LMFDB - Embedded newform 322.2.i.d.85.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{2} +(1.39187 - 0.894499i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-1.27474 - 2.79128i) q^{5} +(-0.235462 + 1.63768i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.109077 + 0.238845i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{2} +(1.39187 - 0.894499i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-1.27474 - 2.79128i) q^{5} +(-0.235462 + 1.63768i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.109077 + 0.238845i) q^{9} +(2.94429 + 0.864520i) q^{10} +(-1.60338 - 1.85040i) q^{11} +(-1.08348 - 1.25040i) q^{12} +(0.227911 + 0.0669208i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(-4.27107 - 2.74485i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.786144 - 5.46775i) q^{17} +(-0.109077 - 0.238845i) q^{18} +(-0.408174 - 2.83891i) q^{19} +(-2.58146 + 1.65900i) q^{20} +(1.08348 - 1.25040i) q^{21} +2.44842 q^{22} +(0.294813 - 4.78676i) q^{23} +1.65452 q^{24} +(-2.89200 + 3.33755i) q^{25} +(-0.199826 + 0.128420i) q^{26} +(0.768213 + 5.34304i) q^{27} +(-0.415415 - 0.909632i) q^{28} +(-0.445425 + 3.09800i) q^{29} +(4.87137 - 1.43036i) q^{30} +(4.62969 + 2.97532i) q^{31} +(0.415415 - 0.909632i) q^{32} +(-3.88687 - 1.14129i) q^{33} +(3.61743 + 4.17474i) q^{34} +(-2.00950 - 2.31908i) q^{35} +(0.251937 + 0.0739754i) q^{36} +(-1.89888 + 4.15797i) q^{37} +(2.41280 + 1.55061i) q^{38} +(0.377083 - 0.110722i) q^{39} +(0.436705 - 3.03735i) q^{40} +(1.02386 + 2.24195i) q^{41} +(0.235462 + 1.63768i) q^{42} +(1.86556 - 1.19892i) q^{43} +(-1.60338 + 1.85040i) q^{44} +0.805728 q^{45} +(3.42453 + 3.35747i) q^{46} +11.6979 q^{47} +(-1.08348 + 1.25040i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.628493 - 4.37126i) q^{50} +(-3.79669 - 8.31359i) q^{51} +(0.0338045 - 0.235115i) q^{52} +(4.42280 - 1.29865i) q^{53} +(-4.54107 - 2.91837i) q^{54} +(-3.12109 + 6.83424i) q^{55} +(0.959493 + 0.281733i) q^{56} +(-3.10753 - 3.58628i) q^{57} +(-2.04962 - 2.36539i) q^{58} +(-7.23756 - 2.12514i) q^{59} +(-2.10907 + 4.61823i) q^{60} +(10.8606 + 6.97967i) q^{61} +(-5.28041 + 1.55047i) q^{62} +(-0.0373681 + 0.259901i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.103732 - 0.721471i) q^{65} +(3.40788 - 2.19011i) q^{66} +(-9.60399 + 11.0836i) q^{67} -5.52397 q^{68} +(-3.87141 - 6.92625i) q^{69} +3.06858 q^{70} +(-3.38848 + 3.91051i) q^{71} +(-0.220891 + 0.141958i) q^{72} +(-1.06964 - 7.43953i) q^{73} +(-1.89888 - 4.15797i) q^{74} +(-1.03985 + 7.23233i) q^{75} +(-2.75192 + 0.808038i) q^{76} +(-2.05975 - 1.32372i) q^{77} +(-0.163259 + 0.357488i) q^{78} +(3.12023 + 0.916182i) q^{79} +(2.00950 + 2.31908i) q^{80} +(5.33275 + 6.15432i) q^{81} +(-2.36484 - 0.694379i) q^{82} +(-5.51635 + 12.0791i) q^{83} +(-1.39187 - 0.894499i) q^{84} +(-16.2642 + 4.77559i) q^{85} +(-0.315597 + 2.19503i) q^{86} +(2.15119 + 4.71044i) q^{87} +(-0.348447 - 2.42350i) q^{88} +(10.5002 - 6.74806i) q^{89} +(-0.527640 + 0.608929i) q^{90} +0.237533 q^{91} +(-4.78000 + 0.389415i) q^{92} +9.10535 q^{93} +(-7.66050 + 8.84068i) q^{94} +(-7.40389 + 4.75819i) q^{95} +(-0.235462 - 1.63768i) q^{96} +(1.83545 + 4.01907i) q^{97} +(-0.142315 + 0.989821i) q^{98} +(0.616849 - 0.181123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$3$	1.39187	−	0.894499i	0.803596	−	0.516440i	−0.0731918	−	0.997318i	$-0.523319\pi$
$3$	1.39187	−	0.894499i	0.803596	−	0.516440i	0.876787	+	0.480878i	$0.159682\pi$
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	−1.27474	−	2.79128i	−0.570079	−	1.24830i	−0.946755	−	0.321955i	$-0.895660\pi$
$5$	−1.27474	−	2.79128i	−0.570079	−	1.24830i	0.376676	−	0.926345i	$-0.377067\pi$
$6$	−0.235462	+	1.63768i	−0.0961271	+	0.668579i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$	−0.109077	+	0.238845i	−0.0363590	+	0.0796150i
$10$	2.94429	+	0.864520i	0.931065	+	0.273385i
$11$	−1.60338	−	1.85040i	−0.483436	−	0.557915i	0.460664	−	0.887575i	$-0.347611\pi$
$11$	−1.60338	−	1.85040i	−0.483436	−	0.557915i	−0.944100	+	0.329660i	$0.893066\pi$
$12$	−1.08348	−	1.25040i	−0.312773	−	0.360960i
$13$	0.227911	+	0.0669208i	0.0632112	+	0.0185605i	0.313185	−	0.949692i	$-0.398604\pi$
$13$	0.227911	+	0.0669208i	0.0632112	+	0.0185605i	−0.249974	+	0.968253i	$0.580422\pi$
$14$	−0.415415	+	0.909632i	−0.111024	+	0.243109i
$15$	−4.27107	−	2.74485i	−1.10278	−	0.708717i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.786144	−	5.46775i	0.190668	−	1.32612i	−0.639578	−	0.768726i	$-0.720891\pi$
$17$	0.786144	−	5.46775i	0.190668	−	1.32612i	0.830246	−	0.557397i	$-0.188200\pi$
$18$	−0.109077	−	0.238845i	−0.0257097	−	0.0562963i
$19$	−0.408174	−	2.83891i	−0.0936414	−	0.651290i	−0.981541	−	0.191253i	$-0.938745\pi$
$19$	−0.408174	−	2.83891i	−0.0936414	−	0.651290i	0.887899	−	0.460038i	$-0.152164\pi$
$20$	−2.58146	+	1.65900i	−0.577232	+	0.370964i
$21$	1.08348	−	1.25040i	0.236434	−	0.272860i
$22$	2.44842			0.522006
$23$	0.294813	−	4.78676i	0.0614728	−	0.998109i
$23$	0.294813	−	4.78676i	0.0614728	−	0.998109i
$24$	1.65452			0.337727
$25$	−2.89200	+	3.33755i	−0.578401	+	0.667510i
$26$	−0.199826	+	0.128420i	−0.0391890	+	0.0251852i
$27$	0.768213	+	5.34304i	0.147843	+	1.02827i
$28$	−0.415415	−	0.909632i	−0.0785061	−	0.171904i
$29$	−0.445425	+	3.09800i	−0.0827134	+	0.575284i	0.905749	+	0.423815i	$0.139309\pi$
$29$	−0.445425	+	3.09800i	−0.0827134	+	0.575284i	−0.988462	+	0.151469i	$0.951600\pi$
$30$	4.87137	−	1.43036i	0.889387	−	0.261147i
$31$	4.62969	+	2.97532i	0.831518	+	0.534384i	0.885760	−	0.464144i	$-0.153638\pi$
$31$	4.62969	+	2.97532i	0.831518	+	0.534384i	−0.0542421	+	0.998528i	$0.517274\pi$
$32$	0.415415	−	0.909632i	0.0734357	−	0.160802i
$33$	−3.88687	−	1.14129i	−0.676617	−	0.198673i
$34$	3.61743	+	4.17474i	0.620385	+	0.715962i
$35$	−2.00950	−	2.31908i	−0.339667	−	0.391996i
$36$	0.251937	+	0.0739754i	0.0419895	+	0.0123292i
$37$	−1.89888	+	4.15797i	−0.312174	+	0.683566i	−0.999067	−	0.0431929i	$-0.986247\pi$
$37$	−1.89888	+	4.15797i	−0.312174	+	0.683566i	0.686893	+	0.726759i	$0.258974\pi$
$38$	2.41280	+	1.55061i	0.391408	+	0.251543i
$39$	0.377083	−	0.110722i	0.0603816	−	0.0177296i
$40$	0.436705	−	3.03735i	0.0690491	−	0.480247i
$41$	1.02386	+	2.24195i	0.159900	+	0.350133i	0.972577	−	0.232582i	$-0.0747175\pi$
$41$	1.02386	+	2.24195i	0.159900	+	0.350133i	−0.812676	+	0.582715i	$0.801990\pi$
$42$	0.235462	+	1.63768i	0.0363326	+	0.252699i
$43$	1.86556	−	1.19892i	0.284496	−	0.182834i	−0.390608	−	0.920557i	$-0.627735\pi$
$43$	1.86556	−	1.19892i	0.284496	−	0.182834i	0.675104	+	0.737723i	$0.264099\pi$
$44$	−1.60338	+	1.85040i	−0.241718	+	0.278958i
$45$	0.805728			0.120111
$46$	3.42453	+	3.35747i	0.504920	+	0.495032i
$47$	11.6979			1.70631			0.853157	−	0.521654i	$-0.174685\pi$
$47$	11.6979			1.70631			0.853157	+	0.521654i	$0.174685\pi$
$48$	−1.08348	+	1.25040i	−0.156387	+	0.180480i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	−0.628493	−	4.37126i	−0.0888823	−	0.618190i
$51$	−3.79669	−	8.31359i	−0.531643	−	1.16414i
$52$	0.0338045	−	0.235115i	0.00468784	−	0.0326046i
$53$	4.42280	−	1.29865i	0.607518	−	0.178383i	0.0365174	−	0.999333i	$-0.488374\pi$
$53$	4.42280	−	1.29865i	0.607518	−	0.178383i	0.571001	+	0.820950i	$0.306555\pi$
$54$	−4.54107	−	2.91837i	−0.617962	−	0.397140i
$55$	−3.12109	+	6.83424i	−0.420848	+	0.921529i
$56$	0.959493	+	0.281733i	0.128218	+	0.0376481i
$57$	−3.10753	−	3.58628i	−0.411602	−	0.475014i
$58$	−2.04962	−	2.36539i	−0.269128	−	0.310591i
$59$	−7.23756	−	2.12514i	−0.942250	−	0.276670i	−0.225693	−	0.974198i	$-0.572465\pi$
$59$	−7.23756	−	2.12514i	−0.942250	−	0.276670i	−0.716557	+	0.697529i	$0.754283\pi$
$60$	−2.10907	+	4.61823i	−0.272280	+	0.596210i
$61$	10.8606	+	6.97967i	1.39055	+	0.893655i	0.999642	−	0.0267735i	$-0.00852329\pi$
$61$	10.8606	+	6.97967i	1.39055	+	0.893655i	0.390912	+	0.920428i	$0.372160\pi$
$62$	−5.28041	+	1.55047i	−0.670612	+	0.196909i
$63$	−0.0373681	+	0.259901i	−0.00470793	+	0.0327444i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−0.103732	−	0.721471i	−0.0128664	−	0.0894875i
$66$	3.40788	−	2.19011i	0.419481	−	0.269584i
$67$	−9.60399	+	11.0836i	−1.17331	+	1.35408i	−0.250835	+	0.968030i	$0.580705\pi$
$67$	−9.60399	+	11.0836i	−1.17331	+	1.35408i	−0.922479	+	0.386047i	$0.873840\pi$
$68$	−5.52397			−0.669880
$69$	−3.87141	−	6.92625i	−0.466064	−	0.833823i
$70$	3.06858			0.366766
$71$	−3.38848	+	3.91051i	−0.402138	+	0.464092i	−0.920313	−	0.391182i	$-0.872066\pi$
$71$	−3.38848	+	3.91051i	−0.402138	+	0.464092i	0.518175	+	0.855275i	$0.326612\pi$
$72$	−0.220891	+	0.141958i	−0.0260322	+	0.0167299i
$73$	−1.06964	−	7.43953i	−0.125192	−	0.870731i	−0.951530	−	0.307556i	$-0.900489\pi$
$73$	−1.06964	−	7.43953i	−0.125192	−	0.870731i	0.826338	−	0.563175i	$-0.190420\pi$
$74$	−1.89888	−	4.15797i	−0.220740	−	0.483354i
$75$	−1.03985	+	7.23233i	−0.120072	+	0.835117i
$76$	−2.75192	+	0.808038i	−0.315667	+	0.0926883i
$77$	−2.05975	−	1.32372i	−0.234730	−	0.150852i
$78$	−0.163259	+	0.357488i	−0.0184855	+	0.0404775i
$79$	3.12023	+	0.916182i	0.351053	+	0.103078i	0.452505	−	0.891762i	$-0.350531\pi$
$79$	3.12023	+	0.916182i	0.351053	+	0.103078i	−0.101452	+	0.994840i	$0.532349\pi$
$80$	2.00950	+	2.31908i	0.224668	+	0.259281i
$81$	5.33275	+	6.15432i	0.592528	+	0.683814i
$82$	−2.36484	−	0.694379i	−0.261153	−	0.0766813i
$83$	−5.51635	+	12.0791i	−0.605498	+	1.32586i	0.320113	+	0.947380i	$0.396279\pi$
$83$	−5.51635	+	12.0791i	−0.605498	+	1.32586i	−0.925611	+	0.378477i	$0.876448\pi$
$84$	−1.39187	−	0.894499i	−0.151865	−	0.0975979i
$85$	−16.2642	+	4.77559i	−1.76410	+	0.517985i
$86$	−0.315597	+	2.19503i	−0.0340317	+	0.236696i
$87$	2.15119	+	4.71044i	0.230631	+	0.505012i
$88$	−0.348447	−	2.42350i	−0.0371446	−	0.258346i
$89$	10.5002	−	6.74806i	1.11302	−	0.715293i	0.151070	−	0.988523i	$-0.451728\pi$
$89$	10.5002	−	6.74806i	1.11302	−	0.715293i	0.961949	+	0.273230i	$0.0880919\pi$
$90$	−0.527640	+	0.608929i	−0.0556181	+	0.0641867i
$91$	0.237533			0.0249002
$92$	−4.78000	+	0.389415i	−0.498349	+	0.0405993i
$93$	9.10535			0.944181
$94$	−7.66050	+	8.84068i	−0.790120	+	0.911847i
$95$	−7.40389	+	4.75819i	−0.759623	+	0.488180i
$96$	−0.235462	−	1.63768i	−0.0240318	−	0.167145i
$97$	1.83545	+	4.01907i	0.186361	+	0.408074i	0.979634	−	0.200792i	$-0.0643517\pi$
$97$	1.83545	+	4.01907i	0.186361	+	0.408074i	−0.793273	+	0.608867i	$0.791624\pi$
$98$	−0.142315	+	0.989821i	−0.0143760	+	0.0999871i
$99$	0.616849	−	0.181123i	0.0619957	−	0.0182036i
$100$	3.71515	+	2.38758i	0.371515	+	0.238758i
$101$	−0.0835059	+	0.182852i	−0.00830914	+	0.0181945i	−0.913741	−	0.406297i	$-0.866820\pi$
$101$	−0.0835059	+	0.182852i	−0.00830914	+	0.0181945i	0.905432	+	0.424491i	$0.139547\pi$
$102$	8.76930	+	2.57490i	0.868290	+	0.254953i
$103$	1.05203	+	1.21411i	0.103660	+	0.119630i	0.805209	−	0.592992i	$-0.202053\pi$
$103$	1.05203	+	1.21411i	0.103660	+	0.119630i	−0.701549	+	0.712621i	$0.747508\pi$
$104$	0.155551	+	0.179515i	0.0152530	+	0.0176029i
$105$	−4.87137	−	1.43036i	−0.475397	−	0.139589i
$106$	−1.91486	+	4.19296i	−0.185988	+	0.407257i
$107$	−3.62202	−	2.32773i	−0.350154	−	0.225031i	0.353726	−	0.935349i	$-0.384915\pi$
$107$	−3.62202	−	2.32773i	−0.350154	−	0.225031i	−0.703880	+	0.710319i	$0.748551\pi$
$108$	5.17933	−	1.52079i	0.498381	−	0.146338i
$109$	−0.631961	+	4.39539i	−0.0605309	+	0.421002i	0.936914	+	0.349560i	$0.113669\pi$
$109$	−0.631961	+	4.39539i	−0.0605309	+	0.421002i	−0.997445	+	0.0714414i	$0.977240\pi$
$110$	−3.12109	−	6.83424i	−0.297585	−	0.651620i
$111$	1.07631	+	7.48589i	0.102159	+	0.710530i
$112$	−0.841254	+	0.540641i	−0.0794910	+	0.0510858i
$113$	11.6274	−	13.4187i	1.09381	−	1.26233i	0.131226	−	0.991353i	$-0.458109\pi$
$113$	11.6274	−	13.4187i	1.09381	−	1.26233i	0.962587	−	0.270974i	$-0.0873458\pi$
$114$	4.74532			0.444440
$115$	−13.7370	+	5.27895i	−1.28098	+	0.492265i
$116$	3.12986			0.290600
$117$	−0.0408436	+	0.0471360i	−0.00377599	+	0.00435772i
$118$	6.34567	−	4.07811i	0.584166	−	0.375421i
$119$	−0.786144	−	5.46775i	−0.0720657	−	0.501228i
$120$	−2.10907	−	4.61823i	−0.192531	−	0.421584i
$121$	0.712317	−	4.95427i	0.0647561	−	0.450389i
$122$	−12.3870	+	3.63716i	−1.12147	+	0.329293i
$123$	3.43050	+	2.20465i	0.309318	+	0.198787i
$124$	2.28617	−	5.00600i	0.205304	−	0.449552i
$125$	−1.71884	−	0.504696i	−0.153737	−	0.0451414i
$126$	−0.171949	−	0.198440i	−0.0153184	−	0.0176784i
$127$	6.89139	+	7.95309i	0.611512	+	0.705723i	0.974072	−	0.226238i	$-0.0726426\pi$
$127$	6.89139	+	7.95309i	0.611512	+	0.705723i	−0.362560	+	0.931961i	$0.618097\pi$
$128$	−0.959493	−	0.281733i	−0.0848080	−	0.0249019i
$129$	1.52418	−	3.33749i	0.134197	−	0.293850i
$130$	0.613182	+	0.394068i	0.0537796	+	0.0345620i
$131$	−18.4629	+	5.42119i	−1.61311	+	0.473652i	−0.959155	−	0.282882i	$-0.908709\pi$
$131$	−18.4629	+	5.42119i	−1.61311	+	0.473652i	−0.653954	+	0.756534i	$0.726891\pi$
$132$	−0.576512	+	4.00973i	−0.0501789	+	0.349002i
$133$	−1.19145	−	2.60892i	−0.103312	−	0.226222i
$134$	−2.08715	−	14.5164i	−0.180302	−	1.25403i
$135$	13.9347	−	8.95527i	1.19931	−	0.770747i
$136$	3.61743	−	4.17474i	0.310192	−	0.357981i
$137$	6.53221			0.558085			0.279042	−	0.960279i	$-0.409983\pi$
$137$	6.53221			0.558085			0.279042	+	0.960279i	$0.409983\pi$
$138$	7.76975	+	1.60991i	0.661405	+	0.137045i
$139$	11.3443			0.962209			0.481105	−	0.876663i	$-0.340236\pi$
$139$	11.3443			0.962209			0.481105	+	0.876663i	$0.340236\pi$
$140$	−2.00950	+	2.31908i	−0.169833	+	0.195998i
$141$	16.2819	−	10.4638i	1.37119	−	0.881208i
$142$	−0.736387	−	5.12168i	−0.0617962	−	0.429802i
$143$	−0.241598	−	0.529025i	−0.0202034	−	0.0442393i
$144$	0.0373681	−	0.259901i	0.00311401	−	0.0216584i
$145$	9.21520	−	2.70583i	0.765280	−	0.224707i
$146$	6.32289	+	4.06347i	0.523286	+	0.336295i
$147$	0.687311	−	1.50500i	0.0566885	−	0.124130i
$148$	4.38589	+	1.28781i	0.360518	+	0.105858i
$149$	−13.8634	−	15.9992i	−1.13574	−	1.31071i	−0.944256	−	0.329212i	$-0.893217\pi$
$149$	−13.8634	−	15.9992i	−1.13574	−	1.31071i	−0.191479	−	0.981497i	$-0.561328\pi$
$150$	−4.78487	−	5.52204i	−0.390683	−	0.450872i
$151$	−3.04307	−	0.893525i	−0.247641	−	0.0727140i	0.155556	−	0.987827i	$-0.450283\pi$
$151$	−3.04307	−	0.893525i	−0.247641	−	0.0727140i	−0.403197	+	0.915113i	$0.632101\pi$
$152$	1.19145	−	2.60892i	0.0966396	−	0.211611i
$153$	1.22019	+	0.784171i	0.0986469	+	0.0633965i
$154$	2.34925	−	0.689801i	0.189308	−	0.0555857i
$155$	2.40333	−	16.7155i	0.193040	−	1.34262i
$156$	−0.163259	−	0.357488i	−0.0130712	−	0.0286219i
$157$	0.409310	+	2.84682i	0.0326665	+	0.227201i	0.999614	−	0.0277741i	$-0.00884192\pi$
$157$	0.409310	+	2.84682i	0.0326665	+	0.227201i	−0.966948	+	0.254975i	$0.917933\pi$
$158$	−2.73572	+	1.75814i	−0.217642	+	0.139870i
$159$	4.99431	−	5.76374i	0.396075	−	0.457094i
$160$	−3.06858			−0.242593
$161$	−1.06572	−	4.67592i	−0.0839901	−	0.368514i
$162$	−8.14334			−0.639801
$163$	2.77191	−	3.19895i	0.217113	−	0.250561i	−0.636737	−	0.771081i	$-0.719716\pi$
$163$	2.77191	−	3.19895i	0.217113	−	0.250561i	0.853850	+	0.520520i	$0.174262\pi$
$164$	2.07342	−	1.33250i	0.161907	−	0.104051i
$165$	1.76907	+	12.3042i	0.137722	+	0.957879i
$166$	−5.51635	−	12.0791i	−0.428152	−	0.937522i
$167$	−1.85731	+	12.9178i	−0.143723	+	0.999613i	0.782504	+	0.622646i	$0.213942\pi$
$167$	−1.85731	+	12.9178i	−0.143723	+	0.999613i	−0.926227	+	0.376967i	$0.876967\pi$
$168$	1.58750	−	0.466131i	0.122478	−	0.0359628i
$169$	−10.8888	−	6.99783i	−0.837602	−	0.538294i
$170$	7.04161	−	15.4190i	0.540067	−	1.18258i
$171$	0.722582	+	0.212169i	0.0552572	+	0.0162250i
$172$	−1.45222	−	1.67595i	−0.110731	−	0.127790i
$173$	9.06703	+	10.4639i	0.689353	+	0.795556i	0.987273	−	0.159035i	$-0.0508382\pi$
$173$	9.06703	+	10.4639i	0.689353	+	0.795556i	−0.297920	+	0.954591i	$0.596293\pi$
$174$	−4.96864	−	1.45893i	−0.376672	−	0.110601i
$175$	−1.83456	+	4.01713i	−0.138680	+	0.303666i
$176$	2.05975	+	1.32372i	0.155259	+	0.0997790i
$177$	−11.9747	+	3.51608i	−0.900071	+	0.264285i
$178$	−1.77632	+	12.3546i	−0.133141	+	0.926013i
$179$	−6.70477	−	14.6814i	−0.501138	−	1.09734i	−0.976098	−	0.217332i	$-0.930265\pi$
$179$	−6.70477	−	14.6814i	−0.501138	−	1.09734i	0.474960	−	0.880008i	$-0.342463\pi$
$180$	−0.114667	−	0.797527i	−0.00854678	−	0.0594442i
$181$	17.4817	−	11.2348i	1.29941	−	0.835078i	0.306260	−	0.951948i	$-0.400922\pi$
$181$	17.4817	−	11.2348i	1.29941	−	0.835078i	0.993147	+	0.116870i	$0.0372860\pi$
$182$	−0.155551	+	0.179515i	−0.0115302	+	0.0133066i
$183$	21.3598			1.57896
$184$	2.83593	−	3.86749i	0.209068	−	0.285115i
$185$	14.0266			1.03126
$186$	−5.96274	+	6.88137i	−0.437209	+	0.504566i
$187$	−11.3780	+	7.31218i	−0.832040	+	0.534720i
$188$	−1.66479	−	11.5788i	−0.121417	−	0.844473i
$189$	2.24240	+	4.91018i	0.163111	+	0.357163i
$190$	1.25252	−	8.71143i	0.0908670	−	0.631994i
$191$	−0.0219530	+	0.00644597i	−0.00158846	+	0.000466414i	−0.282527	−	0.959259i	$-0.591173\pi$
$191$	−0.0219530	+	0.00644597i	−0.00158846	+	0.000466414i	0.280938	+	0.959726i	$0.409354\pi$
$192$	1.39187	+	0.894499i	0.100449	+	0.0645549i
$193$	8.63448	−	18.9069i	0.621524	−	1.36095i	−0.292882	−	0.956148i	$-0.594614\pi$
$193$	8.63448	−	18.9069i	0.621524	−	1.36095i	0.914406	−	0.404798i	$-0.132658\pi$
$194$	−4.23937	−	1.24479i	−0.304369	−	0.0893708i
$195$	−0.789737	−	0.911405i	−0.0565542	−	0.0652671i
$196$	−0.654861	−	0.755750i	−0.0467758	−	0.0539821i
$197$	20.2926	+	5.95846i	1.44579	+	0.424523i	0.908148	−	0.418650i	$-0.137496\pi$
$197$	20.2926	+	5.95846i	1.44579	+	0.424523i	0.537643	+	0.843172i	$0.319315\pi$
$198$	−0.267066	+	0.584794i	−0.0189796	+	0.0415595i
$199$	6.23456	+	4.00671i	0.441956	+	0.284028i	0.742634	−	0.669698i	$-0.233576\pi$
$199$	6.23456	+	4.00671i	0.441956	+	0.284028i	−0.300677	+	0.953726i	$0.597213\pi$
$200$	−4.23733	+	1.24419i	−0.299624	+	0.0879776i
$201$	−3.45322	+	24.0177i	−0.243571	+	1.69408i
$202$	−0.0835059	−	0.182852i	−0.00587545	−	0.0128654i
$203$	0.445425	+	3.09800i	0.0312627	+	0.217437i
$204$	−7.68864	+	4.94119i	−0.538313	+	0.345953i
$205$	4.95275	−	5.71578i	0.345915	−	0.399207i
$206$	−1.60650			−0.111930
$207$	1.11114	+	0.592540i	0.0772294	+	0.0411844i
$208$	−0.237533			−0.0164700
$209$	−4.59865	+	5.30712i	−0.318095	+	0.367101i
$210$	4.27107	−	2.74485i	0.294732	−	0.189412i
$211$	3.64880	+	25.3779i	0.251193	+	1.74709i	0.591071	+	0.806619i	$0.298705\pi$
$211$	3.64880	+	25.3779i	0.251193	+	1.74709i	−0.339878	+	0.940470i	$0.610386\pi$
$212$	−1.91486	−	4.19296i	−0.131513	−	0.287974i
$213$	−1.21836	+	8.47391i	−0.0834809	+	0.580623i
$214$	4.13111	−	1.21300i	0.282397	−	0.0829191i
$215$	−5.72464	−	3.67900i	−0.390417	−	0.250906i
$216$	−2.24240	+	4.91018i	−0.152576	+	0.334095i
$217$	5.28041	+	1.55047i	0.358457	+	0.105253i
$218$	−2.90796	−	3.35597i	−0.196952	−	0.227295i
$219$	−8.14345	−	9.39805i	−0.550284	−	0.635061i
$220$	7.20886	+	2.11671i	0.486021	+	0.142709i
$221$	0.545077	−	1.19355i	0.0366658	−	0.0802870i
$222$	−6.36229	−	4.08880i	−0.427009	−	0.274422i
$223$	−14.1681	+	4.16014i	−0.948768	+	0.278583i	−0.719274	−	0.694727i	$-0.755525\pi$
$223$	−14.1681	+	4.16014i	−0.948768	+	0.278583i	−0.229494	+	0.973310i	$0.573707\pi$
$224$	0.142315	−	0.989821i	0.00950881	−	0.0661352i
$225$	−0.481707	−	1.05479i	−0.0321138	−	0.0703194i
$226$	2.52687	+	17.5748i	0.168085	+	1.16906i
$227$	−18.3410	+	11.7870i	−1.21733	+	0.782332i	−0.981871	−	0.189551i	$-0.939297\pi$
$227$	−18.3410	+	11.7870i	−1.21733	+	0.782332i	−0.235462	+	0.971884i	$0.575660\pi$
$228$	−3.10753	+	3.58628i	−0.205801	+	0.237507i
$229$	−1.55495			−0.102754			−0.0513771	−	0.998679i	$-0.516361\pi$
$229$	−1.55495			−0.102754			−0.0513771	+	0.998679i	$0.516361\pi$
$230$	5.00627	−	13.8387i	0.330103	−	0.912498i
$231$	−4.05096			−0.266534
$232$	−2.04962	+	2.36539i	−0.134564	+	0.155295i
$233$	−21.0256	+	13.5123i	−1.37743	+	0.885223i	−0.999180	−	0.0404791i	$-0.987112\pi$
$233$	−21.0256	+	13.5123i	−1.37743	+	0.885223i	−0.378253	+	0.925702i	$0.623475\pi$
$234$	−0.00887615	−	0.0617350i	−0.000580252	−	0.00403574i
$235$	−14.9117	−	32.6522i	−0.972735	−	2.12999i
$236$	−1.07350	+	7.46633i	−0.0698787	+	0.486017i
$237$	5.16247	−	1.51584i	0.335339	−	0.0984643i
$238$	4.64706	+	2.98649i	0.301224	+	0.193585i
$239$	5.09292	−	11.1519i	0.329434	−	0.721359i	−0.670352	−	0.742043i	$-0.733857\pi$
$239$	5.09292	−	11.1519i	0.329434	−	0.721359i	0.999786	+	0.0206838i	$0.00658433\pi$
$240$	4.87137	+	1.43036i	0.314446	+	0.0923296i
$241$	−5.79960	−	6.69309i	−0.373585	−	0.431140i	0.537560	−	0.843225i	$-0.319346\pi$
$241$	−5.79960	−	6.69309i	−0.373585	−	0.431140i	−0.911145	+	0.412085i	$0.864801\pi$
$242$	3.27772	+	3.78269i	0.210700	+	0.243161i
$243$	−2.61046	−	0.766499i	−0.167461	−	0.0491709i
$244$	5.36300	−	11.7433i	0.343331	−	0.751790i
$245$	−2.58146	−	1.65900i	−0.164923	−	0.105990i
$246$	−3.91266	+	1.14886i	−0.249462	+	0.0732488i
$247$	0.0969547	−	0.674335i	0.00616908	−	0.0429069i
$248$	2.28617	+	5.00600i	0.145172	+	0.317882i
$249$	3.12674	+	21.7469i	0.198149	+	1.37816i
$250$	1.50702	−	0.968504i	0.0953124	−	0.0612536i
$251$	6.81567	−	7.86571i	0.430201	−	0.496479i	−0.498716	−	0.866765i	$-0.666195\pi$
$251$	6.81567	−	7.86571i	0.430201	−	0.496479i	0.928918	+	0.370286i	$0.120740\pi$
$252$	0.262573			0.0165406
$253$	−9.33010	+	7.12946i	−0.586578	+	0.448225i
$254$	−10.5235			−0.660300
$255$	−18.3658	+	21.1953i	−1.15011	+	1.32730i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	0.333818	+	2.32176i	0.0208230	+	0.144827i	0.997581	−	0.0695198i	$-0.0221467\pi$
$257$	0.333818	+	2.32176i	0.0208230	+	0.144827i	−0.976758	+	0.214347i	$0.931238\pi$
$258$	1.52418	+	3.33749i	0.0948913	+	0.207783i
$259$	−0.650528	+	4.52452i	−0.0404218	+	0.281140i
$260$	−0.699365	+	0.205352i	−0.0433728	+	0.0127354i
$261$	−0.691357	−	0.444308i	−0.0427939	−	0.0275020i
$262$	7.99355	−	17.5034i	0.493843	−	1.08137i
$263$	−24.4773	−	7.18718i	−1.50933	−	0.443181i	−0.580682	−	0.814131i	$-0.697214\pi$
$263$	−24.4773	−	7.18718i	−1.50933	−	0.443181i	−0.928653	+	0.370950i	$0.879032\pi$
$264$	−2.65281	−	3.06151i	−0.163269	−	0.188423i
$265$	−9.26280	−	10.6898i	−0.569009	−	0.656672i
$266$	2.75192	+	0.808038i	0.168731	+	0.0495440i
$267$	8.57875	−	18.7848i	0.525011	−	1.14961i
$268$	12.3376	+	7.92888i	0.753637	+	0.484333i
$269$	−0.343815	+	0.100953i	−0.0209628	+	0.00615523i	−0.292197	−	0.956358i	$-0.594386\pi$
$269$	−0.343815	+	0.100953i	−0.0209628	+	0.00615523i	0.271234	+	0.962513i	$0.412568\pi$
$270$	−2.35733	+	16.3956i	−0.143462	+	0.997803i
$271$	−9.65746	−	21.1469i	−0.586649	−	1.28458i	−0.937446	−	0.348131i	$-0.886817\pi$
$271$	−9.65746	−	21.1469i	−0.586649	−	1.28458i	0.350797	−	0.936452i	$-0.385911\pi$
$272$	0.786144	+	5.46775i	0.0476670	+	0.331531i
$273$	0.330615	−	0.212473i	0.0200097	−	0.0128595i
$274$	−4.27769	+	4.93672i	−0.258425	+	0.298238i
$275$	10.8128			0.652034
$276$	−6.30479	+	4.81772i	−0.379504	+	0.289993i
$277$	−7.26885			−0.436743			−0.218371	−	0.975866i	$-0.570074\pi$
$277$	−7.26885			−0.436743			−0.218371	+	0.975866i	$0.570074\pi$
$278$	−7.42892	+	8.57343i	−0.445557	+	0.514200i
$279$	−1.21563	+	0.781241i	−0.0727781	+	0.0467717i
$280$	−0.436705	−	3.03735i	−0.0260981	−	0.181516i
$281$	5.86253	+	12.8372i	0.349729	+	0.765801i	0.999982	+	0.00608208i	$0.00193600\pi$
$281$	5.86253	+	12.8372i	0.349729	+	0.765801i	−0.650252	+	0.759719i	$0.725337\pi$
$282$	−2.75442	+	19.1574i	−0.164023	+	1.14081i
$283$	−3.31697	+	0.973951i	−0.197174	+	0.0578954i	−0.378828	−	0.925467i	$-0.623673\pi$
$283$	−3.31697	+	0.973951i	−0.197174	+	0.0578954i	0.181655	+	0.983362i	$0.441855\pi$
$284$	4.35294	+	2.79746i	0.258299	+	0.165999i
$285$	−6.04904	+	13.2455i	−0.358314	+	0.784598i
$286$	0.558023	+	0.163850i	0.0329966	+	0.00968868i
$287$	1.61402	+	1.86268i	0.0952725	+	0.109950i
$288$	0.171949	+	0.198440i	0.0101322	+	0.0116932i
$289$	−12.9669	−	3.80742i	−0.762757	−	0.223966i
$290$	−3.98974	+	8.73632i	−0.234286	+	0.513014i
$291$	6.14975	+	3.95220i	0.360505	+	0.231682i
$292$	−7.21158	+	2.11751i	−0.422026	+	0.123918i
$293$	−3.83532	+	26.6753i	−0.224062	+	1.55839i	0.498383	+	0.866957i	$0.333927\pi$
$293$	−3.83532	+	26.6753i	−0.224062	+	1.55839i	−0.722445	+	0.691428i	$0.756982\pi$
$294$	0.687311	+	1.50500i	0.0400848	+	0.0877735i
$295$	3.29411	+	22.9111i	0.191791	+	1.33393i
$296$	−3.84541	+	2.47129i	−0.223510	+	0.143641i
$297$	8.65500	−	9.98840i	0.502214	−	0.579586i
$298$	21.1700			1.22635
$299$	0.387525	−	1.07123i	0.0224112	−	0.0619507i
$300$	7.30670			0.421852
$301$	1.45222	−	1.67595i	0.0837045	−	0.0966001i
$302$	2.66807	−	1.71466i	0.153530	−	0.0986677i
$303$	0.0473322	+	0.329202i	0.00271916	+	0.0189122i
$304$	1.19145	+	2.60892i	0.0683345	+	0.149632i
$305$	5.63786	−	39.2122i	0.322823	−	2.24528i
$306$	−1.39169	+	0.408638i	−0.0795579	+	0.0233603i
$307$	8.05152	+	5.17440i	0.459524	+	0.295318i	0.749848	−	0.661610i	$-0.230127\pi$
$307$	8.05152	+	5.17440i	0.459524	+	0.295318i	−0.290324	+	0.956929i	$0.593763\pi$
$308$	−1.01711	+	2.22716i	−0.0579553	+	0.126904i
$309$	2.55031	+	0.748839i	0.145082	+	0.0425999i
$310$	11.0589	+	12.7627i	0.628104	+	0.724871i
$311$	2.34472	+	2.70595i	0.132957	+	0.153440i	0.818324	−	0.574758i	$-0.194904\pi$
$311$	2.34472	+	2.70595i	0.132957	+	0.153440i	−0.685367	+	0.728198i	$0.740358\pi$
$312$	0.377083	+	0.110722i	0.0213481	+	0.00626838i
$313$	8.15096	−	17.8481i	0.460719	−	1.00883i	−0.526604	−	0.850111i	$-0.676535\pi$
$313$	8.15096	−	17.8481i	0.460719	−	1.00883i	0.987323	−	0.158724i	$-0.0507380\pi$
$314$	−2.41952	−	1.55493i	−0.136541	−	0.0877499i
$315$	0.773091	−	0.227000i	0.0435587	−	0.0127900i
$316$	0.462802	−	3.21886i	0.0260346	−	0.181075i
$317$	9.62577	+	21.0775i	0.540637	+	1.18383i	0.961019	+	0.276483i	$0.0891688\pi$
$317$	9.62577	+	21.0775i	0.540637	+	1.18383i	−0.420382	+	0.907347i	$0.638104\pi$
$318$	1.08537	+	7.54890i	0.0608644	+	0.423321i
$319$	6.44671	−	4.14305i	0.360947	−	0.231966i
$320$	2.00950	−	2.31908i	0.112334	−	0.129641i
$321$	−7.12354			−0.397597
$322$	4.23172	+	2.25666i	0.235825	+	0.125759i
$323$	−15.8433			−0.881546
$324$	5.33275	−	6.15432i	0.296264	−	0.341907i
$325$	−0.882472	+	0.567130i	−0.0489507	+	0.0314587i
$326$	0.602393	+	4.18974i	0.0333635	+	0.232048i
$327$	3.05206	+	6.68309i	0.168780	+	0.369576i
$328$	−0.350760	+	2.43959i	−0.0193675	+	0.134704i
$329$	11.2241	−	3.29568i	0.618802	−	0.181697i
$330$	−10.4574	−	6.72055i	−0.575660	−	0.369954i
$331$	5.68738	−	12.4536i	0.312607	−	0.684513i	−0.686484	−	0.727145i	$-0.740847\pi$
$331$	5.68738	−	12.4536i	0.312607	−	0.684513i	0.999091	+	0.0426316i	$0.0135742\pi$
$332$	12.7412	+	3.74116i	0.699266	+	0.205323i
$333$	−0.785987	−	0.907077i	−0.0430718	−	0.0497075i
$334$	−8.54638	−	9.86305i	−0.467637	−	0.539682i
$335$	43.1800	+	12.6788i	2.35918	+	0.692717i
$336$	−0.687311	+	1.50500i	−0.0374959	+	0.0821046i
$337$	−4.02364	−	2.58584i	−0.219182	−	0.140860i	0.426443	−	0.904515i	$-0.359767\pi$
$337$	−4.02364	−	2.58584i	−0.219182	−	0.140860i	−0.645625	+	0.763655i	$0.723403\pi$
$338$	12.4193	−	3.64663i	0.675519	−	0.198350i
$339$	4.18075	−	29.0778i	0.227067	−	1.57929i
$340$	7.04161	+	15.4190i	0.381885	+	0.836211i
$341$	−1.91762	−	13.3373i	−0.103845	−	0.722257i
$342$	−0.633537	+	0.407150i	−0.0342578	+	0.0220161i
$343$	0.654861	−	0.755750i	0.0353592	−	0.0408066i
$344$	2.21760			0.119565
$345$	−14.3981	+	19.6354i	−0.775167	+	1.05713i
$346$	−13.8457			−0.744351
$347$	−1.84818	+	2.13291i	−0.0992155	+	0.114501i	−0.803186	−	0.595729i	$-0.796863\pi$
$347$	−1.84818	+	2.13291i	−0.0992155	+	0.114501i	0.703970	+	0.710229i	$0.251409\pi$
$348$	4.35635	−	2.79966i	0.233525	−	0.150077i
$349$	−4.39316	−	30.5551i	−0.235160	−	1.63558i	−0.675227	−	0.737610i	$-0.735954\pi$
$349$	−4.39316	−	30.5551i	−0.235160	−	1.63558i	0.440066	−	0.897965i	$-0.354955\pi$
$350$	−1.83456	−	4.01713i	−0.0980614	−	0.214725i
$351$	−0.182476	+	1.26915i	−0.00973985	+	0.0677421i
$352$	−2.34925	+	0.689801i	−0.125215	+	0.0367665i
$353$	−14.7218	−	9.46113i	−0.783562	−	0.503565i	0.0866518	−	0.996239i	$-0.472383\pi$
$353$	−14.7218	−	9.46113i	−0.783562	−	0.503565i	−0.870214	+	0.492674i	$0.836020\pi$
$354$	5.18446	−	11.3524i	0.275551	−	0.603373i
$355$	15.2348	+	4.47333i	0.808577	+	0.237420i
$356$	−8.17371	−	9.43297i	−0.433206	−	0.499946i
$357$	−5.98511	−	6.90718i	−0.316765	−	0.365567i
$358$	15.4862	+	4.54715i	0.818469	+	0.240324i
$359$	−8.84754	+	19.3734i	−0.466955	+	1.02249i	0.518891	+	0.854840i	$0.326345\pi$
$359$	−8.84754	+	19.3734i	−0.466955	+	1.02249i	−0.985847	+	0.167649i	$0.946382\pi$
$360$	0.677822	+	0.435610i	0.0357243	+	0.0229586i
$361$	10.3376	−	3.03538i	0.544082	−	0.159757i
$362$	−2.95738	+	20.5691i	−0.155437	+	1.08109i
$363$	−3.44014	−	7.53287i	−0.180561	−	0.395373i
$364$	−0.0338045	−	0.235115i	−0.00177184	−	0.0123234i
$365$	−19.4023	+	12.4691i	−1.01556	+	0.652663i
$366$	−13.9877	+	16.1427i	−0.731148	+	0.843790i
$367$	17.2499			0.900435			0.450218	−	0.892919i	$-0.351346\pi$
$367$	17.2499			0.900435			0.450218	+	0.892919i	$0.351346\pi$
$368$	1.06572	+	4.67592i	0.0555543	+	0.243749i
$369$	−0.647158			−0.0336897
$370$	−9.18550	+	10.6006i	−0.477531	+	0.551100i
$371$	3.87777	−	2.49209i	0.201324	−	0.129383i
$372$	−1.29583	−	9.01267i	−0.0671855	−	0.467285i
$373$	8.41201	+	18.4197i	0.435557	+	0.953737i	0.992393	+	0.123114i	$0.0392882\pi$
$373$	8.41201	+	18.4197i	0.435557	+	0.953737i	−0.556835	+	0.830623i	$0.687985\pi$
$374$	1.92481	−	13.3874i	0.0995297	−	0.692244i
$375$	−2.84384	+	0.835028i	−0.146855	+	0.0431207i
$376$	9.84090	+	6.32436i	0.507506	+	0.326154i
$377$	−0.308838	+	0.676261i	−0.0159060	+	0.0348292i
$378$	−5.17933	−	1.52079i	−0.266396	−	0.0782209i
$379$	−20.1266	−	23.2273i	−1.03383	−	1.19311i	−0.980901	−	0.194508i	$-0.937689\pi$
$379$	−20.1266	−	23.2273i	−1.03383	−	1.19311i	−0.0529312	−	0.998598i	$-0.516856\pi$
$380$	5.76344	+	6.65136i	0.295658	+	0.341208i
$381$	16.7060	+	4.90531i	0.855872	+	0.251307i
$382$	0.00950459	−	0.0208122i	0.000486297	−	0.00106484i
$383$	14.4563	+	9.29051i	0.738683	+	0.474723i	0.855091	−	0.518479i	$-0.173501\pi$
$383$	14.4563	+	9.29051i	0.738683	+	0.474723i	−0.116407	+	0.993202i	$0.537138\pi$
$384$	−1.58750	+	0.466131i	−0.0810116	+	0.0237872i
$385$	−1.06924	+	7.43672i	−0.0544935	+	0.379010i
$386$	8.63448	+	18.9069i	0.439484	+	0.962335i
$387$	0.0828674	+	0.576355i	0.00421239	+	0.0292978i
$388$	3.71695	−	2.38874i	0.188699	−	0.121270i
$389$	11.1067	−	12.8178i	0.563131	−	0.649888i	−0.400761	−	0.916183i	$-0.631254\pi$
$389$	11.1067	−	12.8178i	0.563131	−	0.649888i	0.963892	+	0.266295i	$0.0857995\pi$
$390$	1.20596			0.0610662
$391$	−25.9410	−	5.37505i	−1.31189	−	0.271828i
$392$	1.00000			0.0505076
$393$	−20.8486	+	24.0606i	−1.05167	+	1.21370i
$394$	−17.7920	+	11.4342i	−0.896346	+	0.576047i
$395$	−1.42015	−	9.87733i	−0.0714553	−	0.496982i
$396$	−0.267066	−	0.584794i	−0.0134206	−	0.0293870i
$397$	−1.03987	+	7.23243i	−0.0521894	+	0.362985i	0.946945	+	0.321395i	$0.104152\pi$
$397$	−1.03987	+	7.23243i	−0.0521894	+	0.362985i	−0.999135	+	0.0415905i	$0.986758\pi$
$398$	−7.11084	+	2.08793i	−0.356434	+	0.104658i
$399$	−3.99202	−	2.56552i	−0.199851	−	0.128436i
$400$	1.83456	−	4.01713i	0.0917281	−	0.200856i
$401$	−34.4926	−	10.1280i	−1.72248	−	0.505766i	−0.737049	−	0.675839i	$-0.763781\pi$
$401$	−34.4926	−	10.1280i	−1.72248	−	0.505766i	−0.985431	+	0.170073i	$0.945600\pi$
$402$	−15.8900	−	18.3380i	−0.792520	−	0.914616i
$403$	0.856049	+	0.987933i	0.0426428	+	0.0492124i
$404$	0.192875	+	0.0566333i	0.00959590	+	0.00281761i
$405$	10.3806	−	22.7304i	0.515816	−	1.12948i
$406$	−2.63300	−	1.69213i	−0.130674	−	0.0839790i
$407$	10.7385	−	3.15311i	0.532288	−	0.156294i
$408$	1.30069	−	9.04648i	0.0643936	−	0.447868i
$409$	−0.0542109	−	0.118705i	−0.00268056	−	0.00586961i	0.908287	−	0.418348i	$-0.137391\pi$
$409$	−0.0542109	−	0.118705i	−0.00268056	−	0.00586961i	−0.910968	+	0.412478i	$0.864663\pi$
$410$	1.07634	+	7.48608i	0.0531564	+	0.369711i
$411$	9.09198	−	5.84306i	0.448474	−	0.288217i
$412$	1.05203	−	1.21411i	0.0518299	−	0.0598149i
$413$	−7.54311			−0.371172
$414$	−1.17545	+	0.451710i	−0.0577703	+	0.0222004i
$415$	40.7482			2.00025
$416$	0.155551	−	0.179515i	0.00762652	−	0.00880147i
$417$	15.7897	−	10.1475i	0.773227	−	0.496923i
$418$	−0.999382	−	6.95085i	−0.0488814	−	0.339977i
$419$	−13.1220	−	28.7331i	−0.641049	−	1.40370i	−0.899174	−	0.437591i	$-0.855832\pi$
$419$	−13.1220	−	28.7331i	−0.641049	−	1.40370i	0.258125	−	0.966112i	$-0.416895\pi$
$420$	−0.722536	+	5.02535i	−0.0352562	+	0.245212i
$421$	−36.9358	+	10.8453i	−1.80014	+	0.528570i	−0.997677	−	0.0681275i	$-0.978298\pi$
$421$	−36.9358	+	10.8453i	−1.80014	+	0.528570i	−0.802466	+	0.596697i	$0.796479\pi$
$422$	−21.5688	−	13.8614i	−1.04995	−	0.674764i
$423$	−1.27597	+	2.79399i	−0.0620398	+	0.135848i
$424$	4.42280	+	1.29865i	0.214790	+	0.0630681i
$425$	15.9754	+	18.4365i	0.774919	+	0.894304i
$426$	−5.60629	−	6.47001i	−0.271626	−	0.313473i
$427$	12.3870	+	3.63716i	0.599451	+	0.176015i
$428$	−1.78857	+	3.91643i	−0.0864539	+	0.189308i
$429$	−0.809485	−	0.520224i	−0.0390823	−	0.0251167i
$430$	6.52924	−	1.91716i	0.314868	−	0.0924536i
$431$	−3.26641	+	22.7184i	−0.157337	+	1.09430i	0.746177	+	0.665747i	$0.231887\pi$
$431$	−3.26641	+	22.7184i	−0.157337	+	1.09430i	−0.903515	+	0.428557i	$0.859022\pi$
$432$	−2.24240	−	4.91018i	−0.107888	−	0.236241i
$433$	−0.782112	−	5.43971i	−0.0375859	−	0.261416i	0.962360	−	0.271776i	$-0.0876111\pi$
$433$	−0.782112	−	5.43971i	−0.0375859	−	0.261416i	−0.999946	+	0.0103607i	$0.996702\pi$
$434$	−4.62969	+	2.97532i	−0.222232	+	0.142820i
$435$	10.4060	−	12.0091i	0.498929	−	0.575794i
$436$	4.44058			0.212665
$437$	−13.7095	+	1.11688i	−0.655815	+	0.0534277i
$438$	12.4354			0.594186
$439$	2.33201	−	2.69128i	0.111301	−	0.128448i	−0.697365	−	0.716716i	$-0.745644\pi$
$439$	2.33201	−	2.69128i	0.111301	−	0.128448i	0.808666	+	0.588268i	$0.200190\pi$
$440$	−6.32050	+	4.06194i	−0.301318	+	0.193645i
$441$	0.0373681	+	0.259901i	0.00177943	+	0.0123762i
$442$	0.545077	+	1.19355i	0.0259267	+	0.0567715i
$443$	−2.58559	+	17.9832i	−0.122845	+	0.854408i	0.831462	+	0.555581i	$0.187504\pi$
$443$	−2.58559	+	17.9832i	−0.122845	+	0.854408i	−0.954307	+	0.298827i	$0.903405\pi$
$444$	7.25652	−	2.13071i	0.344379	−	0.101119i
$445$	−32.2207	−	20.7070i	−1.52741	−	0.981606i
$446$	6.13413	−	13.4319i	0.290459	−	0.636017i
$447$	−33.6074	−	9.86801i	−1.58957	−	0.466741i
$448$	0.654861	+	0.755750i	0.0309393	+	0.0357058i
$449$	22.9649	+	26.5029i	1.08378	+	1.25075i	0.966229	+	0.257684i	$0.0829592\pi$
$449$	22.9649	+	26.5029i	1.08378	+	1.25075i	0.117552	+	0.993067i	$0.462495\pi$
$450$	1.11261	+	0.326691i	0.0524489	+	0.0154004i
$451$	2.50685	−	5.48924i	0.118043	−	0.258478i
$452$	−14.9369	−	9.59935i	−0.702572	−	0.451516i
$453$	−5.03481	+	1.47835i	−0.236556	+	0.0694591i
$454$	3.10274	−	21.5800i	0.145619	−	1.01280i
$455$	−0.302792	−	0.663022i	−0.0141951	−	0.0310829i
$456$	−0.675330	−	4.69702i	−0.0316252	−	0.219958i
$457$	−12.2040	+	7.84306i	−0.570881	+	0.366883i	−0.794009	−	0.607906i	$-0.792010\pi$
$457$	−12.2040	+	7.84306i	−0.570881	+	0.366883i	0.223128	+	0.974789i	$0.428373\pi$
$458$	1.01828	−	1.17516i	0.0475810	−	0.0549114i
$459$	29.8183			1.39180
$460$	7.18020	+	12.8459i	0.334779	+	0.598944i
$461$	20.0961			0.935969			0.467984	−	0.883737i	$-0.344980\pi$
$461$	20.0961			0.935969			0.467984	+	0.883737i	$0.344980\pi$
$462$	2.65281	−	3.06151i	0.123420	−	0.142434i
$463$	−22.9485	+	14.7481i	−1.06651	+	0.685401i	−0.951402	−	0.307952i	$-0.900356\pi$
$463$	−22.9485	+	14.7481i	−1.06651	+	0.685401i	−0.115103	+	0.993354i	$0.536720\pi$
$464$	−0.445425	−	3.09800i	−0.0206784	−	0.143821i
$465$	−11.6069	−	25.4156i	−0.538258	−	1.17862i
$466$	3.55690	−	24.7388i	0.164770	−	1.14600i
$467$	38.9023	−	11.4227i	1.80018	−	0.528582i	0.802503	−	0.596648i	$-0.203501\pi$
$467$	38.9023	−	11.4227i	1.80018	−	0.528582i	0.997681	+	0.0680661i	$0.0216829\pi$
$468$	0.0524688	+	0.0337197i	0.00242537	+	0.00155869i
$469$	−6.09235	+	13.3404i	−0.281319	+	0.616002i
$470$	34.4420	+	10.1131i	1.58869	+	0.466481i
$471$	3.11618	+	3.59626i	0.143586	+	0.165707i
$472$	−4.93969	−	5.70070i	−0.227367	−	0.262396i
$473$	−5.20968	−	1.52970i	−0.239542	−	0.0703357i
$474$	−2.23511	+	4.89420i	−0.102662	+	0.224798i
$475$	10.6554	+	6.84784i	0.488905	+	0.314200i
$476$	−5.30021	+	1.55628i	−0.242935	+	0.0713321i
$477$	−0.172249	+	1.19802i	−0.00788673	+	0.0548534i
$478$	5.09292	+	11.1519i	0.232945	+	0.510078i
$479$	−2.86838	−	19.9500i	−0.131059	−	0.911538i	−0.944177	−	0.329439i	$-0.893140\pi$
$479$	−2.86838	−	19.9500i	−0.131059	−	0.911538i	0.813117	−	0.582100i	$-0.197769\pi$
$480$	−4.27107	+	2.74485i	−0.194947	+	0.125285i
$481$	−0.711031	+	0.820574i	−0.0324202	+	0.0374149i
$482$	8.85623			0.403390
$483$	−5.66595	−	5.55499i	−0.257809	−	0.252761i
$484$	−5.00522			−0.227510
$485$	8.87864	−	10.2465i	0.403158	−	0.465269i
$486$	2.28877	−	1.47090i	0.103821	−	0.0667214i
$487$	4.09059	+	28.4507i	0.185362	+	1.28922i	0.843828	+	0.536613i	$0.180297\pi$
$487$	4.09059	+	28.4507i	0.185362	+	1.28922i	−0.658466	+	0.752611i	$0.728794\pi$
$488$	5.36300	+	11.7433i	0.242772	+	0.531596i
$489$	0.996670	−	6.93199i	0.0450710	−	0.313476i
$490$	2.94429	−	0.864520i	0.133009	−	0.0390550i
$491$	5.65143	+	3.63195i	0.255045	+	0.163908i	0.661916	−	0.749578i	$-0.269744\pi$
$491$	5.65143	+	3.63195i	0.255045	+	0.163908i	−0.406871	+	0.913486i	$0.633380\pi$
$492$	1.69400	−	3.70934i	0.0763713	−	0.167230i
$493$	16.5889	+	4.87095i	0.747127	+	0.219376i
$494$	0.446136	+	0.514869i	0.0200726	+	0.0231650i
$495$	−1.29189	−	1.49092i	−0.0580660	−	0.0670117i
$496$	−5.28041	−	1.55047i	−0.237097	−	0.0696180i
$497$	−2.14950	+	4.70675i	−0.0964183	+	0.211127i
$498$	−18.4828	−	11.8782i	−0.828234	−	0.532274i
$499$	−12.7834	+	3.75355i	−0.572265	+	0.168032i	−0.555046	−	0.831820i	$-0.687299\pi$
$499$	−12.7834	+	3.75355i	−0.572265	+	0.168032i	−0.0172187	+	0.999852i	$0.505481\pi$
$500$	−0.254943	+	1.77317i	−0.0114014	+	0.0792984i
$501$	8.96988	+	19.6413i	0.400745	+	0.877508i
$502$	1.48119	+	10.3019i	0.0661086	+	0.459796i
$503$	2.44800	−	1.57323i	0.109151	−	0.0701470i	−0.484927	−	0.874555i	$-0.661154\pi$
$503$	2.44800	−	1.57323i	0.109151	−	0.0701470i	0.594077	+	0.804408i	$0.297517\pi$
$504$	−0.171949	+	0.198440i	−0.00765921	+	0.00883920i
$505$	0.616841			0.0274490
$506$	0.721828	−	11.7200i	0.0320892	−	0.521018i
$507$	−21.4154			−0.951090
$508$	6.89139	−	7.95309i	0.305756	−	0.352861i
$509$	−6.95376	+	4.46891i	−0.308220	+	0.198081i	−0.685602	−	0.727977i	$-0.740461\pi$
$509$	−6.95376	+	4.46891i	−0.308220	+	0.198081i	0.377382	+	0.926058i	$0.376824\pi$
$510$	−3.99127	−	27.7599i	−0.176736	−	1.22923i
$511$	−3.12227	−	6.83682i	−0.138121	−	0.302443i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$	14.8548	−	4.36177i	0.655857	−	0.192577i
$514$	−1.97327	−	1.26814i	−0.0870373	−	0.0559355i
$515$	2.04786	−	4.48419i	0.0902395	−	0.197597i
$516$	−3.52043	−	1.03369i	−0.154978	−	0.0455058i
$517$	−18.7561	−	21.6457i	−0.824894	−	0.951979i
$518$	−2.99340	−	3.45457i	−0.131522	−	0.151785i
$519$	21.9801	+	6.45393i	0.964818	+	0.283296i
$520$	0.302792	−	0.663022i	0.0132783	−	0.0290754i
$521$	−2.88977	−	1.85714i	−0.126603	−	0.0813629i	0.475807	−	0.879550i	$-0.342156\pi$
$521$	−2.88977	−	1.85714i	−0.126603	−	0.0813629i	−0.602410	+	0.798187i	$0.705793\pi$
$522$	0.788528	−	0.231533i	0.0345129	−	0.0101339i
$523$	−3.84610	+	26.7502i	−0.168178	+	1.16971i	0.714468	+	0.699668i	$0.246669\pi$
$523$	−3.84610	+	26.7502i	−0.168178	+	1.16971i	−0.882646	+	0.470038i	$0.844240\pi$
$524$	7.99355	+	17.5034i	0.349200	+	0.764641i
$525$	1.03985	+	7.23233i	0.0453829	+	0.315645i
$526$	21.4609	−	13.7921i	0.935741	−	0.601364i
$527$	19.9079	−	22.9750i	0.867203	−	1.00081i
$528$	4.05096			0.176295
$529$	−22.8262	−	2.82240i	−0.992442	−	0.122713i
$530$	14.1447			0.614406
$531$	1.29703	−	1.49685i	0.0562863	−	0.0649578i
$532$	−2.41280	+	1.55061i	−0.104608	+	0.0672276i
$533$	0.0833170	+	0.579483i	0.00360886	+	0.0251002i
$534$	8.57875	+	18.7848i	0.371239	+	0.812899i
$535$	−1.88024	+	13.0773i	−0.0812898	+	0.565383i
$536$	−14.0716	+	4.13181i	−0.607802	+	0.178467i
$537$	−22.4647	−	14.4372i	−0.969422	−	0.623010i
$538$	0.148856	−	0.325948i	0.00641762	−	0.0140526i
$539$	−2.34925	−	0.689801i	−0.101189	−	0.0297118i
$540$	−10.8472	−	12.5184i	−0.466790	−	0.538705i
$541$	−12.4812	−	14.4041i	−0.536609	−	0.619280i	0.421101	−	0.907014i	$-0.361644\pi$
$541$	−12.4812	−	14.4041i	−0.536609	−	0.619280i	−0.957710	+	0.287734i	$0.907098\pi$
$542$	22.3060	+	6.54965i	0.958127	+	0.281331i
$543$	14.2827	−	31.2748i	0.612930	−	1.34213i
$544$	−4.64706	−	2.98649i	−0.199241	−	0.128045i
$545$	13.0743	−	3.83898i	0.560044	−	0.164444i
$546$	−0.0559301	+	0.389002i	−0.00239359	+	0.0166478i
$547$	−9.87983	−	21.6338i	−0.422431	−	0.924995i	−0.994495	−	0.104786i	$-0.966584\pi$
$547$	−9.87983	−	21.6338i	−0.422431	−	0.924995i	0.572064	−	0.820209i	$-0.306143\pi$
$548$	−0.929631	−	6.46573i	−0.0397119	−	0.276202i
$549$	−2.85170	+	1.83267i	−0.121707	+	0.0782166i
$550$	−7.08085	+	8.17174i	−0.301929	+	0.348444i
$551$	8.97675			0.382423
$552$	0.487773	−	7.91978i	0.0207610	−	0.337088i
$553$	3.25196			0.138287
$554$	4.76008	−	5.49343i	0.202237	−	0.233394i
$555$	19.5232	−	12.5468i	0.828715	−	0.532583i
$556$	−1.61446	−	11.2288i	−0.0684683	−	0.476208i
$557$	−16.0748	−	35.1990i	−0.681113	−	1.49143i	−0.861460	−	0.507826i	$-0.830449\pi$
$557$	−16.0748	−	35.1990i	−0.681113	−	1.49143i	0.180347	−	0.983603i	$-0.442278\pi$
$558$	0.205649	−	1.43032i	0.00870581	−	0.0605502i
$559$	0.505416	−	0.148403i	0.0213768	−	0.00627680i
$560$	2.58146	+	1.65900i	0.109087	+	0.0701056i
$561$	−9.29591	+	20.3552i	−0.392473	+	0.859397i
$562$	−13.5408	−	3.97594i	−0.571185	−	0.167715i
$563$	27.1080	+	31.2842i	1.14246	+	1.31847i	0.940778	+	0.339024i	$0.110097\pi$
$563$	27.1080	+	31.2842i	1.14246	+	1.31847i	0.201686	+	0.979450i	$0.435358\pi$
$564$	−12.6744	−	14.6271i	−0.533689	−	0.615910i
$565$	−52.2773	−	15.3500i	−2.19932	−	0.645779i
$566$	1.43609	−	3.14460i	0.0603635	−	0.132178i
$567$	6.85061	+	4.40262i	0.287699	+	0.184893i
$568$	−4.96475	+	1.45778i	−0.208316	+	0.0611672i
$569$	−5.50172	+	38.2653i	−0.230644	+	1.60416i	0.464688	+	0.885475i	$0.346167\pi$
$569$	−5.50172	+	38.2653i	−0.230644	+	1.60416i	−0.695331	+	0.718689i	$0.744742\pi$
$570$	−6.04904	−	13.2455i	−0.253366	−	0.554795i
$571$	1.24867	+	8.68471i	0.0522554	+	0.363444i	0.999125	+	0.0418261i	$0.0133175\pi$
$571$	1.24867	+	8.68471i	0.0522554	+	0.363444i	−0.946870	+	0.321618i	$0.895773\pi$
$572$	−0.489258	+	0.314427i	−0.0204569	+	0.0131468i
$573$	−0.0247897	+	0.0286089i	−0.00103561	+	0.00119515i
$574$	−2.46467			−0.102874
$575$	15.1235	+	14.8273i	0.630692	+	0.618341i
$576$	−0.262573			−0.0109406
$577$	18.0554	−	20.8370i	0.751656	−	0.867458i	−0.243071	−	0.970008i	$-0.578155\pi$
$577$	18.0554	−	20.8370i	0.751656	−	0.867458i	0.994728	+	0.102551i	$0.0327004\pi$
$578$	11.3689	−	7.30638i	0.472886	−	0.303905i
$579$	−4.89413	−	34.0394i	−0.203393	−	1.41463i
$580$	−3.98974	−	8.73632i	−0.165665	−	0.362756i
$581$	−1.88982	+	13.1440i	−0.0784029	+	0.545304i
$582$	−7.01411	+	2.05953i	−0.290744	+	0.0853702i
$583$	−9.49443	−	6.10170i	−0.393219	−	0.252707i
$584$	3.12227	−	6.83682i	0.129201	−	0.282910i
$585$	0.183635	+	0.0539200i	0.00759236	+	0.00222932i
$586$	−17.6482	−	20.3671i	−0.729041	−	0.841358i
$587$	26.6176	+	30.7184i	1.09863	+	1.26788i	0.960745	+	0.277434i	$0.0894841\pi$
$587$	26.6176	+	30.7184i	1.09863	+	1.26788i	0.137882	+	0.990449i	$0.455970\pi$
$588$	−1.58750	−	0.466131i	−0.0654673	−	0.0192229i
$589$	6.55696	−	14.3577i	0.270175	−	0.591600i
$590$	−19.4722	−	12.5140i	−0.801659	−	0.515195i
$591$	33.5745	−	9.85837i	1.38107	−	0.405519i
$592$	0.650528	−	4.52452i	0.0267365	−	0.185957i
$593$	16.8138	+	36.8171i	0.690460	+	1.51190i	0.851167	+	0.524895i	$0.175895\pi$
$593$	16.8138	+	36.8171i	0.690460	+	1.51190i	−0.160707	+	0.987002i	$0.551377\pi$
$594$	1.88091	+	13.0820i	0.0771747	+	0.536762i
$595$	−14.2599	+	9.16429i	−0.584599	+	0.375699i
$596$	−13.8634	+	15.9992i	−0.567868	+	0.655354i
$597$	12.2617			0.501837
$598$	0.555805	+	0.994377i	0.0227286	+	0.0406631i
$599$	−23.5674			−0.962937			−0.481469	−	0.876463i	$-0.659896\pi$
$599$	−23.5674			−0.962937			−0.481469	+	0.876463i	$0.659896\pi$
$600$	−4.78487	+	5.52204i	−0.195342	+	0.225436i
$601$	17.6205	−	11.3240i	0.718756	−	0.461916i	−0.129448	−	0.991586i	$-0.541321\pi$
$601$	17.6205	−	11.3240i	0.718756	−	0.461916i	0.848204	+	0.529670i	$0.177684\pi$
$602$	0.315597	+	2.19503i	0.0128628	+	0.0894626i
$603$	−1.59969	−	3.50283i	−0.0651444	−	0.142646i
$604$	−0.451357	+	3.13926i	−0.0183654	+	0.127734i
$605$	−14.7368	+	4.32711i	−0.599136	+	0.175922i
$606$	−0.279791	−	0.179810i	−0.0113657	−	0.00730430i
$607$	−13.9707	+	30.5917i	−0.567055	+	1.24168i	0.381296	+	0.924453i	$0.375478\pi$
$607$	−13.9707	+	30.5917i	−0.567055	+	1.24168i	−0.948351	+	0.317224i	$0.897249\pi$
$608$	−2.75192	−	0.808038i	−0.111605	−	0.0327703i
$609$	3.39113	+	3.91358i	0.137416	+	0.158586i
$610$	25.9426	+	29.9393i	1.05038	+	1.21221i
$611$	2.66608	+	0.782833i	0.107858	+	0.0316700i
$612$	0.602538	−	1.31937i	0.0243562	−	0.0533325i
$613$	−2.94883	−	1.89510i	−0.119102	−	0.0765424i	0.479733	−	0.877414i	$-0.340733\pi$
$613$	−2.94883	−	1.89510i	−0.119102	−	0.0765424i	−0.598836	+	0.800872i	$0.704370\pi$
$614$	−9.18317	+	2.69642i	−0.370603	+	0.108819i
$615$	1.78082	−	12.3858i	0.0718094	−	0.499446i
$616$	−1.01711	−	2.22716i	−0.0409806	−	0.0897350i
$617$	−1.10955	−	7.71709i	−0.0446688	−	0.310679i	−0.999891	−	0.0147879i	$-0.995293\pi$
$617$	−1.10955	−	7.71709i	−0.0446688	−	0.310679i	0.955222	−	0.295891i	$-0.0956164\pi$
$618$	−2.23603	+	1.43701i	−0.0899464	+	0.0578051i
$619$	11.2169	−	12.9450i	0.450847	−	0.520305i	−0.484139	−	0.874991i	$-0.660867\pi$
$619$	11.2169	−	12.9450i	0.450847	−	0.520305i	0.934985	+	0.354687i	$0.115412\pi$
$620$	−16.8874			−0.678216
$621$	25.8023	−	2.10205i	1.03541	−	0.0843525i
$622$	−3.58048			−0.143564
$623$	8.17371	−	9.43297i	0.327473	−	0.377924i
$624$	−0.330615	+	0.212473i	−0.0132352	+	0.00850573i
$625$	3.92478	+	27.2974i	0.156991	+	1.09190i
$626$	8.15096	+	17.8481i	0.325778	+	0.713354i
$627$	−1.65349	+	11.5003i	−0.0660342	+	0.459278i
$628$	2.75959	−	0.810288i	0.110120	−	0.0323340i
$629$	21.2419	+	13.6514i	0.846972	+	0.544316i
$630$	−0.334712	+	0.732916i	−0.0133352	+	0.0292001i
$631$	40.6561	+	11.9377i	1.61850	+	0.475233i	0.960614	−	0.277888i	$-0.0896344\pi$
$631$	40.6561	+	11.9377i	1.61850	+	0.475233i	0.657882	+	0.753121i	$0.271453\pi$
$632$	2.12958	+	2.45766i	0.0847101	+	0.0977606i
$633$	27.7792	+	32.0589i	1.10412	+	1.27423i
$634$	−22.2328	−	6.52815i	−0.882979	−	0.259266i
$635$	13.4146	−	29.3739i	0.532343	−	1.16567i
$636$	−6.41584	−	4.12321i	−0.254405	−	0.163496i
$637$	0.227911	−	0.0669208i	0.00903017	−	0.00265150i
$638$	−1.09059	+	7.58522i	−0.0431769	+	0.300302i
$639$	−0.564402	−	1.23587i	−0.0223274	−	0.0488902i
$640$	0.436705	+	3.03735i	0.0172623	+	0.120062i
$641$	−6.79861	+	4.36920i	−0.268529	+	0.172573i	−0.667975	−	0.744184i	$-0.732839\pi$
$641$	−6.79861	+	4.36920i	−0.268529	+	0.172573i	0.399446	+	0.916757i	$0.369202\pi$
$642$	4.66493	−	5.38361i	0.184110	−	0.212474i
$643$	−43.4125			−1.71202			−0.856010	−	0.516959i	$-0.827064\pi$
$643$	−43.4125			−1.71202			−0.856010	+	0.516959i	$0.827064\pi$
$644$	−4.47666	+	1.72032i	−0.176405	+	0.0677901i
$645$	−11.2588			−0.443315
$646$	10.3752	−	11.9736i	0.408206	−	0.471094i
$647$	−10.6222	+	6.82647i	−0.417601	+	0.268376i	−0.732524	−	0.680741i	$-0.761658\pi$
$647$	−10.6222	+	6.82647i	−0.417601	+	0.268376i	0.314923	+	0.949117i	$0.398021\pi$
$648$	1.15892	+	8.06045i	0.0455266	+	0.316644i
$649$	7.67219	+	16.7997i	0.301160	+	0.659448i
$650$	0.149288	−	1.03832i	0.00585555	−	0.0407262i
$651$	8.73652	−	2.56527i	0.342411	−	0.100541i
$652$	−3.56088	−	2.28844i	−0.139455	−	0.0896221i
$653$	−2.36223	+	5.17257i	−0.0924414	+	0.202418i	−0.950205	−	0.311626i	$-0.899126\pi$
$653$	−2.36223	+	5.17257i	−0.0924414	+	0.202418i	0.857763	+	0.514045i	$0.171854\pi$
$654$	−7.04942	−	2.06990i	−0.275654	−	0.0809393i
$655$	38.6674	+	44.6245i	1.51086	+	1.74362i
$656$	−1.61402	−	1.86268i	−0.0630168	−	0.0727253i
$657$	1.89357	+	0.556002i	0.0738751	+	0.0216917i
$658$	−4.85948	+	10.6408i	−0.189442	+	0.414821i
$659$	−19.6158	−	12.6063i	−0.764121	−	0.491071i	0.0996082	−	0.995027i	$-0.468241\pi$
$659$	−19.6158	−	12.6063i	−0.764121	−	0.491071i	−0.863729	+	0.503956i	$0.831877\pi$
$660$	11.9272	−	3.50214i	0.464265	−	0.136320i
$661$	1.82464	−	12.6907i	0.0709704	−	0.493610i	−0.923073	−	0.384625i	$-0.874331\pi$
$661$	1.82464	−	12.6907i	0.0709704	−	0.493610i	0.994043	−	0.108985i	$-0.0347601\pi$
$662$	5.68738	+	12.4536i	0.221046	+	0.484024i
$663$	−0.308956	−	2.14884i	−0.0119989	−	0.0834540i
$664$	−11.1711	+	7.17924i	−0.433523	+	0.278609i
$665$	−5.76344	+	6.65136i	−0.223497	+	0.257929i
$666$	1.20023			0.0465081
$667$	14.6981	+	3.04548i	0.569112	+	0.117921i
$668$	13.0507			0.504946
$669$	−15.9989	+	18.4637i	−0.618554	+	0.713849i
$670$	−37.8589	+	24.3304i	−1.46262	+	0.939967i
$671$	−4.49845	−	31.2874i	−0.173661	−	1.20784i
$672$	−0.687311	−	1.50500i	−0.0265136	−	0.0580567i
$673$	−6.12512	+	42.6011i	−0.236106	+	1.64215i	0.434739	+	0.900556i	$0.356840\pi$
$673$	−6.12512	+	42.6011i	−0.236106	+	1.64215i	−0.670845	+	0.741597i	$0.734069\pi$
$674$	4.58917	−	1.34750i	0.176768	−	0.0519039i
$675$	−20.0543	−	12.8881i	−0.771892	−	0.496065i
$676$	−5.37696	+	11.7739i	−0.206806	+	0.452842i
$677$	35.1450	+	10.3195i	1.35073	+	0.396611i	0.875487	−	0.483242i	$-0.160541\pi$
$677$	35.1450	+	10.3195i	1.35073	+	0.396611i	0.475246	+	0.879853i	$0.342359\pi$
$678$	19.2377	+	22.2015i	0.738820	+	0.852643i
$679$	2.89340	+	3.33916i	0.111038	+	0.128145i
$680$	−16.2642	−	4.77559i	−0.623702	−	0.183135i
$681$	−14.9847	+	32.8120i	−0.574216	+	1.25736i
$682$	11.3355	+	7.28486i	0.434057	+	0.278952i
$683$	−25.7458	+	7.55965i	−0.985136	+	0.289262i	−0.734343	−	0.678779i	$-0.762510\pi$
$683$	−25.7458	+	7.55965i	−0.985136	+	0.289262i	−0.250793	+	0.968041i	$0.580691\pi$
$684$	0.107175	−	0.745422i	0.00409796	−	0.0285019i
$685$	−8.32685	−	18.2333i	−0.318153	−	0.696657i
$686$	0.142315	+	0.989821i	0.00543361	+	0.0377916i
$687$	−2.16429	+	1.39090i	−0.0825728	+	0.0530663i
$688$	−1.45222	+	1.67595i	−0.0553653	+	0.0638950i
$689$	1.09491			0.0417128
$690$	−5.41066	−	23.7398i	−0.205980	−	0.903758i
$691$	−7.85627			−0.298867			−0.149433	−	0.988772i	$-0.547745\pi$
$691$	−7.85627			−0.298867			−0.149433	+	0.988772i	$0.547745\pi$
$692$	9.06703	−	10.4639i	0.344677	−	0.397778i
$693$	0.540834	−	0.347573i	0.0205446	−	0.0132032i
$694$	−0.401648	−	2.79352i	−0.0152464	−	0.106041i
$695$	−14.4610	−	31.6651i	−0.548536	−	1.20113i
$696$	−0.736964	+	5.12570i	−0.0279345	+	0.194289i
$697$	13.0633	−	3.83573i	0.494808	−	0.145289i
$698$	25.9689	+	16.6892i	0.982937	+	0.631695i
$699$	−17.1781	+	37.6148i	−0.649736	+	1.42272i
$700$	4.23733	+	1.24419i	0.160156	+	0.0470260i
$701$	17.1051	+	19.7403i	0.646051	+	0.745583i	0.980433	−	0.196855i	$-0.0630729\pi$
$701$	17.1051	+	19.7403i	0.646051	+	0.745583i	−0.334382	+	0.942438i	$0.608527\pi$
$702$	−0.839662	−	0.969022i	−0.0316910	−	0.0365734i
$703$	12.5792	+	3.69358i	0.474432	+	0.139306i
$704$	1.01711	−	2.22716i	0.0383339	−	0.0839394i
$705$	−49.9625	−	32.1090i	−1.88170	−	1.20929i
$706$	16.7910	−	4.93027i	0.631936	−	0.185553i
$707$	−0.0286078	+	0.198972i	−0.00107591	+	0.00748311i
$708$	5.18446	+	11.3524i	0.194844	+	0.426649i
$709$	2.22593	+	15.4817i	0.0835964	+	0.581426i	0.987965	+	0.154675i	$0.0494330\pi$
$709$	2.22593	+	15.4817i	0.0835964	+	0.581426i	−0.904369	+	0.426751i	$0.859658\pi$
$710$	−13.3574	+	8.58426i	−0.501293	+	0.322161i
$711$	−0.559170	+	0.645317i	−0.0209705	+	0.0242013i
$712$	12.4816			0.467768
$713$	15.6071	−	21.2841i	0.584489	−	0.797095i
$714$	9.13951			0.342038
$715$	−1.16869	+	1.34874i	−0.0437064	+	0.0504398i
$716$	−13.5778	+	8.72591i	−0.507425	+	0.326102i
$717$	−2.88673	−	20.0776i	−0.107807	−	0.749814i
$718$	−8.84754	−	19.3734i	−0.330187	−	0.723009i
$719$	−1.42880	+	9.93754i	−0.0532853	+	0.370608i	0.945679	+	0.325103i	$0.105399\pi$
$719$	−1.42880	+	9.93754i	−0.0532853	+	0.370608i	−0.998964	+	0.0455051i	$0.985510\pi$
$720$	−0.773091	+	0.227000i	−0.0288114	+	0.00845979i
$721$	1.35147	+	0.868538i	0.0503314	+	0.0323460i
$722$	−4.47568	+	9.80037i	−0.166567	+	0.364732i
$723$	−14.0592	−	4.12817i	−0.522869	−	0.153528i
$724$	−13.6084	−	15.7049i	−0.505752	−	0.583668i
$725$	−9.05156	−	10.4461i	−0.336167	−	0.387957i
$726$	7.94577	+	2.33309i	0.294895	+	0.0865891i
$727$	4.60773	−	10.0895i	0.170891	−	0.374200i	−0.804736	−	0.593632i	$-0.797693\pi$
$727$	4.60773	−	10.0895i	0.170891	−	0.374200i	0.975628	+	0.219433i	$0.0704206\pi$
$728$	0.199826	+	0.128420i	0.00740603	+	0.00475956i
$729$	−27.7595	+	8.15091i	−1.02813	+	0.301886i
$730$	3.28229	−	22.8288i	0.121483	−	0.844932i
$731$	−5.08882	−	11.1430i	−0.188217	−	0.412137i
$732$	−3.03982	−	21.1424i	−0.112355	−	0.781445i
$733$	−14.9707	+	9.62109i	−0.552956	+	0.355363i	−0.787087	−	0.616842i	$-0.788412\pi$
$733$	−14.9707	+	9.62109i	−0.552956	+	0.355363i	0.234131	+	0.972205i	$0.424775\pi$
$734$	−11.2963	+	13.0366i	−0.416952	+	0.481189i
$735$	−5.07703			−0.187269
$736$	−4.23172	−	2.25666i	−0.155983	−	0.0831817i
$737$	35.9079			1.32268
$738$	0.423798	−	0.489089i	0.0156002	−	0.0180036i
$739$	−12.5704	+	8.07853i	−0.462411	+	0.297173i	−0.751027	−	0.660271i	$-0.770441\pi$
$739$	−12.5704	+	8.07853i	−0.462411	+	0.297173i	0.288616	+	0.957445i	$0.406805\pi$
$740$	−1.99620	−	13.8839i	−0.0733817	−	0.510381i
$741$	−0.468244	−	1.02531i	−0.0172014	−	0.0376657i
$742$	−0.656003	+	4.56260i	−0.0240826	+	0.167498i
$743$	−14.6597	+	4.30448i	−0.537813	+	0.157916i	−0.539349	−	0.842083i	$-0.681329\pi$
$743$	−14.6597	+	4.30448i	−0.537813	+	0.157916i	0.00153535	+	0.999999i	$0.499511\pi$
$744$	7.65991	+	4.92272i	0.280826	+	0.180476i
$745$	−26.9862	+	59.0915i	−0.988698	+	2.16495i
$746$	−19.4294	−	5.70498i	−0.711361	−	0.208874i
$747$	−2.28333	−	2.63511i	−0.0835428	−	0.0964135i
$748$	8.85701	+	10.2215i	0.323844	+	0.373736i
$749$	−4.13111	−	1.21300i	−0.150947	−	0.0443221i
$750$	1.23125	−	2.69606i	0.0449589	−	0.0984462i
$751$	10.4077	+	6.68860i	0.379781	+	0.244070i	0.716578	−	0.697507i	$-0.245707\pi$
$751$	10.4077	+	6.68860i	0.379781	+	0.244070i	−0.336797	+	0.941577i	$0.609344\pi$
$752$	−11.2241	+	3.29568i	−0.409299	+	0.120181i
$753$	2.45065	−	17.0446i	0.0893066	−	0.621141i
$754$	−0.308838	−	0.676261i	−0.0112472	−	0.0246280i
$755$	1.38503	+	9.63307i	0.0504063	+	0.350583i
$756$	4.54107	−	2.91837i	0.165157	−	0.106140i
$757$	22.2552	−	25.6838i	0.808877	−	0.933494i	−0.189956	−	0.981793i	$-0.560834\pi$
$757$	22.2552	−	25.6838i	0.808877	−	0.933494i	0.998833	+	0.0482985i	$0.0153799\pi$
$758$	30.7341			1.11631
$759$	−6.60897	+	18.2690i	−0.239890	+	0.663124i
$760$	−8.80102			−0.319246
$761$	0.168497	−	0.194456i	0.00610800	−	0.00704901i	−0.752687	−	0.658378i	$-0.771243\pi$
$761$	0.168497	−	0.194456i	0.00610800	−	0.00704901i	0.758795	+	0.651329i	$0.225788\pi$
$762$	−14.6473	+	9.41322i	−0.530614	+	0.341005i
$763$	0.631961	+	4.39539i	0.0228785	+	0.159124i
$764$	0.00950459	+	0.0208122i	0.000343864	+	0.000752958i
$765$	0.633418	−	4.40552i	0.0229013	−	0.159282i
$766$	−16.4882	+	4.84136i	−0.595742	+	0.174926i
$767$	−1.50731	−	0.968686i	−0.0544256	−	0.0349772i
$768$	0.687311	−	1.50500i	0.0248012	−	0.0543071i
$769$	6.67131	+	1.95887i	0.240574	+	0.0706388i	0.399797	−	0.916604i	$-0.369081\pi$
$769$	6.67131	+	1.95887i	0.240574	+	0.0706388i	−0.159223	+	0.987243i	$0.550899\pi$
$770$	−4.92010	−	5.67809i	−0.177308	−	0.204624i
$771$	2.54144	+	2.93298i	0.0915278	+	0.105629i
$772$	−19.9432	−	5.85587i	−0.717773	−	0.210757i
$773$	−6.14407	+	13.4536i	−0.220987	+	0.483894i	−0.987358	−	0.158504i	$-0.949333\pi$
$773$	−6.14407	+	13.4536i	−0.220987	+	0.483894i	0.766372	+	0.642398i	$0.222060\pi$
$774$	−0.489847	−	0.314806i	−0.0176072	−	0.0113155i
$775$	−23.3194	+	6.84719i	−0.837657	+	0.245958i
$776$	−0.628796	+	4.37337i	−0.0225724	+	0.156995i
$777$	3.14173	+	6.87943i	0.112709	+	0.246798i
$778$	2.41371	+	16.7877i	0.0865358	+	0.601869i
$779$	5.94677	−	3.82176i	0.213065	−	0.136929i
$780$	−0.789737	+	0.911405i	−0.0282771	+	0.0326335i
$781$	12.6690			0.453332
$782$	21.0500	−	16.0850i	0.752745	−	0.575199i
$783$	−16.8949			−0.603775
$784$	−0.654861	+	0.755750i	−0.0233879	+	0.0269911i
$785$	7.42451	−	4.77144i	0.264992	−	0.170300i
$786$	−4.53084	−	31.5127i	−0.161610	−	1.12402i
$787$	−18.7338	−	41.0213i	−0.667787	−	1.46225i	−0.875083	−	0.483972i	$-0.839194\pi$
$787$	−18.7338	−	41.0213i	−0.667787	−	1.46225i	0.207296	−	0.978278i	$-0.433534\pi$
$788$	3.00987	−	20.9341i	0.107222	−	0.745745i
$789$	−40.4981	+	11.8913i	−1.44177	+	0.423342i
$790$	8.39479	+	5.39500i	0.298673	+	0.191946i
$791$	7.37590	−	16.1510i	0.262257	−	0.574263i
$792$	0.616849	+	0.181123i	0.0219188	+	0.00643593i
$793$	2.00816	+	2.31754i	0.0713119	+	0.0822983i
$794$	−4.78494	−	5.52211i	−0.169811	−	0.195972i
$795$	−22.4547	−	6.59328i	−0.796385	−	0.233840i
$796$	3.07866	−	6.74131i	0.109120	−	0.238940i
$797$	11.5187	+	7.40261i	0.408013	+	0.262214i	0.728510	−	0.685036i	$-0.240213\pi$
$797$	11.5187	+	7.40261i	0.408013	+	0.262214i	−0.320497	+	0.947250i	$0.603850\pi$
$798$	4.55311	−	1.33691i	0.161178	−	0.0473262i
$799$	9.19623	−	63.9612i	0.325339	−	2.26278i
$800$	1.83456	+	4.01713i	0.0648615	+	0.142027i
$801$	0.466414	+	3.24398i	0.0164799	+	0.114620i
$802$	30.2421	−	19.4354i	1.06788	−	0.686288i
$803$	−12.0510	+	13.9076i	−0.425271	+	0.490789i
$804$	24.2647			0.855748
$805$	−11.6933	+	8.93528i	−0.412135	+	0.314927i
$806$	−1.30722			−0.0460449
$807$	−0.388243	+	0.448056i	−0.0136668	+	0.0157723i
$808$	−0.169107	+	0.108679i	−0.00594917	+	0.00382330i
$809$	7.22025	+	50.2180i	0.253851	+	1.76557i	0.574628	+	0.818415i	$0.305147\pi$
$809$	7.22025	+	50.2180i	0.253851	+	1.76557i	−0.320778	+	0.947155i	$0.603944\pi$
$810$	10.3806	+	22.7304i	0.364737	+	0.798663i
$811$	1.47880	−	10.2853i	0.0519278	−	0.361166i	−0.947245	−	0.320509i	$-0.896146\pi$
$811$	1.47880	−	10.2853i	0.0519278	−	0.361166i	0.999173	−	0.0406567i	$-0.0129450\pi$
$812$	3.00308	−	0.881783i	0.105387	−	0.0309445i
$813$	−32.3578	−	20.7951i	−1.13484	−	0.729316i
$814$	−4.64927	+	10.1805i	−0.162957	+	0.356825i
$815$	−12.4626	−	3.65936i	−0.436547	−	0.128182i
$816$	5.98511	+	6.90718i	0.209521	+	0.241800i
$817$	−4.16511	−	4.80679i	−0.145719	−	0.168168i
$818$	0.125212	+	0.0367656i	0.00437794	+	0.00128548i
$819$	−0.0259094	+	0.0567336i	−0.000905346	+	0.00198243i
$820$	−6.36245	−	4.08890i	−0.222186	−	0.142791i
$821$	4.40099	−	1.29225i	0.153595	−	0.0450997i	−0.204031	−	0.978964i	$-0.565404\pi$
$821$	4.40099	−	1.29225i	0.153595	−	0.0450997i	0.357626	+	0.933865i	$0.383586\pi$
$822$	−1.53809	+	10.6977i	−0.0536471	+	0.373124i
$823$	19.2363	+	42.1217i	0.670536	+	1.46827i	0.872368	+	0.488849i	$0.162583\pi$
$823$	19.2363	+	42.1217i	0.670536	+	1.46827i	−0.201833	+	0.979420i	$0.564690\pi$
$824$	0.228628	+	1.59015i	0.00796465	+	0.0553953i
$825$	15.0499	−	9.67201i	0.523972	−	0.336736i
$826$	4.93969	−	5.70070i	0.171874	−	0.198353i
$827$	−19.8472			−0.690155			−0.345077	−	0.938574i	$-0.612147\pi$
$827$	−19.8472			−0.690155			−0.345077	+	0.938574i	$0.612147\pi$
$828$	0.428377	−	1.18415i	0.0148871	−	0.0411522i
$829$	46.9878			1.63195			0.815977	−	0.578084i	$-0.196200\pi$
$829$	46.9878			1.63195			0.815977	+	0.578084i	$0.196200\pi$
$830$	−26.6844	+	30.7954i	−0.926228	+	1.06892i
$831$	−10.1173	+	6.50198i	−0.350965	+	0.225551i
$832$	0.0338045	+	0.235115i	0.00117196	+	0.00815116i
$833$	−2.29474	−	5.02478i	−0.0795081	−	0.174098i
$834$	−2.67115	+	18.5783i	−0.0924944	+	0.643313i
$835$	38.4249	−	11.2826i	1.32975	−	0.390450i
$836$	5.90756	+	3.79656i	0.204317	+	0.131307i
$837$	−12.3407	+	27.0223i	−0.426556	+	0.934028i
$838$	30.3081	+	8.89925i	1.04697	+	0.307419i
$839$	−5.93765	−	6.85241i	−0.204990	−	0.236572i	0.643940	−	0.765076i	$-0.277299\pi$
$839$	−5.93765	−	6.85241i	−0.204990	−	0.236572i	−0.848931	+	0.528504i	$0.822753\pi$
$840$	−3.32474	−	3.83696i	−0.114715	−	0.132388i
$841$	18.4261	+	5.41039i	0.635382	+	0.186565i
$842$	15.9915	−	35.0164i	0.551103	−	1.20675i
$843$	19.6427	+	12.6236i	0.676531	+	0.434780i
$844$	24.6003	−	7.22331i	0.846779	−	0.248637i
$845$	−5.65253	+	39.3142i	−0.194453	+	1.35245i
$846$	−1.27597	−	2.79399i	−0.0438688	−	0.0960592i
$847$	−0.712317	−	4.95427i	−0.0244755	−	0.170231i
$848$	−3.87777	+	2.49209i	−0.133163	+	0.0855788i
$849$	−3.74559	+	4.32264i	−0.128548	+	0.148353i
$850$	−24.3950			−0.836743
$851$	19.3434	+	10.3153i	0.663083	+	0.353604i
$852$	8.56105			0.293297
$853$	31.8479	−	36.7545i	1.09045	−	1.25845i	0.126617	−	0.991952i	$-0.459588\pi$
$853$	31.8479	−	36.7545i	1.09045	−	1.25845i	0.963836	−	0.266497i	$-0.0858664\pi$
$854$	−10.8606	+	6.97967i	−0.371641	+	0.238839i
$855$	−0.328877	−	2.28739i	−0.0112474	−	0.0782271i
$856$	−1.78857	−	3.91643i	−0.0611322	−	0.133861i
$857$	4.43553	−	30.8498i	0.151515	−	1.05381i	−0.762168	−	0.647379i	$-0.775865\pi$
$857$	4.43553	−	30.8498i	0.151515	−	1.05381i	0.913683	−	0.406428i	$-0.133226\pi$
$858$	0.923259	−	0.271093i	0.0315196	−	0.00925498i
$859$	10.2151	+	6.56485i	0.348535	+	0.223990i	0.703181	−	0.711011i	$-0.251762\pi$
$859$	10.2151	+	6.56485i	0.348535	+	0.223990i	−0.354646	+	0.935001i	$0.615399\pi$
$860$	−2.82685	+	6.18995i	−0.0963949	+	0.211075i
$861$	3.91266	+	1.14886i	0.133343	+	0.0391531i
$862$	−15.0303	−	17.3459i	−0.511936	−	0.590805i
$863$	−11.5258	−	13.3014i	−0.392342	−	0.452786i	0.524873	−	0.851181i	$-0.324113\pi$
$863$	−11.5258	−	13.3014i	−0.392342	−	0.452786i	−0.917214	+	0.398394i	$0.869568\pi$
$864$	5.17933	+	1.52079i	0.176204	+	0.0517382i
$865$	17.6497	−	38.6474i	0.600106	−	1.31405i
$866$	4.62323	+	2.97117i	0.157104	+	0.100965i
$867$	−21.4539	+	6.29943i	−0.728613	+	0.213940i
$868$	0.783205	−	5.44731i	0.0265837	−	0.184894i
$869$	−3.30760	−	7.24264i	−0.112203	−	0.245690i
$870$	2.26144	+	15.7286i	0.0766699	+	0.533251i
$871$	−2.93058	+	1.88337i	−0.0992990	+	0.0638156i
$872$	−2.90796	+	3.35597i	−0.0984761	+	0.113647i
$873$	−1.16014			−0.0392647
$874$	8.13374	−	11.0924i	0.275128	−	0.375205i
$875$	−1.79140			−0.0605604
$876$	−8.14345	+	9.39805i	−0.275142	+	0.317531i
$877$	32.4023	−	20.8237i	1.09415	−	0.703167i	0.136366	−	0.990659i	$-0.456458\pi$
$877$	32.4023	−	20.8237i	1.09415	−	0.703167i	0.957783	+	0.287491i	$0.0928213\pi$
$878$	0.506794	+	3.52483i	0.0171035	+	0.118957i
$879$	18.5227	+	40.5591i	0.624757	+	1.36803i
$880$	1.06924	−	7.43672i	0.0360441	−	0.250692i
$881$	−17.1343	+	5.03108i	−0.577269	+	0.169501i	−0.557317	−	0.830300i	$-0.688169\pi$
$881$	−17.1343	+	5.03108i	−0.577269	+	0.169501i	−0.0199515	+	0.999801i	$0.506351\pi$
$882$	−0.220891	−	0.141958i	−0.00743778	−	0.00477997i
$883$	20.4478	−	44.7745i	0.688123	−	1.50678i	−0.165677	−	0.986180i	$-0.552981\pi$
$883$	20.4478	−	44.7745i	0.688123	−	1.50678i	0.853801	−	0.520600i	$-0.174292\pi$
$884$	−1.25898	−	0.369669i	−0.0423439	−	0.0124333i
$885$	25.0789	+	28.9426i	0.843018	+	0.972895i
$886$	−11.8976	−	13.7306i	−0.399708	−	0.461287i
$887$	−17.4661	−	5.12850i	−0.586453	−	0.172198i	−0.0249728	−	0.999688i	$-0.507950\pi$
$887$	−17.4661	−	5.12850i	−0.586453	−	0.172198i	−0.561481	+	0.827490i	$0.689768\pi$
$888$	−3.14173	+	6.87943i	−0.105430	+	0.230859i
$889$	8.85289	+	5.68941i	0.296916	+	0.190817i
$890$	36.7494	−	10.7906i	1.23184	−	0.361702i
$891$	2.83752	−	19.7354i	0.0950605	−	0.661161i
$892$	6.13413	+	13.4319i	0.205386	+	0.449732i
$893$	−4.77477	−	33.2093i	−0.159782	−	1.11131i
$894$	29.4659	−	18.9366i	0.985486	−	0.633334i
$895$	−32.4331	+	37.4298i	−1.08412	+	1.25114i
$896$	−1.00000			−0.0334077
$897$	−0.418829	−	1.83765i	−0.0139843	−	0.0613573i
$898$	−35.0684			−1.17025
$899$	−11.2797	+	13.0175i	−0.376200	+	0.434158i
$900$	−0.975500	+	0.626916i	−0.0325167	+	0.0208972i
$901$	−3.62374	−	25.2037i	−0.120724	−	0.839656i
$902$	2.50685	+	5.48924i	0.0834690	+	0.182772i
$903$	0.522161	−	3.63171i	0.0173764	−	0.120856i
$904$	17.0363	−	5.00230i	0.566618	−	0.166374i
$905$	−53.6442	−	34.4750i	−1.78319	−	1.14599i
$906$	2.17983	−	4.77317i	0.0724201	−	0.158578i
$907$	−24.1957	−	7.10450i	−0.803406	−	0.235901i	−0.145850	−	0.989307i	$-0.546592\pi$
$907$	−24.1957	−	7.10450i	−0.803406	−	0.235901i	−0.657556	+	0.753406i	$0.728410\pi$
$908$	14.2772	+	16.4768i	0.473807	+	0.546802i
$909$	−0.0345648	−	0.0398899i	−0.00114644	−	0.00132307i
$910$	0.699365	+	0.205352i	0.0231837	+	0.00680736i
$911$	−6.77735	+	14.8403i	−0.224544	+	0.491682i	−0.988053	−	0.154115i	$-0.950747\pi$
$911$	−6.77735	+	14.8403i	−0.224544	+	0.491682i	0.763509	+	0.645797i	$0.223475\pi$
$912$	3.99202	+	2.56552i	0.132189	+	0.0849527i
$913$	31.1959	−	9.15996i	1.03244	−	0.303150i
$914$	2.06456	−	14.3593i	0.0682895	−	0.474964i
$915$	−27.2281	−	59.6212i	−0.900133	−	1.97102i
$916$	0.221293	+	1.53913i	0.00731172	+	0.0508542i
$917$	−16.1877	+	10.4032i	−0.534564	+	0.343544i
$918$	−19.5268	+	22.5352i	−0.644482	+	0.743772i
$919$	−0.0260504			−0.000859322			−0.000429661	−	1.00000i	$-0.500137\pi$
$919$	−0.0260504			−0.000859322			−0.000429661		1.00000i	$0.500137\pi$
$920$	−14.4103	−	2.98585i	−0.475094	−	0.0984407i
$921$	15.8351			0.521786
$922$	−13.1601	+	15.1876i	−0.433406	+	0.500178i
$923$	−1.03397	+	0.664490i	−0.0340334	+	0.0218720i
$924$	0.576512	+	4.00973i	0.0189658	+	0.131910i
$925$	−8.38586	−	18.3625i	−0.275725	−	0.603755i
$926$	3.88219	−	27.0012i	0.127577	−	0.887315i
$927$	−0.404736	+	0.118841i	−0.0132933	+	0.00390326i
$928$	2.63300	+	1.69213i	0.0864326	+	0.0555469i
$929$	24.8942	−	54.5107i	0.816752	−	1.78844i	0.241635	−	0.970367i	$-0.422316\pi$
$929$	24.8942	−	54.5107i	0.816752	−	1.78844i	0.575118	−	0.818071i	$-0.304956\pi$
$930$	26.8088	+	7.87176i	0.879094	+	0.258125i
$931$	−1.87821	−	2.16757i	−0.0615558	−	0.0710391i
$932$	16.3671	+	18.8886i	0.536121	+	0.618717i
$933$	5.68400	+	1.66897i	0.186086	+	0.0546397i
$934$	−16.8429	+	36.8807i	−0.551115	+	1.20677i
$935$	34.9143	+	22.4381i	1.14182	+	0.733803i
$936$	−0.0598434	+	0.0175716i	−0.00195604	+	0.000574346i
$937$	−6.03454	+	41.9712i	−0.197140	+	1.37114i	0.615392	+	0.788221i	$0.288998\pi$
$937$	−6.03454	+	41.9712i	−0.197140	+	1.37114i	−0.812532	+	0.582917i	$0.801911\pi$
$938$	−6.09235	−	13.3404i	−0.198922	−	0.435579i
$939$	−4.62006	−	32.1332i	−0.150770	−	1.04863i
$940$	−30.1976	+	19.4068i	−0.984938	+	0.632982i
$941$	−16.1848	+	18.6783i	−0.527611	+	0.608895i	−0.955520	−	0.294926i	$-0.904705\pi$
$941$	−16.1848	+	18.6783i	−0.527611	+	0.608895i	0.427909	+	0.903822i	$0.359250\pi$
$942$	−4.75854			−0.155042
$943$	11.0335	−	4.24003i	0.359301	−	0.138074i
$944$	7.54311			0.245507
$945$	10.8472	−	12.5184i	0.352860	−	0.407222i
$946$	4.56769	−	2.93548i	0.148508	−	0.0954405i
$947$	4.07679	+	28.3547i	0.132478	+	0.921405i	0.942310	+	0.334743i	$0.108649\pi$
$947$	4.07679	+	28.3547i	0.132478	+	0.921405i	−0.809832	+	0.586662i	$0.800442\pi$
$948$	−2.23511	−	4.89420i	−0.0725929	−	0.158956i
$949$	0.254075	−	1.76713i	0.00824764	−	0.0573636i
$950$	−12.1531	+	3.56847i	−0.394298	+	0.115776i
$951$	32.2516	+	20.7268i	1.04583	+	0.672114i
$952$	2.29474	−	5.02478i	0.0743730	−	0.162854i
$953$	2.79749	+	0.821418i	0.0906197	+	0.0266084i	0.326728	−	0.945118i	$-0.394054\pi$
$953$	2.79749	+	0.821418i	0.0906197	+	0.0266084i	−0.236108	+	0.971727i	$0.575872\pi$
$954$	−0.792601	−	0.914711i	−0.0256614	−	0.0296149i
$955$	0.0459768	+	0.0530600i	0.00148777	+	0.00171698i
$956$	−11.7632	−	3.45400i	−0.380450	−	0.111710i
$957$	5.26702	−	11.5332i	0.170258	−	0.372814i
$958$	16.9556	+	10.8967i	0.547810	+	0.352056i
$959$	6.26761	−	1.84034i	0.202392	−	0.0594276i
$960$	0.722536	−	5.02535i	0.0233198	−	0.162192i
$961$	−0.296345	−	0.648904i	−0.00955950	−	0.0209324i
$962$	−0.154522	−	1.07472i	−0.00498198	−	0.0346505i
$963$	0.951047	−	0.611201i	0.0306471	−	0.0196957i
$964$	−5.79960	+	6.69309i	−0.186793	+	0.215570i
$965$	−63.7811			−2.05319
$966$	7.90858	−	0.644293i	0.254455	−	0.0207298i
$967$	−2.51963			−0.0810257			−0.0405129	−	0.999179i	$-0.512899\pi$
$967$	−2.51963			−0.0810257			−0.0405129	+	0.999179i	$0.512899\pi$
$968$	3.27772	−	3.78269i	0.105350	−	0.121580i
$969$	−22.0518	+	14.1718i	−0.708407	+	0.455265i
$970$	1.92951	+	13.4201i	0.0619529	+	0.430892i
$971$	15.0533	+	32.9621i	0.483083	+	1.05780i	0.981604	+	0.190927i	$0.0611494\pi$
$971$	15.0533	+	32.9621i	0.483083	+	1.05780i	−0.498521	+	0.866878i	$0.666123\pi$
$972$	−0.387191	+	2.69297i	−0.0124191	+	0.0863770i
$973$	10.8848	−	3.19605i	0.348949	−	0.102461i
$974$	−24.1804	−	15.5398i	−0.774789	−	0.497927i
$975$	−0.720987	+	1.57874i	−0.0230901	+	0.0505602i
$976$	−12.3870	−	3.63716i	−0.396499	−	0.116423i
$977$	39.9475	+	46.1019i	1.27803	+	1.47493i	0.804251	+	0.594289i	$0.202567\pi$
$977$	39.9475	+	46.1019i	1.27803	+	1.47493i	0.473783	+	0.880641i	$0.342888\pi$
$978$	4.58617	+	5.29272i	0.146650	+	0.169243i
$979$	−29.3224	−	8.60982i	−0.937146	−	0.275171i
$980$	−1.27474	+	2.79128i	−0.0407200	+	0.0891643i
$981$	−0.980884	−	0.630376i	−0.0313172	−	0.0201263i
$982$	−6.44574	+	1.89264i	−0.205692	+	0.0603966i
$983$	6.82387	−	47.4611i	0.217648	−	1.51377i	−0.529039	−	0.848597i	$-0.677448\pi$
$983$	6.82387	−	47.4611i	0.217648	−	1.51377i	0.746687	−	0.665176i	$-0.231643\pi$
$984$	1.69400	+	3.70934i	0.0540027	+	0.118249i
$985$	−9.23603	−	64.2380i	−0.294284	−	2.04679i
$986$	−14.5446	+	9.34728i	−0.463196	+	0.297678i
$987$	12.6744	−	14.6271i	0.403431	−	0.465585i
$988$	−0.681269			−0.0216741
$989$	−5.18897	−	9.28346i	−0.165000	−	0.295197i
$990$	1.97276			0.0626986
$991$	18.0715	−	20.8556i	0.574060	−	0.662500i	−0.392257	−	0.919856i	$-0.628306\pi$
$991$	18.0715	−	20.8556i	0.574060	−	0.662500i	0.966317	+	0.257355i	$0.0828511\pi$
$992$	4.62969	−	2.97532i	0.146993	−	0.0944666i
$993$	−3.22368	−	22.4212i	−0.102300	−	0.711514i
$994$	−2.14950	−	4.70675i	−0.0681781	−	0.149289i
$995$	3.23644	−	22.5099i	0.102602	−	0.713612i
$996$	21.0806	−	6.18982i	0.667964	−	0.196132i
$997$	−26.8871	−	17.2793i	−0.851523	−	0.547241i	0.0405263	−	0.999178i	$-0.487097\pi$
$997$	−26.8871	−	17.2793i	−0.851523	−	0.547241i	−0.892049	+	0.451938i	$0.850733\pi$
$998$	5.53462	−	12.1191i	0.175195	−	0.383624i
$999$	−23.6749	−	6.95159i	−0.749042	−	0.219939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.d.85.3	✓	40
23.6	even	11		7406.2.a.bu.1.13		20
23.13	even	11	inner	322.2.i.d.197.3	yes	40
23.17	odd	22		7406.2.a.bv.1.13		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.85.3	✓	40	1.1	even	1	trivial
322.2.i.d.197.3	yes	40	23.13	even	11	inner
7406.2.a.bu.1.13		20	23.6	even	11
7406.2.a.bv.1.13		20	23.17	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{2} +(1.39187 - 0.894499i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-1.27474 - 2.79128i) q^{5} +(-0.235462 + 1.63768i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.109077 + 0.238845i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{2} +(1.39187 - 0.894499i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-1.27474 - 2.79128i) q^{5} +(-0.235462 + 1.63768i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.109077 + 0.238845i) q^{9} +(2.94429 + 0.864520i) q^{10} +(-1.60338 - 1.85040i) q^{11} +(-1.08348 - 1.25040i) q^{12} +(0.227911 + 0.0669208i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(-4.27107 - 2.74485i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.786144 - 5.46775i) q^{17} +(-0.109077 - 0.238845i) q^{18} +(-0.408174 - 2.83891i) q^{19} +(-2.58146 + 1.65900i) q^{20} +(1.08348 - 1.25040i) q^{21} +2.44842 q^{22} +(0.294813 - 4.78676i) q^{23} +1.65452 q^{24} +(-2.89200 + 3.33755i) q^{25} +(-0.199826 + 0.128420i) q^{26} +(0.768213 + 5.34304i) q^{27} +(-0.415415 - 0.909632i) q^{28} +(-0.445425 + 3.09800i) q^{29} +(4.87137 - 1.43036i) q^{30} +(4.62969 + 2.97532i) q^{31} +(0.415415 - 0.909632i) q^{32} +(-3.88687 - 1.14129i) q^{33} +(3.61743 + 4.17474i) q^{34} +(-2.00950 - 2.31908i) q^{35} +(0.251937 + 0.0739754i) q^{36} +(-1.89888 + 4.15797i) q^{37} +(2.41280 + 1.55061i) q^{38} +(0.377083 - 0.110722i) q^{39} +(0.436705 - 3.03735i) q^{40} +(1.02386 + 2.24195i) q^{41} +(0.235462 + 1.63768i) q^{42} +(1.86556 - 1.19892i) q^{43} +(-1.60338 + 1.85040i) q^{44} +0.805728 q^{45} +(3.42453 + 3.35747i) q^{46} +11.6979 q^{47} +(-1.08348 + 1.25040i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.628493 - 4.37126i) q^{50} +(-3.79669 - 8.31359i) q^{51} +(0.0338045 - 0.235115i) q^{52} +(4.42280 - 1.29865i) q^{53} +(-4.54107 - 2.91837i) q^{54} +(-3.12109 + 6.83424i) q^{55} +(0.959493 + 0.281733i) q^{56} +(-3.10753 - 3.58628i) q^{57} +(-2.04962 - 2.36539i) q^{58} +(-7.23756 - 2.12514i) q^{59} +(-2.10907 + 4.61823i) q^{60} +(10.8606 + 6.97967i) q^{61} +(-5.28041 + 1.55047i) q^{62} +(-0.0373681 + 0.259901i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.103732 - 0.721471i) q^{65} +(3.40788 - 2.19011i) q^{66} +(-9.60399 + 11.0836i) q^{67} -5.52397 q^{68} +(-3.87141 - 6.92625i) q^{69} +3.06858 q^{70} +(-3.38848 + 3.91051i) q^{71} +(-0.220891 + 0.141958i) q^{72} +(-1.06964 - 7.43953i) q^{73} +(-1.89888 - 4.15797i) q^{74} +(-1.03985 + 7.23233i) q^{75} +(-2.75192 + 0.808038i) q^{76} +(-2.05975 - 1.32372i) q^{77} +(-0.163259 + 0.357488i) q^{78} +(3.12023 + 0.916182i) q^{79} +(2.00950 + 2.31908i) q^{80} +(5.33275 + 6.15432i) q^{81} +(-2.36484 - 0.694379i) q^{82} +(-5.51635 + 12.0791i) q^{83} +(-1.39187 - 0.894499i) q^{84} +(-16.2642 + 4.77559i) q^{85} +(-0.315597 + 2.19503i) q^{86} +(2.15119 + 4.71044i) q^{87} +(-0.348447 - 2.42350i) q^{88} +(10.5002 - 6.74806i) q^{89} +(-0.527640 + 0.608929i) q^{90} +0.237533 q^{91} +(-4.78000 + 0.389415i) q^{92} +9.10535 q^{93} +(-7.66050 + 8.84068i) q^{94} +(-7.40389 + 4.75819i) q^{95} +(-0.235462 - 1.63768i) q^{96} +(1.83545 + 4.01907i) q^{97} +(-0.142315 + 0.989821i) q^{98} +(0.616849 - 0.181123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Introduction

L-functions

Modular forms

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