LMFDB - Embedded newform 78.3.l.c.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,3,Mod(7,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("78.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	78.l (of order $12$, degree $4$, 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:	$2.12534606201$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 82x^{5} + 5053x^{4} - 6736x^{3} + 6728x^{2} + 275384x + 5635876 $ x^8 - 2x^7 + 2x^6 + 82x^5 + 5053x^4 - 6736x^3 + 6728x^2 + 275384*x + 5635876
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.1
Root			$-4.04651 - 4.04651i$ of defining polynomial
Character	$\chi$	$=$	78.19
Dual form			78.3.l.c.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-5.04651 + 5.04651i) q^{5} +(2.36603 + 0.633975i) q^{6} +(-1.34715 + 5.02764i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-5.04651 + 5.04651i) q^{5} +(2.36603 + 0.633975i) q^{6} +(-1.34715 + 5.02764i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(8.74082 + 5.04651i) q^{10} +(-7.32323 + 1.96225i) q^{11} -3.46410i q^{12} +(12.9213 + 1.42820i) q^{13} +7.36098 q^{14} +(-3.19936 - 11.9402i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-13.9968 + 8.08105i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(9.87664 + 2.64644i) q^{19} +(3.69431 - 13.7873i) q^{20} +(-6.37479 - 6.37479i) q^{21} +(5.36098 + 9.28549i) q^{22} +(-8.29191 - 4.78733i) q^{23} +(-4.73205 + 1.26795i) q^{24} -25.9346i q^{25} +(-2.77857 - 18.1736i) q^{26} +5.19615 q^{27} +(-2.69431 - 10.0553i) q^{28} +(16.5880 - 28.7312i) q^{29} +(-15.1395 + 8.74082i) q^{30} +(-34.2312 + 34.2312i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(3.39872 - 12.6842i) q^{33} +(16.1621 + 16.1621i) q^{34} +(-18.5736 - 32.1705i) q^{35} +(5.19615 + 3.00000i) q^{36} +(63.2267 - 16.9415i) q^{37} -14.4604i q^{38} +(-13.3325 + 18.1451i) q^{39} -20.1861 q^{40} +(14.0962 + 52.6079i) q^{41} +(-6.37479 + 11.0415i) q^{42} +(-40.7432 + 23.5231i) q^{43} +(10.7220 - 10.7220i) q^{44} +(20.6810 + 5.54146i) q^{45} +(-3.50457 + 13.0792i) q^{46} +(47.8214 + 47.8214i) q^{47} +(3.46410 + 6.00000i) q^{48} +(18.9729 + 10.9540i) q^{49} +(-35.4274 + 9.49273i) q^{50} -27.9936i q^{51} +(-23.8086 + 10.4476i) q^{52} +67.5177 q^{53} +(-1.90192 - 7.09808i) q^{54} +(27.0543 - 46.8594i) q^{55} +(-12.7496 + 7.36098i) q^{56} +(-12.5231 + 12.5231i) q^{57} +(-45.3192 - 12.1432i) q^{58} +(-19.4918 + 72.7442i) q^{59} +(17.4816 + 17.4816i) q^{60} +(-35.2597 - 61.0716i) q^{61} +(59.2902 + 34.2312i) q^{62} +(15.0829 - 4.04146i) q^{63} +8.00000i q^{64} +(-72.4150 + 58.0001i) q^{65} -18.5710 q^{66} +(11.1841 + 41.7395i) q^{67} +(16.1621 - 27.9936i) q^{68} +(14.3620 - 8.29191i) q^{69} +(-37.1473 + 37.1473i) q^{70} +(-106.797 - 28.6161i) q^{71} +(2.19615 - 8.19615i) q^{72} +(-36.8385 - 36.8385i) q^{73} +(-46.2851 - 80.1682i) q^{74} +(38.9019 + 22.4600i) q^{75} +(-19.7533 + 5.29288i) q^{76} -39.4621i q^{77} +(29.6667 + 11.5709i) q^{78} -13.3867 q^{79} +(7.38861 + 27.5747i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(66.7041 - 38.5116i) q^{82} +(93.1237 - 93.1237i) q^{83} +(17.4163 + 4.66667i) q^{84} +(29.8539 - 111.416i) q^{85} +(47.0461 + 47.0461i) q^{86} +(28.7312 + 49.7639i) q^{87} +(-18.5710 - 10.7220i) q^{88} +(48.6137 - 13.0260i) q^{89} -30.2791i q^{90} +(-24.5875 + 63.0397i) q^{91} +19.1493 q^{92} +(-21.7017 - 80.9919i) q^{93} +(47.8214 - 82.8291i) q^{94} +(-63.1979 + 36.4873i) q^{95} +(6.92820 - 6.92820i) q^{96} +(-52.5419 - 14.0786i) q^{97} +(8.01888 - 29.9269i) q^{98} +(16.0829 + 16.0829i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 6 q^{5} + 12 q^{6} + 10 q^{7} + 16 q^{8} - 12 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - 6 * q^5 + 12 * q^6 + 10 * q^7 + 16 * q^8 - 12 * q^9	$ 8 q + 4 q^{2} - 6 q^{5} + 12 q^{6} + 10 q^{7} + 16 q^{8} - 12 q^{9} - 6 q^{10} + 24 q^{11} + 4 q^{14} - 12 q^{15} + 16 q^{16} - 84 q^{17} - 24 q^{18} + 10 q^{19} - 12 q^{20} + 18 q^{21} - 12 q^{22} - 12 q^{23} - 24 q^{24} + 26 q^{26} + 20 q^{28} + 36 q^{29} - 18 q^{30} - 94 q^{31} - 16 q^{32} + 60 q^{34} - 204 q^{35} + 140 q^{37} + 66 q^{39} - 24 q^{40} + 72 q^{41} + 18 q^{42} - 222 q^{43} - 24 q^{44} - 84 q^{46} + 300 q^{47} + 42 q^{49} - 62 q^{50} + 44 q^{52} + 84 q^{53} - 36 q^{54} + 396 q^{55} + 36 q^{56} + 24 q^{57} - 66 q^{58} - 60 q^{59} - 12 q^{60} - 90 q^{61} + 198 q^{62} - 24 q^{63} - 108 q^{65} + 72 q^{66} + 304 q^{67} + 60 q^{68} - 216 q^{69} - 408 q^{70} - 192 q^{71} - 24 q^{72} + 16 q^{73} - 46 q^{74} + 312 q^{75} - 20 q^{76} + 114 q^{78} - 96 q^{79} - 24 q^{80} - 36 q^{81} + 114 q^{82} - 12 q^{84} - 390 q^{85} + 168 q^{86} + 30 q^{87} + 72 q^{88} + 354 q^{89} - 218 q^{91} - 288 q^{92} - 42 q^{93} + 300 q^{94} - 576 q^{95} - 460 q^{97} + 58 q^{98} - 36 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 6 * q^5 + 12 * q^6 + 10 * q^7 + 16 * q^8 - 12 * q^9 - 6 * q^10 + 24 * q^11 + 4 * q^14 - 12 * q^15 + 16 * q^16 - 84 * q^17 - 24 * q^18 + 10 * q^19 - 12 * q^20 + 18 * q^21 - 12 * q^22 - 12 * q^23 - 24 * q^24 + 26 * q^26 + 20 * q^28 + 36 * q^29 - 18 * q^30 - 94 * q^31 - 16 * q^32 + 60 * q^34 - 204 * q^35 + 140 * q^37 + 66 * q^39 - 24 * q^40 + 72 * q^41 + 18 * q^42 - 222 * q^43 - 24 * q^44 - 84 * q^46 + 300 * q^47 + 42 * q^49 - 62 * q^50 + 44 * q^52 + 84 * q^53 - 36 * q^54 + 396 * q^55 + 36 * q^56 + 24 * q^57 - 66 * q^58 - 60 * q^59 - 12 * q^60 - 90 * q^61 + 198 * q^62 - 24 * q^63 - 108 * q^65 + 72 * q^66 + 304 * q^67 + 60 * q^68 - 216 * q^69 - 408 * q^70 - 192 * q^71 - 24 * q^72 + 16 * q^73 - 46 * q^74 + 312 * q^75 - 20 * q^76 + 114 * q^78 - 96 * q^79 - 24 * q^80 - 36 * q^81 + 114 * q^82 - 12 * q^84 - 390 * q^85 + 168 * q^86 + 30 * q^87 + 72 * q^88 + 354 * q^89 - 218 * q^91 - 288 * q^92 - 42 * q^93 + 300 * q^94 - 576 * q^95 - 460 * q^97 + 58 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$	−5.04651	+	5.04651i	−1.00930	+	1.00930i	−0.00934664	+	0.999956i	$0.502975\pi$
$5$	−5.04651	+	5.04651i	−1.00930	+	1.00930i	−0.999956	+	0.00934664i	$0.997025\pi$
$6$	2.36603	+	0.633975i	0.394338	+	0.105662i
$7$	−1.34715	+	5.02764i	−0.192450	+	0.718235i	0.800462	+	0.599384i	$0.204588\pi$
$7$	−1.34715	+	5.02764i	−0.192450	+	0.718235i	−0.992912	+	0.118851i	$0.962079\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$	8.74082	+	5.04651i	0.874082	+	0.504651i
$11$	−7.32323	+	1.96225i	−0.665748	+	0.178387i	−0.575839	−	0.817563i	$-0.695324\pi$
$11$	−7.32323	+	1.96225i	−0.665748	+	0.178387i	−0.0899095	+	0.995950i	$0.528658\pi$
$12$		−	3.46410i		−	0.288675i
$13$	12.9213	+	1.42820i	0.993947	+	0.109862i
$13$	12.9213	+	1.42820i	0.993947	+	0.109862i
$14$	7.36098			0.525784
$15$	−3.19936	−	11.9402i	−0.213291	−	0.796012i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−13.9968	+	8.08105i	−0.823341	+	0.475356i	−0.851567	−	0.524246i	$-0.824347\pi$
$17$	−13.9968	+	8.08105i	−0.823341	+	0.475356i	0.0282265	+	0.999602i	$0.491014\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$	9.87664	+	2.64644i	0.519823	+	0.139286i	0.509185	−	0.860657i	$-0.329947\pi$
$19$	9.87664	+	2.64644i	0.519823	+	0.139286i	0.0106384	+	0.999943i	$0.496614\pi$
$20$	3.69431	−	13.7873i	0.184715	−	0.689367i
$21$	−6.37479	−	6.37479i	−0.303562	−	0.303562i
$22$	5.36098	+	9.28549i	0.243681	+	0.422068i
$23$	−8.29191	−	4.78733i	−0.360518	−	0.208145i	0.308790	−	0.951130i	$-0.400076\pi$
$23$	−8.29191	−	4.78733i	−0.360518	−	0.208145i	−0.669308	+	0.742985i	$0.733409\pi$
$24$	−4.73205	+	1.26795i	−0.197169	+	0.0528312i
$25$		−	25.9346i		−	1.03738i
$26$	−2.77857	−	18.1736i	−0.106868	−	0.698984i
$27$	5.19615			0.192450
$28$	−2.69431	−	10.0553i	−0.0962252	−	0.359117i
$29$	16.5880	−	28.7312i	0.571999	−	0.990731i	−0.424362	−	0.905493i	$-0.639501\pi$
$29$	16.5880	−	28.7312i	0.571999	−	0.990731i	0.996361	−	0.0852386i	$-0.0271652\pi$
$30$	−15.1395	+	8.74082i	−0.504651	+	0.291361i
$31$	−34.2312	+	34.2312i	−1.10423	+	1.10423i	−0.110338	+	0.993894i	$0.535193\pi$
$31$	−34.2312	+	34.2312i	−1.10423	+	1.10423i	−0.993894	+	0.110338i	$0.964807\pi$
$32$	−5.46410	−	1.46410i	−0.170753	−	0.0457532i
$33$	3.39872	−	12.6842i	0.102992	−	0.384370i
$34$	16.1621	+	16.1621i	0.475356	+	0.475356i
$35$	−18.5736	−	32.1705i	−0.530676	−	0.919157i
$36$	5.19615	+	3.00000i	0.144338	+	0.0833333i
$37$	63.2267	−	16.9415i	1.70883	−	0.457879i	0.733692	−	0.679482i	$-0.237796\pi$
$37$	63.2267	−	16.9415i	1.70883	−	0.457879i	0.975137	+	0.221603i	$0.0711289\pi$
$38$		−	14.4604i		−	0.380537i
$39$	−13.3325	+	18.1451i	−0.341859	+	0.465259i
$40$	−20.1861			−0.504651
$41$	14.0962	+	52.6079i	0.343811	+	1.28312i	0.893995	+	0.448076i	$0.147891\pi$
$41$	14.0962	+	52.6079i	0.343811	+	1.28312i	−0.550185	+	0.835043i	$0.685443\pi$
$42$	−6.37479	+	11.0415i	−0.151781	+	0.262892i
$43$	−40.7432	+	23.5231i	−0.947515	+	0.547048i	−0.892308	−	0.451427i	$-0.850915\pi$
$43$	−40.7432	+	23.5231i	−0.947515	+	0.547048i	−0.0552070	+	0.998475i	$0.517582\pi$
$44$	10.7220	−	10.7220i	0.243681	−	0.243681i
$45$	20.6810	+	5.54146i	0.459578	+	0.123144i
$46$	−3.50457	+	13.0792i	−0.0761864	+	0.284331i
$47$	47.8214	+	47.8214i	1.01748	+	1.01748i	0.999845	+	0.0176317i	$0.00561265\pi$
$47$	47.8214	+	47.8214i	1.01748	+	1.01748i	0.0176317	+	0.999845i	$0.494387\pi$
$48$	3.46410	+	6.00000i	0.0721688	+	0.125000i
$49$	18.9729	+	10.9540i	0.387202	+	0.223551i
$50$	−35.4274	+	9.49273i	−0.708547	+	0.189855i
$51$		−	27.9936i		−	0.548894i
$52$	−23.8086	+	10.4476i	−0.457857	+	0.200915i
$53$	67.5177			1.27392			0.636959	−	0.770897i	$-0.280192\pi$
$53$	67.5177			1.27392			0.636959	+	0.770897i	$0.280192\pi$
$54$	−1.90192	−	7.09808i	−0.0352208	−	0.131446i
$55$	27.0543	−	46.8594i	0.491896	−	0.851988i
$56$	−12.7496	+	7.36098i	−0.227671	+	0.131446i
$57$	−12.5231	+	12.5231i	−0.219703	+	0.219703i
$58$	−45.3192	−	12.1432i	−0.781365	−	0.209366i
$59$	−19.4918	+	72.7442i	−0.330369	+	1.23295i	0.578435	+	0.815729i	$0.303664\pi$
$59$	−19.4918	+	72.7442i	−0.330369	+	1.23295i	−0.908804	+	0.417224i	$0.863003\pi$
$60$	17.4816	+	17.4816i	0.291361	+	0.291361i
$61$	−35.2597	−	61.0716i	−0.578028	−	1.00117i	−0.995705	−	0.0925789i	$-0.970489\pi$
$61$	−35.2597	−	61.0716i	−0.578028	−	1.00117i	0.417677	−	0.908596i	$-0.362844\pi$
$62$	59.2902	+	34.2312i	0.956293	+	0.552116i
$63$	15.0829	−	4.04146i	0.239412	−	0.0641501i
$64$			8.00000i			0.125000i
$65$	−72.4150	+	58.0001i	−1.11408	+	0.892310i
$66$	−18.5710			−0.281378
$67$	11.1841	+	41.7395i	0.166926	+	0.622977i	0.997787	+	0.0664962i	$0.0211820\pi$
$67$	11.1841	+	41.7395i	0.166926	+	0.622977i	−0.830860	+	0.556481i	$0.812151\pi$
$68$	16.1621	−	27.9936i	0.237678	−	0.411670i
$69$	14.3620	−	8.29191i	0.208145	−	0.120173i
$70$	−37.1473	+	37.1473i	−0.530676	+	0.530676i
$71$	−106.797	−	28.6161i	−1.50418	−	0.403044i	−0.589682	−	0.807635i	$-0.700747\pi$
$71$	−106.797	−	28.6161i	−1.50418	−	0.403044i	−0.914498	+	0.404591i	$0.867414\pi$
$72$	2.19615	−	8.19615i	0.0305021	−	0.113835i
$73$	−36.8385	−	36.8385i	−0.504638	−	0.504638i	0.408238	−	0.912876i	$-0.366143\pi$
$73$	−36.8385	−	36.8385i	−0.504638	−	0.504638i	−0.912876	+	0.408238i	$0.866143\pi$
$74$	−46.2851	−	80.1682i	−0.625475	−	1.08335i
$75$	38.9019	+	22.4600i	0.518692	+	0.299467i
$76$	−19.7533	+	5.29288i	−0.259912	+	0.0696431i
$77$		−	39.4621i		−	0.512494i
$78$	29.6667	+	11.5709i	0.380342	+	0.148345i
$79$	−13.3867			−0.169452			−0.0847259	−	0.996404i	$-0.527001\pi$
$79$	−13.3867			−0.169452			−0.0847259	+	0.996404i	$0.527001\pi$
$80$	7.38861	+	27.5747i	0.0923576	+	0.344683i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	66.7041	−	38.5116i	0.813465	−	0.469654i
$83$	93.1237	−	93.1237i	1.12197	−	1.12197i	0.130528	−	0.991445i	$-0.458333\pi$
$83$	93.1237	−	93.1237i	1.12197	−	1.12197i	0.991445	−	0.130528i	$-0.0416671\pi$
$84$	17.4163	+	4.66667i	0.207336	+	0.0555556i
$85$	29.8539	−	111.416i	0.351222	−	1.31078i
$86$	47.0461	+	47.0461i	0.547048	+	0.547048i
$87$	28.7312	+	49.7639i	0.330244	+	0.571999i
$88$	−18.5710	−	10.7220i	−0.211034	−	0.121840i
$89$	48.6137	−	13.0260i	0.546222	−	0.146360i	0.0248529	−	0.999691i	$-0.492088\pi$
$89$	48.6137	−	13.0260i	0.546222	−	0.146360i	0.521369	+	0.853331i	$0.325422\pi$
$90$		−	30.2791i		−	0.336434i
$91$	−24.5875	+	63.0397i	−0.270192	+	0.692744i
$92$	19.1493			0.208145
$93$	−21.7017	−	80.9919i	−0.233352	−	0.870881i
$94$	47.8214	−	82.8291i	0.508738	−	0.881160i
$95$	−63.1979	+	36.4873i	−0.665241	+	0.384077i
$96$	6.92820	−	6.92820i	0.0721688	−	0.0721688i
$97$	−52.5419	−	14.0786i	−0.541669	−	0.145140i	−0.0223976	−	0.999749i	$-0.507130\pi$
$97$	−52.5419	−	14.0786i	−0.541669	−	0.145140i	−0.519271	+	0.854609i	$0.673797\pi$
$98$	8.01888	−	29.9269i	0.0818253	−	0.305376i
$99$	16.0829	+	16.0829i	0.162454	+	0.162454i
$100$	25.9346	+	44.9201i	0.259346	+	0.449201i
$101$	19.5286	+	11.2749i	0.193353	+	0.111632i	0.593551	−	0.804796i	$-0.297725\pi$
$101$	19.5286	+	11.2749i	0.193353	+	0.111632i	−0.400198	+	0.916428i	$0.631059\pi$
$102$	−38.2399	+	10.2464i	−0.374901	+	0.100455i
$103$		−	109.385i		−	1.06199i	−0.847374	−	0.530996i	$-0.821818\pi$
$103$		−	109.385i		−	1.06199i	0.847374	−	0.530996i	$-0.178182\pi$
$104$	22.9862	+	28.6990i	0.221021	+	0.275952i
$105$	64.3410			0.612771
$106$	−24.7132	−	92.2309i	−0.233143	−	0.870103i
$107$	16.4375	−	28.4706i	0.153621	−	0.266080i	−0.778935	−	0.627105i	$-0.784240\pi$
$107$	16.4375	−	28.4706i	0.153621	−	0.266080i	0.932556	+	0.361025i	$0.117573\pi$
$108$	−9.00000	+	5.19615i	−0.0833333	+	0.0481125i
$109$	−150.086	+	150.086i	−1.37693	+	1.37693i	−0.527183	+	0.849752i	$0.676752\pi$
$109$	−150.086	+	150.086i	−1.37693	+	1.37693i	−0.849752	+	0.527183i	$0.823248\pi$
$110$	−73.9136	−	19.8051i	−0.671942	−	0.180046i
$111$	−29.3436	+	109.512i	−0.264357	+	0.986593i
$112$	14.7220	+	14.7220i	0.131446	+	0.131446i
$113$	59.3938	+	102.873i	0.525609	+	0.910382i	0.999555	+	0.0298278i	$0.00949589\pi$
$113$	59.3938	+	102.873i	0.525609	+	0.910382i	−0.473946	+	0.880554i	$0.657171\pi$
$114$	21.6906	+	12.5231i	0.190269	+	0.109852i
$115$	66.0046	−	17.6859i	0.573953	−	0.153790i
$116$			66.3519i			0.571999i
$117$	−15.6714	−	35.7129i	−0.133943	−	0.305238i
$118$	106.505			0.902584
$119$	−21.7728	−	81.2573i	−0.182965	−	0.682834i
$120$	17.4816	−	30.2791i	0.145680	−	0.252326i
$121$	−55.0098	+	31.7599i	−0.454626	+	0.262479i
$122$	−70.5195	+	70.5195i	−0.578028	+	0.578028i
$123$	−91.1195	−	24.4154i	−0.740809	−	0.198499i
$124$	25.0590	−	93.5214i	0.202089	−	0.754205i
$125$	4.71659	+	4.71659i	0.0377327	+	0.0377327i
$126$	−11.0415	−	19.1244i	−0.0876307	−	0.151781i
$127$	−57.5499	−	33.2265i	−0.453149	−	0.261626i	0.256010	−	0.966674i	$-0.417592\pi$
$127$	−57.5499	−	33.2265i	−0.453149	−	0.261626i	−0.709159	+	0.705048i	$0.750925\pi$
$128$	10.9282	−	2.92820i	0.0853766	−	0.0228766i
$129$		−	81.4863i		−	0.631677i
$130$	105.735	+	77.6912i	0.813349	+	0.597625i
$131$	−28.3277			−0.216242			−0.108121	−	0.994138i	$-0.534483\pi$
$131$	−28.3277			−0.216242			−0.108121	+	0.994138i	$0.534483\pi$
$132$	6.79745	+	25.3684i	0.0514958	+	0.192185i
$133$	−26.6107	+	46.0911i	−0.200080	+	0.346549i
$134$	52.9235	−	30.5554i	0.394952	−	0.228025i
$135$	−26.2225	+	26.2225i	−0.194240	+	0.194240i
$136$	−44.1557	−	11.8315i	−0.324674	−	0.0869962i
$137$	13.0272	−	48.6183i	0.0950892	−	0.354878i	−0.901944	−	0.431854i	$-0.857860\pi$
$137$	13.0272	−	48.6183i	0.0950892	−	0.354878i	0.997033	+	0.0769757i	$0.0245264\pi$
$138$	−16.5838	−	16.5838i	−0.120173	−	0.120173i
$139$	74.1420	+	128.418i	0.533396	+	0.923868i	0.999239	+	0.0390012i	$0.0124176\pi$
$139$	74.1420	+	128.418i	0.533396	+	0.923868i	−0.465844	+	0.884867i	$0.654249\pi$
$140$	64.3410	+	37.1473i	0.459579	+	0.265338i
$141$	−113.147	+	30.3175i	−0.802458	+	0.215018i
$142$			156.361i			1.10114i
$143$	−97.4283	+	14.8958i	−0.681316	+	0.104167i
$144$	−12.0000			−0.0833333
$145$	61.2810	+	228.704i	0.422628	+	1.57727i
$146$	−36.8385	+	63.8062i	−0.252319	+	0.437029i
$147$	−32.8620	+	18.9729i	−0.223551	+	0.129067i
$148$	−92.5703	+	92.5703i	−0.625475	+	0.625475i
$149$	−40.4254	−	10.8320i	−0.271312	−	0.0726977i	0.120598	−	0.992701i	$-0.461519\pi$
$149$	−40.4254	−	10.8320i	−0.271312	−	0.0726977i	−0.391910	+	0.920004i	$0.628185\pi$
$150$	16.4419	−	61.3620i	0.109613	−	0.409080i
$151$	−2.57635	−	2.57635i	−0.0170619	−	0.0170619i	0.698524	−	0.715586i	$-0.253840\pi$
$151$	−2.57635	−	2.57635i	−0.0170619	−	0.0170619i	−0.715586	+	0.698524i	$0.753840\pi$
$152$	14.4604	+	25.0462i	0.0951343	+	0.164777i
$153$	41.9904	+	24.2432i	0.274447	+	0.158452i
$154$	−53.9062	+	14.4441i	−0.350040	+	0.0937929i
$155$		−	345.497i		−	2.22901i
$156$	4.94744	−	44.7607i	0.0317144	−	0.286928i
$157$	275.987			1.75788			0.878939	−	0.476934i	$-0.158252\pi$
$157$	275.987			1.75788			0.878939	+	0.476934i	$0.158252\pi$
$158$	4.89987	+	18.2866i	0.0310118	+	0.115738i
$159$	−58.4720	+	101.277i	−0.367749	+	0.636959i
$160$	34.9633	−	20.1861i	0.218520	−	0.126163i
$161$	35.2395	−	35.2395i	0.218879	−	0.218879i
$162$	12.2942	+	3.29423i	0.0758903	+	0.0203347i
$163$	−36.3840	+	135.787i	−0.223214	+	0.833048i	0.759898	+	0.650043i	$0.225249\pi$
$163$	−36.3840	+	135.787i	−0.223214	+	0.833048i	−0.983112	+	0.183005i	$0.941418\pi$
$164$	−77.0233	−	77.0233i	−0.469654	−	0.469654i
$165$	46.8594	+	81.1628i	0.283996	+	0.491896i
$166$	−161.295	−	93.1237i	−0.971657	−	0.560986i
$167$	189.805	−	50.8582i	1.13656	−	0.304540i	0.358992	−	0.933341i	$-0.383121\pi$
$167$	189.805	−	50.8582i	1.13656	−	0.304540i	0.777566	+	0.628801i	$0.216454\pi$
$168$		−	25.4992i		−	0.151781i
$169$	164.920	+	36.9085i	0.975861	+	0.218394i
$170$	−163.125			−0.959556
$171$	−7.93931	−	29.6299i	−0.0464287	−	0.173274i
$172$	47.0461	−	81.4863i	0.273524	−	0.473758i
$173$	114.533	−	66.1255i	0.662039	−	0.382228i	−0.131015	−	0.991380i	$-0.541823\pi$
$173$	114.533	−	66.1255i	0.662039	−	0.382228i	0.793053	+	0.609152i	$0.208490\pi$
$174$	57.4624	−	57.4624i	0.330244	−	0.330244i
$175$	130.390	+	34.9379i	0.745086	+	0.199645i
$176$	−7.84902	+	29.2929i	−0.0445967	+	0.166437i
$177$	−92.2360	−	92.2360i	−0.521107	−	0.521107i
$178$	−35.5877	−	61.6398i	−0.199931	−	0.346291i
$179$	30.6843	+	17.7156i	0.171421	+	0.0989697i	0.583255	−	0.812289i	$-0.301779\pi$
$179$	30.6843	+	17.7156i	0.171421	+	0.0989697i	−0.411835	+	0.911258i	$0.635112\pi$
$180$	−41.3620	+	11.0829i	−0.229789	+	0.0615718i
$181$		−	121.119i		−	0.669163i	−0.942367	−	0.334582i	$-0.891405\pi$
$181$		−	121.119i		−	0.669163i	0.942367	−	0.334582i	$-0.108595\pi$
$182$	95.1135	+	10.5130i	0.522602	+	0.0577636i
$183$	122.143			0.667450
$184$	−7.00914	−	26.1585i	−0.0380932	−	0.142166i
$185$	−233.579	+	404.570i	−1.26259	+	2.18686i
$186$	−102.694	+	59.2902i	−0.552116	+	0.318764i
$187$	86.6447	−	86.6447i	0.463341	−	0.463341i
$188$	−130.650	−	35.0077i	−0.694949	−	0.186211i
$189$	−7.00001	+	26.1244i	−0.0370371	+	0.138224i
$190$	72.9747	+	72.9747i	0.384077	+	0.384077i
$191$	−100.282	−	173.693i	−0.525036	−	0.909389i	−0.999575	−	0.0291545i	$-0.990719\pi$
$191$	−100.282	−	173.693i	−0.525036	−	0.909389i	0.474539	−	0.880235i	$-0.342615\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	25.2721	−	6.77163i	0.130943	−	0.0350862i	−0.192752	−	0.981247i	$-0.561741\pi$
$193$	25.2721	−	6.77163i	0.130943	−	0.0350862i	0.323695	+	0.946161i	$0.395075\pi$
$194$			76.9267i			0.396529i
$195$	−24.2869	−	158.852i	−0.124548	−	0.814626i
$196$	−43.8160			−0.223551
$197$	−24.5163	−	91.4962i	−0.124448	−	0.464448i	0.875371	−	0.483452i	$-0.160617\pi$
$197$	−24.5163	−	91.4962i	−0.124448	−	0.464448i	−0.999819	+	0.0190039i	$0.993950\pi$
$198$	16.0829	−	27.8565i	0.0812270	−	0.140689i
$199$	170.780	−	98.5996i	0.858188	−	0.495475i	−0.00521676	−	0.999986i	$-0.501661\pi$
$199$	170.780	−	98.5996i	0.858188	−	0.495475i	0.863405	+	0.504511i	$0.168327\pi$
$200$	51.8692	−	51.8692i	0.259346	−	0.259346i
$201$	−72.2949	−	19.3713i	−0.359676	−	0.0963749i
$202$	8.25377	−	30.8035i	0.0408602	−	0.152492i
$203$	122.104	+	122.104i	0.601496	+	0.601496i
$204$	27.9936	+	48.4863i	0.137223	+	0.237678i
$205$	−336.623	−	194.350i	−1.64207	−	0.948047i
$206$	−149.423	+	40.0378i	−0.725354	+	0.194358i
$207$			28.7240i			0.138763i
$208$	30.7901	−	41.9043i	0.148029	−	0.201463i
$209$	−77.5219			−0.370918
$210$	−23.5504	−	87.8914i	−0.112145	−	0.418531i
$211$	97.4174	−	168.732i	0.461694	−	0.799677i	−0.537352	−	0.843358i	$-0.680575\pi$
$211$	97.4174	−	168.732i	0.461694	−	0.799677i	0.999046	+	0.0436812i	$0.0139086\pi$
$212$	−116.944	+	67.5177i	−0.551623	+	0.318480i
$213$	135.413	−	135.413i	0.635741	−	0.635741i
$214$	−44.9081	−	12.0331i	−0.209851	−	0.0562294i
$215$	86.9014	−	324.320i	0.404193	−	1.50847i
$216$	10.3923	+	10.3923i	0.0481125	+	0.0481125i
$217$	−125.988	−	218.217i	−0.580588	−	1.00561i
$218$	259.956	+	150.086i	1.19246	+	0.688467i
$219$	87.1609	−	23.3547i	0.397995	−	0.106642i
$220$			108.217i			0.491896i
$221$	−192.398	+	84.4275i	−0.870580	+	0.382025i
$222$	160.336			0.722236
$223$	106.021	+	395.676i	0.475431	+	1.77433i	0.619750	+	0.784800i	$0.287234\pi$
$223$	106.021	+	395.676i	0.475431	+	1.77433i	−0.144319	+	0.989531i	$0.546099\pi$
$224$	14.7220	−	25.4992i	0.0657230	−	0.113836i
$225$	−67.3801	+	38.9019i	−0.299467	+	0.172897i
$226$	118.788	−	118.788i	0.525609	−	0.525609i
$227$	241.186	+	64.6255i	1.06249	+	0.284694i	0.747405	−	0.664369i	$-0.231300\pi$
$227$	241.186	+	64.6255i	1.06249	+	0.284694i	0.315087	+	0.949063i	$0.397966\pi$
$228$	9.16753	−	34.2137i	0.0402085	−	0.150060i
$229$	−174.256	−	174.256i	−0.760945	−	0.760945i	0.215548	−	0.976493i	$-0.430846\pi$
$229$	−174.256	−	174.256i	−0.760945	−	0.760945i	−0.976493	+	0.215548i	$0.930846\pi$
$230$	−48.3187	−	83.6905i	−0.210081	−	0.363872i
$231$	59.1931	+	34.1751i	0.256247	+	0.147944i
$232$	90.6384	−	24.2865i	0.390683	−	0.104683i
$233$			290.609i			1.24725i	0.781724	+	0.623624i	$0.214340\pi$
$233$			290.609i			1.24725i	−0.781724	+	0.623624i	$0.785660\pi$
$234$	−43.0485	+	34.4793i	−0.183968	+	0.147348i
$235$	−482.663			−2.05388
$236$	−38.9835	−	145.488i	−0.165184	−	0.616476i
$237$	11.5932	−	20.0800i	0.0489165	−	0.0847259i
$238$	−103.030	+	59.4844i	−0.432899	+	0.249935i
$239$	215.875	−	215.875i	0.903243	−	0.903243i	−0.0924720	−	0.995715i	$-0.529477\pi$
$239$	215.875	−	215.875i	0.903243	−	0.903243i	0.995715	+	0.0924720i	$0.0294769\pi$
$240$	−47.7607	−	12.7974i	−0.199003	−	0.0533227i
$241$	−31.0933	+	116.042i	−0.129018	+	0.481502i	−0.999951	−	0.00989998i	$-0.996849\pi$
$241$	−31.0933	+	116.042i	−0.129018	+	0.481502i	0.870933	+	0.491402i	$0.163515\pi$
$242$	63.5198	+	63.5198i	0.262479	+	0.262479i
$243$	−7.79423	−	13.5000i	−0.0320750	−	0.0555556i
$244$	122.143	+	70.5195i	0.500587	+	0.289014i
$245$	−151.026	+	40.4674i	−0.616434	+	0.165173i
$246$			133.408i			0.542310i
$247$	123.839	+	48.3013i	0.501374	+	0.195552i
$248$	−136.925			−0.552116
$249$	59.0381	+	220.333i	0.237101	+	0.884872i
$250$	4.71659	−	8.16937i	0.0188663	−	0.0326775i
$251$	−151.116	+	87.2471i	−0.602057	+	0.347598i	−0.769850	−	0.638224i	$-0.779669\pi$
$251$	−151.116	+	87.2471i	−0.602057	+	0.347598i	0.167793	+	0.985822i	$0.446336\pi$
$252$	−22.0829	+	22.0829i	−0.0876307	+	0.0876307i
$253$	70.1175	+	18.7879i	0.277144	+	0.0742606i
$254$	−24.3235	+	90.7764i	−0.0957617	+	0.357387i
$255$	141.270	+	141.270i	0.554000	+	0.554000i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−4.02596	−	2.32439i	−0.0156652	−	0.00904433i	0.492147	−	0.870512i	$-0.336212\pi$
$257$	−4.02596	−	2.32439i	−0.0156652	−	0.00904433i	−0.507812	+	0.861468i	$0.669546\pi$
$258$	−111.312	+	29.8261i	−0.431443	+	0.115605i
$259$			340.704i			1.31546i
$260$	67.4264	−	172.874i	0.259332	−	0.664901i
$261$	−99.5278			−0.381333
$262$	10.3687	+	38.6964i	0.0395750	+	0.147696i
$263$	−6.92157	+	11.9885i	−0.0263177	+	0.0455837i	−0.878884	−	0.477035i	$-0.841711\pi$
$263$	−6.92157	+	11.9885i	−0.0263177	+	0.0455837i	0.852567	+	0.522619i	$0.175045\pi$
$264$	32.1659	−	18.5710i	0.121840	−	0.0703446i
$265$	−340.729	+	340.729i	−1.28577	+	1.28577i
$266$	72.7018	+	19.4804i	0.273315	+	0.0732345i
$267$	−22.5617	+	84.2015i	−0.0845008	+	0.315361i
$268$	−61.1108	−	61.1108i	−0.228025	−	0.228025i
$269$	230.126	+	398.590i	0.855487	+	1.48175i	0.876193	+	0.481961i	$0.160075\pi$
$269$	230.126	+	398.590i	0.855487	+	1.48175i	−0.0207059	+	0.999786i	$0.506591\pi$
$270$	45.4186	+	26.2225i	0.168217	+	0.0971202i
$271$	143.260	−	38.3864i	0.528635	−	0.141647i	0.0153773	−	0.999882i	$-0.495105\pi$
$271$	143.260	−	38.3864i	0.528635	−	0.141647i	0.513258	+	0.858234i	$0.328438\pi$
$272$			64.6484i			0.237678i
$273$	−73.2662	−	91.4752i	−0.268374	−	0.335074i
$274$	−71.1821			−0.259789
$275$	50.8903	+	189.925i	0.185056	+	0.690637i
$276$	−16.5838	+	28.7240i	−0.0600863	+	0.104072i
$277$	323.280	−	186.646i	1.16707	−	0.673811i	0.214085	−	0.976815i	$-0.431323\pi$
$277$	323.280	−	186.646i	1.16707	−	0.673811i	0.952989	+	0.303004i	$0.0979896\pi$
$278$	148.284	−	148.284i	0.533396	−	0.533396i
$279$	140.282	+	37.5885i	0.502803	+	0.134726i
$280$	27.1937	−	101.488i	0.0971204	−	0.362458i
$281$	−136.099	−	136.099i	−0.484337	−	0.484337i	0.422177	−	0.906514i	$-0.361266\pi$
$281$	−136.099	−	136.099i	−0.484337	−	0.484337i	−0.906514	+	0.422177i	$0.861266\pi$
$282$	82.8291	+	143.464i	0.293720	+	0.508738i
$283$	−329.692	−	190.347i	−1.16499	−	0.672606i	−0.212493	−	0.977162i	$-0.568158\pi$
$283$	−329.692	−	190.347i	−1.16499	−	0.672606i	−0.952494	+	0.304557i	$0.901492\pi$
$284$	213.594	−	57.2322i	0.752090	−	0.201522i
$285$		−	126.396i		−	0.443494i
$286$	56.0093	+	127.637i	0.195837	+	0.446284i
$287$	−283.483			−0.987747
$288$	4.39230	+	16.3923i	0.0152511	+	0.0569177i
$289$	−13.8932	+	24.0638i	−0.0480735	+	0.0832657i
$290$	289.985	−	167.423i	0.999948	−	0.577320i
$291$	66.6205	−	66.6205i	0.228936	−	0.228936i
$292$	100.645	+	26.9677i	0.344674	+	0.0923551i
$293$	−1.43061	+	5.33910i	−0.00488262	+	0.0182222i	−0.968324	−	0.249696i	$-0.919669\pi$
$293$	−1.43061	+	5.33910i	−0.00488262	+	0.0182222i	0.963442	+	0.267919i	$0.0863358\pi$
$294$	37.9458	+	37.9458i	0.129067	+	0.129067i
$295$	−268.739	−	465.470i	−0.910981	−	1.57787i
$296$	160.336	+	92.5703i	0.541677	+	0.312737i
$297$	−38.0526	+	10.1962i	−0.128123	+	0.0343305i
$298$			59.1870i			0.198614i
$299$	−100.305	−	73.7012i	−0.335468	−	0.246492i
$300$	−89.8402			−0.299467
$301$	−63.3783	−	236.531i	−0.210559	−	0.785818i
$302$	−2.57635	+	4.46237i	−0.00853096	+	0.0147760i
$303$	−33.8246	+	19.5286i	−0.111632	+	0.0644509i
$304$	28.9208	−	28.9208i	0.0951343	−	0.0951343i
$305$	486.138	+	130.260i	1.59389	+	0.427083i
$306$	17.7472	−	66.2335i	0.0579974	−	0.216449i
$307$	−227.287	−	227.287i	−0.740349	−	0.740349i	0.232296	−	0.972645i	$-0.425376\pi$
$307$	−227.287	−	227.287i	−0.740349	−	0.740349i	−0.972645	+	0.232296i	$0.925376\pi$
$308$	39.4621	+	68.3503i	0.128124	+	0.221916i
$309$	164.078	+	94.7304i	0.530996	+	0.306571i
$310$	−471.957	+	126.461i	−1.52244	+	0.407937i
$311$			308.864i			0.993132i	0.867999	+	0.496566i	$0.165406\pi$
$311$			308.864i			0.993132i	−0.867999	+	0.496566i	$0.834594\pi$
$312$	−62.9552	+	9.62523i	−0.201779	+	0.0308501i
$313$	2.51660			0.00804026			0.00402013	−	0.999992i	$-0.498720\pi$
$313$	2.51660			0.00804026			0.00402013	+	0.999992i	$0.498720\pi$
$314$	−101.018	−	377.005i	−0.321714	−	1.20065i
$315$	−55.7209	+	96.5115i	−0.176892	+	0.306386i
$316$	23.1864	−	13.3867i	0.0733748	−	0.0423630i
$317$	46.8460	−	46.8460i	0.147779	−	0.147779i	−0.629346	−	0.777125i	$-0.716677\pi$
$317$	46.8460	−	46.8460i	0.147779	−	0.147779i	0.777125	+	0.629346i	$0.216677\pi$
$318$	159.749	+	42.8045i	0.502354	+	0.134605i
$319$	−65.0996	+	242.955i	−0.204074	+	0.761615i
$320$	−40.3721	−	40.3721i	−0.126163	−	0.126163i
$321$	28.4706	+	49.3125i	0.0886934	+	0.153621i
$322$	−61.0366	−	35.2395i	−0.189555	−	0.109439i
$323$	−159.627	+	42.7720i	−0.494202	+	0.132421i
$324$		−	18.0000i		−	0.0555556i
$325$	37.0399	−	335.109i	0.113969	−	1.03111i
$326$	198.806			0.609833
$327$	−95.1507	−	355.107i	−0.290981	−	1.08595i
$328$	−77.0233	+	133.408i	−0.234827	+	0.406732i
$329$	−304.852	+	176.006i	−0.926600	+	0.534973i
$330$	93.7187	−	93.7187i	0.283996	−	0.283996i
$331$	232.042	+	62.1755i	0.701033	+	0.187841i	0.591693	−	0.806163i	$-0.298460\pi$
$331$	232.042	+	62.1755i	0.701033	+	0.187841i	0.109340	+	0.994004i	$0.465126\pi$
$332$	−68.1713	+	254.419i	−0.205335	+	0.766321i
$333$	−138.855	−	138.855i	−0.416983	−	0.416983i
$334$	−138.947	−	240.663i	−0.416009	−	0.720549i
$335$	−267.079	−	154.198i	−0.797252	−	0.460293i
$336$	−34.8325	+	9.33335i	−0.103668	+	0.0277778i
$337$			5.72952i			0.0170015i	0.999964	+	0.00850077i	$0.00270591\pi$
$337$			5.72952i			0.0170015i	−0.999964	+	0.00850077i	$0.997294\pi$
$338$	−9.94712	−	238.795i	−0.0294293	−	0.706494i
$339$	−205.746			−0.606921
$340$	59.7077	+	222.832i	0.175611	+	0.655389i
$341$	183.513	−	317.853i	0.538161	−	0.932121i
$342$	−37.5692	+	21.6906i	−0.109852	+	0.0634228i
$343$	−260.976	+	260.976i	−0.760863	+	0.760863i
$344$	−128.532	−	34.4402i	−0.373641	−	0.100117i
$345$	−30.6328	+	114.323i	−0.0887908	+	0.331372i
$346$	−132.251	−	132.251i	−0.382228	−	0.382228i
$347$	51.4856	+	89.1757i	0.148373	+	0.256990i	0.930626	−	0.365971i	$-0.119263\pi$
$347$	51.4856	+	89.1757i	0.148373	+	0.256990i	−0.782253	+	0.622961i	$0.785930\pi$
$348$	−99.5278	−	57.4624i	−0.286000	−	0.165122i
$349$	468.190	−	125.451i	1.34152	−	0.359459i	0.484521	−	0.874780i	$-0.338994\pi$
$349$	468.190	−	125.451i	1.34152	−	0.359459i	0.856997	+	0.515321i	$0.172327\pi$
$350$		−	190.904i		−	0.545441i
$351$	67.1411	+	7.42116i	0.191285	+	0.0211429i
$352$	42.8878			0.121840
$353$	−50.9642	−	190.201i	−0.144375	−	0.538813i	−0.999782	−	0.0208583i	$-0.993360\pi$
$353$	−50.9642	−	190.201i	−0.144375	−	0.538813i	0.855408	−	0.517955i	$-0.173307\pi$
$354$	−92.2360	+	159.757i	−0.260554	+	0.451292i
$355$	683.363	−	394.540i	1.92497	−	1.11138i
$356$	−71.1755	+	71.1755i	−0.199931	+	0.199931i
$357$	140.742	+	37.7116i	0.394234	+	0.105635i
$358$	12.9687	−	48.3998i	0.0362254	−	0.135195i
$359$	−54.1215	−	54.1215i	−0.150756	−	0.150756i	0.627699	−	0.778456i	$-0.283997\pi$
$359$	−54.1215	−	54.1215i	−0.150756	−	0.150756i	−0.778456	+	0.627699i	$0.783997\pi$
$360$	30.2791	+	52.4449i	0.0841086	+	0.145680i
$361$	−222.091	−	128.224i	−0.615210	−	0.355192i
$362$	−165.451	+	44.3325i	−0.457047	+	0.122465i
$363$		−	110.020i		−	0.303084i
$364$	−20.4530	−	133.775i	−0.0561895	−	0.367515i
$365$	371.812			1.01866
$366$	−44.7075	−	166.851i	−0.122152	−	0.455877i
$367$	107.824	−	186.757i	0.293799	−	0.508875i	−0.680906	−	0.732371i	$-0.738414\pi$
$367$	107.824	−	186.757i	0.293799	−	0.508875i	0.974705	+	0.223496i	$0.0717470\pi$
$368$	−33.1676	+	19.1493i	−0.0901294	+	0.0520362i
$369$	115.535	−	115.535i	0.313103	−	0.313103i
$370$	638.149	+	170.991i	1.72473	+	0.462139i
$371$	−90.9566	+	339.455i	−0.245166	+	0.914972i
$372$	118.580	+	118.580i	0.318764	+	0.318764i
$373$	315.693	+	546.797i	0.846363	+	1.46594i	0.884432	+	0.466669i	$0.154546\pi$
$373$	315.693	+	546.797i	0.846363	+	1.46594i	−0.0380693	+	0.999275i	$0.512121\pi$
$374$	−150.073	−	86.6447i	−0.401265	−	0.231670i
$375$	−11.1596	+	2.99020i	−0.0297588	+	0.00797386i
$376$			191.286i			0.508738i
$377$	255.372	−	347.554i	0.677380	−	0.921894i
$378$	38.2488			0.101187
$379$	−64.5160	−	240.777i	−0.170227	−	0.635296i	−0.997316	−	0.0732240i	$-0.976671\pi$
$379$	−64.5160	−	240.777i	−0.170227	−	0.635296i	0.827089	−	0.562072i	$-0.189995\pi$
$380$	72.9747	−	126.396i	0.192039	−	0.332621i
$381$	99.6794	−	57.5499i	0.261626	−	0.151050i
$382$	−200.564	+	200.564i	−0.525036	+	0.525036i
$383$	271.369	+	72.7131i	0.708535	+	0.189851i	0.595050	−	0.803688i	$-0.297132\pi$
$383$	271.369	+	72.7131i	0.708535	+	0.189851i	0.113485	+	0.993540i	$0.463799\pi$
$384$	−5.07180	+	18.9282i	−0.0132078	+	0.0492922i
$385$	199.146	+	199.146i	0.517262	+	0.517262i
$386$	−18.5004	−	32.0437i	−0.0479286	−	0.0830148i
$387$	122.229	+	70.5692i	0.315838	+	0.182349i
$388$	105.084	−	28.1571i	0.270835	−	0.0725699i
$389$		−	265.150i		−	0.681620i	−0.940132	−	0.340810i	$-0.889299\pi$
$389$		−	265.150i		−	0.681620i	0.940132	−	0.340810i	$-0.110701\pi$
$390$	−208.106	+	91.3205i	−0.533606	+	0.234155i
$391$	154.747			0.395772
$392$	16.0378	+	59.8538i	0.0409127	+	0.152688i
$393$	24.5325	−	42.4916i	0.0624237	−	0.108121i
$394$	−116.013	+	66.9799i	−0.294448	+	0.170000i
$395$	67.5561	−	67.5561i	0.171028	−	0.171028i
$396$	−43.9394	−	11.7735i	−0.110958	−	0.0297311i
$397$	−32.5780	+	121.583i	−0.0820604	+	0.306253i	−0.994741	−	0.102419i	$-0.967342\pi$
$397$	−32.5780	+	121.583i	−0.0820604	+	0.306253i	0.912681	+	0.408673i	$0.134008\pi$
$398$	−197.199	−	197.199i	−0.495475	−	0.495475i
$399$	−46.0911	−	79.8321i	−0.115516	−	0.200080i
$400$	−89.8402	−	51.8692i	−0.224600	−	0.129673i
$401$	−537.968	+	144.148i	−1.34157	+	0.359472i	−0.857015	−	0.515291i	$-0.827684\pi$
$401$	−537.968	+	144.148i	−1.34157	+	0.359472i	−0.484551	+	0.874763i	$0.661017\pi$
$402$			105.847i			0.263301i
$403$	−491.201	+	393.423i	−1.21886	+	0.976235i
$404$	−45.0994			−0.111632
$405$	−16.6244	−	62.0430i	−0.0410478	−	0.153193i
$406$	122.104	−	211.490i	0.300748	−	0.520911i
$407$	−429.780	+	248.134i	−1.05597	+	0.609665i
$408$	55.9872	−	55.9872i	0.137223	−	0.137223i
$409$	199.444	+	53.4410i	0.487639	+	0.130663i	0.494257	−	0.869316i	$-0.335440\pi$
$409$	199.444	+	53.4410i	0.487639	+	0.130663i	−0.00661830	+	0.999978i	$0.502107\pi$
$410$	−142.274	+	530.973i	−0.347009	+	1.29506i
$411$	61.6455	+	61.6455i	0.149989	+	0.149989i
$412$	109.385	+	189.461i	0.265498	+	0.459856i
$413$	−339.474	−	195.995i	−0.821970	−	0.474564i
$414$	39.2377	−	10.5137i	0.0947771	−	0.0253955i
$415$			939.900i			2.26482i
$416$	−68.5123	−	26.7220i	−0.164693	−	0.0642355i
$417$	−256.835			−0.615912
$418$	28.3750	+	105.897i	0.0678828	+	0.253342i
$419$	−167.706	+	290.475i	−0.400253	+	0.693259i	−0.993756	−	0.111573i	$-0.964411\pi$
$419$	−167.706	+	290.475i	−0.400253	+	0.693259i	0.593503	+	0.804832i	$0.297744\pi$
$420$	−111.442	+	64.3410i	−0.265338	+	0.153193i
$421$	274.627	−	274.627i	0.652321	−	0.652321i	−0.301230	−	0.953551i	$-0.597397\pi$
$421$	274.627	−	274.627i	0.652321	−	0.652321i	0.953551	+	0.301230i	$0.0973973\pi$
$422$	−266.149	−	71.3145i	−0.630685	−	0.168992i
$423$	52.5115	−	195.976i	0.124141	−	0.463299i
$424$	135.035	+	135.035i	0.318480	+	0.318480i
$425$	209.579	+	363.001i	0.493127	+	0.854121i
$426$	−234.542	−	135.413i	−0.550568	−	0.317871i
$427$	354.547	−	95.0005i	0.830320	−	0.222484i
$428$			65.7500i			0.153621i
$429$	62.0316	−	159.043i	0.144596	−	0.370729i
$430$	−474.838			−1.10427
$431$	35.5849	+	132.805i	0.0825635	+	0.308131i	0.994842	−	0.101440i	$-0.0323450\pi$
$431$	35.5849	+	132.805i	0.0825635	+	0.308131i	−0.912278	+	0.409571i	$0.865678\pi$
$432$	10.3923	−	18.0000i	0.0240563	−	0.0416667i
$433$	−364.107	+	210.217i	−0.840893	+	0.485490i	−0.857568	−	0.514371i	$-0.828025\pi$
$433$	−364.107	+	210.217i	−0.840893	+	0.485490i	0.0166746	+	0.999861i	$0.494692\pi$
$434$	−251.975	+	251.975i	−0.580588	+	0.580588i
$435$	−396.127	−	106.142i	−0.910636	−	0.244004i
$436$	109.871	−	410.042i	0.251997	−	0.940464i
$437$	−69.2268	−	69.2268i	−0.158414	−	0.158414i
$438$	−63.8062	−	110.516i	−0.145676	−	0.252319i
$439$	645.502	+	372.680i	1.47039	+	0.848930i	0.999448	−	0.0332332i	$-0.0105804\pi$
$439$	645.502	+	372.680i	1.47039	+	0.848930i	0.470943	+	0.882164i	$0.343914\pi$
$440$	147.827	−	39.6102i	0.335971	−	0.0900231i
$441$		−	65.7240i		−	0.149034i
$442$	185.753	+	231.918i	0.420255	+	0.524702i
$443$	661.917			1.49417			0.747084	−	0.664729i	$-0.231453\pi$
$443$	661.917			1.49417			0.747084	+	0.664729i	$0.231453\pi$
$444$	−58.6872	−	219.024i	−0.132178	−	0.493296i
$445$	−179.594	+	311.066i	−0.403582	+	0.699025i
$446$	501.697	−	289.655i	1.12488	−	0.649450i
$447$	51.2574	−	51.2574i	0.114670	−	0.114670i
$448$	−40.2211	−	10.7772i	−0.0897793	−	0.0240563i
$449$	−8.12050	+	30.3061i	−0.0180857	+	0.0674969i	−0.974379	−	0.224913i	$-0.927790\pi$
$449$	−8.12050	+	30.3061i	−0.0180857	+	0.0674969i	0.956293	+	0.292409i	$0.0944570\pi$
$450$	77.8039	+	77.8039i	0.172897	+	0.172897i
$451$	−206.460	−	357.599i	−0.457783	−	0.792903i
$452$	−205.746	−	118.788i	−0.455191	−	0.262805i
$453$	6.09571	−	1.63334i	0.0134563	−	0.00360561i
$454$		−	353.120i		−	0.777798i
$455$	−194.050	−	442.212i	−0.426483	−	0.971894i
$456$	−50.0923			−0.109852
$457$	−42.0960	−	157.104i	−0.0921137	−	0.343773i	0.904452	−	0.426575i	$-0.140280\pi$
$457$	−42.0960	−	157.104i	−0.0921137	−	0.343773i	−0.996566	+	0.0828016i	$0.973613\pi$
$458$	−174.256	+	301.821i	−0.380472	+	0.658997i
$459$	−72.7295	+	41.9904i	−0.158452	+	0.0914823i
$460$	−96.6374	+	96.6374i	−0.210081	+	0.210081i
$461$	−77.8033	−	20.8473i	−0.168771	−	0.0452220i	0.173444	−	0.984844i	$-0.444510\pi$
$461$	−77.8033	−	20.8473i	−0.168771	−	0.0452220i	−0.342215	+	0.939622i	$0.611177\pi$
$462$	25.0179	−	93.3682i	0.0541514	−	0.202096i
$463$	−172.856	−	172.856i	−0.373338	−	0.373338i	0.495353	−	0.868692i	$-0.335039\pi$
$463$	−172.856	−	172.856i	−0.373338	−	0.373338i	−0.868692	+	0.495353i	$0.835039\pi$
$464$	−66.3519	−	114.925i	−0.143000	−	0.247683i
$465$	518.245	+	299.209i	1.11450	+	0.643460i
$466$	396.979	−	106.370i	0.851887	−	0.228262i
$467$			649.970i			1.39180i	0.718139	+	0.695899i	$0.244994\pi$
$467$			649.970i			1.39180i	−0.718139	+	0.695899i	$0.755006\pi$
$468$	62.8565	+	46.1851i	0.134309	+	0.0986861i
$469$	−224.918			−0.479569
$470$	176.667	+	659.329i	0.375887	+	1.40283i
$471$	−239.012	+	413.980i	−0.507456	+	0.878939i
$472$	−184.472	+	106.505i	−0.390830	+	0.225646i
$473$	252.213	−	252.213i	0.533221	−	0.533221i
$474$	−31.6733	−	8.48682i	−0.0668212	−	0.0179047i
$475$	68.6344	−	256.147i	0.144493	−	0.539257i
$476$	118.969	+	118.969i	0.249935	+	0.249935i
$477$	−101.277	−	175.416i	−0.212320	−	0.367749i
$478$	−373.907	−	215.875i	−0.782232	−	0.451622i
$479$	−490.789	+	131.507i	−1.02461	+	0.274544i	−0.731723	−	0.681602i	$-0.761283\pi$
$479$	−490.789	+	131.507i	−1.02461	+	0.274544i	−0.292890	+	0.956146i	$0.594617\pi$
$480$			69.9266i			0.145680i
$481$	841.167	−	128.606i	1.74879	−	0.267373i
$482$	169.897			0.352484
$483$	22.3409	+	83.3775i	0.0462545	+	0.172624i
$484$	63.5198	−	110.020i	0.131239	−	0.227313i
$485$	336.201	−	194.106i	0.693198	−	0.400218i
$486$	−15.5885	+	15.5885i	−0.0320750	+	0.0320750i
$487$	−749.567	−	200.846i	−1.53915	−	0.412415i	−0.613161	−	0.789958i	$-0.710102\pi$
$487$	−749.567	−	200.846i	−1.53915	−	0.412415i	−0.925992	+	0.377544i	$0.876769\pi$
$488$	51.6238	−	192.663i	0.105787	−	0.394801i
$489$	−172.171	−	172.171i	−0.352087	−	0.352087i
$490$	110.559	+	191.494i	0.225631	+	0.390804i
$491$	−108.265	−	62.5068i	−0.220499	−	0.127305i	0.385682	−	0.922632i	$-0.373966\pi$
$491$	−108.265	−	62.5068i	−0.220499	−	0.127305i	−0.606181	+	0.795327i	$0.707299\pi$
$492$	182.239	−	48.8308i	0.370405	−	0.0992496i
$493$			536.193i			1.08761i
$494$	20.6524	−	186.847i	0.0418065	−	0.378234i
$495$	−162.326			−0.327930
$496$	50.1180	+	187.043i	0.101044	+	0.377102i
$497$	287.743	−	498.386i	0.578960	−	1.00279i
$498$	279.371	−	161.295i	0.560986	−	0.323886i
$499$	151.406	−	151.406i	0.303419	−	0.303419i	−0.538931	−	0.842350i	$-0.681172\pi$
$499$	151.406	−	151.406i	0.303419	−	0.303419i	0.842350	+	0.538931i	$0.181172\pi$
$500$	−12.8860	−	3.45278i	−0.0257719	−	0.00690556i
$501$	−88.0889	+	328.752i	−0.175826	+	0.656192i
$502$	174.494	+	174.494i	0.347598	+	0.347598i
$503$	−263.256	−	455.973i	−0.523372	−	0.906506i	−0.999630	−	0.0272010i	$-0.991341\pi$
$503$	−263.256	−	455.973i	−0.523372	−	0.906506i	0.476258	−	0.879305i	$-0.341993\pi$
$504$	38.2488	+	22.0829i	0.0758904	+	0.0438153i
$505$	−155.450	+	41.6527i	−0.307822	+	0.0824807i
$506$		−	102.659i		−	0.202884i
$507$	−198.188	+	215.417i	−0.390904	+	0.424886i
$508$	132.906			0.261626
$509$	−249.649	−	931.702i	−0.490469	−	1.83046i	−0.554056	−	0.832479i	$-0.686921\pi$
$509$	−249.649	−	931.702i	−0.490469	−	1.83046i	0.0635873	−	0.997976i	$-0.479746\pi$
$510$	141.270	−	244.687i	0.277000	−	0.479778i
$511$	234.838	−	135.584i	0.459566	−	0.265330i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	51.3205	+	13.7513i	0.100040	+	0.0268056i
$514$	−1.70157	+	6.35036i	−0.00331045	+	0.0123548i
$515$	552.014	+	552.014i	1.07187	+	1.07187i
$516$	81.4863	+	141.138i	0.157919	+	0.273524i
$517$	−444.045	−	256.369i	−0.858888	−	0.495879i
$518$	465.410	−	124.706i	0.898475	−	0.240746i
$519$			229.065i			0.441359i
$520$	−260.830	−	28.8298i	−0.501597	−	0.0554419i
$521$	−158.382			−0.303997			−0.151998	−	0.988381i	$-0.548571\pi$
$521$	−158.382			−0.303997			−0.151998	+	0.988381i	$0.548571\pi$
$522$	36.4297	+	135.958i	0.0697887	+	0.260455i
$523$	114.739	−	198.734i	0.219386	−	0.379989i	−0.735234	−	0.677813i	$-0.762928\pi$
$523$	114.739	−	198.734i	0.219386	−	0.379989i	0.954621	+	0.297825i	$0.0962611\pi$
$524$	49.0650	−	28.3277i	0.0936356	−	0.0540605i
$525$	−165.328	+	165.328i	−0.314910	+	0.314910i
$526$	18.9101	+	5.06694i	0.0359507	+	0.00963296i
$527$	202.503	−	755.751i	0.384256	−	1.43406i
$528$	−37.1420	−	37.1420i	−0.0703446	−	0.0703446i
$529$	−218.663	−	378.735i	−0.413351	−	0.715945i
$530$	590.160	+	340.729i	1.11351	+	0.642885i
$531$	218.233	−	58.4753i	0.410984	−	0.110123i
$532$		−	106.443i		−	0.200080i
$533$	107.007	+	699.895i	0.200764	+	1.31312i
$534$	123.280			0.230860
$535$	60.7251	+	226.629i	0.113505	+	0.423606i
$536$	−61.1108	+	105.847i	−0.114013	+	0.197476i
$537$	−53.1467	+	30.6843i	−0.0989697	+	0.0571402i
$538$	460.252	−	460.252i	0.855487	−	0.855487i
$539$	−160.437	−	42.9891i	−0.297657	−	0.0797571i
$540$	19.1962	−	71.6411i	0.0355485	−	0.132669i
$541$	606.240	+	606.240i	1.12059	+	1.12059i	0.991653	+	0.128938i	$0.0411569\pi$
$541$	606.240	+	606.240i	1.12059	+	1.12059i	0.128938	+	0.991653i	$0.458843\pi$
$542$	−104.874	−	181.647i	−0.193494	−	0.335141i
$543$	181.678	+	104.892i	0.334582	+	0.193171i
$544$	88.3114	−	23.6630i	0.162337	−	0.0434981i
$545$		−	1514.82i		−	2.77949i
$546$	−98.1402	+	133.566i	−0.179744	+	0.244626i
$547$	−790.673			−1.44547			−0.722736	−	0.691124i	$-0.757116\pi$
$547$	−790.673			−1.44547			−0.722736	+	0.691124i	$0.757116\pi$
$548$	26.0545	+	97.2365i	0.0475446	+	0.177439i
$549$	−105.779	+	183.215i	−0.192676	+	0.333725i
$550$	240.816	−	139.035i	0.437847	−	0.252791i
$551$	239.869	−	239.869i	0.435334	−	0.435334i
$552$	45.3078	+	12.1402i	0.0820794	+	0.0219931i
$553$	18.0339	−	67.3035i	0.0326111	−	0.121706i
$554$	−373.291	−	373.291i	−0.673811	−	0.673811i
$555$	−404.570	−	700.736i	−0.728955	−	1.26259i
$556$	−256.835	−	148.284i	−0.461934	−	0.266698i
$557$	−414.689	+	111.116i	−0.744505	+	0.199490i	−0.611080	−	0.791569i	$-0.709264\pi$
$557$	−414.689	+	111.116i	−0.744505	+	0.199490i	−0.133426	+	0.991059i	$0.542598\pi$
$558$		−	205.387i		−	0.368077i
$559$	−560.051	+	245.759i	−1.00188	+	0.439641i
$560$	−148.589			−0.265338
$561$	54.9305	+	205.004i	0.0979154	+	0.365425i
$562$	−136.099	+	235.730i	−0.242168	+	0.419448i
$563$	−276.549	+	159.665i	−0.491206	+	0.283598i	−0.725074	−	0.688671i	$-0.758195\pi$
$563$	−276.549	+	159.665i	−0.491206	+	0.283598i	0.233869	+	0.972268i	$0.424861\pi$
$564$	165.658	−	165.658i	0.293720	−	0.293720i
$565$	−818.883	−	219.419i	−1.44935	−	0.388352i
$566$	−139.344	+	520.039i	−0.246191	+	0.918797i
$567$	−33.1244	−	33.1244i	−0.0584205	−	0.0584205i
$568$	−156.361	−	270.826i	−0.275284	−	0.476806i
$569$	687.019	+	396.650i	1.20741	+	0.697101i	0.962194	−	0.272366i	$-0.0878063\pi$
$569$	687.019	+	396.650i	1.20741	+	0.697101i	0.245221	+	0.969467i	$0.421140\pi$
$570$	−172.660	+	46.2641i	−0.302912	+	0.0811651i
$571$		−	852.111i		−	1.49231i	−0.665771	−	0.746156i	$-0.731897\pi$
$571$		−	852.111i		−	1.49231i	0.665771	−	0.746156i	$-0.268103\pi$
$572$	153.855	−	123.229i	0.268977	−	0.215435i
$573$	347.387			0.606259
$574$	103.762	+	387.245i	0.180770	+	0.674644i
$575$	−124.158	+	215.047i	−0.215926	+	0.373996i
$576$	20.7846	−	12.0000i	0.0360844	−	0.0208333i
$577$	−186.391	+	186.391i	−0.323035	+	0.323035i	−0.849930	−	0.526895i	$-0.823356\pi$
$577$	−186.391	+	186.391i	−0.323035	+	0.323035i	0.526895	+	0.849930i	$0.323356\pi$
$578$	37.9570	+	10.1706i	0.0656696	+	0.0175961i
$579$	−11.7288	+	43.7725i	−0.0202570	+	0.0756002i
$580$	−334.846	−	334.846i	−0.577320	−	0.577320i
$581$	342.741	+	593.644i	0.589915	+	1.02176i
$582$	−115.390	−	66.6205i	−0.198265	−	0.114468i
$583$	−494.448	+	132.487i	−0.848109	+	0.227250i
$584$		−	147.354i		−	0.252319i
$585$	259.311	+	101.140i	0.443267	+	0.172888i
$586$	7.81698			0.0133396
$587$	203.087	+	757.931i	0.345975	+	1.29119i	0.891469	+	0.453081i	$0.149675\pi$
$587$	203.087	+	757.931i	0.345975	+	1.29119i	−0.545495	+	0.838114i	$0.683658\pi$
$588$	37.9458	−	65.7240i	0.0645336	−	0.111775i
$589$	−428.680	+	247.499i	−0.727810	+	0.420201i
$590$	−537.479	+	537.479i	−0.910981	+	0.910981i
$591$	158.476	+	42.4635i	0.268149	+	0.0718503i
$592$	67.7661	−	252.907i	0.114470	−	0.427207i
$593$	−375.307	−	375.307i	−0.632895	−	0.632895i	0.315898	−	0.948793i	$-0.397694\pi$
$593$	−375.307	−	375.307i	−0.632895	−	0.632895i	−0.948793	+	0.315898i	$0.897694\pi$
$594$	27.8565	+	48.2488i	0.0468964	+	0.0812270i
$595$	519.943	+	300.189i	0.873853	+	0.504520i
$596$	80.8509	−	21.6639i	0.135656	−	0.0363489i
$597$			341.559i			0.572126i
$598$	−63.9635	+	163.996i	−0.106962	+	0.274240i
$599$	320.645			0.535300			0.267650	−	0.963516i	$-0.413753\pi$
$599$	320.645			0.535300			0.267650	+	0.963516i	$0.413753\pi$
$600$	32.8838	+	122.724i	0.0548063	+	0.204540i
$601$	29.2104	−	50.5939i	0.0486030	−	0.0841828i	−0.840700	−	0.541500i	$-0.817856\pi$
$601$	29.2104	−	50.5939i	0.0486030	−	0.0841828i	0.889303	+	0.457318i	$0.151190\pi$
$602$	−299.909	+	173.153i	−0.498188	+	0.287629i
$603$	91.6662	−	91.6662i	0.152017	−	0.152017i
$604$	7.03871	+	1.88602i	0.0116535	+	0.00312255i
$605$	117.331	−	437.884i	0.193935	−	0.723776i
$606$	39.0572	+	39.0572i	0.0644509	+	0.0644509i
$607$	327.926	+	567.984i	0.540240	+	0.935724i	0.998890	+	0.0471065i	$0.0150000\pi$
$607$	327.926	+	567.984i	0.540240	+	0.935724i	−0.458649	+	0.888617i	$0.651667\pi$
$608$	−50.0923	−	28.9208i	−0.0823887	−	0.0475671i
$609$	−288.900	+	77.4107i	−0.474385	+	0.127111i
$610$		−	711.755i		−	1.16681i
$611$	549.616	+	686.214i	0.899536	+	1.12310i
$612$	−96.9726			−0.158452
$613$	−49.8176	−	185.922i	−0.0812686	−	0.303298i	0.913313	−	0.407259i	$-0.133515\pi$
$613$	−49.8176	−	185.922i	−0.0812686	−	0.303298i	−0.994581	+	0.103960i	$0.966849\pi$
$614$	−227.287	+	393.673i	−0.370174	+	0.641161i
$615$	583.049	−	336.623i	0.948047	−	0.547355i
$616$	78.9241	−	78.9241i	0.128124	−	0.128124i
$617$	19.1730	+	5.13739i	0.0310745	+	0.00832640i	0.274323	−	0.961638i	$-0.411546\pi$
$617$	19.1730	+	5.13739i	0.0310745	+	0.00832640i	−0.243248	+	0.969964i	$0.578213\pi$
$618$	69.3474	−	258.808i	0.112213	−	0.418783i
$619$	−319.972	−	319.972i	−0.516917	−	0.516917i	0.399720	−	0.916637i	$-0.369107\pi$
$619$	−319.972	−	319.972i	−0.516917	−	0.516917i	−0.916637	+	0.399720i	$0.869107\pi$
$620$	345.497	+	598.418i	0.557252	+	0.965190i
$621$	−43.0860	−	24.8757i	−0.0693817	−	0.0400575i
$622$	421.916	−	113.052i	0.678322	−	0.181756i
$623$			261.961i			0.420482i
$624$	36.1915	+	82.4753i	0.0579992	+	0.132172i
$625$	600.761			0.961217
$626$	−0.921140	−	3.43774i	−0.00147147	−	0.00549160i
$627$	67.1360	−	116.283i	0.107075	−	0.185459i
$628$	−478.023	+	275.987i	−0.761184	+	0.439470i
$629$	−748.065	+	748.065i	−1.18929	+	1.18929i
$630$	152.232	+	40.7906i	0.241639	+	0.0647469i
$631$	113.387	−	423.167i	0.179695	−	0.670629i	−0.816010	−	0.578038i	$-0.803818\pi$
$631$	113.387	−	423.167i	0.179695	−	0.670629i	0.995704	−	0.0925909i	$-0.0295149\pi$
$632$	−26.7734	−	26.7734i	−0.0423630	−	0.0423630i
$633$	168.732	+	292.252i	0.266559	+	0.461694i
$634$	−81.1397	−	46.8460i	−0.127981	−	0.0738896i
$635$	458.104	−	122.749i	0.721424	−	0.193305i
$636$		−	233.888i		−	0.367749i
$637$	229.510	+	168.637i	0.360298	+	0.264736i
$638$	355.711			0.557541
$639$	85.8483	+	320.390i	0.134348	+	0.501393i
$640$	−40.3721	+	69.9266i	−0.0630814	+	0.109260i
$641$	−536.275	+	309.618i	−0.836622	+	0.483024i	−0.856115	−	0.516786i	$-0.827128\pi$
$641$	−536.275	+	309.618i	−0.836622	+	0.483024i	0.0194927	+	0.999810i	$0.493795\pi$
$642$	56.9412	−	56.9412i	0.0886934	−	0.0886934i
$643$	−389.853	−	104.461i	−0.606304	−	0.162459i	−0.0574099	−	0.998351i	$-0.518284\pi$
$643$	−389.853	−	104.461i	−0.606304	−	0.162459i	−0.548894	+	0.835892i	$0.684951\pi$
$644$	−25.7971	+	96.2760i	−0.0400576	+	0.149497i
$645$	411.222	+	411.222i	0.637553	+	0.637553i
$646$	116.855	+	202.399i	0.180891	+	0.313312i
$647$	−216.586	−	125.046i	−0.334754	−	0.193270i	0.323196	−	0.946332i	$-0.395243\pi$
$647$	−216.586	−	125.046i	−0.334754	−	0.193270i	−0.657950	+	0.753062i	$0.728576\pi$
$648$	−24.5885	+	6.58846i	−0.0379452	+	0.0101674i
$649$		−	570.971i		−	0.879770i
$650$	−471.325	+	72.0611i	−0.725116	+	0.110863i
$651$	436.434			0.670405
$652$	−72.7679	−	271.574i	−0.111607	−	0.416524i
$653$	195.830	−	339.188i	0.299894	−	0.519431i	−0.676218	−	0.736702i	$-0.736382\pi$
$653$	195.830	−	339.188i	0.299894	−	0.519431i	0.976111	+	0.217271i	$0.0697155\pi$
$654$	−450.258	+	259.956i	−0.688467	+	0.397487i
$655$	142.956	−	142.956i	0.218254	−	0.218254i
$656$	210.432	+	56.3850i	0.320780	+	0.0859527i
$657$	−40.4515	+	150.967i	−0.0615701	+	0.229783i
$658$	352.012	+	352.012i	0.534973	+	0.534973i
$659$	305.994	+	529.997i	0.464330	+	0.804244i	0.999171	−	0.0407093i	$-0.0129617\pi$
$659$	305.994	+	529.997i	0.464330	+	0.804244i	−0.534841	+	0.844953i	$0.679628\pi$
$660$	−162.326	−	93.7187i	−0.245948	−	0.141998i
$661$	−585.429	+	156.865i	−0.885671	+	0.237315i	−0.672852	−	0.739777i	$-0.734931\pi$
$661$	−585.429	+	156.865i	−0.885671	+	0.237315i	−0.212819	+	0.977092i	$0.568264\pi$
$662$		−	339.733i		−	0.513192i
$663$	39.9805	−	361.714i	0.0603024	−	0.545571i
$664$	372.495			0.560986
$665$	−98.3080	−	366.890i	−0.147832	−	0.551715i
$666$	−138.855	+	240.505i	−0.208492	+	0.361118i
$667$	−275.092	+	158.824i	−0.412432	+	0.238117i
$668$	−277.894	+	277.894i	−0.416009	+	0.416009i
$669$	−685.331	−	183.634i	−1.02441	−	0.274490i
$670$	−112.881	+	421.278i	−0.168479	+	0.628773i
$671$	378.053	+	378.053i	0.563418	+	0.563418i
$672$	25.4992	+	44.1659i	0.0379452	+	0.0657230i
$673$	680.049	+	392.627i	1.01047	+	0.583398i	0.911331	−	0.411675i	$-0.135056\pi$
$673$	680.049	+	392.627i	1.01047	+	0.583398i	0.0991438	+	0.995073i	$0.468390\pi$
$674$	7.82667	−	2.09715i	0.0116123	−	0.00311150i
$675$		−	134.760i		−	0.199645i
$676$	−322.559	+	100.993i	−0.477159	+	0.149398i
$677$	−622.197			−0.919051			−0.459525	−	0.888165i	$-0.651980\pi$
$677$	−622.197			−0.919051			−0.459525	+	0.888165i	$0.651980\pi$
$678$	75.3084	+	281.055i	0.111074	+	0.414535i
$679$	141.564	−	245.196i	0.208489	−	0.361113i
$680$	282.540	−	163.125i	0.415500	−	0.239889i
$681$	−305.811	+	305.811i	−0.449062	+	0.449062i
$682$	−501.366	−	134.341i	−0.735141	−	0.196980i
$683$	218.794	−	816.549i	0.320342	−	1.19553i	−0.598570	−	0.801071i	$-0.704264\pi$
$683$	218.794	−	816.549i	0.320342	−	1.19553i	0.918912	−	0.394462i	$-0.129069\pi$
$684$	43.3812	+	43.3812i	0.0634228	+	0.0634228i
$685$	179.611	+	311.095i	0.262205	+	0.454153i
$686$	452.024	+	260.976i	0.658927	+	0.380432i
$687$	412.295	−	110.474i	0.600138	−	0.160807i
$688$			188.185i			0.273524i
$689$	872.417	+	96.4290i	1.26621	+	0.139955i
$690$	167.381			0.242581
$691$	172.573	+	644.052i	0.249744	+	0.932058i	0.970939	+	0.239326i	$0.0769264\pi$
$691$	172.573	+	644.052i	0.249744	+	0.932058i	−0.721195	+	0.692732i	$0.756407\pi$
$692$	−132.251	+	229.065i	−0.191114	+	0.331019i
$693$	−102.525	+	59.1931i	−0.147944	+	0.0854157i
$694$	102.971	−	102.971i	0.148373	−	0.148373i
$695$	−1022.22	−	273.903i	−1.47082	−	0.394105i
$696$	−42.0654	+	156.990i	−0.0604388	+	0.225561i
$697$	−622.429	−	622.429i	−0.893012	−	0.893012i
$698$	−342.739	−	593.641i	−0.491030	−	0.850488i
$699$	−435.913	−	251.675i	−0.623624	−	0.360050i
$700$	−260.780	+	69.8758i	−0.372543	+	0.0998226i
$701$			299.776i			0.427640i	0.976873	+	0.213820i	$0.0685907\pi$
$701$			299.776i			0.427640i	−0.976873	+	0.213820i	$0.931409\pi$
$702$	−14.4379	−	94.4328i	−0.0205667	−	0.134520i
$703$	669.302			0.952065
$704$	−15.6980	−	58.5859i	−0.0222983	−	0.0832186i
$705$	417.998	−	723.994i	0.592905	−	1.02694i
$706$	−241.165	+	139.237i	−0.341594	+	0.197219i
$707$	−82.9940	+	82.9940i	−0.117389	+	0.117389i
$708$	251.993	+	67.5214i	0.355923	+	0.0953692i
$709$	−88.7405	+	331.184i	−0.125163	+	0.467114i	−0.999845	−	0.0175820i	$-0.994403\pi$
$709$	−88.7405	+	331.184i	−0.125163	+	0.467114i	0.874683	+	0.484696i	$0.161070\pi$
$710$	−789.080	−	789.080i	−1.11138	−	1.11138i
$711$	20.0800	+	34.7796i	0.0282420	+	0.0489165i
$712$	123.280	+	71.1755i	0.173145	+	0.0999655i
$713$	447.718	−	119.966i	0.627936	−	0.168255i
$714$		−	206.060i		−	0.288600i
$715$	416.501	−	566.845i	0.582519	−	0.792790i
$716$	−70.8623			−0.0989697
$717$	136.859	+	510.766i	0.190878	+	0.712365i
$718$	−54.1215	+	93.7412i	−0.0753781	+	0.130559i
$719$	551.827	−	318.597i	0.767492	−	0.443112i	−0.0644873	−	0.997919i	$-0.520541\pi$
$719$	551.827	−	318.597i	0.767492	−	0.443112i	0.831979	+	0.554807i	$0.187208\pi$
$720$	60.5582	−	60.5582i	0.0841086	−	0.0841086i
$721$	549.950	+	147.359i	0.762759	+	0.204381i
$722$	−93.8666	+	350.315i	−0.130009	+	0.485201i
$723$	−147.135	−	147.135i	−0.203507	−	0.203507i
$724$	121.119	+	209.783i	0.167291	+	0.289756i
$725$	−745.133	−	430.203i	−1.02777	−	0.593383i
$726$	−150.289	+	40.2699i	−0.207010	+	0.0554682i
$727$		−	617.181i		−	0.848943i	−0.905441	−	0.424471i	$-0.860460\pi$
$727$		−	617.181i		−	0.848943i	0.905441	−	0.424471i	$-0.139540\pi$
$728$	−175.254	+	76.9045i	−0.240734	+	0.105638i
$729$	27.0000			0.0370370
$730$	−136.093	−	507.905i	−0.186429	−	0.695761i
$731$	380.182	−	658.495i	0.520085	−	0.900814i
$732$	−211.558	+	122.143i	−0.289014	+	0.166862i
$733$	−932.866	+	932.866i	−1.27267	+	1.27267i	−0.327985	+	0.944683i	$0.606369\pi$
$733$	−932.866	+	932.866i	−1.27267	+	1.27267i	−0.944683	+	0.327985i	$0.893631\pi$
$734$	−294.581	−	78.9329i	−0.401337	−	0.107538i
$735$	70.0916	−	261.585i	0.0953627	−	0.355899i
$736$	38.2987	+	38.2987i	0.0520362	+	0.0520362i
$737$	−163.807	−	283.722i	−0.222262	−	0.384969i
$738$	−200.112	−	115.535i	−0.271155	−	0.156551i
$739$	195.134	−	52.2859i	0.264051	−	0.0707523i	−0.124364	−	0.992237i	$-0.539689\pi$
$739$	195.134	−	52.2859i	0.264051	−	0.0707523i	0.388416	+	0.921484i	$0.373023\pi$
$740$		−	934.314i		−	1.26259i
$741$	−179.700	+	143.929i	−0.242510	+	0.194236i
$742$	496.996			0.669806
$743$	−271.553	−	1013.45i	−0.365482	−	1.36400i	−0.866766	−	0.498716i	$-0.833805\pi$
$743$	−271.553	−	1013.45i	−0.365482	−	1.36400i	0.501283	−	0.865283i	$-0.332861\pi$
$744$	118.580	−	205.387i	0.159382	−	0.276058i
$745$	258.671	−	149.344i	0.347210	−	0.200462i
$746$	631.387	−	631.387i	0.846363	−	0.846363i
$747$	−381.628	−	102.257i	−0.510881	−	0.136890i
$748$	−63.4283	+	236.718i	−0.0847972	+	0.316467i
$749$	120.996	+	120.996i	0.161543	+	0.161543i
$750$	8.16937	+	14.1498i	0.0108925	+	0.0188663i
$751$	1272.00	+	734.389i	1.69374	+	0.977881i	0.951451	+	0.307800i	$0.0995929\pi$
$751$	1272.00	+	734.389i	1.69374	+	0.977881i	0.742288	+	0.670080i	$0.233740\pi$
$752$	261.301	−	70.0154i	0.347475	−	0.0931055i
$753$		−	302.233i		−	0.401371i
$754$	−568.240	−	221.632i	−0.753634	−	0.293941i
$755$	26.0032			0.0344413
$756$	−14.0000	−	52.2488i	−0.0185185	−	0.0691122i
$757$	427.864	−	741.082i	0.565210	−	0.978972i	−0.431821	−	0.901960i	$-0.642129\pi$
$757$	427.864	−	741.082i	0.565210	−	0.978972i	0.997030	−	0.0770121i	$-0.0245380\pi$
$758$	−305.293	+	176.261i	−0.402761	+	0.232534i
$759$	−88.9055	+	88.9055i	−0.117135	+	0.117135i
$760$	−199.370	−	53.4212i	−0.262330	−	0.0702910i
$761$	111.078	−	414.549i	0.145963	−	0.544743i	−0.853747	−	0.520688i	$-0.825676\pi$
$761$	111.078	−	414.549i	0.145963	−	0.544743i	0.999711	−	0.0240550i	$-0.00765767\pi$
$762$	−115.100	−	115.100i	−0.151050	−	0.151050i
$763$	−552.390	−	956.767i	−0.723971	−	1.25395i
$764$	347.387	+	200.564i	0.454694	+	0.262518i
$765$	−334.248	+	89.5616i	−0.436926	+	0.117074i
$766$		−	397.312i		−	0.518684i
$767$	−355.753	+	912.112i	−0.463823	+	1.18919i
$768$	27.7128			0.0360844
$769$	114.020	+	425.529i	0.148271	+	0.553354i	0.999588	+	0.0287025i	$0.00913755\pi$
$769$	114.020	+	425.529i	0.148271	+	0.553354i	−0.851317	+	0.524651i	$0.824196\pi$
$770$	199.146	−	344.931i	0.258631	−	0.447962i
$771$	6.97318	−	4.02596i	0.00904433	−	0.00522174i
$772$	−37.0009	+	37.0009i	−0.0479286	+	0.0479286i
$773$	1154.86	+	309.443i	1.49399	+	0.400315i	0.911084	−	0.412221i	$-0.135247\pi$
$773$	1154.86	+	309.443i	1.49399	+	0.400315i	0.582911	+	0.812536i	$0.301914\pi$
$774$	51.6602	−	192.799i	0.0667445	−	0.249094i
$775$	887.773	+	887.773i	1.14551	+	1.14551i
$776$	−76.9267	−	133.241i	−0.0991323	−	0.171702i
$777$	−511.056	−	295.058i	−0.657729	−	0.379740i
$778$	−362.202	+	97.0517i	−0.465555	+	0.124745i
$779$			556.894i			0.714883i
$780$	200.918	+	250.853i	0.257588	+	0.321606i
$781$	838.250			1.07330
$782$	−56.6413	−	211.388i	−0.0724313	−	0.270317i
$783$	86.1936	−	149.292i	0.110081	−	0.190666i
$784$	75.8915	−	43.8160i	0.0968004	−	0.0558877i
$785$	−1392.77	+	1392.77i	−1.77423	+	1.77423i
$786$	−67.0241	−	17.9591i	−0.0852724	−	0.0228487i
$787$	84.2515	−	314.431i	0.107054	−	0.399531i	−0.891516	−	0.452989i	$-0.850358\pi$
$787$	84.2515	−	314.431i	0.107054	−	0.399531i	0.998570	+	0.0534580i	$0.0170243\pi$
$788$	133.960	+	133.960i	0.170000	+	0.170000i
$789$	−11.9885	−	20.7647i	−0.0151946	−	0.0263177i
$790$	−117.011	−	67.5561i	−0.148115	−	0.0855141i
$791$	−597.222	+	160.025i	−0.755021	+	0.202307i
$792$			64.3317i			0.0812270i
$793$	−368.379	−	839.484i	−0.464539	−	1.05862i
$794$	178.009			0.224193
$795$	−216.014	−	806.173i	−0.271715	−	1.01405i
$796$	−197.199	+	341.559i	−0.247738	+	0.429094i
$797$	2.24946	−	1.29872i	0.00282241	−	0.00162952i	−0.498588	−	0.866839i	$-0.666148\pi$
$797$	2.24946	−	1.29872i	0.00282241	−	0.00162952i	0.501411	+	0.865209i	$0.332815\pi$
$798$	−92.1821	+	92.1821i	−0.115516	+	0.115516i
$799$	−1055.79	−	282.899i	−1.32139	−	0.354066i
$800$	−37.9709	+	141.709i	−0.0474637	+	0.177137i
$801$	−106.763	−	106.763i	−0.133287	−	0.133287i
$802$	393.820	+	682.116i	0.491047	+	0.850519i
$803$	342.064	+	197.491i	0.425982	+	0.245941i
$804$	144.590	−	38.7427i	0.179838	−	0.0481874i
$805$			355.673i			0.441830i
$806$	717.218	+	526.990i	0.889848	+	0.653834i
$807$	−797.180			−0.987831
$808$	16.5075	+	61.6069i	0.0204301	+	0.0762462i
$809$	56.2400	−	97.4105i	0.0695179	−	0.120409i	−0.829171	−	0.558995i	$-0.811187\pi$
$809$	56.2400	−	97.4105i	0.0695179	−	0.120409i	0.898689	+	0.438586i	$0.144521\pi$
$810$	−78.6674	+	45.4186i	−0.0971202	+	0.0560724i
$811$	725.545	−	725.545i	0.894630	−	0.894630i	−0.100324	−	0.994955i	$-0.531988\pi$
$811$	725.545	−	725.545i	0.894630	−	0.894630i	0.994955	+	0.100324i	$0.0319881\pi$
$812$	−333.594	−	89.3861i	−0.410829	−	0.110081i
$813$	−66.4873	+	248.134i	−0.0817802	+	0.305208i
$814$	496.267	+	496.267i	0.609665	+	0.609665i
$815$	−501.638	−	868.862i	−0.615506	−	1.06609i
$816$	−96.9726	−	55.9872i	−0.118839	−	0.0686117i
$817$	−464.658	+	124.505i	−0.568737	+	0.152393i
$818$		−	292.007i		−	0.356977i
$819$	200.663	−	30.6794i	0.245010	−	0.0374596i
$820$	777.398			0.948047
$821$	−143.499	−	535.547i	−0.174786	−	0.652311i	−0.996588	−	0.0825373i	$-0.973698\pi$
$821$	−143.499	−	535.547i	−0.174786	−	0.652311i	0.821802	−	0.569773i	$-0.192969\pi$
$822$	61.6455	−	106.773i	0.0749945	−	0.129894i
$823$	−96.1533	+	55.5142i	−0.116833	+	0.0674534i	−0.557278	−	0.830326i	$-0.688154\pi$
$823$	−96.1533	+	55.5142i	−0.116833	+	0.0674534i	0.440445	+	0.897780i	$0.354821\pi$
$824$	218.770	−	218.770i	0.265498	−	0.265498i
$825$	−328.960	−	88.1446i	−0.398740	−	0.106842i
$826$	−143.478	+	535.469i	−0.173703	+	0.648267i
$827$	878.475	+	878.475i	1.06224	+	1.06224i	0.997930	+	0.0643137i	$0.0204858\pi$
$827$	878.475	+	878.475i	1.06224	+	1.06224i	0.0643137	+	0.997930i	$0.479514\pi$
$828$	−28.7240	−	49.7514i	−0.0346908	−	0.0600863i
$829$	715.780	+	413.256i	0.863425	+	0.498499i	0.865158	−	0.501500i	$-0.167218\pi$
$829$	715.780	+	413.256i	0.863425	+	0.498499i	−0.00173250	+	0.999998i	$0.500551\pi$
$830$	1283.93	−	344.027i	1.54690	−	0.414491i
$831$			646.559i			0.778050i
$832$	−11.4256	+	103.370i	−0.0137327	+	0.124243i
$833$	−354.079			−0.425065
$834$	94.0083	+	350.844i	0.112720	+	0.420676i
$835$	−701.199	+	1214.51i	−0.839759	+	1.45450i
$836$	134.272	−	77.5219i	0.160612	−	0.0927296i
$837$	−177.871	+	177.871i	−0.212510	+	0.212510i
$838$	458.181	+	122.769i	0.546756	+	0.146503i
$839$	−80.6696	+	301.063i	−0.0961497	+	0.358836i	−0.997191	−	0.0748971i	$-0.976137\pi$
$839$	−80.6696	+	301.063i	−0.0961497	+	0.358836i	0.901042	+	0.433733i	$0.142804\pi$
$840$	128.682	+	128.682i	0.153193	+	0.153193i
$841$	−129.822	−	224.858i	−0.154366	−	0.267369i
$842$	−475.668	−	274.627i	−0.564927	−	0.326161i
$843$	322.013	−	86.2831i	0.381984	−	0.102352i
$844$			389.670i			0.461694i
$845$	−1018.53	+	646.014i	−1.20536	+	0.764514i
$846$	−286.928			−0.339159
$847$	−85.5709	−	319.355i	−0.101028	−	0.377042i
$848$	135.035	−	233.888i	0.159240	−	0.275811i
$849$	571.042	−	329.692i	0.672606	−	0.388329i
$850$	419.158	−	419.158i	0.493127	−	0.493127i
$851$	−605.374	−	162.210i	−0.711368	−	0.190611i
$852$	−99.1291	+	369.955i	−0.116349	+	0.434219i
$853$	724.409	+	724.409i	0.849249	+	0.849249i	0.990039	−	0.140791i	$-0.0449645\pi$
$853$	724.409	+	724.409i	0.849249	+	0.849249i	−0.140791	+	0.990039i	$0.544964\pi$
$854$	−259.546	−	449.547i	−0.303918	−	0.526402i
$855$	189.594	+	109.462i	0.221747	+	0.128026i
$856$	89.8161	−	24.0662i	0.104925	−	0.0281147i
$857$			49.0244i			0.0572047i	0.999591	+	0.0286023i	$0.00910565\pi$
$857$			49.0244i			0.0572047i	−0.999591	+	0.0286023i	$0.990894\pi$
$858$	−239.961	−	26.5231i	−0.279675	−	0.0309127i
$859$	−584.617			−0.680578			−0.340289	−	0.940321i	$-0.610525\pi$
$859$	−584.617			−0.680578			−0.340289	+	0.940321i	$0.610525\pi$
$860$	173.803	+	648.641i	0.202096	+	0.754234i
$861$	245.504	−	425.225i	0.285138	−	0.493873i
$862$	168.389	−	97.2197i	0.195347	−	0.112784i
$863$	458.022	−	458.022i	0.530732	−	0.530732i	−0.390058	−	0.920790i	$-0.627545\pi$
$863$	458.022	−	458.022i	0.530732	−	0.530732i	0.920790	+	0.390058i	$0.127545\pi$
$864$	−28.3923	−	7.60770i	−0.0328615	−	0.00880520i
$865$	−244.288	+	911.694i	−0.282414	+	1.05398i
$866$	420.434	+	420.434i	0.485490	+	0.485490i
$867$	−24.0638	−	41.6797i	−0.0277552	−	0.0480735i
$868$	436.434	+	251.975i	0.502804	+	0.290294i
$869$	98.0339	−	26.2681i	0.112812	−	0.0302280i
$870$			579.970i			0.666632i
$871$	84.9002	+	555.302i	0.0974744	+	0.637545i
$872$	−600.344			−0.688467
$873$	42.2357	+	157.626i	0.0483799	+	0.180556i
$874$	−69.2268	+	119.904i	−0.0792069	+	0.137190i
$875$	−30.0673	+	17.3593i	−0.0343626	+	0.0198393i
$876$	−127.612	+	127.612i	−0.145676	+	0.145676i
$877$	−311.620	−	83.4983i	−0.355325	−	0.0952090i	0.0767411	−	0.997051i	$-0.475549\pi$
$877$	−311.620	−	83.4983i	−0.355325	−	0.0952090i	−0.432066	+	0.901842i	$0.642215\pi$
$878$	272.821	−	1018.18i	0.310730	−	1.15966i
$879$	−6.76970	−	6.76970i	−0.00770160	−	0.00770160i
$880$	−108.217	−	187.437i	−0.122974	−	0.212997i
$881$	−1090.72	−	629.725i	−1.23804	−	0.714785i	−0.269349	−	0.963043i	$-0.586809\pi$
$881$	−1090.72	−	629.725i	−1.23804	−	0.714785i	−0.968694	+	0.248258i	$0.920142\pi$
$882$	−89.7806	+	24.0566i	−0.101792	+	0.0272751i
$883$			213.692i			0.242007i	0.992652	+	0.121003i	$0.0386112\pi$
$883$			213.692i			0.242007i	−0.992652	+	0.121003i	$0.961389\pi$
$884$	248.816	−	338.631i	0.281466	−	0.383067i
$885$	930.940			1.05191
$886$	−242.278	−	904.195i	−0.273452	−	1.02054i
$887$	133.786	−	231.725i	0.150830	−	0.261245i	−0.780703	−	0.624903i	$-0.785139\pi$
$887$	133.786	−	231.725i	0.150830	−	0.261245i	0.931533	+	0.363657i	$0.118472\pi$
$888$	−277.711	+	160.336i	−0.312737	+	0.180559i
$889$	244.579	−	244.579i	0.275117	−	0.275117i
$890$	490.660	+	131.472i	0.551303	+	0.147721i
$891$	17.6603	−	65.9091i	0.0198208	−	0.0739721i
$892$	−579.310	−	579.310i	−0.649450	−	0.649450i
$893$	345.758	+	598.871i	0.387187	+	0.670628i
$894$	−88.7804	−	51.2574i	−0.0993070	−	0.0573349i
$895$	−244.251	+	65.4467i	−0.272906	+	0.0731248i
$896$			58.8878i			0.0657230i
$897$	197.418	−	86.6304i	0.220087	−	0.0965780i
$898$	44.3712			0.0494112
$899$	415.678	+	1551.33i	0.462378	+	1.72562i
$900$	77.8039	−	134.760i	0.0864487	−	0.149734i
$901$	−945.031	+	545.614i	−1.04887	+	0.605565i
$902$	−412.920	+	412.920i	−0.457783	+	0.457783i
$903$	409.684	+	109.774i	0.453692	+	0.121566i
$904$	−86.9586	+	324.534i	−0.0961932	+	0.358998i
$905$	611.226	+	611.226i	0.675388	+	0.675388i
$906$	−4.46237	−	7.72905i	−0.00492535	−	0.00853096i
$907$	43.1528	+	24.9143i	0.0475776	+	0.0274689i	0.523600	−	0.851964i	$-0.324589\pi$
$907$	43.1528	+	24.9143i	0.0475776	+	0.0274689i	−0.476023	+	0.879433i	$0.657922\pi$
$908$	−482.371	+	129.251i	−0.531246	+	0.142347i
$909$		−	67.6491i		−	0.0744215i
$910$	−533.045	+	426.938i	−0.585764	+	0.469162i
$911$	−465.226			−0.510676			−0.255338	−	0.966852i	$-0.582187\pi$
$911$	−465.226			−0.510676			−0.255338	+	0.966852i	$0.582187\pi$
$912$	18.3351	+	68.4274i	0.0201042	+	0.0750300i
$913$	−499.234	+	864.699i	−0.546806	+	0.947096i
$914$	−199.200	+	115.008i	−0.217943	+	0.125830i
$915$	−616.398	+	616.398i	−0.673659	+	0.673659i
$916$	476.077	+	127.564i	0.519735	+	0.139263i
$917$	38.1618	−	142.422i	0.0416159	−	0.155313i
$918$	83.9807	+	83.9807i	0.0914823	+	0.0914823i
$919$	−334.402	−	579.201i	−0.363876	−	0.630251i	0.624719	−	0.780849i	$-0.285213\pi$
$919$	−334.402	−	579.201i	−0.363876	−	0.630251i	−0.988595	+	0.150598i	$0.951880\pi$
$920$	167.381	+	96.6374i	0.181936	+	0.105041i
$921$	537.767	−	144.094i	0.583894	−	0.156454i
$922$			113.912i			0.123549i
$923$	−1339.08	−	522.285i	−1.45080	−	0.565856i
$924$	−136.701			−0.147944
$925$	−439.372	−	1639.76i	−0.474997	−	1.77271i
$926$	−172.856	+	299.395i	−0.186669	+	0.323321i
$927$	−284.191	+	164.078i	−0.306571	+	0.176999i
$928$	−132.704	+	132.704i	−0.143000	+	0.143000i
$929$	−655.978	−	175.769i	−0.706112	−	0.189202i	−0.112145	−	0.993692i	$-0.535772\pi$
$929$	−655.978	−	175.769i	−0.706112	−	0.189202i	−0.593966	+	0.804490i	$0.702439\pi$
$930$	219.036	−	817.454i	0.235523	−	0.878982i
$931$	158.399	+	158.399i	0.170139	+	0.170139i
$932$	−290.609	−	503.349i	−0.311812	−	0.540074i
$933$	−463.296	−	267.484i	−0.496566	−	0.286693i
$934$	887.875	−	237.906i	0.950616	−	0.254717i
$935$			874.507i			0.935302i
$936$	40.0829	−	102.768i	0.0428236	−	0.109795i
$937$	−210.517			−0.224671			−0.112336	−	0.993670i	$-0.535833\pi$
$937$	−210.517			−0.224671			−0.112336	+	0.993670i	$0.535833\pi$
$938$	82.3256	+	307.243i	0.0877671	+	0.327551i
$939$	−2.17944	+	3.77490i	−0.00232102	+	0.00402013i
$940$	835.996	−	482.663i	0.889358	−	0.513471i
$941$	447.841	−	447.841i	0.475920	−	0.475920i	−0.427904	−	0.903824i	$-0.640748\pi$
$941$	447.841	−	447.841i	0.475920	−	0.475920i	0.903824	+	0.427904i	$0.140748\pi$
$942$	652.992	+	174.969i	0.693198	+	0.185742i
$943$	134.967	−	503.703i	0.143125	−	0.534150i
$944$	213.010	+	213.010i	0.225646	+	0.225646i
$945$	−96.5115	−	167.163i	−0.102129	−	0.176892i
$946$	−436.846	−	252.213i	−0.461783	−	0.266610i
$947$	569.069	−	152.482i	0.600918	−	0.161015i	0.0544795	−	0.998515i	$-0.482650\pi$
$947$	569.069	−	152.482i	0.600918	−	0.161015i	0.546438	+	0.837500i	$0.315983\pi$
$948$			46.3729i			0.0489165i
$949$	−423.389	−	528.615i	−0.446143	−	0.557023i
$950$	−375.025			−0.394763
$951$	29.6992	+	110.839i	0.0312294	+	0.116550i
$952$	118.969	−	206.060i	0.124967	−	0.216450i
$953$	333.275	−	192.416i	0.349711	−	0.201906i	−0.314847	−	0.949142i	$-0.601953\pi$
$953$	333.275	−	192.416i	0.349711	−	0.201906i	0.664558	+	0.747237i	$0.268620\pi$
$954$	−202.553	+	202.553i	−0.212320	+	0.212320i
$955$	1382.62	+	370.472i	1.44777	+	0.387929i
$956$	−158.032	+	589.782i	−0.165305	+	0.616927i
$957$	−308.055	−	308.055i	−0.321896	−	0.321896i
$958$	359.283	+	622.296i	0.375034	+	0.649578i
$959$	226.886	+	130.992i	0.236586	+	0.136593i
$960$	95.5215	−	25.5949i	0.0995015	−	0.0266614i
$961$		−	1382.55i		−	1.43866i
$962$	−483.568	−	1101.98i	−0.502669	−	1.14551i
$963$	−98.6250			−0.102414
$964$	−62.1867	−	232.084i	−0.0645090	−	0.240751i
$965$	−93.3627	+	161.709i	−0.0967490	+	0.167574i
$966$	105.718	−	61.0366i	0.109439	−	0.0631848i
$967$	1196.08	−	1196.08i	1.23690	−	1.23690i	0.275638	−	0.961262i	$-0.411111\pi$
$967$	1196.08	−	1196.08i	1.23690	−	1.23690i	0.961262	−	0.275638i	$-0.0888891\pi$
$968$	−173.539	−	46.4997i	−0.179276	−	0.0480369i
$969$	74.0833	−	276.483i	0.0764533	−	0.285328i
$970$	−388.212	−	388.212i	−0.400218	−	0.400218i
$971$	−149.962	−	259.741i	−0.154440	−	0.267499i	0.778415	−	0.627750i	$-0.216024\pi$
$971$	−149.962	−	259.741i	−0.154440	−	0.267499i	−0.932855	+	0.360252i	$0.882691\pi$
$972$	27.0000	+	15.5885i	0.0277778	+	0.0160375i
$973$	−745.519	+	199.761i	−0.766206	+	0.205304i
$974$			1097.44i			1.12674i
$975$	470.586	+	345.773i	0.482653	+	0.354639i
$976$	−282.078			−0.289014
$977$	62.1492	+	231.944i	0.0636123	+	0.237404i	0.990411	−	0.138155i	$-0.0441173\pi$
$977$	62.1492	+	231.944i	0.0636123	+	0.237404i	−0.926798	+	0.375559i	$0.877451\pi$
$978$	−172.171	+	298.208i	−0.176044	+	0.304917i
$979$	−330.449	+	190.785i	−0.337538	+	0.194877i
$980$	221.118	−	221.118i	0.225631	−	0.225631i
$981$	615.063	+	164.806i	0.626976	+	0.167998i
$982$	−45.7581	+	170.772i	−0.0465969	+	0.173902i
$983$	−503.122	−	503.122i	−0.511823	−	0.511823i	0.403261	−	0.915085i	$-0.367877\pi$
$983$	−503.122	−	503.122i	−0.511823	−	0.511823i	−0.915085	+	0.403261i	$0.867877\pi$
$984$	−133.408	−	231.070i	−0.135577	−	0.234827i
$985$	585.459	+	338.015i	0.594375	+	0.343162i
$986$	732.453	−	196.260i	0.742853	−	0.199047i
$987$		−	609.703i		−	0.617734i
$988$	−262.798	+	40.1792i	−0.265989	+	0.0406672i
$989$	450.451			0.455461
$990$	59.4153	+	221.741i	0.0600154	+	0.223981i
$991$	268.482	−	465.025i	0.270921	−	0.469249i	−0.698177	−	0.715925i	$-0.746005\pi$
$991$	268.482	−	465.025i	0.270921	−	0.469249i	0.969098	+	0.246677i	$0.0793385\pi$
$992$	237.161	−	136.925i	0.239073	−	0.138029i
$993$	−294.217	+	294.217i	−0.296291	+	0.296291i
$994$	−786.129	−	210.643i	−0.790874	−	0.211914i
$995$	−364.257	+	1359.43i	−0.366087	+	1.36626i
$996$	−322.590	−	322.590i	−0.323886	−	0.323886i
$997$	509.605	+	882.662i	0.511139	+	0.885318i	0.999917	+	0.0129099i	$0.00410948\pi$
$997$	509.605	+	882.662i	0.511139	+	0.885318i	−0.488778	+	0.872408i	$0.662557\pi$
$998$	−262.243	−	151.406i	−0.262768	−	0.151709i
$999$	328.535	−	88.0308i	0.328864	−	0.0881189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.3.l.c.19.1	✓	8
3.2	odd	2		234.3.bb.d.19.2		8
13.4	even	6		1014.3.f.j.577.4		8
13.6	odd	12		1014.3.f.j.775.4		8
13.7	odd	12		1014.3.f.h.775.3		8
13.9	even	3		1014.3.f.h.577.3		8
13.11	odd	12	inner	78.3.l.c.37.1	yes	8
39.11	even	12		234.3.bb.d.37.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.c.19.1	✓	8	1.1	even	1	trivial
78.3.l.c.37.1	yes	8	13.11	odd	12	inner
234.3.bb.d.19.2		8	3.2	odd	2
234.3.bb.d.37.2		8	39.11	even	12
1014.3.f.h.577.3		8	13.9	even	3
1014.3.f.h.775.3		8	13.7	odd	12
1014.3.f.j.577.4		8	13.4	even	6
1014.3.f.j.775.4		8	13.6	odd	12

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	78.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-5.04651 + 5.04651i) q^{5} +(2.36603 + 0.633975i) q^{6} +(-1.34715 + 5.02764i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-5.04651 + 5.04651i) q^{5} +(2.36603 + 0.633975i) q^{6} +(-1.34715 + 5.02764i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(8.74082 + 5.04651i) q^{10} +(-7.32323 + 1.96225i) q^{11} -3.46410i q^{12} +(12.9213 + 1.42820i) q^{13} +7.36098 q^{14} +(-3.19936 - 11.9402i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-13.9968 + 8.08105i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(9.87664 + 2.64644i) q^{19} +(3.69431 - 13.7873i) q^{20} +(-6.37479 - 6.37479i) q^{21} +(5.36098 + 9.28549i) q^{22} +(-8.29191 - 4.78733i) q^{23} +(-4.73205 + 1.26795i) q^{24} -25.9346i q^{25} +(-2.77857 - 18.1736i) q^{26} +5.19615 q^{27} +(-2.69431 - 10.0553i) q^{28} +(16.5880 - 28.7312i) q^{29} +(-15.1395 + 8.74082i) q^{30} +(-34.2312 + 34.2312i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(3.39872 - 12.6842i) q^{33} +(16.1621 + 16.1621i) q^{34} +(-18.5736 - 32.1705i) q^{35} +(5.19615 + 3.00000i) q^{36} +(63.2267 - 16.9415i) q^{37} -14.4604i q^{38} +(-13.3325 + 18.1451i) q^{39} -20.1861 q^{40} +(14.0962 + 52.6079i) q^{41} +(-6.37479 + 11.0415i) q^{42} +(-40.7432 + 23.5231i) q^{43} +(10.7220 - 10.7220i) q^{44} +(20.6810 + 5.54146i) q^{45} +(-3.50457 + 13.0792i) q^{46} +(47.8214 + 47.8214i) q^{47} +(3.46410 + 6.00000i) q^{48} +(18.9729 + 10.9540i) q^{49} +(-35.4274 + 9.49273i) q^{50} -27.9936i q^{51} +(-23.8086 + 10.4476i) q^{52} +67.5177 q^{53} +(-1.90192 - 7.09808i) q^{54} +(27.0543 - 46.8594i) q^{55} +(-12.7496 + 7.36098i) q^{56} +(-12.5231 + 12.5231i) q^{57} +(-45.3192 - 12.1432i) q^{58} +(-19.4918 + 72.7442i) q^{59} +(17.4816 + 17.4816i) q^{60} +(-35.2597 - 61.0716i) q^{61} +(59.2902 + 34.2312i) q^{62} +(15.0829 - 4.04146i) q^{63} +8.00000i q^{64} +(-72.4150 + 58.0001i) q^{65} -18.5710 q^{66} +(11.1841 + 41.7395i) q^{67} +(16.1621 - 27.9936i) q^{68} +(14.3620 - 8.29191i) q^{69} +(-37.1473 + 37.1473i) q^{70} +(-106.797 - 28.6161i) q^{71} +(2.19615 - 8.19615i) q^{72} +(-36.8385 - 36.8385i) q^{73} +(-46.2851 - 80.1682i) q^{74} +(38.9019 + 22.4600i) q^{75} +(-19.7533 + 5.29288i) q^{76} -39.4621i q^{77} +(29.6667 + 11.5709i) q^{78} -13.3867 q^{79} +(7.38861 + 27.5747i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(66.7041 - 38.5116i) q^{82} +(93.1237 - 93.1237i) q^{83} +(17.4163 + 4.66667i) q^{84} +(29.8539 - 111.416i) q^{85} +(47.0461 + 47.0461i) q^{86} +(28.7312 + 49.7639i) q^{87} +(-18.5710 - 10.7220i) q^{88} +(48.6137 - 13.0260i) q^{89} -30.2791i q^{90} +(-24.5875 + 63.0397i) q^{91} +19.1493 q^{92} +(-21.7017 - 80.9919i) q^{93} +(47.8214 - 82.8291i) q^{94} +(-63.1979 + 36.4873i) q^{95} +(6.92820 - 6.92820i) q^{96} +(-52.5419 - 14.0786i) q^{97} +(8.01888 - 29.9269i) q^{98} +(16.0829 + 16.0829i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 6 q^{5} + 12 q^{6} + 10 q^{7} + 16 q^{8} - 12 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - 6 * q^5 + 12 * q^6 + 10 * q^7 + 16 * q^8 - 12 * q^9	\( 8 q + 4 q^{2} - 6 q^{5} + 12 q^{6} + 10 q^{7} + 16 q^{8} - 12 q^{9} - 6 q^{10} + 24 q^{11} + 4 q^{14} - 12 q^{15} + 16 q^{16} - 84 q^{17} - 24 q^{18} + 10 q^{19} - 12 q^{20} + 18 q^{21} - 12 q^{22} - 12 q^{23} - 24 q^{24} + 26 q^{26} + 20 q^{28} + 36 q^{29} - 18 q^{30} - 94 q^{31} - 16 q^{32} + 60 q^{34} - 204 q^{35} + 140 q^{37} + 66 q^{39} - 24 q^{40} + 72 q^{41} + 18 q^{42} - 222 q^{43} - 24 q^{44} - 84 q^{46} + 300 q^{47} + 42 q^{49} - 62 q^{50} + 44 q^{52} + 84 q^{53} - 36 q^{54} + 396 q^{55} + 36 q^{56} + 24 q^{57} - 66 q^{58} - 60 q^{59} - 12 q^{60} - 90 q^{61} + 198 q^{62} - 24 q^{63} - 108 q^{65} + 72 q^{66} + 304 q^{67} + 60 q^{68} - 216 q^{69} - 408 q^{70} - 192 q^{71} - 24 q^{72} + 16 q^{73} - 46 q^{74} + 312 q^{75} - 20 q^{76} + 114 q^{78} - 96 q^{79} - 24 q^{80} - 36 q^{81} + 114 q^{82} - 12 q^{84} - 390 q^{85} + 168 q^{86} + 30 q^{87} + 72 q^{88} + 354 q^{89} - 218 q^{91} - 288 q^{92} - 42 q^{93} + 300 q^{94} - 576 q^{95} - 460 q^{97} + 58 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 6 * q^5 + 12 * q^6 + 10 * q^7 + 16 * q^8 - 12 * q^9 - 6 * q^10 + 24 * q^11 + 4 * q^14 - 12 * q^15 + 16 * q^16 - 84 * q^17 - 24 * q^18 + 10 * q^19 - 12 * q^20 + 18 * q^21 - 12 * q^22 - 12 * q^23 - 24 * q^24 + 26 * q^26 + 20 * q^28 + 36 * q^29 - 18 * q^30 - 94 * q^31 - 16 * q^32 + 60 * q^34 - 204 * q^35 + 140 * q^37 + 66 * q^39 - 24 * q^40 + 72 * q^41 + 18 * q^42 - 222 * q^43 - 24 * q^44 - 84 * q^46 + 300 * q^47 + 42 * q^49 - 62 * q^50 + 44 * q^52 + 84 * q^53 - 36 * q^54 + 396 * q^55 + 36 * q^56 + 24 * q^57 - 66 * q^58 - 60 * q^59 - 12 * q^60 - 90 * q^61 + 198 * q^62 - 24 * q^63 - 108 * q^65 + 72 * q^66 + 304 * q^67 + 60 * q^68 - 216 * q^69 - 408 * q^70 - 192 * q^71 - 24 * q^72 + 16 * q^73 - 46 * q^74 + 312 * q^75 - 20 * q^76 + 114 * q^78 - 96 * q^79 - 24 * q^80 - 36 * q^81 + 114 * q^82 - 12 * q^84 - 390 * q^85 + 168 * q^86 + 30 * q^87 + 72 * q^88 + 354 * q^89 - 218 * q^91 - 288 * q^92 - 42 * q^93 + 300 * q^94 - 576 * q^95 - 460 * q^97 + 58 * q^98 - 36 * q^99

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