LMFDB - Embedded newform 690.2.m.f.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 36 x^{18} - 172 x^{17} + 691 x^{16} - 2342 x^{15} + 7870 x^{14} - 23240 x^{13} + \cdots + 123904 $ x^20 - 6x^19 + 36x^18 - 172x^17 + 691x^16 - 2342x^15 + 7870x^14 - 23240x^13 + 63837x^12 - 154607x^11 + 334467x^10 - 664202x^9 + 1099560x^8 - 1331000x^7 + 1218096x^6 + 395648x^5 - 588544x^4 + 665984x^3 + 2323200x^2 + 991232*x + 123904
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			211.1
Root			$2.64328 + 1.69874i$ of defining polynomial
Character	$\chi$	$=$	690.211
Dual form			690.2.m.f.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.0123285 + 0.0857467i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.0123285 + 0.0857467i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-0.142315 + 0.989821i) q^{10} +(-0.0149014 + 0.0326296i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(0.472833 - 3.28862i) q^{13} +(0.0728765 - 0.0468349i) q^{14} +(-0.959493 - 0.281733i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(0.115248 + 0.133003i) q^{17} +(-0.841254 - 0.540641i) q^{18} +(4.96186 - 5.72629i) q^{19} +(0.959493 - 0.281733i) q^{20} +(0.0359868 + 0.0788000i) q^{21} +0.0358712 q^{22} +(-3.25873 - 3.51862i) q^{23} +1.00000 q^{24} +(0.415415 + 0.909632i) q^{25} +(-3.18786 + 0.936040i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-0.0728765 - 0.0468349i) q^{28} +(-3.67108 - 4.23665i) q^{29} +(0.142315 + 0.989821i) q^{30} +(0.778319 + 0.228535i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(-0.00510500 + 0.0355061i) q^{33} +(0.0731080 - 0.160084i) q^{34} +(0.0359868 - 0.0788000i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(4.18076 - 2.68681i) q^{37} +(-7.27005 - 2.13468i) q^{38} +(-0.472833 - 3.28862i) q^{39} +(-0.654861 - 0.755750i) q^{40} +(2.07374 + 1.33271i) q^{41} +(0.0567296 - 0.0654694i) q^{42} +(-2.62056 + 0.769467i) q^{43} +(-0.0149014 - 0.0326296i) q^{44} -1.00000 q^{45} +(-1.84693 + 4.42593i) q^{46} -7.00973 q^{47} +(-0.415415 - 0.909632i) q^{48} +(6.70925 - 1.97001i) q^{49} +(0.654861 - 0.755750i) q^{50} +(0.148050 + 0.0951463i) q^{51} +(2.17574 + 2.51093i) q^{52} +(-0.706993 - 4.91724i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(0.0301768 - 0.0193934i) q^{55} +(-0.0123285 + 0.0857467i) q^{56} +(3.14759 - 6.89226i) q^{57} +(-2.32877 + 5.09929i) q^{58} +(0.652267 - 4.53662i) q^{59} +(0.841254 - 0.540641i) q^{60} +(0.338503 + 0.0993936i) q^{61} +(-0.115443 - 0.802920i) q^{62} +(0.0567296 + 0.0654694i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-2.17574 + 2.51093i) q^{65} +(0.0344182 - 0.0101061i) q^{66} +(2.11154 + 4.62363i) q^{67} -0.175988 q^{68} +(-4.11803 - 2.45800i) q^{69} -0.0866285 q^{70} +(4.92817 + 10.7912i) q^{71} +(0.959493 - 0.281733i) q^{72} +(-5.10207 + 5.88810i) q^{73} +(-4.18076 - 2.68681i) q^{74} +(0.654861 + 0.755750i) q^{75} +(1.07832 + 7.49985i) q^{76} +(-0.00298159 - 0.000875475i) q^{77} +(-2.79502 + 1.79625i) q^{78} +(-1.07167 + 7.45363i) q^{79} +(-0.415415 + 0.909632i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.350814 - 2.43997i) q^{82} +(6.46184 - 4.15277i) q^{83} +(-0.0831194 - 0.0244061i) q^{84} +(-0.0250457 - 0.174197i) q^{85} +(1.78855 + 2.06410i) q^{86} +(-4.71597 - 3.03077i) q^{87} +(-0.0234906 + 0.0271096i) q^{88} +(1.10436 - 0.324268i) q^{89} +(0.415415 + 0.909632i) q^{90} +0.287818 q^{91} +(4.79321 - 0.158572i) q^{92} +0.811177 q^{93} +(2.91195 + 6.37628i) q^{94} +(-7.27005 + 2.13468i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(-2.62704 - 1.68830i) q^{97} +(-4.57911 - 5.28458i) q^{98} +(0.00510500 + 0.0355061i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + 18 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 13 * q^21 + 26 * q^22 + 20 * q^24 - 2 * q^25 + 9 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 + 8 * q^31 + 2 * q^32 + 4 * q^33 + 13 * q^34 + 13 * q^35 - 2 * q^36 + 16 * q^37 - 15 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 + 9 * q^42 - 16 * q^43 + 18 * q^44 - 20 * q^45 - 34 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 - 9 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 7 * q^55 + 2 * q^56 + 29 * q^57 + 16 * q^58 + 25 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 9 * q^63 - 2 * q^64 - 2 * q^65 - 15 * q^66 + 20 * q^67 - 2 * q^68 - 22 * q^69 - 2 * q^70 - q^71 + 2 * q^72 - q^73 - 16 * q^74 + 2 * q^75 + 4 * q^76 + 53 * q^77 + 2 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 - 25 * q^82 + 9 * q^83 - 9 * q^84 - 9 * q^85 - 28 * q^86 - 6 * q^87 - 7 * q^88 - 31 * q^89 - 2 * q^90 - 26 * q^91 + 11 * q^92 - 30 * q^93 + q^94 - 15 * q^95 - 2 * q^96 - 35 * q^97 - 5 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{11}\right)$

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 $

$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$	−0.654861	+	0.755750i	−0.327430	+	0.377875i
$5$	−0.841254	−	0.540641i	−0.376220	−	0.241782i
$5$	−0.841254	−	0.540641i	−0.376220	−	0.241782i
$6$	−0.654861	−	0.755750i	−0.267346	−	0.308533i
$7$	0.0123285	+	0.0857467i	0.00465974	+	0.0324092i	0.992019	−	0.126091i	$-0.0402432\pi$
$7$	0.0123285	+	0.0857467i	0.00465974	+	0.0324092i	−0.987359	+	0.158500i	$0.949334\pi$
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	−0.142315	+	0.989821i	−0.0450039	+	0.313009i
$11$	−0.0149014	+	0.0326296i	−0.00449295	+	0.00983819i	−0.911865	−	0.410490i	$-0.865358\pi$
$11$	−0.0149014	+	0.0326296i	−0.00449295	+	0.00983819i	0.907372	+	0.420328i	$0.138085\pi$
$12$	−0.415415	+	0.909632i	−0.119920	+	0.262588i
$13$	0.472833	−	3.28862i	0.131140	−	0.912100i	−0.812931	−	0.582359i	$-0.802130\pi$
$13$	0.472833	−	3.28862i	0.131140	−	0.912100i	0.944072	−	0.329741i	$-0.106961\pi$
$14$	0.0728765	−	0.0468349i	0.0194771	−	0.0125172i
$15$	−0.959493	−	0.281733i	−0.247740	−	0.0727430i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	0.115248	+	0.133003i	0.0279516	+	0.0322579i	0.769553	−	0.638583i	$-0.220479\pi$
$17$	0.115248	+	0.133003i	0.0279516	+	0.0322579i	−0.741602	+	0.670841i	$0.765933\pi$
$18$	−0.841254	−	0.540641i	−0.198285	−	0.127430i
$19$	4.96186	−	5.72629i	1.13833	−	1.31370i	0.195394	−	0.980725i	$-0.437401\pi$
$19$	4.96186	−	5.72629i	1.13833	−	1.31370i	0.942935	−	0.332977i	$-0.108053\pi$
$20$	0.959493	−	0.281733i	0.214549	−	0.0629973i
$21$	0.0359868	+	0.0788000i	0.00785296	+	0.0171956i
$22$	0.0358712			0.00764777
$23$	−3.25873	−	3.51862i	−0.679491	−	0.733684i
$23$	−3.25873	−	3.51862i	−0.679491	−	0.733684i
$24$	1.00000			0.204124
$25$	0.415415	+	0.909632i	0.0830830	+	0.181926i
$26$	−3.18786	+	0.936040i	−0.625191	+	0.183573i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	−0.0728765	−	0.0468349i	−0.0137724	−	0.00885096i
$29$	−3.67108	−	4.23665i	−0.681702	−	0.786726i	0.304458	−	0.952526i	$-0.401525\pi$
$29$	−3.67108	−	4.23665i	−0.681702	−	0.786726i	−0.986159	+	0.165800i	$0.946979\pi$
$30$	0.142315	+	0.989821i	0.0259830	+	0.180716i
$31$	0.778319	+	0.228535i	0.139790	+	0.0410461i	0.350879	−	0.936421i	$-0.385883\pi$
$31$	0.778319	+	0.228535i	0.139790	+	0.0410461i	−0.211089	+	0.977467i	$0.567701\pi$
$32$	−0.841254	+	0.540641i	−0.148714	+	0.0955727i
$33$	−0.00510500	+	0.0355061i	−0.000888667	+	0.00618082i
$34$	0.0731080	−	0.160084i	0.0125379	−	0.0274542i
$35$	0.0359868	−	0.0788000i	0.00608288	−	0.0133196i
$36$	−0.142315	+	0.989821i	−0.0237191	+	0.164970i
$37$	4.18076	−	2.68681i	0.687313	−	0.441709i	−0.149817	−	0.988714i	$-0.547868\pi$
$37$	4.18076	−	2.68681i	0.687313	−	0.441709i	0.837129	+	0.547005i	$0.184232\pi$
$38$	−7.27005	−	2.13468i	−1.17936	−	0.346291i
$39$	−0.472833	−	3.28862i	−0.0757138	−	0.526601i
$40$	−0.654861	−	0.755750i	−0.103543	−	0.119494i
$41$	2.07374	+	1.33271i	0.323863	+	0.208134i	0.692462	−	0.721454i	$-0.256526\pi$
$41$	2.07374	+	1.33271i	0.323863	+	0.208134i	−0.368599	+	0.929589i	$0.620162\pi$
$42$	0.0567296	−	0.0654694i	0.00875357	−	0.0101022i
$43$	−2.62056	+	0.769467i	−0.399632	+	0.117343i	−0.475372	−	0.879785i	$-0.657686\pi$
$43$	−2.62056	+	0.769467i	−0.399632	+	0.117343i	0.0757395	+	0.997128i	$0.475868\pi$
$44$	−0.0149014	−	0.0326296i	−0.00224648	−	0.00491910i
$45$	−1.00000			−0.149071
$46$	−1.84693	+	4.42593i	−0.272315	+	0.652568i
$47$	−7.00973			−1.02247			−0.511237	−	0.859440i	$-0.670813\pi$
$47$	−7.00973			−1.02247			−0.511237	+	0.859440i	$0.670813\pi$
$48$	−0.415415	−	0.909632i	−0.0599600	−	0.131294i
$49$	6.70925	−	1.97001i	0.958464	−	0.281431i
$50$	0.654861	−	0.755750i	0.0926113	−	0.106879i
$51$	0.148050	+	0.0951463i	0.0207312	+	0.0133231i
$52$	2.17574	+	2.51093i	0.301720	+	0.348204i
$53$	−0.706993	−	4.91724i	−0.0971130	−	0.675435i	−0.978983	−	0.203943i	$-0.934624\pi$
$53$	−0.706993	−	4.91724i	−0.0971130	−	0.675435i	0.881870	−	0.471493i	$-0.156285\pi$
$54$	−0.959493	−	0.281733i	−0.130570	−	0.0383389i
$55$	0.0301768	−	0.0193934i	0.00406904	−	0.00261501i
$56$	−0.0123285	+	0.0857467i	−0.00164747	+	0.0114584i
$57$	3.14759	−	6.89226i	0.416908	−	0.912902i
$58$	−2.32877	+	5.09929i	−0.305782	+	0.669570i
$59$	0.652267	−	4.53662i	0.0849179	−	0.590617i	−0.902284	−	0.431142i	$-0.858111\pi$
$59$	0.652267	−	4.53662i	0.0849179	−	0.590617i	0.987202	−	0.159475i	$-0.0509802\pi$
$60$	0.841254	−	0.540641i	0.108605	−	0.0697964i
$61$	0.338503	+	0.0993936i	0.0433409	+	0.0127260i	0.303331	−	0.952885i	$-0.401901\pi$
$61$	0.338503	+	0.0993936i	0.0433409	+	0.0127260i	−0.259990	+	0.965611i	$0.583719\pi$
$62$	−0.115443	−	0.802920i	−0.0146612	−	0.101971i
$63$	0.0567296	+	0.0654694i	0.00714726	+	0.00824838i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−2.17574	+	2.51093i	−0.269867	+	0.311443i
$66$	0.0344182	−	0.0101061i	0.00423658	−	0.00124397i
$67$	2.11154	+	4.62363i	0.257966	+	0.564866i	0.993657	−	0.112451i	$-0.0358700\pi$
$67$	2.11154	+	4.62363i	0.257966	+	0.564866i	−0.735692	+	0.677317i	$0.763143\pi$
$68$	−0.175988			−0.0213417
$69$	−4.11803	−	2.45800i	−0.495753	−	0.295909i
$70$	−0.0866285			−0.0103541
$71$	4.92817	+	10.7912i	0.584867	+	1.28068i	0.938495	+	0.345293i	$0.112221\pi$
$71$	4.92817	+	10.7912i	0.584867	+	1.28068i	−0.353628	+	0.935386i	$0.615052\pi$
$72$	0.959493	−	0.281733i	0.113077	−	0.0332025i
$73$	−5.10207	+	5.88810i	−0.597152	+	0.689150i	−0.971202	−	0.238258i	$-0.923423\pi$
$73$	−5.10207	+	5.88810i	−0.597152	+	0.689150i	0.374050	+	0.927409i	$0.377969\pi$
$74$	−4.18076	−	2.68681i	−0.486003	−	0.312335i
$75$	0.654861	+	0.755750i	0.0756168	+	0.0872664i
$76$	1.07832	+	7.49985i	0.123691	+	0.860292i
$77$	−0.00298159		0.000875475i	−0.000339784		9.97696e-5i
$78$	−2.79502	+	1.79625i	−0.316473	+	0.203385i
$79$	−1.07167	+	7.45363i	−0.120572	+	0.838598i	0.836338	+	0.548214i	$0.184692\pi$
$79$	−1.07167	+	7.45363i	−0.120572	+	0.838598i	−0.956910	+	0.290384i	$0.906217\pi$
$80$	−0.415415	+	0.909632i	−0.0464448	+	0.101700i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	0.350814	−	2.43997i	0.0387409	−	0.269449i
$83$	6.46184	−	4.15277i	0.709279	−	0.455826i	−0.135614	−	0.990762i	$-0.543301\pi$
$83$	6.46184	−	4.15277i	0.709279	−	0.455826i	0.844893	+	0.534936i	$0.179664\pi$
$84$	−0.0831194	−	0.0244061i	−0.00906907	−	0.00266292i
$85$	−0.0250457	−	0.174197i	−0.00271659	−	0.0188943i
$86$	1.78855	+	2.06410i	0.192865	+	0.222578i
$87$	−4.71597	−	3.03077i	−0.505605	−	0.324933i
$88$	−0.0234906	+	0.0271096i	−0.00250411	+	0.00288990i
$89$	1.10436	−	0.324268i	0.117061	−	0.0343723i	−0.222677	−	0.974892i	$-0.571480\pi$
$89$	1.10436	−	0.324268i	0.117061	−	0.0343723i	0.339739	+	0.940520i	$0.389661\pi$
$90$	0.415415	+	0.909632i	0.0437886	+	0.0958836i
$91$	0.287818			0.0301715
$92$	4.79321	−	0.158572i	0.499727	−	0.0165323i
$93$	0.811177			0.0841151
$94$	2.91195	+	6.37628i	0.300345	+	0.657663i
$95$	−7.27005	+	2.13468i	−0.745892	+	0.219014i
$96$	−0.654861	+	0.755750i	−0.0668364	+	0.0771334i
$97$	−2.62704	−	1.68830i	−0.266736	−	0.171421i	0.400436	−	0.916325i	$-0.368859\pi$
$97$	−2.62704	−	1.68830i	−0.266736	−	0.171421i	−0.667171	+	0.744904i	$0.732495\pi$
$98$	−4.57911	−	5.28458i	−0.462560	−	0.533823i
$99$	0.00510500	+	0.0355061i	0.000513072	+	0.00356850i
$100$	−0.959493	−	0.281733i	−0.0959493	−	0.0281733i
$101$	−9.22397	+	5.92789i	−0.917820	+	0.589847i	−0.912024	−	0.410136i	$-0.865481\pi$
$101$	−9.22397	+	5.92789i	−0.917820	+	0.589847i	−0.00579553	+	0.999983i	$0.501845\pi$
$102$	0.0250457	−	0.174197i	0.00247989	−	0.0172480i
$103$	5.62705	−	12.3215i	0.554450	−	1.21408i	−0.400222	−	0.916418i	$-0.631067\pi$
$103$	5.62705	−	12.3215i	0.554450	−	1.21408i	0.954672	−	0.297658i	$-0.0962056\pi$
$104$	1.38019	−	3.02220i	0.135339	−	0.296351i
$105$	0.0123285	−	0.0857467i	0.00120314	−	0.00836803i
$106$	−4.17919	+	2.68580i	−0.405919	+	0.260868i
$107$	−6.25406	−	1.83636i	−0.604602	−	0.177527i	−0.0349171	−	0.999390i	$-0.511117\pi$
$107$	−6.25406	−	1.83636i	−0.604602	−	0.177527i	−0.569685	+	0.821863i	$0.692935\pi$
$108$	0.142315	+	0.989821i	0.0136943	+	0.0952456i
$109$	4.29273	+	4.95407i	0.411169	+	0.474514i	0.923126	−	0.384497i	$-0.125625\pi$
$109$	4.29273	+	4.95407i	0.411169	+	0.474514i	−0.511958	+	0.859011i	$0.671080\pi$
$110$	−0.0301768	−	0.0193934i	−0.00287724	−	0.00184909i
$111$	3.25445	−	3.75583i	0.308898	−	0.356488i
$112$	0.0831194	−	0.0244061i	0.00785405	−	0.00230616i
$113$	−0.599677	−	1.31311i	−0.0564128	−	0.123527i	0.879326	−	0.476220i	$-0.157993\pi$
$113$	−0.599677	−	1.31311i	−0.0564128	−	0.123527i	−0.935739	+	0.352693i	$0.885266\pi$
$114$	−7.57697			−0.709648
$115$	0.839103	+	4.72185i	0.0782468	+	0.440315i
$116$	5.60589			0.520494
$117$	−1.38019	−	3.02220i	−0.127599	−	0.279402i
$118$	−4.39761	+	1.29126i	−0.404833	+	0.118870i
$119$	−0.00998373	+	0.0115218i	−0.000915207	+	0.00105620i
$120$	−0.841254	−	0.540641i	−0.0767956	−	0.0493535i
$121$	7.20263	+	8.31227i	0.654784	+	0.755661i
$122$	−0.0502078	−	0.349203i	−0.00454560	−	0.0316154i
$123$	2.36520	+	0.694487i	0.213263	+	0.0626198i
$124$	−0.682405	+	0.438555i	−0.0612818	+	0.0393834i
$125$	0.142315	−	0.989821i	0.0127290	−	0.0885323i
$126$	0.0359868	−	0.0788000i	0.00320596	−	0.00702007i
$127$	4.92683	−	10.7883i	0.437185	−	0.957302i	−0.554921	−	0.831903i	$-0.687252\pi$
$127$	4.92683	−	10.7883i	0.437185	−	0.957302i	0.992106	−	0.125399i	$-0.0400212\pi$
$128$	0.142315	−	0.989821i	0.0125790	−	0.0874887i
$129$	−2.29763	+	1.47660i	−0.202295	+	0.130007i
$130$	3.18786	+	0.936040i	0.279594	+	0.0820961i
$131$	2.46138	+	17.1193i	0.215052	+	1.49572i	0.755950	+	0.654629i	$0.227175\pi$
$131$	2.46138	+	17.1193i	0.215052	+	1.49572i	−0.540899	+	0.841088i	$0.681916\pi$
$132$	−0.0234906	−	0.0271096i	−0.00204460	−	0.00235959i
$133$	0.552183	+	0.354867i	0.0478804	+	0.0307708i
$134$	3.32863	−	3.84145i	0.287550	−	0.331851i
$135$	−0.959493	+	0.281733i	−0.0825800	+	0.0242477i
$136$	0.0731080	+	0.160084i	0.00626896	+	0.0137271i
$137$	−7.24055			−0.618602			−0.309301	−	0.950964i	$-0.600095\pi$
$137$	−7.24055			−0.618602			−0.309301	+	0.950964i	$0.600095\pi$
$138$	−0.525186	+	4.76699i	−0.0447068	+	0.405793i
$139$	6.17673			0.523904			0.261952	−	0.965081i	$-0.415634\pi$
$139$	6.17673			0.523904			0.261952	+	0.965081i	$0.415634\pi$
$140$	0.0359868	+	0.0788000i	0.00304144	+	0.00665982i
$141$	−6.72579	+	1.97487i	−0.566414	+	0.166314i
$142$	7.76878	−	8.96565i	0.651942	−	0.752381i
$143$	0.100261	+	0.0644336i	0.00838421	+	0.00538820i
$144$	−0.654861	−	0.755750i	−0.0545717	−	0.0629791i
$145$	0.797801	+	5.54883i	0.0662538	+	0.460805i
$146$	7.47548	+	2.19500i	0.618675	+	0.181659i
$147$	5.88246	−	3.78043i	0.485177	−	0.311804i
$148$	−0.707259	+	4.91909i	−0.0581363	+	0.404347i
$149$	5.66207	−	12.3982i	0.463855	−	1.01570i	−0.522737	−	0.852494i	$-0.675089\pi$
$149$	5.66207	−	12.3982i	0.463855	−	1.01570i	0.986592	−	0.163207i	$-0.0521837\pi$
$150$	0.415415	−	0.909632i	0.0339185	−	0.0742711i
$151$	−2.39215	+	16.6378i	−0.194670	+	1.35396i	0.624775	+	0.780805i	$0.285191\pi$
$151$	−2.39215	+	16.6378i	−0.194670	+	1.35396i	−0.819446	+	0.573157i	$0.805719\pi$
$152$	6.37415	−	4.09642i	0.517012	−	0.332264i
$153$	0.168859	+	0.0495815i	0.0136515	+	0.00400843i
$154$	0.000442239		0.00307584i	3.56366e−5		0.000247858i
$155$	−0.531208	−	0.613047i	−0.0426676	−	0.0492411i
$156$	2.79502	+	1.79625i	0.223780	+	0.143815i
$157$	−5.83029	+	6.72851i	−0.465307	+	0.536993i	−0.939100	−	0.343643i	$-0.888339\pi$
$157$	−5.83029	+	6.72851i	−0.465307	+	0.536993i	0.473793	+	0.880636i	$0.342884\pi$
$158$	7.22524	−	2.12152i	0.574810	−	0.168779i
$159$	−2.06370	−	4.51888i	−0.163662	−	0.358370i
$160$	1.00000			0.0790569
$161$	0.261535	−	0.322805i	0.0206119	−	0.0254406i
$162$	−1.00000			−0.0785674
$163$	8.28159	+	18.1341i	0.648664	+	1.42038i	0.892719	+	0.450614i	$0.148795\pi$
$163$	8.28159	+	18.1341i	0.648664	+	1.42038i	−0.244055	+	0.969761i	$0.578478\pi$
$164$	−2.36520	+	0.694487i	−0.184691	+	0.0542303i
$165$	0.0234906	−	0.0271096i	0.00182874	−	0.00211048i
$166$	−6.46184	−	4.15277i	−0.501536	−	0.322318i
$167$	12.0125	+	13.8632i	0.929558	+	1.07277i	0.997179	+	0.0750565i	$0.0239137\pi$
$167$	12.0125	+	13.8632i	0.929558	+	1.07277i	−0.0676208	+	0.997711i	$0.521541\pi$
$168$	0.0123285	+	0.0857467i	0.000951166	+	0.00661550i
$169$	1.88193	+	0.552586i	0.144764	+	0.0425066i
$170$	−0.148050	+	0.0951463i	−0.0113550	+	0.00729739i
$171$	1.07832	−	7.49985i	0.0824608	−	0.573528i
$172$	1.13458	−	2.48438i	0.0865109	−	0.189433i
$173$	4.47648	−	9.80212i	0.340340	−	0.745241i	−0.659640	−	0.751582i	$-0.729291\pi$
$173$	4.47648	−	9.80212i	0.340340	−	0.745241i	0.999980	+	0.00634085i	$0.00201837\pi$
$174$	−0.797801	+	5.54883i	−0.0604811	+	0.420656i
$175$	−0.0728765	+	0.0468349i	−0.00550895	+	0.00354039i
$176$	0.0344182	+	0.0101061i	0.00259437	+	0.000761775i
$177$	−0.652267	−	4.53662i	−0.0490274	−	0.340993i
$178$	−0.753730	−	0.869851i	−0.0564945	−	0.0651981i
$179$	13.5641	+	8.71713i	1.01383	+	0.651549i	0.938382	−	0.345600i	$-0.112325\pi$
$179$	13.5641	+	8.71713i	1.01383	+	0.651549i	0.0754487	+	0.997150i	$0.475961\pi$
$180$	0.654861	−	0.755750i	0.0488104	−	0.0563302i
$181$	21.9395	−	6.44202i	1.63075	−	0.478832i	0.666872	−	0.745172i	$-0.267633\pi$
$181$	21.9395	−	6.44202i	1.63075	−	0.478832i	0.963879	+	0.266341i	$0.0858147\pi$
$182$	−0.119564	−	0.261809i	−0.00886267	−	0.0194065i
$183$	0.352794			0.0260793
$184$	−2.13541	−	4.29418i	−0.157425	−	0.316571i
$185$	−4.96968			−0.365378
$186$	−0.336975	−	0.737873i	−0.0247082	−	0.0541034i
$187$	−0.00605718	+	0.00177855i	−0.000442945	+	0.000130060i
$188$	4.59040	−	5.29760i	0.334789	−	0.386367i
$189$	0.0728765	+	0.0468349i	0.00530099	+	0.00340674i
$190$	4.96186	+	5.72629i	0.359971	+	0.415429i
$191$	2.80546	+	19.5124i	0.202996	+	1.41187i	0.795331	+	0.606176i	$0.207297\pi$
$191$	2.80546	+	19.5124i	0.202996	+	1.41187i	−0.592335	+	0.805692i	$0.701794\pi$
$192$	0.959493	+	0.281733i	0.0692454	+	0.0203323i
$193$	−6.97727	+	4.48402i	−0.502235	+	0.322767i	−0.767110	−	0.641516i	$-0.778306\pi$
$193$	−6.97727	+	4.48402i	−0.502235	+	0.322767i	0.264875	+	0.964283i	$0.414669\pi$
$194$	−0.444417	+	3.09099i	−0.0319073	+	0.221920i
$195$	−1.38019	+	3.02220i	−0.0988376	+	0.216424i
$196$	−2.90479	+	6.36060i	−0.207485	+	0.454328i
$197$	0.734007	−	5.10513i	0.0522958	−	0.363726i	−0.946823	−	0.321755i	$-0.895727\pi$
$197$	0.734007	−	5.10513i	0.0522958	−	0.363726i	0.999119	−	0.0419707i	$-0.0133636\pi$
$198$	0.0301768	−	0.0193934i	0.00214457	−	0.00137823i
$199$	0.563797	+	0.165546i	0.0399665	+	0.0117352i	0.301655	−	0.953417i	$-0.402461\pi$
$199$	0.563797	+	0.165546i	0.0399665	+	0.0117352i	−0.261688	+	0.965152i	$0.584279\pi$
$200$	0.142315	+	0.989821i	0.0100632	+	0.0699909i
$201$	3.32863	+	3.84145i	0.234784	+	0.270955i
$202$	9.22397	+	5.92789i	0.648997	+	0.417085i
$203$	0.318020	−	0.367014i	0.0223206	−	0.0257594i
$204$	−0.168859	+	0.0495815i	−0.0118225	+	0.00347140i
$205$	−1.02402	−	2.24229i	−0.0715208	−	0.156609i
$206$	−13.5456			−0.943768
$207$	−4.64373	−	1.19825i	−0.322761	−	0.0832844i
$208$	−3.32244			−0.230370
$209$	0.112908	+	0.247234i	0.00780999	+	0.0171015i
$210$	−0.0831194	+	0.0244061i	−0.00573579	+	0.00168418i
$211$	−9.95243	+	11.4857i	−0.685154	+	0.790709i	−0.986667	−	0.162753i	$-0.947963\pi$
$211$	−9.95243	+	11.4857i	−0.685154	+	0.790709i	0.301513	+	0.953462i	$0.402508\pi$
$212$	4.17919	+	2.68580i	0.287028	+	0.184462i
$213$	7.76878	+	8.96565i	0.532308	+	0.614316i
$214$	0.927620	+	6.45174i	0.0634108	+	0.441032i
$215$	2.62056	+	0.769467i	0.178721	+	0.0524772i
$216$	0.841254	−	0.540641i	0.0572401	−	0.0367859i
$217$	−0.0100006	+	0.0695558i	−0.000678886	+	0.00472175i
$218$	2.72312	−	5.96280i	0.184433	−	0.403852i
$219$	−3.23653	+	7.08701i	−0.218704	+	0.478896i
$220$	−0.00510500	+	0.0355061i	−0.000344179	+	0.00239382i
$221$	0.491889	−	0.316118i	0.0330880	−	0.0212644i
$222$	−4.76837	−	1.40012i	−0.320032	−	0.0939699i
$223$	−0.571472	−	3.97467i	−0.0382686	−	0.266164i	0.961700	−	0.274105i	$-0.0883814\pi$
$223$	−0.571472	−	3.97467i	−0.0382686	−	0.266164i	−0.999968	+	0.00794079i	$0.997472\pi$
$224$	−0.0567296	−	0.0654694i	−0.00379041	−	0.00437436i
$225$	0.841254	+	0.540641i	0.0560836	+	0.0360427i
$226$	−0.945331	+	1.09097i	−0.0628825	+	0.0725703i
$227$	1.58539	−	0.465512i	0.105226	−	0.0308971i	−0.228696	−	0.973498i	$-0.573446\pi$
$227$	1.58539	−	0.465512i	0.105226	−	0.0308971i	0.333922	+	0.942601i	$0.391628\pi$
$228$	3.14759	+	6.89226i	0.208454	+	0.456451i
$229$	−8.93673			−0.590556			−0.295278	−	0.955411i	$-0.595412\pi$
$229$	−8.93673			−0.590556			−0.295278	+	0.955411i	$0.595412\pi$
$230$	3.94657	−	2.72480i	0.260229	−	0.179668i
$231$	−0.00310747			−0.000204456
$232$	−2.32877	−	5.09929i	−0.152891	−	0.334785i
$233$	5.38881	−	1.58230i	0.353032	−	0.103660i	−0.100408	−	0.994946i	$-0.532015\pi$
$233$	5.38881	−	1.58230i	0.353032	−	0.103660i	0.453440	+	0.891287i	$0.350197\pi$
$234$	−2.17574	+	2.51093i	−0.142232	+	0.164145i
$235$	5.89696	+	3.78975i	0.384676	+	0.247216i
$236$	3.00140	+	3.46380i	0.195375	+	0.225474i
$237$	1.07167	+	7.45363i	0.0696124	+	0.484165i
$238$	0.0146280	+	0.00429517i	0.000948194	+	0.000278415i
$239$	−18.7894	+	12.0752i	−1.21538	+	0.781079i	−0.981552	−	0.191198i	$-0.938763\pi$
$239$	−18.7894	+	12.0752i	−1.21538	+	0.781079i	−0.233832	+	0.972277i	$0.575127\pi$
$240$	−0.142315	+	0.989821i	−0.00918638	+	0.0638927i
$241$	9.57391	−	20.9639i	0.616710	−	1.35041i	−0.301178	−	0.953568i	$-0.597380\pi$
$241$	9.57391	−	20.9639i	0.616710	−	1.35041i	0.917888	−	0.396839i	$-0.129893\pi$
$242$	4.56903	−	10.0048i	0.293708	−	0.643132i
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$	−0.296789	+	0.190735i	−0.0190000	+	0.0122105i
$245$	−6.70925	−	1.97001i	−0.428638	−	0.125860i
$246$	−0.350814	−	2.43997i	−0.0223671	−	0.155567i
$247$	−16.4855	−	19.0253i	−1.04895	−	1.21055i
$248$	0.682405	+	0.438555i	0.0433328	+	0.0278483i
$249$	5.03012	−	5.80507i	0.318771	−	0.367881i
$250$	−0.959493	+	0.281733i	−0.0606837	+	0.0178183i
$251$	8.81737	+	19.3073i	0.556547	+	1.21867i	0.953657	+	0.300897i	$0.0972861\pi$
$251$	8.81737	+	19.3073i	0.556547	+	1.21867i	−0.397109	+	0.917771i	$0.629987\pi$
$252$	−0.0866285			−0.00545708
$253$	0.163371	−	0.0538984i	0.0102710	−	0.00338856i
$254$	−11.8600			−0.744164
$255$	−0.0731080	−	0.160084i	−0.00457820	−	0.0100249i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	11.1492	−	12.8669i	0.695470	−	0.802615i	−0.292663	−	0.956216i	$-0.594542\pi$
$257$	11.1492	−	12.8669i	0.695470	−	0.802615i	0.988133	+	0.153601i	$0.0490870\pi$
$258$	2.29763	+	1.47660i	0.143044	+	0.0919289i
$259$	0.281928	+	0.325362i	0.0175181	+	0.0202170i
$260$	−0.472833	−	3.28862i	−0.0293238	−	0.203952i
$261$	−5.37881	−	1.57936i	−0.332940	−	0.0977600i
$262$	14.5497	−	9.35054i	0.898885	−	0.577679i
$263$	0.732384	−	5.09384i	0.0451607	−	0.314100i	−0.954703	−	0.297562i	$-0.903827\pi$
$263$	0.732384	−	5.09384i	0.0451607	−	0.314100i	0.999863	−	0.0165379i	$-0.00526440\pi$
$264$	−0.0149014	+	0.0326296i	−0.000917120	+	0.00200821i
$265$	−2.06370	+	4.51888i	−0.126772	+	0.277593i
$266$	0.0934128	−	0.649701i	0.00572751	−	0.0398357i
$267$	0.968264	−	0.622266i	0.0592568	−	0.0380820i
$268$	−4.87707	−	1.43204i	−0.297914	−	0.0874756i
$269$	0.989705	+	6.88355i	0.0603434	+	0.419697i	0.997493	+	0.0707689i	$0.0225453\pi$
$269$	0.989705	+	6.88355i	0.0603434	+	0.419697i	−0.937149	+	0.348928i	$0.886546\pi$
$270$	0.654861	+	0.755750i	0.0398536	+	0.0459935i
$271$	−22.4822	−	14.4485i	−1.36570	−	0.877681i	−0.367078	−	0.930190i	$-0.619642\pi$
$271$	−22.4822	−	14.4485i	−1.36570	−	0.877681i	−0.998620	+	0.0525090i	$0.983278\pi$
$272$	0.115248	−	0.133003i	0.00698791	−	0.00806448i
$273$	0.276159	−	0.0810877i	0.0167139	−	0.00490765i
$274$	3.00783	+	6.58624i	0.181710	+	0.397889i
$275$	−0.0358712			−0.00216311
$276$	4.55438	−	1.50255i	0.274141	−	0.0904430i
$277$	−12.7252			−0.764585			−0.382292	−	0.924041i	$-0.624865\pi$
$277$	−12.7252			−0.764585			−0.382292	+	0.924041i	$0.624865\pi$
$278$	−2.56591	−	5.61855i	−0.153893	−	0.336978i
$279$	0.778319	−	0.228535i	0.0465967	−	0.0136820i
$280$	0.0567296	−	0.0654694i	0.00339024	−	0.00391255i
$281$	−24.6842	−	15.8635i	−1.47253	−	0.946340i	−0.997806	−	0.0662067i	$-0.978910\pi$
$281$	−24.6842	−	15.8635i	−1.47253	−	0.946340i	−0.474727	−	0.880133i	$-0.657453\pi$
$282$	4.59040	+	5.29760i	0.273354	+	0.315468i
$283$	1.30801	+	9.09741i	0.0777531	+	0.540785i	0.991050	+	0.133490i	$0.0426186\pi$
$283$	1.30801	+	9.09741i	0.0777531	+	0.540785i	−0.913297	+	0.407294i	$0.866472\pi$
$284$	−11.3827	−	3.34227i	−0.675440	−	0.198327i
$285$	−6.37415	+	4.09642i	−0.377572	+	0.242651i
$286$	0.0169611	−	0.117967i	0.00100293	−	0.00697553i
$287$	−0.0887095	+	0.194247i	−0.00523635	+	0.0114660i
$288$	−0.415415	+	0.909632i	−0.0244786	+	0.0536006i
$289$	2.41494	−	16.7963i	0.142056	−	0.988018i
$290$	4.71597	−	3.03077i	0.276931	−	0.177973i
$291$	−2.99628	−	0.879787i	−0.175645	−	0.0515740i
$292$	−1.10879	−	7.71177i	−0.0648868	−	0.451297i
$293$	0.328543	+	0.379158i	0.0191937	+	0.0221507i	0.765265	−	0.643715i	$-0.222608\pi$
$293$	0.328543	+	0.379158i	0.0191937	+	0.0221507i	−0.746072	+	0.665866i	$0.768062\pi$
$294$	−5.88246	−	3.78043i	−0.343072	−	0.220479i
$295$	−3.00140	+	3.46380i	−0.174748	+	0.201670i
$296$	4.76837	−	1.40012i	0.277156	−	0.0813803i
$297$	0.0149014	+	0.0326296i	0.000864669	+	0.00189336i
$298$	−13.6299			−0.789560
$299$	−13.1123	+	9.05300i	−0.758301	+	0.523549i
$300$	−1.00000			−0.0577350
$301$	−0.0982870	−	0.215218i	−0.00566517	−	0.0124050i
$302$	16.1280	−	4.73560i	0.928061	−	0.272503i
$303$	−7.18026	+	8.28646i	−0.412495	+	0.476045i
$304$	−6.37415	−	4.09642i	−0.365583	−	0.234946i
$305$	−0.231031	−	0.266624i	−0.0132288	−	0.0152668i
$306$	−0.0250457	−	0.174197i	−0.00143177	−	0.00995816i
$307$	−3.11324	−	0.914129i	−0.177682	−	0.0521721i	0.191681	−	0.981457i	$-0.438606\pi$
$307$	−3.11324	−	0.914129i	−0.177682	−	0.0521721i	−0.369363	+	0.929285i	$0.620424\pi$
$308$	0.00261417	−	0.00168002i	0.000148956	−	9.57283e-5i
$309$	1.92774	−	13.4077i	0.109665	−	0.762740i
$310$	−0.336975	+	0.737873i	−0.0191389	+	0.0419083i
$311$	−7.89387	+	17.2852i	−0.447620	+	0.980152i	0.542516	+	0.840045i	$0.317472\pi$
$311$	−7.89387	+	17.2852i	−0.447620	+	0.980152i	−0.990136	+	0.140106i	$0.955256\pi$
$312$	0.472833	−	3.28862i	0.0267689	−	0.186182i
$313$	9.67922	−	6.22046i	0.547102	−	0.351601i	−0.237709	−	0.971336i	$-0.576396\pi$
$313$	9.67922	−	6.22046i	0.547102	−	0.351601i	0.784811	+	0.619735i	$0.212760\pi$
$314$	8.54245	+	2.50829i	0.482079	+	0.141551i
$315$	−0.0123285	−	0.0857467i	−0.000694633	−	0.00483128i
$316$	−4.93128	−	5.69100i	−0.277406	−	0.320144i
$317$	−6.56031	−	4.21606i	−0.368464	−	0.236797i	0.343285	−	0.939231i	$-0.388460\pi$
$317$	−6.56031	−	4.21606i	−0.368464	−	0.236797i	−0.711749	+	0.702434i	$0.752097\pi$
$318$	−3.25322	+	3.75442i	−0.182432	+	0.210537i
$319$	0.192944	−	0.0566536i	0.0108028	−	0.00317199i
$320$	−0.415415	−	0.909632i	−0.0232224	−	0.0508500i
$321$	−6.51808			−0.363804
$322$	−0.402279	−	0.103803i	−0.0224181	−	0.00578471i
$323$	1.33346			0.0741955
$324$	0.415415	+	0.909632i	0.0230786	+	0.0505351i
$325$	3.18786	−	0.936040i	0.176831	−	0.0519221i
$326$	13.0551	−	15.0664i	0.723055	−	0.834450i
$327$	5.51457	+	3.54400i	0.304956	+	0.195983i
$328$	1.61427	+	1.86297i	0.0891331	+	0.102865i
$329$	−0.0864197	−	0.601062i	−0.00476447	−	0.0331376i
$330$	−0.0344182	−	0.0101061i	−0.00189466	−	0.000556322i
$331$	−14.9419	+	9.60258i	−0.821281	+	0.527805i	−0.882496	−	0.470319i	$-0.844139\pi$
$331$	−14.9419	+	9.60258i	−0.821281	+	0.527805i	0.0612152	+	0.998125i	$0.480502\pi$
$332$	−1.09315	+	7.60302i	−0.0599944	+	0.417270i
$333$	2.06448	−	4.52058i	0.113133	−	0.247726i
$334$	7.62023	−	16.6860i	0.416961	−	0.913016i
$335$	0.723381	−	5.03123i	0.0395226	−	0.274885i
$336$	0.0728765	−	0.0468349i	0.00397574	−	0.00255505i
$337$	−22.3972	−	6.57640i	−1.22005	−	0.358240i	−0.392565	−	0.919724i	$-0.628412\pi$
$337$	−22.3972	−	6.57640i	−1.22005	−	0.358240i	−0.827487	+	0.561485i	$0.810230\pi$
$338$	−0.279134	−	1.94142i	−0.0151829	−	0.105599i
$339$	−0.945331	−	1.09097i	−0.0513433	−	0.0592534i
$340$	0.148050	+	0.0951463i	0.00802916	+	0.00516003i
$341$	−0.0190551	+	0.0219907i	−0.00103189	+	0.00119086i
$342$	−7.27005	+	2.13468i	−0.393119	+	0.115430i
$343$	0.503545	+	1.10261i	0.0271889	+	0.0595353i
$344$	−2.73120			−0.147256
$345$	2.13541	+	4.29418i	0.114967	+	0.231191i
$346$	−10.7759			−0.579317
$347$	5.12918	+	11.2313i	0.275349	+	0.602930i	0.995899	−	0.0904732i	$-0.0288380\pi$
$347$	5.12918	+	11.2313i	0.275349	+	0.602930i	−0.720550	+	0.693403i	$0.756111\pi$
$348$	5.37881	−	1.57936i	0.288334	−	0.0846626i
$349$	−2.52285	+	2.91153i	−0.135045	+	0.155850i	−0.819244	−	0.573445i	$-0.805607\pi$
$349$	−2.52285	+	2.91153i	−0.135045	+	0.155850i	0.684199	+	0.729296i	$0.260152\pi$
$350$	0.0728765	+	0.0468349i	0.00389541	+	0.00250343i
$351$	−2.17574	−	2.51093i	−0.116132	−	0.134024i
$352$	−0.00510500	−	0.0355061i	−0.000272098	−	0.00189248i
$353$	−5.77000	−	1.69422i	−0.307106	−	0.0901745i	0.124548	−	0.992214i	$-0.460252\pi$
$353$	−5.77000	−	1.69422i	−0.307106	−	0.0901745i	−0.431654	+	0.902039i	$0.642070\pi$
$354$	−3.85569	+	2.47790i	−0.204928	+	0.131699i
$355$	1.68832	−	11.7425i	0.0896066	−	0.623228i
$356$	−0.478134	+	1.04697i	−0.0253410	+	0.0554891i
$357$	−0.00633324	+	0.0138679i	−0.000335191	+	0.000733965i
$358$	2.29464	−	15.9596i	0.121276	−	0.843491i
$359$	17.0360	−	10.9484i	0.899126	−	0.577833i	−0.00740477	−	0.999973i	$-0.502357\pi$
$359$	17.0360	−	10.9484i	0.899126	−	0.577833i	0.906531	+	0.422139i	$0.138721\pi$
$360$	−0.959493	−	0.281733i	−0.0505697	−	0.0148486i
$361$	−5.46638	−	38.0195i	−0.287704	−	2.00103i
$362$	−14.9739	−	17.2808i	−0.787009	−	0.908257i
$363$	9.25271	+	5.94635i	0.485641	+	0.312103i
$364$	−0.188481	+	0.217518i	−0.00987908	+	0.0114011i
$365$	7.47548	−	2.19500i	0.391285	−	0.114892i
$366$	−0.146556	−	0.320913i	−0.00766060	−	0.0167744i
$367$	−12.3855			−0.646520			−0.323260	−	0.946310i	$-0.604779\pi$
$367$	−12.3855			−0.646520			−0.323260	+	0.946310i	$0.604779\pi$
$368$	−3.01904	+	3.72631i	−0.157379	+	0.194247i
$369$	2.46506			0.128326
$370$	2.06448	+	4.52058i	0.107327	+	0.235014i
$371$	0.412922	−	0.121245i	0.0214378	−	0.00629471i
$372$	−0.531208	+	0.613047i	−0.0275418	+	0.0317850i
$373$	−11.4602	−	7.36501i	−0.593385	−	0.381346i	0.209209	−	0.977871i	$-0.432911\pi$
$373$	−11.4602	−	7.36501i	−0.593385	−	0.381346i	−0.802594	+	0.596525i	$0.796547\pi$
$374$	0.00413407	+	0.00477097i	0.000213768	+	0.000246701i
$375$	−0.142315	−	0.989821i	−0.00734911	−	0.0511142i
$376$	−6.72579	−	1.97487i	−0.346856	−	0.101846i
$377$	−15.6685	+	10.0696i	−0.806971	+	0.518609i
$378$	0.0123285	−	0.0857467i	0.000634111	−	0.00441034i
$379$	11.3264	−	24.8015i	0.581801	−	1.27397i	−0.358471	−	0.933541i	$-0.616702\pi$
$379$	11.3264	−	24.8015i	0.581801	−	1.27397i	0.940272	−	0.340425i	$-0.110571\pi$
$380$	3.14759	−	6.89226i	0.161468	−	0.353565i
$381$	1.68786	−	11.7393i	0.0864715	−	0.601422i
$382$	16.5837	−	10.6577i	0.848495	−	0.545294i
$383$	5.53290	+	1.62461i	0.282718	+	0.0830134i	0.420017	−	0.907516i	$-0.362024\pi$
$383$	5.53290	+	1.62461i	0.282718	+	0.0830134i	−0.137299	+	0.990530i	$0.543842\pi$
$384$	−0.142315	−	0.989821i	−0.00726247	−	0.0505116i
$385$	0.00203496	+	0.00234847i	0.000103711	+	0.000119689i
$386$	6.97727	+	4.48402i	0.355134	+	0.228231i
$387$	−1.78855	+	2.06410i	−0.0909173	+	0.104924i
$388$	2.99628	−	0.879787i	0.152113	−	0.0446644i
$389$	−10.6397	−	23.2977i	−0.539454	−	1.18124i	−0.961535	−	0.274682i	$-0.911427\pi$
$389$	−10.6397	−	23.2977i	−0.539454	−	1.18124i	0.422081	−	0.906558i	$-0.361300\pi$
$390$	3.32244			0.168238
$391$	0.0924265	−	0.838933i	0.00467421	−	0.0424266i
$392$	6.99250			0.353174
$393$	7.18473	+	15.7324i	0.362422	+	0.793592i
$394$	−4.94871	+	1.45307i	−0.249312	+	0.0732047i
$395$	4.93128	−	5.69100i	0.248120	−	0.286345i
$396$	−0.0301768	−	0.0193934i	−0.00151644	−	0.000974557i
$397$	−16.6302	−	19.1922i	−0.834644	−	0.963231i	0.165090	−	0.986279i	$-0.447209\pi$
$397$	−16.6302	−	19.1922i	−0.834644	−	0.963231i	−0.999734	+	0.0230475i	$0.992663\pi$
$398$	−0.0836241	−	0.581618i	−0.00419170	−	0.0291539i
$399$	0.629794	+	0.184924i	0.0315291	+	0.00925778i
$400$	0.841254	−	0.540641i	0.0420627	−	0.0270320i
$401$	−2.16604	+	15.0652i	−0.108167	+	0.752318i	0.861477	+	0.507797i	$0.169540\pi$
$401$	−2.16604	+	15.0652i	−0.108167	+	0.752318i	−0.969644	+	0.244521i	$0.921369\pi$
$402$	2.11154	−	4.62363i	0.105314	−	0.230606i
$403$	1.11958	−	2.45154i	0.0557702	−	0.122120i
$404$	1.56042	−	10.8530i	0.0776338	−	0.539955i
$405$	−0.841254	+	0.540641i	−0.0418022	+	0.0268647i
$406$	−0.465958	−	0.136818i	−0.0231251	−	0.00679015i
$407$	0.0253702	+	0.176454i	0.00125756	+	0.00874649i
$408$	0.115248	+	0.133003i	0.00570561	+	0.00658462i
$409$	19.7028	+	12.6622i	0.974238	+	0.626105i	0.927903	−	0.372821i	$-0.121609\pi$
$409$	19.7028	+	12.6622i	0.974238	+	0.626105i	0.0463351	+	0.998926i	$0.485246\pi$
$410$	−1.61427	+	1.86297i	−0.0797231	+	0.0920053i
$411$	−6.94726	+	2.03990i	−0.342683	+	0.100621i
$412$	5.62705	+	12.3215i	0.277225	+	0.607038i
$413$	0.397042			0.0195371
$414$	0.839103	+	4.72185i	0.0412397	+	0.232066i
$415$	−7.68120			−0.377055
$416$	1.38019	+	3.02220i	0.0676695	+	0.148175i
$417$	5.92653	−	1.74019i	0.290223	−	0.0852173i
$418$	0.177988	−	0.205409i	0.00870567	−	0.0100469i
$419$	29.8800	+	19.2027i	1.45974	+	0.938115i	0.998713	+	0.0507273i	$0.0161539\pi$
$419$	29.8800	+	19.2027i	1.45974	+	0.938115i	0.461023	+	0.887388i	$0.347482\pi$
$420$	0.0567296	+	0.0654694i	0.00276812	+	0.00319458i
$421$	−1.02464	−	7.12653i	−0.0499379	−	0.347326i	−0.999437	−	0.0335556i	$-0.989317\pi$
$421$	−1.02464	−	7.12653i	−0.0499379	−	0.347326i	0.949499	−	0.313770i	$-0.101592\pi$
$422$	14.5822	+	4.28171i	0.709849	+	0.208430i
$423$	−5.89696	+	3.78975i	−0.286720	+	0.184264i
$424$	0.706993	−	4.91724i	0.0343346	−	0.238802i
$425$	−0.0731080	+	0.160084i	−0.00354626	+	0.00776523i
$426$	4.92817	−	10.7912i	0.238771	−	0.522835i
$427$	−0.00434943	+	0.0302509i	−0.000210484	+	0.00146395i
$428$	5.48336	−	3.52394i	0.265048	−	0.170336i
$429$	0.114352	+	0.0335769i	0.00552098	+	0.00162111i
$430$	−0.388690	−	2.70340i	−0.0187443	−	0.130369i
$431$	−7.51633	−	8.67431i	−0.362049	−	0.417827i	0.545276	−	0.838257i	$-0.316425\pi$
$431$	−7.51633	−	8.67431i	−0.362049	−	0.417827i	−0.907325	+	0.420430i	$0.861879\pi$
$432$	−0.841254	−	0.540641i	−0.0404748	−	0.0260116i
$433$	−21.3627	+	24.6539i	−1.02663	+	1.18479i	−0.0440316	+	0.999030i	$0.514020\pi$
$433$	−21.3627	+	24.6539i	−1.02663	+	1.18479i	−0.982595	+	0.185760i	$0.940525\pi$
$434$	0.0674246	−	0.0197976i	0.00323648	−	0.000950317i
$435$	2.32877	+	5.09929i	0.111656	+	0.244492i
$436$	−6.55518			−0.313936
$437$	−36.3180	+	1.20150i	−1.73733	+	0.0574755i
$438$	7.79107			0.372272
$439$	2.68938	+	5.88893i	0.128357	+	0.281063i	0.962890	−	0.269896i	$-0.0869893\pi$
$439$	2.68938	+	5.88893i	0.128357	+	0.281063i	−0.834532	+	0.550959i	$0.814262\pi$
$440$	0.0344182	−	0.0101061i	0.00164082	−	0.000481789i
$441$	4.57911	−	5.28458i	0.218053	−	0.251646i
$442$	−0.491889	−	0.316118i	−0.0233968	−	0.0150362i
$443$	−14.5733	−	16.8185i	−0.692401	−	0.799073i	0.295304	−	0.955403i	$-0.404579\pi$
$443$	−14.5733	−	16.8185i	−0.692401	−	0.799073i	−0.987705	+	0.156330i	$0.950034\pi$
$444$	0.707259	+	4.91909i	0.0335650	+	0.233450i
$445$	−1.10436	−	0.324268i	−0.0523515	−	0.0153718i
$446$	−3.37809	+	2.17097i	−0.159957	+	0.102798i
$447$	1.93974	−	13.4912i	0.0917465	−	0.638111i
$448$	−0.0359868	+	0.0788000i	−0.00170022	+	0.00372295i
$449$	−1.83527	+	4.01869i	−0.0866120	+	0.189654i	−0.947982	−	0.318325i	$-0.896880\pi$
$449$	−1.83527	+	4.01869i	−0.0866120	+	0.189654i	0.861370	+	0.507978i	$0.169607\pi$
$450$	0.142315	−	0.989821i	0.00670879	−	0.0466606i
$451$	−0.0743875	+	0.0478059i	−0.00350277	+	0.00225109i
$452$	1.38509	+	0.406698i	0.0651490	+	0.0191295i
$453$	2.39215	+	16.6378i	0.112393	+	0.781710i
$454$	−1.08204	−	1.24874i	−0.0507825	−	0.0586062i
$455$	−0.242128	−	0.155606i	−0.0113511	−	0.00729493i
$456$	4.96186	−	5.72629i	0.232360	−	0.268158i
$457$	−4.13036	+	1.21278i	−0.193210	+	0.0567316i	−0.376906	−	0.926252i	$-0.623012\pi$
$457$	−4.13036	+	1.21278i	−0.193210	+	0.0567316i	0.183696	+	0.982983i	$0.441194\pi$
$458$	3.71245	+	8.12913i	0.173471	+	0.379849i
$459$	0.175988			0.00821441
$460$	−4.11803	−	2.45800i	−0.192004	−	0.114605i
$461$	12.1243			0.564685			0.282342	−	0.959314i	$-0.408889\pi$
$461$	12.1243			0.564685			0.282342	+	0.959314i	$0.408889\pi$
$462$	0.00129089	+	0.00282665i	6.00576e−5	+	0.000131508i
$463$	−6.43568	+	1.88968i	−0.299091	+	0.0878211i	−0.427835	−	0.903857i	$-0.640724\pi$
$463$	−6.43568	+	1.88968i	−0.299091	+	0.0878211i	0.128744	+	0.991678i	$0.458905\pi$
$464$	−3.67108	+	4.23665i	−0.170425	+	0.196681i
$465$	−0.682405	−	0.438555i	−0.0316458	−	0.0203375i
$466$	−3.67790	−	4.24452i	−0.170375	−	0.196624i
$467$	5.17694	+	36.0064i	0.239560	+	1.66618i	0.654298	+	0.756237i	$0.272964\pi$
$467$	5.17694	+	36.0064i	0.239560	+	1.66618i	−0.414737	+	0.909941i	$0.636127\pi$
$468$	3.18786	+	0.936040i	0.147359	+	0.0432685i
$469$	−0.370429	+	0.238060i	−0.0171048	+	0.0109926i
$470$	0.997589	−	6.93839i	0.0460154	−	0.320044i
$471$	−3.69848	+	8.09854i	−0.170417	+	0.373161i
$472$	1.90396	−	4.16909i	0.0876368	−	0.191898i
$473$	0.0139428	−	0.0969741i	0.000641089	−	0.00445887i
$474$	6.33487	−	4.07117i	0.290970	−	0.186995i
$475$	7.27005	+	2.13468i	0.333573	+	0.0979458i
$476$	−0.00216967	−	0.0150904i	−9.94467e−5	−	0.000691667i
$477$	−3.25322	−	3.75442i	−0.148955	−	0.171903i
$478$	18.7894	+	12.0752i	0.859406	+	0.552307i
$479$	−5.78714	+	6.67872i	−0.264421	+	0.305158i	−0.872398	−	0.488797i	$-0.837436\pi$
$479$	−5.78714	+	6.67872i	−0.264421	+	0.305158i	0.607977	+	0.793955i	$0.291981\pi$
$480$	0.959493	−	0.281733i	0.0437947	−	0.0128593i
$481$	−6.85911	−	15.0194i	−0.312749	−	0.684824i
$482$	−23.0466			−1.04974
$483$	0.159997	−	0.383412i	0.00728010	−	0.0174458i
$484$	−10.9987			−0.499942
$485$	1.29725	+	2.84057i	0.0589049	+	0.128984i
$486$	−0.959493	+	0.281733i	−0.0435235	+	0.0127796i
$487$	−10.7522	+	12.4087i	−0.487228	+	0.562291i	−0.945123	−	0.326716i	$-0.894058\pi$
$487$	−10.7522	+	12.4087i	−0.487228	+	0.562291i	0.457895	+	0.889006i	$0.348604\pi$
$488$	0.296789	+	0.190735i	0.0134350	+	0.00863416i
$489$	13.0551	+	15.0664i	0.590372	+	0.681326i
$490$	0.995136	+	6.92132i	0.0449557	+	0.312673i
$491$	9.98400	+	2.93157i	0.450571	+	0.132300i	0.499142	−	0.866520i	$-0.333648\pi$
$491$	9.98400	+	2.93157i	0.450571	+	0.132300i	−0.0485709	+	0.998820i	$0.515467\pi$
$492$	−2.07374	+	1.33271i	−0.0934913	+	0.0600832i
$493$	0.140403	−	0.976527i	0.00632345	−	0.0439806i
$494$	−10.4577	+	22.8991i	−0.470513	+	1.03028i
$495$	0.0149014	−	0.0326296i	0.000669770	−	0.00146659i
$496$	0.115443	−	0.802920i	0.00518352	−	0.0360522i
$497$	−0.864553	+	0.555614i	−0.0387805	+	0.0249227i
$498$	−7.37006	−	2.16404i	−0.330260	−	0.0969732i
$499$	−1.58820	−	11.0462i	−0.0710978	−	0.494496i	−0.993993	−	0.109445i	$-0.965093\pi$
$499$	−1.58820	−	11.0462i	−0.0710978	−	0.494496i	0.922895	−	0.385051i	$-0.125816\pi$
$500$	0.654861	+	0.755750i	0.0292863	+	0.0337981i
$501$	15.4317	+	9.91733i	0.689436	+	0.443074i
$502$	13.8997	−	16.0411i	0.620374	−	0.715950i
$503$	19.5644	−	5.74463i	0.872334	−	0.256141i	0.185227	−	0.982696i	$-0.440698\pi$
$503$	19.5644	−	5.74463i	0.872334	−	0.256141i	0.687108	+	0.726555i	$0.258880\pi$
$504$	0.0359868	+	0.0788000i	0.00160298	+	0.00351003i
$505$	10.9646			0.487917
$506$	−0.116894	−	0.126217i	−0.00519659	−	0.00561104i
$507$	1.96138			0.0871081
$508$	4.92683	+	10.7883i	0.218593	+	0.478651i
$509$	22.1919	−	6.51612i	0.983637	−	0.288822i	0.249912	−	0.968269i	$-0.419598\pi$
$509$	22.1919	−	6.51612i	0.983637	−	0.288822i	0.733725	+	0.679447i	$0.237780\pi$
$510$	−0.115248	+	0.133003i	−0.00510325	+	0.00588946i
$511$	−0.567786	−	0.364894i	−0.0251174	−	0.0161420i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	−1.07832	−	7.49985i	−0.0476088	−	0.331126i
$514$	−16.3357	−	4.79659i	−0.720536	−	0.211569i
$515$	−11.3953	+	7.32332i	−0.502137	+	0.322704i
$516$	0.388690	−	2.70340i	0.0171111	−	0.119010i
$517$	0.104455	−	0.228725i	0.00459393	−	0.0100593i
$518$	0.178843	−	0.391611i	0.00785790	−	0.0172064i
$519$	1.53357	−	10.6662i	0.0673164	−	0.468196i
$520$	−2.79502	+	1.79625i	−0.122570	+	0.0787707i
$521$	33.4371	+	9.81801i	1.46491	+	0.430135i	0.914439	−	0.404723i	$-0.132632\pi$
$521$	33.4371	+	9.81801i	1.46491	+	0.430135i	0.550466	+	0.834858i	$0.314450\pi$
$522$	0.797801	+	5.54883i	0.0349188	+	0.242866i
$523$	1.10407	+	1.27417i	0.0482777	+	0.0557155i	0.779375	−	0.626558i	$-0.215537\pi$
$523$	1.10407	+	1.27417i	0.0482777	+	0.0557155i	−0.731097	+	0.682273i	$0.760991\pi$
$524$	−14.5497	−	9.35054i	−0.635608	−	0.408480i
$525$	−0.0567296	+	0.0654694i	−0.00247588	+	0.00285732i
$526$	−4.93777	+	1.44986i	−0.215297	+	0.0632169i
$527$	0.0593036	+	0.129857i	0.00258330	+	0.00565665i
$528$	0.0358712			0.00156109
$529$	−1.76142	+	22.9325i	−0.0765833	+	0.997063i
$530$	4.96781			0.215788
$531$	−1.90396	−	4.16909i	−0.0826248	−	0.180923i
$532$	−0.629794	+	0.184924i	−0.0273050	+	0.00801748i
$533$	5.36331	−	6.18959i	0.232311	−	0.268101i
$534$	−0.968264	−	0.622266i	−0.0419009	−	0.0269281i
$535$	4.26844	+	4.92604i	0.184541	+	0.212971i
$536$	0.723381	+	5.03123i	0.0312453	+	0.217316i
$537$	15.4706	+	4.54257i	0.667605	+	0.196027i
$538$	5.85036	−	3.75980i	0.252227	−	0.162096i
$539$	−0.0356967	+	0.248276i	−0.00153757	+	0.0106940i
$540$	0.415415	−	0.909632i	0.0178766	−	0.0391443i
$541$	2.74897	−	6.01940i	0.118187	−	0.258794i	−0.841288	−	0.540588i	$-0.818202\pi$
$541$	2.74897	−	6.01940i	0.118187	−	0.258794i	0.959475	+	0.281793i	$0.0909292\pi$
$542$	−3.80332	+	26.4527i	−0.163367	+	1.13624i
$543$	19.2359	−	12.3621i	0.825490	−	0.530511i
$544$	−0.168859	−	0.0495815i	−0.00723978	−	0.00212579i
$545$	−0.932899	−	6.48846i	−0.0399610	−	0.277935i
$546$	−0.188481	−	0.217518i	−0.00806623	−	0.00930893i
$547$	23.4910	+	15.0967i	1.00440	+	0.645490i	0.935938	−	0.352164i	$-0.114554\pi$
$547$	23.4910	+	15.0967i	1.00440	+	0.645490i	0.0684632	+	0.997654i	$0.478190\pi$
$548$	4.74155	−	5.47205i	0.202549	−	0.233754i
$549$	0.338503	−	0.0993936i	0.0144470	−	0.00424201i
$550$	0.0149014	+	0.0326296i	0.000635399	+	0.00139133i
$551$	−42.4757			−1.80952
$552$	−3.25873	−	3.51862i	−0.138701	−	0.149763i
$553$	−0.652336			−0.0277402
$554$	5.28625	+	11.5753i	0.224591	+	0.491786i
$555$	−4.76837	+	1.40012i	−0.202406	+	0.0594318i
$556$	−4.04490	+	4.66806i	−0.171542	+	0.197970i
$557$	20.6233	+	13.2538i	0.873838	+	0.561581i	0.898924	−	0.438104i	$-0.144350\pi$
$557$	20.6233	+	13.2538i	0.873838	+	0.561581i	−0.0250867	+	0.999685i	$0.507986\pi$
$558$	−0.531208	−	0.613047i	−0.0224878	−	0.0259523i
$559$	1.29140	+	8.98188i	0.0546204	+	0.379893i
$560$	−0.0831194	−	0.0244061i	−0.00351244	−	0.00103134i
$561$	−0.00531075	+	0.00341301i	−0.000224220	+	0.000144097i
$562$	−4.17582	+	29.0435i	−0.176146	+	1.22512i
$563$	15.9337	−	34.8900i	0.671527	−	1.47044i	−0.199851	−	0.979826i	$-0.564046\pi$
$563$	15.9337	−	34.8900i	0.671527	−	1.47044i	0.871378	−	0.490612i	$-0.163227\pi$
$564$	2.91195	−	6.37628i	0.122615	−	0.268490i
$565$	−0.205440	+	1.42887i	−0.00864293	+	0.0601129i
$566$	7.73193	−	4.96901i	0.324997	−	0.208863i
$567$	0.0831194	+	0.0244061i	0.00349069	+	0.00102496i
$568$	1.68832	+	11.7425i	0.0708402	+	0.492705i
$569$	−7.82197	−	9.02703i	−0.327914	−	0.378433i	0.567722	−	0.823220i	$-0.307825\pi$
$569$	−7.82197	−	9.02703i	−0.327914	−	0.378433i	−0.895636	+	0.444787i	$0.853279\pi$
$570$	6.37415	+	4.09642i	0.266984	+	0.171580i
$571$	15.7995	−	18.2336i	0.661190	−	0.763054i	−0.321781	−	0.946814i	$-0.604282\pi$
$571$	15.7995	−	18.2336i	0.661190	−	0.763054i	0.982971	+	0.183760i	$0.0588270\pi$
$572$	−0.114352	+	0.0335769i	−0.00478131	+	0.00140392i
$573$	8.18910	+	17.9316i	0.342104	+	0.749104i
$574$	0.213544			0.00891316
$575$	1.84693	−	4.42593i	0.0770222	−	0.184574i
$576$	1.00000			0.0416667
$577$	14.6737	+	32.1309i	0.610874	+	1.33763i	0.921975	+	0.387250i	$0.126575\pi$
$577$	14.6737	+	32.1309i	0.610874	+	1.33763i	−0.311101	+	0.950377i	$0.600698\pi$
$578$	−16.2817	+	4.78073i	−0.677228	+	0.198852i
$579$	−5.43135	+	6.26811i	−0.225719	+	0.260494i
$580$	−4.71597	−	3.03077i	−0.195820	−	0.125846i
$581$	0.435752	+	0.502884i	0.0180780	+	0.0208631i
$582$	0.444417	+	3.09099i	0.0184217	+	0.128126i
$583$	0.170983	+	0.0502051i	0.00708139	+	0.00207928i
$584$	−6.55427	+	4.21217i	−0.271218	+	0.174301i
$585$	−0.472833	+	3.28862i	−0.0195492	+	0.135968i
$586$	0.208413	−	0.456361i	0.00860947	−	0.0188521i
$587$	−14.1583	+	31.0024i	−0.584377	+	1.27961i	0.354404	+	0.935092i	$0.384684\pi$
$587$	−14.1583	+	31.0024i	−0.584377	+	1.27961i	−0.938781	+	0.344514i	$0.888044\pi$
$588$	−0.995136	+	6.92132i	−0.0410387	+	0.285431i
$589$	5.17057	−	3.32292i	0.213050	−	0.136919i
$590$	4.39761	+	1.29126i	0.181047	+	0.0531602i
$591$	−0.734007	−	5.10513i	−0.0301930	−	0.209997i
$592$	−3.25445	−	3.75583i	−0.133757	−	0.154364i
$593$	−25.9833	−	16.6985i	−1.06701	−	0.685724i	−0.115487	−	0.993309i	$-0.536843\pi$
$593$	−25.9833	−	16.6985i	−1.06701	−	0.685724i	−0.951521	+	0.307585i	$0.900479\pi$
$594$	0.0234906	−	0.0271096i	0.000963833	−	0.00111232i
$595$	0.0146280	−	0.00429517i	0.000599690	−	0.000176085i
$596$	5.66207	+	12.3982i	0.231927	+	0.507850i
$597$	0.587599			0.0240488
$598$	13.6819	+	8.16658i	0.559496	+	0.333956i
$599$	−14.1833			−0.579513			−0.289757	−	0.957100i	$-0.593574\pi$
$599$	−14.1833			−0.579513			−0.289757	+	0.957100i	$0.593574\pi$
$600$	0.415415	+	0.909632i	0.0169592	+	0.0371356i
$601$	42.1219	−	12.3681i	1.71819	−	0.504506i	0.733629	−	0.679550i	$-0.237825\pi$
$601$	42.1219	−	12.3681i	1.71819	−	0.504506i	0.984561	+	0.175044i	$0.0560069\pi$
$602$	−0.154940	+	0.178810i	−0.00631487	+	0.00728775i
$603$	4.27606	+	2.74806i	0.174135	+	0.111910i
$604$	−11.0075	−	12.7033i	−0.447887	−	0.516889i
$605$	−1.56528	−	10.8868i	−0.0636377	−	0.442610i
$606$	10.5204	+	3.08907i	0.427363	+	0.125485i
$607$	−18.6489	+	11.9849i	−0.756934	+	0.486452i	−0.861306	−	0.508087i	$-0.830353\pi$
$607$	−18.6489	+	11.9849i	−0.756934	+	0.486452i	0.104372	+	0.994538i	$0.466717\pi$
$608$	−1.07832	+	7.49985i	−0.0437315	+	0.304159i
$609$	0.201738	−	0.441744i	0.00817483	−	0.0179004i
$610$	−0.146556	+	0.320913i	−0.00593388	+	0.0129934i
$611$	−3.31443	+	23.0524i	−0.134088	+	0.932599i
$612$	−0.148050	+	0.0951463i	−0.00598459	+	0.00384606i
$613$	−3.00138	−	0.881284i	−0.121225	−	0.0355947i	0.220558	−	0.975374i	$-0.429212\pi$
$613$	−3.00138	−	0.881284i	−0.121225	−	0.0355947i	−0.341782	+	0.939779i	$0.611030\pi$
$614$	0.461765	+	3.21165i	0.0186353	+	0.129611i
$615$	−1.61427	−	1.86297i	−0.0650936	−	0.0751220i
$616$	−0.00261417	−	0.00168002i	−0.000105328	−	6.76901e-5i
$617$	12.8298	−	14.8064i	0.516510	−	0.596084i	−0.436244	−	0.899829i	$-0.643691\pi$
$617$	12.8298	−	14.8064i	0.516510	−	0.596084i	0.952754	+	0.303744i	$0.0982368\pi$
$618$	−12.9969	+	3.81624i	−0.522813	+	0.153512i
$619$	−6.31691	−	13.8321i	−0.253898	−	0.555959i	0.739168	−	0.673522i	$-0.235219\pi$
$619$	−6.31691	−	13.8321i	−0.253898	−	0.555959i	−0.993065	+	0.117563i	$0.962492\pi$
$620$	0.811177			0.0325777
$621$	−4.79321	+	0.158572i	−0.192345	+	0.00636329i
$622$	19.0024			0.761926
$623$	0.0414200	+	0.0906971i	0.00165946	+	0.00363370i
$624$	−3.18786	+	0.936040i	−0.127616	+	0.0374716i
$625$	−0.654861	+	0.755750i	−0.0261944	+	0.0302300i
$626$	−9.67922	−	6.22046i	−0.386860	−	0.248620i
$627$	0.177988	+	0.205409i	0.00710815	+	0.00820325i
$628$	−1.26704	−	8.81247i	−0.0505605	−	0.351656i
$629$	0.839176	+	0.246404i	0.0334601	+	0.00982478i
$630$	−0.0728765	+	0.0468349i	−0.00290347	+	0.00186595i
$631$	6.99693	−	48.6647i	0.278543	−	1.93731i	−0.0643250	−	0.997929i	$-0.520489\pi$
$631$	6.99693	−	48.6647i	0.278543	−	1.93731i	0.342868	−	0.939383i	$-0.388601\pi$
$632$	−3.12819	+	6.84978i	−0.124433	+	0.272470i
$633$	−6.31339	+	13.8244i	−0.250935	+	0.549470i
$634$	−1.10981	+	7.71889i	−0.0440761	+	0.306556i
$635$	−9.97728	+	6.41201i	−0.395936	+	0.254453i
$636$	4.76658	+	1.39959i	0.189007	+	0.0554975i
$637$	−3.30628	−	22.9957i	−0.131000	−	0.911122i
$638$	−0.131686	−	0.151974i	−0.00521349	−	0.00601669i
$639$	9.98001	+	6.41376i	0.394803	+	0.253724i
$640$	−0.654861	+	0.755750i	−0.0258856	+	0.0298736i
$641$	18.8174	−	5.52528i	0.743242	−	0.218236i	0.111878	−	0.993722i	$-0.464313\pi$
$641$	18.8174	−	5.52528i	0.743242	−	0.218236i	0.631364	+	0.775486i	$0.282495\pi$
$642$	2.70771	+	5.92906i	0.106865	+	0.234001i
$643$	−2.60190			−0.102609			−0.0513045	−	0.998683i	$-0.516338\pi$
$643$	−2.60190			−0.102609			−0.0513045	+	0.998683i	$0.516338\pi$
$644$	0.0726902	+	0.409047i	0.00286440	+	0.0161187i
$645$	2.73120			0.107541
$646$	−0.553938	−	1.21295i	−0.0217944	−	0.0477230i
$647$	25.3360	−	7.43932i	0.996060	−	0.292470i	0.257222	−	0.966352i	$-0.417193\pi$
$647$	25.3360	−	7.43932i	0.996060	−	0.292470i	0.738838	+	0.673883i	$0.235375\pi$
$648$	0.654861	−	0.755750i	0.0257254	−	0.0296886i
$649$	0.138308	+	0.0888853i	0.00542907	+	0.00348905i
$650$	−2.17574	−	2.51093i	−0.0853394	−	0.0984869i
$651$	0.0100006	+	0.0695558i	0.000391955	+	0.00272611i
$652$	−19.1282	−	5.61653i	−0.749116	−	0.219960i
$653$	−21.7206	+	13.9590i	−0.849993	+	0.546257i	−0.891573	−	0.452878i	$-0.850397\pi$
$653$	−21.7206	+	13.9590i	−0.849993	+	0.546257i	0.0415796	+	0.999135i	$0.486761\pi$
$654$	0.932899	−	6.48846i	0.0364792	−	0.253719i
$655$	7.18473	−	15.7324i	0.280731	−	0.614714i
$656$	1.02402	−	2.24229i	0.0399813	−	0.0875469i
$657$	−1.10879	+	7.71177i	−0.0432578	+	0.300865i
$658$	−0.510845	+	0.328300i	−0.0199148	+	0.0127985i
$659$	22.4107	+	6.58038i	0.872997	+	0.256335i	0.687390	−	0.726289i	$-0.258757\pi$
$659$	22.4107	+	6.58038i	0.872997	+	0.256335i	0.185607	+	0.982624i	$0.440575\pi$
$660$	0.00510500	+	0.0355061i	0.000198712	+	0.00138207i
$661$	−11.3750	−	13.1274i	−0.442435	−	0.510597i	0.490105	−	0.871663i	$-0.336958\pi$
$661$	−11.3750	−	13.1274i	−0.442435	−	0.510597i	−0.932540	+	0.361066i	$0.882413\pi$
$662$	14.9419	+	9.60258i	0.580733	+	0.373215i
$663$	0.382903	−	0.441894i	0.0148707	−	0.0171617i
$664$	7.37006	−	2.16404i	0.286014	−	0.0839812i
$665$	−0.272671	−	0.597066i	−0.0105737	−	0.0231532i
$666$	−4.96968			−0.192571
$667$	−2.94414	+	26.7232i	−0.113997	+	1.03473i
$668$	−18.3437			−0.709737
$669$	−1.66812	−	3.65267i	−0.0644932	−	0.141220i
$670$	−4.87707	+	1.43204i	−0.188418	+	0.0553244i
$671$	−0.00828736	+	0.00956412i	−0.000319930	+	0.000369219i
$672$	−0.0728765	−	0.0468349i	−0.00281127	−	0.00180670i
$673$	20.1631	+	23.2694i	0.777230	+	0.896971i	0.996906	−	0.0786020i	$-0.0250456\pi$
$673$	20.1631	+	23.2694i	0.777230	+	0.896971i	−0.219676	+	0.975573i	$0.570500\pi$
$674$	3.32202	+	23.1051i	0.127959	+	0.889976i
$675$	0.959493	+	0.281733i	0.0369309	+	0.0108439i
$676$	−1.65002	+	1.06040i	−0.0634624	+	0.0407848i
$677$	1.66649	−	11.5907i	0.0640486	−	0.445468i	−0.932411	−	0.361399i	$-0.882299\pi$
$677$	1.66649	−	11.5907i	0.0640486	−	0.445468i	0.996460	−	0.0840689i	$-0.0267916\pi$
$678$	−0.599677	+	1.31311i	−0.0230304	+	0.0504296i
$679$	0.112379	−	0.246075i	0.00431269	−	0.00944348i
$680$	0.0250457	−	0.174197i	0.000960459	−	0.00668014i
$681$	1.39002	−	0.893310i	0.0532656	−	0.0342317i
$682$	0.0279192	+	0.00819782i	0.00106908	+	0.000313911i
$683$	4.82065	+	33.5283i	0.184457	+	1.28293i	0.846066	+	0.533078i	$0.178965\pi$
$683$	4.82065	+	33.5283i	0.184457	+	1.28293i	−0.661609	+	0.749849i	$0.730126\pi$
$684$	4.96186	+	5.72629i	0.189722	+	0.218950i
$685$	6.09114	+	3.91454i	0.232731	+	0.149567i
$686$	0.793789	−	0.916081i	0.0303070	−	0.0349761i
$687$	−8.57473	+	2.51777i	−0.327146	+	0.0960588i
$688$	1.13458	+	2.48438i	0.0432555	+	0.0947163i
$689$	−16.5053			−0.628800
$690$	3.01904	−	3.72631i	0.114933	−	0.141858i
$691$	2.83905			0.108003			0.0540014	−	0.998541i	$-0.482802\pi$
$691$	2.83905			0.108003			0.0540014	+	0.998541i	$0.482802\pi$
$692$	4.47648	+	9.80212i	0.170170	+	0.372621i
$693$	−0.00298159		0.000875475i	−0.000113261		3.32565e-5i
$694$	8.08564	−	9.33133i	0.306927	−	0.354212i
$695$	−5.19620	−	3.33939i	−0.197103	−	0.126670i
$696$	−3.67108	−	4.23665i	−0.139152	−	0.160590i
$697$	0.0617391	+	0.429405i	0.00233853	+	0.0162649i
$698$	3.69645	+	1.08538i	0.139913	+	0.0410821i
$699$	4.72474	−	3.03640i	0.178706	−	0.114847i
$700$	0.0123285	−	0.0857467i	0.000465974	−	0.00324092i
$701$	9.88951	−	21.6550i	0.373522	−	0.817899i	−0.625760	−	0.780015i	$-0.715211\pi$
$701$	9.88951	−	21.6550i	0.373522	−	0.817899i	0.999282	−	0.0378833i	$-0.0120615\pi$
$702$	−1.38019	+	3.02220i	−0.0520920	+	0.114066i
$703$	5.35888	−	37.2718i	0.202114	−	1.40573i
$704$	−0.0301768	+	0.0193934i	−0.00113733	+	0.000730918i
$705$	6.72579	+	1.97487i	0.253308	+	0.0743779i
$706$	0.855823	+	5.95238i	0.0322093	+	0.224021i
$707$	−0.622015	−	0.717844i	−0.0233933	−	0.0269973i
$708$	3.85569	+	2.47790i	0.144906	+	0.0931253i
$709$	1.95607	−	2.25742i	0.0734617	−	0.0847793i	−0.717829	−	0.696219i	$-0.754864\pi$
$709$	1.95607	−	2.25742i	0.0734617	−	0.0847793i	0.791291	+	0.611440i	$0.209409\pi$
$710$	−11.3827	+	3.34227i	−0.427186	+	0.125433i
$711$	3.12819	+	6.84978i	0.117316	+	0.256887i
$712$	1.15098			0.0431347
$713$	−1.73220	−	3.48334i	−0.0648713	−	0.130452i
$714$	0.0152456			0.000570551
$715$	−0.0495091	−	0.108410i	−0.00185154	−	0.00405430i
$716$	−15.4706	+	4.54257i	−0.578163	+	0.169764i
$717$	−14.6263	+	16.8796i	−0.546229	+	0.630382i
$718$	−17.0360	−	10.9484i	−0.635778	−	0.408590i
$719$	11.9165	+	13.7523i	0.444409	+	0.512876i	0.933117	−	0.359572i	$-0.117077\pi$
$719$	11.9165	+	13.7523i	0.444409	+	0.512876i	−0.488708	+	0.872447i	$0.662532\pi$
$720$	0.142315	+	0.989821i	0.00530376	+	0.0368885i
$721$	1.12590	+	0.330595i	0.0419309	+	0.0123120i
$722$	−32.3130	+	20.7663i	−1.20256	+	0.772841i
$723$	3.27988	−	22.8120i	0.121980	−	0.848389i
$724$	−9.49877	+	20.7994i	−0.353019	+	0.773004i
$725$	2.32877	−	5.09929i	0.0864883	−	0.189383i
$726$	1.56528	−	10.8868i	0.0580930	−	0.404046i
$727$	−37.8147	+	24.3020i	−1.40247	+	0.901313i	−0.999901	−	0.0140764i	$-0.995519\pi$
$727$	−37.8147	+	24.3020i	−1.40247	+	0.901313i	−0.402569	+	0.915389i	$0.631883\pi$
$728$	0.276159	+	0.0810877i	0.0102351	+	0.00300531i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	−5.10207	−	5.88810i	−0.188836	−	0.217928i
$731$	−0.404355	−	0.259863i	−0.0149556	−	0.00961139i
$732$	−0.231031	+	0.266624i	−0.00853915	+	0.00985470i
$733$	−12.6990	+	3.72875i	−0.469047	+	0.137725i	−0.507711	−	0.861528i	$-0.669508\pi$
$733$	−12.6990	+	3.72875i	−0.469047	+	0.137725i	0.0386637	+	0.999252i	$0.487690\pi$
$734$	5.14514	+	11.2663i	0.189911	+	0.415846i
$735$	−6.99250			−0.257922
$736$	4.64373	+	1.19825i	0.171170	+	0.0441682i
$737$	−0.182332			−0.00671629
$738$	−1.02402	−	2.24229i	−0.0376948	−	0.0825400i
$739$	33.8673	−	9.94434i	1.24583	−	0.365809i	0.408627	−	0.912701i	$-0.366008\pi$
$739$	33.8673	−	9.94434i	1.24583	−	0.365809i	0.837203	+	0.546893i	$0.184189\pi$
$740$	3.25445	−	3.75583i	0.119636	−	0.138067i
$741$	−21.1778	−	13.6101i	−0.777984	−	0.499980i
$742$	−0.281822	−	0.325240i	−0.0103460	−	0.0119399i
$743$	−5.11707	−	35.5900i	−0.187727	−	1.30567i	−0.837875	−	0.545862i	$-0.816202\pi$
$743$	−5.11707	−	35.5900i	−0.187727	−	1.30567i	0.650148	−	0.759808i	$-0.274707\pi$
$744$	0.778319	+	0.228535i	0.0285345	+	0.00837850i
$745$	−11.4662	+	7.36889i	−0.420090	+	0.269975i
$746$	−1.93872	+	13.4841i	−0.0709815	+	0.493687i
$747$	3.19089	−	6.98707i	0.116748	−	0.255643i
$748$	0.00262247	−	0.00574242i	9.58871e−5	−	0.000209963i
$749$	0.0803583	−	0.558904i	0.00293623	−	0.0204219i
$750$	−0.841254	+	0.540641i	−0.0307182	+	0.0197414i
$751$	14.0521	+	4.12606i	0.512767	+	0.150562i	0.527872	−	0.849324i	$-0.322990\pi$
$751$	14.0521	+	4.12606i	0.512767	+	0.150562i	−0.0151050	+	0.999886i	$0.504808\pi$
$752$	0.997589	+	6.93839i	0.0363783	+	0.253017i
$753$	13.8997	+	16.0411i	0.506533	+	0.584571i
$754$	15.6685	+	10.0696i	0.570615	+	0.366712i
$755$	11.0075	−	12.7033i	0.400602	−	0.462320i
$756$	−0.0831194	+	0.0244061i	−0.00302302	+	0.000887640i
$757$	18.0384	+	39.4985i	0.655615	+	1.43560i	0.886552	+	0.462629i	$0.153094\pi$
$757$	18.0384	+	39.4985i	0.655615	+	1.43560i	−0.230937	+	0.972969i	$0.574179\pi$
$758$	−27.2654			−0.990323
$759$	0.141568	−	0.0977420i	0.00513861	−	0.00354781i
$760$	−7.57697			−0.274846
$761$	−7.98734	−	17.4898i	−0.289541	−	0.634006i	0.707837	−	0.706376i	$-0.249671\pi$
$761$	−7.98734	−	17.4898i	−0.289541	−	0.634006i	−0.997378	+	0.0723699i	$0.976944\pi$
$762$	−11.3796	+	3.34135i	−0.412239	+	0.121044i
$763$	−0.371873	+	0.429164i	−0.0134627	+	0.0155368i
$764$	−16.5837	−	10.6577i	−0.599976	−	0.385581i
$765$	−0.115248	−	0.133003i	−0.00416679	−	0.00480873i
$766$	−0.820656	−	5.70779i	−0.0296515	−	0.206231i
$767$	−14.6108	−	4.29012i	−0.527566	−	0.154907i
$768$	−0.841254	+	0.540641i	−0.0303561	+	0.0195087i
$769$	−5.11457	+	35.5726i	−0.184436	+	1.28278i	0.661681	+	0.749785i	$0.269843\pi$
$769$	−5.11457	+	35.5726i	−0.184436	+	1.28278i	−0.846117	+	0.532996i	$0.821066\pi$
$770$	0.00129089	−	0.00282665i	4.65204e−5	−	0.000101865i
$771$	7.07258	−	15.4868i	0.254713	−	0.557743i
$772$	1.18035	−	8.20948i	0.0424816	−	0.295466i
$773$	28.9356	−	18.5958i	1.04074	−	0.668844i	0.0955718	−	0.995423i	$-0.469532\pi$
$773$	28.9356	−	18.5958i	1.04074	−	0.668844i	0.945170	+	0.326578i	$0.105896\pi$
$774$	2.62056	+	0.769467i	0.0941942	+	0.0276579i
$775$	0.115443	+	0.802920i	0.00414682	+	0.0288418i
$776$	−2.04498	−	2.36003i	−0.0734105	−	0.0847203i
$777$	0.362173	+	0.232754i	0.0129929	+	0.00835002i
$778$	−16.7724	+	19.3564i	−0.601321	+	0.693962i
$779$	17.9211	−	5.26211i	0.642090	−	0.188535i
$780$	−1.38019	−	3.02220i	−0.0494188	−	0.108212i
$781$	−0.425549			−0.0152274
$782$	−0.801515	+	0.264431i	−0.0286621	+	0.00945604i
$783$	−5.60589			−0.200338
$784$	−2.90479	−	6.36060i	−0.103742	−	0.227164i
$785$	8.54245	−	2.50829i	0.304893	−	0.0895247i
$786$	11.3260	−	13.0709i	0.403985	−	0.466224i
$787$	−37.6255	−	24.1804i	−1.34120	−	0.861939i	−0.344170	−	0.938907i	$-0.611840\pi$
$787$	−37.6255	−	24.1804i	−1.34120	−	0.861939i	−0.997034	+	0.0769681i	$0.975476\pi$
$788$	3.37753	+	3.89788i	0.120319	+	0.138856i
$789$	−0.732384	−	5.09384i	−0.0260736	−	0.181346i
$790$	−7.22524	−	2.12152i	−0.257063	−	0.0754804i
$791$	0.105202	−	0.0676090i	0.00374054	−	0.00240390i
$792$	−0.00510500	+	0.0355061i	−0.000181398	+	0.00126165i
$793$	0.486923	−	1.06621i	0.0172912	−	0.0378624i
$794$	−10.5495	+	23.1001i	−0.374386	+	0.819791i
$795$	−0.706993	+	4.91724i	−0.0250745	+	0.174397i
$796$	−0.494320	+	0.317680i	−0.0175207	+	0.0112599i
$797$	49.2370	+	14.4573i	1.74406	+	0.512103i	0.989551	−	0.144183i	$-0.0460554\pi$
$797$	49.2370	+	14.4573i	1.74406	+	0.512103i	0.754512	+	0.656286i	$0.227874\pi$
$798$	−0.0934128	−	0.649701i	−0.00330678	−	0.0229992i
$799$	−0.807855	−	0.932314i	−0.0285799	−	0.0329829i
$800$	−0.841254	−	0.540641i	−0.0297428	−	0.0191145i
$801$	0.753730	−	0.869851i	0.0266318	−	0.0307347i
$802$	14.6036	−	4.28799i	0.515670	−	0.151414i
$803$	−0.116098	−	0.254220i	−0.00409702	−	0.00897121i
$804$	−5.08297			−0.179262
$805$	−0.394539	+	0.130164i	−0.0139057	+	0.00458767i
$806$	−2.69509			−0.0949304
$807$	2.88893	+	6.32588i	0.101695	+	0.222682i
$808$	−10.5204	+	3.08907i	−0.370107	+	0.108673i
$809$	3.53447	−	4.07900i	0.124265	−	0.143410i	−0.690207	−	0.723612i	$-0.742481\pi$
$809$	3.53447	−	4.07900i	0.124265	−	0.143410i	0.814473	+	0.580202i	$0.197026\pi$
$810$	0.841254	+	0.540641i	0.0295586	+	0.0189962i
$811$	24.4600	+	28.2283i	0.858907	+	0.991231i	0.999999	+	0.00123490i	$0.000393080\pi$
$811$	24.4600	+	28.2283i	0.858907	+	0.991231i	−0.141092	+	0.989996i	$0.545061\pi$
$812$	0.0691123	+	0.480687i	0.00242537	+	0.0168688i
$813$	−25.6421	−	7.52921i	−0.899309	−	0.264061i
$814$	0.149969	−	0.0963791i	0.00525641	−	0.00337809i
$815$	2.83714	−	19.7328i	0.0993808	−	0.691209i
$816$	0.0731080	−	0.160084i	0.00255929	−	0.00560407i
$817$	−8.59668	+	18.8241i	−0.300760	+	0.658572i
$818$	3.33311	−	23.1823i	0.116540	−	0.810551i
$819$	0.242128	−	0.155606i	0.00846064	−	0.00543732i
$820$	2.36520	+	0.694487i	0.0825965	+	0.0242525i
$821$	0.930226	+	6.46986i	0.0324651	+	0.225800i	0.999594	−	0.0284862i	$-0.00906867\pi$
$821$	0.930226	+	6.46986i	0.0324651	+	0.225800i	−0.967129	+	0.254286i	$0.918160\pi$
$822$	4.74155	+	5.47205i	0.165381	+	0.190860i
$823$	29.7428	+	19.1145i	1.03677	+	0.666291i	0.944185	−	0.329414i	$-0.106851\pi$
$823$	29.7428	+	19.1145i	1.03677	+	0.666291i	0.0925829	+	0.995705i	$0.470488\pi$
$824$	8.87049	−	10.2371i	0.309018	−	0.356626i
$825$	−0.0344182	+	0.0101061i	−0.00119829	+	0.000351849i
$826$	−0.164937	−	0.361162i	−0.00573889	−	0.0125664i
$827$	34.5074			1.19994			0.599970	−	0.800022i	$-0.295179\pi$
$827$	34.5074			1.19994			0.599970	+	0.800022i	$0.295179\pi$
$828$	3.94657	−	2.72480i	0.137153	−	0.0946935i
$829$	−46.4115			−1.61194			−0.805969	−	0.591958i	$-0.798355\pi$
$829$	−46.4115			−1.61194			−0.805969	+	0.591958i	$0.798355\pi$
$830$	3.19089	+	6.98707i	0.110757	+	0.242525i
$831$	−12.2098	+	3.58511i	−0.423552	+	0.124366i
$832$	2.17574	−	2.51093i	0.0754301	−	0.0870510i
$833$	1.03524	+	0.665310i	0.0358690	+	0.0230516i
$834$	−4.04490	−	4.66806i	−0.140063	−	0.161642i
$835$	−2.61057	−	18.1569i	−0.0903427	−	0.628347i
$836$	−0.260785	−	0.0765735i	−0.00901945	−	0.00264835i
$837$	0.682405	−	0.438555i	0.0235874	−	0.0151587i
$838$	5.05481	−	35.1570i	0.174615	−	1.21448i
$839$	−7.33861	+	16.0693i	−0.253357	+	0.554774i	−0.992985	−	0.118242i	$-0.962274\pi$
$839$	−7.33861	+	16.0693i	−0.253357	+	0.554774i	0.739628	+	0.673016i	$0.235001\pi$
$840$	0.0359868	−	0.0788000i	0.00124166	−	0.00271886i
$841$	−0.345253	+	2.40128i	−0.0119053	+	0.0828029i
$842$	−6.05687	+	3.89251i	−0.208734	+	0.134145i
$843$	−28.1535	−	8.26663i	−0.969660	−	0.284718i
$844$	−2.16287	−	15.0431i	−0.0744491	−	0.517805i
$845$	−1.28443	−	1.48232i	−0.0441859	−	0.0509932i
$846$	5.89696	+	3.78975i	0.202742	+	0.130294i
$847$	−0.623953	+	0.720080i	−0.0214393	+	0.0247422i
$848$	−4.76658	+	1.39959i	−0.163685	+	0.0480622i
$849$	3.81806	+	8.36039i	0.131036	+	0.286928i
$850$	0.175988			0.00603634
$851$	−23.0778	−	5.95494i	−0.791098	−	0.204133i
$852$	−11.8633			−0.406428
$853$	21.8336	+	47.8090i	0.747569	+	1.63695i	0.770686	+	0.637216i	$0.219914\pi$
$853$	21.8336	+	47.8090i	0.747569	+	1.63695i	−0.0231164	+	0.999733i	$0.507359\pi$
$854$	0.0293240	−	0.00861031i	0.00100345	−	0.000294639i
$855$	−4.96186	+	5.72629i	−0.169692	+	0.195835i
$856$	−5.48336	−	3.52394i	−0.187417	−	0.120446i
$857$	−8.89533	−	10.2658i	−0.303859	−	0.350671i	0.583200	−	0.812329i	$-0.301800\pi$
$857$	−8.89533	−	10.2658i	−0.303859	−	0.350671i	−0.887058	+	0.461657i	$0.847255\pi$
$858$	−0.0169611	−	0.117967i	−0.000579042	−	0.00402732i
$859$	−48.6880	−	14.2961i	−1.66121	−	0.487776i	−0.689568	−	0.724221i	$-0.742200\pi$
$859$	−48.6880	−	14.2961i	−1.66121	−	0.487776i	−0.971645	+	0.236445i	$0.924018\pi$
$860$	−2.29763	+	1.47660i	−0.0783485	+	0.0503515i
$861$	−0.0303905	+	0.211371i	−0.00103571	+	0.00720349i
$862$	−4.76803	+	10.4405i	−0.162400	+	0.355606i
$863$	0.330016	−	0.722634i	0.0112339	−	0.0245988i	−0.903932	−	0.427676i	$-0.859332\pi$
$863$	0.330016	−	0.722634i	0.0112339	−	0.0245988i	0.915166	+	0.403078i	$0.132060\pi$
$864$	−0.142315	+	0.989821i	−0.00484165	+	0.0336744i
$865$	−9.06528	+	5.82590i	−0.308229	+	0.198087i
$866$	31.3004	+	9.19062i	1.06363	+	0.312310i
$867$	−2.41494	−	16.7963i	−0.0820158	−	0.570433i
$868$	−0.0460177	−	0.0531073i	−0.00156194	−	0.00180258i
$869$	−0.227239	−	0.146038i	−0.00770857	−	0.00495400i
$870$	3.67108	−	4.23665i	0.124461	−	0.143636i
$871$	16.2038	−	4.75786i	0.549044	−	0.161214i
$872$	2.72312	+	5.96280i	0.0922165	+	0.201926i
$873$	−3.12277			−0.105690
$874$	16.1800	+	32.5369i	0.547296	+	1.10058i
$875$	0.0866285			0.00292858
$876$	−3.23653	−	7.08701i	−0.109352	−	0.239448i
$877$	9.77623	−	2.87056i	0.330120	−	0.0969319i	−0.112473	−	0.993655i	$-0.535877\pi$
$877$	9.77623	−	2.87056i	0.330120	−	0.0969319i	0.442592	+	0.896723i	$0.354059\pi$
$878$	4.23955	−	4.89270i	0.143078	−	0.165121i
$879$	0.422056	+	0.271239i	0.0142356	+	0.00914866i
$880$	−0.0234906	−	0.0271096i	−0.000791869	−	0.000913866i
$881$	−2.25799	−	15.7047i	−0.0760736	−	0.529104i	−0.991850	−	0.127414i	$-0.959332\pi$
$881$	−2.25799	−	15.7047i	−0.0760736	−	0.529104i	0.915776	−	0.401689i	$-0.131577\pi$
$882$	−6.70925	−	1.97001i	−0.225912	−	0.0663338i
$883$	7.39653	−	4.75346i	0.248913	−	0.159967i	−0.410235	−	0.911980i	$-0.634553\pi$
$883$	7.39653	−	4.75346i	0.248913	−	0.159967i	0.659148	+	0.752013i	$0.270917\pi$
$884$	−0.0832129	+	0.578758i	−0.00279875	+	0.0194657i
$885$	−1.90396	+	4.16909i	−0.0640009	+	0.140142i
$886$	−9.24470	+	20.2431i	−0.310582	+	0.680079i
$887$	0.970794	−	6.75202i	0.0325961	−	0.226711i	−0.967011	−	0.254734i	$-0.918012\pi$
$887$	0.970794	−	6.75202i	0.0325961	−	0.226711i	0.999607	+	0.0280232i	$0.00892121\pi$
$888$	4.18076	−	2.68681i	0.140297	−	0.0901635i
$889$	0.985798	+	0.289456i	0.0330626	+	0.00970805i
$890$	0.163801	+	1.13926i	0.00549063	+	0.0381882i
$891$	0.0234906	+	0.0271096i	0.000786966	+	0.000908207i
$892$	3.37809	+	2.17097i	0.113107	+	0.0726894i
$893$	−34.7813	+	40.1398i	−1.16391	+	1.34323i
$894$	−13.0778	+	3.83999i	−0.437387	+	0.128429i
$895$	−6.69803	−	14.6666i	−0.223890	−	0.490252i
$896$	0.0866285			0.00289405
$897$	−10.0306	+	12.3804i	−0.334912	+	0.413371i
$898$	4.41793			0.147428
$899$	−1.88904	−	4.13643i	−0.0630032	−	0.137958i
$900$	−0.959493	+	0.281733i	−0.0319831	+	0.00939109i
$901$	0.572528	−	0.660733i	0.0190737	−	0.0220122i
$902$	0.0743875	+	0.0478059i	0.00247683	+	0.00159176i
$903$	−0.154940	−	0.178810i	−0.00515607	−	0.00595042i
$904$	−0.205440	−	1.42887i	−0.00683284	−	0.0475234i
$905$	−21.9395	−	6.44202i	−0.729294	−	0.214140i
$906$	14.1405	−	9.08755i	0.469787	−	0.301914i
$907$	−3.77328	+	26.2437i	−0.125290	+	0.871409i	0.826123	+	0.563490i	$0.190542\pi$
$907$	−3.77328	+	26.2437i	−0.125290	+	0.871409i	−0.951413	+	0.307919i	$0.900367\pi$
$908$	−0.686397	+	1.50300i	−0.0227789	+	0.0498788i
$909$	−4.55484	+	9.97371i	−0.151075	+	0.330807i
$910$	−0.0409608	+	0.284889i	−0.00135784	+	0.00944396i
$911$	7.61395	−	4.89319i	0.252261	−	0.162119i	−0.408399	−	0.912804i	$-0.633913\pi$
$911$	7.61395	−	4.89319i	0.252261	−	0.162119i	0.660660	+	0.750685i	$0.270276\pi$
$912$	−7.27005	−	2.13468i	−0.240735	−	0.0706863i
$913$	0.0392126	+	0.272729i	0.00129775	+	0.00902603i
$914$	2.81900	+	3.25330i	0.0932443	+	0.107610i
$915$	−0.296789	−	0.190735i	−0.00981155	−	0.00630550i
$916$	5.85231	−	6.75393i	0.193366	−	0.223156i
$917$	−1.43758	+	0.422110i	−0.0474729	+	0.0139393i
$918$	−0.0731080	−	0.160084i	−0.00241292	−	0.00528357i
$919$	−40.9287			−1.35011			−0.675056	−	0.737766i	$-0.735881\pi$
$919$	−40.9287			−1.35011			−0.675056	+	0.737766i	$0.735881\pi$
$920$	−0.525186	+	4.76699i	−0.0173149	+	0.157163i
$921$	−3.24467			−0.106916
$922$	−5.03661	−	11.0286i	−0.165872	−	0.363209i
$923$	37.8184	−	11.1045i	1.24481	−	0.365508i
$924$	0.00203496	−	0.00234847i	6.69452e−5	−	7.72589e-5i
$925$	4.18076	+	2.68681i	0.137463	+	0.0883418i
$926$	4.39239	+	5.06909i	0.144343	+	0.166581i
$927$	−1.92774	−	13.4077i	−0.0633154	−	0.440368i
$928$	5.37881	+	1.57936i	0.176568	+	0.0518451i
$929$	−16.6088	+	10.6738i	−0.544918	+	0.350197i	−0.783960	−	0.620812i	$-0.786803\pi$
$929$	−16.6088	+	10.6738i	−0.544918	+	0.350197i	0.239042	+	0.971009i	$0.423167\pi$
$930$	−0.115443	+	0.802920i	−0.00378551	+	0.0263288i
$931$	22.0095	−	48.1941i	0.721332	−	1.57950i
$932$	−2.33310	+	5.10877i	−0.0764232	+	0.167343i
$933$	−2.70432	+	18.8090i	−0.0885354	+	0.615777i
$934$	30.6020	−	19.6667i	1.00133	−	0.643515i
$935$	0.00605718	+	0.00177855i	0.000198091	+	5.81648e-5i
$936$	−0.472833	−	3.28862i	−0.0154550	−	0.107492i
$937$	9.94618	+	11.4785i	0.324928	+	0.374986i	0.894587	−	0.446895i	$-0.147470\pi$
$937$	9.94618	+	11.4785i	0.324928	+	0.374986i	−0.569659	+	0.821881i	$0.692925\pi$
$938$	0.370429	+	0.238060i	0.0120949	+	0.00777294i
$939$	7.53464	−	8.69544i	0.245884	−	0.283765i
$940$	−6.72579	+	1.97487i	−0.219371	+	0.0644132i
$941$	−6.55088	−	14.3444i	−0.213553	−	0.467615i	0.772294	−	0.635265i	$-0.219109\pi$
$941$	−6.55088	−	14.3444i	−0.213553	−	0.467615i	−0.985847	+	0.167650i	$0.946382\pi$
$942$	8.90309			0.290078
$943$	−2.06844	−	11.6396i	−0.0673576	−	0.379039i
$944$	−4.58327			−0.149173
$945$	−0.0359868	−	0.0788000i	−0.00117065	−	0.00256337i
$946$	−0.0940028	+	0.0276017i	−0.00305629	+	0.000897409i
$947$	23.1983	−	26.7722i	0.753842	−	0.869980i	−0.241093	−	0.970502i	$-0.577506\pi$
$947$	23.1983	−	26.7722i	0.753842	−	0.869980i	0.994935	+	0.100522i	$0.0320512\pi$
$948$	−6.33487	−	4.07117i	−0.205747	−	0.132226i
$949$	16.9513	+	19.5629i	0.550263	+	0.635038i
$950$	−1.07832	−	7.49985i	−0.0349852	−	0.243327i
$951$	−7.48238	−	2.19702i	−0.242633	−	0.0712434i
$952$	−0.0128254	+	0.00824238i	−0.000415673	+	0.000267137i
$953$	6.55653	−	45.6017i	0.212387	−	1.47718i	−0.552767	−	0.833336i	$-0.686428\pi$
$953$	6.55653	−	45.6017i	0.212387	−	1.47718i	0.765154	−	0.643847i	$-0.222663\pi$
$954$	−2.06370	+	4.51888i	−0.0668148	+	0.146304i
$955$	8.18910	−	17.9316i	0.264993	−	0.580254i
$956$	3.17860	−	22.1076i	0.102803	−	0.715012i
$957$	0.169168	−	0.108717i	0.00546841	−	0.00351434i
$958$	8.47924	+	2.48973i	0.273952	+	0.0804395i
$959$	−0.0892653	−	0.620854i	−0.00288253	−	0.0200484i
$960$	−0.654861	−	0.755750i	−0.0211355	−	0.0243917i
$961$	−25.5253	−	16.4041i	−0.823397	−	0.529165i
$962$	−10.8127	+	12.4785i	−0.348616	+	0.402324i
$963$	−6.25406	+	1.83636i	−0.201534	+	0.0591758i
$964$	9.57391	+	20.9639i	0.308355	+	0.675203i
$965$	8.29390			0.266990
$966$	−0.415228	+	0.0137369i	−0.0133598	+	0.000441977i
$967$	33.6239			1.08127			0.540637	−	0.841256i	$-0.318183\pi$
$967$	33.6239			1.08127			0.540637	+	0.841256i	$0.318183\pi$
$968$	4.56903	+	10.0048i	0.146854	+	0.321566i
$969$	1.27944	−	0.375678i	0.0411016	−	0.0120685i
$970$	2.04498	−	2.36003i	0.0656604	−	0.0757761i
$971$	8.47124	+	5.44413i	0.271855	+	0.174711i	0.669464	−	0.742844i	$-0.266524\pi$
$971$	8.47124	+	5.44413i	0.271855	+	0.174711i	−0.397609	+	0.917555i	$0.630160\pi$
$972$	0.654861	+	0.755750i	0.0210047	+	0.0242407i
$973$	0.0761500	+	0.529635i	0.00244126	+	0.0169793i
$974$	15.7539	+	4.62577i	0.504789	+	0.148219i
$975$	2.79502	−	1.79625i	0.0895121	−	0.0575260i
$976$	0.0502078	−	0.349203i	0.00160711	−	0.0111777i
$977$	6.10904	−	13.3769i	0.195446	−	0.427966i	−0.786382	−	0.617740i	$-0.788048\pi$
$977$	6.10904	−	13.3769i	0.195446	−	0.427966i	0.981828	+	0.189774i	$0.0607756\pi$
$978$	8.28159	−	18.1341i	0.264816	−	0.579866i
$979$	−0.00587575	+	0.0408667i	−0.000187790	+	0.00130611i
$980$	5.88246	−	3.78043i	0.187908	−	0.120761i
$981$	6.28965	+	1.84681i	0.200813	+	0.0589640i
$982$	−1.48086	−	10.2996i	−0.0472560	−	0.328673i
$983$	−31.5092	−	36.3636i	−1.00499	−	1.15982i	−0.987121	−	0.159977i	$-0.948858\pi$
$983$	−31.5092	−	36.3636i	−1.00499	−	1.15982i	−0.0178669	−	0.999840i	$-0.505688\pi$
$984$	2.07374	+	1.33271i	0.0661084	+	0.0424853i
$985$	−3.37753	+	3.89788i	−0.107617	+	0.124197i
$986$	−0.946606	+	0.277949i	−0.0301461	+	0.00885168i
$987$	−0.252258	−	0.552367i	−0.00802945	−	0.0175820i
$988$	25.1740			0.800893
$989$	11.2472	+	6.71330i	0.357639	+	0.213470i
$990$	−0.0358712			−0.00114006
$991$	7.22123	+	15.8123i	0.229390	+	0.502294i	0.988969	−	0.148121i	$-0.0473224\pi$
$991$	7.22123	+	15.8123i	0.229390	+	0.502294i	−0.759579	+	0.650415i	$0.774595\pi$
$992$	−0.778319	+	0.228535i	−0.0247116	+	0.00725599i
$993$	−11.6313	+	13.4232i	−0.369108	+	0.425973i
$994$	0.864553	+	0.555614i	0.0274220	+	0.0176230i
$995$	−0.384796	−	0.444078i	−0.0121988	−	0.0140782i
$996$	1.09315	+	7.60302i	0.0346378	+	0.240911i
$997$	54.0875	+	15.8815i	1.71297	+	0.502973i	0.983479	−	0.181021i	$-0.0579401\pi$
$997$	54.0875	+	15.8815i	1.71297	+	0.502973i	0.729488	+	0.683993i	$0.239758\pi$
$998$	−9.38822	+	6.03344i	−0.297179	+	0.190985i
$999$	0.707259	−	4.91909i	0.0223767	−	0.155633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.f.211.1	yes	20
23.6	even	11	inner	690.2.m.f.121.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.f.121.1	✓	20	23.6	even	11	inner
690.2.m.f.211.1	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.0123285 + 0.0857467i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.0123285 + 0.0857467i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-0.142315 + 0.989821i) q^{10} +(-0.0149014 + 0.0326296i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(0.472833 - 3.28862i) q^{13} +(0.0728765 - 0.0468349i) q^{14} +(-0.959493 - 0.281733i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(0.115248 + 0.133003i) q^{17} +(-0.841254 - 0.540641i) q^{18} +(4.96186 - 5.72629i) q^{19} +(0.959493 - 0.281733i) q^{20} +(0.0359868 + 0.0788000i) q^{21} +0.0358712 q^{22} +(-3.25873 - 3.51862i) q^{23} +1.00000 q^{24} +(0.415415 + 0.909632i) q^{25} +(-3.18786 + 0.936040i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-0.0728765 - 0.0468349i) q^{28} +(-3.67108 - 4.23665i) q^{29} +(0.142315 + 0.989821i) q^{30} +(0.778319 + 0.228535i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(-0.00510500 + 0.0355061i) q^{33} +(0.0731080 - 0.160084i) q^{34} +(0.0359868 - 0.0788000i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(4.18076 - 2.68681i) q^{37} +(-7.27005 - 2.13468i) q^{38} +(-0.472833 - 3.28862i) q^{39} +(-0.654861 - 0.755750i) q^{40} +(2.07374 + 1.33271i) q^{41} +(0.0567296 - 0.0654694i) q^{42} +(-2.62056 + 0.769467i) q^{43} +(-0.0149014 - 0.0326296i) q^{44} -1.00000 q^{45} +(-1.84693 + 4.42593i) q^{46} -7.00973 q^{47} +(-0.415415 - 0.909632i) q^{48} +(6.70925 - 1.97001i) q^{49} +(0.654861 - 0.755750i) q^{50} +(0.148050 + 0.0951463i) q^{51} +(2.17574 + 2.51093i) q^{52} +(-0.706993 - 4.91724i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(0.0301768 - 0.0193934i) q^{55} +(-0.0123285 + 0.0857467i) q^{56} +(3.14759 - 6.89226i) q^{57} +(-2.32877 + 5.09929i) q^{58} +(0.652267 - 4.53662i) q^{59} +(0.841254 - 0.540641i) q^{60} +(0.338503 + 0.0993936i) q^{61} +(-0.115443 - 0.802920i) q^{62} +(0.0567296 + 0.0654694i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-2.17574 + 2.51093i) q^{65} +(0.0344182 - 0.0101061i) q^{66} +(2.11154 + 4.62363i) q^{67} -0.175988 q^{68} +(-4.11803 - 2.45800i) q^{69} -0.0866285 q^{70} +(4.92817 + 10.7912i) q^{71} +(0.959493 - 0.281733i) q^{72} +(-5.10207 + 5.88810i) q^{73} +(-4.18076 - 2.68681i) q^{74} +(0.654861 + 0.755750i) q^{75} +(1.07832 + 7.49985i) q^{76} +(-0.00298159 - 0.000875475i) q^{77} +(-2.79502 + 1.79625i) q^{78} +(-1.07167 + 7.45363i) q^{79} +(-0.415415 + 0.909632i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.350814 - 2.43997i) q^{82} +(6.46184 - 4.15277i) q^{83} +(-0.0831194 - 0.0244061i) q^{84} +(-0.0250457 - 0.174197i) q^{85} +(1.78855 + 2.06410i) q^{86} +(-4.71597 - 3.03077i) q^{87} +(-0.0234906 + 0.0271096i) q^{88} +(1.10436 - 0.324268i) q^{89} +(0.415415 + 0.909632i) q^{90} +0.287818 q^{91} +(4.79321 - 0.158572i) q^{92} +0.811177 q^{93} +(2.91195 + 6.37628i) q^{94} +(-7.27005 + 2.13468i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(-2.62704 - 1.68830i) q^{97} +(-4.57911 - 5.28458i) q^{98} +(0.00510500 + 0.0355061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + 18 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 13 * q^21 + 26 * q^22 + 20 * q^24 - 2 * q^25 + 9 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 + 8 * q^31 + 2 * q^32 + 4 * q^33 + 13 * q^34 + 13 * q^35 - 2 * q^36 + 16 * q^37 - 15 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 + 9 * q^42 - 16 * q^43 + 18 * q^44 - 20 * q^45 - 34 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 - 9 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 7 * q^55 + 2 * q^56 + 29 * q^57 + 16 * q^58 + 25 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 9 * q^63 - 2 * q^64 - 2 * q^65 - 15 * q^66 + 20 * q^67 - 2 * q^68 - 22 * q^69 - 2 * q^70 - q^71 + 2 * q^72 - q^73 - 16 * q^74 + 2 * q^75 + 4 * q^76 + 53 * q^77 + 2 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 - 25 * q^82 + 9 * q^83 - 9 * q^84 - 9 * q^85 - 28 * q^86 - 6 * q^87 - 7 * q^88 - 31 * q^89 - 2 * q^90 - 26 * q^91 + 11 * q^92 - 30 * q^93 + q^94 - 15 * q^95 - 2 * q^96 - 35 * q^97 - 5 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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