LMFDB - Embedded newform 95.2.k.b.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,2,Mod(6,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("95.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.k (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} + \cdots + 361 $ x^18 + 12x^16 - 8x^15 + 96x^14 - 75x^13 + 448x^12 - 405x^11 + 1521x^10 - 1294x^9 + 3333x^8 - 2616x^7 + 5113x^6 - 3126x^5 + 4032x^4 - 1359x^3 + 1698x^2 - 513x + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.1
Root			$-0.841804 - 1.45805i$ of defining polynomial
Character	$\chi$	$=$	95.61
Dual form			95.2.k.b.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58207 - 0.575828i) q^{2} +(-0.564707 - 3.20261i) q^{3} +(0.639290 + 0.536428i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-0.950745 + 5.39194i) q^{6} +(0.274194 - 0.474919i) q^{7} +(0.981094 + 1.69930i) q^{8} +(-7.11876 + 2.59101i) q^{9} +O(q^{10})$	\(q+(-1.58207 - 0.575828i) q^{2} +(-0.564707 - 3.20261i) q^{3} +(0.639290 + 0.536428i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-0.950745 + 5.39194i) q^{6} +(0.274194 - 0.474919i) q^{7} +(0.981094 + 1.69930i) q^{8} +(-7.11876 + 2.59101i) q^{9} +(1.58207 - 0.575828i) q^{10} +(-0.165601 - 0.286829i) q^{11} +(1.35696 - 2.35032i) q^{12} +(0.837254 - 4.74830i) q^{13} +(-0.707267 + 0.593468i) q^{14} +(2.49119 + 2.09036i) q^{15} +(-0.863487 - 4.89708i) q^{16} +(-4.96227 - 1.80612i) q^{17} +12.7544 q^{18} +(4.30704 + 0.670409i) q^{19} -0.834534 q^{20} +(-1.67582 - 0.609949i) q^{21} +(0.0968286 + 0.549142i) q^{22} +(-0.850350 - 0.713529i) q^{23} +(4.88818 - 4.10167i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-4.05880 + 7.03005i) q^{26} +(7.44000 + 12.8865i) q^{27} +(0.430050 - 0.156525i) q^{28} +(3.01199 - 1.09627i) q^{29} +(-2.73756 - 4.74159i) q^{30} +(3.01060 - 5.21452i) q^{31} +(-0.772312 + 4.38000i) q^{32} +(-0.825087 + 0.692330i) q^{33} +(6.81067 + 5.71483i) q^{34} +(0.0952268 + 0.540058i) q^{35} +(-5.94084 - 2.16229i) q^{36} -6.67261 q^{37} +(-6.42801 - 3.54075i) q^{38} -15.6798 q^{39} +(-1.84385 - 0.671108i) q^{40} +(-1.37380 - 7.79121i) q^{41} +(2.30005 + 1.92997i) q^{42} +(1.25559 - 1.05356i) q^{43} +(0.0479962 - 0.272200i) q^{44} +(3.78781 - 6.56068i) q^{45} +(0.934447 + 1.61851i) q^{46} +(4.32380 - 1.57373i) q^{47} +(-15.1958 + 5.53083i) q^{48} +(3.34963 + 5.80174i) q^{49} +(-0.841804 + 1.45805i) q^{50} +(-2.98207 + 16.9122i) q^{51} +(3.08237 - 2.58642i) q^{52} +(5.15257 + 4.32352i) q^{53} +(-4.35025 - 24.6715i) q^{54} +(0.311228 + 0.113278i) q^{55} +1.07604 q^{56} +(-0.285152 - 14.1723i) q^{57} -5.39645 q^{58} +(6.39331 + 2.32697i) q^{59} +(0.471267 + 2.67269i) q^{60} +(0.520640 + 0.436869i) q^{61} +(-7.76566 + 6.51616i) q^{62} +(-0.721402 + 4.09127i) q^{63} +(-1.22864 + 2.12807i) q^{64} +(2.41078 + 4.17559i) q^{65} +(1.70401 - 0.620209i) q^{66} +(7.30324 - 2.65816i) q^{67} +(-2.20348 - 3.81654i) q^{68} +(-1.80496 + 3.12628i) q^{69} +(0.160324 - 0.909245i) q^{70} +(-0.832574 + 0.698612i) q^{71} +(-11.3871 - 9.55490i) q^{72} +(2.42261 + 13.7393i) q^{73} +(10.5566 + 3.84227i) q^{74} -3.25202 q^{75} +(2.39382 + 2.73900i) q^{76} -0.181627 q^{77} +(24.8065 + 9.02885i) q^{78} +(-0.243868 - 1.38304i) q^{79} +(3.80925 + 3.19634i) q^{80} +(19.6591 - 16.4960i) q^{81} +(-2.31294 + 13.1173i) q^{82} +(0.427439 - 0.740346i) q^{83} +(-0.744142 - 1.28889i) q^{84} +(4.96227 - 1.80612i) q^{85} +(-2.59310 + 0.943812i) q^{86} +(-5.21183 - 9.02715i) q^{87} +(0.324940 - 0.562813i) q^{88} +(2.52694 - 14.3310i) q^{89} +(-9.77042 + 8.19835i) q^{90} +(-2.02549 - 1.69959i) q^{91} +(-0.160864 - 0.912304i) q^{92} +(-18.4002 - 6.69712i) q^{93} -7.74677 q^{94} +(-3.73031 + 2.25495i) q^{95} +14.4636 q^{96} +(6.59799 + 2.40147i) q^{97} +(-1.95857 - 11.1076i) q^{98} +(1.92205 + 1.61279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{6} - 12 q^{8} - 21 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^6 - 12 * q^8 - 21 * q^9	\( 18 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{6} - 12 q^{8} - 21 q^{9} - 3 q^{10} + 6 q^{12} - 3 q^{13} + 24 q^{14} + 3 q^{15} + 21 q^{16} - 24 q^{17} - 12 q^{18} - 12 q^{19} - 12 q^{20} + 3 q^{21} + 15 q^{22} + 21 q^{23} + 21 q^{24} - 21 q^{26} + 6 q^{27} - 24 q^{28} - 9 q^{29} - 12 q^{30} + 30 q^{31} + 45 q^{32} - 3 q^{33} + 24 q^{34} - 6 q^{35} - 21 q^{36} - 60 q^{37} - 15 q^{38} + 12 q^{39} - 6 q^{40} - 6 q^{41} + 39 q^{42} - 6 q^{43} - 30 q^{44} + 6 q^{45} + 21 q^{46} + 33 q^{47} - 63 q^{48} - 3 q^{49} + 27 q^{51} + 9 q^{52} + 24 q^{53} + 30 q^{54} - 3 q^{55} - 72 q^{56} - 30 q^{57} + 36 q^{58} + 18 q^{59} + 15 q^{60} + 6 q^{61} + 12 q^{62} + 24 q^{63} - 24 q^{64} + 3 q^{65} - 33 q^{66} - 24 q^{67} - 3 q^{68} + 27 q^{69} + 39 q^{70} + 24 q^{71} + 18 q^{72} + 6 q^{73} - 39 q^{74} - 6 q^{75} + 27 q^{76} + 24 q^{77} + 72 q^{78} + 9 q^{79} + 33 q^{80} + 15 q^{81} - 57 q^{82} - 12 q^{84} + 24 q^{85} - 33 q^{86} - 45 q^{87} + 39 q^{88} - 6 q^{89} - 21 q^{90} - 6 q^{91} - 66 q^{92} - 72 q^{93} - 66 q^{94} - 15 q^{95} - 18 q^{96} - 87 q^{97} + 39 q^{98} + 3 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^6 - 12 * q^8 - 21 * q^9 - 3 * q^10 + 6 * q^12 - 3 * q^13 + 24 * q^14 + 3 * q^15 + 21 * q^16 - 24 * q^17 - 12 * q^18 - 12 * q^19 - 12 * q^20 + 3 * q^21 + 15 * q^22 + 21 * q^23 + 21 * q^24 - 21 * q^26 + 6 * q^27 - 24 * q^28 - 9 * q^29 - 12 * q^30 + 30 * q^31 + 45 * q^32 - 3 * q^33 + 24 * q^34 - 6 * q^35 - 21 * q^36 - 60 * q^37 - 15 * q^38 + 12 * q^39 - 6 * q^40 - 6 * q^41 + 39 * q^42 - 6 * q^43 - 30 * q^44 + 6 * q^45 + 21 * q^46 + 33 * q^47 - 63 * q^48 - 3 * q^49 + 27 * q^51 + 9 * q^52 + 24 * q^53 + 30 * q^54 - 3 * q^55 - 72 * q^56 - 30 * q^57 + 36 * q^58 + 18 * q^59 + 15 * q^60 + 6 * q^61 + 12 * q^62 + 24 * q^63 - 24 * q^64 + 3 * q^65 - 33 * q^66 - 24 * q^67 - 3 * q^68 + 27 * q^69 + 39 * q^70 + 24 * q^71 + 18 * q^72 + 6 * q^73 - 39 * q^74 - 6 * q^75 + 27 * q^76 + 24 * q^77 + 72 * q^78 + 9 * q^79 + 33 * q^80 + 15 * q^81 - 57 * q^82 - 12 * q^84 + 24 * q^85 - 33 * q^86 - 45 * q^87 + 39 * q^88 - 6 * q^89 - 21 * q^90 - 6 * q^91 - 66 * q^92 - 72 * q^93 - 66 * q^94 - 15 * q^95 - 18 * q^96 - 87 * q^97 + 39 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.58207	−	0.575828i	−1.11869	−	0.407172i	−0.284519	−	0.958670i	$-0.591834\pi$
$2$	−1.58207	−	0.575828i	−1.11869	−	0.407172i	−0.834176	+	0.551499i	$0.814056\pi$
$3$	−0.564707	−	3.20261i	−0.326034	−	1.84903i	−0.502309	−	0.864688i	$-0.667516\pi$
$3$	−0.564707	−	3.20261i	−0.326034	−	1.84903i	0.176275	−	0.984341i	$-0.443595\pi$
$4$	0.639290	+	0.536428i	0.319645	+	0.268214i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$6$	−0.950745	+	5.39194i	−0.388140	+	2.20125i
$7$	0.274194	−	0.474919i	0.103636	−	0.179502i	−0.809544	−	0.587059i	$-0.800286\pi$
$7$	0.274194	−	0.474919i	0.103636	−	0.179502i	0.913180	+	0.407556i	$0.133619\pi$
$8$	0.981094	+	1.69930i	0.346869	+	0.600795i
$9$	−7.11876	+	2.59101i	−2.37292	+	0.863672i
$10$	1.58207	−	0.575828i	0.500296	−	0.182093i
$11$	−0.165601	−	0.286829i	−0.0499306	−	0.0864823i	0.839980	−	0.542617i	$-0.182567\pi$
$11$	−0.165601	−	0.286829i	−0.0499306	−	0.0864823i	−0.889910	+	0.456135i	$0.849233\pi$
$12$	1.35696	−	2.35032i	0.391720	−	0.678480i
$13$	0.837254	−	4.74830i	0.232212	−	1.31694i	−0.616193	−	0.787595i	$-0.711326\pi$
$13$	0.837254	−	4.74830i	0.232212	−	1.31694i	0.848406	−	0.529347i	$-0.177563\pi$
$14$	−0.707267	+	0.593468i	−0.189025	+	0.158611i
$15$	2.49119	+	2.09036i	0.643223	+	0.539728i
$16$	−0.863487	−	4.89708i	−0.215872	−	1.22427i
$17$	−4.96227	−	1.80612i	−1.20353	−	0.438048i	−0.339074	−	0.940760i	$-0.610114\pi$
$17$	−4.96227	−	1.80612i	−1.20353	−	0.438048i	−0.864454	+	0.502711i	$0.832336\pi$
$18$	12.7544			3.00623
$19$	4.30704	+	0.670409i	0.988102	+	0.153802i
$19$	4.30704	+	0.670409i	0.988102	+	0.153802i
$20$	−0.834534			−0.186607
$21$	−1.67582	−	0.609949i	−0.365694	−	0.133102i
$22$	0.0968286	+	0.549142i	0.0206439	+	0.117078i
$23$	−0.850350	−	0.713529i	−0.177310	−	0.148781i	0.549813	−	0.835288i	$-0.314699\pi$
$23$	−0.850350	−	0.713529i	−0.177310	−	0.148781i	−0.727124	+	0.686507i	$0.759143\pi$
$24$	4.88818	−	4.10167i	0.997796	−	0.837250i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	−4.05880	+	7.03005i	−0.795996	+	1.37871i
$27$	7.44000	+	12.8865i	1.43183	+	2.48000i
$28$	0.430050	−	0.156525i	0.0812717	−	0.0295805i
$29$	3.01199	−	1.09627i	0.559312	−	0.203573i	−0.0468671	−	0.998901i	$-0.514924\pi$
$29$	3.01199	−	1.09627i	0.559312	−	0.203573i	0.606179	+	0.795328i	$0.292702\pi$
$30$	−2.73756	−	4.74159i	−0.499808	−	0.865693i
$31$	3.01060	−	5.21452i	0.540720	−	0.936555i	−0.458142	−	0.888879i	$-0.651485\pi$
$31$	3.01060	−	5.21452i	0.540720	−	0.936555i	0.998863	−	0.0476765i	$-0.0151816\pi$
$32$	−0.772312	+	4.38000i	−0.136527	+	0.774282i
$33$	−0.825087	+	0.692330i	−0.143629	+	0.120519i
$34$	6.81067	+	5.71483i	1.16802	+	0.980085i
$35$	0.0952268	+	0.540058i	0.0160963	+	0.0912864i
$36$	−5.94084	−	2.16229i	−0.990140	−	0.360382i
$37$	−6.67261			−1.09697			−0.548485	−	0.836161i	$-0.684795\pi$
$37$	−6.67261			−1.09697			−0.548485	+	0.836161i	$0.684795\pi$
$38$	−6.42801	−	3.54075i	−1.04276	−	0.574385i
$39$	−15.6798			−2.51077
$40$	−1.84385	−	0.671108i	−0.291539	−	0.106111i
$41$	−1.37380	−	7.79121i	−0.214552	−	1.21678i	−0.881683	−	0.471842i	$-0.843589\pi$
$41$	−1.37380	−	7.79121i	−0.214552	−	1.21678i	0.667131	−	0.744940i	$-0.267522\pi$
$42$	2.30005	+	1.92997i	0.354905	+	0.297800i
$43$	1.25559	−	1.05356i	0.191475	−	0.160667i	−0.542010	−	0.840372i	$-0.682337\pi$
$43$	1.25559	−	1.05356i	0.191475	−	0.160667i	0.733486	+	0.679705i	$0.237892\pi$
$44$	0.0479962	−	0.272200i	0.00723570	−	0.0410357i
$45$	3.78781	−	6.56068i	0.564653	−	0.978008i
$46$	0.934447	+	1.61851i	0.137777	+	0.238636i
$47$	4.32380	−	1.57373i	0.630691	−	0.229553i	−0.00684117	−	0.999977i	$-0.502178\pi$
$47$	4.32380	−	1.57373i	0.630691	−	0.229553i	0.637532	+	0.770424i	$0.279955\pi$
$48$	−15.1958	+	5.53083i	−2.19333	+	0.798306i
$49$	3.34963	+	5.80174i	0.478519	+	0.828820i
$50$	−0.841804	+	1.45805i	−0.119049	+	0.206199i
$51$	−2.98207	+	16.9122i	−0.417574	+	2.36818i
$52$	3.08237	−	2.58642i	0.427448	−	0.358671i
$53$	5.15257	+	4.32352i	0.707759	+	0.593881i	0.923970	−	0.382466i	$-0.124925\pi$
$53$	5.15257	+	4.32352i	0.707759	+	0.593881i	−0.216210	+	0.976347i	$0.569370\pi$
$54$	−4.35025	−	24.6715i	−0.591994	−	3.35736i
$55$	0.311228	+	0.113278i	0.0419660	+	0.0152744i
$56$	1.07604			0.143792
$57$	−0.285152	−	14.1723i	−0.0377693	−	1.87717i
$58$	−5.39645			−0.708588
$59$	6.39331	+	2.32697i	0.832338	+	0.302946i	0.722818	−	0.691038i	$-0.242846\pi$
$59$	6.39331	+	2.32697i	0.832338	+	0.302946i	0.109520	+	0.993985i	$0.465069\pi$
$60$	0.471267	+	2.67269i	0.0608403	+	0.345043i
$61$	0.520640	+	0.436869i	0.0666612	+	0.0559354i	0.675509	−	0.737351i	$-0.263924\pi$
$61$	0.520640	+	0.436869i	0.0666612	+	0.0559354i	−0.608848	+	0.793287i	$0.708368\pi$
$62$	−7.76566	+	6.51616i	−0.986240	+	0.827554i
$63$	−0.721402	+	4.09127i	−0.0908881	+	0.515452i
$64$	−1.22864	+	2.12807i	−0.153580	+	0.266009i
$65$	2.41078	+	4.17559i	0.299020	+	0.517918i
$66$	1.70401	−	0.620209i	0.209749	−	0.0763425i
$67$	7.30324	−	2.65816i	0.892232	−	0.324746i	0.145097	−	0.989418i	$-0.453651\pi$
$67$	7.30324	−	2.65816i	0.892232	−	0.324746i	0.747136	+	0.664672i	$0.231429\pi$
$68$	−2.20348	−	3.81654i	−0.267211	−	0.462823i
$69$	−1.80496	+	3.12628i	−0.217291	+	0.376360i
$70$	0.160324	−	0.909245i	0.0191624	−	0.108676i
$71$	−0.832574	+	0.698612i	−0.0988083	+	0.0829101i	−0.690854	−	0.722995i	$-0.742765\pi$
$71$	−0.832574	+	0.698612i	−0.0988083	+	0.0829101i	0.592045	+	0.805905i	$0.298321\pi$
$72$	−11.3871	−	9.55490i	−1.34198	−	1.12606i
$73$	2.42261	+	13.7393i	0.283545	+	1.60806i	0.710437	+	0.703761i	$0.248497\pi$
$73$	2.42261	+	13.7393i	0.283545	+	1.60806i	−0.426892	+	0.904302i	$0.640392\pi$
$74$	10.5566	+	3.84227i	1.22717	+	0.446655i
$75$	−3.25202			−0.375511
$76$	2.39382	+	2.73900i	0.274590	+	0.314185i
$77$	−0.181627			−0.0206984
$78$	24.8065	+	9.02885i	2.80879	+	1.02232i
$79$	−0.243868	−	1.38304i	−0.0274373	−	0.155605i	0.968011	−	0.250908i	$-0.0807291\pi$
$79$	−0.243868	−	1.38304i	−0.0274373	−	0.155605i	−0.995448	+	0.0953032i	$0.969618\pi$
$80$	3.80925	+	3.19634i	0.425887	+	0.357362i
$81$	19.6591	−	16.4960i	2.18435	−	1.83289i
$82$	−2.31294	+	13.1173i	−0.255422	+	1.44857i
$83$	0.427439	−	0.740346i	0.0469176	−	0.0812636i	−0.841613	−	0.540081i	$-0.818394\pi$
$83$	0.427439	−	0.740346i	0.0469176	−	0.0812636i	0.888530	+	0.458818i	$0.151727\pi$
$84$	−0.744142	−	1.28889i	−0.0811925	−	0.140630i
$85$	4.96227	−	1.80612i	0.538234	−	0.195901i
$86$	−2.59310	+	0.943812i	−0.279621	+	0.101774i
$87$	−5.21183	−	9.02715i	−0.558767	−	0.967812i
$88$	0.324940	−	0.562813i	0.0346387	−	0.0599960i
$89$	2.52694	−	14.3310i	0.267855	−	1.51908i	−0.492926	−	0.870071i	$-0.664073\pi$
$89$	2.52694	−	14.3310i	0.267855	−	1.51908i	0.760781	−	0.649009i	$-0.224816\pi$
$90$	−9.77042	+	8.19835i	−1.02989	+	0.864182i
$91$	−2.02549	−	1.69959i	−0.212329	−	0.178165i
$92$	−0.160864	−	0.912304i	−0.0167712	−	0.0951142i
$93$	−18.4002	−	6.69712i	−1.90801	−	0.694459i
$94$	−7.74677			−0.799018
$95$	−3.73031	+	2.25495i	−0.382722	+	0.231353i
$96$	14.4636			1.47618
$97$	6.59799	+	2.40147i	0.669924	+	0.243832i	0.654515	−	0.756049i	$-0.272873\pi$
$97$	6.59799	+	2.40147i	0.669924	+	0.243832i	0.0154088	+	0.999881i	$0.495095\pi$
$98$	−1.95857	−	11.1076i	−0.197845	−	1.12204i
$99$	1.92205	+	1.61279i	0.193173	+	0.162092i
$100$	0.639290	−	0.536428i	0.0639290	−	0.0536428i
$101$	−1.25144	+	7.09728i	−0.124523	+	0.706206i	0.857067	+	0.515205i	$0.172284\pi$
$101$	−1.25144	+	7.09728i	−0.124523	+	0.706206i	−0.981590	+	0.191000i	$0.938827\pi$
$102$	14.4563	−	25.0391i	1.43139	−	2.47924i
$103$	−3.53759	−	6.12729i	−0.348569	−	0.603739i	0.637426	−	0.770511i	$-0.279999\pi$
$103$	−3.53759	−	6.12729i	−0.348569	−	0.603739i	−0.985996	+	0.166772i	$0.946666\pi$
$104$	8.89023	−	3.23578i	0.871759	−	0.317294i
$105$	1.67582	−	0.609949i	0.163543	−	0.0595249i
$106$	−5.66214	−	9.80711i	−0.549956	−	0.952551i
$107$	3.25053	−	5.63008i	0.314241	−	0.544281i	−0.665035	−	0.746812i	$-0.731583\pi$
$107$	3.25053	−	5.63008i	0.314241	−	0.544281i	0.979276	+	0.202531i	$0.0649168\pi$
$108$	−2.15634	+	12.2292i	−0.207494	+	1.17676i
$109$	−13.5289	+	11.3521i	−1.29583	+	1.08733i	−0.304980	+	0.952359i	$0.598650\pi$
$109$	−13.5289	+	11.3521i	−1.29583	+	1.08733i	−0.990850	+	0.134971i	$0.956906\pi$
$110$	−0.427157	−	0.358427i	−0.0407278	−	0.0341747i
$111$	3.76807	+	21.3698i	0.357649	+	2.02833i
$112$	−2.56248	−	0.932665i	−0.242131	−	0.0881286i
$113$	−4.86487			−0.457649			−0.228824	−	0.973468i	$-0.573488\pi$
$113$	−4.86487			−0.457649			−0.228824	+	0.973468i	$0.573488\pi$
$114$	−7.70970	+	22.5859i	−0.722079	+	2.11536i
$115$	1.11005			0.103513
$116$	2.51360	+	0.914877i	0.233382	+	0.0849442i
$117$	6.34272	+	35.9713i	0.586384	+	3.32555i
$118$	−8.77475	−	7.36289i	−0.807781	−	0.677809i
$119$	−2.21839	+	1.86145i	−0.203359	+	0.170639i
$120$	−1.10806	+	6.28413i	−0.101152	+	0.573660i
$121$	5.44515	−	9.43128i	0.495014	−	0.857389i
$122$	−0.572130	−	0.990958i	−0.0517982	−	0.0897171i
$123$	−24.1764	+	8.79950i	−2.17992	+	0.793424i
$124$	4.72186	−	1.71862i	0.424036	−	0.154336i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	3.49718	−	6.05729i	0.311553	−	0.539626i
$127$	−0.515613	+	2.92418i	−0.0457532	+	0.259479i	−0.999101	−	0.0423950i	$-0.986501\pi$
$127$	−0.515613	+	2.92418i	−0.0457532	+	0.259479i	0.953348	+	0.301874i	$0.0976123\pi$
$128$	9.98327	−	8.37696i	0.882405	−	0.740426i
$129$	−4.08319	−	3.42620i	−0.359505	−	0.301660i
$130$	−1.40961	−	7.99427i	−0.123631	−	0.701144i
$131$	7.51285	+	2.73445i	0.656400	+	0.238910i	0.648682	−	0.761060i	$-0.275321\pi$
$131$	7.51285	+	2.73445i	0.656400	+	0.238910i	0.00771895	+	0.999970i	$0.497543\pi$
$132$	−0.898855			−0.0782353
$133$	1.49936	−	1.86167i	0.130011	−	0.161427i
$134$	−13.0849			−1.13036
$135$	−13.9826	−	5.08926i	−1.20343	−	0.438014i
$136$	−1.79931	−	10.2044i	−0.154289	−	0.875019i
$137$	0.705354	+	0.591862i	0.0602625	+	0.0505662i	0.672421	−	0.740169i	$-0.265254\pi$
$137$	0.705354	+	0.591862i	0.0602625	+	0.0505662i	−0.612159	+	0.790735i	$0.709699\pi$
$138$	4.65577	−	3.90666i	0.396326	−	0.332557i
$139$	−0.0173742	+	0.0985339i	−0.00147366	+	0.00835754i	−0.985536	−	0.169468i	$-0.945795\pi$
$139$	−0.0173742	+	0.0985339i	−0.00147366	+	0.00835754i	0.984062	+	0.177825i	$0.0569062\pi$
$140$	−0.228825	+	0.396336i	−0.0193392	+	0.0334965i
$141$	−7.48174	−	12.9588i	−0.630076	−	1.09132i
$142$	1.71947	−	0.625837i	0.144295	−	0.0525191i
$143$	−1.50060	+	0.546174i	−0.125487	+	0.0456734i
$144$	18.8353	+	32.6238i	1.56961	+	2.71865i
$145$	−1.60264	+	2.77586i	−0.133092	+	0.230523i
$146$	4.07872	−	23.1316i	0.337557	−	1.91438i
$147$	16.6892	−	14.0039i	1.37650	−	1.15502i
$148$	−4.26573	−	3.57937i	−0.350641	−	0.294223i
$149$	−3.00368	−	17.0347i	−0.246071	−	1.39554i	−0.817992	−	0.575229i	$-0.804913\pi$
$149$	−3.00368	−	17.0347i	−0.246071	−	1.39554i	0.571922	−	0.820308i	$-0.306198\pi$
$150$	5.14493	+	1.87260i	0.420082	+	0.152897i
$151$	−19.2178			−1.56393			−0.781963	−	0.623325i	$-0.785781\pi$
$151$	−19.2178			−1.56393			−0.781963	+	0.623325i	$0.785781\pi$
$152$	3.08638	+	7.97670i	0.250338	+	0.646996i
$153$	40.0049			3.23420
$154$	0.287348	+	0.104586i	0.0231552	+	0.00842779i
$155$	1.04557	+	5.92973i	0.0839823	+	0.476288i
$156$	−10.0239	−	8.41107i	−0.802556	−	0.673424i
$157$	−5.04261	+	4.23125i	−0.402444	+	0.337690i	−0.821437	−	0.570299i	$-0.806827\pi$
$157$	−5.04261	+	4.23125i	−0.402444	+	0.337690i	0.418994	+	0.907989i	$0.362383\pi$
$158$	−0.410578	+	2.32850i	−0.0326638	+	0.185246i
$159$	10.9369	−	18.9432i	0.867349	−	1.50229i
$160$	−2.22378	−	3.85171i	−0.175806	−	0.304504i
$161$	−0.572030	+	0.208202i	−0.0450822	+	0.0164086i
$162$	−40.6010	+	14.7776i	−3.18992	+	1.16104i
$163$	7.29637	+	12.6377i	0.571496	+	0.989860i	0.996413	+	0.0846275i	$0.0269700\pi$
$163$	7.29637	+	12.6377i	0.571496	+	0.989860i	−0.424917	+	0.905232i	$0.639697\pi$
$164$	3.30117	−	5.71779i	0.257778	−	0.446484i
$165$	0.187032	−	1.06071i	0.0145604	−	0.0825763i
$166$	−1.10255	+	0.925151i	−0.0855746	+	0.0718057i
$167$	2.68854	+	2.25595i	0.208045	+	0.174571i	0.740856	−	0.671664i	$-0.234420\pi$
$167$	2.68854	+	2.25595i	0.208045	+	0.174571i	−0.532811	+	0.846234i	$0.678864\pi$
$168$	−0.607648	−	3.44615i	−0.0468811	−	0.265876i
$169$	−9.62936	−	3.50480i	−0.740720	−	0.269600i
$170$	−8.89069			−0.681885
$171$	−32.3978	+	6.38711i	−2.47752	+	0.488435i
$172$	1.36784			0.104297
$173$	−2.35200	−	0.856059i	−0.178819	−	0.0650849i	0.251059	−	0.967972i	$-0.419221\pi$
$173$	−2.35200	−	0.856059i	−0.178819	−	0.0650849i	−0.429878	+	0.902887i	$0.641443\pi$
$174$	3.04741	+	17.2827i	0.231024	+	1.31020i
$175$	−0.420090	−	0.352498i	−0.0317558	−	0.0266463i
$176$	−1.26163	+	1.05863i	−0.0950990	+	0.0797975i
$177$	3.84205	−	21.7894i	0.288786	−	1.63779i
$178$	−12.2500	+	21.2176i	−0.918174	+	1.59032i
$179$	2.51029	+	4.34795i	0.187628	+	0.324981i	0.944459	−	0.328630i	$-0.106587\pi$
$179$	2.51029	+	4.34795i	0.187628	+	0.324981i	−0.756831	+	0.653610i	$0.773253\pi$
$180$	5.94084	−	2.16229i	0.442804	−	0.161168i
$181$	5.09429	−	1.85417i	0.378656	−	0.137819i	−0.145678	−	0.989332i	$-0.546536\pi$
$181$	5.09429	−	1.85417i	0.378656	−	0.137819i	0.524334	+	0.851513i	$0.324314\pi$
$182$	2.22580	+	3.85520i	0.164987	+	0.285766i
$183$	1.10511	−	1.91411i	0.0816923	−	0.141495i
$184$	0.378229	−	2.14504i	0.0278834	−	0.158135i
$185$	5.11151	−	4.28907i	0.375806	−	0.315339i
$186$	25.2541	+	21.1907i	1.85172	+	1.55378i
$187$	0.303709	+	1.72242i	0.0222094	+	0.125956i
$188$	3.60836	+	1.31333i	0.263166	+	0.0957847i
$189$	8.16003			0.593555
$190$	7.20009	−	1.41947i	0.522349	−	0.102979i
$191$	5.98517			0.433071			0.216536	−	0.976275i	$-0.430524\pi$
$191$	5.98517			0.433071			0.216536	+	0.976275i	$0.430524\pi$
$192$	7.50921	+	2.73313i	0.541931	+	0.197247i
$193$	0.376572	+	2.13565i	0.0271063	+	0.153727i	0.995357	−	0.0962548i	$-0.0306864\pi$
$193$	0.376572	+	2.13565i	0.0271063	+	0.153727i	−0.968250	+	0.249982i	$0.919575\pi$
$194$	−9.05567	−	7.59861i	−0.650159	−	0.545548i
$195$	12.0114	−	10.0788i	0.860154	−	0.721755i
$196$	−0.970827	+	5.50583i	−0.0693448	+	0.393274i
$197$	−8.28327	+	14.3471i	−0.590159	+	1.02219i	0.404052	+	0.914736i	$0.367602\pi$
$197$	−8.28327	+	14.3471i	−0.590159	+	1.02219i	−0.994211	+	0.107449i	$0.965732\pi$
$198$	−2.11214	−	3.65833i	−0.150103	−	0.259986i
$199$	−13.1370	+	4.78149i	−0.931259	+	0.338951i	−0.762709	−	0.646742i	$-0.776131\pi$
$199$	−13.1370	+	4.78149i	−0.931259	+	0.338951i	−0.168551	+	0.985693i	$0.553909\pi$
$200$	1.84385	−	0.671108i	0.130380	−	0.0474545i
$201$	−12.6372	−	21.8884i	−0.891363	−	1.54389i
$202$	6.06668	−	10.5078i	0.426850	−	0.739327i
$203$	0.305229	−	1.73104i	0.0214229	−	0.121495i
$204$	−10.9786	+	9.21211i	−0.768654	+	0.644977i
$205$	6.06049	+	5.08535i	0.423283	+	0.355176i
$206$	2.06847	+	11.7309i	0.144117	+	0.817328i
$207$	7.90220	+	2.87617i	0.549241	+	0.199907i
$208$	−23.9757			−1.66242
$209$	−0.520956	−	1.34640i	−0.0360353	−	0.0931327i
$210$	−3.00250			−0.207192
$211$	16.9908	+	6.18415i	1.16970	+	0.425735i	0.852552	−	0.522643i	$-0.175054\pi$
$211$	16.9908	+	6.18415i	1.16970	+	0.425735i	0.317145	+	0.948377i	$0.397276\pi$
$212$	0.974729	+	5.52796i	0.0669447	+	0.379662i
$213$	2.70755	+	2.27190i	0.185518	+	0.155668i
$214$	−8.38453	+	7.03546i	−0.573155	+	0.480934i
$215$	−0.284618	+	1.61415i	−0.0194108	+	0.110084i
$216$	−14.5987	+	25.2856i	−0.993314	+	1.72047i
$217$	−1.65098	−	2.85958i	−0.112076	−	0.194121i
$218$	27.9405	−	10.1695i	1.89237	−	0.688766i
$219$	42.6336	−	15.5174i	2.88091	−	1.04857i
$220$	0.138200	+	0.239369i	0.00931741	+	0.0161382i
$221$	−12.7307	+	22.0502i	−0.856358	+	1.48326i
$222$	6.34395	−	35.9783i	0.425778	−	2.41471i
$223$	20.1214	−	16.8838i	1.34743	−	1.13062i	0.367775	−	0.929915i	$-0.380119\pi$
$223$	20.1214	−	16.8838i	1.34743	−	1.13062i	0.979651	−	0.200710i	$-0.0643250\pi$
$224$	1.86838	+	1.56776i	0.124836	+	0.104750i
$225$	1.31549	+	7.46053i	0.0876995	+	0.497369i
$226$	7.69659	+	2.80133i	0.511969	+	0.186342i
$227$	6.97401			0.462881			0.231441	−	0.972849i	$-0.425656\pi$
$227$	6.97401			0.462881			0.231441	+	0.972849i	$0.425656\pi$
$228$	7.42015	−	9.21321i	0.491411	−	0.610159i
$229$	2.62489			0.173458			0.0867288	−	0.996232i	$-0.472359\pi$
$229$	2.62489			0.173458			0.0867288	+	0.996232i	$0.472359\pi$
$230$	−1.75619	−	0.639200i	−0.115799	−	0.0421476i
$231$	0.102566	+	0.581682i	0.00674837	+	0.0382719i
$232$	4.81794	+	4.04273i	0.316313	+	0.265419i
$233$	−20.4217	+	17.1358i	−1.33787	+	1.12260i	−0.355700	+	0.934600i	$0.615757\pi$
$233$	−20.4217	+	17.1358i	−1.33787	+	1.12260i	−0.982168	+	0.188004i	$0.939798\pi$
$234$	10.6786	−	60.5616i	0.698085	−	3.95904i
$235$	−2.30064	+	3.98483i	−0.150078	+	0.259942i
$236$	2.83892	+	4.91716i	0.184798	+	0.320080i
$237$	−4.29164	+	1.56203i	−0.278772	+	0.101465i
$238$	4.58153	−	1.66754i	0.296976	−	0.108091i
$239$	−6.55369	−	11.3513i	−0.423923	−	0.734256i	0.572396	−	0.819977i	$-0.306014\pi$
$239$	−6.55369	−	11.3513i	−0.423923	−	0.734256i	−0.996319	+	0.0857211i	$0.972681\pi$
$240$	8.08553	−	14.0045i	0.521918	−	0.903989i
$241$	−2.63284	+	14.9316i	−0.169596	+	0.961828i	0.774602	+	0.632449i	$0.217950\pi$
$241$	−2.63284	+	14.9316i	−0.169596	+	0.961828i	−0.944198	+	0.329379i	$0.893161\pi$
$242$	−14.0454	+	11.7855i	−0.902874	+	0.757601i
$243$	−29.7356	−	24.9511i	−1.90754	−	1.60062i
$244$	0.0984913	+	0.558572i	0.00630526	+	0.0357589i
$245$	−6.29525	−	2.29129i	−0.402189	−	0.146385i
$246$	43.3159			2.76172
$247$	6.78939	−	19.8898i	0.431998	−	1.26556i
$248$	11.8147			0.750237
$249$	−2.61242	−	0.950843i	−0.165555	−	0.0602573i
$250$	−0.292355	−	1.65803i	−0.0184902	−	0.104863i
$251$	14.5597	+	12.2170i	0.919001	+	0.771133i	0.973810	−	0.227364i	$-0.0730106\pi$
$251$	14.5597	+	12.2170i	0.919001	+	0.771133i	−0.0548090	+	0.998497i	$0.517455\pi$
$252$	−2.65586	+	2.22853i	−0.167303	+	0.140384i
$253$	−0.0638421	+	0.362066i	−0.00401372	+	0.0227629i
$254$	2.49956	−	4.32937i	0.156837	−	0.271649i
$255$	−8.58653	−	14.8723i	−0.537710	−	0.931340i
$256$	−15.9998	+	5.82344i	−0.999986	+	0.363965i
$257$	−20.5212	+	7.46911i	−1.28008	+	0.465910i	−0.890458	−	0.455066i	$-0.849616\pi$
$257$	−20.5212	+	7.46911i	−1.28008	+	0.465910i	−0.389620	+	0.920976i	$0.627394\pi$
$258$	4.48701	+	7.77172i	0.279349	+	0.483846i
$259$	−1.82959	+	3.16895i	−0.113685	+	0.196909i
$260$	−0.698716	+	3.96262i	−0.0433326	+	0.245751i
$261$	−18.6011	+	15.6082i	−1.15138	+	0.966124i
$262$	−10.3113	−	8.65221i	−0.637034	−	0.534535i
$263$	−3.40719	−	19.3231i	−0.210096	−	1.19152i	−0.889216	−	0.457488i	$-0.848749\pi$
$263$	−3.40719	−	19.3231i	−0.210096	−	1.19152i	0.679119	−	0.734028i	$-0.262362\pi$
$264$	−1.98597	−	0.722833i	−0.122228	−	0.0444873i
$265$	−6.72620			−0.413187
$266$	−3.44409	+	2.08193i	−0.211171	+	0.127651i
$267$	−47.3235			−2.89615
$268$	6.09480	+	2.21832i	0.372299	+	0.135506i
$269$	−0.293697	−	1.66564i	−0.0179070	−	0.101556i	0.974544	−	0.224195i	$-0.0719753\pi$
$269$	−0.293697	−	1.66564i	−0.0179070	−	0.101556i	−0.992451	+	0.122639i	$0.960864\pi$
$270$	19.1910	+	16.1032i	1.16793	+	0.980008i
$271$	−6.08215	+	5.10353i	−0.369465	+	0.310018i	−0.808550	−	0.588428i	$-0.799747\pi$
$271$	−6.08215	+	5.10353i	−0.369465	+	0.310018i	0.439085	+	0.898445i	$0.355303\pi$
$272$	−4.55985	+	25.8602i	−0.276481	+	1.56800i
$273$	−4.29931	+	7.44662i	−0.260206	+	0.450690i
$274$	−0.775111	−	1.34253i	−0.0468262	−	0.0811053i
$275$	−0.311228	+	0.113278i	−0.0187678	+	0.00683090i
$276$	−2.83091	+	1.03037i	−0.170401	+	0.0620209i
$277$	4.73698	+	8.20468i	0.284617	+	0.492972i	0.972516	−	0.232835i	$-0.0748002\pi$
$277$	4.73698	+	8.20468i	0.284617	+	0.492972i	−0.687899	+	0.725806i	$0.741467\pi$
$278$	0.0842258	−	0.145883i	0.00505153	−	0.00874950i
$279$	−7.92086	+	44.9214i	−0.474209	+	2.68937i
$280$	−0.824296	+	0.691666i	−0.0492611	+	0.0413350i
$281$	−9.62922	−	8.07988i	−0.574431	−	0.482005i	0.308682	−	0.951165i	$-0.400112\pi$
$281$	−9.62922	−	8.07988i	−0.574431	−	0.482005i	−0.883113	+	0.469160i	$0.844557\pi$
$282$	4.37465	+	24.8099i	0.260507	+	1.47741i
$283$	17.4632	+	6.35609i	1.03808	+	0.377830i	0.804152	−	0.594424i	$-0.202620\pi$
$283$	17.4632	+	6.35609i	1.03808	+	0.377830i	0.233928	+	0.972254i	$0.424842\pi$
$284$	−0.907012			−0.0538212
$285$	9.32825	+	10.6734i	0.552558	+	0.632235i
$286$	2.68856			0.158978
$287$	−4.07688	−	1.48386i	−0.240651	−	0.0875897i
$288$	−5.85074	−	33.1812i	−0.344758	−	1.95522i
$289$	8.33933	+	6.99753i	0.490549	+	0.411619i
$290$	4.13392	−	3.46877i	0.242752	−	0.203693i
$291$	3.96505	−	22.4869i	0.232435	−	1.31821i
$292$	−5.82139	+	10.0830i	−0.340671	+	0.590060i
$293$	8.68253	+	15.0386i	0.507239	+	0.878563i	0.999965	+	0.00837865i	$0.00266704\pi$
$293$	8.68253	+	15.0386i	0.507239	+	0.878563i	−0.492726	+	0.870184i	$0.664000\pi$
$294$	−34.4673	+	12.5451i	−2.01017	+	0.731643i
$295$	−6.39331	+	2.32697i	−0.372233	+	0.135482i
$296$	−6.54645	−	11.3388i	−0.380505	−	0.659054i
$297$	2.46414	−	4.26802i	0.142984	−	0.247656i
$298$	−5.05701	+	28.6798i	−0.292945	+	1.66137i
$299$	−4.10001	+	3.44032i	−0.237110	+	0.198959i
$300$	−2.07898	−	1.74447i	−0.120030	−	0.100717i
$301$	−0.156082	−	0.885183i	−0.00899639	−	0.0510211i
$302$	30.4040	+	11.0662i	1.74956	+	0.636786i
$303$	23.4365			1.34639
$304$	−0.436022	−	21.6708i	−0.0250076	−	1.24290i
$305$	−0.679648			−0.0389165
$306$	−63.2907	−	23.0359i	−3.61809	−	1.31688i
$307$	−4.34996	−	24.6698i	−0.248265	−	1.40798i	−0.812786	−	0.582563i	$-0.802050\pi$
$307$	−4.34996	−	24.6698i	−0.248265	−	1.40798i	0.564521	−	0.825419i	$-0.309061\pi$
$308$	−0.116113	−	0.0974301i	−0.00661613	−	0.00555159i
$309$	−17.6256	+	14.7897i	−1.00269	+	0.841354i
$310$	1.76033	−	9.98334i	0.0999802	−	0.567016i
$311$	2.79206	−	4.83598i	0.158323	−	0.274223i	−0.775941	−	0.630805i	$-0.782725\pi$
$311$	2.79206	−	4.83598i	0.158323	−	0.274223i	0.934264	+	0.356582i	$0.116058\pi$
$312$	−15.3833	−	26.6447i	−0.870909	−	1.50846i
$313$	0.771588	−	0.280835i	0.0436127	−	0.0158737i	−0.320122	−	0.947376i	$-0.603724\pi$
$313$	0.771588	−	0.280835i	0.0436127	−	0.0158737i	0.363734	+	0.931503i	$0.381502\pi$
$314$	10.4142	−	3.79048i	0.587710	−	0.213909i
$315$	−2.07719	−	3.59780i	−0.117037	−	0.202713i
$316$	0.586001	−	1.01498i	0.0329651	−	0.0570973i
$317$	5.82285	−	33.0230i	0.327044	−	1.85476i	−0.167860	−	0.985811i	$-0.553686\pi$
$317$	5.82285	−	33.0230i	0.327044	−	1.85476i	0.494904	−	0.868948i	$-0.335203\pi$
$318$	−28.2109	+	23.6718i	−1.58199	+	1.32745i
$319$	−0.813231	−	0.682382i	−0.0455322	−	0.0382061i
$320$	−0.426703	−	2.41995i	−0.0238534	−	0.135280i
$321$	−19.8666	−	7.23084i	−1.10884	−	0.403586i
$322$	1.02488			0.0571144
$323$	−20.1618	−	11.1058i	−1.12184	−	0.617942i
$324$	21.4168			1.18982
$325$	−4.53078	−	1.64907i	−0.251322	−	0.0914738i
$326$	−4.26627	−	24.1952i	−0.236287	−	1.34005i
$327$	43.9961	+	36.9171i	2.43299	+	2.04152i
$328$	11.8918	−	9.97841i	0.656615	−	0.550966i
$329$	0.438166	−	2.48496i	0.0241569	−	0.137000i
$330$	−0.906685	+	1.57042i	−0.0499114	+	0.0864490i
$331$	−5.63364	−	9.75775i	−0.309653	−	0.536334i	0.668634	−	0.743592i	$-0.266879\pi$
$331$	−5.63364	−	9.75775i	−0.309653	−	0.536334i	−0.978286	+	0.207258i	$0.933546\pi$
$332$	0.670400	−	0.244006i	0.0367930	−	0.0133916i
$333$	47.5006	−	17.2888i	2.60302	−	0.947421i
$334$	−2.95442	−	5.11721i	−0.161659	−	0.280001i
$335$	−3.88597	+	6.73070i	−0.212313	+	0.367737i
$336$	−1.53992	+	8.73330i	−0.0840093	+	0.476441i
$337$	4.82284	−	4.04684i	0.262717	−	0.220445i	−0.501909	−	0.864921i	$-0.667369\pi$
$337$	4.82284	−	4.04684i	0.262717	−	0.220445i	0.764625	+	0.644475i	$0.222924\pi$
$338$	13.2162	+	11.0897i	0.718866	+	0.603201i
$339$	2.74723	+	15.5803i	0.149209	+	0.846206i
$340$	4.14118	+	1.50727i	0.224587	+	0.0817431i
$341$	−1.99424			−0.107994
$342$	54.9335	+	8.55065i	2.97046	+	0.462366i
$343$	7.51253			0.405638
$344$	3.02217	+	1.09998i	0.162945	+	0.0593070i
$345$	−0.626855	−	3.55507i	−0.0337487	−	0.191399i
$346$	3.22810	+	2.70870i	0.173544	+	0.145620i
$347$	−13.4490	+	11.2851i	−0.721981	+	0.605814i	−0.927932	−	0.372749i	$-0.878415\pi$
$347$	−13.4490	+	11.2851i	−0.721981	+	0.605814i	0.205952	+	0.978562i	$0.433971\pi$
$348$	1.51055	−	8.56674i	0.0809738	−	0.459225i
$349$	−6.25844	+	10.8399i	−0.335007	+	0.580248i	−0.983486	−	0.180984i	$-0.942072\pi$
$349$	−6.25844	+	10.8399i	−0.335007	+	0.580248i	0.648480	+	0.761232i	$0.275405\pi$
$350$	0.461636	+	0.799577i	0.0246755	+	0.0427392i
$351$	67.4180	−	24.5381i	3.59850	−	1.30975i
$352$	1.38421	−	0.503810i	0.0737785	−	0.0268532i
$353$	−2.91409	−	5.04735i	−0.155101	−	0.268643i	0.777995	−	0.628271i	$-0.216237\pi$
$353$	−2.91409	−	5.04735i	−0.155101	−	0.268643i	−0.933096	+	0.359628i	$0.882904\pi$
$354$	−18.6253	+	32.2600i	−0.989924	+	1.71460i
$355$	0.188729	−	1.07034i	0.0100167	−	0.0568076i
$356$	9.30298	−	7.80613i	0.493057	−	0.413724i
$357$	7.21424	+	6.05346i	0.381818	+	0.320383i
$358$	−1.46779	−	8.32426i	−0.0775752	−	0.439951i
$359$	−0.544588	−	0.198214i	−0.0287423	−	0.0104613i	0.327609	−	0.944813i	$-0.393757\pi$
$359$	−0.544588	−	0.198214i	−0.0287423	−	0.0104613i	−0.356351	+	0.934352i	$0.615979\pi$
$360$	14.8648			0.783443
$361$	18.1011	+	5.77495i	0.952690	+	0.303945i
$362$	−9.12723			−0.479717
$363$	−33.2797	−	12.1128i	−1.74673	−	0.635757i
$364$	−0.383168	−	2.17306i	−0.0200835	−	0.113899i
$365$	−10.6873	−	8.96769i	−0.559398	−	0.469390i
$366$	−2.85057	+	2.39191i	−0.149002	+	0.125027i
$367$	−1.37291	+	7.78614i	−0.0716651	+	0.406433i	0.927780	+	0.373127i	$0.121715\pi$
$367$	−1.37291	+	7.78614i	−0.0716651	+	0.406433i	−0.999445	+	0.0333057i	$0.989397\pi$
$368$	−2.75994	+	4.78035i	−0.143872	+	0.249193i
$369$	29.9669	+	51.9042i	1.56001	+	2.70202i
$370$	−10.5566	+	3.84227i	−0.548809	+	0.199750i
$371$	3.46613	−	1.26157i	0.179952	−	0.0654973i
$372$	−8.17054	−	14.1518i	−0.423623	−	0.733736i
$373$	4.15310	−	7.19338i	0.215039	−	0.372459i	−0.738245	−	0.674532i	$-0.764345\pi$
$373$	4.15310	−	7.19338i	0.215039	−	0.372459i	0.953285	+	0.302073i	$0.0976787\pi$
$374$	0.511327	−	2.89988i	0.0264401	−	0.149949i
$375$	2.49119	−	2.09036i	0.128645	−	0.107946i
$376$	6.91630	+	5.80347i	0.356681	+	0.299291i
$377$	−2.68364	−	15.2197i	−0.138214	−	0.783853i
$378$	−12.9098	−	4.69877i	−0.664007	−	0.241679i
$379$	10.2928			0.528707			0.264354	−	0.964426i	$-0.414841\pi$
$379$	10.2928			0.528707			0.264354	+	0.964426i	$0.414841\pi$
$380$	−3.59437	−	0.559479i	−0.184387	−	0.0287007i
$381$	9.65620			0.494702
$382$	−9.46897	−	3.44642i	−0.484475	−	0.176334i
$383$	5.56168	+	31.5418i	0.284188	+	1.61171i	0.708170	+	0.706042i	$0.249521\pi$
$383$	5.56168	+	31.5418i	0.284188	+	1.61171i	−0.423981	+	0.905671i	$0.639368\pi$
$384$	−32.4658	−	27.2420i	−1.65676	−	1.39019i
$385$	0.139135	−	0.116748i	0.00709096	−	0.00595002i
$386$	0.634000	−	3.59559i	0.0322698	−	0.183011i
$387$	−6.20842	+	10.7533i	−0.315592	+	0.546621i
$388$	2.92981	+	5.07458i	0.148739	+	0.257623i
$389$	28.7624	−	10.4686i	1.45831	−	0.530781i	0.513411	−	0.858143i	$-0.328382\pi$
$389$	28.7624	−	10.4686i	1.45831	−	0.530781i	0.944899	+	0.327362i	$0.106160\pi$
$390$	−24.8065	+	9.02885i	−1.25613	+	0.457193i
$391$	2.93095	+	5.07656i	0.148225	+	0.256733i
$392$	−6.57261	+	11.3841i	−0.331967	+	0.574984i
$393$	4.51483	−	25.6049i	0.227743	−	1.29160i
$394$	21.3662	−	17.9284i	1.07641	−	0.903217i
$395$	1.07582	+	0.902717i	0.0541302	+	0.0454206i
$396$	0.363601	+	2.06208i	0.0182716	+	0.103624i
$397$	−9.97995	−	3.63241i	−0.500880	−	0.182305i	0.0792100	−	0.996858i	$-0.474760\pi$
$397$	−9.97995	−	3.63241i	−0.500880	−	0.182305i	−0.580090	+	0.814553i	$0.696982\pi$
$398$	23.5371			1.17981
$399$	−6.80890	−	3.75056i	−0.340871	−	0.187763i
$400$	−4.97262			−0.248631
$401$	14.3159	+	5.21056i	0.714901	+	0.260203i	0.673760	−	0.738950i	$-0.264678\pi$
$401$	14.3159	+	5.21056i	0.714901	+	0.260203i	0.0411417	+	0.999153i	$0.486901\pi$
$402$	7.38913	+	41.9059i	0.368536	+	2.09007i
$403$	−22.2395	−	18.6611i	−1.10783	−	0.929577i
$404$	−4.60721	+	3.86591i	−0.229217	+	0.192336i
$405$	−4.45636	+	25.2733i	−0.221438	+	1.25584i
$406$	−1.47968	+	2.56287i	−0.0734351	+	0.127193i
$407$	1.10499	+	1.91390i	0.0547723	+	0.0948684i
$408$	−31.6646	+	11.5250i	−1.56763	+	0.570571i
$409$	10.9607	−	3.98936i	0.541971	−	0.197261i	−0.0565046	−	0.998402i	$-0.517996\pi$
$409$	10.9607	−	3.98936i	0.541971	−	0.197261i	0.598476	+	0.801141i	$0.295773\pi$
$410$	−6.65985	−	11.5352i	−0.328906	−	0.569683i
$411$	1.49719	−	2.59320i	0.0738508	−	0.127913i
$412$	1.02530	−	5.81478i	0.0505130	−	0.286473i
$413$	2.85813	−	2.39826i	0.140640	−	0.118011i
$414$	−10.8457	−	9.10061i	−0.533036	−	0.447271i
$415$	0.148448	+	0.841891i	0.00728703	+	0.0413268i
$416$	20.1509	+	7.33434i	0.987981	+	0.359595i
$417$	0.325377			0.0159338
$418$	0.0488942	+	2.43009i	0.00239149	+	0.118860i
$419$	17.7028			0.864840			0.432420	−	0.901672i	$-0.357660\pi$
$419$	17.7028			0.864840			0.432420	+	0.901672i	$0.357660\pi$
$420$	1.39853	+	0.509023i	0.0682412	+	0.0248378i
$421$	3.57756	+	20.2893i	0.174359	+	0.988841i	0.938881	+	0.344243i	$0.111864\pi$
$421$	3.57756	+	20.2893i	0.174359	+	0.988841i	−0.764521	+	0.644599i	$0.777025\pi$
$422$	−23.3197	−	19.5676i	−1.13519	−	0.952534i
$423$	−26.7025	+	22.4061i	−1.29832	+	1.08942i
$424$	−2.29182	+	12.9976i	−0.111301	+	0.631217i
$425$	−2.64037	+	4.57326i	−0.128077	+	0.221835i
$426$	−2.97531	−	5.15339i	−0.144154	−	0.249683i
$427$	0.350234	−	0.127475i	0.0169490	−	0.00616894i
$428$	5.09817	−	1.85558i	0.246429	−	0.0896929i
$429$	2.59658	+	4.49742i	0.125364	+	0.217137i
$430$	1.37976	−	2.38981i	0.0665379	−	0.115247i
$431$	1.44676	−	8.20498i	0.0696879	−	0.395220i	−0.929934	−	0.367726i	$-0.880136\pi$
$431$	1.44676	−	8.20498i	0.0696879	−	0.395220i	0.999622	−	0.0274936i	$-0.00875258\pi$
$432$	56.6816	−	47.5615i	2.72710	−	2.28831i
$433$	21.5979	+	18.1228i	1.03793	+	0.870926i	0.991773	−	0.128008i	$-0.0408584\pi$
$433$	21.5979	+	18.1228i	1.03793	+	0.870926i	0.0461560	+	0.998934i	$0.485303\pi$
$434$	0.965347	+	5.47475i	0.0463381	+	0.262797i
$435$	9.79503	+	3.56510i	0.469636	+	0.170934i
$436$	−14.7384			−0.705843
$437$	−3.18413	−	3.64328i	−0.152318	−	0.174282i
$438$	−76.3848			−3.64981
$439$	−28.5501	−	10.3914i	−1.36262	−	0.495954i	−0.445759	−	0.895153i	$-0.647066\pi$
$439$	−28.5501	−	10.3914i	−1.36262	−	0.495954i	−0.916864	+	0.399199i	$0.869288\pi$
$440$	0.112850	+	0.640007i	0.00537994	+	0.0305111i
$441$	−38.8776	−	32.6222i	−1.85132	−	1.55344i
$442$	32.8380	−	27.5543i	1.56194	−	1.31063i
$443$	4.25799	−	24.1482i	0.202303	−	1.14732i	−0.699325	−	0.714804i	$-0.746516\pi$
$443$	4.25799	−	24.1482i	0.202303	−	1.14732i	0.901628	−	0.432513i	$-0.142373\pi$
$444$	−9.05446	+	15.6828i	−0.429705	+	0.744272i
$445$	7.27602	+	12.6024i	0.344917	+	0.597413i
$446$	−41.5556	+	15.1250i	−1.96772	+	0.716190i
$447$	−52.8594	+	19.2392i	−2.50016	+	0.909984i
$448$	0.673774	+	1.16701i	0.0318328	+	0.0551361i
$449$	−12.3444	+	21.3812i	−0.582570	+	1.00904i	0.412604	+	0.910911i	$0.364619\pi$
$449$	−12.3444	+	21.3812i	−0.582570	+	1.00904i	−0.995174	+	0.0981300i	$0.968714\pi$
$450$	2.21477	−	12.5606i	0.104405	−	0.592113i
$451$	−2.00724	+	1.68428i	−0.0945174	+	0.0793095i
$452$	−3.11007	−	2.60965i	−0.146285	−	0.122748i
$453$	10.8525	+	61.5473i	0.509893	+	2.89175i
$454$	−11.0334	−	4.01583i	−0.517823	−	0.188472i
$455$	2.64409			0.123957
$456$	23.8034	−	14.3890i	1.11469	−	0.673825i
$457$	7.16480			0.335155			0.167578	−	0.985859i	$-0.446406\pi$
$457$	7.16480			0.335155			0.167578	+	0.985859i	$0.446406\pi$
$458$	−4.15277	−	1.51148i	−0.194046	−	0.0706270i
$459$	−13.6448	−	77.3837i	−0.636886	−	3.61196i
$460$	0.709646	+	0.595464i	0.0330874	+	0.0277636i
$461$	16.6388	−	13.9616i	0.774947	−	0.650258i	−0.167024	−	0.985953i	$-0.553416\pi$
$461$	16.6388	−	13.9616i	0.774947	−	0.650258i	0.941971	+	0.335695i	$0.108971\pi$
$462$	0.172681	−	0.979325i	0.00803386	−	0.0455623i
$463$	15.9642	−	27.6508i	0.741918	−	1.28504i	−0.209703	−	0.977765i	$-0.567250\pi$
$463$	15.9642	−	27.6508i	0.741918	−	1.28504i	0.951621	−	0.307274i	$-0.0994169\pi$
$464$	−7.96934	−	13.8033i	−0.369968	−	0.640803i
$465$	18.4002	−	6.69712i	0.853289	−	0.310572i
$466$	42.1759	−	15.3508i	1.95376	−	0.711110i
$467$	9.76911	+	16.9206i	0.452061	+	0.782992i	0.998514	−	0.0544977i	$-0.0173558\pi$
$467$	9.76911	+	16.9206i	0.452061	+	0.782992i	−0.546453	+	0.837490i	$0.684022\pi$
$468$	−15.2412	+	26.3985i	−0.704524	+	1.22027i
$469$	0.740097	−	4.19730i	0.0341745	−	0.193813i
$470$	5.93437	−	4.97952i	0.273732	−	0.229688i
$471$	16.3986	+	13.7601i	0.755610	+	0.634032i
$472$	2.31820	+	13.1472i	0.106704	+	0.605147i
$473$	−0.510119	−	0.185668i	−0.0234553	−	0.00853703i
$474$	7.68914			0.353174
$475$	1.40813	−	4.12519i	0.0646096	−	0.189277i
$476$	−2.41673			−0.110770
$477$	−47.8822	−	17.4277i	−2.19237	−	0.797959i
$478$	3.83201	+	21.7324i	0.175272	+	0.994018i
$479$	−9.37543	−	7.86692i	−0.428374	−	0.359449i	0.402964	−	0.915216i	$-0.367980\pi$
$479$	−9.37543	−	7.86692i	−0.428374	−	0.359449i	−0.831338	+	0.555767i	$0.812425\pi$
$480$	−11.0797	+	9.29700i	−0.505718	+	0.424348i
$481$	−5.58666	+	31.6835i	−0.254730	+	1.44464i
$482$	12.7634	−	22.1068i	0.581356	−	1.00694i
$483$	0.989819	+	1.71442i	0.0450383	+	0.0780086i
$484$	8.54024	−	3.10839i	0.388193	−	0.141291i
$485$	−6.59799	+	2.40147i	−0.299599	+	0.109045i
$486$	32.6764	+	56.5971i	1.48223	+	2.56730i
$487$	7.05086	−	12.2125i	0.319505	−	0.553399i	−0.660880	−	0.750492i	$-0.729817\pi$
$487$	7.05086	−	12.2125i	0.319505	−	0.553399i	0.980385	+	0.197093i	$0.0631500\pi$
$488$	−0.231577	+	1.31334i	−0.0104830	+	0.0594519i
$489$	36.3533	−	30.5040i	1.64395	−	1.37944i
$490$	8.64017	+	7.24996i	0.390323	+	0.327520i
$491$	−3.45329	−	19.5846i	−0.155845	−	0.883839i	−0.958009	−	0.286737i	$-0.907430\pi$
$491$	−3.45329	−	19.5846i	−0.155845	−	0.883839i	0.802165	−	0.597103i	$-0.203682\pi$
$492$	−20.1761	−	7.34348i	−0.909607	−	0.331070i
$493$	−16.9263			−0.762322
$494$	−22.1944	+	27.5576i	−0.998573	+	1.23988i
$495$	−2.50906			−0.112774
$496$	−28.1355	−	10.2405i	−1.26332	−	0.459812i
$497$	0.103497	+	0.586961i	0.00464248	+	0.0263288i
$498$	3.58552	+	3.00861i	0.160671	+	0.134819i
$499$	−5.69739	+	4.78068i	−0.255050	+	0.214013i	−0.761343	−	0.648349i	$-0.775460\pi$
$499$	−5.69739	+	4.78068i	−0.255050	+	0.214013i	0.506293	+	0.862362i	$0.331015\pi$
$500$	−0.144915	+	0.821855i	−0.00648081	+	0.0367545i
$501$	5.70670	−	9.88429i	0.254956	−	0.441598i
$502$	−15.9996	−	27.7122i	−0.714098	−	1.23685i
$503$	12.6972	−	4.62141i	0.566141	−	0.206059i	−0.0430624	−	0.999072i	$-0.513711\pi$
$503$	12.6972	−	4.62141i	0.566141	−	0.206059i	0.609204	+	0.793014i	$0.291489\pi$
$504$	−7.66008	+	2.78804i	−0.341207	+	0.124189i
$505$	−3.60338	−	6.24124i	−0.160348	−	0.277732i
$506$	0.309491	−	0.536054i	0.0137585	−	0.0238305i
$507$	−5.78675	+	32.8183i	−0.256999	+	1.45751i
$508$	−1.89824	+	1.59281i	−0.0842208	+	0.0706696i
$509$	−26.9446	−	22.6092i	−1.19430	−	1.00214i	−0.999774	−	0.0212383i	$-0.993239\pi$
$509$	−26.9446	−	22.6092i	−1.19430	−	1.00214i	−0.194525	−	0.980898i	$-0.562316\pi$
$510$	5.02064	+	28.4734i	0.222318	+	1.26083i
$511$	7.18932	+	2.61670i	0.318037	+	0.115756i
$512$	2.60163			0.114977
$513$	23.4051	+	60.4903i	1.03336	+	2.67071i
$514$	36.7670			1.62172
$515$	6.64850	+	2.41985i	0.292968	+	0.106632i
$516$	−0.772431	−	4.38068i	−0.0340044	−	0.192849i
$517$	−1.16742	−	0.979580i	−0.0513430	−	0.0430819i
$518$	4.71931	−	3.95998i	0.207355	−	0.173991i
$519$	−1.41343	+	8.01597i	−0.0620428	+	0.351862i
$520$	−4.73039	+	8.19328i	−0.207441	+	0.359299i
$521$	2.92797	+	5.07140i	0.128277	+	0.222182i	0.923009	−	0.384778i	$-0.125722\pi$
$521$	2.92797	+	5.07140i	0.128277	+	0.222182i	−0.794732	+	0.606960i	$0.792389\pi$
$522$	38.4160	−	13.9823i	1.68142	−	0.611988i
$523$	−10.8529	+	3.95014i	−0.474565	+	0.172727i	−0.568219	−	0.822877i	$-0.692367\pi$
$523$	−10.8529	+	3.95014i	−0.474565	+	0.172727i	0.0936543	+	0.995605i	$0.470145\pi$
$524$	3.33605	+	5.77821i	0.145736	+	0.252422i
$525$	−0.891685	+	1.54444i	−0.0389163	+	0.0674051i
$526$	−5.73637	+	32.5326i	−0.250118	+	1.41849i
$527$	−24.3575	+	20.4384i	−1.06103	+	0.890309i
$528$	4.10284	+	3.44270i	0.178553	+	0.149824i
$529$	−3.77994	−	21.4371i	−0.164345	−	0.932047i
$530$	10.6413	+	3.87313i	0.462230	+	0.168238i
$531$	−51.5416			−2.23672
$532$	1.95717	−	0.385851i	0.0848543	−	0.0167287i
$533$	−38.1452			−1.65225
$534$	74.8693	+	27.2502i	3.23991	+	1.17923i
$535$	1.12890	+	6.40229i	0.0488065	+	0.276795i
$536$	11.6822	+	9.80251i	0.504593	+	0.423404i
$537$	12.5072	−	10.4948i	0.539726	−	0.452884i
$538$	−0.494470	+	2.80428i	−0.0213181	+	0.120901i
$539$	1.10941	−	1.92155i	0.0477855	−	0.0827669i
$540$	−6.20893	−	10.7542i	−0.267190	−	0.462787i
$541$	−11.0424	+	4.01909i	−0.474748	+	0.172794i	−0.568302	−	0.822820i	$-0.692399\pi$
$541$	−11.0424	+	4.01909i	−0.474748	+	0.172794i	0.0935540	+	0.995614i	$0.470177\pi$
$542$	12.5612	−	4.57189i	0.539548	−	0.196380i
$543$	−8.81497	−	15.2680i	−0.378287	−	0.655212i
$544$	11.7432	−	20.3399i	0.503487	−	0.872064i
$545$	3.06674	−	17.3924i	0.131365	−	0.745007i
$546$	11.0898	−	9.30544i	0.474599	−	0.398236i
$547$	−22.1845	−	18.6150i	−0.948541	−	0.795920i	0.0305106	−	0.999534i	$-0.490287\pi$
$547$	−22.1845	−	18.6150i	−0.948541	−	0.795920i	−0.979051	+	0.203614i	$0.934731\pi$
$548$	0.133434	+	0.756743i	0.00570003	+	0.0323265i
$549$	−4.83825	−	1.76098i	−0.206491	−	0.0751567i
$550$	0.557614			0.0237767
$551$	13.7077	−	2.70242i	0.583967	−	0.115127i
$552$	−7.08333			−0.301486
$553$	−0.723700	−	0.263405i	−0.0307749	−	0.0112011i
$554$	−2.76976	−	15.7081i	−0.117676	−	0.667373i
$555$	−16.6227	−	13.9481i	−0.705596	−	0.592065i
$556$	−0.0639635	+	0.0536718i	−0.00271266	+	0.00227619i
$557$	−4.20497	+	23.8476i	−0.178170	+	1.01045i	0.756250	+	0.654282i	$0.227029\pi$
$557$	−4.20497	+	23.8476i	−0.178170	+	1.01045i	−0.934421	+	0.356171i	$0.884082\pi$
$558$	38.3984	−	66.5079i	1.62553	−	2.81550i
$559$	−3.95139	−	6.84400i	−0.167126	−	0.289470i
$560$	2.56248	−	0.932665i	0.108284	−	0.0394123i
$561$	5.34474	−	1.94533i	0.225655	−	0.0821317i
$562$	10.5815	+	18.3277i	0.446355	+	0.773109i
$563$	−22.7232	+	39.3578i	−0.957669	+	1.65873i	−0.229531	+	0.973301i	$0.573719\pi$
$563$	−22.7232	+	39.3578i	−0.957669	+	1.65873i	−0.728138	+	0.685431i	$0.759614\pi$
$564$	2.16844	−	12.2978i	0.0913076	−	0.517831i
$565$	3.72671	−	3.12708i	0.156784	−	0.131557i
$566$	−23.9681	−	20.1116i	−1.00745	−	0.845354i
$567$	−2.44382	−	13.8596i	−0.102631	−	0.582048i
$568$	−2.00399	−	0.729392i	−0.0840855	−	0.0306046i
$569$	28.1695			1.18093			0.590463	−	0.807065i	$-0.298945\pi$
$569$	28.1695			1.18093			0.590463	+	0.807065i	$0.298945\pi$
$570$	−8.61196	−	22.2575i	−0.360715	−	0.932264i
$571$	18.2742			0.764752			0.382376	−	0.924007i	$-0.375106\pi$
$571$	18.2742			0.764752			0.382376	+	0.924007i	$0.375106\pi$
$572$	−1.25230	−	0.455801i	−0.0523614	−	0.0190580i
$573$	−3.37987	−	19.1682i	−0.141196	−	0.800762i
$574$	5.59547	+	4.69516i	0.233551	+	0.195972i
$575$	−0.850350	+	0.713529i	−0.0354621	+	0.0297562i
$576$	3.23254	−	18.3327i	0.134689	−	0.763861i
$577$	10.0919	−	17.4797i	0.420132	−	0.727689i	−0.575820	−	0.817576i	$-0.695317\pi$
$577$	10.0919	−	17.4797i	0.420132	−	0.727689i	0.995952	+	0.0898868i	$0.0286505\pi$
$578$	−9.16406	−	15.8726i	−0.381175	−	0.660214i
$579$	6.62700	−	2.41203i	0.275409	−	0.100241i
$580$	−2.51360	+	0.914877i	−0.104372	+	0.0379882i
$581$	−0.234403	−	0.405998i	−0.00972467	−	0.0168436i
$582$	−19.2216	+	33.2928i	−0.796761	+	1.38003i
$583$	0.386841	−	2.19389i	0.0160213	−	0.0908614i
$584$	−20.9704	+	17.5963i	−0.867763	+	0.728140i
$585$	−27.9807	−	23.4786i	−1.15686	−	0.970721i
$586$	−5.07677	−	28.7918i	−0.209719	−	1.18938i
$587$	17.3771	+	6.32474i	0.717229	+	0.261050i	0.674749	−	0.738047i	$-0.264252\pi$
$587$	17.3771	+	6.32474i	0.717229	+	0.261050i	0.0424803	+	0.999097i	$0.486474\pi$
$588$	18.1813			0.749783
$589$	16.4626	−	20.4408i	0.678331	−	0.842248i
$590$	11.4546			0.471579
$591$	50.6257	+	18.4262i	2.08246	+	0.757954i
$592$	5.76170	+	32.6763i	0.236805	+	1.34299i
$593$	−3.91012	−	3.28098i	−0.160569	−	0.134734i	0.558963	−	0.829193i	$-0.311199\pi$
$593$	−3.91012	−	3.28098i	−0.160569	−	0.134734i	−0.719532	+	0.694459i	$0.755644\pi$
$594$	−6.35610	+	5.33340i	−0.260794	+	0.218832i
$595$	0.502868	−	2.85190i	0.0206156	−	0.116917i
$596$	7.21767	−	12.5014i	0.295647	−	0.512076i
$597$	22.7318	+	39.3727i	0.930352	+	1.61142i
$598$	8.46754	−	3.08193i	0.346264	−	0.126030i
$599$	−33.6127	+	12.2340i	−1.37338	+	0.499869i	−0.920164	−	0.391532i	$-0.871945\pi$
$599$	−33.6127	+	12.2340i	−1.37338	+	0.499869i	−0.453215	+	0.891401i	$0.649723\pi$
$600$	−3.19053	−	5.52617i	−0.130253	−	0.225605i
$601$	−17.1676	+	29.7352i	−0.700281	+	1.21292i	0.268087	+	0.963395i	$0.413609\pi$
$601$	−17.1676	+	29.7352i	−0.700281	+	1.21292i	−0.968368	+	0.249528i	$0.919725\pi$
$602$	−0.262780	+	1.49030i	−0.0107101	+	0.0607401i
$603$	−45.1026	+	37.8456i	−1.83672	+	1.54119i
$604$	−12.2858	−	10.3090i	−0.499901	−	0.419467i
$605$	1.89108	+	10.7249i	0.0768834	+	0.436027i
$606$	−37.0783	−	13.4954i	−1.50620	−	0.548213i
$607$	−3.43239			−0.139316			−0.0696582	−	0.997571i	$-0.522191\pi$
$607$	−3.43239			−0.139316			−0.0696582	+	0.997571i	$0.522191\pi$
$608$	−6.26277	+	18.3470i	−0.253989	+	0.744071i
$609$	−5.71622			−0.231633
$610$	1.07525	+	0.391360i	0.0435357	+	0.0158457i
$611$	−3.85245	−	21.8483i	−0.155853	−	0.883888i
$612$	25.5747	+	21.4597i	1.03380	+	0.867459i
$613$	21.5266	−	18.0630i	0.869451	−	0.729556i	−0.0945313	−	0.995522i	$-0.530135\pi$
$613$	21.5266	−	18.0630i	0.869451	−	0.729556i	0.963982	+	0.265966i	$0.0856908\pi$
$614$	−7.32362	+	41.5343i	−0.295557	+	1.67619i
$615$	12.8640	−	22.2811i	0.518727	−	0.898461i
$616$	−0.178194	−	0.308640i	−0.00717962	−	0.0124355i
$617$	11.2044	−	4.07805i	0.451070	−	0.164176i	−0.106488	−	0.994314i	$-0.533961\pi$
$617$	11.2044	−	4.07805i	0.451070	−	0.164176i	0.557558	+	0.830138i	$0.311738\pi$
$618$	36.4013	−	13.2490i	1.46428	−	0.532953i
$619$	13.9457	+	24.1547i	0.560525	+	0.970858i	0.997451	+	0.0713602i	$0.0227340\pi$
$619$	13.9457	+	24.1547i	0.560525	+	0.970858i	−0.436926	+	0.899498i	$0.643933\pi$
$620$	−2.51245	+	4.35169i	−0.100902	+	0.174768i
$621$	2.86825	−	16.2667i	0.115099	−	0.652759i
$622$	−7.20193	+	6.04314i	−0.288771	+	0.242308i
$623$	−6.11318	−	5.12956i	−0.244919	−	0.205512i
$624$	13.5393	+	76.7850i	0.542005	+	3.07386i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	−1.38242			−0.0552527
$627$	−4.01782	+	2.42874i	−0.160456	+	0.0969947i
$628$	−5.49345			−0.219212
$629$	33.1113	+	12.0515i	1.32023	+	0.480526i
$630$	1.21456	+	6.88810i	0.0483891	+	0.274428i
$631$	14.3666	+	12.0550i	0.571927	+	0.479904i	0.882285	−	0.470716i	$-0.156004\pi$
$631$	14.3666	+	12.0550i	0.571927	+	0.479904i	−0.310358	+	0.950620i	$0.600449\pi$
$632$	2.11095	−	1.77130i	0.0839692	−	0.0704586i
$633$	10.2106	−	57.9073i	0.405835	−	2.30161i
$634$	−28.2278	+	48.8919i	−1.12107	+	1.94175i
$635$	−1.48465	−	2.57148i	−0.0589164	−	0.102046i
$636$	17.1535	−	6.24336i	0.680180	−	0.247565i
$637$	30.3529	−	11.0475i	1.20263	−	0.437720i
$638$	0.893657	+	1.54786i	0.0353802	+	0.0612803i
$639$	4.11677	−	7.13046i	0.162857	−	0.282077i
$640$	−2.26302	+	12.8342i	−0.0894539	+	0.507318i
$641$	−16.7076	+	14.0193i	−0.659909	+	0.553729i	−0.910059	−	0.414478i	$-0.863964\pi$
$641$	−16.7076	+	14.0193i	−0.659909	+	0.553729i	0.250151	+	0.968207i	$0.419520\pi$
$642$	27.2667	+	22.8794i	1.07613	+	0.902980i
$643$	−8.24656	−	46.7686i	−0.325213	−	1.84437i	−0.508176	−	0.861253i	$-0.669680\pi$
$643$	−8.24656	−	46.7686i	−0.325213	−	1.84437i	0.182964	−	0.983120i	$-0.441431\pi$
$644$	−0.477378	−	0.173751i	−0.0188113	−	0.00684676i
$645$	5.33023			0.209877
$646$	25.5025	+	29.1799i	1.00338	+	1.14807i
$647$	35.0985			1.37986			0.689932	−	0.723874i	$-0.257640\pi$
$647$	35.0985			1.37986			0.689932	+	0.723874i	$0.257640\pi$
$648$	47.3191	+	17.2227i	1.85887	+	0.676573i
$649$	−0.391294	−	2.21914i	−0.0153596	−	0.0871087i
$650$	6.21844	+	5.21789i	0.243907	+	0.204663i
$651$	−8.22582	+	6.90228i	−0.322395	+	0.270522i
$652$	−2.11471	+	11.9931i	−0.0828185	+	0.469687i
$653$	−23.2582	+	40.2844i	−0.910163	+	1.57645i	−0.0963305	+	0.995349i	$0.530711\pi$
$653$	−23.2582	+	40.2844i	−0.910163	+	1.57645i	−0.813833	+	0.581099i	$0.802623\pi$
$654$	−48.3472	−	83.7397i	−1.89052	−	3.27448i
$655$	−7.51285	+	2.73445i	−0.293551	+	0.106844i
$656$	−36.9679	+	13.4552i	−1.44335	+	0.525338i
$657$	−52.8447	−	91.5297i	−2.06167	−	3.57091i
$658$	−2.12412	+	3.67908i	−0.0828068	+	0.143426i
$659$	−7.50737	+	42.5764i	−0.292445	+	1.65854i	0.384962	+	0.922932i	$0.374215\pi$
$659$	−7.50737	+	42.5764i	−0.292445	+	1.65854i	−0.677407	+	0.735608i	$0.736897\pi$
$660$	0.688563	−	0.577773i	0.0268023	−	0.0224898i
$661$	−35.9309	−	30.1496i	−1.39755	−	1.17268i	−0.962174	−	0.272436i	$-0.912171\pi$
$661$	−35.9309	−	30.1496i	−1.39755	−	1.17268i	−0.435376	−	0.900249i	$-0.643385\pi$
$662$	3.29405	+	18.6815i	0.128027	+	0.726076i
$663$	77.8073	+	28.3195i	3.02179	+	1.09984i
$664$	1.67743			0.0650970
$665$	0.0480853	+	2.38989i	0.00186467	+	0.0926759i
$666$	−85.1049			−3.29775
$667$	−3.34347	−	1.21692i	−0.129460	−	0.0471194i
$668$	0.508600	+	2.88441i	0.0196783	+	0.111601i
$669$	−65.4350	−	54.9065i	−2.52986	−	2.12281i
$670$	10.0236	−	8.41081i	0.387246	−	0.324938i
$671$	0.0390883	−	0.221681i	0.00150899	−	0.00855789i
$672$	3.96583	−	6.86902i	0.152985	−	0.264978i
$673$	−7.15589	−	12.3944i	−0.275839	−	0.477768i	0.694507	−	0.719486i	$-0.255622\pi$
$673$	−7.15589	−	12.3944i	−0.275839	−	0.477768i	−0.970347	+	0.241718i	$0.922289\pi$
$674$	−9.96036	+	3.62528i	−0.383659	+	0.139640i
$675$	13.9826	−	5.08926i	0.538192	−	0.195886i
$676$	−4.27588	−	7.40605i	−0.164457	−	0.284848i
$677$	13.8430	−	23.9767i	0.532029	−	0.921501i	−0.467272	−	0.884114i	$-0.654763\pi$
$677$	13.8430	−	23.9767i	0.532029	−	0.921501i	0.999301	−	0.0373874i	$-0.0119036\pi$
$678$	4.62525	−	26.2311i	0.177632	−	1.00740i
$679$	2.94963	−	2.47504i	0.113197	−	0.0949832i
$680$	7.93760	+	6.66044i	0.304393	+	0.255416i
$681$	−3.93827	−	22.3350i	−0.150915	−	0.855881i
$682$	3.15503	+	1.14834i	0.120812	+	0.0439721i
$683$	20.0771			0.768228			0.384114	−	0.923286i	$-0.374507\pi$
$683$	20.0771			0.768228			0.384114	+	0.923286i	$0.374507\pi$
$684$	−24.1378	−	13.2959i	−0.922932	−	0.508380i
$685$	−0.920774			−0.0351810
$686$	−11.8854	−	4.32592i	−0.453786	−	0.165164i
$687$	−1.48229	−	8.40651i	−0.0565531	−	0.320728i
$688$	−6.24356	−	5.23897i	−0.238033	−	0.199734i
$689$	24.8434	−	20.8461i	0.946457	−	0.794172i
$690$	−1.05538	+	5.98534i	−0.0401775	+	0.227858i
$691$	14.3678	−	24.8857i	0.546577	−	0.946698i	−0.451929	−	0.892054i	$-0.649264\pi$
$691$	14.3678	−	24.8857i	0.546577	−	0.946698i	0.998506	−	0.0546446i	$-0.0174026\pi$
$692$	−1.04440	−	1.80895i	−0.0397020	−	0.0687659i
$693$	1.29296	−	0.470599i	0.0491155	−	0.0178766i
$694$	27.7756	−	10.1095i	1.05435	−	0.383751i
$695$	−0.0500270	−	0.0866493i	−0.00189763	−	0.00328680i
$696$	10.2266	−	17.7130i	0.387638	−	0.671408i
$697$	−7.25468	+	41.1434i	−0.274791	+	1.55842i
$698$	16.1432	−	13.5458i	0.611031	−	0.512716i
$699$	66.4116	+	55.7260i	2.51192	+	2.10775i
$700$	−0.0794699	−	0.450696i	−0.00300368	−	0.0170347i
$701$	25.2861	+	9.20337i	0.955041	+	0.347607i	0.772089	−	0.635515i	$-0.219212\pi$
$701$	25.2861	+	9.20337i	0.955041	+	0.347607i	0.182953	+	0.983122i	$0.441434\pi$
$702$	−120.790			−4.55892
$703$	−28.7391	−	4.47338i	−1.08392	−	0.168717i
$704$	0.813858			0.0306734
$705$	14.0611	+	5.11781i	0.529570	+	0.192748i
$706$	1.70390	+	9.66329i	0.0641271	+	0.363683i
$707$	3.02749	+	2.54037i	0.113861	+	0.0955404i
$708$	14.1446	−	11.8687i	0.531587	−	0.446054i
$709$	−1.74216	+	9.88027i	−0.0654281	+	0.371061i	0.934460	+	0.356069i	$0.115883\pi$
$709$	−1.74216	+	9.88027i	−0.0654281	+	0.371061i	−0.999888	+	0.0149918i	$0.995228\pi$
$710$	−0.914913	+	1.58468i	−0.0343361	+	0.0594718i
$711$	5.31952	+	9.21368i	0.199498	+	0.345540i
$712$	26.8318	−	9.76599i	1.00557	−	0.365996i
$713$	−6.28078	+	2.28602i	−0.235217	+	0.0856120i
$714$	−7.92770	−	13.7312i	−0.296687	−	0.513877i
$715$	0.798453	−	1.38296i	0.0298605	−	0.0517198i
$716$	−0.727558	+	4.12619i	−0.0271901	+	0.154203i
$717$	−32.6530	+	27.3991i	−1.21945	+	1.02324i
$718$	0.747441	+	0.627178i	0.0278943	+	0.0234061i
$719$	4.57974	+	25.9730i	0.170796	+	0.968630i	0.942886	+	0.333117i	$0.108100\pi$
$719$	4.57974	+	25.9730i	0.170796	+	0.968630i	−0.772090	+	0.635513i	$0.780789\pi$
$720$	−35.3989	−	12.8841i	−1.31924	−	0.480163i
$721$	−3.87995			−0.144497
$722$	−25.3119	−	19.5595i	−0.942011	−	0.727930i
$723$	49.3069			1.83374
$724$	4.25136	+	1.54737i	0.158001	+	0.0575075i
$725$	−0.556593	−	3.15659i	−0.0206713	−	0.117233i
$726$	45.6760	+	38.3267i	1.69519	+	1.42244i
$727$	−37.0863	+	31.1191i	−1.37546	+	1.15414i	−0.404595	+	0.914496i	$0.632588\pi$
$727$	−37.0863	+	31.1191i	−1.37546	+	1.15414i	−0.970860	+	0.239648i	$0.922968\pi$
$728$	0.900920	−	5.10937i	0.0333903	−	0.189366i
$729$	−24.6222	+	42.6469i	−0.911932	+	1.57951i
$730$	11.7442	+	20.3416i	0.434673	+	0.752875i
$731$	−8.13342	+	2.96032i	−0.300826	+	0.109492i
$732$	1.73327	−	0.630859i	0.0640636	−	0.0233172i
$733$	17.6687	+	30.6031i	0.652610	+	1.13035i	0.982487	+	0.186329i	$0.0596591\pi$
$733$	17.6687	+	30.6031i	0.652610	+	1.13035i	−0.329878	+	0.944024i	$0.607008\pi$
$734$	6.65551	−	11.5277i	0.245659	−	0.425495i
$735$	−3.78312	+	21.4552i	−0.139543	+	0.791386i
$736$	3.78199	−	3.17347i	0.139406	−	0.116976i
$737$	−1.97186	−	1.65459i	−0.0726344	−	0.0609475i
$738$	−17.5220	−	99.3720i	−0.644992	−	3.65793i
$739$	−18.2924	−	6.65787i	−0.672895	−	0.244914i	−0.0171013	−	0.999854i	$-0.505444\pi$
$739$	−18.2924	−	6.65787i	−0.672895	−	0.244914i	−0.655794	+	0.754940i	$0.727666\pi$
$740$	5.56851			0.204703
$741$	−67.5333	−	10.5119i	−2.48090	−	0.386163i
$742$	−6.21011			−0.227980
$743$	−26.8764	−	9.78221i	−0.986000	−	0.358875i	−0.201830	−	0.979421i	$-0.564689\pi$
$743$	−26.8764	−	9.78221i	−0.986000	−	0.358875i	−0.784170	+	0.620546i	$0.786911\pi$
$744$	−6.67187	−	37.8380i	−0.244602	−	1.38721i
$745$	13.2506	+	11.1186i	0.485466	+	0.407354i
$746$	−10.7127	+	8.98899i	−0.392218	+	0.329110i
$747$	−1.12459	+	6.37785i	−0.0411465	+	0.233353i
$748$	−0.729796	+	1.26404i	−0.0266840	+	0.0462180i
$749$	−1.78255	−	3.08748i	−0.0651331	−	0.112814i
$750$	−5.14493	+	1.87260i	−0.187866	+	0.0683778i
$751$	−44.7071	+	16.2721i	−1.63139	+	0.593776i	−0.985503	−	0.169660i	$-0.945733\pi$
$751$	−44.7071	+	16.2721i	−1.63139	+	0.593776i	−0.645883	+	0.763436i	$0.723511\pi$
$752$	−11.4402	−	19.8151i	−0.417182	−	0.722581i
$753$	30.9045	−	53.5282i	1.12622	−	1.95068i
$754$	−4.51820	+	25.6240i	−0.164543	+	0.933170i
$755$	14.7217	−	12.3530i	0.535778	−	0.449571i
$756$	5.21663	+	4.37727i	0.189727	+	0.159200i
$757$	2.06236	+	11.6962i	0.0749578	+	0.425107i	0.999075	+	0.0429980i	$0.0136909\pi$
$757$	2.06236	+	11.6962i	0.0749578	+	0.425107i	−0.924117	+	0.382109i	$0.875198\pi$
$758$	−16.2840	−	5.92689i	−0.591462	−	0.215274i
$759$	1.19561			0.0433979
$760$	−7.49162	−	4.12662i	−0.271750	−	0.149688i
$761$	28.1049			1.01880			0.509401	−	0.860530i	$-0.329867\pi$
$761$	28.1049			1.01880			0.509401	+	0.860530i	$0.329867\pi$
$762$	−15.2768	−	5.56031i	−0.553421	−	0.201429i
$763$	1.68177	+	9.53778i	0.0608841	+	0.345291i
$764$	3.82626	+	3.21061i	0.138429	+	0.116156i
$765$	−30.6455	+	25.7146i	−1.10799	+	0.929715i
$766$	9.36368	−	53.1041i	0.338324	−	1.91873i
$767$	16.4020	−	28.4091i	0.592242	−	1.02579i
$768$	27.6854	+	47.9525i	0.999011	+	1.73034i
$769$	−52.0340	+	18.9388i	−1.87639	+	0.682952i	−0.918909	+	0.394471i	$0.870928\pi$
$769$	−52.0340	+	18.9388i	−1.87639	+	0.682952i	−0.957486	+	0.288481i	$0.906850\pi$
$770$	−0.287348	+	0.104586i	−0.0103553	+	0.00376902i
$771$	35.5091	+	61.5036i	1.27883	+	2.21500i
$772$	−0.904883	+	1.56730i	−0.0325674	+	0.0564085i
$773$	3.10626	−	17.6165i	0.111725	−	0.633621i	−0.876595	−	0.481228i	$-0.840191\pi$
$773$	3.10626	−	17.6165i	0.111725	−	0.633621i	0.988320	−	0.152393i	$-0.0486980\pi$
$774$	16.0142	−	13.4375i	0.575619	−	0.483002i
$775$	−4.61251	−	3.87036i	−0.165686	−	0.139027i
$776$	2.39241	+	13.5681i	0.0858826	+	0.487065i
$777$	11.1821	+	4.06995i	0.401155	+	0.146009i
$778$	−51.5323			−1.84752
$779$	−0.693708	−	34.4780i	−0.0248547	−	1.23530i
$780$	13.0853			0.468529
$781$	0.338258	+	0.123116i	0.0121038	+	0.00440542i
$782$	−1.71376	−	9.71921i	−0.0612839	−	0.347558i
$783$	36.5363	+	30.6576i	1.30570	+	1.09561i
$784$	25.5192	−	21.4131i	0.911399	−	0.764755i
$785$	1.14307	−	6.48265i	0.0407978	−	0.231376i
$786$	−21.8868	+	37.9091i	−0.780677	+	1.35217i
$787$	−3.70147	−	6.41114i	−0.131943	−	0.228532i	0.792482	−	0.609895i	$-0.208788\pi$
$787$	−3.70147	−	6.41114i	−0.131943	−	0.228532i	−0.924426	+	0.381362i	$0.875455\pi$
$788$	−12.9916	+	4.72855i	−0.462806	+	0.168448i
$789$	−59.9605	+	21.8238i	−2.13465	+	0.776949i
$790$	−1.18221	−	2.04765i	−0.0420612	−	0.0728521i
$791$	−1.33392	+	2.31042i	−0.0474288	+	0.0821491i
$792$	−0.854913	+	4.84845i	−0.0303780	+	0.172282i
$793$	2.51029	−	2.10639i	0.0891432	−	0.0748000i
$794$	13.6974	+	11.4935i	0.486102	+	0.407888i
$795$	3.79833	+	21.5414i	0.134713	+	0.763995i
$796$	−10.9633	−	3.99031i	−0.388584	−	0.141433i
$797$	45.6568			1.61725			0.808624	−	0.588326i	$-0.200213\pi$
$797$	45.6568			1.61725			0.808624	+	0.588326i	$0.200213\pi$
$798$	8.61251	+	9.85441i	0.304880	+	0.348842i
$799$	−24.2982			−0.859609
$800$	4.17935	+	1.52116i	0.147762	+	0.0537810i
$801$	19.1431	+	108.566i	0.676389	+	3.83599i
$802$	−19.6484	−	16.4870i	−0.693809	−	0.582175i
$803$	3.53965	−	2.97012i	0.124911	−	0.104813i
$804$	3.66266	−	20.7720i	0.129172	−	0.732571i
$805$	0.304371	−	0.527185i	0.0107277	−	0.0185808i
$806$	24.4389	+	42.3294i	0.860823	+	1.49099i
$807$	−5.16853	+	1.88119i	−0.181941	+	0.0662211i
$808$	−13.2882	+	4.83652i	−0.467478	+	0.170148i
$809$	9.67626	+	16.7598i	0.340199	+	0.589242i	0.984469	−	0.175556i	$-0.0561722\pi$
$809$	9.67626	+	16.7598i	0.340199	+	0.589242i	−0.644270	+	0.764798i	$0.722839\pi$
$810$	21.6034	−	37.4181i	0.759064	−	1.31474i
$811$	3.61818	−	20.5197i	0.127052	−	0.720546i	−0.853016	−	0.521884i	$-0.825229\pi$
$811$	3.61818	−	20.5197i	0.127052	−	0.720546i	0.980068	−	0.198662i	$-0.0636595\pi$
$812$	1.12371	−	0.942904i	0.0394345	−	0.0330894i
$813$	19.7793	+	16.5968i	0.693689	+	0.582075i
$814$	−0.646099	−	3.66421i	−0.0226458	−	0.128431i
$815$	−13.7127	−	4.99101i	−0.480335	−	0.174828i
$816$	85.3951			2.98943
$817$	6.11417	−	3.69597i	0.213908	−	0.129306i
$818$	−19.6378			−0.686619
$819$	18.8226	+	6.85087i	0.657715	+	0.239389i
$820$	1.14648	+	6.50203i	0.0400369	+	0.227061i
$821$	−23.4739	−	19.6969i	−0.819244	−	0.687427i	0.133551	−	0.991042i	$-0.457362\pi$
$821$	−23.4739	−	19.6969i	−0.819244	−	0.687427i	−0.952795	+	0.303615i	$0.901806\pi$
$822$	−3.86190	+	3.24052i	−0.134699	+	0.113026i
$823$	1.40229	−	7.95277i	0.0488807	−	0.277216i	−0.950564	−	0.310528i	$-0.899494\pi$
$823$	1.40229	−	7.95277i	0.0488807	−	0.277216i	0.999445	+	0.0333116i	$0.0106054\pi$
$824$	6.94142	−	12.0229i	0.241816	−	0.418837i
$825$	0.538537	+	0.932774i	0.0187495	+	0.0324750i
$826$	−5.90276	+	2.14843i	−0.205383	+	0.0747534i
$827$	34.3375	−	12.4978i	1.19403	−	0.434593i	0.332895	−	0.942964i	$-0.391974\pi$
$827$	34.3375	−	12.4978i	1.19403	−	0.434593i	0.861138	+	0.508371i	$0.169752\pi$
$828$	3.50894	+	6.07767i	0.121944	+	0.211213i
$829$	21.3514	−	36.9817i	0.741564	−	1.28443i	−0.210218	−	0.977654i	$-0.567418\pi$
$829$	21.3514	−	36.9817i	0.741564	−	1.28443i	0.951783	−	0.306773i	$-0.0992491\pi$
$830$	0.249928	−	1.41741i	0.00867514	−	0.0491992i
$831$	23.6014	−	19.8039i	0.818724	−	0.686991i
$832$	9.07604	+	7.61570i	0.314655	+	0.264027i
$833$	−6.14317	−	34.8396i	−0.212848	−	1.20712i
$834$	−0.514771	−	0.187361i	−0.0178251	−	0.00648779i
$835$	−3.50963			−0.121456
$836$	0.389207	−	1.14020i	0.0134610	−	0.0394346i
$837$	89.5956			3.09688
$838$	−28.0072	−	10.1938i	−0.967492	−	0.352138i
$839$	8.35614	+	47.3900i	0.288486	+	1.63609i	0.692561	+	0.721360i	$0.256482\pi$
$839$	8.35614	+	47.3900i	0.288486	+	1.63609i	−0.404075	+	0.914726i	$0.632406\pi$
$840$	2.68063	+	2.24931i	0.0924904	+	0.0776086i
$841$	−14.3450	+	12.0369i	−0.494657	+	0.415066i
$842$	6.02320	−	34.1593i	0.207573	−	1.17721i
$843$	−20.4390	+	35.4014i	−0.703958	+	1.21929i
$844$	7.54471	+	13.0678i	0.259700	+	0.449813i
$845$	9.62936	−	3.50480i	0.331260	−	0.120569i
$846$	55.1473	−	20.0720i	1.89600	−	0.690089i
$847$	−2.98606	−	5.17201i	−0.102602	−	0.177712i
$848$	16.7234	−	28.9658i	0.574285	−	0.994690i
$849$	10.4945	−	59.5172i	0.360170	−	2.04263i
$850$	6.81067	−	5.71483i	0.233604	−	0.196017i
$851$	5.67405	+	4.76110i	0.194504	+	0.163208i
$852$	0.512196	+	2.90481i	0.0175475	+	0.0995170i
$853$	−30.4917	−	11.0981i	−1.04402	−	0.379991i	−0.237615	−	0.971359i	$-0.576366\pi$
$853$	−30.4917	−	11.0981i	−1.04402	−	0.379991i	−0.806402	+	0.591368i	$0.798588\pi$
$854$	−0.627500			−0.0214726
$855$	20.7126	−	25.7177i	0.708355	−	0.879527i
$856$	12.7563			0.436001
$857$	−28.3576	−	10.3213i	−0.968677	−	0.352569i	−0.191249	−	0.981542i	$-0.561254\pi$
$857$	−28.3576	−	10.3213i	−0.968677	−	0.352569i	−0.777428	+	0.628972i	$0.783476\pi$
$858$	−1.51825	−	8.61043i	−0.0518322	−	0.293955i
$859$	20.3519	+	17.0772i	0.694396	+	0.582668i	0.920173	−	0.391511i	$-0.128048\pi$
$859$	20.3519	+	17.0772i	0.694396	+	0.582668i	−0.225777	+	0.974179i	$0.572492\pi$
$860$	−1.04783	+	0.879234i	−0.0357307	+	0.0299816i
$861$	−2.45000	+	13.8946i	−0.0834956	+	0.473527i
$862$	−7.01353	+	12.1478i	−0.238882	+	0.413756i
$863$	−5.77830	−	10.0083i	−0.196696	−	0.340687i	0.750759	−	0.660576i	$-0.229688\pi$
$863$	−5.77830	−	10.0083i	−0.196696	−	0.340687i	−0.947455	+	0.319889i	$0.896354\pi$
$864$	−62.1887	+	22.6348i	−2.11570	+	0.770052i
$865$	2.35200	−	0.856059i	0.0799705	−	0.0291069i
$866$	−23.7339	−	41.1083i	−0.806510	−	1.39692i
$867$	17.7011	−	30.6592i	0.601161	−	1.04124i
$868$	0.478505	−	2.71374i	0.0162415	−	0.0921102i
$869$	−0.356312	+	0.298982i	−0.0120871	+	0.0101423i
$870$	−13.4436	−	11.2805i	−0.455780	−	0.382445i
$871$	−6.50709	−	36.9035i	−0.220484	−	1.25043i
$872$	−32.5637	−	11.8522i	−1.10275	−	0.401366i
$873$	−53.1917			−1.80027
$874$	2.93963	+	7.59744i	0.0994346	+	0.256987i
$875$	0.548389			0.0185389
$876$	35.5792	+	12.9498i	1.20211	+	0.437532i
$877$	3.15457	+	17.8905i	0.106522	+	0.604118i	0.990601	+	0.136781i	$0.0436756\pi$
$877$	3.15457	+	17.8905i	0.106522	+	0.604118i	−0.884079	+	0.467338i	$0.845213\pi$
$878$	39.1847	+	32.8799i	1.32242	+	1.10964i
$879$	43.2596	−	36.2992i	1.45911	−	1.22434i
$880$	0.285988	−	1.62192i	0.00964067	−	0.0546749i
$881$	19.9306	−	34.5209i	0.671480	−	1.16304i	−0.306004	−	0.952030i	$-0.598992\pi$
$881$	19.9306	−	34.5209i	0.671480	−	1.16304i	0.977484	−	0.211008i	$-0.0676745\pi$
$882$	42.7225	+	73.9975i	1.43854	+	2.49163i
$883$	24.7626	−	9.01286i	0.833329	−	0.303307i	0.110104	−	0.993920i	$-0.464882\pi$
$883$	24.7626	−	9.01286i	0.833329	−	0.303307i	0.723224	+	0.690613i	$0.242659\pi$
$884$	−19.9669	+	7.26737i	−0.671561	+	0.244428i
$885$	11.0627	+	19.1612i	0.371870	+	0.644098i
$886$	−20.6417	+	35.7524i	−0.693470	+	1.20113i
$887$	9.71703	−	55.1080i	0.326266	−	1.85035i	−0.174360	−	0.984682i	$-0.555786\pi$
$887$	9.71703	−	55.1080i	0.326266	−	1.85035i	0.500626	−	0.865664i	$-0.333103\pi$
$888$	−32.6169	+	27.3688i	−1.09455	+	0.918438i
$889$	1.24737	+	1.04667i	0.0418355	+	0.0351042i
$890$	−4.25437	−	24.1277i	−0.142607	−	0.808763i
$891$	−7.98710	−	2.90707i	−0.267578	−	0.0973903i
$892$	21.9203			0.733947
$893$	19.6778	−	3.87941i	0.658492	−	0.129820i
$894$	94.7059			3.16744
$895$	−4.71780	−	1.71714i	−0.157699	−	0.0573976i
$896$	−1.24102	−	7.03816i	−0.0414595	−	0.235128i
$897$	13.3333	+	11.1880i	0.445186	+	0.373555i
$898$	31.8417	−	26.7183i	1.06257	−	0.891603i
$899$	3.35136	−	19.0065i	0.111774	−	0.633903i
$900$	−3.16106	+	5.47511i	−0.105369	+	0.182504i
$901$	−17.7597	−	30.7606i	−0.591660	−	1.02479i
$902$	4.14546	−	1.50882i	0.138029	−	0.0502384i
$903$	−2.74676	+	0.999738i	−0.0914064	+	0.0332692i
$904$	−4.77290	−	8.26690i	−0.158744	−	0.274953i
$905$	−2.71062	+	4.69493i	−0.0901040	+	0.156065i
$906$	18.2713	−	103.622i	0.607022	−	3.44259i
$907$	−35.3239	+	29.6403i	−1.17291	+	0.984188i	−1.00000		0.000749224i	$-0.999762\pi$
$907$	−35.3239	+	29.6403i	−1.17291	+	0.984188i	−0.172910	+	0.984938i	$0.555317\pi$
$908$	4.45841	+	3.74105i	0.147958	+	0.124151i
$909$	−9.48045	−	53.7663i	−0.314447	−	1.78332i
$910$	−4.18314	−	1.52254i	−0.138670	−	0.0504716i
$911$	1.40625			0.0465912			0.0232956	−	0.999729i	$-0.492584\pi$
$911$	1.40625			0.0465912			0.0232956	+	0.999729i	$0.492584\pi$
$912$	−69.1568	+	13.6340i	−2.29001	+	0.451468i
$913$	−0.283137			−0.00937048
$914$	−11.3352	−	4.12569i	−0.374936	−	0.136466i
$915$	0.383802	+	2.17665i	0.0126881	+	0.0719578i
$916$	1.67807	+	1.40807i	0.0554449	+	0.0465238i
$917$	3.35862	−	2.81822i	0.110912	−	0.0930658i
$918$	−22.9725	+	130.284i	−0.758207	+	4.30000i
$919$	−23.5177	+	40.7338i	−0.775777	+	1.34369i	0.158579	+	0.987346i	$0.449309\pi$
$919$	−23.5177	+	40.7338i	−0.775777	+	1.34369i	−0.934357	+	0.356339i	$0.884025\pi$
$920$	1.08907	+	1.88632i	0.0359055	+	0.0621901i
$921$	−76.5515	+	27.8625i	−2.52246	+	0.918099i
$922$	−34.3633	+	12.5072i	−1.13170	+	0.411903i
$923$	2.62015	+	4.53823i	0.0862432	+	0.149378i
$924$	−0.246461	+	0.426883i	−0.00810798	+	0.0140434i
$925$	−1.15869	+	6.57123i	−0.0380974	+	0.216061i
$926$	−41.1786	+	34.5529i	−1.35321	+	1.13548i
$927$	41.0591	+	34.4527i	1.34856	+	1.13158i
$928$	2.47548	+	14.0392i	0.0812617	+	0.460858i
$929$	0.927569	+	0.337607i	0.0304325	+	0.0110765i	0.357192	−	0.934031i	$-0.383734\pi$
$929$	0.927569	+	0.337607i	0.0304325	+	0.0110765i	−0.326759	+	0.945108i	$0.605957\pi$
$930$	−32.9668			−1.08103
$931$	10.5375	+	27.2339i	0.345351	+	0.892555i
$932$	−22.2475			−0.728741
$933$	−17.0645	−	6.21096i	−0.558666	−	0.203338i
$934$	−5.71210	−	32.3950i	−0.186906	−	1.06000i
$935$	−1.33980	−	1.12423i	−0.0438163	−	0.0367662i
$936$	−54.9034	+	46.0694i	−1.79457	+	1.50583i
$937$	−1.84463	+	10.4614i	−0.0602615	+	0.341760i	−1.00000		0.000134284i	$-0.999957\pi$
$937$	−1.84463	+	10.4614i	−0.0602615	+	0.341760i	0.939739	+	0.341894i	$0.111068\pi$
$938$	−3.58781	+	6.21426i	−0.117146	+	0.202903i
$939$	−1.33513	−	2.31251i	−0.0435702	−	0.0754659i
$940$	−3.60836	+	1.31333i	−0.117692	+	0.0428362i
$941$	9.88893	−	3.59928i	0.322370	−	0.117333i	−0.175766	−	0.984432i	$-0.556240\pi$
$941$	9.88893	−	3.59928i	0.322370	−	0.117333i	0.498136	+	0.867099i	$0.334018\pi$
$942$	−18.0204	−	31.2123i	−0.587137	−	1.01695i
$943$	−4.39104	+	7.60550i	−0.142992	+	0.247669i
$944$	5.87483	−	33.3178i	0.191210	−	1.08440i
$945$	−6.25095	+	5.24517i	−0.203343	+	0.170625i
$946$	0.700133	+	0.587481i	0.0227633	+	0.0191007i
$947$	6.09701	+	34.5779i	0.198126	+	1.12363i	0.907896	+	0.419196i	$0.137688\pi$
$947$	6.09701	+	34.5779i	0.198126	+	1.12363i	−0.709770	+	0.704434i	$0.751201\pi$
$948$	−3.58152	−	1.30357i	−0.116322	−	0.0423378i
$949$	67.2667			2.18357
$950$	−4.60317	+	5.71551i	−0.149346	+	0.185435i
$951$	−109.048			−3.53613
$952$	−5.33961	−	1.94346i	−0.173058	−	0.0629879i
$953$	3.66011	+	20.7575i	0.118563	+	0.672402i	0.984924	+	0.172985i	$0.0553413\pi$
$953$	3.66011	+	20.7575i	0.118563	+	0.672402i	−0.866362	+	0.499417i	$0.833548\pi$
$954$	65.7178	+	55.1437i	2.12769	+	1.78534i
$955$	−4.58490	+	3.84719i	−0.148364	+	0.124492i
$956$	1.89946	−	10.7724i	0.0614329	−	0.348403i
$957$	−1.72617	+	2.98981i	−0.0557991	+	0.0966468i
$958$	10.3026	+	17.8447i	0.332863	+	0.576535i
$959$	0.474491	−	0.172701i	0.0153221	−	0.00557679i
$960$	−7.50921	+	2.73313i	−0.242359	+	0.0882114i
$961$	−2.62747	−	4.55092i	−0.0847572	−	0.146804i
$962$	27.0828	−	46.9087i	0.873183	−	1.51240i
$963$	−8.55210	+	48.5014i	−0.275587	+	1.56293i
$964$	−9.69287	+	8.13329i	−0.312186	+	0.261956i
$965$	−1.66124	−	1.39395i	−0.0534772	−	0.0448727i
$966$	−0.578758	−	3.28230i	−0.0186212	−	0.105606i
$967$	−44.5471	−	16.2138i	−1.43254	−	0.521401i	−0.494881	−	0.868961i	$-0.664788\pi$
$967$	−44.5471	−	16.2138i	−1.43254	−	0.521401i	−0.937658	+	0.347560i	$0.887010\pi$
$968$	21.3688			0.686820
$969$	−24.1820	+	70.8421i	−0.776836	+	2.27578i
$970$	11.8213			0.379560
$971$	30.6348	+	11.1502i	0.983117	+	0.357825i	0.783051	−	0.621957i	$-0.213662\pi$
$971$	30.6348	+	11.1502i	0.983117	+	0.357825i	0.200066	+	0.979782i	$0.435884\pi$
$972$	−5.62519	−	31.9020i	−0.180428	−	1.02326i
$973$	0.0420317	+	0.0352688i	0.00134747	+	0.00113067i
$974$	−18.1873	+	15.2609i	−0.582757	+	0.488991i
$975$	−2.72276	+	15.4416i	−0.0871982	+	0.494526i
$976$	1.68982	−	2.92685i	0.0540897	−	0.0936861i
$977$	11.9957	+	20.7772i	0.383777	+	0.664721i	0.991599	−	0.129353i	$-0.0412899\pi$
$977$	11.9957	+	20.7772i	0.383777	+	0.664721i	−0.607822	+	0.794073i	$0.707957\pi$
$978$	−75.0787	+	27.3264i	−2.40075	+	0.873802i
$979$	−4.52900	+	1.64842i	−0.144748	+	0.0526838i
$980$	−2.79538	−	4.84175i	−0.0892953	−	0.154664i
$981$	66.8953	−	115.866i	2.13580	−	3.69932i
$982$	−5.81398	+	32.9727i	−0.185532	+	1.05220i
$983$	3.28438	−	2.75592i	0.104756	−	0.0879003i	−0.588906	−	0.808202i	$-0.700441\pi$
$983$	3.28438	−	2.75592i	0.104756	−	0.0879003i	0.693661	+	0.720302i	$0.255997\pi$
$984$	−38.6724	−	32.4500i	−1.23283	−	1.03447i
$985$	−2.87675	−	16.3149i	−0.0916609	−	0.519835i
$986$	26.7787	+	9.74663i	0.852806	+	0.310396i
$987$	−8.20581			−0.261194
$988$	15.0098	−	9.07333i	0.477526	−	0.288661i
$989$	−1.81944			−0.0578547
$990$	3.96952	+	1.44479i	0.126160	+	0.0459183i
$991$	−7.94255	−	45.0444i	−0.252303	−	1.43088i	−0.802901	−	0.596113i	$-0.796711\pi$
$991$	−7.94255	−	45.0444i	−0.252303	−	1.43088i	0.550597	−	0.834771i	$-0.314400\pi$
$992$	20.5145	+	17.2137i	0.651335	+	0.546535i
$993$	−28.0689	+	23.5526i	−0.890741	+	0.747420i
$994$	0.174248	−	0.988211i	0.00552682	−	0.0313442i
$995$	6.99007	−	12.1072i	0.221600	−	0.383822i
$996$	−1.16004	−	2.00924i	−0.0367571	−	0.0636652i
$997$	−11.2503	+	4.09478i	−0.356301	+	0.129683i	−0.513968	−	0.857809i	$-0.671825\pi$
$997$	−11.2503	+	4.09478i	−0.356301	+	0.129683i	0.157667	+	0.987492i	$0.449603\pi$
$998$	11.7665	−	4.28267i	0.372463	−	0.135566i
$999$	−49.6442	−	85.9863i	−1.57067	−	2.72048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.k.b.61.1	✓	18
3.2	odd	2		855.2.bs.b.631.3		18
5.2	odd	4		475.2.u.c.99.5		36
5.3	odd	4		475.2.u.c.99.2		36
5.4	even	2		475.2.l.b.251.3		18
19.5	even	9	inner	95.2.k.b.81.1	yes	18
19.9	even	9		1805.2.a.t.1.7		9
19.10	odd	18		1805.2.a.u.1.3		9
57.5	odd	18		855.2.bs.b.271.3		18
95.9	even	18		9025.2.a.ce.1.3		9
95.24	even	18		475.2.l.b.176.3		18
95.29	odd	18		9025.2.a.cd.1.7		9
95.43	odd	36		475.2.u.c.24.5		36
95.62	odd	36		475.2.u.c.24.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.61.1	✓	18	1.1	even	1	trivial
95.2.k.b.81.1	yes	18	19.5	even	9	inner
475.2.l.b.176.3		18	95.24	even	18
475.2.l.b.251.3		18	5.4	even	2
475.2.u.c.24.2		36	95.62	odd	36
475.2.u.c.24.5		36	95.43	odd	36
475.2.u.c.99.2		36	5.3	odd	4
475.2.u.c.99.5		36	5.2	odd	4
855.2.bs.b.271.3		18	57.5	odd	18
855.2.bs.b.631.3		18	3.2	odd	2
1805.2.a.t.1.7		9	19.9	even	9
1805.2.a.u.1.3		9	19.10	odd	18
9025.2.a.cd.1.7		9	95.29	odd	18
9025.2.a.ce.1.3		9	95.9	even	18

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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58207 - 0.575828i) q^{2} +(-0.564707 - 3.20261i) q^{3} +(0.639290 + 0.536428i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-0.950745 + 5.39194i) q^{6} +(0.274194 - 0.474919i) q^{7} +(0.981094 + 1.69930i) q^{8} +(-7.11876 + 2.59101i) q^{9} +O(q^{10})\)	\(q+(-1.58207 - 0.575828i) q^{2} +(-0.564707 - 3.20261i) q^{3} +(0.639290 + 0.536428i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-0.950745 + 5.39194i) q^{6} +(0.274194 - 0.474919i) q^{7} +(0.981094 + 1.69930i) q^{8} +(-7.11876 + 2.59101i) q^{9} +(1.58207 - 0.575828i) q^{10} +(-0.165601 - 0.286829i) q^{11} +(1.35696 - 2.35032i) q^{12} +(0.837254 - 4.74830i) q^{13} +(-0.707267 + 0.593468i) q^{14} +(2.49119 + 2.09036i) q^{15} +(-0.863487 - 4.89708i) q^{16} +(-4.96227 - 1.80612i) q^{17} +12.7544 q^{18} +(4.30704 + 0.670409i) q^{19} -0.834534 q^{20} +(-1.67582 - 0.609949i) q^{21} +(0.0968286 + 0.549142i) q^{22} +(-0.850350 - 0.713529i) q^{23} +(4.88818 - 4.10167i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-4.05880 + 7.03005i) q^{26} +(7.44000 + 12.8865i) q^{27} +(0.430050 - 0.156525i) q^{28} +(3.01199 - 1.09627i) q^{29} +(-2.73756 - 4.74159i) q^{30} +(3.01060 - 5.21452i) q^{31} +(-0.772312 + 4.38000i) q^{32} +(-0.825087 + 0.692330i) q^{33} +(6.81067 + 5.71483i) q^{34} +(0.0952268 + 0.540058i) q^{35} +(-5.94084 - 2.16229i) q^{36} -6.67261 q^{37} +(-6.42801 - 3.54075i) q^{38} -15.6798 q^{39} +(-1.84385 - 0.671108i) q^{40} +(-1.37380 - 7.79121i) q^{41} +(2.30005 + 1.92997i) q^{42} +(1.25559 - 1.05356i) q^{43} +(0.0479962 - 0.272200i) q^{44} +(3.78781 - 6.56068i) q^{45} +(0.934447 + 1.61851i) q^{46} +(4.32380 - 1.57373i) q^{47} +(-15.1958 + 5.53083i) q^{48} +(3.34963 + 5.80174i) q^{49} +(-0.841804 + 1.45805i) q^{50} +(-2.98207 + 16.9122i) q^{51} +(3.08237 - 2.58642i) q^{52} +(5.15257 + 4.32352i) q^{53} +(-4.35025 - 24.6715i) q^{54} +(0.311228 + 0.113278i) q^{55} +1.07604 q^{56} +(-0.285152 - 14.1723i) q^{57} -5.39645 q^{58} +(6.39331 + 2.32697i) q^{59} +(0.471267 + 2.67269i) q^{60} +(0.520640 + 0.436869i) q^{61} +(-7.76566 + 6.51616i) q^{62} +(-0.721402 + 4.09127i) q^{63} +(-1.22864 + 2.12807i) q^{64} +(2.41078 + 4.17559i) q^{65} +(1.70401 - 0.620209i) q^{66} +(7.30324 - 2.65816i) q^{67} +(-2.20348 - 3.81654i) q^{68} +(-1.80496 + 3.12628i) q^{69} +(0.160324 - 0.909245i) q^{70} +(-0.832574 + 0.698612i) q^{71} +(-11.3871 - 9.55490i) q^{72} +(2.42261 + 13.7393i) q^{73} +(10.5566 + 3.84227i) q^{74} -3.25202 q^{75} +(2.39382 + 2.73900i) q^{76} -0.181627 q^{77} +(24.8065 + 9.02885i) q^{78} +(-0.243868 - 1.38304i) q^{79} +(3.80925 + 3.19634i) q^{80} +(19.6591 - 16.4960i) q^{81} +(-2.31294 + 13.1173i) q^{82} +(0.427439 - 0.740346i) q^{83} +(-0.744142 - 1.28889i) q^{84} +(4.96227 - 1.80612i) q^{85} +(-2.59310 + 0.943812i) q^{86} +(-5.21183 - 9.02715i) q^{87} +(0.324940 - 0.562813i) q^{88} +(2.52694 - 14.3310i) q^{89} +(-9.77042 + 8.19835i) q^{90} +(-2.02549 - 1.69959i) q^{91} +(-0.160864 - 0.912304i) q^{92} +(-18.4002 - 6.69712i) q^{93} -7.74677 q^{94} +(-3.73031 + 2.25495i) q^{95} +14.4636 q^{96} +(6.59799 + 2.40147i) q^{97} +(-1.95857 - 11.1076i) q^{98} +(1.92205 + 1.61279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{6} - 12 q^{8} - 21 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^6 - 12 * q^8 - 21 * q^9	\( 18 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{6} - 12 q^{8} - 21 q^{9} - 3 q^{10} + 6 q^{12} - 3 q^{13} + 24 q^{14} + 3 q^{15} + 21 q^{16} - 24 q^{17} - 12 q^{18} - 12 q^{19} - 12 q^{20} + 3 q^{21} + 15 q^{22} + 21 q^{23} + 21 q^{24} - 21 q^{26} + 6 q^{27} - 24 q^{28} - 9 q^{29} - 12 q^{30} + 30 q^{31} + 45 q^{32} - 3 q^{33} + 24 q^{34} - 6 q^{35} - 21 q^{36} - 60 q^{37} - 15 q^{38} + 12 q^{39} - 6 q^{40} - 6 q^{41} + 39 q^{42} - 6 q^{43} - 30 q^{44} + 6 q^{45} + 21 q^{46} + 33 q^{47} - 63 q^{48} - 3 q^{49} + 27 q^{51} + 9 q^{52} + 24 q^{53} + 30 q^{54} - 3 q^{55} - 72 q^{56} - 30 q^{57} + 36 q^{58} + 18 q^{59} + 15 q^{60} + 6 q^{61} + 12 q^{62} + 24 q^{63} - 24 q^{64} + 3 q^{65} - 33 q^{66} - 24 q^{67} - 3 q^{68} + 27 q^{69} + 39 q^{70} + 24 q^{71} + 18 q^{72} + 6 q^{73} - 39 q^{74} - 6 q^{75} + 27 q^{76} + 24 q^{77} + 72 q^{78} + 9 q^{79} + 33 q^{80} + 15 q^{81} - 57 q^{82} - 12 q^{84} + 24 q^{85} - 33 q^{86} - 45 q^{87} + 39 q^{88} - 6 q^{89} - 21 q^{90} - 6 q^{91} - 66 q^{92} - 72 q^{93} - 66 q^{94} - 15 q^{95} - 18 q^{96} - 87 q^{97} + 39 q^{98} + 3 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^6 - 12 * q^8 - 21 * q^9 - 3 * q^10 + 6 * q^12 - 3 * q^13 + 24 * q^14 + 3 * q^15 + 21 * q^16 - 24 * q^17 - 12 * q^18 - 12 * q^19 - 12 * q^20 + 3 * q^21 + 15 * q^22 + 21 * q^23 + 21 * q^24 - 21 * q^26 + 6 * q^27 - 24 * q^28 - 9 * q^29 - 12 * q^30 + 30 * q^31 + 45 * q^32 - 3 * q^33 + 24 * q^34 - 6 * q^35 - 21 * q^36 - 60 * q^37 - 15 * q^38 + 12 * q^39 - 6 * q^40 - 6 * q^41 + 39 * q^42 - 6 * q^43 - 30 * q^44 + 6 * q^45 + 21 * q^46 + 33 * q^47 - 63 * q^48 - 3 * q^49 + 27 * q^51 + 9 * q^52 + 24 * q^53 + 30 * q^54 - 3 * q^55 - 72 * q^56 - 30 * q^57 + 36 * q^58 + 18 * q^59 + 15 * q^60 + 6 * q^61 + 12 * q^62 + 24 * q^63 - 24 * q^64 + 3 * q^65 - 33 * q^66 - 24 * q^67 - 3 * q^68 + 27 * q^69 + 39 * q^70 + 24 * q^71 + 18 * q^72 + 6 * q^73 - 39 * q^74 - 6 * q^75 + 27 * q^76 + 24 * q^77 + 72 * q^78 + 9 * q^79 + 33 * q^80 + 15 * q^81 - 57 * q^82 - 12 * q^84 + 24 * q^85 - 33 * q^86 - 45 * q^87 + 39 * q^88 - 6 * q^89 - 21 * q^90 - 6 * q^91 - 66 * q^92 - 72 * q^93 - 66 * q^94 - 15 * q^95 - 18 * q^96 - 87 * q^97 + 39 * q^98 + 3 * q^99

Introduction

L-functions

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