LMFDB - Embedded newform 1183.2.e.k.170.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.10
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.k.508.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.308759 + 0.534786i) q^{2} +(-1.53664 - 2.66155i) q^{3} +(0.809336 + 1.40181i) q^{4} +(0.698024 - 1.20901i) q^{5} +1.89781 q^{6} +(-2.36540 + 1.18527i) q^{7} -2.23459 q^{8} +(-3.22255 + 5.58162i) q^{9} +O(q^{10})$	\(q+(-0.308759 + 0.534786i) q^{2} +(-1.53664 - 2.66155i) q^{3} +(0.809336 + 1.40181i) q^{4} +(0.698024 - 1.20901i) q^{5} +1.89781 q^{6} +(-2.36540 + 1.18527i) q^{7} -2.23459 q^{8} +(-3.22255 + 5.58162i) q^{9} +(0.431043 + 0.746588i) q^{10} +(-0.111926 - 0.193862i) q^{11} +(2.48732 - 4.30817i) q^{12} +(0.0964736 - 1.63095i) q^{14} -4.29046 q^{15} +(-0.928721 + 1.60859i) q^{16} +(1.10151 + 1.90787i) q^{17} +(-1.98998 - 3.44675i) q^{18} +(4.07853 - 7.06422i) q^{19} +2.25974 q^{20} +(6.78943 + 4.47429i) q^{21} +0.138233 q^{22} +(-2.72842 + 4.72576i) q^{23} +(3.43378 + 5.94748i) q^{24} +(1.52552 + 2.64228i) q^{25} +10.5878 q^{27} +(-3.57593 - 2.35657i) q^{28} +8.94660 q^{29} +(1.32472 - 2.29448i) q^{30} +(2.36176 + 4.09069i) q^{31} +(-2.80810 - 4.86377i) q^{32} +(-0.343981 + 0.595792i) q^{33} -1.36040 q^{34} +(-0.218102 + 3.68715i) q^{35} -10.4325 q^{36} +(0.859375 - 1.48848i) q^{37} +(2.51856 + 4.36228i) q^{38} +(-1.55980 + 2.70166i) q^{40} -2.09513 q^{41} +(-4.48909 + 2.24942i) q^{42} -2.39709 q^{43} +(0.181171 - 0.313798i) q^{44} +(4.49884 + 7.79222i) q^{45} +(-1.68485 - 2.91824i) q^{46} +(2.34791 - 4.06670i) q^{47} +5.70845 q^{48} +(4.19027 - 5.60728i) q^{49} -1.88408 q^{50} +(3.38525 - 5.86343i) q^{51} +(5.61288 + 9.72179i) q^{53} +(-3.26908 + 5.66220i) q^{54} -0.312508 q^{55} +(5.28572 - 2.64860i) q^{56} -25.0690 q^{57} +(-2.76234 + 4.78452i) q^{58} +(0.743148 + 1.28717i) q^{59} +(-3.47242 - 6.01441i) q^{60} +(6.25979 - 10.8423i) q^{61} -2.91686 q^{62} +(1.00691 - 17.0224i) q^{63} -0.246783 q^{64} +(-0.212414 - 0.367913i) q^{66} +(-0.845719 - 1.46483i) q^{67} +(-1.78298 + 3.08821i) q^{68} +16.7704 q^{69} +(-1.90450 - 1.25508i) q^{70} +7.64780 q^{71} +(7.20109 - 12.4727i) q^{72} +(2.25564 + 3.90689i) q^{73} +(0.530680 + 0.919164i) q^{74} +(4.68837 - 8.12050i) q^{75} +13.2036 q^{76} +(0.494529 + 0.325898i) q^{77} +(4.78709 - 8.29148i) q^{79} +(1.29654 + 2.24567i) q^{80} +(-6.60202 - 11.4350i) q^{81} +(0.646891 - 1.12045i) q^{82} +8.77718 q^{83} +(-0.777179 + 13.1387i) q^{84} +3.07552 q^{85} +(0.740125 - 1.28193i) q^{86} +(-13.7477 - 23.8118i) q^{87} +(0.250109 + 0.433202i) q^{88} +(-5.36613 + 9.29441i) q^{89} -5.55623 q^{90} -8.83282 q^{92} +(7.25837 - 12.5719i) q^{93} +(1.44988 + 2.51126i) q^{94} +(-5.69382 - 9.86199i) q^{95} +(-8.63009 + 14.9478i) q^{96} -13.0629 q^{97} +(1.70491 + 3.97220i) q^{98} +1.44275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9}+O(q^{10}) $ 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9	\( 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9} - 5 q^{10} - q^{11} - 5 q^{12} - 2 q^{14} - 10 q^{15} - 17 q^{16} + 5 q^{17} + 24 q^{19} - 68 q^{20} + q^{21} - 28 q^{22} - 11 q^{23} + 32 q^{24} - 33 q^{25} - 42 q^{27} + 15 q^{28} + 8 q^{29} + 22 q^{30} + 40 q^{31} - 6 q^{32} + 24 q^{33} - 72 q^{34} + 44 q^{35} - 30 q^{36} - 4 q^{37} + 29 q^{38} + 4 q^{40} - 98 q^{41} - 9 q^{42} + 26 q^{43} + 10 q^{44} + 58 q^{45} - 10 q^{46} + 62 q^{47} + 178 q^{48} + 31 q^{49} + 46 q^{50} + 21 q^{51} + 18 q^{53} + 12 q^{54} - 28 q^{55} - 56 q^{56} + 26 q^{57} + 56 q^{58} + 79 q^{59} + 22 q^{60} - 13 q^{61} + 24 q^{62} - 22 q^{63} + 36 q^{64} + 38 q^{66} - 2 q^{67} + 12 q^{68} - 56 q^{69} - 85 q^{70} + 38 q^{71} + 81 q^{72} + 17 q^{73} - 17 q^{74} - 24 q^{75} - 116 q^{76} - 30 q^{77} + 9 q^{79} + 63 q^{80} - 16 q^{81} + 22 q^{82} - 162 q^{83} - 203 q^{84} + 68 q^{85} + 22 q^{86} - 70 q^{87} + 33 q^{88} + 72 q^{89} + 2 q^{90} - 8 q^{92} + 19 q^{93} + 30 q^{94} - 13 q^{95} + 11 q^{96} - 90 q^{97} - 81 q^{98} + 78 q^{99}+O(q^{100}) \) 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9 - 5 * q^10 - q^11 - 5 * q^12 - 2 * q^14 - 10 * q^15 - 17 * q^16 + 5 * q^17 + 24 * q^19 - 68 * q^20 + q^21 - 28 * q^22 - 11 * q^23 + 32 * q^24 - 33 * q^25 - 42 * q^27 + 15 * q^28 + 8 * q^29 + 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 - 72 * q^34 + 44 * q^35 - 30 * q^36 - 4 * q^37 + 29 * q^38 + 4 * q^40 - 98 * q^41 - 9 * q^42 + 26 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 178 * q^48 + 31 * q^49 + 46 * q^50 + 21 * q^51 + 18 * q^53 + 12 * q^54 - 28 * q^55 - 56 * q^56 + 26 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 - 13 * q^61 + 24 * q^62 - 22 * q^63 + 36 * q^64 + 38 * q^66 - 2 * q^67 + 12 * q^68 - 56 * q^69 - 85 * q^70 + 38 * q^71 + 81 * q^72 + 17 * q^73 - 17 * q^74 - 24 * q^75 - 116 * q^76 - 30 * q^77 + 9 * q^79 + 63 * q^80 - 16 * q^81 + 22 * q^82 - 162 * q^83 - 203 * q^84 + 68 * q^85 + 22 * q^86 - 70 * q^87 + 33 * q^88 + 72 * q^89 + 2 * q^90 - 8 * q^92 + 19 * q^93 + 30 * q^94 - 13 * q^95 + 11 * q^96 - 90 * q^97 - 81 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.308759	+	0.534786i	−0.218326	+	0.378151i	−0.954296	−	0.298863i	$-0.903393\pi$
$2$	−0.308759	+	0.534786i	−0.218326	+	0.378151i	0.735971	+	0.677013i	$0.236726\pi$
$3$	−1.53664	−	2.66155i	−0.887182	−	1.53664i	−0.843192	−	0.537612i	$-0.819326\pi$
$3$	−1.53664	−	2.66155i	−0.887182	−	1.53664i	−0.0439897	−	0.999032i	$-0.514007\pi$
$4$	0.809336	+	1.40181i	0.404668	+	0.700905i
$5$	0.698024	−	1.20901i	0.312166	−	0.540687i	−0.666665	−	0.745357i	$-0.732279\pi$
$5$	0.698024	−	1.20901i	0.312166	−	0.540687i	0.978831	+	0.204670i	$0.0656121\pi$
$6$	1.89781			0.774778
$7$	−2.36540	+	1.18527i	−0.894039	+	0.447990i
$7$	−2.36540	+	1.18527i	−0.894039	+	0.447990i
$8$	−2.23459			−0.790048
$9$	−3.22255	+	5.58162i	−1.07418	+	1.86054i
$10$	0.431043	+	0.746588i	0.136308	+	0.236092i
$11$	−0.111926	−	0.193862i	−0.0337470	−	0.0584515i	0.848659	−	0.528941i	$-0.177411\pi$
$11$	−0.111926	−	0.193862i	−0.0337470	−	0.0584515i	−0.882406	+	0.470489i	$0.844077\pi$
$12$	2.48732	−	4.30817i	0.718028	−	1.24366i
$13$		0			0
$13$		0			0
$14$	0.0964736	−	1.63095i	0.0257837	−	0.435889i
$15$	−4.29046			−1.10779
$16$	−0.928721	+	1.60859i	−0.232180	+	0.402148i
$17$	1.10151	+	1.90787i	0.267155	+	0.462726i	0.968126	−	0.250464i	$-0.0805831\pi$
$17$	1.10151	+	1.90787i	0.267155	+	0.462726i	−0.700971	+	0.713190i	$0.747250\pi$
$18$	−1.98998	−	3.44675i	−0.469043	−	0.812407i
$19$	4.07853	−	7.06422i	0.935678	−	1.62064i	0.162258	−	0.986748i	$-0.448122\pi$
$19$	4.07853	−	7.06422i	0.935678	−	1.62064i	0.773420	−	0.633894i	$-0.218544\pi$
$20$	2.25974			0.505294
$21$	6.78943	+	4.47429i	1.48158	+	0.976371i
$22$	0.138233			0.0294713
$23$	−2.72842	+	4.72576i	−0.568914	+	0.985388i	0.427759	+	0.903893i	$0.359303\pi$
$23$	−2.72842	+	4.72576i	−0.568914	+	0.985388i	−0.996674	+	0.0814958i	$0.974030\pi$
$24$	3.43378	+	5.94748i	0.700917	+	1.21402i
$25$	1.52552	+	2.64228i	0.305105	+	0.528457i
$26$		0			0
$27$	10.5878			2.03762
$28$	−3.57593	−	2.35657i	−0.675787	−	0.445349i
$29$	8.94660			1.66134			0.830671	−	0.556764i	$-0.187957\pi$
$29$	8.94660			1.66134			0.830671	+	0.556764i	$0.187957\pi$
$30$	1.32472	−	2.29448i	0.241859	−	0.418913i
$31$	2.36176	+	4.09069i	0.424184	+	0.734709i	0.996344	−	0.0854334i	$-0.0272275\pi$
$31$	2.36176	+	4.09069i	0.424184	+	0.734709i	−0.572159	+	0.820142i	$0.693894\pi$
$32$	−2.80810	−	4.86377i	−0.496406	−	0.859800i
$33$	−0.343981	+	0.595792i	−0.0598794	+	0.103714i
$34$	−1.36040			−0.233307
$35$	−0.218102	+	3.68715i	−0.0368660	+	0.623243i
$36$	−10.4325			−1.73875
$37$	0.859375	−	1.48848i	0.141280	−	0.244705i	−0.786699	−	0.617337i	$-0.788211\pi$
$37$	0.859375	−	1.48848i	0.141280	−	0.244705i	0.927979	+	0.372632i	$0.121545\pi$
$38$	2.51856	+	4.36228i	0.408565	+	0.707655i
$39$		0			0
$40$	−1.55980	+	2.70166i	−0.246626	+	0.427169i
$41$	−2.09513			−0.327205			−0.163602	−	0.986526i	$-0.552311\pi$
$41$	−2.09513			−0.327205			−0.163602	+	0.986526i	$0.552311\pi$
$42$	−4.48909	+	2.24942i	−0.692681	+	0.347093i
$43$	−2.39709			−0.365554			−0.182777	−	0.983154i	$-0.558509\pi$
$43$	−2.39709			−0.365554			−0.182777	+	0.983154i	$0.558509\pi$
$44$	0.181171	−	0.313798i	0.0273126	−	0.0473069i
$45$	4.49884	+	7.79222i	0.670647	+	1.16160i
$46$	−1.68485	−	2.91824i	−0.248417	−	0.430271i
$47$	2.34791	−	4.06670i	0.342478	−	0.593189i	−0.642414	−	0.766358i	$-0.722067\pi$
$47$	2.34791	−	4.06670i	0.342478	−	0.593189i	0.984892	+	0.173168i	$0.0554004\pi$
$48$	5.70845			0.823944
$49$	4.19027	−	5.60728i	0.598610	−	0.801041i
$50$	−1.88408			−0.266449
$51$	3.38525	−	5.86343i	0.474030	−	0.821044i
$52$		0			0
$53$	5.61288	+	9.72179i	0.770988	+	1.33539i	0.937022	+	0.349271i	$0.113571\pi$
$53$	5.61288	+	9.72179i	0.770988	+	1.33539i	−0.166033	+	0.986120i	$0.553096\pi$
$54$	−3.26908	+	5.66220i	−0.444865	+	0.770528i
$55$	−0.312508			−0.0421386
$56$	5.28572	−	2.64860i	0.706334	−	0.353934i
$57$	−25.0690			−3.32047
$58$	−2.76234	+	4.78452i	−0.362713	+	0.628238i
$59$	0.743148	+	1.28717i	0.0967496	+	0.167575i	0.910337	−	0.413867i	$-0.135822\pi$
$59$	0.743148	+	1.28717i	0.0967496	+	0.167575i	−0.813588	+	0.581442i	$0.802489\pi$
$60$	−3.47242	−	6.01441i	−0.448288	−	0.776458i
$61$	6.25979	−	10.8423i	0.801484	−	1.38821i	−0.117156	−	0.993114i	$-0.537378\pi$
$61$	6.25979	−	10.8423i	0.801484	−	1.38821i	0.918640	−	0.395097i	$-0.129289\pi$
$62$	−2.91686			−0.370441
$63$	1.00691	−	17.0224i	0.126858	−	2.14462i
$64$	−0.246783			−0.0308479
$65$		0			0
$66$	−0.212414	−	0.367913i	−0.0261464	−	0.0452869i
$67$	−0.845719	−	1.46483i	−0.103321	−	0.178957i	0.809730	−	0.586803i	$-0.199614\pi$
$67$	−0.845719	−	1.46483i	−0.103321	−	0.178957i	−0.913051	+	0.407845i	$0.866280\pi$
$68$	−1.78298	+	3.08821i	−0.216218	+	0.374501i
$69$	16.7704			2.01892
$70$	−1.90450	−	1.25508i	−0.227631	−	0.150011i
$71$	7.64780			0.907627			0.453813	−	0.891097i	$-0.350063\pi$
$71$	7.64780			0.907627			0.453813	+	0.891097i	$0.350063\pi$
$72$	7.20109	−	12.4727i	0.848657	−	1.46992i
$73$	2.25564	+	3.90689i	0.264003	+	0.457267i	0.967302	−	0.253628i	$-0.0816238\pi$
$73$	2.25564	+	3.90689i	0.264003	+	0.457267i	−0.703299	+	0.710894i	$0.748290\pi$
$74$	0.530680	+	0.919164i	0.0616903	+	0.106851i
$75$	4.68837	−	8.12050i	0.541367	−	0.937675i
$76$	13.2036			1.51456
$77$	0.494529	+	0.325898i	0.0563568	+	0.0371396i
$78$		0			0
$79$	4.78709	−	8.29148i	0.538589	−	0.932864i	−0.460391	−	0.887716i	$-0.652291\pi$
$79$	4.78709	−	8.29148i	0.538589	−	0.932864i	0.998980	−	0.0451477i	$-0.0143758\pi$
$80$	1.29654	+	2.24567i	0.144958	+	0.251074i
$81$	−6.60202	−	11.4350i	−0.733557	−	1.27056i
$82$	0.646891	−	1.12045i	0.0714372	−	0.123733i
$83$	8.77718			0.963421			0.481710	−	0.876330i	$-0.340016\pi$
$83$	8.77718			0.963421			0.481710	+	0.876330i	$0.340016\pi$
$84$	−0.777179	+	13.1387i	−0.0847972	+	1.43355i
$85$	3.07552			0.333587
$86$	0.740125	−	1.28193i	0.0798097	−	0.138234i
$87$	−13.7477	−	23.8118i	−1.47391	−	2.55289i
$88$	0.250109	+	0.433202i	0.0266617	+	0.0461795i
$89$	−5.36613	+	9.29441i	−0.568809	+	0.985205i	0.427875	+	0.903838i	$0.359262\pi$
$89$	−5.36613	+	9.29441i	−0.568809	+	0.985205i	−0.996684	+	0.0813678i	$0.974071\pi$
$90$	−5.55623			−0.585678
$91$		0			0
$92$	−8.83282			−0.920885
$93$	7.25837	−	12.5719i	0.752658	−	1.30364i
$94$	1.44988	+	2.51126i	0.149543	+	0.259017i
$95$	−5.69382	−	9.86199i	−0.584174	−	1.01182i
$96$	−8.63009	+	14.9478i	−0.880805	+	1.52560i
$97$	−13.0629			−1.32633			−0.663167	−	0.748472i	$-0.730788\pi$
$97$	−13.0629			−1.32633			−0.663167	+	0.748472i	$0.730788\pi$
$98$	1.70491	+	3.97220i	0.172222	+	0.401253i
$99$	1.44275			0.145002
$100$	−2.46932	+	4.27699i	−0.246932	+	0.427699i
$101$	6.22759	+	10.7865i	0.619669	+	1.07330i	0.989546	+	0.144217i	$0.0460663\pi$
$101$	6.22759	+	10.7865i	0.619669	+	1.07330i	−0.369877	+	0.929081i	$0.620600\pi$
$102$	2.09045	+	3.62077i	0.206986	+	0.358510i
$103$	−0.198175	+	0.343249i	−0.0195267	+	0.0338213i	−0.875624	−	0.482994i	$-0.839549\pi$
$103$	−0.198175	+	0.343249i	−0.0195267	+	0.0338213i	0.856097	+	0.516815i	$0.172883\pi$
$104$		0			0
$105$	10.1487	−	5.08535i	0.990409	−	0.496280i
$106$	−6.93211			−0.673306
$107$	−3.22973	+	5.59405i	−0.312230	+	0.540797i	−0.978845	−	0.204605i	$-0.934409\pi$
$107$	−3.22973	+	5.59405i	−0.312230	+	0.540797i	0.666615	+	0.745402i	$0.267742\pi$
$108$	8.56908	+	14.8421i	0.824560	+	1.42818i
$109$	2.01350	+	3.48749i	0.192858	+	0.334041i	0.946196	−	0.323593i	$-0.104891\pi$
$109$	2.01350	+	3.48749i	0.192858	+	0.334041i	−0.753338	+	0.657634i	$0.771558\pi$
$110$	0.0964898	−	0.167125i	0.00919994	−	0.0159348i
$111$	−5.28222			−0.501366
$112$	0.290184	−	4.90575i	0.0274199	−	0.463550i
$113$	9.54275			0.897707			0.448853	−	0.893605i	$-0.351833\pi$
$113$	9.54275			0.897707			0.448853	+	0.893605i	$0.351833\pi$
$114$	7.74027	−	13.4065i	0.724943	−	1.25564i
$115$	3.80900	+	6.59739i	0.355191	+	0.615210i
$116$	7.24080	+	12.5414i	0.672292	+	1.16444i
$117$		0			0
$118$	−0.917814			−0.0844916
$119$	−4.86685	−	3.20729i	−0.446143	−	0.294012i
$120$	9.58744			0.875210
$121$	5.47495	−	9.48288i	0.497722	−	0.862080i
$122$	3.86553	+	6.69529i	0.349969	+	0.606164i
$123$	3.21947	+	5.57629i	0.290290	+	0.502797i
$124$	−3.82291	+	6.62148i	−0.343308	+	0.594626i
$125$	11.2397			1.00531
$126$	8.79244	+	5.79429i	0.783293	+	0.516197i
$127$	5.41025			0.480082			0.240041	−	0.970763i	$-0.422839\pi$
$127$	5.41025			0.480082			0.240041	+	0.970763i	$0.422839\pi$
$128$	5.69239	−	9.85951i	0.503141	−	0.871465i
$129$	3.68348	+	6.37998i	0.324313	+	0.561726i
$130$		0			0
$131$	1.49474	−	2.58897i	0.130596	−	0.226199i	−0.793310	−	0.608817i	$-0.791644\pi$
$131$	1.49474	−	2.58897i	0.130596	−	0.226199i	0.923907	+	0.382618i	$0.124978\pi$
$132$	−1.11358			−0.0969251
$133$	−1.27436	+	21.5439i	−0.110501	+	1.86809i
$134$	1.04449			0.0902304
$135$	7.39054	−	12.8008i	0.636076	−	1.10172i
$136$	−2.46142	−	4.26331i	−0.211065	−	0.365576i
$137$	8.07420	+	13.9849i	0.689825	+	1.19481i	0.971894	+	0.235418i	$0.0756460\pi$
$137$	8.07420	+	13.9849i	0.689825	+	1.19481i	−0.282069	+	0.959394i	$0.591021\pi$
$138$	−5.17802	+	8.96859i	−0.440782	+	0.763457i
$139$	−0.657502			−0.0557686			−0.0278843	−	0.999611i	$-0.508877\pi$
$139$	−0.657502			−0.0557686			−0.0278843	+	0.999611i	$0.508877\pi$
$140$	−5.34521	+	2.67841i	−0.451753	+	0.226367i
$141$	−14.4316			−1.21536
$142$	−2.36133	+	4.08994i	−0.198158	+	0.343220i
$143$		0			0
$144$	−5.98570	−	10.3675i	−0.498808	−	0.863961i
$145$	6.24494	−	10.8166i	0.518614	−	0.898266i
$146$	−2.78580			−0.230554
$147$	−21.3630	−	2.53620i	−1.76199	−	0.209182i
$148$	2.78209			0.228687
$149$	7.92219	−	13.7216i	0.649011	−	1.12412i	−0.334349	−	0.942449i	$-0.608516\pi$
$149$	7.92219	−	13.7216i	0.649011	−	1.12412i	0.983359	−	0.181670i	$-0.0581504\pi$
$150$	2.89516	+	5.01456i	0.236388	+	0.409437i
$151$	0.932800	+	1.61566i	0.0759102	+	0.131480i	0.901482	−	0.432817i	$-0.142480\pi$
$151$	0.932800	+	1.61566i	0.0759102	+	0.131480i	−0.825572	+	0.564298i	$0.809147\pi$
$152$	−9.11385	+	15.7857i	−0.739231	+	1.28039i
$153$	−14.1987			−1.14789
$154$	−0.326976	+	0.163843i	−0.0263485	+	0.0132028i
$155$	6.59426			0.529664
$156$		0			0
$157$	3.44305	+	5.96355i	0.274786	+	0.475943i	0.970081	−	0.242781i	$-0.0780598\pi$
$157$	3.44305	+	5.96355i	0.274786	+	0.475943i	−0.695295	+	0.718724i	$0.744726\pi$
$158$	2.95611	+	5.12013i	0.235176	+	0.407336i
$159$	17.2500	−	29.8779i	1.36801	−	2.36947i
$160$	−7.84048			−0.619844
$161$	0.852511	−	14.4122i	0.0671873	−	1.13584i
$162$	8.15373			0.640617
$163$	6.06366	−	10.5026i	0.474943	−	0.822625i	−0.524645	−	0.851321i	$-0.675802\pi$
$163$	6.06366	−	10.5026i	0.474943	−	0.822625i	0.999588	+	0.0286959i	$0.00913543\pi$
$164$	−1.69567	−	2.93698i	−0.132409	−	0.229340i
$165$	0.480214	+	0.831755i	0.0373846	+	0.0647521i
$166$	−2.71003	+	4.69392i	−0.210339	+	0.364319i
$167$	−12.6717			−0.980563			−0.490282	−	0.871564i	$-0.663106\pi$
$167$	−12.6717			−0.980563			−0.490282	+	0.871564i	$0.663106\pi$
$168$	−15.1716	−	9.99823i	−1.17052	−	0.771380i
$169$		0			0
$170$	−0.949594	+	1.64475i	−0.0728305	+	0.126146i
$171$	26.2865	+	45.5296i	2.01018	+	3.48173i
$172$	−1.94005	−	3.36027i	−0.147928	−	0.256218i
$173$	−6.22592	+	10.7836i	−0.473348	+	0.819862i	−0.999535	−	0.0305066i	$-0.990288\pi$
$173$	−6.22592	+	10.7836i	−0.473348	+	0.819862i	0.526187	+	0.850369i	$0.323621\pi$
$174$	16.9789			1.28717
$175$	−6.74030	−	4.44191i	−0.509519	−	0.335777i
$176$	0.415792			0.0313415
$177$	2.28391	−	3.95584i	0.171669	−	0.297339i
$178$	−3.31368	−	5.73946i	−0.248371	−	0.430191i
$179$	2.17356	+	3.76472i	0.162460	+	0.281388i	0.935750	−	0.352663i	$-0.114724\pi$
$179$	2.17356	+	3.76472i	0.162460	+	0.281388i	−0.773291	+	0.634052i	$0.781391\pi$
$180$	−7.28214	+	12.6130i	−0.542779	+	0.940121i
$181$	1.20804			0.0897930			0.0448965	−	0.998992i	$-0.485704\pi$
$181$	1.20804			0.0897930			0.0448965	+	0.998992i	$0.485704\pi$
$182$		0			0
$183$	−38.4763			−2.84425
$184$	6.09691	−	10.5602i	0.449470	−	0.778505i
$185$	−1.19973	−	2.07799i	−0.0882059	−	0.152777i
$186$	4.48217	+	7.76335i	0.328649	+	0.569236i
$187$	0.246575	−	0.427080i	0.0180313	−	0.0312312i
$188$	7.60100			0.554360
$189$	−25.0444	+	12.5494i	−1.82171	+	0.912834i
$190$	7.03207			0.510160
$191$	−11.6337	+	20.1502i	−0.841787	+	1.45802i	0.0465964	+	0.998914i	$0.485163\pi$
$191$	−11.6337	+	20.1502i	−0.841787	+	1.45802i	−0.888383	+	0.459103i	$0.848171\pi$
$192$	0.379218	+	0.656825i	0.0273677	+	0.0474023i
$193$	4.90744	+	8.49994i	0.353245	+	0.611839i	0.986816	−	0.161846i	$-0.0517448\pi$
$193$	4.90744	+	8.49994i	0.353245	+	0.611839i	−0.633571	+	0.773685i	$0.718411\pi$
$194$	4.03328	−	6.98584i	0.289573	−	0.501554i
$195$		0			0
$196$	11.2517	+	1.33579i	0.803692	+	0.0954136i
$197$	−11.6979			−0.833440			−0.416720	−	0.909035i	$-0.636820\pi$
$197$	−11.6979			−0.833440			−0.416720	+	0.909035i	$0.636820\pi$
$198$	−0.445462	+	0.771562i	−0.0316576	+	0.0548325i
$199$	−1.36587	−	2.36576i	−0.0968240	−	0.167704i	0.813544	−	0.581503i	$-0.197535\pi$
$199$	−1.36587	−	2.36576i	−0.0968240	−	0.167704i	−0.910368	+	0.413799i	$0.864202\pi$
$200$	−3.40893	−	5.90443i	−0.241048	−	0.417507i
$201$	−2.59914	+	4.50184i	−0.183329	+	0.317535i
$202$	−7.69130			−0.541158
$203$	−21.1623	+	10.6041i	−1.48530	+	0.744264i
$204$	10.9592			0.767299
$205$	−1.46245	+	2.53304i	−0.102142	+	0.176916i
$206$	−0.122376	−	0.211962i	−0.00852637	−	0.0147681i
$207$	−17.5849	−	30.4580i	−1.22224	−	2.11698i
$208$		0			0
$209$	−1.82597			−0.126305
$210$	−0.413916	+	6.99752i	−0.0285629	+	0.482875i
$211$	−5.39966			−0.371728			−0.185864	−	0.982575i	$-0.559508\pi$
$211$	−5.39966			−0.371728			−0.185864	+	0.982575i	$0.559508\pi$
$212$	−9.08541	+	15.7364i	−0.623989	+	1.08078i
$213$	−11.7519	−	20.3550i	−0.805230	−	1.39470i
$214$	−1.99441	−	3.45443i	−0.136335	−	0.236140i
$215$	−1.67323	+	2.89812i	−0.114113	+	0.197650i
$216$	−23.6594			−1.60982
$217$	−10.4351	−	6.87680i	−0.708380	−	0.466828i
$218$	−2.48675			−0.168424
$219$	6.93224	−	12.0070i	0.468438	−	0.811358i
$220$	−0.252924	−	0.438078i	−0.0170521	−	0.0295352i
$221$		0			0
$222$	1.63093	−	2.82486i	0.109461	−	0.189592i
$223$	−4.36362			−0.292210			−0.146105	−	0.989269i	$-0.546674\pi$
$223$	−4.36362			−0.292210			−0.146105	+	0.989269i	$0.546674\pi$
$224$	12.4072	+	8.17642i	0.828988	+	0.546310i
$225$	−19.6643			−1.31095
$226$	−2.94641	+	5.10333i	−0.195992	+	0.339469i
$227$	−7.73843	−	13.4034i	−0.513618	−	0.889612i	−0.999875	−	0.0157967i	$-0.994972\pi$
$227$	−7.73843	−	13.4034i	−0.513618	−	0.889612i	0.486257	−	0.873816i	$-0.338362\pi$
$228$	−20.2892	−	35.1420i	−1.34369	−	2.32733i
$229$	−2.46927	+	4.27691i	−0.163174	+	0.282626i	−0.936005	−	0.351986i	$-0.885507\pi$
$229$	−2.46927	+	4.27691i	−0.163174	+	0.282626i	0.772831	+	0.634612i	$0.218840\pi$
$230$	−4.70426			−0.310189
$231$	0.107479	−	1.81700i	0.00707160	−	0.119550i
$232$	−19.9920			−1.31254
$233$	−0.299732	+	0.519151i	−0.0196361	+	0.0340107i	−0.875676	−	0.482898i	$-0.839584\pi$
$233$	−0.299732	+	0.519151i	−0.0196361	+	0.0340107i	0.856040	+	0.516909i	$0.172917\pi$
$234$		0			0
$235$	−3.27780	−	5.67731i	−0.213820	−	0.370347i
$236$	−1.20291	+	2.08350i	−0.0783029	+	0.135625i
$237$	−29.4242			−1.91131
$238$	3.21790	−	1.61244i	0.208586	−	0.104519i
$239$	9.54890			0.617667			0.308834	−	0.951116i	$-0.400061\pi$
$239$	9.54890			0.617667			0.308834	+	0.951116i	$0.400061\pi$
$240$	3.98464	−	6.90160i	0.257207	−	0.445496i
$241$	11.9898	+	20.7670i	0.772332	+	1.33772i	0.936282	+	0.351249i	$0.114243\pi$
$241$	11.9898	+	20.7670i	0.772332	+	1.33772i	−0.163951	+	0.986469i	$0.552424\pi$
$242$	3.38088	+	5.85585i	0.217331	+	0.376428i
$243$	−4.40821	+	7.63525i	−0.282787	+	0.489801i
$244$	20.2651			1.29734
$245$	−3.85437	−	8.98012i	−0.246247	−	0.573719i
$246$	−3.97617			−0.253511
$247$		0			0
$248$	−5.27757	−	9.14103i	−0.335126	−	0.580456i
$249$	−13.4874	−	23.3609i	−0.854730	−	1.48044i
$250$	−3.47034	+	6.01081i	−0.219484	+	0.380157i
$251$	−23.6573			−1.49324			−0.746618	−	0.665253i	$-0.768324\pi$
$251$	−23.6573			−1.49324			−0.746618	+	0.665253i	$0.768324\pi$
$252$	24.6771	−	12.3653i	1.55451	−	0.778943i
$253$	1.22152			0.0767965
$254$	−1.67046	+	2.89333i	−0.104814	+	0.181543i
$255$	−4.72598	−	8.18563i	−0.295952	−	0.512604i
$256$	3.26837	+	5.66098i	0.204273	+	0.353811i
$257$	−8.52294	+	14.7622i	−0.531647	+	0.920839i	0.467671	+	0.883903i	$0.345093\pi$
$257$	−8.52294	+	14.7622i	−0.531647	+	0.920839i	−0.999318	+	0.0369364i	$0.988240\pi$
$258$	−4.54923			−0.283223
$259$	−0.268517	+	4.53945i	−0.0166848	+	0.282068i
$260$		0			0
$261$	−28.8309	+	49.9365i	−1.78459	+	3.09099i
$262$	0.923030	+	1.59873i	0.0570250	+	0.0987701i
$263$	1.63379	+	2.82981i	0.100744	+	0.174494i	0.911991	−	0.410209i	$-0.134544\pi$
$263$	1.63379	+	2.82981i	0.100744	+	0.174494i	−0.811247	+	0.584703i	$0.801211\pi$
$264$	0.768658	−	1.33135i	0.0473076	−	0.0819392i
$265$	15.6717			0.962706
$266$	−11.1279	−	7.33338i	−0.682295	−	0.449638i
$267$	32.9833			2.01855
$268$	1.36894	−	2.37107i	0.0836214	−	0.144836i
$269$	0.204756	+	0.354647i	0.0124842	+	0.0216232i	0.872200	−	0.489149i	$-0.162693\pi$
$269$	0.204756	+	0.354647i	0.0124842	+	0.0216232i	−0.859716	+	0.510773i	$0.829359\pi$
$270$	4.56379	+	7.90471i	0.277743	+	0.481066i
$271$	6.48223	−	11.2276i	0.393768	−	0.682025i	−0.599175	−	0.800618i	$-0.704505\pi$
$271$	6.48223	−	11.2276i	0.393768	−	0.682025i	0.992943	+	0.118592i	$0.0378381\pi$
$272$	−4.09197			−0.248112
$273$		0			0
$274$	−9.97192			−0.602426
$275$	0.341492	−	0.591481i	0.0205927	−	0.0356676i
$276$	13.5729	+	23.5090i	0.816993	+	1.41507i
$277$	−2.54766	−	4.41267i	−0.153074	−	0.265132i	0.779282	−	0.626673i	$-0.215584\pi$
$277$	−2.54766	−	4.41267i	−0.153074	−	0.265132i	−0.932356	+	0.361542i	$0.882251\pi$
$278$	0.203010	−	0.351623i	0.0121757	−	0.0210890i
$279$	−30.4436			−1.82261
$280$	0.487370	−	8.23929i	0.0291259	−	0.492392i
$281$	−21.5831			−1.28754			−0.643770	−	0.765219i	$-0.722631\pi$
$281$	−21.5831			−1.28754			−0.643770	+	0.765219i	$0.722631\pi$
$282$	4.45589	−	7.71783i	0.265344	−	0.459590i
$283$	7.14447	+	12.3746i	0.424694	+	0.735592i	0.996392	−	0.0848723i	$-0.0270482\pi$
$283$	7.14447	+	12.3746i	0.424694	+	0.735592i	−0.571697	+	0.820465i	$0.693715\pi$
$284$	6.18964	+	10.7208i	0.367287	+	0.636160i
$285$	−17.4988	+	30.3087i	−1.03654	+	1.79533i
$286$		0			0
$287$	4.95584	−	2.48330i	0.292534	−	0.146584i
$288$	36.1969			2.13292
$289$	6.07336	−	10.5194i	0.357256	−	0.618786i
$290$	3.85636	+	6.67942i	0.226454	+	0.392229i
$291$	20.0730	+	34.7674i	1.17670	+	2.03810i
$292$	−3.65115	+	6.32397i	−0.213667	+	0.370082i
$293$	−11.8059			−0.689710			−0.344855	−	0.938656i	$-0.612072\pi$
$293$	−11.8059			−0.689710			−0.344855	+	0.938656i	$0.612072\pi$
$294$	7.95234	−	10.6416i	0.463790	−	0.620629i
$295$	2.07494			0.120808
$296$	−1.92036	+	3.32615i	−0.111618	+	0.193329i
$297$	−1.18505	−	2.05257i	−0.0687635	−	0.119102i
$298$	4.89209	+	8.47335i	0.283391	+	0.490848i
$299$		0			0
$300$	15.1779			0.876295
$301$	5.67010	−	2.84120i	0.326819	−	0.163764i
$302$	−1.15204			−0.0662926
$303$	19.1392	−	33.1500i	1.09952	−	1.90442i
$304$	7.57562	+	13.1214i	0.434492	+	0.752562i
$305$	−8.73897	−	15.1363i	−0.500392	−	0.866704i
$306$	4.38397	−	7.59325i	0.250615	−	0.434077i
$307$	21.1587			1.20759			0.603794	−	0.797140i	$-0.293655\pi$
$307$	21.1587			1.20759			0.603794	+	0.797140i	$0.293655\pi$
$308$	−0.0566081	+	0.956997i	−0.00322555	+	0.0545299i
$309$	1.21810			0.0692951
$310$	−2.03604	+	3.52652i	−0.115639	+	0.200293i
$311$	4.04735	+	7.01021i	0.229504	+	0.397513i	0.957661	−	0.287897i	$-0.0929562\pi$
$311$	4.04735	+	7.01021i	0.229504	+	0.397513i	−0.728157	+	0.685410i	$0.759623\pi$
$312$		0			0
$313$	−0.762374	+	1.32047i	−0.0430919	+	0.0746374i	−0.886767	−	0.462217i	$-0.847054\pi$
$313$	−0.762374	+	1.32047i	−0.0430919	+	0.0746374i	0.843675	+	0.536854i	$0.180388\pi$
$314$	−4.25230			−0.239971
$315$	−19.8775	−	13.0994i	−1.11997	−	0.738068i
$316$	15.4974			0.871799
$317$	−7.70500	+	13.3454i	−0.432756	+	0.749555i	−0.997109	−	0.0759781i	$-0.975792\pi$
$317$	−7.70500	+	13.3454i	−0.432756	+	0.749555i	0.564354	+	0.825533i	$0.309125\pi$
$318$	10.6522	+	18.4501i	0.597345	+	1.03463i
$319$	−1.00136	−	1.73440i	−0.0560652	−	0.0971078i
$320$	−0.172261	+	0.298364i	−0.00962967	+	0.0166791i
$321$	19.8518			1.10802
$322$	7.44424	+	4.90582i	0.414851	+	0.273390i
$323$	17.9701			0.999884
$324$	10.6865	−	18.5096i	0.593694	−	1.02831i
$325$		0			0
$326$	3.74442	+	6.48553i	0.207384	+	0.359200i
$327$	6.18807	−	10.7181i	0.342201	−	0.592710i
$328$	4.68177			0.258508
$329$	−0.733619	+	12.4023i	−0.0404457	+	0.683761i
$330$	−0.593082			−0.0326481
$331$	−14.8023	+	25.6384i	−0.813609	+	1.40921i	0.0967133	+	0.995312i	$0.469167\pi$
$331$	−14.8023	+	25.6384i	−0.813609	+	1.40921i	−0.910322	+	0.413900i	$0.864166\pi$
$332$	7.10369	+	12.3039i	0.389866	+	0.675267i
$333$	5.53876	+	9.59342i	0.303522	+	0.525716i
$334$	3.91249	−	6.77663i	0.214082	−	0.370801i
$335$	−2.36133			−0.129013
$336$	−13.5028	+	6.76606i	−0.736638	+	0.369119i
$337$	0.432568			0.0235635			0.0117817	−	0.999931i	$-0.496250\pi$
$337$	0.432568			0.0235635			0.0117817	+	0.999931i	$0.496250\pi$
$338$		0			0
$339$	−14.6638	−	25.3985i	−0.796429	−	1.37946i
$340$	2.48913	+	4.31130i	0.134992	+	0.233813i
$341$	0.528685	−	0.915709i	0.0286299	−	0.0495884i
$342$	−32.4648			−1.75549
$343$	−3.26554	+	18.2301i	−0.176322	+	0.984332i
$344$	5.35654			0.288805
$345$	11.7062	−	20.2757i	0.630239	−	1.09161i
$346$	−3.84462	−	6.65907i	−0.206688	−	0.357994i
$347$	0.419474	+	0.726550i	0.0225185	+	0.0390032i	0.877065	−	0.480372i	$-0.159498\pi$
$347$	0.419474	+	0.726550i	0.0225185	+	0.0390032i	−0.854547	+	0.519375i	$0.826165\pi$
$348$	22.2531	−	38.5435i	1.19289	−	2.06615i
$349$	17.7261			0.948857			0.474428	−	0.880294i	$-0.342655\pi$
$349$	17.7261			0.948857			0.474428	+	0.880294i	$0.342655\pi$
$350$	4.45660	−	2.23314i	0.238215	−	0.119366i
$351$		0			0
$352$	−0.628598	+	1.08876i	−0.0335044	+	0.0580313i
$353$	−4.91218	−	8.50815i	−0.261449	−	0.452843i	0.705178	−	0.709030i	$-0.250867\pi$
$353$	−4.91218	−	8.50815i	−0.261449	−	0.452843i	−0.966627	+	0.256187i	$0.917534\pi$
$354$	1.41035	+	2.44280i	0.0749594	+	0.129834i
$355$	5.33835	−	9.24629i	0.283330	−	0.490742i
$356$	−17.3720			−0.920714
$357$	−1.05774	+	17.8818i	−0.0559817	+	0.946406i
$358$	−2.68443			−0.141876
$359$	−12.5078	+	21.6641i	−0.660136	+	1.14339i	0.320443	+	0.947268i	$0.396168\pi$
$359$	−12.5078	+	21.6641i	−0.660136	+	1.14339i	−0.980579	+	0.196122i	$0.937165\pi$
$360$	−10.0531	−	17.4124i	−0.529844	−	0.917716i
$361$	−23.7688	−	41.1687i	−1.25099	−	2.16677i
$362$	−0.372993	+	0.646044i	−0.0196041	+	0.0339553i
$363$	−33.6522			−1.76628
$364$		0			0
$365$	6.29798			0.329651
$366$	11.8799	−	20.5766i	0.620972	−	1.07555i
$367$	−5.73131	−	9.92692i	−0.299172	−	0.518181i	0.676775	−	0.736190i	$-0.263377\pi$
$367$	−5.73131	−	9.92692i	−0.299172	−	0.518181i	−0.975947	+	0.218009i	$0.930044\pi$
$368$	−5.06787	−	8.77782i	−0.264181	−	0.457575i
$369$	6.75167	−	11.6942i	0.351478	−	0.608778i
$370$	1.48171			0.0770304
$371$	−24.7997	−	16.3432i	−1.28754	−	0.848496i
$372$	23.4978			1.21831
$373$	3.49602	−	6.05529i	0.181017	−	0.313531i	−0.761210	−	0.648505i	$-0.775394\pi$
$373$	3.49602	−	6.05529i	0.181017	−	0.313531i	0.942227	+	0.334974i	$0.108728\pi$
$374$	0.152264	+	0.263730i	0.00787340	+	0.0136371i
$375$	−17.2714	−	29.9149i	−0.891889	−	1.54480i
$376$	−5.24663	+	9.08743i	−0.270574	+	0.468648i
$377$		0			0
$378$	1.02144	−	17.2681i	0.0525373	−	0.888177i
$379$	20.6039			1.05835			0.529175	−	0.848513i	$-0.322501\pi$
$379$	20.6039			1.05835			0.529175	+	0.848513i	$0.322501\pi$
$380$	9.21643	−	15.9633i	0.472793	−	0.818901i
$381$	−8.31363	−	14.3996i	−0.425920	−	0.737715i
$382$	−7.18403	−	12.4431i	−0.367567	−	0.636645i
$383$	5.23529	−	9.06778i	0.267511	−	0.463342i	−0.700708	−	0.713448i	$-0.747132\pi$
$383$	5.23529	−	9.06778i	0.267511	−	0.463342i	0.968218	+	0.250106i	$0.0804656\pi$
$384$	−34.9887			−1.78551
$385$	0.739209	−	0.370407i	0.0376736	−	0.0188777i
$386$	−6.06086			−0.308490
$387$	7.72476	−	13.3797i	0.392672	−	0.680127i
$388$	−10.5723	−	18.3117i	−0.536725	−	0.929634i
$389$	−10.8387	−	18.7732i	−0.549545	−	0.951840i	−0.998306	−	0.0581880i	$-0.981468\pi$
$389$	−10.8387	−	18.7732i	−0.549545	−	0.951840i	0.448761	−	0.893652i	$-0.351866\pi$
$390$		0			0
$391$	−12.0215			−0.607953
$392$	−9.36356	+	12.5300i	−0.472931	+	0.632861i
$393$	−9.18754			−0.463450
$394$	3.61183	−	6.25587i	0.181961	−	0.315166i
$395$	−6.68301	−	11.5753i	−0.336258	−	0.582417i
$396$	1.16767	+	2.02246i	0.0586776	+	0.101633i
$397$	14.1276	−	24.4698i	0.709046	−	1.22810i	−0.256166	−	0.966633i	$-0.582459\pi$
$397$	14.1276	−	24.4698i	0.709046	−	1.22810i	0.965212	−	0.261470i	$-0.0842073\pi$
$398$	1.68690			0.0845566
$399$	59.2983	−	29.7135i	2.96863	−	1.48754i
$400$	−5.66714			−0.283357
$401$	−15.3570	+	26.5990i	−0.766890	+	1.32829i	0.172352	+	0.985035i	$0.444863\pi$
$401$	−15.3570	+	26.5990i	−0.766890	+	1.32829i	−0.939242	+	0.343257i	$0.888470\pi$
$402$	−1.60501	−	2.77997i	−0.0800508	−	0.138652i
$403$		0			0
$404$	−10.0804	+	17.4598i	−0.501520	+	0.868658i
$405$	−18.4335			−0.915967
$406$	0.863111	−	14.5914i	0.0428355	−	0.724161i
$407$	−0.384746			−0.0190711
$408$	−7.56467	+	13.1024i	−0.374507	+	0.648665i
$409$	19.0877	+	33.0609i	0.943826	+	1.63476i	0.758084	+	0.652157i	$0.226136\pi$
$409$	19.0877	+	33.0609i	0.943826	+	1.63476i	0.185742	+	0.982599i	$0.440531\pi$
$410$	−0.903092	−	1.56420i	−0.0446005	−	0.0772504i
$411$	24.8143	−	42.9797i	1.22400	−	2.12003i
$412$	−0.641560			−0.0316074
$413$	−3.28349	−	2.16384i	−0.161570	−	0.106476i
$414$	21.7180			1.06738
$415$	6.12669	−	10.6117i	0.300747	−	0.520910i
$416$		0			0
$417$	1.01035	+	1.74997i	0.0494769	+	0.0856965i
$418$	0.563786	−	0.976505i	0.0275757	−	0.0477624i
$419$	9.23952			0.451380			0.225690	−	0.974199i	$-0.427536\pi$
$419$	9.23952			0.451380			0.225690	+	0.974199i	$0.427536\pi$
$420$	15.3424	+	10.1108i	0.748632	+	0.493355i
$421$	0.392086			0.0191091			0.00955455	−	0.999954i	$-0.496959\pi$
$421$	0.392086			0.0191091			0.00955455	+	0.999954i	$0.496959\pi$
$422$	1.66719	−	2.88767i	0.0811577	−	0.140569i
$423$	15.1325	+	26.2103i	0.735769	+	1.27439i
$424$	−12.5425	−	21.7243i	−0.609118	−	1.05502i
$425$	−3.36075	+	5.82100i	−0.163021	+	0.282360i
$426$	14.5141			0.703209
$427$	−1.95591	+	33.0659i	−0.0946531	+	1.60017i
$428$	−10.4557			−0.505397
$429$		0			0
$430$	−1.03325	−	1.78964i	−0.0498277	−	0.0863042i
$431$	7.68006	+	13.3022i	0.369935	+	0.640747i	0.989555	−	0.144155i	$-0.0460465\pi$
$431$	7.68006	+	13.3022i	0.369935	+	0.640747i	−0.619620	+	0.784902i	$0.712713\pi$
$432$	−9.83310	+	17.0314i	−0.473095	+	0.819425i
$433$	14.5885			0.701080			0.350540	−	0.936548i	$-0.385998\pi$
$433$	14.5885			0.701080			0.350540	+	0.936548i	$0.385998\pi$
$434$	6.89954	−	3.45726i	0.331189	−	0.165954i
$435$	−38.3850			−1.84042
$436$	−3.25920	+	5.64510i	−0.156087	+	0.270351i
$437$	22.2558	+	38.5482i	1.06464	+	1.84401i
$438$	4.28078	+	7.41454i	0.204544	+	0.354280i
$439$	−0.321846	+	0.557453i	−0.0153609	+	0.0266058i	−0.873604	−	0.486638i	$-0.838223\pi$
$439$	−0.321846	+	0.557453i	−0.0153609	+	0.0266058i	0.858243	+	0.513244i	$0.171556\pi$
$440$	0.698330			0.0332916
$441$	17.7944	+	41.4583i	0.847351	+	1.97420i
$442$		0			0
$443$	8.99976	−	15.5880i	0.427591	−	0.740610i	−0.569067	−	0.822291i	$-0.692696\pi$
$443$	8.99976	−	15.5880i	0.427591	−	0.740610i	0.996659	+	0.0816812i	$0.0260289\pi$
$444$	−4.27509	−	7.40467i	−0.202887	−	0.351410i
$445$	7.49138	+	12.9755i	0.355125	+	0.615095i
$446$	1.34731	−	2.33360i	0.0637968	−	0.110499i
$447$	−48.6943			−2.30316
$448$	0.583742	−	0.292505i	0.0275792	−	0.0138196i
$449$	−3.13150			−0.147784			−0.0738922	−	0.997266i	$-0.523542\pi$
$449$	−3.13150			−0.147784			−0.0738922	+	0.997266i	$0.523542\pi$
$450$	6.07153	−	10.5162i	0.286215	−	0.495739i
$451$	0.234500	+	0.406166i	0.0110422	+	0.0191256i
$452$	7.72329	+	13.3771i	0.363273	+	0.629207i
$453$	2.86676	−	4.96538i	0.134692	−	0.233294i
$454$	9.55724			0.448544
$455$		0			0
$456$	56.0190			2.62333
$457$	7.48525	−	12.9648i	0.350145	−	0.606470i	−0.636129	−	0.771583i	$-0.719466\pi$
$457$	7.48525	−	12.9648i	0.350145	−	0.606470i	0.986275	+	0.165113i	$0.0527988\pi$
$458$	−1.52482	−	2.64107i	−0.0712502	−	0.123409i
$459$	11.6625	+	20.2001i	0.544361	+	0.942860i
$460$	−6.16553	+	10.6790i	−0.287469	+	0.497911i
$461$	25.3290			1.17969			0.589845	−	0.807517i	$-0.299189\pi$
$461$	25.3290			1.17969			0.589845	+	0.807517i	$0.299189\pi$
$462$	0.938521	+	0.618493i	0.0436640	+	0.0287749i
$463$	−32.0644			−1.49016			−0.745080	−	0.666975i	$-0.767589\pi$
$463$	−32.0644			−1.49016			−0.745080	+	0.666975i	$0.767589\pi$
$464$	−8.30889	+	14.3914i	−0.385731	+	0.668105i
$465$	−10.1330	−	17.5509i	−0.469908	−	0.813905i
$466$	−0.185090	−	0.320585i	−0.00857412	−	0.0148508i
$467$	20.2766	−	35.1201i	0.938290	−	1.62517i	0.169630	−	0.985508i	$-0.445743\pi$
$467$	20.2766	−	35.1201i	0.938290	−	1.62517i	0.768660	−	0.639658i	$-0.220924\pi$
$468$		0			0
$469$	3.73668	+	2.46250i	0.172544	+	0.113708i
$470$	4.04820			0.186730
$471$	10.5815	−	18.3277i	0.487570	−	0.844496i
$472$	−1.66063	−	2.87630i	−0.0764369	−	0.132393i
$473$	0.268297	+	0.464705i	0.0123363	+	0.0213671i
$474$	9.08498	−	15.7356i	0.417287	−	0.722762i
$475$	24.8876			1.14192
$476$	0.557103	−	9.41818i	0.0255348	−	0.431682i
$477$	−72.3512			−3.31273
$478$	−2.94831	+	5.10662i	−0.134852	+	0.233571i
$479$	−4.86636	−	8.42878i	−0.222350	−	0.385121i	0.733171	−	0.680044i	$-0.238039\pi$
$479$	−4.86636	−	8.42878i	−0.222350	−	0.385121i	−0.955521	+	0.294923i	$0.904706\pi$
$480$	12.0480	+	20.8678i	0.549915	+	0.952480i
$481$		0			0
$482$	−14.8078			−0.674479
$483$	−39.6688	+	19.8775i	−1.80499	+	0.904457i
$484$	17.7243			0.805649
$485$	−9.11820	+	15.7932i	−0.414036	+	0.717132i
$486$	−2.72215	−	4.71490i	−0.123479	−	0.213872i
$487$	−7.25354	−	12.5635i	−0.328689	−	0.569307i	0.653563	−	0.756872i	$-0.273274\pi$
$487$	−7.25354	−	12.5635i	−0.328689	−	0.569307i	−0.982252	+	0.187566i	$0.939940\pi$
$488$	−13.9881	+	24.2281i	−0.633211	+	1.09675i
$489$	−37.2708			−1.68544
$490$	5.99251	+	0.711426i	0.270714	+	0.0321390i
$491$	19.9592			0.900748			0.450374	−	0.892840i	$-0.351291\pi$
$491$	19.9592			0.900748			0.450374	+	0.892840i	$0.351291\pi$
$492$	−5.21127	+	9.02619i	−0.234942	+	0.406932i
$493$	9.85475	+	17.0689i	0.443836	+	0.768746i
$494$		0			0
$495$	1.00707	−	1.74430i	0.0452646	−	0.0784006i
$496$	−8.77366			−0.393949
$497$	−18.0901	+	9.06470i	−0.811453	+	0.406608i
$498$	16.6574			0.746437
$499$	−5.92205	+	10.2573i	−0.265107	+	0.459179i	−0.967592	−	0.252520i	$-0.918741\pi$
$499$	−5.92205	+	10.2573i	−0.265107	+	0.459179i	0.702484	+	0.711699i	$0.252074\pi$
$500$	9.09666	+	15.7559i	0.406815	+	0.704624i
$501$	19.4718	+	33.7262i	0.869938	+	1.50678i
$502$	7.30440	−	12.6516i	0.326011	−	0.564668i
$503$	16.4363			0.732857			0.366429	−	0.930446i	$-0.380580\pi$
$503$	16.4363			0.732857			0.366429	+	0.930446i	$0.380580\pi$
$504$	−2.25003	+	38.0381i	−0.100224	+	1.69435i
$505$	17.3880			0.773758
$506$	−0.377156	+	0.653254i	−0.0167666	+	0.0290407i
$507$		0			0
$508$	4.37871	+	7.58414i	0.194274	+	0.336492i
$509$	−0.864455	+	1.49728i	−0.0383163	+	0.0663658i	−0.884548	−	0.466450i	$-0.845533\pi$
$509$	−0.864455	+	1.49728i	−0.0383163	+	0.0663658i	0.846231	+	0.532816i	$0.178866\pi$
$510$	5.83675			0.258456
$511$	−9.96623	−	6.56782i	−0.440880	−	0.290543i
$512$	18.7330			0.827890
$513$	43.1826	−	74.7944i	1.90656	−	3.30226i
$514$	−5.26307	−	9.11591i	−0.232144	−	0.402085i
$515$	0.276662	+	0.479192i	0.0121912	+	0.0211157i
$516$	−5.96235	+	10.3271i	−0.262478	+	0.454625i
$517$	−1.05117			−0.0462304
$518$	−2.34473	−	1.54520i	−0.103021	−	0.0678920i
$519$	38.2681			1.67978
$520$		0			0
$521$	−14.0118	−	24.2692i	−0.613868	−	1.06325i	−0.990582	−	0.136922i	$-0.956279\pi$
$521$	−14.0118	−	24.2692i	−0.613868	−	1.06325i	0.376713	−	0.926330i	$-0.377054\pi$
$522$	−17.8036	−	30.8367i	−0.779241	−	1.34969i
$523$	−4.10838	+	7.11592i	−0.179647	+	0.311157i	−0.941760	−	0.336287i	$-0.890829\pi$
$523$	−4.10838	+	7.11592i	−0.179647	+	0.311157i	0.762113	+	0.647444i	$0.224162\pi$
$524$	4.83899			0.211392
$525$	−1.46491	+	24.7653i	−0.0639340	+	1.08084i
$526$	−2.01779			−0.0879799
$527$	−5.20299	+	9.01185i	−0.226646	+	0.392562i
$528$	−0.638924	−	1.10665i	−0.0278056	−	0.0481607i
$529$	−3.38852	−	5.86909i	−0.147327	−	0.255178i
$530$	−4.83878	+	8.38101i	−0.210183	+	0.364048i
$531$	−9.57932			−0.415707
$532$	−31.2318	+	15.6498i	−1.35407	+	0.678506i
$533$		0			0
$534$	−10.1839	+	17.6390i	−0.440700	+	0.763315i
$535$	4.50886	+	7.80957i	0.194935	+	0.337637i
$536$	1.88984	+	3.27330i	0.0816286	+	0.141385i
$537$	6.67998	−	11.5701i	0.288262	−	0.499285i
$538$	−0.252881			−0.0109025
$539$	−1.55604	−	0.184731i	−0.0670233	−	0.00795695i
$540$	23.9257			1.02960
$541$	−11.8917	+	20.5970i	−0.511263	+	0.885534i	0.488652	+	0.872479i	$0.337489\pi$
$541$	−11.8917	+	20.5970i	−0.511263	+	0.885534i	−0.999915	+	0.0130547i	$0.995844\pi$
$542$	4.00289	+	6.93322i	0.171939	+	0.297807i
$543$	−1.85633	−	3.21526i	−0.0796627	−	0.137980i
$544$	6.18628	−	10.7150i	0.265235	−	0.459400i
$545$	5.62189			0.240815
$546$		0			0
$547$	22.7663			0.973418			0.486709	−	0.873564i	$-0.338197\pi$
$547$	22.7663			0.973418			0.486709	+	0.873564i	$0.338197\pi$
$548$	−13.0695	+	22.6370i	−0.558300	+	0.967005i
$549$	40.3450	+	69.8795i	1.72188	+	2.98239i
$550$	0.210877	+	0.365250i	0.00899183	+	0.0155743i
$551$	36.4889	−	63.2007i	1.55448	−	2.69244i
$552$	−37.4751			−1.59505
$553$	−1.49575	+	25.2867i	−0.0636059	+	1.07530i
$554$	3.14645			0.133680
$555$	−3.68712	+	6.38627i	−0.156509	+	0.271082i
$556$	−0.532140	−	0.921694i	−0.0225678	−	0.0390885i
$557$	2.04298	+	3.53854i	0.0865638	+	0.149933i	0.906056	−	0.423157i	$-0.139078\pi$
$557$	2.04298	+	3.53854i	0.0865638	+	0.149933i	−0.819493	+	0.573090i	$0.805745\pi$
$558$	9.39972	−	16.2808i	0.397922	−	0.689221i
$559$		0			0
$560$	−5.72857	−	3.77517i	−0.242076	−	0.159530i
$561$	−1.51559			−0.0639883
$562$	6.66397	−	11.5423i	0.281103	−	0.486884i
$563$	11.1914	+	19.3840i	0.471659	+	0.816938i	0.999474	−	0.0324214i	$-0.0103219\pi$
$563$	11.1914	+	19.3840i	0.471659	+	0.816938i	−0.527815	+	0.849359i	$0.676989\pi$
$564$	−11.6800	−	20.2304i	−0.491818	−	0.851853i
$565$	6.66108	−	11.5373i	0.280234	−	0.485379i
$566$	−8.82367			−0.370887
$567$	29.1700	+	19.2233i	1.22503	+	0.807302i
$568$	−17.0897			−0.717069
$569$	−16.9618	+	29.3788i	−0.711078	+	1.23162i	0.253375	+	0.967368i	$0.418459\pi$
$569$	−16.9618	+	29.3788i	−0.711078	+	1.23162i	−0.964453	+	0.264255i	$0.914874\pi$
$570$	−10.8058	−	18.7162i	−0.452605	−	0.783935i
$571$	−17.5546	−	30.4055i	−0.734638	−	1.27243i	−0.954882	−	0.296986i	$-0.904019\pi$
$571$	−17.5546	−	30.4055i	−0.734638	−	1.27243i	0.220244	−	0.975445i	$-0.429315\pi$
$572$		0			0
$573$	71.5076			2.98727
$574$	−0.202125	+	3.41705i	−0.00843654	+	0.142625i
$575$	−16.6491			−0.694314
$576$	0.795272	−	1.37745i	0.0331363	−	0.0573938i
$577$	−20.4359	−	35.3960i	−0.850758	−	1.47356i	−0.880525	−	0.473999i	$-0.842810\pi$
$577$	−20.4359	−	35.3960i	−0.850758	−	1.47356i	0.0297676	−	0.999557i	$-0.490523\pi$
$578$	3.75041	+	6.49590i	0.155996	+	0.270194i
$579$	15.0820	−	26.1228i	0.626786	−	1.08562i
$580$	20.2170			0.839466
$581$	−20.7616	+	10.4033i	−0.861335	+	0.431603i
$582$	−24.7909			−1.02761
$583$	1.25645	−	2.17624i	0.0520370	−	0.0901308i
$584$	−5.04045	−	8.73031i	−0.208575	−	0.361263i
$585$		0			0
$586$	3.64519	−	6.31365i	0.150581	−	0.260815i
$587$	−32.3939			−1.33704			−0.668520	−	0.743694i	$-0.733072\pi$
$587$	−32.3939			−1.33704			−0.668520	+	0.743694i	$0.733072\pi$
$588$	−13.7346	−	31.9995i	−0.566404	−	1.31964i
$589$	38.5300			1.58760
$590$	−0.640657	+	1.10965i	−0.0263754	+	0.0456836i
$591$	17.9755	+	31.1345i	0.739413	+	1.28070i
$592$	1.59624	+	2.76477i	0.0656050	+	0.113631i
$593$	5.49276	−	9.51374i	0.225561	−	0.390682i	−0.730927	−	0.682456i	$-0.760912\pi$
$593$	5.49276	−	9.51374i	0.225561	−	0.390682i	0.956487	+	0.291773i	$0.0942453\pi$
$594$	1.46358			0.0600513
$595$	−7.27484	+	3.64532i	−0.298240	+	0.149444i
$596$	25.6468			1.05054
$597$	−4.19772	+	7.27066i	−0.171801	+	0.297568i
$598$		0			0
$599$	14.3485	+	24.8523i	0.586264	+	1.01544i	0.994717	+	0.102659i	$0.0327351\pi$
$599$	14.3485	+	24.8523i	0.586264	+	1.01544i	−0.408453	+	0.912779i	$0.633932\pi$
$600$	−10.4766	+	18.1460i	−0.427706	+	0.740809i
$601$	−34.3272			−1.40023			−0.700117	−	0.714028i	$-0.746869\pi$
$601$	−34.3272			−1.40023			−0.700117	+	0.714028i	$0.746869\pi$
$602$	−0.231256	+	3.90954i	−0.00942531	+	0.159341i
$603$	10.9015			0.443943
$604$	−1.50990	+	2.61522i	−0.0614369	+	0.106412i
$605$	−7.64329	−	13.2386i	−0.310744	−	0.538224i
$606$	11.8188	+	20.4707i	0.480106	+	0.831567i
$607$	5.68723	−	9.85057i	0.230838	−	0.399822i	−0.727217	−	0.686407i	$-0.759187\pi$
$607$	5.68723	−	9.85057i	0.230838	−	0.399822i	0.958055	+	0.286585i	$0.0925201\pi$
$608$	−45.8116			−1.85790
$609$	60.7423	+	40.0297i	2.46140	+	1.62209i
$610$	10.7929			0.436993
$611$		0			0
$612$	−11.4915	−	19.9038i	−0.464516	−	0.804565i
$613$	10.7871	+	18.6838i	0.435687	+	0.754632i	0.997351	−	0.0727330i	$-0.0231721\pi$
$613$	10.7871	+	18.6838i	0.435687	+	0.754632i	−0.561664	+	0.827365i	$0.689839\pi$
$614$	−6.53293	+	11.3154i	−0.263647	+	0.456651i
$615$	8.98909			0.362475
$616$	−1.10507	−	0.728251i	−0.0445246	−	0.0293421i
$617$	30.5920			1.23159			0.615793	−	0.787908i	$-0.288836\pi$
$617$	30.5920			1.23159			0.615793	+	0.787908i	$0.288836\pi$
$618$	−0.376098	+	0.651421i	−0.0151289	+	0.0262040i
$619$	0.658832	+	1.14113i	0.0264807	+	0.0458659i	0.878962	−	0.476892i	$-0.158237\pi$
$619$	0.658832	+	1.14113i	0.0264807	+	0.0458659i	−0.852481	+	0.522758i	$0.824903\pi$
$620$	5.33697	+	9.24391i	0.214338	+	0.371244i
$621$	−28.8879	+	50.0353i	−1.15923	+	2.00785i
$622$	−4.99862			−0.200426
$623$	1.67668	−	28.3453i	0.0671748	−	1.13563i
$624$		0			0
$625$	0.217936	−	0.377476i	0.00871743	−	0.0150990i
$626$	−0.470780	−	0.815415i	−0.0188161	−	0.0325905i
$627$	2.80587	+	4.85991i	0.112056	+	0.194086i
$628$	−5.57318	+	9.65302i	−0.222394	+	0.385198i
$629$	3.78644			0.150975
$630$	13.1427	−	6.58563i	0.523618	−	0.262378i
$631$	−21.3548			−0.850120			−0.425060	−	0.905165i	$-0.639747\pi$
$631$	−21.3548			−0.850120			−0.425060	+	0.905165i	$0.639747\pi$
$632$	−10.6972	+	18.5281i	−0.425512	+	0.737008i
$633$	8.29736	+	14.3715i	0.329790	+	0.571214i
$634$	−4.75797	−	8.24105i	−0.188963	−	0.327294i
$635$	3.77649	−	6.54106i	0.149865	−	0.259574i
$636$	55.8442			2.21437
$637$		0			0
$638$	1.23671			0.0489619
$639$	−24.6454	+	42.6871i	−0.974958	+	1.68868i
$640$	−7.94685	−	13.7644i	−0.314127	−	0.544084i
$641$	15.0198	+	26.0150i	0.593245	+	1.02753i	0.993792	+	0.111254i	$0.0354866\pi$
$641$	15.0198	+	26.0150i	0.593245	+	1.02753i	−0.400547	+	0.916276i	$0.631180\pi$
$642$	−6.12941	+	10.6165i	−0.241909	+	0.418998i
$643$	17.8164			0.702610			0.351305	−	0.936261i	$-0.385738\pi$
$643$	17.8164			0.702610			0.351305	+	0.936261i	$0.385738\pi$
$644$	20.8932	−	10.4693i	0.823307	−	0.412547i
$645$	10.2846			0.404957
$646$	−5.54844	+	9.61017i	−0.218300	+	0.378107i
$647$	−9.76093	−	16.9064i	−0.383742	−	0.664660i	0.607852	−	0.794050i	$-0.292031\pi$
$647$	−9.76093	−	16.9064i	−0.383742	−	0.664660i	−0.991594	+	0.129390i	$0.958698\pi$
$648$	14.7528	+	25.5526i	0.579546	+	1.00380i
$649$	0.166355	−	0.288136i	0.00653001	−	0.0113103i
$650$		0			0
$651$	−2.26792	+	38.3407i	−0.0888869	+	1.50269i
$652$	19.6302			0.768776
$653$	19.3055	−	33.4381i	0.755484	−	1.30854i	−0.189650	−	0.981852i	$-0.560735\pi$
$653$	19.3055	−	33.4381i	0.755484	−	1.30854i	0.945134	−	0.326684i	$-0.105931\pi$
$654$	3.82124	+	6.61859i	0.149422	+	0.258807i
$655$	−2.08673	−	3.61433i	−0.0815354	−	0.141223i
$656$	1.94579	−	3.37021i	0.0759705	−	0.131585i
$657$	−29.0757			−1.13435
$658$	−6.40607	−	4.22165i	−0.249735	−	0.164577i
$659$	−45.5235			−1.77334			−0.886671	−	0.462400i	$-0.846988\pi$
$659$	−45.5235			−1.77334			−0.886671	+	0.462400i	$0.846988\pi$
$660$	−0.777309	+	1.34634i	−0.0302567	+	0.0524062i
$661$	−19.4116	−	33.6219i	−0.755024	−	1.30774i	−0.945362	−	0.326021i	$-0.894292\pi$
$661$	−19.4116	−	33.6219i	−0.755024	−	1.30774i	0.190339	−	0.981718i	$-0.439041\pi$
$662$	−9.14070	−	15.8322i	−0.355263	−	0.615334i
$663$		0			0
$664$	−19.6134			−0.761149
$665$	25.1573	+	16.5789i	0.975559	+	0.642901i
$666$	−6.84057			−0.265067
$667$	−24.4100	+	42.2794i	−0.945161	+	1.63707i
$668$	−10.2556	−	17.7633i	−0.396802	−	0.687282i
$669$	6.70533	+	11.6140i	0.259243	+	0.449022i
$670$	0.729081	−	1.26281i	0.0281669	−	0.0487865i
$671$	−2.80253			−0.108191
$672$	2.69652	−	45.5865i	0.104021	−	1.75854i
$673$	37.4770			1.44463			0.722316	−	0.691563i	$-0.243078\pi$
$673$	37.4770			1.44463			0.722316	+	0.691563i	$0.243078\pi$
$674$	−0.133559	+	0.231331i	−0.00514451	+	0.00891055i
$675$	16.1519	+	27.9760i	0.621688	+	1.07680i
$676$		0			0
$677$	15.3224	−	26.5391i	0.588886	−	1.01998i	−0.405493	−	0.914098i	$-0.632900\pi$
$677$	15.3224	−	26.5391i	0.588886	−	1.01998i	0.994379	−	0.105882i	$-0.0337666\pi$
$678$	18.1103			0.695523
$679$	30.8990	−	15.4830i	1.18579	−	0.594184i
$680$	−6.87254			−0.263550
$681$	−23.7824	+	41.1924i	−0.911345	+	1.57850i
$682$	0.326472	+	0.565466i	0.0125013	+	0.0216528i
$683$	−22.7328	−	39.3743i	−0.869846	−	1.50662i	−0.862154	−	0.506647i	$-0.830885\pi$
$683$	−22.7328	−	39.3743i	−0.869846	−	1.50662i	−0.00769249	−	0.999970i	$-0.502449\pi$
$684$	−42.5492	+	73.6974i	−1.62691	+	2.81789i
$685$	22.5439			0.861360
$686$	−8.74094	−	7.37507i	−0.333731	−	0.281581i
$687$	15.1776			0.579061
$688$	2.22623	−	3.85595i	0.0848743	−	0.147007i
$689$		0			0
$690$	7.22877	+	12.5206i	0.275194	+	0.476651i
$691$	3.55615	−	6.15944i	0.135283	−	0.234316i	−0.790423	−	0.612562i	$-0.790139\pi$
$691$	3.55615	−	6.15944i	0.135283	−	0.234316i	0.925705	+	0.378245i	$0.123472\pi$
$692$	−20.1554			−0.766195
$693$	−3.41268	+	1.71005i	−0.129637	+	0.0649593i
$694$	−0.518065			−0.0196655
$695$	−0.458953	+	0.794930i	−0.0174091	+	0.0301534i
$696$	30.7206	+	53.2097i	1.16446	+	2.01691i
$697$	−2.30781	−	3.99724i	−0.0874144	−	0.151406i
$698$	−5.47309	+	9.47968i	−0.207160	+	0.358811i
$699$	1.84233			0.0696832
$700$	0.771555	−	13.0436i	0.0291620	−	0.493003i
$701$	−17.8807			−0.675345			−0.337672	−	0.941264i	$-0.609640\pi$
$701$	−17.8807			−0.675345			−0.337672	+	0.941264i	$0.609640\pi$
$702$		0			0
$703$	−7.00997	−	12.1416i	−0.264386	−	0.457930i
$704$	0.0276215	+	0.0478418i	0.00104102	+	0.00180311i
$705$	−10.0736	+	17.4480i	−0.379395	+	0.657131i
$706$	6.06672			0.228324
$707$	−27.5157	−	18.1331i	−1.03483	−	0.681964i
$708$	7.39379			0.277876
$709$	20.2506	−	35.0751i	0.760529	−	1.31727i	−0.182049	−	0.983289i	$-0.558273\pi$
$709$	20.2506	−	35.0751i	0.760529	−	1.31727i	0.942578	−	0.333985i	$-0.108394\pi$
$710$	3.29653	+	5.70975i	0.123716	+	0.214283i
$711$	30.8533	+	53.4394i	1.15709	+	2.00413i
$712$	11.9911	−	20.7692i	0.449386	−	0.778360i
$713$	−25.7755			−0.965298
$714$	−9.23636	−	6.08684i	−0.345662	−	0.227794i
$715$		0			0
$716$	−3.51828	+	6.09384i	−0.131484	+	0.227738i
$717$	−14.6733	−	25.4148i	−0.547983	−	0.949134i
$718$	−7.72379	−	13.3780i	−0.288249	−	0.499262i
$719$	22.4680	−	38.9157i	0.837916	−	1.45131i	−0.0537189	−	0.998556i	$-0.517107\pi$
$719$	22.4680	−	38.9157i	0.837916	−	1.45131i	0.891634	−	0.452756i	$-0.149559\pi$
$720$	−16.7127			−0.622844
$721$	0.0619209	−	1.04681i	0.00230606	−	0.0389853i
$722$	29.3553			1.09249
$723$	36.8481	−	63.8229i	1.37040	−	2.37360i
$724$	0.977711	+	1.69344i	0.0363363	+	0.0629364i
$725$	13.6482	+	23.6395i	0.506883	+	0.877947i
$726$	10.3904	−	17.9967i	0.385624	−	0.667921i
$727$	20.3358			0.754214			0.377107	−	0.926170i	$-0.376919\pi$
$727$	20.3358			0.754214			0.377107	+	0.926170i	$0.376919\pi$
$728$		0			0
$729$	−12.5167			−0.463581
$730$	−1.94456	+	3.36807i	−0.0719713	+	0.124658i
$731$	−2.64042	−	4.57334i	−0.0976595	−	0.169151i
$732$	−31.1402	−	53.9364i	−1.15098	−	1.99355i
$733$	−12.5447	+	21.7280i	−0.463349	+	0.802543i	−0.999125	−	0.0418165i	$-0.986686\pi$
$733$	−12.5447	+	21.7280i	−0.463349	+	0.802543i	0.535777	+	0.844360i	$0.320019\pi$
$734$	7.07838			0.261268
$735$	−17.9782	+	24.0578i	−0.663136	+	0.887386i
$736$	30.6466			1.12965
$737$	−0.189316	+	0.327905i	−0.00697354	+	0.0120785i
$738$	4.16928	+	7.22140i	0.153473	+	0.265824i
$739$	−20.9406	−	36.2702i	−0.770313	−	1.33422i	−0.937391	−	0.348278i	$-0.886766\pi$
$739$	−20.9406	−	36.2702i	−0.770313	−	1.33422i	0.167078	−	0.985944i	$-0.446567\pi$
$740$	1.94197	−	3.36359i	0.0713882	−	0.123648i
$741$		0			0
$742$	16.3972	−	8.21642i	0.601961	−	0.301634i
$743$	−3.10309			−0.113841			−0.0569207	−	0.998379i	$-0.518128\pi$
$743$	−3.10309			−0.113841			−0.0569207	+	0.998379i	$0.518128\pi$
$744$	−16.2195	+	28.0930i	−0.594636	+	1.02994i
$745$	−11.0598	−	19.1561i	−0.405198	−	0.701824i
$746$	2.15886	+	3.73925i	0.0790414	+	0.136904i
$747$	−28.2849	+	48.9909i	−1.03489	+	1.79248i
$748$	0.798248			0.0291868
$749$	1.00915	−	17.0603i	0.0368735	−	0.623369i
$750$	21.3307			0.778888
$751$	15.3116	−	26.5204i	0.558727	−	0.967744i	−0.438876	−	0.898548i	$-0.644623\pi$
$751$	15.3116	−	26.5204i	0.558727	−	0.967744i	0.997603	−	0.0691960i	$-0.0220434\pi$
$752$	4.36111	+	7.55366i	0.159033	+	0.275454i
$753$	36.3529	+	62.9650i	1.32477	+	2.29457i
$754$		0			0
$755$	2.60447			0.0947864
$756$	−37.8612	−	24.9508i	−1.37700	−	0.907453i
$757$	−20.8805			−0.758916			−0.379458	−	0.925209i	$-0.623890\pi$
$757$	−20.8805			−0.758916			−0.379458	+	0.925209i	$0.623890\pi$
$758$	−6.36163	+	11.0187i	−0.231065	+	0.400216i
$759$	−1.87705	−	3.25114i	−0.0681325	−	0.118009i
$760$	12.7234	+	22.0375i	0.461526	+	0.799386i
$761$	−9.10333	+	15.7674i	−0.329995	+	0.571569i	−0.982511	−	0.186207i	$-0.940381\pi$
$761$	−9.10333	+	15.7674i	−0.329995	+	0.571569i	0.652515	+	0.757776i	$0.273714\pi$
$762$	10.2676			0.371957
$763$	−8.89636	−	5.86277i	−0.322070	−	0.212247i
$764$	−37.6623			−1.36258
$765$	−9.91102	+	17.1664i	−0.358334	+	0.620652i
$766$	3.23288	+	5.59952i	0.116809	+	0.202319i
$767$		0			0
$768$	10.0446	−	17.3978i	0.362455	−	0.627790i
$769$	−24.1128			−0.869531			−0.434765	−	0.900544i	$-0.643169\pi$
$769$	−24.1128			−0.869531			−0.434765	+	0.900544i	$0.643169\pi$
$770$	−0.0301488	+	0.509685i	−0.00108649	+	0.0183678i
$771$	52.3869			1.88667
$772$	−7.94353	+	13.7586i	−0.285894	+	0.495183i
$773$	−18.2416	−	31.5953i	−0.656103	−	1.13640i	−0.981616	−	0.190867i	$-0.938870\pi$
$773$	−18.2416	−	31.5953i	−0.656103	−	1.13640i	0.325512	−	0.945538i	$-0.394463\pi$
$774$	4.77018	+	8.26219i	0.171461	+	0.296978i
$775$	−7.20584	+	12.4809i	−0.258841	+	0.448326i
$776$	29.1902			1.04787
$777$	12.4946	−	6.26085i	0.448240	−	0.224607i
$778$	13.3862			0.479919
$779$	−8.54506	+	14.8005i	−0.306158	+	0.530282i
$780$		0			0
$781$	−0.855988	−	1.48261i	−0.0306296	−	0.0530521i
$782$	3.71174	−	6.42893i	0.132732	−	0.229898i
$783$	94.7247			3.38518
$784$	5.12824	+	11.9480i	0.183151	+	0.426715i
$785$	9.61335			0.343115
$786$	2.83674	−	4.91337i	0.101183	−	0.175254i
$787$	−12.9385	−	22.4101i	−0.461207	−	0.798835i	0.537814	−	0.843063i	$-0.319250\pi$
$787$	−12.9385	−	22.4101i	−0.461207	−	0.798835i	−0.999021	+	0.0442289i	$0.985917\pi$
$788$	−9.46752	−	16.3982i	−0.337266	−	0.584162i
$789$	5.02111	−	8.69682i	0.178756	−	0.309615i
$790$	8.25375			0.293655
$791$	−22.5725	+	11.3107i	−0.802584	+	0.402164i
$792$	−3.22396			−0.114558
$793$		0			0
$794$	8.72407	+	15.1105i	0.309605	+	0.536252i
$795$	−24.0818	−	41.7110i	−0.854095	−	1.47934i
$796$	2.21090	−	3.82939i	0.0783632	−	0.135729i
$797$	−2.54530			−0.0901592			−0.0450796	−	0.998983i	$-0.514354\pi$
$797$	−2.54530			−0.0901592			−0.0450796	+	0.998983i	$0.514354\pi$
$798$	−2.41850	+	40.8862i	−0.0856138	+	1.44736i
$799$	10.3450			0.365979
$800$	8.56763	−	14.8396i	0.302912	−	0.524658i
$801$	−34.5853	−	59.9034i	−1.22201	−	2.11658i
$802$	−9.48319	−	16.4254i	−0.334863	−	0.580000i
$803$	0.504930	−	0.874565i	0.0178186	−	0.0308627i
$804$	−8.41430			−0.296749
$805$	−16.8295	−	11.0908i	−0.593162	−	0.390899i
$806$		0			0
$807$	0.629273	−	1.08993i	0.0221515	−	0.0383675i
$808$	−13.9161	−	24.1035i	−0.489568	−	0.847957i
$809$	4.77591	+	8.27213i	0.167912	+	0.290832i	0.937686	−	0.347485i	$-0.112964\pi$
$809$	4.77591	+	8.27213i	0.167912	+	0.290832i	−0.769773	+	0.638317i	$0.779631\pi$
$810$	5.69150	−	9.85797i	0.199979	−	0.346374i
$811$	9.19410			0.322849			0.161424	−	0.986885i	$-0.448391\pi$
$811$	9.19410			0.322849			0.161424	+	0.986885i	$0.448391\pi$
$812$	−31.9924	−	21.0833i	−1.12271	−	0.739877i
$813$	−39.8435			−1.39737
$814$	0.118794	−	0.205757i	0.00416372	−	0.00721177i
$815$	−8.46517	−	14.6621i	−0.296522	−	0.513591i
$816$	6.28791	+	10.8910i	0.220121	+	0.381260i
$817$	−9.77662	+	16.9336i	−0.342040	+	0.592431i
$818$	−23.5740			−0.824246
$819$		0			0
$820$	−4.73447			−0.165335
$821$	15.9628	−	27.6483i	0.557104	−	0.964933i	−0.440632	−	0.897688i	$-0.645246\pi$
$821$	15.9628	−	27.6483i	0.557104	−	0.964933i	0.997736	−	0.0672453i	$-0.0214210\pi$
$822$	15.3233	+	26.5407i	0.534461	+	0.925714i
$823$	−6.05776	−	10.4924i	−0.211160	−	0.365740i	0.740918	−	0.671596i	$-0.234391\pi$
$823$	−6.05776	−	10.4924i	−0.211160	−	0.365740i	−0.952078	+	0.305855i	$0.901058\pi$
$824$	0.442840	−	0.767022i	0.0154271	−	0.0267205i
$825$	−2.09900			−0.0730780
$826$	2.17100	−	1.08786i	0.0755388	−	0.0378514i
$827$	26.0883			0.907179			0.453589	−	0.891211i	$-0.350143\pi$
$827$	26.0883			0.907179			0.453589	+	0.891211i	$0.350143\pi$
$828$	28.4642	−	49.3015i	0.989200	−	1.71334i
$829$	−17.6835	−	30.6288i	−0.614174	−	1.06378i	−0.990529	−	0.137305i	$-0.956156\pi$
$829$	−17.6835	−	30.6288i	−0.614174	−	1.06378i	0.376354	−	0.926476i	$-0.377177\pi$
$830$	3.78334	+	6.55294i	0.131322	+	0.227456i
$831$	−7.82968	+	13.5614i	−0.271609	+	0.470440i
$832$		0			0
$833$	15.3136	+	1.81801i	0.530584	+	0.0629905i
$834$	−1.24782			−0.0432083
$835$	−8.84513	+	15.3202i	−0.306098	+	0.530178i
$836$	−1.47783	−	2.55967i	−0.0511117	−	0.0885280i
$837$	25.0058	+	43.3113i	0.864327	+	1.49706i
$838$	−2.85278	+	4.94117i	−0.0985478	+	0.170690i
$839$	14.4481			0.498803			0.249402	−	0.968400i	$-0.419766\pi$
$839$	14.4481			0.498803			0.249402	+	0.968400i	$0.419766\pi$
$840$	−22.6782	+	11.3637i	−0.782471	+	0.392085i
$841$	51.0416			1.76006
$842$	−0.121060	+	0.209682i	−0.00417201	+	0.00722613i
$843$	33.1655	+	57.4444i	1.14228	+	1.97849i
$844$	−4.37014	−	7.56931i	−0.150426	−	0.260546i
$845$		0			0
$846$	−18.6892			−0.642548
$847$	−1.71068	+	28.9201i	−0.0587797	+	0.993708i
$848$	−20.8512			−0.716033
$849$	21.9570	−	38.0306i	0.753562	−	1.30521i
$850$	−2.07533	−	3.59457i	−0.0711831	−	0.123293i
$851$	4.68947	+	8.12240i	0.160753	+	0.278432i
$852$	19.0225	−	32.9480i	0.651701	−	1.12878i
$853$	27.6047			0.945166			0.472583	−	0.881286i	$-0.343322\pi$
$853$	27.6047			0.945166			0.472583	+	0.881286i	$0.343322\pi$
$854$	−17.0793	−	11.2554i	−0.584441	−	0.385151i
$855$	73.3945			2.51004
$856$	7.21713	−	12.5004i	0.246676	−	0.427256i
$857$	−16.0597	−	27.8162i	−0.548588	−	0.950182i	−0.998372	−	0.0570444i	$-0.981832\pi$
$857$	−16.0597	−	27.8162i	−0.548588	−	0.950182i	0.449784	−	0.893137i	$-0.351501\pi$
$858$		0			0
$859$	−12.6152	+	21.8501i	−0.430424	+	0.745517i	−0.996910	−	0.0785549i	$-0.974969\pi$
$859$	−12.6152	+	21.8501i	−0.430424	+	0.745517i	0.566485	+	0.824072i	$0.308303\pi$
$860$	−5.41682			−0.184712
$861$	−14.2248	−	9.37424i	−0.484779	−	0.319473i
$862$	−9.48515			−0.323065
$863$	9.03603	−	15.6509i	0.307590	−	0.532762i	−0.670245	−	0.742140i	$-0.733811\pi$
$863$	9.03603	−	15.6509i	0.307590	−	0.532762i	0.977835	+	0.209379i	$0.0671441\pi$
$864$	−29.7315	−	51.4965i	−1.01149	−	1.75195i
$865$	8.69169	+	15.0544i	0.295526	+	0.511866i
$866$	−4.50434	+	7.80175i	−0.153064	+	0.265114i
$867$	−37.3304			−1.26781
$868$	1.19449	−	20.1937i	0.0405437	−	0.685417i
$869$	−2.14320			−0.0727030
$870$	11.8517	−	20.5278i	0.401811	−	0.695957i
$871$		0			0
$872$	−4.49936	−	7.79312i	−0.152368	−	0.263908i
$873$	42.0958	−	72.9120i	1.42473	−	2.46770i
$874$	−27.4868			−0.929754
$875$	−26.5863	+	13.3220i	−0.898782	+	0.450367i
$876$	22.4420			0.758247
$877$	−11.2787	+	19.5353i	−0.380855	+	0.659659i	−0.991185	−	0.132488i	$-0.957703\pi$
$877$	−11.2787	+	19.5353i	−0.380855	+	0.659659i	0.610330	+	0.792147i	$0.291037\pi$
$878$	−0.198746	−	0.344237i	−0.00670734	−	0.0116175i
$879$	18.1415	+	31.4221i	0.611899	+	1.05984i
$880$	0.290233	−	0.502698i	0.00978375	−	0.0169460i
$881$	41.8834			1.41109			0.705544	−	0.708666i	$-0.250703\pi$
$881$	41.8834			1.41109			0.705544	+	0.708666i	$0.250703\pi$
$882$	−27.6655	−	3.28442i	−0.931545	−	0.110592i
$883$	3.20950			0.108008			0.0540041	−	0.998541i	$-0.482802\pi$
$883$	3.20950			0.108008			0.0540041	+	0.998541i	$0.482802\pi$
$884$		0			0
$885$	−3.18845	−	5.52255i	−0.107178	−	0.185638i
$886$	5.55751	+	9.62589i	0.186708	+	0.323388i
$887$	15.7498	−	27.2794i	0.528826	−	0.915953i	−0.470609	−	0.882342i	$-0.655966\pi$
$887$	15.7498	−	27.2794i	0.528826	−	0.915953i	0.999435	−	0.0336115i	$-0.0107009\pi$
$888$	11.8036			0.396103
$889$	−12.7974	+	6.41260i	−0.429212	+	0.215072i
$890$	−9.25212			−0.310132
$891$	−1.47787	+	2.55975i	−0.0495107	+	0.0857550i
$892$	−3.53163	−	6.11697i	−0.118248	−	0.204811i
$893$	−19.1520	−	33.1723i	−0.640899	−	1.11007i
$894$	15.0348	−	26.0411i	0.502839	−	0.870943i
$895$	6.06879			0.202857
$896$	−1.77862	+	30.0687i	−0.0594196	+	1.00453i
$897$		0			0
$898$	0.966878	−	1.67468i	0.0322651	−	0.0558848i
$899$	21.1297	+	36.5977i	0.704715	+	1.22060i
$900$	−15.9150	−	27.5656i	−0.530501	−	0.918855i
$901$	−12.3653	+	21.4173i	−0.411947	+	0.713513i
$902$	−0.289616			−0.00964315
$903$	−16.2749	−	10.7253i	−0.541595	−	0.356916i
$904$	−21.3242			−0.709232
$905$	0.843242	−	1.46054i	0.0280303	−	0.0485499i
$906$	1.77028	+	3.06621i	0.0588136	+	0.101868i
$907$	−10.8853	−	18.8538i	−0.361439	−	0.626031i	0.626759	−	0.779213i	$-0.284381\pi$
$907$	−10.8853	−	18.8538i	−0.361439	−	0.626031i	−0.988198	+	0.153182i	$0.951048\pi$
$908$	12.5260	−	21.6956i	0.415689	−	0.719995i
$909$	−80.2749			−2.66255
$910$		0			0
$911$	14.1386			0.468434			0.234217	−	0.972184i	$-0.424747\pi$
$911$	14.1386			0.468434			0.234217	+	0.972184i	$0.424747\pi$
$912$	23.2821	−	40.3257i	0.770947	−	1.33532i
$913$	−0.982395	−	1.70156i	−0.0325125	−	0.0563134i
$914$	4.62228	+	8.00602i	0.152891	+	0.264816i
$915$	−26.8574	+	46.5183i	−0.887877	+	1.53785i
$916$	−7.99388			−0.264125
$917$	−0.467041	+	7.89563i	−0.0154231	+	0.260737i
$918$	−14.4037			−0.475391
$919$	13.0955	−	22.6821i	0.431982	−	0.748215i	−0.565062	−	0.825048i	$-0.691148\pi$
$919$	13.0955	−	22.6821i	0.431982	−	0.748215i	0.997044	+	0.0768338i	$0.0244811\pi$
$920$	−8.51158	−	14.7425i	−0.280618	−	0.486045i
$921$	−32.5133	−	56.3148i	−1.07135	−	1.85563i
$922$	−7.82056	+	13.5456i	−0.257556	+	0.446101i
$923$		0			0
$924$	2.63408	−	1.31990i	0.0866548	−	0.0434215i
$925$	5.24399			0.172421
$926$	9.90018	−	17.1476i	0.325340	−	0.563506i
$927$	−1.27726	−	2.21227i	−0.0419506	−	0.0726606i
$928$	−25.1229	−	43.5141i	−0.824700	−	1.42842i
$929$	−20.2615	+	35.0939i	−0.664757	+	1.15139i	0.314594	+	0.949226i	$0.398131\pi$
$929$	−20.2615	+	35.0939i	−0.664757	+	1.15139i	−0.979351	+	0.202166i	$0.935202\pi$
$930$	12.5147			0.410372
$931$	−22.5209	−	52.4704i	−0.738094	−	1.71965i
$932$	−0.970335			−0.0317844
$933$	12.4387	−	21.5444i	0.407224	−	0.705332i
$934$	12.5212	+	21.6873i	0.409705	+	0.709630i
$935$	−0.344231	−	0.596225i	−0.0112575	−	0.0194986i
$936$		0			0
$937$	9.04873			0.295609			0.147805	−	0.989017i	$-0.452779\pi$
$937$	9.04873			0.295609			0.147805	+	0.989017i	$0.452779\pi$
$938$	−2.47065	+	1.23801i	−0.0806695	+	0.0404223i
$939$	4.68599			0.152922
$940$	5.30568	−	9.18971i	0.173052	−	0.299735i
$941$	0.709932	+	1.22964i	0.0231431	+	0.0400850i	0.877365	−	0.479824i	$-0.159299\pi$
$941$	0.709932	+	1.22964i	0.0231431	+	0.0400850i	−0.854222	+	0.519909i	$0.825966\pi$
$942$	6.53427	+	11.3177i	0.212898	+	0.368750i
$943$	5.71640	−	9.90109i	0.186151	−	0.322424i
$944$	−2.76071			−0.0898533
$945$	−2.30922	+	39.0388i	−0.0751189	+	1.26993i
$946$	−0.331357			−0.0107733
$947$	−12.0854	+	20.9325i	−0.392723	+	0.680216i	−0.992808	−	0.119720i	$-0.961800\pi$
$947$	−12.0854	+	20.9325i	−0.392723	+	0.680216i	0.600085	+	0.799937i	$0.295134\pi$
$948$	−23.8140	−	41.2471i	−0.773444	−	1.33964i
$949$		0			0
$950$	−7.68426	+	13.3095i	−0.249310	+	0.431818i
$951$	47.3594			1.53573
$952$	10.8754	+	7.16700i	0.352475	+	0.232284i
$953$	−2.59826			−0.0841658			−0.0420829	−	0.999114i	$-0.513399\pi$
$953$	−2.59826			−0.0841658			−0.0420829	+	0.999114i	$0.513399\pi$
$954$	22.3391	−	38.6924i	0.723254	−	1.25271i
$955$	16.2412	+	28.1307i	0.525554	+	0.910287i
$956$	7.72827	+	13.3858i	0.249950	+	0.432926i
$957$	−3.07746	+	5.33032i	−0.0994801	+	0.172305i
$958$	6.01013			0.194178
$959$	−35.6746	−	23.5099i	−1.15199	−	0.759174i
$960$	1.05881			0.0341731
$961$	4.34419	−	7.52435i	0.140135	−	0.242721i
$962$		0			0
$963$	−20.8159	−	36.0542i	−0.670784	−	1.16183i
$964$	−19.4076	+	33.6149i	−0.625076	+	1.08266i
$965$	13.7021			0.441085
$966$	1.61790	−	27.3517i	0.0520552	−	0.880026i
$967$	−3.70258			−0.119067			−0.0595335	−	0.998226i	$-0.518961\pi$
$967$	−3.70258			−0.119067			−0.0595335	+	0.998226i	$0.518961\pi$
$968$	−12.2343	+	21.1904i	−0.393225	+	0.681085i
$969$	−27.6137	−	47.8283i	−0.887079	−	1.53647i
$970$	−5.63065	−	9.75258i	−0.180789	−	0.313136i
$971$	−16.1778	+	28.0207i	−0.519169	+	0.899228i	0.480583	+	0.876949i	$0.340425\pi$
$971$	−16.1778	+	28.0207i	−0.519169	+	0.899228i	−0.999752	+	0.0222781i	$0.992908\pi$
$972$	−14.2709			−0.457739
$973$	1.55526	−	0.779318i	0.0498593	−	0.0249838i
$974$	8.95838			0.287045
$975$		0			0
$976$	11.6272	+	20.1389i	0.372177	+	0.644630i
$977$	24.7045	+	42.7895i	0.790368	+	1.36896i	0.925739	+	0.378162i	$0.123444\pi$
$977$	24.7045	+	42.7895i	0.790368	+	1.36896i	−0.135372	+	0.990795i	$0.543223\pi$
$978$	11.5077	−	19.9319i	0.367975	−	0.637352i
$979$	2.40244			0.0767823
$980$	9.46894	−	12.6710i	0.302474	−	0.404761i
$981$	−25.9544			−0.828662
$982$	−6.16260	+	10.6739i	−0.196656	+	0.340619i
$983$	9.73790	+	16.8665i	0.310591	+	0.537959i	0.978490	−	0.206292i	$-0.0661398\pi$
$983$	9.73790	+	16.8665i	0.310591	+	0.537959i	−0.667900	+	0.744251i	$0.732806\pi$
$984$	−7.19422	−	12.4608i	−0.229343	−	0.397234i
$985$	−8.16541	+	14.1429i	−0.260172	+	0.450630i
$986$	−12.1710			−0.387603
$987$	34.1366	−	17.1054i	1.08658	−	0.544470i
$988$		0			0
$989$	6.54027	−	11.3281i	0.207969	−	0.360212i
$990$	0.621886	+	1.07714i	0.0197648	+	0.0342337i
$991$	−10.7071	−	18.5453i	−0.340123	−	0.589111i	0.644332	−	0.764746i	$-0.277135\pi$
$991$	−10.7071	−	18.5453i	−0.340123	−	0.589111i	−0.984455	+	0.175635i	$0.943802\pi$
$992$	13.2641	−	22.9741i	0.421135	−	0.729428i
$993$	90.9836			2.88728
$994$	0.737811	−	12.4732i	0.0234019	−	0.395625i
$995$	−3.81365			−0.120901
$996$	21.8317	−	37.8136i	0.691763	−	1.19817i
$997$	21.0273	+	36.4203i	0.665941	+	1.15344i	0.979029	+	0.203719i	$0.0653031\pi$
$997$	21.0273	+	36.4203i	0.665941	+	1.15344i	−0.313088	+	0.949724i	$0.601364\pi$
$998$	−3.65697	−	6.33406i	−0.115759	−	0.200501i
$999$	9.09889	−	15.7597i	0.287876	−	0.498616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.k.170.10	✓	48
7.2	even	3		8281.2.a.cv.1.15		24
7.4	even	3	inner	1183.2.e.k.508.10	yes	48
7.5	odd	6		8281.2.a.cw.1.15		24
13.12	even	2		1183.2.e.l.170.15	yes	48
91.12	odd	6		8281.2.a.ct.1.10		24
91.25	even	6		1183.2.e.l.508.15	yes	48
91.51	even	6		8281.2.a.cu.1.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.e.k.170.10	✓	48	1.1	even	1	trivial
1183.2.e.k.508.10	yes	48	7.4	even	3	inner
1183.2.e.l.170.15	yes	48	13.12	even	2
1183.2.e.l.508.15	yes	48	91.25	even	6
8281.2.a.ct.1.10		24	91.12	odd	6
8281.2.a.cu.1.10		24	91.51	even	6
8281.2.a.cv.1.15		24	7.2	even	3
8281.2.a.cw.1.15		24	7.5	odd	6

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.308759 + 0.534786i) q^{2} +(-1.53664 - 2.66155i) q^{3} +(0.809336 + 1.40181i) q^{4} +(0.698024 - 1.20901i) q^{5} +1.89781 q^{6} +(-2.36540 + 1.18527i) q^{7} -2.23459 q^{8} +(-3.22255 + 5.58162i) q^{9} +O(q^{10})\)	\(q+(-0.308759 + 0.534786i) q^{2} +(-1.53664 - 2.66155i) q^{3} +(0.809336 + 1.40181i) q^{4} +(0.698024 - 1.20901i) q^{5} +1.89781 q^{6} +(-2.36540 + 1.18527i) q^{7} -2.23459 q^{8} +(-3.22255 + 5.58162i) q^{9} +(0.431043 + 0.746588i) q^{10} +(-0.111926 - 0.193862i) q^{11} +(2.48732 - 4.30817i) q^{12} +(0.0964736 - 1.63095i) q^{14} -4.29046 q^{15} +(-0.928721 + 1.60859i) q^{16} +(1.10151 + 1.90787i) q^{17} +(-1.98998 - 3.44675i) q^{18} +(4.07853 - 7.06422i) q^{19} +2.25974 q^{20} +(6.78943 + 4.47429i) q^{21} +0.138233 q^{22} +(-2.72842 + 4.72576i) q^{23} +(3.43378 + 5.94748i) q^{24} +(1.52552 + 2.64228i) q^{25} +10.5878 q^{27} +(-3.57593 - 2.35657i) q^{28} +8.94660 q^{29} +(1.32472 - 2.29448i) q^{30} +(2.36176 + 4.09069i) q^{31} +(-2.80810 - 4.86377i) q^{32} +(-0.343981 + 0.595792i) q^{33} -1.36040 q^{34} +(-0.218102 + 3.68715i) q^{35} -10.4325 q^{36} +(0.859375 - 1.48848i) q^{37} +(2.51856 + 4.36228i) q^{38} +(-1.55980 + 2.70166i) q^{40} -2.09513 q^{41} +(-4.48909 + 2.24942i) q^{42} -2.39709 q^{43} +(0.181171 - 0.313798i) q^{44} +(4.49884 + 7.79222i) q^{45} +(-1.68485 - 2.91824i) q^{46} +(2.34791 - 4.06670i) q^{47} +5.70845 q^{48} +(4.19027 - 5.60728i) q^{49} -1.88408 q^{50} +(3.38525 - 5.86343i) q^{51} +(5.61288 + 9.72179i) q^{53} +(-3.26908 + 5.66220i) q^{54} -0.312508 q^{55} +(5.28572 - 2.64860i) q^{56} -25.0690 q^{57} +(-2.76234 + 4.78452i) q^{58} +(0.743148 + 1.28717i) q^{59} +(-3.47242 - 6.01441i) q^{60} +(6.25979 - 10.8423i) q^{61} -2.91686 q^{62} +(1.00691 - 17.0224i) q^{63} -0.246783 q^{64} +(-0.212414 - 0.367913i) q^{66} +(-0.845719 - 1.46483i) q^{67} +(-1.78298 + 3.08821i) q^{68} +16.7704 q^{69} +(-1.90450 - 1.25508i) q^{70} +7.64780 q^{71} +(7.20109 - 12.4727i) q^{72} +(2.25564 + 3.90689i) q^{73} +(0.530680 + 0.919164i) q^{74} +(4.68837 - 8.12050i) q^{75} +13.2036 q^{76} +(0.494529 + 0.325898i) q^{77} +(4.78709 - 8.29148i) q^{79} +(1.29654 + 2.24567i) q^{80} +(-6.60202 - 11.4350i) q^{81} +(0.646891 - 1.12045i) q^{82} +8.77718 q^{83} +(-0.777179 + 13.1387i) q^{84} +3.07552 q^{85} +(0.740125 - 1.28193i) q^{86} +(-13.7477 - 23.8118i) q^{87} +(0.250109 + 0.433202i) q^{88} +(-5.36613 + 9.29441i) q^{89} -5.55623 q^{90} -8.83282 q^{92} +(7.25837 - 12.5719i) q^{93} +(1.44988 + 2.51126i) q^{94} +(-5.69382 - 9.86199i) q^{95} +(-8.63009 + 14.9478i) q^{96} -13.0629 q^{97} +(1.70491 + 3.97220i) q^{98} +1.44275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9}+O(q^{10}) \) 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9	\( 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9} - 5 q^{10} - q^{11} - 5 q^{12} - 2 q^{14} - 10 q^{15} - 17 q^{16} + 5 q^{17} + 24 q^{19} - 68 q^{20} + q^{21} - 28 q^{22} - 11 q^{23} + 32 q^{24} - 33 q^{25} - 42 q^{27} + 15 q^{28} + 8 q^{29} + 22 q^{30} + 40 q^{31} - 6 q^{32} + 24 q^{33} - 72 q^{34} + 44 q^{35} - 30 q^{36} - 4 q^{37} + 29 q^{38} + 4 q^{40} - 98 q^{41} - 9 q^{42} + 26 q^{43} + 10 q^{44} + 58 q^{45} - 10 q^{46} + 62 q^{47} + 178 q^{48} + 31 q^{49} + 46 q^{50} + 21 q^{51} + 18 q^{53} + 12 q^{54} - 28 q^{55} - 56 q^{56} + 26 q^{57} + 56 q^{58} + 79 q^{59} + 22 q^{60} - 13 q^{61} + 24 q^{62} - 22 q^{63} + 36 q^{64} + 38 q^{66} - 2 q^{67} + 12 q^{68} - 56 q^{69} - 85 q^{70} + 38 q^{71} + 81 q^{72} + 17 q^{73} - 17 q^{74} - 24 q^{75} - 116 q^{76} - 30 q^{77} + 9 q^{79} + 63 q^{80} - 16 q^{81} + 22 q^{82} - 162 q^{83} - 203 q^{84} + 68 q^{85} + 22 q^{86} - 70 q^{87} + 33 q^{88} + 72 q^{89} + 2 q^{90} - 8 q^{92} + 19 q^{93} + 30 q^{94} - 13 q^{95} + 11 q^{96} - 90 q^{97} - 81 q^{98} + 78 q^{99}+O(q^{100}) \) 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9 - 5 * q^10 - q^11 - 5 * q^12 - 2 * q^14 - 10 * q^15 - 17 * q^16 + 5 * q^17 + 24 * q^19 - 68 * q^20 + q^21 - 28 * q^22 - 11 * q^23 + 32 * q^24 - 33 * q^25 - 42 * q^27 + 15 * q^28 + 8 * q^29 + 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 - 72 * q^34 + 44 * q^35 - 30 * q^36 - 4 * q^37 + 29 * q^38 + 4 * q^40 - 98 * q^41 - 9 * q^42 + 26 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 178 * q^48 + 31 * q^49 + 46 * q^50 + 21 * q^51 + 18 * q^53 + 12 * q^54 - 28 * q^55 - 56 * q^56 + 26 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 - 13 * q^61 + 24 * q^62 - 22 * q^63 + 36 * q^64 + 38 * q^66 - 2 * q^67 + 12 * q^68 - 56 * q^69 - 85 * q^70 + 38 * q^71 + 81 * q^72 + 17 * q^73 - 17 * q^74 - 24 * q^75 - 116 * q^76 - 30 * q^77 + 9 * q^79 + 63 * q^80 - 16 * q^81 + 22 * q^82 - 162 * q^83 - 203 * q^84 + 68 * q^85 + 22 * q^86 - 70 * q^87 + 33 * q^88 + 72 * q^89 + 2 * q^90 - 8 * q^92 + 19 * q^93 + 30 * q^94 - 13 * q^95 + 11 * q^96 - 90 * q^97 - 81 * q^98 + 78 * q^99

Introduction

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