LMFDB - Embedded newform 115.2.g.b.101.2

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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 12 x^{18} - 12 x^{17} + 56 x^{16} - 155 x^{15} + 551 x^{14} - 1189 x^{13} + \cdots + 1437601 $ x^20 - x^19 + 12x^18 - 12x^17 + 56x^16 - 155x^15 + 551x^14 - 1189x^13 + 3851x^12 - 10594x^11 + 18470x^10 - 22715x^9 + 56089x^8 + 1474x^7 - 31240x^6 + 12001x^5 + 243089x^4 + 225907x^3 + 23958x^2 + 857285x + 1437601
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			101.2
Root			$2.10016 - 0.616663i$ of defining polynomial
Character	$\chi$	$=$	115.101
Dual form			115.2.g.b.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61435 + 0.474017i) q^{2} +(1.43337 + 1.65420i) q^{3} +(0.698939 - 0.449181i) q^{4} +(0.142315 + 0.989821i) q^{5} +(-3.09809 - 1.99102i) q^{6} +(-0.775475 + 1.69805i) q^{7} +(1.28820 - 1.48666i) q^{8} +(-0.254878 + 1.77272i) q^{9} +O(q^{10})$	\(q+(-1.61435 + 0.474017i) q^{2} +(1.43337 + 1.65420i) q^{3} +(0.698939 - 0.449181i) q^{4} +(0.142315 + 0.989821i) q^{5} +(-3.09809 - 1.99102i) q^{6} +(-0.775475 + 1.69805i) q^{7} +(1.28820 - 1.48666i) q^{8} +(-0.254878 + 1.77272i) q^{9} +(-0.698939 - 1.53046i) q^{10} +(-4.02174 - 1.18089i) q^{11} +(1.74488 + 0.512342i) q^{12} +(2.36374 + 5.17587i) q^{13} +(0.446985 - 3.10885i) q^{14} +(-1.43337 + 1.65420i) q^{15} +(-2.06519 + 4.52213i) q^{16} +(-0.151987 - 0.0976762i) q^{17} +(-0.428834 - 2.98261i) q^{18} +(2.74511 - 1.76418i) q^{19} +(0.544078 + 0.627899i) q^{20} +(-3.92047 + 1.15115i) q^{21} +7.05228 q^{22} +(3.75681 - 2.98100i) q^{23} +4.30571 q^{24} +(-0.959493 + 0.281733i) q^{25} +(-6.26937 - 7.23523i) q^{26} +(2.22630 - 1.43076i) q^{27} +(0.220723 + 1.53516i) q^{28} +(-0.637100 - 0.409439i) q^{29} +(1.52985 - 3.34991i) q^{30} +(7.00791 - 8.08755i) q^{31} +(0.630471 - 4.38502i) q^{32} +(-3.81123 - 8.34543i) q^{33} +(0.291661 + 0.0856394i) q^{34} +(-1.79113 - 0.525924i) q^{35} +(0.618126 + 1.35351i) q^{36} +(0.204624 - 1.42319i) q^{37} +(-3.59533 + 4.14923i) q^{38} +(-5.17381 + 11.3291i) q^{39} +(1.65486 + 1.06351i) q^{40} +(0.414944 + 2.88600i) q^{41} +(5.78336 - 3.71674i) q^{42} +(3.64309 + 4.20435i) q^{43} +(-3.34138 + 0.981119i) q^{44} -1.79095 q^{45} +(-4.65178 + 6.59318i) q^{46} -2.05166 q^{47} +(-10.4407 + 3.06567i) q^{48} +(2.30200 + 2.65665i) q^{49} +(1.41542 - 0.909632i) q^{50} +(-0.0562783 - 0.391424i) q^{51} +(3.97701 + 2.55587i) q^{52} +(-1.10445 + 2.41842i) q^{53} +(-2.91583 + 3.36505i) q^{54} +(0.596517 - 4.14886i) q^{55} +(1.52547 + 3.34030i) q^{56} +(6.85307 + 2.01224i) q^{57} +(1.22259 + 0.358983i) q^{58} +(-4.12836 - 9.03985i) q^{59} +(-0.258805 + 1.80003i) q^{60} +(0.277718 - 0.320503i) q^{61} +(-7.47960 + 16.3780i) q^{62} +(-2.81252 - 1.80749i) q^{63} +(-0.354232 - 2.46373i) q^{64} +(-4.78679 + 3.07629i) q^{65} +(10.1085 + 11.6659i) q^{66} +(-13.0871 + 3.84272i) q^{67} -0.150104 q^{68} +(10.3161 + 1.94164i) q^{69} +3.14082 q^{70} +(8.95568 - 2.62962i) q^{71} +(2.30710 + 2.66253i) q^{72} +(-10.0300 + 6.44590i) q^{73} +(0.344281 + 2.39453i) q^{74} +(-1.84135 - 1.18337i) q^{75} +(1.12623 - 2.46610i) q^{76} +(5.12398 - 5.91338i) q^{77} +(2.98219 - 20.7416i) q^{78} +(-5.10681 - 11.1824i) q^{79} +(-4.77001 - 1.40060i) q^{80} +(10.7131 + 3.14564i) q^{81} +(-2.03788 - 4.46234i) q^{82} +(0.859580 - 5.97851i) q^{83} +(-2.22309 + 2.56559i) q^{84} +(0.0750520 - 0.164341i) q^{85} +(-7.87417 - 5.06042i) q^{86} +(-0.235907 - 1.64077i) q^{87} +(-6.93640 + 4.45775i) q^{88} +(-0.992535 - 1.14545i) q^{89} +(2.89122 - 0.848939i) q^{90} -10.6219 q^{91} +(1.28678 - 3.77102i) q^{92} +23.4234 q^{93} +(3.31210 - 0.972520i) q^{94} +(2.13689 + 2.46610i) q^{95} +(8.15741 - 5.24245i) q^{96} +(-2.19640 - 15.2763i) q^{97} +(-4.97554 - 3.19758i) q^{98} +(3.11844 - 6.82842i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} + 10 q^{13} + 3 q^{14} - q^{15} - 36 q^{16} - 9 q^{17} + 10 q^{18} + 24 q^{19} + 4 q^{20} + 25 q^{21} + 6 q^{22} + 11 q^{23} - 2 q^{25} - 2 q^{26} + 28 q^{27} - 8 q^{28} + 12 q^{29} - 2 q^{30} + 10 q^{31} - 50 q^{32} - 49 q^{33} - 7 q^{34} + 4 q^{35} + 43 q^{36} - 18 q^{37} - 29 q^{38} - 52 q^{39} + 22 q^{40} + 10 q^{41} - 5 q^{42} + 35 q^{43} + 6 q^{44} - 38 q^{45} - 33 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 18 q^{50} + 50 q^{51} + 9 q^{52} - 5 q^{53} + 23 q^{54} + 8 q^{55} + 33 q^{57} + 35 q^{58} + 41 q^{59} - 2 q^{60} - 13 q^{61} - 2 q^{62} - 46 q^{63} + 16 q^{64} - 10 q^{65} + 56 q^{66} - 9 q^{67} + 26 q^{68} - 45 q^{69} + 8 q^{70} - 19 q^{71} - 27 q^{73} + 8 q^{74} + q^{75} + 4 q^{76} - 64 q^{77} - 27 q^{78} - 83 q^{79} - 8 q^{80} + 12 q^{81} + 31 q^{82} + 67 q^{83} + 28 q^{84} - 13 q^{85} - 73 q^{86} + 69 q^{87} + 22 q^{88} - 5 q^{89} - 10 q^{90} - 84 q^{91} + 11 q^{92} + 28 q^{93} - 37 q^{94} - 2 q^{95} + 14 q^{96} + 18 q^{97} + 8 q^{98} + 62 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 10 * q^13 + 3 * q^14 - q^15 - 36 * q^16 - 9 * q^17 + 10 * q^18 + 24 * q^19 + 4 * q^20 + 25 * q^21 + 6 * q^22 + 11 * q^23 - 2 * q^25 - 2 * q^26 + 28 * q^27 - 8 * q^28 + 12 * q^29 - 2 * q^30 + 10 * q^31 - 50 * q^32 - 49 * q^33 - 7 * q^34 + 4 * q^35 + 43 * q^36 - 18 * q^37 - 29 * q^38 - 52 * q^39 + 22 * q^40 + 10 * q^41 - 5 * q^42 + 35 * q^43 + 6 * q^44 - 38 * q^45 - 33 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 18 * q^50 + 50 * q^51 + 9 * q^52 - 5 * q^53 + 23 * q^54 + 8 * q^55 + 33 * q^57 + 35 * q^58 + 41 * q^59 - 2 * q^60 - 13 * q^61 - 2 * q^62 - 46 * q^63 + 16 * q^64 - 10 * q^65 + 56 * q^66 - 9 * q^67 + 26 * q^68 - 45 * q^69 + 8 * q^70 - 19 * q^71 - 27 * q^73 + 8 * q^74 + q^75 + 4 * q^76 - 64 * q^77 - 27 * q^78 - 83 * q^79 - 8 * q^80 + 12 * q^81 + 31 * q^82 + 67 * q^83 + 28 * q^84 - 13 * q^85 - 73 * q^86 + 69 * q^87 + 22 * q^88 - 5 * q^89 - 10 * q^90 - 84 * q^91 + 11 * q^92 + 28 * q^93 - 37 * q^94 - 2 * q^95 + 14 * q^96 + 18 * q^97 + 8 * q^98 + 62 * 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 $

$2$	−1.61435	+	0.474017i	−1.14152	+	0.335181i	−0.797226	−	0.603681i	$-0.793700\pi$
$2$	−1.61435	+	0.474017i	−1.14152	+	0.335181i	−0.344295	+	0.938862i	$0.611882\pi$
$3$	1.43337	+	1.65420i	0.827559	+	0.955054i	0.999549	−	0.0300448i	$-0.00956501\pi$
$3$	1.43337	+	1.65420i	0.827559	+	0.955054i	−0.171990	+	0.985099i	$0.555020\pi$
$4$	0.698939	−	0.449181i	0.349469	−	0.224590i
$5$	0.142315	+	0.989821i	0.0636451	+	0.442662i
$5$	0.142315	+	0.989821i	0.0636451	+	0.442662i
$6$	−3.09809	−	1.99102i	−1.26479	−	0.812832i
$7$	−0.775475	+	1.69805i	−0.293102	+	0.641804i	−0.997699	−	0.0678041i	$-0.978401\pi$
$7$	−0.775475	+	1.69805i	−0.293102	+	0.641804i	0.704597	+	0.709608i	$0.251128\pi$
$8$	1.28820	−	1.48666i	0.455448	−	0.525615i
$9$	−0.254878	+	1.77272i	−0.0849594	+	0.590905i
$10$	−0.698939	−	1.53046i	−0.221024	−	0.483975i
$11$	−4.02174	−	1.18089i	−1.21260	−	0.356052i	−0.387943	−	0.921683i	$-0.626814\pi$
$11$	−4.02174	−	1.18089i	−1.21260	−	0.356052i	−0.824658	+	0.565632i	$0.808632\pi$
$12$	1.74488	+	0.512342i	0.503702	+	0.147900i
$13$	2.36374	+	5.17587i	0.655584	+	1.43553i	0.886581	+	0.462574i	$0.153074\pi$
$13$	2.36374	+	5.17587i	0.655584	+	1.43553i	−0.230997	+	0.972955i	$0.574199\pi$
$14$	0.446985	−	3.10885i	0.119462	−	0.830875i
$15$	−1.43337	+	1.65420i	−0.370096	+	0.427113i
$16$	−2.06519	+	4.52213i	−0.516297	+	1.13053i
$17$	−0.151987	−	0.0976762i	−0.0368623	−	0.0236900i	0.522080	−	0.852897i	$-0.325156\pi$
$17$	−0.151987	−	0.0976762i	−0.0368623	−	0.0236900i	−0.558942	+	0.829207i	$0.688793\pi$
$18$	−0.428834	−	2.98261i	−0.101077	−	0.703007i
$19$	2.74511	−	1.76418i	0.629771	−	0.404730i	−0.186453	−	0.982464i	$-0.559699\pi$
$19$	2.74511	−	1.76418i	0.629771	−	0.404730i	0.816225	+	0.577734i	$0.196063\pi$
$20$	0.544078	+	0.627899i	0.121660	+	0.140403i
$21$	−3.92047	+	1.15115i	−0.855517	+	0.251202i
$22$	7.05228			1.50355
$23$	3.75681	−	2.98100i	0.783350	−	0.621581i
$23$	3.75681	−	2.98100i	0.783350	−	0.621581i
$24$	4.30571			0.878900
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$	−6.26937	−	7.23523i	−1.22952	−	1.41895i
$27$	2.22630	−	1.43076i	0.428451	−	0.275349i
$28$	0.220723	+	1.53516i	0.0417128	+	0.290119i
$29$	−0.637100	−	0.409439i	−0.118306	−	0.0760309i	0.480149	−	0.877187i	$-0.340582\pi$
$29$	−0.637100	−	0.409439i	−0.118306	−	0.0760309i	−0.598456	+	0.801156i	$0.704219\pi$
$30$	1.52985	−	3.34991i	0.279312	−	0.611607i
$31$	7.00791	−	8.08755i	1.25866	−	1.45257i	0.420356	−	0.907359i	$-0.361905\pi$
$31$	7.00791	−	8.08755i	1.25866	−	1.45257i	0.838301	−	0.545208i	$-0.183549\pi$
$32$	0.630471	−	4.38502i	0.111452	−	0.775169i
$33$	−3.81123	−	8.34543i	−0.663450	−	1.45275i
$34$	0.291661	+	0.0856394i	0.0500195	+	0.0146870i
$35$	−1.79113	−	0.525924i	−0.302757	−	0.0888973i
$36$	0.618126	+	1.35351i	0.103021	+	0.225584i
$37$	0.204624	−	1.42319i	0.0336399	−	0.233971i	−0.966064	−	0.258303i	$-0.916837\pi$
$37$	0.204624	−	1.42319i	0.0336399	−	0.233971i	0.999704	+	0.0243319i	$0.00774585\pi$
$38$	−3.59533	+	4.14923i	−0.583239	+	0.673094i
$39$	−5.17381	+	11.3291i	−0.828473	+	1.81410i
$40$	1.65486	+	1.06351i	0.261656	+	0.168156i
$41$	0.414944	+	2.88600i	0.0648034	+	0.450718i	0.996227	+	0.0867816i	$0.0276582\pi$
$41$	0.414944	+	2.88600i	0.0648034	+	0.450718i	−0.931424	+	0.363936i	$0.881433\pi$
$42$	5.78336	−	3.71674i	0.892392	−	0.573505i
$43$	3.64309	+	4.20435i	0.555566	+	0.641158i	0.962171	−	0.272447i	$-0.0878328\pi$
$43$	3.64309	+	4.20435i	0.555566	+	0.641158i	−0.406605	+	0.913604i	$0.633287\pi$
$44$	−3.34138	+	0.981119i	−0.503733	+	0.147909i
$45$	−1.79095			−0.266978
$46$	−4.65178	+	6.59318i	−0.685868	+	0.972111i
$47$	−2.05166			−0.299265			−0.149632	−	0.988742i	$-0.547809\pi$
$47$	−2.05166			−0.299265			−0.149632	+	0.988742i	$0.547809\pi$
$48$	−10.4407	+	3.06567i	−1.50698	+	0.442491i
$49$	2.30200	+	2.65665i	0.328857	+	0.379521i
$50$	1.41542	−	0.909632i	0.200170	−	0.128641i
$51$	−0.0562783	−	0.391424i	−0.00788053	−	0.0548103i
$52$	3.97701	+	2.55587i	0.551512	+	0.354435i
$53$	−1.10445	+	2.41842i	−0.151709	+	0.332195i	−0.970193	−	0.242333i	$-0.922087\pi$
$53$	−1.10445	+	2.41842i	−0.151709	+	0.332195i	0.818485	+	0.574529i	$0.194815\pi$
$54$	−2.91583	+	3.36505i	−0.396794	+	0.457925i
$55$	0.596517	−	4.14886i	0.0804343	−	0.559433i
$56$	1.52547	+	3.34030i	0.203849	+	0.446367i
$57$	6.85307	+	2.01224i	0.907712	+	0.266528i
$58$	1.22259	+	0.358983i	0.160533	+	0.0471368i
$59$	−4.12836	−	9.03985i	−0.537467	−	1.17689i	−0.962393	−	0.271661i	$-0.912427\pi$
$59$	−4.12836	−	9.03985i	−0.537467	−	1.17689i	0.424926	−	0.905228i	$-0.360300\pi$
$60$	−0.258805	+	1.80003i	−0.0334116	+	0.232383i
$61$	0.277718	−	0.320503i	0.0355581	−	0.0410363i	−0.737692	−	0.675137i	$-0.764084\pi$
$61$	0.277718	−	0.320503i	0.0355581	−	0.0410363i	0.773250	+	0.634101i	$0.218630\pi$
$62$	−7.47960	+	16.3780i	−0.949910	+	2.08001i
$63$	−2.81252	−	1.80749i	−0.354344	−	0.227723i
$64$	−0.354232	−	2.46373i	−0.0442789	−	0.307967i
$65$	−4.78679	+	3.07629i	−0.593729	+	0.381566i
$66$	10.1085	+	11.6659i	1.24428	+	1.43597i
$67$	−13.0871	+	3.84272i	−1.59884	+	0.469463i	−0.955224	−	0.295882i	$-0.904386\pi$
$67$	−13.0871	+	3.84272i	−1.59884	+	0.469463i	−0.643620	+	0.765345i	$0.722568\pi$
$68$	−0.150104			−0.0182028
$69$	10.3161	+	1.94164i	1.24191	+	0.233746i
$70$	3.14082			0.375399
$71$	8.95568	−	2.62962i	1.06284	−	0.312079i	0.296848	−	0.954925i	$-0.404065\pi$
$71$	8.95568	−	2.62962i	1.06284	−	0.312079i	0.765996	+	0.642846i	$0.222246\pi$
$72$	2.30710	+	2.66253i	0.271894	+	0.313782i
$73$	−10.0300	+	6.44590i	−1.17392	+	0.754435i	−0.974259	−	0.225429i	$-0.927621\pi$
$73$	−10.0300	+	6.44590i	−1.17392	+	0.754435i	−0.199664	+	0.979864i	$0.563985\pi$
$74$	0.344281	+	2.39453i	0.0400219	+	0.278358i
$75$	−1.84135	−	1.18337i	−0.212621	−	0.136643i
$76$	1.12623	−	2.46610i	0.129187	−	0.282881i
$77$	5.12398	−	5.91338i	0.583931	−	0.673893i
$78$	2.98219	−	20.7416i	0.337667	−	2.34852i
$79$	−5.10681	−	11.1824i	−0.574561	−	1.25811i	−0.944333	−	0.328991i	$-0.893291\pi$
$79$	−5.10681	−	11.1824i	−0.574561	−	1.25811i	0.369772	−	0.929123i	$-0.379436\pi$
$80$	−4.77001	−	1.40060i	−0.533303	−	0.156592i
$81$	10.7131	+	3.14564i	1.19034	+	0.349516i
$82$	−2.03788	−	4.46234i	−0.225046	−	0.492783i
$83$	0.859580	−	5.97851i	0.0943512	−	0.656227i	−0.886681	−	0.462382i	$-0.846995\pi$
$83$	0.859580	−	5.97851i	0.0943512	−	0.656227i	0.981032	−	0.193845i	$-0.0620960\pi$
$84$	−2.22309	+	2.56559i	−0.242559	+	0.279928i
$85$	0.0750520	−	0.164341i	0.00814053	−	0.0178253i
$86$	−7.87417	−	5.06042i	−0.849094	−	0.545679i
$87$	−0.235907	−	1.64077i	−0.0252919	−	0.175909i
$88$	−6.93640	+	4.45775i	−0.739422	+	0.475198i
$89$	−0.992535	−	1.14545i	−0.105208	−	0.121417i	0.700703	−	0.713453i	$-0.252870\pi$
$89$	−0.992535	−	1.14545i	−0.105208	−	0.121417i	−0.805912	+	0.592036i	$0.798324\pi$
$90$	2.89122	−	0.848939i	0.304761	−	0.0894860i
$91$	−10.6219			−1.11348
$92$	1.28678	−	3.77102i	0.134156	−	0.393156i
$93$	23.4234			2.42889
$94$	3.31210	−	0.972520i	0.341617	−	0.100308i
$95$	2.13689	+	2.46610i	0.219240	+	0.253017i
$96$	8.15741	−	5.24245i	0.832562	−	0.535055i
$97$	−2.19640	−	15.2763i	−0.223010	−	1.55107i	−0.726559	−	0.687105i	$-0.758881\pi$
$97$	−2.19640	−	15.2763i	−0.223010	−	1.55107i	0.503548	−	0.863967i	$-0.332028\pi$
$98$	−4.97554	−	3.19758i	−0.502605	−	0.323005i
$99$	3.11844	−	6.82842i	0.313415	−	0.686282i
$100$	−0.544078	+	0.627899i	−0.0544078	+	0.0627899i
$101$	−1.18326	+	8.22973i	−0.117738	+	0.818888i	0.842298	+	0.539012i	$0.181202\pi$
$101$	−1.18326	+	8.22973i	−0.117738	+	0.818888i	−0.960036	+	0.279876i	$0.909707\pi$
$102$	0.276395	+	0.605220i	0.0273671	+	0.0599257i
$103$	−4.64717	−	1.36453i	−0.457899	−	0.134451i	0.0446449	−	0.999003i	$-0.485784\pi$
$103$	−4.64717	−	1.36453i	−0.457899	−	0.134451i	−0.502544	+	0.864552i	$0.667603\pi$
$104$	10.7397	+	3.15347i	1.05312	+	0.309224i
$105$	−1.69738	−	3.71674i	−0.165647	−	0.362717i
$106$	0.636609	−	4.42771i	0.0618329	−	0.430058i
$107$	−11.4206	+	13.1801i	−1.10407	+	1.27417i	−0.145489	+	0.989360i	$0.546476\pi$
$107$	−11.4206	+	13.1801i	−1.10407	+	1.27417i	−0.958584	+	0.284809i	$0.908070\pi$
$108$	0.913379	−	2.00002i	0.0878899	−	0.192452i
$109$	4.20400	+	2.70175i	0.402671	+	0.258781i	0.726264	−	0.687415i	$-0.241255\pi$
$109$	4.20400	+	2.70175i	0.402671	+	0.258781i	−0.323594	+	0.946196i	$0.604891\pi$
$110$	1.00364	+	6.98049i	0.0956937	+	0.665564i
$111$	2.64755	−	1.70147i	0.251294	−	0.161497i
$112$	−6.07732	−	7.01360i	−0.574252	−	0.662723i
$113$	9.17803	−	2.69491i	0.863396	−	0.253516i	0.180092	−	0.983650i	$-0.442360\pi$
$113$	9.17803	−	2.69491i	0.863396	−	0.253516i	0.683304	+	0.730134i	$0.260542\pi$
$114$	−12.0171			−1.12551
$115$	3.48531	+	3.29433i	0.325006	+	0.307198i
$116$	−0.629206			−0.0584203
$117$	−9.77782	+	2.87103i	−0.903960	+	0.265426i
$118$	10.9497	+	12.6366i	1.00800	+	1.16329i
$119$	0.283722	−	0.182337i	0.0260087	−	0.0167148i
$120$	0.612767	+	4.26189i	0.0559377	+	0.389055i
$121$	5.52612	+	3.55142i	0.502374	+	0.322856i
$122$	−0.296411	+	0.649049i	−0.0268358	+	0.0587621i
$123$	−4.17926	+	4.82312i	−0.376831	+	0.434886i
$124$	1.26532	−	8.80052i	0.113629	−	0.790310i
$125$	−0.415415	−	0.909632i	−0.0371558	−	0.0813600i
$126$	5.39718	+	1.58475i	0.480819	+	0.141181i
$127$	9.64499	+	2.83203i	0.855855	+	0.251302i	0.680088	−	0.733130i	$-0.261941\pi$
$127$	9.64499	+	2.83203i	0.855855	+	0.251302i	0.175767	+	0.984432i	$0.443760\pi$
$128$	5.42038	+	11.8690i	0.479098	+	1.04908i
$129$	−1.73293	+	12.0528i	−0.152576	+	1.06119i
$130$	6.26937	−	7.23523i	0.549860	−	0.634572i
$131$	1.41825	−	3.10554i	0.123913	−	0.271332i	−0.837502	−	0.546435i	$-0.815985\pi$
$131$	1.41825	−	3.10554i	0.123913	−	0.271332i	0.961415	+	0.275103i	$0.0887119\pi$
$132$	−6.41242	−	4.12101i	−0.558130	−	0.358688i
$133$	0.866900	+	6.02942i	0.0751697	+	0.522817i
$134$	19.3057	−	12.4070i	1.66776	−	1.07180i
$135$	1.73303	+	2.00002i	0.149155	+	0.172134i
$136$	−0.341001	+	0.100127i	−0.0292406	+	0.00858582i
$137$	−23.3656			−1.99626			−0.998130	−	0.0611196i	$-0.980533\pi$
$137$	−23.3656			−1.99626			−0.998130	+	0.0611196i	$0.980533\pi$
$138$	−17.5742	+	1.75550i	−1.49601	+	0.149438i
$139$	−20.3624			−1.72712			−0.863560	−	0.504247i	$-0.831770\pi$
$139$	−20.3624			−1.72712			−0.863560	+	0.504247i	$0.831770\pi$
$140$	−1.48813	+	0.436953i	−0.125770	+	0.0369293i
$141$	−2.94079	−	3.39385i	−0.247659	−	0.285814i
$142$	−13.2111	+	8.49029i	−1.10865	+	0.712489i
$143$	−3.39422	−	23.6073i	−0.283839	−	1.97414i
$144$	−7.49008	−	4.81358i	−0.624173	−	0.401132i
$145$	0.314603	−	0.688884i	0.0261263	−	0.0572087i
$146$	13.1365	−	15.1603i	1.08719	−	1.25468i
$147$	−1.09501	+	7.61594i	−0.0903147	+	0.628153i
$148$	−0.496250	−	1.08664i	−0.0407915	−	0.0893209i
$149$	−8.98747	−	2.63896i	−0.736282	−	0.216192i	−0.107971	−	0.994154i	$-0.534435\pi$
$149$	−8.98747	−	2.63896i	−0.736282	−	0.216192i	−0.628311	+	0.777962i	$0.716254\pi$
$150$	3.53353	+	1.03754i	0.288512	+	0.0847147i
$151$	−7.73868	−	16.9454i	−0.629765	−	1.37899i	−0.908199	−	0.418538i	$-0.862543\pi$
$151$	−7.73868	−	16.9454i	−0.629765	−	1.37899i	0.278434	−	0.960455i	$-0.410185\pi$
$152$	0.913519	−	6.35366i	0.0740962	−	0.515350i
$153$	0.211890	−	0.244534i	0.0171303	−	0.0197694i
$154$	−5.46887	+	11.9751i	−0.440694	+	0.964985i
$155$	9.00256	+	5.78560i	0.723103	+	0.464710i
$156$	1.47262	+	10.2423i	0.117904	+	0.820040i
$157$	18.1477	−	11.6628i	1.44834	−	0.930795i	0.449040	−	0.893512i	$-0.351766\pi$
$157$	18.1477	−	11.6628i	1.44834	−	0.930795i	0.999305	−	0.0372831i	$-0.0118703\pi$
$158$	13.5448	+	15.6316i	1.07757	+	1.24358i
$159$	−5.58365	+	1.63951i	−0.442812	+	0.130021i
$160$	4.43011			0.350231
$161$	2.14858	+	8.69096i	0.169332	+	0.684944i
$162$	−18.7858			−1.47595
$163$	5.25225	−	1.54220i	0.411388	−	0.120794i	−0.0694884	−	0.997583i	$-0.522137\pi$
$163$	5.25225	−	1.54220i	0.411388	−	0.120794i	0.480877	+	0.876788i	$0.340319\pi$
$164$	1.58636	+	1.83075i	0.123874	+	0.142958i
$165$	7.71809	−	4.96012i	0.600853	−	0.386145i
$166$	1.44625	+	10.0589i	0.112251	+	0.780721i
$167$	6.57321	+	4.22434i	0.508650	+	0.326890i	0.769668	−	0.638444i	$-0.220422\pi$
$167$	6.57321	+	4.22434i	0.508650	+	0.326890i	−0.261018	+	0.965334i	$0.584058\pi$
$168$	−3.33897	+	7.31133i	−0.257607	+	0.564082i
$169$	−12.6892	+	14.6441i	−0.976091	+	1.12647i
$170$	−0.0432600	+	0.300880i	−0.00331789	+	0.0230765i
$171$	2.42771	+	5.31595i	0.185652	+	0.406521i
$172$	4.43481	+	1.30218i	0.338151	+	0.0992901i
$173$	3.41709	+	1.00335i	0.259797	+	0.0762832i	0.409037	−	0.912518i	$-0.365865\pi$
$173$	3.41709	+	1.00335i	0.259797	+	0.0762832i	−0.149240	+	0.988801i	$0.547683\pi$
$174$	1.15859	+	2.53696i	0.0878326	+	0.192326i
$175$	0.265666	−	1.84775i	0.0200825	−	0.139677i
$176$	13.6458	−	15.7481i	1.02859	−	1.18706i
$177$	9.03625	−	19.7866i	0.679207	−	1.48725i
$178$	2.14526	+	1.37868i	0.160794	+	0.103336i
$179$	0.553320	+	3.84843i	0.0413571	+	0.287645i	0.999995	+	0.00301799i	$0.000960658\pi$
$179$	0.553320	+	3.84843i	0.0413571	+	0.287645i	−0.958638	+	0.284627i	$0.908130\pi$
$180$	−1.25176	+	0.804458i	−0.0933008	+	0.0599608i
$181$	9.87450	+	11.3958i	0.733966	+	0.847042i	0.992912	−	0.118850i	$-0.0379207\pi$
$181$	9.87450	+	11.3958i	0.733966	+	0.847042i	−0.258946	+	0.965892i	$0.583375\pi$
$182$	17.1476	−	5.03498i	1.27106	−	0.373217i
$183$	0.928251			0.0686183
$184$	0.407791	−	9.42524i	0.0300628	−	0.694838i
$185$	1.43782			0.105711
$186$	−37.8136	+	11.1031i	−2.77263	+	0.814118i
$187$	0.495908	+	0.572308i	0.0362644	+	0.0418513i
$188$	−1.43398	+	0.921564i	−0.104584	+	0.0672120i
$189$	0.703060	+	4.88989i	0.0511401	+	0.355687i
$190$	−4.61867	−	2.96824i	−0.335073	−	0.215339i
$191$	−7.50723	+	16.4385i	−0.543204	+	1.18945i	0.416680	+	0.909053i	$0.363194\pi$
$191$	−7.50723	+	16.4385i	−0.543204	+	1.18945i	−0.959884	+	0.280398i	$0.909534\pi$
$192$	3.56777	−	4.11742i	0.257482	−	0.297149i
$193$	2.42144	−	16.8415i	0.174299	−	1.21228i	−0.695373	−	0.718649i	$-0.744761\pi$
$193$	2.42144	−	16.8415i	0.174299	−	1.21228i	0.869672	−	0.493630i	$-0.164330\pi$
$194$	10.7870	+	23.6202i	0.774460	+	1.69583i
$195$	−11.9501	−	3.50886i	−0.855762	−	0.251274i
$196$	2.80227	+	0.822821i	0.200162	+	0.0587730i
$197$	6.27410	+	13.7384i	0.447011	+	0.978818i	0.990258	+	0.139245i	$0.0444674\pi$
$197$	6.27410	+	13.7384i	0.447011	+	0.978818i	−0.543247	+	0.839573i	$0.682805\pi$
$198$	−1.79747	+	12.5017i	−0.127741	+	0.888456i
$199$	9.33637	−	10.7747i	0.661838	−	0.763802i	−0.321238	−	0.946998i	$-0.604099\pi$
$199$	9.33637	−	10.7747i	0.661838	−	0.763802i	0.983076	+	0.183197i	$0.0586445\pi$
$200$	−0.817178	+	1.78937i	−0.0577832	+	0.126528i
$201$	−25.1154	−	16.1407i	−1.77150	−	1.13847i
$202$	−1.99084	−	13.8466i	−0.140075	−	0.974242i
$203$	1.18930	−	0.764320i	0.0834728	−	0.0536447i
$204$	−0.215155	−	0.248302i	−0.0150639	−	0.0173846i
$205$	−2.79757	+	0.821442i	−0.195391	+	0.0573720i
$206$	8.14898			0.567767
$207$	4.32693	+	7.41956i	0.300743	+	0.515695i
$208$	−28.2875			−1.96139
$209$	−13.1234	+	3.85338i	−0.907766	+	0.266544i
$210$	4.50197	+	5.19555i	0.310665	+	0.358527i
$211$	−5.26949	+	3.38650i	−0.362767	+	0.233136i	−0.709308	−	0.704899i	$-0.750992\pi$
$211$	−5.26949	+	3.38650i	−0.362767	+	0.233136i	0.346541	+	0.938035i	$0.387356\pi$
$212$	0.314361	+	2.18643i	0.0215904	+	0.150164i
$213$	17.1868	+	11.0453i	1.17762	+	0.756809i
$214$	12.1893	−	26.6909i	0.833246	−	1.82455i
$215$	−3.64309	+	4.20435i	−0.248457	+	0.286734i
$216$	0.740869	−	5.15285i	0.0504097	−	0.350607i
$217$	8.29865	+	18.1715i	0.563349	+	1.23356i
$218$	−8.06742	−	2.36881i	−0.546395	−	0.160436i
$219$	−25.0396	−	7.35228i	−1.69202	−	0.496821i
$220$	−1.44666	−	3.16775i	−0.0975339	−	0.213569i
$221$	0.146301	−	1.01755i	0.00984128	−	0.0684476i
$222$	−3.46755	+	4.00176i	−0.232727	+	0.268581i
$223$	2.88508	−	6.31744i	0.193199	−	0.423047i	−0.788097	−	0.615551i	$-0.788933\pi$
$223$	2.88508	−	6.31744i	0.193199	−	0.423047i	0.981296	+	0.192504i	$0.0616608\pi$
$224$	6.95708	+	4.47105i	0.464840	+	0.298734i
$225$	−0.254878	−	1.77272i	−0.0169919	−	0.118181i
$226$	−13.5391	+	8.70108i	−0.900611	+	0.578787i
$227$	−1.80305	−	2.08083i	−0.119673	−	0.138109i	0.692752	−	0.721176i	$-0.256398\pi$
$227$	−1.80305	−	2.08083i	−0.119673	−	0.138109i	−0.812424	+	0.583067i	$0.801853\pi$
$228$	5.69374	−	1.67183i	0.377077	−	0.110720i
$229$	12.7030			0.839440			0.419720	−	0.907654i	$-0.362128\pi$
$229$	12.7030			0.839440			0.419720	+	0.907654i	$0.362128\pi$
$230$	−7.18809	−	3.66613i	−0.473968	−	0.241737i
$231$	17.1265			1.12684
$232$	−1.42941	+	0.419713i	−0.0938454	+	0.0275555i
$233$	3.64245	+	4.20362i	0.238625	+	0.275388i	0.862413	−	0.506206i	$-0.168952\pi$
$233$	3.64245	+	4.20362i	0.238625	+	0.275388i	−0.623788	+	0.781594i	$0.714407\pi$
$234$	14.4239	−	9.26970i	0.942923	−	0.605980i
$235$	−0.291981	−	2.03077i	−0.0190467	−	0.132473i
$236$	−6.94600	−	4.46392i	−0.452146	−	0.290577i
$237$	11.1779	−	24.4762i	0.726083	−	1.58990i
$238$	−0.371596	+	0.428845i	−0.0240870	+	0.0277979i
$239$	−2.60938	+	18.1486i	−0.168787	+	1.17394i	0.712609	+	0.701561i	$0.247513\pi$
$239$	−2.60938	+	18.1486i	−0.168787	+	1.17394i	−0.881396	+	0.472378i	$0.843396\pi$
$240$	−4.52033	−	9.89814i	−0.291786	−	0.638922i
$241$	1.25465	+	0.368399i	0.0808192	+	0.0237307i	0.321892	−	0.946776i	$-0.395681\pi$
$241$	1.25465	+	0.368399i	0.0808192	+	0.0237307i	−0.241073	+	0.970507i	$0.577499\pi$
$242$	−10.6045	−	3.11377i	−0.681686	−	0.200161i
$243$	6.85425	+	15.0087i	0.439700	+	0.962809i
$244$	0.0501438	−	0.348758i	0.00321013	−	0.0223269i
$245$	−2.30200	+	2.65665i	−0.147069	+	0.169727i
$246$	4.46056	−	9.76726i	0.284395	−	0.622738i
$247$	15.6199	+	10.0383i	0.993869	+	0.638721i
$248$	−2.99588	−	20.8368i	−0.190238	−	1.32314i
$249$	11.1218	−	7.14753i	0.704813	−	0.452956i
$250$	1.10181	+	1.27155i	0.0696844	+	0.0804201i
$251$	22.0337	−	6.46968i	1.39076	−	0.408363i	0.501256	−	0.865299i	$-0.332871\pi$
$251$	22.0337	−	6.46968i	1.39076	−	0.408363i	0.889500	+	0.456936i	$0.151053\pi$
$252$	−2.77767			−0.174977
$253$	−18.6292	+	7.55242i	−1.17121	+	0.474817i
$254$	−16.9129			−1.06121
$255$	0.379430	−	0.111411i	0.0237609	−	0.00697682i
$256$	−11.1165	−	12.8291i	−0.694782	−	0.801821i
$257$	−0.603853	+	0.388073i	−0.0376673	+	0.0242073i	−0.559339	−	0.828939i	$-0.688945\pi$
$257$	−0.603853	+	0.388073i	−0.0376673	+	0.0242073i	0.521672	+	0.853146i	$0.325309\pi$
$258$	−2.91567	−	20.2790i	−0.181522	−	1.26251i
$259$	2.25797	+	1.45111i	0.140304	+	0.0901676i
$260$	−1.96387	+	4.30027i	−0.121794	+	0.266691i
$261$	0.888202	−	1.02504i	0.0549783	−	0.0634484i
$262$	−0.817482	+	5.68571i	−0.0505042	+	0.351264i
$263$	−6.95418	−	15.2275i	−0.428813	−	0.938970i	−0.993518	−	0.113677i	$-0.963737\pi$
$263$	−6.95418	−	15.2275i	−0.428813	−	0.938970i	0.564705	−	0.825293i	$-0.308990\pi$
$264$	−17.3165	−	5.08457i	−1.06576	−	0.312934i
$265$	−2.55098	−	0.749036i	−0.156706	−	0.0460129i
$266$	−4.25753	−	9.32269i	−0.261046	−	0.571611i
$267$	0.472126	−	3.28371i	0.0288936	−	0.200959i
$268$	−7.42101	+	8.56430i	−0.453310	+	0.523148i
$269$	3.45265	−	7.56025i	0.210512	−	0.460957i	−0.774693	−	0.632338i	$-0.782096\pi$
$269$	3.45265	−	7.56025i	0.210512	−	0.460957i	0.985205	+	0.171381i	$0.0548228\pi$
$270$	−3.74576	−	2.40726i	−0.227960	−	0.146501i
$271$	1.61856	+	11.2573i	0.0983205	+	0.683834i	0.978052	+	0.208363i	$0.0668135\pi$
$271$	1.61856	+	11.2573i	0.0983205	+	0.683834i	−0.879731	+	0.475472i	$0.842277\pi$
$272$	0.755586	−	0.485586i	0.0458141	−	0.0294429i
$273$	−15.2252	−	17.5708i	−0.921471	−	1.06343i
$274$	37.7204	−	11.0757i	2.27877	−	0.669108i
$275$	4.19153			0.252759
$276$	8.08246	−	3.27670i	0.486507	−	0.197234i
$277$	4.54850			0.273293			0.136647	−	0.990620i	$-0.456368\pi$
$277$	4.54850			0.273293			0.136647	+	0.990620i	$0.456368\pi$
$278$	32.8722	−	9.65214i	1.97154	−	0.578897i
$279$	12.5508	+	14.4844i	0.751395	+	0.867156i
$280$	−3.08921	+	1.98531i	−0.184616	+	0.118645i
$281$	0.774924	+	5.38972i	0.0462281	+	0.321524i	0.999793	+	0.0203365i	$0.00647377\pi$
$281$	0.774924	+	5.38972i	0.0462281	+	0.321524i	−0.953565	+	0.301187i	$0.902617\pi$
$282$	6.35622	+	4.08489i	0.378507	+	0.243252i
$283$	−5.28963	+	11.5827i	−0.314436	+	0.688518i	−0.999189	−	0.0402564i	$-0.987183\pi$
$283$	−5.28963	+	11.5827i	−0.314436	+	0.688518i	0.684754	+	0.728775i	$0.259910\pi$
$284$	5.07829	−	5.86066i	0.301341	−	0.347766i
$285$	−1.01647	+	7.06969i	−0.0602104	+	0.418772i
$286$	16.6698	+	36.5017i	0.985703	+	2.15839i
$287$	−5.22236	−	1.53342i	−0.308266	−	0.0905152i
$288$	7.61270	+	2.23529i	0.448583	+	0.131716i
$289$	−7.04850	−	15.4341i	−0.414617	−	0.907885i
$290$	−0.181337	+	1.26123i	−0.0106485	+	0.0740620i
$291$	22.1218	−	25.5299i	1.29680	−	1.49659i
$292$	−4.11499	+	9.01057i	−0.240812	+	0.527304i
$293$	−20.8224	−	13.3817i	−1.21646	−	0.781768i	−0.234728	−	0.972061i	$-0.575420\pi$
$293$	−20.8224	−	13.3817i	−1.21646	−	0.781768i	−0.981727	+	0.190293i	$0.939056\pi$
$294$	−1.84236	−	12.8139i	−0.107448	−	0.747321i
$295$	8.36031	−	5.37285i	0.486756	−	0.312819i
$296$	−1.85221	−	2.13756i	−0.107657	−	0.124243i
$297$	−10.6432	+	3.12511i	−0.617579	+	0.181338i
$298$	15.7599			0.912945
$299$	24.3094	+	12.3985i	1.40585	+	0.717023i
$300$	−1.81854			−0.104993
$301$	−9.96434	+	2.92580i	−0.574335	+	0.168640i
$302$	20.5254	+	23.6875i	1.18110	+	1.36306i
$303$	−15.3097	+	9.83893i	−0.879518	+	0.565232i
$304$	2.30866	+	16.0571i	0.132411	+	0.920937i
$305$	0.356764	+	0.229279i	0.0204283	+	0.0131285i
$306$	−0.226152	+	0.495205i	−0.0129283	+	0.0283090i
$307$	−12.3617	+	14.2662i	−0.705519	+	0.814213i	−0.989487	−	0.144621i	$-0.953804\pi$
$307$	−12.3617	+	14.2662i	−0.705519	+	0.814213i	0.283968	+	0.958834i	$0.408349\pi$
$308$	0.925168	−	6.43468i	0.0527163	−	0.366650i
$309$	−4.40392	−	9.64324i	−0.250530	−	0.548585i
$310$	−17.2758	−	5.07263i	−0.981199	−	0.288106i
$311$	−10.6970	−	3.14092i	−0.606570	−	0.178105i	−0.0359970	−	0.999352i	$-0.511461\pi$
$311$	−10.6970	−	3.14092i	−0.606570	−	0.178105i	−0.570573	+	0.821247i	$0.693279\pi$
$312$	10.1776	+	22.2858i	0.576193	+	1.26169i
$313$	−1.64619	+	11.4495i	−0.0930480	+	0.647163i	0.888913	+	0.458077i	$0.151462\pi$
$313$	−1.64619	+	11.4495i	−0.0930480	+	0.647163i	−0.981961	+	0.189086i	$0.939447\pi$
$314$	−23.7684	+	27.4302i	−1.34133	+	1.54798i
$315$	1.38883	−	3.04112i	0.0782519	−	0.171348i
$316$	−8.59225	−	5.52190i	−0.483352	−	0.310631i
$317$	1.07700	+	7.49070i	0.0604904	+	0.420720i	0.997455	+	0.0712960i	$0.0227135\pi$
$317$	1.07700	+	7.49070i	0.0604904	+	0.420720i	−0.936965	+	0.349424i	$0.886377\pi$
$318$	8.23683	−	5.29349i	0.461899	−	0.296844i
$319$	2.07875	+	2.39900i	0.116388	+	0.134318i
$320$	2.38825	−	0.701252i	0.133507	−	0.0392012i
$321$	−38.1726			−2.13059
$322$	−7.58823	−	13.0118i	−0.422876	−	0.725121i
$323$	−0.589539			−0.0328028
$324$	8.90074	−	2.61349i	0.494486	−	0.145194i
$325$	−3.72621	−	4.30027i	−0.206693	−	0.238536i
$326$	−7.74796	+	4.97931i	−0.429120	+	0.275779i
$327$	1.55667	+	10.8269i	0.0860841	+	0.598728i
$328$	4.82504	+	3.10087i	0.266418	+	0.171217i
$329$	1.59101	−	3.48382i	0.0877151	−	0.192069i
$330$	−10.1085	+	11.6659i	−0.556457	+	0.642186i
$331$	0.814080	−	5.66205i	0.0447459	−	0.311214i	−0.955141	−	0.296152i	$-0.904296\pi$
$331$	0.814080	−	5.66205i	0.0447459	−	0.311214i	0.999887	−	0.0150619i	$-0.00479455\pi$
$332$	−2.08464	−	4.56472i	−0.114409	−	0.250522i
$333$	2.47076	+	0.725480i	0.135397	+	0.0397561i
$334$	−12.6139	−	3.70377i	−0.690202	−	0.202661i
$335$	−5.66610	−	12.4070i	−0.309572	−	0.677868i
$336$	2.89084	−	20.1062i	0.157708	−	1.09688i
$337$	11.9630	−	13.8060i	0.651665	−	0.752061i	−0.329727	−	0.944076i	$-0.606957\pi$
$337$	11.9630	−	13.8060i	0.651665	−	0.752061i	0.981392	+	0.192015i	$0.0615023\pi$
$338$	13.5433	−	29.6557i	0.736657	−	1.61305i
$339$	17.6135	+	11.3195i	0.956633	+	0.614790i
$340$	−0.0213620	−	0.148576i	−0.00115852	−	0.00805767i
$341$	−37.7345	+	24.2505i	−2.04344	+	1.31324i
$342$	−6.43904	−	7.43105i	−0.348183	−	0.401825i
$343$	−18.8342	+	5.53022i	−1.01695	+	0.298604i
$344$	10.9435			0.590033
$345$	−0.453747	+	10.4874i	−0.0244289	+	0.564623i
$346$	−5.99200			−0.322132
$347$	33.5607	−	9.85431i	1.80163	−	0.529007i	0.803806	−	0.594892i	$-0.202805\pi$
$347$	33.5607	−	9.85431i	1.80163	−	0.529007i	0.997827	+	0.0658849i	$0.0209870\pi$
$348$	−0.901887	−	1.04083i	−0.0483462	−	0.0557945i
$349$	8.55813	−	5.49998i	0.458106	−	0.294407i	−0.291162	−	0.956674i	$-0.594042\pi$
$349$	8.55813	−	5.49998i	0.458106	−	0.294407i	0.749268	+	0.662267i	$0.230405\pi$
$350$	0.446985	+	3.10885i	0.0238923	+	0.166175i
$351$	12.6678	+	8.14110i	0.676157	+	0.434540i
$352$	−7.71381	+	16.8909i	−0.411148	+	0.900288i
$353$	−12.0510	+	13.9076i	−0.641409	+	0.740226i	−0.979623	−	0.200843i	$-0.935632\pi$
$353$	−12.0510	+	13.9076i	−0.641409	+	0.740226i	0.338214	+	0.941069i	$0.390177\pi$
$354$	−5.20851	+	36.2260i	−0.276829	+	1.92539i
$355$	3.87738	+	8.49029i	0.205790	+	0.450618i
$356$	−1.20823	−	0.354769i	−0.0640362	−	0.0188027i
$357$	0.708301	+	0.207976i	0.0374873	+	0.0110073i
$358$	−2.71748	−	5.95044i	−0.143623	−	0.314491i
$359$	4.09979	−	28.5147i	0.216379	−	1.50495i	−0.534875	−	0.844931i	$-0.679641\pi$
$359$	4.09979	−	28.5147i	0.216379	−	1.50495i	0.751253	−	0.660014i	$-0.229450\pi$
$360$	−2.30710	+	2.66253i	−0.121595	+	0.140328i
$361$	−3.46957	+	7.59730i	−0.182609	+	0.399858i
$362$	−21.3427	−	13.7161i	−1.12175	−	0.720905i
$363$	2.04623	+	14.2318i	0.107399	+	0.746977i
$364$	−7.42408	+	4.77117i	−0.389128	+	0.250077i
$365$	−7.80770	−	9.01057i	−0.408674	−	0.471635i
$366$	−1.49853	+	0.440007i	−0.0783292	+	0.0229995i
$367$	−7.35897			−0.384135			−0.192068	−	0.981382i	$-0.561519\pi$
$367$	−7.35897			−0.384135			−0.192068	+	0.981382i	$0.561519\pi$
$368$	5.72193	+	23.1451i	0.298276	+	1.20652i
$369$	−5.22182			−0.271837
$370$	−2.32116	+	0.681553i	−0.120671	+	0.0354323i
$371$	−3.25013	−	3.75085i	−0.168738	−	0.194734i
$372$	16.3715	−	10.5213i	0.848824	−	0.545506i
$373$	1.76363	+	12.2663i	0.0913171	+	0.635124i	0.983156	+	0.182770i	$0.0585065\pi$
$373$	1.76363	+	12.2663i	0.0913171	+	0.635124i	−0.891839	+	0.452354i	$0.850584\pi$
$374$	−1.07185	−	0.688839i	−0.0554243	−	0.0356190i
$375$	0.909270	−	1.99102i	0.0469545	−	0.102816i
$376$	−2.64294	+	3.05012i	−0.136299	+	0.157298i
$377$	0.613265	−	4.26535i	0.0315848	−	0.219677i
$378$	−3.45288	−	7.56075i	−0.177597	−	0.388883i
$379$	13.8688	+	4.07226i	0.712394	+	0.209178i	0.617797	−	0.786338i	$-0.288025\pi$
$379$	13.8688	+	4.07226i	0.712394	+	0.209178i	0.0945974	+	0.995516i	$0.469844\pi$
$380$	2.60128	+	0.763804i	0.133443	+	0.0391823i
$381$	9.14014	+	20.0141i	0.468264	+	1.02535i
$382$	4.32718	−	30.0962i	0.221398	−	1.53985i
$383$	−11.9801	+	13.8258i	−0.612155	+	0.706465i	−0.974198	−	0.225697i	$-0.927534\pi$
$383$	−11.9801	+	13.8258i	−0.612155	+	0.706465i	0.362042	+	0.932162i	$0.382080\pi$
$384$	−11.8642	+	25.9791i	−0.605445	+	1.32574i
$385$	6.58241	+	4.23026i	0.335471	+	0.215594i
$386$	4.07410	+	28.3360i	0.207366	+	1.44226i
$387$	−8.38167	+	5.38657i	−0.426064	+	0.273815i
$388$	−8.39696	−	9.69061i	−0.426291	−	0.491966i
$389$	−27.3273	+	8.02401i	−1.38555	+	0.406833i	−0.887696	−	0.460429i	$-0.847696\pi$
$389$	−27.3273	+	8.02401i	−1.38555	+	0.406833i	−0.497851	+	0.867263i	$0.665877\pi$
$390$	20.9549			1.06109
$391$	−0.862160	+	0.0861220i	−0.0436013	+	0.00435538i
$392$	6.91498			0.349259
$393$	7.17007	−	2.10532i	0.361682	−	0.106199i
$394$	−16.6408	−	19.2045i	−0.838353	−	0.967511i
$395$	10.3418	−	6.64625i	0.520351	−	0.334409i
$396$	−0.887600	−	6.17339i	−0.0446036	−	0.310225i
$397$	3.16061	+	2.03120i	0.158626	+	0.101943i	0.617546	−	0.786535i	$-0.288127\pi$
$397$	3.16061	+	2.03120i	0.158626	+	0.101943i	−0.458919	+	0.888478i	$0.651763\pi$
$398$	−9.96479	+	21.8199i	−0.499490	+	1.09373i
$399$	−8.73129	+	10.0764i	−0.437111	+	0.504453i
$400$	0.707501	−	4.92078i	0.0353751	−	0.246039i
$401$	−6.87471	−	15.0535i	−0.343307	−	0.751737i	0.656690	−	0.754160i	$-0.271956\pi$
$401$	−6.87471	−	15.0535i	−0.343307	−	0.751737i	−0.999997	+	0.00242326i	$0.999229\pi$
$402$	48.1960	+	14.1516i	2.40380	+	0.705819i
$403$	58.4250	+	17.1551i	2.91036	+	0.854558i
$404$	2.86961	+	6.28357i	0.142768	+	0.312619i
$405$	−1.58900	+	11.0517i	−0.0789578	+	0.549164i
$406$	−1.55766	+	1.79763i	−0.0773053	+	0.0892150i
$407$	−2.50357	+	5.48206i	−0.124098	+	0.271736i
$408$	−0.654413	−	0.420566i	−0.0323983	−	0.0208211i
$409$	−1.72576	−	12.0029i	−0.0853331	−	0.593505i	−0.986957	−	0.160984i	$-0.948533\pi$
$409$	−1.72576	−	12.0029i	−0.0853331	−	0.593505i	0.901624	−	0.432521i	$-0.142376\pi$
$410$	4.12689	−	2.65219i	0.203813	−	0.130983i
$411$	−33.4917	−	38.6515i	−1.65202	−	1.90654i
$412$	−3.86101	+	1.13369i	−0.190218	+	0.0558531i
$413$	18.5516			0.912865
$414$	−10.5022	−	9.92675i	−0.516155	−	0.487873i
$415$	6.03999			0.296492
$416$	24.1866	−	7.10182i	1.18584	−	0.348195i
$417$	−29.1870	−	33.6836i	−1.42929	−	1.64949i
$418$	19.3593	−	12.4414i	0.946893	−	0.608531i
$419$	0.160557	+	1.11670i	0.00784370	+	0.0545541i	0.993367	−	0.114984i	$-0.0366816\pi$
$419$	0.160557	+	1.11670i	0.00784370	+	0.0545541i	−0.985524	+	0.169538i	$0.945772\pi$
$420$	−2.85585	−	1.83534i	−0.139351	−	0.0895556i
$421$	16.3966	−	35.9035i	0.799121	−	1.74983i	0.150654	−	0.988587i	$-0.451862\pi$
$421$	16.3966	−	35.9035i	0.799121	−	1.74983i	0.648466	−	0.761243i	$-0.275411\pi$
$422$	6.90157	−	7.96484i	0.335963	−	0.387722i
$423$	0.522922	−	3.63700i	0.0254253	−	0.176837i
$424$	2.17261	+	4.75736i	0.105511	+	0.231038i
$425$	0.173349	+	0.0508999i	0.00840867	+	0.00246901i
$426$	−32.9812	−	9.68414i	−1.59794	−	0.469198i
$427$	0.328869	+	0.720122i	0.0159151	+	0.0348492i
$428$	−2.06207	+	14.3420i	−0.0996739	+	0.693247i
$429$	34.1861	−	39.4529i	1.65052	−	1.90480i
$430$	3.88830	−	8.51420i	0.187511	−	0.410591i
$431$	11.3983	+	7.32526i	0.549038	+	0.352845i	0.785565	−	0.618780i	$-0.212373\pi$
$431$	11.3983	+	7.32526i	0.549038	+	0.352845i	−0.236526	+	0.971625i	$0.576009\pi$
$432$	1.87234	+	13.0224i	0.0900828	+	0.626540i
$433$	−25.5241	+	16.4033i	−1.22661	+	0.788293i	−0.983359	−	0.181671i	$-0.941850\pi$
$433$	−25.5241	+	16.4033i	−1.22661	+	0.788293i	−0.243249	+	0.969964i	$0.578213\pi$
$434$	−22.0105	−	25.4015i	−1.05654	−	1.21931i
$435$	1.59050	−	0.467012i	0.0762585	−	0.0223915i
$436$	4.15191			0.198841
$437$	5.05387	−	14.8108i	0.241759	−	0.708499i
$438$	43.9078			2.09800
$439$	−3.39276	+	0.996204i	−0.161928	+	0.0475462i	−0.361692	−	0.932298i	$-0.617801\pi$
$439$	−3.39276	+	0.996204i	−0.161928	+	0.0475462i	0.199764	+	0.979844i	$0.435982\pi$
$440$	−5.39953	−	6.23139i	−0.257412	−	0.297070i
$441$	−5.29621	+	3.40367i	−0.252201	+	0.162080i
$442$	0.246153	+	1.71203i	0.0117083	+	0.0814330i
$443$	−1.10906	−	0.712752i	−0.0526932	−	0.0338638i	0.514029	−	0.857773i	$-0.328152\pi$
$443$	−1.10906	−	0.712752i	−0.0526932	−	0.0338638i	−0.566722	+	0.823909i	$0.691789\pi$
$444$	1.08620	−	2.37845i	0.0515489	−	0.112876i
$445$	0.992535	−	1.14545i	0.0470507	−	0.0542993i
$446$	−1.66296	+	11.5662i	−0.0787436	+	0.547674i
$447$	−8.51704	−	18.6497i	−0.402842	−	0.882101i
$448$	4.45825	+	1.30906i	0.210633	+	0.0618473i
$449$	−12.6114	−	3.70305i	−0.595170	−	0.174758i	−0.0297453	−	0.999558i	$-0.509470\pi$
$449$	−12.6114	−	3.70305i	−0.595170	−	0.174758i	−0.565425	+	0.824800i	$0.691288\pi$
$450$	1.25176	+	2.74097i	0.0590086	+	0.129211i
$451$	1.73925	−	12.0968i	0.0818981	−	0.569614i
$452$	5.20438	−	6.00617i	0.244793	−	0.282506i
$453$	16.9386	−	37.0904i	0.795845	−	1.74266i
$454$	3.89711	+	2.50452i	0.182900	+	0.117543i
$455$	−1.51166	−	10.5138i	−0.0708677	−	0.492895i
$456$	11.8197	−	7.59603i	0.553506	−	0.355717i
$457$	6.80244	+	7.85043i	0.318205	+	0.367228i	0.892208	−	0.451626i	$-0.149156\pi$
$457$	6.80244	+	7.85043i	0.318205	+	0.367228i	−0.574003	+	0.818853i	$0.694610\pi$
$458$	−20.5072	+	6.02145i	−0.958238	+	0.281364i
$459$	−0.478119			−0.0223167
$460$	3.91577	+	0.737006i	0.182574	+	0.0343631i
$461$	8.79964			0.409840			0.204920	−	0.978779i	$-0.434307\pi$
$461$	8.79964			0.409840			0.204920	+	0.978779i	$0.434307\pi$
$462$	−27.6482	+	8.11826i	−1.28631	+	0.377695i
$463$	−11.9406	−	13.7802i	−0.554929	−	0.640422i	0.407095	−	0.913386i	$-0.366542\pi$
$463$	−11.9406	−	13.7802i	−0.554929	−	0.640422i	−0.962024	+	0.272963i	$0.911996\pi$
$464$	3.16727	−	2.03548i	0.147037	−	0.0944947i
$465$	3.33350	+	23.1850i	0.154587	+	1.07518i
$466$	−7.87279	−	5.05954i	−0.364700	−	0.234379i
$467$	8.55146	−	18.7251i	0.395714	−	0.866494i	−0.601972	−	0.798517i	$-0.705618\pi$
$467$	8.55146	−	18.7251i	0.395714	−	0.866494i	0.997687	−	0.0679769i	$-0.0216544\pi$
$468$	−5.54449	+	6.39868i	−0.256294	+	0.295779i
$469$	3.62358	−	25.2025i	0.167321	−	1.16375i
$470$	1.43398	+	3.13998i	0.0661446	+	0.144837i
$471$	45.3051	+	13.3028i	2.08755	+	0.612960i
$472$	−18.7574	−	5.50766i	−0.863378	−	0.253511i
$473$	−9.68670	−	21.2109i	−0.445395	−	0.975279i
$474$	−6.44296	+	44.8118i	−0.295935	+	2.05827i
$475$	−2.13689	+	2.46610i	−0.0980472	+	0.113152i
$476$	0.116402	−	0.254885i	0.00533527	−	0.0116826i
$477$	−4.00567	−	2.57429i	−0.183407	−	0.117868i
$478$	−4.39030	−	30.5352i	−0.200808	−	1.39665i
$479$	−19.7563	+	12.6966i	−0.902688	+	0.580122i	−0.907586	−	0.419866i	$-0.862077\pi$
$479$	−19.7563	+	12.6966i	−0.902688	+	0.580122i	0.00489857	+	0.999988i	$0.498441\pi$
$480$	6.35001	+	7.32830i	0.289837	+	0.334490i
$481$	7.84993	−	2.30495i	0.357926	−	0.105097i
$482$	−2.20008			−0.100211
$483$	−11.2969	+	16.0116i	−0.514026	+	0.728552i
$484$	5.45765			0.248075
$485$	14.8082	−	4.34808i	0.672406	−	0.197436i
$486$	−18.1796	−	20.9803i	−0.824642	−	0.951687i
$487$	−16.1988	+	10.4103i	−0.734037	+	0.471737i	−0.853494	−	0.521103i	$-0.825521\pi$
$487$	−16.1988	+	10.4103i	−0.734037	+	0.471737i	0.119457	+	0.992839i	$0.461884\pi$
$488$	−0.118724	−	0.825745i	−0.00537439	−	0.0373797i
$489$	10.0796	+	6.47774i	0.455813	+	0.292933i
$490$	2.45694	−	5.37996i	0.110993	−	0.243042i
$491$	6.58009	−	7.59383i	0.296955	−	0.342705i	−0.587590	−	0.809159i	$-0.699923\pi$
$491$	6.58009	−	7.59383i	0.296955	−	0.342705i	0.884545	+	0.466454i	$0.154469\pi$
$492$	−0.754593	+	5.24831i	−0.0340197	+	0.236612i
$493$	0.0568385	+	0.124459i	0.00255988	+	0.00560535i
$494$	−29.9743	−	8.80126i	−1.34861	−	0.395987i
$495$	7.20272	+	2.11491i	0.323738	+	0.0950581i
$496$	22.1003	+	48.3929i	0.992334	+	2.17291i
$497$	−2.47966	+	17.2464i	−0.111228	+	0.773608i
$498$	−14.5664	+	16.8105i	−0.652737	+	0.753298i
$499$	−1.89978	+	4.15993i	−0.0850456	+	0.186224i	−0.947377	−	0.320121i	$-0.896276\pi$
$499$	−1.89978	+	4.15993i	−0.0850456	+	0.186224i	0.862331	+	0.506345i	$0.169004\pi$
$500$	−0.698939	−	0.449181i	−0.0312575	−	0.0200880i
$501$	2.43395	+	16.9285i	0.108741	+	0.756309i
$502$	−32.5035	+	20.8887i	−1.45070	+	0.932309i
$503$	5.23760	+	6.04451i	0.233533	+	0.269511i	0.860405	−	0.509611i	$-0.170211\pi$
$503$	5.23760	+	6.04451i	0.233533	+	0.269511i	−0.626872	+	0.779122i	$0.715665\pi$
$504$	−6.31022	+	1.85285i	−0.281080	+	0.0825324i
$505$	−8.31436			−0.369984
$506$	26.4941	−	21.0228i	1.17781	−	0.934578i
$507$	−42.4127			−1.88361
$508$	8.01335	−	2.35293i	0.355535	−	0.104394i
$509$	20.5087	+	23.6683i	0.909031	+	1.04908i	0.998589	+	0.0530966i	$0.0169091\pi$
$509$	20.5087	+	23.6683i	0.909031	+	1.04908i	−0.0895579	+	0.995982i	$0.528545\pi$
$510$	−0.559724	+	0.359713i	−0.0247850	+	0.0159284i
$511$	−3.16745	−	22.0301i	−0.140120	−	0.974555i
$512$	2.07369	+	1.33268i	0.0916449	+	0.0588966i
$513$	3.58733	−	7.85516i	0.158385	−	0.346814i
$514$	0.790879	−	0.912723i	0.0348842	−	0.0402585i
$515$	0.689282	−	4.79406i	0.0303734	−	0.211252i
$516$	4.20268	+	9.20258i	0.185013	+	0.405121i
$517$	8.25123	+	2.42278i	0.362889	+	0.106554i
$518$	−4.33302	−	1.27229i	−0.190382	−	0.0559012i
$519$	3.23823	+	7.09074i	0.142143	+	0.311249i
$520$	−1.59295	+	11.0792i	−0.0698555	+	0.485856i
$521$	−16.7402	+	19.3192i	−0.733401	+	0.846389i	−0.992850	−	0.119367i	$-0.961913\pi$
$521$	−16.7402	+	19.3192i	−0.733401	+	0.846389i	0.259450	+	0.965757i	$0.416459\pi$
$522$	−0.947986	+	2.07580i	−0.0414922	+	0.0908553i
$523$	−12.7441	−	8.19012i	−0.557260	−	0.358129i	0.231496	−	0.972836i	$-0.425638\pi$
$523$	−12.7441	−	8.19012i	−0.557260	−	0.358129i	−0.788756	+	0.614707i	$0.789274\pi$
$524$	−0.403676	−	2.80763i	−0.0176347	−	0.122652i
$525$	3.43735	−	2.20905i	0.150018	−	0.0964108i
$526$	18.4446	+	21.2862i	0.804223	+	0.928123i
$527$	−1.85507	+	0.544698i	−0.0808082	+	0.0237274i
$528$	45.6100			1.98492
$529$	5.22730	−	22.3981i	0.227274	−	0.973831i
$530$	4.47324			0.194305
$531$	17.0773	−	5.01435i	0.741093	−	0.217604i
$532$	3.31421	+	3.82480i	0.143689	+	0.165826i
$533$	−13.9568	+	8.96946i	−0.604534	+	0.388510i
$534$	0.794355	+	5.52486i	0.0343751	+	0.239084i
$535$	−14.6713	−	9.42865i	−0.634294	−	0.407636i
$536$	−11.1460	+	24.4063i	−0.481433	+	1.05419i
$537$	−5.57296	+	6.43154i	−0.240491	+	0.277541i
$538$	−1.99011	+	13.8415i	−0.0857999	+	0.596751i
$539$	−6.12084	−	13.4028i	−0.263643	−	0.577298i
$540$	2.10965	+	0.619449i	0.0907849	+	0.0266569i
$541$	−12.6787	−	3.72279i	−0.545098	−	0.160055i	−0.00242175	−	0.999997i	$-0.500771\pi$
$541$	−12.6787	−	3.72279i	−0.545098	−	0.160055i	−0.542677	+	0.839942i	$0.682589\pi$
$542$	−7.94910	−	17.4061i	−0.341443	−	0.747656i
$543$	−4.69707	+	32.6688i	−0.201571	+	1.40195i
$544$	−0.524135	+	0.604884i	−0.0224721	+	0.0259342i
$545$	−2.07596	+	4.54571i	−0.0889242	+	0.194717i
$546$	32.9077	+	21.1485i	1.40832	+	0.905073i
$547$	1.00052	+	6.95877i	0.0427792	+	0.297536i	0.999967	+	0.00806959i	$0.00256866\pi$
$547$	1.00052	+	6.95877i	0.0427792	+	0.297536i	−0.957188	+	0.289466i	$0.906522\pi$
$548$	−16.3311	+	10.4954i	−0.697632	+	0.448341i
$549$	0.497377	+	0.574004i	0.0212275	+	0.0244979i
$550$	−6.76661	+	1.98686i	−0.288529	+	0.0847198i
$551$	−2.47123			−0.105278
$552$	16.1758	−	12.8353i	0.688486	−	0.546308i
$553$	22.9485			0.975868
$554$	−7.34289	+	2.15607i	−0.311970	+	0.0916025i
$555$	2.06094	+	2.37845i	0.0874821	+	0.100960i
$556$	−14.2321	+	9.14641i	−0.603575	+	0.387894i
$557$	−2.31738	−	16.1178i	−0.0981907	−	0.682931i	−0.978153	−	0.207887i	$-0.933341\pi$
$557$	−2.31738	−	16.1178i	−0.0981907	−	0.682931i	0.879962	−	0.475044i	$-0.157568\pi$
$558$	−27.1272	−	17.4336i	−1.14839	−	0.738024i
$559$	−13.1499	+	28.7942i	−0.556180	+	1.21786i
$560$	6.07732	−	7.01360i	0.256813	−	0.296379i
$561$	−0.235892	+	1.64066i	−0.00995936	+	0.0692689i
$562$	−3.80582	−	8.33358i	−0.160539	−	0.351531i
$563$	−2.46734	−	0.724477i	−0.103986	−	0.0305331i	0.229326	−	0.973350i	$-0.426348\pi$
$563$	−2.46734	−	0.724477i	−0.103986	−	0.0305331i	−0.333312	+	0.942817i	$0.608166\pi$
$564$	−3.57989	−	1.05115i	−0.150740	−	0.0442614i
$565$	3.97365	+	8.70108i	0.167173	+	0.366057i
$566$	3.04895	−	21.2059i	0.128157	−	0.891350i
$567$	−13.6492	+	15.7520i	−0.573212	+	0.661522i
$568$	7.62734	−	16.7016i	0.320036	−	0.700782i
$569$	23.4788	+	15.0889i	0.984281	+	0.632559i	0.930615	−	0.366000i	$-0.119273\pi$
$569$	23.4788	+	15.0889i	0.984281	+	0.632559i	0.0536659	+	0.998559i	$0.482909\pi$
$570$	−1.71021	−	11.8948i	−0.0716330	−	0.498218i
$571$	0.961243	−	0.617753i	0.0402268	−	0.0258522i	−0.520373	−	0.853939i	$-0.674207\pi$
$571$	0.961243	−	0.617753i	0.0402268	−	0.0258522i	0.560600	+	0.828087i	$0.310571\pi$
$572$	−12.9763	−	14.9755i	−0.542567	−	0.626156i
$573$	−37.9533	+	11.1441i	−1.58552	+	0.465552i
$574$	9.15761			0.382231
$575$	−2.76479	+	3.91866i	−0.115300	+	0.163420i
$576$	4.45779			0.185741
$577$	−0.329327	+	0.0966992i	−0.0137101	+	0.00402564i	−0.288580	−	0.957456i	$-0.593183\pi$
$577$	−0.329327	+	0.0966992i	−0.0137101	+	0.00402564i	0.274870	+	0.961481i	$0.411365\pi$
$578$	18.6948	+	21.5749i	0.777600	+	0.897398i
$579$	31.3301	−	20.1346i	1.30203	−	0.836767i
$580$	−0.0895453	−	0.622801i	−0.00371817	−	0.0258604i
$581$	9.48525	+	6.09580i	0.393515	+	0.252897i
$582$	−23.6108	+	51.7004i	−0.978699	+	2.14305i
$583$	7.29772	−	8.42202i	0.302241	−	0.348804i
$584$	−3.33779	+	23.2148i	−0.138119	+	0.960637i
$585$	−4.23333	−	9.26970i	−0.175027	−	0.383255i
$586$	39.9578	+	11.7327i	1.65064	+	0.484672i
$587$	−8.22173	−	2.41412i	−0.339347	−	0.0996414i	0.107619	−	0.994192i	$-0.465677\pi$
$587$	−8.22173	−	2.41412i	−0.339347	−	0.0996414i	−0.446966	+	0.894551i	$0.647496\pi$
$588$	2.65559	+	5.81493i	0.109515	+	0.239804i
$589$	4.96961	−	34.5644i	0.204769	−	1.42420i
$590$	−10.9497	+	12.6366i	−0.450791	+	0.520241i
$591$	−13.7329	+	30.0708i	−0.564896	+	1.23695i
$592$	6.01326	+	3.86449i	0.247143	+	0.158829i
$593$	−5.58081	−	38.8154i	−0.229177	−	1.59396i	−0.701590	−	0.712581i	$-0.747526\pi$
$593$	−5.58081	−	38.8154i	−0.229177	−	1.59396i	0.472414	−	0.881377i	$-0.343383\pi$
$594$	15.7005	−	10.0901i	0.644198	−	0.414001i
$595$	0.220859	+	0.254885i	0.00905432	+	0.0104492i
$596$	−7.46706	+	2.19253i	−0.305863	+	0.0898094i
$597$	31.2061			1.27718
$598$	−45.1211	−	8.49246i	−1.84514	−	0.347283i
$599$	19.3791			0.791809			0.395905	−	0.918292i	$-0.370431\pi$
$599$	19.3791			0.791809			0.395905	+	0.918292i	$0.370431\pi$
$600$	−4.13130	+	1.21306i	−0.168660	+	0.0495230i
$601$	−13.3216	−	15.3739i	−0.543398	−	0.627115i	0.415934	−	0.909395i	$-0.363455\pi$
$601$	−13.3216	−	15.3739i	−0.543398	−	0.627115i	−0.959332	+	0.282280i	$0.908909\pi$
$602$	14.6991	−	9.44654i	0.599091	−	0.385012i
$603$	−3.47644	−	24.1792i	−0.141571	−	0.984651i
$604$	−13.0204	−	8.36770i	−0.529792	−	0.340477i
$605$	−2.72882	+	5.97529i	−0.110942	+	0.242930i
$606$	20.0514	−	23.1406i	0.814533	−	0.940021i
$607$	−5.79082	+	40.2761i	−0.235042	+	1.63476i	0.440726	+	0.897642i	$0.354721\pi$
$607$	−5.79082	+	40.2761i	−0.235042	+	1.63476i	−0.675769	+	0.737114i	$0.736188\pi$
$608$	−6.00523	−	13.1496i	−0.243544	−	0.533288i
$609$	2.96906	+	0.871794i	0.120312	+	0.0353269i
$610$	−0.684626	−	0.201024i	−0.0277197	−	0.00813924i
$611$	−4.84958	−	10.6191i	−0.196193	−	0.429603i
$612$	0.0382582	−	0.266092i	0.00154650	−	0.0107561i
$613$	5.76724	−	6.65575i	0.232937	−	0.268823i	−0.627233	−	0.778832i	$-0.715812\pi$
$613$	5.76724	−	6.65575i	0.232937	−	0.268823i	0.860169	+	0.510009i	$0.170358\pi$
$614$	13.1938	−	28.8903i	0.532457	−	1.16592i
$615$	−5.36880	−	3.45032i	−0.216491	−	0.139130i
$616$	−2.19050	−	15.2352i	−0.0882577	−	0.613846i
$617$	−4.83429	+	3.10681i	−0.194621	+	0.125075i	−0.634322	−	0.773069i	$-0.718721\pi$
$617$	−4.83429	+	3.10681i	−0.194621	+	0.125075i	0.439701	+	0.898144i	$0.355084\pi$
$618$	11.6805	+	13.4801i	0.469860	+	0.542248i
$619$	9.44084	−	2.77208i	0.379459	−	0.111419i	−0.0864400	−	0.996257i	$-0.527549\pi$
$619$	9.44084	−	2.77208i	0.379459	−	0.111419i	0.465899	+	0.884838i	$0.345731\pi$
$620$	8.89102			0.357072
$621$	4.09871	−	12.0117i	0.164476	−	0.482012i
$622$	18.7576			0.752109
$623$	2.71472	−	0.797112i	0.108763	−	0.0319356i
$624$	−40.5466	−	46.7933i	−1.62316	−	1.87323i
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$	−2.76972	−	19.2638i	−0.110700	−	0.769938i
$627$	−25.1850	−	16.1854i	−1.00579	−	0.646385i
$628$	7.44542	−	16.3032i	0.297105	−	0.650568i
$629$	−0.170112	+	0.196320i	−0.00678281	+	0.00782778i
$630$	−0.800526	+	5.56778i	−0.0318937	+	0.221826i
$631$	3.55896	+	7.79304i	0.141680	+	0.310236i	0.967148	−	0.254212i	$-0.0818162\pi$
$631$	3.55896	+	7.79304i	0.141680	+	0.310236i	−0.825468	+	0.564448i	$0.809089\pi$
$632$	−23.2030	−	6.81301i	−0.922966	−	0.271007i
$633$	−13.1551	−	3.86269i	−0.522869	−	0.153528i
$634$	−5.28938	−	11.5821i	−0.210068	−	0.459985i
$635$	−1.43057	+	9.94986i	−0.0567706	+	0.394848i
$636$	−3.16619	+	3.65398i	−0.125548	+	0.144890i
$637$	−8.30914	+	18.1945i	−0.329220	+	0.720892i
$638$	−4.49300	−	2.88748i	−0.177880	−	0.114316i
$639$	2.37897	+	16.5461i	0.0941106	+	0.654554i
$640$	−10.9768	+	7.05434i	−0.433895	+	0.278847i
$641$	13.0089	+	15.0131i	0.513821	+	0.592981i	0.952073	−	0.305871i	$-0.0989476\pi$
$641$	13.0089	+	15.0131i	0.513821	+	0.592981i	−0.438252	+	0.898852i	$0.644402\pi$
$642$	61.6240	−	18.0945i	2.43211	−	0.714131i
$643$	5.55314			0.218994			0.109497	−	0.993987i	$-0.465076\pi$
$643$	5.55314			0.218994			0.109497	+	0.993987i	$0.465076\pi$
$644$	5.40554	+	5.10935i	0.213008	+	0.201337i
$645$	−12.1768			−0.479459
$646$	0.951725	−	0.279452i	0.0374451	−	0.0109949i
$647$	−20.7709	−	23.9709i	−0.816587	−	0.942392i	0.182580	−	0.983191i	$-0.441555\pi$
$647$	−20.7709	−	23.9709i	−0.816587	−	0.942392i	−0.999167	+	0.0407993i	$0.987010\pi$
$648$	18.4771	−	11.8745i	0.725849	−	0.466475i
$649$	5.92814	+	41.2311i	0.232700	+	1.61846i
$650$	8.05381	+	5.17587i	0.315897	+	0.203014i
$651$	−18.1643	+	39.7742i	−0.711914	+	1.55887i
$652$	2.97828	−	3.43711i	0.116638	−	0.134608i
$653$	−2.82965	+	19.6807i	−0.110733	+	0.770163i	0.856477	+	0.516185i	$0.172648\pi$
$653$	−2.82965	+	19.6807i	−0.110733	+	0.770163i	−0.967210	+	0.253978i	$0.918261\pi$
$654$	−7.64515	−	16.7405i	−0.298949	−	0.654607i
$655$	3.27577	+	0.961852i	0.127995	+	0.0375827i
$656$	−13.9078	−	4.08370i	−0.543008	−	0.159442i
$657$	−8.87031	−	19.4233i	−0.346064	−	0.757774i
$658$	−0.917059	+	6.37829i	−0.0357507	+	0.248652i
$659$	−15.8818	+	18.3285i	−0.618666	+	0.713979i	−0.975453	−	0.220207i	$-0.929327\pi$
$659$	−15.8818	+	18.3285i	−0.618666	+	0.713979i	0.356787	+	0.934186i	$0.383872\pi$
$660$	3.16648	−	6.93363i	0.123255	−	0.269891i
$661$	39.9894	+	25.6996i	1.55541	+	0.999598i	0.983842	+	0.179041i	$0.0572994\pi$
$661$	39.9894	+	25.6996i	1.55541	+	0.999598i	0.571564	+	0.820558i	$0.306337\pi$
$662$	1.36970	+	9.52644i	0.0532347	+	0.370256i
$663$	1.89293	−	1.21651i	0.0735154	−	0.0472455i
$664$	−7.78072	−	8.97943i	−0.301951	−	0.348469i
$665$	−5.84468	+	1.71615i	−0.226647	+	0.0665495i
$666$	−4.33257			−0.167884
$667$	−3.61400	+	0.361006i	−0.139935	+	0.0139782i
$668$	6.49176			0.251174
$669$	14.5857	−	4.28276i	0.563917	−	0.165581i
$670$	15.0282	+	17.3435i	0.580591	+	0.670038i
$671$	−1.49539	+	0.961028i	−0.0577288	+	0.0371001i
$672$	2.57609	+	17.9171i	0.0993749	+	0.691167i
$673$	0.724077	+	0.465336i	0.0279111	+	0.0179374i	0.554522	−	0.832169i	$-0.312901\pi$
$673$	0.724077	+	0.465336i	0.0279111	+	0.0179374i	−0.526611	+	0.850106i	$0.676537\pi$
$674$	−12.7682	+	27.9584i	−0.491812	+	1.07692i
$675$	−1.73303	+	2.00002i	−0.0667043	+	0.0769808i
$676$	−2.29112	+	15.9351i	−0.0881199	+	0.612887i
$677$	18.6306	+	40.7952i	0.716030	+	1.56789i	0.819385	+	0.573243i	$0.194315\pi$
$677$	18.6306	+	40.7952i	0.716030	+	1.56789i	−0.103355	+	0.994645i	$0.532958\pi$
$678$	−33.8000	−	9.92458i	−1.29808	−	0.381151i
$679$	27.6432	+	8.11678i	1.06085	+	0.311493i
$680$	−0.147637	−	0.323281i	−0.00566164	−	0.0123973i
$681$	0.857668	−	5.96521i	0.0328659	−	0.228587i
$682$	49.4217	−	57.0357i	1.89245	−	2.18401i
$683$	−4.36723	+	9.56290i	−0.167107	+	0.365914i	−0.974596	−	0.223969i	$-0.928099\pi$
$683$	−4.36723	+	9.56290i	−0.167107	+	0.365914i	0.807489	+	0.589883i	$0.200826\pi$
$684$	4.08465	+	2.62504i	0.156180	+	0.100371i
$685$	−3.32528	−	23.1278i	−0.127052	−	0.883668i
$686$	27.7836	−	17.8555i	1.06078	−	0.681725i
$687$	18.2082	+	21.0134i	0.694686	+	0.801711i
$688$	−26.5363	+	7.79175i	−1.01169	+	0.297058i
$689$	−15.1281			−0.576334
$690$	−4.23870	−	17.1455i	−0.161365	−	0.652717i
$691$	−6.52956			−0.248396			−0.124198	−	0.992257i	$-0.539636\pi$
$691$	−6.52956			−0.248396			−0.124198	+	0.992257i	$0.539636\pi$
$692$	2.83902	−	0.833613i	0.107924	−	0.0316892i
$693$	9.17676	+	10.5905i	0.348596	+	0.402302i
$694$	−49.5077	+	31.8167i	−1.87929	+	1.20774i
$695$	−2.89788	−	20.1552i	−0.109923	−	0.764529i
$696$	−2.74317	−	1.76293i	−0.103980	−	0.0668236i
$697$	0.218827	−	0.479165i	0.00828868	−	0.0181497i
$698$	−11.2088	+	12.9356i	−0.424258	+	0.489620i
$699$	−1.73263	+	12.0507i	−0.0655341	+	0.455800i
$700$	−0.644288	−	1.41079i	−0.0243518	−	0.0533230i
$701$	21.1250	+	6.20285i	0.797879	+	0.234279i	0.655165	−	0.755485i	$-0.272599\pi$
$701$	21.1250	+	6.20285i	0.797879	+	0.234279i	0.142714	+	0.989764i	$0.454417\pi$
$702$	−24.3093	−	7.13786i	−0.917497	−	0.269401i
$703$	−1.94904	−	4.26781i	−0.0735095	−	0.160963i
$704$	−1.48477	+	10.3268i	−0.0559594	+	0.389206i
$705$	2.94079	−	3.39385i	0.110757	−	0.127820i
$706$	12.8621	−	28.1641i	0.484072	−	1.05997i
$707$	−13.0569	−	8.39118i	−0.491057	−	0.315583i
$708$	−2.57199	−	17.8886i	−0.0966612	−	0.672293i
$709$	−4.51994	+	2.90479i	−0.169750	+	0.109092i	−0.622757	−	0.782415i	$-0.713988\pi$
$709$	−4.51994	+	2.90479i	−0.169750	+	0.109092i	0.453007	+	0.891507i	$0.350351\pi$
$710$	−10.2840	−	11.8684i	−0.385952	−	0.445412i
$711$	21.1248	−	6.20279i	0.792241	−	0.232623i
$712$	−2.98148			−0.111736
$713$	2.21841	−	51.2740i	0.0830803	−	1.92023i
$714$	−1.24203			−0.0464819
$715$	22.8840	−	6.71935i	0.855813	−	0.251289i
$716$	2.11538	+	2.44127i	0.0790553	+	0.0912347i
$717$	−33.7618	+	21.6974i	−1.26086	+	0.810303i
$718$	6.89792	+	47.9761i	0.257428	+	1.79045i
$719$	−38.7855	−	24.9259i	−1.44646	−	0.929581i	−0.999384	−	0.0350829i	$-0.988830\pi$
$719$	−38.7855	−	24.9259i	−1.44646	−	0.929581i	−0.447072	−	0.894498i	$-0.647533\pi$
$720$	3.69864	−	8.09888i	0.137840	−	0.301828i
$721$	5.92081	−	6.83298i	0.220503	−	0.254474i
$722$	1.99986	−	13.9094i	0.0744272	−	0.517653i
$723$	1.18898	+	2.60350i	0.0442186	+	0.0968252i
$724$	12.0204	+	3.52952i	0.446736	+	0.131174i
$725$	0.726645	+	0.213362i	0.0269869	+	0.00792407i
$726$	−10.0495	−	22.0053i	−0.372971	−	0.816692i
$727$	0.846412	−	5.88693i	0.0313917	−	0.218334i	−0.968087	−	0.250614i	$-0.919368\pi$
$727$	0.846412	−	5.88693i	0.0313917	−	0.218334i	0.999479	+	0.0322797i	$0.0102767\pi$
$728$	−13.6832	+	15.7912i	−0.507132	+	0.585262i
$729$	−1.08797	+	2.38232i	−0.0402951	+	0.0882340i
$730$	16.8756	+	10.8453i	0.624593	+	0.401401i
$731$	−0.143038	−	0.994850i	−0.00529045	−	0.0367959i
$732$	0.648790	−	0.416952i	0.0239800	−	0.0154110i
$733$	−4.60649	−	5.31618i	−0.170145	−	0.196357i	0.664273	−	0.747490i	$-0.268741\pi$
$733$	−4.60649	−	5.31618i	−0.170145	−	0.196357i	−0.834418	+	0.551133i	$0.814196\pi$
$734$	11.8800	−	3.48828i	0.438498	−	0.128755i
$735$	−7.69426			−0.283807
$736$	−10.7032	−	18.3531i	−0.394524	−	0.676505i
$737$	57.1708			2.10591
$738$	8.42987	−	2.47523i	0.310308	−	0.0911145i
$739$	10.0255	+	11.5700i	0.368794	+	0.425611i	0.909567	−	0.415558i	$-0.136414\pi$
$739$	10.0255	+	11.5700i	0.368794	+	0.425611i	−0.540773	+	0.841169i	$0.681868\pi$
$740$	1.00495	−	0.645843i	0.0369427	−	0.0237417i
$741$	5.78378	+	40.2270i	0.212472	+	1.47778i
$742$	7.02482	+	4.51458i	0.257889	+	0.165735i
$743$	6.04602	−	13.2389i	0.221807	−	0.485690i	−0.765713	−	0.643182i	$-0.777614\pi$
$743$	6.04602	−	13.2389i	0.221807	−	0.485690i	0.987520	+	0.157493i	$0.0503410\pi$
$744$	30.1740	−	34.8227i	1.10623	−	1.27666i
$745$	1.33305	−	9.27155i	0.0488391	−	0.339683i
$746$	−8.66154	−	18.9661i	−0.317122	−	0.694399i
$747$	10.3791	+	3.04758i	0.379752	+	0.111505i
$748$	0.603679	+	0.177256i	0.0220727	+	0.00648113i
$749$	−13.5241	−	29.6137i	−0.494160	−	1.08206i
$750$	−0.524104	+	3.64523i	−0.0191376	+	0.133105i
$751$	−8.25603	+	9.52797i	−0.301267	+	0.347680i	−0.886118	−	0.463460i	$-0.846608\pi$
$751$	−8.25603	+	9.52797i	−0.301267	+	0.347680i	0.584851	+	0.811141i	$0.301153\pi$
$752$	4.23705	−	9.27785i	0.154509	−	0.338328i
$753$	42.2847	+	27.1747i	1.54094	+	0.990303i
$754$	1.03182	+	7.17649i	0.0375768	+	0.261352i
$755$	15.6715	−	10.0715i	0.570346	−	0.366539i
$756$	2.68784	+	3.10193i	0.0977558	+	0.112816i
$757$	−40.4999	+	11.8918i	−1.47199	+	0.432217i	−0.916747	−	0.399469i	$-0.869195\pi$
$757$	−40.4999	+	11.8918i	−1.47199	+	0.432217i	−0.555247	+	0.831685i	$0.687376\pi$
$758$	−24.3195			−0.883325
$759$	−39.1958	−	19.9910i	−1.42272	−	0.725626i
$760$	6.41900			0.232842
$761$	−22.9030	+	6.72492i	−0.830232	+	0.243778i	−0.669117	−	0.743157i	$-0.733327\pi$
$761$	−22.9030	+	6.72492i	−0.830232	+	0.243778i	−0.161115	+	0.986936i	$0.551509\pi$
$762$	−24.2425	−	27.9773i	−0.878212	−	1.01351i
$763$	−7.84782	+	5.04349i	−0.284110	+	0.182586i
$764$	2.13678	+	14.8616i	0.0773060	+	0.537675i
$765$	0.272201	+	0.174933i	0.00984143	+	0.00632471i
$766$	12.7865	−	27.9985i	0.461994	−	1.01163i
$767$	37.0307	−	42.7358i	1.33710	−	1.54310i
$768$	5.28786	−	36.7779i	0.190809	−	1.32711i
$769$	18.1511	+	39.7453i	0.654544	+	1.43325i	0.887520	+	0.460770i	$0.152427\pi$
$769$	18.1511	+	39.7453i	0.654544	+	1.43325i	−0.232975	+	0.972483i	$0.574846\pi$
$770$	−12.6316	−	3.70896i	−0.455210	−	0.133662i
$771$	−1.50750	−	0.442641i	−0.0542912	−	0.0159413i
$772$	−5.87244	−	12.8589i	−0.211354	−	0.462800i
$773$	−6.52823	+	45.4048i	−0.234804	+	1.63310i	0.442057	+	0.896987i	$0.354249\pi$
$773$	−6.52823	+	45.4048i	−0.234804	+	1.63310i	−0.676861	+	0.736111i	$0.736660\pi$
$774$	10.9776	−	12.6689i	0.394583	−	0.455374i
$775$	−4.44551	+	9.73431i	−0.159687	+	0.349667i
$776$	−25.5401	−	16.4136i	−0.916836	−	0.589214i
$777$	0.836089	+	5.81513i	0.0299945	+	0.208617i
$778$	40.3124	−	25.9072i	1.44527	−	0.928817i
$779$	6.23048	+	7.19036i	0.223230	+	0.257621i
$780$	−9.92847	+	2.91526i	−0.355496	+	0.104383i
$781$	−39.1227			−1.39992
$782$	1.35101	−	0.547710i	0.0483119	−	0.0195861i
$783$	−2.00418			−0.0716236
$784$	−16.7678	+	4.92346i	−0.598849	+	0.175838i
$785$	14.1268	+	16.3032i	0.504207	+	0.581886i
$786$	−10.5771	+	6.79747i	−0.377272	+	0.242458i
$787$	−0.406574	−	2.82779i	−0.0144928	−	0.100800i	0.981291	−	0.192530i	$-0.0616693\pi$
$787$	−0.406574	−	2.82779i	−0.0144928	−	0.100800i	−0.995784	+	0.0917304i	$0.970760\pi$
$788$	10.5562	+	6.78407i	0.376050	+	0.241672i
$789$	15.2215	−	33.3304i	0.541899	−	1.18659i
$790$	−13.5448	+	15.6316i	−0.481903	+	0.556146i
$791$	−2.54123	+	17.6746i	−0.0903556	+	0.628437i
$792$	−6.13439	−	13.4324i	−0.217976	−	0.477301i
$793$	2.31534	+	0.679844i	0.0822200	+	0.0241420i
$794$	−6.06517	−	1.78089i	−0.215245	−	0.0632016i
$795$	−2.41746	−	5.29349i	−0.0857383	−	0.187741i
$796$	1.68574	−	11.7246i	0.0597496	−	0.415568i
$797$	−2.11156	+	2.43687i	−0.0747951	+	0.0863182i	−0.791914	−	0.610633i	$-0.790915\pi$
$797$	−2.11156	+	2.43687i	−0.0747951	+	0.0863182i	0.717119	+	0.696951i	$0.245461\pi$
$798$	9.31898	−	20.4057i	0.329888	−	0.722355i
$799$	0.311825	+	0.200398i	0.0110316	+	0.00708957i
$800$	0.630471	+	4.38502i	0.0222905	+	0.155034i
$801$	2.28353	−	1.46753i	0.0806844	−	0.0518527i
$802$	18.2338	+	21.0430i	0.643860	+	0.743054i
$803$	47.9500	−	14.0794i	1.69212	−	0.496851i
$804$	−24.8042			−0.874776
$805$	−8.29673	+	3.36356i	−0.292421	+	0.118550i
$806$	−102.450			−3.60866
$807$	17.4551	−	5.12529i	0.614450	−	0.180419i
$808$	10.7106	+	12.3606i	0.376796	+	0.434846i
$809$	14.0729	−	9.04409i	0.494776	−	0.317973i	−0.269348	−	0.963043i	$-0.586808\pi$
$809$	14.0729	−	9.04409i	0.494776	−	0.317973i	0.764124	+	0.645070i	$0.223172\pi$
$810$	−2.67350	−	18.5946i	−0.0939371	−	0.653347i
$811$	−17.2105	−	11.0605i	−0.604343	−	0.388387i	0.202389	−	0.979305i	$-0.435129\pi$
$811$	−17.2105	−	11.0605i	−0.604343	−	0.388387i	−0.806732	+	0.590918i	$0.798766\pi$
$812$	0.487933	−	1.06843i	0.0171231	−	0.0374944i
$813$	−16.3019	+	18.8134i	−0.571733	+	0.659815i
$814$	1.44306	−	10.0367i	0.0505793	−	0.351787i
$815$	2.27398	+	4.97931i	0.0796539	+	0.174418i
$816$	1.88629	+	0.553866i	0.0660335	+	0.0193892i
$817$	17.4179	+	5.11436i	0.609375	+	0.178929i
$818$	8.47555	+	18.5589i	0.296341	+	0.648896i
$819$	2.70730	−	18.8297i	0.0946007	−	0.657962i
$820$	−1.58636	+	1.83075i	−0.0553980	+	0.0639327i
$821$	−13.1269	+	28.7439i	−0.458131	+	1.00317i	0.529778	+	0.848136i	$0.322275\pi$
$821$	−13.1269	+	28.7439i	−0.458131	+	1.00317i	−0.987910	+	0.155031i	$0.950452\pi$
$822$	72.3889	+	46.5215i	2.52485	+	1.62262i
$823$	1.30283	+	9.06140i	0.0454139	+	0.315861i	0.999848	+	0.0174386i	$0.00555116\pi$
$823$	1.30283	+	9.06140i	0.0454139	+	0.315861i	−0.954434	+	0.298422i	$0.903540\pi$
$824$	−8.01508	+	5.15098i	−0.279219	+	0.179443i
$825$	6.00803	+	6.93363i	0.209173	+	0.241398i
$826$	−29.9488	+	8.79378i	−1.04205	+	0.305975i
$827$	9.64265			0.335308			0.167654	−	0.985846i	$-0.446381\pi$
$827$	9.64265			0.335308			0.167654	+	0.985846i	$0.446381\pi$
$828$	6.35698	+	3.24224i	0.220920	+	0.112676i
$829$	15.3137			0.531865			0.265933	−	0.963992i	$-0.414320\pi$
$829$	15.3137			0.531865			0.265933	+	0.963992i	$0.414320\pi$
$830$	−9.75068	+	2.86306i	−0.338451	+	0.0993782i
$831$	6.51971	+	7.52414i	0.226166	+	0.261010i
$832$	11.9147	−	7.65709i	0.413067	−	0.265462i
$833$	−0.0903829	−	0.628627i	−0.00313158	−	0.0217806i
$834$	63.0847	+	40.5421i	2.18444	+	1.40386i
$835$	−3.24588	+	7.10749i	−0.112328	+	0.245965i
$836$	−7.44160	+	8.58807i	−0.257373	+	0.297024i
$837$	4.03038	−	28.0319i	0.139310	−	0.968924i
$838$	−0.788528	−	1.72663i	−0.0272392	−	0.0596456i
$839$	54.5455	+	16.0160i	1.88312	+	0.552934i	0.995775	+	0.0918269i	$0.0292706\pi$
$839$	54.5455	+	16.0160i	1.88312	+	0.552934i	0.887345	+	0.461107i	$0.152548\pi$
$840$	−7.71210	−	2.26448i	−0.266093	−	0.0781319i
$841$	−11.8088	−	25.8576i	−0.407199	−	0.891642i
$842$	−9.45101	+	65.7332i	−0.325703	+	2.26532i
$843$	−7.80492	+	9.00736i	−0.268816	+	0.310230i
$844$	−2.16190	+	4.73391i	−0.0744158	+	0.162948i
$845$	−16.3009	−	10.4760i	−0.560768	−	0.360384i
$846$	0.879820	+	6.11928i	0.0302488	+	0.210385i
$847$	−10.3159	+	6.62961i	−0.354457	+	0.227796i
$848$	−8.65549	−	9.98897i	−0.297231	−	0.343023i
$849$	−26.7421	+	7.85219i	−0.917786	+	0.269486i
$850$	−0.303974			−0.0104262
$851$	−3.47379	−	5.95664i	−0.119080	−	0.204191i
$852$	16.9738			0.581513
$853$	−1.23598	+	0.362916i	−0.0423190	+	0.0124260i	−0.302824	−	0.953047i	$-0.597929\pi$
$853$	−1.23598	+	0.362916i	−0.0423190	+	0.0124260i	0.260505	+	0.965473i	$0.416111\pi$
$854$	−0.872261	−	1.00664i	−0.0298481	−	0.0344466i
$855$	−4.91634	+	3.15954i	−0.168135	+	0.108054i
$856$	4.88231	+	33.9572i	0.166874	+	1.16063i
$857$	−31.2563	−	20.0872i	−1.06770	−	0.686167i	−0.116013	−	0.993248i	$-0.537011\pi$
$857$	−31.2563	−	20.0872i	−1.06770	−	0.686167i	−0.951683	+	0.307081i	$0.900648\pi$
$858$	−36.4871	+	79.8957i	−1.24565	+	2.72759i
$859$	−19.1111	+	22.0553i	−0.652061	+	0.752518i	−0.981459	−	0.191673i	$-0.938609\pi$
$859$	−19.1111	+	22.0553i	−0.652061	+	0.752518i	0.329398	+	0.944191i	$0.393154\pi$
$860$	−0.657784	+	4.57499i	−0.0224303	+	0.156006i
$861$	−4.94901	−	10.8368i	−0.168662	−	0.369318i
$862$	−21.8732	−	6.42256i	−0.745005	−	0.218753i
$863$	0.728362	+	0.213866i	0.0247937	+	0.00728010i	0.294106	−	0.955773i	$-0.404978\pi$
$863$	0.728362	+	0.213866i	0.0247937	+	0.00728010i	−0.269312	+	0.963053i	$0.586796\pi$
$864$	−4.87027	−	10.6644i	−0.165690	−	0.362811i
$865$	−0.506834	+	3.52510i	−0.0172329	+	0.119857i
$866$	33.4294	−	38.5796i	1.13598	−	1.31099i
$867$	15.4279	−	33.7824i	0.523959	−	1.14731i
$868$	13.9625	+	8.97317i	0.473919	+	0.304569i
$869$	7.33314	+	51.0031i	0.248760	+	1.73016i
$870$	−2.34625	+	1.50785i	−0.0795454	+	0.0511207i
$871$	−50.8240	−	58.6540i	−1.72210	−	1.98741i
$872$	9.43219	−	2.76954i	0.319414	−	0.0937885i
$873$	27.6403			0.935484
$874$	−1.13813	+	26.3056i	−0.0384979	+	0.889799i
$875$	1.86675			0.0631076
$876$	−20.8036	+	6.10850i	−0.702889	+	0.206387i
$877$	15.6416	+	18.0513i	0.528178	+	0.609550i	0.955659	−	0.294474i	$-0.0951446\pi$
$877$	15.6416	+	18.0513i	0.528178	+	0.609550i	−0.427482	+	0.904024i	$0.640599\pi$
$878$	5.00490	−	3.21645i	0.168907	−	0.108550i
$879$	−7.71017	−	53.6254i	−0.260058	−	1.80874i
$880$	17.5298	+	11.2657i	0.590929	+	0.379767i
$881$	8.04422	−	17.6144i	0.271017	−	0.593444i	−0.724368	−	0.689414i	$-0.757868\pi$
$881$	8.04422	−	17.6144i	0.271017	−	0.593444i	0.995384	+	0.0959704i	$0.0305954\pi$
$882$	6.93657	−	8.00522i	0.233566	−	0.269550i
$883$	5.82242	−	40.4958i	0.195940	−	1.36279i	−0.619976	−	0.784621i	$-0.712858\pi$
$883$	5.82242	−	40.4958i	0.195940	−	1.36279i	0.815916	−	0.578171i	$-0.196233\pi$
$884$	−0.354807	−	0.776919i	−0.0119334	−	0.0261306i
$885$	20.8712	+	6.12835i	0.701579	+	0.206002i
$886$	2.12828	+	0.624918i	0.0715008	+	0.0209945i
$887$	−5.61342	−	12.2917i	−0.188480	−	0.412714i	0.791676	−	0.610941i	$-0.209209\pi$
$887$	−5.61342	−	12.2917i	−0.188480	−	0.412714i	−0.980156	+	0.198227i	$0.936482\pi$
$888$	0.881052	−	6.12785i	0.0295662	−	0.205637i
$889$	−12.2884	+	14.1816i	−0.412139	+	0.475634i
$890$	−1.05934	+	2.31963i	−0.0355092	+	0.0777543i
$891$	−39.3706	−	25.3019i	−1.31896	−	0.847646i
$892$	−0.821179	−	5.71143i	−0.0274951	−	0.191233i
$893$	−5.63202	+	3.61948i	−0.188468	+	0.121121i
$894$	22.5898	+	26.0700i	0.755516	+	0.871911i
$895$	−3.73051	+	1.09538i	−0.124697	+	0.0366144i
$896$	−24.3575			−0.813728
$897$	14.3349	+	57.9843i	0.478628	+	1.93604i
$898$	22.1146			0.737975
$899$	−7.77609	+	2.28327i	−0.259347	+	0.0761512i
$900$	−0.974414	−	1.12453i	−0.0324805	−	0.0374845i
$901$	0.404085	−	0.259690i	0.0134620	−	0.00865151i
$902$	2.92630	+	20.3529i	0.0974352	+	0.677677i
$903$	−19.1225	−	12.2893i	−0.636357	−	0.408962i
$904$	7.81671	−	17.1162i	0.259980	−	0.569277i
$905$	−9.87450	+	11.3958i	−0.328240	+	0.378809i
$906$	−9.76343	+	67.9062i	−0.324368	+	2.25603i
$907$	−0.294344	−	0.644524i	−0.00977354	−	0.0214011i	0.904682	−	0.426087i	$-0.140108\pi$
$907$	−0.294344	−	0.644524i	−0.00977354	−	0.0214011i	−0.914456	+	0.404686i	$0.867381\pi$
$908$	−2.19489	−	0.644478i	−0.0728399	−	0.0213877i
$909$	−14.2874	−	4.19515i	−0.473883	−	0.139145i
$910$	7.42408	+	16.2565i	0.246106	+	0.538897i
$911$	−1.90438	+	13.2452i	−0.0630948	+	0.438834i	0.933648	+	0.358191i	$0.116606\pi$
$911$	−1.90438	+	13.2452i	−0.0630948	+	0.438834i	−0.996743	+	0.0806428i	$0.974303\pi$
$912$	−23.2525	+	26.8348i	−0.769967	+	0.888589i
$913$	−10.5170	+	23.0290i	−0.348061	+	0.762147i
$914$	−14.7028	−	9.44890i	−0.486325	−	0.312542i
$915$	0.132104	+	0.918802i	0.00436722	+	0.0303747i
$916$	8.87864	−	5.70596i	0.293359	−	0.188530i
$917$	4.17355	+	4.81654i	0.137823	+	0.159056i
$918$	0.771854	−	0.226637i	0.0254750	−	0.00748013i
$919$	22.0123			0.726118			0.363059	−	0.931766i	$-0.381732\pi$
$919$	22.0123			0.726118			0.363059	+	0.931766i	$0.381732\pi$
$920$	9.38734	−	0.937711i	0.309491	−	0.0309154i
$921$	−41.3181			−1.36148
$922$	−14.2057	+	4.17118i	−0.467841	+	0.137370i
$923$	34.7795	+	40.1377i	1.14478	+	1.32115i
$924$	11.9704	−	7.69289i	0.393797	−	0.253078i
$925$	0.204624	+	1.42319i	0.00672799	+	0.0467942i
$926$	25.8085	+	16.5861i	0.848120	+	0.545054i
$927$	3.60339	−	7.89032i	0.118351	−	0.259152i
$928$	−2.19707	+	2.53555i	−0.0721224	+	0.0832337i
$929$	5.42338	−	37.7204i	0.177935	−	1.23757i	−0.683596	−	0.729861i	$-0.739585\pi$
$929$	5.42338	−	37.7204i	0.177935	−	1.23757i	0.861531	−	0.507705i	$-0.169506\pi$
$930$	−16.3715	−	35.8486i	−0.536843	−	1.17552i
$931$	11.0060	+	3.23166i	0.360708	+	0.105914i
$932$	4.43403	+	1.30195i	0.145242	+	0.0426468i
$933$	−10.1371	−	22.1971i	−0.331873	−	0.726699i
$934$	−4.92907	+	34.2825i	−0.161284	+	1.12176i
$935$	−0.495908	+	0.572308i	−0.0162179	+	0.0187165i
$936$	−8.32754	+	18.2348i	−0.272194	+	0.596022i
$937$	−25.7574	−	16.5533i	−0.841458	−	0.540772i	0.0474415	−	0.998874i	$-0.484893\pi$
$937$	−25.7574	−	16.5533i	−0.841458	−	0.540772i	−0.888900	+	0.458102i	$0.848530\pi$
$938$	6.09670	+	42.4035i	0.199064	+	1.38452i
$939$	−21.2994	+	13.6883i	−0.695078	+	0.446700i
$940$	−1.11626	−	1.28823i	−0.0364084	−	0.0420175i
$941$	8.78312	−	2.57896i	0.286322	−	0.0840716i	−0.135418	−	0.990789i	$-0.543238\pi$
$941$	8.78312	−	2.57896i	0.286322	−	0.0840716i	0.421740	+	0.906717i	$0.361420\pi$
$942$	−79.4442			−2.58843
$943$	10.1620	+	9.60522i	0.330921	+	0.312789i
$944$	49.4052			1.60800
$945$	−4.74006	+	1.39181i	−0.154194	+	0.0452755i
$946$	25.6921	+	29.6502i	0.835322	+	0.964013i
$947$	2.49086	−	1.60078i	0.0809421	−	0.0520183i	−0.499544	−	0.866289i	$-0.666499\pi$
$947$	2.49086	−	1.60078i	0.0809421	−	0.0520183i	0.580486	+	0.814270i	$0.302863\pi$
$948$	−3.18156	−	22.1283i	−0.103332	−	0.718693i
$949$	−57.0715	−	36.6776i	−1.85262	−	1.19061i
$950$	2.28072	−	4.99408i	0.0739963	−	0.162029i
$951$	−10.8474	+	12.5186i	−0.351751	+	0.405942i
$952$	0.0944170	−	0.656685i	0.00306007	−	0.0212833i
$953$	−14.2839	−	31.2773i	−0.462699	−	1.01317i	−0.986864	−	0.161553i	$-0.948350\pi$
$953$	−14.2839	−	31.2773i	−0.462699	−	1.01317i	0.524164	−	0.851617i	$-0.324378\pi$
$954$	7.68682	+	2.25705i	0.248870	+	0.0730748i
$955$	−17.3396	−	5.09137i	−0.561097	−	0.164753i
$956$	6.32822	+	13.8569i	0.204669	+	0.448163i
$957$	−0.988812	+	6.87734i	−0.0319637	+	0.222313i
$958$	25.8752	−	29.8616i	0.835991	−	0.964785i
$959$	18.1195	−	39.6761i	0.585108	−	1.28121i
$960$	4.58326	+	2.94548i	0.147924	+	0.0950651i
$961$	−11.8860	−	82.6692i	−0.383420	−	2.66675i
$962$	−11.5800	+	7.44200i	−0.373353	+	0.239940i
$963$	−20.4537	−	23.6048i	−0.659112	−	0.760655i
$964$	1.04240	−	0.306077i	0.0335735	−	0.00985807i
$965$	17.0147			0.547723
$966$	10.6474	−	31.2033i	0.342575	−	1.00395i
$967$	−40.8856			−1.31479			−0.657396	−	0.753545i	$-0.728342\pi$
$967$	−40.8856			−1.31479			−0.657396	+	0.753545i	$0.728342\pi$
$968$	12.3985	−	3.64053i	0.398503	−	0.117011i
$969$	−0.845030	−	0.975217i	−0.0271463	−	0.0313285i
$970$	−21.8446	+	14.0387i	−0.701389	+	0.450755i
$971$	−5.41965	−	37.6945i	−0.173925	−	1.20967i	−0.870492	−	0.492183i	$-0.836199\pi$
$971$	−5.41965	−	37.6945i	−0.173925	−	1.20967i	0.696567	−	0.717492i	$-0.254710\pi$
$972$	11.5323	+	7.41137i	0.369899	+	0.237720i
$973$	15.7906	−	34.5765i	0.506222	−	1.10847i
$974$	21.2159	−	24.4844i	0.679801	−	0.784532i
$975$	1.77247	−	12.3278i	0.0567644	−	0.394805i
$976$	0.875818	+	1.91777i	0.0280343	+	0.0613865i
$977$	14.0214	+	4.11705i	0.448584	+	0.131716i	0.498219	−	0.867051i	$-0.333988\pi$
$977$	14.0214	+	4.11705i	0.448584	+	0.131716i	−0.0496348	+	0.998767i	$0.515806\pi$
$978$	−19.3425	−	5.67948i	−0.618506	−	0.181610i
$979$	2.63907	+	5.77876i	0.0843451	+	0.184690i
$980$	−0.415641	+	2.89085i	−0.0132772	+	0.0923448i
$981$	−5.86094	+	6.76389i	−0.187126	+	0.215954i
$982$	−7.02299	+	15.3782i	−0.224113	+	0.490738i
$983$	38.4815	+	24.7305i	1.22737	+	0.788781i	0.983479	−	0.181022i	$-0.0579405\pi$
$983$	38.4815	+	24.7305i	1.22737	+	0.788781i	0.243889	+	0.969803i	$0.421577\pi$
$984$	1.78663	+	12.4263i	0.0569557	+	0.396136i
$985$	−12.7056	+	8.16541i	−0.404835	+	0.260172i
$986$	−0.150753	−	0.173978i	−0.00480096	−	0.00554060i
$987$	8.04346	−	2.36177i	0.256026	−	0.0751760i
$988$	15.4263			0.490777
$989$	26.2196	+	4.93492i	0.833734	+	0.156921i
$990$	−12.6302			−0.401415
$991$	44.2321	−	12.9877i	1.40508	−	0.412569i	0.510654	−	0.859786i	$-0.329403\pi$
$991$	44.2321	−	12.9877i	1.40508	−	0.412569i	0.894425	+	0.447218i	$0.147585\pi$
$992$	−31.0458	−	35.8288i	−0.985705	−	1.13756i
$993$	10.5331	−	6.76918i	0.334256	−	0.214814i
$994$	−4.17205	−	29.0172i	−0.132329	−	0.920371i
$995$	11.9938	+	7.70794i	0.380228	+	0.244358i
$996$	4.56290	−	9.99136i	0.144581	−	0.316589i
$997$	−3.27109	+	3.77504i	−0.103596	+	0.119557i	−0.805180	−	0.593031i	$-0.797931\pi$
$997$	−3.27109	+	3.77504i	−0.103596	+	0.119557i	0.701583	+	0.712587i	$0.252477\pi$
$998$	1.09503	−	7.61612i	0.0346627	−	0.241084i
$999$	−1.58068	−	3.46121i	−0.0500106	−	0.109508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.b.101.2	yes	20
5.2	odd	4		575.2.p.c.124.2		40
5.3	odd	4		575.2.p.c.124.3		40
5.4	even	2		575.2.k.c.101.1		20
23.8	even	11		2645.2.a.t.1.9		10
23.15	odd	22		2645.2.a.u.1.9		10
23.18	even	11	inner	115.2.g.b.41.2	✓	20
115.18	odd	44		575.2.p.c.524.2		40
115.64	even	22		575.2.k.c.501.1		20
115.87	odd	44		575.2.p.c.524.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.b.41.2	✓	20	23.18	even	11	inner
115.2.g.b.101.2	yes	20	1.1	even	1	trivial
575.2.k.c.101.1		20	5.4	even	2
575.2.k.c.501.1		20	115.64	even	22
575.2.p.c.124.2		40	5.2	odd	4
575.2.p.c.124.3		40	5.3	odd	4
575.2.p.c.524.2		40	115.18	odd	44
575.2.p.c.524.3		40	115.87	odd	44
2645.2.a.t.1.9		10	23.8	even	11
2645.2.a.u.1.9		10	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)

\(f(q)\)	\(=\)	\(q+(-1.61435 + 0.474017i) q^{2} +(1.43337 + 1.65420i) q^{3} +(0.698939 - 0.449181i) q^{4} +(0.142315 + 0.989821i) q^{5} +(-3.09809 - 1.99102i) q^{6} +(-0.775475 + 1.69805i) q^{7} +(1.28820 - 1.48666i) q^{8} +(-0.254878 + 1.77272i) q^{9} +O(q^{10})\)	\(q+(-1.61435 + 0.474017i) q^{2} +(1.43337 + 1.65420i) q^{3} +(0.698939 - 0.449181i) q^{4} +(0.142315 + 0.989821i) q^{5} +(-3.09809 - 1.99102i) q^{6} +(-0.775475 + 1.69805i) q^{7} +(1.28820 - 1.48666i) q^{8} +(-0.254878 + 1.77272i) q^{9} +(-0.698939 - 1.53046i) q^{10} +(-4.02174 - 1.18089i) q^{11} +(1.74488 + 0.512342i) q^{12} +(2.36374 + 5.17587i) q^{13} +(0.446985 - 3.10885i) q^{14} +(-1.43337 + 1.65420i) q^{15} +(-2.06519 + 4.52213i) q^{16} +(-0.151987 - 0.0976762i) q^{17} +(-0.428834 - 2.98261i) q^{18} +(2.74511 - 1.76418i) q^{19} +(0.544078 + 0.627899i) q^{20} +(-3.92047 + 1.15115i) q^{21} +7.05228 q^{22} +(3.75681 - 2.98100i) q^{23} +4.30571 q^{24} +(-0.959493 + 0.281733i) q^{25} +(-6.26937 - 7.23523i) q^{26} +(2.22630 - 1.43076i) q^{27} +(0.220723 + 1.53516i) q^{28} +(-0.637100 - 0.409439i) q^{29} +(1.52985 - 3.34991i) q^{30} +(7.00791 - 8.08755i) q^{31} +(0.630471 - 4.38502i) q^{32} +(-3.81123 - 8.34543i) q^{33} +(0.291661 + 0.0856394i) q^{34} +(-1.79113 - 0.525924i) q^{35} +(0.618126 + 1.35351i) q^{36} +(0.204624 - 1.42319i) q^{37} +(-3.59533 + 4.14923i) q^{38} +(-5.17381 + 11.3291i) q^{39} +(1.65486 + 1.06351i) q^{40} +(0.414944 + 2.88600i) q^{41} +(5.78336 - 3.71674i) q^{42} +(3.64309 + 4.20435i) q^{43} +(-3.34138 + 0.981119i) q^{44} -1.79095 q^{45} +(-4.65178 + 6.59318i) q^{46} -2.05166 q^{47} +(-10.4407 + 3.06567i) q^{48} +(2.30200 + 2.65665i) q^{49} +(1.41542 - 0.909632i) q^{50} +(-0.0562783 - 0.391424i) q^{51} +(3.97701 + 2.55587i) q^{52} +(-1.10445 + 2.41842i) q^{53} +(-2.91583 + 3.36505i) q^{54} +(0.596517 - 4.14886i) q^{55} +(1.52547 + 3.34030i) q^{56} +(6.85307 + 2.01224i) q^{57} +(1.22259 + 0.358983i) q^{58} +(-4.12836 - 9.03985i) q^{59} +(-0.258805 + 1.80003i) q^{60} +(0.277718 - 0.320503i) q^{61} +(-7.47960 + 16.3780i) q^{62} +(-2.81252 - 1.80749i) q^{63} +(-0.354232 - 2.46373i) q^{64} +(-4.78679 + 3.07629i) q^{65} +(10.1085 + 11.6659i) q^{66} +(-13.0871 + 3.84272i) q^{67} -0.150104 q^{68} +(10.3161 + 1.94164i) q^{69} +3.14082 q^{70} +(8.95568 - 2.62962i) q^{71} +(2.30710 + 2.66253i) q^{72} +(-10.0300 + 6.44590i) q^{73} +(0.344281 + 2.39453i) q^{74} +(-1.84135 - 1.18337i) q^{75} +(1.12623 - 2.46610i) q^{76} +(5.12398 - 5.91338i) q^{77} +(2.98219 - 20.7416i) q^{78} +(-5.10681 - 11.1824i) q^{79} +(-4.77001 - 1.40060i) q^{80} +(10.7131 + 3.14564i) q^{81} +(-2.03788 - 4.46234i) q^{82} +(0.859580 - 5.97851i) q^{83} +(-2.22309 + 2.56559i) q^{84} +(0.0750520 - 0.164341i) q^{85} +(-7.87417 - 5.06042i) q^{86} +(-0.235907 - 1.64077i) q^{87} +(-6.93640 + 4.45775i) q^{88} +(-0.992535 - 1.14545i) q^{89} +(2.89122 - 0.848939i) q^{90} -10.6219 q^{91} +(1.28678 - 3.77102i) q^{92} +23.4234 q^{93} +(3.31210 - 0.972520i) q^{94} +(2.13689 + 2.46610i) q^{95} +(8.15741 - 5.24245i) q^{96} +(-2.19640 - 15.2763i) q^{97} +(-4.97554 - 3.19758i) q^{98} +(3.11844 - 6.82842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} + 10 q^{13} + 3 q^{14} - q^{15} - 36 q^{16} - 9 q^{17} + 10 q^{18} + 24 q^{19} + 4 q^{20} + 25 q^{21} + 6 q^{22} + 11 q^{23} - 2 q^{25} - 2 q^{26} + 28 q^{27} - 8 q^{28} + 12 q^{29} - 2 q^{30} + 10 q^{31} - 50 q^{32} - 49 q^{33} - 7 q^{34} + 4 q^{35} + 43 q^{36} - 18 q^{37} - 29 q^{38} - 52 q^{39} + 22 q^{40} + 10 q^{41} - 5 q^{42} + 35 q^{43} + 6 q^{44} - 38 q^{45} - 33 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 18 q^{50} + 50 q^{51} + 9 q^{52} - 5 q^{53} + 23 q^{54} + 8 q^{55} + 33 q^{57} + 35 q^{58} + 41 q^{59} - 2 q^{60} - 13 q^{61} - 2 q^{62} - 46 q^{63} + 16 q^{64} - 10 q^{65} + 56 q^{66} - 9 q^{67} + 26 q^{68} - 45 q^{69} + 8 q^{70} - 19 q^{71} - 27 q^{73} + 8 q^{74} + q^{75} + 4 q^{76} - 64 q^{77} - 27 q^{78} - 83 q^{79} - 8 q^{80} + 12 q^{81} + 31 q^{82} + 67 q^{83} + 28 q^{84} - 13 q^{85} - 73 q^{86} + 69 q^{87} + 22 q^{88} - 5 q^{89} - 10 q^{90} - 84 q^{91} + 11 q^{92} + 28 q^{93} - 37 q^{94} - 2 q^{95} + 14 q^{96} + 18 q^{97} + 8 q^{98} + 62 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 10 * q^13 + 3 * q^14 - q^15 - 36 * q^16 - 9 * q^17 + 10 * q^18 + 24 * q^19 + 4 * q^20 + 25 * q^21 + 6 * q^22 + 11 * q^23 - 2 * q^25 - 2 * q^26 + 28 * q^27 - 8 * q^28 + 12 * q^29 - 2 * q^30 + 10 * q^31 - 50 * q^32 - 49 * q^33 - 7 * q^34 + 4 * q^35 + 43 * q^36 - 18 * q^37 - 29 * q^38 - 52 * q^39 + 22 * q^40 + 10 * q^41 - 5 * q^42 + 35 * q^43 + 6 * q^44 - 38 * q^45 - 33 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 18 * q^50 + 50 * q^51 + 9 * q^52 - 5 * q^53 + 23 * q^54 + 8 * q^55 + 33 * q^57 + 35 * q^58 + 41 * q^59 - 2 * q^60 - 13 * q^61 - 2 * q^62 - 46 * q^63 + 16 * q^64 - 10 * q^65 + 56 * q^66 - 9 * q^67 + 26 * q^68 - 45 * q^69 + 8 * q^70 - 19 * q^71 - 27 * q^73 + 8 * q^74 + q^75 + 4 * q^76 - 64 * q^77 - 27 * q^78 - 83 * q^79 - 8 * q^80 + 12 * q^81 + 31 * q^82 + 67 * q^83 + 28 * q^84 - 13 * q^85 - 73 * q^86 + 69 * q^87 + 22 * q^88 - 5 * q^89 - 10 * q^90 - 84 * q^91 + 11 * q^92 + 28 * q^93 - 37 * q^94 - 2 * q^95 + 14 * q^96 + 18 * q^97 + 8 * q^98 + 62 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more