LMFDB - Embedded newform 76.2.k.a.15.5

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			15.5
Character	$\chi$	$=$	76.15
Dual form			76.2.k.a.71.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0238852 - 1.41401i) q^{2} +(-0.306623 - 1.73895i) q^{3} +(-1.99886 + 0.0675479i) q^{4} +(-0.220151 + 0.184728i) q^{5} +(-2.45157 + 0.475104i) q^{6} +(0.588321 + 0.339668i) q^{7} +(0.143257 + 2.82480i) q^{8} +(-0.110838 + 0.0403418i) q^{9} +O(q^{10})$	\(q+(-0.0238852 - 1.41401i) q^{2} +(-0.306623 - 1.73895i) q^{3} +(-1.99886 + 0.0675479i) q^{4} +(-0.220151 + 0.184728i) q^{5} +(-2.45157 + 0.475104i) q^{6} +(0.588321 + 0.339668i) q^{7} +(0.143257 + 2.82480i) q^{8} +(-0.110838 + 0.0403418i) q^{9} +(0.266467 + 0.306884i) q^{10} +(3.85060 - 2.22314i) q^{11} +(0.730359 + 3.45520i) q^{12} +(-3.41466 - 0.602096i) q^{13} +(0.466242 - 0.840006i) q^{14} +(0.388736 + 0.326188i) q^{15} +(3.99087 - 0.270038i) 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} +(-3.23552 - 5.39169i) q^{22} +(-0.347253 + 0.413840i) q^{23} +(4.86824 - 1.11526i) q^{24} +(-0.853899 + 4.84270i) q^{25} +(-0.769811 + 4.84275i) q^{26} +(-2.54452 - 4.40724i) q^{27} +(-1.19892 - 0.639208i) q^{28} +(1.03930 + 2.85545i) q^{29} +(0.451949 - 0.557469i) q^{30} +(-5.24551 + 9.08550i) q^{31} +(-0.477159 - 5.63669i) q^{32} +(-5.04661 - 6.01432i) q^{33} +(2.03749 - 5.90649i) q^{34} +(-0.192266 + 0.0339016i) q^{35} +(0.218825 - 0.0881245i) q^{36} -8.82897i q^{37} +(5.67982 + 2.39576i) q^{38} +6.12252i q^{39} +(-0.553358 - 0.595418i) q^{40} +(1.85222 - 0.326596i) q^{41} +(-1.60369 - 0.553204i) q^{42} +(-3.49849 - 4.16933i) q^{43} +(-7.54663 + 4.70385i) q^{44} +(0.0169489 - 0.0293563i) q^{45} +(0.593469 + 0.481135i) q^{46} +(-0.419777 - 1.15333i) q^{47} +(-1.69328 - 6.85712i) q^{48} +(-3.26925 - 5.66251i) q^{49} +(6.86803 + 1.09175i) q^{50} +(1.35467 - 7.68271i) q^{51} +(6.86609 + 0.972852i) q^{52} +(-6.41208 + 7.64162i) q^{53} +(-6.17111 + 3.70325i) 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} +(-0.799062 - 0.625746i) q^{60} +(6.04529 + 5.07260i) q^{61} +(12.9723 + 7.20021i) q^{62} +(-0.0789113 - 0.0139142i) q^{63} +(-7.95896 + 0.809342i) q^{64} +(0.862964 - 0.498232i) q^{65} +(-8.38378 + 7.27962i) q^{66} +(4.66099 - 1.69646i) q^{67} +(-8.40051 - 2.73995i) q^{68} +(0.826122 + 0.476961i) q^{69} +(0.0525296 + 0.271056i) q^{70} +(6.81908 - 5.72189i) q^{71} +(-0.129836 - 0.307316i) q^{72} +(0.591231 + 3.35304i) q^{73} +(-12.4843 + 0.210882i) q^{74} +8.68302 q^{75} +(3.25197 - 8.08855i) q^{76} +3.02052 q^{77} +(8.65732 - 0.146238i) q^{78} +(1.43865 + 8.15896i) q^{79} +(-0.828711 + 0.796677i) q^{80} +(-7.15481 + 6.00360i) q^{81} +(-0.506052 - 2.61126i) q^{82} +(-8.64879 - 4.99338i) q^{83} +(-0.743932 + 2.28085i) q^{84} +(-1.19311 + 0.434257i) q^{85} +(-5.81192 + 5.04649i) q^{86} +(4.64680 - 2.68283i) q^{87} +(6.83155 + 10.5587i) q^{88} +(-10.6299 - 1.87434i) q^{89} +(-0.0419149 - 0.0232647i) q^{90} +(-1.80440 - 1.51407i) q^{91} +(0.666156 - 0.850664i) 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} +(-7.92877 + 4.75801i) 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 $

$2$	−0.0238852	−	1.41401i	−0.0168894	−	0.999857i
$2$	−0.0238852	−	1.41401i	−0.0168894	−	0.999857i
$3$	−0.306623	−	1.73895i	−0.177029	−	1.00398i	−0.935776	−	0.352595i	$-0.885299\pi$
$3$	−0.306623	−	1.73895i	−0.177029	−	1.00398i	0.758747	−	0.651386i	$-0.225812\pi$
$4$	−1.99886	+	0.0675479i	−0.999429	+	0.0337740i
$5$	−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	$0.298247\pi$
$6$	−2.45157	+	0.475104i	−1.00085	+	0.193960i
$7$	0.588321	+	0.339668i	0.222365	+	0.128382i	0.607045	−	0.794668i	$-0.292355\pi$
$7$	0.588321	+	0.339668i	0.222365	+	0.128382i	−0.384680	+	0.923050i	$0.625688\pi$
$8$	0.143257	+	2.82480i	0.0506489	+	0.998717i
$9$	−0.110838	+	0.0403418i	−0.0369461	+	0.0134473i
$10$	0.266467	+	0.306884i	0.0842641	+	0.0970451i
$11$	3.85060	−	2.22314i	1.16100	−	0.670303i	0.209456	−	0.977818i	$-0.432831\pi$
$11$	3.85060	−	2.22314i	1.16100	−	0.670303i	0.951543	+	0.307515i	$0.0994974\pi$
$12$	0.730359	+	3.45520i	0.210836	+	0.997429i
$13$	−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	$0.715221\pi$
$14$	0.466242	−	0.840006i	0.124608	−	0.224501i
$15$	0.388736	+	0.326188i	0.100371	+	0.0842215i
$16$	3.99087	−	0.270038i	0.997719	−	0.0675094i
$17$	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
$22$	−3.23552	−	5.39169i	−0.689816	−	1.14951i
$23$	−0.347253	+	0.413840i	−0.0724073	+	0.0862916i	−0.801032	−	0.598621i	$-0.795715\pi$
$23$	−0.347253	+	0.413840i	−0.0724073	+	0.0862916i	0.728625	+	0.684913i	$0.240160\pi$
$24$	4.86824	−	1.11526i	0.993726	−	0.227652i
$25$	−0.853899	+	4.84270i	−0.170780	+	0.968541i
$26$	−0.769811	+	4.84275i	−0.150972	+	0.949741i
$27$	−2.54452	−	4.40724i	−0.489693	−	0.848174i
$28$	−1.19892	−	0.639208i	−0.226574	−	0.120799i
$29$	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	$0.797846\pi$
$30$	0.451949	−	0.557469i	0.0825143	−	0.101779i
$31$	−5.24551	+	9.08550i	−0.942122	+	1.63180i	−0.180709	+	0.983537i	$0.557839\pi$
$31$	−5.24551	+	9.08550i	−0.942122	+	1.63180i	−0.761413	+	0.648267i	$0.775494\pi$
$32$	−0.477159	−	5.63669i	−0.0843506	−	0.996436i
$33$	−5.04661	−	6.01432i	−0.878502	−	1.04696i
$34$	2.03749	−	5.90649i	0.349426	−	1.01295i
$35$	−0.192266	+	0.0339016i	−0.0324988	+	0.00573042i
$36$	0.218825	−	0.0881245i	0.0364708	−	0.0146874i
$37$		−	8.82897i		−	1.45147i	−0.687972	−	0.725737i	$-0.741499\pi$
$37$		−	8.82897i		−	1.45147i	0.687972	−	0.725737i	$-0.258501\pi$
$38$	5.67982	+	2.39576i	0.921388	+	0.388644i
$39$			6.12252i			0.980388i
$40$	−0.553358	−	0.595418i	−0.0874937	−	0.0941438i
$41$	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	$0.397526\pi$
$42$	−1.60369	−	0.553204i	−0.247454	−	0.0853612i
$43$	−3.49849	−	4.16933i	−0.533514	−	0.635817i	0.430207	−	0.902730i	$-0.358441\pi$
$43$	−3.49849	−	4.16933i	−0.533514	−	0.635817i	−0.963721	+	0.266913i	$0.913996\pi$
$44$	−7.54663	+	4.70385i	−1.13770	+	0.709132i
$45$	0.0169489	−	0.0293563i	0.00252659	−	0.00437617i
$46$	0.593469	+	0.481135i	0.0875022	+	0.0709395i
$47$	−0.419777	−	1.15333i	−0.0612307	−	0.168230i	0.905305	−	0.424762i	$-0.139642\pi$
$47$	−0.419777	−	1.15333i	−0.0612307	−	0.168230i	−0.966536	+	0.256532i	$0.917420\pi$
$48$	−1.69328	−	6.85712i	−0.244403	−	0.989739i
$49$	−3.26925	−	5.66251i	−0.467036	−	0.808930i
$50$	6.86803	+	1.09175i	0.971287	+	0.154397i
$51$	1.35467	−	7.68271i	0.189692	−	1.07580i
$52$	6.86609	+	0.972852i	0.952155	+	0.134910i
$53$	−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	$0.981974\pi$
$54$	−6.17111	+	3.70325i	−0.839782	+	0.503948i
$55$	−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	0.600916	−	0.799312i	$-0.294803\pi$
$59$	4.20510	+	1.53053i	0.547457	+	0.199258i	−0.0534593	+	0.998570i	$0.517025\pi$
$60$	−0.799062	−	0.625746i	−0.103158	−	0.0807835i
$61$	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	$0.553639\pi$
$62$	12.9723	+	7.20021i	1.64748	+	0.914428i
$63$	−0.0789113	−	0.0139142i	−0.00994189	−	0.00175302i
$64$	−7.95896	+	0.809342i	−0.994869	+	0.101168i
$65$	0.862964	−	0.498232i	0.107037	−	0.0617981i
$66$	−8.38378	+	7.27962i	−1.03197	+	0.896059i
$67$	4.66099	−	1.69646i	0.569430	−	0.207256i	−0.0412282	−	0.999150i	$-0.513127\pi$
$67$	4.66099	−	1.69646i	0.569430	−	0.207256i	0.610658	+	0.791894i	$0.290905\pi$
$68$	−8.40051	−	2.73995i	−1.01871	−	0.332268i
$69$	0.826122	+	0.476961i	0.0994533	+	0.0574194i
$70$	0.0525296	+	0.271056i	0.00627849	+	0.0323974i
$71$	6.81908	−	5.72189i	0.809276	−	0.679064i	−0.141159	−	0.989987i	$-0.545083\pi$
$71$	6.81908	−	5.72189i	0.809276	−	0.679064i	0.950435	+	0.310923i	$0.100638\pi$
$72$	−0.129836	−	0.307316i	−0.0153013	−	0.0362176i
$73$	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	$0.880594\pi$
$74$	−12.4843	+	0.210882i	−1.45127	+	0.0245145i
$75$	8.68302			1.00263
$76$	3.25197	−	8.08855i	0.373027	−	0.927821i
$77$	3.02052			0.344220
$78$	8.65732	−	0.146238i	0.980248	−	0.0165582i
$79$	1.43865	+	8.15896i	0.161860	+	0.917955i	0.952243	+	0.305342i	$0.0987707\pi$
$79$	1.43865	+	8.15896i	0.161860	+	0.917955i	−0.790383	+	0.612614i	$0.790118\pi$
$80$	−0.828711	+	0.796677i	−0.0926527	+	0.0890712i
$81$	−7.15481	+	6.00360i	−0.794979	+	0.667067i
$82$	−0.506052	−	2.61126i	−0.0558841	−	0.288365i
$83$	−8.64879	−	4.99338i	−0.949328	−	0.548095i	−0.0564561	−	0.998405i	$-0.517980\pi$
$83$	−8.64879	−	4.99338i	−0.949328	−	0.548095i	−0.892872	+	0.450310i	$0.851313\pi$
$84$	−0.743932	+	2.28085i	−0.0811697	+	0.248861i
$85$	−1.19311	+	0.434257i	−0.129411	+	0.0471018i
$86$	−5.81192	+	5.04649i	−0.626716	+	0.544177i
$87$	4.64680	−	2.68283i	0.498189	−	0.287630i
$88$	6.83155	+	10.5587i	0.728246	+	1.12556i
$89$	−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	$0.749417\pi$
$90$	−0.0419149	−	0.0232647i	−0.00441822	−	0.00245231i
$91$	−1.80440	−	1.51407i	−0.189153	−	0.158718i
$92$	0.666156	−	0.850664i	0.0694516	−	0.0886879i
$93$	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	$0.170044\pi$
$98$	−7.92877	+	4.75801i	−0.800927	+	0.480632i
$99$	−0.337108	+	0.401750i	−0.0338806	+	0.0403774i
$100$	1.37971	−	9.73756i	0.137971	−	0.973756i
$101$	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	$-0.130978\pi$
$102$	−10.8958	−	1.73202i	−1.07885	−	0.171495i
$103$	−1.44865	−	2.50913i	−0.142740	−	0.247232i	0.785788	−	0.618496i	$-0.212258\pi$
$103$	−1.44865	−	2.50913i	−0.142740	−	0.247232i	−0.928527	+	0.371264i	$0.878924\pi$
$104$	1.21163	−	9.73197i	0.118810	−	0.954298i
$105$	0.117906	+	0.323945i	0.0115065	+	0.0316138i
$106$	10.9585	+	8.88424i	1.06438	+	0.862913i
$107$	4.67836	−	8.10316i	0.452274	−	0.783362i	−0.546253	−	0.837620i	$-0.683946\pi$
$107$	4.67836	−	8.10316i	0.452274	−	0.783362i	0.998527	+	0.0542585i	$0.0172795\pi$
$108$	5.38384	+	8.63757i	0.518060	+	0.831151i
$109$	−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	$0.924528\pi$
$110$	1.70830	+	0.589292i	0.162880	+	0.0561868i
$111$	−15.3531	+	2.70717i	−1.45725	+	0.256953i
$112$	2.43964	+	1.19670i	0.230524	+	0.113078i
$113$		−	13.7103i		−	1.28976i	−0.764285	−	0.644879i	$-0.776908\pi$
$113$		−	13.7103i		−	1.28976i	0.764285	−	0.644879i	$-0.223092\pi$
$114$	2.42454	−	10.6115i	0.227079	−	0.993857i
$115$		−	0.155255i		−	0.0144776i
$116$	−2.27029	−	5.63744i	−0.210791	−	0.523423i
$117$	0.402764	−	0.0710182i	0.0372356	−	0.00656564i
$118$	2.06375	−	5.98261i	0.189983	−	0.550744i
$119$	1.92921	+	2.29915i	0.176851	+	0.210762i
$120$	−0.865727	+	1.14483i	−0.0790297	+	0.104508i
$121$	4.38474	−	7.59459i	0.398613	−	0.690417i
$122$	7.02832	−	8.66927i	0.636315	−	0.784879i
$123$	−1.13587	−	3.12077i	−0.102418	−	0.281390i
$124$	9.87134	−	18.5149i	0.886472	−	1.66269i
$125$	−1.42506	−	2.46828i	−0.127462	−	0.220770i
$126$	−0.0177900	+	0.111914i	−0.00158486	+	0.00997008i
$127$	−0.878075	+	4.97981i	−0.0779165	+	0.441887i	0.920745	+	0.390165i	$0.127582\pi$
$127$	−0.878075	+	4.97981i	−0.0779165	+	0.441887i	−0.998662	+	0.0517217i	$0.983529\pi$
$128$	1.33452	+	11.2347i	0.117956	+	0.993019i
$129$	−6.17753	+	7.36209i	−0.543901	+	0.648196i
$130$	−0.725119	−	1.20834i	−0.0635971	−	0.105978i
$131$	−5.78998	+	15.9078i	−0.505873	+	1.38987i	0.379586	+	0.925156i	$0.376066\pi$
$131$	−5.78998	+	15.9078i	−0.505873	+	1.38987i	−0.885459	+	0.464718i	$0.846156\pi$
$132$	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
$136$	−3.67368	+	11.9439i	−0.315015	+	1.02418i
$137$	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	$0.561883\pi$
$138$	0.654697	−	1.17954i	0.0557315	−	0.100409i
$139$	1.86185	+	0.328295i	0.157920	+	0.0278456i	0.252049	−	0.967714i	$-0.418895\pi$
$139$	1.86185	+	0.328295i	0.157920	+	0.0278456i	−0.0941290	+	0.995560i	$0.530007\pi$
$140$	0.382022	−	0.0807517i	0.0322868	−	0.00682477i
$141$	−1.87686	+	1.08361i	−0.158060	+	0.0912561i
$142$	−8.25370	−	9.50560i	−0.692635	−	0.797692i
$143$	−14.4870	+	5.27284i	−1.21147	+	0.440937i
$144$	−0.431448	+	0.190930i	−0.0359540	+	0.0159108i
$145$	−0.756285	−	0.436641i	−0.0628061	−	0.0362611i
$146$	4.72711	−	0.916096i	0.391219	−	0.0758166i
$147$	−8.84437	+	7.42131i	−0.729472	+	0.612099i
$148$	0.596379	+	17.6479i	0.0490220	+	1.45065i
$149$	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	$0.909164\pi$
$150$	−0.207396	−	12.2779i	−0.0169338	−	1.00249i
$151$	12.9100			1.05060			0.525302	−	0.850916i	$-0.323952\pi$
$151$	12.9100			1.05060			0.525302	+	0.850916i	$0.323952\pi$
$152$	−11.5150	−	4.40513i	−0.933988	−	0.357303i
$153$	−0.521114			−0.0421295
$154$	−0.0721457	−	4.27105i	−0.00581367	−	0.344171i
$155$	−0.523546	−	2.96917i	−0.0420522	−	0.238490i
$156$	−0.413564	−	12.2381i	−0.0331116	−	0.979829i
$157$	−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	$0.870511\pi$
$158$	11.5025	−	2.22914i	0.915090	−	0.177341i
$159$	15.2545	+	8.80717i	1.20976	+	0.698454i
$160$	1.14630	+	1.15278i	0.0906233	+	0.0911351i
$161$	−0.344864	+	0.125520i	−0.0271791	+	0.00989239i
$162$	8.66005	+	9.97359i	0.680398	+	0.783599i
$163$	−9.16976	+	5.29416i	−0.718231	+	0.414671i	−0.814101	−	0.580723i	$-0.802770\pi$
$163$	−9.16976	+	5.29416i	−0.718231	+	0.414671i	0.0958702	+	0.995394i	$0.469437\pi$
$164$	−3.68026	+	0.777933i	−0.287380	+	0.0607464i
$165$	2.22203	+	0.391804i	0.172985	+	0.0305019i
$166$	−6.85412	+	12.3488i	−0.531983	+	0.958450i
$167$	−12.2979	−	10.3192i	−0.951640	−	0.798521i	0.0279326	−	0.999610i	$-0.491108\pi$
$167$	−12.2979	−	10.3192i	−0.951640	−	0.798521i	−0.979573	+	0.201089i	$0.935552\pi$
$168$	3.24291	+	0.997451i	0.250196	+	0.0769550i
$169$	−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	$0.0401570\pi$
$174$	−3.90454	−	6.50655i	−0.296003	−	0.493260i
$175$	−2.14728	+	2.55902i	−0.162319	+	0.193444i
$176$	14.7669	−	9.91210i	1.11310	−	0.747152i
$177$	1.37213	−	7.78173i	0.103136	−	0.584911i
$178$	−2.39644	+	15.0756i	−0.179621	+	1.12996i
$179$	11.9517	+	20.7009i	0.893312	+	1.54726i	0.835880	+	0.548912i	$0.184958\pi$
$179$	11.9517	+	20.7009i	0.893312	+	1.54726i	0.0574313	+	0.998349i	$0.481709\pi$
$180$	−0.0318954	+	0.0598239i	−0.00237734	+	0.00445901i
$181$	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	$0.823980\pi$
$182$	−2.09782	+	2.58761i	−0.155501	+	0.191807i
$183$	6.96735	−	12.0678i	0.515042	−	0.892078i
$184$	−1.21876	−	0.921634i	−0.0898482	−	0.0679438i
$185$	1.63096	+	1.94371i	0.119911	+	0.142904i
$186$	8.54317	−	24.7659i	0.626416	−	1.81592i
$187$	19.3454	−	3.41112i	1.41468	−	0.249445i
$188$	0.916979	+	2.27698i	0.0668776	+	0.166066i
$189$		−	3.45716i		−	0.251472i
$190$	−1.69298	+	0.521795i	−0.122822	+	0.0378550i
$191$		−	22.7901i		−	1.64904i	−0.565835	−	0.824518i	$-0.691446\pi$
$191$		−	22.7901i		−	1.64904i	0.565835	−	0.824518i	$-0.308554\pi$
$192$	3.84780	+	13.5920i	0.277691	+	0.980920i
$193$	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	$0.181372\pi$
$194$	4.84772	+	1.67226i	0.348046	+	0.120061i
$195$	−1.13100	−	1.34788i	−0.0809929	−	0.0965236i
$196$	6.91726	+	11.0977i	0.494090	+	0.792695i
$197$	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	$0.112295\pi$
$198$	0.576131	+	0.467079i	0.0409438	+	0.0331938i
$199$	−2.00612	−	5.51177i	−0.142210	−	0.390719i	0.848056	−	0.529907i	$-0.177773\pi$
$199$	−2.00612	−	5.51177i	−0.142210	−	0.390719i	−0.990266	+	0.139188i	$0.955551\pi$
$200$	−13.8020	−	1.71834i	−0.975947	−	0.121505i
$201$	−4.37922	−	7.58503i	−0.308886	−	0.535007i
$202$	−15.5255	−	2.46796i	−1.09237	−	0.173645i
$203$	−0.358462	+	2.03294i	−0.0251591	+	0.142684i
$204$	−2.18884	+	15.4482i	−0.153250	+	1.08159i
$205$	−0.347436	+	0.414058i	−0.0242660	+	0.0289191i
$206$	−3.51334	+	2.10834i	−0.244786	+	0.146895i
$207$	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	−0.272695	−	0.962101i	$-0.587915\pi$
$211$	−15.9787	−	5.81576i	−1.10002	−	0.400374i	−0.827323	+	0.561727i	$0.810137\pi$
$212$	12.3007	−	15.7076i	0.844813	−	1.07881i
$213$	−12.0410	−	10.1036i	−0.825032	−	0.692284i
$214$	−11.5697	−	6.42171i	−0.790889	−	0.438979i
$215$	1.54039	+	0.271612i	0.105054	+	0.0185238i
$216$	12.0850	−	7.81912i	0.822282	−	0.532024i
$217$	−6.17210	+	3.56346i	−0.418989	+	0.241904i
$218$	−9.91937	+	8.61298i	−0.671825	+	0.583344i
$219$	5.64947	−	2.05624i	0.381756	−	0.138948i
$220$	0.792462	−	2.42963i	0.0534278	−	0.163806i
$221$	−13.2665	−	7.65939i	−0.892398	−	0.515226i
$222$	4.19468	+	21.6448i	0.281528	+	1.45271i
$223$	10.5804	−	8.87801i	0.708516	−	0.594515i	−0.215667	−	0.976467i	$-0.569192\pi$
$223$	10.5804	−	8.87801i	0.708516	−	0.594515i	0.924182	+	0.381952i	$0.124748\pi$
$224$	1.63388	−	3.47826i	0.109168	−	0.232401i
$225$	−0.100719	−	0.571205i	−0.00671459	−	0.0380803i
$226$	−19.3866	+	0.327474i	−1.28957	+	0.0217832i
$227$	−11.2959			−0.749734			−0.374867	−	0.927079i	$-0.622312\pi$
$227$	−11.2959			−0.749734			−0.374867	+	0.927079i	$0.622312\pi$
$228$	−15.0627	−	3.17487i	−0.997551	−	0.210261i
$229$	5.17443			0.341936			0.170968	−	0.985277i	$-0.445311\pi$
$229$	5.17443			0.341936			0.170968	+	0.985277i	$0.445311\pi$
$230$	−0.219532	+	0.00370829i	−0.0144755	+	0.000244518i
$231$	−0.926161	−	5.25252i	−0.0609369	−	0.345590i
$232$	−7.91718	+	3.34487i	−0.519788	+	0.219601i
$233$	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	$0.212904\pi$
$234$	−0.110041	−	0.567817i	−0.00719359	−	0.0371194i
$235$	0.305467	+	0.176361i	0.0199264	+	0.0115045i
$236$	−8.50878	−	2.77527i	−0.553874	−	0.180655i
$237$	13.7469	−	5.00345i	0.892956	−	0.325009i
$238$	3.20494	−	2.78284i	0.207745	−	0.180385i
$239$	−6.82870	+	3.94255i	−0.441712	+	0.255023i	−0.704324	−	0.709879i	$-0.748750\pi$
$239$	−6.82870	+	3.94255i	−0.441712	+	0.255023i	0.262612	+	0.964902i	$0.415416\pi$
$240$	1.63948	+	1.19680i	0.105828	+	0.0772533i
$241$	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	$0.389629\pi$
$242$	−10.8436	−	6.01868i	−0.697051	−	0.386895i
$243$	0.938472	+	0.787471i	0.0602030	+	0.0505163i
$244$	−12.4263	−	9.73107i	−0.795514	−	0.622968i
$245$	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
$250$	−3.45615	+	2.07401i	−0.218586	+	0.131172i
$251$	−5.32272	+	6.34338i	−0.335967	+	0.400390i	−0.907406	−	0.420254i	$-0.861941\pi$
$251$	−5.32272	+	6.34338i	−0.335967	+	0.400390i	0.571439	+	0.820644i	$0.306385\pi$
$252$	0.158673	+	0.0224822i	0.00999543	+	0.00141625i
$253$	−0.417106	+	2.36553i	−0.0262232	+	0.148719i
$254$	7.06248	+	1.12266i	0.443140	+	0.0704422i
$255$	1.12098	+	1.94160i	0.0701988	+	0.121588i
$256$	15.8542	−	2.15537i	0.990885	−	0.134711i
$257$	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	$0.830939\pi$
$258$	10.5576	+	8.55925i	0.657290	+	0.532876i
$259$	2.99892	−	5.19427i	0.186344	−	0.322756i
$260$	−1.69129	+	1.05419i	−0.104889	+	0.0653780i
$261$	−0.230388	−	0.274566i	−0.0142607	−	0.0169952i
$262$	22.6322	+	7.80714i	1.39822	+	0.482327i
$263$	18.2994	−	3.22667i	1.12839	−	0.198965i	0.421867	−	0.906658i	$-0.361375\pi$
$263$	18.2994	−	3.22667i	1.12839	−	0.198965i	0.706520	+	0.707693i	$0.250264\pi$
$264$	16.2663	−	15.1172i	1.00112	−	0.930402i
$265$		−	2.86680i		−	0.176106i
$266$	2.52780	+	3.33873i	0.154989	+	0.204710i
$267$			19.0596i			1.16643i
$268$	−9.20206	+	3.70583i	−0.562106	+	0.226369i
$269$	−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	$0.460280\pi$
$270$	0.674479	−	1.95525i	0.0410475	−	0.118993i
$271$	−13.9309	−	16.6022i	−0.846242	−	1.00851i	−0.999792	−	0.0203711i	$-0.993515\pi$
$271$	−13.9309	−	16.6022i	−0.846242	−	1.00851i	0.153551	−	0.988141i	$-0.450929\pi$
$272$	16.9765	+	4.90935i	1.02935	+	0.297673i
$273$	−2.07962	+	3.60201i	−0.125864	+	0.218004i
$274$	10.0634	−	12.4130i	0.607952	−	0.749894i
$275$	7.47800	+	20.5456i	0.450941	+	1.23895i
$276$	−1.68352	−	0.897576i	−0.101336	−	0.0540277i
$277$	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	$0.666689\pi$
$278$	0.419742	−	2.64052i	0.0251745	−	0.158368i
$279$	0.214878	−	1.21863i	0.0128644	−	0.0729577i
$280$	−0.123309	−	0.538255i	−0.00736910	−	0.0321669i
$281$	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	$0.0735986\pi$
$282$	1.57706	+	2.62802i	0.0939126	+	0.156496i
$283$	2.29727	−	6.31170i	0.136559	−	0.375192i	−0.852498	−	0.522731i	$-0.824913\pi$
$283$	2.29727	−	6.31170i	0.136559	−	0.375192i	0.989056	+	0.147540i	$0.0471354\pi$
$284$	−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
$288$	0.280282	+	0.605512i	0.0165158	+	0.0356801i
$289$	1.92965	+	1.61917i	0.113509	+	0.0952452i
$290$	−0.599352	+	1.07983i	−0.0351952	+	0.0634095i
$291$	6.30555	+	1.11184i	0.369638	+	0.0651771i
$292$	−1.40828	−	6.66232i	−0.0824133	−	0.389883i
$293$	−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	$0.358609\pi$
$294$	10.7051	+	12.3288i	0.624332	+	0.719030i
$295$	−1.20849	+	0.439854i	−0.0703609	+	0.0256093i
$296$	24.9401	−	1.26481i	1.44961	−	0.0735156i
$297$	−19.5959	−	11.3137i	−1.13707	−	0.656486i
$298$	3.74913	−	0.726567i	0.217181	−	0.0420889i
$299$	1.43492	−	1.20404i	0.0829837	−	0.0696316i
$300$	−17.3561	+	0.586520i	−1.00206	+	0.0338628i
$301$	−0.642047	−	3.64123i	−0.0370070	−	0.209877i
$302$	−0.308359	−	18.2549i	−0.0177441	−	1.05045i
$303$	−19.6283			−1.12762
$304$	−5.95387	+	16.3875i	−0.341478	+	0.939890i
$305$	−2.26793			−0.129861
$306$	0.0124469	+	0.736861i	0.000711542	+	0.0421235i
$307$	0.847455	+	4.80616i	0.0483668	+	0.274302i	0.999394	−	0.0348050i	$-0.0110810\pi$
$307$	0.847455	+	4.80616i	0.0483668	+	0.274302i	−0.951027	+	0.309107i	$0.899970\pi$
$308$	−6.03759	+	0.204030i	−0.344024	+	0.0116257i
$309$	−3.91906	+	3.28848i	−0.222947	+	0.187075i
$310$	−4.18594	+	0.811219i	−0.237746	+	0.0460741i
$311$	7.86197	+	4.53911i	0.445811	+	0.257389i	0.706060	−	0.708153i	$-0.250471\pi$
$311$	7.86197	+	4.53911i	0.445811	+	0.257389i	−0.260248	+	0.965542i	$0.583804\pi$
$312$	−17.2949	+	0.877092i	−0.979130	+	0.0496556i
$313$	−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	$0.396745\pi$
$314$	22.2566	+	25.6325i	1.25601	+	1.44652i
$315$	0.0199427	−	0.0115139i	0.00112365	−	0.000648737i
$316$	−3.42677	−	16.2114i	−0.192771	−	0.911965i
$317$	−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	$0.798109\pi$
$318$	12.0891	−	21.7803i	0.677922	−	1.22138i
$319$	10.3500	+	8.68468i	0.579489	+	0.486249i
$320$	1.60266	−	1.64842i	0.0895915	−	0.0921496i
$321$	−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
$326$	7.70503	+	12.8397i	0.426742	+	0.711125i
$327$	−10.5434	+	12.5651i	−0.583049	+	0.694851i
$328$	1.18791	+	5.18536i	0.0655914	+	0.286313i
$329$	0.144784	−	0.821111i	0.00798221	−	0.0452693i
$330$	0.500942	−	3.15134i	0.0275759	−	0.173475i
$331$	−3.60843	−	6.24998i	−0.198337	−	0.343530i	0.749652	−	0.661832i	$-0.230221\pi$
$331$	−3.60843	−	6.24998i	−0.198337	−	0.343530i	−0.947989	+	0.318302i	$0.896887\pi$
$332$	17.6250	+	9.39686i	0.967298	+	0.515720i
$333$	0.356177	+	0.978588i	0.0195184	+	0.0536263i
$334$	−14.2977	+	17.6359i	−0.782335	+	0.964991i
$335$	−0.712736	+	1.23449i	−0.0389409	+	0.0674476i
$336$	1.33295	−	4.60934i	0.0727184	−	0.251460i
$337$	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	$0.752503\pi$
$338$	−0.450843	+	1.30695i	−0.0245226	+	0.0710887i
$339$	−23.8415	+	4.20390i	−1.29489	+	0.228325i
$340$	2.35553	−	0.948610i	0.127746	−	0.0514456i
$341$			46.6461i			2.52603i
$342$	−0.726191	−	0.0364078i	−0.0392679	−	0.00196871i
$343$		−	9.19718i		−	0.496601i
$344$	11.2763	−	10.4798i	0.607979	−	0.565033i
$345$	−0.269980	+	0.0476047i	−0.0145352	+	0.00256295i
$346$	−7.77461	−	2.68191i	−0.417966	−	0.144180i
$347$	19.7749	+	23.5668i	1.06157	+	1.26513i	0.962856	+	0.270016i	$0.0870291\pi$
$347$	19.7749	+	23.5668i	1.06157	+	1.26513i	0.0987161	+	0.995116i	$0.468526\pi$
$348$	−9.10708	+	5.67648i	−0.488191	+	0.304291i
$349$	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	$-0.150598\pi$
$350$	3.66978	+	2.97515i	0.196158	+	0.159028i
$351$	6.03508	+	16.5813i	0.322129	+	0.885042i
$352$	−14.3685	−	20.6439i	−0.765845	−	1.10032i
$353$	−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	$0.916912\pi$
$354$	−11.0362	−	1.75434i	−0.586569	−	0.0932421i
$355$	−0.444231	+	2.51936i	−0.0235773	+	0.133714i
$356$	21.3743	+	3.02851i	1.13284	+	0.160511i
$357$	3.40655	−	4.05977i	0.180294	−	0.214866i
$358$	28.9859	−	17.3943i	1.53195	−	0.919317i
$359$	11.1764	−	30.7070i	0.589870	−	1.62066i	−0.180871	−	0.983507i	$-0.557892\pi$
$359$	11.1764	−	30.7070i	0.589870	−	1.62066i	0.770741	−	0.637148i	$-0.219886\pi$
$360$	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
$364$	3.70902	+	2.90454i	0.194406	+	0.152239i
$365$	−0.749562	−	0.628957i	−0.0392339	−	0.0329211i
$366$	−17.2304	−	9.56368i	−0.900650	−	0.499901i
$367$	−25.0700	−	4.42052i	−1.30864	−	0.230749i	−0.524544	−	0.851384i	$-0.675764\pi$
$367$	−25.0700	−	4.42052i	−1.30864	−	0.230749i	−0.784100	+	0.620634i	$0.786875\pi$
$368$	−1.27409	+	1.74536i	−0.0664166	+	0.0909829i
$369$	−0.192121	+	0.110921i	−0.0100014	+	0.00577433i
$370$	2.70947	−	2.35263i	0.140858	−	0.122307i
$371$	−6.36797	+	2.31775i	−0.330609	+	0.120332i
$372$	−35.2233	−	11.4886i	−1.82624	−	0.595657i
$373$	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	$0.429901\pi$
$374$	−5.28543	−	27.2731i	−0.273303	−	1.41026i
$375$	−3.85526	+	3.23494i	−0.199085	+	0.167052i
$376$	3.19778	−	1.35101i	0.164913	−	0.0696728i
$377$	−1.82959	−	10.3761i	−0.0942288	−	0.534398i
$378$	−4.88847	+	0.0825751i	−0.251436	+	0.00424720i
$379$	−11.3746			−0.584276			−0.292138	−	0.956376i	$-0.594367\pi$
$379$	−11.3746			−0.584276			−0.292138	+	0.956376i	$0.594367\pi$
$380$	0.778262	+	2.38143i	0.0399240	+	0.122165i
$381$	8.92886			0.457439
$382$	−32.2255	+	0.544347i	−1.64880	+	0.0278512i
$383$	2.72109	+	15.4321i	0.139041	+	0.788543i	0.971960	+	0.235147i	$0.0755572\pi$
$383$	2.72109	+	15.4321i	0.139041	+	0.788543i	−0.832918	+	0.553396i	$0.813332\pi$
$384$	19.1274	−	5.76549i	0.976090	−	0.294219i
$385$	−0.664970	+	0.557976i	−0.0338900	+	0.0284371i
$386$	−5.49882	−	28.3743i	−0.279883	−	1.44421i
$387$	0.555965	+	0.320986i	0.0282613	+	0.0163167i
$388$	2.24880	−	6.89467i	0.114166	−	0.350024i
$389$	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	$0.255470\pi$
$390$	−1.87890	+	1.63145i	−0.0951419	+	0.0826116i
$391$	−2.06699	+	1.19338i	−0.104532	+	0.0603516i
$392$	15.5271	−	10.0462i	0.784237	−	0.507408i
$393$	29.4382	+	5.19075i	1.48496	+	0.261839i
$394$	−5.90025	−	3.27491i	−0.297251	−	0.164988i
$395$	−1.82391	−	1.53044i	−0.0917710	−	0.0770050i
$396$	0.646694	−	0.825812i	0.0324976	−	0.0414986i
$397$	−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	$0.950599\pi$
$402$	−10.6207	+	6.37344i	−0.529714	+	0.317878i
$403$	23.3820	−	27.8656i	1.16474	−	1.38808i
$404$	−3.11889	+	22.0122i	−0.155171	+	1.09515i
$405$	0.466102	−	2.64339i	0.0231608	−	0.131351i
$406$	2.88316	+	0.458312i	0.143089	+	0.0227456i
$407$	−19.6281	−	33.9968i	−0.972928	−	1.68516i
$408$	21.8962	+	2.72607i	1.08402	+	0.134960i
$409$	−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	$0.958356\pi$
$410$	0.593782	+	0.481389i	0.0293248	+	0.0237741i
$411$	9.97609	−	17.2791i	0.492084	−	0.852315i
$412$	3.06513	+	4.91755i	0.151008	+	0.242270i
$413$	1.95408	+	2.32878i	0.0961538	+	0.114592i
$414$	−0.0851890	−	0.0293866i	−0.00418681	−	0.00144427i
$415$	2.82646	−	0.498381i	0.138745	−	0.0244646i
$416$	−1.76450	+	19.5347i	−0.0865116	+	0.957766i
$417$		−	3.33832i		−	0.163478i
$418$	27.1968	−	3.40194i	1.33024	−	0.166394i
$419$			15.7998i			0.771873i	0.922525	+	0.385936i	$0.126122\pi$
$419$			15.7998i			0.771873i	−0.922525	+	0.385936i	$0.873878\pi$
$420$	−0.257560	−	0.639555i	−0.0125676	−	0.0312071i
$421$	−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	$0.657263\pi$
$422$	−7.84191	+	22.7330i	−0.381738	+	1.10662i
$423$	0.0930547	+	0.110898i	0.00452447	+	0.00539206i
$424$	−22.5046	−	17.0181i	−1.09292	−	0.826473i
$425$	−10.8626	+	18.8146i	−0.526915	+	0.912643i
$426$	−13.9989	+	17.2674i	−0.678251	+	0.836607i
$427$	1.83358	+	5.03771i	0.0887329	+	0.243792i
$428$	−8.80403	+	16.5131i	−0.425559	+	0.798190i
$429$	13.6112	+	23.5754i	0.657157	+	1.13823i
$430$	0.347270	−	2.18462i	0.0167469	−	0.105352i
$431$	1.17478	−	6.66249i	0.0565870	−	0.320921i	−0.943354	−	0.331788i	$-0.892348\pi$
$431$	1.17478	−	6.66249i	0.0565870	−	0.320921i	0.999941	+	0.0108673i	$0.00345924\pi$
$432$	−11.3450	−	16.9016i	−0.545836	−	0.813180i
$433$	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	$0.151434\pi$
$434$	5.18620	+	8.64230i	0.248945	+	0.414844i
$435$	−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	0.966832	−	0.255414i	$-0.0822119\pi$
$439$	32.3355	+	11.7692i	1.54329	+	0.561712i	0.576459	+	0.817126i	$0.304434\pi$
$440$	−3.45446	−	1.06252i	−0.164685	−	0.0506536i
$441$	0.590794	+	0.495735i	0.0281331	+	0.0236064i
$442$	−10.5136	+	18.9419i	−0.500081	+	0.900973i
$443$	23.1576	+	4.08330i	1.10025	+	0.194004i	0.694154	−	0.719827i	$-0.255779\pi$
$443$	23.1576	+	4.08330i	1.10025	+	0.194004i	0.406096	+	0.913831i	$0.366890\pi$
$444$	30.5058	−	6.44832i	1.44774	−	0.306024i
$445$	2.68643	−	1.55101i	0.127349	−	0.0735249i
$446$	−12.8063	−	14.7488i	−0.606397	−	0.698374i
$447$	4.48066	−	1.63083i	0.211928	−	0.0771355i
$448$	−4.95733	−	2.22725i	−0.234212	−	0.105227i
$449$	−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	$0.688913\pi$
$450$	−0.805284	+	0.156061i	−0.0379615	+	0.00735678i
$451$	6.40608	−	5.37534i	0.301651	−	0.253115i
$452$	0.926103	+	27.4050i	0.0435602	+	1.28902i
$453$	−3.95851	−	22.4499i	−0.185987	−	1.05479i
$454$	0.269805	+	15.9725i	0.0126626	+	0.749627i
$455$	0.676933			0.0317351
$456$	−4.12952	+	21.3747i	−0.193383	+	1.00096i
$457$	−27.5794			−1.29011			−0.645054	−	0.764137i	$-0.723165\pi$
$457$	−27.5794			−1.29011			−0.645054	+	0.764137i	$0.723165\pi$
$458$	−0.123592	−	7.31670i	−0.00577509	−	0.341887i
$459$	−3.90422	−	22.1420i	−0.182234	−	1.03350i
$460$	0.0104871	+	0.310332i	0.000488965	+	0.0144693i
$461$	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	$0.0178387\pi$
$462$	−7.40500	+	1.43506i	−0.344512	+	0.0667650i
$463$	−1.35838	−	0.784262i	−0.0631294	−	0.0364478i	0.468103	−	0.883674i	$-0.344938\pi$
$463$	−1.35838	−	0.784262i	−0.0631294	−	0.0364478i	−0.531232	+	0.847226i	$0.678271\pi$
$464$	4.91879	+	11.1151i	0.228349	+	0.516005i
$465$	−5.00270	+	1.82084i	−0.231995	+	0.0844392i
$466$	−5.72921	−	6.59820i	−0.265400	−	0.305656i
$467$	16.4940	−	9.52284i	0.763253	−	0.440664i	−0.0672096	−	0.997739i	$-0.521410\pi$
$467$	16.4940	−	9.52284i	0.763253	−	0.440664i	0.830462	+	0.557075i	$0.188076\pi$
$468$	−0.800272	+	0.169161i	−0.0369926	+	0.00781949i
$469$	3.31839	+	0.585122i	0.153229	+	0.0270184i
$470$	0.242081	−	0.436146i	0.0111663	−	0.0201179i
$471$	32.4692	+	27.2449i	1.49610	+	1.25538i
$472$	−3.72103	+	12.0978i	−0.171274	+	0.556847i
$473$	−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
$478$	5.73792	+	9.56170i	0.262446	+	0.437342i
$479$	14.9412	−	17.8062i	0.682680	−	0.813586i	−0.307770	−	0.951461i	$-0.599583\pi$
$479$	14.9412	−	17.8062i	0.682680	−	0.813586i	0.990450	+	0.137874i	$0.0440270\pi$
$480$	1.65314	−	2.34683i	0.0754549	−	0.107118i
$481$	−5.31589	+	30.1479i	−0.242384	+	1.37463i
$482$	3.43276	−	21.5949i	0.156358	−	0.983620i
$483$	0.324017	+	0.561213i	0.0147433	+	0.0255361i
$484$	−8.25148	+	15.4767i	−0.375067	+	0.703486i
$485$	−0.356414	−	0.979239i	−0.0161839	−	0.0444649i
$486$	1.09108	−	1.34582i	0.0494923	−	0.0610476i
$487$	−18.8848	+	32.7094i	−0.855752	+	1.48221i	0.0201932	+	0.999796i	$0.493572\pi$
$487$	−18.8848	+	32.7094i	−0.855752	+	1.48221i	−0.875945	+	0.482410i	$0.839761\pi$
$488$	−13.4630	+	17.8034i	−0.609443	+	0.805922i
$489$	12.0179	+	14.3224i	0.543469	+	0.647682i
$490$	0.866585	−	2.51215i	0.0391483	−	0.113487i
$491$	10.7823	−	1.90120i	0.486596	−	0.0858001i	0.0750327	−	0.997181i	$-0.476094\pi$
$491$	10.7823	−	1.90120i	0.486596	−	0.0858001i	0.411564	+	0.911381i	$0.364983\pi$
$492$	2.48124	+	6.16125i	0.111863	+	0.277771i
$493$			13.4251i			0.604636i
$494$	−17.9522	−	11.6005i	−0.807706	−	0.521931i
$495$		−	0.150719i		−	0.00677431i
$496$	−18.4808	+	37.6756i	−0.829811	+	1.69168i
$497$	5.95535	−	1.05009i	0.267134	−	0.0471030i
$498$	23.5755	+	8.13254i	1.05644	+	0.364428i
$499$	−12.5333	−	14.9366i	−0.561067	−	0.668654i	0.408705	−	0.912667i	$-0.365980\pi$
$499$	−12.5333	−	14.9366i	−0.561067	−	0.668654i	−0.969772	+	0.244013i	$0.921536\pi$
$500$	3.01523	+	4.83749i	0.134845	+	0.216339i
$501$	−14.1737	+	24.5495i	−0.633232	+	1.09679i
$502$	9.09674	+	7.37488i	0.406007	+	0.329157i
$503$	−6.17225	−	16.9581i	−0.275207	−	0.756125i	−0.997889	−	0.0649441i	$-0.979313\pi$
$503$	−6.17225	−	16.9581i	−0.275207	−	0.756125i	0.722682	−	0.691181i	$-0.242909\pi$
$504$	0.0280002	−	0.224902i	0.00124723	−	0.0100179i
$505$	1.59730	+	2.76660i	0.0710787	+	0.123112i
$506$	3.35484	+	0.533292i	0.149141	+	0.0237077i
$507$	−0.299753	+	1.69998i	−0.0133125	+	0.0754989i
$508$	1.41877	−	10.0132i	0.0629478	−	0.444266i
$509$	−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	$0.268833\pi$
$510$	2.71867	−	1.63146i	0.120385	−	0.0722423i
$511$	−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
$516$	11.8507	−	15.1331i	0.521699	−	0.666196i
$517$	−4.18040	−	3.50778i	−0.183854	−	0.154272i
$518$	−7.41639	−	4.11644i	−0.325858	−	0.180866i
$519$	−10.1126	−	1.78313i	−0.443895	−	0.0782707i
$520$	1.53103	+	2.36632i	0.0671401	+	0.103770i
$521$	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	$0.0130915\pi$
$522$	−0.382736	+	0.332330i	−0.0167519	+	0.0145457i
$523$	14.7646	−	5.37386i	0.645609	−	0.234982i	0.00159809	−	0.999999i	$-0.499491\pi$
$523$	14.7646	−	5.37386i	0.645609	−	0.234982i	0.644011	+	0.765016i	$0.277269\pi$
$524$	10.4988	−	32.1886i	0.458643	−	1.40617i
$525$	5.10841	+	2.94934i	0.222949	+	0.128720i
$526$	−4.99964	−	25.7985i	−0.217995	−	1.12487i
$527$	−35.5059	+	29.7930i	−1.54666	+	1.29780i
$528$	−21.7645	−	22.6396i	−0.947177	−	0.985262i
$529$	3.94323	+	22.3632i	0.171445	+	0.972311i
$530$	−4.05369	+	0.0684742i	−0.176081	+	0.00297433i
$531$	−0.527830			−0.0229059
$532$	4.66062	−	3.65408i	0.202064	−	0.158424i
$533$	−6.52134			−0.282470
$534$	26.9504	−	0.455242i	1.16626	−	0.0197002i
$535$	0.466939	+	2.64814i	0.0201875	+	0.114489i
$536$	5.45987	+	12.9233i	0.235831	+	0.558202i
$537$	32.3332	−	27.1307i	1.39528	−	1.17078i
$538$	0.438895	+	2.26473i	0.0189221	+	0.0976393i
$539$	−25.1772	−	14.5360i	−1.08446	−	0.626111i
$540$	−2.78086	−	0.907020i	−0.119669	−	0.0390319i
$541$	−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	$0.451679\pi$
$542$	−23.1430	+	20.0950i	−0.994076	+	0.863154i
$543$	8.33246	−	4.81075i	0.357580	−	0.206449i
$544$	6.53638	−	24.1223i	0.280245	−	1.03423i
$545$	2.62902	+	0.463568i	0.112615	+	0.0198571i
$546$	5.14296	+	2.85458i	0.220098	+	0.122165i
$547$	−0.345374	−	0.289803i	−0.0147671	−	0.0123911i	0.635374	−	0.772204i	$-0.280846\pi$
$547$	−0.345374	−	0.289803i	−0.0147671	−	0.0123911i	−0.650141	+	0.759813i	$0.725290\pi$
$548$	−17.7924	−	13.9333i	−0.760055	−	0.595200i
$549$	−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
$554$	20.1797	−	12.1097i	0.857355	−	0.514494i
$555$	2.87991	−	3.43214i	0.122245	−	0.145686i
$556$	−3.74376	−	0.530451i	−0.158771	−	0.0224961i
$557$	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	$-0.0890682\pi$
$558$	−1.72830	−	0.274733i	−0.0731646	−	0.0116304i
$559$	9.43579	+	16.3433i	0.399091	+	0.691247i
$560$	−0.758153	+	0.187216i	−0.0320378	+	0.00791132i
$561$	−11.8635	−	32.5947i	−0.500877	−	1.37615i
$562$	−16.5785	−	13.4404i	−0.699320	−	0.566950i
$563$	−17.7749	+	30.7871i	−0.749125	+	1.29752i	0.199118	+	0.979976i	$0.436192\pi$
$563$	−17.7749	+	30.7871i	−0.749125	+	1.29752i	−0.948243	+	0.317546i	$0.897141\pi$
$564$	3.67838	−	2.29275i	0.154888	−	0.0965423i
$565$	2.53269	+	3.01834i	0.106551	+	0.126982i
$566$	−8.97969	−	3.09761i	−0.377445	−	0.130202i
$567$	−6.24856	+	1.10179i	−0.262415	+	0.0462708i
$568$	17.1401	+	18.4428i	0.719181	+	0.773844i
$569$			1.64769i			0.0690748i	0.999403	+	0.0345374i	$0.0109958\pi$
$569$			1.64769i			0.0690748i	−0.999403	+	0.0345374i	$0.989004\pi$
$570$	1.42648	+	2.78401i	0.0597487	+	0.116609i
$571$			13.5132i			0.565511i	0.959192	+	0.282755i	$0.0912484\pi$
$571$			13.5132i			0.565511i	−0.959192	+	0.282755i	$0.908752\pi$
$572$	28.6013	−	11.5182i	1.19588	−	0.481602i
$573$	−39.6308	+	6.98798i	−1.65560	+	0.291927i
$574$	0.589239	−	1.70815i	0.0245944	−	0.0712968i
$575$	−1.70759	−	2.03502i	−0.0712112	−	0.0848662i
$576$	0.849507	−	0.410785i	0.0353961	−	0.0171160i
$577$	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	$0.0415272\pi$
$578$	2.24343	−	2.76722i	0.0933145	−	0.115101i
$579$	−12.3425	−	33.9107i	−0.512936	−	1.40928i
$580$	1.54120	+	0.821699i	0.0639949	+	0.0341192i
$581$	−3.39218	−	5.87543i	−0.140731	−	0.243754i
$582$	1.42154	−	8.94267i	0.0589248	−	0.370686i
$583$	−7.70193	+	43.6798i	−0.318981	+	1.80903i
$584$	−9.38696	+	2.15045i	−0.388435	+	0.0889864i
$585$	−0.0755498	+	0.0900368i	−0.00312360	+	0.00372256i
$586$	1.97609	+	3.29297i	0.0816317	+	0.136031i
$587$	0.260988	−	0.717059i	0.0107721	−	0.0295962i	−0.934190	−	0.356776i	$-0.883876\pi$
$587$	0.260988	−	0.717059i	0.0107721	−	0.0295962i	0.944962	+	0.327180i	$0.106098\pi$
$588$	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
$592$	−2.38415	−	35.2353i	−0.0979881	−	1.44816i
$593$	−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	$0.771513\pi$
$594$	−15.5296	+	27.9790i	−0.637188	+	1.14799i
$595$	−0.849435	−	0.149778i	−0.0348235	−	0.00614031i
$596$	−1.11692	−	5.28396i	−0.0457509	−	0.216440i
$597$	−8.96956	+	5.17858i	−0.367100	+	0.211945i
$598$	−1.73680	−	2.00024i	−0.0710232	−	0.0817958i
$599$	−3.55846	+	1.29517i	−0.145395	+	0.0529194i	−0.413693	−	0.910417i	$-0.635761\pi$
$599$	−3.55846	+	1.29517i	−0.145395	+	0.0529194i	0.268298	+	0.963336i	$0.413539\pi$
$600$	1.24390	+	24.5278i	0.0507821	+	1.00134i
$601$	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	$0.572297\pi$
$602$	−5.13341	+	0.994834i	−0.209222	+	0.0405464i
$603$	−0.448177	+	0.376066i	−0.0182512	+	0.0153146i
$604$	−25.8053	+	0.872046i	−1.05000	+	0.0354830i
$605$	0.437633	+	2.48194i	0.0177923	+	0.100905i
$606$	0.468827	+	27.7547i	0.0190448	+	1.12746i
$607$	17.3937			0.705987			0.352993	−	0.935626i	$-0.385164\pi$
$607$	17.3937			0.705987			0.352993	+	0.935626i	$0.385164\pi$
$608$	23.3144	+	8.02742i	0.945523	+	0.325555i
$609$	3.64508			0.147706
$610$	0.0541699	+	3.20688i	0.00219328	+	0.129843i
$611$	0.738980	+	4.19096i	0.0298959	+	0.169548i
$612$	1.04163	−	0.0352001i	0.0421055	−	0.00142288i
$613$	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	$0.275589\pi$
$614$	6.77572	−	1.31311i	0.273446	−	0.0529927i
$615$	0.826557	+	0.477213i	0.0333300	+	0.0192431i
$616$	0.432710	+	8.53235i	0.0174344	+	0.343778i
$617$	−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	$0.700550\pi$
$618$	4.74356	+	5.46305i	0.190814	+	0.219756i
$619$	−16.6044	+	9.58653i	−0.667386	+	0.385315i	−0.795085	−	0.606498i	$-0.792574\pi$
$619$	−16.6044	+	9.58653i	−0.667386	+	0.385315i	0.127700	+	0.991813i	$0.459241\pi$
$620$	1.24706	+	5.89960i	0.0500830	+	0.236934i
$621$	2.70748	+	0.477403i	0.108648	+	0.0191575i
$622$	6.23057	−	11.2253i	0.249823	−	0.450095i
$623$	−5.61715	−	4.71335i	−0.225046	−	0.188836i
$624$	1.65331	+	24.4342i	0.0661854	+	0.978152i
$625$	−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
$630$	−0.0167572	−	0.0279243i	−0.000667623	−	0.00111253i
$631$	−22.7701	+	27.1363i	−0.906462	+	1.08028i	0.0899749	+	0.995944i	$0.471321\pi$
$631$	−22.7701	+	27.1363i	−0.906462	+	1.08028i	−0.996437	+	0.0843359i	$0.973123\pi$
$632$	−22.8413	+	5.23271i	−0.908579	+	0.208146i
$633$	−5.21387	+	29.5693i	−0.207233	+	1.17527i
$634$	−5.45797	+	34.3352i	−0.216764	+	1.36362i
$635$	−0.726604	−	1.25851i	−0.0288344	−	0.0499426i
$636$	−31.0864	−	16.5739i	−1.23266	−	0.657197i
$637$	7.75400	+	21.3039i	0.307225	+	0.844093i
$638$	12.0330	−	14.8425i	0.476392	−	0.587618i
$639$	−0.524984	+	0.909299i	−0.0207680	+	0.0359713i
$640$	−2.36917	−	2.22681i	−0.0936496	−	0.0880224i
$641$	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	$0.607807\pi$
$642$	−7.61947	+	22.0881i	−0.300717	+	0.871749i
$643$	−2.51226	+	0.442980i	−0.0990740	+	0.0174694i	−0.222965	−	0.974826i	$-0.571574\pi$
$643$	−2.51226	+	0.442980i	−0.0990740	+	0.0174694i	0.123891	+	0.992296i	$0.460463\pi$
$644$	0.680857	−	0.274192i	0.0268295	−	0.0108047i
$645$		−	2.76194i		−	0.108751i
$646$	19.9601	+	18.5287i	0.785321	+	0.729003i
$647$		−	16.5839i		−	0.651979i	−0.945373	−	0.325989i	$-0.894303\pi$
$647$		−	16.5839i		−	0.651979i	0.945373	−	0.325989i	$-0.105697\pi$
$648$	−17.9839	−	19.3508i	−0.706475	−	0.760172i
$649$	19.5947	−	3.45508i	0.769160	−	0.135624i
$650$	−22.7946	−	7.86319i	−0.894079	−	0.308420i
$651$	8.08917	+	9.64030i	0.317040	+	0.377833i
$652$	17.9714	−	11.2017i	0.703816	−	0.438692i
$653$	−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	$0.844415\pi$
$654$	18.0190	+	14.6083i	0.704599	+	0.571230i
$655$	−1.66396	−	4.57170i	−0.0650164	−	0.178631i
$656$	7.30378	−	1.80357i	0.285165	−	0.0704177i
$657$	−0.200799	−	0.347794i	−0.00783391	−	0.0135687i
$658$	−1.16452	−	0.185114i	−0.0453977	−	0.00721650i
$659$	5.07827	−	28.8003i	0.197821	−	1.12190i	−0.710522	−	0.703675i	$-0.751541\pi$
$659$	5.07827	−	28.8003i	0.197821	−	1.12190i	0.908344	−	0.418225i	$-0.137348\pi$
$660$	−4.46799	−	0.633067i	−0.173916	−	0.0246421i
$661$	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	$-0.0218405\pi$
$662$	−8.75136	+	5.25164i	−0.340131	+	0.204111i
$663$	−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
$668$	25.2788	+	19.7959i	0.978067	+	0.765925i
$669$	−18.6826	−	15.6765i	−0.722310	−	0.606090i
$670$	1.76261	+	0.978330i	0.0680957	+	0.0377962i
$671$	34.5551	+	6.09300i	1.33399	+	0.235218i
$672$	−6.54950	−	1.77471i	−0.252652	−	0.0684610i
$673$	−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	$0.467710\pi$
$674$	3.10982	−	2.70026i	0.119786	−	0.104010i
$675$	23.5157	−	8.55902i	0.905120	−	0.329437i
$676$	1.85881	+	0.606280i	0.0714928	+	0.0233185i
$677$	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	$0.525669\pi$
$678$	6.51382	+	33.6118i	0.250162	+	1.29085i
$679$	−1.88701	+	1.58339i	−0.0724168	+	0.0607649i
$680$	−1.39761	−	3.30808i	−0.0535958	−	0.126859i
$681$	3.46358	+	19.6429i	0.132725	+	0.752719i
$682$	65.9582	−	1.11415i	2.52567	−	0.0426631i
$683$	4.25657			0.162873			0.0814366	−	0.996679i	$-0.474049\pi$
$683$	4.25657			0.162873			0.0814366	+	0.996679i	$0.474049\pi$
$684$	−0.0341359	+	1.02771i	−0.00130522	+	0.0392955i
$685$	−3.24730			−0.124073
$686$	−13.0049	+	0.219677i	−0.496530	+	0.00838729i
$687$	−1.58660	−	8.99805i	−0.0605325	−	0.343297i
$688$	−15.0879	−	15.6946i	−0.575221	−	0.598350i
$689$	26.4960	−	22.2328i	1.00942	−	0.847003i
$690$	0.0737621	+	0.380617i	0.00280808	+	0.0144899i
$691$	−4.43757	−	2.56203i	−0.168813	−	0.0974643i	0.413213	−	0.910634i	$-0.364407\pi$
$691$	−4.43757	−	2.56203i	−0.168813	−	0.0974643i	−0.582026	+	0.813170i	$0.697740\pi$
$692$	−3.60656	+	11.0575i	−0.137101	+	0.420341i
$693$	−0.334789	+	0.121853i	−0.0127176	+	0.00462882i
$694$	32.8514	−	28.5248i	1.24702	−	1.08279i
$695$	−0.470534	+	0.271663i	−0.0178484	+	0.0103048i
$696$	8.24414	+	12.7419i	0.312493	+	0.482982i
$697$	8.18316	+	1.44291i	0.309959	+	0.0546542i
$698$	−38.7937	−	21.5323i	−1.46836	−	0.815008i
$699$	−8.35809	−	7.01327i	−0.316132	−	0.265266i
$700$	4.11924	−	5.26017i	0.155693	−	0.198816i
$701$	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
$706$	−11.8274	+	7.09755i	−0.445130	+	0.267120i
$707$	4.85401	−	5.78478i	0.182554	−	0.217559i
$708$	−2.21705	+	15.6473i	−0.0833220	+	0.588061i
$709$	−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	$0.0960169\pi$
$710$	3.57301	+	0.567972i	0.134093	+	0.0213156i
$711$	−0.488605	−	0.846288i	−0.0183241	−	0.0317383i
$712$	3.77182	−	30.2959i	0.141355	−	1.13539i
$713$	−1.93842	−	5.32577i	−0.0725945	−	0.199452i
$714$	−5.82193	−	4.71993i	−0.217880	−	0.176639i
$715$	2.21528	−	3.83699i	0.0828470	−	0.143495i
$716$	−25.2881	−	40.5710i	−0.945059	−	1.51621i
$717$	8.94972	+	10.6659i	0.334234	+	0.398324i
$718$	−43.6871	−	15.0702i	−1.63039	−	0.562414i
$719$	−28.0650	+	4.94861i	−1.04665	+	0.184552i	−0.670425	−	0.741977i	$-0.733888\pi$
$719$	−28.0650	+	4.94861i	−1.04665	+	0.184552i	−0.376222	+	0.926529i	$0.622777\pi$
$720$	0.0597134	−	0.121734i	0.00222539	−	0.00453676i
$721$		−	1.96823i		−	0.0733009i
$722$	−19.5579	+	18.4252i	−0.727869	+	0.685717i
$723$		−	27.3017i		−	1.01536i
$724$	−4.07100	−	10.1088i	−0.151297	−	0.375692i
$725$	−14.7155	+	2.59475i	−0.546522	+	0.0963665i
$726$	−7.14126	+	20.7019i	−0.265037	+	0.768318i
$727$	23.5241	+	28.0349i	0.872461	+	1.03976i	0.998858	+	0.0477786i	$0.0152142\pi$
$727$	23.5241	+	28.0349i	0.872461	+	1.03976i	−0.126397	+	0.991980i	$0.540341\pi$
$728$	4.01846	−	5.31397i	0.148934	−	0.196949i
$729$	−12.9283	+	22.3925i	−0.478826	+	0.829351i
$730$	−0.871449	+	1.07491i	−0.0322538	+	0.0397843i
$731$	−8.22418	−	22.5958i	−0.304182	−	0.835734i
$732$	−13.1116	+	24.5925i	−0.484619	+	0.908964i
$733$	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	$0.636224\pi$
$734$	−5.65186	+	35.5549i	−0.208614	+	1.31235i
$735$	0.576169	−	3.26761i	0.0212523	−	0.120528i
$736$	2.49839	+	1.75989i	0.0920917	+	0.0648705i
$737$	14.1761	−	16.8944i	0.522184	−	0.622315i
$738$	0.161433	+	0.269012i	0.00594243	+	0.00990248i
$739$	12.5256	−	34.4138i	0.460762	−	1.26593i	−0.464152	−	0.885756i	$-0.653641\pi$
$739$	12.5256	−	34.4138i	0.460762	−	1.26593i	0.924914	−	0.380177i	$-0.124137\pi$
$740$	−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	0.658235	−	0.752813i	$-0.271303\pi$
$743$	18.4966	+	6.73220i	0.678573	+	0.246980i	0.0203384	+	0.999793i	$0.493526\pi$
$744$	−15.4037	+	50.0805i	−0.564728	+	1.83604i
$745$	−0.594486	−	0.498833i	−0.0217803	−	0.0182758i
$746$	17.9501	−	32.3399i	0.657200	−	1.18405i
$747$	1.16006	+	0.204550i	0.0424444	+	0.00748408i
$748$	−38.4383	+	8.12508i	−1.40544	+	0.297082i
$749$	5.50476	−	3.17817i	0.201140	−	0.116128i
$750$	4.66633	+	5.37411i	0.170390	+	0.196235i
$751$	−10.9116	+	3.97149i	−0.398169	+	0.144922i	−0.533341	−	0.845900i	$-0.679064\pi$
$751$	−10.9116	+	3.97149i	−0.398169	+	0.144922i	0.135171	+	0.990822i	$0.456841\pi$
$752$	−1.98672	−	4.48943i	−0.0724481	−	0.163713i
$753$	12.6629	+	7.31090i	0.461460	+	0.266424i
$754$	−14.6283	+	2.83490i	−0.532731	+	0.103241i
$755$	−2.84215	+	2.38485i	−0.103437	+	0.0867936i
$756$	0.233524	+	6.91038i	0.00849319	+	0.251328i
$757$	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	$0.850998\pi$
$758$	0.271686	+	16.0839i	0.00986807	+	0.584193i
$759$	4.24142			0.153954
$760$	3.34879	−	1.15735i	0.121473	−	0.0419816i
$761$	−7.73239			−0.280299			−0.140149	−	0.990130i	$-0.544758\pi$
$761$	−7.73239			−0.280299			−0.140149	+	0.990130i	$0.544758\pi$
$762$	−0.213268	−	12.6255i	−0.00772587	−	0.457374i
$763$	−1.09580	−	6.21459i	−0.0396706	−	0.224983i
$764$	1.53943	+	45.5543i	0.0556945	+	1.64810i
$765$	0.114724	−	0.0962645i	0.00414784	−	0.00348045i
$766$	21.7562	−	4.21626i	0.786082	−	0.152340i
$767$	−13.4374	−	7.75811i	−0.485198	−	0.280129i
$768$	−8.60933	−	26.9086i	−0.310662	−	0.970982i
$769$	−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	$0.544671\pi$
$770$	0.804867	+	0.926948i	0.0290054	+	0.0334049i
$771$	8.87699	−	5.12513i	0.319697	−	0.184577i
$772$	−39.9902	+	8.45312i	−1.43928	+	0.304235i
$773$	−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	$0.629796\pi$
$774$	0.440599	−	0.793807i	0.0158370	−	0.0285328i
$775$	−39.5192	−	33.1606i	−1.41957	−	1.19116i
$776$	−9.80286	−	3.01515i	−0.351902	−	0.108238i
$777$	−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
$782$	1.73682	+	2.89424i	0.0621085	+	0.103498i
$783$	9.94013	−	11.8462i	0.355231	−	0.423348i
$784$	−14.5763	−	21.7155i	−0.520581	−	0.775555i
$785$	1.19790	−	6.79361i	0.0427548	−	0.242474i
$786$	6.63665	−	41.7500i	0.236721	−	1.48917i
$787$	5.14544	+	8.91217i	0.183415	+	0.317684i	0.943041	−	0.332676i	$-0.107951\pi$
$787$	5.14544	+	8.91217i	0.183415	+	0.317684i	−0.759626	+	0.650360i	$0.774618\pi$
$788$	−4.48983	+	8.42125i	−0.159944	+	0.299995i
$789$	−11.2220	−	30.8322i	−0.399514	−	1.09766i
$790$	−2.12050	+	2.61559i	−0.0754440	+	0.0930584i
$791$	4.65695	−	8.06607i	0.165582	−	0.286797i
$792$	−1.18315	−	0.894708i	−0.0420416	−	0.0317921i
$793$	−17.5884	−	20.9610i	−0.624582	−	0.744348i
$794$	−4.36583	+	12.6561i	−0.154937	+	0.449149i
$795$	−4.98521	+	0.879028i	−0.176807	+	0.0311759i
$796$	4.38226	+	10.8818i	0.155325	+	0.385693i
$797$		−	1.81305i		−	0.0642216i	−0.999484	−	0.0321108i	$-0.989777\pi$
$797$		−	1.81305i		−	0.0642216i	0.999484	−	0.0321108i	$-0.0102230\pi$
$798$	5.03079	−	5.41943i	0.178088	−	0.191846i
$799$		−	5.42245i		−	0.191832i
$800$	27.7043	+	2.50243i	0.979494	+	0.0884742i
$801$	1.25382	−	0.221082i	0.0443014	−	0.00781153i
$802$	25.8700	+	8.92404i	0.913500	+	0.315119i
$803$	9.73088	+	11.5968i	0.343395	+	0.409243i
$804$	9.26580	+	14.8656i	0.326779	+	0.524269i
$805$	0.0527350	−	0.0913397i	0.00185866	−	0.00321930i
$806$	−39.9607	−	32.3968i	−1.40756	−	1.14113i
$807$	0.985129	+	2.70662i	0.0346782	+	0.0952775i
$808$	31.1999	+	3.88438i	1.09761	+	0.136652i
$809$	−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	$0.925972\pi$
$810$	−3.74892	−	0.595935i	−0.131724	−	0.0209390i
$811$	−2.81946	+	15.9900i	−0.0990047	+	0.561484i	0.894442	+	0.447185i	$0.147573\pi$
$811$	−2.81946	+	15.9900i	−0.0990047	+	0.561484i	−0.993446	+	0.114299i	$0.963538\pi$
$812$	0.579194	−	4.08777i	0.0203257	−	0.143453i
$813$	−24.5988	+	29.3157i	−0.862718	+	1.02815i
$814$	−47.6031	+	28.5664i	−1.66849	+	1.00125i
$815$	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
$820$	0.666507	−	0.851112i	0.0232754	−	0.0297221i
$821$	−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	$0.794840\pi$
$822$	−24.6711	−	13.6936i	−0.860504	−	0.477619i
$823$	−20.9188	−	3.68856i	−0.729185	−	0.128575i	−0.203283	−	0.979120i	$-0.565161\pi$
$823$	−20.9188	−	3.68856i	−0.729185	−	0.128575i	−0.525902	+	0.850545i	$0.676272\pi$
$824$	6.88026	−	4.45159i	0.239685	−	0.155078i
$825$	33.4348	−	19.3036i	1.16405	−	0.672066i
$826$	3.24625	−	2.81871i	0.112951	−	0.0980755i
$827$	19.5621	−	7.12001i	0.680240	−	0.247587i	0.0212892	−	0.999773i	$-0.493223\pi$
$827$	19.5621	−	7.12001i	0.680240	−	0.247587i	0.658950	+	0.752186i	$0.271001\pi$
$828$	−0.0395182	+	0.121160i	−0.00137335	+	0.00421060i
$829$	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	$0.502854\pi$
$830$	−0.772227	−	3.98474i	−0.0268044	−	0.138312i
$831$	22.5101	−	18.8882i	0.780865	−	0.655224i
$832$	27.6644	+	2.02843i	0.959091	+	0.0703232i
$833$	−5.01623	−	28.4484i	−0.173802	−	0.985680i
$834$	−4.72043	+	0.0797366i	−0.163455	+	0.00276105i
$835$	4.61364			0.159661
$836$	−5.45998	−	38.3754i	−0.188837	−	1.32724i
$837$	53.3893			1.84540
$838$	22.3412	−	0.377382i	0.771763	−	0.0130365i
$839$	−2.04975	−	11.6247i	−0.0707652	−	0.401329i	−0.999530	−	0.0306595i	$-0.990239\pi$
$839$	−2.04975	−	11.6247i	−0.0707652	−	0.401329i	0.928765	−	0.370670i	$-0.120872\pi$
$840$	−0.898187	+	0.379468i	−0.0309904	+	0.0130929i
$841$	15.1418	−	12.7055i	0.522132	−	0.438121i
$842$	6.84435	+	35.3173i	0.235872	+	1.21711i
$843$	−23.0776	−	13.3238i	−0.794833	−	0.458897i
$844$	32.3320	+	10.5456i	1.11291	+	0.362993i
$845$	0.264004	−	0.0960896i	0.00908201	−	0.00330558i
$846$	0.154589	−	0.134229i	0.00531487	−	0.00461490i
$847$	5.15927	−	2.97871i	0.177275	−	0.102350i
$848$	−23.5263	+	32.2282i	−0.807896	+	1.10672i
$849$	−11.6801	−	2.05952i	−0.400860	−	0.0706825i
$850$	26.8636	+	14.9105i	0.921412	+	0.511426i
$851$	3.65378	+	3.06589i	0.125250	+	0.105097i
$852$	24.7506	+	19.3822i	0.847943	+	0.664025i
$853$	−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	$0.871330\pi$
$858$	33.0108	−	19.8096i	1.12697	−	0.676288i
$859$	−26.2991	+	31.3421i	−0.897314	+	1.06938i	0.0999155	+	0.994996i	$0.468143\pi$
$859$	−26.2991	+	31.3421i	−0.897314	+	1.06938i	−0.997230	+	0.0743817i	$0.976302\pi$
$860$	−3.09737	−	0.438864i	−0.105619	−	0.0149651i
$861$	0.391769	−	2.22183i	0.0133514	−	0.0757198i
$862$	−9.44889	−	1.50201i	−0.321831	−	0.0511588i
$863$	21.1102	+	36.5639i	0.718598	+	1.24465i	0.961555	+	0.274611i	$0.0885492\pi$
$863$	21.1102	+	36.5639i	0.718598	+	1.24465i	−0.242957	+	0.970037i	$0.578117\pi$
$864$	−23.6281	+	16.4456i	−0.803845	+	0.559492i
$865$	0.571605	+	1.57047i	0.0194351	+	0.0533976i
$866$	−10.0836	−	8.17496i	−0.342655	−	0.277796i
$867$	2.22397	−	3.85203i	0.0755300	−	0.130822i
$868$	12.0964	−	7.53977i	0.410580	−	0.255916i
$869$	23.6782	+	28.2186i	0.803228	+	0.957250i
$870$	2.06153	+	0.711142i	0.0698925	+	0.0241100i
$871$	−16.9371	+	2.98647i	−0.573892	+	0.101193i
$872$	19.2456	−	17.8862i	0.651740	−	0.605702i
$873$		−	0.427701i		−	0.0144755i
$874$	−2.96380	+	1.51860i	−0.100252	+	0.0513674i
$875$		−	1.93619i		−	0.0654553i
$876$	−11.1536	+	4.49174i	−0.376845	+	0.151762i
$877$	−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	$0.468559\pi$
$878$	15.8694	−	46.0039i	0.535566	−	1.55256i
$879$	3.08221	+	3.67324i	0.103960	+	0.123895i
$880$	−1.41990	+	4.91003i	−0.0478650	+	0.165517i
$881$	−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	$0.904091\pi$
$882$	0.686864	−	0.847231i	0.0231279	−	0.0285277i
$883$	10.7642	+	29.5744i	0.362244	+	0.995257i	0.978234	+	0.207503i	$0.0665337\pi$
$883$	10.7642	+	29.5744i	0.362244	+	0.995257i	−0.615991	+	0.787754i	$0.711244\pi$
$884$	27.0351	+	14.4139i	0.909290	+	0.484793i
$885$	1.13543	+	1.96663i	0.0381671	+	0.0661074i
$886$	5.22072	−	32.8426i	0.175393	−	1.10337i
$887$	4.01156	−	22.7507i	0.134695	−	0.763893i	−0.840377	−	0.542003i	$-0.817666\pi$
$887$	4.01156	−	22.7507i	0.134695	−	0.763893i	0.975072	−	0.221890i	$-0.0712227\pi$
$888$	−9.84663	−	42.9816i	−0.330431	−	1.44237i
$889$	−2.20807	+	2.63147i	−0.0740563	+	0.0882568i
$890$	−2.25731	−	3.76159i	−0.0756653	−	0.126089i
$891$	−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
$896$	−3.03094	+	7.06292i	−0.101257	+	0.235956i
$897$	−2.53375	−	2.12606i	−0.0845993	−	0.0709872i
$898$	−2.03113	+	3.65940i	−0.0677798	+	0.122116i
$899$	−31.3948	−	5.53575i	−1.04708	−	0.184628i
$900$	0.239906	+	1.13495i	0.00799688	+	0.0378318i
$901$	−38.1672	+	22.0359i	−1.27153	+	0.734121i
$902$	−7.75381	−	8.92989i	−0.258174	−	0.297333i
$903$	−6.13504	+	2.23297i	−0.204161	+	0.0743086i
$904$	38.7289	−	1.96410i	1.28810	−	0.0653248i
$905$	−1.35614	−	0.782968i	−0.0450796	−	0.0260267i
$906$	−31.6498	+	6.13361i	−1.05149	+	0.203775i
$907$	−2.28571	+	1.91794i	−0.0758956	+	0.0636840i	−0.679946	−	0.733262i	$-0.737997\pi$
$907$	−2.28571	+	1.91794i	−0.0758956	+	0.0636840i	0.604051	+	0.796946i	$0.293552\pi$
$908$	22.5789	−	0.763014i	0.749307	−	0.0253215i
$909$	0.227679	+	1.29123i	0.00755164	+	0.0428275i
$910$	−0.0161687	−	0.957192i	−0.000535987	−	0.0317306i
$911$	−9.69320			−0.321150			−0.160575	−	0.987024i	$-0.551335\pi$
$911$	−9.69320			−0.321150			−0.160575	+	0.987024i	$0.551335\pi$
$912$	30.3226	+	5.32866i	1.00408	+	0.176449i
$913$	−44.4040			−1.46956
$914$	0.658739	+	38.9975i	0.0217891	+	1.28992i
$915$	0.695399	+	3.94381i	0.0229892	+	0.130378i
$916$	−10.3429	+	0.349522i	−0.341741	+	0.0115485i
$917$	−8.80974	+	7.39225i	−0.290923	+	0.244114i
$918$	−31.2157	+	6.04948i	−1.03027	+	0.199663i
$919$	18.5828	+	10.7288i	0.612989	+	0.353909i	0.774134	−	0.633021i	$-0.218185\pi$
$919$	18.5828	+	10.7288i	0.612989	+	0.353909i	−0.161145	+	0.986931i	$0.551519\pi$
$920$	0.438563	−	0.0222413i	0.0144590	−	0.000733274i
$921$	8.09780	−	2.94736i	0.266832	−	0.0971188i
$922$	−29.0193	−	33.4209i	−0.955701	−	1.10066i
$923$	−26.7300	+	15.4326i	−0.879828	+	0.507969i
$924$	2.20606	+	10.4365i	0.0725741	+	0.343335i
$925$	42.7561	+	7.53905i	1.40581	+	0.247883i
$926$	−1.07651	+	1.93950i	−0.0353763	+	0.0637359i
$927$	0.261789	+	0.219667i	0.00859827	+	0.00721480i
$928$	15.5994	−	7.22071i	0.512075	−	0.237031i
$929$	−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
$934$	−13.8594	−	23.0953i	−0.453492	−	0.755701i
$935$	−3.62877	+	4.32460i	−0.118674	+	0.141430i
$936$	0.258311	+	1.12755i	0.00844315	+	0.0368553i
$937$	−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	$0.811691\pi$
$938$	0.748109	−	4.70622i	0.0244266	−	0.153664i
$939$	0.770982	+	1.33538i	0.0251600	+	0.0435785i
$940$	−0.622497	−	0.331887i	−0.0203036	−	0.0108250i
$941$	−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	$0.907012\pi$
$942$	37.7491	−	46.5626i	1.22993	−	1.51709i
$943$	−0.508030	+	0.879934i	−0.0165437	+	0.0286546i
$944$	17.1953	+	4.97262i	0.559660	+	0.161845i
$945$	0.638637	+	0.761097i	0.0207748	+	0.0247585i
$946$	−11.1603	+	32.3527i	−0.362853	+	1.05188i
$947$	20.9000	−	3.68524i	0.679159	−	0.119754i	0.176581	−	0.984286i	$-0.443496\pi$
$947$	20.9000	−	3.68524i	0.679159	−	0.119754i	0.502578	+	0.864532i	$0.332385\pi$
$948$	−27.1401	+	10.9298i	−0.881469	+	0.354982i
$949$		−	11.8055i		−	0.383221i
$950$	−16.4520	+	25.4599i	−0.533772	+	0.826029i
$951$			43.4088i			1.40763i
$952$	−6.21825	+	5.77900i	−0.201535	+	0.187299i
$953$	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	$0.364466\pi$
$954$	−1.57303	−	0.542628i	−0.0509286	−	0.0175682i
$955$	4.20999	+	5.01727i	0.136232	+	0.162355i
$956$	13.3833	−	8.34187i	0.432847	−	0.269795i
$957$	11.9286	−	20.6610i	0.385598	−	0.667876i
$958$	−25.5351	−	20.7017i	−0.825000	−	0.668842i
$959$	2.62537	+	7.21316i	0.0847778	+	0.232925i
$960$	−3.35793	−	2.28150i	−0.108377	−	0.0736350i
$961$	−39.5308	−	68.4694i	−1.27519	−	2.20869i
$962$	42.7565	+	6.79664i	1.37852	+	0.219133i
$963$	−0.191645	+	1.08687i	−0.00617568	+	0.0350240i
$964$	−30.6174	−	4.33817i	−0.986121	−	0.139723i
$965$	−3.77528	+	4.49921i	−0.121531	+	0.144835i
$966$	0.785823	−	0.471568i	0.0252834	−	0.0151725i
$967$	−7.30654	+	20.0745i	−0.234962	+	0.645554i	0.765036	+	0.643987i	$0.222721\pi$
$967$	−7.30654	+	20.0745i	−0.234962	+	0.645554i	−0.999999	+	0.00156674i	$0.999501\pi$
$968$	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	0.748247	−	0.663420i	$-0.230896\pi$
$971$	27.8889	+	10.1507i	0.894999	+	0.325753i	0.146752	+	0.989173i	$0.453118\pi$
$972$	−1.92906	−	1.51065i	−0.0618748	−	0.0484542i
$973$	0.983857	+	0.825554i	0.0315410	+	0.0264660i
$974$	46.7026	+	25.9221i	1.49645	+	0.830597i
$975$	−29.6496	−	5.22802i	−0.949546	−	0.167431i
$976$	25.4958	+	18.6117i	0.816100	+	0.595745i
$977$	−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	$0.471822\pi$
$978$	19.9650	−	17.3356i	0.638410	−	0.554331i
$979$	−45.0985	+	16.4145i	−1.44135	+	0.524610i
$980$	−3.57291	−	1.16536i	−0.114132	−	0.0372260i
$981$	0.948880	+	0.547836i	0.0302954	+	0.0174911i
$982$	−2.94586	−	15.2008i	−0.0940062	−	0.485078i
$983$	28.8985	−	24.2487i	0.921718	−	0.773414i	−0.0525936	−	0.998616i	$-0.516749\pi$
$983$	28.8985	−	24.2487i	0.921718	−	0.773414i	0.974312	+	0.225202i	$0.0723044\pi$
$984$	8.65282	−	3.65566i	0.275842	−	0.116538i
$985$	0.238127	+	1.35049i	0.00758736	+	0.0430300i
$986$	18.9832	−	0.320661i	0.604549	−	0.0102119i
$987$	−1.47226			−0.0468626
$988$	−15.9745	+	25.6616i	−0.508215	+	0.816405i
$989$	2.94030			0.0934960
$990$	−0.213118	+	0.00359995i	−0.00677335	+	0.000114414i
$991$	−3.04240	−	17.2543i	−0.0966449	−	0.548100i	−0.994231	−	0.107261i	$-0.965792\pi$
$991$	−3.04240	−	17.2543i	−0.0966449	−	0.548100i	0.897586	−	0.440839i	$-0.145319\pi$
$992$	53.7151	+	25.2321i	1.70546	+	0.801121i
$993$	−9.76195	+	8.19125i	−0.309786	+	0.259941i
$994$	−1.62708	−	8.39586i	−0.0516080	−	0.266300i
$995$	1.45983	+	0.842834i	0.0462798	+	0.0267196i
$996$	10.9364	−	33.5302i	0.346533	−	1.06245i
$997$	−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	$0.457688\pi$
$998$	−20.8212	+	18.0790i	−0.659082	+	0.572280i
$999$	−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.15.5	✓	48
3.2	odd	2		684.2.cf.a.91.4		48
4.3	odd	2	inner	76.2.k.a.15.7	yes	48
12.11	even	2		684.2.cf.a.91.2		48
19.14	odd	18	inner	76.2.k.a.71.7	yes	48
57.14	even	18		684.2.cf.a.451.2		48
76.71	even	18	inner	76.2.k.a.71.5	yes	48
228.71	odd	18		684.2.cf.a.451.4		48

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.0238852 - 1.41401i) q^{2} +(-0.306623 - 1.73895i) q^{3} +(-1.99886 + 0.0675479i) q^{4} +(-0.220151 + 0.184728i) q^{5} +(-2.45157 + 0.475104i) q^{6} +(0.588321 + 0.339668i) q^{7} +(0.143257 + 2.82480i) q^{8} +(-0.110838 + 0.0403418i) q^{9} +O(q^{10})\)	\(q+(-0.0238852 - 1.41401i) q^{2} +(-0.306623 - 1.73895i) q^{3} +(-1.99886 + 0.0675479i) q^{4} +(-0.220151 + 0.184728i) q^{5} +(-2.45157 + 0.475104i) q^{6} +(0.588321 + 0.339668i) q^{7} +(0.143257 + 2.82480i) q^{8} +(-0.110838 + 0.0403418i) q^{9} +(0.266467 + 0.306884i) q^{10} +(3.85060 - 2.22314i) q^{11} +(0.730359 + 3.45520i) q^{12} +(-3.41466 - 0.602096i) q^{13} +(0.466242 - 0.840006i) q^{14} +(0.388736 + 0.326188i) q^{15} +(3.99087 - 0.270038i) 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} +(-3.23552 - 5.39169i) q^{22} +(-0.347253 + 0.413840i) q^{23} +(4.86824 - 1.11526i) q^{24} +(-0.853899 + 4.84270i) q^{25} +(-0.769811 + 4.84275i) q^{26} +(-2.54452 - 4.40724i) q^{27} +(-1.19892 - 0.639208i) q^{28} +(1.03930 + 2.85545i) q^{29} +(0.451949 - 0.557469i) q^{30} +(-5.24551 + 9.08550i) q^{31} +(-0.477159 - 5.63669i) q^{32} +(-5.04661 - 6.01432i) q^{33} +(2.03749 - 5.90649i) q^{34} +(-0.192266 + 0.0339016i) q^{35} +(0.218825 - 0.0881245i) q^{36} -8.82897i q^{37} +(5.67982 + 2.39576i) q^{38} +6.12252i q^{39} +(-0.553358 - 0.595418i) q^{40} +(1.85222 - 0.326596i) q^{41} +(-1.60369 - 0.553204i) q^{42} +(-3.49849 - 4.16933i) q^{43} +(-7.54663 + 4.70385i) q^{44} +(0.0169489 - 0.0293563i) q^{45} +(0.593469 + 0.481135i) q^{46} +(-0.419777 - 1.15333i) q^{47} +(-1.69328 - 6.85712i) q^{48} +(-3.26925 - 5.66251i) q^{49} +(6.86803 + 1.09175i) q^{50} +(1.35467 - 7.68271i) q^{51} +(6.86609 + 0.972852i) q^{52} +(-6.41208 + 7.64162i) q^{53} +(-6.17111 + 3.70325i) 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} +(-0.799062 - 0.625746i) q^{60} +(6.04529 + 5.07260i) q^{61} +(12.9723 + 7.20021i) q^{62} +(-0.0789113 - 0.0139142i) q^{63} +(-7.95896 + 0.809342i) q^{64} +(0.862964 - 0.498232i) q^{65} +(-8.38378 + 7.27962i) q^{66} +(4.66099 - 1.69646i) q^{67} +(-8.40051 - 2.73995i) q^{68} +(0.826122 + 0.476961i) q^{69} +(0.0525296 + 0.271056i) q^{70} +(6.81908 - 5.72189i) q^{71} +(-0.129836 - 0.307316i) q^{72} +(0.591231 + 3.35304i) q^{73} +(-12.4843 + 0.210882i) q^{74} +8.68302 q^{75} +(3.25197 - 8.08855i) q^{76} +3.02052 q^{77} +(8.65732 - 0.146238i) q^{78} +(1.43865 + 8.15896i) q^{79} +(-0.828711 + 0.796677i) q^{80} +(-7.15481 + 6.00360i) q^{81} +(-0.506052 - 2.61126i) q^{82} +(-8.64879 - 4.99338i) q^{83} +(-0.743932 + 2.28085i) q^{84} +(-1.19311 + 0.434257i) q^{85} +(-5.81192 + 5.04649i) q^{86} +(4.64680 - 2.68283i) q^{87} +(6.83155 + 10.5587i) q^{88} +(-10.6299 - 1.87434i) q^{89} +(-0.0419149 - 0.0232647i) q^{90} +(-1.80440 - 1.51407i) q^{91} +(0.666156 - 0.850664i) 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} +(-7.92877 + 4.75801i) 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

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