LMFDB - Embedded newform 115.2.g.a.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, 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("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			101.1
Root			$0.654861 - 0.755750i$ of defining polynomial
Character	$\chi$	$=$	115.101
Dual form			115.2.g.a.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31718 - 0.386758i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-0.0971309 + 0.0624222i) q^{4} +(0.142315 + 0.989821i) q^{5} +(1.15486 + 0.742184i) q^{6} +(0.925839 - 2.02730i) q^{7} +(-1.90176 + 2.19475i) q^{8} +(0.284630 - 1.97964i) q^{9} +O(q^{10})$	\(q+(1.31718 - 0.386758i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-0.0971309 + 0.0624222i) q^{4} +(0.142315 + 0.989821i) q^{5} +(1.15486 + 0.742184i) q^{6} +(0.925839 - 2.02730i) q^{7} +(-1.90176 + 2.19475i) q^{8} +(0.284630 - 1.97964i) q^{9} +(0.570276 + 1.24873i) q^{10} +(-1.98926 - 0.584100i) q^{11} +(-0.110783 - 0.0325288i) q^{12} +(-0.425839 - 0.932456i) q^{13} +(0.435418 - 3.02840i) q^{14} +(-0.654861 + 0.755750i) q^{15} +(-1.56019 + 3.41635i) q^{16} +(-3.33083 - 2.14059i) q^{17} +(-0.390736 - 2.71763i) q^{18} +(-0.879900 + 0.565477i) q^{19} +(-0.0756100 - 0.0872586i) q^{20} +(2.13843 - 0.627899i) q^{21} -2.84612 q^{22} +(2.01691 + 4.35110i) q^{23} -2.90407 q^{24} +(-0.959493 + 0.281733i) q^{25} +(-0.921540 - 1.06351i) q^{26} +(4.20627 - 2.70320i) q^{27} +(0.0366213 + 0.254707i) q^{28} +(4.95274 + 3.18293i) q^{29} +(-0.570276 + 1.24873i) q^{30} +(-2.78201 + 3.21061i) q^{31} +(0.0928329 - 0.645667i) q^{32} +(-0.861256 - 1.88589i) q^{33} +(-5.21519 - 1.53132i) q^{34} +(2.13843 + 0.627899i) q^{35} +(0.0959274 + 0.210052i) q^{36} +(0.851751 - 5.92406i) q^{37} +(-0.940282 + 1.08514i) q^{38} +(0.425839 - 0.932456i) q^{39} +(-2.44306 - 1.57006i) q^{40} +(1.36297 + 9.47964i) q^{41} +(2.57385 - 1.65411i) q^{42} +(-1.23278 - 1.42270i) q^{43} +(0.229680 - 0.0674400i) q^{44} +2.00000 q^{45} +(4.33945 + 4.95112i) q^{46} -7.61130 q^{47} +(-3.60362 + 1.05812i) q^{48} +(1.33124 + 1.53634i) q^{49} +(-1.15486 + 0.742184i) q^{50} +(-0.563476 - 3.91906i) q^{51} +(0.0995681 + 0.0639885i) q^{52} +(4.95792 - 10.8563i) q^{53} +(4.49492 - 5.18741i) q^{54} +(0.295053 - 2.05214i) q^{55} +(2.68870 + 5.88744i) q^{56} +(-1.00357 - 0.294675i) q^{57} +(7.75466 + 2.27697i) q^{58} +(4.75662 + 10.4155i) q^{59} +(0.0164316 - 0.114284i) q^{60} +(4.20330 - 4.85087i) q^{61} +(-2.42267 + 5.30490i) q^{62} +(-3.74982 - 2.40986i) q^{63} +(-1.19644 - 8.32140i) q^{64} +(0.862362 - 0.554206i) q^{65} +(-1.86381 - 2.15095i) q^{66} +(3.93196 - 1.15453i) q^{67} +0.457147 q^{68} +(-1.96755 + 4.37364i) q^{69} +3.05954 q^{70} +(-9.69553 + 2.84686i) q^{71} +(3.80353 + 4.38950i) q^{72} +(7.65481 - 4.91945i) q^{73} +(-1.16927 - 8.13247i) q^{74} +(-0.841254 - 0.540641i) q^{75} +(0.0501671 - 0.109851i) q^{76} +(-3.02588 + 3.49206i) q^{77} +(0.200270 - 1.39291i) q^{78} +(1.59168 + 3.48530i) q^{79} +(-3.60362 - 1.05812i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(5.46160 + 11.9592i) q^{82} +(-1.03645 + 7.20866i) q^{83} +(-0.168513 + 0.194474i) q^{84} +(1.64478 - 3.60157i) q^{85} +(-2.17403 - 1.39717i) q^{86} +(0.837855 + 5.82741i) q^{87} +(5.06506 - 3.25512i) q^{88} +(6.80606 + 7.85461i) q^{89} +(2.63436 - 0.773517i) q^{90} -2.28463 q^{91} +(-0.467509 - 0.296726i) q^{92} -4.24824 q^{93} +(-10.0254 + 2.94373i) q^{94} +(-0.684944 - 0.790468i) q^{95} +(0.548755 - 0.352663i) q^{96} +(-0.207978 - 1.44652i) q^{97} +(2.34767 + 1.50876i) q^{98} +(-1.72251 + 3.77178i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9} - 5 q^{10} + 8 q^{11} + q^{12} - 3 q^{14} - q^{15} + 5 q^{16} - 23 q^{17} - 10 q^{18} - 13 q^{19} + q^{20} + 6 q^{21} + 4 q^{22} - 21 q^{23} - 6 q^{24} - q^{25} + 11 q^{26} - 5 q^{27} - 6 q^{28} + 2 q^{29} + 5 q^{30} - 20 q^{31} - 15 q^{32} + 3 q^{33} + 16 q^{34} + 6 q^{35} + 24 q^{36} + 13 q^{37} + 21 q^{38} - 6 q^{40} - 5 q^{41} + 3 q^{42} + 15 q^{43} + 19 q^{44} + 20 q^{45} - 16 q^{46} - 52 q^{47} + 6 q^{48} + 4 q^{49} - 6 q^{50} - 10 q^{51} + 22 q^{52} + 6 q^{53} - 30 q^{54} + 3 q^{55} + 3 q^{56} + 2 q^{57} + 45 q^{58} + 5 q^{59} + 10 q^{60} - 3 q^{61} - 54 q^{62} - 10 q^{63} - 34 q^{64} - 4 q^{66} + 20 q^{67} + 32 q^{68} - q^{69} - 8 q^{70} - 22 q^{71} + 32 q^{72} + 43 q^{73} + q^{74} + q^{75} - 2 q^{76} + 4 q^{77} + 11 q^{78} + 51 q^{79} + 6 q^{80} - q^{81} + 58 q^{82} - 17 q^{83} + 6 q^{84} + q^{85} - 9 q^{86} - 2 q^{87} + 7 q^{88} + 57 q^{89} + 10 q^{90} - 22 q^{91} - 43 q^{92} + 20 q^{93} - 81 q^{94} - 9 q^{95} - 7 q^{96} + 52 q^{97} + 24 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9 - 5 * q^10 + 8 * q^11 + q^12 - 3 * q^14 - q^15 + 5 * q^16 - 23 * q^17 - 10 * q^18 - 13 * q^19 + q^20 + 6 * q^21 + 4 * q^22 - 21 * q^23 - 6 * q^24 - q^25 + 11 * q^26 - 5 * q^27 - 6 * q^28 + 2 * q^29 + 5 * q^30 - 20 * q^31 - 15 * q^32 + 3 * q^33 + 16 * q^34 + 6 * q^35 + 24 * q^36 + 13 * q^37 + 21 * q^38 - 6 * q^40 - 5 * q^41 + 3 * q^42 + 15 * q^43 + 19 * q^44 + 20 * q^45 - 16 * q^46 - 52 * q^47 + 6 * q^48 + 4 * q^49 - 6 * q^50 - 10 * q^51 + 22 * q^52 + 6 * q^53 - 30 * q^54 + 3 * q^55 + 3 * q^56 + 2 * q^57 + 45 * q^58 + 5 * q^59 + 10 * q^60 - 3 * q^61 - 54 * q^62 - 10 * q^63 - 34 * q^64 - 4 * q^66 + 20 * q^67 + 32 * q^68 - q^69 - 8 * q^70 - 22 * q^71 + 32 * q^72 + 43 * q^73 + q^74 + q^75 - 2 * q^76 + 4 * q^77 + 11 * q^78 + 51 * q^79 + 6 * q^80 - q^81 + 58 * q^82 - 17 * q^83 + 6 * q^84 + q^85 - 9 * q^86 - 2 * q^87 + 7 * q^88 + 57 * q^89 + 10 * q^90 - 22 * q^91 - 43 * q^92 + 20 * q^93 - 81 * q^94 - 9 * q^95 - 7 * q^96 + 52 * q^97 + 24 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$

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 $

$2$	1.31718	−	0.386758i	0.931386	−	0.273479i	0.219369	−	0.975642i	$-0.429600\pi$
$2$	1.31718	−	0.386758i	0.931386	−	0.273479i	0.712017	+	0.702163i	$0.247782\pi$
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i	0.912617	−	0.408815i	$-0.134058\pi$
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i	−0.534533	+	0.845148i	$0.679513\pi$
$4$	−0.0971309	+	0.0624222i	−0.0485654	+	0.0312111i
$5$	0.142315	+	0.989821i	0.0636451	+	0.442662i
$5$	0.142315	+	0.989821i	0.0636451	+	0.442662i
$6$	1.15486	+	0.742184i	0.471470	+	0.302995i
$7$	0.925839	−	2.02730i	0.349934	−	0.766249i	−0.650046	−	0.759895i	$-0.725250\pi$
$7$	0.925839	−	2.02730i	0.349934	−	0.766249i	0.999980	−	0.00635365i	$-0.00202244\pi$
$8$	−1.90176	+	2.19475i	−0.672375	+	0.775962i
$9$	0.284630	−	1.97964i	0.0948766	−	0.659881i
$10$	0.570276	+	1.24873i	0.180337	+	0.394883i
$11$	−1.98926	−	0.584100i	−0.599785	−	0.176113i	−0.0322746	−	0.999479i	$-0.510275\pi$
$11$	−1.98926	−	0.584100i	−0.599785	−	0.176113i	−0.567510	+	0.823366i	$0.692093\pi$
$12$	−0.110783	−	0.0325288i	−0.0319802	−	0.00939024i
$13$	−0.425839	−	0.932456i	−0.118106	−	0.258617i	0.841341	−	0.540505i	$-0.181767\pi$
$13$	−0.425839	−	0.932456i	−0.118106	−	0.258617i	−0.959447	+	0.281888i	$0.909039\pi$
$14$	0.435418	−	3.02840i	0.116370	−	0.809373i
$15$	−0.654861	+	0.755750i	−0.169084	+	0.195134i
$16$	−1.56019	+	3.41635i	−0.390049	+	0.854088i
$17$	−3.33083	−	2.14059i	−0.807845	−	0.519170i	0.0703222	−	0.997524i	$-0.477597\pi$
$17$	−3.33083	−	2.14059i	−0.807845	−	0.519170i	−0.878167	+	0.478354i	$0.841234\pi$
$18$	−0.390736	−	2.71763i	−0.0920972	−	0.640550i
$19$	−0.879900	+	0.565477i	−0.201863	+	0.129729i	−0.637667	−	0.770312i	$-0.720100\pi$
$19$	−0.879900	+	0.565477i	−0.201863	+	0.129729i	0.435804	+	0.900042i	$0.356464\pi$
$20$	−0.0756100	−	0.0872586i	−0.0169069	−	0.0195116i
$21$	2.13843	−	0.627899i	0.466643	−	0.137019i
$22$	−2.84612			−0.606794
$23$	2.01691	+	4.35110i	0.420554	+	0.907267i
$23$	2.01691	+	4.35110i	0.420554	+	0.907267i
$24$	−2.90407			−0.592791
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$	−0.921540	−	1.06351i	−0.180729	−	0.208572i
$27$	4.20627	−	2.70320i	0.809497	−	0.520232i
$28$	0.0366213	+	0.254707i	0.00692077	+	0.0481350i
$29$	4.95274	+	3.18293i	0.919700	+	0.591056i	0.912571	−	0.408919i	$-0.134094\pi$
$29$	4.95274	+	3.18293i	0.919700	+	0.591056i	0.00712969	+	0.999975i	$0.497731\pi$
$30$	−0.570276	+	1.24873i	−0.104118	+	0.227986i
$31$	−2.78201	+	3.21061i	−0.499663	+	0.576642i	−0.948422	−	0.317011i	$-0.897321\pi$
$31$	−2.78201	+	3.21061i	−0.499663	+	0.576642i	0.448759	+	0.893653i	$0.351866\pi$
$32$	0.0928329	−	0.645667i	0.0164107	−	0.114139i
$33$	−0.861256	−	1.88589i	−0.149925	−	0.328291i
$34$	−5.21519	−	1.53132i	−0.894398	−	0.262619i
$35$	2.13843	+	0.627899i	0.361460	+	0.106134i
$36$	0.0959274	+	0.210052i	0.0159879	+	0.0350086i
$37$	0.851751	−	5.92406i	0.140027	−	0.973910i	−0.791741	−	0.610857i	$-0.790825\pi$
$37$	0.851751	−	5.92406i	0.140027	−	0.973910i	0.931768	−	0.363053i	$-0.118266\pi$
$38$	−0.940282	+	1.08514i	−0.152534	+	0.176033i
$39$	0.425839	−	0.932456i	0.0681887	−	0.149313i
$40$	−2.44306	−	1.57006i	−0.386282	−	0.248248i
$41$	1.36297	+	9.47964i	0.212860	+	1.48047i	0.763543	+	0.645757i	$0.223458\pi$
$41$	1.36297	+	9.47964i	0.212860	+	1.48047i	−0.550684	+	0.834714i	$0.685633\pi$
$42$	2.57385	−	1.65411i	0.397153	−	0.255235i
$43$	−1.23278	−	1.42270i	−0.187997	−	0.216960i	0.653925	−	0.756560i	$-0.273121\pi$
$43$	−1.23278	−	1.42270i	−0.187997	−	0.216960i	−0.841922	+	0.539599i	$0.818576\pi$
$44$	0.229680	−	0.0674400i	0.0346255	−	0.0101670i
$45$	2.00000			0.298142
$46$	4.33945	+	4.95112i	0.639817	+	0.730003i
$47$	−7.61130			−1.11022			−0.555111	−	0.831776i	$-0.687324\pi$
$47$	−7.61130			−1.11022			−0.555111	+	0.831776i	$0.687324\pi$
$48$	−3.60362	+	1.05812i	−0.520137	+	0.152726i
$49$	1.33124	+	1.53634i	0.190177	+	0.219477i
$50$	−1.15486	+	0.742184i	−0.163322	+	0.104961i
$51$	−0.563476	−	3.91906i	−0.0789025	−	0.548779i
$52$	0.0995681	+	0.0639885i	0.0138076	+	0.00887361i
$53$	4.95792	−	10.8563i	0.681022	−	1.49123i	−0.180534	−	0.983569i	$-0.557783\pi$
$53$	4.95792	−	10.8563i	0.681022	−	1.49123i	0.861556	−	0.507662i	$-0.169490\pi$
$54$	4.49492	−	5.18741i	0.611681	−	0.705917i
$55$	0.295053	−	2.05214i	0.0397850	−	0.276710i
$56$	2.68870	+	5.88744i	0.359293	+	0.786742i
$57$	−1.00357	−	0.294675i	−0.132926	−	0.0390307i
$58$	7.75466	+	2.27697i	1.01824	+	0.298981i
$59$	4.75662	+	10.4155i	0.619259	+	1.35599i	0.916057	+	0.401047i	$0.131354\pi$
$59$	4.75662	+	10.4155i	0.619259	+	1.35599i	−0.296799	+	0.954940i	$0.595919\pi$
$60$	0.0164316	−	0.114284i	0.00212131	−	0.0147541i
$61$	4.20330	−	4.85087i	0.538178	−	0.621090i	−0.419910	−	0.907566i	$-0.637938\pi$
$61$	4.20330	−	4.85087i	0.538178	−	0.621090i	0.958087	+	0.286476i	$0.0924838\pi$
$62$	−2.42267	+	5.30490i	−0.307679	+	0.673723i
$63$	−3.74982	−	2.40986i	−0.472432	−	0.303614i
$64$	−1.19644	−	8.32140i	−0.149555	−	1.04018i
$65$	0.862362	−	0.554206i	0.106963	−	0.0687409i
$66$	−1.86381	−	2.15095i	−0.229419	−	0.264764i
$67$	3.93196	−	1.15453i	0.480366	−	0.141048i	−0.0325800	−	0.999469i	$-0.510372\pi$
$67$	3.93196	−	1.15453i	0.480366	−	0.141048i	0.512946	+	0.858421i	$0.328554\pi$
$68$	0.457147			0.0554372
$69$	−1.96755	+	4.37364i	−0.236865	+	0.526525i
$70$	3.05954			0.365685
$71$	−9.69553	+	2.84686i	−1.15065	+	0.337861i	−0.800792	−	0.598943i	$-0.795588\pi$
$71$	−9.69553	+	2.84686i	−1.15065	+	0.337861i	−0.349856	+	0.936804i	$0.613769\pi$
$72$	3.80353	+	4.38950i	0.448250	+	0.517308i
$73$	7.65481	−	4.91945i	0.895927	−	0.575778i	−0.00965241	−	0.999953i	$-0.503073\pi$
$73$	7.65481	−	4.91945i	0.895927	−	0.575778i	0.905580	+	0.424176i	$0.139436\pi$
$74$	−1.16927	−	8.13247i	−0.135925	−	0.945380i
$75$	−0.841254	−	0.540641i	−0.0971396	−	0.0624278i
$76$	0.0501671	−	0.109851i	0.00575456	−	0.0126007i
$77$	−3.02588	+	3.49206i	−0.344831	+	0.397957i
$78$	0.200270	−	1.39291i	0.0226761	−	0.157716i
$79$	1.59168	+	3.48530i	0.179078	+	0.392127i	0.977790	−	0.209587i	$-0.0672120\pi$
$79$	1.59168	+	3.48530i	0.179078	+	0.392127i	−0.798712	+	0.601714i	$0.794485\pi$
$80$	−3.60362	−	1.05812i	−0.402896	−	0.118301i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	5.46160	+	11.9592i	0.603133	+	1.32068i
$83$	−1.03645	+	7.20866i	−0.113765	+	0.791254i	0.850435	+	0.526079i	$0.176339\pi$
$83$	−1.03645	+	7.20866i	−0.113765	+	0.791254i	−0.964201	+	0.265174i	$0.914571\pi$
$84$	−0.168513	+	0.194474i	−0.0183862	+	0.0212188i
$85$	1.64478	−	3.60157i	0.178401	−	0.390645i
$86$	−2.17403	−	1.39717i	−0.234432	−	0.150660i
$87$	0.837855	+	5.82741i	0.0898274	+	0.624764i
$88$	5.06506	−	3.25512i	0.539937	−	0.346996i
$89$	6.80606	+	7.85461i	0.721441	+	0.832587i	0.991480	−	0.130262i	$-0.0415819\pi$
$89$	6.80606	+	7.85461i	0.721441	+	0.832587i	−0.270039	+	0.962850i	$0.587036\pi$
$90$	2.63436	−	0.773517i	0.277686	−	0.0815358i
$91$	−2.28463			−0.239494
$92$	−0.467509	−	0.296726i	−0.0487412	−	0.0309359i
$93$	−4.24824			−0.440522
$94$	−10.0254	+	2.94373i	−1.03404	+	0.303623i
$95$	−0.684944	−	0.790468i	−0.0702738	−	0.0811003i
$96$	0.548755	−	0.352663i	0.0560071	−	0.0359936i
$97$	−0.207978	−	1.44652i	−0.0211169	−	0.146872i	0.976535	−	0.215358i	$-0.0690920\pi$
$97$	−0.207978	−	1.44652i	−0.0211169	−	0.146872i	−0.997652	+	0.0684868i	$0.978183\pi$
$98$	2.34767	+	1.50876i	0.237151	+	0.152408i
$99$	−1.72251	+	3.77178i	−0.173119	+	0.379078i
$100$	0.0756100	−	0.0872586i	0.00756100	−	0.00872586i
$101$	1.70976	−	11.8916i	0.170127	−	1.18326i	−0.708485	−	0.705726i	$-0.750621\pi$
$101$	1.70976	−	11.8916i	0.170127	−	1.18326i	0.878612	−	0.477536i	$-0.158470\pi$
$102$	−2.25793	−	4.94418i	−0.223568	−	0.489546i
$103$	−16.1958	−	4.75552i	−1.59582	−	0.468575i	−0.641442	−	0.767172i	$-0.721663\pi$
$103$	−16.1958	−	4.75552i	−1.59582	−	0.468575i	−0.954380	+	0.298596i	$0.903482\pi$
$104$	2.85635	+	0.838701i	0.280089	+	0.0822414i
$105$	0.925839	+	2.02730i	0.0903526	+	0.197845i
$106$	2.33169	−	16.2172i	0.226473	−	1.57516i
$107$	−2.88497	+	3.32943i	−0.278900	+	0.321868i	−0.877866	−	0.478907i	$-0.841033\pi$
$107$	−2.88497	+	3.32943i	−0.278900	+	0.321868i	0.598965	+	0.800775i	$0.295579\pi$
$108$	−0.239818	+	0.525129i	−0.0230765	+	0.0505306i
$109$	−15.3342	−	9.85470i	−1.46875	−	0.943910i	−0.998102	−	0.0615897i	$-0.980383\pi$
$109$	−15.3342	−	9.85470i	−1.46875	−	0.943910i	−0.470650	−	0.882320i	$-0.655981\pi$
$110$	−0.405045	−	2.81715i	−0.0386195	−	0.268605i
$111$	5.03489	−	3.23572i	0.477890	−	0.307121i
$112$	5.48149	+	6.32598i	0.517952	+	0.597749i
$113$	−9.90588	+	2.90863i	−0.931867	+	0.273621i	−0.712218	−	0.701958i	$-0.752309\pi$
$113$	−9.90588	+	2.90863i	−0.931867	+	0.273621i	−0.219649	+	0.975579i	$0.570491\pi$
$114$	−1.43585			−0.134480
$115$	−4.01978	+	2.61561i	−0.374846	+	0.243906i
$116$	−0.679749			−0.0631132
$117$	−1.96714	+	0.577603i	−0.181862	+	0.0533995i
$118$	10.2936	+	11.8795i	0.947603	+	1.09359i
$119$	−7.42345	+	4.77076i	−0.680506	+	0.437335i
$120$	−0.413293	−	2.87451i	−0.0377283	−	0.262406i
$121$	−5.63780	−	3.62319i	−0.512527	−	0.329381i
$122$	3.66038	−	8.01512i	0.331395	−	0.725655i
$123$	−6.27168	+	7.23790i	−0.565498	+	0.652620i
$124$	0.0698055	−	0.485508i	0.00626872	−	0.0435999i
$125$	−0.415415	−	0.909632i	−0.0371558	−	0.0813600i
$126$	−5.87121	−	1.72394i	−0.523049	−	0.153581i
$127$	7.91056	+	2.32275i	0.701948	+	0.206111i	0.613182	−	0.789942i	$-0.289889\pi$
$127$	7.91056	+	2.32275i	0.701948	+	0.206111i	0.0887666	+	0.996052i	$0.471707\pi$
$128$	−4.25234	−	9.31132i	−0.375857	−	0.823012i
$129$	0.267909	−	1.86335i	0.0235881	−	0.164058i
$130$	0.921540	−	1.06351i	0.0808244	−	0.0932764i
$131$	−1.70938	+	3.74303i	−0.149350	+	0.327030i	−0.969489	−	0.245133i	$-0.921168\pi$
$131$	−1.70938	+	3.74303i	−0.149350	+	0.327030i	0.820140	+	0.572163i	$0.193896\pi$
$132$	0.201376	+	0.129416i	0.0175275	+	0.0112643i
$133$	0.331749	+	2.30736i	0.0287663	+	0.200074i
$134$	4.73257	−	3.04144i	0.408832	−	0.262740i
$135$	3.27430	+	3.77875i	0.281807	+	0.325223i
$136$	11.0325	−	3.23944i	0.946031	−	0.277780i
$137$	−11.8468			−1.01214			−0.506068	−	0.862493i	$-0.668902\pi$
$137$	−11.8468			−1.01214			−0.506068	+	0.862493i	$0.668902\pi$
$138$	−0.900070	+	6.52183i	−0.0766190	+	0.555175i
$139$	−2.26434			−0.192058			−0.0960292	−	0.995379i	$-0.530614\pi$
$139$	−2.26434			−0.192058			−0.0960292	+	0.995379i	$0.530614\pi$
$140$	−0.246902	+	0.0724971i	−0.0208671	+	0.00612712i
$141$	−4.98434	−	5.75223i	−0.419757	−	0.484426i
$142$	−11.6697	+	7.49965i	−0.979299	+	0.629357i
$143$	0.302457	+	2.10363i	0.0252927	+	0.175915i
$144$	6.31908	+	4.06102i	0.526590	+	0.338419i
$145$	−2.44569	+	5.35530i	−0.203103	+	0.444734i
$146$	8.18011	−	9.44035i	0.676991	−	0.781289i
$147$	−0.289307	+	2.01217i	−0.0238616	+	0.165961i
$148$	0.287062	+	0.628578i	0.0235963	+	0.0516688i
$149$	18.0514	+	5.30037i	1.47883	+	0.434223i	0.918957	−	0.394357i	$-0.129033\pi$
$149$	18.0514	+	5.30037i	1.47883	+	0.434223i	0.559871	+	0.828580i	$0.310851\pi$
$150$	−1.31718	−	0.386758i	−0.107547	−	0.0315787i
$151$	−7.49577	−	16.4134i	−0.609997	−	1.33571i	−0.922576	−	0.385815i	$-0.873920\pi$
$151$	−7.49577	−	16.4134i	−0.609997	−	1.33571i	0.312579	−	0.949892i	$-0.398807\pi$
$152$	0.432279	−	3.00657i	0.0350624	−	0.243865i
$153$	−5.18567	+	5.98458i	−0.419236	+	0.483824i
$154$	−2.63505	+	5.76994i	−0.212338	+	0.464955i
$155$	−3.57385	−	2.29677i	−0.287058	−	0.184481i
$156$	0.0168439	+	0.117152i	0.00134859	+	0.00937967i
$157$	5.43674	−	3.49398i	0.433899	−	0.278850i	−0.305404	−	0.952223i	$-0.598792\pi$
$157$	5.43674	−	3.49398i	0.433899	−	0.278850i	0.739303	+	0.673373i	$0.235155\pi$
$158$	3.44450	+	3.97516i	0.274030	+	0.316247i
$159$	11.4514	−	3.36244i	0.908156	−	0.266659i
$160$	0.652306			0.0515693
$161$	10.6883	−	0.0604677i	0.842359	−	0.00476552i
$162$	−1.37279			−0.107856
$163$	14.6662	−	4.30640i	1.14875	−	0.337303i	0.348698	−	0.937235i	$-0.386624\pi$
$163$	14.6662	−	4.30640i	1.14875	−	0.337303i	0.800051	+	0.599932i	$0.204806\pi$
$164$	−0.724126	−	0.835686i	−0.0565448	−	0.0652561i
$165$	1.74412	−	1.12088i	0.135780	−	0.0872604i
$166$	1.42282	+	9.89595i	0.110432	+	0.768075i
$167$	12.2681	+	7.88422i	0.949333	+	0.610100i	0.921027	−	0.389500i	$-0.127352\pi$
$167$	12.2681	+	7.88422i	0.949333	+	0.610100i	0.0283068	+	0.999599i	$0.490988\pi$
$168$	−2.68870	+	5.88744i	−0.207438	+	0.454226i
$169$	7.82505	−	9.03059i	0.601927	−	0.694661i
$170$	0.773532	−	5.38004i	0.0593272	−	0.412630i
$171$	0.868997	+	1.90284i	0.0664539	+	0.145514i
$172$	0.208549	+	0.0612356i	0.0159017	+	0.00466917i
$173$	1.78842	+	0.525127i	0.135971	+	0.0399246i	0.349010	−	0.937119i	$-0.386518\pi$
$173$	1.78842	+	0.525127i	0.135971	+	0.0399246i	−0.213039	+	0.977044i	$0.568336\pi$
$174$	3.35740	+	7.35168i	0.254524	+	0.557330i
$175$	−0.317178	+	2.20602i	−0.0239764	+	0.166760i
$176$	5.09913	−	5.88470i	0.384361	−	0.443576i
$177$	−4.75662	+	10.4155i	−0.357529	+	0.782880i
$178$	12.0026	+	7.71362i	0.899635	+	0.578161i
$179$	1.86792	+	12.9917i	0.139615	+	0.971043i	0.932371	+	0.361504i	$0.117736\pi$
$179$	1.86792	+	12.9917i	0.139615	+	0.971043i	−0.792756	+	0.609539i	$0.791354\pi$
$180$	−0.194262	+	0.124844i	−0.0144794	+	0.00930536i
$181$	9.52938	+	10.9975i	0.708314	+	0.817437i	0.989850	−	0.142113i	$-0.0453896\pi$
$181$	9.52938	+	10.9975i	0.708314	+	0.817437i	−0.281537	+	0.959550i	$0.590844\pi$
$182$	−3.00926	+	0.883600i	−0.223062	+	0.0654968i
$183$	6.41862			0.474478
$184$	−13.3853	−	3.84815i	−0.986775	−	0.283690i
$185$	5.98498			0.440024
$186$	−5.59569	+	1.64304i	−0.410296	+	0.120474i
$187$	5.37557	+	6.20374i	0.393101	+	0.453662i
$188$	0.739292	−	0.475114i	0.0539184	−	0.0346513i
$189$	−1.58589	−	11.0301i	−0.115357	−	0.802323i
$190$	−1.20791	−	0.776279i	−0.0876313	−	0.0563172i
$191$	6.96203	−	15.2447i	0.503755	−	1.10307i	−0.471476	−	0.881879i	$-0.656278\pi$
$191$	6.96203	−	15.2447i	0.503755	−	1.10307i	0.975231	−	0.221191i	$-0.0709943\pi$
$192$	5.50540	−	6.35357i	0.397318	−	0.458529i
$193$	2.12000	−	14.7449i	0.152601	−	1.06136i	−0.759238	−	0.650813i	$-0.774428\pi$
$193$	2.12000	−	14.7449i	0.152601	−	1.06136i	0.911839	−	0.410549i	$-0.134663\pi$
$194$	−0.833396	−	1.82488i	−0.0598344	−	0.131019i
$195$	0.983568	+	0.288802i	0.0704348	+	0.0206815i
$196$	−0.225206	−	0.0661265i	−0.0160862	−	0.00472332i
$197$	−7.85139	−	17.1922i	−0.559389	−	1.22489i	−0.952258	−	0.305296i	$-0.901245\pi$
$197$	−7.85139	−	17.1922i	−0.559389	−	1.22489i	0.392869	−	0.919594i	$-0.371483\pi$
$198$	−0.810090	+	5.63430i	−0.0575706	+	0.400412i
$199$	−9.61092	+	11.0916i	−0.681300	+	0.786262i	−0.986100	−	0.166154i	$-0.946865\pi$
$199$	−9.61092	+	11.0916i	−0.681300	+	0.786262i	0.304800	+	0.952416i	$0.401410\pi$
$200$	1.20640	−	2.64164i	0.0853050	−	0.186792i
$201$	3.44742	+	2.21552i	0.243163	+	0.156271i
$202$	−2.34713	−	16.3247i	−0.165144	−	1.14860i
$203$	11.0382	−	7.09382i	0.774730	−	0.497889i
$204$	0.299368	+	0.345489i	0.0209599	+	0.0241891i
$205$	−9.18918	+	2.69819i	−0.641800	+	0.188450i
$206$	−23.1720			−1.61447
$207$	9.18770	−	2.75431i	0.638589	−	0.191437i
$208$	3.84999			0.266949
$209$	2.08065	−	0.610933i	0.143921	−	0.0422591i
$210$	2.00357	+	2.31224i	0.138260	+	0.159560i
$211$	0.131272	−	0.0843634i	0.00903714	−	0.00580782i	−0.536114	−	0.844145i	$-0.680108\pi$
$211$	0.131272	−	0.0843634i	0.00903714	−	0.00580782i	0.545152	+	0.838337i	$0.316472\pi$
$212$	0.196109	+	1.36397i	0.0134688	+	0.0936777i
$213$	−8.50074	−	5.46309i	−0.582461	−	0.374325i
$214$	−2.51233	+	5.50124i	−0.171740	+	0.376057i
$215$	1.23278	−	1.42270i	0.0840749	−	0.0970276i
$216$	−2.06646	+	14.3726i	−0.140605	+	0.977929i
$217$	3.93318	+	8.61247i	0.267002	+	0.584653i
$218$	−24.0093	−	7.04976i	−1.62611	−	0.477470i
$219$	8.73070	+	2.56357i	0.589966	+	0.173230i
$220$	0.0994404	+	0.217744i	0.00670427	+	0.0146803i
$221$	−0.577615	+	4.01740i	−0.0388546	+	0.270240i
$222$	5.38040	−	6.20931i	0.361109	−	0.416742i
$223$	−8.21192	+	17.9816i	−0.549911	+	1.20414i	0.406912	+	0.913467i	$0.366605\pi$
$223$	−8.21192	+	17.9816i	−0.549911	+	1.20414i	−0.956823	+	0.290670i	$0.906122\pi$
$224$	−1.22301	−	0.785983i	−0.0817161	−	0.0525157i
$225$	0.284630	+	1.97964i	0.0189753	+	0.131976i
$226$	−11.9229	+	7.66236i	−0.793098	+	0.509693i
$227$	−8.62362	−	9.95219i	−0.572370	−	0.660550i	0.393577	−	0.919292i	$-0.371238\pi$
$227$	−8.62362	−	9.95219i	−0.572370	−	0.660550i	−0.965946	+	0.258742i	$0.916692\pi$
$228$	0.115872	−	0.0340231i	0.00767381	−	0.00225323i
$229$	−13.1012			−0.865752			−0.432876	−	0.901454i	$-0.642501\pi$
$229$	−13.1012			−0.865752			−0.432876	+	0.901454i	$0.642501\pi$
$230$	−4.28316	+	4.99990i	−0.282423	+	0.329684i
$231$	−4.62065			−0.304017
$232$	−16.4047	+	4.81685i	−1.07702	+	0.316242i
$233$	6.68832	+	7.71874i	0.438167	+	0.505671i	0.931285	−	0.364291i	$-0.118689\pi$
$233$	6.68832	+	7.71874i	0.438167	+	0.505671i	−0.493119	+	0.869962i	$0.664143\pi$
$234$	−2.36768	+	1.52161i	−0.154780	+	0.0994710i
$235$	−1.08320	−	7.53383i	−0.0706602	−	0.491453i
$236$	−1.11218	−	0.714752i	−0.0723964	−	0.0465264i
$237$	−1.59168	+	3.48530i	−0.103391	+	0.226394i
$238$	−7.93287	+	9.15502i	−0.514212	+	0.593432i
$239$	3.92361	−	27.2893i	0.253797	−	1.76520i	−0.321170	−	0.947022i	$-0.604076\pi$
$239$	3.92361	−	27.2893i	0.253797	−	1.76520i	0.574967	−	0.818177i	$-0.305015\pi$
$240$	−1.56019	−	3.41635i	−0.100710	−	0.220524i
$241$	14.6163	+	4.29174i	0.941521	+	0.276456i	0.716253	−	0.697841i	$-0.245856\pi$
$241$	14.6163	+	4.29174i	0.941521	+	0.276456i	0.225269	+	0.974297i	$0.427674\pi$
$242$	−8.82729	−	2.59193i	−0.567439	−	0.166615i
$243$	−6.64664	−	14.5541i	−0.426382	−	0.933647i
$244$	−0.105468	+	0.733548i	−0.00675192	+	0.0469606i
$245$	−1.33124	+	1.53634i	−0.0850500	+	0.0981529i
$246$	−5.46160	+	11.9592i	−0.348219	+	0.762493i
$247$	0.901978	+	0.579666i	0.0573915	+	0.0368833i
$248$	−1.75577	−	12.2116i	−0.111491	−	0.775439i
$249$	−6.12667	+	3.93737i	−0.388262	+	0.249521i
$250$	−0.898983	−	1.03748i	−0.0568567	−	0.0656161i
$251$	−14.1510	+	4.15511i	−0.893203	+	0.262268i	−0.695955	−	0.718086i	$-0.745019\pi$
$251$	−14.1510	+	4.15511i	−0.893203	+	0.262268i	−0.197248	+	0.980354i	$0.563200\pi$
$252$	0.514652			0.0324200
$253$	−1.47068	−	9.83355i	−0.0924609	−	0.618230i
$254$	11.3180			0.710152
$255$	3.79898	−	1.11548i	0.237902	−	0.0698542i
$256$	1.80848	+	2.08709i	0.113030	+	0.130443i
$257$	2.31178	−	1.48569i	0.144205	−	0.0926749i	−0.466549	−	0.884495i	$-0.654503\pi$
$257$	2.31178	−	1.48569i	0.144205	−	0.0926749i	0.610754	+	0.791820i	$0.290866\pi$
$258$	−0.367781	−	2.55797i	−0.0228971	−	0.159253i
$259$	−11.2213	−	7.21148i	−0.697257	−	0.448100i
$260$	−0.0491672	+	0.107661i	−0.00304922	+	0.00667686i
$261$	7.71076	−	8.89870i	0.477284	−	0.550815i
$262$	−0.803915	+	5.59135i	−0.0496660	+	0.345435i
$263$	−11.4364	−	25.0422i	−0.705198	−	1.54417i	−0.833552	−	0.552441i	$-0.813697\pi$
$263$	−11.4364	−	25.0422i	−0.705198	−	1.54417i	0.128354	−	0.991728i	$-0.459031\pi$
$264$	5.77696	+	1.69627i	0.355547	+	0.104398i
$265$	11.4514	+	3.36244i	0.703454	+	0.206553i
$266$	1.32936	+	2.91090i	0.0815086	+	0.178479i
$267$	−1.47910	+	10.2874i	−0.0905194	+	0.629576i
$268$	−0.309847	+	0.357582i	−0.0189269	+	0.0218428i
$269$	6.34388	−	13.8912i	0.386793	−	0.846959i	−0.611647	−	0.791131i	$-0.709493\pi$
$269$	6.34388	−	13.8912i	0.386793	−	0.846959i	0.998440	−	0.0558282i	$-0.0177799\pi$
$270$	5.77430	+	3.71092i	0.351413	+	0.225839i
$271$	3.44290	+	23.9459i	0.209141	+	1.45461i	0.775969	+	0.630771i	$0.217261\pi$
$271$	3.44290	+	23.9459i	0.209141	+	1.45461i	−0.566828	+	0.823836i	$0.691830\pi$
$272$	12.5098	−	8.03954i	0.758516	−	0.487469i
$273$	−1.49611	−	1.72661i	−0.0905490	−	0.104499i
$274$	−15.6043	+	4.58183i	−0.942689	+	0.276799i
$275$	2.07324			0.125021
$276$	−0.0819027	−	0.547635i	−0.00492997	−	0.0329637i
$277$	0.826290			0.0496470			0.0248235	−	0.999692i	$-0.492098\pi$
$277$	0.826290			0.0496470			0.0248235	+	0.999692i	$0.492098\pi$
$278$	−2.98253	+	0.875751i	−0.178880	+	0.0525241i
$279$	5.56401	+	6.42121i	0.333109	+	0.384428i
$280$	−5.44487	+	3.49920i	−0.325393	+	0.209117i
$281$	3.78346	+	26.3146i	0.225702	+	1.56979i	0.715912	+	0.698190i	$0.246011\pi$
$281$	3.78346	+	26.3146i	0.225702	+	1.56979i	−0.490210	+	0.871604i	$0.663080\pi$
$282$	−8.78999	−	5.64898i	−0.523436	−	0.336392i
$283$	5.78812	−	12.6742i	0.344068	−	0.753404i	−0.655931	−	0.754821i	$-0.727724\pi$
$283$	5.78812	−	12.6742i	0.344068	−	0.753404i	0.999999	+	0.00141703i	$0.000451056\pi$
$284$	0.764028	−	0.881735i	0.0453367	−	0.0523213i
$285$	0.148853	−	1.03529i	0.00881727	−	0.0613254i
$286$	1.21199	+	2.65388i	0.0716663	+	0.156927i
$287$	20.4800	+	6.01347i	1.20890	+	0.354964i
$288$	−1.25177	−	0.367552i	−0.0737610	−	0.0216582i
$289$	−0.549771	−	1.20383i	−0.0323395	−	0.0708136i
$290$	−1.15019	+	7.99978i	−0.0675418	+	0.469763i
$291$	0.957008	−	1.10445i	0.0561008	−	0.0647438i
$292$	−0.436435	+	0.955660i	−0.0255405	+	0.0559258i
$293$	22.4409	+	14.4219i	1.31101	+	0.842537i	0.994365	−	0.106007i	$-0.0338065\pi$
$293$	22.4409	+	14.4219i	1.31101	+	0.842537i	0.316647	+	0.948543i	$0.397443\pi$
$294$	0.397156	+	2.76228i	0.0231626	+	0.161099i
$295$	−9.63258	+	6.19048i	−0.560831	+	0.360424i
$296$	11.3820	+	13.1355i	0.661566	+	0.763488i
$297$	−9.94631	+	2.92050i	−0.577143	+	0.169465i
$298$	25.8269			1.49611
$299$	3.19833	−	3.73355i	0.184964	−	0.215916i
$300$	0.115460			0.00666607
$301$	−4.02561	+	1.18203i	−0.232032	+	0.0681308i
$302$	−16.2213	−	18.7204i	−0.933431	−	1.07724i
$303$	10.1068	−	6.49522i	0.580618	−	0.373140i
$304$	−0.559053	−	3.88830i	−0.0320639	−	0.223009i
$305$	5.39968	+	3.47017i	0.309185	+	0.198701i
$306$	−4.51586	+	9.88835i	−0.258155	+	0.565280i
$307$	8.78398	−	10.1373i	0.501328	−	0.578564i	−0.447529	−	0.894269i	$-0.647696\pi$
$307$	8.78398	−	10.1373i	0.501328	−	0.578564i	0.948857	+	0.315706i	$0.102241\pi$
$308$	0.0759248	−	0.528069i	0.00432622	−	0.0300895i
$309$	−7.01202	−	15.3542i	−0.398900	−	0.873469i
$310$	−5.59569	−	1.64304i	−0.317814	−	0.0933185i
$311$	−13.6718	−	4.01440i	−0.775256	−	0.227636i	−0.129910	−	0.991526i	$-0.541469\pi$
$311$	−13.6718	−	4.01440i	−0.775256	−	0.227636i	−0.645346	+	0.763890i	$0.723287\pi$
$312$	1.23667	+	2.70792i	0.0700124	+	0.153306i
$313$	−2.61950	+	18.2190i	−0.148063	+	1.02980i	0.771323	+	0.636444i	$0.219595\pi$
$313$	−2.61950	+	18.2190i	−0.148063	+	1.02980i	−0.919386	+	0.393356i	$0.871314\pi$
$314$	5.80983	−	6.70490i	0.327868	−	0.378379i
$315$	1.85168	−	4.05461i	0.104330	−	0.228451i
$316$	−0.372162	−	0.239174i	−0.0209357	−	0.0134546i
$317$	0.296225	+	2.06029i	0.0166377	+	0.115717i	0.996448	−	0.0842128i	$-0.0268375\pi$
$317$	0.296225	+	2.06029i	0.0166377	+	0.115717i	−0.979810	+	0.199930i	$0.935928\pi$
$318$	13.7831	−	8.85786i	0.772917	−	0.496724i
$319$	−7.99314	−	9.22458i	−0.447530	−	0.516477i
$320$	8.06643	−	2.36852i	0.450927	−	0.132404i
$321$	−4.40547			−0.245889
$322$	14.0551	−	4.21345i	0.783258	−	0.234806i
$323$	4.14125			0.230426
$324$	0.110783	−	0.0325288i	0.00615460	−	0.00180715i
$325$	0.671292	+	0.774713i	0.0372366	+	0.0429733i
$326$	17.6525	−	11.3446i	0.977682	−	0.628318i
$327$	−2.59409	−	18.0423i	−0.143453	−	0.997741i
$328$	−23.3975	−	15.0367i	−1.29191	−	0.830260i
$329$	−7.04683	+	15.4304i	−0.388504	+	0.850706i
$330$	1.86381	−	2.15095i	0.102599	−	0.118406i
$331$	−4.67886	+	32.5422i	−0.257173	+	1.78868i	0.295562	+	0.955323i	$0.404493\pi$
$331$	−4.67886	+	32.5422i	−0.257173	+	1.78868i	−0.552736	+	0.833357i	$0.686416\pi$
$332$	−0.349310	−	0.764881i	−0.0191709	−	0.0419783i
$333$	−11.4851	−	3.37233i	−0.629379	−	0.184802i
$334$	19.2086	+	5.64014i	1.05105	+	0.308615i
$335$	1.70235	+	3.72764i	0.0930095	+	0.203662i
$336$	−1.19124	+	8.28527i	−0.0649876	+	0.451998i
$337$	−3.72890	+	4.30338i	−0.203126	+	0.234420i	−0.848168	−	0.529727i	$-0.822294\pi$
$337$	−3.72890	+	4.30338i	−0.203126	+	0.234420i	0.645042	+	0.764147i	$0.276840\pi$
$338$	6.81433	−	14.9213i	0.370651	−	0.811612i
$339$	−8.68517	−	5.58162i	−0.471714	−	0.303152i
$340$	0.0650588	+	0.452494i	0.00352831	+	0.0245399i
$341$	7.40945	−	4.76177i	0.401244	−	0.257864i
$342$	1.88056	+	2.17029i	0.101689	+	0.117356i
$343$	19.3161	−	5.67173i	1.04297	−	0.306245i
$344$	5.46694			0.294758
$345$	−4.60914	−	1.32509i	−0.248148	−	0.0713403i
$346$	2.55876			0.137560
$347$	6.75284	−	1.98281i	0.362511	−	0.106443i	−0.0954043	−	0.995439i	$-0.530414\pi$
$347$	6.75284	−	1.98281i	0.362511	−	0.106443i	0.457916	+	0.888996i	$0.348596\pi$
$348$	−0.445141	−	0.513720i	−0.0238621	−	0.0275383i
$349$	−19.1203	+	12.2879i	−1.02349	+	0.657754i	−0.940849	−	0.338826i	$-0.889970\pi$
$349$	−19.1203	+	12.2879i	−1.02349	+	0.657754i	−0.0826359	+	0.996580i	$0.526334\pi$
$350$	0.435418	+	3.02840i	0.0232740	+	0.161875i
$351$	−4.31181	−	2.77103i	−0.230147	−	0.147907i
$352$	−0.561803	+	1.23018i	−0.0299442	+	0.0655686i
$353$	−18.1886	+	20.9908i	−0.968083	+	1.11723i	0.0249855	+	0.999688i	$0.492046\pi$
$353$	−18.1886	+	20.9908i	−0.968083	+	1.11723i	−0.993068	+	0.117539i	$0.962499\pi$
$354$	−2.23701	+	15.5588i	−0.118896	+	0.826940i
$355$	−4.19771	−	9.19169i	−0.222791	−	0.487844i
$356$	−1.15138	−	0.338076i	−0.0610231	−	0.0179180i
$357$	−8.46682	−	2.48608i	−0.448112	−	0.131577i
$358$	7.48502	+	16.3899i	0.395596	+	0.866233i
$359$	1.92267	−	13.3725i	0.101475	−	0.705771i	−0.874043	−	0.485849i	$-0.838511\pi$
$359$	1.92267	−	13.3725i	0.101475	−	0.705771i	0.975517	−	0.219922i	$-0.0705804\pi$
$360$	−3.80353	+	4.38950i	−0.200463	+	0.231347i
$361$	−7.43843	+	16.2879i	−0.391496	+	0.857257i
$362$	16.8053	+	10.8001i	0.883265	+	0.567640i
$363$	−0.953746	−	6.63345i	−0.0500587	−	0.348166i
$364$	0.221908	−	0.142612i	0.0116311	−	0.00747488i
$365$	5.95877	+	6.87678i	0.311896	+	0.359947i
$366$	8.45446	−	2.48245i	0.441922	−	0.129760i
$367$	6.91397			0.360906			0.180453	−	0.983584i	$-0.442244\pi$
$367$	6.91397			0.360906			0.180453	+	0.983584i	$0.442244\pi$
$368$	−18.0117	+	0.101898i	−0.938922	+	0.00531182i
$369$	19.1542			0.997130
$370$	7.88329	−	2.31474i	0.409832	−	0.120338i
$371$	−17.4188	−	20.1024i	−0.904341	−	1.04366i
$372$	0.412635	−	0.265185i	0.0213941	−	0.0137492i
$373$	2.67794	+	18.6255i	0.138658	+	0.964391i	0.933756	+	0.357910i	$0.116510\pi$
$373$	2.67794	+	18.6255i	0.138658	+	0.964391i	−0.795098	+	0.606481i	$0.792580\pi$
$374$	9.47993	+	6.09238i	0.490196	+	0.315030i
$375$	0.415415	−	0.909632i	0.0214519	−	0.0469732i
$376$	14.4749	−	16.7049i	0.746485	−	0.861490i
$377$	0.858878	−	5.97363i	0.0442345	−	0.307657i
$378$	−6.35489	−	13.9153i	−0.326860	−	0.715724i
$379$	30.5138	+	8.95965i	1.56739	+	0.460226i	0.946239	−	0.323467i	$-0.104849\pi$
$379$	30.5138	+	8.95965i	1.56739	+	0.460226i	0.621147	+	0.783694i	$0.286667\pi$
$380$	0.115872	+	0.0340231i	0.00594411	+	0.00174535i
$381$	3.42490	+	7.49948i	0.175463	+	0.384210i
$382$	3.27421	−	22.7726i	0.167523	−	1.16515i
$383$	−14.2255	+	16.4171i	−0.726890	+	0.838875i	−0.992118	−	0.125310i	$-0.960007\pi$
$383$	−14.2255	+	16.4171i	−0.726890	+	0.838875i	0.265228	+	0.964186i	$0.414553\pi$
$384$	4.25234	−	9.31132i	0.217001	−	0.475166i
$385$	−3.88714	−	2.49811i	−0.198107	−	0.127316i
$386$	−2.91030	−	20.2416i	−0.148131	−	1.03027i
$387$	−3.16733	+	2.03552i	−0.161005	+	0.103471i
$388$	0.110496	+	0.127519i	0.00560958	+	0.00647380i
$389$	−26.2813	+	7.71690i	−1.33252	+	0.391262i	−0.868994	−	0.494823i	$-0.835233\pi$
$389$	−26.2813	+	7.71690i	−1.33252	+	0.391262i	−0.463523	+	0.886085i	$0.653415\pi$
$390$	1.40723			0.0712579
$391$	2.59597	−	18.8102i	0.131284	−	0.951271i
$392$	−5.90358			−0.298176
$393$	−3.94820	+	1.15930i	−0.199160	+	0.0584787i
$394$	−16.9909	−	19.6085i	−0.855989	−	0.987864i
$395$	−3.22330	+	2.07149i	−0.162182	+	0.104228i
$396$	−0.0681335	−	0.473879i	−0.00342384	−	0.0238133i
$397$	−13.3628	−	8.58774i	−0.670659	−	0.431006i	0.160504	−	0.987035i	$-0.448688\pi$
$397$	−13.3628	−	8.58774i	−0.670659	−	0.431006i	−0.831163	+	0.556029i	$0.812324\pi$
$398$	−8.36953	+	18.3267i	−0.419526	+	0.918635i
$399$	−1.52654	+	1.76172i	−0.0764226	+	0.0881964i
$400$	0.534499	−	3.71752i	0.0267249	−	0.185876i
$401$	7.96308	+	17.4367i	0.397657	+	0.870748i	0.997502	+	0.0706320i	$0.0225016\pi$
$401$	7.96308	+	17.4367i	0.397657	+	0.870748i	−0.599845	+	0.800116i	$0.704771\pi$
$402$	5.39774	+	1.58492i	0.269215	+	0.0790487i
$403$	4.17843	+	1.22690i	0.208143	+	0.0611162i
$404$	0.576232	+	1.26177i	0.0286686	+	0.0627755i
$405$	0.142315	−	0.989821i	0.00707168	−	0.0491846i
$406$	11.7957	−	13.6129i	0.585410	−	0.675599i
$407$	−5.15460	+	11.2870i	−0.255504	+	0.559476i
$408$	9.67297	+	6.21644i	0.478883	+	0.307760i
$409$	−0.531076	−	3.69371i	−0.0262600	−	0.182642i	0.972470	−	0.233029i	$-0.0748637\pi$
$409$	−0.531076	−	3.69371i	−0.0262600	−	0.182642i	−0.998730	+	0.0503867i	$0.983955\pi$
$410$	−11.0602	+	7.10798i	−0.546226	+	0.351038i
$411$	−7.75797	−	8.95318i	−0.382673	−	0.441628i
$412$	1.86996	−	0.549071i	0.0921265	−	0.0270508i
$413$	25.5193			1.25572
$414$	11.0366	−	7.18133i	0.542419	−	0.352943i
$415$	−7.28279			−0.357498
$416$	−0.641588	+	0.188387i	−0.0314564	+	0.00923644i
$417$	−1.48282	−	1.71127i	−0.0726142	−	0.0838013i
$418$	2.50430	−	1.60941i	0.122489	−	0.0787190i
$419$	−1.45389	−	10.1120i	−0.0710270	−	0.494004i	−0.994021	−	0.109189i	$-0.965175\pi$
$419$	−1.45389	−	10.1120i	−0.0710270	−	0.494004i	0.922994	−	0.384814i	$-0.125735\pi$
$420$	−0.216476	−	0.139121i	−0.0105630	−	0.00678840i
$421$	10.8236	−	23.7004i	0.527510	−	1.15509i	−0.439007	−	0.898484i	$-0.644670\pi$
$421$	10.8236	−	23.7004i	0.527510	−	1.15509i	0.966517	−	0.256602i	$-0.0826030\pi$
$422$	0.140280	−	0.161892i	0.00682875	−	0.00788079i
$423$	−2.16640	+	15.0677i	−0.105334	+	0.732614i
$424$	14.3982	+	31.5276i	0.699236	+	1.53111i
$425$	3.79898	+	1.11548i	0.184278	+	0.0541088i
$426$	−13.3099	−	3.90813i	−0.644866	−	0.189350i
$427$	−5.94260	−	13.0125i	−0.287583	−	0.629718i
$428$	0.0723890	−	0.503477i	0.00349906	−	0.0243365i
$429$	−1.39175	+	1.60617i	−0.0671944	+	0.0775465i
$430$	1.07355	−	2.35074i	0.0517711	−	0.113363i
$431$	−4.59454	−	2.95273i	−0.221311	−	0.142228i	0.425288	−	0.905058i	$-0.360173\pi$
$431$	−4.59454	−	2.95273i	−0.221311	−	0.142228i	−0.646599	+	0.762830i	$0.723809\pi$
$432$	2.67249	+	18.5876i	0.128580	+	0.894297i
$433$	−28.8567	+	18.5451i	−1.38677	+	0.891221i	−0.999527	−	0.0307586i	$-0.990208\pi$
$433$	−28.8567	+	18.5451i	−1.38677	+	0.891221i	−0.387239	+	0.921979i	$0.626571\pi$
$434$	8.51165	+	9.82297i	0.408572	+	0.471518i
$435$	−5.64885	+	1.65865i	−0.270842	+	0.0795263i
$436$	2.10458			0.100791
$437$	−4.23513	−	2.68802i	−0.202594	−	0.128585i
$438$	12.4914			0.596861
$439$	38.5316	−	11.3139i	1.83901	−	0.539982i	0.839019	−	0.544102i	$-0.183130\pi$
$439$	38.5316	−	11.3139i	1.83901	−	0.539982i	0.999992	+	0.00411984i	$0.00131139\pi$
$440$	3.94282	+	4.55025i	0.187966	+	0.216925i
$441$	3.42031	−	2.19810i	0.162872	−	0.104671i
$442$	0.792942	+	5.51503i	0.0377164	+	0.262323i
$443$	−1.99646	−	1.28305i	−0.0948546	−	0.0609593i	0.492354	−	0.870395i	$-0.336137\pi$
$443$	−1.99646	−	1.28305i	−0.0948546	−	0.0609593i	−0.587208	+	0.809436i	$0.699773\pi$
$444$	−0.287062	+	0.628578i	−0.0136233	+	0.0298310i
$445$	−6.80606	+	7.85461i	−0.322638	+	0.372344i
$446$	−3.86203	+	26.8610i	−0.182872	+	1.27191i
$447$	7.81540	+	17.1133i	0.369656	+	0.809433i
$448$	−17.9777	−	5.27874i	−0.849368	−	0.249397i
$449$	−21.7260	−	6.37934i	−1.02531	−	0.301060i	−0.274510	−	0.961584i	$-0.588516\pi$
$449$	−21.7260	−	6.37934i	−1.02531	−	0.301060i	−0.750804	+	0.660525i	$0.770334\pi$
$450$	1.14055	+	2.49746i	0.0537661	+	0.117731i
$451$	2.82576	−	19.6536i	0.133060	−	0.925451i
$452$	0.780604	−	0.900865i	0.0367165	−	0.0423731i
$453$	7.49577	−	16.4134i	0.352182	−	0.771171i
$454$	−15.2079	−	9.77354i	−0.713744	−	0.458695i
$455$	−0.325137	−	2.26138i	−0.0152426	−	0.106015i
$456$	2.55529	−	1.64219i	0.119663	−	0.0769024i
$457$	−13.7735	−	15.8955i	−0.644297	−	0.743558i	0.335832	−	0.941922i	$-0.390983\pi$
$457$	−13.7735	−	15.8955i	−0.644297	−	0.743558i	−0.980128	+	0.198364i	$0.936437\pi$
$458$	−17.2566	+	5.06700i	−0.806349	+	0.236765i
$459$	−19.7968			−0.924037
$460$	0.227173	−	0.504979i	0.0105920	−	0.0235448i
$461$	−10.7755			−0.501863			−0.250932	−	0.968005i	$-0.580737\pi$
$461$	−10.7755			−0.501863			−0.250932	+	0.968005i	$0.580737\pi$
$462$	−6.08622	+	1.78708i	−0.283157	+	0.0831423i
$463$	19.8770	+	22.9392i	0.923761	+	1.06608i	0.997630	+	0.0688089i	$0.0219199\pi$
$463$	19.8770	+	22.9392i	0.923761	+	1.06608i	−0.0738690	+	0.997268i	$0.523535\pi$
$464$	−18.6012	+	11.9543i	−0.863541	+	0.554964i
$465$	−0.604588	−	4.20500i	−0.0280371	−	0.195002i
$466$	11.7950	+	7.58019i	0.546393	+	0.351145i
$467$	−8.86498	+	19.4116i	−0.410223	+	0.898262i	0.585908	+	0.810377i	$0.300738\pi$
$467$	−8.86498	+	19.4116i	−0.410223	+	0.898262i	−0.996131	+	0.0878846i	$0.971989\pi$
$468$	0.155014	−	0.178896i	0.00716554	−	0.00826948i
$469$	1.29978	−	9.04019i	0.0600184	−	0.417437i
$470$	−4.34054	−	9.50445i	−0.200214	−	0.438408i
$471$	6.20088	+	1.82074i	0.285721	+	0.0838954i
$472$	−31.9055	−	9.36829i	−1.46857	−	0.431211i
$473$	1.62132	+	3.55020i	0.0745484	+	0.163238i
$474$	−0.748561	+	5.20636i	−0.0343825	+	0.239136i
$475$	0.684944	−	0.790468i	0.0314274	−	0.0362692i
$476$	0.423244	−	0.926776i	0.0193994	−	0.0424787i
$477$	−20.0805	−	12.9049i	−0.919422	−	0.590876i
$478$	−5.38627	−	37.4624i	−0.246362	−	1.71349i
$479$	−19.4779	+	12.5177i	−0.889966	+	0.571947i	−0.903799	−	0.427958i	$-0.859233\pi$
$479$	−19.4779	+	12.5177i	−0.889966	+	0.571947i	0.0138325	+	0.999904i	$0.495597\pi$
$480$	0.427170	+	0.492980i	0.0194975	+	0.0225014i
$481$	−5.88664	+	1.72847i	−0.268408	+	0.0788116i
$482$	20.9122			0.952524
$483$	7.04507	+	8.03811i	0.320562	+	0.365746i
$484$	0.773772			0.0351715
$485$	1.40220	−	0.411722i	0.0636704	−	0.0186953i
$486$	−14.3837	−	16.5997i	−0.652459	−	0.752978i
$487$	3.38506	−	2.17545i	0.153392	−	0.0985790i	−0.461693	−	0.887040i	$-0.652758\pi$
$487$	3.38506	−	2.17545i	0.153392	−	0.0985790i	0.615085	+	0.788461i	$0.289122\pi$
$488$	2.65277	+	18.4504i	0.120085	+	0.835210i
$489$	12.8589	+	8.26391i	0.581500	+	0.373707i
$490$	−1.15929	+	2.53850i	−0.0523715	+	0.114678i
$491$	2.57592	−	2.97277i	0.116250	−	0.134159i	−0.694642	−	0.719356i	$-0.744437\pi$
$491$	2.57592	−	2.97277i	0.116250	−	0.134159i	0.810892	+	0.585196i	$0.198983\pi$
$492$	0.157368	−	1.09452i	0.00709468	−	0.0493446i
$493$	−9.68336	−	21.2036i	−0.436117	−	0.954962i
$494$	1.41226	+	0.414676i	0.0635404	+	0.0186572i
$495$	−3.97852	−	1.16820i	−0.178821	−	0.0525067i
$496$	−6.62808	−	14.5135i	−0.297610	−	0.651674i
$497$	−3.20504	+	22.2915i	−0.143766	+	0.999911i
$498$	−6.54711	+	7.55577i	−0.293383	+	0.338582i
$499$	0.0891762	−	0.195269i	0.00399208	−	0.00874143i	−0.907625	−	0.419781i	$-0.862107\pi$
$499$	0.0891762	−	0.195269i	0.00399208	−	0.00874143i	0.911618	+	0.411040i	$0.134834\pi$
$500$	0.0971309	+	0.0624222i	0.00434383	+	0.00279161i
$501$	2.07539	+	14.4347i	0.0927217	+	0.644894i
$502$	−17.0324	+	10.9460i	−0.760191	+	0.488545i
$503$	−5.39214	−	6.22287i	−0.240424	−	0.277464i	0.622695	−	0.782465i	$-0.286038\pi$
$503$	−5.39214	−	6.22287i	−0.240424	−	0.277464i	−0.863119	+	0.505001i	$0.831492\pi$
$504$	12.4203	−	3.64693i	0.553244	−	0.162447i
$505$	12.0139			0.534613
$506$	−5.74036	−	12.3837i	−0.255190	−	0.550525i
$507$	11.9492			0.530682
$508$	−0.913351	+	0.268184i	−0.0405234	+	0.0118987i
$509$	−8.08242	−	9.32761i	−0.358247	−	0.413439i	0.547805	−	0.836606i	$-0.315464\pi$
$509$	−8.08242	−	9.32761i	−0.358247	−	0.413439i	−0.906052	+	0.423167i	$0.860918\pi$
$510$	4.57252	−	2.93858i	0.202474	−	0.130122i
$511$	−2.88609	−	20.0732i	−0.127673	−	0.887987i
$512$	20.4120	+	13.1180i	0.902093	+	0.579740i
$513$	−2.17249	+	4.75710i	−0.0959179	+	0.210031i
$514$	2.47042	−	2.85102i	0.108966	−	0.125753i
$515$	2.40221	−	16.7077i	0.105854	−	0.736231i
$516$	0.0902920	+	0.197712i	0.00397488	+	0.00870378i
$517$	15.1409	+	4.44576i	0.665894	+	0.195524i
$518$	−17.5695	−	5.15888i	−0.771961	−	0.226668i
$519$	0.774300	+	1.69548i	0.0339880	+	0.0744233i
$520$	−0.423663	+	2.94664i	−0.0185788	+	0.129219i
$521$	12.2617	−	14.1507i	0.537194	−	0.619955i	−0.420657	−	0.907220i	$-0.638201\pi$
$521$	12.2617	−	14.1507i	0.537194	−	0.619955i	0.957851	+	0.287265i	$0.0927460\pi$
$522$	6.71480	−	14.7034i	0.293899	−	0.643549i
$523$	28.9341	+	18.5948i	1.26520	+	0.813094i	0.988987	−	0.148003i	$-0.0472844\pi$
$523$	28.9341	+	18.5948i	1.26520	+	0.813094i	0.276212	+	0.961097i	$0.410921\pi$
$524$	−0.0676142	−	0.470267i	−0.00295374	−	0.0205437i
$525$	−1.87491	+	1.20493i	−0.0818277	+	0.0525875i
$526$	−24.7491	−	28.5619i	−1.07911	−	1.24536i
$527$	16.1390	−	4.73884i	0.703025	−	0.206427i
$528$	7.78658			0.338867
$529$	−14.8642	+	17.5515i	−0.646268	+	0.763111i
$530$	16.3840			0.711675
$531$	21.9729	−	6.45183i	0.953543	−	0.279986i
$532$	−0.176254	−	0.203408i	−0.00764158	−	0.00881885i
$533$	8.25894	−	5.30770i	0.357735	−	0.229902i
$534$	2.03048	+	14.1223i	0.0878677	+	0.611133i
$535$	−3.70612	−	2.38178i	−0.160229	−	0.102973i
$536$	−4.94376	+	10.8253i	−0.213538	+	0.467583i
$537$	−8.59522	+	9.91941i	−0.370911	+	0.428054i
$538$	2.98350	−	20.7507i	0.128628	−	0.894625i
$539$	−1.75082	−	3.83375i	−0.0754130	−	0.165131i
$540$	−0.553914	−	0.162644i	−0.0238367	−	0.00699907i
$541$	8.52969	+	2.50454i	0.366720	+	0.107679i	0.459900	−	0.887971i	$-0.347885\pi$
$541$	8.52969	+	2.50454i	0.366720	+	0.107679i	−0.0931803	+	0.995649i	$0.529703\pi$
$542$	13.7962	+	30.2094i	0.592596	+	1.29760i
$543$	−2.07093	+	14.4037i	−0.0888722	+	0.618120i
$544$	−1.69132	+	1.95189i	−0.0725148	+	0.0836865i
$545$	7.57211	−	16.5806i	0.324354	−	0.710235i
$546$	−2.63843	−	1.69562i	−0.112914	−	0.0725656i
$547$	−2.64852	−	18.4209i	−0.113243	−	0.787619i	−0.964729	−	0.263243i	$-0.915208\pi$
$547$	−2.64852	−	18.4209i	−0.113243	−	0.787619i	0.851487	−	0.524376i	$-0.175701\pi$
$548$	1.15069	−	0.739501i	0.0491548	−	0.0315899i
$549$	−8.40660	−	9.70174i	−0.358785	−	0.414060i
$550$	2.73083	−	0.801844i	0.116443	−	0.0341907i
$551$	−6.15779			−0.262331
$552$	−5.85725	−	12.6359i	−0.249301	−	0.537820i
$553$	8.53940			0.363132
$554$	1.08837	−	0.319575i	0.0462405	−	0.0135774i
$555$	3.91933	+	4.52315i	0.166366	+	0.191997i
$556$	0.219937	−	0.141345i	0.00932740	−	0.00599436i
$557$	5.47182	+	38.0574i	0.231849	+	1.61254i	0.690096	+	0.723718i	$0.257568\pi$
$557$	5.47182	+	38.0574i	0.231849	+	1.61254i	−0.458248	+	0.888825i	$0.651523\pi$
$558$	9.81225	+	6.30595i	0.415386	+	0.266952i
$559$	−0.801644	+	1.75536i	−0.0339059	+	0.0742436i
$560$	−5.48149	+	6.32598i	−0.231635	+	0.267321i
$561$	−1.16822	+	8.12517i	−0.0493224	+	0.343045i
$562$	15.1609	+	33.1977i	0.639523	+	1.40036i
$563$	−23.1732	−	6.80428i	−0.976635	−	0.286766i	−0.245801	−	0.969320i	$-0.579051\pi$
$563$	−23.1732	−	6.80428i	−0.976635	−	0.286766i	−0.730835	+	0.682554i	$0.760869\pi$
$564$	0.843201	+	0.247586i	0.0355052	+	0.0104253i
$565$	−4.28878	−	9.39111i	−0.180430	−	0.395087i
$566$	2.72213	−	18.9328i	0.114419	−	0.795805i
$567$	−1.45949	+	1.68434i	−0.0612929	+	0.0707358i
$568$	12.1904	−	26.6933i	0.511500	−	1.12003i
$569$	14.3173	+	9.20115i	0.600211	+	0.385732i	0.805175	−	0.593037i	$-0.202071\pi$
$569$	14.3173	+	9.20115i	0.600211	+	0.385732i	−0.204964	+	0.978770i	$0.565708\pi$
$570$	−0.204343	−	1.42123i	−0.00855897	−	0.0595290i
$571$	−21.2061	+	13.6283i	−0.887446	+	0.570327i	−0.903042	−	0.429551i	$-0.858672\pi$
$571$	−21.2061	+	13.6283i	−0.887446	+	0.570327i	0.0155964	+	0.999878i	$0.495035\pi$
$572$	−0.160691	−	0.185448i	−0.00671884	−	0.00775395i
$573$	16.0804	−	4.72162i	0.671767	−	0.197248i
$574$	29.3016			1.22302
$575$	−3.16106	−	3.60662i	−0.131825	−	0.150407i
$576$	−16.8140			−0.700581
$577$	23.6388	−	6.94098i	0.984096	−	0.288957i	0.250182	−	0.968199i	$-0.419510\pi$
$577$	23.6388	−	6.94098i	0.984096	−	0.288957i	0.733914	+	0.679242i	$0.237691\pi$
$578$	−1.18974	−	1.37303i	−0.0494866	−	0.0571106i
$579$	12.5318	−	8.05368i	0.520802	−	0.334699i
$580$	−0.0967384	−	0.672831i	−0.00401684	−	0.0279378i
$581$	13.6546	+	8.77526i	0.566487	+	0.364059i
$582$	0.833396	−	1.82488i	0.0345454	−	0.0756439i
$583$	−16.2038	+	18.7001i	−0.671092	+	0.774481i
$584$	−3.76067	+	26.1560i	−0.155618	+	1.08234i
$585$	−0.851677	−	1.86491i	−0.0352125	−	0.0771046i
$586$	35.1365	+	10.3170i	1.45147	+	0.426191i
$587$	28.8958	+	8.48458i	1.19266	+	0.350196i	0.817042	−	0.576579i	$-0.195613\pi$
$587$	28.8958	+	8.48458i	1.19266	+	0.350196i	0.375617	+	0.926775i	$0.377431\pi$
$588$	−0.0975036	−	0.213503i	−0.00402098	−	0.00880472i
$589$	0.632362	−	4.39817i	0.0260560	−	0.181223i
$590$	−10.2936	+	11.8795i	−0.423781	+	0.489069i
$591$	7.85139	−	17.1922i	0.322963	−	0.707191i
$592$	18.9098	+	12.1526i	0.777187	+	0.499468i
$593$	1.29455	+	9.00378i	0.0531607	+	0.369741i	0.998984	+	0.0450599i	$0.0143479\pi$
$593$	1.29455	+	9.00378i	0.0531607	+	0.369741i	−0.945824	+	0.324681i	$0.894743\pi$
$594$	−11.9715	+	7.69364i	−0.491198	+	0.315674i
$595$	−5.77867	−	6.66894i	−0.236902	−	0.273400i
$596$	−2.08421	+	0.611979i	−0.0853725	+	0.0250676i
$597$	−14.6763			−0.600660
$598$	2.76880	−	6.15473i	0.113225	−	0.251685i
$599$	−10.3891			−0.424487			−0.212244	−	0.977217i	$-0.568077\pi$
$599$	−10.3891			−0.424487			−0.212244	+	0.977217i	$0.568077\pi$
$600$	2.78644	−	0.818172i	0.113756	−	0.0334017i
$601$	−8.58709	−	9.91003i	−0.350275	−	0.404238i	0.553083	−	0.833126i	$-0.313451\pi$
$601$	−8.58709	−	9.91003i	−0.350275	−	0.404238i	−0.903358	+	0.428888i	$0.858906\pi$
$602$	−4.84529	+	3.11388i	−0.197479	+	0.126912i
$603$	−1.16640	−	8.11250i	−0.0474995	−	0.330366i
$604$	1.75263	+	1.12635i	0.0713137	+	0.0458305i
$605$	2.78397	−	6.09605i	0.113185	−	0.247840i
$606$	10.8003	−	12.4642i	0.438733	−	0.506325i
$607$	−5.35147	+	37.2203i	−0.217209	+	1.51072i	0.531063	+	0.847332i	$0.321793\pi$
$607$	−5.35147	+	37.2203i	−0.217209	+	1.51072i	−0.748272	+	0.663392i	$0.769116\pi$
$608$	0.283426	+	0.620617i	0.0114944	+	0.0251693i
$609$	12.5896	+	3.69665i	0.510158	+	0.149796i
$610$	8.45446	+	2.48245i	0.342311	+	0.100512i
$611$	3.24118	+	7.09720i	0.131124	+	0.287122i
$612$	0.130118	−	0.904988i	0.00525969	−	0.0365820i
$613$	9.46277	−	10.9206i	0.382198	−	0.441079i	−0.531756	−	0.846897i	$-0.678468\pi$
$613$	9.46277	−	10.9206i	0.382198	−	0.441079i	0.913954	+	0.405818i	$0.133013\pi$
$614$	7.64940	−	16.7498i	0.308705	−	0.675969i
$615$	−8.05679	−	5.17778i	−0.324881	−	0.208788i
$616$	−1.90968	−	13.2821i	−0.0769432	−	0.535152i
$617$	−1.68450	+	1.08256i	−0.0678154	+	0.0435823i	−0.574109	−	0.818779i	$-0.694651\pi$
$617$	−1.68450	+	1.08256i	−0.0678154	+	0.0435823i	0.506294	+	0.862361i	$0.331015\pi$
$618$	−15.1744	−	17.5122i	−0.610406	−	0.704446i
$619$	16.0496	−	4.71258i	0.645087	−	0.189415i	0.0572062	−	0.998362i	$-0.481781\pi$
$619$	16.0496	−	4.71258i	0.645087	−	0.189415i	0.587880	+	0.808948i	$0.299963\pi$
$620$	0.490500			0.0196990
$621$	20.2456	+	12.8498i	0.812427	+	0.515644i
$622$	−19.5608			−0.784316
$623$	22.2250	−	6.52585i	0.890426	−	0.261453i
$624$	2.52121	+	2.90963i	0.100929	+	0.116478i
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$	3.59601	+	25.0108i	0.143726	+	0.999633i
$627$	1.82425	+	1.17237i	0.0728534	+	0.0468200i
$628$	−0.309973	+	0.678747i	−0.0123693	+	0.0270849i
$629$	−15.5181	+	17.9088i	−0.618745	+	0.714070i
$630$	0.870835	−	6.05679i	0.0346949	−	0.241308i
$631$	8.42520	+	18.4486i	0.335402	+	0.734427i	0.999917	−	0.0128469i	$-0.00408942\pi$
$631$	8.42520	+	18.4486i	0.335402	+	0.734427i	−0.664516	+	0.747274i	$0.731362\pi$
$632$	−10.6764	−	3.13486i	−0.424683	−	0.124698i
$633$	0.149723	+	0.0439625i	0.00595094	+	0.00174735i
$634$	1.18702	+	2.59920i	0.0471424	+	0.103227i
$635$	−1.17332	+	8.16060i	−0.0465617	+	0.323844i
$636$	−0.902394	+	1.04142i	−0.0357823	+	0.0412949i
$637$	0.865671	−	1.89556i	0.0342992	−	0.0751047i
$638$	−14.0961	−	9.05900i	−0.558069	−	0.358649i
$639$	2.87614	+	20.0040i	0.113778	+	0.791346i
$640$	8.61138	−	5.53420i	0.340395	−	0.218758i
$641$	−4.19160	−	4.83737i	−0.165558	−	0.191065i	0.666908	−	0.745140i	$-0.267617\pi$
$641$	−4.19160	−	4.83737i	−0.165558	−	0.191065i	−0.832466	+	0.554075i	$0.813072\pi$
$642$	−5.80279	+	1.70385i	−0.229018	+	0.0672457i
$643$	0.222671			0.00878128			0.00439064	−	0.999990i	$-0.498602\pi$
$643$	0.222671			0.00878128			0.00439064	+	0.999990i	$0.498602\pi$
$644$	−1.03439	+	0.673063i	−0.0407608	+	0.0265224i
$645$	1.88251			0.0741237
$646$	5.45477	−	1.60166i	0.214615	−	0.0630167i
$647$	−26.1092	−	30.1316i	−1.02646	−	1.18460i	−0.982633	−	0.185557i	$-0.940591\pi$
$647$	−26.1092	−	30.1316i	−1.02646	−	1.18460i	−0.0438252	−	0.999039i	$-0.513954\pi$
$648$	2.44306	−	1.57006i	0.0959725	−	0.0616778i
$649$	−3.37844	−	23.4976i	−0.132615	−	0.922360i
$650$	1.18384	+	0.760807i	0.0464340	+	0.0298413i
$651$	−3.93318	+	8.61247i	−0.154154	+	0.337549i
$652$	−1.15573	+	1.33378i	−0.0452619	+	0.0522350i
$653$	3.25524	−	22.6407i	0.127387	−	0.885999i	−0.821460	−	0.570266i	$-0.806840\pi$
$653$	3.25524	−	22.6407i	0.127387	−	0.885999i	0.948848	−	0.315734i	$-0.102251\pi$
$654$	−10.3949	−	22.7616i	−0.406472	−	0.890050i
$655$	−3.94820	−	1.15930i	−0.154269	−	0.0452974i
$656$	−34.5123	−	10.1337i	−1.34748	−	0.395655i
$657$	−7.55996	−	16.5540i	−0.294942	−	0.645833i
$658$	−3.31409	+	23.0500i	−0.129197	+	0.898583i
$659$	16.6284	−	19.1902i	0.647751	−	0.747545i	−0.332974	−	0.942936i	$-0.608052\pi$
$659$	16.6284	−	19.1902i	0.647751	−	0.747545i	0.980725	+	0.195391i	$0.0625976\pi$
$660$	−0.0994404	+	0.217744i	−0.00387071	+	0.00847568i
$661$	3.12575	+	2.00880i	0.121578	+	0.0781333i	0.600016	−	0.799988i	$-0.295161\pi$
$661$	3.12575	+	2.00880i	0.121578	+	0.0781333i	−0.478439	+	0.878121i	$0.658797\pi$
$662$	6.42307	+	44.6734i	0.249640	+	1.73628i
$663$	−3.41441	+	2.19431i	−0.132605	+	0.0852198i
$664$	−13.8501	−	15.9839i	−0.537490	−	0.620296i
$665$	−2.23667	+	0.656744i	−0.0867342	+	0.0254675i
$666$	−16.4322			−0.636734
$667$	−3.86004	+	27.9695i	−0.149461	+	1.08299i
$668$	−1.68376			−0.0651467
$669$	−18.9673	+	5.56929i	−0.733317	+	0.215321i
$670$	3.68400	+	4.25156i	0.142325	+	0.164252i
$671$	−11.1949	+	7.19450i	−0.432173	+	0.277741i
$672$	−0.206897	−	1.43900i	−0.00798124	−	0.0555107i
$673$	2.75389	+	1.76982i	0.106155	+	0.0682214i	0.592641	−	0.805467i	$-0.298085\pi$
$673$	2.75389	+	1.76982i	0.106155	+	0.0682214i	−0.486486	+	0.873688i	$0.661722\pi$
$674$	−3.24725	+	7.11049i	−0.125080	+	0.273886i
$675$	−3.27430	+	3.77875i	−0.126028	+	0.145444i
$676$	−0.196345	+	1.36561i	−0.00755172	+	0.0525233i
$677$	−8.00017	−	17.5179i	−0.307472	−	0.673269i	0.691313	−	0.722555i	$-0.257033\pi$
$677$	−8.00017	−	17.5179i	−0.307472	−	0.673269i	−0.998785	+	0.0492865i	$0.984305\pi$
$678$	−13.5986	−	3.99292i	−0.522253	−	0.153347i
$679$	−3.12508	−	0.917607i	−0.119930	−	0.0352145i
$680$	4.77656	+	10.4592i	0.183173	+	0.401092i
$681$	1.87409	−	13.0346i	0.0718153	−	0.499487i
$682$	7.91791	−	9.13776i	0.303193	−	0.349903i
$683$	10.9067	−	23.8823i	0.417333	−	0.913831i	−0.577882	−	0.816120i	$-0.696121\pi$
$683$	10.9067	−	23.8823i	0.417333	−	0.913831i	0.995215	−	0.0977109i	$-0.0311521\pi$
$684$	−0.203186	−	0.130580i	−0.00776901	−	0.00499284i
$685$	−1.68597	−	11.7262i	−0.0644175	−	0.448034i
$686$	23.2492	−	14.9414i	0.887659	−	0.570464i
$687$	−8.57946	−	9.90123i	−0.327327	−	0.377755i
$688$	6.78383	−	1.99191i	0.258631	−	0.0759410i
$689$	−12.2343			−0.466090
$690$	−6.58354	+	0.0372454i	−0.250631	+	0.00141791i
$691$	−41.0885			−1.56308			−0.781541	−	0.623854i	$-0.785566\pi$
$691$	−41.0885			−1.56308			−0.781541	+	0.623854i	$0.785566\pi$
$692$	−0.206490	+	0.0606310i	−0.00784957	+	0.00230484i
$693$	6.05177	+	6.98411i	0.229888	+	0.265304i
$694$	8.12782	−	5.22343i	0.308528	−	0.198279i
$695$	−0.322249	−	2.24129i	−0.0122236	−	0.0850169i
$696$	−14.3831	−	9.24346i	−0.545190	−	0.350373i
$697$	15.7523	−	34.4926i	0.596659	−	1.30650i
$698$	−20.4324	+	23.5802i	−0.773377	+	0.892525i
$699$	−1.45351	+	10.1094i	−0.0549769	+	0.382372i
$700$	−0.106897	−	0.234072i	−0.00404033	−	0.00884709i
$701$	29.9345	+	8.78957i	1.13061	+	0.331977i	0.792948	−	0.609289i	$-0.208545\pi$
$701$	29.9345	+	8.78957i	1.13061	+	0.331977i	0.337664	+	0.941267i	$0.390363\pi$
$702$	−6.75114	−	1.98231i	−0.254805	−	0.0748176i
$703$	2.60047	+	5.69423i	0.0980784	+	0.214762i
$704$	−2.48050	+	17.2523i	−0.0934875	+	0.650220i
$705$	4.98434	−	5.75223i	0.187721	−	0.216642i
$706$	−15.8393	+	34.6832i	−0.596120	+	1.30532i
$707$	−22.5250	−	14.4759i	−0.847140	−	0.544424i
$708$	−0.188147	−	1.30859i	−0.00707098	−	0.0491798i
$709$	−23.4807	+	15.0902i	−0.881838	+	0.566723i	−0.901352	−	0.433087i	$-0.857424\pi$
$709$	−23.4807	+	15.0902i	−0.881838	+	0.566723i	0.0195142	+	0.999810i	$0.493788\pi$
$710$	−9.08409	−	10.4836i	−0.340920	−	0.393442i
$711$	7.35269	−	2.15894i	0.275747	−	0.0809667i
$712$	−30.1824			−1.13113
$713$	−19.5807	−	5.62929i	−0.733304	−	0.210819i
$714$	−12.1138			−0.453349
$715$	−2.03918	+	0.598756i	−0.0762609	+	0.0223922i
$716$	−0.992402	−	1.14529i	−0.0370878	−	0.0428016i
$717$	23.1933	−	14.9054i	0.866170	−	0.556653i
$718$	−2.63941	−	18.3575i	−0.0985020	−	0.685096i
$719$	−8.72996	−	5.61040i	−0.325572	−	0.209233i	0.367636	−	0.929970i	$-0.380167\pi$
$719$	−8.72996	−	5.61040i	−0.325572	−	0.209233i	−0.693209	+	0.720737i	$0.743804\pi$
$720$	−3.12039	+	6.83270i	−0.116290	+	0.254640i
$721$	−24.6356	+	28.4310i	−0.917478	+	1.05883i
$722$	−3.49826	+	24.3309i	−0.130192	+	0.905503i
$723$	6.32818	+	13.8568i	0.235348	+	0.515339i
$724$	−1.61209	−	0.473351i	−0.0599127	−	0.0175920i
$725$	−5.64885	−	1.65865i	−0.209793	−	0.0616008i
$726$	−3.82180	−	8.36857i	−0.141840	−	0.310587i
$727$	2.35904	−	16.4075i	0.0874919	−	0.608519i	−0.898152	−	0.439684i	$-0.855090\pi$
$727$	2.35904	−	16.4075i	0.0874919	−	0.608519i	0.985644	−	0.168835i	$-0.0540006\pi$
$728$	4.34482	−	5.01419i	0.161030	−	0.185838i
$729$	5.40040	−	11.8252i	0.200015	−	0.437971i
$730$	10.5084	+	6.75334i	0.388934	+	0.249953i
$731$	1.06075	+	7.37767i	0.0392332	+	0.272873i
$732$	−0.623446	+	0.400664i	−0.0230432	+	0.0148090i
$733$	−9.13396	−	10.5411i	−0.337370	−	0.389346i	0.561561	−	0.827435i	$-0.310201\pi$
$733$	−9.13396	−	10.5411i	−0.337370	−	0.389346i	−0.898932	+	0.438089i	$0.855655\pi$
$734$	9.10693	−	2.67404i	0.336143	−	0.0987005i
$735$	−2.03286			−0.0749833
$736$	2.99660	−	0.898325i	0.110456	−	0.0331127i
$737$	−8.49607			−0.312957
$738$	25.2295	−	7.40806i	0.928712	−	0.272695i
$739$	7.96631	+	9.19361i	0.293046	+	0.338193i	0.883112	−	0.469162i	$-0.155444\pi$
$739$	7.96631	+	9.19361i	0.293046	+	0.338193i	−0.590067	+	0.807355i	$0.700899\pi$
$740$	−0.581326	+	0.373596i	−0.0213700	+	0.0137337i
$741$	0.152588	+	1.06127i	0.00560545	+	0.0389867i
$742$	−30.7185	−	19.7416i	−1.12771	−	0.724736i
$743$	8.95858	−	19.6166i	0.328658	−	0.719662i	−0.671106	−	0.741361i	$-0.734181\pi$
$743$	8.95858	−	19.6166i	0.328658	−	0.719662i	0.999765	+	0.0216997i	$0.00690778\pi$
$744$	8.07915	−	9.32383i	0.296196	−	0.341828i
$745$	−2.67744	+	18.6220i	−0.0980937	+	0.682257i
$746$	10.7309	+	23.4974i	0.392886	+	0.860300i
$747$	13.9756	+	4.10360i	0.511340	+	0.150143i
$748$	−0.909385	−	0.267020i	−0.0332504	−	0.00976320i
$749$	4.07875	+	8.93122i	0.149034	+	0.326340i
$750$	0.195368	−	1.35881i	0.00713382	−	0.0496168i
$751$	17.2589	−	19.9179i	0.629788	−	0.726814i	−0.347747	−	0.937588i	$-0.613053\pi$
$751$	17.2589	−	19.9179i	0.629788	−	0.726814i	0.977535	+	0.210774i	$0.0675986\pi$
$752$	11.8751	−	26.0029i	0.433041	−	0.948227i
$753$	−12.4072	−	7.97359i	−0.452142	−	0.290574i
$754$	−1.17906	−	8.20051i	−0.0429387	−	0.298645i
$755$	15.1796	−	9.75535i	0.552443	−	0.355034i
$756$	0.842563	+	0.972370i	0.0306437	+	0.0353647i
$757$	−11.0340	+	3.23988i	−0.401038	+	0.117755i	−0.476030	−	0.879429i	$-0.657925\pi$
$757$	−11.0340	+	3.23988i	−0.401038	+	0.117755i	0.0749928	+	0.997184i	$0.476107\pi$
$758$	43.6573			1.58570
$759$	6.46861	−	7.55107i	0.234796	−	0.274087i
$760$	3.03748			0.110181
$761$	−30.1077	+	8.84043i	−1.09140	+	0.320465i	−0.777432	−	0.628967i	$-0.783478\pi$
$761$	−30.1077	+	8.84043i	−1.09140	+	0.320465i	−0.313973	+	0.949432i	$0.601660\pi$
$762$	7.41168	+	8.55354i	0.268497	+	0.309862i
$763$	−34.1755	+	21.9633i	−1.23724	+	0.795123i
$764$	0.275381	+	1.91532i	0.00996295	+	0.0692938i
$765$	−6.66166	−	4.28119i	−0.240853	−	0.154787i
$766$	−12.3881	+	27.1261i	−0.447599	+	0.980106i
$767$	7.68648	−	8.87067i	0.277543	−	0.320301i
$768$	−0.393020	+	2.73351i	−0.0141819	+	0.0986371i
$769$	14.5909	+	31.9496i	0.526160	+	1.15213i	0.967054	+	0.254571i	$0.0819343\pi$
$769$	14.5909	+	31.9496i	0.526160	+	1.15213i	−0.440894	+	0.897559i	$0.645338\pi$
$770$	−6.08622	−	1.78708i	−0.219332	−	0.0644017i
$771$	2.63671	+	0.774207i	0.0949587	+	0.0278824i
$772$	0.714493	+	1.56452i	0.0257152	+	0.0563083i
$773$	−4.92870	+	34.2799i	−0.177273	+	1.23296i	0.685765	+	0.727823i	$0.259468\pi$
$773$	−4.92870	+	34.2799i	−0.177273	+	1.23296i	−0.863038	+	0.505139i	$0.831441\pi$
$774$	−3.38469	+	3.90614i	−0.121660	+	0.140403i
$775$	1.76478	−	3.86433i	0.0633929	−	0.138811i
$776$	3.57027	+	2.29447i	0.128165	+	0.0823668i
$777$	−1.89830	−	13.2030i	−0.0681013	−	0.473655i
$778$	−31.6326	+	20.3291i	−1.13408	+	0.728832i
$779$	−6.55979	−	7.57040i	−0.235029	−	0.271238i
$780$	−0.113563	+	0.0333450i	−0.00406619	+	0.00119394i
$781$	20.9498			0.749643
$782$	−3.85564	−	25.7803i	−0.137877	−	0.921903i
$783$	29.4367			1.05198
$784$	−7.32566	+	2.15101i	−0.261631	+	0.0768217i
$785$	4.23214	+	4.88416i	0.151052	+	0.174323i
$786$	−4.75211	+	3.05400i	−0.169502	+	0.108933i
$787$	1.83031	+	12.7301i	0.0652437	+	0.453780i	0.996088	+	0.0883643i	$0.0281640\pi$
$787$	1.83031	+	12.7301i	0.0652437	+	0.453780i	−0.930845	+	0.365415i	$0.880927\pi$
$788$	1.83579	+	1.17979i	0.0653971	+	0.0420282i
$789$	11.4364	−	25.0422i	0.407146	−	0.891526i
$790$	−3.44450	+	3.97516i	−0.122550	+	0.141430i
$791$	−3.27457	+	22.7751i	−0.116430	+	0.809791i
$792$	−5.00230	−	10.9535i	−0.177749	−	0.389216i
$793$	−6.31315	−	1.85371i	−0.224187	−	0.0658271i
$794$	−20.9225	−	6.14341i	−0.742513	−	0.218022i
$795$	4.95792	+	10.8563i	0.175839	+	0.385034i
$796$	0.241155	−	1.67727i	0.00854752	−	0.0594493i
$797$	32.7198	−	37.7607i	1.15900	−	1.33755i	0.227509	−	0.973776i	$-0.426942\pi$
$797$	32.7198	−	37.7607i	1.15900	−	1.33755i	0.931486	−	0.363777i	$-0.118513\pi$
$798$	−1.32936	+	2.91090i	−0.0470590	+	0.103045i
$799$	25.3519	+	16.2927i	0.896887	+	0.576394i
$800$	0.0928329	+	0.645667i	0.00328214	+	0.0228278i
$801$	17.4865	−	11.2379i	0.617856	−	0.397072i
$802$	17.2326	+	19.8875i	0.608504	+	0.702251i
$803$	−18.1009	+	5.31489i	−0.638766	+	0.187559i
$804$	−0.473149			−0.0166867
$805$	1.58096	+	10.5709i	0.0557215	+	0.372577i
$806$	5.97826			0.210575
$807$	14.6526	−	4.30239i	0.515796	−	0.151451i
$808$	22.8476	+	26.3676i	0.803777	+	0.927608i
$809$	26.0076	−	16.7141i	0.914380	−	0.587636i	0.00335807	−	0.999994i	$-0.498931\pi$
$809$	26.0076	−	16.7141i	0.914380	−	0.587636i	0.911022	+	0.412358i	$0.135295\pi$
$810$	−0.195368	−	1.35881i	−0.00686452	−	0.0477438i
$811$	−3.70472	−	2.38088i	−0.130090	−	0.0836040i	0.473977	−	0.880537i	$-0.342818\pi$
$811$	−3.70472	−	2.38088i	−0.130090	−	0.0836040i	−0.604068	+	0.796933i	$0.706454\pi$
$812$	−0.629338	+	1.37806i	−0.0220854	+	0.0483604i
$813$	−15.8425	+	18.2832i	−0.555619	+	0.641219i
$814$	−2.42418	+	16.8606i	−0.0849676	+	0.590963i
$815$	6.34979	+	13.9041i	0.222423	+	0.487039i
$816$	14.2680	+	4.18947i	0.499481	+	0.146661i
$817$	1.88923	+	0.554728i	0.0660958	+	0.0194075i
$818$	−2.12809	−	4.65988i	−0.0744071	−	0.162929i
$819$	−0.650273	+	4.52275i	−0.0227224	+	0.158038i
$820$	0.724126	−	0.835686i	0.0252876	−	0.0291834i
$821$	18.0805	−	39.5908i	0.631014	−	1.38173i	−0.276217	−	0.961095i	$-0.589081\pi$
$821$	18.0805	−	39.5908i	0.631014	−	1.38173i	0.907231	−	0.420633i	$-0.138192\pi$
$822$	−13.6813	−	8.79247i	−0.477192	−	0.306673i
$823$	−0.404970	−	2.81663i	−0.0141164	−	0.0981814i	0.981545	−	0.191230i	$-0.0612478\pi$
$823$	−0.404970	−	2.81663i	−0.0141164	−	0.0981814i	−0.995662	+	0.0930490i	$0.970339\pi$
$824$	41.2378	−	26.5019i	1.43659	−	0.923238i
$825$	1.35769	+	1.56685i	0.0472685	+	0.0545508i
$826$	33.6135	−	9.86981i	1.16956	−	0.343414i
$827$	−9.22615			−0.320825			−0.160412	−	0.987050i	$-0.551282\pi$
$827$	−9.22615			−0.320825			−0.160412	+	0.987050i	$0.551282\pi$
$828$	−0.720479	+	0.841045i	−0.0250384	+	0.0292283i
$829$	7.15078			0.248357			0.124178	−	0.992260i	$-0.460370\pi$
$829$	7.15078			0.248357			0.124178	+	0.992260i	$0.460370\pi$
$830$	−9.59273	+	2.81668i	−0.332969	+	0.0977684i
$831$	0.541105	+	0.624468i	0.0187707	+	0.0216626i
$832$	−7.24986	+	4.65920i	−0.251344	+	0.161529i
$833$	−1.14547	−	7.96692i	−0.0396882	−	0.276038i
$834$	−2.61499	−	1.68055i	−0.0905498	−	0.0581928i
$835$	−6.05804	+	13.2653i	−0.209647	+	0.459063i
$836$	−0.163959	+	0.189219i	−0.00567065	+	0.00654428i
$837$	−3.02294	+	21.0250i	−0.104488	+	0.726730i
$838$	−5.82593	−	12.7570i	−0.201253	−	0.440683i
$839$	−23.3760	−	6.86382i	−0.807030	−	0.236965i	−0.147907	−	0.989001i	$-0.547254\pi$
$839$	−23.3760	−	6.86382i	−0.807030	−	0.236965i	−0.659122	+	0.752036i	$0.729072\pi$
$840$	−6.21015	−	1.82347i	−0.214271	−	0.0629155i
$841$	2.35153	+	5.14912i	0.0810871	+	0.177556i
$842$	5.09029	−	35.4037i	0.175423	−	1.22009i
$843$	−17.4096	+	20.0917i	−0.599617	+	0.691995i
$844$	−0.00748442	+	0.0163886i	−0.000257624	+	0.000564119i
$845$	10.0523	+	6.46022i	0.345809	+	0.222238i
$846$	2.97400	+	20.6847i	0.102248	+	0.711153i
$847$	−12.5650	+	8.07504i	−0.431739	+	0.277462i
$848$	29.3537	+	33.8760i	1.00801	+	1.16331i
$849$	13.3689	−	3.92548i	0.458821	−	0.134722i
$850$	5.43536			0.186431
$851$	27.4941	−	8.24223i	0.942485	−	0.282540i
$852$	1.16670			0.0399706
$853$	11.7696	−	3.45587i	0.402984	−	0.118327i	−0.0739585	−	0.997261i	$-0.523563\pi$
$853$	11.7696	−	3.45587i	0.402984	−	0.118327i	0.476942	+	0.878935i	$0.341745\pi$
$854$	−12.8602	−	14.8414i	−0.440065	−	0.507863i
$855$	−1.75980	+	1.13095i	−0.0601839	+	0.0386778i
$856$	−1.82075	−	12.6636i	−0.0622319	−	0.432832i
$857$	33.6103	+	21.6000i	1.14811	+	0.737842i	0.969261	−	0.246035i	$-0.0791278\pi$
$857$	33.6103	+	21.6000i	1.14811	+	0.737842i	0.178844	+	0.983877i	$0.442764\pi$
$858$	−1.21199	+	2.65388i	−0.0413765	+	0.0906020i
$859$	18.7267	−	21.6117i	0.638945	−	0.737382i	−0.340243	−	0.940338i	$-0.610509\pi$
$859$	18.7267	−	21.6117i	0.638945	−	0.737382i	0.979188	+	0.202955i	$0.0650547\pi$
$860$	−0.0309327	+	0.215141i	−0.00105480	+	0.00733626i
$861$	8.86687	+	19.4157i	0.302182	+	0.661686i
$862$	−7.19383	−	2.11230i	−0.245023	−	0.0719452i
$863$	7.09190	+	2.08237i	0.241411	+	0.0708847i	0.400200	−	0.916428i	$-0.368941\pi$
$863$	7.09190	+	2.08237i	0.241411	+	0.0708847i	−0.158789	+	0.987313i	$0.550759\pi$
$864$	−1.35489	−	2.96679i	−0.0460943	−	0.100932i
$865$	−0.265263	+	1.84495i	−0.00901922	+	0.0627301i
$866$	−30.8370	+	35.5878i	−1.04788	+	1.20932i
$867$	0.549771	−	1.20383i	0.0186712	−	0.0408843i
$868$	−0.919643	−	0.591019i	−0.0312147	−	0.0200605i
$869$	−1.13051	−	7.86287i	−0.0383499	−	0.266730i
$870$	−6.79905	+	4.36948i	−0.230509	+	0.148139i
$871$	−2.75093	−	3.17474i	−0.0932117	−	0.107572i
$872$	50.7907	−	14.9135i	1.71999	−	0.505035i
$873$	−2.92278			−0.0989212
$874$	−6.61803	−	1.90263i	−0.223858	−	0.0643573i
$875$	−2.22871			−0.0753441
$876$	−1.00804	+	0.295989i	−0.0340587	+	0.0100005i
$877$	−11.9415	−	13.7812i	−0.403234	−	0.465357i	0.517423	−	0.855730i	$-0.326892\pi$
$877$	−11.9415	−	13.7812i	−0.403234	−	0.465357i	−0.920657	+	0.390373i	$0.872346\pi$
$878$	46.3772	−	29.8048i	1.56515	−	1.00586i
$879$	3.79633	+	26.4041i	0.128047	+	0.890587i
$880$	6.55049	+	4.20974i	0.220817	+	0.141910i
$881$	15.0799	−	33.0203i	0.508054	−	1.11248i	−0.465713	−	0.884936i	$-0.654202\pi$
$881$	15.0799	−	33.0203i	0.508054	−	1.11248i	0.973767	−	0.227547i	$-0.0730706\pi$
$882$	3.65502	−	4.21812i	0.123071	−	0.142031i
$883$	2.69561	−	18.7483i	0.0907143	−	0.630932i	−0.892847	−	0.450360i	$-0.851296\pi$
$883$	2.69561	−	18.7483i	0.0907143	−	0.630932i	0.983562	−	0.180573i	$-0.0577951\pi$
$884$	−0.194671	−	0.426270i	−0.00654749	−	0.0143370i
$885$	−10.9865	−	3.22591i	−0.369306	−	0.108438i
$886$	−3.12592	−	0.917853i	−0.105017	−	0.0308359i
$887$	−13.3895	−	29.3189i	−0.449576	−	0.984433i	−0.989741	−	0.142874i	$-0.954366\pi$
$887$	−13.3895	−	29.3189i	−0.449576	−	0.984433i	0.540165	−	0.841559i	$-0.318362\pi$
$888$	−2.47355	+	17.2039i	−0.0830068	+	0.577325i
$889$	12.0328	−	13.8866i	0.403568	−	0.465742i
$890$	−5.92696	+	12.9782i	−0.198672	+	0.435031i
$891$	1.74412	+	1.12088i	0.0584303	+	0.0375509i
$892$	−0.324820	−	2.25918i	−0.0108758	−	0.0756428i
$893$	6.69718	−	4.30402i	0.224113	−	0.144028i
$894$	16.9130	+	19.5186i	0.565655	+	0.652801i
$895$	−12.5936	+	3.69781i	−0.420958	+	0.123604i
$896$	−22.8139			−0.762158
$897$	4.91609	−	0.0278121i	0.164143	−	0.000928618i
$898$	−31.0843			−1.03730
$899$	−23.9977	+	7.04635i	−0.800367	+	0.235009i
$900$	−0.151220	−	0.174517i	−0.00504067	−	0.00581724i
$901$	−39.7530	+	25.5477i	−1.32436	+	0.851117i
$902$	−3.87916	−	26.9802i	−0.129162	−	0.898341i
$903$	−3.52953	−	2.26829i	−0.117455	−	0.0754840i
$904$	12.4549	−	27.2725i	0.414244	−	0.907069i
$905$	−9.52938	+	10.9975i	−0.316767	+	0.365569i
$906$	3.52523	−	24.5185i	0.117118	−	0.814572i
$907$	−0.898972	−	1.96847i	−0.0298499	−	0.0653621i	0.894120	−	0.447828i	$-0.147802\pi$
$907$	−0.898972	−	1.96847i	−0.0298499	−	0.0653621i	−0.923970	+	0.382466i	$0.875075\pi$
$908$	1.45886	+	0.428359i	0.0484139	+	0.0142156i
$909$	−23.0545	−	6.76943i	−0.764671	−	0.224528i
$910$	−1.30287	−	2.85288i	−0.0431897	−	0.0945722i
$911$	−0.324606	+	2.25769i	−0.0107547	+	0.0748005i	−0.994492	−	0.104813i	$-0.966576\pi$
$911$	−0.324606	+	2.25769i	−0.0107547	+	0.0748005i	0.983737	+	0.179613i	$0.0574847\pi$
$912$	2.57248	−	2.96880i	0.0851833	−	0.0983068i
$913$	6.27235	−	13.7345i	0.207584	−	0.454547i
$914$	−24.2898	−	15.6101i	−0.803436	−	0.516337i
$915$	0.913465	+	6.35329i	0.0301982	+	0.210033i
$916$	1.27253	−	0.817806i	0.0420456	−	0.0270211i
$917$	6.00564	+	6.93088i	0.198324	+	0.228878i
$918$	−26.0759	+	7.65659i	−0.860634	+	0.252705i
$919$	21.9965			0.725596			0.362798	−	0.931868i	$-0.381821\pi$
$919$	21.9965			0.725596			0.362798	+	0.931868i	$0.381821\pi$
$920$	1.90406	−	13.7967i	0.0627750	−	0.454863i
$921$	13.4135			0.441990
$922$	−14.1932	+	4.16750i	−0.467428	+	0.137249i
$923$	6.78331	+	7.82835i	0.223275	+	0.257673i
$924$	0.448808	−	0.288431i	0.0147647	−	0.00948869i
$925$	0.851751	+	5.92406i	0.0280054	+	0.194782i
$926$	35.0534	+	22.5275i	1.15193	+	0.740299i
$927$	−14.0240	+	30.7084i	−0.460610	+	1.00860i
$928$	2.51489	−	2.90234i	0.0825553	−	0.0952739i
$929$	3.87661	−	26.9624i	0.127188	−	0.884609i	−0.821908	−	0.569620i	$-0.807090\pi$
$929$	3.87661	−	26.9624i	0.127188	−	0.884609i	0.949096	−	0.314988i	$-0.102001\pi$
$930$	−2.42267	−	5.30490i	−0.0794424	−	0.173955i
$931$	−2.04012	−	0.599034i	−0.0668623	−	0.0196325i
$932$	−1.13146	−	0.332228i	−0.0370623	−	0.0108825i
$933$	−5.91924	−	12.9613i	−0.193787	−	0.424335i
$934$	−4.16916	+	28.9972i	−0.136419	+	0.948816i
$935$	−5.37557	+	6.20374i	−0.175800	+	0.202884i
$936$	2.47333	−	5.41584i	0.0808434	−	0.177022i
$937$	26.1742	+	16.8211i	0.855073	+	0.549522i	0.893153	−	0.449752i	$-0.148488\pi$
$937$	26.1742	+	16.8211i	0.855073	+	0.549522i	−0.0380798	+	0.999275i	$0.512124\pi$
$938$	−1.78432	−	12.4102i	−0.0582602	−	0.405209i
$939$	−15.4844	+	9.95124i	−0.505315	+	0.324746i
$940$	0.575490	+	0.664151i	0.0187704	+	0.0216622i
$941$	−21.8554	+	6.41733i	−0.712466	+	0.209199i	−0.617828	−	0.786313i	$-0.711987\pi$
$941$	−21.8554	+	6.41733i	−0.712466	+	0.209199i	−0.0946374	+	0.995512i	$0.530169\pi$
$942$	8.87185			0.289061
$943$	−38.4979	+	25.0500i	−1.25366	+	0.815739i
$944$	−43.0044			−1.39967
$945$	10.6921	−	3.13950i	0.347816	−	0.102128i
$946$	3.50864	+	4.04918i	0.114076	+	0.131650i
$947$	−26.7831	+	17.2124i	−0.870332	+	0.559329i	−0.897854	−	0.440293i	$-0.854875\pi$
$947$	−26.7831	+	17.2124i	−0.870332	+	0.559329i	0.0275220	+	0.999621i	$0.491238\pi$
$948$	−0.0629586	−	0.437887i	−0.00204480	−	0.0142219i
$949$	−7.84688	−	5.04288i	−0.254721	−	0.163699i
$950$	0.596474	−	1.30609i	0.0193522	−	0.0423753i
$951$	−1.36308	+	1.57308i	−0.0442008	+	0.0510105i
$952$	3.64700	−	25.3655i	0.118200	−	0.822100i
$953$	−5.84093	−	12.7898i	−0.189206	−	0.414304i	0.791127	−	0.611651i	$-0.209494\pi$
$953$	−5.84093	−	12.7898i	−0.189206	−	0.414304i	−0.980334	+	0.197348i	$0.936767\pi$
$954$	−31.4407	−	9.23181i	−1.01793	−	0.298891i
$955$	16.0804	+	4.72162i	0.520348	+	0.152788i
$956$	1.32236	+	2.89555i	0.0427680	+	0.0936489i
$957$	1.73708	−	12.0816i	0.0561517	−	0.390544i
$958$	−20.8145	+	24.0212i	−0.672486	+	0.776090i
$959$	−10.9682	+	24.0170i	−0.354181	+	0.775548i
$960$	7.07240	+	4.54515i	0.228261	+	0.146694i
$961$	1.84333	+	12.8206i	0.0594622	+	0.413568i
$962$	−7.08525	+	4.55341i	−0.228438	+	0.146808i
$963$	5.76994	+	6.65886i	0.185934	+	0.214579i
$964$	−1.68760	+	0.495524i	−0.0543539	+	0.0159597i
$965$	14.8965			0.479536
$966$	12.3884	+	7.86288i	0.398591	+	0.252984i
$967$	21.5282			0.692301			0.346151	−	0.938179i	$-0.387489\pi$
$967$	21.5282			0.692301			0.346151	+	0.938179i	$0.387489\pi$
$968$	18.6738	−	5.48311i	0.600198	−	0.176234i
$969$	2.71194	+	3.12975i	0.0871202	+	0.100542i
$970$	1.68770	−	1.08462i	0.0541889	−	0.0348251i
$971$	−4.68869	−	32.6106i	−0.150467	−	1.04652i	−0.915438	−	0.402458i	$-0.868156\pi$
$971$	−4.68869	−	32.6106i	−0.150467	−	1.04652i	0.764971	−	0.644065i	$-0.222753\pi$
$972$	1.55409	+	0.998756i	0.0498476	+	0.0320351i
$973$	−2.09641	+	4.59050i	−0.0672078	+	0.147165i
$974$	3.61736	−	4.17465i	0.115908	−	0.133765i
$975$	−0.145886	+	1.01466i	−0.00467208	+	0.0324951i
$976$	10.0143	+	21.9282i	0.320550	+	0.701906i
$977$	−30.5120	−	8.95913i	−0.976166	−	0.286628i	−0.245525	−	0.969390i	$-0.578960\pi$
$977$	−30.5120	−	8.95913i	−0.976166	−	0.286628i	−0.730641	+	0.682762i	$0.760779\pi$
$978$	20.1336	+	5.91176i	0.643802	+	0.189037i
$979$	−8.95116	−	19.6003i	−0.286080	−	0.626428i
$980$	0.0334033	−	0.232325i	0.00106703	−	0.00742134i
$981$	−23.8734	+	27.5513i	−0.762218	+	0.879647i
$982$	2.24320	−	4.91193i	0.0715835	−	0.156746i
$983$	0.688292	+	0.442339i	0.0219531	+	0.0141084i	0.551571	−	0.834128i	$-0.314028\pi$
$983$	0.688292	+	0.442339i	0.0219531	+	0.0141084i	−0.529618	+	0.848236i	$0.677665\pi$
$984$	−3.95815	−	27.5296i	−0.126181	−	0.877610i
$985$	15.8998	−	10.2182i	0.506610	−	0.325578i
$986$	−20.9554	−	24.1838i	−0.667355	−	0.770169i
$987$	−16.2762	+	4.77913i	−0.518078	+	0.152121i
$988$	−0.123794			−0.00393841
$989$	3.70393	−	8.23342i	0.117778	−	0.261807i
$990$	−5.69224			−0.180911
$991$	−18.8980	+	5.54895i	−0.600314	+	0.176268i	−0.567749	−	0.823201i	$-0.692186\pi$
$991$	−18.8980	+	5.54895i	−0.600314	+	0.176268i	−0.0325649	+	0.999470i	$0.510368\pi$
$992$	1.81472	+	2.09430i	0.0576174	+	0.0664940i
$993$	−27.6577	+	17.7746i	−0.877692	+	0.564058i
$994$	4.39983	+	30.6015i	0.139554	+	0.970620i
$995$	−12.3465	−	7.93460i	−0.391409	−	0.251544i
$996$	0.349310	−	0.764881i	0.0110683	−	0.0242362i
$997$	20.3424	−	23.4764i	0.644251	−	0.743505i	−0.335869	−	0.941909i	$-0.609030\pi$
$997$	20.3424	−	23.4764i	0.644251	−	0.743505i	0.980121	+	0.198403i	$0.0635755\pi$
$998$	0.0419392	−	0.291693i	0.00132756	−	0.00923339i
$999$	−12.4313	−	27.2206i	−0.393307	−	0.861223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.a.101.1	yes	10
5.2	odd	4		575.2.p.a.124.2		20
5.3	odd	4		575.2.p.a.124.1		20
5.4	even	2		575.2.k.a.101.1		10
23.8	even	11		2645.2.a.n.1.3		5
23.15	odd	22		2645.2.a.o.1.3		5
23.18	even	11	inner	115.2.g.a.41.1	✓	10
115.18	odd	44		575.2.p.a.524.2		20
115.64	even	22		575.2.k.a.501.1		10
115.87	odd	44		575.2.p.a.524.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.a.41.1	✓	10	23.18	even	11	inner
115.2.g.a.101.1	yes	10	1.1	even	1	trivial
575.2.k.a.101.1		10	5.4	even	2
575.2.k.a.501.1		10	115.64	even	22
575.2.p.a.124.1		20	5.3	odd	4
575.2.p.a.124.2		20	5.2	odd	4
575.2.p.a.524.1		20	115.87	odd	44
575.2.p.a.524.2		20	115.18	odd	44
2645.2.a.n.1.3		5	23.8	even	11
2645.2.a.o.1.3		5	23.15	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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31718 - 0.386758i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-0.0971309 + 0.0624222i) q^{4} +(0.142315 + 0.989821i) q^{5} +(1.15486 + 0.742184i) q^{6} +(0.925839 - 2.02730i) q^{7} +(-1.90176 + 2.19475i) q^{8} +(0.284630 - 1.97964i) q^{9} +O(q^{10})\)	\(q+(1.31718 - 0.386758i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-0.0971309 + 0.0624222i) q^{4} +(0.142315 + 0.989821i) q^{5} +(1.15486 + 0.742184i) q^{6} +(0.925839 - 2.02730i) q^{7} +(-1.90176 + 2.19475i) q^{8} +(0.284630 - 1.97964i) q^{9} +(0.570276 + 1.24873i) q^{10} +(-1.98926 - 0.584100i) q^{11} +(-0.110783 - 0.0325288i) q^{12} +(-0.425839 - 0.932456i) q^{13} +(0.435418 - 3.02840i) q^{14} +(-0.654861 + 0.755750i) q^{15} +(-1.56019 + 3.41635i) q^{16} +(-3.33083 - 2.14059i) q^{17} +(-0.390736 - 2.71763i) q^{18} +(-0.879900 + 0.565477i) q^{19} +(-0.0756100 - 0.0872586i) q^{20} +(2.13843 - 0.627899i) q^{21} -2.84612 q^{22} +(2.01691 + 4.35110i) q^{23} -2.90407 q^{24} +(-0.959493 + 0.281733i) q^{25} +(-0.921540 - 1.06351i) q^{26} +(4.20627 - 2.70320i) q^{27} +(0.0366213 + 0.254707i) q^{28} +(4.95274 + 3.18293i) q^{29} +(-0.570276 + 1.24873i) q^{30} +(-2.78201 + 3.21061i) q^{31} +(0.0928329 - 0.645667i) q^{32} +(-0.861256 - 1.88589i) q^{33} +(-5.21519 - 1.53132i) q^{34} +(2.13843 + 0.627899i) q^{35} +(0.0959274 + 0.210052i) q^{36} +(0.851751 - 5.92406i) q^{37} +(-0.940282 + 1.08514i) q^{38} +(0.425839 - 0.932456i) q^{39} +(-2.44306 - 1.57006i) q^{40} +(1.36297 + 9.47964i) q^{41} +(2.57385 - 1.65411i) q^{42} +(-1.23278 - 1.42270i) q^{43} +(0.229680 - 0.0674400i) q^{44} +2.00000 q^{45} +(4.33945 + 4.95112i) q^{46} -7.61130 q^{47} +(-3.60362 + 1.05812i) q^{48} +(1.33124 + 1.53634i) q^{49} +(-1.15486 + 0.742184i) q^{50} +(-0.563476 - 3.91906i) q^{51} +(0.0995681 + 0.0639885i) q^{52} +(4.95792 - 10.8563i) q^{53} +(4.49492 - 5.18741i) q^{54} +(0.295053 - 2.05214i) q^{55} +(2.68870 + 5.88744i) q^{56} +(-1.00357 - 0.294675i) q^{57} +(7.75466 + 2.27697i) q^{58} +(4.75662 + 10.4155i) q^{59} +(0.0164316 - 0.114284i) q^{60} +(4.20330 - 4.85087i) q^{61} +(-2.42267 + 5.30490i) q^{62} +(-3.74982 - 2.40986i) q^{63} +(-1.19644 - 8.32140i) q^{64} +(0.862362 - 0.554206i) q^{65} +(-1.86381 - 2.15095i) q^{66} +(3.93196 - 1.15453i) q^{67} +0.457147 q^{68} +(-1.96755 + 4.37364i) q^{69} +3.05954 q^{70} +(-9.69553 + 2.84686i) q^{71} +(3.80353 + 4.38950i) q^{72} +(7.65481 - 4.91945i) q^{73} +(-1.16927 - 8.13247i) q^{74} +(-0.841254 - 0.540641i) q^{75} +(0.0501671 - 0.109851i) q^{76} +(-3.02588 + 3.49206i) q^{77} +(0.200270 - 1.39291i) q^{78} +(1.59168 + 3.48530i) q^{79} +(-3.60362 - 1.05812i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(5.46160 + 11.9592i) q^{82} +(-1.03645 + 7.20866i) q^{83} +(-0.168513 + 0.194474i) q^{84} +(1.64478 - 3.60157i) q^{85} +(-2.17403 - 1.39717i) q^{86} +(0.837855 + 5.82741i) q^{87} +(5.06506 - 3.25512i) q^{88} +(6.80606 + 7.85461i) q^{89} +(2.63436 - 0.773517i) q^{90} -2.28463 q^{91} +(-0.467509 - 0.296726i) q^{92} -4.24824 q^{93} +(-10.0254 + 2.94373i) q^{94} +(-0.684944 - 0.790468i) q^{95} +(0.548755 - 0.352663i) q^{96} +(-0.207978 - 1.44652i) q^{97} +(2.34767 + 1.50876i) q^{98} +(-1.72251 + 3.77178i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9} - 5 q^{10} + 8 q^{11} + q^{12} - 3 q^{14} - q^{15} + 5 q^{16} - 23 q^{17} - 10 q^{18} - 13 q^{19} + q^{20} + 6 q^{21} + 4 q^{22} - 21 q^{23} - 6 q^{24} - q^{25} + 11 q^{26} - 5 q^{27} - 6 q^{28} + 2 q^{29} + 5 q^{30} - 20 q^{31} - 15 q^{32} + 3 q^{33} + 16 q^{34} + 6 q^{35} + 24 q^{36} + 13 q^{37} + 21 q^{38} - 6 q^{40} - 5 q^{41} + 3 q^{42} + 15 q^{43} + 19 q^{44} + 20 q^{45} - 16 q^{46} - 52 q^{47} + 6 q^{48} + 4 q^{49} - 6 q^{50} - 10 q^{51} + 22 q^{52} + 6 q^{53} - 30 q^{54} + 3 q^{55} + 3 q^{56} + 2 q^{57} + 45 q^{58} + 5 q^{59} + 10 q^{60} - 3 q^{61} - 54 q^{62} - 10 q^{63} - 34 q^{64} - 4 q^{66} + 20 q^{67} + 32 q^{68} - q^{69} - 8 q^{70} - 22 q^{71} + 32 q^{72} + 43 q^{73} + q^{74} + q^{75} - 2 q^{76} + 4 q^{77} + 11 q^{78} + 51 q^{79} + 6 q^{80} - q^{81} + 58 q^{82} - 17 q^{83} + 6 q^{84} + q^{85} - 9 q^{86} - 2 q^{87} + 7 q^{88} + 57 q^{89} + 10 q^{90} - 22 q^{91} - 43 q^{92} + 20 q^{93} - 81 q^{94} - 9 q^{95} - 7 q^{96} + 52 q^{97} + 24 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9 - 5 * q^10 + 8 * q^11 + q^12 - 3 * q^14 - q^15 + 5 * q^16 - 23 * q^17 - 10 * q^18 - 13 * q^19 + q^20 + 6 * q^21 + 4 * q^22 - 21 * q^23 - 6 * q^24 - q^25 + 11 * q^26 - 5 * q^27 - 6 * q^28 + 2 * q^29 + 5 * q^30 - 20 * q^31 - 15 * q^32 + 3 * q^33 + 16 * q^34 + 6 * q^35 + 24 * q^36 + 13 * q^37 + 21 * q^38 - 6 * q^40 - 5 * q^41 + 3 * q^42 + 15 * q^43 + 19 * q^44 + 20 * q^45 - 16 * q^46 - 52 * q^47 + 6 * q^48 + 4 * q^49 - 6 * q^50 - 10 * q^51 + 22 * q^52 + 6 * q^53 - 30 * q^54 + 3 * q^55 + 3 * q^56 + 2 * q^57 + 45 * q^58 + 5 * q^59 + 10 * q^60 - 3 * q^61 - 54 * q^62 - 10 * q^63 - 34 * q^64 - 4 * q^66 + 20 * q^67 + 32 * q^68 - q^69 - 8 * q^70 - 22 * q^71 + 32 * q^72 + 43 * q^73 + q^74 + q^75 - 2 * q^76 + 4 * q^77 + 11 * q^78 + 51 * q^79 + 6 * q^80 - q^81 + 58 * q^82 - 17 * q^83 + 6 * q^84 + q^85 - 9 * q^86 - 2 * q^87 + 7 * q^88 + 57 * q^89 + 10 * q^90 - 22 * q^91 - 43 * q^92 + 20 * q^93 - 81 * q^94 - 9 * q^95 - 7 * q^96 + 52 * q^97 + 24 * q^98 + 6 * q^99

Introduction

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