LMFDB - Embedded newform 418.2.q.a.21.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(21,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("418.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.q (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.7
Character	$\chi$	$=$	418.21
Dual form			418.2.q.a.219.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(0.144347 - 0.172026i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-2.86607 + 1.04316i) q^{5} +(0.144347 + 0.172026i) q^{6} +(0.416271 - 0.240334i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.512188 + 2.90476i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(0.144347 - 0.172026i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-2.86607 + 1.04316i) q^{5} +(0.144347 + 0.172026i) q^{6} +(0.416271 - 0.240334i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.512188 + 2.90476i) q^{9} +(-0.529628 - 3.00367i) q^{10} +(-2.85690 - 1.68468i) q^{11} +(-0.194478 + 0.112282i) q^{12} +(1.28361 - 1.07708i) q^{13} +(0.164398 + 0.451681i) q^{14} +(-0.234257 + 0.643617i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-6.73559 - 1.18767i) q^{17} -2.94957 q^{18} +(-1.17941 - 4.19631i) q^{19} +3.05001 q^{20} +(0.0187438 - 0.106301i) q^{21} +(2.15518 - 2.52095i) q^{22} +(-8.00046 - 2.91193i) q^{23} +(-0.0768055 - 0.211022i) q^{24} +(3.29594 - 2.76562i) q^{25} +(0.837817 + 1.45114i) q^{26} +(1.15706 + 0.668031i) q^{27} +(-0.473366 + 0.0834672i) q^{28} +(-0.535611 - 3.03760i) q^{29} +(-0.593161 - 0.342462i) q^{30} +(-4.09905 + 2.36659i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-0.702194 + 0.248283i) q^{33} +(2.33924 - 6.42702i) q^{34} +(-0.942354 + 1.12305i) q^{35} +(0.512188 - 2.90476i) q^{36} +10.7581i q^{37} +(4.33736 - 0.432811i) q^{38} -0.376288i q^{39} +(-0.529628 + 3.00367i) q^{40} +(5.39386 + 4.52598i) q^{41} +(0.101431 + 0.0369180i) q^{42} +(1.49518 + 4.10797i) q^{43} +(2.10841 + 2.56019i) q^{44} +(-4.49811 - 7.79095i) q^{45} +(4.25696 - 7.37326i) q^{46} +(-0.724581 - 4.10930i) q^{47} +(0.221153 - 0.0389952i) q^{48} +(-3.38448 + 5.86209i) q^{49} +(2.15127 + 3.72611i) q^{50} +(-1.17657 + 0.987262i) q^{51} +(-1.57458 + 0.573101i) q^{52} +(1.51502 - 4.16247i) q^{53} +(-0.858804 + 1.02348i) q^{54} +(9.94546 + 1.84818i) q^{55} -0.480668i q^{56} +(-0.892120 - 0.402836i) q^{57} +3.08446 q^{58} +(7.03232 + 1.23999i) q^{59} +(0.440260 - 0.524682i) q^{60} +(0.344560 - 0.946671i) q^{61} +(-1.61884 - 4.44773i) q^{62} +(0.911322 + 1.08607i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.55535 + 4.42600i) q^{65} +(-0.122577 - 0.734640i) q^{66} +(11.8120 - 2.08278i) q^{67} +(5.92318 + 3.41975i) q^{68} +(-1.65577 + 0.955961i) q^{69} +(-0.942354 - 1.12305i) q^{70} +(2.30809 + 6.34142i) q^{71} +(2.77169 + 1.00881i) q^{72} +(1.60948 - 1.91810i) q^{73} +(-10.5946 - 1.86812i) q^{74} -0.966199i q^{75} +(-0.326939 + 4.34662i) q^{76} +(-1.59413 - 0.0146713i) q^{77} +(0.370571 + 0.0653417i) q^{78} +(-7.42007 - 6.22618i) q^{79} +(-2.86607 - 1.04316i) q^{80} +(-8.03313 + 2.92382i) q^{81} +(-5.39386 + 4.52598i) q^{82} +(-11.3910 + 6.57657i) q^{83} +(-0.0539705 + 0.0934797i) q^{84} +(20.5436 - 3.62239i) q^{85} +(-4.30520 + 0.759123i) q^{86} +(-0.599861 - 0.346330i) q^{87} +(-2.88742 + 1.63181i) q^{88} +(-8.94689 - 10.6625i) q^{89} +(8.45368 - 3.07689i) q^{90} +(0.275471 - 0.756852i) q^{91} +(6.52203 + 5.47264i) q^{92} +(-0.184571 + 1.04676i) q^{93} +4.17269 q^{94} +(7.75771 + 10.7966i) q^{95} +0.224564i q^{96} +(-3.31865 - 0.585168i) q^{97} +(-5.18532 - 4.35100i) q^{98} +(3.43031 - 9.16147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9}+O(q^{10}) $ 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9	$ 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9} + 3 q^{11} + 6 q^{13} - 12 q^{14} + 24 q^{15} - 6 q^{17} + 60 q^{18} - 30 q^{19} - 12 q^{20} + 12 q^{21} + 12 q^{22} + 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} + 6 q^{28} - 3 q^{29} - 9 q^{31} - 42 q^{33} - 6 q^{34} - 24 q^{35} - 3 q^{36} + 6 q^{38} + 15 q^{41} + 6 q^{42} - 3 q^{43} + 12 q^{44} - 48 q^{45} + 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} + 36 q^{50} - 45 q^{51} - 3 q^{52} + 24 q^{53} - 27 q^{54} + 6 q^{55} + 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} + 54 q^{61} - 66 q^{63} - 30 q^{64} - 63 q^{66} + 9 q^{67} - 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 36 q^{79} - 93 q^{81} - 15 q^{82} - 36 q^{83} + 24 q^{84} - 60 q^{85} - 3 q^{86} + 54 q^{87} - 3 q^{88} - 3 q^{89} - 24 q^{90} - 12 q^{91} - 102 q^{93} - 12 q^{94} + 24 q^{95} - 6 q^{97} - 18 q^{98} - 78 q^{99}+O(q^{100}) $ 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9 + 3 * q^11 + 6 * q^13 - 12 * q^14 + 24 * q^15 - 6 * q^17 + 60 * q^18 - 30 * q^19 - 12 * q^20 + 12 * q^21 + 12 * q^22 + 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 + 6 * q^28 - 3 * q^29 - 9 * q^31 - 42 * q^33 - 6 * q^34 - 24 * q^35 - 3 * q^36 + 6 * q^38 + 15 * q^41 + 6 * q^42 - 3 * q^43 + 12 * q^44 - 48 * q^45 + 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 + 36 * q^50 - 45 * q^51 - 3 * q^52 + 24 * q^53 - 27 * q^54 + 6 * q^55 + 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 + 54 * q^61 - 66 * q^63 - 30 * q^64 - 63 * q^66 + 9 * q^67 - 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 36 * q^79 - 93 * q^81 - 15 * q^82 - 36 * q^83 + 24 * q^84 - 60 * q^85 - 3 * q^86 + 54 * q^87 - 3 * q^88 - 3 * q^89 - 24 * q^90 - 12 * q^91 - 102 * q^93 - 12 * q^94 + 24 * q^95 - 6 * q^97 - 18 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	0.144347	−	0.172026i	0.0833389	−	0.0993194i	−0.722764	−	0.691095i	$-0.757128\pi$
$3$	0.144347	−	0.172026i	0.0833389	−	0.0993194i	0.806103	+	0.591776i	$0.201573\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−2.86607	+	1.04316i	−1.28175	+	0.466517i	−0.891009	−	0.453986i	$-0.850002\pi$
$5$	−2.86607	+	1.04316i	−1.28175	+	0.466517i	−0.390736	+	0.920503i	$0.627780\pi$
$6$	0.144347	+	0.172026i	0.0589295	+	0.0702294i
$7$	0.416271	−	0.240334i	0.157336	−	0.0908378i	−0.419265	−	0.907864i	$-0.637712\pi$
$7$	0.416271	−	0.240334i	0.157336	−	0.0908378i	0.576601	+	0.817026i	$0.304379\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.512188	+	2.90476i	0.170729	+	0.968253i
$10$	−0.529628	−	3.00367i	−0.167483	−	0.949844i
$11$	−2.85690	−	1.68468i	−0.861387	−	0.507949i
$11$	−2.85690	−	1.68468i	−0.861387	−	0.507949i
$12$	−0.194478	+	0.112282i	−0.0561411	+	0.0324131i
$13$	1.28361	−	1.07708i	0.356010	−	0.298728i	−0.447188	−	0.894440i	$-0.647575\pi$
$13$	1.28361	−	1.07708i	0.356010	−	0.298728i	0.803198	+	0.595712i	$0.203130\pi$
$14$	0.164398	+	0.451681i	0.0439373	+	0.120717i
$15$	−0.234257	+	0.643617i	−0.0604850	+	0.166181i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−6.73559	−	1.18767i	−1.63362	−	0.288051i	−0.719803	−	0.694178i	$-0.755768\pi$
$17$	−6.73559	−	1.18767i	−1.63362	−	0.288051i	−0.913817	+	0.406127i	$0.866879\pi$
$18$	−2.94957			−0.695221
$19$	−1.17941	−	4.19631i	−0.270575	−	0.962699i
$19$	−1.17941	−	4.19631i	−0.270575	−	0.962699i
$20$	3.05001			0.682002
$21$	0.0187438	−	0.106301i	0.00409022	−	0.0231968i
$22$	2.15518	−	2.52095i	0.459485	−	0.537469i
$23$	−8.00046	−	2.91193i	−1.66821	−	0.607179i	−0.676590	−	0.736360i	$-0.736543\pi$
$23$	−8.00046	−	2.91193i	−1.66821	−	0.607179i	−0.991621	+	0.129181i	$0.958765\pi$
$24$	−0.0768055	−	0.211022i	−0.0156779	−	0.0430746i
$25$	3.29594	−	2.76562i	0.659188	−	0.553125i
$26$	0.837817	+	1.45114i	0.164310	+	0.284592i
$27$	1.15706	+	0.668031i	0.222677	+	0.128563i
$28$	−0.473366	+	0.0834672i	−0.0894578	+	0.0157738i
$29$	−0.535611	−	3.03760i	−0.0994604	−	0.564068i	−0.993289	−	0.115659i	$-0.963102\pi$
$29$	−0.535611	−	3.03760i	−0.0994604	−	0.564068i	0.893829	−	0.448409i	$-0.148009\pi$
$30$	−0.593161	−	0.342462i	−0.108296	−	0.0625246i
$31$	−4.09905	+	2.36659i	−0.736211	+	0.425052i	−0.820690	−	0.571373i	$-0.806411\pi$
$31$	−4.09905	+	2.36659i	−0.736211	+	0.425052i	0.0844787	+	0.996425i	$0.473077\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	−0.702194	+	0.248283i	−0.122236	+	0.0432206i
$34$	2.33924	−	6.42702i	0.401177	−	1.10223i
$35$	−0.942354	+	1.12305i	−0.159287	+	0.189831i
$36$	0.512188	−	2.90476i	0.0853646	−	0.484127i
$37$			10.7581i			1.76862i	0.466903	+	0.884309i	$0.345370\pi$
$37$			10.7581i			1.76862i	−0.466903	+	0.884309i	$0.654630\pi$
$38$	4.33736	−	0.432811i	0.703612	−	0.0702112i
$39$		−	0.376288i		−	0.0602543i
$40$	−0.529628	+	3.00367i	−0.0837416	+	0.474922i
$41$	5.39386	+	4.52598i	0.842379	+	0.706840i	0.958097	−	0.286442i	$-0.0924727\pi$
$41$	5.39386	+	4.52598i	0.842379	+	0.706840i	−0.115719	+	0.993282i	$0.536917\pi$
$42$	0.101431	+	0.0369180i	0.0156512	+	0.00569657i
$43$	1.49518	+	4.10797i	0.228013	+	0.626460i	0.999957	−	0.00922987i	$-0.00293800\pi$
$43$	1.49518	+	4.10797i	0.228013	+	0.626460i	−0.771945	+	0.635690i	$0.780716\pi$
$44$	2.10841	+	2.56019i	0.317855	+	0.385964i
$45$	−4.49811	−	7.79095i	−0.670538	−	1.16141i
$46$	4.25696	−	7.37326i	0.627654	−	1.08713i
$47$	−0.724581	−	4.10930i	−0.105691	−	0.599403i	−0.990942	−	0.134290i	$-0.957125\pi$
$47$	−0.724581	−	4.10930i	−0.105691	−	0.599403i	0.885251	−	0.465113i	$-0.153986\pi$
$48$	0.221153	−	0.0389952i	0.0319207	−	0.00562847i
$49$	−3.38448	+	5.86209i	−0.483497	+	0.837441i
$50$	2.15127	+	3.72611i	0.304236	+	0.526952i
$51$	−1.17657	+	0.987262i	−0.164753	+	0.138244i
$52$	−1.57458	+	0.573101i	−0.218355	+	0.0794748i
$53$	1.51502	−	4.16247i	0.208103	−	0.571760i	−0.791099	−	0.611688i	$-0.790491\pi$
$53$	1.51502	−	4.16247i	0.208103	−	0.571760i	0.999203	+	0.0399284i	$0.0127130\pi$
$54$	−0.858804	+	1.02348i	−0.116868	+	0.139278i
$55$	9.94546	+	1.84818i	1.34105	+	0.249209i
$56$		−	0.480668i		−	0.0642320i
$57$	−0.892120	−	0.402836i	−0.118164	−	0.0533569i
$58$	3.08446			0.405009
$59$	7.03232	+	1.23999i	0.915531	+	0.161433i	0.611514	−	0.791234i	$-0.290561\pi$
$59$	7.03232	+	1.23999i	0.915531	+	0.161433i	0.304017	+	0.952667i	$0.401672\pi$
$60$	0.440260	−	0.524682i	0.0568373	−	0.0677361i
$61$	0.344560	−	0.946671i	0.0441164	−	0.121209i	−0.915678	−	0.401913i	$-0.868346\pi$
$61$	0.344560	−	0.946671i	0.0441164	−	0.121209i	0.959794	+	0.280704i	$0.0905678\pi$
$62$	−1.61884	−	4.44773i	−0.205593	−	0.564863i
$63$	0.911322	+	1.08607i	0.114816	+	0.136832i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.55535	+	4.42600i	−0.316952	+	0.548977i
$66$	−0.122577	−	0.734640i	−0.0150882	−	0.0904279i
$67$	11.8120	−	2.08278i	1.44307	−	0.254452i	0.603351	−	0.797476i	$-0.293832\pi$
$67$	11.8120	−	2.08278i	1.44307	−	0.254452i	0.839717	+	0.543024i	$0.182721\pi$
$68$	5.92318	+	3.41975i	0.718291	+	0.414705i
$69$	−1.65577	+	0.955961i	−0.199332	+	0.115084i
$70$	−0.942354	−	1.12305i	−0.112633	−	0.134231i
$71$	2.30809	+	6.34142i	0.273920	+	0.752588i	0.998020	+	0.0628938i	$0.0200329\pi$
$71$	2.30809	+	6.34142i	0.273920	+	0.752588i	−0.724100	+	0.689694i	$0.757745\pi$
$72$	2.77169	+	1.00881i	0.326647	+	0.118890i
$73$	1.60948	−	1.91810i	0.188375	−	0.224496i	−0.663589	−	0.748098i	$-0.730967\pi$
$73$	1.60948	−	1.91810i	0.188375	−	0.224496i	0.851963	+	0.523601i	$0.175412\pi$
$74$	−10.5946	−	1.86812i	−1.23160	−	0.217165i
$75$		−	0.966199i		−	0.111567i
$76$	−0.326939	+	4.34662i	−0.0375024	+	0.498592i
$77$	−1.59413	−	0.0146713i	−0.181668	−	0.00167195i
$78$	0.370571	+	0.0653417i	0.0419589	+	0.00739849i
$79$	−7.42007	−	6.22618i	−0.834823	−	0.700500i	0.121570	−	0.992583i	$-0.461207\pi$
$79$	−7.42007	−	6.22618i	−0.834823	−	0.700500i	−0.956393	+	0.292083i	$0.905652\pi$
$80$	−2.86607	−	1.04316i	−0.320436	−	0.116629i
$81$	−8.03313	+	2.92382i	−0.892570	+	0.324869i
$82$	−5.39386	+	4.52598i	−0.595652	+	0.499811i
$83$	−11.3910	+	6.57657i	−1.25032	+	0.721873i	−0.971173	−	0.238376i	$-0.923385\pi$
$83$	−11.3910	+	6.57657i	−1.25032	+	0.721873i	−0.279147	+	0.960248i	$0.590052\pi$
$84$	−0.0539705	+	0.0934797i	−0.00588867	+	0.0101995i
$85$	20.5436	−	3.62239i	2.22827	−	0.392903i
$86$	−4.30520	+	0.759123i	−0.464241	+	0.0818583i
$87$	−0.599861	−	0.346330i	−0.0643118	−	0.0371304i
$88$	−2.88742	+	1.63181i	−0.307800	+	0.173951i
$89$	−8.94689	−	10.6625i	−0.948368	−	1.13022i	−0.991363	−	0.131146i	$-0.958134\pi$
$89$	−8.94689	−	10.6625i	−0.948368	−	1.13022i	0.0429948	−	0.999075i	$-0.486310\pi$
$90$	8.45368	−	3.07689i	0.891096	−	0.324332i
$91$	0.275471	−	0.756852i	0.0288773	−	0.0793396i
$92$	6.52203	+	5.47264i	0.679969	+	0.570562i
$93$	−0.184571	+	1.04676i	−0.0191391	+	0.108543i
$94$	4.17269			0.430381
$95$	7.75771	+	10.7966i	0.795924	+	1.10771i
$96$			0.224564i			0.0229195i
$97$	−3.31865	−	0.585168i	−0.336958	−	0.0594148i	0.00260899	−	0.999997i	$-0.499170\pi$
$97$	−3.31865	−	0.585168i	−0.336958	−	0.0594148i	−0.339567	+	0.940582i	$0.610281\pi$
$98$	−5.18532	−	4.35100i	−0.523797	−	0.439518i
$99$	3.43031	−	9.16147i	0.344759	−	0.920763i
$100$	−4.04307	+	1.47156i	−0.404307	+	0.147156i
$101$	4.08737	+	4.87114i	0.406709	+	0.484697i	0.930053	−	0.367424i	$-0.119760\pi$
$101$	4.08737	+	4.87114i	0.406709	+	0.484697i	−0.523345	+	0.852121i	$0.675316\pi$
$102$	−0.767953	−	1.33013i	−0.0760387	−	0.131703i
$103$	0.308717	+	0.178238i	0.0304188	+	0.0175623i	0.515132	−	0.857111i	$-0.327743\pi$
$103$	0.308717	+	0.178238i	0.0304188	+	0.0175623i	−0.484714	+	0.874673i	$0.661076\pi$
$104$	−0.290971	−	1.65018i	−0.0285320	−	0.161813i
$105$	0.0571686	+	0.324219i	0.00557908	+	0.0316406i
$106$	3.83616	+	2.21481i	0.372600	+	0.215121i
$107$	3.22070	+	5.57842i	0.311357	+	0.539286i	0.978656	−	0.205504i	$-0.0658833\pi$
$107$	3.22070	+	5.57842i	0.311357	+	0.539286i	−0.667300	+	0.744789i	$0.732550\pi$
$108$	−0.858804	−	1.02348i	−0.0826385	−	0.0984847i
$109$	−15.7541	+	5.73403i	−1.50897	+	0.549220i	−0.958365	−	0.285545i	$-0.907825\pi$
$109$	−15.7541	+	5.73403i	−1.50897	+	0.549220i	−0.550605	+	0.834766i	$0.685603\pi$
$110$	−3.54712	+	9.47343i	−0.338204	+	0.903257i
$111$	1.85067	+	1.55290i	0.175658	+	0.147395i
$112$	0.473366	+	0.0834672i	0.0447289	+	0.00788691i
$113$			7.59906i			0.714860i	0.933940	+	0.357430i	$0.116347\pi$
$113$			7.59906i			0.714860i	−0.933940	+	0.357430i	$0.883653\pi$
$114$	0.551631	−	0.808615i	0.0516649	−	0.0757337i
$115$	25.9675			2.42148
$116$	−0.535611	+	3.03760i	−0.0497302	+	0.282034i
$117$	3.78610	+	3.17692i	0.350025	+	0.293706i
$118$	−2.44230	+	6.71017i	−0.224832	+	0.617721i
$119$	−3.08927	+	1.12440i	−0.283193	+	0.103074i
$120$	0.440260	+	0.524682i	0.0401901	+	0.0478967i
$121$	5.32374	+	9.62589i	0.483976	+	0.875081i
$122$	0.872457	+	0.503713i	0.0789885	+	0.0456041i
$123$	1.55718	−	0.274572i	0.140406	−	0.0247573i
$124$	4.66127	−	0.821908i	0.418594	−	0.0738095i
$125$	1.06362	−	1.84224i	0.0951331	−	0.164775i
$126$	−1.22782	+	0.708883i	−0.109383	+	0.0631523i
$127$	0.588699	−	0.493977i	0.0522386	−	0.0438334i	−0.616295	−	0.787516i	$-0.711367\pi$
$127$	0.588699	−	0.493977i	0.0522386	−	0.0438334i	0.668533	+	0.743682i	$0.266922\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	0.922504	+	0.335764i	0.0812220	+	0.0295624i
$130$	−3.91502	−	3.28509i	−0.343370	−	0.288122i
$131$	20.0999	+	3.54415i	1.75613	+	0.309654i	0.956694	−	0.291094i	$-0.0940194\pi$
$131$	20.0999	+	3.54415i	1.75613	+	0.309654i	0.799438	+	0.600748i	$0.205130\pi$
$132$	0.744764	+	0.00685432i	0.0648234	+	0.000596592i
$133$	−1.49947	−	1.46335i	−0.130021	−	0.126888i
$134$			11.9942i			1.03614i
$135$	−4.01309	−	0.707616i	−0.345392	−	0.0609019i
$136$	−4.39634	+	5.23936i	−0.376983	+	0.449271i
$137$	−14.9149	−	5.42858i	−1.27427	−	0.463795i	−0.385734	−	0.922610i	$-0.626052\pi$
$137$	−14.9149	−	5.42858i	−1.27427	−	0.463795i	−0.888531	+	0.458816i	$0.848274\pi$
$138$	−0.653916	−	1.79662i	−0.0556650	−	0.152938i
$139$	−0.0454408	−	0.0541542i	−0.00385424	−	0.00459330i	0.764114	−	0.645081i	$-0.223177\pi$
$139$	−0.0454408	−	0.0541542i	−0.00385424	−	0.00459330i	−0.767968	+	0.640488i	$0.778732\pi$
$140$	1.26963	−	0.733021i	0.107303	−	0.0619516i
$141$	−0.811499	−	0.468519i	−0.0683406	−	0.0394564i
$142$	−6.64588	+	1.17185i	−0.557710	+	0.0983392i
$143$	−5.48167	+	0.914633i	−0.458400	+	0.0764854i
$144$	−1.47479	+	2.55440i	−0.122899	+	0.212867i
$145$	4.70381	+	8.14724i	0.390630	+	0.676591i
$146$	1.60948	+	1.91810i	0.133201	+	0.158743i
$147$	0.519894	+	1.42840i	0.0428801	+	0.117812i
$148$	3.67948	−	10.1093i	0.302451	−	0.830978i
$149$	−11.2252	+	13.3776i	−0.919601	+	1.09594i	0.0755070	+	0.997145i	$0.475942\pi$
$149$	−11.2252	+	13.3776i	−0.919601	+	1.09594i	−0.995108	+	0.0987925i	$0.968502\pi$
$150$	0.951520	+	0.167779i	0.0776913	+	0.0136991i
$151$	−13.4259			−1.09259			−0.546293	−	0.837594i	$-0.683961\pi$
$151$	−13.4259			−1.09259			−0.546293	+	0.837594i	$0.683961\pi$
$152$	−4.22381	−	1.07675i	−0.342597	−	0.0873363i
$153$		−	20.1736i		−	1.63094i
$154$	0.291266	−	1.56736i	0.0234709	−	0.126302i
$155$	9.27943	−	11.0588i	0.745342	−	0.888264i
$156$	−0.128698	+	0.353595i	−0.0103041	+	0.0283103i
$157$	−12.8739	+	4.68571i	−1.02745	+	0.373960i	−0.800109	−	0.599855i	$-0.795225\pi$
$157$	−12.8739	+	4.68571i	−1.02745	+	0.373960i	−0.227339	+	0.973816i	$0.573003\pi$
$158$	7.42007	−	6.22618i	0.590309	−	0.495328i
$159$	−0.497367	−	0.861464i	−0.0394437	−	0.0683185i
$160$	1.52500	−	2.64138i	0.120562	−	0.208820i
$161$	−4.03020	+	0.710632i	−0.317624	+	0.0560057i
$162$	−1.48446	−	8.41881i	−0.116630	−	0.661444i
$163$	9.21394	−	15.9590i	0.721692	−	1.25001i	−0.238630	−	0.971111i	$-0.576698\pi$
$163$	9.21394	−	15.9590i	0.721692	−	1.25001i	0.960321	−	0.278896i	$-0.0899684\pi$
$164$	−3.52059	−	6.09784i	−0.274912	−	0.476161i
$165$	1.75354	−	1.44410i	0.136513	−	0.112423i
$166$	−4.49864	−	12.3599i	−0.349162	−	0.959316i
$167$	−13.4659	−	4.90119i	−1.04202	−	0.379266i	−0.236377	−	0.971662i	$-0.575960\pi$
$167$	−13.4659	−	4.90119i	−1.04202	−	0.379266i	−0.805647	+	0.592396i	$0.798182\pi$
$168$	−0.0826876	−	0.0693831i	−0.00637949	−	0.00535303i
$169$	−1.76987	+	10.0374i	−0.136143	+	0.772108i
$170$			20.8605i			1.59993i
$171$	11.5852	−	5.57520i	0.885941	−	0.426346i
$172$		−	4.37161i		−	0.333332i
$173$	2.57605	−	14.6095i	0.195854	−	1.11074i	−0.715344	−	0.698772i	$-0.753730\pi$
$173$	2.57605	−	14.6095i	0.195854	−	1.11074i	0.911198	−	0.411969i	$-0.135159\pi$
$174$	0.445233	−	0.530608i	0.0337530	−	0.0402253i
$175$	0.707331	−	1.94338i	0.0534692	−	0.146905i
$176$	−1.10562	−	3.12692i	−0.0833394	−	0.235700i
$177$	1.22841	−	1.03076i	0.0923327	−	0.0774764i
$178$	12.0541	−	6.95944i	0.903494	−	0.521632i
$179$	14.3189	+	8.26704i	1.07025	+	0.617908i	0.928249	−	0.371959i	$-0.121314\pi$
$179$	14.3189	+	8.26704i	1.07025	+	0.617908i	0.141999	+	0.989867i	$0.454647\pi$
$180$	1.56218	+	8.85954i	0.116438	+	0.660351i
$181$	3.19670	−	0.563665i	0.237609	−	0.0418969i	−0.0535754	−	0.998564i	$-0.517062\pi$
$181$	3.19670	−	0.563665i	0.237609	−	0.0418969i	0.291185	+	0.956667i	$0.405951\pi$
$182$	0.697518	+	0.402712i	0.0517035	+	0.0298510i
$183$	−0.113116	−	0.195923i	−0.00836178	−	0.0144830i
$184$	−6.52203	+	5.47264i	−0.480811	+	0.403448i
$185$	−11.2224	−	30.8334i	−0.825090	−	2.26692i
$186$	−0.998802	−	0.363534i	−0.0732357	−	0.0266556i
$187$	17.2421	+	14.7403i	1.26086	+	1.07792i
$188$	−0.724581	+	4.10930i	−0.0528455	+	0.299702i
$189$	0.642203			0.0467134
$190$	−11.9797	+	5.76504i	−0.869097	+	0.418240i
$191$	15.2836			1.10588			0.552941	−	0.833220i	$-0.313505\pi$
$191$	15.2836			1.10588			0.552941	+	0.833220i	$0.313505\pi$
$192$	−0.221153	−	0.0389952i	−0.0159603	−	0.00281424i
$193$	−12.8127	−	10.7511i	−0.922278	−	0.773883i	0.0521370	−	0.998640i	$-0.483397\pi$
$193$	−12.8127	−	10.7511i	−0.922278	−	0.773883i	−0.974415	+	0.224757i	$0.927841\pi$
$194$	1.15256	−	3.16662i	0.0827488	−	0.227350i
$195$	0.392530	+	1.07847i	0.0281097	+	0.0772307i
$196$	5.18532	−	4.35100i	0.370380	−	0.310786i
$197$	−10.8757	+	6.27908i	−0.774861	+	0.447366i	−0.834606	−	0.550847i	$-0.814305\pi$
$197$	−10.8757	+	6.27908i	−0.774861	+	0.447366i	0.0597449	+	0.998214i	$0.480971\pi$
$198$	8.42662	+	4.96907i	0.598854	+	0.353136i
$199$	−3.22288	−	18.2779i	−0.228464	−	1.29568i	−0.855951	−	0.517057i	$-0.827028\pi$
$199$	−3.22288	−	18.2779i	−0.228464	−	1.29568i	0.627487	−	0.778627i	$-0.284083\pi$
$200$	−0.747129	−	4.23718i	−0.0528300	−	0.299614i
$201$	1.34674	−	2.33262i	0.0949917	−	0.164530i
$202$	−5.50690	+	3.17941i	−0.387464	+	0.223703i
$203$	−0.952998	−	1.13574i	−0.0668873	−	0.0797132i
$204$	1.44328	−	0.525311i	0.101050	−	0.0367791i
$205$	−20.1805	−	7.34510i	−1.40947	−	0.513004i
$206$	−0.229138	+	0.273076i	−0.0159648	+	0.0190261i
$207$	4.36072	−	24.7309i	0.303091	−	1.71891i
$208$	1.67563			0.116184
$209$	−3.69996	+	13.9753i	−0.255932	+	0.966695i
$210$	−0.329221			−0.0227184
$211$	3.49466	−	19.8192i	0.240582	−	1.36441i	−0.589951	−	0.807439i	$-0.700853\pi$
$211$	3.49466	−	19.8192i	0.240582	−	1.36441i	0.830533	−	0.556970i	$-0.188036\pi$
$212$	−2.84730	+	3.39328i	−0.195553	+	0.233051i
$213$	1.42406	+	0.518315i	0.0975748	+	0.0355143i
$214$	−6.05293	+	2.20309i	−0.413770	+	0.150600i
$215$	−8.57058	−	10.2140i	−0.584509	−	0.696590i
$216$	1.15706	−	0.668031i	0.0787282	−	0.0454537i
$217$	−1.13754	+	1.97028i	−0.0772216	+	0.133752i
$218$	−2.91124	−	16.5105i	−0.197174	−	1.11823i
$219$	−0.0976401	−	0.553744i	−0.00659791	−	0.0374186i
$220$	−8.71356	−	5.13827i	−0.587468	−	0.346422i
$221$	−9.92508	+	5.73025i	−0.667633	+	0.385458i
$222$	−1.85067	+	1.55290i	−0.124209	+	0.104224i
$223$	−4.28745	−	11.7797i	−0.287109	−	0.788824i	−0.996468	−	0.0839771i	$-0.973238\pi$
$223$	−4.28745	−	11.7797i	−0.287109	−	0.788824i	0.709359	−	0.704847i	$-0.248984\pi$
$224$	−0.164398	+	0.451681i	−0.0109843	+	0.0301792i
$225$	9.72161	+	8.15740i	0.648107	+	0.543827i
$226$	−7.48362	−	1.31956i	−0.497803	−	0.0877761i
$227$	−21.2020			−1.40723			−0.703613	−	0.710583i	$-0.748431\pi$
$227$	−21.2020			−1.40723			−0.703613	+	0.710583i	$0.748431\pi$
$228$	0.700540	+	0.683665i	0.0463944	+	0.0452768i
$229$	3.10350			0.205085			0.102543	−	0.994729i	$-0.467302\pi$
$229$	3.10350			0.205085			0.102543	+	0.994729i	$0.467302\pi$
$230$	−4.50921	+	25.5730i	−0.297328	+	1.68623i
$231$	−0.232632	+	0.272114i	−0.0153061	+	0.0179038i
$232$	−2.89844	−	1.05495i	−0.190292	−	0.0692606i
$233$	3.25013	+	8.92965i	0.212923	+	0.585001i	0.999471	−	0.0325283i	$-0.0103559\pi$
$233$	3.25013	+	8.92965i	0.212923	+	0.585001i	−0.786548	+	0.617529i	$0.788134\pi$
$234$	−3.78610	+	3.17692i	−0.247505	+	0.207681i
$235$	6.36338	+	11.0217i	0.415101	+	0.718976i
$236$	−6.18412	−	3.57040i	−0.402552	−	0.232414i
$237$	−2.14213	+	0.377716i	−0.139147	+	0.0245353i
$238$	−0.570873	−	3.23758i	−0.0370042	−	0.209861i
$239$	2.07376	+	1.19728i	0.134140	+	0.0774459i	0.565568	−	0.824701i	$-0.308657\pi$
$239$	2.07376	+	1.19728i	0.134140	+	0.0774459i	−0.431428	+	0.902147i	$0.641990\pi$
$240$	−0.593161	+	0.342462i	−0.0382884	+	0.0221058i
$241$	18.9308	−	15.8848i	1.21944	−	1.02323i	0.220587	−	0.975367i	$-0.429203\pi$
$241$	18.9308	−	15.8848i	1.21944	−	1.02323i	0.998854	−	0.0478650i	$-0.0152417\pi$
$242$	−10.4041	+	3.57134i	−0.668802	+	0.229574i
$243$	−2.02747	+	5.57042i	−0.130062	+	0.357342i
$244$	−0.647561	+	0.771733i	−0.0414559	+	0.0494052i
$245$	3.58503	−	20.3317i	0.229039	−	1.29895i
$246$			1.58120i			0.100814i
$247$	−6.03365	−	4.11611i	−0.383912	−	0.261902i
$248$			4.73318i			0.300557i
$249$	−0.512910	+	2.90885i	−0.0325043	+	0.184341i
$250$	1.62956	+	1.36736i	0.103062	+	0.0864797i
$251$	18.3044	+	6.66224i	1.15536	+	0.420517i	0.847438	−	0.530895i	$-0.178144\pi$
$251$	18.3044	+	6.66224i	1.15536	+	0.420517i	0.307923	+	0.951411i	$0.400366\pi$
$252$	−0.484904	−	1.33226i	−0.0305461	−	0.0839247i
$253$	17.9508	+	21.7973i	1.12856	+	1.37038i
$254$	0.384246	+	0.665533i	0.0241097	+	0.0417593i
$255$	2.34226	−	4.05692i	0.146678	−	0.254054i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	11.0763	−	1.95304i	0.690919	−	0.121828i	0.182846	−	0.983142i	$-0.441469\pi$
$257$	11.0763	−	1.95304i	0.690919	−	0.121828i	0.508073	+	0.861314i	$0.330358\pi$
$258$	−0.490854	+	0.850185i	−0.0305593	+	0.0529302i
$259$	2.58553	+	4.47828i	0.160657	+	0.278267i
$260$	3.91502	−	3.28509i	0.242799	−	0.203733i
$261$	8.54916	−	3.11164i	0.529180	−	0.192606i
$262$	−6.98061	+	19.1791i	−0.431263	+	1.18489i
$263$	−5.69533	+	6.78743i	−0.351189	+	0.418531i	−0.912502	−	0.409073i	$-0.865852\pi$
$263$	−5.69533	+	6.78743i	−0.351189	+	0.418531i	0.561313	+	0.827604i	$0.310297\pi$
$264$	−0.136077	+	0.732259i	−0.00837497	+	0.0450675i
$265$			13.5103i			0.829934i
$266$	1.70150	−	1.22258i	0.104325	−	0.0749613i
$267$	−3.12569			−0.191289
$268$	−11.8120	−	2.08278i	−0.721534	−	0.127226i
$269$	−8.41035	+	10.0231i	−0.512788	+	0.611117i	−0.958860	−	0.283880i	$-0.908378\pi$
$269$	−8.41035	+	10.0231i	−0.512788	+	0.611117i	0.446072	+	0.894997i	$0.352823\pi$
$270$	1.39373	−	3.82925i	0.0848198	−	0.233040i
$271$	0.769615	+	2.11450i	0.0467508	+	0.128447i	0.960871	−	0.276997i	$-0.0893392\pi$
$271$	0.769615	+	2.11450i	0.0467508	+	0.128447i	−0.914120	+	0.405444i	$0.867117\pi$
$272$	−4.39634	−	5.23936i	−0.266567	−	0.317683i
$273$	−0.0904349	−	0.156638i	−0.00547337	−	0.00948015i
$274$	7.93605	−	13.7456i	0.479434	−	0.830404i
$275$	−14.0753	+	2.34851i	−0.848775	+	0.141621i
$276$	1.88288	−	0.332002i	0.113336	−	0.0199842i
$277$	−24.3220	−	14.0423i	−1.46137	−	0.843721i	−0.462292	−	0.886728i	$-0.652973\pi$
$277$	−24.3220	−	14.0423i	−1.46137	−	0.843721i	−0.999075	+	0.0430069i	$0.986306\pi$
$278$	0.0612222	−	0.0353467i	0.00367186	−	0.00211995i
$279$	−8.97386	−	10.6946i	−0.537251	−	0.640271i
$280$	0.501416	+	1.37763i	0.0299653	+	0.0823291i
$281$	17.6763	+	6.43364i	1.05448	+	0.383799i	0.810351	−	0.585945i	$-0.199276\pi$
$281$	17.6763	+	6.43364i	1.05448	+	0.383799i	0.244127	+	0.969743i	$0.421499\pi$
$282$	0.602317	−	0.717813i	0.0358674	−	0.0427452i
$283$	3.23853	+	0.571040i	0.192511	+	0.0339448i	0.269072	−	0.963120i	$-0.413283\pi$
$283$	3.23853	+	0.571040i	0.192511	+	0.0339448i	−0.0765614	+	0.997065i	$0.524394\pi$
$284$		−	6.74840i		−	0.400444i
$285$	2.97710	+	0.223928i	0.176348	+	0.0132643i
$286$	0.0511450	−	5.55722i	0.00302427	−	0.328605i
$287$	3.33305	+	0.587707i	0.196744	+	0.0346913i
$288$	−2.25950	−	1.89595i	−0.133142	−	0.111720i
$289$	27.9828	+	10.1849i	1.64605	+	0.599112i
$290$	−8.84027	+	3.21760i	−0.519119	+	0.188944i
$291$	−0.579703	+	0.486429i	−0.0339828	+	0.0285149i
$292$	−2.16844	+	1.25195i	−0.126898	+	0.0732648i
$293$	2.33247	−	4.03996i	0.136264	−	0.236017i	−0.789815	−	0.613345i	$-0.789824\pi$
$293$	2.33247	−	4.03996i	0.136264	−	0.236017i	0.926080	+	0.377328i	$0.123157\pi$
$294$	−1.49697	+	0.263957i	−0.0873053	+	0.0153943i
$295$	−21.4486	+	3.78197i	−1.24879	+	0.220195i
$296$	9.31677	+	5.37904i	0.541526	+	0.312650i
$297$	−2.18020	−	3.85777i	−0.126508	−	0.223851i
$298$	−11.2252	−	13.3776i	−0.650256	−	0.774945i
$299$	−13.4059	+	4.87933i	−0.775280	+	0.282179i
$300$	−0.330459	+	0.907930i	−0.0190791	+	0.0524193i
$301$	1.60969	+	1.35069i	0.0927808	+	0.0778523i
$302$	2.33138	−	13.2219i	0.134156	−	0.760837i
$303$	1.42797			0.0820345
$304$	1.79385	−	3.97267i	0.102885	−	0.227848i
$305$			3.07266i			0.175940i
$306$	19.8671	+	3.50310i	1.13573	+	0.200259i
$307$	11.1550	+	9.36017i	0.636650	+	0.534213i	0.902987	−	0.429667i	$-0.141369\pi$
$307$	11.1550	+	9.36017i	0.636650	+	0.534213i	−0.266337	+	0.963880i	$0.585813\pi$
$308$	1.49297	+	0.559011i	0.0850701	+	0.0318526i
$309$	0.0752240	−	0.0273793i	0.00427934	−	0.00155755i
$310$	9.27943	+	11.0588i	0.527036	+	0.628097i
$311$	5.48075	+	9.49294i	0.310785	+	0.538295i	0.978533	−	0.206092i	$-0.0660748\pi$
$311$	5.48075	+	9.49294i	0.310785	+	0.538295i	−0.667748	+	0.744388i	$0.732741\pi$
$312$	−0.325875	−	0.188144i	−0.0184490	−	0.0106516i
$313$	−3.39166	−	19.2351i	−0.191708	−	1.08723i	−0.917029	−	0.398820i	$-0.869420\pi$
$313$	−3.39166	−	19.2351i	−0.191708	−	1.08723i	0.725321	−	0.688411i	$-0.241691\pi$
$314$	−2.37900	−	13.4920i	−0.134255	−	0.761396i
$315$	−3.74486	−	2.16210i	−0.210999	−	0.121820i
$316$	4.84311	+	8.38851i	0.272446	+	0.471891i
$317$	0.988408	+	1.17794i	0.0555145	+	0.0661596i	0.793087	−	0.609108i	$-0.208472\pi$
$317$	0.988408	+	1.17794i	0.0555145	+	0.0661596i	−0.737573	+	0.675268i	$0.764028\pi$
$318$	0.934743	−	0.340219i	0.0524178	−	0.0190785i
$319$	−3.58718	+	9.58044i	−0.200844	+	0.536402i
$320$	2.33644	+	1.96051i	0.130611	+	0.109596i
$321$	1.42453	+	0.251184i	0.0795097	+	0.0140197i
$322$		−	4.09237i		−	0.228059i
$323$	2.96021	+	29.6653i	0.164710	+	1.65062i
$324$	8.54868			0.474927
$325$	1.25192	−	7.09997i	0.0694438	−	0.393835i
$326$	14.1166	+	11.8452i	0.781845	+	0.656046i
$327$	−1.28766	+	3.53781i	−0.0712077	+	0.195642i
$328$	6.61654	−	2.40822i	0.365338	−	0.132972i
$329$	−1.28923	−	1.53644i	−0.0710774	−	0.0847068i
$330$	1.11766	+	1.97766i	0.0615253	+	0.108867i
$331$	−13.7932	−	7.96353i	−0.758145	−	0.437715i	0.0704841	−	0.997513i	$-0.477546\pi$
$331$	−13.7932	−	7.96353i	−0.758145	−	0.437715i	−0.828629	+	0.559797i	$0.810879\pi$
$332$	12.9533	−	2.28402i	0.710906	−	0.125352i
$333$	−31.2496	+	5.51015i	−1.71247	+	0.301955i
$334$	7.16506	−	12.4103i	0.392055	−	0.679059i
$335$	−31.6814	+	18.2913i	−1.73094	+	0.999358i
$336$	0.0826876	−	0.0693831i	0.00451098	−	0.00378516i
$337$	3.80432	−	1.38466i	0.207234	−	0.0754271i	−0.236317	−	0.971676i	$-0.575940\pi$
$337$	3.80432	−	1.38466i	0.207234	−	0.0754271i	0.443552	+	0.896249i	$0.353718\pi$
$338$	−9.57758	−	3.48595i	−0.520952	−	0.189611i
$339$	1.30724	+	1.09690i	0.0709995	+	0.0595756i
$340$	−20.5436	−	3.62239i	−1.11413	−	0.196452i
$341$	15.6975	+	0.144470i	0.850068	+	0.00782347i
$342$	3.47875	+	12.3773i	0.188109	+	0.669288i
$343$			6.61830i			0.357355i
$344$	4.30520	+	0.759123i	0.232121	+	0.0409291i
$345$	3.74834	−	4.46709i	0.201804	−	0.240500i
$346$	13.9402	+	5.07383i	0.749432	+	0.272771i
$347$	1.70738	+	4.69098i	0.0916569	+	0.251825i	0.977047	−	0.213023i	$-0.0683310\pi$
$347$	1.70738	+	4.69098i	0.0916569	+	0.251825i	−0.885390	+	0.464849i	$0.846109\pi$
$348$	0.445233	+	0.530608i	0.0238670	+	0.0284436i
$349$	9.61813	−	5.55303i	0.514847	−	0.297247i	−0.219977	−	0.975505i	$-0.570598\pi$
$349$	9.61813	−	5.55303i	0.514847	−	0.297247i	0.734824	+	0.678258i	$0.237265\pi$
$350$	1.79103	+	1.03405i	0.0957343	+	0.0552722i
$351$	2.20474	−	0.388755i	0.117680	−	0.0207502i
$352$	3.27140	−	0.545842i	0.174366	−	0.0290935i
$353$	10.0733	−	17.4475i	0.536148	−	0.928635i	−0.462959	−	0.886380i	$-0.653212\pi$
$353$	10.0733	−	17.4475i	0.536148	−	0.928635i	0.999107	−	0.0422555i	$-0.0134543\pi$
$354$	0.801786	+	1.38873i	0.0426144	+	0.0738104i
$355$	−13.2303	−	15.7672i	−0.702191	−	0.836838i
$356$	4.76054	+	13.0795i	0.252308	+	0.693211i
$357$	−0.252500	+	0.693739i	−0.0133637	+	0.0367166i
$358$	−10.6279	+	12.6658i	−0.561702	+	0.669411i
$359$	−3.22982	−	0.569505i	−0.170463	−	0.0300573i	0.0877649	−	0.996141i	$-0.472028\pi$
$359$	−3.22982	−	0.569505i	−0.170463	−	0.0300573i	−0.258228	+	0.966084i	$0.583139\pi$
$360$	−8.99621			−0.474142
$361$	−16.2180	+	9.89833i	−0.853578	+	0.520965i
$362$			3.24602i			0.170607i
$363$	2.42437	+	0.473648i	0.127247	+	0.0248601i
$364$	−0.517717	+	0.616991i	−0.0271357	+	0.0323391i
$365$	−2.61198	+	7.17635i	−0.136717	+	0.375627i
$366$	0.212589	−	0.0773759i	0.0111122	−	0.00404451i
$367$	−12.7681	+	10.7137i	−0.666489	+	0.559251i	−0.912024	−	0.410137i	$-0.865481\pi$
$367$	−12.7681	+	10.7137i	−0.666489	+	0.559251i	0.245535	+	0.969388i	$0.421037\pi$
$368$	−4.25696	−	7.37326i	−0.221909	−	0.384358i
$369$	−10.3842	+	17.9860i	−0.540581	+	0.936314i
$370$	32.3137	−	5.69778i	1.67991	−	0.296214i
$371$	−0.369727	−	2.09683i	−0.0191953	−	0.108862i
$372$	0.531452	−	0.920501i	0.0275545	−	0.0477258i
$373$	−8.55855	−	14.8238i	−0.443145	−	0.767550i	0.554776	−	0.832000i	$-0.312804\pi$
$373$	−8.55855	−	14.8238i	−0.443145	−	0.767550i	−0.997921	+	0.0644502i	$0.979471\pi$
$374$	−17.5104	+	14.4205i	−0.905443	+	0.745665i
$375$	−0.163384	−	0.448894i	−0.00843711	−	0.0231808i
$376$	−3.92105	−	1.42715i	−0.202213	−	0.0735994i
$377$	−3.95924	−	3.32220i	−0.203911	−	0.171102i
$378$	−0.111517	+	0.632446i	−0.00573583	+	0.0325295i
$379$			1.95757i			0.100554i	0.998735	+	0.0502769i	$0.0160104\pi$
$379$			1.95757i			0.100554i	−0.998735	+	0.0502769i	$0.983990\pi$
$380$	−3.59721	−	12.7988i	−0.184533	−	0.656563i
$381$		−	0.172576i		−	0.00884133i
$382$	−2.65397	+	15.0514i	−0.135789	+	0.770097i
$383$	−7.21970	+	8.60411i	−0.368910	+	0.439649i	−0.918281	−	0.395929i	$-0.870423\pi$
$383$	−7.21970	+	8.60411i	−0.368910	+	0.439649i	0.549372	+	0.835578i	$0.314867\pi$
$384$	0.0768055	−	0.211022i	0.00391947	−	0.0107686i
$385$	4.58419	−	1.62089i	0.233632	−	0.0826082i
$386$	12.8127	−	10.7511i	0.652149	−	0.547218i
$387$	−11.1669	+	6.44719i	−0.567643	+	0.327729i
$388$	2.91838	+	1.68493i	0.148158	+	0.0855391i
$389$	1.93049	+	10.9484i	0.0978797	+	0.555103i	0.993827	+	0.110943i	$0.0353870\pi$
$389$	1.93049	+	10.9484i	0.0978797	+	0.555103i	−0.895947	+	0.444161i	$0.853502\pi$
$390$	−1.13025	+	0.199293i	−0.0572322	+	0.0100916i
$391$	50.4294	+	29.1154i	2.55032	+	1.47243i
$392$	3.38448	+	5.86209i	0.170942	+	0.296080i
$393$	3.51105	−	2.94612i	0.177109	−	0.148612i
$394$	−4.29515	−	11.8008i	−0.216386	−	0.594517i
$395$	27.7614	+	10.1043i	1.39683	+	0.508403i
$396$	−6.35685	+	7.43573i	−0.319444	+	0.373660i
$397$	3.50220	−	19.8619i	0.175770	−	0.996842i	−0.761481	−	0.648187i	$-0.775527\pi$
$397$	3.50220	−	19.8619i	0.175770	−	0.996842i	0.937251	−	0.348655i	$-0.113362\pi$
$398$	18.5598			0.930320
$399$	−0.468179	+	0.0467181i	−0.0234383	+	0.00233883i
$400$	4.30255			0.215127
$401$	15.9699	+	2.81593i	0.797501	+	0.140621i	0.557527	−	0.830159i	$-0.311750\pi$
$401$	15.9699	+	2.81593i	0.797501	+	0.140621i	0.239973	+	0.970779i	$0.422861\pi$
$402$	2.06332	+	1.73133i	0.102909	+	0.0863511i
$403$	−2.71259	+	7.45278i	−0.135124	+	0.371249i
$404$	−2.17485	−	5.97534i	−0.108203	−	0.297284i
$405$	19.9735	−	16.7597i	0.992491	−	0.832799i
$406$	1.28397	−	0.741301i	0.0637224	−	0.0367901i
$407$	18.1239	−	30.7347i	0.898367	−	1.52346i
$408$	0.266707	+	1.51257i	0.0132040	+	0.0748835i
$409$	5.24487	+	29.7451i	0.259342	+	1.47080i	0.784676	+	0.619906i	$0.212829\pi$
$409$	5.24487	+	29.7451i	0.259342	+	1.47080i	−0.525334	+	0.850896i	$0.676060\pi$
$410$	10.7378	−	18.5985i	0.530303	−	0.918512i
$411$	−3.08678	+	1.78215i	−0.152260	+	0.0879072i
$412$	−0.229138	−	0.273076i	−0.0112888	−	0.0134535i
$413$	3.22536	−	1.17394i	0.158710	−	0.0577656i
$414$	23.5979	+	8.58894i	1.15977	+	0.422123i
$415$	25.7868	−	30.7316i	1.26583	−	1.50855i
$416$	−0.290971	+	1.65018i	−0.0142660	+	0.0809066i
$417$	−0.0158752			−0.000777412
$418$	−13.1205	−	6.07054i	−0.641746	−	0.296920i
$419$	−8.89095			−0.434351			−0.217176	−	0.976133i	$-0.569684\pi$
$419$	−8.89095			−0.434351			−0.217176	+	0.976133i	$0.569684\pi$
$420$	0.0571686	−	0.324219i	0.00278954	−	0.0158203i
$421$	−12.7427	+	15.1862i	−0.621043	+	0.740130i	−0.981249	−	0.192743i	$-0.938262\pi$
$421$	−12.7427	+	15.1862i	−0.621043	+	0.740130i	0.360207	+	0.932873i	$0.382706\pi$
$422$	18.9112	+	6.88313i	0.920585	+	0.335066i
$423$	11.5654	−	4.20947i	0.562330	−	0.204671i
$424$	−2.84730	−	3.39328i	−0.138277	−	0.164792i
$425$	−25.4847	+	14.7136i	−1.23619	+	0.713715i
$426$	−0.757725	+	1.31242i	−0.0367119	+	0.0635869i
$427$	−0.0840871	−	0.476881i	−0.00406926	−	0.0230779i
$428$	−1.11854	−	6.34354i	−0.0540665	−	0.306627i
$429$	−0.633923	+	1.07502i	−0.0306061	+	0.0519023i
$430$	11.5471	−	6.66673i	0.556851	−	0.321498i
$431$	−24.7964	+	20.8067i	−1.19440	+	1.00222i	−0.194630	+	0.980877i	$0.562351\pi$
$431$	−24.7964	+	20.8067i	−1.19440	+	1.00222i	−0.999772	+	0.0213459i	$0.993205\pi$
$432$	0.456960	+	1.25549i	0.0219855	+	0.0604047i
$433$	−5.91130	+	16.2412i	−0.284079	+	0.780501i	0.712786	+	0.701382i	$0.247433\pi$
$433$	−5.91130	+	16.2412i	−0.284079	+	0.780501i	−0.996865	+	0.0791195i	$0.974789\pi$
$434$	−1.74282	−	1.46240i	−0.0836580	−	0.0701974i
$435$	2.08052	+	0.366852i	0.0997534	+	0.0175892i
$436$	16.7652			0.802906
$437$	−2.78353	+	37.0067i	−0.133154	+	1.77027i
$438$	0.562287			0.0268671
$439$	−2.97821	+	16.8902i	−0.142142	+	0.806127i	0.827476	+	0.561502i	$0.189776\pi$
$439$	−2.97821	+	16.8902i	−0.142142	+	0.806127i	−0.969618	+	0.244626i	$0.921335\pi$
$440$	6.57331	−	7.68893i	0.313370	−	0.366555i
$441$	−18.7615	−	6.82861i	−0.893402	−	0.325172i
$442$	−3.91972	−	10.7693i	−0.186442	−	0.512245i
$443$	14.6849	−	12.3221i	0.697703	−	0.585442i	−0.223416	−	0.974723i	$-0.571721\pi$
$443$	14.6849	−	12.3221i	0.697703	−	0.585442i	0.921119	+	0.389281i	$0.127277\pi$
$444$	−1.20794	−	2.09221i	−0.0573263	−	0.0992921i
$445$	36.7651	+	21.2264i	1.74283	+	1.00623i
$446$	12.3452	−	2.17679i	0.584562	−	0.103074i
$447$	0.680983	+	3.86205i	0.0322094	+	0.182669i
$448$	−0.416271	−	0.240334i	−0.0196670	−	0.0113547i
$449$	−28.5420	+	16.4788i	−1.34698	+	0.777680i	−0.987821	−	0.155595i	$-0.950270\pi$
$449$	−28.5420	+	16.4788i	−1.34698	+	0.777680i	−0.359161	+	0.933276i	$0.616937\pi$
$450$	−9.72161	+	8.15740i	−0.458281	+	0.384544i
$451$	−7.78489	−	22.0172i	−0.366576	−	1.03675i
$452$	2.59903	−	7.14079i	0.122248	−	0.335874i
$453$	−1.93799	+	2.30961i	−0.0910548	+	0.108515i
$454$	3.68169	−	20.8799i	0.172790	−	0.979942i
$455$			2.45655i			0.115165i
$456$	−0.794926	+	0.571181i	−0.0372258	+	0.0267480i
$457$		−	24.3274i		−	1.13799i	−0.822342	−	0.568994i	$-0.807333\pi$
$457$		−	24.3274i		−	1.13799i	0.822342	−	0.568994i	$-0.192667\pi$
$458$	−0.538918	+	3.05635i	−0.0251820	+	0.142814i
$459$	−7.00010	−	5.87378i	−0.326737	−	0.274165i
$460$	−24.4015	−	8.88141i	−1.13772	−	0.414098i
$461$	−2.61279	−	7.17858i	−0.121690	−	0.334340i	0.863859	−	0.503735i	$-0.168041\pi$
$461$	−2.61279	−	7.17858i	−0.121690	−	0.334340i	−0.985548	+	0.169395i	$0.945819\pi$
$462$	−0.227584	−	0.276350i	−0.0105882	−	0.0128570i
$463$	−8.43133	−	14.6035i	−0.391837	−	0.678681i	0.600855	−	0.799358i	$-0.294827\pi$
$463$	−8.43133	−	14.6035i	−0.391837	−	0.678681i	−0.992692	+	0.120677i	$0.961494\pi$
$464$	1.54223	−	2.67122i	0.0715962	−	0.124008i
$465$	−0.562944	−	3.19261i	−0.0261059	−	0.148054i
$466$	−9.35837	+	1.65013i	−0.433518	+	0.0764409i
$467$	−0.922553	+	1.59791i	−0.0426907	+	0.0739424i	−0.886581	−	0.462573i	$-0.846926\pi$
$467$	−0.922553	+	1.59791i	−0.0426907	+	0.0739424i	0.843891	+	0.536515i	$0.180260\pi$
$468$	−2.47120	−	4.28025i	−0.114231	−	0.197854i
$469$	4.41644	−	3.70583i	0.203932	−	0.171119i
$470$	−11.9592	+	4.35280i	−0.551638	+	0.200780i
$471$	−1.05224	+	2.89102i	−0.0484848	+	0.133211i
$472$	4.59002	−	5.47018i	0.211273	−	0.251785i
$473$	2.64902	−	14.2550i	0.121802	−	0.655443i
$474$		−	2.17518i		−	0.0999093i
$475$	−15.4927	−	10.5690i	−0.710852	−	0.484938i
$476$	3.28753			0.150684
$477$	12.8670	+	2.26879i	0.589138	+	0.103881i
$478$	−1.53920	+	1.83435i	−0.0704013	+	0.0839010i
$479$	11.0670	−	30.4062i	0.505662	−	1.38930i	−0.380009	−	0.924983i	$-0.624079\pi$
$479$	11.0670	−	30.4062i	0.505662	−	1.38930i	0.885671	−	0.464313i	$-0.153699\pi$
$480$	−0.234257	−	0.643617i	−0.0106923	−	0.0293770i
$481$	11.5873	+	13.8092i	0.528335	+	0.629645i
$482$	12.3562	+	21.4016i	0.562810	+	0.974815i
$483$	−0.459500	+	0.795878i	−0.0209080	+	0.0362137i
$484$	−1.71043	−	10.8662i	−0.0777466	−	0.493918i
$485$	10.1219	−	1.78477i	0.459613	−	0.0810421i
$486$	−5.13372	−	2.96396i	−0.232870	−	0.134448i
$487$	8.70643	−	5.02666i	0.394526	−	0.227780i	−0.289593	−	0.957150i	$-0.593520\pi$
$487$	8.70643	−	5.02666i	0.394526	−	0.227780i	0.684119	+	0.729370i	$0.260187\pi$
$488$	−0.647561	−	0.771733i	−0.0293137	−	0.0349347i
$489$	−1.41536	−	3.88868i	−0.0640049	−	0.175852i
$490$	19.4003	+	7.06113i	0.876416	+	0.318989i
$491$	7.95446	−	9.47975i	0.358980	−	0.427815i	−0.556083	−	0.831127i	$-0.687696\pi$
$491$	7.95446	−	9.47975i	0.358980	−	0.427815i	0.915063	+	0.403311i	$0.132141\pi$
$492$	−1.55718	−	0.274572i	−0.0702029	−	0.0123787i
$493$			21.0961i			0.950122i
$494$	5.10131	−	5.22723i	0.229519	−	0.235184i
$495$	−0.274589	+	29.8358i	−0.0123419	+	1.34102i
$496$	−4.66127	−	0.821908i	−0.209297	−	0.0369047i
$497$	2.48485	+	2.08504i	0.111461	+	0.0935267i
$498$	−2.77560	−	1.01023i	−0.124377	−	0.0452697i
$499$	−18.7127	+	6.81085i	−0.837693	+	0.304895i	−0.725012	−	0.688736i	$-0.758166\pi$
$499$	−18.7127	+	6.81085i	−0.837693	+	0.304895i	−0.112681	+	0.993631i	$0.535944\pi$
$500$	−1.62956	+	1.36736i	−0.0728762	+	0.0611504i
$501$	−2.78690	+	1.60902i	−0.124510	+	0.0718856i
$502$	−9.73954	+	16.8694i	−0.434697	+	0.752917i
$503$	−20.5109	+	3.61662i	−0.914535	+	0.161257i	−0.611062	−	0.791583i	$-0.709257\pi$
$503$	−20.5109	+	3.61662i	−0.914535	+	0.161257i	−0.303473	+	0.952840i	$0.598146\pi$
$504$	1.39623	−	0.246192i	0.0621929	−	0.0109663i
$505$	−16.7961	−	9.69723i	−0.747416	−	0.431521i
$506$	−24.5832	+	13.8931i	−1.09286	+	0.617623i
$507$	1.47122	+	1.75333i	0.0653393	+	0.0778683i
$508$	−0.722146	+	0.262840i	−0.0320400	+	0.0116616i
$509$	10.2540	−	28.1726i	0.454500	−	1.24873i	−0.475026	−	0.879972i	$-0.657561\pi$
$509$	10.2540	−	28.1726i	0.454500	−	1.24873i	0.929526	−	0.368757i	$-0.120217\pi$
$510$	3.58856	+	3.01116i	0.158904	+	0.133336i
$511$	0.208994	−	1.18526i	0.00924533	−	0.0524329i
$512$	−1.00000			−0.0441942
$513$	1.43861	−	5.64328i	0.0635162	−	0.249157i
$514$			11.2471i			0.496090i
$515$	−1.07073	−	0.188799i	−0.0471822	−	0.00831950i
$516$	−0.752032	−	0.631030i	−0.0331064	−	0.0277796i
$517$	−4.85279	+	12.9605i	−0.213425	+	0.570004i
$518$	−4.85921	+	1.76861i	−0.213502	+	0.0777082i
$519$	−2.14137	−	2.55199i	−0.0939959	−	0.112020i
$520$	2.55535	+	4.42600i	0.112059	+	0.194093i
$521$	−14.6834	−	8.47749i	−0.643294	−	0.371406i	0.142589	−	0.989782i	$-0.454457\pi$
$521$	−14.6834	−	8.47749i	−0.643294	−	0.371406i	−0.785882	+	0.618376i	$0.787791\pi$
$522$	1.57982	+	8.95961i	0.0691469	+	0.392152i
$523$	−1.42295	−	8.06997i	−0.0622214	−	0.352875i	−0.999984	−	0.00559895i	$-0.998218\pi$
$523$	−1.42295	−	8.06997i	−0.0622214	−	0.352875i	0.937763	−	0.347276i	$-0.112893\pi$
$524$	−17.6755	−	10.2050i	−0.772159	−	0.445806i
$525$	−0.232211	−	0.402201i	−0.0101345	−	0.0175535i
$526$	−5.69533	−	6.78743i	−0.248328	−	0.295946i
$527$	30.4202	−	11.0721i	1.32513	−	0.482307i
$528$	−0.697505	−	0.261165i	−0.0303550	−	0.0113658i
$529$	37.9090	+	31.8094i	1.64822	+	1.38302i
$530$	−13.3051	−	2.34605i	−0.577936	−	0.101906i
$531$			21.0623i			0.914027i
$532$	0.908547	+	1.88795i	0.0393905	+	0.0818529i
$533$	11.7984			0.511047
$534$	0.542770	−	3.07820i	0.0234879	−	0.133207i
$535$	−15.0500	−	12.6284i	−0.650666	−	0.545974i
$536$	4.10227	−	11.2709i	0.177191	−	0.486829i
$537$	3.48905	−	1.26991i	0.150564	−	0.0548006i
$538$	−8.41035	−	10.0231i	−0.362596	−	0.432125i
$539$	19.5448	−	11.0456i	0.841855	−	0.475770i
$540$	3.52905	+	2.03750i	0.151866	+	0.0876800i
$541$	2.93650	−	0.517785i	0.126250	−	0.0222613i	−0.110166	−	0.993913i	$-0.535138\pi$
$541$	2.93650	−	0.517785i	0.126250	−	0.0222613i	0.236416	+	0.971652i	$0.424027\pi$
$542$	−2.21602	+	0.390744i	−0.0951861	+	0.0167839i
$543$	0.364470	−	0.631281i	0.0156409	−	0.0270909i
$544$	5.92318	−	3.41975i	0.253954	−	0.146620i
$545$	39.1709	−	32.8682i	1.67790	−	1.40792i
$546$	0.169962	−	0.0618611i	0.00727370	−	0.00264741i
$547$	−41.8015	−	15.2145i	−1.78730	−	0.650525i	−0.999397	−	0.0347304i	$-0.988943\pi$
$547$	−41.8015	−	15.2145i	−1.78730	−	0.650525i	−0.787907	−	0.615795i	$-0.788835\pi$
$548$	12.1587	+	10.2024i	0.519395	+	0.435824i
$549$	2.92633	+	0.515991i	0.124893	+	0.0220220i
$550$	0.131326	−	14.2693i	0.00559974	−	0.608446i
$551$	−12.1150	+	5.83016i	−0.516116	+	0.248373i
$552$			1.91192i			0.0813768i
$553$	−4.58513	−	0.808481i	−0.194979	−	0.0343801i
$554$	18.0524	−	21.5141i	0.766975	−	0.914045i
$555$	−6.92408	−	2.52016i	−0.293911	−	0.106975i
$556$	0.0241785	+	0.0664300i	0.00102540	+	0.00281726i
$557$	−22.4116	−	26.7091i	−0.949610	−	1.13170i	−0.991174	−	0.132565i	$-0.957679\pi$
$557$	−22.4116	−	26.7091i	−0.949610	−	1.13170i	0.0415644	−	0.999136i	$-0.486766\pi$
$558$	12.0904	−	6.98042i	0.511829	−	0.295505i
$559$	6.34383	+	3.66261i	0.268316	+	0.154912i
$560$	−1.44377	+	0.254576i	−0.0610104	+	0.0107578i
$561$	5.02457	−	0.838363i	0.212137	−	0.0353957i
$562$	−9.40535	+	16.2905i	−0.396741	+	0.687175i
$563$	7.37482	+	12.7736i	0.310812	+	0.538342i	0.978538	−	0.206065i	$-0.0660658\pi$
$563$	7.37482	+	12.7736i	0.310812	+	0.538342i	−0.667727	+	0.744407i	$0.732732\pi$
$564$	0.602317	+	0.717813i	0.0253621	+	0.0302254i
$565$	−7.92707	−	21.7794i	−0.333494	−	0.916268i
$566$	−1.12473	+	3.09017i	−0.0472759	+	0.129890i
$567$	−2.64127	+	3.14774i	−0.110923	+	0.132193i
$568$	6.64588	+	1.17185i	0.278855	+	0.0491696i
$569$	−10.0803			−0.422590			−0.211295	−	0.977422i	$-0.567768\pi$
$569$	−10.0803			−0.422590			−0.211295	+	0.977422i	$0.567768\pi$
$570$	−0.737494	+	2.89299i	−0.0308902	+	0.121174i
$571$			5.53983i			0.231835i	0.993259	+	0.115917i	$0.0369807\pi$
$571$			5.53983i			0.231835i	−0.993259	+	0.115917i	$0.963019\pi$
$572$	5.46391	+	1.01537i	0.228458	+	0.0424547i
$573$	2.20615	−	2.62918i	0.0921631	−	0.109836i
$574$	−1.15756	+	3.18036i	−0.0483155	+	0.132746i
$575$	−34.4223	+	12.5287i	−1.43551	+	0.522483i
$576$	2.25950	−	1.89595i	0.0941459	−	0.0789978i
$577$	−2.60864	−	4.51830i	−0.108599	−	0.188099i	0.806604	−	0.591093i	$-0.201303\pi$
$577$	−2.60864	−	4.51830i	−0.108599	−	0.188099i	−0.915203	+	0.402993i	$0.867970\pi$
$578$	−14.8893	+	25.7891i	−0.619315	+	1.07268i
$579$	−3.69895	+	0.652225i	−0.153723	+	0.0271056i
$580$	−1.63362	−	9.26470i	−0.0678322	−	0.384696i
$581$	−3.16115	+	5.47527i	−0.131147	+	0.227153i
$582$	−0.378374	−	0.655363i	−0.0156841	−	0.0271657i
$583$	−11.3407	+	9.33945i	−0.469682	+	0.386801i
$584$	−0.856384	−	2.35290i	−0.0354374	−	0.0973636i
$585$	−14.1653	−	5.15574i	−0.585662	−	0.213164i
$586$	3.57355	+	2.99857i	0.147622	+	0.123870i
$587$	4.52810	−	25.6801i	0.186895	−	1.05993i	−0.736602	−	0.676326i	$-0.763571\pi$
$587$	4.52810	−	25.6801i	0.186895	−	1.05993i	0.923497	−	0.383606i	$-0.125318\pi$
$588$		−	1.52007i		−	0.0626865i
$589$	14.7654	+	14.4097i	0.608398	+	0.593741i
$590$		−	21.7795i		−	0.896649i
$591$	−0.489708	+	2.77727i	−0.0201439	+	0.114242i
$592$	−6.91516	+	8.24117i	−0.284211	+	0.338710i
$593$	−3.07964	+	8.46124i	−0.126466	+	0.347462i	−0.986726	−	0.162393i	$-0.948079\pi$
$593$	−3.07964	+	8.46124i	−0.126466	+	0.347462i	0.860260	+	0.509855i	$0.170301\pi$
$594$	4.17775	−	1.47718i	0.171415	−	0.0606094i
$595$	7.68112	−	6.44522i	0.314895	−	0.264228i
$596$	15.1236	−	8.73163i	0.619488	−	0.357661i
$597$	−3.60949	−	2.08394i	−0.147726	−	0.0852899i
$598$	−2.47730	−	14.0495i	−0.101304	−	0.574526i
$599$	−11.9946	+	2.11497i	−0.490085	+	0.0864152i	−0.413229	−	0.910627i	$-0.635599\pi$
$599$	−11.9946	+	2.11497i	−0.490085	+	0.0864152i	−0.0768557	+	0.997042i	$0.524488\pi$
$600$	−0.836753	−	0.483099i	−0.0341603	−	0.0197224i
$601$	2.26282	+	3.91932i	0.0923024	+	0.159872i	0.908480	−	0.417929i	$-0.137244\pi$
$601$	2.26282	+	3.91932i	0.0923024	+	0.159872i	−0.816177	+	0.577802i	$0.803911\pi$
$602$	−1.60969	+	1.35069i	−0.0656059	+	0.0550499i
$603$	12.0999	+	33.2443i	0.492748	+	1.35381i
$604$	12.6162	+	4.59193i	0.513347	+	0.186843i
$605$	−25.2996	−	22.0350i	−1.02857	−	0.895848i
$606$	−0.247964	+	1.40627i	−0.0100728	+	0.0571259i
$607$	−34.1802			−1.38733			−0.693665	−	0.720298i	$-0.744005\pi$
$607$	−34.1802			−1.38733			−0.693665	+	0.720298i	$0.744005\pi$
$608$	3.60081	+	2.45645i	0.146032	+	0.0996221i
$609$	−0.332940			−0.0134914
$610$	−3.02598	−	0.533562i	−0.122518	−	0.0216033i
$611$	−5.35612	−	4.49431i	−0.216685	−	0.181821i
$612$	−6.89977	+	18.9570i	−0.278907	+	0.766290i
$613$	11.0326	+	30.3119i	0.445604	+	1.22429i	0.935756	+	0.352649i	$0.114719\pi$
$613$	11.0326	+	30.3119i	0.445604	+	1.22429i	−0.490152	+	0.871637i	$0.663059\pi$
$614$	−11.1550	+	9.36017i	−0.450180	+	0.377746i
$615$	−4.17655	+	2.41133i	−0.168415	+	0.0972343i
$616$	−0.809770	+	1.37322i	−0.0326266	+	0.0553286i
$617$	−1.31948	−	7.48314i	−0.0531203	−	0.301260i	0.946660	−	0.322235i	$-0.104434\pi$
$617$	−1.31948	−	7.48314i	−0.0531203	−	0.301260i	−0.999780	+	0.0209749i	$0.993323\pi$
$618$	0.0139008	+	0.0788355i	0.000559173	+	0.00317123i
$619$	0.625169	−	1.08282i	0.0251276	−	0.0435224i	−0.853188	−	0.521603i	$-0.825334\pi$
$619$	0.625169	−	1.08282i	0.0251276	−	0.0435224i	0.878316	+	0.478081i	$0.158667\pi$
$620$	−12.5021	+	7.21811i	−0.502098	+	0.289886i
$621$	−7.31178	−	8.71384i	−0.293412	−	0.349674i
$622$	−10.3004	+	3.74906i	−0.413010	+	0.150323i
$623$	−6.28689	−	2.28824i	−0.251879	−	0.0916764i
$624$	0.241873	−	0.288253i	0.00968268	−	0.0115394i
$625$	−4.86229	+	27.5754i	−0.194492	+	1.10302i
$626$	19.5318			0.780648
$627$	1.87005	+	2.65379i	0.0746825	+	0.105982i
$628$	13.7001			0.546694
$629$	12.7770	−	72.4620i	0.509452	−	2.88925i
$630$	2.77954	−	3.31253i	0.110739	−	0.131974i
$631$	−1.91248	−	0.696087i	−0.0761347	−	0.0277108i	0.303672	−	0.952777i	$-0.401787\pi$
$631$	−1.91248	−	0.696087i	−0.0761347	−	0.0277108i	−0.379807	+	0.925066i	$0.624010\pi$
$632$	−9.10207	+	3.31288i	−0.362061	+	0.131779i
$633$	−2.90498	−	3.46202i	−0.115462	−	0.137603i
$634$	−1.33168	+	0.768845i	−0.0528877	+	0.0305347i
$635$	−1.17195	+	2.02988i	−0.0465075	+	0.0805534i
$636$	0.172734	+	0.979621i	0.00684933	+	0.0388445i
$637$	1.96957	+	11.1700i	0.0780372	+	0.442571i
$638$	−8.81198	−	5.19631i	−0.348870	−	0.205724i
$639$	−17.2381	+	9.95244i	−0.681930	+	0.393713i
$640$	−2.33644	+	1.96051i	−0.0923560	+	0.0774958i
$641$	9.53568	+	26.1991i	0.376637	+	1.03480i	0.972741	+	0.231894i	$0.0744922\pi$
$641$	9.53568	+	26.1991i	0.376637	+	1.03480i	−0.596104	+	0.802907i	$0.703286\pi$
$642$	−0.494735	+	1.35927i	−0.0195256	+	0.0536463i
$643$	−6.32336	−	5.30593i	−0.249369	−	0.209245i	0.509532	−	0.860452i	$-0.329819\pi$
$643$	−6.32336	−	5.30593i	−0.249369	−	0.209245i	−0.758901	+	0.651207i	$0.774263\pi$
$644$	4.03020	+	0.710632i	0.158812	+	0.0280028i
$645$	−2.99422			−0.117897
$646$	−29.7287	−	2.23609i	−1.16966	−	0.0879780i
$647$	18.0741			0.710567			0.355283	−	0.934759i	$-0.384384\pi$
$647$	18.0741			0.710567			0.355283	+	0.934759i	$0.384384\pi$
$648$	−1.48446	+	8.41881i	−0.0583152	+	0.330722i
$649$	−18.0017	−	15.3897i	−0.706627	−	0.604099i
$650$	6.77471	+	2.46579i	0.265726	+	0.0967163i
$651$	0.174739	+	0.480093i	0.00684858	+	0.0188163i
$652$	−14.1166	+	11.8452i	−0.552848	+	0.463894i
$653$	7.28814	+	12.6234i	0.285207	+	0.493993i	0.972659	−	0.232237i	$-0.0746044\pi$
$653$	7.28814	+	12.6234i	0.285207	+	0.493993i	−0.687452	+	0.726229i	$0.741271\pi$
$654$	−3.26047	−	1.88243i	−0.127494	−	0.0736089i
$655$	−61.3047	+	10.8097i	−2.39537	+	0.422369i
$656$	1.22269	+	6.93421i	0.0477379	+	0.270735i
$657$	6.39597	+	3.69272i	0.249531	+	0.144067i
$658$	1.73697	−	1.00284i	0.0677142	−	0.0390948i
$659$	13.1734	−	11.0538i	0.513162	−	0.430594i	−0.349078	−	0.937094i	$-0.613505\pi$
$659$	13.1734	−	11.0538i	0.513162	−	0.430594i	0.862240	+	0.506499i	$0.169061\pi$
$660$	−2.14170	+	0.757266i	−0.0833654	+	0.0294766i
$661$	−6.47851	+	17.7995i	−0.251985	+	0.692322i	0.747618	+	0.664129i	$0.231198\pi$
$661$	−6.47851	+	17.7995i	−0.251985	+	0.692322i	−0.999602	+	0.0281930i	$0.991025\pi$
$662$	10.2377	−	12.2008i	0.397900	−	0.474199i
$663$	−0.446904	+	2.53452i	−0.0173563	+	0.0984326i
$664$			13.1531i			0.510441i
$665$	5.82410	+	2.62987i	0.225849	+	0.101982i
$666$		−	31.7317i		−	1.22958i
$667$	−4.56014	+	25.8618i	−0.176569	+	1.00137i
$668$	10.9775	+	9.21123i	0.424733	+	0.356393i
$669$	−2.64529	−	0.962808i	−0.102273	−	0.0372243i
$670$	−12.5120	−	34.3763i	−0.483379	−	1.32807i
$671$	−2.57921	+	2.12407i	−0.0995692	+	0.0819989i
$672$	0.0539705	+	0.0934797i	0.00208196	+	0.00360606i
$673$	−16.6268	+	28.7984i	−0.640915	+	1.11010i	0.344313	+	0.938855i	$0.388112\pi$
$673$	−16.6268	+	28.7984i	−0.640915	+	1.11010i	−0.985229	+	0.171243i	$0.945222\pi$
$674$	0.703009	+	3.98696i	0.0270789	+	0.153572i
$675$	5.66113	−	0.998211i	0.217897	−	0.0384212i
$676$	5.09612	−	8.82675i	0.196005	−	0.339490i
$677$	−20.6635	−	35.7902i	−0.794162	−	1.37553i	−0.923370	−	0.383912i	$-0.874577\pi$
$677$	−20.6635	−	35.7902i	−0.794162	−	1.37553i	0.129208	−	0.991618i	$-0.458757\pi$
$678$	−1.30724	+	1.09690i	−0.0502042	+	0.0421263i
$679$	−1.52210	+	0.553998i	−0.0584127	+	0.0212605i
$680$	7.13471	−	19.6025i	0.273604	−	0.751720i
$681$	−3.06045	+	3.64730i	−0.117277	+	0.139765i
$682$	−2.86812	+	15.4339i	−0.109826	+	0.590996i
$683$			22.7795i			0.871634i	0.900035	+	0.435817i	$0.143540\pi$
$683$			22.7795i			0.871634i	−0.900035	+	0.435817i	$0.856460\pi$
$684$	−12.7933	+	1.27661i	−0.489166	+	0.0488123i
$685$	48.4100			1.84965
$686$	−6.51776	−	1.14926i	−0.248849	−	0.0438788i
$687$	0.447982	−	0.533884i	0.0170916	−	0.0203690i
$688$	−1.49518	+	4.10797i	−0.0570032	+	0.156615i
$689$	−2.53861	−	6.97479i	−0.0967135	−	0.265718i
$690$	3.74834	+	4.46709i	0.142697	+	0.170059i
$691$	−10.8613	−	18.8124i	−0.413184	−	0.715656i	0.582052	−	0.813152i	$-0.302250\pi$
$691$	−10.8613	−	18.8124i	−0.413184	−	0.715656i	−0.995236	+	0.0974960i	$0.968917\pi$
$692$	−7.41744	+	12.8474i	−0.281969	+	0.488385i
$693$	−0.773877	−	4.63808i	−0.0293971	−	0.176186i
$694$	−4.91620	+	0.866859i	−0.186616	+	0.0329055i
$695$	0.186728	+	0.107808i	0.00708300	+	0.00408937i
$696$	−0.599861	+	0.346330i	−0.0227377	+	0.0131276i
$697$	−30.9554	−	36.8912i	−1.17252	−	1.39736i
$698$	3.79850	+	10.4363i	0.143775	+	0.395019i
$699$	2.00528	+	0.729863i	0.0758467	+	0.0276060i
$700$	−1.32935	+	1.58425i	−0.0502446	+	0.0598792i
$701$	37.9705	+	6.69522i	1.43412	+	0.252875i	0.836089	−	0.548594i	$-0.184837\pi$
$701$	37.9705	+	6.69522i	1.43412	+	0.252875i	0.598036	+	0.801469i	$0.295948\pi$
$702$			2.23875i			0.0844962i
$703$	45.1442	−	12.6882i	1.70265	−	0.478544i
$704$	−0.0305227	+	3.31648i	−0.00115037	+	0.124995i
$705$	2.81456	+	0.496282i	0.106002	+	0.0186911i
$706$	15.4332	+	12.9500i	0.580836	+	0.487379i
$707$	2.87216	+	1.04538i	0.108019	+	0.0393156i
$708$	−1.50686	+	0.548454i	−0.0566314	+	0.0206122i
$709$	−22.6599	+	19.0139i	−0.851012	+	0.714084i	−0.960012	−	0.279958i	$-0.909679\pi$
$709$	−22.6599	+	19.0139i	−0.851012	+	0.714084i	0.109001	+	0.994042i	$0.465235\pi$
$710$	17.8251	−	10.2913i	0.668965	−	0.386227i
$711$	14.2851	−	24.7425i	0.535733	−	0.927916i
$712$	−13.7074	+	2.41699i	−0.513708	+	0.0905805i
$713$	39.6856	−	6.99765i	1.48624	−	0.262064i
$714$	−0.639354	−	0.369131i	−0.0239272	−	0.0138144i
$715$	14.7567	−	8.33968i	0.551871	−	0.311886i
$716$	−10.6279	−	12.6658i	−0.397184	−	0.473345i
$717$	0.505306	−	0.183916i	0.0188710	−	0.00686848i
$718$	1.12170	−	3.08186i	0.0418617	−	0.115014i
$719$	−0.654458	−	0.549156i	−0.0244072	−	0.0204801i	0.630502	−	0.776187i	$-0.282849\pi$
$719$	−0.654458	−	0.549156i	−0.0244072	−	0.0204801i	−0.654910	+	0.755707i	$0.727293\pi$
$720$	1.56218	−	8.85954i	0.0582189	−	0.330176i
$721$	0.171346			0.00638128
$722$	−6.93173	−	17.6904i	−0.257972	−	0.658369i
$723$		−	5.54953i		−	0.206389i
$724$	−3.19670	−	0.563665i	−0.118805	−	0.0209485i
$725$	−10.1662	−	8.53045i	−0.377563	−	0.316813i
$726$	−0.887441	+	2.30529i	−0.0329360	+	0.0855575i
$727$	3.04864	−	1.10961i	0.113068	−	0.0411533i	−0.284867	−	0.958567i	$-0.591949\pi$
$727$	3.04864	−	1.10961i	0.113068	−	0.0411533i	0.397935	+	0.917414i	$0.369727\pi$
$728$	−0.517717	−	0.616991i	−0.0191879	−	0.0228672i
$729$	−12.1574	−	21.0573i	−0.450275	−	0.779899i
$730$	−6.61376	−	3.81846i	−0.244786	−	0.141327i
$731$	−5.19201	−	29.4454i	−0.192034	−	1.08908i
$732$	0.0392848	+	0.222795i	0.00145201	+	0.00823475i
$733$	−12.9279	−	7.46395i	−0.477504	−	0.275687i	0.241872	−	0.970308i	$-0.422239\pi$
$733$	−12.9279	−	7.46395i	−0.477504	−	0.275687i	−0.719376	+	0.694621i	$0.755572\pi$
$734$	−8.33379	−	14.4345i	−0.307606	−	0.532789i
$735$	−2.98010	−	3.55155i	−0.109923	−	0.131001i
$736$	8.00046	−	2.91193i	0.294901	−	0.107335i
$737$	−37.2545	−	13.9491i	−1.37229	−	0.513823i
$738$	−15.9096	−	13.3497i	−0.585639	−	0.491409i
$739$	3.07535	+	0.542268i	0.113129	+	0.0199476i	0.229926	−	0.973208i	$-0.426152\pi$
$739$	3.07535	+	0.542268i	0.113129	+	0.0199476i	−0.116797	+	0.993156i	$0.537263\pi$
$740$			32.8122i			1.20620i
$741$	−1.57902	+	0.443798i	−0.0580067	+	0.0163033i
$742$	2.12917			0.0781644
$743$	−2.80843	+	15.9274i	−0.103031	+	0.584319i	0.888957	+	0.457990i	$0.151431\pi$
$743$	−2.80843	+	15.9274i	−0.103031	+	0.584319i	−0.991988	+	0.126329i	$0.959681\pi$
$744$	0.814231	+	0.683221i	0.0298512	+	0.0250481i
$745$	18.2170	−	50.0509i	0.667420	−	1.83372i
$746$	16.0848	−	5.85439i	0.588907	−	0.214345i
$747$	−24.9377	−	29.7196i	−0.912422	−	1.08738i
$748$	−11.1607	−	19.7485i	−0.408077	−	0.722077i
$749$	2.68137	+	1.54809i	0.0979750	+	0.0565659i
$750$	0.470445	−	0.0829522i	0.0171782	−	0.00302899i
$751$	36.3169	−	6.40365i	1.32522	−	0.233673i	0.534148	−	0.845391i	$-0.320633\pi$
$751$	36.3169	−	6.40365i	1.32522	−	0.233673i	0.791076	+	0.611718i	$0.209521\pi$
$752$	2.08635	−	3.61366i	0.0760813	−	0.131777i
$753$	3.78826	−	2.18715i	0.138052	−	0.0797043i
$754$	3.95924	−	3.32220i	0.144187	−	0.120987i
$755$	38.4796	−	14.0054i	1.40042	−	0.509710i
$756$	−0.603473	−	0.219646i	−0.0219481	−	0.00798846i
$757$	7.72532	+	6.48231i	0.280782	+	0.235604i	0.772292	−	0.635268i	$-0.219110\pi$
$757$	7.72532	+	6.48231i	0.280782	+	0.235604i	−0.491510	+	0.870872i	$0.663555\pi$
$758$	−1.92783	−	0.339929i	−0.0700221	−	0.0123468i
$759$	6.34086	+	0.0583571i	0.230159	+	0.00211823i
$760$	13.2290	−	1.32008i	0.479865	−	0.0478842i
$761$			33.1094i			1.20022i	0.799919	+	0.600108i	$0.204876\pi$
$761$			33.1094i			1.20022i	−0.799919	+	0.600108i	$0.795124\pi$
$762$	0.169954	+	0.0299675i	0.00615678	+	0.00108561i
$763$	−5.17990	+	6.17316i	−0.187525	+	0.223483i
$764$	−14.3619	−	5.22730i	−0.519595	−	0.189117i
$765$	21.0443	+	57.8189i	0.760860	+	2.09045i
$766$	−7.21970	−	8.60411i	−0.260858	−	0.310879i
$767$	10.3623	−	5.98269i	0.374162	−	0.216023i
$768$	0.194478	+	0.112282i	0.00701764	+	0.00405163i
$769$	−31.3748	+	5.53222i	−1.13140	+	0.199497i	−0.707842	−	0.706370i	$-0.750331\pi$
$769$	−31.3748	+	5.53222i	−1.13140	+	0.199497i	−0.423561	+	0.905867i	$0.639220\pi$
$770$	0.800228	+	4.79601i	0.0288382	+	0.172836i
$771$	1.26285	−	2.18733i	0.0454806	−	0.0787746i
$772$	8.36289	+	14.4850i	0.300987	+	0.521325i
$773$	5.27079	+	6.28148i	0.189577	+	0.225929i	0.852458	−	0.522796i	$-0.175111\pi$
$773$	5.27079	+	6.28148i	0.189577	+	0.225929i	−0.662881	+	0.748725i	$0.730666\pi$
$774$	−4.41014	−	12.1168i	−0.158519	−	0.435528i
$775$	−6.96514	+	19.1366i	−0.250195	+	0.687406i
$776$	−2.16610	+	2.58146i	−0.0777584	+	0.0926688i
$777$	1.14360	+	0.201647i	0.0410263	+	0.00723404i
$778$	−11.1172			−0.398573
$779$	12.6308	−	27.9723i	0.452547	−	1.00221i
$780$		−	1.14768i		−	0.0410936i
$781$	4.08926	−	22.0052i	0.146325	−	0.787407i
$782$	−37.4301	+	44.6074i	−1.33850	+	1.59516i
$783$	1.40947	−	3.87250i	0.0503705	−	0.138392i
$784$	−6.36074	+	2.31512i	−0.227169	+	0.0826829i
$785$	32.0095	−	26.8591i	1.14247	−	0.958644i
$786$	2.29167	+	3.96929i	0.0817412	+	0.141580i
$787$	−3.57700	+	6.19554i	−0.127506	+	0.220847i	−0.922710	−	0.385495i	$-0.874031\pi$
$787$	−3.57700	+	6.19554i	−0.127506	+	0.220847i	0.795204	+	0.606342i	$0.207364\pi$
$788$	12.3674	−	2.18070i	0.440570	−	0.0776843i
$789$	0.345511	+	1.95949i	0.0123005	+	0.0697598i
$790$	−14.7715	+	25.5850i	−0.525547	+	0.910274i
$791$	1.82632	+	3.16327i	0.0649363	+	0.112473i
$792$	−6.21891	−	7.55147i	−0.220979	−	0.268330i
$793$	−0.577357	−	1.58628i	−0.0205025	−	0.0563303i
$794$	18.9520	+	6.89798i	0.672583	+	0.244800i
$795$	2.32414	+	1.95018i	0.0824286	+	0.0691658i
$796$	−3.22288	+	18.2779i	−0.114232	+	0.647842i
$797$		−	46.5224i		−	1.64791i	−0.566657	−	0.823954i	$-0.691764\pi$
$797$		−	46.5224i		−	1.64791i	0.566657	−	0.823954i	$-0.308236\pi$
$798$	0.0352901	−	0.469179i	0.00124926	−	0.0166087i
$799$			28.5391i			1.00964i
$800$	−0.747129	+	4.23718i	−0.0264150	+	0.149807i
$801$	26.3895	−	31.4498i	0.932426	−	1.11122i
$802$	−5.54630	+	15.2383i	−0.195847	+	0.538085i
$803$	−7.82948	+	2.76837i	−0.276296	+	0.0976936i
$804$	−2.06332	+	1.73133i	−0.0727678	+	0.0610595i
$805$	10.8095	−	6.24088i	0.380985	−	0.219962i
$806$	−6.86851	−	3.96554i	−0.241933	−	0.139680i
$807$	0.510220	+	2.89360i	0.0179606	+	0.101860i
$808$	6.26222	−	1.10420i	0.220304	−	0.0388456i
$809$	26.0149	+	15.0197i	0.914634	+	0.528064i	0.881919	−	0.471400i	$-0.156251\pi$
$809$	26.0149	+	15.0197i	0.914634	+	0.528064i	0.0327149	+	0.999465i	$0.489585\pi$
$810$	13.0368	+	22.5803i	0.458065	+	0.793393i
$811$	−11.4248	+	9.58652i	−0.401178	+	0.336628i	−0.820949	−	0.571002i	$-0.806555\pi$
$811$	−11.4248	+	9.58652i	−0.401178	+	0.336628i	0.419771	+	0.907630i	$0.362110\pi$
$812$	0.507080	+	1.39319i	0.0177950	+	0.0488914i
$813$	0.474841	+	0.172828i	0.0166534	+	0.00606135i
$814$	27.1206	+	23.1856i	0.950578	+	0.812653i
$815$	−9.75993	+	55.3513i	−0.341875	+	1.93887i
$816$	−1.53591			−0.0537675
$817$	15.4749	−	11.1192i	0.541398	−	0.389012i
$818$	−30.2040			−1.05606
$819$	2.33957	+	0.412529i	0.0817510	+	0.0144149i
$820$	16.4513	+	13.8043i	0.574504	+	0.482066i
$821$	−15.9032	+	43.6936i	−0.555025	+	1.52492i	0.271741	+	0.962370i	$0.412401\pi$
$821$	−15.9032	+	43.6936i	−0.555025	+	1.52492i	−0.826765	+	0.562547i	$0.809822\pi$
$822$	−1.21906	−	3.34935i	−0.0425198	−	0.116822i
$823$	−21.9336	+	18.4045i	−0.764557	+	0.641539i	−0.939309	−	0.343073i	$-0.888532\pi$
$823$	−21.9336	+	18.4045i	−0.764557	+	0.641539i	0.174752	+	0.984612i	$0.444088\pi$
$824$	0.308717	−	0.178238i	0.0107547	−	0.00620920i
$825$	−1.62773	+	2.76033i	−0.0566703	+	0.0961024i
$826$	0.596023	+	3.38022i	0.0207383	+	0.117613i
$827$	3.88122	+	22.0115i	0.134963	+	0.765415i	0.974885	+	0.222708i	$0.0714896\pi$
$827$	3.88122	+	22.0115i	0.134963	+	0.765415i	−0.839922	+	0.542707i	$0.817399\pi$
$828$	−12.5562	+	21.7480i	−0.436358	+	0.755794i
$829$	46.8670	−	27.0586i	1.62776	−	0.939786i	0.642996	−	0.765869i	$-0.277691\pi$
$829$	46.8670	−	27.0586i	1.62776	−	0.939786i	0.984760	−	0.173916i	$-0.0556422\pi$
$830$	25.7868	+	30.7316i	0.895074	+	1.06671i
$831$	−5.92646	+	2.15705i	−0.205587	+	0.0748274i
$832$	−1.57458	−	0.573101i	−0.0545888	−	0.0198687i
$833$	29.7587	−	35.4650i	1.03108	−	1.22879i
$834$	0.00275670	−	0.0156340i	9.54567e−5	−	0.000541362i
$835$	43.7070			1.51254
$836$	8.25668	−	11.8671i	0.285563	−	0.410431i
$837$	−6.32382			−0.218583
$838$	1.54390	−	8.75588i	0.0533331	−	0.302467i
$839$	−18.1179	+	21.5921i	−0.625501	+	0.745443i	−0.982006	−	0.188851i	$-0.939524\pi$
$839$	−18.1179	+	21.5921i	−0.625501	+	0.745443i	0.356505	+	0.934293i	$0.383968\pi$
$840$	0.309366	+	0.112600i	0.0106742	+	0.00388508i
$841$	18.3110	−	6.66465i	0.631412	−	0.229815i
$842$	−12.7427	−	15.1862i	−0.439143	−	0.523351i
$843$	3.65827	−	2.11211i	0.125998	−	0.0727448i
$844$	−10.0625	+	17.4287i	−0.346364	+	0.599921i
$845$	−5.39810	−	30.6142i	−0.185700	−	1.05316i
$846$	2.13720	+	12.1207i	0.0734785	+	0.416717i
$847$	4.52955	+	2.72751i	0.155637	+	0.0937182i
$848$	3.83616	−	2.21481i	0.131734	−	0.0760567i
$849$	0.565707	−	0.474684i	0.0194150	−	0.0162911i
$850$	−10.0647	−	27.6526i	−0.345217	−	0.948475i
$851$	31.3268	−	86.0696i	1.07387	−	2.95043i
$852$	−1.16090	−	0.974113i	−0.0397719	−	0.0333726i
$853$	−24.7736	−	4.36825i	−0.848232	−	0.149566i	−0.267396	−	0.963587i	$-0.586163\pi$
$853$	−24.7736	−	4.36825i	−0.848232	−	0.149566i	−0.580836	+	0.814021i	$0.697274\pi$
$854$	0.484238			0.0165703
$855$	−27.3881	+	28.0642i	−0.936653	+	0.959774i
$856$	6.44140			0.220162
$857$	−0.336821	+	1.91020i	−0.0115056	+	0.0652513i	−0.990020	−	0.140927i	$-0.954992\pi$
$857$	−0.336821	+	1.91020i	−0.0115056	+	0.0652513i	0.978514	+	0.206179i	$0.0661028\pi$
$858$	−0.948605	−	0.810967i	−0.0323848	−	0.0276860i
$859$	32.4727	+	11.8191i	1.10795	+	0.403262i	0.830242	−	0.557403i	$-0.188202\pi$
$859$	32.4727	+	11.8191i	1.10795	+	0.403262i	0.277711	+	0.960665i	$0.410424\pi$
$860$	4.56031	+	12.5293i	0.155505	+	0.427247i
$861$	0.582218	−	0.488539i	0.0198419	−	0.0166494i
$862$	−16.1847	−	28.0328i	−0.551254	−	0.954800i
$863$	−25.5247	−	14.7367i	−0.868870	−	0.501642i	−0.00189730	−	0.999998i	$-0.500604\pi$
$863$	−25.5247	−	14.7367i	−0.868870	−	0.501642i	−0.866972	+	0.498356i	$0.833937\pi$
$864$	−1.31576	+	0.232005i	−0.0447632	+	0.00789296i
$865$	7.85698	+	44.5591i	0.267145	+	1.51506i
$866$	−14.9679	−	8.64175i	−0.508632	−	0.293659i
$867$	5.79131	−	3.34362i	0.196683	−	0.113555i
$868$	1.74282	−	1.46240i	0.0591551	−	0.0496371i
$869$	10.7093	+	30.2880i	0.363288	+	1.02745i
$870$	−0.722557	+	1.98521i	−0.0244970	+	0.0673049i
$871$	12.9187	−	15.3959i	0.437734	−	0.521671i
$872$	−2.91124	+	16.5105i	−0.0985871	+	0.559115i
$873$		−	9.93961i		−	0.336405i
$874$	−35.9612	−	9.16739i	−1.21640	−	0.310092i
$875$		−	1.02250i		−	0.0345667i
$876$	−0.0976401	+	0.553744i	−0.00329895	+	0.0187093i
$877$	37.5612	+	31.5176i	1.26835	+	1.06427i	0.994740	+	0.102434i	$0.0326632\pi$
$877$	37.5612	+	31.5176i	1.26835	+	1.06427i	0.273613	+	0.961840i	$0.411781\pi$
$878$	−16.1165	−	5.86592i	−0.543905	−	0.197965i
$879$	−0.358293	−	0.984403i	−0.0120849	−	0.0332031i
$880$	6.43068	+	7.80861i	0.216778	+	0.263228i
$881$	7.13438	+	12.3571i	0.240363	+	0.416322i	0.960818	−	0.277181i	$-0.0894001\pi$
$881$	7.13438	+	12.3571i	0.240363	+	0.416322i	−0.720454	+	0.693502i	$0.756067\pi$
$882$	9.98276	−	17.2906i	0.336137	−	0.582206i
$883$	6.59567	+	37.4059i	0.221962	+	1.25881i	0.868408	+	0.495850i	$0.165143\pi$
$883$	6.59567	+	37.4059i	0.221962	+	1.25881i	−0.646446	+	0.762959i	$0.723746\pi$
$884$	11.2864	−	1.99009i	0.379602	−	0.0669341i
$885$	−2.44545	+	4.23565i	−0.0822030	+	0.142380i
$886$	9.58492	+	16.6016i	0.322012	+	0.557740i
$887$	27.8203	−	23.3440i	0.934115	−	0.783816i	−0.0424364	−	0.999099i	$-0.513512\pi$
$887$	27.8203	−	23.3440i	0.934115	−	0.783816i	0.976552	+	0.215283i	$0.0690675\pi$
$888$	2.27019	−	0.826280i	0.0761825	−	0.0277281i
$889$	0.126339	−	0.347113i	0.00423726	−	0.0116418i
$890$	−27.2881	+	32.5207i	−0.914698	+	1.09010i
$891$	27.8755	+	5.18016i	0.933865	+	0.173542i
$892$			12.5357i			0.419725i
$893$	−16.3893	+	7.88712i	−0.548448	+	0.263932i
$894$	−3.92162			−0.131159
$895$	−49.6630	−	8.75692i	−1.66005	−	0.292712i
$896$	0.308968	−	0.368213i	0.0103219	−	0.0123011i
$897$	−1.09572	+	3.01048i	−0.0365852	+	0.100517i
$898$	−11.2721	−	30.9699i	−0.376156	−	1.03348i
$899$	9.38424	+	11.1837i	0.312982	+	0.372997i
$900$	−6.34533	−	10.9904i	−0.211511	−	0.366348i
$901$	−15.1481	+	26.2374i	−0.504658	+	0.874093i
$902$	23.0345	−	3.84337i	0.766965	−	0.127970i
$903$	0.464707	−	0.0819405i	0.0154645	−	0.00272681i
$904$	6.58098	+	3.79953i	0.218880	+	0.126371i
$905$	−8.57398	+	4.95019i	−0.285009	+	0.164550i
$906$	−1.93799	−	2.30961i	−0.0643855	−	0.0767316i
$907$	−7.06970	−	19.4238i	−0.234746	−	0.644958i	−0.999999	−	0.00122933i	$-0.999609\pi$
$907$	−7.06970	−	19.4238i	−0.234746	−	0.644958i	0.765254	−	0.643729i	$-0.222614\pi$
$908$	19.9234	+	7.25151i	0.661180	+	0.240650i
$909$	−12.0560	+	14.3678i	−0.399872	+	0.476549i
$910$	−2.41923	−	0.426576i	−0.0801967	−	0.0141408i
$911$			14.9150i			0.494156i	0.968996	+	0.247078i	$0.0794704\pi$
$911$			14.9150i			0.494156i	−0.968996	+	0.247078i	$0.920530\pi$
$912$	−0.424466	−	0.882034i	−0.0140555	−	0.0292070i
$913$	43.6222	+	0.401470i	1.44368	+	0.0132867i
$914$	23.9578	+	4.22441i	0.792454	+	0.139731i
$915$	0.528578	+	0.443530i	0.0174743	+	0.0146626i
$916$	−2.91634	−	1.06146i	−0.0963586	−	0.0350716i
$917$	9.21877	−	3.35536i	0.304431	−	0.110804i
$918$	7.00010	−	5.87378i	0.231038	−	0.193864i
$919$	−22.9698	+	13.2616i	−0.757703	+	0.437460i	−0.828470	−	0.560033i	$-0.810788\pi$
$919$	−22.9698	+	13.2616i	−0.757703	+	0.437460i	0.0707676	+	0.997493i	$0.477455\pi$
$920$	12.9837	−	22.4885i	0.428061	−	0.741424i
$921$	3.22039	−	0.567842i	0.106115	−	0.0187110i
$922$	7.52323	−	1.32655i	0.247764	−	0.0436876i
$923$	9.79289	+	5.65393i	0.322337	+	0.186101i
$924$	0.311671	−	0.176139i	0.0102532	−	0.00579455i
$925$	29.7528	+	35.4580i	0.978266	+	1.16585i
$926$	15.8457	−	5.76737i	0.520722	−	0.189527i
$927$	−0.359617	+	0.988039i	−0.0118114	+	0.0324515i
$928$	2.36283	+	1.98265i	0.0775638	+	0.0650837i
$929$	0.975707	−	5.53351i	0.0320119	−	0.181549i	−0.964609	−	0.263683i	$-0.915063\pi$
$929$	0.975707	−	5.53351i	0.0320119	−	0.181549i	0.996621	+	0.0821347i	$0.0261738\pi$
$930$	3.24186			0.106305
$931$	28.5908	+	7.28851i	0.937026	+	0.238871i
$932$		−	9.50274i		−	0.311273i
$933$	2.42417	+	0.427446i	0.0793637	+	0.0139940i
$934$	−1.41343	−	1.18601i	−0.0462489	−	0.0388075i
$935$	−64.7935	−	24.2605i	−2.11897	−	0.793403i
$936$	4.64434	−	1.69040i	0.151805	−	0.0552525i
$937$	30.1971	+	35.9875i	0.986497	+	1.17566i	0.984450	+	0.175664i	$0.0562072\pi$
$937$	30.1971	+	35.9875i	0.986497	+	1.17566i	0.00204720	+	0.999998i	$0.499348\pi$
$938$	2.88263	+	4.99285i	0.0941211	+	0.163022i
$939$	−3.79852	−	2.19307i	−0.123960	−	0.0715683i
$940$	−2.20998	−	12.5334i	−0.0720815	−	0.408795i
$941$	−4.62488	−	26.2290i	−0.150767	−	0.855040i	−0.962555	−	0.271088i	$-0.912617\pi$
$941$	−4.62488	−	26.2290i	−0.150767	−	0.855040i	0.811788	−	0.583952i	$-0.198495\pi$
$942$	−2.66437	−	1.53828i	−0.0868100	−	0.0501198i
$943$	−29.9740	−	51.9165i	−0.976087	−	1.69063i
$944$	4.59002	+	5.47018i	0.149393	+	0.178039i
$945$	−1.84060	+	0.669923i	−0.0598746	+	0.0217926i
$946$	13.5784	+	5.08413i	0.441471	+	0.165299i
$947$	−0.584078	−	0.490100i	−0.0189800	−	0.0159261i	0.633248	−	0.773949i	$-0.281721\pi$
$947$	−0.584078	−	0.490100i	−0.0189800	−	0.0159261i	−0.652228	+	0.758023i	$0.726166\pi$
$948$	2.14213	+	0.377716i	0.0695733	+	0.0122676i
$949$		−	4.19562i		−	0.136196i
$950$	13.0987	−	13.4220i	0.424977	−	0.435468i
$951$	0.345310			0.0111975
$952$	−0.570873	+	3.23758i	−0.0185021	+	0.104931i
$953$	−7.00482	−	5.87774i	−0.226908	−	0.190399i	0.522245	−	0.852796i	$-0.325095\pi$
$953$	−7.00482	−	5.87774i	−0.226908	−	0.190399i	−0.749153	+	0.662397i	$0.769539\pi$
$954$	−4.46865	+	12.2775i	−0.144678	+	0.397499i
$955$	−43.8039	+	15.9433i	−1.41746	+	0.515913i
$956$	−1.53920	−	1.83435i	−0.0497813	−	0.0593270i
$957$	1.13029	+	2.00000i	0.0365370	+	0.0646508i
$958$	28.0225	+	16.1788i	0.905367	+	0.522714i
$959$	−7.51331	+	1.32480i	−0.242617	+	0.0427800i
$960$	0.674518	−	0.118936i	0.0217700	−	0.00383863i
$961$	−4.29851	+	7.44525i	−0.138662	+	0.240169i
$962$	−15.6115	+	9.01331i	−0.503335	+	0.290601i
$963$	−14.5544	+	12.2126i	−0.469008	+	0.393544i
$964$	−23.2221	+	8.45215i	−0.747933	+	0.272225i
$965$	47.9373	+	17.4477i	1.54315	+	0.561662i
$966$	−0.703995	−	0.590722i	−0.0226507	−	0.0190062i
$967$	−4.95059	−	0.872922i	−0.159200	−	0.0280713i	0.0934799	−	0.995621i	$-0.470201\pi$
$967$	−4.95059	−	0.872922i	−0.159200	−	0.0280713i	−0.252680	+	0.967550i	$0.581312\pi$
$968$	10.9981	+	0.202456i	0.353494	+	0.00650720i
$969$	5.53052	+	3.77287i	0.177666	+	0.121202i
$970$			10.2781i			0.330009i
$971$	−20.3902	−	3.59534i	−0.654352	−	0.115380i	−0.163391	−	0.986561i	$-0.552243\pi$
$971$	−20.3902	−	3.59534i	−0.654352	−	0.115380i	−0.490961	+	0.871182i	$0.663354\pi$
$972$	3.81039	−	4.54105i	0.122218	−	0.145654i
$973$	−0.0319308	−	0.0116219i	−0.00102365	−	0.000372580i
$974$	3.43844	+	9.44703i	0.110175	+	0.302702i
$975$	−1.04067	−	1.24022i	−0.0333281	−	0.0397189i
$976$	0.872457	−	0.503713i	0.0279267	−	0.0161235i
$977$	24.0166	+	13.8660i	0.768358	+	0.443612i	0.832289	−	0.554343i	$-0.187030\pi$
$977$	24.0166	+	13.8660i	0.768358	+	0.443612i	−0.0639304	+	0.997954i	$0.520364\pi$
$978$	4.07538	−	0.718599i	0.130316	−	0.0229783i
$979$	7.59752	+	45.5342i	0.242818	+	1.45528i
$980$	−10.3227	+	17.8794i	−0.329746	+	0.571137i
$981$	−24.7250	−	42.8250i	−0.789410	−	1.36730i
$982$	7.95446	+	9.47975i	0.253837	+	0.302511i
$983$	−7.70737	−	21.1758i	−0.245827	−	0.675404i	−0.999828	−	0.0185313i	$-0.994101\pi$
$983$	−7.70737	−	21.1758i	−0.245827	−	0.675404i	0.754001	−	0.656873i	$-0.228121\pi$
$984$	0.540802	−	1.48584i	0.0172401	−	0.0473669i
$985$	24.6204	−	29.3414i	0.784470	−	0.934895i
$986$	−20.7756	−	3.66330i	−0.661631	−	0.116663i
$987$	−0.450405			−0.0143365
$988$	4.26198	+	5.93151i	0.135592	+	0.188706i
$989$		−	37.2195i		−	1.18351i
$990$	−29.3348	−	5.45135i	−0.932323	−	0.173255i
$991$	30.6506	−	36.5280i	0.973649	−	1.16035i	−0.0133969	−	0.999910i	$-0.504265\pi$
$991$	30.6506	−	36.5280i	0.973649	−	1.16035i	0.987046	−	0.160439i	$-0.0512910\pi$
$992$	1.61884	−	4.44773i	0.0513983	−	0.141216i
$993$	−3.36095	+	1.22329i	−0.106657	+	0.0388198i
$994$	−2.48485	+	2.08504i	−0.0788147	+	0.0661334i
$995$	28.3038	+	49.0236i	0.897291	+	1.55415i
$996$	1.47686	−	2.55800i	0.0467962	−	0.0810535i
$997$	5.18432	−	0.914136i	0.164189	−	0.0289510i	−0.0909492	−	0.995856i	$-0.528990\pi$
$997$	5.18432	−	0.914136i	0.164189	−	0.0289510i	0.255138	+	0.966905i	$0.417879\pi$
$998$	−3.45796	−	19.6111i	−0.109460	−	0.620777i
$999$	−7.18673	+	12.4478i	−0.227378	+	0.393830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.q.a.21.7	✓	60
11.10	odd	2		418.2.q.b.21.7	yes	60
19.10	odd	18		418.2.q.b.219.7	yes	60
209.10	even	18	inner	418.2.q.a.219.7	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.q.a.21.7	✓	60	1.1	even	1	trivial
418.2.q.a.219.7	yes	60	209.10	even	18	inner
418.2.q.b.21.7	yes	60	11.10	odd	2
418.2.q.b.219.7	yes	60	19.10	odd	18

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.q (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.144347 - 0.172026i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-2.86607 + 1.04316i) q^{5} +(0.144347 + 0.172026i) q^{6} +(0.416271 - 0.240334i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.512188 + 2.90476i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.144347 - 0.172026i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-2.86607 + 1.04316i) q^{5} +(0.144347 + 0.172026i) q^{6} +(0.416271 - 0.240334i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.512188 + 2.90476i) q^{9} +(-0.529628 - 3.00367i) q^{10} +(-2.85690 - 1.68468i) q^{11} +(-0.194478 + 0.112282i) q^{12} +(1.28361 - 1.07708i) q^{13} +(0.164398 + 0.451681i) q^{14} +(-0.234257 + 0.643617i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-6.73559 - 1.18767i) q^{17} -2.94957 q^{18} +(-1.17941 - 4.19631i) q^{19} +3.05001 q^{20} +(0.0187438 - 0.106301i) q^{21} +(2.15518 - 2.52095i) q^{22} +(-8.00046 - 2.91193i) q^{23} +(-0.0768055 - 0.211022i) q^{24} +(3.29594 - 2.76562i) q^{25} +(0.837817 + 1.45114i) q^{26} +(1.15706 + 0.668031i) q^{27} +(-0.473366 + 0.0834672i) q^{28} +(-0.535611 - 3.03760i) q^{29} +(-0.593161 - 0.342462i) q^{30} +(-4.09905 + 2.36659i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-0.702194 + 0.248283i) q^{33} +(2.33924 - 6.42702i) q^{34} +(-0.942354 + 1.12305i) q^{35} +(0.512188 - 2.90476i) q^{36} +10.7581i q^{37} +(4.33736 - 0.432811i) q^{38} -0.376288i q^{39} +(-0.529628 + 3.00367i) q^{40} +(5.39386 + 4.52598i) q^{41} +(0.101431 + 0.0369180i) q^{42} +(1.49518 + 4.10797i) q^{43} +(2.10841 + 2.56019i) q^{44} +(-4.49811 - 7.79095i) q^{45} +(4.25696 - 7.37326i) q^{46} +(-0.724581 - 4.10930i) q^{47} +(0.221153 - 0.0389952i) q^{48} +(-3.38448 + 5.86209i) q^{49} +(2.15127 + 3.72611i) q^{50} +(-1.17657 + 0.987262i) q^{51} +(-1.57458 + 0.573101i) q^{52} +(1.51502 - 4.16247i) q^{53} +(-0.858804 + 1.02348i) q^{54} +(9.94546 + 1.84818i) q^{55} -0.480668i q^{56} +(-0.892120 - 0.402836i) q^{57} +3.08446 q^{58} +(7.03232 + 1.23999i) q^{59} +(0.440260 - 0.524682i) q^{60} +(0.344560 - 0.946671i) q^{61} +(-1.61884 - 4.44773i) q^{62} +(0.911322 + 1.08607i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.55535 + 4.42600i) q^{65} +(-0.122577 - 0.734640i) q^{66} +(11.8120 - 2.08278i) q^{67} +(5.92318 + 3.41975i) q^{68} +(-1.65577 + 0.955961i) q^{69} +(-0.942354 - 1.12305i) q^{70} +(2.30809 + 6.34142i) q^{71} +(2.77169 + 1.00881i) q^{72} +(1.60948 - 1.91810i) q^{73} +(-10.5946 - 1.86812i) q^{74} -0.966199i q^{75} +(-0.326939 + 4.34662i) q^{76} +(-1.59413 - 0.0146713i) q^{77} +(0.370571 + 0.0653417i) q^{78} +(-7.42007 - 6.22618i) q^{79} +(-2.86607 - 1.04316i) q^{80} +(-8.03313 + 2.92382i) q^{81} +(-5.39386 + 4.52598i) q^{82} +(-11.3910 + 6.57657i) q^{83} +(-0.0539705 + 0.0934797i) q^{84} +(20.5436 - 3.62239i) q^{85} +(-4.30520 + 0.759123i) q^{86} +(-0.599861 - 0.346330i) q^{87} +(-2.88742 + 1.63181i) q^{88} +(-8.94689 - 10.6625i) q^{89} +(8.45368 - 3.07689i) q^{90} +(0.275471 - 0.756852i) q^{91} +(6.52203 + 5.47264i) q^{92} +(-0.184571 + 1.04676i) q^{93} +4.17269 q^{94} +(7.75771 + 10.7966i) q^{95} +0.224564i q^{96} +(-3.31865 - 0.585168i) q^{97} +(-5.18532 - 4.35100i) q^{98} +(3.43031 - 9.16147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9}+O(q^{10}) \) 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9	\( 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9} + 3 q^{11} + 6 q^{13} - 12 q^{14} + 24 q^{15} - 6 q^{17} + 60 q^{18} - 30 q^{19} - 12 q^{20} + 12 q^{21} + 12 q^{22} + 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} + 6 q^{28} - 3 q^{29} - 9 q^{31} - 42 q^{33} - 6 q^{34} - 24 q^{35} - 3 q^{36} + 6 q^{38} + 15 q^{41} + 6 q^{42} - 3 q^{43} + 12 q^{44} - 48 q^{45} + 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} + 36 q^{50} - 45 q^{51} - 3 q^{52} + 24 q^{53} - 27 q^{54} + 6 q^{55} + 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} + 54 q^{61} - 66 q^{63} - 30 q^{64} - 63 q^{66} + 9 q^{67} - 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 36 q^{79} - 93 q^{81} - 15 q^{82} - 36 q^{83} + 24 q^{84} - 60 q^{85} - 3 q^{86} + 54 q^{87} - 3 q^{88} - 3 q^{89} - 24 q^{90} - 12 q^{91} - 102 q^{93} - 12 q^{94} + 24 q^{95} - 6 q^{97} - 18 q^{98} - 78 q^{99}+O(q^{100}) \) 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9 + 3 * q^11 + 6 * q^13 - 12 * q^14 + 24 * q^15 - 6 * q^17 + 60 * q^18 - 30 * q^19 - 12 * q^20 + 12 * q^21 + 12 * q^22 + 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 + 6 * q^28 - 3 * q^29 - 9 * q^31 - 42 * q^33 - 6 * q^34 - 24 * q^35 - 3 * q^36 + 6 * q^38 + 15 * q^41 + 6 * q^42 - 3 * q^43 + 12 * q^44 - 48 * q^45 + 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 + 36 * q^50 - 45 * q^51 - 3 * q^52 + 24 * q^53 - 27 * q^54 + 6 * q^55 + 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 + 54 * q^61 - 66 * q^63 - 30 * q^64 - 63 * q^66 + 9 * q^67 - 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 36 * q^79 - 93 * q^81 - 15 * q^82 - 36 * q^83 + 24 * q^84 - 60 * q^85 - 3 * q^86 + 54 * q^87 - 3 * q^88 - 3 * q^89 - 24 * q^90 - 12 * q^91 - 102 * q^93 - 12 * q^94 + 24 * q^95 - 6 * q^97 - 18 * q^98 - 78 * q^99

Introduction

L-functions

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