LMFDB - Embedded newform 322.2.i.e.85.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.3
Character	$\chi$	$=$	322.85
Dual form			322.2.i.e.197.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(2.09228 - 1.34463i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.762523 - 1.66969i) q^{5} +(0.353951 - 2.46178i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(1.32337 - 2.89778i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(2.09228 - 1.34463i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.762523 - 1.66969i) q^{5} +(0.353951 - 2.46178i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(1.32337 - 2.89778i) q^{9} +(-1.76122 - 0.517140i) q^{10} +(4.20713 + 4.85528i) q^{11} +(-1.62870 - 1.87962i) q^{12} +(-4.06149 - 1.19256i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(-3.84053 - 2.46816i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.235227 - 1.63604i) q^{17} +(-1.32337 - 2.89778i) q^{18} +(0.662572 + 4.60829i) q^{19} +(-1.54418 + 0.992384i) q^{20} +(-1.62870 + 1.87962i) q^{21} +6.42446 q^{22} +(2.63677 - 4.00593i) q^{23} -2.48710 q^{24} +(1.06787 - 1.23239i) q^{25} +(-3.56099 + 2.28851i) q^{26} +(-0.0657159 - 0.457064i) q^{27} +(0.415415 + 0.909632i) q^{28} +(-1.02042 + 7.09719i) q^{29} +(-4.38032 + 1.28618i) q^{30} +(0.894714 + 0.574998i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(15.3310 + 4.50160i) q^{33} +(-1.08240 - 1.24915i) q^{34} +(1.20204 + 1.38723i) q^{35} +(-3.05662 - 0.897505i) q^{36} +(-0.165185 + 0.361704i) q^{37} +(3.91661 + 2.51705i) q^{38} +(-10.1013 + 2.96602i) q^{39} +(-0.261229 + 1.81689i) q^{40} +(-2.68205 - 5.87287i) q^{41} +(0.353951 + 2.46178i) q^{42} +(6.34229 - 4.07594i) q^{43} +(4.20713 - 4.85528i) q^{44} -5.84751 q^{45} +(-1.30076 - 4.61606i) q^{46} -2.26932 q^{47} +(-1.62870 + 1.87962i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.232070 - 1.61408i) q^{50} +(-1.70770 - 3.73935i) q^{51} +(-0.602413 + 4.18987i) q^{52} +(-4.95145 + 1.45388i) q^{53} +(-0.388460 - 0.249648i) q^{54} +(4.89880 - 10.7269i) q^{55} +(0.959493 + 0.281733i) q^{56} +(7.58272 + 8.75093i) q^{57} +(4.69547 + 5.41886i) q^{58} +(-12.7975 - 3.75769i) q^{59} +(-1.89647 + 4.15269i) q^{60} +(12.0714 + 7.75779i) q^{61} +(1.02047 - 0.299636i) q^{62} +(-0.453367 + 3.15324i) q^{63} +(0.415415 + 0.909632i) q^{64} +(1.10577 + 7.69081i) q^{65} +(13.4418 - 8.63851i) q^{66} +(0.679222 - 0.783864i) q^{67} -1.65286 q^{68} +(0.130383 - 11.9270i) q^{69} +1.83557 q^{70} +(-8.01366 + 9.24826i) q^{71} +(-2.67995 + 1.72230i) q^{72} +(-0.415057 - 2.88678i) q^{73} +(0.165185 + 0.361704i) q^{74} +(0.577182 - 4.01439i) q^{75} +(4.46709 - 1.31166i) q^{76} +(-5.40460 - 3.47333i) q^{77} +(-4.37340 + 9.57641i) q^{78} +(-2.26835 - 0.666047i) q^{79} +(1.20204 + 1.38723i) q^{80} +(5.50642 + 6.35475i) q^{81} +(-6.19478 - 1.81895i) q^{82} +(-1.35321 + 2.96311i) q^{83} +(2.09228 + 1.34463i) q^{84} +(-2.91105 + 0.854761i) q^{85} +(1.07292 - 7.46236i) q^{86} +(7.40807 + 16.2214i) q^{87} +(-0.914296 - 6.35907i) q^{88} +(-8.37800 + 5.38421i) q^{89} +(-3.82930 + 4.41925i) q^{90} +4.23296 q^{91} +(-4.34040 - 2.03983i) q^{92} +2.64515 q^{93} +(-1.48609 + 1.71503i) q^{94} +(7.18921 - 4.62022i) q^{95} +(0.353951 + 2.46178i) q^{96} +(0.297701 + 0.651875i) q^{97} +(0.142315 - 0.989821i) q^{98} +(19.6372 - 5.76599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	$ 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} + 2 q^{12} + 4 q^{13} + 4 q^{14} - 11 q^{15} - 4 q^{16} - 21 q^{17} + 4 q^{19} + 2 q^{20} + 2 q^{21} - 11 q^{23} - 2 q^{24} + 5 q^{25} - 15 q^{26} + 95 q^{27} - 4 q^{28} + 22 q^{30} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 10 q^{34} - 9 q^{35} + 41 q^{37} + 7 q^{38} - 38 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} - 59 q^{43} - 6 q^{45} + 11 q^{46} - 60 q^{47} + 2 q^{48} - 4 q^{49} + 61 q^{50} - 87 q^{51} + 4 q^{52} + 47 q^{53} - 29 q^{54} - 30 q^{55} + 4 q^{56} + 20 q^{57} - 96 q^{59} - 11 q^{60} + 84 q^{61} - 65 q^{62} - 4 q^{64} + 52 q^{65} - 3 q^{66} + 11 q^{67} - 10 q^{68} - 42 q^{69} - 2 q^{70} - 13 q^{71} + 11 q^{72} - 48 q^{73} - 41 q^{74} + 23 q^{75} + 26 q^{76} - 83 q^{78} + 80 q^{79} - 9 q^{80} + 2 q^{81} + 30 q^{82} - 20 q^{83} + 2 q^{84} - 71 q^{85} - 40 q^{86} + 99 q^{87} - 30 q^{89} + 116 q^{90} + 26 q^{91} - 22 q^{92} + 20 q^{93} - 17 q^{94} - 4 q^{95} - 2 q^{96} - 56 q^{97} + 4 q^{98} + 138 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 + 2 * q^12 + 4 * q^13 + 4 * q^14 - 11 * q^15 - 4 * q^16 - 21 * q^17 + 4 * q^19 + 2 * q^20 + 2 * q^21 - 11 * q^23 - 2 * q^24 + 5 * q^25 - 15 * q^26 + 95 * q^27 - 4 * q^28 + 22 * q^30 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 10 * q^34 - 9 * q^35 + 41 * q^37 + 7 * q^38 - 38 * q^39 - 13 * q^40 + 25 * q^41 - 2 * q^42 - 59 * q^43 - 6 * q^45 + 11 * q^46 - 60 * q^47 + 2 * q^48 - 4 * q^49 + 61 * q^50 - 87 * q^51 + 4 * q^52 + 47 * q^53 - 29 * q^54 - 30 * q^55 + 4 * q^56 + 20 * q^57 - 96 * q^59 - 11 * q^60 + 84 * q^61 - 65 * q^62 - 4 * q^64 + 52 * q^65 - 3 * q^66 + 11 * q^67 - 10 * q^68 - 42 * q^69 - 2 * q^70 - 13 * q^71 + 11 * q^72 - 48 * q^73 - 41 * q^74 + 23 * q^75 + 26 * q^76 - 83 * q^78 + 80 * q^79 - 9 * q^80 + 2 * q^81 + 30 * q^82 - 20 * q^83 + 2 * q^84 - 71 * q^85 - 40 * q^86 + 99 * q^87 - 30 * q^89 + 116 * q^90 + 26 * q^91 - 22 * q^92 + 20 * q^93 - 17 * q^94 - 4 * q^95 - 2 * q^96 - 56 * q^97 + 4 * q^98 + 138 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$3$	2.09228	−	1.34463i	1.20798	−	0.776321i	0.227660	−	0.973741i	$-0.426893\pi$
$3$	2.09228	−	1.34463i	1.20798	−	0.776321i	0.980319	+	0.197420i	$0.0632562\pi$
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	−0.762523	−	1.66969i	−0.341011	−	0.746710i	0.658974	−	0.752165i	$-0.270991\pi$
$5$	−0.762523	−	1.66969i	−0.341011	−	0.746710i	−0.999985	+	0.00545589i	$0.998263\pi$
$6$	0.353951	−	2.46178i	0.144500	−	1.00502i
$7$	−0.959493	+	0.281733i	−0.362654	+	0.106485i
$7$	−0.959493	+	0.281733i	−0.362654	+	0.106485i
$8$	−0.841254	−	0.540641i	−0.297428	−	0.191145i
$9$	1.32337	−	2.89778i	0.441124	−	0.965927i
$10$	−1.76122	−	0.517140i	−0.556946	−	0.163534i
$11$	4.20713	+	4.85528i	1.26850	+	1.46392i	0.822369	+	0.568954i	$0.192652\pi$
$11$	4.20713	+	4.85528i	1.26850	+	1.46392i	0.446127	+	0.894969i	$0.352803\pi$
$12$	−1.62870	−	1.87962i	−0.470166	−	0.542601i
$13$	−4.06149	−	1.19256i	−1.12646	−	0.330757i	−0.335142	−	0.942168i	$-0.608784\pi$
$13$	−4.06149	−	1.19256i	−1.12646	−	0.330757i	−0.791314	+	0.611410i	$0.790603\pi$
$14$	−0.415415	+	0.909632i	−0.111024	+	0.243109i
$15$	−3.84053	−	2.46816i	−0.991620	−	0.637276i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.235227	−	1.63604i	0.0570509	−	0.396798i	−0.941209	−	0.337826i	$-0.890309\pi$
$17$	0.235227	−	1.63604i	0.0570509	−	0.396798i	0.998260	−	0.0589722i	$-0.0187823\pi$
$18$	−1.32337	−	2.89778i	−0.311922	−	0.683014i
$19$	0.662572	+	4.60829i	0.152005	+	1.05721i	0.912854	+	0.408286i	$0.133873\pi$
$19$	0.662572	+	4.60829i	0.152005	+	1.05721i	−0.760849	+	0.648929i	$0.775217\pi$
$20$	−1.54418	+	0.992384i	−0.345289	+	0.221904i
$21$	−1.62870	+	1.87962i	−0.355412	+	0.410168i
$22$	6.42446			1.36970
$23$	2.63677	−	4.00593i	0.549804	−	0.835293i
$23$	2.63677	−	4.00593i	0.549804	−	0.835293i
$24$	−2.48710			−0.507677
$25$	1.06787	−	1.23239i	0.213574	−	0.246477i
$26$	−3.56099	+	2.28851i	−0.698368	+	0.448814i
$27$	−0.0657159	−	0.457064i	−0.0126470	−	0.0879620i
$28$	0.415415	+	0.909632i	0.0785061	+	0.171904i
$29$	−1.02042	+	7.09719i	−0.189488	+	1.31792i	0.643850	+	0.765152i	$0.277336\pi$
$29$	−1.02042	+	7.09719i	−0.189488	+	1.31792i	−0.833338	+	0.552764i	$0.813573\pi$
$30$	−4.38032	+	1.28618i	−0.799734	+	0.234823i
$31$	0.894714	+	0.574998i	0.160695	+	0.103273i	0.618517	−	0.785771i	$-0.287734\pi$
$31$	0.894714	+	0.574998i	0.160695	+	0.103273i	−0.457822	+	0.889044i	$0.651370\pi$
$32$	−0.415415	+	0.909632i	−0.0734357	+	0.160802i
$33$	15.3310	+	4.50160i	2.66879	+	0.783628i
$34$	−1.08240	−	1.24915i	−0.185629	−	0.214228i
$35$	1.20204	+	1.38723i	0.203182	+	0.234485i
$36$	−3.05662	−	0.897505i	−0.509437	−	0.149584i
$37$	−0.165185	+	0.361704i	−0.0271562	+	0.0594637i	−0.922724	−	0.385461i	$-0.874042\pi$
$37$	−0.165185	+	0.361704i	−0.0271562	+	0.0594637i	0.895568	+	0.444925i	$0.146770\pi$
$38$	3.91661	+	2.51705i	0.635358	+	0.408320i
$39$	−10.1013	+	2.96602i	−1.61751	+	0.474944i
$40$	−0.261229	+	1.81689i	−0.0413039	+	0.287275i
$41$	−2.68205	−	5.87287i	−0.418866	−	0.917188i	−0.995004	−	0.0998355i	$-0.968168\pi$
$41$	−2.68205	−	5.87287i	−0.418866	−	0.917188i	0.576138	−	0.817352i	$-0.304559\pi$
$42$	0.353951	+	2.46178i	0.0546158	+	0.379862i
$43$	6.34229	−	4.07594i	0.967190	−	0.621575i	0.0412110	−	0.999150i	$-0.486878\pi$
$43$	6.34229	−	4.07594i	0.967190	−	0.621575i	0.925979	+	0.377575i	$0.123242\pi$
$44$	4.20713	−	4.85528i	0.634248	−	0.731962i
$45$	−5.84751			−0.871695
$46$	−1.30076	−	4.61606i	−0.191787	−	0.680601i
$47$	−2.26932			−0.331014			−0.165507	−	0.986209i	$-0.552926\pi$
$47$	−2.26932			−0.331014			−0.165507	+	0.986209i	$0.552926\pi$
$48$	−1.62870	+	1.87962i	−0.235083	+	0.271300i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	−0.232070	−	1.61408i	−0.0328197	−	0.228266i
$51$	−1.70770	−	3.73935i	−0.239126	−	0.523613i
$52$	−0.602413	+	4.18987i	−0.0835396	+	0.581031i
$53$	−4.95145	+	1.45388i	−0.680134	+	0.199705i	−0.603511	−	0.797355i	$-0.706232\pi$
$53$	−4.95145	+	1.45388i	−0.680134	+	0.199705i	−0.0766231	+	0.997060i	$0.524414\pi$
$54$	−0.388460	−	0.249648i	−0.0528628	−	0.0339728i
$55$	4.89880	−	10.7269i	0.660554	−	1.44641i
$56$	0.959493	+	0.281733i	0.128218	+	0.0376481i
$57$	7.58272	+	8.75093i	1.00436	+	1.15909i
$58$	4.69547	+	5.41886i	0.616545	+	0.711531i
$59$	−12.7975	−	3.75769i	−1.66610	−	0.489210i	−0.693257	−	0.720691i	$-0.743825\pi$
$59$	−12.7975	−	3.75769i	−1.66610	−	0.489210i	−0.972839	+	0.231481i	$0.925643\pi$
$60$	−1.89647	+	4.15269i	−0.244833	+	0.536110i
$61$	12.0714	+	7.75779i	1.54558	+	0.993284i	0.986424	+	0.164221i	$0.0525110\pi$
$61$	12.0714	+	7.75779i	1.54558	+	0.993284i	0.559156	+	0.829063i	$0.311125\pi$
$62$	1.02047	−	0.299636i	0.129600	−	0.0380539i
$63$	−0.453367	+	3.15324i	−0.0571189	+	0.397271i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	1.10577	+	7.69081i	0.137154	+	0.953927i
$66$	13.4418	−	8.63851i	1.65457	−	1.06333i
$67$	0.679222	−	0.783864i	0.0829802	−	0.0957642i	−0.712741	−	0.701427i	$-0.752547\pi$
$67$	0.679222	−	0.783864i	0.0829802	−	0.0957642i	0.795721	+	0.605663i	$0.207092\pi$
$68$	−1.65286			−0.200439
$69$	0.130383	−	11.9270i	0.0156962	−	1.43584i
$70$	1.83557			0.219393
$71$	−8.01366	+	9.24826i	−0.951047	+	1.09757i	0.0440861	+	0.999028i	$0.485962\pi$
$71$	−8.01366	+	9.24826i	−0.951047	+	1.09757i	−0.995133	+	0.0985391i	$0.968583\pi$
$72$	−2.67995	+	1.72230i	−0.315835	+	0.202975i
$73$	−0.415057	−	2.88678i	−0.0485787	−	0.337872i	−0.999588	−	0.0287095i	$-0.990860\pi$
$73$	−0.415057	−	2.88678i	−0.0485787	−	0.337872i	0.951009	−	0.309163i	$-0.100049\pi$
$74$	0.165185	+	0.361704i	0.0192023	+	0.0420472i
$75$	0.577182	−	4.01439i	0.0666472	−	0.463542i
$76$	4.46709	−	1.31166i	0.512411	−	0.150457i
$77$	−5.40460	−	3.47333i	−0.615912	−	0.395822i
$78$	−4.37340	+	9.57641i	−0.495190	+	1.08432i
$79$	−2.26835	−	0.666047i	−0.255209	−	0.0749361i	0.151626	−	0.988438i	$-0.451549\pi$
$79$	−2.26835	−	0.666047i	−0.255209	−	0.0749361i	−0.406834	+	0.913502i	$0.633367\pi$
$80$	1.20204	+	1.38723i	0.134392	+	0.155097i
$81$	5.50642	+	6.35475i	0.611825	+	0.706083i
$82$	−6.19478	−	1.81895i	−0.684099	−	0.200870i
$83$	−1.35321	+	2.96311i	−0.148534	+	0.325243i	−0.969244	−	0.246101i	$-0.920851\pi$
$83$	−1.35321	+	2.96311i	−0.148534	+	0.325243i	0.820711	+	0.571344i	$0.193578\pi$
$84$	2.09228	+	1.34463i	0.228287	+	0.146711i
$85$	−2.91105	+	0.854761i	−0.315748	+	0.0927119i
$86$	1.07292	−	7.46236i	0.115696	−	0.804686i
$87$	7.40807	+	16.2214i	0.794228	+	1.73912i
$88$	−0.914296	−	6.35907i	−0.0974643	−	0.677879i
$89$	−8.37800	+	5.38421i	−0.888066	+	0.570725i	−0.903229	−	0.429160i	$-0.858810\pi$
$89$	−8.37800	+	5.38421i	−0.888066	+	0.570725i	0.0151628	+	0.999885i	$0.495173\pi$
$90$	−3.82930	+	4.41925i	−0.403644	+	0.465830i
$91$	4.23296			0.443735
$92$	−4.34040	−	2.03983i	−0.452518	−	0.212667i
$93$	2.64515			0.274289
$94$	−1.48609	+	1.71503i	−0.153278	+	0.176892i
$95$	7.18921	−	4.62022i	0.737597	−	0.474025i
$96$	0.353951	+	2.46178i	0.0361250	+	0.251255i
$97$	0.297701	+	0.651875i	0.0302270	+	0.0661879i	0.924143	−	0.382046i	$-0.124780\pi$
$97$	0.297701	+	0.651875i	0.0302270	+	0.0661879i	−0.893916	+	0.448234i	$0.852053\pi$
$98$	0.142315	−	0.989821i	0.0143760	−	0.0999871i
$99$	19.6372	−	5.76599i	1.97361	−	0.579504i
$100$	−1.37182	−	0.881613i	−0.137182	−	0.0881613i
$101$	2.39342	−	5.24087i	0.238155	−	0.521486i	−0.752383	−	0.658726i	$-0.771096\pi$
$101$	2.39342	−	5.24087i	0.238155	−	0.521486i	0.990538	+	0.137240i	$0.0438231\pi$
$102$	−3.94432	−	1.15816i	−0.390546	−	0.114675i
$103$	−7.36911	−	8.50441i	−0.726100	−	0.837965i	0.265926	−	0.963993i	$-0.414322\pi$
$103$	−7.36911	−	8.50441i	−0.726100	−	0.837965i	−0.992027	+	0.126029i	$0.959777\pi$
$104$	2.77200	+	3.19906i	0.271817	+	0.313693i
$105$	4.38032	+	1.28618i	0.427476	+	0.125518i
$106$	−2.14374	+	4.69414i	−0.208219	+	0.455936i
$107$	14.3138	+	9.19891i	1.38377	+	0.889292i	0.999425	−	0.0338989i	$-0.0107924\pi$
$107$	14.3138	+	9.19891i	1.38377	+	0.889292i	0.384341	+	0.923191i	$0.374429\pi$
$108$	−0.443059	+	0.130094i	−0.0426334	+	0.0125183i
$109$	0.110494	−	0.768501i	0.0105834	−	0.0736090i	−0.983845	−	0.179021i	$-0.942707\pi$
$109$	0.110494	−	0.768501i	0.0105834	−	0.0736090i	0.994429	+	0.105412i	$0.0336161\pi$
$110$	−4.89880	−	10.7269i	−0.467083	−	1.02277i
$111$	0.140744	+	0.978898i	0.0133589	+	0.0929129i
$112$	0.841254	−	0.540641i	0.0794910	−	0.0510858i
$113$	−13.0397	+	15.0487i	−1.22668	+	1.41566i	−0.348509	+	0.937306i	$0.613312\pi$
$113$	−13.0397	+	15.0487i	−1.22668	+	1.41566i	−0.878167	+	0.478354i	$0.841234\pi$
$114$	11.5791			1.08449
$115$	−8.69927	−	1.34798i	−0.811211	−	0.125700i
$116$	7.17017			0.665734
$117$	−8.83066	+	10.1911i	−0.816394	+	0.942169i
$118$	−11.2205	+	7.21096i	−1.03293	+	0.663823i
$119$	0.235227	+	1.63604i	0.0215632	+	0.149975i
$120$	1.89647	+	4.15269i	0.173123	+	0.379087i
$121$	−4.30840	+	29.9656i	−0.391673	+	2.72414i
$122$	13.7680	−	4.04265i	1.24650	−	0.366005i
$123$	−13.5084	−	8.68133i	−1.21801	−	0.782769i
$124$	0.441814	−	0.967438i	0.0396761	−	0.0868785i
$125$	−11.6781	−	3.42899i	−1.04452	−	0.306698i
$126$	2.08617	+	2.40756i	0.185850	+	0.214483i
$127$	−7.44956	−	8.59725i	−0.661041	−	0.762882i	0.321906	−	0.946772i	$-0.395677\pi$
$127$	−7.44956	−	8.59725i	−0.661041	−	0.762882i	−0.982947	+	0.183889i	$0.941131\pi$
$128$	0.959493	+	0.281733i	0.0848080	+	0.0249019i
$129$	7.78923	−	17.0560i	0.685803	−	1.50170i
$130$	6.53645	+	4.20072i	0.573285	+	0.368428i
$131$	13.0405	−	3.82903i	1.13935	−	0.334544i	0.342974	−	0.939345i	$-0.388566\pi$
$131$	13.0405	−	3.82903i	1.13935	−	0.334544i	0.796377	+	0.604801i	$0.206747\pi$
$132$	2.27395	−	15.8156i	0.197922	−	1.37657i
$133$	−1.93404	−	4.23496i	−0.167703	−	0.367217i
$134$	−0.147609	−	1.02664i	−0.0127515	−	0.0886885i
$135$	−0.713047	+	0.458247i	−0.0613693	+	0.0394396i
$136$	−1.08240	+	1.24915i	−0.0928146	+	0.107114i
$137$	−7.09880			−0.606491			−0.303246	−	0.952912i	$-0.598070\pi$
$137$	−7.09880			−0.606491			−0.303246	+	0.952912i	$0.598070\pi$
$138$	−8.92844	−	7.90906i	−0.760039	−	0.673264i
$139$	−9.40131			−0.797409			−0.398704	−	0.917080i	$-0.630540\pi$
$139$	−9.40131			−0.797409			−0.398704	+	0.917080i	$0.630540\pi$
$140$	1.20204	−	1.38723i	0.101591	−	0.117242i
$141$	−4.74805	+	3.05138i	−0.399858	+	0.256973i
$142$	1.74154	+	12.1126i	0.146146	+	1.01647i
$143$	−11.2970	−	24.7370i	−0.944702	−	2.06861i
$144$	−0.453367	+	3.15324i	−0.0377806	+	0.262770i
$145$	12.6282	−	3.70798i	1.04872	−	0.307931i
$146$	−2.45349	−	1.57676i	−0.203052	−	0.130494i
$147$	1.03318	−	2.26235i	0.0852151	−	0.186595i
$148$	0.381530	+	0.112027i	0.0313616	+	0.00920860i
$149$	−3.98914	−	4.60372i	−0.326803	−	0.377151i	0.568443	−	0.822723i	$-0.307546\pi$
$149$	−3.98914	−	4.60372i	−0.326803	−	0.377151i	−0.895246	+	0.445571i	$0.853001\pi$
$150$	−2.65590	−	3.06507i	−0.216853	−	0.250262i
$151$	4.50311	+	1.32223i	0.366458	+	0.107602i	0.459777	−	0.888034i	$-0.347929\pi$
$151$	4.50311	+	1.32223i	0.366458	+	0.107602i	−0.0933187	+	0.995636i	$0.529748\pi$
$152$	1.93404	−	4.23496i	0.156871	−	0.343500i
$153$	−4.42959	−	2.84673i	−0.358111	−	0.230144i
$154$	−6.16423	+	1.80998i	−0.496728	+	0.145852i
$155$	0.277830	−	1.93235i	0.0223158	−	0.155210i
$156$	4.37340	+	9.57641i	0.350152	+	0.766727i
$157$	−3.13085	−	21.7756i	−0.249869	−	1.73788i	−0.598951	−	0.800786i	$-0.704415\pi$
$157$	−3.13085	−	21.7756i	−0.249869	−	1.73788i	0.349082	−	0.937092i	$-0.386494\pi$
$158$	−1.98882	+	1.27813i	−0.158222	+	0.101683i
$159$	−8.40490	+	9.69978i	−0.666552	+	0.769242i
$160$	1.83557			0.145115
$161$	−1.40136	+	4.58652i	−0.110443	+	0.361469i
$162$	8.40854			0.660637
$163$	9.95256	−	11.4859i	0.779545	−	0.899642i	−0.217532	−	0.976053i	$-0.569801\pi$
$163$	9.95256	−	11.4859i	0.779545	−	0.899642i	0.997076	+	0.0764109i	$0.0243461\pi$
$164$	−5.43139	+	3.49054i	−0.424121	+	0.272566i
$165$	−4.17399	−	29.0307i	−0.324944	−	2.26004i
$166$	1.35321	+	2.96311i	0.105029	+	0.229982i
$167$	2.43169	−	16.9128i	0.188170	−	1.30875i	−0.648573	−	0.761152i	$-0.724634\pi$
$167$	2.43169	−	16.9128i	0.188170	−	1.30875i	0.836743	−	0.547596i	$-0.184457\pi$
$168$	2.38635	−	0.700697i	0.184111	−	0.0540599i
$169$	4.13724	+	2.65884i	0.318249	+	0.204526i
$170$	−1.26035	+	2.75977i	−0.0966642	+	0.211665i
$171$	14.2307	+	4.17850i	1.08825	+	0.319538i
$172$	−4.93706	−	5.69767i	−0.376447	−	0.434443i
$173$	5.02204	+	5.79574i	0.381818	+	0.440642i	0.913831	−	0.406095i	$-0.133110\pi$
$173$	5.02204	+	5.79574i	0.381818	+	0.440642i	−0.532013	+	0.846736i	$0.678564\pi$
$174$	17.1106	+	5.02412i	1.29715	+	0.380877i
$175$	−0.677410	+	1.48332i	−0.0512074	+	0.112128i
$176$	−5.40460	−	3.47333i	−0.407387	−	0.261812i
$177$	−31.8287	+	9.34576i	−2.39239	+	0.702470i
$178$	−1.41731	+	9.85758i	−0.106232	+	0.738857i
$179$	−6.45288	−	14.1298i	−0.482311	−	1.05611i	−0.981822	−	0.189806i	$-0.939214\pi$
$179$	−6.45288	−	14.1298i	−0.482311	−	1.05611i	0.499511	−	0.866308i	$-0.333513\pi$
$180$	0.832187	+	5.78799i	0.0620276	+	0.431411i
$181$	5.95238	−	3.82536i	0.442437	−	0.284337i	−0.300395	−	0.953815i	$-0.597119\pi$
$181$	5.95238	−	3.82536i	0.442437	−	0.284337i	0.742832	+	0.669478i	$0.233482\pi$
$182$	2.77200	−	3.19906i	0.205474	−	0.237130i
$183$	35.6880			2.63813
$184$	−4.38396	+	1.94446i	−0.323190	+	0.143347i
$185$	0.729892			0.0536627
$186$	1.73221	−	1.99907i	0.127012	−	0.146579i
$187$	8.93307	−	5.74093i	0.653250	−	0.419819i
$188$	0.322957	+	2.24622i	0.0235541	+	0.163822i
$189$	0.191824	+	0.420035i	0.0139531	+	0.0305531i
$190$	1.21620	−	8.45884i	0.0882323	−	0.613669i
$191$	−11.6402	+	3.41788i	−0.842258	+	0.247309i	−0.674275	−	0.738480i	$-0.735544\pi$
$191$	−11.6402	+	3.41788i	−0.842258	+	0.247309i	−0.167984	+	0.985790i	$0.553726\pi$
$192$	2.09228	+	1.34463i	0.150997	+	0.0970401i
$193$	−0.326594	+	0.715142i	−0.0235088	+	0.0514771i	−0.921022	−	0.389510i	$-0.872644\pi$
$193$	−0.326594	+	0.715142i	−0.0235088	+	0.0514771i	0.897513	+	0.440987i	$0.145372\pi$
$194$	0.687607	+	0.201900i	0.0493673	+	0.0144956i
$195$	12.6549	+	14.6045i	0.906233	+	1.04585i
$196$	−0.654861	−	0.755750i	−0.0467758	−	0.0539821i
$197$	−3.51664	−	1.03258i	−0.250550	−	0.0735681i	0.154046	−	0.988064i	$-0.450770\pi$
$197$	−3.51664	−	1.03258i	−0.250550	−	0.0735681i	−0.404596	+	0.914496i	$0.632588\pi$
$198$	8.50196	−	18.6167i	0.604208	−	1.32303i
$199$	3.47802	+	2.23519i	0.246550	+	0.158448i	0.658080	−	0.752948i	$-0.271369\pi$
$199$	3.47802	+	2.23519i	0.246550	+	0.158448i	−0.411529	+	0.911396i	$0.635005\pi$
$200$	−1.56463	+	0.459416i	−0.110636	+	0.0324856i
$201$	0.367118	−	2.55336i	0.0258945	−	0.180100i
$202$	−2.39342	−	5.24087i	−0.168401	−	0.368746i
$203$	−1.02042	−	7.09719i	−0.0716196	−	0.498125i
$204$	−3.45825	+	2.22249i	−0.242126	+	0.155605i
$205$	−7.76076	+	8.95640i	−0.542035	+	0.625542i
$206$	−11.2529			−0.784030
$207$	−8.11887	−	12.9421i	−0.564301	−	0.899539i
$208$	4.23296			0.293503
$209$	−19.5870	+	22.6047i	−1.35486	+	1.56360i
$210$	3.84053	−	2.46816i	0.265022	−	0.170319i
$211$	−3.13892	−	21.8317i	−0.216092	−	1.50296i	−0.752273	−	0.658852i	$-0.771042\pi$
$211$	−3.13892	−	21.8317i	−0.216092	−	1.50296i	0.536180	−	0.844104i	$-0.319867\pi$
$212$	2.14374	+	4.69414i	0.147233	+	0.322395i
$213$	−4.33137	+	30.1254i	−0.296781	+	2.06416i
$214$	16.3256	−	4.79363i	1.11600	−	0.327686i
$215$	−11.6417	−	7.48168i	−0.793958	−	0.510246i
$216$	−0.191824	+	0.420035i	−0.0130519	+	0.0285798i
$217$	−1.02047	−	0.299636i	−0.0692739	−	0.0203406i
$218$	−0.508436	−	0.586767i	−0.0344356	−	0.0397408i
$219$	−4.75006	−	5.48187i	−0.320980	−	0.370430i
$220$	−11.3149	−	3.32235i	−0.762848	−	0.223993i
$221$	−2.90645	+	6.36424i	−0.195509	+	0.428105i
$222$	0.831969	+	0.534674i	0.0558381	+	0.0358850i
$223$	−4.31421	+	1.26677i	−0.288901	+	0.0848289i	−0.422972	−	0.906143i	$-0.639013\pi$
$223$	−4.31421	+	1.26677i	−0.288901	+	0.0848289i	0.134071	+	0.990972i	$0.457195\pi$
$224$	0.142315	−	0.989821i	0.00950881	−	0.0661352i
$225$	−2.15800	−	4.72536i	−0.143867	−	0.315024i
$226$	2.83381	+	19.7096i	0.188502	+	1.31106i
$227$	−13.8513	+	8.90168i	−0.919342	+	0.590825i	−0.912467	−	0.409151i	$-0.865825\pi$
$227$	−13.8513	+	8.90168i	−0.919342	+	0.590825i	−0.00687560	+	0.999976i	$0.502189\pi$
$228$	7.58272	−	8.75093i	0.502178	−	0.579545i
$229$	8.76301			0.579076			0.289538	−	0.957167i	$-0.406498\pi$
$229$	8.76301			0.579076			0.289538	+	0.957167i	$0.406498\pi$
$230$	−6.71555	+	5.69173i	−0.442810	+	0.375301i
$231$	−15.9783			−1.05129
$232$	4.69547	−	5.41886i	0.308272	−	0.355765i
$233$	−13.5110	+	8.68301i	−0.885137	+	0.568843i	−0.902348	−	0.431009i	$-0.858158\pi$
$233$	−13.5110	+	8.68301i	−0.885137	+	0.568843i	0.0172109	+	0.999852i	$0.494521\pi$
$234$	1.91908	+	13.3475i	0.125455	+	0.872555i
$235$	1.73041	+	3.78906i	0.112879	+	0.247171i
$236$	−1.89817	+	13.2020i	−0.123560	+	0.859380i
$237$	−5.64160	+	1.65652i	−0.366461	+	0.107603i
$238$	1.39048	+	0.893605i	0.0901312	+	0.0579238i
$239$	2.24599	−	4.91803i	0.145281	−	0.318121i	−0.822977	−	0.568075i	$-0.807688\pi$
$239$	2.24599	−	4.91803i	0.145281	−	0.318121i	0.968258	+	0.249954i	$0.0804156\pi$
$240$	4.38032	+	1.28618i	0.282749	+	0.0830225i
$241$	7.37084	+	8.50640i	0.474797	+	0.547945i	0.941740	−	0.336342i	$-0.109190\pi$
$241$	7.37084	+	8.50640i	0.474797	+	0.547945i	−0.466942	+	0.884288i	$0.654644\pi$
$242$	19.8251	+	22.8793i	1.27440	+	1.47074i
$243$	21.3949	+	6.28212i	1.37249	+	0.402998i
$244$	5.96090	−	13.0525i	0.381607	−	0.835603i
$245$	−1.54418	−	0.992384i	−0.0986540	−	0.0634011i
$246$	−15.4070	+	4.52392i	−0.982317	+	0.288434i
$247$	2.80464	−	19.5067i	0.178455	−	1.24118i
$248$	−0.441814	−	0.967438i	−0.0280552	−	0.0614324i
$249$	1.15299	+	8.01921i	0.0730677	+	0.508197i
$250$	−10.2390	+	6.58018i	−0.647569	+	0.416167i
$251$	12.5139	−	14.4418i	0.789868	−	0.911556i	−0.207912	−	0.978147i	$-0.566667\pi$
$251$	12.5139	−	14.4418i	0.789868	−	0.911556i	0.997780	+	0.0665912i	$0.0212123\pi$
$252$	3.18566			0.200678
$253$	30.5431	−	4.05118i	1.92023	−	0.254696i
$254$	−11.3758			−0.713780
$255$	−4.94140	+	5.70268i	−0.309442	+	0.357116i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−3.87902	−	26.9792i	−0.241966	−	1.68291i	−0.642229	−	0.766513i	$-0.721990\pi$
$257$	−3.87902	−	26.9792i	−0.241966	−	1.68291i	0.400262	−	0.916401i	$-0.368919\pi$
$258$	−7.78923	−	17.0560i	−0.484936	−	1.06186i
$259$	0.0565897	−	0.393590i	0.00351631	−	0.0244565i
$260$	7.45516	−	2.18903i	0.462349	−	0.135758i
$261$	19.2157	+	12.3492i	1.18942	+	0.764396i
$262$	5.64590	−	12.3628i	0.348805	−	0.763777i
$263$	22.8171	+	6.69969i	1.40696	+	0.413121i	0.895068	−	0.445929i	$-0.147127\pi$
$263$	22.8171	+	6.69969i	1.40696	+	0.413121i	0.511892	+	0.859050i	$0.328945\pi$
$264$	−10.4635	−	12.0756i	−0.643987	−	0.743200i
$265$	6.20313	+	7.15879i	0.381055	+	0.439761i
$266$	−4.46709	−	1.31166i	−0.273895	−	0.0804228i
$267$	−10.2894	+	22.5306i	−0.629699	+	1.37885i
$268$	−0.872549	−	0.560753i	−0.0532994	−	0.0342534i
$269$	1.81991	−	0.534375i	0.110962	−	0.0325814i	−0.225780	−	0.974178i	$-0.572493\pi$
$269$	1.81991	−	0.534375i	0.110962	−	0.0325814i	0.336742	+	0.941597i	$0.390675\pi$
$270$	−0.120626	+	0.838973i	−0.00734107	+	0.0510583i
$271$	12.5135	+	27.4007i	0.760141	+	1.66448i	0.747235	+	0.664559i	$0.231381\pi$
$271$	12.5135	+	27.4007i	0.760141	+	1.66448i	0.0129053	+	0.999917i	$0.495892\pi$
$272$	0.235227	+	1.63604i	0.0142627	+	0.0991995i
$273$	8.85654	−	5.69175i	0.536022	−	0.344481i
$274$	−4.64873	+	5.36492i	−0.280840	+	0.324106i
$275$	10.4763			0.631742
$276$	−11.8242	+	1.56833i	−0.711730	+	0.0944026i
$277$	11.1020			0.667057			0.333529	−	0.942740i	$-0.391761\pi$
$277$	11.1020			0.667057			0.333529	+	0.942740i	$0.391761\pi$
$278$	−6.15655	+	7.10504i	−0.369245	+	0.426132i
$279$	2.85026	−	1.83175i	0.170641	−	0.109664i
$280$	−0.261229	−	1.81689i	−0.0156114	−	0.108580i
$281$	−8.43134	−	18.4621i	−0.502972	−	1.10135i	−0.975492	−	0.220035i	$-0.929383\pi$
$281$	−8.43134	−	18.4621i	−0.502972	−	1.10135i	0.472520	−	0.881320i	$-0.343344\pi$
$282$	−0.803227	+	5.58656i	−0.0478315	+	0.332675i
$283$	−8.13842	+	2.38965i	−0.483779	+	0.142050i	−0.514522	−	0.857477i	$-0.672031\pi$
$283$	−8.13842	+	2.38965i	−0.483779	+	0.142050i	0.0307435	+	0.999527i	$0.490212\pi$
$284$	10.2946	+	6.61593i	0.610872	+	0.392583i
$285$	8.82937	−	19.3336i	0.523007	−	1.14522i
$286$	−26.0929	−	7.66157i	−1.54291	−	0.453038i
$287$	4.22798	+	4.87935i	0.249570	+	0.288019i
$288$	2.08617	+	2.40756i	0.122929	+	0.141867i
$289$	13.6901	+	4.01977i	0.805299	+	0.236457i
$290$	5.46743	−	11.9720i	0.321058	−	0.703020i
$291$	1.49940	+	0.963609i	0.0878966	+	0.0564877i
$292$	−2.79833	+	0.821664i	−0.163760	+	0.0480843i
$293$	−3.27748	+	22.7954i	−0.191473	+	1.33172i	0.636641	+	0.771161i	$0.280324\pi$
$293$	−3.27748	+	22.7954i	−0.191473	+	1.33172i	−0.828113	+	0.560561i	$0.810586\pi$
$294$	−1.03318	−	2.26235i	−0.0602562	−	0.131943i
$295$	3.48422	+	24.2333i	0.202859	+	1.41092i
$296$	0.334514	−	0.214979i	0.0194432	−	0.0124954i
$297$	1.94270	−	2.24200i	0.112727	−	0.130094i
$298$	−6.09159			−0.352876
$299$	−15.4865	+	13.1255i	−0.895610	+	0.759069i
$300$	−4.05567			−0.234154
$301$	−4.93706	+	5.69767i	−0.284567	+	0.328408i
$302$	3.94819	−	2.53735i	0.227193	−	0.146008i
$303$	−2.03930	−	14.1836i	−0.117155	−	0.814828i
$304$	−1.93404	−	4.23496i	−0.110925	−	0.242891i
$305$	3.74844	−	26.0710i	0.214635	−	1.49282i
$306$	−5.05218	+	1.48345i	−0.288814	+	0.0848034i
$307$	0.249588	+	0.160401i	0.0142447	+	0.00915454i	0.547744	−	0.836646i	$-0.315487\pi$
$307$	0.249588	+	0.160401i	0.0142447	+	0.00915454i	−0.533499	+	0.845801i	$0.679123\pi$
$308$	−2.66882	+	5.84390i	−0.152070	+	0.332987i
$309$	−26.8535	−	7.88491i	−1.52764	−	0.448557i
$310$	−1.27843	−	1.47539i	−0.0726100	−	0.0837964i
$311$	8.05702	+	9.29830i	0.456872	+	0.527258i	0.936713	−	0.350097i	$-0.113851\pi$
$311$	8.05702	+	9.29830i	0.456872	+	0.527258i	−0.479842	+	0.877355i	$0.659306\pi$
$312$	10.1013	+	2.96602i	0.571876	+	0.167918i
$313$	−2.39530	+	5.24497i	−0.135390	+	0.296463i	−0.965168	−	0.261631i	$-0.915740\pi$
$313$	−2.39530	+	5.24497i	−0.135390	+	0.296463i	0.829778	+	0.558094i	$0.188467\pi$
$314$	−18.5071	−	11.8938i	−1.04442	−	0.671207i
$315$	5.61064	−	1.64743i	0.316124	−	0.0928224i
$316$	−0.336448	+	2.34005i	−0.0189267	+	0.131638i
$317$	−1.50679	−	3.29941i	−0.0846299	−	0.185314i	0.862586	−	0.505911i	$-0.168844\pi$
$317$	−1.50679	−	3.29941i	−0.0846299	−	0.185314i	−0.947216	+	0.320597i	$0.896116\pi$
$318$	1.82656	+	12.7040i	0.102428	+	0.712405i
$319$	−38.7519	+	24.9044i	−2.16969	+	1.39438i
$320$	1.20204	−	1.38723i	0.0671962	−	0.0775486i
$321$	42.3176			2.36194
$322$	2.54857	+	4.06261i	0.142026	+	0.226400i
$323$	7.69520			0.428173
$324$	5.50642	−	6.35475i	0.305912	−	0.353042i
$325$	−5.80685	+	3.73183i	−0.322106	+	0.207005i
$326$	−2.16290	−	15.0433i	−0.119792	−	0.833170i
$327$	−0.802163	−	1.75649i	−0.0443597	−	0.0971343i
$328$	−0.918829	+	6.39059i	−0.0507338	+	0.352862i
$329$	2.17739	−	0.639340i	0.120044	−	0.0352480i
$330$	−24.6733	−	15.8566i	−1.35822	−	0.872876i
$331$	7.44598	−	16.3044i	0.409268	−	0.896172i	−0.586978	−	0.809603i	$-0.699682\pi$
$331$	7.44598	−	16.3044i	0.409268	−	0.896172i	0.996246	−	0.0865692i	$-0.0275904\pi$
$332$	3.12553	+	0.917738i	0.171536	+	0.0503674i
$333$	0.829538	+	0.957338i	0.0454584	+	0.0524618i
$334$	−11.1894	−	12.9132i	−0.612256	−	0.706581i
$335$	−1.82674	−	0.536378i	−0.0998052	−	0.0293055i
$336$	1.03318	−	2.26235i	0.0563645	−	0.123421i
$337$	23.3398	+	14.9996i	1.27140	+	0.817079i	0.989801	−	0.142454i	$-0.0454992\pi$
$337$	23.3398	+	14.9996i	1.27140	+	0.817079i	0.281598	+	0.959533i	$0.409136\pi$
$338$	4.71873	−	1.38554i	0.256665	−	0.0753637i
$339$	−7.04796	+	49.0196i	−0.382793	+	2.66238i
$340$	1.26035	+	2.75977i	0.0683519	+	0.149670i
$341$	0.972399	+	6.76318i	0.0526584	+	0.366247i
$342$	12.4770	−	8.01848i	0.674679	−	0.433590i
$343$	−0.654861	+	0.755750i	−0.0353592	+	0.0408066i
$344$	−7.53909			−0.406481
$345$	−20.0138	+	8.87692i	−1.07751	+	0.477917i
$346$	7.66886			0.412280
$347$	−10.7293	+	12.3823i	−0.575979	+	0.664716i	−0.966735	−	0.255779i	$-0.917668\pi$
$347$	−10.7293	+	12.3823i	−0.575979	+	0.664716i	0.390756	+	0.920494i	$0.372214\pi$
$348$	15.0020	−	9.64121i	0.804193	−	0.516823i
$349$	−1.37998	−	9.59796i	−0.0738685	−	0.513767i	−0.992841	−	0.119445i	$-0.961889\pi$
$349$	−1.37998	−	9.59796i	−0.0738685	−	0.513767i	0.918972	−	0.394322i	$-0.129021\pi$
$350$	0.677410	+	1.48332i	0.0362091	+	0.0792868i
$351$	−0.278173	+	1.93473i	−0.0148478	+	0.103268i
$352$	−6.16423	+	1.80998i	−0.328554	+	0.0964723i
$353$	11.1640	+	7.17468i	0.594200	+	0.381869i	0.802903	−	0.596110i	$-0.203288\pi$
$353$	11.1640	+	7.17468i	0.594200	+	0.381869i	−0.208703	+	0.977979i	$0.566924\pi$
$354$	−13.7803	+	30.1747i	−0.732416	+	1.60377i
$355$	21.5524	+	6.32835i	1.14388	+	0.335874i
$356$	6.52172	+	7.52647i	0.345651	+	0.398902i
$357$	2.69202	+	3.10676i	0.142477	+	0.164427i
$358$	−14.9044	−	4.37631i	−0.787719	−	0.231295i
$359$	1.95671	−	4.28461i	0.103271	−	0.226133i	−0.850942	−	0.525260i	$-0.823968\pi$
$359$	1.95671	−	4.28461i	0.103271	−	0.226133i	0.954213	+	0.299127i	$0.0966954\pi$
$360$	4.91924	+	3.16140i	0.259267	+	0.166621i
$361$	−2.56699	+	0.753737i	−0.135105	+	0.0396704i
$362$	1.00696	−	7.00358i	0.0529248	−	0.368100i
$363$	31.2782	+	68.4896i	1.64168	+	3.59477i
$364$	−0.602413	−	4.18987i	−0.0315750	−	0.219609i
$365$	−4.50355	+	2.89426i	−0.235727	+	0.151492i
$366$	23.3707	−	26.9712i	1.22161	−	1.40981i
$367$	5.10699			0.266583			0.133291	−	0.991077i	$-0.457445\pi$
$367$	5.10699			0.266583			0.133291	+	0.991077i	$0.457445\pi$
$368$	−1.40136	+	4.58652i	−0.0730510	+	0.239089i
$369$	−20.5676			−1.07071
$370$	0.477977	−	0.551615i	0.0248489	−	0.0286771i
$371$	4.34128	−	2.78997i	0.225388	−	0.144848i
$372$	−0.376444	−	2.61823i	−0.0195177	−	0.135749i
$373$	−5.11954	−	11.2102i	−0.265080	−	0.580443i	0.729552	−	0.683926i	$-0.239729\pi$
$373$	−5.11954	−	11.2102i	−0.265080	−	0.580443i	−0.994631	+	0.103482i	$0.967001\pi$
$374$	1.51121	−	10.5107i	0.0781426	−	0.543494i
$375$	−29.0445	+	8.52824i	−1.49985	+	0.440396i
$376$	1.90907	+	1.22688i	0.0984527	+	0.0632717i
$377$	12.6083	−	27.6083i	0.649360	−	1.42190i
$378$	0.443059	+	0.130094i	0.0227885	+	0.00669131i
$379$	−8.20589	−	9.47011i	−0.421508	−	0.486447i	0.504787	−	0.863244i	$-0.331571\pi$
$379$	−8.20589	−	9.47011i	−0.421508	−	0.486447i	−0.926296	+	0.376797i	$0.877025\pi$
$380$	−5.59633	−	6.45851i	−0.287086	−	0.331314i
$381$	−27.1467	−	7.97098i	−1.39077	−	0.408366i
$382$	−5.03967	+	11.0353i	−0.257852	+	0.564617i
$383$	−7.29685	−	4.68940i	−0.372852	−	0.239617i	0.340773	−	0.940146i	$-0.389311\pi$
$383$	−7.29685	−	4.68940i	−0.372852	−	0.239617i	−0.713624	+	0.700528i	$0.752948\pi$
$384$	2.38635	−	0.700697i	0.121778	−	0.0357573i
$385$	−1.67826	+	11.6725i	−0.0855318	+	0.594887i
$386$	0.326594	+	0.715142i	0.0166232	+	0.0363998i
$387$	−3.41798	−	23.7726i	−0.173746	−	1.20843i
$388$	0.602873	−	0.387443i	0.0306062	−	0.0196694i
$389$	14.2499	−	16.4452i	0.722497	−	0.833806i	−0.269108	−	0.963110i	$-0.586729\pi$
$389$	14.2499	−	16.4452i	0.722497	−	0.833806i	0.991605	+	0.129304i	$0.0412744\pi$
$390$	19.3245			0.978534
$391$	−5.93361	−	5.25616i	−0.300076	−	0.265815i
$392$	−1.00000			−0.0505076
$393$	22.1357	−	25.5460i	1.11660	−	1.28862i
$394$	−3.08328	+	1.98150i	−0.155333	+	0.0998266i
$395$	0.617574	+	4.29532i	0.0310735	+	0.216121i
$396$	−8.50196	−	18.6167i	−0.427239	−	0.935524i
$397$	−1.70429	+	11.8536i	−0.0855360	+	0.594916i	0.901300	+	0.433194i	$0.142614\pi$
$397$	−1.70429	+	11.8536i	−0.0855360	+	0.594916i	−0.986836	+	0.161721i	$0.948295\pi$
$398$	3.96686	−	1.16478i	0.198841	−	0.0583850i
$399$	−9.74099	−	6.26016i	−0.487660	−	0.313400i
$400$	−0.677410	+	1.48332i	−0.0338705	+	0.0741660i
$401$	26.0151	+	7.63871i	1.29913	+	0.381459i	0.856919	−	0.515451i	$-0.172376\pi$
$401$	26.0151	+	7.63871i	1.29913	+	0.381459i	0.442212	+	0.896911i	$0.354194\pi$
$402$	−1.68929	−	1.94955i	−0.0842543	−	0.0972346i
$403$	−2.94816	−	3.40235i	−0.146858	−	0.169483i
$404$	−5.52814	−	1.62321i	−0.275035	−	0.0807577i
$405$	6.41171	−	14.0397i	0.318600	−	0.697637i
$406$	−6.03193	−	3.87649i	−0.299360	−	0.192387i
$407$	−2.45113	+	0.719716i	−0.121498	+	0.0356750i
$408$	−0.585033	+	4.06899i	−0.0289634	+	0.201445i
$409$	−0.0767771	−	0.168118i	−0.00379638	−	0.00831292i	0.907724	−	0.419567i	$-0.137818\pi$
$409$	−0.0767771	−	0.168118i	−0.00379638	−	0.00831292i	−0.911521	+	0.411254i	$0.865091\pi$
$410$	1.68657	+	11.7304i	0.0832940	+	0.579322i
$411$	−14.8527	+	9.54524i	−0.732629	+	0.470832i
$412$	−7.36911	+	8.50441i	−0.363050	+	0.418982i
$413$	13.3378			0.656310
$414$	−15.0977	−	2.33945i	−0.742013	−	0.114978i
$415$	5.97933			0.293514
$416$	2.77200	−	3.19906i	0.135908	−	0.156847i
$417$	−19.6702	+	12.6413i	−0.963253	+	0.619045i
$418$	4.25667	+	29.6058i	0.208201	+	1.44807i
$419$	11.5893	+	25.3771i	0.566176	+	1.23975i	0.948808	+	0.315852i	$0.102290\pi$
$419$	11.5893	+	25.3771i	0.566176	+	1.23975i	−0.382632	+	0.923901i	$0.624982\pi$
$420$	0.649702	−	4.51878i	0.0317022	−	0.220494i
$421$	−13.0395	+	3.82876i	−0.635508	+	0.186602i	−0.583589	−	0.812049i	$-0.698352\pi$
$421$	−13.0395	+	3.82876i	−0.635508	+	0.186602i	−0.0519194	+	0.998651i	$0.516534\pi$
$422$	−18.5548	−	11.9245i	−0.903236	−	0.580474i
$423$	−3.00315	+	6.57598i	−0.146018	+	0.319735i
$424$	4.95145	+	1.45388i	0.240464	+	0.0706065i
$425$	−1.76504	−	2.03697i	−0.0856171	−	0.0988074i
$426$	19.9308	+	23.0013i	0.965650	+	1.11442i
$427$	−13.7680	−	4.04265i	−0.666281	−	0.195638i
$428$	7.06822	−	15.4772i	0.341655	−	0.748120i
$429$	−56.8985	−	36.5665i	−2.74709	−	1.76544i
$430$	−13.2780	+	3.89877i	−0.640321	+	0.188015i
$431$	−3.97859	+	27.6717i	−0.191642	+	1.33290i	0.636019	+	0.771673i	$0.280580\pi$
$431$	−3.97859	+	27.6717i	−0.191642	+	1.33290i	−0.827662	+	0.561227i	$0.810329\pi$
$432$	0.191824	+	0.420035i	0.00922912	+	0.0202090i
$433$	0.130184	+	0.905447i	0.00625622	+	0.0435130i	0.992710	−	0.120524i	$-0.0384575\pi$
$433$	0.130184	+	0.905447i	0.00625622	+	0.0435130i	−0.986454	+	0.164037i	$0.947548\pi$
$434$	−0.894714	+	0.574998i	−0.0429477	+	0.0276008i
$435$	21.4360	−	24.7384i	1.02778	−	1.18612i
$436$	−0.776403			−0.0371830
$437$	20.2075	+	9.49679i	0.966657	+	0.454293i
$438$	−7.25355			−0.346588
$439$	15.3922	−	17.7635i	0.734629	−	0.847807i	−0.258355	−	0.966050i	$-0.583181\pi$
$439$	15.3922	−	17.7635i	0.734629	−	0.847807i	0.992985	+	0.118242i	$0.0377260\pi$
$440$	−9.92053	+	6.37553i	−0.472943	+	0.303942i
$441$	−0.453367	−	3.15324i	−0.0215889	−	0.150154i
$442$	2.90645	+	6.36424i	0.138246	+	0.302716i
$443$	1.85955	−	12.9335i	0.0883499	−	0.614487i	−0.896754	−	0.442529i	$-0.854081\pi$
$443$	1.85955	−	12.9335i	0.0883499	−	0.614487i	0.985104	−	0.171958i	$-0.0550094\pi$
$444$	0.948904	−	0.278623i	0.0450330	−	0.0132229i
$445$	15.3784	+	9.88310i	0.729006	+	0.468504i
$446$	−1.86785	+	4.09001i	−0.0884451	+	0.193668i
$447$	−14.5367	−	4.26836i	−0.687562	−	0.201886i
$448$	−0.654861	−	0.755750i	−0.0309393	−	0.0357058i
$449$	−8.89384	−	10.2640i	−0.419726	−	0.484390i	0.506027	−	0.862518i	$-0.331114\pi$
$449$	−8.89384	−	10.2640i	−0.419726	−	0.484390i	−0.925754	+	0.378128i	$0.876568\pi$
$450$	−4.98438	−	1.46355i	−0.234966	−	0.0689922i
$451$	17.2307	−	37.7300i	0.811363	−	1.77664i
$452$	16.7512	+	10.7654i	0.787912	+	0.506360i
$453$	11.1997	−	3.28853i	0.526207	−	0.154508i
$454$	−2.34322	+	16.2975i	−0.109973	+	0.764878i
$455$	−3.22773	−	7.06774i	−0.151318	−	0.331341i
$456$	−1.64788	−	11.4613i	−0.0771692	−	0.536724i
$457$	17.9413	−	11.5302i	0.839259	−	0.539359i	−0.0489488	−	0.998801i	$-0.515587\pi$
$457$	17.9413	−	11.5302i	0.839259	−	0.539359i	0.888208	+	0.459442i	$0.151951\pi$
$458$	5.73855	−	6.62264i	0.268145	−	0.309456i
$459$	−0.763232			−0.0356246
$460$	−0.0962272	+	8.80256i	−0.00448662	+	0.410421i
$461$	20.2440			0.942858			0.471429	−	0.881904i	$-0.343738\pi$
$461$	20.2440			0.942858			0.471429	+	0.881904i	$0.343738\pi$
$462$	−10.4635	+	12.0756i	−0.486808	+	0.561807i
$463$	−28.6258	+	18.3967i	−1.33036	+	0.854968i	−0.996161	−	0.0875363i	$-0.972101\pi$
$463$	−28.6258	+	18.3967i	−1.33036	+	0.854968i	−0.334195	+	0.942504i	$0.608464\pi$
$464$	−1.02042	−	7.09719i	−0.0473719	−	0.329479i
$465$	−2.01699	−	4.41659i	−0.0935357	−	0.204815i
$466$	−2.28566	+	15.8971i	−0.105881	+	0.736420i
$467$	−1.41304	+	0.414907i	−0.0653879	+	0.0191996i	−0.314263	−	0.949336i	$-0.601757\pi$
$467$	−1.41304	+	0.414907i	−0.0653879	+	0.0191996i	0.248875	+	0.968536i	$0.419939\pi$
$468$	11.3441	+	7.29042i	0.524382	+	0.337000i
$469$	−0.430869	+	0.943471i	−0.0198957	+	0.0435654i
$470$	3.99676	+	1.17355i	0.184357	+	0.0541320i
$471$	−35.8306	−	41.3507i	−1.65099	−	1.90534i
$472$	8.73440	+	10.0800i	0.402033	+	0.463971i
$473$	46.4727	+	13.6456i	2.13682	+	0.627426i
$474$	−2.44255	+	5.34843i	−0.112190	+	0.245662i
$475$	6.38674	+	4.10451i	0.293044	+	0.188328i
$476$	1.58591	−	0.465665i	0.0726901	−	0.0213437i
$477$	−2.33960	+	16.2722i	−0.107123	+	0.745055i
$478$	−2.24599	−	4.91803i	−0.102729	−	0.224945i
$479$	4.46153	+	31.0306i	0.203853	+	1.41783i	0.792715	+	0.609592i	$0.208667\pi$
$479$	4.46153	+	31.0306i	0.203853	+	1.41783i	−0.588862	+	0.808233i	$0.700424\pi$
$480$	3.84053	−	2.46816i	0.175295	−	0.112655i
$481$	1.10225	−	1.27207i	0.0502583	−	0.0580012i
$482$	11.2556			0.512678
$483$	3.23512	+	11.4806i	0.147203	+	0.522386i
$484$	30.2737			1.37608
$485$	0.861427	−	0.994140i	0.0391154	−	0.0451416i
$486$	18.7584	−	12.0553i	0.850899	−	0.546839i
$487$	−6.07840	−	42.2762i	−0.275438	−	1.91572i	−0.387227	−	0.921984i	$-0.626567\pi$
$487$	−6.07840	−	42.2762i	−0.275438	−	1.91572i	0.111789	−	0.993732i	$-0.464342\pi$
$488$	−5.96090	−	13.0525i	−0.269837	−	0.590861i
$489$	5.37934	−	37.4141i	0.243262	−	1.69193i
$490$	−1.76122	+	0.517140i	−0.0795637	+	0.0233620i
$491$	−30.4369	−	19.5606i	−1.37360	−	0.882759i	−0.374587	−	0.927192i	$-0.622216\pi$
$491$	−30.4369	−	19.5606i	−1.37360	−	0.882759i	−0.999012	+	0.0444328i	$0.985852\pi$
$492$	−6.67052	+	14.6064i	−0.300730	+	0.658507i
$493$	11.3713	+	3.33890i	0.512136	+	0.150377i
$494$	−12.9055	−	14.8938i	−0.580648	−	0.670103i
$495$	−24.6012	−	28.3913i	−1.10574	−	1.27610i
$496$	−1.02047	−	0.299636i	−0.0458204	−	0.0134541i
$497$	5.08352	−	11.1314i	0.228027	−	0.499309i
$498$	6.81556	+	4.38010i	0.305413	+	0.196277i
$499$	2.66093	−	0.781319i	0.119119	−	0.0349766i	−0.221630	−	0.975131i	$-0.571138\pi$
$499$	2.66093	−	0.781319i	0.119119	−	0.0349766i	0.340749	+	0.940154i	$0.389319\pi$
$500$	−1.73213	+	12.0472i	−0.0774630	+	0.538767i
$501$	−17.6536	−	38.6559i	−0.788704	−	1.72702i
$502$	−2.71952	−	18.9147i	−0.121378	−	0.844204i
$503$	12.2908	−	7.89880i	0.548019	−	0.352190i	−0.237149	−	0.971473i	$-0.576213\pi$
$503$	12.2908	−	7.89880i	0.548019	−	0.352190i	0.785168	+	0.619283i	$0.212577\pi$
$504$	2.08617	−	2.40756i	0.0929252	−	0.107241i
$505$	−10.5757			−0.470612
$506$	16.9398	−	25.7359i	0.753067	−	1.14410i
$507$	12.2314			0.543216
$508$	−7.44956	+	8.59725i	−0.330521	+	0.381441i
$509$	2.15852	−	1.38720i	0.0956747	−	0.0614864i	−0.491929	−	0.870636i	$-0.663708\pi$
$509$	2.15852	−	1.38720i	0.0956747	−	0.0614864i	0.587603	+	0.809149i	$0.300072\pi$
$510$	1.07387	+	7.46892i	0.0475517	+	0.330729i
$511$	1.21155	+	2.65291i	0.0535956	+	0.117358i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	2.06274	−	0.605676i	0.0910723	−	0.0267412i
$514$	−22.9297	−	14.7360i	−1.01139	−	0.649978i
$515$	−8.58064	+	18.7890i	−0.378108	+	0.827941i
$516$	−17.9909	−	5.28262i	−0.792007	−	0.232554i
$517$	−9.54730	−	11.0182i	−0.419890	−	0.484579i
$518$	−0.260397	−	0.300514i	−0.0114412	−	0.0132038i
$519$	18.3006	+	5.37355i	0.803308	+	0.235873i
$520$	3.22773	−	7.06774i	0.141545	−	0.309941i
$521$	−34.4744	−	22.1553i	−1.51035	−	0.970643i	−0.993409	−	0.114621i	$-0.963435\pi$
$521$	−34.4744	−	22.1553i	−1.51035	−	0.970643i	−0.516940	−	0.856022i	$-0.672929\pi$
$522$	21.9165	−	6.43527i	0.959260	−	0.281664i
$523$	3.74764	−	26.0654i	0.163873	−	1.13976i	−0.727373	−	0.686242i	$-0.759259\pi$
$523$	3.74764	−	26.0654i	0.163873	−	1.13976i	0.891246	−	0.453520i	$-0.149832\pi$
$524$	−5.64590	−	12.3628i	−0.246643	−	0.540072i
$525$	0.577182	+	4.01439i	0.0251903	+	0.175202i
$526$	20.0053	−	12.8566i	0.872272	−	0.560575i
$527$	1.15118	−	1.32853i	0.0501462	−	0.0578718i
$528$	−15.9783			−0.695365
$529$	−9.09490	−	21.1254i	−0.395430	−	0.918496i
$530$	9.47243			0.411456
$531$	−27.8249	+	32.1116i	−1.20750	+	1.39353i
$532$	−3.91661	+	2.51705i	−0.169806	+	0.109128i
$533$	3.88936	+	27.0511i	0.168467	+	1.17171i
$534$	10.2894	+	22.5306i	0.445264	+	0.974993i
$535$	4.44477	−	30.9140i	0.192164	−	1.33653i
$536$	−0.995187	+	0.292213i	−0.0429855	+	0.0126217i
$537$	−32.5006	−	20.8869i	−1.40250	−	0.901335i
$538$	0.787936	−	1.72534i	0.0339703	−	0.0743847i
$539$	6.16423	+	1.80998i	0.265512	+	0.0779614i
$540$	0.555060	+	0.640573i	0.0238860	+	0.0275659i
$541$	21.4390	+	24.7419i	0.921734	+	1.06374i	0.997778	+	0.0666337i	$0.0212259\pi$
$541$	21.4390	+	24.7419i	0.921734	+	1.06374i	−0.0760431	+	0.997105i	$0.524229\pi$
$542$	28.9027	+	8.48660i	1.24148	+	0.364531i
$543$	7.31036	−	16.0075i	0.313718	−	0.686946i
$544$	1.39048	+	0.893605i	0.0596162	+	0.0383130i
$545$	−1.36741	+	0.401509i	−0.0585736	+	0.0171988i
$546$	1.49826	−	10.4206i	0.0641196	−	0.445962i
$547$	−1.65304	−	3.61965i	−0.0706788	−	0.154765i	0.870995	−	0.491292i	$-0.163475\pi$
$547$	−1.65304	−	3.61965i	−0.0706788	−	0.154765i	−0.941674	+	0.336527i	$0.890748\pi$
$548$	1.01026	+	7.02654i	0.0431564	+	0.300159i
$549$	38.4553	−	24.7137i	1.64123	−	1.05476i
$550$	6.86049	−	7.91743i	0.292532	−	0.337600i
$551$	−33.3820			−1.42212
$552$	−6.55791	+	9.96314i	−0.279123	+	0.424059i
$553$	2.36411			0.100532
$554$	7.27029	−	8.39037i	0.308885	−	0.356472i
$555$	1.52714	−	0.981432i	0.0648234	−	0.0416595i
$556$	1.33795	+	9.30562i	0.0567415	+	0.394646i
$557$	9.40569	+	20.5956i	0.398532	+	0.872663i	0.997417	+	0.0718283i	$0.0228834\pi$
$557$	9.40569	+	20.5956i	0.398532	+	0.872663i	−0.598885	+	0.800835i	$0.704389\pi$
$558$	0.482178	−	3.35362i	0.0204122	−	0.141970i
$559$	−30.6200	+	8.99084i	−1.29509	+	0.380272i
$560$	−1.54418	−	0.992384i	−0.0652535	−	0.0419359i
$561$	10.9711	−	24.0233i	0.463199	−	1.01426i
$562$	−19.4741	−	5.71810i	−0.821463	−	0.241203i
$563$	5.37021	+	6.19756i	0.226328	+	0.261196i	0.857544	−	0.514411i	$-0.171989\pi$
$563$	5.37021	+	6.19756i	0.226328	+	0.261196i	−0.631216	+	0.775607i	$0.717444\pi$
$564$	3.69604	+	4.26546i	0.155631	+	0.179608i
$565$	35.0698	+	10.2974i	1.47540	+	0.433215i
$566$	−3.52355	+	7.71550i	−0.148106	+	0.324306i
$567$	−7.07371	−	4.54600i	−0.297068	−	0.190914i
$568$	11.7415	−	3.44762i	0.492663	−	0.144659i
$569$	1.01807	−	7.08087i	0.0426799	−	0.296845i	−0.957290	−	0.289128i	$-0.906635\pi$
$569$	1.01807	−	7.08087i	0.0426799	−	0.296845i	0.999970	−	0.00771686i	$-0.00245638\pi$
$570$	−8.82937	−	19.3336i	−0.369821	−	0.809796i
$571$	5.39796	+	37.5436i	0.225898	+	1.57115i	0.715125	+	0.698996i	$0.246370\pi$
$571$	5.39796	+	37.5436i	0.225898	+	1.57115i	−0.489228	+	0.872156i	$0.662721\pi$
$572$	−22.8775	+	14.7024i	−0.956555	+	0.614740i
$573$	−19.7589	+	22.8030i	−0.825439	+	0.952608i
$574$	6.45631			0.269481
$575$	−2.12113	−	7.52733i	−0.0884571	−	0.313911i
$576$	3.18566			0.132736
$577$	−19.2728	+	22.2420i	−0.802339	+	0.925948i	−0.998507	−	0.0546220i	$-0.982605\pi$
$577$	−19.2728	+	22.2420i	−0.802339	+	0.925948i	0.196168	+	0.980570i	$0.437150\pi$
$578$	12.0030	−	7.71389i	0.499261	−	0.320855i
$579$	0.278272	+	1.93543i	0.0115646	+	0.0804336i
$580$	−5.46743	−	11.9720i	−0.227022	−	0.497110i
$581$	0.463588	−	3.22432i	0.0192329	−	0.133767i
$582$	1.71015	−	0.502145i	0.0708879	−	0.0208146i
$583$	−27.8904	−	17.9241i	−1.15510	−	0.742338i
$584$	−1.21155	+	2.65291i	−0.0501341	+	0.109778i
$585$	23.7496	+	6.97352i	0.981926	+	0.288320i
$586$	15.0813	+	17.4048i	0.623004	+	0.718984i
$587$	−5.05714	−	5.83625i	−0.208730	−	0.240888i	0.641725	−	0.766935i	$-0.278219\pi$
$587$	−5.05714	−	5.83625i	−0.208730	−	0.240888i	−0.850456	+	0.526047i	$0.823674\pi$
$588$	−2.38635	−	0.700697i	−0.0984116	−	0.0288963i
$589$	−2.05695	+	4.50408i	−0.0847550	+	0.185588i
$590$	20.5960	+	13.2362i	0.847923	+	0.544927i
$591$	−8.74622	+	2.56812i	−0.359772	+	0.105638i
$592$	0.0565897	−	0.393590i	0.00232582	−	0.0161765i
$593$	15.2804	+	33.4595i	0.627492	+	1.37402i	0.909943	+	0.414734i	$0.136125\pi$
$593$	15.2804	+	33.4595i	0.627492	+	1.37402i	−0.282451	+	0.959282i	$0.591147\pi$
$594$	−0.422189	−	2.93639i	−0.0173226	−	0.120482i
$595$	2.55232	−	1.64028i	0.104635	−	0.0672447i
$596$	−3.98914	+	4.60372i	−0.163402	+	0.188576i
$597$	10.2825			0.420835
$598$	−0.221907	+	20.2993i	−0.00907445	+	0.830102i
$599$	44.4439			1.81593			0.907965	−	0.419046i	$-0.137635\pi$
$599$	44.4439			1.81593			0.907965	+	0.419046i	$0.137635\pi$
$600$	−2.65590	+	3.06507i	−0.108427	+	0.125131i
$601$	−2.72530	+	1.75144i	−0.111167	+	0.0714428i	−0.595043	−	0.803694i	$-0.702865\pi$
$601$	−2.72530	+	1.75144i	−0.111167	+	0.0714428i	0.483876	+	0.875137i	$0.339229\pi$
$602$	1.07292	+	7.46236i	0.0437291	+	0.304143i
$603$	−1.37260	−	3.00558i	−0.0558967	−	0.122397i
$604$	0.667915	−	4.64545i	0.0271771	−	0.189021i
$605$	53.3186	−	15.6557i	2.16771	−	0.636497i
$606$	−12.0547	−	7.74710i	−0.489690	−	0.314705i
$607$	−6.11287	+	13.3853i	−0.248114	+	0.543293i	−0.992180	−	0.124812i	$-0.960167\pi$
$607$	−6.11287	+	13.3853i	−0.248114	+	0.543293i	0.744067	+	0.668105i	$0.232894\pi$
$608$	−4.46709	−	1.31166i	−0.181165	−	0.0531947i
$609$	−11.6781	−	13.4772i	−0.473220	−	0.546125i
$610$	−17.2484	−	19.9057i	−0.698368	−	0.805960i
$611$	9.21681	+	2.70630i	0.372872	+	0.109485i
$612$	−2.18735	+	4.78964i	−0.0884185	+	0.193610i
$613$	14.9215	+	9.58949i	0.602675	+	0.387316i	0.806104	−	0.591774i	$-0.201572\pi$
$613$	14.9215	+	9.58949i	0.602675	+	0.387316i	−0.203429	+	0.979090i	$0.565208\pi$
$614$	0.284668	−	0.0835861i	0.0114883	−	0.00337326i
$615$	−4.19468	+	29.1746i	−0.169146	+	1.17643i
$616$	2.66882	+	5.84390i	0.107530	+	0.235457i
$617$	0.648439	+	4.50999i	0.0261052	+	0.181565i	0.998702	−	0.0509323i	$-0.0162193\pi$
$617$	0.648439	+	4.50999i	0.0261052	+	0.181565i	−0.972597	+	0.232498i	$0.925310\pi$
$618$	−23.5443	+	15.1310i	−0.947092	+	0.608659i
$619$	−12.0590	+	13.9168i	−0.484691	+	0.559363i	−0.944439	−	0.328686i	$-0.893394\pi$
$619$	−12.0590	+	13.9168i	−0.484691	+	0.559363i	0.459748	+	0.888049i	$0.347940\pi$
$620$	−1.95222			−0.0784030
$621$	−2.00424	−	0.941919i	−0.0804274	−	0.0377979i
$622$	12.3034			0.493322
$623$	6.52172	−	7.52647i	0.261287	−	0.301542i
$624$	8.85654	−	5.69175i	0.354545	−	0.227852i
$625$	2.01909	+	14.0431i	0.0807635	+	0.561722i
$626$	2.39530	+	5.24497i	0.0957354	+	0.209631i
$627$	−10.5868	+	73.6326i	−0.422795	+	2.94060i
$628$	−21.1083	+	6.19797i	−0.842315	+	0.247326i
$629$	0.552906	+	0.355331i	0.0220458	+	0.0141680i
$630$	2.42914	−	5.31908i	0.0967794	−	0.211917i
$631$	−15.5604	−	4.56894i	−0.619449	−	0.181887i	−0.0430737	−	0.999072i	$-0.513715\pi$
$631$	−15.5604	−	4.56894i	−0.619449	−	0.181887i	−0.576375	+	0.817185i	$0.695533\pi$
$632$	1.54816	+	1.78667i	0.0615826	+	0.0710701i
$633$	−35.9230	−	41.4574i	−1.42781	−	1.64778i
$634$	−3.48027	−	1.02190i	−0.138219	−	0.0405848i
$635$	−8.67431	+	18.9941i	−0.344229	+	0.753757i
$636$	10.7972	+	6.93893i	0.428136	+	0.275147i
$637$	−4.06149	+	1.19256i	−0.160922	+	0.0472510i
$638$	−6.55566	+	45.5956i	−0.259541	+	1.80515i
$639$	16.1944	+	35.4607i	0.640640	+	1.40281i
$640$	−0.261229	−	1.81689i	−0.0103260	−	0.0718188i
$641$	−13.9254	+	8.94932i	−0.550021	+	0.353477i	−0.785947	−	0.618294i	$-0.787824\pi$
$641$	−13.9254	+	8.94932i	−0.550021	+	0.353477i	0.235926	+	0.971771i	$0.424188\pi$
$642$	27.7121	−	31.9815i	1.09371	−	1.26221i
$643$	−3.24627			−0.128021			−0.0640103	−	0.997949i	$-0.520389\pi$
$643$	−3.24627			−0.128021			−0.0640103	+	0.997949i	$0.520389\pi$
$644$	4.73927	+	0.734367i	0.186754	+	0.0289381i
$645$	−34.4178			−1.35520
$646$	5.03929	−	5.81565i	0.198268	−	0.228814i
$647$	−17.4499	+	11.2144i	−0.686026	+	0.440882i	−0.836671	−	0.547706i	$-0.815501\pi$
$647$	−17.4499	+	11.2144i	−0.686026	+	0.440882i	0.150645	+	0.988588i	$0.451865\pi$
$648$	−1.19666	−	8.32295i	−0.0470092	−	0.326956i
$649$	−35.5962	−	77.9447i	−1.39727	−	3.05960i
$650$	−0.982344	+	6.83235i	−0.0385307	+	0.267987i
$651$	−2.53800	+	0.745225i	−0.0994722	+	0.0292077i
$652$	−12.7854	−	8.21665i	−0.500713	−	0.321789i
$653$	0.0371334	−	0.0813108i	0.00145314	−	0.00318194i	−0.908904	−	0.417005i	$-0.863080\pi$
$653$	0.0371334	−	0.0813108i	0.00145314	−	0.00318194i	0.910357	+	0.413823i	$0.135807\pi$
$654$	−1.85277	−	0.544023i	−0.0724492	−	0.0212730i
$655$	−16.3370	−	18.8539i	−0.638338	−	0.736681i
$656$	4.22798	+	4.87935i	0.165075	+	0.190507i
$657$	−8.91454	−	2.61755i	−0.347789	−	0.102120i
$658$	0.942708	−	2.06424i	0.0367506	−	0.0804725i
$659$	−32.9850	−	21.1982i	−1.28491	−	0.825764i	−0.293429	−	0.955981i	$-0.594796\pi$
$659$	−32.9850	−	21.1982i	−1.28491	−	0.825764i	−0.991486	+	0.130216i	$0.958433\pi$
$660$	−28.1412	+	8.26300i	−1.09540	+	0.321637i
$661$	3.90620	−	27.1682i	0.151934	−	1.05672i	−0.761041	−	0.648704i	$-0.775311\pi$
$661$	3.90620	−	27.1682i	0.151934	−	1.05672i	0.912974	−	0.408017i	$-0.133780\pi$
$662$	−7.44598	−	16.3044i	−0.289396	−	0.633690i
$663$	2.47642	+	17.2239i	0.0961762	+	0.668920i
$664$	2.74037	−	1.76113i	0.106347	−	0.0683450i
$665$	−5.59633	+	6.45851i	−0.217016	+	0.250450i
$666$	1.26674			0.0490852
$667$	25.7402	+	22.8014i	0.996665	+	0.882873i
$668$	−17.0867			−0.661103
$669$	−7.32321	+	8.45143i	−0.283131	+	0.326751i
$670$	−1.60162	+	1.02930i	−0.0618762	+	0.0397654i
$671$	13.1195	+	91.2479i	0.506472	+	3.52259i
$672$	−1.03318	−	2.26235i	−0.0398557	−	0.0872719i
$673$	−5.86417	+	40.7862i	−0.226047	+	1.57219i	0.488474	+	0.872578i	$0.337554\pi$
$673$	−5.86417	+	40.7862i	−0.226047	+	1.57219i	−0.714521	+	0.699614i	$0.753355\pi$
$674$	26.6202	−	7.81640i	1.02537	−	0.301077i
$675$	−0.633456	−	0.407097i	−0.0243817	−	0.0156692i
$676$	2.04299	−	4.47352i	0.0785764	−	0.172058i
$677$	−31.7030	−	9.30885i	−1.21845	−	0.357768i	−0.391568	−	0.920149i	$-0.628067\pi$
$677$	−31.7030	−	9.30885i	−1.21845	−	0.357768i	−0.826878	+	0.562381i	$0.809885\pi$
$678$	32.4311	+	37.4275i	1.24551	+	1.43740i
$679$	−0.469297	−	0.541597i	−0.0180100	−	0.0207846i
$680$	2.91105	+	0.854761i	0.111634	+	0.0327786i
$681$	−17.0113	+	37.2496i	−0.651876	+	1.42741i
$682$	5.74806	+	3.69405i	0.220105	+	0.141453i
$683$	25.7674	−	7.56599i	0.985961	−	0.289504i	0.251278	−	0.967915i	$-0.419149\pi$
$683$	25.7674	−	7.56599i	0.985961	−	0.289504i	0.734683	+	0.678410i	$0.237331\pi$
$684$	2.11073	−	14.6805i	0.0807059	−	0.561322i
$685$	5.41300	+	11.8528i	0.206820	+	0.452873i
$686$	0.142315	+	0.989821i	0.00543361	+	0.0377916i
$687$	18.3347	−	11.7830i	0.699512	−	0.449549i
$688$	−4.93706	+	5.69767i	−0.188223	+	0.217221i
$689$	21.8441			0.832195
$690$	−6.39756	+	20.9386i	−0.243551	+	0.797119i
$691$	41.7628			1.58873			0.794366	−	0.607439i	$-0.207803\pi$
$691$	41.7628			1.58873			0.794366	+	0.607439i	$0.207803\pi$
$692$	5.02204	−	5.79574i	0.190909	−	0.220321i
$693$	−17.2172	+	11.0648i	−0.654029	+	0.420319i
$694$	2.33170	+	16.2173i	0.0885102	+	0.615602i
$695$	7.16872	+	15.6973i	0.271925	+	0.595433i
$696$	2.53789	−	17.6514i	0.0961985	−	0.669075i
$697$	−10.2391	+	3.00648i	−0.387835	+	0.113879i
$698$	−8.15735	−	5.24241i	−0.308760	−	0.198428i
$699$	−16.5935	+	36.3346i	−0.627622	+	1.37430i
$700$	1.56463	+	0.459416i	0.0591374	+	0.0173643i
$701$	2.18368	+	2.52010i	0.0824763	+	0.0951827i	0.795488	−	0.605970i	$-0.207215\pi$
$701$	2.18368	+	2.52010i	0.0824763	+	0.0951827i	−0.713011	+	0.701152i	$0.752669\pi$
$702$	1.28001	+	1.47721i	0.0483108	+	0.0557537i
$703$	−1.77628	−	0.521564i	−0.0669938	−	0.0196712i
$704$	−2.66882	+	5.84390i	−0.100585	+	0.220250i
$705$	8.71537	+	5.60103i	0.328240	+	0.210947i
$706$	12.7331	−	3.73879i	0.479218	−	0.140711i
$707$	−0.819950	+	5.70288i	−0.0308374	+	0.214479i
$708$	13.7803	+	30.1747i	0.517897	+	1.13404i
$709$	2.27698	+	15.8368i	0.0855139	+	0.594763i	0.986850	+	0.161641i	$0.0516787\pi$
$709$	2.27698	+	15.8368i	0.0855139	+	0.594763i	−0.901336	+	0.433121i	$0.857412\pi$
$710$	18.8964	−	12.1440i	0.709171	−	0.455757i
$711$	−4.93192	+	5.69174i	−0.184962	+	0.213457i
$712$	9.95894			0.373227
$713$	4.66255	−	2.06802i	0.174614	−	0.0774481i
$714$	4.11083			0.153844
$715$	−32.6889	+	37.7250i	−1.22250	+	1.41084i
$716$	−13.0677	+	8.39808i	−0.488362	+	0.313851i
$717$	−1.91368	−	13.3099i	−0.0714676	−	0.497068i
$718$	−1.95671	−	4.28461i	−0.0730239	−	0.159900i
$719$	4.48914	−	31.2227i	0.167417	−	1.16441i	−0.716782	−	0.697298i	$-0.754386\pi$
$719$	4.48914	−	31.2227i	0.167417	−	1.16441i	0.884199	−	0.467111i	$-0.154705\pi$
$720$	5.61064	−	1.64743i	0.209096	−	0.0613962i
$721$	9.46658	+	6.08380i	0.352554	+	0.226573i
$722$	−1.11139	+	2.43360i	−0.0413615	+	0.0905691i
$723$	26.8598	+	7.88675i	0.998927	+	0.293311i
$724$	−4.63354	−	5.34738i	−0.172204	−	0.198734i
$725$	7.65681	+	8.83643i	0.284367	+	0.328177i
$726$	72.2438	+	21.2127i	2.68122	+	0.787277i
$727$	6.07101	−	13.2937i	0.225161	−	0.493035i	−0.763010	−	0.646386i	$-0.776279\pi$
$727$	6.07101	−	13.2937i	0.225161	−	0.493035i	0.988172	+	0.153352i	$0.0490068\pi$
$728$	−3.56099	−	2.28851i	−0.131979	−	0.0848178i
$729$	29.0075	−	8.51738i	1.07435	−	0.315458i
$730$	−0.761866	+	5.29889i	−0.0281979	+	0.196121i
$731$	−5.17652	−	11.3350i	−0.191461	−	0.419240i
$732$	−5.07893	−	35.3248i	−0.187723	−	1.30564i
$733$	−32.5781	+	20.9367i	−1.20330	+	0.773314i	−0.979524	−	0.201326i	$-0.935475\pi$
$733$	−32.5781	+	20.9367i	−1.20330	+	0.773314i	−0.223776	+	0.974641i	$0.571838\pi$
$734$	3.34437	−	3.85961i	0.123443	−	0.142461i
$735$	−4.56525			−0.168392
$736$	2.54857	+	4.06261i	0.0939414	+	0.149750i
$737$	6.66346			0.245452
$738$	−13.4689	+	15.5440i	−0.495798	+	0.572182i
$739$	19.2468	−	12.3692i	0.708006	−	0.455008i	−0.136440	−	0.990648i	$-0.543566\pi$
$739$	19.2468	−	12.3692i	0.708006	−	0.455008i	0.844446	+	0.535640i	$0.179930\pi$
$740$	−0.103874	−	0.722462i	−0.00381850	−	0.0265582i
$741$	−20.3612	−	44.5847i	−0.747986	−	1.63786i
$742$	0.734414	−	5.10796i	0.0269612	−	0.187519i
$743$	24.5686	−	7.21399i	0.901335	−	0.264656i	0.201946	−	0.979397i	$-0.435274\pi$
$743$	24.5686	−	7.21399i	0.901335	−	0.264656i	0.699389	+	0.714741i	$0.253455\pi$
$744$	−2.22524	−	1.43008i	−0.0815814	−	0.0524292i
$745$	−4.64498	+	10.1711i	−0.170179	+	0.372640i
$746$	−11.8247	−	3.47205i	−0.432933	−	0.127121i
$747$	6.79564	+	7.84259i	0.248640	+	0.286945i
$748$	−6.95381	−	8.02512i	−0.254256	−	0.293427i
$749$	−16.3256	−	4.79363i	−0.596525	−	0.175156i
$750$	−12.5749	+	27.5352i	−0.459170	+	1.00544i
$751$	−17.5851	−	11.3012i	−0.641688	−	0.412388i	0.178933	−	0.983861i	$-0.442736\pi$
$751$	−17.5851	−	11.3012i	−0.641688	−	0.412388i	−0.820620	+	0.571474i	$0.806372\pi$
$752$	2.17739	−	0.639340i	0.0794013	−	0.0233143i
$753$	6.76372	−	47.0427i	0.246484	−	1.71433i
$754$	−12.6083	−	27.6083i	−0.459167	−	1.00543i
$755$	−1.22601	−	8.52705i	−0.0446189	−	0.310331i
$756$	0.388460	−	0.249648i	0.0141282	−	0.00907962i
$757$	8.42895	−	9.72753i	0.306355	−	0.353553i	−0.581606	−	0.813470i	$-0.697576\pi$
$757$	8.42895	−	9.72753i	0.306355	−	0.353553i	0.887962	+	0.459917i	$0.152121\pi$
$758$	−12.5307			−0.455137
$759$	58.4575	−	49.5454i	2.12187	−	1.79838i
$760$	−8.54583			−0.309990
$761$	−3.91472	+	4.51783i	−0.141909	+	0.163771i	−0.822255	−	0.569120i	$-0.807284\pi$
$761$	−3.91472	+	4.51783i	−0.141909	+	0.163771i	0.680346	+	0.732891i	$0.261830\pi$
$762$	−23.8013	+	15.2962i	−0.862232	+	0.554123i
$763$	0.110494	+	0.768501i	0.00400014	+	0.0278216i
$764$	5.03967	+	11.0353i	0.182329	+	0.399245i
$765$	−1.37549	+	9.56675i	−0.0497310	+	0.345887i
$766$	−8.32244	+	2.44369i	−0.300702	+	0.0882940i
$767$	47.4958	+	30.5237i	1.71497	+	1.10215i
$768$	1.03318	−	2.26235i	0.0372816	−	0.0816354i
$769$	−3.42047	−	1.00434i	−0.123345	−	0.0362174i	0.219477	−	0.975618i	$-0.429565\pi$
$769$	−3.42047	−	1.00434i	−0.123345	−	0.0362174i	−0.342823	+	0.939400i	$0.611383\pi$
$770$	7.72248	+	8.91222i	0.278299	+	0.321174i
$771$	−44.3929	−	51.2322i	−1.59877	−	1.84508i
$772$	0.754342	+	0.221495i	0.0271494	+	0.00797177i
$773$	−3.58131	+	7.84197i	−0.128811	+	0.282056i	−0.963038	−	0.269364i	$-0.913187\pi$
$773$	−3.58131	+	7.84197i	−0.128811	+	0.282056i	0.834228	+	0.551420i	$0.185914\pi$
$774$	−20.2044	−	12.9846i	−0.726232	−	0.466721i
$775$	1.66406	−	0.488612i	0.0597747	−	0.0175514i
$776$	0.101988	−	0.709342i	0.00366115	−	0.0254639i
$777$	−0.410830	−	0.899593i	−0.0147385	−	0.0322727i
$778$	−3.09679	−	21.5387i	−0.111025	−	0.772198i
$779$	25.2868	−	16.2509i	0.905995	−	0.582248i
$780$	12.6549	−	14.6045i	0.453116	−	0.522924i
$781$	−78.6175			−2.81315
$782$	−7.85803	+	1.04227i	−0.281003	+	0.0372717i
$783$	3.31093			0.118323
$784$	−0.654861	+	0.755750i	−0.0233879	+	0.0269911i
$785$	−33.9711	+	21.8319i	−1.21248	+	0.779215i
$786$	−4.81055	−	33.4581i	−0.171587	−	1.19341i
$787$	−3.76870	−	8.25231i	−0.134340	−	0.294163i	0.830492	−	0.557030i	$-0.188059\pi$
$787$	−3.76870	−	8.25231i	−0.134340	−	0.294163i	−0.964832	+	0.262867i	$0.915332\pi$
$788$	−0.521598	+	3.62779i	−0.0185812	+	0.129235i
$789$	56.7483	−	16.6628i	2.02029	−	0.593211i
$790$	3.65061	+	2.34610i	0.129883	+	0.0834707i
$791$	8.27184	−	18.1128i	0.294113	−	0.644017i
$792$	−19.6372	−	5.76599i	−0.697776	−	0.204885i
$793$	−39.7761	−	45.9041i	−1.41249	−	1.63010i
$794$	7.84229	+	9.05049i	0.278312	+	0.321190i
$795$	22.6046	+	6.63731i	0.801702	+	0.235401i
$796$	1.71746	−	3.76072i	0.0608739	−	0.133295i
$797$	31.6065	+	20.3123i	1.11956	+	0.719498i	0.963356	−	0.268227i	$-0.0864378\pi$
$797$	31.6065	+	20.3123i	1.11956	+	0.719498i	0.156204	+	0.987725i	$0.450074\pi$
$798$	−11.1101	+	3.26222i	−0.393293	+	0.115481i
$799$	−0.533804	+	3.71269i	−0.0188846	+	0.131345i
$800$	0.677410	+	1.48332i	0.0239501	+	0.0524433i
$801$	4.51506	+	31.4029i	0.159532	+	1.10957i
$802$	22.8092	−	14.6586i	0.805421	−	0.517613i
$803$	12.2700	−	14.1603i	0.432997	−	0.499706i
$804$	−2.57962			−0.0909762
$805$	8.72666	−	1.15749i	0.307574	−	0.0407961i
$806$	−4.50196			−0.158575
$807$	3.08924	−	3.56517i	0.108746	−	0.125500i
$808$	−4.84690	+	3.11492i	−0.170513	+	0.109582i
$809$	−5.66042	−	39.3691i	−0.199010	−	1.38414i	−0.807165	−	0.590326i	$-0.798999\pi$
$809$	−5.66042	−	39.3691i	−0.199010	−	1.38414i	0.608155	−	0.793818i	$-0.291910\pi$
$810$	−6.41171	−	14.0397i	−0.225284	−	0.493304i
$811$	4.53079	−	31.5123i	0.159098	−	1.10655i	−0.741203	−	0.671280i	$-0.765745\pi$
$811$	4.53079	−	31.5123i	0.159098	−	1.10655i	0.900301	−	0.435268i	$-0.143346\pi$
$812$	−6.87973	+	2.02007i	−0.241431	+	0.0708906i
$813$	63.0255	+	40.5041i	2.21040	+	1.42054i
$814$	−1.06122	+	2.32375i	−0.0371958	+	0.0814475i
$815$	−26.7669	−	7.85948i	−0.937605	−	0.275306i
$816$	2.69202	+	3.10676i	0.0942397	+	0.108758i
$817$	22.9854	+	26.5265i	0.804156	+	0.928045i
$818$	−0.177334	−	0.0520699i	−0.00620033	−	0.00182058i
$819$	5.60178	−	12.2662i	0.195742	−	0.428615i
$820$	9.96970	+	6.40714i	0.348157	+	0.223747i
$821$	8.53023	−	2.50470i	0.297707	−	0.0874147i	−0.129468	−	0.991584i	$-0.541327\pi$
$821$	8.53023	−	2.50470i	0.297707	−	0.0874147i	0.427175	+	0.904169i	$0.359509\pi$
$822$	−2.51263	+	17.4757i	−0.0876380	+	0.609536i
$823$	13.2053	+	28.9156i	0.460309	+	1.00794i	0.987417	+	0.158138i	$0.0505489\pi$
$823$	13.2053	+	28.9156i	0.460309	+	1.00794i	−0.527108	+	0.849798i	$0.676724\pi$
$824$	1.60146	+	11.1384i	0.0557896	+	0.388025i
$825$	21.9193	−	14.0867i	0.763131	−	0.490435i
$826$	8.73440	−	10.0800i	0.303909	−	0.350729i
$827$	30.0480			1.04487			0.522436	−	0.852678i	$-0.325023\pi$
$827$	30.0480			1.04487			0.522436	+	0.852678i	$0.325023\pi$
$828$	−11.6549	+	9.87809i	−0.405037	+	0.343287i
$829$	−33.8571			−1.17590			−0.587952	−	0.808895i	$-0.700066\pi$
$829$	−33.8571			−1.17590			−0.587952	+	0.808895i	$0.700066\pi$
$830$	3.91563	−	4.51888i	0.135914	−	0.156853i
$831$	23.2286	−	14.9281i	0.805791	−	0.517851i
$832$	−0.602413	−	4.18987i	−0.0208849	−	0.145258i
$833$	−0.686624	−	1.50350i	−0.0237901	−	0.0520931i
$834$	−3.32760	+	23.1440i	−0.115226	+	0.801411i
$835$	−30.0933	+	8.83620i	−1.04142	+	0.305789i
$836$	25.1621	+	16.1707i	0.870249	+	0.559275i
$837$	0.204014	−	0.446728i	0.00705175	−	0.0154412i
$838$	26.7681	+	7.85983i	0.924690	+	0.271513i
$839$	−35.0909	−	40.4970i	−1.21147	−	1.39811i	−0.892925	−	0.450205i	$-0.851351\pi$
$839$	−35.0909	−	40.4970i	−1.21147	−	1.39811i	−0.318546	−	0.947908i	$-0.603194\pi$
$840$	−2.98960	−	3.45018i	−0.103151	−	0.119043i
$841$	−21.5036	−	6.31402i	−0.741503	−	0.217725i
$842$	−5.64550	+	12.3619i	−0.194557	+	0.426020i
$843$	−42.4653	−	27.2908i	−1.46258	−	0.939946i
$844$	−21.1628	+	6.21395i	−0.728452	+	0.213893i
$845$	1.28471	−	8.93535i	0.0441953	−	0.307385i
$846$	3.00315	+	6.57598i	0.103250	+	0.226087i
$847$	−4.30840	−	29.9656i	−0.148038	−	1.02963i
$848$	4.34128	−	2.78997i	0.149080	−	0.0958079i
$849$	−13.8147	+	15.9430i	−0.474118	+	0.547161i
$850$	−2.69529			−0.0924478
$851$	1.01341	+	1.61545i	0.0347391	+	0.0553768i
$852$	30.4351			1.04269
$853$	23.2805	−	26.8671i	0.797109	−	0.919913i	−0.201110	−	0.979569i	$-0.564455\pi$
$853$	23.2805	−	26.8671i	0.797109	−	0.919913i	0.998219	+	0.0596555i	$0.0190002\pi$
$854$	−12.0714	+	7.75779i	−0.413073	+	0.265466i
$855$	−3.87440	−	26.9470i	−0.132502	−	0.921569i
$856$	−7.06822	−	15.4772i	−0.241587	−	0.529001i
$857$	1.14551	−	7.96717i	0.0391297	−	0.272153i	−0.960858	−	0.277040i	$-0.910646\pi$
$857$	1.14551	−	7.96717i	0.0391297	−	0.272153i	0.999988	+	0.00488693i	$0.00155556\pi$
$858$	−64.8957	+	19.0551i	−2.21550	+	0.650530i
$859$	−2.05857	−	1.32296i	−0.0702376	−	0.0451390i	0.505051	−	0.863090i	$-0.331474\pi$
$859$	−2.05857	−	1.32296i	−0.0702376	−	0.0451390i	−0.575288	+	0.817951i	$0.695110\pi$
$860$	−5.74873	+	12.5880i	−0.196030	+	0.429246i
$861$	15.4070	+	4.52392i	0.525071	+	0.154175i
$862$	18.3075	+	21.1280i	0.623555	+	0.719621i
$863$	35.9114	+	41.4440i	1.22244	+	1.41077i	0.882495	+	0.470323i	$0.155862\pi$
$863$	35.9114	+	41.4440i	1.22244	+	1.41077i	0.339943	+	0.940446i	$0.389592\pi$
$864$	0.443059	+	0.130094i	0.0150732	+	0.00442588i
$865$	5.84769	−	12.8046i	0.198827	−	0.435371i
$866$	0.769543	+	0.494555i	0.0261501	+	0.0168057i
$867$	34.0486	−	9.99757i	1.15635	−	0.339535i
$868$	−0.151359	+	1.05272i	−0.00513745	+	0.0357318i
$869$	−6.30938	−	13.8156i	−0.214031	−	0.468662i
$870$	−4.65848	−	32.4004i	−0.157937	−	1.09848i
$871$	−3.69346	+	2.37364i	−0.125148	+	0.0804279i
$872$	−0.508436	+	0.586767i	−0.0172178	+	0.0198704i
$873$	2.28296			0.0772665
$874$	20.4103	−	9.05276i	0.690389	−	0.306214i
$875$	12.1711			0.411458
$876$	−4.75006	+	5.48187i	−0.160490	+	0.185215i
$877$	35.2677	−	22.6652i	1.19091	−	0.765349i	0.213547	−	0.976933i	$-0.431498\pi$
$877$	35.2677	−	22.6652i	1.19091	−	0.765349i	0.977360	+	0.211584i	$0.0678620\pi$
$878$	−3.34504	−	23.2653i	−0.112890	−	0.785165i
$879$	23.7939	+	52.1014i	0.802548	+	1.75734i
$880$	−1.67826	+	11.6725i	−0.0565740	+	0.393481i
$881$	−48.7423	+	14.3120i	−1.64217	+	0.482185i	−0.966851	−	0.255341i	$-0.917812\pi$
$881$	−48.7423	+	14.3120i	−1.64217	+	0.482185i	−0.675319	+	0.737526i	$0.735994\pi$
$882$	−2.67995	−	1.72230i	−0.0902386	−	0.0579929i
$883$	20.2498	−	44.3409i	0.681460	−	1.49219i	−0.179628	−	0.983735i	$-0.557489\pi$
$883$	20.2498	−	44.3409i	0.681460	−	1.49219i	0.861088	−	0.508455i	$-0.169783\pi$
$884$	6.71309	+	1.97114i	0.225786	+	0.0662967i
$885$	39.8747	+	46.0179i	1.34037	+	1.54687i
$886$	−8.55671	−	9.87497i	−0.287468	−	0.331756i
$887$	−54.4203	−	15.9793i	−1.82726	−	0.536531i	−0.827565	−	0.561370i	$-0.810274\pi$
$887$	−54.4203	−	15.9793i	−1.82726	−	0.536531i	−0.999691	+	0.0248393i	$0.992093\pi$
$888$	0.410830	−	0.899593i	0.0137866	−	0.0301884i
$889$	9.56992	+	6.15022i	0.320965	+	0.206272i
$890$	17.5399	−	5.15017i	0.587937	−	0.172634i
$891$	−7.68790	+	53.4705i	−0.257554	+	1.79133i
$892$	1.86785	+	4.09001i	0.0625401	+	0.136944i
$893$	−1.50359	−	10.4577i	−0.0503156	−	0.349953i
$894$	−12.7453	+	8.19092i	−0.426267	+	0.273945i
$895$	−18.6720	+	21.5487i	−0.624137	+	0.720292i
$896$	−1.00000			−0.0334077
$897$	−14.7532	+	48.2859i	−0.492596	+	1.61222i
$898$	−13.5813			−0.453213
$899$	−4.99386	+	5.76322i	−0.166554	+	0.192214i
$900$	−4.37015	+	2.80852i	−0.145672	+	0.0936174i
$901$	1.21389	+	8.44276i	0.0404404	+	0.281269i
$902$	−17.2307	−	37.7300i	−0.573720	−	1.25627i
$903$	−2.66847	+	18.5596i	−0.0888011	+	0.617625i
$904$	19.1057	−	5.60993i	0.635445	−	0.186583i
$905$	−10.9260	−	7.02172i	−0.363193	−	0.233410i
$906$	4.84894	−	10.6177i	0.161095	−	0.352749i
$907$	27.5673	+	8.09448i	0.915356	+	0.268773i	0.705294	−	0.708915i	$-0.250815\pi$
$907$	27.5673	+	8.09448i	0.915356	+	0.268773i	0.210062	+	0.977688i	$0.432633\pi$
$908$	10.7823	+	12.4435i	0.357824	+	0.412951i
$909$	−12.0195	−	13.8712i	−0.398662	−	0.460080i
$910$	−7.45516	−	2.18903i	−0.247136	−	0.0725657i
$911$	8.93646	−	19.5681i	0.296078	−	0.648321i	−0.701873	−	0.712302i	$-0.747653\pi$
$911$	8.93646	−	19.5681i	0.296078	−	0.648321i	0.997951	+	0.0639814i	$0.0203798\pi$
$912$	−9.74099	−	6.26016i	−0.322557	−	0.207294i
$913$	−20.0798	+	5.89597i	−0.664546	+	0.195128i
$914$	3.03513	−	21.1098i	0.100393	−	0.698250i
$915$	−27.2130	−	59.5881i	−0.899632	−	1.96992i
$916$	−1.24711	−	8.67381i	−0.0412055	−	0.286591i
$917$	−11.4335	+	7.34785i	−0.377567	+	0.242647i
$918$	−0.499811	+	0.576813i	−0.0164962	+	0.0190377i
$919$	−33.9103			−1.11860			−0.559299	−	0.828966i	$-0.688930\pi$
$919$	−33.9103			−1.11860			−0.559299	+	0.828966i	$0.688930\pi$
$920$	6.58952	+	5.83717i	0.217250	+	0.192446i
$921$	0.737888			0.0243142
$922$	13.2570	−	15.2994i	0.436596	−	0.503859i
$923$	43.5766	−	28.0050i	1.43434	−	0.921795i
$924$	2.27395	+	15.8156i	0.0748073	+	0.520296i
$925$	0.269364	+	0.589824i	0.00885662	+	0.0193933i
$926$	−4.84263	+	33.6813i	−0.159139	+	1.10683i
$927$	−34.3960	+	10.0996i	−1.12971	+	0.331714i
$928$	−6.03193	−	3.87649i	−0.198008	−	0.127252i
$929$	−9.65877	+	21.1498i	−0.316894	+	0.693901i	−0.999313	−	0.0370601i	$-0.988201\pi$
$929$	−9.65877	+	21.1498i	−0.316894	+	0.693901i	0.682419	+	0.730961i	$0.260928\pi$
$930$	−4.65869	−	1.36791i	−0.152764	−	0.0448557i
$931$	3.04882	+	3.51853i	0.0999211	+	0.115315i
$932$	10.5174	+	12.1378i	0.344510	+	0.397586i
$933$	29.3603	+	8.62096i	0.961213	+	0.282238i
$934$	−0.611781	+	1.33961i	−0.0200181	+	0.0438335i
$935$	−16.3973	−	10.5379i	−0.536248	−	0.344626i
$936$	12.9386	−	3.79910i	0.422910	−	0.124178i
$937$	2.49824	−	17.3757i	0.0816140	−	0.567638i	−0.907451	−	0.420158i	$-0.861975\pi$
$937$	2.49824	−	17.3757i	0.0816140	−	0.567638i	0.989065	−	0.147480i	$-0.0471163\pi$
$938$	0.430869	+	0.943471i	0.0140684	+	0.0308054i
$939$	2.04090	+	14.1947i	0.0666021	+	0.463228i
$940$	3.50423	−	2.25203i	0.114295	−	0.0734532i
$941$	−16.2084	+	18.7055i	−0.528378	+	0.609781i	−0.955709	−	0.294315i	$-0.904909\pi$
$941$	−16.2084	+	18.7055i	−0.528378	+	0.609781i	0.427330	+	0.904096i	$0.359454\pi$
$942$	−54.7149			−1.78271
$943$	−30.5982	−	4.74130i	−0.996415	−	0.154398i
$944$	13.3378			0.434108
$945$	0.555060	−	0.640573i	0.0180561	−	0.0208379i
$946$	40.7458	−	26.1857i	1.32476	−	0.851371i
$947$	−3.16858	−	22.0379i	−0.102965	−	0.716136i	−0.974268	−	0.225392i	$-0.927634\pi$
$947$	−3.16858	−	22.0379i	−0.102965	−	0.716136i	0.871303	−	0.490745i	$-0.163275\pi$
$948$	2.44255	+	5.34843i	0.0793302	+	0.173709i
$949$	−1.75692	+	12.2196i	−0.0570320	+	0.396666i
$950$	7.28441	−	2.13890i	0.236337	−	0.0693949i
$951$	−7.58911	−	4.87723i	−0.246094	−	0.158155i
$952$	0.686624	−	1.50350i	0.0222536	−	0.0487286i
$953$	−10.9081	−	3.20290i	−0.353347	−	0.103752i	0.100242	−	0.994963i	$-0.468038\pi$
$953$	−10.9081	−	3.20290i	−0.353347	−	0.103752i	−0.453589	+	0.891211i	$0.649856\pi$
$954$	10.7656	+	12.4242i	0.348550	+	0.402248i
$955$	14.5828	+	16.8294i	0.471888	+	0.544587i
$956$	−5.18761	−	1.52322i	−0.167779	−	0.0492644i
$957$	−47.5929	+	104.214i	−1.53846	+	3.36875i
$958$	26.3731	+	16.9489i	0.852075	+	0.547595i
$959$	6.81125	−	1.99996i	0.219947	−	0.0645822i
$960$	0.649702	−	4.51878i	0.0209690	−	0.145843i
$961$	−12.4080	−	27.1697i	−0.400257	−	0.876441i
$962$	−0.239542	−	1.66605i	−0.00772314	−	0.0537156i
$963$	45.5989	−	29.3046i	1.46940	−	0.944329i
$964$	7.37084	−	8.50640i	0.237399	−	0.273973i
$965$	1.44310			0.0464552
$966$	10.7950	+	5.07325i	0.347324	+	0.163229i
$967$	16.1045			0.517887			0.258943	−	0.965893i	$-0.416626\pi$
$967$	16.1045			0.517887			0.258943	+	0.965893i	$0.416626\pi$
$968$	19.8251	−	22.8793i	0.637202	−	0.735370i
$969$	16.1005	−	10.3472i	0.517223	−	0.332399i
$970$	−0.187206	−	1.30205i	−0.00601082	−	0.0418062i
$971$	16.8709	+	36.9422i	0.541414	+	1.18553i	0.960677	+	0.277667i	$0.0895612\pi$
$971$	16.8709	+	36.9422i	0.541414	+	1.18553i	−0.419263	+	0.907865i	$0.637712\pi$
$972$	3.17336	−	22.0712i	0.101786	−	0.707934i
$973$	9.02049	−	2.64866i	0.289184	−	0.0849120i
$974$	−35.9307	−	23.0913i	−1.15129	−	0.739892i
$975$	−7.13163	+	15.6161i	−0.228395	+	0.500115i
$976$	−13.7680	−	4.04265i	−0.440703	−	0.129402i
$977$	−33.0957	−	38.1944i	−1.05882	−	1.22195i	−0.974236	−	0.225532i	$-0.927588\pi$
$977$	−33.0957	−	38.1944i	−1.05882	−	1.22195i	−0.0845880	−	0.996416i	$-0.526957\pi$
$978$	−24.7530	−	28.5665i	−0.791514	−	0.913456i
$979$	−61.3892	−	18.0255i	−1.96201	−	0.576097i
$980$	−0.762523	+	1.66969i	−0.0243579	+	0.0533364i
$981$	−2.08072	−	1.33720i	−0.0664324	−	0.0426935i
$982$	−34.7149	+	10.1932i	−1.10780	+	0.325278i
$983$	−5.94643	+	41.3584i	−0.189662	+	1.31913i	0.643222	+	0.765679i	$0.277597\pi$
$983$	−5.94643	+	41.3584i	−0.189662	+	1.31913i	−0.832884	+	0.553447i	$0.813312\pi$
$984$	6.67052	+	14.6064i	0.212648	+	0.465635i
$985$	0.957430	+	6.65907i	0.0305062	+	0.212176i
$986$	9.96996	−	6.40730i	0.317508	−	0.204050i
$987$	3.69604	−	4.26546i	0.117646	−	0.135771i
$988$	−19.7073			−0.626973
$989$	0.395226	−	36.1541i	0.0125675	−	1.14963i
$990$	−37.5671			−1.19396
$991$	32.1411	−	37.0928i	1.02100	−	1.17829i	0.0371448	−	0.999310i	$-0.488174\pi$
$991$	32.1411	−	37.0928i	1.02100	−	1.17829i	0.983852	−	0.178983i	$-0.0572808\pi$
$992$	−0.894714	+	0.574998i	−0.0284072	+	0.0182562i
$993$	−6.34429	−	44.1255i	−0.201330	−	1.40028i
$994$	−5.08352	−	11.1314i	−0.161239	−	0.353065i
$995$	1.08001	−	7.51162i	0.0342385	−	0.238134i
$996$	7.77350	−	2.28251i	0.246313	−	0.0723240i
$997$	23.3208	+	14.9874i	0.738577	+	0.474655i	0.855054	−	0.518538i	$-0.173524\pi$
$997$	23.3208	+	14.9874i	0.738577	+	0.474655i	−0.116477	+	0.993193i	$0.537160\pi$
$998$	1.15206	−	2.52265i	0.0364677	−	0.0798531i
$999$	0.176177	+	0.0517302i	0.00557399	+	0.00163667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.e.85.3	✓	40
23.6	even	11		7406.2.a.bt.1.16		20
23.13	even	11	inner	322.2.i.e.197.3	yes	40
23.17	odd	22		7406.2.a.bs.1.16		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.e.85.3	✓	40	1.1	even	1	trivial
322.2.i.e.197.3	yes	40	23.13	even	11	inner
7406.2.a.bs.1.16		20	23.17	odd	22
7406.2.a.bt.1.16		20	23.6	even	11

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(2.09228 - 1.34463i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.762523 - 1.66969i) q^{5} +(0.353951 - 2.46178i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(1.32337 - 2.89778i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(2.09228 - 1.34463i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.762523 - 1.66969i) q^{5} +(0.353951 - 2.46178i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(1.32337 - 2.89778i) q^{9} +(-1.76122 - 0.517140i) q^{10} +(4.20713 + 4.85528i) q^{11} +(-1.62870 - 1.87962i) q^{12} +(-4.06149 - 1.19256i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(-3.84053 - 2.46816i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.235227 - 1.63604i) q^{17} +(-1.32337 - 2.89778i) q^{18} +(0.662572 + 4.60829i) q^{19} +(-1.54418 + 0.992384i) q^{20} +(-1.62870 + 1.87962i) q^{21} +6.42446 q^{22} +(2.63677 - 4.00593i) q^{23} -2.48710 q^{24} +(1.06787 - 1.23239i) q^{25} +(-3.56099 + 2.28851i) q^{26} +(-0.0657159 - 0.457064i) q^{27} +(0.415415 + 0.909632i) q^{28} +(-1.02042 + 7.09719i) q^{29} +(-4.38032 + 1.28618i) q^{30} +(0.894714 + 0.574998i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(15.3310 + 4.50160i) q^{33} +(-1.08240 - 1.24915i) q^{34} +(1.20204 + 1.38723i) q^{35} +(-3.05662 - 0.897505i) q^{36} +(-0.165185 + 0.361704i) q^{37} +(3.91661 + 2.51705i) q^{38} +(-10.1013 + 2.96602i) q^{39} +(-0.261229 + 1.81689i) q^{40} +(-2.68205 - 5.87287i) q^{41} +(0.353951 + 2.46178i) q^{42} +(6.34229 - 4.07594i) q^{43} +(4.20713 - 4.85528i) q^{44} -5.84751 q^{45} +(-1.30076 - 4.61606i) q^{46} -2.26932 q^{47} +(-1.62870 + 1.87962i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.232070 - 1.61408i) q^{50} +(-1.70770 - 3.73935i) q^{51} +(-0.602413 + 4.18987i) q^{52} +(-4.95145 + 1.45388i) q^{53} +(-0.388460 - 0.249648i) q^{54} +(4.89880 - 10.7269i) q^{55} +(0.959493 + 0.281733i) q^{56} +(7.58272 + 8.75093i) q^{57} +(4.69547 + 5.41886i) q^{58} +(-12.7975 - 3.75769i) q^{59} +(-1.89647 + 4.15269i) q^{60} +(12.0714 + 7.75779i) q^{61} +(1.02047 - 0.299636i) q^{62} +(-0.453367 + 3.15324i) q^{63} +(0.415415 + 0.909632i) q^{64} +(1.10577 + 7.69081i) q^{65} +(13.4418 - 8.63851i) q^{66} +(0.679222 - 0.783864i) q^{67} -1.65286 q^{68} +(0.130383 - 11.9270i) q^{69} +1.83557 q^{70} +(-8.01366 + 9.24826i) q^{71} +(-2.67995 + 1.72230i) q^{72} +(-0.415057 - 2.88678i) q^{73} +(0.165185 + 0.361704i) q^{74} +(0.577182 - 4.01439i) q^{75} +(4.46709 - 1.31166i) q^{76} +(-5.40460 - 3.47333i) q^{77} +(-4.37340 + 9.57641i) q^{78} +(-2.26835 - 0.666047i) q^{79} +(1.20204 + 1.38723i) q^{80} +(5.50642 + 6.35475i) q^{81} +(-6.19478 - 1.81895i) q^{82} +(-1.35321 + 2.96311i) q^{83} +(2.09228 + 1.34463i) q^{84} +(-2.91105 + 0.854761i) q^{85} +(1.07292 - 7.46236i) q^{86} +(7.40807 + 16.2214i) q^{87} +(-0.914296 - 6.35907i) q^{88} +(-8.37800 + 5.38421i) q^{89} +(-3.82930 + 4.41925i) q^{90} +4.23296 q^{91} +(-4.34040 - 2.03983i) q^{92} +2.64515 q^{93} +(-1.48609 + 1.71503i) q^{94} +(7.18921 - 4.62022i) q^{95} +(0.353951 + 2.46178i) q^{96} +(0.297701 + 0.651875i) q^{97} +(0.142315 - 0.989821i) q^{98} +(19.6372 - 5.76599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	\( 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} + 2 q^{12} + 4 q^{13} + 4 q^{14} - 11 q^{15} - 4 q^{16} - 21 q^{17} + 4 q^{19} + 2 q^{20} + 2 q^{21} - 11 q^{23} - 2 q^{24} + 5 q^{25} - 15 q^{26} + 95 q^{27} - 4 q^{28} + 22 q^{30} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 10 q^{34} - 9 q^{35} + 41 q^{37} + 7 q^{38} - 38 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} - 59 q^{43} - 6 q^{45} + 11 q^{46} - 60 q^{47} + 2 q^{48} - 4 q^{49} + 61 q^{50} - 87 q^{51} + 4 q^{52} + 47 q^{53} - 29 q^{54} - 30 q^{55} + 4 q^{56} + 20 q^{57} - 96 q^{59} - 11 q^{60} + 84 q^{61} - 65 q^{62} - 4 q^{64} + 52 q^{65} - 3 q^{66} + 11 q^{67} - 10 q^{68} - 42 q^{69} - 2 q^{70} - 13 q^{71} + 11 q^{72} - 48 q^{73} - 41 q^{74} + 23 q^{75} + 26 q^{76} - 83 q^{78} + 80 q^{79} - 9 q^{80} + 2 q^{81} + 30 q^{82} - 20 q^{83} + 2 q^{84} - 71 q^{85} - 40 q^{86} + 99 q^{87} - 30 q^{89} + 116 q^{90} + 26 q^{91} - 22 q^{92} + 20 q^{93} - 17 q^{94} - 4 q^{95} - 2 q^{96} - 56 q^{97} + 4 q^{98} + 138 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 + 2 * q^12 + 4 * q^13 + 4 * q^14 - 11 * q^15 - 4 * q^16 - 21 * q^17 + 4 * q^19 + 2 * q^20 + 2 * q^21 - 11 * q^23 - 2 * q^24 + 5 * q^25 - 15 * q^26 + 95 * q^27 - 4 * q^28 + 22 * q^30 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 10 * q^34 - 9 * q^35 + 41 * q^37 + 7 * q^38 - 38 * q^39 - 13 * q^40 + 25 * q^41 - 2 * q^42 - 59 * q^43 - 6 * q^45 + 11 * q^46 - 60 * q^47 + 2 * q^48 - 4 * q^49 + 61 * q^50 - 87 * q^51 + 4 * q^52 + 47 * q^53 - 29 * q^54 - 30 * q^55 + 4 * q^56 + 20 * q^57 - 96 * q^59 - 11 * q^60 + 84 * q^61 - 65 * q^62 - 4 * q^64 + 52 * q^65 - 3 * q^66 + 11 * q^67 - 10 * q^68 - 42 * q^69 - 2 * q^70 - 13 * q^71 + 11 * q^72 - 48 * q^73 - 41 * q^74 + 23 * q^75 + 26 * q^76 - 83 * q^78 + 80 * q^79 - 9 * q^80 + 2 * q^81 + 30 * q^82 - 20 * q^83 + 2 * q^84 - 71 * q^85 - 40 * q^86 + 99 * q^87 - 30 * q^89 + 116 * q^90 + 26 * q^91 - 22 * q^92 + 20 * q^93 - 17 * q^94 - 4 * q^95 - 2 * q^96 - 56 * q^97 + 4 * q^98 + 138 * q^99

Introduction

L-functions

Modular forms

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