LMFDB - Embedded newform 170.2.r.a.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(23,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([12, 15]))

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

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

chi := DirichletCharacter("170.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.r (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	170.37
Dual form			170.2.r.a.23.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.923880 - 0.382683i) q^{2} +(2.33925 - 1.56304i) q^{3} +(0.707107 + 0.707107i) q^{4} +(0.438207 - 2.19271i) q^{5} +(-2.75933 + 0.548865i) q^{6} +(-1.27851 + 0.254312i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(1.88095 - 4.54102i) q^{9} +O(q^{10})$	\(q+(-0.923880 - 0.382683i) q^{2} +(2.33925 - 1.56304i) q^{3} +(0.707107 + 0.707107i) q^{4} +(0.438207 - 2.19271i) q^{5} +(-2.75933 + 0.548865i) q^{6} +(-1.27851 + 0.254312i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(1.88095 - 4.54102i) q^{9} +(-1.24396 + 1.85810i) q^{10} +(1.14054 + 5.73386i) q^{11} +(2.75933 + 0.548865i) q^{12} -5.33794 q^{13} +(1.27851 + 0.254312i) q^{14} +(-2.40221 - 5.81423i) q^{15} +1.00000i q^{16} +(3.93717 + 1.22423i) q^{17} +(-3.47555 + 3.47555i) q^{18} +(0.311731 + 0.752584i) q^{19} +(1.86034 - 1.24062i) q^{20} +(-2.59326 + 2.59326i) q^{21} +(1.14054 - 5.73386i) q^{22} +(3.88994 - 5.82170i) q^{23} +(-2.33925 - 1.56304i) q^{24} +(-4.61595 - 1.92172i) q^{25} +(4.93161 + 2.04274i) q^{26} +(-1.05117 - 5.28458i) q^{27} +(-1.08387 - 0.724218i) q^{28} +(1.17050 + 1.75178i) q^{29} +(-0.00565639 + 6.29093i) q^{30} +(0.301321 - 1.51484i) q^{31} +(0.382683 - 0.923880i) q^{32} +(11.6302 + 11.6302i) q^{33} +(-3.16897 - 2.63773i) q^{34} +(-0.00262084 + 2.91484i) q^{35} +(4.54102 - 1.88095i) q^{36} +(3.87014 + 5.79208i) q^{37} -0.814591i q^{38} +(-12.4868 + 8.34339i) q^{39} +(-2.19349 + 0.434263i) q^{40} +(-4.40455 + 6.59188i) q^{41} +(3.38825 - 1.40346i) q^{42} +(-1.31384 + 0.544211i) q^{43} +(-3.24797 + 4.86093i) q^{44} +(-9.13290 - 6.11429i) q^{45} +(-5.82170 + 3.88994i) q^{46} -0.109944i q^{47} +(1.56304 + 2.33925i) q^{48} +(-4.89724 + 2.02850i) q^{49} +(3.52917 + 3.54189i) q^{50} +(11.1235 - 3.29016i) q^{51} +(-3.77449 - 3.77449i) q^{52} +(0.379151 - 0.915351i) q^{53} +(-1.05117 + 5.28458i) q^{54} +(13.0725 + 0.0117539i) q^{55} +(0.724218 + 1.08387i) q^{56} +(1.90553 + 1.27324i) q^{57} +(-0.411026 - 2.06637i) q^{58} +(5.08359 + 2.10569i) q^{59} +(2.41266 - 5.80990i) q^{60} +(-4.82682 - 3.22518i) q^{61} +(-0.858089 + 1.28422i) q^{62} +(-1.24998 + 6.28410i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(-2.33912 + 11.7045i) q^{65} +(-6.29423 - 15.1956i) q^{66} +(4.12405 - 4.12405i) q^{67} +(1.91834 + 3.64966i) q^{68} -19.6985i q^{69} +(1.11788 - 2.69196i) q^{70} +(-5.38952 - 1.07204i) q^{71} -4.91517 q^{72} +(-8.02579 - 1.59643i) q^{73} +(-1.35901 - 6.83222i) q^{74} +(-13.8016 + 2.71951i) q^{75} +(-0.311731 + 0.752584i) q^{76} +(-2.91637 - 7.04075i) q^{77} +(14.7291 - 2.92981i) q^{78} +(5.01247 - 0.997043i) q^{79} +(2.19271 + 0.438207i) q^{80} +(-0.292298 - 0.292298i) q^{81} +(6.59188 - 4.40455i) q^{82} +(-2.38399 - 0.987480i) q^{83} -3.66742 q^{84} +(4.40967 - 8.09659i) q^{85} +1.42209 q^{86} +(5.47620 + 2.26832i) q^{87} +(4.86093 - 3.24797i) q^{88} +(-0.779290 - 0.779290i) q^{89} +(6.09786 + 9.14388i) q^{90} +(6.82461 - 1.35750i) q^{91} +(6.86717 - 1.36596i) q^{92} +(-1.66289 - 4.01457i) q^{93} +(-0.0420738 + 0.101575i) q^{94} +(1.78680 - 0.353747i) q^{95} +(-0.548865 - 2.75933i) q^{96} +(-14.7649 - 2.93692i) q^{97} +5.30073 q^{98} +(28.1829 + 5.60592i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} - 48 q^{15} + 16 q^{18} - 24 q^{25} + 8 q^{26} + 24 q^{27} - 8 q^{28} - 8 q^{29} - 16 q^{30} - 16 q^{31} + 64 q^{33} + 24 q^{34} + 32 q^{35} - 32 q^{37} - 32 q^{39} + 16 q^{41} - 24 q^{42} - 16 q^{43} - 16 q^{44} - 24 q^{45} - 16 q^{49} - 32 q^{50} + 32 q^{51} - 16 q^{52} + 16 q^{53} + 24 q^{54} - 8 q^{55} + 8 q^{56} - 24 q^{57} - 16 q^{58} - 64 q^{59} + 40 q^{60} - 24 q^{61} - 40 q^{62} - 24 q^{63} + 32 q^{65} + 16 q^{67} + 40 q^{70} + 8 q^{71} - 16 q^{72} + 32 q^{73} + 8 q^{74} - 56 q^{75} + 24 q^{77} + 32 q^{78} + 72 q^{79} + 8 q^{80} + 48 q^{81} + 48 q^{82} + 16 q^{83} + 8 q^{85} - 64 q^{86} + 40 q^{87} + 32 q^{88} + 16 q^{89} + 24 q^{90} + 48 q^{91} + 24 q^{92} - 8 q^{93} + 8 q^{94} + 56 q^{95} - 48 q^{97} - 64 q^{99}+O(q^{100}) $ 32 * q - 8 * q^10 - 48 * q^15 + 16 * q^18 - 24 * q^25 + 8 * q^26 + 24 * q^27 - 8 * q^28 - 8 * q^29 - 16 * q^30 - 16 * q^31 + 64 * q^33 + 24 * q^34 + 32 * q^35 - 32 * q^37 - 32 * q^39 + 16 * q^41 - 24 * q^42 - 16 * q^43 - 16 * q^44 - 24 * q^45 - 16 * q^49 - 32 * q^50 + 32 * q^51 - 16 * q^52 + 16 * q^53 + 24 * q^54 - 8 * q^55 + 8 * q^56 - 24 * q^57 - 16 * q^58 - 64 * q^59 + 40 * q^60 - 24 * q^61 - 40 * q^62 - 24 * q^63 + 32 * q^65 + 16 * q^67 + 40 * q^70 + 8 * q^71 - 16 * q^72 + 32 * q^73 + 8 * q^74 - 56 * q^75 + 24 * q^77 + 32 * q^78 + 72 * q^79 + 8 * q^80 + 48 * q^81 + 48 * q^82 + 16 * q^83 + 8 * q^85 - 64 * q^86 + 40 * q^87 + 32 * q^88 + 16 * q^89 + 24 * q^90 + 48 * q^91 + 24 * q^92 - 8 * q^93 + 8 * q^94 + 56 * q^95 - 48 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.923880	−	0.382683i	−0.653281	−	0.270598i
$2$	−0.923880	−	0.382683i	−0.653281	−	0.270598i
$3$	2.33925	−	1.56304i	1.35057	−	0.902419i	0.351141	−	0.936323i	$-0.385794\pi$
$3$	2.33925	−	1.56304i	1.35057	−	0.902419i	0.999425	+	0.0339033i	$0.0107938\pi$
$4$	0.707107	+	0.707107i	0.353553	+	0.353553i
$5$	0.438207	−	2.19271i	0.195972	−	0.980609i
$5$	0.438207	−	2.19271i	0.195972	−	0.980609i
$6$	−2.75933	+	0.548865i	−1.12649	+	0.224073i
$7$	−1.27851	+	0.254312i	−0.483232	+	0.0961208i	−0.430694	−	0.902498i	$-0.641731\pi$
$7$	−1.27851	+	0.254312i	−0.483232	+	0.0961208i	−0.0525381	+	0.998619i	$0.516731\pi$
$8$	−0.382683	−	0.923880i	−0.135299	−	0.326641i
$9$	1.88095	−	4.54102i	0.626984	−	1.51367i
$10$	−1.24396	+	1.85810i	−0.393376	+	0.587584i
$11$	1.14054	+	5.73386i	0.343884	+	1.72882i	0.635335	+	0.772237i	$0.280862\pi$
$11$	1.14054	+	5.73386i	0.343884	+	1.72882i	−0.291450	+	0.956586i	$0.594138\pi$
$12$	2.75933	+	0.548865i	0.796551	+	0.158444i
$13$	−5.33794			−1.48048			−0.740239	−	0.672344i	$-0.765288\pi$
$13$	−5.33794			−1.48048			−0.740239	+	0.672344i	$0.765288\pi$
$14$	1.27851	+	0.254312i	0.341696	+	0.0679677i
$15$	−2.40221	−	5.81423i	−0.620248	−	1.50123i
$16$			1.00000i			0.250000i
$17$	3.93717	+	1.22423i	0.954903	+	0.296919i
$17$	3.93717	+	1.22423i	0.954903	+	0.296919i
$18$	−3.47555	+	3.47555i	−0.819195	+	0.819195i
$19$	0.311731	+	0.752584i	0.0715159	+	0.172655i	0.955595	−	0.294682i	$-0.0952137\pi$
$19$	0.311731	+	0.752584i	0.0715159	+	0.172655i	−0.884080	+	0.467336i	$0.845214\pi$
$20$	1.86034	−	1.24062i	0.415984	−	0.277411i
$21$	−2.59326	+	2.59326i	−0.565895	+	0.565895i
$22$	1.14054	−	5.73386i	0.243163	−	1.22246i
$23$	3.88994	−	5.82170i	0.811108	−	1.21391i	−0.162731	−	0.986670i	$-0.552030\pi$
$23$	3.88994	−	5.82170i	0.811108	−	1.21391i	0.973839	−	0.227239i	$-0.0729697\pi$
$24$	−2.33925	−	1.56304i	−0.477497	−	0.319053i
$25$	−4.61595	−	1.92172i	−0.923190	−	0.384344i
$26$	4.93161	+	2.04274i	0.967168	+	0.400614i
$27$	−1.05117	−	5.28458i	−0.202298	−	1.01702i
$28$	−1.08387	−	0.724218i	−0.204832	−	0.136864i
$29$	1.17050	+	1.75178i	0.217357	+	0.325298i	0.924085	−	0.382188i	$-0.124829\pi$
$29$	1.17050	+	1.75178i	0.217357	+	0.325298i	−0.706727	+	0.707486i	$0.749829\pi$
$30$	−0.00565639	+	6.29093i	−0.00103271	+	1.14856i
$31$	0.301321	−	1.51484i	0.0541188	−	0.272074i	−0.944246	−	0.329241i	$-0.893207\pi$
$31$	0.301321	−	1.51484i	0.0541188	−	0.272074i	0.998365	+	0.0571677i	$0.0182070\pi$
$32$	0.382683	−	0.923880i	0.0676495	−	0.163320i
$33$	11.6302	+	11.6302i	2.02456	+	2.02456i
$34$	−3.16897	−	2.63773i	−0.543475	−	0.452366i
$35$	−0.00262084	+	2.91484i	−0.000443002	+	0.492699i
$36$	4.54102	−	1.88095i	0.756837	−	0.313492i
$37$	3.87014	+	5.79208i	0.636248	+	0.952212i	0.999787	+	0.0206333i	$0.00656823\pi$
$37$	3.87014	+	5.79208i	0.636248	+	0.952212i	−0.363539	+	0.931579i	$0.618432\pi$
$38$		−	0.814591i		−	0.132144i
$39$	−12.4868	+	8.34339i	−1.99948	+	1.33601i
$40$	−2.19349	+	0.434263i	−0.346822	+	0.0686630i
$41$	−4.40455	+	6.59188i	−0.687876	+	1.02948i	0.309044	+	0.951048i	$0.399991\pi$
$41$	−4.40455	+	6.59188i	−0.687876	+	1.02948i	−0.996920	+	0.0784311i	$0.975009\pi$
$42$	3.38825	−	1.40346i	0.522819	−	0.216559i
$43$	−1.31384	+	0.544211i	−0.200359	+	0.0829914i	−0.480607	−	0.876936i	$-0.659583\pi$
$43$	−1.31384	+	0.544211i	−0.200359	+	0.0829914i	0.280248	+	0.959928i	$0.409583\pi$
$44$	−3.24797	+	4.86093i	−0.489650	+	0.732813i
$45$	−9.13290	−	6.11429i	−1.36145	−	0.911465i
$46$	−5.82170	+	3.88994i	−0.858363	+	0.573540i
$47$		−	0.109944i		−	0.0160370i	−0.999968	−	0.00801850i	$-0.997448\pi$
$47$		−	0.109944i		−	0.0160370i	0.999968	−	0.00801850i	$-0.00255240\pi$
$48$	1.56304	+	2.33925i	0.225605	+	0.337642i
$49$	−4.89724	+	2.02850i	−0.699606	+	0.289786i
$50$	3.52917	+	3.54189i	0.499100	+	0.500898i
$51$	11.1235	−	3.29016i	1.55760	−	0.460715i
$52$	−3.77449	−	3.77449i	−0.523428	−	0.523428i
$53$	0.379151	−	0.915351i	0.0520804	−	0.125733i	−0.895698	−	0.444663i	$-0.853323\pi$
$53$	0.379151	−	0.915351i	0.0520804	−	0.125733i	0.947778	+	0.318930i	$0.103323\pi$
$54$	−1.05117	+	5.28458i	−0.143046	+	0.719141i
$55$	13.0725	+	0.0117539i	1.76269	+	0.00158490i
$56$	0.724218	+	1.08387i	0.0967778	+	0.144838i
$57$	1.90553	+	1.27324i	0.252394	+	0.168644i
$58$	−0.411026	−	2.06637i	−0.0539704	−	0.271328i
$59$	5.08359	+	2.10569i	0.661827	+	0.274138i	0.688207	−	0.725514i	$-0.258398\pi$
$59$	5.08359	+	2.10569i	0.661827	+	0.274138i	−0.0263799	+	0.999652i	$0.508398\pi$
$60$	2.41266	−	5.80990i	0.311473	−	0.750055i
$61$	−4.82682	−	3.22518i	−0.618011	−	0.412942i	0.206774	−	0.978389i	$-0.433704\pi$
$61$	−4.82682	−	3.22518i	−0.618011	−	0.412942i	−0.824785	+	0.565447i	$0.808704\pi$
$62$	−0.858089	+	1.28422i	−0.108977	+	0.163096i
$63$	−1.24998	+	6.28410i	−0.157483	+	0.791722i
$64$	−0.707107	+	0.707107i	−0.0883883	+	0.0883883i
$65$	−2.33912	+	11.7045i	−0.290132	+	1.45177i
$66$	−6.29423	−	15.1956i	−0.774766	−	1.87045i
$67$	4.12405	−	4.12405i	0.503833	−	0.503833i	−0.408794	−	0.912627i	$-0.634050\pi$
$67$	4.12405	−	4.12405i	0.503833	−	0.503833i	0.912627	+	0.408794i	$0.134050\pi$
$68$	1.91834	+	3.64966i	0.232633	+	0.442586i
$69$		−	19.6985i		−	2.37142i
$70$	1.11788	−	2.69196i	0.133613	−	0.321751i
$71$	−5.38952	−	1.07204i	−0.639618	−	0.127228i	−0.135382	−	0.990794i	$-0.543226\pi$
$71$	−5.38952	−	1.07204i	−0.639618	−	0.127228i	−0.504237	+	0.863566i	$0.668226\pi$
$72$	−4.91517			−0.579258
$73$	−8.02579	−	1.59643i	−0.939348	−	0.186848i	−0.298407	−	0.954439i	$-0.596455\pi$
$73$	−8.02579	−	1.59643i	−0.939348	−	0.186848i	−0.640940	+	0.767591i	$0.721455\pi$
$74$	−1.35901	−	6.83222i	−0.157982	−	0.794230i
$75$	−13.8016	+	2.71951i	−1.59367	+	0.314022i
$76$	−0.311731	+	0.752584i	−0.0357580	+	0.0863273i
$77$	−2.91637	−	7.04075i	−0.332352	−	0.802368i
$78$	14.7291	−	2.92981i	1.66775	−	0.331736i
$79$	5.01247	−	0.997043i	0.563947	−	0.112176i	0.0951198	−	0.995466i	$-0.469677\pi$
$79$	5.01247	−	0.997043i	0.563947	−	0.112176i	0.468828	+	0.883290i	$0.344677\pi$
$80$	2.19271	+	0.438207i	0.245152	+	0.0489930i
$81$	−0.292298	−	0.292298i	−0.0324776	−	0.0324776i
$82$	6.59188	−	4.40455i	0.727952	−	0.486402i
$83$	−2.38399	−	0.987480i	−0.261677	−	0.108390i	0.247988	−	0.968763i	$-0.420231\pi$
$83$	−2.38399	−	0.987480i	−0.261677	−	0.108390i	−0.509665	+	0.860373i	$0.670231\pi$
$84$	−3.66742			−0.400148
$85$	4.40967	−	8.09659i	0.478296	−	0.878199i
$86$	1.42209			0.153348
$87$	5.47620	+	2.26832i	0.587110	+	0.243189i
$88$	4.86093	−	3.24797i	0.518177	−	0.346235i
$89$	−0.779290	−	0.779290i	−0.0826045	−	0.0826045i	0.664597	−	0.747202i	$-0.268603\pi$
$89$	−0.779290	−	0.779290i	−0.0826045	−	0.0826045i	−0.747202	+	0.664597i	$0.768603\pi$
$90$	6.09786	+	9.14388i	0.642771	+	0.963849i
$91$	6.82461	−	1.35750i	0.715414	−	0.142305i
$92$	6.86717	−	1.36596i	0.715952	−	0.142412i
$93$	−1.66289	−	4.01457i	−0.172434	−	0.416291i
$94$	−0.0420738	+	0.101575i	−0.00433958	+	0.0104767i
$95$	1.78680	−	0.353747i	0.183322	−	0.0362937i
$96$	−0.548865	−	2.75933i	−0.0560183	−	0.281623i
$97$	−14.7649	−	2.93692i	−1.49915	−	0.298199i	−0.623758	−	0.781617i	$-0.714395\pi$
$97$	−14.7649	−	2.93692i	−1.49915	−	0.298199i	−0.875389	+	0.483418i	$0.839395\pi$
$98$	5.30073			0.535455
$99$	28.1829	+	5.60592i	2.83249	+	0.563416i
$100$	−1.90511	−	4.62283i	−0.190511	−	0.462283i
$101$		−	6.75581i		−	0.672228i	−0.941821	−	0.336114i	$-0.890887\pi$
$101$		−	6.75581i		−	0.672228i	0.941821	−	0.336114i	$-0.109113\pi$
$102$	−11.5359	−	1.21708i	−1.14222	−	0.120508i
$103$	−4.75400	+	4.75400i	−0.468426	+	0.468426i	−0.901404	−	0.432978i	$-0.857463\pi$
$103$	−4.75400	+	4.75400i	−0.468426	+	0.468426i	0.432978	+	0.901404i	$0.357463\pi$
$104$	2.04274	+	4.93161i	0.200307	+	0.483584i
$105$	4.54988	+	6.82264i	0.444023	+	0.665822i
$106$	−0.700579	+	0.700579i	−0.0680463	+	0.0680463i
$107$	3.26275	−	16.4030i	0.315422	−	1.58573i	−0.419611	−	0.907704i	$-0.637834\pi$
$107$	3.26275	−	16.4030i	0.315422	−	1.58573i	0.735033	−	0.678031i	$-0.237166\pi$
$108$	2.99348	−	4.48005i	0.288047	−	0.431093i
$109$	2.02154	+	1.35075i	0.193628	+	0.129378i	0.648605	−	0.761125i	$-0.275353\pi$
$109$	2.02154	+	1.35075i	0.193628	+	0.129378i	−0.454977	+	0.890503i	$0.650353\pi$
$110$	−12.0729	−	5.01348i	−1.15111	−	0.478016i
$111$	18.1065	+	7.49994i	1.71859	+	0.711863i
$112$	−0.254312	−	1.27851i	−0.0240302	−	0.120808i
$113$	−9.40688	−	6.28548i	−0.884925	−	0.591288i	0.0279127	−	0.999610i	$-0.491114\pi$
$113$	−9.40688	−	6.28548i	−0.884925	−	0.591288i	−0.912838	+	0.408322i	$0.866114\pi$
$114$	−1.27324	−	1.90553i	−0.119249	−	0.178469i
$115$	−11.0607	−	11.0806i	−1.03142	−	1.03327i
$116$	−0.411026	+	2.06637i	−0.0381628	+	0.191858i
$117$	−10.0404	+	24.2397i	−0.928236	+	2.24096i
$118$	−3.89081	−	3.89081i	−0.358178	−	0.358178i
$119$	−5.34504	−	0.563921i	−0.489979	−	0.0516945i
$120$	−4.45236	+	4.44436i	−0.406443	+	0.405713i
$121$	−21.4136	+	8.86981i	−1.94669	+	0.806347i
$122$	3.22518	+	4.82682i	0.291994	+	0.437000i
$123$			22.3045i			2.01113i
$124$	1.28422	−	0.858089i	0.115326	−	0.0770587i
$125$	−6.23652	+	9.27932i	−0.557811	+	0.829968i
$126$	3.55966	−	5.32740i	0.317119	−	0.474603i
$127$	−3.29207	+	1.36362i	−0.292124	+	0.121002i	−0.523933	−	0.851760i	$-0.675536\pi$
$127$	−3.29207	+	1.36362i	−0.292124	+	0.121002i	0.231809	+	0.972761i	$0.425536\pi$
$128$	0.923880	−	0.382683i	0.0816602	−	0.0338248i
$129$	−2.22278	+	3.32663i	−0.195705	+	0.292893i
$130$	6.64020	−	9.91845i	0.582384	−	0.869905i
$131$	9.80467	−	6.55127i	0.856638	−	0.572387i	−0.0478655	−	0.998854i	$-0.515242\pi$
$131$	9.80467	−	6.55127i	0.856638	−	0.572387i	0.904503	+	0.426467i	$0.140242\pi$
$132$			16.4476i			1.43158i
$133$	−0.589942	−	0.882911i	−0.0511545	−	0.0765581i
$134$	−5.38834	+	2.23192i	−0.465481	+	0.192809i
$135$	−12.0482	−	0.0108329i	−1.03694	−	0.000932351i
$136$	−0.375650	−	4.10596i	−0.0322117	−	0.352083i
$137$	9.59397	+	9.59397i	0.819668	+	0.819668i	0.986060	−	0.166391i	$-0.0532115\pi$
$137$	9.59397	+	9.59397i	0.819668	+	0.819668i	−0.166391	+	0.986060i	$0.553212\pi$
$138$	−7.53830	+	18.1991i	−0.641703	+	1.54921i
$139$	−2.01112	+	10.1106i	−0.170581	+	0.857570i	0.796800	+	0.604244i	$0.206525\pi$
$139$	−2.01112	+	10.1106i	−0.170581	+	0.857570i	−0.967381	+	0.253326i	$0.918475\pi$
$140$	−2.06296	+	2.05925i	−0.174352	+	0.174039i
$141$	−0.171847	−	0.257187i	−0.0144721	−	0.0216590i
$142$	4.56901	+	3.05292i	0.383423	+	0.256195i
$143$	−6.08810	−	30.6070i	−0.509113	−	2.55948i
$144$	4.54102	+	1.88095i	0.378419	+	0.156746i
$145$	4.35408	−	1.79893i	0.361586	−	0.149393i
$146$	6.80394	+	4.54625i	0.563098	+	0.376250i
$147$	−8.28524	+	12.3997i	−0.683355	+	1.02271i
$148$	−1.35901	+	6.83222i	−0.111710	+	0.561605i
$149$	13.6274	−	13.6274i	1.11640	−	1.11640i	0.124139	−	0.992265i	$-0.460383\pi$
$149$	13.6274	−	13.6274i	1.11640	−	1.11640i	0.992265	−	0.124139i	$-0.0396170\pi$
$150$	13.7917	+	2.76913i	1.12609	+	0.226099i
$151$	3.26423	+	7.88055i	0.265639	+	0.641310i	0.999269	−	0.0382398i	$-0.0121751\pi$
$151$	3.26423	+	7.88055i	0.265639	+	0.641310i	−0.733629	+	0.679550i	$0.762175\pi$
$152$	0.576003	−	0.576003i	0.0467200	−	0.0467200i
$153$	12.9649	−	15.5760i	1.04815	−	1.25925i
$154$			7.62085i			0.614106i
$155$	−3.18957	−	1.32452i	−0.256192	−	0.106388i
$156$	−14.7291	−	2.92981i	−1.17928	−	0.234572i
$157$	−0.880010			−0.0702324			−0.0351162	−	0.999383i	$-0.511180\pi$
$157$	−0.880010			−0.0702324			−0.0351162	+	0.999383i	$0.511180\pi$
$158$	−5.01247	−	0.997043i	−0.398771	−	0.0793205i
$159$	−0.543799	−	2.73386i	−0.0431260	−	0.216809i
$160$	−1.85810	−	1.24396i	−0.146896	−	0.0983440i
$161$	−3.49280	+	8.43237i	−0.275271	+	0.664564i
$162$	0.158191	+	0.381906i	0.0124286	+	0.0300054i
$163$	6.68221	−	1.32917i	0.523391	−	0.104109i	0.0736779	−	0.997282i	$-0.476526\pi$
$163$	6.68221	−	1.32917i	0.523391	−	0.104109i	0.449713	+	0.893173i	$0.351526\pi$
$164$	−7.77565	+	1.54667i	−0.607177	+	0.120775i
$165$	30.5981	−	20.4053i	2.38206	−	1.58855i
$166$	1.82463	+	1.82463i	0.141618	+	0.141618i
$167$	−11.1600	+	7.45689i	−0.863589	+	0.577032i	−0.906575	−	0.422044i	$-0.861313\pi$
$167$	−11.1600	+	7.45689i	−0.863589	+	0.577032i	0.0429863	+	0.999076i	$0.486313\pi$
$168$	3.38825	+	1.40346i	0.261409	+	0.108279i
$169$	15.4936			1.19181
$170$	−7.17243	+	5.79277i	−0.550101	+	0.444285i
$171$	4.00385			0.306182
$172$	−1.31384	−	0.544211i	−0.100180	−	0.0414957i
$173$	−19.6568	+	13.1343i	−1.49448	+	0.998580i	−0.503585	+	0.863945i	$0.667986\pi$
$173$	−19.6568	+	13.1343i	−1.49448	+	0.998580i	−0.990895	+	0.134635i	$0.957014\pi$
$174$	−4.19130	−	4.19130i	−0.317742	−	0.317742i
$175$	6.39026	+	1.28305i	0.483058	+	0.0969896i
$176$	−5.73386	+	1.14054i	−0.432206	+	0.0859711i
$177$	15.1831	−	3.02010i	1.14123	−	0.227005i
$178$	0.421748	+	1.01819i	0.0316114	+	0.0763166i
$179$	9.49226	−	22.9163i	0.709485	−	1.71285i	0.00820077	−	0.999966i	$-0.497390\pi$
$179$	9.49226	−	22.9163i	0.709485	−	1.71285i	0.701284	−	0.712882i	$-0.252610\pi$
$180$	−2.13448	−	10.7814i	−0.159094	−	0.803597i
$181$	−1.10723	−	5.56640i	−0.0822995	−	0.413747i	−0.999869	−	0.0161726i	$-0.994852\pi$
$181$	−1.10723	−	5.56640i	−0.0822995	−	0.413747i	0.917570	−	0.397575i	$-0.130148\pi$
$182$	−6.82461	−	1.35750i	−0.505874	−	0.100625i
$183$	−16.3322			−1.20731
$184$	−6.86717	−	1.36596i	−0.506254	−	0.100700i
$185$	14.3963	−	5.94797i	1.05844	−	0.437304i
$186$			4.34534i			0.318616i
$187$	−2.52907	+	23.9714i	−0.184944	+	1.75296i
$188$	0.0777423	−	0.0777423i	0.00566994	−	0.00566994i
$189$	2.68786	+	6.48908i	0.195513	+	0.472011i
$190$	−1.78616	−	0.356960i	−0.129582	−	0.0258966i
$191$	−0.202904	+	0.202904i	−0.0146816	+	0.0146816i	−0.714409	−	0.699728i	$-0.753305\pi$
$191$	−0.202904	+	0.202904i	−0.0146816	+	0.0146816i	0.699728	+	0.714409i	$0.253305\pi$
$192$	−0.548865	+	2.75933i	−0.0396109	+	0.199138i
$193$	13.6206	−	20.3846i	0.980429	−	1.46732i	0.0989501	−	0.995092i	$-0.468452\pi$
$193$	13.6206	−	20.3846i	0.980429	−	1.46732i	0.881479	−	0.472223i	$-0.156548\pi$
$194$	12.5171	+	8.36364i	0.898673	+	0.600474i
$195$	12.8228	+	31.0360i	0.918263	+	2.22253i
$196$	−4.89724	−	2.02850i	−0.349803	−	0.144893i
$197$	0.490864	+	2.46774i	0.0349726	+	0.175819i	0.994324	−	0.106396i	$-0.0339310\pi$
$197$	0.490864	+	2.46774i	0.0349726	+	0.175819i	−0.959351	+	0.282215i	$0.908931\pi$
$198$	−23.8923	−	15.9643i	−1.69795	−	1.13453i
$199$	−7.18214	−	10.7488i	−0.509128	−	0.761964i	0.484485	−	0.874799i	$-0.339007\pi$
$199$	−7.18214	−	10.7488i	−0.509128	−	0.761964i	−0.993614	+	0.112835i	$0.964007\pi$
$200$	−0.00899134	+	4.99999i	−0.000635784	+	0.353553i
$201$	3.20114	−	16.0932i	0.225791	−	1.13513i
$202$	−2.58533	+	6.24155i	−0.181904	+	0.439154i
$203$	−1.94200	−	1.94200i	−0.136302	−	0.136302i
$204$	10.1920	+	5.53902i	0.713584	+	0.387809i
$205$	12.5240	+	12.5465i	0.874712	+	0.876287i
$206$	6.21141	−	2.57285i	0.432769	−	0.179259i
$207$	−19.1197	−	28.6146i	−1.32891	−	1.98886i
$208$		−	5.33794i		−	0.370119i
$209$	−3.95967	+	2.64577i	−0.273896	+	0.183012i
$210$	−1.59263	−	8.04446i	−0.109902	−	0.555121i
$211$	7.92328	−	11.8580i	0.545461	−	0.816340i	−0.451658	−	0.892191i	$-0.649167\pi$
$211$	7.92328	−	11.8580i	0.545461	−	0.816340i	0.997119	+	0.0758509i	$0.0241673\pi$
$212$	0.915351	−	0.379151i	0.0628666	−	0.0260402i
$213$	−14.2831	+	5.91624i	−0.978660	+	0.405374i
$214$	−9.29153	+	13.9058i	−0.635156	+	0.950578i
$215$	0.617562	+	3.11935i	0.0421174	+	0.212738i
$216$	−4.48005	+	2.99348i	−0.304829	+	0.203680i
$217$			2.01337i			0.136677i
$218$	−1.35075	−	2.02154i	−0.0914842	−	0.136916i
$219$	−21.2696	+	8.81016i	−1.43727	+	0.595335i
$220$	9.23532	+	9.25195i	0.622645	+	0.623766i
$221$	−21.0163	−	6.53485i	−1.41371	−	0.439581i
$222$	−13.8581	−	13.8581i	−0.930094	−	0.930094i
$223$	−5.22346	+	12.6106i	−0.349789	+	0.844465i	0.646856	+	0.762613i	$0.276084\pi$
$223$	−5.22346	+	12.6106i	−0.349789	+	0.844465i	−0.996644	+	0.0818526i	$0.973916\pi$
$224$	−0.254312	+	1.27851i	−0.0169919	+	0.0854241i
$225$	−17.4090	+	17.3465i	−1.16060	+	1.15643i
$226$	6.28548	+	9.40688i	0.418104	+	0.625737i
$227$	−6.55814	−	4.38201i	−0.435279	−	0.290844i	0.318561	−	0.947902i	$-0.396801\pi$
$227$	−6.55814	−	4.38201i	−0.435279	−	0.290844i	−0.753840	+	0.657058i	$0.771801\pi$
$228$	0.447101	+	2.24773i	0.0296100	+	0.148859i
$229$	−9.79199	−	4.05598i	−0.647073	−	0.268026i	0.0349144	−	0.999390i	$-0.488884\pi$
$229$	−9.79199	−	4.05598i	−0.647073	−	0.268026i	−0.681987	+	0.731364i	$0.738884\pi$
$230$	5.97839	+	14.4699i	0.394204	+	0.954117i
$231$	−17.8271	−	11.9117i	−1.17294	−	0.783730i
$232$	1.17050	−	1.75178i	0.0768474	−	0.115010i
$233$	0.465778	−	2.34162i	0.0305141	−	0.153405i	−0.962524	−	0.271195i	$-0.912581\pi$
$233$	0.465778	−	2.34162i	0.0305141	−	0.153405i	0.993038	+	0.117790i	$0.0375811\pi$
$234$	18.5523	−	18.5523i	1.21280	−	1.21280i
$235$	−0.241076	−	0.0481783i	−0.0157260	−	0.00314281i
$236$	2.10569	+	5.08359i	0.137069	+	0.330914i
$237$	10.1670	−	10.1670i	0.660418	−	0.660418i
$238$	4.72237	+	2.56645i	0.306106	+	0.166359i
$239$			10.4783i			0.677786i	0.940825	+	0.338893i	$0.110053\pi$
$239$			10.4783i			0.677786i	−0.940825	+	0.338893i	$0.889947\pi$
$240$	5.81423	−	2.40221i	0.375307	−	0.155062i
$241$	6.35785	+	1.26466i	0.409545	+	0.0814636i	0.395564	−	0.918439i	$-0.370549\pi$
$241$	6.35785	+	1.26466i	0.409545	+	0.0814636i	0.0139818	+	0.999902i	$0.495549\pi$
$242$	23.1779			1.48993
$243$	14.7131	+	2.92662i	0.943847	+	0.187743i
$244$	−1.13253	−	5.69362i	−0.0725029	−	0.364497i
$245$	2.30191	+	11.6271i	0.147064	+	0.742830i
$246$	8.53557	−	20.6067i	0.544208	−	1.31384i
$247$	−1.66400	−	4.01725i	−0.105878	−	0.255611i
$248$	−1.51484	+	0.301321i	−0.0961926	+	0.0191339i
$249$	−7.12021	+	1.41630i	−0.451225	+	0.0897542i
$250$	9.31283	−	6.18637i	0.588995	−	0.391260i
$251$	15.4336	+	15.4336i	0.974160	+	0.974160i	0.999674	−	0.0255144i	$-0.00812236\pi$
$251$	15.4336	+	15.4336i	0.974160	+	0.974160i	−0.0255144	+	0.999674i	$0.508122\pi$
$252$	−5.32740	+	3.55966i	−0.335595	+	0.224237i
$253$	37.8174	+	15.6645i	2.37756	+	0.984818i
$254$	3.56331			0.223582
$255$	−2.33996	−	25.8324i	−0.146534	−	1.61769i
$256$	−1.00000			−0.0625000
$257$	8.96619	+	3.71392i	0.559296	+	0.231668i	0.644379	−	0.764706i	$-0.277116\pi$
$257$	8.96619	+	3.71392i	0.559296	+	0.231668i	−0.0850837	+	0.996374i	$0.527116\pi$
$258$	3.32663	−	2.22278i	0.207107	−	0.138384i
$259$	−6.42102	−	6.42102i	−0.398983	−	0.398983i
$260$	−9.93037	+	6.62236i	−0.615856	+	0.410701i
$261$	10.1566	−	2.02026i	0.628675	−	0.125051i
$262$	−11.5654	+	2.30050i	−0.714512	+	0.142125i
$263$	−6.13000	−	14.7991i	−0.377992	−	0.912553i	−0.992342	−	0.123520i	$-0.960582\pi$
$263$	−6.13000	−	14.7991i	−0.377992	−	0.912553i	0.614350	−	0.789033i	$-0.289418\pi$
$264$	6.29423	−	15.1956i	0.387383	−	0.935226i
$265$	−1.84095	−	1.23248i	−0.113089	−	0.0757107i
$266$	0.207160	+	1.04146i	0.0127018	+	0.0638563i
$267$	−3.04101	−	0.604895i	−0.186107	−	0.0370189i
$268$	5.83229			0.356264
$269$	−16.1671	−	3.21583i	−0.985724	−	0.196073i	−0.324194	−	0.945991i	$-0.605093\pi$
$269$	−16.1671	−	3.21583i	−0.985724	−	0.196073i	−0.661531	+	0.749918i	$0.730093\pi$
$270$	11.1269	+	4.62065i	0.677163	+	0.281204i
$271$		−	5.17301i		−	0.314238i	−0.987580	−	0.157119i	$-0.949779\pi$
$271$		−	5.17301i		−	0.314238i	0.987580	−	0.157119i	$-0.0502206\pi$
$272$	−1.22423	+	3.93717i	−0.0742297	+	0.238726i
$273$	13.8426	−	13.8426i	0.837795	−	0.837795i
$274$	−5.19222	−	12.5351i	−0.313673	−	0.757275i
$275$	5.75422	−	28.6590i	0.346993	−	1.72820i
$276$	13.9290	−	13.9290i	0.838425	−	0.838425i
$277$	−4.03287	+	20.2746i	−0.242312	+	1.21818i	0.647575	+	0.762002i	$0.275783\pi$
$277$	−4.03287	+	20.2746i	−0.242312	+	1.21818i	−0.889886	+	0.456182i	$0.849217\pi$
$278$	5.72719	−	8.57135i	0.343494	−	0.514076i
$279$	−6.31216	−	4.21765i	−0.377899	−	0.252504i
$280$	2.69397	−	1.11304i	0.160995	−	0.0665169i
$281$	−1.20815	−	0.500433i	−0.0720724	−	0.0298534i	0.346356	−	0.938103i	$-0.387419\pi$
$281$	−1.20815	−	0.500433i	−0.0720724	−	0.0298534i	−0.418428	+	0.908250i	$0.637419\pi$
$282$	0.0603445	+	0.303372i	0.00359347	+	0.0180656i
$283$	3.79127	+	2.53325i	0.225368	+	0.150586i	0.663128	−	0.748506i	$-0.269228\pi$
$283$	3.79127	+	2.53325i	0.225368	+	0.150586i	−0.437761	+	0.899091i	$0.644228\pi$
$284$	−3.05292	−	4.56901i	−0.181157	−	0.271121i
$285$	3.62685	−	3.62034i	0.214836	−	0.214450i
$286$	−6.08810	+	30.6070i	−0.359997	+	1.80983i
$287$	3.95488	−	9.54792i	0.233449	−	0.563596i
$288$	−3.47555	−	3.47555i	−0.204799	−	0.204799i
$289$	14.0025	+	9.63997i	0.823679	+	0.567057i
$290$	−4.71106	−	0.00423588i	−0.276643	−	0.000248739i
$291$	−39.1293	+	16.2079i	−2.29380	+	0.950122i
$292$	−4.54625	−	6.80394i	−0.266049	−	0.398170i
$293$			31.2813i			1.82747i	0.406310	+	0.913735i	$0.366815\pi$
$293$			31.2813i			1.82747i	−0.406310	+	0.913735i	$0.633185\pi$
$294$	12.3997	−	8.28524i	0.723167	−	0.483205i
$295$	6.84484	−	10.2241i	0.398522	−	0.595271i
$296$	3.87014	−	5.79208i	0.224948	−	0.336658i
$297$	29.1022	−	12.0545i	1.68868	−	0.699474i
$298$	−17.8051	+	7.37512i	−1.03142	+	0.427229i
$299$	−20.7642	+	31.0759i	−1.20083	+	1.79716i
$300$	−11.6822	−	7.83620i	−0.674471	−	0.452423i
$301$	1.54136	−	1.02991i	0.0888426	−	0.0593628i
$302$		−	8.52985i		−	0.490838i
$303$	−10.5596	−	15.8035i	−0.606631	−	0.907888i
$304$	−0.752584	+	0.311731i	−0.0431637	+	0.0178790i
$305$	−9.18703	+	9.17052i	−0.526048	+	0.525102i
$306$	−17.9387	+	9.42895i	−1.02549	+	0.539017i
$307$	−12.1175	−	12.1175i	−0.691579	−	0.691579i	0.271000	−	0.962579i	$-0.412646\pi$
$307$	−12.1175	−	12.1175i	−0.691579	−	0.691579i	−0.962579	+	0.271000i	$0.912646\pi$
$308$	2.91637	−	7.04075i	0.166176	−	0.401184i
$309$	−3.69012	+	18.5515i	−0.209924	+	1.05536i
$310$	2.43990	+	2.44430i	0.138577	+	0.138827i
$311$	−3.04967	−	4.56416i	−0.172931	−	0.258810i	0.734872	−	0.678205i	$-0.237242\pi$
$311$	−3.04967	−	4.56416i	−0.172931	−	0.258810i	−0.907804	+	0.419396i	$0.862242\pi$
$312$	12.4868	+	8.34339i	0.706924	+	0.472351i
$313$	1.25044	+	6.28639i	0.0706791	+	0.355328i	0.999899	−	0.0141989i	$-0.00451980\pi$
$313$	1.25044	+	6.28639i	0.0706791	+	0.355328i	−0.929220	+	0.369527i	$0.879520\pi$
$314$	0.813023	+	0.336765i	0.0458815	+	0.0190048i
$315$	13.2314	+	5.49459i	0.745508	+	0.309585i
$316$	4.24937	+	2.83934i	0.239046	+	0.159725i
$317$	10.7218	−	16.0464i	0.602199	−	0.901254i	−0.397669	−	0.917529i	$-0.630181\pi$
$317$	10.7218	−	16.0464i	0.602199	−	0.901254i	0.999868	+	0.0162752i	$0.00518078\pi$
$318$	−0.543799	+	2.73386i	−0.0304947	+	0.153307i
$319$	−8.70947	+	8.70947i	−0.487637	+	0.487637i
$320$	1.24062	+	1.86034i	0.0693528	+	0.103996i
$321$	−18.0060	−	43.4704i	−1.00500	−	2.42628i
$322$	6.45386	−	6.45386i	0.359659	−	0.359659i
$323$	0.306001	+	3.34468i	0.0170263	+	0.186103i
$324$		−	0.413372i		−	0.0229651i
$325$	24.6396	+	10.2580i	1.36676	+	0.569013i
$326$	−6.68221	−	1.32917i	−0.370093	−	0.0736161i
$327$	6.84014			0.378261
$328$	7.77565	+	1.54667i	0.429339	+	0.0854008i
$329$	0.0279601	+	0.140565i	0.00154149	+	0.00774959i
$330$	−36.0777	+	7.14259i	−1.98601	+	0.393187i
$331$	−5.53455	+	13.3616i	−0.304207	+	0.734420i	0.695665	+	0.718367i	$0.255110\pi$
$331$	−5.53455	+	13.3616i	−0.304207	+	0.734420i	−0.999871	+	0.0160529i	$0.994890\pi$
$332$	−0.987480	−	2.38399i	−0.0541950	−	0.130838i
$333$	33.5815	−	6.67978i	1.84026	−	0.366050i
$334$	13.1642	−	2.61851i	0.720310	−	0.143279i
$335$	−7.23566	−	10.8500i	−0.395326	−	0.592801i
$336$	−2.59326	−	2.59326i	−0.141474	−	0.141474i
$337$	−7.15312	+	4.77956i	−0.389655	+	0.260359i	−0.734931	−	0.678142i	$-0.762785\pi$
$337$	−7.15312	+	4.77956i	−0.389655	+	0.260359i	0.345276	+	0.938501i	$0.387785\pi$
$338$	−14.3142	−	5.92913i	−0.778590	−	0.322502i
$339$	−31.8295			−1.72874
$340$	8.84326	−	2.60705i	0.479593	−	0.141387i
$341$	9.02956			0.488978
$342$	−3.69908	−	1.53221i	−0.200023	−	0.0828523i
$343$	13.3324	−	8.90842i	0.719881	−	0.481009i
$344$	1.00557	+	1.00557i	0.0542168	+	0.0542168i
$345$	−43.1931	−	8.63203i	−2.32544	−	0.464733i
$346$	23.1868	−	4.61214i	1.24653	−	0.247950i
$347$	33.4249	−	6.64863i	1.79434	−	0.356917i	0.818350	−	0.574720i	$-0.194889\pi$
$347$	33.4249	−	6.64863i	1.79434	−	0.356917i	0.975993	+	0.217802i	$0.0698888\pi$
$348$	2.26832	+	5.47620i	0.121595	+	0.293555i
$349$	2.62113	−	6.32796i	0.140306	−	0.338728i	−0.838070	−	0.545562i	$-0.816316\pi$
$349$	2.62113	−	6.32796i	0.140306	−	0.338728i	0.978376	+	0.206834i	$0.0663161\pi$
$350$	−5.41283	−	3.63083i	−0.289328	−	0.194076i
$351$	5.61108	+	28.2088i	0.299497	+	1.50567i
$352$	5.73386	+	1.14054i	0.305616	+	0.0607907i
$353$	−23.7210			−1.26254			−0.631270	−	0.775563i	$-0.717466\pi$
$353$	−23.7210			−1.26254			−0.631270	+	0.775563i	$0.717466\pi$
$354$	−15.1831	−	3.02010i	−0.806971	−	0.160516i
$355$	−4.71240	+	11.3479i	−0.250108	+	0.602283i
$356$		−	1.10208i		−	0.0584102i
$357$	−13.3848	+	7.03535i	−0.708400	+	0.372350i
$358$	−17.5394	+	17.5394i	−0.926987	+	0.926987i
$359$	10.0001	+	24.1423i	0.527783	+	1.27418i	0.932972	+	0.359948i	$0.117206\pi$
$359$	10.0001	+	24.1423i	0.527783	+	1.27418i	−0.405189	+	0.914233i	$0.632794\pi$
$360$	−2.15386	+	10.7775i	−0.113518	+	0.568026i
$361$	12.9658	−	12.9658i	0.682412	−	0.682412i
$362$	−1.10723	+	5.56640i	−0.0581945	+	0.292564i
$363$	−36.2280	+	54.2190i	−1.90147	+	2.84576i
$364$	5.78563	+	3.86583i	0.303249	+	0.202625i
$365$	−7.01746	+	16.8987i	−0.367311	+	0.884516i
$366$	15.0890	+	6.25006i	0.788714	+	0.326696i
$367$	2.97569	+	14.9598i	0.155330	+	0.780894i	0.977382	+	0.211482i	$0.0678291\pi$
$367$	2.97569	+	14.9598i	0.155330	+	0.780894i	−0.822052	+	0.569412i	$0.807171\pi$
$368$	5.82170	+	3.88994i	0.303477	+	0.202777i
$369$	21.6491	+	32.4002i	1.12701	+	1.68669i
$370$	−15.5766	−	0.0140055i	−0.809790	−	0.000728110i
$371$	−0.251964	+	1.26671i	−0.0130813	+	0.0657643i
$372$	1.66289	−	4.01457i	0.0862168	−	0.208146i
$373$	−3.61554	−	3.61554i	−0.187206	−	0.187206i	0.607281	−	0.794487i	$-0.292260\pi$
$373$	−3.61554	−	3.61554i	−0.187206	−	0.187206i	−0.794487	+	0.607281i	$0.792260\pi$
$374$	11.5100	−	21.1789i	0.595169	−	1.09513i
$375$	−0.0848458	+	31.4546i	−0.00438142	+	1.62431i
$376$	−0.101575	+	0.0420738i	−0.00523834	+	0.00216979i
$377$	−6.24808	−	9.35091i	−0.321792	−	0.481596i
$378$		−	7.02373i		−	0.361261i
$379$	20.5807	−	13.7516i	1.05716	−	0.706372i	0.0997236	−	0.995015i	$-0.468204\pi$
$379$	20.5807	−	13.7516i	1.05716	−	0.706372i	0.957437	+	0.288643i	$0.0932042\pi$
$380$	1.51360	+	1.01332i	0.0776458	+	0.0519823i
$381$	−5.56959	+	8.33548i	−0.285339	+	0.427039i
$382$	0.265107	−	0.109811i	0.0135641	−	0.00561842i
$383$	15.5006	−	6.42058i	0.792046	−	0.328076i	0.0502803	−	0.998735i	$-0.483989\pi$
$383$	15.5006	−	6.42058i	0.792046	−	0.328076i	0.741766	+	0.670659i	$0.233989\pi$
$384$	1.56304	−	2.33925i	0.0797634	−	0.119374i
$385$	−16.7163	+	3.30946i	−0.851941	+	0.168665i
$386$	−20.3846	+	13.6206i	−1.03755	+	0.693268i
$387$			6.98982i			0.355313i
$388$	−8.36364	−	12.5171i	−0.424599	−	0.635458i
$389$	10.3937	−	4.30522i	0.526983	−	0.218283i	−0.103298	−	0.994650i	$-0.532940\pi$
$389$	10.3937	−	4.30522i	0.526983	−	0.218283i	0.630281	+	0.776367i	$0.282940\pi$
$390$	0.0301935	−	33.5806i	0.00152891	−	1.70042i
$391$	22.4424	−	18.1588i	1.13496	−	0.918332i
$392$	3.74819	+	3.74819i	0.189312	+	0.189312i
$393$	12.6957	−	30.6501i	0.640413	−	1.54609i
$394$	0.490864	−	2.46774i	0.0247294	−	0.124323i
$395$	0.0102751	−	11.4278i	0.000516998	−	0.574995i
$396$	15.9643	+	23.8923i	0.802237	+	1.20063i
$397$	−31.0249	−	20.7302i	−1.55710	−	1.04042i	−0.973588	−	0.228311i	$-0.926680\pi$
$397$	−31.0249	−	20.7302i	−1.55710	−	1.04042i	−0.583508	−	0.812107i	$-0.698320\pi$
$398$	2.52203	+	12.6791i	0.126418	+	0.635546i
$399$	−2.76004	−	1.14325i	−0.138175	−	0.0572339i
$400$	1.92172	−	4.61595i	0.0960860	−	0.230797i
$401$	−3.29578	−	2.20217i	−0.164583	−	0.109971i	0.470551	−	0.882373i	$-0.344055\pi$
$401$	−3.29578	−	2.20217i	−0.164583	−	0.109971i	−0.635134	+	0.772402i	$0.719055\pi$
$402$	−9.11608	+	13.6432i	−0.454669	+	0.680460i
$403$	−1.60843	+	8.08613i	−0.0801217	+	0.402799i
$404$	4.77708	−	4.77708i	0.237668	−	0.237668i
$405$	−0.769012	+	0.512838i	−0.0382125	+	0.0254831i
$406$	1.05100	+	2.53735i	0.0521604	+	0.125926i
$407$	−28.7969	+	28.7969i	−1.42741	+	1.42741i
$408$	−7.29650	−	9.01770i	−0.361230	−	0.446443i
$409$			0.304764i			0.0150696i	0.999972	+	0.00753480i	$0.00239842\pi$
$409$			0.304764i			0.0150696i	−0.999972	+	0.00753480i	$0.997602\pi$
$410$	−6.76930	−	16.3842i	−0.334312	−	0.809157i
$411$	37.4384	+	7.44696i	1.84670	+	0.367332i
$412$	−6.72318			−0.331227
$413$	−7.03493	−	1.39933i	−0.346166	−	0.0688568i
$414$	6.71394	+	33.7533i	0.329972	+	1.65888i
$415$	−3.20994	+	4.79467i	−0.157570	+	0.235361i
$416$	−2.04274	+	4.93161i	−0.100154	+	0.241792i
$417$	11.0987	+	26.7947i	0.543506	+	1.31214i
$418$	4.67075	−	0.929070i	0.228454	−	0.0454423i
$419$	35.8559	−	7.13218i	1.75168	−	0.348430i	0.788035	−	0.615631i	$-0.211099\pi$
$419$	35.8559	−	7.13218i	1.75168	−	0.348430i	0.963641	+	0.267201i	$0.0860988\pi$
$420$	−1.60709	+	8.04159i	−0.0784179	+	0.392389i
$421$	15.7246	+	15.7246i	0.766371	+	0.766371i	0.977466	−	0.211095i	$-0.0677029\pi$
$421$	15.7246	+	15.7246i	0.766371	+	0.766371i	−0.211095	+	0.977466i	$0.567703\pi$
$422$	−11.8580	+	7.92328i	−0.577240	+	0.385699i
$423$	−0.499259	−	0.206800i	−0.0242748	−	0.0100550i
$424$	−0.990769			−0.0481160
$425$	−15.8211	−	13.2171i	−0.767438	−	0.641124i
$426$	15.4599			0.749034
$427$	6.99134	+	2.89591i	0.338335	+	0.140143i
$428$	13.9058	−	9.29153i	0.672160	−	0.449123i
$429$	−62.0814	−	62.0814i	−2.99732	−	2.99732i
$430$	0.623171	−	3.11823i	0.0300520	−	0.150375i
$431$	−34.8166	+	6.92546i	−1.67706	+	0.333588i	−0.939722	−	0.341939i	$-0.888916\pi$
$431$	−34.8166	+	6.92546i	−1.67706	+	0.333588i	−0.737336	+	0.675526i	$0.763916\pi$
$432$	5.28458	−	1.05117i	0.254255	−	0.0505744i
$433$	−1.80184	−	4.35002i	−0.0865907	−	0.209048i	0.874652	−	0.484751i	$-0.161090\pi$
$433$	−1.80184	−	4.35002i	−0.0865907	−	0.209048i	−0.961243	+	0.275702i	$0.911090\pi$
$434$	0.770484	−	1.86011i	0.0369844	−	0.0892883i
$435$	7.37347	−	11.0137i	0.353531	−	0.528068i
$436$	0.474319	+	2.38457i	0.0227158	+	0.114200i
$437$	5.59393	+	1.11270i	0.267594	+	0.0532278i
$438$	23.0220			1.10004
$439$	16.6816	+	3.31818i	0.796170	+	0.158368i	0.576383	−	0.817180i	$-0.304464\pi$
$439$	16.6816	+	3.31818i	0.796170	+	0.158368i	0.219787	+	0.975548i	$0.429464\pi$
$440$	−4.99176	−	12.0819i	−0.237973	−	0.575981i
$441$			26.0540i			1.24067i
$442$	16.9158	+	14.0800i	0.804602	+	0.669718i
$443$	8.08098	−	8.08098i	0.383939	−	0.383939i	−0.488580	−	0.872519i	$-0.662485\pi$
$443$	8.08098	−	8.08098i	0.383939	−	0.383939i	0.872519	+	0.488580i	$0.162485\pi$
$444$	7.49994	+	18.1065i	0.355931	+	0.859295i
$445$	−2.05025	+	1.36727i	−0.0971910	+	0.0648146i
$446$	9.65170	−	9.65170i	0.457021	−	0.457021i
$447$	10.5778	−	53.1782i	0.500313	−	2.51524i
$448$	0.724218	−	1.08387i	0.0342161	−	0.0512080i
$449$	−9.49028	−	6.34120i	−0.447874	−	0.299260i	0.311104	−	0.950376i	$-0.399301\pi$
$449$	−9.49028	−	6.34120i	−0.447874	−	0.299260i	−0.758978	+	0.651116i	$0.774301\pi$
$450$	22.7220	−	9.36392i	1.07112	−	0.441419i
$451$	−42.8205	−	17.7368i	−2.01634	−	0.835194i
$452$	−2.20717	−	11.0962i	−0.103816	−	0.521920i
$453$	19.9534	+	13.3325i	0.937494	+	0.626414i
$454$	4.38201	+	6.55814i	0.205658	+	0.307789i
$455$	0.0139899	−	15.5593i	0.000655855	−	0.729429i
$456$	0.447101	−	2.24773i	0.0209374	−	0.105260i
$457$	3.07536	−	7.42458i	0.143859	−	0.347307i	−0.835483	−	0.549516i	$-0.814812\pi$
$457$	3.07536	−	7.42458i	0.143859	−	0.347307i	0.979342	+	0.202209i	$0.0648121\pi$
$458$	7.49447	+	7.49447i	0.350193	+	0.350193i
$459$	2.33090	−	22.0932i	0.108797	−	1.03122i
$460$	0.0140771	−	15.6563i	0.000656348	−	0.729978i
$461$	32.2280	−	13.3493i	1.50101	−	0.621737i	0.527328	−	0.849662i	$-0.323194\pi$
$461$	32.2280	−	13.3493i	1.50101	−	0.621737i	0.973679	+	0.227924i	$0.0731939\pi$
$462$	11.9117	+	17.8271i	0.554181	+	0.829390i
$463$			39.0872i			1.81654i	0.418386	+	0.908269i	$0.362596\pi$
$463$			39.0872i			1.81654i	−0.418386	+	0.908269i	$0.637404\pi$
$464$	−1.75178	+	1.17050i	−0.0813245	+	0.0543393i
$465$	−9.53147	+	1.88702i	−0.442012	+	0.0875085i
$466$	−1.32642	+	1.98513i	−0.0614454	+	0.0919595i
$467$	15.5971	−	6.46053i	0.721748	−	0.298958i	0.00859198	−	0.999963i	$-0.497265\pi$
$467$	15.5971	−	6.46053i	0.721748	−	0.298958i	0.713156	+	0.701005i	$0.247265\pi$
$468$	−24.2397	+	10.0404i	−1.12048	+	0.464118i
$469$	−4.22385	+	6.32144i	−0.195039	+	0.291897i
$470$	0.204288	+	0.136767i	0.00942309	+	0.00630857i
$471$	−2.05856	+	1.37549i	−0.0948535	+	0.0633791i
$472$		−	5.50244i		−	0.253270i
$473$	−4.61891	−	6.91269i	−0.212378	−	0.317846i
$474$	−13.2838	+	5.50235i	−0.610147	+	0.252731i
$475$	0.00732427	−	4.07295i	0.000336060	−	0.186880i
$476$	−3.38077	−	4.17827i	−0.154957	−	0.191511i
$477$	−3.44347	−	3.44347i	−0.157665	−	0.157665i
$478$	4.00988	−	9.68071i	0.183408	−	0.442785i
$479$	1.23929	−	6.23034i	0.0566247	−	0.284672i	−0.942090	−	0.335361i	$-0.891142\pi$
$479$	1.23929	−	6.23034i	0.0566247	−	0.284672i	0.998714	+	0.0506892i	$0.0161418\pi$
$480$	−6.29093	−	0.00565639i	−0.287140	−	0.000258178i
$481$	−20.6586	−	30.9178i	−0.941950	−	1.40973i
$482$	−5.38993	−	3.60143i	−0.245504	−	0.164041i
$483$	5.00957	+	25.1848i	0.227943	+	1.14595i
$484$	−21.4136	−	8.86981i	−0.973346	−	0.403173i
$485$	−12.9099	+	31.0881i	−0.586208	+	1.41164i
$486$	−12.4732	−	8.33431i	−0.565795	−	0.378052i
$487$	−15.0153	+	22.4720i	−0.680407	+	1.01830i	0.317145	+	0.948377i	$0.397276\pi$
$487$	−15.0153	+	22.4720i	−0.680407	+	1.01830i	−0.997552	+	0.0699246i	$0.977724\pi$
$488$	−1.13253	+	5.69362i	−0.0512673	+	0.257738i
$489$	13.5538	−	13.5538i	0.612924	−	0.612924i
$490$	2.32282	−	11.6230i	0.104934	−	0.525072i
$491$	−0.0788074	−	0.190258i	−0.00355653	−	0.00858621i	0.922091	−	0.386972i	$-0.126479\pi$
$491$	−0.0788074	−	0.190258i	−0.00355653	−	0.00858621i	−0.925648	+	0.378386i	$0.876479\pi$
$492$	−15.7717	+	15.7717i	−0.711042	+	0.711042i
$493$	2.46389	+	8.33002i	0.110968	+	0.375165i
$494$			4.34824i			0.195636i
$495$	24.6421	−	59.3403i	1.10758	−	2.66715i
$496$	1.51484	+	0.301321i	0.0680184	+	0.0135297i
$497$	7.16319			0.321313
$498$	7.12021	+	1.41630i	0.319064	+	0.0634658i
$499$	4.34370	+	21.8373i	0.194451	+	0.977570i	0.947536	+	0.319648i	$0.103565\pi$
$499$	4.34370	+	21.8373i	0.194451	+	0.977570i	−0.753086	+	0.657923i	$0.771435\pi$
$500$	−10.9714	+	2.15159i	−0.490654	+	0.0962220i
$501$	−14.4507	+	34.8871i	−0.645609	+	1.55864i
$502$	−8.35260	−	20.1650i	−0.372795	−	0.900007i
$503$	1.59744	−	0.317750i	0.0712262	−	0.0141678i	−0.159349	−	0.987222i	$-0.550939\pi$
$503$	1.59744	−	0.317750i	0.0712262	−	0.0141678i	0.230575	+	0.973055i	$0.425939\pi$
$504$	6.28410	−	1.24998i	0.279916	−	0.0556787i
$505$	−14.8135	−	2.96044i	−0.659193	−	0.131738i
$506$	−28.9442	−	28.9442i	−1.28673	−	1.28673i
$507$	36.2433	−	24.2170i	1.60962	−	1.07552i
$508$	−3.29207	−	1.36362i	−0.146062	−	0.0605009i
$509$	35.1547			1.55820			0.779102	−	0.626897i	$-0.215675\pi$
$509$	35.1547			1.55820			0.779102	+	0.626897i	$0.215675\pi$
$510$	−7.72380	+	24.7615i	−0.342015	+	1.09646i
$511$	10.6671			0.471883
$512$	0.923880	+	0.382683i	0.0408301	+	0.0169124i
$513$	3.64941	−	2.43846i	0.161126	−	0.107661i
$514$	−6.86243	−	6.86243i	−0.302689	−	0.302689i
$515$	8.34091	+	12.5074i	0.367544	+	0.551141i
$516$	−3.92402	+	0.780537i	−0.172746	+	0.0343612i
$517$	0.630404	−	0.125395i	0.0277251	−	0.00551487i
$518$	3.47503	+	8.38946i	0.152684	+	0.368612i
$519$	−25.4529	+	61.4487i	−1.11726	+	2.69730i
$520$	11.7087	−	2.31807i	0.513462	−	0.101654i
$521$	6.77862	+	34.0784i	0.296977	+	1.49300i	0.784629	+	0.619965i	$0.212853\pi$
$521$	6.77862	+	34.0784i	0.296977	+	1.49300i	−0.487653	+	0.873038i	$0.662147\pi$
$522$	−10.1566	−	2.02026i	−0.444540	−	0.0884246i
$523$	−0.224643			−0.00982294			−0.00491147	−	0.999988i	$-0.501563\pi$
$523$	−0.224643			−0.00982294			−0.00491147	+	0.999988i	$0.501563\pi$
$524$	11.5654	+	2.30050i	0.505237	+	0.100498i
$525$	16.9539	−	6.98683i	0.739927	−	0.304930i
$526$			16.0185i			0.698438i
$527$	3.04086	−	5.59530i	0.132462	−	0.243735i
$528$	−11.6302	+	11.6302i	−0.506140	+	0.506140i
$529$	−9.95889	−	24.0429i	−0.432995	−	1.04534i
$530$	1.22917	+	1.84317i	0.0533917	+	0.0800620i
$531$	19.1240	−	19.1240i	0.829911	−	0.829911i
$532$	0.207160	−	1.04146i	0.00898153	−	0.0451532i
$533$	23.5112	−	35.1871i	1.01838	−	1.52412i
$534$	2.57804	+	1.72259i	0.111563	+	0.0745439i
$535$	−34.5372	−	14.3422i	−1.49317	−	0.620066i
$536$	−5.38834	−	2.23192i	−0.232741	−	0.0964043i
$537$	−13.6143	−	68.4438i	−0.587501	−	2.95357i
$538$	13.7058	+	9.15792i	0.590899	+	0.394826i
$539$	−17.2166	−	25.7665i	−0.741572	−	1.10984i
$540$	−8.51170	−	8.52702i	−0.366285	−	0.366944i
$541$	6.22565	−	31.2985i	0.267662	−	1.34563i	−0.579796	−	0.814762i	$-0.696868\pi$
$541$	6.22565	−	31.2985i	0.267662	−	1.34563i	0.847457	−	0.530864i	$-0.178132\pi$
$542$	−1.97962	+	4.77923i	−0.0850321	+	0.205286i
$543$	−11.2906	−	11.2906i	−0.484525	−	0.484525i
$544$	2.63773	−	3.16897i	0.113092	−	0.135869i
$545$	3.84765	−	3.84074i	0.164815	−	0.164519i
$546$	−18.0863	+	7.49159i	−0.774022	+	0.320610i
$547$	−3.82638	−	5.72658i	−0.163604	−	0.244851i	0.740605	−	0.671940i	$-0.234539\pi$
$547$	−3.82638	−	5.72658i	−0.163604	−	0.244851i	−0.904209	+	0.427090i	$0.859539\pi$
$548$			13.5679i			0.579593i
$549$	−23.7246	+	15.8523i	−1.01254	+	0.676559i
$550$	−16.2835	+	24.2754i	−0.694332	+	1.03511i
$551$	−0.953483	+	1.42699i	−0.0406197	+	0.0607917i
$552$	−18.1991	+	7.53830i	−0.774604	+	0.320851i
$553$	−6.15494	+	2.54946i	−0.261735	+	0.108414i
$554$	11.4847	−	17.1880i	0.487936	−	0.730248i
$555$	24.3796	−	36.4157i	1.03486	−	1.54576i
$556$	−8.57135	+	5.72719i	−0.363506	+	0.242887i
$557$		−	33.2286i		−	1.40794i	−0.710228	−	0.703971i	$-0.751408\pi$
$557$		−	33.2286i		−	1.40794i	0.710228	−	0.703971i	$-0.248592\pi$
$558$	4.21765	+	6.31216i	0.178548	+	0.267215i
$559$	7.01321	−	2.90496i	0.296627	−	0.122867i
$560$	−2.91484	−	0.00262084i	−0.123175	−	0.000110751i
$561$	31.5521	+	60.0281i	1.33213	+	2.53439i
$562$	0.924680	+	0.924680i	0.0390053	+	0.0390053i
$563$	8.49755	−	20.5149i	0.358129	−	0.864600i	−0.637434	−	0.770505i	$-0.720004\pi$
$563$	8.49755	−	20.5149i	0.358129	−	0.864600i	0.995563	−	0.0940950i	$-0.0299958\pi$
$564$	0.0603445	−	0.303372i	0.00254096	−	0.0127743i
$565$	−17.9044	+	17.8722i	−0.753243	+	0.751890i
$566$	−2.53325	−	3.79127i	−0.106480	−	0.159359i
$567$	0.448041	+	0.299372i	0.0188160	+	0.0125724i
$568$	1.07204	+	5.38952i	0.0449819	+	0.226139i
$569$	13.2905	+	5.50510i	0.557166	+	0.230786i	0.643454	−	0.765484i	$-0.277501\pi$
$569$	13.2905	+	5.50510i	0.557166	+	0.230786i	−0.0862883	+	0.996270i	$0.527501\pi$
$570$	−4.73622	+	1.95682i	−0.198378	+	0.0819621i
$571$	17.4454	+	11.6566i	0.730068	+	0.487816i	0.864200	−	0.503148i	$-0.167825\pi$
$571$	17.4454	+	11.6566i	0.730068	+	0.487816i	−0.134133	+	0.990963i	$0.542825\pi$
$572$	17.3375	−	25.9473i	0.724915	−	1.08491i
$573$	−0.157497	+	0.791791i	−0.00657953	+	0.0330775i
$574$	−7.30766	+	7.30766i	−0.305016	+	0.305016i
$575$	−29.1434	+	19.3973i	−1.21537	+	0.808924i
$576$	1.88095	+	4.54102i	0.0783731	+	0.189209i
$577$	13.0297	−	13.0297i	0.542435	−	0.542435i	−0.381807	−	0.924242i	$-0.624698\pi$
$577$	13.0297	−	13.0297i	0.542435	−	0.542435i	0.924242	+	0.381807i	$0.124698\pi$
$578$	−9.24760	−	14.2647i	−0.384650	−	0.593334i
$579$		−	68.9741i		−	2.86646i
$580$	4.35083	+	1.80676i	0.180659	+	0.0750216i
$581$	3.29908	+	0.656228i	0.136869	+	0.0272249i
$582$	42.3532			1.75560
$583$	5.68093	+	1.13001i	0.235280	+	0.0468001i
$584$	1.59643	+	8.02579i	0.0660607	+	0.332110i
$585$	48.7508	+	32.6377i	2.01560	+	1.34940i
$586$	11.9708	−	28.9001i	0.494510	−	1.19385i
$587$	8.94250	+	21.5891i	0.369096	+	0.891077i	0.993899	+	0.110295i	$0.0351795\pi$
$587$	8.94250	+	21.5891i	0.369096	+	0.891077i	−0.624803	+	0.780783i	$0.714821\pi$
$588$	−14.6265	+	2.90939i	−0.603186	+	0.119981i
$589$	1.23398	−	0.245453i	0.0508452	−	0.0101137i
$590$	−10.2364	+	6.82644i	−0.421426	+	0.281040i
$591$	5.00542	+	5.00542i	0.205895	+	0.205895i
$592$	−5.79208	+	3.87014i	−0.238053	+	0.159062i
$593$	−25.7677	−	10.6733i	−1.05815	−	0.438301i	−0.215357	−	0.976535i	$-0.569092\pi$
$593$	−25.7677	−	10.6733i	−1.05815	−	0.438301i	−0.842795	+	0.538234i	$0.819092\pi$
$594$	−31.4999			−1.29246
$595$	−3.57875	+	11.4730i	−0.146714	+	0.470348i
$596$	19.2721			0.789417
$597$	−33.6016	−	13.9182i	−1.37522	−	0.569636i
$598$	31.0759	−	20.7642i	1.27079	−	0.849113i
$599$	6.03820	+	6.03820i	0.246714	+	0.246714i	0.819621	−	0.572907i	$-0.194184\pi$
$599$	6.03820	+	6.03820i	0.246714	+	0.246714i	−0.572907	+	0.819621i	$0.694184\pi$
$600$	7.79414	+	11.7103i	0.318194	+	0.478070i
$601$	−1.21570	+	0.241819i	−0.0495896	+	0.00986398i	−0.219823	−	0.975540i	$-0.570548\pi$
$601$	−1.21570	+	0.241819i	−0.0495896	+	0.00986398i	0.170233	+	0.985404i	$0.445548\pi$
$602$	−1.81816	+	0.361655i	−0.0741027	+	0.0147399i
$603$	−10.9703	−	26.4846i	−0.446744	−	1.07854i
$604$	−3.26423	+	7.88055i	−0.132820	+	0.320655i
$605$	10.0653	+	50.8407i	0.409214	+	2.06697i
$606$	3.70803	+	18.6415i	0.150628	+	0.757260i
$607$	35.7149	+	7.10414i	1.44962	+	0.288348i	0.856243	−	0.516574i	$-0.172793\pi$
$607$	35.7149	+	7.10414i	1.44962	+	0.288348i	0.593381	+	0.804922i	$0.297793\pi$
$608$	0.814591			0.0330360
$609$	−7.57824	−	1.50741i	−0.307086	−	0.0610832i
$610$	11.9971	−	4.95673i	0.485749	−	0.200692i
$611$			0.586875i			0.0237424i
$612$	20.1815	−	1.84638i	0.815788	−	0.0746355i
$613$	−1.67709	+	1.67709i	−0.0677372	+	0.0677372i	−0.740164	−	0.672427i	$-0.765252\pi$
$613$	−1.67709	+	1.67709i	−0.0677372	+	0.0677372i	0.672427	+	0.740164i	$0.265252\pi$
$614$	6.55792	+	15.8322i	0.264656	+	0.638936i
$615$	48.9074	+	9.77400i	1.97213	+	0.394126i
$616$	−5.38876	+	5.38876i	−0.217119	+	0.217119i
$617$	−1.85351	+	9.31821i	−0.0746194	+	0.375137i	−0.999992	−	0.00392093i	$-0.998752\pi$
$617$	−1.85351	+	9.31821i	−0.0746194	+	0.375137i	0.925373	+	0.379058i	$0.123752\pi$
$618$	10.5086	−	15.7272i	0.422717	−	0.632640i
$619$	−33.6978	−	22.5162i	−1.35443	−	0.905001i	−0.354877	−	0.934913i	$-0.615477\pi$
$619$	−33.6978	−	22.5162i	−1.35443	−	0.905001i	−0.999553	+	0.0299118i	$0.990477\pi$
$620$	−1.31879	−	3.19195i	−0.0529637	−	0.128192i
$621$	−34.8543	−	14.4371i	−1.39865	−	0.579341i
$622$	1.07090	+	5.38379i	0.0429393	+	0.215870i
$623$	1.19451	+	0.798148i	0.0478571	+	0.0319771i
$624$	−8.34339	−	12.4868i	−0.334003	−	0.499871i
$625$	17.6140	+	17.7411i	0.704559	+	0.709645i
$626$	1.25044	−	6.28639i	0.0499777	−	0.251255i
$627$	−5.12723	+	12.3782i	−0.204762	+	0.494338i
$628$	−0.622261	−	0.622261i	−0.0248309	−	0.0248309i
$629$	8.14658	+	27.5423i	0.324825	+	1.09818i
$630$	−10.1216	−	10.1398i	−0.403253	−	0.403979i
$631$	−12.6410	+	5.23609i	−0.503232	+	0.208446i	−0.619834	−	0.784733i	$-0.712800\pi$
$631$	−12.6410	+	5.23609i	−0.503232	+	0.208446i	0.116602	+	0.993179i	$0.462800\pi$
$632$	−2.83934	−	4.24937i	−0.112943	−	0.169031i
$633$		−	40.1233i		−	1.59476i
$634$	−16.0464	+	10.7218i	−0.637283	+	0.425819i
$635$	1.54742	+	7.81610i	0.0614073	+	0.310173i
$636$	1.54861	−	2.31766i	0.0614063	−	0.0919010i
$637$	26.1412	−	10.8280i	1.03575	−	0.429022i
$638$	11.3795	−	4.71353i	0.450518	−	0.186611i
$639$	−15.0056	+	22.4575i	−0.593613	+	0.888404i
$640$	−0.434263	−	2.19349i	−0.0171658	−	0.0867055i
$641$	−28.3365	+	18.9339i	−1.11923	+	0.747843i	−0.970516	−	0.241038i	$-0.922512\pi$
$641$	−28.3365	+	18.9339i	−1.11923	+	0.747843i	−0.148711	+	0.988881i	$0.547512\pi$
$642$			47.0520i			1.85700i
$643$	6.38975	+	9.56293i	0.251987	+	0.377125i	0.935800	−	0.352532i	$-0.114679\pi$
$643$	6.38975	+	9.56293i	0.251987	+	0.377125i	−0.683813	+	0.729658i	$0.739679\pi$
$644$	−8.43237	+	3.49280i	−0.332282	+	0.137636i
$645$	6.32029	+	6.33167i	0.248861	+	0.249309i
$646$	0.997245	−	3.20718i	0.0392361	−	0.126185i
$647$	22.0524	+	22.0524i	0.866968	+	0.866968i	0.992136	−	0.125168i	$-0.0399469\pi$
$647$	22.0524	+	22.0524i	0.866968	+	0.866968i	−0.125168	+	0.992136i	$0.539947\pi$
$648$	−0.158191	+	0.381906i	−0.00621432	+	0.0150027i
$649$	−6.27573	+	31.5502i	−0.246344	+	1.23845i
$650$	−18.8385	−	18.9064i	−0.738906	−	0.741569i
$651$	3.14697	+	4.70978i	0.123340	+	0.184591i
$652$	5.66490	+	3.78517i	0.221855	+	0.148239i
$653$	9.02163	+	45.3548i	0.353044	+	1.77487i	0.594132	+	0.804368i	$0.297496\pi$
$653$	9.02163	+	45.3548i	0.353044	+	1.77487i	−0.241088	+	0.970503i	$0.577504\pi$
$654$	−6.31947	−	2.61761i	−0.247111	−	0.102357i
$655$	−10.0686	−	24.3696i	−0.393411	−	0.952199i
$656$	−6.59188	−	4.40455i	−0.257370	−	0.171969i
$657$	−22.3456	+	33.4425i	−0.871783	+	1.30472i
$658$	0.0279601	−	0.140565i	0.00109000	−	0.00547979i
$659$	−26.4734	+	26.4734i	−1.03126	+	1.03126i	−0.0317611	+	0.999495i	$0.510112\pi$
$659$	−26.4734	+	26.4734i	−1.03126	+	1.03126i	−0.999495	+	0.0317611i	$0.989888\pi$
$660$	36.0648	+	7.20746i	1.40382	+	0.280550i
$661$	−3.99375	−	9.64176i	−0.155339	−	0.375021i	0.826981	−	0.562229i	$-0.190056\pi$
$661$	−3.99375	−	9.64176i	−0.155339	−	0.375021i	−0.982320	+	0.187208i	$0.940056\pi$
$662$	10.2265	−	10.2265i	0.397465	−	0.397465i
$663$	−59.3767	+	17.5627i	−2.30600	+	0.682077i
$664$			2.58041i			0.100139i
$665$	−2.19448	+	0.906674i	−0.0850984	+	0.0351593i
$666$	−33.5815	−	6.67978i	−1.30126	−	0.258836i
$667$	14.7516			0.571182
$668$	−13.1642	−	2.61851i	−0.509336	−	0.101313i
$669$	7.49177	+	37.6637i	0.289649	+	1.45616i
$670$	2.53275	+	12.7931i	0.0978487	+	0.494241i
$671$	12.9876	−	31.3547i	0.501379	−	1.21044i
$672$	1.40346	+	3.38825i	0.0541397	+	0.130705i
$673$	−9.10724	+	1.81154i	−0.351058	+	0.0698299i	−0.367470	−	0.930035i	$-0.619776\pi$
$673$	−9.10724	+	1.81154i	−0.351058	+	0.0698299i	0.0164114	+	0.999865i	$0.494776\pi$
$674$	8.43768	−	1.67836i	0.325007	−	0.0646480i
$675$	−5.30335	+	26.4134i	−0.204126	+	1.01665i
$676$	10.9556	+	10.9556i	0.421370	+	0.421370i
$677$	−31.7217	+	21.1958i	−1.21916	+	0.814619i	−0.987414	−	0.158157i	$-0.949445\pi$
$677$	−31.7217	+	21.1958i	−1.21916	+	0.814619i	−0.231749	+	0.972776i	$0.574445\pi$
$678$	29.4066	+	12.1806i	1.12935	+	0.467794i
$679$	19.6240			0.753099
$680$	−9.16778	−	0.975568i	−0.351568	−	0.0374113i
$681$	−22.1904			−0.850336
$682$	−8.34222	−	3.45546i	−0.319440	−	0.132316i
$683$	−22.6804	+	15.1546i	−0.867842	+	0.579874i	−0.907836	−	0.419326i	$-0.862266\pi$
$683$	−22.6804	+	15.1546i	−0.867842	+	0.579874i	0.0399935	+	0.999200i	$0.487266\pi$
$684$	2.83115	+	2.83115i	0.108252	+	0.108252i
$685$	25.2409	−	16.8326i	0.964407	−	0.643142i
$686$	−15.7266	+	3.12822i	−0.600445	+	0.119436i
$687$	−29.2455	+	5.81730i	−1.11579	+	0.221944i
$688$	−0.544211	−	1.31384i	−0.0207479	−	0.0500898i
$689$	−2.02388	+	4.88609i	−0.0771038	+	0.186145i
$690$	36.6019	+	24.5043i	1.39341	+	0.932861i
$691$	−5.53015	−	27.8020i	−0.210377	−	1.05764i	−0.931198	−	0.364515i	$-0.881235\pi$
$691$	−5.53015	−	27.8020i	−0.210377	−	1.05764i	0.720821	−	0.693122i	$-0.243765\pi$
$692$	−23.1868	−	4.61214i	−0.881430	−	0.175327i
$693$	−37.4578			−1.42290
$694$	−33.4249	−	6.64863i	−1.26879	−	0.252378i
$695$	21.2883	+	8.84034i	0.807512	+	0.335333i
$696$		−	5.92740i		−	0.224677i
$697$	−25.4114	+	20.5612i	−0.962526	+	0.778809i
$698$	−4.84321	+	4.84321i	−0.183318	+	0.183318i
$699$	−2.57047	−	6.20567i	−0.0972242	−	0.234720i
$700$	3.61134	+	5.42585i	0.136496	+	0.205078i
$701$	−2.93942	+	2.93942i	−0.111020	+	0.111020i	−0.760435	−	0.649414i	$-0.775014\pi$
$701$	−2.93942	+	2.93942i	−0.111020	+	0.111020i	0.649414	+	0.760435i	$0.275014\pi$
$702$	5.61108	−	28.2088i	0.211776	−	1.06467i
$703$	−3.15259	+	4.71818i	−0.118902	+	0.177949i
$704$	−4.86093	−	3.24797i	−0.183203	−	0.122412i
$705$	−0.639240	+	0.264109i	−0.0240752	+	0.00994692i
$706$	21.9153	+	9.07762i	0.824794	+	0.341641i
$707$	1.71808	+	8.63737i	0.0646151	+	0.324842i
$708$	12.8716	+	8.60051i	0.483744	+	0.323227i
$709$	−9.66796	−	14.4691i	−0.363088	−	0.543399i	0.604281	−	0.796771i	$-0.293460\pi$
$709$	−9.66796	−	14.4691i	−0.363088	−	0.543399i	−0.967369	+	0.253372i	$0.918460\pi$
$710$	8.69634	−	8.68071i	0.326368	−	0.325781i
$711$	4.90063	−	24.6371i	0.183788	−	0.923965i
$712$	−0.421748	+	1.01819i	−0.0158057	+	0.0381583i
$713$	−7.64684	−	7.64684i	−0.286377	−	0.286377i
$714$	15.0583	−	1.37767i	0.563542	−	0.0515578i
$715$	−69.7800	−	0.0627416i	−2.60963	−	0.00234640i
$716$	22.9163	−	9.49226i	0.856424	−	0.354742i
$717$	16.3780	+	24.5114i	0.611647	+	0.915395i
$718$		−	26.1314i		−	0.975216i
$719$	−7.89793	+	5.27723i	−0.294543	+	0.196807i	−0.694058	−	0.719919i	$-0.744179\pi$
$719$	−7.89793	+	5.27723i	−0.294543	+	0.196807i	0.399515	+	0.916727i	$0.369179\pi$
$720$	6.11429	−	9.13290i	0.227866	−	0.340363i
$721$	4.86905	−	7.28705i	0.181333	−	0.271384i
$722$	−16.9407	+	7.01705i	−0.630466	+	0.261148i
$723$	16.8493	−	6.97921i	0.626632	−	0.259560i
$724$	3.15311	−	4.71897i	0.117185	−	0.175379i
$725$	−2.03655	−	10.3355i	−0.0756355	−	0.383852i
$726$	54.2190	−	36.2280i	2.01225	−	1.34455i
$727$			11.5433i			0.428116i	0.976821	+	0.214058i	$0.0686681\pi$
$727$			11.5433i			0.428116i	−0.976821	+	0.214058i	$0.931332\pi$
$728$	−3.86583	−	5.78563i	−0.143277	−	0.214430i
$729$	40.1378	−	16.6256i	1.48658	−	0.615764i
$730$	12.9501	−	12.9269i	0.479306	−	0.478445i
$731$	−5.83905	+	0.534208i	−0.215965	+	0.0197584i
$732$	−11.5486	−	11.5486i	−0.426849	−	0.426849i
$733$	1.12997	−	2.72799i	0.0417363	−	0.100760i	−0.901637	−	0.432494i	$-0.857634\pi$
$733$	1.12997	−	2.72799i	0.0417363	−	0.100760i	0.943373	+	0.331734i	$0.107634\pi$
$734$	2.97569	−	14.9598i	0.109835	−	0.552176i
$735$	23.5584	+	23.6008i	0.868964	+	0.870528i
$736$	−3.88994	−	5.82170i	−0.143385	−	0.214591i
$737$	28.3504	+	18.9431i	1.04430	+	0.697778i
$738$	−7.60216	−	38.2186i	−0.279839	−	1.40685i
$739$	9.10333	+	3.77072i	0.334871	+	0.138708i	0.543782	−	0.839226i	$-0.316992\pi$
$739$	9.10333	+	3.77072i	0.334871	+	0.138708i	−0.208911	+	0.977935i	$0.566992\pi$
$740$	14.3856	+	5.97385i	0.528823	+	0.219603i
$741$	−10.1716	−	6.79645i	−0.373663	−	0.249674i
$742$	0.717533	−	1.07386i	0.0263415	−	0.0394228i
$743$	0.496966	−	2.49842i	0.0182319	−	0.0916580i	−0.970598	−	0.240706i	$-0.922621\pi$
$743$	0.496966	−	2.49842i	0.0182319	−	0.0916580i	0.988830	+	0.149048i	$0.0476210\pi$
$744$	−3.07262	+	3.07262i	−0.112648	+	0.112648i
$745$	−23.9094	−	35.8527i	−0.875972	−	1.31354i
$746$	1.95672	+	4.72394i	0.0716406	+	0.172956i
$747$	−8.96834	+	8.96834i	−0.328134	+	0.328134i
$748$	−18.7387	+	15.1620i	−0.685154	+	0.554379i
$749$			21.8011i			0.796596i
$750$	12.1155	−	29.0277i	0.442396	−	1.05994i
$751$	−28.9085	−	5.75025i	−1.05489	−	0.209830i	−0.362964	−	0.931803i	$-0.618235\pi$
$751$	−28.9085	−	5.75025i	−1.05489	−	0.209830i	−0.691921	+	0.721973i	$0.743235\pi$
$752$	0.109944			0.00400925
$753$	60.2263	+	11.9798i	2.19477	+	0.436567i
$754$	2.19403	+	11.0302i	0.0799020	+	0.401694i
$755$	18.7102	−	3.70420i	0.680933	−	0.134810i
$756$	−2.68786	+	6.48908i	−0.0977566	+	0.236005i
$757$	−3.97997	−	9.60850i	−0.144655	−	0.349227i	0.834901	−	0.550400i	$-0.185525\pi$
$757$	−3.97997	−	9.60850i	−0.144655	−	0.349227i	−0.979556	+	0.201173i	$0.935525\pi$
$758$	−24.2766	+	4.82892i	−0.881766	+	0.175394i
$759$	112.949	−	22.4669i	4.09977	−	0.815495i
$760$	−1.01060	−	1.51542i	−0.0366583	−	0.0549699i
$761$	−0.842952	−	0.842952i	−0.0305570	−	0.0305570i	0.691663	−	0.722220i	$-0.256878\pi$
$761$	−0.842952	−	0.842952i	−0.0305570	−	0.0305570i	−0.722220	+	0.691663i	$0.756878\pi$
$762$	8.33548	−	5.56959i	0.301962	−	0.201765i
$763$	−2.92807	−	1.21285i	−0.106003	−	0.0439080i
$764$	−0.286950			−0.0103815
$765$	−28.4724	−	35.2537i	−1.02942	−	1.27460i
$766$	−16.7778			−0.606206
$767$	−27.1359	−	11.2401i	−0.979820	−	0.405855i
$768$	−2.33925	+	1.56304i	−0.0844104	+	0.0564012i
$769$	−5.06321	−	5.06321i	−0.182584	−	0.182584i	0.609897	−	0.792481i	$-0.291211\pi$
$769$	−5.06321	−	5.06321i	−0.182584	−	0.182584i	−0.792481	+	0.609897i	$0.791211\pi$
$770$	16.7103	+	3.33951i	0.602198	+	0.120348i
$771$	26.7791	−	5.32670i	0.964427	−	0.191837i
$772$	24.0453	−	4.78290i	0.865408	−	0.172140i
$773$	−0.443463	−	1.07061i	−0.0159502	−	0.0385073i	0.915704	−	0.401854i	$-0.131634\pi$
$773$	−0.443463	−	1.07061i	−0.0159502	−	0.0385073i	−0.931654	+	0.363347i	$0.881634\pi$
$774$	2.67489	−	6.45775i	0.0961469	−	0.232119i
$775$	−4.30199	+	6.41338i	−0.154532	+	0.230375i
$776$	2.93692	+	14.7649i	0.105429	+	0.530029i
$777$	−25.0566	−	4.98407i	−0.898902	−	0.178803i
$778$	−11.2501			−0.403335
$779$	−6.33398	−	1.25991i	−0.226938	−	0.0451409i
$780$	−12.8786	+	31.0129i	−0.461129	+	1.11044i
$781$		−	32.1254i		−	1.14954i
$782$	−27.6832	+	8.18824i	−0.989948	+	0.292811i
$783$	8.02705	−	8.02705i	0.286863	−	0.286863i
$784$	−2.02850	−	4.89724i	−0.0724465	−	0.174901i
$785$	−0.385626	+	1.92961i	−0.0137636	+	0.0688706i
$786$	−23.4586	+	23.4586i	−0.836740	+	0.836740i
$787$	−7.24294	+	36.4127i	−0.258183	+	1.29797i	0.606270	+	0.795259i	$0.292665\pi$
$787$	−7.24294	+	36.4127i	−0.258183	+	1.29797i	−0.864453	+	0.502714i	$0.832335\pi$
$788$	−1.39786	+	2.09205i	−0.0497968	+	0.0745261i
$789$	−37.4712	−	25.0374i	−1.33401	−	0.891356i
$790$	−4.38273	+	10.5540i	−0.155930	+	0.375494i
$791$	13.6253	+	5.64377i	0.484459	+	0.200669i
$792$	−5.60592	−	28.1829i	−0.199198	−	1.00143i
$793$	25.7653	+	17.2158i	0.914951	+	0.611351i
$794$	20.7302	+	31.0249i	0.735687	+	1.10103i
$795$	−6.23286	−	0.00560418i	−0.221057	−	0.000198760i
$796$	2.52203	−	12.6791i	0.0893911	−	0.449399i
$797$	−0.0157219	+	0.0379559i	−0.000556897	+	0.00134447i	−0.924158	−	0.382011i	$-0.875232\pi$
$797$	−0.0157219	+	0.0379559i	−0.000556897	+	0.00134447i	0.923601	+	0.383356i	$0.125232\pi$
$798$	2.11245	+	2.11245i	0.0747797	+	0.0747797i
$799$	0.134597	−	0.432868i	0.00476169	−	0.0153138i
$800$	−3.54189	+	3.52917i	−0.125225	+	0.124775i
$801$	−5.00458	+	2.07296i	−0.176828	+	0.0732446i
$802$	2.20217	+	3.29578i	0.0777614	+	0.116378i
$803$		−	47.8395i		−	1.68822i
$804$	13.6432	−	9.11608i	0.481158	−	0.321500i
$805$	16.9592	+	11.3538i	0.597732	+	0.400170i
$806$	4.58043	−	6.85509i	0.161339	−	0.241460i
$807$	−42.8453	+	17.7471i	−1.50823	+	0.624727i
$808$	−6.24155	+	2.58533i	−0.219577	+	0.0909518i
$809$	21.2673	−	31.8287i	0.747717	−	1.11904i	−0.241186	−	0.970479i	$-0.577537\pi$
$809$	21.2673	−	31.8287i	0.747717	−	1.11904i	0.988904	−	0.148559i	$-0.0474635\pi$
$810$	0.906729	−	0.179512i	0.0318592	−	0.00630742i
$811$	−3.94173	+	2.63378i	−0.138413	+	0.0924845i	−0.622849	−	0.782342i	$-0.714025\pi$
$811$	−3.94173	+	2.63378i	−0.138413	+	0.0924845i	0.484436	+	0.874827i	$0.339025\pi$
$812$		−	2.74641i		−	0.0963799i
$813$	−8.08560	−	12.1009i	−0.283574	−	0.424399i
$814$	37.6250	−	15.5848i	1.31876	−	0.546246i
$815$	0.0136979	−	15.2346i	0.000479818	−	0.533644i
$816$	3.29016	+	11.1235i	0.115179	+	0.389401i
$817$	−0.819129	−	0.819129i	−0.0286577	−	0.0286577i
$818$	0.116628	−	0.281565i	0.00407780	−	0.00984469i
$819$	6.67234	−	33.5441i	0.233150	−	1.17213i
$820$	−0.0159394	+	17.7275i	−0.000556629	+	0.619072i
$821$	24.1132	+	36.0879i	0.841555	+	1.25948i	0.963706	+	0.266965i	$0.0860208\pi$
$821$	24.1132	+	36.0879i	0.841555	+	1.25948i	−0.122151	+	0.992512i	$0.538979\pi$
$822$	−31.7388	−	21.2072i	−1.10702	−	0.739685i
$823$	−6.32657	−	31.8058i	−0.220531	−	1.10868i	−0.919367	−	0.393401i	$-0.871299\pi$
$823$	−6.32657	−	31.8058i	−0.220531	−	1.10868i	0.698837	−	0.715281i	$-0.253701\pi$
$824$	6.21141	+	2.57285i	0.216385	+	0.0896294i
$825$	−31.3345	−	76.0346i	−1.09093	−	2.64718i
$826$	5.96393	+	3.98497i	0.207512	+	0.138655i
$827$	−24.8130	+	37.1352i	−0.862832	+	1.29132i	0.0924789	+	0.995715i	$0.470521\pi$
$827$	−24.8130	+	37.1352i	−0.862832	+	1.29132i	−0.955311	+	0.295604i	$0.904479\pi$
$828$	6.71394	−	33.7533i	0.233326	−	1.17301i
$829$	24.9924	−	24.9924i	0.868024	−	0.868024i	−0.124230	−	0.992253i	$-0.539646\pi$
$829$	24.9924	−	24.9924i	0.868024	−	0.868024i	0.992253	+	0.124230i	$0.0396460\pi$
$830$	4.80044	−	3.20131i	0.166626	−	0.111119i
$831$	22.2561	+	53.7309i	0.772055	+	1.86390i
$832$	3.77449	−	3.77449i	0.130857	−	0.130857i
$833$	−21.7646	+	1.99122i	−0.754098	+	0.0689917i
$834$		−	29.0023i		−	1.00427i
$835$	11.4604	+	27.7384i	0.396603	+	0.959926i
$836$	−4.67075	−	0.929070i	−0.161541	−	0.0321326i
$837$	−8.32205			−0.287652
$838$	−35.8559	−	7.13218i	−1.23862	−	0.246377i
$839$	−9.26094	−	46.5579i	−0.319723	−	1.60736i	−0.722037	−	0.691855i	$-0.756794\pi$
$839$	−9.26094	−	46.5579i	−0.319723	−	1.60736i	0.402314	−	0.915502i	$-0.368206\pi$
$840$	4.56214	−	6.81445i	0.157409	−	0.235121i
$841$	9.39915	−	22.6916i	0.324109	−	0.782468i
$842$	−8.51010	−	20.5452i	−0.293277	−	0.708034i
$843$	−3.60837	+	0.717749i	−0.124279	+	0.0247206i
$844$	13.9875	−	2.78229i	0.481470	−	0.0957702i
$845$	6.78939	−	33.9729i	0.233562	−	1.16870i
$846$	0.382116	+	0.382116i	0.0131374	+	0.0131374i
$847$	25.1219	−	16.7859i	0.863197	−	0.576770i
$848$	0.915351	+	0.379151i	0.0314333	+	0.0130201i
$849$	12.8283			0.440265
$850$	9.55885	+	18.2655i	0.327866	+	0.626501i
$851$	48.7744			1.67196
$852$	−14.2831	−	5.91624i	−0.489330	−	0.202687i
$853$	−16.1374	+	10.7826i	−0.552533	+	0.369191i	−0.800273	−	0.599636i	$-0.795312\pi$
$853$	−16.1374	+	10.7826i	−0.552533	+	0.369191i	0.247740	+	0.968827i	$0.420312\pi$
$854$	−5.35094	−	5.35094i	−0.183106	−	0.183106i
$855$	1.75452	−	8.77929i	0.0600032	−	0.300245i
$856$	−16.4030	+	3.26275i	−0.560642	+	0.111519i
$857$	12.8130	−	2.54865i	0.437682	−	0.0870604i	0.0286691	−	0.999589i	$-0.490873\pi$
$857$	12.8130	−	2.54865i	0.437682	−	0.0870604i	0.409013	+	0.912529i	$0.365873\pi$
$858$	33.5982	+	81.1133i	1.14702	+	2.76916i
$859$	−8.74774	+	21.1189i	−0.298469	+	0.720568i	0.701500	+	0.712670i	$0.252514\pi$
$859$	−8.74774	+	21.1189i	−0.298469	+	0.720568i	−0.999969	+	0.00789846i	$0.997486\pi$
$860$	−1.76903	+	2.64240i	−0.0603235	+	0.0901050i
$861$	−5.67230	−	28.5166i	−0.193312	−	0.971843i
$862$	34.8166	+	6.92546i	1.18586	+	0.235882i
$863$	48.9670			1.66686			0.833429	−	0.552627i	$-0.186375\pi$
$863$	48.9670			1.66686			0.833429	+	0.552627i	$0.186375\pi$
$864$	−5.28458	−	1.05117i	−0.179785	−	0.0357615i
$865$	20.1859	+	48.8572i	0.686341	+	1.66120i
$866$			4.70842i			0.159999i
$867$	47.8230	+	0.663809i	1.62416	+	0.0225441i
$868$	−1.42367	+	1.42367i	−0.0483225	+	0.0483225i
$869$	11.4338	+	27.6036i	0.387865	+	0.936390i
$870$	−11.0270	+	7.35365i	−0.373849	+	0.249312i
$871$	−22.0139	+	22.0139i	−0.745914	+	0.745914i
$872$	0.474319	−	2.38457i	0.0160625	−	0.0807516i
$873$	−41.1087	+	61.5235i	−1.39132	+	2.08226i
$874$	−4.74231	−	3.16871i	−0.160411	−	0.107183i
$875$	5.61362	−	13.4497i	0.189775	−	0.454684i
$876$	−21.2696	−	8.81016i	−0.718633	−	0.297668i
$877$	−1.88944	−	9.49886i	−0.0638019	−	0.320754i	0.935683	−	0.352841i	$-0.114784\pi$
$877$	−1.88944	−	9.49886i	−0.0638019	−	0.320754i	−0.999485	+	0.0320876i	$0.989784\pi$
$878$	−14.1420	−	9.44938i	−0.477269	−	0.318901i
$879$	48.8937	+	73.1747i	1.64915	+	2.46812i
$880$	−0.0117539	+	13.0725i	−0.000396224	+	0.440673i
$881$	−3.65125	+	18.3561i	−0.123014	+	0.618431i	0.869259	+	0.494356i	$0.164596\pi$
$881$	−3.65125	+	18.3561i	−0.123014	+	0.618431i	−0.992273	+	0.124075i	$0.960404\pi$
$882$	9.97043	−	24.0708i	0.335722	−	0.810505i
$883$	−19.9922	−	19.9922i	−0.672793	−	0.672793i	0.285566	−	0.958359i	$-0.407818\pi$
$883$	−19.9922	−	19.9922i	−0.672793	−	0.672793i	−0.958359	+	0.285566i	$0.907818\pi$
$884$	−10.2400	−	19.4816i	−0.344407	−	0.655238i
$885$	0.0311240	−	34.6155i	0.00104622	−	1.16359i
$886$	−10.5583	+	4.37340i	−0.354713	+	0.146927i
$887$	−29.6178	−	44.3262i	−0.994469	−	1.48833i	−0.868128	−	0.496340i	$-0.834677\pi$
$887$	−29.6178	−	44.3262i	−0.994469	−	1.48833i	−0.126341	−	0.991987i	$-0.540323\pi$
$888$		−	19.5983i		−	0.657676i
$889$	3.86217	−	2.58062i	0.129533	−	0.0865511i
$890$	2.41741	−	0.478594i	0.0810318	−	0.0160425i
$891$	1.34262	−	2.00937i	0.0449795	−	0.0673165i
$892$	−12.6106	+	5.22346i	−0.422233	+	0.174894i
$893$	0.0827422	−	0.0342730i	0.00276886	−	0.00114690i
$894$	−30.1230	+	45.0823i	−1.00746	+	1.50778i
$895$	−46.0893	−	30.8559i	−1.54060	−	1.03140i
$896$	−1.08387	+	0.724218i	−0.0362095	+	0.0241944i
$897$			105.150i			3.51084i
$898$	6.34120	+	9.49028i	0.211609	+	0.316695i
$899$	3.00637	−	1.24528i	0.100268	−	0.0415324i
$900$	−24.5758	−	0.0441939i	−0.819193	−	0.00147313i
$901$	2.61338	−	3.13972i	0.0870642	−	0.104599i
$902$	32.7734	+	32.7734i	1.09123	+	1.09123i
$903$	1.99585	−	4.81841i	0.0664178	−	0.160347i
$904$	−2.20717	+	11.0962i	−0.0734093	+	0.369053i
$905$	−12.6907	−	0.0114106i	−0.421853	−	0.000379303i
$906$	−13.3325	−	19.9534i	−0.442941	−	0.662909i
$907$	−28.6777	−	19.1618i	−0.952226	−	0.636257i	−0.0206435	−	0.999787i	$-0.506572\pi$
$907$	−28.6777	−	19.1618i	−0.952226	−	0.636257i	−0.931583	+	0.363530i	$0.881572\pi$
$908$	−1.53876	−	7.73585i	−0.0510654	−	0.256723i
$909$	−30.6783	−	12.7074i	−1.01753	−	0.421476i
$910$	−5.96720	+	14.3695i	−0.197811	+	0.476345i
$911$	−16.3825	−	10.9464i	−0.542777	−	0.362672i	0.253755	−	0.967269i	$-0.418334\pi$
$911$	−16.3825	−	10.9464i	−0.542777	−	0.362672i	−0.796532	+	0.604597i	$0.793334\pi$
$912$	−1.27324	+	1.90553i	−0.0421610	+	0.0630985i
$913$	2.94305	−	14.7957i	0.0974007	−	0.489666i
$914$	−5.68253	+	5.68253i	−0.187961	+	0.187961i
$915$	−7.15689	+	35.8118i	−0.236599	+	1.18390i
$916$	−4.05598	−	9.79199i	−0.134013	−	0.323537i
$917$	−10.8693	+	10.8693i	−0.358936	+	0.358936i
$918$	−10.6082	+	19.5194i	−0.350121	+	0.644237i
$919$		−	7.48557i		−	0.246926i	−0.992349	−	0.123463i	$-0.960600\pi$
$919$		−	7.48557i		−	0.246926i	0.992349	−	0.123463i	$-0.0394001\pi$
$920$	−6.00440	+	14.4591i	−0.197959	+	0.476703i
$921$	−47.2857	−	9.40572i	−1.55812	−	0.309929i
$922$	−34.8833			−1.14882
$923$	28.7689	+	5.72249i	0.946941	+	0.188358i
$924$	−4.18282	−	21.0285i	−0.137605	−	0.691786i
$925$	−6.73363	−	34.1733i	−0.221400	−	1.12361i
$926$	14.9580	−	36.1119i	0.491552	−	1.18671i
$927$	12.6460	+	30.5301i	0.415349	+	1.00274i
$928$	2.06637	−	0.411026i	0.0678319	−	0.0134926i
$929$	−23.3245	+	4.63954i	−0.765253	+	0.152218i	−0.562258	−	0.826962i	$-0.690067\pi$
$929$	−23.3245	+	4.63954i	−0.765253	+	0.152218i	−0.202995	+	0.979180i	$0.565067\pi$
$930$	9.52806	+	1.90416i	0.312438	+	0.0624398i
$931$	−3.05324	−	3.05324i	−0.100066	−	0.100066i
$932$	1.98513	−	1.32642i	0.0650252	−	0.0434484i
$933$	−14.2679	−	5.90995i	−0.467110	−	0.193483i
$934$	−16.8822			−0.552402
$935$	51.4541	+	16.0499i	1.68273	+	0.524889i
$936$	26.2369			0.857579
$937$	−27.2845	−	11.3016i	−0.891345	−	0.369207i	−0.110459	−	0.993881i	$-0.535232\pi$
$937$	−27.2845	−	11.3016i	−0.891345	−	0.369207i	−0.780886	+	0.624674i	$0.785232\pi$
$938$	6.32144	−	4.22385i	0.206402	−	0.137914i
$939$	12.7510	+	12.7510i	0.416112	+	0.416112i
$940$	−0.136399	−	0.204533i	−0.00444884	−	0.00667114i
$941$	1.26326	−	0.251277i	0.0411810	−	0.00819140i	−0.174457	−	0.984665i	$-0.555817\pi$
$941$	1.26326	−	0.251277i	0.0411810	−	0.00819140i	0.215638	+	0.976473i	$0.430817\pi$
$942$	2.42824	−	0.483007i	0.0791163	−	0.0157372i
$943$	21.2425	+	51.2840i	0.691752	+	1.67004i
$944$	−2.10569	+	5.08359i	−0.0685345	+	0.165457i
$945$	15.4065	−	3.05015i	0.501173	−	0.0992212i
$946$	1.62195	+	8.15407i	0.0527340	+	0.265112i
$947$	36.8415	+	7.32823i	1.19719	+	0.238136i	0.753136	−	0.657865i	$-0.228540\pi$
$947$	36.8415	+	7.32823i	1.19719	+	0.238136i	0.444052	+	0.896001i	$0.353540\pi$
$948$	14.3783			0.466986
$949$	42.8412	+	8.52164i	1.39068	+	0.276624i
$950$	−1.56542	+	3.76011i	−0.0507888	+	0.121994i
$951$		−	54.2951i		−	1.76064i
$952$	1.52447	+	5.15398i	0.0494082	+	0.167041i
$953$	25.9594	−	25.9594i	0.840908	−	0.840908i	−0.148069	−	0.988977i	$-0.547306\pi$
$953$	25.9594	−	25.9594i	0.840908	−	0.840908i	0.988977	+	0.148069i	$0.0473056\pi$
$954$	1.86359	+	4.49910i	0.0603360	+	0.145664i
$955$	0.355996	+	0.533825i	0.0115198	+	0.0172742i
$956$	−7.40929	+	7.40929i	−0.239634	+	0.239634i
$957$	−6.76041	+	33.9869i	−0.218533	+	1.09864i
$958$	−3.52921	+	5.28183i	−0.114023	+	0.170648i
$959$	−14.7059	−	9.82614i	−0.474877	−	0.317303i
$960$	5.80990	+	2.41266i	0.187514	+	0.0778683i
$961$	26.4363	+	10.9503i	0.852784	+	0.353235i
$962$	7.25433	+	36.4700i	0.233889	+	1.17584i
$963$	−68.3492	−	45.6695i	−2.20252	−	1.47168i
$964$	3.60143	+	5.38993i	0.115994	+	0.173598i
$965$	−38.7289	−	38.7986i	−1.24673	−	1.24897i
$966$	5.00957	−	25.1848i	0.161180	−	0.810307i
$967$	9.00902	−	21.7497i	0.289711	−	0.699423i	−0.710279	−	0.703920i	$-0.751431\pi$
$967$	9.00902	−	21.7497i	0.289711	−	0.699423i	0.999990	+	0.00449664i	$0.00143133\pi$
$968$	16.3893	+	16.3893i	0.526771	+	0.526771i
$969$	5.94366	+	7.34574i	0.190938	+	0.235979i
$970$	23.8241	−	23.7813i	0.764946	−	0.763571i
$971$	−16.1076	+	6.67199i	−0.516918	+	0.214114i	−0.625862	−	0.779933i	$-0.715253\pi$
$971$	−16.1076	+	6.67199i	−0.516918	+	0.214114i	0.108945	+	0.994048i	$0.465253\pi$
$972$	8.33431	+	12.4732i	0.267323	+	0.400078i
$973$		−	13.4380i		−	0.430801i
$974$	22.4720	−	15.0153i	0.720048	−	0.481121i
$975$	73.6719	−	14.5166i	2.35939	−	0.464903i
$976$	3.22518	−	4.82682i	0.103235	−	0.154503i
$977$	−11.9048	+	4.93111i	−0.380867	+	0.157760i	−0.564899	−	0.825160i	$-0.691085\pi$
$977$	−11.9048	+	4.93111i	−0.380867	+	0.157760i	0.184032	+	0.982920i	$0.441085\pi$
$978$	−17.7089	+	7.33526i	−0.566268	+	0.234556i
$979$	3.57953	−	5.35714i	0.114402	−	0.171215i
$980$	−6.59392	+	9.84932i	−0.210635	+	0.314625i
$981$	9.93619	−	6.63915i	0.317238	−	0.211972i
$982$			0.205934i			0.00657160i
$983$	18.1782	+	27.2056i	0.579795	+	0.867724i	0.999197	−	0.0400767i	$-0.0127602\pi$
$983$	18.1782	+	27.2056i	0.579795	+	0.867724i	−0.419402	+	0.907801i	$0.637760\pi$
$984$	20.6067	−	8.53557i	0.656918	−	0.272104i
$985$	5.62613	+	0.00505865i	0.179264	+	0.000161182i
$986$	0.911426	−	8.63883i	0.0290257	−	0.275116i
$987$	0.285114	+	0.285114i	0.00907526	+	0.00907526i
$988$	1.66400	−	4.01725i	0.0529388	−	0.127806i
$989$	−1.94253	+	9.76574i	−0.0617688	+	0.310533i
$990$	−45.4749	+	45.3932i	−1.44529	+	1.44269i
$991$	2.85767	+	4.27680i	0.0907767	+	0.135857i	0.874079	−	0.485785i	$-0.161466\pi$
$991$	2.85767	+	4.27680i	0.0907767	+	0.135857i	−0.783302	+	0.621642i	$0.786466\pi$
$992$	−1.28422	−	0.858089i	−0.0407741	−	0.0272444i
$993$	7.93796	+	39.9068i	0.251903	+	1.26640i
$994$	−6.61793	−	2.74124i	−0.209908	−	0.0869467i
$995$	−26.7163	+	11.0381i	−0.846965	+	0.349932i
$996$	−6.03622	−	4.03327i	−0.191265	−	0.127799i
$997$	28.9665	−	43.3514i	0.917378	−	1.37295i	−0.0104506	−	0.999945i	$-0.503327\pi$
$997$	28.9665	−	43.3514i	0.917378	−	1.37295i	0.927828	−	0.373007i	$-0.121673\pi$
$998$	4.34370	−	21.8373i	0.137498	−	0.691247i
$999$	26.5406	−	26.5406i	0.839706	−	0.839706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.r.a.37.4	yes	32
5.2	odd	4		850.2.s.c.343.1		32
5.3	odd	4		170.2.o.a.3.4	✓	32
5.4	even	2		850.2.v.c.207.1		32
17.6	odd	16		170.2.o.a.57.4	yes	32
85.23	even	16	inner	170.2.r.a.23.4	yes	32
85.57	even	16		850.2.v.c.193.1		32
85.74	odd	16		850.2.s.c.57.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.a.3.4	✓	32	5.3	odd	4
170.2.o.a.57.4	yes	32	17.6	odd	16
170.2.r.a.23.4	yes	32	85.23	even	16	inner
170.2.r.a.37.4	yes	32	1.1	even	1	trivial
850.2.s.c.57.1		32	85.74	odd	16
850.2.s.c.343.1		32	5.2	odd	4
850.2.v.c.193.1		32	85.57	even	16
850.2.v.c.207.1		32	5.4	even	2

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.923880 - 0.382683i) q^{2} +(2.33925 - 1.56304i) q^{3} +(0.707107 + 0.707107i) q^{4} +(0.438207 - 2.19271i) q^{5} +(-2.75933 + 0.548865i) q^{6} +(-1.27851 + 0.254312i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(1.88095 - 4.54102i) q^{9} +O(q^{10})\)	\(q+(-0.923880 - 0.382683i) q^{2} +(2.33925 - 1.56304i) q^{3} +(0.707107 + 0.707107i) q^{4} +(0.438207 - 2.19271i) q^{5} +(-2.75933 + 0.548865i) q^{6} +(-1.27851 + 0.254312i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(1.88095 - 4.54102i) q^{9} +(-1.24396 + 1.85810i) q^{10} +(1.14054 + 5.73386i) q^{11} +(2.75933 + 0.548865i) q^{12} -5.33794 q^{13} +(1.27851 + 0.254312i) q^{14} +(-2.40221 - 5.81423i) q^{15} +1.00000i q^{16} +(3.93717 + 1.22423i) q^{17} +(-3.47555 + 3.47555i) q^{18} +(0.311731 + 0.752584i) q^{19} +(1.86034 - 1.24062i) q^{20} +(-2.59326 + 2.59326i) q^{21} +(1.14054 - 5.73386i) q^{22} +(3.88994 - 5.82170i) q^{23} +(-2.33925 - 1.56304i) q^{24} +(-4.61595 - 1.92172i) q^{25} +(4.93161 + 2.04274i) q^{26} +(-1.05117 - 5.28458i) q^{27} +(-1.08387 - 0.724218i) q^{28} +(1.17050 + 1.75178i) q^{29} +(-0.00565639 + 6.29093i) q^{30} +(0.301321 - 1.51484i) q^{31} +(0.382683 - 0.923880i) q^{32} +(11.6302 + 11.6302i) q^{33} +(-3.16897 - 2.63773i) q^{34} +(-0.00262084 + 2.91484i) q^{35} +(4.54102 - 1.88095i) q^{36} +(3.87014 + 5.79208i) q^{37} -0.814591i q^{38} +(-12.4868 + 8.34339i) q^{39} +(-2.19349 + 0.434263i) q^{40} +(-4.40455 + 6.59188i) q^{41} +(3.38825 - 1.40346i) q^{42} +(-1.31384 + 0.544211i) q^{43} +(-3.24797 + 4.86093i) q^{44} +(-9.13290 - 6.11429i) q^{45} +(-5.82170 + 3.88994i) q^{46} -0.109944i q^{47} +(1.56304 + 2.33925i) q^{48} +(-4.89724 + 2.02850i) q^{49} +(3.52917 + 3.54189i) q^{50} +(11.1235 - 3.29016i) q^{51} +(-3.77449 - 3.77449i) q^{52} +(0.379151 - 0.915351i) q^{53} +(-1.05117 + 5.28458i) q^{54} +(13.0725 + 0.0117539i) q^{55} +(0.724218 + 1.08387i) q^{56} +(1.90553 + 1.27324i) q^{57} +(-0.411026 - 2.06637i) q^{58} +(5.08359 + 2.10569i) q^{59} +(2.41266 - 5.80990i) q^{60} +(-4.82682 - 3.22518i) q^{61} +(-0.858089 + 1.28422i) q^{62} +(-1.24998 + 6.28410i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(-2.33912 + 11.7045i) q^{65} +(-6.29423 - 15.1956i) q^{66} +(4.12405 - 4.12405i) q^{67} +(1.91834 + 3.64966i) q^{68} -19.6985i q^{69} +(1.11788 - 2.69196i) q^{70} +(-5.38952 - 1.07204i) q^{71} -4.91517 q^{72} +(-8.02579 - 1.59643i) q^{73} +(-1.35901 - 6.83222i) q^{74} +(-13.8016 + 2.71951i) q^{75} +(-0.311731 + 0.752584i) q^{76} +(-2.91637 - 7.04075i) q^{77} +(14.7291 - 2.92981i) q^{78} +(5.01247 - 0.997043i) q^{79} +(2.19271 + 0.438207i) q^{80} +(-0.292298 - 0.292298i) q^{81} +(6.59188 - 4.40455i) q^{82} +(-2.38399 - 0.987480i) q^{83} -3.66742 q^{84} +(4.40967 - 8.09659i) q^{85} +1.42209 q^{86} +(5.47620 + 2.26832i) q^{87} +(4.86093 - 3.24797i) q^{88} +(-0.779290 - 0.779290i) q^{89} +(6.09786 + 9.14388i) q^{90} +(6.82461 - 1.35750i) q^{91} +(6.86717 - 1.36596i) q^{92} +(-1.66289 - 4.01457i) q^{93} +(-0.0420738 + 0.101575i) q^{94} +(1.78680 - 0.353747i) q^{95} +(-0.548865 - 2.75933i) q^{96} +(-14.7649 - 2.93692i) q^{97} +5.30073 q^{98} +(28.1829 + 5.60592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} - 48 q^{15} + 16 q^{18} - 24 q^{25} + 8 q^{26} + 24 q^{27} - 8 q^{28} - 8 q^{29} - 16 q^{30} - 16 q^{31} + 64 q^{33} + 24 q^{34} + 32 q^{35} - 32 q^{37} - 32 q^{39} + 16 q^{41} - 24 q^{42} - 16 q^{43} - 16 q^{44} - 24 q^{45} - 16 q^{49} - 32 q^{50} + 32 q^{51} - 16 q^{52} + 16 q^{53} + 24 q^{54} - 8 q^{55} + 8 q^{56} - 24 q^{57} - 16 q^{58} - 64 q^{59} + 40 q^{60} - 24 q^{61} - 40 q^{62} - 24 q^{63} + 32 q^{65} + 16 q^{67} + 40 q^{70} + 8 q^{71} - 16 q^{72} + 32 q^{73} + 8 q^{74} - 56 q^{75} + 24 q^{77} + 32 q^{78} + 72 q^{79} + 8 q^{80} + 48 q^{81} + 48 q^{82} + 16 q^{83} + 8 q^{85} - 64 q^{86} + 40 q^{87} + 32 q^{88} + 16 q^{89} + 24 q^{90} + 48 q^{91} + 24 q^{92} - 8 q^{93} + 8 q^{94} + 56 q^{95} - 48 q^{97} - 64 q^{99}+O(q^{100}) \) 32 * q - 8 * q^10 - 48 * q^15 + 16 * q^18 - 24 * q^25 + 8 * q^26 + 24 * q^27 - 8 * q^28 - 8 * q^29 - 16 * q^30 - 16 * q^31 + 64 * q^33 + 24 * q^34 + 32 * q^35 - 32 * q^37 - 32 * q^39 + 16 * q^41 - 24 * q^42 - 16 * q^43 - 16 * q^44 - 24 * q^45 - 16 * q^49 - 32 * q^50 + 32 * q^51 - 16 * q^52 + 16 * q^53 + 24 * q^54 - 8 * q^55 + 8 * q^56 - 24 * q^57 - 16 * q^58 - 64 * q^59 + 40 * q^60 - 24 * q^61 - 40 * q^62 - 24 * q^63 + 32 * q^65 + 16 * q^67 + 40 * q^70 + 8 * q^71 - 16 * q^72 + 32 * q^73 + 8 * q^74 - 56 * q^75 + 24 * q^77 + 32 * q^78 + 72 * q^79 + 8 * q^80 + 48 * q^81 + 48 * q^82 + 16 * q^83 + 8 * q^85 - 64 * q^86 + 40 * q^87 + 32 * q^88 + 16 * q^89 + 24 * q^90 + 48 * q^91 + 24 * q^92 - 8 * q^93 + 8 * q^94 + 56 * q^95 - 48 * q^97 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more