LMFDB - Embedded newform 122.2.i.b.73.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(15,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("122.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.i (of order $15$, degree $8$, 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:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			73.3
Character	$\chi$	$=$	122.73
Dual form			122.2.i.b.117.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.913545 + 0.406737i) q^{2} +(2.23206 - 1.62169i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-3.24270 + 0.689258i) q^{5} +(2.69869 - 0.573623i) q^{6} +(-0.206641 + 1.96606i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.42517 - 4.38623i) q^{9} +O(q^{10})$	\(q+(0.913545 + 0.406737i) q^{2} +(2.23206 - 1.62169i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-3.24270 + 0.689258i) q^{5} +(2.69869 - 0.573623i) q^{6} +(-0.206641 + 1.96606i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.42517 - 4.38623i) q^{9} +(-3.24270 - 0.689258i) q^{10} -1.71534 q^{11} +(2.69869 + 0.573623i) q^{12} +(-3.52952 - 6.11331i) q^{13} +(-0.988443 + 1.71203i) q^{14} +(-6.12015 + 6.79711i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(4.94574 + 5.49280i) q^{17} +(3.08600 - 3.42735i) q^{18} +(-0.229827 - 2.18666i) q^{19} +(-2.68201 - 1.94859i) q^{20} +(2.72709 + 4.72346i) q^{21} +(-1.56705 - 0.697694i) q^{22} +(-1.23012 + 3.78593i) q^{23} +(2.23206 + 1.62169i) q^{24} +(5.47232 - 2.43643i) q^{25} +(-0.737870 - 7.02037i) q^{26} +(-1.37430 - 4.22967i) q^{27} +(-1.59933 + 1.16198i) q^{28} +(-1.30459 + 2.25962i) q^{29} +(-8.35566 + 3.72018i) q^{30} +(4.25575 - 1.89478i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.82875 + 2.78175i) q^{33} +(2.28403 + 7.02953i) q^{34} +(-0.685045 - 6.51777i) q^{35} +(4.21323 - 1.87585i) q^{36} +(-0.748347 - 0.543706i) q^{37} +(0.679437 - 2.09109i) q^{38} +(-17.7920 - 7.92149i) q^{39} +(-1.65757 - 2.87100i) q^{40} +(-3.69381 - 2.68371i) q^{41} +(0.570117 + 5.42430i) q^{42} +(3.98750 - 4.42856i) q^{43} +(-1.14779 - 1.27475i) q^{44} +(-1.59817 + 15.2055i) q^{45} +(-2.66365 + 2.95828i) q^{46} +(3.99965 - 6.92759i) q^{47} +(1.37949 + 2.38934i) q^{48} +(3.02435 + 0.642846i) q^{49} +5.99020 q^{50} +(19.9468 + 4.23982i) q^{51} +(2.18136 - 6.71354i) q^{52} +(0.0463429 + 0.142629i) q^{53} +(0.464873 - 4.42297i) q^{54} +(5.56235 - 1.18232i) q^{55} +(-1.93369 + 0.411018i) q^{56} +(-4.05906 - 4.50804i) q^{57} +(-2.11087 + 1.53364i) q^{58} +(-2.87903 - 1.28183i) q^{59} -9.14641 q^{60} +(5.59001 + 5.45452i) q^{61} +4.65850 q^{62} +(8.32907 + 3.70834i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(15.6588 + 17.3909i) q^{65} +(-4.62918 + 0.983962i) q^{66} +(-9.52519 + 2.02464i) q^{67} +(-0.772600 + 7.35080i) q^{68} +(3.39388 + 10.4453i) q^{69} +(2.02520 - 6.23291i) q^{70} +(-7.61267 - 1.61812i) q^{71} +4.61195 q^{72} +(5.03470 + 1.07016i) q^{73} +(-0.462504 - 0.801080i) q^{74} +(8.26341 - 14.3127i) q^{75} +(1.47122 - 1.63395i) q^{76} +(0.354460 - 3.37247i) q^{77} +(-13.0318 - 14.4733i) q^{78} +(-0.924243 + 1.02648i) q^{79} +(-0.346527 - 3.29699i) q^{80} +(1.26673 + 0.920332i) q^{81} +(-2.28290 - 3.95410i) q^{82} +(-9.96942 - 4.43867i) q^{83} +(-1.68544 + 5.18724i) q^{84} +(-19.8235 - 14.4026i) q^{85} +(5.44402 - 2.42383i) q^{86} +(0.752466 + 7.15923i) q^{87} +(-0.530071 - 1.63139i) q^{88} +(3.10898 - 2.25881i) q^{89} +(-7.64465 + 13.2409i) q^{90} +(12.7484 - 5.67598i) q^{91} +(-3.63660 + 1.61912i) q^{92} +(6.42635 - 11.1308i) q^{93} +(6.47157 - 4.70187i) q^{94} +(2.25243 + 6.93228i) q^{95} +(0.288392 + 2.74386i) q^{96} +(-6.47933 + 2.88478i) q^{97} +(2.50142 + 1.81739i) q^{98} +(-2.44466 + 7.52389i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9	\( 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9} - 12 q^{10} + 6 q^{11} - q^{12} + 5 q^{13} - 4 q^{14} - 9 q^{15} + 3 q^{16} + 16 q^{17} + 17 q^{18} - 2 q^{19} - q^{20} + 10 q^{21} + 7 q^{22} + q^{23} - 3 q^{24} + 11 q^{25} - 9 q^{27} - 7 q^{28} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 12 q^{32} + 7 q^{33} - 17 q^{34} + 9 q^{35} + 2 q^{36} - 38 q^{37} + 4 q^{38} - 40 q^{39} - 7 q^{40} - 10 q^{41} + 15 q^{42} - 5 q^{43} + 2 q^{44} - 96 q^{45} - 8 q^{46} + 3 q^{47} - q^{48} + 19 q^{49} + 38 q^{50} + 102 q^{51} + 20 q^{52} - 37 q^{53} + 17 q^{54} + 33 q^{55} + 6 q^{56} - 71 q^{57} + q^{58} - 17 q^{59} - 22 q^{60} + 70 q^{61} + 72 q^{62} + 146 q^{63} - 6 q^{64} + 2 q^{65} - 86 q^{66} - 4 q^{67} + q^{68} - 2 q^{69} - 28 q^{70} - 76 q^{71} + 46 q^{72} + 84 q^{73} + 19 q^{74} + 9 q^{75} - 2 q^{76} - 10 q^{77} - 5 q^{78} - 56 q^{79} - 7 q^{80} + 59 q^{81} - 20 q^{82} - 9 q^{83} + 25 q^{84} - 37 q^{85} - 65 q^{86} - 25 q^{87} - 4 q^{88} - 45 q^{89} - 31 q^{90} + 2 q^{91} + 7 q^{92} - 47 q^{93} + 24 q^{94} - 39 q^{95} + 9 q^{96} + 6 q^{97} + 7 q^{98} - 24 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9 - 12 * q^10 + 6 * q^11 - q^12 + 5 * q^13 - 4 * q^14 - 9 * q^15 + 3 * q^16 + 16 * q^17 + 17 * q^18 - 2 * q^19 - q^20 + 10 * q^21 + 7 * q^22 + q^23 - 3 * q^24 + 11 * q^25 - 9 * q^27 - 7 * q^28 + 2 * q^29 - 4 * q^30 + 14 * q^31 - 12 * q^32 + 7 * q^33 - 17 * q^34 + 9 * q^35 + 2 * q^36 - 38 * q^37 + 4 * q^38 - 40 * q^39 - 7 * q^40 - 10 * q^41 + 15 * q^42 - 5 * q^43 + 2 * q^44 - 96 * q^45 - 8 * q^46 + 3 * q^47 - q^48 + 19 * q^49 + 38 * q^50 + 102 * q^51 + 20 * q^52 - 37 * q^53 + 17 * q^54 + 33 * q^55 + 6 * q^56 - 71 * q^57 + q^58 - 17 * q^59 - 22 * q^60 + 70 * q^61 + 72 * q^62 + 146 * q^63 - 6 * q^64 + 2 * q^65 - 86 * q^66 - 4 * q^67 + q^68 - 2 * q^69 - 28 * q^70 - 76 * q^71 + 46 * q^72 + 84 * q^73 + 19 * q^74 + 9 * q^75 - 2 * q^76 - 10 * q^77 - 5 * q^78 - 56 * q^79 - 7 * q^80 + 59 * q^81 - 20 * q^82 - 9 * q^83 + 25 * q^84 - 37 * q^85 - 65 * q^86 - 25 * q^87 - 4 * q^88 - 45 * q^89 - 31 * q^90 + 2 * q^91 + 7 * q^92 - 47 * q^93 + 24 * q^94 - 39 * q^95 + 9 * q^96 + 6 * q^97 + 7 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

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 $

$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$3$	2.23206	−	1.62169i	1.28868	−	0.936281i	0.288902	−	0.957359i	$-0.406710\pi$
$3$	2.23206	−	1.62169i	1.28868	−	0.936281i	0.999778	+	0.0210781i	$0.00670985\pi$
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	−3.24270	+	0.689258i	−1.45018	+	0.308246i	−0.864638	−	0.502396i	$-0.832452\pi$
$5$	−3.24270	+	0.689258i	−1.45018	+	0.308246i	−0.585543	+	0.810641i	$0.699119\pi$
$6$	2.69869	−	0.573623i	1.10173	−	0.234181i
$7$	−0.206641	+	1.96606i	−0.0781029	+	0.743100i	0.883458	+	0.468509i	$0.155209\pi$
$7$	−0.206641	+	1.96606i	−0.0781029	+	0.743100i	−0.961561	+	0.274590i	$0.911458\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	1.42517	−	4.38623i	0.475057	−	1.46208i
$10$	−3.24270	−	0.689258i	−1.02543	−	0.217962i
$11$	−1.71534			−0.517196			−0.258598	−	0.965985i	$-0.583260\pi$
$11$	−1.71534			−0.517196			−0.258598	+	0.965985i	$0.583260\pi$
$12$	2.69869	+	0.573623i	0.779044	+	0.165591i
$13$	−3.52952	−	6.11331i	−0.978912	−	1.69553i	−0.666368	−	0.745623i	$-0.732152\pi$
$13$	−3.52952	−	6.11331i	−0.978912	−	1.69553i	−0.312544	−	0.949903i	$-0.601181\pi$
$14$	−0.988443	+	1.71203i	−0.264173	+	0.457560i
$15$	−6.12015	+	6.79711i	−1.58021	+	1.75501i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	4.94574	+	5.49280i	1.19952	+	1.33220i	0.929267	+	0.369409i	$0.120440\pi$
$17$	4.94574	+	5.49280i	1.19952	+	1.33220i	0.270251	+	0.962790i	$0.412893\pi$
$18$	3.08600	−	3.42735i	0.727377	−	0.807834i
$19$	−0.229827	−	2.18666i	−0.0527259	−	0.501654i	−0.988735	−	0.149678i	$-0.952176\pi$
$19$	−0.229827	−	2.18666i	−0.0527259	−	0.501654i	0.936009	−	0.351976i	$-0.114490\pi$
$20$	−2.68201	−	1.94859i	−0.599716	−	0.435719i
$21$	2.72709	+	4.72346i	0.595100	+	1.03074i
$22$	−1.56705	−	0.697694i	−0.334095	−	0.148749i
$23$	−1.23012	+	3.78593i	−0.256498	+	0.789420i	0.737033	+	0.675857i	$0.236226\pi$
$23$	−1.23012	+	3.78593i	−0.256498	+	0.789420i	−0.993531	+	0.113563i	$0.963774\pi$
$24$	2.23206	+	1.62169i	0.455617	+	0.331025i
$25$	5.47232	−	2.43643i	1.09446	−	0.487287i
$26$	−0.737870	−	7.02037i	−0.144708	−	1.37681i
$27$	−1.37430	−	4.22967i	−0.264485	−	0.814000i
$28$	−1.59933	+	1.16198i	−0.302246	+	0.219594i
$29$	−1.30459	+	2.25962i	−0.242256	+	0.419600i	−0.961357	−	0.275306i	$-0.911221\pi$
$29$	−1.30459	+	2.25962i	−0.242256	+	0.419600i	0.719100	+	0.694906i	$0.244554\pi$
$30$	−8.35566	+	3.72018i	−1.52553	+	0.679209i
$31$	4.25575	−	1.89478i	0.764356	−	0.340313i	0.0127438	−	0.999919i	$-0.495943\pi$
$31$	4.25575	−	1.89478i	0.764356	−	0.340313i	0.751612	+	0.659606i	$0.229277\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−3.82875	+	2.78175i	−0.666500	+	0.484241i
$34$	2.28403	+	7.02953i	0.391709	+	1.20556i
$35$	−0.685045	−	6.51777i	−0.115794	−	1.10170i
$36$	4.21323	−	1.87585i	0.702204	−	0.312642i
$37$	−0.748347	−	0.543706i	−0.123027	−	0.0893847i	0.524570	−	0.851367i	$-0.324226\pi$
$37$	−0.748347	−	0.543706i	−0.123027	−	0.0893847i	−0.647597	+	0.761983i	$0.724226\pi$
$38$	0.679437	−	2.09109i	0.110219	−	0.339220i
$39$	−17.7920	−	7.92149i	−2.84899	−	1.26845i
$40$	−1.65757	−	2.87100i	−0.262085	−	0.453945i
$41$	−3.69381	−	2.68371i	−0.576876	−	0.419125i	0.260721	−	0.965414i	$-0.416040\pi$
$41$	−3.69381	−	2.68371i	−0.576876	−	0.419125i	−0.837596	+	0.546290i	$0.816040\pi$
$42$	0.570117	+	5.42430i	0.0879710	+	0.836988i
$43$	3.98750	−	4.42856i	0.608088	−	0.675350i	−0.357953	−	0.933740i	$-0.616525\pi$
$43$	3.98750	−	4.42856i	0.608088	−	0.675350i	0.966041	+	0.258390i	$0.0831919\pi$
$44$	−1.14779	−	1.27475i	−0.173036	−	0.192176i
$45$	−1.59817	+	15.2055i	−0.238241	+	2.26671i
$46$	−2.66365	+	2.95828i	−0.392733	+	0.436175i
$47$	3.99965	−	6.92759i	0.583409	−	1.01049i	−0.411663	−	0.911336i	$-0.635052\pi$
$47$	3.99965	−	6.92759i	0.583409	−	1.01049i	0.995072	−	0.0991574i	$-0.0316147\pi$
$48$	1.37949	+	2.38934i	0.199112	+	0.344872i
$49$	3.02435	+	0.642846i	0.432051	+	0.0918352i
$50$	5.99020			0.847143
$51$	19.9468	+	4.23982i	2.79311	+	0.593693i
$52$	2.18136	−	6.71354i	0.302501	−	0.931001i
$53$	0.0463429	+	0.142629i	0.00636568	+	0.0195915i	0.954189	−	0.299205i	$-0.0967214\pi$
$53$	0.0463429	+	0.142629i	0.00636568	+	0.0195915i	−0.947823	+	0.318796i	$0.896721\pi$
$54$	0.464873	−	4.42297i	0.0632612	−	0.601890i
$55$	5.56235	−	1.18232i	0.750028	−	0.159423i
$56$	−1.93369	+	0.411018i	−0.258400	+	0.0549246i
$57$	−4.05906	−	4.50804i	−0.537636	−	0.597105i
$58$	−2.11087	+	1.53364i	−0.277171	+	0.201377i
$59$	−2.87903	−	1.28183i	−0.374818	−	0.166880i	0.210677	−	0.977556i	$-0.432433\pi$
$59$	−2.87903	−	1.28183i	−0.374818	−	0.166880i	−0.585495	+	0.810676i	$0.699100\pi$
$60$	−9.14641			−1.18080
$61$	5.59001	+	5.45452i	0.715727	+	0.698380i
$61$	5.59001	+	5.45452i	0.715727	+	0.698380i
$62$	4.65850			0.591630
$63$	8.32907	+	3.70834i	1.04936	+	0.467207i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	15.6588	+	17.3909i	1.94224	+	2.15707i
$66$	−4.62918	+	0.983962i	−0.569812	+	0.121117i
$67$	−9.52519	+	2.02464i	−1.16369	+	0.247349i	−0.748972	−	0.662602i	$-0.769452\pi$
$67$	−9.52519	+	2.02464i	−1.16369	+	0.247349i	−0.414716	+	0.909951i	$0.636119\pi$
$68$	−0.772600	+	7.35080i	−0.0936915	+	0.891415i
$69$	3.39388	+	10.4453i	0.408575	+	1.25746i
$70$	2.02520	−	6.23291i	0.242057	−	0.744975i
$71$	−7.61267	−	1.61812i	−0.903458	−	0.192036i	−0.267317	−	0.963609i	$-0.586137\pi$
$71$	−7.61267	−	1.61812i	−0.903458	−	0.192036i	−0.636141	+	0.771573i	$0.719470\pi$
$72$	4.61195			0.543524
$73$	5.03470	+	1.07016i	0.589267	+	0.125253i	0.492889	−	0.870092i	$-0.335941\pi$
$73$	5.03470	+	1.07016i	0.589267	+	0.125253i	0.0963779	+	0.995345i	$0.469274\pi$
$74$	−0.462504	−	0.801080i	−0.0537650	−	0.0931236i
$75$	8.26341	−	14.3127i	0.954177	−	1.65268i
$76$	1.47122	−	1.63395i	0.168760	−	0.187427i
$77$	0.354460	−	3.37247i	0.0403945	−	0.384328i
$78$	−13.0318	−	14.4733i	−1.47556	−	1.63878i
$79$	−0.924243	+	1.02648i	−0.103985	+	0.115488i	−0.792891	−	0.609364i	$-0.791425\pi$
$79$	−0.924243	+	1.02648i	−0.103985	+	0.115488i	0.688905	+	0.724851i	$0.258092\pi$
$80$	−0.346527	−	3.29699i	−0.0387429	−	0.368614i
$81$	1.26673	+	0.920332i	0.140748	+	0.102259i
$82$	−2.28290	−	3.95410i	−0.252104	−	0.436657i
$83$	−9.96942	−	4.43867i	−1.09429	−	0.487208i	−0.221426	−	0.975177i	$-0.571071\pi$
$83$	−9.96942	−	4.43867i	−1.09429	−	0.487208i	−0.872861	+	0.487970i	$0.837738\pi$
$84$	−1.68544	+	5.18724i	−0.183896	+	0.565974i
$85$	−19.8235	−	14.4026i	−2.15016	−	1.56218i
$86$	5.44402	−	2.42383i	0.587044	−	0.261369i
$87$	0.752466	+	7.15923i	0.0806728	+	0.767550i
$88$	−0.530071	−	1.63139i	−0.0565057	−	0.173907i
$89$	3.10898	−	2.25881i	0.329551	−	0.239433i	−0.410689	−	0.911775i	$-0.634712\pi$
$89$	3.10898	−	2.25881i	0.329551	−	0.239433i	0.740240	+	0.672343i	$0.234712\pi$
$90$	−7.64465	+	13.2409i	−0.805817	+	1.39572i
$91$	12.7484	−	5.67598i	1.33640	−	0.595004i
$92$	−3.63660	+	1.61912i	−0.379142	+	0.168805i
$93$	6.42635	−	11.1308i	0.666381	−	1.15421i
$94$	6.47157	−	4.70187i	0.667491	−	0.484961i
$95$	2.25243	+	6.93228i	0.231095	+	0.711236i
$96$	0.288392	+	2.74386i	0.0294338	+	0.280044i
$97$	−6.47933	+	2.88478i	−0.657876	+	0.292905i	−0.708393	−	0.705818i	$-0.750580\pi$
$97$	−6.47933	+	2.88478i	−0.657876	+	0.292905i	0.0505174	+	0.998723i	$0.483913\pi$
$98$	2.50142	+	1.81739i	0.252681	+	0.183584i
$99$	−2.44466	+	7.52389i	−0.245698	+	0.756179i
$100$	5.47232	+	2.43643i	0.547232	+	0.243643i
$101$	3.88693	+	6.73236i	0.386764	+	0.669895i	0.992012	−	0.126142i	$-0.0402595\pi$
$101$	3.88693	+	6.73236i	0.386764	+	0.669895i	−0.605248	+	0.796037i	$0.706926\pi$
$102$	16.4978	+	11.9863i	1.63352	+	1.18683i
$103$	−0.547702	−	5.21104i	−0.0539667	−	0.513459i	−0.987797	−	0.155744i	$-0.950223\pi$
$103$	−0.547702	−	5.21104i	−0.0539667	−	0.513459i	0.933831	−	0.357715i	$-0.116444\pi$
$104$	4.72342	−	5.24589i	0.463169	−	0.514402i
$105$	−12.0988	−	13.4371i	−1.18073	−	1.31133i
$106$	−0.0156760	+	0.149147i	−0.00152259	+	0.0144864i
$107$	−11.9669	+	13.2906i	−1.15689	+	1.28485i	−0.204878	+	0.978787i	$0.565680\pi$
$107$	−11.9669	+	13.2906i	−1.15689	+	1.28485i	−0.952010	+	0.306067i	$0.900987\pi$
$108$	2.22367	−	3.85150i	0.213972	−	0.370611i
$109$	4.78659	+	8.29061i	0.458472	+	0.794097i	0.998880	−	0.0473060i	$-0.0150636\pi$
$109$	4.78659	+	8.29061i	0.458472	+	0.794097i	−0.540408	+	0.841403i	$0.681730\pi$
$110$	5.56235	+	1.18232i	0.530350	+	0.112729i
$111$	−2.55207			−0.242232
$112$	−1.93369	−	0.411018i	−0.182716	−	0.0388375i
$113$	1.95761	−	6.02491i	0.184157	−	0.566776i	−0.815776	−	0.578368i	$-0.803690\pi$
$113$	1.95761	−	6.02491i	0.184157	−	0.566776i	0.999933	+	0.0115917i	$0.00368984\pi$
$114$	−1.87455	−	5.76927i	−0.175568	−	0.540342i
$115$	1.37944	−	13.1245i	0.128634	−	1.22387i
$116$	−2.55216	+	0.542479i	−0.236962	+	0.0503679i
$117$	−31.8445	+	6.76876i	−2.94403	+	0.625772i
$118$	−2.10876	−	2.34201i	−0.194127	−	0.215600i
$119$	−11.8211	+	8.58856i	−1.08364	+	0.787312i
$120$	−8.35566	−	3.72018i	−0.762764	−	0.339605i
$121$	−8.05759			−0.732508
$122$	2.88817	+	7.25662i	0.261483	+	0.656983i
$123$	−12.5969			−1.13583
$124$	4.25575	+	1.89478i	0.382178	+	0.170157i
$125$	−2.65573	+	1.92950i	−0.237536	+	0.172580i
$126$	6.10067	+	6.77548i	0.543491	+	0.603607i
$127$	10.5410	−	2.24055i	0.935360	−	0.198817i	0.285073	−	0.958506i	$-0.407982\pi$
$127$	10.5410	−	2.24055i	0.935360	−	0.198817i	0.650287	+	0.759689i	$0.274649\pi$
$128$	−0.978148	+	0.207912i	−0.0864569	+	0.0183770i
$129$	1.71859	−	16.3513i	0.151313	−	1.43965i
$130$	7.23154	+	22.2564i	0.634248	+	1.95201i
$131$	−1.47942	+	4.55319i	−0.129258	+	0.397814i	−0.994653	−	0.103276i	$-0.967067\pi$
$131$	−1.47942	+	4.55319i	−0.129258	+	0.397814i	0.865395	+	0.501090i	$0.167067\pi$
$132$	−4.62918	−	0.983962i	−0.402918	−	0.0856429i
$133$	4.34659			0.376897
$134$	−9.52519	−	2.02464i	−0.822851	−	0.174902i
$135$	7.37178	+	12.7683i	0.634462	+	1.09892i
$136$	−3.69564	+	6.40104i	−0.316899	+	0.548885i
$137$	2.25269	−	2.50187i	0.192461	−	0.213749i	−0.639189	−	0.769049i	$-0.720730\pi$
$137$	2.25269	−	2.50187i	0.192461	−	0.213749i	0.831650	+	0.555300i	$0.187397\pi$
$138$	−1.14802	+	10.9227i	−0.0977257	+	0.929798i
$139$	−10.8147	−	12.0109i	−0.917291	−	1.01875i	−0.999754	−	0.0221605i	$-0.992946\pi$
$139$	−10.8147	−	12.0109i	−0.917291	−	1.01875i	0.0824637	−	0.996594i	$-0.473721\pi$
$140$	4.38526	−	4.87033i	0.370622	−	0.411618i
$141$	−2.30693	−	21.9490i	−0.194279	−	1.84844i
$142$	−6.29637	−	4.57458i	−0.528380	−	0.383890i
$143$	6.05434	+	10.4864i	0.506290	+	0.876919i
$144$	4.21323	+	1.87585i	0.351102	+	0.156321i
$145$	2.67294	−	8.22647i	0.221976	−	0.683171i
$146$	4.16415	+	3.02543i	0.344628	+	0.250387i
$147$	7.79303	−	3.46968i	0.642759	−	0.286175i
$148$	−0.0966896	−	0.919940i	−0.00794784	−	0.0756186i
$149$	4.94853	+	15.2300i	0.405399	+	1.24769i	0.920561	+	0.390598i	$0.127732\pi$
$149$	4.94853	+	15.2300i	0.405399	+	1.24769i	−0.515162	+	0.857093i	$0.672268\pi$
$150$	13.3705	−	9.71423i	1.09170	−	0.793163i
$151$	−10.7784	+	18.6687i	−0.877133	+	1.51924i	−0.0226593	+	0.999743i	$0.507213\pi$
$151$	−10.7784	+	18.6687i	−0.877133	+	1.51924i	−0.854473	+	0.519495i	$0.826120\pi$
$152$	2.00862	−	0.894293i	0.162920	−	0.0725368i
$153$	31.1412	−	13.8649i	2.51762	−	1.12091i
$154$	1.69552	−	2.93673i	0.136629	−	0.236648i
$155$	−12.4941	+	9.07753i	−1.00355	+	0.729125i
$156$	−6.01833	−	18.5225i	−0.481852	−	1.48299i
$157$	−0.522174	−	4.96815i	−0.0416740	−	0.396502i	−0.995399	−	0.0958203i	$-0.969453\pi$
$157$	−0.522174	−	4.96815i	−0.0416740	−	0.396502i	0.953725	−	0.300681i	$-0.0972141\pi$
$158$	−1.26184	+	0.561809i	−0.100387	+	0.0446951i
$159$	0.334739	+	0.243202i	0.0265465	+	0.0192872i
$160$	1.02444	−	3.15289i	0.0809888	−	0.249258i
$161$	−7.18915	−	3.20082i	−0.566585	−	0.252260i
$162$	0.782881	+	1.35599i	0.0615089	+	0.106537i
$163$	10.5610	+	7.67298i	0.827198	+	0.600995i	0.918765	−	0.394804i	$-0.129188\pi$
$163$	10.5610	+	7.67298i	0.827198	+	0.600995i	−0.0915672	+	0.995799i	$0.529188\pi$
$164$	−0.477256	−	4.54078i	−0.0372674	−	0.354576i
$165$	10.4982	−	11.6594i	0.817281	−	0.907682i
$166$	−7.30215	−	8.10986i	−0.566757	−	0.629447i
$167$	1.47765	−	14.0589i	0.114344	−	1.08791i	−0.775406	−	0.631462i	$-0.782455\pi$
$167$	1.47765	−	14.0589i	0.114344	−	1.08791i	0.889750	−	0.456447i	$-0.150878\pi$
$168$	−3.64956	+	4.05325i	−0.281570	+	0.312715i
$169$	−18.4150	+	31.8957i	−1.41654	+	2.45352i
$170$	−12.2516	−	21.2204i	−0.939655	−	1.62753i
$171$	−9.91872	−	2.10829i	−0.758504	−	0.161225i
$172$	5.95922			0.454386
$173$	19.8036	+	4.20938i	1.50564	+	0.320033i	0.885567	−	0.464511i	$-0.153770\pi$
$173$	19.8036	+	4.20938i	1.50564	+	0.320033i	0.620072	+	0.784545i	$0.287103\pi$
$174$	−2.22451	+	6.84634i	−0.168640	+	0.519020i
$175$	3.65936	+	11.2624i	0.276622	+	0.851355i
$176$	0.179302	−	1.70595i	0.0135154	−	0.128591i
$177$	−8.50488	+	1.80777i	−0.639266	+	0.135880i
$178$	3.75893	−	0.798986i	0.281744	−	0.0598865i
$179$	−5.21774	−	5.79488i	−0.389992	−	0.433130i	0.515894	−	0.856653i	$-0.327460\pi$
$179$	−5.21774	−	5.79488i	−0.389992	−	0.433130i	−0.905885	+	0.423523i	$0.860793\pi$
$180$	−12.3693	+	8.98682i	−0.921953	+	0.669838i
$181$	−6.65002	−	2.96078i	−0.494292	−	0.220073i	0.144423	−	0.989516i	$-0.453867\pi$
$181$	−6.65002	−	2.96078i	−0.494292	−	0.220073i	−0.638716	+	0.769443i	$0.720534\pi$
$182$	13.9549			1.03441
$183$	21.3227	+	3.10958i	1.57622	+	0.229867i
$184$	−3.98076			−0.293465
$185$	2.80142	+	1.24727i	0.205964	+	0.0917013i
$186$	10.3980	−	7.55462i	0.762422	−	0.553932i
$187$	−8.48365	−	9.42204i	−0.620386	−	0.689008i
$188$	7.82449	−	1.66315i	0.570660	−	0.121297i
$189$	8.59975	−	1.82793i	0.625540	−	0.132963i
$190$	−0.761911	+	7.24910i	−0.0552748	+	0.525905i
$191$	−5.55185	−	17.0868i	−0.401718	−	1.23636i	−0.923605	−	0.383346i	$-0.874772\pi$
$191$	−5.55185	−	17.0868i	−0.401718	−	1.23636i	0.521887	−	0.853015i	$-0.325228\pi$
$192$	−0.852571	+	2.62394i	−0.0615290	+	0.189367i
$193$	−0.472467	−	0.100426i	−0.0340089	−	0.00722881i	0.190876	−	0.981614i	$-0.438867\pi$
$193$	−0.472467	−	0.100426i	−0.0340089	−	0.00722881i	−0.224885	+	0.974385i	$0.572201\pi$
$194$	−7.09251			−0.509212
$195$	63.1540	+	13.4238i	4.52255	+	0.961298i
$196$	1.54596	+	2.67768i	0.110426	+	0.191263i
$197$	8.55232	−	14.8131i	0.609328	−	1.05539i	−0.382024	−	0.924152i	$-0.624773\pi$
$197$	8.55232	−	14.8131i	0.609328	−	1.05539i	0.991351	−	0.131234i	$-0.0418939\pi$
$198$	−5.29355	+	5.87908i	−0.376196	+	0.417808i
$199$	1.49976	−	14.2693i	0.106315	−	1.01152i	−0.803160	−	0.595763i	$-0.796850\pi$
$199$	1.49976	−	14.2693i	0.106315	−	1.01152i	0.909475	−	0.415758i	$-0.136484\pi$
$200$	4.00823	+	4.45159i	0.283425	+	0.314775i
$201$	−17.9775	+	19.9660i	−1.26803	+	1.40829i
$202$	0.812590	+	7.73127i	0.0571736	+	0.543971i
$203$	−4.17295	−	3.03183i	−0.292884	−	0.212793i
$204$	10.1962	+	17.6603i	0.713877	+	1.23647i
$205$	13.8277	+	6.15648i	0.965768	+	0.429987i
$206$	1.61917	−	4.98329i	0.112813	−	0.347202i
$207$	14.8528	+	10.7912i	1.03234	+	0.750039i
$208$	6.44875	−	2.87117i	0.447140	−	0.199080i
$209$	0.394233	+	3.75087i	0.0272696	+	0.259453i
$210$	−5.58747	−	17.1965i	−0.385572	−	1.18667i
$211$	−7.84249	+	5.69790i	−0.539899	+	0.392260i	−0.824048	−	0.566521i	$-0.808289\pi$
$211$	−7.84249	+	5.69790i	−0.539899	+	0.392260i	0.284148	+	0.958780i	$0.408289\pi$
$212$	−0.0749843	+	0.129877i	−0.00514994	+	0.00891996i
$213$	−19.6160	+	8.73362i	−1.34407	+	0.598418i
$214$	−16.3381	+	7.27421i	−1.11685	+	0.497255i
$215$	−9.87785	+	17.1089i	−0.673664	+	1.16682i
$216$	3.59797	−	2.61408i	0.244811	−	0.177865i
$217$	2.84584	+	8.75859i	0.193188	+	0.594572i
$218$	1.00067	+	9.52073i	0.0677739	+	0.644825i
$219$	12.9732	−	5.77604i	0.876648	−	0.390309i
$220$	4.60057	+	3.34251i	0.310171	+	0.225352i
$221$	16.1231	−	49.6217i	1.08456	−	3.33792i
$222$	−2.33144	−	1.03802i	−0.156476	−	0.0696675i
$223$	6.77162	+	11.7288i	0.453461	+	0.785418i	0.998598	−	0.0529289i	$-0.0168557\pi$
$223$	6.77162	+	11.7288i	0.453461	+	0.785418i	−0.545137	+	0.838347i	$0.683522\pi$
$224$	−1.59933	−	1.16198i	−0.106860	−	0.0776384i
$225$	−2.88776	−	27.4752i	−0.192517	−	1.83168i
$226$	4.23892	−	4.70780i	0.281969	−	0.313158i
$227$	9.02191	+	10.0198i	0.598805	+	0.665041i	0.964004	−	0.265889i	$-0.0856655\pi$
$227$	9.02191	+	10.0198i	0.598805	+	0.665041i	−0.365198	+	0.930930i	$0.618999\pi$
$228$	0.634087	−	6.03294i	0.0419935	−	0.399541i
$229$	1.86523	−	2.07155i	0.123258	−	0.136892i	−0.678357	−	0.734732i	$-0.737308\pi$
$229$	1.86523	−	2.07155i	0.123258	−	0.136892i	0.801615	+	0.597840i	$0.203974\pi$
$230$	6.59840	−	11.4288i	0.435086	−	0.753591i
$231$	−4.67790	−	8.10236i	−0.307783	−	0.533096i
$232$	−2.55216	−	0.542479i	−0.167558	−	0.0356155i
$233$	−7.44093			−0.487471			−0.243736	−	0.969842i	$-0.578373\pi$
$233$	−7.44093			−0.487471			−0.243736	+	0.969842i	$0.578373\pi$
$234$	−31.8445	−	6.76876i	−2.08174	−	0.442488i
$235$	−8.19477	+	25.2209i	−0.534568	+	1.64523i
$236$	−0.973864	−	2.99724i	−0.0633931	−	0.195104i
$237$	−0.398343	+	3.78999i	−0.0258752	+	0.246186i
$238$	−14.2924	+	3.03795i	−0.926441	+	0.196921i
$239$	−15.5585	+	3.30705i	−1.00639	+	0.213916i	−0.681487	−	0.731830i	$-0.738666\pi$
$239$	−15.5585	+	3.30705i	−1.00639	+	0.213916i	−0.324907	+	0.945746i	$0.605333\pi$
$240$	−6.12015	−	6.79711i	−0.395054	−	0.438752i
$241$	−4.74362	+	3.44644i	−0.305563	+	0.222005i	−0.729990	−	0.683457i	$-0.760475\pi$
$241$	−4.74362	+	3.44644i	−0.305563	+	0.222005i	0.424427	+	0.905462i	$0.360475\pi$
$242$	−7.36098	−	3.27732i	−0.473181	−	0.210674i
$243$	17.6619			1.13301
$244$	−0.313056	+	7.80397i	−0.0200413	+	0.499598i
$245$	−10.2502			−0.654860
$246$	−11.5079	−	5.12363i	−0.733715	−	0.326671i
$247$	−12.5565	+	9.12286i	−0.798953	+	0.580473i
$248$	3.11715	+	3.46194i	0.197939	+	0.219833i
$249$	−29.4505	+	6.25989i	−1.86635	+	0.396704i
$250$	−3.21093	+	0.682505i	−0.203077	+	0.0431654i
$251$	0.586332	−	5.57857i	0.0370089	−	0.352117i	−0.960310	−	0.278936i	$-0.910018\pi$
$251$	0.586332	−	5.57857i	0.0370089	−	0.352117i	0.997319	−	0.0731807i	$-0.0233150\pi$
$252$	2.81740	+	8.67107i	0.177480	+	0.546226i
$253$	2.11008	−	6.49417i	0.132660	−	0.408285i
$254$	10.5410	+	2.24055i	0.661399	+	0.140585i
$255$	−67.6038			−4.23351
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	−6.69350	−	11.5935i	−0.417529	−	0.723181i	0.578161	−	0.815922i	$-0.303770\pi$
$257$	−6.69350	−	11.5935i	−0.417529	−	0.723181i	−0.995690	+	0.0927412i	$0.970437\pi$
$258$	8.22067	−	14.2386i	0.511797	−	0.886458i
$259$	1.22360	−	1.35894i	0.0760305	−	0.0844404i
$260$	−2.44615	+	23.2736i	−0.151704	+	1.44336i
$261$	8.05193	+	8.94257i	0.498402	+	0.553531i
$262$	−3.20347	+	3.55781i	−0.197911	+	0.219802i
$263$	−0.344379	−	3.27655i	−0.0212353	−	0.202040i	0.978760	−	0.205008i	$-0.0657221\pi$
$263$	−0.344379	−	3.27655i	−0.0212353	−	0.202040i	−0.999996	+	0.00296759i	$0.999055\pi$
$264$	−3.82875	−	2.78175i	−0.235643	−	0.171205i
$265$	−0.248584	−	0.430560i	−0.0152704	−	0.0264491i
$266$	3.97080	+	1.76792i	0.243466	+	0.108398i
$267$	3.27635	−	10.0836i	0.200509	−	0.617105i
$268$	−7.87820	−	5.72385i	−0.481238	−	0.349640i
$269$	−28.1429	+	12.5300i	−1.71591	+	0.763970i	−0.718231	+	0.695804i	$0.755048\pi$
$269$	−28.1429	+	12.5300i	−1.71591	+	0.763970i	−0.997674	+	0.0681659i	$0.978285\pi$
$270$	1.54112	+	14.6628i	0.0937897	+	0.892350i
$271$	−0.828348	−	2.54939i	−0.0503185	−	0.154865i	0.922740	−	0.385423i	$-0.125945\pi$
$271$	−0.828348	−	2.54939i	−0.0503185	−	0.154865i	−0.973058	+	0.230559i	$0.925945\pi$
$272$	−5.97968	+	4.34449i	−0.362571	+	0.263423i
$273$	19.2506	−	33.3431i	1.16510	−	2.01802i
$274$	3.07554	−	1.36932i	0.185800	−	0.0827236i
$275$	−9.38692	+	4.17933i	−0.566053	+	0.252023i
$276$	−5.49141	+	9.51140i	−0.330544	+	0.572519i
$277$	20.3074	−	14.7542i	1.22015	−	0.886494i	0.224042	−	0.974580i	$-0.428075\pi$
$277$	20.3074	−	14.7542i	1.22015	−	0.886494i	0.996113	+	0.0880855i	$0.0280749\pi$
$278$	−4.99443	−	15.3713i	−0.299546	−	0.921908i
$279$	−2.24577	−	21.3671i	−0.134451	−	1.27921i
$280$	5.98707	−	2.66562i	0.357796	−	0.159301i
$281$	15.5848	+	11.3230i	0.929710	+	0.675474i	0.945922	−	0.324395i	$-0.105161\pi$
$281$	15.5848	+	11.3230i	0.929710	+	0.675474i	−0.0162119	+	0.999869i	$0.505161\pi$
$282$	6.81997	−	20.9897i	0.406123	−	1.24992i
$283$	20.6773	+	9.20612i	1.22914	+	0.547247i	0.915508	−	0.402299i	$-0.131789\pi$
$283$	20.6773	+	9.20612i	1.22914	+	0.547247i	0.313629	+	0.949546i	$0.398455\pi$
$284$	−3.89137	−	6.74006i	−0.230910	−	0.399949i
$285$	16.2695	+	11.8205i	0.963724	+	0.700186i
$286$	1.26570	+	12.0424i	0.0748425	+	0.712079i
$287$	6.03961	−	6.70767i	0.356507	−	0.395941i
$288$	3.08600	+	3.42735i	0.181844	+	0.201958i
$289$	−3.93353	+	37.4250i	−0.231384	+	2.20147i
$290$	5.78786	−	6.42807i	0.339875	−	0.377469i
$291$	−9.78403	+	16.9464i	−0.573550	+	0.993417i
$292$	2.57359	+	4.45758i	0.150608	+	0.260860i
$293$	19.7371	+	4.19526i	1.15306	+	0.245090i	0.744486	−	0.667638i	$-0.232694\pi$
$293$	19.7371	+	4.19526i	1.15306	+	0.245090i	0.408569	+	0.912727i	$0.366028\pi$
$294$	8.53054			0.497511
$295$	10.2193	+	2.17219i	0.594993	+	0.126470i
$296$	0.285843	−	0.879734i	0.0166143	−	0.0511335i
$297$	2.35740	+	7.25534i	0.136790	+	0.420997i
$298$	−1.67389	+	15.9260i	−0.0969661	+	0.922571i
$299$	27.4863	−	5.84239i	1.58957	−	0.337874i
$300$	16.1657	−	3.43612i	0.933326	−	0.198385i
$301$	7.88283	+	8.75477i	0.454359	+	0.504616i
$302$	−17.4398	+	12.6708i	−1.00355	+	0.729120i
$303$	19.5936	+	8.72364i	1.12562	+	0.501160i
$304$	2.19870			0.126104
$305$	−21.8863	−	13.8344i	−1.25321	−	0.792158i
$306$	34.0883			1.94870
$307$	−8.46731	−	3.76989i	−0.483255	−	0.215159i	0.150624	−	0.988591i	$-0.451872\pi$
$307$	−8.46731	−	3.76989i	−0.483255	−	0.215159i	−0.633879	+	0.773432i	$0.718538\pi$
$308$	2.74341	−	1.99320i	0.156320	−	0.113573i
$309$	−9.67317	−	10.7431i	−0.550287	−	0.611156i
$310$	−15.1061	+	3.21091i	−0.857971	+	0.182367i
$311$	−0.0536889	+	0.0114119i	−0.00304442	+	0.000647111i	−0.209434	−	0.977823i	$-0.567162\pi$
$311$	−0.0536889	+	0.0114119i	−0.00304442	+	0.000647111i	0.206389	+	0.978470i	$0.433829\pi$
$312$	2.03577	−	19.3690i	0.115253	−	1.09656i
$313$	−2.81618	−	8.66731i	−0.159180	−	0.489905i	0.839380	−	0.543544i	$-0.182918\pi$
$313$	−2.81618	−	8.66731i	−0.159180	−	0.489905i	−0.998560	+	0.0536389i	$0.982918\pi$
$314$	1.54370	−	4.75102i	0.0871160	−	0.268116i
$315$	−29.5647	−	6.28417i	−1.66578	−	0.354073i
$316$	−1.38126			−0.0777019
$317$	−2.30065	−	0.489019i	−0.129218	−	0.0274661i	0.142849	−	0.989745i	$-0.454374\pi$
$317$	−2.30065	−	0.489019i	−0.129218	−	0.0274661i	−0.272066	+	0.962278i	$0.587707\pi$
$318$	0.206880	+	0.358327i	0.0116013	+	0.0200940i
$319$	2.23782	−	3.87602i	0.125294	−	0.217016i
$320$	2.21827	−	2.46363i	0.124005	−	0.137721i
$321$	−5.15769	+	49.0721i	−0.287874	+	2.73894i
$322$	−5.26573	−	5.84818i	−0.293448	−	0.325907i
$323$	10.8742	−	12.0770i	0.605057	−	0.671984i
$324$	0.163667	+	1.55718i	0.00909259	+	0.0865102i
$325$	−34.2093	−	24.8545i	−1.89759	−	1.37868i
$326$	6.52703	+	11.3051i	0.361499	+	0.626134i
$327$	24.1287	+	10.7428i	1.33432	+	0.594078i
$328$	1.41091	−	4.34233i	0.0779044	−	0.239765i
$329$	12.7936	+	9.29506i	0.705331	+	0.512453i
$330$	14.3328	−	6.38139i	0.788997	−	0.351284i
$331$	−2.75585	−	26.2202i	−0.151475	−	1.44119i	−0.761169	−	0.648554i	$-0.775374\pi$
$331$	−2.75585	−	26.2202i	−0.151475	−	1.44119i	0.609694	−	0.792637i	$-0.291292\pi$
$332$	−3.37227	−	10.3788i	−0.185077	−	0.569609i
$333$	−3.45134	+	2.50754i	−0.189132	+	0.137413i
$334$	7.06817	−	12.2424i	0.386753	−	0.669876i
$335$	29.4919	−	13.1306i	1.61131	−	0.717403i
$336$	−4.98264	+	2.21842i	−0.271825	+	0.121025i
$337$	3.88034	−	6.72094i	0.211375	−	0.366113i	−0.740770	−	0.671759i	$-0.765539\pi$
$337$	3.88034	−	6.72094i	0.211375	−	0.366113i	0.952145	+	0.305646i	$0.0988724\pi$
$338$	−29.7961	+	21.6481i	−1.62069	+	1.17750i
$339$	−5.40101	−	16.6226i	−0.293342	−	0.902815i
$340$	−2.56128	−	24.3690i	−0.138905	−	1.32159i
$341$	−7.30008	+	3.25021i	−0.395322	+	0.176009i
$342$	−8.20368	−	5.96033i	−0.443604	−	0.322297i
$343$	−6.16507	+	18.9741i	−0.332882	+	1.02451i
$344$	5.44402	+	2.42383i	0.293522	+	0.130684i
$345$	−18.2048	−	31.5317i	−0.980115	−	1.69761i
$346$	16.3794	+	11.9003i	0.880560	+	0.639765i
$347$	−1.82067	−	17.3225i	−0.0977388	−	0.929923i	−0.928008	−	0.372560i	$-0.878480\pi$
$347$	−1.82067	−	17.3225i	−0.0977388	−	0.929923i	0.830269	−	0.557363i	$-0.188187\pi$
$348$	−4.81685	+	5.34965i	−0.258210	+	0.286772i
$349$	18.8674	+	20.9544i	1.00995	+	1.12166i	0.992553	+	0.121813i	$0.0388709\pi$
$349$	18.8674	+	20.9544i	1.00995	+	1.12166i	0.0173960	+	0.999849i	$0.494462\pi$
$350$	−1.23782	+	11.7771i	−0.0661643	+	0.629511i
$351$	−21.0066	+	23.3302i	−1.12125	+	1.24527i
$352$	0.857672	−	1.48553i	0.0457141	−	0.0791791i
$353$	0.509440	+	0.882376i	0.0271147	+	0.0469641i	0.879264	−	0.476334i	$-0.158035\pi$
$353$	0.509440	+	0.882376i	0.0271147	+	0.0469641i	−0.852150	+	0.523298i	$0.824701\pi$
$354$	−8.50488	−	1.80777i	−0.452029	−	0.0960818i
$355$	25.8009			1.36937
$356$	3.75893	+	0.798986i	0.199223	+	0.0423462i
$357$	−12.4575	+	38.3404i	−0.659323	+	2.02919i
$358$	−2.40965	−	7.41613i	−0.127354	−	0.391955i
$359$	0.874048	−	8.31601i	0.0461305	−	0.438902i	−0.946942	−	0.321403i	$-0.895846\pi$
$359$	0.874048	−	8.31601i	0.0461305	−	0.438902i	0.993073	−	0.117499i	$-0.0374878\pi$
$360$	−14.9552	+	3.17882i	−0.788208	+	0.167539i
$361$	13.8561	−	2.94522i	0.729271	−	0.155011i
$362$	−4.87084	−	5.40962i	−0.256006	−	0.284323i
$363$	−17.9850	+	13.0669i	−0.943969	+	0.685833i
$364$	12.7484	+	5.67598i	0.668200	+	0.297502i
$365$	−17.0636			−0.893152
$366$	18.2145	+	11.5135i	0.952088	+	0.601820i
$367$	11.3005			0.589882			0.294941	−	0.955515i	$-0.404700\pi$
$367$	11.3005			0.589882			0.294941	+	0.955515i	$0.404700\pi$
$368$	−3.63660	−	1.61912i	−0.189571	−	0.0844025i
$369$	−17.0357	+	12.3771i	−0.886841	+	0.644328i
$370$	2.05191	+	2.27888i	0.106674	+	0.118473i
$371$	−0.289992	+	0.0616398i	−0.0150556	+	0.00320018i
$372$	12.5718	−	2.67222i	0.651819	−	0.138548i
$373$	2.29415	−	21.8274i	0.118787	−	1.13018i	−0.758988	−	0.651105i	$-0.774306\pi$
$373$	2.29415	−	21.8274i	0.118787	−	1.13018i	0.877774	−	0.479074i	$-0.159028\pi$
$374$	−3.91791	−	12.0581i	−0.202590	−	0.623508i
$375$	−2.79871	+	8.61353i	−0.144525	+	0.444801i
$376$	7.82449	+	1.66315i	0.403517	+	0.0857703i
$377$	18.4183			0.948591
$378$	8.59975	+	1.82793i	0.442323	+	0.0940188i
$379$	−2.96406	−	5.13390i	−0.152254	−	0.263711i	0.779802	−	0.626026i	$-0.215320\pi$
$379$	−2.96406	−	5.13390i	−0.152254	−	0.263711i	−0.932056	+	0.362315i	$0.881986\pi$
$380$	−3.64451	+	6.31248i	−0.186960	+	0.323823i
$381$	19.8946	−	22.0952i	1.01923	−	1.13197i
$382$	1.87798	−	17.8678i	0.0960856	−	0.914194i
$383$	0.255443	+	0.283699i	0.0130525	+	0.0144963i	0.749636	−	0.661851i	$-0.230229\pi$
$383$	0.255443	+	0.283699i	0.0130525	+	0.0144963i	−0.736583	+	0.676347i	$0.763562\pi$
$384$	−1.84612	+	2.05032i	−0.0942092	+	0.104630i
$385$	1.17509	+	11.1802i	0.0598881	+	0.569797i
$386$	−0.390773	−	0.283913i	−0.0198898	−	0.0144508i
$387$	−13.7418	−	23.8015i	−0.698536	−	1.20990i
$388$	−6.47933	−	2.88478i	−0.328938	−	0.146453i
$389$	−0.414084	+	1.27442i	−0.0209949	+	0.0646157i	−0.961005	−	0.276531i	$-0.910815\pi$
$389$	−0.414084	+	1.27442i	−0.0209949	+	0.0646157i	0.940010	+	0.341146i	$0.110815\pi$
$390$	52.2341	+	37.9503i	2.64498	+	1.92169i
$391$	−26.8792	+	11.9674i	−1.35934	+	0.605217i
$392$	0.323194	+	3.07498i	0.0163237	+	0.155310i
$393$	4.08169	+	12.5621i	0.205894	+	0.633676i
$394$	13.8379	−	10.0539i	0.697146	−	0.506506i
$395$	2.28954	−	3.96560i	0.115199	−	0.199531i
$396$	−7.22714	+	3.21773i	−0.363177	+	0.161697i
$397$	14.0006	−	6.23345i	0.702668	−	0.312848i	−0.0241209	−	0.999709i	$-0.507679\pi$
$397$	14.0006	−	6.23345i	0.702668	−	0.312848i	0.726789	+	0.686861i	$0.241012\pi$
$398$	7.17393	−	12.4256i	0.359597	−	0.622839i
$399$	9.70184	−	7.04880i	0.485699	−	0.352881i
$400$	1.85107	+	5.69702i	0.0925537	+	0.284851i
$401$	−2.26742	−	21.5731i	−0.113230	−	1.07731i	−0.892633	−	0.450785i	$-0.851144\pi$
$401$	−2.26742	−	21.5731i	−0.113230	−	1.07731i	0.779403	−	0.626523i	$-0.215523\pi$
$402$	−24.5441	+	10.9277i	−1.22415	+	0.545027i
$403$	−26.6041	−	19.3290i	−1.32525	−	0.962848i
$404$	−2.40225	+	7.39338i	−0.119517	+	0.367834i
$405$	−4.74197	−	2.11126i	−0.235630	−	0.104909i
$406$	−2.57903	−	4.46701i	−0.127995	−	0.221694i
$407$	1.28367	+	0.932643i	0.0636293	+	0.0462294i
$408$	2.13159	+	20.2807i	0.105529	+	1.00404i
$409$	9.66906	−	10.7386i	0.478104	−	0.530989i	−0.455049	−	0.890466i	$-0.650378\pi$
$409$	9.66906	−	10.7386i	0.478104	−	0.530989i	0.933154	+	0.359478i	$0.117045\pi$
$410$	10.1282	+	11.2485i	0.500194	+	0.555522i
$411$	0.970898	−	9.23748i	0.0478909	−	0.455651i
$412$	3.50607	−	3.89389i	0.172732	−	0.191838i
$413$	3.11507	−	5.39546i	0.153282	−	0.265493i
$414$	9.17953	+	15.8994i	0.451149	+	0.781414i
$415$	35.3873	+	7.52180i	1.73709	+	0.369230i
$416$	7.05904			0.346098
$417$	−43.6170	−	9.27108i	−2.13593	−	0.454007i
$418$	−1.16547	+	3.58694i	−0.0570049	+	0.175443i
$419$	7.41085	+	22.8082i	0.362044	+	1.11426i	0.951812	+	0.306683i	$0.0992191\pi$
$419$	7.41085	+	22.8082i	0.362044	+	1.11426i	−0.589768	+	0.807573i	$0.700781\pi$
$420$	1.89002	−	17.9824i	0.0922237	−	0.877450i
$421$	−24.9084	+	5.29444i	−1.21396	+	0.258035i	−0.770019	−	0.638021i	$-0.779753\pi$
$421$	−24.9084	+	5.29444i	−1.21396	+	0.258035i	−0.443940	+	0.896056i	$0.646420\pi$
$422$	−9.48201	+	2.01546i	−0.461577	+	0.0981113i
$423$	−24.6858	−	27.4164i	−1.20027	−	1.33303i
$424$	−0.121327	+	0.0881493i	−0.00589217	+	0.00428091i
$425$	40.4475	+	18.0084i	1.96199	+	0.873535i
$426$	−21.4724			−1.04034
$427$	−11.8790	+	9.86314i	−0.574866	+	0.477311i
$428$	−17.8843			−0.864471
$429$	30.5193	+	13.5881i	1.47349	+	0.656039i
$430$	−15.9827	+	11.6121i	−0.770754	+	0.559985i
$431$	3.07607	+	3.41632i	0.148169	+	0.164558i	0.812660	−	0.582738i	$-0.198018\pi$
$431$	3.07607	+	3.41632i	0.148169	+	0.164558i	−0.664491	+	0.747296i	$0.731352\pi$
$432$	4.35015	−	0.924653i	0.209297	−	0.0444874i
$433$	−14.4328	+	3.06778i	−0.693595	+	0.147428i	−0.541203	−	0.840892i	$-0.682031\pi$
$433$	−14.4328	+	3.06778i	−0.693595	+	0.147428i	−0.152392	+	0.988320i	$0.548698\pi$
$434$	−0.962637	+	9.15888i	−0.0462080	+	0.439640i
$435$	−7.37458	−	22.6966i	−0.353584	−	1.08822i
$436$	−2.95827	+	9.10463i	−0.141676	+	0.436033i
$437$	8.56124	+	1.81975i	0.409540	+	0.0870504i
$438$	14.2009			0.678547
$439$	−29.7733	−	6.32851i	−1.42100	−	0.302043i	−0.567604	−	0.823302i	$-0.692129\pi$
$439$	−29.7733	−	6.32851i	−1.42100	−	0.302043i	−0.853399	+	0.521259i	$0.825463\pi$
$440$	2.84331	+	4.92476i	0.135550	+	0.234779i
$441$	7.12989	−	12.3493i	0.339519	−	0.588064i
$442$	34.9122	−	38.7739i	1.66060	−	1.84428i
$443$	1.66172	−	15.8102i	0.0789505	−	0.751164i	−0.881400	−	0.472370i	$-0.843399\pi$
$443$	1.66172	−	15.8102i	0.0789505	−	0.751164i	0.960351	−	0.278794i	$-0.0899347\pi$
$444$	−1.70767	−	1.89656i	−0.0810425	−	0.0900068i
$445$	−8.52460	+	9.46752i	−0.404105	+	0.448804i
$446$	1.41565	+	13.4691i	0.0670332	+	0.637778i
$447$	35.7437	+	25.9693i	1.69062	+	1.22831i
$448$	−0.988443	−	1.71203i	−0.0466995	−	0.0808860i
$449$	10.2917	+	4.58218i	0.485697	+	0.216246i	0.634951	−	0.772553i	$-0.281020\pi$
$449$	10.2917	+	4.58218i	0.485697	+	0.216246i	−0.149254	+	0.988799i	$0.547687\pi$
$450$	8.53706	−	26.2744i	0.402441	−	1.23859i
$451$	6.33615	+	4.60348i	0.298358	+	0.216770i
$452$	5.78728	−	2.57666i	0.272211	−	0.121196i
$453$	6.21679	+	59.1488i	0.292090	+	2.77905i
$454$	4.16649	+	12.8231i	0.195543	+	0.601819i
$455$	−37.4272	+	27.1925i	−1.75462	+	1.27480i
$456$	3.03309	−	5.25346i	0.142037	−	0.246016i
$457$	25.4353	−	11.3245i	1.18981	−	0.529740i	0.286235	−	0.958159i	$-0.407596\pi$
$457$	25.4353	−	11.3245i	1.18981	−	0.529740i	0.903580	+	0.428420i	$0.140930\pi$
$458$	2.54655	−	1.13380i	0.118993	−	0.0529789i
$459$	16.4358	−	28.4676i	0.767156	−	1.32875i
$460$	10.6764	−	7.75689i	0.497792	−	0.361667i
$461$	−5.72843	−	17.6303i	−0.266800	−	0.821125i	−0.991273	−	0.131823i	$-0.957917\pi$
$461$	−5.72843	−	17.6303i	−0.266800	−	0.821125i	0.724474	−	0.689303i	$-0.242083\pi$
$462$	−0.977948	−	9.30455i	−0.0454983	−	0.432887i
$463$	−20.5868	+	9.16582i	−0.956748	+	0.425972i	−0.824888	−	0.565297i	$-0.808762\pi$
$463$	−20.5868	+	9.16582i	−0.956748	+	0.425972i	−0.131860	+	0.991268i	$0.542095\pi$
$464$	−2.11087	−	1.53364i	−0.0979948	−	0.0711974i
$465$	−13.1668	+	40.5232i	−0.610594	+	1.87922i
$466$	−6.79763	−	3.02650i	−0.314894	−	0.140200i
$467$	−14.6159	−	25.3154i	−0.676341	−	1.17146i	−0.976075	−	0.217434i	$-0.930231\pi$
$467$	−14.6159	−	25.3154i	−0.676341	−	1.17146i	0.299734	−	0.954023i	$-0.403102\pi$
$468$	−26.3383	−	19.1359i	−1.21749	−	0.884557i
$469$	−2.01227	−	19.1454i	−0.0929179	−	0.884054i
$470$	−17.7446	+	19.7073i	−0.818496	+	0.909032i
$471$	−9.22230	−	10.2424i	−0.424941	−	0.471945i
$472$	0.329420	−	3.13422i	0.0151628	−	0.144264i
$473$	−6.83993	+	7.59651i	−0.314500	+	0.349288i
$474$	−1.90543	+	3.30030i	−0.0875193	+	0.151588i
$475$	−6.58534	−	11.4061i	−0.302156	−	0.523350i
$476$	−14.2924	−	3.03795i	−0.655093	−	0.139244i
$477$	0.691648			0.0316684
$478$	−15.5585	−	3.30705i	−0.711628	−	0.151261i
$479$	1.75877	−	5.41293i	0.0803602	−	0.247323i	−0.902803	−	0.430055i	$-0.858494\pi$
$479$	1.75877	−	5.41293i	0.0803602	−	0.247323i	0.983163	+	0.182732i	$0.0584941\pi$
$480$	−2.82640	−	8.69876i	−0.129007	−	0.397042i
$481$	−0.682535	+	6.49389i	−0.0311209	+	0.296096i
$482$	−5.73530	+	1.21908i	−0.261236	+	0.0555274i
$483$	−21.2373	+	4.51413i	−0.966332	+	0.205400i
$484$	−5.39158	−	5.98796i	−0.245072	−	0.272180i
$485$	19.0222	−	13.8204i	0.863752	−	0.627553i
$486$	16.1350	+	7.18374i	0.731896	+	0.325861i
$487$	−11.4906			−0.520690			−0.260345	−	0.965516i	$-0.583836\pi$
$487$	−11.4906			−0.520690			−0.260345	+	0.965516i	$0.583836\pi$
$488$	−3.46015	+	7.00195i	−0.156634	+	0.316964i
$489$	36.0158			1.62869
$490$	−9.36400	−	4.16912i	−0.423022	−	0.188342i
$491$	−3.18480	+	2.31390i	−0.143728	+	0.104425i	−0.657326	−	0.753607i	$-0.728312\pi$
$491$	−3.18480	+	2.31390i	−0.143728	+	0.104425i	0.513598	+	0.858031i	$0.328312\pi$
$492$	−8.42899	−	9.36134i	−0.380008	−	0.422042i
$493$	−18.8638	+	4.00962i	−0.849582	+	0.180584i
$494$	−15.1816	+	3.22694i	−0.683051	+	0.145187i
$495$	2.74141	−	26.0827i	0.123217	−	1.17233i
$496$	1.43956	+	4.43050i	0.0646380	+	0.198935i
$497$	4.75441	−	14.6326i	0.213265	−	0.656361i
$498$	−29.4505	−	6.25989i	−1.31971	−	0.280512i
$499$	10.8362			0.485095			0.242547	−	0.970140i	$-0.422017\pi$
$499$	10.8362			0.485095			0.242547	+	0.970140i	$0.422017\pi$
$500$	−3.21093	−	0.682505i	−0.143597	−	0.0305226i
$501$	−19.5009	−	33.7766i	−0.871236	−	1.50903i
$502$	2.80465	−	4.85780i	0.125178	−	0.216814i
$503$	−5.44474	+	6.04700i	−0.242769	+	0.269622i	−0.852199	−	0.523217i	$-0.824732\pi$
$503$	−5.44474	+	6.04700i	−0.242769	+	0.269622i	0.609430	+	0.792840i	$0.291398\pi$
$504$	−0.953018	+	9.06736i	−0.0424508	+	0.403892i
$505$	−17.2445	−	19.1519i	−0.767370	−	0.852251i
$506$	4.56907	−	5.07447i	0.203120	−	0.225588i
$507$	10.6215	+	101.056i	0.471716	+	4.48808i
$508$	8.71834	+	6.33424i	0.386814	+	0.281037i
$509$	4.08444	+	7.07445i	0.181039	+	0.313569i	0.942235	−	0.334953i	$-0.108721\pi$
$509$	4.08444	+	7.07445i	0.181039	+	0.313569i	−0.761195	+	0.648523i	$0.775387\pi$
$510$	−61.7591	−	27.4969i	−2.73474	−	1.21758i
$511$	−3.14437	+	9.67736i	−0.139099	+	0.428101i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−8.93298	+	3.97722i	−0.394401	+	0.175599i
$514$	−1.39932	−	13.3137i	−0.0617214	−	0.587240i
$515$	5.36778	+	16.5203i	0.236533	+	0.727973i
$516$	13.3013	−	9.66398i	0.585558	−	0.425433i
$517$	−6.86078	+	11.8832i	−0.301737	+	0.522623i
$518$	1.67054	−	0.743773i	0.0733993	−	0.0326795i
$519$	51.0291	−	22.7196i	2.23993	−	0.997280i
$520$	−11.7009	+	20.2665i	−0.513117	+	0.888745i
$521$	−0.522323	+	0.379490i	−0.0228834	+	0.0166258i	−0.599168	−	0.800623i	$-0.704502\pi$
$521$	−0.522323	+	0.379490i	−0.0228834	+	0.0166258i	0.576285	+	0.817249i	$0.304502\pi$
$522$	3.71853	+	11.4445i	0.162756	+	0.500910i
$523$	0.425243	+	4.04592i	0.0185946	+	0.176916i	0.999877	−	0.0156564i	$-0.00498378\pi$
$523$	0.425243	+	4.04592i	0.0185946	+	0.176916i	−0.981283	+	0.192572i	$0.938317\pi$
$524$	−4.37360	+	1.94725i	−0.191062	+	0.0850662i
$525$	26.4319	+	19.2039i	1.15358	+	0.838128i
$526$	1.01809	−	3.13334i	0.0443906	−	0.136620i
$527$	31.4555	+	14.0049i	1.37022	+	0.610062i
$528$	−2.36630	−	4.09855i	−0.102980	−	0.178366i
$529$	5.78735	+	4.20475i	0.251624	+	0.182815i
$530$	−0.0519682	−	0.494445i	−0.00225736	−	0.0214773i
$531$	−9.72549	+	10.8012i	−0.422050	+	0.468734i
$532$	2.90843	+	3.23014i	0.126097	+	0.140044i
$533$	−3.36897	+	32.0536i	−0.145926	+	1.38839i
$534$	7.09445	−	7.87919i	0.307007	−	0.340966i
$535$	29.6446	−	51.3459i	1.28165	−	2.21988i
$536$	−4.86900	−	8.43335i	−0.210309	−	0.364265i
$537$	−21.0438	−	4.47299i	−0.908106	−	0.193024i
$538$	−30.8063			−1.32815
$539$	−5.18781	−	1.10270i	−0.223455	−	0.0474968i
$540$	−4.55601	+	14.0220i	−0.196060	+	0.603409i
$541$	6.14481	+	18.9118i	0.264186	+	0.813081i	0.991880	+	0.127179i	$0.0405921\pi$
$541$	6.14481	+	18.9118i	0.264186	+	0.813081i	−0.727694	+	0.685902i	$0.759408\pi$
$542$	0.280198	−	2.66590i	0.0120355	−	0.114510i
$543$	−19.6447	+	4.17561i	−0.843035	+	0.179193i
$544$	−7.22977	+	1.53674i	−0.309974	+	0.0658870i
$545$	−21.2359	−	23.5848i	−0.909644	−	1.01026i
$546$	31.1482	−	22.6305i	1.33302	−	0.968495i
$547$	7.23084	+	3.21938i	0.309168	+	0.137651i	0.555455	−	0.831546i	$-0.312544\pi$
$547$	7.23084	+	3.21938i	0.309168	+	0.137651i	−0.246287	+	0.969197i	$0.579211\pi$
$548$	3.36660			0.143814
$549$	31.8915	−	16.7454i	1.36110	−	0.714676i
$550$	−10.2753			−0.438139
$551$	5.24084	+	2.33337i	0.223267	+	0.0994050i
$552$	−8.88529	+	6.45554i	−0.378183	+	0.274766i
$553$	−1.82712	−	2.02923i	−0.0776972	−	0.0862914i
$554$	24.5528	−	5.21886i	1.04315	−	0.221728i
$555$	8.27562	−	1.75904i	0.351280	−	0.0746670i
$556$	1.68942	−	16.0738i	0.0716474	−	0.681680i
$557$	7.58864	+	23.3554i	0.321541	+	0.989602i	0.972978	+	0.230899i	$0.0741666\pi$
$557$	7.58864	+	23.3554i	0.321541	+	0.989602i	−0.651437	+	0.758703i	$0.725833\pi$
$558$	6.63916	−	20.4332i	0.281058	−	0.865008i
$559$	−41.1471	−	8.74609i	−1.74034	−	0.369920i
$560$	6.55367			0.276943
$561$	−34.2156	−	7.27275i	−1.44458	−	0.307056i
$562$	9.63192	+	16.6830i	0.406298	+	0.703729i
$563$	−13.4151	+	23.2356i	−0.565379	+	0.979266i	0.431635	+	0.902048i	$0.357937\pi$
$563$	−13.4151	+	23.2356i	−0.565379	+	0.979266i	−0.997014	+	0.0772174i	$0.975396\pi$
$564$	14.7676	−	16.4011i	0.621829	−	0.690611i
$565$	−2.19524	+	20.8863i	−0.0923544	+	0.878694i
$566$	15.1452	+	16.8204i	0.636599	+	0.707015i
$567$	−2.07118	+	2.30028i	−0.0869815	+	0.0966027i
$568$	−0.813518	−	7.74011i	−0.0341345	−	0.324768i
$569$	13.0340	+	9.46972i	0.546412	+	0.396991i	0.826461	−	0.562994i	$-0.190351\pi$
$569$	13.0340	+	9.46972i	0.546412	+	0.396991i	−0.280049	+	0.959986i	$0.590351\pi$
$570$	10.0551	+	17.4160i	0.421163	+	0.729475i
$571$	42.9665	+	19.1299i	1.79809	+	0.800562i	0.971225	+	0.238166i	$0.0765461\pi$
$571$	42.9665	+	19.1299i	1.79809	+	0.800562i	0.826868	+	0.562397i	$0.190121\pi$
$572$	−3.74179	+	11.5160i	−0.156452	+	0.481510i
$573$	−40.1016	−	29.1355i	−1.67527	−	1.21715i
$574$	8.24572	−	3.67123i	0.344170	−	0.153234i
$575$	2.49254	+	23.7149i	0.103946	+	0.988981i
$576$	1.42517	+	4.38623i	0.0593821	+	0.182759i
$577$	4.62024	−	3.35680i	0.192343	−	0.139746i	−0.487446	−	0.873153i	$-0.662071\pi$
$577$	4.62024	−	3.35680i	0.192343	−	0.139746i	0.679789	+	0.733408i	$0.262071\pi$
$578$	−18.8156	+	32.5895i	−0.782625	+	1.35555i
$579$	−1.21743	+	0.542036i	−0.0505948	+	0.0225262i
$580$	7.90200	−	3.51820i	0.328113	−	0.146085i
$581$	10.7868	−	18.6832i	0.447511	−	0.775111i
$582$	−15.8309	+	11.5018i	−0.656211	+	0.476766i
$583$	−0.0794940	−	0.244657i	−0.00329230	−	0.0101327i
$584$	0.538026	+	5.11898i	0.0222637	+	0.211825i
$585$	98.5969	−	43.8982i	4.07648	−	1.81497i
$586$	16.3244	+	11.8604i	0.674355	+	0.489948i
$587$	5.80422	−	17.8636i	0.239566	−	0.737308i	−0.756917	−	0.653511i	$-0.773295\pi$
$587$	5.80422	−	17.8636i	0.239566	−	0.737308i	0.996483	−	0.0837968i	$-0.0267047\pi$
$588$	7.79303	+	3.46968i	0.321379	+	0.143087i
$589$	−5.12133	−	8.87040i	−0.211021	−	0.365499i
$590$	8.45233	+	6.14098i	0.347977	+	0.252820i
$591$	−4.93283	−	46.9328i	−0.202910	−	1.93056i
$592$	0.618951	−	0.687414i	0.0254387	−	0.0282526i
$593$	16.2358	+	18.0317i	0.666726	+	0.740474i	0.977714	−	0.209940i	$-0.0673268\pi$
$593$	16.2358	+	18.0317i	0.666726	+	0.740474i	−0.310989	+	0.950414i	$0.600660\pi$
$594$	−0.797418	+	7.58692i	−0.0327184	+	0.311295i
$595$	32.4127	−	35.9980i	1.32879	−	1.47577i
$596$	−8.00689	+	13.8683i	−0.327975	+	0.568069i
$597$	−19.7927	−	34.2820i	−0.810061	−	1.40307i
$598$	27.4863	+	5.84239i	1.12400	+	0.238913i
$599$	−19.2883			−0.788098			−0.394049	−	0.919089i	$-0.628926\pi$
$599$	−19.2883			−0.788098			−0.394049	+	0.919089i	$0.628926\pi$
$600$	16.1657	+	3.43612i	0.659961	+	0.140279i
$601$	−1.71273	+	5.27124i	−0.0698637	+	0.215018i	−0.979892	−	0.199527i	$-0.936059\pi$
$601$	−1.71273	+	5.27124i	−0.0698637	+	0.215018i	0.910029	+	0.414545i	$0.136059\pi$
$602$	3.64044	+	11.2041i	0.148373	+	0.456645i
$603$	−4.69449	+	44.6651i	−0.191175	+	1.81890i
$604$	−21.0857	+	4.48191i	−0.857965	+	0.182366i
$605$	26.1284	−	5.55376i	1.06227	−	0.225792i
$606$	14.3514	+	15.9389i	0.582988	+	0.647473i
$607$	18.3421	−	13.3263i	0.744483	−	0.540899i	−0.149629	−	0.988742i	$-0.547808\pi$
$607$	18.3421	−	13.3263i	0.744483	−	0.540899i	0.894112	+	0.447843i	$0.147808\pi$
$608$	2.00862	+	0.894293i	0.0814601	+	0.0362684i
$609$	−14.2309			−0.576667
$610$	−14.3672	−	21.5404i	−0.581709	−	0.872144i
$611$	−56.4673			−2.28442
$612$	31.1412	+	13.8649i	1.25881	+	0.560457i
$613$	10.2452	−	7.44358i	0.413800	−	0.300643i	−0.361338	−	0.932435i	$-0.617680\pi$
$613$	10.2452	−	7.44358i	0.413800	−	0.300643i	0.775138	+	0.631791i	$0.217680\pi$
$614$	−6.20192	−	6.88793i	−0.250289	−	0.277974i
$615$	40.8481	−	8.68253i	1.64715	−	0.350113i
$616$	3.31694	−	0.705037i	0.133643	−	0.0284068i
$617$	−0.269597	+	2.56505i	−0.0108536	+	0.103265i	−0.998607	−	0.0527550i	$-0.983200\pi$
$617$	−0.269597	+	2.56505i	−0.0108536	+	0.103265i	0.987754	+	0.156020i	$0.0498664\pi$
$618$	−4.46725	−	13.7488i	−0.179699	−	0.553057i
$619$	6.32407	−	19.4635i	0.254186	−	0.782304i	−0.739803	−	0.672824i	$-0.765081\pi$
$619$	6.32407	−	19.4635i	0.254186	−	0.782304i	0.993989	−	0.109480i	$-0.0349187\pi$
$620$	−15.1061	−	3.21091i	−0.606677	−	0.128953i
$621$	17.7038			0.710428
$622$	−0.0536889	−	0.0114119i	−0.00215273	−	0.000457576i
$623$	3.79850	+	6.57919i	0.152184	+	0.263590i
$624$	9.73786	−	16.8665i	0.389826	−	0.675199i
$625$	−12.7593	+	14.1706i	−0.510372	+	0.566826i
$626$	0.952604	−	9.06343i	0.0380737	−	0.362247i
$627$	6.96269	+	7.73285i	0.278063	+	0.308820i
$628$	3.34265	−	3.71239i	0.133386	−	0.148141i
$629$	−0.714661	−	6.79954i	−0.0284954	−	0.271116i
$630$	−24.4527	−	17.7659i	−0.974219	−	0.707811i
$631$	15.9622	+	27.6473i	0.635445	+	1.10062i	0.986421	+	0.164238i	$0.0525166\pi$
$631$	15.9622	+	27.6473i	0.635445	+	1.10062i	−0.350976	+	0.936385i	$0.614150\pi$
$632$	−1.26184	−	0.561809i	−0.0501934	−	0.0223475i
$633$	−8.26469	+	25.4361i	−0.328492	+	1.01099i
$634$	−1.90285	−	1.38250i	−0.0755718	−	0.0549062i
$635$	−32.6369	+	14.5309i	−1.29516	+	0.576641i
$636$	0.0432497	+	0.411493i	0.00171496	+	0.0163168i
$637$	−6.74460	−	20.7577i	−0.267231	−	0.822452i
$638$	3.62087	−	2.63072i	0.143352	−	0.104151i
$639$	−17.9468	+	31.0848i	−0.709965	+	1.22970i
$640$	3.02854	−	1.34839i	0.119713	−	0.0532999i
$641$	−42.7285	+	19.0240i	−1.68767	+	0.751401i	−0.688005	+	0.725706i	$0.741513\pi$
$641$	−42.7285	+	19.0240i	−1.68767	+	0.751401i	−0.999670	+	0.0256946i	$0.991820\pi$
$642$	−24.6712	+	42.7318i	−0.973695	+	1.68649i
$643$	1.84559	−	1.34090i	0.0727831	−	0.0528800i	−0.550799	−	0.834638i	$-0.685677\pi$
$643$	1.84559	−	1.34090i	0.0727831	−	0.0528800i	0.623582	+	0.781758i	$0.285677\pi$
$644$	−2.43181	−	7.48435i	−0.0958268	−	0.294925i
$645$	5.69738	+	54.2069i	0.224334	+	2.13439i
$646$	14.8463	−	6.60998i	0.584118	−	0.260066i
$647$	−37.6495	−	27.3539i	−1.48015	−	1.07539i	−0.977507	−	0.210902i	$-0.932360\pi$
$647$	−37.6495	−	27.3539i	−1.48015	−	1.07539i	−0.502646	−	0.864492i	$-0.667640\pi$
$648$	−0.483847	+	1.48913i	−0.0190073	+	0.0584985i
$649$	4.93853	+	2.19877i	0.193854	+	0.0863094i
$650$	−21.1425	−	36.6199i	−0.829278	−	1.43635i
$651$	20.5558	+	14.9346i	0.805644	+	0.585334i
$652$	1.36452	+	12.9825i	0.0534388	+	0.508436i
$653$	11.6547	−	12.9439i	0.456085	−	0.506534i	−0.470613	−	0.882340i	$-0.655967\pi$
$653$	11.6547	−	12.9439i	0.456085	−	0.506534i	0.926699	+	0.375806i	$0.122634\pi$
$654$	17.6732	+	19.6281i	0.691076	+	0.767518i
$655$	1.65900	−	15.7843i	0.0648226	−	0.616745i
$656$	3.05511	−	3.39305i	0.119282	−	0.132476i
$657$	11.8693	−	20.5582i	0.463064	−	0.802050i
$658$	7.90685	+	13.6951i	0.308241	+	0.533889i
$659$	0.456915	+	0.0971203i	0.0177989	+	0.00378327i	0.216803	−	0.976215i	$-0.430437\pi$
$659$	0.456915	+	0.0971203i	0.0177989	+	0.00378327i	−0.199004	+	0.979999i	$0.563771\pi$
$660$	15.6893			0.610703
$661$	−11.4991	−	2.44422i	−0.447265	−	0.0950691i	−0.0212276	−	0.999775i	$-0.506757\pi$
$661$	−11.4991	−	2.44422i	−0.447265	−	0.0950691i	−0.426037	+	0.904706i	$0.640091\pi$
$662$	8.14711	−	25.0742i	0.316646	−	0.974537i
$663$	−44.4832	−	136.905i	−1.72758	−	5.31696i
$664$	1.14071	−	10.8531i	0.0442680	−	0.421182i
$665$	−14.0947	+	2.99592i	−0.546569	+	0.116177i
$666$	−4.17286	+	0.886970i	−0.161695	+	0.0343694i
$667$	−6.94994	−	7.71869i	−0.269103	−	0.298869i
$668$	11.4365	−	8.30913i	0.442493	−	0.321490i
$669$	34.1351	+	15.1979i	1.31974	+	0.587585i
$670$	32.2829			1.24720
$671$	−9.58879	−	9.35639i	−0.370171	−	0.361199i
$672$	−5.45418			−0.210400
$673$	7.49290	+	3.33605i	0.288830	+	0.128595i	0.546037	−	0.837761i	$-0.316136\pi$
$673$	7.49290	+	3.33605i	0.288830	+	0.128595i	−0.257207	+	0.966356i	$0.582802\pi$
$674$	6.27852	−	4.56161i	0.241839	−	0.175707i
$675$	−17.8259	−	19.7977i	−0.686120	−	0.762014i
$676$	−36.0252	+	7.65739i	−1.38558	+	0.294515i
$677$	−24.1272	+	5.12840i	−0.927284	+	0.197100i	−0.646714	−	0.762733i	$-0.723857\pi$
$677$	−24.1272	+	5.12840i	−0.927284	+	0.197100i	−0.280571	+	0.959833i	$0.590524\pi$
$678$	1.82695	−	17.3823i	0.0701637	−	0.667563i
$679$	−4.33275	−	13.3348i	−0.166276	−	0.511744i
$680$	7.57191	−	23.3039i	0.290369	−	0.893665i
$681$	36.3865	+	7.73419i	1.39433	+	0.296375i
$682$	−7.99093			−0.305989
$683$	30.3340	+	6.44769i	1.16070	+	0.246714i	0.747712	−	0.664023i	$-0.231152\pi$
$683$	30.3340	+	6.44769i	1.16070	+	0.246714i	0.412986	+	0.910737i	$0.364486\pi$
$684$	−5.07016	−	8.78177i	−0.193862	−	0.335779i
$685$	−5.58038	+	9.66551i	−0.213216	+	0.369300i
$686$	−13.3495	+	14.8262i	−0.509688	+	0.566066i
$687$	0.803905	−	7.64865i	0.0306709	−	0.291814i
$688$	3.98750	+	4.42856i	0.152022	+	0.168837i
$689$	0.708365	−	0.786718i	0.0269865	−	0.0299716i
$690$	−3.80585	−	36.2102i	−0.144886	−	1.37850i
$691$	37.9103	+	27.5434i	1.44217	+	1.04780i	0.987582	+	0.157101i	$0.0502150\pi$
$691$	37.9103	+	27.5434i	1.44217	+	1.04780i	0.454592	+	0.890700i	$0.349785\pi$
$692$	10.1230	+	17.5336i	0.384819	+	0.666526i
$693$	−14.2872	−	6.36108i	−0.542727	−	0.241638i
$694$	5.38245	−	16.5655i	0.204315	−	0.628816i
$695$	43.3475	+	31.4938i	1.64426	+	1.19463i
$696$	−6.57631	+	2.92796i	−0.249274	+	0.110984i
$697$	−3.52753	−	33.5623i	−0.133615	−	1.27126i
$698$	8.71332	+	26.8168i	0.329804	+	1.01503i
$699$	−16.6086	+	12.0668i	−0.628195	+	0.456410i
$700$	−5.92097	+	10.2554i	−0.223792	+	0.387619i
$701$	−45.6596	+	20.3290i	−1.72454	+	0.767814i	−0.727919	+	0.685664i	$0.759512\pi$
$701$	−45.6596	+	20.3290i	−1.72454	+	0.767814i	−0.996620	+	0.0821505i	$0.973821\pi$
$702$	−28.6798	+	12.7691i	−1.08245	+	0.481937i
$703$	−1.01691	+	1.76134i	−0.0383534	+	0.0664301i
$704$	1.38774	−	1.00825i	0.0523025	−	0.0380000i
$705$	22.6092	+	69.5839i	0.851511	+	2.62068i
$706$	0.106502	+	1.01330i	0.00400825	+	0.0381360i
$707$	−14.0394	+	6.25074i	−0.528006	+	0.235083i
$708$	−7.03431	−	5.11072i	−0.264366	−	0.192073i
$709$	−6.17529	+	19.0056i	−0.231918	+	0.713769i	0.765598	+	0.643320i	$0.222443\pi$
$709$	−6.17529	+	19.0056i	−0.231918	+	0.713769i	−0.997515	+	0.0704496i	$0.977557\pi$
$710$	23.5703	+	10.4942i	0.884579	+	0.393840i
$711$	3.18515	+	5.51684i	0.119452	+	0.206898i
$712$	3.10898	+	2.25881i	0.116514	+	0.0846523i
$713$	1.93841	+	18.4428i	0.0725942	+	0.690688i
$714$	−26.9750	+	29.9587i	−1.00951	+	1.12118i
$715$	−26.8603	−	29.8314i	−1.00452	−	1.11563i
$716$	0.815090	−	7.75507i	0.0304614	−	0.289820i
$717$	−29.3644	+	32.6125i	−1.09663	+	1.21794i
$718$	4.18091	−	7.24155i	0.156030	−	0.270252i
$719$	−5.13671	−	8.89704i	−0.191567	−	0.331803i	0.754203	−	0.656642i	$-0.228024\pi$
$719$	−5.13671	−	8.89704i	−0.191567	−	0.331803i	−0.945770	+	0.324838i	$0.894690\pi$
$720$	−14.9552	−	3.17882i	−0.557347	−	0.118468i
$721$	10.3584			0.385766
$722$	13.8561	+	2.94522i	0.515672	+	0.109610i
$723$	−4.99899	+	15.3853i	−0.185914	+	0.572186i
$724$	−2.24945	−	6.92308i	−0.0836000	−	0.257294i
$725$	−1.63373	+	15.5439i	−0.0606752	+	0.577286i
$726$	−21.7449	+	4.62202i	−0.807029	+	0.171539i
$727$	30.6719	−	6.51952i	1.13756	−	0.241795i	0.399631	−	0.916676i	$-0.369138\pi$
$727$	30.6719	−	6.51952i	1.13756	−	0.241795i	0.737927	+	0.674880i	$0.235805\pi$
$728$	9.33766	+	10.3705i	0.346077	+	0.384357i
$729$	35.6222	−	25.8811i	1.31934	−	0.958558i
$730$	−15.5884	−	6.94041i	−0.576953	−	0.256876i
$731$	44.0463			1.62911
$732$	11.9568	+	17.9266i	0.441937	+	0.662586i
$733$	−40.7836			−1.50638			−0.753188	−	0.657805i	$-0.771485\pi$
$733$	−40.7836			−1.50638			−0.753188	+	0.657805i	$0.771485\pi$
$734$	10.3235	+	4.59634i	0.381049	+	0.169654i
$735$	−22.8790	+	16.6226i	−0.843904	+	0.613132i
$736$	−2.66365	−	2.95828i	−0.0981834	−	0.109044i
$737$	16.3390	−	3.47296i	0.601854	−	0.127928i
$738$	−20.5971	+	4.37804i	−0.758189	+	0.161158i
$739$	−5.09310	+	48.4576i	−0.187353	+	1.78254i	0.347584	+	0.937649i	$0.387002\pi$
$739$	−5.09310	+	48.4576i	−0.187353	+	1.78254i	−0.534936	+	0.844892i	$0.679664\pi$
$740$	0.947612	+	2.91645i	0.0348349	+	0.107211i
$741$	−13.2325	+	40.7255i	−0.486109	+	1.49609i
$742$	−0.289992	−	0.0616398i	−0.0106460	−	0.00226287i
$743$	30.1771			1.10709			0.553545	−	0.832819i	$-0.313275\pi$
$743$	30.1771			1.10709			0.553545	+	0.832819i	$0.313275\pi$
$744$	12.5718	+	2.67222i	0.460906	+	0.0979685i
$745$	−26.5440	−	45.9756i	−0.972497	−	1.68441i
$746$	10.9738	−	19.0072i	0.401780	−	0.695903i
$747$	−33.6771	+	37.4023i	−1.23218	+	1.36848i
$748$	1.32528	−	12.6092i	0.0484569	−	0.461036i
$749$	−23.6573	−	26.2741i	−0.864419	−	0.960034i
$750$	−6.06018	+	6.73052i	−0.221287	+	0.245764i
$751$	−2.78799	−	26.5260i	−0.101735	−	0.967947i	−0.919685	−	0.392657i	$-0.871556\pi$
$751$	−2.78799	−	26.5260i	−0.101735	−	0.967947i	0.817949	−	0.575290i	$-0.195111\pi$
$752$	6.47157	+	4.70187i	0.235994	+	0.171460i
$753$	−7.73797	−	13.4026i	−0.281987	−	0.488416i
$754$	16.8260	+	7.49140i	0.612765	+	0.272821i
$755$	22.0836	−	67.9662i	0.803703	−	2.47354i
$756$	7.11278	+	5.16773i	0.258689	+	0.187949i
$757$	−15.1480	+	6.74432i	−0.550563	+	0.245126i	−0.663113	−	0.748520i	$-0.730765\pi$
$757$	−15.1480	+	6.74432i	−0.550563	+	0.245126i	0.112550	+	0.993646i	$0.464098\pi$
$758$	−0.619657	−	5.89565i	−0.0225070	−	0.214139i
$759$	−5.82167	−	17.9173i	−0.211313	−	0.650355i
$760$	−5.89695	+	4.28438i	−0.213905	+	0.155411i
$761$	19.1602	−	33.1864i	0.694556	−	1.20301i	−0.275774	−	0.961222i	$-0.588934\pi$
$761$	19.1602	−	33.1864i	0.694556	−	1.20301i	0.970330	−	0.241784i	$-0.0777324\pi$
$762$	27.1615	−	12.0931i	0.983958	−	0.438086i
$763$	−17.2889	+	7.69752i	−0.625901	+	0.278669i
$764$	8.98309	−	15.5592i	0.324997	−	0.562911i
$765$	−91.4251	+	66.4242i	−3.30548	+	2.40157i
$766$	0.117968	+	0.363070i	0.00426237	+	0.0131182i
$767$	2.32539	+	22.1246i	0.0839650	+	0.798873i
$768$	−2.52045	+	1.12218i	−0.0909489	+	0.0404931i
$769$	−11.8399	−	8.60220i	−0.426958	−	0.310203i	0.353473	−	0.935445i	$-0.385001\pi$
$769$	−11.8399	−	8.60220i	−0.426958	−	0.310203i	−0.780431	+	0.625241i	$0.785001\pi$
$770$	−3.47391	+	10.6916i	−0.125191	+	0.385298i
$771$	−33.7413	−	15.0226i	−1.21516	−	0.541025i
$772$	−0.241511	−	0.418309i	−0.00869217	−	0.0150553i
$773$	−27.1166	−	19.7014i	−0.975316	−	0.708608i	−0.0186589	−	0.999826i	$-0.505940\pi$
$773$	−27.1166	−	19.7014i	−0.975316	−	0.708608i	−0.956657	+	0.291218i	$0.905940\pi$
$774$	−2.87282	−	27.3331i	−0.103261	−	0.982467i
$775$	18.6723	−	20.7377i	0.670730	−	0.744921i
$776$	−4.74581	−	5.27076i	−0.170365	−	0.189209i
$777$	0.527363	−	5.01752i	0.0189190	−	0.180003i
$778$	−0.896638	+	0.995818i	−0.0321460	+	0.0357018i
$779$	−5.01942	+	8.69388i	−0.179839	+	0.311491i
$780$	32.2824	+	55.9148i	1.15590	+	2.00207i
$781$	13.0584	+	2.77564i	0.467265	+	0.0993202i
$782$	−29.4229			−1.05216
$783$	11.3503	+	2.41259i	0.405628	+	0.0862188i
$784$	−0.955456	+	2.94059i	−0.0341234	+	0.105021i
$785$	5.11759	+	15.7503i	0.182655	+	0.562153i
$786$	−1.38068	+	13.1363i	−0.0492471	+	0.468555i
$787$	−42.5337	+	9.04083i	−1.51616	+	0.322271i	−0.889470	−	0.456994i	$-0.848926\pi$
$787$	−42.5337	+	9.04083i	−1.51616	+	0.322271i	−0.626695	+	0.779265i	$0.715593\pi$
$788$	16.7309	−	3.55625i	0.596012	−	0.126686i
$789$	−6.08220	−	6.75497i	−0.216532	−	0.240483i
$790$	3.70455	−	2.69151i	0.131802	−	0.0957598i
$791$	11.4408	+	5.09377i	0.406788	+	0.181114i
$792$	−7.91109			−0.281108
$793$	13.6151	−	53.4253i	0.483488	−	1.89719i
$794$	15.3255			0.543882
$795$	−1.25309	−	0.557910i	−0.0444424	−	0.0197870i
$796$	11.6077	−	8.43346i	0.411423	−	0.298916i
$797$	13.5357	+	15.0329i	0.479459	+	0.532493i	0.933543	−	0.358466i	$-0.116700\pi$
$797$	13.5357	+	15.0329i	0.479459	+	0.532493i	−0.454084	+	0.890959i	$0.650033\pi$
$798$	11.7301	−	2.49330i	0.415240	−	0.0882620i
$799$	57.8331	−	12.2928i	2.04599	−	0.434888i
$800$	−0.626147	+	5.95739i	−0.0221376	+	0.210625i
$801$	−5.47680	−	16.8559i	−0.193513	−	0.595573i
$802$	6.70317	−	20.6302i	0.236697	−	0.728479i
$803$	−8.63624	−	1.83569i	−0.304766	−	0.0647801i
$804$	−26.8669			−0.947522
$805$	25.5185	+	5.42412i	0.899408	+	0.191175i
$806$	−16.4423	−	28.4788i	−0.579154	−	1.00312i
$807$	−42.4969	+	73.6068i	−1.49596	+	2.59108i
$808$	−5.20173	+	5.77710i	−0.182996	+	0.203238i
$809$	−1.42575	+	13.5651i	−0.0501268	+	0.476924i	0.940447	+	0.339941i	$0.110407\pi$
$809$	−1.42575	+	13.5651i	−0.0501268	+	0.476924i	−0.990573	+	0.136983i	$0.956259\pi$
$810$	−3.47328	−	3.85746i	−0.122039	−	0.135537i
$811$	−32.6539	+	36.2658i	−1.14663	+	1.27347i	−0.190125	+	0.981760i	$0.560889\pi$
$811$	−32.6539	+	36.2658i	−1.14663	+	1.27347i	−0.956508	+	0.291706i	$0.905777\pi$
$812$	−0.539163	−	5.12980i	−0.0189209	−	0.180021i
$813$	−5.98323	−	4.34707i	−0.209841	−	0.152458i
$814$	0.793353	+	1.37413i	0.0278070	+	0.0481632i
$815$	−39.5347	−	17.6020i	−1.38484	−	0.616571i
$816$	−6.30160	+	19.3943i	−0.220600	+	0.678937i
$817$	−10.6002	−	7.70149i	−0.370854	−	0.269441i
$818$	13.2009	−	5.87742i	0.461559	−	0.205499i
$819$	−6.72739	−	64.0068i	−0.235074	−	2.23658i
$820$	4.67737	+	14.3955i	0.163341	+	0.502711i
$821$	10.4384	−	7.58391i	0.364301	−	0.264680i	−0.390543	−	0.920585i	$-0.627713\pi$
$821$	10.4384	−	7.58391i	0.364301	−	0.264680i	0.754844	+	0.655905i	$0.227713\pi$
$822$	4.64418	−	8.04396i	0.161984	−	0.280565i
$823$	−23.6159	+	10.5145i	−0.823200	+	0.366512i	−0.774714	−	0.632312i	$-0.782106\pi$
$823$	−23.6159	+	10.5145i	−0.823200	+	0.366512i	−0.0484858	+	0.998824i	$0.515440\pi$
$824$	4.78674	−	2.13119i	0.166754	−	0.0742437i
$825$	−14.1746	+	24.5511i	−0.493496	+	0.854761i
$826$	5.04029	−	3.66198i	0.175374	−	0.127417i
$827$	−16.7571	−	51.5730i	−0.582701	−	1.79337i	−0.608312	−	0.793698i	$-0.708153\pi$
$827$	−16.7571	−	51.5730i	−0.582701	−	1.79337i	0.0256102	−	0.999672i	$-0.491847\pi$
$828$	1.91904	+	18.2585i	0.0666914	+	0.634527i
$829$	−16.8962	+	7.52267i	−0.586829	+	0.261273i	−0.678601	−	0.734507i	$-0.737413\pi$
$829$	−16.8962	+	7.52267i	−0.586829	+	0.261273i	0.0917722	+	0.995780i	$0.470747\pi$
$830$	29.2685	+	21.2648i	1.01592	+	0.738112i
$831$	21.4007	−	65.8645i	0.742381	−	2.28481i
$832$	6.44875	+	2.87117i	0.223570	+	0.0995399i
$833$	11.4266	+	19.7915i	0.395910	+	0.685736i
$834$	−36.0752	−	26.2102i	−1.24918	−	0.907585i
$835$	4.89863	+	46.6073i	0.169524	+	1.61291i
$836$	−2.52365	+	2.80280i	−0.0872822	+	0.0969367i
$837$	−13.8630	−	15.3964i	−0.479175	−	0.532178i
$838$	−2.50680	+	23.8506i	−0.0865960	+	0.823906i
$839$	−32.1256	+	35.6791i	−1.10910	+	1.23178i	−0.138683	+	0.990337i	$0.544287\pi$
$839$	−32.1256	+	35.6791i	−1.10910	+	1.23178i	−0.970415	+	0.241442i	$0.922380\pi$
$840$	9.04071	−	15.6590i	0.311934	−	0.540286i
$841$	11.0961	+	19.2190i	0.382624	+	0.662724i
$842$	−24.9084	−	5.29444i	−0.858399	−	0.182458i
$843$	53.1485			1.83053
$844$	−9.48201	−	2.01546i	−0.326384	−	0.0693751i
$845$	37.7300	−	116.121i	1.29795	−	3.99469i
$846$	−11.4004	−	35.0867i	−0.391953	−	1.20631i
$847$	1.66503	−	15.8417i	0.0572110	−	0.544327i
$848$	−0.146691	+	0.0311802i	−0.00503740	+	0.00107073i
$849$	61.0824	−	12.9835i	2.09634	−	0.445591i
$850$	29.6260	+	32.9030i	1.01616	+	1.12856i
$851$	2.97899	−	2.16436i	0.102118	−	0.0741934i
$852$	−19.6160	−	8.73362i	−0.672034	−	0.299209i
$853$	38.3667			1.31365			0.656825	−	0.754043i	$-0.271899\pi$
$853$	38.3667			1.31365			0.656825	+	0.754043i	$0.271899\pi$
$854$	−14.8637	+	4.17879i	−0.508626	+	0.142995i
$855$	33.6166			1.14966
$856$	−16.3381	−	7.27421i	−0.558426	−	0.248627i
$857$	10.0905	−	7.33119i	0.344686	−	0.250429i	−0.401951	−	0.915661i	$-0.631668\pi$
$857$	10.0905	−	7.33119i	0.344686	−	0.250429i	0.746636	+	0.665233i	$0.231668\pi$
$858$	22.3540	+	24.8267i	0.763154	+	0.847568i
$859$	−8.72989	+	1.85560i	−0.297860	+	0.0633121i	−0.354418	−	0.935087i	$-0.615321\pi$
$859$	−8.72989	+	1.85560i	−0.297860	+	0.0633121i	0.0565577	+	0.998399i	$0.481988\pi$
$860$	−19.3240	+	4.10744i	−0.658942	+	0.140063i
$861$	2.60304	−	24.7663i	0.0887114	−	0.844032i
$862$	1.42059	+	4.37211i	0.0483853	+	0.148915i
$863$	16.2302	−	49.9513i	0.552481	−	1.70036i	−0.150022	−	0.988683i	$-0.547934\pi$
$863$	16.2302	−	49.9513i	0.552481	−	1.70036i	0.702503	−	0.711680i	$-0.252066\pi$
$864$	4.35015	+	0.924653i	0.147995	+	0.0314573i
$865$	−67.1185			−2.28210
$866$	−14.4328	−	3.06778i	−0.490446	−	0.104247i
$867$	51.9117	+	89.9138i	1.76302	+	3.05363i
$868$	−4.60466	+	7.97551i	−0.156292	+	0.270706i
$869$	1.58540	−	1.76076i	0.0537808	−	0.0597297i
$870$	2.49454	−	23.7339i	0.0845727	−	0.804655i
$871$	45.9966	+	51.0844i	1.55854	+	1.73093i
$872$	−6.40571	+	7.11426i	−0.216925	+	0.240919i
$873$	3.41916	+	32.5311i	0.115721	+	1.10101i
$874$	7.08093	+	5.14460i	0.239516	+	0.174019i
$875$	−3.24473	−	5.62004i	−0.109692	−	0.189992i
$876$	12.9732	+	5.77604i	0.438324	+	0.195154i
$877$	−4.47919	+	13.7855i	−0.151251	+	0.465504i	−0.997762	−	0.0668681i	$-0.978699\pi$
$877$	−4.47919	+	13.7855i	−0.151251	+	0.465504i	0.846510	+	0.532372i	$0.178699\pi$
$878$	−24.6252	−	17.8913i	−0.831061	−	0.603801i
$879$	50.8578	−	22.6434i	1.71539	−	0.763742i
$880$	0.594414	+	5.65547i	0.0200377	+	0.190646i
$881$	−2.51590	−	7.74315i	−0.0847629	−	0.260873i	0.899688	−	0.436534i	$-0.143794\pi$
$881$	−2.51590	−	7.74315i	−0.0847629	−	0.260873i	−0.984451	+	0.175660i	$0.943794\pi$
$882$	11.5364	−	8.38169i	0.388451	−	0.282226i
$883$	−16.7002	+	28.9256i	−0.562006	+	0.973423i	0.435315	+	0.900278i	$0.356637\pi$
$883$	−16.7002	+	28.9256i	−0.562006	+	0.973423i	−0.997321	+	0.0731447i	$0.976697\pi$
$884$	47.6646	−	21.2216i	1.60313	−	0.713761i
$885$	26.3328	−	11.7241i	0.885167	−	0.394102i
$886$	7.94863	−	13.7674i	0.267039	−	0.462526i
$887$	17.1739	−	12.4775i	0.576642	−	0.418955i	−0.260870	−	0.965374i	$-0.584009\pi$
$887$	17.1739	−	12.4775i	0.576642	−	0.418955i	0.837512	+	0.546419i	$0.184009\pi$
$888$	−0.788634	−	2.42717i	−0.0264648	−	0.0814504i
$889$	2.22686	+	21.1871i	0.0746864	+	0.710593i
$890$	−11.6384	+	5.18175i	−0.390120	+	0.173693i
$891$	−2.17288	−	1.57869i	−0.0727941	−	0.0528880i
$892$	−4.18509	+	12.8804i	−0.140127	+	0.431267i
$893$	−16.0675	−	7.15372i	−0.537679	−	0.239390i
$894$	22.0908	+	38.2624i	0.738827	+	1.27969i
$895$	20.9137	+	15.1947i	0.699069	+	0.507903i
$896$	−0.206641	−	1.96606i	−0.00690339	−	0.0656813i
$897$	51.8765	−	57.6146i	1.73210	−	1.92370i
$898$	7.53823	+	8.37205i	0.251554	+	0.279379i
$899$	−1.27053	+	12.0883i	−0.0423745	+	0.403167i
$900$	18.4858	−	20.5305i	0.616192	−	0.684350i
$901$	−0.554231	+	0.959956i	−0.0184641	+	0.0319808i
$902$	3.91596	+	6.78264i	0.130387	+	0.225837i
$903$	31.7924	+	6.75769i	1.05799	+	0.224882i
$904$	6.33497			0.210698
$905$	23.6048	+	5.01736i	0.784650	+	0.166783i
$906$	−18.3787	+	56.5637i	−0.610590	+	1.87920i
$907$	8.75450	+	26.9436i	0.290689	+	0.894647i	0.984636	+	0.174621i	$0.0558701\pi$
$907$	8.75450	+	26.9436i	0.290689	+	0.894647i	−0.693947	+	0.720026i	$0.744130\pi$
$908$	−1.40936	+	13.4092i	−0.0467713	+	0.444999i
$909$	35.0692	−	7.45419i	1.16317	−	0.247240i
$910$	−45.2517	+	9.61854i	−1.50008	+	0.318851i
$911$	−9.33647	−	10.3692i	−0.309331	−	0.343547i	0.568355	−	0.822784i	$-0.307580\pi$
$911$	−9.33647	−	10.3692i	−0.309331	−	0.343547i	−0.877686	+	0.479237i	$0.840914\pi$
$912$	4.90763	−	3.56561i	0.162508	−	0.118069i
$913$	17.1010	+	7.61385i	0.565960	+	0.251982i
$914$	27.8424			0.920946
$915$	−71.2866	+	4.61342i	−2.35666	+	0.152515i
$916$	2.78755			0.0921031
$917$	−8.64612	−	3.84950i	−0.285520	−	0.127122i
$918$	26.5936	−	19.3214i	0.877721	−	0.637701i
$919$	10.1168	+	11.2358i	0.333722	+	0.370636i	0.886529	−	0.462674i	$-0.153110\pi$
$919$	10.1168	+	11.2358i	0.333722	+	0.370636i	−0.552807	+	0.833310i	$0.686443\pi$
$920$	12.9084	−	2.74377i	0.425578	−	0.0904594i
$921$	−25.0131	+	5.31670i	−0.824210	+	0.175191i
$922$	1.93771	−	18.4360i	0.0638150	−	0.607159i
$923$	16.9770	+	52.2498i	0.558804	+	1.71982i
$924$	2.89110	−	8.89790i	0.0951103	−	0.292719i
$925$	−5.41990	−	1.15203i	−0.178205	−	0.0378787i
$926$	−22.5350			−0.740547
$927$	−23.6374	−	5.02427i	−0.776353	−	0.165019i
$928$	−1.30459	−	2.25962i	−0.0428253	−	0.0741756i
$929$	14.3754	−	24.8989i	0.471642	−	0.816908i	−0.527832	−	0.849349i	$-0.676995\pi$
$929$	14.3754	−	24.8989i	0.471642	−	0.816908i	0.999474	+	0.0324413i	$0.0103282\pi$
$930$	−28.5107	+	31.6643i	−0.934903	+	1.03831i
$931$	0.710607	−	6.76097i	0.0232892	−	0.221582i
$932$	−4.97895	−	5.52969i	−0.163091	−	0.181131i
$933$	−0.101330	+	0.112539i	−0.00331740	+	0.00368435i
$934$	−3.05555	−	29.0716i	−0.0999805	−	0.951251i
$935$	34.0042	+	24.7055i	1.11206	+	0.807955i
$936$	−16.2780	−	28.1943i	−0.532062	−	0.921558i
$937$	−0.227324	−	0.101211i	−0.00742634	−	0.00330642i	0.403020	−	0.915191i	$-0.367960\pi$
$937$	−0.227324	−	0.101211i	−0.00742634	−	0.00330642i	−0.410446	+	0.911885i	$0.634627\pi$
$938$	5.94886	−	18.3087i	0.194237	−	0.597800i
$939$	−20.3415	−	14.7790i	−0.663821	−	0.482294i
$940$	−24.2262	+	10.7862i	−0.790171	+	0.351807i
$941$	0.922869	+	8.78052i	0.0300847	+	0.286237i	0.999213	+	0.0396779i	$0.0126332\pi$
$941$	0.922869	+	8.78052i	0.0300847	+	0.286237i	−0.969128	+	0.246559i	$0.920700\pi$
$942$	−4.25903	−	13.1080i	−0.138767	−	0.427080i
$943$	14.7042	−	10.6832i	0.478833	−	0.347893i
$944$	1.57574	−	2.72927i	0.0512861	−	0.0888302i
$945$	−26.6265	+	11.8549i	−0.866161	+	0.385640i
$946$	−9.33837	+	4.15771i	−0.303617	+	0.135179i
$947$	6.08676	−	10.5426i	0.197793	−	0.342588i	−0.750019	−	0.661416i	$-0.769956\pi$
$947$	6.08676	−	10.5426i	0.197793	−	0.342588i	0.947813	+	0.318828i	$0.103289\pi$
$948$	−3.08305	+	2.23997i	−0.100133	+	0.0727508i
$949$	−11.2279	−	34.5558i	−0.364472	−	1.12173i
$950$	−1.37671	−	13.0985i	−0.0446664	−	0.424972i
$951$	−5.92823	+	2.63942i	−0.192236	+	0.0855890i
$952$	−11.8211	−	8.58856i	−0.383125	−	0.278357i
$953$	−6.53215	+	20.1039i	−0.211597	+	0.651229i	0.787781	+	0.615956i	$0.211230\pi$
$953$	−6.53215	+	20.1039i	−0.211597	+	0.651229i	−0.999378	+	0.0352730i	$0.988770\pi$
$954$	0.631852	+	0.281319i	0.0204570	+	0.00910802i
$955$	29.7803	+	51.5809i	0.963666	+	1.66912i
$956$	−12.8683	−	9.34934i	−0.416190	−	0.302379i
$957$	−1.29074	−	12.2806i	−0.0417236	−	0.396974i
$958$	3.80835	−	4.22960i	0.123042	−	0.136652i
$959$	4.45332	+	4.94591i	0.143805	+	0.159712i
$960$	0.956061	−	9.09631i	0.0308567	−	0.293582i
$961$	−6.22183	+	6.91004i	−0.200704	+	0.222905i
$962$	−3.26483	+	5.65485i	−0.105262	+	0.182320i
$963$	41.2408	+	71.4312i	1.32897	+	2.30184i
$964$	−5.73530	−	1.21908i	−0.184722	−	0.0392638i
$965$	1.60129			0.0515473
$966$	−21.2373	−	4.51413i	−0.683300	−	0.145240i
$967$	−5.19944	+	16.0022i	−0.167203	+	0.514597i	−0.999192	−	0.0401947i	$-0.987202\pi$
$967$	−5.19944	+	16.0022i	−0.167203	+	0.514597i	0.831989	+	0.554792i	$0.187202\pi$
$968$	−2.48993	−	7.66323i	−0.0800295	−	0.246305i
$969$	4.68672	−	44.5912i	0.150559	−	1.43248i
$970$	22.9989	−	4.88857i	0.738450	−	0.156962i
$971$	−57.0041	+	12.1166i	−1.82935	+	0.388840i	−0.988350	−	0.152199i	$-0.951364\pi$
$971$	−57.0041	+	12.1166i	−1.82935	+	0.388840i	−0.840998	+	0.541039i	$0.818031\pi$
$972$	11.8181	+	13.1254i	0.379066	+	0.420996i
$973$	25.8489	−	18.7804i	0.828679	−	0.602071i
$974$	−10.4972	−	4.67366i	−0.336352	−	0.149754i
$975$	−116.664			−3.73622
$976$	−6.00896	+	4.98923i	−0.192342	+	0.159701i
$977$	3.69924			0.118349			0.0591745	−	0.998248i	$-0.481153\pi$
$977$	3.69924			0.118349			0.0591745	+	0.998248i	$0.481153\pi$
$978$	32.9021	+	14.6490i	1.05209	+	0.468422i
$979$	−5.33297	+	3.87463i	−0.170442	+	0.123834i
$980$	−6.85870	−	7.61736i	−0.219093	−	0.243328i
$981$	43.1862	−	9.17951i	1.37883	−	0.293079i
$982$	−3.85061	+	0.818472i	−0.122878	+	0.0261185i
$983$	−2.67405	+	25.4419i	−0.0852890	+	0.811470i	0.865349	+	0.501169i	$0.167097\pi$
$983$	−2.67405	+	25.4419i	−0.0852890	+	0.811470i	−0.950638	+	0.310301i	$0.899570\pi$
$984$	−3.89266	−	11.9804i	−0.124094	−	0.381921i
$985$	−17.5226	+	53.9291i	−0.558317	+	1.71832i
$986$	−18.8638	−	4.00962i	−0.600745	−	0.127692i
$987$	43.6296			1.38875
$988$	−15.1816	−	3.22694i	−0.482990	−	0.102663i
$989$	11.8611	+	20.5440i	0.377161	+	0.653263i
$990$	13.1132	−	22.7127i	0.416765	−	0.721858i
$991$	−10.0690	+	11.1827i	−0.319852	+	0.355231i	−0.881533	−	0.472122i	$-0.843488\pi$
$991$	−10.0690	+	11.1827i	−0.319852	+	0.355231i	0.561681	+	0.827354i	$0.310155\pi$
$992$	−0.486946	+	4.63298i	−0.0154605	+	0.147097i
$993$	−48.6721	−	54.0558i	−1.54456	−	1.71541i
$994$	10.2950	−	11.4337i	0.326537	−	0.362656i
$995$	4.97192	+	47.3047i	0.157621	+	1.49966i
$996$	−24.3582	−	17.6973i	−0.771819	−	0.560760i
$997$	−19.3413	−	33.5001i	−0.612544	−	1.06096i	−0.990810	−	0.135261i	$-0.956813\pi$
$997$	−19.3413	−	33.5001i	−0.612544	−	1.06096i	0.378266	−	0.925697i	$-0.376521\pi$
$998$	9.89936	+	4.40748i	0.313359	+	0.139516i
$999$	−1.27124	+	3.91247i	−0.0402202	+	0.123785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.i.b.73.3	✓	24
4.3	odd	2		976.2.bw.b.561.1		24
61.19	even	30		7442.2.a.u.1.2		12
61.42	even	15		7442.2.a.w.1.2		12
61.56	even	15	inner	122.2.i.b.117.3	yes	24
244.239	odd	30		976.2.bw.b.849.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.i.b.73.3	✓	24	1.1	even	1	trivial
122.2.i.b.117.3	yes	24	61.56	even	15	inner
976.2.bw.b.561.1		24	4.3	odd	2
976.2.bw.b.849.1		24	244.239	odd	30
7442.2.a.u.1.2		12	61.19	even	30
7442.2.a.w.1.2		12	61.42	even	15

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:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.i (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913545 + 0.406737i) q^{2} +(2.23206 - 1.62169i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-3.24270 + 0.689258i) q^{5} +(2.69869 - 0.573623i) q^{6} +(-0.206641 + 1.96606i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.42517 - 4.38623i) q^{9} +O(q^{10})\)	\(q+(0.913545 + 0.406737i) q^{2} +(2.23206 - 1.62169i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-3.24270 + 0.689258i) q^{5} +(2.69869 - 0.573623i) q^{6} +(-0.206641 + 1.96606i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.42517 - 4.38623i) q^{9} +(-3.24270 - 0.689258i) q^{10} -1.71534 q^{11} +(2.69869 + 0.573623i) q^{12} +(-3.52952 - 6.11331i) q^{13} +(-0.988443 + 1.71203i) q^{14} +(-6.12015 + 6.79711i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(4.94574 + 5.49280i) q^{17} +(3.08600 - 3.42735i) q^{18} +(-0.229827 - 2.18666i) q^{19} +(-2.68201 - 1.94859i) q^{20} +(2.72709 + 4.72346i) q^{21} +(-1.56705 - 0.697694i) q^{22} +(-1.23012 + 3.78593i) q^{23} +(2.23206 + 1.62169i) q^{24} +(5.47232 - 2.43643i) q^{25} +(-0.737870 - 7.02037i) q^{26} +(-1.37430 - 4.22967i) q^{27} +(-1.59933 + 1.16198i) q^{28} +(-1.30459 + 2.25962i) q^{29} +(-8.35566 + 3.72018i) q^{30} +(4.25575 - 1.89478i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.82875 + 2.78175i) q^{33} +(2.28403 + 7.02953i) q^{34} +(-0.685045 - 6.51777i) q^{35} +(4.21323 - 1.87585i) q^{36} +(-0.748347 - 0.543706i) q^{37} +(0.679437 - 2.09109i) q^{38} +(-17.7920 - 7.92149i) q^{39} +(-1.65757 - 2.87100i) q^{40} +(-3.69381 - 2.68371i) q^{41} +(0.570117 + 5.42430i) q^{42} +(3.98750 - 4.42856i) q^{43} +(-1.14779 - 1.27475i) q^{44} +(-1.59817 + 15.2055i) q^{45} +(-2.66365 + 2.95828i) q^{46} +(3.99965 - 6.92759i) q^{47} +(1.37949 + 2.38934i) q^{48} +(3.02435 + 0.642846i) q^{49} +5.99020 q^{50} +(19.9468 + 4.23982i) q^{51} +(2.18136 - 6.71354i) q^{52} +(0.0463429 + 0.142629i) q^{53} +(0.464873 - 4.42297i) q^{54} +(5.56235 - 1.18232i) q^{55} +(-1.93369 + 0.411018i) q^{56} +(-4.05906 - 4.50804i) q^{57} +(-2.11087 + 1.53364i) q^{58} +(-2.87903 - 1.28183i) q^{59} -9.14641 q^{60} +(5.59001 + 5.45452i) q^{61} +4.65850 q^{62} +(8.32907 + 3.70834i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(15.6588 + 17.3909i) q^{65} +(-4.62918 + 0.983962i) q^{66} +(-9.52519 + 2.02464i) q^{67} +(-0.772600 + 7.35080i) q^{68} +(3.39388 + 10.4453i) q^{69} +(2.02520 - 6.23291i) q^{70} +(-7.61267 - 1.61812i) q^{71} +4.61195 q^{72} +(5.03470 + 1.07016i) q^{73} +(-0.462504 - 0.801080i) q^{74} +(8.26341 - 14.3127i) q^{75} +(1.47122 - 1.63395i) q^{76} +(0.354460 - 3.37247i) q^{77} +(-13.0318 - 14.4733i) q^{78} +(-0.924243 + 1.02648i) q^{79} +(-0.346527 - 3.29699i) q^{80} +(1.26673 + 0.920332i) q^{81} +(-2.28290 - 3.95410i) q^{82} +(-9.96942 - 4.43867i) q^{83} +(-1.68544 + 5.18724i) q^{84} +(-19.8235 - 14.4026i) q^{85} +(5.44402 - 2.42383i) q^{86} +(0.752466 + 7.15923i) q^{87} +(-0.530071 - 1.63139i) q^{88} +(3.10898 - 2.25881i) q^{89} +(-7.64465 + 13.2409i) q^{90} +(12.7484 - 5.67598i) q^{91} +(-3.63660 + 1.61912i) q^{92} +(6.42635 - 11.1308i) q^{93} +(6.47157 - 4.70187i) q^{94} +(2.25243 + 6.93228i) q^{95} +(0.288392 + 2.74386i) q^{96} +(-6.47933 + 2.88478i) q^{97} +(2.50142 + 1.81739i) q^{98} +(-2.44466 + 7.52389i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9	\( 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9} - 12 q^{10} + 6 q^{11} - q^{12} + 5 q^{13} - 4 q^{14} - 9 q^{15} + 3 q^{16} + 16 q^{17} + 17 q^{18} - 2 q^{19} - q^{20} + 10 q^{21} + 7 q^{22} + q^{23} - 3 q^{24} + 11 q^{25} - 9 q^{27} - 7 q^{28} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 12 q^{32} + 7 q^{33} - 17 q^{34} + 9 q^{35} + 2 q^{36} - 38 q^{37} + 4 q^{38} - 40 q^{39} - 7 q^{40} - 10 q^{41} + 15 q^{42} - 5 q^{43} + 2 q^{44} - 96 q^{45} - 8 q^{46} + 3 q^{47} - q^{48} + 19 q^{49} + 38 q^{50} + 102 q^{51} + 20 q^{52} - 37 q^{53} + 17 q^{54} + 33 q^{55} + 6 q^{56} - 71 q^{57} + q^{58} - 17 q^{59} - 22 q^{60} + 70 q^{61} + 72 q^{62} + 146 q^{63} - 6 q^{64} + 2 q^{65} - 86 q^{66} - 4 q^{67} + q^{68} - 2 q^{69} - 28 q^{70} - 76 q^{71} + 46 q^{72} + 84 q^{73} + 19 q^{74} + 9 q^{75} - 2 q^{76} - 10 q^{77} - 5 q^{78} - 56 q^{79} - 7 q^{80} + 59 q^{81} - 20 q^{82} - 9 q^{83} + 25 q^{84} - 37 q^{85} - 65 q^{86} - 25 q^{87} - 4 q^{88} - 45 q^{89} - 31 q^{90} + 2 q^{91} + 7 q^{92} - 47 q^{93} + 24 q^{94} - 39 q^{95} + 9 q^{96} + 6 q^{97} + 7 q^{98} - 24 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9 - 12 * q^10 + 6 * q^11 - q^12 + 5 * q^13 - 4 * q^14 - 9 * q^15 + 3 * q^16 + 16 * q^17 + 17 * q^18 - 2 * q^19 - q^20 + 10 * q^21 + 7 * q^22 + q^23 - 3 * q^24 + 11 * q^25 - 9 * q^27 - 7 * q^28 + 2 * q^29 - 4 * q^30 + 14 * q^31 - 12 * q^32 + 7 * q^33 - 17 * q^34 + 9 * q^35 + 2 * q^36 - 38 * q^37 + 4 * q^38 - 40 * q^39 - 7 * q^40 - 10 * q^41 + 15 * q^42 - 5 * q^43 + 2 * q^44 - 96 * q^45 - 8 * q^46 + 3 * q^47 - q^48 + 19 * q^49 + 38 * q^50 + 102 * q^51 + 20 * q^52 - 37 * q^53 + 17 * q^54 + 33 * q^55 + 6 * q^56 - 71 * q^57 + q^58 - 17 * q^59 - 22 * q^60 + 70 * q^61 + 72 * q^62 + 146 * q^63 - 6 * q^64 + 2 * q^65 - 86 * q^66 - 4 * q^67 + q^68 - 2 * q^69 - 28 * q^70 - 76 * q^71 + 46 * q^72 + 84 * q^73 + 19 * q^74 + 9 * q^75 - 2 * q^76 - 10 * q^77 - 5 * q^78 - 56 * q^79 - 7 * q^80 + 59 * q^81 - 20 * q^82 - 9 * q^83 + 25 * q^84 - 37 * q^85 - 65 * q^86 - 25 * q^87 - 4 * q^88 - 45 * q^89 - 31 * q^90 + 2 * q^91 + 7 * q^92 - 47 * q^93 + 24 * q^94 - 39 * q^95 + 9 * q^96 + 6 * q^97 + 7 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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