LMFDB - Embedded newform 110.3.l.a.97.4

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			97.4
Character	$\chi$	$=$	110.97
Dual form			110.3.l.a.93.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26007 - 0.642040i) q^{2} +(-0.00857923 + 0.0541671i) q^{3} +(1.17557 - 1.61803i) q^{4} +(3.95108 + 3.06414i) q^{5} +(0.0239670 + 0.0737628i) q^{6} +(-1.56642 - 9.88997i) q^{7} +(0.442463 - 2.79360i) 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} +(-0.659823 - 1.29498i) q^{13} +(-8.32355 - 11.4564i) q^{14} +(-0.199873 + 0.187731i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(0.191740 - 0.376311i) q^{17} +(12.5670 - 1.99042i) q^{18} +(-18.9077 - 26.0242i) q^{19} +(9.60266 - 2.79087i) q^{20} +0.549150 q^{21} +(7.53732 + 13.6084i) q^{22} +(-20.6006 + 20.6006i) q^{23} +(0.147526 + 0.0479340i) q^{24} +(6.22211 + 24.2133i) q^{25} +(-1.66285 - 1.20813i) q^{26} +(-0.448087 + 0.879421i) q^{27} +(-17.8437 - 9.09184i) q^{28} +(-22.6761 + 31.2110i) q^{29} +(-0.131324 + 0.364881i) q^{30} +(-11.3535 + 34.9426i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.598744 - 0.0737199i) q^{33} -0.597284i q^{34} +(24.1152 - 43.8758i) q^{35} +(14.5574 - 10.5766i) q^{36} +(-4.12530 - 26.0461i) q^{37} +(-40.5337 - 20.6529i) q^{38} +(0.0758059 - 0.0246308i) q^{39} +(10.3082 - 9.68199i) q^{40} +(-18.5293 + 13.4623i) q^{41} +(0.691969 - 0.352576i) 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} +(38.0459 + 6.02588i) q^{47} +(0.216669 - 0.0343169i) q^{48} +(-48.7561 + 15.8418i) q^{49} +(23.3862 + 26.5157i) q^{50} +(0.0187387 + 0.0136145i) q^{51} +(-2.87098 - 0.454719i) q^{52} +(-35.4495 - 69.5736i) q^{53} +1.39582i q^{54} +(-32.1831 + 44.6010i) q^{55} -28.3217 q^{56} +(1.57187 - 0.800909i) q^{57} +(-8.53489 + 53.8872i) q^{58} +(67.8245 - 93.3524i) q^{59} +(0.0687903 + 0.544092i) q^{60} +(19.5547 + 60.1832i) q^{61} +(8.12823 + 51.3196i) q^{62} +(14.0930 - 88.9800i) 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} +(-0.383480 - 0.752622i) q^{68} +(-0.939138 - 1.29261i) q^{69} +(2.21692 - 70.7697i) q^{70} +(0.774125 + 2.38251i) q^{71} +(11.5528 - 22.6737i) q^{72} +(97.1040 - 15.3798i) q^{73} +(-21.9208 - 30.1714i) q^{74} +(-1.36495 + 0.129302i) q^{75} -64.3354 q^{76} +(108.129 - 20.9806i) q^{77} +(0.0797070 - 0.0797070i) q^{78} +(-83.9580 - 27.2796i) q^{79} +(6.77287 - 18.8183i) q^{80} +(65.4647 + 47.5629i) q^{81} +(-14.7049 + 28.8600i) q^{82} +(72.9621 + 37.1761i) q^{83} +(0.645564 - 0.888543i) q^{84} +(1.91065 - 0.899318i) q^{85} +(5.23591 - 16.1145i) q^{86} +(-1.49607 - 1.49607i) q^{87} +(30.8795 + 3.80201i) q^{88} +104.283i q^{89} +(55.7523 + 30.6428i) q^{90} +(-11.7737 + 8.55410i) q^{91} +(9.11501 + 57.5499i) q^{92} +(-1.79534 - 0.914769i) q^{93} +(51.8095 - 16.8339i) q^{94} +(5.03593 - 160.760i) q^{95} +(0.250985 - 0.182352i) q^{96} +(53.1476 - 27.0800i) 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 $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.26007	−	0.642040i	0.630037	−	0.321020i
$2$	1.26007	−	0.642040i	0.630037	−	0.321020i
$3$	−0.00857923	+	0.0541671i	−0.00285974	+	0.0180557i	−0.989077	−	0.147400i	$-0.952910\pi$
$3$	−0.00857923	+	0.0541671i	−0.00285974	+	0.0180557i	0.986217	+	0.165456i	$0.0529095\pi$
$4$	1.17557	−	1.61803i	0.293893	−	0.404508i
$5$	3.95108	+	3.06414i	0.790217	+	0.612828i
$5$	3.95108	+	3.06414i	0.790217	+	0.612828i
$6$	0.0239670	+	0.0737628i	0.00399450	+	0.0122938i
$7$	−1.56642	−	9.88997i	−0.223774	−	1.41285i	−0.802169	−	0.597096i	$-0.796321\pi$
$7$	−1.56642	−	9.88997i	−0.223774	−	1.41285i	0.578396	−	0.815756i	$-0.303679\pi$
$8$	0.442463	−	2.79360i	0.0553079	−	0.349201i
$9$	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
$13$	−0.659823	−	1.29498i	−0.0507556	−	0.0996135i	0.864236	−	0.503087i	$-0.167803\pi$
$13$	−0.659823	−	1.29498i	−0.0507556	−	0.0996135i	−0.914991	+	0.403474i	$0.867803\pi$
$14$	−8.32355	−	11.4564i	−0.594539	−	0.818313i
$15$	−0.199873	+	0.187731i	−0.0133249	+	0.0125154i
$16$	−1.23607	−	3.80423i	−0.0772542	−	0.237764i
$17$	0.191740	−	0.376311i	0.0112788	−	0.0221359i	−0.885298	−	0.465023i	$-0.846046\pi$
$17$	0.191740	−	0.376311i	0.0112788	−	0.0221359i	0.896577	+	0.442888i	$0.146046\pi$
$18$	12.5670	−	1.99042i	0.698168	−	0.110579i
$19$	−18.9077	−	26.0242i	−0.995143	−	1.36970i	−0.928259	−	0.371936i	$-0.878694\pi$
$19$	−18.9077	−	26.0242i	−0.995143	−	1.36970i	−0.0668842	−	0.997761i	$-0.521306\pi$
$20$	9.60266	−	2.79087i	0.480133	−	0.139544i
$21$	0.549150			0.0261500
$22$	7.53732	+	13.6084i	0.342605	+	0.618564i
$23$	−20.6006	+	20.6006i	−0.895678	+	0.895678i	−0.995050	−	0.0993721i	$-0.968317\pi$
$23$	−20.6006	+	20.6006i	−0.895678	+	0.895678i	0.0993721	+	0.995050i	$0.468317\pi$
$24$	0.147526	+	0.0479340i	0.00614690	+	0.00199725i
$25$	6.22211	+	24.2133i	0.248884	+	0.968533i
$26$	−1.66285	−	1.20813i	−0.0639558	−	0.0464666i
$27$	−0.448087	+	0.879421i	−0.0165958	+	0.0325711i
$28$	−17.8437	−	9.09184i	−0.637276	−	0.324709i
$29$	−22.6761	+	31.2110i	−0.781936	+	1.07624i	0.213130	+	0.977024i	$0.431634\pi$
$29$	−22.6761	+	31.2110i	−0.781936	+	1.07624i	−0.995066	+	0.0992182i	$0.968366\pi$
$30$	−0.131324	+	0.364881i	−0.00437746	+	0.0121627i
$31$	−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
$33$	−0.598744	−	0.0737199i	−0.0181438	−	0.00223394i
$34$		−	0.597284i		−	0.0175672i
$35$	24.1152	−	43.8758i	0.689006	−	1.25359i
$36$	14.5574	−	10.5766i	0.404373	−	0.293794i
$37$	−4.12530	−	26.0461i	−0.111495	−	0.703949i	−0.978592	−	0.205810i	$-0.934017\pi$
$37$	−4.12530	−	26.0461i	−0.111495	−	0.703949i	0.867097	−	0.498139i	$-0.165983\pi$
$38$	−40.5337	−	20.6529i	−1.06668	−	0.543499i
$39$	0.0758059	−	0.0246308i	0.00194374	−	0.000631559i
$40$	10.3082	−	9.68199i	0.257705	−	0.242050i
$41$	−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	$0.390106\pi$
$42$	0.691969	−	0.352576i	0.0164755	−	0.00839467i
$43$	8.47188	−	8.47188i	0.197020	−	0.197020i	−0.601701	−	0.798721i	$-0.705510\pi$
$43$	8.47188	−	8.47188i	0.197020	−	0.197020i	0.798721	+	0.601701i	$0.205510\pi$
$44$	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
$47$	38.0459	+	6.02588i	0.809488	+	0.128210i	0.547440	−	0.836845i	$-0.315602\pi$
$47$	38.0459	+	6.02588i	0.809488	+	0.128210i	0.262047	+	0.965055i	$0.415602\pi$
$48$	0.216669	−	0.0343169i	0.00451393	−	0.000714936i
$49$	−48.7561	+	15.8418i	−0.995022	+	0.323302i
$50$	23.3862	+	26.5157i	0.467725	+	0.530315i
$51$	0.0187387	+	0.0136145i	0.000367426	+	0.000266950i
$52$	−2.87098	−	0.454719i	−0.0552112	−	0.00874459i
$53$	−35.4495	−	69.5736i	−0.668859	−	1.31271i	−0.937000	−	0.349329i	$-0.886409\pi$
$53$	−35.4495	−	69.5736i	−0.668859	−	1.31271i	0.268141	−	0.963380i	$-0.413591\pi$
$54$			1.39582i			0.0258486i
$55$	−32.1831	+	44.6010i	−0.585148	+	0.810927i
$56$	−28.3217			−0.505745
$57$	1.57187	−	0.800909i	0.0275767	−	0.0140510i
$58$	−8.53489	+	53.8872i	−0.147153	+	0.929089i
$59$	67.8245	−	93.3524i	1.14957	−	1.58224i	0.405565	−	0.914066i	$-0.367075\pi$
$59$	67.8245	−	93.3524i	1.14957	−	1.58224i	0.744002	−	0.668177i	$-0.232925\pi$
$60$	0.0687903	+	0.544092i	0.00114650	+	0.00906820i
$61$	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	$0.726419\pi$
$62$	8.12823	+	51.3196i	0.131101	+	0.827736i
$63$	14.0930	−	88.9800i	0.223699	−	1.41238i
$64$	−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	0.231400	−	0.972859i	$-0.425669\pi$
$67$	−49.6777	−	49.6777i	−0.741459	−	0.741459i	−0.972859	+	0.231400i	$0.925669\pi$
$68$	−0.383480	−	0.752622i	−0.00563941	−	0.0110680i
$69$	−0.939138	−	1.29261i	−0.0136107	−	0.0187335i
$70$	2.21692	−	70.7697i	0.0316702	−	1.01100i
$71$	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	$0.894384\pi$
$72$	11.5528	−	22.6737i	0.160456	−	0.314913i
$73$	97.1040	−	15.3798i	1.33019	−	0.210682i	0.549445	−	0.835530i	$-0.314839\pi$
$73$	97.1040	−	15.3798i	1.33019	−	0.210682i	0.780746	+	0.624848i	$0.214839\pi$
$74$	−21.9208	−	30.1714i	−0.296227	−	0.407722i
$75$	−1.36495	+	0.129302i	−0.0181993	+	0.00172403i
$76$	−64.3354			−0.846519
$77$	108.129	−	20.9806i	1.40427	−	0.272476i
$78$	0.0797070	−	0.0797070i	0.00102188	−	0.00102188i
$79$	−83.9580	−	27.2796i	−1.06276	−	0.345311i	−0.275096	−	0.961417i	$-0.588710\pi$
$79$	−83.9580	−	27.2796i	−1.06276	−	0.345311i	−0.787664	+	0.616105i	$0.788710\pi$
$80$	6.77287	−	18.8183i	0.0846609	−	0.235229i
$81$	65.4647	+	47.5629i	0.808206	+	0.587196i
$82$	−14.7049	+	28.8600i	−0.179328	+	0.351952i
$83$	72.9621	+	37.1761i	0.879062	+	0.447904i	0.834439	−	0.551100i	$-0.185792\pi$
$83$	72.9621	+	37.1761i	0.879062	+	0.447904i	0.0446222	+	0.999004i	$0.485792\pi$
$84$	0.645564	−	0.888543i	0.00768529	−	0.0105779i
$85$	1.91065	−	0.899318i	0.0224782	−	0.0105802i
$86$	5.23591	−	16.1145i	0.0608826	−	0.187378i
$87$	−1.49607	−	1.49607i	−0.0171962	−	0.0171962i
$88$	30.8795	+	3.80201i	0.350904	+	0.0432047i
$89$			104.283i			1.17172i	0.810411	+	0.585862i	$0.199244\pi$
$89$			104.283i			1.17172i	−0.810411	+	0.585862i	$0.800756\pi$
$90$	55.7523	+	30.6428i	0.619469	+	0.340475i
$91$	−11.7737	+	8.55410i	−0.129381	+	0.0940011i
$92$	9.11501	+	57.5499i	0.0990762	+	0.625543i
$93$	−1.79534	−	0.914769i	−0.0193047	−	0.00983622i
$94$	51.8095	−	16.8339i	0.551165	−	0.179084i
$95$	5.03593	−	160.760i	0.0530098	−	1.69221i
$96$	0.250985	−	0.182352i	0.00261443	−	0.00189950i
$97$	53.1476	−	27.0800i	0.547913	−	0.279176i	−0.158042	−	0.987432i	$-0.550518\pi$
$97$	53.1476	−	27.0800i	0.547913	−	0.279176i	0.705955	+	0.708257i	$0.250518\pi$
$98$	−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	$-0.0917722\pi$
$102$	0.0323532	+	0.00512424i	0.000317188	+	5.02376e-5i
$103$	50.6848	−	8.02769i	0.492086	−	0.0779387i	0.0945399	−	0.995521i	$-0.469862\pi$
$103$	50.6848	−	8.02769i	0.492086	−	0.0779387i	0.397546	+	0.917582i	$0.369862\pi$
$104$	−3.90960	+	1.27030i	−0.0375923	+	0.0122145i
$105$	2.16974	+	1.68267i	0.0206642	+	0.0160254i
$106$	−89.3380	−	64.9078i	−0.842811	−	0.612338i
$107$	−113.307	−	17.9461i	−1.05894	−	0.167720i	−0.397414	−	0.917639i	$-0.630092\pi$
$107$	−113.307	−	17.9461i	−1.05894	−	0.167720i	−0.661529	+	0.749919i	$0.730092\pi$
$108$	0.896175	+	1.75884i	0.00829791	+	0.0162856i
$109$			38.1763i			0.350242i	0.984547	+	0.175121i	$0.0560316\pi$
$109$			38.1763i			0.350242i	−0.984547	+	0.175121i	$0.943968\pi$
$110$	−11.9175	+	76.8633i	−0.108341	+	0.698758i
$111$	1.44624			0.0130292
$112$	−35.6875	+	18.1837i	−0.318638	+	0.162354i
$113$	1.80667	−	11.4068i	0.0159882	−	0.100946i	−0.978404	−	0.206703i	$-0.933727\pi$
$113$	1.80667	−	11.4068i	0.0159882	−	0.100946i	0.994392	+	0.105757i	$0.0337267\pi$
$114$	1.46646	−	2.01841i	0.0128637	−	0.0177053i
$115$	−144.518	+	18.2716i	−1.25668	+	0.158883i
$116$	23.8431	+	73.3815i	0.205544	+	0.632599i
$117$	−2.04555	−	12.9151i	−0.0174833	−	0.110385i
$118$	25.5279	−	161.177i	0.216338	−	1.36591i
$119$	−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
$123$	−0.570248	−	1.11917i	−0.00463616	−	0.00909898i
$124$	43.1914	+	59.4479i	0.348318	+	0.479418i
$125$	−49.6089	+	114.734i	−0.396872	+	0.917874i
$126$	−39.3704	−	121.170i	−0.312463	−	0.961664i
$127$	21.5492	−	42.2926i	0.169678	−	0.333013i	−0.790471	−	0.612499i	$-0.790164\pi$
$127$	21.5492	−	42.2926i	0.169678	−	0.333013i	0.960150	+	0.279487i	$0.0901643\pi$
$128$	−11.1744	+	1.76985i	−0.0873001	+	0.0138270i
$129$	0.386215	+	0.531579i	0.00299391	+	0.00412077i
$130$	−2.86818	−	9.86863i	−0.0220629	−	0.0759126i
$131$	109.294			0.834309			0.417154	−	0.908836i	$-0.363027\pi$
$131$	109.294			0.834309			0.417154	+	0.908836i	$0.363027\pi$
$132$	−0.823147	+	0.882126i	−0.00623597	+	0.00668277i
$133$	−227.761	+	227.761i	−1.71249	+	1.71249i
$134$	−94.4927	−	30.7025i	−0.705169	−	0.229123i
$135$	−4.46510	+	2.10166i	−0.0330748	+	0.0155679i
$136$	−0.966426	−	0.702150i	−0.00710607	−	0.00516287i
$137$	−38.4633	+	75.4884i	−0.280754	+	0.551010i	−0.987720	−	0.156237i	$-0.950063\pi$
$137$	−38.4633	+	75.4884i	−0.280754	+	0.551010i	0.706966	+	0.707248i	$0.250063\pi$
$138$	−2.01329	−	1.02582i	−0.0145891	−	0.00743350i
$139$	−54.3821	+	74.8506i	−0.391238	+	0.538493i	−0.958518	−	0.285032i	$-0.907996\pi$
$139$	−54.3821	+	74.8506i	−0.391238	+	0.538493i	0.567280	+	0.823525i	$0.307996\pi$
$140$	−42.6434	−	90.5983i	−0.304596	−	0.647131i
$141$	−0.652809	+	2.00914i	−0.00462985	+	0.0142492i
$142$	2.50512	+	2.50512i	0.0176417	+	0.0176417i
$143$	13.9853	−	7.74609i	0.0977996	−	0.0541684i
$144$		−	35.9880i		−	0.249916i
$145$	−185.230	+	53.8345i	−1.27745	+	0.371272i
$146$	112.484	−	81.7242i	0.770437	−	0.559755i
$147$	−0.439816	−	2.77689i	−0.00299194	−	0.0188904i
$148$	−46.9931	−	23.9442i	−0.317521	−	0.161785i
$149$	176.898	−	57.4778i	1.18724	−	0.385757i	0.352187	−	0.935930i	$-0.385438\pi$
$149$	176.898	−	57.4778i	1.18724	−	0.385757i	0.835051	+	0.550172i	$0.185438\pi$
$150$	−1.63692	+	1.03928i	−0.0109128	+	0.00692853i
$151$	−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	$0.359448\pi$
$152$	−81.0674	+	41.3059i	−0.533338	+	0.271749i
$153$	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
$157$	−182.277	−	28.8698i	−1.16100	−	0.183884i	−0.453936	−	0.891034i	$-0.649981\pi$
$157$	−182.277	−	28.8698i	−1.16100	−	0.183884i	−0.707064	+	0.707150i	$0.749981\pi$
$158$	−123.308	+	19.5300i	−0.780429	+	0.123608i
$159$	4.07273	−	1.32331i	0.0256147	−	0.00832271i
$160$	−3.54778	−	28.0609i	−0.0221736	−	0.175381i
$161$	236.008	+	171.470i	1.46589	+	1.06503i
$162$	113.028	+	17.9018i	0.697701	+	0.110505i
$163$	64.9646	+	127.500i	0.398556	+	0.782210i	0.999859	−	0.0168112i	$-0.00535143\pi$
$163$	64.9646	+	127.500i	0.398556	+	0.782210i	−0.601303	+	0.799021i	$0.705351\pi$
$164$			45.8069i			0.279310i
$165$	−2.13980	−	2.12591i	−0.0129685	−	0.0128843i
$166$	115.806			0.697627
$167$	32.0214	−	16.3157i	0.191745	−	0.0976988i	−0.355482	−	0.934683i	$-0.615683\pi$
$167$	32.0214	−	16.3157i	0.191745	−	0.0976988i	0.547227	+	0.836984i	$0.315683\pi$
$168$	0.242979	−	1.53411i	0.00144630	−	0.00913159i
$169$	98.0941	−	135.015i	0.580439	−	0.798905i
$170$	1.83016	−	2.35992i	0.0107657	−	0.0138819i
$171$	−89.4335	−	275.248i	−0.523003	−	1.60964i
$172$	−3.74850	−	23.6671i	−0.0217936	−	0.137599i
$173$	−1.12741	+	7.11821i	−0.00651684	+	0.0411457i	−0.990732	−	0.135828i	$-0.956631\pi$
$173$	−1.12741	+	7.11821i	−0.00651684	+	0.0411457i	0.984216	+	0.176973i	$0.0566307\pi$
$174$	−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
$178$	66.9541	+	131.405i	0.376146	+	0.738229i
$179$	58.7250	+	80.8280i	0.328073	+	0.451553i	0.940910	−	0.338655i	$-0.109972\pi$
$179$	58.7250	+	80.8280i	0.328073	+	0.451553i	−0.612838	+	0.790209i	$0.709972\pi$
$180$	89.9258	+	2.81700i	0.499588	+	0.0156500i
$181$	−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	$-0.273136\pi$
$182$	−9.34367	+	18.3380i	−0.0513388	+	0.100758i
$183$	−3.42772	+	0.542897i	−0.0187307	+	0.00296665i
$184$	48.4349	+	66.6649i	0.263233	+	0.362309i
$185$	63.5095	−	115.551i	0.343295	−	0.624599i
$186$	−2.84957			−0.0153203
$187$	4.20985	+	1.96480i	0.0225126	+	0.0105070i
$188$	54.4757	−	54.4757i	0.289765	−	0.289765i
$189$	9.39934	+	3.05403i	0.0497319	+	0.0161589i
$190$	−96.8685	−	205.802i	−0.509834	−	1.08317i
$191$	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	$0.685397\pi$
$192$	0.199183	−	0.390919i	0.00103741	−	0.00203604i
$193$	135.381	+	68.9801i	0.701456	+	0.357410i	0.768067	−	0.640369i	$-0.221219\pi$
$193$	135.381	+	68.9801i	0.701456	+	0.357410i	−0.0666112	+	0.997779i	$0.521219\pi$
$194$	49.5834	−	68.2457i	0.255585	−	0.351782i
$195$	0.374987	+	0.134961i	0.00192301	+	0.000692109i
$196$	−31.6836	+	97.5121i	−0.161651	+	0.497511i
$197$	−167.774	−	167.774i	−0.851645	−	0.851645i	0.138690	−	0.990336i	$-0.455711\pi$
$197$	−167.774	−	167.774i	−0.851645	−	0.851645i	−0.990336	+	0.138690i	$0.955711\pi$
$198$	26.6597	+	137.398i	0.134645	+	0.693928i
$199$			39.4919i			0.198452i	0.995065	+	0.0992258i	$0.0316366\pi$
$199$			39.4919i			0.198452i	−0.995065	+	0.0992258i	$0.968363\pi$
$200$	70.3955	−	6.66859i	0.351978	−	0.0333430i
$201$	3.11710	−	2.26470i	0.0155079	−	0.0112672i
$202$	−25.3242	−	159.891i	−0.125367	−	0.791539i
$203$	344.196	+	175.377i	1.69555	+	0.863925i
$204$	0.0440573	−	0.0143151i	0.000215967	−	7.01720e-5i
$205$	−114.461	−	3.58559i	−0.558347	−	0.0174907i
$206$	58.7125	−	42.6571i	0.285012	−	0.207073i
$207$	−233.546	+	118.998i	−1.12824	+	0.574869i
$208$	−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	$0.00258429\pi$
$212$	−154.246	−	24.4301i	−0.727574	−	0.115236i
$213$	−0.135695	+	0.0214920i	−0.000637067	+	0.000100901i
$214$	−154.297	+	50.1342i	−0.721015	+	0.234272i
$215$	59.4321	−	7.51408i	0.276428	−	0.0349492i
$216$	2.25849	+	1.64089i	0.0104560	+	0.00759671i
$217$	363.365	+	57.5514i	1.67450	+	0.265214i
$218$	24.5107	+	48.1050i	0.112434	+	0.220665i
$219$			5.39179i			0.0246200i
$220$	34.3324	+	104.505i	0.156056	+	0.475023i
$221$	−0.613828			−0.00277750
$222$	1.82236	−	0.928541i	0.00820884	−	0.00418262i
$223$	−17.1612	+	108.352i	−0.0769561	+	0.485882i	0.918866	+	0.394569i	$0.129106\pi$
$223$	−17.1612	+	108.352i	−0.0769561	+	0.485882i	−0.995822	+	0.0913126i	$0.970894\pi$
$224$	−33.2942	+	45.8255i	−0.148635	+	0.204578i
$225$	−14.0781	+	224.484i	−0.0625693	+	0.997706i
$226$	−5.04711	−	15.5334i	−0.0223324	−	0.0687320i
$227$	2.31693	+	14.6285i	0.0102067	+	0.0644427i	0.992266	−	0.124130i	$-0.0396139\pi$
$227$	2.31693	+	14.6285i	0.0102067	+	0.0644427i	−0.982059	+	0.188573i	$0.939614\pi$
$228$	0.551949	−	3.48487i	0.00242083	−	0.0152845i
$229$	−282.436	−	91.7689i	−1.23334	−	0.400738i	−0.381419	−	0.924402i	$-0.624565\pi$
$229$	−282.436	−	91.7689i	−1.23334	−	0.400738i	−0.851925	+	0.523664i	$0.824565\pi$
$230$	−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
$233$	−193.607	−	379.975i	−0.830931	−	1.63079i	−0.774660	−	0.632378i	$-0.782079\pi$
$233$	−193.607	−	379.975i	−0.830931	−	1.63079i	−0.0562713	−	0.998416i	$-0.517921\pi$
$234$	−10.8696	−	14.9607i	−0.0464511	−	0.0639344i
$235$	131.858	+	140.387i	0.561100	+	0.597390i
$236$	−71.3149	−	219.485i	−0.302182	−	0.930019i
$237$	2.19795	−	4.31373i	0.00927406	−	0.0182014i
$238$	−5.90712	+	0.935596i	−0.0248198	+	0.00393108i
$239$	31.6842	+	43.6095i	0.132570	+	0.182467i	0.870141	−	0.492802i	$-0.164027\pi$
$239$	31.6842	+	43.6095i	0.132570	+	0.182467i	−0.737571	+	0.675269i	$0.764027\pi$
$240$	0.961227	+	0.528313i	0.00400511	+	0.00220131i
$241$	255.591			1.06054			0.530272	−	0.847827i	$-0.322090\pi$
$241$	255.591			1.06054			0.530272	+	0.847827i	$0.322090\pi$
$242$	−146.737	+	88.0351i	−0.606352	+	0.363781i
$243$	−9.41919	+	9.41919i	−0.0387621	+	0.0387621i
$244$	120.366	+	39.1094i	0.493305	+	0.160285i
$245$	−241.181	−	86.8031i	−0.984411	−	0.354298i
$246$	−1.43711	−	1.04412i	−0.00584190	−	0.00424439i
$247$	−21.2250	+	41.6564i	−0.0859312	+	0.168649i
$248$	92.5922	+	47.1781i	0.373356	+	0.190234i
$249$	−2.63968	+	3.63321i	−0.0106011	+	0.0145912i
$250$	11.1530	+	176.425i	0.0446121	+	0.705698i
$251$	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
$253$	−234.304	−	218.638i	−0.926102	−	0.864184i
$254$		−	67.1272i		−	0.264280i
$255$	0.0323216	+	0.111210i	0.000126751	+	0.000436117i
$256$	−12.9443	+	9.40456i	−0.0505636	+	0.0367366i
$257$	−2.01278	−	12.7082i	−0.00783182	−	0.0494481i	0.983463	−	0.181110i	$-0.0579688\pi$
$257$	−2.01278	−	12.7082i	−0.00783182	−	0.0494481i	−0.991295	+	0.131661i	$0.957969\pi$
$258$	0.827954	+	0.421864i	0.00320913	+	0.00163513i
$259$	−251.133	+	81.5982i	−0.969627	+	0.315051i
$260$	−9.95017	−	10.5937i	−0.0382699	−	0.0407451i
$261$	−280.805	+	204.017i	−1.07588	+	0.781674i
$262$	137.719	−	70.1714i	0.525645	−	0.267830i
$263$	−238.421	+	238.421i	−0.906544	+	0.906544i	−0.995992	−	0.0894475i	$-0.971490\pi$
$263$	−238.421	+	238.421i	−0.906544	+	0.906544i	0.0894475	+	0.995992i	$0.471490\pi$
$264$	−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
$267$	−5.64873	−	0.894671i	−0.0211563	−	0.00335083i
$268$	−138.780	+	21.9806i	−0.517836	+	0.0820171i
$269$	198.621	−	64.5360i	0.738370	−	0.239911i	0.0844004	−	0.996432i	$-0.473103\pi$
$269$	198.621	−	64.5360i	0.738370	−	0.239911i	0.653969	+	0.756521i	$0.273103\pi$
$270$	−4.27700	+	5.51502i	−0.0158407	+	0.0204260i
$271$	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	$0.648237\pi$
$272$	−1.66858	−	0.264276i	−0.00613447	−	0.000971605i
$273$	−0.362342	−	0.711136i	−0.00132726	−	0.00260489i
$274$			119.816i			0.437284i
$275$	−263.822	+	77.6086i	−0.959352	+	0.282213i
$276$	−3.19551			−0.0115779
$277$	120.258	−	61.2746i	0.434145	−	0.221208i	−0.223239	−	0.974764i	$-0.571663\pi$
$277$	120.258	−	61.2746i	0.434145	−	0.221208i	0.657384	+	0.753556i	$0.271663\pi$
$278$	−20.4685	+	129.233i	−0.0736275	+	0.464866i
$279$	−194.296	+	267.426i	−0.696403	+	0.958516i
$280$	−111.902	−	86.7818i	−0.399648	−	0.309935i
$281$	−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	$0.913594\pi$
$282$	0.467360	+	2.95079i	0.00165730	+	0.0104638i
$283$	48.2434	−	304.597i	0.170471	−	1.07631i	−0.742964	−	0.669331i	$-0.766581\pi$
$283$	48.2434	−	304.597i	0.170471	−	1.07631i	0.913436	−	0.406983i	$-0.133419\pi$
$284$	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
$288$	−23.1057	−	45.3475i	−0.0802281	−	0.157457i
$289$	169.765	+	233.662i	0.587422	+	0.808518i
$290$	−198.840	+	186.761i	−0.685654	+	0.644002i
$291$	1.01088	+	3.11118i	0.00347382	+	0.0106913i
$292$	89.2676	−	175.198i	0.305711	−	0.599992i
$293$	−440.902	+	69.8320i	−1.50479	+	0.238335i	−0.853738	−	0.520702i	$-0.825670\pi$
$293$	−440.902	+	69.8320i	−1.50479	+	0.238335i	−0.651047	+	0.759037i	$0.725670\pi$
$294$	−2.33707	−	3.21670i	−0.00794922	−	0.0109412i
$295$	554.025	−	161.019i	1.87805	−	0.545828i
$296$	−74.5879			−0.251986
$297$	−9.83822	−	4.59164i	−0.0331253	−	0.0154601i
$298$	186.002	−	186.002i	0.624168	−	0.624168i
$299$	40.2700	+	13.0845i	0.134682	+	0.0437609i
$300$	−1.39538	+	2.36054i	−0.00465126	+	0.00786845i
$301$	−97.0571	−	70.5161i	−0.322449	−	0.234273i
$302$	−36.0020	+	70.6580i	−0.119212	+	0.233967i
$303$	5.59353	+	2.85004i	0.0184605	+	0.00940608i
$304$	−75.6308	+	104.097i	−0.248786	+	0.342424i
$305$	−107.147	+	297.707i	−0.351303	+	0.976089i
$306$	1.66058	−	5.11075i	0.00542674	−	0.0167018i
$307$	346.977	+	346.977i	1.13022	+	1.13022i	0.990140	+	0.140078i	$0.0447353\pi$
$307$	346.977	+	346.977i	1.13022	+	1.13022i	0.140078	+	0.990140i	$0.455265\pi$
$308$	93.1660	−	199.621i	0.302487	−	0.648119i
$309$			2.81432i			0.00910784i
$310$	−125.135	+	227.674i	−0.403662	+	0.734433i
$311$	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	$0.262688\pi$
$312$	−0.0352674	−	0.222670i	−0.000113037	−	0.000713685i
$313$	427.854	+	218.003i	1.36695	+	0.696494i	0.974732	−	0.223379i	$-0.0717089\pi$
$313$	427.854	+	218.003i	1.36695	+	0.696494i	0.392215	+	0.919874i	$0.371709\pi$
$314$	−248.218	+	80.6509i	−0.790503	+	0.256850i
$315$	328.330	−	308.384i	1.04232	−	0.978997i
$316$	−142.838	+	103.778i	−0.452019	+	0.328411i
$317$	−193.880	+	98.7868i	−0.611609	+	0.311630i	−0.732219	−	0.681070i	$-0.761515\pi$
$317$	−193.880	+	98.7868i	−0.611609	+	0.311630i	0.120610	+	0.992700i	$0.461515\pi$
$318$	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
$322$	407.479	+	64.5383i	1.26546	+	0.200429i
$323$	−13.4186	+	2.12529i	−0.0415436	+	0.00657985i
$324$	153.917	−	50.0106i	0.475052	−	0.154354i
$325$	27.2502	−	24.0340i	0.0838467	−	0.0739507i
$326$	163.720	+	118.950i	0.502210	+	0.364877i
$327$	−2.06790	−	0.327524i	−0.00632386	−	0.00100160i
$328$	29.4098	+	57.7201i	0.0896641	+	0.175976i
$329$		−	385.712i		−	1.17238i
$330$	−4.06122	−	1.30497i	−0.0123067	−	0.00395444i
$331$	−40.7232			−0.123031			−0.0615155	−	0.998106i	$-0.519593\pi$
$331$	−40.7232			−0.123031			−0.0615155	+	0.998106i	$0.519593\pi$
$332$	145.924	−	74.3521i	0.439531	−	0.223952i
$333$	37.1153	−	234.337i	0.111457	−	0.703714i
$334$	29.8739	−	41.1180i	0.0894430	−	0.123108i
$335$	−44.0614	−	348.500i	−0.131526	−	1.04030i
$336$	−0.678787	−	2.08909i	−0.00202020	−	0.00621753i
$337$	−46.9876	−	296.668i	−0.139429	−	0.880320i	−0.953902	−	0.300119i	$-0.902974\pi$
$337$	−46.9876	−	296.668i	−0.139429	−	0.880320i	0.814473	−	0.580202i	$-0.197026\pi$
$338$	36.9209	−	233.109i	0.109233	−	0.689672i
$339$	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
$343$	10.2972	+	20.2095i	0.0300211	+	0.0589198i
$344$	−19.9186	−	27.4156i	−0.0579028	−	0.0796964i
$345$	0.250133	−	7.98487i	0.000725022	−	0.0231445i
$346$	3.14955	+	9.69331i	0.00910274	+	0.0280153i
$347$	−278.238	+	546.074i	−0.801840	+	1.57370i	0.0171235	+	0.999853i	$0.494549\pi$
$347$	−278.238	+	546.074i	−0.801840	+	1.57370i	−0.818963	+	0.573846i	$0.805451\pi$
$348$	−4.17942	+	0.661955i	−0.0120098	+	0.00190217i
$349$	103.441	+	142.374i	0.296392	+	0.407948i	0.931077	−	0.364822i	$-0.118870\pi$
$349$	103.441	+	142.374i	0.296392	+	0.407948i	−0.634685	+	0.772771i	$0.718870\pi$
$350$	225.607	−	272.824i	0.644592	−	0.779497i
$351$	1.43449			0.00408686
$352$	42.4528	−	45.4946i	0.120605	−	0.129246i
$353$	397.645	−	397.645i	1.12647	−	1.12647i	0.135726	−	0.990746i	$-0.456663\pi$
$353$	397.645	−	397.645i	1.12647	−	1.12647i	0.990746	−	0.135726i	$-0.0433367\pi$
$354$	8.51148	+	2.76555i	0.0240437	+	0.00781228i
$355$	−4.24172	+	11.7855i	−0.0119485	+	0.0331987i
$356$	168.734	+	122.592i	0.473972	+	0.344361i
$357$	0.105294	−	0.206651i	0.000294941	−	0.000578855i
$358$	125.893	+	64.1455i	0.351655	+	0.179177i
$359$	−155.716	+	214.324i	−0.433748	+	0.597003i	−0.968808	−	0.247811i	$-0.920289\pi$
$359$	−155.716	+	214.324i	−0.433748	+	0.597003i	0.535060	+	0.844814i	$0.320289\pi$
$360$	115.122	−	54.1863i	0.319783	−	0.150517i
$361$	−208.204	+	640.786i	−0.576742	+	1.77503i
$362$	−187.333	−	187.333i	−0.517496	−	0.517496i
$363$	0.582781	−	6.61028i	0.00160546	−	0.0182101i
$364$			29.1062i			0.0799621i
$365$	430.792	+	236.773i	1.18025	+	0.648694i
$366$	−3.97061	+	2.88482i	−0.0108487	+	0.00788202i
$367$	34.1633	+	215.699i	0.0930880	+	0.587734i	0.989502	+	0.144517i	$0.0461629\pi$
$367$	34.1633	+	215.699i	0.0930880	+	0.587734i	−0.896414	+	0.443217i	$0.853837\pi$
$368$	103.833	+	52.9056i	0.282155	+	0.143765i
$369$	−195.977	+	63.6767i	−0.531102	+	0.172566i
$370$	5.83845	−	186.378i	0.0157796	−	0.503725i
$371$	−632.552	+	459.576i	−1.70499	+	1.23875i
$372$	−3.59067	+	1.82954i	−0.00965234	+	0.00491811i
$373$	24.0372	−	24.0372i	0.0644428	−	0.0644428i	−0.674151	−	0.738594i	$-0.735490\pi$
$373$	24.0372	−	24.0372i	0.0644428	−	0.0644428i	0.738594	+	0.674151i	$0.235490\pi$
$374$	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
$377$	55.3797	+	8.77129i	0.146896	+	0.0232660i
$378$	13.8047	−	2.18644i	0.0365203	−	0.00578424i
$379$	361.853	−	117.573i	0.954757	−	0.310219i	0.210110	−	0.977678i	$-0.432618\pi$
$379$	361.853	−	117.573i	0.954757	−	0.310219i	0.744647	+	0.667459i	$0.232618\pi$
$380$	−254.195	−	197.133i	−0.668933	−	0.518770i
$381$	2.10599	+	1.53009i	0.00552754	+	0.00401599i
$382$	24.4706	+	3.87576i	0.0640591	+	0.0101460i
$383$	−21.1383	−	41.4863i	−0.0551914	−	0.108319i	0.861763	−	0.507311i	$-0.169360\pi$
$383$	−21.1383	−	41.4863i	−0.0551914	−	0.108319i	−0.916955	+	0.398991i	$0.869360\pi$
$384$		−	0.620470i		−	0.00161581i
$385$	491.514	+	248.426i	1.27666	+	0.645263i
$386$	214.878			0.556679
$387$	96.0446	−	48.9372i	0.248177	−	0.126453i
$388$	18.6623	−	117.829i	0.0480987	−	0.303683i
$389$	291.694	−	401.483i	0.749857	−	1.03209i	−0.248134	−	0.968726i	$-0.579817\pi$
$389$	291.694	−	401.483i	0.749857	−	1.03209i	0.997991	−	0.0633633i	$-0.0201827\pi$
$390$	0.559162	−	0.0706956i	0.00143375	−	0.000181271i
$391$	3.80227	+	11.7022i	0.00972448	+	0.0299289i
$392$	22.6830	+	143.215i	0.0578647	+	0.365343i
$393$	−0.937662	+	5.92017i	−0.00238591	+	0.0150640i
$394$	−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	−0.999794	−	0.0203041i	$-0.993537\pi$
$397$	−404.979	−	404.979i	−1.02010	−	1.02010i	−0.0203041	−	0.999794i	$-0.506463\pi$
$398$	25.3553	+	49.7626i	0.0637069	+	0.125032i
$399$	−10.3832	−	14.2912i	−0.0260230	−	0.0358176i
$400$	84.4220	−	53.5996i	0.211055	−	0.133999i
$401$	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	$0.850117\pi$
$402$	2.47374	−	4.85499i	0.00615359	−	0.0120771i
$403$	52.7411	−	8.35337i	0.130871	−	0.0207280i
$404$	−134.567	−	185.215i	−0.333086	−	0.458453i
$405$	112.917	+	388.518i	0.278808	+	0.959303i
$406$	546.311			1.34559
$407$	284.768	−	55.2544i	0.699675	−	0.135760i
$408$	0.0463246	−	0.0463246i	0.000113541	−	0.000113541i
$409$	90.3434	+	29.3544i	0.220889	+	0.0717711i	0.417371	−	0.908736i	$-0.362952\pi$
$409$	90.3434	+	29.3544i	0.220889	+	0.0717711i	−0.196482	+	0.980507i	$0.562952\pi$
$410$	−146.531	+	68.9704i	−0.357394	+	0.168221i
$411$	−3.75901	−	2.73108i	−0.00914600	−	0.00664496i
$412$	46.5945	−	91.4469i	0.113093	−	0.221958i
$413$	−1029.49	−	524.553i	−2.49272	−	1.27010i
$414$	−217.884	+	299.892i	−0.526291	+	0.724377i
$415$	174.367	+	370.452i	0.420161	+	0.892655i
$416$	−2.54061	+	7.81919i	−0.00610723	+	0.0187961i
$417$	−3.58788	−	3.58788i	−0.00860404	−	0.00860404i
$418$	211.635	−	453.457i	0.506304	−	1.08482i
$419$		−	434.554i		−	1.03712i	−0.855040	−	0.518561i	$-0.826468\pi$
$419$		−	434.554i		−	1.03712i	0.855040	−	0.518561i	$-0.173532\pi$
$420$	5.27330	−	1.53261i	0.0125555	−	0.00364907i
$421$	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	$-0.0425290\pi$
$422$	−28.1280	−	177.593i	−0.0666539	−	0.420836i
$423$	308.792	+	157.337i	0.730005	+	0.371956i
$424$	−210.046	+	68.2481i	−0.495392	+	0.160963i
$425$	10.3048	+	2.30122i	0.0242465	+	0.00541463i
$426$	−0.157187	+	0.114203i	−0.000368984	+	0.000268083i
$427$	564.579	−	287.668i	1.32220	−	0.673694i
$428$	−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	$0.834106\pi$
$432$	3.89938	+	0.617601i	0.00902635	+	0.00142963i
$433$	−657.518	+	104.141i	−1.51852	+	0.240510i	−0.859312	−	0.511452i	$-0.829108\pi$
$433$	−657.518	+	104.141i	−1.51852	+	0.240510i	−0.659206	+	0.751962i	$0.729108\pi$
$434$	494.818	−	160.776i	1.14013	−	0.370452i
$435$	−1.32693	−	10.4952i	−0.00305041	−	0.0241270i
$436$	61.7706	+	44.8790i	0.141676	+	0.102933i
$437$	925.625	+	146.605i	2.11813	+	0.335480i
$438$	3.46174	+	6.79405i	0.00790352	+	0.0155115i
$439$		−	194.650i		−	0.443395i	−0.975115	−	0.221698i	$-0.928840\pi$
$439$		−	194.650i		−	0.443395i	0.975115	−	0.221698i	$-0.0711598\pi$
$440$	110.358	+	109.641i	0.250813	+	0.249185i
$441$	−461.232			−1.04588
$442$	−0.773468	+	0.394102i	−0.00174993	+	0.000891633i
$443$	−82.6731	+	521.977i	−0.186621	+	1.17828i	0.699434	+	0.714697i	$0.253436\pi$
$443$	−82.6731	+	521.977i	−0.186621	+	1.17828i	−0.886055	+	0.463581i	$0.846564\pi$
$444$	1.70015	−	2.34006i	0.00382917	−	0.00527040i
$445$	−319.539	+	412.032i	−0.718065	+	0.925915i
$446$	47.9417	+	147.549i	0.107493	+	0.330828i
$447$	1.59575	+	10.0752i	0.00356992	+	0.0225396i
$448$	−12.5313	+	79.1198i	−0.0279717	+	0.176607i
$449$	−258.084	−	83.8564i	−0.574796	−	0.186763i	0.00717174	−	0.999974i	$-0.497717\pi$
$449$	−258.084	−	83.8564i	−0.574796	−	0.186763i	−0.581968	+	0.813212i	$0.697717\pi$
$450$	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
$453$	−1.39614	−	2.74007i	−0.00308198	−	0.00604873i
$454$	12.3116	+	16.9454i	0.0271180	+	0.0373247i
$455$	−72.7298	−	2.27832i	−0.159846	−	0.00500730i
$456$	−1.54193	−	4.74556i	−0.00338142	−	0.0104069i
$457$	−172.425	+	338.403i	−0.377297	+	0.740487i	−0.999088	−	0.0426961i	$-0.986405\pi$
$457$	−172.425	+	338.403i	−0.377297	+	0.740487i	0.621791	+	0.783183i	$0.286405\pi$
$458$	−414.809	+	65.6993i	−0.905697	+	0.143448i
$459$	0.245019	+	0.337240i	0.000533811	+	0.000734728i
$460$	−140.327	+	255.314i	−0.305058	+	0.555031i
$461$	−104.939			−0.227634			−0.113817	−	0.993502i	$-0.536308\pi$
$461$	−104.939			−0.227634			−0.113817	+	0.993502i	$0.536308\pi$
$462$	4.13912	+	7.47306i	0.00895913	+	0.0161755i
$463$	−65.6026	+	65.6026i	−0.141690	+	0.141690i	−0.774394	−	0.632704i	$-0.781945\pi$
$463$	−65.6026	+	65.6026i	−0.141690	+	0.141690i	0.632704	+	0.774394i	$0.281945\pi$
$464$	146.763	+	47.6862i	0.316300	+	0.102772i
$465$	−4.29054	−	9.11548i	−0.00922696	−	0.0196032i
$466$	−487.918	−	354.493i	−1.04703	−	0.760715i
$467$	−311.761	+	611.865i	−0.667582	+	1.31020i	0.270142	+	0.962821i	$0.412930\pi$
$467$	−311.761	+	611.865i	−0.667582	+	1.31020i	−0.937723	+	0.347383i	$0.887070\pi$
$468$	−23.3018	−	11.8728i	−0.0497901	−	0.0253693i
$469$	−413.495	+	569.127i	−0.881653	+	1.21349i
$470$	256.285	+	92.2393i	0.545288	+	0.196254i
$471$	3.12759	−	9.62574i	0.00664033	−	0.0204368i
$472$	−230.780	−	230.780i	−0.488940	−	0.488940i
$473$	96.3561	+	89.9138i	0.203713	+	0.190093i
$474$		−	6.84678i		−	0.0144447i
$475$	512.488	−	619.744i	1.07892	−	1.30472i
$476$	−6.84272	+	4.97153i	−0.0143755	+	0.0104444i
$477$	−109.899	−	693.874i	−0.230396	−	1.45466i
$478$	67.9235	+	34.6087i	0.142099	+	0.0724032i
$479$	−44.7516	+	14.5407i	−0.0934271	+	0.0303563i	−0.355358	−	0.934730i	$-0.615641\pi$
$479$	−44.7516	+	14.5407i	−0.0934271	+	0.0303563i	0.261930	+	0.965087i	$0.415641\pi$
$480$	1.55041	+	0.0485680i	0.00323003	+	0.000101183i
$481$	−31.0071	+	22.5280i	−0.0644639	+	0.0468357i
$482$	322.064	−	164.100i	0.668182	−	0.340456i
$483$	−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
$487$	−809.873	−	128.271i	−1.66298	−	0.263391i	−0.747064	−	0.664752i	$-0.768537\pi$
$487$	−809.873	−	128.271i	−1.66298	−	0.263391i	−0.915920	+	0.401362i	$0.868537\pi$
$488$	176.780	−	27.9993i	0.362255	−	0.0573755i
$489$	−7.46367	+	2.42509i	−0.0152631	+	0.00495929i
$490$	−359.636	+	45.4693i	−0.733952	+	0.0927945i
$491$	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	$0.669240\pi$
$492$	−2.48123	−	0.392988i	−0.00504315	−	0.000798756i
$493$	7.39713	+	14.5177i	0.0150043	+	0.0294476i
$494$			66.1174i			0.133841i
$495$	−399.380	+	292.159i	−0.806829	+	0.590219i
$496$	146.963			0.296297
$497$	22.3504	−	11.3881i	0.0449706	−	0.0229136i
$498$	−0.993528	+	6.27289i	−0.00199504	+	0.0125962i
$499$	−330.715	+	455.190i	−0.662756	+	0.912205i	−0.999569	−	0.0293667i	$-0.990651\pi$
$499$	−330.715	+	455.190i	−0.662756	+	0.912205i	0.336813	+	0.941572i	$0.390651\pi$
$500$	127.325	+	215.147i	0.254650	+	0.430294i
$501$	0.609056	+	1.87448i	0.00121568	+	0.00374148i
$502$	−54.1303	−	341.765i	−0.107829	−	0.680807i
$503$	46.5066	−	293.631i	0.0924585	−	0.583760i	−0.897346	−	0.441328i	$-0.854508\pi$
$503$	46.5066	−	293.631i	0.0924585	−	0.583760i	0.989805	−	0.142432i	$-0.0454923\pi$
$504$	−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
$508$	−43.0983	−	84.5852i	−0.0848392	−	0.166506i
$509$	159.382	+	219.370i	0.313127	+	0.430982i	0.936353	−	0.351059i	$-0.114178\pi$
$509$	159.382	+	219.370i	0.313127	+	0.430982i	−0.623226	+	0.782042i	$0.714178\pi$
$510$	0.112129	+	0.119381i	0.000219860	+	0.000234080i
$511$	−304.211	−	936.264i	−0.595324	−	1.83222i
$512$	−10.2726	+	20.1612i	−0.0200637	+	0.0393773i
$513$	31.3586	−	4.96671i	0.0611278	−	0.00968169i
$514$	−10.6954	−	14.7210i	−0.0208082	−	0.0286400i
$515$	224.858	+	123.587i	0.436617	+	0.239975i
$516$	1.31414			0.00254678
$517$	−51.7794	+	420.546i	−0.100154	+	0.813435i
$518$	−264.057	+	264.057i	−0.509763	+	0.509763i
$519$	−0.375901	−	0.122137i	−0.000724278	−	0.000235332i
$520$	−19.3395	−	6.96047i	−0.0371914	−	0.0133855i
$521$	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	$0.560980\pi$
$522$	−222.848	+	437.364i	−0.426913	+	0.837863i
$523$	15.5980	+	7.94760i	0.0298242	+	0.0151962i	0.468839	−	0.883284i	$-0.344672\pi$
$523$	15.5980	+	7.94760i	0.0298242	+	0.0151962i	−0.439015	+	0.898480i	$0.644672\pi$
$524$	128.483	−	176.842i	0.245197	−	0.337485i
$525$	3.41687	+	13.2967i	0.00650832	+	0.0253271i
$526$	−147.352	+	453.504i	−0.280138	+	0.862175i
$527$	10.9724	+	10.9724i	0.0208204	+	0.0208204i
$528$	0.459642	+	2.36888i	0.000870533	+	0.00448652i
$529$		−	319.769i		−	0.604479i
$530$	−154.095	−	530.200i	−0.290745	−	1.00038i
$531$	839.890	−	610.216i	1.58171	−	1.14918i
$532$	100.776	+	636.276i	0.189429	+	1.19601i
$533$	29.6594	+	15.1122i	0.0556462	+	0.0283531i
$534$	−7.69223	+	2.49936i	−0.0144049	+	0.00468044i
$535$	−392.696	−	418.094i	−0.734011	−	0.781485i
$536$	−160.761	+	116.799i	−0.299926	+	0.217909i
$537$	−4.88204	+	2.48752i	−0.00909132	+	0.00463226i
$538$	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	$0.197548\pi$
$542$	122.571	+	19.4133i	0.226145	+	0.0358179i
$543$	10.1473	−	1.60718i	0.0186875	−	0.00295981i
$544$	−2.27220	+	0.738284i	−0.00417685	+	0.00135714i
$545$	−116.978	+	150.838i	−0.214638	+	0.276767i
$546$	−0.913154	−	0.663445i	−0.00167244	−	0.00121510i
$547$	−962.318	−	152.416i	−1.75927	−	0.278640i	−0.808487	−	0.588514i	$-0.799713\pi$
$547$	−962.318	−	152.416i	−1.75927	−	0.278640i	−0.950778	+	0.309873i	$0.899713\pi$
$548$	76.9265	+	150.977i	0.140377	+	0.275505i
$549$			569.333i			1.03704i
$550$	−282.607	+	267.177i	−0.513831	+	0.485775i
$551$	1241.00			2.25226
$552$	−4.02658	+	2.05165i	−0.00729453	+	0.00371675i
$553$	−138.281	+	873.073i	−0.250056	+	1.57879i
$554$	112.193	−	154.421i	0.202515	−	0.278738i
$555$	5.71420	+	4.43147i	0.0102959	+	0.00798463i
$556$	57.1808	+	175.984i	0.102843	+	0.316519i
$557$	80.1711	+	506.181i	0.143934	+	0.908762i	0.948931	+	0.315484i	$0.102167\pi$
$557$	80.1711	+	506.181i	0.143934	+	0.908762i	−0.804997	+	0.593279i	$0.797833\pi$
$558$	−73.1297	+	461.722i	−0.131057	+	0.827460i
$559$	−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
$563$	98.0830	+	192.499i	0.174215	+	0.341916i	0.961559	−	0.274597i	$-0.0885446\pi$
$563$	98.0830	+	192.499i	0.174215	+	0.341916i	−0.787344	+	0.616513i	$0.788545\pi$
$564$	2.48343	+	3.41815i	0.00440325	+	0.00606056i
$565$	42.0905	−	39.5335i	0.0744964	−	0.0699708i
$566$	−134.773	−	414.789i	−0.238115	−	0.732843i
$567$	367.850	−	721.947i	0.648766	−	1.27328i
$568$	6.99832	−	1.10842i	0.0123210	−	0.00195145i
$569$	−290.736	−	400.163i	−0.510959	−	0.703275i	0.473122	−	0.880997i	$-0.343127\pi$
$569$	−290.736	−	400.163i	−0.510959	−	0.703275i	−0.984081	+	0.177722i	$0.943127\pi$
$570$	11.9788	−	3.48146i	0.0210154	−	0.00610783i
$571$	−316.381			−0.554083			−0.277041	−	0.960858i	$-0.589354\pi$
$571$	−316.381			−0.554083			−0.277041	+	0.960858i	$0.589354\pi$
$572$	3.90732	−	31.7348i	0.00683098	−	0.0554805i
$573$	−0.679376	+	0.679376i	−0.00118565	+	0.00118565i
$574$	308.459	+	100.224i	0.537385	+	0.174607i
$575$	−626.988	−	370.630i	−1.09041	−	0.644574i
$576$	−58.2298	−	42.3064i	−0.101093	−	0.0734486i
$577$	483.476	−	948.875i	0.837913	−	1.64450i	0.0757362	−	0.997128i	$-0.475869\pi$
$577$	483.476	−	948.875i	0.837913	−	1.64450i	0.762177	−	0.647369i	$-0.224131\pi$
$578$	363.936	+	185.435i	0.629648	+	0.320822i
$579$	−4.89792	+	6.74140i	−0.00845927	+	0.0116432i
$580$	−130.645	+	362.995i	−0.225250	+	0.625853i
$581$	253.381	−	779.826i	0.436112	−	1.34221i
$582$	3.27129	+	3.27129i	0.00562077	+	0.00562077i
$583$	751.373	−	416.165i	1.28881	−	0.713833i
$584$		−	278.075i		−	0.476156i
$585$	31.4915	−	57.2965i	0.0538317	−	0.0979427i
$586$	−510.734	+	371.070i	−0.871560	+	0.633226i
$587$	46.0919	+	291.013i	0.0785212	+	0.495763i	0.995337	+	0.0964539i	$0.0307500\pi$
$587$	46.0919	+	291.013i	0.0785212	+	0.495763i	−0.916816	+	0.399309i	$0.869250\pi$
$588$	−5.01013	−	2.55279i	−0.00852063	−	0.00434148i
$589$	1124.02	−	365.217i	1.90836	−	0.620063i
$590$	594.731	−	558.602i	1.00802	−	0.946783i
$591$	10.5272	−	7.64847i	0.0178125	−	0.0129416i
$592$	−93.9862	+	47.8884i	−0.158760	+	0.0808925i
$593$	−405.664	+	405.664i	−0.684088	+	0.684088i	−0.960919	−	0.276831i	$-0.910716\pi$
$593$	−405.664	+	405.664i	−0.684088	+	0.684088i	0.276831	+	0.960919i	$0.410716\pi$
$594$	−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
$597$	−2.13916	−	0.338810i	−0.00358318	−	0.000567521i
$598$	59.1440	−	9.36748i	0.0989029	−	0.0156647i
$599$	979.953	−	318.406i	1.63598	−	0.531563i	0.660346	−	0.750961i	$-0.270409\pi$
$599$	979.953	−	318.406i	1.63598	−	0.531563i	0.975635	+	0.219398i	$0.0704094\pi$
$600$	−0.242721	+	3.87033i	−0.000404535	+	0.00645056i
$601$	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	$0.395528\pi$
$602$	−167.573	−	26.5410i	−0.278361	−	0.0440880i
$603$	−286.960	−	563.190i	−0.475887	−	0.933980i
$604$			112.149i			0.185677i
$605$	−502.554	−	336.845i	−0.830668	−	0.556768i
$606$	8.87809			0.0146503
$607$	−798.188	+	406.697i	−1.31497	+	0.670011i	−0.963882	−	0.266330i	$-0.914189\pi$
$607$	−798.188	+	406.697i	−1.31497	+	0.670011i	−0.351090	+	0.936342i	$0.614189\pi$
$608$	−28.4661	+	179.728i	−0.0468192	+	0.295605i
$609$	−12.4526	+	17.1395i	−0.0204476	+	0.0281437i
$610$	56.1261	+	443.926i	0.0920101	+	0.727747i
$611$	−17.3002	−	53.2445i	−0.0283146	−	0.0871433i
$612$	−1.18885	−	7.50608i	−0.00194256	−	0.0122648i
$613$	51.0066	−	322.043i	0.0832082	−	0.525356i	−0.910514	−	0.413479i	$-0.864314\pi$
$613$	51.0066	−	322.043i	0.0832082	−	0.525356i	0.993722	−	0.111877i	$-0.0356864\pi$
$614$	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	0.872107	−	0.489315i	$-0.162753\pi$
$617$	236.183	+	236.183i	0.382793	+	0.382793i	−0.489315	+	0.872107i	$0.662753\pi$
$618$	1.80691	+	3.54625i	0.00292380	+	0.00573827i
$619$	7.06702	+	9.72692i	0.0114168	+	0.0157139i	0.814687	−	0.579901i	$-0.196909\pi$
$619$	7.06702	+	9.72692i	0.0114168	+	0.0157139i	−0.803270	+	0.595614i	$0.796909\pi$
$620$	−11.5037	+	367.228i	−0.0185544	+	0.592303i
$621$	−8.88573	−	27.3475i	−0.0143087	−	0.0440378i
$622$	46.7041	−	91.6620i	0.0750870	−	0.147367i
$623$	1031.36	−	163.351i	1.65547	−	0.262201i
$624$	−0.187402	−	0.257937i	−0.000300324	−	0.000413361i
$625$	−547.571	+	301.316i	−0.876113	+	0.482105i
$626$	679.094			1.08482
$627$	9.40238	+	16.9757i	0.0149958	+	0.0270745i
$628$	−260.992	+	260.992i	−0.415592	+	0.415592i
$629$	−10.5924	−	3.44169i	−0.0168401	−	0.00547168i
$630$	215.725	−	599.387i	0.342420	−	0.951409i
$631$	−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	$0.853759\pi$
$632$	−113.357	+	222.475i	−0.179362	+	0.352018i
$633$	6.21280	+	3.16558i	0.00981485	+	0.00500092i
$634$	−180.878	+	248.957i	−0.285297	+	0.392677i
$635$	214.733	−	101.072i	0.338162	−	0.159168i
$636$	2.64662	−	8.14546i	0.00416135	−	0.0128073i
$637$	52.6851	+	52.6851i	0.0827082	+	0.0827082i
$638$	−595.650	−	73.3388i	−0.933620	−	0.114951i
$639$			22.5386i			0.0352716i
$640$	−49.5741	−	27.2471i	−0.0774596	−	0.0425736i
$641$	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	$0.259048\pi$
$642$	−1.39187	−	8.78795i	−0.00216803	−	0.0136884i
$643$	236.684	+	120.596i	0.368093	+	0.187553i	0.628246	−	0.778015i	$-0.283773\pi$
$643$	236.684	+	120.596i	0.368093	+	0.187553i	−0.260153	+	0.965567i	$0.583773\pi$
$644$	554.889	−	180.294i	0.861629	−	0.279960i
$645$	−0.102866	+	3.28373i	−0.000159481	+	0.00509105i
$646$	−15.5439	+	11.2933i	−0.0240617	+	0.0174819i
$647$	409.458	−	208.629i	0.632856	−	0.322456i	−0.107969	−	0.994154i	$-0.534435\pi$
$647$	409.458	−	208.629i	0.632856	−	0.322456i	0.740825	+	0.671698i	$0.234435\pi$
$648$	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
$652$	282.670	+	44.7706i	0.433543	+	0.0686665i
$653$	956.916	−	151.561i	1.46541	−	0.232099i	0.627806	−	0.778370i	$-0.283953\pi$
$653$	956.916	−	151.561i	1.46541	−	0.232099i	0.837608	+	0.546271i	$0.183953\pi$
$654$	−2.81599	+	0.914971i	−0.00430580	+	0.00139904i
$655$	431.831	+	334.893i	0.659285	+	0.511288i
$656$	74.1171	+	53.8492i	0.112983	+	0.0820873i
$657$	873.644	+	138.372i	1.32975	+	0.210611i
$658$	−247.642	−	486.025i	−0.376356	−	0.738641i
$659$			680.077i			1.03198i	0.856593	+	0.515992i	$0.172577\pi$
$659$			680.077i			1.03198i	−0.856593	+	0.515992i	$0.827423\pi$
$660$	−5.95528	+	0.963114i	−0.00902315	+	0.00145926i
$661$	−416.848			−0.630632			−0.315316	−	0.948987i	$-0.602111\pi$
$661$	−416.848			−0.630632			−0.315316	+	0.948987i	$0.602111\pi$
$662$	−51.3143	+	26.1459i	−0.0775140	+	0.0394954i
$663$	0.00526617	−	0.0332493i	7.94294e−6	−	5.01498e-5i
$664$	136.138	−	187.378i	0.205028	−	0.282196i
$665$	−1597.80	+	202.012i	−2.40270	+	0.303777i
$666$	−103.685	−	319.111i	−0.155684	−	0.479146i
$667$	−175.824	−	1110.11i	−0.263604	−	1.66433i
$668$	11.2440	−	70.9919i	0.0168324	−	0.106275i
$669$	−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
$673$	204.518	+	401.389i	0.303890	+	0.596418i	0.991566	−	0.129600i	$-0.0413692\pi$
$673$	204.518	+	401.389i	0.303890	+	0.596418i	−0.687676	+	0.726017i	$0.741369\pi$
$674$	−249.680	−	343.656i	−0.370446	−	0.509875i
$675$	−24.0818	−	5.37783i	−0.0356767	−	0.00796716i
$676$	−103.142	−	317.439i	−0.152577	−	0.469585i
$677$	−406.535	+	797.871i	−0.600495	+	1.17854i	0.368074	+	0.929796i	$0.380017\pi$
$677$	−406.535	+	797.871i	−0.600495	+	1.17854i	−0.968570	+	0.248742i	$0.919983\pi$
$678$	0.884701	−	0.140123i	0.00130487	−	0.000206671i
$679$	−351.072	−	483.209i	−0.517043	−	0.711648i
$680$	−1.66695	−	5.73552i	−0.00245139	−	0.00843458i
$681$	−0.812261			−0.00119275
$682$	−561.088	+	108.870i	−0.822710	+	0.159633i
$683$	−450.561	+	450.561i	−0.659680	+	0.659680i	−0.955304	−	0.295624i	$-0.904472\pi$
$683$	−450.561	+	450.561i	−0.659680	+	0.659680i	0.295624	+	0.955304i	$0.404472\pi$
$684$	−550.496	−	178.867i	−0.804818	−	0.261501i
$685$	−383.279	+	180.404i	−0.559531	+	0.263364i
$686$	25.9506	+	18.8542i	0.0378288	+	0.0274843i
$687$	7.39394	−	14.5114i	0.0107627	−	0.0211229i
$688$	−42.7007	−	21.7571i	−0.0620650	−	0.0316237i
$689$	−66.7057	+	91.8125i	−0.0968152	+	0.133255i
$690$	−4.81142	−	10.2221i	−0.00697307	−	0.0148147i
$691$	−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
$693$	983.553	+	121.099i	1.41927	+	0.174746i
$694$			866.733i			1.24889i
$695$	−444.221	+	129.106i	−0.639167	+	0.185765i
$696$	−4.84138	+	3.51747i	−0.00695600	+	0.00505383i
$697$	1.51321	+	9.55404i	0.00217103	+	0.0137074i
$698$	221.753	+	112.989i	0.317697	+	0.161875i
$699$	22.2432	−	7.22724i	0.0318214	−	0.0103394i
$700$	109.118	−	488.627i	0.155883	−	0.698038i
$701$	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	$0.197585\pi$
$702$	1.80756	−	0.920997i	0.00257487	−	0.00131196i
$703$	−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
$707$	−1132.10	−	179.307i	−1.60127	−	0.253616i
$708$	12.5007	−	1.97991i	0.0176563	−	0.00279649i
$709$	−928.632	+	301.731i	−1.30978	+	0.425572i	−0.878972	−	0.476873i	$-0.841770\pi$
$709$	−928.632	+	301.731i	−1.30978	+	0.425572i	−0.430805	+	0.902445i	$0.641770\pi$
$710$	2.22190	+	17.5740i	0.00312944	+	0.0247521i
$711$	−642.556	−	466.844i	−0.903735	−	0.656602i
$712$	291.327	+	46.1416i	0.409166	+	0.0648056i
$713$	−485.949	−	953.728i	−0.681555	−	1.33763i
$714$		−	0.327999i		−	0.000459382i
$715$	78.9923	+	12.2476i	0.110479	+	0.0171295i
$716$	199.818			0.279075
$717$	−2.63403	+	1.34211i	−0.00367368	+	0.00187183i
$718$	−58.6085	+	370.040i	−0.0816275	+	0.515376i
$719$	−674.882	+	928.896i	−0.938640	+	1.29193i	0.0177523	+	0.999842i	$0.494349\pi$
$719$	−674.882	+	928.896i	−0.938640	+	1.29193i	−0.956392	+	0.292085i	$0.905651\pi$
$720$	110.272	−	142.191i	0.153156	−	0.197488i
$721$	−158.787	−	488.697i	−0.220232	−	0.677804i
$722$	149.058	+	941.113i	0.206451	+	1.30348i
$723$	−2.19278	+	13.8446i	−0.00303289	+	0.0191489i
$724$	−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	0.730416	−	0.683002i	$-0.239326\pi$
$727$	34.4699	+	34.4699i	0.0474139	+	0.0474139i	−0.683002	+	0.730416i	$0.739326\pi$
$728$	18.6873	+	36.6760i	0.0256694	+	0.0503791i
$729$	427.637	+	588.591i	0.586607	+	0.807395i
$730$	694.847	+	21.7666i	0.951845	+	0.0298173i
$731$	−1.56366	−	4.81246i	−0.00213907	−	0.00658339i
$732$	−3.15110	+	6.18438i	−0.00430478	+	0.00844860i
$733$	−1276.25	+	202.138i	−1.74113	+	0.275768i	−0.944454	−	0.328643i	$-0.893409\pi$
$733$	−1276.25	+	202.138i	−1.74113	+	0.275768i	−0.796673	+	0.604410i	$0.793409\pi$
$734$	181.535	+	249.862i	0.247323	+	0.340411i
$735$	6.77102	−	12.3194i	0.00921227	−	0.0167610i
$736$	164.805			0.223920
$737$	527.240	−	565.017i	0.715387	−	0.766644i
$738$	−206.062	+	206.062i	−0.279217	+	0.279217i
$739$	−1054.29	−	342.559i	−1.42664	−	0.463544i	−0.508935	−	0.860805i	$-0.669961\pi$
$739$	−1054.29	−	342.559i	−1.42664	−	0.463544i	−0.917706	+	0.397261i	$0.869961\pi$
$740$	−112.305	−	238.599i	−0.151764	−	0.322431i
$741$	−2.07431	−	1.50708i	−0.00279934	−	0.00203384i
$742$	−501.996	+	985.222i	−0.676544	+	1.32779i
$743$	967.579	+	493.006i	1.30226	+	0.663534i	0.961030	−	0.276446i	$-0.0891566\pi$
$743$	967.579	+	493.006i	1.30226	+	0.663534i	0.341230	+	0.939980i	$0.389157\pi$
$744$	−3.34987	+	4.61070i	−0.00450252	+	0.00619718i
$745$	875.061	+	314.942i	1.17458	+	0.422741i
$746$	14.8558	−	45.7214i	0.0199139	−	0.0612887i
$747$	520.953	+	520.953i	0.697394	+	0.697394i
$748$	8.12809	−	4.50192i	0.0108664	−	0.00601861i
$749$			1148.71i			1.53366i
$750$	−9.65209	−	0.909460i	−0.0128695	−	0.00121261i
$751$	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	$0.0466816\pi$
$752$	−24.1035	−	152.184i	−0.0320526	−	0.202372i
$753$	11.9561	+	6.09194i	0.0158780	+	0.00809022i
$754$	75.4140	−	24.5035i	0.100019	−	0.0324980i
$755$	−280.235	−	8.77859i	−0.371172	−	0.0116273i
$756$	15.9911	−	11.6182i	0.0211523	−	0.0153680i
$757$	−1106.38	+	563.731i	−1.46154	+	0.744691i	−0.990512	−	0.137429i	$-0.956116\pi$
$757$	−1106.38	+	563.731i	−1.46154	+	0.744691i	−0.471026	+	0.882119i	$0.656116\pi$
$758$	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	$0.133887\pi$
$762$	3.63609	+	0.575900i	0.00477177	+	0.000755774i
$763$	377.563	−	59.8001i	0.494840	−	0.0783749i
$764$	33.3231	−	10.8273i	0.0436166	−	0.0141719i
$765$	18.8491	−	2.38311i	0.0246393	−	0.00311518i
$766$	−53.2717	−	38.7041i	−0.0695452	−	0.0505276i
$767$	−165.641	−	26.2350i	−0.215960	−	0.0342047i
$768$	−0.398366	−	0.781838i	−0.000518706	−	0.00101802i
$769$		−	1094.24i		−	1.42294i	−0.702716	−	0.711470i	$-0.748030\pi$
$769$		−	1094.24i		−	1.42294i	0.702716	−	0.711470i	$-0.251970\pi$
$770$	778.844	−	2.53632i	1.01149	−	0.00329392i
$771$	0.705633			0.000915218
$772$	270.762	−	137.960i	0.350728	−	0.178705i
$773$	68.3057	−	431.265i	0.0883645	−	0.557911i	−0.903294	−	0.429021i	$-0.858859\pi$
$773$	68.3057	−	431.265i	0.0883645	−	0.557911i	0.991659	−	0.128890i	$-0.0411414\pi$
$774$	89.6036	−	123.329i	0.115767	−	0.159340i
$775$	−916.719	−	57.4904i	−1.18286	−	0.0741811i
$776$	−52.1351	−	160.455i	−0.0671844	−	0.206772i
$777$	−2.26541	−	14.3032i	−0.00291558	−	0.0184083i
$778$	109.788	−	693.177i	0.141116	−	0.890973i
$779$	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
$783$	−17.2867	−	33.9271i	−0.0220776	−	0.0433297i
$784$	120.532	+	165.898i	0.153739	+	0.211604i
$785$	−631.730	−	672.589i	−0.804752	−	0.856802i
$786$	2.61946	+	8.06186i	0.00333264	+	0.0102568i
$787$	636.291	−	1248.79i	0.808502	−	1.58677i	−0.00124742	−	0.999999i	$-0.500397\pi$
$787$	636.291	−	1248.79i	0.808502	−	1.58677i	0.809750	−	0.586776i	$-0.199603\pi$
$788$	−468.695	+	74.2339i	−0.594790	+	0.0942055i
$789$	−10.8691	−	14.9601i	−0.0137758	−	0.0189608i
$790$	−547.042	−	300.667i	−0.692458	−	0.380592i
$791$	−115.643			−0.146199
$792$	253.655	+	118.384i	0.320271	+	0.149475i
$793$	65.0331	−	65.0331i	0.0820090	−	0.0820090i
$794$	−770.316	−	250.291i	−0.970171	−	0.315228i
$795$	20.1465	+	7.25090i	0.0253415	+	0.00912063i
$796$	63.8992	+	46.4255i	0.0802753	+	0.0583234i
$797$	−53.1272	+	104.268i	−0.0666590	+	0.130826i	−0.921932	−	0.387353i	$-0.873390\pi$
$797$	−53.1272	+	104.268i	−0.0666590	+	0.130826i	0.855273	+	0.518178i	$0.173390\pi$
$798$	−22.2591	−	11.3416i	−0.0278936	−	0.0142125i
$799$	9.56253	−	13.1617i	0.0119681	−	0.0164727i
$800$	71.9649	−	121.742i	0.0899561	−	0.152177i
$801$	−289.931	+	892.316i	−0.361961	+	1.11400i
$802$	125.170	+	125.170i	0.156072	+	0.156072i
$803$	205.997	+	1061.66i	0.256534	+	1.32211i
$804$		−	7.70589i		−	0.00958444i
$805$	407.080	+	1400.66i	0.505690	+	1.73994i
$806$	61.0945	−	44.3877i	0.0757996	−	0.0550716i
$807$	1.79171	+	11.3124i	0.00222021	+	0.0140179i
$808$	−288.479	−	146.988i	−0.357029	−	0.181915i
$809$	−494.845	+	160.785i	−0.611675	+	0.198745i	−0.598441	−	0.801167i	$-0.704213\pi$
$809$	−494.845	+	160.785i	−0.611675	+	0.198745i	−0.0132343	+	0.999912i	$0.504213\pi$
$810$	391.728	+	417.064i	0.483614	+	0.514893i
$811$	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	$0.262922\pi$
$812$	688.393	−	350.754i	0.847774	−	0.431963i
$813$	−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
$817$	−380.658	−	60.2903i	−0.465921	−	0.0737947i
$818$	132.686	−	21.0154i	0.162208	−	0.0256912i
$819$	−124.526	+	40.4609i	−0.152046	+	0.0494028i
$820$	−140.359	+	180.987i	−0.171169	+	0.220716i
$821$	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	$0.442575\pi$
$822$	−6.49008	−	1.02793i	−0.00789548	−	0.00125052i
$823$	417.891	+	820.158i	0.507766	+	0.996547i	0.992541	+	0.121908i	$0.0389013\pi$
$823$	417.891	+	820.158i	0.507766	+	0.996547i	−0.484776	+	0.874639i	$0.661099\pi$
$824$		−	145.145i		−	0.176147i
$825$	−1.94045	−	14.9563i	−0.00235206	−	0.0181288i
$826$	−1634.02			−1.97823
$827$	679.843	−	346.398i	0.822060	−	0.418860i	0.00823175	−	0.999966i	$-0.497380\pi$
$827$	679.843	−	346.398i	0.822060	−	0.418860i	0.813828	+	0.581106i	$0.197380\pi$
$828$	−82.0077	+	517.776i	−0.0990431	+	0.625334i
$829$	456.540	−	628.374i	0.550712	−	0.757990i	−0.439396	−	0.898293i	$-0.644808\pi$
$829$	456.540	−	628.374i	0.550712	−	0.757990i	0.990109	+	0.140303i	$0.0448077\pi$
$830$	457.560	+	354.846i	0.551277	+	0.427525i
$831$	2.28735	+	7.03973i	0.00275252	+	0.00847140i
$832$	1.81888	+	11.4839i	0.00218615	+	0.0138028i
$833$	−3.38704	+	21.3850i	−0.00406608	+	0.0256722i
$834$	−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
$838$	−279.001	−	547.570i	−0.332937	−	0.653425i
$839$	433.961	+	597.296i	0.517236	+	0.711914i	0.985118	−	0.171877i	$-0.0549830\pi$
$839$	433.961	+	597.296i	0.517236	+	0.711914i	−0.467883	+	0.883791i	$0.654983\pi$
$840$	5.66075	−	5.31687i	0.00673899	−	0.00632960i
$841$	−200.037	−	615.652i	−0.237857	−	0.732047i
$842$	475.783	−	933.777i	0.565063	−	1.10900i
$843$	1.29968	−	0.205848i	0.00154173	−	0.000244186i
$844$	−149.465	−	205.721i	−0.177091	−	0.243745i
$845$	801.283	−	232.881i	0.948263	−	0.275599i
$846$	490.118			0.579335
$847$	271.762	+	1180.73i	0.320852	+	1.39402i
$848$	−220.856	+	220.856i	−0.260443	+	0.260443i
$849$	16.0853	+	5.22642i	0.0189461	+	0.00615597i
$850$	14.4622	−	3.71637i	0.0170144	−	0.00437220i
$851$	621.549	+	451.582i	0.730375	+	0.530649i
$852$	−0.124745	+	0.244825i	−0.000146414	+	0.000287353i
$853$	533.213	+	271.686i	0.625103	+	0.318506i	0.737694	−	0.675135i	$-0.235915\pi$
$853$	533.213	+	271.686i	0.625103	+	0.318506i	−0.112590	+	0.993641i	$0.535915\pi$
$854$	526.718	−	724.964i	0.616765	−	0.848905i
$855$	490.039	−	1361.56i	0.573145	−	1.59247i
$856$	−100.268	+	308.594i	−0.117136	+	0.360507i
$857$	−576.629	−	576.629i	−0.672846	−	0.672846i	0.285525	−	0.958371i	$-0.407832\pi$
$857$	−576.629	−	576.629i	−0.672846	−	0.672846i	−0.958371	+	0.285525i	$0.907832\pi$
$858$	0.906559	+	0.845947i	0.00105660	+	0.000985952i
$859$			385.261i			0.448500i	0.974532	+	0.224250i	$0.0719932\pi$
$859$			385.261i			0.448500i	−0.974532	+	0.224250i	$0.928007\pi$
$860$	57.7086	−	104.996i	0.0671030	−	0.122089i
$861$	−10.1754	+	7.39283i	−0.0118181	+	0.00858633i
$862$	141.409	+	892.820i	0.164047	+	1.03575i
$863$	−1425.25	−	726.202i	−1.65151	−	0.841486i	−0.996291	−	0.0860459i	$-0.972577\pi$
$863$	−1425.25	−	726.202i	−1.65151	−	0.841486i	−0.655218	−	0.755440i	$-0.727423\pi$
$864$	5.31003	−	1.72533i	0.00614587	−	0.00199691i
$865$	−26.2657	+	24.6701i	−0.0303649	+	0.0285203i
$866$	−761.659	+	553.378i	−0.879514	+	0.639004i
$867$	−14.1132	+	7.19105i	−0.0162782	+	0.00829418i
$868$	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
$872$	106.650	+	16.8916i	0.122305	+	0.0193711i
$873$	530.054	−	83.9523i	0.607163	−	0.0961652i
$874$	1260.48	−	409.555i	1.44220	−	0.468599i
$875$	1212.43	+	310.909i	1.38563	+	0.355325i
$876$	8.72410	+	6.33843i	0.00995902	+	0.00723565i
$877$	−766.301	−	121.370i	−0.873775	−	0.138392i	−0.296589	−	0.955005i	$-0.595849\pi$
$877$	−766.301	−	121.370i	−0.873775	−	0.138392i	−0.577186	+	0.816613i	$0.695849\pi$
$878$	−124.973	−	245.274i	−0.142339	−	0.279355i
$879$		−	24.4815i		−	0.0278516i
$880$	209.453	+	67.3020i	0.238014	+	0.0764796i
$881$	317.840			0.360772			0.180386	−	0.983596i	$-0.442265\pi$
$881$	317.840			0.360772			0.180386	+	0.983596i	$0.442265\pi$
$882$	−581.187	+	296.129i	−0.658942	+	0.335748i
$883$	245.419	−	1549.52i	0.277938	−	1.75483i	−0.314539	−	0.949244i	$-0.601850\pi$
$883$	245.419	−	1549.52i	0.277938	−	1.75483i	0.592477	−	0.805587i	$-0.298150\pi$
$884$	−0.721598	+	0.993194i	−0.000816287	+	0.00112352i
$885$	3.96885	+	31.3913i	0.00448458	+	0.0354704i
$886$	230.956	+	710.809i	0.260672	+	0.802267i
$887$	−267.345	−	1687.95i	−0.301403	−	1.90298i	−0.415637	−	0.909530i	$-0.636441\pi$
$887$	−267.345	−	1687.95i	−0.301403	−	1.90298i	0.114234	−	0.993454i	$-0.463559\pi$
$888$	0.639907	−	4.04021i	0.000720615	−	0.00454979i
$889$	−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
$893$	−562.542	−	1104.05i	−0.629947	−	1.23634i
$894$	8.47944	+	11.6710i	0.00948484	+	0.0130548i
$895$	−15.6410	+	499.300i	−0.0174759	+	0.557877i
$896$	35.0076	+	107.742i	0.0390710	+	0.120248i
$897$	−1.05424	+	2.06906i	−0.00117529	+	0.00230664i
$898$	−379.043	+	60.0346i	−0.422097	+	0.0668536i
$899$	−833.139	−	1146.72i	−0.926740	−	1.27555i
$900$	346.673	+	286.675i	0.385192	+	0.318528i
$901$	−32.9784			−0.0366020
$902$	−322.862	−	150.684i	−0.357940	−	0.167056i
$903$	4.65233	−	4.65233i	0.00515208	−	0.00515208i
$904$	−31.0668	−	10.0942i	−0.0343660	−	0.0111662i
$905$	317.196	−	881.324i	0.350493	−	0.973839i
$906$	−3.51847	−	2.55632i	−0.00388352	−	0.00282154i
$907$	246.880	−	484.529i	0.272194	−	0.534211i	−0.713931	−	0.700216i	$-0.753087\pi$
$907$	246.880	−	484.529i	0.272194	−	0.534211i	0.986125	+	0.166005i	$0.0530869\pi$
$908$	26.3931	+	13.4480i	0.0290673	+	0.0148105i
$909$	605.348	−	833.190i	0.665949	−	0.916600i
$910$	−93.1077	+	43.8246i	−0.102316	+	0.0481589i
$911$	−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
$913$	−380.951	+	816.239i	−0.417252	+	0.894018i
$914$			537.116i			0.587654i
$915$	−15.2067	−	8.35797i	−0.0166193	−	0.00913439i
$916$	−480.508	+	349.110i	−0.524573	+	0.381124i
$917$	−171.201	−	1080.92i	−0.186697	−	1.17876i
$918$	0.525264	+	0.267635i	0.000572183	+	0.000291542i
$919$	798.077	−	259.311i	0.868419	−	0.282167i	0.159279	−	0.987234i	$-0.449083\pi$
$919$	798.077	−	259.311i	0.868419	−	0.282167i	0.709141	+	0.705067i	$0.249083\pi$
$920$	−12.9003	+	411.810i	−0.0140220	+	0.447620i
$921$	−21.7715	+	15.8180i	−0.0236390	+	0.0171748i
$922$	−132.231	+	67.3752i	−0.143418	+	0.0730750i
$923$	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
$927$	456.011	+	72.2250i	0.491921	+	0.0779127i
$928$	215.549	−	34.1395i	0.232272	−	0.0367883i
$929$	−1241.31	+	403.325i	−1.33618	+	0.434150i	−0.888020	−	0.459805i	$-0.847919\pi$
$929$	−1241.31	+	403.325i	−1.33618	+	0.434150i	−0.448157	+	0.893955i	$0.647919\pi$
$930$	−11.2589	−	8.73148i	−0.0121063	−	0.00938869i
$931$	1334.14	+	969.307i	1.43301	+	1.04115i
$932$	−842.411	−	133.425i	−0.903874	−	0.143160i
$933$	1.81116	+	3.55460i	0.00194122	+	0.00380986i
$934$			971.158i			1.03978i
$935$	10.6130	+	20.6627i	0.0113509	+	0.0220991i
$936$	−36.9848			−0.0395136
$937$	160.001	−	81.5245i	0.170759	−	0.0870059i	−0.366522	−	0.930409i	$-0.619452\pi$
$937$	160.001	−	81.5245i	0.170759	−	0.0870059i	0.537281	+	0.843403i	$0.319452\pi$
$938$	−155.632	+	982.623i	−0.165919	+	1.04757i
$939$	−15.4792	+	21.3053i	−0.0164848	+	0.0226894i
$940$	382.159	−	48.3169i	0.406553	−	0.0514010i
$941$	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	$0.736592\pi$
$942$	−2.23911	−	14.1372i	−0.00237697	−	0.0150076i
$943$	104.383	−	659.046i	0.110692	−	0.698882i
$944$	−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	0.978543	−	0.206043i	$-0.0660587\pi$
$947$	731.557	+	731.557i	0.772500	+	0.772500i	−0.206043	+	0.978543i	$0.566059\pi$
$948$	−4.39591	−	8.62745i	−0.00463703	−	0.00910069i
$949$	−83.9878	−	115.599i	−0.0885014	−	0.121812i
$950$	247.872	−	1109.96i	0.260918	−	1.16838i
$951$	−3.68766	−	11.3494i	−0.00387766	−	0.0119342i
$952$	−5.43041	+	10.6578i	−0.00570422	+	0.0111952i
$953$	−529.916	+	83.9304i	−0.556050	+	0.0880697i	−0.428134	−	0.903715i	$-0.640829\pi$
$953$	−529.916	+	83.9304i	−0.556050	+	0.0880697i	−0.127916	+	0.991785i	$0.540829\pi$
$954$	−583.975	−	803.773i	−0.612133	−	0.842529i
$955$	24.4467	+	84.1144i	0.0255986	+	0.0880780i
$956$	107.809			0.112771
$957$	15.8781	−	17.0157i	0.0165915	−	0.0177803i
$958$	−47.0546	+	47.0546i	−0.0491175	+	0.0491175i
$959$	806.828	+	262.154i	0.841322	+	0.273362i
$960$	1.98482	−	0.934228i	0.00206752	−	0.000973155i
$961$	−314.616	−	228.582i	−0.327384	−	0.237859i
$962$	−24.6074	+	48.2947i	−0.0255794	+	0.0502024i
$963$	−919.633	−	468.577i	−0.954967	−	0.486580i
$964$	300.466	−	413.555i	0.311686	−	0.428999i
$965$	323.537	+	687.372i	0.335271	+	0.712303i
$966$	−6.99171	+	21.5183i	−0.00723779	+	0.0222756i
$967$	607.058	+	607.058i	0.627774	+	0.627774i	0.947508	−	0.319733i	$-0.103593\pi$
$967$	607.058	+	607.058i	0.627774	+	0.627774i	−0.319733	+	0.947508i	$0.603593\pi$
$968$	−30.0562	+	340.917i	−0.0310498	+	0.352187i
$969$		−	0.745079i		−	0.000768915i
$970$	405.022	−	117.714i	0.417549	−	0.121355i
$971$	−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	$0.372233\pi$
$972$	4.16765	+	26.3135i	0.00428770	+	0.0270715i
$973$	825.455	+	420.590i	0.848361	+	0.432262i
$974$	−1102.85	+	358.339i	−1.13229	+	0.367905i
$975$	1.06807	+	1.68226i	0.00109545	+	0.00172539i
$976$	204.780	−	148.781i	0.209815	−	0.152440i
$977$	1181.94	−	602.229i	1.20977	−	0.616406i	0.271539	−	0.962427i	$-0.412467\pi$
$977$	1181.94	−	602.229i	1.20977	−	0.616406i	0.938227	+	0.346021i	$0.112467\pi$
$978$	−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
$982$	132.344	+	20.9612i	0.134770	+	0.0213454i
$983$	−518.491	+	82.1209i	−0.527458	+	0.0835411i	−0.414483	−	0.910057i	$-0.636038\pi$
$983$	−518.491	+	82.1209i	−0.527458	+	0.0835411i	−0.112974	+	0.993598i	$0.536038\pi$
$984$	−3.37884	+	1.09785i	−0.00343378	+	0.00111570i
$985$	−148.806	−	1176.97i	−0.151072	−	1.19490i
$986$	18.6418	+	13.5441i	0.0189065	+	0.0137364i
$987$	20.8929	+	3.30911i	0.0211681	+	0.00335270i
$988$	42.4500	+	83.3128i	0.0429656	+	0.0843247i
$989$			349.051i			0.352934i
$990$	−315.671	+	624.559i	−0.318860	+	0.630868i
$991$	−111.067			−0.112076			−0.0560381	−	0.998429i	$-0.517847\pi$
$991$	−111.067			−0.112076			−0.0560381	+	0.998429i	$0.517847\pi$
$992$	185.184	−	94.3562i	0.186678	−	0.0951171i
$993$	0.349374	−	2.20586i	0.000351837	−	0.00222141i
$994$	20.8515	−	28.6996i	0.0209774	−	0.0288729i
$995$	−121.009	+	156.036i	−0.121617	+	0.156820i
$996$	2.77552	+	8.54218i	0.00278667	+	0.00857649i
$997$	−68.7205	−	433.884i	−0.0689272	−	0.435189i	−0.997885	−	0.0650038i	$-0.979294\pi$
$997$	−68.7205	−	433.884i	−0.0689272	−	0.435189i	0.928958	−	0.370186i	$-0.120706\pi$
$998$	−124.475	+	785.905i	−0.124725	+	0.787480i
$999$	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.97.4	yes	48
5.3	odd	4	inner	110.3.l.a.53.4	yes	48
11.5	even	5	inner	110.3.l.a.27.4	✓	48
55.38	odd	20	inner	110.3.l.a.93.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.3.l.a.27.4	✓	48	11.5	even	5	inner
110.3.l.a.53.4	yes	48	5.3	odd	4	inner
110.3.l.a.93.4	yes	48	55.38	odd	20	inner
110.3.l.a.97.4	yes	48	1.1	even	1	trivial

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+(1.26007 - 0.642040i) q^{2} +(-0.00857923 + 0.0541671i) q^{3} +(1.17557 - 1.61803i) q^{4} +(3.95108 + 3.06414i) q^{5} +(0.0239670 + 0.0737628i) q^{6} +(-1.56642 - 9.88997i) q^{7} +(0.442463 - 2.79360i) 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} +(-0.659823 - 1.29498i) q^{13} +(-8.32355 - 11.4564i) q^{14} +(-0.199873 + 0.187731i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(0.191740 - 0.376311i) q^{17} +(12.5670 - 1.99042i) q^{18} +(-18.9077 - 26.0242i) q^{19} +(9.60266 - 2.79087i) q^{20} +0.549150 q^{21} +(7.53732 + 13.6084i) q^{22} +(-20.6006 + 20.6006i) q^{23} +(0.147526 + 0.0479340i) q^{24} +(6.22211 + 24.2133i) q^{25} +(-1.66285 - 1.20813i) q^{26} +(-0.448087 + 0.879421i) q^{27} +(-17.8437 - 9.09184i) q^{28} +(-22.6761 + 31.2110i) q^{29} +(-0.131324 + 0.364881i) q^{30} +(-11.3535 + 34.9426i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.598744 - 0.0737199i) q^{33} -0.597284i q^{34} +(24.1152 - 43.8758i) q^{35} +(14.5574 - 10.5766i) q^{36} +(-4.12530 - 26.0461i) q^{37} +(-40.5337 - 20.6529i) q^{38} +(0.0758059 - 0.0246308i) q^{39} +(10.3082 - 9.68199i) q^{40} +(-18.5293 + 13.4623i) q^{41} +(0.691969 - 0.352576i) 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} +(38.0459 + 6.02588i) q^{47} +(0.216669 - 0.0343169i) q^{48} +(-48.7561 + 15.8418i) q^{49} +(23.3862 + 26.5157i) q^{50} +(0.0187387 + 0.0136145i) q^{51} +(-2.87098 - 0.454719i) q^{52} +(-35.4495 - 69.5736i) q^{53} +1.39582i q^{54} +(-32.1831 + 44.6010i) q^{55} -28.3217 q^{56} +(1.57187 - 0.800909i) q^{57} +(-8.53489 + 53.8872i) q^{58} +(67.8245 - 93.3524i) q^{59} +(0.0687903 + 0.544092i) q^{60} +(19.5547 + 60.1832i) q^{61} +(8.12823 + 51.3196i) q^{62} +(14.0930 - 88.9800i) 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} +(-0.383480 - 0.752622i) q^{68} +(-0.939138 - 1.29261i) q^{69} +(2.21692 - 70.7697i) q^{70} +(0.774125 + 2.38251i) q^{71} +(11.5528 - 22.6737i) q^{72} +(97.1040 - 15.3798i) q^{73} +(-21.9208 - 30.1714i) q^{74} +(-1.36495 + 0.129302i) q^{75} -64.3354 q^{76} +(108.129 - 20.9806i) q^{77} +(0.0797070 - 0.0797070i) q^{78} +(-83.9580 - 27.2796i) q^{79} +(6.77287 - 18.8183i) q^{80} +(65.4647 + 47.5629i) q^{81} +(-14.7049 + 28.8600i) q^{82} +(72.9621 + 37.1761i) q^{83} +(0.645564 - 0.888543i) q^{84} +(1.91065 - 0.899318i) q^{85} +(5.23591 - 16.1145i) q^{86} +(-1.49607 - 1.49607i) q^{87} +(30.8795 + 3.80201i) q^{88} +104.283i q^{89} +(55.7523 + 30.6428i) q^{90} +(-11.7737 + 8.55410i) q^{91} +(9.11501 + 57.5499i) q^{92} +(-1.79534 - 0.914769i) q^{93} +(51.8095 - 16.8339i) q^{94} +(5.03593 - 160.760i) q^{95} +(0.250985 - 0.182352i) q^{96} +(53.1476 - 27.0800i) 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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