LMFDB - Embedded newform 950.2.e.j.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.e (of order $3$, degree $2$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.1
Root			$1.39564 - 0.228425i$ of defining polynomial
Character	$\chi$	$=$	950.201
Dual form			950.2.e.j.501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.39564 + 2.41733i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.39564 + 2.41733i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(-2.39564 - 4.14938i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.39564 + 2.41733i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.39564 + 2.41733i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(-2.39564 - 4.14938i) q^{9} -3.79129 q^{11} +2.79129 q^{12} +(-0.104356 - 0.180750i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.395644 + 0.685275i) q^{17} -4.79129 q^{18} +(-3.50000 - 2.59808i) q^{19} +(-1.39564 + 2.41733i) q^{21} +(-1.89564 + 3.28335i) q^{22} +(2.29129 + 3.96863i) q^{23} +(1.39564 - 2.41733i) q^{24} -0.208712 q^{26} +5.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-3.39564 - 5.88143i) q^{29} -4.79129 q^{31} +(0.500000 + 0.866025i) q^{32} +(5.29129 - 9.16478i) q^{33} +(0.395644 + 0.685275i) q^{34} +(-2.39564 + 4.14938i) q^{36} -3.58258 q^{37} +(-4.00000 + 1.73205i) q^{38} +0.582576 q^{39} +(5.68693 - 9.85005i) q^{41} +(1.39564 + 2.41733i) q^{42} +(2.89564 - 5.01540i) q^{43} +(1.89564 + 3.28335i) q^{44} +4.58258 q^{46} +(-6.08258 - 10.5353i) q^{47} +(-1.39564 - 2.41733i) q^{48} -6.00000 q^{49} +(-1.10436 - 1.91280i) q^{51} +(-0.104356 + 0.180750i) q^{52} +(-2.29129 - 3.96863i) q^{53} +(2.50000 - 4.33013i) q^{54} -1.00000 q^{56} +(11.1652 - 4.83465i) q^{57} -6.79129 q^{58} +(-2.29129 + 3.96863i) q^{59} +(-0.686932 - 1.18980i) q^{61} +(-2.39564 + 4.14938i) q^{62} +(-2.39564 - 4.14938i) q^{63} +1.00000 q^{64} +(-5.29129 - 9.16478i) q^{66} +(7.79129 + 13.4949i) q^{67} +0.791288 q^{68} -12.7913 q^{69} +(2.29129 - 3.96863i) q^{71} +(2.39564 + 4.14938i) q^{72} +(1.39564 - 2.41733i) q^{73} +(-1.79129 + 3.10260i) q^{74} +(-0.500000 + 4.33013i) q^{76} -3.79129 q^{77} +(0.291288 - 0.504525i) q^{78} +(-7.47822 + 12.9527i) q^{79} +(0.208712 - 0.361500i) q^{81} +(-5.68693 - 9.85005i) q^{82} -3.79129 q^{83} +2.79129 q^{84} +(-2.89564 - 5.01540i) q^{86} +18.9564 q^{87} +3.79129 q^{88} +(-2.29129 - 3.96863i) q^{89} +(-0.104356 - 0.180750i) q^{91} +(2.29129 - 3.96863i) q^{92} +(6.68693 - 11.5821i) q^{93} -12.1652 q^{94} -2.79129 q^{96} +(-6.18693 + 10.7161i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(9.08258 + 15.7315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{6} + 4 q^{7} - 4 q^{8} - 5 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - q^3 - 2 * q^4 + q^6 + 4 * q^7 - 4 * q^8 - 5 * q^9	$ 4 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{6} + 4 q^{7} - 4 q^{8} - 5 q^{9} - 6 q^{11} + 2 q^{12} - 5 q^{13} + 2 q^{14} - 2 q^{16} + 3 q^{17} - 10 q^{18} - 14 q^{19} - q^{21} - 3 q^{22} + q^{24} - 10 q^{26} + 20 q^{27} - 2 q^{28} - 9 q^{29} - 10 q^{31} + 2 q^{32} + 12 q^{33} - 3 q^{34} - 5 q^{36} + 4 q^{37} - 16 q^{38} - 16 q^{39} + 9 q^{41} + q^{42} + 7 q^{43} + 3 q^{44} - 6 q^{47} - q^{48} - 24 q^{49} - 9 q^{51} - 5 q^{52} + 10 q^{54} - 4 q^{56} + 8 q^{57} - 18 q^{58} + 11 q^{61} - 5 q^{62} - 5 q^{63} + 4 q^{64} - 12 q^{66} + 22 q^{67} - 6 q^{68} - 42 q^{69} + 5 q^{72} + q^{73} + 2 q^{74} - 2 q^{76} - 6 q^{77} - 8 q^{78} - 7 q^{79} + 10 q^{81} - 9 q^{82} - 6 q^{83} + 2 q^{84} - 7 q^{86} + 30 q^{87} + 6 q^{88} - 5 q^{91} + 13 q^{93} - 12 q^{94} - 2 q^{96} - 11 q^{97} - 12 q^{98} + 18 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - q^3 - 2 * q^4 + q^6 + 4 * q^7 - 4 * q^8 - 5 * q^9 - 6 * q^11 + 2 * q^12 - 5 * q^13 + 2 * q^14 - 2 * q^16 + 3 * q^17 - 10 * q^18 - 14 * q^19 - q^21 - 3 * q^22 + q^24 - 10 * q^26 + 20 * q^27 - 2 * q^28 - 9 * q^29 - 10 * q^31 + 2 * q^32 + 12 * q^33 - 3 * q^34 - 5 * q^36 + 4 * q^37 - 16 * q^38 - 16 * q^39 + 9 * q^41 + q^42 + 7 * q^43 + 3 * q^44 - 6 * q^47 - q^48 - 24 * q^49 - 9 * q^51 - 5 * q^52 + 10 * q^54 - 4 * q^56 + 8 * q^57 - 18 * q^58 + 11 * q^61 - 5 * q^62 - 5 * q^63 + 4 * q^64 - 12 * q^66 + 22 * q^67 - 6 * q^68 - 42 * q^69 + 5 * q^72 + q^73 + 2 * q^74 - 2 * q^76 - 6 * q^77 - 8 * q^78 - 7 * q^79 + 10 * q^81 - 9 * q^82 - 6 * q^83 + 2 * q^84 - 7 * q^86 + 30 * q^87 + 6 * q^88 - 5 * q^91 + 13 * q^93 - 12 * q^94 - 2 * q^96 - 11 * q^97 - 12 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.39564	+	2.41733i	−0.805775	+	1.39564i	0.109991	+	0.993933i	$0.464918\pi$
$3$	−1.39564	+	2.41733i	−0.805775	+	1.39564i	−0.915766	+	0.401711i	$0.868416\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	1.39564	+	2.41733i	0.569769	+	0.986869i
$7$	1.00000			0.377964			0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000			0.377964			0.188982	+	0.981981i	$0.439481\pi$
$8$	−1.00000			−0.353553
$9$	−2.39564	−	4.14938i	−0.798548	−	1.38313i
$10$		0			0
$11$	−3.79129			−1.14312			−0.571558	−	0.820562i	$-0.693661\pi$
$11$	−3.79129			−1.14312			−0.571558	+	0.820562i	$0.693661\pi$
$12$	2.79129			0.805775
$13$	−0.104356	−	0.180750i	−0.0289432	−	0.0501310i	0.851191	−	0.524856i	$-0.175881\pi$
$13$	−0.104356	−	0.180750i	−0.0289432	−	0.0501310i	−0.880134	+	0.474725i	$0.842548\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.395644	+	0.685275i	−0.0959577	+	0.166204i	−0.910008	−	0.414591i	$-0.863925\pi$
$17$	−0.395644	+	0.685275i	−0.0959577	+	0.166204i	0.814050	+	0.580795i	$0.197258\pi$
$18$	−4.79129			−1.12932
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$20$		0			0
$21$	−1.39564	+	2.41733i	−0.304554	+	0.527504i
$22$	−1.89564	+	3.28335i	−0.404153	+	0.700013i
$23$	2.29129	+	3.96863i	0.477767	+	0.827516i	0.999675	−	0.0254855i	$-0.00811315\pi$
$23$	2.29129	+	3.96863i	0.477767	+	0.827516i	−0.521909	+	0.853001i	$0.674780\pi$
$24$	1.39564	−	2.41733i	0.284885	−	0.493435i
$25$		0			0
$26$	−0.208712			−0.0409318
$27$	5.00000			0.962250
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	−3.39564	−	5.88143i	−0.630555	−	1.09215i	−0.987438	−	0.158005i	$-0.949494\pi$
$29$	−3.39564	−	5.88143i	−0.630555	−	1.09215i	0.356883	−	0.934149i	$-0.383839\pi$
$30$		0			0
$31$	−4.79129			−0.860541			−0.430270	−	0.902700i	$-0.641582\pi$
$31$	−4.79129			−0.860541			−0.430270	+	0.902700i	$0.641582\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	5.29129	−	9.16478i	0.921095	−	1.59538i
$34$	0.395644	+	0.685275i	0.0678524	+	0.117524i
$35$		0			0
$36$	−2.39564	+	4.14938i	−0.399274	+	0.691563i
$37$	−3.58258			−0.588972			−0.294486	−	0.955656i	$-0.595148\pi$
$37$	−3.58258			−0.588972			−0.294486	+	0.955656i	$0.595148\pi$
$38$	−4.00000	+	1.73205i	−0.648886	+	0.280976i
$39$	0.582576			0.0932868
$40$		0			0
$41$	5.68693	−	9.85005i	0.888150	−	1.53832i	0.0460888	−	0.998937i	$-0.485324\pi$
$41$	5.68693	−	9.85005i	0.888150	−	1.53832i	0.842061	−	0.539383i	$-0.181342\pi$
$42$	1.39564	+	2.41733i	0.215353	+	0.373002i
$43$	2.89564	−	5.01540i	0.441582	−	0.764842i	−0.556225	−	0.831031i	$-0.687751\pi$
$43$	2.89564	−	5.01540i	0.441582	−	0.764842i	0.997807	+	0.0661897i	$0.0210843\pi$
$44$	1.89564	+	3.28335i	0.285779	+	0.494984i
$45$		0			0
$46$	4.58258			0.675664
$47$	−6.08258	−	10.5353i	−0.887235	−	1.53674i	−0.843131	−	0.537709i	$-0.819290\pi$
$47$	−6.08258	−	10.5353i	−0.887235	−	1.53674i	−0.0441043	−	0.999027i	$-0.514043\pi$
$48$	−1.39564	−	2.41733i	−0.201444	−	0.348911i
$49$	−6.00000			−0.857143
$50$		0			0
$51$	−1.10436	−	1.91280i	−0.154641	−	0.267846i
$52$	−0.104356	+	0.180750i	−0.0144716	+	0.0250655i
$53$	−2.29129	−	3.96863i	−0.314733	−	0.545133i	0.664648	−	0.747157i	$-0.268582\pi$
$53$	−2.29129	−	3.96863i	−0.314733	−	0.545133i	−0.979381	+	0.202024i	$0.935248\pi$
$54$	2.50000	−	4.33013i	0.340207	−	0.589256i
$55$		0			0
$56$	−1.00000			−0.133631
$57$	11.1652	−	4.83465i	1.47886	−	0.640365i
$58$	−6.79129			−0.891740
$59$	−2.29129	+	3.96863i	−0.298300	+	0.516671i	−0.975747	−	0.218900i	$-0.929753\pi$
$59$	−2.29129	+	3.96863i	−0.298300	+	0.516671i	0.677447	+	0.735572i	$0.263086\pi$
$60$		0			0
$61$	−0.686932	−	1.18980i	−0.0879526	−	0.152338i	0.818693	−	0.574232i	$-0.194699\pi$
$61$	−0.686932	−	1.18980i	−0.0879526	−	0.152338i	−0.906646	+	0.421893i	$0.861366\pi$
$62$	−2.39564	+	4.14938i	−0.304247	+	0.526971i
$63$	−2.39564	−	4.14938i	−0.301823	−	0.522772i
$64$	1.00000			0.125000
$65$		0			0
$66$	−5.29129	−	9.16478i	−0.651313	−	1.12811i
$67$	7.79129	+	13.4949i	0.951857	+	1.64867i	0.741401	+	0.671062i	$0.234162\pi$
$67$	7.79129	+	13.4949i	0.951857	+	1.64867i	0.210456	+	0.977603i	$0.432505\pi$
$68$	0.791288			0.0959577
$69$	−12.7913			−1.53989
$70$		0			0
$71$	2.29129	−	3.96863i	0.271926	−	0.470989i	−0.697429	−	0.716654i	$-0.745673\pi$
$71$	2.29129	−	3.96863i	0.271926	−	0.470989i	0.969355	+	0.245664i	$0.0790061\pi$
$72$	2.39564	+	4.14938i	0.282329	+	0.489009i
$73$	1.39564	−	2.41733i	0.163348	−	0.282927i	−0.772720	−	0.634748i	$-0.781104\pi$
$73$	1.39564	−	2.41733i	0.163348	−	0.282927i	0.936067	+	0.351821i	$0.114437\pi$
$74$	−1.79129	+	3.10260i	−0.208233	+	0.360670i
$75$		0			0
$76$	−0.500000	+	4.33013i	−0.0573539	+	0.496700i
$77$	−3.79129			−0.432057
$78$	0.291288	−	0.504525i	0.0329819	−	0.0571262i
$79$	−7.47822	+	12.9527i	−0.841365	+	1.45729i	0.0473751	+	0.998877i	$0.484914\pi$
$79$	−7.47822	+	12.9527i	−0.841365	+	1.45729i	−0.888741	+	0.458411i	$0.848419\pi$
$80$		0			0
$81$	0.208712	−	0.361500i	0.0231902	−	0.0401667i
$82$	−5.68693	−	9.85005i	−0.628017	−	1.08776i
$83$	−3.79129			−0.416148			−0.208074	−	0.978113i	$-0.566719\pi$
$83$	−3.79129			−0.416148			−0.208074	+	0.978113i	$0.566719\pi$
$84$	2.79129			0.304554
$85$		0			0
$86$	−2.89564	−	5.01540i	−0.312245	−	0.540825i
$87$	18.9564			2.03234
$88$	3.79129			0.404153
$89$	−2.29129	−	3.96863i	−0.242876	−	0.420674i	0.718656	−	0.695365i	$-0.244757\pi$
$89$	−2.29129	−	3.96863i	−0.242876	−	0.420674i	−0.961532	+	0.274692i	$0.911424\pi$
$90$		0			0
$91$	−0.104356	−	0.180750i	−0.0109395	−	0.0189478i
$92$	2.29129	−	3.96863i	0.238883	−	0.413758i
$93$	6.68693	−	11.5821i	0.693403	−	1.20101i
$94$	−12.1652			−1.25474
$95$		0			0
$96$	−2.79129			−0.284885
$97$	−6.18693	+	10.7161i	−0.628188	+	1.08805i	0.359727	+	0.933057i	$0.382870\pi$
$97$	−6.18693	+	10.7161i	−0.628188	+	1.08805i	−0.987915	+	0.154996i	$0.950464\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$	9.08258	+	15.7315i	0.912833	+	1.58107i
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	−2.20871			−0.218695
$103$	−5.16515			−0.508937			−0.254469	−	0.967081i	$-0.581901\pi$
$103$	−5.16515			−0.508937			−0.254469	+	0.967081i	$0.581901\pi$
$104$	0.104356	+	0.180750i	0.0102330	+	0.0177240i
$105$		0			0
$106$	−4.58258			−0.445099
$107$	−18.9564			−1.83259			−0.916294	−	0.400506i	$-0.868834\pi$
$107$	−18.9564			−1.83259			−0.916294	+	0.400506i	$0.868834\pi$
$108$	−2.50000	−	4.33013i	−0.240563	−	0.416667i
$109$	5.87386	−	10.1738i	0.562614	−	0.974476i	−0.434653	−	0.900598i	$-0.643129\pi$
$109$	5.87386	−	10.1738i	0.562614	−	0.974476i	0.997267	−	0.0738783i	$-0.0235376\pi$
$110$		0			0
$111$	5.00000	−	8.66025i	0.474579	−	0.821995i
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	−5.37386			−0.505531			−0.252765	−	0.967528i	$-0.581340\pi$
$113$	−5.37386			−0.505531			−0.252765	+	0.967528i	$0.581340\pi$
$114$	1.39564	−	12.0866i	0.130714	−	1.13202i
$115$		0			0
$116$	−3.39564	+	5.88143i	−0.315278	+	0.546077i
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$	2.29129	+	3.96863i	0.210930	+	0.365342i
$119$	−0.395644	+	0.685275i	−0.0362686	+	0.0628191i
$120$		0			0
$121$	3.37386			0.306715
$122$	−1.37386			−0.124384
$123$	15.8739	+	27.4943i	1.43130	+	2.47908i
$124$	2.39564	+	4.14938i	0.215135	+	0.372625i
$125$		0			0
$126$	−4.79129			−0.426842
$127$	1.31307	+	2.27430i	0.116516	+	0.201812i	0.918385	−	0.395689i	$-0.129494\pi$
$127$	1.31307	+	2.27430i	0.116516	+	0.201812i	−0.801869	+	0.597500i	$0.796161\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	8.08258	+	13.9994i	0.711631	+	1.23258i
$130$		0			0
$131$	−5.76951	+	9.99308i	−0.504084	+	0.873099i	0.495905	+	0.868377i	$0.334837\pi$
$131$	−5.76951	+	9.99308i	−0.504084	+	0.873099i	−0.999989	+	0.00472247i	$0.998497\pi$
$132$	−10.5826			−0.921095
$133$	−3.50000	−	2.59808i	−0.303488	−	0.225282i
$134$	15.5826			1.34613
$135$		0			0
$136$	0.395644	−	0.685275i	0.0339262	−	0.0587619i
$137$	7.66515	+	13.2764i	0.654878	+	1.13428i	0.981924	+	0.189274i	$0.0606134\pi$
$137$	7.66515	+	13.2764i	0.654878	+	1.13428i	−0.327046	+	0.945008i	$0.606053\pi$
$138$	−6.39564	+	11.0776i	−0.544433	+	0.942986i
$139$	6.10436	+	10.5731i	0.517765	+	0.896795i	0.999787	+	0.0206359i	$0.00656907\pi$
$139$	6.10436	+	10.5731i	0.517765	+	0.896795i	−0.482022	+	0.876159i	$0.660098\pi$
$140$		0			0
$141$	33.9564			2.85965
$142$	−2.29129	−	3.96863i	−0.192281	−	0.333040i
$143$	0.395644	+	0.685275i	0.0330854	+	0.0573056i
$144$	4.79129			0.399274
$145$		0			0
$146$	−1.39564	−	2.41733i	−0.115504	−	0.200059i
$147$	8.37386	−	14.5040i	0.690665	−	1.19627i
$148$	1.79129	+	3.10260i	0.147243	+	0.255032i
$149$	11.3739	−	19.7001i	0.931783	−	1.61390i	0.151511	−	0.988456i	$-0.451586\pi$
$149$	11.3739	−	19.7001i	0.931783	−	1.61390i	0.780272	−	0.625440i	$-0.215081\pi$
$150$		0			0
$151$	15.7477			1.28153			0.640766	−	0.767736i	$-0.278617\pi$
$151$	15.7477			1.28153			0.640766	+	0.767736i	$0.278617\pi$
$152$	3.50000	+	2.59808i	0.283887	+	0.210732i
$153$	3.79129			0.306507
$154$	−1.89564	+	3.28335i	−0.152755	+	0.264580i
$155$		0			0
$156$	−0.291288	−	0.504525i	−0.0233217	−	0.0403944i
$157$	−3.97822	+	6.89048i	−0.317496	+	0.549920i	−0.979965	−	0.199170i	$-0.936176\pi$
$157$	−3.97822	+	6.89048i	−0.317496	+	0.549920i	0.662469	+	0.749090i	$0.269509\pi$
$158$	7.47822	+	12.9527i	0.594935	+	1.03046i
$159$	12.7913			1.01442
$160$		0			0
$161$	2.29129	+	3.96863i	0.180579	+	0.312772i
$162$	−0.208712	−	0.361500i	−0.0163980	−	0.0284021i
$163$	14.5826			1.14220			0.571098	−	0.820882i	$-0.306518\pi$
$163$	14.5826			1.14220			0.571098	+	0.820882i	$0.306518\pi$
$164$	−11.3739			−0.888150
$165$		0			0
$166$	−1.89564	+	3.28335i	−0.147131	+	0.254838i
$167$	5.76951	+	9.99308i	0.446458	+	0.773288i	0.998152	−	0.0607584i	$-0.0193519\pi$
$167$	5.76951	+	9.99308i	0.446458	+	0.773288i	−0.551695	+	0.834046i	$0.686019\pi$
$168$	1.39564	−	2.41733i	0.107676	−	0.186501i
$169$	6.47822	−	11.2206i	0.498325	−	0.863124i
$170$		0			0
$171$	−2.39564	+	20.7469i	−0.183199	+	1.58655i
$172$	−5.79129			−0.441582
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	0.122422	+	0.992478i	$0.460934\pi$
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	−0.920722	+	0.390218i	$0.872399\pi$
$174$	9.47822	−	16.4168i	0.718542	−	1.24455i
$175$		0			0
$176$	1.89564	−	3.28335i	0.142890	−	0.247492i
$177$	−6.39564	−	11.0776i	−0.480726	−	0.832642i
$178$	−4.58258			−0.343479
$179$	−16.7477			−1.25178			−0.625892	−	0.779910i	$-0.715265\pi$
$179$	−16.7477			−1.25178			−0.625892	+	0.779910i	$0.715265\pi$
$180$		0			0
$181$	3.81307	+	6.60443i	0.283423	+	0.490903i	0.972226	−	0.234046i	$-0.0751966\pi$
$181$	3.81307	+	6.60443i	0.283423	+	0.490903i	−0.688802	+	0.724949i	$0.741863\pi$
$182$	−0.208712			−0.0154708
$183$	3.83485			0.283480
$184$	−2.29129	−	3.96863i	−0.168916	−	0.292571i
$185$		0			0
$186$	−6.68693	−	11.5821i	−0.490310	−	0.849241i
$187$	1.50000	−	2.59808i	0.109691	−	0.189990i
$188$	−6.08258	+	10.5353i	−0.443617	+	0.768368i
$189$	5.00000			0.363696
$190$		0			0
$191$	15.9564			1.15457			0.577284	−	0.816544i	$-0.304113\pi$
$191$	15.9564			1.15457			0.577284	+	0.816544i	$0.304113\pi$
$192$	−1.39564	+	2.41733i	−0.100722	+	0.174455i
$193$	−1.37386	+	2.37960i	−0.0988929	+	0.171287i	−0.911227	−	0.411905i	$-0.864863\pi$
$193$	−1.37386	+	2.37960i	−0.0988929	+	0.171287i	0.812334	+	0.583193i	$0.198197\pi$
$194$	6.18693	+	10.7161i	0.444196	+	0.769370i
$195$		0			0
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$	−20.2087			−1.43981			−0.719906	−	0.694072i	$-0.755815\pi$
$197$	−20.2087			−1.43981			−0.719906	+	0.694072i	$0.755815\pi$
$198$	18.1652			1.29094
$199$	−1.79129	−	3.10260i	−0.126981	−	0.219938i	0.795525	−	0.605921i	$-0.207195\pi$
$199$	−1.79129	−	3.10260i	−0.126981	−	0.219938i	−0.922506	+	0.385984i	$0.873862\pi$
$200$		0			0
$201$	−43.4955			−3.06793
$202$		0			0
$203$	−3.39564	−	5.88143i	−0.238327	−	0.412795i
$204$	−1.10436	+	1.91280i	−0.0773204	+	0.133923i
$205$		0			0
$206$	−2.58258	+	4.47315i	−0.179937	+	0.311659i
$207$	10.9782	−	19.0148i	0.763039	−	1.32162i
$208$	0.208712			0.0144716
$209$	13.2695	+	9.85005i	0.917871	+	0.681343i
$210$		0			0
$211$	−11.9782	+	20.7469i	−0.824615	+	1.42827i	0.0775988	+	0.996985i	$0.475275\pi$
$211$	−11.9782	+	20.7469i	−0.824615	+	1.42827i	−0.902213	+	0.431290i	$0.858059\pi$
$212$	−2.29129	+	3.96863i	−0.157366	+	0.272566i
$213$	6.39564	+	11.0776i	0.438222	+	0.759023i
$214$	−9.47822	+	16.4168i	−0.647918	+	1.12223i
$215$		0			0
$216$	−5.00000			−0.340207
$217$	−4.79129			−0.325254
$218$	−5.87386	−	10.1738i	−0.397828	−	0.689059i
$219$	3.89564	+	6.74745i	0.263243	+	0.455951i
$220$		0			0
$221$	0.165151			0.0111093
$222$	−5.00000	−	8.66025i	−0.335578	−	0.581238i
$223$	9.60436	−	16.6352i	0.643155	−	1.11398i	−0.341569	−	0.939857i	$-0.610958\pi$
$223$	9.60436	−	16.6352i	0.643155	−	1.11398i	0.984724	−	0.174121i	$-0.0557084\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$	−2.68693	+	4.65390i	−0.178732	+	0.309573i
$227$	−7.74773			−0.514235			−0.257117	−	0.966380i	$-0.582773\pi$
$227$	−7.74773			−0.514235			−0.257117	+	0.966380i	$0.582773\pi$
$228$	−9.76951	−	7.25198i	−0.647001	−	0.480274i
$229$	−25.3303			−1.67387			−0.836937	−	0.547300i	$-0.815656\pi$
$229$	−25.3303			−1.67387			−0.836937	+	0.547300i	$0.815656\pi$
$230$		0			0
$231$	5.29129	−	9.16478i	0.348141	−	0.602998i
$232$	3.39564	+	5.88143i	0.222935	+	0.386135i
$233$	4.58258	−	7.93725i	0.300215	−	0.519987i	−0.675970	−	0.736929i	$-0.736275\pi$
$233$	4.58258	−	7.93725i	0.300215	−	0.519987i	0.976184	+	0.216942i	$0.0696084\pi$
$234$	0.500000	+	0.866025i	0.0326860	+	0.0566139i
$235$		0			0
$236$	4.58258			0.298300
$237$	−20.8739	−	36.1546i	−1.35590	−	2.34849i
$238$	0.395644	+	0.685275i	0.0256458	+	0.0444198i
$239$	16.5826			1.07264			0.536319	−	0.844015i	$-0.319814\pi$
$239$	16.5826			1.07264			0.536319	+	0.844015i	$0.319814\pi$
$240$		0			0
$241$	8.39564	+	14.5417i	0.540811	+	0.936712i	0.998858	+	0.0477840i	$0.0152159\pi$
$241$	8.39564	+	14.5417i	0.540811	+	0.936712i	−0.458047	+	0.888928i	$0.651451\pi$
$242$	1.68693	−	2.92185i	0.108440	−	0.187824i
$243$	8.08258	+	13.9994i	0.518497	+	0.898064i
$244$	−0.686932	+	1.18980i	−0.0439763	+	0.0761692i
$245$		0			0
$246$	31.7477			2.02416
$247$	−0.104356	+	0.903750i	−0.00664002	+	0.0575042i
$248$	4.79129			0.304247
$249$	5.29129	−	9.16478i	0.335322	−	0.580794i
$250$		0			0
$251$	−6.56080	−	11.3636i	−0.414114	−	0.717266i	0.581221	−	0.813746i	$-0.302575\pi$
$251$	−6.56080	−	11.3636i	−0.414114	−	0.717266i	−0.995335	+	0.0964796i	$0.969242\pi$
$252$	−2.39564	+	4.14938i	−0.150911	+	0.261386i
$253$	−8.68693	−	15.0462i	−0.546143	−	0.945947i
$254$	2.62614			0.164778
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.60436	−	9.70703i	−0.349590	−	0.605508i	0.636587	−	0.771205i	$-0.280346\pi$
$257$	−5.60436	−	9.70703i	−0.349590	−	0.605508i	−0.986177	+	0.165697i	$0.947012\pi$
$258$	16.1652			1.00640
$259$	−3.58258			−0.222610
$260$		0			0
$261$	−16.2695	+	28.1796i	−1.00706	+	1.74427i
$262$	5.76951	+	9.99308i	0.356441	+	0.617375i
$263$	−9.70871	+	16.8160i	−0.598665	+	1.03692i	0.394354	+	0.918959i	$0.370969\pi$
$263$	−9.70871	+	16.8160i	−0.598665	+	1.03692i	−0.993018	+	0.117959i	$0.962365\pi$
$264$	−5.29129	+	9.16478i	−0.325656	+	0.564053i
$265$		0			0
$266$	−4.00000	+	1.73205i	−0.245256	+	0.106199i
$267$	12.7913			0.782814
$268$	7.79129	−	13.4949i	0.475929	−	0.824333i
$269$	−6.56080	+	11.3636i	−0.400019	+	0.692853i	−0.993728	−	0.111827i	$-0.964330\pi$
$269$	−6.56080	+	11.3636i	−0.400019	+	0.692853i	0.593709	+	0.804680i	$0.297663\pi$
$270$		0			0
$271$	8.56080	−	14.8277i	0.520031	−	0.900721i	−0.479698	−	0.877434i	$-0.659254\pi$
$271$	8.56080	−	14.8277i	0.520031	−	0.900721i	0.999729	−	0.0232867i	$-0.00741305\pi$
$272$	−0.395644	−	0.685275i	−0.0239894	−	0.0415509i
$273$	0.582576			0.0352591
$274$	15.3303			0.926137
$275$		0			0
$276$	6.39564	+	11.0776i	0.384973	+	0.666792i
$277$	8.74773			0.525600			0.262800	−	0.964850i	$-0.415354\pi$
$277$	8.74773			0.525600			0.262800	+	0.964850i	$0.415354\pi$
$278$	12.2087			0.732230
$279$	11.4782	+	19.8809i	0.687183	+	1.19024i
$280$		0			0
$281$	−5.29129	−	9.16478i	−0.315652	−	0.546725i	0.663924	−	0.747800i	$-0.268890\pi$
$281$	−5.29129	−	9.16478i	−0.315652	−	0.546725i	−0.979576	+	0.201075i	$0.935556\pi$
$282$	16.9782	−	29.4071i	1.01104	−	1.75117i
$283$	10.5608	−	18.2918i	0.627774	−	1.08734i	−0.360223	−	0.932866i	$-0.617299\pi$
$283$	10.5608	−	18.2918i	0.627774	−	1.08734i	0.987997	−	0.154471i	$-0.0493672\pi$
$284$	−4.58258			−0.271926
$285$		0			0
$286$	0.791288			0.0467898
$287$	5.68693	−	9.85005i	0.335689	−	0.581430i
$288$	2.39564	−	4.14938i	0.141165	−	0.244504i
$289$	8.18693	+	14.1802i	0.481584	+	0.834128i
$290$		0			0
$291$	−17.2695	−	29.9117i	−1.01236	−	1.75345i
$292$	−2.79129			−0.163348
$293$	−24.9564			−1.45797			−0.728985	−	0.684529i	$-0.760008\pi$
$293$	−24.9564			−1.45797			−0.728985	+	0.684529i	$0.760008\pi$
$294$	−8.37386	−	14.5040i	−0.488374	−	0.845888i
$295$		0			0
$296$	3.58258			0.208233
$297$	−18.9564			−1.09996
$298$	−11.3739	−	19.7001i	−0.658870	−	1.14120i
$299$	0.478220	−	0.828301i	0.0276562	−	0.0479019i
$300$		0			0
$301$	2.89564	−	5.01540i	0.166902	−	0.289083i
$302$	7.87386	−	13.6379i	0.453090	−	0.784775i
$303$		0			0
$304$	4.00000	−	1.73205i	0.229416	−	0.0993399i
$305$		0			0
$306$	1.89564	−	3.28335i	0.108367	−	0.187697i
$307$	−17.2477	+	29.8739i	−0.984380	+	1.70500i	−0.339719	+	0.940527i	$0.610332\pi$
$307$	−17.2477	+	29.8739i	−0.984380	+	1.70500i	−0.644661	+	0.764469i	$0.723001\pi$
$308$	1.89564	+	3.28335i	0.108014	+	0.187086i
$309$	7.20871	−	12.4859i	0.410089	−	0.710296i
$310$		0			0
$311$	−15.0000			−0.850572			−0.425286	−	0.905059i	$-0.639826\pi$
$311$	−15.0000			−0.850572			−0.425286	+	0.905059i	$0.639826\pi$
$312$	−0.582576			−0.0329819
$313$	−5.87386	−	10.1738i	−0.332010	−	0.575059i	0.650896	−	0.759167i	$-0.274394\pi$
$313$	−5.87386	−	10.1738i	−0.332010	−	0.575059i	−0.982906	+	0.184108i	$0.941060\pi$
$314$	3.97822	+	6.89048i	0.224504	+	0.388852i
$315$		0			0
$316$	14.9564			0.841365
$317$	−4.58258	−	7.93725i	−0.257383	−	0.445801i	0.708157	−	0.706055i	$-0.249527\pi$
$317$	−4.58258	−	7.93725i	−0.257383	−	0.445801i	−0.965540	+	0.260254i	$0.916194\pi$
$318$	6.39564	−	11.0776i	0.358650	−	0.621200i
$319$	12.8739	+	22.2982i	0.720798	+	1.24846i
$320$		0			0
$321$	26.4564	−	45.8239i	1.47665	−	2.55764i
$322$	4.58258			0.255377
$323$	3.16515	−	1.37055i	0.176114	−	0.0762595i
$324$	−0.417424			−0.0231902
$325$		0			0
$326$	7.29129	−	12.6289i	0.403827	−	0.699449i
$327$	16.3956	+	28.3981i	0.906681	+	1.57042i
$328$	−5.68693	+	9.85005i	−0.314008	+	0.543878i
$329$	−6.08258	−	10.5353i	−0.335343	−	0.580832i
$330$		0			0
$331$	−17.9129			−0.984581			−0.492290	−	0.870431i	$-0.663840\pi$
$331$	−17.9129			−0.984581			−0.492290	+	0.870431i	$0.663840\pi$
$332$	1.89564	+	3.28335i	0.104037	+	0.180197i
$333$	8.58258	+	14.8655i	0.470322	+	0.814622i
$334$	11.5390			0.631387
$335$		0			0
$336$	−1.39564	−	2.41733i	−0.0761386	−	0.131876i
$337$	11.6652	−	20.2046i	0.635441	−	1.10062i	−0.350980	−	0.936383i	$-0.614152\pi$
$337$	11.6652	−	20.2046i	0.635441	−	1.10062i	0.986421	−	0.164234i	$-0.0525151\pi$
$338$	−6.47822	−	11.2206i	−0.352369	−	0.610320i
$339$	7.50000	−	12.9904i	0.407344	−	0.705541i
$340$		0			0
$341$	18.1652			0.983698
$342$	16.7695	+	12.4481i	0.906791	+	0.673118i
$343$	−13.0000			−0.701934
$344$	−2.89564	+	5.01540i	−0.156123	+	0.270412i
$345$		0			0
$346$	10.5000	+	18.1865i	0.564483	+	0.977714i
$347$	1.81307	−	3.14033i	0.0973306	−	0.168582i	−0.813248	−	0.581917i	$-0.802303\pi$
$347$	1.81307	−	3.14033i	0.0973306	−	0.168582i	0.910579	+	0.413335i	$0.135636\pi$
$348$	−9.47822	−	16.4168i	−0.508086	−	0.880031i
$349$	−5.41742			−0.289988			−0.144994	−	0.989433i	$-0.546316\pi$
$349$	−5.41742			−0.289988			−0.144994	+	0.989433i	$0.546316\pi$
$350$		0			0
$351$	−0.521780	−	0.903750i	−0.0278506	−	0.0482386i
$352$	−1.89564	−	3.28335i	−0.101038	−	0.175003i
$353$	13.7477			0.731718			0.365859	−	0.930670i	$-0.380775\pi$
$353$	13.7477			0.731718			0.365859	+	0.930670i	$0.380775\pi$
$354$	−12.7913			−0.679849
$355$		0			0
$356$	−2.29129	+	3.96863i	−0.121438	+	0.210337i
$357$	−1.10436	−	1.91280i	−0.0584487	−	0.101236i
$358$	−8.37386	+	14.5040i	−0.442572	+	0.766558i
$359$	17.8521	−	30.9207i	0.942197	−	1.63193i	0.180928	−	0.983496i	$-0.442090\pi$
$359$	17.8521	−	30.9207i	0.942197	−	1.63193i	0.761269	−	0.648437i	$-0.224577\pi$
$360$		0			0
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$	7.62614			0.400821
$363$	−4.70871	+	8.15573i	−0.247143	+	0.428065i
$364$	−0.104356	+	0.180750i	−0.00546974	+	0.00947388i
$365$		0			0
$366$	1.91742	−	3.32108i	0.100225	−	0.173595i
$367$	4.39564	+	7.61348i	0.229451	+	0.397420i	0.957645	−	0.287950i	$-0.0929737\pi$
$367$	4.39564	+	7.61348i	0.229451	+	0.397420i	−0.728195	+	0.685370i	$0.759640\pi$
$368$	−4.58258			−0.238883
$369$	−54.4955			−2.83692
$370$		0			0
$371$	−2.29129	−	3.96863i	−0.118958	−	0.206041i
$372$	−13.3739			−0.693403
$373$	21.3739			1.10670			0.553348	−	0.832950i	$-0.313350\pi$
$373$	21.3739			1.10670			0.553348	+	0.832950i	$0.313350\pi$
$374$	−1.50000	−	2.59808i	−0.0775632	−	0.134343i
$375$		0			0
$376$	6.08258	+	10.5353i	0.313685	+	0.543318i
$377$	−0.708712	+	1.22753i	−0.0365005	+	0.0632208i
$378$	2.50000	−	4.33013i	0.128586	−	0.222718i
$379$	4.83485			0.248349			0.124175	−	0.992260i	$-0.460372\pi$
$379$	4.83485			0.248349			0.124175	+	0.992260i	$0.460372\pi$
$380$		0			0
$381$	−7.33030			−0.375543
$382$	7.97822	−	13.8187i	0.408201	−	0.707025i
$383$	2.29129	−	3.96863i	0.117079	−	0.202787i	−0.801530	−	0.597955i	$-0.795980\pi$
$383$	2.29129	−	3.96863i	0.117079	−	0.202787i	0.918609	+	0.395168i	$0.129313\pi$
$384$	1.39564	+	2.41733i	0.0712212	+	0.123359i
$385$		0			0
$386$	1.37386	+	2.37960i	0.0699278	+	0.121119i
$387$	−27.7477			−1.41050
$388$	12.3739			0.628188
$389$	−9.31307	−	16.1307i	−0.472191	−	0.817859i	0.527302	−	0.849678i	$-0.323204\pi$
$389$	−9.31307	−	16.1307i	−0.472191	−	0.817859i	−0.999494	+	0.0318184i	$0.989870\pi$
$390$		0			0
$391$	−3.62614			−0.183382
$392$	6.00000			0.303046
$393$	−16.1044	−	27.8936i	−0.812357	−	1.40704i
$394$	−10.1044	+	17.5013i	−0.509050	+	0.881701i
$395$		0			0
$396$	9.08258	−	15.7315i	0.456417	−	0.790537i
$397$	−5.70871	+	9.88778i	−0.286512	+	0.496253i	−0.972975	−	0.230912i	$-0.925829\pi$
$397$	−5.70871	+	9.88778i	−0.286512	+	0.496253i	0.686463	+	0.727165i	$0.259163\pi$
$398$	−3.58258			−0.179578
$399$	11.1652	−	4.83465i	0.558957	−	0.242035i
$400$		0			0
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	−0.676425	−	0.736512i	$-0.736472\pi$
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	0.976050	+	0.217545i	$0.0698049\pi$
$402$	−21.7477	+	37.6682i	−1.08468	+	1.87872i
$403$	0.500000	+	0.866025i	0.0249068	+	0.0431398i
$404$		0			0
$405$		0			0
$406$	−6.79129			−0.337046
$407$	13.5826			0.673263
$408$	1.10436	+	1.91280i	0.0546738	+	0.0946978i
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	0.962757	−	0.270367i	$-0.0871450\pi$
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	−0.715523	+	0.698589i	$0.753812\pi$
$410$		0			0
$411$	−42.7913			−2.11074
$412$	2.58258	+	4.47315i	0.127234	+	0.220376i
$413$	−2.29129	+	3.96863i	−0.112747	+	0.195283i
$414$	−10.9782	−	19.0148i	−0.539550	−	0.934528i
$415$		0			0
$416$	0.104356	−	0.180750i	0.00511648	−	0.00886200i
$417$	−34.0780			−1.66881
$418$	15.1652	−	6.56670i	0.741752	−	0.321188i
$419$	−22.7477			−1.11130			−0.555650	−	0.831417i	$-0.687530\pi$
$419$	−22.7477			−1.11130			−0.555650	+	0.831417i	$0.687530\pi$
$420$		0			0
$421$	−10.0000	+	17.3205i	−0.487370	+	0.844150i	−0.999895	−	0.0145228i	$-0.995377\pi$
$421$	−10.0000	+	17.3205i	−0.487370	+	0.844150i	0.512524	+	0.858673i	$0.328710\pi$
$422$	11.9782	+	20.7469i	0.583091	+	1.00994i
$423$	−29.1434	+	50.4778i	−1.41700	+	2.45431i
$424$	2.29129	+	3.96863i	0.111275	+	0.192734i
$425$		0			0
$426$	12.7913			0.619740
$427$	−0.686932	−	1.18980i	−0.0332430	−	0.0575785i
$428$	9.47822	+	16.4168i	0.458147	+	0.793534i
$429$	−2.20871			−0.106638
$430$		0			0
$431$	−4.10436	−	7.10895i	−0.197700	−	0.342426i	0.750082	−	0.661344i	$-0.230014\pi$
$431$	−4.10436	−	7.10895i	−0.197700	−	0.342426i	−0.947782	+	0.318918i	$0.896680\pi$
$432$	−2.50000	+	4.33013i	−0.120281	+	0.208333i
$433$	3.45644	+	5.98673i	0.166106	+	0.287704i	0.937047	−	0.349202i	$-0.113547\pi$
$433$	3.45644	+	5.98673i	0.166106	+	0.287704i	−0.770942	+	0.636906i	$0.780214\pi$
$434$	−2.39564	+	4.14938i	−0.114995	+	0.199176i
$435$		0			0
$436$	−11.7477			−0.562614
$437$	2.29129	−	19.8431i	0.109607	−	0.949226i
$438$	7.79129			0.372282
$439$	12.6652	−	21.9367i	0.604475	−	1.04698i	−0.387660	−	0.921803i	$-0.626716\pi$
$439$	12.6652	−	21.9367i	0.604475	−	1.04698i	0.992134	−	0.125178i	$-0.0399503\pi$
$440$		0			0
$441$	14.3739	+	24.8963i	0.684470	+	1.18554i
$442$	0.0825757	−	0.143025i	0.00392773	−	0.00680302i
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	−0.996551	−	0.0829786i	$-0.973557\pi$
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	0.426414	−	0.904528i	$-0.359777\pi$
$444$	−10.0000			−0.474579
$445$		0			0
$446$	−9.60436	−	16.6352i	−0.454779	−	0.787701i
$447$	31.7477	+	54.9887i	1.50162	+	2.60088i
$448$	1.00000			0.0472456
$449$	3.33030			0.157167			0.0785834	−	0.996908i	$-0.474960\pi$
$449$	3.33030			0.157167			0.0785834	+	0.996908i	$0.474960\pi$
$450$		0			0
$451$	−21.5608	+	37.3444i	−1.01526	+	1.75848i
$452$	2.68693	+	4.65390i	0.126383	+	0.218901i
$453$	−21.9782	+	38.0674i	−1.03263	+	1.78856i
$454$	−3.87386	+	6.70973i	−0.181809	+	0.314903i
$455$		0			0
$456$	−11.1652	+	4.83465i	−0.522856	+	0.226403i
$457$	20.7477			0.970538			0.485269	−	0.874365i	$-0.338722\pi$
$457$	20.7477			0.970538			0.485269	+	0.874365i	$0.338722\pi$
$458$	−12.6652	+	21.9367i	−0.591804	+	1.02503i
$459$	−1.97822	+	3.42638i	−0.0923354	+	0.159930i
$460$		0			0
$461$	−6.39564	+	11.0776i	−0.297875	+	0.515934i	−0.975650	−	0.219335i	$-0.929611\pi$
$461$	−6.39564	+	11.0776i	−0.297875	+	0.515934i	0.677775	+	0.735270i	$0.262944\pi$
$462$	−5.29129	−	9.16478i	−0.246173	−	0.426384i
$463$	−17.9564			−0.834507			−0.417253	−	0.908790i	$-0.637007\pi$
$463$	−17.9564			−0.834507			−0.417253	+	0.908790i	$0.637007\pi$
$464$	6.79129			0.315278
$465$		0			0
$466$	−4.58258	−	7.93725i	−0.212284	−	0.367686i
$467$	12.3303			0.570578			0.285289	−	0.958441i	$-0.407910\pi$
$467$	12.3303			0.570578			0.285289	+	0.958441i	$0.407910\pi$
$468$	1.00000			0.0462250
$469$	7.79129	+	13.4949i	0.359768	+	0.623137i
$470$		0			0
$471$	−11.1044	−	19.2333i	−0.511662	−	0.886224i
$472$	2.29129	−	3.96863i	0.105465	−	0.182671i
$473$	−10.9782	+	19.0148i	−0.504779	+	0.874303i
$474$	−41.7477			−1.91754
$475$		0			0
$476$	0.791288			0.0362686
$477$	−10.9782	+	19.0148i	−0.502658	+	0.870629i
$478$	8.29129	−	14.3609i	0.379235	−	0.656854i
$479$	−15.8739	−	27.4943i	−0.725295	−	1.25625i	−0.958852	−	0.283905i	$-0.908370\pi$
$479$	−15.8739	−	27.4943i	−0.725295	−	1.25625i	0.233557	−	0.972343i	$-0.424963\pi$
$480$		0			0
$481$	0.373864	+	0.647551i	0.0170467	+	0.0295258i
$482$	16.7913			0.764822
$483$	−12.7913			−0.582024
$484$	−1.68693	−	2.92185i	−0.0766787	−	0.132811i
$485$		0			0
$486$	16.1652			0.733266
$487$	−23.0000			−1.04223			−0.521115	−	0.853487i	$-0.674484\pi$
$487$	−23.0000			−1.04223			−0.521115	+	0.853487i	$0.674484\pi$
$488$	0.686932	+	1.18980i	0.0310959	+	0.0538597i
$489$	−20.3521	+	35.2508i	−0.920353	+	1.59410i
$490$		0			0
$491$	15.7087	−	27.2083i	0.708924	−	1.22789i	−0.256332	−	0.966589i	$-0.582514\pi$
$491$	15.7087	−	27.2083i	0.708924	−	1.22789i	0.965257	−	0.261304i	$-0.0841525\pi$
$492$	15.8739	−	27.4943i	0.715649	−	1.23954i
$493$	5.37386			0.242027
$494$	0.730493	+	0.542250i	0.0328664	+	0.0243970i
$495$		0			0
$496$	2.39564	−	4.14938i	0.107568	−	0.186313i
$497$	2.29129	−	3.96863i	0.102778	−	0.178017i
$498$	−5.29129	−	9.16478i	−0.237108	−	0.410684i
$499$	9.66515	−	16.7405i	0.432672	−	0.749409i	−0.564431	−	0.825480i	$-0.690904\pi$
$499$	9.66515	−	16.7405i	0.432672	−	0.749409i	0.997102	+	0.0760712i	$0.0242376\pi$
$500$		0			0
$501$	−32.2087			−1.43898
$502$	−13.1216			−0.585645
$503$	−2.29129	−	3.96863i	−0.102163	−	0.176952i	0.810412	−	0.585860i	$-0.199243\pi$
$503$	−2.29129	−	3.96863i	−0.102163	−	0.176952i	−0.912576	+	0.408908i	$0.865910\pi$
$504$	2.39564	+	4.14938i	0.106710	+	0.184828i
$505$		0			0
$506$	−17.3739			−0.772362
$507$	18.0826	+	31.3199i	0.803075	+	1.39097i
$508$	1.31307	−	2.27430i	0.0582580	−	0.100906i
$509$	−11.2087	−	19.4141i	−0.496817	−	0.860513i	0.503176	−	0.864184i	$-0.332165\pi$
$509$	−11.2087	−	19.4141i	−0.496817	−	0.860513i	−0.999993	+	0.00367102i	$0.998831\pi$
$510$		0			0
$511$	1.39564	−	2.41733i	0.0617397	−	0.106936i
$512$	−1.00000			−0.0441942
$513$	−17.5000	−	12.9904i	−0.772644	−	0.573539i
$514$	−11.2087			−0.494395
$515$		0			0
$516$	8.08258	−	13.9994i	0.355816	−	0.616291i
$517$	23.0608	+	39.9425i	1.01421	+	1.75667i
$518$	−1.79129	+	3.10260i	−0.0787047	+	0.136320i
$519$	−29.3085	−	50.7638i	−1.28650	−	2.22829i
$520$		0			0
$521$	13.2523			0.580593			0.290296	−	0.956937i	$-0.406246\pi$
$521$	13.2523			0.580593			0.290296	+	0.956937i	$0.406246\pi$
$522$	16.2695	+	28.1796i	0.712097	+	1.23339i
$523$	−8.87386	−	15.3700i	−0.388027	−	0.672082i	0.604157	−	0.796865i	$-0.293510\pi$
$523$	−8.87386	−	15.3700i	−0.388027	−	0.672082i	−0.992184	+	0.124783i	$0.960177\pi$
$524$	11.5390			0.504084
$525$		0			0
$526$	9.70871	+	16.8160i	0.423320	+	0.733212i
$527$	1.89564	−	3.28335i	0.0825755	−	0.143025i
$528$	5.29129	+	9.16478i	0.230274	+	0.398846i
$529$	1.00000	−	1.73205i	0.0434783	−	0.0753066i
$530$		0			0
$531$	21.9564			0.952828
$532$	−0.500000	+	4.33013i	−0.0216777	+	0.187735i
$533$	−2.37386			−0.102823
$534$	6.39564	−	11.0776i	0.276767	−	0.479374i
$535$		0			0
$536$	−7.79129	−	13.4949i	−0.336532	−	0.582891i
$537$	23.3739	−	40.4847i	1.00866	−	1.74704i
$538$	6.56080	+	11.3636i	0.282856	+	0.489921i
$539$	22.7477			0.979814
$540$		0			0
$541$	8.56080	+	14.8277i	0.368057	+	0.637494i	0.989262	−	0.146155i	$-0.0466897\pi$
$541$	8.56080	+	14.8277i	0.368057	+	0.637494i	−0.621204	+	0.783649i	$0.713356\pi$
$542$	−8.56080	−	14.8277i	−0.367718	−	0.636906i
$543$	−21.2867			−0.913502
$544$	−0.791288			−0.0339262
$545$		0			0
$546$	0.291288	−	0.504525i	0.0124660	−	0.0215917i
$547$	8.41742	+	14.5794i	0.359903	+	0.623370i	0.987944	−	0.154810i	$-0.0494764\pi$
$547$	8.41742	+	14.5794i	0.359903	+	0.623370i	−0.628041	+	0.778180i	$0.716143\pi$
$548$	7.66515	−	13.2764i	0.327439	−	0.567141i
$549$	−3.29129	+	5.70068i	−0.140469	+	0.243299i
$550$		0			0
$551$	−3.39564	+	29.4071i	−0.144659	+	1.25279i
$552$	12.7913			0.544433
$553$	−7.47822	+	12.9527i	−0.318006	+	0.550803i
$554$	4.37386	−	7.57575i	0.185828	−	0.321863i
$555$		0			0
$556$	6.10436	−	10.5731i	0.258882	−	0.448397i
$557$	4.97822	+	8.62253i	0.210934	+	0.365348i	0.952007	−	0.306076i	$-0.0990162\pi$
$557$	4.97822	+	8.62253i	0.210934	+	0.365348i	−0.741073	+	0.671424i	$0.765683\pi$
$558$	22.9564			0.971824
$559$	−1.20871			−0.0511231
$560$		0			0
$561$	4.18693	+	7.25198i	0.176772	+	0.306179i
$562$	−10.5826			−0.446399
$563$	14.3739			0.605786			0.302893	−	0.953025i	$-0.402047\pi$
$563$	14.3739			0.605786			0.302893	+	0.953025i	$0.402047\pi$
$564$	−16.9782	−	29.4071i	−0.714912	−	1.23826i
$565$		0			0
$566$	−10.5608	−	18.2918i	−0.443903	−	0.768863i
$567$	0.208712	−	0.361500i	0.00876509	−	0.0151816i
$568$	−2.29129	+	3.96863i	−0.0961403	+	0.166520i
$569$	−8.83485			−0.370376			−0.185188	−	0.982703i	$-0.559289\pi$
$569$	−8.83485			−0.370376			−0.185188	+	0.982703i	$0.559289\pi$
$570$		0			0
$571$	−22.0000			−0.920671			−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000			−0.920671			−0.460336	+	0.887745i	$0.652271\pi$
$572$	0.395644	−	0.685275i	0.0165427	−	0.0286528i
$573$	−22.2695	+	38.5719i	−0.930322	+	1.61137i
$574$	−5.68693	−	9.85005i	−0.237368	−	0.411133i
$575$		0			0
$576$	−2.39564	−	4.14938i	−0.0998185	−	0.172891i
$577$	−14.0000			−0.582828			−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000			−0.582828			−0.291414	+	0.956597i	$0.594126\pi$
$578$	16.3739			0.681063
$579$	−3.83485	−	6.64215i	−0.159371	−	0.276038i
$580$		0			0
$581$	−3.79129			−0.157289
$582$	−34.5390			−1.43169
$583$	8.68693	+	15.0462i	0.359776	+	0.623150i
$584$	−1.39564	+	2.41733i	−0.0577522	+	0.100030i
$585$		0			0
$586$	−12.4782	+	21.6129i	−0.515471	+	0.892821i
$587$	−4.74773	+	8.22330i	−0.195960	+	0.339412i	−0.947215	−	0.320600i	$-0.896116\pi$
$587$	−4.74773	+	8.22330i	−0.195960	+	0.339412i	0.751255	+	0.660012i	$0.229449\pi$
$588$	−16.7477			−0.690665
$589$	16.7695	+	12.4481i	0.690976	+	0.512916i
$590$		0			0
$591$	28.2042	−	48.8510i	1.16016	−	2.00946i
$592$	1.79129	−	3.10260i	0.0736215	−	0.127516i
$593$	−5.91742	−	10.2493i	−0.242999	−	0.420887i	0.718568	−	0.695457i	$-0.244798\pi$
$593$	−5.91742	−	10.2493i	−0.242999	−	0.420887i	−0.961567	+	0.274569i	$0.911465\pi$
$594$	−9.47822	+	16.4168i	−0.388896	+	0.673588i
$595$		0			0
$596$	−22.7477			−0.931783
$597$	10.0000			0.409273
$598$	−0.478220	−	0.828301i	−0.0195559	−	0.0338717i
$599$	18.5608	+	32.1482i	0.758374	+	1.31354i	0.943680	+	0.330861i	$0.107339\pi$
$599$	18.5608	+	32.1482i	0.758374	+	1.31354i	−0.185306	+	0.982681i	$0.559328\pi$
$600$		0			0
$601$	9.91288			0.404355			0.202177	−	0.979349i	$-0.435198\pi$
$601$	9.91288			0.404355			0.202177	+	0.979349i	$0.435198\pi$
$602$	−2.89564	−	5.01540i	−0.118018	−	0.204413i
$603$	37.3303	−	64.6580i	1.52021	−	2.63308i
$604$	−7.87386	−	13.6379i	−0.320383	−	0.554920i
$605$		0			0
$606$		0			0
$607$	18.2087			0.739069			0.369534	−	0.929217i	$-0.379517\pi$
$607$	18.2087			0.739069			0.369534	+	0.929217i	$0.379517\pi$
$608$	0.500000	−	4.33013i	0.0202777	−	0.175610i
$609$	18.9564			0.768154
$610$		0			0
$611$	−1.26951	+	2.19885i	−0.0513588	+	0.0889560i
$612$	−1.89564	−	3.28335i	−0.0766269	−	0.132722i
$613$	7.24773	−	12.5534i	0.292733	−	0.507028i	−0.681722	−	0.731611i	$-0.738769\pi$
$613$	7.24773	−	12.5534i	0.292733	−	0.507028i	0.974455	+	0.224583i	$0.0721020\pi$
$614$	17.2477	+	29.8739i	0.696062	+	1.20561i
$615$		0			0
$616$	3.79129			0.152755
$617$	−16.5000	−	28.5788i	−0.664265	−	1.15054i	−0.979484	−	0.201522i	$-0.935411\pi$
$617$	−16.5000	−	28.5788i	−0.664265	−	1.15054i	0.315219	−	0.949019i	$-0.397922\pi$
$618$	−7.20871	−	12.4859i	−0.289977	−	0.502255i
$619$	−24.3739			−0.979668			−0.489834	−	0.871816i	$-0.662943\pi$
$619$	−24.3739			−0.979668			−0.489834	+	0.871816i	$0.662943\pi$
$620$		0			0
$621$	11.4564	+	19.8431i	0.459731	+	0.796278i
$622$	−7.50000	+	12.9904i	−0.300723	+	0.520867i
$623$	−2.29129	−	3.96863i	−0.0917985	−	0.159000i
$624$	−0.291288	+	0.504525i	−0.0116608	+	0.0201972i
$625$		0			0
$626$	−11.7477			−0.469534
$627$	−42.3303	+	18.3296i	−1.69051	+	0.732012i
$628$	7.95644			0.317496
$629$	1.41742	−	2.45505i	0.0565164	−	0.0978893i
$630$		0			0
$631$	18.1044	+	31.3577i	0.720723	+	1.24833i	0.960710	+	0.277553i	$0.0895234\pi$
$631$	18.1044	+	31.3577i	0.720723	+	1.24833i	−0.239987	+	0.970776i	$0.577143\pi$
$632$	7.47822	−	12.9527i	0.297468	−	0.515229i
$633$	−33.4347	−	57.9105i	−1.32891	−	2.30174i
$634$	−9.16515			−0.363995
$635$		0			0
$636$	−6.39564	−	11.0776i	−0.253604	−	0.439255i
$637$	0.626136	+	1.08450i	0.0248084	+	0.0429695i
$638$	25.7477			1.01936
$639$	−21.9564			−0.868583
$640$		0			0
$641$	−8.52178	+	14.7602i	−0.336590	+	0.582991i	−0.983789	−	0.179330i	$-0.942607\pi$
$641$	−8.52178	+	14.7602i	−0.336590	+	0.582991i	0.647199	+	0.762321i	$0.275940\pi$
$642$	−26.4564	−	45.8239i	−1.04415	−	1.80852i
$643$	14.7477	−	25.5438i	0.581594	−	1.00735i	−0.413697	−	0.910415i	$-0.635763\pi$
$643$	14.7477	−	25.5438i	0.581594	−	1.00735i	0.995291	−	0.0969351i	$-0.0309039\pi$
$644$	2.29129	−	3.96863i	0.0902894	−	0.156386i
$645$		0			0
$646$	0.395644	−	3.42638i	0.0155664	−	0.134809i
$647$	−18.7913			−0.738762			−0.369381	−	0.929278i	$-0.620430\pi$
$647$	−18.7913			−0.738762			−0.369381	+	0.929278i	$0.620430\pi$
$648$	−0.208712	+	0.361500i	−0.00819899	+	0.0142011i
$649$	8.68693	−	15.0462i	0.340992	−	0.590615i
$650$		0			0
$651$	6.68693	−	11.5821i	0.262082	−	0.453939i
$652$	−7.29129	−	12.6289i	−0.285549	−	0.494585i
$653$	27.3303			1.06952			0.534759	−	0.845005i	$-0.320403\pi$
$653$	27.3303			1.06952			0.534759	+	0.845005i	$0.320403\pi$
$654$	32.7913			1.28224
$655$		0			0
$656$	5.68693	+	9.85005i	0.222037	+	0.384580i
$657$	−13.3739			−0.521764
$658$	−12.1652			−0.474247
$659$	−0.873864	−	1.51358i	−0.0340409	−	0.0589606i	0.848503	−	0.529190i	$-0.177504\pi$
$659$	−0.873864	−	1.51358i	−0.0340409	−	0.0589606i	−0.882544	+	0.470230i	$0.844171\pi$
$660$		0			0
$661$	−23.4347	−	40.5900i	−0.911503	−	1.57877i	−0.811943	−	0.583737i	$-0.801590\pi$
$661$	−23.4347	−	40.5900i	−0.911503	−	1.57877i	−0.0995599	−	0.995032i	$-0.531744\pi$
$662$	−8.95644	+	15.5130i	−0.348102	+	0.602930i
$663$	−0.230493	+	0.399225i	−0.00895159	+	0.0155046i
$664$	3.79129			0.147131
$665$		0			0
$666$	17.1652			0.665136
$667$	15.5608	−	26.9521i	0.602516	−	1.04359i
$668$	5.76951	−	9.99308i	0.223229	−	0.386644i
$669$	26.8085	+	46.4337i	1.03648	+	1.79523i
$670$		0			0
$671$	2.60436	+	4.51088i	0.100540	+	0.174140i
$672$	−2.79129			−0.107676
$673$	−2.79129			−0.107596			−0.0537981	−	0.998552i	$-0.517133\pi$
$673$	−2.79129			−0.107596			−0.0537981	+	0.998552i	$0.517133\pi$
$674$	−11.6652	−	20.2046i	−0.449325	−	0.778253i
$675$		0			0
$676$	−12.9564			−0.498325
$677$	35.2432			1.35451			0.677253	−	0.735750i	$-0.263170\pi$
$677$	35.2432			1.35451			0.677253	+	0.735750i	$0.263170\pi$
$678$	−7.50000	−	12.9904i	−0.288036	−	0.498893i
$679$	−6.18693	+	10.7161i	−0.237433	+	0.411245i
$680$		0			0
$681$	10.8131	−	18.7288i	0.414358	−	0.717689i
$682$	9.08258	−	15.7315i	0.347790	−	0.602390i
$683$	36.1652			1.38382			0.691911	−	0.721983i	$-0.256769\pi$
$683$	36.1652			1.38382			0.691911	+	0.721983i	$0.256769\pi$
$684$	19.1652	−	8.29875i	0.732798	−	0.317311i
$685$		0			0
$686$	−6.50000	+	11.2583i	−0.248171	+	0.429845i
$687$	35.3521	−	61.2316i	1.34877	−	2.33613i
$688$	2.89564	+	5.01540i	0.110395	+	0.191210i
$689$	−0.478220	+	0.828301i	−0.0182187	+	0.0315557i
$690$		0			0
$691$	−32.1216			−1.22196			−0.610981	−	0.791645i	$-0.709225\pi$
$691$	−32.1216			−1.22196			−0.610981	+	0.791645i	$0.709225\pi$
$692$	21.0000			0.798300
$693$	9.08258	+	15.7315i	0.345019	+	0.597590i
$694$	−1.81307	−	3.14033i	−0.0688231	−	0.119205i
$695$		0			0
$696$	−18.9564			−0.718542
$697$	4.50000	+	7.79423i	0.170450	+	0.295227i
$698$	−2.70871	+	4.69163i	−0.102526	+	0.177581i
$699$	12.7913	+	22.1552i	0.483811	+	0.837985i
$700$		0			0
$701$	6.47822	−	11.2206i	0.244679	−	0.423796i	−0.717362	−	0.696700i	$-0.754651\pi$
$701$	6.47822	−	11.2206i	0.244679	−	0.423796i	0.962041	+	0.272904i	$0.0879841\pi$
$702$	−1.04356			−0.0393867
$703$	12.5390	+	9.30780i	0.472918	+	0.351051i
$704$	−3.79129			−0.142890
$705$		0			0
$706$	6.87386	−	11.9059i	0.258701	−	0.448084i
$707$		0			0
$708$	−6.39564	+	11.0776i	−0.240363	+	0.416321i
$709$	13.3739	+	23.1642i	0.502266	+	0.869950i	0.999997	+	0.00261852i	$0.000833501\pi$
$709$	13.3739	+	23.1642i	0.502266	+	0.869950i	−0.497731	+	0.867332i	$0.665833\pi$
$710$		0			0
$711$	71.6606			2.68748
$712$	2.29129	+	3.96863i	0.0858696	+	0.148731i
$713$	−10.9782	−	19.0148i	−0.411138	−	0.712111i
$714$	−2.20871			−0.0826590
$715$		0			0
$716$	8.37386	+	14.5040i	0.312946	+	0.542038i
$717$	−23.1434	+	40.0855i	−0.864305	+	1.49702i
$718$	−17.8521	−	30.9207i	−0.666234	−	1.15395i
$719$	6.08258	−	10.5353i	0.226842	−	0.392902i	−0.730029	−	0.683417i	$-0.760493\pi$
$719$	6.08258	−	10.5353i	0.226842	−	0.392902i	0.956870	+	0.290515i	$0.0938266\pi$
$720$		0			0
$721$	−5.16515			−0.192360
$722$	18.5000	+	4.33013i	0.688499	+	0.161151i
$723$	−46.8693			−1.74309
$724$	3.81307	−	6.60443i	0.141712	−	0.245452i
$725$		0			0
$726$	4.70871	+	8.15573i	0.174757	+	0.302687i
$727$	−2.08258	+	3.60713i	−0.0772385	+	0.133781i	−0.902058	−	0.431616i	$-0.857944\pi$
$727$	−2.08258	+	3.60713i	−0.0772385	+	0.133781i	0.824819	+	0.565397i	$0.191277\pi$
$728$	0.104356	+	0.180750i	0.00386769	+	0.00669904i
$729$	−43.8693			−1.62479
$730$		0			0
$731$	2.29129	+	3.96863i	0.0847463	+	0.146785i
$732$	−1.91742	−	3.32108i	−0.0708700	−	0.122751i
$733$	−12.7477			−0.470848			−0.235424	−	0.971893i	$-0.575648\pi$
$733$	−12.7477			−0.470848			−0.235424	+	0.971893i	$0.575648\pi$
$734$	8.79129			0.324492
$735$		0			0
$736$	−2.29129	+	3.96863i	−0.0844580	+	0.146286i
$737$	−29.5390	−	51.1631i	−1.08808	−	1.88462i
$738$	−27.2477	+	47.1944i	−1.00300	+	1.73725i
$739$	17.8739	−	30.9584i	0.657501	−	1.13882i	−0.323760	−	0.946139i	$-0.604947\pi$
$739$	17.8739	−	30.9584i	0.657501	−	1.13882i	0.981261	−	0.192685i	$-0.0617197\pi$
$740$		0			0
$741$	−2.03901	−	1.51358i	−0.0749051	−	0.0556026i
$742$	−4.58258			−0.168232
$743$	9.70871	−	16.8160i	0.356178	−	0.616919i	−0.631141	−	0.775668i	$-0.717413\pi$
$743$	9.70871	−	16.8160i	0.356178	−	0.616919i	0.987319	+	0.158750i	$0.0507463\pi$
$744$	−6.68693	+	11.5821i	−0.245155	+	0.424621i
$745$		0			0
$746$	10.6869	−	18.5103i	0.391276	−	0.677711i
$747$	9.08258	+	15.7315i	0.332314	+	0.575585i
$748$	−3.00000			−0.109691
$749$	−18.9564			−0.692653
$750$		0			0
$751$	−10.7913	−	18.6911i	−0.393780	−	0.682046i	0.599165	−	0.800626i	$-0.295499\pi$
$751$	−10.7913	−	18.6911i	−0.393780	−	0.682046i	−0.992945	+	0.118579i	$0.962166\pi$
$752$	12.1652			0.443617
$753$	36.6261			1.33473
$754$	0.708712	+	1.22753i	0.0258098	+	0.0447038i
$755$		0			0
$756$	−2.50000	−	4.33013i	−0.0909241	−	0.157485i
$757$	22.8739	−	39.6187i	0.831365	−	1.43997i	−0.0655915	−	0.997847i	$-0.520893\pi$
$757$	22.8739	−	39.6187i	0.831365	−	1.43997i	0.896956	−	0.442119i	$-0.145773\pi$
$758$	2.41742	−	4.18710i	0.0878048	−	0.152082i
$759$	48.4955			1.76027
$760$		0			0
$761$	25.2523			0.915394			0.457697	−	0.889108i	$-0.348674\pi$
$761$	25.2523			0.915394			0.457697	+	0.889108i	$0.348674\pi$
$762$	−3.66515	+	6.34823i	−0.132774	+	0.229972i
$763$	5.87386	−	10.1738i	0.212648	−	0.368317i
$764$	−7.97822	−	13.8187i	−0.288642	−	0.499942i
$765$		0			0
$766$	−2.29129	−	3.96863i	−0.0827876	−	0.143392i
$767$	0.956439			0.0345350
$768$	2.79129			0.100722
$769$	11.1652	+	19.3386i	0.402626	+	0.697368i	0.994042	−	0.108998i	$-0.0347643\pi$
$769$	11.1652	+	19.3386i	0.402626	+	0.697368i	−0.591416	+	0.806366i	$0.701431\pi$
$770$		0			0
$771$	31.2867			1.12676
$772$	2.74773			0.0988929
$773$	−10.6652	−	18.4726i	−0.383599	−	0.664413i	0.607975	−	0.793956i	$-0.291982\pi$
$773$	−10.6652	−	18.4726i	−0.383599	−	0.664413i	−0.991574	+	0.129544i	$0.958649\pi$
$774$	−13.8739	+	24.0302i	−0.498686	+	0.863749i
$775$		0			0
$776$	6.18693	−	10.7161i	0.222098	−	0.384685i
$777$	5.00000	−	8.66025i	0.179374	−	0.310685i
$778$	−18.6261			−0.667779
$779$	−45.4955	+	19.7001i	−1.63004	+	0.705830i
$780$		0			0
$781$	−8.68693	+	15.0462i	−0.310843	+	0.538396i
$782$	−1.81307	+	3.14033i	−0.0648352	+	0.112298i
$783$	−16.9782	−	29.4071i	−0.606752	−	1.05093i
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$		0			0
$786$	−32.2087			−1.14885
$787$	23.7477			0.846515			0.423258	−	0.906009i	$-0.360887\pi$
$787$	23.7477			0.846515			0.423258	+	0.906009i	$0.360887\pi$
$788$	10.1044	+	17.5013i	0.359953	+	0.623457i
$789$	−27.0998	−	46.9382i	−0.964779	−	1.67105i
$790$		0			0
$791$	−5.37386			−0.191073
$792$	−9.08258	−	15.7315i	−0.322735	−	0.558994i
$793$	−0.143371	+	0.248326i	−0.00509125	+	0.00881831i
$794$	5.70871	+	9.88778i	0.202595	+	0.350904i
$795$		0			0
$796$	−1.79129	+	3.10260i	−0.0634905	+	0.109969i
$797$	38.5390			1.36512			0.682561	−	0.730829i	$-0.260866\pi$
$797$	38.5390			1.36512			0.682561	+	0.730829i	$0.260866\pi$
$798$	1.39564	−	12.0866i	0.0494053	−	0.427862i
$799$	9.62614			0.340548
$800$		0			0
$801$	−10.9782	+	19.0148i	−0.387896	+	0.671856i
$802$	−6.00000	−	10.3923i	−0.211867	−	0.366965i
$803$	−5.29129	+	9.16478i	−0.186725	+	0.323418i
$804$	21.7477	+	37.6682i	0.766983	+	1.32845i
$805$		0			0
$806$	1.00000			0.0352235
$807$	−18.3131	−	31.7192i	−0.644651	−	1.11657i
$808$		0			0
$809$	−2.53901			−0.0892670			−0.0446335	−	0.999003i	$-0.514212\pi$
$809$	−2.53901			−0.0892670			−0.0446335	+	0.999003i	$0.514212\pi$
$810$		0			0
$811$	−12.9347	−	22.4035i	−0.454197	−	0.786693i	0.544444	−	0.838797i	$-0.316741\pi$
$811$	−12.9347	−	22.4035i	−0.454197	−	0.786693i	−0.998642	+	0.0521042i	$0.983407\pi$
$812$	−3.39564	+	5.88143i	−0.119164	+	0.206398i
$813$	23.8956	+	41.3885i	0.838057	+	1.45156i
$814$	6.79129	−	11.7629i	0.238035	−	0.412288i
$815$		0			0
$816$	2.20871			0.0773204
$817$	−23.1652	+	10.0308i	−0.810446	+	0.350933i
$818$	10.0000			0.349642
$819$	−0.500000	+	0.866025i	−0.0174714	+	0.0302614i
$820$		0			0
$821$	18.1652	+	31.4630i	0.633968	+	1.09807i	0.986733	+	0.162353i	$0.0519083\pi$
$821$	18.1652	+	31.4630i	0.633968	+	1.09807i	−0.352765	+	0.935712i	$0.614758\pi$
$822$	−21.3956	+	37.0583i	−0.746259	+	1.29256i
$823$	18.3739	+	31.8245i	0.640473	+	1.10933i	0.985327	+	0.170675i	$0.0545948\pi$
$823$	18.3739	+	31.8245i	0.640473	+	1.10933i	−0.344855	+	0.938656i	$0.612072\pi$
$824$	5.16515			0.179937
$825$		0			0
$826$	2.29129	+	3.96863i	0.0797241	+	0.138086i
$827$	−14.4564	−	25.0393i	−0.502700	−	0.870701i	−0.999995	−	0.00312009i	$-0.999007\pi$
$827$	−14.4564	−	25.0393i	−0.502700	−	0.870701i	0.497295	−	0.867581i	$-0.334326\pi$
$828$	−21.9564			−0.763039
$829$	31.5390			1.09540			0.547698	−	0.836676i	$-0.315504\pi$
$829$	31.5390			1.09540			0.547698	+	0.836676i	$0.315504\pi$
$830$		0			0
$831$	−12.2087	+	21.1461i	−0.423516	+	0.733550i
$832$	−0.104356	−	0.180750i	−0.00361790	−	0.00626638i
$833$	2.37386	−	4.11165i	0.0822495	−	0.142460i
$834$	−17.0390	+	29.5124i	−0.590013	+	1.02193i
$835$		0			0
$836$	1.89564	−	16.4168i	0.0655622	−	0.567785i
$837$	−23.9564			−0.828056
$838$	−11.3739	+	19.7001i	−0.392904	+	0.680529i
$839$	−25.9782	+	44.9956i	−0.896868	+	1.55342i	−0.0653918	+	0.997860i	$0.520830\pi$
$839$	−25.9782	+	44.9956i	−0.896868	+	1.55342i	−0.831476	+	0.555561i	$0.812504\pi$
$840$		0			0
$841$	−8.56080	+	14.8277i	−0.295200	+	0.511301i
$842$	10.0000	+	17.3205i	0.344623	+	0.596904i
$843$	29.5390			1.01738
$844$	23.9564			0.824615
$845$		0			0
$846$	29.1434	+	50.4778i	1.00197	+	1.73546i
$847$	3.37386			0.115927
$848$	4.58258			0.157366
$849$	29.4782	+	51.0578i	1.01169	+	1.75230i
$850$		0			0
$851$	−8.20871	−	14.2179i	−0.281391	−	0.487384i
$852$	6.39564	−	11.0776i	0.219111	−	0.379512i
$853$	−26.0172	+	45.0632i	−0.890813	+	1.54293i	−0.0519108	+	0.998652i	$0.516531\pi$
$853$	−26.0172	+	45.0632i	−0.890813	+	1.54293i	−0.838902	+	0.544282i	$0.816802\pi$
$854$	−1.37386			−0.0470126
$855$		0			0
$856$	18.9564			0.647918
$857$	1.50000	−	2.59808i	0.0512390	−	0.0887486i	−0.839268	−	0.543718i	$-0.817016\pi$
$857$	1.50000	−	2.59808i	0.0512390	−	0.0887486i	0.890507	+	0.454969i	$0.150350\pi$
$858$	−1.10436	+	1.91280i	−0.0377021	+	0.0653019i
$859$	−8.35208	−	14.4662i	−0.284969	−	0.493581i	0.687632	−	0.726059i	$-0.258650\pi$
$859$	−8.35208	−	14.4662i	−0.284969	−	0.493581i	−0.972602	+	0.232478i	$0.925317\pi$
$860$		0			0
$861$	15.8739	+	27.4943i	0.540980	+	0.937005i
$862$	−8.20871			−0.279590
$863$	4.41742			0.150371			0.0751854	−	0.997170i	$-0.476045\pi$
$863$	4.41742			0.150371			0.0751854	+	0.997170i	$0.476045\pi$
$864$	2.50000	+	4.33013i	0.0850517	+	0.147314i
$865$		0			0
$866$	6.91288			0.234909
$867$	−45.7042			−1.55219
$868$	2.39564	+	4.14938i	0.0813135	+	0.140839i
$869$	28.3521	−	49.1072i	0.961779	−	1.66585i
$870$		0			0
$871$	1.62614	−	2.81655i	0.0550995	−	0.0954352i
$872$	−5.87386	+	10.1738i	−0.198914	+	0.344529i
$873$	59.2867			2.00655
$874$	−16.0390	−	11.9059i	−0.542528	−	0.402722i
$875$		0			0
$876$	3.89564	−	6.74745i	0.131622	−	0.227975i
$877$	13.2477	−	22.9457i	0.447344	−	0.774822i	−0.550868	−	0.834592i	$-0.685703\pi$
$877$	13.2477	−	22.9457i	0.447344	−	0.774822i	0.998212	+	0.0597698i	$0.0190367\pi$
$878$	−12.6652	−	21.9367i	−0.427428	−	0.740327i
$879$	34.8303	−	60.3279i	1.17480	−	2.03481i
$880$		0			0
$881$	−0.791288			−0.0266592			−0.0133296	−	0.999911i	$-0.504243\pi$
$881$	−0.791288			−0.0266592			−0.0133296	+	0.999911i	$0.504243\pi$
$882$	28.7477			0.967986
$883$	12.3739	+	21.4322i	0.416414	+	0.721250i	0.995576	−	0.0939628i	$-0.0299535\pi$
$883$	12.3739	+	21.4322i	0.416414	+	0.721250i	−0.579162	+	0.815212i	$0.696620\pi$
$884$	−0.0825757	−	0.143025i	−0.00277732	−	0.00481046i
$885$		0			0
$886$	−24.0000			−0.806296
$887$	−17.0608	−	29.5502i	−0.572845	−	0.992197i	−0.996272	−	0.0862670i	$-0.972506\pi$
$887$	−17.0608	−	29.5502i	−0.572845	−	0.992197i	0.423427	−	0.905930i	$-0.360827\pi$
$888$	−5.00000	+	8.66025i	−0.167789	+	0.290619i
$889$	1.31307	+	2.27430i	0.0440389	+	0.0762776i
$890$		0			0
$891$	−0.791288	+	1.37055i	−0.0265091	+	0.0459152i
$892$	−19.2087			−0.643155
$893$	−6.08258	+	52.6767i	−0.203546	+	1.76276i
$894$	63.4955			2.12361
$895$		0			0
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$	1.33485	+	2.31203i	0.0445693	+	0.0771963i
$898$	1.66515	−	2.88413i	0.0555668	−	0.0962446i
$899$	16.2695	+	28.1796i	0.542618	+	0.939843i
$900$		0			0
$901$	3.62614			0.120804
$902$	21.5608	+	37.3444i	0.717896	+	1.24343i
$903$	8.08258	+	13.9994i	0.268971	+	0.465872i
$904$	5.37386			0.178732
$905$		0			0
$906$	21.9782	+	38.0674i	0.730177	+	1.26470i
$907$	−16.9347	+	29.3317i	−0.562306	+	0.973943i	0.434989	+	0.900436i	$0.356752\pi$
$907$	−16.9347	+	29.3317i	−0.562306	+	0.973943i	−0.997295	+	0.0735068i	$0.976581\pi$
$908$	3.87386	+	6.70973i	0.128559	+	0.222670i
$909$		0			0
$910$		0			0
$911$	−48.6606			−1.61220			−0.806099	−	0.591781i	$-0.798425\pi$
$911$	−48.6606			−1.61220			−0.806099	+	0.591781i	$0.798425\pi$
$912$	−1.39564	+	12.0866i	−0.0462144	+	0.400228i
$913$	14.3739			0.475705
$914$	10.3739	−	17.9681i	0.343137	−	0.594331i
$915$		0			0
$916$	12.6652	+	21.9367i	0.418468	+	0.724808i
$917$	−5.76951	+	9.99308i	−0.190526	+	0.330001i
$918$	1.97822	+	3.42638i	0.0652910	+	0.113087i
$919$	−46.7913			−1.54350			−0.771751	−	0.635925i	$-0.780619\pi$
$919$	−46.7913			−1.54350			−0.771751	+	0.635925i	$0.780619\pi$
$920$		0			0
$921$	−48.1434	−	83.3868i	−1.58638	−	2.74769i
$922$	6.39564	+	11.0776i	0.210629	+	0.364821i
$923$	−0.956439			−0.0314816
$924$	−10.5826			−0.348141
$925$		0			0
$926$	−8.97822	+	15.5507i	−0.295043	+	0.511029i
$927$	12.3739	+	21.4322i	0.406411	+	0.703925i
$928$	3.39564	−	5.88143i	0.111467	−	0.193067i
$929$	−5.43920	+	9.42098i	−0.178455	+	0.309092i	−0.941351	−	0.337428i	$-0.890443\pi$
$929$	−5.43920	+	9.42098i	−0.178455	+	0.309092i	0.762897	+	0.646520i	$0.223776\pi$
$930$		0			0
$931$	21.0000	+	15.5885i	0.688247	+	0.510891i
$932$	−9.16515			−0.300215
$933$	20.9347	−	36.2599i	0.685370	−	1.18710i
$934$	6.16515	−	10.6784i	0.201730	−	0.349406i
$935$		0			0
$936$	0.500000	−	0.866025i	0.0163430	−	0.0283069i
$937$	3.06080	+	5.30145i	0.0999918	+	0.173191i	0.911681	−	0.410899i	$-0.134785\pi$
$937$	3.06080	+	5.30145i	0.0999918	+	0.173191i	−0.811689	+	0.584090i	$0.801452\pi$
$938$	15.5826			0.508789
$939$	32.7913			1.07010
$940$		0			0
$941$	20.2913	+	35.1455i	0.661477	+	1.14571i	0.980228	+	0.197873i	$0.0634034\pi$
$941$	20.2913	+	35.1455i	0.661477	+	1.14571i	−0.318751	+	0.947839i	$0.603263\pi$
$942$	−22.2087			−0.723599
$943$	52.1216			1.69731
$944$	−2.29129	−	3.96863i	−0.0745751	−	0.129168i
$945$		0			0
$946$	10.9782	+	19.0148i	0.356933	+	0.618226i
$947$	−14.2913	+	24.7532i	−0.464404	+	0.804372i	−0.999174	−	0.0406256i	$-0.987065\pi$
$947$	−14.2913	+	24.7532i	−0.464404	+	0.804372i	0.534770	+	0.844998i	$0.320398\pi$
$948$	−20.8739	+	36.1546i	−0.677952	+	1.17425i
$949$	−0.582576			−0.0189112
$950$		0			0
$951$	25.5826			0.829572
$952$	0.395644	−	0.685275i	0.0128229	−	0.0222099i
$953$	−8.06080	+	13.9617i	−0.261115	+	0.452264i	−0.966538	−	0.256522i	$-0.917423\pi$
$953$	−8.06080	+	13.9617i	−0.261115	+	0.452264i	0.705424	+	0.708786i	$0.250757\pi$
$954$	10.9782	+	19.0148i	0.355433	+	0.615628i
$955$		0			0
$956$	−8.29129	−	14.3609i	−0.268159	−	0.464466i
$957$	−71.8693			−2.32321
$958$	−31.7477			−1.02572
$959$	7.66515	+	13.2764i	0.247521	+	0.428718i
$960$		0			0
$961$	−8.04356			−0.259470
$962$	0.747727			0.0241077
$963$	45.4129	+	78.6574i	1.46341	+	2.53470i
$964$	8.39564	−	14.5417i	0.270405	−	0.468356i
$965$		0			0
$966$	−6.39564	+	11.0776i	−0.205776	+	0.356415i
$967$	−25.5390	+	44.2349i	−0.821279	+	1.42250i	0.0834506	+	0.996512i	$0.473406\pi$
$967$	−25.5390	+	44.2349i	−0.821279	+	1.42250i	−0.904730	+	0.425986i	$0.859927\pi$
$968$	−3.37386			−0.108440
$969$	−1.10436	+	9.56400i	−0.0354770	+	0.307240i
$970$		0			0
$971$	0.543561	−	0.941475i	0.0174437	−	0.0302134i	−0.857172	−	0.515031i	$-0.827781\pi$
$971$	0.543561	−	0.941475i	0.0174437	−	0.0302134i	0.874615	+	0.484817i	$0.161114\pi$
$972$	8.08258	−	13.9994i	0.259249	−	0.449032i
$973$	6.10436	+	10.5731i	0.195697	+	0.338957i
$974$	−11.5000	+	19.9186i	−0.368484	+	0.638233i
$975$		0			0
$976$	1.37386			0.0439763
$977$	−32.3739			−1.03573			−0.517866	−	0.855462i	$-0.673273\pi$
$977$	−32.3739			−1.03573			−0.517866	+	0.855462i	$0.673273\pi$
$978$	20.3521	+	35.2508i	0.650788	+	1.12720i
$979$	8.68693	+	15.0462i	0.277636	+	0.480879i
$980$		0			0
$981$	−56.2867			−1.79710
$982$	−15.7087	−	27.2083i	−0.501285	−	0.868251i
$983$	24.7913	−	42.9398i	0.790719	−	1.36957i	−0.134803	−	0.990872i	$-0.543040\pi$
$983$	24.7913	−	42.9398i	0.790719	−	1.36957i	0.925522	−	0.378694i	$-0.123627\pi$
$984$	−15.8739	−	27.4943i	−0.506040	−	0.876487i
$985$		0			0
$986$	2.68693	−	4.65390i	0.0855693	−	0.148210i
$987$	33.9564			1.08085
$988$	0.834849	−	0.361500i	0.0265601	−	0.0115008i
$989$	26.5390			0.843892
$990$		0			0
$991$	−12.0608	+	20.8899i	−0.383124	+	0.663590i	−0.991507	−	0.130054i	$-0.958485\pi$
$991$	−12.0608	+	20.8899i	−0.383124	+	0.663590i	0.608383	+	0.793643i	$0.291818\pi$
$992$	−2.39564	−	4.14938i	−0.0760618	−	0.131743i
$993$	25.0000	−	43.3013i	0.793351	−	1.37412i
$994$	−2.29129	−	3.96863i	−0.0726752	−	0.125877i
$995$		0			0
$996$	−10.5826			−0.335322
$997$	−0.500000	−	0.866025i	−0.0158352	−	0.0274273i	0.857999	−	0.513651i	$-0.171707\pi$
$997$	−0.500000	−	0.866025i	−0.0158352	−	0.0274273i	−0.873834	+	0.486224i	$0.838374\pi$
$998$	−9.66515	−	16.7405i	−0.305945	−	0.529912i
$999$	−17.9129			−0.566738

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.j.201.1	yes	4
5.2	odd	4		950.2.j.h.49.4		8
5.3	odd	4		950.2.j.h.49.1		8
5.4	even	2		950.2.e.i.201.2	✓	4
19.7	even	3	inner	950.2.e.j.501.1	yes	4
95.7	odd	12		950.2.j.h.349.1		8
95.64	even	6		950.2.e.i.501.2	yes	4
95.83	odd	12		950.2.j.h.349.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.e.i.201.2	✓	4	5.4	even	2
950.2.e.i.501.2	yes	4	95.64	even	6
950.2.e.j.201.1	yes	4	1.1	even	1	trivial
950.2.e.j.501.1	yes	4	19.7	even	3	inner
950.2.j.h.49.1		8	5.3	odd	4
950.2.j.h.49.4		8	5.2	odd	4
950.2.j.h.349.1		8	95.7	odd	12
950.2.j.h.349.4		8	95.83	odd	12

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.39564 + 2.41733i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.39564 + 2.41733i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(-2.39564 - 4.14938i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.39564 + 2.41733i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.39564 + 2.41733i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(-2.39564 - 4.14938i) q^{9} -3.79129 q^{11} +2.79129 q^{12} +(-0.104356 - 0.180750i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.395644 + 0.685275i) q^{17} -4.79129 q^{18} +(-3.50000 - 2.59808i) q^{19} +(-1.39564 + 2.41733i) q^{21} +(-1.89564 + 3.28335i) q^{22} +(2.29129 + 3.96863i) q^{23} +(1.39564 - 2.41733i) q^{24} -0.208712 q^{26} +5.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-3.39564 - 5.88143i) q^{29} -4.79129 q^{31} +(0.500000 + 0.866025i) q^{32} +(5.29129 - 9.16478i) q^{33} +(0.395644 + 0.685275i) q^{34} +(-2.39564 + 4.14938i) q^{36} -3.58258 q^{37} +(-4.00000 + 1.73205i) q^{38} +0.582576 q^{39} +(5.68693 - 9.85005i) q^{41} +(1.39564 + 2.41733i) q^{42} +(2.89564 - 5.01540i) q^{43} +(1.89564 + 3.28335i) q^{44} +4.58258 q^{46} +(-6.08258 - 10.5353i) q^{47} +(-1.39564 - 2.41733i) q^{48} -6.00000 q^{49} +(-1.10436 - 1.91280i) q^{51} +(-0.104356 + 0.180750i) q^{52} +(-2.29129 - 3.96863i) q^{53} +(2.50000 - 4.33013i) q^{54} -1.00000 q^{56} +(11.1652 - 4.83465i) q^{57} -6.79129 q^{58} +(-2.29129 + 3.96863i) q^{59} +(-0.686932 - 1.18980i) q^{61} +(-2.39564 + 4.14938i) q^{62} +(-2.39564 - 4.14938i) q^{63} +1.00000 q^{64} +(-5.29129 - 9.16478i) q^{66} +(7.79129 + 13.4949i) q^{67} +0.791288 q^{68} -12.7913 q^{69} +(2.29129 - 3.96863i) q^{71} +(2.39564 + 4.14938i) q^{72} +(1.39564 - 2.41733i) q^{73} +(-1.79129 + 3.10260i) q^{74} +(-0.500000 + 4.33013i) q^{76} -3.79129 q^{77} +(0.291288 - 0.504525i) q^{78} +(-7.47822 + 12.9527i) q^{79} +(0.208712 - 0.361500i) q^{81} +(-5.68693 - 9.85005i) q^{82} -3.79129 q^{83} +2.79129 q^{84} +(-2.89564 - 5.01540i) q^{86} +18.9564 q^{87} +3.79129 q^{88} +(-2.29129 - 3.96863i) q^{89} +(-0.104356 - 0.180750i) q^{91} +(2.29129 - 3.96863i) q^{92} +(6.68693 - 11.5821i) q^{93} -12.1652 q^{94} -2.79129 q^{96} +(-6.18693 + 10.7161i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(9.08258 + 15.7315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{6} + 4 q^{7} - 4 q^{8} - 5 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 + q^6 + 4 * q^7 - 4 * q^8 - 5 * q^9	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{6} + 4 q^{7} - 4 q^{8} - 5 q^{9} - 6 q^{11} + 2 q^{12} - 5 q^{13} + 2 q^{14} - 2 q^{16} + 3 q^{17} - 10 q^{18} - 14 q^{19} - q^{21} - 3 q^{22} + q^{24} - 10 q^{26} + 20 q^{27} - 2 q^{28} - 9 q^{29} - 10 q^{31} + 2 q^{32} + 12 q^{33} - 3 q^{34} - 5 q^{36} + 4 q^{37} - 16 q^{38} - 16 q^{39} + 9 q^{41} + q^{42} + 7 q^{43} + 3 q^{44} - 6 q^{47} - q^{48} - 24 q^{49} - 9 q^{51} - 5 q^{52} + 10 q^{54} - 4 q^{56} + 8 q^{57} - 18 q^{58} + 11 q^{61} - 5 q^{62} - 5 q^{63} + 4 q^{64} - 12 q^{66} + 22 q^{67} - 6 q^{68} - 42 q^{69} + 5 q^{72} + q^{73} + 2 q^{74} - 2 q^{76} - 6 q^{77} - 8 q^{78} - 7 q^{79} + 10 q^{81} - 9 q^{82} - 6 q^{83} + 2 q^{84} - 7 q^{86} + 30 q^{87} + 6 q^{88} - 5 q^{91} + 13 q^{93} - 12 q^{94} - 2 q^{96} - 11 q^{97} - 12 q^{98} + 18 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 + q^6 + 4 * q^7 - 4 * q^8 - 5 * q^9 - 6 * q^11 + 2 * q^12 - 5 * q^13 + 2 * q^14 - 2 * q^16 + 3 * q^17 - 10 * q^18 - 14 * q^19 - q^21 - 3 * q^22 + q^24 - 10 * q^26 + 20 * q^27 - 2 * q^28 - 9 * q^29 - 10 * q^31 + 2 * q^32 + 12 * q^33 - 3 * q^34 - 5 * q^36 + 4 * q^37 - 16 * q^38 - 16 * q^39 + 9 * q^41 + q^42 + 7 * q^43 + 3 * q^44 - 6 * q^47 - q^48 - 24 * q^49 - 9 * q^51 - 5 * q^52 + 10 * q^54 - 4 * q^56 + 8 * q^57 - 18 * q^58 + 11 * q^61 - 5 * q^62 - 5 * q^63 + 4 * q^64 - 12 * q^66 + 22 * q^67 - 6 * q^68 - 42 * q^69 + 5 * q^72 + q^73 + 2 * q^74 - 2 * q^76 - 6 * q^77 - 8 * q^78 - 7 * q^79 + 10 * q^81 - 9 * q^82 - 6 * q^83 + 2 * q^84 - 7 * q^86 + 30 * q^87 + 6 * q^88 - 5 * q^91 + 13 * q^93 - 12 * q^94 - 2 * q^96 - 11 * q^97 - 12 * q^98 + 18 * q^99

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