LMFDB - Embedded newform 133.2.s.d.103.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [133,2,Mod(31,133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(133, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("133.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.s (of order $6$, 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:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26x^{14} + 265x^{12} + 1335x^{10} + 3450x^{8} + 4344x^{6} + 2376x^{4} + 423x^{2} + 9 $ x^16 + 26x^14 + 265x^12 + 1335x^10 + 3450x^8 + 4344x^6 + 2376x^4 + 423*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.8
Root			$-2.53791i$ of defining polynomial
Character	$\chi$	$=$	133.103
Dual form			133.2.s.d.31.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.19790 - 1.26896i) q^{2} -2.88800 q^{3} +(2.22050 - 3.84603i) q^{4} +(2.26105 - 1.30542i) q^{5} +(-6.34752 + 3.66474i) q^{6} +(-2.45775 + 0.979525i) q^{7} -6.19507i q^{8} +5.34052 q^{9} +O(q^{10})$	\(q+(2.19790 - 1.26896i) q^{2} -2.88800 q^{3} +(2.22050 - 3.84603i) q^{4} +(2.26105 - 1.30542i) q^{5} +(-6.34752 + 3.66474i) q^{6} +(-2.45775 + 0.979525i) q^{7} -6.19507i q^{8} +5.34052 q^{9} +(3.31303 - 5.73834i) q^{10} +(1.10109 + 1.90714i) q^{11} +(-6.41281 + 11.1073i) q^{12} +(-0.123499 - 0.213906i) q^{13} +(-4.15891 + 5.27168i) q^{14} +(-6.52989 + 3.77003i) q^{15} +(-3.42027 - 5.92409i) q^{16} +5.04720i q^{17} +(11.7379 - 6.77689i) q^{18} +(4.15176 + 1.32773i) q^{19} -11.5947i q^{20} +(7.09797 - 2.82886i) q^{21} +(4.84015 + 2.79446i) q^{22} -1.97953 q^{23} +17.8913i q^{24} +(0.908220 - 1.57308i) q^{25} +(-0.542875 - 0.313429i) q^{26} -6.75941 q^{27} +(-1.69016 + 11.6276i) q^{28} +(-1.73625 + 1.00243i) q^{29} +(-9.56803 + 16.5723i) q^{30} +(-4.35499 - 7.54306i) q^{31} +(-4.30465 - 2.48529i) q^{32} +(-3.17993 - 5.50780i) q^{33} +(6.40468 + 11.0932i) q^{34} +(-4.27840 + 5.42314i) q^{35} +(11.8586 - 20.5398i) q^{36} +(-6.96980 - 4.02402i) q^{37} +(10.8100 - 2.35019i) q^{38} +(0.356663 + 0.617759i) q^{39} +(-8.08715 - 14.0073i) q^{40} +(-0.155777 + 0.269813i) q^{41} +(12.0109 - 15.2246i) q^{42} +(-3.07717 + 5.32981i) q^{43} +9.77987 q^{44} +(12.0752 - 6.97160i) q^{45} +(-4.35081 + 2.51194i) q^{46} -7.23797i q^{47} +(9.87774 + 17.1087i) q^{48} +(5.08106 - 4.81485i) q^{49} -4.60997i q^{50} -14.5763i q^{51} -1.09692 q^{52} +(-6.46265 - 3.73121i) q^{53} +(-14.8565 + 8.57740i) q^{54} +(4.97921 + 2.87475i) q^{55} +(6.06823 + 15.2259i) q^{56} +(-11.9903 - 3.83449i) q^{57} +(-2.54407 + 4.40646i) q^{58} +0.126296 q^{59} +33.4855i q^{60} +4.91796i q^{61} +(-19.1436 - 11.0526i) q^{62} +(-13.1257 + 5.23117i) q^{63} +1.06620 q^{64} +(-0.558472 - 0.322434i) q^{65} +(-13.9783 - 8.07039i) q^{66} +(12.0731 + 6.97042i) q^{67} +(19.4117 + 11.2073i) q^{68} +5.71688 q^{69} +(-2.52175 + 17.3486i) q^{70} +(-2.22357 - 1.28378i) q^{71} -33.0849i q^{72} +2.64973i q^{73} -20.4252 q^{74} +(-2.62294 + 4.54306i) q^{75} +(14.3255 - 13.0196i) q^{76} +(-4.57428 - 3.60872i) q^{77} +(1.56782 + 0.905181i) q^{78} +(0.870703 - 0.502701i) q^{79} +(-15.4668 - 8.92976i) q^{80} +3.49958 q^{81} +0.790697i q^{82} +3.43226i q^{83} +(4.88119 - 33.5805i) q^{84} +(6.58870 + 11.4120i) q^{85} +15.6192i q^{86} +(5.01429 - 2.89500i) q^{87} +(11.8149 - 6.82131i) q^{88} +1.06925 q^{89} +(17.6933 - 30.6457i) q^{90} +(0.513055 + 0.404757i) q^{91} +(-4.39556 + 7.61333i) q^{92} +(12.5772 + 21.7843i) q^{93} +(-9.18468 - 15.9083i) q^{94} +(11.1206 - 2.41771i) q^{95} +(12.4318 + 7.17750i) q^{96} +(-2.90401 + 5.02990i) q^{97} +(5.05781 - 17.0302i) q^{98} +(5.88037 + 10.1851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 10 q^{4} + 9 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 10 * q^4 + 9 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^9	$ 16 q - 8 q^{3} + 10 q^{4} + 9 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{9} - 2 q^{10} - 9 q^{11} - 17 q^{12} + 15 q^{13} + 3 q^{14} - 12 q^{15} - 22 q^{16} - 3 q^{18} + 8 q^{19} - 10 q^{21} - 27 q^{22} + 30 q^{23} + 13 q^{25} - 9 q^{26} - 38 q^{27} + 35 q^{28} - 18 q^{29} - 32 q^{30} - 27 q^{31} + 27 q^{32} - 12 q^{33} - 16 q^{34} - 6 q^{35} + 4 q^{36} - 39 q^{37} + 27 q^{38} - 9 q^{39} + 9 q^{40} + 9 q^{41} + 48 q^{42} - 9 q^{43} + 18 q^{44} + 75 q^{45} - 36 q^{46} + 35 q^{48} - 8 q^{49} + 18 q^{53} - 18 q^{54} + 15 q^{56} - 22 q^{57} - 20 q^{58} + 18 q^{59} - 45 q^{62} - 46 q^{63} - 22 q^{64} - 36 q^{65} - 45 q^{66} + 18 q^{67} + 63 q^{68} + 30 q^{69} - 19 q^{70} - 9 q^{71} + 18 q^{74} + 10 q^{75} + 98 q^{76} + 30 q^{77} + 54 q^{78} + 21 q^{79} + 27 q^{80} + 40 q^{81} - 34 q^{84} + 31 q^{85} - 48 q^{87} + 18 q^{88} + 24 q^{89} + 28 q^{90} + 15 q^{91} + 54 q^{92} + 6 q^{93} - 49 q^{94} - 66 q^{95} - 69 q^{96} + q^{97} + 15 q^{98} + 18 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 10 * q^4 + 9 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^9 - 2 * q^10 - 9 * q^11 - 17 * q^12 + 15 * q^13 + 3 * q^14 - 12 * q^15 - 22 * q^16 - 3 * q^18 + 8 * q^19 - 10 * q^21 - 27 * q^22 + 30 * q^23 + 13 * q^25 - 9 * q^26 - 38 * q^27 + 35 * q^28 - 18 * q^29 - 32 * q^30 - 27 * q^31 + 27 * q^32 - 12 * q^33 - 16 * q^34 - 6 * q^35 + 4 * q^36 - 39 * q^37 + 27 * q^38 - 9 * q^39 + 9 * q^40 + 9 * q^41 + 48 * q^42 - 9 * q^43 + 18 * q^44 + 75 * q^45 - 36 * q^46 + 35 * q^48 - 8 * q^49 + 18 * q^53 - 18 * q^54 + 15 * q^56 - 22 * q^57 - 20 * q^58 + 18 * q^59 - 45 * q^62 - 46 * q^63 - 22 * q^64 - 36 * q^65 - 45 * q^66 + 18 * q^67 + 63 * q^68 + 30 * q^69 - 19 * q^70 - 9 * q^71 + 18 * q^74 + 10 * q^75 + 98 * q^76 + 30 * q^77 + 54 * q^78 + 21 * q^79 + 27 * q^80 + 40 * q^81 - 34 * q^84 + 31 * q^85 - 48 * q^87 + 18 * q^88 + 24 * q^89 + 28 * q^90 + 15 * q^91 + 54 * q^92 + 6 * q^93 - 49 * q^94 - 66 * q^95 - 69 * q^96 + q^97 + 15 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.19790	−	1.26896i	1.55415	−	0.897288i	0.556352	−	0.830947i	$-0.312201\pi$
$2$	2.19790	−	1.26896i	1.55415	−	0.897288i	0.997797	−	0.0663414i	$-0.0211327\pi$
$3$	−2.88800			−1.66738			−0.833692	−	0.552229i	$-0.813777\pi$
$3$	−2.88800			−1.66738			−0.833692	+	0.552229i	$0.813777\pi$
$4$	2.22050	−	3.84603i	1.11025	−	1.92301i
$5$	2.26105	−	1.30542i	1.01117	−	0.583800i	0.0996365	−	0.995024i	$-0.468232\pi$
$5$	2.26105	−	1.30542i	1.01117	−	0.583800i	0.911534	+	0.411224i	$0.134899\pi$
$6$	−6.34752	+	3.66474i	−2.59136	+	1.49612i
$7$	−2.45775	+	0.979525i	−0.928942	+	0.370226i
$7$	−2.45775	+	0.979525i	−0.928942	+	0.370226i
$8$		−	6.19507i		−	2.19029i
$9$	5.34052			1.78017
$10$	3.31303	−	5.73834i	1.04767	−	1.81462i
$11$	1.10109	+	1.90714i	0.331990	+	0.575023i	0.982902	−	0.184130i	$-0.0589467\pi$
$11$	1.10109	+	1.90714i	0.331990	+	0.575023i	−0.650912	+	0.759153i	$0.725613\pi$
$12$	−6.41281	+	11.1073i	−1.85122	+	3.20640i
$13$	−0.123499	−	0.213906i	−0.0342523	−	0.0593268i	0.848391	−	0.529370i	$-0.177572\pi$
$13$	−0.123499	−	0.213906i	−0.0342523	−	0.0593268i	−0.882643	+	0.470043i	$0.844238\pi$
$14$	−4.15891	+	5.27168i	−1.11151	+	1.40891i
$15$	−6.52989	+	3.77003i	−1.68601	+	0.973419i
$16$	−3.42027	−	5.92409i	−0.855068	−	1.48102i
$17$			5.04720i			1.22413i	0.790809	+	0.612063i	$0.209660\pi$
$17$			5.04720i			1.22413i	−0.790809	+	0.612063i	$0.790340\pi$
$18$	11.7379	−	6.77689i	2.76665	−	1.59733i
$19$	4.15176	+	1.32773i	0.952479	+	0.304603i
$19$	4.15176	+	1.32773i	0.952479	+	0.304603i
$20$		−	11.5947i		−	2.59266i
$21$	7.09797	−	2.82886i	1.54890	−	0.617309i
$22$	4.84015	+	2.79446i	1.03192	+	0.595781i
$23$	−1.97953			−0.412761			−0.206380	−	0.978472i	$-0.566168\pi$
$23$	−1.97953			−0.412761			−0.206380	+	0.978472i	$0.566168\pi$
$24$			17.8913i			3.65206i
$25$	0.908220	−	1.57308i	0.181644	−	0.314617i
$26$	−0.542875	−	0.313429i	−0.106466	−	0.0614684i
$27$	−6.75941			−1.30085
$28$	−1.69016	+	11.6276i	−0.319411	+	2.19741i
$29$	−1.73625	+	1.00243i	−0.322414	+	0.186146i	−0.652468	−	0.757816i	$-0.726266\pi$
$29$	−1.73625	+	1.00243i	−0.322414	+	0.186146i	0.330054	+	0.943962i	$0.392933\pi$
$30$	−9.56803	+	16.5723i	−1.74687	+	3.02568i
$31$	−4.35499	−	7.54306i	−0.782179	−	1.35477i	−0.930670	−	0.365859i	$-0.880775\pi$
$31$	−4.35499	−	7.54306i	−0.782179	−	1.35477i	0.148491	−	0.988914i	$-0.452558\pi$
$32$	−4.30465	−	2.48529i	−0.760961	−	0.439341i
$33$	−3.17993	−	5.50780i	−0.553555	−	0.958785i
$34$	6.40468	+	11.0932i	1.09839	+	1.90247i
$35$	−4.27840	+	5.42314i	−0.723181	+	0.916677i
$36$	11.8586	−	20.5398i	1.97644	−	3.42330i
$37$	−6.96980	−	4.02402i	−1.14583	−	0.661544i	−0.197961	−	0.980210i	$-0.563432\pi$
$37$	−6.96980	−	4.02402i	−1.14583	−	0.661544i	−0.947867	+	0.318665i	$0.896765\pi$
$38$	10.8100	−	2.35019i	1.75361	−	0.381250i
$39$	0.356663	+	0.617759i	0.0571118	+	0.0989206i
$40$	−8.08715	−	14.0073i	−1.27869	−	2.21476i
$41$	−0.155777	+	0.269813i	−0.0243283	+	0.0421378i	−0.877933	−	0.478783i	$-0.841078\pi$
$41$	−0.155777	+	0.269813i	−0.0243283	+	0.0421378i	0.853605	+	0.520921i	$0.174411\pi$
$42$	12.0109	−	15.2246i	1.85332	−	2.34920i
$43$	−3.07717	+	5.32981i	−0.469264	+	0.812789i	−0.999383	−	0.0351347i	$-0.988814\pi$
$43$	−3.07717	+	5.32981i	−0.469264	+	0.812789i	0.530119	+	0.847923i	$0.322147\pi$
$44$	9.77987			1.47437
$45$	12.0752	−	6.97160i	1.80006	−	1.03926i
$46$	−4.35081	+	2.51194i	−0.641492	+	0.370365i
$47$		−	7.23797i		−	1.05577i	−0.849317	−	0.527883i	$-0.822986\pi$
$47$		−	7.23797i		−	1.05577i	0.849317	−	0.527883i	$-0.177014\pi$
$48$	9.87774	+	17.1087i	1.42573	+	2.46943i
$49$	5.08106	−	4.81485i	0.725866	−	0.687836i
$50$		−	4.60997i		−	0.651948i
$51$		−	14.5763i		−	2.04109i
$52$	−1.09692			−0.152115
$53$	−6.46265	−	3.73121i	−0.887714	−	0.512522i	−0.0145197	−	0.999895i	$-0.504622\pi$
$53$	−6.46265	−	3.73121i	−0.887714	−	0.512522i	−0.873194	+	0.487373i	$0.837955\pi$
$54$	−14.8565	+	8.57740i	−2.02171	+	1.16724i
$55$	4.97921	+	2.87475i	0.671397	+	0.387631i
$56$	6.06823	+	15.2259i	0.810901	+	2.03465i
$57$	−11.9903	−	3.83449i	−1.58815	−	0.507890i
$58$	−2.54407	+	4.40646i	−0.334053	+	0.578596i
$59$	0.126296			0.0164423			0.00822116	−	0.999966i	$-0.497383\pi$
$59$	0.126296			0.0164423			0.00822116	+	0.999966i	$0.497383\pi$
$60$			33.4855i			4.32296i
$61$			4.91796i			0.629680i	0.949145	+	0.314840i	$0.101951\pi$
$61$			4.91796i			0.629680i	−0.949145	+	0.314840i	$0.898049\pi$
$62$	−19.1436	−	11.0526i	−2.43124	−	1.40368i
$63$	−13.1257	+	5.23117i	−1.65368	+	0.659066i
$64$	1.06620			0.133274
$65$	−0.558472	−	0.322434i	−0.0692699	−	0.0399930i
$66$	−13.9783	−	8.07039i	−1.72061	−	0.993397i
$67$	12.0731	+	6.97042i	1.47497	+	0.851572i	0.999602	−	0.0282173i	$-0.00898305\pi$
$67$	12.0731	+	6.97042i	1.47497	+	0.851572i	0.475364	+	0.879789i	$0.342316\pi$
$68$	19.4117	+	11.2073i	2.35401	+	1.35909i
$69$	5.71688			0.688231
$70$	−2.52175	+	17.3486i	−0.301407	+	2.07355i
$71$	−2.22357	−	1.28378i	−0.263889	−	0.152357i	0.362218	−	0.932093i	$-0.382020\pi$
$71$	−2.22357	−	1.28378i	−0.263889	−	0.152357i	−0.626107	+	0.779737i	$0.715353\pi$
$72$		−	33.0849i		−	3.89909i
$73$			2.64973i			0.310127i	0.987905	+	0.155064i	$0.0495582\pi$
$73$			2.64973i			0.310127i	−0.987905	+	0.155064i	$0.950442\pi$
$74$	−20.4252			−2.37438
$75$	−2.62294	+	4.54306i	−0.302871	+	0.524587i
$76$	14.3255	−	13.0196i	1.64325	−	1.49344i
$77$	−4.57428	−	3.60872i	−0.521288	−	0.411252i
$78$	1.56782	+	0.905181i	0.177521	+	0.102492i
$79$	0.870703	−	0.502701i	0.0979617	−	0.0565582i	−0.450219	−	0.892918i	$-0.648654\pi$
$79$	0.870703	−	0.502701i	0.0979617	−	0.0565582i	0.548181	+	0.836360i	$0.315321\pi$
$80$	−15.4668	−	8.92976i	−1.72924	−	0.998377i
$81$	3.49958			0.388842
$82$			0.790697i			0.0873178i
$83$			3.43226i			0.376739i	0.982098	+	0.188370i	$0.0603203\pi$
$83$			3.43226i			0.376739i	−0.982098	+	0.188370i	$0.939680\pi$
$84$	4.88119	−	33.5805i	0.532581	−	3.66393i
$85$	6.58870	+	11.4120i	0.714645	+	1.23780i
$86$			15.6192i			1.68426i
$87$	5.01429	−	2.89500i	0.537588	−	0.310377i
$88$	11.8149	−	6.82131i	1.25947	−	0.727154i
$89$	1.06925			0.113340			0.0566700	−	0.998393i	$-0.481952\pi$
$89$	1.06925			0.113340			0.0566700	+	0.998393i	$0.481952\pi$
$90$	17.6933	−	30.6457i	1.86504	−	3.23034i
$91$	0.513055	+	0.404757i	0.0537827	+	0.0424300i
$92$	−4.39556	+	7.61333i	−0.458269	+	0.793745i
$93$	12.5772	+	21.7843i	1.30419	+	2.25893i
$94$	−9.18468	−	15.9083i	−0.947327	−	1.64082i
$95$	11.1206	−	2.41771i	1.14095	−	0.248052i
$96$	12.4318	+	7.17750i	1.26882	+	0.732551i
$97$	−2.90401	+	5.02990i	−0.294858	+	0.510709i	−0.974952	−	0.222416i	$-0.928606\pi$
$97$	−2.90401	+	5.02990i	−0.294858	+	0.510709i	0.680094	+	0.733125i	$0.261939\pi$
$98$	5.05781	−	17.0302i	0.510916	−	1.72031i
$99$	5.88037	+	10.1851i	0.590999	+	1.02364i
$100$	−4.03342	−	6.98608i	−0.403342	−	0.698608i
$101$	−9.09501	−	5.25101i	−0.904987	−	0.522495i	−0.0261723	−	0.999657i	$-0.508332\pi$
$101$	−9.09501	−	5.25101i	−0.904987	−	0.522495i	−0.878815	+	0.477163i	$0.841665\pi$
$102$	−18.4967	−	32.0372i	−1.83145	−	3.17216i
$103$	0.166375	−	0.288171i	0.0163935	−	0.0283943i	−0.857712	−	0.514130i	$-0.828115\pi$
$103$	0.166375	−	0.288171i	0.0163935	−	0.0283943i	0.874106	+	0.485736i	$0.161448\pi$
$104$	−1.32516	+	0.765083i	−0.129943	+	0.0750225i
$105$	12.3560	−	15.6620i	1.20582	−	1.52845i
$106$	−18.9390			−1.83952
$107$	−1.08277	−	0.625137i	−0.104675	−	0.0604343i	0.446748	−	0.894660i	$-0.352582\pi$
$107$	−1.08277	−	0.625137i	−0.104675	−	0.0604343i	−0.551424	+	0.834225i	$0.685915\pi$
$108$	−15.0093	+	25.9969i	−1.44427	+	2.50155i
$109$			15.2055i			1.45642i	0.685353	+	0.728211i	$0.259648\pi$
$109$			15.2055i			1.45642i	−0.685353	+	0.728211i	$0.740352\pi$
$110$	14.5917			1.39127
$111$	20.1288	+	11.6213i	1.91054	+	1.10305i
$112$	14.2090	+	11.2097i	1.34262	+	1.05922i
$113$		−	13.0568i		−	1.22828i	−0.789199	−	0.614138i	$-0.789504\pi$
$113$		−	13.0568i		−	1.22828i	0.789199	−	0.614138i	$-0.210496\pi$
$114$	−31.2192	+	6.78732i	−2.92395	+	0.635691i
$115$	−4.47581	+	2.58411i	−0.417372	+	0.240970i
$116$			8.90356i			0.826675i
$117$	−0.659546	−	1.14237i	−0.0609751	−	0.105612i
$118$	0.277586	−	0.160264i	0.0255538	−	0.0147535i
$119$	−4.94386	−	12.4048i	−0.453203	−	1.13714i
$120$	23.3556	+	40.4532i	2.13207	+	3.69285i
$121$	3.07522	−	5.32644i	0.279565	−	0.484222i
$122$	6.24068	+	10.8092i	0.565004	+	0.978616i
$123$	0.449883	−	0.779220i	0.0405646	−	0.0702599i
$124$	−38.6811			−3.47366
$125$			8.31174i			0.743424i
$126$	−22.2107	+	28.1535i	−1.97869	+	2.50811i
$127$	0.546379	−	0.315452i	0.0484833	−	0.0279918i	−0.475562	−	0.879682i	$-0.657755\pi$
$127$	0.546379	−	0.315452i	0.0484833	−	0.0279918i	0.524046	+	0.851690i	$0.324422\pi$
$128$	10.9527	−	6.32353i	0.968089	−	0.558927i
$129$	8.88685	−	15.3925i	0.782443	−	1.35523i
$130$	−1.63662			−0.143541
$131$	−7.69171	+	4.44081i	−0.672028	+	0.387995i	−0.796845	−	0.604184i	$-0.793499\pi$
$131$	−7.69171	+	4.44081i	−0.672028	+	0.387995i	0.124817	+	0.992180i	$0.460166\pi$
$132$	−28.2442			−2.45834
$133$	−11.5045	+	0.803520i	−0.997570	+	0.0696740i
$134$	35.3806			3.05642
$135$	−15.2833	+	8.82383i	−1.31538	+	0.759435i
$136$	31.2678			2.68119
$137$	10.6876	−	18.5115i	0.913104	−	1.58154i	0.103450	−	0.994635i	$-0.467012\pi$
$137$	10.6876	−	18.5115i	0.913104	−	1.58154i	0.809654	−	0.586907i	$-0.199655\pi$
$138$	12.5651	−	7.25447i	1.06961	−	0.617542i
$139$	15.3517	−	8.86329i	1.30211	−	0.751775i	0.321346	−	0.946962i	$-0.395865\pi$
$139$	15.3517	−	8.86329i	1.30211	−	0.751775i	0.980766	+	0.195187i	$0.0625314\pi$
$140$	11.3573	+	28.4969i	0.959869	+	2.40843i
$141$			20.9032i			1.76037i
$142$	−6.51624			−0.546831
$143$	0.271965	−	0.471057i	0.0227429	−	0.0393918i
$144$	−18.2660	−	31.6377i	−1.52217	−	2.63647i
$145$	−2.61716	+	4.53306i	−0.217344	+	0.376450i
$146$	3.36239	+	5.82383i	0.278273	+	0.481984i
$147$	−14.6741	+	13.9053i	−1.21030	+	1.14689i
$148$	−30.9530	+	17.8707i	−2.54432	+	1.46896i
$149$	−0.329031	−	0.569899i	−0.0269553	−	0.0466879i	0.852233	−	0.523162i	$-0.175248\pi$
$149$	−0.329031	−	0.569899i	−0.0269553	−	0.0466879i	−0.879188	+	0.476474i	$0.841915\pi$
$150$			13.3136i			1.08705i
$151$	−11.2781	+	6.51141i	−0.917798	+	0.529891i	−0.882932	−	0.469501i	$-0.844434\pi$
$151$	−11.2781	+	6.51141i	−0.917798	+	0.529891i	−0.0348661	+	0.999392i	$0.511100\pi$
$152$	8.22540	−	25.7205i	0.667168	−	2.08621i
$153$			26.9547i			2.17916i
$154$	−14.6331	−	2.12704i	−1.17917	−	0.171402i
$155$	−19.6937	−	11.3701i	−1.58183	−	0.913271i
$156$	3.16789			0.253634
$157$			10.4151i			0.831215i	0.909544	+	0.415608i	$0.136431\pi$
$157$			10.4151i			0.831215i	−0.909544	+	0.415608i	$0.863569\pi$
$158$	1.27581	−	2.20977i	0.101498	−	0.175800i
$159$	18.6641	+	10.7757i	1.48016	+	0.854571i
$160$	−12.9773			−1.02595
$161$	4.86519	−	1.93900i	0.383431	−	0.152815i
$162$	7.69172	−	4.44082i	0.604318	−	0.348903i
$163$	6.05774	−	10.4923i	0.474479	−	0.821821i	−0.525094	−	0.851044i	$-0.675970\pi$
$163$	6.05774	−	10.4923i	0.474479	−	0.821821i	0.999573	+	0.0292229i	$0.00930326\pi$
$164$	0.691807	+	1.19824i	0.0540210	+	0.0935671i
$165$	−14.3799	−	8.30226i	−1.11948	−	0.646330i
$166$	4.35539	+	7.54375i	0.338044	+	0.585509i
$167$	−9.54699	−	16.5359i	−0.738768	−	1.27958i	−0.953050	−	0.302813i	$-0.902074\pi$
$167$	−9.54699	−	16.5359i	−0.738768	−	1.27958i	0.214282	−	0.976772i	$-0.431259\pi$
$168$	−17.5250	−	43.9724i	−1.35208	−	3.39255i
$169$	6.46950	−	11.2055i	0.497654	−	0.861961i
$170$	28.9626	+	16.7215i	2.22133	+	1.28248i
$171$	22.1726	+	7.09078i	1.69558	+	0.542246i
$172$	13.6657	+	23.6697i	1.04200	+	1.80480i
$173$	1.96956	+	3.41138i	0.149743	+	0.259362i	0.931132	−	0.364681i	$-0.118822\pi$
$173$	1.96956	+	3.41138i	0.149743	+	0.259362i	−0.781390	+	0.624044i	$0.785489\pi$
$174$	7.34726	−	12.7258i	0.556995	−	0.964743i
$175$	−0.691303	+	4.75587i	−0.0522576	+	0.359510i
$176$	7.53203	−	13.0459i	0.567748	−	0.983369i
$177$	−0.364742			−0.0274157
$178$	2.35010	−	1.35683i	0.176147	−	0.101699i
$179$	5.53790	−	3.19731i	0.413922	−	0.238978i	−0.278552	−	0.960421i	$-0.589854\pi$
$179$	5.53790	−	3.19731i	0.413922	−	0.238978i	0.692473	+	0.721443i	$0.256521\pi$
$180$		−	61.9219i		−	4.61538i
$181$	−3.84073	−	6.65234i	−0.285479	−	0.494464i	0.687246	−	0.726425i	$-0.258819\pi$
$181$	−3.84073	−	6.65234i	−0.285479	−	0.494464i	−0.972725	+	0.231960i	$0.925486\pi$
$182$	1.64126	+	0.238570i	0.121658	+	0.0176840i
$183$		−	14.2030i		−	1.04992i
$184$			12.2633i			0.904066i
$185$	−21.0121			−1.54484
$186$	55.2867	+	31.9198i	4.05382	+	2.34047i
$187$	−9.62570	+	5.55740i	−0.703901	+	0.406398i
$188$	−27.8374	−	16.0720i	−2.03025	−	1.17217i
$189$	16.6129	−	6.62101i	1.20841	−	0.481607i
$190$	21.3739	−	19.4254i	1.55063	−	1.40927i
$191$	6.31399	−	10.9361i	0.456864	−	0.791312i	−0.541929	−	0.840424i	$-0.682306\pi$
$191$	6.31399	−	10.9361i	0.456864	−	0.791312i	0.998793	+	0.0491124i	$0.0156393\pi$
$192$	−3.07917			−0.222220
$193$			4.41740i			0.317971i	0.987281	+	0.158986i	$0.0508223\pi$
$193$			4.41740i			0.317971i	−0.987281	+	0.158986i	$0.949178\pi$
$194$			14.7403i			1.05829i
$195$	1.61286	+	0.931188i	0.115500	+	0.0666837i
$196$	−7.23554	−	30.2333i	−0.516824	−	2.15952i
$197$	−0.105213			−0.00749610			−0.00374805	−	0.999993i	$-0.501193\pi$
$197$	−0.105213			−0.00749610			−0.00374805	+	0.999993i	$0.501193\pi$
$198$	25.8489	+	14.9239i	1.83700	+	1.06059i
$199$	8.77039	+	5.06359i	0.621716	+	0.358948i	0.777537	−	0.628837i	$-0.216469\pi$
$199$	8.77039	+	5.06359i	0.621716	+	0.358948i	−0.155821	+	0.987785i	$0.549802\pi$
$200$	−9.74537	−	5.62649i	−0.689102	−	0.397853i
$201$	−34.8671	−	20.1305i	−2.45934	−	1.41990i
$202$	−26.6532			−1.87531
$203$	3.28537	−	4.16441i	0.230588	−	0.292284i
$204$	−56.0608	−	32.3667i	−3.92504	−	2.26612i
$205$			0.813414i			0.0568113i
$206$		−	0.844493i		−	0.0588386i
$207$	−10.5717			−0.734786
$208$	−0.844798	+	1.46323i	−0.0585762	+	0.101457i
$209$	2.03928	+	9.37992i	0.141060	+	0.648823i
$210$	7.28282	−	50.1027i	0.502562	−	3.45741i
$211$	−11.0321	−	6.36941i	−0.759484	−	0.438488i	0.0696265	−	0.997573i	$-0.477819\pi$
$211$	−11.0321	−	6.36941i	−0.759484	−	0.438488i	−0.829110	+	0.559085i	$0.811153\pi$
$212$	−28.7007	+	16.5704i	−1.97117	+	1.13806i
$213$	6.42166	+	3.70755i	0.440005	+	0.254037i
$214$	−3.17309			−0.216908
$215$			16.0679i			1.09582i
$216$			41.8750i			2.84923i
$217$	18.0921	+	14.2731i	1.22817	+	0.968923i
$218$	19.2951	+	33.4201i	1.30683	+	2.26350i
$219$		−	7.65240i		−	0.517101i
$220$	22.1127	−	12.7668i	1.49084	−	0.860737i
$221$	1.07963	−	0.623322i	0.0726235	−	0.0419292i
$222$	58.9880			3.95901
$223$	−6.21205	+	10.7596i	−0.415989	+	0.720515i	−0.995532	−	0.0944272i	$-0.969898\pi$
$223$	−6.21205	+	10.7596i	−0.415989	+	0.720515i	0.579542	+	0.814942i	$0.303231\pi$
$224$	13.0141	+	1.89171i	0.869544	+	0.126395i
$225$	4.85037	−	8.40108i	0.323358	−	0.560072i
$226$	−16.5685	−	28.6974i	−1.10212	−	1.90892i
$227$	7.84851	+	13.5940i	0.520924	+	0.902267i	0.999704	+	0.0243317i	$0.00774579\pi$
$227$	7.84851	+	13.5940i	0.520924	+	0.902267i	−0.478780	+	0.877935i	$0.658921\pi$
$228$	−41.3720	+	37.6004i	−2.73993	+	2.49015i
$229$	6.77437	+	3.91119i	0.447663	+	0.258458i	0.706843	−	0.707371i	$-0.250119\pi$
$229$	6.77437	+	3.91119i	0.447663	+	0.258458i	−0.259180	+	0.965829i	$0.583452\pi$
$230$	−6.55825	+	11.3592i	−0.432438	+	0.749005i
$231$	13.2105	+	10.4220i	0.869187	+	0.685715i
$232$	6.21010	+	10.7562i	0.407713	+	0.706180i
$233$	3.57201	+	6.18690i	0.234010	+	0.405317i	0.958985	−	0.283458i	$-0.0914818\pi$
$233$	3.57201	+	6.18690i	0.234010	+	0.405317i	−0.724974	+	0.688776i	$0.758148\pi$
$234$	−2.89923	−	1.67387i	−0.189529	−	0.109424i
$235$	−9.44856	−	16.3654i	−0.616356	−	1.06756i
$236$	0.280441	−	0.485738i	0.0182551	−	0.0316188i
$237$	−2.51459	+	1.45180i	−0.163340	+	0.0943043i
$238$	−26.6072	−	20.9908i	−1.72469	−	1.36063i
$239$	−2.93282			−0.189708			−0.0948540	−	0.995491i	$-0.530238\pi$
$239$	−2.93282			−0.189708			−0.0948540	+	0.995491i	$0.530238\pi$
$240$	44.6680	+	25.7891i	2.88331	+	1.66468i
$241$	2.21251	−	3.83217i	0.142520	−	0.246852i	−0.785925	−	0.618322i	$-0.787813\pi$
$241$	2.21251	−	3.83217i	0.142520	−	0.246852i	0.928445	+	0.371470i	$0.121146\pi$
$242$		−	15.6093i		−	1.00340i
$243$	10.1714			0.652499
$244$	18.9146	+	10.9203i	1.21088	+	0.699104i
$245$	5.20313	−	17.5195i	0.332416	−	1.11928i
$246$		−	2.28353i		−	0.145592i
$247$	−0.228727	−	1.05206i	−0.0145535	−	0.0669409i
$248$	−46.7298	+	26.9795i	−2.96735	+	1.71320i
$249$		−	9.91234i		−	0.628169i
$250$	10.5472	+	18.2684i	0.667066	+	1.15539i
$251$	−20.5141	+	11.8438i	−1.29484	+	0.747577i	−0.979508	−	0.201405i	$-0.935449\pi$
$251$	−20.5141	+	11.8438i	−1.29484	+	0.747577i	−0.315332	+	0.948981i	$0.602116\pi$
$252$	−9.02635	+	62.0975i	−0.568607	+	3.91177i
$253$	−2.17963	−	3.77524i	−0.137032	−	0.237347i
$254$	0.800590	−	1.38666i	0.0502335	−	0.0870070i
$255$	−19.0281	−	32.9577i	−1.19159	−	2.06389i
$256$	14.9824	−	25.9503i	0.936400	−	1.62189i
$257$	−7.92773			−0.494518			−0.247259	−	0.968949i	$-0.579530\pi$
$257$	−7.92773			−0.494518			−0.247259	+	0.968949i	$0.579530\pi$
$258$		−	45.1081i		−	2.80831i
$259$	21.0717	+	3.06293i	1.30933	+	0.190321i
$260$	−2.48018	+	1.43193i	−0.153814	+	0.0888047i
$261$	−9.27248	+	5.35347i	−0.573952	+	0.331372i
$262$	−11.2704	+	19.5209i	−0.696288	+	1.20601i
$263$	−26.1748			−1.61401			−0.807004	−	0.590547i	$-0.798912\pi$
$263$	−26.1748			−1.61401			−0.807004	+	0.590547i	$0.798912\pi$
$264$	−34.1212	+	19.6999i	−2.10002	+	1.21245i
$265$	−19.4831			−1.19684
$266$	−24.2662	+	16.3648i	−1.48785	+	1.00339i
$267$	−3.08798			−0.188981
$268$	53.6168	−	30.9557i	3.27517	−	1.89092i
$269$	20.7334			1.26414			0.632069	−	0.774912i	$-0.282206\pi$
$269$	20.7334			1.26414			0.632069	+	0.774912i	$0.282206\pi$
$270$	−22.3941	+	38.7878i	−1.36286	+	2.36055i
$271$	25.2186	−	14.5600i	1.53192	−	0.884454i	0.532647	−	0.846338i	$-0.321198\pi$
$271$	25.2186	−	14.5600i	1.53192	−	0.884454i	0.999273	−	0.0381165i	$-0.0121358\pi$
$272$	29.9001	−	17.2628i	1.81296	−	1.04671i
$273$	−1.48170	−	1.16894i	−0.0896765	−	0.0707472i
$274$		−	54.2485i		−	3.27727i
$275$	4.00011			0.241216
$276$	12.6944	−	21.9873i	0.764110	−	1.32348i
$277$	15.7026	+	27.1977i	0.943479	+	1.63415i	0.758768	+	0.651361i	$0.225802\pi$
$277$	15.7026	+	27.1977i	0.943479	+	1.63415i	0.184711	+	0.982793i	$0.440865\pi$
$278$	22.4943	−	38.9612i	1.34912	−	2.33674i
$279$	−23.2579	−	40.2838i	−1.39241	−	2.41173i
$280$	33.5967	+	26.5050i	2.00779	+	1.58398i
$281$	−10.0752	+	5.81695i	−0.601039	+	0.347010i	−0.769450	−	0.638707i	$-0.779470\pi$
$281$	−10.0752	+	5.81695i	−0.601039	+	0.347010i	0.168411	+	0.985717i	$0.446136\pi$
$282$	26.5253	+	45.9432i	1.57956	+	2.73588i
$283$		−	8.23294i		−	0.489397i	−0.969599	−	0.244699i	$-0.921311\pi$
$283$		−	8.23294i		−	0.489397i	0.969599	−	0.244699i	$-0.0786890\pi$
$284$	−9.87490	+	5.70127i	−0.585967	+	0.338308i
$285$	−32.1162	+	6.98233i	−1.90240	+	0.413598i
$286$		−	1.38045i		−	0.0816276i
$287$	0.118571	−	0.815721i	0.00699905	−	0.0481505i
$288$	−22.9890	−	13.2727i	−1.35464	−	0.782103i
$289$	−8.47425			−0.498485
$290$			13.2843i			0.780080i
$291$	8.38678	−	14.5263i	0.491642	−	0.851549i
$292$	10.1909	+	5.88373i	0.596378	+	0.344319i
$293$	−12.9455			−0.756284			−0.378142	−	0.925748i	$-0.623437\pi$
$293$	−12.9455			−0.756284			−0.378142	+	0.925748i	$0.623437\pi$
$294$	−14.6069	+	49.1832i	−0.851894	+	2.86842i
$295$	0.285561	−	0.164869i	0.0166260	−	0.00959903i
$296$	−24.9291	+	43.1784i	−1.44897	+	2.50970i
$297$	−7.44269	−	12.8911i	−0.431868	−	0.748018i
$298$	−1.44635	−	0.835053i	−0.0837851	−	0.0483733i
$299$	0.244469	+	0.423433i	0.0141380	+	0.0244878i
$300$	11.6485	+	20.1758i	0.672526	+	1.16485i
$301$	2.34222	−	16.1135i	0.135004	−	0.928767i
$302$	−16.5254	+	28.6228i	−0.950930	+	1.64706i
$303$	26.2663	+	15.1649i	1.50896	+	0.871200i
$304$	−6.33455	−	29.1366i	−0.363312	−	1.67110i
$305$	6.41998	+	11.1197i	0.367607	+	0.636714i
$306$	34.2043	+	59.2436i	1.95533	+	3.38673i
$307$	9.82767	−	17.0220i	0.560895	−	0.971498i	−0.436524	−	0.899693i	$-0.643791\pi$
$307$	9.82767	−	17.0220i	0.560895	−	0.971498i	0.997419	−	0.0718057i	$-0.0228762\pi$
$308$	−24.0365	+	9.57962i	−1.36960	+	0.545850i
$309$	−0.480492	+	0.832236i	−0.0273342	+	0.0473442i
$310$	−57.7129			−3.27787
$311$	−16.2475	+	9.38048i	−0.921309	+	0.531918i	−0.884052	−	0.467388i	$-0.845195\pi$
$311$	−16.2475	+	9.38048i	−0.921309	+	0.531918i	−0.0372566	+	0.999306i	$0.511862\pi$
$312$	3.82706	−	2.20956i	0.216665	−	0.125091i
$313$		−	18.6317i		−	1.05313i	−0.850135	−	0.526564i	$-0.823480\pi$
$313$		−	18.6317i		−	1.05313i	0.850135	−	0.526564i	$-0.176520\pi$
$314$	13.2163	+	22.8913i	0.745840	+	1.29183i
$315$	−22.8489	+	28.9624i	−1.28739	+	1.63184i
$316$		−	4.46500i		−	0.251176i
$317$		−	24.2635i		−	1.36277i	−0.731923	−	0.681387i	$-0.761377\pi$
$317$		−	24.2635i		−	1.36277i	0.731923	−	0.681387i	$-0.238623\pi$
$318$	54.6958			3.06719
$319$	−3.82352	−	2.20751i	−0.214076	−	0.123597i
$320$	2.41072	−	1.39183i	0.134763	−	0.0778056i
$321$	3.12703	+	1.80539i	0.174534	+	0.100767i
$322$	8.23269	−	10.4354i	0.458790	−	0.581545i
$323$	−6.70134	+	20.9548i	−0.372872	+	1.16596i
$324$	7.77083	−	13.4595i	0.431713	−	0.747749i
$325$	−0.448656			−0.0248869
$326$		−	30.7480i		−	1.70298i
$327$		−	43.9134i		−	2.42842i
$328$	1.67151	+	0.965049i	0.0922939	+	0.0532859i
$329$	7.08977	+	17.7891i	0.390872	+	0.980746i
$330$	−42.1409			−2.31978
$331$	7.92329	+	4.57452i	0.435504	+	0.251438i	0.701688	−	0.712484i	$-0.252430\pi$
$331$	7.92329	+	4.57452i	0.435504	+	0.251438i	−0.266185	+	0.963922i	$0.585763\pi$
$332$	13.2006	+	7.62134i	0.724475	+	0.418276i
$333$	−37.2224	−	21.4903i	−2.03977	−	1.17766i
$334$	−41.9666	−	24.2294i	−2.29631	−	1.32578i
$335$	36.3972			1.98859
$336$	−41.0354	−	32.3735i	−2.23867	−	1.76612i
$337$	29.5881	+	17.0827i	1.61177	+	0.930554i	0.988961	+	0.148177i	$0.0473404\pi$
$337$	29.5881	+	17.0827i	1.61177	+	0.930554i	0.622805	+	0.782377i	$0.285993\pi$
$338$		−	32.8381i		−	1.78615i
$339$			37.7078i			2.04801i
$340$	58.5209			3.17374
$341$	9.59043	−	16.6111i	0.519351	−	0.899542i
$342$	57.7309	−	12.5512i	3.12173	−	0.678692i
$343$	−7.77170	+	16.8107i	−0.419633	+	0.907694i
$344$	33.0186	+	19.0633i	1.78024	+	1.02782i
$345$	12.9261	−	7.46290i	0.695919	−	0.401789i
$346$	8.65778	+	4.99857i	0.465445	+	0.268725i
$347$	5.59015			0.300095			0.150047	−	0.988679i	$-0.452057\pi$
$347$	5.59015			0.300095			0.150047	+	0.988679i	$0.452057\pi$
$348$		−	25.7134i		−	1.37839i
$349$		−	15.2618i		−	0.816947i	−0.912770	−	0.408474i	$-0.866061\pi$
$349$		−	15.2618i		−	0.816947i	0.912770	−	0.408474i	$-0.133939\pi$
$350$	4.51558	+	11.3302i	0.241368	+	0.605622i
$351$	0.834777	+	1.44588i	0.0445571	+	0.0771752i
$352$		−	10.9461i		−	0.583427i
$353$	3.30845	−	1.91013i	0.176091	−	0.101666i	−0.409364	−	0.912371i	$-0.634249\pi$
$353$	3.30845	−	1.91013i	0.176091	−	0.101666i	0.585455	+	0.810705i	$0.300916\pi$
$354$	−0.801666	+	0.462842i	−0.0426081	+	0.0245998i
$355$	−6.70346			−0.355783
$356$	2.37427	−	4.11236i	0.125836	−	0.217954i
$357$	14.2778	+	35.8249i	0.755664	+	1.89605i
$358$	8.11449	−	14.0547i	0.428864	−	0.742814i
$359$	2.00206	+	3.46767i	0.105665	+	0.183016i	0.914010	−	0.405693i	$-0.132970\pi$
$359$	2.00206	+	3.46767i	0.105665	+	0.183016i	−0.808345	+	0.588709i	$0.799636\pi$
$360$	−43.1896	−	74.8065i	−2.27629	−	3.94265i
$361$	15.4742	+	11.0249i	0.814434	+	0.580256i
$362$	−16.8831	−	9.74744i	−0.887354	−	0.512314i
$363$	−8.88122	+	15.3827i	−0.466143	+	0.807384i
$364$	2.69595	−	1.07446i	0.141306	−	0.0563169i
$365$	3.45899	+	5.99115i	0.181052	+	0.313591i
$366$	−18.0231	−	31.2168i	−0.942080	−	1.63173i
$367$	−22.9445	−	13.2470i	−1.19769	−	0.691487i	−0.237652	−	0.971350i	$-0.576378\pi$
$367$	−22.9445	−	13.2470i	−1.19769	−	0.691487i	−0.960040	+	0.279863i	$0.909711\pi$
$368$	6.77054	+	11.7269i	0.352939	+	0.611308i
$369$	−0.831929	+	1.44094i	−0.0433085	+	0.0750125i
$370$	−46.1824	+	26.6634i	−2.40091	+	1.38616i
$371$	19.5384	+	2.84006i	1.01438	+	0.147448i
$372$	111.711			5.79193
$373$	−15.7308	−	9.08219i	−0.814511	−	0.470258i	0.0340092	−	0.999422i	$-0.489172\pi$
$373$	−15.7308	−	9.08219i	−0.814511	−	0.470258i	−0.848520	+	0.529164i	$0.822506\pi$
$374$	−14.1042	+	24.4292i	−0.729311	+	1.26320i
$375$		−	24.0043i		−	1.23957i
$376$	−44.8398			−2.31243
$377$	0.428849	+	0.247596i	0.0220869	+	0.0127519i
$378$	28.1117	−	35.6334i	1.44591	−	1.83278i
$379$			37.9127i			1.94745i	0.227734	+	0.973723i	$0.426868\pi$
$379$			37.9127i			1.94745i	−0.227734	+	0.973723i	$0.573132\pi$
$380$	15.3947	−	48.1385i	0.789732	−	2.46946i
$381$	−1.57794	+	0.911024i	−0.0808403	+	0.0466732i
$382$		−	32.0487i		−	1.63975i
$383$	8.78815	+	15.2215i	0.449053	+	0.777783i	0.998325	−	0.0578610i	$-0.0184280\pi$
$383$	8.78815	+	15.2215i	0.449053	+	0.777783i	−0.549271	+	0.835644i	$0.685095\pi$
$384$	−31.6313	+	18.2623i	−1.61418	+	0.931946i
$385$	−15.0535	−	2.18815i	−0.767200	−	0.111518i
$386$	5.60549	+	9.70899i	0.285312	+	0.494175i
$387$	−16.4337	+	28.4640i	−0.835370	+	1.44690i
$388$	12.8968	+	22.3378i	0.654734	+	1.13403i
$389$	−1.31189	+	2.27227i	−0.0665156	+	0.115208i	−0.897365	−	0.441288i	$-0.854522\pi$
$389$	−1.31189	+	2.27227i	−0.0665156	+	0.115208i	0.830850	+	0.556497i	$0.187855\pi$
$390$	4.72655			0.239338
$391$		−	9.99110i		−	0.505271i
$392$	−29.8284	−	31.4775i	−1.50656	−	1.58986i
$393$	22.2136	−	12.8250i	1.12053	−	0.646938i
$394$	−0.231247	+	0.133511i	−0.0116501	+	0.00672617i
$395$	1.31247	−	2.27326i	0.0660374	−	0.114380i
$396$	52.2295			2.62463
$397$	−2.11522	+	1.22122i	−0.106160	+	0.0612914i	−0.552140	−	0.833751i	$-0.686189\pi$
$397$	−2.11522	+	1.22122i	−0.106160	+	0.0612914i	0.445980	+	0.895043i	$0.352855\pi$
$398$	25.7019			1.28832
$399$	33.2250	−	2.32056i	1.66333	−	0.116173i
$400$	−12.4254			−0.621272
$401$	−21.9832	+	12.6920i	−1.09779	+	0.633810i	−0.935640	−	0.352956i	$-0.885176\pi$
$401$	−21.9832	+	12.6920i	−1.09779	+	0.633810i	−0.162151	+	0.986766i	$0.551843\pi$
$402$	−102.179			−5.09623
$403$	−1.07567	+	1.86311i	−0.0535829	+	0.0928083i
$404$	−40.3910	+	23.3198i	−2.00953	+	1.16020i
$405$	7.91271	−	4.56840i	0.393186	−	0.227006i
$406$	1.93645	−	13.3220i	0.0961044	−	0.661157i
$407$		−	17.7232i		−	0.878504i
$408$	−90.3012			−4.47058
$409$	−14.3063	+	24.7792i	−0.707401	+	1.22525i	0.258418	+	0.966033i	$0.416799\pi$
$409$	−14.3063	+	24.7792i	−0.707401	+	1.22525i	−0.965818	+	0.259220i	$0.916534\pi$
$410$	1.03219	+	1.78780i	0.0509761	+	0.0882932i
$411$	−30.8658	+	53.4611i	−1.52250	+	2.63704i
$412$	−0.738875	−	1.27977i	−0.0364018	−	0.0630497i
$413$	−0.310404	+	0.123710i	−0.0152740	+	0.00608737i
$414$	−23.2356	+	13.4151i	−1.14197	+	0.659315i
$415$	4.48052	+	7.76049i	0.219940	+	0.380948i
$416$			1.22772i			0.0601938i
$417$	−44.3356	+	25.5972i	−2.17112	+	1.25350i
$418$	16.3848	+	18.0284i	0.801409	+	0.881796i
$419$		−	0.148869i		−	0.00727271i	−0.999993	−	0.00363636i	$-0.998843\pi$
$419$		−	0.148869i		−	0.00727271i	0.999993	−	0.00363636i	$-0.00115749\pi$
$420$	−32.7999	−	82.2990i	−1.60047	−	4.01578i
$421$	13.7501	+	7.93863i	0.670139	+	0.386905i	0.796129	−	0.605127i	$-0.206877\pi$
$421$	13.7501	+	7.93863i	0.670139	+	0.386905i	−0.125990	+	0.992031i	$0.540211\pi$
$422$	−32.3300			−1.57380
$423$		−	38.6545i		−	1.87945i
$424$	−23.1151	+	40.0366i	−1.12257	+	1.94435i
$425$	7.93967	+	4.58397i	0.385131	+	0.222355i
$426$	18.8189			0.911778
$427$	−4.81726	−	12.0871i	−0.233124	−	0.584936i
$428$	−4.80859	+	2.77624i	−0.232432	+	0.134195i
$429$	−0.785434	+	1.36041i	−0.0379211	+	0.0656813i
$430$	20.3895	+	35.3157i	0.983270	+	1.70307i
$431$	28.3530	+	16.3696i	1.36571	+	0.788496i	0.990377	−	0.138393i	$-0.0441936\pi$
$431$	28.3530	+	16.3696i	1.36571	+	0.788496i	0.375337	+	0.926888i	$0.377527\pi$
$432$	23.1190	+	40.0433i	1.11231	+	1.92658i
$433$	−2.03932	−	3.53221i	−0.0980035	−	0.169747i	0.812855	−	0.582467i	$-0.197912\pi$
$433$	−2.03932	−	3.53221i	−0.0980035	−	0.169747i	−0.910858	+	0.412720i	$0.864579\pi$
$434$	57.8765	+	8.41281i	2.77816	+	0.403828i
$435$	7.55836	−	13.0915i	0.362396	−	0.627687i
$436$	58.4808	+	33.7639i	2.80072	+	1.61700i
$437$	−8.21854	−	2.62829i	−0.393146	−	0.125728i
$438$	−9.71057	−	16.8192i	−0.463989	−	0.803652i
$439$	−2.07614	−	3.59598i	−0.0990888	−	0.171627i	0.812219	−	0.583353i	$-0.198259\pi$
$439$	−2.07614	−	3.59598i	−0.0990888	−	0.171627i	−0.911308	+	0.411726i	$0.864926\pi$
$440$	17.8093	−	30.8466i	0.849024	−	1.47055i
$441$	27.1355	−	25.7138i	1.29217	−	1.22447i
$442$	1.58194	−	2.74000i	0.0752451	−	0.130328i
$443$	−35.7204			−1.69713			−0.848564	−	0.529092i	$-0.822532\pi$
$443$	−35.7204			−1.69713			−0.848564	+	0.529092i	$0.822532\pi$
$444$	89.3920	−	51.6105i	4.24236	−	2.44933i
$445$	2.41762	−	1.39581i	0.114606	−	0.0661679i
$446$			31.5313i			1.49305i
$447$	0.950241	+	1.64587i	0.0449448	+	0.0778467i
$448$	−2.62044	+	1.04437i	−0.123804	+	0.0493416i
$449$		−	22.7762i		−	1.07487i	−0.843304	−	0.537437i	$-0.819393\pi$
$449$		−	22.7762i		−	1.07487i	0.843304	−	0.537437i	$-0.180607\pi$
$450$		−	24.6196i		−	1.16058i
$451$	−0.686095			−0.0323069
$452$	−50.2166	−	28.9926i	−2.36199	−	1.36370i
$453$	32.5711	−	18.8049i	1.53032	−	0.883532i
$454$	34.5005	+	19.9188i	1.61919	+	0.934838i
$455$	1.68842	+	0.245424i	0.0791542	+	0.0115057i
$456$	−23.7549	+	74.2806i	−1.11243	+	3.47851i
$457$	15.3124	−	26.5219i	0.716286	−	1.24064i	−0.246176	−	0.969225i	$-0.579174\pi$
$457$	15.3124	−	26.5219i	0.716286	−	1.24064i	0.962462	−	0.271418i	$-0.0874927\pi$
$458$	19.8525			0.927647
$459$		−	34.1161i		−	1.59240i
$460$			22.9521i			1.07015i
$461$	12.5677	+	7.25597i	0.585337	+	0.337944i	0.763251	−	0.646102i	$-0.223602\pi$
$461$	12.5677	+	7.25597i	0.585337	+	0.337944i	−0.177915	+	0.984046i	$0.556935\pi$
$462$	42.2604	+	6.14288i	1.96613	+	0.285792i
$463$	6.60021			0.306738			0.153369	−	0.988169i	$-0.450988\pi$
$463$	6.60021			0.306738			0.153369	+	0.988169i	$0.450988\pi$
$464$	11.8769	+	6.85714i	0.551372	+	0.318335i
$465$	56.8752	+	32.8369i	2.63752	+	1.52277i
$466$	15.7018	+	9.06545i	0.727373	+	0.419949i
$467$	9.00219	+	5.19741i	0.416571	+	0.240508i	0.693609	−	0.720351i	$-0.256019\pi$
$467$	9.00219	+	5.19741i	0.416571	+	0.240508i	−0.277038	+	0.960859i	$0.589353\pi$
$468$	−5.85810			−0.270791
$469$	−36.5004	−	5.30562i	−1.68543	−	0.244991i
$470$	−41.5340	−	23.9796i	−1.91582	−	1.10610i
$471$		−	30.0788i		−	1.38596i
$472$		−	0.782412i		−	0.0360135i
$473$	−13.5529			−0.623163
$474$	−3.68454	+	6.38180i	−0.169236	+	0.293126i
$475$	5.85935	−	5.32519i	0.268845	−	0.244337i
$476$	−58.6869	−	8.53060i	−2.68991	−	0.390999i
$477$	−34.5139	−	19.9266i	−1.58028	−	0.912377i
$478$	−6.44603	+	3.72162i	−0.294835	+	0.170223i
$479$	−32.4077	−	18.7106i	−1.48075	−	0.854909i	−0.480984	−	0.876729i	$-0.659721\pi$
$479$	−32.4077	−	18.7106i	−1.48075	−	0.854909i	−0.999762	+	0.0218202i	$0.993054\pi$
$480$	37.4785			1.71065
$481$			1.98784i			0.0906378i
$482$		−	11.2303i		−	0.511526i
$483$	−14.0507	+	5.59983i	−0.639327	+	0.254801i
$484$	−13.6571	−	23.6548i	−0.620776	−	1.07522i
$485$			15.1638i			0.688552i
$486$	22.3558	−	12.9071i	1.01408	−	0.585479i
$487$	14.9711	−	8.64355i	0.678404	−	0.391677i	−0.120849	−	0.992671i	$-0.538562\pi$
$487$	14.9711	−	8.64355i	0.678404	−	0.391677i	0.799253	+	0.600994i	$0.205228\pi$
$488$	30.4671			1.37918
$489$	−17.4947	+	30.3017i	−0.791139	+	1.37029i
$490$	−10.7956	−	45.1086i	−0.487693	−	2.03780i
$491$	−1.00627	+	1.74292i	−0.0454125	+	0.0786567i	−0.887838	−	0.460156i	$-0.847794\pi$
$491$	−1.00627	+	1.74292i	−0.0454125	+	0.0786567i	0.842426	+	0.538813i	$0.181127\pi$
$492$	−1.99793	−	3.46052i	−0.0900738	−	0.156012i
$493$	−5.05944	−	8.76321i	−0.227866	−	0.394675i
$494$	−1.83774	−	2.02207i	−0.0826837	−	0.0909774i
$495$	26.5916	+	15.3527i	1.19520	+	0.690050i
$496$	−29.7905	+	51.5986i	−1.33763	+	2.31685i
$497$	6.72247	+	0.977164i	0.301544	+	0.0438318i
$498$	−12.5783	−	21.7863i	−0.563649	−	0.976269i
$499$	18.1647	+	31.4622i	0.813164	+	1.40844i	0.910639	+	0.413203i	$0.135590\pi$
$499$	18.1647	+	31.4622i	0.813164	+	1.40844i	−0.0974751	+	0.995238i	$0.531077\pi$
$500$	31.9672	+	18.4563i	1.42962	+	0.825389i
$501$	27.5717	+	47.7555i	1.23181	+	2.13356i
$502$	−30.0587	+	52.0631i	−1.34158	+	2.32369i
$503$	33.1053	−	19.1133i	1.47609	−	0.852222i	0.476455	−	0.879199i	$-0.341922\pi$
$503$	33.1053	−	19.1133i	1.47609	−	0.852222i	0.999636	+	0.0269773i	$0.00858817\pi$
$504$	32.4075	+	81.3144i	1.44354	+	3.62203i
$505$	−27.4190			−1.22013
$506$	−9.58123	−	5.53173i	−0.425938	−	0.245915i
$507$	−18.6839	+	32.3614i	−0.829780	+	1.43722i
$508$		−	2.80185i		−	0.124312i
$509$	25.3821			1.12504			0.562522	−	0.826782i	$-0.309831\pi$
$509$	25.3821			1.12504			0.562522	+	0.826782i	$0.309831\pi$
$510$	−83.6438	−	48.2918i	−3.70381	−	2.13840i
$511$	−2.59547	−	6.51236i	−0.114817	−	0.288090i
$512$		−	50.7539i		−	2.24303i
$513$	−28.0634	−	8.97469i	−1.23903	−	0.396242i
$514$	−17.4243	+	10.0599i	−0.768554	+	0.443725i
$515$		−	0.868757i		−	0.0382820i
$516$	−39.4666	−	68.3581i	−1.73742	−	3.00930i
$517$	13.8038	−	7.96963i	0.607090	−	0.350504i
$518$	50.2001	−	20.0070i	2.20566	−	0.879058i
$519$	−5.68808	−	9.85204i	−0.249679	−	0.432457i
$520$	−1.99750	+	3.45977i	−0.0875963	+	0.151721i
$521$	10.2308	+	17.7203i	0.448220	+	0.776340i	0.998270	−	0.0587919i	$-0.0187249\pi$
$521$	10.2308	+	17.7203i	0.448220	+	0.776340i	−0.550050	+	0.835131i	$0.685392\pi$
$522$	−13.5867	+	23.5328i	−0.594672	+	1.03000i
$523$	21.8931			0.957319			0.478659	−	0.878001i	$-0.341123\pi$
$523$	21.8931			0.957319			0.478659	+	0.878001i	$0.341123\pi$
$524$			39.4434i			1.72309i
$525$	1.99648	−	13.7349i	0.0871335	−	0.599442i
$526$	−57.5295	+	33.2147i	−2.50841	+	1.44823i
$527$	38.0713	−	21.9805i	1.65841	−	0.957485i
$528$	−21.7525	+	37.6764i	−0.946655	+	1.63965i
$529$	−19.0815			−0.829628
$530$	−42.8220	+	24.7233i	−1.86007	+	1.07391i
$531$	0.674486			0.0292702
$532$	−22.4555	+	46.0310i	−0.973570	+	1.99570i
$533$	0.0769529			0.00333320
$534$	−6.78707	+	3.91852i	−0.293705	+	0.169571i
$535$	−3.26425			−0.141126
$536$	43.1822	−	74.7938i	1.86519	−	3.23060i
$537$	−15.9934	+	9.23380i	−0.690167	+	0.398468i
$538$	45.5699	−	26.3098i	1.96466	−	1.13430i
$539$	14.7773	+	4.38871i	0.636502	+	0.189035i
$540$			78.3735i			3.37266i
$541$	−20.3292			−0.874021			−0.437010	−	0.899456i	$-0.643963\pi$
$541$	−20.3292			−0.874021			−0.437010	+	0.899456i	$0.643963\pi$
$542$	36.9519	−	64.0026i	1.58722	−	2.74915i
$543$	11.0920	+	19.2119i	0.476004	+	0.824463i
$544$	12.5438	−	21.7264i	0.537809	−	0.931513i
$545$	19.8495	+	34.3803i	0.850259	+	1.47269i
$546$	−4.73995	−	0.688989i	−0.202851	−	0.0294860i
$547$	36.4975	−	21.0719i	1.56052	−	0.900968i	0.563318	−	0.826240i	$-0.309524\pi$
$547$	36.4975	−	21.0719i	1.56052	−	0.900968i	0.997204	−	0.0747282i	$-0.0238089\pi$
$548$	−47.4638	−	82.2096i	−2.02755	−	3.51182i
$549$			26.2644i			1.12094i
$550$	8.79184	−	5.07597i	0.374885	−	0.216440i
$551$	−8.53946	+	1.85655i	−0.363793	+	0.0790918i
$552$		−	35.4165i		−	1.50743i
$553$	−1.64756	+	2.08839i	−0.0700614	+	0.0888073i
$554$	69.0255	+	39.8519i	2.93261	+	1.69315i
$555$	60.6827			2.57584
$556$		−	78.7239i		−	3.33864i
$557$	−19.1941	+	33.2451i	−0.813280	+	1.40864i	0.0972770	+	0.995257i	$0.468987\pi$
$557$	−19.1941	+	33.2451i	−0.813280	+	1.40864i	−0.910557	+	0.413384i	$0.864347\pi$
$558$	−102.237	−	59.0265i	−4.32803	−	2.49879i
$559$	1.52010			0.0642935
$560$	46.7604	+	6.79699i	1.97599	+	0.287225i
$561$	27.7990	−	16.0498i	1.17367	−	0.677621i
$562$	−14.7629	+	25.5701i	−0.622736	+	1.07861i
$563$	17.3957	+	30.1302i	0.733141	+	1.26984i	0.955534	+	0.294881i	$0.0952799\pi$
$563$	17.3957	+	30.1302i	0.733141	+	1.26984i	−0.222393	+	0.974957i	$0.571387\pi$
$564$	80.3944	+	46.4157i	3.38521	+	1.95445i
$565$	−17.0445	−	29.5219i	−0.717067	−	1.24200i
$566$	−10.4472	−	18.0952i	−0.439130	−	0.760596i
$567$	−8.60109	+	3.42792i	−0.361212	+	0.143959i
$568$	−7.95310	+	13.7752i	−0.333705	+	0.577994i
$569$	−17.2965	−	9.98611i	−0.725105	−	0.418640i	0.0915238	−	0.995803i	$-0.470826\pi$
$569$	−17.2965	−	9.98611i	−0.725105	−	0.418640i	−0.816629	+	0.577163i	$0.804160\pi$
$570$	−61.7278	+	56.1005i	−2.58549	+	2.34979i
$571$	−13.3996	−	23.2087i	−0.560754	−	0.971255i	−0.997431	−	0.0716361i	$-0.977178\pi$
$571$	−13.3996	−	23.2087i	−0.560754	−	0.971255i	0.436677	−	0.899619i	$-0.356155\pi$
$572$	−1.20780	−	2.09197i	−0.0505006	−	0.0874697i
$573$	−18.2348	+	31.5835i	−0.761768	+	1.31942i
$574$	−0.774507	−	1.94333i	−0.0323273	−	0.0811132i
$575$	−1.79785	+	3.11397i	−0.0749756	+	0.129861i
$576$	5.69404			0.237252
$577$	−21.2116	+	12.2465i	−0.883049	+	0.509828i	−0.871662	−	0.490107i	$-0.836958\pi$
$577$	−21.2116	+	12.2465i	−0.883049	+	0.509828i	−0.0113864	+	0.999935i	$0.503624\pi$
$578$	−18.6255	+	10.7535i	−0.774720	+	0.447285i
$579$		−	12.7574i		−	0.530180i
$580$	11.6229	+	20.1314i	0.482613	+	0.835910i
$581$	−3.36198	−	8.43563i	−0.139479	−	0.349969i
$582$		−	42.5699i		−	1.76458i
$583$		−	16.4335i		−	0.680608i
$584$	16.4153			0.679268
$585$	−2.98253	−	1.72196i	−0.123312	−	0.0711945i
$586$	−28.4529	+	16.4273i	−1.17538	+	0.678605i
$587$	−18.7495	−	10.8250i	−0.773873	−	0.446796i	0.0603815	−	0.998175i	$-0.480768\pi$
$587$	−18.7495	−	10.8250i	−0.773873	−	0.446796i	−0.834254	+	0.551380i	$0.814102\pi$
$588$	20.8962	+	87.3137i	0.861745	+	3.60075i
$589$	−8.06570	−	37.0992i	−0.332341	−	1.52865i
$590$	0.418423	−	0.724729i	0.0172262	−	0.0298366i
$591$	0.303854			0.0124989
$592$			55.0530i			2.26266i
$593$			10.9543i			0.449838i	0.974377	+	0.224919i	$0.0722118\pi$
$593$			10.9543i			0.449838i	−0.974377	+	0.224919i	$0.927788\pi$
$594$	−32.7165	−	18.8889i	−1.34238	−	0.775021i
$595$	−27.3717	−	21.5939i	−1.12213	−	0.885265i
$596$	−2.92246			−0.119709
$597$	−25.3288	−	14.6236i	−1.03664	−	0.598505i
$598$	1.07464	+	0.620442i	0.0439452	+	0.0253718i
$599$	−36.2775	−	20.9448i	−1.48226	−	0.855783i	−0.482462	−	0.875917i	$-0.660257\pi$
$599$	−36.2775	−	20.9448i	−1.48226	−	0.855783i	−0.999797	+	0.0201341i	$0.993591\pi$
$600$	28.1446	+	16.2493i	1.14900	+	0.663374i
$601$	−30.4715			−1.24296			−0.621478	−	0.783431i	$-0.713468\pi$
$601$	−30.4715			−1.24296			−0.621478	+	0.783431i	$0.713468\pi$
$602$	−15.2994	−	38.3880i	−0.623556	−	1.56458i
$603$	64.4767	+	37.2256i	2.62569	+	1.51595i
$604$			57.8345i			2.35325i
$605$		−	16.0578i		−	0.652841i
$606$	76.9743			3.12687
$607$	2.40590	−	4.16715i	0.0976526	−	0.169139i	−0.813060	−	0.582180i	$-0.802200\pi$
$607$	2.40590	−	4.16715i	0.0976526	−	0.169139i	0.910713	+	0.413041i	$0.135533\pi$
$608$	−14.5721	−	16.0337i	−0.590975	−	0.650254i
$609$	−9.48814	+	12.0268i	−0.384479	+	0.487351i
$610$	28.2209	+	16.2934i	1.14263	+	0.659699i
$611$	−1.54824	+	0.893879i	−0.0626352	+	0.0361625i
$612$	103.668	+	59.8530i	4.19055	+	2.41941i
$613$	−2.79892			−0.113047			−0.0565237	−	0.998401i	$-0.518002\pi$
$613$	−2.79892			−0.113047			−0.0565237	+	0.998401i	$0.518002\pi$
$614$		−	49.8836i		−	2.01314i
$615$		−	2.34914i		−	0.0947263i
$616$	−22.3563	+	28.3380i	−0.900761	+	1.14177i
$617$	−6.16097	−	10.6711i	−0.248031	−	0.429603i	0.714948	−	0.699177i	$-0.246450\pi$
$617$	−6.16097	−	10.6711i	−0.248031	−	0.429603i	−0.962980	+	0.269575i	$0.913117\pi$
$618$			2.43889i			0.0981067i
$619$	21.6664	−	12.5091i	0.870845	−	0.502782i	0.00321575	−	0.999995i	$-0.498976\pi$
$619$	21.6664	−	12.5091i	0.870845	−	0.502782i	0.867629	+	0.497212i	$0.165643\pi$
$620$	−87.4597	+	50.4949i	−3.51247	+	2.02792i
$621$	13.3805			0.536939
$622$	−23.8068	+	41.2347i	−0.954568	+	1.65336i
$623$	−2.62794	+	1.04736i	−0.105286	+	0.0419614i
$624$	2.43977	−	4.22581i	0.0976691	−	0.169168i
$625$	15.3914	+	26.6586i	0.615655	+	1.06635i
$626$	−23.6429	−	40.9507i	−0.944960	−	1.63672i
$627$	−5.88942	−	27.0892i	−0.235201	−	1.08184i
$628$	40.0567	+	23.1268i	1.59844	+	0.922859i
$629$	20.3100	−	35.1780i	0.809814	−	1.40264i
$630$	−13.4675	+	92.6505i	−0.536557	+	3.69129i
$631$	14.4464	+	25.0219i	0.575103	+	0.996107i	0.996030	+	0.0890131i	$0.0283713\pi$
$631$	14.4464	+	25.0219i	0.575103	+	0.996107i	−0.420928	+	0.907094i	$0.638295\pi$
$632$	−3.11427	−	5.39407i	−0.123879	−	0.214565i
$633$	31.8608	+	18.3948i	1.26635	+	0.731129i
$634$	−30.7893	−	53.3287i	−1.22280	−	2.11795i
$635$	0.823592	−	1.42650i	0.0326833	−	0.0566091i
$636$	82.8875	−	47.8551i	3.28670	−	1.89758i
$637$	−1.65743	−	0.492241i	−0.0656697	−	0.0195033i
$638$	−11.2050			−0.443609
$639$	−11.8750	−	6.85604i	−0.469768	−	0.271221i
$640$	16.5097	−	28.5956i	0.652602	−	1.13034i
$641$			20.2826i			0.801113i	0.916272	+	0.400557i	$0.131183\pi$
$641$			20.2826i			0.801113i	−0.916272	+	0.400557i	$0.868817\pi$
$642$	9.16386			0.361669
$643$	−6.68151	−	3.85757i	−0.263493	−	0.152128i	0.362434	−	0.932009i	$-0.381946\pi$
$643$	−6.68151	−	3.85757i	−0.263493	−	0.152128i	−0.625927	+	0.779882i	$0.715279\pi$
$644$	3.34573	−	23.0172i	0.131840	−	0.907006i
$645$		−	46.4041i		−	1.82716i
$646$	11.8619	+	54.5602i	0.466699	+	2.14664i
$647$	−6.03713	+	3.48554i	−0.237344	+	0.137031i	−0.613955	−	0.789341i	$-0.710423\pi$
$647$	−6.03713	+	3.48554i	−0.237344	+	0.137031i	0.376611	+	0.926371i	$0.377089\pi$
$648$		−	21.6801i		−	0.851677i
$649$	0.139063	+	0.240864i	0.00545869	+	0.00945472i
$650$	−0.986099	+	0.569325i	−0.0386780	+	0.0223308i
$651$	−52.2498	−	41.2207i	−2.04783	−	1.61557i
$652$	−26.9025	−	46.5965i	−1.05358	−	1.82486i
$653$	−0.144616	+	0.250482i	−0.00565926	+	0.00980212i	−0.868841	−	0.495091i	$-0.835135\pi$
$653$	−0.144616	+	0.250482i	−0.00565926	+	0.00980212i	0.863182	+	0.504893i	$0.168468\pi$
$654$	−55.7242	−	96.5172i	−2.17899	−	3.77412i
$655$	−11.5942	+	20.0818i	−0.453023	+	0.784659i
$656$	2.13120			0.0832093
$657$			14.1509i			0.552080i
$658$	38.1562	+	30.1021i	1.48748	+	1.17350i
$659$	−16.8010	+	9.70006i	−0.654474	+	0.377861i	−0.790168	−	0.612890i	$-0.790007\pi$
$659$	−16.8010	+	9.70006i	−0.654474	+	0.377861i	0.135694	+	0.990751i	$0.456674\pi$
$660$	−63.8615	+	36.8704i	−2.48580	+	1.43518i
$661$	−21.7555	+	37.6816i	−0.846189	+	1.46564i	0.0383950	+	0.999263i	$0.487775\pi$
$661$	−21.7555	+	37.6816i	−0.846189	+	1.46564i	−0.884584	+	0.466380i	$0.845558\pi$
$662$	23.2195			0.902450
$663$	−3.11795	+	1.80015i	−0.121091	+	0.0699121i
$664$	21.2631			0.825168
$665$	−24.9634	+	16.8350i	−0.968038	+	0.652833i
$666$	−109.081			−4.22681
$667$	3.43697	−	1.98433i	0.133080	−	0.0768337i
$668$	−84.7966			−3.28088
$669$	17.9404	−	31.0736i	0.693615	−	1.20138i
$670$	79.9973	−	46.1864i	3.09056	−	1.78434i
$671$	−9.37922	+	5.41509i	−0.362081	+	0.209047i
$672$	−37.5848	−	5.46324i	−1.44986	−	0.210749i
$673$			11.3747i			0.438462i	0.975673	+	0.219231i	$0.0703548\pi$
$673$			11.3747i			0.438462i	−0.975673	+	0.219231i	$0.929645\pi$
$674$	86.7088			3.33990
$675$	−6.13903	+	10.6331i	−0.236291	+	0.409269i
$676$	−28.7311	−	49.7637i	−1.10504	−	1.91399i
$677$	5.85059	−	10.1335i	0.224856	−	0.389463i	−0.731420	−	0.681927i	$-0.761142\pi$
$677$	5.85059	−	10.1335i	0.224856	−	0.389463i	0.956276	+	0.292465i	$0.0944754\pi$
$678$	47.8496	+	82.8780i	1.83765	+	3.18291i
$679$	2.21043	−	15.2068i	0.0848283	−	0.583583i
$680$	70.6979	−	40.8175i	2.71114	−	1.56528i
$681$	−22.6665	−	39.2595i	−0.868581	−	1.50443i
$682$		−	48.6794i		−	1.86403i
$683$	8.44959	−	4.87837i	0.323315	−	0.186666i	−0.329554	−	0.944137i	$-0.606899\pi$
$683$	8.44959	−	4.87837i	0.323315	−	0.186666i	0.652869	+	0.757471i	$0.273565\pi$
$684$	76.5056	−	69.5311i	2.92527	−	2.65859i
$685$		−	55.8071i		−	2.13228i
$686$	4.25068	+	46.8102i	0.162292	+	1.78722i
$687$	−19.5644	−	11.2955i	−0.746427	−	0.430950i
$688$	42.0990			1.60501
$689$			1.84320i			0.0702203i
$690$	18.9402	−	32.8054i	0.721041	−	1.24888i
$691$	0.853727	+	0.492899i	0.0324773	+	0.0187508i	0.516151	−	0.856498i	$-0.327364\pi$
$691$	0.853727	+	0.492899i	0.0324773	+	0.0187508i	−0.483673	+	0.875249i	$0.660698\pi$
$692$	17.4937			0.665009
$693$	−24.4290	−	19.2724i	−0.927982	−	0.732100i
$694$	12.2866	−	7.09366i	0.466392	−	0.269272i
$695$	23.1406	−	40.0806i	0.877772	−	1.52035i
$696$	−17.9347	−	31.0639i	−0.679815	−	1.17747i
$697$	−1.36180	−	0.786237i	−0.0515820	−	0.0297809i
$698$	−19.3666	−	33.5440i	−0.733037	−	1.26966i
$699$	−10.3159	−	17.8677i	−0.390185	−	0.675820i
$700$	16.7562	+	13.2192i	0.633323	+	0.499639i
$701$	7.32326	−	12.6843i	0.276596	−	0.479078i	−0.693941	−	0.720032i	$-0.744127\pi$
$701$	7.32326	−	12.6843i	0.276596	−	0.479078i	0.970536	+	0.240954i	$0.0774604\pi$
$702$	3.66951	+	2.11859i	0.138497	+	0.0799611i
$703$	−23.5941	−	25.9608i	−0.889870	−	0.979130i
$704$	1.17397	+	2.03338i	0.0442458	+	0.0766359i
$705$	27.2874	+	47.2632i	1.02770	+	1.78003i
$706$	4.84775	−	8.39655i	0.182448	−	0.316008i
$707$	27.4967	+	3.99687i	1.03412	+	0.150318i
$708$	−0.809911	+	1.40281i	−0.0304383	+	0.0527207i
$709$	2.22737			0.0836506			0.0418253	−	0.999125i	$-0.486683\pi$
$709$	2.22737			0.0836506			0.0418253	+	0.999125i	$0.486683\pi$
$710$	−14.7335	+	8.50640i	−0.552939	+	0.319240i
$711$	4.65000	−	2.68468i	0.174389	−	0.100683i
$712$		−	6.62407i		−	0.248247i
$713$	8.62083	+	14.9317i	0.322853	+	0.559197i
$714$	76.8415	+	60.6215i	2.87572	+	2.26870i
$715$		−	1.42011i		−	0.0531091i
$716$		−	28.3985i		−	1.06130i
$717$	8.46996			0.316316
$718$	8.80064	+	5.08105i	0.328437	+	0.189623i
$719$	−37.8287	+	21.8404i	−1.41077	+	0.814511i	−0.995461	−	0.0951679i	$-0.969661\pi$
$719$	−37.8287	+	21.8404i	−1.41077	+	0.814511i	−0.415313	+	0.909679i	$0.636328\pi$
$720$	−82.6007	−	47.6895i	−3.07835	−	1.77728i
$721$	−0.126639	+	0.871220i	−0.00471627	+	0.0324459i
$722$	48.0009	+	4.59537i	1.78641	+	0.171022i
$723$	−6.38971	+	11.0673i	−0.237636	+	0.411597i
$724$	−34.1134			−1.26782
$725$			3.64169i			0.135249i
$726$			45.0796i			1.67306i
$727$	22.8290	+	13.1803i	0.846681	+	0.488832i	0.859530	−	0.511086i	$-0.170757\pi$
$727$	22.8290	+	13.1803i	0.846681	+	0.488832i	−0.0128485	+	0.999917i	$0.504090\pi$
$728$	2.50750	−	3.17841i	0.0929341	−	0.117800i
$729$	−39.8738			−1.47681
$730$	15.2050	+	8.77863i	0.562764	+	0.324912i
$731$	−26.9006	−	15.5311i	−0.994956	−	0.574438i
$732$	−54.6253	−	31.5379i	−2.01901	−	1.16568i
$733$	10.2430	+	5.91383i	0.378336	+	0.218432i	0.677094	−	0.735897i	$-0.263239\pi$
$733$	10.2430	+	5.91383i	0.378336	+	0.218432i	−0.298758	+	0.954329i	$0.596572\pi$
$734$	−67.2395			−2.48185
$735$	−15.0266	+	50.5963i	−0.554265	+	1.86627i
$736$	8.52118	+	4.91971i	0.314095	+	0.181343i
$737$			30.7001i			1.13085i
$738$			4.22273i			0.155441i
$739$	20.3134			0.747240			0.373620	−	0.927582i	$-0.378116\pi$
$739$	20.3134			0.747240			0.373620	+	0.927582i	$0.378116\pi$
$740$	−46.6574	+	80.8130i	−1.71516	+	2.97074i
$741$	0.660562	+	3.03834i	0.0242664	+	0.111616i
$742$	46.5473	−	18.5512i	1.70881	−	0.681037i
$743$	19.2461	+	11.1117i	0.706069	+	0.407649i	0.809604	−	0.586977i	$-0.199682\pi$
$743$	19.2461	+	11.1117i	0.706069	+	0.407649i	−0.103535	+	0.994626i	$0.533015\pi$
$744$	134.955	−	77.9166i	4.94771	−	2.85656i
$745$	−1.48791	−	0.859045i	−0.0545128	−	0.0314730i
$746$	−46.0996			−1.68783
$747$			18.3300i			0.670661i
$748$			49.3610i			1.80482i
$749$	3.27351	+	0.475830i	0.119611	+	0.0173865i
$750$	−30.4604	−	52.7589i	−1.11226	−	1.92648i
$751$			53.4254i			1.94952i	0.223255	+	0.974760i	$0.428332\pi$
$751$			53.4254i			1.94952i	−0.223255	+	0.974760i	$0.571668\pi$
$752$	−42.8784	+	24.7558i	−1.56361	+	0.902753i
$753$	59.2447	−	34.2050i	2.15900	−	1.24650i
$754$	1.25676			0.0457684
$755$	−17.0002	+	29.4452i	−0.618700	+	1.07162i
$756$	11.4245	−	78.5957i	0.415505	−	2.85850i
$757$	−9.69268	+	16.7882i	−0.352286	+	0.610178i	−0.986650	−	0.162857i	$-0.947929\pi$
$757$	−9.69268	+	16.7882i	−0.352286	+	0.610178i	0.634363	+	0.773035i	$0.281262\pi$
$758$	48.1096	+	83.3283i	1.74742	+	3.02662i
$759$	6.29477	+	10.9029i	0.228486	+	0.395749i
$760$	−14.9779	−	68.8927i	−0.543305	−	2.49900i
$761$	−34.7871	−	20.0843i	−1.26103	−	0.728057i	−0.287757	−	0.957703i	$-0.592910\pi$
$761$	−34.7871	−	20.0843i	−1.26103	−	0.728057i	−0.973274	+	0.229647i	$0.926243\pi$
$762$	−2.31210	+	4.00468i	−0.0837586	+	0.145074i
$763$	−14.8942	−	37.3713i	−0.539205	−	1.35293i
$764$	−28.0405	−	48.5675i	−1.01447	−	1.75711i
$765$	35.1871	+	60.9458i	1.27219	+	2.20350i
$766$	38.6309	+	22.3036i	1.39579	+	0.805860i
$767$	−0.0155974	−	0.0270154i	−0.000563188	−	0.000975471i
$768$	−43.2691	+	74.9442i	−1.56134	+	2.70432i
$769$	21.2368	−	12.2610i	0.765817	−	0.442145i	−0.0655634	−	0.997848i	$-0.520884\pi$
$769$	21.2368	−	12.2610i	0.765817	−	0.442145i	0.831380	+	0.555704i	$0.187551\pi$
$770$	−35.8628	+	14.2930i	−1.29241	+	0.515083i
$771$	22.8952			0.824552
$772$	16.9894	+	9.80885i	0.611463	+	0.353028i
$773$	17.6099	−	30.5012i	0.633382	−	1.09705i	−0.353473	−	0.935445i	$-0.614999\pi$
$773$	17.6099	−	30.5012i	0.633382	−	1.09705i	0.986855	−	0.161606i	$-0.0516673\pi$
$774$			83.4145i			2.99827i
$775$	−15.8211			−0.568312
$776$	31.1606	+	17.9906i	1.11860	+	0.645824i
$777$	−60.8548	−	8.84572i	−2.18316	−	0.317339i
$778$			6.65895i			0.238735i
$779$	−1.00499	+	0.913371i	−0.0360075	+	0.0327249i
$780$	7.16275	−	4.13541i	0.256467	−	0.148072i
$781$		−	5.65420i		−	0.202323i
$782$	−12.6783	−	21.9594i	−0.453374	−	0.785267i
$783$	11.7360	−	6.77580i	0.419412	−	0.242147i
$784$	−45.9022	−	13.6325i	−1.63937	−	0.486876i
$785$	13.5960	+	23.5490i	0.485263	+	0.840500i
$786$	32.5489	−	56.3763i	1.16098	−	2.01088i
$787$	14.5794	+	25.2523i	0.519700	+	0.900147i	0.999738	+	0.0228989i	$0.00728960\pi$
$787$	14.5794	+	25.2523i	0.519700	+	0.900147i	−0.480038	+	0.877248i	$0.659377\pi$
$788$	−0.233626	+	0.404651i	−0.00832257	+	0.0144151i
$789$	75.5927			2.69117
$790$		−	6.66186i		−	0.237018i
$791$	12.7894	+	32.0902i	0.454739	+	1.14100i
$792$	63.0974	−	36.4293i	2.24207	−	1.29446i
$793$	1.05198	−	0.607361i	0.0373569	−	0.0215680i
$794$	−3.09936	+	5.36825i	−0.109992	+	0.190512i
$795$	56.2672			1.99559
$796$	38.9494	−	22.4874i	1.38052	−	0.797046i
$797$	−6.52802			−0.231234			−0.115617	−	0.993294i	$-0.536885\pi$
$797$	−6.52802			−0.231234			−0.115617	+	0.993294i	$0.536885\pi$
$798$	70.0806	−	47.2615i	2.48083	−	1.67304i
$799$	36.5315			1.29239
$800$	−7.81913	+	4.51438i	−0.276448	+	0.159607i
$801$	5.71034			0.201765
$802$	−32.2113	+	55.7916i	−1.13742	+	1.97007i
$803$	−5.05339	+	2.91758i	−0.178330	+	0.102959i
$804$	−154.845	+	89.3999i	−5.46097	+	3.15289i
$805$	8.46922	−	10.7353i	0.298501	−	0.378369i
$806$			5.45991i			0.192317i
$807$	−59.8780			−2.10781
$808$	−32.5304	+	56.3443i	−1.14441	+	1.98218i
$809$	−12.4188	−	21.5101i	−0.436623	−	0.756254i	0.560803	−	0.827949i	$-0.310492\pi$
$809$	−12.4188	−	21.5101i	−0.436623	−	0.756254i	−0.997427	+	0.0716954i	$0.977159\pi$
$810$	11.5942	−	20.0818i	0.407379	−	0.705602i
$811$	−9.72639	−	16.8466i	−0.341540	−	0.591564i	0.643179	−	0.765716i	$-0.277615\pi$
$811$	−9.72639	−	16.8466i	−0.341540	−	0.591564i	−0.984719	+	0.174152i	$0.944282\pi$
$812$	−8.72126	−	21.8827i	−0.306056	−	0.767933i
$813$	−72.8312	+	42.0491i	−2.55430	+	1.47473i
$814$	−22.4899	−	38.9537i	−0.788271	−	1.36533i
$815$		−	31.6315i		−	1.10800i
$816$	−86.3513	+	49.8549i	−3.02290	+	1.74527i
$817$	−19.8522	+	18.0424i	−0.694542	+	0.631225i
$818$			72.6163i			2.53897i
$819$	2.73998	+	2.16161i	0.0957426	+	0.0755328i
$820$	3.12841	+	1.80619i	0.109249	+	0.0630749i
$821$	−9.52572			−0.332450			−0.166225	−	0.986088i	$-0.553158\pi$
$821$	−9.52572			−0.332450			−0.166225	+	0.986088i	$0.553158\pi$
$822$			156.669i			5.46447i
$823$	−9.23375	+	15.9933i	−0.321868	+	0.557492i	−0.980874	−	0.194646i	$-0.937644\pi$
$823$	−9.23375	+	15.9933i	−0.321868	+	0.557492i	0.659005	+	0.752138i	$0.270978\pi$
$824$	−1.78524	−	1.03071i	−0.0621917	−	0.0359064i
$825$	−11.5523			−0.402200
$826$	−0.525253	+	0.665791i	−0.0182759	+	0.0231658i
$827$	−30.8373	+	17.8039i	−1.07232	+	0.619103i	−0.928814	−	0.370547i	$-0.879170\pi$
$827$	−30.8373	+	17.8039i	−1.07232	+	0.619103i	−0.143504	+	0.989650i	$0.545837\pi$
$828$	−23.4746	+	40.6591i	−0.815798	+	1.41300i
$829$	−13.6623	−	23.6638i	−0.474512	−	0.821878i	0.525062	−	0.851064i	$-0.324042\pi$
$829$	−13.6623	−	23.6638i	−0.474512	−	0.821878i	−0.999574	+	0.0291854i	$0.990709\pi$
$830$	19.6955	+	11.3712i	0.683640	+	0.394700i
$831$	−45.3491	−	78.5469i	−1.57314	−	2.72476i
$832$	−0.131674	−	0.228065i	−0.00456496	−	0.00790675i
$833$	24.3015	+	25.6451i	0.841998	+	0.888552i
$834$	−64.9634	+	112.520i	−2.24950	+	3.89624i
$835$	−43.1724	−	24.9256i	−1.49404	−	0.862585i
$836$	40.6037	+	12.9851i	1.40431	+	0.449097i
$837$	29.4371	+	50.9866i	1.01750	+	1.76235i
$838$	−0.188908	−	0.327198i	−0.00652572	−	0.0113029i
$839$	−14.7830	+	25.6050i	−0.510367	+	0.883982i	0.489561	+	0.871969i	$0.337157\pi$
$839$	−14.7830	+	25.6050i	−0.510367	+	0.883982i	−0.999928	+	0.0120125i	$0.996176\pi$
$840$	−97.0272	−	76.5463i	−3.34776	−	2.64110i
$841$	−12.4903	+	21.6338i	−0.430700	+	0.745993i
$842$	40.2951			1.38866
$843$	29.0973	−	16.7993i	1.00216	−	0.578599i
$844$	−48.9938	+	28.2866i	−1.68644	+	0.973665i
$845$		−	33.7815i		−	1.16212i
$846$	−49.0509	−	84.9587i	−1.68641	−	2.92094i
$847$	−2.34074	+	16.1033i	−0.0804288	+	0.553316i
$848$			51.0471i			1.75296i
$849$			23.7767i			0.816014i
$850$	23.2675			0.798067
$851$	13.7969	+	7.96567i	0.472953	+	0.273060i
$852$	28.5187	−	16.4653i	0.977033	−	0.564090i
$853$	−24.0285	−	13.8729i	−0.822720	−	0.474998i	0.0286337	−	0.999590i	$-0.490884\pi$
$853$	−24.0285	−	13.8729i	−0.822720	−	0.474998i	−0.851353	+	0.524592i	$0.824218\pi$
$854$	−25.9259	−	20.4533i	−0.887165	−	0.699899i
$855$	59.3896	−	12.9118i	2.03108	−	0.441575i
$856$	−3.87277	+	6.70783i	−0.132368	+	0.229269i
$857$	20.1931			0.689783			0.344892	−	0.938643i	$-0.387916\pi$
$857$	20.1931			0.689783			0.344892	+	0.938643i	$0.387916\pi$
$858$			3.98673i			0.136105i
$859$			5.54848i			0.189312i	0.995510	+	0.0946559i	$0.0301751\pi$
$859$			5.54848i			0.189312i	−0.995510	+	0.0946559i	$0.969825\pi$
$860$	61.7977	+	35.6789i	2.10728	+	1.21664i
$861$	−0.342434	+	2.35580i	−0.0116701	+	0.0802854i
$862$	83.0893			2.83003
$863$	14.5522	+	8.40174i	0.495364	+	0.285999i	0.726797	−	0.686852i	$-0.241008\pi$
$863$	14.5522	+	8.40174i	0.495364	+	0.285999i	−0.231433	+	0.972851i	$0.574341\pi$
$864$	29.0968	+	16.7991i	0.989895	+	0.571516i
$865$	8.90653	+	5.14219i	0.302831	+	0.174840i
$866$	−8.96444	−	5.17562i	−0.304624	−	0.175875i
$867$	24.4736			0.831167
$868$	95.0684	−	37.8891i	3.22683	−	1.28604i
$869$	1.91744	+	1.10703i	0.0650446	+	0.0375535i
$870$		−	38.3649i		−	1.30069i
$871$		−	3.44335i		−	0.116673i
$872$	94.1992			3.18999
$873$	−15.5089	+	26.8623i	−0.524898	+	0.909150i
$874$	−21.3987	+	4.65227i	−0.723822	+	0.157365i
$875$	−8.14155	−	20.4282i	−0.275235	−	0.690598i
$876$	−29.4313	−	16.9922i	−0.994393	−	0.574113i
$877$	−14.4572	+	8.34688i	−0.488186	+	0.281854i	−0.723821	−	0.689987i	$-0.757616\pi$
$877$	−14.4572	+	8.34688i	−0.488186	+	0.281854i	0.235636	+	0.971841i	$0.424283\pi$
$878$	−9.12630	−	5.26907i	−0.307998	−	0.177822i
$879$	37.3865			1.26102
$880$		−	39.3297i		−	1.32580i
$881$		−	46.9769i		−	1.58269i	−0.611368	−	0.791346i	$-0.709380\pi$
$881$		−	46.9769i		−	1.58269i	0.611368	−	0.791346i	$-0.290620\pi$
$882$	27.0113	−	90.9501i	0.909519	−	3.06245i
$883$	−9.62991	−	16.6795i	−0.324072	−	0.561310i	0.657252	−	0.753671i	$-0.271719\pi$
$883$	−9.62991	−	16.6795i	−0.324072	−	0.561310i	−0.981324	+	0.192361i	$0.938385\pi$
$884$		−	5.53636i		−	0.186208i
$885$	−0.824699	+	0.476140i	−0.0277219	+	0.0160053i
$886$	−78.5099	+	45.3277i	−2.63759	+	1.52281i
$887$	−11.6979			−0.392778			−0.196389	−	0.980526i	$-0.562922\pi$
$887$	−11.6979			−0.392778			−0.196389	+	0.980526i	$0.562922\pi$
$888$	71.9951	−	124.699i	2.41600	−	4.18463i
$889$	−1.03387	+	1.31049i	−0.0346749	+	0.0439526i
$890$	3.54245	−	6.13571i	0.118743	−	0.205669i
$891$	3.85334	+	6.67417i	0.129092	+	0.223593i
$892$	27.5878	+	47.7834i	0.923707	+	1.59991i
$893$	9.61009	−	30.0503i	0.321590	−	1.00560i
$894$	4.17706	+	2.41163i	0.139702	+	0.0806570i
$895$	8.34763	−	14.4585i	0.279030	−	0.483295i
$896$	−20.7249	+	26.2701i	−0.692370	+	0.877622i
$897$	−0.706026	−	1.22287i	−0.0235735	−	0.0408306i
$898$	−28.9020	−	50.0597i	−0.964472	−	1.67051i
$899$	15.1227	+	8.73110i	0.504371	+	0.291198i
$900$	−21.5405	−	37.3093i	−0.718018	−	1.24364i
$901$	18.8322	−	32.6183i	0.627391	−	1.08667i
$902$	−1.50797	+	0.870625i	−0.0502098	+	0.0289886i
$903$	−6.76433	+	46.5357i	−0.225103	+	1.54861i
$904$	−80.8875			−2.69028
$905$	−17.3681	−	10.0275i	−0.577336	−	0.333325i
$906$	47.7253	−	82.6626i	1.58557	−	2.74628i
$907$		−	22.6161i		−	0.750954i	−0.926832	−	0.375477i	$-0.877479\pi$
$907$		−	22.6161i		−	0.750954i	0.926832	−	0.375477i	$-0.122521\pi$
$908$	69.7106			2.31343
$909$	−48.5721	−	28.0431i	−1.61103	−	0.930131i
$910$	4.02240	−	1.60311i	0.133341	−	0.0531426i
$911$		−	45.1634i		−	1.49633i	−0.663513	−	0.748165i	$-0.730935\pi$
$911$		−	45.1634i		−	1.49633i	0.663513	−	0.748165i	$-0.269065\pi$
$912$	18.2942	+	84.1464i	0.605780	+	2.78637i
$913$	−6.54578	+	3.77921i	−0.216634	+	0.125074i
$914$		−	77.7233i		−	2.57086i
$915$	−18.5409	−	32.1137i	−0.612942	−	1.06165i
$916$	30.0851	−	17.3696i	0.994038	−	0.573908i
$917$	14.5544	−	18.4486i	0.480629	−	0.609227i
$918$	−43.2919	−	74.9837i	−1.42884	−	2.47483i
$919$	−6.39950	+	11.0843i	−0.211100	+	0.365636i	−0.952059	−	0.305914i	$-0.901038\pi$
$919$	−6.39950	+	11.0843i	−0.211100	+	0.365636i	0.740959	+	0.671550i	$0.234371\pi$
$920$	16.0088	+	27.7280i	0.527793	+	0.914165i
$921$	−28.3823	+	49.1595i	−0.935228	+	1.61986i
$922$	36.8301			1.21293
$923$			0.634179i			0.0208743i
$924$	69.4172	−	27.6659i	2.28366	−	0.910142i
$925$	−12.6602	+	7.30939i	−0.416266	+	0.240331i
$926$	14.5066	−	8.37538i	0.476716	−	0.275232i
$927$	0.888531	−	1.53898i	0.0291832	−	0.0505468i
$928$	9.96527			0.327126
$929$	30.9075	−	17.8444i	1.01404	−	0.585457i	0.101669	−	0.994818i	$-0.467582\pi$
$929$	30.9075	−	17.8444i	1.01404	−	0.585457i	0.912372	+	0.409361i	$0.134248\pi$
$930$	166.674			5.46547
$931$	27.4882	−	13.2438i	0.900889	−	0.434049i
$932$	31.7267			1.03924
$933$	46.9226	−	27.0908i	1.53618	−	0.886912i
$934$	26.3812			0.863219
$935$	−14.5094	+	25.1311i	−0.474509	+	0.821875i
$936$	−7.07705	+	4.08594i	−0.231321	+	0.133553i
$937$	34.4126	−	19.8681i	1.12421	−	0.649063i	0.181738	−	0.983347i	$-0.441828\pi$
$937$	34.4126	−	19.8681i	1.12421	−	0.649063i	0.942473	+	0.334284i	$0.108494\pi$
$938$	−86.9567	+	34.6562i	−2.83924	+	1.13157i
$939$			53.8084i			1.75597i
$940$	−83.9223			−2.73724
$941$	11.6552	−	20.1874i	0.379948	−	0.658090i	−0.611106	−	0.791549i	$-0.709275\pi$
$941$	11.6552	−	20.1874i	0.379948	−	0.658090i	0.991054	+	0.133459i	$0.0426084\pi$
$942$	−38.1687	−	66.1100i	−1.24360	−	2.15398i
$943$	0.308365	−	0.534104i	0.0100418	−	0.0173928i
$944$	−0.431967	−	0.748188i	−0.0140593	−	0.0243514i
$945$	28.9194	−	36.6572i	0.940749	−	1.19246i
$946$	−29.7879	+	17.1981i	−0.968488	+	0.559157i
$947$	15.8374	+	27.4312i	0.514646	+	0.891393i	0.999856	+	0.0169954i	$0.00541006\pi$
$947$	15.8374	+	27.4312i	0.514646	+	0.891393i	−0.485209	+	0.874398i	$0.661257\pi$
$948$			12.8949i			0.418807i
$949$	0.566792	−	0.327237i	0.0183988	−	0.0106226i
$950$	6.12081	−	19.1395i	0.198585	−	0.620967i
$951$			70.0729i			2.27227i
$952$	−76.8484	+	30.6276i	−2.49067	+	0.992646i
$953$	−20.1414	−	11.6286i	−0.652443	−	0.376688i	0.136949	−	0.990578i	$-0.456271\pi$
$953$	−20.1414	−	11.6286i	−0.652443	−	0.376688i	−0.789392	+	0.613890i	$0.789604\pi$
$954$	−101.144			−3.27466
$955$		−	32.9695i		−	1.06687i
$956$	−6.51233	+	11.2797i	−0.210624	+	0.364811i
$957$	11.0423	+	6.37529i	0.356948	+	0.206084i
$958$	−94.9718			−3.06840
$959$	−8.13500	+	55.9653i	−0.262693	+	1.80722i
$960$	−6.96214	+	4.01960i	−0.224702	+	0.129732i
$961$	−22.4318	+	38.8530i	−0.723607	+	1.25332i
$962$	2.52249	+	4.36907i	0.0813282	+	0.140865i
$963$	−5.78255	−	3.33855i	−0.186340	−	0.107583i
$964$	−9.82576	−	17.0187i	−0.316466	−	0.548136i
$965$	5.76654	+	9.98794i	0.185631	+	0.321523i
$966$	−23.7760	+	30.1375i	−0.764979	+	0.969659i
$967$	−3.02049	+	5.23165i	−0.0971325	+	0.168239i	−0.910497	−	0.413516i	$-0.864300\pi$
$967$	−3.02049	+	5.23165i	−0.0971325	+	0.168239i	0.813364	+	0.581755i	$0.197634\pi$
$968$	−32.9977	−	19.0512i	−1.06059	−	0.612329i
$969$	19.3534	−	60.5173i	0.621722	−	1.94410i
$970$	19.2422	+	33.3285i	0.617830	+	1.07011i
$971$	6.22587	+	10.7835i	0.199798	+	0.346059i	0.948463	−	0.316889i	$-0.102638\pi$
$971$	6.22587	+	10.7835i	0.199798	+	0.346059i	−0.748665	+	0.662948i	$0.769305\pi$
$972$	22.5858	−	39.1197i	0.724438	−	1.25476i
$973$	−29.0487	+	36.8211i	−0.931260	+	1.18043i
$974$	21.9366	−	37.9953i	0.702894	−	1.21745i
$975$	1.29572			0.0414961
$976$	29.1344	−	16.8208i	0.932570	−	0.538420i
$977$	45.5636	−	26.3062i	1.45771	−	0.841609i	0.458811	−	0.888534i	$-0.348275\pi$
$977$	45.5636	−	26.3062i	1.45771	−	0.841609i	0.998898	+	0.0469249i	$0.0149421\pi$
$978$			88.8002i			2.83952i
$979$	1.17733	+	2.03920i	0.0376277	+	0.0651732i
$980$	−55.8269	−	58.9135i	−1.78333	−	1.88192i
$981$			81.2052i			2.59268i
$982$			5.10767i			0.162992i
$983$	−46.8713			−1.49496			−0.747482	−	0.664282i	$-0.768737\pi$
$983$	−46.8713			−1.49496			−0.747482	+	0.664282i	$0.768737\pi$
$984$	−4.82733	−	2.78706i	−0.153890	−	0.0888481i
$985$	−0.237891	+	0.137347i	−0.00757984	+	0.00437622i
$986$	−22.2403	−	12.8404i	−0.708275	−	0.408923i
$987$	−20.4752	−	51.3749i	−0.651734	−	1.63528i
$988$	−4.55414	−	1.45641i	−0.144886	−	0.0463347i
$989$	6.09135	−	10.5505i	0.193694	−	0.335487i
$990$	77.9274			2.47670
$991$			26.2880i			0.835065i	0.908662	+	0.417532i	$0.137105\pi$
$991$			26.2880i			0.835065i	−0.908662	+	0.417532i	$0.862895\pi$
$992$			43.2936i			1.37457i
$993$	−22.8824	−	13.2112i	−0.726152	−	0.419244i
$994$	16.0153	−	6.38282i	0.507974	−	0.202451i
$995$	26.4403			0.838215
$996$	−38.1231	−	22.0104i	−1.20798	−	0.697426i
$997$	47.5428	+	27.4488i	1.50570	+	0.869314i	0.999978	+	0.00661423i	$0.00210539\pi$
$997$	47.5428	+	27.4488i	1.50570	+	0.869314i	0.505717	+	0.862699i	$0.331228\pi$
$998$	79.8483	+	46.1005i	2.52756	+	1.45928i
$999$	47.1117	+	27.2000i	1.49055	+	0.860569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.s.d.103.8	yes	16
7.2	even	3		931.2.p.h.293.1		16
7.3	odd	6		133.2.i.d.122.8	yes	16
7.4	even	3		931.2.i.g.521.8		16
7.5	odd	6		931.2.p.g.293.1		16
7.6	odd	2		931.2.s.g.901.8		16
19.12	odd	6		133.2.i.d.12.1	✓	16
133.12	even	6		931.2.p.h.734.1		16
133.31	even	6	inner	133.2.s.d.31.8	yes	16
133.69	even	6		931.2.i.g.411.1		16
133.88	odd	6		931.2.s.g.31.8		16
133.107	odd	6		931.2.p.g.734.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.i.d.12.1	✓	16	19.12	odd	6
133.2.i.d.122.8	yes	16	7.3	odd	6
133.2.s.d.31.8	yes	16	133.31	even	6	inner
133.2.s.d.103.8	yes	16	1.1	even	1	trivial
931.2.i.g.411.1		16	133.69	even	6
931.2.i.g.521.8		16	7.4	even	3
931.2.p.g.293.1		16	7.5	odd	6
931.2.p.g.734.1		16	133.107	odd	6
931.2.p.h.293.1		16	7.2	even	3
931.2.p.h.734.1		16	133.12	even	6
931.2.s.g.31.8		16	133.88	odd	6
931.2.s.g.901.8		16	7.6	odd	2

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:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.19790 - 1.26896i) q^{2} -2.88800 q^{3} +(2.22050 - 3.84603i) q^{4} +(2.26105 - 1.30542i) q^{5} +(-6.34752 + 3.66474i) q^{6} +(-2.45775 + 0.979525i) q^{7} -6.19507i q^{8} +5.34052 q^{9} +O(q^{10})\)	\(q+(2.19790 - 1.26896i) q^{2} -2.88800 q^{3} +(2.22050 - 3.84603i) q^{4} +(2.26105 - 1.30542i) q^{5} +(-6.34752 + 3.66474i) q^{6} +(-2.45775 + 0.979525i) q^{7} -6.19507i q^{8} +5.34052 q^{9} +(3.31303 - 5.73834i) q^{10} +(1.10109 + 1.90714i) q^{11} +(-6.41281 + 11.1073i) q^{12} +(-0.123499 - 0.213906i) q^{13} +(-4.15891 + 5.27168i) q^{14} +(-6.52989 + 3.77003i) q^{15} +(-3.42027 - 5.92409i) q^{16} +5.04720i q^{17} +(11.7379 - 6.77689i) q^{18} +(4.15176 + 1.32773i) q^{19} -11.5947i q^{20} +(7.09797 - 2.82886i) q^{21} +(4.84015 + 2.79446i) q^{22} -1.97953 q^{23} +17.8913i q^{24} +(0.908220 - 1.57308i) q^{25} +(-0.542875 - 0.313429i) q^{26} -6.75941 q^{27} +(-1.69016 + 11.6276i) q^{28} +(-1.73625 + 1.00243i) q^{29} +(-9.56803 + 16.5723i) q^{30} +(-4.35499 - 7.54306i) q^{31} +(-4.30465 - 2.48529i) q^{32} +(-3.17993 - 5.50780i) q^{33} +(6.40468 + 11.0932i) q^{34} +(-4.27840 + 5.42314i) q^{35} +(11.8586 - 20.5398i) q^{36} +(-6.96980 - 4.02402i) q^{37} +(10.8100 - 2.35019i) q^{38} +(0.356663 + 0.617759i) q^{39} +(-8.08715 - 14.0073i) q^{40} +(-0.155777 + 0.269813i) q^{41} +(12.0109 - 15.2246i) q^{42} +(-3.07717 + 5.32981i) q^{43} +9.77987 q^{44} +(12.0752 - 6.97160i) q^{45} +(-4.35081 + 2.51194i) q^{46} -7.23797i q^{47} +(9.87774 + 17.1087i) q^{48} +(5.08106 - 4.81485i) q^{49} -4.60997i q^{50} -14.5763i q^{51} -1.09692 q^{52} +(-6.46265 - 3.73121i) q^{53} +(-14.8565 + 8.57740i) q^{54} +(4.97921 + 2.87475i) q^{55} +(6.06823 + 15.2259i) q^{56} +(-11.9903 - 3.83449i) q^{57} +(-2.54407 + 4.40646i) q^{58} +0.126296 q^{59} +33.4855i q^{60} +4.91796i q^{61} +(-19.1436 - 11.0526i) q^{62} +(-13.1257 + 5.23117i) q^{63} +1.06620 q^{64} +(-0.558472 - 0.322434i) q^{65} +(-13.9783 - 8.07039i) q^{66} +(12.0731 + 6.97042i) q^{67} +(19.4117 + 11.2073i) q^{68} +5.71688 q^{69} +(-2.52175 + 17.3486i) q^{70} +(-2.22357 - 1.28378i) q^{71} -33.0849i q^{72} +2.64973i q^{73} -20.4252 q^{74} +(-2.62294 + 4.54306i) q^{75} +(14.3255 - 13.0196i) q^{76} +(-4.57428 - 3.60872i) q^{77} +(1.56782 + 0.905181i) q^{78} +(0.870703 - 0.502701i) q^{79} +(-15.4668 - 8.92976i) q^{80} +3.49958 q^{81} +0.790697i q^{82} +3.43226i q^{83} +(4.88119 - 33.5805i) q^{84} +(6.58870 + 11.4120i) q^{85} +15.6192i q^{86} +(5.01429 - 2.89500i) q^{87} +(11.8149 - 6.82131i) q^{88} +1.06925 q^{89} +(17.6933 - 30.6457i) q^{90} +(0.513055 + 0.404757i) q^{91} +(-4.39556 + 7.61333i) q^{92} +(12.5772 + 21.7843i) q^{93} +(-9.18468 - 15.9083i) q^{94} +(11.1206 - 2.41771i) q^{95} +(12.4318 + 7.17750i) q^{96} +(-2.90401 + 5.02990i) q^{97} +(5.05781 - 17.0302i) q^{98} +(5.88037 + 10.1851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 10 q^{4} + 9 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 10 * q^4 + 9 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^9	\( 16 q - 8 q^{3} + 10 q^{4} + 9 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{9} - 2 q^{10} - 9 q^{11} - 17 q^{12} + 15 q^{13} + 3 q^{14} - 12 q^{15} - 22 q^{16} - 3 q^{18} + 8 q^{19} - 10 q^{21} - 27 q^{22} + 30 q^{23} + 13 q^{25} - 9 q^{26} - 38 q^{27} + 35 q^{28} - 18 q^{29} - 32 q^{30} - 27 q^{31} + 27 q^{32} - 12 q^{33} - 16 q^{34} - 6 q^{35} + 4 q^{36} - 39 q^{37} + 27 q^{38} - 9 q^{39} + 9 q^{40} + 9 q^{41} + 48 q^{42} - 9 q^{43} + 18 q^{44} + 75 q^{45} - 36 q^{46} + 35 q^{48} - 8 q^{49} + 18 q^{53} - 18 q^{54} + 15 q^{56} - 22 q^{57} - 20 q^{58} + 18 q^{59} - 45 q^{62} - 46 q^{63} - 22 q^{64} - 36 q^{65} - 45 q^{66} + 18 q^{67} + 63 q^{68} + 30 q^{69} - 19 q^{70} - 9 q^{71} + 18 q^{74} + 10 q^{75} + 98 q^{76} + 30 q^{77} + 54 q^{78} + 21 q^{79} + 27 q^{80} + 40 q^{81} - 34 q^{84} + 31 q^{85} - 48 q^{87} + 18 q^{88} + 24 q^{89} + 28 q^{90} + 15 q^{91} + 54 q^{92} + 6 q^{93} - 49 q^{94} - 66 q^{95} - 69 q^{96} + q^{97} + 15 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 10 * q^4 + 9 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^9 - 2 * q^10 - 9 * q^11 - 17 * q^12 + 15 * q^13 + 3 * q^14 - 12 * q^15 - 22 * q^16 - 3 * q^18 + 8 * q^19 - 10 * q^21 - 27 * q^22 + 30 * q^23 + 13 * q^25 - 9 * q^26 - 38 * q^27 + 35 * q^28 - 18 * q^29 - 32 * q^30 - 27 * q^31 + 27 * q^32 - 12 * q^33 - 16 * q^34 - 6 * q^35 + 4 * q^36 - 39 * q^37 + 27 * q^38 - 9 * q^39 + 9 * q^40 + 9 * q^41 + 48 * q^42 - 9 * q^43 + 18 * q^44 + 75 * q^45 - 36 * q^46 + 35 * q^48 - 8 * q^49 + 18 * q^53 - 18 * q^54 + 15 * q^56 - 22 * q^57 - 20 * q^58 + 18 * q^59 - 45 * q^62 - 46 * q^63 - 22 * q^64 - 36 * q^65 - 45 * q^66 + 18 * q^67 + 63 * q^68 + 30 * q^69 - 19 * q^70 - 9 * q^71 + 18 * q^74 + 10 * q^75 + 98 * q^76 + 30 * q^77 + 54 * q^78 + 21 * q^79 + 27 * q^80 + 40 * q^81 - 34 * q^84 + 31 * q^85 - 48 * q^87 + 18 * q^88 + 24 * q^89 + 28 * q^90 + 15 * q^91 + 54 * q^92 + 6 * q^93 - 49 * q^94 - 66 * q^95 - 69 * q^96 + q^97 + 15 * q^98 + 18 * q^99

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