LMFDB - Embedded newform 110.3.l.a.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,3,Mod(3,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([15, 16]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("110.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	110.l (of order $20$, degree $8$, 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:	$2.99728290796$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			53.4
Character	$\chi$	$=$	110.53
Dual form			110.3.l.a.27.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.642040 - 1.26007i) q^{2} +(-0.0541671 - 0.00857923i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(-1.39544 + 4.80133i) q^{5} +(0.0239670 + 0.0737628i) q^{6} +(-9.88997 + 1.56642i) q^{7} +(2.79360 + 0.442463i) q^{8} +(-8.55665 - 2.78022i) q^{9} +(6.94595 - 1.32429i) q^{10} +(0.380217 + 10.9934i) q^{11} +(0.0775588 - 0.0775588i) q^{12} +(1.29498 - 0.659823i) q^{13} +(8.32355 + 11.4564i) q^{14} +(0.116779 - 0.248102i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(-0.376311 - 0.191740i) q^{17} +(1.99042 + 12.5670i) q^{18} +(18.9077 + 26.0242i) q^{19} +(-6.12828 - 7.90217i) q^{20} +0.549150 q^{21} +(13.6084 - 7.53732i) q^{22} +(-20.6006 - 20.6006i) q^{23} +(-0.147526 - 0.0479340i) q^{24} +(-21.1055 - 13.3999i) q^{25} +(-1.66285 - 1.20813i) q^{26} +(0.879421 + 0.448087i) q^{27} +(9.09184 - 17.8437i) q^{28} +(22.6761 - 31.2110i) q^{29} +(-0.387604 + 0.0121420i) q^{30} +(-11.3535 + 34.9426i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(0.0737199 - 0.598744i) q^{33} +0.597284i q^{34} +(6.27995 - 49.6708i) q^{35} +(14.5574 - 10.5766i) q^{36} +(-26.0461 + 4.12530i) q^{37} +(20.6529 - 40.5337i) q^{38} +(-0.0758059 + 0.0246308i) q^{39} +(-6.02271 + 12.7956i) q^{40} +(-18.5293 + 13.4623i) q^{41} +(-0.352576 - 0.691969i) q^{42} +(8.47188 + 8.47188i) q^{43} +(-18.2347 - 12.3083i) q^{44} +(25.2890 - 37.2037i) q^{45} +(-12.7319 + 39.1847i) q^{46} +(6.02588 - 38.0459i) q^{47} +(0.0343169 + 0.216669i) q^{48} +(48.7561 - 15.8418i) q^{49} +(-3.33430 + 35.1978i) q^{50} +(0.0187387 + 0.0136145i) q^{51} +(-0.454719 + 2.87098i) q^{52} +(69.5736 - 35.4495i) q^{53} -1.39582i q^{54} +(-53.3136 - 13.5151i) q^{55} -28.3217 q^{56} +(-0.800909 - 1.57187i) q^{57} +(-53.8872 - 8.53489i) q^{58} +(-67.8245 + 93.3524i) q^{59} +(0.264157 + 0.480614i) q^{60} +(19.5547 + 60.1832i) q^{61} +(51.3196 - 8.12823i) q^{62} +(88.9800 + 14.0930i) q^{63} +(7.60845 + 2.47214i) q^{64} +(1.36097 + 7.13834i) q^{65} +(-0.801793 + 0.291525i) q^{66} +(-49.6777 + 49.6777i) q^{67} +(0.752622 - 0.383480i) q^{68} +(0.939138 + 1.29261i) q^{69} +(-66.6209 + 23.9774i) q^{70} +(0.774125 + 2.38251i) q^{71} +(-22.6737 - 11.5528i) q^{72} +(15.3798 + 97.1040i) q^{73} +(21.9208 + 30.1714i) q^{74} +(1.02826 + 0.906904i) q^{75} -64.3354 q^{76} +(-20.9806 - 108.129i) q^{77} +(0.0797070 + 0.0797070i) q^{78} +(83.9580 + 27.2796i) q^{79} +(19.9902 - 0.626209i) q^{80} +(65.4647 + 47.5629i) q^{81} +(28.8600 + 14.7049i) q^{82} +(-37.1761 + 72.9621i) q^{83} +(-0.645564 + 0.888543i) q^{84} +(1.44573 - 1.53923i) q^{85} +(5.23591 - 16.1145i) q^{86} +(-1.49607 + 1.49607i) q^{87} +(-3.80201 + 30.8795i) q^{88} -104.283i q^{89} +(-63.1159 - 7.97983i) q^{90} +(-11.7737 + 8.55410i) q^{91} +(57.5499 - 9.11501i) q^{92} +(0.914769 - 1.79534i) q^{93} +(-51.8095 + 16.8339i) q^{94} +(-151.335 + 54.4669i) q^{95} +(0.250985 - 0.182352i) q^{96} +(-27.0800 - 53.1476i) q^{97} +(-51.2652 - 51.2652i) q^{98} +(27.3108 - 95.1240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} + 2 q^{3} + 4 q^{5} + 4 q^{6} + 38 q^{7} + 24 q^{8} + 36 q^{10} + 80 q^{11} - 16 q^{12} - 16 q^{13} + 38 q^{15} + 48 q^{16} - 18 q^{17} - 44 q^{18} + 4 q^{20} + 24 q^{21} + 64 q^{23} + 70 q^{25}+ \cdots - 440 q^{98}+O(q^{100}) $ 48 * q - 12 * q^2 + 2 * q^3 + 4 * q^5 + 4 * q^6 + 38 * q^7 + 24 * q^8 + 36 * q^10 + 80 * q^11 - 16 * q^12 - 16 * q^13 + 38 * q^15 + 48 * q^16 - 18 * q^17 - 44 * q^18 + 4 * q^20 + 24 * q^21 + 64 * q^23 + 70 * q^25 + 8 * q^26 - 82 * q^27 + 64 * q^28 - 14 * q^30 - 116 * q^31 - 192 * q^32 - 312 * q^33 - 288 * q^35 - 88 * q^36 + 22 * q^37 - 72 * q^38 - 24 * q^40 - 196 * q^41 - 96 * q^42 - 484 * q^43 - 56 * q^45 - 132 * q^46 - 310 * q^47 - 8 * q^48 - 128 * q^50 + 256 * q^51 + 8 * q^52 - 82 * q^53 - 264 * q^55 + 48 * q^56 + 744 * q^57 + 168 * q^58 + 196 * q^60 + 528 * q^61 + 144 * q^62 + 814 * q^63 + 840 * q^65 + 436 * q^66 + 192 * q^67 + 36 * q^68 + 230 * q^70 - 292 * q^71 - 48 * q^72 - 108 * q^73 + 258 * q^75 + 96 * q^76 - 200 * q^77 + 88 * q^78 + 24 * q^80 + 628 * q^81 + 24 * q^82 + 360 * q^83 - 368 * q^85 + 532 * q^86 - 328 * q^87 - 40 * q^88 - 766 * q^90 + 72 * q^91 + 68 * q^92 - 66 * q^93 - 232 * q^95 - 16 * q^96 + 6 * q^97 - 440 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.642040	−	1.26007i	−0.321020	−	0.630037i
$2$	−0.642040	−	1.26007i	−0.321020	−	0.630037i
$3$	−0.0541671	−	0.00857923i	−0.0180557	−	0.00285974i	0.147400	−	0.989077i	$-0.452910\pi$
$3$	−0.0541671	−	0.00857923i	−0.0180557	−	0.00285974i	−0.165456	+	0.986217i	$0.552910\pi$
$4$	−1.17557	+	1.61803i	−0.293893	+	0.404508i
$5$	−1.39544	+	4.80133i	−0.279087	+	0.960266i
$5$	−1.39544	+	4.80133i	−0.279087	+	0.960266i
$6$	0.0239670	+	0.0737628i	0.00399450	+	0.0122938i
$7$	−9.88997	+	1.56642i	−1.41285	+	0.223774i	−0.815756	−	0.578396i	$-0.803679\pi$
$7$	−9.88997	+	1.56642i	−1.41285	+	0.223774i	−0.597096	+	0.802169i	$0.703679\pi$
$8$	2.79360	+	0.442463i	0.349201	+	0.0553079i
$9$	−8.55665	−	2.78022i	−0.950739	−	0.308914i
$10$	6.94595	−	1.32429i	0.694595	−	0.132429i
$11$	0.380217	+	10.9934i	0.0345652	+	0.999402i
$11$	0.380217	+	10.9934i	0.0345652	+	0.999402i
$12$	0.0775588	−	0.0775588i	0.00646323	−	0.00646323i
$13$	1.29498	−	0.659823i	0.0996135	−	0.0507556i	−0.403474	−	0.914991i	$-0.632197\pi$
$13$	1.29498	−	0.659823i	0.0996135	−	0.0507556i	0.503087	+	0.864236i	$0.332197\pi$
$14$	8.32355	+	11.4564i	0.594539	+	0.818313i
$15$	0.116779	−	0.248102i	0.00778524	−	0.0165402i
$16$	−1.23607	−	3.80423i	−0.0772542	−	0.237764i
$17$	−0.376311	−	0.191740i	−0.0221359	−	0.0112788i	0.442888	−	0.896577i	$-0.353954\pi$
$17$	−0.376311	−	0.191740i	−0.0221359	−	0.0112788i	−0.465023	+	0.885298i	$0.653954\pi$
$18$	1.99042	+	12.5670i	0.110579	+	0.698168i
$19$	18.9077	+	26.0242i	0.995143	+	1.36970i	0.928259	+	0.371936i	$0.121306\pi$
$19$	18.9077	+	26.0242i	0.995143	+	1.36970i	0.0668842	+	0.997761i	$0.478694\pi$
$20$	−6.12828	−	7.90217i	−0.306414	−	0.395108i
$21$	0.549150			0.0261500
$22$	13.6084	−	7.53732i	0.618564	−	0.342605i
$23$	−20.6006	−	20.6006i	−0.895678	−	0.895678i	0.0993721	−	0.995050i	$-0.468317\pi$
$23$	−20.6006	−	20.6006i	−0.895678	−	0.895678i	−0.995050	+	0.0993721i	$0.968317\pi$
$24$	−0.147526	−	0.0479340i	−0.00614690	−	0.00199725i
$25$	−21.1055	−	13.3999i	−0.844220	−	0.535996i
$26$	−1.66285	−	1.20813i	−0.0639558	−	0.0464666i
$27$	0.879421	+	0.448087i	0.0325711	+	0.0165958i
$28$	9.09184	−	17.8437i	0.324709	−	0.637276i
$29$	22.6761	−	31.2110i	0.781936	−	1.07624i	−0.213130	−	0.977024i	$-0.568366\pi$
$29$	22.6761	−	31.2110i	0.781936	−	1.07624i	0.995066	−	0.0992182i	$-0.0316342\pi$
$30$	−0.387604	+	0.0121420i	−0.0129201	+	0.000404733i
$31$	−11.3535	+	34.9426i	−0.366243	+	1.12718i	0.582956	+	0.812504i	$0.301896\pi$
$31$	−11.3535	+	34.9426i	−0.366243	+	1.12718i	−0.949199	+	0.314676i	$0.898104\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	0.0737199	−	0.598744i	0.00223394	−	0.0181438i
$34$			0.597284i			0.0175672i
$35$	6.27995	−	49.6708i	0.179427	−	1.41917i
$36$	14.5574	−	10.5766i	0.404373	−	0.293794i
$37$	−26.0461	+	4.12530i	−0.703949	+	0.111495i	−0.498139	−	0.867097i	$-0.665983\pi$
$37$	−26.0461	+	4.12530i	−0.703949	+	0.111495i	−0.205810	+	0.978592i	$0.565983\pi$
$38$	20.6529	−	40.5337i	0.543499	−	1.06668i
$39$	−0.0758059	+	0.0246308i	−0.00194374	+	0.000631559i
$40$	−6.02271	+	12.7956i	−0.150568	+	0.319890i
$41$	−18.5293	+	13.4623i	−0.451934	+	0.328349i	−0.790359	−	0.612644i	$-0.790106\pi$
$41$	−18.5293	+	13.4623i	−0.451934	+	0.328349i	0.338425	+	0.940993i	$0.390106\pi$
$42$	−0.352576	−	0.691969i	−0.00839467	−	0.0164755i
$43$	8.47188	+	8.47188i	0.197020	+	0.197020i	0.798721	−	0.601701i	$-0.205510\pi$
$43$	8.47188	+	8.47188i	0.197020	+	0.197020i	−0.601701	+	0.798721i	$0.705510\pi$
$44$	−18.2347	−	12.3083i	−0.414425	−	0.279735i
$45$	25.2890	−	37.2037i	0.561979	−	0.826748i
$46$	−12.7319	+	39.1847i	−0.276780	+	0.851841i
$47$	6.02588	−	38.0459i	0.128210	−	0.809488i	−0.836845	−	0.547440i	$-0.815602\pi$
$47$	6.02588	−	38.0459i	0.128210	−	0.809488i	0.965055	−	0.262047i	$-0.0843977\pi$
$48$	0.0343169	+	0.216669i	0.000714936	+	0.00451393i
$49$	48.7561	−	15.8418i	0.995022	−	0.323302i
$50$	−3.33430	+	35.1978i	−0.0666859	+	0.703955i
$51$	0.0187387	+	0.0136145i	0.000367426	+	0.000266950i
$52$	−0.454719	+	2.87098i	−0.00874459	+	0.0552112i
$53$	69.5736	−	35.4495i	1.31271	−	0.668859i	0.349329	−	0.937000i	$-0.386409\pi$
$53$	69.5736	−	35.4495i	1.31271	−	0.668859i	0.963380	+	0.268141i	$0.0864095\pi$
$54$		−	1.39582i		−	0.0258486i
$55$	−53.3136	−	13.5151i	−0.969339	−	0.245729i
$56$	−28.3217			−0.505745
$57$	−0.800909	−	1.57187i	−0.0140510	−	0.0275767i
$58$	−53.8872	−	8.53489i	−0.929089	−	0.147153i
$59$	−67.8245	+	93.3524i	−1.14957	+	1.58224i	−0.405565	+	0.914066i	$0.632925\pi$
$59$	−67.8245	+	93.3524i	−1.14957	+	1.58224i	−0.744002	+	0.668177i	$0.767075\pi$
$60$	0.264157	+	0.480614i	0.00440261	+	0.00801023i
$61$	19.5547	+	60.1832i	0.320569	+	0.986610i	0.973401	+	0.229107i	$0.0735807\pi$
$61$	19.5547	+	60.1832i	0.320569	+	0.986610i	−0.652832	+	0.757503i	$0.726419\pi$
$62$	51.3196	−	8.12823i	0.827736	−	0.131101i
$63$	88.9800	+	14.0930i	1.41238	+	0.223699i
$64$	7.60845	+	2.47214i	0.118882	+	0.0386271i
$65$	1.36097	+	7.13834i	0.0209380	+	0.109821i
$66$	−0.801793	+	0.291525i	−0.0121484	+	0.00441705i
$67$	−49.6777	+	49.6777i	−0.741459	+	0.741459i	−0.972859	−	0.231400i	$-0.925669\pi$
$67$	−49.6777	+	49.6777i	−0.741459	+	0.741459i	0.231400	+	0.972859i	$0.425669\pi$
$68$	0.752622	−	0.383480i	0.0110680	−	0.00563941i
$69$	0.939138	+	1.29261i	0.0136107	+	0.0187335i
$70$	−66.6209	+	23.9774i	−0.951727	+	0.342535i
$71$	0.774125	+	2.38251i	0.0109032	+	0.0335565i	0.956360	−	0.292191i	$-0.0943842\pi$
$71$	0.774125	+	2.38251i	0.0109032	+	0.0335565i	−0.945457	+	0.325747i	$0.894384\pi$
$72$	−22.6737	−	11.5528i	−0.314913	−	0.160456i
$73$	15.3798	+	97.1040i	0.210682	+	1.33019i	0.835530	+	0.549445i	$0.185161\pi$
$73$	15.3798	+	97.1040i	0.210682	+	1.33019i	−0.624848	+	0.780746i	$0.714839\pi$
$74$	21.9208	+	30.1714i	0.296227	+	0.407722i
$75$	1.02826	+	0.906904i	0.0137102	+	0.0120920i
$76$	−64.3354			−0.846519
$77$	−20.9806	−	108.129i	−0.272476	−	1.40427i
$78$	0.0797070	+	0.0797070i	0.00102188	+	0.00102188i
$79$	83.9580	+	27.2796i	1.06276	+	0.345311i	0.787664	−	0.616105i	$-0.211290\pi$
$79$	83.9580	+	27.2796i	1.06276	+	0.345311i	0.275096	+	0.961417i	$0.411290\pi$
$80$	19.9902	−	0.626209i	0.249877	−	0.00782761i
$81$	65.4647	+	47.5629i	0.808206	+	0.587196i
$82$	28.8600	+	14.7049i	0.351952	+	0.179328i
$83$	−37.1761	+	72.9621i	−0.447904	+	0.879062i	0.551100	+	0.834439i	$0.314208\pi$
$83$	−37.1761	+	72.9621i	−0.447904	+	0.879062i	−0.999004	+	0.0446222i	$0.985792\pi$
$84$	−0.645564	+	0.888543i	−0.00768529	+	0.0105779i
$85$	1.44573	−	1.53923i	0.0170085	−	0.0181086i
$86$	5.23591	−	16.1145i	0.0608826	−	0.187378i
$87$	−1.49607	+	1.49607i	−0.0171962	+	0.0171962i
$88$	−3.80201	+	30.8795i	−0.0432047	+	0.350904i
$89$		−	104.283i		−	1.17172i	−0.810411	−	0.585862i	$-0.800756\pi$
$89$		−	104.283i		−	1.17172i	0.810411	−	0.585862i	$-0.199244\pi$
$90$	−63.1159	−	7.97983i	−0.701288	−	0.0886647i
$91$	−11.7737	+	8.55410i	−0.129381	+	0.0940011i
$92$	57.5499	−	9.11501i	0.625543	−	0.0990762i
$93$	0.914769	−	1.79534i	0.00983622	−	0.0193047i
$94$	−51.8095	+	16.8339i	−0.551165	+	0.179084i
$95$	−151.335	+	54.4669i	−1.59300	+	0.573336i
$96$	0.250985	−	0.182352i	0.00261443	−	0.00189950i
$97$	−27.0800	−	53.1476i	−0.279176	−	0.547913i	0.708257	−	0.705955i	$-0.249482\pi$
$97$	−27.0800	−	53.1476i	−0.279176	−	0.547913i	−0.987432	+	0.158042i	$0.949482\pi$
$98$	−51.2652	−	51.2652i	−0.523114	−	0.523114i
$99$	27.3108	−	95.1240i	0.275867	−	0.960848i
$100$	46.4925	−	18.3969i	0.464925	−	0.183969i
$101$	35.3729	−	108.867i	0.350227	−	1.07789i	−0.608498	−	0.793555i	$-0.708228\pi$
$101$	35.3729	−	108.867i	0.350227	−	1.07789i	0.958726	−	0.284333i	$-0.0917722\pi$
$102$	0.00512424	−	0.0323532i	5.02376e−5	−	0.000317188i
$103$	8.02769	+	50.6848i	0.0779387	+	0.492086i	0.995521	+	0.0945399i	$0.0301380\pi$
$103$	8.02769	+	50.6848i	0.0779387	+	0.492086i	−0.917582	+	0.397546i	$0.869862\pi$
$104$	3.90960	−	1.27030i	0.0375923	−	0.0122145i
$105$	−0.766304	+	2.63665i	−0.00729814	+	0.0251109i
$106$	−89.3380	−	64.9078i	−0.842811	−	0.612338i
$107$	−17.9461	+	113.307i	−0.167720	+	1.05894i	0.749919	+	0.661529i	$0.230092\pi$
$107$	−17.9461	+	113.307i	−0.167720	+	1.05894i	−0.917639	+	0.397414i	$0.869908\pi$
$108$	−1.75884	+	0.896175i	−0.0162856	+	0.00829791i
$109$		−	38.1763i		−	0.350242i	−0.984547	−	0.175121i	$-0.943968\pi$
$109$		−	38.1763i		−	0.350242i	0.984547	−	0.175121i	$-0.0560316\pi$
$110$	17.1994	+	75.8563i	0.156359	+	0.689603i
$111$	1.44624			0.0130292
$112$	18.1837	+	35.6875i	0.162354	+	0.318638i
$113$	11.4068	+	1.80667i	0.100946	+	0.0159882i	0.206703	−	0.978404i	$-0.433727\pi$
$113$	11.4068	+	1.80667i	0.100946	+	0.0159882i	−0.105757	+	0.994392i	$0.533727\pi$
$114$	−1.46646	+	2.01841i	−0.0128637	+	0.0177053i
$115$	127.657	−	70.1634i	1.11006	−	0.610116i
$116$	23.8431	+	73.3815i	0.205544	+	0.632599i
$117$	−12.9151	+	2.04555i	−0.110385	+	0.0174833i
$118$	161.177	+	25.5279i	1.36591	+	0.216338i
$119$	4.02205	+	1.30684i	0.0337987	+	0.0109819i
$120$	0.436009	−	0.641430i	0.00363341	−	0.00534525i
$121$	−120.711	+	8.35978i	−0.997610	+	0.0690891i
$122$	63.2804	−	63.2804i	0.518692	−	0.518692i
$123$	1.11917	−	0.570248i	0.00909898	−	0.00463616i
$124$	−43.1914	−	59.4479i	−0.348318	−	0.479418i
$125$	93.7888	−	82.6358i	0.750310	−	0.661086i
$126$	−39.3704	−	121.170i	−0.312463	−	0.961664i
$127$	−42.2926	−	21.5492i	−0.333013	−	0.169678i	0.279487	−	0.960150i	$-0.409836\pi$
$127$	−42.2926	−	21.5492i	−0.333013	−	0.169678i	−0.612499	+	0.790471i	$0.709836\pi$
$128$	−1.76985	−	11.1744i	−0.0138270	−	0.0873001i
$129$	−0.386215	−	0.531579i	−0.00299391	−	0.00412077i
$130$	8.12104	−	6.29802i	0.0624695	−	0.0484463i
$131$	109.294			0.834309			0.417154	−	0.908836i	$-0.363027\pi$
$131$	109.294			0.834309			0.417154	+	0.908836i	$0.363027\pi$
$132$	0.882126	+	0.823147i	0.00668277	+	0.00623597i
$133$	−227.761	−	227.761i	−1.71249	−	1.71249i
$134$	94.4927	+	30.7025i	0.705169	+	0.229123i
$135$	−3.37859	+	3.59711i	−0.0250266	+	0.0266453i
$136$	−0.966426	−	0.702150i	−0.00710607	−	0.00516287i
$137$	75.4884	+	38.4633i	0.551010	+	0.280754i	0.707248	−	0.706966i	$-0.249937\pi$
$137$	75.4884	+	38.4633i	0.551010	+	0.280754i	−0.156237	+	0.987720i	$0.549937\pi$
$138$	1.02582	−	2.01329i	0.00743350	−	0.0145891i
$139$	54.3821	−	74.8506i	0.391238	−	0.538493i	−0.567280	−	0.823525i	$-0.692004\pi$
$139$	54.3821	−	74.8506i	0.391238	−	0.538493i	0.958518	+	0.285032i	$0.0920041\pi$
$140$	72.9866	+	68.5527i	0.521333	+	0.489662i
$141$	−0.652809	+	2.00914i	−0.00462985	+	0.0142492i
$142$	2.50512	−	2.50512i	0.0176417	−	0.0176417i
$143$	7.74609	+	13.9853i	0.0541684	+	0.0977996i
$144$			35.9880i			0.249916i
$145$	118.211	+	152.429i	0.815250	+	1.05123i
$146$	112.484	−	81.7242i	0.770437	−	0.559755i
$147$	−2.77689	+	0.439816i	−0.0188904	+	0.00299194i
$148$	23.9442	−	46.9931i	0.161785	−	0.317521i
$149$	−176.898	+	57.4778i	−1.18724	+	0.385757i	−0.835051	−	0.550172i	$-0.814562\pi$
$149$	−176.898	+	57.4778i	−1.18724	+	0.385757i	−0.352187	+	0.935930i	$0.614562\pi$
$150$	0.482579	−	1.87796i	0.00321719	−	0.0125197i
$151$	−45.3652	+	32.9598i	−0.300432	+	0.218277i	−0.727780	−	0.685811i	$-0.759448\pi$
$151$	−45.3652	+	32.9598i	−0.300432	+	0.218277i	0.427348	+	0.904087i	$0.359448\pi$
$152$	41.3059	+	81.0674i	0.271749	+	0.533338i
$153$	2.68688	+	2.68688i	0.0175613	+	0.0175613i
$154$	−122.780	+	95.8603i	−0.797274	+	0.622469i
$155$	−151.928	−	103.272i	−0.980179	−	0.666273i
$156$	0.0492616	−	0.151612i	0.000315780	−	0.000971870i
$157$	−28.8698	+	182.277i	−0.183884	+	1.16100i	0.707150	+	0.707064i	$0.249981\pi$
$157$	−28.8698	+	182.277i	−0.183884	+	1.16100i	−0.891034	+	0.453936i	$0.850019\pi$
$158$	−19.5300	−	123.308i	−0.123608	−	0.780429i
$159$	−4.07273	+	1.32331i	−0.0256147	+	0.00832271i
$160$	−13.6236	−	24.7871i	−0.0851473	−	0.154919i
$161$	236.008	+	171.470i	1.46589	+	1.06503i
$162$	17.9018	−	113.028i	0.110505	−	0.697701i
$163$	−127.500	+	64.9646i	−0.782210	+	0.398556i	−0.799021	−	0.601303i	$-0.794649\pi$
$163$	−127.500	+	64.9646i	−0.782210	+	0.398556i	0.0168112	+	0.999859i	$0.494649\pi$
$164$		−	45.8069i		−	0.279310i
$165$	2.77190	+	1.18946i	0.0167994	+	0.00720887i
$166$	115.806			0.697627
$167$	−16.3157	−	32.0214i	−0.0976988	−	0.191745i	0.836984	−	0.547227i	$-0.184317\pi$
$167$	−16.3157	−	32.0214i	−0.0976988	−	0.191745i	−0.934683	+	0.355482i	$0.884317\pi$
$168$	1.53411	+	0.242979i	0.00913159	+	0.00144630i
$169$	−98.0941	+	135.015i	−0.580439	+	0.798905i
$170$	−2.86776	−	0.833473i	−0.0168692	−	0.00490278i
$171$	−89.4335	−	275.248i	−0.523003	−	1.60964i
$172$	−23.6671	+	3.74850i	−0.137599	+	0.0217936i
$173$	−7.11821	−	1.12741i	−0.0411457	−	0.00651684i	0.135828	−	0.990732i	$-0.456631\pi$
$173$	−7.11821	−	1.12741i	−0.0411457	−	0.00651684i	−0.176973	+	0.984216i	$0.556631\pi$
$174$	2.84569	+	0.924621i	0.0163545	+	0.00531391i
$175$	229.723	+	99.4646i	1.31270	+	0.568369i
$176$	41.3515	−	15.0351i	0.234952	−	0.0854264i
$177$	4.47475	−	4.47475i	0.0252811	−	0.0252811i
$178$	−131.405	+	66.9541i	−0.738229	+	0.376146i
$179$	−58.7250	−	80.8280i	−0.328073	−	0.451553i	0.612838	−	0.790209i	$-0.290028\pi$
$179$	−58.7250	−	80.8280i	−0.328073	−	0.451553i	−0.940910	+	0.338655i	$0.890028\pi$
$180$	30.4677	+	84.6540i	0.169265	+	0.470300i
$181$	−57.8892	−	178.165i	−0.319830	−	0.984335i	−0.973721	−	0.227746i	$-0.926864\pi$
$181$	−57.8892	−	178.165i	−0.319830	−	0.984335i	0.653891	−	0.756589i	$-0.273136\pi$
$182$	18.3380	+	9.34367i	0.100758	+	0.0513388i
$183$	−0.542897	−	3.42772i	−0.00296665	−	0.0187307i
$184$	−48.4349	−	66.6649i	−0.263233	−	0.362309i
$185$	16.5388	−	130.813i	0.0893990	−	0.707095i
$186$	−2.84957			−0.0153203
$187$	1.96480	−	4.20985i	0.0105070	−	0.0225126i
$188$	54.4757	+	54.4757i	0.289765	+	0.289765i
$189$	−9.39934	−	3.05403i	−0.0497319	−	0.0161589i
$190$	165.796	+	155.724i	0.872609	+	0.819599i
$191$	14.1732	+	10.2974i	0.0742051	+	0.0539131i	0.624269	−	0.781209i	$-0.285397\pi$
$191$	14.1732	+	10.2974i	0.0742051	+	0.0539131i	−0.550064	+	0.835122i	$0.685397\pi$
$192$	−0.390919	−	0.199183i	−0.00203604	−	0.00103741i
$193$	−68.9801	+	135.381i	−0.357410	+	0.701456i	−0.997779	−	0.0666112i	$-0.978781\pi$
$193$	−68.9801	+	135.381i	−0.357410	+	0.701456i	0.640369	+	0.768067i	$0.278781\pi$
$194$	−49.5834	+	68.2457i	−0.255585	+	0.351782i
$195$	−0.0124783	−	0.398340i	−6.39913e−5	−	0.00204277i
$196$	−31.6836	+	97.5121i	−0.161651	+	0.497511i
$197$	−167.774	+	167.774i	−0.851645	+	0.851645i	−0.990336	−	0.138690i	$-0.955711\pi$
$197$	−167.774	+	167.774i	−0.851645	+	0.851645i	0.138690	+	0.990336i	$0.455711\pi$
$198$	−137.398	+	26.6597i	−0.693928	+	0.134645i
$199$		−	39.4919i		−	0.198452i	−0.995065	−	0.0992258i	$-0.968363\pi$
$199$		−	39.4919i		−	0.198452i	0.995065	−	0.0992258i	$-0.0316366\pi$
$200$	−53.0315	−	46.7725i	−0.265157	−	0.233862i
$201$	3.11710	−	2.26470i	0.0155079	−	0.0112672i
$202$	−159.891	+	25.3242i	−0.791539	+	0.125367i
$203$	−175.377	+	344.196i	−0.863925	+	1.69555i
$204$	−0.0440573	+	0.0143151i	−0.000215967	+	7.01720e-5i
$205$	−38.7805	−	107.751i	−0.189173	−	0.525614i
$206$	58.7125	−	42.6571i	0.285012	−	0.207073i
$207$	118.998	+	233.546i	0.574869	+	1.12824i
$208$	−4.11079	−	4.11079i	−0.0197634	−	0.0197634i
$209$	−278.906	+	217.755i	−1.33448	+	1.04189i
$210$	3.81437	−	0.727233i	0.0181637	−	0.00346302i
$211$	39.2892	−	120.920i	0.186205	−	0.573079i	−0.813762	−	0.581198i	$-0.802584\pi$
$211$	39.2892	−	120.920i	0.186205	−	0.573079i	0.999967	+	0.00811869i	$0.00258429\pi$
$212$	−24.4301	+	154.246i	−0.115236	+	0.727574i
$213$	−0.0214920	−	0.135695i	−0.000100901	−	0.000637067i
$214$	154.297	−	50.1342i	0.721015	−	0.234272i
$215$	−52.4982	+	28.8543i	−0.244178	+	0.134206i
$216$	2.25849	+	1.64089i	0.0104560	+	0.00759671i
$217$	57.5514	−	363.365i	0.265214	−	1.67450i
$218$	−48.1050	+	24.5107i	−0.220665	+	0.112434i
$219$		−	5.39179i		−	0.0246200i
$220$	84.5418	−	70.3753i	0.384281	−	0.319888i
$221$	−0.613828			−0.00277750
$222$	−0.928541	−	1.82236i	−0.00418262	−	0.00820884i
$223$	−108.352	−	17.1612i	−0.485882	−	0.0769561i	−0.0913126	−	0.995822i	$-0.529106\pi$
$223$	−108.352	−	17.1612i	−0.485882	−	0.0769561i	−0.394569	+	0.918866i	$0.629106\pi$
$224$	33.2942	−	45.8255i	0.148635	−	0.204578i
$225$	143.338	+	173.336i	0.637056	+	0.770384i
$226$	−5.04711	−	15.5334i	−0.0223324	−	0.0687320i
$227$	14.6285	−	2.31693i	0.0644427	−	0.0102067i	−0.124130	−	0.992266i	$-0.539614\pi$
$227$	14.6285	−	2.31693i	0.0644427	−	0.0102067i	0.188573	+	0.982059i	$0.439614\pi$
$228$	3.48487	+	0.551949i	0.0152845	+	0.00242083i
$229$	282.436	+	91.7689i	1.23334	+	0.400738i	0.851925	−	0.523664i	$-0.175435\pi$
$229$	282.436	+	91.7689i	1.23334	+	0.400738i	0.381419	+	0.924402i	$0.375435\pi$
$230$	−170.372	−	115.810i	−0.740748	−	0.503520i
$231$	0.208796	+	6.03704i	0.000903880	+	0.0261344i
$232$	77.1579	−	77.1579i	0.332577	−	0.332577i
$233$	379.975	−	193.607i	1.63079	−	0.830931i	0.632378	−	0.774660i	$-0.282079\pi$
$233$	379.975	−	193.607i	1.63079	−	0.830931i	0.998416	−	0.0562713i	$-0.0179212\pi$
$234$	10.8696	+	14.9607i	0.0464511	+	0.0639344i
$235$	174.262	+	82.0229i	0.741541	+	0.349034i
$236$	−71.3149	−	219.485i	−0.302182	−	0.930019i
$237$	−4.31373	−	2.19795i	−0.0182014	−	0.00927406i
$238$	−0.935596	−	5.90712i	−0.00393108	−	0.0248198i
$239$	−31.6842	−	43.6095i	−0.132570	−	0.182467i	0.737571	−	0.675269i	$-0.235973\pi$
$239$	−31.6842	−	43.6095i	−0.132570	−	0.182467i	−0.870141	+	0.492802i	$0.835973\pi$
$240$	−1.08818	−	0.137581i	−0.00453410	−	0.000573252i
$241$	255.591			1.06054			0.530272	−	0.847827i	$-0.322090\pi$
$241$	255.591			1.06054			0.530272	+	0.847827i	$0.322090\pi$
$242$	88.0351	+	146.737i	0.363781	+	0.606352i
$243$	−9.41919	−	9.41919i	−0.0387621	−	0.0387621i
$244$	−120.366	−	39.1094i	−0.493305	−	0.160285i
$245$	8.02568	+	256.200i	0.0327579	+	1.04571i
$246$	−1.43711	−	1.04412i	−0.00584190	−	0.00424439i
$247$	41.6564	+	21.2250i	0.168649	+	0.0859312i
$248$	−47.1781	+	92.5922i	−0.190234	+	0.373356i
$249$	2.63968	−	3.63321i	0.0106011	−	0.0145912i
$250$	−164.343	−	65.1253i	−0.657373	−	0.260501i
$251$	75.6093	−	232.701i	0.301232	−	0.927098i	−0.679824	−	0.733375i	$-0.737944\pi$
$251$	75.6093	−	232.701i	0.301232	−	0.927098i	0.981056	−	0.193722i	$-0.0620561\pi$
$252$	−127.405	+	127.405i	−0.505576	+	0.505576i
$253$	218.638	−	234.304i	0.864184	−	0.926102i
$254$			67.1272i			0.264280i
$255$	−0.0915162	+	0.0709725i	−0.000358887	+	0.000278324i
$256$	−12.9443	+	9.40456i	−0.0505636	+	0.0367366i
$257$	−12.7082	+	2.01278i	−0.0494481	+	0.00783182i	−0.181110	−	0.983463i	$-0.557969\pi$
$257$	−12.7082	+	2.01278i	−0.0494481	+	0.00783182i	0.131661	+	0.991295i	$0.457969\pi$
$258$	−0.421864	+	0.827954i	−0.00163513	+	0.00320913i
$259$	251.133	−	81.5982i	0.969627	−	0.315051i
$260$	−13.1500	−	6.18953i	−0.0505769	−	0.0238059i
$261$	−280.805	+	204.017i	−1.07588	+	0.781674i
$262$	−70.1714	−	137.719i	−0.267830	−	0.525645i
$263$	−238.421	−	238.421i	−0.906544	−	0.906544i	0.0894475	−	0.995992i	$-0.471490\pi$
$263$	−238.421	−	238.421i	−0.906544	−	0.906544i	−0.995992	+	0.0894475i	$0.971490\pi$
$264$	0.470867	−	1.64004i	0.00178359	−	0.00621226i
$265$	73.1192	+	383.513i	0.275921	+	1.44722i
$266$	−140.764	+	433.228i	−0.529189	+	1.62868i
$267$	−0.894671	+	5.64873i	−0.00335083	+	0.0211563i
$268$	−21.9806	−	138.780i	−0.0820171	−	0.517836i
$269$	−198.621	+	64.5360i	−0.738370	+	0.239911i	−0.653969	−	0.756521i	$-0.726897\pi$
$269$	−198.621	+	64.5360i	−0.738370	+	0.239911i	−0.0844004	+	0.996432i	$0.526897\pi$
$270$	6.70181	+	1.94779i	0.0248215	+	0.00721402i
$271$	70.9921	+	51.5788i	0.261963	+	0.190328i	0.711012	−	0.703180i	$-0.248237\pi$
$271$	70.9921	+	51.5788i	0.261963	+	0.190328i	−0.449049	+	0.893507i	$0.648237\pi$
$272$	−0.264276	+	1.66858i	−0.000971605	+	0.00613447i
$273$	0.711136	−	0.362342i	0.00260489	−	0.00132726i
$274$		−	119.816i		−	0.437284i
$275$	139.286	−	237.117i	0.506495	−	0.862243i
$276$	−3.19551			−0.0115779
$277$	−61.2746	−	120.258i	−0.221208	−	0.434145i	0.753556	−	0.657384i	$-0.228337\pi$
$277$	−61.2746	−	120.258i	−0.221208	−	0.434145i	−0.974764	+	0.223239i	$0.928337\pi$
$278$	−129.233	−	20.4685i	−0.464866	−	0.0736275i
$279$	194.296	−	267.426i	0.696403	−	0.958516i
$280$	39.5212	−	135.982i	0.141147	−	0.485650i
$281$	−7.41449	−	22.8195i	−0.0263861	−	0.0812081i	0.936996	−	0.349339i	$-0.113594\pi$
$281$	−7.41449	−	22.8195i	−0.0263861	−	0.0812081i	−0.963382	+	0.268131i	$0.913594\pi$
$282$	2.95079	−	0.467360i	0.0104638	−	0.00165730i
$283$	304.597	+	48.2434i	1.07631	+	0.170471i	0.669331	−	0.742964i	$-0.266581\pi$
$283$	304.597	+	48.2434i	1.07631	+	0.170471i	0.406983	+	0.913436i	$0.366581\pi$
$284$	−4.76502	−	1.54825i	−0.0167783	−	0.00545159i
$285$	8.66469	−	1.65198i	0.0304024	−	0.00579641i
$286$	12.6493	−	18.7398i	0.0442282	−	0.0655237i
$287$	162.166	−	162.166i	0.565040	−	0.565040i
$288$	45.3475	−	23.1057i	0.157457	−	0.0802281i
$289$	−169.765	−	233.662i	−0.587422	−	0.808518i
$290$	116.175	−	246.820i	0.400603	−	0.851103i
$291$	1.01088	+	3.11118i	0.00347382	+	0.0106913i
$292$	−175.198	−	89.2676i	−0.599992	−	0.305711i
$293$	−69.8320	−	440.902i	−0.238335	−	1.50479i	−0.759037	−	0.651047i	$-0.774330\pi$
$293$	−69.8320	−	440.902i	−0.238335	−	1.50479i	0.520702	−	0.853738i	$-0.325670\pi$
$294$	2.33707	+	3.21670i	0.00794922	+	0.0109412i
$295$	−353.571	−	455.915i	−1.19854	−	1.54547i
$296$	−74.5879			−0.251986
$297$	−4.59164	+	9.83822i	−0.0154601	+	0.0331253i
$298$	186.002	+	186.002i	0.624168	+	0.624168i
$299$	−40.2700	−	13.0845i	−0.134682	−	0.0437609i
$300$	−2.67620	+	0.597637i	−0.00892066	+	0.00199212i
$301$	−97.0571	−	70.5161i	−0.322449	−	0.234273i
$302$	70.6580	+	36.0020i	0.233967	+	0.119212i
$303$	−2.85004	+	5.59353i	−0.00940608	+	0.0184605i
$304$	75.6308	−	104.097i	0.248786	−	0.342424i
$305$	−316.247	+	9.90669i	−1.03687	+	0.0324809i
$306$	1.66058	−	5.11075i	0.00542674	−	0.0167018i
$307$	346.977	−	346.977i	1.13022	−	1.13022i	0.140078	−	0.990140i	$-0.455265\pi$
$307$	346.977	−	346.977i	1.13022	−	1.13022i	0.990140	−	0.140078i	$-0.0447353\pi$
$308$	199.621	+	93.1660i	0.648119	+	0.302487i
$309$		−	2.81432i		−	0.00910784i
$310$	−32.5870	+	257.745i	−0.105119	+	0.831435i
$311$	58.8506	−	42.7575i	0.189230	−	0.137484i	−0.489137	−	0.872207i	$-0.662688\pi$
$311$	58.8506	−	42.7575i	0.189230	−	0.137484i	0.678367	+	0.734723i	$0.262688\pi$
$312$	−0.222670	+	0.0352674i	−0.000713685	+	0.000113037i
$313$	−218.003	+	427.854i	−0.696494	+	1.36695i	0.223379	+	0.974732i	$0.428291\pi$
$313$	−218.003	+	427.854i	−0.696494	+	1.36695i	−0.919874	+	0.392215i	$0.871709\pi$
$314$	248.218	−	80.6509i	0.790503	−	0.256850i
$315$	−191.831	+	407.556i	−0.608988	+	1.29383i
$316$	−142.838	+	103.778i	−0.452019	+	0.328411i
$317$	98.7868	+	193.880i	0.311630	+	0.611609i	0.992700	−	0.120610i	$-0.0384849\pi$
$317$	98.7868	+	193.880i	0.311630	+	0.611609i	−0.681070	+	0.732219i	$0.738485\pi$
$318$	4.28232	+	4.28232i	0.0134664	+	0.0134664i
$319$	351.738	+	237.421i	1.10263	+	0.744268i
$320$	−22.4867	+	33.0810i	−0.0702708	+	0.103378i
$321$	1.94417	−	5.98355i	0.00605661	−	0.0186403i
$322$	64.5383	−	407.479i	0.200429	−	1.26546i
$323$	−2.12529	−	13.4186i	−0.00657985	−	0.0415436i
$324$	−153.917	+	50.0106i	−0.475052	+	0.154354i
$325$	−36.1727	−	3.42665i	−0.111301	−	0.0105435i
$326$	163.720	+	118.950i	0.502210	+	0.364877i
$327$	−0.327524	+	2.06790i	−0.00100160	+	0.00632386i
$328$	−57.7201	+	29.4098i	−0.175976	+	0.0896641i
$329$			385.712i			1.17238i
$330$	−0.280856	−	4.25648i	−0.000851078	−	0.0128984i
$331$	−40.7232			−0.123031			−0.0615155	−	0.998106i	$-0.519593\pi$
$331$	−40.7232			−0.123031			−0.0615155	+	0.998106i	$0.519593\pi$
$332$	−74.3521	−	145.924i	−0.223952	−	0.439531i
$333$	234.337	+	37.1153i	0.703714	+	0.111457i
$334$	−29.8739	+	41.1180i	−0.0894430	+	0.123108i
$335$	−169.197	−	307.841i	−0.505066	−	0.918929i
$336$	−0.678787	−	2.08909i	−0.00202020	−	0.00621753i
$337$	−296.668	+	46.9876i	−0.880320	+	0.139429i	−0.580202	−	0.814473i	$-0.697026\pi$
$337$	−296.668	+	46.9876i	−0.880320	+	0.139429i	−0.300119	+	0.953902i	$0.597026\pi$
$338$	233.109	+	36.9209i	0.689672	+	0.109233i
$339$	−0.602377	−	0.195724i	−0.00177692	−	0.000577357i
$340$	0.790977	+	4.14871i	0.00232640	+	0.0122021i
$341$	−388.456	−	111.528i	−1.13917	−	0.327063i
$342$	−289.413	+	289.413i	−0.846236	+	0.846236i
$343$	−20.2095	+	10.2972i	−0.0589198	+	0.0300211i
$344$	19.9186	+	27.4156i	0.0579028	+	0.0796964i
$345$	−7.51677	+	2.70535i	−0.0217877	+	0.00784159i
$346$	3.14955	+	9.69331i	0.00910274	+	0.0280153i
$347$	546.074	+	278.238i	1.57370	+	0.801840i	0.999853	−	0.0171235i	$-0.00545083\pi$
$347$	546.074	+	278.238i	1.57370	+	0.801840i	0.573846	+	0.818963i	$0.305451\pi$
$348$	−0.661955	−	4.17942i	−0.00190217	−	0.0120098i
$349$	−103.441	−	142.374i	−0.296392	−	0.407948i	0.634685	−	0.772771i	$-0.281130\pi$
$349$	−103.441	−	142.374i	−0.296392	−	0.407948i	−0.931077	+	0.364822i	$0.881130\pi$
$350$	−22.1583	−	353.328i	−0.0633094	−	1.00951i
$351$	1.43449			0.00408686
$352$	−45.4946	−	42.4528i	−0.129246	−	0.120605i
$353$	397.645	+	397.645i	1.12647	+	1.12647i	0.990746	+	0.135726i	$0.0433367\pi$
$353$	397.645	+	397.645i	1.12647	+	1.12647i	0.135726	+	0.990746i	$0.456663\pi$
$354$	−8.51148	−	2.76555i	−0.0240437	−	0.00781228i
$355$	−12.5195	+	0.392182i	−0.0352661	+	0.00110474i
$356$	168.734	+	122.592i	0.473972	+	0.344361i
$357$	−0.206651	−	0.105294i	−0.000578855	−	0.000294941i
$358$	−64.1455	+	125.893i	−0.179177	+	0.351655i
$359$	155.716	−	214.324i	0.433748	−	0.597003i	−0.535060	−	0.844814i	$-0.679711\pi$
$359$	155.716	−	214.324i	0.433748	−	0.597003i	0.968808	+	0.247811i	$0.0797111\pi$
$360$	87.1088	−	92.7428i	0.241969	−	0.257619i
$361$	−208.204	+	640.786i	−0.576742	+	1.77503i
$362$	−187.333	+	187.333i	−0.517496	+	0.517496i
$363$	6.61028	+	0.582781i	0.0182101	+	0.00160546i
$364$		−	29.1062i		−	0.0799621i
$365$	−487.690	−	61.6593i	−1.33614	−	0.168929i
$366$	−3.97061	+	2.88482i	−0.0108487	+	0.00788202i
$367$	215.699	−	34.1633i	0.587734	−	0.0930880i	0.144517	−	0.989502i	$-0.453837\pi$
$367$	215.699	−	34.1633i	0.587734	−	0.0930880i	0.443217	+	0.896414i	$0.353837\pi$
$368$	−52.9056	+	103.833i	−0.143765	+	0.282155i
$369$	195.977	−	63.6767i	0.531102	−	0.172566i
$370$	−175.452	+	63.1467i	−0.474195	+	0.170667i
$371$	−632.552	+	459.576i	−1.70499	+	1.23875i
$372$	1.82954	+	3.59067i	0.00491811	+	0.00965234i
$373$	24.0372	+	24.0372i	0.0644428	+	0.0644428i	0.738594	−	0.674151i	$-0.235490\pi$
$373$	24.0372	+	24.0372i	0.0644428	+	0.0644428i	−0.674151	+	0.738594i	$0.735490\pi$
$374$	−6.56620	+	0.227098i	−0.0175567	+	0.000607213i
$375$	−5.78922	+	3.67151i	−0.0154379	+	0.00979068i
$376$	33.6679	−	103.619i	0.0895422	−	0.275582i
$377$	8.77129	−	55.3797i	0.0232660	−	0.146896i
$378$	2.18644	+	13.8047i	0.00578424	+	0.0365203i
$379$	−361.853	+	117.573i	−0.954757	+	0.310219i	−0.744647	−	0.667459i	$-0.767382\pi$
$379$	−361.853	+	117.573i	−0.954757	+	0.310219i	−0.210110	+	0.977678i	$0.567382\pi$
$380$	89.7761	−	308.896i	0.236253	−	0.812883i
$381$	2.10599	+	1.53009i	0.00552754	+	0.00401599i
$382$	3.87576	−	24.4706i	0.0101460	−	0.0640591i
$383$	41.4863	−	21.1383i	0.108319	−	0.0551914i	−0.398991	−	0.916955i	$-0.630640\pi$
$383$	41.4863	−	21.1383i	0.108319	−	0.0551914i	0.507311	+	0.861763i	$0.330640\pi$
$384$			0.620470i			0.00161581i
$385$	548.440	+	50.1525i	1.42452	+	0.130266i
$386$	214.878			0.556679
$387$	−48.9372	−	96.0446i	−0.126453	−	0.248177i
$388$	117.829	+	18.6623i	0.303683	+	0.0480987i
$389$	−291.694	+	401.483i	−0.749857	+	1.03209i	0.248134	+	0.968726i	$0.420183\pi$
$389$	−291.694	+	401.483i	−0.749857	+	1.03209i	−0.997991	+	0.0633633i	$0.979817\pi$
$390$	−0.493926	+	0.271473i	−0.00126648	+	0.000696086i
$391$	3.80227	+	11.7022i	0.00972448	+	0.0299289i
$392$	143.215	−	22.6830i	0.365343	−	0.0578647i
$393$	−5.92017	−	0.937662i	−0.0150640	−	0.00238591i
$394$	319.125	+	103.690i	0.809963	+	0.263173i
$395$	−248.136	+	365.043i	−0.628194	+	0.924159i
$396$	121.808	+	156.015i	0.307596	+	0.393977i
$397$	−404.979	+	404.979i	−1.02010	+	1.02010i	−0.0203041	+	0.999794i	$0.506463\pi$
$397$	−404.979	+	404.979i	−1.02010	+	1.02010i	−0.999794	+	0.0203041i	$0.993537\pi$
$398$	−49.7626	+	25.3553i	−0.125032	+	0.0637069i
$399$	10.3832	+	14.2912i	0.0260230	+	0.0358176i
$400$	−24.8884	+	96.8533i	−0.0622211	+	0.242133i
$401$	38.6795	+	119.043i	0.0964577	+	0.296866i	0.987631	−	0.156797i	$-0.0501168\pi$
$401$	38.6795	+	119.043i	0.0964577	+	0.296866i	−0.891173	+	0.453663i	$0.850117\pi$
$402$	−4.85499	−	2.47374i	−0.0120771	−	0.00615359i
$403$	8.35337	+	52.7411i	0.0207280	+	0.130871i
$404$	134.567	+	185.215i	0.333086	+	0.458453i
$405$	−319.717	+	247.946i	−0.789424	+	0.612213i
$406$	546.311			1.34559
$407$	−55.2544	−	284.768i	−0.135760	−	0.699675i
$408$	0.0463246	+	0.0463246i	0.000113541	+	0.000113541i
$409$	−90.3434	−	29.3544i	−0.220889	−	0.0717711i	0.196482	−	0.980507i	$-0.437048\pi$
$409$	−90.3434	−	29.3544i	−0.220889	−	0.0717711i	−0.417371	+	0.908736i	$0.637048\pi$
$410$	−110.876	+	118.047i	−0.270428	+	0.287919i
$411$	−3.75901	−	2.73108i	−0.00914600	−	0.00664496i
$412$	−91.4469	−	46.5945i	−0.221958	−	0.113093i
$413$	524.553	−	1029.49i	1.27010	−	2.49272i
$414$	217.884	−	299.892i	0.526291	−	0.724377i
$415$	−298.438	−	280.309i	−0.719128	−	0.675442i
$416$	−2.54061	+	7.81919i	−0.00610723	+	0.0187961i
$417$	−3.58788	+	3.58788i	−0.00860404	+	0.00860404i
$418$	453.457	+	211.635i	1.08482	+	0.506304i
$419$			434.554i			1.03712i	0.855040	+	0.518561i	$0.173532\pi$
$419$			434.554i			1.03712i	−0.855040	+	0.518561i	$0.826468\pi$
$420$	−3.36534	−	4.33947i	−0.00801272	−	0.0103321i
$421$	599.522	−	435.578i	1.42404	−	1.03463i	0.432955	−	0.901416i	$-0.357471\pi$
$421$	599.522	−	435.578i	1.42404	−	1.03463i	0.991088	−	0.133212i	$-0.0425290\pi$
$422$	−177.593	+	28.1280i	−0.420836	+	0.0666539i
$423$	−157.337	+	308.792i	−0.371956	+	0.730005i
$424$	210.046	−	68.2481i	0.495392	−	0.160963i
$425$	5.37294	+	9.08930i	0.0126422	+	0.0213866i
$426$	−0.157187	+	0.114203i	−0.000368984	+	0.000268083i
$427$	−287.668	−	564.579i	−0.673694	−	1.32220i
$428$	−162.238	−	162.238i	−0.379060	−	0.379060i
$429$	−0.299600	−	0.824001i	−0.000698368	−	0.00192075i
$430$	70.0645	+	47.6260i	0.162941	+	0.110758i
$431$	−197.520	+	607.904i	−0.458283	+	1.41045i	0.408954	+	0.912555i	$0.365894\pi$
$431$	−197.520	+	607.904i	−0.458283	+	1.41045i	−0.867237	+	0.497896i	$0.834106\pi$
$432$	0.617601	−	3.89938i	0.00142963	−	0.00902635i
$433$	−104.141	−	657.518i	−0.240510	−	1.51852i	−0.751962	−	0.659206i	$-0.770892\pi$
$433$	−104.141	−	657.518i	−0.240510	−	1.51852i	0.511452	−	0.859312i	$-0.329108\pi$
$434$	−494.818	+	160.776i	−1.14013	+	0.370452i
$435$	−5.09544	−	9.27078i	−0.0117137	−	0.0213121i
$436$	61.7706	+	44.8790i	0.141676	+	0.102933i
$437$	146.605	−	925.625i	0.335480	−	2.11813i
$438$	−6.79405	+	3.46174i	−0.0155115	+	0.00790352i
$439$			194.650i			0.443395i	0.975115	+	0.221698i	$0.0711598\pi$
$439$			194.650i			0.443395i	−0.975115	+	0.221698i	$0.928840\pi$
$440$	−142.957	−	61.3452i	−0.324903	−	0.139421i
$441$	−461.232			−1.04588
$442$	0.394102	+	0.773468i	0.000891633	+	0.00174993i
$443$	−521.977	−	82.6731i	−1.17828	−	0.186621i	−0.463581	−	0.886055i	$-0.653436\pi$
$443$	−521.977	−	82.6731i	−1.17828	−	0.186621i	−0.714697	+	0.699434i	$0.753436\pi$
$444$	−1.70015	+	2.34006i	−0.00382917	+	0.00527040i
$445$	500.699	+	145.521i	1.12517	+	0.327013i
$446$	47.9417	+	147.549i	0.107493	+	0.330828i
$447$	10.0752	−	1.59575i	0.0225396	−	0.00356992i
$448$	−79.1198	−	12.5313i	−0.176607	−	0.0279717i
$449$	258.084	+	83.8564i	0.574796	+	0.186763i	0.581968	−	0.813212i	$-0.302283\pi$
$449$	258.084	+	83.8564i	0.574796	+	0.186763i	−0.00717174	+	0.999974i	$0.502283\pi$
$450$	126.388	−	291.905i	0.280862	−	0.648677i
$451$	−155.042	−	198.582i	−0.343774	−	0.440314i
$452$	−16.3328	+	16.3328i	−0.0361345	+	0.0361345i
$453$	2.74007	−	1.39614i	0.00604873	−	0.00308198i
$454$	−12.3116	−	16.9454i	−0.0271180	−	0.0373247i
$455$	−24.6416	−	68.4661i	−0.0541573	−	0.150475i
$456$	−1.54193	−	4.74556i	−0.00338142	−	0.0104069i
$457$	338.403	+	172.425i	0.740487	+	0.377297i	0.783183	−	0.621791i	$-0.213595\pi$
$457$	338.403	+	172.425i	0.740487	+	0.377297i	−0.0426961	+	0.999088i	$0.513595\pi$
$458$	−65.6993	−	414.809i	−0.143448	−	0.905697i
$459$	−0.245019	−	0.337240i	−0.000533811	−	0.000734728i
$460$	−36.5431	+	289.036i	−0.0794416	+	0.628338i
$461$	−104.939			−0.227634			−0.113817	−	0.993502i	$-0.536308\pi$
$461$	−104.939			−0.227634			−0.113817	+	0.993502i	$0.536308\pi$
$462$	7.47306	−	4.13912i	0.0161755	−	0.00895913i
$463$	−65.6026	−	65.6026i	−0.141690	−	0.141690i	0.632704	−	0.774394i	$-0.281945\pi$
$463$	−65.6026	−	65.6026i	−0.141690	−	0.141690i	−0.774394	+	0.632704i	$0.781945\pi$
$464$	−146.763	−	47.6862i	−0.316300	−	0.102772i
$465$	7.34349	+	6.89738i	0.0157925	+	0.0148331i
$466$	−487.918	−	354.493i	−1.04703	−	0.760715i
$467$	611.865	+	311.761i	1.31020	+	0.667582i	0.962821	−	0.270142i	$-0.0870705\pi$
$467$	611.865	+	311.761i	1.31020	+	0.667582i	0.347383	+	0.937723i	$0.387070\pi$
$468$	11.8728	−	23.3018i	0.0253693	−	0.0497901i
$469$	413.495	−	569.127i	0.881653	−	1.21349i
$470$	−8.52830	−	272.245i	−0.0181453	−	0.579245i
$471$	3.12759	−	9.62574i	0.00664033	−	0.0204368i
$472$	−230.780	+	230.780i	−0.488940	+	0.488940i
$473$	−89.9138	+	96.3561i	−0.190093	+	0.203713i
$474$			6.84678i			0.0144447i
$475$	−50.3346	−	802.616i	−0.105968	−	1.68972i
$476$	−6.84272	+	4.97153i	−0.0143755	+	0.0104444i
$477$	−693.874	+	109.899i	−1.45466	+	0.230396i
$478$	−34.6087	+	67.9235i	−0.0724032	+	0.142099i
$479$	44.7516	−	14.5407i	0.0934271	−	0.0303563i	−0.261930	−	0.965087i	$-0.584359\pi$
$479$	44.7516	−	14.5407i	0.0934271	−	0.0303563i	0.355358	+	0.934730i	$0.384359\pi$
$480$	0.525295	+	1.45952i	0.00109437	+	0.00304067i
$481$	−31.0071	+	22.5280i	−0.0644639	+	0.0468357i
$482$	−164.100	−	322.064i	−0.340456	−	0.668182i
$483$	−11.3128	−	11.3128i	−0.0234220	−	0.0234220i
$484$	128.378	−	205.142i	0.265243	−	0.423847i
$485$	292.967	−	55.8561i	0.604057	−	0.115167i
$486$	−5.82138	+	17.9164i	−0.0119781	+	0.0368650i
$487$	−128.271	+	809.873i	−0.263391	+	1.66298i	0.401362	+	0.915920i	$0.368537\pi$
$487$	−128.271	+	809.873i	−0.263391	+	1.66298i	−0.664752	+	0.747064i	$0.731463\pi$
$488$	27.9993	+	176.780i	0.0573755	+	0.362255i
$489$	7.46367	−	2.42509i	0.0152631	−	0.00495929i
$490$	317.678	−	174.604i	0.648323	−	0.356334i
$491$	76.6526	+	55.6914i	0.156115	+	0.113424i	0.663101	−	0.748530i	$-0.269240\pi$
$491$	76.6526	+	55.6914i	0.156115	+	0.113424i	−0.506985	+	0.861955i	$0.669240\pi$
$492$	−0.392988	+	2.48123i	−0.000798756	+	0.00504315i
$493$	−14.5177	+	7.39713i	−0.0294476	+	0.0150043i
$494$		−	66.1174i		−	0.133841i
$495$	418.611	+	263.868i	0.845679	+	0.533066i
$496$	146.963			0.296297
$497$	−11.3881	−	22.3504i	−0.0229136	−	0.0449706i
$498$	−6.27289	−	0.993528i	−0.0125962	−	0.00199504i
$499$	330.715	−	455.190i	0.662756	−	0.912205i	−0.336813	−	0.941572i	$-0.609349\pi$
$499$	330.715	−	455.190i	0.662756	−	0.912205i	0.999569	+	0.0293667i	$0.00934906\pi$
$500$	23.4521	+	248.898i	0.0469043	+	0.497795i
$501$	0.609056	+	1.87448i	0.00121568	+	0.00374148i
$502$	−341.765	+	54.1303i	−0.680807	+	0.107829i
$503$	293.631	+	46.5066i	0.583760	+	0.0924585i	0.441328	−	0.897346i	$-0.354508\pi$
$503$	293.631	+	46.5066i	0.583760	+	0.0924585i	0.142432	+	0.989805i	$0.454508\pi$
$504$	242.339	+	78.7408i	0.480832	+	0.156232i
$505$	473.344	+	321.754i	0.937315	+	0.637136i
$506$	−435.615	−	125.068i	−0.860899	−	0.247170i
$507$	6.47180	−	6.47180i	0.0127649	−	0.0127649i
$508$	84.5852	−	43.0983i	0.166506	−	0.0848392i
$509$	−159.382	−	219.370i	−0.313127	−	0.430982i	0.623226	−	0.782042i	$-0.285822\pi$
$509$	−159.382	−	219.370i	−0.313127	−	0.430982i	−0.936353	+	0.351059i	$0.885822\pi$
$510$	0.148188	+	0.0697500i	0.000290564	+	0.000136765i
$511$	−304.211	−	936.264i	−0.595324	−	1.83222i
$512$	20.1612	+	10.2726i	0.0393773	+	0.0200637i
$513$	4.96671	+	31.3586i	0.00968169	+	0.0611278i
$514$	10.6954	+	14.7210i	0.0208082	+	0.0286400i
$515$	−254.557	−	32.1839i	−0.494285	−	0.0624931i
$516$	1.31414			0.00254678
$517$	420.546	+	51.7794i	0.813435	+	0.100154i
$518$	−264.057	−	264.057i	−0.509763	−	0.509763i
$519$	0.375901	+	0.122137i	0.000724278	+	0.000235332i
$520$	0.643554	+	20.5439i	0.00123760	+	0.0395075i
$521$	356.581	+	259.071i	0.684417	+	0.497258i	0.874820	−	0.484448i	$-0.160980\pi$
$521$	356.581	+	259.071i	0.684417	+	0.497258i	−0.190403	+	0.981706i	$0.560980\pi$
$522$	437.364	+	222.848i	0.837863	+	0.426913i
$523$	−7.94760	+	15.5980i	−0.0151962	+	0.0298242i	−0.898480	−	0.439015i	$-0.855328\pi$
$523$	−7.94760	+	15.5980i	−0.0151962	+	0.0298242i	0.883284	+	0.468839i	$0.155328\pi$
$524$	−128.483	+	176.842i	−0.245197	+	0.337485i
$525$	−11.5901	−	7.35856i	−0.0220764	−	0.0140163i
$526$	−147.352	+	453.504i	−0.280138	+	0.862175i
$527$	10.9724	−	10.9724i	0.0208204	−	0.0208204i
$528$	−2.36888	+	0.459642i	−0.00448652	+	0.000870533i
$529$			319.769i			0.604479i
$530$	436.309	−	338.366i	0.823225	−	0.638427i
$531$	839.890	−	610.216i	1.58171	−	1.14918i
$532$	636.276	−	100.776i	1.19601	−	0.189429i
$533$	−15.1122	+	29.6594i	−0.0283531	+	0.0556462i
$534$	7.69223	−	2.49936i	0.0144049	−	0.00468044i
$535$	−518.981	−	244.278i	−0.970058	−	0.456594i
$536$	−160.761	+	116.799i	−0.299926	+	0.217909i
$537$	2.48752	+	4.88204i	0.00463226	+	0.00909132i
$538$	208.843	+	208.843i	0.388184	+	0.388184i
$539$	192.694	+	529.973i	0.357502	+	0.983252i
$540$	−1.84848	−	9.69533i	−0.00342310	−	0.0179543i
$541$	−100.870	+	310.445i	−0.186450	+	0.573835i	−0.999970	−	0.00770172i	$-0.997548\pi$
$541$	−100.870	+	310.445i	−0.186450	+	0.573835i	0.813520	+	0.581537i	$0.197548\pi$
$542$	19.4133	−	122.571i	0.0358179	−	0.226145i
$543$	1.60718	+	10.1473i	0.00295981	+	0.0186875i
$544$	2.27220	−	0.738284i	0.00417685	−	0.00135714i
$545$	183.297	+	53.2727i	0.336325	+	0.0977480i
$546$	−0.913154	−	0.663445i	−0.00167244	−	0.00121510i
$547$	−152.416	+	962.318i	−0.278640	+	1.75927i	0.309873	+	0.950778i	$0.399713\pi$
$547$	−152.416	+	962.318i	−0.278640	+	1.75927i	−0.588514	+	0.808487i	$0.700287\pi$
$548$	−150.977	+	76.9265i	−0.275505	+	0.140377i
$549$		−	569.333i		−	1.03704i
$550$	−388.212	−	23.2725i	−0.705840	−	0.0423137i
$551$	1241.00			2.25226
$552$	2.05165	+	4.02658i	0.00371675	+	0.00729453i
$553$	−873.073	−	138.281i	−1.57879	−	0.250056i
$554$	−112.193	+	154.421i	−0.202515	+	0.278738i
$555$	−2.01813	+	6.94385i	−0.00363627	+	0.0125114i
$556$	57.1808	+	175.984i	0.102843	+	0.316519i
$557$	506.181	−	80.1711i	0.908762	−	0.143934i	0.315484	−	0.948931i	$-0.397833\pi$
$557$	506.181	−	80.1711i	0.908762	−	0.143934i	0.593279	+	0.804997i	$0.297833\pi$
$558$	−461.722	−	73.1297i	−0.827460	−	0.131057i
$559$	16.5608	+	5.38093i	0.0296258	+	0.00962600i
$560$	−196.722	+	37.5062i	−0.351288	+	0.0669753i
$561$	−0.142545	+	0.211179i	−0.000254091	+	0.000376433i
$562$	−23.9938	+	23.9938i	−0.0426936	+	0.0426936i
$563$	−192.499	+	98.0830i	−0.341916	+	0.174215i	−0.616513	−	0.787344i	$-0.711455\pi$
$563$	−192.499	+	98.0830i	−0.341916	+	0.174215i	0.274597	+	0.961559i	$0.411455\pi$
$564$	−2.48343	−	3.41815i	−0.00440325	−	0.00606056i
$565$	−24.5919	+	52.2469i	−0.0435256	+	0.0924725i
$566$	−134.773	−	414.789i	−0.238115	−	0.732843i
$567$	−721.947	−	367.850i	−1.27328	−	0.648766i
$568$	1.10842	+	6.99832i	0.00195145	+	0.0123210i
$569$	290.736	+	400.163i	0.510959	+	0.703275i	0.984081	−	0.177722i	$-0.0568729\pi$
$569$	290.736	+	400.163i	0.510959	+	0.703275i	−0.473122	+	0.880997i	$0.656873\pi$
$570$	−7.64469	−	9.85751i	−0.0134117	−	0.0172939i
$571$	−316.381			−0.554083			−0.277041	−	0.960858i	$-0.589354\pi$
$571$	−316.381			−0.554083			−0.277041	+	0.960858i	$0.589354\pi$
$572$	−31.7348	−	3.90732i	−0.0554805	−	0.00683098i
$573$	−0.679376	−	0.679376i	−0.00118565	−	0.00118565i
$574$	−308.459	−	100.224i	−0.537385	−	0.174607i
$575$	158.740	+	710.832i	0.276070	+	1.23623i
$576$	−58.2298	−	42.3064i	−0.101093	−	0.0734486i
$577$	−948.875	−	483.476i	−1.64450	−	0.837913i	−0.997128	−	0.0757362i	$-0.975869\pi$
$577$	−948.875	−	483.476i	−1.64450	−	0.837913i	−0.647369	−	0.762177i	$-0.724131\pi$
$578$	−185.435	+	363.936i	−0.320822	+	0.629648i
$579$	4.89792	−	6.74140i	0.00845927	−	0.0116432i
$580$	−385.600	+	12.0792i	−0.664828	+	0.0208263i
$581$	253.381	−	779.826i	0.436112	−	1.34221i
$582$	3.27129	−	3.27129i	0.00562077	−	0.00562077i
$583$	416.165	+	751.373i	0.713833	+	1.28881i
$584$			278.075i			0.476156i
$585$	8.20085	−	64.8641i	0.0140186	−	0.110879i
$586$	−510.734	+	371.070i	−0.871560	+	0.633226i
$587$	291.013	−	46.0919i	0.495763	−	0.0785212i	0.0964539	−	0.995337i	$-0.469250\pi$
$587$	291.013	−	46.0919i	0.495763	−	0.0785212i	0.399309	+	0.916816i	$0.369250\pi$
$588$	2.55279	−	5.01013i	0.00434148	−	0.00852063i
$589$	−1124.02	+	365.217i	−1.90836	+	0.620063i
$590$	−347.480	+	738.240i	−0.588949	+	1.25125i
$591$	10.5272	−	7.64847i	0.0178125	−	0.0129416i
$592$	47.8884	+	93.9862i	0.0808925	+	0.158760i
$593$	−405.664	−	405.664i	−0.684088	−	0.684088i	0.276831	−	0.960919i	$-0.410716\pi$
$593$	−405.664	−	405.664i	−0.684088	−	0.684088i	−0.960919	+	0.276831i	$0.910716\pi$
$594$	15.3449	−	0.530716i	0.0258332	−	0.000893462i
$595$	−11.8871	+	17.4876i	−0.0199783	+	0.0293909i
$596$	114.956	−	353.797i	0.192879	−	0.593619i
$597$	−0.338810	+	2.13916i	−0.000567521	+	0.00358318i
$598$	9.36748	+	59.1440i	0.0156647	+	0.0989029i
$599$	−979.953	+	318.406i	−1.63598	+	0.531563i	−0.975635	−	0.219398i	$-0.929591\pi$
$599$	−979.953	+	318.406i	−1.63598	+	0.531563i	−0.660346	+	0.750961i	$0.729591\pi$
$600$	2.47129	+	2.98850i	0.00411882	+	0.00498083i
$601$	794.671	+	577.362i	1.32225	+	0.960669i	0.999901	+	0.0140473i	$0.00447154\pi$
$601$	794.671	+	577.362i	1.32225	+	0.960669i	0.322346	+	0.946622i	$0.395528\pi$
$602$	−26.5410	+	167.573i	−0.0440880	+	0.278361i
$603$	563.190	−	286.960i	0.933980	−	0.475887i
$604$		−	112.149i		−	0.185677i
$605$	128.306	−	591.238i	0.212077	−	0.977253i
$606$	8.87809			0.0146503
$607$	406.697	+	798.188i	0.670011	+	1.31497i	0.936342	+	0.351090i	$0.114189\pi$
$607$	406.697	+	798.188i	0.670011	+	1.31497i	−0.266330	+	0.963882i	$0.585811\pi$
$608$	−179.728	−	28.4661i	−0.295605	−	0.0468192i
$609$	12.4526	−	17.1395i	0.0204476	−	0.0281437i
$610$	215.526	+	392.134i	0.353321	+	0.642842i
$611$	−17.3002	−	53.2445i	−0.0283146	−	0.0871433i
$612$	−7.50608	+	1.18885i	−0.0122648	+	0.00194256i
$613$	322.043	+	51.0066i	0.525356	+	0.0832082i	0.413479	−	0.910514i	$-0.364314\pi$
$613$	322.043	+	51.0066i	0.525356	+	0.0832082i	0.111877	+	0.993722i	$0.464314\pi$
$614$	−659.990	−	214.444i	−1.07490	−	0.349257i
$615$	1.17621	+	6.16927i	0.00191254	+	0.0100313i
$616$	−10.7684	−	311.353i	−0.0174812	−	0.505443i
$617$	236.183	−	236.183i	0.382793	−	0.382793i	−0.489315	−	0.872107i	$-0.662753\pi$
$617$	236.183	−	236.183i	0.382793	−	0.382793i	0.872107	+	0.489315i	$0.162753\pi$
$618$	−3.54625	+	1.80691i	−0.00573827	+	0.00292380i
$619$	−7.06702	−	9.72692i	−0.0114168	−	0.0157139i	0.803270	−	0.595614i	$-0.203091\pi$
$619$	−7.06702	−	9.72692i	−0.0114168	−	0.0157139i	−0.814687	+	0.579901i	$0.803091\pi$
$620$	345.700	−	124.420i	0.557580	−	0.200678i
$621$	−8.88573	−	27.3475i	−0.0143087	−	0.0440378i
$622$	−91.6620	−	46.7041i	−0.147367	−	0.0750870i
$623$	163.351	+	1031.36i	0.262201	+	1.65547i
$624$	0.187402	+	0.257937i	0.000300324	+	0.000413361i
$625$	265.885	+	565.624i	0.425416	+	0.904998i
$626$	679.094			1.08482
$627$	16.9757	−	9.40238i	0.0270745	−	0.0149958i
$628$	−260.992	−	260.992i	−0.415592	−	0.415592i
$629$	10.5924	+	3.44169i	0.0168401	+	0.00547168i
$630$	636.714	−	19.9456i	1.01066	−	0.0316597i
$631$	−474.225	−	344.545i	−0.751546	−	0.546030i	0.144760	−	0.989467i	$-0.453759\pi$
$631$	−474.225	−	344.545i	−0.751546	−	0.546030i	−0.896306	+	0.443437i	$0.853759\pi$
$632$	222.475	+	113.357i	0.352018	+	0.179362i
$633$	−3.16558	+	6.21280i	−0.00500092	+	0.00981485i
$634$	180.878	−	248.957i	0.285297	−	0.392677i
$635$	162.481	−	172.990i	0.255876	−	0.272425i
$636$	2.64662	−	8.14546i	0.00416135	−	0.0128073i
$637$	52.6851	−	52.6851i	0.0827082	−	0.0827082i
$638$	73.3388	−	595.650i	0.114951	−	0.933620i
$639$		−	22.5386i		−	0.0352716i
$640$	56.1218	+	7.09555i	0.0876903	+	0.0110868i
$641$	133.066	−	96.6783i	0.207592	−	0.150824i	−0.479132	−	0.877743i	$-0.659048\pi$
$641$	133.066	−	96.6783i	0.207592	−	0.150824i	0.686723	+	0.726919i	$0.259048\pi$
$642$	−8.78795	+	1.39187i	−0.0136884	+	0.00216803i
$643$	−120.596	+	236.684i	−0.187553	+	0.368093i	−0.965567	−	0.260153i	$-0.916227\pi$
$643$	−120.596	+	236.684i	−0.187553	+	0.368093i	0.778015	+	0.628246i	$0.216227\pi$
$644$	−554.889	+	180.294i	−0.861629	+	0.279960i
$645$	3.09123	−	1.11256i	0.00479260	−	0.00172490i
$646$	−15.5439	+	11.2933i	−0.0240617	+	0.0174819i
$647$	−208.629	−	409.458i	−0.322456	−	0.632856i	0.671698	−	0.740825i	$-0.265565\pi$
$647$	−208.629	−	409.458i	−0.322456	−	0.632856i	−0.994154	+	0.107969i	$0.965565\pi$
$648$	161.838	+	161.838i	0.249749	+	0.249749i
$649$	−1052.05	−	710.129i	−1.62103	−	1.09419i
$650$	18.9065	+	47.7803i	0.0290869	+	0.0735081i
$651$	−6.23479	+	19.1887i	−0.00957725	+	0.0294758i
$652$	44.7706	−	282.670i	0.0686665	−	0.433543i
$653$	151.561	+	956.916i	0.232099	+	1.46541i	0.778370	+	0.627806i	$0.216047\pi$
$653$	151.561	+	956.916i	0.232099	+	1.46541i	−0.546271	+	0.837608i	$0.683953\pi$
$654$	2.81599	−	0.914971i	0.00430580	−	0.00139904i
$655$	−152.514	+	524.759i	−0.232845	+	0.801158i
$656$	74.1171	+	53.8492i	0.112983	+	0.0820873i
$657$	138.372	−	873.644i	0.210611	−	1.32975i
$658$	486.025	−	247.642i	0.738641	−	0.376356i
$659$		−	680.077i		−	1.03198i	−0.856593	−	0.515992i	$-0.827423\pi$
$659$		−	680.077i		−	1.03198i	0.856593	−	0.515992i	$-0.172577\pi$
$660$	−5.18315	+	3.08673i	−0.00785326	+	0.00467686i
$661$	−416.848			−0.630632			−0.315316	−	0.948987i	$-0.602111\pi$
$661$	−416.848			−0.630632			−0.315316	+	0.948987i	$0.602111\pi$
$662$	26.1459	+	51.3143i	0.0394954	+	0.0775140i
$663$	0.0332493	+	0.00526617i	5.01498e−5	+	7.94294e-6i
$664$	−136.138	+	187.378i	−0.205028	+	0.282196i
$665$	1411.38	−	775.731i	2.12238	−	1.16651i
$666$	−103.685	−	319.111i	−0.155684	−	0.479146i
$667$	−1110.11	+	175.824i	−1.66433	+	0.263604i
$668$	70.9919	+	11.2440i	0.106275	+	0.0168324i
$669$	5.72187	+	1.85915i	0.00855287	+	0.00277900i
$670$	−279.272	+	410.847i	−0.416823	+	0.613204i
$671$	−654.185	+	237.856i	−0.974940	+	0.354480i
$672$	−2.19660	+	2.19660i	−0.00326875	+	0.00326875i
$673$	−401.389	+	204.518i	−0.596418	+	0.303890i	−0.726017	−	0.687676i	$-0.758631\pi$
$673$	−401.389	+	204.518i	−0.596418	+	0.303890i	0.129600	+	0.991566i	$0.458631\pi$
$674$	249.680	+	343.656i	0.370446	+	0.509875i
$675$	−12.5563	−	21.2413i	−0.0186019	−	0.0314685i
$676$	−103.142	−	317.439i	−0.152577	−	0.469585i
$677$	797.871	+	406.535i	1.17854	+	0.600495i	0.929796	−	0.368074i	$-0.119983\pi$
$677$	797.871	+	406.535i	1.17854	+	0.600495i	0.248742	+	0.968570i	$0.419983\pi$
$678$	0.140123	+	0.884701i	0.000206671	+	0.00130487i
$679$	351.072	+	483.209i	0.517043	+	0.711648i
$680$	4.71984	−	3.66032i	0.00694094	−	0.00538283i
$681$	−0.812261			−0.00119275
$682$	108.870	+	561.088i	0.159633	+	0.822710i
$683$	−450.561	−	450.561i	−0.659680	−	0.659680i	0.295624	−	0.955304i	$-0.404472\pi$
$683$	−450.561	−	450.561i	−0.659680	−	0.659680i	−0.955304	+	0.295624i	$0.904472\pi$
$684$	550.496	+	178.867i	0.804818	+	0.261501i
$685$	−290.014	+	308.772i	−0.423378	+	0.450761i
$686$	25.9506	+	18.8542i	0.0378288	+	0.0274843i
$687$	−14.5114	−	7.39394i	−0.0211229	−	0.0107627i
$688$	21.7571	−	42.7007i	0.0316237	−	0.0620650i
$689$	66.7057	−	91.8125i	0.0968152	−	0.133255i
$690$	8.23500	+	7.73474i	0.0119348	+	0.0112098i
$691$	−229.327	+	705.796i	−0.331877	+	1.02141i	0.636363	+	0.771390i	$0.280438\pi$
$691$	−229.327	+	705.796i	−0.331877	+	1.02141i	−0.968240	+	0.250022i	$0.919562\pi$
$692$	10.1921	−	10.1921i	0.0147285	−	0.0147285i
$693$	−121.099	+	983.553i	−0.174746	+	1.41927i
$694$		−	866.733i		−	1.24889i
$695$	283.495	+	365.556i	0.407907	+	0.525980i
$696$	−4.84138	+	3.51747i	−0.00695600	+	0.00505383i
$697$	9.55404	−	1.51321i	0.0137074	−	0.00217103i
$698$	−112.989	+	221.753i	−0.161875	+	0.317697i
$699$	−22.2432	+	7.22724i	−0.0318214	+	0.0103394i
$700$	−430.992	+	254.771i	−0.615703	+	0.363959i
$701$	358.674	−	260.592i	0.511661	−	0.371743i	−0.301792	−	0.953374i	$-0.597585\pi$
$701$	358.674	−	260.592i	0.511661	−	0.371743i	0.813453	+	0.581630i	$0.197585\pi$
$702$	−0.920997	−	1.80756i	−0.00131196	−	0.00257487i
$703$	−599.830	−	599.830i	−0.853244	−	0.853244i
$704$	−24.2844	+	84.5829i	−0.0344949	+	0.120146i
$705$	−8.73559	−	5.93798i	−0.0123909	−	0.00842267i
$706$	245.758	−	756.365i	0.348099	−	1.07134i
$707$	−179.307	+	1132.10i	−0.253616	+	1.60127i
$708$	1.97991	+	12.5007i	0.00279649	+	0.0176563i
$709$	928.632	−	301.731i	1.30978	−	0.425572i	0.430805	−	0.902445i	$-0.358230\pi$
$709$	928.632	−	301.731i	1.30978	−	0.425572i	0.878972	+	0.476873i	$0.158230\pi$
$710$	8.53217	+	15.5237i	0.0120171	+	0.0218643i
$711$	−642.556	−	466.844i	−0.903735	−	0.656602i
$712$	46.1416	−	291.327i	0.0648056	−	0.409166i
$713$	953.728	−	485.949i	1.33763	−	0.681555i
$714$			0.327999i			0.000459382i
$715$	−77.9574	+	17.6758i	−0.109031	+	0.0247214i
$716$	199.818			0.279075
$717$	1.34211	+	2.63403i	0.00187183	+	0.00367368i
$718$	−370.040	−	58.6085i	−0.515376	−	0.0816275i
$719$	674.882	−	928.896i	0.938640	−	1.29193i	−0.0177523	−	0.999842i	$-0.505651\pi$
$719$	674.882	−	928.896i	0.938640	−	1.29193i	0.956392	−	0.292085i	$-0.0943490\pi$
$720$	−172.790	−	50.2190i	−0.239986	−	0.0697486i
$721$	−158.787	−	488.697i	−0.220232	−	0.677804i
$722$	941.113	−	149.058i	1.30348	−	0.206451i
$723$	−13.8446	−	2.19278i	−0.0191489	−	0.00303289i
$724$	356.329	+	115.778i	0.492168	+	0.159915i
$725$	−896.816	+	354.866i	−1.23699	+	0.489471i
$726$	−3.50972	−	8.70361i	−0.00483432	−	0.0119884i
$727$	34.4699	−	34.4699i	0.0474139	−	0.0474139i	−0.683002	−	0.730416i	$-0.739326\pi$
$727$	34.4699	−	34.4699i	0.0474139	−	0.0474139i	0.730416	+	0.683002i	$0.239326\pi$
$728$	−36.6760	+	18.6873i	−0.0503791	+	0.0256694i
$729$	−427.637	−	588.591i	−0.586607	−	0.807395i
$730$	235.421	+	654.112i	0.322494	+	0.896044i
$731$	−1.56366	−	4.81246i	−0.00213907	−	0.00658339i
$732$	6.18438	+	3.15110i	0.00844860	+	0.00430478i
$733$	−202.138	−	1276.25i	−0.275768	−	1.74113i	−0.604410	−	0.796673i	$-0.706591\pi$
$733$	−202.138	−	1276.25i	−0.275768	−	1.74113i	0.328643	−	0.944454i	$-0.393409\pi$
$734$	−181.535	−	249.862i	−0.247323	−	0.340411i
$735$	1.76327	−	13.9465i	0.00239901	−	0.0189748i
$736$	164.805			0.223920
$737$	−565.017	−	527.240i	−0.766644	−	0.715387i
$738$	−206.062	−	206.062i	−0.279217	−	0.279217i
$739$	1054.29	+	342.559i	1.42664	+	0.463544i	0.917706	−	0.397261i	$-0.130039\pi$
$739$	1054.29	+	342.559i	1.42664	+	0.463544i	0.508935	+	0.860805i	$0.330039\pi$
$740$	192.217	+	180.540i	0.259752	+	0.243973i
$741$	−2.07431	−	1.50708i	−0.00279934	−	0.00203384i
$742$	985.222	+	501.996i	1.32779	+	0.676544i
$743$	−493.006	+	967.579i	−0.663534	+	1.30226i	0.276446	+	0.961030i	$0.410843\pi$
$743$	−493.006	+	967.579i	−0.663534	+	1.30226i	−0.939980	+	0.341230i	$0.889157\pi$
$744$	3.34987	−	4.61070i	0.00450252	−	0.00619718i
$745$	−29.1190	−	929.554i	−0.0390860	−	1.24772i
$746$	14.8558	−	45.7214i	0.0199139	−	0.0612887i
$747$	520.953	−	520.953i	0.697394	−	0.697394i
$748$	4.50192	+	8.12809i	0.00601861	+	0.0108664i
$749$		−	1148.71i		−	1.53366i
$750$	8.34328	+	4.93759i	0.0111244	+	0.00658345i
$751$	868.147	−	630.746i	1.15599	−	0.839875i	0.166723	−	0.986004i	$-0.446682\pi$
$751$	868.147	−	630.746i	1.15599	−	0.839875i	0.989265	+	0.146129i	$0.0466816\pi$
$752$	−152.184	+	24.1035i	−0.202372	+	0.0320526i
$753$	−6.09194	+	11.9561i	−0.00809022	+	0.0158780i
$754$	−75.4140	+	24.5035i	−0.100019	+	0.0324980i
$755$	−94.9463	−	263.807i	−0.125757	−	0.349413i
$756$	15.9911	−	11.6182i	0.0211523	−	0.0153680i
$757$	563.731	+	1106.38i	0.744691	+	1.46154i	0.882119	+	0.471026i	$0.156116\pi$
$757$	563.731	+	1106.38i	0.744691	+	1.46154i	−0.137429	+	0.990512i	$0.543884\pi$
$758$	380.475	+	380.475i	0.501945	+	0.501945i
$759$	−13.8532	+	10.8158i	−0.0182519	+	0.0142501i
$760$	−446.871	+	85.1987i	−0.587988	+	0.112104i
$761$	−49.9762	+	153.811i	−0.0656717	+	0.202117i	−0.978508	−	0.206209i	$-0.933887\pi$
$761$	−49.9762	+	153.811i	−0.0656717	+	0.202117i	0.912836	+	0.408326i	$0.133887\pi$
$762$	0.575900	−	3.63609i	0.000755774	−	0.00477177i
$763$	59.8001	+	377.563i	0.0783749	+	0.494840i
$764$	−33.3231	+	10.8273i	−0.0436166	+	0.0141719i
$765$	−16.6500	+	9.15122i	−0.0217647	+	0.0119624i
$766$	−53.2717	−	38.7041i	−0.0695452	−	0.0505276i
$767$	−26.2350	+	165.641i	−0.0342047	+	0.215960i
$768$	0.781838	−	0.398366i	0.00101802	−	0.000518706i
$769$			1094.24i			1.42294i	0.702716	+	0.711470i	$0.251970\pi$
$769$			1094.24i			1.42294i	−0.702716	+	0.711470i	$0.748030\pi$
$770$	−288.925	−	723.275i	−0.375227	−	0.939318i
$771$	0.705633			0.000915218
$772$	−137.960	−	270.762i	−0.178705	−	0.350728i
$773$	431.265	+	68.3057i	0.557911	+	0.0883645i	0.429021	−	0.903294i	$-0.358859\pi$
$773$	431.265	+	68.3057i	0.557911	+	0.0883645i	0.128890	+	0.991659i	$0.458859\pi$
$774$	−89.6036	+	123.329i	−0.115767	+	0.159340i
$775$	707.850	−	585.345i	0.913354	−	0.755284i
$776$	−52.1351	−	160.455i	−0.0671844	−	0.206772i
$777$	−14.3032	+	2.26541i	−0.0184083	+	0.00291558i
$778$	693.177	+	109.788i	0.890973	+	0.141116i
$779$	−700.693	−	227.669i	−0.899477	−	0.292258i
$780$	0.659196	+	0.448086i	0.000845123	+	0.000574469i
$781$	−25.8976	+	9.41616i	−0.0331596	+	0.0120565i
$782$	12.3044	−	12.3044i	0.0157345	−	0.0157345i
$783$	33.9271	−	17.2867i	0.0433297	−	0.0220776i
$784$	−120.532	−	165.898i	−0.153739	−	0.211604i
$785$	−834.886	−	392.970i	−1.06355	−	0.500598i
$786$	2.61946	+	8.06186i	0.00333264	+	0.0102568i
$787$	−1248.79	−	636.291i	−1.58677	−	0.808502i	−0.586776	−	0.809750i	$-0.699603\pi$
$787$	−1248.79	−	636.291i	−1.58677	−	0.808502i	−0.999999	+	0.00124742i	$0.999603\pi$
$788$	−74.2339	−	468.695i	−0.0942055	−	0.594790i
$789$	10.8691	+	14.9601i	0.0137758	+	0.0189608i
$790$	619.294	+	78.2982i	0.783917	+	0.0991117i
$791$	−115.643			−0.146199
$792$	118.384	−	253.655i	0.149475	−	0.320271i
$793$	65.0331	+	65.0331i	0.0820090	+	0.0820090i
$794$	770.316	+	250.291i	0.970171	+	0.315228i
$795$	−0.670407	−	21.4011i	−0.000843280	−	0.0269196i
$796$	63.8992	+	46.4255i	0.0802753	+	0.0583234i
$797$	104.268	+	53.1272i	0.130826	+	0.0666590i	0.518178	−	0.855273i	$-0.326610\pi$
$797$	104.268	+	53.1272i	0.130826	+	0.0666590i	−0.387353	+	0.921932i	$0.626610\pi$
$798$	11.3416	−	22.2591i	0.0142125	−	0.0278936i
$799$	−9.56253	+	13.1617i	−0.0119681	+	0.0164727i
$800$	138.022	−	30.8224i	0.172527	−	0.0385280i
$801$	−289.931	+	892.316i	−0.361961	+	1.11400i
$802$	125.170	−	125.170i	0.156072	−	0.156072i
$803$	−1061.66	+	205.997i	−1.32211	+	0.256534i
$804$			7.70589i			0.00958444i
$805$	−1152.62	+	893.878i	−1.43183	+	1.11041i
$806$	61.0945	−	44.3877i	0.0757996	−	0.0550716i
$807$	11.3124	−	1.79171i	0.0140179	−	0.00222021i
$808$	146.988	−	288.479i	0.181915	−	0.357029i
$809$	494.845	−	160.785i	0.611675	−	0.198745i	0.0132343	−	0.999912i	$-0.495787\pi$
$809$	494.845	−	160.785i	0.611675	−	0.198745i	0.598441	+	0.801167i	$0.295787\pi$
$810$	517.702	+	243.675i	0.639138	+	0.300834i
$811$	152.507	−	110.803i	0.188048	−	0.136625i	−0.489778	−	0.871847i	$-0.662922\pi$
$811$	152.507	−	110.803i	0.188048	−	0.136625i	0.677826	+	0.735222i	$0.262922\pi$
$812$	−350.754	−	688.393i	−0.431963	−	0.847774i
$813$	−3.40293	−	3.40293i	−0.00418565	−	0.00418565i
$814$	−323.353	+	252.457i	−0.397239	+	0.310143i
$815$	−133.998	−	702.825i	−0.164415	−	0.862361i
$816$	0.0286302	−	0.0881147i	3.50860e−5	−	0.000107984i
$817$	−60.2903	+	380.658i	−0.0737947	+	0.465921i
$818$	21.0154	+	132.686i	0.0256912	+	0.162208i
$819$	124.526	−	40.4609i	0.152046	−	0.0494028i
$820$	219.934	+	63.9207i	0.268212	+	0.0779520i
$821$	960.978	+	698.191i	1.17050	+	0.850415i	0.991068	−	0.133356i	$-0.0425753\pi$
$821$	960.978	+	698.191i	1.17050	+	0.850415i	0.179428	+	0.983771i	$0.442575\pi$
$822$	−1.02793	+	6.49008i	−0.00125052	+	0.00789548i
$823$	−820.158	+	417.891i	−0.996547	+	0.507766i	−0.874639	−	0.484776i	$-0.838901\pi$
$823$	−820.158	+	417.891i	−0.996547	+	0.507766i	−0.121908	+	0.992541i	$0.538901\pi$
$824$			145.145i			0.176147i
$825$	−9.57901	+	11.6490i	−0.0116109	+	0.0141200i
$826$	−1634.02			−1.97823
$827$	−346.398	−	679.843i	−0.418860	−	0.822060i	−0.999966	−	0.00823175i	$-0.997380\pi$
$827$	−346.398	−	679.843i	−0.418860	−	0.822060i	0.581106	−	0.813828i	$-0.302620\pi$
$828$	−517.776	−	82.0077i	−0.625334	−	0.0990431i
$829$	−456.540	+	628.374i	−0.550712	+	0.757990i	−0.990109	−	0.140303i	$-0.955192\pi$
$829$	−456.540	+	628.374i	−0.550712	+	0.757990i	0.439396	+	0.898293i	$0.355192\pi$
$830$	−161.600	+	556.023i	−0.194699	+	0.669908i
$831$	2.28735	+	7.03973i	0.00275252	+	0.00847140i
$832$	11.4839	−	1.81888i	0.0138028	−	0.00218615i
$833$	−21.3850	−	3.38704i	−0.0256722	−	0.00406608i
$834$	6.82456	+	2.21743i	0.00818293	+	0.00265879i
$835$	176.513	−	33.6532i	0.211392	−	0.0403033i
$836$	−24.4614	−	707.267i	−0.0292601	−	0.846013i
$837$	−25.6419	+	25.6419i	−0.0306354	+	0.0306354i
$838$	547.570	−	279.001i	0.653425	−	0.332937i
$839$	−433.961	−	597.296i	−0.517236	−	0.711914i	0.467883	−	0.883791i	$-0.345017\pi$
$839$	−433.961	−	597.296i	−0.517236	−	0.711914i	−0.985118	+	0.171877i	$0.945017\pi$
$840$	−3.30737	+	7.02669i	−0.00393735	+	0.00836511i
$841$	−200.037	−	615.652i	−0.237857	−	0.732047i
$842$	−933.777	−	475.783i	−1.10900	−	0.565063i
$843$	0.205848	+	1.29968i	0.000244186	+	0.00154173i
$844$	149.465	+	205.721i	0.177091	+	0.243745i
$845$	−511.367	−	659.387i	−0.605168	−	0.780340i
$846$	490.118			0.579335
$847$	1180.73	−	271.762i	1.39402	−	0.320852i
$848$	−220.856	−	220.856i	−0.260443	−	0.260443i
$849$	−16.0853	−	5.22642i	−0.0189461	−	0.00615597i
$850$	8.00355	−	12.6060i	0.00941594	−	0.0148306i
$851$	621.549	+	451.582i	0.730375	+	0.530649i
$852$	0.244825	+	0.124745i	0.000287353	+	0.000146414i
$853$	−271.686	+	533.213i	−0.318506	+	0.625103i	−0.993641	−	0.112590i	$-0.964085\pi$
$853$	−271.686	+	533.213i	−0.318506	+	0.625103i	0.675135	+	0.737694i	$0.264085\pi$
$854$	−526.718	+	724.964i	−0.616765	+	0.848905i
$855$	1446.35	−	45.3082i	1.69164	−	0.0529921i
$856$	−100.268	+	308.594i	−0.117136	+	0.360507i
$857$	−576.629	+	576.629i	−0.672846	+	0.672846i	−0.958371	−	0.285525i	$-0.907832\pi$
$857$	−576.629	+	576.629i	−0.672846	+	0.672846i	0.285525	+	0.958371i	$0.407832\pi$
$858$	−0.845947	+	0.906559i	−0.000985952	+	0.00105660i
$859$		−	385.261i		−	0.448500i	−0.974532	−	0.224250i	$-0.928007\pi$
$859$		−	385.261i		−	0.448500i	0.974532	−	0.224250i	$-0.0719932\pi$
$860$	15.0282	−	118.864i	0.0174746	−	0.138214i
$861$	−10.1754	+	7.39283i	−0.0118181	+	0.00858633i
$862$	892.820	−	141.409i	1.03575	−	0.164047i
$863$	726.202	−	1425.25i	0.841486	−	1.65151i	0.0860459	−	0.996291i	$-0.472577\pi$
$863$	726.202	−	1425.25i	0.841486	−	1.65151i	0.755440	−	0.655218i	$-0.227423\pi$
$864$	−5.31003	+	1.72533i	−0.00614587	+	0.00199691i
$865$	15.3461	−	32.6036i	0.0177411	−	0.0376920i
$866$	−761.659	+	553.378i	−0.879514	+	0.639004i
$867$	7.19105	+	14.1132i	0.00829418	+	0.0162782i
$868$	520.282	+	520.282i	0.599403	+	0.599403i
$869$	−267.974	+	933.358i	−0.308371	+	1.07406i
$870$	−8.41039	+	12.3728i	−0.00966711	+	0.0142217i
$871$	−31.5529	+	97.1100i	−0.0362261	+	0.111492i
$872$	16.8916	−	106.650i	0.0193711	−	0.122305i
$873$	83.9523	+	530.054i	0.0961652	+	0.607163i
$874$	−1260.48	+	409.555i	−1.44220	+	0.468599i
$875$	−798.126	+	964.177i	−0.912144	+	1.10192i
$876$	8.72410	+	6.33843i	0.00995902	+	0.00723565i
$877$	−121.370	+	766.301i	−0.138392	+	0.873775i	0.816613	+	0.577186i	$0.195849\pi$
$877$	−121.370	+	766.301i	−0.138392	+	0.873775i	−0.955005	+	0.296589i	$0.904151\pi$
$878$	245.274	−	124.973i	0.279355	−	0.142339i
$879$			24.4815i			0.0278516i
$880$	14.4848	+	219.523i	0.0164600	+	0.249458i
$881$	317.840			0.360772			0.180386	−	0.983596i	$-0.442265\pi$
$881$	317.840			0.360772			0.180386	+	0.983596i	$0.442265\pi$
$882$	296.129	+	581.187i	0.335748	+	0.658942i
$883$	1549.52	+	245.419i	1.75483	+	0.277938i	0.949244	−	0.314539i	$-0.101850\pi$
$883$	1549.52	+	245.419i	1.75483	+	0.277938i	0.805587	+	0.592477i	$0.201850\pi$
$884$	0.721598	−	0.993194i	0.000816287	−	0.00112352i
$885$	15.2405	+	27.7290i	0.0172209	+	0.0313322i
$886$	230.956	+	710.809i	0.260672	+	0.802267i
$887$	−1687.95	+	267.345i	−1.90298	+	0.301403i	−0.993454	−	0.114234i	$-0.963559\pi$
$887$	−1687.95	+	267.345i	−1.90298	+	0.301403i	−0.909530	+	0.415637i	$0.863559\pi$
$888$	4.04021	+	0.639907i	0.00454979	+	0.000720615i
$889$	452.027	+	146.873i	0.508467	+	0.165211i
$890$	−138.101	−	724.347i	−0.155170	−	0.813874i
$891$	−497.988	+	737.765i	−0.558909	+	0.828020i
$892$	155.142	−	155.142i	0.173927	−	0.173927i
$893$	1104.05	−	562.542i	1.23634	−	0.629947i
$894$	−8.47944	−	11.6710i	−0.00948484	−	0.0130548i
$895$	470.029	−	169.168i	0.525172	−	0.189014i
$896$	35.0076	+	107.742i	0.0390710	+	0.120248i
$897$	2.06906	+	1.05424i	0.00230664	+	0.00117529i
$898$	−60.0346	−	379.043i	−0.0668536	−	0.422097i
$899$	833.139	+	1146.72i	0.926740	+	1.27555i
$900$	−448.968	+	28.1562i	−0.498853	+	0.0312846i
$901$	−32.9784			−0.0366020
$902$	−150.684	+	322.862i	−0.167056	+	0.357940i
$903$	4.65233	+	4.65233i	0.00515208	+	0.00515208i
$904$	31.0668	+	10.0942i	0.0343660	+	0.0111662i
$905$	936.208	−	29.3275i	1.03448	−	0.0324061i
$906$	−3.51847	−	2.55632i	−0.00388352	−	0.00282154i
$907$	−484.529	−	246.880i	−0.534211	−	0.272194i	0.166005	−	0.986125i	$-0.446913\pi$
$907$	−484.529	−	246.880i	−0.534211	−	0.272194i	−0.700216	+	0.713931i	$0.746913\pi$
$908$	−13.4480	+	26.3931i	−0.0148105	+	0.0290673i
$909$	−605.348	+	833.190i	−0.665949	+	0.916600i
$910$	−70.4515	+	75.0082i	−0.0774192	+	0.0824265i
$911$	−122.977	+	378.484i	−0.134991	+	0.415460i	−0.995589	−	0.0938256i	$-0.970090\pi$
$911$	−122.977	+	378.484i	−0.134991	+	0.415460i	0.860597	+	0.509286i	$0.170090\pi$
$912$	−4.98978	+	4.98978i	−0.00547125	+	0.00547125i
$913$	−816.239	−	380.951i	−0.894018	−	0.417252i
$914$		−	537.116i		−	0.587654i
$915$	17.2152	+	2.17654i	0.0188144	+	0.00237873i
$916$	−480.508	+	349.110i	−0.524573	+	0.381124i
$917$	−1080.92	+	171.201i	−1.17876	+	0.186697i
$918$	−0.267635	+	0.525264i	−0.000291542	+	0.000572183i
$919$	−798.077	+	259.311i	−0.868419	+	0.282167i	−0.709141	−	0.705067i	$-0.750917\pi$
$919$	−798.077	+	259.311i	−0.868419	+	0.282167i	−0.159279	+	0.987234i	$0.550917\pi$
$920$	387.668	−	139.525i	0.421378	−	0.151658i
$921$	−21.7715	+	15.8180i	−0.0236390	+	0.0171748i
$922$	67.3752	+	132.231i	0.0730750	+	0.143418i
$923$	2.57451	+	2.57451i	0.00278928	+	0.00278928i
$924$	−10.0136	−	6.75913i	−0.0108372	−	0.00731507i
$925$	604.995	+	261.949i	0.654049	+	0.283188i
$926$	−40.5446	+	124.784i	−0.0437847	+	0.134755i
$927$	72.2250	−	456.011i	0.0779127	−	0.491921i
$928$	34.1395	+	215.549i	0.0367883	+	0.232272i
$929$	1241.31	−	403.325i	1.33618	−	0.434150i	0.448157	−	0.893955i	$-0.352081\pi$
$929$	1241.31	−	403.325i	1.33618	−	0.434150i	0.888020	+	0.459805i	$0.152081\pi$
$930$	3.97640	−	13.6817i	0.00427570	−	0.0147115i
$931$	1334.14	+	969.307i	1.43301	+	1.04115i
$932$	−133.425	+	842.411i	−0.143160	+	0.903874i
$933$	−3.55460	+	1.81116i	−0.00380986	+	0.00194122i
$934$		−	971.158i		−	1.03978i
$935$	17.4711	+	15.3082i	0.0186857	+	0.0163724i
$936$	−36.9848			−0.0395136
$937$	−81.5245	−	160.001i	−0.0870059	−	0.170759i	0.843403	−	0.537281i	$-0.180548\pi$
$937$	−81.5245	−	160.001i	−0.0870059	−	0.170759i	−0.930409	+	0.366522i	$0.880548\pi$
$938$	−982.623	−	155.632i	−1.04757	−	0.165919i
$939$	15.4792	−	21.3053i	0.0164848	−	0.0226894i
$940$	−337.573	+	185.538i	−0.359121	+	0.197381i
$941$	285.613	+	879.027i	0.303521	+	0.934141i	0.980225	+	0.197886i	$0.0634077\pi$
$941$	285.613	+	879.027i	0.303521	+	0.934141i	−0.676704	+	0.736255i	$0.736592\pi$
$942$	−14.1372	+	2.23911i	−0.0150076	+	0.00237697i
$943$	659.046	+	104.383i	0.698882	+	0.110692i
$944$	438.969	+	142.630i	0.465010	+	0.151091i
$945$	27.7796	−	40.8676i	0.0293964	−	0.0432461i
$946$	179.144	+	51.4336i	0.189370	+	0.0543695i
$947$	731.557	−	731.557i	0.772500	−	0.772500i	−0.206043	−	0.978543i	$-0.566059\pi$
$947$	731.557	−	731.557i	0.772500	−	0.772500i	0.978543	+	0.206043i	$0.0660587\pi$
$948$	8.62745	−	4.39591i	0.00910069	−	0.00463703i
$949$	83.9878	+	115.599i	0.0885014	+	0.121812i
$950$	−979.039	+	578.737i	−1.03057	+	0.609196i
$951$	−3.68766	−	11.3494i	−0.00387766	−	0.0119342i
$952$	10.6578	+	5.43041i	0.0111952	+	0.00570422i
$953$	−83.9304	−	529.916i	−0.0880697	−	0.556050i	−0.991785	−	0.127916i	$-0.959171\pi$
$953$	−83.9304	−	529.916i	−0.0880697	−	0.556050i	0.903715	−	0.428134i	$-0.140829\pi$
$954$	583.975	+	803.773i	0.612133	+	0.842529i
$955$	−69.2190	+	53.6806i	−0.0724806	+	0.0562101i
$956$	107.809			0.112771
$957$	−17.0157	−	15.8781i	−0.0177803	−	0.0165915i
$958$	−47.0546	−	47.0546i	−0.0491175	−	0.0491175i
$959$	−806.828	−	262.154i	−0.841322	−	0.273362i
$960$	1.50185	−	1.59898i	0.00156442	−	0.00166561i
$961$	−314.616	−	228.582i	−0.327384	−	0.237859i
$962$	48.2947	+	24.6074i	0.0502024	+	0.0255794i
$963$	468.577	−	919.633i	0.486580	−	0.954967i
$964$	−300.466	+	413.555i	−0.311686	+	0.428999i
$965$	−553.751	−	520.112i	−0.573835	−	0.538976i
$966$	−6.99171	+	21.5183i	−0.00723779	+	0.0222756i
$967$	607.058	−	607.058i	0.627774	−	0.627774i	−0.319733	−	0.947508i	$-0.603593\pi$
$967$	607.058	−	607.058i	0.627774	−	0.627774i	0.947508	+	0.319733i	$0.103593\pi$
$968$	−340.917	−	30.0562i	−0.352187	−	0.0310498i
$969$			0.745079i			0.000768915i
$970$	−258.479	−	333.299i	−0.266474	−	0.343607i
$971$	−353.473	+	256.813i	−0.364030	+	0.264483i	−0.754731	−	0.656035i	$-0.772233\pi$
$971$	−353.473	+	256.813i	−0.364030	+	0.264483i	0.390701	+	0.920518i	$0.372233\pi$
$972$	26.3135	−	4.16765i	0.0270715	−	0.00428770i
$973$	−420.590	+	825.455i	−0.432262	+	0.848361i
$974$	1102.85	−	358.339i	1.13229	−	0.367905i
$975$	1.92997	+	0.495945i	0.00197946	+	0.000508662i
$976$	204.780	−	148.781i	0.209815	−	0.152440i
$977$	−602.229	−	1181.94i	−0.616406	−	1.20977i	−0.962427	−	0.271539i	$-0.912467\pi$
$977$	−602.229	−	1181.94i	−0.616406	−	1.20977i	0.346021	−	0.938227i	$-0.387533\pi$
$978$	−7.84777	−	7.84777i	−0.00802430	−	0.00802430i
$979$	1146.43	−	39.6503i	1.17102	−	0.0405008i
$980$	−423.975	−	288.196i	−0.432628	−	0.294077i
$981$	−106.139	+	326.661i	−0.108194	+	0.332988i
$982$	20.9612	−	132.344i	0.0213454	−	0.134770i
$983$	−82.1209	−	518.491i	−0.0835411	−	0.527458i	−0.993598	−	0.112974i	$-0.963962\pi$
$983$	−82.1209	−	518.491i	−0.0835411	−	0.527458i	0.910057	−	0.414483i	$-0.136038\pi$
$984$	3.37884	−	1.09785i	0.00343378	−	0.00111570i
$985$	−571.420	−	1039.66i	−0.580122	−	1.05549i
$986$	18.6418	+	13.5441i	0.0189065	+	0.0137364i
$987$	3.30911	−	20.8929i	0.00335270	−	0.0211681i
$988$	−83.3128	+	42.4500i	−0.0843247	+	0.0429656i
$989$		−	349.051i		−	0.352934i
$990$	63.7279	−	696.894i	0.0643716	−	0.703933i
$991$	−111.067			−0.112076			−0.0560381	−	0.998429i	$-0.517847\pi$
$991$	−111.067			−0.112076			−0.0560381	+	0.998429i	$0.517847\pi$
$992$	−94.3562	−	185.184i	−0.0951171	−	0.186678i
$993$	2.20586	+	0.349374i	0.00222141	+	0.000351837i
$994$	−20.8515	+	28.6996i	−0.0209774	+	0.0288729i
$995$	189.613	+	55.1084i	0.190566	+	0.0553853i
$996$	2.77552	+	8.54218i	0.00278667	+	0.00857649i
$997$	−433.884	+	68.7205i	−0.435189	+	0.0689272i	−0.370186	−	0.928958i	$-0.620706\pi$
$997$	−433.884	+	68.7205i	−0.435189	+	0.0689272i	−0.0650038	+	0.997885i	$0.520706\pi$
$998$	−785.905	−	124.475i	−0.787480	−	0.124725i
$999$	−24.7540	−	8.04306i	−0.0247788	−	0.00805111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.3.l.a.53.4	yes	48
5.2	odd	4	inner	110.3.l.a.97.4	yes	48
11.5	even	5	inner	110.3.l.a.93.4	yes	48
55.27	odd	20	inner	110.3.l.a.27.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.3.l.a.27.4	✓	48	55.27	odd	20	inner
110.3.l.a.53.4	yes	48	1.1	even	1	trivial
110.3.l.a.93.4	yes	48	11.5	even	5	inner
110.3.l.a.97.4	yes	48	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	110.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642040 - 1.26007i) q^{2} +(-0.0541671 - 0.00857923i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(-1.39544 + 4.80133i) q^{5} +(0.0239670 + 0.0737628i) q^{6} +(-9.88997 + 1.56642i) q^{7} +(2.79360 + 0.442463i) q^{8} +(-8.55665 - 2.78022i) q^{9} +(6.94595 - 1.32429i) q^{10} +(0.380217 + 10.9934i) q^{11} +(0.0775588 - 0.0775588i) q^{12} +(1.29498 - 0.659823i) q^{13} +(8.32355 + 11.4564i) q^{14} +(0.116779 - 0.248102i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(-0.376311 - 0.191740i) q^{17} +(1.99042 + 12.5670i) q^{18} +(18.9077 + 26.0242i) q^{19} +(-6.12828 - 7.90217i) q^{20} +0.549150 q^{21} +(13.6084 - 7.53732i) q^{22} +(-20.6006 - 20.6006i) q^{23} +(-0.147526 - 0.0479340i) q^{24} +(-21.1055 - 13.3999i) q^{25} +(-1.66285 - 1.20813i) q^{26} +(0.879421 + 0.448087i) q^{27} +(9.09184 - 17.8437i) q^{28} +(22.6761 - 31.2110i) q^{29} +(-0.387604 + 0.0121420i) q^{30} +(-11.3535 + 34.9426i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(0.0737199 - 0.598744i) q^{33} +0.597284i q^{34} +(6.27995 - 49.6708i) q^{35} +(14.5574 - 10.5766i) q^{36} +(-26.0461 + 4.12530i) q^{37} +(20.6529 - 40.5337i) q^{38} +(-0.0758059 + 0.0246308i) q^{39} +(-6.02271 + 12.7956i) q^{40} +(-18.5293 + 13.4623i) q^{41} +(-0.352576 - 0.691969i) q^{42} +(8.47188 + 8.47188i) q^{43} +(-18.2347 - 12.3083i) q^{44} +(25.2890 - 37.2037i) q^{45} +(-12.7319 + 39.1847i) q^{46} +(6.02588 - 38.0459i) q^{47} +(0.0343169 + 0.216669i) q^{48} +(48.7561 - 15.8418i) q^{49} +(-3.33430 + 35.1978i) q^{50} +(0.0187387 + 0.0136145i) q^{51} +(-0.454719 + 2.87098i) q^{52} +(69.5736 - 35.4495i) q^{53} -1.39582i q^{54} +(-53.3136 - 13.5151i) q^{55} -28.3217 q^{56} +(-0.800909 - 1.57187i) q^{57} +(-53.8872 - 8.53489i) q^{58} +(-67.8245 + 93.3524i) q^{59} +(0.264157 + 0.480614i) q^{60} +(19.5547 + 60.1832i) q^{61} +(51.3196 - 8.12823i) q^{62} +(88.9800 + 14.0930i) q^{63} +(7.60845 + 2.47214i) q^{64} +(1.36097 + 7.13834i) q^{65} +(-0.801793 + 0.291525i) q^{66} +(-49.6777 + 49.6777i) q^{67} +(0.752622 - 0.383480i) q^{68} +(0.939138 + 1.29261i) q^{69} +(-66.6209 + 23.9774i) q^{70} +(0.774125 + 2.38251i) q^{71} +(-22.6737 - 11.5528i) q^{72} +(15.3798 + 97.1040i) q^{73} +(21.9208 + 30.1714i) q^{74} +(1.02826 + 0.906904i) q^{75} -64.3354 q^{76} +(-20.9806 - 108.129i) q^{77} +(0.0797070 + 0.0797070i) q^{78} +(83.9580 + 27.2796i) q^{79} +(19.9902 - 0.626209i) q^{80} +(65.4647 + 47.5629i) q^{81} +(28.8600 + 14.7049i) q^{82} +(-37.1761 + 72.9621i) q^{83} +(-0.645564 + 0.888543i) q^{84} +(1.44573 - 1.53923i) q^{85} +(5.23591 - 16.1145i) q^{86} +(-1.49607 + 1.49607i) q^{87} +(-3.80201 + 30.8795i) q^{88} -104.283i q^{89} +(-63.1159 - 7.97983i) q^{90} +(-11.7737 + 8.55410i) q^{91} +(57.5499 - 9.11501i) q^{92} +(0.914769 - 1.79534i) q^{93} +(-51.8095 + 16.8339i) q^{94} +(-151.335 + 54.4669i) q^{95} +(0.250985 - 0.182352i) q^{96} +(-27.0800 - 53.1476i) q^{97} +(-51.2652 - 51.2652i) q^{98} +(27.3108 - 95.1240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} + 2 q^{3} + 4 q^{5} + 4 q^{6} + 38 q^{7} + 24 q^{8} + 36 q^{10} + 80 q^{11} - 16 q^{12} - 16 q^{13} + 38 q^{15} + 48 q^{16} - 18 q^{17} - 44 q^{18} + 4 q^{20} + 24 q^{21} + 64 q^{23} + 70 q^{25}+ \cdots - 440 q^{98}+O(q^{100}) \) 48 * q - 12 * q^2 + 2 * q^3 + 4 * q^5 + 4 * q^6 + 38 * q^7 + 24 * q^8 + 36 * q^10 + 80 * q^11 - 16 * q^12 - 16 * q^13 + 38 * q^15 + 48 * q^16 - 18 * q^17 - 44 * q^18 + 4 * q^20 + 24 * q^21 + 64 * q^23 + 70 * q^25 + 8 * q^26 - 82 * q^27 + 64 * q^28 - 14 * q^30 - 116 * q^31 - 192 * q^32 - 312 * q^33 - 288 * q^35 - 88 * q^36 + 22 * q^37 - 72 * q^38 - 24 * q^40 - 196 * q^41 - 96 * q^42 - 484 * q^43 - 56 * q^45 - 132 * q^46 - 310 * q^47 - 8 * q^48 - 128 * q^50 + 256 * q^51 + 8 * q^52 - 82 * q^53 - 264 * q^55 + 48 * q^56 + 744 * q^57 + 168 * q^58 + 196 * q^60 + 528 * q^61 + 144 * q^62 + 814 * q^63 + 840 * q^65 + 436 * q^66 + 192 * q^67 + 36 * q^68 + 230 * q^70 - 292 * q^71 - 48 * q^72 - 108 * q^73 + 258 * q^75 + 96 * q^76 - 200 * q^77 + 88 * q^78 + 24 * q^80 + 628 * q^81 + 24 * q^82 + 360 * q^83 - 368 * q^85 + 532 * q^86 - 328 * q^87 - 40 * q^88 - 766 * q^90 + 72 * q^91 + 68 * q^92 - 66 * q^93 - 232 * q^95 - 16 * q^96 + 6 * q^97 - 440 * q^98

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