LMFDB - Embedded newform 134.2.e.a.89.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [134,2,Mod(9,134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(134, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("134.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 134 = 2 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	134.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.06999538709$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			89.2
Character	$\chi$	$=$	134.89
Dual form			134.2.e.a.131.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 - 0.281733i) q^{2} +(0.187400 + 1.30339i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-1.59822 + 3.49961i) q^{5} +(0.547017 + 1.19780i) q^{6} +(-0.563661 + 0.165506i) q^{7} +(0.654861 - 0.755750i) q^{8} +(1.21477 - 0.356688i) q^{9} +O(q^{10})$	\(q+(0.959493 - 0.281733i) q^{2} +(0.187400 + 1.30339i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-1.59822 + 3.49961i) q^{5} +(0.547017 + 1.19780i) q^{6} +(-0.563661 + 0.165506i) q^{7} +(0.654861 - 0.755750i) q^{8} +(1.21477 - 0.356688i) q^{9} +(-0.547525 + 3.80812i) q^{10} +(2.56065 - 5.60704i) q^{11} +(0.862318 + 0.995168i) q^{12} +(-3.49705 - 4.03581i) q^{13} +(-0.494200 + 0.317603i) q^{14} +(-4.86087 - 1.42728i) q^{15} +(0.415415 - 0.909632i) q^{16} +(1.23862 + 0.796013i) q^{17} +(1.06507 - 0.684478i) q^{18} +(1.62746 + 0.477867i) q^{19} +(0.547525 + 3.80812i) q^{20} +(-0.321349 - 0.703656i) q^{21} +(0.877239 - 6.10133i) q^{22} +(0.981909 + 6.82933i) q^{23} +(1.10776 + 0.711913i) q^{24} +(-6.41865 - 7.40752i) q^{25} +(-4.49241 - 2.88710i) q^{26} +(2.33360 + 5.10987i) q^{27} +(-0.384703 + 0.443971i) q^{28} -3.91290 q^{29} -5.06608 q^{30} +(2.11922 - 2.44571i) q^{31} +(0.142315 - 0.989821i) q^{32} +(7.78804 + 2.28677i) q^{33} +(1.41271 + 0.414809i) q^{34} +(0.321647 - 2.23711i) q^{35} +(0.829086 - 0.956817i) q^{36} -11.3561 q^{37} +1.69617 q^{38} +(4.60490 - 5.31433i) q^{39} +(1.59822 + 3.49961i) q^{40} +(2.13476 + 1.37193i) q^{41} +(-0.506575 - 0.584618i) q^{42} +(-1.13816 - 0.731454i) q^{43} +(-0.877239 - 6.10133i) q^{44} +(-0.693194 + 4.82127i) q^{45} +(2.86618 + 6.27605i) q^{46} +(-0.490752 - 3.41325i) q^{47} +(1.26346 + 0.370984i) q^{48} +(-5.59845 + 3.59791i) q^{49} +(-8.24559 - 5.29912i) q^{50} +(-0.805401 + 1.76358i) q^{51} +(-5.12383 - 1.50449i) q^{52} +(3.87604 - 2.49098i) q^{53} +(3.67869 + 4.24543i) q^{54} +(15.5300 + 17.9225i) q^{55} +(-0.244039 + 0.534370i) q^{56} +(-0.317862 + 2.21078i) q^{57} +(-3.75440 + 1.10239i) q^{58} +(-0.879824 + 1.01537i) q^{59} +(-4.86087 + 1.42728i) q^{60} +(-2.07921 - 4.55283i) q^{61} +(1.34434 - 2.94369i) q^{62} +(-0.625683 + 0.402102i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(19.7128 - 5.78820i) q^{65} +8.11682 q^{66} +(-6.61753 - 4.81750i) q^{67} +1.47235 q^{68} +(-8.71728 + 2.55962i) q^{69} +(-0.321647 - 2.23711i) q^{70} +(9.82951 - 6.31704i) q^{71} +(0.525936 - 1.15164i) q^{72} +(0.674059 + 1.47598i) q^{73} +(-10.8961 + 3.19938i) q^{74} +(8.45206 - 9.75419i) q^{75} +(1.62746 - 0.477867i) q^{76} +(-0.515341 + 3.58427i) q^{77} +(2.92114 - 6.39641i) q^{78} +(5.18408 + 5.98275i) q^{79} +(2.51943 + 2.90758i) q^{80} +(-3.02764 + 1.94575i) q^{81} +(2.43480 + 0.714922i) q^{82} +(-2.12739 + 4.65834i) q^{83} +(-0.650761 - 0.418219i) q^{84} +(-4.76532 + 3.06249i) q^{85} +(-1.29813 - 0.381167i) q^{86} +(-0.733275 - 5.10004i) q^{87} +(-2.56065 - 5.60704i) q^{88} +(-2.09064 + 14.5407i) q^{89} +(0.693194 + 4.82127i) q^{90} +(2.63910 + 1.69605i) q^{91} +(4.51825 + 5.21433i) q^{92} +(3.58486 + 2.30385i) q^{93} +(-1.43250 - 3.13673i) q^{94} +(-4.27339 + 4.93175i) q^{95} +1.31680 q^{96} -2.16747 q^{97} +(-4.35803 + 5.02943i) q^{98} +(1.11063 - 7.72459i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{8} - 8 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 + q^6 + 3 * q^8 - 8 * q^9	\( 30 q + 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{8} - 8 q^{9} + 3 q^{10} + q^{11} - q^{12} - 11 q^{13} - 22 q^{14} + 18 q^{15} - 3 q^{16} - 8 q^{17} - 3 q^{18} + 16 q^{19} - 3 q^{20} - 27 q^{21} - q^{22} + 12 q^{24} + 2 q^{25} - 11 q^{26} + 14 q^{27} - 11 q^{28} + 26 q^{30} + 18 q^{31} + 3 q^{32} + 9 q^{33} - 14 q^{34} - 90 q^{35} - 8 q^{36} - 48 q^{37} + 28 q^{38} - q^{39} + 3 q^{40} - 51 q^{41} - 17 q^{42} + 10 q^{43} + q^{44} - 4 q^{45} - 11 q^{46} + 10 q^{47} + 10 q^{48} - 19 q^{49} - 24 q^{50} + 4 q^{51} + 11 q^{52} - 8 q^{53} - 25 q^{54} + 25 q^{55} + 31 q^{57} + 22 q^{58} + 66 q^{59} + 18 q^{60} + 34 q^{61} - 29 q^{62} + 80 q^{63} - 3 q^{64} + 26 q^{65} + 90 q^{66} - 3 q^{67} - 8 q^{68} - 46 q^{69} + 90 q^{70} + 39 q^{71} - 3 q^{72} + 78 q^{73} - 18 q^{74} - 11 q^{75} + 16 q^{76} + 73 q^{77} - 10 q^{78} + 34 q^{79} + 8 q^{80} - 134 q^{81} + 7 q^{82} - 11 q^{83} + 6 q^{84} - 31 q^{85} + q^{86} - 110 q^{87} - q^{88} - 30 q^{89} + 4 q^{90} + 14 q^{91} + 11 q^{92} - 13 q^{93} + 23 q^{94} - 39 q^{95} - 10 q^{96} + 24 q^{97} + 19 q^{98} - 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 + q^6 + 3 * q^8 - 8 * q^9 + 3 * q^10 + q^11 - q^12 - 11 * q^13 - 22 * q^14 + 18 * q^15 - 3 * q^16 - 8 * q^17 - 3 * q^18 + 16 * q^19 - 3 * q^20 - 27 * q^21 - q^22 + 12 * q^24 + 2 * q^25 - 11 * q^26 + 14 * q^27 - 11 * q^28 + 26 * q^30 + 18 * q^31 + 3 * q^32 + 9 * q^33 - 14 * q^34 - 90 * q^35 - 8 * q^36 - 48 * q^37 + 28 * q^38 - q^39 + 3 * q^40 - 51 * q^41 - 17 * q^42 + 10 * q^43 + q^44 - 4 * q^45 - 11 * q^46 + 10 * q^47 + 10 * q^48 - 19 * q^49 - 24 * q^50 + 4 * q^51 + 11 * q^52 - 8 * q^53 - 25 * q^54 + 25 * q^55 + 31 * q^57 + 22 * q^58 + 66 * q^59 + 18 * q^60 + 34 * q^61 - 29 * q^62 + 80 * q^63 - 3 * q^64 + 26 * q^65 + 90 * q^66 - 3 * q^67 - 8 * q^68 - 46 * q^69 + 90 * q^70 + 39 * q^71 - 3 * q^72 + 78 * q^73 - 18 * q^74 - 11 * q^75 + 16 * q^76 + 73 * q^77 - 10 * q^78 + 34 * q^79 + 8 * q^80 - 134 * q^81 + 7 * q^82 - 11 * q^83 + 6 * q^84 - 31 * q^85 + q^86 - 110 * q^87 - q^88 - 30 * q^89 + 4 * q^90 + 14 * q^91 + 11 * q^92 - 13 * q^93 + 23 * q^94 - 39 * q^95 - 10 * q^96 + 24 * q^97 + 19 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/134\mathbb{Z}\right)^\times$.

$n$	$69$
$\chi(n)$	$e\left(\frac{10}{11}\right)$

Coefficient data

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

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

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

$2$	0.959493	−	0.281733i	0.678464	−	0.199215i
$2$	0.959493	−	0.281733i	0.678464	−	0.199215i
$3$	0.187400	+	1.30339i	0.108195	+	0.752514i	0.969618	+	0.244625i	$0.0786649\pi$
$3$	0.187400	+	1.30339i	0.108195	+	0.752514i	−0.861423	+	0.507889i	$0.830426\pi$
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	−1.59822	+	3.49961i	−0.714745	+	1.56507i	0.106381	+	0.994325i	$0.466074\pi$
$5$	−1.59822	+	3.49961i	−0.714745	+	1.56507i	−0.821126	+	0.570747i	$0.806654\pi$
$6$	0.547017	+	1.19780i	0.223319	+	0.488999i
$7$	−0.563661	+	0.165506i	−0.213044	+	0.0625553i	−0.386513	−	0.922284i	$-0.626321\pi$
$7$	−0.563661	+	0.165506i	−0.213044	+	0.0625553i	0.173469	+	0.984839i	$0.444502\pi$
$8$	0.654861	−	0.755750i	0.231528	−	0.267198i
$9$	1.21477	−	0.356688i	0.404922	−	0.118896i
$10$	−0.547525	+	3.80812i	−0.173143	+	1.20423i
$11$	2.56065	−	5.60704i	0.772065	−	1.69059i	0.0500114	−	0.998749i	$-0.484074\pi$
$11$	2.56065	−	5.60704i	0.772065	−	1.69059i	0.722053	−	0.691837i	$-0.243198\pi$
$12$	0.862318	+	0.995168i	0.248930	+	0.287280i
$13$	−3.49705	−	4.03581i	−0.969906	−	1.11933i	−0.992823	−	0.119594i	$-0.961841\pi$
$13$	−3.49705	−	4.03581i	−0.969906	−	1.11933i	0.0229165	−	0.999737i	$-0.492705\pi$
$14$	−0.494200	+	0.317603i	−0.132081	+	0.0848831i
$15$	−4.86087	−	1.42728i	−1.25507	−	0.368522i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	1.23862	+	0.796013i	0.300410	+	0.193062i	0.682158	−	0.731205i	$-0.261042\pi$
$17$	1.23862	+	0.796013i	0.300410	+	0.193062i	−0.381748	+	0.924266i	$0.624678\pi$
$18$	1.06507	−	0.684478i	0.251039	−	0.161333i
$19$	1.62746	+	0.477867i	0.373366	+	0.109630i	0.463032	−	0.886342i	$-0.346762\pi$
$19$	1.62746	+	0.477867i	0.373366	+	0.109630i	−0.0896657	+	0.995972i	$0.528580\pi$
$20$	0.547525	+	3.80812i	0.122430	+	0.851521i
$21$	−0.321349	−	0.703656i	−0.0701241	−	0.153550i
$22$	0.877239	−	6.10133i	0.187028	−	1.30081i
$23$	0.981909	+	6.82933i	0.204742	+	1.42401i	0.789971	+	0.613144i	$0.210096\pi$
$23$	0.981909	+	6.82933i	0.204742	+	1.42401i	−0.585229	+	0.810868i	$0.698995\pi$
$24$	1.10776	+	0.711913i	0.226120	+	0.145319i
$25$	−6.41865	−	7.40752i	−1.28373	−	1.48150i
$26$	−4.49241	−	2.88710i	−0.881034	−	0.566206i
$27$	2.33360	+	5.10987i	0.449102	+	0.983395i
$28$	−0.384703	+	0.443971i	−0.0727020	+	0.0839025i
$29$	−3.91290			−0.726607			−0.363303	−	0.931671i	$-0.618351\pi$
$29$	−3.91290			−0.726607			−0.363303	+	0.931671i	$0.618351\pi$
$30$	−5.06608			−0.924935
$31$	2.11922	−	2.44571i	0.380623	−	0.439262i	−0.532820	−	0.846228i	$-0.678868\pi$
$31$	2.11922	−	2.44571i	0.380623	−	0.439262i	0.913443	+	0.406966i	$0.133413\pi$
$32$	0.142315	−	0.989821i	0.0251579	−	0.174977i
$33$	7.78804	+	2.28677i	1.35572	+	0.398076i
$34$	1.41271	+	0.414809i	0.242278	+	0.0711392i
$35$	0.321647	−	2.23711i	0.0543683	−	0.378140i
$36$	0.829086	−	0.956817i	0.138181	−	0.159469i
$37$	−11.3561			−1.86693			−0.933466	−	0.358666i	$-0.883232\pi$
$37$	−11.3561			−1.86693			−0.933466	+	0.358666i	$0.883232\pi$
$38$	1.69617			0.275155
$39$	4.60490	−	5.31433i	0.737373	−	0.850974i
$40$	1.59822	+	3.49961i	0.252700	+	0.553337i
$41$	2.13476	+	1.37193i	0.333393	+	0.214259i	0.696617	−	0.717443i	$-0.254688\pi$
$41$	2.13476	+	1.37193i	0.333393	+	0.214259i	−0.363224	+	0.931702i	$0.618324\pi$
$42$	−0.506575	−	0.584618i	−0.0781662	−	0.0902086i
$43$	−1.13816	−	0.731454i	−0.173568	−	0.111546i	0.450972	−	0.892538i	$-0.351077\pi$
$43$	−1.13816	−	0.731454i	−0.173568	−	0.111546i	−0.624541	+	0.780992i	$0.714714\pi$
$44$	−0.877239	−	6.10133i	−0.132249	−	0.919811i
$45$	−0.693194	+	4.82127i	−0.103335	+	0.718712i
$46$	2.86618	+	6.27605i	0.422595	+	0.925354i
$47$	−0.490752	−	3.41325i	−0.0715835	−	0.497874i	−0.993798	−	0.111197i	$-0.964532\pi$
$47$	−0.490752	−	3.41325i	−0.0715835	−	0.497874i	0.922215	−	0.386678i	$-0.126377\pi$
$48$	1.26346	+	0.370984i	0.182364	+	0.0535469i
$49$	−5.59845	+	3.59791i	−0.799779	+	0.513987i
$50$	−8.24559	−	5.29912i	−1.16610	−	0.749409i
$51$	−0.805401	+	1.76358i	−0.112779	+	0.246951i
$52$	−5.12383	−	1.50449i	−0.710547	−	0.208635i
$53$	3.87604	−	2.49098i	0.532415	−	0.342163i	−0.246651	−	0.969104i	$-0.579330\pi$
$53$	3.87604	−	2.49098i	0.532415	−	0.342163i	0.779066	+	0.626942i	$0.215694\pi$
$54$	3.67869	+	4.24543i	0.500606	+	0.577730i
$55$	15.5300	+	17.9225i	2.09406	+	2.41667i
$56$	−0.244039	+	0.534370i	−0.0326110	+	0.0714082i
$57$	−0.317862	+	2.21078i	−0.0421018	+	0.292824i
$58$	−3.75440	+	1.10239i	−0.492976	+	0.144751i
$59$	−0.879824	+	1.01537i	−0.114543	+	0.132190i	−0.810125	−	0.586257i	$-0.800601\pi$
$59$	−0.879824	+	1.01537i	−0.114543	+	0.132190i	0.695582	+	0.718447i	$0.255147\pi$
$60$	−4.86087	+	1.42728i	−0.627535	+	0.184261i
$61$	−2.07921	−	4.55283i	−0.266215	−	0.582930i	0.728564	−	0.684977i	$-0.240188\pi$
$61$	−2.07921	−	4.55283i	−0.266215	−	0.582930i	−0.994780	+	0.102047i	$0.967461\pi$
$62$	1.34434	−	2.94369i	0.170731	−	0.373849i
$63$	−0.625683	+	0.402102i	−0.0788286	+	0.0506601i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	19.7128	−	5.78820i	2.44507	−	0.717937i
$66$	8.11682			0.999112
$67$	−6.61753	−	4.81750i	−0.808460	−	0.588551i
$67$	−6.61753	−	4.81750i	−0.808460	−	0.588551i
$68$	1.47235			0.178549
$69$	−8.71728	+	2.55962i	−1.04944	+	0.308143i
$70$	−0.321647	−	2.23711i	−0.0384442	−	0.267385i
$71$	9.82951	−	6.31704i	1.16655	−	0.749695i	0.193682	−	0.981064i	$-0.437957\pi$
$71$	9.82951	−	6.31704i	1.16655	−	0.749695i	0.972866	+	0.231370i	$0.0743207\pi$
$72$	0.525936	−	1.15164i	0.0619822	−	0.135722i
$73$	0.674059	+	1.47598i	0.0788927	+	0.172751i	0.944968	−	0.327162i	$-0.106092\pi$
$73$	0.674059	+	1.47598i	0.0788927	+	0.172751i	−0.866075	+	0.499913i	$0.833365\pi$
$74$	−10.8961	+	3.19938i	−1.26665	+	0.371921i
$75$	8.45206	−	9.75419i	0.975959	−	1.12632i
$76$	1.62746	−	0.477867i	0.186683	−	0.0548151i
$77$	−0.515341	+	3.58427i	−0.0587285	+	0.408466i
$78$	2.92114	−	6.39641i	0.330754	−	0.724251i
$79$	5.18408	+	5.98275i	0.583255	+	0.673112i	0.968301	−	0.249785i	$-0.0803600\pi$
$79$	5.18408	+	5.98275i	0.583255	+	0.673112i	−0.385046	+	0.922897i	$0.625815\pi$
$80$	2.51943	+	2.90758i	0.281681	+	0.325077i
$81$	−3.02764	+	1.94575i	−0.336405	+	0.216194i
$82$	2.43480	+	0.714922i	0.268879	+	0.0789499i
$83$	−2.12739	+	4.65834i	−0.233512	+	0.511319i	−0.989721	−	0.143010i	$-0.954322\pi$
$83$	−2.12739	+	4.65834i	−0.233512	+	0.511319i	0.756209	+	0.654330i	$0.227049\pi$
$84$	−0.650761	−	0.418219i	−0.0710038	−	0.0456314i
$85$	−4.76532	+	3.06249i	−0.516872	+	0.332173i
$86$	−1.29813	−	0.381167i	−0.139981	−	0.0411023i
$87$	−0.733275	−	5.10004i	−0.0786153	−	0.546782i
$88$	−2.56065	−	5.60704i	−0.272966	−	0.597712i
$89$	−2.09064	+	14.5407i	−0.221607	+	1.54131i	0.510354	+	0.859964i	$0.329514\pi$
$89$	−2.09064	+	14.5407i	−0.221607	+	1.54131i	−0.731961	+	0.681346i	$0.761395\pi$
$90$	0.693194	+	4.82127i	0.0730691	+	0.508206i
$91$	2.63910	+	1.69605i	0.276653	+	0.177794i
$92$	4.51825	+	5.21433i	0.471060	+	0.543632i
$93$	3.58486	+	2.30385i	0.371732	+	0.238898i
$94$	−1.43250	−	3.13673i	−0.147751	−	0.323529i
$95$	−4.27339	+	4.93175i	−0.438440	+	0.505987i
$96$	1.31680			0.134395
$97$	−2.16747			−0.220073			−0.110036	−	0.993928i	$-0.535097\pi$
$97$	−2.16747			−0.220073			−0.110036	+	0.993928i	$0.535097\pi$
$98$	−4.35803	+	5.02943i	−0.440227	+	0.508049i
$99$	1.11063	−	7.72459i	0.111622	−	0.776351i
$100$	−9.40453	−	2.76142i	−0.940453	−	0.276142i
$101$	−7.38338	−	2.16795i	−0.734673	−	0.215720i	−0.107069	−	0.994252i	$-0.534146\pi$
$101$	−7.38338	−	2.16795i	−0.734673	−	0.215720i	−0.627605	+	0.778532i	$0.715965\pi$
$102$	−0.275918	+	1.91905i	−0.0273199	+	0.190014i
$103$	0.648831	−	0.748791i	0.0639312	−	0.0737806i	−0.722883	−	0.690970i	$-0.757183\pi$
$103$	0.648831	−	0.748791i	0.0639312	−	0.0737806i	0.786814	+	0.617190i	$0.211729\pi$
$104$	−5.34014			−0.523644
$105$	2.97610			0.290438
$106$	3.01724	−	3.48209i	0.293061	−	0.338210i
$107$	2.43028	+	5.32157i	0.234944	+	0.514455i	0.989977	−	0.141232i	$-0.0451063\pi$
$107$	2.43028	+	5.32157i	0.234944	+	0.514455i	−0.755033	+	0.655687i	$0.772379\pi$
$108$	4.72575	+	3.03706i	0.454736	+	0.292241i
$109$	6.64555	+	7.66937i	0.636528	+	0.734593i	0.978757	−	0.205024i	$-0.0657272\pi$
$109$	6.64555	+	7.66937i	0.636528	+	0.734593i	−0.342229	+	0.939617i	$0.611182\pi$
$110$	19.9503	+	12.8213i	1.90218	+	1.22246i
$111$	−2.12813	−	14.8015i	−0.201993	−	1.40489i
$112$	−0.0836039	+	0.581478i	−0.00789982	+	0.0549445i
$113$	2.59620	+	5.68489i	0.244230	+	0.534790i	0.991558	−	0.129666i	$-0.0413906\pi$
$113$	2.59620	+	5.68489i	0.244230	+	0.534790i	−0.747327	+	0.664456i	$0.768663\pi$
$114$	0.317862	+	2.21078i	0.0297705	+	0.207058i
$115$	−25.4693	−	7.47845i	−2.37502	−	0.697369i
$116$	−3.29174	+	2.11547i	−0.305630	+	0.196417i
$117$	−5.68762	−	3.65521i	−0.525820	−	0.337924i
$118$	−0.558122	+	1.22212i	−0.0513793	+	0.112505i
$119$	−0.829907	−	0.243683i	−0.0760775	−	0.0223384i
$120$	−4.26186	+	2.73893i	−0.389053	+	0.250029i
$121$	−17.6785	−	20.4021i	−1.60714	−	1.85473i
$122$	−3.27766	−	3.78263i	−0.296746	−	0.342463i
$123$	−1.38810	+	3.03952i	−0.125161	+	0.274065i
$124$	0.460550	−	3.20320i	0.0413586	−	0.287655i
$125$	17.7246	−	5.20443i	1.58534	−	0.465498i
$126$	−0.487053	+	0.562089i	−0.0433901	+	0.0500749i
$127$	6.79829	−	1.99616i	0.603251	−	0.177131i	0.0341757	−	0.999416i	$-0.489119\pi$
$127$	6.79829	−	1.99616i	0.603251	−	0.177131i	0.569075	+	0.822285i	$0.307301\pi$
$128$	−0.415415	−	0.909632i	−0.0367178	−	0.0804009i
$129$	0.740080	−	1.62055i	0.0651604	−	0.142681i
$130$	17.2836	−	11.1075i	1.51587	−	0.974189i
$131$	−0.447968	−	3.11569i	−0.0391392	−	0.272219i	0.960849	−	0.277072i	$-0.0893642\pi$
$131$	−0.447968	−	3.11569i	−0.0391392	−	0.272219i	−0.999988	+	0.00485344i	$0.998455\pi$
$132$	7.78804	−	2.28677i	0.677862	−	0.199038i
$133$	−0.996428			−0.0864012
$134$	−7.70672	−	2.75798i	−0.665759	−	0.238253i
$135$	−21.6121			−1.86008
$136$	1.41271	−	0.414809i	0.121139	−	0.0355696i
$137$	−1.94473	−	13.5259i	−0.166149	−	1.15559i	−0.886752	−	0.462245i	$-0.847044\pi$
$137$	−1.94473	−	13.5259i	−0.166149	−	1.15559i	0.720603	−	0.693348i	$-0.243865\pi$
$138$	−7.64304	+	4.91188i	−0.650619	+	0.418127i
$139$	5.52236	−	12.0923i	0.468400	−	1.02565i	−0.517092	−	0.855930i	$-0.672985\pi$
$139$	5.52236	−	12.0923i	0.468400	−	1.02565i	0.985492	−	0.169723i	$-0.0542874\pi$
$140$	−0.938884	−	2.05587i	−0.0793502	−	0.173753i
$141$	4.35684	−	1.27928i	0.366912	−	0.107735i
$142$	7.65163	−	8.83045i	0.642110	−	0.741035i
$143$	−31.5836	+	9.27379i	−2.64116	+	0.775514i
$144$	0.180178	−	1.25316i	0.0150148	−	0.104430i
$145$	6.25366	−	13.6936i	0.519338	−	1.13719i
$146$	1.06259	+	1.22629i	0.0879404	+	0.101489i
$147$	−5.73863	−	6.62273i	−0.473314	−	0.546234i
$148$	−9.55336	+	6.13957i	−0.785282	+	0.504670i
$149$	8.35770	+	2.45404i	0.684690	+	0.201043i	0.605534	−	0.795819i	$-0.292959\pi$
$149$	8.35770	+	2.45404i	0.684690	+	0.201043i	0.0791554	+	0.996862i	$0.474778\pi$
$150$	5.36161	−	11.7403i	0.437774	−	0.958591i
$151$	0.993674	+	0.638596i	0.0808641	+	0.0519682i	0.580448	−	0.814297i	$-0.302877\pi$
$151$	0.993674	+	0.638596i	0.0808641	+	0.0519682i	−0.499584	+	0.866265i	$0.666514\pi$
$152$	1.42691	−	0.917019i	0.115738	−	0.0743801i
$153$	1.78856	+	0.525169i	0.144597	+	0.0424574i
$154$	0.515341	+	3.58427i	0.0415273	+	0.288829i
$155$	5.17205	+	11.3252i	0.415429	+	0.909662i
$156$	1.00074	−	6.96030i	0.0801233	−	0.557270i
$157$	2.46070	+	17.1145i	0.196385	+	1.36589i	0.814666	+	0.579930i	$0.196920\pi$
$157$	2.46070	+	17.1145i	0.196385	+	1.36589i	−0.618281	+	0.785957i	$0.712171\pi$
$158$	6.65963	+	4.27988i	0.529811	+	0.340489i
$159$	3.97309	+	4.58519i	0.315087	+	0.363630i
$160$	3.23654	+	2.08000i	0.255871	+	0.164438i
$161$	−1.68376	−	3.68691i	−0.132699	−	0.290569i
$162$	−2.35682	+	2.71992i	−0.185169	+	0.213697i
$163$	−6.18853			−0.484723			−0.242362	−	0.970186i	$-0.577922\pi$
$163$	−6.18853			−0.484723			−0.242362	+	0.970186i	$0.577922\pi$
$164$	2.53759			0.198153
$165$	−20.4498	+	23.6003i	−1.59201	+	1.83728i
$166$	−0.728812	+	5.06900i	−0.0565668	+	0.393431i
$167$	12.1546	+	3.56892i	0.940552	+	0.276171i	0.715848	−	0.698256i	$-0.246040\pi$
$167$	12.1546	+	3.56892i	0.940552	+	0.276171i	0.224704	+	0.974427i	$0.427858\pi$
$168$	−0.742226	−	0.217937i	−0.0572640	−	0.0168142i
$169$	−2.20831	+	15.3591i	−0.169870	+	1.18147i
$170$	−3.70949	+	4.28098i	−0.284505	+	0.328336i
$171$	2.14744			0.164219
$172$	−1.35294			−0.103161
$173$	−9.82101	+	11.3341i	−0.746678	+	0.861712i	−0.994242	−	0.107160i	$-0.965824\pi$
$173$	−9.82101	+	11.3341i	−0.746678	+	0.861712i	0.247564	+	0.968872i	$0.420370\pi$
$174$	−2.14042	−	4.68686i	−0.162265	−	0.355310i
$175$	4.84393	+	3.11301i	0.366167	+	0.235321i
$176$	−4.03661	−	4.65850i	−0.304271	−	0.351147i
$177$	−1.48831	−	0.956476i	−0.111868	−	0.0718931i
$178$	2.09064	+	14.5407i	0.156700	+	1.08987i
$179$	−0.824455	+	5.73421i	−0.0616227	+	0.428595i	0.935534	+	0.353237i	$0.114919\pi$
$179$	−0.824455	+	5.73421i	−0.0616227	+	0.428595i	−0.997157	+	0.0753581i	$0.975990\pi$
$180$	2.02342	+	4.43068i	0.150817	+	0.330243i
$181$	0.337969	+	2.35062i	0.0251210	+	0.174720i	0.998519	−	0.0543993i	$-0.0173244\pi$
$181$	0.337969	+	2.35062i	0.0251210	+	0.174720i	−0.973398	+	0.229120i	$0.926415\pi$
$182$	3.01003	+	0.883824i	0.223118	+	0.0655134i
$183$	5.54448	−	3.56322i	0.409860	−	0.263401i
$184$	5.80427	+	3.73018i	0.427897	+	0.274993i
$185$	18.1495	−	39.7419i	1.33438	−	2.92188i
$186$	4.08871	+	1.20055i	0.299799	+	0.0880289i
$187$	7.63495	−	4.90668i	0.558323	−	0.358812i
$188$	−2.25819	−	2.60609i	−0.164696	−	0.190069i
$189$	−2.16107	−	2.49401i	−0.157195	−	0.181413i
$190$	−2.71085	+	5.93593i	−0.196666	+	0.430638i
$191$	0.312309	−	2.17216i	0.0225979	−	0.157172i	−0.975398	−	0.220451i	$-0.929247\pi$
$191$	0.312309	−	2.17216i	0.0225979	−	0.157172i	0.997996	+	0.0632797i	$0.0201560\pi$
$192$	1.26346	−	0.370984i	0.0911821	−	0.0267735i
$193$	14.8329	−	17.1180i	1.06769	−	1.23218i	0.0961386	−	0.995368i	$-0.469351\pi$
$193$	14.8329	−	17.1180i	1.06769	−	1.23218i	0.971555	−	0.236816i	$-0.0761037\pi$
$194$	−2.07967	+	0.610646i	−0.149312	+	0.0438418i
$195$	11.2385	+	24.6088i	0.804803	+	1.76227i
$196$	−2.76454	+	6.05350i	−0.197467	+	0.432393i
$197$	11.2732	−	7.24484i	0.803182	−	0.516174i	−0.0734709	−	0.997297i	$-0.523408\pi$
$197$	11.2732	−	7.24484i	0.803182	−	0.516174i	0.876653	+	0.481124i	$0.159771\pi$
$198$	−1.11063	−	7.72459i	−0.0789290	−	0.548963i
$199$	−8.57103	+	2.51668i	−0.607584	+	0.178403i	−0.571030	−	0.820929i	$-0.693456\pi$
$199$	−8.57103	+	2.51668i	−0.607584	+	0.178403i	−0.0365536	+	0.999332i	$0.511638\pi$
$200$	−9.80156			−0.693075
$201$	5.03897	−	9.52803i	0.355421	−	0.672056i
$202$	−7.69508			−0.541424
$203$	2.20555	−	0.647607i	0.154799	−	0.0454531i
$204$	0.275918	+	1.91905i	0.0193181	+	0.134360i
$205$	−8.21301	+	5.27818i	−0.573621	+	0.368644i
$206$	0.411590	−	0.901257i	0.0286768	−	0.0627935i
$207$	3.62872	+	7.94580i	0.252214	+	0.552271i
$208$	−5.12383	+	1.50449i	−0.355273	+	0.104318i
$209$	6.84678	−	7.90161i	0.473602	−	0.546566i
$210$	2.85555	−	0.838466i	0.197052	−	0.0578596i
$211$	−2.34783	+	16.3295i	−0.161631	+	1.12417i	0.733928	+	0.679227i	$0.237685\pi$
$211$	−2.34783	+	16.3295i	−0.161631	+	1.12417i	−0.895559	+	0.444943i	$0.853224\pi$
$212$	1.91401	−	4.19109i	0.131455	−	0.287845i
$213$	10.0756	+	11.6279i	0.690371	+	0.796730i
$214$	3.83109	+	4.42132i	0.261888	+	0.302235i
$215$	4.37884	−	2.81411i	0.298634	−	0.191920i
$216$	5.38997	+	1.58264i	0.366741	+	0.107685i
$217$	−0.789742	+	1.72929i	−0.0536112	+	0.117392i
$218$	8.53707	+	5.48644i	0.578203	+	0.371589i
$219$	−1.79747	+	1.15516i	−0.121462	+	0.0780587i
$220$	22.7543	+	6.68126i	1.53409	+	0.450451i
$221$	−1.11896	−	7.78253i	−0.0752693	−	0.523510i
$222$	−6.21198	−	13.6023i	−0.416921	−	0.912929i
$223$	−1.14674	+	7.97574i	−0.0767912	+	0.534095i	0.914721	+	0.404085i	$0.132410\pi$
$223$	−1.14674	+	7.97574i	−0.0767912	+	0.534095i	−0.991513	+	0.130010i	$0.958499\pi$
$224$	0.0836039	+	0.581478i	0.00558602	+	0.0388516i
$225$	−10.4393	−	6.70895i	−0.695956	−	0.447264i
$226$	4.09266	+	4.72318i	0.272240	+	0.314181i
$227$	18.9570	+	12.1830i	1.25822	+	0.808611i	0.988040	−	0.154198i	$-0.0492793\pi$
$227$	18.9570	+	12.1830i	1.25822	+	0.808611i	0.270183	+	0.962809i	$0.412916\pi$
$228$	0.927834	+	2.03167i	0.0614473	+	0.134551i
$229$	15.0957	−	17.4214i	0.997555	−	1.15124i	0.00906372	−	0.999959i	$-0.497115\pi$
$229$	15.0957	−	17.4214i	0.997555	−	1.15124i	0.988491	−	0.151280i	$-0.0483397\pi$
$230$	−26.5445			−1.75029
$231$	−4.76829			−0.313730
$232$	−2.56240	+	2.95717i	−0.168230	+	0.194148i
$233$	−2.40789	+	16.7473i	−0.157746	+	1.09715i	0.745027	+	0.667034i	$0.232436\pi$
$233$	−2.40789	+	16.7473i	−0.157746	+	1.09715i	−0.902774	+	0.430116i	$0.858473\pi$
$234$	−6.48702	−	1.90476i	−0.424070	−	0.124518i
$235$	12.7294	+	3.73768i	0.830373	+	0.243820i
$236$	−0.191204	+	1.32985i	−0.0124463	+	0.0865661i
$237$	−6.82638	+	7.87806i	−0.443421	+	0.511735i
$238$	−0.864943			−0.0560660
$239$	−16.7535			−1.08369			−0.541846	−	0.840478i	$-0.682274\pi$
$239$	−16.7535			−1.08369			−0.541846	+	0.840478i	$0.682274\pi$
$240$	−3.31758	+	3.82869i	−0.214149	+	0.247141i
$241$	0.798551	+	1.74858i	0.0514392	+	0.112636i	0.933606	−	0.358300i	$-0.116644\pi$
$241$	0.798551	+	1.74858i	0.0514392	+	0.112636i	−0.882167	+	0.470936i	$0.843916\pi$
$242$	−22.7103	−	14.5950i	−1.45987	−	0.938205i
$243$	7.93262	+	9.15473i	0.508878	+	0.587276i
$244$	−4.21058	−	2.70598i	−0.269555	−	0.173233i
$245$	−3.64372	−	25.3426i	−0.232789	−	1.61908i
$246$	−0.475543	+	3.30748i	−0.0303195	+	0.210877i
$247$	−3.76274	−	8.23925i	−0.239417	−	0.524251i
$248$	−0.460550	−	3.20320i	−0.0292450	−	0.203403i
$249$	−6.47032	−	1.89986i	−0.410040	−	0.120399i
$250$	15.5404	−	9.98722i	0.982862	−	0.631647i
$251$	−12.1831	−	7.82959i	−0.768989	−	0.494199i	0.0963740	−	0.995345i	$-0.469276\pi$
$251$	−12.1831	−	7.82959i	−0.768989	−	0.494199i	−0.865363	+	0.501146i	$0.832912\pi$
$252$	−0.308965	+	0.676539i	−0.0194630	+	0.0426180i
$253$	40.8066	+	11.9819i	2.56549	+	0.753296i
$254$	5.96053	−	3.83060i	0.373997	−	0.240353i
$255$	−4.88464	−	5.63717i	−0.305888	−	0.353013i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−8.33449	+	18.2500i	−0.519891	+	1.13840i	0.449589	+	0.893235i	$0.351570\pi$
$257$	−8.33449	+	18.2500i	−0.519891	+	1.13840i	−0.969481	+	0.245168i	$0.921157\pi$
$258$	0.253540	−	1.76341i	0.0157847	−	0.109785i
$259$	6.40099	−	1.87950i	0.397738	−	0.116787i
$260$	13.4541	−	15.5269i	0.834389	−	0.962936i
$261$	−4.75325	+	1.39568i	−0.294219	+	0.0863905i
$262$	−1.30761	−	2.86327i	−0.0807846	−	0.176894i
$263$	−1.83482	+	4.01769i	−0.113140	+	0.247742i	−0.957728	−	0.287674i	$-0.907118\pi$
$263$	−1.83482	+	4.01769i	−0.113140	+	0.247742i	0.844588	+	0.535416i	$0.179845\pi$
$264$	6.82831	−	4.38829i	0.420253	−	0.270080i
$265$	2.52270	+	17.5458i	0.154968	+	1.07783i
$266$	−0.956065	+	0.280726i	−0.0586201	+	0.0172124i
$267$	−19.3440			−1.18383
$268$	−8.17156	−	0.475031i	−0.499157	−	0.0290171i
$269$	−9.58439			−0.584370			−0.292185	−	0.956362i	$-0.594382\pi$
$269$	−9.58439			−0.584370			−0.292185	+	0.956362i	$0.594382\pi$
$270$	−20.7367	+	6.08885i	−1.26200	+	0.370555i
$271$	−4.36497	−	30.3590i	−0.265153	−	1.84418i	−0.492432	−	0.870351i	$-0.663892\pi$
$271$	−4.36497	−	30.3590i	−0.265153	−	1.84418i	0.227279	−	0.973830i	$-0.427017\pi$
$272$	1.23862	−	0.796013i	0.0751024	−	0.0482654i
$273$	−1.71605	+	3.75762i	−0.103860	+	0.227421i
$274$	−5.67663	−	12.4301i	−0.342938	−	0.750929i
$275$	−57.9702	+	17.0216i	−3.49573	+	1.02644i
$276$	−5.94961	+	6.86621i	−0.358124	+	0.413297i
$277$	16.2798	−	4.78019i	0.978161	−	0.287214i	0.246696	−	0.969093i	$-0.420655\pi$
$277$	16.2798	−	4.78019i	0.978161	−	0.287214i	0.731465	+	0.681879i	$0.238837\pi$
$278$	1.89188	−	13.1583i	0.113467	−	0.789181i
$279$	1.70200	−	3.72686i	0.101896	−	0.223121i
$280$	−1.48006	−	1.70808i	−0.0884504	−	0.102077i
$281$	17.3124	+	19.9796i	1.03277	+	1.19188i	0.981156	+	0.193215i	$0.0618915\pi$
$281$	17.3124	+	19.9796i	1.03277	+	1.19188i	0.0516153	+	0.998667i	$0.483563\pi$
$282$	3.81994	−	2.45493i	0.227474	−	0.146189i
$283$	−4.29467	−	1.26103i	−0.255292	−	0.0749604i	0.151582	−	0.988445i	$-0.451563\pi$
$283$	−4.29467	−	1.26103i	−0.255292	−	0.0749604i	−0.406874	+	0.913484i	$0.633381\pi$
$284$	4.85386	−	10.6285i	0.288023	−	0.630683i
$285$	−7.22884	−	4.64569i	−0.428199	−	0.275187i
$286$	−27.6916	+	17.7963i	−1.63744	+	1.05232i
$287$	−1.43034	−	0.419986i	−0.0844304	−	0.0247910i
$288$	−0.180178	−	1.25316i	−0.0106171	−	0.0738434i
$289$	−6.16151	−	13.4918i	−0.362442	−	0.793637i
$290$	2.14241	−	14.9008i	0.125807	−	0.875004i
$291$	−0.406182	−	2.82506i	−0.0238108	−	0.165608i
$292$	1.36503	+	0.877253i	0.0798825	+	0.0513373i
$293$	−11.6961	−	13.4981i	−0.683296	−	0.788566i	0.303099	−	0.952959i	$-0.401979\pi$
$293$	−11.6961	−	13.4981i	−0.683296	−	0.788566i	−0.986395	+	0.164393i	$0.947433\pi$
$294$	−7.37202	−	4.73771i	−0.429945	−	0.276309i
$295$	−2.14725	−	4.70182i	−0.125018	−	0.273751i
$296$	−7.43667	+	8.58237i	−0.432247	+	0.498840i
$297$	34.6268			2.00925
$298$	8.71054			0.504588
$299$	24.1281	−	27.8453i	1.39536	−	1.61033i
$300$	1.83681	−	12.7753i	0.106048	−	0.737581i
$301$	0.762599	+	0.223919i	0.0439555	+	0.0129065i
$302$	1.13334	+	0.332778i	0.0652162	+	0.0191492i
$303$	1.44205	−	10.0297i	0.0828439	−	0.576192i
$304$	1.11076	−	1.28188i	0.0637062	−	0.0735209i
$305$	19.2561			1.10260
$306$	1.86407			0.106562
$307$	13.6356	−	15.7364i	0.778227	−	0.898122i	−0.218753	−	0.975780i	$-0.570199\pi$
$307$	13.6356	−	15.7364i	0.778227	−	0.898122i	0.996980	+	0.0776580i	$0.0247442\pi$
$308$	1.50427	+	3.29390i	0.0857138	+	0.187687i
$309$	1.09756	+	0.705358i	0.0624380	+	0.0401264i
$310$	8.15322	+	9.40932i	0.463072	+	0.534413i
$311$	−28.9760	−	18.6217i	−1.64308	−	1.05594i	−0.937897	−	0.346914i	$-0.887230\pi$
$311$	−28.9760	−	18.6217i	−1.64308	−	1.05594i	−0.705181	−	0.709028i	$-0.749134\pi$
$312$	−1.00074	−	6.96030i	−0.0566557	−	0.394049i
$313$	−2.04514	+	14.2243i	−0.115598	+	0.804003i	0.846713	+	0.532051i	$0.178578\pi$
$313$	−2.04514	+	14.2243i	−0.115598	+	0.804003i	−0.962311	+	0.271952i	$0.912331\pi$
$314$	7.18274	+	15.7280i	0.405345	+	0.887583i
$315$	−0.407222	−	2.83229i	−0.0229443	−	0.159581i
$316$	7.59565	+	2.23028i	0.427289	+	0.125463i
$317$	−16.6512	+	10.7010i	−0.935222	+	0.601031i	−0.917036	−	0.398804i	$-0.869425\pi$
$317$	−16.6512	+	10.7010i	−0.935222	+	0.601031i	−0.0181857	+	0.999835i	$0.505789\pi$
$318$	5.10395	+	3.28011i	0.286216	+	0.183940i
$319$	−10.0196	+	21.9398i	−0.560987	+	1.22839i
$320$	3.69144	+	1.08390i	0.206358	+	0.0605921i
$321$	−6.48066	+	4.16487i	−0.361715	+	0.232460i
$322$	−2.65428	−	3.06320i	−0.147917	−	0.170705i
$323$	1.63542	+	1.88738i	0.0909973	+	0.105017i
$324$	−1.49507	+	3.27374i	−0.0830592	+	0.181874i
$325$	−7.44900	+	51.8089i	−0.413196	+	2.87384i
$326$	−5.93785	+	1.74351i	−0.328867	+	0.0965641i
$327$	−8.75083	+	10.0990i	−0.483922	+	0.558476i
$328$	2.43480	−	0.714922i	0.134439	−	0.0394750i
$329$	0.841531	+	1.84270i	0.0463951	+	0.101591i
$330$	−12.9725	+	28.4057i	−0.714110	+	1.56368i
$331$	4.08342	−	2.62425i	0.224445	−	0.144242i	−0.423586	−	0.905856i	$-0.639229\pi$
$331$	4.08342	−	2.62425i	0.224445	−	0.144242i	0.648031	+	0.761614i	$0.275593\pi$
$332$	0.728812	+	5.06900i	0.0399988	+	0.278198i
$333$	−13.7950	+	4.05058i	−0.755962	+	0.221970i
$334$	12.6677			0.693148
$335$	27.4356	−	15.4594i	1.49897	−	0.844635i
$336$	−0.773561			−0.0422012
$337$	21.7695	−	6.39209i	1.18586	−	0.348200i	0.371429	−	0.928461i	$-0.378868\pi$
$337$	21.7695	−	6.39209i	1.18586	−	0.348200i	0.814430	+	0.580262i	$0.197050\pi$
$338$	2.20831	+	15.3591i	0.120116	+	0.835427i
$339$	−6.92312	+	4.44922i	−0.376012	+	0.241648i
$340$	−2.35314	+	5.15265i	−0.127617	+	0.279442i
$341$	−8.28660	−	18.1451i	−0.448745	−	0.982614i
$342$	2.06045	−	0.605003i	0.111416	−	0.0327148i
$343$	5.25307	−	6.06237i	0.283639	−	0.327337i
$344$	−1.29813	+	0.381167i	−0.0699907	+	0.0205511i
$345$	4.97443	−	34.5979i	0.267814	−	1.86269i
$346$	−6.23002	+	13.6418i	−0.334928	+	0.733390i
$347$	−19.6202	−	22.6429i	−1.05327	−	1.21554i	−0.975828	−	0.218540i	$-0.929871\pi$
$347$	−19.6202	−	22.6429i	−1.05327	−	1.21554i	−0.0774407	−	0.996997i	$-0.524675\pi$
$348$	−3.37416	−	3.89399i	−0.180874	−	0.208740i
$349$	2.01675	−	1.29608i	0.107954	−	0.0693778i	−0.485550	−	0.874209i	$-0.661381\pi$
$349$	2.01675	−	1.29608i	0.107954	−	0.0693778i	0.593504	+	0.804831i	$0.297744\pi$
$350$	5.52476	+	1.62221i	0.295311	+	0.0867110i
$351$	12.4617	−	27.2874i	0.665159	−	1.45649i
$352$	−5.18555	−	3.33255i	−0.276391	−	0.177626i
$353$	−17.4044	+	11.1851i	−0.926342	+	0.595324i	−0.914491	−	0.404606i	$-0.867409\pi$
$353$	−17.4044	+	11.1851i	−0.926342	+	0.595324i	−0.0118507	+	0.999930i	$0.503772\pi$
$354$	−1.69749	−	0.498428i	−0.0902205	−	0.0264911i
$355$	6.39748	+	44.4954i	0.339543	+	2.36157i
$356$	6.10254	+	13.3627i	0.323434	+	0.708221i
$357$	0.162090	−	1.12736i	0.00857871	−	0.0596662i
$358$	0.824455	+	5.73421i	0.0435738	+	0.303063i
$359$	29.7526	+	19.1208i	1.57028	+	1.00916i	0.979286	+	0.202483i	$0.0649010\pi$
$359$	29.7526	+	19.1208i	1.57028	+	1.00916i	0.590995	+	0.806675i	$0.298735\pi$
$360$	3.18973	+	3.68114i	0.168113	+	0.194013i
$361$	−13.5635	−	8.71675i	−0.713870	−	0.458777i
$362$	0.986525	+	2.16019i	0.0518506	+	0.113537i
$363$	23.2790	−	26.8654i	1.22183	−	1.41007i
$364$	3.13710			0.164429
$365$	−6.24266			−0.326756
$366$	4.31601	−	4.98094i	0.225602	−	0.260358i
$367$	2.92608	−	20.3513i	0.152740	−	1.06233i	−0.758860	−	0.651253i	$-0.774243\pi$
$367$	2.92608	−	20.3513i	0.152740	−	1.06233i	0.911600	−	0.411077i	$-0.134847\pi$
$368$	6.62007	+	1.94383i	0.345095	+	0.101329i
$369$	3.08258	+	0.905127i	0.160473	+	0.0471190i
$370$	6.21775	−	43.2454i	0.323245	−	2.24822i
$371$	−1.77250	+	2.04558i	−0.0920237	+	0.106201i
$372$	4.26133			0.220940
$373$	−3.14735			−0.162964			−0.0814818	−	0.996675i	$-0.525965\pi$
$373$	−3.14735			−0.162964			−0.0814818	+	0.996675i	$0.525965\pi$
$374$	5.94331	−	6.85894i	0.307321	−	0.354668i
$375$	10.1050	+	22.1269i	0.521820	+	1.14263i
$376$	−2.90094	−	1.86432i	−0.149605	−	0.0961450i
$377$	13.6836	+	15.7917i	0.704740	+	0.813314i
$378$	−2.77618	−	1.78414i	−0.142791	−	0.0917663i
$379$	0.862542	+	5.99911i	0.0443058	+	0.308154i	0.999909	+	0.0134967i	$0.00429625\pi$
$379$	0.862542	+	5.99911i	0.0443058	+	0.308154i	−0.955603	+	0.294657i	$0.904795\pi$
$380$	−0.928696	+	6.45922i	−0.0476411	+	0.331351i
$381$	3.87578	+	8.48677i	0.198562	+	0.434790i
$382$	−0.312309	−	2.17216i	−0.0159791	−	0.111137i
$383$	−6.23482	−	1.83071i	−0.318584	−	0.0935448i	0.118531	−	0.992950i	$-0.462182\pi$
$383$	−6.23482	−	1.83071i	−0.318584	−	0.0935448i	−0.437115	+	0.899406i	$0.644000\pi$
$384$	1.10776	−	0.711913i	0.0565301	−	0.0363297i
$385$	−11.7199	−	7.53194i	−0.597303	−	0.383863i
$386$	9.40932	−	20.6035i	0.478922	−	1.04869i
$387$	−1.64350	−	0.482576i	−0.0835440	−	0.0245307i
$388$	−1.82339	+	1.17182i	−0.0925686	+	0.0594902i
$389$	1.04230	+	1.20288i	0.0528466	+	0.0609882i	0.781557	−	0.623833i	$-0.214426\pi$
$389$	1.04230	+	1.20288i	0.0528466	+	0.0609882i	−0.728711	+	0.684822i	$0.759880\pi$
$390$	17.7163	+	20.4457i	0.897101	+	1.03531i
$391$	−4.22002	+	9.24056i	−0.213416	+	0.467315i
$392$	−0.947090	+	6.58716i	−0.0478353	+	0.332702i
$393$	3.97702	−	1.16776i	0.200614	−	0.0589055i
$394$	8.77544	−	10.1274i	0.442100	−	0.510211i
$395$	−29.2226	+	8.58052i	−1.47035	+	0.431733i
$396$	−3.24191	−	7.09879i	−0.162912	−	0.356728i
$397$	−8.39462	+	18.3816i	−0.421314	+	0.922549i	0.573343	+	0.819315i	$0.305646\pi$
$397$	−8.39462	+	18.3816i	−0.421314	+	0.922549i	−0.994657	+	0.103233i	$0.967081\pi$
$398$	−7.51481	+	4.82947i	−0.376683	+	0.242080i
$399$	−0.186730	−	1.29874i	−0.00934820	−	0.0650181i
$400$	−9.40453	+	2.76142i	−0.470226	+	0.138071i
$401$	11.7504			0.586785			0.293393	−	0.955992i	$-0.405216\pi$
$401$	11.7504			0.586785			0.293393	+	0.955992i	$0.405216\pi$
$402$	2.15050	−	10.5617i	0.107257	−	0.526771i
$403$	−17.2814			−0.860848
$404$	−7.38338	+	2.16795i	−0.367337	+	0.107860i
$405$	−1.97052	−	13.7053i	−0.0979161	−	0.681022i
$406$	1.93376	−	1.24275i	0.0959707	−	0.0616766i
$407$	−29.0790	+	63.6741i	−1.44139	+	3.15621i
$408$	0.805401	+	1.76358i	0.0398733	+	0.0873103i
$409$	−16.4108	+	4.81865i	−0.811463	+	0.238267i	−0.661036	−	0.750354i	$-0.729883\pi$
$409$	−16.4108	+	4.81865i	−0.811463	+	0.238267i	−0.150427	+	0.988621i	$0.548065\pi$
$410$	−6.39329	+	7.37825i	−0.315742	+	0.364386i
$411$	17.2651	−	5.06948i	0.851623	−	0.250059i
$412$	0.141004	−	0.980708i	0.00694679	−	0.0483160i
$413$	0.327873	−	0.717941i	0.0161336	−	0.0353276i
$414$	5.72033	+	6.60161i	0.281139	+	0.324451i
$415$	−12.9023	−	14.8901i	−0.633351	−	0.730925i
$416$	−4.49241	+	2.88710i	−0.220259	+	0.141552i
$417$	16.7959	+	4.93171i	0.822497	+	0.241507i
$418$	4.34330	−	9.51050i	0.212438	−	0.465174i
$419$	2.63295	+	1.69209i	0.128628	+	0.0826641i	0.603372	−	0.797459i	$-0.293823\pi$
$419$	2.63295	+	1.69209i	0.128628	+	0.0826641i	−0.474745	+	0.880124i	$0.657460\pi$
$420$	2.50366	−	1.60900i	0.122166	−	0.0785113i
$421$	20.6806	+	6.07236i	1.00791	+	0.295949i	0.743698	−	0.668516i	$-0.233070\pi$
$421$	20.6806	+	6.07236i	1.00791	+	0.295949i	0.264211	+	0.964465i	$0.414888\pi$
$422$	2.34783	+	16.3295i	0.114291	+	0.794908i
$423$	−1.81361	−	3.97126i	−0.0881809	−	0.193089i
$424$	0.655710	−	4.56056i	0.0318441	−	0.221480i
$425$	−2.05379	−	14.2844i	−0.0996236	−	0.692897i
$426$	12.9434	+	8.31825i	0.627112	+	0.403020i
$427$	1.92549	+	2.22213i	0.0931809	+	0.107536i
$428$	4.92154	+	3.16288i	0.237892	+	0.152884i
$429$	−18.0062	−	39.4280i	−0.869345	−	1.90360i
$430$	3.40864	−	3.93378i	0.164379	−	0.189704i
$431$	14.5966			0.703094			0.351547	−	0.936170i	$-0.385656\pi$
$431$	14.5966			0.703094			0.351547	+	0.936170i	$0.385656\pi$
$432$	5.61751			0.270273
$433$	2.01334	−	2.32351i	0.0967548	−	0.111661i	−0.705307	−	0.708902i	$-0.749191\pi$
$433$	2.01334	−	2.32351i	0.0967548	−	0.111661i	0.802062	+	0.597241i	$0.203736\pi$
$434$	−0.270553	+	1.88174i	−0.0129870	+	0.0903264i
$435$	19.0201	+	5.58480i	0.911943	+	0.267771i
$436$	9.73697	+	2.85903i	0.466316	+	0.136923i
$437$	−1.66548	+	11.5837i	−0.0796709	+	0.554124i
$438$	−1.39921	+	1.61478i	−0.0668569	+	0.0771570i
$439$	27.8802			1.33065			0.665325	−	0.746554i	$-0.268293\pi$
$439$	27.8802			1.33065			0.665325	+	0.746554i	$0.268293\pi$
$440$	23.7149			1.13056
$441$	−5.51748	+	6.36751i	−0.262737	+	0.303215i
$442$	−3.26623	−	7.15204i	−0.155358	−	0.340188i
$443$	−9.18932	−	5.90562i	−0.436598	−	0.280584i	0.303822	−	0.952729i	$-0.401737\pi$
$443$	−9.18932	−	5.90562i	−0.436598	−	0.280584i	−0.740420	+	0.672144i	$0.765373\pi$
$444$	−9.79257	−	11.3012i	−0.464735	−	0.536332i
$445$	−47.5455	−	30.5556i	−2.25387	−	1.44847i
$446$	1.14674	+	7.97574i	0.0542996	+	0.377662i
$447$	−1.63235	+	11.3532i	−0.0772075	+	0.536990i
$448$	0.244039	+	0.534370i	0.0115297	+	0.0252466i
$449$	−0.765316	−	5.32289i	−0.0361175	−	0.251203i	0.963761	−	0.266766i	$-0.0859550\pi$
$449$	−0.765316	−	5.32289i	−0.0361175	−	0.251203i	−0.999879	+	0.0155631i	$0.995046\pi$
$450$	−11.9066	−	3.49609i	−0.561282	−	0.164807i
$451$	13.1588	−	8.45665i	0.619624	−	0.398208i
$452$	5.25755	+	3.37882i	0.247294	+	0.158927i
$453$	−0.646127	+	1.41482i	−0.0303577	+	0.0664740i
$454$	21.6215	+	6.34864i	1.01475	+	0.297957i
$455$	−10.1534	+	6.52516i	−0.475996	+	0.305904i
$456$	1.46264	+	1.68797i	0.0684943	+	0.0790466i
$457$	−18.5445	−	21.4015i	−0.867476	−	1.00112i	−0.999951	−	0.00993390i	$-0.996838\pi$
$457$	−18.5445	−	21.4015i	−0.867476	−	1.00112i	0.132475	−	0.991186i	$-0.457708\pi$
$458$	9.57608	−	20.9687i	0.447461	−	0.979802i
$459$	−1.17708	+	8.18677i	−0.0549414	+	0.382126i
$460$	−25.4693	+	7.47845i	−1.18751	+	0.348685i
$461$	1.01745	−	1.17420i	0.0473872	−	0.0546878i	−0.731561	−	0.681776i	$-0.761208\pi$
$461$	1.01745	−	1.17420i	0.0473872	−	0.0546878i	0.778948	+	0.627088i	$0.215753\pi$
$462$	−4.57514	+	1.34338i	−0.212855	+	0.0624998i
$463$	10.0375	+	21.9791i	0.466483	+	1.02145i	0.985962	+	0.166971i	$0.0533987\pi$
$463$	10.0375	+	21.9791i	0.466483	+	1.02145i	−0.519479	+	0.854483i	$0.673874\pi$
$464$	−1.62548	+	3.55930i	−0.0754608	+	0.165236i
$465$	−13.7919	+	8.86354i	−0.639586	+	0.411037i
$466$	2.40789	+	16.7473i	0.111544	+	0.775802i
$467$	21.4700	−	6.30415i	0.993511	−	0.291721i	0.255721	−	0.966751i	$-0.417687\pi$
$467$	21.4700	−	6.30415i	0.993511	−	0.291721i	0.737791	+	0.675030i	$0.235869\pi$
$468$	−6.76088			−0.312522
$469$	4.52737	+	1.62020i	0.209054	+	0.0748137i
$470$	13.2668			0.611951
$471$	−21.8458	+	6.41451i	−1.00660	+	0.295565i
$472$	0.191204	+	1.32985i	0.00880088	+	0.0612115i
$473$	−7.01573	+	4.50874i	−0.322584	+	0.207312i
$474$	−4.33035	+	9.48215i	−0.198900	+	0.435530i
$475$	−6.90632	−	15.1227i	−0.316884	−	0.693879i
$476$	−0.829907	+	0.243683i	−0.0380387	+	0.0111692i
$477$	3.81998	−	4.40849i	0.174905	−	0.201851i
$478$	−16.0748	+	4.72000i	−0.735246	+	0.215888i
$479$	4.54105	−	31.5837i	0.207486	−	1.44310i	−0.573837	−	0.818969i	$-0.694546\pi$
$479$	4.54105	−	31.5837i	0.207486	−	1.44310i	0.781323	−	0.624127i	$-0.214545\pi$
$480$	−2.10453	+	4.60827i	−0.0960580	+	0.210338i
$481$	39.7128	+	45.8310i	1.81075	+	2.08972i
$482$	1.25884	+	1.45277i	0.0573384	+	0.0661721i
$483$	4.48996	−	2.88552i	0.204300	−	0.131296i
$484$	−25.9023	−	7.60560i	−1.17738	−	0.345709i
$485$	3.46408	−	7.58529i	0.157296	−	0.344430i
$486$	10.1905	+	6.54902i	0.462249	+	0.297070i
$487$	29.1647	−	18.7430i	1.32158	−	0.849327i	0.326195	−	0.945303i	$-0.394233\pi$
$487$	29.1647	−	18.7430i	1.32158	−	0.849327i	0.995384	+	0.0959757i	$0.0305971\pi$
$488$	−4.80239	−	1.41011i	−0.217394	−	0.0638326i
$489$	−1.15973	−	8.06608i	−0.0524447	−	0.364761i
$490$	−10.6360	−	23.2895i	−0.480484	−	1.05211i
$491$	3.19887	−	22.2487i	0.144363	−	1.00407i	−0.780877	−	0.624685i	$-0.785227\pi$
$491$	3.19887	−	22.2487i	0.144363	−	1.00407i	0.925240	−	0.379382i	$-0.123864\pi$
$492$	0.475543	+	3.30748i	0.0214392	+	0.149113i
$493$	−4.84660	−	3.11472i	−0.218280	−	0.140280i
$494$	−5.93159	−	6.84542i	−0.266875	−	0.307990i
$495$	25.2580	+	16.2323i	1.13526	+	0.729590i
$496$	−1.34434	−	2.94369i	−0.0603626	−	0.132176i
$497$	−4.49500	+	5.18751i	−0.201628	+	0.232692i
$498$	−6.74348			−0.302182
$499$	−0.293538			−0.0131406			−0.00657028	−	0.999978i	$-0.502091\pi$
$499$	−0.293538			−0.0131406			−0.00657028	+	0.999978i	$0.502091\pi$
$500$	12.0972	−	13.9609i	0.541003	−	0.624351i
$501$	−2.37393	+	16.5110i	−0.106059	+	0.737659i
$502$	−13.8954	−	4.08006i	−0.620183	−	0.182102i
$503$	0.340084	+	0.0998577i	0.0151636	+	0.00445244i	0.289306	−	0.957237i	$-0.406576\pi$
$503$	0.340084	+	0.0998577i	0.0151636	+	0.00445244i	−0.274142	+	0.961689i	$0.588394\pi$
$504$	−0.105847	+	0.736180i	−0.00471479	+	0.0327921i
$505$	19.3872	−	22.3741i	0.862721	−	0.995633i
$506$	42.5294			1.89066
$507$	−20.4328			−0.907453
$508$	4.63988	−	5.35471i	0.205862	−	0.237577i
$509$	−8.62586	−	18.8880i	−0.382334	−	0.837196i	−0.998760	−	0.0497825i	$-0.984147\pi$
$509$	−8.62586	−	18.8880i	−0.382334	−	0.837196i	0.616426	−	0.787413i	$-0.288580\pi$
$510$	−6.27495	−	4.03267i	−0.277859	−	0.178569i
$511$	−0.624225	−	0.720394i	−0.0276141	−	0.0318684i
$512$	−0.841254	−	0.540641i	−0.0371785	−	0.0238932i
$513$	1.35601	+	9.43128i	0.0598695	+	0.416401i
$514$	−2.85527	+	19.8588i	−0.125941	+	0.875936i
$515$	1.58350	+	3.46739i	0.0697774	+	0.152791i
$516$	−0.253540	−	1.76341i	−0.0111615	−	0.0776298i
$517$	−20.3949	−	5.98848i	−0.896967	−	0.263373i
$518$	5.61219	−	3.60674i	0.246586	−	0.158471i
$519$	−16.6132	−	10.6766i	−0.729237	−	0.468652i
$520$	8.53470	−	18.6884i	0.374271	−	0.819540i
$521$	−22.3040	−	6.54906i	−0.977158	−	0.286919i	−0.246107	−	0.969243i	$-0.579152\pi$
$521$	−22.3040	−	6.54906i	−0.977158	−	0.286919i	−0.731051	+	0.682323i	$0.760970\pi$
$522$	−4.16751	+	2.67829i	−0.182407	+	0.117226i
$523$	5.40011	+	6.23206i	0.236130	+	0.272509i	0.861431	−	0.507875i	$-0.169569\pi$
$523$	5.40011	+	6.23206i	0.236130	+	0.272509i	−0.625300	+	0.780384i	$0.715023\pi$
$524$	−2.06132	−	2.37889i	−0.0900493	−	0.103922i
$525$	−3.14972	+	6.89692i	−0.137465	+	0.301006i
$526$	−0.628581	+	4.37188i	−0.0274074	+	0.190623i
$527$	4.57172	−	1.34238i	0.199147	−	0.0584749i
$528$	5.31539	−	6.13429i	0.231323	−	0.266961i
$529$	−23.6072	+	6.93170i	−1.02640	+	0.301378i
$530$	7.36372	+	16.1243i	0.319860	+	0.700395i
$531$	−0.706610	+	1.54726i	−0.0306643	+	0.0671454i
$532$	−0.838248	+	0.538710i	−0.0363427	+	0.0233560i
$533$	−1.92852	−	13.4132i	−0.0835335	−	0.580988i
$534$	−18.5604	+	5.44984i	−0.803189	+	0.235838i
$535$	−22.5075			−0.973085
$536$	−7.97438	+	1.84640i	−0.344441	+	0.0797525i
$537$	−7.62843			−0.329191
$538$	−9.19615	+	2.70023i	−0.396474	+	0.116415i
$539$	5.83793	+	40.6037i	0.251458	+	1.74893i
$540$	−18.1813	+	11.6844i	−0.782398	+	0.502817i
$541$	0.232725	−	0.509597i	0.0100056	−	0.0219093i	−0.904563	−	0.426340i	$-0.859803\pi$
$541$	0.232725	−	0.509597i	0.0100056	−	0.0219093i	0.914569	+	0.404430i	$0.132530\pi$
$542$	−12.7413	−	27.8995i	−0.547285	−	1.19839i
$543$	−3.00045	+	0.881011i	−0.128762	+	0.0378078i
$544$	0.964185	−	1.11273i	0.0413391	−	0.0477079i
$545$	−37.4608	+	10.9995i	−1.60465	+	0.471167i
$546$	−0.587892	+	4.08888i	−0.0251594	+	0.174988i
$547$	5.01336	−	10.9777i	0.214356	−	0.469374i	−0.771658	−	0.636038i	$-0.780572\pi$
$547$	5.01336	−	10.9777i	0.214356	−	0.469374i	0.986014	+	0.166664i	$0.0532995\pi$
$548$	−8.94865	−	10.3273i	−0.382267	−	0.441160i
$549$	−4.14969	−	4.78899i	−0.177104	−	0.204389i
$550$	−50.8265	+	32.6642i	−2.16725	+	1.39281i
$551$	−6.36810	−	1.86984i	−0.271290	−	0.0796580i
$552$	−3.77417	+	8.26428i	−0.160639	+	0.351751i
$553$	−3.91225	−	2.51425i	−0.166366	−	0.106917i
$554$	14.2737	−	9.17312i	0.606430	−	0.389729i
$555$	55.2005	+	16.2083i	2.34313	+	0.688005i
$556$	−1.89188	−	13.1583i	−0.0802334	−	0.558035i
$557$	9.04658	+	19.8092i	0.383316	+	0.839345i	0.998693	+	0.0511117i	$0.0162765\pi$
$557$	9.04658	+	19.8092i	0.383316	+	0.839345i	−0.615377	+	0.788233i	$0.710996\pi$
$558$	0.583079	−	4.05541i	0.0246837	−	0.171679i
$559$	1.02821	+	7.15134i	0.0434885	+	0.302469i
$560$	−1.90133	−	1.22191i	−0.0803457	−	0.0516351i
$561$	7.82612	+	9.03183i	0.330419	+	0.381324i
$562$	22.2400	+	14.2928i	0.938139	+	0.602905i
$563$	−3.77546	−	8.26711i	−0.159117	−	0.348417i	0.813236	−	0.581934i	$-0.197704\pi$
$563$	−3.77546	−	8.26711i	−0.159117	−	0.348417i	−0.972353	+	0.233517i	$0.924977\pi$
$564$	2.97358	−	3.43169i	0.125210	−	0.144500i
$565$	−24.0442			−1.01155
$566$	−4.47598			−0.188139
$567$	1.38453	−	1.59784i	0.0581449	−	0.0671028i
$568$	1.66286	−	11.5654i	0.0697719	−	0.485275i
$569$	29.3003	+	8.60335i	1.22833	+	0.360671i	0.830621	−	0.556839i	$-0.187986\pi$
$569$	29.3003	+	8.60335i	1.22833	+	0.360671i	0.397713	+	0.917510i	$0.369804\pi$
$570$	−8.24486	−	2.42091i	−0.345339	−	0.101401i
$571$	−6.22808	+	43.3172i	−0.260637	+	1.81277i	0.267442	+	0.963574i	$0.413822\pi$
$571$	−6.22808	+	43.3172i	−0.260637	+	1.81277i	−0.528079	+	0.849195i	$0.677088\pi$
$572$	−21.5561	+	24.8770i	−0.901304	+	1.04016i
$573$	2.88970			0.120719
$574$	−1.49073			−0.0622217
$575$	44.2858	−	51.1086i	1.84685	−	2.13138i
$576$	−0.525936	−	1.15164i	−0.0219140	−	0.0479850i
$577$	−20.6141	−	13.2479i	−0.858176	−	0.551516i	0.0359386	−	0.999354i	$-0.488558\pi$
$577$	−20.6141	−	13.2479i	−0.858176	−	0.551516i	−0.894115	+	0.447838i	$0.852194\pi$
$578$	−9.71301	−	11.2094i	−0.404008	−	0.466250i
$579$	25.0912	+	16.1251i	1.04275	+	0.670138i
$580$	−2.14241	−	14.9008i	−0.0889587	−	0.618721i
$581$	0.428146	−	2.97782i	0.0177625	−	0.123541i
$582$	−1.18564	−	2.59619i	−0.0491464	−	0.107616i
$583$	−4.04184	−	28.1116i	−0.167396	−	1.16427i
$584$	1.55689	+	0.457144i	0.0644246	+	0.0189168i
$585$	21.8818	−	14.0626i	0.904703	−	0.581417i
$586$	−15.0252	−	9.65612i	−0.620686	−	0.398891i
$587$	4.57902	−	10.0266i	0.188996	−	0.413844i	−0.791286	−	0.611446i	$-0.790588\pi$
$587$	4.57902	−	10.0266i	0.188996	−	0.413844i	0.980282	+	0.197602i	$0.0633154\pi$
$588$	−8.40817	−	2.46886i	−0.346747	−	0.101814i
$589$	4.61767	−	2.96760i	0.190268	−	0.122278i
$590$	−3.38493	−	3.90642i	−0.139355	−	0.160825i
$591$	11.5555	+	13.3357i	0.475328	+	0.548558i
$592$	−4.71750	+	10.3299i	−0.193888	+	0.424555i
$593$	4.05417	−	28.1974i	0.166485	−	1.15793i	−0.719595	−	0.694394i	$-0.755672\pi$
$593$	4.05417	−	28.1974i	0.166485	−	1.15793i	0.886080	−	0.463533i	$-0.153419\pi$
$594$	33.2242	−	9.75549i	1.36320	−	0.400273i
$595$	2.17917	−	2.51489i	0.0893371	−	0.103101i
$596$	8.35770	−	2.45404i	0.342345	−	0.100521i
$597$	−4.88643	−	10.6998i	−0.199988	−	0.437913i
$598$	15.3058	−	33.5150i	0.625900	−	1.37053i
$599$	−25.1339	+	16.1526i	−1.02694	+	0.659977i	−0.941724	−	0.336385i	$-0.890796\pi$
$599$	−25.1339	+	16.1526i	−1.02694	+	0.659977i	−0.0852197	+	0.996362i	$0.527159\pi$
$600$	−1.83681	−	12.7753i	−0.0749873	−	0.521548i
$601$	−16.7964	+	4.93186i	−0.685138	+	0.201175i	−0.605733	−	0.795668i	$-0.707120\pi$
$601$	−16.7964	+	4.93186i	−0.685138	+	0.201175i	−0.0794050	+	0.996842i	$0.525302\pi$
$602$	0.794793			0.0323934
$603$	−9.75709	−	3.49174i	−0.397340	−	0.142195i
$604$	1.18118			0.0480616
$605$	99.6534	−	29.2609i	4.05149	−	1.18962i
$606$	−1.44205	−	10.0297i	−0.0585795	−	0.407429i
$607$	−17.7596	+	11.4134i	−0.720839	+	0.463255i	−0.848928	−	0.528508i	$-0.822752\pi$
$607$	−17.7596	+	11.4134i	−0.720839	+	0.463255i	0.128090	+	0.991763i	$0.459115\pi$
$608$	0.704615	−	1.54289i	0.0285759	−	0.0625725i
$609$	1.25740	+	2.75333i	0.0509526	+	0.111571i
$610$	18.4761	−	5.42508i	0.748077	−	0.219655i
$611$	−12.0591	+	13.9169i	−0.487857	+	0.563017i
$612$	1.78856	−	0.525169i	0.0722984	−	0.0212287i
$613$	0.0586327	−	0.407800i	0.00236815	−	0.0164709i	−0.988603	−	0.150545i	$-0.951897\pi$
$613$	0.0586327	−	0.407800i	0.00236815	−	0.0164709i	0.990971	+	0.134074i	$0.0428061\pi$
$614$	8.64986	−	18.9405i	0.349080	−	0.764378i
$615$	−8.41865	−	9.71564i	−0.339473	−	0.391773i
$616$	2.37134	+	2.73667i	0.0955438	+	0.110263i
$617$	−14.9043	+	9.57843i	−0.600026	+	0.385613i	−0.805105	−	0.593132i	$-0.797891\pi$
$617$	−14.9043	+	9.57843i	−0.600026	+	0.385613i	0.205079	+	0.978745i	$0.434255\pi$
$618$	1.25182	+	0.367568i	0.0503557	+	0.0147858i
$619$	5.73359	−	12.5548i	0.230452	−	0.504621i	−0.758713	−	0.651425i	$-0.774172\pi$
$619$	5.73359	−	12.5548i	0.230452	−	0.504621i	0.989166	+	0.146804i	$0.0468988\pi$
$620$	10.4739	+	6.73115i	0.420641	+	0.270329i
$621$	−32.6056	+	20.9543i	−1.30842	+	0.840869i
$622$	−33.0486	−	9.70395i	−1.32513	−	0.389093i
$623$	−1.22816	−	8.54204i	−0.0492052	−	0.342230i
$624$	−2.92114	−	6.39641i	−0.116939	−	0.256061i
$625$	−3.13985	+	21.8382i	−0.125594	+	0.873527i
$626$	2.04514	+	14.2243i	0.0817402	+	0.568516i
$627$	11.5820	+	7.44328i	0.462540	+	0.297256i
$628$	11.3229	+	13.0673i	0.451832	+	0.521442i
$629$	−14.0659	−	9.03961i	−0.560844	−	0.360433i
$630$	−1.18867	−	2.60283i	−0.0473579	−	0.103699i
$631$	12.6733	−	14.6258i	0.504518	−	0.582244i	−0.445169	−	0.895447i	$-0.646856\pi$
$631$	12.6733	−	14.6258i	0.504518	−	0.582244i	0.949686	+	0.313202i	$0.101402\pi$
$632$	7.91631			0.314894
$633$	−21.7237			−0.863441
$634$	−12.9618	+	14.9588i	−0.514780	+	0.594088i
$635$	−3.87938	+	26.9817i	−0.153948	+	1.07073i
$636$	5.82132	+	1.70929i	0.230830	+	0.0677779i
$637$	34.0985	+	10.0122i	1.35103	+	0.396699i
$638$	−3.43255	+	23.8739i	−0.135896	+	0.945176i
$639$	9.68734	−	11.1798i	0.383225	−	0.442266i
$640$	3.84728			0.152077
$641$	45.2138			1.78584			0.892920	−	0.450216i	$-0.148653\pi$
$641$	45.2138			1.78584			0.892920	+	0.450216i	$0.148653\pi$
$642$	−5.04477	+	5.82197i	−0.199101	+	0.229775i
$643$	−10.7006	−	23.4310i	−0.421991	−	0.924030i	−0.994559	−	0.104174i	$-0.966780\pi$
$643$	−10.7006	−	23.4310i	−0.421991	−	0.924030i	0.572569	−	0.819857i	$-0.305947\pi$
$644$	−3.40976	−	2.19132i	−0.134363	−	0.0863501i
$645$	4.48848	+	5.17998i	0.176734	+	0.203961i
$646$	2.10091	+	1.35017i	0.0826593	+	0.0531219i
$647$	4.83801	+	33.6491i	0.190202	+	1.32288i	0.831472	+	0.555567i	$0.187499\pi$
$647$	4.83801	+	33.6491i	0.190202	+	1.32288i	−0.641270	+	0.767315i	$0.721592\pi$
$648$	−0.512186	+	3.56234i	−0.0201206	+	0.139942i
$649$	3.44031	+	7.53322i	0.135044	+	0.295705i
$650$	7.44900	+	51.8089i	0.292174	+	2.03211i
$651$	−2.40194	−	0.705274i	−0.0941396	−	0.0276419i
$652$	−5.20612	+	3.34577i	−0.203888	+	0.131031i
$653$	26.2160	+	16.8480i	1.02591	+	0.659312i	0.941463	−	0.337116i	$-0.109451\pi$
$653$	26.2160	+	16.8480i	1.02591	+	0.659312i	0.0844465	+	0.996428i	$0.473088\pi$
$654$	−5.55114	+	12.1553i	−0.217067	+	0.475310i
$655$	11.6196	+	3.41183i	0.454017	+	0.133311i
$656$	2.13476	−	1.37193i	0.0833483	−	0.0535647i
$657$	1.34529	+	1.55255i	0.0524848	+	0.0605706i
$658$	1.32659	+	1.53097i	0.0517159	+	0.0596833i
$659$	−19.3350	+	42.3377i	−0.753185	+	1.64924i	0.00737197	+	0.999973i	$0.497653\pi$
$659$	−19.3350	+	42.3377i	−0.753185	+	1.64924i	−0.760557	+	0.649272i	$0.775074\pi$
$660$	−4.44416	+	30.9098i	−0.172989	+	1.20316i
$661$	−13.4616	+	3.95269i	−0.523596	+	0.153742i	−0.532841	−	0.846215i	$-0.678876\pi$
$661$	−13.4616	+	3.95269i	−0.523596	+	0.153742i	0.00924443	+	0.999957i	$0.497057\pi$
$662$	3.17868	−	3.66839i	0.123543	−	0.142576i
$663$	9.93400	−	2.91688i	0.385804	−	0.113282i
$664$	2.12739	+	4.65834i	0.0825589	+	0.180779i
$665$	1.59251	−	3.48711i	0.0617548	−	0.135224i
$666$	−12.0950	+	7.77301i	−0.468673	+	0.301198i
$667$	−3.84211	−	26.7224i	−0.148767	−	1.03470i
$668$	12.1546	−	3.56892i	0.470276	−	0.138086i
$669$	−10.6104			−0.410222
$670$	21.9689	−	22.5626i	0.848732	−	0.871671i
$671$	−30.8520			−1.19103
$672$	−0.742226	+	0.217937i	−0.0286320	+	0.00840711i
$673$	−1.48404	−	10.3217i	−0.0572054	−	0.397872i	−0.998227	−	0.0595252i	$-0.981041\pi$
$673$	−1.48404	−	10.3217i	−0.0572054	−	0.397872i	0.941021	−	0.338347i	$-0.109868\pi$
$674$	19.0868	−	12.2663i	0.735196	−	0.472482i
$675$	22.8729	−	50.0847i	0.880379	−	1.92776i
$676$	6.44603	+	14.1148i	0.247924	+	0.542878i
$677$	−14.3901	+	4.22531i	−0.553056	+	0.162392i	−0.546307	−	0.837585i	$-0.683967\pi$
$677$	−14.3901	+	4.22531i	−0.553056	+	0.162392i	−0.00674959	+	0.999977i	$0.502148\pi$
$678$	−5.38920	+	6.21946i	−0.206971	+	0.238857i
$679$	1.22172	−	0.358729i	0.0468852	−	0.0137667i
$680$	−0.806149	+	5.60689i	−0.0309144	+	0.215014i
$681$	−12.3266	+	26.9915i	−0.472357	+	1.03432i
$682$	−13.0630	−	15.0755i	−0.500209	−	0.577272i
$683$	−11.3810	−	13.1344i	−0.435481	−	0.502572i	0.495009	−	0.868888i	$-0.335165\pi$
$683$	−11.3810	−	13.1344i	−0.435481	−	0.502572i	−0.930491	+	0.366315i	$0.880619\pi$
$684$	1.80654	−	1.16099i	0.0690747	−	0.0443916i
$685$	50.4433	+	14.8115i	1.92734	+	0.565918i
$686$	3.33232	−	7.29676i	0.127229	−	0.278592i
$687$	25.5359	+	16.4109i	0.974254	+	0.626115i
$688$	−1.13816	+	0.731454i	−0.0433921	+	0.0278864i
$689$	−23.6078	−	6.93188i	−0.899386	−	0.264084i
$690$	−4.97443	−	34.5979i	−0.189373	−	1.31712i
$691$	11.4138	+	24.9928i	0.434203	+	0.950772i	0.992626	+	0.121216i	$0.0386793\pi$
$691$	11.4138	+	24.9928i	0.434203	+	0.950772i	−0.558423	+	0.829556i	$0.688593\pi$
$692$	−2.13431	+	14.8445i	−0.0811343	+	0.564301i
$693$	0.652447	+	4.53787i	0.0247844	+	0.172379i
$694$	−25.2047	−	16.1981i	−0.956758	−	0.614871i
$695$	33.4923	+	38.6522i	1.27044	+	1.46616i
$696$	−4.33455	−	2.78564i	−0.164301	−	0.105590i
$697$	1.55208	+	3.39859i	0.0587894	+	0.128731i
$698$	1.56991	−	1.81177i	0.0594218	−	0.0685764i
$699$	−22.2795			−0.842688
$700$	5.75800			0.217632
$701$	−31.9338	+	36.8536i	−1.20612	+	1.39194i	−0.308473	+	0.951233i	$0.599818\pi$
$701$	−31.9338	+	36.8536i	−1.20612	+	1.39194i	−0.897651	+	0.440708i	$0.854728\pi$
$702$	4.26920	−	29.6930i	0.161131	−	1.12069i
$703$	−18.4816	−	5.42670i	−0.697049	−	0.204672i
$704$	−5.91439	−	1.73662i	−0.222907	−	0.0654513i
$705$	−2.48619	+	17.2918i	−0.0936353	+	0.651248i
$706$	−13.5482	+	15.6354i	−0.509892	+	0.588447i
$707$	4.52053			0.170012
$708$	−1.76915			−0.0664888
$709$	−21.5229	+	24.8388i	−0.808311	+	0.932841i	−0.998806	−	0.0488475i	$-0.984445\pi$
$709$	−21.5229	+	24.8388i	−0.808311	+	0.932841i	0.190495	+	0.981688i	$0.438991\pi$
$710$	18.6741	+	40.8907i	0.700828	+	1.53460i
$711$	8.43142	+	5.41855i	0.316203	+	0.203211i
$712$	9.62005	+	11.1021i	0.360527	+	0.416070i
$713$	18.7834	+	12.0714i	0.703444	+	0.452076i
$714$	−0.162090	−	1.12736i	−0.00606607	−	0.0421904i
$715$	18.0229	−	125.352i	0.674018	−	4.68790i
$716$	2.40657	+	5.26966i	0.0899379	+	0.196936i
$717$	−3.13959	−	21.8364i	−0.117250	−	0.815494i
$718$	33.9343	+	9.96402i	1.26642	+	0.371854i
$719$	1.20072	−	0.771657i	0.0447794	−	0.0287780i	−0.518060	−	0.855345i	$-0.673345\pi$
$719$	1.20072	−	0.771657i	0.0447794	−	0.0287780i	0.562839	+	0.826567i	$0.309709\pi$
$720$	4.09762	+	2.63338i	0.152709	+	0.0981402i
$721$	−0.241792	+	0.529450i	−0.00900479	+	0.0197177i
$722$	−15.4699	−	4.54238i	−0.575730	−	0.169050i
$723$	−2.12944	+	1.36851i	−0.0791947	+	0.0508954i
$724$	1.55516	+	1.79475i	0.0577971	+	0.0667014i
$725$	25.1155	+	28.9849i	0.932768	+	1.07647i
$726$	14.7672	−	32.3356i	0.548061	−	1.20009i
$727$	−3.61707	+	25.1573i	−0.134150	+	0.933031i	0.805914	+	0.592032i	$0.201674\pi$
$727$	−3.61707	+	25.1573i	−0.134150	+	0.933031i	−0.940064	+	0.340999i	$0.889235\pi$
$728$	3.01003	−	0.883824i	0.111559	−	0.0327567i
$729$	−17.5161	+	20.2147i	−0.648744	+	0.748691i
$730$	−5.98979	+	1.75876i	−0.221692	+	0.0650947i
$731$	−0.827507	−	1.81199i	−0.0306065	−	0.0670188i
$732$	2.73789	−	5.99514i	0.101195	−	0.221587i
$733$	16.6905	−	10.7263i	0.616478	−	0.396186i	−0.194803	−	0.980842i	$-0.562407\pi$
$733$	16.6905	−	10.7263i	0.616478	−	0.396186i	0.811281	+	0.584656i	$0.198770\pi$
$734$	−2.92608	−	20.3513i	−0.108004	−	0.751181i
$735$	32.3486	−	9.49839i	1.19319	−	0.350354i
$736$	6.89955			0.254321
$737$	−43.9571	+	24.7688i	−1.61918	+	0.912371i
$738$	3.21272			0.118262
$739$	−27.9323	+	8.20165i	−1.02751	+	0.301703i	−0.751696	−	0.659510i	$-0.770764\pi$
$739$	−27.9323	+	8.20165i	−1.02751	+	0.301703i	−0.275809	+	0.961212i	$0.588946\pi$
$740$	−6.21775	−	43.2454i	−0.228569	−	1.58973i
$741$	10.0338	−	6.44836i	0.368602	−	0.236886i
$742$	−1.12440	+	2.46209i	−0.0412779	+	0.0903861i
$743$	−15.8032	−	34.6042i	−0.579763	−	1.26950i	−0.941434	−	0.337198i	$-0.890521\pi$
$743$	−15.8032	−	34.6042i	−0.579763	−	1.26950i	0.361671	−	0.932306i	$-0.382206\pi$
$744$	4.08871	−	1.20055i	0.149899	−	0.0440145i
$745$	−21.9456	+	25.3266i	−0.804025	+	0.927894i
$746$	−3.01986	+	0.886711i	−0.110565	+	0.0324648i
$747$	−0.922713	+	6.41761i	−0.0337603	+	0.234808i
$748$	3.77018	−	8.25553i	0.137851	−	0.301852i
$749$	−2.25060	−	2.59734i	−0.0822353	−	0.0949046i
$750$	15.9295	+	18.3837i	0.581664	+	0.671276i
$751$	14.7949	−	9.50813i	0.539875	−	0.346957i	−0.242115	−	0.970248i	$-0.577841\pi$
$751$	14.7949	−	9.50813i	0.539875	−	0.346957i	0.781990	+	0.623291i	$0.214205\pi$
$752$	−3.30867	−	0.971514i	−0.120655	−	0.0354275i
$753$	7.92192	−	17.3466i	0.288691	−	0.632145i
$754$	17.5783	+	11.2969i	0.640165	+	0.411409i
$755$	−3.82294	+	2.45686i	−0.139131	+	0.0894141i
$756$	−3.16637	−	0.929731i	−0.115160	−	0.0338140i
$757$	−2.09223	−	14.5517i	−0.0760432	−	0.528892i	−0.991864	−	0.127304i	$-0.959368\pi$
$757$	−2.09223	−	14.5517i	−0.0760432	−	0.528892i	0.915820	−	0.401588i	$-0.131542\pi$
$758$	2.51775	+	5.51310i	0.0914487	+	0.200245i
$759$	−7.96998	+	55.4324i	−0.289292	+	2.01207i
$760$	0.928696	+	6.45922i	0.0336873	+	0.234301i
$761$	6.06142	+	3.89544i	0.219726	+	0.141209i	0.645874	−	0.763444i	$-0.276493\pi$
$761$	6.06142	+	3.89544i	0.219726	+	0.141209i	−0.426148	+	0.904654i	$0.640130\pi$
$762$	6.10978	+	7.05106i	0.221334	+	0.255433i
$763$	−5.01516	−	3.22305i	−0.181561	−	0.116682i
$764$	−0.911625	−	1.99618i	−0.0329815	−	0.0722193i
$765$	−4.69640	+	5.41993i	−0.169799	+	0.195958i
$766$	−6.49804			−0.234784
$767$	7.17463			0.259061
$768$	0.862318	−	0.995168i	0.0311162	−	0.0359100i
$769$	3.16744	−	22.0300i	0.114221	−	0.794423i	−0.849515	−	0.527564i	$-0.823105\pi$
$769$	3.16744	−	22.0300i	0.114221	−	0.794423i	0.963736	−	0.266858i	$-0.0859856\pi$
$770$	−13.3672	−	3.92496i	−0.481720	−	0.141446i
$771$	−25.3488	−	7.44307i	−0.912914	−	0.268056i
$772$	3.22349	−	22.4199i	0.116016	−	0.806909i
$773$	30.6099	−	35.3258i	1.10096	−	1.27058i	0.141135	−	0.989990i	$-0.454925\pi$
$773$	30.6099	−	35.3258i	1.10096	−	1.27058i	0.959828	−	0.280589i	$-0.0905298\pi$
$774$	−1.71289			−0.0615685
$775$	−31.7192			−1.13939
$776$	−1.41939	+	1.63806i	−0.0509531	+	0.0588030i
$777$	3.64927	+	7.99079i	0.130917	+	0.286668i
$778$	1.33897	+	0.860501i	0.0480043	+	0.0308505i
$779$	2.81864	+	3.25289i	0.100988	+	0.116547i
$780$	22.7589	+	14.6263i	0.814900	+	0.523704i
$781$	−10.2500	−	71.2902i	−0.366773	−	2.55096i
$782$	−1.44571	+	10.0552i	−0.0516986	+	0.359572i
$783$	−9.13114	−	19.9944i	−0.326320	−	0.714542i
$784$	0.947090	+	6.58716i	0.0338246	+	0.235256i
$785$	−63.8268	−	18.7413i	−2.27808	−	0.668904i
$786$	3.48692	−	2.24091i	0.124374	−	0.0799306i
$787$	−19.7324	−	12.6813i	−0.703385	−	0.452038i	0.139436	−	0.990231i	$-0.455471\pi$
$787$	−19.7324	−	12.6813i	−0.703385	−	0.452038i	−0.842822	+	0.538193i	$0.819107\pi$
$788$	5.56676	−	12.1895i	0.198308	−	0.434233i
$789$	−5.58047	−	1.63858i	−0.198670	−	0.0583348i
$790$	−25.6214	+	16.4659i	−0.911570	+	0.585831i
$791$	−2.40426	−	2.77467i	−0.0854857	−	0.0986558i
$792$	−5.11055	−	5.89789i	−0.181596	−	0.209572i
$793$	−11.1033	+	24.3127i	−0.394288	+	0.863370i
$794$	−2.87587	+	20.0021i	−0.102061	+	0.709848i
$795$	−22.3963	+	6.57613i	−0.794313	+	0.233231i
$796$	−5.84979	+	6.75101i	−0.207340	+	0.239283i
$797$	37.7648	−	11.0887i	1.33770	−	0.392784i	0.466850	−	0.884336i	$-0.345389\pi$
$797$	37.7648	−	11.0887i	1.33770	−	0.392784i	0.870848	+	0.491553i	$0.163570\pi$
$798$	−0.545063	−	1.19352i	−0.0192950	−	0.0422502i
$799$	2.10914	−	4.61837i	0.0746160	−	0.163386i
$800$	−8.24559	+	5.29912i	−0.291526	+	0.187352i
$801$	2.64685	+	18.4092i	0.0935219	+	0.650459i
$802$	11.2744	−	3.31046i	0.398113	−	0.116896i
$803$	10.0019			0.352961
$804$	−0.912194	−	10.7398i	−0.0321706	−	0.378762i
$805$	15.5938			0.549608
$806$	−16.5814	+	4.86873i	−0.584054	+	0.171494i
$807$	−1.79611	−	12.4922i	−0.0632261	−	0.439747i
$808$	−6.47351	+	4.16027i	−0.227737	+	0.146358i
$809$	8.75570	−	19.1723i	0.307834	−	0.674062i	−0.690974	−	0.722880i	$-0.742818\pi$
$809$	8.75570	−	19.1723i	0.307834	−	0.674062i	0.998808	+	0.0488174i	$0.0155452\pi$
$810$	−5.75193	−	12.5950i	−0.202102	−	0.442542i
$811$	17.1010	−	5.02130i	0.600497	−	0.176322i	0.0326649	−	0.999466i	$-0.489601\pi$
$811$	17.1010	−	5.02130i	0.600497	−	0.176322i	0.567832	+	0.823145i	$0.307782\pi$
$812$	1.50530	−	1.73721i	0.0528257	−	0.0609642i
$813$	38.7518	−	11.3785i	1.35908	−	0.399063i
$814$	−9.96202	+	69.2874i	−0.349169	+	2.42852i
$815$	9.89062	−	21.6574i	0.346453	−	0.758627i
$816$	1.26963	+	1.46524i	0.0444461	+	0.0512935i
$817$	−1.50278	−	1.73431i	−0.0525758	−	0.0606757i
$818$	−14.3885	+	9.24693i	−0.503082	+	0.323311i
$819$	3.81085	+	1.11897i	0.133162	+	0.0390998i
$820$	−4.05562	+	8.88058i	−0.141628	+	0.310123i
$821$	0.731449	+	0.470074i	0.0255277	+	0.0164057i	0.553342	−	0.832954i	$-0.313352\pi$
$821$	0.731449	+	0.470074i	0.0255277	+	0.0164057i	−0.527815	+	0.849360i	$0.676988\pi$
$822$	15.1375	−	9.72827i	0.527980	−	0.339312i
$823$	−23.9291	−	7.02623i	−0.834117	−	0.244919i	−0.163333	−	0.986571i	$-0.552224\pi$
$823$	−23.9291	−	7.02623i	−0.834117	−	0.244919i	−0.670785	+	0.741652i	$0.734043\pi$
$824$	−0.141004	−	0.980708i	−0.00491212	−	0.0341646i
$825$	−33.0494	−	72.3681i	−1.15063	−	2.51953i
$826$	0.112324	−	0.781232i	0.00390826	−	0.0271825i
$827$	−3.91238	−	27.2112i	−0.136047	−	0.946227i	−0.937454	−	0.348108i	$-0.886824\pi$
$827$	−3.91238	−	27.2112i	−0.136047	−	0.946227i	0.801407	−	0.598119i	$-0.204085\pi$
$828$	7.34850	+	4.72259i	0.255378	+	0.164121i
$829$	−14.0167	−	16.1761i	−0.486819	−	0.561819i	0.458194	−	0.888852i	$-0.348496\pi$
$829$	−14.0167	−	16.1761i	−0.486819	−	0.561819i	−0.945013	+	0.327033i	$0.893951\pi$
$830$	−16.5747	−	10.6519i	−0.575317	−	0.369734i
$831$	9.28130	+	20.3232i	0.321965	+	0.705004i
$832$	−3.49705	+	4.03581i	−0.121238	+	0.139916i
$833$	−9.79834			−0.339492
$834$	17.5049			0.606146
$835$	−31.9155	+	36.8325i	−1.10448	+	1.27464i
$836$	1.48795	−	10.3489i	0.0514617	−	0.357924i
$837$	17.4427	+	5.12163i	0.602906	+	0.177029i
$838$	3.00301	+	0.881763i	0.103737	+	0.0304600i
$839$	−4.08535	+	28.4143i	−0.141042	+	0.980969i	0.789230	+	0.614098i	$0.210480\pi$
$839$	−4.08535	+	28.4143i	−0.141042	+	0.980969i	−0.930272	+	0.366871i	$0.880429\pi$
$840$	1.94893	−	2.24919i	0.0672446	−	0.0776044i
$841$	−13.6892			−0.472043
$842$	21.5536			0.742788
$843$	−22.7969	+	26.3090i	−0.785167	+	0.906131i
$844$	6.85328	+	15.0066i	0.235900	+	0.516548i
$845$	−50.2216	−	32.2755i	−1.72768	−	1.11031i
$846$	−2.85898	−	3.29944i	−0.0982939	−	0.113437i
$847$	13.3413	+	8.57396i	0.458414	+	0.294605i
$848$	−0.655710	−	4.56056i	−0.0225172	−	0.156610i
$849$	0.838796	−	5.83396i	0.0287874	−	0.200221i
$850$	−5.99499	−	13.1272i	−0.205627	−	0.450259i
$851$	−11.1507	−	77.5545i	−0.382240	−	2.65853i
$852$	14.7627	+	4.33471i	0.505761	+	0.148505i
$853$	−29.2004	+	18.7659i	−0.999801	+	0.642533i	−0.934734	−	0.355348i	$-0.884363\pi$
$853$	−29.2004	+	18.7659i	−0.999801	+	0.642533i	−0.0650672	+	0.997881i	$0.520726\pi$
$854$	2.47354	+	1.58965i	0.0846427	+	0.0543966i
$855$	−3.43207	+	7.51519i	−0.117374	+	0.257014i
$856$	5.61327	+	1.64820i	0.191858	+	0.0563345i
$857$	−23.4126	+	15.0464i	−0.799758	+	0.513974i	−0.875537	−	0.483151i	$-0.839492\pi$
$857$	−23.4126	+	15.0464i	−0.799758	+	0.513974i	0.0757785	+	0.997125i	$0.475856\pi$
$858$	−28.3849	−	32.7579i	−0.969045	−	1.11834i
$859$	12.8027	+	14.7751i	0.436821	+	0.504119i	0.930888	−	0.365306i	$-0.119035\pi$
$859$	12.8027	+	14.7751i	0.436821	+	0.504119i	−0.494066	+	0.869424i	$0.664490\pi$
$860$	2.16229	−	4.73475i	0.0737335	−	0.161454i
$861$	0.279361	−	1.94300i	0.00952061	−	0.0662173i
$862$	14.0053	−	4.11234i	0.477024	−	0.140067i
$863$	12.2273	−	14.1111i	0.416223	−	0.480347i	−0.508460	−	0.861086i	$-0.669785\pi$
$863$	12.2273	−	14.1111i	0.416223	−	0.480347i	0.924683	+	0.380739i	$0.124330\pi$
$864$	5.38997	−	1.58264i	0.183370	−	0.0538424i
$865$	−23.9686	−	52.4840i	−0.814958	−	1.78451i
$866$	1.27717	−	2.79662i	0.0434001	−	0.0950329i
$867$	16.4305	−	10.5592i	0.558008	−	0.358610i
$868$	0.270553	+	1.88174i	0.00918318	+	0.0638704i
$869$	46.8201	−	13.7476i	1.58826	−	0.466357i
$870$	19.8230			0.672064
$871$	3.69932	+	43.5541i	0.125347	+	1.47577i
$872$	10.1480			0.343656
$873$	−2.63297	+	0.773109i	−0.0891124	+	0.0261658i
$874$	1.66548	+	11.5837i	0.0563359	+	0.391825i
$875$	−9.12933	+	5.86707i	−0.308628	+	0.198343i
$876$	−0.887598	+	1.94357i	−0.0299892	+	0.0656671i
$877$	−9.80240	−	21.4643i	−0.331003	−	0.724797i	0.668823	−	0.743422i	$-0.266798\pi$
$877$	−9.80240	−	21.4643i	−0.331003	−	0.724797i	−0.999827	+	0.0186251i	$0.994071\pi$
$878$	26.7509	−	7.85477i	0.902798	−	0.265085i
$879$	15.4014	−	17.7742i	0.519477	−	0.599509i
$880$	22.7543	−	6.68126i	0.767047	−	0.225225i
$881$	0.191005	−	1.32847i	0.00643514	−	0.0447574i	−0.986351	−	0.164657i	$-0.947348\pi$
$881$	0.191005	−	1.32847i	0.00643514	−	0.0447574i	0.992786	+	0.119900i	$0.0382573\pi$
$882$	−3.50005	+	7.66404i	−0.117853	+	0.258062i
$883$	13.1850	+	15.2164i	0.443712	+	0.512071i	0.932914	−	0.360100i	$-0.117257\pi$
$883$	13.1850	+	15.2164i	0.443712	+	0.512071i	−0.489202	+	0.872171i	$0.662712\pi$
$884$	−5.14888	−	5.94213i	−0.173176	−	0.199855i
$885$	5.72593	−	3.67983i	0.192475	−	0.123696i
$886$	−10.4809	−	3.07747i	−0.352113	−	0.103390i
$887$	−22.4526	+	49.1642i	−0.753883	+	1.65077i	0.00537692	+	0.999986i	$0.498288\pi$
$887$	−22.4526	+	49.1642i	−0.753883	+	1.65077i	−0.759260	+	0.650788i	$0.774439\pi$
$888$	−12.5798	−	8.08456i	−0.422151	−	0.271300i
$889$	−3.50156	+	2.25031i	−0.117438	+	0.0754731i
$890$	−54.2280	−	15.9228i	−1.81773	−	0.533733i
$891$	3.15716	+	21.9585i	0.105769	+	0.735637i
$892$	3.34731	+	7.32959i	0.112076	+	0.245413i
$893$	0.832399	−	5.78946i	0.0278552	−	0.193737i
$894$	1.63235	+	11.3532i	0.0545940	+	0.379709i
$895$	−18.7498	−	12.0498i	−0.626738	−	0.402780i
$896$	0.384703	+	0.443971i	0.0128520	+	0.0148320i
$897$	40.8149	+	26.2301i	1.36277	+	0.875799i
$898$	−2.23395	−	4.89166i	−0.0745477	−	0.163237i
$899$	−8.29228	+	9.56980i	−0.276563	+	0.319171i
$900$	−12.4093			−0.413642
$901$	6.78380			0.226001
$902$	10.2433	−	11.8214i	0.341063	−	0.393608i
$903$	−0.148944	+	1.03593i	−0.00495654	+	0.0344735i
$904$	5.99651	+	1.76073i	0.199441	+	0.0585611i
$905$	−8.76641	−	2.57405i	−0.291405	−	0.0855643i
$906$	−0.221353	+	1.53954i	−0.00735396	+	0.0511479i
$907$	9.13080	−	10.5375i	0.303183	−	0.349892i	−0.583630	−	0.812020i	$-0.698368\pi$
$907$	9.13080	−	10.5375i	0.303183	−	0.349892i	0.886814	+	0.462127i	$0.152914\pi$
$908$	22.5343			0.747827
$909$	−9.74236			−0.323134
$910$	−7.90372	+	9.12138i	−0.262006	+	0.302371i
$911$	−4.61044	−	10.0955i	−0.152751	−	0.334477i	0.817751	−	0.575572i	$-0.195221\pi$
$911$	−4.61044	−	10.0955i	−0.152751	−	0.334477i	−0.970502	+	0.241095i	$0.922493\pi$
$912$	1.87895	+	1.20753i	0.0622182	+	0.0399852i
$913$	20.6720	+	23.8568i	0.684143	+	0.789543i
$914$	−23.8228	−	15.3100i	−0.787989	−	0.506410i
$915$	3.60859	+	25.0983i	0.119296	+	0.829724i
$916$	3.28062	−	22.8172i	0.108395	−	0.753901i
$917$	0.768167	+	1.68205i	0.0253671	+	0.0555462i
$918$	1.17708	+	8.18677i	0.0388494	+	0.270204i
$919$	56.4781	+	16.5835i	1.86304	+	0.547038i	0.999052	+	0.0435240i	$0.0138585\pi$
$919$	56.4781	+	16.5835i	1.86304	+	0.547038i	0.863987	+	0.503514i	$0.167960\pi$
$920$	−22.3307	+	14.3510i	−0.736220	+	0.473140i
$921$	23.0660	+	14.8236i	0.760050	+	0.488454i
$922$	0.645424	−	1.41328i	0.0212559	−	0.0465440i
$923$	−59.8686	−	17.5790i	−1.97060	−	0.578620i
$924$	−4.01134	+	2.57793i	−0.131963	+	0.0848077i
$925$	72.8909	+	84.1206i	2.39664	+	2.76587i
$926$	15.8231	+	18.2609i	0.519981	+	0.600090i
$927$	0.521094	−	1.14104i	0.0171150	−	0.0374765i
$928$	−0.556863	+	3.87307i	−0.0182799	+	0.127140i
$929$	−6.68296	+	1.96229i	−0.219261	+	0.0643808i	−0.389518	−	0.921019i	$-0.627358\pi$
$929$	−6.68296	+	1.96229i	−0.219261	+	0.0643808i	0.170257	+	0.985400i	$0.445540\pi$
$930$	−10.7361	+	12.3901i	−0.352051	+	0.406289i
$931$	−10.8306	+	3.18015i	−0.354959	+	0.104225i
$932$	7.02861	+	15.3905i	0.230230	+	0.504133i
$933$	18.8413	−	41.2568i	0.616838	−	1.35069i
$934$	18.8242	−	12.0976i	0.615946	−	0.395845i
$935$	4.96916	+	34.5613i	0.162509	+	1.13027i
$936$	−6.48702	+	1.90476i	−0.212035	+	0.0622590i
$937$	−30.2813			−0.989246			−0.494623	−	0.869108i	$-0.664694\pi$
$937$	−30.2813			−0.989246			−0.494623	+	0.869108i	$0.664694\pi$
$938$	4.80044	+	0.279060i	0.156740	+	0.00911165i
$939$	−18.9231			−0.617531
$940$	12.7294	−	3.73768i	0.415187	−	0.121910i
$941$	4.55192	+	31.6593i	0.148388	+	1.03206i	0.918858	+	0.394588i	$0.129113\pi$
$941$	4.55192	+	31.6593i	0.148388	+	1.03206i	−0.770470	+	0.637476i	$0.779978\pi$
$942$	−19.1537	+	12.3093i	−0.624062	+	0.401060i
$943$	−7.27319	+	15.9261i	−0.236848	+	0.518624i
$944$	0.558122	+	1.22212i	0.0181653	+	0.0397765i
$945$	12.1819	−	3.57694i	0.396278	−	0.116358i
$946$	−5.46129	+	6.30266i	−0.177562	+	0.204917i
$947$	20.3262	−	5.96830i	0.660512	−	0.193944i	0.0657381	−	0.997837i	$-0.479060\pi$
$947$	20.3262	−	5.96830i	0.660512	−	0.193944i	0.594774	+	0.803893i	$0.297242\pi$
$948$	−1.48351	+	10.3181i	−0.0481823	+	0.335115i
$949$	3.59957	−	7.88196i	0.116847	−	0.255859i
$950$	−10.8871	−	12.5644i	−0.353225	−	0.407644i
$951$	−17.0681	−	19.6976i	−0.553470	−	0.638739i
$952$	−0.727637	+	0.467624i	−0.0235828	+	0.0151558i
$953$	−4.64217	−	1.36307i	−0.150375	−	0.0441540i	0.205679	−	0.978620i	$-0.434060\pi$
$953$	−4.64217	−	1.36307i	−0.150375	−	0.0441540i	−0.356054	+	0.934466i	$0.615878\pi$
$954$	2.42323	−	5.30613i	0.0784550	−	0.171792i
$955$	7.10256	+	4.56454i	0.229833	+	0.147705i
$956$	−14.0939	+	9.05761i	−0.455830	+	0.292944i
$957$	−30.4738	−	8.94791i	−0.985078	−	0.289245i
$958$	−4.54105	−	31.5837i	−0.146715	−	1.02042i
$959$	3.33478	+	7.30214i	0.107686	+	0.235799i
$960$	−0.720978	+	5.01451i	−0.0232695	+	0.161843i
$961$	2.92136	+	20.3185i	0.0942374	+	0.655435i
$962$	51.0163	+	32.7862i	1.64483	+	1.05707i
$963$	4.85036	+	5.59761i	0.156301	+	0.180381i
$964$	1.61714	+	1.03927i	0.0520845	+	0.0334727i
$965$	36.2003	+	79.2676i	1.16533	+	2.55171i
$966$	3.49514	−	4.03361i	0.112454	−	0.129779i
$967$	−45.6410			−1.46772			−0.733858	−	0.679303i	$-0.762282\pi$
$967$	−45.6410			−1.46772			−0.733858	+	0.679303i	$0.762282\pi$
$968$	−26.9958			−0.867678
$969$	−2.15352	+	2.48529i	−0.0691809	+	0.0798390i
$970$	1.18674	−	8.25398i	0.0381040	−	0.265019i
$971$	30.1936	+	8.86563i	0.968957	+	0.284512i	0.727659	−	0.685939i	$-0.240608\pi$
$971$	30.1936	+	8.86563i	0.968957	+	0.284512i	0.241299	+	0.970451i	$0.422427\pi$
$972$	11.6228	+	3.41275i	0.372800	+	0.109464i
$973$	−1.11140	+	7.72993i	−0.0356297	+	0.247810i
$974$	22.7028	−	26.2004i	0.727445	−	0.839516i
$975$	−68.9233			−2.20731
$976$	−5.00513			−0.160210
$977$	10.1192	−	11.6782i	0.323743	−	0.373620i	−0.570426	−	0.821349i	$-0.693222\pi$
$977$	10.1192	−	11.6782i	0.323743	−	0.373620i	0.894169	+	0.447729i	$0.147767\pi$
$978$	−3.38523	−	7.41262i	−0.108248	−	0.237029i
$979$	76.1769	+	48.9559i	2.43462	+	1.56464i
$980$	−16.7666	−	19.3496i	−0.535588	−	0.618101i
$981$	10.8084	+	6.94611i	0.345084	+	0.221772i
$982$	−3.19887	−	22.2487i	−0.102080	−	0.709983i
$983$	1.77754	−	12.3630i	0.0566946	−	0.394320i	−0.941640	−	0.336623i	$-0.890715\pi$
$983$	1.77754	−	12.3630i	0.0566946	−	0.394320i	0.998334	−	0.0576967i	$-0.0183757\pi$
$984$	1.38810	+	3.03952i	0.0442512	+	0.0968965i
$985$	7.33709	+	51.0306i	0.233779	+	1.62597i
$986$	−5.52779	−	1.62311i	−0.176041	−	0.0516902i
$987$	−2.24405	+	1.44217i	−0.0714290	+	0.0459046i
$988$	−7.61990	−	4.89701i	−0.242421	−	0.155795i
$989$	3.87776	−	8.49111i	0.123306	−	0.270002i
$990$	28.8081	+	8.45881i	0.915581	+	0.268839i
$991$	24.3620	−	15.6565i	0.773885	−	0.497346i	−0.0931138	−	0.995655i	$-0.529682\pi$
$991$	24.3620	−	15.6565i	0.773885	−	0.497346i	0.866999	+	0.498310i	$0.166046\pi$
$992$	−2.11922	−	2.44571i	−0.0672852	−	0.0776513i
$993$	4.18566	+	4.83051i	0.132828	+	0.153292i
$994$	−2.85143	+	6.24377i	−0.0904420	+	0.198040i
$995$	4.89097	−	34.0174i	0.155054	−	1.07843i
$996$	−6.47032	+	1.89986i	−0.205020	+	0.0601993i
$997$	32.0764	−	37.0181i	1.01587	−	1.17237i	0.0309209	−	0.999522i	$-0.490156\pi$
$997$	32.0764	−	37.0181i	1.01587	−	1.17237i	0.984948	−	0.172853i	$-0.0552986\pi$
$998$	−0.281648	+	0.0826992i	−0.00891540	+	0.00261780i
$999$	−26.5006	−	58.0282i	−0.838442	−	1.83593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	134.2.e.a.89.2	✓	30
67.8	odd	22		8978.2.a.l.1.12		15
67.59	even	11		8978.2.a.k.1.4		15
67.64	even	11	inner	134.2.e.a.131.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
134.2.e.a.89.2	✓	30	1.1	even	1	trivial
134.2.e.a.131.2	yes	30	67.64	even	11	inner
8978.2.a.k.1.4		15	67.59	even	11
8978.2.a.l.1.12		15	67.8	odd	22

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:	\( N \)	\(=\)	\( 134 = 2 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	134.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 - 0.281733i) q^{2} +(0.187400 + 1.30339i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-1.59822 + 3.49961i) q^{5} +(0.547017 + 1.19780i) q^{6} +(-0.563661 + 0.165506i) q^{7} +(0.654861 - 0.755750i) q^{8} +(1.21477 - 0.356688i) q^{9} +O(q^{10})\)	\(q+(0.959493 - 0.281733i) q^{2} +(0.187400 + 1.30339i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-1.59822 + 3.49961i) q^{5} +(0.547017 + 1.19780i) q^{6} +(-0.563661 + 0.165506i) q^{7} +(0.654861 - 0.755750i) q^{8} +(1.21477 - 0.356688i) q^{9} +(-0.547525 + 3.80812i) q^{10} +(2.56065 - 5.60704i) q^{11} +(0.862318 + 0.995168i) q^{12} +(-3.49705 - 4.03581i) q^{13} +(-0.494200 + 0.317603i) q^{14} +(-4.86087 - 1.42728i) q^{15} +(0.415415 - 0.909632i) q^{16} +(1.23862 + 0.796013i) q^{17} +(1.06507 - 0.684478i) q^{18} +(1.62746 + 0.477867i) q^{19} +(0.547525 + 3.80812i) q^{20} +(-0.321349 - 0.703656i) q^{21} +(0.877239 - 6.10133i) q^{22} +(0.981909 + 6.82933i) q^{23} +(1.10776 + 0.711913i) q^{24} +(-6.41865 - 7.40752i) q^{25} +(-4.49241 - 2.88710i) q^{26} +(2.33360 + 5.10987i) q^{27} +(-0.384703 + 0.443971i) q^{28} -3.91290 q^{29} -5.06608 q^{30} +(2.11922 - 2.44571i) q^{31} +(0.142315 - 0.989821i) q^{32} +(7.78804 + 2.28677i) q^{33} +(1.41271 + 0.414809i) q^{34} +(0.321647 - 2.23711i) q^{35} +(0.829086 - 0.956817i) q^{36} -11.3561 q^{37} +1.69617 q^{38} +(4.60490 - 5.31433i) q^{39} +(1.59822 + 3.49961i) q^{40} +(2.13476 + 1.37193i) q^{41} +(-0.506575 - 0.584618i) q^{42} +(-1.13816 - 0.731454i) q^{43} +(-0.877239 - 6.10133i) q^{44} +(-0.693194 + 4.82127i) q^{45} +(2.86618 + 6.27605i) q^{46} +(-0.490752 - 3.41325i) q^{47} +(1.26346 + 0.370984i) q^{48} +(-5.59845 + 3.59791i) q^{49} +(-8.24559 - 5.29912i) q^{50} +(-0.805401 + 1.76358i) q^{51} +(-5.12383 - 1.50449i) q^{52} +(3.87604 - 2.49098i) q^{53} +(3.67869 + 4.24543i) q^{54} +(15.5300 + 17.9225i) q^{55} +(-0.244039 + 0.534370i) q^{56} +(-0.317862 + 2.21078i) q^{57} +(-3.75440 + 1.10239i) q^{58} +(-0.879824 + 1.01537i) q^{59} +(-4.86087 + 1.42728i) q^{60} +(-2.07921 - 4.55283i) q^{61} +(1.34434 - 2.94369i) q^{62} +(-0.625683 + 0.402102i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(19.7128 - 5.78820i) q^{65} +8.11682 q^{66} +(-6.61753 - 4.81750i) q^{67} +1.47235 q^{68} +(-8.71728 + 2.55962i) q^{69} +(-0.321647 - 2.23711i) q^{70} +(9.82951 - 6.31704i) q^{71} +(0.525936 - 1.15164i) q^{72} +(0.674059 + 1.47598i) q^{73} +(-10.8961 + 3.19938i) q^{74} +(8.45206 - 9.75419i) q^{75} +(1.62746 - 0.477867i) q^{76} +(-0.515341 + 3.58427i) q^{77} +(2.92114 - 6.39641i) q^{78} +(5.18408 + 5.98275i) q^{79} +(2.51943 + 2.90758i) q^{80} +(-3.02764 + 1.94575i) q^{81} +(2.43480 + 0.714922i) q^{82} +(-2.12739 + 4.65834i) q^{83} +(-0.650761 - 0.418219i) q^{84} +(-4.76532 + 3.06249i) q^{85} +(-1.29813 - 0.381167i) q^{86} +(-0.733275 - 5.10004i) q^{87} +(-2.56065 - 5.60704i) q^{88} +(-2.09064 + 14.5407i) q^{89} +(0.693194 + 4.82127i) q^{90} +(2.63910 + 1.69605i) q^{91} +(4.51825 + 5.21433i) q^{92} +(3.58486 + 2.30385i) q^{93} +(-1.43250 - 3.13673i) q^{94} +(-4.27339 + 4.93175i) q^{95} +1.31680 q^{96} -2.16747 q^{97} +(-4.35803 + 5.02943i) q^{98} +(1.11063 - 7.72459i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{8} - 8 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 + q^6 + 3 * q^8 - 8 * q^9	\( 30 q + 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{8} - 8 q^{9} + 3 q^{10} + q^{11} - q^{12} - 11 q^{13} - 22 q^{14} + 18 q^{15} - 3 q^{16} - 8 q^{17} - 3 q^{18} + 16 q^{19} - 3 q^{20} - 27 q^{21} - q^{22} + 12 q^{24} + 2 q^{25} - 11 q^{26} + 14 q^{27} - 11 q^{28} + 26 q^{30} + 18 q^{31} + 3 q^{32} + 9 q^{33} - 14 q^{34} - 90 q^{35} - 8 q^{36} - 48 q^{37} + 28 q^{38} - q^{39} + 3 q^{40} - 51 q^{41} - 17 q^{42} + 10 q^{43} + q^{44} - 4 q^{45} - 11 q^{46} + 10 q^{47} + 10 q^{48} - 19 q^{49} - 24 q^{50} + 4 q^{51} + 11 q^{52} - 8 q^{53} - 25 q^{54} + 25 q^{55} + 31 q^{57} + 22 q^{58} + 66 q^{59} + 18 q^{60} + 34 q^{61} - 29 q^{62} + 80 q^{63} - 3 q^{64} + 26 q^{65} + 90 q^{66} - 3 q^{67} - 8 q^{68} - 46 q^{69} + 90 q^{70} + 39 q^{71} - 3 q^{72} + 78 q^{73} - 18 q^{74} - 11 q^{75} + 16 q^{76} + 73 q^{77} - 10 q^{78} + 34 q^{79} + 8 q^{80} - 134 q^{81} + 7 q^{82} - 11 q^{83} + 6 q^{84} - 31 q^{85} + q^{86} - 110 q^{87} - q^{88} - 30 q^{89} + 4 q^{90} + 14 q^{91} + 11 q^{92} - 13 q^{93} + 23 q^{94} - 39 q^{95} - 10 q^{96} + 24 q^{97} + 19 q^{98} - 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 + q^6 + 3 * q^8 - 8 * q^9 + 3 * q^10 + q^11 - q^12 - 11 * q^13 - 22 * q^14 + 18 * q^15 - 3 * q^16 - 8 * q^17 - 3 * q^18 + 16 * q^19 - 3 * q^20 - 27 * q^21 - q^22 + 12 * q^24 + 2 * q^25 - 11 * q^26 + 14 * q^27 - 11 * q^28 + 26 * q^30 + 18 * q^31 + 3 * q^32 + 9 * q^33 - 14 * q^34 - 90 * q^35 - 8 * q^36 - 48 * q^37 + 28 * q^38 - q^39 + 3 * q^40 - 51 * q^41 - 17 * q^42 + 10 * q^43 + q^44 - 4 * q^45 - 11 * q^46 + 10 * q^47 + 10 * q^48 - 19 * q^49 - 24 * q^50 + 4 * q^51 + 11 * q^52 - 8 * q^53 - 25 * q^54 + 25 * q^55 + 31 * q^57 + 22 * q^58 + 66 * q^59 + 18 * q^60 + 34 * q^61 - 29 * q^62 + 80 * q^63 - 3 * q^64 + 26 * q^65 + 90 * q^66 - 3 * q^67 - 8 * q^68 - 46 * q^69 + 90 * q^70 + 39 * q^71 - 3 * q^72 + 78 * q^73 - 18 * q^74 - 11 * q^75 + 16 * q^76 + 73 * q^77 - 10 * q^78 + 34 * q^79 + 8 * q^80 - 134 * q^81 + 7 * q^82 - 11 * q^83 + 6 * q^84 - 31 * q^85 + q^86 - 110 * q^87 - q^88 - 30 * q^89 + 4 * q^90 + 14 * q^91 + 11 * q^92 - 13 * q^93 + 23 * q^94 - 39 * q^95 - 10 * q^96 + 24 * q^97 + 19 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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