LMFDB - Embedded newform 93.2.m.b.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(7,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 28]))

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

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

chi := DirichletCharacter("93.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.m (of order $15$, 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:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	93.7
Dual form			93.2.m.b.40.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.362683 + 1.11622i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.503620 - 0.365901i) q^{4} +(-2.03997 + 3.53333i) q^{5} +(-0.586833 - 1.01642i) q^{6} +(1.97984 + 0.881481i) q^{7} +(2.49011 + 1.80917i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})$	\(q+(0.362683 + 1.11622i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.503620 - 0.365901i) q^{4} +(-2.03997 + 3.53333i) q^{5} +(-0.586833 - 1.01642i) q^{6} +(1.97984 + 0.881481i) q^{7} +(2.49011 + 1.80917i) q^{8} +(0.913545 - 0.406737i) q^{9} +(-4.68384 - 0.995581i) q^{10} +(-0.660107 - 6.28050i) q^{11} +(-0.416540 + 0.462614i) q^{12} +(-1.09512 - 1.21625i) q^{13} +(-0.265876 + 2.52964i) q^{14} +(1.26077 - 3.88025i) q^{15} +(-0.731587 + 2.25159i) q^{16} +(0.198947 - 1.89285i) q^{17} +(0.785336 + 0.872204i) q^{18} +(0.411346 - 0.456845i) q^{19} +(0.265481 + 2.52588i) q^{20} +(-2.11984 - 0.450587i) q^{21} +(6.77102 - 3.01465i) q^{22} +(3.79430 + 2.75672i) q^{23} +(-2.81185 - 1.25191i) q^{24} +(-5.82294 - 10.0856i) q^{25} +(0.960427 - 1.66351i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.31962 - 0.280494i) q^{28} +(-0.358068 - 1.10202i) q^{29} +4.78848 q^{30} +(0.846253 + 5.50308i) q^{31} +3.37728 q^{32} +(1.95147 + 6.00601i) q^{33} +(2.18500 - 0.464435i) q^{34} +(-7.15337 + 5.19723i) q^{35} +(0.311254 - 0.539108i) q^{36} +(0.418263 + 0.724452i) q^{37} +(0.659129 + 0.293463i) q^{38} +(1.32406 + 0.961986i) q^{39} +(-11.4722 + 5.10773i) q^{40} +(-4.72618 - 1.00458i) q^{41} +(-0.265876 - 2.52964i) q^{42} +(-2.75174 + 3.05612i) q^{43} +(-2.63049 - 2.92145i) q^{44} +(-0.426470 + 4.05759i) q^{45} +(-1.70099 + 5.23510i) q^{46} +(2.53194 - 7.79252i) q^{47} +(0.247467 - 2.35450i) q^{48} +(-1.54116 - 1.71164i) q^{49} +(9.14593 - 10.1576i) q^{50} +(0.198947 + 1.89285i) q^{51} +(-0.996552 - 0.211824i) q^{52} +(-8.67938 + 3.86431i) q^{53} +(-0.949516 - 0.689863i) q^{54} +(23.5377 + 10.4796i) q^{55} +(3.33527 + 5.77686i) q^{56} +(-0.307373 + 0.532386i) q^{57} +(1.10024 - 0.799368i) q^{58} +(1.41225 - 0.300184i) q^{59} +(-0.784840 - 2.41549i) q^{60} -7.03201 q^{61} +(-5.83574 + 2.94048i) q^{62} +2.16720 q^{63} +(2.68806 + 8.27299i) q^{64} +(6.53142 - 1.38830i) q^{65} +(-5.99628 + 4.35655i) q^{66} +(4.32649 - 7.49370i) q^{67} +(-0.592403 - 1.02607i) q^{68} +(-4.28454 - 1.90760i) q^{69} +(-8.39566 - 6.09981i) q^{70} +(-3.60398 + 1.60459i) q^{71} +(3.01069 + 0.639942i) q^{72} +(0.503825 + 4.79358i) q^{73} +(-0.656953 + 0.729621i) q^{74} +(7.79262 + 8.65458i) q^{75} +(0.0400015 - 0.380589i) q^{76} +(4.22923 - 13.0162i) q^{77} +(-0.593577 + 1.82684i) q^{78} +(-0.0545741 + 0.519238i) q^{79} +(-6.46321 - 7.17812i) q^{80} +(0.669131 - 0.743145i) q^{81} +(-0.592768 - 5.63981i) q^{82} +(-6.84291 - 1.45450i) q^{83} +(-1.23247 + 0.548729i) q^{84} +(6.28222 + 4.56430i) q^{85} +(-4.40932 - 1.96316i) q^{86} +(0.579367 + 1.00349i) q^{87} +(9.71876 - 16.8334i) q^{88} +(4.12530 - 2.99720i) q^{89} +(-4.68384 + 0.995581i) q^{90} +(-1.09605 - 3.37331i) q^{91} +2.91957 q^{92} +(-1.97191 - 5.20688i) q^{93} +9.61648 q^{94} +(0.775054 + 2.38537i) q^{95} +(-3.30348 + 0.702177i) q^{96} +(4.05910 - 2.94911i) q^{97} +(1.35161 - 2.34106i) q^{98} +(-3.15755 - 5.46903i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{14}{15}\right)$

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 $

$2$	0.362683	+	1.11622i	0.256455	+	0.789288i	0.993539	+	0.113487i	$0.0362022\pi$
$2$	0.362683	+	1.11622i	0.256455	+	0.789288i	−0.737084	+	0.675801i	$0.763798\pi$
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i
$4$	0.503620	−	0.365901i	0.251810	−	0.182951i
$5$	−2.03997	+	3.53333i	−0.912302	+	1.58015i	−0.101497	+	0.994836i	$0.532363\pi$
$5$	−2.03997	+	3.53333i	−0.912302	+	1.58015i	−0.810805	+	0.585317i	$0.800970\pi$
$6$	−0.586833	−	1.01642i	−0.239574	−	0.414953i
$7$	1.97984	+	0.881481i	0.748308	+	0.333168i	0.745213	−	0.666827i	$-0.232348\pi$
$7$	1.97984	+	0.881481i	0.748308	+	0.333168i	0.00309570	+	0.999995i	$0.499015\pi$
$8$	2.49011	+	1.80917i	0.880388	+	0.639639i
$9$	0.913545	−	0.406737i	0.304515	−	0.135579i
$10$	−4.68384	−	0.995581i	−1.48116	−	0.314830i
$11$	−0.660107	−	6.28050i	−0.199030	−	1.89364i	−0.403826	−	0.914836i	$-0.632320\pi$
$11$	−0.660107	−	6.28050i	−0.199030	−	1.89364i	0.204796	−	0.978805i	$-0.434347\pi$
$12$	−0.416540	+	0.462614i	−0.120245	+	0.133545i
$13$	−1.09512	−	1.21625i	−0.303731	−	0.337328i	0.571886	−	0.820333i	$-0.306212\pi$
$13$	−1.09512	−	1.21625i	−0.303731	−	0.337328i	−0.875617	+	0.483005i	$0.839545\pi$
$14$	−0.265876	+	2.52964i	−0.0710582	+	0.676074i
$15$	1.26077	−	3.88025i	0.325529	−	1.00188i
$16$	−0.731587	+	2.25159i	−0.182897	+	0.562898i
$17$	0.198947	−	1.89285i	0.0482516	−	0.459084i	−0.943544	−	0.331248i	$-0.892530\pi$
$17$	0.198947	−	1.89285i	0.0482516	−	0.459084i	0.991795	−	0.127836i	$-0.0408030\pi$
$18$	0.785336	+	0.872204i	0.185105	+	0.205580i
$19$	0.411346	−	0.456845i	0.0943691	−	0.104808i	−0.694110	−	0.719869i	$-0.744202\pi$
$19$	0.411346	−	0.456845i	0.0943691	−	0.104808i	0.788479	+	0.615061i	$0.210869\pi$
$20$	0.265481	+	2.52588i	0.0593634	+	0.564805i
$21$	−2.11984	−	0.450587i	−0.462588	−	0.0983261i
$22$	6.77102	−	3.01465i	1.44359	−	0.642726i
$23$	3.79430	+	2.75672i	0.791166	+	0.574816i	0.908309	−	0.418299i	$-0.137374\pi$
$23$	3.79430	+	2.75672i	0.791166	+	0.574816i	−0.117143	+	0.993115i	$0.537374\pi$
$24$	−2.81185	−	1.25191i	−0.573966	−	0.255546i
$25$	−5.82294	−	10.0856i	−1.16459	−	2.01713i
$26$	0.960427	−	1.66351i	0.188355	−	0.326241i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	1.31962	−	0.280494i	0.249385	−	0.0530084i
$29$	−0.358068	−	1.10202i	−0.0664916	−	0.204640i	0.912291	−	0.409543i	$-0.134312\pi$
$29$	−0.358068	−	1.10202i	−0.0664916	−	0.204640i	−0.978782	+	0.204903i	$0.934312\pi$
$30$	4.78848			0.874253
$31$	0.846253	+	5.50308i	0.151992	+	0.988382i
$31$	0.846253	+	5.50308i	0.151992	+	0.988382i
$32$	3.37728			0.597025
$33$	1.95147	+	6.00601i	0.339707	+	1.04551i
$34$	2.18500	−	0.464435i	0.374724	−	0.0796500i
$35$	−7.15337	+	5.19723i	−1.20914	+	0.878492i
$36$	0.311254	−	0.539108i	0.0518757	−	0.0898514i
$37$	0.418263	+	0.724452i	0.0687620	+	0.119099i	0.898357	−	0.439267i	$-0.144762\pi$
$37$	0.418263	+	0.724452i	0.0687620	+	0.119099i	−0.829595	+	0.558366i	$0.811428\pi$
$38$	0.659129	+	0.293463i	0.106925	+	0.0476060i
$39$	1.32406	+	0.961986i	0.212019	+	0.154041i
$40$	−11.4722	+	5.10773i	−1.81391	+	0.807603i
$41$	−4.72618	−	1.00458i	−0.738105	−	0.156889i	−0.176507	−	0.984299i	$-0.556480\pi$
$41$	−4.72618	−	1.00458i	−0.738105	−	0.156889i	−0.561598	+	0.827410i	$0.689813\pi$
$42$	−0.265876	−	2.52964i	−0.0410255	−	0.390331i
$43$	−2.75174	+	3.05612i	−0.419637	+	0.466054i	−0.915483	−	0.402356i	$-0.868191\pi$
$43$	−2.75174	+	3.05612i	−0.419637	+	0.466054i	0.495846	+	0.868410i	$0.334858\pi$
$44$	−2.63049	−	2.92145i	−0.396561	−	0.440425i
$45$	−0.426470	+	4.05759i	−0.0635743	+	0.604869i
$46$	−1.70099	+	5.23510i	−0.250797	+	0.771873i
$47$	2.53194	−	7.79252i	0.369322	−	1.13666i	−0.577908	−	0.816102i	$-0.696131\pi$
$47$	2.53194	−	7.79252i	0.369322	−	1.13666i	0.947230	−	0.320554i	$-0.103869\pi$
$48$	0.247467	−	2.35450i	0.0357189	−	0.339842i
$49$	−1.54116	−	1.71164i	−0.220166	−	0.244519i
$50$	9.14593	−	10.1576i	1.29343	−	1.43650i
$51$	0.198947	+	1.89285i	0.0278581	+	0.265052i
$52$	−0.996552	−	0.211824i	−0.138197	−	0.0293747i
$53$	−8.67938	+	3.86431i	−1.19220	+	0.530804i	−0.904317	−	0.426861i	$-0.859619\pi$
$53$	−8.67938	+	3.86431i	−1.19220	+	0.530804i	−0.287887	+	0.957664i	$0.592953\pi$
$54$	−0.949516	−	0.689863i	−0.129213	−	0.0938785i
$55$	23.5377	+	10.4796i	3.17382	+	1.41307i
$56$	3.33527	+	5.77686i	0.445694	+	0.771965i
$57$	−0.307373	+	0.532386i	−0.0407126	+	0.0705162i
$58$	1.10024	−	0.799368i	0.144468	−	0.104962i
$59$	1.41225	−	0.300184i	0.183860	−	0.0390806i	−0.115062	−	0.993358i	$-0.536707\pi$
$59$	1.41225	−	0.300184i	0.183860	−	0.0390806i	0.298921	+	0.954278i	$0.403373\pi$
$60$	−0.784840	−	2.41549i	−0.101322	−	0.311838i
$61$	−7.03201			−0.900356			−0.450178	−	0.892939i	$-0.648639\pi$
$61$	−7.03201			−0.900356			−0.450178	+	0.892939i	$0.648639\pi$
$62$	−5.83574	+	2.94048i	−0.741139	+	0.373441i
$63$	2.16720			0.273042
$64$	2.68806	+	8.27299i	0.336007	+	1.03412i
$65$	6.53142	−	1.38830i	0.810124	−	0.172197i
$66$	−5.99628	+	4.35655i	−0.738091	+	0.536254i
$67$	4.32649	−	7.49370i	0.528565	−	0.915501i	−0.470881	−	0.882197i	$-0.656064\pi$
$67$	4.32649	−	7.49370i	0.528565	−	0.915501i	0.999445	−	0.0333040i	$-0.0106030\pi$
$68$	−0.592403	−	1.02607i	−0.0718394	−	0.124430i
$69$	−4.28454	−	1.90760i	−0.515798	−	0.229648i
$70$	−8.39566	−	6.09981i	−1.00347	−	0.729066i
$71$	−3.60398	+	1.60459i	−0.427713	+	0.190430i	−0.609292	−	0.792946i	$-0.708546\pi$
$71$	−3.60398	+	1.60459i	−0.427713	+	0.190430i	0.181578	+	0.983376i	$0.441879\pi$
$72$	3.01069	+	0.639942i	0.354813	+	0.0754178i
$73$	0.503825	+	4.79358i	0.0589683	+	0.561046i	0.983623	+	0.180239i	$0.0576871\pi$
$73$	0.503825	+	4.79358i	0.0589683	+	0.561046i	−0.924655	+	0.380807i	$0.875646\pi$
$74$	−0.656953	+	0.729621i	−0.0763693	+	0.0848167i
$75$	7.79262	+	8.65458i	0.899814	+	0.999345i
$76$	0.0400015	−	0.380589i	0.00458848	−	0.0436565i
$77$	4.22923	−	13.0162i	0.481966	−	1.48334i
$78$	−0.593577	+	1.82684i	−0.0672093	+	0.206849i
$79$	−0.0545741	+	0.519238i	−0.00614007	+	0.0584188i	−0.997163	−	0.0752740i	$-0.976017\pi$
$79$	−0.0545741	+	0.519238i	−0.00614007	+	0.0584188i	0.991023	+	0.133693i	$0.0426835\pi$
$80$	−6.46321	−	7.17812i	−0.722608	−	0.802538i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	−0.592768	−	5.63981i	−0.0654603	−	0.622813i
$83$	−6.84291	−	1.45450i	−0.751106	−	0.159653i	−0.183577	−	0.983005i	$-0.558768\pi$
$83$	−6.84291	−	1.45450i	−0.751106	−	0.159653i	−0.567530	+	0.823353i	$0.692101\pi$
$84$	−1.23247	+	0.548729i	−0.134473	+	0.0598713i
$85$	6.28222	+	4.56430i	0.681402	+	0.495068i
$86$	−4.40932	−	1.96316i	−0.475469	−	0.211693i
$87$	0.579367	+	1.00349i	0.0621146	+	0.107586i
$88$	9.71876	−	16.8334i	1.03602	−	1.79445i
$89$	4.12530	−	2.99720i	0.437281	−	0.317703i	−0.347273	−	0.937764i	$-0.612892\pi$
$89$	4.12530	−	2.99720i	0.437281	−	0.317703i	0.784553	+	0.620061i	$0.212892\pi$
$90$	−4.68384	+	0.995581i	−0.493720	+	0.104943i
$91$	−1.09605	−	3.37331i	−0.114898	−	0.353619i
$92$	2.91957			0.304387
$93$	−1.97191	−	5.20688i	−0.204478	−	0.539928i
$94$	9.61648			0.991864
$95$	0.775054	+	2.38537i	0.0795188	+	0.244734i
$96$	−3.30348	+	0.702177i	−0.337160	+	0.0716656i
$97$	4.05910	−	2.94911i	0.412139	−	0.299436i	−0.362328	−	0.932051i	$-0.618018\pi$
$97$	4.05910	−	2.94911i	0.412139	−	0.299436i	0.774467	+	0.632614i	$0.218018\pi$
$98$	1.35161	−	2.34106i	0.136534	−	0.236483i
$99$	−3.15755	−	5.46903i	−0.317345	−	0.549658i
$100$	−6.62290	−	2.94871i	−0.662290	−	0.294871i
$101$	−7.50890	−	5.45554i	−0.747164	−	0.542846i	0.147783	−	0.989020i	$-0.452786\pi$
$101$	−7.50890	−	5.45554i	−0.747164	−	0.542846i	−0.894946	+	0.446174i	$0.852786\pi$
$102$	−2.04069	+	0.908573i	−0.202058	+	0.0899621i
$103$	4.21671	+	0.896290i	0.415485	+	0.0883141i	0.410911	−	0.911675i	$-0.365211\pi$
$103$	4.21671	+	0.896290i	0.415485	+	0.0883141i	0.00457417	+	0.999990i	$0.498544\pi$
$104$	−0.526558	−	5.00986i	−0.0516332	−	0.491257i
$105$	5.91649	−	6.57092i	0.577390	−	0.641256i
$106$	−7.46129	−	8.28660i	−0.724705	−	0.804866i
$107$	−0.418666	+	3.98334i	−0.0404740	+	0.385084i	0.955469	+	0.295093i	$0.0953506\pi$
$107$	−0.418666	+	3.98334i	−0.0404740	+	0.385084i	−0.995943	+	0.0899913i	$0.971316\pi$
$108$	−0.192366	+	0.592041i	−0.0185104	+	0.0569692i
$109$	−3.10456	+	9.55485i	−0.297363	+	0.915189i	0.685055	+	0.728492i	$0.259778\pi$
$109$	−3.10456	+	9.55485i	−0.297363	+	0.915189i	−0.982418	+	0.186697i	$0.940222\pi$
$110$	−3.16091	+	30.0740i	−0.301381	+	2.86745i
$111$	−0.559745	−	0.621660i	−0.0531286	−	0.0590053i
$112$	−3.43316	+	3.81291i	−0.324403	+	0.360286i
$113$	1.24292	+	11.8256i	0.116924	+	1.11246i	0.882890	+	0.469579i	$0.155594\pi$
$113$	1.24292	+	11.8256i	0.116924	+	1.11246i	−0.765966	+	0.642881i	$0.777739\pi$
$114$	−0.705740	−	0.150010i	−0.0660986	−	0.0140497i
$115$	−17.4807	+	7.78289i	−1.63008	+	0.725758i
$116$	−0.583561	−	0.423982i	−0.0541823	−	0.0393658i
$117$	−1.49513	−	0.665677i	−0.138225	−	0.0615418i
$118$	0.847272	+	1.46752i	0.0779977	+	0.135096i
$119$	2.06239	−	3.57217i	0.189059	−	0.327460i
$120$	10.1595	−	7.38131i	0.927432	−	0.673818i
$121$	−28.2493	+	6.00457i	−2.56811	+	0.545870i
$122$	−2.55039	−	7.84928i	−0.230901	−	0.710641i
$123$	4.83177			0.435666
$124$	2.43977	+	2.46182i	0.219098	+	0.221078i
$125$	27.1148			2.42522
$126$	0.786007	+	2.41908i	0.0700230	+	0.215509i
$127$	−1.85665	+	0.394644i	−0.164751	+	0.0350190i	−0.289549	−	0.957163i	$-0.593505\pi$
$127$	−1.85665	+	0.394644i	−0.164751	+	0.0350190i	0.124797	+	0.992182i	$0.460172\pi$
$128$	−2.79502	+	2.03070i	−0.247047	+	0.179490i
$129$	2.05621	−	3.56146i	0.181039	−	0.313569i
$130$	3.91848	+	6.78701i	0.343674	+	0.595260i
$131$	12.2079	+	5.43529i	1.06661	+	0.474884i	0.863540	−	0.504281i	$-0.168242\pi$
$131$	12.2079	+	5.43529i	1.06661	+	0.474884i	0.203067	+	0.979165i	$0.434909\pi$
$132$	3.18041	+	2.31070i	0.276819	+	0.201121i
$133$	1.21710	−	0.541887i	0.105536	−	0.0469876i
$134$	9.93378	+	2.11149i	0.858148	+	0.182405i
$135$	−0.426470	−	4.05759i	−0.0367047	−	0.349221i
$136$	3.91989	−	4.35348i	0.336128	−	0.373308i
$137$	13.7269	+	15.2452i	1.17277	+	1.30249i	0.944357	+	0.328924i	$0.106686\pi$
$137$	13.7269	+	15.2452i	1.17277	+	1.30249i	0.228410	+	0.973565i	$0.426647\pi$
$138$	0.575378	−	5.47435i	0.0489794	−	0.466008i
$139$	2.47889	−	7.62924i	0.210257	−	0.647104i	−0.789200	−	0.614137i	$-0.789504\pi$
$139$	2.47889	−	7.62924i	0.210257	−	0.647104i	0.999456	−	0.0329669i	$-0.0104956\pi$
$140$	−1.70091	+	5.23486i	−0.143753	+	0.442426i
$141$	−0.856458	+	8.14866i	−0.0721268	+	0.686241i
$142$	−3.09818	−	3.44088i	−0.259994	−	0.288752i
$143$	−6.91577	+	7.68074i	−0.578326	+	0.642296i
$144$	0.247467	+	2.35450i	0.0206223	+	0.196208i
$145$	4.62425	+	0.982915i	0.384023	+	0.0816266i
$146$	−5.16797	+	2.30093i	−0.427704	+	0.190426i
$147$	1.86336	+	1.35381i	0.153687	+	0.111660i
$148$	0.475724	+	0.211806i	0.0391043	+	0.0174103i
$149$	−7.68422	−	13.3095i	−0.629515	−	1.09035i	−0.987649	−	0.156682i	$-0.949920\pi$
$149$	−7.68422	−	13.3095i	−0.629515	−	1.09035i	0.358134	−	0.933670i	$-0.383413\pi$
$150$	−6.83419	+	11.8372i	−0.558009	+	0.966500i
$151$	12.3031	−	8.93873i	1.00121	−	0.727423i	0.0388646	−	0.999244i	$-0.487626\pi$
$151$	12.3031	−	8.93873i	1.00121	−	0.727423i	0.962348	+	0.271821i	$0.0876259\pi$
$152$	1.85081	−	0.393402i	0.150120	−	0.0319091i
$153$	−0.588145	−	1.81012i	−0.0475487	−	0.146340i
$154$	16.0629			1.29438
$155$	−21.1705	−	8.23601i	−1.70046	−	0.661532i
$156$	1.01882			0.0815705
$157$	3.66481	+	11.2791i	0.292483	+	0.900172i	0.984055	+	0.177864i	$0.0569186\pi$
$157$	3.66481	+	11.2791i	0.292483	+	0.900172i	−0.691572	+	0.722308i	$0.743081\pi$
$158$	−0.599378	+	0.127402i	−0.0476840	+	0.0101355i
$159$	7.68628	−	5.58441i	0.609562	−	0.442872i
$160$	−6.88955	+	11.9331i	−0.544667	+	0.943391i
$161$	5.08210	+	8.80246i	0.400526	+	0.693731i
$162$	1.07220	+	0.477373i	0.0842398	+	0.0375060i
$163$	−11.2082	−	8.14322i	−0.877893	−	0.637826i	0.0548004	−	0.998497i	$-0.482548\pi$
$163$	−11.2082	−	8.14322i	−0.877893	−	0.637826i	−0.932693	+	0.360671i	$0.882548\pi$
$164$	−2.74778	+	1.22339i	−0.214565	+	0.0955307i
$165$	−25.2021	−	5.35688i	−1.96198	−	0.417033i
$166$	−0.858253	−	8.16573i	−0.0666133	−	0.633783i
$167$	−9.02006	+	10.0178i	−0.697993	+	0.775200i	−0.983055	−	0.183309i	$-0.941319\pi$
$167$	−9.02006	+	10.0178i	−0.697993	+	0.775200i	0.285062	+	0.958509i	$0.407986\pi$
$168$	−4.46346	−	4.95718i	−0.344363	−	0.382454i
$169$	1.07889	−	10.2649i	0.0829912	−	0.789608i
$170$	−2.81632	+	8.66775i	−0.216002	+	0.664786i
$171$	0.189967	−	0.584658i	0.0145271	−	0.0447099i
$172$	−0.267595	+	2.54599i	−0.0204039	+	0.194130i
$173$	2.98361	+	3.31363i	0.226840	+	0.251931i	0.845811	−	0.533483i	$-0.179117\pi$
$173$	2.98361	+	3.31363i	0.226840	+	0.251931i	−0.618971	+	0.785413i	$0.712450\pi$
$174$	−0.909994	+	1.01065i	−0.0689865	+	0.0766173i
$175$	−2.63819	−	25.1007i	−0.199429	−	1.89744i
$176$	14.6240	+	3.10844i	1.10233	+	0.234307i
$177$	−1.31898	+	0.587248i	−0.0991406	+	0.0441403i
$178$	4.84172	+	3.51771i	0.362902	+	0.263664i
$179$	−4.42059	−	1.96817i	−0.330410	−	0.147108i	0.234826	−	0.972038i	$-0.424548\pi$
$179$	−4.42059	−	1.96817i	−0.330410	−	0.147108i	−0.565236	+	0.824929i	$0.691215\pi$
$180$	1.26990	+	2.19953i	0.0946526	+	0.163943i
$181$	−0.677370	+	1.17324i	−0.0503485	+	0.0872062i	−0.890101	−	0.455763i	$-0.849367\pi$
$181$	−0.677370	+	1.17324i	−0.0503485	+	0.0872062i	0.839753	+	0.542969i	$0.182700\pi$
$182$	3.36784	−	2.44688i	0.249641	−	0.181375i
$183$	6.87834	−	1.46204i	0.508462	−	0.108077i
$184$	4.46085	+	13.7291i	0.328858	+	1.01212i
$185$	−3.41297			−0.250927
$186$	5.09685	−	4.08954i	0.373719	−	0.299860i
$187$	−12.0194			−0.878943
$188$	−1.57616	−	4.85091i	−0.114953	−	0.353789i
$189$	−2.11984	+	0.450587i	−0.154196	+	0.0327754i
$190$	−2.38150	+	1.73026i	−0.172772	+	0.125527i
$191$	−1.83796	+	3.18343i	−0.132990	+	0.230345i	−0.924828	−	0.380386i	$-0.875791\pi$
$191$	−1.83796	+	3.18343i	−0.132990	+	0.230345i	0.791838	+	0.610731i	$0.209124\pi$
$192$	−4.34937	−	7.53332i	−0.313889	−	0.543671i
$193$	2.92641	+	1.30292i	0.210648	+	0.0937864i	0.509348	−	0.860560i	$-0.329887\pi$
$193$	2.92641	+	1.30292i	0.210648	+	0.0937864i	−0.298701	+	0.954347i	$0.596553\pi$
$194$	4.76402	+	3.46126i	0.342037	+	0.248504i
$195$	−6.10005	+	2.71592i	−0.436834	+	0.194491i
$196$	−1.40245	−	0.298100i	−0.100175	−	0.0212929i
$197$	−1.21355	−	11.5462i	−0.0864620	−	0.822631i	−0.948711	−	0.316146i	$-0.897611\pi$
$197$	−1.21355	−	11.5462i	−0.0864620	−	0.822631i	0.862249	−	0.506485i	$-0.169056\pi$
$198$	4.95947	−	5.50804i	0.352454	−	0.391440i
$199$	−5.15164	−	5.72148i	−0.365190	−	0.405585i	0.532345	−	0.846527i	$-0.321311\pi$
$199$	−5.15164	−	5.72148i	−0.365190	−	0.405585i	−0.897535	+	0.440943i	$0.854644\pi$
$200$	3.74687	−	35.6491i	0.264944	−	2.52077i
$201$	−2.67392	+	8.22947i	−0.188604	+	0.580462i
$202$	3.36624	−	10.3602i	0.236848	−	0.728943i
$203$	0.262493	−	2.49745i	0.0184234	−	0.175287i
$204$	0.792790	+	0.880483i	0.0555064	+	0.0616461i
$205$	13.1908	−	14.6498i	0.921284	−	1.02319i
$206$	0.528870	+	5.03186i	0.0368481	+	0.350586i
$207$	4.58753	+	0.975109i	0.318855	+	0.0677747i
$208$	3.53968	−	1.57597i	0.245433	−	0.109274i
$209$	−3.14075	−	2.28189i	−0.217250	−	0.157841i
$210$	9.48042	+	4.22095i	0.654211	+	0.291274i
$211$	11.7626	+	20.3734i	0.809771	+	1.40256i	0.913023	+	0.407909i	$0.133742\pi$
$211$	11.7626	+	20.3734i	0.809771	+	1.40256i	−0.103252	+	0.994655i	$0.532925\pi$
$212$	−2.95715	+	5.12194i	−0.203098	+	0.351776i
$213$	3.19161	−	2.31884i	0.218685	−	0.158884i
$214$	−4.59814	+	0.977365i	−0.314322	+	0.0668113i
$215$	−5.18481	−	15.9572i	−0.353601	−	1.08827i
$216$	−3.07795			−0.209428
$217$	−3.17541	+	11.6412i	−0.215561	+	0.790253i
$218$	−11.7913			−0.798608
$219$	−1.48946	−	4.58407i	−0.100648	−	0.309763i
$220$	15.6886	−	3.33471i	1.05772	−	0.224826i
$221$	−2.52005	+	1.83093i	−0.169517	+	0.123161i
$222$	0.490901	−	0.850265i	0.0329471	−	0.0570660i
$223$	−12.2489	−	21.2156i	−0.820244	−	1.42070i	−0.905501	−	0.424345i	$-0.860504\pi$
$223$	−12.2489	−	21.2156i	−0.820244	−	1.42070i	0.0852566	−	0.996359i	$-0.472829\pi$
$224$	6.68648	+	2.97701i	0.446759	+	0.198910i
$225$	−9.42172	−	6.84528i	−0.628115	−	0.456352i
$226$	−12.7492	+	5.67632i	−0.848066	+	0.377583i
$227$	20.1636	+	4.28590i	1.33830	+	0.284465i	0.820800	−	0.571216i	$-0.193528\pi$
$227$	20.1636	+	4.28590i	1.33830	+	0.284465i	0.517503	+	0.855681i	$0.326861\pi$
$228$	0.0400015	+	0.380589i	0.00264916	+	0.0252051i
$229$	−12.5097	+	13.8935i	−0.826666	+	0.918105i	−0.997743	−	0.0671524i	$-0.978609\pi$
$229$	−12.5097	+	13.8935i	−0.826666	+	0.918105i	0.171077	+	0.985258i	$0.445275\pi$
$230$	−15.0274	−	16.6896i	−0.990875	−	1.10048i
$231$	−1.43058	+	13.6111i	−0.0941256	+	0.895545i
$232$	1.10212	−	3.39196i	0.0723574	−	0.222693i
$233$	−7.25908	+	22.3411i	−0.475558	+	1.46362i	0.369646	+	0.929173i	$0.379479\pi$
$233$	−7.25908	+	22.3411i	−0.475558	+	1.46362i	−0.845204	+	0.534444i	$0.820521\pi$
$234$	0.200784	−	1.91033i	0.0131257	−	0.124882i
$235$	22.3685	+	24.8427i	1.45916	+	1.62056i
$236$	0.601402	−	0.667924i	0.0391479	−	0.0434782i
$237$	−0.0545741	−	0.519238i	−0.00354497	−	0.0337281i
$238$	4.73533	+	1.00653i	0.306946	+	0.0652434i
$239$	12.2657	−	5.46105i	0.793403	−	0.353246i	0.0303152	−	0.999540i	$-0.490349\pi$
$239$	12.2657	−	5.46105i	0.793403	−	0.353246i	0.763088	+	0.646295i	$0.223682\pi$
$240$	7.81438	+	5.67748i	0.504416	+	0.366480i
$241$	−9.35927	−	4.16701i	−0.602883	−	0.268421i	0.0825144	−	0.996590i	$-0.473705\pi$
$241$	−9.35927	−	4.16701i	−0.602883	−	0.268421i	−0.685398	+	0.728169i	$0.740372\pi$
$242$	−16.9479	−	29.3547i	−1.08946	−	1.88699i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−3.54146	+	2.57302i	−0.226719	+	0.164721i
$245$	9.19170	−	1.95376i	0.587236	−	0.124821i
$246$	1.75240	+	5.39333i	0.111729	+	0.343866i
$247$	−1.00611			−0.0640173
$248$	−7.84875	+	15.2343i	−0.498396	+	0.967379i
$249$	6.99578			0.443340
$250$	9.83407	+	30.2661i	0.621961	+	1.91420i
$251$	17.1089	−	3.63661i	1.07990	−	0.229541i	0.366588	−	0.930383i	$-0.380526\pi$
$251$	17.1089	−	3.63661i	1.07990	−	0.229541i	0.713316	+	0.700843i	$0.247193\pi$
$252$	1.09145	−	0.792983i	0.0687547	−	0.0499532i
$253$	14.8089	−	25.6498i	0.931029	−	1.61259i
$254$	−1.11389	−	1.92931i	−0.0698915	−	0.121056i
$255$	−7.09391	−	3.15841i	−0.444238	−	0.197787i
$256$	10.7944	+	7.84261i	0.674652	+	0.490163i
$257$	2.32175	−	1.03371i	0.144827	−	0.0644810i	−0.333043	−	0.942911i	$-0.608076\pi$
$257$	2.32175	−	1.03371i	0.144827	−	0.0644810i	0.477870	+	0.878430i	$0.341409\pi$
$258$	4.72113	+	1.00351i	0.293925	+	0.0624756i
$259$	0.189502	+	1.80299i	0.0117751	+	0.112032i
$260$	2.78138	−	3.08903i	0.172494	−	0.191574i
$261$	−0.775344	−	0.861106i	−0.0479926	−	0.0533012i
$262$	−1.63941	+	15.5980i	−0.101283	+	0.963646i
$263$	4.72208	−	14.5331i	0.291176	−	0.896147i	−0.693304	−	0.720646i	$-0.743845\pi$
$263$	4.72208	−	14.5331i	0.291176	−	0.896147i	0.984479	−	0.175501i	$-0.0561545\pi$
$264$	−6.00653	+	18.4862i	−0.369676	+	1.13775i
$265$	4.05179	−	38.5502i	0.248899	−	2.36812i
$266$	1.04629	+	1.16202i	0.0641519	+	0.0712480i
$267$	−3.41200	+	3.78940i	−0.208811	+	0.231908i
$268$	−0.563048	−	5.35705i	−0.0343936	−	0.327234i
$269$	14.4300	+	3.06720i	0.879815	+	0.187010i	0.625606	−	0.780139i	$-0.284852\pi$
$269$	14.4300	+	3.06720i	0.879815	+	0.187010i	0.254209	+	0.967149i	$0.418185\pi$
$270$	4.37450	−	1.94765i	0.266223	−	0.118530i
$271$	4.09591	+	2.97585i	0.248809	+	0.180770i	0.705199	−	0.709010i	$-0.250858\pi$
$271$	4.09591	+	2.97585i	0.248809	+	0.180770i	−0.456390	+	0.889780i	$0.650858\pi$
$272$	4.11638	+	1.83273i	0.249592	+	0.111126i
$273$	1.77345	+	3.07171i	0.107334	+	0.185908i
$274$	−12.0386	+	20.8514i	−0.727277	+	1.25968i
$275$	−59.4990	+	43.2286i	−3.58793	+	2.60678i
$276$	−2.85577	+	0.607014i	−0.171897	+	0.0365379i
$277$	4.19136	+	12.8997i	0.251834	+	0.775066i	0.994437	+	0.105334i	$0.0335912\pi$
$277$	4.19136	+	12.8997i	0.251834	+	0.775066i	−0.742603	+	0.669732i	$0.766409\pi$
$278$	9.41498			0.564673
$279$	3.01139	+	4.68311i	0.180287	+	0.280370i
$280$	−27.2154			−1.62643
$281$	−9.51390	−	29.2808i	−0.567552	−	1.74674i	−0.660245	−	0.751050i	$-0.729548\pi$
$281$	−9.51390	−	29.2808i	−0.567552	−	1.74674i	0.0926937	−	0.995695i	$-0.470452\pi$
$282$	−9.40634	+	1.99938i	−0.560139	+	0.119061i
$283$	−19.7183	+	14.3262i	−1.17213	+	0.851605i	−0.991263	−	0.131901i	$-0.957892\pi$
$283$	−19.7183	+	14.3262i	−1.17213	+	0.851605i	−0.180871	+	0.983507i	$0.557892\pi$
$284$	−1.22791	+	2.12681i	−0.0728632	+	0.126203i
$285$	−1.25406	−	2.17210i	−0.0742843	−	0.128664i
$286$	−11.0816	−	4.93387i	−0.655271	−	0.291746i
$287$	−8.47155	−	6.15494i	−0.500060	−	0.363315i
$288$	3.08530	−	1.37367i	0.181803	−	0.0809440i
$289$	13.0852	+	2.78135i	0.769718	+	0.163609i
$290$	0.579984	+	5.51818i	0.0340578	+	0.324039i
$291$	−3.35724	+	3.72859i	−0.196805	+	0.218574i
$292$	2.00771	+	2.22979i	0.117493	+	0.130489i
$293$	−1.69342	+	16.1119i	−0.0989309	+	0.941265i	0.826650	+	0.562716i	$0.190243\pi$
$293$	−1.69342	+	16.1119i	−0.0989309	+	0.941265i	−0.925581	+	0.378549i	$0.876423\pi$
$294$	−0.835343	+	2.57092i	−0.0487182	+	0.149939i
$295$	−1.82030	+	5.60232i	−0.105982	+	0.326180i
$296$	−0.269138	+	2.56068i	−0.0156433	+	0.148836i
$297$	4.22562	+	4.69303i	0.245195	+	0.272317i
$298$	12.0694	−	13.4044i	0.699160	−	0.776496i
$299$	−0.802340	−	7.63376i	−0.0464005	−	0.441472i
$300$	7.09124	+	1.50729i	0.409413	+	0.0870235i
$301$	−8.14192	+	3.62502i	−0.469293	+	0.208942i
$302$	14.4397	+	10.4911i	0.830913	+	0.603694i
$303$	8.47908	+	3.77513i	0.487111	+	0.216876i
$304$	0.727695	+	1.26040i	0.0417362	+	0.0722892i
$305$	14.3451	−	24.8464i	0.821396	−	1.42270i
$306$	1.80719	−	1.31300i	0.103310	−	0.0750593i
$307$	15.2223	−	3.23561i	0.868785	−	0.184666i	0.248108	−	0.968732i	$-0.420191\pi$
$307$	15.2223	−	3.23561i	0.868785	−	0.184666i	0.620677	+	0.784066i	$0.286858\pi$
$308$	−2.63273	−	8.10272i	−0.150014	−	0.461695i
$309$	−4.31092			−0.245240
$310$	1.51504	−	26.6181i	0.0860488	−	1.51180i
$311$	7.31140			0.414591			0.207296	−	0.978278i	$-0.433534\pi$
$311$	7.31140			0.414591			0.207296	+	0.978278i	$0.433534\pi$
$312$	1.55666	+	4.79091i	0.0881285	+	0.271232i
$313$	−7.78598	+	1.65496i	−0.440090	+	0.0935440i	−0.422627	−	0.906304i	$-0.638892\pi$
$313$	−7.78598	+	1.65496i	−0.440090	+	0.0935440i	−0.0174624	+	0.999848i	$0.505559\pi$
$314$	−11.2608	+	8.18148i	−0.635486	+	0.461708i
$315$	−4.42102	+	7.65744i	−0.249097	+	0.431448i
$316$	0.162505	+	0.281467i	0.00914164	+	0.0158338i
$317$	28.8783	+	12.8574i	1.62197	+	0.722146i	0.998229	−	0.0594889i	$-0.0189471\pi$
$317$	28.8783	+	12.8574i	1.62197	+	0.722146i	0.623737	+	0.781635i	$0.285614\pi$
$318$	9.02112	+	6.55423i	0.505880	+	0.367543i
$319$	−6.68487	+	2.97630i	−0.374281	+	0.166641i
$320$	−34.7147	−	7.37885i	−1.94061	−	0.412490i
$321$	−0.418666	−	3.98334i	−0.0233677	−	0.222328i
$322$	−7.98231	+	8.86526i	−0.444837	+	0.494042i
$323$	−0.782904	−	0.869503i	−0.0435620	−	0.0483805i
$324$	0.0650699	−	0.619099i	0.00361499	−	0.0343944i
$325$	−5.88986	+	18.1271i	−0.326711	+	1.00551i
$326$	5.02463	−	15.4642i	0.278289	−	0.856485i
$327$	1.05015	−	9.99153i	0.0580735	−	0.552533i
$328$	−9.95126	−	11.0520i	−0.549467	−	0.610244i
$329$	11.8818	−	13.1961i	0.655065	−	0.727523i
$330$	−3.16091	−	30.0740i	−0.174002	−	1.65552i
$331$	10.5505	+	2.24258i	0.579908	+	0.123263i	0.488521	−	0.872552i	$-0.337537\pi$
$331$	10.5505	+	2.24258i	0.579908	+	0.123263i	0.0913871	+	0.995815i	$0.470870\pi$
$332$	−3.97843	+	1.77131i	−0.218345	+	0.0972134i
$333$	0.676763	+	0.491697i	0.0370864	+	0.0269449i
$334$	−14.4535	−	6.43512i	−0.790861	−	0.352114i
$335$	17.6518	+	30.5738i	0.964421	+	1.67043i
$336$	2.56539	−	4.44338i	0.139953	−	0.242406i
$337$	−0.322529	+	0.234331i	−0.0175693	+	0.0127648i	−0.596535	−	0.802587i	$-0.703456\pi$
$337$	−0.322529	+	0.234331i	−0.0175693	+	0.0127648i	0.578966	+	0.815352i	$0.303456\pi$
$338$	11.8492	−	2.51863i	0.644512	−	0.136995i
$339$	−3.67445	−	11.3088i	−0.199568	−	0.614209i
$340$	4.83394			0.262157
$341$	34.0034	−	8.94751i	1.84139	−	0.484535i
$342$	0.721507			0.0390146
$343$	−6.23040	−	19.1752i	−0.336410	−	1.03536i
$344$	−12.3812	+	2.63171i	−0.667550	+	0.141892i
$345$	15.4805	−	11.2472i	0.833442	−	0.605531i
$346$	−2.61665	+	4.53217i	−0.140672	+	0.243651i
$347$	−1.34355	−	2.32709i	−0.0721255	−	0.124925i	0.827707	−	0.561160i	$-0.189645\pi$
$347$	−1.34355	−	2.32709i	−0.0721255	−	0.124925i	−0.899833	+	0.436235i	$0.856312\pi$
$348$	0.658960	+	0.293388i	0.0353240	+	0.0157272i
$349$	16.3542	+	11.8820i	0.875421	+	0.636031i	0.932036	−	0.362365i	$-0.118031\pi$
$349$	16.3542	+	11.8820i	0.875421	+	0.636031i	−0.0566151	+	0.998396i	$0.518031\pi$
$350$	27.0612	−	12.0484i	1.44648	−	0.644015i
$351$	1.60086	+	0.340274i	0.0854478	+	0.0181625i
$352$	−2.22937	−	21.2110i	−0.118826	−	1.13055i
$353$	−15.9247	+	17.6862i	−0.847587	+	0.941341i	−0.998888	−	0.0471468i	$-0.984987\pi$
$353$	−15.9247	+	17.6862i	−0.847587	+	0.941341i	0.151301	+	0.988488i	$0.451654\pi$
$354$	−1.13387	−	1.25929i	−0.0602645	−	0.0669306i
$355$	1.68244	−	16.0074i	0.0892947	−	0.849582i
$356$	0.980901	−	3.01890i	0.0519877	−	0.160002i
$357$	−1.27463	+	3.92290i	−0.0674605	+	0.207622i
$358$	0.593647	−	5.64818i	0.0313752	−	0.298515i
$359$	−9.43388	−	10.4774i	−0.497901	−	0.552975i	0.440846	−	0.897583i	$-0.354679\pi$
$359$	−9.43388	−	10.4774i	−0.497901	−	0.552975i	−0.938747	+	0.344608i	$0.888012\pi$
$360$	−8.40283	+	9.33229i	−0.442868	+	0.491855i
$361$	1.94654	+	18.5201i	0.102449	+	0.974741i
$362$	−1.55527	−	0.330582i	−0.0817430	−	0.0173750i
$363$	26.3835	−	11.7467i	1.38478	−	0.616542i
$364$	−1.78629	−	1.29782i	−0.0936272	−	0.0680241i
$365$	−17.9651	−	7.99857i	−0.940335	−	0.418664i
$366$	4.12661	+	7.14750i	0.215701	+	0.373606i
$367$	−16.8113	+	29.1179i	−0.877540	+	1.51994i	−0.0235084	+	0.999724i	$0.507484\pi$
$367$	−16.8113	+	29.1179i	−0.877540	+	1.51994i	−0.854032	+	0.520221i	$0.825850\pi$
$368$	−8.98287	+	6.52644i	−0.468265	+	0.340214i
$369$	−4.72618	+	1.00458i	−0.246035	+	0.0522964i
$370$	−1.23783	−	3.80964i	−0.0643515	−	0.198054i
$371$	−20.5901			−1.06898
$372$	−2.89830	−	1.90076i	−0.150270	−	0.0985499i
$373$	−0.511040			−0.0264607			−0.0132303	−	0.999912i	$-0.504211\pi$
$373$	−0.511040			−0.0264607			−0.0132303	+	0.999912i	$0.504211\pi$
$374$	−4.35922	−	13.4163i	−0.225410	−	0.693740i
$375$	−26.5223	+	5.63748i	−1.36960	+	0.291118i
$376$	20.4028	−	14.8235i	1.05220	−	0.764465i
$377$	−0.948208	+	1.64234i	−0.0488352	+	0.0845850i
$378$	−1.27179	−	2.20280i	−0.0654136	−	0.113300i
$379$	−19.1777	−	8.53848i	−0.985095	−	0.438592i	−0.149992	−	0.988687i	$-0.547925\pi$
$379$	−19.1777	−	8.53848i	−0.985095	−	0.438592i	−0.835102	+	0.550095i	$0.814592\pi$
$380$	1.26314	+	0.917727i	0.0647979	+	0.0470784i
$381$	1.73403	−	0.772041i	0.0888371	−	0.0395528i
$382$	−4.22001	−	0.896992i	−0.215915	−	0.0458941i
$383$	0.227051	+	2.16025i	0.0116018	+	0.110383i	0.998790	−	0.0491757i	$-0.0156594\pi$
$383$	0.227051	+	2.16025i	0.0116018	+	0.110383i	−0.987188	+	0.159559i	$0.948993\pi$
$384$	2.31174	−	2.56744i	0.117970	−	0.131019i
$385$	37.3631	+	41.4960i	1.90420	+	2.11483i
$386$	−0.392992	+	3.73907i	−0.0200028	+	0.190314i
$387$	−1.27081	+	3.91114i	−0.0645987	+	0.198815i
$388$	0.965161	−	2.97046i	0.0489986	−	0.150802i
$389$	−3.95570	+	37.6360i	−0.200562	+	1.90822i	0.180337	+	0.983605i	$0.442281\pi$
$389$	−3.95570	+	37.6360i	−0.200562	+	1.90822i	−0.380899	+	0.924617i	$0.624385\pi$
$390$	−5.24395	−	5.82400i	−0.265538	−	0.294910i
$391$	5.97292	−	6.63360i	0.302064	−	0.335476i
$392$	−0.741027	−	7.05040i	−0.0374275	−	0.356099i
$393$	−13.0712	−	2.77836i	−0.659353	−	0.140150i
$394$	12.4480	−	5.54219i	0.627120	−	0.279212i
$395$	−1.72331	−	1.25206i	−0.0867091	−	0.0629978i
$396$	−3.59133	−	1.59896i	−0.180471	−	0.0803509i
$397$	−16.1115	−	27.9060i	−0.808615	−	1.40056i	−0.913824	−	0.406112i	$-0.866884\pi$
$397$	−16.1115	−	27.9060i	−0.808615	−	1.40056i	0.105209	−	0.994450i	$-0.466449\pi$
$398$	4.51803	−	7.82546i	0.226468	−	0.392255i
$399$	−1.07784	+	0.783094i	−0.0539593	+	0.0392037i
$400$	26.9687	−	5.73238i	1.34844	−	0.286619i
$401$	4.32570	+	13.3131i	0.216015	+	0.664827i	0.999080	+	0.0428864i	$0.0136553\pi$
$401$	4.32570	+	13.3131i	0.216015	+	0.664827i	−0.783065	+	0.621940i	$0.786345\pi$
$402$	−10.1557			−0.506520
$403$	5.76638	−	7.05578i	0.287244	−	0.351473i
$404$	−5.77782			−0.287457
$405$	1.26077	+	3.88025i	0.0626482	+	0.192811i
$406$	2.88291	−	0.612782i	0.143077	−	0.0304119i
$407$	4.27382	−	3.10511i	0.211845	−	0.153915i
$408$	−2.92909	+	5.07334i	−0.145012	+	0.251168i
$409$	−17.0590	−	29.5471i	−0.843515	−	1.46101i	−0.886904	−	0.461953i	$-0.847149\pi$
$409$	−17.0590	−	29.5471i	−0.843515	−	1.46101i	0.0433888	−	0.999058i	$-0.486185\pi$
$410$	21.1365	+	9.41060i	1.04386	+	0.464756i
$411$	−16.5966	−	12.0581i	−0.818649	−	0.594783i
$412$	2.45158	−	1.09151i	0.120781	−	0.0537750i
$413$	3.06064	+	0.650559i	0.150604	+	0.0320119i
$414$	0.575378	+	5.47435i	0.0282783	+	0.269050i
$415$	19.0986	−	21.2111i	0.937511	−	1.04121i
$416$	−3.69853	−	4.10763i	−0.181335	−	0.201393i
$417$	−0.838512	+	7.97791i	−0.0410621	+	0.390680i
$418$	1.40800	−	4.33337i	0.0688675	−	0.211952i
$419$	1.05723	−	3.25383i	0.0516492	−	0.158960i	−0.921905	−	0.387416i	$-0.873368\pi$
$419$	1.05723	−	3.25383i	0.0516492	−	0.158960i	0.973554	+	0.228456i	$0.0733677\pi$
$420$	0.575351	−	5.47410i	0.0280743	−	0.267109i
$421$	4.95175	+	5.49948i	0.241334	+	0.268028i	0.851628	−	0.524146i	$-0.175616\pi$
$421$	4.95175	+	5.49948i	0.241334	+	0.268028i	−0.610294	+	0.792175i	$0.708949\pi$
$422$	−18.4752	+	20.5188i	−0.899357	+	0.998838i
$423$	−0.856458	−	8.14866i	−0.0416424	−	0.396201i
$424$	−28.6038	−	6.07993i	−1.38913	−	0.295268i
$425$	−20.2491	+	9.01546i	−0.982223	+	0.437314i
$426$	3.74588	+	2.72154i	0.181488	+	0.131859i
$427$	−13.9222	−	6.19858i	−0.673744	−	0.299970i
$428$	1.24666	+	2.15928i	0.0602597	+	0.104373i
$429$	5.16773	−	8.95077i	0.249500	−	0.432147i
$430$	15.9314	−	11.5748i	0.768278	−	0.558187i
$431$	−3.09123	+	0.657062i	−0.148900	+	0.0316496i	−0.281758	−	0.959485i	$-0.590918\pi$
$431$	−3.09123	+	0.657062i	−0.148900	+	0.0316496i	0.132859	+	0.991135i	$0.457584\pi$
$432$	−0.731587	−	2.25159i	−0.0351985	−	0.108330i
$433$	−10.9053			−0.524074			−0.262037	−	0.965058i	$-0.584394\pi$
$433$	−10.9053			−0.524074			−0.262037	+	0.965058i	$0.584394\pi$
$434$	−14.1458	+	0.677580i	−0.679019	+	0.0325249i
$435$	−4.72756			−0.226669
$436$	1.93262	+	5.94798i	0.0925555	+	0.284857i
$437$	2.82016	−	0.599444i	0.134907	−	0.0286753i
$438$	4.57665	−	3.32513i	0.218681	−	0.158881i
$439$	14.7205	−	25.4967i	0.702573	−	1.21689i	−0.264988	−	0.964252i	$-0.585368\pi$
$439$	14.7205	−	25.4967i	0.702573	−	1.21689i	0.967560	−	0.252640i	$-0.0812988\pi$
$440$	39.6519	+	68.6792i	1.89033	+	3.27415i
$441$	−2.10411	−	0.936810i	−0.100196	−	0.0446100i
$442$	−2.95770	−	2.14889i	−0.140683	−	0.102212i
$443$	−11.5653	+	5.14918i	−0.549482	+	0.244645i	−0.662648	−	0.748931i	$-0.730567\pi$
$443$	−11.5653	+	5.14918i	−0.549482	+	0.244645i	0.113166	+	0.993576i	$0.463901\pi$
$444$	−0.509365	−	0.108269i	−0.0241734	−	0.00513821i
$445$	2.17463	+	20.6902i	0.103087	+	0.980811i
$446$	19.2389	−	21.3670i	0.910989	−	1.01176i
$447$	10.2835	+	11.4210i	0.486392	+	0.540193i
$448$	−1.97056	+	18.7486i	−0.0931003	+	0.885790i
$449$	−8.39097	+	25.8248i	−0.395994	+	1.21875i	0.532190	+	0.846625i	$0.321369\pi$
$449$	−8.39097	+	25.8248i	−0.395994	+	1.21875i	−0.928184	+	0.372121i	$0.878631\pi$
$450$	4.22376	−	12.9994i	0.199110	−	0.612798i
$451$	−3.18948	+	30.3459i	−0.150187	+	1.42893i
$452$	4.95297	+	5.50083i	0.232968	+	0.258737i
$453$	−10.1758	+	11.3014i	−0.478100	+	0.530984i
$454$	2.52896	+	24.0615i	0.118690	+	1.12926i
$455$	14.1549	+	3.00872i	0.663593	+	0.141051i
$456$	−1.72857	+	0.769610i	−0.0809478	+	0.0360403i
$457$	−10.0094	−	7.27226i	−0.468220	−	0.340182i	0.328527	−	0.944495i	$-0.393448\pi$
$457$	−10.0094	−	7.27226i	−0.468220	−	0.340182i	−0.796747	+	0.604313i	$0.793448\pi$
$458$	−20.0452	−	8.92472i	−0.936653	−	0.417025i
$459$	0.951638	+	1.64829i	0.0444187	+	0.0769354i
$460$	−5.95584	+	10.3158i	−0.277692	+	0.480977i
$461$	30.2111	−	21.9497i	1.40707	−	1.02230i	0.413332	−	0.910581i	$-0.364365\pi$
$461$	30.2111	−	21.9497i	1.40707	−	1.02230i	0.993740	−	0.111717i	$-0.0356350\pi$
$462$	−15.7119	+	3.33966i	−0.730982	+	0.155375i
$463$	8.64949	+	26.6204i	0.401976	+	1.23715i	0.923394	+	0.383853i	$0.125403\pi$
$463$	8.64949	+	26.6204i	0.401976	+	1.23715i	−0.521418	+	0.853301i	$0.674597\pi$
$464$	2.74326			0.127353
$465$	22.4202	+	3.65444i	1.03971	+	0.169471i
$466$	−27.5704			−1.27718
$467$	−9.90232	−	30.4762i	−0.458225	−	1.41027i	−0.867307	−	0.497773i	$-0.834151\pi$
$467$	−9.90232	−	30.4762i	−0.458225	−	1.41027i	0.409083	−	0.912497i	$-0.365849\pi$
$468$	−0.996552	+	0.211824i	−0.0460656	+	0.00979155i
$469$	15.1713	−	11.0226i	0.700545	−	0.508976i
$470$	−19.6173	+	33.9782i	−0.904879	+	1.56730i
$471$	−5.92978	−	10.2707i	−0.273230	−	0.473248i
$472$	4.05975	+	1.80752i	0.186865	+	0.0831978i
$473$	21.0104	+	15.2650i	0.966059	+	0.701883i
$474$	0.559792	−	0.249235i	0.0257121	−	0.0114478i
$475$	−7.00282	−	1.48849i	−0.321311	−	0.0682968i
$476$	−0.268399	−	2.55365i	−0.0123021	−	0.117046i
$477$	−6.35725	+	7.06044i	−0.291079	+	0.323276i
$478$	10.5443	+	11.7106i	0.482285	+	0.535632i
$479$	0.291342	−	2.77194i	0.0133118	−	0.126653i	−0.985848	−	0.167643i	$-0.946384\pi$
$479$	0.291342	−	2.77194i	0.0133118	−	0.126653i	0.999160	+	0.0409898i	$0.0130511\pi$
$480$	4.25798	−	13.1047i	0.194349	−	0.598146i
$481$	0.423069	−	1.30207i	0.0192903	−	0.0593695i
$482$	1.25687	−	11.9583i	0.0572489	−	0.544687i
$483$	−6.80118	−	7.55348i	−0.309465	−	0.343695i
$484$	−12.0298	+	13.3605i	−0.546810	+	0.607294i
$485$	2.13973	+	20.3582i	0.0971603	+	0.924419i
$486$	−1.14802	−	0.244019i	−0.0520752	−	0.0110689i
$487$	4.44109	−	1.97730i	0.201245	−	0.0896001i	−0.303639	−	0.952787i	$-0.598202\pi$
$487$	4.44109	−	1.97730i	0.201245	−	0.0896001i	0.504884	+	0.863187i	$0.331535\pi$
$488$	−17.5105	−	12.7221i	−0.792663	−	0.575903i
$489$	12.6563	+	5.63496i	0.572339	+	0.254822i
$490$	5.51450	+	9.55139i	0.249120	+	0.431488i
$491$	15.7163	−	27.2214i	0.709265	−	1.22848i	−0.255865	−	0.966713i	$-0.582360\pi$
$491$	15.7163	−	27.2214i	0.709265	−	1.22848i	0.965130	−	0.261771i	$-0.0843065\pi$
$492$	2.43338	−	1.76795i	0.109705	−	0.0797054i
$493$	−2.15720	+	0.458526i	−0.0971553	+	0.0206510i
$494$	−0.364899	−	1.12304i	−0.0164176	−	0.0505281i
$495$	25.7652			1.15806
$496$	−13.0098	−	2.12056i	−0.584157	−	0.0952160i
$497$	−8.54971			−0.383507
$498$	2.53725	+	7.80885i	0.113697	+	0.349923i
$499$	11.1868	−	2.37783i	0.500791	−	0.106446i	0.0494116	−	0.998778i	$-0.484265\pi$
$499$	11.1868	−	2.37783i	0.500791	−	0.106446i	0.451380	+	0.892332i	$0.350932\pi$
$500$	13.6556	−	9.92135i	0.610695	−	0.443696i
$501$	6.74014	−	11.6743i	0.301127	−	0.521567i
$502$	10.2644	+	17.7784i	0.458121	+	0.793489i
$503$	−38.1453	−	16.9834i	−1.70082	−	0.757252i	−0.998991	−	0.0449025i	$-0.985702\pi$
$503$	−38.1453	−	16.9834i	−1.70082	−	0.757252i	−0.701825	−	0.712350i	$-0.747631\pi$
$504$	5.39658	+	3.92084i	0.240383	+	0.174648i
$505$	34.5941	−	15.4023i	1.53942	−	0.685393i
$506$	34.0018	+	7.22731i	1.51157	+	0.321293i
$507$	1.07889	+	10.2649i	0.0479150	+	0.455880i
$508$	−0.790648	+	0.878104i	−0.0350793	+	0.0389595i
$509$	−17.9150	−	19.8966i	−0.794068	−	0.881902i	0.201152	−	0.979560i	$-0.435532\pi$
$509$	−17.9150	−	19.8966i	−0.794068	−	0.881902i	−0.995220	+	0.0976578i	$0.968865\pi$
$510$	0.952652	−	9.06388i	0.0421842	−	0.401355i
$511$	−3.22795	+	9.93462i	−0.142796	+	0.439482i
$512$	−6.97435	+	21.4648i	−0.308226	+	0.948621i
$513$	−0.0642585	+	0.611379i	−0.00283708	+	0.0269930i
$514$	1.99591	+	2.21668i	0.0880357	+	0.0977735i
$515$	−11.7689	+	13.0706i	−0.518598	+	0.575961i
$516$	−0.267595	−	2.54599i	−0.0117802	−	0.112081i
$517$	−50.6123	−	10.7580i	−2.22592	−	0.473135i
$518$	−1.94381	+	0.865439i	−0.0854060	+	0.0380252i
$519$	−3.60735	−	2.62089i	−0.158345	−	0.115045i
$520$	18.7757	+	8.35946i	0.823367	+	0.366587i
$521$	−2.93514	−	5.08382i	−0.128591	−	0.222726i	0.794540	−	0.607212i	$-0.207712\pi$
$521$	−2.93514	−	5.08382i	−0.128591	−	0.222726i	−0.923131	+	0.384486i	$0.874379\pi$
$522$	0.679983	−	1.17776i	0.0297620	−	0.0515494i
$523$	−20.4541	+	14.8608i	−0.894397	+	0.649818i	−0.937021	−	0.349274i	$-0.886428\pi$
$523$	−20.4541	+	14.8608i	−0.894397	+	0.649818i	0.0426236	+	0.999091i	$0.486428\pi$
$524$	8.13691	−	1.72955i	0.355463	−	0.0755559i
$525$	7.79928	+	24.0037i	0.340388	+	1.04761i
$526$	17.9347			0.781992
$527$	10.5849	−	0.507012i	0.461084	−	0.0220858i
$528$	−14.9508			−0.650648
$529$	−0.310184	−	0.954649i	−0.0134863	−	0.0415065i
$530$	44.5001	−	9.45879i	1.93296	−	0.410863i
$531$	1.16806	−	0.848647i	0.0506896	−	0.0368281i
$532$	0.414678	−	0.718243i	0.0179786	−	0.0311398i
$533$	3.95390	+	6.84836i	0.171263	+	0.296635i
$534$	−5.46729	−	2.43419i	−0.236593	−	0.105338i
$535$	−13.2204	−	9.60518i	−0.571567	−	0.415268i
$536$	24.3308	−	10.8328i	1.05093	−	0.467905i
$537$	4.73319	+	1.00607i	0.204252	+	0.0434152i
$538$	1.80985	+	17.2196i	0.0780281	+	0.742388i
$539$	−9.73259	+	10.8091i	−0.419212	+	0.465582i
$540$	−1.69946	−	1.88744i	−0.0731329	−	0.0812223i
$541$	3.91912	−	37.2879i	0.168496	−	1.60313i	−0.504450	−	0.863441i	$-0.668305\pi$
$541$	3.91912	−	37.2879i	0.168496	−	1.60313i	0.672946	−	0.739692i	$-0.265029\pi$
$542$	−1.83620	+	5.65124i	−0.0788715	+	0.242742i
$543$	0.418638	−	1.28843i	0.0179655	−	0.0552920i
$544$	0.671899	−	6.39269i	0.0288074	−	0.274085i
$545$	−27.4272	−	30.4610i	−1.17485	−	1.30481i
$546$	−2.78551	+	3.09362i	−0.119209	+	0.132395i
$547$	0.315074	+	2.99773i	0.0134716	+	0.128174i	0.999191	−	0.0402244i	$-0.0128073\pi$
$547$	0.315074	+	2.99773i	0.0134716	+	0.128174i	−0.985719	+	0.168398i	$0.946141\pi$
$548$	12.4914	+	2.65513i	0.533606	+	0.113421i
$549$	−6.42406	+	2.86017i	−0.274172	+	0.122069i
$550$	−69.8320	−	50.7359i	−2.97764	−	2.16339i
$551$	−0.650743	−	0.289729i	−0.0277226	−	0.0123429i
$552$	−7.21781	−	12.5016i	−0.307210	−	0.532104i
$553$	−0.565746	+	0.979901i	−0.0240580	+	0.0416696i
$554$	−12.8788	+	9.35698i	−0.547167	+	0.397540i
$555$	3.33839	−	0.709597i	0.141707	−	0.0301207i
$556$	−1.54313	−	4.74927i	−0.0654433	−	0.201414i
$557$	−6.64939			−0.281744			−0.140872	−	0.990028i	$-0.544991\pi$
$557$	−6.64939			−0.281744			−0.140872	+	0.990028i	$0.544991\pi$
$558$	−4.13521	+	5.05987i	−0.175057	+	0.214201i
$559$	6.73050			0.284670
$560$	−6.46873	−	19.9087i	−0.273354	−	0.841296i
$561$	11.7567	−	2.49897i	0.496369	−	0.105506i
$562$	29.2333	−	21.2393i	1.23313	−	0.895924i
$563$	3.96138	−	6.86132i	0.166952	−	0.289170i	−0.770395	−	0.637567i	$-0.779941\pi$
$563$	3.96138	−	6.86132i	0.166952	−	0.289170i	0.937347	+	0.348397i	$0.113274\pi$
$564$	2.55028	+	4.41721i	0.107386	+	0.185998i
$565$	−44.3193	−	19.7322i	−1.86453	−	0.830141i
$566$	−23.1427	−	16.8142i	−0.972762	−	0.706753i
$567$	1.97984	−	0.881481i	0.0831454	−	0.0370187i
$568$	−11.8773	−	2.52460i	−0.498360	−	0.105930i
$569$	2.07339	+	19.7270i	0.0869212	+	0.827000i	0.947945	+	0.318435i	$0.103157\pi$
$569$	2.07339	+	19.7270i	0.0869212	+	0.827000i	−0.861024	+	0.508565i	$0.830176\pi$
$570$	1.96972	−	2.18760i	0.0825025	−	0.0916283i
$571$	−18.9332	−	21.0275i	−0.792331	−	0.879973i	0.202730	−	0.979235i	$-0.435018\pi$
$571$	−18.9332	−	21.0275i	−0.792331	−	0.879973i	−0.995061	+	0.0992620i	$0.968352\pi$
$572$	−0.672527	+	6.39867i	−0.0281198	+	0.267542i
$573$	1.13592	−	3.49600i	0.0474537	−	0.146047i
$574$	3.79780	−	11.6884i	0.158517	−	0.487866i
$575$	5.70928	−	54.3202i	0.238093	−	2.26531i
$576$	5.82059	+	6.46442i	0.242525	+	0.269351i
$577$	−8.83262	+	9.80962i	−0.367707	+	0.408380i	−0.898396	−	0.439187i	$-0.855267\pi$
$577$	−8.83262	+	9.80962i	−0.367707	+	0.408380i	0.530689	+	0.847567i	$0.321933\pi$
$578$	1.64118	+	15.6147i	0.0682639	+	0.649488i
$579$	−3.13335	−	0.666015i	−0.130218	−	0.0276786i
$580$	2.68852	−	1.19700i	0.111635	−	0.0497029i
$581$	−12.2657	−	8.91157i	−0.508868	−	0.369714i
$582$	−5.37955	−	2.39513i	−0.222990	−	0.0992814i
$583$	29.9991	+	51.9600i	1.24244	+	2.15196i
$584$	−7.41783	+	12.8481i	−0.306952	+	0.531656i
$585$	5.40208	−	3.92484i	0.223349	−	0.162272i
$586$	−18.5986	+	3.95325i	−0.768301	+	0.163307i
$587$	1.86720	+	5.74664i	0.0770675	+	0.237189i	0.982167	−	0.188010i	$-0.0602038\pi$
$587$	1.86720	+	5.74664i	0.0770675	+	0.237189i	−0.905100	+	0.425200i	$0.860204\pi$
$588$	1.43378			0.0591282
$589$	2.86216	+	1.87706i	0.117933	+	0.0773429i
$590$	−6.91363			−0.284630
$591$	3.58762	+	11.0416i	0.147575	+	0.454189i
$592$	−1.93717	+	0.411758i	−0.0796171	+	0.0169231i
$593$	−19.1031	+	13.8792i	−0.784469	+	0.569950i	−0.906317	−	0.422599i	$-0.861118\pi$
$593$	−19.1031	+	13.8792i	−0.784469	+	0.569950i	0.121848	+	0.992549i	$0.461118\pi$
$594$	−3.70590	+	6.41881i	−0.152055	+	0.263367i
$595$	8.41443	+	14.5742i	0.344958	+	0.597485i
$596$	−8.73987	−	3.89124i	−0.357999	−	0.159392i
$597$	6.22863	+	4.52536i	0.254921	+	0.185211i
$598$	8.22998	−	3.66422i	0.336549	−	0.149841i
$599$	30.7108	+	6.52778i	1.25481	+	0.266718i	0.786912	−	0.617065i	$-0.211678\pi$
$599$	30.7108	+	6.52778i	1.25481	+	0.266718i	0.467897	+	0.883783i	$0.345012\pi$
$600$	3.74687	+	35.6491i	0.152965	+	1.45537i
$601$	30.7772	−	34.1816i	1.25543	−	1.39429i	0.370324	−	0.928903i	$-0.379247\pi$
$601$	30.7772	−	34.1816i	1.25543	−	1.39429i	0.885105	−	0.465392i	$-0.154087\pi$
$602$	−6.99926	−	7.77346i	−0.285268	−	0.316823i
$603$	0.904482	−	8.60558i	0.0368334	−	0.350446i
$604$	2.92540	−	9.00345i	0.119033	−	0.366345i
$605$	36.4115	−	112.063i	1.48034	−	4.55601i
$606$	−1.13867	+	10.8337i	−0.0462553	+	0.440090i
$607$	10.9617	+	12.1742i	0.444920	+	0.494134i	0.923333	−	0.384001i	$-0.125454\pi$
$607$	10.9617	+	12.1742i	0.444920	+	0.494134i	−0.478412	+	0.878135i	$0.658788\pi$
$608$	1.38923	−	1.54290i	0.0563408	−	0.0625727i
$609$	0.262493	+	2.49745i	0.0106367	+	0.101202i
$610$	32.9368	+	7.00093i	1.33357	+	0.283460i
$611$	−12.2504	+	5.45425i	−0.495600	+	0.220655i
$612$	−0.958529	−	0.696412i	−0.0387462	−	0.0281508i
$613$	39.0859	+	17.4022i	1.57867	+	0.702867i	0.994099	−	0.108479i	$-0.0345979\pi$
$613$	39.0859	+	17.4022i	1.57867	+	0.702867i	0.584567	+	0.811346i	$0.301265\pi$
$614$	9.13254	+	15.8180i	0.368559	+	0.638363i
$615$	−9.85665	+	17.0722i	−0.397459	+	0.688418i
$616$	34.0799	−	24.7605i	1.37312	−	0.997628i
$617$	−9.16115	+	1.94726i	−0.368814	+	0.0783938i	−0.388590	−	0.921411i	$-0.627038\pi$
$617$	−9.16115	+	1.94726i	−0.368814	+	0.0783938i	0.0197764	+	0.999804i	$0.493705\pi$
$618$	−1.56350	−	4.81194i	−0.0628930	−	0.193565i
$619$	−11.4230			−0.459129			−0.229564	−	0.973293i	$-0.573730\pi$
$619$	−11.4230			−0.459129			−0.229564	+	0.973293i	$0.573730\pi$
$620$	−13.6755	+	3.59850i	−0.549220	+	0.144519i
$621$	−4.69001			−0.188204
$622$	2.65172	+	8.16115i	0.106324	+	0.327232i
$623$	10.8094	−	2.29761i	0.433069	−	0.0920517i
$624$	−3.13467	+	2.27747i	−0.125487	+	0.0911717i
$625$	−26.1986	+	45.3773i	−1.04794	+	1.81509i
$626$	−4.67115	−	8.09066i	−0.186697	−	0.323368i
$627$	3.54655	+	1.57902i	0.141635	+	0.0630601i
$628$	5.97272	+	4.33943i	0.238337	+	0.173162i
$629$	1.45449	−	0.647582i	0.0579944	−	0.0258208i
$630$	−10.1508	−	2.15763i	−0.404419	−	0.0859619i
$631$	0.597211	+	5.68208i	0.0237746	+	0.226200i	0.999957	+	0.00924972i	$0.00294432\pi$
$631$	0.597211	+	5.68208i	0.0237746	+	0.226200i	−0.976183	+	0.216950i	$0.930389\pi$
$632$	−1.07529	+	1.19423i	−0.0427726	+	0.0475038i
$633$	−15.7414	−	17.4826i	−0.625666	−	0.694872i
$634$	−3.87811	+	36.8977i	−0.154019	+	1.46540i
$635$	2.39311	−	7.36523i	0.0949677	−	0.292280i
$636$	1.82762	−	5.62484i	0.0724699	−	0.223040i
$637$	−0.394024	+	3.74889i	−0.0156118	+	0.148536i
$638$	−5.74670	−	6.38235i	−0.227514	−	0.252680i
$639$	−2.63975	+	2.93174i	−0.104427	+	0.115978i
$640$	−1.47338	−	14.0183i	−0.0582406	−	0.554122i
$641$	−42.1982	−	8.96950i	−1.66673	−	0.354274i	−0.724507	−	0.689267i	$-0.757933\pi$
$641$	−42.1982	−	8.96950i	−1.66673	−	0.354274i	−0.942221	+	0.334993i	$0.891266\pi$
$642$	4.29445	−	1.91201i	0.169489	−	0.0754612i
$643$	24.7667	+	17.9940i	0.976703	+	0.709616i	0.956969	−	0.290189i	$-0.0937183\pi$
$643$	24.7667	+	17.9940i	0.976703	+	0.709616i	0.0197333	+	0.999805i	$0.493718\pi$
$644$	5.78028	+	2.57355i	0.227775	+	0.101412i
$645$	8.38920	+	14.5305i	0.330325	+	0.572139i
$646$	0.686613	−	1.18925i	0.0270144	−	0.0467904i
$647$	0.893652	−	0.649276i	0.0351331	−	0.0255257i	−0.570080	−	0.821589i	$-0.693088\pi$
$647$	0.893652	−	0.649276i	0.0351331	−	0.0255257i	0.605213	+	0.796063i	$0.293088\pi$
$648$	3.01069	−	0.639942i	0.118271	−	0.0251393i
$649$	−2.81754	−	8.67150i	−0.110598	−	0.340386i
$650$	−22.3701			−0.877426
$651$	0.685689	−	12.0470i	0.0268743	−	0.472158i
$652$	−8.62429			−0.337753
$653$	−2.51588	−	7.74308i	−0.0984540	−	0.303010i	0.889684	−	0.456576i	$-0.150924\pi$
$653$	−2.51588	−	7.74308i	−0.0984540	−	0.303010i	−0.988138	+	0.153566i	$0.950924\pi$
$654$	11.5336	−	2.45155i	0.451001	−	0.0958632i
$655$	−44.1083	+	32.0466i	−1.72346	+	1.25216i
$656$	5.71952	−	9.90650i	0.223310	−	0.386784i
$657$	2.40999	+	4.17423i	0.0940227	+	0.162852i
$658$	19.0391	+	8.47674i	0.742220	+	0.330458i
$659$	5.92816	+	4.30706i	0.230928	+	0.167779i	0.697232	−	0.716845i	$-0.254415\pi$
$659$	5.92816	+	4.30706i	0.230928	+	0.167779i	−0.466304	+	0.884625i	$0.654415\pi$
$660$	−14.6524	+	6.52367i	−0.570344	+	0.253933i
$661$	19.8582	+	4.22098i	0.772393	+	0.164177i	0.577217	−	0.816591i	$-0.304139\pi$
$661$	19.8582	+	4.22098i	0.772393	+	0.164177i	0.195176	+	0.980768i	$0.437472\pi$
$662$	1.32327	+	12.5900i	0.0514303	+	0.489326i
$663$	2.08431	−	2.31486i	0.0809480	−	0.0899019i
$664$	−14.4082	−	16.0019i	−0.559145	−	0.620993i
$665$	−0.568177	+	5.40584i	−0.0220329	+	0.209629i
$666$	−0.303393	+	0.933749i	−0.0117563	+	0.0361820i
$667$	1.67934	−	5.16849i	0.0650245	−	0.200125i
$668$	−0.877160	+	8.34562i	−0.0339383	+	0.322902i
$669$	16.3922	+	18.2053i	0.633758	+	0.703859i
$670$	−27.7252	+	30.7919i	−1.07112	+	1.18960i
$671$	4.64187	+	44.1645i	0.179198	+	1.70495i
$672$	−7.15932	−	1.52176i	−0.276177	−	0.0587032i
$673$	38.2059	−	17.0104i	1.47273	−	0.655701i	0.495640	−	0.868528i	$-0.334934\pi$
$673$	38.2059	−	17.0104i	1.47273	−	0.655701i	0.977090	+	0.212827i	$0.0682671\pi$
$674$	−0.378542	−	0.275027i	−0.0145809	−	0.0105936i
$675$	10.6390	+	4.73681i	0.409497	+	0.182320i
$676$	−3.21260	−	5.56438i	−0.123561	−	0.214015i
$677$	3.06884	−	5.31538i	0.117945	−	0.204287i	−0.801008	−	0.598653i	$-0.795703\pi$
$677$	3.06884	−	5.31538i	0.117945	−	0.204287i	0.918953	+	0.394367i	$0.129036\pi$
$678$	11.2905	−	8.20300i	0.433607	−	0.315034i
$679$	10.6359	−	2.26074i	0.408170	−	0.0867591i
$680$	7.38583	+	22.7312i	0.283234	+	0.871703i
$681$	−20.6140			−0.789932
$682$	22.3199	+	34.7103i	0.854672	+	1.32913i
$683$	10.8856			0.416525			0.208263	−	0.978073i	$-0.433219\pi$
$683$	10.8856			0.416525			0.208263	+	0.978073i	$0.433219\pi$
$684$	−0.118256	−	0.363955i	−0.00452164	−	0.0139162i
$685$	−81.8688	+	17.4018i	−3.12805	+	0.664887i
$686$	19.1441	−	13.9090i	0.730926	−	0.531049i
$687$	9.34774	−	16.1908i	0.356639	−	0.617716i
$688$	−4.86800	−	8.43163i	−0.185591	−	0.321453i
$689$	14.2049	+	6.32444i	0.541164	+	0.240942i
$690$	18.1689	+	13.2005i	0.691680	+	0.502535i
$691$	20.6433	−	9.19100i	0.785309	−	0.349642i	0.0254051	−	0.999677i	$-0.491912\pi$
$691$	20.6433	−	9.19100i	0.785309	−	0.349642i	0.759904	+	0.650035i	$0.225246\pi$
$692$	2.71507	+	0.577106i	0.103211	+	0.0219383i
$693$	−1.43058	−	13.6111i	−0.0543434	−	0.517043i
$694$	2.11027	−	2.34370i	0.0801049	−	0.0889655i
$695$	21.8998	+	24.3221i	0.830705	+	0.922591i
$696$	−0.372803	+	3.54698i	−0.0141311	+	0.134448i
$697$	−2.84178	+	8.74610i	−0.107640	+	0.331282i
$698$	−7.33160	+	22.5643i	−0.277505	+	0.854073i
$699$	2.45546	−	23.3622i	0.0928742	−	0.883639i
$700$	−10.5130	−	11.6759i	−0.397356	−	0.441308i
$701$	−5.18594	+	5.75957i	−0.195870	+	0.217536i	−0.833077	−	0.553157i	$-0.813423\pi$
$701$	−5.18594	+	5.75957i	−0.195870	+	0.217536i	0.637207	+	0.770693i	$0.280090\pi$
$702$	0.200784	+	1.91033i	0.00757810	+	0.0721008i
$703$	0.503013	+	0.106919i	0.0189715	+	0.00403252i
$704$	50.1841	−	22.3434i	1.89138	−	0.842098i
$705$	−27.0447	−	19.6492i	−1.01856	−	0.740030i
$706$	−25.5173	−	11.3611i	−0.960358	−	0.427579i
$707$	−10.0575	−	17.4200i	−0.378250	−	0.655148i
$708$	−0.449390	+	0.778367i	−0.0168891	+	0.0292528i
$709$	−24.2192	+	17.5963i	−0.909570	+	0.660842i	−0.940906	−	0.338667i	$-0.890024\pi$
$709$	−24.2192	+	17.5963i	−0.909570	+	0.660842i	0.0313358	+	0.999509i	$0.490024\pi$
$710$	18.4780	−	3.92761i	0.693465	−	0.147401i
$711$	0.161337	+	0.496545i	0.00605062	+	0.0186219i
$712$	15.6949			0.588192
$713$	−11.9595	+	23.2132i	−0.447887	+	0.869342i
$714$	−4.84112			−0.181174
$715$	−13.0306	−	40.1042i	−0.487318	−	1.49981i
$716$	−2.94645	+	0.626288i	−0.110114	+	0.0234055i
$717$	−10.8623	+	7.89190i	−0.405659	+	0.294728i
$718$	8.27359	−	14.3303i	0.308767	−	0.534801i
$719$	−9.16478	−	15.8739i	−0.341789	−	0.591996i	0.642976	−	0.765886i	$-0.277699\pi$
$719$	−9.16478	−	15.8739i	−0.341789	−	0.591996i	−0.984765	+	0.173891i	$0.944366\pi$
$720$	−8.82404	−	3.92871i	−0.328852	−	0.146415i
$721$	7.55835	+	5.49146i	0.281488	+	0.204513i
$722$	−19.9665	+	8.88968i	−0.743078	+	0.330840i
$723$	10.0211	+	2.13005i	0.372689	+	0.0792175i
$724$	0.0881528	+	0.838717i	0.00327617	+	0.0311707i
$725$	−9.02957	+	10.0283i	−0.335350	+	0.372444i
$726$	22.6808	+	25.1896i	0.841763	+	0.934872i
$727$	−3.57552	+	34.0188i	−0.132609	+	1.26169i	0.702532	+	0.711652i	$0.252053\pi$
$727$	−3.57552	+	34.0188i	−0.132609	+	1.26169i	−0.835141	+	0.550036i	$0.814614\pi$
$728$	3.37360	−	10.3829i	0.125034	−	0.384815i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	2.41256	−	22.9540i	0.0892928	−	0.849564i
$731$	5.23733	+	5.81665i	0.193710	+	0.215136i
$732$	2.92911	−	3.25311i	0.108263	−	0.120238i
$733$	0.0482823	+	0.459376i	0.00178335	+	0.0169674i	0.995377	−	0.0960409i	$-0.0306180\pi$
$733$	0.0482823	+	0.459376i	0.00178335	+	0.0169674i	−0.993594	+	0.113008i	$0.963951\pi$
$734$	−38.5993	−	8.20452i	−1.42472	−	0.302835i
$735$	−8.58463	+	3.82212i	−0.316649	+	0.140981i
$736$	12.8144	+	9.31023i	0.472346	+	0.343180i
$737$	−49.9201	−	22.2259i	−1.83883	−	0.818700i
$738$	−2.83544	−	4.91113i	−0.104374	−	0.180781i
$739$	21.2177	−	36.7501i	0.780504	−	1.35187i	−0.151144	−	0.988512i	$-0.548296\pi$
$739$	21.2177	−	36.7501i	0.780504	−	1.35187i	0.931648	−	0.363361i	$-0.118371\pi$
$740$	−1.71884	+	1.24881i	−0.0631859	+	0.0459072i
$741$	0.984125	−	0.209182i	0.0361527	−	0.00768450i
$742$	−7.46767	−	22.9831i	−0.274147	−	0.843737i
$743$	1.56364			0.0573645			0.0286822	−	0.999589i	$-0.490869\pi$
$743$	1.56364			0.0573645			0.0286822	+	0.999589i	$0.490869\pi$
$744$	4.50985	−	16.5332i	0.165339	−	0.606138i
$745$	62.7022			2.29723
$746$	−0.185345	−	0.570434i	−0.00678598	−	0.0208851i
$747$	−6.84291	+	1.45450i	−0.250369	+	0.0532175i
$748$	−6.05319	+	4.39790i	−0.221327	+	0.160803i
$749$	−4.34013	+	7.51733i	−0.158585	+	0.274677i
$750$	−15.9119	−	27.5601i	−0.581019	−	1.00635i
$751$	25.4799	+	11.3444i	0.929775	+	0.413962i	0.815021	−	0.579432i	$-0.196725\pi$
$751$	25.4799	+	11.3444i	0.929775	+	0.413962i	0.114754	+	0.993394i	$0.463392\pi$
$752$	15.6933	+	11.4018i	0.572274	+	0.415781i
$753$	−15.9789	+	7.11428i	−0.582304	+	0.259259i
$754$	−2.17712	−	0.462761i	−0.0792860	−	0.0168528i
$755$	6.48552	+	61.7056i	0.236032	+	2.24570i
$756$	−0.902726	+	1.00258i	−0.0328318	+	0.0364634i
$757$	5.04494	+	5.60297i	0.183361	+	0.203643i	0.827817	−	0.560998i	$-0.189583\pi$
$757$	5.04494	+	5.60297i	0.183361	+	0.203643i	−0.644456	+	0.764642i	$0.722916\pi$
$758$	2.57541	−	24.5034i	0.0935431	−	0.890003i
$759$	−9.15242	+	28.1683i	−0.332212	+	1.02244i
$760$	−2.38557	+	7.34204i	−0.0865339	+	0.266324i
$761$	−0.601396	+	5.72190i	−0.0218006	+	0.207419i	−1.00000		0.000249232i	$-0.999921\pi$
$761$	−0.601396	+	5.72190i	−0.0218006	+	0.207419i	0.978199	+	0.207668i	$0.0665873\pi$
$762$	1.49067	+	1.65556i	0.0540014	+	0.0599746i
$763$	−14.5689	+	16.1804i	−0.527431	+	0.585772i
$764$	0.239191	+	2.27575i	0.00865363	+	0.0823338i
$765$	7.59556	+	1.61449i	0.274618	+	0.0583719i
$766$	−2.32897	+	1.03692i	−0.0841490	+	0.0374656i
$767$	−1.91168	−	1.38892i	−0.0690269	−	0.0501510i
$768$	−12.1891	−	5.42694i	−0.439837	−	0.195828i
$769$	−15.8741	−	27.4947i	−0.572433	−	0.991483i	−0.996315	−	0.0857659i	$-0.972666\pi$
$769$	−15.8741	−	27.4947i	−0.572433	−	0.991483i	0.423882	−	0.905717i	$-0.360667\pi$
$770$	−32.7678	+	56.7554i	−1.18087	+	2.04532i
$771$	−2.05609	+	1.49384i	−0.0740484	+	0.0537993i
$772$	1.95054	−	0.414600i	0.0702015	−	0.0149218i
$773$	−0.165911	−	0.510622i	−0.00596741	−	0.0183658i	0.948028	−	0.318185i	$-0.103073\pi$
$773$	−0.165911	−	0.510622i	−0.00596741	−	0.0183658i	−0.953996	+	0.299820i	$0.903073\pi$
$774$	−4.82660			−0.173489
$775$	50.5743	−	40.5791i	1.81668	−	1.45764i
$776$	15.4430			0.554373
$777$	−0.560223	−	1.72419i	−0.0200979	−	0.0618550i
$778$	−43.4448	+	9.23448i	−1.55757	+	0.331072i
$779$	−2.40303	+	1.74590i	−0.0860975	+	0.0625535i
$780$	−2.07835	+	3.59981i	−0.0744169	+	0.128894i
$781$	12.4566	+	21.5755i	0.445734	+	0.772034i
$782$	9.57085	+	4.26122i	0.342253	+	0.152381i
$783$	0.937435	+	0.681086i	0.0335012	+	0.0243400i
$784$	4.98140	−	2.21786i	0.177907	−	0.0792094i
$785$	−47.3289	−	10.0601i	−1.68924	−	0.359059i
$786$	−1.63941	−	15.5980i	−0.0584760	−	0.556362i
$787$	26.5041	−	29.4358i	0.944771	−	1.04927i	−0.0539419	−	0.998544i	$-0.517179\pi$
$787$	26.5041	−	29.4358i	0.944771	−	1.04927i	0.998712	−	0.0507299i	$-0.0161548\pi$
$788$	−4.83593	−	5.37085i	−0.172273	−	0.191329i
$789$	−1.59730	+	15.1972i	−0.0568652	+	0.541036i
$790$	0.772560	−	2.37770i	0.0274865	−	0.0845946i
$791$	−7.96327	+	24.5084i	−0.283141	+	0.871419i
$792$	2.03177	−	19.3310i	0.0721960	−	0.686899i
$793$	7.70088	+	8.55269i	0.273466	+	0.303715i
$794$	25.3059	−	28.1051i	0.898074	−	0.997412i
$795$	4.05179	+	38.5502i	0.143702	+	1.36723i
$796$	−4.68797	−	0.996458i	−0.166161	−	0.0353185i
$797$	−14.3903	+	6.40698i	−0.509731	+	0.226947i	−0.645453	−	0.763800i	$-0.723331\pi$
$797$	−14.3903	+	6.40698i	−0.509731	+	0.226947i	0.135722	+	0.990747i	$0.456665\pi$
$798$	−1.26502	−	0.919091i	−0.0447812	−	0.0325355i
$799$	−14.2464	−	6.34289i	−0.504000	−	0.224395i
$800$	−19.6657	−	34.0621i	−0.695289	−	1.20428i
$801$	2.54957	−	4.41599i	0.0900847	−	0.156031i
$802$	−13.2916	+	9.65689i	−0.469342	+	0.340997i
$803$	29.7735	−	6.32854i	1.05068	−	0.223329i
$804$	1.66454	+	5.12292i	0.0587037	+	0.180671i
$805$	−41.4693			−1.46160
$806$	9.96718	+	3.87756i	0.351079	+	0.136581i
$807$	−14.7524			−0.519310
$808$	−8.82800	−	27.1698i	−0.310568	−	0.955830i
$809$	−18.5583	+	3.94470i	−0.652477	+	0.138688i	−0.522245	−	0.852795i	$-0.674905\pi$
$809$	−18.5583	+	3.94470i	−0.652477	+	0.138688i	−0.130231	+	0.991484i	$0.541572\pi$
$810$	−3.87396	+	2.81460i	−0.136117	+	0.0988949i
$811$	−16.2093	+	28.0753i	−0.569186	+	0.985858i	0.427461	+	0.904034i	$0.359408\pi$
$811$	−16.2093	+	28.0753i	−0.569186	+	0.985858i	−0.996647	+	0.0818246i	$0.973925\pi$
$812$	−0.781625	−	1.35381i	−0.0274297	−	0.0475096i
$813$	−4.62512	−	2.05924i	−0.162210	−	0.0722206i
$814$	5.01604	+	3.64437i	0.175812	+	0.127735i
$815$	51.6370	−	22.9903i	1.80877	−	0.805315i
$816$	−4.40748	−	0.936838i	−0.154293	−	0.0327959i
$817$	0.264258	+	2.51424i	0.00924521	+	0.0879623i
$818$	26.7942	−	29.7579i	0.936835	−	1.04046i
$819$	−2.37334	−	2.63586i	−0.0829313	−	0.0921045i
$820$	1.28274	−	12.2045i	0.0447953	−	0.426199i
$821$	2.99628	−	9.22160i	0.104571	−	0.321836i	−0.885059	−	0.465480i	$-0.845882\pi$
$821$	2.99628	−	9.22160i	0.104571	−	0.321836i	0.989629	+	0.143644i	$0.0458819\pi$
$822$	7.44025	−	22.8987i	0.259509	−	0.798685i
$823$	2.67999	−	25.4984i	0.0934187	−	0.888820i	−0.842995	−	0.537922i	$-0.819210\pi$
$823$	2.67999	−	25.4984i	0.0934187	−	0.888820i	0.936414	−	0.350898i	$-0.114124\pi$
$824$	8.87855	+	9.86063i	0.309299	+	0.343511i
$825$	49.2111	−	54.6545i	1.71331	−	1.90282i
$826$	0.383872	+	3.65230i	0.0133566	+	0.127080i
$827$	32.4592	+	6.89941i	1.12872	+	0.239916i	0.734173	−	0.678962i	$-0.237570\pi$
$827$	32.4592	+	6.89941i	1.12872	+	0.239916i	0.394542	+	0.918878i	$0.370903\pi$
$828$	2.66716	−	1.18750i	0.0926904	−	0.0412684i
$829$	15.5025	+	11.2632i	0.538423	+	0.391187i	0.823499	−	0.567318i	$-0.192019\pi$
$829$	15.5025	+	11.2632i	0.538423	+	0.391187i	−0.285076	+	0.958505i	$0.592019\pi$
$830$	30.6030	+	13.6253i	1.06225	+	0.472942i
$831$	−6.78176	−	11.7464i	−0.235257	−	0.407477i
$832$	7.11830	−	12.3293i	0.246783	−	0.427440i
$833$	−3.54648	+	2.57667i	−0.122878	+	0.0892763i
$834$	−9.20924	+	1.95748i	−0.318890	+	0.0677821i
$835$	−16.9955	−	52.3068i	−0.588154	−	1.81015i
$836$	−2.41669			−0.0835830
$837$	−3.91926	−	3.95467i	−0.135469	−	0.136693i
$838$	4.01544			0.138711
$839$	5.82339	+	17.9226i	0.201046	+	0.618755i	0.999853	+	0.0171676i	$0.00546489\pi$
$839$	5.82339	+	17.9226i	0.201046	+	0.618755i	−0.798807	+	0.601588i	$0.794535\pi$
$840$	26.6207	−	5.65839i	0.918500	−	0.195233i
$841$	22.3753	−	16.2566i	0.771561	−	0.560572i
$842$	−4.34273	+	7.52182i	−0.149660	+	0.259219i
$843$	15.3938	+	26.6629i	0.530191	+	0.918318i
$844$	13.3785	+	5.95651i	0.460509	+	0.205032i
$845$	34.0684	+	24.7521i	1.17199	+	0.851500i
$846$	8.78509	−	3.91137i	0.302038	−	0.134476i
$847$	−61.2219	−	13.0131i	−2.10361	−	0.447136i
$848$	−2.35113	−	22.3695i	−0.0807382	−	0.768172i
$849$	16.3089	−	18.1128i	0.559719	−	0.621631i
$850$	−17.4072	−	19.3327i	−0.597063	−	0.663106i
$851$	−0.410098	+	3.90182i	−0.0140580	+	0.133753i
$852$	0.758891	−	2.33563i	0.0259992	−	0.0800173i
$853$	9.57434	−	29.4668i	0.327819	−	1.00892i	−0.642333	−	0.766426i	$-0.722033\pi$
$853$	9.57434	−	29.4668i	0.327819	−	1.00892i	0.970152	−	0.242498i	$-0.0779666\pi$
$854$	1.86964	−	17.7884i	0.0639777	−	0.608707i
$855$	1.67826	+	1.86390i	0.0573954	+	0.0637441i
$856$	−8.24908	+	9.16153i	−0.281948	+	0.313135i
$857$	−1.43844	−	13.6858i	−0.0491362	−	0.467500i	−0.991230	−	0.132150i	$-0.957812\pi$
$857$	−1.43844	−	13.6858i	−0.0491362	−	0.467500i	0.942094	−	0.335350i	$-0.108855\pi$
$858$	11.8653	+	2.52205i	0.405074	+	0.0861012i
$859$	1.06535	−	0.474325i	0.0363493	−	0.0161838i	−0.388481	−	0.921457i	$-0.627000\pi$
$859$	1.06535	−	0.474325i	0.0363493	−	0.0161838i	0.424831	+	0.905273i	$0.360334\pi$
$860$	−8.44994	−	6.13924i	−0.288141	−	0.209346i
$861$	9.56611	+	4.25911i	0.326012	+	0.145150i
$862$	−1.85456	−	3.21220i	−0.0631667	−	0.109408i
$863$	−20.9010	+	36.2016i	−0.711478	+	1.23232i	0.252824	+	0.967512i	$0.418641\pi$
$863$	−20.9010	+	36.2016i	−0.711478	+	1.23232i	−0.964302	+	0.264804i	$0.914693\pi$
$864$	−2.73228	+	1.98512i	−0.0929541	+	0.0675351i
$865$	−17.7946	+	3.78236i	−0.605035	+	0.128604i
$866$	−3.95515	−	12.1727i	−0.134402	−	0.413645i
$867$	−13.3775			−0.454325
$868$	2.66032	+	7.02461i	0.0902970	+	0.238431i
$869$	3.29710			0.111846
$870$	−1.71460	−	5.27701i	−0.0581305	−	0.178907i
$871$	−13.8522	+	2.94438i	−0.469365	+	0.0997667i
$872$	−25.0171	+	18.1760i	−0.847185	+	0.615516i
$873$	2.50866	−	4.34513i	0.0849053	−	0.147060i
$874$	1.69194	+	2.93052i	0.0572306	+	0.0991264i
$875$	53.6829	+	23.9012i	1.81481	+	0.808007i
$876$	−2.42744	−	1.76364i	−0.0820156	−	0.0595878i
$877$	−6.36912	+	2.83571i	−0.215070	+	0.0957553i	−0.511444	−	0.859317i	$-0.670889\pi$
$877$	−6.36912	+	2.83571i	−0.215070	+	0.0957553i	0.296374	+	0.955072i	$0.404223\pi$
$878$	33.7989	+	7.18417i	1.14066	+	0.242454i
$879$	−1.69342	−	16.1119i	−0.0571178	−	0.543439i
$880$	−40.8157	+	45.3305i	−1.37590	+	1.52809i
$881$	10.3561	+	11.5016i	0.348905	+	0.387499i	0.891896	−	0.452240i	$-0.149375\pi$
$881$	10.3561	+	11.5016i	0.348905	+	0.387499i	−0.542991	+	0.839738i	$0.682708\pi$
$882$	0.282564	−	2.68842i	0.00951443	−	0.0905237i
$883$	−2.26607	+	6.97424i	−0.0762592	+	0.234702i	−0.981918	−	0.189305i	$-0.939377\pi$
$883$	−2.26607	+	6.97424i	−0.0762592	+	0.234702i	0.905659	+	0.424006i	$0.139377\pi$
$884$	−0.599211	+	1.84418i	−0.0201537	+	0.0620266i
$885$	0.615738	−	5.85836i	0.0206978	−	0.196927i
$886$	−9.94215	−	11.0419i	−0.334013	−	0.370959i
$887$	37.8752	−	42.0647i	1.27173	−	1.41239i	0.404455	−	0.914558i	$-0.367461\pi$
$887$	37.8752	−	42.0647i	1.27173	−	1.41239i	0.867271	−	0.497836i	$-0.165872\pi$
$888$	−0.269138	−	2.56068i	−0.00903168	−	0.0859307i
$889$	−4.02375	−	0.855274i	−0.134952	−	0.0286850i
$890$	−22.3062	+	9.93136i	−0.747705	+	0.332900i
$891$	−5.10902	−	3.71192i	−0.171158	−	0.124354i
$892$	−13.9316	−	6.20275i	−0.466465	−	0.207683i
$893$	−2.51847	−	4.36213i	−0.0842775	−	0.145973i
$894$	−9.01870	+	15.6208i	−0.301630	+	0.522439i
$895$	15.9721	−	11.6044i	0.533887	−	0.387892i
$896$	−7.32371	+	1.55670i	−0.244668	+	0.0520058i
$897$	2.37196	+	7.30013i	0.0791973	+	0.243744i
$898$	−31.8694			−1.06350
$899$	5.76149	−	2.90307i	0.192156	−	0.0968227i
$900$	−7.24967			−0.241656
$901$	5.58783	+	17.1976i	0.186157	+	0.572934i
$902$	−35.0295	+	7.44576i	−1.16636	+	0.247917i
$903$	7.21032	−	5.23860i	0.239944	−	0.174330i
$904$	−18.2996	+	31.6958i	−0.608635	+	1.05419i
$905$	−2.76363	−	4.78674i	−0.0918660	−	0.159117i
$906$	−16.3054	−	7.25963i	−0.541711	−	0.241185i
$907$	11.4419	+	8.31302i	0.379922	+	0.276029i	0.761313	−	0.648384i	$-0.224555\pi$
$907$	11.4419	+	8.31302i	0.379922	+	0.276029i	−0.381392	+	0.924414i	$0.624555\pi$
$908$	11.7230	−	5.21942i	0.389041	−	0.173212i
$909$	−9.07869	−	1.92973i	−0.301121	−	0.0640053i
$910$	1.77534	+	16.8912i	0.0588520	+	0.559939i
$911$	−39.6606	+	44.0475i	−1.31401	+	1.45936i	−0.516181	+	0.856480i	$0.672647\pi$
$911$	−39.6606	+	44.0475i	−1.31401	+	1.45936i	−0.797832	+	0.602880i	$0.794020\pi$
$912$	−0.973846	−	1.08157i	−0.0322473	−	0.0358142i
$913$	−4.61796	+	43.9370i	−0.152832	+	1.45410i
$914$	4.48722	−	13.8102i	0.148424	−	0.456802i
$915$	−8.86574	+	27.2859i	−0.293092	+	0.902046i
$916$	−1.21651	+	11.5743i	−0.0401947	+	0.382427i
$917$	19.3785	+	21.5220i	0.639934	+	0.710719i
$918$	−1.49471	+	1.66004i	−0.0493328	+	0.0547896i
$919$	−2.79660	−	26.6079i	−0.0922515	−	0.877714i	−0.938582	−	0.345056i	$-0.887860\pi$
$919$	−2.79660	−	26.6079i	−0.0922515	−	0.877714i	0.846331	−	0.532658i	$-0.178807\pi$
$920$	−57.6094	−	12.2453i	−1.89933	−	0.403714i
$921$	−14.2170	+	6.32981i	−0.468465	+	0.208574i
$922$	35.4577	+	25.7616i	1.16774	+	0.848412i
$923$	5.89837	+	2.62612i	0.194147	+	0.0864399i
$924$	4.25985	+	7.37828i	0.140139	+	0.242728i
$925$	4.87104	−	8.43689i	0.160159	−	0.277403i
$926$	−26.5773	+	19.3095i	−0.873383	+	0.634550i
$927$	4.21671	−	0.896290i	0.138495	−	0.0294380i
$928$	−1.20930	−	3.72184i	−0.0396972	−	0.122175i
$929$	−47.9515			−1.57324			−0.786619	−	0.617439i	$-0.788170\pi$
$929$	−47.9515			−1.57324			−0.786619	+	0.617439i	$0.788170\pi$
$930$	4.05227	+	26.3514i	0.132879	+	0.864096i
$931$	−1.41590			−0.0464044
$932$	4.51884	+	13.9076i	0.148019	+	0.455557i
$933$	−7.15163	+	1.52012i	−0.234134	+	0.0497667i
$934$	30.4268	−	22.1064i	0.995596	−	0.723343i
$935$	24.5191	−	42.4684i	0.801861	−	1.38886i
$936$	−2.51873	−	4.36257i	−0.0823272	−	0.142595i
$937$	37.0491	+	16.4953i	1.21034	+	0.538879i	0.909863	−	0.414909i	$-0.136186\pi$
$937$	37.0491	+	16.4953i	1.21034	+	0.538879i	0.300480	+	0.953788i	$0.402853\pi$
$938$	17.8060	+	12.9368i	0.581388	+	0.422403i
$939$	7.27175	−	3.23759i	0.237305	−	0.105655i
$940$	20.3552	+	4.32663i	0.663913	+	0.141119i
$941$	1.14673	+	10.9104i	0.0373823	+	0.355669i	0.997184	+	0.0749908i	$0.0238927\pi$
$941$	1.14673	+	10.9104i	0.0373823	+	0.355669i	−0.959802	+	0.280678i	$0.909441\pi$
$942$	9.31374	−	10.3440i	0.303458	−	0.337024i
$943$	−15.1632	−	16.8404i	−0.493782	−	0.548400i
$944$	−0.357295	+	3.39943i	−0.0116289	+	0.110642i
$945$	2.73234	−	8.40929i	0.0888831	−	0.273554i
$946$	−9.41897	+	28.9886i	−0.306237	+	0.942501i
$947$	2.64060	−	25.1236i	0.0858080	−	0.816408i	−0.863983	−	0.503522i	$-0.832037\pi$
$947$	2.64060	−	25.1236i	0.0858080	−	0.816408i	0.949790	−	0.312887i	$-0.101296\pi$
$948$	−0.217475	−	0.241530i	−0.00706324	−	0.00784453i
$949$	5.27845	−	5.86231i	0.171346	−	0.190299i
$950$	−0.878309	−	8.35655i	−0.0284961	−	0.271122i
$951$	−30.9204	−	6.57234i	−1.00266	−	0.213123i
$952$	11.5983	−	5.16388i	0.375902	−	0.167362i
$953$	−10.2988	−	7.48251i	−0.333611	−	0.242382i	0.408351	−	0.912825i	$-0.366104\pi$
$953$	−10.2988	−	7.48251i	−0.333611	−	0.242382i	−0.741961	+	0.670443i	$0.766104\pi$
$954$	−10.1867	−	4.53541i	−0.329806	−	0.146839i
$955$	−7.49874	−	12.9882i	−0.242654	−	0.420289i
$956$	4.17906	−	7.23834i	0.135160	−	0.234105i
$957$	5.91999	−	4.30112i	0.191366	−	0.139035i
$958$	3.19976	−	0.680131i	0.103380	−	0.0219740i
$959$	13.7386	+	42.2831i	0.443643	+	1.36539i
$960$	35.4903			1.14544
$961$	−29.5677	+	9.31399i	−0.953797	+	0.300451i
$962$	1.60684			0.0518067
$963$	1.23770	+	3.80925i	0.0398843	+	0.122751i
$964$	−6.23823	+	1.32598i	−0.200920	+	0.0427068i
$965$	−10.5734	+	7.68205i	−0.340371	+	0.247294i
$966$	5.96469	−	10.3311i	0.191911	−	0.332399i
$967$	−4.36890	−	7.56715i	−0.140494	−	0.243343i	0.787189	−	0.616712i	$-0.211536\pi$
$967$	−4.36890	−	7.56715i	−0.140494	−	0.243343i	−0.927683	+	0.373369i	$0.878203\pi$
$968$	−81.2071	−	36.1557i	−2.61010	−	1.16209i
$969$	0.946576	+	0.687728i	0.0304084	+	0.0220930i
$970$	−21.9482	+	9.77199i	−0.704716	+	0.313760i
$971$	31.1417	+	6.61938i	0.999386	+	0.212426i	0.678428	−	0.734667i	$-0.262662\pi$
$971$	31.1417	+	6.61938i	0.999386	+	0.212426i	0.320959	+	0.947093i	$0.395995\pi$
$972$	0.0650699	+	0.619099i	0.00208712	+	0.0198576i
$973$	11.6328	−	12.9196i	0.372931	−	0.414182i
$974$	3.81782	+	4.24012i	0.122331	+	0.135862i
$975$	1.99231	−	18.9556i	0.0638050	−	0.607064i
$976$	5.14452	−	15.8332i	0.164672	−	0.506809i
$977$	−1.14807	+	3.53339i	−0.0367300	+	0.113043i	−0.967740	−	0.251949i	$-0.918928\pi$
$977$	−1.14807	+	3.53339i	−0.0367300	+	0.113043i	0.931010	+	0.364992i	$0.118928\pi$
$978$	−1.69964	+	16.1710i	−0.0543484	+	0.517091i
$979$	−21.5471	−	23.9304i	−0.688647	−	0.764820i
$980$	3.91424	−	4.34721i	0.125036	−	0.138866i
$981$	1.05015	+	9.99153i	0.0335288	+	0.319005i
$982$	36.0851	+	7.67013i	1.15152	+	0.244764i
$983$	17.4750	−	7.78036i	0.557365	−	0.248155i	−0.108667	−	0.994078i	$-0.534658\pi$
$983$	17.4750	−	7.78036i	0.557365	−	0.248155i	0.666032	+	0.745923i	$0.267991\pi$
$984$	12.0316	+	8.74150i	0.383555	+	0.278669i
$985$	43.2721	+	19.2660i	1.37876	+	0.613865i
$986$	−1.29420	−	2.24161i	−0.0412156	−	0.0713875i
$987$	−8.87853	+	15.3781i	−0.282607	+	0.489489i
$988$	−0.506698	+	0.368138i	−0.0161202	+	0.0117120i
$989$	−18.8658	+	4.01005i	−0.599898	+	0.127512i
$990$	9.34458	+	28.7597i	0.296990	+	0.914042i
$991$	17.7063			0.562458			0.281229	−	0.959641i	$-0.409258\pi$
$991$	17.7063			0.562458			0.281229	+	0.959641i	$0.409258\pi$
$992$	2.85804	+	18.5855i	0.0907428	+	0.590089i
$993$	−10.7862			−0.342290
$994$	−3.10083	−	9.54337i	−0.0983523	−	0.302697i
$995$	30.7250	−	6.53081i	0.974049	−	0.207041i
$996$	3.52322	−	2.55977i	0.111637	−	0.0811093i
$997$	−13.4064	+	23.2206i	−0.424585	+	0.735403i	−0.996382	−	0.0849923i	$-0.972913\pi$
$997$	−13.4064	+	23.2206i	−0.424585	+	0.735403i	0.571796	+	0.820396i	$0.306247\pi$
$998$	6.71146	+	11.6246i	0.212448	+	0.367970i
$999$	−0.764204	−	0.340246i	−0.0241783	−	0.0107649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.m.b.7.2	✓	24
3.2	odd	2		279.2.y.d.100.2		24
31.3	odd	30		2883.2.a.s.1.8		12
31.9	even	15	inner	93.2.m.b.40.2	yes	24
31.28	even	15		2883.2.a.t.1.8		12
93.59	odd	30		8649.2.a.bk.1.5		12
93.65	even	30		8649.2.a.bl.1.5		12
93.71	odd	30		279.2.y.d.226.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.b.7.2	✓	24	1.1	even	1	trivial
93.2.m.b.40.2	yes	24	31.9	even	15	inner
279.2.y.d.100.2		24	3.2	odd	2
279.2.y.d.226.2		24	93.71	odd	30
2883.2.a.s.1.8		12	31.3	odd	30
2883.2.a.t.1.8		12	31.28	even	15
8649.2.a.bk.1.5		12	93.59	odd	30
8649.2.a.bl.1.5		12	93.65	even	30

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.362683 + 1.11622i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.503620 - 0.365901i) q^{4} +(-2.03997 + 3.53333i) q^{5} +(-0.586833 - 1.01642i) q^{6} +(1.97984 + 0.881481i) q^{7} +(2.49011 + 1.80917i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})\)	\(q+(0.362683 + 1.11622i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.503620 - 0.365901i) q^{4} +(-2.03997 + 3.53333i) q^{5} +(-0.586833 - 1.01642i) q^{6} +(1.97984 + 0.881481i) q^{7} +(2.49011 + 1.80917i) q^{8} +(0.913545 - 0.406737i) q^{9} +(-4.68384 - 0.995581i) q^{10} +(-0.660107 - 6.28050i) q^{11} +(-0.416540 + 0.462614i) q^{12} +(-1.09512 - 1.21625i) q^{13} +(-0.265876 + 2.52964i) q^{14} +(1.26077 - 3.88025i) q^{15} +(-0.731587 + 2.25159i) q^{16} +(0.198947 - 1.89285i) q^{17} +(0.785336 + 0.872204i) q^{18} +(0.411346 - 0.456845i) q^{19} +(0.265481 + 2.52588i) q^{20} +(-2.11984 - 0.450587i) q^{21} +(6.77102 - 3.01465i) q^{22} +(3.79430 + 2.75672i) q^{23} +(-2.81185 - 1.25191i) q^{24} +(-5.82294 - 10.0856i) q^{25} +(0.960427 - 1.66351i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.31962 - 0.280494i) q^{28} +(-0.358068 - 1.10202i) q^{29} +4.78848 q^{30} +(0.846253 + 5.50308i) q^{31} +3.37728 q^{32} +(1.95147 + 6.00601i) q^{33} +(2.18500 - 0.464435i) q^{34} +(-7.15337 + 5.19723i) q^{35} +(0.311254 - 0.539108i) q^{36} +(0.418263 + 0.724452i) q^{37} +(0.659129 + 0.293463i) q^{38} +(1.32406 + 0.961986i) q^{39} +(-11.4722 + 5.10773i) q^{40} +(-4.72618 - 1.00458i) q^{41} +(-0.265876 - 2.52964i) q^{42} +(-2.75174 + 3.05612i) q^{43} +(-2.63049 - 2.92145i) q^{44} +(-0.426470 + 4.05759i) q^{45} +(-1.70099 + 5.23510i) q^{46} +(2.53194 - 7.79252i) q^{47} +(0.247467 - 2.35450i) q^{48} +(-1.54116 - 1.71164i) q^{49} +(9.14593 - 10.1576i) q^{50} +(0.198947 + 1.89285i) q^{51} +(-0.996552 - 0.211824i) q^{52} +(-8.67938 + 3.86431i) q^{53} +(-0.949516 - 0.689863i) q^{54} +(23.5377 + 10.4796i) q^{55} +(3.33527 + 5.77686i) q^{56} +(-0.307373 + 0.532386i) q^{57} +(1.10024 - 0.799368i) q^{58} +(1.41225 - 0.300184i) q^{59} +(-0.784840 - 2.41549i) q^{60} -7.03201 q^{61} +(-5.83574 + 2.94048i) q^{62} +2.16720 q^{63} +(2.68806 + 8.27299i) q^{64} +(6.53142 - 1.38830i) q^{65} +(-5.99628 + 4.35655i) q^{66} +(4.32649 - 7.49370i) q^{67} +(-0.592403 - 1.02607i) q^{68} +(-4.28454 - 1.90760i) q^{69} +(-8.39566 - 6.09981i) q^{70} +(-3.60398 + 1.60459i) q^{71} +(3.01069 + 0.639942i) q^{72} +(0.503825 + 4.79358i) q^{73} +(-0.656953 + 0.729621i) q^{74} +(7.79262 + 8.65458i) q^{75} +(0.0400015 - 0.380589i) q^{76} +(4.22923 - 13.0162i) q^{77} +(-0.593577 + 1.82684i) q^{78} +(-0.0545741 + 0.519238i) q^{79} +(-6.46321 - 7.17812i) q^{80} +(0.669131 - 0.743145i) q^{81} +(-0.592768 - 5.63981i) q^{82} +(-6.84291 - 1.45450i) q^{83} +(-1.23247 + 0.548729i) q^{84} +(6.28222 + 4.56430i) q^{85} +(-4.40932 - 1.96316i) q^{86} +(0.579367 + 1.00349i) q^{87} +(9.71876 - 16.8334i) q^{88} +(4.12530 - 2.99720i) q^{89} +(-4.68384 + 0.995581i) q^{90} +(-1.09605 - 3.37331i) q^{91} +2.91957 q^{92} +(-1.97191 - 5.20688i) q^{93} +9.61648 q^{94} +(0.775054 + 2.38537i) q^{95} +(-3.30348 + 0.702177i) q^{96} +(4.05910 - 2.94911i) q^{97} +(1.35161 - 2.34106i) q^{98} +(-3.15755 - 5.46903i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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