LMFDB - Embedded newform 945.2.cq.a.59.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(59,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 9, 3]))

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

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

chi := DirichletCharacter("945.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cq (of order $18$, degree $6$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.17
Character	$\chi$	$=$	945.59
Dual form			945.2.cq.a.929.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18094 - 0.793796i) q^{2} +(0.224921 - 1.71738i) q^{3} +(2.59428 + 2.17686i) q^{4} +(1.01687 + 1.99148i) q^{5} +(-1.85379 + 3.56696i) q^{6} +(0.0155159 + 2.64571i) q^{7} +(-1.60908 - 2.78700i) q^{8} +(-2.89882 - 0.772553i) q^{9} +O(q^{10})$	\(q+(-2.18094 - 0.793796i) q^{2} +(0.224921 - 1.71738i) q^{3} +(2.59428 + 2.17686i) q^{4} +(1.01687 + 1.99148i) q^{5} +(-1.85379 + 3.56696i) q^{6} +(0.0155159 + 2.64571i) q^{7} +(-1.60908 - 2.78700i) q^{8} +(-2.89882 - 0.772553i) q^{9} +(-0.636893 - 5.15047i) q^{10} +(3.04282 + 3.62629i) q^{11} +(4.32202 - 3.96576i) q^{12} +(-2.46136 - 2.06532i) q^{13} +(2.06631 - 5.78243i) q^{14} +(3.64885 - 1.29842i) q^{15} +(0.120830 + 0.685259i) q^{16} +(2.52506 - 1.45785i) q^{17} +(5.70889 + 3.98596i) q^{18} +(-6.25127 - 3.60917i) q^{19} +(-1.69713 + 7.38003i) q^{20} +(4.54718 + 0.568429i) q^{21} +(-3.75766 - 10.3241i) q^{22} +(1.16190 - 0.422899i) q^{23} +(-5.14827 + 2.13655i) q^{24} +(-2.93197 + 4.05013i) q^{25} +(3.72862 + 6.45816i) q^{26} +(-1.97878 + 4.80463i) q^{27} +(-5.71908 + 6.89748i) q^{28} +(4.21789 + 5.02668i) q^{29} +(-8.98859 - 0.0646607i) q^{30} +(-0.00365117 + 0.00435129i) q^{31} +(-0.837218 + 4.74810i) q^{32} +(6.91213 - 4.41006i) q^{33} +(-6.66423 + 1.17508i) q^{34} +(-5.25309 + 2.72123i) q^{35} +(-5.83862 - 8.31455i) q^{36} +11.8943i q^{37} +(10.7687 + 12.8336i) q^{38} +(-4.10057 + 3.76256i) q^{39} +(3.91404 - 6.03844i) q^{40} +(-3.67394 - 3.08281i) q^{41} +(-9.46590 - 4.84924i) q^{42} +(0.149570 - 0.410940i) q^{43} +16.0314i q^{44} +(-1.40919 - 6.55852i) q^{45} -2.86973 q^{46} +(-2.20608 - 2.62911i) q^{47} +(1.20403 - 0.0533816i) q^{48} +(-6.99952 + 0.0821008i) q^{49} +(9.60941 - 6.50569i) q^{50} +(-1.93574 - 4.66441i) q^{51} +(-1.88953 - 10.7161i) q^{52} +(-2.37616 + 4.11562i) q^{53} +(8.12948 - 8.90784i) q^{54} +(-4.12754 + 9.74715i) q^{55} +(7.34862 - 4.30038i) q^{56} +(-7.60438 + 9.92405i) q^{57} +(-5.20878 - 14.3110i) q^{58} +(-2.00484 + 11.3700i) q^{59} +(12.2926 + 4.57456i) q^{60} +(-4.16948 - 4.96899i) q^{61} +(0.0114170 - 0.00659161i) q^{62} +(1.99897 - 7.68141i) q^{63} +(6.29077 - 10.8959i) q^{64} +(1.61018 - 7.00190i) q^{65} +(-18.5756 + 4.13124i) q^{66} +(4.06185 + 11.1598i) q^{67} +(9.72425 + 1.71465i) q^{68} +(-0.464942 - 2.09056i) q^{69} +(13.6167 - 1.76494i) q^{70} +(-7.50774 - 4.33460i) q^{71} +(2.51132 + 9.32211i) q^{72} +0.250759 q^{73} +(9.44167 - 25.9408i) q^{74} +(6.29617 + 5.94628i) q^{75} +(-8.36088 - 22.9713i) q^{76} +(-9.54688 + 8.10666i) q^{77} +(11.9298 - 4.95090i) q^{78} +(10.3962 + 3.78391i) q^{79} +(-1.24181 + 0.937446i) q^{80} +(7.80632 + 4.47899i) q^{81} +(5.56552 + 9.63976i) q^{82} +(7.10287 + 8.46487i) q^{83} +(10.5593 + 11.3733i) q^{84} +(5.47092 + 3.54617i) q^{85} +(-0.652404 + 0.777505i) q^{86} +(9.58144 - 6.11313i) q^{87} +(5.21034 - 14.3153i) q^{88} +(-4.22538 + 7.31858i) q^{89} +(-2.13277 + 15.4223i) q^{90} +(5.42605 - 6.54407i) q^{91} +(3.93490 + 1.43219i) q^{92} +(0.00665162 + 0.00724916i) q^{93} +(2.72435 + 7.48510i) q^{94} +(0.830883 - 16.1193i) q^{95} +(7.96601 + 2.50577i) q^{96} +(-4.55306 - 1.65718i) q^{97} +(15.3307 + 5.37713i) q^{98} +(-6.01908 - 12.8627i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 6 q^{4} - 9 q^{5} + 18 q^{6} + 6 q^{9}+O(q^{10}) $ 840 * q - 6 * q^4 - 9 * q^5 + 18 * q^6 + 6 * q^9	$ 840 q - 6 q^{4} - 9 q^{5} + 18 q^{6} + 6 q^{9} - 9 q^{10} + 6 q^{11} - 6 q^{14} + 18 q^{16} - 18 q^{19} + 18 q^{20} - 30 q^{21} + 36 q^{24} - 3 q^{25} - 42 q^{29} + 33 q^{30} - 18 q^{31} - 36 q^{34} - 9 q^{35} - 42 q^{36} - 90 q^{39} - 9 q^{40} - 9 q^{45} - 12 q^{46} - 48 q^{49} - 48 q^{50} - 42 q^{51} - 144 q^{54} - 42 q^{56} - 18 q^{59} + 57 q^{60} - 72 q^{61} - 348 q^{64} - 54 q^{65} - 18 q^{66} + 21 q^{70} - 36 q^{71} + 42 q^{74} - 9 q^{75} - 72 q^{76} + 12 q^{79} + 72 q^{80} - 162 q^{81} + 78 q^{84} + 3 q^{85} + 168 q^{86} - 18 q^{89} - 81 q^{90} - 6 q^{91} - 18 q^{94} - 93 q^{95} - 18 q^{96} - 60 q^{99}+O(q^{100}) $ 840 * q - 6 * q^4 - 9 * q^5 + 18 * q^6 + 6 * q^9 - 9 * q^10 + 6 * q^11 - 6 * q^14 + 18 * q^16 - 18 * q^19 + 18 * q^20 - 30 * q^21 + 36 * q^24 - 3 * q^25 - 42 * q^29 + 33 * q^30 - 18 * q^31 - 36 * q^34 - 9 * q^35 - 42 * q^36 - 90 * q^39 - 9 * q^40 - 9 * q^45 - 12 * q^46 - 48 * q^49 - 48 * q^50 - 42 * q^51 - 144 * q^54 - 42 * q^56 - 18 * q^59 + 57 * q^60 - 72 * q^61 - 348 * q^64 - 54 * q^65 - 18 * q^66 + 21 * q^70 - 36 * q^71 + 42 * q^74 - 9 * q^75 - 72 * q^76 + 12 * q^79 + 72 * q^80 - 162 * q^81 + 78 * q^84 + 3 * q^85 + 168 * q^86 - 18 * q^89 - 81 * q^90 - 6 * q^91 - 18 * q^94 - 93 * q^95 - 18 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	−2.18094	−	0.793796i	−1.54215	−	0.561298i	−0.575594	−	0.817736i	$-0.695229\pi$
$2$	−2.18094	−	0.793796i	−1.54215	−	0.561298i	−0.966561	+	0.256437i	$0.917451\pi$
$3$	0.224921	−	1.71738i	0.129858	−	0.991533i
$3$	0.224921	−	1.71738i	0.129858	−	0.991533i
$4$	2.59428	+	2.17686i	1.29714	+	1.08843i
$5$	1.01687	+	1.99148i	0.454756	+	0.890616i
$5$	1.01687	+	1.99148i	0.454756	+	0.890616i
$6$	−1.85379	+	3.56696i	−0.756807	+	1.45621i
$7$	0.0155159	+	2.64571i	0.00586444	+	0.999983i
$7$	0.0155159	+	2.64571i	0.00586444	+	0.999983i
$8$	−1.60908	−	2.78700i	−0.568894	−	0.985353i
$9$	−2.89882	−	0.772553i	−0.966274	−	0.257518i
$10$	−0.636893	−	5.15047i	−0.201403	−	1.62872i
$11$	3.04282	+	3.62629i	0.917444	+	1.09337i	0.995342	+	0.0964058i	$0.0307346\pi$
$11$	3.04282	+	3.62629i	0.917444	+	1.09337i	−0.0778982	+	0.996961i	$0.524821\pi$
$12$	4.32202	−	3.96576i	1.24766	−	1.14482i
$13$	−2.46136	−	2.06532i	−0.682658	−	0.572818i	0.234124	−	0.972207i	$-0.424778\pi$
$13$	−2.46136	−	2.06532i	−0.682658	−	0.572818i	−0.916782	+	0.399389i	$0.869222\pi$
$14$	2.06631	−	5.78243i	0.552245	−	1.54542i
$15$	3.64885	−	1.29842i	0.942129	−	0.335252i
$16$	0.120830	+	0.685259i	0.0302074	+	0.171315i
$17$	2.52506	−	1.45785i	0.612418	−	0.353580i	−0.161493	−	0.986874i	$-0.551631\pi$
$17$	2.52506	−	1.45785i	0.612418	−	0.353580i	0.773911	+	0.633294i	$0.218298\pi$
$18$	5.70889	+	3.98596i	1.34560	+	0.939500i
$19$	−6.25127	−	3.60917i	−1.43414	−	0.828001i	−0.436706	−	0.899604i	$-0.643855\pi$
$19$	−6.25127	−	3.60917i	−1.43414	−	0.828001i	−0.997433	+	0.0716037i	$0.977188\pi$
$20$	−1.69713	+	7.38003i	−0.379491	+	1.65022i
$21$	4.54718	+	0.568429i	0.992277	+	0.124041i
$22$	−3.75766	−	10.3241i	−0.801135	−	2.20110i
$23$	1.16190	−	0.422899i	0.242274	−	0.0881804i	−0.218029	−	0.975942i	$-0.569963\pi$
$23$	1.16190	−	0.422899i	0.242274	−	0.0881804i	0.460303	+	0.887762i	$0.347741\pi$
$24$	−5.14827	+	2.13655i	−1.05089	+	0.436121i
$25$	−2.93197	+	4.05013i	−0.586393	+	0.810026i
$26$	3.72862	+	6.45816i	0.731242	+	1.26655i
$27$	−1.97878	+	4.80463i	−0.380816	+	0.924651i
$28$	−5.71908	+	6.89748i	−1.08080	+	1.30350i
$29$	4.21789	+	5.02668i	0.783242	+	0.933431i	0.999075	−	0.0429989i	$-0.0136912\pi$
$29$	4.21789	+	5.02668i	0.783242	+	0.933431i	−0.215833	+	0.976430i	$0.569247\pi$
$30$	−8.98859	−	0.0646607i	−1.64108	−	0.0118054i
$31$	−0.00365117	+	0.00435129i	−0.000655769	+	0.000781515i	−0.766372	−	0.642397i	$-0.777940\pi$
$31$	−0.00365117	+	0.00435129i	−0.000655769	+	0.000781515i	0.765716	+	0.643178i	$0.222385\pi$
$32$	−0.837218	+	4.74810i	−0.148001	+	0.839353i
$33$	6.91213	−	4.41006i	1.20325	−	0.767693i
$34$	−6.66423	+	1.17508i	−1.14291	+	0.201525i
$35$	−5.25309	+	2.72123i	−0.887934	+	0.459971i
$36$	−5.83862	−	8.31455i	−0.973103	−	1.38576i
$37$			11.8943i			1.95542i	0.209967	+	0.977708i	$0.432664\pi$
$37$			11.8943i			1.95542i	−0.209967	+	0.977708i	$0.567336\pi$
$38$	10.7687	+	12.8336i	1.74691	+	2.08188i
$39$	−4.10057	+	3.76256i	−0.656617	+	0.602492i
$40$	3.91404	−	6.03844i	0.618863	−	0.954762i
$41$	−3.67394	−	3.08281i	−0.573774	−	0.481453i	0.309122	−	0.951022i	$-0.399965\pi$
$41$	−3.67394	−	3.08281i	−0.573774	−	0.481453i	−0.882896	+	0.469569i	$0.844409\pi$
$42$	−9.46590	−	4.84924i	−1.46062	−	0.748255i
$43$	0.149570	−	0.410940i	0.0228092	−	0.0626677i	−0.927765	−	0.373164i	$-0.878273\pi$
$43$	0.149570	−	0.410940i	0.0228092	−	0.0626677i	0.950575	+	0.310496i	$0.100495\pi$
$44$			16.0314i			2.41682i
$45$	−1.40919	−	6.55852i	−0.210070	−	0.977686i
$46$	−2.86973			−0.423119
$47$	−2.20608	−	2.62911i	−0.321791	−	0.383495i	0.580763	−	0.814073i	$-0.302754\pi$
$47$	−2.20608	−	2.62911i	−0.321791	−	0.383495i	−0.902554	+	0.430578i	$0.858310\pi$
$48$	1.20403	−	0.0533816i	0.173787	−	0.00770497i
$49$	−6.99952	+	0.0821008i	−0.999931	+	0.0117287i
$50$	9.60941	−	6.50569i	1.35898	−	0.920044i
$51$	−1.93574	−	4.66441i	−0.271058	−	0.653147i
$52$	−1.88953	−	10.7161i	−0.262031	−	1.48605i
$53$	−2.37616	+	4.11562i	−0.326390	+	0.565325i	−0.981793	−	0.189955i	$-0.939166\pi$
$53$	−2.37616	+	4.11562i	−0.326390	+	0.565325i	0.655402	+	0.755280i	$0.272499\pi$
$54$	8.12948	−	8.90784i	1.10628	−	1.21220i
$55$	−4.12754	+	9.74715i	−0.556557	+	1.31431i
$56$	7.34862	−	4.30038i	0.982000	−	0.574663i
$57$	−7.60438	+	9.92405i	−1.00722	+	1.31447i
$58$	−5.20878	−	14.3110i	−0.683947	−	1.87913i
$59$	−2.00484	+	11.3700i	−0.261008	+	1.48025i	0.519160	+	0.854677i	$0.326245\pi$
$59$	−2.00484	+	11.3700i	−0.261008	+	1.48025i	−0.780168	+	0.625571i	$0.784866\pi$
$60$	12.2926	+	4.57456i	1.58697	+	0.590573i
$61$	−4.16948	−	4.96899i	−0.533847	−	0.636214i	0.429949	−	0.902853i	$-0.358531\pi$
$61$	−4.16948	−	4.96899i	−0.533847	−	0.636214i	−0.963797	+	0.266639i	$0.914087\pi$
$62$	0.0114170	−	0.00659161i	0.00144996	−	0.000837135i
$63$	1.99897	−	7.68141i	0.251847	−	0.967767i
$64$	6.29077	−	10.8959i	0.786346	−	1.36199i
$65$	1.61018	−	7.00190i	0.199718	−	0.868479i
$66$	−18.5756	+	4.13124i	−2.28650	+	0.508520i
$67$	4.06185	+	11.1598i	0.496234	+	1.36339i	0.894888	+	0.446290i	$0.147255\pi$
$67$	4.06185	+	11.1598i	0.496234	+	1.36339i	−0.398655	+	0.917101i	$0.630523\pi$
$68$	9.72425	+	1.71465i	1.17924	+	0.207932i
$69$	−0.464942	−	2.09056i	−0.0559725	−	0.251673i
$70$	13.6167	−	1.76494i	1.62751	−	0.210951i
$71$	−7.50774	−	4.33460i	−0.891005	−	0.514422i	−0.0167341	−	0.999860i	$-0.505327\pi$
$71$	−7.50774	−	4.33460i	−0.891005	−	0.514422i	−0.874271	+	0.485438i	$0.838660\pi$
$72$	2.51132	+	9.32211i	0.295961	+	1.09862i
$73$	0.250759			0.0293491			0.0146746	−	0.999892i	$-0.495329\pi$
$73$	0.250759			0.0293491			0.0146746	+	0.999892i	$0.495329\pi$
$74$	9.44167	−	25.9408i	1.09757	−	3.01556i
$75$	6.29617	+	5.94628i	0.727019	+	0.686617i
$76$	−8.36088	−	22.9713i	−0.959059	−	2.63499i
$77$	−9.54688	+	8.10666i	−1.08797	+	0.923840i
$78$	11.9298	−	4.95090i	1.35078	−	0.560578i
$79$	10.3962	+	3.78391i	1.16966	+	0.425723i	0.852541	−	0.522661i	$-0.175061\pi$
$79$	10.3962	+	3.78391i	1.16966	+	0.425723i	0.317124	+	0.948384i	$0.397283\pi$
$80$	−1.24181	+	0.937446i	−0.138839	+	0.104810i
$81$	7.80632	+	4.47899i	0.867369	+	0.497665i
$82$	5.56552	+	9.63976i	0.614609	+	1.06453i
$83$	7.10287	+	8.46487i	0.779641	+	0.929140i	0.998917	−	0.0465225i	$-0.0148139\pi$
$83$	7.10287	+	8.46487i	0.779641	+	0.929140i	−0.219276	+	0.975663i	$0.570369\pi$
$84$	10.5593	+	11.3733i	1.15211	+	1.24092i
$85$	5.47092	+	3.54617i	0.593404	+	0.384636i
$86$	−0.652404	+	0.777505i	−0.0703506	+	0.0838405i
$87$	9.58144	−	6.11313i	1.02724	−	0.655396i
$88$	5.21034	−	14.3153i	0.555425	−	1.52602i
$89$	−4.22538	+	7.31858i	−0.447890	+	0.775768i	−0.998248	−	0.0591607i	$-0.981158\pi$
$89$	−4.22538	+	7.31858i	−0.447890	+	0.775768i	0.550359	+	0.834928i	$0.314491\pi$
$90$	−2.13277	+	15.4223i	−0.224814	+	1.62566i
$91$	5.42605	−	6.54407i	0.568805	−	0.686005i
$92$	3.93490	+	1.43219i	0.410241	+	0.149316i
$93$	0.00665162	+	0.00724916i	0.000689740	+	0.000751703i
$94$	2.72435	+	7.48510i	0.280996	+	0.772029i
$95$	0.830883	−	16.1193i	0.0852468	−	1.65381i
$96$	7.96601	+	2.50577i	0.813027	+	0.255745i
$97$	−4.55306	−	1.65718i	−0.462293	−	0.168261i	0.100365	−	0.994951i	$-0.467999\pi$
$97$	−4.55306	−	1.65718i	−0.462293	−	0.168261i	−0.562658	+	0.826690i	$0.690221\pi$
$98$	15.3307	+	5.37713i	1.54863	+	0.543172i
$99$	−6.01908	−	12.8627i	−0.604940	−	1.29275i
$100$	−16.4229	+	4.12470i	−1.64229	+	0.412470i
$101$	10.3929	+	3.78269i	1.03413	+	0.376392i	0.802652	−	0.596448i	$-0.203422\pi$
$101$	10.3929	+	3.78269i	1.03413	+	0.376392i	0.231477	+	0.972840i	$0.425644\pi$
$102$	0.519143	+	11.7094i	0.0514028	+	1.15940i
$103$	−1.32747	−	1.11388i	−0.130799	−	0.109754i	0.575041	−	0.818124i	$-0.304986\pi$
$103$	−1.32747	−	1.11388i	−0.130799	−	0.109754i	−0.705840	+	0.708371i	$0.749430\pi$
$104$	−1.79555	+	10.1831i	−0.176068	+	0.998532i
$105$	3.49186	+	9.63363i	0.340771	+	0.940146i
$106$	8.44921	−	7.08973i	0.820660	−	0.688616i
$107$	−0.100836	−	0.174653i	−0.00974817	−	0.0168843i	0.861110	−	0.508418i	$-0.169770\pi$
$107$	−0.100836	−	0.174653i	−0.00974817	−	0.0168843i	−0.870858	+	0.491534i	$0.836436\pi$
$108$	−15.5925	+	8.15703i	−1.50039	+	0.784911i
$109$	−0.705525	+	1.22201i	−0.0675771	+	0.117047i	−0.897834	−	0.440334i	$-0.854860\pi$
$109$	−0.705525	+	1.22201i	−0.0675771	+	0.117047i	0.830257	+	0.557380i	$0.188194\pi$
$110$	16.7391	−	17.9815i	1.59601	−	1.71447i
$111$	20.4272	+	2.67529i	1.93886	+	0.253927i
$112$	−1.81112	+	0.330312i	−0.171135	+	0.0312116i
$113$	−6.50995	+	2.36943i	−0.612405	+	0.222897i	−0.629555	−	0.776956i	$-0.716763\pi$
$113$	−6.50995	+	2.36943i	−0.612405	+	0.222897i	0.0171504	+	0.999853i	$0.494541\pi$
$114$	24.4623	−	15.6074i	2.29111	−	1.46177i
$115$	2.02369	+	1.88388i	0.188710	+	0.175672i
$116$			22.2224i			2.06330i
$117$	5.53946	+	7.88854i	0.512124	+	0.729295i
$118$	13.3979	−	23.2058i	1.23337	−	2.13627i
$119$	3.89621	+	6.65795i	0.357165	+	0.610334i
$120$	−9.48998	−	8.08008i	−0.866313	−	0.737607i
$121$	−1.98110	+	11.2354i	−0.180100	+	1.02140i
$122$	5.14900	+	14.1468i	0.466169	+	1.28079i
$123$	−6.12071	+	5.61619i	−0.551886	+	0.506395i
$124$	−0.0189443	+	0.00334039i	−0.00170125	+	0.000299976i
$125$	−11.0472	−	1.72051i	−0.988088	−	0.153887i
$126$	−10.4571	+	15.1659i	−0.931593	+	1.35109i
$127$	−16.9236	+	9.77086i	−1.50173	+	0.867024i	−0.501731	+	0.865024i	$0.667303\pi$
$127$	−16.9236	+	9.77086i	−1.50173	+	0.867024i	−0.999998	+	0.00199967i	$0.999363\pi$
$128$	−14.9822	+	12.5715i	−1.32425	+	1.11118i
$129$	−0.672100	−	0.349298i	−0.0591751	−	0.0307540i
$130$	−9.06977	+	13.9925i	−0.795472	+	1.22723i
$131$	−1.47235	+	0.535891i	−0.128640	+	0.0468210i	−0.405538	−	0.914078i	$-0.632916\pi$
$131$	−1.47235	+	0.535891i	−0.128640	+	0.0468210i	0.276898	+	0.960899i	$0.410694\pi$
$132$	27.5321	+	3.60581i	2.39636	+	0.313845i
$133$	9.45181	−	16.5950i	0.819576	−	1.43897i
$134$		−	27.5632i		−	2.38110i
$135$	−11.5805	+	0.944969i	−0.996687	+	0.0813300i
$136$	−8.12603	−	4.69157i	−0.696802	−	0.402299i
$137$	−0.552949	−	3.13593i	−0.0472416	−	0.267920i	0.952033	−	0.305994i	$-0.0989889\pi$
$137$	−0.552949	−	3.13593i	−0.0472416	−	0.267920i	−0.999275	+	0.0380739i	$0.987878\pi$
$138$	−0.645465	+	4.92844i	−0.0549456	+	0.419536i
$139$	−5.94607	−	1.04845i	−0.504339	−	0.0889285i	−0.0843104	−	0.996440i	$-0.526869\pi$
$139$	−5.94607	−	1.04845i	−0.504339	−	0.0889285i	−0.420028	+	0.907511i	$0.637980\pi$
$140$	−19.5517	−	4.37561i	−1.65242	−	0.369806i
$141$	−5.01139	+	3.19735i	−0.422035	+	0.269266i
$142$	12.9331	+	15.4131i	1.08532	+	1.29344i
$143$		−	15.2100i		−	1.27192i
$144$	0.179135	−	2.07979i	0.0149280	−	0.173316i
$145$	−5.72150	+	13.5113i	−0.475145	+	1.12205i
$146$	−0.546890	−	0.199052i	−0.0452609	−	0.0164736i
$147$	−1.43334	+	12.0393i	−0.118220	+	0.992987i
$148$	−25.8923	+	30.8573i	−2.12833	+	2.53645i
$149$	18.2752	+	3.22241i	1.49716	+	0.263990i	0.861413	−	0.507905i	$-0.169580\pi$
$149$	18.2752	+	3.22241i	1.49716	+	0.263990i	0.635750	+	0.771895i	$0.280691\pi$
$150$	−9.01142	−	17.9663i	−0.735779	−	1.46694i
$151$	7.15200	−	6.00124i	0.582021	−	0.488374i	−0.303589	−	0.952803i	$-0.598185\pi$
$151$	7.15200	−	6.00124i	0.582021	−	0.488374i	0.885610	+	0.464429i	$0.153741\pi$
$152$			23.2297i			1.88418i
$153$	−8.44597	+	2.27529i	−0.682816	+	0.183946i
$154$	27.2562	−	10.1018i	2.19636	−	0.814030i
$155$	−0.0123782	−	0.00284654i	−0.000994245	−	0.000228639i
$156$	−18.8286	+	0.834780i	−1.50749	+	0.0668359i
$157$	3.36893	−	19.1062i	0.268870	−	1.52484i	−0.488914	−	0.872332i	$-0.662607\pi$
$157$	3.36893	−	19.1062i	0.268870	−	1.52484i	0.757784	−	0.652505i	$-0.226282\pi$
$158$	−19.6698	−	16.5049i	−1.56485	−	1.31306i
$159$	6.53366	+	5.00647i	0.518153	+	0.397039i
$160$	−10.3071	+	3.16088i	−0.814846	+	0.249889i
$161$	1.13689	+	3.06750i	0.0895997	+	0.241752i
$162$	−13.4697	−	15.9650i	−1.05828	−	1.25433i
$163$	13.8267	−	7.98283i	1.08299	−	0.625264i	0.151287	−	0.988490i	$-0.451658\pi$
$163$	13.8267	−	7.98283i	1.08299	−	0.625264i	0.931701	+	0.363226i	$0.118325\pi$
$164$	−2.82041	−	15.9953i	−0.220237	−	1.24903i
$165$	15.8112	+	9.28091i	1.23090	+	0.722518i
$166$	−8.77153	−	24.0996i	−0.680803	−	1.87049i
$167$	3.35249	+	9.21090i	0.259424	+	0.712761i	0.999203	+	0.0399116i	$0.0127076\pi$
$167$	3.35249	+	9.21090i	0.259424	+	0.712761i	−0.739779	+	0.672850i	$0.765070\pi$
$168$	−5.73255	−	13.5877i	−0.442276	−	1.04831i
$169$	−0.464709	−	2.63549i	−0.0357468	−	0.202730i
$170$	−9.11678	−	12.0768i	−0.699225	−	0.926246i
$171$	15.3330	+	15.2918i	1.17255	+	1.16939i
$172$	1.28258	−	0.740501i	0.0977962	−	0.0564626i
$173$	3.35261	−	0.591155i	0.254894	−	0.0449447i	−0.0447409	−	0.998999i	$-0.514246\pi$
$173$	3.35261	−	0.591155i	0.254894	−	0.0449447i	0.299635	+	0.954054i	$0.403135\pi$
$174$	−25.7491	+	5.72663i	−1.95203	+	0.434135i
$175$	−10.7609	−	7.69428i	−0.813451	−	0.581633i
$176$	−2.11728	+	2.52328i	−0.159596	+	0.190199i
$177$	19.0757	+	6.00043i	1.43382	+	0.451020i
$178$	15.0247	−	12.6073i	1.12615	−	0.944954i
$179$	−8.52569	+	4.92231i	−0.637240	+	0.367911i	−0.783551	−	0.621328i	$-0.786594\pi$
$179$	−8.52569	+	4.92231i	−0.637240	+	0.367911i	0.146310	+	0.989239i	$0.453260\pi$
$180$	10.6211	−	20.0823i	0.791654	−	1.49684i
$181$	−10.1144	+	5.83954i	−0.751796	+	0.434049i	−0.826342	−	0.563168i	$-0.809582\pi$
$181$	−10.1144	+	5.83954i	−0.751796	+	0.434049i	0.0745467	+	0.997218i	$0.476249\pi$
$182$	−17.0285	+	9.96503i	−1.26224	+	0.738657i
$183$	−9.47148	+	6.04297i	−0.700152	+	0.446709i
$184$	−3.04821	−	2.55775i	−0.224717	−	0.188560i
$185$	−23.6873	+	12.0949i	−1.74153	+	0.889238i
$186$	−0.00875240	−	0.0210900i	−0.000641757	−	0.00154639i
$187$	12.9699	+	4.72065i	0.948451	+	0.345208i
$188$		−	11.6230i		−	0.847694i
$189$	−12.7423	−	5.16072i	−0.926868	−	0.375387i
$190$	−14.6075	+	34.4956i	−1.05974	+	2.50258i
$191$	0.394924	−	1.08504i	0.0285757	−	0.0785111i	−0.924584	−	0.380977i	$-0.875588\pi$
$191$	0.394924	−	1.08504i	0.0285757	−	0.0785111i	0.953160	+	0.302466i	$0.0978099\pi$
$192$	−17.2976	−	13.2544i	−1.24835	−	0.956554i
$193$	10.1039	−	12.0414i	0.727296	−	0.866757i	−0.268022	−	0.963413i	$-0.586370\pi$
$193$	10.1039	−	12.0414i	0.727296	−	0.866757i	0.995318	+	0.0966554i	$0.0308145\pi$
$194$	8.61448	+	7.22840i	0.618483	+	0.518969i
$195$	−11.6628	−	4.34017i	−0.835190	−	0.310806i
$196$	−18.3374	−	15.0240i	−1.30982	−	1.07314i
$197$	−11.3786	−	19.7083i	−0.810690	−	1.40416i	−0.912382	−	0.409340i	$-0.865759\pi$
$197$	−11.3786	−	19.7083i	−0.810690	−	1.40416i	0.101692	−	0.994816i	$-0.467574\pi$
$198$	2.91688	+	32.8306i	0.207293	+	2.33317i
$199$	−7.70965	+	4.45117i	−0.546523	+	0.315535i	−0.747718	−	0.664016i	$-0.768851\pi$
$199$	−7.70965	+	4.45117i	−0.546523	+	0.315535i	0.201196	+	0.979551i	$0.435517\pi$
$200$	16.0055	+	1.65443i	1.13176	+	0.116986i
$201$	20.0793	−	4.46567i	1.41629	−	0.314984i
$202$	−19.6635	−	16.4996i	−1.38352	−	1.16091i
$203$	−13.2337	+	11.2373i	−0.928822	+	0.788702i
$204$	5.13190	−	16.3146i	0.359305	−	1.14225i
$205$	2.40343	−	10.4514i	0.167863	−	0.729956i
$206$	2.01093	+	3.48303i	0.140108	+	0.242675i
$207$	−3.69486	+	0.328274i	−0.256811	+	0.0228166i
$208$	1.11788	−	1.93622i	0.0775108	−	0.134253i
$209$	−5.93357	−	33.6509i	−0.410434	−	2.32768i
$210$	0.0316077	−	23.7822i	0.00218114	−	1.64113i
$211$	−12.9032	+	4.69640i	−0.888296	+	0.323313i	−0.745553	−	0.666446i	$-0.767814\pi$
$211$	−12.9032	+	4.69640i	−0.888296	+	0.323313i	−0.142743	+	0.989760i	$0.545592\pi$
$212$	−15.1236	+	5.50453i	−1.03869	+	0.378052i
$213$	−9.13282	+	11.9187i	−0.625771	+	0.816659i
$214$	0.0812779	+	0.460950i	0.00555604	+	0.0315099i
$215$	0.970470	−	0.120006i	0.0661855	−	0.00818431i
$216$	16.5745	−	2.21615i	1.12775	−	0.150790i
$217$	−0.0115689	−	0.00959240i	−0.000785347	−	0.000651175i
$218$	2.50873	−	2.10507i	0.169913	−	0.142574i
$219$	0.0564011	−	0.430650i	0.00381123	−	0.0291006i
$220$	−31.9262	+	16.3018i	−2.15246	+	1.09907i
$221$	−9.22601	−	1.62679i	−0.620609	−	0.109430i
$222$	−42.4267	−	22.0496i	−2.84749	−	1.47987i
$223$	1.35036	+	7.65828i	0.0904269	+	0.512836i	0.996053	+	0.0887594i	$0.0282902\pi$
$223$	1.35036	+	7.65828i	0.0904269	+	0.512836i	−0.905626	+	0.424077i	$0.860599\pi$
$224$	−12.5751	−	2.14136i	−0.840207	−	0.143076i
$225$	11.6282	−	9.47551i	0.775213	−	0.631700i
$226$	16.0786			1.06953
$227$	17.8346	+	21.2545i	1.18373	+	1.41071i	0.890692	+	0.454607i	$0.150220\pi$
$227$	17.8346	+	21.2545i	1.18373	+	1.41071i	0.293034	+	0.956102i	$0.405335\pi$
$228$	−41.3312	+	9.19211i	−2.73722	+	0.608762i
$229$	14.1132	+	2.48854i	0.932628	+	0.164448i	0.619262	−	0.785185i	$-0.287432\pi$
$229$	14.1132	+	2.48854i	0.932628	+	0.164448i	0.313367	+	0.949632i	$0.398543\pi$
$230$	−2.91813	−	5.71501i	−0.192416	−	0.376837i
$231$	11.7750	+	18.2190i	0.774736	+	1.19872i
$232$	7.22247	−	19.8436i	0.474178	−	1.30279i
$233$	7.53433			0.493590			0.246795	−	0.969068i	$-0.420623\pi$
$233$	7.53433			0.493590			0.246795	+	0.969068i	$0.420623\pi$
$234$	−5.81933	−	21.6016i	−0.380421	−	1.41214i
$235$	2.99252	−	7.06682i	0.195211	−	0.460989i
$236$	−29.9520	+	25.1327i	−1.94971	+	1.63600i
$237$	8.83676	−	17.0032i	0.574009	−	1.10448i
$238$	−3.21233	−	17.6134i	−0.208224	−	1.14170i
$239$	15.3398	+	2.70483i	0.992252	+	0.174961i	0.646129	−	0.763228i	$-0.276387\pi$
$239$	15.3398	+	2.70483i	0.992252	+	0.174961i	0.346123	+	0.938189i	$0.387498\pi$
$240$	1.33065	+	2.34352i	0.0858928	+	0.151273i
$241$	−0.788256	+	0.138991i	−0.0507760	+	0.00895318i	−0.198978	−	0.980004i	$-0.563762\pi$
$241$	−0.788256	+	0.138991i	−0.0507760	+	0.00895318i	0.148202	+	0.988957i	$0.452651\pi$
$242$	13.2393	−	22.9311i	0.851051	−	1.47406i
$243$	9.44795	−	12.3990i	0.606086	−	0.795399i
$244$		−	21.9673i		−	1.40632i
$245$	−7.28107	−	13.8559i	−0.465171	−	0.885221i
$246$	17.8070	−	7.38995i	1.13533	−	0.471166i
$247$	7.93250	+	21.7944i	0.504733	+	1.38674i
$248$	0.0180021	+	0.00317425i	0.00114313	+	0.000201565i
$249$	16.1350	−	10.2944i	1.02252	−	0.652383i
$250$	22.7274	+	12.5215i	1.43741	+	0.791930i
$251$	−6.01802	−	10.4235i	−0.379854	−	0.657927i	0.611187	−	0.791487i	$-0.290692\pi$
$251$	−6.01802	−	10.4235i	−0.379854	−	0.657927i	−0.991041	+	0.133560i	$0.957359\pi$
$252$	21.9073	−	15.5763i	1.38003	−	0.981213i
$253$	5.06901	+	2.92660i	0.318686	+	0.183994i
$254$	44.6654	−	7.87572i	2.80256	−	0.494166i
$255$	7.32067	−	8.59806i	0.458438	−	0.538431i
$256$	19.0089	−	6.91866i	1.18805	−	0.432416i
$257$	−24.3052	−	4.28567i	−1.51612	−	0.267332i	−0.647212	−	0.762310i	$-0.724065\pi$
$257$	−24.3052	−	4.28567i	−1.51612	−	0.267332i	−0.868906	+	0.494978i	$0.835176\pi$
$258$	1.18854	+	1.29531i	0.0739950	+	0.0806423i
$259$	−31.4689	+	0.184551i	−1.95538	+	0.0114674i
$260$	19.4194	−	14.6598i	1.20434	−	0.909160i
$261$	−8.34352	−	17.8300i	−0.516451	−	1.10365i
$262$	3.63648			0.224663
$263$	25.5476	+	9.29856i	1.57533	+	0.573374i	0.974182	−	0.225762i	$-0.0724873\pi$
$263$	25.5476	+	9.29856i	1.57533	+	0.573374i	0.601150	+	0.799136i	$0.294710\pi$
$264$	−23.4130	−	12.1680i	−1.44097	−	0.748888i
$265$	−10.6124	−	0.547025i	−0.651915	−	0.0336035i
$266$	−33.7868	+	28.6899i	−2.07160	+	1.75909i
$267$	11.6184	+	8.90271i	0.711037	+	0.544837i
$268$	−13.7558	+	37.7938i	−0.840271	+	2.30863i
$269$	13.5428	−	23.4568i	0.825718	−	1.43019i	−0.0756510	−	0.997134i	$-0.524103\pi$
$269$	13.5428	−	23.4568i	0.825718	−	1.43019i	0.901369	−	0.433052i	$-0.142563\pi$
$270$	26.0064	+	7.13160i	1.58270	+	0.434015i
$271$	−12.9669	+	7.48642i	−0.787681	+	0.454768i	−0.839145	−	0.543907i	$-0.816944\pi$
$271$	−12.9669	+	7.48642i	−0.787681	+	0.454768i	0.0514646	+	0.998675i	$0.483611\pi$
$272$	1.30410	+	1.55417i	0.0790729	+	0.0942355i
$273$	−10.0183	−	10.7905i	−0.606333	−	0.653072i
$274$	−1.28334	+	7.27819i	−0.0775295	+	0.439691i
$275$	−23.6084	+	1.69165i	−1.42364	+	0.102010i
$276$	3.34466	−	6.43560i	0.201325	−	0.387378i
$277$	5.20324	−	14.2958i	0.312633	−	0.858951i	−0.679491	−	0.733684i	$-0.737799\pi$
$277$	5.20324	−	14.2958i	0.312633	−	0.858951i	0.992123	−	0.125267i	$-0.0399786\pi$
$278$	12.1357	+	7.00657i	0.727853	+	0.420226i
$279$	0.0139457	−	0.00979289i	0.000834906	−	0.000586285i
$280$	16.0367	+	10.2617i	0.958375	+	0.613254i
$281$	−1.53763	+	4.22459i	−0.0917270	+	0.252018i	−0.977069	−	0.212922i	$-0.931702\pi$
$281$	−1.53763	+	4.22459i	−0.0917270	+	0.252018i	0.885342	+	0.464940i	$0.153924\pi$
$282$	13.4676	−	2.99520i	0.801982	−	0.178362i
$283$	−1.66504	+	0.606026i	−0.0989765	+	0.0360245i	−0.391034	−	0.920376i	$-0.627882\pi$
$283$	−1.66504	+	0.606026i	−0.0989765	+	0.0360245i	0.292057	+	0.956401i	$0.405660\pi$
$284$	−10.0414	−	27.5885i	−0.595847	−	1.63708i
$285$	−27.4962	−	5.05252i	−1.62873	−	0.299286i
$286$	−12.0736	+	33.1720i	−0.713929	+	1.96150i
$287$	8.09919	−	9.76801i	0.478080	−	0.576587i
$288$	6.09510	−	13.1171i	0.359157	−	0.772932i
$289$	−4.24937	+	7.36013i	−0.249963	+	0.432949i
$290$	23.2034	−	24.9256i	1.36255	−	1.46368i
$291$	−3.87010	+	7.44663i	−0.226869	+	0.436529i
$292$	0.650540	+	0.545868i	0.0380700	+	0.0319445i
$293$	16.8867	+	2.97758i	0.986531	+	0.173952i	0.643562	−	0.765394i	$-0.277456\pi$
$293$	16.8867	+	2.97758i	0.986531	+	0.173952i	0.342970	+	0.939346i	$0.388567\pi$
$294$	12.6828	−	25.1192i	0.739676	−	1.46498i
$295$	−24.6817	+	7.56917i	−1.43703	+	0.440694i
$296$	33.1495	−	19.1389i	1.92678	−	1.11242i
$297$	−23.4440	+	7.44398i	−1.36036	+	0.431944i
$298$	−37.2991	−	21.5347i	−2.16068	−	1.24747i
$299$	−3.73329	−	1.35880i	−0.215901	−	0.0785817i
$300$	3.38983	+	29.1322i	0.195712	+	1.68195i
$301$	1.08955	+	0.389342i	0.0628004	+	0.0224413i
$302$	−20.3618	+	7.41109i	−1.17169	+	0.426460i
$303$	8.83392	−	16.9977i	0.507495	−	0.976495i
$304$	1.71788	−	4.71983i	0.0985271	−	0.270701i
$305$	5.65584	−	13.3562i	0.323852	−	0.764775i
$306$	20.2262	+	1.74212i	1.15626	+	0.0995901i
$307$	−2.39703	+	4.15178i	−0.136806	+	0.236955i	−0.926286	−	0.376822i	$-0.877017\pi$
$307$	−2.39703	+	4.15178i	−0.136806	+	0.236955i	0.789480	+	0.613776i	$0.210350\pi$
$308$	−42.4144	+	0.248741i	−2.41678	+	0.0141733i
$309$	−2.21153	+	2.02924i	−0.125810	+	0.115439i
$310$	0.0247366	+	0.0160339i	0.00140494	+	0.000910665i
$311$	−25.7267	+	9.36375i	−1.45883	+	0.530969i	−0.945042	−	0.326950i	$-0.893979\pi$
$311$	−25.7267	+	9.36375i	−1.45883	+	0.530969i	−0.513785	+	0.857919i	$0.671757\pi$
$312$	17.0844	+	5.37404i	0.967213	+	0.304245i
$313$	2.24961	+	12.7582i	0.127155	+	0.721134i	0.980004	+	0.198976i	$0.0637616\pi$
$313$	2.24961	+	12.7582i	0.127155	+	0.721134i	−0.852849	+	0.522158i	$0.825127\pi$
$314$	−22.5138	+	38.9950i	−1.27053	+	2.20062i
$315$	17.3300	−	3.83006i	0.976438	−	0.215800i
$316$	18.7336	+	32.4476i	1.05385	+	1.82532i
$317$	−9.75438	+	8.18489i	−0.547860	+	0.459709i	−0.874216	−	0.485538i	$-0.838624\pi$
$317$	−9.75438	+	8.18489i	−0.547860	+	0.459709i	0.326355	+	0.945247i	$0.394179\pi$
$318$	−10.2754	−	16.1052i	−0.576215	−	0.903134i
$319$	−5.39394	+	30.5905i	−0.302003	+	1.71274i
$320$	28.0959	+	1.44823i	1.57061	+	0.0809583i
$321$	−0.322626	+	0.133891i	−0.0180072	+	0.00747306i
$322$	−0.0445264	−	7.59247i	−0.00248136	−	0.423112i
$323$	−21.0465			−1.17106
$324$	10.5017	+	28.6130i	0.583426	+	1.58961i
$325$	15.5815	−	3.91336i	0.864304	−	0.217074i
$326$	−36.4918	+	6.43449i	−2.02110	+	0.356374i
$327$	1.93997	+	1.48651i	0.107280	+	0.0822044i
$328$	−2.68013	+	15.1998i	−0.147985	+	0.839266i
$329$	6.92162	−	5.87744i	0.381601	−	0.324034i
$330$	−27.1162	−	32.7920i	−1.49270	−	1.80514i
$331$	−18.0647	+	15.1581i	−0.992928	+	0.833165i	−0.985989	−	0.166810i	$-0.946653\pi$
$331$	−18.0647	+	15.1581i	−0.992928	+	0.833165i	−0.00693897	+	0.999976i	$0.502209\pi$
$332$			37.4222i			2.05381i
$333$	9.18901	−	34.4795i	0.503554	−	1.88947i
$334$		−	22.7496i		−	1.24480i
$335$	−18.0942	+	19.4371i	−0.988592	+	1.06196i
$336$	0.159914	+	3.18468i	0.00872400	+	0.173739i
$337$	14.7048	−	17.5244i	0.801019	−	0.954617i	−0.198657	−	0.980069i	$-0.563658\pi$
$337$	14.7048	−	17.5244i	0.801019	−	0.954617i	0.999676	+	0.0254520i	$0.00810250\pi$
$338$	−1.07854	+	6.11673i	−0.0586651	+	0.332706i
$339$	2.60499	+	11.7130i	0.141484	+	0.636164i
$340$	6.47358	+	21.1092i	0.351079	+	1.14481i
$341$	−0.0268889			−0.00145611
$342$	−21.3018	−	45.5217i	−1.15187	−	2.46153i
$343$	−0.325818	−	18.5174i	−0.0175925	−	0.999845i
$344$	−1.38596	+	0.244382i	−0.0747258	+	0.0131762i
$345$	3.69051	−	3.05174i	0.198690	−	0.164300i
$346$	−7.78108	−	1.37201i	−0.418313	−	0.0737599i
$347$	14.2949	+	11.9948i	0.767389	+	0.643916i	0.940039	−	0.341067i	$-0.110788\pi$
$347$	14.2949	+	11.9948i	0.767389	+	0.643916i	−0.172650	+	0.984983i	$0.555233\pi$
$348$	38.1644	+	4.99829i	2.04583	+	0.267936i
$349$	13.8348	+	16.4877i	0.740559	+	0.882564i	0.996454	−	0.0841404i	$-0.0268144\pi$
$349$	13.8348	+	16.4877i	0.740559	+	0.882564i	−0.255894	+	0.966705i	$0.582370\pi$
$350$	17.3613	+	25.3227i	0.927998	+	1.35356i
$351$	14.7936	−	7.73909i	0.789624	−	0.413082i
$352$	−19.7655	+	11.4116i	−1.05350	+	0.608241i
$353$	−2.12621	+	0.374909i	−0.113167	+	0.0199544i	−0.229945	−	0.973204i	$-0.573855\pi$
$353$	−2.12621	+	0.374909i	−0.113167	+	0.0199544i	0.116778	+	0.993158i	$0.462743\pi$
$354$	−36.8398	−	28.2288i	−1.95801	−	1.50034i
$355$	0.997887	−	19.3592i	0.0529623	−	1.02748i
$356$	−26.8933	+	9.78838i	−1.42534	+	0.518783i
$357$	12.3106	−	5.19377i	0.651547	−	0.274884i
$358$	22.5013	−	3.96759i	1.18923	−	0.209693i
$359$	−14.5479	−	8.39921i	−0.767807	−	0.443293i	0.0642849	−	0.997932i	$-0.479523\pi$
$359$	−14.5479	−	8.39921i	−0.767807	−	0.443293i	−0.832092	+	0.554638i	$0.812857\pi$
$360$	−16.0111	+	14.4806i	−0.843859	+	0.763193i
$361$	16.5522	+	28.6693i	0.871170	+	1.50891i
$362$	26.6942	−	4.70691i	1.40302	−	0.247390i
$363$	18.8499	+	5.92939i	0.989362	+	0.311212i
$364$	28.3222	−	5.16541i	1.48449	−	0.270741i
$365$	0.254988	+	0.499381i	0.0133467	+	0.0261388i
$366$	25.4536	−	5.66091i	1.33048	−	0.295900i
$367$	5.86250	−	4.91922i	0.306020	−	0.256781i	−0.476825	−	0.878998i	$-0.658212\pi$
$367$	5.86250	−	4.91922i	0.306020	−	0.256781i	0.782845	+	0.622217i	$0.213768\pi$
$368$	0.430188	+	0.745107i	0.0224251	+	0.0388414i
$369$	8.26848	+	11.7748i	0.430440	+	0.612973i
$370$	61.2614	−	7.57542i	3.18483	−	0.393827i
$371$	−10.9256	−	6.22276i	−0.567229	−	0.323069i
$372$	0.00147576	+	0.0332860i	7.65146e−5	+	0.00172580i
$373$	7.30443	−	8.70508i	0.378209	−	0.450732i	−0.543039	−	0.839707i	$-0.682726\pi$
$373$	7.30443	−	8.70508i	0.378209	−	0.450732i	0.921248	+	0.388976i	$0.127171\pi$
$374$	−24.5392	−	20.5909i	−1.26889	−	1.06473i
$375$	−5.43952	+	18.5853i	−0.280895	+	0.959738i
$376$	−3.77757	+	10.3788i	−0.194813	+	0.535245i
$377$		−	21.0838i		−	1.08587i
$378$	23.6937	+	21.3700i	1.21867	+	1.09915i
$379$	22.7732			1.16978			0.584890	−	0.811113i	$-0.301138\pi$
$379$	22.7732			1.16978			0.584890	+	0.811113i	$0.301138\pi$
$380$	37.2450	−	40.0093i	1.91063	−	2.05243i
$381$	12.9738	+	31.2620i	0.664670	+	1.60160i
$382$	−1.72261	+	2.05292i	−0.0881363	+	0.105037i
$383$	9.07332	−	10.8132i	0.463625	−	0.552527i	−0.482682	−	0.875796i	$-0.660337\pi$
$383$	9.07332	−	10.8132i	0.463625	−	0.552527i	0.946307	+	0.323269i	$0.104782\pi$
$384$	18.2204	+	28.5578i	0.929804	+	1.45733i
$385$	−25.8521	−	10.7690i	−1.31755	−	0.548840i
$386$	−31.5944	+	18.2410i	−1.60811	+	0.928444i
$387$	−0.751049	+	1.07569i	−0.0381780	+	0.0546804i
$388$	−8.20448	−	14.2106i	−0.416519	−	0.721433i
$389$	−18.8452	−	22.4589i	−0.955492	−	1.13871i	−0.990248	−	0.139315i	$-0.955510\pi$
$389$	−18.8452	−	22.4589i	−0.955492	−	1.13871i	0.0347563	−	0.999396i	$-0.488934\pi$
$390$	21.9906	+	18.7235i	1.11354	+	0.948102i
$391$	2.31736	−	2.76172i	0.117194	−	0.139666i
$392$	11.4916	+	19.3756i	0.580412	+	0.978613i
$393$	0.589168	+	2.64912i	0.0297196	+	0.133630i
$394$	9.17160	+	52.0147i	0.462059	+	2.62046i
$395$	3.03598	+	24.5515i	0.152757	+	1.23532i
$396$	12.3851	−	46.4722i	0.622375	−	2.33531i
$397$	11.4214	−	19.7825i	0.573225	−	0.992854i	−0.423007	−	0.906126i	$-0.639026\pi$
$397$	11.4214	−	19.7825i	0.573225	−	0.992854i	0.996232	−	0.0867280i	$-0.0276411\pi$
$398$	20.3476	−	3.58783i	1.01993	−	0.179841i
$399$	−26.3741	−	19.9650i	−1.32036	−	0.999499i
$400$	−3.12966	−	1.51978i	−0.156483	−	0.0759891i
$401$	−5.86126	−	16.1037i	−0.292697	−	0.804179i	−0.995670	−	0.0929620i	$-0.970367\pi$
$401$	−5.86126	−	16.1037i	−0.292697	−	0.804179i	0.702972	−	0.711217i	$-0.251856\pi$
$402$	−47.3366	−	6.19955i	−2.36093	−	0.309205i
$403$	0.0179737	−	0.00316924i	0.000895332	−	0.000157871i
$404$	18.7276	+	32.4372i	0.931734	+	1.61381i
$405$	−0.981817	+	20.1006i	−0.0487869	+	0.998809i
$406$	37.7819	−	14.0030i	1.87508	−	0.694955i
$407$	−43.1323	+	36.1923i	−2.13799	+	1.79399i
$408$	−9.88494	+	12.9003i	−0.489378	+	0.638660i
$409$	13.6877	−	16.3123i	0.676811	−	0.806592i	−0.312883	−	0.949792i	$-0.601295\pi$
$409$	13.6877	−	16.3123i	0.676811	−	0.806592i	0.989694	+	0.143200i	$0.0457392\pi$
$410$	−13.5380	+	20.8860i	−0.668594	+	1.03148i
$411$	−5.50997	+	0.244288i	−0.271787	+	0.0120499i
$412$	−1.01907	−	5.77943i	−0.0502059	−	0.284732i
$413$	−30.1128	−	5.12779i	−1.48175	−	0.252322i
$414$	8.31884	+	2.21702i	0.408849	+	0.108961i
$415$	−9.63494	+	22.7528i	−0.472960	+	1.11689i
$416$	11.8671	−	9.95765i	0.581831	−	0.488214i
$417$	−3.13799	+	9.97586i	−0.153668	+	0.488520i
$418$	−13.7712	+	78.1006i	−0.673574	+	3.82003i
$419$	7.13616	+	5.98795i	0.348624	+	0.292530i	0.800237	−	0.599684i	$-0.204707\pi$
$419$	7.13616	+	5.98795i	0.348624	+	0.292530i	−0.451613	+	0.892214i	$0.649151\pi$
$420$	−11.9122	+	32.5937i	−0.581256	+	1.59041i
$421$	6.58807	+	2.39786i	0.321083	+	0.116865i	0.497533	−	0.867445i	$-0.334239\pi$
$421$	6.58807	+	2.39786i	0.321083	+	0.116865i	−0.176450	+	0.984310i	$0.556461\pi$
$422$	31.8691			1.55136
$423$	4.36392	+	9.32563i	0.212181	+	0.453428i
$424$	15.2937			0.742726
$425$	−1.49893	+	14.5012i	−0.0727090	+	0.703411i
$426$	29.3792	−	18.7444i	1.42342	−	0.908170i
$427$	13.0818	−	11.1083i	0.633073	−	0.537569i
$428$	0.118598	−	0.672604i	0.00573266	−	0.0325116i
$429$	−26.1214	−	3.42105i	−1.26115	−	0.165170i
$430$	−2.21179	−	0.508630i	−0.106662	−	0.0245283i
$431$	23.8672	+	13.7798i	1.14964	+	0.663747i	0.948800	−	0.315876i	$-0.102298\pi$
$431$	23.8672	+	13.7798i	1.14964	+	0.663747i	0.200844	+	0.979623i	$0.435632\pi$
$432$	−3.53151	−	0.775434i	−0.169910	−	0.0373081i
$433$	1.37621			0.0661367			0.0330683	−	0.999453i	$-0.489472\pi$
$433$	1.37621			0.0661367			0.0330683	+	0.999453i	$0.489472\pi$
$434$	0.0176166	+	0.0301037i	0.000845624	+	0.00144503i
$435$	21.9172	+	12.8650i	1.05085	+	0.616829i
$436$	−4.49047	+	1.63440i	−0.215054	+	0.0782734i
$437$	−8.78969	−	1.54986i	−0.420468	−	0.0741398i
$438$	−0.464855	+	0.894449i	−0.0222116	+	0.0427384i
$439$	−2.09716	−	2.49930i	−0.100092	−	0.119285i	0.713673	−	0.700479i	$-0.247030\pi$
$439$	−2.09716	−	2.49930i	−0.100092	−	0.119285i	−0.813765	+	0.581194i	$0.802586\pi$
$440$	33.8068	−	4.18046i	1.61168	−	0.199296i
$441$	20.3538	+	5.16950i	0.969227	+	0.246167i
$442$	18.8300	+	10.8715i	0.895651	+	0.517105i
$443$	−1.72630	−	9.79032i	−0.0820189	−	0.465152i	−0.997960	−	0.0638399i	$-0.979665\pi$
$443$	−1.72630	−	9.79032i	−0.0820189	−	0.465152i	0.915941	−	0.401312i	$-0.131446\pi$
$444$	47.1700	+	51.4075i	2.23859	+	2.43969i
$445$	−18.8714	−	0.972744i	−0.894592	−	0.0461125i
$446$	3.13406	−	17.7741i	0.148402	−	0.841629i
$447$	9.64460	−	30.6608i	0.456174	−	1.45020i
$448$	28.9250	+	16.4745i	1.36658	+	0.778346i
$449$	18.1130	+	10.4576i	0.854807	+	0.493523i	0.862270	−	0.506449i	$-0.169042\pi$
$449$	18.1130	+	10.4576i	0.854807	+	0.493523i	−0.00746259	+	0.999972i	$0.502375\pi$
$450$	−32.8820	+	11.4351i	−1.55007	+	0.539054i
$451$		−	22.7032i		−	1.06905i
$452$	−22.0466	−	8.02429i	−1.03698	−	0.377431i
$453$	−8.69780	−	13.6325i	−0.408658	−	0.640512i
$454$	−22.0245	−	60.5117i	−1.03366	−	2.83996i
$455$	18.5499	+	4.15141i	0.869635	+	0.194621i
$456$	39.8944	+	5.22486i	1.86822	+	0.244676i
$457$	1.21315	−	3.33311i	0.0567489	−	0.155916i	−0.908079	−	0.418799i	$-0.862451\pi$
$457$	1.21315	−	3.33311i	0.0567489	−	0.155916i	0.964828	+	0.262883i	$0.0846733\pi$
$458$	−28.8047	−	16.6304i	−1.34595	−	0.777086i
$459$	2.00787	+	15.0167i	0.0937192	+	0.700921i
$460$	1.14910	+	9.29260i	0.0535769	+	0.433270i
$461$	6.60502	−	5.54227i	0.307626	−	0.258129i	−0.475884	−	0.879508i	$-0.657872\pi$
$461$	6.60502	−	5.54227i	0.307626	−	0.258129i	0.783510	+	0.621379i	$0.213427\pi$
$462$	−11.2183	−	49.0815i	−0.521920	−	2.28348i
$463$	24.6708	+	4.35014i	1.14655	+	0.202168i	0.714470	−	0.699666i	$-0.246668\pi$
$463$	24.6708	+	4.35014i	1.14655	+	0.202168i	0.432082	+	0.901834i	$0.357779\pi$
$464$	−2.93493	+	3.49772i	−0.136251	+	0.162377i
$465$	−0.00767273	+	0.0206180i	−0.000355814	+	0.000956135i
$466$	−16.4319	−	5.98072i	−0.761193	−	0.277052i
$467$	18.0907	+	10.4447i	0.837140	+	0.483323i	0.856291	−	0.516494i	$-0.172763\pi$
$467$	18.0907	+	10.4447i	0.837140	+	0.483323i	−0.0191511	+	0.999817i	$0.506096\pi$
$468$	−2.80132	+	32.5237i	−0.129491	+	1.50341i
$469$	−29.4626	+	10.9196i	−1.36046	+	0.504221i
$470$	−12.1361	+	13.0368i	−0.559797	+	0.601344i
$471$	−32.0549	−	10.0831i	−1.47701	−	0.464606i
$472$	34.9141	−	12.7077i	1.60705	−	0.584919i
$473$	1.94530	−	0.708031i	0.0894450	−	0.0325553i
$474$	−32.7695	+	30.0683i	−1.50515	+	1.38108i
$475$	32.9461	−	14.7365i	1.51167	−	0.676156i
$476$	−4.38557	+	25.7541i	−0.201012	+	1.18044i
$477$	10.0676	−	10.0948i	0.460963	−	0.462207i
$478$	−31.3081	−	18.0758i	−1.43200	−	0.826766i
$479$	19.4167	+	7.06710i	0.887172	+	0.322904i	0.745100	−	0.666952i	$-0.232401\pi$
$479$	19.4167	+	7.06710i	0.887172	+	0.322904i	0.142071	+	0.989856i	$0.454624\pi$
$480$	3.11016	+	18.4122i	0.141959	+	0.840396i
$481$	24.5657	−	29.2762i	1.12010	−	1.33488i
$482$	1.82947	+	0.322584i	0.0833299	+	0.0146933i
$483$	5.52378	−	1.26254i	0.251341	−	0.0574474i
$484$	−29.5974	+	24.8352i	−1.34534	+	1.12887i
$485$	−1.32962	−	10.7525i	−0.0603749	−	0.488244i
$486$	−30.4477	+	19.5418i	−1.38114	+	0.886433i
$487$	−23.2776	−	13.4393i	−1.05481	−	0.608993i	−0.130816	−	0.991407i	$-0.541760\pi$
$487$	−23.2776	−	13.4393i	−1.05481	−	0.608993i	−0.923991	+	0.382414i	$0.875093\pi$
$488$	−7.13958	+	19.6158i	−0.323194	+	0.887967i
$489$	−10.5997	−	25.5412i	−0.479334	−	1.15501i
$490$	4.88080	+	35.9985i	0.220492	+	1.62625i
$491$	9.80755	+	26.9460i	0.442609	+	1.21606i	0.937770	+	0.347257i	$0.112887\pi$
$491$	9.80755	+	26.9460i	0.442609	+	1.21606i	−0.495161	+	0.868801i	$0.664891\pi$
$492$	−28.1045	+	1.24603i	−1.26705	+	0.0561756i
$493$	17.9786	+	6.54366i	0.809713	+	0.294712i
$494$		−	53.8289i		−	2.42188i
$495$	19.4952	−	25.0665i	0.876243	−	1.12666i
$496$	−0.00342293	−	0.00197623i	−0.000153694	−	8.87353e-5i
$497$	11.3516	−	19.9305i	0.509188	−	0.894007i
$498$	−43.3611	+	9.64358i	−1.94306	+	0.432139i
$499$	−4.76568	+	27.0275i	−0.213341	+	1.20992i	0.670420	+	0.741982i	$0.266114\pi$
$499$	−4.76568	+	27.0275i	−0.213341	+	1.20992i	−0.883762	+	0.467937i	$0.844997\pi$
$500$	−24.9142	−	28.5116i	−1.11419	−	1.27508i
$501$	16.5727	−	3.68579i	0.740414	−	0.164669i
$502$	4.85077	+	27.5101i	0.216501	+	1.22784i
$503$	−10.2556	−	5.92109i	−0.457276	−	0.264008i	0.253622	−	0.967303i	$-0.418378\pi$
$503$	−10.2556	−	5.92109i	−0.457276	−	0.264008i	−0.710898	+	0.703295i	$0.751711\pi$
$504$	−24.6246	+	6.78884i	−1.09687	+	0.302399i
$505$	3.03500	+	24.5437i	0.135056	+	1.09218i
$506$	−8.73208	−	10.4065i	−0.388188	−	0.462625i
$507$	−4.63068	+	0.205305i	−0.205656	+	0.00911790i
$508$	−65.1744	−	11.4920i	−2.89165	−	0.509876i
$509$	−23.7687	+	8.65108i	−1.05353	+	0.383453i	−0.809993	−	0.586440i	$-0.800529\pi$
$509$	−23.7687	+	8.65108i	−1.05353	+	0.383453i	−0.243534	+	0.969892i	$0.578307\pi$
$510$	−22.7910	+	12.9407i	−1.00920	+	0.573024i
$511$	0.00389074	+	0.663435i	0.000172116	+	0.0293486i
$512$	−7.83341			−0.346191
$513$	29.7106	−	22.8933i	1.31175	−	1.01076i
$514$	49.6062	+	28.6401i	2.18803	+	1.26326i
$515$	0.868406	−	3.77629i	0.0382665	−	0.166403i
$516$	−0.983244	−	2.36925i	−0.0432849	−	0.104300i
$517$	2.82120	−	15.9998i	0.124076	−	0.703670i
$518$	68.7782	+	24.5774i	3.02194	+	1.07987i
$519$	−0.261168	−	5.89068i	−0.0114640	−	0.258572i
$520$	−22.1052	+	6.77902i	−0.969377	+	0.297280i
$521$	36.2284			1.58720			0.793598	−	0.608442i	$-0.208205\pi$
$521$	36.2284			1.58720			0.793598	+	0.608442i	$0.208205\pi$
$522$	4.04331	+	45.5091i	0.176971	+	1.99188i
$523$	−20.1072			−0.879226			−0.439613	−	0.898187i	$-0.644884\pi$
$523$	−20.1072			−0.879226			−0.439613	+	0.898187i	$0.644884\pi$
$524$	−4.98624	−	1.81484i	−0.217825	−	0.0792819i
$525$	−15.6344	+	16.7501i	−0.682342	+	0.731033i
$526$	−48.3365	−	40.5591i	−2.10757	−	1.76846i
$527$	−0.00287591	+	0.0163101i	−0.000125277	+	0.000710480i
$528$	3.85722	+	4.20373i	0.167864	+	0.182944i
$529$	−16.4478	+	13.8014i	−0.715124	+	0.600060i
$530$	22.7108	+	9.61711i	0.986492	+	0.417741i
$531$	14.5956	−	31.4107i	0.633395	−	1.36311i
$532$	60.6457	−	22.4769i	2.62932	−	0.974496i
$533$	2.67590	+	15.1758i	0.115906	+	0.657336i
$534$	−18.2721	−	28.6389i	−0.790712	−	1.23933i
$535$	0.245281	−	0.378411i	0.0106044	−	0.0163601i
$536$	24.5667	−	29.2774i	1.06112	−	1.26459i
$537$	6.53589	+	15.7490i	0.282045	+	0.679621i
$538$	−48.1559	+	40.4076i	−2.07615	+	1.74209i
$539$	−21.5960	−	25.1325i	−0.930205	−	1.08253i
$540$	−32.1000	−	22.7575i	−1.38137	−	0.979328i
$541$	−20.6733	−	35.8071i	−0.888813	−	1.53947i	−0.841280	−	0.540599i	$-0.818198\pi$
$541$	−20.6733	−	35.8071i	−0.888813	−	1.53947i	−0.0475322	−	0.998870i	$-0.515136\pi$
$542$	34.2226	−	6.03437i	1.46999	−	0.259198i
$543$	7.75379	+	18.6837i	0.332747	+	0.801795i
$544$	4.80797	+	13.2098i	0.206140	+	0.566365i
$545$	−3.15102	−	0.162422i	−0.134975	−	0.00695740i
$546$	13.2837	+	31.4859i	0.568490	+	1.34747i
$547$	−30.9558	+	5.45834i	−1.32357	+	0.233382i	−0.790383	−	0.612613i	$-0.790119\pi$
$547$	−30.9558	+	5.45834i	−1.32357	+	0.233382i	−0.533191	+	0.845995i	$0.679007\pi$
$548$	5.39197	−	9.33917i	0.230334	−	0.398950i
$549$	8.24777	+	17.6254i	0.352006	+	0.752232i
$550$	52.8312	+	15.0509i	2.25273	+	0.641771i
$551$	−8.22498	−	46.6462i	−0.350396	−	1.98720i
$552$	−5.07825	+	4.65966i	−0.216145	+	0.198328i
$553$	−9.84981	+	27.5640i	−0.418856	+	1.17214i
$554$	−22.6959	+	27.0479i	−0.964256	+	1.14916i
$555$	15.4439	+	43.4006i	0.655557	+	1.84225i
$556$	−13.1434	−	15.6637i	−0.557406	−	0.664290i
$557$	−8.28355	−	14.3475i	−0.350985	−	0.607924i	0.635437	−	0.772153i	$-0.280820\pi$
$557$	−8.28355	−	14.3475i	−0.350985	−	0.607924i	−0.986422	+	0.164228i	$0.947487\pi$
$558$	−0.0381882	+	0.0102876i	−0.00161664	+	0.000435511i
$559$	−1.21687	+	0.702559i	−0.0514681	+	0.0297151i
$560$	−2.49947	−	3.27092i	−0.105622	−	0.138222i
$561$	11.0244	−	21.2125i	0.465449	−	0.895592i
$562$	6.70692	−	7.99300i	0.282915	−	0.337164i
$563$	21.2750	−	25.3546i	0.896635	−	1.06857i	−0.100650	−	0.994922i	$-0.532092\pi$
$563$	21.2750	−	25.3546i	0.896635	−	1.06857i	0.997284	−	0.0736459i	$-0.0234635\pi$
$564$	−19.9611	−	2.61426i	−0.840516	−	0.110080i
$565$	−11.3384	−	10.5550i	−0.477011	−	0.444054i
$566$	4.11241			0.172858
$567$	−11.7290	+	20.7227i	−0.492570	+	0.870273i
$568$			27.8988i			1.17061i
$569$	5.22086	−	14.3442i	0.218870	−	0.601340i	−0.780857	−	0.624710i	$-0.785217\pi$
$569$	5.22086	−	14.3442i	0.218870	−	0.601340i	0.999727	+	0.0233697i	$0.00743948\pi$
$570$	55.9567	+	32.8456i	2.34377	+	1.37575i
$571$	−34.7582	−	29.1656i	−1.45459	−	1.22054i	−0.929146	−	0.369712i	$-0.879456\pi$
$571$	−34.7582	−	29.1656i	−1.45459	−	1.22054i	−0.525440	−	0.850831i	$-0.676099\pi$
$572$	33.1100	−	39.4590i	1.38440	−	1.64986i
$573$	−1.77461	−	0.922286i	−0.0741355	−	0.0385291i
$574$	−25.4176	+	14.8743i	−1.06091	+	0.620841i
$575$	−1.69387	+	5.94579i	−0.0706393	+	0.247957i
$576$	−26.6535	+	26.7254i	−1.11056	+	1.11356i
$577$	−5.84508	−	10.1240i	−0.243334	−	0.421467i	0.718328	−	0.695705i	$-0.244908\pi$
$577$	−5.84508	−	10.1240i	−0.243334	−	0.421467i	−0.961662	+	0.274238i	$0.911574\pi$
$578$	15.1100	−	12.6788i	0.628495	−	0.527370i
$579$	−18.4071	−	20.0607i	−0.764973	−	0.833693i
$580$	−44.2554	+	22.5972i	−1.83760	+	0.938297i
$581$	−22.2854	+	18.9234i	−0.924552	+	0.785077i
$582$	14.3515	−	13.1685i	0.594890	−	0.545854i
$583$	−22.1547	+	3.90646i	−0.917552	+	0.161789i
$584$	−0.403490	−	0.698866i	−0.0166965	−	0.0289193i
$585$	−10.0770	+	19.0533i	−0.416631	+	0.787757i
$586$	−34.4652	−	19.8985i	−1.42374	−	0.822000i
$587$	1.87813	−	0.331165i	0.0775187	−	0.0136686i	−0.134754	−	0.990879i	$-0.543025\pi$
$587$	1.87813	−	0.331165i	0.0775187	−	0.0136686i	0.212273	+	0.977210i	$0.431913\pi$
$588$	−29.9264	+	28.1132i	−1.23415	+	1.15937i
$589$	0.0385290	−	0.0140234i	0.00158756	−	0.000577824i
$590$	59.8377	+	3.08438i	2.46348	+	0.126982i
$591$	−36.4060	+	15.1086i	−1.49754	+	0.621484i
$592$	−8.15070	+	1.43719i	−0.334992	+	0.0590681i
$593$	−6.28615	+	3.62931i	−0.258141	+	0.149038i	−0.623486	−	0.781834i	$-0.714284\pi$
$593$	−6.28615	+	3.62931i	−0.258141	+	0.149038i	0.365345	+	0.930872i	$0.380951\pi$
$594$	57.0389	+	2.37492i	2.34034	+	0.0974440i
$595$	−9.29724	+	14.5295i	−0.381150	+	0.595650i
$596$	40.3963	+	48.1424i	1.65470	+	1.97199i
$597$	5.91030	+	14.2416i	0.241893	+	0.582870i
$598$	7.06344	+	5.92693i	0.288846	+	0.242370i
$599$	42.6366	+	7.51798i	1.74208	+	0.307176i	0.952062	−	0.305905i	$-0.0989588\pi$
$599$	42.6366	+	7.51798i	1.74208	+	0.307176i	0.790020	+	0.613081i	$0.210070\pi$
$600$	6.44126	−	27.1154i	0.262963	−	1.10698i
$601$	40.5055	−	7.14221i	1.65225	−	0.291337i	0.731604	−	0.681730i	$-0.238772\pi$
$601$	40.5055	−	7.14221i	1.65225	−	0.291337i	0.920648	+	0.390393i	$0.127661\pi$
$602$	−2.06717	−	1.71401i	−0.0842517	−	0.0698577i
$603$	−3.15300	−	35.4884i	−0.128400	−	1.44520i
$604$	31.6181			1.28652
$605$	−24.3895	+	7.47956i	−0.991575	+	0.304087i
$606$	−32.7589	+	30.0587i	−1.33074	+	1.22105i
$607$	3.51163	−	19.9155i	0.142533	−	0.808343i	−0.826782	−	0.562522i	$-0.809831\pi$
$607$	3.51163	−	19.9155i	0.142533	−	0.808343i	0.969315	−	0.245821i	$-0.0790577\pi$
$608$	22.3704	−	26.6600i	0.907239	−	1.08120i
$609$	16.3222	+	25.2548i	0.661409	+	1.02338i
$610$	−22.9371	+	24.6395i	−0.928698	+	0.997624i
$611$			11.0275i			0.446123i
$612$	−26.8642	−	12.4830i	−1.08592	−	0.504594i
$613$			6.76585i			0.273270i	0.990621	+	0.136635i	$0.0436288\pi$
$613$			6.76585i			0.273270i	−0.990621	+	0.136635i	$0.956371\pi$
$614$	8.52344	−	7.15202i	0.343978	−	0.288632i
$615$	−17.4085	−	6.47835i	−0.701977	−	0.261232i
$616$	37.9549	+	13.5629i	1.52925	+	0.546466i
$617$	−2.01623	+	11.4346i	−0.0811702	+	0.460339i	0.916947	+	0.399008i	$0.130646\pi$
$617$	−2.01623	+	11.4346i	−0.0811702	+	0.460339i	−0.998118	+	0.0613307i	$0.980466\pi$
$618$	6.43401	−	2.67013i	0.258814	−	0.107409i
$619$	18.8165	−	3.31785i	0.756298	−	0.133356i	0.217813	−	0.975991i	$-0.430108\pi$
$619$	18.8165	−	3.31785i	0.756298	−	0.133356i	0.538485	+	0.842635i	$0.318997\pi$
$620$	−0.0259161	−	0.0343304i	−0.00104082	−	0.00137874i
$621$	−0.267280	+	6.41934i	−0.0107256	+	0.257599i
$622$	63.5412			2.54777
$623$	−19.4284	−	11.0656i	−0.778381	−	0.443332i
$624$	−3.07380	−	2.35532i	−0.123051	−	0.0942884i
$625$	−7.80713	−	23.7497i	−0.312285	−	0.949988i
$626$	5.22112	−	29.6105i	0.208678	−	1.18347i
$627$	−59.1262	+	2.62140i	−2.36127	+	0.104689i
$628$	50.3314	−	42.2330i	2.00844	−	1.68528i
$629$	17.3401	+	30.0339i	0.691395	+	1.19753i
$630$	−40.8360	−	5.40340i	−1.62695	−	0.215277i
$631$	1.51428	−	2.62280i	0.0602824	−	0.104412i	−0.834309	−	0.551297i	$-0.814133\pi$
$631$	1.51428	−	2.62280i	0.0602824	−	0.104412i	0.894592	+	0.446885i	$0.147467\pi$
$632$	−6.18252	−	35.0628i	−0.245928	−	1.39472i
$633$	5.16330	+	23.2162i	0.205223	+	0.922759i
$634$	27.7708	−	10.1077i	1.10292	−	0.401430i
$635$	−36.6675	−	23.7674i	−1.45511	−	0.943179i
$636$	6.05178	+	27.2111i	0.239969	+	1.07899i
$637$	17.3979	+	14.2542i	0.689329	+	0.564772i
$638$	36.0465	−	62.4343i	1.42709	−	2.47180i
$639$	18.4149	+	18.3654i	0.728482	+	0.726522i
$640$	−40.2708	−	17.0531i	−1.59184	−	0.674083i
$641$	−14.6328	+	40.2032i	−0.577960	+	1.58793i	0.213654	+	0.976909i	$0.431464\pi$
$641$	−14.6328	+	40.2032i	−0.577960	+	1.58793i	−0.791614	+	0.611022i	$0.790759\pi$
$642$	0.809909	−	0.0359079i	0.0319646	−	0.00141717i
$643$	2.68049	−	0.975620i	0.105708	−	0.0384747i	−0.288625	−	0.957442i	$-0.593198\pi$
$643$	2.68049	−	0.975620i	0.105708	−	0.0384747i	0.394333	+	0.918968i	$0.370976\pi$
$644$	−3.72809	+	10.4328i	−0.146907	+	0.411110i
$645$	0.0121836	−	1.69366i	0.000479729	−	0.0666879i
$646$	45.9010	+	16.7066i	1.80595	+	0.657312i
$647$	7.22516	+	4.17145i	0.284050	+	0.163996i	0.635256	−	0.772302i	$-0.280895\pi$
$647$	7.22516	+	4.17145i	0.284050	+	0.163996i	−0.351205	+	0.936298i	$0.614228\pi$
$648$	−0.0780274	−	28.9633i	−0.00306521	−	1.13778i
$649$	−47.3312	+	27.3267i	−1.85791	+	1.07267i
$650$	−37.0886	−	3.83371i	−1.45473	−	0.150370i
$651$	−0.0190759	+	0.0177107i	−0.000747645	+	0.000694137i
$652$	53.2478	+	9.38902i	2.08534	+	0.367702i
$653$	−19.9890	−	16.7727i	−0.782229	−	0.656368i	0.161580	−	0.986860i	$-0.448341\pi$
$653$	−19.9890	−	16.7727i	−0.782229	−	0.656368i	−0.943809	+	0.330492i	$0.892785\pi$
$654$	−3.05095	−	4.78193i	−0.119302	−	0.186988i
$655$	−2.56440	−	2.38722i	−0.100199	−	0.0932764i
$656$	1.66860	−	2.89010i	0.0651478	−	0.112839i
$657$	−0.726906	−	0.193725i	−0.0283593	−	0.00755792i
$658$	−19.7611	+	7.32398i	−0.770368	+	0.285518i
$659$	2.19670	−	6.03539i	0.0855714	−	0.235105i	−0.889525	−	0.456886i	$-0.848965\pi$
$659$	2.19670	−	6.03539i	0.0855714	−	0.235105i	0.975097	+	0.221781i	$0.0711869\pi$
$660$	20.8156	+	58.4962i	0.810244	+	2.27696i
$661$	−16.3385	−	44.8898i	−0.635496	−	1.74601i	−0.665433	−	0.746458i	$-0.731753\pi$
$661$	−16.3385	−	44.8898i	−0.635496	−	1.74601i	0.0299370	−	0.999552i	$-0.490469\pi$
$662$	51.4305	−	18.7192i	1.99890	−	0.727541i
$663$	−4.86896	+	15.4787i	−0.189095	+	0.601143i
$664$	12.1625	−	33.4163i	0.471998	−	1.29680i
$665$	42.6598	+	1.94817i	1.65428	+	0.0755467i
$666$	−47.4104	+	67.9035i	−1.83711	+	2.63121i
$667$	7.02656	+	4.05678i	0.272069	+	0.157079i
$668$	−11.3535	+	31.1936i	−0.439282	+	1.20692i
$669$	13.4559	−	0.596579i	0.520236	−	0.0230651i
$670$	54.8914	−	28.0280i	2.12064	−	1.08282i
$671$	5.33204	−	30.2395i	0.205841	−	1.16738i
$672$	−6.50594	+	21.1146i	−0.250972	+	0.814513i
$673$	14.2424	+	16.9734i	0.549004	+	0.654277i	0.967181	−	0.254088i	$-0.0817754\pi$
$673$	14.2424	+	16.9734i	0.549004	+	0.654277i	−0.418177	+	0.908365i	$0.637331\pi$
$674$	−45.9809	+	26.5471i	−1.77112	+	1.02256i
$675$	−13.6577	−	22.1013i	−0.525684	−	0.850680i
$676$	4.53152	−	7.84882i	0.174289	−	0.301878i
$677$	12.0167	−	33.0155i	0.461838	−	1.26889i	−0.462263	−	0.886743i	$-0.652963\pi$
$677$	12.0167	−	33.0155i	0.461838	−	1.26889i	0.924101	−	0.382147i	$-0.124815\pi$
$678$	3.61643	−	27.6132i	0.138888	−	1.06048i
$679$	4.31376	−	12.0718i	0.165547	−	0.463272i
$680$	1.08007	−	20.9535i	0.0414186	−	0.803530i
$681$	40.5135	−	25.8483i	1.55248	−	0.990510i
$682$	0.0586429	+	0.0213443i	0.00224555	+	0.000817314i
$683$	−0.249475			−0.00954588			−0.00477294	−	0.999989i	$-0.501519\pi$
$683$	−0.249475			−0.00954588			−0.00477294	+	0.999989i	$0.501519\pi$
$684$	6.49012	+	73.0490i	0.248156	+	2.79310i
$685$	5.68286	−	4.29000i	0.217131	−	0.163913i
$686$	−13.9884	+	40.6439i	−0.534081	+	1.55179i
$687$	7.44815	−	23.6781i	0.284165	−	0.903376i
$688$	0.299673	+	0.0528404i	0.0114249	+	0.00201452i
$689$	14.3487	−	5.22249i	0.546641	−	0.198961i
$690$	−10.4712	+	3.72613i	−0.398633	+	0.141851i
$691$	18.4875	−	3.25985i	0.703298	−	0.124010i	0.189448	−	0.981891i	$-0.439330\pi$
$691$	18.4875	−	3.25985i	0.703298	−	0.124010i	0.513850	+	0.857880i	$0.328219\pi$
$692$	9.98447	+	5.76454i	0.379553	+	0.219135i
$693$	33.9375	−	16.1243i	1.28918	−	0.612511i
$694$	−21.6548	−	37.5072i	−0.822004	−	1.42375i
$695$	−3.95838	−	12.9076i	−0.150150	−	0.489613i
$696$	−32.4545	−	16.8670i	−1.23019	−	0.639342i
$697$	−13.7712	−	2.42823i	−0.521621	−	0.0919759i
$698$	−17.0850	−	46.9405i	−0.646675	−	1.77673i
$699$	1.69463	−	12.9393i	0.0640969	−	0.489411i
$700$	−11.1676	−	43.3862i	−0.422094	−	1.63984i
$701$			1.49711i			0.0565452i	0.999600	+	0.0282726i	$0.00900064\pi$
$701$			1.49711i			0.0565452i	−0.999600	+	0.0282726i	$0.990999\pi$
$702$	−38.4071	+	5.13536i	−1.44958	+	0.193822i
$703$	42.9287	−	74.3547i	1.61909	−	2.80434i
$704$	58.6535	−	10.3422i	2.21059	−	0.389786i
$705$	−11.4634	−	6.72879i	−0.431735	−	0.253421i
$706$	4.93473	+	0.870127i	0.185721	+	0.0327476i
$707$	−9.84664	+	27.5552i	−0.370321	+	1.03632i
$708$	36.4257	+	57.0920i	1.36896	+	2.14565i
$709$	20.2700	−	17.0086i	0.761257	−	0.638771i	−0.177197	−	0.984175i	$-0.556703\pi$
$709$	20.2700	−	17.0086i	0.761257	−	0.638771i	0.938454	+	0.345405i	$0.112258\pi$
$710$	−17.5436	+	41.4291i	−0.658399	+	1.55481i
$711$	−27.2135	−	19.0005i	−1.02058	−	0.712574i
$712$	27.1958			1.01921
$713$	−0.00240215	+	0.00659986i	−8.99613e−5	+	0.000247167i
$714$	−30.9714	+	1.55518i	−1.15908	+	0.0582011i
$715$	30.2904	−	15.4665i	1.13280	−	0.578415i
$716$	−32.8332	−	5.78939i	−1.22704	−	0.216359i
$717$	8.09549	−	25.7360i	0.302332	−	0.961130i
$718$	25.0607	+	29.8662i	0.935257	+	1.11460i
$719$	2.57482			0.0960246			0.0480123	−	0.998847i	$-0.484711\pi$
$719$	2.57482			0.0960246			0.0480123	+	0.998847i	$0.484711\pi$
$720$	4.32401	−	1.75812i	0.161146	−	0.0655214i
$721$	2.92640	−	3.52937i	0.108985	−	0.131441i
$722$	−13.3418	−	75.6650i	−0.496530	−	2.81596i
$723$	0.0614050	+	1.38500i	0.00228368	+	0.0515087i
$724$	−38.9514	−	6.86818i	−1.44762	−	0.255254i
$725$	−32.7254	+	2.34493i	−1.21539	+	0.0870885i
$726$	−36.4037	−	27.8946i	−1.35107	−	1.03526i
$727$	−26.5542	+	22.2816i	−0.984840	+	0.826379i	−0.984812	−	0.173621i	$-0.944453\pi$
$727$	−26.5542	+	22.2816i	−0.984840	+	0.826379i	−2.71941e−5		1.00000i	$0.500009\pi$
$728$	−26.9693	−	4.59250i	−0.999547	−	0.170209i
$729$	−19.1689	−	19.0146i	−0.709958	−	0.704244i
$730$	−0.159707	−	1.29153i	−0.00591101	−	0.0478016i
$731$	−0.221413	−	1.25570i	−0.00818927	−	0.0464437i
$732$	−37.7264	−	4.94093i	−1.39441	−	0.182622i
$733$	−40.0849	+	14.5897i	−1.48057	+	0.538883i	−0.950948	−	0.309351i	$-0.899888\pi$
$733$	−40.0849	+	14.5897i	−1.48057	+	0.538883i	−0.529621	+	0.848234i	$0.677666\pi$
$734$	−16.6906	+	6.07488i	−0.616061	+	0.224228i
$735$	−25.4336	+	9.38792i	−0.938132	+	0.346279i
$736$	1.03520	+	5.87090i	0.0381579	+	0.216404i
$737$	−28.1093	+	48.6868i	−1.03542	+	1.79340i
$738$	−8.68622	−	32.2436i	−0.319744	−	1.18690i
$739$	−16.3665	−	28.3475i	−0.602050	−	1.04278i	−0.992510	−	0.122162i	$-0.961017\pi$
$739$	−16.3665	−	28.3475i	−0.602050	−	1.04278i	0.390460	−	0.920620i	$-0.372316\pi$
$740$	−87.7805	−	20.1863i	−3.22688	−	0.742062i
$741$	39.2135	−	8.72113i	1.44054	−	0.320379i
$742$	18.8884	+	22.2441i	0.693416	+	0.816608i
$743$	10.8226	+	9.08125i	0.397043	+	0.333159i	0.819349	−	0.573294i	$-0.194335\pi$
$743$	10.8226	+	9.08125i	0.397043	+	0.333159i	−0.422306	+	0.906453i	$0.638779\pi$
$744$	0.00950045	−	0.0302025i	0.000348303	−	0.00110728i
$745$	12.1661	+	39.6714i	0.445730	+	1.45345i
$746$	−22.8405	+	13.1870i	−0.836252	+	0.482810i
$747$	−14.0504	−	30.0255i	−0.514077	−	1.09858i
$748$	23.3713	+	40.4803i	0.854540	+	1.48011i
$749$	0.460515	−	0.269492i	0.0168269	−	0.00984702i
$750$	26.6161	−	36.2154i	0.971884	−	1.32240i
$751$	12.9838	+	10.8947i	0.473787	+	0.397555i	0.848174	−	0.529718i	$-0.177702\pi$
$751$	12.9838	+	10.8947i	0.473787	+	0.397555i	−0.374387	+	0.927273i	$0.622147\pi$
$752$	1.53506	−	1.82941i	0.0559779	−	0.0667119i
$753$	−19.2548	+	7.99079i	−0.701683	+	0.291200i
$754$	−16.7362	+	45.9824i	−0.609497	+	1.67458i
$755$	19.2240	+	8.14059i	0.699631	+	0.296266i
$756$	−21.8230	−	41.1266i	−0.793696	−	1.49576i
$757$		−	22.3006i		−	0.810531i	−0.914199	−	0.405265i	$-0.867179\pi$
$757$		−	22.3006i		−	0.810531i	0.914199	−	0.405265i	$-0.132821\pi$
$758$	−49.6668	−	18.0772i	−1.80398	−	0.656595i
$759$	6.16622	−	8.04719i	0.223820	−	0.292095i
$760$	−46.2615	+	23.6215i	−1.67808	+	0.856842i
$761$	−10.8650	−	9.11682i	−0.393856	−	0.330485i	0.424257	−	0.905542i	$-0.360535\pi$
$761$	−10.8650	−	9.11682i	−0.393856	−	0.330485i	−0.818113	+	0.575057i	$0.804980\pi$
$762$	−3.47943	−	78.4791i	−0.126046	−	2.84300i
$763$	−3.24402	−	1.84765i	−0.117441	−	0.0668895i
$764$	3.38654	−	1.95522i	0.122521	−	0.0707373i
$765$	−13.1196	−	14.5063i	−0.474340	−	0.524476i
$766$	−28.3718	+	16.3805i	−1.02511	+	0.591850i
$767$	28.4174	−	23.8450i	1.02609	−	0.860993i
$768$	−7.60650	−	34.2017i	−0.274476	−	1.23415i
$769$	−0.150947	+	0.179892i	−0.00544330	+	0.00648708i	−0.768759	−	0.639538i	$-0.779126\pi$
$769$	−0.150947	+	0.179892i	−0.00544330	+	0.00648708i	0.763316	+	0.646025i	$0.223570\pi$
$770$	47.8335	+	44.0078i	1.72380	+	1.58593i
$771$	−12.8269	+	40.7775i	−0.461950	+	1.46856i
$772$	52.4248	−	9.24391i	1.88681	−	0.332695i
$773$	28.2997	−	16.3388i	1.01787	−	0.587667i	0.104383	−	0.994537i	$-0.466713\pi$
$773$	28.2997	−	16.3388i	1.01787	−	0.587667i	0.913486	+	0.406870i	$0.133380\pi$
$774$	2.49187	−	1.74983i	0.0895683	−	0.0628964i
$775$	−0.00691820	−	0.0275456i	−0.000248509	−	0.000989465i
$776$	2.70766	+	15.3559i	0.0971994	+	0.551245i
$777$	−6.76109	+	54.0857i	−0.242553	+	1.94032i
$778$	23.2725	+	63.9407i	0.834360	+	2.29238i
$779$	11.8404	+	32.5313i	0.424228	+	1.16556i
$780$	−20.8086	−	36.6479i	−0.745068	−	1.31220i
$781$	−7.12619	−	40.4146i	−0.254995	−	1.44615i
$782$	−7.24626	+	4.18363i	−0.259126	+	0.149606i
$783$	−32.4976	+	10.3187i	−1.16137	+	0.368760i
$784$	−0.902010	−	4.78656i	−0.0322146	−	0.170949i
$785$	41.4752	−	12.7192i	1.48031	−	0.453969i
$786$	0.817923	−	6.24524i	0.0291744	−	0.222760i
$787$	6.49334	+	5.44856i	0.231463	+	0.194220i	0.751141	−	0.660142i	$-0.229504\pi$
$787$	6.49334	+	5.44856i	0.231463	+	0.194220i	−0.519678	+	0.854362i	$0.673948\pi$
$788$	13.3829	−	75.8984i	0.476747	−	2.70377i
$789$	21.7154	−	41.7836i	0.773089	−	1.48754i
$790$	12.8676	−	55.9553i	0.457810	−	1.99080i
$791$	−6.36982	−	17.1867i	−0.226485	−	0.611087i
$792$	−26.1632	+	37.4722i	−0.929668	+	1.33152i
$793$			20.8418i			0.740114i
$794$	−40.6126	+	34.0780i	−1.44129	+	1.20938i
$795$	−3.32641	+	18.1026i	−0.117976	+	0.642031i
$796$	−29.6906	−	5.23525i	−1.05235	−	0.185558i
$797$	−18.0610	+	21.5243i	−0.639754	+	0.762429i	−0.984331	−	0.176329i	$-0.943578\pi$
$797$	−18.0610	+	21.5243i	−0.639754	+	0.762429i	0.344577	+	0.938758i	$0.388022\pi$
$798$	41.6721	+	64.4780i	1.47518	+	2.28250i
$799$	−9.40334	−	3.42254i	−0.332666	−	0.121081i
$800$	−16.7757	−	17.3121i	−0.593112	−	0.612076i
$801$	17.9026	−	17.9509i	0.632558	−	0.634264i
$802$			39.7737i			1.40446i
$803$	0.763014	+	0.909325i	0.0269262	+	0.0320894i
$804$	61.8126	+	32.1247i	2.17996	+	1.13295i
$805$	−4.95278	+	5.38333i	−0.174563	+	0.189737i
$806$	−0.0417151	−	0.00735550i	−0.00146935	−	0.000259087i
$807$	−37.2383	−	28.5341i	−1.31085	−	1.00445i
$808$	−6.18053	−	35.0516i	−0.217430	−	1.23311i
$809$	18.4329	+	10.6422i	0.648065	+	0.374161i	0.787715	−	0.616040i	$-0.211264\pi$
$809$	18.4329	+	10.6422i	0.648065	+	0.374161i	−0.139649	+	0.990201i	$0.544598\pi$
$810$	18.0971	−	43.0589i	0.635867	−	1.51293i
$811$		−	35.7637i		−	1.25583i	−0.778280	−	0.627917i	$-0.783908\pi$
$811$		−	35.7637i		−	1.25583i	0.778280	−	0.627917i	$-0.216092\pi$
$812$	−58.7939	+	0.344799i	−2.06326	+	0.0121001i
$813$	9.94054	+	23.9529i	0.348630	+	0.840067i
$814$	122.798	−	44.6948i	4.30407	−	1.56655i
$815$	29.9575	+	19.4180i	1.04937	+	0.680184i
$816$	2.96243	−	1.89008i	0.103706	−	0.0661661i
$817$	−2.41815	+	2.02907i	−0.0846004	+	0.0709882i
$818$	−42.8005	+	24.7109i	−1.49649	+	0.863996i
$819$	−20.7848	+	14.7782i	−0.726280	+	0.516392i
$820$	28.9864	−	21.8819i	1.01225	−	0.764149i
$821$	−12.9786	+	2.28848i	−0.452957	+	0.0798685i	−0.395472	−	0.918478i	$-0.629419\pi$
$821$	−12.9786	+	2.28848i	−0.452957	+	0.0798685i	−0.0574845	+	0.998346i	$0.518308\pi$
$822$	12.2108	+	3.84101i	0.425900	+	0.133971i
$823$	−1.74843	−	4.80376i	−0.0609463	−	0.167449i	0.905482	−	0.424384i	$-0.139509\pi$
$823$	−1.74843	−	4.80376i	−0.0609463	−	0.167449i	−0.966429	+	0.256936i	$0.917287\pi$
$824$	−0.968382	+	5.49197i	−0.0337352	+	0.191322i
$825$	−2.40482	+	40.9252i	−0.0837249	+	1.42483i
$826$	61.6036	+	35.0868i	2.14346	+	1.22083i
$827$	−9.78948	+	16.9559i	−0.340414	+	0.589614i	−0.984510	−	0.175331i	$-0.943900\pi$
$827$	−9.78948	+	16.9559i	−0.340414	+	0.589614i	0.644096	+	0.764945i	$0.277234\pi$
$828$	−10.3001	−	7.19157i	−0.357954	−	0.249924i
$829$		−	1.62578i		−	0.0564657i	−0.999601	−	0.0282328i	$-0.991012\pi$
$829$		−	1.62578i		−	0.0564657i	0.999601	−	0.0282328i	$-0.00898798\pi$
$830$	39.0743	−	41.9743i	1.35629	−	1.45695i
$831$	−23.3811	−	12.1514i	−0.811080	−	0.421527i
$832$	−37.9875	+	13.8263i	−1.31698	+	0.479341i
$833$	−17.5545	+	10.4115i	−0.608229	+	0.360738i
$834$	14.7626	−	19.2658i	0.511186	−	0.667120i
$835$	−14.9343	+	16.0427i	−0.516822	+	0.555180i
$836$	57.8601	−	100.217i	2.00113	−	3.46606i
$837$	−0.0136815	−	0.0261527i	−0.000472901	−	0.000903971i
$838$	−10.8103	−	18.7240i	−0.373435	−	0.646809i
$839$	4.27500	−	3.58715i	0.147589	−	0.123842i	−0.566003	−	0.824403i	$-0.691511\pi$
$839$	4.27500	−	3.58715i	0.147589	−	0.123842i	0.713593	+	0.700561i	$0.247067\pi$
$840$	21.2303	−	25.2331i	0.732514	−	0.870623i
$841$	−2.44116	+	13.8445i	−0.0841780	+	0.477397i
$842$	−12.4647	−	10.4592i	−0.429564	−	0.360447i
$843$	6.90940	+	3.59089i	0.237972	+	0.123677i
$844$	−43.6980	−	15.9048i	−1.50415	−	0.547465i
$845$	4.77598	−	3.60540i	0.164299	−	0.124030i
$846$	−2.11478	−	23.8027i	−0.0727075	−	0.818353i
$847$	−29.7563	−	5.06708i	−1.02244	−	0.174107i
$848$	−3.10738	−	1.13099i	−0.106708	−	0.0388385i
$849$	0.666276	+	2.99583i	0.0228665	+	0.102816i
$850$	14.7801	−	30.4363i	0.506952	−	1.04396i
$851$	5.03010	+	13.8201i	0.172430	+	0.473746i
$852$	−49.6386	+	11.0397i	−1.70059	+	0.378213i
$853$	9.96952	+	3.62861i	0.341350	+	0.124241i	0.507006	−	0.861942i	$-0.330752\pi$
$853$	9.96952	+	3.62861i	0.341350	+	0.124241i	−0.165656	+	0.986184i	$0.552974\pi$
$854$	−37.3483	+	13.8423i	−1.27803	+	0.473672i
$855$	−14.8616	+	46.0851i	−0.508256	+	1.57608i
$856$	−0.324505	+	0.562059i	−0.0110914	+	0.0192108i
$857$	5.71768	−	15.7092i	0.195312	−	0.536615i	−0.802918	−	0.596090i	$-0.796720\pi$
$857$	5.71768	−	15.7092i	0.195312	−	0.536615i	0.998230	+	0.0594743i	$0.0189424\pi$
$858$	54.2535	+	28.1962i	1.85219	+	0.962602i
$859$	3.22842	−	3.84748i	0.110152	−	0.131274i	−0.708151	−	0.706061i	$-0.750471\pi$
$859$	3.22842	−	3.84748i	0.110152	−	0.131274i	0.818303	+	0.574787i	$0.194915\pi$
$860$	2.77891	+	1.80125i	0.0947599	+	0.0614221i
$861$	−14.9537	−	16.1065i	−0.509622	−	0.548907i
$862$	−41.1146	−	48.9985i	−1.40037	−	1.66889i
$863$	−15.4606	−	26.7785i	−0.526285	−	0.911552i	−0.999531	−	0.0306219i	$-0.990251\pi$
$863$	−15.4606	−	26.7785i	−0.526285	−	0.911552i	0.473246	−	0.880930i	$-0.343082\pi$
$864$	−21.1562	−	13.4180i	−0.719748	−	0.456488i
$865$	4.58642	+	6.07552i	0.155943	+	0.206574i
$866$	−3.00144	−	1.09243i	−0.101993	−	0.0371224i
$867$	11.6844	+	8.95326i	0.396823	+	0.304069i
$868$	−0.00913163	−	0.0500692i	−0.000309948	−	0.00169946i
$869$	17.9122	+	49.2134i	0.607630	+	1.66945i
$870$	−37.5878	−	45.4555i	−1.27435	−	1.54109i
$871$	13.0510	−	35.8574i	0.442217	−	1.21498i
$872$	4.54097			0.153777
$873$	11.9183	+	8.32135i	0.403372	+	0.281635i
$874$	17.9395	+	10.3574i	0.606812	+	0.350343i
$875$	4.38055	−	29.2542i	0.148090	−	0.988974i
$876$	1.08378	−	0.994450i	0.0366177	−	0.0335993i
$877$	−8.21026	−	1.44769i	−0.277241	−	0.0488850i	0.0332989	−	0.999445i	$-0.489399\pi$
$877$	−8.21026	−	1.44769i	−0.277241	−	0.0488850i	−0.310540	+	0.950560i	$0.600510\pi$
$878$	2.58984	+	7.11552i	0.0874028	+	0.240137i
$879$	8.91183	−	28.3312i	0.300589	−	0.955589i
$880$	−7.17805	−	1.65069i	−0.241972	−	0.0556446i
$881$	−5.05615	+	8.75751i	−0.170346	+	0.295048i	−0.938541	−	0.345168i	$-0.887822\pi$
$881$	−5.05615	+	8.75751i	−0.170346	+	0.295048i	0.768195	+	0.640216i	$0.221155\pi$
$882$	−40.2868	−	27.4311i	−1.35653	−	0.923653i
$883$	5.68611	−	3.28288i	0.191353	−	0.110478i	−0.401263	−	0.915963i	$-0.631429\pi$
$883$	5.68611	−	3.28288i	0.191353	−	0.110478i	0.592616	+	0.805485i	$0.298095\pi$
$884$	−20.3936	−	24.3041i	−0.685910	−	0.817435i
$885$	7.44773	+	44.0905i	0.250353	+	1.48209i
$886$	−4.00657	+	22.7224i	−0.134603	+	0.763374i
$887$	1.78309	+	4.89901i	0.0598704	+	0.164493i	0.966022	−	0.258461i	$-0.0832155\pi$
$887$	1.78309	+	4.89901i	0.0598704	+	0.164493i	−0.906151	+	0.422954i	$0.860993\pi$
$888$	−25.4128	−	61.2352i	−0.852797	−	2.05492i
$889$	−26.1134	−	44.6233i	−0.875815	−	1.49662i
$890$	40.3852	+	17.1016i	1.35372	+	0.573245i
$891$	7.51112	+	41.9367i	0.251632	+	1.40493i
$892$	−13.1678	+	22.8073i	−0.440890	+	0.763644i
$893$	4.30192	+	24.3974i	0.143958	+	0.816428i
$894$	−45.3727	+	59.2133i	−1.51749	+	1.98039i
$895$	−18.4722	−	11.9734i	−0.617456	−	0.400227i
$896$	−33.4931	−	39.4434i	−1.11893	−	1.31771i
$897$	−3.17329	+	6.10586i	−0.105953	+	0.203869i
$898$	−31.2022	−	37.1854i	−1.04123	−	1.24089i
$899$	−0.0372728			−0.00124312
$900$	50.7937	+	0.730821i	1.69312	+	0.0243607i
$901$			13.8563i			0.461620i
$902$	−18.0217	+	49.5142i	−0.600057	+	1.64864i
$903$	0.913712	−	1.78360i	0.0304064	−	0.0593544i
$904$	17.0786	+	14.3306i	0.568026	+	0.476630i
$905$	−21.9143	−	14.2045i	−0.728455	−	0.472174i
$906$	8.14789	+	36.6360i	0.270695	+	1.21715i
$907$	16.2925	+	19.4166i	0.540982	+	0.644717i	0.965408	−	0.260746i	$-0.0839684\pi$
$907$	16.2925	+	19.4166i	0.540982	+	0.644717i	−0.424426	+	0.905463i	$0.639524\pi$
$908$			93.9636i			3.11829i
$909$	−27.2047	−	18.9944i	−0.902324	−	0.630004i
$910$	−37.1609	−	23.7788i	−1.23187	−	0.788261i
$911$	13.0656	−	2.30382i	0.432882	−	0.0763288i	0.0470388	−	0.998893i	$-0.485022\pi$
$911$	13.0656	−	2.30382i	0.432882	−	0.0763288i	0.385844	+	0.922564i	$0.373910\pi$
$912$	−7.71938	−	4.01185i	−0.255614	−	0.132846i
$913$	−9.08333	+	51.5141i	−0.300614	+	1.70487i
$914$	−5.29162	+	6.30630i	−0.175031	+	0.208594i
$915$	−21.6657	−	12.7174i	−0.716245	−	0.420423i
$916$	31.1965	+	37.1785i	1.03076	+	1.22841i
$917$	−1.44065	−	3.88708i	−0.0475746	−	0.128363i
$918$	7.54119	−	34.3444i	0.248897	−	1.13353i
$919$	−9.36009	−	16.2122i	−0.308761	−	0.534790i	0.669331	−	0.742965i	$-0.266581\pi$
$919$	−9.36009	−	16.2122i	−0.308761	−	0.534790i	−0.978092	+	0.208175i	$0.933248\pi$
$920$	1.99409	−	8.67133i	0.0657430	−	0.285885i
$921$	6.59107	+	5.05045i	0.217183	+	0.166418i
$922$	−18.8045	+	6.84429i	−0.619295	+	0.225405i
$923$	9.52689	+	26.1749i	0.313582	+	0.861558i
$924$	−9.11272	+	72.8977i	−0.299786	+	2.39816i
$925$	−48.1736	−	34.8738i	−1.58394	−	1.14664i
$926$	−50.3524	−	29.0710i	−1.65468	−	0.955332i
$927$	2.98756	+	4.25447i	0.0981244	+	0.139735i
$928$	−27.3985	+	15.8185i	−0.899399	+	0.519268i
$929$	3.63223	+	20.5994i	0.119170	+	0.675844i	0.984601	+	0.174817i	$0.0559333\pi$
$929$	3.63223	+	20.5994i	0.119170	+	0.675844i	−0.865431	+	0.501027i	$0.832956\pi$
$930$	0.0331002	−	0.0388759i	0.00108540	−	0.00127479i
$931$	44.0522	+	24.7492i	1.44375	+	0.811123i
$932$	19.5462	+	16.4012i	0.640256	+	0.537239i
$933$	10.2947	+	46.2887i	0.337033	+	1.51542i
$934$	−31.1638	−	37.1396i	−1.01971	−	1.21524i
$935$	3.78756	+	30.6295i	0.123866	+	1.00169i
$936$	13.0719	−	28.1317i	0.427270	−	0.919514i
$937$	−12.2889	−	21.2850i	−0.401460	−	0.695349i	0.592442	−	0.805613i	$-0.298164\pi$
$937$	−12.2889	−	21.2850i	−0.401460	−	0.695349i	−0.993902	+	0.110264i	$0.964830\pi$
$938$	72.9240	−	0.427666i	2.38105	−	0.0139638i
$939$	22.4166	−	0.993859i	0.731540	−	0.0324334i
$940$	23.1469	−	11.8190i	0.754969	−	0.385494i
$941$	−19.5182	−	16.3777i	−0.636274	−	0.533897i	0.266598	−	0.963808i	$-0.414101\pi$
$941$	−19.5182	−	16.3777i	−0.636274	−	0.533897i	−0.902871	+	0.429911i	$0.858545\pi$
$942$	61.9057	+	47.4357i	2.01700	+	1.54554i
$943$	−5.57249	−	2.02822i	−0.181465	−	0.0660479i
$944$	−8.03364			−0.261473
$945$	−2.67979	−	30.6238i	−0.0871736	−	0.996193i
$946$	−4.80461			−0.156211
$947$	30.8444	+	11.2264i	1.00231	+	0.364810i	0.790474	−	0.612496i	$-0.209834\pi$
$947$	30.8444	+	11.2264i	1.00231	+	0.364810i	0.211834	+	0.977306i	$0.432057\pi$
$948$	59.9386	−	24.8747i	1.94672	−	0.807893i
$949$	−0.617208	−	0.517899i	−0.0200354	−	0.0168117i
$950$	−83.5512	+	5.98683i	−2.71076	+	0.194238i
$951$	11.8626	+	18.5930i	0.384673	+	0.602918i
$952$	12.2864	−	21.5719i	0.398205	−	0.699149i
$953$	−10.6122	−	18.3808i	−0.343762	−	0.595413i	0.641366	−	0.767235i	$-0.278368\pi$
$953$	−10.6122	−	18.3808i	−0.343762	−	0.595413i	−0.985128	+	0.171822i	$0.945035\pi$
$954$	−29.9699	+	14.0244i	−0.970313	+	0.454057i
$955$	2.56243	−	0.316863i	0.0829182	−	0.0102534i
$956$	33.9078	+	40.4098i	1.09666	+	1.30695i
$957$	51.3225	+	16.1439i	1.65902	+	0.521859i
$958$	−36.7368	−	30.8258i	−1.18691	−	0.995936i
$959$	8.28816	−	1.51160i	0.267639	−	0.0488120i
$960$	8.80653	−	47.9257i	0.284229	−	1.54680i
$961$	5.38309	+	30.5290i	0.173648	+	0.984807i
$962$	−76.8155	+	44.3494i	−2.47663	+	1.42988i
$963$	0.157376	+	0.584188i	0.00507139	+	0.0188252i
$964$	−2.34752	−	1.35534i	−0.0756085	−	0.0436526i
$965$	34.2545	+	7.87726i	1.10269	+	0.253578i
$966$	−13.0492	−	1.63124i	−0.419851	−	0.0524843i
$967$	3.59244	+	9.87013i	0.115525	+	0.317402i	0.983957	−	0.178406i	$-0.0570941\pi$
$967$	3.59244	+	9.87013i	0.115525	+	0.317402i	−0.868432	+	0.495808i	$0.834872\pi$
$968$	34.5008	−	12.5572i	1.10890	−	0.403605i
$969$	−4.73380	+	36.1449i	−0.152072	+	1.16114i
$970$	−5.63544	+	24.5059i	−0.180943	+	0.786836i
$971$	0.699752	+	1.21201i	0.0224561	+	0.0388951i	0.877035	−	0.480426i	$-0.159518\pi$
$971$	0.699752	+	1.21201i	0.0224561	+	0.0388951i	−0.854579	+	0.519321i	$0.826185\pi$
$972$	51.5016	−	11.5997i	1.65192	−	0.372061i
$973$	2.68164	−	15.7478i	0.0859693	−	0.504852i
$974$	40.0988	+	47.7879i	1.28485	+	1.53122i
$975$	−3.21614	−	27.6396i	−0.102999	−	0.885174i
$976$	2.90125	−	3.45758i	0.0928668	−	0.110674i
$977$	−10.0066	+	56.7502i	−0.320139	+	1.81560i	0.221697	+	0.975116i	$0.428840\pi$
$977$	−10.0066	+	56.7502i	−0.320139	+	1.81560i	−0.541836	+	0.840484i	$0.682271\pi$
$978$	2.84271	+	64.1178i	0.0908998	+	2.05026i
$979$	−39.3963	+	6.94664i	−1.25911	+	0.222015i
$980$	11.2732	−	51.7960i	0.360109	−	1.65456i
$981$	2.98926	−	2.99732i	0.0954396	−	0.0956971i
$982$		−	66.5528i		−	2.12378i
$983$	−13.1768	−	15.7035i	−0.420275	−	0.500864i	0.513815	−	0.857901i	$-0.328232\pi$
$983$	−13.1768	−	15.7035i	−0.420275	−	0.500864i	−0.934090	+	0.357036i	$0.883787\pi$
$984$	25.5010	+	8.02156i	0.812942	+	0.255718i
$985$	27.6781	−	42.7008i	0.881897	−	1.36056i
$986$	−34.0157	−	28.5426i	−1.08328	−	0.908982i
$987$	−8.53701	−	13.2090i	−0.271736	−	0.420449i
$988$	−26.8641	+	73.8086i	−0.854662	+	2.34817i
$989$		−	0.540725i		−	0.0171941i
$990$	−62.4154	+	39.1933i	−1.98369	+	1.24564i
$991$	−33.7586			−1.07238			−0.536189	−	0.844098i	$-0.680137\pi$
$991$	−33.7586			−1.07238			−0.536189	+	0.844098i	$0.680137\pi$
$992$	−0.0176035	−	0.0209791i	−0.000558913	−	0.000666087i
$993$	21.9692	+	34.4335i	0.697171	+	1.09271i
$994$	−40.5779	+	34.4564i	−1.28705	+	1.09289i
$995$	−16.7041	−	10.8274i	−0.529555	−	0.343250i
$996$	64.2683	+	8.41706i	2.03642	+	0.266705i
$997$	1.37897	+	7.82055i	0.0436725	+	0.247679i	0.998827	−	0.0484301i	$-0.0154218\pi$
$997$	1.37897	+	7.82055i	0.0436725	+	0.247679i	−0.955154	+	0.296109i	$0.904311\pi$
$998$	31.8480	−	55.1624i	1.00813	−	1.74613i
$999$	−57.1478	−	23.5362i	−1.80808	−	0.744654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cq.a.59.17	yes	840
5.4	even	2	inner	945.2.cq.a.59.124	yes	840
7.5	odd	6		945.2.cl.a.194.124	yes	840
27.11	odd	18		945.2.cl.a.794.17	yes	840
35.19	odd	6		945.2.cl.a.194.17	✓	840
135.119	odd	18		945.2.cl.a.794.124	yes	840
189.173	even	18	inner	945.2.cq.a.929.124	yes	840
945.929	even	18	inner	945.2.cq.a.929.17	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cl.a.194.17	✓	840	35.19	odd	6
945.2.cl.a.194.124	yes	840	7.5	odd	6
945.2.cl.a.794.17	yes	840	27.11	odd	18
945.2.cl.a.794.124	yes	840	135.119	odd	18
945.2.cq.a.59.17	yes	840	1.1	even	1	trivial
945.2.cq.a.59.124	yes	840	5.4	even	2	inner
945.2.cq.a.929.17	yes	840	945.929	even	18	inner
945.2.cq.a.929.124	yes	840	189.173	even	18	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cq (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.18094 - 0.793796i) q^{2} +(0.224921 - 1.71738i) q^{3} +(2.59428 + 2.17686i) q^{4} +(1.01687 + 1.99148i) q^{5} +(-1.85379 + 3.56696i) q^{6} +(0.0155159 + 2.64571i) q^{7} +(-1.60908 - 2.78700i) q^{8} +(-2.89882 - 0.772553i) q^{9} +O(q^{10})\)	\(q+(-2.18094 - 0.793796i) q^{2} +(0.224921 - 1.71738i) q^{3} +(2.59428 + 2.17686i) q^{4} +(1.01687 + 1.99148i) q^{5} +(-1.85379 + 3.56696i) q^{6} +(0.0155159 + 2.64571i) q^{7} +(-1.60908 - 2.78700i) q^{8} +(-2.89882 - 0.772553i) q^{9} +(-0.636893 - 5.15047i) q^{10} +(3.04282 + 3.62629i) q^{11} +(4.32202 - 3.96576i) q^{12} +(-2.46136 - 2.06532i) q^{13} +(2.06631 - 5.78243i) q^{14} +(3.64885 - 1.29842i) q^{15} +(0.120830 + 0.685259i) q^{16} +(2.52506 - 1.45785i) q^{17} +(5.70889 + 3.98596i) q^{18} +(-6.25127 - 3.60917i) q^{19} +(-1.69713 + 7.38003i) q^{20} +(4.54718 + 0.568429i) q^{21} +(-3.75766 - 10.3241i) q^{22} +(1.16190 - 0.422899i) q^{23} +(-5.14827 + 2.13655i) q^{24} +(-2.93197 + 4.05013i) q^{25} +(3.72862 + 6.45816i) q^{26} +(-1.97878 + 4.80463i) q^{27} +(-5.71908 + 6.89748i) q^{28} +(4.21789 + 5.02668i) q^{29} +(-8.98859 - 0.0646607i) q^{30} +(-0.00365117 + 0.00435129i) q^{31} +(-0.837218 + 4.74810i) q^{32} +(6.91213 - 4.41006i) q^{33} +(-6.66423 + 1.17508i) q^{34} +(-5.25309 + 2.72123i) q^{35} +(-5.83862 - 8.31455i) q^{36} +11.8943i q^{37} +(10.7687 + 12.8336i) q^{38} +(-4.10057 + 3.76256i) q^{39} +(3.91404 - 6.03844i) q^{40} +(-3.67394 - 3.08281i) q^{41} +(-9.46590 - 4.84924i) q^{42} +(0.149570 - 0.410940i) q^{43} +16.0314i q^{44} +(-1.40919 - 6.55852i) q^{45} -2.86973 q^{46} +(-2.20608 - 2.62911i) q^{47} +(1.20403 - 0.0533816i) q^{48} +(-6.99952 + 0.0821008i) q^{49} +(9.60941 - 6.50569i) q^{50} +(-1.93574 - 4.66441i) q^{51} +(-1.88953 - 10.7161i) q^{52} +(-2.37616 + 4.11562i) q^{53} +(8.12948 - 8.90784i) q^{54} +(-4.12754 + 9.74715i) q^{55} +(7.34862 - 4.30038i) q^{56} +(-7.60438 + 9.92405i) q^{57} +(-5.20878 - 14.3110i) q^{58} +(-2.00484 + 11.3700i) q^{59} +(12.2926 + 4.57456i) q^{60} +(-4.16948 - 4.96899i) q^{61} +(0.0114170 - 0.00659161i) q^{62} +(1.99897 - 7.68141i) q^{63} +(6.29077 - 10.8959i) q^{64} +(1.61018 - 7.00190i) q^{65} +(-18.5756 + 4.13124i) q^{66} +(4.06185 + 11.1598i) q^{67} +(9.72425 + 1.71465i) q^{68} +(-0.464942 - 2.09056i) q^{69} +(13.6167 - 1.76494i) q^{70} +(-7.50774 - 4.33460i) q^{71} +(2.51132 + 9.32211i) q^{72} +0.250759 q^{73} +(9.44167 - 25.9408i) q^{74} +(6.29617 + 5.94628i) q^{75} +(-8.36088 - 22.9713i) q^{76} +(-9.54688 + 8.10666i) q^{77} +(11.9298 - 4.95090i) q^{78} +(10.3962 + 3.78391i) q^{79} +(-1.24181 + 0.937446i) q^{80} +(7.80632 + 4.47899i) q^{81} +(5.56552 + 9.63976i) q^{82} +(7.10287 + 8.46487i) q^{83} +(10.5593 + 11.3733i) q^{84} +(5.47092 + 3.54617i) q^{85} +(-0.652404 + 0.777505i) q^{86} +(9.58144 - 6.11313i) q^{87} +(5.21034 - 14.3153i) q^{88} +(-4.22538 + 7.31858i) q^{89} +(-2.13277 + 15.4223i) q^{90} +(5.42605 - 6.54407i) q^{91} +(3.93490 + 1.43219i) q^{92} +(0.00665162 + 0.00724916i) q^{93} +(2.72435 + 7.48510i) q^{94} +(0.830883 - 16.1193i) q^{95} +(7.96601 + 2.50577i) q^{96} +(-4.55306 - 1.65718i) q^{97} +(15.3307 + 5.37713i) q^{98} +(-6.01908 - 12.8627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 6 q^{4} - 9 q^{5} + 18 q^{6} + 6 q^{9}+O(q^{10}) \) 840 * q - 6 * q^4 - 9 * q^5 + 18 * q^6 + 6 * q^9	\( 840 q - 6 q^{4} - 9 q^{5} + 18 q^{6} + 6 q^{9} - 9 q^{10} + 6 q^{11} - 6 q^{14} + 18 q^{16} - 18 q^{19} + 18 q^{20} - 30 q^{21} + 36 q^{24} - 3 q^{25} - 42 q^{29} + 33 q^{30} - 18 q^{31} - 36 q^{34} - 9 q^{35} - 42 q^{36} - 90 q^{39} - 9 q^{40} - 9 q^{45} - 12 q^{46} - 48 q^{49} - 48 q^{50} - 42 q^{51} - 144 q^{54} - 42 q^{56} - 18 q^{59} + 57 q^{60} - 72 q^{61} - 348 q^{64} - 54 q^{65} - 18 q^{66} + 21 q^{70} - 36 q^{71} + 42 q^{74} - 9 q^{75} - 72 q^{76} + 12 q^{79} + 72 q^{80} - 162 q^{81} + 78 q^{84} + 3 q^{85} + 168 q^{86} - 18 q^{89} - 81 q^{90} - 6 q^{91} - 18 q^{94} - 93 q^{95} - 18 q^{96} - 60 q^{99}+O(q^{100}) \) 840 * q - 6 * q^4 - 9 * q^5 + 18 * q^6 + 6 * q^9 - 9 * q^10 + 6 * q^11 - 6 * q^14 + 18 * q^16 - 18 * q^19 + 18 * q^20 - 30 * q^21 + 36 * q^24 - 3 * q^25 - 42 * q^29 + 33 * q^30 - 18 * q^31 - 36 * q^34 - 9 * q^35 - 42 * q^36 - 90 * q^39 - 9 * q^40 - 9 * q^45 - 12 * q^46 - 48 * q^49 - 48 * q^50 - 42 * q^51 - 144 * q^54 - 42 * q^56 - 18 * q^59 + 57 * q^60 - 72 * q^61 - 348 * q^64 - 54 * q^65 - 18 * q^66 + 21 * q^70 - 36 * q^71 + 42 * q^74 - 9 * q^75 - 72 * q^76 + 12 * q^79 + 72 * q^80 - 162 * q^81 + 78 * q^84 + 3 * q^85 + 168 * q^86 - 18 * q^89 - 81 * q^90 - 6 * q^91 - 18 * q^94 - 93 * q^95 - 18 * q^96 - 60 * q^99

Introduction

L-functions

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