LMFDB - Embedded newform 91.2.q.a.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(36,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("91.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.q (of order $6$, degree $2$, 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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.1
Root			$-1.12906 + 0.851598i$ of defining polynomial
Character	$\chi$	$=$	91.43
Dual form			91.2.q.a.36.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.34104 - 1.35160i) q^{2} +(0.172975 - 0.299601i) q^{3} +(2.65363 + 4.59623i) q^{4} +3.25812i q^{5} +(-0.809880 + 0.467584i) q^{6} +(0.866025 - 0.500000i) q^{7} -8.94020i q^{8} +(1.44016 + 2.49443i) q^{9} +O(q^{10})$	\(q+(-2.34104 - 1.35160i) q^{2} +(0.172975 - 0.299601i) q^{3} +(2.65363 + 4.59623i) q^{4} +3.25812i q^{5} +(-0.809880 + 0.467584i) q^{6} +(0.866025 - 0.500000i) q^{7} -8.94020i q^{8} +(1.44016 + 2.49443i) q^{9} +(4.40367 - 7.62739i) q^{10} +(-1.59871 - 0.923014i) q^{11} +1.83605 q^{12} +(3.60550 - 0.0186461i) q^{13} -2.70320 q^{14} +(0.976136 + 0.563573i) q^{15} +(-6.77628 + 11.7369i) q^{16} +(1.07657 + 1.86467i) q^{17} -7.78607i q^{18} +(-2.07929 + 1.20048i) q^{19} +(-14.9751 + 8.64587i) q^{20} -0.345949i q^{21} +(2.49509 + 4.32162i) q^{22} +(0.906314 - 1.56978i) q^{23} +(-2.67849 - 1.54643i) q^{24} -5.61537 q^{25} +(-8.46582 - 4.82954i) q^{26} +2.03429 q^{27} +(4.59623 + 2.65363i) q^{28} +(1.36703 - 2.36777i) q^{29} +(-1.52345 - 2.63869i) q^{30} +1.74236i q^{31} +(16.2422 - 9.37743i) q^{32} +(-0.553071 + 0.319316i) q^{33} -5.82036i q^{34} +(1.62906 + 2.82162i) q^{35} +(-7.64331 + 13.2386i) q^{36} +(-5.14042 - 2.96783i) q^{37} +6.49025 q^{38} +(0.618074 - 1.08344i) q^{39} +29.1283 q^{40} +(3.65577 + 2.11066i) q^{41} +(-0.467584 + 0.809880i) q^{42} +(-4.34111 - 7.51903i) q^{43} -9.79737i q^{44} +(-8.12716 + 4.69222i) q^{45} +(-4.24343 + 2.44994i) q^{46} -5.87774i q^{47} +(2.34425 + 4.06036i) q^{48} +(0.500000 - 0.866025i) q^{49} +(13.1458 + 7.58972i) q^{50} +0.744877 q^{51} +(9.65339 + 16.5222i) q^{52} -9.30628 q^{53} +(-4.76235 - 2.74954i) q^{54} +(3.00729 - 5.20878i) q^{55} +(-4.47010 - 7.74244i) q^{56} +0.830609i q^{57} +(-6.40054 + 3.69535i) q^{58} +(9.31173 - 5.37613i) q^{59} +5.98206i q^{60} +(-5.05504 - 8.75558i) q^{61} +(2.35497 - 4.07893i) q^{62} +(2.49443 + 1.44016i) q^{63} -23.5929 q^{64} +(0.0607514 + 11.7472i) q^{65} +1.72635 q^{66} +(0.716130 + 0.413458i) q^{67} +(-5.71365 + 9.89633i) q^{68} +(-0.313538 - 0.543065i) q^{69} -8.80735i q^{70} +(-2.03884 + 1.17712i) q^{71} +(22.3007 - 12.8753i) q^{72} -3.19482i q^{73} +(8.02261 + 13.8956i) q^{74} +(-0.971316 + 1.68237i) q^{75} +(-11.0353 - 6.37126i) q^{76} -1.84603 q^{77} +(-2.91130 + 1.70098i) q^{78} +0.801911 q^{79} +(-38.2402 - 22.0780i) q^{80} +(-3.96860 + 6.87381i) q^{81} +(-5.70552 - 9.88225i) q^{82} +9.97031i q^{83} +(1.59006 - 0.918023i) q^{84} +(-6.07534 + 3.50760i) q^{85} +23.4698i q^{86} +(-0.472923 - 0.819127i) q^{87} +(-8.25193 + 14.2928i) q^{88} +(13.0886 + 7.55674i) q^{89} +25.3680 q^{90} +(3.11313 - 1.81890i) q^{91} +9.62010 q^{92} +(0.522012 + 0.301384i) q^{93} +(-7.94435 + 13.7600i) q^{94} +(-3.91130 - 6.77458i) q^{95} -6.48823i q^{96} +(7.99489 - 4.61585i) q^{97} +(-2.34104 + 1.35160i) q^{98} -5.31715i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9	$ 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9} + 12 q^{10} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 8 q^{14} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 12 q^{24} - 20 q^{25} - 42 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} - 30 q^{33} + 6 q^{35} - 10 q^{36} - 42 q^{37} + 4 q^{38} - 4 q^{39} + 92 q^{40} + 30 q^{41} + 4 q^{42} + 2 q^{43} + 12 q^{46} - 2 q^{48} + 6 q^{49} - 18 q^{50} + 52 q^{51} + 2 q^{52} - 44 q^{53} + 12 q^{54} - 6 q^{55} - 12 q^{56} - 12 q^{58} + 18 q^{59} + 14 q^{61} - 4 q^{62} + 12 q^{63} - 52 q^{64} + 60 q^{65} - 52 q^{66} - 24 q^{67} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} + 46 q^{75} - 18 q^{76} + 8 q^{77} - 10 q^{78} - 56 q^{79} - 72 q^{80} + 2 q^{81} + 14 q^{82} + 18 q^{84} - 48 q^{85} - 2 q^{87} - 14 q^{88} - 12 q^{89} + 24 q^{90} + 14 q^{91} + 24 q^{92} - 18 q^{93} + 4 q^{94} - 22 q^{95} + 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9 + 12 * q^10 + 6 * q^11 - 4 * q^12 + 4 * q^13 - 8 * q^14 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 12 * q^24 - 20 * q^25 - 42 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 - 30 * q^33 + 6 * q^35 - 10 * q^36 - 42 * q^37 + 4 * q^38 - 4 * q^39 + 92 * q^40 + 30 * q^41 + 4 * q^42 + 2 * q^43 + 12 * q^46 - 2 * q^48 + 6 * q^49 - 18 * q^50 + 52 * q^51 + 2 * q^52 - 44 * q^53 + 12 * q^54 - 6 * q^55 - 12 * q^56 - 12 * q^58 + 18 * q^59 + 14 * q^61 - 4 * q^62 + 12 * q^63 - 52 * q^64 + 60 * q^65 - 52 * q^66 - 24 * q^67 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 + 46 * q^75 - 18 * q^76 + 8 * q^77 - 10 * q^78 - 56 * q^79 - 72 * q^80 + 2 * q^81 + 14 * q^82 + 18 * q^84 - 48 * q^85 - 2 * q^87 - 14 * q^88 - 12 * q^89 + 24 * q^90 + 14 * q^91 + 24 * q^92 - 18 * q^93 + 4 * q^94 - 22 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−2.34104	−	1.35160i	−1.65536	−	0.955724i	−0.974813	−	0.223022i	$-0.928408\pi$
$2$	−2.34104	−	1.35160i	−1.65536	−	0.955724i	−0.680549	−	0.732702i	$-0.738259\pi$
$3$	0.172975	−	0.299601i	0.0998669	−	0.172975i	−0.811763	−	0.583988i	$-0.801492\pi$
$3$	0.172975	−	0.299601i	0.0998669	−	0.172975i	0.911629	+	0.411013i	$0.134825\pi$
$4$	2.65363	+	4.59623i	1.32682	+	2.29811i
$5$			3.25812i			1.45708i	0.685005	+	0.728539i	$0.259800\pi$
$5$			3.25812i			1.45708i	−0.685005	+	0.728539i	$0.740200\pi$
$6$	−0.809880	+	0.467584i	−0.330632	+	0.190890i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$		−	8.94020i		−	3.16084i
$9$	1.44016	+	2.49443i	0.480053	+	0.831477i
$10$	4.40367	−	7.62739i	1.39256	−	2.41199i
$11$	−1.59871	−	0.923014i	−0.482028	−	0.278299i	0.239233	−	0.970962i	$-0.423104\pi$
$11$	−1.59871	−	0.923014i	−0.482028	−	0.278299i	−0.721261	+	0.692663i	$0.756437\pi$
$12$	1.83605			0.530021
$13$	3.60550	−	0.0186461i	0.999987	−	0.00517151i
$13$	3.60550	−	0.0186461i	0.999987	−	0.00517151i
$14$	−2.70320			−0.722460
$15$	0.976136	+	0.563573i	0.252037	+	0.145514i
$16$	−6.77628	+	11.7369i	−1.69407	+	2.93422i
$17$	1.07657	+	1.86467i	0.261107	+	0.452250i	0.966536	−	0.256530i	$-0.0825793\pi$
$17$	1.07657	+	1.86467i	0.261107	+	0.452250i	−0.705430	+	0.708780i	$0.749246\pi$
$18$		−	7.78607i		−	1.83519i
$19$	−2.07929	+	1.20048i	−0.477021	+	0.275408i	−0.719174	−	0.694830i	$-0.755480\pi$
$19$	−2.07929	+	1.20048i	−0.477021	+	0.275408i	0.242153	+	0.970238i	$0.422146\pi$
$20$	−14.9751	+	8.64587i	−3.34853	+	1.93328i
$21$		−	0.345949i		−	0.0754923i
$22$	2.49509	+	4.32162i	0.531954	+	0.921372i
$23$	0.906314	−	1.56978i	0.188979	−	0.327322i	−0.755931	−	0.654652i	$-0.772815\pi$
$23$	0.906314	−	1.56978i	0.188979	−	0.327322i	0.944910	+	0.327329i	$0.106149\pi$
$24$	−2.67849	−	1.54643i	−0.546744	−	0.315663i
$25$	−5.61537			−1.12307
$26$	−8.46582	−	4.82954i	−1.66028	−	0.947151i
$27$	2.03429			0.391500
$28$	4.59623	+	2.65363i	0.868606	+	0.501490i
$29$	1.36703	−	2.36777i	0.253851	−	0.439683i	−0.710732	−	0.703463i	$-0.751636\pi$
$29$	1.36703	−	2.36777i	0.253851	−	0.439683i	0.964583	+	0.263780i	$0.0849693\pi$
$30$	−1.52345	−	2.63869i	−0.278142	−	0.481756i
$31$			1.74236i			0.312937i	0.987683	+	0.156468i	$0.0500110\pi$
$31$			1.74236i			0.312937i	−0.987683	+	0.156468i	$0.949989\pi$
$32$	16.2422	−	9.37743i	2.87124	−	1.65771i
$33$	−0.553071	+	0.319316i	−0.0962774	+	0.0555858i
$34$		−	5.82036i		−	0.998183i
$35$	1.62906	+	2.82162i	0.275362	+	0.476940i
$36$	−7.64331	+	13.2386i	−1.27389	+	2.20643i
$37$	−5.14042	−	2.96783i	−0.845081	−	0.487908i	0.0139073	−	0.999903i	$-0.495573\pi$
$37$	−5.14042	−	2.96783i	−0.845081	−	0.487908i	−0.858988	+	0.511996i	$0.828906\pi$
$38$	6.49025			1.05286
$39$	0.618074	−	1.08344i	0.0989710	−	0.173489i
$40$	29.1283			4.60558
$41$	3.65577	+	2.11066i	0.570935	+	0.329629i	0.757523	−	0.652809i	$-0.226410\pi$
$41$	3.65577	+	2.11066i	0.570935	+	0.329629i	−0.186588	+	0.982438i	$0.559743\pi$
$42$	−0.467584	+	0.809880i	−0.0721498	+	0.124967i
$43$	−4.34111	−	7.51903i	−0.662014	−	1.14664i	−0.980086	−	0.198575i	$-0.936369\pi$
$43$	−4.34111	−	7.51903i	−0.662014	−	1.14664i	0.318072	−	0.948067i	$-0.396965\pi$
$44$		−	9.79737i		−	1.47701i
$45$	−8.12716	+	4.69222i	−1.21153	+	0.699475i
$46$	−4.24343	+	2.44994i	−0.625659	+	0.361224i
$47$		−	5.87774i		−	0.857357i	−0.903457	−	0.428678i	$-0.858979\pi$
$47$		−	5.87774i		−	0.857357i	0.903457	−	0.428678i	$-0.141021\pi$
$48$	2.34425	+	4.06036i	0.338363	+	0.586062i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	13.1458	+	7.58972i	1.85910	+	1.07335i
$51$	0.744877			0.104304
$52$	9.65339	+	16.5222i	1.33868	+	2.29122i
$53$	−9.30628			−1.27832			−0.639158	−	0.769076i	$-0.720717\pi$
$53$	−9.30628			−1.27832			−0.639158	+	0.769076i	$0.720717\pi$
$54$	−4.76235	−	2.74954i	−0.648074	−	0.374166i
$55$	3.00729	−	5.20878i	0.405503	−	0.702352i
$56$	−4.47010	−	7.74244i	−0.597342	−	1.03463i
$57$			0.830609i			0.110017i
$58$	−6.40054	+	3.69535i	−0.840432	+	0.485224i
$59$	9.31173	−	5.37613i	1.21228	−	0.699912i	0.249028	−	0.968496i	$-0.419889\pi$
$59$	9.31173	−	5.37613i	1.21228	−	0.699912i	0.963256	+	0.268584i	$0.0865557\pi$
$60$			5.98206i			0.772281i
$61$	−5.05504	−	8.75558i	−0.647231	−	1.12104i	−0.983781	−	0.179371i	$-0.942594\pi$
$61$	−5.05504	−	8.75558i	−0.647231	−	1.12104i	0.336550	−	0.941665i	$-0.390740\pi$
$62$	2.35497	−	4.07893i	0.299081	−	0.518024i
$63$	2.49443	+	1.44016i	0.314269	+	0.181443i
$64$	−23.5929			−2.94911
$65$	0.0607514	+	11.7472i	0.00753529	+	1.45706i
$66$	1.72635			0.212499
$67$	0.716130	+	0.413458i	0.0874892	+	0.0505119i	0.543106	−	0.839664i	$-0.317248\pi$
$67$	0.716130	+	0.413458i	0.0874892	+	0.0505119i	−0.455617	+	0.890176i	$0.650581\pi$
$68$	−5.71365	+	9.89633i	−0.692881	+	1.20011i
$69$	−0.313538	−	0.543065i	−0.0377456	−	0.0653773i
$70$		−	8.80735i		−	1.05268i
$71$	−2.03884	+	1.17712i	−0.241965	+	0.139699i	−0.616080	−	0.787684i	$-0.711280\pi$
$71$	−2.03884	+	1.17712i	−0.241965	+	0.139699i	0.374114	+	0.927383i	$0.377947\pi$
$72$	22.3007	−	12.8753i	2.62816	−	1.51737i
$73$		−	3.19482i		−	0.373925i	−0.982367	−	0.186963i	$-0.940136\pi$
$73$		−	3.19482i		−	0.373925i	0.982367	−	0.186963i	$-0.0598644\pi$
$74$	8.02261	+	13.8956i	0.932610	+	1.61533i
$75$	−0.971316	+	1.68237i	−0.112158	+	0.194263i
$76$	−11.0353	−	6.37126i	−1.26584	−	0.730833i
$77$	−1.84603			−0.210374
$78$	−2.91130	+	1.70098i	−0.329640	+	0.192598i
$79$	0.801911			0.0902220			0.0451110	−	0.998982i	$-0.485636\pi$
$79$	0.801911			0.0902220			0.0451110	+	0.998982i	$0.485636\pi$
$80$	−38.2402	−	22.0780i	−4.27538	−	2.46839i
$81$	−3.96860	+	6.87381i	−0.440955	+	0.763757i
$82$	−5.70552	−	9.88225i	−0.630069	−	1.09131i
$83$			9.97031i			1.09438i	0.837007	+	0.547192i	$0.184303\pi$
$83$			9.97031i			1.09438i	−0.837007	+	0.547192i	$0.815697\pi$
$84$	1.59006	−	0.918023i	0.173490	−	0.100164i
$85$	−6.07534	+	3.50760i	−0.658963	+	0.380452i
$86$			23.4698i			2.53081i
$87$	−0.472923	−	0.819127i	−0.0507027	−	0.0878196i
$88$	−8.25193	+	14.2928i	−0.879658	+	1.52361i
$89$	13.0886	+	7.55674i	1.38739	+	0.801012i	0.993021	−	0.117938i	$-0.0376284\pi$
$89$	13.0886	+	7.55674i	1.38739	+	0.801012i	0.394373	+	0.918950i	$0.370962\pi$
$90$	25.3680			2.67402
$91$	3.11313	−	1.81890i	0.326345	−	0.190672i
$92$	9.62010			1.00296
$93$	0.522012	+	0.301384i	0.0541301	+	0.0312520i
$94$	−7.94435	+	13.7600i	−0.819397	+	1.41924i
$95$	−3.91130	−	6.77458i	−0.401291	−	0.695057i
$96$		−	6.48823i		−	0.662202i
$97$	7.99489	−	4.61585i	0.811758	−	0.468669i	−0.0358079	−	0.999359i	$-0.511400\pi$
$97$	7.99489	−	4.61585i	0.811758	−	0.468669i	0.847566	+	0.530690i	$0.178067\pi$
$98$	−2.34104	+	1.35160i	−0.236480	+	0.136532i
$99$		−	5.31715i		−	0.534394i
$100$	−14.9011	−	25.8095i	−1.49011	−	2.58095i
$101$	7.41169	−	12.8374i	0.737491	−	1.27737i	−0.216131	−	0.976364i	$-0.569344\pi$
$101$	7.41169	−	12.8374i	0.737491	−	1.27737i	0.953622	−	0.301007i	$-0.0973228\pi$
$102$	−1.74378	−	1.00677i	−0.172660	−	0.0996855i
$103$	4.28286			0.422003			0.211001	−	0.977486i	$-0.432328\pi$
$103$	4.28286			0.422003			0.211001	+	0.977486i	$0.432328\pi$
$104$	−0.166700	−	32.2339i	−0.0163463	−	3.16079i
$105$	1.12715			0.109998
$106$	21.7863	+	12.5783i	2.11608	+	1.22172i
$107$	9.56289	−	16.5634i	0.924479	−	1.60124i	0.132082	−	0.991239i	$-0.457834\pi$
$107$	9.56289	−	16.5634i	0.924479	−	1.60124i	0.792397	−	0.610006i	$-0.208833\pi$
$108$	5.39827	+	9.35007i	0.519448	+	0.899711i
$109$			4.27153i			0.409139i	0.978852	+	0.204569i	$0.0655794\pi$
$109$			4.27153i			0.409139i	−0.978852	+	0.204569i	$0.934421\pi$
$110$	−14.0804	+	8.12930i	−1.34251	+	0.775099i
$111$	−1.77833	+	1.02672i	−0.168791	+	0.0974516i
$112$			13.5526i			1.28060i
$113$	−1.37488	−	2.38137i	−0.129338	−	0.224020i	0.794082	−	0.607810i	$-0.207952\pi$
$113$	−1.37488	−	2.38137i	−0.129338	−	0.224020i	−0.923420	+	0.383790i	$0.874619\pi$
$114$	1.12265	−	1.94448i	0.105146	−	0.182118i
$115$	5.11454	+	2.95288i	0.476934	+	0.275358i
$116$	14.5104			1.34726
$117$	5.23901	+	8.96682i	0.484347	+	0.828983i
$118$	−29.0655			−2.67569
$119$	1.86467	+	1.07657i	0.170934	+	0.0986890i
$120$	5.03845	−	8.72685i	0.459945	−	0.796649i
$121$	−3.79609	−	6.57502i	−0.345099	−	0.597729i
$122$			27.3295i			2.47430i
$123$	1.26471	−	0.730180i	0.114035	−	0.0658381i
$124$	−8.00828	+	4.62358i	−0.719165	+	0.415210i
$125$		−	2.00495i		−	0.179329i
$126$	−3.89303	−	6.74293i	−0.346819	−	0.600708i
$127$	−4.86719	+	8.43022i	−0.431893	+	0.748061i	−0.997036	−	0.0769320i	$-0.975488\pi$
$127$	−4.86719	+	8.43022i	−0.431893	+	0.748061i	0.565143	+	0.824993i	$0.308821\pi$
$128$	22.7475	+	13.1333i	2.01061	+	1.16083i
$129$	−3.00361			−0.264453
$130$	15.7352	−	27.5827i	1.38007	−	2.41916i
$131$	−18.6615			−1.63046			−0.815230	−	0.579138i	$-0.803389\pi$
$131$	−18.6615			−1.63046			−0.815230	+	0.579138i	$0.803389\pi$
$132$	−2.93530	−	1.69470i	−0.255485	−	0.147504i
$133$	−1.20048	+	2.07929i	−0.104095	+	0.180297i
$134$	−1.11766	−	1.93584i	−0.0965509	−	0.167231i
$135$			6.62797i			0.570445i
$136$	16.6706	−	9.62475i	1.42949	−	0.825315i
$137$	−7.29328	+	4.21078i	−0.623107	+	0.359751i	−0.778078	−	0.628168i	$-0.783805\pi$
$137$	−7.29328	+	4.21078i	−0.623107	+	0.359751i	0.154971	+	0.987919i	$0.450472\pi$
$138$			1.69511i			0.144298i
$139$	8.81809	+	15.2734i	0.747941	+	1.29547i	0.948808	+	0.315853i	$0.102291\pi$
$139$	8.81809	+	15.2734i	0.747941	+	1.29547i	−0.200867	+	0.979619i	$0.564376\pi$
$140$	−8.64587	+	14.9751i	−0.730709	+	1.26563i
$141$	−1.76098	−	1.01670i	−0.148301	−	0.0856216i
$142$	6.36399			0.534054
$143$	−5.78135	−	3.29812i	−0.483461	−	0.275803i
$144$	−39.0357			−3.25298
$145$	7.71448	+	4.45396i	0.640653	+	0.369881i
$146$	−4.31811	+	7.47919i	−0.357370	+	0.618982i
$147$	−0.172975	−	0.299601i	−0.0142667	−	0.0247107i
$148$		−	31.5021i		−	2.58946i
$149$	−3.48232	+	2.01052i	−0.285283	+	0.164708i	−0.635813	−	0.771843i	$-0.719335\pi$
$149$	−3.48232	+	2.01052i	−0.285283	+	0.164708i	0.350530	+	0.936552i	$0.386002\pi$
$150$	4.54777	−	2.62566i	0.371324	−	0.214384i
$151$		−	18.9010i		−	1.53814i	−0.639165	−	0.769069i	$-0.720720\pi$
$151$		−	18.9010i		−	1.53814i	0.639165	−	0.769069i	$-0.279280\pi$
$152$	10.7325	+	18.5892i	0.870521	+	1.50779i
$153$	−3.10086	+	5.37086i	−0.250690	+	0.434208i
$154$	4.32162	+	2.49509i	0.348246	+	0.201060i
$155$	−5.67682			−0.455973
$156$	6.61987	−	0.0342352i	0.530014	−	0.00274101i
$157$	−11.5735			−0.923670			−0.461835	−	0.886966i	$-0.652809\pi$
$157$	−11.5735			−0.923670			−0.461835	+	0.886966i	$0.652809\pi$
$158$	−1.87730	−	1.08386i	−0.149350	−	0.0862273i
$159$	−1.60975	+	2.78817i	−0.127661	+	0.221116i
$160$	30.5528	+	52.9190i	2.41541	+	4.18362i
$161$		−	1.81263i		−	0.142855i
$162$	18.5813	−	10.7279i	1.45988	−	0.842863i
$163$	−3.81520	+	2.20271i	−0.298830	+	0.172529i	−0.641917	−	0.766774i	$-0.721861\pi$
$163$	−3.81520	+	2.20271i	−0.298830	+	0.172529i	0.343087	+	0.939304i	$0.388527\pi$
$164$			22.4037i			1.74943i
$165$	−1.04037	−	1.80197i	−0.0809927	−	0.140284i
$166$	13.4759	−	23.3409i	1.04593	−	1.81160i
$167$	−7.81076	−	4.50954i	−0.604415	−	0.348959i	0.166362	−	0.986065i	$-0.446798\pi$
$167$	−7.81076	−	4.50954i	−0.604415	−	0.348959i	−0.770776	+	0.637106i	$0.780131\pi$
$168$	−3.09285			−0.238619
$169$	12.9993	−	0.134457i	0.999947	−	0.0103429i
$170$	18.9635			1.45443
$171$	−5.98901	−	3.45776i	−0.457991	−	0.264421i
$172$	23.0395	−	39.9055i	1.75674	−	3.04277i
$173$	3.04600	+	5.27583i	0.231583	+	0.401114i	0.958274	−	0.285851i	$-0.0922761\pi$
$173$	3.04600	+	5.27583i	0.231583	+	0.401114i	−0.726691	+	0.686964i	$0.758943\pi$
$174$			2.55681i			0.193831i
$175$	−4.86305	+	2.80769i	−0.367612	+	0.212241i
$176$	21.6666	−	12.5092i	1.63318	−	0.942917i
$177$		−	3.71974i		−	0.279592i
$178$	−20.4273	−	35.3812i	−1.53109	−	2.65193i
$179$	1.93982	−	3.35987i	0.144989	−	0.251128i	−0.784380	−	0.620281i	$-0.787019\pi$
$179$	1.93982	−	3.35987i	0.144989	−	0.251128i	0.929369	+	0.369152i	$0.120352\pi$
$180$	−43.1330	−	24.9029i	−3.21495	−	1.85615i
$181$	−6.58392			−0.489379			−0.244690	−	0.969601i	$-0.578686\pi$
$181$	−6.58392			−0.489379			−0.244690	+	0.969601i	$0.578686\pi$
$182$	−9.74638	+	0.0504042i	−0.722450	+	0.00373621i
$183$	−3.49757			−0.258548
$184$	−14.0342	−	8.10262i	−1.03461	−	0.597333i
$185$	9.66954	−	16.7481i	0.710919	−	1.23135i
$186$	−0.814700	−	1.41110i	−0.0597367	−	0.103467i
$187$		−	3.97476i		−	0.290663i
$188$	27.0155	−	15.5974i	1.97030	−	1.13756i
$189$	1.76175	−	1.01715i	0.128148	−	0.0739865i
$190$			21.1460i			1.53410i
$191$	6.87168	+	11.9021i	0.497218	+	0.861206i	0.999995	−	0.00320983i	$-0.00102172\pi$
$191$	6.87168	+	11.9021i	0.497218	+	0.861206i	−0.502777	+	0.864416i	$0.667688\pi$
$192$	−4.08097	+	7.06845i	−0.294519	+	0.510122i
$193$	19.7047	+	11.3765i	1.41838	+	0.818899i	0.996156	−	0.0875946i	$-0.0279180\pi$
$193$	19.7047	+	11.3765i	1.41838	+	0.818899i	0.422219	+	0.906494i	$0.361251\pi$
$194$	−24.9551			−1.79167
$195$	3.52997	+	2.01376i	0.252786	+	0.144208i
$196$	5.30727			0.379091
$197$	−12.5809	−	7.26358i	−0.896352	−	0.517509i	−0.0203371	−	0.999793i	$-0.506474\pi$
$197$	−12.5809	−	7.26358i	−0.896352	−	0.517509i	−0.876015	+	0.482284i	$0.839807\pi$
$198$	−7.18665	+	12.4476i	−0.510733	+	0.884615i
$199$	11.9202	+	20.6464i	0.845001	+	1.46358i	0.885620	+	0.464410i	$0.153734\pi$
$199$	11.9202	+	20.6464i	0.845001	+	1.46358i	−0.0406192	+	0.999175i	$0.512933\pi$
$200$			50.2025i			3.54985i
$201$	0.247745	−	0.143035i	0.0174746	−	0.0100889i
$202$	−34.7021	+	20.0353i	−2.44163	+	1.40968i
$203$		−	2.73406i		−	0.191894i
$204$	1.97663	+	3.42363i	0.138392	+	0.239702i
$205$	−6.87678	+	11.9109i	−0.480295	+	0.831896i
$206$	−10.0263	−	5.78871i	−0.698568	−	0.403318i
$207$	5.22095			0.362881
$208$	−24.2131	+	42.4437i	−1.67887	+	2.94294i
$209$	4.43223			0.306584
$210$	−2.63869	−	1.52345i	−0.182087	−	0.105128i
$211$	−2.15764	+	3.73714i	−0.148538	+	0.257275i	−0.930687	−	0.365816i	$-0.880790\pi$
$211$	−2.15764	+	3.73714i	−0.148538	+	0.257275i	0.782149	+	0.623091i	$0.214123\pi$
$212$	−24.6955	−	42.7738i	−1.69609	−	2.93772i
$213$			0.814450i			0.0558052i
$214$	−44.7741	+	25.8504i	−3.06070	+	1.76709i
$215$	24.4979	−	14.1439i	1.67075	−	0.964605i
$216$		−	18.1870i		−	1.23747i
$217$	0.871180	+	1.50893i	0.0591395	+	0.102433i
$218$	5.77339	−	9.99981i	0.391024	−	0.677273i
$219$	−0.957171	−	0.552623i	−0.0646796	−	0.0373428i
$220$	31.9210			2.15212
$221$	3.91635	+	6.70301i	0.263442	+	0.450893i
$222$	5.55083			0.372548
$223$	−20.2604	−	11.6973i	−1.35674	−	0.783312i	−0.367553	−	0.930003i	$-0.619804\pi$
$223$	−20.2604	−	11.6973i	−1.35674	−	0.783312i	−0.989182	+	0.146691i	$0.953138\pi$
$224$	9.37743	−	16.2422i	0.626556	−	1.08523i
$225$	−8.08703	−	14.0071i	−0.539135	−	0.933810i
$226$			7.43315i			0.494446i
$227$	−23.1427	+	13.3614i	−1.53603	+	0.886829i	−0.536968	+	0.843602i	$0.680431\pi$
$227$	−23.1427	+	13.3614i	−1.53603	+	0.886829i	−0.999065	+	0.0432270i	$0.986236\pi$
$228$	−3.81767	+	2.20413i	−0.252831	+	0.145972i
$229$			3.00670i			0.198688i	0.995053	+	0.0993442i	$0.0316745\pi$
$229$			3.00670i			0.198688i	−0.995053	+	0.0993442i	$0.968326\pi$
$230$	−7.98222	−	13.8256i	−0.526332	−	0.911634i
$231$	−0.319316	+	0.553071i	−0.0210094	+	0.0363894i
$232$	−21.1683	−	12.2215i	−1.38977	−	0.802383i
$233$	11.7148			0.767462			0.383731	−	0.923445i	$-0.374639\pi$
$233$	11.7148			0.767462			0.383731	+	0.923445i	$0.374639\pi$
$234$	−0.145180	−	28.0727i	−0.00949072	−	1.83517i
$235$	19.1504			1.24924
$236$	49.4199	+	28.5326i	3.21696	+	1.85731i
$237$	0.138710	−	0.240253i	0.00901019	−	0.0156061i
$238$	−2.91018	−	5.04058i	−0.188639	−	0.326732i
$239$		−	1.42797i		−	0.0923677i	−0.998933	−	0.0461838i	$-0.985294\pi$
$239$		−	1.42797i		−	0.0923677i	0.998933	−	0.0461838i	$-0.0147060\pi$
$240$	−13.2292	+	7.63786i	−0.853938	+	0.493021i
$241$	−2.32068	+	1.33984i	−0.149488	+	0.0863069i	−0.572878	−	0.819640i	$-0.694173\pi$
$241$	−2.32068	+	1.33984i	−0.149488	+	0.0863069i	0.423390	+	0.905947i	$0.360840\pi$
$242$			20.5232i			1.31928i
$243$	4.42437	+	7.66323i	0.283824	+	0.491597i
$244$	26.8284	−	46.4682i	1.71751	−	2.97482i
$245$	2.82162	+	1.62906i	0.180267	+	0.104077i
$246$	−3.94764			−0.251692
$247$	−7.47450	+	4.36710i	−0.475591	+	0.277872i
$248$	15.5770			0.989143
$249$	2.98711	+	1.72461i	0.189301	+	0.109293i
$250$	−2.70989	+	4.69367i	−0.171389	+	0.296854i
$251$	5.46696	+	9.46906i	0.345072	+	0.597681i	0.985367	−	0.170447i	$-0.0545213\pi$
$251$	5.46696	+	9.46906i	0.345072	+	0.597681i	−0.640295	+	0.768129i	$0.721188\pi$
$252$			15.2866i			0.962967i
$253$	−2.89786	+	1.67308i	−0.182187	+	0.105186i
$254$	22.7885	−	13.1570i	1.42988	−	0.825541i
$255$			2.42690i			0.151978i
$256$	−11.9089	−	20.6268i	−0.744307	−	1.28918i
$257$	2.07569	−	3.59520i	0.129478	−	0.224262i	−0.793996	−	0.607922i	$-0.792003\pi$
$257$	2.07569	−	3.59520i	0.129478	−	0.224262i	0.923474	+	0.383660i	$0.125337\pi$
$258$	7.03156	+	4.05967i	0.437766	+	0.252744i
$259$	−5.93565			−0.368823
$260$	−53.8315	+	31.4519i	−3.33849	+	1.95057i
$261$	7.87497			0.487448
$262$	43.6872	+	25.2228i	2.69900	+	1.55827i
$263$	−2.02680	+	3.51052i	−0.124978	+	0.216468i	−0.921724	−	0.387846i	$-0.873219\pi$
$263$	−2.02680	+	3.51052i	−0.124978	+	0.216468i	0.796747	+	0.604314i	$0.206553\pi$
$264$	2.85475	+	4.94457i	0.175698	+	0.304317i
$265$		−	30.3210i		−	1.86260i
$266$	5.62072	−	3.24513i	0.344629	−	0.198971i
$267$	4.52801	−	2.61425i	0.277110	−	0.159989i
$268$			4.38866i			0.268080i
$269$	−2.00011	−	3.46430i	−0.121949	−	0.211222i	0.798587	−	0.601879i	$-0.205581\pi$
$269$	−2.00011	−	3.46430i	−0.121949	−	0.211222i	−0.920536	+	0.390657i	$0.872248\pi$
$270$	8.95836	−	15.5163i	0.545188	−	0.944294i
$271$	−2.41189	−	1.39251i	−0.146512	−	0.0845888i	0.424952	−	0.905216i	$-0.360291\pi$
$271$	−2.41189	−	1.39251i	−0.146512	−	0.0845888i	−0.571464	+	0.820627i	$0.693624\pi$
$272$	−29.1806			−1.76933
$273$	−0.00645062	−	1.24732i	−0.000390409	−	0.0754913i
$274$	22.7651			1.37529
$275$	8.97733	+	5.18306i	0.541353	+	0.312551i
$276$	1.66403	−	2.88219i	0.100163	−	0.173487i
$277$	8.34618	+	14.4560i	0.501474	+	0.868578i	0.999999	+	0.00170243i	$0.000541901\pi$
$277$	8.34618	+	14.4560i	0.501474	+	0.868578i	−0.498525	+	0.866875i	$0.666125\pi$
$278$		−	47.6741i		−	2.85930i
$279$	−4.34619	+	2.50928i	−0.260200	+	0.150226i
$280$	25.2258	−	14.5641i	1.50753	−	0.870373i
$281$		−	13.3731i		−	0.797774i	−0.917000	−	0.398887i	$-0.869397\pi$
$281$		−	13.3731i		−	0.797774i	0.917000	−	0.398887i	$-0.130603\pi$
$282$	2.74834	+	4.76026i	0.163661	+	0.283470i
$283$	−9.44312	+	16.3560i	−0.561335	+	0.972261i	0.436045	+	0.899925i	$0.356379\pi$
$283$	−9.44312	+	16.3560i	−0.561335	+	0.972261i	−0.997380	+	0.0723362i	$0.976955\pi$
$284$	−10.8207	−	6.24731i	−0.642088	−	0.370710i
$285$	−2.70623			−0.160303
$286$	9.07663	+	15.5351i	0.536712	+	0.918609i
$287$	4.22131			0.249176
$288$	46.7827	+	27.0100i	2.75669	+	1.59158i
$289$	6.18199	−	10.7075i	0.363647	−	0.629855i
$290$	−12.0399	−	20.8537i	−0.707008	−	1.22457i
$291$		−	3.19370i		−	0.187218i
$292$	14.6841	−	8.47789i	0.859324	−	0.496131i
$293$	−2.95999	+	1.70895i	−0.172925	+	0.0998380i	−0.583964	−	0.811779i	$-0.698499\pi$
$293$	−2.95999	+	1.70895i	−0.172925	+	0.0998380i	0.411040	+	0.911617i	$0.365166\pi$
$294$			0.935168i			0.0545401i
$295$	17.5161	+	30.3388i	1.01983	+	1.76639i
$296$	−26.5329	+	45.9564i	−1.54220	+	2.67116i
$297$	−3.25224	−	1.87768i	−0.188714	−	0.108954i
$298$	10.8697			0.629663
$299$	3.23845	−	5.67675i	0.187284	−	0.328295i
$300$	−10.3101			−0.595252
$301$	−7.51903	−	4.34111i	−0.433390	−	0.250218i
$302$	−25.5465	+	44.2479i	−1.47004	+	2.54618i
$303$	−2.56407	−	4.44110i	−0.147302	−	0.255134i
$304$		−	32.5391i		−	1.86625i
$305$	28.5268	−	16.4699i	1.63344	−	0.943066i
$306$	14.5185	−	8.38225i	0.829966	−	0.479181i
$307$			16.3679i			0.934165i	0.884214	+	0.467083i	$0.154695\pi$
$307$			16.3679i			0.934165i	−0.884214	+	0.467083i	$0.845305\pi$
$308$	−4.89868	−	8.48477i	−0.279128	−	0.483464i
$309$	0.740826	−	1.28315i	0.0421441	−	0.0729958i
$310$	13.2896	+	7.67278i	0.754801	+	0.435785i
$311$	−23.6979			−1.34378			−0.671891	−	0.740650i	$-0.734518\pi$
$311$	−23.6979			−1.34378			−0.671891	+	0.740650i	$0.734518\pi$
$312$	−9.68614	−	5.52570i	−0.548370	−	0.312831i
$313$	−5.18025			−0.292805			−0.146403	−	0.989225i	$-0.546769\pi$
$313$	−5.18025			−0.292805			−0.146403	+	0.989225i	$0.546769\pi$
$314$	27.0941	+	15.6428i	1.52901	+	0.882774i
$315$	−4.69222	+	8.12716i	−0.264377	+	0.457914i
$316$	2.12798	+	3.68577i	0.119708	+	0.207341i
$317$			6.06537i			0.340665i	0.985387	+	0.170332i	$0.0544842\pi$
$317$			6.06537i			0.340665i	−0.985387	+	0.170332i	$0.945516\pi$
$318$	7.53697	−	4.35147i	0.422652	−	0.244018i
$319$	−4.37096	+	2.52358i	−0.244727	+	0.141293i
$320$		−	76.8686i		−	4.29709i
$321$	−3.30827	−	5.73010i	−0.184650	−	0.319823i
$322$	−2.44994	+	4.24343i	−0.136530	+	0.236477i
$323$	−4.47700	−	2.58480i	−0.249107	−	0.143822i
$324$	−42.1248			−2.34027
$325$	−20.2462	+	0.104705i	−1.12306	+	0.00580799i
$326$	11.9087			0.659562
$327$	1.27975	+	0.738866i	0.0707706	+	0.0408594i
$328$	18.8697	−	32.6833i	1.04190	−	1.80463i
$329$	−2.93887	−	5.09027i	−0.162025	−	0.280636i
$330$			5.62465i			0.309627i
$331$	14.9605	−	8.63743i	0.822301	−	0.474756i	−0.0289082	−	0.999582i	$-0.509203\pi$
$331$	14.9605	−	8.63743i	0.822301	−	0.474756i	0.851209	+	0.524826i	$0.175870\pi$
$332$	−45.8258	+	26.4576i	−2.51502	+	1.45205i
$333$		−	17.0966i		−	0.936886i
$334$	12.1902	+	21.1140i	0.667017	+	1.15531i
$335$	−1.34710	+	2.33324i	−0.0735998	+	0.127479i
$336$	4.06036	+	2.34425i	0.221511	+	0.127889i
$337$	−8.35464			−0.455106			−0.227553	−	0.973766i	$-0.573073\pi$
$337$	−8.35464			−0.455106			−0.227553	+	0.973766i	$0.573073\pi$
$338$	−30.6136	−	17.2551i	−1.66516	−	0.938552i
$339$	−0.951279			−0.0516664
$340$	−32.2435	−	18.6158i	−1.74865	−	1.00958i
$341$	1.60822	−	2.78552i	0.0870901	−	0.150844i
$342$	9.34700	+	16.1895i	0.505428	+	0.875427i
$343$		−	1.00000i		−	0.0539949i
$344$	−67.2216	+	38.8104i	−3.62435	+	2.09252i
$345$	1.76937	−	1.02155i	0.0952598	−	0.0549983i
$346$		−	16.4679i		−	0.885318i
$347$	−14.4110	−	24.9606i	−0.773623	−	1.33995i	−0.935565	−	0.353154i	$-0.885109\pi$
$347$	−14.4110	−	24.9606i	−0.773623	−	1.33995i	0.161942	−	0.986800i	$-0.448224\pi$
$348$	2.50993	−	4.34733i	0.134546	−	0.233041i
$349$	−10.1516	−	5.86103i	−0.543403	−	0.313734i	0.203054	−	0.979167i	$-0.434913\pi$
$349$	−10.1516	−	5.86103i	−0.543403	−	0.313734i	−0.746457	+	0.665434i	$0.768247\pi$
$350$	15.1794			0.811376
$351$	7.33464	−	0.0379317i	0.391494	−	0.00202464i
$352$	−34.6220			−1.84536
$353$	15.4466	+	8.91811i	0.822141	+	0.474663i	0.851154	−	0.524916i	$-0.175903\pi$
$353$	15.4466	+	8.91811i	0.822141	+	0.474663i	−0.0290134	+	0.999579i	$0.509237\pi$
$354$	−5.02759	+	8.70804i	−0.267213	+	0.462827i
$355$	−3.83521	−	6.64278i	−0.203552	−	0.352562i
$356$			80.2113i			4.25119i
$357$	0.645082	−	0.372438i	0.0341414	−	0.0197115i
$358$	−9.08239	+	5.24372i	−0.480019	+	0.277139i
$359$			5.68162i			0.299864i	0.988696	+	0.149932i	$0.0479055\pi$
$359$			5.68162i			0.299864i	−0.988696	+	0.149932i	$0.952094\pi$
$360$	41.9494	+	72.6584i	2.21093	+	3.82943i
$361$	−6.61771	+	11.4622i	−0.348300	+	0.603274i
$362$	15.4132	+	8.89882i	0.810100	+	0.467712i
$363$	−2.62651			−0.137856
$364$	16.6212	+	9.48199i	0.871188	+	0.496991i
$365$	10.4091			0.544838
$366$	8.18794	+	4.72731i	0.427991	+	0.247100i
$367$	9.81580	−	17.0015i	0.512381	−	0.887469i	−0.487516	−	0.873114i	$-0.662097\pi$
$367$	9.81580	−	17.0015i	0.512381	−	0.887469i	0.999897	−	0.0143554i	$-0.00456964\pi$
$368$	12.2829	+	21.2746i	0.640289	+	1.10901i
$369$			12.1587i			0.632958i
$370$	−45.2735	+	26.1387i	−2.35366	+	1.35888i
$371$	−8.05947	+	4.65314i	−0.418427	+	0.241579i
$372$			3.19905i			0.165863i
$373$	−16.0323	−	27.7687i	−0.830119	−	1.43781i	−0.897943	−	0.440111i	$-0.854939\pi$
$373$	−16.0323	−	27.7687i	−0.830119	−	1.43781i	0.0678240	−	0.997697i	$-0.478394\pi$
$374$	−5.37227	+	9.30505i	−0.277794	+	0.481153i
$375$	−0.600686	−	0.346806i	−0.0310193	−	0.0179090i
$376$	−52.5482			−2.70997
$377$	4.88468	−	8.56248i	0.251574	−	0.440990i
$378$	−5.49909			−0.282843
$379$	−16.4745	−	9.51154i	−0.846237	−	0.488575i	0.0131425	−	0.999914i	$-0.495816\pi$
$379$	−16.4745	−	9.51154i	−0.846237	−	0.488575i	−0.859379	+	0.511339i	$0.829150\pi$
$380$	20.7583	−	35.9545i	1.06488	−	1.84443i
$381$	1.68380	+	2.91643i	0.0862637	+	0.149413i
$382$		−	37.1510i		−	1.90081i
$383$	0.606070	−	0.349915i	0.0309687	−	0.0178798i	−0.484436	−	0.874827i	$-0.660975\pi$
$383$	0.606070	−	0.349915i	0.0309687	−	0.0178798i	0.515404	+	0.856947i	$0.327642\pi$
$384$	7.86948	−	4.54345i	0.401588	−	0.231857i
$385$		−	6.01459i		−	0.306532i
$386$	−30.7529	−	53.2657i	−1.56528	−	2.71115i
$387$	12.5038	−	21.6572i	0.635604	−	1.10090i
$388$	42.4310	+	24.4976i	2.15411	+	1.24368i
$389$	20.0547			1.01681			0.508407	−	0.861117i	$-0.330235\pi$
$389$	20.0547			1.01681			0.508407	+	0.861117i	$0.330235\pi$
$390$	−5.54200	−	9.48539i	−0.280630	−	0.480311i
$391$	3.90284			0.197375
$392$	−7.74244	−	4.47010i	−0.391052	−	0.225774i
$393$	−3.22796	+	5.59099i	−0.162829	+	0.282028i
$394$	19.6349	+	34.0086i	0.989192	+	1.71333i
$395$			2.61272i			0.131460i
$396$	24.4388	−	14.1098i	1.22810	−	0.709043i
$397$	−19.2953	+	11.1401i	−0.968403	+	0.559108i	−0.898749	−	0.438463i	$-0.855523\pi$
$397$	−19.2953	+	11.1401i	−0.968403	+	0.559108i	−0.0696541	+	0.997571i	$0.522190\pi$
$398$		−	64.4453i		−	3.23035i
$399$	0.415304	+	0.719328i	0.0207912	+	0.0360114i
$400$	38.0513	−	65.9069i	1.90257	−	3.29534i
$401$	−4.16341	−	2.40374i	−0.207911	−	0.120037i	0.392429	−	0.919782i	$-0.371635\pi$
$401$	−4.16341	−	2.40374i	−0.207911	−	0.120037i	−0.600340	+	0.799745i	$0.704968\pi$
$402$	−0.773306			−0.0385690
$403$	0.0324883	+	6.28208i	0.00161836	+	0.312933i
$404$	78.6717			3.91406
$405$	−22.3957	−	12.9302i	−1.11285	−	0.642506i
$406$	−3.69535	+	6.40054i	−0.183397	+	0.317653i
$407$	5.47869	+	9.48937i	0.271568	+	0.470370i
$408$		−	6.65935i		−	0.329687i
$409$	31.8727	−	18.4017i	1.57601	−	0.909907i	0.580597	−	0.814191i	$-0.302819\pi$
$409$	31.8727	−	18.4017i	1.57601	−	0.909907i	0.995409	−	0.0957164i	$-0.0305142\pi$
$410$	32.1976	−	18.5893i	1.59013	−	0.918060i
$411$			2.91343i			0.143709i
$412$	11.3651	+	19.6850i	0.559921	+	0.969811i
$413$	5.37613	−	9.31173i	0.264542	−	0.458200i
$414$	−12.2224	−	7.05662i	−0.600699	−	0.346814i
$415$	−32.4845			−1.59460
$416$	58.3864	−	34.1132i	2.86263	−	1.67254i
$417$	6.10122			0.298778
$418$	−10.3760	−	5.99059i	−0.507507	−	0.293009i
$419$	−14.6334	+	25.3457i	−0.714887	+	1.23822i	0.248116	+	0.968730i	$0.420188\pi$
$419$	−14.6334	+	25.3457i	−0.714887	+	1.23822i	−0.963003	+	0.269490i	$0.913145\pi$
$420$	2.99103	+	5.18062i	0.145947	+	0.252788i
$421$			7.53862i			0.367410i	0.982981	+	0.183705i	$0.0588091\pi$
$421$			7.53862i			0.367410i	−0.982981	+	0.183705i	$0.941191\pi$
$422$	10.1022	−	5.83251i	0.491768	−	0.283922i
$423$	14.6616	−	8.46489i	0.712872	−	0.411577i
$424$			83.2000i			4.04055i
$425$	−6.04534	−	10.4708i	−0.293242	−	0.507910i
$426$	1.10081	−	1.90666i	0.0533343	−	0.0923778i
$427$	−8.75558	−	5.05504i	−0.423712	−	0.244630i
$428$	101.506			4.90646
$429$	−1.98815	+	1.16161i	−0.0959886	+	0.0560829i
$430$	−76.4674			−3.68759
$431$	−27.0426	−	15.6131i	−1.30260	−	0.752055i	−0.321748	−	0.946825i	$-0.604270\pi$
$431$	−27.0426	−	15.6131i	−1.30260	−	0.752055i	−0.980849	+	0.194771i	$0.937604\pi$
$432$	−13.7849	+	23.8762i	−0.663228	+	1.14874i
$433$	2.94202	+	5.09573i	0.141384	+	0.244885i	0.928018	−	0.372535i	$-0.121511\pi$
$433$	2.94202	+	5.09573i	0.141384	+	0.244885i	−0.786634	+	0.617420i	$0.788178\pi$
$434$		−	4.70994i		−	0.226084i
$435$	2.66882	−	1.54084i	0.127960	−	0.0738777i
$436$	−19.6329	+	11.3351i	−0.940247	+	0.542852i
$437$			4.35204i			0.208186i
$438$	1.49385	+	2.58742i	0.0713788	+	0.123632i
$439$	−4.97821	+	8.62251i	−0.237597	+	0.411530i	−0.960024	−	0.279917i	$-0.909693\pi$
$439$	−4.97821	+	8.62251i	−0.237597	+	0.411530i	0.722427	+	0.691447i	$0.243026\pi$
$440$	−46.5676	−	26.8858i	−2.22002	−	1.28173i
$441$	2.88032			0.137158
$442$	−0.108527	−	20.9853i	−0.00516212	−	0.998170i
$443$	−35.8813			−1.70477			−0.852385	−	0.522915i	$-0.824845\pi$
$443$	−35.8813			−1.70477			−0.852385	+	0.522915i	$0.824845\pi$
$444$	−9.43805	−	5.44906i	−0.447910	−	0.258601i
$445$	−24.6208	+	42.6444i	−1.16714	+	2.02154i
$446$	31.6202	+	54.7678i	1.49726	+	2.59333i
$447$			1.39108i			0.0657956i
$448$	−20.4321	+	11.7965i	−0.965324	+	0.557330i
$449$	3.46001	−	1.99764i	0.163288	−	0.0942744i	−0.416129	−	0.909306i	$-0.636614\pi$
$449$	3.46001	−	1.99764i	0.163288	−	0.0942744i	0.579417	+	0.815031i	$0.303280\pi$
$450$			43.7217i			2.06106i
$451$	−3.89633	−	6.74864i	−0.183471	−	0.317781i
$452$	7.29687	−	12.6386i	0.343216	−	0.594467i
$453$	−5.66274	−	3.26939i	−0.266059	−	0.153609i
$454$	72.2371			3.39026
$455$	5.92620	+	10.1430i	0.277825	+	0.475510i
$456$	7.42580			0.347745
$457$	35.6995	+	20.6111i	1.66995	+	0.964147i	0.967660	+	0.252257i	$0.0811729\pi$
$457$	35.6995	+	20.6111i	1.66995	+	0.964147i	0.702291	+	0.711890i	$0.252160\pi$
$458$	4.06385	−	7.03880i	0.189891	−	0.328901i
$459$	2.19006	+	3.79329i	0.102223	+	0.177056i
$460$			31.3435i			1.46140i
$461$	21.4139	−	12.3633i	0.997343	−	0.575816i	0.0898818	−	0.995952i	$-0.471351\pi$
$461$	21.4139	−	12.3633i	0.997343	−	0.575816i	0.907461	+	0.420136i	$0.138018\pi$
$462$	1.49506	−	0.863173i	0.0695565	−	0.0401585i
$463$			24.4057i			1.13423i	0.823639	+	0.567115i	$0.191940\pi$
$463$			24.4057i			1.13423i	−0.823639	+	0.567115i	$0.808060\pi$
$464$	18.5268	+	32.0893i	0.860084	+	1.48971i
$465$	−0.981946	+	1.70078i	−0.0455366	+	0.0788718i
$466$	−27.4248	−	15.8337i	−1.27043	−	0.733482i
$467$	4.44860			0.205857			0.102928	−	0.994689i	$-0.467179\pi$
$467$	4.44860			0.205857			0.102928	+	0.994689i	$0.467179\pi$
$468$	−27.3111	+	47.8744i	−1.26246	+	2.21299i
$469$	0.826916			0.0381834
$470$	−44.8318	−	25.8837i	−2.06794	−	1.19392i
$471$	−2.00193	+	3.46744i	−0.0922441	+	0.159771i
$472$	−48.0637	−	83.2487i	−2.21231	−	3.83183i
$473$			16.0276i			0.736951i
$474$	−0.649451	+	0.374961i	−0.0298303	+	0.0172225i
$475$	11.6760	−	6.74113i	0.535730	−	0.309304i
$476$			11.4273i			0.523769i
$477$	−13.4025	−	23.2139i	−0.613660	−	1.06289i
$478$	−1.93004	+	3.34293i	−0.0882780	+	0.152902i
$479$	−27.4328	−	15.8383i	−1.25343	−	0.723671i	−0.281645	−	0.959519i	$-0.590880\pi$
$479$	−27.4328	−	15.8383i	−1.25343	−	0.723671i	−0.971790	+	0.235848i	$0.924213\pi$
$480$	21.1394			0.964879
$481$	−18.5892	−	10.6047i	−0.847593	−	0.483531i
$482$	7.24372			0.329942
$483$	−0.543065	−	0.313538i	−0.0247103	−	0.0142665i
$484$	20.1469	−	34.8954i	0.915767	−	1.58616i
$485$	15.0390	+	26.0483i	0.682887	+	1.18279i
$486$		−	23.9199i		−	1.08503i
$487$	23.3096	−	13.4578i	1.05626	−	0.609832i	0.131864	−	0.991268i	$-0.457904\pi$
$487$	23.3096	−	13.4578i	1.05626	−	0.609832i	0.924395	+	0.381436i	$0.124570\pi$
$488$	−78.2766	+	45.1930i	−3.54341	+	2.04579i
$489$			1.52405i			0.0689200i
$490$	−4.40367	−	7.62739i	−0.198938	−	0.344570i
$491$	4.86358	−	8.42396i	0.219490	−	0.380168i	−0.735162	−	0.677891i	$-0.762894\pi$
$491$	4.86358	−	8.42396i	0.219490	−	0.380168i	0.954652	+	0.297723i	$0.0962273\pi$
$492$	6.71215	+	3.87526i	0.302607	+	0.174710i
$493$	5.88682			0.265129
$494$	23.4006	−	0.121018i	1.05284	−	0.00544487i
$495$	17.3239			0.778653
$496$	−20.4498	−	11.8067i	−0.918225	−	0.530137i
$497$	−1.17712	+	2.03884i	−0.0528012	+	0.0914543i
$498$	−4.66196	−	8.07475i	−0.208907	−	0.361838i
$499$		−	7.87525i		−	0.352545i	−0.984341	−	0.176272i	$-0.943596\pi$
$499$		−	7.87525i		−	0.352545i	0.984341	−	0.176272i	$-0.0564039\pi$
$500$	9.21523	−	5.32042i	0.412118	−	0.237936i
$501$	−2.70213	+	1.56007i	−0.120722	+	0.0696989i
$502$		−	29.5565i		−	1.31917i
$503$	4.87603	+	8.44553i	0.217411	+	0.376568i	0.954016	−	0.299756i	$-0.0969053\pi$
$503$	4.87603	+	8.44553i	0.217411	+	0.376568i	−0.736604	+	0.676324i	$0.763572\pi$
$504$	12.8753	−	22.3007i	0.573512	−	0.993352i
$505$	41.8259	+	24.1482i	1.86123	+	1.07458i
$506$	9.04533			0.402114
$507$	2.20827	−	3.91786i	0.0980725	−	0.173998i
$508$	−51.6630			−2.29217
$509$	−19.9407	−	11.5128i	−0.883857	−	0.510295i	−0.0119288	−	0.999929i	$-0.503797\pi$
$509$	−19.9407	−	11.5128i	−0.883857	−	0.510295i	−0.871928	+	0.489634i	$0.837130\pi$
$510$	3.28019	−	5.68146i	0.145249	−	0.251579i
$511$	−1.59741	−	2.76680i	−0.0706653	−	0.122396i
$512$			11.8512i			0.523752i
$513$	−4.22988	+	2.44212i	−0.186754	+	0.107822i
$514$	−9.71853	+	5.61100i	−0.428666	+	0.247490i
$515$			13.9541i			0.614891i
$516$	−7.97048	−	13.8053i	−0.350881	−	0.607744i
$517$	−5.42524	+	9.39679i	−0.238602	+	0.413270i
$518$	13.8956	+	8.02261i	0.610537	+	0.352493i
$519$	2.10752			0.0925100
$520$	105.022	−	0.543130i	4.60552	−	0.0238178i
$521$	0.486481			0.0213131			0.0106566	−	0.999943i	$-0.496608\pi$
$521$	0.486481			0.0213131			0.0106566	+	0.999943i	$0.496608\pi$
$522$	−18.4356	−	10.6438i	−0.806904	−	0.465866i
$523$	17.3135	−	29.9878i	0.757065	−	1.31128i	−0.187275	−	0.982307i	$-0.559966\pi$
$523$	17.3135	−	29.9878i	0.757065	−	1.31128i	0.944341	−	0.328968i	$-0.106701\pi$
$524$	−49.5207	−	85.7724i	−2.16332	−	3.74698i
$525$			1.94263i			0.0847834i
$526$	9.48962	−	5.47883i	0.413767	−	0.238888i
$527$	−3.24893	+	1.87577i	−0.141526	+	0.0817099i
$528$		−	8.65510i		−	0.376665i
$529$	9.85719	+	17.0732i	0.428574	+	0.742311i
$530$	−40.9818	+	70.9826i	−1.78014	+	3.08329i
$531$	26.8208	+	15.4850i	1.16392	+	0.671990i
$532$	−12.7425			−0.552458
$533$	13.2202	+	7.54182i	0.572632	+	0.326672i
$534$	−14.1336			−0.611622
$535$	53.9656	+	31.1571i	2.33314	+	1.34704i
$536$	3.69639	−	6.40234i	0.159660	−	0.276539i
$537$	−0.671080	−	1.16234i	−0.0289592	−	0.0501589i
$538$			10.8134i			0.466198i
$539$	−1.59871	+	0.923014i	−0.0688612	+	0.0397570i
$540$	−30.4637	+	17.5882i	−1.31095	+	0.756876i
$541$		−	22.5384i		−	0.969002i	−0.874791	−	0.484501i	$-0.839001\pi$
$541$		−	22.5384i		−	0.969002i	0.874791	−	0.484501i	$-0.160999\pi$
$542$	3.76422	+	6.51982i	0.161687	+	0.280050i
$543$	−1.13885	+	1.97255i	−0.0488728	+	0.0846502i
$544$	34.9717	+	20.1909i	1.49940	+	0.865678i
$545$	−13.9172			−0.596146
$546$	−1.67078	+	2.92874i	−0.0715026	+	0.125339i
$547$	39.3716			1.68341			0.841704	−	0.539940i	$-0.181553\pi$
$547$	39.3716			1.68341			0.841704	+	0.539940i	$0.181553\pi$
$548$	−38.7074	−	22.3477i	−1.65350	−	0.954648i
$549$	14.5601	−	25.2189i	0.621411	−	1.07631i
$550$	−14.0108	−	24.2675i	−0.597424	−	1.03477i
$551$			6.56436i			0.279651i
$552$	−4.85510	+	2.80310i	−0.206647	+	0.119308i
$553$	0.694475	−	0.400955i	0.0295321	−	0.0170504i
$554$		−	45.1227i		−	1.91708i
$555$	−3.34517	−	5.79401i	−0.141995	−	0.245942i
$556$	−46.8000	+	81.0600i	−1.98476	+	3.43771i
$557$	0.629579	+	0.363487i	0.0266761	+	0.0154015i	0.513279	−	0.858222i	$-0.328431\pi$
$557$	0.629579	+	0.363487i	0.0266761	+	0.0154015i	−0.486603	+	0.873623i	$0.661764\pi$
$558$	13.5661			0.574300
$559$	−15.7921	−	27.0289i	−0.667935	−	1.14320i
$560$	−44.1559			−1.86593
$561$	−1.19084	−	0.687532i	−0.0502773	−	0.0290276i
$562$	−18.0751	+	31.3070i	−0.762452	+	1.32061i
$563$	20.8038	+	36.0333i	0.876777	+	1.51862i	0.854857	+	0.518863i	$0.173645\pi$
$563$	20.8038	+	36.0333i	0.876777	+	1.51862i	0.0219200	+	0.999760i	$0.493022\pi$
$564$		−	10.7918i		−	0.454417i
$565$	7.75879	−	4.47954i	0.326415	−	0.188456i
$566$	44.2134	−	25.5266i	1.85843	−	1.07296i
$567$			7.93720i			0.333331i
$568$	10.5237	+	18.2276i	0.441565	+	0.764813i
$569$	−12.6944	+	21.9873i	−0.532177	+	0.921757i	0.467118	+	0.884195i	$0.345292\pi$
$569$	−12.6944	+	21.9873i	−0.532177	+	0.921757i	−0.999294	+	0.0375618i	$0.988041\pi$
$570$	6.33537	+	3.65773i	0.265360	+	0.153205i
$571$	−16.9992			−0.711393			−0.355697	−	0.934602i	$-0.615756\pi$
$571$	−16.9992			−0.711393			−0.355697	+	0.934602i	$0.615756\pi$
$572$	−0.182683	−	35.3244i	−0.00763836	−	1.47699i
$573$	4.75451			0.198622
$574$	−9.88225	−	5.70552i	−0.412477	−	0.238144i
$575$	−5.08929	+	8.81490i	−0.212238	+	0.367607i
$576$	−33.9776	−	58.8508i	−1.41573	−	2.45212i
$577$			15.9759i			0.665084i	0.943088	+	0.332542i	$0.107906\pi$
$577$			15.9759i			0.665084i	−0.943088	+	0.332542i	$0.892094\pi$
$578$	−28.9445	+	16.7111i	−1.20393	+	0.695092i
$579$	6.81682	−	3.93570i	0.283298	−	0.163562i
$580$			47.2767i			1.96306i
$581$	4.98516	+	8.63454i	0.206819	+	0.358221i
$582$	−4.31660	+	7.47657i	−0.178929	+	0.309914i
$583$	14.8780	+	8.58982i	0.616184	+	0.355754i
$584$	−28.5623			−1.18192
$585$	−29.2150	+	17.0693i	−1.20789	+	0.705731i
$586$	9.23926			0.381670
$587$	−13.8404	−	7.99075i	−0.571254	−	0.329814i	0.186396	−	0.982475i	$-0.440319\pi$
$587$	−13.8404	−	7.99075i	−0.571254	−	0.329814i	−0.757650	+	0.652661i	$0.773653\pi$
$588$	0.918023	−	1.59006i	0.0378586	−	0.0655730i
$589$	−2.09166	−	3.62287i	−0.0861855	−	0.149278i
$590$		−	94.6989i		−	3.89869i
$591$	−4.35235	+	2.51283i	−0.179032	+	0.103364i
$592$	69.6660	−	40.2217i	2.86325	−	1.65310i
$593$			29.0532i			1.19307i	0.802586	+	0.596536i	$0.203457\pi$
$593$			29.0532i			1.19307i	−0.802586	+	0.596536i	$0.796543\pi$
$594$	5.07574	+	8.79143i	0.208260	+	0.360717i
$595$	−3.50760	+	6.07534i	−0.143797	+	0.249065i
$596$	−18.4816	−	10.6704i	−0.757037	−	0.437075i
$597$	8.24757			0.337551
$598$	−15.2540	+	8.91240i	−0.623783	+	0.364455i
$599$	3.45554			0.141190			0.0705948	−	0.997505i	$-0.477510\pi$
$599$	3.45554			0.141190			0.0705948	+	0.997505i	$0.477510\pi$
$600$	15.0407	+	8.68376i	0.614035	+	0.354513i
$601$	−7.76518	+	13.4497i	−0.316748	+	0.548624i	−0.979808	−	0.199943i	$-0.935924\pi$
$601$	−7.76518	+	13.4497i	−0.316748	+	0.548624i	0.663059	+	0.748567i	$0.269258\pi$
$602$	11.7349	+	20.3254i	0.478278	+	0.828402i
$603$			2.38178i			0.0969936i
$604$	86.8732	−	50.1563i	3.53482	−	2.04083i
$605$	21.4222	−	12.3681i	0.870938	−	0.502836i
$606$			13.8624i			0.563120i
$607$	−7.73922	−	13.4047i	−0.314125	−	0.544081i	0.665126	−	0.746731i	$-0.268378\pi$
$607$	−7.73922	−	13.4047i	−0.314125	−	0.544081i	−0.979251	+	0.202650i	$0.935044\pi$
$608$	−22.5148	+	38.9967i	−0.913095	+	1.58153i
$609$	−0.819127	−	0.472923i	−0.0331927	−	0.0191638i
$610$	−89.0429			−3.60524
$611$	−0.109597	−	21.1922i	−0.00443383	−	0.857345i
$612$	−32.9142			−1.33048
$613$	−6.17669	−	3.56611i	−0.249474	−	0.144034i	0.370049	−	0.929012i	$-0.379341\pi$
$613$	−6.17669	−	3.56611i	−0.249474	−	0.144034i	−0.619523	+	0.784978i	$0.712674\pi$
$614$	22.1228	−	38.3178i	0.892804	−	1.54638i
$615$	2.37902	+	4.12058i	0.0959312	+	0.166158i
$616$			16.5039i			0.664959i
$617$	−4.30142	+	2.48342i	−0.173168	+	0.0999789i	−0.584079	−	0.811697i	$-0.698544\pi$
$617$	−4.30142	+	2.48342i	−0.173168	+	0.0999789i	0.410911	+	0.911676i	$0.365211\pi$
$618$	−3.46860	+	2.00260i	−0.139528	+	0.0805563i
$619$			42.3570i			1.70247i	0.524784	+	0.851235i	$0.324146\pi$
$619$			42.3570i			1.70247i	−0.524784	+	0.851235i	$0.675854\pi$
$620$	−15.0642	−	26.0920i	−0.604993	−	1.04788i
$621$	1.84371	−	3.19339i	0.0739854	−	0.128146i
$622$	55.4776	+	32.0300i	2.22445	+	1.28429i
$623$	15.1135			0.605508
$624$	8.52791	+	14.5959i	0.341390	+	0.584305i
$625$	−21.5445			−0.861779
$626$	12.1272	+	7.00162i	0.484699	+	0.279841i
$627$	0.766663	−	1.32790i	0.0306176	−	0.0530312i
$628$	−30.7120	−	53.1947i	−1.22554	−	2.12270i
$629$		−	12.7803i		−	0.509583i
$630$	21.9693	−	12.6840i	0.875278	−	0.505342i
$631$	−5.42803	+	3.13387i	−0.216086	+	0.124758i	−0.604137	−	0.796881i	$-0.706482\pi$
$631$	−5.42803	+	3.13387i	−0.216086	+	0.124758i	0.388050	+	0.921638i	$0.373149\pi$
$632$		−	7.16924i		−	0.285177i
$633$	0.746432	+	1.29286i	0.0296680	+	0.0513865i
$634$	8.19794	−	14.1992i	0.325582	−	0.563924i
$635$	−27.4667	−	15.8579i	−1.08998	−	0.629302i
$636$	−17.0868			−0.677534
$637$	1.78660	−	3.13178i	0.0707878	−	0.124086i
$638$	13.6434			0.540149
$639$	−5.87250	−	3.39049i	−0.232313	−	0.134126i
$640$	−42.7898	+	74.1142i	−1.69142	+	2.92962i
$641$	−15.7818	−	27.3350i	−0.623345	−	1.07967i	−0.988858	−	0.148860i	$-0.952440\pi$
$641$	−15.7818	−	27.3350i	−0.623345	−	1.07967i	0.365513	−	0.930806i	$-0.380894\pi$
$642$			17.8858i			0.705897i
$643$	15.8053	−	9.12520i	0.623300	−	0.359863i	−0.154852	−	0.987938i	$-0.549490\pi$
$643$	15.8053	−	9.12520i	0.623300	−	0.359863i	0.778153	+	0.628075i	$0.216157\pi$
$644$	8.33125	−	4.81005i	0.328297	−	0.189543i
$645$		−	9.78613i		−	0.385329i
$646$	6.98721	+	12.1022i	0.274908	+	0.476155i
$647$	11.5137	−	19.9423i	0.452649	−	0.784011i	−0.545901	−	0.837850i	$-0.683812\pi$
$647$	11.5137	−	19.9423i	0.452649	−	0.784011i	0.998550	+	0.0538387i	$0.0171457\pi$
$648$	61.4532	+	35.4800i	2.41411	+	1.39379i
$649$	−19.8490			−0.779140
$650$	47.5387	+	27.1197i	1.86462	+	1.06372i
$651$	0.602768			0.0236243
$652$	−20.2483	−	11.6904i	−0.792985	−	0.457830i
$653$	−14.4062	+	24.9523i	−0.563759	+	0.976459i	0.433405	+	0.901199i	$0.357312\pi$
$653$	−14.4062	+	24.9523i	−0.563759	+	0.976459i	−0.997164	+	0.0752597i	$0.976021\pi$
$654$	−1.99730	−	3.45943i	−0.0781006	−	0.135274i
$655$		−	60.8014i		−	2.37571i
$656$	−49.5450	+	28.6048i	−1.93441	+	1.11683i
$657$	7.96926	−	4.60105i	0.310910	−	0.179504i
$658$			15.8887i			0.619406i
$659$	15.6114	+	27.0397i	0.608134	+	1.05332i	0.991548	+	0.129742i	$0.0414149\pi$
$659$	15.6114	+	27.0397i	0.608134	+	1.05332i	−0.383414	+	0.923577i	$0.625252\pi$
$660$	5.52153	−	9.56356i	0.214925	−	0.372261i
$661$	−23.0000	−	13.2791i	−0.894598	−	0.516496i	−0.0191541	−	0.999817i	$-0.506097\pi$
$661$	−23.0000	−	13.2791i	−0.894598	−	0.516496i	−0.875444	+	0.483320i	$0.839431\pi$
$662$	−46.6973			−1.81494
$663$	2.68566	−	0.0138891i	0.104302	−	0.000539407i
$664$	89.1366			3.45917
$665$	−6.77458	−	3.91130i	−0.262707	−	0.151674i
$666$	−23.1077	+	40.0237i	−0.895405	+	1.55089i
$667$	−2.47792	−	4.29188i	−0.0959454	−	0.166182i
$668$		−	47.8667i		−	1.85202i
$669$	−7.00906	+	4.04668i	−0.270986	+	0.156454i
$670$	6.30721	−	3.64147i	0.243669	−	0.140682i
$671$			18.6635i			0.720495i
$672$	−3.24411	−	5.61897i	−0.125144	−	0.216756i
$673$	−9.86930	+	17.0941i	−0.380434	+	0.658930i	−0.991124	−	0.132939i	$-0.957559\pi$
$673$	−9.86930	+	17.0941i	−0.380434	+	0.658930i	0.610691	+	0.791869i	$0.290892\pi$
$674$	19.5585	+	11.2921i	0.753366	+	0.434956i
$675$	−11.4233			−0.439683
$676$	35.1134	+	59.3910i	1.35052	+	2.28427i
$677$	−13.1440			−0.505163			−0.252582	−	0.967576i	$-0.581280\pi$
$677$	−13.1440			−0.505163			−0.252582	+	0.967576i	$0.581280\pi$
$678$	2.22698	+	1.28575i	0.0855266	+	0.0493788i
$679$	4.61585	−	7.99489i	0.177140	−	0.306816i
$680$	31.3586	+	54.3147i	1.20255	+	2.08287i
$681$			9.24475i			0.354260i
$682$	−7.52981	+	4.34734i	−0.288331	+	0.166468i
$683$	−5.85654	+	3.38128i	−0.224094	+	0.129381i	−0.607845	−	0.794056i	$-0.707966\pi$
$683$	−5.85654	+	3.38128i	−0.224094	+	0.129381i	0.383750	+	0.923437i	$0.374632\pi$
$684$		−	36.7025i		−	1.40336i
$685$	−13.7192	−	23.7624i	−0.524185	−	0.907915i
$686$	−1.35160	+	2.34104i	−0.0516043	+	0.0893812i
$687$	0.900810	+	0.520083i	0.0343681	+	0.0198424i
$688$	117.666			4.48599
$689$	−33.5538	+	0.173526i	−1.27830	+	0.00661082i
$690$	−5.52288			−0.210253
$691$	7.94223	+	4.58545i	0.302137	+	0.174439i	0.643402	−	0.765528i	$-0.277522\pi$
$691$	7.94223	+	4.58545i	0.302137	+	0.174439i	−0.341266	+	0.939967i	$0.610856\pi$
$692$	−16.1659	+	28.0002i	−0.614537	+	1.06441i
$693$	−2.65857	−	4.60479i	−0.100991	−	0.174921i
$694$			77.9115i			2.95748i
$695$	−49.7626	+	28.7304i	−1.88760	+	1.08981i
$696$	−7.32316	+	4.22803i	−0.277584	+	0.160263i
$697$			9.08908i			0.344273i
$698$	15.8435	+	27.4418i	0.599686	+	1.03869i
$699$	2.02636	−	3.50976i	0.0766440	−	0.132751i
$700$	−25.8095	−	14.9011i	−0.975509	−	0.563210i
$701$	47.4700			1.79292			0.896459	−	0.443127i	$-0.146131\pi$
$701$	47.4700			1.79292			0.896459	+	0.443127i	$0.146131\pi$
$702$	−17.2219	−	9.82469i	−0.650000	−	0.370809i
$703$	14.2512			0.537495
$704$	37.7181	+	21.7766i	1.42156	+	0.820736i
$705$	3.31253	−	5.73748i	0.124757	−	0.216086i
$706$	−24.1074	−	41.7552i	−0.907294	−	1.57148i
$707$		−	14.8234i		−	0.557491i
$708$	17.0968	−	9.87082i	0.642535	−	0.370968i
$709$	30.2866	−	17.4860i	1.13744	−	0.656699i	0.191642	−	0.981465i	$-0.438619\pi$
$709$	30.2866	−	17.4860i	1.13744	−	0.656699i	0.945795	+	0.324766i	$0.105285\pi$
$710$			20.7347i			0.778158i
$711$	1.15488	+	2.00031i	0.0433114	+	0.0750175i
$712$	67.5587	−	117.015i	2.53187	−	4.38533i
$713$	2.73512	+	1.57912i	0.102431	+	0.0591387i
$714$	−2.01355			−0.0753552
$715$	10.7457	−	18.8364i	0.401866	−	0.704440i
$716$	20.5903			0.769496
$717$	−0.427821	−	0.247002i	−0.0159773	−	0.00922448i
$718$	7.67926	−	13.3009i	0.286588	−	0.496384i
$719$	−4.18051	−	7.24085i	−0.155907	−	0.270038i	0.777482	−	0.628905i	$-0.216497\pi$
$719$	−4.18051	−	7.24085i	−0.155907	−	0.270038i	−0.933389	+	0.358867i	$0.883163\pi$
$720$		−	127.183i		−	4.73984i
$721$	3.70907	−	2.14143i	0.138133	−	0.0797511i
$722$	30.9846	−	17.8890i	1.15313	−	0.665758i
$723$			0.927035i			0.0344768i
$724$	−17.4713	−	30.2612i	−0.649317	−	1.12465i
$725$	−7.67639	+	13.2959i	−0.285094	+	0.493797i
$726$	6.14875	+	3.54998i	0.228202	+	0.131752i
$727$	−27.4014			−1.01626			−0.508131	−	0.861280i	$-0.669663\pi$
$727$	−27.4014			−1.01626			−0.508131	+	0.861280i	$0.669663\pi$
$728$	−16.2613	−	27.8320i	−0.602685	−	1.03152i
$729$	−20.7504			−0.768532
$730$	−24.3681	−	14.0689i	−0.901905	−	0.520715i
$731$	9.34703	−	16.1895i	0.345712	−	0.598791i
$732$	−9.28127	−	16.0756i	−0.343046	−	0.594173i
$733$			12.1569i			0.449026i	0.974471	+	0.224513i	$0.0720792\pi$
$733$			12.1569i			0.449026i	−0.974471	+	0.224513i	$0.927921\pi$
$734$	−45.9583	+	26.5340i	−1.69635	+	0.979389i
$735$	0.976136	−	0.563573i	0.0360053	−	0.0207877i
$736$		−	33.9956i		−	1.25309i
$737$	−0.763255	−	1.32200i	−0.0281148	−	0.0486963i
$738$	16.4337	−	28.4640i	0.604934	−	1.04778i
$739$	−41.9537	−	24.2220i	−1.54329	−	0.891019i	−0.998628	−	0.0523634i	$-0.983325\pi$
$739$	−41.9537	−	24.2220i	−1.54329	−	0.891019i	−0.544662	−	0.838656i	$-0.683342\pi$
$740$	102.638			3.77304
$741$	0.0154876	+	2.99476i	0.000568953	+	0.110015i
$742$	25.1567			0.923531
$743$	−14.7143	−	8.49532i	−0.539816	−	0.311663i	0.205188	−	0.978722i	$-0.434219\pi$
$743$	−14.7143	−	8.49532i	−0.539816	−	0.311663i	−0.745004	+	0.667060i	$0.767553\pi$
$744$	2.69443	−	4.66689i	0.0987826	−	0.171097i
$745$	−6.55052	−	11.3458i	−0.239993	−	0.415679i
$746$			86.6767i			3.17346i
$747$	−24.8702	+	14.3588i	−0.909955	+	0.525363i
$748$	18.2689	−	10.5475i	0.667977	−	0.385657i
$749$		−	19.1258i		−	0.698841i
$750$	0.937485	+	1.62377i	0.0342321	+	0.0592917i
$751$	21.5162	−	37.2671i	0.785136	−	1.35990i	−0.143781	−	0.989610i	$-0.545926\pi$
$751$	21.5162	−	37.2671i	0.785136	−	1.35990i	0.928918	−	0.370287i	$-0.120741\pi$
$752$	68.9863	+	39.8292i	2.51567	+	1.45242i
$753$	3.78258			0.137845
$754$	−23.0083	+	13.4430i	−0.837911	+	0.489563i
$755$	61.5817			2.24119
$756$	9.35007	+	5.39827i	0.340059	+	0.196333i
$757$	−14.5892	+	25.2693i	−0.530255	+	0.918428i	0.469122	+	0.883133i	$0.344570\pi$
$757$	−14.5892	+	25.2693i	−0.530255	+	0.918428i	−0.999377	+	0.0352949i	$0.988763\pi$
$758$	25.7116	+	44.5337i	0.933886	+	1.61754i
$759$			1.15760i			0.0420183i
$760$	−60.5661	+	34.9678i	−2.19696	+	1.26842i
$761$	−25.4829	+	14.7126i	−0.923754	+	0.533330i	−0.884831	−	0.465912i	$-0.845726\pi$
$761$	−25.4829	+	14.7126i	−0.923754	+	0.533330i	−0.0389234	+	0.999242i	$0.512393\pi$
$762$		−	9.10328i		−	0.329777i
$763$	2.13577	+	3.69925i	0.0773199	+	0.133922i
$764$	−36.4699	+	63.1677i	−1.31943	+	2.28533i
$765$	−17.4989	−	10.1030i	−0.632675	−	0.365275i
$766$	−1.89178			−0.0683526
$767$	33.4732	−	19.5573i	1.20865	−	0.706172i
$768$	−8.23976			−0.297327
$769$	14.8839	+	8.59322i	0.536727	+	0.309879i	0.743751	−	0.668456i	$-0.233045\pi$
$769$	14.8839	+	8.59322i	0.536727	+	0.309879i	−0.207024	+	0.978336i	$0.566378\pi$
$770$	−8.12930	+	14.0804i	−0.292960	+	0.507421i

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.34104 - 1.35160i) q^{2} +(0.172975 - 0.299601i) q^{3} +(2.65363 + 4.59623i) q^{4} +3.25812i q^{5} +(-0.809880 + 0.467584i) q^{6} +(0.866025 - 0.500000i) q^{7} -8.94020i q^{8} +(1.44016 + 2.49443i) q^{9} +O(q^{10})\)	\(q+(-2.34104 - 1.35160i) q^{2} +(0.172975 - 0.299601i) q^{3} +(2.65363 + 4.59623i) q^{4} +3.25812i q^{5} +(-0.809880 + 0.467584i) q^{6} +(0.866025 - 0.500000i) q^{7} -8.94020i q^{8} +(1.44016 + 2.49443i) q^{9} +(4.40367 - 7.62739i) q^{10} +(-1.59871 - 0.923014i) q^{11} +1.83605 q^{12} +(3.60550 - 0.0186461i) q^{13} -2.70320 q^{14} +(0.976136 + 0.563573i) q^{15} +(-6.77628 + 11.7369i) q^{16} +(1.07657 + 1.86467i) q^{17} -7.78607i q^{18} +(-2.07929 + 1.20048i) q^{19} +(-14.9751 + 8.64587i) q^{20} -0.345949i q^{21} +(2.49509 + 4.32162i) q^{22} +(0.906314 - 1.56978i) q^{23} +(-2.67849 - 1.54643i) q^{24} -5.61537 q^{25} +(-8.46582 - 4.82954i) q^{26} +2.03429 q^{27} +(4.59623 + 2.65363i) q^{28} +(1.36703 - 2.36777i) q^{29} +(-1.52345 - 2.63869i) q^{30} +1.74236i q^{31} +(16.2422 - 9.37743i) q^{32} +(-0.553071 + 0.319316i) q^{33} -5.82036i q^{34} +(1.62906 + 2.82162i) q^{35} +(-7.64331 + 13.2386i) q^{36} +(-5.14042 - 2.96783i) q^{37} +6.49025 q^{38} +(0.618074 - 1.08344i) q^{39} +29.1283 q^{40} +(3.65577 + 2.11066i) q^{41} +(-0.467584 + 0.809880i) q^{42} +(-4.34111 - 7.51903i) q^{43} -9.79737i q^{44} +(-8.12716 + 4.69222i) q^{45} +(-4.24343 + 2.44994i) q^{46} -5.87774i q^{47} +(2.34425 + 4.06036i) q^{48} +(0.500000 - 0.866025i) q^{49} +(13.1458 + 7.58972i) q^{50} +0.744877 q^{51} +(9.65339 + 16.5222i) q^{52} -9.30628 q^{53} +(-4.76235 - 2.74954i) q^{54} +(3.00729 - 5.20878i) q^{55} +(-4.47010 - 7.74244i) q^{56} +0.830609i q^{57} +(-6.40054 + 3.69535i) q^{58} +(9.31173 - 5.37613i) q^{59} +5.98206i q^{60} +(-5.05504 - 8.75558i) q^{61} +(2.35497 - 4.07893i) q^{62} +(2.49443 + 1.44016i) q^{63} -23.5929 q^{64} +(0.0607514 + 11.7472i) q^{65} +1.72635 q^{66} +(0.716130 + 0.413458i) q^{67} +(-5.71365 + 9.89633i) q^{68} +(-0.313538 - 0.543065i) q^{69} -8.80735i q^{70} +(-2.03884 + 1.17712i) q^{71} +(22.3007 - 12.8753i) q^{72} -3.19482i q^{73} +(8.02261 + 13.8956i) q^{74} +(-0.971316 + 1.68237i) q^{75} +(-11.0353 - 6.37126i) q^{76} -1.84603 q^{77} +(-2.91130 + 1.70098i) q^{78} +0.801911 q^{79} +(-38.2402 - 22.0780i) q^{80} +(-3.96860 + 6.87381i) q^{81} +(-5.70552 - 9.88225i) q^{82} +9.97031i q^{83} +(1.59006 - 0.918023i) q^{84} +(-6.07534 + 3.50760i) q^{85} +23.4698i q^{86} +(-0.472923 - 0.819127i) q^{87} +(-8.25193 + 14.2928i) q^{88} +(13.0886 + 7.55674i) q^{89} +25.3680 q^{90} +(3.11313 - 1.81890i) q^{91} +9.62010 q^{92} +(0.522012 + 0.301384i) q^{93} +(-7.94435 + 13.7600i) q^{94} +(-3.91130 - 6.77458i) q^{95} -6.48823i q^{96} +(7.99489 - 4.61585i) q^{97} +(-2.34104 + 1.35160i) q^{98} -5.31715i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9	\( 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9} + 12 q^{10} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 8 q^{14} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 12 q^{24} - 20 q^{25} - 42 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} - 30 q^{33} + 6 q^{35} - 10 q^{36} - 42 q^{37} + 4 q^{38} - 4 q^{39} + 92 q^{40} + 30 q^{41} + 4 q^{42} + 2 q^{43} + 12 q^{46} - 2 q^{48} + 6 q^{49} - 18 q^{50} + 52 q^{51} + 2 q^{52} - 44 q^{53} + 12 q^{54} - 6 q^{55} - 12 q^{56} - 12 q^{58} + 18 q^{59} + 14 q^{61} - 4 q^{62} + 12 q^{63} - 52 q^{64} + 60 q^{65} - 52 q^{66} - 24 q^{67} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} + 46 q^{75} - 18 q^{76} + 8 q^{77} - 10 q^{78} - 56 q^{79} - 72 q^{80} + 2 q^{81} + 14 q^{82} + 18 q^{84} - 48 q^{85} - 2 q^{87} - 14 q^{88} - 12 q^{89} + 24 q^{90} + 14 q^{91} + 24 q^{92} - 18 q^{93} + 4 q^{94} - 22 q^{95} + 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9 + 12 * q^10 + 6 * q^11 - 4 * q^12 + 4 * q^13 - 8 * q^14 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 12 * q^24 - 20 * q^25 - 42 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 - 30 * q^33 + 6 * q^35 - 10 * q^36 - 42 * q^37 + 4 * q^38 - 4 * q^39 + 92 * q^40 + 30 * q^41 + 4 * q^42 + 2 * q^43 + 12 * q^46 - 2 * q^48 + 6 * q^49 - 18 * q^50 + 52 * q^51 + 2 * q^52 - 44 * q^53 + 12 * q^54 - 6 * q^55 - 12 * q^56 - 12 * q^58 + 18 * q^59 + 14 * q^61 - 4 * q^62 + 12 * q^63 - 52 * q^64 + 60 * q^65 - 52 * q^66 - 24 * q^67 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 + 46 * q^75 - 18 * q^76 + 8 * q^77 - 10 * q^78 - 56 * q^79 - 72 * q^80 + 2 * q^81 + 14 * q^82 + 18 * q^84 - 48 * q^85 - 2 * q^87 - 14 * q^88 - 12 * q^89 + 24 * q^90 + 14 * q^91 + 24 * q^92 - 18 * q^93 + 4 * q^94 - 22 * q^95 + 6 * q^97

Introduction

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