−	7.41629i	0.160117	−	0.375539i
$391$	0.775891			0.0392385
$392$	5.82828	−	3.36496i	0.294373	−	0.169956i
$393$	−4.50210	+	16.8021i	−0.227101	+	0.847552i
$394$	−6.06986	+	10.5133i	−0.305795	+	0.529653i
$395$	33.0645	−	13.7824i	1.66366	−	0.693468i
$396$	0.222514	+	0.830435i	0.0111818	+	0.0417309i
$397$	−7.12070	+	12.3334i	−0.357378	+	0.618996i	−0.987522	−	0.157482i	$-0.949662\pi$
$397$	−7.12070	+	12.3334i	−0.357378	+	0.618996i	0.630144	+	0.776478i	$0.282996\pi$
$398$		−	4.07610i		−	0.204317i
$399$	0.0251117	+	0.0144982i	0.00125716	+	0.000725819i
$400$	4.83536	+	1.27250i	0.241768	+	0.0636251i
$401$	−8.08823	+	30.1857i	−0.403907	+	1.50740i	0.402155	+	0.915571i	$0.368261\pi$
$401$	−8.08823	+	30.1857i	−0.403907	+	1.50740i	−0.806062	+	0.591830i	$0.798405\pi$
$402$	9.69723	+	9.69723i	0.483654	+	0.483654i
$403$	−4.28243	+	15.2151i	−0.213323	+	0.757917i
$404$		−	5.07001i		−	0.252243i
$405$	1.35727	−	1.77703i	0.0674430	−	0.0883013i
$406$	−1.88239	−	3.26039i	−0.0934212	−	0.161810i
$407$	0.187430	−	0.0502218i	0.00929057	−	0.00248940i
$408$	−4.22888			−0.209361
$409$	−32.5735	+	8.72803i	−1.61065	+	0.431573i	−0.948237	−	0.317563i	$-0.897136\pi$
$409$	−32.5735	+	8.72803i	−1.61065	+	0.431573i	−0.662416	+	0.749136i	$0.730469\pi$
$410$	0.0396496	+	0.0514340i	0.00195815	+	0.00254015i
$411$	−6.42548	−	6.42548i	−0.316946	−	0.316946i
$412$	2.17876	+	8.13124i	0.107340	+	0.400597i
$413$	2.54402	+	0.681667i	0.125183	+	0.0335426i
$414$	−0.177222	−	0.0474866i	−0.00871001	−	0.00233384i
$415$	4.15620	+	9.97090i	0.204020	+	0.489452i
$416$	3.60527	+	0.0452920i	0.176763	+	0.00222062i
$417$	−1.90829	+	1.90829i	−0.0934492	+	0.0934492i
$418$	0.0239844	+	0.0415422i	0.00117311	+	0.00203189i
$419$	−9.64226	+	5.56696i	−0.471055	+	0.271964i	−0.716681	−	0.697401i	$-0.754340\pi$
$419$	−9.64226	+	5.56696i	−0.471055	+	0.271964i	0.245626	+	0.969365i	$0.421006\pi$
$420$	0.709483	+	0.920352i	0.0346192	+	0.0449086i
$421$	20.6313	−	20.6313i	1.00551	−	1.00551i	0.00552546	−	0.999985i	$-0.498241\pi$
$421$	20.6313	−	20.6313i	1.00551	−	1.00551i	0.999985	−	0.00552546i	$-0.00175882\pi$
$422$	12.7914	+	7.38509i	0.622673	+	0.359501i
$423$	−4.79551	−	2.76869i	−0.233166	−	0.134618i
$424$	2.49867	−	2.49867i	0.121346	−	0.121346i
$425$	−10.4903	+	18.3587i	−0.508853	+	0.890526i
$426$	−5.95877	+	3.44030i	−0.288703	+	0.166683i
$427$	−3.75102	−	6.49695i	−0.181524	−	0.314409i
$428$	4.95978	−	4.95978i	0.239740	−	0.239740i
$429$	3.09956	+	0.0389389i	0.149648	+	0.00187999i
$430$	4.08196	−	9.91734i	0.196850	−	0.478257i
$431$	16.8679	+	4.51975i	0.812500	+	0.217709i	0.641065	−	0.767487i	$-0.278493\pi$
$431$	16.8679	+	4.51975i	0.812500	+	0.217709i	0.171435	+	0.985195i	$0.445160\pi$
$432$	0.965926	+	0.258819i	0.0464731	+	0.0124524i
$433$	−0.575332	−	2.14717i	−0.0276487	−	0.103186i	0.950723	−	0.310043i	$-0.100343\pi$
$433$	−0.575332	−	2.14717i	−0.0276487	−	0.103186i	−0.978371	+	0.206856i	$0.933677\pi$
$434$	−1.61098	−	1.61098i	−0.0773296	−	0.0773296i
$435$	−12.8291	+	9.88971i	−0.615107	+	0.474175i
$436$	−8.51759	+	2.28228i	−0.407919	+	0.109302i
$437$	−0.0102370			−0.000489701
$438$	2.32329	−	0.622524i	0.111011	−	0.0297453i
$439$	18.9701	+	32.8571i	0.905392	+	1.56819i	0.820390	+	0.571805i	$0.193757\pi$
$439$	18.9701	+	32.8571i	0.905392	+	1.56819i	0.0850025	+	0.996381i	$0.472910\pi$
$440$	0.255183	+	1.90540i	0.0121654	+	0.0908365i
$441$		−	6.72992i		−	0.320472i
$442$	−4.13103	+	14.6772i	−0.196493	+	0.698122i
$443$	15.4941	+	15.4941i	0.736149	+	0.736149i	0.971830	−	0.235681i	$-0.0757322\pi$
$443$	15.4941	+	15.4941i	0.736149	+	0.736149i	−0.235681	+	0.971830i	$0.575732\pi$
$444$	0.0584158	−	0.218011i	0.00277229	−	0.0103463i
$445$	−4.58166	−	34.2103i	−0.217191	−	1.62173i
$446$	2.75364	+	1.58981i	0.130388	+	0.0752798i
$447$			4.15800i			0.196666i
$448$	−0.259847	+	0.450069i	−0.0122766	+	0.0212638i
$449$	−4.09810	−	15.2943i	−0.193402	−	0.721784i	−0.992675	−	0.120817i	$-0.961449\pi$
$449$	−4.09810	−	15.2943i	−0.193402	−	0.721784i	0.799273	−	0.600968i	$-0.205218\pi$
$450$	3.51970	−	3.55130i	0.165920	−	0.167410i
$451$	−0.0124847	+	0.0216241i	−0.000587880	+	0.00101824i
$452$	−1.51348	+	5.64837i	−0.0711879	+	0.265677i
$453$	3.42183	−	1.97560i	0.160772	−	0.0928216i
$454$	−28.9659			−1.35944
$455$	3.88733	−	1.56335i	0.182241	−	0.0732908i
$456$	0.0557952			0.00261285
$457$	−33.9453	+	19.5983i	−1.58789	+	0.916771i	−0.594240	+	0.804288i	$0.702547\pi$
$457$	−33.9453	+	19.5983i	−1.58789	+	0.916771i	−0.993654	+	0.112483i	$0.964120\pi$
$458$	3.12345	−	11.6569i	0.145949	−	0.544691i
$459$	−2.11444	+	3.66232i	−0.0986937	+	0.170943i
$460$	−0.379381	−	0.156153i	−0.0176887	−	0.00728066i
$461$	−2.72197	−	10.1585i	−0.126775	−	0.473130i	0.873122	−	0.487502i	$-0.162092\pi$
$461$	−2.72197	−	10.1585i	−0.126775	−	0.473130i	−0.999897	+	0.0143717i	$0.995425\pi$
$462$	−0.223399	+	0.386938i	−0.0103934	+	0.0180020i
$463$		−	31.3265i		−	1.45586i	−0.685649	−	0.727932i	$-0.740482\pi$
$463$		−	31.3265i		−	1.45586i	0.685649	−	0.727932i	$-0.259518\pi$
$464$	−6.27365	−	3.62210i	−0.291247	−	0.168152i
$465$	−5.95007	+	7.79026i	−0.275928	+	0.361265i
$466$	−2.60452	+	9.72020i	−0.120652	+	0.450280i
$467$	17.1532	+	17.1532i	0.793754	+	0.793754i	0.982102	−	0.188349i	$-0.0603135\pi$
$467$	17.1532	+	17.1532i	0.793754	+	0.793754i	−0.188349	+	0.982102i	$0.560313\pi$
$468$	1.84186	−	3.09961i	0.0851399	−	0.143279i
$469$			7.12707i			0.329098i
$470$	−9.84008	−	7.51569i	−0.453889	−	0.346673i
$471$	6.63981	+	11.5005i	0.305946	+	0.529915i
$472$	4.89521	−	1.31167i	0.225320	−	0.0603744i
$473$	4.12341			0.189595
$474$	15.4742	−	4.14631i	0.710755	−	0.190446i
$475$	0.138407	−	0.242221i	0.00635055	−	0.0111139i
$476$	−1.55403	−	1.55403i	−0.0712288	−	0.0712288i
$477$	−0.914577	−	3.41325i	−0.0418756	−	0.156282i
$478$	−21.4528	−	5.74827i	−0.981230	−	0.262920i
$479$	−11.2332	−	3.00994i	−0.513260	−	0.137528i	−0.00711279	−	0.999975i	$-0.502264\pi$
$479$	−11.2332	−	3.00994i	−0.513260	−	0.137528i	−0.506147	+	0.862447i	$0.668931\pi$
$480$	2.06776	+	0.851088i	0.0943801	+	0.0388467i
$481$	−0.699585	−	0.415709i	−0.0318983	−	0.0189547i
$482$	17.6925	−	17.6925i	0.805871	−	0.805871i
$483$	−0.0476753	−	0.0825761i	−0.00216930	−	0.00375734i
$484$	8.88617	−	5.13043i	0.403917	−	0.233201i
$485$	−1.80566	+	13.9562i	−0.0819908	+	0.633720i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	7.91564	+	4.57010i	0.358692	+	0.207091i	0.668507	−	0.743706i	$-0.266934\pi$
$487$	7.91564	+	4.57010i	0.358692	+	0.207091i	−0.309815	+	0.950797i	$0.600267\pi$
$488$	−12.5015	−	7.21773i	−0.565915	−	0.326731i
$489$	−16.1341	+	16.1341i	−0.729609	+	0.729609i
$490$	1.93089	−	14.9242i	0.0872288	−	0.674205i
$491$	−6.88995	+	3.97792i	−0.310939	+	0.179521i	−0.647347	−	0.762196i	$-0.724121\pi$
$491$	−6.88995	+	3.97792i	−0.310939	+	0.179521i	0.336407	+	0.941717i	$0.390788\pi$
$492$	0.0145216	+	0.0251522i	0.000654685	+	0.00113395i
$493$	21.6621	−	21.6621i	0.975612	−	0.975612i
$494$	0.0545041	−	0.193648i	0.00245225	−	0.00871264i
$495$	1.77772	+	0.731706i	0.0799025	+	0.0328877i
$496$	−4.23449	−	1.13463i	−0.190134	−	0.0509463i
$497$	−3.45397	−	0.925487i	−0.154932	−	0.0415138i
$498$	1.25035	+	4.66639i	0.0560297	+	0.209106i
$499$	−21.9284	−	21.9284i	−0.981650	−	0.981650i	0.0181843	−	0.999835i	$-0.494211\pi$
$499$	−21.9284	−	21.9284i	−0.981650	−	0.981650i	−0.999835	+	0.0181843i	$0.994211\pi$
$500$	8.82414	−	6.86546i	0.394628	−	0.307033i
$501$	−12.8623	+	3.44643i	−0.574644	+	0.153975i
$502$	−27.3728			−1.22171
$503$	−18.5020	+	4.95760i	−0.824964	+	0.221049i	−0.646516	−	0.762901i	$-0.723775\pi$
$503$	−18.5020	+	4.95760i	−0.824964	+	0.221049i	−0.178449	+	0.983949i	$0.557108\pi$
$504$	0.259847	+	0.450069i	0.0115745	+	0.0200477i
$505$	−9.00956	−	6.88135i	−0.400920	−	0.306216i
$506$		−	0.157738i		−	0.00701232i
$507$	−8.95856	−	9.42041i	−0.397864	−	0.418375i
$508$	7.35039	+	7.35039i	0.326121	+	0.326121i
$509$	8.14806	−	30.4090i	0.361156	−	1.34785i	−0.511401	−	0.859342i	$-0.670873\pi$
$509$	8.14806	−	30.4090i	0.361156	−	1.34785i	0.872557	−	0.488512i	$-0.162460\pi$
$510$	−5.73972	+	7.51485i	−0.254159	+	0.332763i
$511$	1.08253	+	0.624997i	0.0478882	+	0.0276482i
$512$			1.00000i			0.0441942i
$513$	0.0278976	−	0.0483200i	0.00123171	−	0.00213338i
$514$	0.0669693	+	0.249933i	0.00295389	+	0.0110241i
$515$	17.4066	+	7.16453i	0.767027	+	0.315707i
$516$	2.39808	−	4.15360i	0.105570	−	0.182852i
$517$	1.23215	−	4.59843i	0.0541898	−	0.202239i
$518$	0.101581	−	0.0586479i	0.00446322	−	0.00257684i
$519$	−19.2850			−0.846517
$520$	4.97379	−	6.34519i	0.218115	−	0.278255i
$521$	38.1901			1.67314			0.836568	−	0.547862i	$-0.184558\pi$
$521$	38.1901			1.67314			0.836568	+	0.547862i	$0.184558\pi$
$522$	−6.27365	+	3.62210i	−0.274590	+	0.158535i
$523$	−0.379154	+	1.41502i	−0.0165793	+	0.0618747i	−0.973720	−	0.227749i	$-0.926863\pi$
$523$	−0.379154	+	1.41502i	−0.0165793	+	0.0618747i	0.957141	+	0.289624i	$0.0935301\pi$
$524$	−8.69738	+	15.0643i	−0.379947	+	0.658087i
$525$	2.59845	−	0.0116110i	0.113406	−	0.000506746i
$526$	1.60883	+	6.00425i	0.0701485	+	0.261798i
$527$	9.26943	−	16.0551i	0.403783	−	0.699372i
$528$			0.859730i			0.0374149i
$529$	−19.8894	−	11.4832i	−0.864758	−	0.499268i
$530$	−1.04885	−	7.83157i	−0.0455592	−	0.340182i
$531$	1.31167	−	4.89521i	0.0569215	−	0.212434i
$532$	0.0205036	+	0.0205036i	0.000888944	+	0.000888944i
$533$	0.101481	−	0.0258300i	0.00439564	−	0.00111882i
$534$		−	15.4359i		−	0.667978i
$535$	−2.08194	−	15.5454i	−0.0900099	−	0.672087i
$536$	6.85698	+	11.8766i	0.296176	+	0.512993i
$537$	19.5852	−	5.24784i	0.845165	−	0.226461i
$538$	−0.390528			−0.0168369
$539$	5.58876	−	1.49750i	0.240725	−	0.0645021i
$540$	1.77095	−	1.36519i	0.0762094	−	0.0587485i
$541$	−21.3618	−	21.3618i	−0.918417	−	0.918417i	0.0784970	−	0.996914i	$-0.474988\pi$
$541$	−21.3618	−	21.3618i	−0.918417	−	0.918417i	−0.996914	+	0.0784970i	$0.974988\pi$
$542$	4.36922	+	16.3061i	0.187674	+	0.700409i
$543$	−13.8246	−	3.70429i	−0.593271	−	0.158966i
$544$	−4.08479	−	1.09452i	−0.175134	−	0.0469270i
$545$	−7.50495	+	18.2337i	−0.321477	+	0.781045i
$546$	1.81589	−	0.462197i	0.0777128	−	0.0197802i
$547$	13.4041	−	13.4041i	0.573116	−	0.573116i	−0.359882	−	0.932998i	$-0.617183\pi$
$547$	13.4041	−	13.4041i	0.573116	−	0.573116i	0.932998	+	0.359882i	$0.117183\pi$
$548$	−4.54350	−	7.86958i	−0.194089	−	0.336172i
$549$	−12.5015	+	7.21773i	−0.533550	+	0.308045i
$550$	3.73231	+	2.13267i	0.159146	+	0.0909373i
$551$	−0.285806	+	0.285806i	−0.0121758	+	0.0121758i
$552$	−0.158893	−	0.0917371i	−0.00676295	−	0.00390459i
$553$	7.21015	+	4.16278i	0.306607	+	0.177019i
$554$	−0.747388	+	0.747388i	−0.0317535	+	0.0317535i
$555$	−0.308126	−	0.399705i	−0.0130792	−	0.0169665i
$556$	−2.33716	+	1.34936i	−0.0991178	+	0.0572257i
$557$	16.6586	+	28.8536i	0.705848	+	1.22256i	0.966385	+	0.257101i	$0.0827673\pi$
$557$	16.6586	+	28.8536i	0.705848	+	1.22256i	−0.260536	+	0.965464i	$0.583899\pi$
$558$	−3.09986	+	3.09986i	−0.131228	+	0.131228i
$559$	−12.0733	−	12.3805i	−0.510647	−	0.523640i
$560$	0.447104	+	1.07262i	0.0188936	+	0.0453264i
$561$	−3.51181	−	0.940988i	−0.148269	−	0.0397285i
$562$	13.1111	+	3.51311i	0.553059	+	0.148192i
$563$	−6.90115	−	25.7554i	−0.290849	−	1.08546i	−0.944458	−	0.328631i	$-0.893413\pi$
$563$	−6.90115	−	25.7554i	−0.290849	−	1.08546i	0.653610	−	0.756832i	$-0.273254\pi$
$564$	−3.91552	−	3.91552i	−0.164873	−	0.164873i
$565$	7.98313	+	10.3558i	0.335853	+	0.435673i
$566$	9.27878	−	2.48624i	0.390016	−	0.104505i
$567$	0.519695			0.0218251
$568$	−6.64614	+	1.78083i	−0.278866	+	0.0747219i
$569$	−20.0582	−	34.7418i	−0.840883	−	1.45645i	−0.889149	−	0.457618i	$-0.848703\pi$
$569$	−20.0582	−	34.7418i	−0.840883	−	1.45645i	0.0482653	−	0.998835i	$-0.484631\pi$
$570$	0.0757288	−	0.0991496i	0.00317193	−	0.00415292i
$571$			5.59408i			0.234105i	0.993126	+	0.117053i	$0.0373446\pi$
$571$			5.59408i			0.234105i	−0.993126	+	0.117053i	$0.962655\pi$
$572$	2.98386	+	0.839836i	0.124762	+	0.0351153i
$573$	9.04369	+	9.04369i	0.377806	+	0.377806i
$574$	−0.00390652	+	0.0145793i	−0.000163055	+	0.000608529i
$575$	−0.792409	+	0.462231i	−0.0330457	+	0.0192764i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$		−	12.9781i		−	0.540287i	−0.962820	−	0.270144i	$-0.912929\pi$
$577$		−	12.9781i		−	0.540287i	0.962820	−	0.270144i	$-0.0870712\pi$
$578$	0.441732	−	0.765102i	0.0183736	−	0.0318240i
$579$	0.571737	+	2.13375i	0.0237606	+	0.0886757i
$580$	−14.9516	+	6.23232i	−0.620831	+	0.258783i
$581$	−1.25532	+	2.17428i	−0.0520796	+	0.0902045i
$582$	−1.62886	+	6.07899i	−0.0675185	+	0.251982i
$583$	2.63097	−	1.51899i	0.108964	−	0.0629103i
$584$	2.40525			0.0995298
$585$	−3.00820	−	7.48002i	−0.124374	−	0.309261i
$586$	−5.82718			−0.240718
$587$	36.2188	−	20.9109i	1.49491	−	0.863086i	0.494926	−	0.868935i	$-0.335195\pi$
$587$	36.2188	−	20.9109i	1.49491	−	0.863086i	0.999983	+	0.00584852i	$0.00186165\pi$
$588$	1.74183	−	6.50060i	0.0718319	−	0.268080i
$589$	−0.122299	+	0.211829i	−0.00503925	+	0.00872824i
$590$	4.31323	−	10.4792i	0.177573	−	0.431422i
$591$	3.14199	+	11.7261i	0.129244	+	0.482346i
$592$	0.112851	−	0.195463i	0.00463813	−	0.00803348i
$593$			6.42791i			0.263963i	0.991252	+	0.131981i	$0.0421339\pi$
$593$			6.42791i			0.263963i	−0.991252	+	0.131981i	$0.957866\pi$
$594$	0.744548	+	0.429865i	0.0305492	+	0.0176376i
$595$	−4.87079	+	0.652325i	−0.199683	+	0.0267427i
$596$	−1.07617	+	4.01632i	−0.0440816	+	0.164515i
$597$	−2.88224	−	2.88224i	−0.117962	−	0.117962i
$598$	−0.473608	+	0.461856i	−0.0193673	+	0.0188867i
$599$		−	17.8641i		−	0.729906i	−0.931026	−	0.364953i	$-0.881085\pi$
$599$		−	17.8641i		−	0.729906i	0.931026	−	0.364953i	$-0.118915\pi$
$600$	4.31891	−	2.51932i	0.176319	−	0.102851i
$601$	−16.6635	−	28.8620i	−0.679717	−	1.17730i	−0.975066	−	0.221914i	$-0.928769\pi$
$601$	−16.6635	−	28.8620i	−0.679717	−	1.17730i	0.295349	−	0.955389i	$-0.404564\pi$
$602$	2.40761	−	0.645118i	0.0981270	−	0.0262930i
$603$	13.7140			0.558476
$604$	3.81656	−	1.02264i	0.155293	−	0.0416108i
$605$	2.94396	−	22.7543i	0.119689	−	0.925095i
$606$	−3.58504	−	3.58504i	−0.145632	−	0.145632i
$607$	4.37259	+	16.3187i	0.177478	+	0.662357i	0.996116	+	0.0880472i	$0.0280626\pi$
$607$	4.37259	+	16.3187i	0.177478	+	0.662357i	−0.818638	+	0.574309i	$0.805271\pi$
$608$	0.0538940	+	0.0144409i	0.00218569	+	0.000585654i
$609$	−3.63649	−	0.974394i	−0.147358	−	0.0394844i
$610$	−29.7939	+	12.4191i	−1.20632	+	0.502835i
$611$	−17.4145	+	9.76467i	−0.704515	+	0.395036i
$612$	−2.99027	+	2.99027i	−0.120875	+	0.120875i
$613$	−19.8507	−	34.3825i	−0.801763	−	1.38869i	−0.918455	−	0.395526i	$-0.870562\pi$
$613$	−19.8507	−	34.3825i	−0.801763	−	1.38869i	0.116692	−	0.993168i	$-0.462771\pi$
$614$	3.92039	−	2.26344i	0.158214	−	0.0913450i
$615$	0.0644058	+	0.00833284i	0.00259709	+	0.000336013i
$616$	−0.315933	+	0.315933i	−0.0127293	+	0.0127293i
$617$	−20.2554	−	11.6945i	−0.815453	−	0.470802i	0.0333930	−	0.999442i	$-0.489369\pi$
$617$	−20.2554	−	11.6945i	−0.815453	−	0.470802i	−0.848846	+	0.528640i	$0.822702\pi$
$618$	7.29027	+	4.20904i	0.293258	+	0.169312i
$619$	9.00079	−	9.00079i	0.361772	−	0.361772i	−0.502693	−	0.864465i	$-0.667657\pi$
$619$	9.00079	−	9.00079i	0.361772	−	0.361772i	0.864465	+	0.502693i	$0.167657\pi$
$620$	−7.76359	+	5.98482i	−0.311793	+	0.240356i
$621$	−0.158893	+	0.0917371i	−0.00637617	+	0.00368128i
$622$	−13.8185	−	23.9343i	−0.554071	−	0.959680i
$623$	5.67239	−	5.67239i	0.227259	−	0.227259i
$624$	2.58133	−	2.51728i	0.103336	−	0.100772i
$625$	−0.223417	−	24.9990i	−0.00893670	−	0.999960i
$626$	30.7305	+	8.23422i	1.22824	+	0.329106i
$627$	0.0463343	+	0.0124152i	0.00185041	+	0.000495817i
$628$	3.43702	+	12.8271i	0.137152	+	0.511858i
$629$	0.674908	+	0.674908i	0.0269104	+	0.0269104i
$630$	1.15247	+	0.149107i	0.0459154	+	0.00594055i
$631$	−5.22065	+	1.39887i	−0.207831	+	0.0556881i	−0.361232	−	0.932476i	$-0.617644\pi$
$631$	−5.22065	+	1.39887i	−0.207831	+	0.0556881i	0.153401	+	0.988164i	$0.450977\pi$
$632$	16.0201			0.637245
$633$	14.2669	−	3.82280i	0.567058	−	0.151943i
$634$	0.902361	+	1.56294i	0.0358373	+	0.0620721i
$635$	23.0383	−	3.08543i	0.914247	−	0.122442i
$636$		−	3.53365i		−	0.140118i
$637$	−20.8601	−	12.3955i	−0.826507	−	0.491129i
$638$	−4.40390	−	4.40390i	−0.174352	−	0.174352i
$639$	−1.78083	+	6.64614i	−0.0704485	+	0.262917i
$640$	1.77703	+	1.35727i	0.0702432	+	0.0536506i
$641$	−7.68152	−	4.43492i	−0.303402	−	0.175169i	0.340568	−	0.940220i	$-0.389381\pi$
$641$	−7.68152	−	4.43492i	−0.303402	−	0.175169i	−0.643970	+	0.765051i	$0.722714\pi$
$642$		−	7.01419i		−	0.276828i
$643$	−8.83093	+	15.2956i	−0.348258	+	0.603201i	−0.985940	−	0.167099i	$-0.946560\pi$
$643$	−8.83093	+	15.2956i	−0.348258	+	0.603201i	0.637682	+	0.770300i	$0.279893\pi$
$644$	−0.0246786	−	0.0921016i	−0.000972471	−	0.00362931i
$645$	−4.12624	−	9.89901i	−0.162470	−	0.389773i
$646$	−0.117976	+	0.204340i	−0.00464169	+	0.00803964i
$647$	11.3799	−	42.4705i	0.447391	−	1.66969i	−0.262154	−	0.965026i	$-0.584433\pi$
$647$	11.3799	−	42.4705i	0.447391	−	1.66969i	0.709545	−	0.704660i	$-0.248900\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	4.35702			0.171028
$650$	−4.52484	−	17.4507i	−0.177479	−	0.684472i
$651$	−2.27827			−0.0892926
$652$	−19.7602	+	11.4085i	−0.773867	+	0.446792i
$653$	5.90050	−	22.0209i	0.230904	−	0.861746i	−0.749048	−	0.662515i	$-0.769489\pi$
$653$	5.90050	−	22.0209i	0.230904	−	0.861746i	0.979953	−	0.199231i	$-0.0638444\pi$
$654$	−4.40903	+	7.63667i	−0.172407	+	0.298617i
$655$	14.9651	+	35.9018i	0.584733	+	1.40280i
$656$	0.00751694	+	0.0280536i	0.000293487	+	0.00109531i
$657$	1.20262	−	2.08300i	0.0469188	−	0.0812657i
$658$		−	2.87775i		−	0.112186i
$659$	0.951098	+	0.549117i	0.0370495	+	0.0213906i	0.518410	−	0.855132i	$-0.326524\pi$
$659$	0.951098	+	0.549117i	0.0370495	+	0.0213906i	−0.481361	+	0.876523i	$0.659857\pi$
$660$	1.52776	+	1.16688i	0.0594682	+	0.0454208i
$661$	−6.39522	+	23.8673i	−0.248745	+	0.928330i	0.722719	+	0.691142i	$0.242892\pi$
$661$	−6.39522	+	23.8673i	−0.248745	+	0.928330i	−0.971464	+	0.237187i	$0.923774\pi$
$662$	14.3606	+	14.3606i	0.558142	+	0.558142i
$663$	7.45725	+	13.2994i	0.289616	+	0.516506i
$664$			4.83100i			0.187479i
$665$	0.0642643	−	0.00860667i	0.00249206	−	0.000333752i
$666$	−0.112851	−	0.195463i	−0.00437287	−	0.00757404i
$667$	1.28383	−	0.344002i	0.0497102	−	0.0133198i
$668$	−13.3160			−0.515211
$669$	3.07128	−	0.822948i	0.118743	−	0.0318170i
$670$	30.4119	+	3.93469i	1.17491	+	0.152010i
$671$	−8.77561	−	8.77561i	−0.338779	−	0.338779i
$672$	0.134507	+	0.501987i	0.00518872	+	0.0193646i
$673$	7.25006	+	1.94265i	0.279469	+	0.0748836i	0.395831	−	0.918323i	$-0.370457\pi$
$673$	7.25006	+	1.94265i	0.279469	+	0.0748836i	−0.116362	+	0.993207i	$0.537123\pi$
$674$	21.8897	+	5.86533i	0.843160	+	0.225924i
$675$	−0.0223420	−	4.99995i	−0.000859943	−	0.192448i
$676$	−6.21512	−	11.4181i	−0.239043	−	0.439156i
$677$	−29.5301	+	29.5301i	−1.13493	+	1.13493i	−0.145589	+	0.989345i	$0.546508\pi$
$677$	−29.5301	+	29.5301i	−1.13493	+	1.13493i	−0.989345	+	0.145589i	$0.953492\pi$
$678$	2.92381	+	5.06419i	0.112288	+	0.194489i
$679$	−2.83248	+	1.63533i	−0.108701	+	0.0627583i
$680$	−7.48913	+	5.77324i	−0.287195	+	0.221394i
$681$	−20.4820	+	20.4820i	−0.784871	+	0.784871i
$682$	−3.26400	−	1.88447i	−0.124985	−	0.0721601i
$683$	−19.5774	−	11.3030i	−0.749110	−	0.432499i	0.0762622	−	0.997088i	$-0.475701\pi$
$683$	−19.5774	−	11.3030i	−0.749110	−	0.432499i	−0.825372	+	0.564589i	$0.809035\pi$
$684$	0.0394531	−	0.0394531i	0.00150853	−	0.00150853i
$685$	−20.1512	−	2.60717i	−0.769938	−	0.0996147i
$686$	6.17941	−	3.56768i	0.235931	−	0.136215i
$687$	−6.03405	−	10.4513i	−0.230213	−	0.398741i
$688$	3.39140	−	3.39140i	0.129296	−	0.129296i
$689$	−12.2642	−	3.45189i	−0.467230	−	0.131506i
$690$	−0.378680	+	0.157846i	−0.0144161	+	0.00600911i
$691$	18.9019	+	5.06476i	0.719063	+	0.192672i	0.599754	−	0.800185i	$-0.295265\pi$
$691$	18.9019	+	5.06476i	0.719063	+	0.192672i	0.119310	+	0.992857i	$0.461932\pi$
$692$	−18.6279	−	4.99132i	−0.708126	−	0.189742i
$693$	0.115640	+	0.431573i	0.00439279	+	0.0163941i
$694$	25.5041	+	25.5041i	0.968124	+	0.968124i
$695$	−0.774295	+	5.98465i	−0.0293707	+	0.227011i
$696$	−6.99735	+	1.87494i	−0.265234	+	0.0710692i
$697$	−0.122821			−0.00465216
$698$	3.51575	−	0.942042i	0.133073	−	0.0356568i
$699$	5.03155	+	8.71490i	0.190311	+	0.329628i
$700$	2.51291	+	0.661313i	0.0949792	+	0.0249953i
$701$		−	29.4470i		−	1.11220i	−0.831116	−	0.556098i	$-0.812298\pi$
$701$		−	29.4470i		−	1.11220i	0.831116	−	0.556098i	$-0.187702\pi$
$702$	−0.889363	−	3.49414i	−0.0335668	−	0.131878i
$703$	−0.00890462	−	0.00890462i	−0.000335844	−	0.000335844i
$704$	−0.222514	+	0.830435i	−0.00838633	+	0.0312982i
$705$	−12.2724	+	1.64359i	−0.462205	+	0.0619013i
$706$	24.5055	+	14.1482i	0.922275	+	0.532476i
$707$		−	2.63486i		−	0.0990941i
$708$	2.53395	−	4.38892i	0.0952315	−	0.164946i
$709$	10.6145	+	39.6139i	0.398636	+	1.48773i	0.815497	+	0.578761i	$0.196463\pi$
$709$	10.6145	+	39.6139i	0.398636	+	1.48773i	−0.416861	+	0.908970i	$0.636870\pi$
$710$	−5.85599	+	14.2274i	−0.219771	+	0.533946i
$711$	8.01005	−	13.8738i	0.300400	−	0.520308i
$712$	3.99511	−	14.9100i	0.149723	−	0.558774i
$713$	0.696567	−	0.402163i	0.0260866	−	0.0150611i
$714$	−2.19773			−0.0822480
$715$	5.54231	−	4.16253i	0.207270	−	0.155670i
$716$	20.2761			0.757754
$717$	−19.2341	+	11.1048i	−0.718310	+	0.414717i
$718$	−1.74502	+	6.51252i	−0.0651237	+	0.243045i
$719$	15.8538	−	27.4596i	0.591246	−	1.02407i	−0.402819	−	0.915280i	$-0.631969\pi$
$719$	15.8538	−	27.4596i	0.591246	−	1.02407i	0.994065	−	0.108789i	$-0.0346972\pi$
$720$	2.06394	−	0.860320i	0.0769185	−	0.0320622i
$721$	1.13229	+	4.22576i	0.0421687	+	0.157376i
$722$	−9.49844	+	16.4518i	−0.353495	+	0.612272i
$723$		−	25.0210i		−	0.930540i
$724$	−12.3948	−	7.15615i	−0.460649	−	0.265956i
$725$	−9.21825	+	35.0283i	−0.342357	+	1.30092i
$726$	2.65571	−	9.91123i	0.0985625	−	0.367840i
$727$	13.5130	+	13.5130i	0.501169	+	0.501169i	0.911801	−	0.410632i	$-0.134692\pi$
$727$	13.5130	+	13.5130i	0.501169	+	0.501169i	−0.410632	+	0.911801i	$0.634692\pi$
$728$	1.87364	+	0.0235380i	0.0694417	+	0.000872377i
$729$		−	1.00000i		−	0.0370370i
$730$	3.26456	−	4.27419i	0.120827	−	0.158195i
$731$	10.1412	+	17.5651i	0.375087	+	0.649669i
$732$	−13.9436	+	3.73617i	−0.515369	+	0.138093i
$733$	−10.4942			−0.387612			−0.193806	−	0.981040i	$-0.562083\pi$
$733$	−10.4942			−0.387612			−0.193806	+	0.981040i	$0.562083\pi$
$734$	30.0541	−	8.05298i	1.10932	−	0.297241i
$735$	−9.18763	−	11.9183i	−0.338891	−	0.439614i
$736$	−0.129736	−	0.129736i	−0.00478213	−	0.00478213i
$737$	3.05155	+	11.3886i	0.112405	+	0.419503i
$738$	0.0280536	+	0.00751694i	0.00103267	+	0.000276703i
$739$	10.6866	+	2.86346i	0.393112	+	0.105334i	0.449960	−	0.893049i	$-0.351438\pi$
$739$	10.6866	+	2.86346i	0.393112	+	0.105334i	−0.0568477	+	0.998383i	$0.518105\pi$
$740$	−0.194175	−	0.465834i	−0.00713802	−	0.0171244i
$741$	−0.0983897	−	0.175470i	−0.00361444	−	0.00644606i
$742$	1.29855	−	1.29855i	0.0476711	−	0.0476711i
$743$	18.1763	+	31.4823i	0.666825	+	1.15498i	0.978787	+	0.204881i	$0.0656806\pi$
$743$	18.1763	+	31.4823i	0.666825	+	1.15498i	−0.311962	+	0.950095i	$0.600986\pi$
$744$	−3.79654	+	2.19193i	−0.139188	+	0.0803602i
$745$	5.67646	+	7.36359i	0.207969	+	0.269781i
$746$	15.9587	−	15.9587i	0.584291	−	0.584291i
$747$	4.18377	+	2.41550i	0.153076	+	0.0883785i
$748$	−3.14861	−	1.81785i	−0.115124	−	0.0664671i
$749$	2.57757	−	2.57757i	0.0941824	−	0.0941824i
$750$	1.38500	−	11.0942i	0.0505730	−	0.405104i
$751$	−42.3079	+	24.4265i	−1.54384	+	0.891335i	−0.545246	+	0.838276i	$0.683564\pi$
$751$	−42.3079	+	24.4265i	−1.54384	+	0.891335i	−0.998591	+	0.0530591i	$0.983103\pi$
$752$	−2.76869	−	4.79551i	−0.100964	−	0.174874i
$753$	−19.3555	+	19.3555i	−0.705354	+	0.705354i
$754$	−0.328104	+	26.1172i	−0.0119488	+	0.951134i
$755$	3.36281	−	8.17013i	0.122385	−	0.297341i
$756$	0.501987	+	0.134507i	0.0182571	+	0.00489197i
$757$	−26.0534	−	6.98099i	−0.946927	−	0.253728i	−0.247869	−	0.968794i	$-0.579730\pi$
$757$	−26.0534	−	6.98099i	−0.946927	−	0.253728i	−0.699058	+	0.715065i	$0.746397\pi$
$758$	−3.85119	−	14.3728i	−0.139881	−	0.522045i
$759$	−0.111538	−	0.111538i	−0.00404857	−	0.00404857i
$760$	0.0988102	−	0.0761711i	0.00358422	−	0.00276302i
$761$	−21.6967	+	5.81362i	−0.786505	+	0.210743i	−0.629651	−	0.776878i	$-0.716802\pi$
$761$	−21.6967	+	5.81362i	−0.786505	+	0.210743i	−0.156855	+	0.987622i	$0.550135\pi$
$762$	10.3950			0.376572
$763$	−4.42655	+	1.18609i	−0.160252	+	0.0429394i
$764$	6.39485	+	11.0762i	0.231358	+	0.400723i
$765$	1.25521	+	9.37239i	0.0453821	+	0.338860i
$766$		−	11.3636i		−	0.410583i
$767$	−12.7573	−	13.0819i	−0.460640	−	0.472361i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	3.23891	−	12.0878i	0.116798	−	0.435897i	−0.882617	−	0.470093i	$-0.844220\pi$
$769$	3.23891	−	12.0878i	0.116798	−	0.435897i	0.999415	+	0.0341962i	$0.0108871\pi$
$770$	0.132617	+	0.990228i	0.00477920	+	0.0356853i
$771$	0.224083	+	0.129375i	0.00807017	+	0.00465931i
$772$			2.20902i			0.0795045i
$773$	10.2670	−	17.7829i	0.369278	−	0.639607i	−0.620175	−	0.784463i	$-0.712939\pi$
$773$	10.2670	−	17.7829i	0.369278	−	0.639607i	0.989453	+	0.144856i	$0.0462718\pi$
$774$	−1.24134	−	4.63274i	−0.0446190	−	0.166520i
$775$	0.0979442	+	21.9191i	0.00351826	+	0.787358i
$776$	−3.14672	+	5.45027i	−0.112961	+	0.195653i
$777$	0.0303584	−	0.113299i	0.00108910	−	0.00406458i
$778$	−0.678214	+	0.391567i	−0.0243151	+	0.0140384i
$779$	0.00162047			5.80594e−5
$780$	−0.969728	−	8.00373i	−0.0347218	−	0.286579i
$781$	−5.91545			−0.211671
$782$	0.671942	−	0.387946i	0.0240286	−	0.0138729i
$783$	−1.87494	+	6.99735i	−0.0670047	+	0.250065i
$784$	3.36496	−	5.82828i	0.120177	−	0.208153i
$785$	27.4591	+	11.3021i	0.980059	+	0.403391i
$786$	4.50210	+	16.8021i	0.160584	+	0.599309i
$787$	12.7381	−	22.0630i	0.454064	−	0.786462i	−0.544570	−	0.838716i	$-0.683307\pi$
$787$	12.7381	−	22.0630i	0.454064	−	0.786462i	0.998634	+	0.0522536i	$0.0166404\pi$
$788$			12.1397i			0.432460i
$789$	5.38327	+	3.10803i	0.191649	+	0.110649i
$790$	21.7435	−	28.4682i	0.773599	−	1.01285i
$791$	−0.786546	+	2.93543i	−0.0279664	+	0.104372i
$792$	0.607921	+	0.607921i	0.0216015	+	0.0216015i
$793$	−0.653810	+	52.0437i	−0.0232175	+	1.84812i
$794$			14.2414i			0.505409i
$795$	−6.27940	−	4.79610i	−0.222707	−	0.170100i
$796$	−2.03805	−	3.53001i	−0.0722368	−	0.125118i
$797$	−22.3516	+	5.98910i	−0.791735	+	0.212145i	−0.631952	−	0.775008i	$-0.717746\pi$
$797$	−22.3516	+	5.98910i	−0.791735	+	0.212145i	−0.159783	+	0.987152i	$0.551079\pi$
$798$	0.0289965			0.00102646
$799$	22.6190	−	6.06075i	0.800203	−	0.214414i
$800$	4.82380	−	1.31566i	0.170547	−	0.0465157i
$801$	−10.9148	−	10.9148i	−0.385657	−	0.385657i
$802$	8.08823	+	30.1857i	0.285605	+	1.06589i
$803$	1.99740	+	0.535202i	0.0704868	+	0.0188869i
$804$	13.2467	+	3.54943i	0.467174	+	0.125179i
$805$	−0.197163	−	0.0811518i	−0.00694907	−	0.00286023i
$806$	3.89885	+	15.3179i	0.137331	+	0.539548i
$807$	−0.276145	+	0.276145i	−0.00972077	+	0.00972077i
$808$	−2.53501	−	4.39076i	−0.0891812	−	0.154466i
$809$	−20.3578	+	11.7536i	−0.715742	+	0.413234i	−0.813184	−	0.582007i	$-0.802267\pi$
$809$	−20.3578	+	11.7536i	−0.715742	+	0.413234i	0.0974414	+	0.995241i	$0.468934\pi$
$810$	0.286912	−	2.21758i	0.0100810	−	0.0779180i
$811$	−18.5083	+	18.5083i	−0.649915	+	0.649915i	−0.952972	−	0.303057i	$-0.901993\pi$
$811$	−18.5083	+	18.5083i	−0.649915	+	0.649915i	0.303057	+	0.952972i	$0.401993\pi$
$812$	−3.26039	−	1.88239i	−0.114417	−	0.0660588i
$813$	14.6197	+	8.44068i	0.512735	+	0.296028i
$814$	0.137208	−	0.137208i	0.00480915	−	0.00480915i
$815$	−6.54648	+	50.5988i	−0.229313	+	1.77240i
$816$	−3.66232	+	2.11444i	−0.128207	+	0.0740203i
$817$	−0.133801	−	0.231751i	−0.00468112	−	0.00810794i
$818$	−23.8454	+	23.8454i	−0.833736	+	0.833736i
$819$	0.957204	−	1.61085i	0.0334474	−	0.0562876i
$820$	0.0600546	+	0.0247184i	0.00209720	+	0.000863203i
$821$	49.9927	+	13.3955i	1.74476	+	0.467506i	0.983495	−	0.180938i	$-0.0579132\pi$
$821$	49.9927	+	13.3955i	1.74476	+	0.467506i	0.761263	+	0.648444i	$0.224580\pi$
$822$	−8.77737	−	2.35189i	−0.306146	−	0.0820316i
$823$	−7.56435	−	28.2305i	−0.263677	−	0.984054i	−0.963055	−	0.269303i	$-0.913207\pi$
$823$	−7.56435	−	28.2305i	−0.263677	−	0.984054i	0.699379	−	0.714751i	$-0.253460\pi$
$824$	5.95248	+	5.95248i	0.207364	+	0.207364i
$825$	4.14716	−	1.13111i	0.144386	−	0.0393804i
$826$	2.54402	−	0.681667i	0.0885176	−	0.0237182i
$827$	−8.43549			−0.293331			−0.146665	−	0.989186i	$-0.546854\pi$
$827$	−8.43549			−0.293331			−0.146665	+	0.989186i	$0.546854\pi$
$828$	−0.177222	+	0.0474866i	−0.00615891	+	0.00165027i
$829$	10.4506	+	18.1010i	0.362965	+	0.628674i	0.988447	−	0.151564i	$-0.0484310\pi$
$829$	10.4506	+	18.1010i	0.362965	+	0.628674i	−0.625482	+	0.780238i	$0.715098\pi$
$830$	8.58483	+	6.55695i	0.297984	+	0.227595i
$831$			1.05697i			0.0366657i
$832$	3.14490	−	1.76341i	0.109030	−	0.0611352i
$833$	20.1243	+	20.1243i	0.697265	+	0.697265i
$834$	−0.698481	+	2.60677i	−0.0241864	+	0.0902650i
$835$	−18.0733	+	23.6629i	−0.625454	+	0.818889i
$836$	0.0415422	+	0.0239844i	0.00143677	+	0.000829517i
$837$			4.38387i			0.151529i
$838$	−5.56696	+	9.64226i	−0.192307	+	0.333086i
$839$	8.60452	+	32.1125i	0.297061	+	1.10865i	0.939567	+	0.342366i	$0.111228\pi$
$839$	8.60452	+	32.1125i	0.297061	+	1.10865i	−0.642505	+	0.766281i	$0.722105\pi$
$840$	1.07461	+	0.442306i	0.0370774	+	0.0152610i
$841$	11.7392	−	20.3328i	0.404799	−	0.701132i
$842$	7.55160	−	28.1829i	0.260245	−	0.971248i
$843$	11.7551	−	6.78681i	0.404867	−	0.233750i
$844$	14.7702			0.508411
$845$	−28.7258	−	4.45289i	−0.988198	−	0.153184i
$846$	−5.53738			−0.190379
$847$	4.61810	−	2.66626i	0.158680	−	0.0916138i
$848$	0.914577	−	3.41325i	0.0314067	−	0.117211i
$849$	4.80305	−	8.31913i	0.164840	−	0.285512i
$850$	0.0944816	+	21.1442i	0.00324069	+	0.725240i
$851$	0.0107178	+	0.0399993i	0.000367401	+	0.00137116i
$852$	−3.44030	+	5.95877i	−0.117863	+	0.204144i
$853$		−	12.3935i		−	0.424344i	−0.977232	−	0.212172i	$-0.931946\pi$
$853$		−	12.3935i		−	0.424344i	0.977232	−	0.212172i	$-0.0680538\pi$
$854$	−6.49695	−	3.75102i	−0.222321	−	0.128357i
$855$	−0.0165610	−	0.123658i	−0.000566374	−	0.00422900i
$856$	1.81541	−	6.77519i	0.0620493	−	0.231571i
$857$	11.9224	+	11.9224i	0.407262	+	0.407262i	0.880783	−	0.473520i	$-0.157017\pi$
$857$	11.9224	+	11.9224i	0.407262	+	0.407262i	−0.473520	+	0.880783i	$0.657017\pi$
$858$	2.70376	−	1.51606i	0.0923050	−	0.0517573i
$859$			37.7546i			1.28817i	0.764954	+	0.644085i	$0.222762\pi$
$859$			37.7546i			1.28817i	−0.764954	+	0.644085i	$0.777238\pi$
$860$	−1.42359	−	10.6297i	−0.0485439	−	0.362468i
$861$	0.00754681	+	0.0130715i	0.000257195	+	0.000445474i
$862$	16.8679	−	4.51975i	0.574524	−	0.153943i
$863$	−34.7009			−1.18123			−0.590615	−	0.806953i	$-0.701115\pi$
$863$	−34.7009			−1.18123			−0.590615	+	0.806953i	$0.701115\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	−34.1527	+	26.3277i	−1.16123	+	0.895169i
$866$	−1.57183	−	1.57183i	−0.0534131	−	0.0534131i
$867$	−0.228657	−	0.853360i	−0.00776560	−	0.0289816i
$868$	−2.20064	−	0.589661i	−0.0746947	−	0.0200144i
$869$	13.3037	+	3.56470i	0.451295	+	0.120924i
$870$	−6.16545	+	14.9793i	−0.209028	+	0.507845i
$871$	25.2592	−	42.5079i	0.855874	−	1.44032i
$872$	−6.23531	+	6.23531i	−0.211154	+	0.211154i
$873$	3.14672	+	5.45027i	0.106500	+	0.184464i
$874$	−0.00886548	+	0.00511849i	−0.000299879	+	0.000173135i
$875$	4.58586	−	3.56794i	0.155030	−	0.120619i
$876$	1.70077	−	1.70077i	0.0574636	−	0.0574636i
$877$	26.6926	+	15.4110i	0.901344	+	0.520391i	0.877636	−	0.479328i	$-0.159120\pi$
$877$	26.6926	+	15.4110i	0.901344	+	0.520391i	0.0237079	+	0.999719i	$0.492453\pi$
$878$	32.8571	+	18.9701i	1.10887	+	0.640209i
$879$	−4.12044	+	4.12044i	−0.138979	+	0.138979i
$880$	1.17370	+	1.52254i	0.0395653	+	0.0513247i
$881$	24.9249	−	14.3904i	0.839740	−	0.484824i	−0.0174360	−	0.999848i	$-0.505550\pi$
$881$	24.9249	−	14.3904i	0.839740	−	0.484824i	0.857176	+	0.515024i	$0.172217\pi$
$882$	−3.36496	−	5.82828i	−0.113304	−	0.196248i
$883$	12.4407	−	12.4407i	0.418662	−	0.418662i	−0.466080	−	0.884742i	$-0.654334\pi$
$883$	12.4407	−	12.4407i	0.418662	−	0.418662i	0.884742	+	0.466080i	$0.154334\pi$
$884$	3.76101	+	14.7763i	0.126497	+	0.496982i
$885$	−4.36001	−	10.4598i	−0.146560	−	0.351603i
$886$	21.1654	+	5.67125i	0.711065	+	0.190529i
$887$	−37.1375	−	9.95096i	−1.24695	−	0.334121i	−0.425796	−	0.904819i	$-0.640006\pi$
$887$	−37.1375	−	9.95096i	−1.24695	−	0.334121i	−0.821159	+	0.570699i	$0.806672\pi$
$888$	−0.0584158	−	0.218011i	−0.00196031	−	0.00731596i
$889$	3.81996	+	3.81996i	0.128117	+	0.128117i
$890$	−21.0730	−	27.3362i	−0.706368	−	0.916311i
$891$	0.830435	−	0.222514i	0.0278206	−	0.00745451i
$892$	3.17963			0.106462
$893$	−0.298431	+	0.0799645i	−0.00998663	+	0.00267591i
$894$	2.07900	+	3.60093i	0.0695321	+	0.120433i
$895$	27.5201	−	36.0312i	0.919894	−	1.20439i
$896$			0.519695i			0.0173618i
$897$	−0.00830991	+	0.661473i	−0.000277460	+	0.0220860i
$898$	−11.1962	−	11.1962i	−0.373623	−	0.373623i
$899$	8.21947	−	30.6755i	0.274135	−	1.02308i
$900$	1.27250	−	4.83536i	0.0424167	−	0.161179i
$901$	12.9414	+	7.47171i	0.431140	+	0.248919i
$902$			0.0249693i			0.000831388i
$903$	1.24627	−	2.15861i	0.0414733	−	0.0718339i
$904$	1.51348	+	5.64837i	0.0503375	+	0.187862i
$905$	−29.5397	+	12.3131i	−0.981934	+	0.409303i
$906$	1.97560	−	3.42183i	0.0656348	−	0.113683i
$907$	11.9123	−	44.4572i	0.395540	−	1.47618i	−0.425318	−	0.905044i	$-0.639838\pi$
$907$	11.9123	−	44.4572i	0.395540	−	1.47618i	0.820858	−	0.571132i	$-0.193495\pi$
$908$	−25.0852	+	14.4830i	−0.832482	+	0.480634i
$909$	−5.07001			−0.168162
$910$	2.58485	−	3.29756i	0.0856870	−	0.109313i
$911$	−34.0825			−1.12920			−0.564602	−	0.825363i	$-0.690970\pi$
$911$	−34.0825			−1.12920			−0.564602	+	0.825363i	$0.690970\pi$
$912$	0.0483200	−	0.0278976i	0.00160004	−	0.000923781i
$913$	−1.07497	+	4.01183i	−0.0355762	+	0.132772i
$914$	−19.5983	+	33.9453i	−0.648255	+	1.12281i
$915$	−12.2858	+	29.8491i	−0.406158	+	0.986781i
$916$	−3.12345	−	11.6569i	−0.103202	−	0.385154i
$917$	−4.51999	+	7.82884i	−0.149263	+	0.258531i
$918$			4.22888i			0.139574i
$919$	6.13874	+	3.54420i	0.202498	+	0.116913i	0.597820	−	0.801630i	$-0.296034\pi$
$919$	6.13874	+	3.54420i	0.202498	+	0.116913i	−0.395322	+	0.918543i	$0.629367\pi$
$920$	−0.406630	+	0.0544584i	−0.0134062	+	0.00179544i
$921$	1.17164	−	4.37263i	0.0386070	−	0.144083i
$922$	−7.43657	−	7.43657i	−0.244910	−	0.244910i
$923$	17.3204	+	17.7611i	0.570108	+	0.584614i
$924$			0.446797i			0.0146985i
$925$	−1.09135	−	0.287205i	−0.0358833	−	0.00944325i
$926$	−15.6632	−	27.1295i	−0.514726	−	0.891531i
$927$	8.13124	−	2.17876i	0.267065	−	0.0715598i
$928$	−7.24419			−0.237802
$929$	23.6705	−	6.34249i	0.776604	−	0.208090i	0.151317	−	0.988485i	$-0.451649\pi$
$929$	23.6705	−	6.34249i	0.776604	−	0.208090i	0.625287	+	0.780395i	$0.284982\pi$
$930$	−1.25778	+	9.72160i	−0.0412443	+	0.318784i
$931$	−0.265516	−	0.265516i	−0.00870195	−	0.00870195i
$932$	2.60452	+	9.72020i	0.0853139	+	0.318396i
$933$	−26.6953	−	7.15298i	−0.873964	−	0.234178i
$934$	23.4317	+	6.27849i	0.766707	+	0.205439i
$935$	−7.50386	+	3.12786i	−0.245403	+	0.102292i
$936$	0.0452920	−	3.60527i	0.00148041	−	0.117842i
$937$	23.5857	−	23.5857i	0.770510	−	0.770510i	−0.207685	−	0.978196i	$-0.566593\pi$
$937$	23.5857	−	23.5857i	0.770510	−	0.770510i	0.978196	+	0.207685i	$0.0665930\pi$
$938$	3.56354	+	6.17223i	0.116354	+	0.201530i
$939$	27.5522	−	15.9073i	0.899133	−	0.519115i
$940$	−12.2796	−	1.58874i	−0.400517	−	0.0518189i
$941$	−3.01039	+	3.01039i	−0.0981360	+	0.0981360i	−0.754470	−	0.656334i	$-0.772106\pi$
$941$	−3.01039	+	3.01039i	−0.0981360	+	0.0981360i	0.656334	+	0.754470i	$0.272106\pi$
$942$	11.5005	+	6.63981i	0.374706	+	0.216337i
$943$	−0.00461478	−	0.00266434i	−0.000150278	−	8.67629e-5i
$944$	3.58354	−	3.58354i	0.116634	−	0.116634i
$945$	0.920352	−	0.709483i	0.0299390	−	0.0230795i
$946$	3.57098	−	2.06170i	0.116102	−	0.0670318i
$947$	−22.5692	−	39.0911i	−0.733402	−	1.27029i	−0.955421	−	0.295247i	$-0.904598\pi$
$947$	−22.5692	−	39.0911i	−0.733402	−	1.27029i	0.222020	−	0.975042i	$-0.428735\pi$
$948$	11.3279	−	11.3279i	0.367914	−	0.367914i
$949$	−4.24143	−	7.56426i	−0.137683	−	0.245546i
$950$	−0.00124657	−	0.278973i	−4.04442e−5	−	0.00905108i
$951$	1.74323	+	0.467097i	0.0565280	+	0.0151466i
$952$	−2.12284	−	0.568814i	−0.0688018	−	0.0184354i
$953$	3.28613	+	12.2640i	0.106448	+	0.397271i	0.998505	−	0.0546521i	$-0.0174050\pi$
$953$	3.28613	+	12.2640i	0.106448	+	0.397271i	−0.892057	+	0.451923i	$0.850738\pi$
$954$	−2.49867	−	2.49867i	−0.0808974	−	0.0808974i
$955$	28.3623	+	3.66952i	0.917781	+	0.118743i
$956$	−21.4528	+	5.74827i	−0.693835	+	0.185912i
$957$	−6.22805			−0.201324
$958$	−11.2332	+	3.00994i	−0.362930	+	0.0972467i
$959$	−2.36124	−	4.08978i	−0.0762483	−	0.132066i
$960$	2.21628	−	0.296818i	0.0715301	−	0.00957975i
$961$			11.7817i			0.380055i
$962$	−0.813713	−	0.0102225i	−0.0262352	−	0.000329585i
$963$	−4.95978	−	4.95978i	−0.159827	−	0.159827i
$964$	6.47591	−	24.1684i	0.208575	−	0.778412i
$965$	3.92550	+	2.99823i	0.126366	+	0.0965165i
$966$	−0.0825761	−	0.0476753i	−0.00265684	−	0.00153393i
$967$		−	27.7803i		−	0.893353i	−0.894695	−	0.446677i	$-0.852607\pi$
$967$		−	27.7803i		−	0.893353i	0.894695	−	0.446677i	$-0.147393\pi$
$968$	5.13043	−	8.88617i	0.164898	−	0.285612i
$969$	0.0610687	+	0.227911i	0.00196181	+	0.00732157i
$970$	5.41437	+	12.9893i	0.173845	+	0.417061i
$971$	−0.0689099	+	0.119355i	−0.00221142	+	0.00383030i	−0.867129	−	0.498084i	$-0.834037\pi$
$971$	−0.0689099	+	0.119355i	−0.00221142	+	0.00383030i	0.864918	+	0.501914i	$0.167371\pi$
$972$	0.258819	−	0.965926i	0.00830162	−	0.0309821i
$973$	−1.21461	+	0.701257i	−0.0389387	+	0.0224813i
$974$	9.14019			0.292871
$975$	−15.5390	−	9.13994i	−0.497647	−	0.292712i
$976$	−14.4355			−0.462068
$977$	−21.9169	+	12.6538i	−0.701185	+	0.404829i	−0.807789	−	0.589472i	$-0.799336\pi$
$977$	−21.9169	+	12.6538i	−0.701185	+	0.404829i	0.106604	+	0.994302i	$0.466002\pi$
$978$	−5.90549	+	22.0396i	−0.188837	+	0.704748i
$979$	6.63536	−	11.4928i	0.212067	−	0.367311i
$980$	−5.78988	−	13.8901i	−0.184951	−	0.443705i
$981$	2.28228	+	8.51759i	0.0728677	+	0.271946i
$982$	−3.97792	+	6.88995i	−0.126940	+	0.219867i
$983$			19.2981i			0.615512i	0.951465	+	0.307756i	$0.0995781\pi$
$983$			19.2981i			0.615512i	−0.951465	+	0.307756i	$0.900422\pi$
$984$	0.0251522	+	0.0145216i	0.000801822	+	0.000462932i
$985$	21.5726	+	16.4768i	0.687361	+	0.524995i
$986$	7.92888	−	29.5910i	0.252507	−	0.942369i
$987$	−2.03487	−	2.03487i	−0.0647708	−	0.0647708i
$988$	−0.0496222	−	0.194956i	−0.00157869	−	0.00620238i
$989$			0.879973i			0.0279815i
$990$	1.90540	−	0.255183i	0.0605577	−	0.00811025i
$991$	8.95513	+	15.5107i	0.284469	+	0.492715i	0.972480	−	0.232985i	$-0.0748493\pi$
$991$	8.95513	+	15.5107i	0.284469	+	0.492715i	−0.688011	+	0.725700i	$0.741516\pi$
$992$	−4.23449	+	1.13463i	−0.134445	+	0.0360245i
$993$	20.3090			0.644486
$994$	−3.45397	+	0.925487i	−0.109553	+	0.0293547i
$995$	−9.03911	−	1.16948i	−0.286559	−	0.0370751i
$996$	3.41603	+	3.41603i	0.108241	+	0.108241i
$997$	−9.71246	−	36.2474i	−0.307597	−	1.14797i	−0.930687	−	0.365816i	$-0.880790\pi$
$997$	−9.71246	−	36.2474i	−0.307597	−	1.14797i	0.623090	−	0.782150i	$-0.285877\pi$
$998$	−29.9548	−	8.02635i	−0.948201	−	0.254070i
$999$	−0.218011	−	0.0584158i	−0.00689755	−	0.00184819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bd.b.223.3	yes	16
5.2	odd	4		390.2.bn.b.67.2	yes	16
13.7	odd	12		390.2.bn.b.163.2	yes	16
65.7	even	12	inner	390.2.bd.b.7.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.b.7.3	✓	16	65.7	even	12	inner
390.2.bd.b.223.3	yes	16	1.1	even	1	trivial
390.2.bn.b.67.2	yes	16	5.2	odd	4
390.2.bn.b.163.2	yes	16	13.7	odd	12

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.860320 - 2.06394i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.259847 - 0.450069i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.860320 - 2.06394i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.259847 - 0.450069i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.77703 - 1.35727i) q^{10} +(0.222514 - 0.830435i) q^{11} +(-0.707107 - 0.707107i) q^{12} +(-3.14490 + 1.76341i) q^{13} -0.519695i q^{14} +(-2.21628 + 0.296818i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.08479 - 1.09452i) q^{17} -1.00000 q^{18} +(-0.0538940 + 0.0144409i) q^{19} +(-2.21758 - 0.286912i) q^{20} +(-0.367480 - 0.367480i) q^{21} +(-0.222514 - 0.830435i) q^{22} +(0.177222 + 0.0474866i) q^{23} +(-0.965926 - 0.258819i) q^{24} +(-3.51970 + 3.55130i) q^{25} +(-1.84186 + 3.09961i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.259847 - 0.450069i) q^{28} +(6.27365 - 3.62210i) q^{29} +(-1.77095 + 1.36519i) q^{30} +(3.09986 - 3.09986i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.744548 - 0.429865i) q^{33} +(2.99027 - 2.99027i) q^{34} +(-1.15247 - 0.149107i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(0.112851 + 0.195463i) q^{37} +(-0.0394531 + 0.0394531i) q^{38} +(0.889363 + 3.49414i) q^{39} +(-2.06394 + 0.860320i) q^{40} +(-0.0280536 - 0.00751694i) q^{41} +(-0.501987 - 0.134507i) q^{42} +(1.24134 + 4.63274i) q^{43} +(-0.607921 - 0.607921i) q^{44} +(-0.286912 + 2.21758i) q^{45} +(0.177222 - 0.0474866i) q^{46} +5.53738 q^{47} +(-0.965926 + 0.258819i) q^{48} +(3.36496 + 5.82828i) q^{49} +(-1.27250 + 4.83536i) q^{50} -4.22888i q^{51} +(-0.0452920 + 3.60527i) q^{52} +(2.49867 + 2.49867i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(-1.90540 + 0.255183i) q^{55} +(-0.450069 - 0.259847i) q^{56} +0.0557952i q^{57} +(3.62210 - 6.27365i) q^{58} +(1.31167 + 4.89521i) q^{59} +(-0.851088 + 2.06776i) q^{60} +(7.21773 - 12.5015i) q^{61} +(1.13463 - 4.23449i) q^{62} +(-0.450069 + 0.259847i) q^{63} -1.00000 q^{64} +(6.34519 + 4.97379i) q^{65} -0.859730 q^{66} +(-11.8766 + 6.85698i) q^{67} +(1.09452 - 4.08479i) q^{68} +(0.0917371 - 0.158893i) q^{69} +(-1.07262 + 0.447104i) q^{70} +(-1.78083 - 6.64614i) q^{71} +(-0.500000 + 0.866025i) q^{72} +2.40525i q^{73} +(0.195463 + 0.112851i) q^{74} +(2.51932 + 4.31891i) q^{75} +(-0.0144409 + 0.0538940i) q^{76} +(-0.315933 - 0.315933i) q^{77} +(2.51728 + 2.58133i) q^{78} +16.0201i q^{79} +(-1.35727 + 1.77703i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.0280536 + 0.00751694i) q^{82} -4.83100 q^{83} +(-0.501987 + 0.134507i) q^{84} +(-5.77324 - 7.48913i) q^{85} +(3.39140 + 3.39140i) q^{86} +(-1.87494 - 6.99735i) q^{87} +(-0.830435 - 0.222514i) q^{88} +(14.9100 + 3.99511i) q^{89} +(0.860320 + 2.06394i) q^{90} +(-0.0235380 + 1.87364i) q^{91} +(0.129736 - 0.129736i) q^{92} +(-2.19193 - 3.79654i) q^{93} +(4.79551 - 2.76869i) q^{94} +(0.0761711 + 0.0988102i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(-5.45027 - 3.14672i) q^{97} +(5.82828 + 3.36496i) q^{98} +(-0.607921 + 0.607921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7	\( 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7} + 12 q^{11} - 8 q^{13} + 12 q^{15} - 8 q^{16} + 16 q^{17} - 16 q^{18} + 4 q^{19} - 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{25} + 4 q^{26} - 4 q^{28} + 48 q^{29} - 8 q^{30} + 16 q^{31} + 20 q^{34} + 12 q^{35} + 20 q^{37} - 4 q^{38} - 4 q^{39} - 12 q^{41} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 64 q^{47} + 4 q^{49} + 16 q^{50} - 16 q^{52} + 32 q^{53} - 44 q^{55} - 24 q^{56} - 12 q^{58} - 4 q^{59} + 12 q^{60} + 4 q^{61} - 20 q^{62} - 24 q^{63} - 16 q^{64} - 8 q^{65} + 32 q^{66} - 36 q^{67} - 4 q^{68} - 4 q^{69} - 36 q^{71} - 8 q^{72} - 12 q^{74} + 8 q^{76} - 4 q^{77} - 12 q^{78} - 8 q^{80} + 8 q^{81} - 12 q^{82} + 24 q^{83} - 52 q^{85} + 16 q^{86} - 12 q^{87} + 24 q^{89} - 4 q^{90} - 8 q^{92} - 36 q^{94} - 44 q^{95} + 60 q^{97} + 12 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7 + 12 * q^11 - 8 * q^13 + 12 * q^15 - 8 * q^16 + 16 * q^17 - 16 * q^18 + 4 * q^19 - 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^25 + 4 * q^26 - 4 * q^28 + 48 * q^29 - 8 * q^30 + 16 * q^31 + 20 * q^34 + 12 * q^35 + 20 * q^37 - 4 * q^38 - 4 * q^39 - 12 * q^41 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 64 * q^47 + 4 * q^49 + 16 * q^50 - 16 * q^52 + 32 * q^53 - 44 * q^55 - 24 * q^56 - 12 * q^58 - 4 * q^59 + 12 * q^60 + 4 * q^61 - 20 * q^62 - 24 * q^63 - 16 * q^64 - 8 * q^65 + 32 * q^66 - 36 * q^67 - 4 * q^68 - 4 * q^69 - 36 * q^71 - 8 * q^72 - 12 * q^74 + 8 * q^76 - 4 * q^77 - 12 * q^78 - 8 * q^80 + 8 * q^81 - 12 * q^82 + 24 * q^83 - 52 * q^85 + 16 * q^86 - 12 * q^87 + 24 * q^89 - 4 * q^90 - 8 * q^92 - 36 * q^94 - 44 * q^95 + 60 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more