LMFDB - Embedded newform 322.2.i.e.211.4

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			211.4
Character	$\chi$	$=$	322.211
Dual form			322.2.i.e.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{2} +(3.20046 - 0.939739i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-3.28037 - 2.10817i) q^{5} +(-2.18434 - 2.52086i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(6.83607 - 4.39327i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{2} +(3.20046 - 0.939739i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-3.28037 - 2.10817i) q^{5} +(-2.18434 - 2.52086i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(6.83607 - 4.39327i) q^{9} +(-0.554941 + 3.85970i) q^{10} +(-1.52693 + 3.34350i) q^{11} +(-1.38565 + 3.03414i) q^{12} +(0.481108 - 3.34618i) q^{13} +(-0.841254 + 0.540641i) q^{14} +(-12.4798 - 3.66441i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-0.142967 - 0.164993i) q^{17} +(-6.83607 - 4.39327i) q^{18} +(2.07555 - 2.39532i) q^{19} +(3.74144 - 1.09858i) q^{20} +(-1.38565 - 3.03414i) q^{21} +3.67566 q^{22} +(-2.14172 + 4.29104i) q^{23} +3.33557 q^{24} +(4.23941 + 9.28300i) q^{25} +(-3.24365 + 0.952422i) q^{26} +(11.1970 - 12.9220i) q^{27} +(0.841254 + 0.540641i) q^{28} +(2.71964 + 3.13863i) q^{29} +(1.85105 + 12.8743i) q^{30} +(2.23895 + 0.657415i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(-1.74484 + 12.1356i) q^{33} +(-0.0906919 + 0.198588i) q^{34} +(-1.61986 + 3.54701i) q^{35} +(-1.15646 + 8.04334i) q^{36} +(5.22013 - 3.35478i) q^{37} +(-3.04107 - 0.892940i) q^{38} +(-1.60477 - 11.1614i) q^{39} +(-2.55356 - 2.94696i) q^{40} +(5.39716 + 3.46855i) q^{41} +(-2.18434 + 2.52086i) q^{42} +(2.00778 - 0.589537i) q^{43} +(-1.52693 - 3.34350i) q^{44} -31.6866 q^{45} +(4.79297 + 0.165613i) q^{46} -6.78064 q^{47} +(-1.38565 - 3.03414i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(6.68300 - 7.71260i) q^{50} +(-0.612610 - 0.393700i) q^{51} +(2.21381 + 2.55488i) q^{52} +(0.803989 + 5.59186i) q^{53} +(-16.4057 - 4.81715i) q^{54} +(12.0575 - 7.74892i) q^{55} +(0.142315 - 0.989821i) q^{56} +(4.39175 - 9.61660i) q^{57} +(1.72522 - 3.77771i) q^{58} +(-0.0301153 + 0.209457i) q^{59} +(10.9419 - 7.03195i) q^{60} +(2.40151 + 0.705146i) q^{61} +(-0.332088 - 2.30972i) q^{62} +(-5.32143 - 6.14126i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-8.63252 + 9.96246i) q^{65} +(11.7638 - 3.45417i) q^{66} +(2.10017 + 4.59873i) q^{67} +0.218316 q^{68} +(-2.82202 + 15.7460i) q^{69} +3.89939 q^{70} +(-3.35153 - 7.33884i) q^{71} +(7.79689 - 2.28937i) q^{72} +(-5.08026 + 5.86293i) q^{73} +(-5.22013 - 3.35478i) q^{74} +(22.2916 + 25.7259i) q^{75} +(0.451061 + 3.13720i) q^{76} +(3.52677 + 1.03555i) q^{77} +(-9.48614 + 6.09637i) q^{78} +(-0.900001 + 6.25965i) q^{79} +(-1.61986 + 3.54701i) q^{80} +(13.5652 - 29.7036i) q^{81} +(0.913038 - 6.35032i) q^{82} +(-10.9994 + 7.06888i) q^{83} +(3.20046 + 0.939739i) q^{84} +(0.121153 + 0.842636i) q^{85} +(-1.37032 - 1.58144i) q^{86} +(11.6536 + 7.48931i) q^{87} +(-2.40705 + 2.77788i) q^{88} +(17.9303 - 5.26482i) q^{89} +(13.1631 + 28.8232i) q^{90} -3.38059 q^{91} +(-1.84043 - 4.42864i) q^{92} +7.78347 q^{93} +(2.81678 + 6.16789i) q^{94} +(-11.8583 + 3.48192i) q^{95} +(-2.18434 + 2.52086i) q^{96} +(-12.1133 - 7.78473i) q^{97} +(0.654861 + 0.755750i) q^{98} +(4.25075 + 29.5646i) 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 $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$

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 $

$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$3$	3.20046	−	0.939739i	1.84779	−	0.542559i	0.847862	−	0.530217i	$-0.177890\pi$
$3$	3.20046	−	0.939739i	1.84779	−	0.542559i	0.999924	−	0.0123418i	$-0.00392861\pi$
$4$	−0.654861	+	0.755750i	−0.327430	+	0.377875i
$5$	−3.28037	−	2.10817i	−1.46703	−	0.942802i	−0.998228	−	0.0594970i	$-0.981050\pi$
$5$	−3.28037	−	2.10817i	−1.46703	−	0.942802i	−0.468799	−	0.883305i	$-0.655313\pi$
$6$	−2.18434	−	2.52086i	−0.891751	−	1.02914i
$7$	−0.142315	−	0.989821i	−0.0537900	−	0.374117i
$7$	−0.142315	−	0.989821i	−0.0537900	−	0.374117i
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	6.83607	−	4.39327i	2.27869	−	1.46442i
$10$	−0.554941	+	3.85970i	−0.175488	+	1.22054i
$11$	−1.52693	+	3.34350i	−0.460385	+	1.00810i	0.527014	+	0.849856i	$0.323311\pi$
$11$	−1.52693	+	3.34350i	−0.460385	+	1.00810i	−0.987400	+	0.158247i	$0.949416\pi$
$12$	−1.38565	+	3.03414i	−0.400002	+	0.875882i
$13$	0.481108	−	3.34618i	0.133435	−	0.928063i	−0.807594	−	0.589739i	$-0.799231\pi$
$13$	0.481108	−	3.34618i	0.133435	−	0.928063i	0.941030	−	0.338324i	$-0.109860\pi$
$14$	−0.841254	+	0.540641i	−0.224834	+	0.144492i
$15$	−12.4798	−	3.66441i	−3.22228	−	0.946146i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	−0.142967	−	0.164993i	−0.0346746	−	0.0400166i	0.738147	−	0.674639i	$-0.235701\pi$
$17$	−0.142967	−	0.164993i	−0.0346746	−	0.0400166i	−0.772822	+	0.634623i	$0.781155\pi$
$18$	−6.83607	−	4.39327i	−1.61128	−	1.03550i
$19$	2.07555	−	2.39532i	0.476165	−	0.549524i	−0.465951	−	0.884810i	$-0.654288\pi$
$19$	2.07555	−	2.39532i	0.476165	−	0.549524i	0.942116	+	0.335287i	$0.108833\pi$
$20$	3.74144	−	1.09858i	0.836610	−	0.245651i
$21$	−1.38565	−	3.03414i	−0.302373	−	0.662104i
$22$	3.67566			0.783654
$23$	−2.14172	+	4.29104i	−0.446579	+	0.894744i
$23$	−2.14172	+	4.29104i	−0.446579	+	0.894744i
$24$	3.33557			0.680871
$25$	4.23941	+	9.28300i	0.847881	+	1.85660i
$26$	−3.24365	+	0.952422i	−0.636132	+	0.186785i
$27$	11.1970	−	12.9220i	2.15487	−	2.48685i
$28$	0.841254	+	0.540641i	0.158982	+	0.102172i
$29$	2.71964	+	3.13863i	0.505025	+	0.582830i	0.949818	−	0.312804i	$-0.101268\pi$
$29$	2.71964	+	3.13863i	0.505025	+	0.582830i	−0.444793	+	0.895633i	$0.646723\pi$
$30$	1.85105	+	12.8743i	0.337953	+	2.35052i
$31$	2.23895	+	0.657415i	0.402127	+	0.118075i	0.476541	−	0.879152i	$-0.341890\pi$
$31$	2.23895	+	0.657415i	0.402127	+	0.118075i	−0.0744136	+	0.997227i	$0.523709\pi$
$32$	−0.841254	+	0.540641i	−0.148714	+	0.0955727i
$33$	−1.74484	+	12.1356i	−0.303738	+	2.11255i
$34$	−0.0906919	+	0.198588i	−0.0155535	+	0.0340575i
$35$	−1.61986	+	3.54701i	−0.273807	+	0.599554i
$36$	−1.15646	+	8.04334i	−0.192743	+	1.34056i
$37$	5.22013	−	3.35478i	0.858185	−	0.551522i	−0.0359329	−	0.999354i	$-0.511440\pi$
$37$	5.22013	−	3.35478i	0.858185	−	0.551522i	0.894117	+	0.447832i	$0.147804\pi$
$38$	−3.04107	−	0.892940i	−0.493327	−	0.144854i
$39$	−1.60477	−	11.1614i	−0.256969	−	1.78726i
$40$	−2.55356	−	2.94696i	−0.403753	−	0.465955i
$41$	5.39716	+	3.46855i	0.842895	+	0.541696i	0.889351	−	0.457224i	$-0.151156\pi$
$41$	5.39716	+	3.46855i	0.842895	+	0.541696i	−0.0464561	+	0.998920i	$0.514793\pi$
$42$	−2.18434	+	2.52086i	−0.337050	+	0.388977i
$43$	2.00778	−	0.589537i	0.306184	−	0.0899036i	−0.125031	−	0.992153i	$-0.539903\pi$
$43$	2.00778	−	0.589537i	0.306184	−	0.0899036i	0.431215	+	0.902249i	$0.358085\pi$
$44$	−1.52693	−	3.34350i	−0.230193	−	0.504052i
$45$	−31.6866			−4.72356
$46$	4.79297	+	0.165613i	0.706685	+	0.0244183i
$47$	−6.78064			−0.989059			−0.494529	−	0.869161i	$-0.664660\pi$
$47$	−6.78064			−0.989059			−0.494529	+	0.869161i	$0.664660\pi$
$48$	−1.38565	−	3.03414i	−0.200001	−	0.437941i
$49$	−0.959493	+	0.281733i	−0.137070	+	0.0402475i
$50$	6.68300	−	7.71260i	0.945119	−	1.09073i
$51$	−0.612610	−	0.393700i	−0.0857825	−	0.0551291i
$52$	2.21381	+	2.55488i	0.307001	+	0.354298i
$53$	0.803989	+	5.59186i	0.110436	+	0.768102i	0.967496	+	0.252885i	$0.0813794\pi$
$53$	0.803989	+	5.59186i	0.110436	+	0.768102i	−0.857060	+	0.515217i	$0.827711\pi$
$54$	−16.4057	−	4.81715i	−2.23253	−	0.655531i
$55$	12.0575	−	7.74892i	1.62584	−	1.04486i
$56$	0.142315	−	0.989821i	0.0190176	−	0.132270i
$57$	4.39175	−	9.61660i	0.581702	−	1.27375i
$58$	1.72522	−	3.77771i	0.226533	−	0.496037i
$59$	−0.0301153	+	0.209457i	−0.00392068	+	0.0272690i	−0.991688	−	0.128667i	$-0.958930\pi$
$59$	−0.0301153	+	0.209457i	−0.00392068	+	0.0272690i	0.987767	+	0.155936i	$0.0498393\pi$
$60$	10.9419	−	7.03195i	1.41260	−	0.907821i
$61$	2.40151	+	0.705146i	0.307482	+	0.0902847i	0.431833	−	0.901953i	$-0.357867\pi$
$61$	2.40151	+	0.705146i	0.307482	+	0.0902847i	−0.124352	+	0.992238i	$0.539685\pi$
$62$	−0.332088	−	2.30972i	−0.0421752	−	0.293335i
$63$	−5.32143	−	6.14126i	−0.670437	−	0.773726i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−8.63252	+	9.96246i	−1.07073	+	1.23569i
$66$	11.7638	−	3.45417i	1.44802	−	0.425178i
$67$	2.10017	+	4.59873i	0.256576	+	0.561824i	0.993458	−	0.114198i	$-0.0364297\pi$
$67$	2.10017	+	4.59873i	0.256576	+	0.561824i	−0.736882	+	0.676022i	$0.763702\pi$
$68$	0.218316			0.0264748
$69$	−2.82202	+	15.7460i	−0.339732	+	1.89559i
$70$	3.89939			0.466066
$71$	−3.35153	−	7.33884i	−0.397754	−	0.870960i	−0.997493	−	0.0707640i	$-0.977456\pi$
$71$	−3.35153	−	7.33884i	−0.397754	−	0.870960i	0.599739	−	0.800196i	$-0.295271\pi$
$72$	7.79689	−	2.28937i	0.918872	−	0.269805i
$73$	−5.08026	+	5.86293i	−0.594599	+	0.686204i	−0.970678	−	0.240384i	$-0.922727\pi$
$73$	−5.08026	+	5.86293i	−0.594599	+	0.686204i	0.376079	+	0.926588i	$0.377272\pi$
$74$	−5.22013	−	3.35478i	−0.606828	−	0.389985i
$75$	22.2916	+	25.7259i	2.57402	+	2.97057i
$76$	0.451061	+	3.13720i	0.0517403	+	0.359861i
$77$	3.52677	+	1.03555i	0.401913	+	0.118012i
$78$	−9.48614	+	6.09637i	−1.07409	+	0.690278i
$79$	−0.900001	+	6.25965i	−0.101258	+	0.704265i	0.874438	+	0.485137i	$0.161230\pi$
$79$	−0.900001	+	6.25965i	−0.101258	+	0.704265i	−0.975696	+	0.219128i	$0.929679\pi$
$80$	−1.61986	+	3.54701i	−0.181106	+	0.396568i
$81$	13.5652	−	29.7036i	1.50724	−	3.30040i
$82$	0.913038	−	6.35032i	0.100828	−	0.701275i
$83$	−10.9994	+	7.06888i	−1.20734	+	0.775910i	−0.980211	−	0.197955i	$-0.936570\pi$
$83$	−10.9994	+	7.06888i	−1.20734	+	0.775910i	−0.227128	+	0.973865i	$0.572934\pi$
$84$	3.20046	+	0.939739i	0.349199	+	0.102534i
$85$	0.121153	+	0.842636i	0.0131409	+	0.0913967i
$86$	−1.37032	−	1.58144i	−0.147766	−	0.170531i
$87$	11.6536	+	7.48931i	1.24940	+	0.802939i
$88$	−2.40705	+	2.77788i	−0.256592	+	0.296123i
$89$	17.9303	−	5.26482i	1.90061	−	0.558070i	0.911410	−	0.411499i	$-0.134995\pi$
$89$	17.9303	−	5.26482i	1.90061	−	0.558070i	0.989200	−	0.146571i	$-0.0468237\pi$
$90$	13.1631	+	28.8232i	1.38751	+	3.03823i
$91$	−3.38059			−0.354382
$92$	−1.84043	−	4.42864i	−0.191878	−	0.461717i
$93$	7.78347			0.807108
$94$	2.81678	+	6.16789i	0.290529	+	0.636169i
$95$	−11.8583	+	3.48192i	−1.21664	+	0.357237i
$96$	−2.18434	+	2.52086i	−0.222938	+	0.257284i
$97$	−12.1133	−	7.78473i	−1.22992	−	0.790420i	−0.246039	−	0.969260i	$-0.579129\pi$
$97$	−12.1133	−	7.78473i	−1.22992	−	0.790420i	−0.983878	+	0.178840i	$0.942765\pi$
$98$	0.654861	+	0.755750i	0.0661509	+	0.0763422i
$99$	4.25075	+	29.5646i	0.427216	+	2.97135i
$100$	−9.79185	−	2.87515i	−0.979185	−	0.287515i
$101$	9.72668	−	6.25096i	0.967841	−	0.621994i	0.0416837	−	0.999131i	$-0.486728\pi$
$101$	9.72668	−	6.25096i	0.967841	−	0.621994i	0.926157	+	0.377137i	$0.123091\pi$
$102$	−0.103635	+	0.720798i	−0.0102614	+	0.0713697i
$103$	−3.37148	+	7.38251i	−0.332202	+	0.727420i	−0.999855	−	0.0170526i	$-0.994572\pi$
$103$	−3.37148	+	7.38251i	−0.332202	+	0.727420i	0.667653	+	0.744473i	$0.267299\pi$
$104$	1.40435	−	3.07509i	0.137708	−	0.301538i
$105$	−1.85105	+	12.8743i	−0.180644	+	1.25640i
$106$	4.75255	−	3.05428i	0.461608	−	0.296658i
$107$	7.92684	+	2.32753i	0.766317	+	0.225011i	0.641452	−	0.767163i	$-0.278332\pi$
$107$	7.92684	+	2.32753i	0.766317	+	0.225011i	0.124864	+	0.992174i	$0.460150\pi$
$108$	2.43334	+	16.9243i	0.234148	+	1.62854i
$109$	−3.34915	−	3.86513i	−0.320790	−	0.370212i	0.572335	−	0.820020i	$-0.306038\pi$
$109$	−3.34915	−	3.86513i	−0.320790	−	0.370212i	−0.893125	+	0.449808i	$0.851492\pi$
$110$	−12.0575	−	7.74892i	−1.14964	−	0.738830i
$111$	13.5542	−	15.6424i	1.28651	−	1.48471i
$112$	−0.959493	+	0.281733i	−0.0906636	+	0.0266212i
$113$	−3.25814	−	7.13433i	−0.306500	−	0.671141i	0.692222	−	0.721685i	$-0.256632\pi$
$113$	−3.25814	−	7.13433i	−0.306500	−	0.671141i	−0.998722	+	0.0505435i	$0.983905\pi$
$114$	−10.5720			−0.990155
$115$	16.0719	−	9.56112i	1.49871	−	0.891579i
$116$	−4.15301			−0.385597
$117$	−11.4118	−	24.9883i	−1.05502	−	2.31017i
$118$	0.203039	−	0.0596176i	0.0186913	−	0.00548825i
$119$	−0.142967	+	0.164993i	−0.0131058	+	0.0151248i
$120$	−10.9419	−	7.03195i	−0.998857	−	0.641926i
$121$	−1.64403	−	1.89731i	−0.149457	−	0.172482i
$122$	−0.356199	−	2.47742i	−0.0322487	−	0.224295i
$123$	20.5329	+	6.02901i	1.85139	+	0.543618i
$124$	−1.96304	+	1.26157i	−0.176286	+	0.113292i
$125$	2.88859	−	20.0906i	0.258364	−	1.79696i
$126$	−3.37568	+	7.39171i	−0.300730	+	0.658506i
$127$	−5.93800	+	13.0024i	−0.526912	+	1.15378i	0.439844	+	0.898074i	$0.355034\pi$
$127$	−5.93800	+	13.0024i	−0.526912	+	1.15378i	−0.966756	+	0.255702i	$0.917693\pi$
$128$	0.142315	−	0.989821i	0.0125790	−	0.0874887i
$129$	5.87181	−	3.77358i	0.516984	−	0.332245i
$130$	12.6483	+	3.71386i	1.10933	+	0.325727i
$131$	0.853351	+	5.93519i	0.0745576	+	0.518560i	0.992538	+	0.121934i	$0.0389097\pi$
$131$	0.853351	+	5.93519i	0.0745576	+	0.518560i	−0.917981	+	0.396625i	$0.870181\pi$
$132$	−8.02888	−	9.26582i	−0.698824	−	0.806486i
$133$	−2.66632	−	1.71354i	−0.231199	−	0.148583i
$134$	3.31071	−	3.82076i	0.286002	−	0.330064i
$135$	−63.9722	+	18.7839i	−5.50585	+	1.61666i
$136$	−0.0906919	−	0.198588i	−0.00777677	−	0.0170287i
$137$	−16.7334			−1.42963			−0.714813	−	0.699315i	$-0.753488\pi$
$137$	−16.7334			−1.42963			−0.714813	+	0.699315i	$0.753488\pi$
$138$	15.4953	−	3.97411i	1.31905	−	0.338298i
$139$	−8.62071			−0.731199			−0.365600	−	0.930772i	$-0.619136\pi$
$139$	−8.62071			−0.731199			−0.365600	+	0.930772i	$0.619136\pi$
$140$	−1.61986	−	3.54701i	−0.136904	−	0.299777i
$141$	−21.7012	+	6.37204i	−1.82757	+	0.536623i
$142$	−5.28336	+	6.09732i	−0.443370	+	0.511676i
$143$	10.4533	+	6.71795i	0.874152	+	0.561783i
$144$	−5.32143	−	6.14126i	−0.443452	−	0.511771i
$145$	−2.30467	−	16.0294i	−0.191393	−	1.33117i
$146$	7.44352	+	2.18562i	0.616030	+	0.180883i
$147$	−2.80606	+	1.80335i	−0.231440	+	0.148738i
$148$	−0.883090	+	6.14202i	−0.0725895	+	0.504871i
$149$	−0.387266	+	0.847995i	−0.0317261	+	0.0694704i	−0.924832	−	0.380377i	$-0.875794\pi$
$149$	−0.387266	+	0.847995i	−0.0317261	+	0.0694704i	0.893106	+	0.449847i	$0.148522\pi$
$150$	14.1408	−	30.9641i	1.15460	−	2.52821i
$151$	−0.373430	+	2.59726i	−0.0303893	+	0.211362i	−0.999358	−	0.0358203i	$-0.988596\pi$
$151$	−0.373430	+	2.59726i	−0.0303893	+	0.211362i	0.968969	+	0.247182i	$0.0795047\pi$
$152$	2.66632	−	1.71354i	0.216267	−	0.138986i
$153$	−1.70219	−	0.499808i	−0.137614	−	0.0404070i
$154$	−0.523101	−	3.63825i	−0.0421527	−	0.293179i
$155$	−5.95866	−	6.87665i	−0.478611	−	0.552346i
$156$	9.48614	+	6.09637i	0.759499	+	0.488101i
$157$	−2.03190	+	2.34493i	−0.162163	+	0.187146i	−0.831016	−	0.556249i	$-0.812240\pi$
$157$	−2.03190	+	2.34493i	−0.162163	+	0.187146i	0.668853	+	0.743395i	$0.266786\pi$
$158$	6.06785	−	1.78168i	0.482732	−	0.141743i
$159$	7.82803	+	17.1410i	0.620803	+	1.35937i
$160$	3.89939			0.308274
$161$	4.55216	+	1.50924i	0.358761	+	0.118945i
$162$	−32.6545			−2.56558
$163$	−4.94298	−	10.8236i	−0.387164	−	0.847772i	−0.998412	−	0.0563324i	$-0.982059\pi$
$163$	−4.94298	−	10.8236i	−0.387164	−	0.847772i	0.611248	−	0.791439i	$-0.290668\pi$
$164$	−6.15574	+	1.80749i	−0.480683	+	0.141141i
$165$	31.3077	−	36.1310i	2.43730	−	2.81280i
$166$	10.9994	+	7.06888i	0.853718	+	0.548651i
$167$	−14.7927	−	17.0717i	−1.14469	−	1.32105i	−0.939588	−	0.342308i	$-0.888791\pi$
$167$	−14.7927	−	17.0717i	−1.14469	−	1.32105i	−0.205107	−	0.978740i	$-0.565754\pi$
$168$	−0.474702	−	3.30162i	−0.0366240	−	0.254726i
$169$	1.50796	+	0.442777i	0.115997	+	0.0340597i
$170$	0.716160	−	0.460248i	0.0549269	−	0.0352994i
$171$	3.66534	−	25.4930i	0.280296	−	1.94950i
$172$	−0.869274	+	1.90344i	−0.0662815	+	0.145136i
$173$	−7.24121	+	15.8560i	−0.550539	+	1.20551i	0.405991	+	0.913877i	$0.366927\pi$
$173$	−7.24121	+	15.8560i	−0.550539	+	1.20551i	−0.956530	+	0.291635i	$0.905801\pi$
$174$	1.97144	−	13.7117i	0.149454	−	1.03948i
$175$	8.58519	−	5.51736i	0.648979	−	0.417073i
$176$	3.52677	+	1.03555i	0.265840	+	0.0780578i
$177$	0.100452	+	0.698659i	0.00755043	+	0.0525144i
$178$	−12.2376	−	14.1229i	−0.917245	−	1.05856i
$179$	−8.66927	−	5.57140i	−0.647972	−	0.416426i	0.174953	−	0.984577i	$-0.444023\pi$
$179$	−8.66927	−	5.57140i	−0.647972	−	0.416426i	−0.822925	+	0.568151i	$0.807659\pi$
$180$	20.7503	−	23.9471i	1.54664	−	1.78491i
$181$	20.6474	−	6.06263i	1.53471	−	0.450632i	0.598222	−	0.801330i	$-0.295874\pi$
$181$	20.6474	−	6.06263i	1.53471	−	0.450632i	0.936489	+	0.350698i	$0.114056\pi$
$182$	1.40435	+	3.07509i	0.104097	+	0.227941i
$183$	8.34858			0.617145
$184$	−3.26389	+	3.51383i	−0.240617	+	0.259043i
$185$	−24.1964			−1.77896
$186$	−3.23337	−	7.08009i	−0.237082	−	0.519138i
$187$	0.769952	−	0.226078i	0.0563045	−	0.0165325i
$188$	4.44038	−	5.12447i	0.323848	−	0.373740i
$189$	−14.3840	−	9.24404i	−1.04628	−	0.672405i
$190$	8.09339	+	9.34028i	0.587157	+	0.677615i
$191$	−0.951934	−	6.62084i	−0.0688795	−	0.479067i	−0.994841	−	0.101449i	$-0.967652\pi$
$191$	−0.951934	−	6.62084i	−0.0688795	−	0.479067i	0.925961	−	0.377619i	$-0.123257\pi$
$192$	3.20046	+	0.939739i	0.230973	+	0.0678199i
$193$	−21.1165	+	13.5708i	−1.52000	+	0.976846i	−0.528192	+	0.849125i	$0.677130\pi$
$193$	−21.1165	+	13.5708i	−1.52000	+	0.976846i	−0.991810	+	0.127721i	$0.959234\pi$
$194$	−2.04920	+	14.2525i	−0.147124	+	1.02327i
$195$	−18.2659	+	39.9968i	−1.30805	+	2.86423i
$196$	0.415415	−	0.909632i	0.0296725	−	0.0649737i
$197$	1.34123	−	9.32847i	0.0955587	−	0.664626i	−0.884591	−	0.466367i	$-0.845562\pi$
$197$	1.34123	−	9.32847i	0.0955587	−	0.664626i	0.980150	−	0.198258i	$-0.0635285\pi$
$198$	25.1271	−	16.1482i	1.78570	−	1.14760i
$199$	9.56785	+	2.80937i	0.678247	+	0.199151i	0.602672	−	0.797989i	$-0.294103\pi$
$199$	9.56785	+	2.80937i	0.678247	+	0.199151i	0.0755748	+	0.997140i	$0.475921\pi$
$200$	1.45236	+	10.1014i	0.102697	+	0.714274i
$201$	11.0431	+	12.7444i	0.778921	+	0.898923i
$202$	−9.72668	−	6.25096i	−0.684367	−	0.439816i
$203$	2.71964	−	3.13863i	0.190881	−	0.220289i
$204$	0.698713	−	0.205161i	0.0489197	−	0.0143641i
$205$	−10.3924	−	22.7563i	−0.725839	−	1.58937i
$206$	8.11593			0.565463
$207$	4.21078	+	38.7430i	0.292670	+	2.69282i
$208$	−3.38059			−0.234402
$209$	4.83953	+	10.5971i	0.334757	+	0.733016i
$210$	12.4798	−	3.66441i	0.861190	−	0.252868i
$211$	−7.40800	+	8.54929i	−0.509988	+	0.588557i	−0.951095	−	0.308897i	$-0.900040\pi$
$211$	−7.40800	+	8.54929i	−0.509988	+	0.588557i	0.441108	+	0.897454i	$0.354586\pi$
$212$	−4.75255	−	3.05428i	−0.326406	−	0.209769i
$213$	−17.6230	−	20.3381i	−1.20751	−	1.39354i
$214$	−1.17573	−	8.17740i	−0.0803714	−	0.558995i
$215$	−7.82911	−	2.29884i	−0.533941	−	0.156779i
$216$	14.3840	−	9.24404i	0.978708	−	0.628977i
$217$	0.332088	−	2.30972i	0.0225436	−	0.156794i
$218$	−2.12455	+	4.65213i	−0.143893	+	0.315082i
$219$	−10.7495	+	23.5382i	−0.726386	+	1.59056i
$220$	−2.03978	+	14.1869i	−0.137522	+	0.956484i
$221$	−0.620877	+	0.399014i	−0.0417647	+	0.0268406i
$222$	−19.8594	−	5.83126i	−1.33288	−	0.391368i
$223$	3.31988	+	23.0902i	0.222315	+	1.54624i	0.729247	+	0.684251i	$0.239871\pi$
$223$	3.31988	+	23.0902i	0.222315	+	1.54624i	−0.506931	+	0.861986i	$0.669220\pi$
$224$	0.654861	+	0.755750i	0.0437547	+	0.0504956i
$225$	69.7636	+	44.8344i	4.65091	+	2.98896i
$226$	−5.13613	+	5.92741i	−0.341651	+	0.394286i
$227$	7.53467	−	2.21238i	0.500094	−	0.146841i	−0.0219508	−	0.999759i	$-0.506988\pi$
$227$	7.53467	−	2.21238i	0.500094	−	0.146841i	0.522044	+	0.852918i	$0.325170\pi$
$228$	4.39175	+	9.61660i	0.290851	+	0.636875i
$229$	−10.2591			−0.677942			−0.338971	−	0.940797i	$-0.610079\pi$
$229$	−10.2591			−0.677942			−0.338971	+	0.940797i	$0.610079\pi$
$230$	−15.3736	−	10.6477i	−1.01371	−	0.702086i
$231$	12.2604			0.806678
$232$	1.72522	+	3.77771i	0.113266	+	0.248019i
$233$	−10.2751	+	3.01703i	−0.673141	+	0.197652i	−0.600401	−	0.799699i	$-0.704992\pi$
$233$	−10.2751	+	3.01703i	−0.673141	+	0.197652i	−0.0727398	+	0.997351i	$0.523174\pi$
$234$	−17.9896	+	20.7611i	−1.17601	+	1.35719i
$235$	22.2431	+	14.2947i	1.45098	+	0.932486i
$236$	−0.138576	−	0.159925i	−0.00902050	−	0.0104102i
$237$	3.00202	+	20.8795i	0.195002	+	1.35627i
$238$	0.209473	+	0.0615069i	0.0135781	+	0.00398690i
$239$	−8.99639	+	5.78163i	−0.581928	+	0.373982i	−0.798238	−	0.602342i	$-0.794234\pi$
$239$	−8.99639	+	5.78163i	−0.581928	+	0.373982i	0.216310	+	0.976325i	$0.430598\pi$
$240$	−1.85105	+	12.8743i	−0.119484	+	0.831033i
$241$	−0.606514	+	1.32808i	−0.0390690	+	0.0855491i	−0.928160	−	0.372181i	$-0.878610\pi$
$241$	−0.606514	+	1.32808i	−0.0390690	+	0.0855491i	0.889091	+	0.457730i	$0.151337\pi$
$242$	−1.04290	+	2.28363i	−0.0670400	+	0.146797i
$243$	8.20111	−	57.0400i	0.526102	−	3.65912i
$244$	−2.10557	+	1.35317i	−0.134795	+	0.0866276i
$245$	3.74144	+	1.09858i	0.239032	+	0.0701860i
$246$	−3.04550	−	21.1820i	−0.194174	−	1.35051i
$247$	−7.01660	−	8.09759i	−0.446455	−	0.515237i
$248$	1.96304	+	1.26157i	0.124653	+	0.0801098i
$249$	−28.5602	+	32.9602i	−1.80993	+	2.08877i
$250$	−19.4750	+	5.71839i	−1.23171	+	0.361662i
$251$	0.806725	+	1.76648i	0.0509200	+	0.111499i	0.933382	−	0.358884i	$-0.116843\pi$
$251$	0.806725	+	1.76648i	0.0509200	+	0.111499i	−0.882462	+	0.470384i	$0.844116\pi$
$252$	8.12605			0.511893
$253$	−11.0769	−	13.7129i	−0.696396	−	0.862125i
$254$	14.2941			0.896894
$255$	1.17960	+	2.58297i	0.0738696	+	0.161752i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	15.1196	−	17.4489i	0.943133	−	1.08843i	−0.0528237	−	0.998604i	$-0.516822\pi$
$257$	15.1196	−	17.4489i	0.943133	−	1.08843i	0.995957	−	0.0898301i	$-0.0286324\pi$
$258$	−5.87181	−	3.77358i	−0.365563	−	0.234933i
$259$	−4.06353	−	4.68957i	−0.252496	−	0.291395i
$260$	−1.87603	−	13.0481i	−0.116346	−	0.809206i
$261$	32.3805	+	9.50778i	2.00430	+	0.588517i
$262$	5.04434	−	3.24180i	0.311640	−	0.200279i
$263$	3.06909	−	21.3460i	0.189248	−	1.31625i	−0.644712	−	0.764425i	$-0.723023\pi$
$263$	3.06909	−	21.3460i	0.189248	−	1.31625i	0.833961	−	0.551824i	$-0.186068\pi$
$264$	−5.09317	+	11.1525i	−0.313463	+	0.686388i
$265$	9.15121	−	20.0383i	0.562154	−	1.23095i
$266$	−0.451061	+	3.13720i	−0.0276563	+	0.192354i
$267$	52.4377	−	33.6997i	3.20914	−	2.06239i
$268$	−4.85081	−	1.42433i	−0.296310	−	0.0870045i
$269$	−4.53693	−	31.5550i	−0.276621	−	1.92394i	−0.371456	−	0.928451i	$-0.621141\pi$
$269$	−4.53693	−	31.5550i	−0.276621	−	1.92394i	0.0948348	−	0.995493i	$-0.469768\pi$
$270$	43.6615	+	50.3880i	2.65715	+	3.06652i
$271$	7.67758	+	4.93408i	0.466380	+	0.299724i	0.752645	−	0.658426i	$-0.228778\pi$
$271$	7.67758	+	4.93408i	0.466380	+	0.299724i	−0.286266	+	0.958150i	$0.592414\pi$
$272$	−0.142967	+	0.164993i	−0.00866864	+	0.0100041i
$273$	−10.8194	+	3.17687i	−0.654822	+	0.192273i
$274$	6.95128	+	15.2212i	0.419942	+	0.919546i
$275$	−37.5110			−2.26200
$276$	−10.0520	−	12.4442i	−0.605058	−	0.749050i
$277$	−1.55360			−0.0933466			−0.0466733	−	0.998910i	$-0.514862\pi$
$277$	−1.55360			−0.0933466			−0.0466733	+	0.998910i	$0.514862\pi$
$278$	3.58117	+	7.84168i	0.214785	+	0.470313i
$279$	18.1938	−	5.34219i	1.08924	−	0.319828i
$280$	−2.55356	+	2.94696i	−0.152604	+	0.176115i
$281$	−8.00033	−	5.14150i	−0.477260	−	0.306716i	0.279804	−	0.960057i	$-0.409730\pi$
$281$	−8.00033	−	5.14150i	−0.477260	−	0.306716i	−0.757064	+	0.653341i	$0.773367\pi$
$282$	14.8112	+	17.0930i	0.881994	+	1.01788i
$283$	−1.24998	−	8.69381i	−0.0743037	−	0.516793i	−0.992650	−	0.121017i	$-0.961385\pi$
$283$	−1.24998	−	8.69381i	−0.0743037	−	0.516793i	0.918347	−	0.395777i	$-0.129525\pi$
$284$	7.74111	+	2.27299i	0.459350	+	0.134877i
$285$	−34.6800	+	22.2875i	−2.05427	+	1.32020i
$286$	1.76839	−	12.2994i	0.104567	−	0.727280i
$287$	2.66515	−	5.83585i	0.157319	−	0.344480i
$288$	−3.37568	+	7.39171i	−0.198914	+	0.435561i
$289$	2.41257	−	16.7798i	0.141916	−	0.987046i
$290$	−13.6234	+	8.75524i	−0.799995	+	0.514125i
$291$	−46.0837	−	13.5314i	−2.70147	−	0.793224i
$292$	−1.10405	−	7.67880i	−0.0646094	−	0.449368i
$293$	3.74417	+	4.32101i	0.218737	+	0.252436i	0.854504	−	0.519445i	$-0.173861\pi$
$293$	3.74417	+	4.32101i	0.218737	+	0.252436i	−0.635767	+	0.771881i	$0.719316\pi$
$294$	2.80606	+	1.80335i	0.163653	+	0.105173i
$295$	0.540360	−	0.623609i	0.0314610	−	0.0363079i
$296$	5.95383	−	1.74820i	0.346059	−	0.101612i
$297$	26.1078	+	57.1682i	1.51493	+	3.31723i
$298$	0.932239			0.0540032
$299$	13.3282	+	9.23103i	0.770789	+	0.533844i
$300$	−34.0403			−1.96532
$301$	−0.869274	−	1.90344i	−0.0501041	−	0.109713i
$302$	2.51768	−	0.739258i	0.144876	−	0.0425395i
$303$	25.2556	−	29.1465i	1.45089	−	1.67442i
$304$	−2.66632	−	1.71354i	−0.152924	−	0.0982782i
$305$	−6.39128	−	7.37593i	−0.365963	−	0.422344i
$306$	0.252474	+	1.75599i	0.0144330	+	0.100383i
$307$	19.4915	+	5.72321i	1.11244	+	0.326641i	0.785783	−	0.618503i	$-0.212260\pi$
$307$	19.4915	+	5.72321i	1.11244	+	0.326641i	0.326655	+	0.945144i	$0.394079\pi$
$308$	−3.09216	+	1.98721i	−0.176192	+	0.113232i
$309$	−3.85264	+	26.7957i	−0.219169	+	1.52436i
$310$	−3.77991	+	8.27685i	−0.214684	+	0.470093i
$311$	−8.75771	+	19.1767i	−0.496604	+	1.08741i	0.480954	+	0.876746i	$0.340290\pi$
$311$	−8.75771	+	19.1767i	−0.496604	+	1.08741i	−0.977558	+	0.210666i	$0.932437\pi$
$312$	1.60477	−	11.1614i	0.0908522	−	0.631891i
$313$	−5.84921	+	3.75906i	−0.330617	+	0.212474i	−0.695408	−	0.718615i	$-0.744777\pi$
$313$	−5.84921	+	3.75906i	−0.330617	+	0.212474i	0.364792	+	0.931089i	$0.381140\pi$
$314$	2.97711	+	0.874157i	0.168008	+	0.0493316i
$315$	4.50948	+	31.3641i	0.254080	+	1.76717i
$316$	−4.14135	−	4.77937i	−0.232969	−	0.268861i
$317$	8.29606	+	5.33156i	0.465953	+	0.299450i	0.752472	−	0.658625i	$-0.228862\pi$
$317$	8.29606	+	5.33156i	0.465953	+	0.299450i	−0.286518	+	0.958075i	$0.592498\pi$
$318$	12.3401	−	14.2412i	0.691999	−	0.798610i
$319$	−14.6467	+	4.30066i	−0.820059	+	0.240791i
$320$	−1.61986	−	3.54701i	−0.0905532	−	0.198284i
$321$	27.5568			1.53807
$322$	−0.518183	−	4.76775i	−0.0288772	−	0.265697i
$323$	−0.691945			−0.0385009
$324$	13.5652	+	29.7036i	0.753621	+	1.65020i
$325$	33.1022	−	9.71968i	1.83618	−	0.539151i
$326$	−7.79213	+	8.99259i	−0.431566	+	0.498054i
$327$	−14.3510	−	9.22285i	−0.793614	−	0.510025i
$328$	4.20134	+	4.84860i	0.231980	+	0.267719i
$329$	0.964986	+	6.71163i	0.0532014	+	0.370024i
$330$	−45.8717	−	13.4691i	−2.52515	−	0.741451i
$331$	20.7258	−	13.3197i	1.13920	−	0.732117i	0.171736	−	0.985143i	$-0.445062\pi$
$331$	20.7258	−	13.3197i	1.13920	−	0.732117i	0.967459	+	0.253026i	$0.0814260\pi$
$332$	1.86077	−	12.9419i	0.102123	−	0.710280i
$333$	20.9467	−	45.8669i	1.14787	−	2.51349i
$334$	−9.38385	+	20.5478i	−0.513461	+	1.12432i
$335$	2.80555	−	19.5131i	0.153284	−	1.06611i
$336$	−2.80606	+	1.80335i	−0.153083	+	0.0983806i
$337$	−15.7564	−	4.62650i	−0.858306	−	0.252021i	−0.177172	−	0.984180i	$-0.556695\pi$
$337$	−15.7564	−	4.62650i	−0.858306	−	0.252021i	−0.681134	+	0.732158i	$0.738513\pi$
$338$	−0.223665	−	1.55562i	−0.0121658	−	0.0846148i
$339$	−17.1319	−	19.7713i	−0.930480	−	1.07383i
$340$	−0.716160	−	0.460248i	−0.0388392	−	0.0249604i
$341$	−5.61678	+	6.48211i	−0.304166	+	0.351026i
$342$	−24.7119	+	7.25607i	−1.33627	+	0.392364i
$343$	0.415415	+	0.909632i	0.0224303	+	0.0491155i
$344$	2.09254			0.112822
$345$	42.4524	−	45.7033i	2.28556	−	2.46059i
$346$	17.4313			0.937111
$347$	10.5190	+	23.0334i	0.564691	+	1.23650i	0.949576	+	0.313536i	$0.101514\pi$
$347$	10.5190	+	23.0334i	0.564691	+	1.23650i	−0.384886	+	0.922964i	$0.625759\pi$
$348$	−13.2915	+	3.90275i	−0.712501	+	0.209209i
$349$	−14.2286	+	16.4207i	−0.761642	+	0.878981i	−0.995642	−	0.0932552i	$-0.970273\pi$
$349$	−14.2286	+	16.4207i	−0.761642	+	0.878981i	0.234001	+	0.972236i	$0.424818\pi$
$350$	−8.58519	−	5.51736i	−0.458897	−	0.294915i
$351$	−37.8525	−	43.6841i	−2.02042	−	2.33168i
$352$	−0.523101	−	3.63825i	−0.0278814	−	0.193919i
$353$	−22.4910	−	6.60395i	−1.19707	−	0.351493i	−0.378341	−	0.925666i	$-0.623505\pi$
$353$	−22.4910	−	6.60395i	−1.19707	−	0.351493i	−0.818733	+	0.574174i	$0.805323\pi$
$354$	0.593793	−	0.381608i	0.0315597	−	0.0202822i
$355$	−4.47722	+	31.1397i	−0.237626	+	1.65272i
$356$	−7.76298	+	16.9986i	−0.411437	+	0.900922i
$357$	−0.302510	+	0.662404i	−0.0160105	+	0.0350581i
$358$	−1.46658	+	10.2003i	−0.0775112	+	0.539102i
$359$	−25.0286	+	16.0849i	−1.32096	+	0.848930i	−0.995327	−	0.0965654i	$-0.969214\pi$
$359$	−25.0286	+	16.0849i	−1.32096	+	0.848930i	−0.325635	+	0.945496i	$0.605578\pi$
$360$	−30.4031	−	8.92715i	−1.60238	−	0.470502i
$361$	1.27436	+	8.86338i	0.0670717	+	0.466494i
$362$	−14.0920	−	16.2631i	−0.740660	−	0.854767i
$363$	−7.04461	−	4.52730i	−0.369746	−	0.237621i
$364$	2.21381	−	2.55488i	0.116035	−	0.133912i
$365$	29.0252	−	8.52256i	1.51925	−	0.446091i
$366$	−3.46813	−	7.59414i	−0.181282	−	0.396952i
$367$	1.45360			0.0758773			0.0379386	−	0.999280i	$-0.487921\pi$
$367$	1.45360			0.0758773			0.0379386	+	0.999280i	$0.487921\pi$
$368$	4.55216	+	1.50924i	0.237298	+	0.0786746i
$369$	52.1336			2.71397
$370$	10.0516	+	22.0098i	0.522556	+	1.14424i
$371$	5.42053	−	1.59161i	0.281420	−	0.0826323i
$372$	−5.09709	+	5.88235i	−0.264272	+	0.304986i
$373$	3.89557	+	2.50353i	0.201705	+	0.129628i	0.637594	−	0.770372i	$-0.279930\pi$
$373$	3.89557	+	2.50353i	0.201705	+	0.129628i	−0.435889	+	0.900000i	$0.643566\pi$
$374$	−0.525498	−	0.606457i	−0.0271729	−	0.0313591i
$375$	−9.63512	−	67.0137i	−0.497555	−	3.46057i
$376$	−6.50598	−	1.91033i	−0.335520	−	0.0985177i
$377$	11.8109	−	7.59039i	0.608291	−	0.390925i
$378$	−2.43334	+	16.9243i	−0.125158	+	0.870490i
$379$	−5.54543	+	12.1428i	−0.284850	+	0.623734i	−0.996924	−	0.0783697i	$-0.975029\pi$
$379$	−5.54543	+	12.1428i	−0.284850	+	0.623734i	0.712075	+	0.702104i	$0.247756\pi$
$380$	5.13410	−	11.2421i	0.263374	−	0.576708i
$381$	−6.78545	+	47.1938i	−0.347629	+	2.41781i
$382$	−5.62708	+	3.61631i	−0.287907	+	0.185026i
$383$	24.3576	+	7.15205i	1.24462	+	0.365453i	0.836748	−	0.547588i	$-0.184454\pi$
$383$	24.3576	+	7.15205i	1.24462	+	0.365453i	0.407869	+	0.913040i	$0.366272\pi$
$384$	−0.474702	−	3.30162i	−0.0242245	−	0.168485i
$385$	−9.38601	−	10.8320i	−0.478355	−	0.552052i
$386$	21.1165	+	13.5708i	1.07480	+	0.690734i
$387$	11.1353	−	12.8508i	0.566040	−	0.653245i
$388$	13.8158	−	4.05669i	0.701392	−	0.205947i
$389$	9.35957	+	20.4946i	0.474549	+	1.03912i	0.983926	+	0.178574i	$0.0571484\pi$
$389$	9.35957	+	20.4946i	0.474549	+	1.03912i	−0.509377	+	0.860543i	$0.670124\pi$
$390$	43.9703			2.22652
$391$	1.01418	−	0.260109i	0.0512895	−	0.0131543i
$392$	−1.00000			−0.0505076
$393$	8.30865	+	18.1934i	0.419116	+	0.917735i
$394$	−9.04264	+	2.65516i	−0.455562	+	0.133765i
$395$	16.1487	−	18.6366i	0.812531	−	0.937711i
$396$	−25.1271	−	16.1482i	−1.26268	−	0.811477i
$397$	−2.02227	−	2.33383i	−0.101495	−	0.117132i	0.702729	−	0.711457i	$-0.251964\pi$
$397$	−2.02227	−	2.33383i	−0.101495	−	0.117132i	−0.804224	+	0.594326i	$0.797419\pi$
$398$	−1.41913	−	9.87028i	−0.0711347	−	0.494752i
$399$	−10.1437	−	2.97847i	−0.507822	−	0.149110i
$400$	8.58519	−	5.51736i	0.429259	−	0.275868i
$401$	−0.787700	+	5.47858i	−0.0393359	+	0.273587i	−0.999991	−	0.00415573i	$-0.998677\pi$
$401$	−0.787700	+	5.47858i	−0.0393359	+	0.273587i	0.960655	+	0.277743i	$0.0895863\pi$
$402$	7.00527	−	15.3394i	0.349391	−	0.765060i
$403$	3.27701	−	7.17564i	0.163239	−	0.357444i
$404$	−1.64546	+	11.4444i	−0.0818648	+	0.569382i
$405$	−107.119	+	68.8412i	−5.32278	+	3.42075i
$406$	−3.98478	−	1.17004i	−0.197761	−	0.0580680i
$407$	3.24594	+	22.5760i	0.160895	+	1.11905i
$408$	−0.476876	−	0.550345i	−0.0236089	−	0.0272461i
$409$	15.0188	+	9.65201i	0.742633	+	0.477261i	0.856443	−	0.516241i	$-0.172669\pi$
$409$	15.0188	+	9.65201i	0.742633	+	0.477261i	−0.113810	+	0.993503i	$0.536306\pi$
$410$	−16.3826	+	18.9066i	−0.809081	+	0.933730i
$411$	−53.5544	+	15.7250i	−2.64164	+	0.775657i
$412$	−3.37148	−	7.38251i	−0.166101	−	0.363710i
$413$	0.211611			0.0104127
$414$	33.4927	−	19.9247i	1.64607	−	0.979245i
$415$	50.9845			2.50273
$416$	1.40435	+	3.07509i	0.0688538	+	0.150769i
$417$	−27.5902	+	8.10123i	−1.35110	+	0.396719i
$418$	7.62904	−	8.80438i	0.373149	−	0.430636i
$419$	6.75051	+	4.33829i	0.329784	+	0.211939i	0.695046	−	0.718965i	$-0.255384\pi$
$419$	6.75051	+	4.33829i	0.329784	+	0.211939i	−0.365262	+	0.930905i	$0.619020\pi$
$420$	−8.51757	−	9.82980i	−0.415615	−	0.479645i
$421$	−3.02125	−	21.0132i	−0.147247	−	1.02412i	−0.920700	−	0.390270i	$-0.872382\pi$
$421$	−3.02125	−	21.0132i	−0.147247	−	1.02412i	0.773454	−	0.633853i	$-0.218527\pi$
$422$	10.8541	+	3.18705i	0.528369	+	0.155143i
$423$	−46.3529	+	29.7892i	−2.25376	+	1.44840i
$424$	−0.803989	+	5.59186i	−0.0390451	+	0.271565i
$425$	0.925532	−	2.02663i	0.0448949	−	0.0983061i
$426$	−11.1793	+	24.4792i	−0.541638	+	1.18602i
$427$	0.356199	−	2.47742i	0.0172377	−	0.119891i
$428$	−6.95001	+	4.46650i	−0.335941	+	0.215896i
$429$	39.7686	+	11.6771i	1.92005	+	0.563776i
$430$	1.16124	+	8.07658i	0.0559998	+	0.389487i
$431$	20.2898	+	23.4157i	0.977325	+	1.12789i	0.991775	+	0.127997i	$0.0408548\pi$
$431$	20.2898	+	23.4157i	0.977325	+	1.12789i	−0.0144500	+	0.999896i	$0.504600\pi$
$432$	−14.3840	−	9.24404i	−0.692051	−	0.444754i
$433$	−3.15761	+	3.64407i	−0.151745	+	0.175123i	−0.826532	−	0.562889i	$-0.809690\pi$
$433$	−3.15761	+	3.64407i	−0.151745	+	0.175123i	0.674787	+	0.738012i	$0.264235\pi$
$434$	−2.23895	+	0.657415i	−0.107473	+	0.0315569i
$435$	−22.4394	−	49.1355i	−1.07589	−	2.35587i
$436$	5.11429			0.244930
$437$	5.83315	+	14.0364i	0.279038	+	0.671452i
$438$	25.8766			1.23643
$439$	−4.09201	−	8.96026i	−0.195301	−	0.427650i	0.786493	−	0.617600i	$-0.211895\pi$
$439$	−4.09201	−	8.96026i	−0.195301	−	0.427650i	−0.981794	+	0.189950i	$0.939167\pi$
$440$	13.7523	−	4.03803i	0.655613	−	0.192505i
$441$	−5.32143	+	6.14126i	−0.253401	+	0.292441i
$442$	0.620877	+	0.399014i	0.0295321	+	0.0189791i
$443$	−1.30686	−	1.50820i	−0.0620908	−	0.0716566i	0.723854	−	0.689953i	$-0.242369\pi$
$443$	−1.30686	−	1.50820i	−0.0620908	−	0.0716566i	−0.785945	+	0.618296i	$0.787823\pi$
$444$	2.94561	+	20.4872i	0.139792	+	0.972278i
$445$	−69.9173	−	20.5296i	−3.31440	−	0.973195i
$446$	19.6245	−	12.6119i	0.929247	−	0.597191i
$447$	−0.442535	+	3.07790i	−0.0209312	+	0.145580i
$448$	0.415415	−	0.909632i	0.0196265	−	0.0429761i
$449$	6.72702	−	14.7301i	0.317468	−	0.695157i	−0.681873	−	0.731471i	$-0.738834\pi$
$449$	6.72702	−	14.7301i	0.317468	−	0.695157i	0.999340	+	0.0363136i	$0.0115615\pi$
$450$	11.8019	−	82.0841i	0.556347	−	3.86948i
$451$	−19.8382	+	12.7492i	−0.934142	+	0.600337i
$452$	7.52539	+	2.20965i	0.353965	+	0.103933i
$453$	1.24560	+	8.66336i	0.0585235	+	0.407040i
$454$	−5.14246	−	5.93472i	−0.241348	−	0.278530i
$455$	11.0896	+	7.12685i	0.519888	+	0.334112i
$456$	6.92317	−	7.98976i	0.324207	−	0.374155i
$457$	17.2469	−	5.06415i	0.806777	−	0.236891i	0.147764	−	0.989023i	$-0.452792\pi$
$457$	17.2469	−	5.06415i	0.806777	−	0.236891i	0.659013	+	0.752132i	$0.270974\pi$
$458$	4.26180	+	9.33203i	0.199141	+	0.436057i
$459$	−3.73284			−0.174234
$460$	−3.29903	+	18.4075i	−0.153818	+	0.858255i
$461$	−1.18118			−0.0550129			−0.0275065	−	0.999622i	$-0.508757\pi$
$461$	−1.18118			−0.0550129			−0.0275065	+	0.999622i	$0.508757\pi$
$462$	−5.09317	−	11.1525i	−0.236956	−	0.518861i
$463$	15.0125	−	4.40806i	0.697689	−	0.204860i	0.0863918	−	0.996261i	$-0.472466\pi$
$463$	15.0125	−	4.40806i	0.697689	−	0.204860i	0.611297	+	0.791401i	$0.290648\pi$
$464$	2.71964	−	3.13863i	0.126256	−	0.145707i
$465$	−25.5327	−	16.4089i	−1.18405	−	0.760943i
$466$	7.01280	+	8.09320i	0.324861	+	0.374910i
$467$	−2.99988	−	20.8646i	−0.138818	−	0.965501i	−0.933526	−	0.358509i	$-0.883285\pi$
$467$	−2.99988	−	20.8646i	−0.138818	−	0.965501i	0.794708	−	0.606992i	$-0.207624\pi$
$468$	26.3581	+	7.73943i	1.21840	+	0.357755i
$469$	4.25304	−	2.73326i	0.196387	−	0.126210i
$470$	3.76286	−	26.1712i	0.173568	−	1.20719i
$471$	−4.29937	+	9.41432i	−0.198105	+	0.433789i
$472$	−0.0879063	+	0.192488i	−0.00404621	+	0.00885997i
$473$	−1.09461	+	7.61319i	−0.0503303	+	0.350055i
$474$	17.7456	−	11.4044i	0.815082	−	0.523821i
$475$	31.0349	+	9.11266i	1.42398	+	0.418117i
$476$	−0.0310697	−	0.216094i	−0.00142408	−	0.00990467i
$477$	30.0627	+	34.6942i	1.37648	+	1.58854i
$478$	8.99639	+	5.78163i	0.411485	+	0.264445i
$479$	−10.5578	+	12.1844i	−0.482400	+	0.556719i	−0.943819	−	0.330463i	$-0.892795\pi$
$479$	−10.5578	+	12.1844i	−0.482400	+	0.556719i	0.461419	+	0.887182i	$0.347341\pi$
$480$	12.4798	−	3.66441i	0.569624	−	0.167257i
$481$	−8.71423	−	19.0815i	−0.397335	−	0.870042i
$482$	1.46002			0.0665020
$483$	15.9873	+	0.552415i	0.727448	+	0.0251358i
$484$	2.51050			0.114114
$485$	23.3246	+	51.0737i	1.05911	+	2.31914i
$486$	−55.2923	+	16.2353i	−2.50811	+	0.736447i
$487$	−2.57297	+	2.96937i	−0.116593	+	0.134555i	−0.811045	−	0.584983i	$-0.801101\pi$
$487$	−2.57297	+	2.96937i	−0.116593	+	0.134555i	0.694453	+	0.719538i	$0.255647\pi$
$488$	2.10557	+	1.35317i	0.0953146	+	0.0612549i
$489$	−25.9912	−	29.9954i	−1.17536	−	1.35644i
$490$	−0.554941	−	3.85970i	−0.0250697	−	0.174363i
$491$	17.9779	+	5.27878i	0.811329	+	0.238228i	0.660978	−	0.750405i	$-0.270141\pi$
$491$	17.9779	+	5.27878i	0.811329	+	0.238228i	0.150351	+	0.988633i	$0.451960\pi$
$492$	−18.0026	+	11.5696i	−0.811621	+	0.521597i
$493$	0.129033	−	0.897441i	0.00581134	−	0.0404187i
$494$	−4.45102	+	9.74638i	−0.200261	+	0.438510i
$495$	48.3831	−	105.944i	2.17466	−	4.76184i
$496$	0.332088	−	2.30972i	0.0149112	−	0.103710i
$497$	−6.78716	+	4.36185i	−0.304446	+	0.195656i
$498$	41.8460	+	12.2871i	1.87516	+	0.550598i
$499$	−2.66828	−	18.5583i	−0.119449	−	0.830785i	−0.958165	−	0.286216i	$-0.907602\pi$
$499$	−2.66828	−	18.5583i	−0.119449	−	0.830785i	0.838716	−	0.544569i	$-0.183307\pi$
$500$	13.2918	+	15.3396i	0.594429	+	0.686008i
$501$	−63.3864	−	40.7360i	−2.83190	−	1.81995i
$502$	1.27172	−	1.46765i	0.0567597	−	0.0655042i
$503$	24.9677	−	7.33116i	1.11325	−	0.326880i	0.327147	−	0.944973i	$-0.393913\pi$
$503$	24.9677	−	7.33116i	1.11325	−	0.326880i	0.786105	+	0.618093i	$0.212094\pi$
$504$	−3.37568	−	7.39171i	−0.150365	−	0.329253i
$505$	−45.0852			−2.00627
$506$	−7.87224	+	15.7724i	−0.349964	+	0.701170i
$507$	5.24225			0.232817
$508$	−5.93800	−	13.0024i	−0.263456	−	0.576888i
$509$	27.8767	−	8.18533i	1.23561	−	0.362808i	0.402247	−	0.915531i	$-0.368229\pi$
$509$	27.8767	−	8.18533i	1.23561	−	0.362808i	0.833365	+	0.552723i	$0.186411\pi$
$510$	1.85953	−	2.14601i	0.0823412	−	0.0950268i
$511$	6.52625	+	4.19417i	0.288704	+	0.185539i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	−7.71238	−	53.6408i	−0.340510	−	2.36830i
$514$	−22.1530	−	6.50471i	−0.977127	−	0.286910i
$515$	26.6233	−	17.1097i	1.17316	−	0.753945i
$516$	−0.993333	+	6.90878i	−0.0437291	+	0.304142i
$517$	10.3535	−	22.6711i	0.455348	−	0.997073i
$518$	−2.57773	+	5.64443i	−0.113259	+	0.248002i
$519$	−8.27465	+	57.5514i	−0.363217	+	2.52623i
$520$	−11.0896	+	7.12685i	−0.486311	+	0.312533i
$521$	−32.5835	−	9.56739i	−1.42751	−	0.419155i	−0.525473	−	0.850811i	$-0.676111\pi$
$521$	−32.5835	−	9.56739i	−1.42751	−	0.419155i	−0.902039	+	0.431656i	$0.857930\pi$
$522$	−4.80277	−	33.4040i	−0.210212	−	1.46205i
$523$	6.08425	+	7.02160i	0.266046	+	0.307033i	0.873016	−	0.487691i	$-0.162161\pi$
$523$	6.08425	+	7.02160i	0.266046	+	0.307033i	−0.606971	+	0.794724i	$0.707615\pi$
$524$	−5.04434	−	3.24180i	−0.220363	−	0.141619i
$525$	22.2916	−	25.7259i	0.972887	−	1.12277i
$526$	−20.6919	+	6.07570i	−0.902211	+	0.264913i
$527$	−0.211627	−	0.463399i	−0.00921863	−	0.0201860i
$528$	12.2604			0.533567
$529$	−13.8261	−	18.3804i	−0.601134	−	0.799148i
$530$	−22.0291			−0.956882
$531$	0.714330	+	1.56417i	0.0309993	+	0.0678790i
$532$	3.04107	−	0.892940i	0.131847	−	0.0387139i
$533$	14.2030	−	16.3911i	0.615200	−	0.709979i
$534$	−52.4377	−	33.6997i	−2.26920	−	1.45833i
$535$	−21.0962	−	24.3463i	−0.912067	−	1.05258i
$536$	0.719486	+	5.00413i	0.0310771	+	0.216146i
$537$	−32.9813	−	9.68419i	−1.42325	−	0.417904i
$538$	−26.8187	+	17.2354i	−1.15624	+	0.743069i
$539$	0.523101	−	3.63825i	0.0225316	−	0.156711i
$540$	27.6969	−	60.6478i	1.19189	−	2.60987i
$541$	−3.54939	+	7.77208i	−0.152600	+	0.334148i	−0.970457	−	0.241274i	$-0.922435\pi$
$541$	−3.54939	+	7.77208i	−0.152600	+	0.334148i	0.817857	+	0.575422i	$0.195162\pi$
$542$	1.29882	−	9.03346i	0.0557889	−	0.388020i
$543$	60.3839	−	38.8064i	2.59132	−	1.66534i
$544$	0.209473	+	0.0615069i	0.00898109	+	0.00263708i
$545$	2.83813	+	19.7396i	0.121572	+	0.845553i
$546$	7.38434	+	8.52198i	0.316021	+	0.364707i
$547$	14.6813	+	9.43512i	0.627728	+	0.403416i	0.815468	−	0.578802i	$-0.196480\pi$
$547$	14.6813	+	9.43512i	0.627728	+	0.403416i	−0.187740	+	0.982219i	$0.560116\pi$
$548$	10.9580	−	12.6462i	0.468103	−	0.540220i
$549$	19.5148	−	5.73005i	0.832870	−	0.244553i
$550$	15.5826	+	34.1212i	0.664445	+	1.45493i
$551$	13.1628			0.560754
$552$	−7.14386	+	14.3131i	−0.304063	+	0.609205i
$553$	6.32402			0.268925
$554$	0.645388	+	1.41320i	0.0274199	+	0.0600412i
$555$	−77.4397	+	22.7383i	−3.28713	+	0.965189i
$556$	5.64537	−	6.51510i	0.239417	−	0.276302i
$557$	28.2745	+	18.1709i	1.19803	+	0.769926i	0.978614	−	0.205706i	$-0.0659490\pi$
$557$	28.2745	+	18.1709i	1.19803	+	0.769926i	0.219414	+	0.975632i	$0.429585\pi$
$558$	−12.4174	−	14.3305i	−0.525671	−	0.606657i
$559$	−1.00674	−	7.00202i	−0.0425805	−	0.296154i
$560$	3.74144	+	1.09858i	0.158105	+	0.0464237i
$561$	2.25175	−	1.44711i	0.0950688	−	0.0610970i
$562$	−1.35342	+	9.41321i	−0.0570904	+	0.397072i
$563$	−5.25474	+	11.5063i	−0.221461	+	0.484932i	−0.987452	−	0.157919i	$-0.949521\pi$
$563$	−5.25474	+	11.5063i	−0.221461	+	0.484932i	0.765991	+	0.642851i	$0.222249\pi$
$564$	9.39558	−	20.5735i	0.395625	−	0.866299i
$565$	−4.35245	+	30.2720i	−0.183109	+	1.27355i
$566$	−7.38891	+	4.74856i	−0.310579	+	0.199597i
$567$	−31.3318	−	9.19984i	−1.31581	−	0.386357i
$568$	−1.14818	−	7.98580i	−0.0481767	−	0.335077i
$569$	18.3938	+	21.2276i	0.771107	+	0.889905i	0.996434	−	0.0843779i	$-0.0268903\pi$
$569$	18.3938	+	21.2276i	0.771107	+	0.889905i	−0.225326	+	0.974283i	$0.572345\pi$
$570$	34.6800	+	22.2875i	1.45259	+	0.933520i
$571$	7.57032	−	8.73662i	0.316808	−	0.365616i	−0.574903	−	0.818222i	$-0.694960\pi$
$571$	7.57032	−	8.73662i	0.316808	−	0.365616i	0.891711	+	0.452606i	$0.149505\pi$
$572$	−11.9226	+	3.50078i	−0.498508	+	0.146375i
$573$	−9.26849	−	20.2952i	−0.387197	−	0.847843i
$574$	−6.41562			−0.267783
$575$	−48.9134	−	1.69012i	−2.03983	−	0.0704829i
$576$	8.12605			0.338585
$577$	2.16229	+	4.73475i	0.0900172	+	0.197110i	0.949286	−	0.314415i	$-0.101808\pi$
$577$	2.16229	+	4.73475i	0.0900172	+	0.197110i	−0.859269	+	0.511525i	$0.829081\pi$
$578$	−16.2656	+	4.77603i	−0.676562	+	0.198656i
$579$	−54.8296	+	63.2768i	−2.27864	+	2.62969i
$580$	13.6234	+	8.75524i	0.565682	+	0.363542i
$581$	8.56230	+	9.88142i	0.355224	+	0.409950i
$582$	6.83527	+	47.5403i	0.283331	+	1.97061i
$583$	−19.9240	−	5.85022i	−0.825169	−	0.242291i
$584$	−6.52625	+	4.19417i	−0.270058	+	0.173556i
$585$	−15.2447	+	106.029i	−0.630290	+	4.38376i
$586$	2.37514	−	5.20083i	0.0981161	−	0.214844i
$587$	8.03622	−	17.5969i	0.331690	−	0.726300i	−0.668153	−	0.744024i	$-0.732915\pi$
$587$	8.03622	−	17.5969i	0.331690	−	0.726300i	0.999843	+	0.0177239i	$0.00564198\pi$
$588$	0.474702	−	3.30162i	0.0195764	−	0.136157i
$589$	6.22179	−	3.99850i	0.256364	−	0.164755i
$590$	−0.791728	−	0.232472i	−0.0325949	−	0.00957073i
$591$	−4.47377	−	31.1158i	−0.184026	−	1.27993i
$592$	−4.06353	−	4.68957i	−0.167010	−	0.192740i
$593$	0.694203	+	0.446137i	0.0285075	+	0.0183207i	0.554817	−	0.831972i	$-0.312788\pi$
$593$	0.694203	+	0.446137i	0.0285075	+	0.0183207i	−0.526309	+	0.850293i	$0.676425\pi$
$594$	41.1564	−	47.4970i	1.68867	−	1.94883i
$595$	0.816817	−	0.239839i	0.0334862	−	0.00983244i
$596$	−0.387266	−	0.847995i	−0.0158630	−	0.0347352i
$597$	33.2616			1.36131
$598$	2.86011	−	15.9585i	0.116959	−	0.652590i
$599$	−7.27687			−0.297325			−0.148662	−	0.988888i	$-0.547497\pi$
$599$	−7.27687			−0.297325			−0.148662	+	0.988888i	$0.547497\pi$
$600$	14.1408	+	30.9641i	0.577298	+	1.26411i
$601$	−29.2180	+	8.57918i	−1.19183	+	0.349952i	−0.816723	−	0.577030i	$-0.804211\pi$
$601$	−29.2180	+	8.57918i	−1.19183	+	0.349952i	−0.375105	+	0.926983i	$0.622393\pi$
$602$	−1.37032	+	1.58144i	−0.0558502	+	0.0644546i
$603$	34.5604	+	22.2106i	1.40741	+	0.904485i
$604$	−1.71834	−	1.98306i	−0.0699181	−	0.0806898i
$605$	1.39318	+	9.68976i	0.0566407	+	0.393945i
$606$	−37.0041	−	10.8654i	−1.50319	−	0.441376i
$607$	−15.3408	+	9.85892i	−0.622663	+	0.400161i	−0.813587	−	0.581444i	$-0.802488\pi$
$607$	−15.3408	+	9.85892i	−0.622663	+	0.400161i	0.190924	+	0.981605i	$0.438852\pi$
$608$	−0.451061	+	3.13720i	−0.0182929	+	0.127230i
$609$	5.75460	−	12.6008i	0.233188	−	0.510611i
$610$	−4.05435	+	8.87778i	−0.164156	+	0.359451i
$611$	−3.26222	+	22.6893i	−0.131975	+	0.917909i
$612$	1.49243	−	0.959124i	0.0603277	−	0.0387703i
$613$	18.3555	+	5.38965i	0.741370	+	0.217686i	0.630543	−	0.776154i	$-0.282832\pi$
$613$	18.3555	+	5.38965i	0.741370	+	0.217686i	0.110826	+	0.993840i	$0.464650\pi$
$614$	−2.89103	−	20.1076i	−0.116673	−	0.811476i
$615$	−54.6455	−	63.0643i	−2.20352	−	2.54300i
$616$	3.09216	+	1.98721i	0.124587	+	0.0800671i
$617$	23.5956	−	27.2308i	0.949924	−	1.09627i	−0.0453316	−	0.998972i	$-0.514434\pi$
$617$	23.5956	−	27.2308i	0.949924	−	1.09627i	0.995255	−	0.0972984i	$-0.0310201\pi$
$618$	25.9747	−	7.62686i	1.04486	−	0.306797i
$619$	0.0242412	+	0.0530807i	0.000974335	+	0.00213350i	0.910119	−	0.414348i	$-0.135990\pi$
$619$	0.0242412	+	0.0530807i	0.000974335	+	0.00213350i	−0.909144	+	0.416481i	$0.863263\pi$
$620$	9.09912			0.365429
$621$	31.4681	+	75.7222i	1.26277	+	3.03863i
$622$	21.0818			0.845305
$623$	−7.76298	−	16.9986i	−0.311017	−	0.681033i
$624$	−10.8194	+	3.17687i	−0.433124	+	0.127177i
$625$	−18.4151	+	21.2521i	−0.736602	+	0.850084i
$626$	5.84921	+	3.75906i	0.233781	+	0.150242i
$627$	25.4472	+	29.3677i	1.01626	+	1.17283i
$628$	−0.441573	−	3.07121i	−0.0176207	−	0.122555i
$629$	−1.29982	−	0.381661i	−0.0518272	−	0.0152178i
$630$	26.6565	−	17.1311i	1.06202	−	0.682518i
$631$	−0.120772	+	0.839985i	−0.00480784	+	0.0334393i	−0.992084	−	0.125575i	$-0.959922\pi$
$631$	−0.120772	+	0.839985i	−0.00480784	+	0.0334393i	0.987276	+	0.159014i	$0.0508316\pi$
$632$	−2.62709	+	5.75253i	−0.104500	+	0.228823i
$633$	−15.6749	+	34.3232i	−0.623021	+	1.36423i
$634$	1.40344	−	9.76117i	0.0557379	−	0.387666i
$635$	46.8901	−	30.1344i	1.86078	−	1.19585i
$636$	−18.0806	−	5.30893i	−0.716941	−	0.210513i
$637$	0.481108	+	3.34618i	0.0190622	+	0.132580i
$638$	9.99649	+	11.5366i	0.395765	+	0.456737i
$639$	−55.1528	−	35.4446i	−2.18181	−	1.40217i
$640$	−2.55356	+	2.94696i	−0.100938	+	0.116489i
$641$	−39.1399	+	11.4925i	−1.54593	+	0.453927i	−0.939882	−	0.341499i	$-0.889065\pi$
$641$	−39.1399	+	11.4925i	−1.54593	+	0.453927i	−0.606051	+	0.795426i	$0.707247\pi$
$642$	−11.4475	−	25.0665i	−0.451797	−	0.989298i
$643$	−23.2323			−0.916191			−0.458095	−	0.888903i	$-0.651468\pi$
$643$	−23.2323			−0.916191			−0.458095	+	0.888903i	$0.651468\pi$
$644$	−4.12164	+	2.45195i	−0.162415	+	0.0966205i
$645$	−27.2171			−1.07167
$646$	0.287444	+	0.629416i	0.0113094	+	0.0247640i
$647$	10.7246	−	3.14902i	0.421627	−	0.123801i	−0.0640348	−	0.997948i	$-0.520397\pi$
$647$	10.7246	−	3.14902i	0.421627	−	0.123801i	0.485662	+	0.874147i	$0.338579\pi$
$648$	21.3841	−	24.6786i	0.840049	−	0.969468i
$649$	−0.654335	−	0.420516i	−0.0256849	−	0.0165067i
$650$	−22.5925	−	26.0731i	−0.886150	−	1.02267i
$651$	−1.10770	−	7.70425i	−0.0434143	−	0.301953i
$652$	11.4169	+	3.35231i	0.447121	+	0.131287i
$653$	−1.56173	+	1.00366i	−0.0611151	+	0.0392763i	−0.570842	−	0.821060i	$-0.693383\pi$
$653$	−1.56173	+	1.00366i	−0.0611151	+	0.0392763i	0.509726	+	0.860337i	$0.329747\pi$
$654$	−2.42776	+	16.8855i	−0.0949331	+	0.660274i
$655$	9.71306	−	21.2686i	0.379521	−	0.831035i
$656$	2.66515	−	5.83585i	0.104056	−	0.227852i
$657$	−8.97152	+	62.3983i	−0.350012	+	2.43439i
$658$	5.70424	−	3.66589i	0.222374	−	0.142911i
$659$	15.8739	+	4.66099i	0.618358	+	0.181566i	0.575884	−	0.817531i	$-0.304658\pi$
$659$	15.8739	+	4.66099i	0.618358	+	0.181566i	0.0424738	+	0.999098i	$0.486476\pi$
$660$	6.80382	+	47.3216i	0.264838	+	1.84199i
$661$	−3.29353	−	3.80094i	−0.128104	−	0.147839i	0.688074	−	0.725641i	$-0.258456\pi$
$661$	−3.29353	−	3.80094i	−0.128104	−	0.147839i	−0.816178	+	0.577801i	$0.803911\pi$
$662$	−20.7258	−	13.3197i	−0.805533	−	0.517685i
$663$	−1.61212	+	1.86049i	−0.0626097	+	0.0722554i
$664$	−12.5454	+	3.68365i	−0.486855	+	0.142953i
$665$	5.13410	+	11.2421i	0.199092	+	0.435950i
$666$	−50.4236			−1.95388
$667$	−19.2927	+	4.94802i	−0.747017	+	0.191588i
$668$	22.5891			0.873998
$669$	32.3239	+	70.7796i	1.24972	+	2.73650i
$670$	−18.9152	+	5.55400i	−0.730757	+	0.214570i
$671$	−6.02458	+	6.95274i	−0.232576	+	0.268407i
$672$	2.80606	+	1.80335i	0.108246	+	0.0695656i
$673$	−29.9508	−	34.5651i	−1.15452	−	1.33239i	−0.934112	−	0.356979i	$-0.883807\pi$
$673$	−29.9508	−	34.5651i	−1.15452	−	1.33239i	−0.220408	−	0.975408i	$-0.570739\pi$
$674$	2.33704	+	16.2544i	0.0900193	+	0.626098i
$675$	167.424	+	49.1601i	6.44415	+	1.89217i
$676$	−1.32213	+	0.849682i	−0.0508512	+	0.0326801i
$677$	6.76055	−	47.0206i	0.259829	−	1.80715i	−0.274188	−	0.961676i	$-0.588409\pi$
$677$	6.76055	−	47.0206i	0.259829	−	1.80715i	0.534017	−	0.845474i	$-0.320682\pi$
$678$	−10.8678	+	23.7971i	−0.417374	+	0.913921i
$679$	−5.98159	+	13.0979i	−0.229553	+	0.502650i
$680$	−0.121153	+	0.842636i	−0.00464599	+	0.0323136i
$681$	22.0353	−	14.1613i	0.844396	−	0.542660i
$682$	8.22963	+	2.41644i	0.315129	+	0.0925302i
$683$	0.686180	+	4.77248i	0.0262559	+	0.182614i	0.998729	−	0.0504010i	$-0.0160499\pi$
$683$	0.686180	+	4.77248i	0.0262559	+	0.182614i	−0.972473	+	0.233015i	$0.925141\pi$
$684$	16.8661	+	19.4645i	0.644890	+	0.744243i
$685$	54.8917	+	35.2767i	2.09730	+	1.34785i
$686$	0.654861	−	0.755750i	0.0250027	−	0.0288547i
$687$	−32.8339	+	9.64091i	−1.25269	+	0.367824i
$688$	−0.869274	−	1.90344i	−0.0331408	−	0.0725681i
$689$	19.0982			0.727583
$690$	−59.2086	−	19.6302i	−2.25403	−	0.747310i
$691$	36.4464			1.38648			0.693242	−	0.720704i	$-0.256182\pi$
$691$	36.4464			1.38648			0.693242	+	0.720704i	$0.256182\pi$
$692$	−7.24121	−	15.8560i	−0.275269	−	0.602756i
$693$	28.6587	−	8.41496i	1.08865	−	0.319658i
$694$	16.5822	−	19.1369i	0.629452	−	0.726426i
$695$	28.2792	+	18.1739i	1.07269	+	0.689376i
$696$	9.07156	+	10.4691i	0.343857	+	0.396832i
$697$	−0.199331	−	1.38638i	−0.00755021	−	0.0525128i
$698$	20.8476	+	6.12141i	0.789094	+	0.231699i
$699$	−30.0497	+	19.3117i	−1.13658	+	0.730437i
$700$	−1.45236	+	10.1014i	−0.0548939	+	0.381795i
$701$	−1.41832	+	3.10570i	−0.0535694	+	0.117301i	−0.934524	−	0.355900i	$-0.884174\pi$
$701$	−1.41832	+	3.10570i	−0.0535694	+	0.117301i	0.880955	+	0.473201i	$0.156902\pi$
$702$	−24.0120	+	52.5789i	−0.906273	+	1.98446i
$703$	2.79892	−	19.4669i	0.105563	−	0.734208i
$704$	−3.09216	+	1.98721i	−0.116540	+	0.0748959i
$705$	84.6213	+	24.8471i	3.18702	+	0.935794i
$706$	3.33593	+	23.2019i	0.125549	+	0.873215i
$707$	−7.57159	−	8.73808i	−0.284759	−	0.328629i
$708$	−0.593793	−	0.381608i	−0.0223161	−	0.0143417i
$709$	−7.79522	+	8.99616i	−0.292756	+	0.337858i	−0.883006	−	0.469363i	$-0.844484\pi$
$709$	−7.79522	+	8.99616i	−0.292756	+	0.337858i	0.590250	+	0.807221i	$0.299029\pi$
$710$	30.1856	−	8.86329i	1.13285	−	0.332633i
$711$	21.3479	+	46.7453i	0.800608	+	1.75309i
$712$	18.6873			0.700336
$713$	−7.61620	+	8.19943i	−0.285229	+	0.307071i
$714$	0.728210			0.0272526
$715$	−20.1283	−	44.0748i	−0.752755	−	1.64830i
$716$	9.88775	−	2.90331i	0.369523	−	0.108502i
$717$	−23.3593	+	26.9581i	−0.872371	+	1.00677i
$718$	25.0286	+	16.0849i	0.934061	+	0.600284i
$719$	−31.4384	−	36.2819i	−1.17246	−	1.35309i	−0.923046	−	0.384689i	$-0.874309\pi$
$719$	−31.4384	−	36.2819i	−1.17246	−	1.35309i	−0.249410	−	0.968398i	$-0.580237\pi$
$720$	4.50948	+	31.3641i	0.168058	+	1.16887i
$721$	7.78718	+	2.28652i	0.290010	+	0.0851545i
$722$	7.53302	−	4.84118i	0.280350	−	0.180170i
$723$	−0.693073	+	4.82043i	−0.0257757	+	0.179274i
$724$	−8.93936	+	19.5745i	−0.332229	+	0.727479i
$725$	−17.6063	+	38.5524i	−0.653881	+	1.43180i
$726$	−1.19174	+	8.28871i	−0.0442295	+	0.307623i
$727$	−6.41192	+	4.12069i	−0.237805	+	0.152828i	−0.654116	−	0.756394i	$-0.726959\pi$
$727$	−6.41192	+	4.12069i	−0.237805	+	0.152828i	0.416311	+	0.909222i	$0.363323\pi$
$728$	−3.24365	−	0.952422i	−0.120218	−	0.0352991i
$729$	−13.4138	−	93.2947i	−0.496806	−	3.45536i
$730$	−19.8099	−	22.8618i	−0.733197	−	0.846154i
$731$	−0.384315	−	0.246984i	−0.0142144	−	0.00913505i
$732$	−5.46716	+	6.30944i	−0.202072	+	0.233203i
$733$	19.9319	−	5.85252i	0.736200	−	0.216168i	0.107925	−	0.994159i	$-0.465579\pi$
$733$	19.9319	−	5.85252i	0.736200	−	0.216168i	0.628275	+	0.777991i	$0.283761\pi$
$734$	−0.603847	−	1.32224i	−0.0222884	−	0.0488048i
$735$	13.0067			0.479759
$736$	−0.518183	−	4.76775i	−0.0191005	−	0.175742i
$737$	−18.5827			−0.684501
$738$	−21.6571	−	47.4224i	−0.797209	−	1.74564i
$739$	−33.0803	+	9.71324i	−1.21688	+	0.357307i	−0.826283	−	0.563256i	$-0.809549\pi$
$739$	−33.0803	+	9.71324i	−1.21688	+	0.357307i	−0.390594	+	0.920563i	$0.627730\pi$
$740$	15.8453	−	18.2864i	0.582484	−	0.672223i
$741$	−30.0660	−	19.3222i	−1.10450	−	0.709819i
$742$	−3.69955	−	4.26951i	−0.135815	−	0.156738i
$743$	6.56405	+	45.6540i	0.240812	+	1.67488i	0.648079	+	0.761573i	$0.275573\pi$
$743$	6.56405	+	45.6540i	0.240812	+	1.67488i	−0.407267	+	0.913309i	$0.633518\pi$
$744$	7.46818	+	2.19286i	0.273797	+	0.0803940i
$745$	3.05809	−	1.96532i	0.112040	−	0.0720037i
$746$	0.659014	−	4.58354i	0.0241282	−	0.167815i
$747$	−44.1370	+	96.6466i	−1.61489	+	3.53611i
$748$	−0.333353	+	0.729941i	−0.0121886	+	0.0266893i
$749$	1.17573	−	8.17740i	0.0429603	−	0.298796i
$750$	−56.9552	+	36.6029i	−2.07971	+	1.33655i
$751$	−5.73615	−	1.68429i	−0.209315	−	0.0614604i	0.175394	−	0.984498i	$-0.443880\pi$
$751$	−5.73615	−	1.68429i	−0.209315	−	0.0614604i	−0.384709	+	0.923038i	$0.625698\pi$
$752$	0.964986	+	6.71163i	0.0351894	+	0.244748i
$753$	4.24192	+	4.89544i	0.154584	+	0.178400i
$754$	−11.8109	−	7.59039i	−0.430127	−	0.276426i
$755$	6.70046	−	7.73274i	0.243855	−	0.281423i
$756$	16.4057	−	4.81715i	0.596670	−	0.175198i
$757$	2.33930	+	5.12235i	0.0850233	+	0.186175i	0.947368	−	0.320147i	$-0.103732\pi$
$757$	2.33930	+	5.12235i	0.0850233	+	0.186175i	−0.862345	+	0.506322i	$0.831005\pi$
$758$	13.3491			0.484863
$759$	−48.3376	−	33.4783i	−1.75454	−	1.21519i
$760$	−12.3590			−0.448306
$761$	−8.44888	−	18.5005i	−0.306272	−	0.670641i	0.692435	−	0.721480i	$-0.256538\pi$
$761$	−8.44888	−	18.5005i	−0.306272	−	0.670641i	−0.998707	+	0.0508387i	$0.983811\pi$
$762$	45.7478	−	13.4328i	1.65727	−	0.486618i
$763$	−3.34915	+	3.86513i	−0.121247	+	0.139927i
$764$	5.62708	+	3.61631i	0.203581	+	0.130833i
$765$	4.53014	+	5.22806i	0.163787	+	0.189021i
$766$	−3.61280	−	25.1276i	−0.130536	−	0.907896i
$767$	0.686391	+	0.201543i	0.0247842	+	0.00727728i
$768$	−2.80606	+	1.80335i	−0.101255	+	0.0650727i
$769$	2.14385	−	14.9108i	0.0773091	−	0.537697i	−0.913956	−	0.405813i	$-0.866988\pi$
$769$	2.14385	−	14.9108i	0.0773091	−	0.537697i	0.991265	−	0.131884i	$-0.0421025\pi$
$770$	−5.95408	+	13.0376i	−0.214570	+	0.469843i
$771$	31.9921	−	70.0530i	1.15217	−	2.52290i
$772$	3.57229	−	24.8458i	0.128569	−	0.894220i
$773$	−6.18725	+	3.97630i	−0.222540	+	0.143018i	−0.647161	−	0.762354i	$-0.724044\pi$
$773$	−6.18725	+	3.97630i	−0.222540	+	0.143018i	0.424621	+	0.905371i	$0.360407\pi$
$774$	−16.3153	−	4.79061i	−0.586442	−	0.172195i
$775$	3.38903	+	23.5712i	0.121738	+	0.846704i
$776$	−9.42939	−	10.8821i	−0.338495	−	0.390645i
$777$	−17.4121	−	11.1901i	−0.624657	−	0.401443i
$778$	14.7544	−	17.0275i	0.528972	−	0.610466i
$779$	19.5104	−	5.72876i	0.699032	−	0.205254i
$780$	−18.2659	−	39.9968i	−0.654025	−	1.43211i
$781$	29.6549			1.06114
$782$	−0.657911	−	0.814482i	−0.0235269	−	0.0291258i
$783$	71.0094			2.53767
$784$	0.415415	+	0.909632i	0.0148363	+	0.0324869i
$785$	11.6089	−	3.40868i	0.414339	−	0.121661i
$786$	13.0978	−	15.1156i	0.467182	−	0.539156i
$787$	−30.4104	−	19.5436i	−1.08401	−	0.696654i	−0.128533	−	0.991705i	$-0.541027\pi$
$787$	−30.4104	−	19.5436i	−1.08401	−	0.696654i	−0.955481	+	0.295052i	$0.904663\pi$
$788$	6.17166	+	7.12248i	0.219856	+	0.253728i
$789$	−10.2372	−	71.2011i	−0.364453	−	2.53482i
$790$	−23.6609	−	6.94747i	−0.841817	−	0.247180i
$791$	−6.59803	+	4.24030i	−0.234599	+	0.150768i
$792$	−4.25075	+	29.5646i	−0.151044	+	1.05053i
$793$	3.51493	−	7.69662i	0.124819	−	0.273315i
$794$	−1.28284	+	2.80903i	−0.0455264	+	0.0996889i
$795$	10.4572	−	72.7317i	0.370880	−	2.57953i
$796$	−8.38879	+	5.39115i	−0.297333	+	0.191084i
$797$	−38.0112	−	11.1611i	−1.34643	−	0.395346i	−0.472468	−	0.881348i	$-0.656637\pi$
$797$	−38.0112	−	11.1611i	−1.34643	−	0.395346i	−0.873958	+	0.486002i	$0.838455\pi$
$798$	1.50455	+	10.4644i	0.0532604	+	0.370434i
$799$	0.969408	+	1.11876i	0.0342952	+	0.0395787i
$800$	−8.58519	−	5.51736i	−0.303532	−	0.195068i
$801$	99.4431	−	114.763i	3.51365	−	4.05497i
$802$	5.31071	−	1.55937i	0.187528	−	0.0550631i
$803$	−11.8455	−	25.9381i	−0.418020	−	0.915336i
$804$	−16.8633			−0.594723
$805$	−11.7511	−	14.5476i	−0.414171	−	0.512736i
$806$	−7.88851			−0.277861
$807$	−44.1737	−	96.7270i	−1.55499	−	3.40495i
$808$	11.0938	−	3.25743i	0.390278	−	0.114596i
$809$	−0.312539	+	0.360689i	−0.0109883	+	0.0126812i	−0.761217	−	0.648497i	$-0.775398\pi$
$809$	−0.312539	+	0.360689i	−0.0109883	+	0.0126812i	0.750229	+	0.661178i	$0.229943\pi$
$810$	107.119	+	68.8412i	3.76378	+	2.41883i
$811$	33.9770	+	39.2115i	1.19309	+	1.37690i	0.908302	+	0.418314i	$0.137379\pi$
$811$	33.9770	+	39.2115i	1.19309	+	1.37690i	0.284791	+	0.958590i	$0.408076\pi$
$812$	0.591035	+	4.11074i	0.0207412	+	0.144259i
$813$	29.2085	+	8.57640i	1.02439	+	0.300787i
$814$	19.1874	−	12.3310i	0.672520	−	0.432202i
$815$	−6.60319	+	45.9262i	−0.231300	+	1.60872i
$816$	−0.302510	+	0.662404i	−0.0105900	+	0.0231888i
$817$	2.75513	−	6.03289i	0.0963897	−	0.211064i
$818$	2.54073	−	17.6712i	0.0888347	−	0.617859i
$819$	−23.1099	+	14.8518i	−0.807526	+	0.518966i
$820$	24.0036	+	7.04810i	0.838243	+	0.246130i
$821$	7.29690	+	50.7511i	0.254664	+	1.77122i	0.569415	+	0.822050i	$0.307170\pi$
$821$	7.29690	+	50.7511i	0.254664	+	1.77122i	−0.314751	+	0.949174i	$0.601921\pi$
$822$	36.5513	+	42.1824i	1.27487	+	1.47128i
$823$	17.0661	+	10.9677i	0.594885	+	0.382310i	0.803162	−	0.595760i	$-0.203149\pi$
$823$	17.0661	+	10.9677i	0.594885	+	0.382310i	−0.208277	+	0.978070i	$0.566786\pi$
$824$	−5.31480	+	6.13361i	−0.185150	+	0.213674i
$825$	−120.052	+	35.2506i	−4.17969	+	1.22727i
$826$	−0.0879063	−	0.192488i	−0.00305865	−	0.00669751i
$827$	−30.8432			−1.07252			−0.536262	−	0.844052i	$-0.680164\pi$
$827$	−30.8432			−1.07252			−0.536262	+	0.844052i	$0.680164\pi$
$828$	−32.0375	−	22.1890i	−1.11338	−	0.771120i
$829$	39.1185			1.35864			0.679322	−	0.733841i	$-0.262274\pi$
$829$	39.1185			1.35864			0.679322	+	0.733841i	$0.262274\pi$
$830$	−21.1797	−	46.3771i	−0.735159	−	1.60977i
$831$	−4.97223	+	1.45998i	−0.172485	+	0.0506460i
$832$	2.21381	−	2.55488i	0.0767502	−	0.0885745i
$833$	0.183659	+	0.118031i	0.00636342	+	0.00408952i
$834$	18.8305	+	21.7316i	0.652048	+	0.752504i
$835$	12.5356	+	87.1871i	0.433813	+	3.01723i
$836$	−11.1780	−	3.28215i	−0.386598	−	0.113515i
$837$	33.5647	−	21.5707i	1.16017	−	0.745593i
$838$	1.14198	−	7.94268i	0.0394492	−	0.274375i
$839$	−10.0585	+	22.0251i	−0.347259	+	0.760392i	0.652737	+	0.757585i	$0.273621\pi$
$839$	−10.0585	+	22.0251i	−0.347259	+	0.760392i	−0.999996	+	0.00280703i	$0.999106\pi$
$840$	−5.40318	+	11.8313i	−0.186427	+	0.408219i
$841$	1.67256	−	11.6329i	0.0576745	−	0.401135i
$842$	−17.8592	+	11.4774i	−0.615470	+	0.395539i
$843$	−30.4364	−	8.93693i	−1.04829	−	0.307804i
$844$	−1.60991	−	11.1972i	−0.0554155	−	0.385423i
$845$	−4.01322	−	4.63150i	−0.138059	−	0.159329i
$846$	46.3529	+	29.7892i	1.59365	+	1.02417i
$847$	−1.64403	+	1.89731i	−0.0564894	+	0.0651922i
$848$	5.42053	−	1.59161i	0.186142	−	0.0546561i
$849$	−12.1704	−	26.6495i	−0.417688	−	0.914609i
$850$	−2.22797			−0.0764187
$851$	3.21542	+	29.5848i	0.110223	+	1.01415i
$852$	26.9111			0.921960
$853$	−11.6671	−	25.5474i	−0.399474	−	0.874726i	−0.997323	−	0.0731176i	$-0.976705\pi$
$853$	−11.6671	−	25.5474i	−0.399474	−	0.874726i	0.597849	−	0.801609i	$-0.296022\pi$
$854$	−2.40151	+	0.705146i	−0.0821779	+	0.0241296i
$855$	−65.7673	+	75.8995i	−2.24919	+	2.59571i
$856$	6.95001	+	4.46650i	0.237546	+	0.152662i
$857$	0.0107745	+	0.0124345i	0.000368051	+	0.000424753i	0.755934	−	0.654648i	$-0.227183\pi$
$857$	0.0107745	+	0.0124345i	0.000368051	+	0.000424753i	−0.755566	+	0.655073i	$0.772638\pi$
$858$	−5.89860	−	41.0256i	−0.201375	−	1.40059i
$859$	−33.9673	−	9.97369i	−1.15895	−	0.340298i	−0.354924	−	0.934895i	$-0.615493\pi$
$859$	−33.9673	−	9.97369i	−1.15895	−	0.340298i	−0.804024	+	0.594597i	$0.797312\pi$
$860$	6.86432	−	4.41143i	0.234071	−	0.150429i
$861$	3.04550	−	21.1820i	0.103791	−	0.721879i
$862$	12.8710	−	28.1835i	0.438386	−	0.959932i
$863$	−13.6304	+	29.8464i	−0.463983	+	1.01598i	0.522578	+	0.852591i	$0.324970\pi$
$863$	−13.6304	+	29.8464i	−0.463983	+	1.01598i	−0.986561	+	0.163390i	$0.947757\pi$
$864$	−2.43334	+	16.9243i	−0.0827840	+	0.575775i
$865$	57.1811	−	36.7480i	1.94421	−	1.24947i
$866$	4.62648	+	1.35846i	0.157214	+	0.0461623i
$867$	−8.04730	−	55.9702i	−0.273301	−	1.90085i
$868$	1.52810	+	1.76352i	0.0518671	+	0.0598578i
$869$	−19.5549	−	12.5672i	−0.663355	−	0.426312i
$870$	−35.3735	+	40.8232i	−1.19928	+	1.38404i
$871$	16.3986	−	4.81506i	0.555645	−	0.163152i
$872$	−2.12455	−	4.65213i	−0.0719465	−	0.157541i
$873$	−117.008			−3.96011
$874$	10.3448	−	11.1370i	0.349917	−	0.376713i
$875$	−20.2972			−0.686171
$876$	−10.7495	−	23.5382i	−0.363193	−	0.795281i
$877$	−15.9538	+	4.68446i	−0.538722	+	0.158183i	−0.539764	−	0.841817i	$-0.681486\pi$
$877$	−15.9538	+	4.68446i	−0.538722	+	0.158183i	0.00104218	+	0.999999i	$0.499668\pi$
$878$	−6.45066	+	7.44445i	−0.217699	+	0.251238i
$879$	16.0437	+	10.3107i	0.541140	+	0.347770i
$880$	−9.38601	−	10.8320i	−0.316402	−	0.365148i
$881$	−0.463098	−	3.22092i	−0.0156022	−	0.108515i	0.980532	−	0.196359i	$-0.0629117\pi$
$881$	−0.463098	−	3.22092i	−0.0156022	−	0.108515i	−0.996134	+	0.0878431i	$0.972003\pi$
$882$	7.79689	+	2.28937i	0.262535	+	0.0770872i
$883$	−6.86920	+	4.41457i	−0.231167	+	0.148562i	−0.651097	−	0.758994i	$-0.725691\pi$
$883$	−6.86920	+	4.41457i	−0.231167	+	0.148562i	0.419930	+	0.907556i	$0.362055\pi$
$884$	0.105034	−	0.730526i	0.00353267	−	0.0245702i
$885$	1.14337	−	2.50363i	0.0384340	−	0.0841586i
$886$	−0.829015	+	1.81529i	−0.0278513	+	0.0609858i
$887$	−2.01865	+	14.0400i	−0.0677796	+	0.471417i	0.927457	+	0.373929i	$0.121990\pi$
$887$	−2.01865	+	14.0400i	−0.0677796	+	0.471417i	−0.995237	+	0.0974878i	$0.968919\pi$
$888$	17.4121	−	11.1901i	0.584313	−	0.375515i
$889$	13.7151	+	4.02712i	0.459990	+	0.135065i
$890$	10.3703	+	72.1273i	0.347615	+	2.41771i
$891$	78.6009	+	90.7103i	2.63323	+	3.03891i
$892$	−19.6245	−	12.6119i	−0.657077	−	0.422278i
$893$	−14.0736	+	16.2418i	−0.470955	+	0.543511i
$894$	2.98359	−	0.876062i	0.0997863	−	0.0292999i
$895$	16.6930	+	36.5526i	0.557986	+	1.22182i
$896$	−1.00000			−0.0334077
$897$	51.3311	+	17.0185i	1.71390	+	0.568231i
$898$	−16.1935			−0.540384
$899$	4.02576	+	8.81518i	0.134267	+	0.294003i
$900$	−79.5690	+	23.3636i	−2.65230	+	0.778786i
$901$	0.807672	−	0.932103i	0.0269075	−	0.0310529i
$902$	19.8382	+	12.7492i	0.660538	+	0.424502i
$903$	−4.57082	−	5.27500i	−0.152107	−	0.175541i
$904$	−1.11619	−	7.76326i	−0.0371239	−	0.258202i
$905$	−80.5123	−	23.6406i	−2.67632	−	0.785839i
$906$	7.36303	−	4.73193i	0.244620	−	0.157208i
$907$	6.41982	−	44.6508i	0.213167	−	1.48261i	−0.549325	−	0.835609i	$-0.685115\pi$
$907$	6.41982	−	44.6508i	0.213167	−	1.48261i	0.762492	−	0.646998i	$-0.223976\pi$
$908$	−3.26215	+	7.14312i	−0.108258	+	0.237053i
$909$	39.0301	−	85.4639i	1.29455	−	2.83466i
$910$	1.87603	−	13.0481i	0.0621897	−	0.432539i
$911$	8.14380	−	5.23370i	0.269816	−	0.173400i	−0.398736	−	0.917066i	$-0.630551\pi$
$911$	8.14380	−	5.23370i	0.269816	−	0.173400i	0.668552	+	0.743666i	$0.266915\pi$
$912$	−10.1437	−	2.97847i	−0.335892	−	0.0986269i
$913$	−6.83955	−	47.5701i	−0.226356	−	1.57434i
$914$	−11.7711	−	13.5846i	−0.389355	−	0.449340i
$915$	−27.3865	−	17.6002i	−0.905369	−	0.581845i
$916$	6.71830	−	7.75333i	0.221979	−	0.256177i
$917$	5.75333	−	1.68933i	0.189992	−	0.0557866i
$918$	1.55068	+	3.39551i	0.0511800	+	0.112069i
$919$	48.4435			1.59800			0.799002	−	0.601329i	$-0.205362\pi$
$919$	48.4435			1.59800			0.799002	+	0.601329i	$0.205362\pi$
$920$	18.1145	−	4.64585i	0.597218	−	0.153169i
$921$	67.7600			2.23277
$922$	0.490679	+	1.07444i	0.0161597	+	0.0353847i
$923$	−26.1695	+	7.68406i	−0.861380	+	0.252924i
$924$	−8.02888	+	9.26582i	−0.264131	+	0.304823i
$925$	53.2727	+	34.2363i	1.75159	+	1.12568i
$926$	−10.2461	−	11.8246i	−0.336708	−	0.388582i
$927$	9.38572	+	65.2791i	0.308268	+	2.14405i
$928$	−3.98478	−	1.17004i	−0.130807	−	0.0384084i
$929$	−2.86491	+	1.84117i	−0.0939948	+	0.0604068i	−0.586794	−	0.809736i	$-0.699610\pi$
$929$	−2.86491	+	1.84117i	−0.0939948	+	0.0604068i	0.492799	+	0.870143i	$0.335974\pi$
$930$	−4.31937	+	30.0418i	−0.141638	+	0.985111i
$931$	−1.31664	+	2.88304i	−0.0431512	+	0.0944879i
$932$	4.44861	−	9.74110i	0.145719	−	0.319080i
$933$	−10.0076	+	69.6042i	−0.327633	+	2.27874i
$934$	−17.7330	+	11.3963i	−0.580240	+	0.372898i
$935$	−3.00234	−	0.881568i	−0.0981871	−	0.0288303i
$936$	−3.90951	−	27.1912i	−0.127786	−	0.888772i
$937$	−23.1258	−	26.6886i	−0.755487	−	0.871878i	0.239601	−	0.970871i	$-0.422983\pi$
$937$	−23.1258	−	26.6886i	−0.755487	−	0.871878i	−0.995088	+	0.0989930i	$0.968438\pi$
$938$	−4.25304	−	2.73326i	−0.138867	−	0.0892441i
$939$	−15.1876	+	17.5274i	−0.495629	+	0.571986i
$940$	−25.3693	+	7.44911i	−0.827457	+	0.242963i
$941$	5.45520	+	11.9452i	0.177835	+	0.389403i	0.977468	−	0.211086i	$-0.0676999\pi$
$941$	5.45520	+	11.9452i	0.177835	+	0.389403i	−0.799633	+	0.600489i	$0.794973\pi$
$942$	10.3496			0.337208
$943$	−26.4429	+	15.7308i	−0.861099	+	0.512265i
$944$	0.211611			0.00688734
$945$	27.6969	+	60.6478i	0.900981	+	1.97287i
$946$	7.37992	−	2.16694i	0.239942	−	0.0704533i
$947$	35.3913	−	40.8437i	1.15006	−	1.32724i	0.213419	−	0.976961i	$-0.431540\pi$
$947$	35.3913	−	40.8437i	1.15006	−	1.32724i	0.936644	−	0.350282i	$-0.113914\pi$
$948$	−17.7456	−	11.4044i	−0.576350	−	0.370398i
$949$	17.1743	+	19.8201i	0.557500	+	0.643389i
$950$	−4.60318	−	32.0158i	−0.149347	−	1.03873i
$951$	31.5615	+	9.26729i	1.02345	+	0.300512i
$952$	−0.183659	+	0.118031i	−0.00595244	+	0.00382540i
$953$	4.59380	−	31.9506i	0.148808	−	1.03498i	−0.769368	−	0.638806i	$-0.779429\pi$
$953$	4.59380	−	31.9506i	0.148808	−	1.03498i	0.918175	−	0.396174i	$-0.129662\pi$
$954$	19.0705	−	41.7585i	0.617429	−	1.35198i
$955$	−10.8352	+	23.7257i	−0.350617	+	0.767745i
$956$	1.52192	−	10.5852i	0.0492224	−	0.342349i
$957$	−42.8347	+	27.5282i	−1.38465	+	0.889860i
$958$	15.4692	+	4.54217i	0.499787	+	0.146751i
$959$	2.38140	+	16.5630i	0.0768995	+	0.534848i
$960$	−8.51757	−	9.82980i	−0.274903	−	0.317256i
$961$	−21.4982	−	13.8160i	−0.693489	−	0.445678i
$962$	−13.7371	+	15.8535i	−0.442903	+	0.511137i
$963$	64.4139	−	18.9136i	2.07571	−	0.609483i
$964$	−0.606514	−	1.32808i	−0.0195345	−	0.0427746i
$965$	97.8797			3.15086
$966$	−6.13887	−	14.7720i	−0.197515	−	0.475283i
$967$	−38.4000			−1.23486			−0.617431	−	0.786625i	$-0.711827\pi$
$967$	−38.4000			−1.23486			−0.617431	+	0.786625i	$0.711827\pi$
$968$	−1.04290	−	2.28363i	−0.0335200	−	0.0733986i
$969$	−2.21454	+	0.650248i	−0.0711414	+	0.0208890i
$970$	36.7689	−	42.4335i	1.18058	−	1.36246i
$971$	−24.6627	−	15.8497i	−0.791463	−	0.508642i	0.0813570	−	0.996685i	$-0.474075\pi$
$971$	−24.6627	−	15.8497i	−0.791463	−	0.508642i	−0.872820	+	0.488043i	$0.837711\pi$
$972$	37.7374	+	43.5512i	1.21043	+	1.39691i
$973$	1.22686	+	8.53297i	0.0393312	+	0.273554i
$974$	3.76989	+	1.10694i	0.120795	+	0.0354686i
$975$	96.8083	−	62.2149i	3.10035	−	1.99247i
$976$	0.356199	−	2.47742i	0.0114016	−	0.0793002i
$977$	−2.14650	+	4.70018i	−0.0686726	+	0.150372i	−0.940856	−	0.338808i	$-0.889976\pi$
$977$	−2.14650	+	4.70018i	−0.0686726	+	0.150372i	0.872183	+	0.489180i	$0.162704\pi$
$978$	−16.4877	+	36.1030i	−0.527218	+	1.15445i
$979$	−9.77535	+	67.9890i	−0.312421	+	2.17294i
$980$	−3.28037	+	2.10817i	−0.104788	+	0.0673430i
$981$	−39.8756	−	11.7085i	−1.27313	−	0.373824i
$982$	−2.66653	−	18.5461i	−0.0850924	−	0.591830i
$983$	−31.4833	−	36.3336i	−1.00416	−	1.15886i	−0.987278	−	0.159005i	$-0.949171\pi$
$983$	−31.4833	−	36.3336i	−1.00416	−	1.15886i	−0.0168824	−	0.999857i	$-0.505374\pi$
$984$	18.0026	+	11.5696i	0.573903	+	0.368825i
$985$	−24.0657	+	27.7733i	−0.766798	+	0.884932i
$986$	−0.869943	+	0.255438i	−0.0277046	+	0.00813482i
$987$	9.39558	+	20.5735i	0.299065	+	0.654860i
$988$	10.7146			0.340878
$989$	−1.77037	+	9.87809i	−0.0562945	+	0.314105i
$990$	−116.469			−3.70164
$991$	−19.1481	−	41.9285i	−0.608260	−	1.33190i	−0.923758	−	0.382977i	$-0.874899\pi$
$991$	−19.1481	−	41.9285i	−0.608260	−	1.33190i	0.315499	−	0.948926i	$-0.397828\pi$
$992$	−2.23895	+	0.657415i	−0.0710868	+	0.0208730i
$993$	53.8152	−	62.1060i	1.70777	−	1.97088i
$994$	6.78716	+	4.36185i	0.215276	+	0.138349i
$995$	−25.4635	−	29.3864i	−0.807247	−	0.931613i
$996$	−6.20672	−	43.1687i	−0.196667	−	1.36785i
$997$	−44.8923	−	13.1816i	−1.42175	−	0.417465i	−0.521657	−	0.853155i	$-0.674686\pi$
$997$	−44.8923	−	13.1816i	−1.42175	−	0.417465i	−0.900097	+	0.435690i	$0.856504\pi$
$998$	−15.7728	+	10.1366i	−0.499279	+	0.320867i
$999$	15.0993	−	105.018i	0.477722	−	3.32263i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.e.211.4	yes	40
23.6	even	11	inner	322.2.i.e.29.4	✓	40
23.11	odd	22		7406.2.a.bs.1.1		20
23.12	even	11		7406.2.a.bt.1.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.e.29.4	✓	40	23.6	even	11	inner
322.2.i.e.211.4	yes	40	1.1	even	1	trivial
7406.2.a.bs.1.1		20	23.11	odd	22
7406.2.a.bt.1.1		20	23.12	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)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{2} +(3.20046 - 0.939739i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-3.28037 - 2.10817i) q^{5} +(-2.18434 - 2.52086i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(6.83607 - 4.39327i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{2} +(3.20046 - 0.939739i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-3.28037 - 2.10817i) q^{5} +(-2.18434 - 2.52086i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(6.83607 - 4.39327i) q^{9} +(-0.554941 + 3.85970i) q^{10} +(-1.52693 + 3.34350i) q^{11} +(-1.38565 + 3.03414i) q^{12} +(0.481108 - 3.34618i) q^{13} +(-0.841254 + 0.540641i) q^{14} +(-12.4798 - 3.66441i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-0.142967 - 0.164993i) q^{17} +(-6.83607 - 4.39327i) q^{18} +(2.07555 - 2.39532i) q^{19} +(3.74144 - 1.09858i) q^{20} +(-1.38565 - 3.03414i) q^{21} +3.67566 q^{22} +(-2.14172 + 4.29104i) q^{23} +3.33557 q^{24} +(4.23941 + 9.28300i) q^{25} +(-3.24365 + 0.952422i) q^{26} +(11.1970 - 12.9220i) q^{27} +(0.841254 + 0.540641i) q^{28} +(2.71964 + 3.13863i) q^{29} +(1.85105 + 12.8743i) q^{30} +(2.23895 + 0.657415i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(-1.74484 + 12.1356i) q^{33} +(-0.0906919 + 0.198588i) q^{34} +(-1.61986 + 3.54701i) q^{35} +(-1.15646 + 8.04334i) q^{36} +(5.22013 - 3.35478i) q^{37} +(-3.04107 - 0.892940i) q^{38} +(-1.60477 - 11.1614i) q^{39} +(-2.55356 - 2.94696i) q^{40} +(5.39716 + 3.46855i) q^{41} +(-2.18434 + 2.52086i) q^{42} +(2.00778 - 0.589537i) q^{43} +(-1.52693 - 3.34350i) q^{44} -31.6866 q^{45} +(4.79297 + 0.165613i) q^{46} -6.78064 q^{47} +(-1.38565 - 3.03414i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(6.68300 - 7.71260i) q^{50} +(-0.612610 - 0.393700i) q^{51} +(2.21381 + 2.55488i) q^{52} +(0.803989 + 5.59186i) q^{53} +(-16.4057 - 4.81715i) q^{54} +(12.0575 - 7.74892i) q^{55} +(0.142315 - 0.989821i) q^{56} +(4.39175 - 9.61660i) q^{57} +(1.72522 - 3.77771i) q^{58} +(-0.0301153 + 0.209457i) q^{59} +(10.9419 - 7.03195i) q^{60} +(2.40151 + 0.705146i) q^{61} +(-0.332088 - 2.30972i) q^{62} +(-5.32143 - 6.14126i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-8.63252 + 9.96246i) q^{65} +(11.7638 - 3.45417i) q^{66} +(2.10017 + 4.59873i) q^{67} +0.218316 q^{68} +(-2.82202 + 15.7460i) q^{69} +3.89939 q^{70} +(-3.35153 - 7.33884i) q^{71} +(7.79689 - 2.28937i) q^{72} +(-5.08026 + 5.86293i) q^{73} +(-5.22013 - 3.35478i) q^{74} +(22.2916 + 25.7259i) q^{75} +(0.451061 + 3.13720i) q^{76} +(3.52677 + 1.03555i) q^{77} +(-9.48614 + 6.09637i) q^{78} +(-0.900001 + 6.25965i) q^{79} +(-1.61986 + 3.54701i) q^{80} +(13.5652 - 29.7036i) q^{81} +(0.913038 - 6.35032i) q^{82} +(-10.9994 + 7.06888i) q^{83} +(3.20046 + 0.939739i) q^{84} +(0.121153 + 0.842636i) q^{85} +(-1.37032 - 1.58144i) q^{86} +(11.6536 + 7.48931i) q^{87} +(-2.40705 + 2.77788i) q^{88} +(17.9303 - 5.26482i) q^{89} +(13.1631 + 28.8232i) q^{90} -3.38059 q^{91} +(-1.84043 - 4.42864i) q^{92} +7.78347 q^{93} +(2.81678 + 6.16789i) q^{94} +(-11.8583 + 3.48192i) q^{95} +(-2.18434 + 2.52086i) q^{96} +(-12.1133 - 7.78473i) q^{97} +(0.654861 + 0.755750i) q^{98} +(4.25075 + 29.5646i) 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

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