LMFDB - Embedded newform 950.2.j.h.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(49,950)]

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([3, 4]))

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

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

chi := DirichletCharacter("950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.j (of order $6$, degree $2$, not 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Root			$0.228425 + 1.39564i$ of defining polynomial
Character	$\chi$	$=$	950.49
Dual form			950.2.j.h.349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	2.41733	+	1.39564i	1.39564	+	0.805775i	0.993933	−	0.109991i	$-0.0350822\pi$
$3$	2.41733	+	1.39564i	1.39564	+	0.805775i	0.401711	+	0.915766i	$0.368416\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.39564	+	2.41733i	0.569769	+	0.986869i
$7$			1.00000i			0.377964i	0.981981	+	0.188982i	$0.0605189\pi$
$7$			1.00000i			0.377964i	−0.981981	+	0.188982i	$0.939481\pi$
$8$			1.00000i			0.353553i
$9$	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	$0.693661\pi$
$12$			2.79129i			0.805775i
$13$	−0.180750	+	0.104356i	−0.0501310	+	0.0289432i	−0.524856	−	0.851191i	$-0.675881\pi$
$13$	−0.180750	+	0.104356i	−0.0501310	+	0.0289432i	0.474725	+	0.880134i	$0.342548\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.685275	−	0.395644i	−0.166204	−	0.0959577i	0.414591	−	0.910008i	$-0.363925\pi$
$17$	−0.685275	−	0.395644i	−0.166204	−	0.0959577i	−0.580795	+	0.814050i	$0.697258\pi$
$18$			4.79129i			1.12932i
$19$	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
$22$	−3.28335	−	1.89564i	−0.700013	−	0.404153i
$23$	3.96863	−	2.29129i	0.827516	−	0.477767i	−0.0254855	−	0.999675i	$-0.508113\pi$
$23$	3.96863	−	2.29129i	0.827516	−	0.477767i	0.853001	+	0.521909i	$0.174780\pi$
$24$	−1.39564	+	2.41733i	−0.284885	+	0.493435i
$25$		0			0
$26$	−0.208712			−0.0409318
$27$			5.00000i			0.962250i
$28$	−0.866025	+	0.500000i	−0.163663	+	0.0944911i
$29$	3.39564	+	5.88143i	0.630555	+	1.09215i	0.987438	+	0.158005i	$0.0505061\pi$
$29$	3.39564	+	5.88143i	0.630555	+	1.09215i	−0.356883	+	0.934149i	$0.616161\pi$
$30$		0			0
$31$	−4.79129			−0.860541			−0.430270	−	0.902700i	$-0.641582\pi$
$31$	−4.79129			−0.860541			−0.430270	+	0.902700i	$0.641582\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−9.16478	−	5.29129i	−1.59538	−	0.921095i
$34$	−0.395644	−	0.685275i	−0.0678524	−	0.117524i
$35$		0			0
$36$	−2.39564	+	4.14938i	−0.399274	+	0.691563i
$37$		−	3.58258i		−	0.588972i	−0.955656	−	0.294486i	$-0.904852\pi$
$37$		−	3.58258i		−	0.588972i	0.955656	−	0.294486i	$-0.0951484\pi$
$38$	1.73205	+	4.00000i	0.280976	+	0.648886i
$39$	−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	$-0.181342\pi$
$42$	−2.41733	+	1.39564i	−0.373002	+	0.215353i
$43$	−5.01540	−	2.89564i	−0.764842	−	0.441582i	0.0661897	−	0.997807i	$-0.478916\pi$
$43$	−5.01540	−	2.89564i	−0.764842	−	0.441582i	−0.831031	+	0.556225i	$0.812249\pi$
$44$	−1.89564	−	3.28335i	−0.285779	−	0.494984i
$45$		0			0
$46$	4.58258			0.675664
$47$	10.5353	−	6.08258i	1.53674	−	0.887235i	0.537709	−	0.843131i	$-0.319290\pi$
$47$	10.5353	−	6.08258i	1.53674	−	0.887235i	0.999027	−	0.0441043i	$-0.0140434\pi$
$48$	−2.41733	+	1.39564i	−0.348911	+	0.201444i
$49$	6.00000			0.857143
$50$		0			0
$51$	−1.10436	−	1.91280i	−0.154641	−	0.267846i
$52$	−0.180750	−	0.104356i	−0.0250655	−	0.0144716i
$53$	−3.96863	+	2.29129i	−0.545133	+	0.314733i	−0.747157	−	0.664648i	$-0.768582\pi$
$53$	−3.96863	+	2.29129i	−0.545133	+	0.314733i	0.202024	+	0.979381i	$0.435248\pi$
$54$	−2.50000	+	4.33013i	−0.340207	+	0.589256i
$55$		0			0
$56$	−1.00000			−0.133631
$57$	4.83465	+	11.1652i	0.640365	+	1.47886i
$58$			6.79129i			0.891740i
$59$	2.29129	−	3.96863i	0.298300	−	0.516671i	−0.677447	−	0.735572i	$-0.736914\pi$
$59$	2.29129	−	3.96863i	0.298300	−	0.516671i	0.975747	+	0.218900i	$0.0702470\pi$
$60$		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	$0.861366\pi$
$62$	−4.14938	−	2.39564i	−0.526971	−	0.304247i
$63$	−4.14938	+	2.39564i	−0.522772	+	0.301823i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−5.29129	−	9.16478i	−0.651313	−	1.12811i
$67$	−13.4949	+	7.79129i	−1.64867	+	0.951857i	−0.671062	+	0.741401i	$0.734162\pi$
$67$	−13.4949	+	7.79129i	−1.64867	+	0.951857i	−0.977603	+	0.210456i	$0.932505\pi$
$68$		−	0.791288i		−	0.0959577i
$69$	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	$0.0790061\pi$
$72$	−4.14938	+	2.39564i	−0.489009	+	0.282329i
$73$	−2.41733	−	1.39564i	−0.282927	−	0.163348i	0.351821	−	0.936067i	$-0.385563\pi$
$73$	−2.41733	−	1.39564i	−0.282927	−	0.163348i	−0.634748	+	0.772720i	$0.718896\pi$
$74$	1.79129	−	3.10260i	0.208233	−	0.360670i
$75$		0			0
$76$	−0.500000	+	4.33013i	−0.0573539	+	0.496700i
$77$		−	3.79129i		−	0.432057i
$78$	−0.504525	−	0.291288i	−0.0571262	−	0.0329819i
$79$	7.47822	−	12.9527i	0.841365	−	1.45729i	−0.0473751	−	0.998877i	$-0.515086\pi$
$79$	7.47822	−	12.9527i	0.841365	−	1.45729i	0.888741	−	0.458411i	$-0.151581\pi$
$80$		0			0
$81$	0.208712	−	0.361500i	0.0231902	−	0.0401667i
$82$	9.85005	−	5.68693i	1.08776	−	0.628017i
$83$			3.79129i			0.416148i	0.978113	+	0.208074i	$0.0667195\pi$
$83$			3.79129i			0.416148i	−0.978113	+	0.208074i	$0.933281\pi$
$84$	−2.79129			−0.304554
$85$		0			0
$86$	−2.89564	−	5.01540i	−0.312245	−	0.540825i
$87$			18.9564i			2.03234i
$88$		−	3.79129i		−	0.404153i
$89$	2.29129	+	3.96863i	0.242876	+	0.420674i	0.961532	−	0.274692i	$-0.0885758\pi$
$89$	2.29129	+	3.96863i	0.242876	+	0.420674i	−0.718656	+	0.695365i	$0.755243\pi$
$90$		0			0
$91$	−0.104356	−	0.180750i	−0.0109395	−	0.0189478i
$92$	3.96863	+	2.29129i	0.413758	+	0.238883i
$93$	−11.5821	−	6.68693i	−1.20101	−	0.693403i
$94$	12.1652			1.25474
$95$		0			0
$96$	−2.79129			−0.284885
$97$	−10.7161	−	6.18693i	−1.08805	−	0.628188i	−0.154996	−	0.987915i	$-0.549536\pi$
$97$	−10.7161	−	6.18693i	−1.08805	−	0.628188i	−0.933057	+	0.359727i	$0.882870\pi$
$98$	5.19615	+	3.00000i	0.524891	+	0.303046i
$99$	−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	$0.833333\pi$
$102$		−	2.20871i		−	0.218695i
$103$			5.16515i			0.508937i	0.967081	+	0.254469i	$0.0819006\pi$
$103$			5.16515i			0.508937i	−0.967081	+	0.254469i	$0.918099\pi$
$104$	−0.104356	−	0.180750i	−0.0102330	−	0.0177240i
$105$		0			0
$106$	−4.58258			−0.445099
$107$		−	18.9564i		−	1.83259i	−0.400506	−	0.916294i	$-0.631166\pi$
$107$		−	18.9564i		−	1.83259i	0.400506	−	0.916294i	$-0.368834\pi$
$108$	−4.33013	+	2.50000i	−0.416667	+	0.240563i
$109$	−5.87386	+	10.1738i	−0.562614	+	0.974476i	0.434653	+	0.900598i	$0.356871\pi$
$109$	−5.87386	+	10.1738i	−0.562614	+	0.974476i	−0.997267	+	0.0738783i	$0.976462\pi$
$110$		0			0
$111$	5.00000	−	8.66025i	0.474579	−	0.821995i
$112$	−0.866025	−	0.500000i	−0.0818317	−	0.0472456i
$113$			5.37386i			0.505531i	0.967528	+	0.252765i	$0.0813400\pi$
$113$			5.37386i			0.505531i	−0.967528	+	0.252765i	$0.918660\pi$
$114$	−1.39564	+	12.0866i	−0.130714	+	1.13202i
$115$		0			0
$116$	−3.39564	+	5.88143i	−0.315278	+	0.546077i
$117$	−0.866025	−	0.500000i	−0.0800641	−	0.0462250i
$118$	3.96863	−	2.29129i	0.365342	−	0.210930i
$119$	0.395644	−	0.685275i	0.0362686	−	0.0628191i
$120$		0			0
$121$	3.37386			0.306715
$122$		−	1.37386i		−	0.124384i
$123$	27.4943	−	15.8739i	2.47908	−	1.43130i
$124$	−2.39564	−	4.14938i	−0.215135	−	0.372625i
$125$		0			0
$126$	−4.79129			−0.426842
$127$	−2.27430	+	1.31307i	−0.201812	+	0.116516i	−0.597500	−	0.801869i	$-0.703839\pi$
$127$	−2.27430	+	1.31307i	−0.201812	+	0.116516i	0.395689	+	0.918385i	$0.370506\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−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	$0.998497\pi$
$132$		−	10.5826i		−	0.921095i
$133$	−2.59808	+	3.50000i	−0.225282	+	0.303488i
$134$	−15.5826			−1.34613
$135$		0			0
$136$	0.395644	−	0.685275i	0.0339262	−	0.0587619i
$137$	−13.2764	+	7.66515i	−1.13428	+	0.654878i	−0.945008	−	0.327046i	$-0.893947\pi$
$137$	−13.2764	+	7.66515i	−1.13428	+	0.654878i	−0.189274	+	0.981924i	$0.560613\pi$
$138$	11.0776	+	6.39564i	0.942986	+	0.544433i
$139$	−6.10436	−	10.5731i	−0.517765	−	0.896795i	−0.999787	−	0.0206359i	$-0.993431\pi$
$139$	−6.10436	−	10.5731i	−0.517765	−	0.896795i	0.482022	−	0.876159i	$-0.339902\pi$
$140$		0			0
$141$	33.9564			2.85965
$142$	3.96863	−	2.29129i	0.333040	−	0.192281i
$143$	0.685275	−	0.395644i	0.0573056	−	0.0330854i
$144$	−4.79129			−0.399274
$145$		0			0
$146$	−1.39564	−	2.41733i	−0.115504	−	0.200059i
$147$	14.5040	+	8.37386i	1.19627	+	0.690665i
$148$	3.10260	−	1.79129i	0.255032	−	0.147243i
$149$	−11.3739	+	19.7001i	−0.931783	+	1.61390i	−0.151511	+	0.988456i	$0.548414\pi$
$149$	−11.3739	+	19.7001i	−0.931783	+	1.61390i	−0.780272	+	0.625440i	$0.784919\pi$
$150$		0			0
$151$	15.7477			1.28153			0.640766	−	0.767736i	$-0.278617\pi$
$151$	15.7477			1.28153			0.640766	+	0.767736i	$0.278617\pi$
$152$	−2.59808	+	3.50000i	−0.210732	+	0.283887i
$153$		−	3.79129i		−	0.306507i
$154$	1.89564	−	3.28335i	0.152755	−	0.264580i
$155$		0			0
$156$	−0.291288	−	0.504525i	−0.0233217	−	0.0403944i
$157$	−6.89048	−	3.97822i	−0.549920	−	0.317496i	0.199170	−	0.979965i	$-0.436176\pi$
$157$	−6.89048	−	3.97822i	−0.549920	−	0.317496i	−0.749090	+	0.662469i	$0.769509\pi$
$158$	12.9527	−	7.47822i	1.03046	−	0.594935i
$159$	−12.7913			−1.01442
$160$		0			0
$161$	2.29129	+	3.96863i	0.180579	+	0.312772i
$162$	0.361500	−	0.208712i	0.0284021	−	0.0163980i
$163$		−	14.5826i		−	1.14220i	−0.820882	−	0.571098i	$-0.806518\pi$
$163$		−	14.5826i		−	1.14220i	0.820882	−	0.571098i	$-0.193482\pi$
$164$	11.3739			0.888150
$165$		0			0
$166$	−1.89564	+	3.28335i	−0.147131	+	0.254838i
$167$	−9.99308	+	5.76951i	−0.773288	+	0.446458i	−0.834046	−	0.551695i	$-0.813981\pi$
$167$	−9.99308	+	5.76951i	−0.773288	+	0.446458i	0.0607584	+	0.998152i	$0.480648\pi$
$168$	−2.41733	−	1.39564i	−0.186501	−	0.107676i
$169$	−6.47822	+	11.2206i	−0.498325	+	0.863124i
$170$		0			0
$171$	−2.39564	+	20.7469i	−0.183199	+	1.58655i
$172$		−	5.79129i		−	0.441582i
$173$	18.1865	+	10.5000i	1.38270	+	0.798300i	0.992478	−	0.122422i	$-0.0390662\pi$
$173$	18.1865	+	10.5000i	1.38270	+	0.798300i	0.390218	+	0.920722i	$0.372399\pi$
$174$	−9.47822	+	16.4168i	−0.718542	+	1.24455i
$175$		0			0
$176$	1.89564	−	3.28335i	0.142890	−	0.247492i
$177$	11.0776	−	6.39564i	0.832642	−	0.480726i
$178$			4.58258i			0.343479i
$179$	16.7477			1.25178			0.625892	−	0.779910i	$-0.284735\pi$
$179$	16.7477			1.25178			0.625892	+	0.779910i	$0.284735\pi$
$180$		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	$0.741863\pi$
$182$		−	0.208712i		−	0.0154708i
$183$		−	3.83485i		−	0.283480i
$184$	2.29129	+	3.96863i	0.168916	+	0.292571i
$185$		0			0
$186$	−6.68693	−	11.5821i	−0.490310	−	0.849241i
$187$	2.59808	+	1.50000i	0.189990	+	0.109691i
$188$	10.5353	+	6.08258i	0.768368	+	0.443617i
$189$	−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	$0.304113\pi$
$192$	−2.41733	−	1.39564i	−0.174455	−	0.100722i
$193$	2.37960	+	1.37386i	0.171287	+	0.0988929i	0.583193	−	0.812334i	$-0.301803\pi$
$193$	2.37960	+	1.37386i	0.171287	+	0.0988929i	−0.411905	+	0.911227i	$0.635137\pi$
$194$	−6.18693	−	10.7161i	−0.444196	−	0.769370i
$195$		0			0
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$		−	20.2087i		−	1.43981i	−0.694072	−	0.719906i	$-0.744185\pi$
$197$		−	20.2087i		−	1.43981i	0.694072	−	0.719906i	$-0.255815\pi$
$198$		−	18.1652i		−	1.29094i
$199$	1.79129	+	3.10260i	0.126981	+	0.219938i	0.922506	−	0.385984i	$-0.126138\pi$
$199$	1.79129	+	3.10260i	0.126981	+	0.219938i	−0.795525	+	0.605921i	$0.792805\pi$
$200$		0			0
$201$	−43.4955			−3.06793
$202$		0			0
$203$	−5.88143	+	3.39564i	−0.412795	+	0.238327i
$204$	1.10436	−	1.91280i	0.0773204	−	0.133923i
$205$		0			0
$206$	−2.58258	+	4.47315i	−0.179937	+	0.311659i
$207$	19.0148	+	10.9782i	1.32162	+	0.763039i
$208$		−	0.208712i		−	0.0144716i
$209$	−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	$0.858059\pi$
$212$	−3.96863	−	2.29129i	−0.272566	−	0.157366i
$213$	11.0776	−	6.39564i	0.759023	−	0.438222i
$214$	9.47822	−	16.4168i	0.647918	−	1.12223i
$215$		0			0
$216$	−5.00000			−0.340207
$217$		−	4.79129i		−	0.325254i
$218$	−10.1738	+	5.87386i	−0.689059	+	0.397828i
$219$	−3.89564	−	6.74745i	−0.263243	−	0.455951i
$220$		0			0
$221$	0.165151			0.0111093
$222$	8.66025	−	5.00000i	0.581238	−	0.335578i
$223$	−16.6352	−	9.60436i	−1.11398	−	0.643155i	−0.174121	−	0.984724i	$-0.555708\pi$
$223$	−16.6352	−	9.60436i	−1.11398	−	0.643155i	−0.939857	+	0.341569i	$0.889042\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$	−2.68693	+	4.65390i	−0.178732	+	0.309573i
$227$		−	7.74773i		−	0.514235i	−0.966380	−	0.257117i	$-0.917227\pi$
$227$		−	7.74773i		−	0.514235i	0.966380	−	0.257117i	$-0.0827727\pi$
$228$	−7.25198	+	9.76951i	−0.480274	+	0.647001i
$229$	25.3303			1.67387			0.836937	−	0.547300i	$-0.184344\pi$
$229$	25.3303			1.67387			0.836937	+	0.547300i	$0.184344\pi$
$230$		0			0
$231$	5.29129	−	9.16478i	0.348141	−	0.602998i
$232$	−5.88143	+	3.39564i	−0.386135	+	0.222935i
$233$	−7.93725	−	4.58258i	−0.519987	−	0.300215i	0.216942	−	0.976184i	$-0.430392\pi$
$233$	−7.93725	−	4.58258i	−0.519987	−	0.300215i	−0.736929	+	0.675970i	$0.763725\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$		0			0
$236$	4.58258			0.298300
$237$	36.1546	−	20.8739i	2.34849	−	1.35590i
$238$	0.685275	−	0.395644i	0.0444198	−	0.0256458i
$239$	−16.5826			−1.07264			−0.536319	−	0.844015i	$-0.680186\pi$
$239$	−16.5826			−1.07264			−0.536319	+	0.844015i	$0.680186\pi$
$240$		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	$0.651451\pi$
$242$	2.92185	+	1.68693i	0.187824	+	0.108440i
$243$	13.9994	−	8.08258i	0.898064	−	0.518497i
$244$	0.686932	−	1.18980i	0.0439763	−	0.0761692i
$245$		0			0
$246$	31.7477			2.02416
$247$	−0.903750	−	0.104356i	−0.0575042	−	0.00664002i
$248$		−	4.79129i		−	0.304247i
$249$	−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	$0.969242\pi$
$252$	−4.14938	−	2.39564i	−0.261386	−	0.150911i
$253$	−15.0462	+	8.68693i	−0.945947	+	0.546143i
$254$	−2.62614			−0.164778
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.70703	−	5.60436i	0.605508	−	0.349590i	−0.165697	−	0.986177i	$-0.552988\pi$
$257$	9.70703	−	5.60436i	0.605508	−	0.349590i	0.771205	+	0.636587i	$0.219654\pi$
$258$		−	16.1652i		−	1.00640i
$259$	3.58258			0.222610
$260$		0			0
$261$	−16.2695	+	28.1796i	−1.00706	+	1.74427i
$262$	−9.99308	+	5.76951i	−0.617375	+	0.356441i
$263$	16.8160	+	9.70871i	1.03692	+	0.598665i	0.918959	−	0.394354i	$-0.129031\pi$
$263$	16.8160	+	9.70871i	1.03692	+	0.598665i	0.117959	+	0.993018i	$0.462365\pi$
$264$	5.29129	−	9.16478i	0.325656	−	0.564053i
$265$		0			0
$266$	−4.00000	+	1.73205i	−0.245256	+	0.106199i
$267$			12.7913i			0.782814i
$268$	−13.4949	−	7.79129i	−0.824333	−	0.475929i
$269$	6.56080	−	11.3636i	0.400019	−	0.692853i	−0.593709	−	0.804680i	$-0.702337\pi$
$269$	6.56080	−	11.3636i	0.400019	−	0.692853i	0.993728	+	0.111827i	$0.0356703\pi$
$270$		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	$-0.00741305\pi$
$272$	0.685275	−	0.395644i	0.0415509	−	0.0239894i
$273$		−	0.582576i		−	0.0352591i
$274$	−15.3303			−0.926137
$275$		0			0
$276$	6.39564	+	11.0776i	0.384973	+	0.666792i
$277$			8.74773i			0.525600i	0.964850	+	0.262800i	$0.0846459\pi$
$277$			8.74773i			0.525600i	−0.964850	+	0.262800i	$0.915354\pi$
$278$		−	12.2087i		−	0.732230i
$279$	−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	$0.935556\pi$
$282$	29.4071	+	16.9782i	1.75117	+	1.01104i
$283$	−18.2918	−	10.5608i	−1.08734	−	0.627774i	−0.154471	−	0.987997i	$-0.549367\pi$
$283$	−18.2918	−	10.5608i	−1.08734	−	0.627774i	−0.932866	+	0.360223i	$0.882701\pi$
$284$	4.58258			0.271926
$285$		0			0
$286$	0.791288			0.0467898
$287$	9.85005	+	5.68693i	0.581430	+	0.335689i
$288$	−4.14938	−	2.39564i	−0.244504	−	0.141165i
$289$	−8.18693	−	14.1802i	−0.481584	−	0.834128i
$290$		0			0
$291$	−17.2695	−	29.9117i	−1.01236	−	1.75345i
$292$		−	2.79129i		−	0.163348i
$293$			24.9564i			1.45797i	0.684529	+	0.728985i	$0.260008\pi$
$293$			24.9564i			1.45797i	−0.684529	+	0.728985i	$0.739992\pi$
$294$	8.37386	+	14.5040i	0.488374	+	0.845888i
$295$		0			0
$296$	3.58258			0.208233
$297$		−	18.9564i		−	1.09996i
$298$	−19.7001	+	11.3739i	−1.14120	+	0.658870i
$299$	−0.478220	+	0.828301i	−0.0276562	+	0.0479019i
$300$		0			0
$301$	2.89564	−	5.01540i	0.166902	−	0.289083i
$302$	13.6379	+	7.87386i	0.784775	+	0.453090i
$303$		0			0
$304$	−4.00000	+	1.73205i	−0.229416	+	0.0993399i
$305$		0			0
$306$	1.89564	−	3.28335i	0.108367	−	0.187697i
$307$	−29.8739	−	17.2477i	−1.70500	−	0.984380i	−0.940527	−	0.339719i	$-0.889668\pi$
$307$	−29.8739	−	17.2477i	−1.70500	−	0.984380i	−0.764469	−	0.644661i	$-0.776999\pi$
$308$	3.28335	−	1.89564i	0.187086	−	0.108014i
$309$	−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	$0.639826\pi$
$312$		−	0.582576i		−	0.0329819i
$313$	−10.1738	+	5.87386i	−0.575059	+	0.332010i	−0.759167	−	0.650896i	$-0.774394\pi$
$313$	−10.1738	+	5.87386i	−0.575059	+	0.332010i	0.184108	+	0.982906i	$0.441060\pi$
$314$	−3.97822	−	6.89048i	−0.224504	−	0.388852i
$315$		0			0
$316$	14.9564			0.841365
$317$	7.93725	−	4.58258i	0.445801	−	0.257383i	−0.260254	−	0.965540i	$-0.583806\pi$
$317$	7.93725	−	4.58258i	0.445801	−	0.257383i	0.706055	+	0.708157i	$0.250473\pi$
$318$	−11.0776	−	6.39564i	−0.621200	−	0.358650i
$319$	−12.8739	−	22.2982i	−0.720798	−	1.24846i
$320$		0			0
$321$	26.4564	−	45.8239i	1.47665	−	2.55764i
$322$			4.58258i			0.255377i
$323$	−1.37055	−	3.16515i	−0.0762595	−	0.176114i
$324$	0.417424			0.0231902
$325$		0			0
$326$	7.29129	−	12.6289i	0.403827	−	0.699449i
$327$	−28.3981	+	16.3956i	−1.57042	+	0.906681i
$328$	9.85005	+	5.68693i	0.543878	+	0.314008i
$329$	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	$0.663840\pi$
$332$	−3.28335	+	1.89564i	−0.180197	+	0.104037i
$333$	14.8655	−	8.58258i	0.814622	−	0.470322i
$334$	−11.5390			−0.631387
$335$		0			0
$336$	−1.39564	−	2.41733i	−0.0761386	−	0.131876i
$337$	20.2046	+	11.6652i	1.10062	+	0.635441i	0.936383	−	0.350980i	$-0.114152\pi$
$337$	20.2046	+	11.6652i	1.10062	+	0.635441i	0.164234	+	0.986421i	$0.447485\pi$
$338$	−11.2206	+	6.47822i	−0.610320	+	0.352369i
$339$	−7.50000	+	12.9904i	−0.407344	+	0.705541i
$340$		0			0
$341$	18.1652			0.983698
$342$	−12.4481	+	16.7695i	−0.673118	+	0.906791i
$343$			13.0000i			0.701934i
$344$	2.89564	−	5.01540i	0.156123	−	0.270412i
$345$		0			0
$346$	10.5000	+	18.1865i	0.564483	+	0.977714i
$347$	3.14033	+	1.81307i	0.168582	+	0.0973306i	0.581917	−	0.813248i	$-0.302303\pi$
$347$	3.14033	+	1.81307i	0.168582	+	0.0973306i	−0.413335	+	0.910579i	$0.635636\pi$
$348$	−16.4168	+	9.47822i	−0.880031	+	0.508086i
$349$	5.41742			0.289988			0.144994	−	0.989433i	$-0.453684\pi$
$349$	5.41742			0.289988			0.144994	+	0.989433i	$0.453684\pi$
$350$		0			0
$351$	−0.521780	−	0.903750i	−0.0278506	−	0.0482386i
$352$	3.28335	−	1.89564i	0.175003	−	0.101038i
$353$		−	13.7477i		−	0.731718i	−0.930670	−	0.365859i	$-0.880775\pi$
$353$		−	13.7477i		−	0.731718i	0.930670	−	0.365859i	$-0.119225\pi$
$354$	12.7913			0.679849
$355$		0			0
$356$	−2.29129	+	3.96863i	−0.121438	+	0.210337i
$357$	1.91280	−	1.10436i	0.101236	−	0.0584487i
$358$	14.5040	+	8.37386i	0.766558	+	0.442572i
$359$	−17.8521	+	30.9207i	−0.942197	+	1.63193i	−0.180928	+	0.983496i	$0.557910\pi$
$359$	−17.8521	+	30.9207i	−0.942197	+	1.63193i	−0.761269	+	0.648437i	$0.775423\pi$
$360$		0			0
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$			7.62614i			0.400821i
$363$	8.15573	+	4.70871i	0.428065	+	0.247143i
$364$	0.104356	−	0.180750i	0.00546974	−	0.00947388i
$365$		0			0
$366$	1.91742	−	3.32108i	0.100225	−	0.173595i
$367$	−7.61348	+	4.39564i	−0.397420	+	0.229451i	−0.685370	−	0.728195i	$-0.740360\pi$
$367$	−7.61348	+	4.39564i	−0.397420	+	0.229451i	0.287950	+	0.957645i	$0.407026\pi$
$368$			4.58258i			0.238883i
$369$	54.4955			2.83692
$370$		0			0
$371$	−2.29129	−	3.96863i	−0.118958	−	0.206041i
$372$		−	13.3739i		−	0.693403i
$373$		−	21.3739i		−	1.10670i	−0.832950	−	0.553348i	$-0.813350\pi$
$373$		−	21.3739i		−	1.10670i	0.832950	−	0.553348i	$-0.186650\pi$
$374$	1.50000	+	2.59808i	0.0775632	+	0.134343i
$375$		0			0
$376$	6.08258	+	10.5353i	0.313685	+	0.543318i
$377$	−1.22753	−	0.708712i	−0.0632208	−	0.0365005i
$378$	−4.33013	−	2.50000i	−0.222718	−	0.128586i
$379$	−4.83485			−0.248349			−0.124175	−	0.992260i	$-0.539628\pi$
$379$	−4.83485			−0.248349			−0.124175	+	0.992260i	$0.539628\pi$
$380$		0			0
$381$	−7.33030			−0.375543
$382$	13.8187	+	7.97822i	0.707025	+	0.408201i
$383$	−3.96863	−	2.29129i	−0.202787	−	0.117079i	0.395168	−	0.918609i	$-0.370687\pi$
$383$	−3.96863	−	2.29129i	−0.202787	−	0.117079i	−0.597955	+	0.801530i	$0.704020\pi$
$384$	−1.39564	−	2.41733i	−0.0712212	−	0.123359i
$385$		0			0
$386$	1.37386	+	2.37960i	0.0699278	+	0.121119i
$387$		−	27.7477i		−	1.41050i
$388$		−	12.3739i		−	0.628188i
$389$	9.31307	+	16.1307i	0.472191	+	0.817859i	0.999494	−	0.0318184i	$-0.0101298\pi$
$389$	9.31307	+	16.1307i	0.472191	+	0.817859i	−0.527302	+	0.849678i	$0.676796\pi$
$390$		0			0
$391$	−3.62614			−0.183382
$392$			6.00000i			0.303046i
$393$	−27.8936	+	16.1044i	−1.40704	+	0.812357i
$394$	10.1044	−	17.5013i	0.509050	−	0.881701i
$395$		0			0
$396$	9.08258	−	15.7315i	0.456417	−	0.790537i
$397$	−9.88778	−	5.70871i	−0.496253	−	0.286512i	0.230912	−	0.972975i	$-0.425829\pi$
$397$	−9.88778	−	5.70871i	−0.496253	−	0.286512i	−0.727165	+	0.686463i	$0.759163\pi$
$398$			3.58258i			0.179578i
$399$	−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	$0.0698049\pi$
$402$	−37.6682	−	21.7477i	−1.87872	−	1.08468i
$403$	0.866025	−	0.500000i	0.0431398	−	0.0249068i
$404$		0			0
$405$		0			0
$406$	−6.79129			−0.337046
$407$			13.5826i			0.673263i
$408$	1.91280	−	1.10436i	0.0946978	−	0.0546738i
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$		0			0
$411$	−42.7913			−2.11074
$412$	−4.47315	+	2.58258i	−0.220376	+	0.127234i
$413$	3.96863	+	2.29129i	0.195283	+	0.112747i
$414$	10.9782	+	19.0148i	0.539550	+	0.934528i
$415$		0			0
$416$	0.104356	−	0.180750i	0.00511648	−	0.00886200i
$417$		−	34.0780i		−	1.66881i
$418$	−6.56670	−	15.1652i	−0.321188	−	0.741752i
$419$	22.7477			1.11130			0.555650	−	0.831417i	$-0.312470\pi$
$419$	22.7477			1.11130			0.555650	+	0.831417i	$0.312470\pi$
$420$		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	$0.328710\pi$
$422$	−20.7469	+	11.9782i	−1.00994	+	0.583091i
$423$	50.4778	+	29.1434i	2.45431	+	1.41700i
$424$	−2.29129	−	3.96863i	−0.111275	−	0.192734i
$425$		0			0
$426$	12.7913			0.619740
$427$	1.18980	−	0.686932i	0.0575785	−	0.0332430i
$428$	16.4168	−	9.47822i	0.793534	−	0.458147i
$429$	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	$0.896680\pi$
$432$	−4.33013	−	2.50000i	−0.208333	−	0.120281i
$433$	5.98673	−	3.45644i	0.287704	−	0.166106i	−0.349202	−	0.937047i	$-0.613547\pi$
$433$	5.98673	−	3.45644i	0.287704	−	0.166106i	0.636906	+	0.770942i	$0.280214\pi$
$434$	2.39564	−	4.14938i	0.114995	−	0.199176i
$435$		0			0
$436$	−11.7477			−0.562614
$437$	19.8431	+	2.29129i	0.949226	+	0.109607i
$438$		−	7.79129i		−	0.372282i
$439$	−12.6652	+	21.9367i	−0.604475	+	1.04698i	0.387660	+	0.921803i	$0.373284\pi$
$439$	−12.6652	+	21.9367i	−0.604475	+	1.04698i	−0.992134	+	0.125178i	$0.960050\pi$
$440$		0			0
$441$	14.3739	+	24.8963i	0.684470	+	1.18554i
$442$	0.143025	+	0.0825757i	0.00680302	+	0.00392773i
$443$	−20.7846	+	12.0000i	−0.987507	+	0.570137i	−0.904528	−	0.426414i	$-0.859777\pi$
$443$	−20.7846	+	12.0000i	−0.987507	+	0.570137i	−0.0829786	+	0.996551i	$0.526443\pi$
$444$	10.0000			0.474579
$445$		0			0
$446$	−9.60436	−	16.6352i	−0.454779	−	0.787701i
$447$	−54.9887	+	31.7477i	−2.60088	+	1.50162i
$448$		−	1.00000i		−	0.0472456i
$449$	−3.33030			−0.157167			−0.0785834	−	0.996908i	$-0.525040\pi$
$449$	−3.33030			−0.157167			−0.0785834	+	0.996908i	$0.525040\pi$
$450$		0			0
$451$	−21.5608	+	37.3444i	−1.01526	+	1.75848i
$452$	−4.65390	+	2.68693i	−0.218901	+	0.126383i
$453$	38.0674	+	21.9782i	1.78856	+	1.03263i
$454$	3.87386	−	6.70973i	0.181809	−	0.314903i
$455$		0			0
$456$	−11.1652	+	4.83465i	−0.522856	+	0.226403i
$457$			20.7477i			0.970538i	0.874365	+	0.485269i	$0.161278\pi$
$457$			20.7477i			0.970538i	−0.874365	+	0.485269i	$0.838722\pi$
$458$	21.9367	+	12.6652i	1.02503	+	0.591804i
$459$	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	$0.262944\pi$
$462$	9.16478	−	5.29129i	0.426384	−	0.246173i
$463$			17.9564i			0.834507i	0.908790	+	0.417253i	$0.137007\pi$
$463$			17.9564i			0.834507i	−0.908790	+	0.417253i	$0.862993\pi$
$464$	−6.79129			−0.315278
$465$		0			0
$466$	−4.58258	−	7.93725i	−0.212284	−	0.367686i
$467$			12.3303i			0.570578i	0.958441	+	0.285289i	$0.0920896\pi$
$467$			12.3303i			0.570578i	−0.958441	+	0.285289i	$0.907910\pi$
$468$		−	1.00000i		−	0.0462250i
$469$	−7.79129	−	13.4949i	−0.359768	−	0.623137i
$470$		0			0
$471$	−11.1044	−	19.2333i	−0.511662	−	0.886224i
$472$	3.96863	+	2.29129i	0.182671	+	0.105465i
$473$	19.0148	+	10.9782i	0.874303	+	0.504779i
$474$	41.7477			1.91754
$475$		0			0
$476$	0.791288			0.0362686
$477$	−19.0148	−	10.9782i	−0.870629	−	0.502658i
$478$	−14.3609	−	8.29129i	−0.656854	−	0.379235i
$479$	15.8739	+	27.4943i	0.725295	+	1.25625i	0.958852	+	0.283905i	$0.0916301\pi$
$479$	15.8739	+	27.4943i	0.725295	+	1.25625i	−0.233557	+	0.972343i	$0.575037\pi$
$480$		0			0
$481$	0.373864	+	0.647551i	0.0170467	+	0.0295258i
$482$			16.7913i			0.764822i
$483$			12.7913i			0.582024i
$484$	1.68693	+	2.92185i	0.0766787	+	0.132811i
$485$		0			0
$486$	16.1652			0.733266
$487$		−	23.0000i		−	1.04223i	−0.853487	−	0.521115i	$-0.825516\pi$
$487$		−	23.0000i		−	1.04223i	0.853487	−	0.521115i	$-0.174484\pi$
$488$	1.18980	−	0.686932i	0.0538597	−	0.0310959i
$489$	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	$-0.0841525\pi$
$492$	27.4943	+	15.8739i	1.23954	+	0.715649i
$493$		−	5.37386i		−	0.242027i
$494$	−0.730493	−	0.542250i	−0.0328664	−	0.0243970i
$495$		0			0
$496$	2.39564	−	4.14938i	0.107568	−	0.186313i
$497$	3.96863	+	2.29129i	0.178017	+	0.102778i
$498$	−9.16478	+	5.29129i	−0.410684	+	0.237108i
$499$	−9.66515	+	16.7405i	−0.432672	+	0.749409i	−0.997102	−	0.0760712i	$-0.975762\pi$
$499$	−9.66515	+	16.7405i	−0.432672	+	0.749409i	0.564431	+	0.825480i	$0.309096\pi$
$500$		0			0
$501$	−32.2087			−1.43898
$502$		−	13.1216i		−	0.585645i
$503$	−3.96863	+	2.29129i	−0.176952	+	0.102163i	−0.585860	−	0.810412i	$-0.699243\pi$
$503$	−3.96863	+	2.29129i	−0.176952	+	0.102163i	0.408908	+	0.912576i	$0.365910\pi$
$504$	−2.39564	−	4.14938i	−0.106710	−	0.184828i
$505$		0			0
$506$	−17.3739			−0.772362
$507$	−31.3199	+	18.0826i	−1.39097	+	0.803075i
$508$	−2.27430	−	1.31307i	−0.100906	−	0.0582580i
$509$	11.2087	+	19.4141i	0.496817	+	0.860513i	0.999993	−	0.00367102i	$-0.00116853\pi$
$509$	11.2087	+	19.4141i	0.496817	+	0.860513i	−0.503176	+	0.864184i	$0.667835\pi$
$510$		0			0
$511$	1.39564	−	2.41733i	0.0617397	−	0.106936i
$512$		−	1.00000i		−	0.0441942i
$513$	−12.9904	+	17.5000i	−0.573539	+	0.772644i
$514$	11.2087			0.494395
$515$		0			0
$516$	8.08258	−	13.9994i	0.355816	−	0.616291i
$517$	−39.9425	+	23.0608i	−1.75667	+	1.01421i
$518$	3.10260	+	1.79129i	0.136320	+	0.0787047i
$519$	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	$0.406246\pi$
$522$	−28.1796	+	16.2695i	−1.23339	+	0.712097i
$523$	−15.3700	+	8.87386i	−0.672082	+	0.388027i	−0.796865	−	0.604157i	$-0.793510\pi$
$523$	−15.3700	+	8.87386i	−0.672082	+	0.388027i	0.124783	+	0.992184i	$0.460177\pi$
$524$	−11.5390			−0.504084
$525$		0			0
$526$	9.70871	+	16.8160i	0.423320	+	0.733212i
$527$	3.28335	+	1.89564i	0.143025	+	0.0825755i
$528$	9.16478	−	5.29129i	0.398846	−	0.230274i
$529$	−1.00000	+	1.73205i	−0.0434783	+	0.0753066i
$530$		0			0
$531$	21.9564			0.952828
$532$	−4.33013	−	0.500000i	−0.187735	−	0.0216777i
$533$			2.37386i			0.102823i
$534$	−6.39564	+	11.0776i	−0.276767	+	0.479374i
$535$		0			0
$536$	−7.79129	−	13.4949i	−0.336532	−	0.582891i
$537$	40.4847	+	23.3739i	1.74704	+	1.00866i
$538$	11.3636	−	6.56080i	0.489921	−	0.282856i
$539$	−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	$0.713356\pi$
$542$	14.8277	−	8.56080i	0.636906	−	0.367718i
$543$			21.2867i			0.913502i
$544$	0.791288			0.0339262
$545$		0			0
$546$	0.291288	−	0.504525i	0.0124660	−	0.0215917i
$547$	−14.5794	+	8.41742i	−0.623370	+	0.359903i	−0.778180	−	0.628041i	$-0.783857\pi$
$547$	−14.5794	+	8.41742i	−0.623370	+	0.359903i	0.154810	+	0.987944i	$0.450524\pi$
$548$	−13.2764	−	7.66515i	−0.567141	−	0.327439i
$549$	3.29129	−	5.70068i	0.140469	−	0.243299i
$550$		0			0
$551$	−3.39564	+	29.4071i	−0.144659	+	1.25279i
$552$			12.7913i			0.544433i
$553$	12.9527	+	7.47822i	0.550803	+	0.318006i
$554$	−4.37386	+	7.57575i	−0.185828	+	0.321863i
$555$		0			0
$556$	6.10436	−	10.5731i	0.258882	−	0.448397i
$557$	−8.62253	+	4.97822i	−0.365348	+	0.210934i	−0.671424	−	0.741073i	$-0.734317\pi$
$557$	−8.62253	+	4.97822i	−0.365348	+	0.210934i	0.306076	+	0.952007i	$0.400984\pi$
$558$		−	22.9564i		−	0.971824i
$559$	1.20871			0.0511231
$560$		0			0
$561$	4.18693	+	7.25198i	0.176772	+	0.306179i
$562$		−	10.5826i		−	0.446399i
$563$		−	14.3739i		−	0.605786i	−0.953025	−	0.302893i	$-0.902047\pi$
$563$		−	14.3739i		−	0.605786i	0.953025	−	0.302893i	$-0.0979525\pi$
$564$	16.9782	+	29.4071i	0.714912	+	1.23826i
$565$		0			0
$566$	−10.5608	−	18.2918i	−0.443903	−	0.768863i
$567$	0.361500	+	0.208712i	0.0151816	+	0.00876509i
$568$	3.96863	+	2.29129i	0.166520	+	0.0961403i
$569$	8.83485			0.370376			0.185188	−	0.982703i	$-0.440711\pi$
$569$	8.83485			0.370376			0.185188	+	0.982703i	$0.440711\pi$
$570$		0			0
$571$	−22.0000			−0.920671			−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000			−0.920671			−0.460336	+	0.887745i	$0.652271\pi$
$572$	0.685275	+	0.395644i	0.0286528	+	0.0165427i
$573$	38.5719	+	22.2695i	1.61137	+	0.930322i
$574$	5.68693	+	9.85005i	0.237368	+	0.411133i
$575$		0			0
$576$	−2.39564	−	4.14938i	−0.0998185	−	0.172891i
$577$		−	14.0000i		−	0.582828i	−0.956597	−	0.291414i	$-0.905874\pi$
$577$		−	14.0000i		−	0.582828i	0.956597	−	0.291414i	$-0.0941257\pi$
$578$		−	16.3739i		−	0.681063i
$579$	3.83485	+	6.64215i	0.159371	+	0.276038i
$580$		0			0
$581$	−3.79129			−0.157289
$582$		−	34.5390i		−	1.43169i
$583$	15.0462	−	8.68693i	0.623150	−	0.359776i
$584$	1.39564	−	2.41733i	0.0577522	−	0.100030i
$585$		0			0
$586$	−12.4782	+	21.6129i	−0.515471	+	0.892821i
$587$	−8.22330	−	4.74773i	−0.339412	−	0.195960i	0.320600	−	0.947215i	$-0.396116\pi$
$587$	−8.22330	−	4.74773i	−0.339412	−	0.195960i	−0.660012	+	0.751255i	$0.729449\pi$
$588$			16.7477i			0.690665i
$589$	−16.7695	−	12.4481i	−0.690976	−	0.512916i
$590$		0			0
$591$	28.2042	−	48.8510i	1.16016	−	2.00946i
$592$	3.10260	+	1.79129i	0.127516	+	0.0736215i
$593$	−10.2493	+	5.91742i	−0.420887	+	0.242999i	−0.695457	−	0.718568i	$-0.744798\pi$
$593$	−10.2493	+	5.91742i	−0.420887	+	0.242999i	0.274569	+	0.961567i	$0.411465\pi$
$594$	9.47822	−	16.4168i	0.388896	−	0.673588i
$595$		0			0
$596$	−22.7477			−0.931783
$597$			10.0000i			0.409273i
$598$	−0.828301	+	0.478220i	−0.0338717	+	0.0195559i
$599$	−18.5608	−	32.1482i	−0.758374	−	1.31354i	−0.943680	−	0.330861i	$-0.892661\pi$
$599$	−18.5608	−	32.1482i	−0.758374	−	1.31354i	0.185306	−	0.982681i	$-0.440672\pi$
$600$		0			0
$601$	9.91288			0.404355			0.202177	−	0.979349i	$-0.435198\pi$
$601$	9.91288			0.404355			0.202177	+	0.979349i	$0.435198\pi$
$602$	5.01540	−	2.89564i	0.204413	−	0.118018i
$603$	−64.6580	−	37.3303i	−2.63308	−	1.52021i
$604$	7.87386	+	13.6379i	0.320383	+	0.554920i
$605$		0			0
$606$		0			0
$607$			18.2087i			0.739069i	0.929217	+	0.369534i	$0.120483\pi$
$607$			18.2087i			0.739069i	−0.929217	+	0.369534i	$0.879517\pi$
$608$	−4.33013	−	0.500000i	−0.175610	−	0.0202777i
$609$	−18.9564			−0.768154
$610$		0			0
$611$	−1.26951	+	2.19885i	−0.0513588	+	0.0889560i
$612$	3.28335	−	1.89564i	0.132722	−	0.0766269i
$613$	−12.5534	−	7.24773i	−0.507028	−	0.292733i	0.224583	−	0.974455i	$-0.427898\pi$
$613$	−12.5534	−	7.24773i	−0.507028	−	0.292733i	−0.731611	+	0.681722i	$0.761231\pi$
$614$	−17.2477	−	29.8739i	−0.696062	−	1.20561i
$615$		0			0
$616$	3.79129			0.152755
$617$	28.5788	−	16.5000i	1.15054	−	0.664265i	0.201522	−	0.979484i	$-0.435411\pi$
$617$	28.5788	−	16.5000i	1.15054	−	0.664265i	0.949019	+	0.315219i	$0.102078\pi$
$618$	−12.4859	+	7.20871i	−0.502255	+	0.289977i
$619$	24.3739			0.979668			0.489834	−	0.871816i	$-0.337057\pi$
$619$	24.3739			0.979668			0.489834	+	0.871816i	$0.337057\pi$
$620$		0			0
$621$	11.4564	+	19.8431i	0.459731	+	0.796278i
$622$	−12.9904	−	7.50000i	−0.520867	−	0.300723i
$623$	−3.96863	+	2.29129i	−0.159000	+	0.0917985i
$624$	0.291288	−	0.504525i	0.0116608	−	0.0201972i
$625$		0			0
$626$	−11.7477			−0.469534
$627$	−18.3296	−	42.3303i	−0.732012	−	1.69051i
$628$		−	7.95644i		−	0.317496i
$629$	−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	$0.577143\pi$
$632$	12.9527	+	7.47822i	0.515229	+	0.297468i
$633$	−57.9105	+	33.4347i	−2.30174	+	1.32891i
$634$	9.16515			0.363995
$635$		0			0
$636$	−6.39564	−	11.0776i	−0.253604	−	0.439255i
$637$	−1.08450	+	0.626136i	−0.0429695	+	0.0248084i
$638$		−	25.7477i		−	1.01936i
$639$	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	$0.275940\pi$
$642$	45.8239	−	26.4564i	1.80852	−	1.04415i
$643$	−25.5438	−	14.7477i	−1.00735	−	0.581594i	−0.0969351	−	0.995291i	$-0.530904\pi$
$643$	−25.5438	−	14.7477i	−1.00735	−	0.581594i	−0.910415	+	0.413697i	$0.864237\pi$
$644$	−2.29129	+	3.96863i	−0.0902894	+	0.156386i
$645$		0			0
$646$	0.395644	−	3.42638i	0.0155664	−	0.134809i
$647$		−	18.7913i		−	0.738762i	−0.929278	−	0.369381i	$-0.879570\pi$
$647$		−	18.7913i		−	0.738762i	0.929278	−	0.369381i	$-0.120430\pi$
$648$	0.361500	+	0.208712i	0.0142011	+	0.00819899i
$649$	−8.68693	+	15.0462i	−0.340992	+	0.590615i
$650$		0			0
$651$	6.68693	−	11.5821i	0.262082	−	0.453939i
$652$	12.6289	−	7.29129i	0.494585	−	0.285549i
$653$		−	27.3303i		−	1.06952i	−0.845005	−	0.534759i	$-0.820403\pi$
$653$		−	27.3303i		−	1.06952i	0.845005	−	0.534759i	$-0.179597\pi$
$654$	−32.7913			−1.28224
$655$		0			0
$656$	5.68693	+	9.85005i	0.222037	+	0.384580i
$657$		−	13.3739i		−	0.521764i
$658$			12.1652i			0.474247i
$659$	0.873864	+	1.51358i	0.0340409	+	0.0589606i	0.882544	−	0.470230i	$-0.155829\pi$
$659$	0.873864	+	1.51358i	0.0340409	+	0.0589606i	−0.848503	+	0.529190i	$0.822496\pi$
$660$		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	$-0.531744\pi$
$662$	−15.5130	−	8.95644i	−0.602930	−	0.348102i
$663$	0.399225	+	0.230493i	0.0155046	+	0.00895159i
$664$	−3.79129			−0.147131
$665$		0			0
$666$	17.1652			0.665136
$667$	26.9521	+	15.5608i	1.04359	+	0.602516i
$668$	−9.99308	−	5.76951i	−0.386644	−	0.223229i
$669$	−26.8085	−	46.4337i	−1.03648	−	1.79523i
$670$		0			0
$671$	2.60436	+	4.51088i	0.100540	+	0.174140i
$672$		−	2.79129i		−	0.107676i
$673$			2.79129i			0.107596i	0.998552	+	0.0537981i	$0.0171327\pi$
$673$			2.79129i			0.107596i	−0.998552	+	0.0537981i	$0.982867\pi$
$674$	11.6652	+	20.2046i	0.449325	+	0.778253i
$675$		0			0
$676$	−12.9564			−0.498325
$677$			35.2432i			1.35451i	0.735750	+	0.677253i	$0.236830\pi$
$677$			35.2432i			1.35451i	−0.735750	+	0.677253i	$0.763170\pi$
$678$	−12.9904	+	7.50000i	−0.498893	+	0.288036i
$679$	6.18693	−	10.7161i	0.237433	−	0.411245i
$680$		0			0
$681$	10.8131	−	18.7288i	0.414358	−	0.717689i
$682$	15.7315	+	9.08258i	0.602390	+	0.347790i
$683$		−	36.1652i		−	1.38382i	−0.721983	−	0.691911i	$-0.756769\pi$
$683$		−	36.1652i		−	1.38382i	0.721983	−	0.691911i	$-0.243231\pi$
$684$	−19.1652	+	8.29875i	−0.732798	+	0.317311i
$685$		0			0
$686$	−6.50000	+	11.2583i	−0.248171	+	0.429845i
$687$	61.2316	+	35.3521i	2.33613	+	1.34877i
$688$	5.01540	−	2.89564i	0.191210	−	0.110395i
$689$	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	$0.709225\pi$
$692$			21.0000i			0.798300i
$693$	15.7315	−	9.08258i	0.597590	−	0.345019i
$694$	1.81307	+	3.14033i	0.0688231	+	0.119205i
$695$		0			0
$696$	−18.9564			−0.718542
$697$	−7.79423	+	4.50000i	−0.295227	+	0.170450i
$698$	4.69163	+	2.70871i	0.177581	+	0.102526i
$699$	−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	$0.0879841\pi$
$702$		−	1.04356i		−	0.0393867i
$703$	9.30780	−	12.5390i	0.351051	−	0.472918i
$704$	3.79129			0.142890
$705$		0			0
$706$	6.87386	−	11.9059i	0.258701	−	0.448084i
$707$		0			0
$708$	11.0776	+	6.39564i	0.416321	+	0.240363i
$709$	−13.3739	−	23.1642i	−0.502266	−	0.869950i	−0.999997	−	0.00261852i	$-0.999166\pi$
$709$	−13.3739	−	23.1642i	−0.502266	−	0.869950i	0.497731	−	0.867332i	$-0.334167\pi$
$710$		0			0
$711$	71.6606			2.68748
$712$	−3.96863	+	2.29129i	−0.148731	+	0.0858696i
$713$	−19.0148	+	10.9782i	−0.712111	+	0.411138i
$714$	2.20871			0.0826590
$715$		0			0
$716$	8.37386	+	14.5040i	0.312946	+	0.542038i
$717$	−40.0855	−	23.1434i	−1.49702	−	0.864305i
$718$	−30.9207	+	17.8521i	−1.15395	+	0.666234i
$719$	−6.08258	+	10.5353i	−0.226842	+	0.392902i	−0.956870	−	0.290515i	$-0.906173\pi$
$719$	−6.08258	+	10.5353i	−0.226842	+	0.392902i	0.730029	+	0.683417i	$0.239507\pi$
$720$		0			0
$721$	−5.16515			−0.192360
$722$	−4.33013	+	18.5000i	−0.161151	+	0.688499i
$723$			46.8693i			1.74309i
$724$	−3.81307	+	6.60443i	−0.141712	+	0.245452i
$725$		0			0
$726$	4.70871	+	8.15573i	0.174757	+	0.302687i
$727$	−3.60713	−	2.08258i	−0.133781	−	0.0772385i	0.431616	−	0.902058i	$-0.357944\pi$
$727$	−3.60713	−	2.08258i	−0.133781	−	0.0772385i	−0.565397	+	0.824819i	$0.691277\pi$
$728$	0.180750	−	0.104356i	0.00669904	−	0.00386769i
$729$	43.8693			1.62479
$730$		0			0
$731$	2.29129	+	3.96863i	0.0847463	+	0.146785i
$732$	3.32108	−	1.91742i	0.122751	−	0.0708700i
$733$			12.7477i			0.470848i	0.971893	+	0.235424i	$0.0756479\pi$
$733$			12.7477i			0.470848i	−0.971893	+	0.235424i	$0.924352\pi$
$734$	−8.79129			−0.324492
$735$		0			0
$736$	−2.29129	+	3.96863i	−0.0844580	+	0.146286i
$737$	51.1631	−	29.5390i	1.88462	−	1.08808i
$738$	47.1944	+	27.2477i	1.73725	+	1.00300i
$739$	−17.8739	+	30.9584i	−0.657501	+	1.13882i	0.323760	+	0.946139i	$0.395053\pi$
$739$	−17.8739	+	30.9584i	−0.657501	+	1.13882i	−0.981261	+	0.192685i	$0.938280\pi$
$740$		0			0
$741$	−2.03901	−	1.51358i	−0.0749051	−	0.0556026i
$742$		−	4.58258i		−	0.168232i
$743$	−16.8160	−	9.70871i	−0.616919	−	0.356178i	0.158750	−	0.987319i	$-0.449254\pi$
$743$	−16.8160	−	9.70871i	−0.616919	−	0.356178i	−0.775668	+	0.631141i	$0.782587\pi$
$744$	6.68693	−	11.5821i	0.245155	−	0.424621i
$745$		0			0
$746$	10.6869	−	18.5103i	0.391276	−	0.677711i
$747$	−15.7315	+	9.08258i	−0.575585	+	0.332314i
$748$			3.00000i			0.109691i
$749$	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	$0.962166\pi$
$752$			12.1652i			0.443617i
$753$		−	36.6261i		−	1.33473i
$754$	−0.708712	−	1.22753i	−0.0258098	−	0.0447038i
$755$		0			0
$756$	−2.50000	−	4.33013i	−0.0909241	−	0.157485i
$757$	39.6187	+	22.8739i	1.43997	+	0.831365i	0.997847	−	0.0655915i	$-0.0208934\pi$
$757$	39.6187	+	22.8739i	1.43997	+	0.831365i	0.442119	+	0.896956i	$0.354227\pi$
$758$	−4.18710	−	2.41742i	−0.152082	−	0.0878048i
$759$	−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	$0.348674\pi$
$762$	−6.34823	−	3.66515i	−0.229972	−	0.132774i
$763$	−10.1738	−	5.87386i	−0.368317	−	0.212648i
$764$	7.97822	+	13.8187i	0.288642	+	0.499942i
$765$		0			0
$766$	−2.29129	−	3.96863i	−0.0827876	−	0.143392i
$767$			0.956439i			0.0345350i
$768$		−	2.79129i		−	0.100722i
$769$	−11.1652	−	19.3386i	−0.402626	−	0.697368i	0.591416	−	0.806366i	$-0.298569\pi$
$769$	−11.1652	−	19.3386i	−0.402626	−	0.697368i	−0.994042	+	0.108998i	$0.965236\pi$
$770$		0			0
$771$	31.2867			1.12676
$772$			2.74773i			0.0988929i
$773$	−18.4726	+	10.6652i	−0.664413	+	0.383599i	−0.793956	−	0.607975i	$-0.791982\pi$
$773$	−18.4726	+	10.6652i	−0.664413	+	0.383599i	0.129544	+	0.991574i	$0.458649\pi$
$774$	13.8739	−	24.0302i	0.498686	−	0.863749i
$775$		0			0
$776$	6.18693	−	10.7161i	0.222098	−	0.384685i
$777$	8.66025	+	5.00000i	0.310685	+	0.179374i
$778$			18.6261i			0.667779i
$779$	45.4955	−	19.7001i	1.63004	−	0.705830i
$780$		0			0
$781$	−8.68693	+	15.0462i	−0.310843	+	0.538396i
$782$	−3.14033	−	1.81307i	−0.112298	−	0.0648352i
$783$	−29.4071	+	16.9782i	−1.05093	+	0.606752i
$784$	−3.00000	+	5.19615i	−0.107143	+	0.185577i
$785$		0			0
$786$	−32.2087			−1.14885
$787$			23.7477i			0.846515i	0.906009	+	0.423258i	$0.139113\pi$
$787$			23.7477i			0.846515i	−0.906009	+	0.423258i	$0.860887\pi$
$788$	17.5013	−	10.1044i	0.623457	−	0.359953i
$789$	27.0998	+	46.9382i	0.964779	+	1.67105i
$790$		0			0
$791$	−5.37386			−0.191073
$792$	15.7315	−	9.08258i	0.558994	−	0.322735i
$793$	0.248326	+	0.143371i	0.00881831	+	0.00509125i
$794$	−5.70871	−	9.88778i	−0.202595	−	0.350904i
$795$		0			0
$796$	−1.79129	+	3.10260i	−0.0634905	+	0.109969i
$797$			38.5390i			1.36512i	0.730829	+	0.682561i	$0.239134\pi$
$797$			38.5390i			1.36512i	−0.730829	+	0.682561i	$0.760866\pi$
$798$	−12.0866	−	1.39564i	−0.427862	−	0.0494053i
$799$	−9.62614			−0.340548
$800$		0			0
$801$	−10.9782	+	19.0148i	−0.387896	+	0.671856i
$802$	10.3923	−	6.00000i	0.366965	−	0.211867i
$803$	9.16478	+	5.29129i	0.323418	+	0.186725i
$804$	−21.7477	−	37.6682i	−0.766983	−	1.32845i
$805$		0			0
$806$	1.00000			0.0352235
$807$	31.7192	−	18.3131i	1.11657	−	0.644651i
$808$		0			0
$809$	2.53901			0.0892670			0.0446335	−	0.999003i	$-0.485788\pi$
$809$	2.53901			0.0892670			0.0446335	+	0.999003i	$0.485788\pi$
$810$		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	$0.983407\pi$
$812$	−5.88143	−	3.39564i	−0.206398	−	0.119164i
$813$	41.3885	−	23.8956i	1.45156	−	0.838057i
$814$	−6.79129	+	11.7629i	−0.238035	+	0.412288i
$815$		0			0
$816$	2.20871			0.0773204
$817$	−10.0308	−	23.1652i	−0.350933	−	0.810446i
$818$		−	10.0000i		−	0.349642i
$819$	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	$0.614758\pi$
$822$	−37.0583	−	21.3956i	−1.29256	−	0.746259i
$823$	31.8245	−	18.3739i	1.10933	−	0.640473i	0.170675	−	0.985327i	$-0.445405\pi$
$823$	31.8245	−	18.3739i	1.10933	−	0.640473i	0.938656	+	0.344855i	$0.112072\pi$
$824$	−5.16515			−0.179937
$825$		0			0
$826$	2.29129	+	3.96863i	0.0797241	+	0.138086i
$827$	25.0393	−	14.4564i	0.870701	−	0.502700i	0.00312009	−	0.999995i	$-0.499007\pi$
$827$	25.0393	−	14.4564i	0.870701	−	0.502700i	0.867581	+	0.497295i	$0.165674\pi$
$828$			21.9564i			0.763039i
$829$	−31.5390			−1.09540			−0.547698	−	0.836676i	$-0.684496\pi$
$829$	−31.5390			−1.09540			−0.547698	+	0.836676i	$0.684496\pi$
$830$		0			0
$831$	−12.2087	+	21.1461i	−0.423516	+	0.733550i
$832$	0.180750	−	0.104356i	0.00626638	−	0.00361790i
$833$	−4.11165	−	2.37386i	−0.142460	−	0.0822495i
$834$	17.0390	−	29.5124i	0.590013	−	1.02193i
$835$		0			0
$836$	1.89564	−	16.4168i	0.0655622	−	0.567785i
$837$		−	23.9564i		−	0.828056i
$838$	19.7001	+	11.3739i	0.680529	+	0.392904i
$839$	25.9782	−	44.9956i	0.896868	−	1.55342i	0.0653918	−	0.997860i	$-0.479170\pi$
$839$	25.9782	−	44.9956i	0.896868	−	1.55342i	0.831476	−	0.555561i	$-0.187496\pi$
$840$		0			0
$841$	−8.56080	+	14.8277i	−0.295200	+	0.511301i
$842$	−17.3205	+	10.0000i	−0.596904	+	0.344623i
$843$		−	29.5390i		−	1.01738i
$844$	−23.9564			−0.824615
$845$		0			0
$846$	29.1434	+	50.4778i	1.00197	+	1.73546i
$847$			3.37386i			0.115927i
$848$		−	4.58258i		−	0.157366i
$849$	−29.4782	−	51.0578i	−1.01169	−	1.75230i
$850$		0			0
$851$	−8.20871	−	14.2179i	−0.281391	−	0.487384i
$852$	11.0776	+	6.39564i	0.379512	+	0.219111i
$853$	45.0632	+	26.0172i	1.54293	+	0.890813i	0.998652	+	0.0519108i	$0.0165311\pi$
$853$	45.0632	+	26.0172i	1.54293	+	0.890813i	0.544282	+	0.838902i	$0.316802\pi$
$854$	1.37386			0.0470126
$855$		0			0
$856$	18.9564			0.647918
$857$	2.59808	+	1.50000i	0.0887486	+	0.0512390i	0.543718	−	0.839268i	$-0.317016\pi$
$857$	2.59808	+	1.50000i	0.0887486	+	0.0512390i	−0.454969	+	0.890507i	$0.650350\pi$
$858$	1.91280	+	1.10436i	0.0653019	+	0.0377021i
$859$	8.35208	+	14.4662i	0.284969	+	0.493581i	0.972602	−	0.232478i	$-0.0746832\pi$
$859$	8.35208	+	14.4662i	0.284969	+	0.493581i	−0.687632	+	0.726059i	$0.741350\pi$
$860$		0			0
$861$	15.8739	+	27.4943i	0.540980	+	0.937005i
$862$		−	8.20871i		−	0.279590i
$863$		−	4.41742i		−	0.150371i	−0.997170	−	0.0751854i	$-0.976045\pi$
$863$		−	4.41742i		−	0.150371i	0.997170	−	0.0751854i	$-0.0239549\pi$
$864$	−2.50000	−	4.33013i	−0.0850517	−	0.147314i
$865$		0			0
$866$	6.91288			0.234909
$867$		−	45.7042i		−	1.55219i
$868$	4.14938	−	2.39564i	0.140839	−	0.0813135i
$869$	−28.3521	+	49.1072i	−0.961779	+	1.66585i
$870$		0			0
$871$	1.62614	−	2.81655i	0.0550995	−	0.0954352i
$872$	−10.1738	−	5.87386i	−0.344529	−	0.198914i
$873$		−	59.2867i		−	2.00655i
$874$	16.0390	+	11.9059i	0.542528	+	0.402722i
$875$		0			0
$876$	3.89564	−	6.74745i	0.131622	−	0.227975i
$877$	22.9457	+	13.2477i	0.774822	+	0.447344i	0.834592	−	0.550868i	$-0.185703\pi$
$877$	22.9457	+	13.2477i	0.774822	+	0.447344i	−0.0597698	+	0.998212i	$0.519037\pi$
$878$	−21.9367	+	12.6652i	−0.740327	+	0.427428i
$879$	−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	$0.504243\pi$
$882$			28.7477i			0.967986i
$883$	21.4322	−	12.3739i	0.721250	−	0.416414i	−0.0939628	−	0.995576i	$-0.529953\pi$
$883$	21.4322	−	12.3739i	0.721250	−	0.416414i	0.815212	+	0.579162i	$0.196620\pi$
$884$	0.0825757	+	0.143025i	0.00277732	+	0.00481046i
$885$		0			0
$886$	−24.0000			−0.806296
$887$	29.5502	−	17.0608i	0.992197	−	0.572845i	0.0862670	−	0.996272i	$-0.472506\pi$
$887$	29.5502	−	17.0608i	0.992197	−	0.572845i	0.905930	+	0.423427i	$0.139173\pi$
$888$	8.66025	+	5.00000i	0.290619	+	0.167789i
$889$	−1.31307	−	2.27430i	−0.0440389	−	0.0762776i
$890$		0			0
$891$	−0.791288	+	1.37055i	−0.0265091	+	0.0459152i
$892$		−	19.2087i		−	0.643155i
$893$	52.6767	+	6.08258i	1.76276	+	0.203546i
$894$	−63.4955			−2.12361
$895$		0			0
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$	−2.31203	+	1.33485i	−0.0771963	+	0.0445693i
$898$	−2.88413	−	1.66515i	−0.0962446	−	0.0555668i
$899$	−16.2695	−	28.1796i	−0.542618	−	0.939843i
$900$		0			0
$901$	3.62614			0.120804
$902$	−37.3444	+	21.5608i	−1.24343	+	0.717896i
$903$	13.9994	−	8.08258i	0.465872	−	0.268971i
$904$	−5.37386			−0.178732
$905$		0			0
$906$	21.9782	+	38.0674i	0.730177	+	1.26470i
$907$	−29.3317	−	16.9347i	−0.973943	−	0.562306i	−0.0735068	−	0.997295i	$-0.523419\pi$
$907$	−29.3317	−	16.9347i	−0.973943	−	0.562306i	−0.900436	+	0.434989i	$0.856752\pi$
$908$	6.70973	−	3.87386i	0.222670	−	0.128559i
$909$		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	$0.798425\pi$
$912$	−12.0866	−	1.39564i	−0.400228	−	0.0462144i
$913$		−	14.3739i		−	0.475705i
$914$	−10.3739	+	17.9681i	−0.343137	+	0.594331i
$915$		0			0
$916$	12.6652	+	21.9367i	0.418468	+	0.724808i
$917$	−9.99308	−	5.76951i	−0.330001	−	0.190526i
$918$	3.42638	−	1.97822i	0.113087	−	0.0652910i
$919$	46.7913			1.54350			0.771751	−	0.635925i	$-0.219381\pi$
$919$	46.7913			1.54350			0.771751	+	0.635925i	$0.219381\pi$
$920$		0			0
$921$	−48.1434	−	83.3868i	−1.58638	−	2.74769i
$922$	−11.0776	+	6.39564i	−0.364821	+	0.210629i
$923$			0.956439i			0.0314816i
$924$	10.5826			0.348141
$925$		0			0
$926$	−8.97822	+	15.5507i	−0.295043	+	0.511029i
$927$	−21.4322	+	12.3739i	−0.703925	+	0.406411i
$928$	−5.88143	−	3.39564i	−0.193067	−	0.111467i
$929$	5.43920	−	9.42098i	0.178455	−	0.309092i	−0.762897	−	0.646520i	$-0.776224\pi$
$929$	5.43920	−	9.42098i	0.178455	−	0.309092i	0.941351	+	0.337428i	$0.109557\pi$
$930$		0			0
$931$	21.0000	+	15.5885i	0.688247	+	0.510891i
$932$		−	9.16515i		−	0.300215i
$933$	−36.2599	−	20.9347i	−1.18710	−	0.685370i
$934$	−6.16515	+	10.6784i	−0.201730	+	0.349406i
$935$		0			0
$936$	0.500000	−	0.866025i	0.0163430	−	0.0283069i
$937$	−5.30145	+	3.06080i	−0.173191	+	0.0999918i	−0.584090	−	0.811689i	$-0.698548\pi$
$937$	−5.30145	+	3.06080i	−0.173191	+	0.0999918i	0.410899	+	0.911681i	$0.365215\pi$
$938$		−	15.5826i		−	0.508789i
$939$	−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	$0.603263\pi$
$942$		−	22.2087i		−	0.723599i
$943$		−	52.1216i		−	1.69731i
$944$	2.29129	+	3.96863i	0.0745751	+	0.129168i
$945$		0			0
$946$	10.9782	+	19.0148i	0.356933	+	0.618226i
$947$	−24.7532	−	14.2913i	−0.804372	−	0.464404i	0.0406256	−	0.999174i	$-0.487065\pi$
$947$	−24.7532	−	14.2913i	−0.804372	−	0.464404i	−0.844998	+	0.534770i	$0.820398\pi$
$948$	36.1546	+	20.8739i	1.17425	+	0.677952i
$949$	0.582576			0.0189112
$950$		0			0
$951$	25.5826			0.829572
$952$	0.685275	+	0.395644i	0.0222099	+	0.0128229i
$953$	13.9617	+	8.06080i	0.452264	+	0.261115i	0.708786	−	0.705424i	$-0.249243\pi$
$953$	13.9617	+	8.06080i	0.452264	+	0.261115i	−0.256522	+	0.966538i	$0.582577\pi$
$954$	−10.9782	−	19.0148i	−0.355433	−	0.615628i
$955$		0			0
$956$	−8.29129	−	14.3609i	−0.268159	−	0.464466i
$957$		−	71.8693i		−	2.32321i
$958$			31.7477i			1.02572i
$959$	−7.66515	−	13.2764i	−0.247521	−	0.428718i
$960$		0			0
$961$	−8.04356			−0.259470
$962$			0.747727i			0.0241077i
$963$	78.6574	−	45.4129i	2.53470	−	1.46341i
$964$	−8.39564	+	14.5417i	−0.270405	+	0.468356i
$965$		0			0
$966$	−6.39564	+	11.0776i	−0.205776	+	0.356415i
$967$	−44.2349	−	25.5390i	−1.42250	−	0.821279i	−0.425986	−	0.904730i	$-0.640073\pi$
$967$	−44.2349	−	25.5390i	−1.42250	−	0.821279i	−0.996512	+	0.0834506i	$0.973406\pi$
$968$			3.37386i			0.108440i
$969$	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	$0.161114\pi$
$972$	13.9994	+	8.08258i	0.449032	+	0.259249i
$973$	10.5731	−	6.10436i	0.338957	−	0.195697i
$974$	11.5000	−	19.9186i	0.368484	−	0.638233i
$975$		0			0
$976$	1.37386			0.0439763
$977$		−	32.3739i		−	1.03573i	−0.855462	−	0.517866i	$-0.826727\pi$
$977$		−	32.3739i		−	1.03573i	0.855462	−	0.517866i	$-0.173273\pi$
$978$	35.2508	−	20.3521i	1.12720	−	0.650788i
$979$	−8.68693	−	15.0462i	−0.277636	−	0.480879i
$980$		0			0
$981$	−56.2867			−1.79710
$982$	27.2083	−	15.7087i	0.868251	−	0.501285i
$983$	−42.9398	−	24.7913i	−1.36957	−	0.790719i	−0.378694	−	0.925522i	$-0.623627\pi$
$983$	−42.9398	−	24.7913i	−1.36957	−	0.790719i	−0.990872	+	0.134803i	$0.956960\pi$
$984$	15.8739	+	27.4943i	0.506040	+	0.876487i
$985$		0			0
$986$	2.68693	−	4.65390i	0.0855693	−	0.148210i
$987$			33.9564i			1.08085i
$988$	−0.361500	−	0.834849i	−0.0115008	−	0.0265601i
$989$	−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	$0.291818\pi$
$992$	4.14938	−	2.39564i	0.131743	−	0.0760618i
$993$	−43.3013	−	25.0000i	−1.37412	−	0.793351i
$994$	2.29129	+	3.96863i	0.0726752	+	0.125877i
$995$		0			0
$996$	−10.5826			−0.335322
$997$	0.866025	−	0.500000i	0.0274273	−	0.0158352i	−0.486224	−	0.873834i	$-0.661626\pi$
$997$	0.866025	−	0.500000i	0.0274273	−	0.0158352i	0.513651	+	0.857999i	$0.328293\pi$
$998$	−16.7405	+	9.66515i	−0.529912	+	0.305945i
$999$	17.9129			0.566738

Twists

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

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

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.j (of order \(6\), degree \(2\), not minimal)

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

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