LMFDB - Embedded newform 847.2.n.e.130.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(9,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 18]))

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

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

chi := DirichletCharacter("847.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			130.1
Character	$\chi$	$=$	847.130
Dual form			847.2.n.e.632.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79416 + 0.381361i) q^{2} +(0.229826 + 2.18665i) q^{3} +(1.24649 - 0.554971i) q^{4} +(-0.425267 + 0.472307i) q^{5} +(-1.24625 - 3.83555i) q^{6} +(1.28679 - 2.31175i) q^{7} +(0.943117 - 0.685215i) q^{8} +(-1.79416 + 0.381361i) q^{9} +O(q^{10})$	\(q+(-1.79416 + 0.381361i) q^{2} +(0.229826 + 2.18665i) q^{3} +(1.24649 - 0.554971i) q^{4} +(-0.425267 + 0.472307i) q^{5} +(-1.24625 - 3.83555i) q^{6} +(1.28679 - 2.31175i) q^{7} +(0.943117 - 0.685215i) q^{8} +(-1.79416 + 0.381361i) q^{9} +(0.582878 - 1.00958i) q^{10} +(1.50000 + 2.59808i) q^{12} +(-0.556635 + 1.71315i) q^{13} +(-1.42710 + 4.63838i) q^{14} +(-1.13051 - 0.821361i) q^{15} +(-3.25678 + 3.61702i) q^{16} +(2.77231 + 0.589272i) q^{17} +(3.07358 - 1.36844i) q^{18} +(-5.08218 - 2.26273i) q^{19} +(-0.267973 + 0.824735i) q^{20} +(5.35071 + 2.28245i) q^{21} +(-1.08288 - 1.87560i) q^{23} +(1.71507 + 1.90478i) q^{24} +(0.480421 + 4.57090i) q^{25} +(0.345366 - 3.28594i) q^{26} +(0.792054 + 2.43769i) q^{27} +(0.321012 - 3.59569i) q^{28} +(8.43830 + 6.13079i) q^{29} +(2.34154 + 1.04252i) q^{30} +(4.30272 + 4.77866i) q^{31} +(3.29804 - 5.71237i) q^{32} -5.19869 q^{34} +(0.544625 + 1.59087i) q^{35} +(-2.02475 + 1.47107i) q^{36} +(-0.634056 + 6.03264i) q^{37} +(9.98117 + 2.12156i) q^{38} +(-3.87397 - 0.823439i) q^{39} +(-0.0774450 + 0.736840i) q^{40} +(-6.09648 + 4.42935i) q^{41} +(-10.4705 - 2.05454i) q^{42} -4.86718 q^{43} +(0.582878 - 1.00958i) q^{45} +(2.65814 + 2.95216i) q^{46} +(-2.58921 - 1.15279i) q^{47} +(-8.65763 - 6.29014i) q^{48} +(-3.68835 - 5.94946i) q^{49} +(-2.60511 - 8.01771i) q^{50} +(-0.651382 + 6.19749i) q^{51} +(0.256909 + 2.44433i) q^{52} +(4.99827 + 5.55114i) q^{53} +(-2.35071 - 4.07155i) q^{54} +(-0.370450 - 3.06197i) q^{56} +(3.77978 - 11.6330i) q^{57} +(-17.4777 - 7.78158i) q^{58} +(10.7860 - 4.80225i) q^{59} +(-1.86499 - 0.396416i) q^{60} +(-2.89835 + 3.21894i) q^{61} +(-9.54217 - 6.93279i) q^{62} +(-1.42710 + 4.63838i) q^{63} +(-0.730655 + 2.24872i) q^{64} +(-0.572413 - 0.991448i) q^{65} +(0.801309 - 1.38791i) q^{67} +(3.78267 - 0.804031i) q^{68} +(3.85240 - 2.79893i) q^{69} +(-1.58384 - 2.64658i) q^{70} +(1.32631 + 4.08197i) q^{71} +(-1.43079 + 1.58905i) q^{72} +(-14.6107 + 6.50512i) q^{73} +(-1.16301 - 11.0653i) q^{74} +(-9.88452 + 2.10102i) q^{75} -7.59061 q^{76} +7.26456 q^{78} +(-4.65777 + 0.990040i) q^{79} +(-0.323343 - 3.07640i) q^{80} +(-10.1753 + 4.53035i) q^{81} +(9.24888 - 10.2719i) q^{82} +(-2.85273 - 8.77980i) q^{83} +(7.93628 - 0.124443i) q^{84} +(-1.45729 + 1.05878i) q^{85} +(8.73250 - 1.85615i) q^{86} +(-11.4665 + 19.8606i) q^{87} +(-0.182224 - 0.315621i) q^{89} +(-0.660765 + 2.03363i) q^{90} +(3.24409 + 3.49126i) q^{91} +(-2.39070 - 1.73694i) q^{92} +(-9.46036 + 10.5068i) q^{93} +(5.08509 + 1.08087i) q^{94} +(3.22999 - 1.43808i) q^{95} +(13.2489 + 5.89879i) q^{96} +(-0.802231 + 2.46901i) q^{97} +(8.88637 + 9.26770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8}+O(q^{10}) $ 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} + 36 q^{10} + 36 q^{12} + 22 q^{13} - 12 q^{14} + 14 q^{15} + 2 q^{16} - 3 q^{17} + 10 q^{18} - 11 q^{19} - 28 q^{20} + 40 q^{21} - 48 q^{23} + 2 q^{24} + 3 q^{25} + q^{26} - 4 q^{27} - 13 q^{28} + 18 q^{29} + 2 q^{30} - 3 q^{31} + 12 q^{32} - 80 q^{34} - 9 q^{35} + 18 q^{36} - 4 q^{37} + 8 q^{38} - 5 q^{39} - 3 q^{40} + 10 q^{41} + 2 q^{42} + 16 q^{43} + 36 q^{45} - 10 q^{46} - 3 q^{47} - 20 q^{48} + 24 q^{49} + 6 q^{50} + 2 q^{51} - 7 q^{52} + 17 q^{53} + 32 q^{54} + 12 q^{56} - 40 q^{57} - 13 q^{58} + 8 q^{59} + 6 q^{60} - 24 q^{61} - 26 q^{62} - 12 q^{63} + 14 q^{64} - 60 q^{65} + 64 q^{67} + 5 q^{68} + 6 q^{69} + 27 q^{70} - 14 q^{71} + 10 q^{72} - 20 q^{73} + 22 q^{74} + 25 q^{75} - 312 q^{76} - 48 q^{78} + 3 q^{79} + 9 q^{80} - 17 q^{81} + 41 q^{82} + 22 q^{83} - 12 q^{84} - 22 q^{85} - 21 q^{86} - 120 q^{87} - 4 q^{89} - 20 q^{90} + 15 q^{91} - 50 q^{92} - 26 q^{93} - 10 q^{94} - 17 q^{95} + 27 q^{96} - 18 q^{97} - 96 q^{98}+O(q^{100}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 + 36 * q^10 + 36 * q^12 + 22 * q^13 - 12 * q^14 + 14 * q^15 + 2 * q^16 - 3 * q^17 + 10 * q^18 - 11 * q^19 - 28 * q^20 + 40 * q^21 - 48 * q^23 + 2 * q^24 + 3 * q^25 + q^26 - 4 * q^27 - 13 * q^28 + 18 * q^29 + 2 * q^30 - 3 * q^31 + 12 * q^32 - 80 * q^34 - 9 * q^35 + 18 * q^36 - 4 * q^37 + 8 * q^38 - 5 * q^39 - 3 * q^40 + 10 * q^41 + 2 * q^42 + 16 * q^43 + 36 * q^45 - 10 * q^46 - 3 * q^47 - 20 * q^48 + 24 * q^49 + 6 * q^50 + 2 * q^51 - 7 * q^52 + 17 * q^53 + 32 * q^54 + 12 * q^56 - 40 * q^57 - 13 * q^58 + 8 * q^59 + 6 * q^60 - 24 * q^61 - 26 * q^62 - 12 * q^63 + 14 * q^64 - 60 * q^65 + 64 * q^67 + 5 * q^68 + 6 * q^69 + 27 * q^70 - 14 * q^71 + 10 * q^72 - 20 * q^73 + 22 * q^74 + 25 * q^75 - 312 * q^76 - 48 * q^78 + 3 * q^79 + 9 * q^80 - 17 * q^81 + 41 * q^82 + 22 * q^83 - 12 * q^84 - 22 * q^85 - 21 * q^86 - 120 * q^87 - 4 * q^89 - 20 * q^90 + 15 * q^91 - 50 * q^92 - 26 * q^93 - 10 * q^94 - 17 * q^95 + 27 * q^96 - 18 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−1.79416	+	0.381361i	−1.26866	+	0.269663i	−0.792596	−	0.609747i	$-0.791271\pi$
$2$	−1.79416	+	0.381361i	−1.26866	+	0.269663i	−0.476067	+	0.879409i	$0.657938\pi$
$3$	0.229826	+	2.18665i	0.132690	+	1.26246i	0.834864	+	0.550456i	$0.185546\pi$
$3$	0.229826	+	2.18665i	0.132690	+	1.26246i	−0.702174	+	0.712005i	$0.747787\pi$
$4$	1.24649	−	0.554971i	0.623243	−	0.277486i
$5$	−0.425267	+	0.472307i	−0.190185	+	0.211222i	−0.830695	−	0.556728i	$-0.812057\pi$
$5$	−0.425267	+	0.472307i	−0.190185	+	0.211222i	0.640510	+	0.767950i	$0.278723\pi$
$6$	−1.24625	−	3.83555i	−0.508778	−	1.56586i
$7$	1.28679	−	2.31175i	0.486361	−	0.873758i
$7$	1.28679	−	2.31175i	0.486361	−	0.873758i
$8$	0.943117	−	0.685215i	0.333442	−	0.242260i
$9$	−1.79416	+	0.381361i	−0.598054	+	0.127120i
$10$	0.582878	−	1.00958i	0.184322	−	0.319256i
$11$		0			0
$11$		0			0
$12$	1.50000	+	2.59808i	0.433013	+	0.750000i
$13$	−0.556635	+	1.71315i	−0.154383	+	0.475141i	−0.998098	−	0.0616500i	$-0.980364\pi$
$13$	−0.556635	+	1.71315i	−0.154383	+	0.475141i	0.843715	+	0.536791i	$0.180364\pi$
$14$	−1.42710	+	4.63838i	−0.381408	+	1.23966i
$15$	−1.13051	−	0.821361i	−0.291895	−	0.212074i
$16$	−3.25678	+	3.61702i	−0.814194	+	0.904254i
$17$	2.77231	+	0.589272i	0.672383	+	0.142920i	0.531437	−	0.847098i	$-0.321652\pi$
$17$	2.77231	+	0.589272i	0.672383	+	0.142920i	0.140946	+	0.990017i	$0.454986\pi$
$18$	3.07358	−	1.36844i	0.724449	−	0.322545i
$19$	−5.08218	−	2.26273i	−1.16593	−	0.519106i	−0.269810	−	0.962914i	$-0.586961\pi$
$19$	−5.08218	−	2.26273i	−1.16593	−	0.519106i	−0.896122	+	0.443807i	$0.853628\pi$
$20$	−0.267973	+	0.824735i	−0.0599205	+	0.184416i
$21$	5.35071	+	2.28245i	1.16762	+	0.498073i
$22$		0			0
$23$	−1.08288	−	1.87560i	−0.225796	−	0.391090i	0.730762	−	0.682632i	$-0.239165\pi$
$23$	−1.08288	−	1.87560i	−0.225796	−	0.391090i	−0.956558	+	0.291542i	$0.905832\pi$
$24$	1.71507	+	1.90478i	0.350088	+	0.388812i
$25$	0.480421	+	4.57090i	0.0960841	+	0.914179i
$26$	0.345366	−	3.28594i	0.0677319	−	0.644426i
$27$	0.792054	+	2.43769i	0.152431	+	0.469134i
$28$	0.321012	−	3.59569i	0.0606655	−	0.679521i
$29$	8.43830	+	6.13079i	1.56695	+	1.13846i	0.930002	+	0.367555i	$0.119805\pi$
$29$	8.43830	+	6.13079i	1.56695	+	1.13846i	0.636952	+	0.770904i	$0.280195\pi$
$30$	2.34154	+	1.04252i	0.427506	+	0.190338i
$31$	4.30272	+	4.77866i	0.772792	+	0.858272i	0.993114	−	0.117155i	$-0.0373775\pi$
$31$	4.30272	+	4.77866i	0.772792	+	0.858272i	−0.220322	+	0.975427i	$0.570711\pi$
$32$	3.29804	−	5.71237i	0.583016	−	1.00981i
$33$		0			0
$34$	−5.19869			−0.891568
$35$	0.544625	+	1.59087i	0.0920584	+	0.268906i
$36$	−2.02475	+	1.47107i	−0.337458	+	0.245178i
$37$	−0.634056	+	6.03264i	−0.104238	+	0.991760i	0.809958	+	0.586488i	$0.199490\pi$
$37$	−0.634056	+	6.03264i	−0.104238	+	0.991760i	−0.914196	+	0.405272i	$0.867177\pi$
$38$	9.98117	+	2.12156i	1.61916	+	0.344163i
$39$	−3.87397	−	0.823439i	−0.620332	−	0.131856i
$40$	−0.0774450	+	0.736840i	−0.0122451	+	0.116505i
$41$	−6.09648	+	4.42935i	−0.952110	+	0.691749i	−0.951305	−	0.308251i	$-0.900256\pi$
$41$	−6.09648	+	4.42935i	−0.952110	+	0.691749i	−0.000805217		1.00000i	$0.500256\pi$
$42$	−10.4705	−	2.05454i	−1.61563	−	0.317022i
$43$	−4.86718			−0.742238			−0.371119	−	0.928585i	$-0.621026\pi$
$43$	−4.86718			−0.742238			−0.371119	+	0.928585i	$0.621026\pi$
$44$		0			0
$45$	0.582878	−	1.00958i	0.0868904	−	0.150499i
$46$	2.65814	+	2.95216i	0.391921	+	0.435272i
$47$	−2.58921	−	1.15279i	−0.377675	−	0.168152i	0.209115	−	0.977891i	$-0.432942\pi$
$47$	−2.58921	−	1.15279i	−0.377675	−	0.168152i	−0.586790	+	0.809739i	$0.699608\pi$
$48$	−8.65763	−	6.29014i	−1.24962	−	0.907903i
$49$	−3.68835	−	5.94946i	−0.526906	−	0.849923i
$50$	−2.60511	−	8.01771i	−0.368418	−	1.13388i
$51$	−0.651382	+	6.19749i	−0.0912118	+	0.867822i
$52$	0.256909	+	2.44433i	0.0356269	+	0.338967i
$53$	4.99827	+	5.55114i	0.686565	+	0.762508i	0.981177	−	0.193109i	$-0.0618572\pi$
$53$	4.99827	+	5.55114i	0.686565	+	0.762508i	−0.294612	+	0.955617i	$0.595190\pi$
$54$	−2.35071	−	4.07155i	−0.319891	−	0.554068i
$55$		0			0
$56$	−0.370450	−	3.06197i	−0.0495034	−	0.409174i
$57$	3.77978	−	11.6330i	0.500644	−	1.54082i
$58$	−17.4777	−	7.78158i	−2.29494	−	1.02177i
$59$	10.7860	−	4.80225i	1.40422	−	0.625199i	0.441887	−	0.897071i	$-0.354309\pi$
$59$	10.7860	−	4.80225i	1.40422	−	0.625199i	0.962333	+	0.271872i	$0.0876427\pi$
$60$	−1.86499	−	0.396416i	−0.240769	−	0.0511771i
$61$	−2.89835	+	3.21894i	−0.371095	+	0.412143i	−0.899550	−	0.436819i	$-0.856105\pi$
$61$	−2.89835	+	3.21894i	−0.371095	+	0.412143i	0.528454	+	0.848962i	$0.322772\pi$
$62$	−9.54217	−	6.93279i	−1.21186	−	0.880465i
$63$	−1.42710	+	4.63838i	−0.179797	+	0.584380i
$64$	−0.730655	+	2.24872i	−0.0913318	+	0.281090i
$65$	−0.572413	−	0.991448i	−0.0709990	−	0.122974i
$66$		0			0
$67$	0.801309	−	1.38791i	0.0978954	−	0.169560i	−0.812918	−	0.582378i	$-0.802122\pi$
$67$	0.801309	−	1.38791i	0.0978954	−	0.169560i	0.910813	+	0.412818i	$0.135456\pi$
$68$	3.78267	−	0.804031i	0.458716	−	0.0975031i
$69$	3.85240	−	2.79893i	0.463775	−	0.336952i
$70$	−1.58384	−	2.64658i	−0.189305	−	0.316327i
$71$	1.32631	+	4.08197i	0.157404	+	0.484441i	0.998397	−	0.0566066i	$-0.0180281\pi$
$71$	1.32631	+	4.08197i	0.157404	+	0.484441i	−0.840992	+	0.541047i	$0.818028\pi$
$72$	−1.43079	+	1.58905i	−0.168620	+	0.187272i
$73$	−14.6107	+	6.50512i	−1.71006	+	0.761367i	−0.711800	+	0.702382i	$0.752120\pi$
$73$	−14.6107	+	6.50512i	−1.71006	+	0.761367i	−0.998259	+	0.0589850i	$0.981214\pi$
$74$	−1.16301	−	11.0653i	−0.135197	−	1.28632i
$75$	−9.88452	+	2.10102i	−1.14137	+	0.242605i
$76$	−7.59061			−0.870703
$77$		0			0
$78$	7.26456			0.822549
$79$	−4.65777	+	0.990040i	−0.524040	+	0.111388i	−0.462334	−	0.886706i	$-0.652988\pi$
$79$	−4.65777	+	0.990040i	−0.524040	+	0.111388i	−0.0617069	+	0.998094i	$0.519654\pi$
$80$	−0.323343	−	3.07640i	−0.0361508	−	0.343952i
$81$	−10.1753	+	4.53035i	−1.13059	+	0.503372i
$82$	9.24888	−	10.2719i	1.02137	−	1.13434i
$83$	−2.85273	−	8.77980i	−0.313128	−	0.963708i	−0.976518	−	0.215435i	$-0.930883\pi$
$83$	−2.85273	−	8.77980i	−0.313128	−	0.963708i	0.663391	−	0.748273i	$-0.269117\pi$
$84$	7.93628	−	0.124443i	0.865919	−	0.0135778i
$85$	−1.45729	+	1.05878i	−0.158065	+	0.114841i
$86$	8.73250	−	1.85615i	0.941649	−	0.200154i
$87$	−11.4665	+	19.8606i	−1.22934	+	2.12928i
$88$		0			0
$89$	−0.182224	−	0.315621i	−0.0193157	−	0.0334558i	0.856206	−	0.516635i	$-0.172815\pi$
$89$	−0.182224	−	0.315621i	−0.0193157	−	0.0334558i	−0.875522	+	0.483179i	$0.839482\pi$
$90$	−0.660765	+	2.03363i	−0.0696508	+	0.214363i
$91$	3.24409	+	3.49126i	0.340073	+	0.365983i
$92$	−2.39070	−	1.73694i	−0.249247	−	0.181089i
$93$	−9.46036	+	10.5068i	−0.980993	+	1.08950i
$94$	5.08509	+	1.08087i	0.524487	+	0.111483i
$95$	3.22999	−	1.43808i	0.331390	−	0.147544i
$96$	13.2489	+	5.89879i	1.35221	+	0.602043i
$97$	−0.802231	+	2.46901i	−0.0814542	+	0.250690i	−0.983487	−	0.180976i	$-0.942074\pi$
$97$	−0.802231	+	2.46901i	−0.0814542	+	0.250690i	0.902033	+	0.431667i	$0.142074\pi$
$98$	8.88637	+	9.26770i	0.897659	+	0.936179i
$99$		0			0
$100$	3.13555	+	5.43094i	0.313555	+	0.543094i
$101$	−6.62447	−	7.35722i	−0.659159	−	0.732070i	0.317168	−	0.948369i	$-0.397268\pi$
$101$	−6.62447	−	7.35722i	−0.659159	−	0.732070i	−0.976327	+	0.216299i	$0.930601\pi$
$102$	−1.19479	−	11.3677i	−0.118302	−	1.12557i
$103$	−0.651382	+	6.19749i	−0.0641826	+	0.610657i	0.914401	+	0.404809i	$0.132662\pi$
$103$	−0.651382	+	6.19749i	−0.0641826	+	0.610657i	−0.978584	+	0.205848i	$0.934005\pi$
$104$	0.648901	+	1.99711i	0.0636300	+	0.195833i
$105$	−3.35350	+	1.55653i	−0.327268	+	0.151901i
$106$	−11.0847	−	8.05349i	−1.07664	−	0.782224i
$107$	10.1393	+	4.51429i	0.980199	+	0.436413i	0.833350	−	0.552746i	$-0.186420\pi$
$107$	10.1393	+	4.51429i	0.980199	+	0.436413i	0.146850	+	0.989159i	$0.453087\pi$
$108$	2.34013	+	2.59898i	0.225179	+	0.250087i
$109$	7.15202	−	12.3877i	0.685039	−	1.18652i	−0.288385	−	0.957514i	$-0.593118\pi$
$109$	7.15202	−	12.3877i	0.685039	−	1.18652i	0.973424	−	0.229008i	$-0.0735483\pi$
$110$		0			0
$111$	−13.3370			−1.26589
$112$	4.17084	+	12.1832i	0.394107	+	1.15120i
$113$	7.02989	−	5.10751i	0.661316	−	0.480474i	−0.205791	−	0.978596i	$-0.565977\pi$
$113$	7.02989	−	5.10751i	0.661316	−	0.480474i	0.867107	+	0.498122i	$0.165977\pi$
$114$	−2.34518	+	22.3129i	−0.219646	+	2.08979i
$115$	1.34637	+	0.286180i	0.125550	+	0.0266864i
$116$	13.9206	+	2.95892i	1.29250	+	0.274729i
$117$	0.345366	−	3.28594i	0.0319291	−	0.303785i
$118$	−17.5205	+	12.7294i	−1.61289	+	1.17183i
$119$	4.92963	−	5.65060i	0.451898	−	0.517990i
$120$	−1.62901			−0.148707
$121$		0			0
$122$	3.97252	−	6.88061i	0.359655	−	0.622942i
$123$	−11.0866	−	12.3129i	−0.999641	−	1.11021i
$124$	8.01530	+	3.56864i	0.719795	+	0.320473i
$125$	−4.93404	−	3.58479i	−0.441314	−	0.320633i
$126$	0.791549	−	8.86623i	0.0705168	−	0.789866i
$127$	6.48902	+	19.9712i	0.575808	+	1.77215i	0.633413	+	0.773814i	$0.281654\pi$
$127$	6.48902	+	19.9712i	0.575808	+	1.77215i	−0.0576053	+	0.998339i	$0.518346\pi$
$128$	−0.925618	+	8.80667i	−0.0818138	+	0.778407i
$129$	−1.11860	−	10.6428i	−0.0984875	−	0.937046i
$130$	1.40510	+	1.56052i	0.123235	+	0.136867i
$131$	6.85071	+	11.8658i	0.598549	+	1.03672i	0.993035	+	0.117816i	$0.0375893\pi$
$131$	6.85071	+	11.8658i	0.598549	+	1.03672i	−0.394486	+	0.918902i	$0.629077\pi$
$132$		0			0
$133$	−11.7706	+	8.83705i	−1.02064	+	0.766270i
$134$	−0.908383	+	2.79572i	−0.0784724	+	0.241513i
$135$	−1.48817	−	0.662577i	−0.128082	−	0.0570256i
$136$	3.01839	−	1.34387i	0.258825	−	0.115236i
$137$	−7.10581	−	1.51039i	−0.607090	−	0.129041i	−0.105898	−	0.994377i	$-0.533772\pi$
$137$	−7.10581	−	1.51039i	−0.607090	−	0.129041i	−0.501192	+	0.865336i	$0.667105\pi$
$138$	−5.84442	+	6.49089i	−0.497510	+	0.552541i
$139$	2.10556	+	1.52978i	0.178591	+	0.129754i	0.673490	−	0.739197i	$-0.264795\pi$
$139$	2.10556	+	1.52978i	0.178591	+	0.129754i	−0.494898	+	0.868951i	$0.664795\pi$
$140$	1.56175	+	1.68075i	0.131992	+	0.142049i
$141$	1.92568	−	5.92663i	0.162171	−	0.499112i
$142$	−3.93632	−	6.81790i	−0.330328	−	0.572146i
$143$		0			0
$144$	4.46379	−	7.73152i	0.371983	−	0.644293i
$145$	−6.48415	+	1.37825i	−0.538479	+	0.114457i
$146$	23.7332	−	17.2432i	1.96418	−	1.42706i
$147$	12.1617	−	9.43245i	1.00308	−	0.777975i
$148$	2.55760	+	7.87148i	0.210233	+	0.647032i
$149$	−0.669131	+	0.743145i	−0.0548173	+	0.0608808i	−0.769930	−	0.638129i	$-0.779709\pi$
$149$	−0.669131	+	0.743145i	−0.0548173	+	0.0608808i	0.715112	+	0.699009i	$0.246375\pi$
$150$	16.9332	−	7.53913i	1.38259	−	0.615568i
$151$	−0.181403	−	1.72593i	−0.0147624	−	0.140454i	0.984658	−	0.174495i	$-0.0558292\pi$
$151$	−0.181403	−	1.72593i	−0.0147624	−	0.140454i	−0.999420	+	0.0340403i	$0.989163\pi$
$152$	−6.34355	+	1.34836i	−0.514530	+	0.109367i
$153$	−5.19869			−0.420289
$154$		0			0
$155$	−4.08680			−0.328260
$156$	−5.28584	+	1.12354i	−0.423206	+	0.0899551i
$157$	0.829913	+	7.89610i	0.0662343	+	0.630177i	0.976406	+	0.215945i	$0.0692832\pi$
$157$	0.829913	+	7.89610i	0.0662343	+	0.630177i	−0.910171	+	0.414232i	$0.864050\pi$
$158$	7.97923	−	3.55258i	0.634793	−	0.282628i
$159$	−10.9896	+	12.2052i	−0.871536	+	0.967939i
$160$	1.29544	+	3.98697i	0.102414	+	0.315198i
$161$	−5.72935	+	0.0898375i	−0.451536	+	0.00708019i
$162$	16.5285	−	12.0086i	1.29860	−	0.943488i
$163$	15.6557	−	3.32772i	1.22625	−	0.260647i	0.451128	−	0.892459i	$-0.351022\pi$
$163$	15.6557	−	3.32772i	1.22625	−	0.260647i	0.775122	+	0.631812i	$0.217689\pi$
$164$	−5.14101	+	8.90449i	−0.401446	+	0.695324i
$165$		0			0
$166$	8.46652	+	14.6644i	0.657130	+	1.13818i
$167$	0.358217	−	1.10248i	0.0277196	−	0.0853122i	−0.936240	−	0.351362i	$-0.885719\pi$
$167$	0.358217	−	1.10248i	0.0277196	−	0.0853122i	0.963959	+	0.266050i	$0.0857186\pi$
$168$	6.61032	−	1.51376i	0.509997	−	0.116789i
$169$	7.89219	+	5.73401i	0.607092	+	0.441078i
$170$	2.21083	−	2.45538i	0.169563	−	0.188319i
$171$	9.98117	+	2.12156i	0.763279	+	0.162240i
$172$	−6.06687	+	2.70114i	−0.462594	+	0.205960i
$173$	−0.907567	−	0.404075i	−0.0690011	−	0.0307213i	0.371946	−	0.928254i	$-0.378691\pi$
$173$	−0.907567	−	0.404075i	−0.0690011	−	0.0307213i	−0.440947	+	0.897533i	$0.645357\pi$
$174$	12.9987	−	40.0060i	0.985431	−	3.03285i
$175$	11.1850	+	4.77117i	0.845503	+	0.360667i
$176$		0			0
$177$	12.9797	+	22.4815i	0.975615	+	1.68982i
$178$	0.447305	+	0.496782i	0.0335269	+	0.0372354i
$179$	2.05523	+	19.5542i	0.153615	+	1.46155i	0.751374	+	0.659876i	$0.229391\pi$
$179$	2.05523	+	19.5542i	0.153615	+	1.46155i	−0.597759	+	0.801676i	$0.703942\pi$
$180$	0.166265	−	1.58190i	0.0123926	−	0.117908i
$181$	−7.37705	−	22.7042i	−0.548332	−	1.68759i	−0.712933	−	0.701232i	$-0.752634\pi$
$181$	−7.37705	−	22.7042i	−0.548332	−	1.68759i	0.164602	−	0.986360i	$-0.447366\pi$
$182$	−7.15184	−	5.02671i	−0.530130	−	0.372605i
$183$	−7.70480	−	5.59787i	−0.569555	−	0.413806i
$184$	−2.30647	−	1.02691i	−0.170035	−	0.0757046i
$185$	−2.57962	−	2.86495i	−0.189657	−	0.210636i
$186$	12.9665	−	22.4587i	0.950752	−	1.64675i
$187$		0			0
$188$	−3.86718			−0.282043
$189$	6.65453	+	1.30577i	0.484046	+	0.0949806i
$190$	−5.24669	+	3.81194i	−0.380635	+	0.276548i
$191$	1.16358	−	11.0708i	0.0841939	−	0.801052i	−0.868207	−	0.496203i	$-0.834727\pi$
$191$	1.16358	−	11.0708i	0.0841939	−	0.801052i	0.952401	−	0.304849i	$-0.0986060\pi$
$192$	−5.08509	−	1.08087i	−0.366985	−	0.0780050i
$193$	−3.53563	−	0.751522i	−0.254500	−	0.0540957i	0.0788946	−	0.996883i	$-0.474861\pi$
$193$	−3.53563	−	0.751522i	−0.254500	−	0.0540957i	−0.333395	+	0.942787i	$0.608194\pi$
$194$	0.497747	−	4.73574i	0.0357361	−	0.340007i
$195$	2.03639	−	1.47952i	0.145829	−	0.105951i
$196$	−7.89925	−	5.36899i	−0.564232	−	0.383500i
$197$	2.41831			0.172298			0.0861489	−	0.996282i	$-0.472544\pi$
$197$	2.41831			0.172298			0.0861489	+	0.996282i	$0.472544\pi$
$198$		0			0
$199$	9.24809	−	16.0182i	0.655580	−	1.13550i	−0.326168	−	0.945312i	$-0.605758\pi$
$199$	9.24809	−	16.0182i	0.655580	−	1.13550i	0.981748	−	0.190186i	$-0.0609091\pi$
$200$	3.58514	+	3.98170i	0.253508	+	0.281549i
$201$	3.21902	+	1.43320i	0.227052	+	0.101090i
$202$	14.6911	+	10.6737i	1.03366	+	0.751000i
$203$	25.0311	−	11.6182i	1.75684	−	0.815437i
$204$	2.62749	+	8.08658i	0.183961	+	0.566174i
$205$	0.500619	−	4.76307i	0.0349647	−	0.332667i
$206$	−1.19479	−	11.3677i	−0.0832452	−	0.792025i
$207$	2.65814	+	2.95216i	0.184753	+	0.205189i
$208$	−4.38364	−	7.59270i	−0.303951	−	0.526459i
$209$		0			0
$210$	5.42312	−	4.07155i	0.374231	−	0.280964i
$211$	−2.42738	+	7.47072i	−0.167108	+	0.514305i	−0.999185	−	0.0403541i	$-0.987151\pi$
$211$	−2.42738	+	7.47072i	−0.167108	+	0.514305i	0.832078	+	0.554659i	$0.187151\pi$
$212$	9.31099	+	4.14552i	0.639481	+	0.284715i
$213$	−8.62100	+	3.83832i	−0.590701	+	0.262997i
$214$	−19.9130	−	4.23265i	−1.36123	−	0.289338i
$215$	2.06985	−	2.29880i	0.141163	−	0.156777i
$216$	2.41734	+	1.75630i	0.164479	+	0.119501i
$217$	16.5837	−	3.79768i	1.12578	−	0.257803i
$218$	−8.10771	+	24.9530i	−0.549123	+	1.69003i
$219$	−17.5823	−	30.4535i	−1.18810	−	2.05786i
$220$		0			0
$221$	−2.55267	+	4.42136i	−0.171711	+	0.297413i
$222$	23.9287	−	5.08620i	1.60599	−	0.341363i
$223$	−16.4530	+	11.9538i	−1.10177	+	0.800484i	−0.981348	−	0.192239i	$-0.938425\pi$
$223$	−16.4530	+	11.9538i	−1.10177	+	0.800484i	−0.120423	+	0.992723i	$0.538425\pi$
$224$	−8.96167	−	14.9748i	−0.598777	−	1.00055i
$225$	−2.60511	−	8.01771i	−0.173674	−	0.534514i
$226$	−10.6649	+	11.8446i	−0.709421	+	0.787892i
$227$	6.59545	−	2.93649i	0.437756	−	0.194901i	−0.176012	−	0.984388i	$-0.556320\pi$
$227$	6.59545	−	2.93649i	0.437756	−	0.194901i	0.613768	+	0.789487i	$0.289653\pi$
$228$	−1.74452	−	16.5980i	−0.115534	−	1.09923i
$229$	−11.8075	+	2.50977i	−0.780264	+	0.165850i	−0.580791	−	0.814053i	$-0.697257\pi$
$229$	−11.8075	+	2.50977i	−0.780264	+	0.165850i	−0.199474	+	0.979903i	$0.563923\pi$
$230$	−2.52475			−0.166477
$231$		0			0
$232$	12.1592			0.798291
$233$	7.37739	−	1.56811i	0.483309	−	0.102731i	0.0401877	−	0.999192i	$-0.487204\pi$
$233$	7.37739	−	1.56811i	0.483309	−	0.102731i	0.443121	+	0.896462i	$0.353871\pi$
$234$	0.633485	+	6.02721i	0.0414122	+	0.394011i
$235$	1.64558	−	0.732658i	0.107346	−	0.0477934i
$236$	10.7795	−	11.9719i	0.701686	−	0.779301i
$237$	−3.23534	−	9.95737i	−0.210158	−	0.646800i
$238$	−6.68962	+	12.0181i	−0.433624	+	0.779015i
$239$	7.96578	−	5.78748i	0.515264	−	0.374361i	−0.299553	−	0.954080i	$-0.596838\pi$
$239$	7.96578	−	5.78748i	0.515264	−	0.374361i	0.814817	+	0.579719i	$0.196838\pi$
$240$	6.65268	−	1.41407i	0.429429	−	0.0912779i
$241$	0.837515	−	1.45062i	0.0539491	−	0.0934426i	−0.837790	−	0.545993i	$-0.816152\pi$
$241$	0.837515	−	1.45062i	0.0539491	−	0.0934426i	0.891739	+	0.452551i	$0.149486\pi$
$242$		0			0
$243$	−8.40011	−	14.5494i	−0.538867	−	0.933346i
$244$	−1.82633	+	5.62086i	−0.116919	+	0.359839i
$245$	4.37851	+	0.788080i	0.279733	+	0.0503486i
$246$	24.5867	+	17.8633i	1.56759	+	1.13892i
$247$	6.70531	−	7.44700i	0.426649	−	0.473841i
$248$	7.33238	+	1.55854i	0.465606	+	0.0989677i
$249$	18.5427	−	8.25573i	1.17509	−	0.523186i
$250$	10.2195	+	4.55004i	0.646341	+	0.287770i
$251$	6.11045	−	18.8060i	0.385688	−	1.18703i	−0.550292	−	0.834973i	$-0.685483\pi$
$251$	6.11045	−	18.8060i	0.385688	−	1.18703i	0.935980	−	0.352054i	$-0.114517\pi$
$252$	0.795307	+	6.57367i	0.0500997	+	0.414102i
$253$		0			0
$254$	−19.2586	−	33.3568i	−1.20839	−	2.09299i
$255$	−2.65011	−	2.94324i	−0.165956	−	0.184313i
$256$	−2.19211	−	20.8566i	−0.137007	−	1.30353i
$257$	−0.284314	+	2.70507i	−0.0177350	+	0.168737i	−0.999804	−	0.0197829i	$-0.993702\pi$
$257$	−0.284314	+	2.70507i	−0.0177350	+	0.168737i	0.982069	+	0.188520i	$0.0603692\pi$
$258$	6.06570	+	18.6683i	0.377634	+	1.16224i
$259$	13.1300	+	9.22851i	0.815861	+	0.573432i
$260$	−1.26373	−	0.918153i	−0.0783731	−	0.0569414i
$261$	−17.4777	−	7.78158i	−1.08184	−	0.481668i
$262$	−16.8164	−	18.6765i	−1.03892	−	1.15384i
$263$	−6.34744	+	10.9941i	−0.391400	+	0.677924i	−0.992634	−	0.121148i	$-0.961342\pi$
$263$	−6.34744	+	10.9941i	−0.391400	+	0.677924i	0.601235	+	0.799073i	$0.294676\pi$
$264$		0			0
$265$	−4.74744			−0.291633
$266$	17.7482	−	20.3439i	1.08821	−	1.24737i
$267$	0.648272	−	0.470997i	0.0396736	−	0.0288246i
$268$	0.228571	−	2.17471i	0.0139622	−	0.132842i
$269$	6.93834	+	1.47479i	0.423038	+	0.0899195i	0.414511	−	0.910044i	$-0.363953\pi$
$269$	6.93834	+	1.47479i	0.423038	+	0.0899195i	0.00852661	+	0.999964i	$0.497286\pi$
$270$	2.92270	+	0.621240i	0.177870	+	0.0378074i
$271$	1.90411	−	18.1164i	0.115666	−	1.10049i	−0.770601	−	0.637317i	$-0.780044\pi$
$271$	1.90411	−	18.1164i	0.115666	−	1.10049i	0.886268	−	0.463173i	$-0.153289\pi$
$272$	−11.1602	+	8.10836i	−0.676686	+	0.491642i
$273$	−6.88857	+	7.89606i	−0.416915	+	0.477891i
$274$	13.3250			0.804991
$275$		0			0
$276$	3.24864	−	5.62680i	0.195545	−	0.338694i
$277$	9.26654	+	10.2915i	0.556773	+	0.618359i	0.954162	−	0.299292i	$-0.0967503\pi$
$277$	9.26654	+	10.2915i	0.556773	+	0.618359i	−0.397389	+	0.917650i	$0.630084\pi$
$278$	−4.36111	−	1.94169i	−0.261562	−	0.116455i
$279$	−9.54217	−	6.93279i	−0.571274	−	0.415055i
$280$	1.60373	+	1.12719i	0.0958414	+	0.0673626i
$281$	6.49953	+	20.0035i	0.387730	+	1.19331i	0.934481	+	0.356014i	$0.115864\pi$
$281$	6.49953	+	20.0035i	0.387730	+	1.19331i	−0.546751	+	0.837295i	$0.684136\pi$
$282$	−1.19479	+	11.3677i	−0.0711489	+	0.676937i
$283$	−0.0368406	−	0.350514i	−0.00218994	−	0.0208359i	0.993372	−	0.114941i	$-0.0366678\pi$
$283$	−0.0368406	−	0.350514i	−0.00218994	−	0.0208359i	−0.995562	+	0.0941048i	$0.970001\pi$
$284$	3.91860	+	4.35205i	0.232526	+	0.258247i
$285$	3.88692	+	6.73234i	0.230241	+	0.398789i
$286$		0			0
$287$	2.39465	+	19.7932i	0.141352	+	1.16835i
$288$	−3.73874	+	11.5066i	−0.220307	+	0.678036i
$289$	−8.19182	−	3.64723i	−0.481872	−	0.214543i
$290$	11.1080	−	4.94560i	0.652284	−	0.290415i
$291$	−5.58323	−	1.18675i	−0.327295	−	0.0695687i
$292$	−14.6019	+	16.2171i	−0.854513	+	0.949033i
$293$	2.80183	+	2.03565i	0.163685	+	0.118924i	0.666612	−	0.745405i	$-0.267744\pi$
$293$	2.80183	+	2.03565i	0.163685	+	0.118924i	−0.502928	+	0.864329i	$0.667744\pi$
$294$	−18.2229	+	21.5613i	−1.06278	+	1.25748i
$295$	−2.31881	+	7.13655i	−0.135006	+	0.415506i
$296$	3.53566	+	6.12395i	0.205506	+	0.355947i
$297$		0			0
$298$	0.917122	−	1.58850i	0.0531274	−	0.0920194i
$299$	3.81595	−	0.811104i	0.220682	−	0.0469074i
$300$	−11.1549	+	8.10451i	−0.644029	+	0.467914i
$301$	−6.26303	+	11.2517i	−0.360995	+	0.648536i
$302$	0.983669	+	3.02742i	0.0566038	+	0.174209i
$303$	14.5652	−	16.1762i	0.836747	−	0.929301i
$304$	24.7359	−	11.0131i	1.41870	−	0.631646i
$305$	−0.287757	−	2.73782i	−0.0164769	−	0.156767i
$306$	9.32729	−	1.98258i	0.533205	−	0.113336i
$307$	−6.51473			−0.371815			−0.185908	−	0.982567i	$-0.559523\pi$
$307$	−6.51473			−0.371815			−0.185908	+	0.982567i	$0.559523\pi$
$308$		0			0
$309$	−13.7014			−0.779447
$310$	7.33238	−	1.55854i	0.416451	−	0.0885194i
$311$	−1.21568	−	11.5664i	−0.0689346	−	0.655869i	−0.973367	−	0.229252i	$-0.926372\pi$
$311$	−1.21568	−	11.5664i	−0.0689346	−	0.655869i	0.904432	−	0.426617i	$-0.140295\pi$
$312$	−4.21784	+	1.87791i	−0.238788	+	0.106315i
$313$	−18.1319	+	20.1375i	−1.02488	+	1.13824i	−0.0345612	+	0.999403i	$0.511003\pi$
$313$	−18.1319	+	20.1375i	−1.02488	+	1.13824i	−0.990315	+	0.138838i	$0.955663\pi$
$314$	−4.50026	−	13.8504i	−0.253964	−	0.781622i
$315$	−1.58384	−	2.64658i	−0.0892393	−	0.149118i
$316$	−5.25640	+	3.81900i	−0.295696	+	0.214836i
$317$	−3.77733	+	0.802896i	−0.212156	+	0.0450952i	−0.312763	−	0.949831i	$-0.601255\pi$
$317$	−3.77733	+	0.802896i	−0.212156	+	0.0450952i	0.100607	+	0.994926i	$0.467921\pi$
$318$	15.0626	−	26.0892i	0.844668	−	1.46301i
$319$		0			0
$320$	−0.751365	−	1.30140i	−0.0420026	−	0.0727506i
$321$	−7.54089	+	23.2085i	−0.420892	+	1.29537i
$322$	10.2451	−	2.34613i	0.570938	−	0.130745i
$323$	−12.7560	−	9.26778i	−0.709763	−	0.515673i
$324$	−10.1692	+	11.2940i	−0.564955	+	0.627446i
$325$	−8.09803	−	1.72129i	−0.449198	−	0.0954800i
$326$	−26.8198	+	11.9409i	−1.48541	+	0.661347i
$327$	28.7312	+	12.7919i	1.58884	+	0.707396i
$328$	−2.71464	+	8.35480i	−0.149891	+	0.461316i
$329$	−5.99673	+	4.50220i	−0.330610	+	0.248214i
$330$		0			0
$331$	−3.07514	−	5.32630i	−0.169025	−	0.292760i	0.769052	−	0.639186i	$-0.220729\pi$
$331$	−3.07514	−	5.32630i	−0.169025	−	0.292760i	−0.938077	+	0.346426i	$0.887395\pi$
$332$	−8.42842	−	9.36071i	−0.462570	−	0.513736i
$333$	−1.16301	−	11.0653i	−0.0637327	−	0.606376i
$334$	−0.222257	+	2.11463i	−0.0121613	+	0.115707i
$335$	0.314748	+	0.968695i	0.0171965	+	0.0529255i
$336$	−25.6818	+	11.9202i	−1.40105	+	0.650298i
$337$	9.51464	+	6.91279i	0.518296	+	0.376564i	0.815961	−	0.578106i	$-0.196208\pi$
$337$	9.51464	+	6.91279i	0.518296	+	0.376564i	−0.297666	+	0.954670i	$0.596208\pi$
$338$	−16.3466	−	7.27797i	−0.889137	−	0.395869i
$339$	12.7840	+	14.1980i	0.694330	+	0.771132i
$340$	−1.22890	+	2.12851i	−0.0666462	+	0.115435i
$341$		0			0
$342$	−18.7169			−1.01209
$343$	−18.4998	+	0.870813i	−0.998894	+	0.0470195i
$344$	−4.59032	+	3.33506i	−0.247493	+	0.179814i
$345$	−0.316344	+	3.00981i	−0.0170314	+	0.162043i
$346$	1.78242	+	0.378865i	0.0958235	+	0.0203679i
$347$	0.822414	+	0.174809i	0.0441495	+	0.00938426i	0.229933	−	0.973206i	$-0.426149\pi$
$347$	0.822414	+	0.174809i	0.0441495	+	0.00938426i	−0.185784	+	0.982591i	$0.559482\pi$
$348$	−3.27079	+	31.1195i	−0.175333	+	1.66818i
$349$	−7.38773	+	5.36750i	−0.395456	+	0.287316i	−0.767688	−	0.640824i	$-0.778593\pi$
$349$	−7.38773	+	5.36750i	−0.395456	+	0.287316i	0.372231	+	0.928140i	$0.378593\pi$
$350$	−21.8871	−	4.29475i	−1.16992	−	0.229564i
$351$	−4.61701			−0.246438
$352$		0			0
$353$	−11.3639	+	19.6829i	−0.604840	+	1.04761i	0.387237	+	0.921980i	$0.373429\pi$
$353$	−11.3639	+	19.6829i	−0.604840	+	1.04761i	−0.992077	+	0.125633i	$0.959904\pi$
$354$	−31.8613	−	35.3855i	−1.69341	−	1.88072i
$355$	−2.49198	−	1.10950i	−0.132261	−	0.0588862i
$356$	−0.402300	−	0.292288i	−0.0213219	−	0.0154912i
$357$	13.4888	+	9.48069i	0.713905	+	0.501772i
$358$	−11.1446	−	34.2996i	−0.589012	−	1.81279i
$359$	2.74058	−	26.0749i	0.144642	−	1.37618i	−0.645735	−	0.763561i	$-0.723449\pi$
$359$	2.74058	−	26.0749i	0.144642	−	1.37618i	0.790378	−	0.612620i	$-0.209884\pi$
$360$	−0.142053	−	1.35154i	−0.00748685	−	0.0712326i
$361$	7.99512	+	8.87948i	0.420796	+	0.467341i
$362$	21.8941	+	37.9217i	1.15073	+	1.99312i
$363$		0			0
$364$	5.98126	+	2.55143i	0.313503	+	0.133731i
$365$	3.14106	−	9.66718i	0.164410	−	0.506003i
$366$	15.9585	+	7.10516i	0.834162	+	0.371393i
$367$	−3.49179	+	1.55465i	−0.182270	+	0.0811518i	−0.495843	−	0.868412i	$-0.665141\pi$
$367$	−3.49179	+	1.55465i	−0.182270	+	0.0811518i	0.313573	+	0.949564i	$0.398474\pi$
$368$	10.3108	+	2.19162i	0.537486	+	0.114246i
$369$	9.24888	−	10.2719i	0.481478	−	0.534735i
$370$	5.72082	+	4.15642i	0.297412	+	0.216082i
$371$	19.2645	−	4.41158i	1.00017	−	0.229038i
$372$	−5.96123	+	18.3468i	−0.309075	+	0.951236i
$373$	−7.55387	−	13.0837i	−0.391124	−	0.677447i	0.601474	−	0.798893i	$-0.294580\pi$
$373$	−7.55387	−	13.0837i	−0.391124	−	0.677447i	−0.992598	+	0.121445i	$0.961247\pi$
$374$		0			0
$375$	6.70469	−	11.6129i	0.346229	−	0.599686i
$376$	−3.23184	+	0.686948i	−0.166669	+	0.0354266i
$377$	−15.2000	+	11.0434i	−0.782839	+	0.568766i
$378$	−12.4373	+	0.195019i	−0.639704	+	0.0100307i
$379$	−3.51552	−	10.8196i	−0.180580	−	0.555768i	0.819264	−	0.573416i	$-0.194382\pi$
$379$	−3.51552	−	10.8196i	−0.180580	−	0.555768i	−0.999844	+	0.0176481i	$0.994382\pi$
$380$	3.22804	−	3.58510i	0.165595	−	0.183912i
$381$	−42.1785	+	18.7791i	−2.16087	+	0.962082i
$382$	2.13429	+	20.3065i	0.109200	+	1.03897i
$383$	−8.69155	+	1.84745i	−0.444117	+	0.0944001i	−0.424542	−	0.905408i	$-0.639565\pi$
$383$	−8.69155	+	1.84745i	−0.444117	+	0.0944001i	−0.0195756	+	0.999808i	$0.506231\pi$
$384$	−19.4698			−0.993564
$385$		0			0
$386$	6.63009			0.337463
$387$	8.73250	−	1.85615i	0.443898	−	0.0943534i
$388$	0.370262	+	3.52280i	0.0187972	+	0.178843i
$389$	−18.1787	+	8.09366i	−0.921695	+	0.410365i	−0.812038	−	0.583604i	$-0.801642\pi$
$389$	−18.1787	+	8.09366i	−0.921695	+	0.410365i	−0.109657	+	0.993970i	$0.534975\pi$
$390$	−3.08938	+	3.43110i	−0.156437	+	0.173741i
$391$	−1.89683	−	5.83785i	−0.0959270	−	0.295233i
$392$	−7.55520	−	3.08373i	−0.381595	−	0.155752i
$393$	−24.3718	+	17.7071i	−1.22939	+	0.893207i
$394$	−4.33884	+	0.922250i	−0.218588	+	0.0464623i
$395$	1.51320	−	2.62093i	0.0761371	−	0.131873i
$396$		0			0
$397$	17.4303	+	30.1902i	0.874803	+	1.51520i	0.856973	+	0.515361i	$0.172342\pi$
$397$	17.4303	+	30.1902i	0.874803	+	1.51520i	0.0178296	+	0.999841i	$0.494324\pi$
$398$	−10.4839	+	32.2660i	−0.525509	+	1.61735i
$399$	−22.0287	−	23.7071i	−1.10281	−	1.18684i
$400$	−18.0976	−	13.1487i	−0.904882	−	0.657435i
$401$	7.62561	−	8.46910i	0.380805	−	0.422927i	−0.522021	−	0.852932i	$-0.674822\pi$
$401$	7.62561	−	8.46910i	0.380805	−	0.422927i	0.902826	+	0.430006i	$0.141489\pi$
$402$	−6.32201	−	1.34379i	−0.315313	−	0.0670219i
$403$	−10.5816	+	4.71122i	−0.527106	+	0.234683i
$404$	−12.3403	−	5.49428i	−0.613955	−	0.273350i
$405$	2.18752	−	6.73249i	0.108699	−	0.334540i
$406$	−40.4792	+	30.3908i	−2.00895	+	1.50827i
$407$		0			0
$408$	3.63228	+	6.29129i	0.179825	+	0.311465i
$409$	−2.73533	−	3.03789i	−0.135253	−	0.150214i	0.671713	−	0.740811i	$-0.265559\pi$
$409$	−2.73533	−	3.03789i	−0.135253	−	0.150214i	−0.806966	+	0.590597i	$0.798892\pi$
$410$	0.918257	+	8.73663i	0.0453495	+	0.431471i
$411$	1.66958	−	15.8850i	0.0823545	−	0.783551i
$412$	2.62749	+	8.08658i	0.129447	+	0.398397i
$413$	2.77776	−	31.1140i	0.136685	−	1.53102i
$414$	−5.89496	−	4.28294i	−0.289722	−	0.210495i
$415$	5.35993	+	2.38640i	0.263109	+	0.117144i
$416$	7.95032	+	8.82972i	0.389796	+	0.432913i
$417$	−2.86118	+	4.95570i	−0.140112	+	0.242682i
$418$		0			0
$419$	32.8002			1.60240			0.801198	−	0.598399i	$-0.204196\pi$
$419$	32.8002			1.60240			0.801198	+	0.598399i	$0.204196\pi$
$420$	−3.31626	+	3.80128i	−0.161817	+	0.185484i
$421$	6.89386	−	5.00868i	0.335986	−	0.244108i	−0.406980	−	0.913437i	$-0.633418\pi$
$421$	6.89386	−	5.00868i	0.335986	−	0.244108i	0.742966	+	0.669329i	$0.233418\pi$
$422$	1.50608	−	14.3294i	0.0733147	−	0.697543i
$423$	5.08509	+	1.08087i	0.247245	+	0.0525536i
$424$	8.51767	+	1.81049i	0.413655	+	0.0879251i
$425$	−1.36163	+	12.9550i	−0.0660487	+	0.628411i
$426$	14.0037	−	10.1743i	0.678480	−	0.492945i
$427$	3.71181	+	10.8423i	0.179627	+	0.524698i
$428$	15.1437			0.732000
$429$		0			0
$430$	−2.83697	+	4.91378i	−0.136811	+	0.236964i
$431$	−11.1975	−	12.4360i	−0.539363	−	0.599023i	0.410434	−	0.911890i	$-0.365377\pi$
$431$	−11.1975	−	12.4360i	−0.539363	−	0.599023i	−0.949797	+	0.312867i	$0.898711\pi$
$432$	−11.3967	−	5.07414i	−0.548325	−	0.244130i
$433$	20.9261	+	15.2037i	1.00564	+	0.730644i	0.963291	−	0.268459i	$-0.0865144\pi$
$433$	20.9261	+	15.2037i	1.00564	+	0.730644i	0.0423535	+	0.999103i	$0.486514\pi$
$434$	−28.3056	+	13.1380i	−1.35871	+	0.630646i
$435$	−4.50397	−	13.8618i	−0.215949	−	0.664622i
$436$	2.04009	−	19.4102i	0.0977028	−	0.929580i
$437$	1.25940	+	11.9824i	0.0602453	+	0.573196i
$438$	43.1593	+	47.9333i	2.06223	+	2.29034i
$439$	4.78430	+	8.28665i	0.228342	+	0.395500i	0.957317	−	0.289040i	$-0.0933362\pi$
$439$	4.78430	+	8.28665i	0.228342	+	0.395500i	−0.728975	+	0.684541i	$0.760003\pi$
$440$		0			0
$441$	8.88637	+	9.26770i	0.423161	+	0.441319i
$442$	2.89377	−	8.90612i	0.137643	−	0.423621i
$443$	17.3875	+	7.74139i	0.826103	+	0.367805i	0.775839	−	0.630931i	$-0.217327\pi$
$443$	17.3875	+	7.74139i	0.826103	+	0.367805i	0.0502640	+	0.998736i	$0.483994\pi$
$444$	−16.6243	+	7.40163i	−0.788956	+	0.351266i
$445$	0.226564	+	0.0481577i	0.0107402	+	0.00228289i
$446$	24.9605	−	27.7215i	1.18192	−	1.31265i
$447$	−1.77878	−	1.29236i	−0.0841333	−	0.0611264i
$448$	4.25828	+	4.58272i	0.201185	+	0.216513i
$449$	10.3034	−	31.7105i	0.486246	−	1.49651i	−0.343921	−	0.938999i	$-0.611755\pi$
$449$	10.3034	−	31.7105i	0.486246	−	1.49651i	0.830167	−	0.557514i	$-0.188245\pi$
$450$	7.73163	+	13.3916i	0.364472	+	0.631285i
$451$		0			0
$452$	5.92813	−	10.2678i	0.278836	−	0.482958i
$453$	3.73231	−	0.793328i	0.175359	−	0.0372738i
$454$	−10.7134	+	7.78377i	−0.502807	+	0.365311i
$455$	−3.02855	+	0.0474884i	−0.141981	+	0.00222629i
$456$	−4.40630	−	13.5612i	−0.206344	−	0.635062i
$457$	8.00315	−	8.88840i	0.374372	−	0.415782i	−0.526289	−	0.850306i	$-0.676417\pi$
$457$	8.00315	−	8.88840i	0.374372	−	0.415782i	0.900660	+	0.434524i	$0.143083\pi$
$458$	20.2275	−	9.00586i	0.945169	−	0.420816i
$459$	0.759353	+	7.22476i	0.0354436	+	0.337223i
$460$	1.83705	−	0.390478i	0.0856531	−	0.0182061i
$461$	12.4896			0.581701			0.290850	−	0.956769i	$-0.406062\pi$
$461$	12.4896			0.581701			0.290850	+	0.956769i	$0.406062\pi$
$462$		0			0
$463$	12.3095			0.572071			0.286035	−	0.958219i	$-0.407662\pi$
$463$	12.3095			0.572071			0.286035	+	0.958219i	$0.407662\pi$
$464$	−49.6568	+	10.5549i	−2.30526	+	0.489998i
$465$	−0.939252	−	8.93639i	−0.0435568	−	0.414415i
$466$	−12.6382	+	5.62689i	−0.585454	+	0.260661i
$467$	21.9212	−	24.3460i	1.01439	−	1.12660i	0.0224711	−	0.999747i	$-0.492847\pi$
$467$	21.9212	−	24.3460i	1.01439	−	1.12660i	0.991922	−	0.126850i	$-0.0404867\pi$
$468$	−1.39311	−	4.28754i	−0.0643964	−	0.198192i
$469$	−2.17737	−	3.63837i	−0.100542	−	0.168004i
$470$	−2.67302	+	1.94206i	−0.123297	+	0.0895808i
$471$	−17.0752	+	3.62945i	−0.786785	+	0.167236i
$472$	6.88191	−	11.9198i	0.316766	−	0.548654i
$473$		0			0
$474$	9.60208	+	16.6313i	0.441038	+	0.763900i
$475$	7.90113	−	24.3172i	0.362529	−	1.11575i
$476$	3.00878	−	9.77920i	0.137907	−	0.448229i
$477$	−11.0847	−	8.05349i	−0.507533	−	0.368744i
$478$	−12.0848	+	13.4215i	−0.552745	+	0.613885i
$479$	−25.4103	−	5.40113i	−1.16103	−	0.246784i	−0.413176	−	0.910651i	$-0.635581\pi$
$479$	−25.4103	−	5.40113i	−1.16103	−	0.246784i	−0.747850	+	0.663867i	$0.768914\pi$
$480$	−8.42037	+	3.74899i	−0.384335	+	0.171117i
$481$	−9.98186	−	4.44421i	−0.455133	−	0.202638i
$482$	−0.949428	+	2.92204i	−0.0432452	+	0.133095i
$483$	−1.51320	−	12.5074i	−0.0688528	−	0.569107i
$484$		0			0
$485$	−0.824970	−	1.42889i	−0.0374600	−	0.0648825i
$486$	20.6197	+	22.9005i	0.935330	+	1.03879i
$487$	−1.51939	−	14.4560i	−0.0688502	−	0.655066i	−0.973465	−	0.228836i	$-0.926508\pi$
$487$	−1.51939	−	14.4560i	−0.0688502	−	0.655066i	0.904615	−	0.426230i	$-0.140159\pi$
$488$	−0.527816	+	5.02183i	−0.0238931	+	0.227328i
$489$	10.8746	+	33.4687i	0.491768	+	1.51351i
$490$	−8.15629	+	0.255848i	−0.368463	+	0.0115580i
$491$	31.8714	+	23.1559i	1.43834	+	1.04501i	0.988387	+	0.151958i	$0.0485579\pi$
$491$	31.8714	+	23.1559i	1.43834	+	1.04501i	0.449949	+	0.893054i	$0.351442\pi$
$492$	−20.6525	−	9.19509i	−0.931087	−	0.414547i
$493$	19.7809	+	21.9689i	0.890886	+	0.989429i
$494$	−9.19041	+	15.9183i	−0.413496	+	0.716196i
$495$		0			0
$496$	−31.2975			−1.40530
$497$	11.1432	+	2.18654i	0.499839	+	0.0980796i
$498$	−30.1201	+	21.8836i	−1.34972	+	0.980626i
$499$	2.74184	−	26.0868i	0.122742	−	1.16781i	−0.743695	−	0.668520i	$-0.766928\pi$
$499$	2.74184	−	26.0868i	0.122742	−	1.16781i	0.866436	−	0.499288i	$-0.166405\pi$
$500$	−8.13966	−	1.73014i	−0.364016	−	0.0773741i
$501$	2.49306	+	0.529915i	0.111381	+	0.0236749i
$502$	−3.79125	+	36.0713i	−0.169212	+	1.60994i
$503$	−3.19249	+	2.31948i	−0.142346	+	0.103420i	−0.656679	−	0.754170i	$-0.728039\pi$
$503$	−3.19249	+	2.31948i	−0.142346	+	0.103420i	0.514333	+	0.857590i	$0.328039\pi$
$504$	1.83236	+	5.35240i	0.0816199	+	0.238415i
$505$	6.29204			0.279992
$506$		0			0
$507$	−10.7244	+	18.5753i	−0.476289	+	0.824956i
$508$	19.1719	+	21.2925i	0.850615	+	0.944703i
$509$	15.4440	+	6.87612i	0.684544	+	0.304778i	0.719382	−	0.694615i	$-0.244425\pi$
$509$	15.4440	+	6.87612i	0.684544	+	0.304778i	−0.0348386	+	0.999393i	$0.511092\pi$
$510$	5.87715	+	4.27000i	0.260245	+	0.189079i
$511$	−3.76276	+	42.1471i	−0.166455	+	1.86448i
$512$	6.41407	+	19.7405i	0.283465	+	0.872414i
$513$	1.49048	−	14.1810i	0.0658064	−	0.626106i
$514$	−0.521501	−	4.96175i	−0.0230024	−	0.218853i
$515$	−2.65011	−	2.94324i	−0.116778	−	0.129695i
$516$	−7.30077	−	12.6453i	−0.321398	−	0.556678i
$517$		0			0
$518$	−27.0768	−	11.5502i	−1.18969	−	0.507485i
$519$	0.674987	−	2.07740i	0.0296286	−	0.0911876i
$520$	−1.21921	−	0.542826i	−0.0534658	−	0.0238045i
$521$	1.42301	−	0.633566i	0.0623433	−	0.0277570i	−0.375328	−	0.926892i	$-0.622470\pi$
$521$	1.42301	−	0.633566i	0.0623433	−	0.0277570i	0.437671	+	0.899135i	$0.355803\pi$
$522$	34.3254	+	7.29609i	1.50238	+	0.319341i
$523$	−8.36596	+	9.29134i	−0.365818	+	0.406282i	−0.897750	−	0.440505i	$-0.854799\pi$
$523$	−8.36596	+	9.29134i	−0.365818	+	0.406282i	0.531932	+	0.846787i	$0.321466\pi$
$524$	15.1245	+	10.9886i	0.660716	+	0.480038i
$525$	−7.86227	+	25.5541i	−0.343138	+	1.11527i
$526$	7.19561	−	22.1458i	0.313744	−	0.965604i
$527$	9.11254	+	15.7834i	0.396949	+	0.687535i
$528$		0			0
$529$	9.15475	−	15.8565i	0.398033	−	0.689413i
$530$	8.51767	−	1.81049i	0.369984	−	0.0786426i
$531$	−17.5205	+	12.7294i	−0.760323	+	0.552407i
$532$	−9.76752	+	17.5476i	−0.423476	+	0.760784i
$533$	−4.19461	−	12.9097i	−0.181689	−	0.559181i
$534$	−0.983485	+	1.09227i	−0.0425596	+	0.0472672i
$535$	−6.44403	+	2.86907i	−0.278600	+	0.124041i
$536$	−0.195287	−	1.85803i	−0.00843510	−	0.0802546i
$537$	−42.2858	+	8.98813i	−1.82477	+	0.387867i
$538$	−13.0109			−0.560941
$539$		0			0
$540$	−2.22270			−0.0956497
$541$	16.2001	−	3.44344i	0.696498	−	0.148045i	0.153961	−	0.988077i	$-0.450797\pi$
$541$	16.2001	−	3.44344i	0.696498	−	0.148045i	0.542537	+	0.840032i	$0.317464\pi$
$542$	3.49259	+	33.2298i	0.150020	+	1.42734i
$543$	47.9507	−	21.3490i	2.05776	−	0.916174i
$544$	12.5093	−	13.8930i	0.536332	−	0.595658i
$545$	2.80926	+	8.64602i	0.120336	+	0.370355i
$546$	9.34796	−	16.7938i	0.400056	−	0.718709i
$547$	5.37550	−	3.90553i	0.229840	−	0.166988i	−0.466905	−	0.884307i	$-0.654631\pi$
$547$	5.37550	−	3.90553i	0.229840	−	0.166988i	0.696745	+	0.717319i	$0.254631\pi$
$548$	−9.69551	+	2.06084i	−0.414172	+	0.0880349i
$549$	3.97252	−	6.88061i	0.169543	−	0.293657i
$550$		0			0
$551$	−29.0127	−	50.2514i	−1.23598	−	2.14078i
$552$	1.71540	−	5.27944i	0.0730121	−	0.224708i
$553$	−3.70485	+	12.0416i	−0.157546	+	0.512059i
$554$	−20.5505	−	14.9308i	−0.873105	−	0.634348i
$555$	5.67178	−	6.29915i	0.240754	−	0.267384i
$556$	3.47354	+	0.738323i	0.147311	+	0.0313119i
$557$	11.9783	−	5.33309i	0.507537	−	0.225970i	−0.136960	−	0.990577i	$-0.543733\pi$
$557$	11.9783	−	5.33309i	0.507537	−	0.225970i	0.644498	+	0.764606i	$0.277067\pi$
$558$	19.7641	+	8.79953i	0.836680	+	0.372514i
$559$	2.70924	−	8.33819i	0.114589	−	0.352668i
$560$	−7.52793	−	3.21119i	−0.318113	−	0.135698i
$561$		0			0
$562$	−19.2898	−	33.4108i	−0.813689	−	1.40935i
$563$	20.4008	+	22.6574i	0.859792	+	0.954896i	0.999376	−	0.0353141i	$-0.0112432\pi$
$563$	20.4008	+	22.6574i	0.859792	+	0.954896i	−0.139584	+	0.990210i	$0.544577\pi$
$564$	−0.888777	−	8.45615i	−0.0374243	−	0.356068i
$565$	−0.577266	+	5.49232i	−0.0242858	+	0.231064i
$566$	0.199770	+	0.614830i	0.00839697	+	0.0258432i
$567$	−2.62049	+	29.3524i	−0.110050	+	1.23268i
$568$	4.04789	+	2.94097i	0.169846	+	0.123400i
$569$	−32.3011	−	14.3814i	−1.35413	−	0.602898i	−0.404003	−	0.914758i	$-0.632381\pi$
$569$	−32.3011	−	14.3814i	−1.35413	−	0.602898i	−0.950128	+	0.311860i	$0.899048\pi$
$570$	−9.54120	−	10.5966i	−0.399637	−	0.443842i
$571$	20.6422	−	35.7533i	0.863849	−	1.49623i	−0.00433587	−	0.999991i	$-0.501380\pi$
$571$	20.6422	−	35.7533i	0.863849	−	1.49623i	0.868185	−	0.496240i	$-0.165287\pi$
$572$		0			0
$573$	24.4753			1.02247
$574$	−11.8447	−	34.5989i	−0.494389	−	1.44413i
$575$	8.05294	−	5.85080i	0.335831	−	0.243995i
$576$	0.453337	−	4.31321i	0.0188890	−	0.179717i
$577$	−8.51233	−	1.80935i	−0.354373	−	0.0753243i	0.0272855	−	0.999628i	$-0.491314\pi$
$577$	−8.51233	−	1.80935i	−0.354373	−	0.0753243i	−0.381659	+	0.924303i	$0.624647\pi$
$578$	16.0884	+	3.41969i	0.669187	+	0.142240i
$579$	0.830733	−	7.90390i	0.0345241	−	0.328475i
$580$	−7.31751	+	5.31648i	−0.303843	+	0.220755i
$581$	−23.9675	−	4.70296i	−0.994341	−	0.195112i
$582$	10.4698			0.433987
$583$		0			0
$584$	−9.32224	+	16.1466i	−0.385757	+	0.668151i
$585$	1.40510	+	1.56052i	0.0580937	+	0.0645196i
$586$	−5.80325	−	2.58377i	−0.239730	−	0.106735i
$587$	18.6510	+	13.5507i	0.769808	+	0.559298i	0.901903	−	0.431939i	$-0.142170\pi$
$587$	18.6510	+	13.5507i	0.769808	+	0.559298i	−0.132095	+	0.991237i	$0.542170\pi$
$588$	9.92464	−	18.5068i	0.409285	−	0.763207i
$589$	−11.0544	−	34.0219i	−0.455488	−	1.40185i
$590$	1.43871	−	13.6884i	0.0592308	−	0.563543i
$591$	0.555791	+	5.28800i	0.0228622	+	0.217519i
$592$	−19.7552	−	21.9404i	−0.811933	−	0.901743i
$593$	−15.0494	−	26.0663i	−0.618005	−	1.07042i	−0.989849	−	0.142121i	$-0.954608\pi$
$593$	−15.0494	−	26.0663i	−0.618005	−	1.07042i	0.371844	−	0.928295i	$-0.378725\pi$
$594$		0			0
$595$	0.572413	+	4.73131i	0.0234666	+	0.193965i
$596$	−0.421638	+	1.29767i	−0.0172710	+	0.0531545i
$597$	37.1515	+	16.5409i	1.52051	+	0.676975i
$598$	−6.53710	+	2.91050i	−0.267322	+	0.119019i
$599$	−28.6123	−	6.08172i	−1.16907	−	0.248492i	−0.417829	−	0.908526i	$-0.637209\pi$
$599$	−28.6123	−	6.08172i	−1.16907	−	0.248492i	−0.751236	+	0.660033i	$0.770542\pi$
$600$	−7.88261	+	8.75453i	−0.321806	+	0.357402i
$601$	21.6996	+	15.7657i	0.885147	+	0.643097i	0.934608	−	0.355679i	$-0.115750\pi$
$601$	21.6996	+	15.7657i	0.885147	+	0.643097i	−0.0494611	+	0.998776i	$0.515750\pi$
$602$	6.94594	−	22.5758i	0.283095	−	0.920121i
$603$	−0.908383	+	2.79572i	−0.0369922	+	0.113850i
$604$	−1.18396	−	2.05068i	−0.0481746	−	0.0834409i
$605$		0			0
$606$	−19.9633	+	34.5774i	−0.810952	+	1.40461i
$607$	−31.5058	+	6.69675i	−1.27878	+	0.271813i	−0.796732	−	0.604333i	$-0.793440\pi$
$607$	−31.5058	+	6.69675i	−1.27878	+	0.271813i	−0.482047	+	0.876145i	$0.660107\pi$
$608$	−29.6868	+	21.5687i	−1.20396	+	0.874727i
$609$	31.1577	+	52.0641i	1.26257	+	2.10974i
$610$	1.56038	+	4.80235i	0.0631779	+	0.194442i
$611$	3.41614	−	3.79401i	0.138202	−	0.153489i
$612$	−6.48009	+	2.88512i	−0.261942	+	0.116624i
$613$	−4.66145	−	44.3507i	−0.188274	−	1.79131i	−0.526431	−	0.850218i	$-0.676470\pi$
$613$	−4.66145	−	44.3507i	−0.188274	−	1.79131i	0.338157	−	0.941090i	$-0.390197\pi$
$614$	11.6885	−	2.48446i	0.471709	−	0.100265i
$615$	10.5302			0.424619
$616$		0			0
$617$	−0.531290			−0.0213889			−0.0106945	−	0.999943i	$-0.503404\pi$
$617$	−0.531290			−0.0213889			−0.0106945	+	0.999943i	$0.503404\pi$
$618$	24.5825	−	5.22518i	0.988855	−	0.210188i
$619$	−4.36357	−	41.5166i	−0.175387	−	1.66869i	−0.628933	−	0.777460i	$-0.716508\pi$
$619$	−4.36357	−	41.5166i	−0.175387	−	1.66869i	0.453546	−	0.891233i	$-0.350159\pi$
$620$	−5.09414	+	2.26806i	−0.204585	+	0.0910873i
$621$	3.71444	−	4.12530i	0.149055	−	0.165543i
$622$	6.59208	+	20.2883i	0.264318	+	0.813488i
$623$	−0.964120	+	0.0151176i	−0.0386267	+	0.000605675i
$624$	15.5951	−	11.3305i	0.624302	−	0.453582i
$625$	−18.6868	+	3.97200i	−0.747472	+	0.158880i
$626$	24.8519	−	43.0448i	0.993282	−	1.72041i
$627$		0			0
$628$	5.41658	+	9.38179i	0.216145	+	0.374374i
$629$	−5.31267	+	16.3507i	−0.211830	+	0.651945i
$630$	3.85096	+	4.14437i	0.153426	+	0.165116i
$631$	0.175749	+	0.127689i	0.00699646	+	0.00508323i	0.591278	−	0.806468i	$-0.298624\pi$
$631$	0.175749	+	0.127689i	0.00699646	+	0.00508323i	−0.584282	+	0.811551i	$0.698624\pi$
$632$	−3.71444	+	4.12530i	−0.147752	+	0.164096i
$633$	−16.8937	−	3.59086i	−0.671464	−	0.142724i
$634$	6.47094	−	2.88105i	0.256994	−	0.114421i
$635$	−12.1921	−	5.42827i	−0.483828	−	0.215414i
$636$	−6.92488	+	21.3126i	−0.274589	+	0.845099i
$637$	12.2454	−	3.00700i	0.485179	−	0.119142i
$638$		0			0
$639$	−3.93632	−	6.81790i	−0.155718	−	0.269712i
$640$	−3.76582	−	4.18236i	−0.148857	−	0.165322i
$641$	1.01293	+	9.63742i	0.0400085	+	0.380655i	0.996144	+	0.0877311i	$0.0279616\pi$
$641$	1.01293	+	9.63742i	0.0400085	+	0.380655i	−0.956136	+	0.292924i	$0.905372\pi$
$642$	4.67877	−	44.5155i	0.184656	−	1.75689i
$643$	5.08742	+	15.6575i	0.200628	+	0.617471i	0.999865	+	0.0164538i	$0.00523763\pi$
$643$	5.08742	+	15.6575i	0.200628	+	0.617471i	−0.799236	+	0.601017i	$0.794762\pi$
$644$	−7.09169	+	3.29160i	−0.279452	+	0.129707i
$645$	5.50237	+	3.99771i	0.216656	+	0.157410i
$646$	26.4207	+	11.7632i	1.03951	+	0.462819i
$647$	0.584634	+	0.649302i	0.0229843	+	0.0255267i	0.754527	−	0.656269i	$-0.227866\pi$
$647$	0.584634	+	0.649302i	0.0229843	+	0.0255267i	−0.731543	+	0.681795i	$0.761199\pi$
$648$	−6.49226	+	11.2449i	−0.255040	+	0.441743i
$649$		0			0
$650$	15.1856			0.595628
$651$	12.1155	+	35.3900i	0.474846	+	1.38704i
$652$	17.6678	−	12.8364i	0.691925	−	0.502713i
$653$	4.17414	−	39.7143i	0.163347	−	1.55414i	−0.539000	−	0.842306i	$-0.681198\pi$
$653$	4.17414	−	39.7143i	0.163347	−	1.55414i	0.702347	−	0.711835i	$-0.252135\pi$
$654$	−56.4266	−	11.9939i	−2.20646	−	0.468997i
$655$	−8.51767	−	1.81049i	−0.332813	−	0.0707416i
$656$	3.83383	−	36.4765i	0.149686	−	1.42417i
$657$	23.7332	−	17.2432i	0.925922	−	0.672721i
$658$	9.04213	−	10.3646i	0.352499	−	0.404054i
$659$	−6.89465			−0.268578			−0.134289	−	0.990942i	$-0.542875\pi$
$659$	−6.89465			−0.268578			−0.134289	+	0.990942i	$0.542875\pi$
$660$		0			0
$661$	20.0072	−	34.6535i	0.778190	−	1.34786i	−0.154795	−	0.987947i	$-0.549472\pi$
$661$	20.0072	−	34.6535i	0.778190	−	1.34786i	0.932984	−	0.359917i	$-0.117195\pi$
$662$	7.54854	+	8.38350i	0.293382	+	0.325834i
$663$	−10.2546	−	4.56565i	−0.398257	−	0.177315i
$664$	−8.70650	−	6.32565i	−0.337878	−	0.245483i
$665$	0.831831	−	9.31743i	0.0322570	−	0.361314i
$666$	6.30651	+	19.4094i	0.244372	+	0.752101i
$667$	2.36125	−	22.4658i	0.0914279	−	0.869879i
$668$	−0.165331	−	1.57302i	−0.00639686	−	0.0608620i
$669$	−29.9200	−	33.2295i	−1.15677	−	1.28473i
$670$	−0.934131	−	1.61796i	−0.0360886	−	0.0625073i
$671$		0			0
$672$	30.6851	−	23.0376i	1.18370	−	0.888695i
$673$	9.69659	−	29.8430i	0.373776	−	1.15036i	−0.570524	−	0.821281i	$-0.693260\pi$
$673$	9.69659	−	29.8430i	0.373776	−	1.15036i	0.944301	−	0.329084i	$-0.106740\pi$
$674$	−19.7071	−	8.77415i	−0.759088	−	0.337968i
$675$	−10.7619	+	4.79151i	−0.414226	+	0.184425i
$676$	13.0197	+	2.76743i	0.500758	+	0.106439i
$677$	−24.4443	+	27.1482i	−0.939473	+	1.04339i	0.0595071	+	0.998228i	$0.481047\pi$
$677$	−24.4443	+	27.1482i	−0.939473	+	1.04339i	−0.998980	+	0.0451622i	$0.985620\pi$
$678$	−28.3511	−	20.5983i	−1.08882	−	0.791071i
$679$	4.67543	+	5.03165i	0.179427	+	0.193097i
$680$	−0.648901	+	1.99711i	−0.0248842	+	0.0765858i
$681$	7.93686	+	13.7470i	0.304141	+	0.526788i
$682$		0			0
$683$	7.63501	−	13.2242i	0.292146	−	0.506011i	−0.682171	−	0.731192i	$-0.738964\pi$
$683$	7.63501	−	13.2242i	0.292146	−	0.506011i	0.974317	+	0.225181i	$0.0722975\pi$
$684$	13.6188	−	2.89476i	0.520727	−	0.110684i
$685$	3.73524	−	2.71381i	0.142716	−	0.103689i
$686$	32.8595	−	8.61746i	1.25458	−	0.329016i
$687$	−8.20166	−	25.2421i	−0.312913	−	0.963046i
$688$	15.8513	−	17.6047i	0.604326	−	0.671172i
$689$	−12.2921	+	5.47281i	−0.468293	+	0.208497i
$690$	−0.580252	−	5.52073i	−0.0220898	−	0.210170i
$691$	37.5455	−	7.98054i	1.42830	−	0.303594i	0.572076	−	0.820201i	$-0.306138\pi$
$691$	37.5455	−	7.98054i	1.42830	−	0.303594i	0.856223	+	0.516607i	$0.172805\pi$
$692$	−1.35552			−0.0515291
$693$		0			0
$694$	−1.54221			−0.0585414
$695$	−1.61795	+	0.343906i	−0.0613724	+	0.0130451i
$696$	2.79450	+	26.5879i	0.105925	+	1.00781i
$697$	−19.5114	+	8.68704i	−0.739048	+	0.329045i
$698$	11.2078	−	12.4475i	0.424222	−	0.471147i
$699$	5.12442	+	15.7714i	0.193824	+	0.596528i
$700$	16.5897	−	0.260131i	0.627033	−	0.00983202i
$701$	−14.4859	+	10.5246i	−0.547125	+	0.397510i	−0.826724	−	0.562607i	$-0.809798\pi$
$701$	−14.4859	+	10.5246i	−0.547125	+	0.397510i	0.279599	+	0.960117i	$0.409798\pi$
$702$	8.28365	−	1.76074i	0.312646	−	0.0664550i
$703$	16.8726	−	29.2243i	0.636364	−	1.10221i
$704$		0			0
$705$	1.98026	+	3.42991i	0.0745809	+	0.129178i
$706$	12.8824	−	39.6480i	0.484836	−	1.49217i
$707$	−25.5323	+	5.84690i	−0.960242	+	0.219895i
$708$	28.6556	+	20.8195i	1.07694	+	0.782446i
$709$	23.0177	−	25.5637i	0.864447	−	0.960065i	−0.135080	−	0.990835i	$-0.543129\pi$
$709$	23.0177	−	25.5637i	0.864447	−	0.960065i	0.999527	+	0.0307693i	$0.00979571\pi$
$710$	4.89413	+	1.04028i	0.183673	+	0.0390410i
$711$	7.97923	−	3.55258i	0.299245	−	0.133232i
$712$	−0.388127	−	0.172805i	−0.0145457	−	0.00647615i
$713$	4.30353	−	13.2449i	0.161168	−	0.496025i
$714$	−27.8167	−	11.8658i	−1.04101	−	0.444066i
$715$		0			0
$716$	13.4138	+	23.2335i	0.501299	+	0.868276i
$717$	14.4859	+	16.0882i	0.540986	+	0.600826i
$718$	5.02690	+	47.8277i	0.187602	+	1.78491i
$719$	−5.16551	+	49.1465i	−0.192641	+	1.83286i	0.289987	+	0.957030i	$0.406349\pi$
$719$	−5.16551	+	49.1465i	−0.192641	+	1.83286i	−0.482628	+	0.875825i	$0.660318\pi$
$720$	1.75335	+	5.39624i	0.0653433	+	0.201106i
$721$	13.4888	+	9.48069i	0.502350	+	0.353079i
$722$	−17.7308	−	12.8822i	−0.659873	−	0.479425i
$723$	3.36447	+	1.49796i	0.125126	+	0.0557097i
$724$	−21.7956	−	24.2064i	−0.810026	−	0.899625i
$725$	−23.9693	+	41.5160i	−0.890196	+	1.54186i
$726$		0			0
$727$	−19.8201			−0.735086			−0.367543	−	0.930007i	$-0.619801\pi$
$727$	−19.8201			−0.735086			−0.367543	+	0.930007i	$0.619801\pi$
$728$	5.45182	+	1.06977i	0.202058	+	0.0396482i
$729$	2.85070	−	2.07116i	0.105582	−	0.0767095i
$730$	−1.94888	+	18.5423i	−0.0721312	+	0.686283i
$731$	−13.4933	−	2.86809i	−0.499068	−	0.106080i
$732$	−12.7106	−	2.70172i	−0.469797	−	0.0998583i
$733$	3.20354	−	30.4797i	0.118326	−	1.12579i	−0.760729	−	0.649070i	$-0.775158\pi$
$733$	3.20354	−	30.4797i	0.118326	−	1.12579i	0.879054	−	0.476722i	$-0.158175\pi$
$734$	5.67195	−	4.12091i	0.209356	−	0.152106i
$735$	−0.716959	+	9.75537i	−0.0264454	+	0.359832i
$736$	−14.2855			−0.526570
$737$		0			0
$738$	−12.6767	+	21.9566i	−0.466635	+	0.808235i
$739$	11.4434	+	12.7092i	0.420952	+	0.467514i	0.915899	−	0.401409i	$-0.131479\pi$
$739$	11.4434	+	12.7092i	0.420952	+	0.467514i	−0.494947	+	0.868923i	$0.664813\pi$
$740$	−4.80542	−	2.13951i	−0.176651	−	0.0786500i
$741$	17.8250	+	12.9506i	0.654818	+	0.475753i
$742$	−32.8813	+	15.2618i	−1.20711	+	0.560279i
$743$	−2.15463	−	6.63127i	−0.0790457	−	0.243278i	0.903723	−	0.428118i	$-0.140823\pi$
$743$	−2.15463	−	6.63127i	−0.0790457	−	0.243278i	−0.982769	+	0.184840i	$0.940823\pi$
$744$	−1.72282	+	16.3915i	−0.0631615	+	0.600942i
$745$	−0.0664333	−	0.632070i	−0.00243393	−	0.0231573i
$746$	18.5424	+	20.5935i	0.678887	+	0.753981i
$747$	8.46652	+	14.6644i	0.309774	+	0.536544i
$748$		0			0
$749$	23.4830	−	17.6305i	0.858050	−	0.644203i
$750$	−7.60060	+	23.3923i	−0.277535	+	0.854164i
$751$	13.9158	+	6.19570i	0.507794	+	0.226084i	0.644609	−	0.764512i	$-0.277020\pi$
$751$	13.9158	+	6.19570i	0.507794	+	0.226084i	−0.136815	+	0.990597i	$0.543687\pi$
$752$	12.6021	−	5.61084i	0.459553	−	0.204606i
$753$	42.5265	+	9.03928i	1.54975	+	0.329410i
$754$	23.0597	−	25.6104i	0.839784	−	0.932675i
$755$	0.892315	+	0.648305i	0.0324747	+	0.0235942i
$756$	9.01944	−	2.06545i	0.328034	−	0.0751197i
$757$	−4.49082	+	13.8213i	−0.163222	+	0.502344i	−0.998901	−	0.0468735i	$-0.985074\pi$
$757$	−4.49082	+	13.8213i	−0.163222	+	0.502344i	0.835679	+	0.549218i	$0.185074\pi$
$758$	10.4336	+	18.0715i	0.378965	+	0.656387i
$759$		0			0
$760$	2.06086	−	3.56952i	0.0747553	−	0.129480i
$761$	1.67598	−	0.356241i	0.0607543	−	0.0129137i	−0.177434	−	0.984133i	$-0.556780\pi$
$761$	1.67598	−	0.356241i	0.0607543	−	0.0129137i	0.238189	+	0.971219i	$0.423446\pi$
$762$	68.5134	−	49.7779i	2.48198	−	1.80326i
$763$	−19.4340	−	32.4740i	−0.703558	−	1.17564i
$764$	−4.69356	−	14.4453i	−0.169807	−	0.522612i
$765$	2.21083	−	2.45538i	0.0799328	−	0.0887744i
$766$	14.8895	−	6.62923i	0.537979	−	0.239524i
$767$	2.22307	+	21.1511i	0.0802705	+	0.763723i
$768$	45.1021	−	9.58675i	1.62748	−	0.345932i
$769$	−36.5874			−1.31937			−0.659687	−	0.751540i	$-0.729311\pi$
$769$	−36.5874			−1.31937			−0.659687	+	0.751540i	$0.729311\pi$
$770$		0			0
$771$	−5.98037			−0.215378
$772$	−4.82419	+	1.02541i	−0.173626	+	0.0369054i
$773$	−2.80357	−	26.6742i	−0.100838	−	0.959405i	−0.921601	−	0.388138i	$-0.873119\pi$
$773$	−2.80357	−	26.6742i	−0.100838	−	0.959405i	0.820764	−	0.571268i	$-0.193548\pi$
$774$	−14.9596	+	6.66046i	−0.537713	+	0.239405i
$775$	−19.7756	+	21.9631i	−0.710361	+	0.788936i
$776$	0.935206	+	2.87827i	0.0335719	+	0.103324i
$777$	−17.1619	+	30.8317i	−0.615679	+	1.10608i
$778$	29.5288	−	21.4540i	1.05866	−	0.769162i
$779$	41.0059	−	8.71606i	1.46919	−	0.312285i
$780$	1.71724	−	2.97434i	0.0614870	−	0.106499i
$781$		0			0
$782$	5.62955	+	9.75067i	0.201312	+	0.348683i
$783$	−8.26137	+	25.4259i	−0.295237	+	0.908647i
$784$	33.5314	+	6.03527i	1.19755	+	0.215545i
$785$	−4.08232	−	2.96598i	−0.145704	−	0.105860i
$786$	36.9741	−	41.0639i	1.31882	−	1.46470i
$787$	−4.84339	−	1.02949i	−0.172648	−	0.0366975i	0.120776	−	0.992680i	$-0.461462\pi$
$787$	−4.84339	−	1.02949i	−0.172648	−	0.0366975i	−0.293425	+	0.955982i	$0.594795\pi$
$788$	3.01439	−	1.34209i	0.107383	−	0.0478101i
$789$	−25.4990	−	11.3529i	−0.907788	−	0.404173i
$790$	−1.71540	+	5.27944i	−0.0610310	+	0.187834i
$791$	−2.76129	−	22.8236i	−0.0981801	−	0.811514i
$792$		0			0
$793$	−3.90120	−	6.75707i	−0.138536	−	0.239951i
$794$	−42.7861	−	47.5188i	−1.51842	−	1.68638i
$795$	−1.09108	−	10.3810i	−0.0386968	−	0.368175i
$796$	2.63799	−	25.0988i	0.0935012	−	0.889605i
$797$	−8.24513	−	25.3759i	−0.292057	−	0.898860i	−0.984194	−	0.177094i	$-0.943330\pi$
$797$	−8.24513	−	25.3759i	−0.292057	−	0.898860i	0.692137	−	0.721766i	$-0.256670\pi$
$798$	48.5640	+	34.1334i	1.71915	+	1.20831i
$799$	−6.49878	−	4.72164i	−0.229910	−	0.167040i
$800$	27.6951	+	12.3306i	0.979169	+	0.435954i
$801$	0.447305	+	0.496782i	0.0158047	+	0.0175529i
$802$	−10.4518	+	18.1030i	−0.369066	+	0.639240i
$803$		0			0
$804$	4.80785			0.169560
$805$	2.39407	−	2.74422i	0.0843800	−	0.0967210i
$806$	17.1884	−	12.4881i	0.605435	−	0.439874i
$807$	−1.63023	+	15.5106i	−0.0573869	+	0.546000i
$808$	−11.2889	−	2.39953i	−0.397143	−	0.0844153i
$809$	38.6760	+	8.22084i	1.35978	+	0.289029i	0.829363	−	0.558710i	$-0.188704\pi$
$809$	38.6760	+	8.22084i	1.35978	+	0.289029i	0.530413	+	0.847740i	$0.322037\pi$
$810$	−1.35725	+	12.9134i	−0.0476890	+	0.453731i
$811$	27.0651	−	19.6640i	0.950385	−	0.690495i	−0.000513088	−	1.00000i	$-0.500163\pi$
$811$	27.0651	−	19.6640i	0.950385	−	0.690495i	0.950898	+	0.309505i	$0.100163\pi$
$812$	24.7532	−	28.3735i	0.868667	−	0.995713i
$813$	40.0517			1.40467
$814$		0			0
$815$	−5.08615	+	8.80947i	−0.178160	+	0.308582i
$816$	−20.2950	−	22.5399i	−0.710468	−	0.789054i
$817$	24.7359	+	11.0131i	0.865399	+	0.385300i
$818$	6.06615	+	4.40732i	0.212098	+	0.154098i
$819$	−7.15184	−	5.02671i	−0.249906	−	0.175647i
$820$	−2.01935	−	6.21493i	−0.0705188	−	0.217035i
$821$	−5.94369	+	56.5504i	−0.207436	+	1.97362i	0.0198779	+	0.999802i	$0.493672\pi$
$821$	−5.94369	+	56.5504i	−0.207436	+	1.97362i	−0.227314	+	0.973821i	$0.572994\pi$
$822$	3.06242	+	29.1370i	0.106814	+	1.01627i
$823$	−26.8827	−	29.8563i	−0.937073	−	1.04072i	−0.999090	−	0.0426495i	$-0.986420\pi$
$823$	−26.8827	−	29.8563i	−0.937073	−	1.04072i	0.0620175	−	0.998075i	$-0.480247\pi$
$824$	3.63228	+	6.29129i	0.126536	+	0.219168i
$825$		0			0
$826$	6.88191	+	56.8829i	0.239452	+	1.97921i
$827$	−1.77235	+	5.45473i	−0.0616306	+	0.189679i	−0.977131	−	0.212637i	$-0.931795\pi$
$827$	−1.77235	+	5.45473i	−0.0616306	+	0.189679i	0.915501	+	0.402316i	$0.131795\pi$
$828$	4.95169	+	2.20464i	0.172083	+	0.0766164i
$829$	−32.5186	+	14.4782i	−1.12942	+	0.502850i	−0.884428	−	0.466676i	$-0.845451\pi$
$829$	−32.5186	+	14.4782i	−1.12942	+	0.502850i	−0.244990	+	0.969526i	$0.578785\pi$
$830$	−10.5267	−	2.23751i	−0.365386	−	0.0776651i
$831$	−20.3743	+	22.6279i	−0.706775	+	0.784954i
$832$	−3.44569	−	2.50344i	−0.119458	−	0.0867911i
$833$	−6.71938	−	18.6672i	−0.232813	−	0.646780i
$834$	3.24350	−	9.98247i	0.112313	−	0.345665i
$835$	0.368370	+	0.638036i	0.0127480	+	0.0220801i
$836$		0			0
$837$	−8.24090	+	14.2737i	−0.284847	+	0.493370i
$838$	−58.8489	+	12.5087i	−2.03290	+	0.432106i
$839$	33.7949	−	24.5534i	1.16673	−	0.847678i	0.176115	−	0.984370i	$-0.443647\pi$
$839$	33.7949	−	24.5534i	1.16673	−	0.847678i	0.990614	+	0.136692i	$0.0436471\pi$
$840$	−2.09619	+	3.76585i	−0.0723255	+	0.129934i
$841$	24.6569	+	75.8862i	0.850239	+	2.61677i
$842$	−10.4586	+	11.6154i	−0.360426	+	0.400294i
$843$	−42.2468	+	18.8095i	−1.45506	+	0.647834i
$844$	1.12033	+	10.6593i	0.0385635	+	0.366907i
$845$	−6.06451	+	1.28905i	−0.208625	+	0.0443447i
$846$	−9.53566			−0.327843
$847$		0			0
$848$	−36.3568			−1.24850
$849$	0.757984	−	0.161115i	0.0260140	−	0.00552944i
$850$	−2.49756	−	23.7627i	−0.0856655	−	0.815053i
$851$	12.0014	−	5.34338i	0.411404	−	0.183169i
$852$	−8.61580	+	9.56881i	−0.295172	+	0.327822i
$853$	15.3851	+	47.3504i	0.526775	+	1.62125i	0.760779	+	0.649011i	$0.224817\pi$
$853$	15.3851	+	47.3504i	0.526775	+	1.62125i	−0.234005	+	0.972236i	$0.575183\pi$
$854$	−10.7944	−	18.0374i	−0.369378	−	0.617226i
$855$	−5.24669	+	3.81194i	−0.179433	+	0.130366i
$856$	12.6558	−	2.69007i	0.432565	−	0.0919446i
$857$	−12.7394	+	22.0652i	−0.435168	+	0.753734i	−0.997309	−	0.0733077i	$-0.976644\pi$
$857$	−12.7394	+	22.0652i	−0.435168	+	0.753734i	0.562141	+	0.827041i	$0.309978\pi$
$858$		0			0
$859$	−8.08080	−	13.9964i	−0.275713	−	0.477549i	0.694602	−	0.719395i	$-0.255581\pi$
$859$	−8.08080	−	13.9964i	−0.275713	−	0.477549i	−0.970315	+	0.241845i	$0.922247\pi$
$860$	1.30427	−	4.01413i	0.0444752	−	0.136881i
$861$	−42.7303	+	9.78524i	−1.45624	+	0.333480i
$862$	24.8327	+	18.0420i	0.845804	+	0.614513i
$863$	1.93983	−	2.15440i	0.0660325	−	0.0733365i	−0.709223	−	0.704984i	$-0.750954\pi$
$863$	1.93983	−	2.15440i	0.0660325	−	0.0733365i	0.775256	+	0.631647i	$0.217621\pi$
$864$	16.5372	+	3.51509i	0.562607	+	0.119586i
$865$	0.576806	−	0.256811i	0.0196120	−	0.00873183i
$866$	−43.3429	−	19.2975i	−1.47285	−	0.655756i
$867$	6.09252	−	18.7508i	0.206913	−	0.636812i
$868$	18.5638	−	13.9372i	0.630096	−	0.473061i
$869$		0			0
$870$	13.3672	+	23.1526i	0.453190	+	0.784948i
$871$	1.93165	+	2.14532i	0.0654515	+	0.0726913i
$872$	−1.74302	−	16.5837i	−0.0590259	−	0.561594i
$873$	0.497747	−	4.73574i	0.0168462	−	0.160281i
$874$	−6.82919	−	21.0181i	−0.231001	−	0.710947i
$875$	−14.6362	+	6.79337i	−0.494793	+	0.229658i
$876$	−38.8169	−	28.2022i	−1.31150	−	0.952862i
$877$	−7.68734	−	3.42263i	−0.259583	−	0.115574i	0.272819	−	0.962065i	$-0.412044\pi$
$877$	−7.68734	−	3.42263i	−0.259583	−	0.115574i	−0.532402	+	0.846491i	$0.678711\pi$
$878$	−11.7440	−	13.0430i	−0.396341	−	0.440181i
$879$	−3.80731	+	6.59445i	−0.128417	+	0.222425i
$880$		0			0
$881$	41.5335			1.39930			0.699649	−	0.714486i	$-0.253340\pi$
$881$	41.5335			1.39930			0.699649	+	0.714486i	$0.253340\pi$
$882$	−19.4779	−	13.2388i	−0.655856	−	0.445775i
$883$	45.6894	−	33.1953i	1.53757	−	1.11711i	0.585737	−	0.810501i	$-0.300805\pi$
$883$	45.6894	−	33.1953i	1.53757	−	1.11711i	0.951835	−	0.306610i	$-0.0991948\pi$
$884$	−0.728143	+	6.92782i	−0.0244901	+	0.233008i
$885$	−16.1380	−	3.43025i	−0.542474	−	0.115306i
$886$	−34.1481	−	7.25841i	−1.14723	−	0.243851i
$887$	3.61454	−	34.3901i	0.121365	−	1.15471i	−0.749094	−	0.662464i	$-0.769511\pi$
$887$	3.61454	−	34.3901i	0.121365	−	1.15471i	0.870458	−	0.492242i	$-0.163823\pi$
$888$	−12.5783	+	9.13869i	−0.422101	+	0.306674i
$889$	54.5183	+	10.6977i	1.82848	+	0.358789i
$890$	−0.424858			−0.0142413
$891$		0			0
$892$	−13.8744	+	24.0311i	−0.464548	+	0.804621i
$893$	10.5504	+	11.7174i	0.353055	+	0.392107i
$894$	3.68427	+	1.64034i	0.123220	+	0.0548613i
$895$	−10.1096	−	7.34507i	−0.337928	−	0.245519i
$896$	19.1677	+	13.4721i	0.640348	+	0.450072i
$897$	2.65060	+	8.15771i	0.0885010	+	0.272378i
$898$	−6.39277	+	60.8231i	−0.213329	+	2.02969i
$899$	7.01075	+	66.7028i	0.233822	+	2.22466i
$900$	−7.69683	−	8.54819i	−0.256561	−	0.284940i
$901$	10.5856	+	18.3348i	0.352658	+	0.610821i
$902$		0			0
$903$	−26.0429	−	11.1091i	−0.866652	−	0.369688i
$904$	3.13026	−	9.63396i	0.104111	−	0.320421i
$905$	13.8606	+	6.17113i	0.460741	+	0.205135i
$906$	−6.39383	+	2.84672i	−0.212421	+	0.0945758i
$907$	−8.21922	−	1.74705i	−0.272915	−	0.0580098i	0.0694212	−	0.997587i	$-0.477885\pi$
$907$	−8.21922	−	1.74705i	−0.272915	−	0.0580098i	−0.342336	+	0.939578i	$0.611218\pi$
$908$	6.59147	−	7.32057i	0.218746	−	0.242942i
$909$	14.6911	+	10.6737i	0.487273	+	0.354025i
$910$	5.41560	−	1.24017i	0.179525	−	0.0411113i
$911$	−0.183460	+	0.564632i	−0.00607830	+	0.0187071i	−0.954050	−	0.299649i	$-0.903131\pi$
$911$	−0.183460	+	0.564632i	−0.00607830	+	0.0187071i	0.947971	+	0.318356i	$0.103131\pi$
$912$	29.7667	+	51.5575i	0.985675	+	1.70724i
$913$		0			0
$914$	−10.9693	+	18.9993i	−0.362831	+	0.628441i
$915$	5.92051	−	1.25844i	0.195726	−	0.0416029i
$916$	−13.3251	+	9.68123i	−0.440273	+	0.319877i
$917$	36.2461	−	0.568347i	1.19695	−	0.0187685i
$918$	−4.11764	−	12.6728i	−0.135902	−	0.418265i
$919$	−10.9316	+	12.1407i	−0.360599	+	0.400486i	−0.895958	−	0.444139i	$-0.853510\pi$
$919$	−10.9316	+	12.1407i	−0.360599	+	0.400486i	0.535359	+	0.844625i	$0.320176\pi$
$920$	1.46588	−	0.652652i	0.0483287	−	0.0215173i
$921$	−1.49725	−	14.2454i	−0.0493362	−	0.469402i
$922$	−22.4084	+	4.76306i	−0.737982	+	0.156863i
$923$	−7.73128			−0.254478
$924$		0			0
$925$	−27.8792			−0.916662
$926$	−22.0852	+	4.69436i	−0.725765	+	0.154266i
$927$	−1.19479	−	11.3677i	−0.0392422	−	0.373364i
$928$	62.8511	−	27.9831i	2.06319	−	0.918591i
$929$	5.95606	−	6.61488i	0.195412	−	0.217027i	−0.637474	−	0.770472i	$-0.720020\pi$
$929$	5.95606	−	6.61488i	0.195412	−	0.217027i	0.832886	+	0.553445i	$0.186687\pi$
$930$	5.09316	+	15.6751i	0.167011	+	0.514007i
$931$	5.28279	+	38.5820i	0.173137	+	1.26447i
$932$	8.32555	−	6.04887i	0.272713	−	0.198137i
$933$	25.0122	−	5.31651i	0.818863	−	0.174055i
$934$	−30.0456	+	52.0405i	−0.983122	+	1.70282i
$935$		0			0
$936$	−1.92585	−	3.33567i	−0.0629485	−	0.109030i
$937$	13.9787	−	43.0220i	0.456664	−	1.40547i	−0.412506	−	0.910955i	$-0.635347\pi$
$937$	13.9787	−	43.0220i	0.456664	−	1.40547i	0.869170	−	0.494513i	$-0.164653\pi$
$938$	5.29409	+	5.69745i	0.172858	+	0.186028i
$939$	−48.2008	−	35.0200i	−1.57298	−	1.14283i
$940$	1.64458	−	1.82650i	0.0536404	−	0.0595737i
$941$	6.78154	+	1.44146i	0.221072	+	0.0469903i	0.317116	−	0.948387i	$-0.397286\pi$
$941$	6.78154	+	1.44146i	0.221072	+	0.0469903i	−0.0960439	+	0.995377i	$0.530619\pi$
$942$	29.2516	−	13.0236i	0.953068	−	0.424333i
$943$	14.9094	+	6.63811i	0.485518	+	0.216167i
$944$	−17.7579	+	54.6531i	−0.577969	+	1.77881i
$945$	−3.44668	+	2.58768i	−0.112120	+	0.0841773i
$946$		0			0
$947$	−10.3716	−	17.9642i	−0.337033	−	0.583758i	0.646840	−	0.762626i	$-0.276090\pi$
$947$	−10.3716	−	17.9642i	−0.337033	−	0.583758i	−0.983873	+	0.178867i	$0.942757\pi$
$948$	−9.55886	−	10.6162i	−0.310457	−	0.344798i
$949$	−3.01138	−	28.6513i	−0.0977534	−	0.930062i
$950$	−4.90228	+	46.6421i	−0.159051	+	1.51327i
$951$	−2.62378	−	8.07516i	−0.0850819	−	0.261855i
$952$	0.777337	−	8.70703i	0.0251936	−	0.282197i
$953$	−16.3483	−	11.8777i	−0.529574	−	0.384758i	0.290625	−	0.956837i	$-0.406137\pi$
$953$	−16.3483	−	11.8777i	−0.529574	−	0.384758i	−0.820198	+	0.572079i	$0.806137\pi$
$954$	22.9590	+	10.2220i	0.743325	+	0.330949i
$955$	4.73396	+	5.25760i	0.153187	+	0.170132i
$956$	6.71735	−	11.6348i	0.217254	−	0.376296i
$957$		0			0
$958$	47.6499			1.53950
$959$	−12.6353	+	14.4833i	−0.408016	+	0.467690i
$960$	2.67302	−	1.94206i	0.0862715	−	0.0626799i
$961$	−1.08176	+	10.2923i	−0.0348956	+	0.332009i
$962$	19.6039	+	4.16694i	0.632055	+	0.134347i
$963$	−19.9130	−	4.23265i	−0.641689	−	0.136395i
$964$	0.238899	−	2.27297i	0.00769442	−	0.0732075i
$965$	1.85854	−	1.35031i	0.0598284	−	0.0434679i
$966$	7.48475	+	21.8632i	0.240818	+	0.703438i
$967$	−7.98254			−0.256701			−0.128351	−	0.991729i	$-0.540968\pi$
$967$	−7.98254			−0.256701			−0.128351	+	0.991729i	$0.540968\pi$
$968$		0			0
$969$	17.3337	−	30.0229i	0.556839	−	0.964473i
$970$	2.02505	+	2.24905i	0.0650205	+	0.0722125i
$971$	−12.5880	−	5.60454i	−0.403968	−	0.179858i	0.194686	−	0.980866i	$-0.437631\pi$
$971$	−12.5880	−	5.60454i	−0.403968	−	0.179858i	−0.598655	+	0.801007i	$0.704298\pi$
$972$	−18.5451	−	13.4738i	−0.594835	−	0.432173i
$973$	6.24588	−	2.89902i	0.200234	−	0.0929383i
$974$	8.23899	+	25.3570i	0.263994	+	0.812491i
$975$	1.90272	−	18.1031i	0.0609357	−	0.579764i
$976$	−2.20369	−	20.9668i	−0.0705386	−	0.671129i
$977$	8.04357	+	8.93329i	0.257337	+	0.285801i	0.857944	−	0.513742i	$-0.171741\pi$
$977$	8.04357	+	8.93329i	0.257337	+	0.285801i	−0.600608	+	0.799544i	$0.705075\pi$
$978$	−32.2745	−	55.9010i	−1.03202	−	1.78752i
$979$		0			0
$980$	5.89511	−	1.44761i	0.188312	−	0.0462423i
$981$	−8.10771	+	24.9530i	−0.258859	+	0.796686i
$982$	−66.0132	−	29.3910i	−2.10656	−	0.937903i
$983$	−40.7937	+	18.1625i	−1.30112	+	0.579295i	−0.936109	−	0.351709i	$-0.885601\pi$
$983$	−40.7937	+	18.1625i	−1.30112	+	0.579295i	−0.365009	+	0.931004i	$0.618934\pi$
$984$	−18.8929	−	4.01581i	−0.602283	−	0.128019i
$985$	−1.02843	+	1.14219i	−0.0327685	+	0.0363931i
$986$	−43.8681	−	31.8721i	−1.39705	−	1.01501i
$987$	−11.2229	−	12.0780i	−0.357229	−	0.384447i
$988$	4.22520	−	13.0038i	0.134422	−	0.413707i
$989$	5.27056	+	9.12888i	0.167594	+	0.290282i
$990$		0			0
$991$	11.4830	−	19.8891i	0.364769	−	0.631799i	−0.623970	−	0.781448i	$-0.714481\pi$
$991$	11.4830	−	19.8891i	0.364769	−	0.631799i	0.988739	+	0.149650i	$0.0478146\pi$
$992$	41.4880	−	8.81854i	1.31724	−	0.279989i
$993$	10.9400	−	7.94837i	0.347170	−	0.252234i
$994$	−20.8265	+	0.326564i	−0.660576	+	0.0103580i
$995$	3.63258	+	11.1799i	0.115161	+	0.354428i
$996$	18.5315	−	20.5813i	0.587193	−	0.652144i
$997$	1.23235	−	0.548678i	0.0390289	−	0.0173768i	−0.387129	−	0.922025i	$-0.626533\pi$
$997$	1.23235	−	0.548678i	0.0390289	−	0.0173768i	0.426158	+	0.904649i	$0.359867\pi$
$998$	5.02920	+	47.8496i	0.159196	+	1.51465i
$999$	−15.2079	+	3.23254i	−0.481157	+	0.102273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.e.130.1		24
7.2	even	3	inner	847.2.n.e.9.3		24
11.2	odd	10		847.2.n.d.487.1		24
11.3	even	5	inner	847.2.n.e.81.1		24
11.4	even	5		77.2.e.b.67.1	yes	6
11.5	even	5	inner	847.2.n.e.753.3		24
11.6	odd	10		847.2.n.d.753.1		24
11.7	odd	10		847.2.e.d.606.3		6
11.8	odd	10		847.2.n.d.81.3		24
11.9	even	5	inner	847.2.n.e.487.3		24
11.10	odd	2		847.2.n.d.130.3		24
33.26	odd	10		693.2.i.g.298.3		6
44.15	odd	10		1232.2.q.k.529.1		6
77.2	odd	30		847.2.n.d.366.3		24
77.4	even	15		539.2.a.h.1.3		3
77.9	even	15	inner	847.2.n.e.366.1		24
77.16	even	15	inner	847.2.n.e.632.1		24
77.18	odd	30		5929.2.a.v.1.1		3
77.26	odd	30		539.2.e.l.177.1		6
77.30	odd	30		847.2.n.d.807.1		24
77.37	even	15		77.2.e.b.23.1	✓	6
77.48	odd	10		539.2.e.l.67.1		6
77.51	odd	30		847.2.e.d.485.3		6
77.58	even	15	inner	847.2.n.e.807.3		24
77.59	odd	30		539.2.a.i.1.3		3
77.65	odd	6		847.2.n.d.9.1		24
77.72	odd	30		847.2.n.d.632.3		24
77.73	even	30		5929.2.a.w.1.1		3
231.59	even	30		4851.2.a.bn.1.1		3
231.158	odd	30		4851.2.a.bo.1.1		3
231.191	odd	30		693.2.i.g.100.3		6
308.59	even	30		8624.2.a.ck.1.1		3
308.191	odd	30		1232.2.q.k.177.1		6
308.235	odd	30		8624.2.a.cl.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.1	✓	6	77.37	even	15
77.2.e.b.67.1	yes	6	11.4	even	5
539.2.a.h.1.3		3	77.4	even	15
539.2.a.i.1.3		3	77.59	odd	30
539.2.e.l.67.1		6	77.48	odd	10
539.2.e.l.177.1		6	77.26	odd	30
693.2.i.g.100.3		6	231.191	odd	30
693.2.i.g.298.3		6	33.26	odd	10
847.2.e.d.485.3		6	77.51	odd	30
847.2.e.d.606.3		6	11.7	odd	10
847.2.n.d.9.1		24	77.65	odd	6
847.2.n.d.81.3		24	11.8	odd	10
847.2.n.d.130.3		24	11.10	odd	2
847.2.n.d.366.3		24	77.2	odd	30
847.2.n.d.487.1		24	11.2	odd	10
847.2.n.d.632.3		24	77.72	odd	30
847.2.n.d.753.1		24	11.6	odd	10
847.2.n.d.807.1		24	77.30	odd	30
847.2.n.e.9.3		24	7.2	even	3	inner
847.2.n.e.81.1		24	11.3	even	5	inner
847.2.n.e.130.1		24	1.1	even	1	trivial
847.2.n.e.366.1		24	77.9	even	15	inner
847.2.n.e.487.3		24	11.9	even	5	inner
847.2.n.e.632.1		24	77.16	even	15	inner
847.2.n.e.753.3		24	11.5	even	5	inner
847.2.n.e.807.3		24	77.58	even	15	inner
1232.2.q.k.177.1		6	308.191	odd	30
1232.2.q.k.529.1		6	44.15	odd	10
4851.2.a.bn.1.1		3	231.59	even	30
4851.2.a.bo.1.1		3	231.158	odd	30
5929.2.a.v.1.1		3	77.18	odd	30
5929.2.a.w.1.1		3	77.73	even	30
8624.2.a.ck.1.1		3	308.59	even	30
8624.2.a.cl.1.3		3	308.235	odd	30

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.79416 + 0.381361i) q^{2} +(0.229826 + 2.18665i) q^{3} +(1.24649 - 0.554971i) q^{4} +(-0.425267 + 0.472307i) q^{5} +(-1.24625 - 3.83555i) q^{6} +(1.28679 - 2.31175i) q^{7} +(0.943117 - 0.685215i) q^{8} +(-1.79416 + 0.381361i) q^{9} +O(q^{10})\)	\(q+(-1.79416 + 0.381361i) q^{2} +(0.229826 + 2.18665i) q^{3} +(1.24649 - 0.554971i) q^{4} +(-0.425267 + 0.472307i) q^{5} +(-1.24625 - 3.83555i) q^{6} +(1.28679 - 2.31175i) q^{7} +(0.943117 - 0.685215i) q^{8} +(-1.79416 + 0.381361i) q^{9} +(0.582878 - 1.00958i) q^{10} +(1.50000 + 2.59808i) q^{12} +(-0.556635 + 1.71315i) q^{13} +(-1.42710 + 4.63838i) q^{14} +(-1.13051 - 0.821361i) q^{15} +(-3.25678 + 3.61702i) q^{16} +(2.77231 + 0.589272i) q^{17} +(3.07358 - 1.36844i) q^{18} +(-5.08218 - 2.26273i) q^{19} +(-0.267973 + 0.824735i) q^{20} +(5.35071 + 2.28245i) q^{21} +(-1.08288 - 1.87560i) q^{23} +(1.71507 + 1.90478i) q^{24} +(0.480421 + 4.57090i) q^{25} +(0.345366 - 3.28594i) q^{26} +(0.792054 + 2.43769i) q^{27} +(0.321012 - 3.59569i) q^{28} +(8.43830 + 6.13079i) q^{29} +(2.34154 + 1.04252i) q^{30} +(4.30272 + 4.77866i) q^{31} +(3.29804 - 5.71237i) q^{32} -5.19869 q^{34} +(0.544625 + 1.59087i) q^{35} +(-2.02475 + 1.47107i) q^{36} +(-0.634056 + 6.03264i) q^{37} +(9.98117 + 2.12156i) q^{38} +(-3.87397 - 0.823439i) q^{39} +(-0.0774450 + 0.736840i) q^{40} +(-6.09648 + 4.42935i) q^{41} +(-10.4705 - 2.05454i) q^{42} -4.86718 q^{43} +(0.582878 - 1.00958i) q^{45} +(2.65814 + 2.95216i) q^{46} +(-2.58921 - 1.15279i) q^{47} +(-8.65763 - 6.29014i) q^{48} +(-3.68835 - 5.94946i) q^{49} +(-2.60511 - 8.01771i) q^{50} +(-0.651382 + 6.19749i) q^{51} +(0.256909 + 2.44433i) q^{52} +(4.99827 + 5.55114i) q^{53} +(-2.35071 - 4.07155i) q^{54} +(-0.370450 - 3.06197i) q^{56} +(3.77978 - 11.6330i) q^{57} +(-17.4777 - 7.78158i) q^{58} +(10.7860 - 4.80225i) q^{59} +(-1.86499 - 0.396416i) q^{60} +(-2.89835 + 3.21894i) q^{61} +(-9.54217 - 6.93279i) q^{62} +(-1.42710 + 4.63838i) q^{63} +(-0.730655 + 2.24872i) q^{64} +(-0.572413 - 0.991448i) q^{65} +(0.801309 - 1.38791i) q^{67} +(3.78267 - 0.804031i) q^{68} +(3.85240 - 2.79893i) q^{69} +(-1.58384 - 2.64658i) q^{70} +(1.32631 + 4.08197i) q^{71} +(-1.43079 + 1.58905i) q^{72} +(-14.6107 + 6.50512i) q^{73} +(-1.16301 - 11.0653i) q^{74} +(-9.88452 + 2.10102i) q^{75} -7.59061 q^{76} +7.26456 q^{78} +(-4.65777 + 0.990040i) q^{79} +(-0.323343 - 3.07640i) q^{80} +(-10.1753 + 4.53035i) q^{81} +(9.24888 - 10.2719i) q^{82} +(-2.85273 - 8.77980i) q^{83} +(7.93628 - 0.124443i) q^{84} +(-1.45729 + 1.05878i) q^{85} +(8.73250 - 1.85615i) q^{86} +(-11.4665 + 19.8606i) q^{87} +(-0.182224 - 0.315621i) q^{89} +(-0.660765 + 2.03363i) q^{90} +(3.24409 + 3.49126i) q^{91} +(-2.39070 - 1.73694i) q^{92} +(-9.46036 + 10.5068i) q^{93} +(5.08509 + 1.08087i) q^{94} +(3.22999 - 1.43808i) q^{95} +(13.2489 + 5.89879i) q^{96} +(-0.802231 + 2.46901i) q^{97} +(8.88637 + 9.26770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8}+O(q^{10}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} + 36 q^{10} + 36 q^{12} + 22 q^{13} - 12 q^{14} + 14 q^{15} + 2 q^{16} - 3 q^{17} + 10 q^{18} - 11 q^{19} - 28 q^{20} + 40 q^{21} - 48 q^{23} + 2 q^{24} + 3 q^{25} + q^{26} - 4 q^{27} - 13 q^{28} + 18 q^{29} + 2 q^{30} - 3 q^{31} + 12 q^{32} - 80 q^{34} - 9 q^{35} + 18 q^{36} - 4 q^{37} + 8 q^{38} - 5 q^{39} - 3 q^{40} + 10 q^{41} + 2 q^{42} + 16 q^{43} + 36 q^{45} - 10 q^{46} - 3 q^{47} - 20 q^{48} + 24 q^{49} + 6 q^{50} + 2 q^{51} - 7 q^{52} + 17 q^{53} + 32 q^{54} + 12 q^{56} - 40 q^{57} - 13 q^{58} + 8 q^{59} + 6 q^{60} - 24 q^{61} - 26 q^{62} - 12 q^{63} + 14 q^{64} - 60 q^{65} + 64 q^{67} + 5 q^{68} + 6 q^{69} + 27 q^{70} - 14 q^{71} + 10 q^{72} - 20 q^{73} + 22 q^{74} + 25 q^{75} - 312 q^{76} - 48 q^{78} + 3 q^{79} + 9 q^{80} - 17 q^{81} + 41 q^{82} + 22 q^{83} - 12 q^{84} - 22 q^{85} - 21 q^{86} - 120 q^{87} - 4 q^{89} - 20 q^{90} + 15 q^{91} - 50 q^{92} - 26 q^{93} - 10 q^{94} - 17 q^{95} + 27 q^{96} - 18 q^{97} - 96 q^{98}+O(q^{100}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 + 36 * q^10 + 36 * q^12 + 22 * q^13 - 12 * q^14 + 14 * q^15 + 2 * q^16 - 3 * q^17 + 10 * q^18 - 11 * q^19 - 28 * q^20 + 40 * q^21 - 48 * q^23 + 2 * q^24 + 3 * q^25 + q^26 - 4 * q^27 - 13 * q^28 + 18 * q^29 + 2 * q^30 - 3 * q^31 + 12 * q^32 - 80 * q^34 - 9 * q^35 + 18 * q^36 - 4 * q^37 + 8 * q^38 - 5 * q^39 - 3 * q^40 + 10 * q^41 + 2 * q^42 + 16 * q^43 + 36 * q^45 - 10 * q^46 - 3 * q^47 - 20 * q^48 + 24 * q^49 + 6 * q^50 + 2 * q^51 - 7 * q^52 + 17 * q^53 + 32 * q^54 + 12 * q^56 - 40 * q^57 - 13 * q^58 + 8 * q^59 + 6 * q^60 - 24 * q^61 - 26 * q^62 - 12 * q^63 + 14 * q^64 - 60 * q^65 + 64 * q^67 + 5 * q^68 + 6 * q^69 + 27 * q^70 - 14 * q^71 + 10 * q^72 - 20 * q^73 + 22 * q^74 + 25 * q^75 - 312 * q^76 - 48 * q^78 + 3 * q^79 + 9 * q^80 - 17 * q^81 + 41 * q^82 + 22 * q^83 - 12 * q^84 - 22 * q^85 - 21 * q^86 - 120 * q^87 - 4 * q^89 - 20 * q^90 + 15 * q^91 - 50 * q^92 - 26 * q^93 - 10 * q^94 - 17 * q^95 + 27 * q^96 - 18 * q^97 - 96 * q^98

Introduction

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