LMFDB - Embedded newform 76.2.k.a.15.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			15.7
Character	$\chi$	$=$	76.15
Dual form			76.2.k.a.71.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.927206 - 1.06784i) q^{2} +(0.306623 + 1.73895i) q^{3} +(-0.280577 - 1.98022i) q^{4} +(-0.220151 + 0.184728i) q^{5} +(2.14122 + 1.28494i) q^{6} +(-0.588321 - 0.339668i) q^{7} +(-2.37472 - 1.53646i) q^{8} +(-0.110838 + 0.0403418i) q^{9} +O(q^{10})$	\(q+(0.927206 - 1.06784i) q^{2} +(0.306623 + 1.73895i) q^{3} +(-0.280577 - 1.98022i) q^{4} +(-0.220151 + 0.184728i) q^{5} +(2.14122 + 1.28494i) q^{6} +(-0.588321 - 0.339668i) q^{7} +(-2.37472 - 1.53646i) q^{8} +(-0.110838 + 0.0403418i) q^{9} +(-0.00686428 + 0.406368i) q^{10} +(-3.85060 + 2.22314i) q^{11} +(3.35747 - 1.09509i) q^{12} +(-3.41466 - 0.602096i) q^{13} +(-0.908207 + 0.313293i) q^{14} +(-0.388736 - 0.326188i) q^{15} +(-3.84255 + 1.11121i) q^{16} +(4.15159 + 1.51105i) q^{17} +(-0.0596912 + 0.155763i) q^{18} +(1.76165 - 3.98705i) q^{19} +(0.427572 + 0.384117i) q^{20} +(0.410271 - 1.12721i) q^{21} +(-1.19633 + 6.17315i) q^{22} +(0.347253 - 0.413840i) q^{23} +(1.94368 - 4.60062i) q^{24} +(-0.853899 + 4.84270i) q^{25} +(-3.80904 + 3.08805i) q^{26} +(2.54452 + 4.40724i) q^{27} +(-0.507548 + 1.26031i) q^{28} +(1.03930 + 2.85545i) q^{29} +(-0.708757 + 0.112665i) q^{30} +(5.24551 - 9.08550i) q^{31} +(-2.37625 + 5.13356i) q^{32} +(-5.04661 - 6.01432i) q^{33} +(5.46295 - 3.03218i) q^{34} +(0.192266 - 0.0339016i) q^{35} +(0.110984 + 0.208165i) q^{36} -8.82897i q^{37} +(-2.62413 - 5.57799i) q^{38} -6.12252i q^{39} +(0.806624 - 0.100424i) q^{40} +(1.85222 - 0.326596i) q^{41} +(-0.823277 - 1.48326i) q^{42} +(3.49849 + 4.16933i) q^{43} +(5.48271 + 7.00128i) q^{44} +(0.0169489 - 0.0293563i) q^{45} +(-0.119941 - 0.754527i) q^{46} +(0.419777 + 1.15333i) q^{47} +(-3.11055 - 6.34127i) q^{48} +(-3.26925 - 5.66251i) q^{49} +(4.37950 + 5.40201i) q^{50} +(-1.35467 + 7.68271i) q^{51} +(-0.234211 + 6.93071i) q^{52} +(-6.41208 + 7.64162i) q^{53} +(7.06553 + 1.36927i) q^{54} +(0.437034 - 1.20074i) q^{55} +(0.875211 + 1.71055i) q^{56} +(7.47343 + 1.84089i) q^{57} +(4.01281 + 1.53778i) q^{58} +(-4.20510 - 1.53053i) q^{59} +(-0.536855 + 0.861304i) q^{60} +(6.04529 + 5.07260i) q^{61} +(-4.83821 - 14.0255i) q^{62} +(0.0789113 + 0.0139142i) q^{63} +(3.27857 + 7.29733i) q^{64} +(0.862964 - 0.498232i) q^{65} +(-11.1016 - 0.187526i) q^{66} +(-4.66099 + 1.69646i) q^{67} +(1.82738 - 8.64503i) q^{68} +(0.826122 + 0.476961i) q^{69} +(0.142068 - 0.236743i) q^{70} +(-6.81908 + 5.72189i) q^{71} +(0.325193 + 0.0744984i) q^{72} +(0.591231 + 3.35304i) q^{73} +(-9.42796 - 8.18628i) q^{74} -8.68302 q^{75} +(-8.38953 - 2.36978i) q^{76} +3.02052 q^{77} +(-6.53789 - 5.67684i) q^{78} +(-1.43865 - 8.15896i) q^{79} +(0.640670 - 0.954462i) q^{80} +(-7.15481 + 6.00360i) q^{81} +(1.36864 - 2.28070i) q^{82} +(8.64879 + 4.99338i) q^{83} +(-2.34724 - 0.496158i) q^{84} +(-1.19311 + 0.434257i) q^{85} +(7.69601 + 0.129999i) q^{86} +(-4.64680 + 2.68283i) q^{87} +(12.5599 + 0.636961i) q^{88} +(-10.6299 - 1.87434i) q^{89} +(-0.0156328 - 0.0453180i) q^{90} +(1.80440 + 1.51407i) q^{91} +(-0.916926 - 0.571524i) q^{92} +(17.4076 + 6.33584i) q^{93} +(1.62079 + 0.621117i) q^{94} +(0.348694 + 1.20318i) q^{95} +(-9.65560 - 2.55809i) q^{96} +(-1.24019 + 3.40739i) q^{97} +(-9.07794 - 1.75927i) q^{98} +(0.337108 - 0.401750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.927206	−	1.06784i	0.655634	−	0.755079i
$2$	0.927206	−	1.06784i	0.655634	−	0.755079i
$3$	0.306623	+	1.73895i	0.177029	+	1.00398i	0.935776	+	0.352595i	$0.114701\pi$
$3$	0.306623	+	1.73895i	0.177029	+	1.00398i	−0.758747	+	0.651386i	$0.774188\pi$
$4$	−0.280577	−	1.98022i	−0.140288	−	0.990111i
$5$	−0.220151	+	0.184728i	−0.0984544	+	0.0826131i	−0.690686	−	0.723155i	$-0.742691\pi$
$5$	−0.220151	+	0.184728i	−0.0984544	+	0.0826131i	0.592232	+	0.805768i	$0.298247\pi$
$6$	2.14122	+	1.28494i	0.874151	+	0.524573i
$7$	−0.588321	−	0.339668i	−0.222365	−	0.128382i	0.384680	−	0.923050i	$-0.374312\pi$
$7$	−0.588321	−	0.339668i	−0.222365	−	0.128382i	−0.607045	+	0.794668i	$0.707645\pi$
$8$	−2.37472	−	1.53646i	−0.839589	−	0.543221i
$9$	−0.110838	+	0.0403418i	−0.0369461	+	0.0134473i
$10$	−0.00686428	+	0.406368i	−0.00217068	+	0.128505i
$11$	−3.85060	+	2.22314i	−1.16100	+	0.670303i	−0.951543	−	0.307515i	$-0.900503\pi$
$11$	−3.85060	+	2.22314i	−1.16100	+	0.670303i	−0.209456	+	0.977818i	$0.567169\pi$
$12$	3.35747	−	1.09509i	0.969217	−	0.316125i
$13$	−3.41466	−	0.602096i	−0.947056	−	0.166991i	−0.321271	−	0.946987i	$-0.604110\pi$
$13$	−3.41466	−	0.602096i	−0.947056	−	0.166991i	−0.625785	+	0.779996i	$0.715221\pi$
$14$	−0.908207	+	0.313293i	−0.242728	+	0.0837310i
$15$	−0.388736	−	0.326188i	−0.100371	−	0.0842215i
$16$	−3.84255	+	1.11121i	−0.960638	+	0.277802i
$17$	4.15159	+	1.51105i	1.00691	+	0.366485i	0.792245	−	0.610203i	$-0.208912\pi$
$17$	4.15159	+	1.51105i	1.00691	+	0.366485i	0.214663	+	0.976688i	$0.431135\pi$
$18$	−0.0596912	+	0.155763i	−0.0140694	+	0.0367137i
$19$	1.76165	−	3.98705i	0.404150	−	0.914693i
$19$	1.76165	−	3.98705i	0.404150	−	0.914693i
$20$	0.427572	+	0.384117i	0.0956081	+	0.0858911i
$21$	0.410271	−	1.12721i	0.0895284	−	0.245977i
$22$	−1.19633	+	6.17315i	−0.255059	+	1.31612i
$23$	0.347253	−	0.413840i	0.0724073	−	0.0862916i	−0.728625	−	0.684913i	$-0.759840\pi$
$23$	0.347253	−	0.413840i	0.0724073	−	0.0862916i	0.801032	+	0.598621i	$0.204285\pi$
$24$	1.94368	−	4.60062i	0.396752	−	0.939098i
$25$	−0.853899	+	4.84270i	−0.170780	+	0.968541i
$26$	−3.80904	+	3.08805i	−0.747014	+	0.605616i
$27$	2.54452	+	4.40724i	0.489693	+	0.848174i
$28$	−0.507548	+	1.26031i	−0.0959175	+	0.238176i
$29$	1.03930	+	2.85545i	0.192993	+	0.530244i	0.998013	−	0.0630035i	$-0.0200679\pi$
$29$	1.03930	+	2.85545i	0.192993	+	0.530244i	−0.805020	+	0.593247i	$0.797846\pi$
$30$	−0.708757	+	0.112665i	−0.129401	+	0.0205698i
$31$	5.24551	−	9.08550i	0.942122	−	1.63180i	0.180709	−	0.983537i	$-0.442161\pi$
$31$	5.24551	−	9.08550i	0.942122	−	1.63180i	0.761413	−	0.648267i	$-0.224506\pi$
$32$	−2.37625	+	5.13356i	−0.420065	+	0.907494i
$33$	−5.04661	−	6.01432i	−0.878502	−	1.04696i
$34$	5.46295	−	3.03218i	0.936888	−	0.520015i
$35$	0.192266	−	0.0339016i	0.0324988	−	0.00573042i
$36$	0.110984	+	0.208165i	0.0184974	+	0.0346942i
$37$		−	8.82897i		−	1.45147i	−0.687972	−	0.725737i	$-0.741499\pi$
$37$		−	8.82897i		−	1.45147i	0.687972	−	0.725737i	$-0.258501\pi$
$38$	−2.62413	−	5.57799i	−0.425691	−	0.904869i
$39$		−	6.12252i		−	0.980388i
$40$	0.806624	−	0.100424i	0.127538	−	0.0158785i
$41$	1.85222	−	0.326596i	0.289268	−	0.0510058i	−0.0271312	−	0.999632i	$-0.508637\pi$
$41$	1.85222	−	0.326596i	0.289268	−	0.0510058i	0.316399	+	0.948626i	$0.397526\pi$
$42$	−0.823277	−	1.48326i	−0.127034	−	0.228872i
$43$	3.49849	+	4.16933i	0.533514	+	0.635817i	0.963721	−	0.266913i	$-0.0860037\pi$
$43$	3.49849	+	4.16933i	0.533514	+	0.635817i	−0.430207	+	0.902730i	$0.641559\pi$
$44$	5.48271	+	7.00128i	0.826549	+	1.05548i
$45$	0.0169489	−	0.0293563i	0.00252659	−	0.00437617i
$46$	−0.119941	−	0.754527i	−0.0176843	−	0.111249i
$47$	0.419777	+	1.15333i	0.0612307	+	0.168230i	0.966536	−	0.256532i	$-0.0825799\pi$
$47$	0.419777	+	1.15333i	0.0612307	+	0.168230i	−0.905305	+	0.424762i	$0.860358\pi$
$48$	−3.11055	−	6.34127i	−0.448969	−	0.915284i
$49$	−3.26925	−	5.66251i	−0.467036	−	0.808930i
$50$	4.37950	+	5.40201i	0.619355	+	0.763960i
$51$	−1.35467	+	7.68271i	−0.189692	+	1.07580i
$52$	−0.234211	+	6.93071i	−0.0324793	+	0.961117i
$53$	−6.41208	+	7.64162i	−0.880767	+	1.04966i	0.117630	+	0.993057i	$0.462470\pi$
$53$	−6.41208	+	7.64162i	−0.880767	+	1.04966i	−0.998397	+	0.0565997i	$0.981974\pi$
$54$	7.06553	+	1.36927i	0.961497	+	0.186334i
$55$	0.437034	−	1.20074i	0.0589297	−	0.161908i
$56$	0.875211	+	1.71055i	0.116955	+	0.228582i
$57$	7.47343	+	1.84089i	0.989880	+	0.243832i
$58$	4.01281	+	1.53778i	0.526908	+	0.201921i
$59$	−4.20510	−	1.53053i	−0.547457	−	0.199258i	0.0534593	−	0.998570i	$-0.482975\pi$
$59$	−4.20510	−	1.53053i	−0.547457	−	0.199258i	−0.600916	+	0.799312i	$0.705197\pi$
$60$	−0.536855	+	0.861304i	−0.0693077	+	0.111194i
$61$	6.04529	+	5.07260i	0.774020	+	0.649480i	0.941735	−	0.336356i	$-0.109194\pi$
$61$	6.04529	+	5.07260i	0.774020	+	0.649480i	−0.167715	+	0.985836i	$0.553639\pi$
$62$	−4.83821	−	14.0255i	−0.614453	−	1.78124i
$63$	0.0789113	+	0.0139142i	0.00994189	+	0.00175302i
$64$	3.27857	+	7.29733i	0.409821	+	0.912166i
$65$	0.862964	−	0.498232i	0.107037	−	0.0617981i
$66$	−11.1016	−	0.187526i	−1.36651	−	0.0230828i
$67$	−4.66099	+	1.69646i	−0.569430	+	0.207256i	−0.610658	−	0.791894i	$-0.709095\pi$
$67$	−4.66099	+	1.69646i	−0.569430	+	0.207256i	0.0412282	+	0.999150i	$0.486873\pi$
$68$	1.82738	−	8.64503i	0.221603	−	1.04836i
$69$	0.826122	+	0.476961i	0.0994533	+	0.0574194i
$70$	0.142068	−	0.236743i	0.0169804	−	0.0282962i
$71$	−6.81908	+	5.72189i	−0.809276	+	0.679064i	−0.950435	−	0.310923i	$-0.899362\pi$
$71$	−6.81908	+	5.72189i	−0.809276	+	0.679064i	0.141159	+	0.989987i	$0.454917\pi$
$72$	0.325193	+	0.0744984i	0.0383244	+	0.00877972i
$73$	0.591231	+	3.35304i	0.0691984	+	0.392444i	0.999661	+	0.0260554i	$0.00829463\pi$
$73$	0.591231	+	3.35304i	0.0691984	+	0.392444i	−0.930462	+	0.366388i	$0.880594\pi$
$74$	−9.42796	−	8.18628i	−1.09598	−	0.951636i
$75$	−8.68302			−1.00263
$76$	−8.38953	−	2.36978i	−0.962345	−	0.271833i
$77$	3.02052			0.344220
$78$	−6.53789	−	5.67684i	−0.740270	−	0.642776i
$79$	−1.43865	−	8.15896i	−0.161860	−	0.917955i	−0.952243	−	0.305342i	$-0.901229\pi$
$79$	−1.43865	−	8.15896i	−0.161860	−	0.917955i	0.790383	−	0.612614i	$-0.209882\pi$
$80$	0.640670	−	0.954462i	0.0716290	−	0.106712i
$81$	−7.15481	+	6.00360i	−0.794979	+	0.667067i
$82$	1.36864	−	2.28070i	0.151141	−	0.251861i
$83$	8.64879	+	4.99338i	0.949328	+	0.548095i	0.892872	−	0.450310i	$-0.148687\pi$
$83$	8.64879	+	4.99338i	0.949328	+	0.548095i	0.0564561	+	0.998405i	$0.482020\pi$
$84$	−2.34724	−	0.496158i	−0.256104	−	0.0541353i
$85$	−1.19311	+	0.434257i	−0.129411	+	0.0471018i
$86$	7.69601	+	0.129999i	0.829882	+	0.0140182i
$87$	−4.64680	+	2.68283i	−0.498189	+	0.287630i
$88$	12.5599	+	0.636961i	1.33889	+	0.0679002i
$89$	−10.6299	−	1.87434i	−1.12677	−	0.198680i	−0.420958	−	0.907080i	$-0.638306\pi$
$89$	−10.6299	−	1.87434i	−1.12677	−	0.198680i	−0.705811	+	0.708401i	$0.749417\pi$
$90$	−0.0156328	−	0.0453180i	−0.00164784	−	0.00477694i
$91$	1.80440	+	1.51407i	0.189153	+	0.158718i
$92$	−0.916926	−	0.571524i	−0.0955962	−	0.0595855i
$93$	17.4076	+	6.33584i	1.80508	+	0.656996i
$94$	1.62079	+	0.621117i	0.167172	+	0.0640633i
$95$	0.348694	+	1.20318i	0.0357752	+	0.123444i
$96$	−9.65560	−	2.55809i	−0.985471	−	0.261084i
$97$	−1.24019	+	3.40739i	−0.125922	+	0.345968i	−0.986595	−	0.163191i	$-0.947821\pi$
$97$	−1.24019	+	3.40739i	−0.125922	+	0.345968i	0.860672	+	0.509159i	$0.170044\pi$
$98$	−9.07794	−	1.75927i	−0.917011	−	0.177713i
$99$	0.337108	−	0.401750i	0.0338806	−	0.0403774i
$100$	9.82921	+	0.332161i	0.982921	+	0.0332161i
$101$	1.93027	−	10.9471i	0.192069	−	1.08928i	−0.724461	−	0.689316i	$-0.757911\pi$
$101$	1.93027	−	10.9471i	0.192069	−	1.08928i	0.916531	−	0.399965i	$-0.130978\pi$
$102$	6.94787	+	8.57004i	0.687942	+	0.848560i
$103$	1.44865	+	2.50913i	0.142740	+	0.247232i	0.928527	−	0.371264i	$-0.121076\pi$
$103$	1.44865	+	2.50913i	0.142740	+	0.247232i	−0.785788	+	0.618496i	$0.787742\pi$
$104$	7.18375	+	6.67630i	0.704425	+	0.654665i
$105$	0.117906	+	0.323945i	0.0115065	+	0.0316138i
$106$	2.21473	+	13.9325i	0.215113	+	1.35324i
$107$	−4.67836	+	8.10316i	−0.452274	+	0.783362i	−0.998527	−	0.0542585i	$-0.982720\pi$
$107$	−4.67836	+	8.10316i	−0.452274	+	0.783362i	0.546253	+	0.837620i	$0.316054\pi$
$108$	8.01338	−	6.27528i	0.771087	−	0.603839i
$109$	−5.97096	−	7.11592i	−0.571915	−	0.681581i	0.400108	−	0.916468i	$-0.368973\pi$
$109$	−5.97096	−	7.11592i	−0.571915	−	0.681581i	−0.972023	+	0.234887i	$0.924528\pi$
$110$	−0.876983	−	1.58002i	−0.0836170	−	0.150649i
$111$	15.3531	−	2.70717i	1.45725	−	0.256953i
$112$	2.63810	+	0.651444i	0.249277	+	0.0615556i
$113$		−	13.7103i		−	1.28976i	−0.764285	−	0.644879i	$-0.776908\pi$
$113$		−	13.7103i		−	1.28976i	0.764285	−	0.644879i	$-0.223092\pi$
$114$	8.89520	−	6.27357i	0.833112	−	0.587573i
$115$			0.155255i			0.0144776i
$116$	5.36282	−	2.85921i	0.497925	−	0.265471i
$117$	0.402764	−	0.0710182i	0.0372356	−	0.00656564i
$118$	−5.53336	+	3.07127i	−0.509387	+	0.282733i
$119$	−1.92921	−	2.29915i	−0.176851	−	0.210762i
$120$	0.421962	+	1.37188i	0.0385197	+	0.125235i
$121$	4.38474	−	7.59459i	0.398613	−	0.690417i
$122$	11.0220	−	1.75207i	0.997882	−	0.158625i
$123$	1.13587	+	3.12077i	0.102418	+	0.281390i
$124$	−19.4631	−	7.83810i	−1.74783	−	0.703882i
$125$	−1.42506	−	2.46828i	−0.127462	−	0.220770i
$126$	0.0880253	−	0.0713636i	0.00784191	−	0.00635757i
$127$	0.878075	−	4.97981i	0.0779165	−	0.441887i	−0.920745	−	0.390165i	$-0.872418\pi$
$127$	0.878075	−	4.97981i	0.0779165	−	0.441887i	0.998662	−	0.0517217i	$-0.0164709\pi$
$128$	10.8323	+	3.26514i	0.957450	+	0.288600i
$129$	−6.17753	+	7.36209i	−0.543901	+	0.648196i
$130$	0.268112	−	1.38347i	0.0235150	−	0.121339i
$131$	5.78998	−	15.9078i	0.505873	−	1.38987i	−0.379586	−	0.925156i	$-0.623934\pi$
$131$	5.78998	−	15.9078i	0.505873	−	1.38987i	0.885459	−	0.464718i	$-0.153844\pi$
$132$	−10.4937	+	11.6809i	−0.913361	+	1.01669i
$133$	−2.39069	+	1.74729i	−0.207299	+	0.151510i
$134$	−2.51014	+	6.55017i	−0.216843	+	0.565849i
$135$	−1.37432	−	0.500212i	−0.118283	−	0.0430514i
$136$	−7.53717	−	9.96709i	−0.646307	−	0.854671i
$137$	8.65585	+	7.26312i	0.739519	+	0.620530i	0.932708	−	0.360631i	$-0.117439\pi$
$137$	8.65585	+	7.26312i	0.739519	+	0.620530i	−0.193189	+	0.981161i	$0.561883\pi$
$138$	1.27531	−	0.439926i	0.108561	−	0.0374490i
$139$	−1.86185	−	0.328295i	−0.157920	−	0.0278456i	0.0941290	−	0.995560i	$-0.469993\pi$
$139$	−1.86185	−	0.328295i	−0.157920	−	0.0278456i	−0.252049	+	0.967714i	$0.581105\pi$
$140$	−0.121078	−	0.371217i	−0.0102330	−	0.0313735i
$141$	−1.87686	+	1.08361i	−0.158060	+	0.0912561i
$142$	−0.212619	+	12.5871i	−0.0178425	+	1.05628i
$143$	14.4870	−	5.27284i	1.21147	−	0.440937i
$144$	0.381074	−	0.278180i	0.0317562	−	0.0231817i
$145$	−0.756285	−	0.436641i	−0.0628061	−	0.0362611i
$146$	4.12871	+	2.47762i	0.341695	+	0.205049i
$147$	8.84437	−	7.42131i	0.729472	−	0.612099i
$148$	−17.4833	+	2.47720i	−1.43712	+	0.203625i
$149$	0.468913	+	2.65934i	0.0384148	+	0.217861i	0.997972	−	0.0636520i	$-0.0202748\pi$
$149$	0.468913	+	2.65934i	0.0384148	+	0.217861i	−0.959557	+	0.281513i	$0.909164\pi$
$150$	−8.05096	+	9.27211i	−0.657358	+	0.757064i
$151$	−12.9100			−1.05060			−0.525302	−	0.850916i	$-0.676048\pi$
$151$	−12.9100			−1.05060			−0.525302	+	0.850916i	$0.676048\pi$
$152$	−10.3094	+	6.76142i	−0.836201	+	0.548423i
$153$	−0.521114			−0.0421295
$154$	2.80064	−	3.22544i	0.225682	−	0.259913i
$155$	0.523546	+	2.96917i	0.0420522	+	0.238490i
$156$	−12.1240	+	1.71784i	−0.970693	+	0.137537i
$157$	−18.3881	+	15.4295i	−1.46753	+	1.23140i	−0.549140	+	0.835730i	$0.685045\pi$
$157$	−18.3881	+	15.4295i	−1.46753	+	1.23140i	−0.918391	+	0.395674i	$0.870511\pi$
$158$	−10.0464	−	6.02880i	−0.799250	−	0.479625i
$159$	−15.2545	−	8.80717i	−1.20976	−	0.698454i
$160$	−0.425182	−	1.56912i	−0.0336136	−	0.124050i
$161$	−0.344864	+	0.125520i	−0.0271791	+	0.00989239i
$162$	−0.223086	+	13.2068i	−0.0175273	+	1.03762i
$163$	9.16976	−	5.29416i	0.718231	−	0.414671i	−0.0958702	−	0.995394i	$-0.530563\pi$
$163$	9.16976	−	5.29416i	0.718231	−	0.414671i	0.814101	+	0.580723i	$0.197230\pi$
$164$	−1.16642	−	3.57617i	−0.0910823	−	0.279252i
$165$	2.22203	+	0.391804i	0.172985	+	0.0305019i
$166$	13.3514	−	4.60565i	1.03627	−	0.357468i
$167$	12.2979	+	10.3192i	0.951640	+	0.798521i	0.979573	−	0.201089i	$-0.0644479\pi$
$167$	12.2979	+	10.3192i	0.951640	+	0.798521i	−0.0279326	+	0.999610i	$0.508892\pi$
$168$	−2.70619	+	2.04644i	−0.208787	+	0.157886i
$169$	−0.918638	−	0.334357i	−0.0706644	−	0.0257198i
$170$	−0.642542	+	1.67670i	−0.0492807	+	0.128597i
$171$	−0.0344131	+	0.512986i	−0.00263164	+	0.0392290i
$172$	7.27461	−	8.09759i	0.554684	−	0.617436i
$173$	1.98898	−	5.46467i	0.151219	−	0.415471i	−0.840834	−	0.541294i	$-0.817935\pi$
$173$	1.98898	−	5.46467i	0.151219	−	0.415471i	0.992053	+	0.125823i	$0.0401570\pi$
$174$	−1.44370	+	7.44959i	−0.109447	+	0.564752i
$175$	2.14728	−	2.55902i	0.162319	−	0.193444i
$176$	12.3258	−	12.8214i	0.929089	−	0.966447i
$177$	1.37213	−	7.78173i	0.103136	−	0.584911i
$178$	−11.8576	+	9.61318i	−0.888767	+	0.720538i
$179$	−11.9517	−	20.7009i	−0.893312	−	1.54726i	−0.835880	−	0.548912i	$-0.815042\pi$
$179$	−11.9517	−	20.7009i	−0.893312	−	1.54726i	−0.0574313	−	0.998349i	$-0.518291\pi$
$180$	−0.0628874	−	0.0253258i	−0.00468735	−	0.00188767i
$181$	1.86363	+	5.12028i	0.138522	+	0.380587i	0.989484	−	0.144640i	$-0.0462024\pi$
$181$	1.86363	+	5.12028i	0.138522	+	0.380587i	−0.850962	+	0.525227i	$0.823980\pi$
$182$	3.28985	−	0.522960i	0.243860	−	0.0387644i
$183$	−6.96735	+	12.0678i	−0.515042	+	0.892078i
$184$	−1.46048	+	0.449212i	−0.107668	+	0.0331164i
$185$	1.63096	+	1.94371i	0.119911	+	0.142904i
$186$	22.9061	−	12.7139i	1.67956	−	0.932231i
$187$	−19.3454	+	3.41112i	−1.41468	+	0.249445i
$188$	2.16606	−	1.15485i	0.157976	−	0.0842259i
$189$		−	3.45716i		−	0.251472i
$190$	1.60812	+	0.743246i	0.116665	+	0.0539207i
$191$			22.7901i			1.64904i	0.565835	+	0.824518i	$0.308554\pi$
$191$			22.7901i			1.64904i	−0.565835	+	0.824518i	$0.691446\pi$
$192$	−11.6844	+	7.93878i	−0.843247	+	0.572932i
$193$	20.1265	−	3.54884i	1.44873	−	0.255451i	0.606724	−	0.794913i	$-0.292483\pi$
$193$	20.1265	−	3.54884i	1.44873	−	0.255451i	0.842010	+	0.539462i	$0.181372\pi$
$194$	2.48865	+	4.48369i	0.178675	+	0.321910i
$195$	1.13100	+	1.34788i	0.0809929	+	0.0965236i
$196$	−10.2957	+	8.06261i	−0.735411	+	0.575901i
$197$	2.38584	−	4.13240i	0.169984	−	0.294422i	−0.768430	−	0.639934i	$-0.778962\pi$
$197$	2.38584	−	4.13240i	0.169984	−	0.294422i	0.938414	+	0.345513i	$0.112295\pi$
$198$	−0.116437	−	0.732483i	−0.00827480	−	0.0520553i
$199$	2.00612	+	5.51177i	0.142210	+	0.390719i	0.990266	−	0.139188i	$-0.0444491\pi$
$199$	2.00612	+	5.51177i	0.142210	+	0.390719i	−0.848056	+	0.529907i	$0.822227\pi$
$200$	9.46840	−	10.1881i	0.669517	−	0.720405i
$201$	−4.37922	−	7.58503i	−0.308886	−	0.535007i
$202$	−9.90005	−	12.2115i	−0.696565	−	0.859197i
$203$	0.358462	−	2.03294i	0.0251591	−	0.142684i
$204$	15.5936	+	0.526957i	1.09177	+	0.0368944i
$205$	−0.347436	+	0.414058i	−0.0242660	+	0.0289191i
$206$	4.02255	+	0.779555i	0.280265	+	0.0543142i
$207$	−0.0217939	+	0.0598782i	−0.00151478	+	0.00416182i
$208$	13.7901	−	1.48080i	0.956169	−	0.102675i
$209$	2.08039	+	19.2689i	0.143904	+	1.33286i
$210$	0.455245	+	0.174458i	0.0314149	+	0.0120388i
$211$	15.9787	+	5.81576i	1.10002	+	0.400374i	0.827323	−	0.561727i	$-0.189863\pi$
$211$	15.9787	+	5.81576i	1.10002	+	0.400374i	0.272695	+	0.962101i	$0.412085\pi$
$212$	16.9312	+	10.5533i	1.16284	+	0.724802i
$213$	−12.0410	−	10.1036i	−0.825032	−	0.692284i
$214$	4.31509	+	12.5091i	0.294974	+	0.855101i
$215$	−1.54039	−	0.271612i	−0.105054	−	0.0185238i
$216$	0.729039	−	14.3755i	0.0496048	−	0.978129i
$217$	−6.17210	+	3.56346i	−0.418989	+	0.241904i
$218$	−13.1350	−	0.221874i	−0.889614	−	0.0150272i
$219$	−5.64947	+	2.05624i	−0.381756	+	0.138948i
$220$	−2.50036	−	0.528525i	−0.168574	−	0.0356331i
$221$	−13.2665	−	7.65939i	−0.892398	−	0.515226i
$222$	11.3447	−	18.9048i	0.761405	−	1.26881i
$223$	−10.5804	+	8.87801i	−0.708516	+	0.594515i	−0.924182	−	0.381952i	$-0.875252\pi$
$223$	−10.5804	+	8.87801i	−0.708516	+	0.594515i	0.215667	+	0.976467i	$0.430808\pi$
$224$	3.14170	−	2.21305i	0.209914	−	0.147866i
$225$	−0.100719	−	0.571205i	−0.00671459	−	0.0380803i
$226$	−14.6405	−	12.7123i	−0.973869	−	0.845609i
$227$	11.2959			0.749734			0.374867	−	0.927079i	$-0.377688\pi$
$227$	11.2959			0.749734			0.374867	+	0.927079i	$0.377688\pi$
$228$	1.54850	−	15.3156i	0.102552	−	1.01430i
$229$	5.17443			0.341936			0.170968	−	0.985277i	$-0.445311\pi$
$229$	5.17443			0.341936			0.170968	+	0.985277i	$0.445311\pi$
$230$	0.165788	+	0.143953i	0.0109317	+	0.00949199i
$231$	0.926161	+	5.25252i	0.0609369	+	0.345590i
$232$	1.91925	−	8.37773i	0.126005	−	0.550025i
$233$	4.73339	−	3.97179i	0.310095	−	0.260200i	−0.474436	−	0.880290i	$-0.657348\pi$
$233$	4.73339	−	3.97179i	0.310095	−	0.260200i	0.784531	+	0.620089i	$0.212904\pi$
$234$	0.297609	−	0.495938i	0.0194553	−	0.0324205i
$235$	−0.305467	−	0.176361i	−0.0199264	−	0.0115045i
$236$	−1.85094	+	8.75645i	−0.120486	+	0.569997i
$237$	13.7469	−	5.00345i	0.892956	−	0.325009i
$238$	−4.24390	−	0.0716872i	−0.275091	−	0.00464679i
$239$	6.82870	−	3.94255i	0.441712	−	0.255023i	−0.262612	−	0.964902i	$-0.584584\pi$
$239$	6.82870	−	3.94255i	0.441712	−	0.255023i	0.704324	+	0.709879i	$0.251250\pi$
$240$	1.85620	+	0.821430i	0.119817	+	0.0530231i
$241$	15.2267	+	2.68488i	0.980839	+	0.172948i	0.641005	−	0.767537i	$-0.278518\pi$
$241$	15.2267	+	2.68488i	0.980839	+	0.172948i	0.339834	+	0.940485i	$0.389629\pi$
$242$	−4.04427	−	11.7240i	−0.259976	−	0.753645i
$243$	−0.938472	−	0.787471i	−0.0602030	−	0.0505163i
$244$	8.34871	−	13.3943i	0.534471	−	0.857480i
$245$	1.76576	+	0.642682i	0.112810	+	0.0410595i
$246$	4.38567	+	1.68067i	0.279620	+	0.107156i
$247$	−8.41602	+	12.5537i	−0.535498	+	0.798775i
$248$	−26.4161	+	13.5160i	−1.67743	+	0.858264i
$249$	−6.03130	+	16.5709i	−0.382218	+	1.05014i
$250$	−3.95707	−	0.766864i	−0.250267	−	0.0485007i
$251$	5.32272	−	6.34338i	0.335967	−	0.400390i	−0.571439	−	0.820644i	$-0.693615\pi$
$251$	5.32272	−	6.34338i	0.335967	−	0.400390i	0.907406	+	0.420254i	$0.138059\pi$
$252$	0.00541253	−	0.160166i	0.000340957	−	0.0100895i
$253$	−0.417106	+	2.36553i	−0.0262232	+	0.148719i
$254$	−4.50350	−	5.55496i	−0.282575	−	0.348549i
$255$	−1.12098	−	1.94160i	−0.0701988	−	0.121588i
$256$	13.5304	−	8.53975i	0.845652	−	0.533734i
$257$	1.98542	+	5.45489i	0.123847	+	0.340267i	0.986086	−	0.166234i	$-0.0531608\pi$
$257$	1.98542	+	5.45489i	0.123847	+	0.340267i	−0.862239	+	0.506501i	$0.830939\pi$
$258$	2.13371	+	13.4228i	0.132839	+	0.835668i
$259$	−2.99892	+	5.19427i	−0.186344	+	0.322756i
$260$	−1.22874	−	1.56907i	−0.0762031	−	0.0973094i
$261$	−0.230388	−	0.274566i	−0.0142607	−	0.0169952i
$262$	−11.6186	−	20.9326i	−0.717797	−	1.29322i
$263$	−18.2994	+	3.22667i	−1.12839	+	0.198965i	−0.706520	−	0.707693i	$-0.749736\pi$
$263$	−18.2994	+	3.22667i	−1.12839	+	0.198965i	−0.421867	+	0.906658i	$0.638625\pi$
$264$	2.74350	+	22.0362i	0.168851	+	1.35624i
$265$		−	2.86680i		−	0.176106i
$266$	−0.350827	+	4.17298i	−0.0215106	+	0.255862i
$267$		−	19.0596i		−	1.16643i
$268$	4.66713	+	8.75380i	0.285090	+	0.534723i
$269$	−1.60642	+	0.283255i	−0.0979449	+	0.0172703i	−0.222406	−	0.974954i	$-0.571391\pi$
$269$	−1.60642	+	0.283255i	−0.0979449	+	0.0172703i	0.124461	+	0.992225i	$0.460280\pi$
$270$	−1.80843	+	1.00376i	−0.110057	+	0.0610868i
$271$	13.9309	+	16.6022i	0.846242	+	1.00851i	0.999792	+	0.0203711i	$0.00648477\pi$
$271$	13.9309	+	16.6022i	0.846242	+	1.00851i	−0.153551	+	0.988141i	$0.549071\pi$
$272$	−17.6318	−	1.19303i	−1.06908	−	0.0723383i
$273$	−2.07962	+	3.60201i	−0.125864	+	0.218004i
$274$	15.7816	−	2.50867i	0.953403	−	0.151555i
$275$	−7.47800	−	20.5456i	−0.450941	−	1.23895i
$276$	0.712699	−	1.76973i	0.0428994	−	0.106525i
$277$	8.32066	+	14.4118i	0.499940	+	0.865922i	1.00000		6.89371e-5i	$-2.19434e-5\pi$
$277$	8.32066	+	14.4118i	0.499940	+	0.865922i	−0.500060	+	0.865991i	$0.666689\pi$
$278$	−2.07689	+	1.68377i	−0.124564	+	0.100986i
$279$	−0.214878	+	1.21863i	−0.0128644	+	0.0729577i
$280$	−0.508665	−	0.214902i	−0.0303986	−	0.0128429i
$281$	9.70045	−	11.5605i	0.578681	−	0.689645i	−0.394708	−	0.918807i	$-0.629154\pi$
$281$	9.70045	−	11.5605i	0.578681	−	0.689645i	0.973388	+	0.229162i	$0.0735986\pi$
$282$	−0.583116	+	3.00892i	−0.0347241	+	0.179178i
$283$	−2.29727	+	6.31170i	−0.136559	+	0.375192i	−0.989056	−	0.147540i	$-0.952865\pi$
$283$	−2.29727	+	6.31170i	−0.136559	+	0.375192i	0.852498	+	0.522731i	$0.175087\pi$
$284$	13.2439	+	11.8979i	0.785880	+	0.706009i
$285$	−1.98535	+	0.975282i	−0.117602	+	0.0577707i
$286$	7.80189	−	20.3589i	0.461335	−	1.20385i
$287$	−1.20063	−	0.436995i	−0.0708712	−	0.0257950i
$288$	0.0562817	−	0.664857i	0.00331643	−	0.0391771i
$289$	1.92965	+	1.61917i	0.113509	+	0.0952452i
$290$	−1.16750	+	0.402737i	−0.0685578	+	0.0236495i
$291$	−6.30555	−	1.11184i	−0.369638	−	0.0651771i
$292$	6.47387	−	2.11155i	0.378855	−	0.123569i
$293$	−2.35175	+	1.35778i	−0.137391	+	0.0793225i	−0.567120	−	0.823635i	$-0.691942\pi$
$293$	−2.35175	+	1.35778i	−0.137391	+	0.0793225i	0.429729	+	0.902958i	$0.358609\pi$
$294$	0.275767	−	16.3255i	0.0160830	−	0.952122i
$295$	1.20849	−	0.439854i	0.0703609	−	0.0256093i
$296$	−13.5654	+	20.9663i	−0.788472	+	1.21864i
$297$	−19.5959	−	11.3137i	−1.13707	−	0.656486i
$298$	3.27453	+	1.96503i	0.189688	+	0.113831i
$299$	−1.43492	+	1.20404i	−0.0829837	+	0.0696316i
$300$	2.43625	+	17.1943i	0.140657	+	0.992714i
$301$	−0.642047	−	3.64123i	−0.0370070	−	0.209877i
$302$	−11.9703	+	13.7859i	−0.688811	+	0.793289i
$303$	19.6283			1.12762
$304$	−2.33879	+	17.2780i	−0.134139	+	0.990963i
$305$	−2.26793			−0.129861
$306$	−0.483180	+	0.556468i	−0.0276216	+	0.0318111i
$307$	−0.847455	−	4.80616i	−0.0483668	−	0.274302i	0.951027	−	0.309107i	$-0.100030\pi$
$307$	−0.847455	−	4.80616i	−0.0483668	−	0.274302i	−0.999394	+	0.0348050i	$0.988919\pi$
$308$	−0.847487	−	5.98130i	−0.0482900	−	0.340816i
$309$	−3.91906	+	3.28848i	−0.222947	+	0.187075i
$310$	3.65605	+	2.19397i	0.207650	+	0.124609i
$311$	−7.86197	−	4.53911i	−0.445811	−	0.257389i	0.260248	−	0.965542i	$-0.416196\pi$
$311$	−7.86197	−	4.53911i	−0.445811	−	0.257389i	−0.706060	+	0.708153i	$0.749529\pi$
$312$	−9.40703	+	14.5393i	−0.532568	+	0.823124i
$313$	−0.820588	+	0.298670i	−0.0463824	+	0.0168818i	−0.365107	−	0.930966i	$-0.618968\pi$
$313$	−0.820588	+	0.298670i	−0.0463824	+	0.0168818i	0.318725	+	0.947847i	$0.396745\pi$
$314$	−0.573340	+	33.9419i	−0.0323554	+	1.91545i
$315$	−0.0199427	+	0.0115139i	−0.00112365	+	0.000648737i
$316$	−15.7529	+	5.13805i	−0.886170	+	0.289038i
$317$	−24.2100	−	4.26887i	−1.35977	−	0.239764i	−0.554257	−	0.832345i	$-0.686998\pi$
$317$	−24.2100	−	4.26887i	−1.35977	−	0.239764i	−0.805510	+	0.592582i	$0.798109\pi$
$318$	−23.5487	+	8.12330i	−1.32055	+	0.455532i
$319$	−10.3500	−	8.68468i	−0.579489	−	0.486249i
$320$	−2.06980	−	1.00087i	−0.115706	−	0.0559502i
$321$	−15.5254	−	5.65080i	−0.866546	−	0.315397i
$322$	−0.185724	+	0.484644i	−0.0103500	+	0.0270082i
$323$	13.3383	−	13.8907i	0.742163	−	0.772897i
$324$	13.8959	+	12.4836i	0.771996	+	0.693536i
$325$	5.83155	−	16.0220i	0.323476	−	0.888743i
$326$	2.84893	−	14.7006i	0.157787	−	0.814194i
$327$	10.5434	−	12.5651i	0.583049	−	0.694851i
$328$	−4.90030	−	2.07029i	−0.270574	−	0.114313i
$329$	0.144784	−	0.821111i	0.00798221	−	0.0452693i
$330$	2.47867	−	2.00950i	0.136446	−	0.110619i
$331$	3.60843	+	6.24998i	0.198337	+	0.343530i	0.947989	−	0.318302i	$-0.103113\pi$
$331$	3.60843	+	6.24998i	0.198337	+	0.343530i	−0.749652	+	0.661832i	$0.769779\pi$
$332$	7.46135	−	18.5275i	0.409495	−	1.01683i
$333$	0.356177	+	0.978588i	0.0195184	+	0.0536263i
$334$	22.4219	−	3.56423i	1.22687	−	0.195026i
$335$	0.712736	−	1.23449i	0.0389409	−	0.0674476i
$336$	−0.323924	+	4.78726i	−0.0176715	+	0.261166i
$337$	1.87196	+	2.23091i	0.101972	+	0.121526i	0.814617	−	0.580000i	$-0.196947\pi$
$337$	1.87196	+	2.23091i	0.101972	+	0.121526i	−0.712645	+	0.701525i	$0.752503\pi$
$338$	−1.20881	+	0.670943i	−0.0657504	+	0.0364945i
$339$	23.8415	−	4.20390i	1.29489	−	0.228325i
$340$	1.19468	+	2.24078i	0.0647908	+	0.121523i
$341$			46.6461i			2.52603i
$342$	0.515881	+	0.512392i	0.0278956	+	0.0277070i
$343$			9.19718i			0.496601i
$344$	−1.90189	−	15.2763i	−0.102543	−	0.823642i
$345$	−0.269980	+	0.0476047i	−0.0145352	+	0.00256295i
$346$	−3.99121	−	7.19079i	−0.214569	−	0.386579i
$347$	−19.7749	−	23.5668i	−1.06157	−	1.26513i	−0.962856	−	0.270016i	$-0.912971\pi$
$347$	−19.7749	−	23.5668i	−1.06157	−	1.26513i	−0.0987161	−	0.995116i	$-0.531474\pi$
$348$	6.61638	+	8.44895i	0.354675	+	0.452911i
$349$	15.6867	−	27.1702i	0.839692	−	1.45439i	−0.0504605	−	0.998726i	$-0.516069\pi$
$349$	15.6867	−	27.1702i	0.839692	−	1.45439i	0.890152	−	0.455663i	$-0.150598\pi$
$350$	−0.741667	−	4.66570i	−0.0396438	−	0.249392i
$351$	−6.03508	−	16.5813i	−0.322129	−	0.885042i
$352$	−2.26268	−	25.0500i	−0.120601	−	1.33517i
$353$	−4.87676	−	8.44680i	−0.259564	−	0.449578i	0.706561	−	0.707652i	$-0.250245\pi$
$353$	−4.87676	−	8.44680i	−0.259564	−	0.449578i	−0.966125	+	0.258074i	$0.916912\pi$
$354$	−7.03742	−	8.68049i	−0.374035	−	0.461363i
$355$	0.444231	−	2.51936i	0.0235773	−	0.133714i
$356$	−0.729105	+	21.5755i	−0.0386425	+	1.14350i
$357$	3.40655	−	4.05977i	0.180294	−	0.214866i
$358$	−33.1870	−	6.43152i	−1.75399	−	0.339916i
$359$	−11.1764	+	30.7070i	−0.589870	+	1.62066i	0.180871	+	0.983507i	$0.442108\pi$
$359$	−11.1764	+	30.7070i	−0.589870	+	1.62066i	−0.770741	+	0.637148i	$0.780114\pi$
$360$	−0.0853535	+	0.0436716i	−0.00449853	+	0.00230169i
$361$	−12.7932	−	14.0476i	−0.673325	−	0.739346i
$362$	7.19562	+	2.75749i	0.378194	+	0.144931i
$363$	14.5510	+	5.29615i	0.763732	+	0.277976i
$364$	2.49193	−	3.99793i	0.130613	−	0.209549i
$365$	−0.749562	−	0.628957i	−0.0392339	−	0.0329211i
$366$	6.42635	+	18.6294i	0.335911	+	0.973774i
$367$	25.0700	+	4.42052i	1.30864	+	0.230749i	0.784100	−	0.620634i	$-0.213125\pi$
$367$	25.0700	+	4.42052i	1.30864	+	0.230749i	0.524544	+	0.851384i	$0.324236\pi$
$368$	−0.874477	+	1.97607i	−0.0455852	+	0.103010i
$369$	−0.192121	+	0.110921i	−0.0100014	+	0.00577433i
$370$	3.58781	+	0.0606046i	0.186521	+	0.00315068i
$371$	6.36797	−	2.31775i	0.330609	−	0.120332i
$372$	7.66221	−	36.2486i	0.397267	−	1.87940i
$373$	22.6501	+	13.0771i	1.17278	+	0.677104i	0.954333	−	0.298745i	$-0.0965680\pi$
$373$	22.6501	+	13.0771i	1.17278	+	0.677104i	0.218446	+	0.975849i	$0.429901\pi$
$374$	−14.2946	+	23.8206i	−0.739158	+	1.23174i
$375$	3.85526	−	3.23494i	0.199085	−	0.167052i
$376$	0.775193	−	3.38380i	0.0399775	−	0.174506i
$377$	−1.82959	−	10.3761i	−0.0942288	−	0.534398i
$378$	−3.69171	−	3.20550i	−0.189881	−	0.164873i
$379$	11.3746			0.584276			0.292138	−	0.956376i	$-0.405633\pi$
$379$	11.3746			0.584276			0.292138	+	0.956376i	$0.405633\pi$
$380$	2.28473	−	1.02807i	0.117204	−	0.0527391i
$381$	8.92886			0.457439
$382$	24.3363	+	21.1312i	1.24515	+	1.08116i
$383$	−2.72109	−	15.4321i	−0.139041	−	0.788543i	−0.971960	−	0.235147i	$-0.924443\pi$
$383$	−2.72109	−	15.4321i	−0.139041	−	0.788543i	0.832918	−	0.553396i	$-0.186668\pi$
$384$	−2.35646	+	19.8380i	−0.120253	+	1.01235i
$385$	−0.664970	+	0.557976i	−0.0338900	+	0.0284371i
$386$	14.8718	−	24.7824i	0.756954	−	1.26139i
$387$	−0.555965	−	0.320986i	−0.0282613	−	0.0163167i
$388$	7.09536	+	1.49982i	0.360212	+	0.0761416i
$389$	15.0858	−	5.49077i	0.764878	−	0.278393i	0.0700257	−	0.997545i	$-0.477692\pi$
$389$	15.0858	−	5.49077i	0.764878	−	0.278393i	0.694852	+	0.719152i	$0.255470\pi$
$390$	2.48800	+	0.0420267i	0.125985	+	0.00212811i
$391$	2.06699	−	1.19338i	0.104532	−	0.0603516i
$392$	−0.936685	+	18.4699i	−0.0473097	+	0.932873i
$393$	29.4382	+	5.19075i	1.48496	+	0.261839i
$394$	−2.20059	−	6.37930i	−0.110864	−	0.321384i
$395$	1.82391	+	1.53044i	0.0917710	+	0.0770050i
$396$	−0.890138	−	0.554827i	−0.0447311	−	0.0278811i
$397$	−8.89582	−	3.23781i	−0.446468	−	0.162501i	0.108995	−	0.994042i	$-0.465237\pi$
$397$	−8.89582	−	3.23781i	−0.446468	−	0.162501i	−0.555463	+	0.831541i	$0.687459\pi$
$398$	7.74580	+	2.96833i	0.388262	+	0.148789i
$399$	−3.77149	−	3.62152i	−0.188811	−	0.181303i
$400$	−2.10009	−	19.5572i	−0.105005	−	0.977860i
$401$	−6.61831	+	18.1836i	−0.330502	+	0.908048i	0.657479	+	0.753473i	$0.271623\pi$
$401$	−6.61831	+	18.1836i	−0.330502	+	0.908048i	−0.987981	+	0.154575i	$0.950599\pi$
$402$	−12.1601	−	2.35657i	−0.606489	−	0.117535i
$403$	−23.3820	+	27.8656i	−1.16474	+	1.38808i
$404$	−22.2193	−	0.750863i	−1.10545	−	0.0373568i
$405$	0.466102	−	2.64339i	0.0231608	−	0.131351i
$406$	−1.83849	−	2.26773i	−0.0912427	−	0.112546i
$407$	19.6281	+	33.9968i	0.972928	+	1.68516i
$408$	15.0212	−	16.1629i	0.743658	−	0.800182i
$409$	−2.99514	−	8.22908i	−0.148100	−	0.406902i	0.843354	−	0.537359i	$-0.180578\pi$
$409$	−2.99514	−	8.22908i	−0.148100	−	0.406902i	−0.991454	+	0.130457i	$0.958356\pi$
$410$	0.120004	+	0.754924i	0.00592658	+	0.0372831i
$411$	−9.97609	+	17.2791i	−0.492084	+	0.852315i
$412$	4.56218	−	3.57265i	0.224762	−	0.176012i
$413$	1.95408	+	2.32878i	0.0961538	+	0.114592i
$414$	0.0437330	+	0.0787918i	0.00214936	+	0.00387241i
$415$	−2.82646	+	0.498381i	−0.138745	+	0.0244646i
$416$	11.2050	−	16.0986i	0.549369	−	0.789300i
$417$		−	3.33832i		−	0.163478i
$418$	22.5052	+	15.6448i	1.10076	+	0.765210i
$419$		−	15.7998i		−	0.771873i	−0.922525	−	0.385936i	$-0.873878\pi$
$419$		−	15.7998i		−	0.771873i	0.922525	−	0.385936i	$-0.126122\pi$
$420$	0.608400	−	0.324372i	0.0296869	−	0.0158277i
$421$	−25.0513	+	4.41722i	−1.22092	+	0.215282i	−0.746724	−	0.665135i	$-0.768374\pi$
$421$	−25.0513	+	4.41722i	−1.22092	+	0.215282i	−0.474201	+	0.880416i	$0.657263\pi$
$422$	21.0259	−	11.6703i	1.02352	−	0.568102i
$423$	−0.0930547	−	0.110898i	−0.00452447	−	0.00539206i
$424$	26.9679	−	8.29477i	1.30968	−	0.402830i
$425$	−10.8626	+	18.8146i	−0.526915	+	0.912643i
$426$	−21.9535	+	3.48976i	−1.06365	+	0.169079i
$427$	−1.83358	−	5.03771i	−0.0887329	−	0.243792i
$428$	17.3587	+	6.99063i	0.839064	+	0.337905i
$429$	13.6112	+	23.5754i	0.657157	+	1.13823i
$430$	−1.71830	+	1.39305i	−0.0828637	+	0.0671790i
$431$	−1.17478	+	6.66249i	−0.0565870	+	0.320921i	−0.999941	−	0.0108673i	$-0.996541\pi$
$431$	−1.17478	+	6.66249i	−0.0565870	+	0.320921i	0.943354	+	0.331788i	$0.107652\pi$
$432$	−14.6748	−	14.1076i	−0.706042	−	0.678750i
$433$	5.90017	−	7.03155i	0.283544	−	0.337915i	−0.605408	−	0.795916i	$-0.706990\pi$
$433$	5.90017	−	7.03155i	0.283544	−	0.337915i	0.888952	+	0.458001i	$0.151434\pi$
$434$	−1.91759	+	9.89489i	−0.0920473	+	0.474970i
$435$	0.527401	−	1.44902i	0.0252870	−	0.0694754i
$436$	−12.4158	+	13.8204i	−0.594608	+	0.661877i
$437$	−1.03826	−	2.11356i	−0.0496669	−	0.101105i
$438$	−3.04248	+	7.93930i	−0.145376	+	0.379355i
$439$	−32.3355	−	11.7692i	−1.54329	−	0.561712i	−0.576459	−	0.817126i	$-0.695566\pi$
$439$	−32.3355	−	11.7692i	−1.54329	−	0.561712i	−0.966832	+	0.255414i	$0.917788\pi$
$440$	−2.88273	+	2.17994i	−0.137429	+	0.103924i
$441$	0.590794	+	0.495735i	0.0281331	+	0.0236064i
$442$	−20.4798	+	7.06465i	−0.974123	+	0.336031i
$443$	−23.1576	−	4.08330i	−1.10025	−	0.194004i	−0.406096	−	0.913831i	$-0.633110\pi$
$443$	−23.1576	−	4.08330i	−1.10025	−	0.194004i	−0.694154	+	0.719827i	$0.744221\pi$
$444$	−9.66851	−	29.6430i	−0.458847	−	1.40679i
$445$	2.68643	−	1.55101i	0.127349	−	0.0735249i
$446$	−0.329896	+	19.5299i	−0.0156210	+	0.924770i
$447$	−4.48066	+	1.63083i	−0.211928	+	0.0771355i
$448$	0.549815	−	5.40680i	0.0259763	−	0.255447i
$449$	−2.56296	−	1.47973i	−0.120954	−	0.0698325i	0.438303	−	0.898827i	$-0.355580\pi$
$449$	−2.56296	−	1.47973i	−0.120954	−	0.0698325i	−0.559256	+	0.828995i	$0.688913\pi$
$450$	−0.703344	−	0.422073i	−0.0331559	−	0.0198967i
$451$	−6.40608	+	5.37534i	−0.301651	+	0.253115i
$452$	−27.1495	+	3.84679i	−1.27700	+	0.180938i
$453$	−3.95851	−	22.4499i	−0.185987	−	1.05479i
$454$	10.4736	−	12.0622i	0.491551	−	0.566109i
$455$	−0.676933			−0.0317351
$456$	−14.9188	−	15.8542i	−0.698638	−	0.742443i
$457$	−27.5794			−1.29011			−0.645054	−	0.764137i	$-0.723165\pi$
$457$	−27.5794			−1.29011			−0.645054	+	0.764137i	$0.723165\pi$
$458$	4.79776	−	5.52547i	0.224185	−	0.258188i
$459$	3.90422	+	22.1420i	0.182234	+	1.03350i
$460$	0.307439	−	0.0435608i	0.0143344	−	0.00203103i
$461$	23.9754	−	20.1177i	1.11664	−	0.936976i	0.118214	−	0.992988i	$-0.462283\pi$
$461$	23.9754	−	20.1177i	1.11664	−	0.936976i	0.998430	+	0.0560127i	$0.0178387\pi$
$462$	6.46761	+	3.88118i	0.300900	+	0.180569i
$463$	1.35838	+	0.784262i	0.0631294	+	0.0364478i	0.531232	−	0.847226i	$-0.321729\pi$
$463$	1.35838	+	0.784262i	0.0631294	+	0.0364478i	−0.468103	+	0.883674i	$0.655062\pi$
$464$	−7.16656	−	9.81734i	−0.332699	−	0.455759i
$465$	−5.00270	+	1.82084i	−0.231995	+	0.0844392i
$466$	0.147587	−	8.73718i	0.00683682	−	0.404742i
$467$	−16.4940	+	9.52284i	−0.763253	+	0.440664i	−0.830462	−	0.557075i	$-0.811924\pi$
$467$	−16.4940	+	9.52284i	−0.763253	+	0.440664i	0.0672096	+	0.997739i	$0.478590\pi$
$468$	−0.253638	−	0.777637i	−0.0117244	−	0.0359463i
$469$	3.31839	+	0.585122i	0.153229	+	0.0270184i
$470$	−0.471557	+	0.162667i	−0.0217513	+	0.00750327i
$471$	−32.4692	−	27.2449i	−1.49610	−	1.25538i
$472$	7.63432	+	10.0956i	0.351398	+	0.464685i
$473$	−22.7403	−	8.27679i	−1.04560	−	0.380567i
$474$	7.40329	−	19.3187i	0.340044	−	0.887339i
$475$	17.8038	+	11.9357i	0.816896	+	0.547647i
$476$	−4.01153	+	4.46535i	−0.183868	+	0.204669i
$477$	0.402427	−	1.10566i	0.0184259	−	0.0506246i
$478$	2.12159	−	10.9475i	0.0970392	−	0.500729i
$479$	−14.9412	+	17.8062i	−0.682680	+	0.813586i	−0.990450	−	0.137874i	$-0.955973\pi$
$479$	−14.9412	+	17.8062i	−0.682680	+	0.813586i	0.307770	+	0.951461i	$0.400417\pi$
$480$	2.59824	−	1.22050i	0.118593	−	0.0557078i
$481$	−5.31589	+	30.1479i	−0.242384	+	1.37463i
$482$	16.9853	−	13.7703i	0.773661	−	0.627220i
$483$	−0.324017	−	0.561213i	−0.0147433	−	0.0255361i
$484$	−16.2692	−	6.55189i	−0.739510	−	0.297813i
$485$	−0.356414	−	0.979239i	−0.0161839	−	0.0444649i
$486$	−1.71105	+	0.271992i	−0.0776149	+	0.0123378i
$487$	18.8848	−	32.7094i	0.855752	−	1.48221i	−0.0201932	−	0.999796i	$-0.506428\pi$
$487$	18.8848	−	32.7094i	0.855752	−	1.48221i	0.875945	−	0.482410i	$-0.160239\pi$
$488$	−6.56200	−	21.3344i	−0.297048	−	0.965761i
$489$	12.0179	+	14.3224i	0.543469	+	0.647682i
$490$	2.32350	−	1.28965i	0.104965	−	0.0582604i
$491$	−10.7823	+	1.90120i	−0.486596	+	0.0858001i	−0.411564	−	0.911381i	$-0.635017\pi$
$491$	−10.7823	+	1.90120i	−0.486596	+	0.0858001i	−0.0750327	+	0.997181i	$0.523906\pi$
$492$	5.86111	−	3.12488i	0.264239	−	0.140881i
$493$			13.4251i			0.604636i
$494$	5.60203	+	20.6269i	0.252047	+	0.928048i
$495$			0.150719i			0.00677431i
$496$	−10.0603	+	40.7404i	−0.451721	+	1.82930i
$497$	5.95535	−	1.05009i	0.267134	−	0.0471030i
$498$	12.1028	+	21.8051i	0.542340	+	0.977110i
$499$	12.5333	+	14.9366i	0.561067	+	0.668654i	0.969772	−	0.244013i	$-0.0784640\pi$
$499$	12.5333	+	14.9366i	0.561067	+	0.668654i	−0.408705	+	0.912667i	$0.634020\pi$
$500$	−4.48791	+	3.51449i	−0.200705	+	0.157173i
$501$	−14.1737	+	24.5495i	−0.633232	+	1.09679i
$502$	−1.83846	−	11.5655i	−0.0820547	−	0.516191i
$503$	6.17225	+	16.9581i	0.275207	+	0.756125i	0.997889	+	0.0649441i	$0.0206869\pi$
$503$	6.17225	+	16.9581i	0.275207	+	0.756125i	−0.722682	+	0.691181i	$0.757091\pi$
$504$	−0.166013	−	0.154287i	−0.00739483	−	0.00687247i
$505$	1.59730	+	2.76660i	0.0710787	+	0.123112i
$506$	2.13927	+	2.63873i	0.0951020	+	0.117306i
$507$	0.299753	−	1.69998i	0.0133125	−	0.0754989i
$508$	−10.1075	−	0.341565i	−0.448447	−	0.0151545i
$509$	−4.23195	+	5.04344i	−0.187578	+	0.223546i	−0.851635	−	0.524135i	$-0.824389\pi$
$509$	−4.23195	+	5.04344i	−0.187578	+	0.223546i	0.664057	+	0.747682i	$0.268833\pi$
$510$	−3.11271	−	0.603231i	−0.137833	−	0.0267115i
$511$	0.791084	−	2.17349i	0.0349955	−	0.0961494i
$512$	3.42640	−	22.3665i	0.151427	−	0.988468i
$513$	22.0544	−	2.38113i	0.973728	−	0.105129i
$514$	7.66586	+	2.93770i	0.338126	+	0.129576i
$515$	−0.782429	−	0.284781i	−0.0344779	−	0.0125489i
$516$	16.3118	+	10.1672i	0.718089	+	0.447588i
$517$	−4.18040	−	3.50778i	−0.183854	−	0.154272i
$518$	2.76605	+	8.01853i	0.121533	+	0.352314i
$519$	10.1126	+	1.78313i	0.443895	+	0.0782707i
$520$	−2.81481	−	0.142750i	−0.123438	−	0.00626001i
$521$	33.3964	−	19.2814i	1.46312	−	0.844735i	0.463969	−	0.885851i	$-0.346425\pi$
$521$	33.3964	−	19.2814i	1.46312	−	0.844735i	0.999154	+	0.0411164i	$0.0130915\pi$
$522$	−0.506810	−	0.00856094i	−0.0221825	−	0.000374702i
$523$	−14.7646	+	5.37386i	−0.645609	+	0.234982i	−0.644011	−	0.765016i	$-0.722731\pi$
$523$	−14.7646	+	5.37386i	−0.645609	+	0.234982i	−0.00159809	+	0.999999i	$0.500509\pi$
$524$	−33.1256	−	7.00207i	−1.44710	−	0.305887i
$525$	5.10841	+	2.94934i	0.222949	+	0.128720i
$526$	−13.5217	+	22.5326i	−0.589575	+	0.982470i
$527$	35.5059	−	29.7930i	1.54666	−	1.29780i
$528$	26.0750	+	17.5025i	1.13477	+	0.761699i
$529$	3.94323	+	22.3632i	0.171445	+	0.972311i
$530$	−3.06129	−	2.65812i	−0.132974	−	0.115461i
$531$	0.527830			0.0229059
$532$	4.13080	+	4.24384i	0.179093	+	0.183994i
$533$	−6.52134			−0.282470
$534$	−20.3526	−	17.6721i	−0.880744	−	0.764749i
$535$	−0.466939	−	2.64814i	−0.0201875	−	0.114489i
$536$	13.6751	+	3.13282i	0.590673	+	0.135317i
$537$	32.3332	−	27.1307i	1.39528	−	1.17078i
$538$	−1.18701	+	1.97804i	−0.0511756	+	0.0852792i
$539$	25.1772	+	14.5360i	1.08446	+	0.626111i
$540$	−0.604928	+	2.86181i	−0.0260320	+	0.123153i
$541$	−8.56708	+	3.11816i	−0.368328	+	0.134060i	−0.519551	−	0.854439i	$-0.673901\pi$
$541$	−8.56708	+	3.11816i	−0.368328	+	0.134060i	0.151224	+	0.988500i	$0.451679\pi$
$542$	30.6454	+	0.517655i	1.31633	+	0.0222352i
$543$	−8.33246	+	4.81075i	−0.357580	+	0.206449i
$544$	−17.6223	+	17.7218i	−0.755549	+	0.759816i
$545$	2.62902	+	0.463568i	0.112615	+	0.0198571i
$546$	1.91814	+	5.56052i	0.0820889	+	0.237968i
$547$	0.345374	+	0.289803i	0.0147671	+	0.0123911i	0.650141	−	0.759813i	$-0.274710\pi$
$547$	0.345374	+	0.289803i	0.0147671	+	0.0123911i	−0.635374	+	0.772204i	$0.719154\pi$
$548$	11.9540	−	19.1784i	0.510648	−	0.819259i
$549$	−0.874688	−	0.318360i	−0.0373308	−	0.0135873i
$550$	−28.8732	−	11.0647i	−1.23116	−	0.471801i
$551$	13.2157	+	0.886562i	0.563008	+	0.0377688i
$552$	−1.22897	−	2.40195i	−0.0523085	−	0.102234i
$553$	−1.92495	+	5.28875i	−0.0818572	+	0.224901i
$554$	23.1045	+	4.47756i	0.981617	+	0.190233i
$555$	−2.87991	+	3.43214i	−0.122245	+	0.145686i
$556$	−0.127704	+	3.77899i	−0.00541587	+	0.160265i
$557$	3.59725	−	20.4010i	0.152420	−	0.864419i	−0.808686	−	0.588241i	$-0.799821\pi$
$557$	3.59725	−	20.4010i	0.152420	−	0.864419i	0.961106	−	0.276179i	$-0.0890682\pi$
$558$	1.10207	+	1.35938i	0.0466545	+	0.0575472i
$559$	−9.43579	−	16.3433i	−0.399091	−	0.691247i
$560$	−0.701119	+	0.343916i	−0.0296277	+	0.0145331i
$561$	−11.8635	−	32.5947i	−0.500877	−	1.37615i
$562$	−3.35053	−	21.0776i	−0.141333	−	0.889104i
$563$	17.7749	−	30.7871i	0.749125	−	1.29752i	−0.199118	−	0.979976i	$-0.563808\pi$
$563$	17.7749	−	30.7871i	0.749125	−	1.29752i	0.948243	−	0.317546i	$-0.102859\pi$
$564$	2.67238	+	3.41256i	0.112528	+	0.143695i
$565$	2.53269	+	3.01834i	0.106551	+	0.126982i
$566$	4.60986	+	8.30537i	0.193767	+	0.349101i
$567$	6.24856	−	1.10179i	0.262415	−	0.0462708i
$568$	24.9849	−	3.11061i	1.04834	−	0.130518i
$569$			1.64769i			0.0690748i	0.999403	+	0.0345374i	$0.0109958\pi$
$569$			1.64769i			0.0690748i	−0.999403	+	0.0345374i	$0.989004\pi$
$570$	−0.799379	+	3.02433i	−0.0334823	+	0.126675i
$571$		−	13.5132i		−	0.565511i	−0.959192	−	0.282755i	$-0.908752\pi$
$571$		−	13.5132i		−	0.565511i	0.959192	−	0.282755i	$-0.0912484\pi$
$572$	−14.5061	−	27.2081i	−0.606531	−	1.13763i
$573$	−39.6308	+	6.98798i	−1.65560	+	0.291927i
$574$	−1.57988	+	0.876904i	−0.0659428	+	0.0366013i
$575$	1.70759	+	2.03502i	0.0712112	+	0.0848662i
$576$	−0.657778	−	0.676560i	−0.0274074	−	0.0281900i
$577$	9.20209	−	15.9385i	0.383088	−	0.663528i	−0.608414	−	0.793620i	$-0.708194\pi$
$577$	9.20209	−	15.9385i	0.383088	−	0.663528i	0.991502	+	0.130092i	$0.0415272\pi$
$578$	3.51820	−	0.559259i	0.146338	−	0.0232621i
$579$	12.3425	+	33.9107i	0.512936	+	1.40928i
$580$	−0.652451	+	1.62012i	−0.0270915	+	0.0672720i
$581$	−3.39218	−	5.87543i	−0.140731	−	0.243754i
$582$	−7.03381	+	5.70243i	−0.291561	+	0.236373i
$583$	7.70193	−	43.6798i	0.318981	−	1.80903i
$584$	3.74781	−	8.87092i	0.155086	−	0.367081i
$585$	−0.0755498	+	0.0900368i	−0.00312360	+	0.00372256i
$586$	−0.730658	+	3.77024i	−0.0301832	+	0.155747i
$587$	−0.260988	+	0.717059i	−0.0107721	+	0.0295962i	−0.944962	−	0.327180i	$-0.893902\pi$
$587$	−0.260988	+	0.717059i	−0.0107721	+	0.0295962i	0.934190	+	0.356776i	$0.116124\pi$
$588$	−17.1774	−	15.4316i	−0.708382	−	0.636387i
$589$	−26.9836	−	36.9196i	−1.11184	−	1.52125i
$590$	0.650823	−	1.69831i	0.0267940	−	0.0699183i
$591$	7.91758	+	2.88176i	0.325686	+	0.118540i
$592$	9.81082	+	33.9258i	0.403222	+	1.39434i
$593$	−5.75424	−	4.82838i	−0.236298	−	0.198278i	0.516947	−	0.856017i	$-0.327068\pi$
$593$	−5.75424	−	4.82838i	−0.236298	−	0.198278i	−0.753245	+	0.657740i	$0.771513\pi$
$594$	−30.2506	+	10.4352i	−1.24120	+	0.428161i
$595$	0.849435	+	0.149778i	0.0348235	+	0.00614031i
$596$	5.13451	−	1.67470i	0.210318	−	0.0685983i
$597$	−8.96956	+	5.17858i	−0.367100	+	0.211945i
$598$	−0.0447408	+	2.64867i	−0.00182959	+	0.108312i
$599$	3.55846	−	1.29517i	0.145395	−	0.0529194i	−0.268298	−	0.963336i	$-0.586461\pi$
$599$	3.55846	−	1.29517i	0.145395	−	0.0529194i	0.413693	+	0.910417i	$0.364239\pi$
$600$	20.6197	+	13.3411i	0.841797	+	0.544650i
$601$	12.4051	+	7.16208i	0.506014	+	0.292147i	0.731194	−	0.682170i	$-0.238964\pi$
$601$	12.4051	+	7.16208i	0.506014	+	0.292147i	−0.225180	+	0.974317i	$0.572297\pi$
$602$	−4.48357	−	2.69057i	−0.182737	−	0.109659i
$603$	0.448177	−	0.376066i	0.0182512	−	0.0153146i
$604$	3.62225	+	25.5647i	0.147387	+	1.04021i
$605$	0.437633	+	2.48194i	0.0177923	+	0.100905i
$606$	18.1995	−	20.9600i	0.739305	−	0.851441i
$607$	−17.3937			−0.705987			−0.352993	−	0.935626i	$-0.614836\pi$
$607$	−17.3937			−0.705987			−0.352993	+	0.935626i	$0.614836\pi$
$608$	16.2817	+	18.5178i	0.660309	+	0.750994i
$609$	3.64508			0.147706
$610$	−2.10284	+	2.42179i	−0.0851414	+	0.0980555i
$611$	−0.738980	−	4.19096i	−0.0298959	−	0.169548i
$612$	0.146212	+	1.03192i	0.00591028	+	0.0417129i
$613$	0.260867	−	0.218894i	0.0105363	−	0.00884103i	−0.637504	−	0.770447i	$-0.720033\pi$
$613$	0.260867	−	0.218894i	0.0105363	−	0.00884103i	0.648041	+	0.761606i	$0.275589\pi$
$614$	−5.91799	−	3.55135i	−0.238831	−	0.143321i
$615$	−0.826557	−	0.477213i	−0.0333300	−	0.0192431i
$616$	−7.17288	−	4.64091i	−0.289004	−	0.186988i
$617$	−38.7470	+	14.1028i	−1.55990	+	0.567755i	−0.970712	−	0.240244i	$-0.922772\pi$
$617$	−38.7470	+	14.1028i	−1.55990	+	0.567755i	−0.589183	+	0.808000i	$0.700550\pi$
$618$	−0.122196	+	7.23403i	−0.00491544	+	0.290996i
$619$	16.6044	−	9.58653i	0.667386	−	0.385315i	−0.127700	−	0.991813i	$-0.540759\pi$
$619$	16.6044	−	9.58653i	0.667386	−	0.385315i	0.795085	+	0.606498i	$0.207426\pi$
$620$	5.73273	−	1.86982i	0.230232	−	0.0750937i
$621$	2.70748	+	0.477403i	0.108648	+	0.0191575i
$622$	−12.1367	+	4.18665i	−0.486638	+	0.167870i
$623$	5.61715	+	4.71335i	0.225046	+	0.188836i
$624$	6.80339	+	23.5261i	0.272354	+	0.941799i
$625$	−22.3346	−	8.12912i	−0.893383	−	0.325165i
$626$	−0.441922	+	1.15319i	−0.0176628	+	0.0460906i
$627$	−32.8698	+	9.52599i	−1.31269	+	0.380431i
$628$	35.7130	+	32.0834i	1.42510	+	1.28027i
$629$	13.3411	−	36.6543i	0.531943	−	1.46150i
$630$	−0.00619595	+	0.0319715i	−0.000246853	+	0.00127378i
$631$	22.7701	−	27.1363i	0.906462	−	1.08028i	−0.0899749	−	0.995944i	$-0.528679\pi$
$631$	22.7701	−	27.1363i	0.906462	−	1.08028i	0.996437	−	0.0843359i	$-0.0268769\pi$
$632$	−9.11956	+	21.5857i	−0.362757	+	0.858631i
$633$	−5.21387	+	29.5693i	−0.207233	+	1.17527i
$634$	−27.0061	+	21.8943i	−1.07255	+	0.869535i
$635$	0.726604	+	1.25851i	0.0288344	+	0.0499426i
$636$	−13.1601	+	32.6783i	−0.521832	+	1.29578i
$637$	7.75400	+	21.3039i	0.307225	+	0.844093i
$638$	−18.8705	+	2.99968i	−0.747088	+	0.118758i
$639$	0.524984	−	0.909299i	0.0207680	−	0.0359713i
$640$	−2.98790	+	1.28221i	−0.118107	+	0.0506839i
$641$	16.5658	+	19.7424i	0.654310	+	0.779777i	0.986557	−	0.163416i	$-0.0522512\pi$
$641$	16.5658	+	19.7424i	0.654310	+	0.779777i	−0.332247	+	0.943192i	$0.607807\pi$
$642$	−20.4295	+	11.3393i	−0.806287	+	0.447526i
$643$	2.51226	−	0.442980i	0.0990740	−	0.0174694i	−0.123891	−	0.992296i	$-0.539537\pi$
$643$	2.51226	−	0.442980i	0.0990740	−	0.0174694i	0.222965	+	0.974826i	$0.428426\pi$
$644$	0.345319	+	0.647690i	0.0136075	+	0.0255226i
$645$		−	2.76194i		−	0.108751i
$646$	−2.46568	−	27.1227i	−0.0970109	−	1.06713i
$647$			16.5839i			0.651979i	0.945373	+	0.325989i	$0.105697\pi$
$647$			16.5839i			0.651979i	−0.945373	+	0.325989i	$0.894303\pi$
$648$	26.2150	−	3.26375i	1.02982	−	0.128212i
$649$	19.5947	−	3.45508i	0.769160	−	0.135624i
$650$	−11.7020	−	21.0829i	−0.458989	−	0.826940i
$651$	−8.08917	−	9.64030i	−0.317040	−	0.377833i
$652$	−13.0564	−	16.6727i	−0.511330	−	0.652955i
$653$	−21.6722	+	37.5373i	−0.848098	+	1.46895i	0.0348059	+	0.999394i	$0.488919\pi$
$653$	−21.6722	+	37.5373i	−0.848098	+	1.46895i	−0.882904	+	0.469554i	$0.844415\pi$
$654$	−3.64167	−	22.9091i	−0.142400	−	0.895816i
$655$	1.66396	+	4.57170i	0.0650164	+	0.178631i
$656$	−6.75434	+	3.31316i	−0.263713	+	0.129357i
$657$	−0.200799	−	0.347794i	−0.00783391	−	0.0135687i
$658$	−0.742573	−	0.915946i	−0.0289485	−	0.0357073i
$659$	−5.07827	+	28.8003i	−0.197821	+	1.12190i	0.710522	+	0.703675i	$0.248459\pi$
$659$	−5.07827	+	28.8003i	−0.197821	+	1.12190i	−0.908344	+	0.418225i	$0.862652\pi$
$660$	0.152409	−	4.51004i	0.00593251	−	0.175553i
$661$	22.9313	−	27.3285i	0.891926	−	1.06296i	−0.105721	−	0.994396i	$-0.533715\pi$
$661$	22.9313	−	27.3285i	0.891926	−	1.06296i	0.997647	−	0.0685600i	$-0.0218405\pi$
$662$	10.0198	+	1.94179i	0.389429	+	0.0754697i
$663$	9.25147	−	25.4182i	0.359297	−	0.987161i
$664$	−12.8663	−	25.1464i	−0.499309	−	0.975870i
$665$	0.203537	−	0.826296i	0.00789283	−	0.0320424i
$666$	1.37523	+	0.527012i	0.0532890	+	0.0204213i
$667$	1.54260	+	0.561460i	0.0597297	+	0.0217398i
$668$	16.9837	−	27.2479i	0.657120	−	1.05425i
$669$	−18.6826	−	15.6765i	−0.722310	−	0.606090i
$670$	−0.657393	−	1.90572i	−0.0253973	−	0.0736244i
$671$	−34.5551	−	6.09300i	−1.33399	−	0.235218i
$672$	4.81169	+	4.78468i	0.185615	+	0.184573i
$673$	−18.4104	+	10.6293i	−0.709669	+	0.409727i	−0.810938	−	0.585132i	$-0.801043\pi$
$673$	−18.4104	+	10.6293i	−0.709669	+	0.409727i	0.101270	+	0.994859i	$0.467710\pi$
$674$	4.11795	+	0.0695597i	0.158618	+	0.00267934i
$675$	−23.5157	+	8.55902i	−0.905120	+	0.329437i
$676$	−0.404352	+	1.91292i	−0.0155520	+	0.0735738i
$677$	19.3161	+	11.1522i	0.742379	+	0.428613i	0.822934	−	0.568138i	$-0.192336\pi$
$677$	19.3161	+	11.1522i	0.742379	+	0.428613i	−0.0805548	+	0.996750i	$0.525669\pi$
$678$	17.6169	−	29.3569i	0.676573	−	1.12744i
$679$	1.88701	−	1.58339i	0.0724168	−	0.0607649i
$680$	3.50052	+	0.801932i	0.134239	+	0.0307527i
$681$	3.46358	+	19.6429i	0.132725	+	0.752719i
$682$	49.8107	+	43.2506i	1.90735	+	1.65615i
$683$	−4.25657			−0.162873			−0.0814366	−	0.996679i	$-0.525951\pi$
$683$	−4.25657			−0.162873			−0.0814366	+	0.996679i	$0.525951\pi$
$684$	1.02548	−	0.0757862i	0.0392103	−	0.00289776i
$685$	−3.24730			−0.124073
$686$	9.82114	+	8.52768i	0.374973	+	0.325588i
$687$	1.58660	+	8.99805i	0.0605325	+	0.343297i
$688$	−18.0761	−	12.1333i	−0.689145	−	0.462579i
$689$	26.4960	−	22.2328i	1.00942	−	0.847003i
$690$	−0.199493	+	0.332435i	−0.00759455	+	0.0126556i
$691$	4.43757	+	2.56203i	0.168813	+	0.0974643i	0.582026	−	0.813170i	$-0.302260\pi$
$691$	4.43757	+	2.56203i	0.168813	+	0.0974643i	−0.413213	+	0.910634i	$0.635593\pi$
$692$	−11.3793	−	2.40536i	−0.432577	−	0.0914379i
$693$	−0.334789	+	0.121853i	−0.0127176	+	0.00462882i
$694$	−43.5010	−	0.734811i	−1.65128	−	0.0278930i
$695$	0.470534	−	0.271663i	0.0178484	−	0.0103048i
$696$	15.1569	+	0.768667i	0.574521	+	0.0291362i
$697$	8.18316	+	1.44291i	0.309959	+	0.0546542i
$698$	−14.4687	−	41.9434i	−0.547648	−	1.58758i
$699$	8.35809	+	7.01327i	0.316132	+	0.265266i
$700$	−5.66991	−	3.53408i	−0.214302	−	0.133576i
$701$	39.1100	+	14.2349i	1.47717	+	0.537644i	0.950036	−	0.312140i	$-0.101046\pi$
$701$	39.1100	+	14.2349i	1.47717	+	0.537644i	0.527130	+	0.849785i	$0.323268\pi$
$702$	−23.3019	−	8.92973i	−0.879475	−	0.337031i
$703$	−35.2016	−	15.5536i	−1.32765	−	0.586613i
$704$	−28.8475	−	20.8104i	−1.08723	−	0.784320i
$705$	0.213019	−	0.585266i	0.00802278	−	0.0220424i
$706$	−13.5416	−	2.62431i	−0.509646	−	0.0987673i
$707$	−4.85401	+	5.78478i	−0.182554	+	0.217559i
$708$	−15.7945	−	0.533749i	−0.593595	−	0.0200595i
$709$	−1.17231	+	6.64851i	−0.0440271	+	0.249690i	−0.998876	−	0.0474022i	$-0.984906\pi$
$709$	−1.17231	+	6.64851i	−0.0440271	+	0.249690i	0.954849	+	0.297092i	$0.0960169\pi$
$710$	−2.27838	−	2.81033i	−0.0855062	−	0.105470i
$711$	0.488605	+	0.846288i	0.0183241	+	0.0317383i
$712$	22.3632	+	20.7835i	0.838096	+	0.778894i
$713$	−1.93842	−	5.32577i	−0.0725945	−	0.199452i
$714$	−1.17662	−	7.40190i	−0.0440339	−	0.277009i
$715$	−2.21528	+	3.83699i	−0.0828470	+	0.143495i
$716$	−37.6391	+	29.4752i	−1.40664	+	1.10154i
$717$	8.94972	+	10.6659i	0.334234	+	0.398324i
$718$	22.4274	+	40.4064i	0.836984	+	1.50796i
$719$	28.0650	−	4.94861i	1.04665	−	0.184552i	0.376222	−	0.926529i	$-0.377223\pi$
$719$	28.0650	−	4.94861i	1.04665	−	0.184552i	0.670425	+	0.741977i	$0.266112\pi$
$720$	−0.0325060	+	0.131637i	−0.00121143	+	0.00490581i
$721$		−	1.96823i		−	0.0733009i
$722$	−26.8625	+	0.636104i	−0.999720	+	0.0236734i
$723$			27.3017i			1.01536i
$724$	9.61640	−	5.12703i	0.357391	−	0.190545i
$725$	−14.7155	+	2.59475i	−0.546522	+	0.0963665i
$726$	19.1473	−	10.6276i	0.710622	−	0.394428i
$727$	−23.5241	−	28.0349i	−0.872461	−	1.03976i	−0.998858	−	0.0477786i	$-0.984786\pi$
$727$	−23.5241	−	28.0349i	−0.872461	−	1.03976i	0.126397	−	0.991980i	$-0.459659\pi$
$728$	−1.95863	−	6.36790i	−0.0725917	−	0.236010i
$729$	−12.9283	+	22.3925i	−0.478826	+	0.829351i
$730$	−1.36663	+	0.217241i	−0.0505811	+	0.00804046i
$731$	8.22418	+	22.5958i	0.304182	+	0.835734i
$732$	25.8518	+	10.4110i	0.955510	+	0.384800i
$733$	15.7141	+	27.2176i	0.580413	+	1.00531i	0.995430	+	0.0954919i	$0.0304424\pi$
$733$	15.7141	+	27.2176i	0.580413	+	1.00531i	−0.415017	+	0.909814i	$0.636224\pi$
$734$	27.9655	−	22.6721i	1.03222	−	0.836842i
$735$	−0.576169	+	3.26761i	−0.0212523	+	0.120528i
$736$	1.29932	+	2.76603i	0.0478934	+	0.101957i
$737$	14.1761	−	16.8944i	0.522184	−	0.622315i
$738$	−0.0596896	+	0.308002i	−0.00219721	+	0.0113377i
$739$	−12.5256	+	34.4138i	−0.460762	+	1.26593i	0.464152	+	0.885756i	$0.346359\pi$
$739$	−12.5256	+	34.4138i	−0.460762	+	1.26593i	−0.924914	+	0.380177i	$0.875863\pi$
$740$	3.39136	−	3.77503i	0.124669	−	0.138773i
$741$	−24.4108	−	10.7857i	−0.896754	−	0.396224i
$742$	3.42943	−	8.94903i	0.125898	−	0.328529i
$743$	−18.4966	−	6.73220i	−0.678573	−	0.246980i	−0.0203384	−	0.999793i	$-0.506474\pi$
$743$	−18.4966	−	6.73220i	−0.678573	−	0.246980i	−0.658235	+	0.752813i	$0.728697\pi$
$744$	−31.6033	−	41.7919i	−1.15863	−	1.53217i
$745$	−0.594486	−	0.498833i	−0.0217803	−	0.0182758i
$746$	34.9656	−	12.0616i	1.28018	−	0.441608i
$747$	−1.16006	−	0.204550i	−0.0424444	−	0.00748408i
$748$	12.1826	+	37.3511i	0.445441	+	1.36569i
$749$	5.50476	−	3.17817i	0.201140	−	0.116128i
$750$	0.120207	−	7.11627i	0.00438932	−	0.259849i
$751$	10.9116	−	3.97149i	0.398169	−	0.144922i	−0.135171	−	0.990822i	$-0.543159\pi$
$751$	10.9116	−	3.97149i	0.398169	−	0.144922i	0.533341	+	0.845900i	$0.320936\pi$
$752$	−2.89460	−	3.96526i	−0.105555	−	0.144598i
$753$	12.6629	+	7.31090i	0.461460	+	0.266424i
$754$	−12.7765	−	7.66710i	−0.465293	−	0.279219i
$755$	2.84215	−	2.38485i	0.103437	−	0.0867936i
$756$	−6.84595	+	0.969999i	−0.248985	+	0.0352785i
$757$	2.76506	+	15.6814i	0.100498	+	0.569952i	0.992923	+	0.118757i	$0.0378909\pi$
$757$	2.76506	+	15.6814i	0.100498	+	0.569952i	−0.892426	+	0.451195i	$0.850998\pi$
$758$	10.5466	−	12.1463i	0.383071	−	0.441175i
$759$	−4.24142			−0.153954
$760$	1.02059	−	3.39297i	0.0370207	−	0.123076i
$761$	−7.73239			−0.280299			−0.140149	−	0.990130i	$-0.544758\pi$
$761$	−7.73239			−0.280299			−0.140149	+	0.990130i	$0.544758\pi$
$762$	8.27890	−	9.53462i	0.299913	−	0.345403i
$763$	1.09580	+	6.21459i	0.0396706	+	0.224983i
$764$	45.1295	−	6.39438i	1.63273	−	0.231340i
$765$	0.114724	−	0.0962645i	0.00414784	−	0.00348045i
$766$	−19.0021	−	11.4030i	−0.686572	−	0.412008i
$767$	13.4374	+	7.75811i	0.485198	+	0.280129i
$768$	18.9989	+	20.9102i	0.685564	+	0.754533i
$769$	−24.5001	+	8.91731i	−0.883496	+	0.321566i	−0.743620	−	0.668603i	$-0.766893\pi$
$769$	−24.5001	+	8.91731i	−0.883496	+	0.321566i	−0.139877	+	0.990169i	$0.544671\pi$
$770$	−0.0207337	+	1.22744i	−0.000747191	+	0.0442339i
$771$	−8.87699	+	5.12513i	−0.319697	+	0.184577i
$772$	−12.6745	−	38.8591i	−0.456165	−	1.39857i
$773$	−12.6566	−	2.23170i	−0.455226	−	0.0802686i	−0.0586663	−	0.998278i	$-0.518685\pi$
$773$	−12.6566	−	2.23170i	−0.455226	−	0.0802686i	−0.396559	+	0.918009i	$0.629796\pi$
$774$	−0.858257	+	0.296062i	−0.0308494	+	0.0106417i
$775$	39.5192	+	33.1606i	1.41957	+	1.19116i
$776$	8.18043	−	6.18609i	0.293660	−	0.222068i
$777$	−9.95210	−	3.62227i	−0.357030	−	0.129948i
$778$	8.12433	−	21.2003i	0.291271	−	0.760067i
$779$	1.96080	−	7.96025i	0.0702531	−	0.285205i
$780$	2.35176	−	2.61782i	0.0842067	−	0.0937330i
$781$	13.5370	−	37.1925i	0.484391	−	1.33085i
$782$	0.642186	−	3.31372i	0.0229645	−	0.118498i
$783$	−9.94013	+	11.8462i	−0.355231	+	0.423348i
$784$	18.8545	+	18.1257i	0.673375	+	0.647346i
$785$	1.19790	−	6.79361i	0.0427548	−	0.242474i
$786$	32.8382	−	26.6225i	1.17130	−	0.949593i
$787$	−5.14544	−	8.91217i	−0.183415	−	0.317684i	0.759626	−	0.650360i	$-0.225382\pi$
$787$	−5.14544	−	8.91217i	−0.183415	−	0.317684i	−0.943041	+	0.332676i	$0.892049\pi$
$788$	−8.85249	−	3.56504i	−0.315357	−	0.126999i
$789$	−11.2220	−	30.8322i	−0.399514	−	1.09766i
$790$	3.32542	−	0.528614i	0.118313	−	0.0188072i
$791$	−4.65695	+	8.06607i	−0.165582	+	0.286797i
$792$	−1.41781	+	0.436088i	−0.0503797	+	0.0154957i
$793$	−17.5884	−	20.9610i	−0.624582	−	0.744348i
$794$	−11.7057	+	6.49721i	−0.415421	+	0.230577i
$795$	4.98521	−	0.879028i	0.176807	−	0.0311759i
$796$	10.3517	−	5.51904i	0.366905	−	0.195617i
$797$		−	1.81305i		−	0.0642216i	−0.999484	−	0.0321108i	$-0.989777\pi$
$797$		−	1.81305i		−	0.0642216i	0.999484	−	0.0321108i	$-0.0102230\pi$
$798$	−7.36416	+	0.669464i	−0.260688	+	0.0236988i
$799$			5.42245i			0.191832i
$800$	−22.8312	−	15.8910i	−0.807206	−	0.561832i
$801$	1.25382	−	0.221082i	0.0443014	−	0.00781153i
$802$	13.2807	+	23.9273i	0.468959	+	0.844902i
$803$	−9.73088	−	11.5968i	−0.343395	−	0.409243i
$804$	−13.7913	+	10.8000i	−0.486383	+	0.380887i
$805$	0.0527350	−	0.0913397i	0.00185866	−	0.00321930i
$806$	8.07611	+	50.8054i	0.284469	+	1.78954i
$807$	−0.985129	−	2.70662i	−0.0346782	−	0.0952775i
$808$	−21.4037	+	23.0305i	−0.752980	+	0.810212i
$809$	−8.16147	−	14.1361i	−0.286942	−	0.496998i	0.686136	−	0.727473i	$-0.259305\pi$
$809$	−8.16147	−	14.1361i	−0.286942	−	0.496998i	−0.973078	+	0.230475i	$0.925972\pi$
$810$	−2.39056	−	2.94870i	−0.0839956	−	0.103607i
$811$	2.81946	−	15.9900i	0.0990047	−	0.561484i	−0.894442	−	0.447185i	$-0.852427\pi$
$811$	2.81946	−	15.9900i	0.0990047	−	0.561484i	0.993446	−	0.114299i	$-0.0364622\pi$
$812$	−4.12624	−	0.139439i	−0.144803	−	0.00489335i
$813$	−24.5988	+	29.3157i	−0.862718	+	1.02815i
$814$	54.5026	+	10.5624i	1.91031	+	0.370211i
$815$	−1.04075	+	2.85943i	−0.0364558	+	0.100161i
$816$	−3.33170	−	31.0266i	−0.116633	−	1.08615i
$817$	22.7865	−	6.60375i	0.797197	−	0.231036i
$818$	−11.5645	−	4.43172i	−0.404342	−	0.154951i
$819$	−0.261078	−	0.0950244i	−0.00912279	−	0.00332042i
$820$	0.917409	+	0.571825i	0.0320373	+	0.0199690i
$821$	−9.92828	−	8.33081i	−0.346499	−	0.290747i	0.452883	−	0.891570i	$-0.350395\pi$
$821$	−9.92828	−	8.33081i	−0.346499	−	0.290747i	−0.799382	+	0.600822i	$0.794840\pi$
$822$	9.20146	+	26.6742i	0.320938	+	0.930369i
$823$	20.9188	+	3.68856i	0.729185	+	0.128575i	0.525902	−	0.850545i	$-0.323728\pi$
$823$	20.9188	+	3.68856i	0.729185	+	0.128575i	0.203283	+	0.979120i	$0.434839\pi$
$824$	0.415057	−	8.18427i	0.0144592	−	0.285113i
$825$	33.4348	−	19.3036i	1.16405	−	0.672066i
$826$	4.29860	+	0.0726111i	0.149567	+	0.00252646i
$827$	−19.5621	+	7.12001i	−0.680240	+	0.247587i	−0.658950	−	0.752186i	$-0.728999\pi$
$827$	−19.5621	+	7.12001i	−0.680240	+	0.247587i	−0.0212892	+	0.999773i	$0.506777\pi$
$828$	0.124687	+	0.0263563i	0.00433317	+	0.000915944i
$829$	24.5467	+	14.1720i	0.852542	+	0.492215i	0.861508	−	0.507744i	$-0.169521\pi$
$829$	24.5467	+	14.1720i	0.852542	+	0.492215i	−0.00896572	+	0.999960i	$0.502854\pi$
$830$	−2.08852	+	3.48032i	−0.0724935	+	0.120803i
$831$	−22.5101	+	18.8882i	−0.780865	+	0.655224i
$832$	−6.80149	−	26.8919i	−0.235799	−	0.932309i
$833$	−5.01623	−	28.4484i	−0.173802	−	0.985680i
$834$	−3.56481	−	3.09532i	−0.123439	−	0.107182i
$835$	−4.61364			−0.159661
$836$	37.5731	−	9.52604i	1.29949	−	0.329465i
$837$	53.3893			1.84540
$838$	−16.8717	−	14.6497i	−0.582825	−	0.506066i
$839$	2.04975	+	11.6247i	0.0707652	+	0.401329i	0.999530	+	0.0306595i	$0.00976076\pi$
$839$	2.04975	+	11.6247i	0.0707652	+	0.401329i	−0.928765	+	0.370670i	$0.879128\pi$
$840$	0.217735	−	0.950435i	0.00751257	−	0.0327931i
$841$	15.1418	−	12.7055i	0.522132	−	0.438121i
$842$	−18.5108	+	30.8465i	−0.637925	+	1.06304i
$843$	23.0776	+	13.3238i	0.794833	+	0.458897i
$844$	7.03326	−	33.2731i	0.242095	−	1.14531i
$845$	0.264004	−	0.0960896i	0.00908201	−	0.00330558i
$846$	−0.204703	−	0.00345780i	−0.00703783	−	0.000118882i
$847$	−5.15927	+	2.97871i	−0.177275	+	0.102350i
$848$	16.1473	−	36.4885i	0.554502	−	1.25302i
$849$	−11.6801	−	2.05952i	−0.400860	−	0.0706825i
$850$	10.0192	+	29.0446i	0.343654	+	0.996222i
$851$	−3.65378	−	3.06589i	−0.125250	−	0.105097i
$852$	−16.6289	+	26.6786i	−0.569696	+	0.913993i
$853$	−11.7778	−	4.28675i	−0.403263	−	0.146776i	0.132422	−	0.991193i	$-0.457724\pi$
$853$	−11.7778	−	4.28675i	−0.403263	−	0.146776i	−0.535685	+	0.844418i	$0.679947\pi$
$854$	−7.07958	−	2.71302i	−0.242258	−	0.0928378i
$855$	−0.0871871	−	0.119291i	−0.00298174	−	0.00407968i
$856$	23.5600	−	12.0546i	0.805264	−	0.412017i
$857$	−13.6980	+	37.6349i	−0.467915	+	1.28559i	0.451491	+	0.892276i	$0.350892\pi$
$857$	−13.6980	+	37.6349i	−0.467915	+	1.28559i	−0.919406	+	0.393310i	$0.871330\pi$
$858$	37.7952	+	7.32457i	1.29031	+	0.250057i
$859$	26.2991	−	31.3421i	0.897314	−	1.06938i	−0.0999155	−	0.994996i	$-0.531857\pi$
$859$	26.2991	−	31.3421i	0.897314	−	1.06938i	0.997230	−	0.0743817i	$-0.0236983\pi$
$860$	−0.105655	+	3.12652i	−0.00360281	+	0.106613i
$861$	0.391769	−	2.22183i	0.0133514	−	0.0757198i
$862$	6.02523	+	7.43198i	0.205220	+	0.253134i
$863$	−21.1102	−	36.5639i	−0.718598	−	1.24465i	−0.961555	−	0.274611i	$-0.911451\pi$
$863$	−21.1102	−	36.5639i	−0.718598	−	1.24465i	0.242957	−	0.970037i	$-0.421883\pi$
$864$	−28.6712	+	2.58977i	−0.975415	+	0.0881058i
$865$	0.571605	+	1.57047i	0.0194351	+	0.0533976i
$866$	−2.03791	−	12.8202i	−0.0692511	−	0.435646i
$867$	−2.22397	+	3.85203i	−0.0755300	+	0.130822i
$868$	8.78819	+	11.2223i	0.298291	+	0.380909i
$869$	23.6782	+	28.2186i	0.803228	+	0.957250i
$870$	−1.05832	−	1.90673i	−0.0358804	−	0.0646440i
$871$	16.9371	−	2.98647i	0.573892	−	0.101193i
$872$	3.24601	+	26.0725i	0.109924	+	0.882925i
$873$		−	0.427701i		−	0.0144755i
$874$	−3.21963	−	0.851001i	−0.108906	−	0.0287855i
$875$			1.93619i			0.0654553i
$876$	5.65692	+	10.6103i	0.191129	+	0.358488i
$877$	−4.41466	+	0.778423i	−0.149072	+	0.0262855i	−0.247686	−	0.968840i	$-0.579670\pi$
$877$	−4.41466	+	0.778423i	−0.149072	+	0.0262855i	0.0986139	+	0.995126i	$0.468559\pi$
$878$	−42.5493	+	23.6168i	−1.43597	+	0.797029i
$879$	−3.08221	−	3.67324i	−0.103960	−	0.123895i
$880$	−0.345055	+	5.09955i	−0.0116318	+	0.171906i
$881$	−21.8007	+	37.7599i	−0.734484	+	1.27216i	0.220465	+	0.975395i	$0.429243\pi$
$881$	−21.8007	+	37.7599i	−0.734484	+	1.27216i	−0.954949	+	0.296769i	$0.904091\pi$
$882$	1.07716	−	0.171227i	0.0362697	−	0.00576550i
$883$	−10.7642	−	29.5744i	−0.362244	−	0.995257i	−0.978234	−	0.207503i	$-0.933466\pi$
$883$	−10.7642	−	29.5744i	−0.362244	−	0.995257i	0.615991	−	0.787754i	$-0.288756\pi$
$884$	−11.4450	+	28.4196i	−0.384938	+	0.955853i
$885$	1.13543	+	1.96663i	0.0381671	+	0.0661074i
$886$	−25.8322	+	20.9426i	−0.867849	+	0.703580i
$887$	−4.01156	+	22.7507i	−0.134695	+	0.763893i	0.840377	+	0.542003i	$0.182334\pi$
$887$	−4.01156	+	22.7507i	−0.134695	+	0.763893i	−0.975072	+	0.221890i	$0.928777\pi$
$888$	−40.6188	−	17.1607i	−1.36308	−	0.575876i
$889$	−2.20807	+	2.63147i	−0.0740563	+	0.0882568i
$890$	0.834638	−	4.30679i	0.0279771	−	0.144364i
$891$	14.2034	−	39.0236i	0.475833	−	1.30734i
$892$	20.5490	+	18.4606i	0.688032	+	0.618105i
$893$	5.33788	+	0.358086i	0.178625	+	0.0119829i
$894$	−2.41303	+	6.29676i	−0.0807038	+	0.210595i
$895$	6.45523	+	2.34951i	0.215774	+	0.0785355i
$896$	−5.26382	−	5.60033i	−0.175852	−	0.187094i
$897$	−2.53375	−	2.12606i	−0.0845993	−	0.0709872i
$898$	−3.95651	+	1.36483i	−0.132030	+	0.0455449i
$899$	31.3948	+	5.53575i	1.04708	+	0.184628i
$900$	−1.10285	+	0.359712i	−0.0367617	+	0.0119904i
$901$	−38.1672	+	22.0359i	−1.27153	+	0.734121i
$902$	−0.199741	+	11.8247i	−0.00665065	+	0.393721i
$903$	6.13504	−	2.23297i	0.204161	−	0.0743086i
$904$	−21.0654	+	32.5581i	−0.700624	+	1.08287i
$905$	−1.35614	−	0.782968i	−0.0450796	−	0.0260267i
$906$	−27.6433	−	16.5886i	−0.918386	−	0.551119i
$907$	2.28571	−	1.91794i	0.0758956	−	0.0636840i	−0.604051	−	0.796946i	$-0.706448\pi$
$907$	2.28571	−	1.91794i	0.0758956	−	0.0636840i	0.679946	+	0.733262i	$0.262003\pi$
$908$	−3.16936	−	22.3684i	−0.105179	−	0.742320i
$909$	0.227679	+	1.29123i	0.00755164	+	0.0428275i
$910$	−0.627657	+	0.722859i	−0.0208066	+	0.0239625i
$911$	9.69320			0.321150			0.160575	−	0.987024i	$-0.448665\pi$
$911$	9.69320			0.321150			0.160575	+	0.987024i	$0.448665\pi$
$912$	−30.7627	+	1.23081i	−1.01865	+	0.0407562i
$913$	−44.4040			−1.46956
$914$	−25.5718	+	29.4504i	−0.845838	+	0.974133i
$915$	−0.695399	−	3.94381i	−0.0229892	−	0.130378i
$916$	−1.45182	−	10.2465i	−0.0479696	−	0.338554i
$917$	−8.80974	+	7.39225i	−0.290923	+	0.244114i
$918$	27.2641	+	16.3611i	0.899851	+	0.539996i
$919$	−18.5828	−	10.7288i	−0.612989	−	0.353909i	0.161145	−	0.986931i	$-0.448481\pi$
$919$	−18.5828	−	10.7288i	−0.612989	−	0.353909i	−0.774134	+	0.633021i	$0.781815\pi$
$920$	0.238543	−	0.368686i	0.00786453	−	0.0121552i
$921$	8.09780	−	2.94736i	0.266832	−	0.0971188i
$922$	0.747550	−	44.2552i	0.0246192	−	1.45747i
$923$	26.7300	−	15.4326i	0.879828	−	0.507969i
$924$	10.1413	−	3.30774i	0.333624	−	0.108817i
$925$	42.7561	+	7.53905i	1.40581	+	0.247883i
$926$	2.09697	−	0.723366i	0.0689107	−	0.0237713i
$927$	−0.261789	−	0.219667i	−0.00859827	−	0.00721480i
$928$	−17.1283	−	1.44995i	−0.562262	−	0.0475968i
$929$	−21.7707	−	7.92390i	−0.714275	−	0.259975i	−0.0407817	−	0.999168i	$-0.512985\pi$
$929$	−21.7707	−	7.92390i	−0.714275	−	0.259975i	−0.673493	+	0.739193i	$0.735207\pi$
$930$	−2.69417	+	7.03039i	−0.0883454	+	0.230536i
$931$	−28.3360	+	3.05932i	−0.928675	+	0.100265i
$932$	−9.19309	−	8.25877i	−0.301130	−	0.270525i
$933$	5.48260	−	15.0633i	0.179492	−	0.493151i
$934$	−5.12448	+	26.4427i	−0.167678	+	0.865231i
$935$	3.62877	−	4.32460i	0.118674	−	0.141430i
$936$	−1.06557	−	0.450184i	−0.0348292	−	0.0147147i
$937$	−7.37091	+	41.8025i	−0.240797	+	1.36563i	0.589258	+	0.807945i	$0.299420\pi$
$937$	−7.37091	+	41.8025i	−0.240797	+	1.36563i	−0.830055	+	0.557682i	$0.811691\pi$
$938$	3.70165	−	3.00099i	0.120863	−	0.0979858i
$939$	−0.770982	−	1.33538i	−0.0251600	−	0.0435785i
$940$	−0.263527	+	0.654374i	−0.00859532	+	0.0213433i
$941$	−1.19406	−	3.28065i	−0.0389252	−	0.106946i	0.918707	−	0.394939i	$-0.129234\pi$
$941$	−1.19406	−	3.28065i	−0.0389252	−	0.106946i	−0.957633	+	0.287993i	$0.907012\pi$
$942$	−59.1989	+	9.41036i	−1.92881	+	0.306606i
$943$	0.508030	−	0.879934i	0.0165437	−	0.0286546i
$944$	17.8590	+	1.20841i	0.581262	+	0.0393304i
$945$	0.638637	+	0.761097i	0.0207748	+	0.0247585i
$946$	−29.9233	+	16.6088i	−0.972889	+	0.539998i
$947$	−20.9000	+	3.68524i	−0.679159	+	0.119754i	−0.502578	−	0.864532i	$-0.667615\pi$
$947$	−20.9000	+	3.68524i	−0.679159	+	0.119754i	−0.176581	+	0.984286i	$0.556504\pi$
$948$	−13.7650	−	25.8180i	−0.447066	−	0.838530i
$949$		−	11.8055i		−	0.383221i
$950$	29.2533	−	7.94486i	0.949101	−	0.257765i
$951$		−	43.4088i		−	1.40763i
$952$	1.04878	+	8.42398i	0.0339913	+	0.273023i
$953$	15.1172	−	2.66558i	0.489695	−	0.0863465i	0.0766521	−	0.997058i	$-0.475577\pi$
$953$	15.1172	−	2.66558i	0.489695	−	0.0863465i	0.413043	+	0.910711i	$0.364466\pi$
$954$	−0.807537	−	1.45490i	−0.0261450	−	0.0471042i
$955$	−4.20999	−	5.01727i	−0.136232	−	0.162355i
$956$	−9.72310	−	12.4162i	−0.314468	−	0.401567i
$957$	11.9286	−	20.6610i	0.385598	−	0.667876i
$958$	5.16067	+	32.4649i	0.166734	+	1.04889i
$959$	−2.62537	−	7.21316i	−0.0847778	−	0.232925i
$960$	1.10581	−	3.90617i	0.0356897	−	0.126071i
$961$	−39.5308	−	68.4694i	−1.27519	−	2.20869i
$962$	27.2643	+	33.6299i	0.879037	+	1.08427i
$963$	0.191645	−	1.08687i	0.00617568	−	0.0350240i
$964$	1.04440	−	30.9056i	0.0336379	−	0.995402i
$965$	−3.77528	+	4.49921i	−0.121531	+	0.144835i
$966$	−0.899718	−	0.174362i	−0.0289479	−	0.00561000i
$967$	7.30654	−	20.0745i	0.234962	−	0.645554i	−0.765036	−	0.643987i	$-0.777279\pi$
$967$	7.30654	−	20.0745i	0.234962	−	0.645554i	0.999999	−	0.00156674i	$-0.000498709\pi$
$968$	−22.0813	+	11.2980i	−0.709721	+	0.363132i
$969$	28.2449	+	18.9354i	0.907358	+	0.608292i
$970$	−1.37614	−	0.527363i	−0.0441853	−	0.0169326i
$971$	−27.8889	−	10.1507i	−0.894999	−	0.325753i	−0.146752	−	0.989173i	$-0.546882\pi$
$971$	−27.8889	−	10.1507i	−0.894999	−	0.325753i	−0.748247	+	0.663420i	$0.769104\pi$
$972$	−1.29605	+	2.07933i	−0.0415710	+	0.0666945i
$973$	0.983857	+	0.825554i	0.0315410	+	0.0264660i
$974$	−17.4184	−	50.4944i	−0.558122	−	1.61795i
$975$	29.6496	+	5.22802i	0.949546	+	0.167431i
$976$	−28.8661	−	12.7742i	−0.923980	−	0.408891i
$977$	−22.8183	+	13.1741i	−0.730021	+	0.421478i	−0.818430	−	0.574607i	$-0.805155\pi$
$977$	−22.8183	+	13.1741i	−0.730021	+	0.421478i	0.0884090	+	0.996084i	$0.471822\pi$
$978$	26.4372	+	0.446572i	0.845368	+	0.0142798i
$979$	45.0985	−	16.4145i	1.44135	−	0.524610i
$980$	0.777224	−	3.67691i	0.0248275	−	0.117455i
$981$	0.948880	+	0.547836i	0.0302954	+	0.0174911i
$982$	−7.96719	+	13.2766i	−0.254243	+	0.423672i
$983$	−28.8985	+	24.2487i	−0.921718	+	0.773414i	−0.974312	−	0.225202i	$-0.927696\pi$
$983$	−28.8985	+	24.2487i	−0.921718	+	0.773414i	0.0525936	+	0.998616i	$0.483251\pi$
$984$	2.09758	−	9.15616i	0.0668684	−	0.291888i
$985$	0.238127	+	1.35049i	0.00758736	+	0.0430300i
$986$	14.3359	+	12.4478i	0.456548	+	0.396420i
$987$	1.47226			0.0468626
$988$	27.2205	+	13.1433i	0.866000	+	0.418144i
$989$	2.94030			0.0934960
$990$	0.160944	+	0.139748i	0.00511514	+	0.00444147i
$991$	3.04240	+	17.2543i	0.0966449	+	0.548100i	0.994231	+	0.107261i	$0.0342081\pi$
$991$	3.04240	+	17.2543i	0.0966449	+	0.548100i	−0.897586	+	0.440839i	$0.854681\pi$
$992$	34.1763	+	48.5175i	1.08510	+	1.54043i
$993$	−9.76195	+	8.19125i	−0.309786	+	0.259941i
$994$	4.40051	−	7.33303i	0.139576	−	0.232590i
$995$	−1.45983	−	0.842834i	−0.0462798	−	0.0267196i
$996$	34.5062	+	7.29392i	1.09337	+	0.231117i
$997$	−12.7266	+	4.63209i	−0.403054	+	0.146700i	−0.535589	−	0.844479i	$-0.679910\pi$
$997$	−12.7266	+	4.63209i	−0.403054	+	0.146700i	0.132535	+	0.991178i	$0.457688\pi$
$998$	27.5709	+	0.465722i	0.872741	+	0.0147422i
$999$	38.9114	−	22.4655i	1.23110	−	0.710777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.15.7	yes	48
3.2	odd	2		684.2.cf.a.91.2		48
4.3	odd	2	inner	76.2.k.a.15.5	✓	48
12.11	even	2		684.2.cf.a.91.4		48
19.14	odd	18	inner	76.2.k.a.71.5	yes	48
57.14	even	18		684.2.cf.a.451.4		48
76.71	even	18	inner	76.2.k.a.71.7	yes	48
228.71	odd	18		684.2.cf.a.451.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.15.5	✓	48	4.3	odd	2	inner
76.2.k.a.15.7	yes	48	1.1	even	1	trivial
76.2.k.a.71.5	yes	48	19.14	odd	18	inner
76.2.k.a.71.7	yes	48	76.71	even	18	inner
684.2.cf.a.91.2		48	3.2	odd	2
684.2.cf.a.91.4		48	12.11	even	2
684.2.cf.a.451.2		48	228.71	odd	18
684.2.cf.a.451.4		48	57.14	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.927206 - 1.06784i) q^{2} +(0.306623 + 1.73895i) q^{3} +(-0.280577 - 1.98022i) q^{4} +(-0.220151 + 0.184728i) q^{5} +(2.14122 + 1.28494i) q^{6} +(-0.588321 - 0.339668i) q^{7} +(-2.37472 - 1.53646i) q^{8} +(-0.110838 + 0.0403418i) q^{9} +O(q^{10})\)	\(q+(0.927206 - 1.06784i) q^{2} +(0.306623 + 1.73895i) q^{3} +(-0.280577 - 1.98022i) q^{4} +(-0.220151 + 0.184728i) q^{5} +(2.14122 + 1.28494i) q^{6} +(-0.588321 - 0.339668i) q^{7} +(-2.37472 - 1.53646i) q^{8} +(-0.110838 + 0.0403418i) q^{9} +(-0.00686428 + 0.406368i) q^{10} +(-3.85060 + 2.22314i) q^{11} +(3.35747 - 1.09509i) q^{12} +(-3.41466 - 0.602096i) q^{13} +(-0.908207 + 0.313293i) q^{14} +(-0.388736 - 0.326188i) q^{15} +(-3.84255 + 1.11121i) q^{16} +(4.15159 + 1.51105i) q^{17} +(-0.0596912 + 0.155763i) q^{18} +(1.76165 - 3.98705i) q^{19} +(0.427572 + 0.384117i) q^{20} +(0.410271 - 1.12721i) q^{21} +(-1.19633 + 6.17315i) q^{22} +(0.347253 - 0.413840i) q^{23} +(1.94368 - 4.60062i) q^{24} +(-0.853899 + 4.84270i) q^{25} +(-3.80904 + 3.08805i) q^{26} +(2.54452 + 4.40724i) q^{27} +(-0.507548 + 1.26031i) q^{28} +(1.03930 + 2.85545i) q^{29} +(-0.708757 + 0.112665i) q^{30} +(5.24551 - 9.08550i) q^{31} +(-2.37625 + 5.13356i) q^{32} +(-5.04661 - 6.01432i) q^{33} +(5.46295 - 3.03218i) q^{34} +(0.192266 - 0.0339016i) q^{35} +(0.110984 + 0.208165i) q^{36} -8.82897i q^{37} +(-2.62413 - 5.57799i) q^{38} -6.12252i q^{39} +(0.806624 - 0.100424i) q^{40} +(1.85222 - 0.326596i) q^{41} +(-0.823277 - 1.48326i) q^{42} +(3.49849 + 4.16933i) q^{43} +(5.48271 + 7.00128i) q^{44} +(0.0169489 - 0.0293563i) q^{45} +(-0.119941 - 0.754527i) q^{46} +(0.419777 + 1.15333i) q^{47} +(-3.11055 - 6.34127i) q^{48} +(-3.26925 - 5.66251i) q^{49} +(4.37950 + 5.40201i) q^{50} +(-1.35467 + 7.68271i) q^{51} +(-0.234211 + 6.93071i) q^{52} +(-6.41208 + 7.64162i) q^{53} +(7.06553 + 1.36927i) q^{54} +(0.437034 - 1.20074i) q^{55} +(0.875211 + 1.71055i) q^{56} +(7.47343 + 1.84089i) q^{57} +(4.01281 + 1.53778i) q^{58} +(-4.20510 - 1.53053i) q^{59} +(-0.536855 + 0.861304i) q^{60} +(6.04529 + 5.07260i) q^{61} +(-4.83821 - 14.0255i) q^{62} +(0.0789113 + 0.0139142i) q^{63} +(3.27857 + 7.29733i) q^{64} +(0.862964 - 0.498232i) q^{65} +(-11.1016 - 0.187526i) q^{66} +(-4.66099 + 1.69646i) q^{67} +(1.82738 - 8.64503i) q^{68} +(0.826122 + 0.476961i) q^{69} +(0.142068 - 0.236743i) q^{70} +(-6.81908 + 5.72189i) q^{71} +(0.325193 + 0.0744984i) q^{72} +(0.591231 + 3.35304i) q^{73} +(-9.42796 - 8.18628i) q^{74} -8.68302 q^{75} +(-8.38953 - 2.36978i) q^{76} +3.02052 q^{77} +(-6.53789 - 5.67684i) q^{78} +(-1.43865 - 8.15896i) q^{79} +(0.640670 - 0.954462i) q^{80} +(-7.15481 + 6.00360i) q^{81} +(1.36864 - 2.28070i) q^{82} +(8.64879 + 4.99338i) q^{83} +(-2.34724 - 0.496158i) q^{84} +(-1.19311 + 0.434257i) q^{85} +(7.69601 + 0.129999i) q^{86} +(-4.64680 + 2.68283i) q^{87} +(12.5599 + 0.636961i) q^{88} +(-10.6299 - 1.87434i) q^{89} +(-0.0156328 - 0.0453180i) q^{90} +(1.80440 + 1.51407i) q^{91} +(-0.916926 - 0.571524i) q^{92} +(17.4076 + 6.33584i) q^{93} +(1.62079 + 0.621117i) q^{94} +(0.348694 + 1.20318i) q^{95} +(-9.65560 - 2.55809i) q^{96} +(-1.24019 + 3.40739i) q^{97} +(-9.07794 - 1.75927i) q^{98} +(0.337108 - 0.401750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Introduction

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