LMFDB - Embedded newform 798.2.bp.f.613.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(289,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 6, 2]))

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

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

chi := DirichletCharacter("798.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bp (of order $9$, 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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			613.2
Character	$\chi$	$=$	798.613
Dual form			798.2.bp.f.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.553438 + 3.13870i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-2.64367 + 0.104962i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.553438 + 3.13870i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-2.64367 + 0.104962i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-2.44148 + 2.04864i) q^{10} +(-1.34575 - 2.33091i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.287261 + 1.62914i) q^{13} +(-2.09264 - 1.61891i) q^{14} +(2.44148 - 2.04864i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.0114883 - 0.0651533i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.344703 - 4.34525i) q^{19} -3.18712 q^{20} +(2.09264 + 1.61891i) q^{21} +(0.467374 - 2.65061i) q^{22} +(-7.18746 - 2.61602i) q^{23} +(0.939693 - 0.342020i) q^{24} +(-4.84670 - 1.76406i) q^{25} +(-0.827135 + 1.43264i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.562436 - 2.58528i) q^{28} +(-7.72548 - 2.81185i) q^{29} +3.18712 q^{30} +0.361043 q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.467374 + 2.65061i) q^{33} +(0.0506802 - 0.0425258i) q^{34} +(1.13366 - 8.35578i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(-0.0261417 - 0.0452787i) q^{37} +(3.05713 - 3.10708i) q^{38} +(0.827135 - 1.43264i) q^{39} +(-2.44148 - 2.04864i) q^{40} +(-1.44584 + 8.19974i) q^{41} +(0.562436 + 2.58528i) q^{42} +(-0.00422135 - 0.00354213i) q^{43} +(2.06181 - 1.73006i) q^{44} -3.18712 q^{45} +(-3.82437 - 6.62400i) q^{46} +(1.53504 + 8.70563i) q^{47} +(0.939693 + 0.342020i) q^{48} +(6.97797 - 0.554970i) q^{49} +(-2.57888 - 4.46675i) q^{50} +(-0.0506802 + 0.0425258i) q^{51} +(-1.55451 + 0.565794i) q^{52} +(1.99891 + 11.3364i) q^{53} +(0.939693 - 0.342020i) q^{54} +(8.06082 - 2.93390i) q^{55} +(1.23093 - 2.34197i) q^{56} +(-3.05713 + 3.10708i) q^{57} +(-4.11064 - 7.11984i) q^{58} +(-0.935231 + 5.30396i) q^{59} +(2.44148 + 2.04864i) q^{60} +(-5.13290 - 1.86822i) q^{61} +(0.276575 + 0.232074i) q^{62} +(-0.562436 - 2.58528i) q^{63} +(-0.500000 - 0.866025i) q^{64} -5.27236 q^{65} +(-2.06181 + 1.73006i) q^{66} +(1.75360 - 1.47144i) q^{67} +0.0661583 q^{68} +(3.82437 + 6.62400i) q^{69} +(6.23943 - 5.67220i) q^{70} +(-7.69202 - 6.45437i) q^{71} +(-0.939693 - 0.342020i) q^{72} +(-4.08387 - 3.42677i) q^{73} +(0.00907891 - 0.0514891i) q^{74} +(2.57888 + 4.46675i) q^{75} +(4.33909 - 0.415078i) q^{76} +(3.80237 + 6.02089i) q^{77} +(1.55451 - 0.565794i) q^{78} +(-10.4695 + 3.81058i) q^{79} +(-0.553438 - 3.13870i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-6.37827 + 5.35200i) q^{82} +(-0.339057 - 0.587265i) q^{83} +(-1.23093 + 2.34197i) q^{84} +(0.198139 + 0.0721166i) q^{85} +(-0.000956903 - 0.00542686i) q^{86} +(4.11064 + 7.11984i) q^{87} +2.69150 q^{88} +(9.84107 - 8.25764i) q^{89} +(-2.44148 - 2.04864i) q^{90} +(-0.930421 - 4.27675i) q^{91} +(1.32819 - 7.53254i) q^{92} +(-0.276575 - 0.232074i) q^{93} +(-4.41996 + 7.65560i) q^{94} +(13.4477 + 3.48675i) q^{95} +(0.500000 + 0.866025i) q^{96} +(-0.496199 + 0.180602i) q^{97} +(5.70216 + 4.06022i) q^{98} +(2.06181 - 1.73006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 6 q^{5} - 21 q^{8}+O(q^{10}) $ 42 * q + 6 * q^5 - 21 * q^8	$ 42 q + 6 q^{5} - 21 q^{8} - 3 q^{10} - 9 q^{11} + 21 q^{12} - 24 q^{13} - 3 q^{14} + 3 q^{15} - 21 q^{18} + 18 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{22} + 15 q^{23} - 18 q^{25} + 9 q^{26} + 21 q^{27} - 12 q^{28} + 9 q^{29} + 6 q^{30} - 6 q^{31} + 3 q^{33} + 9 q^{34} + 12 q^{35} - 15 q^{37} + 9 q^{38} - 9 q^{39} - 3 q^{40} + 3 q^{41} + 12 q^{42} + 6 q^{44} - 6 q^{45} - 18 q^{46} + 15 q^{47} - 30 q^{50} - 9 q^{51} + 21 q^{52} + 12 q^{53} - 15 q^{55} - 9 q^{57} - 18 q^{58} + 6 q^{59} + 3 q^{60} - 3 q^{61} + 6 q^{62} - 12 q^{63} - 21 q^{64} + 72 q^{65} - 6 q^{66} + 3 q^{67} - 36 q^{68} + 18 q^{69} - 6 q^{70} + 12 q^{71} + 9 q^{73} + 12 q^{74} + 30 q^{75} + 51 q^{77} - 21 q^{78} - 51 q^{79} + 6 q^{80} + 12 q^{82} + 24 q^{83} - 6 q^{85} + 9 q^{86} + 18 q^{87} + 18 q^{88} + 12 q^{89} - 3 q^{90} + 6 q^{92} - 6 q^{93} + 30 q^{94} - 21 q^{95} + 21 q^{96} - 27 q^{97} + 36 q^{98} + 6 q^{99}+O(q^{100}) $ 42 * q + 6 * q^5 - 21 * q^8 - 3 * q^10 - 9 * q^11 + 21 * q^12 - 24 * q^13 - 3 * q^14 + 3 * q^15 - 21 * q^18 + 18 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^22 + 15 * q^23 - 18 * q^25 + 9 * q^26 + 21 * q^27 - 12 * q^28 + 9 * q^29 + 6 * q^30 - 6 * q^31 + 3 * q^33 + 9 * q^34 + 12 * q^35 - 15 * q^37 + 9 * q^38 - 9 * q^39 - 3 * q^40 + 3 * q^41 + 12 * q^42 + 6 * q^44 - 6 * q^45 - 18 * q^46 + 15 * q^47 - 30 * q^50 - 9 * q^51 + 21 * q^52 + 12 * q^53 - 15 * q^55 - 9 * q^57 - 18 * q^58 + 6 * q^59 + 3 * q^60 - 3 * q^61 + 6 * q^62 - 12 * q^63 - 21 * q^64 + 72 * q^65 - 6 * q^66 + 3 * q^67 - 36 * q^68 + 18 * q^69 - 6 * q^70 + 12 * q^71 + 9 * q^73 + 12 * q^74 + 30 * q^75 + 51 * q^77 - 21 * q^78 - 51 * q^79 + 6 * q^80 + 12 * q^82 + 24 * q^83 - 6 * q^85 + 9 * q^86 + 18 * q^87 + 18 * q^88 + 12 * q^89 - 3 * q^90 + 6 * q^92 - 6 * q^93 + 30 * q^94 - 21 * q^95 + 21 * q^96 - 27 * q^97 + 36 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.553438	+	3.13870i	−0.247505	+	1.40367i	0.567097	+	0.823651i	$0.308066\pi$
$5$	−0.553438	+	3.13870i	−0.247505	+	1.40367i	−0.814602	+	0.580020i	$0.803045\pi$
$6$	−0.173648	−	0.984808i	−0.0708916	−	0.402046i
$7$	−2.64367	+	0.104962i	−0.999213	+	0.0396720i
$7$	−2.64367	+	0.104962i	−0.999213	+	0.0396720i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	−2.44148	+	2.04864i	−0.772063	+	0.647838i
$11$	−1.34575	−	2.33091i	−0.405759	−	0.702795i	0.588651	−	0.808388i	$-0.299659\pi$
$11$	−1.34575	−	2.33091i	−0.405759	−	0.702795i	−0.994409	+	0.105593i	$0.966326\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	0.287261	+	1.62914i	0.0796719	+	0.451842i	0.998380	+	0.0569037i	$0.0181228\pi$
$13$	0.287261	+	1.62914i	0.0796719	+	0.451842i	−0.918708	+	0.394938i	$0.870766\pi$
$14$	−2.09264	−	1.61891i	−0.559280	−	0.432672i
$15$	2.44148	−	2.04864i	0.630387	−	0.528957i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	0.0114883	−	0.0651533i	0.00278632	−	0.0158020i	−0.983383	−	0.181544i	$-0.941891\pi$
$17$	0.0114883	−	0.0651533i	0.00278632	−	0.0158020i	0.986169	+	0.165742i	$0.0530018\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	0.344703	−	4.34525i	0.0790803	−	0.996868i
$19$	0.344703	−	4.34525i	0.0790803	−	0.996868i
$20$	−3.18712			−0.712662
$21$	2.09264	+	1.61891i	0.456651	+	0.353275i
$22$	0.467374	−	2.65061i	0.0996445	−	0.565112i
$23$	−7.18746	−	2.61602i	−1.49869	−	0.545479i	−0.542969	−	0.839753i	$-0.682700\pi$
$23$	−7.18746	−	2.61602i	−1.49869	−	0.545479i	−0.955721	+	0.294274i	$0.904922\pi$
$24$	0.939693	−	0.342020i	0.191814	−	0.0698146i
$25$	−4.84670	−	1.76406i	−0.969341	−	0.352811i
$26$	−0.827135	+	1.43264i	−0.162215	+	0.280964i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	−0.562436	−	2.58528i	−0.106290	−	0.488572i
$29$	−7.72548	−	2.81185i	−1.43459	−	0.522147i	−0.496344	−	0.868126i	$-0.665324\pi$
$29$	−7.72548	−	2.81185i	−1.43459	−	0.522147i	−0.938242	+	0.345979i	$0.887547\pi$
$30$	3.18712			0.581886
$31$	0.361043			0.0648453			0.0324227	−	0.999474i	$-0.489678\pi$
$31$	0.361043			0.0648453			0.0324227	+	0.999474i	$0.489678\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−0.467374	+	2.65061i	−0.0813594	+	0.461412i
$34$	0.0506802	−	0.0425258i	0.00869159	−	0.00729311i
$35$	1.13366	−	8.35578i	0.191624	−	1.41238i
$36$	−0.939693	+	0.342020i	−0.156615	+	0.0570034i
$37$	−0.0261417	−	0.0452787i	−0.00429767	−	0.00744378i	0.863869	−	0.503717i	$-0.168035\pi$
$37$	−0.0261417	−	0.0452787i	−0.00429767	−	0.00744378i	−0.868166	+	0.496273i	$0.834701\pi$
$38$	3.05713	−	3.10708i	0.495932	−	0.504035i
$39$	0.827135	−	1.43264i	0.132448	−	0.229406i
$40$	−2.44148	−	2.04864i	−0.386032	−	0.323919i
$41$	−1.44584	+	8.19974i	−0.225802	+	1.28058i	0.635345	+	0.772228i	$0.280858\pi$
$41$	−1.44584	+	8.19974i	−0.225802	+	1.28058i	−0.861147	+	0.508356i	$0.830253\pi$
$42$	0.562436	+	2.58528i	0.0867857	+	0.398917i
$43$	−0.00422135	−	0.00354213i	−0.000643750	−	0.000540170i	0.642466	−	0.766314i	$-0.277912\pi$
$43$	−0.00422135	−	0.00354213i	−0.000643750	−	0.000540170i	−0.643109	+	0.765774i	$0.722356\pi$
$44$	2.06181	−	1.73006i	0.310829	−	0.260817i
$45$	−3.18712			−0.475108
$46$	−3.82437	−	6.62400i	−0.563873	−	0.976656i
$47$	1.53504	+	8.70563i	0.223908	+	1.26985i	0.864761	+	0.502183i	$0.167470\pi$
$47$	1.53504	+	8.70563i	0.223908	+	1.26985i	−0.640853	+	0.767663i	$0.721419\pi$
$48$	0.939693	+	0.342020i	0.135633	+	0.0493664i
$49$	6.97797	−	0.554970i	0.996852	−	0.0792814i
$50$	−2.57888	−	4.46675i	−0.364708	−	0.631693i
$51$	−0.0506802	+	0.0425258i	−0.00709665	+	0.00595480i
$52$	−1.55451	+	0.565794i	−0.215571	+	0.0784615i
$53$	1.99891	+	11.3364i	0.274572	+	1.55717i	0.740318	+	0.672256i	$0.234675\pi$
$53$	1.99891	+	11.3364i	0.274572	+	1.55717i	−0.465746	+	0.884918i	$0.654214\pi$
$54$	0.939693	−	0.342020i	0.127876	−	0.0465430i
$55$	8.06082	−	2.93390i	1.08692	−	0.395607i
$56$	1.23093	−	2.34197i	0.164491	−	0.312958i
$57$	−3.05713	+	3.10708i	−0.404927	+	0.411543i
$58$	−4.11064	−	7.11984i	−0.539754	−	0.934881i
$59$	−0.935231	+	5.30396i	−0.121757	+	0.690517i	0.861425	+	0.507885i	$0.169573\pi$
$59$	−0.935231	+	5.30396i	−0.121757	+	0.690517i	−0.983181	+	0.182631i	$0.941539\pi$
$60$	2.44148	+	2.04864i	0.315193	+	0.264479i
$61$	−5.13290	−	1.86822i	−0.657201	−	0.239201i	−0.00817335	−	0.999967i	$-0.502602\pi$
$61$	−5.13290	−	1.86822i	−0.657201	−	0.239201i	−0.649027	+	0.760765i	$0.724824\pi$
$62$	0.276575	+	0.232074i	0.0351251	+	0.0294735i
$63$	−0.562436	−	2.58528i	−0.0708602	−	0.325715i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−5.27236			−0.653956
$66$	−2.06181	+	1.73006i	−0.253791	+	0.212956i
$67$	1.75360	−	1.47144i	0.214236	−	0.179765i	−0.529354	−	0.848401i	$-0.677566\pi$
$67$	1.75360	−	1.47144i	0.214236	−	0.179765i	0.743590	+	0.668636i	$0.233121\pi$
$68$	0.0661583			0.00802288
$69$	3.82437	+	6.62400i	0.460400	+	0.797436i
$70$	6.23943	−	5.67220i	0.745754	−	0.677957i
$71$	−7.69202	−	6.45437i	−0.912875	−	0.765993i	0.0597888	−	0.998211i	$-0.480957\pi$
$71$	−7.69202	−	6.45437i	−0.912875	−	0.765993i	−0.972664	+	0.232218i	$0.925402\pi$
$72$	−0.939693	−	0.342020i	−0.110744	−	0.0403075i
$73$	−4.08387	−	3.42677i	−0.477980	−	0.401073i	0.371715	−	0.928347i	$-0.378770\pi$
$73$	−4.08387	−	3.42677i	−0.477980	−	0.401073i	−0.849695	+	0.527274i	$0.823214\pi$
$74$	0.00907891	−	0.0514891i	0.00105540	−	0.00598548i
$75$	2.57888	+	4.46675i	0.297783	+	0.515775i
$76$	4.33909	−	0.415078i	0.497728	−	0.0476127i
$77$	3.80237	+	6.02089i	0.433321	+	0.686144i
$78$	1.55451	−	0.565794i	0.176013	−	0.0640635i
$79$	−10.4695	+	3.81058i	−1.17791	+	0.428724i	−0.855463	−	0.517864i	$-0.826727\pi$
$79$	−10.4695	+	3.81058i	−1.17791	+	0.428724i	−0.322446	+	0.946588i	$0.604505\pi$
$80$	−0.553438	−	3.13870i	−0.0618763	−	0.350918i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−6.37827	+	5.35200i	−0.704362	+	0.591030i
$83$	−0.339057	−	0.587265i	−0.0372164	−	0.0644607i	0.846817	−	0.531884i	$-0.178516\pi$
$83$	−0.339057	−	0.587265i	−0.0372164	−	0.0644607i	−0.884034	+	0.467423i	$0.845182\pi$
$84$	−1.23093	+	2.34197i	−0.134306	+	0.255529i
$85$	0.198139	+	0.0721166i	0.0214912	+	0.00782214i
$86$	−0.000956903	−	0.00542686i	−0.000103185	−	0.000585194i
$87$	4.11064	+	7.11984i	0.440707	+	0.763327i
$88$	2.69150			0.286915
$89$	9.84107	−	8.25764i	1.04315	−	0.875308i	0.0507948	−	0.998709i	$-0.483825\pi$
$89$	9.84107	−	8.25764i	1.04315	−	0.875308i	0.992357	+	0.123401i	$0.0393801\pi$
$90$	−2.44148	−	2.04864i	−0.257354	−	0.215946i
$91$	−0.930421	−	4.27675i	−0.0975346	−	0.448325i
$92$	1.32819	−	7.53254i	0.138473	−	0.785321i
$93$	−0.276575	−	0.232074i	−0.0286795	−	0.0240650i
$94$	−4.41996	+	7.65560i	−0.455884	+	0.789615i
$95$	13.4477	+	3.48675i	1.37970	+	0.357733i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−0.496199	+	0.180602i	−0.0503813	+	0.0183373i	−0.367088	−	0.930186i	$-0.619645\pi$
$97$	−0.496199	+	0.180602i	−0.0503813	+	0.0183373i	0.316707	+	0.948524i	$0.397423\pi$
$98$	5.70216	+	4.06022i	0.576005	+	0.410144i
$99$	2.06181	−	1.73006i	0.207220	−	0.173878i
$100$	0.895634	−	5.07940i	0.0895634	−	0.507940i
$101$	7.20500	+	2.62240i	0.716924	+	0.260939i	0.674619	−	0.738166i	$-0.264308\pi$
$101$	7.20500	+	2.62240i	0.716924	+	0.260939i	0.0423046	+	0.999105i	$0.486530\pi$
$102$	−0.0661583			−0.00655065
$103$	0.273326			0.0269316			0.0134658	−	0.999909i	$-0.495714\pi$
$103$	0.273326			0.0269316			0.0134658	+	0.999909i	$0.495714\pi$
$104$	−1.55451	−	0.565794i	−0.152432	−	0.0554806i
$105$	−6.23943	+	5.67220i	−0.608906	+	0.553550i
$106$	−5.75564	+	9.96907i	−0.559037	+	0.968281i
$107$	−2.72982	+	4.72818i	−0.263901	+	0.457090i	−0.967275	−	0.253730i	$-0.918343\pi$
$107$	−2.72982	+	4.72818i	−0.263901	+	0.457090i	0.703374	+	0.710820i	$0.251676\pi$
$108$	0.939693	+	0.342020i	0.0904220	+	0.0329109i
$109$	−9.25599	+	3.36891i	−0.886563	+	0.322683i	−0.744856	−	0.667226i	$-0.767482\pi$
$109$	−9.25599	+	3.36891i	−0.886563	+	0.322683i	−0.141708	+	0.989909i	$0.545259\pi$
$110$	8.06082	+	2.93390i	0.768569	+	0.279736i
$111$	−0.00907891	+	0.0514891i	−0.000861732	+	0.00488713i
$112$	2.44834	−	1.00282i	0.231346	−	0.0947576i
$113$	2.49719			0.234915			0.117458	−	0.993078i	$-0.462526\pi$
$113$	2.49719			0.234915			0.117458	+	0.993078i	$0.462526\pi$
$114$	−4.33909	+	0.415078i	−0.406393	+	0.0388756i
$115$	12.1887	−	21.1115i	1.13661	−	1.96866i
$116$	1.42761	−	8.09639i	0.132550	−	0.751731i
$117$	−1.55451	+	0.565794i	−0.143714	+	0.0523076i
$118$	−4.12575	+	3.46191i	−0.379806	+	0.318695i
$119$	−0.0235326	+	0.173449i	−0.00215723	+	0.0159001i
$120$	0.553438	+	3.13870i	0.0505218	+	0.286523i
$121$	1.87791	−	3.25264i	0.170720	−	0.295695i
$122$	−2.73116	−	4.73051i	−0.247268	−	0.428280i
$123$	6.37827	−	5.35200i	0.575109	−	0.482574i
$124$	0.0626945	+	0.355558i	0.00563013	+	0.0319301i
$125$	0.251390	−	0.435420i	0.0224850	−	0.0389451i
$126$	1.23093	−	2.34197i	0.109660	−	0.208639i
$127$	2.17413	+	12.3301i	0.192923	+	1.09412i	0.915346	+	0.402667i	$0.131917\pi$
$127$	2.17413	+	12.3301i	0.192923	+	1.09412i	−0.722424	+	0.691450i	$0.756972\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	0.000956903		0.00542686i	8.42506e−5		0.000477809i
$130$	−4.03886	−	3.38901i	−0.354232	−	0.297236i
$131$	10.2458	+	8.59724i	0.895179	+	0.751144i	0.969242	−	0.246109i	$-0.0791522\pi$
$131$	10.2458	+	8.59724i	0.895179	+	0.751144i	−0.0740632	+	0.997254i	$0.523597\pi$
$132$	−2.69150			−0.234265
$133$	−0.455194	+	11.5236i	−0.0394703	+	0.999221i
$134$	2.28916			0.197753
$135$	2.44148	+	2.04864i	0.210129	+	0.176319i
$136$	0.0506802	+	0.0425258i	0.00434579	+	0.00364655i
$137$	2.26972	+	12.8722i	0.193915	+	1.09975i	0.913955	+	0.405815i	$0.133012\pi$
$137$	2.26972	+	12.8722i	0.193915	+	1.09975i	−0.720040	+	0.693933i	$0.755877\pi$
$138$	−1.32819	+	7.53254i	−0.113063	+	0.641212i
$139$	4.00450	+	22.7107i	0.339657	+	1.92629i	0.375244	+	0.926926i	$0.377559\pi$
$139$	4.00450	+	22.7107i	0.339657	+	1.92629i	−0.0355862	+	0.999367i	$0.511330\pi$
$140$	8.42570	−	0.334527i	0.712101	−	0.0282727i
$141$	4.41996	−	7.65560i	0.372228	−	0.644718i
$142$	−1.74364	−	9.88867i	−0.146323	−	0.829839i
$143$	3.41079	−	2.86199i	0.285224	−	0.239332i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	13.1011	−	22.6918i	1.08799	−	1.88445i
$146$	−0.925737	−	5.25012i	−0.0766145	−	0.434503i
$147$	−5.70216	−	4.06022i	−0.470306	−	0.334881i
$148$	0.0400514	−	0.0336071i	0.00329220	−	0.00276249i
$149$	−16.6685	+	6.06684i	−1.36554	+	0.497015i	−0.917762	−	0.397131i	$-0.870006\pi$
$149$	−16.6685	+	6.06684i	−1.36554	+	0.497015i	−0.447776	+	0.894146i	$0.647784\pi$
$150$	−0.895634	+	5.07940i	−0.0731282	+	0.414731i
$151$	8.08043	−	13.9957i	0.657576	−	1.13896i	−0.323665	−	0.946172i	$-0.604915\pi$
$151$	8.08043	−	13.9957i	0.657576	−	1.13896i	0.981241	−	0.192784i	$-0.0617517\pi$
$152$	3.59074	+	2.47115i	0.291248	+	0.200436i
$153$	0.0661583			0.00534859
$154$	−0.957368	+	7.05639i	−0.0771469	+	0.568620i
$155$	−0.199815	+	1.13321i	−0.0160495	+	0.0910215i
$156$	1.55451	+	0.565794i	0.124460	+	0.0452998i
$157$	7.51016	−	2.73348i	0.599376	−	0.218155i	−0.0244721	−	0.999701i	$-0.507791\pi$
$157$	7.51016	−	2.73348i	0.599376	−	0.218155i	0.623848	+	0.781545i	$0.285568\pi$
$158$	−10.4695	−	3.81058i	−0.832908	−	0.303154i
$159$	5.75564	−	9.96907i	0.456452	−	0.790598i
$160$	1.59356	−	2.76013i	0.125982	−	0.218207i
$161$	19.2759	+	6.16149i	1.51915	+	0.485593i
$162$	−0.939693	−	0.342020i	−0.0738292	−	0.0268716i
$163$	0.295615			0.0231544			0.0115772	−	0.999933i	$-0.496315\pi$
$163$	0.295615			0.0231544			0.0115772	+	0.999933i	$0.496315\pi$
$164$	−8.32624			−0.650170
$165$	−8.06082	−	2.93390i	−0.627534	−	0.228404i
$166$	0.117753	−	0.667813i	0.00913944	−	0.0518323i
$167$	−3.30835	+	2.77604i	−0.256008	+	0.214816i	−0.761754	−	0.647866i	$-0.775662\pi$
$167$	−3.30835	+	2.77604i	−0.256008	+	0.214816i	0.505746	+	0.862682i	$0.331217\pi$
$168$	−2.44834	+	1.00282i	−0.188893	+	0.0773692i
$169$	9.64443	−	3.51029i	0.741879	−	0.270022i
$170$	0.105427	+	0.182606i	0.00808591	+	0.0140052i
$171$	4.33909	−	0.415078i	0.331819	−	0.0317418i
$172$	0.00275529	−	0.00477230i	0.000210089	−	0.000363885i
$173$	14.8475	+	12.4585i	1.12883	+	0.947202i	0.999017	−	0.0443365i	$-0.0141174\pi$
$173$	14.8475	+	12.4585i	1.12883	+	0.947202i	0.129814	+	0.991538i	$0.458562\pi$
$174$	−1.42761	+	8.09639i	−0.108227	+	0.613785i
$175$	12.9982	+	4.15486i	0.982574	+	0.314078i
$176$	2.06181	+	1.73006i	0.155415	+	0.130408i
$177$	4.12575	−	3.46191i	0.310110	−	0.260213i
$178$	12.8466			0.962894
$179$	−11.6463	−	20.1719i	−0.870482	−	1.50772i	−0.861499	−	0.507759i	$-0.830474\pi$
$179$	−11.6463	−	20.1719i	−0.870482	−	1.50772i	−0.00898281	−	0.999960i	$-0.502859\pi$
$180$	−0.553438	−	3.13870i	−0.0412508	−	0.233945i
$181$	−11.9212	−	4.33895i	−0.886093	−	0.322511i	−0.141427	−	0.989949i	$-0.545169\pi$
$181$	−11.9212	−	4.33895i	−0.886093	−	0.322511i	−0.744666	+	0.667437i	$0.767391\pi$
$182$	2.03630	−	3.87424i	0.150940	−	0.287178i
$183$	2.73116	+	4.73051i	0.201893	+	0.349689i
$184$	5.85927	−	4.91652i	0.431951	−	0.362450i
$185$	0.156584	−	0.0569920i	0.0115123	−	0.00419014i
$186$	−0.0626945	−	0.355558i	−0.00459699	−	0.0260708i
$187$	−0.167327	+	0.0609019i	−0.0122361	+	0.00445359i
$188$	−8.30681	+	3.02343i	−0.605837	+	0.220506i
$189$	−1.23093	+	2.34197i	−0.0895373	+	0.170353i
$190$	8.06028	+	11.3150i	0.584754	+	0.820876i
$191$	−5.05012	−	8.74706i	−0.365414	−	0.632915i	0.623429	−	0.781880i	$-0.285739\pi$
$191$	−5.05012	−	8.74706i	−0.365414	−	0.632915i	−0.988842	+	0.148965i	$0.952406\pi$
$192$	−0.173648	+	0.984808i	−0.0125320	+	0.0710724i
$193$	−12.9192	−	10.8405i	−0.929942	−	0.780314i	0.0458651	−	0.998948i	$-0.485396\pi$
$193$	−12.9192	−	10.8405i	−0.929942	−	0.780314i	−0.975807	+	0.218634i	$0.929840\pi$
$194$	−0.496199	−	0.180602i	−0.0356250	−	0.0129664i
$195$	4.03886	+	3.38901i	0.289229	+	0.242692i
$196$	1.75825	+	6.77559i	0.125589	+	0.483970i
$197$	5.61999	+	9.73412i	0.400408	+	0.693527i	0.993775	−	0.111405i	$-0.0355351\pi$
$197$	5.61999	+	9.73412i	0.400408	+	0.693527i	−0.593367	+	0.804932i	$0.702202\pi$
$198$	2.69150			0.191277
$199$	−5.24926	+	4.40465i	−0.372110	+	0.312238i	−0.809596	−	0.586988i	$-0.800314\pi$
$199$	−5.24926	+	4.40465i	−0.372110	+	0.312238i	0.437485	+	0.899225i	$0.355869\pi$
$200$	3.95107	−	3.31534i	0.279383	−	0.234430i
$201$	−2.28916			−0.161465
$202$	3.83370	+	6.64016i	0.269738	+	0.467200i
$203$	20.7187	+	6.62270i	1.45417	+	0.464823i
$204$	−0.0506802	−	0.0425258i	−0.00354833	−	0.00297740i
$205$	−24.9364	−	9.07610i	−1.74163	−	0.633902i
$206$	0.209380	+	0.175690i	0.0145882	+	0.0122409i
$207$	1.32819	−	7.53254i	0.0923156	−	0.523548i
$208$	−0.827135	−	1.43264i	−0.0573515	−	0.0993357i
$209$	−10.5923	+	5.04415i	−0.732681	+	0.348911i
$210$	−8.42570	+	0.334527i	−0.581428	+	0.0230846i
$211$	24.4762	−	8.90859i	1.68501	−	0.613293i	0.691025	−	0.722831i	$-0.257159\pi$
$211$	24.4762	−	8.90859i	1.68501	−	0.613293i	0.993983	+	0.109538i	$0.0349372\pi$
$212$	−10.8171	+	3.93709i	−0.742919	+	0.270401i
$213$	1.74364	+	9.88867i	0.119472	+	0.677561i
$214$	−5.13038	+	1.86730i	−0.350705	+	0.127646i
$215$	0.0134540	−	0.0112892i	0.000917553	−	0.000769918i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	−0.954479	+	0.0378959i	−0.0647943	+	0.00257254i
$218$	−9.25599	−	3.36891i	−0.626895	−	0.228171i
$219$	0.925737	+	5.25012i	0.0625555	+	0.354770i
$220$	4.28907	+	7.42889i	0.289169	+	0.500856i
$221$	0.109444			0.00736199
$222$	−0.0400514	+	0.0336071i	−0.00268807	+	0.00225556i
$223$	0.671876	+	0.563771i	0.0449921	+	0.0377529i	0.665006	−	0.746838i	$-0.268429\pi$
$223$	0.671876	+	0.563771i	0.0449921	+	0.0377529i	−0.620014	+	0.784591i	$0.712873\pi$
$224$	2.52013	+	0.805556i	0.168384	+	0.0538235i
$225$	0.895634	−	5.07940i	0.0597090	−	0.338626i
$226$	1.91295	+	1.60516i	0.127248	+	0.106774i
$227$	−12.6540	+	21.9174i	−0.839878	+	1.45471i	0.0501188	+	0.998743i	$0.484040\pi$
$227$	−12.6540	+	21.9174i	−0.839878	+	1.45471i	−0.889996	+	0.455967i	$0.849293\pi$
$228$	−3.59074	−	2.47115i	−0.237803	−	0.163656i
$229$	0.407357	+	0.705562i	0.0269189	+	0.0466249i	0.879171	−	0.476506i	$-0.158097\pi$
$229$	0.407357	+	0.705562i	0.0269189	+	0.0466249i	−0.852252	+	0.523131i	$0.824764\pi$
$230$	22.9073	−	8.33759i	1.51046	−	0.549764i
$231$	0.957368	−	7.05639i	0.0629902	−	0.464276i
$232$	6.29787	−	5.28454i	0.413475	−	0.346947i
$233$	0.0484970	−	0.275040i	0.00317715	−	0.0180185i	−0.983178	−	0.182650i	$-0.941532\pi$
$233$	0.0484970	−	0.275040i	0.00317715	−	0.0180185i	0.986355	+	0.164632i	$0.0526435\pi$
$234$	−1.55451	−	0.565794i	−0.101621	−	0.0369871i
$235$	−28.1739			−1.83786
$236$	−5.38578			−0.350584
$237$	10.4695	+	3.81058i	0.680066	+	0.247524i
$238$	−0.129518	+	0.117744i	−0.00839541	+	0.00763218i
$239$	−9.01884	+	15.6211i	−0.583380	+	1.01044i	0.411695	+	0.911322i	$0.364937\pi$
$239$	−9.01884	+	15.6211i	−0.583380	+	1.01044i	−0.995075	+	0.0991225i	$0.968396\pi$
$240$	−1.59356	+	2.76013i	−0.102864	+	0.178166i
$241$	−20.3656	−	7.41247i	−1.31186	−	0.477479i	−0.411020	−	0.911626i	$-0.634828\pi$
$241$	−20.3656	−	7.41247i	−1.31186	−	0.477479i	−0.900842	+	0.434147i	$0.857050\pi$
$242$	3.52933	−	1.28457i	0.226874	−	0.0825752i
$243$	0.939693	+	0.342020i	0.0602813	+	0.0219406i
$244$	0.948522	−	5.37933i	0.0607229	−	0.344377i
$245$	−2.11999	+	22.2089i	−0.135441	+	1.41888i
$246$	8.32624			0.530862
$247$	7.17803	−	0.686651i	0.456727	−	0.0436906i
$248$	−0.180522	+	0.312673i	−0.0114631	+	0.0198547i
$249$	−0.117753	+	0.667813i	−0.00746232	+	0.0423209i
$250$	0.472458	−	0.171961i	0.0298809	−	0.0108757i
$251$	−2.08638	+	1.75068i	−0.131691	+	0.110502i	−0.706254	−	0.707958i	$-0.749616\pi$
$251$	−2.08638	+	1.75068i	−0.131691	+	0.110502i	0.574563	+	0.818460i	$0.305172\pi$
$252$	2.44834	−	1.00282i	0.154231	−	0.0631717i
$253$	3.57482	+	20.2738i	0.224747	+	1.27460i
$254$	−6.26015	+	10.8429i	−0.392797	+	0.680344i
$255$	−0.105427	−	0.182606i	−0.00660212	−	0.0114352i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−2.40987	−	13.6671i	−0.150324	−	0.852528i	−0.962937	−	0.269725i	$-0.913067\pi$
$257$	−2.40987	−	13.6671i	−0.150324	−	0.852528i	0.812614	−	0.582803i	$-0.198044\pi$
$258$	−0.00275529	+	0.00477230i	−0.000171537	+	0.000297111i
$259$	0.0738625	+	0.116958i	0.00458959	+	0.00726742i
$260$	−0.915536	−	5.19226i	−0.0567791	−	0.322011i
$261$	1.42761	−	8.09639i	0.0883669	−	0.501154i
$262$	2.32253	+	13.1717i	0.143487	+	0.813752i
$263$	−7.68938	−	6.45215i	−0.474147	−	0.397857i	0.374157	−	0.927365i	$-0.377932\pi$
$263$	−7.68938	−	6.45215i	−0.474147	−	0.397857i	−0.848305	+	0.529508i	$0.822376\pi$
$264$	−2.06181	−	1.73006i	−0.126896	−	0.106478i
$265$	−36.6879			−2.25372
$266$	−7.75591	+	8.53498i	−0.475545	+	0.523313i
$267$	−12.8466			−0.786200
$268$	1.75360	+	1.47144i	0.107118	+	0.0898826i
$269$	9.32163	+	7.82177i	0.568350	+	0.476902i	0.881098	−	0.472934i	$-0.156805\pi$
$269$	9.32163	+	7.82177i	0.568350	+	0.476902i	−0.312748	+	0.949836i	$0.601250\pi$
$270$	0.553438	+	3.13870i	0.0336812	+	0.191015i
$271$	0.274922	−	1.55916i	0.0167003	−	0.0947123i	−0.975318	−	0.220803i	$-0.929132\pi$
$271$	0.274922	−	1.55916i	0.0167003	−	0.0947123i	0.992019	+	0.126091i	$0.0402432\pi$
$272$	0.0114883	+	0.0651533i	0.000696579	+	0.00395050i
$273$	−2.03630	+	3.87424i	−0.123242	+	0.234480i
$274$	−6.53540	+	11.3196i	−0.394818	+	0.683844i
$275$	2.41060	+	13.6712i	0.145365	+	0.824404i
$276$	−5.85927	+	4.91652i	−0.352687	+	0.295939i
$277$	−4.87865	−	8.45007i	−0.293130	−	0.507715i	0.681418	−	0.731894i	$-0.261363\pi$
$277$	−4.87865	−	8.45007i	−0.293130	−	0.507715i	−0.974548	+	0.224179i	$0.928030\pi$
$278$	−11.5305	+	19.9714i	−0.691554	+	1.19781i
$279$	0.0626945	+	0.355558i	0.00375342	+	0.0212867i
$280$	6.66949	+	5.15967i	0.398578	+	0.308349i
$281$	−11.0488	+	9.27103i	−0.659115	+	0.553063i	−0.909821	−	0.415000i	$-0.863782\pi$
$281$	−11.0488	+	9.27103i	−0.659115	+	0.553063i	0.250706	+	0.968063i	$0.419337\pi$
$282$	8.30681	−	3.02343i	0.494664	−	0.180043i
$283$	1.94760	−	11.0454i	0.115773	−	0.656580i	−0.870592	−	0.492006i	$-0.836264\pi$
$283$	1.94760	−	11.0454i	0.115773	−	0.656580i	0.986365	−	0.164574i	$-0.0526251\pi$
$284$	5.02061	−	8.69595i	0.297918	−	0.516010i
$285$	−8.06028	−	11.3150i	−0.477450	−	0.670243i
$286$	4.45247			0.263280
$287$	2.96165	−	21.8292i	0.174821	−	1.28853i
$288$	0.173648	−	0.984808i	0.0102323	−	0.0580304i
$289$	15.9707	+	5.81285i	0.939451	+	0.341932i
$290$	24.6221	−	8.96170i	1.44586	−	0.526249i
$291$	0.496199	+	0.180602i	0.0290877	+	0.0105871i
$292$	2.66555	−	4.61687i	0.155990	−	0.270182i
$293$	−9.88218	+	17.1164i	−0.577323	+	0.999953i	0.418462	+	0.908234i	$0.362569\pi$
$293$	−9.88218	+	17.1164i	−0.577323	+	0.999953i	−0.995785	+	0.0917186i	$0.970764\pi$
$294$	−1.75825	−	6.77559i	−0.102543	−	0.395160i
$295$	−16.1300	−	5.87083i	−0.939123	−	0.341813i
$296$	0.0522834			0.00303891
$297$	−2.69150			−0.156177
$298$	−16.6685	−	6.06684i	−0.965581	−	0.351443i
$299$	2.19718	−	12.4609i	0.127066	−	0.720630i
$300$	−3.95107	+	3.31534i	−0.228115	+	0.191411i
$301$	0.0115316	+	0.00892115i	0.000664673	+	0.000514206i
$302$	15.1862	−	5.52734i	0.873870	−	0.318063i
$303$	−3.83370	−	6.64016i	−0.220240	−	0.381467i
$304$	1.16225	+	4.20109i	0.0666595	+	0.240949i
$305$	8.70454	−	15.0767i	0.498421	−	0.863290i
$306$	0.0506802	+	0.0425258i	0.00289720	+	0.00243104i
$307$	−2.46983	+	14.0071i	−0.140961	+	0.799428i	0.829561	+	0.558416i	$0.188591\pi$
$307$	−2.46983	+	14.0071i	−0.140961	+	0.799428i	−0.970522	+	0.241013i	$0.922521\pi$
$308$	−5.26915	+	4.79012i	−0.300237	+	0.272943i
$309$	−0.209380	−	0.175690i	−0.0119112	−	0.00999468i
$310$	−0.881479	+	0.739649i	−0.0500647	+	0.0420092i
$311$	−29.2379			−1.65793			−0.828964	−	0.559303i	$-0.811069\pi$
$311$	−29.2379			−1.65793			−0.828964	+	0.559303i	$0.811069\pi$
$312$	0.827135	+	1.43264i	0.0468273	+	0.0811073i
$313$	−3.98972	−	22.6268i	−0.225512	−	1.27894i	−0.861704	−	0.507412i	$-0.830602\pi$
$313$	−3.98972	−	22.6268i	−0.225512	−	1.27894i	0.636192	−	0.771531i	$-0.280509\pi$
$314$	7.51016	+	2.73348i	0.423823	+	0.154259i
$315$	8.42570	−	0.334527i	0.474734	−	0.0188485i
$316$	−5.57070	−	9.64873i	−0.313376	−	0.542784i
$317$	11.3201	−	9.49871i	0.635802	−	0.533501i	−0.266924	−	0.963718i	$-0.586007\pi$
$317$	11.3201	−	9.49871i	0.635802	−	0.533501i	0.902726	+	0.430217i	$0.141563\pi$
$318$	10.8171	−	3.93709i	0.606591	−	0.220781i
$319$	3.84242	+	21.7914i	0.215134	+	1.22009i
$320$	2.99492	−	1.09006i	0.167421	−	0.0609362i
$321$	5.13038	−	1.86730i	0.286350	−	0.104223i
$322$	10.8056	+	17.1103i	0.602175	+	0.953517i
$323$	−0.279147	−	0.0723779i	−0.0155322	−	0.00402722i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	1.48162	−	8.40269i	0.0821856	−	0.466098i
$326$	0.226455	+	0.190018i	0.0125422	+	0.0105241i
$327$	9.25599	+	3.36891i	0.511858	+	0.186301i
$328$	−6.37827	−	5.35200i	−0.352181	−	0.295515i
$329$	−4.97189	−	22.8537i	−0.274109	−	1.25996i
$330$	−4.28907	−	7.42889i	−0.236106	−	0.408947i
$331$	3.55665			0.195491			0.0977457	−	0.995211i	$-0.468837\pi$
$331$	3.55665			0.195491			0.0977457	+	0.995211i	$0.468837\pi$
$332$	0.519466	−	0.435884i	0.0285094	−	0.0239222i
$333$	0.0400514	−	0.0336071i	0.00219480	−	0.00184166i
$334$	−4.31875			−0.236311
$335$	3.64791	+	6.31837i	0.199307	+	0.345209i
$336$	−2.52013	−	0.805556i	−0.137485	−	0.0439467i
$337$	9.59349	+	8.04990i	0.522591	+	0.438506i	0.865534	−	0.500850i	$-0.166979\pi$
$337$	9.59349	+	8.04990i	0.522591	+	0.438506i	−0.342943	+	0.939356i	$0.611424\pi$
$338$	9.64443	+	3.51029i	0.524588	+	0.190934i
$339$	−1.91295	−	1.60516i	−0.103897	−	0.0871803i
$340$	−0.0366146	+	0.207651i	−0.00198570	+	0.0112615i
$341$	−0.485874	−	0.841559i	−0.0263116	−	0.0455729i
$342$	3.59074	+	2.47115i	0.194165	+	0.133624i
$343$	−18.3892	+	2.19958i	−0.992922	+	0.118766i
$344$	0.00517825	−	0.00188473i	0.000279193	−	0.000101618i
$345$	−22.9073	+	8.33759i	−1.23329	+	0.448881i
$346$	3.36564	+	19.0875i	0.180938	+	1.02615i
$347$	26.7259	−	9.72743i	1.43472	−	0.522196i	0.496441	−	0.868071i	$-0.334640\pi$
$347$	26.7259	−	9.72743i	1.43472	−	0.522196i	0.938281	+	0.345875i	$0.112418\pi$
$348$	−6.29787	+	5.28454i	−0.337601	+	0.283281i
$349$	−17.1705	−	29.7401i	−0.919113	−	1.59195i	−0.800765	−	0.598979i	$-0.795573\pi$
$349$	−17.1705	−	29.7401i	−0.919113	−	1.59195i	−0.118349	−	0.992972i	$-0.537760\pi$
$350$	7.28653	+	11.5379i	0.389482	+	0.616727i
$351$	1.55451	+	0.565794i	0.0829734	+	0.0301998i
$352$	0.467374	+	2.65061i	0.0249111	+	0.141278i
$353$	−4.22096	−	7.31092i	−0.224659	−	0.389121i	0.731558	−	0.681779i	$-0.238793\pi$
$353$	−4.22096	−	7.31092i	−0.224659	−	0.389121i	−0.956217	+	0.292658i	$0.905460\pi$
$354$	5.38578			0.286251
$355$	24.5154	−	20.5709i	1.30114	−	1.09179i
$356$	9.84107	+	8.25764i	0.521576	+	0.437654i
$357$	0.129518	−	0.117744i	0.00685483	−	0.00623165i
$358$	4.04470	−	22.9386i	0.213769	−	1.21234i
$359$	17.7690	+	14.9099i	0.937811	+	0.786917i	0.977203	−	0.212307i	$-0.0680977\pi$
$359$	17.7690	+	14.9099i	0.937811	+	0.786917i	−0.0393922	+	0.999224i	$0.512542\pi$
$360$	1.59356	−	2.76013i	0.0839881	−	0.145472i
$361$	−18.7624	−	2.99564i	−0.987493	−	0.157665i
$362$	−6.34312	−	10.9866i	−0.333387	−	0.577443i
$363$	−3.52933	+	1.28457i	−0.185242	+	0.0674224i
$364$	4.05021	−	1.65894i	0.212289	−	0.0869518i
$365$	13.0158	−	10.9215i	0.681277	−	0.571659i
$366$	−0.948522	+	5.37933i	−0.0495800	+	0.281182i
$367$	6.02362	+	2.19242i	0.314430	+	0.114443i	0.494415	−	0.869226i	$-0.335382\pi$
$367$	6.02362	+	2.19242i	0.314430	+	0.114443i	−0.179984	+	0.983669i	$0.557605\pi$
$368$	7.64874			0.398718
$369$	−8.32624			−0.433447
$370$	0.156584	+	0.0569920i	0.00814043	+	0.00296287i
$371$	−6.47436	−	29.7599i	−0.336132	−	1.54506i
$372$	0.180522	−	0.312673i	0.00935961	−	0.0162113i
$373$	9.73437	−	16.8604i	0.504026	−	0.872999i	−0.495963	−	0.868344i	$-0.665185\pi$
$373$	9.73437	−	16.8604i	0.504026	−	0.872999i	0.999989	−	0.00465564i	$-0.00148194\pi$
$374$	−0.167327	−	0.0609019i	−0.00865225	−	0.00314916i
$375$	−0.472458	+	0.171961i	−0.0243976	+	0.00888001i
$376$	−8.30681	−	3.02343i	−0.428391	−	0.155922i
$377$	2.36165	−	13.3936i	0.121631	−	0.689806i
$378$	−2.44834	+	1.00282i	−0.125929	+	0.0515795i
$379$	33.7731			1.73481			0.867405	−	0.497603i	$-0.165786\pi$
$379$	33.7731			1.73481			0.867405	+	0.497603i	$0.165786\pi$
$380$	−1.09861	+	13.8488i	−0.0563576	+	0.710430i
$381$	6.26015	−	10.8429i	0.320717	−	0.555498i
$382$	1.75389	−	9.94679i	0.0897367	−	0.508922i
$383$	23.2319	−	8.45574i	1.18710	−	0.432068i	0.328394	−	0.944541i	$-0.393493\pi$
$383$	23.2319	−	8.45574i	1.18710	−	0.432068i	0.858703	+	0.512473i	$0.171270\pi$
$384$	−0.766044	+	0.642788i	−0.0390920	+	0.0328021i
$385$	−21.0022	+	8.60233i	−1.07037	+	0.438415i
$386$	−2.92854	−	16.6086i	−0.149059	−	0.845353i
$387$	0.00275529	−	0.00477230i	0.000140059	−	0.000242590i
$388$	−0.264022	−	0.457299i	−0.0134037	−	0.0232158i
$389$	−26.9831	+	22.6415i	−1.36810	+	1.14797i	−0.394712	+	0.918805i	$0.629156\pi$
$389$	−26.9831	+	22.6415i	−1.36810	+	1.14797i	−0.973387	+	0.229167i	$0.926400\pi$
$390$	0.915536	+	5.19226i	0.0463600	+	0.262920i
$391$	−0.253014	+	0.438233i	−0.0127955	+	0.0221624i
$392$	−3.00836	+	6.32058i	−0.151945	+	0.319238i
$393$	−2.32253	−	13.1717i	−0.117156	−	0.664426i
$394$	−1.95180	+	11.0692i	−0.0983305	+	0.557660i
$395$	−6.16607	−	34.9695i	−0.310249	−	1.75951i
$396$	2.06181	+	1.73006i	0.103610	+	0.0869389i
$397$	28.7103	+	24.0908i	1.44093	+	1.20908i	0.938882	+	0.344239i	$0.111863\pi$
$397$	28.7103	+	24.0908i	1.44093	+	1.20908i	0.502044	+	0.864842i	$0.332581\pi$
$398$	−6.85242			−0.343481
$399$	7.75591	−	8.53498i	0.388281	−	0.427283i
$400$	5.15775			0.257888
$401$	−13.1590	−	11.0417i	−0.657127	−	0.551395i	0.252097	−	0.967702i	$-0.418880\pi$
$401$	−13.1590	−	11.0417i	−0.657127	−	0.551395i	−0.909224	+	0.416307i	$0.863324\pi$
$402$	−1.75360	−	1.47144i	−0.0874614	−	0.0733888i
$403$	0.103714	+	0.588189i	0.00516635	+	0.0292998i
$404$	−1.33143	+	7.55091i	−0.0662411	+	0.375672i
$405$	−0.553438	−	3.13870i	−0.0275006	−	0.155963i
$406$	11.6145	+	18.3910i	0.576417	+	0.912732i
$407$	−0.0703603	+	0.121868i	−0.00348763	+	0.00604076i
$408$	−0.0114883	−	0.0651533i	−0.000568754	−	0.00322557i
$409$	−19.8504	+	16.6564i	−0.981537	+	0.823608i	−0.984321	−	0.176389i	$-0.943558\pi$
$409$	−19.8504	+	16.6564i	−0.981537	+	0.823608i	0.00278333	+	0.999996i	$0.499114\pi$
$410$	−13.2684	−	22.9815i	−0.655278	−	1.13498i
$411$	6.53540	−	11.3196i	0.322367	−	0.558356i
$412$	0.0474625	+	0.269173i	0.00233831	+	0.0132612i
$413$	1.91573	−	14.1201i	0.0942667	−	0.694803i
$414$	5.85927	−	4.91652i	0.287968	−	0.241634i
$415$	2.03090	−	0.739186i	0.0996928	−	0.0362852i
$416$	0.287261	−	1.62914i	0.0140841	−	0.0798751i
$417$	11.5305	−	19.9714i	0.564651	−	0.978005i
$418$	−11.3565	−	2.94453i	−0.555462	−	0.144022i
$419$	−10.4652			−0.511256			−0.255628	−	0.966775i	$-0.582282\pi$
$419$	−10.4652			−0.511256			−0.255628	+	0.966775i	$0.582282\pi$
$420$	−6.66949	−	5.15967i	−0.325438	−	0.251766i
$421$	−0.505230	+	2.86530i	−0.0246234	+	0.139646i	−0.994641	−	0.103388i	$-0.967032\pi$
$421$	−0.505230	+	2.86530i	−0.0246234	+	0.139646i	0.970018	+	0.243034i	$0.0781428\pi$
$422$	24.4762	+	8.90859i	1.19148	+	0.433663i
$423$	−8.30681	+	3.02343i	−0.403891	+	0.147004i
$424$	−10.8171	−	3.93709i	−0.525323	−	0.191202i
$425$	−0.170614	+	0.295513i	−0.00827601	+	0.0143345i
$426$	−5.02061	+	8.69595i	−0.243249	+	0.421320i
$427$	13.7658	+	4.40020i	0.666173	+	0.212941i
$428$	−5.13038	−	1.86730i	−0.247986	−	0.0902595i
$429$	−4.45247			−0.214967
$430$	0.0175629			0.000846959
$431$	−19.5055	−	7.09943i	−0.939548	−	0.341967i	−0.173560	−	0.984823i	$-0.555527\pi$
$431$	−19.5055	−	7.09943i	−0.939548	−	0.341967i	−0.765987	+	0.642856i	$0.777749\pi$
$432$	−0.173648	+	0.984808i	−0.00835465	+	0.0473816i
$433$	−5.86533	+	4.92160i	−0.281870	+	0.236517i	−0.772750	−	0.634710i	$-0.781120\pi$
$433$	−5.86533	+	4.92160i	−0.281870	+	0.236517i	0.490881	+	0.871227i	$0.336675\pi$
$434$	−0.755532	−	0.584497i	−0.0362667	−	0.0280568i
$435$	−24.6221	+	8.96170i	−1.18054	+	0.429680i
$436$	−4.92501	−	8.53037i	−0.235865	−	0.408531i
$437$	−13.8448	+	30.3296i	−0.662287	+	1.45086i
$438$	−2.66555	+	4.61687i	−0.127365	+	0.220603i
$439$	7.91612	+	6.64242i	0.377816	+	0.317025i	0.811844	−	0.583874i	$-0.198464\pi$
$439$	7.91612	+	6.64242i	0.377816	+	0.317025i	−0.434028	+	0.900899i	$0.642908\pi$
$440$	−1.48958	+	8.44782i	−0.0710129	+	0.402734i
$441$	1.75825	+	6.77559i	0.0837262	+	0.322647i
$442$	0.0838388	+	0.0703491i	0.00398781	+	0.00334617i
$443$	−15.9399	+	13.3752i	−0.757327	+	0.635473i	−0.937429	−	0.348175i	$-0.886801\pi$
$443$	−15.9399	+	13.3752i	−0.757327	+	0.635473i	0.180103	+	0.983648i	$0.442357\pi$
$444$	−0.0522834			−0.00248126
$445$	20.4719	+	35.4583i	0.970459	+	1.68088i
$446$	0.152302	+	0.863747i	0.00721170	+	0.0408996i
$447$	16.6685	+	6.06684i	0.788394	+	0.286952i
$448$	1.41273	+	2.23700i	0.0667454	+	0.105688i
$449$	−14.5336	−	25.1729i	−0.685881	−	1.18798i	−0.973159	−	0.230134i	$-0.926084\pi$
$449$	−14.5336	−	25.1729i	−0.685881	−	1.18798i	0.287278	−	0.957847i	$-0.407250\pi$
$450$	3.95107	−	3.31534i	0.186255	−	0.156287i
$451$	21.0586	−	7.66469i	0.991610	−	0.360916i
$452$	0.433632	+	2.45925i	0.0203963	+	0.115673i
$453$	−15.1862	+	5.52734i	−0.713512	+	0.259697i
$454$	−23.7818	+	8.65587i	−1.11614	+	0.406240i
$455$	13.9384	−	0.553398i	0.653441	−	0.0259437i
$456$	−1.16225	−	4.20109i	−0.0544272	−	0.196734i
$457$	7.53283	+	13.0472i	0.352371	+	0.610324i	0.986664	−	0.162768i	$-0.0520423\pi$
$457$	7.53283	+	13.0472i	0.352371	+	0.610324i	−0.634294	+	0.773092i	$0.718709\pi$
$458$	−0.141473	+	0.802336i	−0.00661062	+	0.0374907i
$459$	−0.0506802	−	0.0425258i	−0.00236555	−	0.00198493i
$460$	22.9073	+	8.33759i	1.06806	+	0.388742i
$461$	−27.9579	−	23.4595i	−1.30213	−	1.09262i	−0.989773	−	0.142653i	$-0.954437\pi$
$461$	−27.9579	−	23.4595i	−1.30213	−	1.09262i	−0.312358	−	0.949964i	$-0.601119\pi$
$462$	5.26915	−	4.79012i	0.245143	−	0.222857i
$463$	−17.9295	−	31.0549i	−0.833256	−	1.44324i	−0.895442	−	0.445178i	$-0.853140\pi$
$463$	−17.9295	−	31.0549i	−0.833256	−	1.44324i	0.0621857	−	0.998065i	$-0.480193\pi$
$464$	8.22129			0.381664
$465$	0.881479	−	0.739649i	0.0408776	−	0.0343004i
$466$	0.213943	−	0.179520i	0.00991074	−	0.00831610i
$467$	17.9518			0.830710			0.415355	−	0.909659i	$-0.363657\pi$
$467$	17.9518			0.830710			0.415355	+	0.909659i	$0.363657\pi$
$468$	−0.827135	−	1.43264i	−0.0382343	−	0.0662238i
$469$	−4.48148	+	4.07407i	−0.206936	+	0.188123i
$470$	−21.5825	−	18.1099i	−0.995526	−	0.835345i
$471$	−7.51016	−	2.73348i	−0.346050	−	0.125952i
$472$	−4.12575	−	3.46191i	−0.189903	−	0.159347i
$473$	−0.00257550	+	0.0146064i	−0.000118422	+	0.000671603i
$474$	5.57070	+	9.64873i	0.255871	+	0.443181i
$475$	−9.33593	+	20.4520i	−0.428362	+	0.938404i
$476$	−0.174901	+	0.00694412i	−0.00801656	+	0.000318283i
$477$	−10.8171	+	3.93709i	−0.495280	+	0.180267i
$478$	−16.9499	+	6.16925i	−0.775269	+	0.282175i
$479$	−4.35355	−	24.6902i	−0.198919	−	1.12813i	−0.906726	−	0.421720i	$-0.861427\pi$
$479$	−4.35355	−	24.6902i	−0.198919	−	1.12813i	0.707807	−	0.706406i	$-0.249685\pi$
$480$	−2.99492	+	1.09006i	−0.136699	+	0.0497542i
$481$	0.0662558	−	0.0555952i	0.00302100	−	0.00253492i
$482$	−10.8363	−	18.7690i	−0.493580	−	0.854905i
$483$	−10.8056	−	17.1103i	−0.491673	−	0.778544i
$484$	3.52933	+	1.28457i	0.160424	+	0.0583895i
$485$	−0.292239	−	1.65737i	−0.0132699	−	0.0752574i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−16.7265			−0.757950			−0.378975	−	0.925407i	$-0.623723\pi$
$487$	−16.7265			−0.757950			−0.378975	+	0.925407i	$0.623723\pi$
$488$	4.18438	−	3.51111i	0.189418	−	0.158941i
$489$	−0.226455	−	0.190018i	−0.0102406	−	0.00859291i
$490$	−15.8996	+	15.6503i	−0.718271	+	0.707009i
$491$	−2.05995	+	11.6825i	−0.0929641	+	0.527226i	0.902388	+	0.430924i	$0.141812\pi$
$491$	−2.05995	+	11.6825i	−0.0929641	+	0.527226i	−0.995352	+	0.0963014i	$0.969299\pi$
$492$	6.37827	+	5.35200i	0.287555	+	0.241287i
$493$	−0.271953	+	0.471037i	−0.0122482	+	0.0212144i
$494$	5.94006	+	4.08794i	0.267256	+	0.183925i
$495$	4.28907	+	7.42889i	0.192779	+	0.333904i
$496$	−0.339270	+	0.123484i	−0.0152337	+	0.00554460i
$497$	21.0126	+	16.2558i	0.942545	+	0.729174i
$498$	−0.519466	+	0.435884i	−0.0232778	+	0.0195324i
$499$	−0.987416	+	5.59991i	−0.0442028	+	0.250687i	−0.998900	−	0.0468926i	$-0.985068\pi$
$499$	−0.987416	+	5.59991i	−0.0442028	+	0.250687i	0.954697	+	0.297579i	$0.0961792\pi$
$500$	0.472458	+	0.171961i	0.0211290	+	0.00769032i
$501$	4.31875			0.192947
$502$	−2.72357			−0.121559
$503$	32.1734	+	11.7102i	1.43454	+	0.522131i	0.938230	−	0.346013i	$-0.112465\pi$
$503$	32.1734	+	11.7102i	1.43454	+	0.522131i	0.496313	+	0.868144i	$0.334687\pi$
$504$	2.52013	+	0.805556i	0.112256	+	0.0358823i
$505$	−12.2185	+	21.1630i	−0.543715	+	0.941742i
$506$	−10.2933	+	17.8285i	−0.457593	+	0.792574i
$507$	−9.64443	−	3.51029i	−0.428324	−	0.155897i
$508$	−11.7652	+	4.28219i	−0.521998	+	0.189992i
$509$	−0.697230	−	0.253771i	−0.0309042	−	0.0112482i	0.326522	−	0.945190i	$-0.394123\pi$
$509$	−0.697230	−	0.253771i	−0.0309042	−	0.0112482i	−0.357426	+	0.933941i	$0.616346\pi$
$510$	0.0366146	−	0.207651i	0.00162132	−	0.00919496i
$511$	11.1561	+	8.63059i	0.493515	+	0.381795i
$512$	1.00000			0.0441942
$513$	−3.59074	−	2.47115i	−0.158535	−	0.109104i
$514$	6.93895	−	12.0186i	0.306064	−	0.530118i
$515$	−0.151269	+	0.857889i	−0.00666571	+	0.0378031i
$516$	−0.00517825	+	0.00188473i	−0.000227960	+	8.29706e-5i
$517$	18.2262	−	15.2936i	0.801589	−	0.672613i
$518$	−0.0185972	+	0.137073i	−0.000817115	+	0.00602264i
$519$	−3.36564	−	19.0875i	−0.147735	−	0.837849i
$520$	2.63618	−	4.56600i	0.115604	−	0.200232i
$521$	−8.31070	−	14.3946i	−0.364098	−	0.630637i	0.624533	−	0.780999i	$-0.285290\pi$
$521$	−8.31070	−	14.3946i	−0.364098	−	0.630637i	−0.988631	+	0.150362i	$0.951956\pi$
$522$	6.29787	−	5.28454i	0.275650	−	0.231298i
$523$	0.736705	+	4.17806i	0.0322139	+	0.182694i	0.996669	−	0.0815526i	$-0.0259879\pi$
$523$	0.736705	+	4.17806i	0.0322139	+	0.182694i	−0.964455	+	0.264247i	$0.914877\pi$
$524$	−6.68746	+	11.5830i	−0.292143	+	0.506007i
$525$	−7.28653	−	11.5379i	−0.318010	−	0.503556i
$526$	−1.74304	−	9.88527i	−0.0760002	−	0.431018i
$527$	0.00414777	−	0.0235231i	0.000180680	−	0.00102468i
$528$	−0.467374	−	2.65061i	−0.0203398	−	0.115353i
$529$	27.1970	+	22.8210i	1.18248	+	0.992219i
$530$	−28.1045	−	23.5825i	−1.22078	−	1.02436i
$531$	−5.38578			−0.233723
$532$	−11.4276	+	1.55277i	−0.495447	+	0.0673211i
$533$	−13.7738			−0.596612
$534$	−9.84107	−	8.25764i	−0.425865	−	0.357343i
$535$	−13.3296	−	11.1848i	−0.576288	−	0.483563i
$536$	0.397508	+	2.25438i	0.0171697	+	0.0973744i
$537$	−4.04470	+	22.9386i	−0.174542	+	0.989875i
$538$	2.11304	+	11.9837i	0.0910997	+	0.516652i
$539$	−10.6842	−	15.5181i	−0.460200	−	0.668414i
$540$	−1.59356	+	2.76013i	−0.0685760	+	0.118777i
$541$	5.48217	+	31.0909i	0.235697	+	1.33670i	0.841141	+	0.540816i	$0.181884\pi$
$541$	5.48217	+	31.0909i	0.235697	+	1.33670i	−0.605444	+	0.795888i	$0.707004\pi$
$542$	1.21281	−	1.01767i	0.0520947	−	0.0437127i
$543$	6.34312	+	10.9866i	0.272209	+	0.471480i
$544$	−0.0330792	+	0.0572948i	−0.00141826	+	0.00245649i
$545$	−5.45138	−	30.9163i	−0.233511	−	1.32431i
$546$	−4.05021	+	1.65894i	−0.173333	+	0.0709959i
$547$	−10.0018	+	8.39251i	−0.427646	+	0.358838i	−0.831063	−	0.556179i	$-0.812267\pi$
$547$	−10.0018	+	8.39251i	−0.427646	+	0.358838i	0.403416	+	0.915016i	$0.367823\pi$
$548$	−12.2825	+	4.47047i	−0.524683	+	0.190969i
$549$	0.948522	−	5.37933i	0.0404819	−	0.229584i
$550$	−6.94105	+	12.0222i	−0.295967	+	0.512630i
$551$	−14.8812	+	32.5999i	−0.633959	+	1.38880i
$552$	−7.64874			−0.325552
$553$	27.2779	−	11.1728i	1.15997	−	0.475116i
$554$	1.69434	−	9.60906i	0.0719855	−	0.408250i
$555$	−0.156584	−	0.0569920i	−0.00664663	−	0.00241918i
$556$	−21.6703	+	7.88733i	−0.919024	+	0.334497i
$557$	40.2494	+	14.6496i	1.70542	+	0.620722i	0.996424	−	0.0844907i	$-0.0269263\pi$
$557$	40.2494	+	14.6496i	1.70542	+	0.620722i	0.708996	+	0.705213i	$0.249149\pi$
$558$	−0.180522	+	0.312673i	−0.00764209	+	0.0132365i
$559$	0.00455800	−	0.00789468i	0.000192783	−	0.000333909i
$560$	1.79255	+	8.23960i	0.0757491	+	0.348187i
$561$	0.167327	+	0.0609019i	0.00706453	+	0.00257128i
$562$	−14.4232			−0.608404
$563$	−39.3379			−1.65790			−0.828948	−	0.559326i	$-0.811060\pi$
$563$	−39.3379			−1.65790			−0.828948	+	0.559326i	$0.811060\pi$
$564$	8.30681	+	3.02343i	0.349780	+	0.127309i
$565$	−1.38204	+	7.83792i	−0.0581428	+	0.329744i
$566$	8.59179	−	7.20937i	0.361140	−	0.303032i
$567$	2.44834	−	1.00282i	0.102820	−	0.0421145i
$568$	9.43566	−	3.43430i	0.395912	−	0.144100i
$569$	−7.39179	−	12.8030i	−0.309880	−	0.536728i	0.668456	−	0.743752i	$-0.266956\pi$
$569$	−7.39179	−	12.8030i	−0.309880	−	0.536728i	−0.978336	+	0.207024i	$0.933622\pi$
$570$	1.09861	−	13.8488i	0.0460158	−	0.580064i
$571$	16.1866	−	28.0360i	0.677387	−	1.17327i	−0.298377	−	0.954448i	$-0.596445\pi$
$571$	16.1866	−	28.0360i	0.677387	−	1.17327i	0.975765	−	0.218821i	$-0.0702212\pi$
$572$	3.41079	+	2.86199i	0.142612	+	0.119666i
$573$	−1.75389	+	9.94679i	−0.0732697	+	0.415533i
$574$	16.3003	−	14.8184i	0.680360	−	0.618508i
$575$	30.2207	+	25.3582i	1.26029	+	1.05751i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	15.8059			0.658007			0.329004	−	0.944329i	$-0.393287\pi$
$577$	15.8059			0.658007			0.329004	+	0.944329i	$0.393287\pi$
$578$	8.49781	+	14.7186i	0.353462	+	0.612215i
$579$	2.92854	+	16.6086i	0.121706	+	0.690228i
$580$	24.6221	+	8.96170i	1.02238	+	0.372114i
$581$	0.957996	+	1.51694i	0.0397444	+	0.0629335i
$582$	0.264022	+	0.457299i	0.0109441	+	0.0189557i
$583$	23.7341	−	19.9152i	0.982964	−	0.824805i
$584$	5.00960	−	1.82335i	0.207299	−	0.0754506i
$585$	−0.915536	−	5.19226i	−0.0378528	−	0.214674i
$586$	−18.5724	+	6.75981i	−0.767220	+	0.279245i
$587$	−43.2984	+	15.7593i	−1.78712	+	0.650458i	−0.787710	+	0.616046i	$0.788733\pi$
$587$	−43.2984	+	15.7593i	−1.78712	+	0.650458i	−0.999408	+	0.0344115i	$0.989044\pi$
$588$	3.00836	−	6.32058i	0.124063	−	0.260656i
$589$	0.124453	−	1.56882i	0.00512799	−	0.0646422i
$590$	−8.58257	−	14.8655i	−0.353339	−	0.612001i
$591$	1.95180	−	11.0692i	0.0802865	−	0.455327i
$592$	0.0400514	+	0.0336071i	0.00164610	+	0.00138124i
$593$	−16.3075	−	5.93544i	−0.669669	−	0.243739i	−0.0152635	−	0.999884i	$-0.504859\pi$
$593$	−16.3075	−	5.93544i	−0.669669	−	0.243739i	−0.654405	+	0.756144i	$0.727081\pi$
$594$	−2.06181	−	1.73006i	−0.0845970	−	0.0709853i
$595$	−0.531383	−	0.169855i	−0.0217846	−	0.00696339i
$596$	−8.86913	−	15.3618i	−0.363294	−	0.629243i
$597$	6.85242			0.280451
$598$	9.69282	−	8.13324i	0.396369	−	0.332593i
$599$	36.7342	−	30.8236i	1.50092	−	1.25942i	0.621459	−	0.783447i	$-0.286540\pi$
$599$	36.7342	−	30.8236i	1.50092	−	1.25942i	0.879460	−	0.475973i	$-0.157904\pi$
$600$	−5.15775			−0.210564
$601$	21.5881	+	37.3917i	0.880598	+	1.52524i	0.850678	+	0.525687i	$0.176192\pi$
$601$	21.5881	+	37.3917i	0.880598	+	1.52524i	0.0299198	+	0.999552i	$0.490475\pi$
$602$	0.00309935	+	0.0142464i	0.000126320	+	0.000580640i
$603$	1.75360	+	1.47144i	0.0714120	+	0.0599217i
$604$	15.1862	+	5.52734i	0.617920	+	0.224904i
$605$	9.16978	+	7.69435i	0.372804	+	0.312820i
$606$	1.33143	−	7.55091i	0.0540856	−	0.306735i
$607$	−13.1203	−	22.7251i	−0.532538	−	0.922382i	−0.999278	−	0.0379879i	$-0.987905\pi$
$607$	−13.1203	−	22.7251i	−0.532538	−	0.922382i	0.466741	−	0.884394i	$-0.345428\pi$
$608$	−1.81008	+	3.96530i	−0.0734083	+	0.160814i
$609$	−11.6145	−	18.3910i	−0.470643	−	0.745243i
$610$	16.3592	−	5.95426i	0.662364	−	0.241081i
$611$	−13.7417	+	5.00157i	−0.555930	+	0.202342i
$612$	0.0114883	+	0.0651533i	0.000464386	+	0.00263366i
$613$	−20.1084	+	7.31884i	−0.812169	+	0.295605i	−0.714519	−	0.699616i	$-0.753355\pi$
$613$	−20.1084	+	7.31884i	−0.812169	+	0.295605i	−0.0976494	+	0.995221i	$0.531132\pi$
$614$	−10.8956	+	9.14250i	−0.439711	+	0.368961i
$615$	13.2684	+	22.9815i	0.535032	+	0.926703i
$616$	−7.11543	+	0.282506i	−0.286689	+	0.0113825i
$617$	39.2730	+	14.2942i	1.58107	+	0.575463i	0.975437	−	0.220279i	$-0.0706967\pi$
$617$	39.2730	+	14.2942i	1.58107	+	0.575463i	0.605636	+	0.795742i	$0.292919\pi$
$618$	−0.0474625	−	0.269173i	−0.00190922	−	0.0108277i
$619$	10.5602	+	18.2908i	0.424451	+	0.735171i	0.996369	−	0.0851399i	$-0.0271337\pi$
$619$	10.5602	+	18.2908i	0.424451	+	0.735171i	−0.571918	+	0.820311i	$0.693800\pi$
$620$	−1.15069			−0.0462128
$621$	−5.85927	+	4.91652i	−0.235125	+	0.197293i
$622$	−22.3975	−	18.7937i	−0.898058	−	0.753560i
$623$	−25.1498	+	22.8634i	−1.00761	+	0.916003i
$624$	−0.287261	+	1.62914i	−0.0114996	+	0.0652177i
$625$	−18.5278	−	15.5467i	−0.741113	−	0.621867i
$626$	11.4879	−	19.8977i	0.459150	−	0.795271i
$627$	11.3565	+	2.94453i	0.453533	+	0.117593i
$628$	3.99607	+	6.92140i	0.159461	+	0.276194i
$629$	−0.00325038	+	0.00118304i	−0.000129601	+	4.71709e-5i
$630$	6.66949	+	5.15967i	0.265719	+	0.205566i
$631$	1.09663	−	0.920181i	0.0436561	−	0.0366318i	−0.620699	−	0.784049i	$-0.713151\pi$
$631$	1.09663	−	0.920181i	0.0436561	−	0.0366318i	0.664355	+	0.747417i	$0.268706\pi$
$632$	1.93468	−	10.9721i	0.0769576	−	0.436448i
$633$	−24.4762	−	8.90859i	−0.972840	−	0.354085i
$634$	14.7774			0.586885
$635$	−39.9037			−1.58353
$636$	10.8171	+	3.93709i	0.428925	+	0.156116i
$637$	2.90862	+	11.2086i	0.115244	+	0.444103i
$638$	−11.0638	+	19.1631i	−0.438020	+	0.758673i
$639$	5.02061	−	8.69595i	0.198612	−	0.344007i
$640$	2.99492	+	1.09006i	0.118384	+	0.0430884i
$641$	22.8420	−	8.31381i	0.902205	−	0.328376i	0.151069	−	0.988523i	$-0.451729\pi$
$641$	22.8420	−	8.31381i	0.902205	−	0.328376i	0.751136	+	0.660148i	$0.229506\pi$
$642$	5.13038	+	1.86730i	0.202480	+	0.0736966i
$643$	0.00615884	−	0.0349285i	0.000242881	−	0.00137745i	−0.984686	−	0.174337i	$-0.944222\pi$
$643$	0.00615884	−	0.0349285i	0.000242881	−	0.00137745i	0.984929	+	0.172959i	$0.0553329\pi$
$644$	−2.72066	+	20.0529i	−0.107209	+	0.790197i
$645$	−0.0175629			−0.000691539
$646$	−0.167315	−	0.234877i	−0.00658294	−	0.00924111i
$647$	−12.5218	+	21.6884i	−0.492283	+	0.852659i	−0.999961	−	0.00888793i	$-0.997171\pi$
$647$	−12.5218	+	21.6884i	−0.492283	+	0.852659i	0.507677	+	0.861547i	$0.330504\pi$
$648$	0.173648	−	0.984808i	0.00682154	−	0.0386869i
$649$	13.6216	−	4.95786i	0.534695	−	0.194613i
$650$	6.53613	−	5.48447i	0.256368	−	0.215119i
$651$	0.755532	+	0.584497i	0.0296116	+	0.0229083i
$652$	0.0513331	+	0.291124i	0.00201036	+	0.0114013i
$653$	−7.05482	+	12.2193i	−0.276077	+	0.478179i	−0.970406	−	0.241478i	$-0.922368\pi$
$653$	−7.05482	+	12.2193i	−0.276077	+	0.478179i	0.694330	+	0.719657i	$0.255701\pi$
$654$	4.92501	+	8.53037i	0.192583	+	0.333564i
$655$	−32.6546	+	27.4005i	−1.27592	+	1.07062i
$656$	−1.44584	−	8.19974i	−0.0564504	−	0.320146i
$657$	2.66555	−	4.61687i	0.103993	−	0.180121i
$658$	10.8814	−	20.7028i	0.424200	−	0.807079i
$659$	−6.49889	−	36.8570i	−0.253161	−	1.43575i	−0.800750	−	0.598999i	$-0.795565\pi$
$659$	−6.49889	−	36.8570i	−0.253161	−	1.43575i	0.547589	−	0.836747i	$-0.315546\pi$
$660$	1.48958	−	8.44782i	0.0579818	−	0.328831i
$661$	−6.40465	−	36.3226i	−0.249112	−	1.41278i	−0.810746	−	0.585399i	$-0.800938\pi$
$661$	−6.40465	−	36.3226i	−0.249112	−	1.41278i	0.561633	−	0.827386i	$-0.310173\pi$
$662$	2.72455	+	2.28617i	0.105893	+	0.0888546i
$663$	−0.0838388	−	0.0703491i	−0.00325603	−	0.00273213i
$664$	0.678115			0.0263160
$665$	−35.9172	−	7.80631i	−1.39281	−	0.302716i
$666$	0.0522834			0.00202594
$667$	48.1708	+	40.4201i	1.86518	+	1.56507i
$668$	−3.30835	−	2.77604i	−0.128004	−	0.107408i
$669$	−0.152302	−	0.863747i	−0.00588833	−	0.0333944i
$670$	−1.26691	+	7.18499i	−0.0489449	+	0.277580i
$671$	2.55295	+	14.4785i	0.0985554	+	0.558935i
$672$	−1.41273	−	2.23700i	−0.0544974	−	0.0862943i
$673$	−12.3256	+	21.3486i	−0.475117	+	0.822927i	−0.999594	−	0.0284980i	$-0.990928\pi$
$673$	−12.3256	+	21.3486i	−0.475117	+	0.822927i	0.524477	+	0.851425i	$0.324261\pi$
$674$	2.17467	+	12.3332i	0.0837651	+	0.475055i
$675$	−3.95107	+	3.31534i	−0.152077	+	0.127607i
$676$	5.13170	+	8.88836i	0.197373	+	0.341860i
$677$	17.0800	−	29.5833i	0.656436	−	1.13698i	−0.325096	−	0.945681i	$-0.605397\pi$
$677$	17.0800	−	29.5833i	0.656436	−	1.13698i	0.981532	−	0.191299i	$-0.0612701\pi$
$678$	−0.433632	−	2.45925i	−0.0166535	−	0.0944468i
$679$	1.29283	−	0.529533i	0.0496142	−	0.0203216i
$680$	−0.161524	+	0.135535i	−0.00619417	+	0.00519752i
$681$	23.7818	−	8.65587i	0.911321	−	0.331694i
$682$	0.168742	−	0.956985i	0.00646148	−	0.0366449i
$683$	19.3741	−	33.5569i	0.741329	−	1.28402i	−0.210562	−	0.977581i	$-0.567529\pi$
$683$	19.3741	−	33.5569i	0.741329	−	1.28402i	0.951890	−	0.306439i	$-0.0991374\pi$
$684$	1.16225	+	4.20109i	0.0444396	+	0.160633i
$685$	−41.6582			−1.59168
$686$	−15.5008	−	10.1354i	−0.591823	−	0.386970i
$687$	0.141473	−	0.802336i	0.00539755	−	0.0306110i
$688$	0.00517825	+	0.00188473i	0.000197419	+	7.18547e-5i
$689$	−17.8944	+	6.51301i	−0.681721	+	0.248126i
$690$	−22.9073	−	8.33759i	−0.872067	−	0.317407i
$691$	−7.97394	+	13.8113i	−0.303343	+	0.525406i	−0.976891	−	0.213738i	$-0.931436\pi$
$691$	−7.97394	+	13.8113i	−0.303343	+	0.525406i	0.673548	+	0.739144i	$0.264770\pi$
$692$	−9.69099	+	16.7853i	−0.368396	+	0.638081i
$693$	−5.26915	+	4.79012i	−0.200158	+	0.181962i
$694$	26.7259	+	9.72743i	1.01450	+	0.369248i
$695$	−73.4983			−2.78795
$696$	−8.22129			−0.311627
$697$	0.517630	+	0.188402i	0.0196066	+	0.00713623i
$698$	5.96324	−	33.8192i	0.225712	−	1.28008i
$699$	−0.213943	+	0.179520i	−0.00809208	+	0.00679006i
$700$	−1.83462	+	13.5222i	−0.0693420	+	0.511093i
$701$	23.9665	−	8.72309i	0.905202	−	0.329466i	0.152866	−	0.988247i	$-0.451150\pi$
$701$	23.9665	−	8.72309i	0.905202	−	0.329466i	0.752335	+	0.658780i	$0.228927\pi$
$702$	0.827135	+	1.43264i	0.0312182	+	0.0540715i
$703$	−0.205758	+	0.0979844i	−0.00776032	+	0.00369555i
$704$	−1.34575	+	2.33091i	−0.0507199	+	0.0878494i
$705$	21.5825	+	18.1099i	0.812843	+	0.682057i
$706$	1.46592	−	8.31367i	0.0551708	−	0.312889i
$707$	−19.3229	−	6.17652i	−0.726712	−	0.232292i
$708$	4.12575	+	3.46191i	0.155055	+	0.130107i
$709$	10.9954	−	9.22627i	0.412942	−	0.346500i	−0.412528	−	0.910945i	$-0.635354\pi$
$709$	10.9954	−	9.22627i	0.412942	−	0.346500i	0.825471	+	0.564445i	$0.190910\pi$
$710$	32.0026			1.20104
$711$	−5.57070	−	9.64873i	−0.208917	−	0.361856i
$712$	2.23079	+	12.6514i	0.0836024	+	0.474133i
$713$	−2.59499	−	0.944498i	−0.0971830	−	0.0353717i
$714$	0.174901	−	0.00694412i	0.00654550	−	0.000259877i
$715$	7.09528	+	12.2894i	0.265348	+	0.459597i
$716$	17.8431	−	14.9721i	0.666828	−	0.559535i
$717$	16.9499	−	6.16925i	0.633005	−	0.230395i
$718$	4.02790	+	22.8434i	0.150320	+	0.852507i
$719$	−7.75146	+	2.82130i	−0.289081	+	0.105217i	−0.482490	−	0.875901i	$-0.660268\pi$
$719$	−7.75146	+	2.82130i	−0.289081	+	0.105217i	0.193410	+	0.981118i	$0.438045\pi$
$720$	2.99492	−	1.09006i	0.111614	−	0.0406241i
$721$	−0.722583	+	0.0286889i	−0.0269104	+	0.00106843i
$722$	−12.4472	−	14.3550i	−0.463238	−	0.534238i
$723$	10.8363	+	18.7690i	0.403006	+	0.698027i
$724$	2.20294	−	12.4935i	0.0818717	−	0.464317i
$725$	32.4829	+	27.2564i	1.20638	+	1.01228i
$726$	−3.52933	−	1.28457i	−0.130986	−	0.0476748i
$727$	−13.4450	−	11.2817i	−0.498649	−	0.418416i	0.358465	−	0.933543i	$-0.383300\pi$
$727$	−13.4450	−	11.2817i	−0.498649	−	0.418416i	−0.857114	+	0.515127i	$0.827745\pi$
$728$	4.16898	+	1.33261i	0.154513	+	0.0493897i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	16.9909			0.628861
$731$	−0.000279278	0	0.000234342i	−1.03295e−5	0	8.66744e-6i
$732$	−4.18438	+	3.51111i	−0.154659	+	0.129774i
$733$	42.4702			1.56867			0.784337	−	0.620335i	$-0.213004\pi$
$733$	42.4702			1.56867			0.784337	+	0.620335i	$0.213004\pi$
$734$	3.20510	+	5.55140i	0.118302	+	0.204906i
$735$	15.8996	−	15.6503i	0.586466	−	0.577270i
$736$	5.85927	+	4.91652i	0.215976	+	0.181225i
$737$	−5.78970	−	2.10728i	−0.213266	−	0.0776225i
$738$	−6.37827	−	5.35200i	−0.234787	−	0.197010i
$739$	−2.40182	+	13.6214i	−0.0883522	+	0.501070i	0.908231	+	0.418470i	$0.137434\pi$
$739$	−2.40182	+	13.6214i	−0.0883522	+	0.501070i	−0.996583	+	0.0826002i	$0.973678\pi$
$740$	0.0833168	+	0.144309i	0.00306278	+	0.00530490i
$741$	−5.94006	−	4.08794i	−0.218214	−	0.150174i
$742$	14.1696	−	26.9590i	0.520184	−	0.989697i
$743$	8.00418	−	2.91328i	0.293645	−	0.106878i	−0.190997	−	0.981591i	$-0.561172\pi$
$743$	8.00418	−	2.91328i	0.293645	−	0.106878i	0.484642	+	0.874713i	$0.338950\pi$
$744$	0.339270	−	0.123484i	0.0124382	−	0.00452715i
$745$	−9.81703	−	55.6751i	−0.359668	−	2.03978i
$746$	18.2946	−	6.65870i	0.669814	−	0.243792i
$747$	0.519466	−	0.435884i	0.0190063	−	0.0159482i
$748$	−0.0890326	−	0.154209i	−0.00325535	−	0.00563844i
$749$	6.72045	−	12.7863i	0.245560	−	0.467200i
$750$	−0.472458	−	0.171961i	−0.0172517	−	0.00627912i
$751$	−3.16868	−	17.9705i	−0.115627	−	0.655752i	−0.986438	−	0.164134i	$-0.947517\pi$
$751$	−3.16868	−	17.9705i	−0.115627	−	0.655752i	0.870811	−	0.491618i	$-0.163594\pi$
$752$	−4.41996	−	7.65560i	−0.161179	−	0.279171i
$753$	2.72357			0.0992525
$754$	10.4184	−	8.74206i	0.379415	−	0.318367i
$755$	39.4564	+	33.1079i	1.43597	+	1.20492i
$756$	−2.52013	−	0.805556i	−0.0916564	−	0.0292978i
$757$	−3.44863	+	19.5582i	−0.125343	+	0.710854i	0.855761	+	0.517371i	$0.173089\pi$
$757$	−3.44863	+	19.5582i	−0.125343	+	0.710854i	−0.981104	+	0.193482i	$0.938022\pi$
$758$	25.8717	+	21.7090i	0.939704	+	0.788505i
$759$	10.2933	−	17.8285i	0.373623	−	0.647134i
$760$	−9.74345	+	9.90265i	−0.353432	+	0.359207i
$761$	6.51541	+	11.2850i	0.236183	+	0.409082i	0.959616	−	0.281313i	$-0.0907701\pi$
$761$	6.51541	+	11.2850i	0.236183	+	0.409082i	−0.723433	+	0.690395i	$0.757437\pi$
$762$	11.7652	−	4.28219i	0.426209	−	0.155127i
$763$	24.1162	−	9.87780i	0.873064	−	0.357600i
$764$	7.73723	−	6.49231i	0.279923	−	0.234883i
$765$	−0.0366146	+	0.207651i	−0.00132380	+	0.00750765i
$766$	23.2319	+	8.45574i	0.839404	+	0.305518i
$767$	−8.90954			−0.321705
$768$	−1.00000			−0.0360844
$769$	33.0000	+	12.0110i	1.19001	+	0.433129i	0.859727	−	0.510753i	$-0.170633\pi$
$769$	33.0000	+	12.0110i	1.19001	+	0.433129i	0.330284	+	0.943882i	$0.392856\pi$
$770$	−21.6181	−	6.91017i	−0.779061	−	0.249025i
$771$	−6.93895	+	12.0186i	−0.249900	+	0.432840i
$772$	8.43239	−	14.6053i	0.303488	−	0.525657i
$773$	−8.13341	−	2.96032i	−0.292539	−	0.106475i	0.191582	−	0.981477i	$-0.438638\pi$
$773$	−8.13341	−	2.96032i	−0.292539	−	0.106475i	−0.484121	+	0.875001i	$0.660860\pi$
$774$	0.00517825	−	0.00188473i	0.000186129	−	6.77452e-5i
$775$	−1.74987	−	0.636901i	−0.0628572	−	0.0228781i
$776$	0.0916938	−	0.520021i	0.00329162	−	0.0186677i
$777$	0.0185972	−	0.137073i	0.000667172	−	0.00491746i
$778$	−35.2240			−1.26284
$779$	35.1315	+	9.10899i	1.25872	+	0.326364i
$780$	−2.63618	+	4.56600i	−0.0943904	+	0.163489i
$781$	−4.69301	+	26.6154i	−0.167929	+	0.952372i
$782$	−0.475511	+	0.173072i	−0.0170042	+	0.00618903i
$783$	−6.29787	+	5.28454i	−0.225068	+	0.188854i
$784$	−6.36733	+	2.90811i	−0.227405	+	0.103861i
$785$	4.42316	+	25.0850i	0.157869	+	0.895321i
$786$	6.68746	−	11.5830i	0.238534	−	0.413153i
$787$	18.6611	+	32.3220i	0.665196	+	1.15215i	0.979232	+	0.202742i	$0.0649854\pi$
$787$	18.6611	+	32.3220i	0.665196	+	1.15215i	−0.314036	+	0.949411i	$0.601681\pi$
$788$	−8.61033	+	7.22493i	−0.306730	+	0.257377i
$789$	1.74304	+	9.88527i	0.0620539	+	0.351925i
$790$	17.7545	−	30.7517i	0.631677	−	1.09410i
$791$	−6.60173	+	0.262110i	−0.234730	+	0.00931955i
$792$	0.467374	+	2.65061i	0.0166074	+	0.0941853i
$793$	1.56911	−	8.89887i	0.0557208	−	0.316008i
$794$	6.50809	+	36.9092i	0.230963	+	1.30986i
$795$	28.1045	+	23.5825i	0.996766	+	0.836386i
$796$	−5.24926	−	4.40465i	−0.186055	−	0.156119i
$797$	18.2787			0.647465			0.323733	−	0.946149i	$-0.395062\pi$
$797$	18.2787			0.647465			0.323733	+	0.946149i	$0.395062\pi$
$798$	11.4276	−	1.55277i	0.404531	−	0.0549674i
$799$	0.584835			0.0206900
$800$	3.95107	+	3.31534i	0.139691	+	0.117215i
$801$	9.84107	+	8.25764i	0.347717	+	0.291769i
$802$	−2.98290	−	16.9168i	−0.105330	−	0.597354i
$803$	−2.49162	+	14.1307i	−0.0879274	+	0.498661i
$804$	−0.397508	−	2.25438i	−0.0140190	−	0.0795058i
$805$	−30.0071	+	57.0912i	−1.05761	+	2.01220i
$806$	−0.298632	+	0.517245i	−0.0105189	+	0.0182192i
$807$	−2.11304	−	11.9837i	−0.0743826	−	0.421845i
$808$	−5.87357	+	4.92851i	−0.206631	+	0.173384i
$809$	−1.05192	−	1.82198i	−0.0369835	−	0.0640574i	0.846941	−	0.531687i	$-0.178442\pi$
$809$	−1.05192	−	1.82198i	−0.0369835	−	0.0640574i	−0.883925	+	0.467629i	$0.845108\pi$
$810$	1.59356	−	2.76013i	0.0559920	−	0.0969811i
$811$	0.532138	+	3.01790i	0.0186859	+	0.105973i	0.992724	−	0.120410i	$-0.0384210\pi$
$811$	0.532138	+	3.01790i	0.0186859	+	0.105973i	−0.974038	+	0.226383i	$0.927310\pi$
$812$	−2.92432	+	21.5540i	−0.102623	+	0.756397i
$813$	−1.21281	+	1.01767i	−0.0425352	+	0.0356913i
$814$	−0.132234	+	0.0481293i	−0.00463481	+	0.00168693i
$815$	−0.163605	+	0.927849i	−0.00573083	+	0.0325011i
$816$	0.0330792	−	0.0572948i	0.00115800	−	0.00200572i
$817$	−0.0168466	+	0.0171218i	−0.000589387	+	0.000599017i
$818$	−25.9128			−0.906020
$819$	4.05021	−	1.65894i	0.141526	−	0.0579679i
$820$	4.60806	−	26.1336i	0.160920	−	0.912625i
$821$	48.7107	+	17.7292i	1.70002	+	0.618755i	0.995827	−	0.0912586i	$-0.0290890\pi$
$821$	48.7107	+	17.7292i	1.70002	+	0.618755i	0.704188	+	0.710014i	$0.251311\pi$
$822$	12.2825	−	4.47047i	0.428402	−	0.155926i
$823$	−40.6974	−	14.8127i	−1.41862	−	0.516337i	−0.484975	−	0.874528i	$-0.661171\pi$
$823$	−40.6974	−	14.8127i	−1.41862	−	0.516337i	−0.933648	+	0.358191i	$0.883394\pi$
$824$	−0.136663	+	0.236707i	−0.00476088	+	0.00824608i
$825$	6.94105	−	12.0222i	0.241656	−	0.418561i
$826$	10.5437	−	9.58520i	0.366864	−	0.333512i
$827$	12.8699	+	4.68425i	0.447530	+	0.162887i	0.555947	−	0.831218i	$-0.312356\pi$
$827$	12.8699	+	4.68425i	0.447530	+	0.162887i	−0.108417	+	0.994106i	$0.534578\pi$
$828$	7.64874			0.265812
$829$	55.0163			1.91079			0.955397	−	0.295325i	$-0.0954278\pi$
$829$	55.0163			1.91079			0.955397	+	0.295325i	$0.0954278\pi$
$830$	2.03090	+	0.739186i	0.0704935	+	0.0256575i
$831$	−1.69434	+	9.60906i	−0.0587759	+	0.333335i
$832$	1.26724	−	1.06334i	0.0439338	−	0.0368648i
$833$	0.0440067	−	0.461013i	0.00152474	−	0.0159731i
$834$	21.6703	−	7.88733i	0.750380	−	0.273116i
$835$	−6.88219	−	11.9203i	−0.238168	−	0.412519i
$836$	−6.80684	−	9.55543i	−0.235419	−	0.330481i
$837$	0.180522	−	0.312673i	0.00623974	−	0.0108076i
$838$	−8.01677	−	6.72687i	−0.276935	−	0.232376i
$839$	−0.237366	+	1.34617i	−0.00819479	+	0.0464750i	−0.988631	−	0.150362i	$-0.951956\pi$
$839$	−0.237366	+	1.34617i	−0.00819479	+	0.0464750i	0.980436	+	0.196837i	$0.0630671\pi$
$840$	−1.79255	−	8.23960i	−0.0618489	−	0.284293i
$841$	29.5613	+	24.8049i	1.01936	+	0.855341i
$842$	−2.22881	+	1.87019i	−0.0768098	+	0.0644511i
$843$	14.4232			0.496760
$844$	13.0235	+	22.5573i	0.448287	+	0.776456i
$845$	5.68015	+	32.2137i	0.195403	+	1.10819i
$846$	−8.30681	−	3.02343i	−0.285594	−	0.103948i
$847$	−4.62318	+	8.79602i	−0.158854	+	0.302235i
$848$	−5.75564	−	9.96907i	−0.197650	−	0.342339i
$849$	−8.59179	+	7.20937i	−0.294869	+	0.247425i
$850$	−0.320650	+	0.116707i	−0.0109982	+	0.00400302i
$851$	0.0694422	+	0.393826i	0.00238045	+	0.0135002i
$852$	−9.43566	+	3.43430i	−0.323260	+	0.117657i
$853$	27.8362	−	10.1316i	0.953095	−	0.346898i	0.181771	−	0.983341i	$-0.441817\pi$
$853$	27.8362	−	10.1316i	0.953095	−	0.346898i	0.771324	+	0.636443i	$0.219595\pi$
$854$	7.71680	+	12.2192i	0.264064	+	0.418133i
$855$	−1.09861	+	13.8488i	−0.0375717	+	0.473620i
$856$	−2.72982	−	4.72818i	−0.0933032	−	0.161606i
$857$	−6.77873	+	38.4441i	−0.231557	+	1.31322i	0.618188	+	0.786030i	$0.287867\pi$
$857$	−6.77873	+	38.4441i	−0.231557	+	1.31322i	−0.849745	+	0.527194i	$0.823244\pi$
$858$	−3.41079	−	2.86199i	−0.116442	−	0.0977068i
$859$	−16.1042	−	5.86144i	−0.549467	−	0.199990i	0.0523424	−	0.998629i	$-0.483331\pi$
$859$	−16.1042	−	5.86144i	−0.549467	−	0.199990i	−0.601810	+	0.798639i	$0.705553\pi$
$860$	0.0134540	+	0.0112892i	0.000458776	+	0.000384959i
$861$	−16.3003	+	14.8184i	−0.555512	+	0.505010i
$862$	−10.3787	−	17.9764i	−0.353499	−	0.612278i
$863$	−11.8045			−0.401830			−0.200915	−	0.979609i	$-0.564391\pi$
$863$	−11.8045			−0.401830			−0.200915	+	0.979609i	$0.564391\pi$
$864$	−0.766044	+	0.642788i	−0.0260614	+	0.0218681i
$865$	−47.3207	+	39.7068i	−1.60895	+	1.35007i
$866$	−7.65665			−0.260183
$867$	−8.49781	−	14.7186i	−0.288601	−	0.499871i
$868$	−0.203064	−	0.933398i	−0.00689243	−	0.0316816i
$869$	22.9714	+	19.2753i	0.779252	+	0.653870i
$870$	−24.6221	−	8.96170i	−0.834766	−	0.303830i
$871$	2.90092	+	2.43416i	0.0982940	+	0.0824784i
$872$	1.71044	−	9.70038i	0.0579228	−	0.328496i
$873$	−0.264022	−	0.457299i	−0.00893578	−	0.0154772i
$874$	−30.1012	+	14.3345i	−1.01819	+	0.484872i
$875$	−0.618888	+	1.17749i	−0.0209222	+	0.0398065i
$876$	−5.00960	+	1.82335i	−0.169259	+	0.0616052i
$877$	−15.3231	+	5.57715i	−0.517424	+	0.188327i	−0.587515	−	0.809214i	$-0.699894\pi$
$877$	−15.3231	+	5.57715i	−0.517424	+	0.188327i	0.0700902	+	0.997541i	$0.477671\pi$
$878$	1.79444	+	10.1768i	0.0605594	+	0.343449i
$879$	18.5724	−	6.75981i	0.626432	−	0.228003i
$880$	−6.57124	+	5.51392i	−0.221516	+	0.185874i
$881$	−8.08353	−	14.0011i	−0.272341	−	0.471709i	0.697120	−	0.716955i	$-0.254465\pi$
$881$	−8.08353	−	14.0011i	−0.272341	−	0.471709i	−0.969461	+	0.245246i	$0.921131\pi$
$882$	−3.00836	+	6.32058i	−0.101297	+	0.212825i
$883$	6.84403	+	2.49102i	0.230320	+	0.0838296i	0.454602	−	0.890695i	$-0.349781\pi$
$883$	6.84403	+	2.49102i	0.230320	+	0.0838296i	−0.224282	+	0.974524i	$0.572004\pi$
$884$	0.0190047	+	0.107781i	0.000639198	+	0.00362507i
$885$	8.58257	+	14.8655i	0.288500	+	0.499697i
$886$	−20.8080			−0.699060
$887$	31.2969	−	26.2612i	1.05085	−	0.881764i	0.0576637	−	0.998336i	$-0.481635\pi$
$887$	31.2969	−	26.2612i	1.05085	−	0.881764i	0.993182	+	0.116572i	$0.0371904\pi$
$888$	−0.0400514	−	0.0336071i	−0.00134404	−	0.00112778i
$889$	−7.04186	−	32.3684i	−0.236176	−	1.08560i
$890$	−7.10980	+	40.3217i	−0.238321	+	1.35159i
$891$	2.06181	+	1.73006i	0.0690732	+	0.0579593i
$892$	−0.438536	+	0.759566i	−0.0146833	+	0.0254322i
$893$	38.3572	−	3.66926i	1.28358	−	0.122787i
$894$	8.86913	+	15.3618i	0.296628	+	0.513775i
$895$	69.7591	−	25.3902i	2.33179	−	0.848702i
$896$	−0.355701	+	2.62173i	−0.0118831	+	0.0875859i
$897$	−9.69282	+	8.13324i	−0.323634	+	0.271561i
$898$	5.04745	−	28.6255i	0.168436	−	0.955246i
$899$	−2.78923	−	1.01520i	−0.0930262	−	0.0338588i
$900$	5.15775			0.171925
$901$	0.761568			0.0253715
$902$	21.0586	+	7.66469i	0.701174	+	0.255206i
$903$	−0.00309935	−	0.0142464i	−0.000103140	−	0.000474090i
$904$	−1.24859	+	2.16263i	−0.0415276	+	0.0719279i
$905$	20.2163	−	35.0157i	0.672012	−	1.16396i
$906$	−15.1862	−	5.52734i	−0.504529	−	0.183634i
$907$	7.47018	−	2.71892i	0.248043	−	0.0902803i	−0.215007	−	0.976613i	$-0.568977\pi$
$907$	7.47018	−	2.71892i	0.248043	−	0.0902803i	0.463050	+	0.886332i	$0.346755\pi$
$908$	−23.7818	−	8.65587i	−0.789227	−	0.287255i
$909$	−1.33143	+	7.55091i	−0.0441607	+	0.250448i
$910$	11.0331	+	8.53549i	0.365745	+	0.282949i
$911$	−1.22323			−0.0405275			−0.0202637	−	0.999795i	$-0.506451\pi$
$911$	−1.22323			−0.0405275			−0.0202637	+	0.999795i	$0.506451\pi$
$912$	1.81008	−	3.96530i	0.0599376	−	0.131304i
$913$	−0.912573	+	1.58062i	−0.0302018	+	0.0523110i
$914$	−2.61612	+	14.8368i	−0.0865337	+	0.490757i
$915$	−16.3592	+	5.95426i	−0.540818	+	0.196842i
$916$	−0.624106	+	0.523687i	−0.0206211	+	0.0173031i
$917$	−27.9889	−	21.6528i	−0.924273	−	0.715039i
$918$	−0.0114883	−	0.0651533i	−0.000379170	−	0.00215038i
$919$	−8.82242	+	15.2809i	−0.291025	+	0.504070i	−0.974052	−	0.226323i	$-0.927330\pi$
$919$	−8.82242	+	15.2809i	−0.291025	+	0.504070i	0.683028	+	0.730393i	$0.260663\pi$
$920$	12.1887	+	21.1115i	0.401851	+	0.696026i
$921$	10.8956	−	9.14250i	0.359022	−	0.301255i
$922$	−6.33755	−	35.9420i	−0.208716	−	1.18369i
$923$	8.30545	−	14.3855i	0.273377	−	0.473503i
$924$	7.11543	−	0.282506i	0.234081	−	0.00929375i
$925$	0.0468268	+	0.265568i	0.00153966	+	0.00873182i
$926$	6.22686	−	35.3143i	0.204627	−	1.16050i
$927$	0.0474625	+	0.269173i	0.00155887	+	0.00884081i
$928$	6.29787	+	5.28454i	0.206738	+	0.173474i
$929$	1.85779	+	1.55887i	0.0609523	+	0.0511450i	0.672755	−	0.739865i	$-0.265111\pi$
$929$	1.85779	+	1.55887i	0.0609523	+	0.0511450i	−0.611803	+	0.791010i	$0.709555\pi$
$930$	1.15069			0.0377326
$931$	−0.00615636	−	30.5123i	−0.000201766	−	1.00000i
$932$	0.279283			0.00914823
$933$	22.3975	+	18.7937i	0.733261	+	0.615279i
$934$	13.7519	+	11.5392i	0.449975	+	0.377574i
$935$	−0.0985481	−	0.558894i	−0.00322287	−	0.0182778i
$936$	0.287261	−	1.62914i	0.00938942	−	0.0532500i
$937$	5.85739	+	33.2189i	0.191353	+	1.08522i	0.917518	+	0.397695i	$0.130190\pi$
$937$	5.85739	+	33.2189i	0.191353	+	1.08522i	−0.726165	+	0.687520i	$0.758699\pi$
$938$	−6.05177	+	0.240275i	−0.197597	+	0.00784525i
$939$	−11.4879	+	19.8977i	−0.374895	+	0.649336i
$940$	−4.89235	−	27.7459i	−0.159571	−	0.904972i
$941$	20.4037	−	17.1207i	0.665142	−	0.558120i	−0.246481	−	0.969148i	$-0.579274\pi$
$941$	20.4037	−	17.1207i	0.665142	−	0.558120i	0.911623	+	0.411027i	$0.134830\pi$
$942$	−3.99607	−	6.92140i	−0.130199	−	0.225511i
$943$	31.8426	−	55.1530i	1.03694	−	1.79603i
$944$	−0.935231	−	5.30396i	−0.0304392	−	0.172629i
$945$	−6.66949	−	5.15967i	−0.216958	−	0.167844i
$946$	−0.0113618	+	0.00953365i	−0.000369403	+	0.000309966i
$947$	52.7625	−	19.2040i	1.71455	−	0.624045i	0.717206	−	0.696862i	$-0.245421\pi$
$947$	52.7625	−	19.2040i	1.71455	−	0.624045i	0.997345	+	0.0728162i	$0.0231986\pi$
$948$	−1.93468	+	10.9721i	−0.0628356	+	0.356358i
$949$	4.40955	−	7.63756i	0.143140	−	0.247926i
$950$	−20.2981	+	9.66616i	−0.658556	+	0.313612i
$951$	−14.7774			−0.479189
$952$	−0.138445	−	0.107105i	−0.00448704	−	0.00347128i
$953$	−0.0454608	+	0.257821i	−0.00147262	+	0.00835164i	−0.985535	−	0.169471i	$-0.945794\pi$
$953$	−0.0454608	+	0.257821i	−0.00147262	+	0.00835164i	0.984063	+	0.177822i	$0.0569053\pi$
$954$	−10.8171	−	3.93709i	−0.350216	−	0.127468i
$955$	30.2494	−	11.0099i	0.978847	−	0.356271i
$956$	−16.9499	−	6.16925i	−0.548198	−	0.199528i
$957$	11.0638	−	19.1631i	0.357642	−	0.619454i
$958$	12.5356	−	21.7122i	0.405006	−	0.701490i
$959$	−7.35148	−	33.7916i	−0.237392	−	1.09119i
$960$	−2.99492	−	1.09006i	−0.0966605	−	0.0351815i
$961$	−30.8696			−0.995795
$962$	0.0864908			0.00278858
$963$	−5.13038	−	1.86730i	−0.165324	−	0.0601730i
$964$	3.76341	−	21.3433i	0.121211	−	0.687423i
$965$	41.1750	−	34.5499i	1.32547	−	1.11220i
$966$	2.72066	−	20.0529i	0.0875359	−	0.645193i
$967$	−55.5662	+	20.2244i	−1.78689	+	0.650374i	−0.787467	+	0.616357i	$0.788608\pi$
$967$	−55.5662	+	20.2244i	−1.78689	+	0.650374i	−0.999421	+	0.0340165i	$0.989170\pi$
$968$	1.87791	+	3.25264i	0.0603585	+	0.104544i
$969$	0.167315	+	0.234877i	0.00537494	+	0.00754533i
$970$	0.841470	−	1.45747i	0.0270180	−	0.0467965i
$971$	−30.3105	−	25.4336i	−0.972712	−	0.816202i	0.0102623	−	0.999947i	$-0.496733\pi$
$971$	−30.3105	−	25.4336i	−0.972712	−	0.816202i	−0.982974	+	0.183745i	$0.941178\pi$
$972$	−0.173648	+	0.984808i	−0.00556977	+	0.0315877i
$973$	−12.9703	−	59.6191i	−0.415810	−	1.91130i
$974$	−12.8132	−	10.7516i	−0.410563	−	0.344503i
$975$	−6.53613	+	5.48447i	−0.209324	+	0.175644i
$976$	5.46232			0.174845
$977$	−5.43239	−	9.40917i	−0.173798	−	0.301026i	0.765947	−	0.642904i	$-0.222270\pi$
$977$	−5.43239	−	9.40917i	−0.173798	−	0.301026i	−0.939744	+	0.341878i	$0.888937\pi$
$978$	−0.0513331	−	0.291124i	−0.00164145	−	0.00930913i
$979$	−32.4914	−	11.8259i	−1.03843	−	0.377958i
$980$	−22.2396	+	1.76876i	−0.710419	+	0.0565009i
$981$	−4.92501	−	8.53037i	−0.157244	−	0.272354i
$982$	−9.08740	+	7.62524i	−0.289991	+	0.243331i
$983$	−31.4132	+	11.4335i	−1.00193	+	0.364671i	−0.790327	−	0.612686i	$-0.790089\pi$
$983$	−31.4132	+	11.4335i	−1.00193	+	0.364671i	−0.211598	+	0.977357i	$0.567867\pi$
$984$	1.44584	+	8.19974i	0.0460916	+	0.261398i
$985$	−33.6628	+	12.2523i	−1.07259	+	0.390390i
$986$	−0.511105	+	0.186027i	−0.0162769	+	0.00592431i
$987$	−10.8814	+	20.7028i	−0.346358	+	0.658977i
$988$	1.92267	+	6.94974i	0.0611683	+	0.221101i
$989$	0.0210745	+	0.0365021i	0.000670130	+	0.00116070i
$990$	−1.48958	+	8.44782i	−0.0473419	+	0.268489i
$991$	−18.4939	−	15.5182i	−0.587479	−	0.492953i	0.299915	−	0.953966i	$-0.403042\pi$
$991$	−18.4939	−	15.5182i	−0.587479	−	0.492953i	−0.887393	+	0.461013i	$0.847486\pi$
$992$	−0.339270	−	0.123484i	−0.0107718	−	0.00392062i
$993$	−2.72455	−	2.28617i	−0.0864611	−	0.0725495i
$994$	5.64754	+	25.9594i	0.179129	+	0.823381i
$995$	−10.9198	−	18.9136i	−0.346180	−	0.599601i
$996$	−0.678115			−0.0214869
$997$	−32.5228	+	27.2899i	−1.03001	+	0.864279i	−0.990852	−	0.134954i	$-0.956911\pi$
$997$	−32.5228	+	27.2899i	−1.03001	+	0.864279i	−0.0391562	+	0.999233i	$0.512467\pi$
$998$	−4.35596	+	3.65508i	−0.137886	+	0.115700i
$999$	−0.0522834			−0.00165417

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bp.f.613.2	yes	42
7.2	even	3		798.2.bq.e.499.6	yes	42
19.4	even	9		798.2.bq.e.403.6	yes	42
133.23	even	9	inner	798.2.bp.f.289.2	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bp.f.289.2	✓	42	133.23	even	9	inner
798.2.bp.f.613.2	yes	42	1.1	even	1	trivial
798.2.bq.e.403.6	yes	42	19.4	even	9
798.2.bq.e.499.6	yes	42	7.2	even	3

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bp (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.553438 + 3.13870i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-2.64367 + 0.104962i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.553438 + 3.13870i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-2.64367 + 0.104962i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-2.44148 + 2.04864i) q^{10} +(-1.34575 - 2.33091i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.287261 + 1.62914i) q^{13} +(-2.09264 - 1.61891i) q^{14} +(2.44148 - 2.04864i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.0114883 - 0.0651533i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.344703 - 4.34525i) q^{19} -3.18712 q^{20} +(2.09264 + 1.61891i) q^{21} +(0.467374 - 2.65061i) q^{22} +(-7.18746 - 2.61602i) q^{23} +(0.939693 - 0.342020i) q^{24} +(-4.84670 - 1.76406i) q^{25} +(-0.827135 + 1.43264i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.562436 - 2.58528i) q^{28} +(-7.72548 - 2.81185i) q^{29} +3.18712 q^{30} +0.361043 q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.467374 + 2.65061i) q^{33} +(0.0506802 - 0.0425258i) q^{34} +(1.13366 - 8.35578i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(-0.0261417 - 0.0452787i) q^{37} +(3.05713 - 3.10708i) q^{38} +(0.827135 - 1.43264i) q^{39} +(-2.44148 - 2.04864i) q^{40} +(-1.44584 + 8.19974i) q^{41} +(0.562436 + 2.58528i) q^{42} +(-0.00422135 - 0.00354213i) q^{43} +(2.06181 - 1.73006i) q^{44} -3.18712 q^{45} +(-3.82437 - 6.62400i) q^{46} +(1.53504 + 8.70563i) q^{47} +(0.939693 + 0.342020i) q^{48} +(6.97797 - 0.554970i) q^{49} +(-2.57888 - 4.46675i) q^{50} +(-0.0506802 + 0.0425258i) q^{51} +(-1.55451 + 0.565794i) q^{52} +(1.99891 + 11.3364i) q^{53} +(0.939693 - 0.342020i) q^{54} +(8.06082 - 2.93390i) q^{55} +(1.23093 - 2.34197i) q^{56} +(-3.05713 + 3.10708i) q^{57} +(-4.11064 - 7.11984i) q^{58} +(-0.935231 + 5.30396i) q^{59} +(2.44148 + 2.04864i) q^{60} +(-5.13290 - 1.86822i) q^{61} +(0.276575 + 0.232074i) q^{62} +(-0.562436 - 2.58528i) q^{63} +(-0.500000 - 0.866025i) q^{64} -5.27236 q^{65} +(-2.06181 + 1.73006i) q^{66} +(1.75360 - 1.47144i) q^{67} +0.0661583 q^{68} +(3.82437 + 6.62400i) q^{69} +(6.23943 - 5.67220i) q^{70} +(-7.69202 - 6.45437i) q^{71} +(-0.939693 - 0.342020i) q^{72} +(-4.08387 - 3.42677i) q^{73} +(0.00907891 - 0.0514891i) q^{74} +(2.57888 + 4.46675i) q^{75} +(4.33909 - 0.415078i) q^{76} +(3.80237 + 6.02089i) q^{77} +(1.55451 - 0.565794i) q^{78} +(-10.4695 + 3.81058i) q^{79} +(-0.553438 - 3.13870i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-6.37827 + 5.35200i) q^{82} +(-0.339057 - 0.587265i) q^{83} +(-1.23093 + 2.34197i) q^{84} +(0.198139 + 0.0721166i) q^{85} +(-0.000956903 - 0.00542686i) q^{86} +(4.11064 + 7.11984i) q^{87} +2.69150 q^{88} +(9.84107 - 8.25764i) q^{89} +(-2.44148 - 2.04864i) q^{90} +(-0.930421 - 4.27675i) q^{91} +(1.32819 - 7.53254i) q^{92} +(-0.276575 - 0.232074i) q^{93} +(-4.41996 + 7.65560i) q^{94} +(13.4477 + 3.48675i) q^{95} +(0.500000 + 0.866025i) q^{96} +(-0.496199 + 0.180602i) q^{97} +(5.70216 + 4.06022i) q^{98} +(2.06181 - 1.73006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 6 q^{5} - 21 q^{8}+O(q^{10}) \) 42 * q + 6 * q^5 - 21 * q^8	\( 42 q + 6 q^{5} - 21 q^{8} - 3 q^{10} - 9 q^{11} + 21 q^{12} - 24 q^{13} - 3 q^{14} + 3 q^{15} - 21 q^{18} + 18 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{22} + 15 q^{23} - 18 q^{25} + 9 q^{26} + 21 q^{27} - 12 q^{28} + 9 q^{29} + 6 q^{30} - 6 q^{31} + 3 q^{33} + 9 q^{34} + 12 q^{35} - 15 q^{37} + 9 q^{38} - 9 q^{39} - 3 q^{40} + 3 q^{41} + 12 q^{42} + 6 q^{44} - 6 q^{45} - 18 q^{46} + 15 q^{47} - 30 q^{50} - 9 q^{51} + 21 q^{52} + 12 q^{53} - 15 q^{55} - 9 q^{57} - 18 q^{58} + 6 q^{59} + 3 q^{60} - 3 q^{61} + 6 q^{62} - 12 q^{63} - 21 q^{64} + 72 q^{65} - 6 q^{66} + 3 q^{67} - 36 q^{68} + 18 q^{69} - 6 q^{70} + 12 q^{71} + 9 q^{73} + 12 q^{74} + 30 q^{75} + 51 q^{77} - 21 q^{78} - 51 q^{79} + 6 q^{80} + 12 q^{82} + 24 q^{83} - 6 q^{85} + 9 q^{86} + 18 q^{87} + 18 q^{88} + 12 q^{89} - 3 q^{90} + 6 q^{92} - 6 q^{93} + 30 q^{94} - 21 q^{95} + 21 q^{96} - 27 q^{97} + 36 q^{98} + 6 q^{99}+O(q^{100}) \) 42 * q + 6 * q^5 - 21 * q^8 - 3 * q^10 - 9 * q^11 + 21 * q^12 - 24 * q^13 - 3 * q^14 + 3 * q^15 - 21 * q^18 + 18 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^22 + 15 * q^23 - 18 * q^25 + 9 * q^26 + 21 * q^27 - 12 * q^28 + 9 * q^29 + 6 * q^30 - 6 * q^31 + 3 * q^33 + 9 * q^34 + 12 * q^35 - 15 * q^37 + 9 * q^38 - 9 * q^39 - 3 * q^40 + 3 * q^41 + 12 * q^42 + 6 * q^44 - 6 * q^45 - 18 * q^46 + 15 * q^47 - 30 * q^50 - 9 * q^51 + 21 * q^52 + 12 * q^53 - 15 * q^55 - 9 * q^57 - 18 * q^58 + 6 * q^59 + 3 * q^60 - 3 * q^61 + 6 * q^62 - 12 * q^63 - 21 * q^64 + 72 * q^65 - 6 * q^66 + 3 * q^67 - 36 * q^68 + 18 * q^69 - 6 * q^70 + 12 * q^71 + 9 * q^73 + 12 * q^74 + 30 * q^75 + 51 * q^77 - 21 * q^78 - 51 * q^79 + 6 * q^80 + 12 * q^82 + 24 * q^83 - 6 * q^85 + 9 * q^86 + 18 * q^87 + 18 * q^88 + 12 * q^89 - 3 * q^90 + 6 * q^92 - 6 * q^93 + 30 * q^94 - 21 * q^95 + 21 * q^96 - 27 * q^97 + 36 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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