LMFDB - Embedded newform 945.2.dh.a.137.122

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(23,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 27, 12]))

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

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

chi := DirichletCharacter("945.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.dh (of order $36$, degree $12$, 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:	$1680$
Relative dimension:	$140$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			137.122
Character	$\chi$	$=$	945.137
Dual form			945.2.dh.a.338.122

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.932323 - 1.99937i) q^{2} +(1.33056 - 1.10888i) q^{3} +(-1.84269 - 2.19603i) q^{4} +(1.73673 + 1.40846i) q^{5} +(-0.976541 - 3.69412i) q^{6} +(1.91548 - 1.82509i) q^{7} +(-1.84688 + 0.494869i) q^{8} +(0.540792 - 2.95085i) q^{9} +O(q^{10})$	\(q+(0.932323 - 1.99937i) q^{2} +(1.33056 - 1.10888i) q^{3} +(-1.84269 - 2.19603i) q^{4} +(1.73673 + 1.40846i) q^{5} +(-0.976541 - 3.69412i) q^{6} +(1.91548 - 1.82509i) q^{7} +(-1.84688 + 0.494869i) q^{8} +(0.540792 - 2.95085i) q^{9} +(4.43524 - 2.15923i) q^{10} +(1.45451 + 3.99622i) q^{11} +(-4.88694 - 0.878644i) q^{12} +(0.104503 + 0.0731741i) q^{13} +(-1.86319 - 5.53132i) q^{14} +(3.87264 - 0.0517672i) q^{15} +(0.263142 - 1.49235i) q^{16} +(-1.34669 + 1.34669i) q^{17} +(-5.39567 - 3.83239i) q^{18} +2.56978i q^{19} +(-0.107221 - 6.40927i) q^{20} +(0.524868 - 4.55242i) q^{21} +(9.34601 + 0.817670i) q^{22} +(-3.04390 + 4.34714i) q^{23} +(-1.90864 + 2.70641i) q^{24} +(1.03246 + 4.89224i) q^{25} +(0.243733 - 0.140719i) q^{26} +(-2.55257 - 4.52597i) q^{27} +(-7.53758 - 0.843380i) q^{28} +(0.465271 - 2.63868i) q^{29} +(3.50705 - 7.79111i) q^{30} +(-0.139069 + 0.116692i) q^{31} +(-5.87092 - 4.11086i) q^{32} +(6.36662 + 3.70436i) q^{33} +(1.43699 + 3.94810i) q^{34} +(5.89724 - 0.471802i) q^{35} +(-7.47668 + 4.24991i) q^{36} +(-0.829150 + 0.222170i) q^{37} +(5.13794 + 2.39586i) q^{38} +(0.220189 - 0.0185186i) q^{39} +(-3.90453 - 1.74181i) q^{40} +(-10.1168 + 1.78386i) q^{41} +(-8.61263 - 5.29373i) q^{42} +(-12.2381 + 1.07069i) q^{43} +(6.09563 - 10.5579i) q^{44} +(5.09538 - 4.36315i) q^{45} +(5.85365 + 10.1388i) q^{46} +(3.87980 - 0.339439i) q^{47} +(-1.30471 - 2.27746i) q^{48} +(0.338110 - 6.99183i) q^{49} +(10.7440 + 2.49688i) q^{50} +(-0.298545 + 3.28518i) q^{51} +(-0.0318747 - 0.364330i) q^{52} +(-10.6064 + 2.84198i) q^{53} +(-11.4289 + 0.883883i) q^{54} +(-3.10245 + 8.98898i) q^{55} +(-2.63447 + 4.31862i) q^{56} +(2.84956 + 3.41925i) q^{57} +(-4.84192 - 3.39035i) q^{58} +(0.718579 + 4.07526i) q^{59} +(-7.24975 - 8.40904i) q^{60} +(1.73808 + 1.45842i) q^{61} +(0.103655 + 0.386845i) q^{62} +(-4.34969 - 6.63929i) q^{63} +(-11.0680 + 6.39013i) q^{64} +(0.0784311 + 0.274273i) q^{65} +(13.3421 - 9.27560i) q^{66} +(-5.72038 - 12.2674i) q^{67} +(5.43892 + 0.475844i) q^{68} +(0.770337 + 9.15944i) q^{69} +(4.55482 - 12.2306i) q^{70} +(3.39061 - 1.95757i) q^{71} +(0.461512 + 5.71749i) q^{72} +(-6.39550 - 1.71367i) q^{73} +(-0.328835 + 1.86491i) q^{74} +(6.79864 + 5.36456i) q^{75} +(5.64331 - 4.73530i) q^{76} +(10.0795 + 5.00008i) q^{77} +(0.168262 - 0.457506i) q^{78} +(4.32870 + 11.8930i) q^{79} +(2.55893 - 2.22119i) q^{80} +(-8.41509 - 3.19159i) q^{81} +(-5.86550 + 21.8903i) q^{82} +(2.43111 - 1.70228i) q^{83} +(-10.9644 + 7.23606i) q^{84} +(-4.23562 + 0.442073i) q^{85} +(-9.26912 + 25.4667i) q^{86} +(-2.30690 - 4.02686i) q^{87} +(-4.66390 - 6.66074i) q^{88} +16.4623 q^{89} +(-3.97302 - 14.2554i) q^{90} +(0.333723 - 0.0505646i) q^{91} +(15.1554 - 1.32593i) q^{92} +(-0.0556421 + 0.309476i) q^{93} +(2.93856 - 8.07363i) q^{94} +(-3.61944 + 4.46301i) q^{95} +(-12.3701 + 1.04036i) q^{96} +(-0.505228 - 5.77479i) q^{97} +(-13.6640 - 7.19465i) q^{98} +(12.5789 - 2.13091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1680 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 36 q^{6} - 12 q^{7} - 36 q^{8}+O(q^{10}) $ 1680 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 36 * q^6 - 12 * q^7 - 36 * q^8	$ 1680 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 36 q^{6} - 12 q^{7} - 36 q^{8} - 12 q^{10} - 24 q^{11} - 6 q^{12} - 24 q^{13} - 24 q^{15} - 12 q^{16} - 6 q^{18} - 24 q^{20} - 24 q^{21} - 24 q^{22} - 30 q^{23} - 6 q^{25} - 24 q^{27} - 24 q^{28} + 30 q^{30} - 12 q^{31} - 18 q^{32} - 6 q^{33} - 72 q^{35} - 84 q^{36} + 6 q^{37} + 42 q^{38} + 90 q^{40} - 72 q^{41} + 36 q^{42} - 24 q^{43} - 6 q^{45} + 12 q^{46} - 6 q^{47} - 96 q^{48} - 72 q^{50} - 12 q^{51} - 30 q^{52} + 90 q^{53} - 48 q^{55} - 180 q^{56} - 24 q^{57} - 6 q^{58} - 102 q^{60} - 84 q^{61} - 36 q^{62} - 54 q^{63} - 78 q^{65} - 12 q^{66} - 6 q^{67} - 246 q^{68} - 12 q^{70} - 72 q^{71} - 126 q^{72} + 6 q^{73} + 66 q^{75} - 12 q^{77} - 84 q^{78} - 24 q^{81} - 12 q^{82} - 24 q^{83} - 24 q^{85} + 204 q^{86} - 102 q^{87} - 78 q^{88} + 30 q^{90} - 12 q^{91} + 108 q^{92} - 78 q^{93} + 114 q^{95} + 204 q^{96} - 24 q^{97} - 18 q^{98}+O(q^{100}) $ 1680 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 36 * q^6 - 12 * q^7 - 36 * q^8 - 12 * q^10 - 24 * q^11 - 6 * q^12 - 24 * q^13 - 24 * q^15 - 12 * q^16 - 6 * q^18 - 24 * q^20 - 24 * q^21 - 24 * q^22 - 30 * q^23 - 6 * q^25 - 24 * q^27 - 24 * q^28 + 30 * q^30 - 12 * q^31 - 18 * q^32 - 6 * q^33 - 72 * q^35 - 84 * q^36 + 6 * q^37 + 42 * q^38 + 90 * q^40 - 72 * q^41 + 36 * q^42 - 24 * q^43 - 6 * q^45 + 12 * q^46 - 6 * q^47 - 96 * q^48 - 72 * q^50 - 12 * q^51 - 30 * q^52 + 90 * q^53 - 48 * q^55 - 180 * q^56 - 24 * q^57 - 6 * q^58 - 102 * q^60 - 84 * q^61 - 36 * q^62 - 54 * q^63 - 78 * q^65 - 12 * q^66 - 6 * q^67 - 246 * q^68 - 12 * q^70 - 72 * q^71 - 126 * q^72 + 6 * q^73 + 66 * q^75 - 12 * q^77 - 84 * q^78 - 24 * q^81 - 12 * q^82 - 24 * q^83 - 24 * q^85 + 204 * q^86 - 102 * q^87 - 78 * q^88 + 30 * q^90 - 12 * q^91 + 108 * q^92 - 78 * q^93 + 114 * q^95 + 204 * q^96 - 24 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.932323	−	1.99937i	0.659252	−	1.41377i	−0.237567	−	0.971371i	$-0.576350\pi$
$2$	0.932323	−	1.99937i	0.659252	−	1.41377i	0.896819	−	0.442399i	$-0.145872\pi$
$3$	1.33056	−	1.10888i	0.768200	−	0.640209i
$3$	1.33056	−	1.10888i	0.768200	−	0.640209i
$4$	−1.84269	−	2.19603i	−0.921344	−	1.09802i
$5$	1.73673	+	1.40846i	0.776689	+	0.629884i
$5$	1.73673	+	1.40846i	0.776689	+	0.629884i
$6$	−0.976541	−	3.69412i	−0.398671	−	1.50812i
$7$	1.91548	−	1.82509i	0.723983	−	0.689818i
$7$	1.91548	−	1.82509i	0.723983	−	0.689818i
$8$	−1.84688	+	0.494869i	−0.652970	+	0.174963i
$9$	0.540792	−	2.95085i	0.180264	−	0.983618i
$10$	4.43524	−	2.15923i	1.40254	−	0.682807i
$11$	1.45451	+	3.99622i	0.438550	+	1.20491i	0.940435	+	0.339973i	$0.110418\pi$
$11$	1.45451	+	3.99622i	0.438550	+	1.20491i	−0.501885	+	0.864934i	$0.667360\pi$
$12$	−4.88694	−	0.878644i	−1.41074	−	0.253643i
$13$	0.104503	+	0.0731741i	0.0289840	+	0.0202948i	0.587979	−	0.808876i	$-0.299924\pi$
$13$	0.104503	+	0.0731741i	0.0289840	+	0.0202948i	−0.558995	+	0.829171i	$0.688813\pi$
$14$	−1.86319	−	5.53132i	−0.497957	−	1.47831i
$15$	3.87264	−	0.0517672i	0.999911	−	0.0133662i
$16$	0.263142	−	1.49235i	0.0657856	−	0.373089i
$17$	−1.34669	+	1.34669i	−0.326621	+	0.326621i	−0.851300	−	0.524679i	$-0.824185\pi$
$17$	−1.34669	+	1.34669i	−0.326621	+	0.326621i	0.524679	+	0.851300i	$0.324185\pi$
$18$	−5.39567	−	3.83239i	−1.27177	−	0.903304i
$19$			2.56978i			0.589547i	0.955567	+	0.294774i	$0.0952442\pi$
$19$			2.56978i			0.589547i	−0.955567	+	0.294774i	$0.904756\pi$
$20$	−0.107221	−	6.40927i	−0.0239754	−	1.43316i
$21$	0.524868	−	4.55242i	0.114536	−	0.993419i
$22$	9.34601	+	0.817670i	1.99258	+	0.174328i
$23$	−3.04390	+	4.34714i	−0.634697	+	0.906441i	−0.999698	−	0.0245660i	$-0.992180\pi$
$23$	−3.04390	+	4.34714i	−0.634697	+	0.906441i	0.365001	+	0.931007i	$0.381069\pi$
$24$	−1.90864	+	2.70641i	−0.389599	+	0.552444i
$25$	1.03246	+	4.89224i	0.206492	+	0.978448i
$26$	0.243733	−	0.140719i	0.0478000	−	0.0275974i
$27$	−2.55257	−	4.52597i	−0.491243	−	0.871023i
$28$	−7.53758	−	0.843380i	−1.42447	−	0.159384i
$29$	0.465271	−	2.63868i	0.0863986	−	0.489991i	−0.910647	−	0.413184i	$-0.864417\pi$
$29$	0.465271	−	2.63868i	0.0863986	−	0.489991i	0.997046	−	0.0768065i	$-0.0244724\pi$
$30$	3.50705	−	7.79111i	0.640296	−	1.42246i
$31$	−0.139069	+	0.116692i	−0.0249775	+	0.0209586i	−0.655191	−	0.755463i	$-0.727412\pi$
$31$	−0.139069	+	0.116692i	−0.0249775	+	0.0209586i	0.630213	+	0.776422i	$0.282967\pi$
$32$	−5.87092	−	4.11086i	−1.03784	−	0.726705i
$33$	6.36662	+	3.70436i	1.10829	+	0.644846i
$34$	1.43699	+	3.94810i	0.246442	+	0.677093i
$35$	5.89724	−	0.471802i	0.996815	−	0.0797491i
$36$	−7.47668	+	4.24991i	−1.24611	+	0.708319i
$37$	−0.829150	+	0.222170i	−0.136311	+	0.0365245i	−0.326330	−	0.945256i	$-0.605812\pi$
$37$	−0.829150	+	0.222170i	−0.136311	+	0.0365245i	0.190018	+	0.981781i	$0.439145\pi$
$38$	5.13794	+	2.39586i	0.833484	+	0.388660i
$39$	0.220189	−	0.0185186i	0.0352585	−	0.00296535i
$40$	−3.90453	−	1.74181i	−0.617360	−	0.275404i
$41$	−10.1168	+	1.78386i	−1.57997	+	0.278592i	−0.893671	−	0.448723i	$-0.851879\pi$
$41$	−10.1168	+	1.78386i	−1.57997	+	0.278592i	−0.686304	+	0.727315i	$0.740768\pi$
$42$	−8.61263	−	5.29373i	−1.32896	−	0.816840i
$43$	−12.2381	+	1.07069i	−1.86629	+	0.163279i	−0.963658	−	0.267139i	$-0.913922\pi$
$43$	−12.2381	+	1.07069i	−1.86629	+	0.163279i	−0.902630	+	0.430418i	$0.858366\pi$
$44$	6.09563	−	10.5579i	0.918951	−	1.59167i
$45$	5.09538	−	4.36315i	0.759575	−	0.650420i
$46$	5.85365	+	10.1388i	0.863074	+	1.49489i
$47$	3.87980	−	0.339439i	0.565927	−	0.0495122i	0.199398	−	0.979919i	$-0.436101\pi$
$47$	3.87980	−	0.339439i	0.565927	−	0.0495122i	0.366529	+	0.930406i	$0.380546\pi$
$48$	−1.30471	−	2.27746i	−0.188318	−	0.328723i
$49$	0.338110	−	6.99183i	0.0483015	−	0.998833i
$50$	10.7440	+	2.49688i	1.51943	+	0.353112i
$51$	−0.298545	+	3.28518i	−0.0418046	+	0.460017i
$52$	−0.0318747	−	0.364330i	−0.00442023	−	0.0505235i
$53$	−10.6064	+	2.84198i	−1.45690	+	0.390375i	−0.898418	−	0.439141i	$-0.855283\pi$
$53$	−10.6064	+	2.84198i	−1.45690	+	0.390375i	−0.558483	+	0.829516i	$0.688616\pi$
$54$	−11.4289	+	0.883883i	−1.55528	+	0.120281i
$55$	−3.10245	+	8.98898i	−0.418335	+	1.21207i
$56$	−2.63447	+	4.31862i	−0.352046	+	0.577100i
$57$	2.84956	+	3.41925i	0.377434	+	0.452890i
$58$	−4.84192	−	3.39035i	−0.635776	−	0.445175i
$59$	0.718579	+	4.07526i	0.0935510	+	0.530554i	0.995182	+	0.0980473i	$0.0312597\pi$
$59$	0.718579	+	4.07526i	0.0935510	+	0.530554i	−0.901631	+	0.432507i	$0.857629\pi$
$60$	−7.24975	−	8.40904i	−0.935938	−	1.08560i
$61$	1.73808	+	1.45842i	0.222539	+	0.186732i	0.747240	−	0.664554i	$-0.231379\pi$
$61$	1.73808	+	1.45842i	0.222539	+	0.186732i	−0.524701	+	0.851286i	$0.675823\pi$
$62$	0.103655	+	0.386845i	0.0131642	+	0.0491294i
$63$	−4.34969	−	6.63929i	−0.548010	−	0.836472i
$64$	−11.0680	+	6.39013i	−1.38350	+	0.798766i
$65$	0.0784311	+	0.274273i	0.00972819	+	0.0340194i
$66$	13.3421	−	9.27560i	1.64230	−	1.14175i
$67$	−5.72038	−	12.2674i	−0.698856	−	1.49870i	−0.859200	−	0.511640i	$-0.829038\pi$
$67$	−5.72038	−	12.2674i	−0.698856	−	1.49870i	0.160345	−	0.987061i	$-0.448739\pi$
$68$	5.43892	+	0.475844i	0.659566	+	0.0577046i
$69$	0.770337	+	9.15944i	0.0927377	+	1.10267i
$70$	4.55482	−	12.2306i	0.544405	−	1.46184i
$71$	3.39061	−	1.95757i	0.402391	−	0.232321i	−0.285124	−	0.958491i	$-0.592035\pi$
$71$	3.39061	−	1.95757i	0.402391	−	0.232321i	0.687515	+	0.726170i	$0.258701\pi$
$72$	0.461512	+	5.71749i	0.0543897	+	0.673812i
$73$	−6.39550	−	1.71367i	−0.748536	−	0.200570i	−0.135668	−	0.990754i	$-0.543318\pi$
$73$	−6.39550	−	1.71367i	−0.748536	−	0.200570i	−0.612869	+	0.790185i	$0.709985\pi$
$74$	−0.328835	+	1.86491i	−0.0382263	+	0.216792i
$75$	6.79864	+	5.36456i	0.785039	+	0.619447i
$76$	5.64331	−	4.73530i	0.647332	−	0.543176i
$77$	10.0795	+	5.00008i	1.14867	+	0.569812i
$78$	0.168262	−	0.457506i	0.0190519	−	0.0518023i
$79$	4.32870	+	11.8930i	0.487017	+	1.33807i	0.903369	+	0.428864i	$0.141086\pi$
$79$	4.32870	+	11.8930i	0.487017	+	1.33807i	−0.416352	+	0.909203i	$0.636692\pi$
$80$	2.55893	−	2.22119i	0.286098	−	0.248336i
$81$	−8.41509	−	3.19159i	−0.935010	−	0.354622i
$82$	−5.86550	+	21.8903i	−0.647736	+	2.41738i
$83$	2.43111	−	1.70228i	0.266849	−	0.186850i	−0.432492	−	0.901638i	$-0.642366\pi$
$83$	2.43111	−	1.70228i	0.266849	−	0.186850i	0.699341	+	0.714788i	$0.253477\pi$
$84$	−10.9644	+	7.23606i	−1.19632	+	0.789519i
$85$	−4.23562	+	0.442073i	−0.459417	+	0.0479496i
$86$	−9.26912	+	25.4667i	−0.999514	+	2.74614i
$87$	−2.30690	−	4.02686i	−0.247325	−	0.431724i
$88$	−4.66390	−	6.66074i	−0.497174	−	0.710038i
$89$	16.4623			1.74500			0.872499	−	0.488616i	$-0.162498\pi$
$89$	16.4623			1.74500			0.872499	+	0.488616i	$0.162498\pi$
$90$	−3.97302	−	14.2554i	−0.418793	−	1.50265i
$91$	0.333723	−	0.0505646i	0.0349837	−	0.00530061i
$92$	15.1554	−	1.32593i	1.58006	−	0.138237i
$93$	−0.0556421	+	0.309476i	−0.00576982	+	0.0320912i
$94$	2.93856	−	8.07363i	0.303089	−	0.832731i
$95$	−3.61944	+	4.46301i	−0.371346	+	0.457895i
$96$	−12.3701	+	1.04036i	−1.26251	+	0.106181i
$97$	−0.505228	−	5.77479i	−0.0512982	−	0.586341i	−0.977728	−	0.209874i	$-0.932695\pi$
$97$	−0.505228	−	5.77479i	−0.0512982	−	0.586341i	0.926430	−	0.376467i	$-0.122861\pi$
$98$	−13.6640	−	7.19465i	−1.38028	−	0.726769i
$99$	12.5789	−	2.13091i	1.26422	−	0.214165i
$100$	8.84102	−	11.2822i	0.884102	−	1.12822i
$101$	10.0069	+	1.76449i	0.995724	+	0.175573i	0.647686	−	0.761908i	$-0.275737\pi$
$101$	10.0069	+	1.76449i	0.995724	+	0.175573i	0.348038	+	0.937480i	$0.386848\pi$
$102$	6.28995	+	3.65975i	0.622798	+	0.362369i
$103$	−3.81245	+	1.77777i	−0.375652	+	0.175169i	−0.601269	−	0.799047i	$-0.705338\pi$
$103$	−3.81245	+	1.77777i	−0.375652	+	0.175169i	0.225617	+	0.974216i	$0.427560\pi$
$104$	−0.229217	−	0.0834280i	−0.0224765	−	0.00818079i
$105$	7.32347	−	7.16706i	0.714698	−	0.699434i
$106$	−4.20642	+	23.8558i	−0.408563	+	2.31708i
$107$	3.95536	+	1.05984i	0.382379	+	0.102458i	0.444888	−	0.895586i	$-0.353244\pi$
$107$	3.95536	+	1.05984i	0.382379	+	0.102458i	−0.0625089	+	0.998044i	$0.519910\pi$
$108$	−5.23556	+	13.9455i	−0.503792	+	1.34190i
$109$	2.74723	+	1.58611i	0.263137	+	0.151922i	0.625765	−	0.780012i	$-0.284787\pi$
$109$	2.74723	+	1.58611i	0.263137	+	0.151922i	−0.362628	+	0.931934i	$0.618120\pi$
$110$	15.0798	+	14.5836i	1.43781	+	1.39049i
$111$	−0.856877	+	1.21504i	−0.0813312	+	0.115326i
$112$	−2.21963	−	3.33883i	−0.209736	−	0.315490i
$113$	−2.75320	−	0.240874i	−0.259000	−	0.0226595i	−0.0430836	−	0.999071i	$-0.513718\pi$
$113$	−2.75320	−	0.240874i	−0.259000	−	0.0226595i	−0.215916	+	0.976412i	$0.569274\pi$
$114$	9.49306	−	2.50949i	0.889106	−	0.235035i
$115$	−11.4092	+	3.26258i	−1.06391	+	0.304237i
$116$	−6.65197	+	3.84052i	−0.617620	+	0.356583i
$117$	0.272441	−	0.268803i	0.0251872	−	0.0248508i
$118$	8.81791	+	2.36275i	0.811755	+	0.217509i
$119$	−0.121728	+	5.03740i	−0.0111588	+	0.461778i
$120$	−7.12667	+	2.01206i	−0.650573	+	0.183675i
$121$	−5.42773	+	4.55440i	−0.493430	+	0.414037i
$122$	4.53639	−	2.11535i	0.410705	−	0.191515i
$123$	−11.4829	+	13.5918i	−1.03538	+	1.22553i
$124$	0.512521	+	0.0903712i	0.0460257	+	0.00811557i
$125$	−5.09745	+	9.95068i	−0.455929	+	0.890016i
$126$	−17.3297	+	2.50670i	−1.54385	+	0.223315i
$127$	−7.16793	+	1.92064i	−0.636051	+	0.170429i	−0.562414	−	0.826856i	$-0.690127\pi$
$127$	−7.16793	+	1.92064i	−0.636051	+	0.170429i	−0.0736371	+	0.997285i	$0.523461\pi$
$128$	1.20797	+	13.8072i	0.106771	+	1.22039i
$129$	−15.0962	+	14.9951i	−1.32915	+	1.32025i
$130$	0.621497	+	0.0988979i	0.0545089	+	0.00867392i
$131$	7.75558	−	1.36752i	0.677608	−	0.119481i	0.175756	−	0.984434i	$-0.443763\pi$
$131$	7.75558	−	1.36752i	0.677608	−	0.119481i	0.501853	+	0.864953i	$0.332652\pi$
$132$	−3.59682	−	20.8073i	−0.313063	−	1.81104i
$133$	4.69007	+	4.92235i	0.406680	+	0.426822i
$134$	−29.8603			−2.57954
$135$	1.94153	−	11.4556i	0.167100	−	0.985940i
$136$	1.82074	−	3.15362i	0.156127	−	0.270420i
$137$	15.8642	−	1.38794i	1.35537	−	0.118580i	0.613804	−	0.789459i	$-0.289639\pi$
$137$	15.8642	−	1.38794i	1.35537	−	0.118580i	0.741567	+	0.670879i	$0.234083\pi$
$138$	19.0313	+	6.99936i	1.62006	+	0.595825i
$139$	7.80023	−	21.4310i	0.661607	−	1.81775i	0.0921223	−	0.995748i	$-0.470635\pi$
$139$	7.80023	−	21.4310i	0.661607	−	1.81775i	0.569485	−	0.822002i	$-0.307143\pi$
$140$	−11.9029	−	12.0811i	−1.00598	−	1.02104i
$141$	4.78592	−	4.75386i	0.403047	−	0.400347i
$142$	−0.752768	−	8.60417i	−0.0631709	−	0.722046i
$143$	−0.140419	+	0.524051i	−0.0117424	+	0.0438234i
$144$	−4.26142	−	1.58355i	−0.355118	−	0.131962i
$145$	4.52454	−	3.92736i	0.375742	−	0.326149i
$146$	−9.38893	+	11.1893i	−0.777033	+	0.926032i
$147$	−7.30319	−	9.67799i	−0.602357	−	0.798227i
$148$	2.01576	+	1.41145i	0.165694	+	0.116020i
$149$	−1.24619	+	1.04567i	−0.102092	+	0.0856650i	−0.692405	−	0.721509i	$-0.743449\pi$
$149$	−1.24619	+	1.04567i	−0.102092	+	0.0856650i	0.590313	+	0.807174i	$0.299004\pi$
$150$	17.0643	−	8.59150i	1.39329	−	0.701493i
$151$	1.39993	−	0.509532i	0.113924	−	0.0414651i	−0.284429	−	0.958697i	$-0.591804\pi$
$151$	1.39993	−	0.509532i	0.113924	−	0.0414651i	0.398353	+	0.917232i	$0.369582\pi$
$152$	−1.27170	−	4.74606i	−0.103149	−	0.384956i
$153$	3.24562	+	4.70218i	0.262393	+	0.380149i
$154$	19.3944	−	15.4911i	1.56284	−	1.24830i
$155$	−0.405882	+	0.00679003i	−0.0326012	+	0.000545388i
$156$	−0.446408	−	0.449419i	−0.0357412	−	0.0359823i
$157$	5.09485	−	7.27620i	0.406614	−	0.580704i	−0.562660	−	0.826688i	$-0.690222\pi$
$157$	5.09485	−	7.27620i	0.406614	−	0.580704i	0.969274	+	0.245984i	$0.0791110\pi$
$158$	27.8143	+	2.43343i	2.21279	+	0.193594i
$159$	−10.9611	+	15.5426i	−0.869270	+	1.23261i
$160$	−4.40620	−	15.4084i	−0.348341	−	1.21814i
$161$	2.10339	+	13.8822i	0.165770	+	1.09407i
$162$	−14.2268	+	13.8493i	−1.11776	+	1.08810i
$163$	−0.167712	−	0.0449382i	−0.0131362	−	0.00351983i	0.252245	−	0.967663i	$-0.418831\pi$
$163$	−0.167712	−	0.0449382i	−0.0131362	−	0.00351983i	−0.265381	+	0.964144i	$0.585498\pi$
$164$	22.5595	+	18.9297i	1.76160	+	1.47816i
$165$	5.83965	+	15.4006i	0.454616	+	1.19894i
$166$	−1.13692	−	6.44778i	−0.0882419	−	0.500445i
$167$	2.00334	−	22.8982i	0.155023	−	1.77192i	−0.377988	−	0.925811i	$-0.623384\pi$
$167$	2.00334	−	22.8982i	0.155023	−	1.77192i	0.533011	−	0.846109i	$-0.321061\pi$
$168$	1.28349	+	8.66750i	0.0990230	+	0.668712i
$169$	−4.44070	−	12.2007i	−0.341592	−	0.938516i
$170$	−3.06509	+	8.88073i	−0.235082	+	0.681121i
$171$	7.58304	+	1.38971i	0.579889	+	0.106274i
$172$	24.9022	+	24.9022i	1.89878	+	1.89878i
$173$	−5.39871	+	3.78022i	−0.410457	+	0.287405i	−0.760512	−	0.649324i	$-0.775052\pi$
$173$	−5.39871	+	3.78022i	−0.410457	+	0.287405i	0.350055	+	0.936729i	$0.386163\pi$
$174$	−10.2020	+	0.858016i	−0.773408	+	0.0650460i
$175$	10.9064	+	7.48665i	0.824448	+	0.565938i
$176$	6.34652	−	1.11906i	0.478387	−	0.0843526i
$177$	5.47507	+	4.62558i	0.411531	+	0.347680i
$178$	15.3482	−	32.9142i	1.15039	−	2.46702i
$179$	10.0682			0.752533			0.376266	−	0.926512i	$-0.377208\pi$
$179$	10.0682			0.752533			0.376266	+	0.926512i	$0.377208\pi$
$180$	−18.9708	−	3.14969i	−1.41400	−	0.234764i
$181$	1.31310	−	2.27436i	0.0976020	−	0.169052i	−0.813090	−	0.582139i	$-0.802216\pi$
$181$	1.31310	−	2.27436i	0.0976020	−	0.169052i	0.910692	+	0.413087i	$0.135549\pi$
$182$	0.210040	−	0.714379i	0.0155692	−	0.0529533i
$183$	3.92984	+	0.0132078i	0.290502	+	0.000976345i
$184$	3.47044	−	9.53496i	0.255844	−	0.702927i
$185$	−1.75293	−	0.781979i	−0.128878	−	0.0574922i
$186$	0.566882	+	0.399781i	0.0415658	+	0.0293134i
$187$	−7.34047	−	3.42292i	−0.536788	−	0.250309i
$188$	−7.89468	−	7.89468i	−0.575779	−	0.575779i
$189$	−13.1497	−	4.01072i	−0.956499	−	0.291737i
$190$	5.54873	+	11.3976i	0.402547	+	0.826866i
$191$	2.80784	+	7.71448i	0.203168	+	0.558201i	0.998872	−	0.0474858i	$-0.0151209\pi$
$191$	2.80784	+	7.71448i	0.203168	+	0.558201i	−0.795704	+	0.605686i	$0.792899\pi$
$192$	−7.64084	+	20.7755i	−0.551430	+	1.49934i
$193$	−0.949558	+	10.8535i	−0.0683507	+	0.781252i	0.882239	+	0.470802i	$0.156035\pi$
$193$	−0.949558	+	10.8535i	−0.0683507	+	0.781252i	−0.950590	+	0.310450i	$0.899520\pi$
$194$	−12.0170	−	4.37382i	−0.862769	−	0.314022i
$195$	0.408492	+	0.277967i	0.0292527	+	0.0199056i
$196$	−15.9773	+	12.1413i	−1.14124	+	0.867233i
$197$	5.71010	+	21.3104i	0.406828	+	1.51830i	0.800660	+	0.599119i	$0.204482\pi$
$197$	5.71010	+	21.3104i	0.406828	+	1.51830i	−0.393832	+	0.919182i	$0.628851\pi$
$198$	7.46707	−	27.1365i	0.530661	−	1.92851i
$199$		−	4.06958i		−	0.288485i	−0.989542	−	0.144242i	$-0.953925\pi$
$199$		−	4.06958i		−	0.288485i	0.989542	−	0.144242i	$-0.0460745\pi$
$200$	−4.32784	−	8.52444i	−0.306025	−	0.602769i
$201$	−21.2143	−	9.97934i	−1.49634	−	0.703889i
$202$	12.8575	−	18.3624i	0.904652	−	1.29198i
$203$	−3.92461	−	5.90349i	−0.275454	−	0.414344i
$204$	7.76448	−	5.39795i	0.543622	−	0.377932i
$205$	−20.0826	−	11.1510i	−1.40263	−	0.778822i
$206$			9.27996i			0.646565i
$207$	11.1817	+	11.3330i	0.777179	+	0.787698i
$208$	0.136701	−	0.136701i	0.00947851	−	0.00947851i
$209$	−10.2694	+	3.73776i	−0.710349	+	0.258546i
$210$	−7.50179	−	21.3244i	−0.517672	−	1.47152i
$211$	7.13070	−	5.98336i	0.490897	−	0.411912i	−0.363450	−	0.931614i	$-0.618401\pi$
$211$	7.13070	−	5.98336i	0.490897	−	0.411912i	0.854348	+	0.519702i	$0.173957\pi$
$212$	25.7854	+	18.0551i	1.77095	+	1.24003i
$213$	2.34072	−	6.36443i	0.160383	−	0.436083i
$214$	5.80668	−	6.92013i	0.396936	−	0.473050i
$215$	−22.7622	−	15.3774i	−1.55237	−	1.04873i
$216$	6.95405	+	7.09571i	0.473163	+	0.482802i
$217$	−0.0534090	+	0.477334i	−0.00362564	+	0.0324036i
$218$	5.73254	−	4.01396i	0.388256	−	0.271860i
$219$	−10.4098	+	4.81167i	−0.703432	+	0.325142i
$220$	25.4569	−	9.75081i	1.71631	−	0.657399i
$221$	−0.239277	+	0.0421911i	−0.0160955	+	0.00283808i
$222$	1.63042	+	2.84602i	0.109427	+	0.191012i
$223$	6.49943	−	13.9381i	0.435234	−	0.933362i	−0.559302	−	0.828964i	$-0.688931\pi$
$223$	6.49943	−	13.9381i	0.435234	−	0.933362i	0.994536	−	0.104398i	$-0.0332915\pi$
$224$	−18.7483	+	2.84068i	−1.25267	+	0.189801i
$225$	14.9946	−	0.400951i	0.999643	−	0.0267301i
$226$	−3.04847	+	5.28011i	−0.202781	+	0.351228i
$227$	10.8123	−	23.1870i	0.717636	−	1.53898i	−0.120017	−	0.992772i	$-0.538295\pi$
$227$	10.8123	−	23.1870i	0.717636	−	1.53898i	0.837653	−	0.546203i	$-0.183927\pi$
$228$	2.25792	−	12.5583i	0.149534	−	0.831696i
$229$	−2.16128	−	2.57571i	−0.142821	−	0.170208i	0.689892	−	0.723913i	$-0.257658\pi$
$229$	−2.16128	−	2.57571i	−0.142821	−	0.170208i	−0.832713	+	0.553705i	$0.813214\pi$
$230$	−4.11396	+	25.8531i	−0.271266	+	1.70470i
$231$	18.9559	−	4.52403i	1.24721	−	0.297659i
$232$	0.446504	+	5.10357i	0.0293144	+	0.335066i
$233$	18.6362	−	4.99355i	1.22090	−	0.327138i	0.409869	−	0.912145i	$-0.365575\pi$
$233$	18.6362	−	4.99355i	1.22090	−	0.327138i	0.811029	+	0.585006i	$0.198908\pi$
$234$	−0.283434	−	0.795321i	−0.0185286	−	0.0519918i
$235$	7.21625	+	4.87505i	0.470736	+	0.318013i
$236$	7.62528	−	9.08746i	0.496364	−	0.591543i
$237$	18.9475	+	11.0244i	1.23077	+	0.716111i
$238$	9.95815	+	4.93986i	0.645491	+	0.320204i
$239$	−26.0992	−	9.49934i	−1.68822	−	0.614461i	−0.693819	−	0.720149i	$-0.744073\pi$
$239$	−26.0992	−	9.49934i	−1.68822	−	0.614461i	−0.994399	+	0.105688i	$0.966295\pi$
$240$	0.941800	−	5.79297i	0.0607929	−	0.373935i
$241$	11.7550	+	9.86358i	0.757204	+	0.635369i	0.937397	−	0.348262i	$-0.113228\pi$
$241$	11.7550	+	9.86358i	0.757204	+	0.635369i	−0.180194	+	0.983631i	$0.557672\pi$
$242$	4.04556	+	15.0982i	0.260058	+	0.970550i
$243$	−14.7359	+	5.08467i	−0.945307	+	0.326182i
$244$		−	6.50431i		−	0.416396i
$245$	10.4349	−	11.6667i	0.666664	−	0.745358i
$246$	16.4692	+	35.6306i	1.05004	+	2.27172i
$247$	−0.188041	+	0.268551i	−0.0119648	+	0.0170875i
$248$	0.199095	−	0.284337i	0.0126426	−	0.0180554i
$249$	1.34713	−	4.96080i	0.0853708	−	0.314378i
$250$	15.1427	+	19.4689i	0.957705	+	1.23132i
$251$	−12.5196	−	7.22819i	−0.790230	−	0.456240i	0.0498135	−	0.998759i	$-0.484137\pi$
$251$	−12.5196	−	7.22819i	−0.790230	−	0.456240i	−0.840044	+	0.542519i	$0.817471\pi$
$252$	−6.56495	+	21.7862i	−0.413553	+	1.37240i
$253$	−21.7995	−	5.84116i	−1.37052	−	0.367231i
$254$	−2.84275	+	16.1220i	−0.178370	+	1.01159i
$255$	−5.14555	+	5.28498i	−0.322227	+	0.330958i
$256$	4.71287	+	1.71535i	0.294554	+	0.107209i
$257$	1.82346	−	20.8422i	0.113744	−	1.30010i	−0.698003	−	0.716095i	$-0.745928\pi$
$257$	1.82346	−	20.8422i	0.113744	−	1.30010i	0.811747	−	0.584009i	$-0.198517\pi$
$258$	15.9062	+	44.1633i	0.990279	+	2.74949i
$259$	−1.18274	+	1.93883i	−0.0734918	+	0.120473i
$260$	0.457788	−	0.677637i	0.0283908	−	0.0420253i
$261$	−7.53475	−	2.79992i	−0.466389	−	0.173311i
$262$	4.49653	−	16.7813i	0.277796	−	1.03675i
$263$	25.2144	−	17.6553i	1.55478	−	1.08867i	0.596592	−	0.802545i	$-0.296521\pi$
$263$	25.2144	−	17.6553i	1.55478	−	1.08867i	0.958192	−	0.286126i	$-0.0923677\pi$
$264$	−13.5915	−	3.69085i	−0.836502	−	0.227156i
$265$	−22.4233	−	10.0030i	−1.37745	−	0.614479i
$266$	14.2143	−	4.78797i	0.871532	−	0.293569i
$267$	21.9041	−	18.2546i	1.34051	−	1.11716i
$268$	−16.3987	+	35.1671i	−1.00171	+	2.14817i
$269$	−9.42540	+	16.3253i	−0.574677	+	0.995369i	0.421400	+	0.906875i	$0.361539\pi$
$269$	−9.42540	+	16.3253i	−0.574677	+	0.995369i	−0.996077	+	0.0884943i	$0.971794\pi$
$270$	−21.0938	−	14.5621i	−1.28373	−	0.886224i
$271$	−8.64270	−	14.9696i	−0.525007	−	0.909339i	−0.999576	−	0.0291203i	$-0.990729\pi$
$271$	−8.64270	−	14.9696i	−0.525007	−	0.909339i	0.474569	−	0.880218i	$-0.342604\pi$
$272$	1.65537	+	2.36412i	0.100372	+	0.143346i
$273$	0.387970	−	0.437337i	0.0234810	−	0.0264688i
$274$	12.0156	−	33.0125i	0.725886	−	1.99436i
$275$	−18.0488	+	11.2417i	−1.08838	+	0.677902i
$276$	18.6949	−	18.5697i	1.12530	−	1.11776i
$277$	−13.6222	+	9.53839i	−0.818481	+	0.573106i	−0.906108	−	0.423047i	$-0.860961\pi$
$277$	−13.6222	+	9.53839i	−0.818481	+	0.573106i	0.0876270	+	0.996153i	$0.472072\pi$
$278$	−35.5761	−	35.5761i	−2.13371	−	2.13371i
$279$	0.269135	+	0.473478i	0.0161127	+	0.0283464i
$280$	−10.6580	+	3.78972i	−0.636937	+	0.226479i
$281$	−10.1467	+	12.0923i	−0.605298	+	0.721367i	−0.978468	−	0.206396i	$-0.933826\pi$
$281$	−10.1467	+	12.0923i	−0.605298	+	0.721367i	0.373170	+	0.927763i	$0.378271\pi$
$282$	−5.04271	−	14.0010i	−0.300289	−	0.833745i
$283$	6.97677	−	3.25332i	0.414726	−	0.193390i	−0.204045	−	0.978962i	$-0.565409\pi$
$283$	6.97677	−	3.25332i	0.414726	−	0.193390i	0.618771	+	0.785572i	$0.287631\pi$
$284$	−10.5467	−	3.83869i	−0.625832	−	0.227784i
$285$	0.133030	+	9.95181i	0.00788003	+	0.589494i
$286$	0.916858	+	0.769335i	0.0542149	+	0.0454917i
$287$	−16.1228	+	21.8809i	−0.951696	+	1.29159i
$288$	−15.3055	+	15.1011i	−0.901885	+	0.889842i
$289$			13.3728i			0.786637i
$290$	−3.63392	−	12.7078i	−0.213391	−	0.746228i
$291$	−7.07576	−	7.12348i	−0.414788	−	0.417586i
$292$	8.02164	+	17.2025i	0.469431	+	1.00670i
$293$	12.4030	+	26.5984i	0.724593	+	1.55389i	0.828930	+	0.559353i	$0.188950\pi$
$293$	12.4030	+	26.5984i	0.724593	+	1.55389i	−0.104337	+	0.994542i	$0.533272\pi$
$294$	−26.1588	+	5.57879i	−1.52561	+	0.325362i
$295$	−4.49188	+	8.08972i	−0.261528	+	0.471002i
$296$	1.42139	−	0.820642i	0.0826168	−	0.0476988i
$297$	14.3740	−	16.7837i	0.834066	−	0.973889i
$298$	0.928845	+	3.46650i	0.0538065	+	0.200809i
$299$	−0.636196	+	0.231556i	−0.0367922	+	0.0133913i
$300$	−0.747019	−	24.8152i	−0.0431292	−	1.43271i
$301$	−21.4876	+	24.3864i	−1.23853	+	1.40561i
$302$	0.286440	−	3.27402i	0.0164828	−	0.188399i
$303$	15.2714	−	8.74864i	0.877319	−	0.502596i
$304$	3.83502	+	0.676217i	0.219953	+	0.0387837i
$305$	0.964441	+	4.98092i	0.0552237	+	0.285206i
$306$	12.4274	−	2.10525i	0.710426	−	0.120349i
$307$	−7.32095	+	27.3222i	−0.417829	+	1.55936i	0.361273	+	0.932460i	$0.382342\pi$
$307$	−7.32095	+	27.3222i	−0.417829	+	1.55936i	−0.779102	+	0.626898i	$0.784324\pi$
$308$	−7.59312	−	31.3486i	−0.432658	−	1.78625i
$309$	−3.10137	+	6.59297i	−0.176431	+	0.375061i
$310$	−0.364837	+	0.817839i	−0.0207213	+	0.0464502i
$311$	9.35087	−	25.6913i	0.530239	−	1.45682i	−0.328548	−	0.944487i	$-0.606559\pi$
$311$	9.35087	−	25.6913i	0.530239	−	1.45682i	0.858787	−	0.512333i	$-0.171219\pi$
$312$	−0.397498	+	0.143166i	−0.0225039	+	0.00810520i
$313$	11.2459	+	16.0608i	0.635657	+	0.907813i	0.999722	−	0.0235607i	$-0.00750029\pi$
$313$	11.2459	+	16.0608i	0.635657	+	0.907813i	−0.364065	+	0.931374i	$0.618611\pi$
$314$	−9.79779	−	16.9703i	−0.552921	−	0.957688i
$315$	1.79696	−	17.6570i	0.101247	−	0.994861i
$316$	18.1410	−	31.4211i	1.02051	−	1.76757i
$317$	8.08048	−	0.706950i	0.453845	−	0.0397063i	0.142058	−	0.989858i	$-0.454628\pi$
$317$	8.08048	−	0.706950i	0.453845	−	0.0397063i	0.311787	+	0.950152i	$0.399072\pi$
$318$	20.8562	+	36.4060i	1.16956	+	2.04155i
$319$	11.2215	−	1.97865i	0.628283	−	0.110783i
$320$	−28.2224	−	4.49099i	−1.57768	−	0.251054i
$321$	6.43808	−	2.97582i	0.359338	−	0.166094i
$322$	29.7168	+	8.73726i	1.65605	+	0.486909i
$323$	−3.46070	−	3.46070i	−0.192559	−	0.192559i
$324$	8.49755	+	24.3609i	0.472086	+	1.35338i
$325$	−0.250090	+	0.586805i	−0.0138725	+	0.0325501i
$326$	−0.246209	+	0.293421i	−0.0136363	+	0.0162511i
$327$	5.41416	−	0.935912i	0.299404	−	0.0517560i
$328$	17.8017	−	8.30105i	0.982932	−	0.458349i
$329$	6.81217	−	7.73116i	0.375567	−	0.426233i
$330$	36.2360	+	2.68272i	1.99473	+	0.147679i
$331$	9.34851	+	7.84433i	0.513841	+	0.431163i	0.862478	−	0.506094i	$-0.168911\pi$
$331$	9.34851	+	7.84433i	0.513841	+	0.431163i	−0.348638	+	0.937258i	$0.613356\pi$
$332$	−8.21806	−	2.20202i	−0.451024	−	0.120852i
$333$	0.207194	+	2.56685i	0.0113542	+	0.140662i
$334$	−43.9144	−	25.3540i	−2.40289	−	1.38731i
$335$	7.34343	−	29.3621i	0.401214	−	1.60422i
$336$	−6.65571	−	1.98122i	−0.363098	−	0.108085i
$337$	−17.7527	+	25.3535i	−0.967051	+	1.38109i	−0.0428932	+	0.999080i	$0.513658\pi$
$337$	−17.7527	+	25.3535i	−0.967051	+	1.38109i	−0.924157	+	0.382012i	$0.875231\pi$
$338$	−28.5339	−	2.49639i	−1.55204	−	0.135786i
$339$	−3.93041	+	2.73246i	−0.213470	+	0.148407i
$340$	8.77573	+	8.48694i	0.475931	+	0.460269i
$341$	−0.668606	−	0.386020i	−0.0362070	−	0.0209041i
$342$	9.84839	−	13.8657i	0.532540	−	0.749769i
$343$	−12.1131	−	14.0098i	−0.654044	−	0.756457i
$344$	22.0724	−	8.03368i	1.19006	−	0.433147i
$345$	−11.5629	+	16.9925i	−0.622524	+	0.914844i
$346$	2.52472	+	14.3184i	0.135730	+	0.769763i
$347$	−2.69032	+	30.7505i	−0.144424	+	1.65078i	0.485586	+	0.874189i	$0.338606\pi$
$347$	−2.69032	+	30.7505i	−0.144424	+	1.65078i	−0.630010	+	0.776587i	$0.716949\pi$
$348$	−4.59221	+	12.4863i	−0.246168	+	0.669334i
$349$	22.8884	+	4.03584i	1.22519	+	0.216033i	0.748557	−	0.663071i	$-0.230747\pi$
$349$	22.8884	+	4.03584i	1.22519	+	0.216033i	0.476630	+	0.879104i	$0.341858\pi$
$350$	25.1369	−	14.8260i	1.34362	−	0.792484i
$351$	0.0644308	−	0.659761i	0.00343906	−	0.0352155i
$352$	7.88864	−	29.4408i	0.420466	−	1.56920i
$353$	1.27288	+	14.5490i	0.0677483	+	0.774367i	0.951748	+	0.306880i	$0.0992849\pi$
$353$	1.27288	+	14.5490i	0.0677483	+	0.774367i	−0.884000	+	0.467487i	$0.845159\pi$
$354$	14.3528	−	6.63418i	0.762842	−	0.352602i
$355$	8.64573	+	1.37578i	0.458868	+	0.0730190i
$356$	−30.3348	−	36.1517i	−1.60774	−	1.91603i
$357$	5.42388	+	6.83756i	0.287062	+	0.361882i
$358$	9.38681	−	20.1301i	0.496109	−	1.06391i
$359$	23.0635			1.21725			0.608623	−	0.793460i	$-0.291722\pi$
$359$	23.0635			1.21725			0.608623	+	0.793460i	$0.291722\pi$
$360$	−7.25135	+	10.5797i	−0.382180	+	0.557602i
$361$	12.3963			0.652434
$362$	−3.32305	−	4.74581i	−0.174656	−	0.249434i
$363$	−2.17166	+	12.0786i	−0.113983	+	0.633961i
$364$	−0.725989	−	0.639692i	−0.0380522	−	0.0335290i
$365$	−8.69361	−	11.9840i	−0.455044	−	0.627271i
$366$	3.69028	−	7.84489i	0.192894	−	0.410059i
$367$	−8.08175	−	3.76858i	−0.421864	−	0.196718i	0.200081	−	0.979779i	$-0.435879\pi$
$367$	−8.08175	−	3.76858i	−0.421864	−	0.196718i	−0.621945	+	0.783061i	$0.713657\pi$
$368$	5.68649	+	5.68649i	0.296429	+	0.296429i
$369$	−0.207153	+	30.8178i	−0.0107840	+	1.60431i
$370$	−3.19776	+	2.77570i	−0.166244	+	0.144302i
$371$	−15.1295	+	24.8013i	−0.785483	+	1.28762i
$372$	0.782151	−	0.448077i	0.0405526	−	0.0232317i
$373$	2.33371	−	1.08823i	0.120835	−	0.0563463i	−0.361261	−	0.932465i	$-0.617654\pi$
$373$	2.33371	−	1.08823i	0.120835	−	0.0563463i	0.482096	+	0.876119i	$0.339876\pi$
$374$	−13.6874	+	11.4851i	−0.707757	+	0.593879i
$375$	4.25159	+	18.8924i	0.219551	+	0.975601i
$376$	−6.99753	+	2.54689i	−0.360870	+	0.131346i
$377$	0.241706	−	0.241706i	0.0124485	−	0.0124485i
$378$	−20.2787	+	22.5518i	−1.04302	+	1.15994i
$379$			9.42082i			0.483915i	0.970287	+	0.241957i	$0.0777894\pi$
$379$			9.42082i			0.483915i	−0.970287	+	0.241957i	$0.922211\pi$
$380$	16.4704	−	0.275534i	0.844913	−	0.0141346i
$381$	−7.40763	+	10.5039i	−0.379504	+	0.538130i
$382$	18.0419	+	1.57847i	0.923106	+	0.0807613i
$383$	−1.24617	−	2.67241i	−0.0636761	−	0.136554i	0.871894	−	0.489694i	$-0.162892\pi$
$383$	−1.24617	−	2.67241i	−0.0636761	−	0.136554i	−0.935570	+	0.353140i	$0.885114\pi$
$384$	16.9177	+	17.0318i	0.863328	+	0.869151i
$385$	10.4630	+	22.8804i	0.533244	+	1.16610i
$386$	20.8149	+	12.0175i	1.05945	+	0.611674i
$387$	−3.45879	+	36.6918i	−0.175820	+	1.86515i
$388$	−11.7506	+	11.7506i	−0.596548	+	0.596548i
$389$	−6.98007	+	2.54054i	−0.353904	+	0.128810i	−0.512853	−	0.858476i	$-0.671411\pi$
$389$	−6.98007	+	2.54054i	−0.353904	+	0.128810i	0.158950	+	0.987287i	$0.449189\pi$
$390$	0.936606	−	0.557573i	0.0474269	−	0.0282338i
$391$	−1.75507	−	9.95347i	−0.0887575	−	0.503369i
$392$	2.83559	+	13.0804i	0.143219	+	0.660658i
$393$	8.80288	−	10.4195i	0.444046	−	0.525596i
$394$	47.9310	+	8.45153i	2.41473	+	0.425782i
$395$	−9.23309	+	26.7517i	−0.464567	+	1.34603i
$396$	−27.8585	−	23.6970i	−1.39994	−	1.19082i
$397$	−15.4154	−	15.4154i	−0.773678	−	0.773678i	0.205070	−	0.978747i	$-0.434258\pi$
$397$	−15.4154	−	15.4154i	−0.773678	−	0.773678i	−0.978747	+	0.205070i	$0.934258\pi$
$398$	−8.13661	−	3.79416i	−0.407851	−	0.190184i
$399$	11.6987	+	1.34879i	0.585667	+	0.0675241i
$400$	7.57264	−	0.253437i	0.378632	−	0.0126719i
$401$	−3.76938	+	0.664643i	−0.188234	+	0.0331907i	−0.266970	−	0.963705i	$-0.586023\pi$
$401$	−3.76938	+	0.664643i	−0.188234	+	0.0331907i	0.0787365	+	0.996895i	$0.474911\pi$
$402$	−39.7310	+	33.1114i	−1.98160	+	1.65145i
$403$	−0.0230720	+	0.00201854i	−0.00114930	+	0.000100551i
$404$	−14.5647	−	25.2269i	−0.724623	−	1.25508i
$405$	−10.1195	−	17.3953i	−0.502841	−	0.864379i
$406$	−15.4623	+	2.34279i	−0.767380	+	0.116271i
$407$	−2.09385	−	2.99032i	−0.103788	−	0.148225i
$408$	−1.07436	−	6.21506i	−0.0531886	−	0.307691i
$409$	14.7762	+	17.6096i	0.730635	+	0.870737i	0.995618	−	0.0935161i	$-0.0298107\pi$
$409$	14.7762	+	17.6096i	0.730635	+	0.870737i	−0.264983	+	0.964253i	$0.585366\pi$
$410$	−41.0185	+	29.7562i	−2.02576	+	1.46956i
$411$	19.5693	−	19.4382i	0.965281	−	0.958814i
$412$	10.9292	+	5.09637i	0.538443	+	0.251080i
$413$	8.81413	+	6.49460i	0.433715	+	0.319579i
$414$	33.0838	−	11.7903i	1.62598	−	0.579461i
$415$	6.61979	+	0.467729i	0.324953	+	0.0229599i
$416$	−0.312723	−	0.859199i	−0.0153325	−	0.0421257i
$417$	−13.3856	−	37.1647i	−0.655494	−	1.81996i
$418$	−2.10123	+	24.0171i	−0.102774	+	1.17472i
$419$	5.17645	+	29.3571i	0.252886	+	1.43419i	0.801442	+	0.598073i	$0.204067\pi$
$419$	5.17645	+	29.3571i	0.252886	+	1.43419i	−0.548556	+	0.836114i	$0.684822\pi$
$420$	−29.2340	−	2.87591i	−1.42647	−	0.140330i
$421$	−13.7480	−	11.5360i	−0.670038	−	0.562229i	0.243039	−	0.970017i	$-0.421856\pi$
$421$	−13.7480	−	11.5360i	−0.670038	−	0.562229i	−0.913077	+	0.407788i	$0.866300\pi$
$422$	−5.31486	−	19.8353i	−0.258724	−	0.965569i
$423$	1.09653	−	11.6323i	0.0533151	−	0.565581i
$424$	18.1823	−	10.4976i	0.883011	−	0.509806i
$425$	−7.97876	−	5.19795i	−0.387027	−	0.252138i
$426$	−10.5426	−	10.6137i	−0.510789	−	0.514234i
$427$	5.99101	−	0.378573i	0.289925	−	0.0183205i
$428$	−4.96106	−	10.6390i	−0.239802	−	0.514257i
$429$	0.394271	+	0.852990i	0.0190356	+	0.0411828i
$430$	−51.9669	+	31.1735i	−2.50606	+	1.50332i
$431$	15.4453	+	8.91734i	0.743973	+	0.429533i	0.823512	−	0.567299i	$-0.192011\pi$
$431$	15.4453	+	8.91734i	0.743973	+	0.429533i	−0.0795389	+	0.996832i	$0.525345\pi$
$432$	−7.42603	+	2.61837i	−0.357285	+	0.125976i
$433$	24.2832	−	24.2832i	1.16698	−	1.16698i	0.184060	−	0.982915i	$-0.441076\pi$
$433$	24.2832	−	24.2832i	1.16698	−	1.16698i	0.982915	−	0.184060i	$-0.0589241\pi$
$434$	0.904575	+	0.551814i	0.0434210	+	0.0264879i
$435$	1.66523	−	10.2427i	0.0798415	−	0.491102i
$436$	−1.57913	−	8.95571i	−0.0756268	−	0.428901i
$437$	−11.1712	−	7.82214i	−0.534390	−	0.374184i
$438$	−0.0850278	+	25.2992i	−0.00406278	+	1.20884i
$439$	0.950478	−	1.13274i	0.0453638	−	0.0540625i	−0.742885	−	0.669419i	$-0.766543\pi$
$439$	0.950478	−	1.13274i	0.0453638	−	0.0540625i	0.788249	+	0.615356i	$0.210988\pi$
$440$	1.28148	−	18.1368i	0.0610922	−	0.864640i
$441$	−20.4490	−	4.77884i	−0.973763	−	0.227564i
$442$	−0.138728	+	0.517740i	−0.00659862	+	0.0246264i
$443$	−0.169786	+	0.118885i	−0.00806678	+	0.00564842i	−0.577603	−	0.816318i	$-0.696012\pi$
$443$	−0.169786	+	0.118885i	−0.00806678	+	0.00564842i	0.569536	+	0.821966i	$0.307123\pi$
$444$	4.24721	−	0.357204i	0.201564	−	0.0169521i
$445$	28.5905	+	23.1865i	1.35532	+	1.09915i
$446$	−21.8078	−	25.9895i	−1.03263	−	1.23064i
$447$	−0.498606	+	2.77320i	−0.0235832	+	0.131168i
$448$	−9.53802	+	32.4403i	−0.450629	+	1.53266i
$449$	−7.92140	−	13.7203i	−0.373834	−	0.647499i	0.616318	−	0.787497i	$-0.288624\pi$
$449$	−7.92140	−	13.7203i	−0.373834	−	0.647499i	−0.990152	+	0.139998i	$0.955290\pi$
$450$	13.1782	−	30.3537i	0.621226	−	1.43089i
$451$	−21.8436	−	37.8343i	−1.02858	−	1.78155i
$452$	4.54433	+	6.48998i	0.213747	+	0.305263i
$453$	1.29768	−	2.23031i	0.0609704	−	0.104789i
$454$	−36.2789	−	43.2355i	−1.70265	−	2.02914i
$455$	0.650805	+	0.382220i	0.0305102	+	0.0179188i
$456$	−6.95487	−	4.90477i	−0.325692	−	0.229687i
$457$	−38.2058	−	17.8157i	−1.78719	−	0.833382i	−0.964130	−	0.265431i	$-0.914486\pi$
$457$	−38.2058	−	17.8157i	−1.78719	−	0.833382i	−0.823063	−	0.567950i	$-0.807737\pi$
$458$	−7.16482	+	1.91981i	−0.334790	+	0.0897067i
$459$	9.53263	+	2.65756i	0.444945	+	0.124044i
$460$	28.1884	+	19.0431i	1.31429	+	0.887888i
$461$	−32.6444	−	5.75608i	−1.52040	−	0.268087i	−0.649809	−	0.760097i	$-0.725151\pi$
$461$	−32.6444	−	5.75608i	−1.52040	−	0.268087i	−0.870590	+	0.492010i	$0.836262\pi$
$462$	8.62779	−	42.1178i	0.401401	−	1.95950i
$463$	−27.3328	+	12.7455i	−1.27026	+	0.592333i	−0.936613	−	0.350365i	$-0.886057\pi$
$463$	−27.3328	+	12.7455i	−1.27026	+	0.592333i	−0.333648	+	0.942698i	$0.608280\pi$
$464$	−3.81541	−	1.38870i	−0.177126	−	0.0644687i
$465$	−0.532522	+	0.459107i	−0.0246951	+	0.0212906i
$466$	7.39097	−	41.9163i	0.342380	−	1.94173i
$467$	0.503655	−	0.503655i	0.0233064	−	0.0233064i	−0.695358	−	0.718664i	$-0.744754\pi$
$467$	0.503655	−	0.503655i	0.0233064	−	0.0233064i	0.718664	+	0.695358i	$0.244754\pi$
$468$	−1.09232	−	0.102969i	−0.0504926	−	0.00475974i
$469$	−33.3463	−	13.0577i	−1.53979	−	0.602950i
$470$	16.4749	−	9.88285i	0.759931	−	0.455862i
$471$	−1.28938	−	15.3310i	−0.0594117	−	0.706415i
$472$	−3.34385	−	7.17090i	−0.153913	−	0.330068i
$473$	−22.0791	−	47.3487i	−1.01520	−	2.17710i
$474$	39.7070	−	27.6047i	1.82380	−	1.26793i
$475$	−12.5720	+	2.65319i	−0.576841	+	0.121737i
$476$	11.2866	−	9.01504i	0.517320	−	0.413204i
$477$	2.65041	+	32.8349i	0.121354	+	1.50340i
$478$	−43.3256	+	43.3256i	−1.98167	+	1.98167i
$479$	5.39793	−	30.6132i	0.246638	−	1.39875i	−0.570020	−	0.821631i	$-0.693065\pi$
$479$	5.39793	−	30.6132i	0.246638	−	1.39875i	0.816658	−	0.577122i	$-0.195824\pi$
$480$	−22.9488	−	15.6160i	−1.04746	−	0.712768i
$481$	−0.102906	−	0.0374548i	−0.00469212	−	0.00170779i
$482$	30.6804	−	14.3065i	1.39745	−	0.651643i
$483$	18.1923	+	16.1388i	0.827781	+	0.734340i
$484$	20.0032	+	3.52711i	0.909237	+	0.160323i
$485$	7.25613	−	10.7408i	0.329484	−	0.487716i
$486$	−3.57245	+	34.2031i	−0.162050	+	1.55148i
$487$	7.12957	−	1.91036i	0.323072	−	0.0865668i	−0.0936384	−	0.995606i	$-0.529850\pi$
$487$	7.12957	−	1.91036i	0.323072	−	0.0865668i	0.416710	+	0.909040i	$0.363183\pi$
$488$	−3.93175	−	1.83341i	−0.177982	−	0.0829944i
$489$	−0.272982	+	0.126178i	−0.0123447	+	0.00570598i
$490$	−13.5973	−	31.7405i	−0.614265	−	1.43389i
$491$	14.5682	+	17.3617i	0.657453	+	0.783522i	0.987018	−	0.160611i	$-0.0513464\pi$
$491$	14.5682	+	17.3617i	0.657453	+	0.783522i	−0.329565	+	0.944133i	$0.606902\pi$
$492$	51.0074	+	0.171430i	2.29959	+	0.00772867i
$493$	2.92692	+	4.18008i	0.131822	+	0.188261i
$494$	0.361617	+	0.626340i	0.0162699	+	0.0281804i
$495$	24.8474	+	14.0161i	1.11681	+	0.629975i
$496$	0.137552	+	0.238246i	0.00617625	+	0.0106976i
$497$	2.92190	−	9.93784i	0.131065	−	0.445773i
$498$	−8.66252	−	7.31847i	−0.388177	−	0.327949i
$499$	−8.99702	−	10.7222i	−0.402762	−	0.479993i	0.526098	−	0.850424i	$-0.323655\pi$
$499$	−8.99702	−	10.7222i	−0.402762	−	0.479993i	−0.928860	+	0.370431i	$0.879210\pi$
$500$	31.2450	−	7.14186i	1.39732	−	0.319394i
$501$	−22.7257	−	32.6890i	−1.01531	−	1.46044i
$502$	−26.1242	+	18.2923i	−1.16598	+	0.816427i
$503$	2.38649	−	8.90651i	0.106408	−	0.397122i	−0.892093	−	0.451852i	$-0.850763\pi$
$503$	2.38649	−	8.90651i	0.106408	−	0.397122i	0.998501	+	0.0547308i	$0.0174301\pi$
$504$	11.3189	+	10.1094i	0.504185	+	0.450309i
$505$	14.8941	+	17.1588i	0.662777	+	0.763556i
$506$	−32.0028	+	38.1395i	−1.42270	+	1.69551i
$507$	−19.4377	−	11.3096i	−0.863258	−	0.502278i
$508$	17.4261	+	12.2019i	0.773156	+	0.541370i
$509$	4.29642	+	24.3662i	0.190435	+	1.08001i	0.918771	+	0.394791i	$0.129183\pi$
$509$	4.29642	+	24.3662i	0.190435	+	1.08001i	−0.728335	+	0.685221i	$0.759706\pi$
$510$	5.76932	+	15.2152i	0.255470	+	0.673739i
$511$	−15.3780	+	8.38985i	−0.680284	+	0.371145i
$512$	−11.7774	+	11.7774i	−0.520490	+	0.520490i
$513$	11.6307	−	6.55954i	0.513509	−	0.289611i
$514$	−39.9714	−	23.0775i	−1.76306	−	1.01790i
$515$	−9.12512	−	2.28218i	−0.402101	−	0.100565i
$516$	60.7474	+	5.52050i	2.67426	+	0.243026i
$517$	6.99967	+	15.0108i	0.307845	+	0.660176i
$518$	2.77376	+	4.17235i	0.121872	+	0.183323i
$519$	−2.99153	+	11.0163i	−0.131314	+	0.483563i
$520$	−0.280582	−	0.467735i	−0.0123043	−	0.0205115i
$521$	−31.9301	+	18.4349i	−1.39888	+	0.807646i	−0.994276	−	0.106844i	$-0.965925\pi$
$521$	−31.9301	+	18.4349i	−1.39888	+	0.807646i	−0.404608	+	0.914490i	$0.632592\pi$
$522$	−12.6229	+	12.4543i	−0.552490	+	0.545112i
$523$	6.24483	+	23.3060i	0.273068	+	1.01910i	0.957125	+	0.289674i	$0.0935469\pi$
$523$	6.24483	+	23.3060i	0.273068	+	1.01910i	−0.684058	+	0.729428i	$0.739786\pi$
$524$	−17.2942	−	14.5116i	−0.755502	−	0.633942i
$525$	22.8134	−	2.13240i	0.995660	−	0.0930656i
$526$	−11.7916	−	66.8733i	−0.514137	−	2.91581i
$527$	0.0301339	−	0.344432i	0.00131265	−	0.0150037i
$528$	7.20354	−	8.52649i	0.313494	−	0.371068i
$529$	−1.76583	−	4.85157i	−0.0767751	−	0.210938i
$530$	−40.9054	+	35.5064i	−1.77682	+	1.54230i
$531$	12.4141	+	0.0834458i	0.538726	+	0.00362124i
$532$	2.16730	−	19.3699i	0.0939643	−	0.839791i
$533$	−1.18777	−	0.553866i	−0.0514480	−	0.0239906i
$534$	−16.0761	−	60.8136i	−0.695680	−	2.63166i
$535$	5.37665	+	7.41163i	0.232453	+	0.320433i
$536$	16.6356	+	19.8255i	0.718548	+	0.856332i
$537$	13.3964	−	11.1644i	0.578096	−	0.481779i
$538$	23.8528	+	34.0653i	1.02837	+	1.46866i
$539$	28.4327	−	8.81850i	1.22468	−	0.379840i
$540$	−28.7345	+	16.8454i	−1.23653	+	0.724911i
$541$	−17.1878	−	29.7702i	−0.738962	−	1.27992i	−0.952963	−	0.303087i	$-0.901983\pi$
$541$	−17.1878	−	29.7702i	−0.738962	−	1.27992i	0.214001	−	0.976834i	$-0.431351\pi$
$542$	−37.9876	+	3.32348i	−1.63171	+	0.142756i
$543$	−0.774816	−	4.48224i	−0.0332505	−	0.192351i
$544$	13.4424	−	2.37026i	0.576339	−	0.101624i
$545$	2.53721	+	6.62402i	0.108682	+	0.283742i
$546$	−0.512686	−	1.18343i	−0.0219409	−	0.0506463i
$547$	−29.2636	−	13.6459i	−1.25122	−	0.583455i	−0.319831	−	0.947475i	$-0.603626\pi$
$547$	−29.2636	−	13.6459i	−1.25122	−	0.583455i	−0.931391	+	0.364020i	$0.881404\pi$
$548$	−32.2807	−	32.2807i	−1.37897	−	1.37897i
$549$	5.24354	−	4.34013i	0.223789	−	0.185232i
$550$	5.64912	+	46.5671i	0.240879	+	1.98563i
$551$	6.78082	+	1.19564i	0.288873	+	0.0509360i
$552$	−5.95544	−	16.5351i	−0.253480	−	0.703783i
$553$	29.9973	+	14.8805i	1.27561	+	0.632784i
$554$	6.37048	+	36.1288i	0.270656	+	1.53496i
$555$	−3.19950	+	0.903307i	−0.135811	+	0.0383433i
$556$	−61.4364	+	22.3610i	−2.60549	+	0.948319i
$557$	20.1841	−	20.1841i	0.855229	−	0.855229i	−0.135543	−	0.990772i	$-0.543278\pi$
$557$	20.1841	−	20.1841i	0.855229	−	0.855229i	0.990772	+	0.135543i	$0.0432778\pi$
$558$	1.19758	−	0.0966678i	0.0506976	−	0.00409228i
$559$	−1.35727	−	0.783619i	−0.0574063	−	0.0331435i
$560$	0.847717	−	8.92492i	0.0358226	−	0.377147i
$561$	−13.5625	+	3.58526i	−0.572611	+	0.151370i
$562$	14.7171	+	31.5609i	0.620802	+	1.33131i
$563$	−12.1049	−	1.05904i	−0.510162	−	0.0446334i	−0.170831	−	0.985300i	$-0.554645\pi$
$563$	−12.1049	−	1.05904i	−0.510162	−	0.0446334i	−0.339331	+	0.940667i	$0.610201\pi$
$564$	−19.2586	−	1.75015i	−0.810933	−	0.0736945i
$565$	−4.44231	−	4.29612i	−0.186889	−	0.180739i
$566$		−	16.9823i		−	0.713820i
$567$	−21.9439	+	9.24485i	−0.921555	+	0.388247i
$568$	−5.29330	+	5.29330i	−0.222102	+	0.222102i
$569$	−8.53609	+	3.10688i	−0.357851	+	0.130247i	−0.514689	−	0.857377i	$-0.672092\pi$
$569$	−8.53609	+	3.10688i	−0.357851	+	0.130247i	0.156837	+	0.987624i	$0.449870\pi$
$570$	20.0214	+	9.01232i	0.838604	+	0.377485i
$571$	−24.2074	+	20.3124i	−1.01305	+	0.850048i	−0.988738	−	0.149656i	$-0.952183\pi$
$571$	−24.2074	+	20.3124i	−1.01305	+	0.850048i	−0.0243102	+	0.999704i	$0.507739\pi$
$572$	1.40958	−	0.657299i	0.0589376	−	0.0274830i
$573$	12.2904	+	7.15105i	0.513439	+	0.298740i
$574$	28.7165	+	52.6355i	1.19861	+	2.19696i
$575$	−24.4100	−	10.4033i	−1.01797	−	0.433846i
$576$	12.8708	+	36.1159i	0.536285	+	1.50483i
$577$	−22.0641	−	22.0641i	−0.918541	−	0.918541i	0.0783826	−	0.996923i	$-0.475024\pi$
$577$	−22.0641	−	22.0641i	−0.918541	−	0.918541i	−0.996923	+	0.0783826i	$0.975024\pi$
$578$	26.7373	+	12.4678i	1.11212	+	0.518592i
$579$	10.7717	+	15.4942i	0.447658	+	0.643917i
$580$	−16.9619	−	2.69912i	−0.704305	−	0.112075i
$581$	1.54993	−	7.69769i	0.0643018	−	0.319354i
$582$	−20.8394	+	7.50569i	−0.863820	+	0.311121i
$583$	−26.7842	−	38.2519i	−1.10929	−	1.58423i
$584$	12.6597			0.523864
$585$	0.851755	−	0.0831144i	0.0352157	−	0.00343636i
$586$	64.7437			2.67454
$587$	−9.96163	+	21.3628i	−0.411161	+	0.881737i	0.586271	+	0.810115i	$0.300595\pi$
$587$	−9.96163	+	21.3628i	−0.411161	+	0.881737i	−0.997432	+	0.0716220i	$0.977182\pi$
$588$	−7.79565	+	33.8715i	−0.321487	+	1.39684i
$589$	−0.299874	−	0.357375i	−0.0123561	−	0.0147254i
$590$	11.9865	+	16.5232i	0.493475	+	0.680248i
$591$	31.2282	+	22.0230i	1.28456	+	0.905905i
$592$	0.113372	+	1.29585i	0.00465956	+	0.0532590i
$593$	4.28377	−	15.9873i	0.175914	−	0.656518i	−0.820481	−	0.571674i	$-0.806294\pi$
$593$	4.28377	−	15.9873i	0.175914	−	0.656518i	0.996394	−	0.0848440i	$-0.0270392\pi$
$594$	−20.1556	−	44.3869i	−0.826995	−	1.82122i
$595$	−7.30641	+	8.57715i	−0.299533	+	0.351629i
$596$	4.59267	+	0.809811i	0.188123	+	0.0331711i
$597$	−4.51266	−	5.41483i	−0.184691	−	0.221614i
$598$	−0.130172	+	1.48788i	−0.00532315	+	0.0608439i
$599$	2.18512	+	12.3925i	0.0892817	+	0.506342i	0.996350	+	0.0853589i	$0.0272037\pi$
$599$	2.18512	+	12.3925i	0.0892817	+	0.506342i	−0.907069	+	0.420983i	$0.861685\pi$
$600$	−15.2110	−	6.54325i	−0.620986	−	0.267127i
$601$	1.79328	−	0.652699i	0.0731493	−	0.0266242i	−0.305186	−	0.952293i	$-0.598719\pi$
$601$	1.79328	−	0.652699i	0.0731493	−	0.0266242i	0.378336	+	0.925668i	$0.376497\pi$
$602$	28.7241	+	65.6978i	1.17071	+	2.67764i
$603$	−39.2928	+	10.2459i	−1.60013	+	0.417246i
$604$	−3.69858	−	2.13537i	−0.150493	−	0.0868871i
$605$	−15.8412	+	0.265009i	−0.644037	+	0.0107741i
$606$	−3.25393	−	38.6898i	−0.132182	−	1.57166i
$607$	9.51560	+	0.832507i	0.386226	+	0.0337904i	0.278616	−	0.960403i	$-0.410124\pi$
$607$	9.51560	+	0.832507i	0.386226	+	0.0337904i	0.107611	+	0.994193i	$0.465680\pi$
$608$	10.5640	−	15.0870i	0.428427	−	0.611857i
$609$	−11.7682	−	3.50307i	−0.476871	−	0.141951i
$610$	10.8579	+	2.71554i	0.439622	+	0.109949i
$611$	0.430291	+	0.248428i	0.0174077	+	0.0100503i
$612$	4.34547	−	15.7921i	0.175655	−	0.638359i
$613$	−8.54052	−	2.28843i	−0.344948	−	0.0924286i	0.0821854	−	0.996617i	$-0.473810\pi$
$613$	−8.54052	−	2.28843i	−0.344948	−	0.0924286i	−0.427134	+	0.904188i	$0.640477\pi$
$614$	47.8017	+	40.1104i	1.92912	+	1.61872i
$615$	−39.0863	+	7.43196i	−1.57611	+	0.299686i
$616$	−21.0900	−	4.24647i	−0.849742	−	0.171095i
$617$	−7.77786	+	3.62688i	−0.313125	+	0.146013i	−0.572827	−	0.819676i	$-0.694153\pi$
$617$	−7.77786	+	3.62688i	−0.313125	+	0.146013i	0.259702	+	0.965689i	$0.416376\pi$
$618$	10.2903	+	12.3476i	0.413937	+	0.496692i
$619$	4.87043	−	5.80435i	0.195759	−	0.233297i	−0.659232	−	0.751940i	$-0.729118\pi$
$619$	4.87043	−	5.80435i	0.195759	−	0.233297i	0.854991	+	0.518643i	$0.173563\pi$
$620$	0.762825	+	0.878817i	0.0306358	+	0.0352941i
$621$	27.4448	+	2.68020i	1.10132	+	0.107553i
$622$	−42.6485	−	42.6485i	−1.71005	−	1.71005i
$623$	31.5331	−	30.0451i	1.26335	−	1.20373i
$624$	0.0303048	−	0.333473i	0.00121316	−	0.0133496i
$625$	−22.8681	+	10.1021i	−0.914722	+	0.404083i
$626$	42.5964	−	7.51090i	1.70250	−	0.300196i
$627$	−9.51937	+	16.3608i	−0.380167	+	0.653387i
$628$	−25.3670	+	2.21932i	−1.01225	+	0.0885607i
$629$	0.817417	−	1.41581i	0.0325925	−	0.0564519i
$630$	−33.6276	−	20.0548i	−1.33976	−	0.799004i
$631$	−19.1622	−	33.1899i	−0.762836	−	1.32127i	−0.941383	−	0.337339i	$-0.890473\pi$
$631$	−19.1622	−	33.1899i	−0.762836	−	1.32127i	0.178547	−	0.983931i	$-0.442860\pi$
$632$	−13.8801	−	19.8228i	−0.552119	−	0.788507i
$633$	2.85303	−	15.8683i	0.113398	−	0.630708i
$634$	6.12016	−	16.8150i	0.243063	−	0.667809i
$635$	−15.1539	−	6.76014i	−0.601365	−	0.268268i
$636$	54.3299	−	4.56931i	2.15432	−	0.181185i
$637$	0.546955	−	0.705930i	0.0216711	−	0.0279699i
$638$	6.50599	−	24.2807i	0.257575	−	0.961282i
$639$	−3.94289	−	11.0638i	−0.155978	−	0.437678i
$640$	−17.3490	+	25.6807i	−0.685779	+	1.01512i
$641$	19.9950	+	3.52565i	0.789754	+	0.139255i	0.553954	−	0.832547i	$-0.313118\pi$
$641$	19.9950	+	3.52565i	0.789754	+	0.139255i	0.235799	+	0.971802i	$0.424229\pi$
$642$	0.0525863	−	15.6465i	0.00207542	−	0.617520i
$643$	2.52694	−	28.8830i	0.0996527	−	1.13904i	−0.767519	−	0.641026i	$-0.778509\pi$
$643$	2.52694	−	28.8830i	0.0996527	−	1.13904i	0.867172	−	0.498009i	$-0.165936\pi$
$644$	26.6099	−	30.1997i	1.04858	−	1.19004i
$645$	−47.3382	+	4.77993i	−1.86394	+	0.188210i
$646$	−10.1457	+	3.69274i	−0.399178	+	0.145289i
$647$	−5.73550	−	21.4052i	−0.225486	−	0.841524i	−0.982209	−	0.187789i	$-0.939868\pi$
$647$	−5.73550	−	21.4052i	−0.225486	−	0.841524i	0.756724	−	0.653735i	$-0.226799\pi$
$648$	17.1211	+	1.73011i	0.672579	+	0.0679653i
$649$	−15.2405	+	8.79910i	−0.598241	+	0.345395i
$650$	0.940078	+	1.04711i	0.0368729	+	0.0410712i
$651$	0.458240	+	0.694347i	0.0179599	+	0.0272136i
$652$	0.210355	+	0.451107i	0.00823812	+	0.0176667i
$653$	7.72665	+	16.5699i	0.302367	+	0.648429i	0.997516	−	0.0704370i	$-0.0224394\pi$
$653$	7.72665	+	16.5699i	0.302367	+	0.648429i	−0.695149	+	0.718866i	$0.744662\pi$
$654$	3.17651	−	11.6975i	0.124211	−	0.457408i
$655$	15.3954	+	8.54845i	0.601550	+	0.334016i
$656$			15.5672i			0.607798i
$657$	−8.51542	+	17.9454i	−0.332218	+	0.700118i
$658$	−9.10633	−	20.8280i	−0.355002	−	0.811960i
$659$	31.4861	+	26.4200i	1.22653	+	1.02918i	0.998457	+	0.0555315i	$0.0176853\pi$
$659$	31.4861	+	26.4200i	1.22653	+	1.02918i	0.228068	+	0.973645i	$0.426759\pi$
$660$	23.0596	−	41.2026i	0.897594	−	1.60381i
$661$	−12.2743	−	4.46747i	−0.477414	−	0.173764i	0.0920942	−	0.995750i	$-0.470644\pi$
$661$	−12.2743	−	4.46747i	−0.477414	−	0.173764i	−0.569508	+	0.821986i	$0.692866\pi$
$662$	24.3996	−	11.3777i	0.948316	−	0.442207i
$663$	−0.271589	+	0.321467i	−0.0105476	+	0.0124847i
$664$	−3.64756	+	4.34699i	−0.141553	+	0.168696i
$665$	1.21243	+	15.1546i	0.0470158	+	0.587669i
$666$	5.32526	+	1.97887i	0.206350	+	0.0766798i
$667$	10.0545	+	10.0545i	0.389311	+	0.389311i
$668$	−53.9768	+	37.7949i	−2.08842	+	1.46233i
$669$	−6.80768	−	25.7525i	−0.263200	−	0.995650i
$670$	−51.8593	−	42.0572i	−2.00350	−	1.62481i
$671$	−3.30014	+	9.06706i	−0.127400	+	0.350030i
$672$	−21.7958	+	24.5692i	−0.840792	+	0.947778i
$673$	16.7885	+	23.9765i	0.647149	+	0.924225i	0.999934	−	0.0114794i	$-0.00365410\pi$
$673$	16.7885	+	23.9765i	0.647149	+	0.924225i	−0.352785	+	0.935705i	$0.614765\pi$
$674$	34.1398	+	59.1318i	1.31502	+	2.27767i
$675$	19.5067	−	17.1607i	0.750813	−	0.660515i
$676$	−18.6103	+	32.2340i	−0.715781	+	1.23977i
$677$	5.71218	−	12.2498i	0.219537	−	0.470799i	−0.765435	−	0.643513i	$-0.777476\pi$
$677$	5.71218	−	12.2498i	0.219537	−	0.470799i	0.984972	+	0.172715i	$0.0552539\pi$
$678$	1.79880	+	10.4059i	0.0690825	+	0.399636i
$679$	−11.5072	−	10.1394i	−0.441608	−	0.389114i
$680$	7.60389	−	2.91253i	0.291596	−	0.111690i
$681$	−11.3251	−	42.8412i	−0.433978	−	1.64168i
$682$	−1.39515	+	0.976897i	−0.0534232	+	0.0374073i
$683$	0.261452	−	0.975751i	0.0100042	−	0.0373361i	−0.960743	−	0.277439i	$-0.910514\pi$
$683$	0.261452	−	0.975751i	0.0100042	−	0.0373361i	0.970748	+	0.240103i	$0.0771811\pi$
$684$	−10.9213	−	19.2134i	−0.417587	−	0.734642i
$685$	29.5067	+	19.9337i	1.12739	+	0.761627i
$686$	−39.3040	+	11.1569i	−1.50063	+	0.425972i
$687$	−5.73186	−	1.03056i	−0.218684	−	0.0393182i
$688$	−1.62250	+	18.5453i	−0.0618573	+	0.707032i
$689$	−1.31636	−	0.479117i	−0.0501495	−	0.0182529i
$690$	23.1939	+	38.9610i	0.882978	+	1.48322i
$691$	−1.43285	+	8.12611i	−0.0545083	+	0.309132i	−0.999857	−	0.0169302i	$-0.994611\pi$
$691$	−1.43285	+	8.12611i	−0.0545083	+	0.309132i	0.945348	+	0.326062i	$0.105722\pi$
$692$	18.2496	+	4.88997i	0.693747	+	0.185889i
$693$	20.2054	−	27.0392i	0.767541	−	1.02714i
$694$	58.9735	+	34.0484i	2.23861	+	1.29246i
$695$	43.7316	−	26.2334i	1.65883	−	0.995091i
$696$	6.25332	+	6.29550i	0.237032	+	0.238630i
$697$	11.2219	−	16.0265i	0.425060	−	0.607048i
$698$	29.4085	−	41.9997i	1.11313	−	1.58971i
$699$	19.2594	−	27.3094i	0.728457	−	1.03294i
$700$	−3.65622	−	37.7464i	−0.138192	−	1.42668i
$701$		−	25.3011i		−	0.955610i	−0.878466	−	0.477805i	$-0.841433\pi$
$701$		−	25.3011i		−	0.955610i	0.878466	−	0.477805i	$-0.158567\pi$
$702$	−1.25904	−	0.743932i	−0.0475193	−	0.0280779i
$703$	−0.570928	−	2.13073i	−0.0215329	−	0.0803620i
$704$	−41.6349	−	34.9358i	−1.56917	−	1.31669i
$705$	15.0075	−	1.51537i	0.565215	−	0.0570721i
$706$	30.2757	+	11.0194i	1.13944	+	0.414722i
$707$	22.3883	−	14.8836i	0.842000	−	0.559757i
$708$	0.0690559	−	20.5469i	0.00259528	−	0.772201i
$709$	−18.6376	+	22.2115i	−0.699951	+	0.834169i	−0.992521	−	0.122075i	$-0.961045\pi$
$709$	−18.6376	+	22.2115i	−0.699951	+	0.834169i	0.292570	+	0.956244i	$0.405490\pi$
$710$	10.8113	−	16.0034i	0.405741	−	0.600596i
$711$	37.4354	−	6.34173i	1.40394	−	0.237833i
$712$	−30.4038	+	8.14667i	−1.13943	+	0.305309i
$713$	−0.0839673	−	0.959751i	−0.00314460	−	0.0359430i
$714$	18.7276	−	4.46955i	0.700864	−	0.167269i
$715$	−0.981978	+	0.712360i	−0.0367239	+	0.0266408i
$716$	−18.5526	−	22.1101i	−0.693342	−	0.826293i
$717$	−45.2602	+	16.3013i	−1.69027	+	0.608784i
$718$	21.5026	−	46.1125i	0.802471	−	1.72090i
$719$	3.68739	−	6.38675i	0.137516	−	0.238185i	−0.789039	−	0.614342i	$-0.789421\pi$
$719$	3.68739	−	6.38675i	0.137516	−	0.238185i	0.926556	+	0.376157i	$0.122755\pi$
$720$	−5.17056	−	8.75224i	−0.192695	−	0.326177i
$721$	−4.05807	+	10.3633i	−0.151130	+	0.385951i
$722$	11.5573	−	24.7847i	0.430118	−	0.922392i
$723$	26.5782	+	0.0893264i	0.988454	+	0.00332208i
$724$	−7.41419	+	1.30732i	−0.275546	+	0.0485863i
$725$	13.3894	−	0.448111i	0.497271	−	0.0166424i
$726$	22.1249	+	15.6031i	0.821132	+	0.579085i
$727$	29.2018	−	20.4474i	1.08304	−	0.758350i	0.111151	−	0.993804i	$-0.464546\pi$
$727$	29.2018	−	20.4474i	1.08304	−	0.758350i	0.971886	+	0.235453i	$0.0756575\pi$
$728$	−0.591323	+	0.258536i	−0.0219159	+	0.00958198i
$729$	−13.9687	+	23.1057i	−0.517361	+	0.855767i
$730$	−32.0657	+	6.20880i	−1.18681	+	0.229798i
$731$	15.0390	−	17.9228i	0.556239	−	0.662900i
$732$	−7.21246	−	8.65438i	−0.266580	−	0.319875i
$733$	22.4604	+	15.7270i	0.829595	+	0.580889i	0.909400	−	0.415922i	$-0.136541\pi$
$733$	22.4604	+	15.7270i	0.829595	+	0.580889i	−0.0798055	+	0.996810i	$0.525430\pi$
$734$	−15.0696	+	12.6449i	−0.556229	+	0.466732i
$735$	0.947431	−	27.0943i	0.0349465	−	0.999389i
$736$	35.7410	−	13.0087i	1.31743	−	0.479505i
$737$	40.7029	−	40.7029i	1.49931	−	1.49931i
$738$	61.4232	+	29.1463i	2.26102	+	1.07289i
$739$			32.5183i			1.19621i	0.801419	+	0.598103i	$0.204079\pi$
$739$			32.5183i			1.19621i	−0.801419	+	0.598103i	$0.795921\pi$
$740$	1.51285	+	5.29043i	0.0556135	+	0.194480i
$741$	0.0475886	+	0.565837i	0.00174821	+	0.0207866i
$742$	35.4816	+	53.3723i	1.30257	+	1.95936i
$743$	−18.1794	+	25.9629i	−0.666939	+	0.952487i	0.333016	+	0.942921i	$0.391934\pi$
$743$	−18.1794	+	25.9629i	−0.666939	+	0.952487i	−0.999954	+	0.00956573i	$0.996955\pi$
$744$	−0.0503862	−	0.599100i	−0.00184725	−	0.0219641i
$745$	−3.63708	+	0.0608450i	−0.133252	+	0.00222919i
$746$		−	5.68054i		−	0.207979i
$747$	−3.70847	−	8.09445i	−0.135686	−	0.296160i
$748$	6.00937	+	22.4273i	0.219724	+	0.820022i
$749$	9.51070	−	5.18879i	0.347513	−	0.189594i
$750$	41.7369	+	9.11332i	1.52401	+	0.332771i
$751$	8.67823	+	3.15862i	0.316673	+	0.115260i	0.495467	−	0.868627i	$-0.334997\pi$
$751$	8.67823	+	3.15862i	0.316673	+	0.115260i	−0.178793	+	0.983887i	$0.557219\pi$
$752$	0.514377	−	5.87936i	0.0187574	−	0.214398i
$753$	−24.6733	+	4.26511i	−0.899144	+	0.155429i
$754$	−0.257912	−	0.708607i	−0.00939259	−	0.0258059i
$755$	3.14895	+	1.08683i	0.114602	+	0.0395537i
$756$	15.4231	+	36.2676i	0.560933	+	1.31904i
$757$	−26.4769	−	26.4769i	−0.962320	−	0.962320i	0.0369950	−	0.999315i	$-0.488221\pi$
$757$	−26.4769	−	26.4769i	−0.962320	−	0.962320i	−0.999315	+	0.0369950i	$0.988221\pi$
$758$	18.8357	+	8.78324i	0.684144	+	0.319022i
$759$	−35.4827	+	16.4009i	−1.28794	+	0.595315i
$760$	4.47605	−	10.0338i	0.162363	−	0.363963i
$761$	−15.4255	+	42.3812i	−0.559174	+	1.53632i	0.261666	+	0.965159i	$0.415728\pi$
$761$	−15.4255	+	42.3812i	−0.559174	+	1.53632i	−0.820840	+	0.571159i	$0.806494\pi$
$762$	14.0949	+	24.6036i	0.510603	+	0.891295i
$763$	8.15705	−	1.97577i	0.295305	−	0.0715276i
$764$	11.7673	−	20.3815i	0.425725	−	0.737377i
$765$	−0.986091	+	12.7378i	−0.0356522	+	0.460535i
$766$	−6.50498			−0.235034
$767$	−0.223110	+	0.478460i	−0.00805603	+	0.0172762i
$768$	8.17287	−	2.94361i	0.294913	−	0.106219i
$769$	−28.3491	+	4.99871i	−1.02230	+	0.180258i	−0.659574	−	0.751640i	$-0.729263\pi$
$769$	−28.3491	+	4.99871i	−1.02230	+	0.180258i	−0.362721	+	0.931898i	$0.618152\pi$
$770$	55.5014	+	0.412529i	2.00013	+	0.0148665i
$771$	−20.6852	−	29.7539i	−0.744960	−	1.07156i
$772$	25.5844	−	17.9144i	0.920801	−	0.644752i
$773$	−1.18110	−	1.18110i	−0.0424813	−	0.0424813i	0.685547	−	0.728028i	$-0.259563\pi$
$773$	−1.18110	−	1.18110i	−0.0424813	−	0.0424813i	−0.728028	+	0.685547i	$0.759563\pi$
$774$	70.1358	+	41.1240i	2.52098	+	1.47817i
$775$	−0.714470	−	0.559878i	−0.0256645	−	0.0201114i
$776$	3.79086	+	10.4153i	0.136084	+	0.373887i
$777$	0.576217	+	3.89125i	0.0206717	+	0.139598i
$778$	−1.42820	+	16.3244i	−0.0512033	+	0.585257i
$779$	−4.58412	−	25.9978i	−0.164243	−	0.931470i
$780$	−0.142300	−	1.40927i	−0.00509515	−	0.0504599i
$781$	12.7545	+	10.7023i	0.456393	+	0.382960i
$782$	−21.5370	−	5.77082i	−0.770161	−	0.206364i
$783$	−13.1302	+	4.62963i	−0.469236	+	0.165449i
$784$	−10.3453	−	2.34443i	−0.369476	−	0.0837295i
$785$	19.0967	−	5.46088i	0.681589	−	0.194907i
$786$	−12.6254	−	27.3146i	−0.450334	−	0.974280i
$787$	44.6073	+	3.90263i	1.59008	+	0.139114i	0.847555	−	0.530708i	$-0.178074\pi$
$787$	44.6073	+	3.90263i	1.59008	+	0.139114i	0.742522	+	0.669821i	$0.233629\pi$
$788$	36.2763	−	51.8079i	1.29229	−	1.84558i
$789$	13.9718	−	51.4510i	0.497408	−	1.83170i
$790$	44.8785	+	43.4016i	1.59670	+	1.54416i
$791$	−5.71332	+	4.56345i	−0.203142	+	0.162258i
$792$	−22.1771	+	10.1604i	−0.788028	+	0.361035i
$793$	0.0749167	+	0.279593i	0.00266037	+	0.00992864i
$794$	−45.1933	+	16.4490i	−1.60385	+	0.583754i
$795$	−40.9276	+	11.5550i	−1.45155	+	0.409814i
$796$	−8.93693	+	7.49897i	−0.316761	+	0.265794i
$797$	−5.56190	−	3.89448i	−0.197013	−	0.137950i	0.470908	−	0.882182i	$-0.343926\pi$
$797$	−5.56190	−	3.89448i	−0.197013	−	0.137950i	−0.667920	+	0.744233i	$0.732815\pi$
$798$	13.6037	−	22.1325i	0.481566	−	0.783483i
$799$	−4.76779	+	5.68203i	−0.168672	+	0.201016i
$800$	14.0499	−	32.9663i	0.496737	−	1.16553i
$801$	8.90266	−	48.5778i	0.314560	−	1.71641i
$802$	−2.18541	+	8.15605i	−0.0771694	+	0.288000i
$803$	−2.45409	−	28.0504i	−0.0866030	−	0.989876i
$804$	17.1765	+	64.9761i	0.605767	+	2.29153i
$805$	−15.8996	+	27.0722i	−0.560387	+	0.954170i
$806$	−0.0174748	+	0.0480115i	−0.000615522	+	0.00169113i
$807$	5.56161	+	32.1734i	0.195778	+	1.13256i
$808$	−19.3547	+	1.69332i	−0.680896	+	0.0595707i
$809$	1.18960	−	2.06045i	0.0418241	−	0.0724415i	−0.844356	−	0.535783i	$-0.820016\pi$
$809$	1.18960	−	2.06045i	0.0418241	−	0.0724415i	0.886180	+	0.463342i	$0.153350\pi$
$810$	−44.2143	+	4.01460i	−1.55353	+	0.141059i
$811$	34.7681			1.22087			0.610436	−	0.792065i	$-0.290994\pi$
$811$	34.7681			1.22087			0.610436	+	0.792065i	$0.290994\pi$
$812$	−5.73243	+	19.4969i	−0.201169	+	0.684206i
$813$	−28.0991	−	10.3343i	−0.985478	−	0.362440i
$814$	−7.93091	+	1.39843i	−0.277978	+	0.0490150i
$815$	−0.227976	−	0.314261i	−0.00798565	−	0.0110081i
$816$	4.82409	+	1.31000i	0.168877	+	0.0458593i
$817$	−2.75144	−	31.4491i	−0.0962607	−	1.10026i
$818$	48.9843	−	13.1253i	1.71269	−	0.458915i
$819$	0.0312659	−	1.01211i	0.00109252	−	0.0353661i
$820$	12.5180	+	64.6499i	0.437147	+	2.25767i
$821$	−0.358992	−	0.0633000i	−0.0125289	−	0.00220919i	0.167380	−	0.985892i	$-0.446469\pi$
$821$	−0.358992	−	0.0633000i	−0.0125289	−	0.00220919i	−0.179909	+	0.983683i	$0.557580\pi$
$822$	−20.6193	−	57.2489i	−0.719179	−	1.99678i
$823$	6.26564	−	2.92172i	0.218407	−	0.101845i	−0.310336	−	0.950627i	$-0.600442\pi$
$823$	6.26564	−	2.92172i	0.218407	−	0.101845i	0.528742	+	0.848782i	$0.322664\pi$
$824$	6.16136	−	5.16999i	0.214641	−	0.180105i
$825$	−11.5493	+	34.9717i	−0.402096	+	1.21756i
$826$	21.2027	−	11.5677i	0.737738	−	0.402490i
$827$	14.5273	+	3.89257i	0.505162	+	0.135358i	0.502395	−	0.864638i	$-0.332452\pi$
$827$	14.5273	+	3.89257i	0.505162	+	0.135358i	0.00276736	+	0.999996i	$0.499119\pi$
$828$	4.28330	−	45.4385i	0.148855	−	1.57910i
$829$	17.3710	−	10.0291i	0.603319	−	0.348327i	−0.167027	−	0.985952i	$-0.553417\pi$
$829$	17.3710	−	10.0291i	0.603319	−	0.348327i	0.770346	+	0.637626i	$0.220083\pi$
$830$	7.10695	−	12.7994i	0.246686	−	0.444272i
$831$	−7.54834	+	27.7968i	−0.261849	+	0.964260i
$832$	−1.62424	−	0.142103i	−0.0563104	−	0.00492652i
$833$	8.96053	+	9.87119i	0.310464	+	0.342017i
$834$	−86.7857	−	7.88676i	−3.00514	−	0.273096i
$835$	35.7306	−	36.9464i	1.23651	−	1.27858i
$836$	27.1315	+	15.6644i	0.938364	+	0.541765i
$837$	0.883129	+	0.331554i	0.0305254	+	0.0114602i
$838$	63.5218	+	17.0206i	2.19433	+	0.587968i
$839$	4.67340	−	26.5041i	0.161344	−	0.915025i	−0.791411	−	0.611284i	$-0.790653\pi$
$839$	4.67340	−	26.5041i	0.161344	−	0.915025i	0.952755	−	0.303741i	$-0.0982356\pi$
$840$	−9.97879	+	16.8608i	−0.344301	+	0.581754i
$841$	20.5049	+	7.46318i	0.707066	+	0.257351i
$842$	−35.8823	+	16.7322i	−1.23659	+	0.576629i
$843$	−0.0918899	+	27.3409i	−0.00316486	+	0.941672i
$844$	−26.2793	−	4.63375i	−0.904571	−	0.159500i
$845$	9.47198	−	27.4439i	0.325846	−	0.944099i
$846$	−22.2350	−	13.0374i	−0.764454	−	0.448236i
$847$	−2.08450	+	18.6299i	−0.0716244	+	0.640132i
$848$	1.45024	+	16.5763i	0.0498015	+	0.569234i
$849$	5.67550	−	12.0651i	0.194783	−	0.414074i
$850$	−17.8314	+	11.1064i	−0.611613	+	0.380945i
$851$	1.55805	−	4.28069i	0.0534091	−	0.146740i
$852$	−18.2897	+	6.58738i	−0.626595	+	0.225680i
$853$	−15.1332	+	1.32398i	−0.518151	+	0.0453323i	−0.343232	−	0.939251i	$-0.611522\pi$
$853$	−15.1332	+	1.32398i	−0.518151	+	0.0453323i	−0.174919	+	0.984583i	$0.555966\pi$
$854$	4.82865	−	12.3312i	0.165233	−	0.421965i
$855$	11.2123	+	13.0940i	0.383453	+	0.447805i
$856$	−7.82954			−0.267608
$857$	−8.86175	−	12.6559i	−0.302712	−	0.432317i	0.638762	−	0.769405i	$-0.279447\pi$
$857$	−8.86175	−	12.6559i	−0.302712	−	0.432317i	−0.941473	+	0.337088i	$0.890558\pi$
$858$	2.07303	+	0.00696724i	0.0707722	+	0.000237858i
$859$	−9.10662	+	25.0202i	−0.310714	+	0.853679i	0.681799	+	0.731539i	$0.261198\pi$
$859$	−9.10662	+	25.0202i	−0.310714	+	0.853679i	−0.992513	+	0.122140i	$0.961024\pi$
$860$	8.17454	+	78.3223i	0.278749	+	2.67077i
$861$	2.81091	+	46.9921i	0.0957955	+	1.60149i
$862$	32.2291	−	22.5670i	1.09773	−	0.768636i
$863$	−5.22300	+	19.4925i	−0.177793	+	0.663532i	0.818266	+	0.574840i	$0.194936\pi$
$863$	−5.22300	+	19.4925i	−0.177793	+	0.663532i	−0.996059	+	0.0886927i	$0.971731\pi$
$864$	−3.61967	+	37.0649i	−0.123144	+	1.26097i
$865$	−14.7004	−	1.03867i	−0.499829	−	0.0353160i
$866$	−25.9114	−	71.1909i	−0.880504	−	2.41916i
$867$	14.8288	+	17.7934i	0.503612	+	0.604295i
$868$	1.14666	−	0.762291i	0.0389201	−	0.0258738i
$869$	−41.2310	+	34.5969i	−1.39867	+	1.17362i
$870$	−18.9265	−	12.8789i	−0.641669	−	0.436637i
$871$	0.299856	−	1.70057i	0.0101602	−	0.0576216i
$872$	−5.85871	−	1.56984i	−0.198401	−	0.0531614i
$873$	−17.3138	−	1.63210i	−0.585983	−	0.0552382i
$874$	−26.0545	+	15.0426i	−0.881307	+	0.508823i
$875$	8.39682	+	28.3636i	0.283864	+	0.958864i
$876$	29.7487	+	13.9940i	1.00511	+	0.472812i
$877$	−50.5101	−	4.41906i	−1.70560	−	0.149221i	−0.807753	−	0.589521i	$-0.799316\pi$
$877$	−50.5101	−	4.41906i	−1.70560	−	0.149221i	−0.897851	+	0.440300i	$0.854872\pi$
$878$	−1.37861	−	2.95643i	−0.0465258	−	0.0997748i
$879$	45.9973	+	21.6374i	1.55145	+	0.729811i
$880$	12.5984	+	6.99534i	0.424690	+	0.235813i
$881$	−0.590192	+	0.340747i	−0.0198841	+	0.0114801i	−0.509909	−	0.860228i	$-0.670321\pi$
$881$	−0.590192	+	0.340747i	−0.0198841	+	0.0114801i	0.490025	+	0.871708i	$0.336988\pi$
$882$	−28.6198	+	36.4298i	−0.963678	+	1.22666i
$883$	−8.29706	−	30.9651i	−0.279218	−	1.04206i	−0.952961	−	0.303091i	$-0.901981\pi$
$883$	−8.29706	−	30.9651i	−0.279218	−	1.04206i	0.673743	−	0.738966i	$-0.264685\pi$
$884$	0.533567	+	0.447716i	0.0179458	+	0.0150583i
$885$	2.99376	+	15.7448i	0.100634	+	0.529256i
$886$	0.0794009	+	0.450305i	0.00266753	+	0.0151283i
$887$	23.2191	+	16.2582i	0.779620	+	0.545896i	0.894279	−	0.447509i	$-0.147689\pi$
$887$	23.2191	+	16.2582i	0.779620	+	0.545896i	−0.114659	+	0.993405i	$0.536578\pi$
$888$	0.981263	−	2.66806i	0.0329290	−	0.0895343i
$889$	−10.2247	+	16.7611i	−0.342925	+	0.562148i
$890$	73.0141	−	35.5458i	2.44744	−	1.19150i
$891$	0.514524	−	38.2708i	0.0172372	−	1.28212i
$892$	−42.5848	+	11.4106i	−1.42585	+	0.382054i
$893$	0.872281	+	9.97022i	0.0291898	+	0.333641i
$894$	5.07980	+	3.58241i	0.169894	+	0.119814i
$895$	17.4857	+	14.1807i	0.584484	+	0.474009i
$896$	27.5131	+	24.2427i	0.919150	+	0.809891i
$897$	−0.589731	+	1.01356i	−0.0196906	+	0.0338419i
$898$	−34.8172	+	3.04611i	−1.16187	+	0.101650i
$899$	0.243210	+	0.421252i	0.00811150	+	0.0140495i
$900$	−28.5110	−	32.1899i	−0.950365	−	1.07300i
$901$	10.4563	−	18.1109i	0.348350	−	0.603360i
$902$	−96.0101	+	8.39979i	−3.19679	+	0.279683i
$903$	−1.54913	+	56.2748i	−0.0515518	+	1.87271i
$904$	5.20403	−	0.917611i	0.173083	−	0.0305193i
$905$	5.48385	−	2.10049i	0.182289	−	0.0698226i
$906$	−3.24936	−	4.67392i	−0.107953	−	0.155280i
$907$	24.3714	+	11.3646i	0.809240	+	0.377355i	0.782783	−	0.622295i	$-0.213800\pi$
$907$	24.3714	+	11.3646i	0.809240	+	0.377355i	0.0264571	+	0.999650i	$0.491577\pi$
$908$	−70.8430	+	18.9823i	−2.35101	+	0.629951i
$909$	10.6184	−	28.5747i	0.352190	−	0.947763i
$910$	1.37096	−	0.944850i	0.0454469	−	0.0313215i
$911$	−13.4026	−	36.8233i	−0.444047	−	1.22001i	−0.936808	−	0.349844i	$-0.886234\pi$
$911$	−13.4026	−	36.8233i	−0.444047	−	1.22001i	0.492761	−	0.870165i	$-0.335988\pi$
$912$	5.85257	−	3.35281i	0.193798	−	0.111022i
$913$	10.3388	+	7.23929i	0.342164	+	0.239586i
$914$	−71.2403	+	59.7777i	−2.35642	+	1.97727i
$915$	6.80646	+	5.55797i	0.225015	+	0.183741i
$916$	−1.67378	+	9.49247i	−0.0553032	+	0.313640i
$917$	12.3598	−	16.7741i	0.408157	−	0.553929i
$918$	14.2009	−	16.5816i	0.468701	−	0.547274i
$919$	−9.23068	+	5.32934i	−0.304492	+	0.175799i	−0.644459	−	0.764639i	$-0.722917\pi$
$919$	−9.23068	+	5.32934i	−0.304492	+	0.175799i	0.339967	+	0.940437i	$0.389584\pi$
$920$	19.4569	−	11.6717i	0.641474	−	0.384803i
$921$	20.5559	+	44.4718i	0.677339	+	1.46540i
$922$	−41.9436	+	59.9017i	−1.38134	+	1.97276i
$923$	0.497574	+	0.0435321i	0.0163778	+	0.00143288i
$924$	−44.8647	−	33.2914i	−1.47594	−	1.09521i
$925$	−1.94297	−	3.82702i	−0.0638846	−	0.125832i
$926$			66.5313i			2.18635i
$927$	3.18421	+	12.2114i	0.104583	+	0.401075i
$928$	−13.5788	+	13.5788i	−0.445747	+	0.445747i
$929$	−4.55438	+	25.8292i	−0.149424	+	0.847428i	0.814283	+	0.580468i	$0.197130\pi$
$929$	−4.55438	+	25.8292i	−0.149424	+	0.847428i	−0.963708	+	0.266960i	$0.913981\pi$
$930$	0.421443	+	1.49274i	0.0138197	+	0.0489490i
$931$	17.9674	+	0.868868i	0.588859	+	0.0284760i
$932$	−45.3067	−	31.7241i	−1.48407	−	1.03916i
$933$	−16.0465	−	44.5528i	−0.525340	−	1.45859i
$934$	−0.537425	−	1.47656i	−0.0175851	−	0.0483146i
$935$	−7.92735	−	16.2835i	−0.259252	−	0.532526i
$936$	−0.370142	+	0.631268i	−0.0120985	+	0.0206336i
$937$	42.7407	−	11.4523i	1.39628	−	0.374131i	0.519270	−	0.854610i	$-0.326204\pi$
$937$	42.7407	−	11.4523i	1.39628	−	0.374131i	0.877006	+	0.480479i	$0.159537\pi$
$938$	−57.1968	+	54.4977i	−1.86754	+	1.77941i
$939$	32.7729	+	8.89963i	1.06950	+	0.290428i
$940$	−2.59155	−	24.8303i	−0.0845271	−	0.809875i
$941$	15.8294	+	18.8647i	0.516022	+	0.614971i	0.959635	−	0.281247i	$-0.0907480\pi$
$941$	15.8294	+	18.8647i	0.516022	+	0.614971i	−0.443613	+	0.896218i	$0.646304\pi$
$942$	−31.8545	−	11.7155i	−1.03788	−	0.381711i
$943$	23.0398	−	49.4089i	0.750278	−	1.60898i
$944$	6.27082			0.204098
$945$	−17.1885	−	25.4864i	−0.559142	−	0.829072i
$946$	−115.253			−3.74718
$947$	11.8565	−	25.4264i	0.385285	−	0.826246i	−0.614032	−	0.789281i	$-0.710453\pi$
$947$	11.8565	−	25.4264i	0.385285	−	0.826246i	0.999317	−	0.0369648i	$-0.0117689\pi$
$948$	−10.7044	−	61.9237i	−0.347661	−	2.01119i
$949$	−0.542955	−	0.647069i	−0.0176251	−	0.0210048i
$950$	−6.41642	+	27.6097i	−0.208176	+	0.895776i
$951$	9.96766	−	9.90089i	0.323224	−	0.321058i
$952$	−2.26804	−	9.36370i	−0.0735075	−	0.303479i
$953$	−31.7286	+	8.50165i	−1.02779	+	0.275396i	−0.733045	−	0.680180i	$-0.761901\pi$
$953$	−31.7286	+	8.50165i	−1.02779	+	0.275396i	−0.294745	+	0.955576i	$0.595235\pi$
$954$	68.1201	+	25.3135i	2.20547	+	0.819556i
$955$	−5.98911	+	17.3527i	−0.193803	+	0.561521i
$956$	27.2319	+	74.8190i	0.880742	+	2.41982i
$957$	12.7368	−	15.0760i	0.411723	−	0.487337i
$958$	−56.1746	−	39.3339i	−1.81492	−	1.27082i
$959$	27.8544	−	31.6121i	0.899466	−	1.02081i
$960$	−42.5317	+	25.3196i	−1.37270	+	0.817187i
$961$	−5.37737	+	30.4966i	−0.173464	+	0.983761i
$962$	−0.170828	+	0.170828i	−0.00550771	+	0.00550771i
$963$	5.26645	−	11.0985i	0.169709	−	0.357645i
$964$		−	43.9898i		−	1.41682i
$965$	−16.9359	+	17.5122i	−0.545185	+	0.563737i
$966$	49.2286	−	21.3267i	1.58390	−	0.686176i
$967$	−39.4566	−	3.45200i	−1.26884	−	0.111009i	−0.567222	−	0.823565i	$-0.691982\pi$
$967$	−39.4566	−	3.45200i	−1.26884	−	0.111009i	−0.701615	+	0.712556i	$0.747538\pi$
$968$	7.77051	−	11.0974i	0.249754	−	0.356685i
$969$	−8.44217	−	0.767193i	−0.271202	−	0.0246458i
$970$	−14.7099	−	24.5216i	−0.472306	−	0.787342i
$971$	−35.5260	+	20.5109i	−1.14008	+	0.658228i	−0.946451	−	0.322847i	$-0.895360\pi$
$971$	−35.5260	+	20.5109i	−1.14008	+	0.658228i	−0.193632	+	0.981074i	$0.562027\pi$
$972$	38.3197	+	22.9910i	1.22911	+	0.737436i
$973$	−24.1722	−	55.2866i	−0.774925	−	1.77241i
$974$	2.82753	−	16.0357i	0.0906000	−	0.513818i
$975$	0.317934	+	1.05810i	0.0101820	+	0.0338863i
$976$	2.63385	−	2.21006i	0.0843074	−	0.0707423i
$977$	−27.9345	−	19.5600i	−0.893704	−	0.625778i	0.0338665	−	0.999426i	$-0.489218\pi$
$977$	−27.9345	−	19.5600i	−0.893704	−	0.625778i	−0.927571	+	0.373648i	$0.878107\pi$
$978$	−0.00222972	+	0.663431i	−7.12985e−5	+	0.0212142i
$979$	23.9445	+	65.7869i	0.765269	+	2.10256i
$980$	−44.8488	−	1.41737i	−1.43264	−	0.0452762i
$981$	6.16607	−	7.24892i	0.196867	−	0.231440i
$982$	48.2947	−	12.9405i	1.54115	−	0.412949i
$983$	13.6838	+	6.38086i	0.436445	+	0.203518i	0.628407	−	0.777885i	$-0.283707\pi$
$983$	13.6838	+	6.38086i	0.436445	+	0.203518i	−0.191962	+	0.981402i	$0.561485\pi$
$984$	14.4814	−	30.7849i	0.461650	−	0.981386i
$985$	−20.0980	+	45.0528i	−0.640376	+	1.43550i
$986$	11.0864	−	1.95482i	0.353062	−	0.0622543i
$987$	0.491116	−	17.8406i	0.0156324	−	0.567874i
$988$	0.936246	−	0.0819110i	0.0297860	−	0.00260593i
$989$	32.5970	−	56.4597i	1.03652	−	1.79531i
$990$	51.1891	−	36.6117i	1.62690	−	1.16360i
$991$	−3.52178	−	6.09990i	−0.111873	−	0.193770i	0.804652	−	0.593746i	$-0.202352\pi$
$991$	−3.52178	−	6.09990i	−0.111873	−	0.193770i	−0.916525	+	0.399976i	$0.869018\pi$
$992$	1.29617	−	0.113400i	0.0411534	−	0.00360045i
$993$	21.1372	+	0.0710397i	0.670767	+	0.00225438i
$994$	−17.1453	−	15.1072i	−0.543815	−	0.479172i
$995$	5.73186	−	7.06776i	0.181712	−	0.224063i
$996$	−13.3764	+	6.18287i	−0.423848	+	0.195912i
$997$	−1.27496	−	14.5729i	−0.0403784	−	0.461528i	−0.989288	−	0.145979i	$-0.953367\pi$
$997$	−1.27496	−	14.5729i	−0.0403784	−	0.461528i	0.948909	−	0.315549i	$-0.102189\pi$
$998$	−29.8259	+	7.99182i	−0.944121	+	0.252977i
$999$	3.12200	+	3.18560i	0.0987757	+	0.100788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.dh.a.137.122	✓	1680
5.3	odd	4	inner	945.2.dh.a.893.19	yes	1680
7.2	even	3		945.2.do.a.2.19	yes	1680
27.14	odd	18		945.2.do.a.662.122	yes	1680
35.23	odd	12		945.2.do.a.758.122	yes	1680
135.68	even	36		945.2.do.a.473.19	yes	1680
189.149	odd	18	inner	945.2.dh.a.527.19	yes	1680
945.338	even	36	inner	945.2.dh.a.338.122	yes	1680

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.dh.a.137.122	✓	1680	1.1	even	1	trivial
945.2.dh.a.338.122	yes	1680	945.338	even	36	inner
945.2.dh.a.527.19	yes	1680	189.149	odd	18	inner
945.2.dh.a.893.19	yes	1680	5.3	odd	4	inner
945.2.do.a.2.19	yes	1680	7.2	even	3
945.2.do.a.473.19	yes	1680	135.68	even	36
945.2.do.a.662.122	yes	1680	27.14	odd	18
945.2.do.a.758.122	yes	1680	35.23	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.dh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.932323 - 1.99937i) q^{2} +(1.33056 - 1.10888i) q^{3} +(-1.84269 - 2.19603i) q^{4} +(1.73673 + 1.40846i) q^{5} +(-0.976541 - 3.69412i) q^{6} +(1.91548 - 1.82509i) q^{7} +(-1.84688 + 0.494869i) q^{8} +(0.540792 - 2.95085i) q^{9} +O(q^{10})\)	\(q+(0.932323 - 1.99937i) q^{2} +(1.33056 - 1.10888i) q^{3} +(-1.84269 - 2.19603i) q^{4} +(1.73673 + 1.40846i) q^{5} +(-0.976541 - 3.69412i) q^{6} +(1.91548 - 1.82509i) q^{7} +(-1.84688 + 0.494869i) q^{8} +(0.540792 - 2.95085i) q^{9} +(4.43524 - 2.15923i) q^{10} +(1.45451 + 3.99622i) q^{11} +(-4.88694 - 0.878644i) q^{12} +(0.104503 + 0.0731741i) q^{13} +(-1.86319 - 5.53132i) q^{14} +(3.87264 - 0.0517672i) q^{15} +(0.263142 - 1.49235i) q^{16} +(-1.34669 + 1.34669i) q^{17} +(-5.39567 - 3.83239i) q^{18} +2.56978i q^{19} +(-0.107221 - 6.40927i) q^{20} +(0.524868 - 4.55242i) q^{21} +(9.34601 + 0.817670i) q^{22} +(-3.04390 + 4.34714i) q^{23} +(-1.90864 + 2.70641i) q^{24} +(1.03246 + 4.89224i) q^{25} +(0.243733 - 0.140719i) q^{26} +(-2.55257 - 4.52597i) q^{27} +(-7.53758 - 0.843380i) q^{28} +(0.465271 - 2.63868i) q^{29} +(3.50705 - 7.79111i) q^{30} +(-0.139069 + 0.116692i) q^{31} +(-5.87092 - 4.11086i) q^{32} +(6.36662 + 3.70436i) q^{33} +(1.43699 + 3.94810i) q^{34} +(5.89724 - 0.471802i) q^{35} +(-7.47668 + 4.24991i) q^{36} +(-0.829150 + 0.222170i) q^{37} +(5.13794 + 2.39586i) q^{38} +(0.220189 - 0.0185186i) q^{39} +(-3.90453 - 1.74181i) q^{40} +(-10.1168 + 1.78386i) q^{41} +(-8.61263 - 5.29373i) q^{42} +(-12.2381 + 1.07069i) q^{43} +(6.09563 - 10.5579i) q^{44} +(5.09538 - 4.36315i) q^{45} +(5.85365 + 10.1388i) q^{46} +(3.87980 - 0.339439i) q^{47} +(-1.30471 - 2.27746i) q^{48} +(0.338110 - 6.99183i) q^{49} +(10.7440 + 2.49688i) q^{50} +(-0.298545 + 3.28518i) q^{51} +(-0.0318747 - 0.364330i) q^{52} +(-10.6064 + 2.84198i) q^{53} +(-11.4289 + 0.883883i) q^{54} +(-3.10245 + 8.98898i) q^{55} +(-2.63447 + 4.31862i) q^{56} +(2.84956 + 3.41925i) q^{57} +(-4.84192 - 3.39035i) q^{58} +(0.718579 + 4.07526i) q^{59} +(-7.24975 - 8.40904i) q^{60} +(1.73808 + 1.45842i) q^{61} +(0.103655 + 0.386845i) q^{62} +(-4.34969 - 6.63929i) q^{63} +(-11.0680 + 6.39013i) q^{64} +(0.0784311 + 0.274273i) q^{65} +(13.3421 - 9.27560i) q^{66} +(-5.72038 - 12.2674i) q^{67} +(5.43892 + 0.475844i) q^{68} +(0.770337 + 9.15944i) q^{69} +(4.55482 - 12.2306i) q^{70} +(3.39061 - 1.95757i) q^{71} +(0.461512 + 5.71749i) q^{72} +(-6.39550 - 1.71367i) q^{73} +(-0.328835 + 1.86491i) q^{74} +(6.79864 + 5.36456i) q^{75} +(5.64331 - 4.73530i) q^{76} +(10.0795 + 5.00008i) q^{77} +(0.168262 - 0.457506i) q^{78} +(4.32870 + 11.8930i) q^{79} +(2.55893 - 2.22119i) q^{80} +(-8.41509 - 3.19159i) q^{81} +(-5.86550 + 21.8903i) q^{82} +(2.43111 - 1.70228i) q^{83} +(-10.9644 + 7.23606i) q^{84} +(-4.23562 + 0.442073i) q^{85} +(-9.26912 + 25.4667i) q^{86} +(-2.30690 - 4.02686i) q^{87} +(-4.66390 - 6.66074i) q^{88} +16.4623 q^{89} +(-3.97302 - 14.2554i) q^{90} +(0.333723 - 0.0505646i) q^{91} +(15.1554 - 1.32593i) q^{92} +(-0.0556421 + 0.309476i) q^{93} +(2.93856 - 8.07363i) q^{94} +(-3.61944 + 4.46301i) q^{95} +(-12.3701 + 1.04036i) q^{96} +(-0.505228 - 5.77479i) q^{97} +(-13.6640 - 7.19465i) q^{98} +(12.5789 - 2.13091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1680 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 36 q^{6} - 12 q^{7} - 36 q^{8}+O(q^{10}) \) 1680 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 36 * q^6 - 12 * q^7 - 36 * q^8	\( 1680 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 36 q^{6} - 12 q^{7} - 36 q^{8} - 12 q^{10} - 24 q^{11} - 6 q^{12} - 24 q^{13} - 24 q^{15} - 12 q^{16} - 6 q^{18} - 24 q^{20} - 24 q^{21} - 24 q^{22} - 30 q^{23} - 6 q^{25} - 24 q^{27} - 24 q^{28} + 30 q^{30} - 12 q^{31} - 18 q^{32} - 6 q^{33} - 72 q^{35} - 84 q^{36} + 6 q^{37} + 42 q^{38} + 90 q^{40} - 72 q^{41} + 36 q^{42} - 24 q^{43} - 6 q^{45} + 12 q^{46} - 6 q^{47} - 96 q^{48} - 72 q^{50} - 12 q^{51} - 30 q^{52} + 90 q^{53} - 48 q^{55} - 180 q^{56} - 24 q^{57} - 6 q^{58} - 102 q^{60} - 84 q^{61} - 36 q^{62} - 54 q^{63} - 78 q^{65} - 12 q^{66} - 6 q^{67} - 246 q^{68} - 12 q^{70} - 72 q^{71} - 126 q^{72} + 6 q^{73} + 66 q^{75} - 12 q^{77} - 84 q^{78} - 24 q^{81} - 12 q^{82} - 24 q^{83} - 24 q^{85} + 204 q^{86} - 102 q^{87} - 78 q^{88} + 30 q^{90} - 12 q^{91} + 108 q^{92} - 78 q^{93} + 114 q^{95} + 204 q^{96} - 24 q^{97} - 18 q^{98}+O(q^{100}) \) 1680 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 36 * q^6 - 12 * q^7 - 36 * q^8 - 12 * q^10 - 24 * q^11 - 6 * q^12 - 24 * q^13 - 24 * q^15 - 12 * q^16 - 6 * q^18 - 24 * q^20 - 24 * q^21 - 24 * q^22 - 30 * q^23 - 6 * q^25 - 24 * q^27 - 24 * q^28 + 30 * q^30 - 12 * q^31 - 18 * q^32 - 6 * q^33 - 72 * q^35 - 84 * q^36 + 6 * q^37 + 42 * q^38 + 90 * q^40 - 72 * q^41 + 36 * q^42 - 24 * q^43 - 6 * q^45 + 12 * q^46 - 6 * q^47 - 96 * q^48 - 72 * q^50 - 12 * q^51 - 30 * q^52 + 90 * q^53 - 48 * q^55 - 180 * q^56 - 24 * q^57 - 6 * q^58 - 102 * q^60 - 84 * q^61 - 36 * q^62 - 54 * q^63 - 78 * q^65 - 12 * q^66 - 6 * q^67 - 246 * q^68 - 12 * q^70 - 72 * q^71 - 126 * q^72 + 6 * q^73 + 66 * q^75 - 12 * q^77 - 84 * q^78 - 24 * q^81 - 12 * q^82 - 24 * q^83 - 24 * q^85 + 204 * q^86 - 102 * q^87 - 78 * q^88 + 30 * q^90 - 12 * q^91 + 108 * q^92 - 78 * q^93 + 114 * q^95 + 204 * q^96 - 24 * q^97 - 18 * q^98

Introduction

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