LMFDB - Embedded newform 210.3.v.a.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(37,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("210.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.v (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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.2
Character	$\chi$	$=$	210.193
Dual form			210.3.v.a.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 0.366025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.25847 + 4.83903i) q^{5} +2.44949 q^{6} +(5.72194 - 4.03230i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(-1.36603 - 0.366025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.25847 + 4.83903i) q^{5} +2.44949 q^{6} +(5.72194 - 4.03230i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(3.49032 - 6.14961i) q^{10} +(-5.44212 + 9.42602i) q^{11} +(-3.34607 - 0.896575i) q^{12} +(-4.13640 - 4.13640i) q^{13} +(-9.29223 + 3.41385i) q^{14} +(-0.0638118 - 8.66002i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-0.489455 - 1.82667i) q^{17} +(-4.09808 + 1.09808i) q^{18} +(-27.1044 + 15.6487i) q^{19} +(-7.01877 + 7.12298i) q^{20} +(-7.76535 + 9.31124i) q^{21} +(10.8842 - 10.8842i) q^{22} +(-5.85291 + 21.8434i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-21.8325 - 12.1796i) q^{25} +(4.13640 + 7.16445i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(13.9430 - 1.26221i) q^{28} +35.4354i q^{29} +(-3.08262 + 11.8532i) q^{30} +(-7.10988 + 12.3147i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(4.87927 - 18.2097i) q^{33} +2.67443i q^{34} +(12.3115 + 32.7632i) q^{35} +6.00000 q^{36} +(13.4546 + 3.60515i) q^{37} +(42.7531 - 11.4557i) q^{38} +(8.77462 + 5.06603i) q^{39} +(12.1950 - 7.16112i) q^{40} -75.8676 q^{41} +(14.0158 - 9.87708i) q^{42} +(-5.54001 - 5.54001i) q^{43} +(-18.8520 + 10.8842i) q^{44} +(3.98894 + 14.4599i) q^{45} +(15.9904 - 27.6963i) q^{46} +(-89.5659 - 23.9991i) q^{47} +(-4.89898 - 4.89898i) q^{48} +(16.4811 - 46.1451i) q^{49} +(25.3657 + 24.6289i) q^{50} +(1.63775 + 2.83666i) q^{51} +(-3.02805 - 11.3008i) q^{52} +(73.5205 - 19.6998i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-38.7641 - 38.1970i) q^{55} +(-19.5085 - 3.37927i) q^{56} +(38.3314 - 38.3314i) q^{57} +(12.9703 - 48.4057i) q^{58} +(39.8083 + 22.9834i) q^{59} +(8.54949 - 15.0634i) q^{60} +(46.7047 + 80.8948i) q^{61} +(14.2198 - 14.2198i) q^{62} +(8.81757 - 19.0591i) q^{63} +8.00000i q^{64} +(25.2217 - 14.8106i) q^{65} +(-13.3304 + 23.0889i) q^{66} +(-6.47966 - 24.1824i) q^{67} +(0.978910 - 3.65334i) q^{68} -39.1684i q^{69} +(-4.82571 - 49.2617i) q^{70} +4.10846 q^{71} +(-8.19615 - 2.19615i) q^{72} +(94.5138 - 25.3249i) q^{73} +(-17.0598 - 9.84945i) q^{74} +(41.9864 + 10.5896i) q^{75} -62.5949 q^{76} +(6.86912 + 75.8794i) q^{77} +(-10.1321 - 10.1321i) q^{78} +(25.8988 - 14.9527i) q^{79} +(-19.2799 + 5.31859i) q^{80} +(4.50000 - 7.79423i) q^{81} +(103.637 + 27.7695i) q^{82} +(-42.2562 - 42.2562i) q^{83} +(-22.7612 + 8.36220i) q^{84} +(9.45529 - 0.0696718i) q^{85} +(5.54001 + 9.59557i) q^{86} +(-15.8853 - 59.2847i) q^{87} +(29.7363 - 7.96781i) q^{88} +(71.6953 - 41.3933i) q^{89} +(-0.156306 - 21.2126i) q^{90} +(-40.3474 - 6.98900i) q^{91} +(-31.9809 + 31.9809i) q^{92} +(6.37455 - 23.7901i) q^{93} +(113.565 + 65.5668i) q^{94} +(-41.6146 - 150.853i) q^{95} +(4.89898 + 8.48528i) q^{96} +(-60.0597 + 60.0597i) q^{97} +(-39.4039 + 57.0029i) q^{98} +32.6527i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 8 q^{7} - 64 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 8 * q^7 - 64 * q^8	$ 32 q - 16 q^{2} - 8 q^{7} - 64 q^{8} + 4 q^{10} - 32 q^{11} - 32 q^{13} + 64 q^{16} - 56 q^{17} - 48 q^{18} - 16 q^{20} - 48 q^{21} + 64 q^{22} - 48 q^{23} + 68 q^{25} + 32 q^{26} + 40 q^{28} + 12 q^{30} + 160 q^{31} + 64 q^{32} + 12 q^{33} + 152 q^{35} + 192 q^{36} + 44 q^{37} - 64 q^{38} + 8 q^{40} - 80 q^{41} - 48 q^{42} - 184 q^{43} - 12 q^{45} - 96 q^{46} - 228 q^{47} - 96 q^{50} + 192 q^{51} + 32 q^{52} + 48 q^{53} + 104 q^{55} + 32 q^{56} + 144 q^{57} - 112 q^{58} + 24 q^{60} + 216 q^{61} - 320 q^{62} + 84 q^{63} - 384 q^{65} + 24 q^{66} + 112 q^{68} - 24 q^{70} + 368 q^{71} - 96 q^{72} + 52 q^{73} + 48 q^{75} + 256 q^{76} - 836 q^{77} - 240 q^{78} + 144 q^{81} + 40 q^{82} - 736 q^{83} - 72 q^{85} + 184 q^{86} - 72 q^{87} + 64 q^{88} + 24 q^{90} + 216 q^{91} + 192 q^{92} - 216 q^{93} + 272 q^{95} - 408 q^{97} + 200 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 - 8 * q^7 - 64 * q^8 + 4 * q^10 - 32 * q^11 - 32 * q^13 + 64 * q^16 - 56 * q^17 - 48 * q^18 - 16 * q^20 - 48 * q^21 + 64 * q^22 - 48 * q^23 + 68 * q^25 + 32 * q^26 + 40 * q^28 + 12 * q^30 + 160 * q^31 + 64 * q^32 + 12 * q^33 + 152 * q^35 + 192 * q^36 + 44 * q^37 - 64 * q^38 + 8 * q^40 - 80 * q^41 - 48 * q^42 - 184 * q^43 - 12 * q^45 - 96 * q^46 - 228 * q^47 - 96 * q^50 + 192 * q^51 + 32 * q^52 + 48 * q^53 + 104 * q^55 + 32 * q^56 + 144 * q^57 - 112 * q^58 + 24 * q^60 + 216 * q^61 - 320 * q^62 + 84 * q^63 - 384 * q^65 + 24 * q^66 + 112 * q^68 - 24 * q^70 + 368 * q^71 - 96 * q^72 + 52 * q^73 + 48 * q^75 + 256 * q^76 - 836 * q^77 - 240 * q^78 + 144 * q^81 + 40 * q^82 - 736 * q^83 - 72 * q^85 + 184 * q^86 - 72 * q^87 + 64 * q^88 + 24 * q^90 + 216 * q^91 + 192 * q^92 - 216 * q^93 + 272 * q^95 - 408 * q^97 + 200 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$3$	−1.67303	+	0.448288i	−0.557678	+	0.149429i
$3$	−1.67303	+	0.448288i	−0.557678	+	0.149429i
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$	−1.25847	+	4.83903i	−0.251695	+	0.967807i
$5$	−1.25847	+	4.83903i	−0.251695	+	0.967807i
$6$	2.44949			0.408248
$7$	5.72194	−	4.03230i	0.817419	−	0.576043i
$7$	5.72194	−	4.03230i	0.817419	−	0.576043i
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	2.59808	−	1.50000i	0.288675	−	0.166667i
$10$	3.49032	−	6.14961i	0.349032	−	0.614961i
$11$	−5.44212	+	9.42602i	−0.494738	+	0.856911i	−0.999982	−	0.00606548i	$-0.998069\pi$
$11$	−5.44212	+	9.42602i	−0.494738	+	0.856911i	0.505244	+	0.862977i	$0.331403\pi$
$12$	−3.34607	−	0.896575i	−0.278839	−	0.0747146i
$13$	−4.13640	−	4.13640i	−0.318184	−	0.318184i	0.529885	−	0.848069i	$-0.322235\pi$
$13$	−4.13640	−	4.13640i	−0.318184	−	0.318184i	−0.848069	+	0.529885i	$0.822235\pi$
$14$	−9.29223	+	3.41385i	−0.663731	+	0.243847i
$15$	−0.0638118	−	8.66002i	−0.00425412	−	0.577335i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	−0.489455	−	1.82667i	−0.0287915	−	0.107451i	0.950035	−	0.312144i	$-0.101047\pi$
$17$	−0.489455	−	1.82667i	−0.0287915	−	0.107451i	−0.978826	+	0.204693i	$0.934380\pi$
$18$	−4.09808	+	1.09808i	−0.227671	+	0.0610042i
$19$	−27.1044	+	15.6487i	−1.42655	+	0.823618i	−0.996847	−	0.0793537i	$-0.974714\pi$
$19$	−27.1044	+	15.6487i	−1.42655	+	0.823618i	−0.429701	+	0.902971i	$0.641381\pi$
$20$	−7.01877	+	7.12298i	−0.350939	+	0.356149i
$21$	−7.76535	+	9.31124i	−0.369779	+	0.443393i
$22$	10.8842	−	10.8842i	0.494738	−	0.494738i
$23$	−5.85291	+	21.8434i	−0.254474	+	0.949711i	0.713908	+	0.700240i	$0.246923\pi$
$23$	−5.85291	+	21.8434i	−0.254474	+	0.949711i	−0.968382	+	0.249471i	$0.919743\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$	−21.8325	−	12.1796i	−0.873300	−	0.487184i
$26$	4.13640	+	7.16445i	0.159092	+	0.275556i
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	13.9430	−	1.26221i	0.497964	−	0.0450791i
$29$			35.4354i			1.22191i	0.791665	+	0.610956i	$0.209215\pi$
$29$			35.4354i			1.22191i	−0.791665	+	0.610956i	$0.790785\pi$
$30$	−3.08262	+	11.8532i	−0.102754	+	0.395105i
$31$	−7.10988	+	12.3147i	−0.229351	+	0.397248i	−0.957616	−	0.288048i	$-0.906994\pi$
$31$	−7.10988	+	12.3147i	−0.229351	+	0.397248i	0.728265	+	0.685296i	$0.240327\pi$
$32$	−1.46410	−	5.46410i	−0.0457532	−	0.170753i
$33$	4.87927	−	18.2097i	0.147857	−	0.551808i
$34$			2.67443i			0.0786598i
$35$	12.3115	+	32.7632i	0.351758	+	0.936091i
$36$	6.00000			0.166667
$37$	13.4546	+	3.60515i	0.363638	+	0.0974365i	0.436011	−	0.899941i	$-0.356391\pi$
$37$	13.4546	+	3.60515i	0.363638	+	0.0974365i	−0.0723735	+	0.997378i	$0.523057\pi$
$38$	42.7531	−	11.4557i	1.12508	−	0.301465i
$39$	8.77462	+	5.06603i	0.224990	+	0.129898i
$40$	12.1950	−	7.16112i	0.304875	−	0.179028i
$41$	−75.8676			−1.85043			−0.925215	−	0.379443i	$-0.876115\pi$
$41$	−75.8676			−1.85043			−0.925215	+	0.379443i	$0.876115\pi$
$42$	14.0158	−	9.87708i	0.333710	−	0.235169i
$43$	−5.54001	−	5.54001i	−0.128837	−	0.128837i	0.639748	−	0.768585i	$-0.279039\pi$
$43$	−5.54001	−	5.54001i	−0.128837	−	0.128837i	−0.768585	+	0.639748i	$0.779039\pi$
$44$	−18.8520	+	10.8842i	−0.428456	+	0.247369i
$45$	3.98894	+	14.4599i	0.0886431	+	0.321331i
$46$	15.9904	−	27.6963i	0.347618	−	0.602093i
$47$	−89.5659	−	23.9991i	−1.90566	−	0.510619i	−0.995305	−	0.0967860i	$-0.969144\pi$
$47$	−89.5659	−	23.9991i	−1.90566	−	0.510619i	−0.910353	−	0.413833i	$-0.864190\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$	16.4811	−	46.1451i	0.336349	−	0.941737i
$50$	25.3657	+	24.6289i	0.507314	+	0.492578i
$51$	1.63775	+	2.83666i	0.0321127	+	0.0556209i
$52$	−3.02805	−	11.3008i	−0.0582318	−	0.217324i
$53$	73.5205	−	19.6998i	1.38718	−	0.371694i	0.513456	−	0.858116i	$-0.328365\pi$
$53$	73.5205	−	19.6998i	1.38718	−	0.371694i	0.873724	+	0.486422i	$0.161698\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$	−38.7641	−	38.1970i	−0.704801	−	0.694491i
$56$	−19.5085	−	3.37927i	−0.348366	−	0.0603441i
$57$	38.3314	−	38.3314i	0.672481	−	0.672481i
$58$	12.9703	−	48.4057i	0.223625	−	0.834581i
$59$	39.8083	+	22.9834i	0.674718	+	0.389548i	0.797862	−	0.602840i	$-0.205964\pi$
$59$	39.8083	+	22.9834i	0.674718	+	0.389548i	−0.123144	+	0.992389i	$0.539298\pi$
$60$	8.54949	−	15.0634i	0.142492	−	0.251057i
$61$	46.7047	+	80.8948i	0.765650	+	1.32615i	0.939902	+	0.341444i	$0.110916\pi$
$61$	46.7047	+	80.8948i	0.765650	+	1.32615i	−0.174252	+	0.984701i	$0.555751\pi$
$62$	14.2198	−	14.2198i	0.229351	−	0.229351i
$63$	8.81757	−	19.0591i	0.139961	−	0.302526i
$64$			8.00000i			0.125000i
$65$	25.2217	−	14.8106i	0.388026	−	0.227856i
$66$	−13.3304	+	23.0889i	−0.201976	+	0.349833i
$67$	−6.47966	−	24.1824i	−0.0967113	−	0.360932i	0.900562	−	0.434728i	$-0.143155\pi$
$67$	−6.47966	−	24.1824i	−0.0967113	−	0.360932i	−0.997273	+	0.0737959i	$0.976489\pi$
$68$	0.978910	−	3.65334i	0.0143957	−	0.0537256i
$69$		−	39.1684i		−	0.567658i
$70$	−4.82571	−	49.2617i	−0.0689387	−	0.703738i
$71$	4.10846			0.0578656			0.0289328	−	0.999581i	$-0.490789\pi$
$71$	4.10846			0.0578656			0.0289328	+	0.999581i	$0.490789\pi$
$72$	−8.19615	−	2.19615i	−0.113835	−	0.0305021i
$73$	94.5138	−	25.3249i	1.29471	−	0.346916i	0.455262	−	0.890357i	$-0.349545\pi$
$73$	94.5138	−	25.3249i	1.29471	−	0.346916i	0.839448	+	0.543441i	$0.182879\pi$
$74$	−17.0598	−	9.84945i	−0.230537	−	0.133101i
$75$	41.9864	+	10.5896i	0.559819	+	0.141195i
$76$	−62.5949			−0.823618
$77$	6.86912	+	75.8794i	0.0892094	+	0.985446i
$78$	−10.1321	−	10.1321i	−0.129898	−	0.129898i
$79$	25.8988	−	14.9527i	0.327833	−	0.189274i	−0.327046	−	0.945009i	$-0.606053\pi$
$79$	25.8988	−	14.9527i	0.327833	−	0.189274i	0.654879	+	0.755734i	$0.272720\pi$
$80$	−19.2799	+	5.31859i	−0.240998	+	0.0664823i
$81$	4.50000	−	7.79423i	0.0555556	−	0.0962250i
$82$	103.637	+	27.7695i	1.26387	+	0.338652i
$83$	−42.2562	−	42.2562i	−0.509111	−	0.509111i	0.405142	−	0.914254i	$-0.367222\pi$
$83$	−42.2562	−	42.2562i	−0.509111	−	0.509111i	−0.914254	+	0.405142i	$0.867222\pi$
$84$	−22.7612	+	8.36220i	−0.270967	+	0.0995499i
$85$	9.45529	−	0.0696718i	0.111239	−	0.000819668i
$86$	5.54001	+	9.59557i	0.0644187	+	0.111576i
$87$	−15.8853	−	59.2847i	−0.182589	−	0.681433i
$88$	29.7363	−	7.96781i	0.337912	−	0.0905433i
$89$	71.6953	−	41.3933i	0.805565	−	0.465093i	−0.0398483	−	0.999206i	$-0.512687\pi$
$89$	71.6953	−	41.3933i	0.805565	−	0.465093i	0.845413	+	0.534113i	$0.179354\pi$
$90$	−0.156306	−	21.2126i	−0.00173674	−	0.235696i
$91$	−40.3474	−	6.98900i	−0.443378	−	0.0768022i
$92$	−31.9809	+	31.9809i	−0.347618	+	0.347618i
$93$	6.37455	−	23.7901i	0.0685435	−	0.255808i
$94$	113.565	+	65.5668i	1.20814	+	0.697519i
$95$	−41.6146	−	150.853i	−0.438048	−	1.58792i
$96$	4.89898	+	8.48528i	0.0510310	+	0.0883883i
$97$	−60.0597	+	60.0597i	−0.619172	+	0.619172i	−0.945319	−	0.326147i	$-0.894249\pi$
$97$	−60.0597	+	60.0597i	−0.619172	+	0.619172i	0.326147	+	0.945319i	$0.394249\pi$
$98$	−39.4039	+	57.0029i	−0.402080	+	0.581663i
$99$			32.6527i			0.329825i
$100$	−25.6354	−	42.9282i	−0.256354	−	0.429282i
$101$	−13.8942	+	24.0654i	−0.137566	+	0.238272i	−0.926575	−	0.376110i	$-0.877261\pi$
$101$	−13.8942	+	24.0654i	−0.137566	+	0.238272i	0.789009	+	0.614382i	$0.210595\pi$
$102$	−1.19892	−	4.47441i	−0.0117541	−	0.0438668i
$103$	−37.1298	+	138.570i	−0.360483	+	1.34534i	0.512959	+	0.858413i	$0.328549\pi$
$103$	−37.1298	+	138.570i	−0.360483	+	1.34534i	−0.873442	+	0.486928i	$0.838117\pi$
$104$			16.5456i			0.159092i
$105$	−35.2849	−	49.2948i	−0.336047	−	0.469474i
$106$	−107.642			−1.01549
$107$	−123.124	−	32.9910i	−1.15069	−	0.308328i	−0.367451	−	0.930043i	$-0.619769\pi$
$107$	−123.124	−	32.9910i	−1.15069	−	0.308328i	−0.783243	+	0.621715i	$0.786436\pi$
$108$	−10.0382	+	2.68973i	−0.0929463	+	0.0249049i
$109$	59.7045	+	34.4704i	0.547748	+	0.316242i	0.748213	−	0.663458i	$-0.230912\pi$
$109$	59.7045	+	34.4704i	0.547748	+	0.316242i	−0.200465	+	0.979701i	$0.564245\pi$
$110$	38.9717	+	66.3667i	0.354288	+	0.603334i
$111$	−24.1261			−0.217353
$112$	25.4122	+	11.7568i	0.226894	+	0.104971i
$113$	133.742	+	133.742i	1.18356	+	1.18356i	0.978816	+	0.204742i	$0.0656356\pi$
$113$	133.742	+	133.742i	1.18356	+	1.18356i	0.204742	+	0.978816i	$0.434364\pi$
$114$	−66.3920	+	38.3314i	−0.582386	+	0.336240i
$115$	−98.3350	−	55.8117i	−0.855087	−	0.485319i
$116$	−35.4354	+	61.3760i	−0.305478	+	0.529103i
$117$	−16.9513	−	4.54208i	−0.144883	−	0.0388212i
$118$	−45.9667	−	45.9667i	−0.389548	−	0.389548i
$119$	−10.1663	−	8.47847i	−0.0854313	−	0.0712476i
$120$	−17.1924	+	17.4477i	−0.143270	+	0.145397i
$121$	1.26672	+	2.19402i	0.0104687	+	0.0181324i
$122$	−34.1902	−	127.600i	−0.280247	−	1.04590i
$123$	126.929	−	34.0105i	1.03194	−	0.276508i
$124$	−24.6294	+	14.2198i	−0.198624	+	0.114676i
$125$	86.4131	−	90.3204i	0.691305	−	0.722564i
$126$	−19.0212	+	22.8078i	−0.150962	+	0.181014i
$127$	25.4322	−	25.4322i	0.200254	−	0.200254i	−0.599855	−	0.800109i	$-0.704775\pi$
$127$	25.4322	−	25.4322i	0.200254	−	0.200254i	0.800109	+	0.599855i	$0.204775\pi$
$128$	2.92820	−	10.9282i	0.0228766	−	0.0853766i
$129$	11.7521	+	6.78509i	0.0911018	+	0.0525976i
$130$	−39.8746	+	10.9999i	−0.306727	+	0.0846145i
$131$	43.4151	+	75.1971i	0.331413	+	0.574024i	0.982789	−	0.184731i	$-0.0591414\pi$
$131$	43.4151	+	75.1971i	0.331413	+	0.574024i	−0.651376	+	0.758755i	$0.725808\pi$
$132$	26.6608	−	26.6608i	0.201976	−	0.201976i
$133$	−91.9892	+	198.834i	−0.691648	+	1.49499i
$134$			35.4055i			0.264220i
$135$	−13.1558	−	22.4037i	−0.0974505	−	0.165953i
$136$	−2.67443	+	4.63225i	−0.0196649	+	0.0340607i
$137$	6.08183	+	22.6977i	0.0443929	+	0.165677i	0.984564	−	0.175027i	$-0.0560013\pi$
$137$	6.08183	+	22.6977i	0.0443929	+	0.165677i	−0.940171	+	0.340704i	$0.889335\pi$
$138$	−14.3366	+	53.5051i	−0.103889	+	0.387718i
$139$			123.024i			0.885067i	0.896752	+	0.442533i	$0.145920\pi$
$139$			123.024i			0.885067i	−0.896752	+	0.442533i	$0.854080\pi$
$140$	−11.4390	+	69.0590i	−0.0817070	+	0.493279i
$141$	160.605			1.13904
$142$	−5.61226	−	1.50380i	−0.0395230	−	0.0105901i
$143$	61.5005	−	16.4790i	0.430074	−	0.115238i
$144$	10.3923	+	6.00000i	0.0721688	+	0.0416667i
$145$	−171.473	−	44.5946i	−1.18257	−	0.307549i
$146$	−138.378			−0.947793
$147$	−6.88711	+	84.5906i	−0.0468511	+	0.575446i
$148$	19.6989	+	19.6989i	0.133101	+	0.133101i
$149$	32.9396	−	19.0177i	0.221071	−	0.127635i	−0.385375	−	0.922760i	$-0.625928\pi$
$149$	32.9396	−	19.0177i	0.221071	−	0.127635i	0.606446	+	0.795125i	$0.292595\pi$
$150$	−53.4785	−	29.8338i	−0.356523	−	0.198892i
$151$	82.2319	−	142.430i	0.544582	−	0.943244i	−0.454051	−	0.890976i	$-0.650022\pi$
$151$	82.2319	−	142.430i	0.544582	−	0.943244i	0.998633	−	0.0522683i	$-0.0166451\pi$
$152$	85.5063	+	22.9113i	0.562541	+	0.150732i
$153$	−4.01165	−	4.01165i	−0.0262199	−	0.0262199i
$154$	18.3904	−	106.167i	0.119418	−	0.689399i
$155$	−50.6435	−	49.9027i	−0.326733	−	0.321953i
$156$	10.1321	+	17.5492i	0.0649491	+	0.112495i
$157$	−0.0693474	−	0.258808i	−0.000441703	−	0.00164846i	0.965705	−	0.259643i	$-0.0836049\pi$
$157$	−0.0693474	−	0.258808i	−0.000441703	−	0.00164846i	−0.966146	+	0.257995i	$0.916938\pi$
$158$	−40.8515	+	10.9461i	−0.258554	+	0.0692792i
$159$	−114.171	+	65.9167i	−0.718057	+	0.414571i
$160$	28.2835	−	0.208408i	0.176772	−	0.00130255i
$161$	54.5890	+	148.587i	0.339062	+	0.922900i
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	−60.2372	+	224.808i	−0.369553	+	1.37919i	0.491589	+	0.870827i	$0.336416\pi$
$163$	−60.2372	+	224.808i	−0.369553	+	1.37919i	−0.861142	+	0.508364i	$0.830250\pi$
$164$	−131.407	−	75.8676i	−0.801260	−	0.462607i
$165$	81.9768	+	46.5273i	0.496829	+	0.281984i
$166$	42.2562	+	73.1899i	0.254556	+	0.440903i
$167$	12.1342	−	12.1342i	0.0726601	−	0.0726601i	−0.669843	−	0.742503i	$-0.733639\pi$
$167$	12.1342	−	12.1342i	0.0726601	−	0.0726601i	0.742503	+	0.669843i	$0.233639\pi$
$168$	34.1532	−	3.09178i	0.203293	−	0.0184035i
$169$		−	134.780i		−	0.797517i
$170$	−12.9417	−	3.36570i	−0.0761275	−	0.0197983i
$171$	−46.9462	+	81.3132i	−0.274539	+	0.475516i
$172$	−4.05557	−	15.1356i	−0.0235789	−	0.0879975i
$173$	64.8931	−	242.184i	0.375104	−	1.39991i	−0.478088	−	0.878312i	$-0.658670\pi$
$173$	64.8931	−	242.184i	0.375104	−	1.39991i	0.853192	−	0.521597i	$-0.174663\pi$
$174$			86.7988i			0.498844i
$175$	−174.036	+	18.3443i	−0.994491	+	0.104825i
$176$	−43.5369			−0.247369
$177$	−76.9038	−	20.6063i	−0.434485	−	0.116420i
$178$	−113.089	+	30.3020i	−0.635329	+	0.170236i
$179$	−44.2012	−	25.5196i	−0.246934	−	0.142567i	0.371425	−	0.928463i	$-0.378869\pi$
$179$	−44.2012	−	25.5196i	−0.246934	−	0.142567i	−0.618360	+	0.785895i	$0.712202\pi$
$180$	−7.55084	+	29.0342i	−0.0419491	+	0.161301i
$181$	−183.017			−1.01114			−0.505572	−	0.862785i	$-0.668718\pi$
$181$	−183.017			−1.01114			−0.505572	+	0.862785i	$0.668718\pi$
$182$	52.5574	+	24.3153i	0.288777	+	0.133601i
$183$	−114.403	−	114.403i	−0.625151	−	0.625151i
$184$	55.3925	−	31.9809i	0.301046	−	0.173809i
$185$	−34.3777	+	60.5703i	−0.185825	+	0.327407i
$186$	−17.4156	+	30.1647i	−0.0936322	+	0.162176i
$187$	19.8819	+	5.32735i	0.106320	+	0.0284885i
$188$	−131.134	−	131.134i	−0.697519	−	0.697519i
$189$	−6.20811	+	35.8394i	−0.0328472	+	0.189626i
$190$	1.63066	+	221.301i	0.00858244	+	1.16474i
$191$	−68.2455	−	118.205i	−0.357307	−	0.618873i	0.630203	−	0.776430i	$-0.282972\pi$
$191$	−68.2455	−	118.205i	−0.357307	−	0.618873i	−0.987510	+	0.157557i	$0.949638\pi$
$192$	−3.58630	−	13.3843i	−0.0186787	−	0.0697097i
$193$	−58.1367	+	15.5777i	−0.301227	+	0.0807134i	−0.406267	−	0.913755i	$-0.633170\pi$
$193$	−58.1367	+	15.5777i	−0.301227	+	0.0807134i	0.105040	+	0.994468i	$0.466503\pi$
$194$	104.026	−	60.0597i	0.536218	−	0.309586i
$195$	−35.5573	+	36.0852i	−0.182345	+	0.185052i
$196$	74.6912	−	63.4446i	0.381078	−	0.323697i
$197$	160.750	−	160.750i	0.815988	−	0.815988i	−0.169536	−	0.985524i	$-0.554227\pi$
$197$	160.750	−	160.750i	0.815988	−	0.815988i	0.985524	+	0.169536i	$0.0542270\pi$
$198$	11.9517	−	44.6044i	0.0603622	−	0.225275i
$199$	195.772	+	113.029i	0.983780	+	0.567986i	0.903409	−	0.428779i	$-0.141056\pi$
$199$	195.772	+	113.029i	0.983780	+	0.567986i	0.0803711	+	0.996765i	$0.474389\pi$
$200$	19.3058	+	68.0242i	0.0965290	+	0.340121i
$201$	21.6814	+	37.5532i	0.107867	+	0.186832i
$202$	27.7884	−	27.7884i	0.137566	−	0.137566i
$203$	142.886	+	202.759i	0.703874	+	0.998815i
$204$			6.55100i			0.0321127i
$205$	95.4774	−	367.126i	0.465743	−	1.79086i
$206$	101.440	−	175.700i	0.492429	−	0.852912i
$207$	17.5587	+	65.5301i	0.0848248	+	0.316570i
$208$	6.05611	−	22.6017i	0.0291159	−	0.108662i
$209$		−	340.649i		−	1.62990i
$210$	30.1570	+	80.2531i	0.143605	+	0.382158i
$211$	320.337			1.51819			0.759093	−	0.650982i	$-0.225643\pi$
$211$	320.337			1.51819			0.759093	+	0.650982i	$0.225643\pi$
$212$	147.041	+	39.3995i	0.693590	+	0.185847i
$213$	−6.87359	+	1.84177i	−0.0322704	+	0.00864682i
$214$	156.115	+	90.1332i	0.729511	+	0.421183i
$215$	33.7802	−	19.8363i	0.157117	−	0.0922620i
$216$	14.6969			0.0680414
$217$	8.97420	+	99.1330i	0.0413558	+	0.456834i
$218$	−68.9409	−	68.9409i	−0.316242	−	0.316242i
$219$	−146.772	+	84.7388i	−0.670191	+	0.386935i
$220$	−28.9444	−	104.923i	−0.131565	−	0.476924i
$221$	−5.53126	+	9.58042i	−0.0250283	+	0.0433503i
$222$	32.9569	+	8.83078i	0.148455	+	0.0397783i
$223$	134.141	+	134.141i	0.601528	+	0.601528i	0.940718	−	0.339190i	$-0.110153\pi$
$223$	134.141	+	134.141i	0.601528	+	0.601528i	−0.339190	+	0.940718i	$0.610153\pi$
$224$	−30.4104	−	25.3615i	−0.135761	−	0.113221i
$225$	−74.9919	+	1.10522i	−0.333297	+	0.00491210i
$226$	−133.742	−	231.648i	−0.591779	−	1.02499i
$227$	−1.96173	−	7.32127i	−0.00864198	−	0.0322523i	0.961470	−	0.274909i	$-0.0886478\pi$
$227$	−1.96173	−	7.32127i	−0.00864198	−	0.0322523i	−0.970112	+	0.242657i	$0.921981\pi$
$228$	104.723	−	28.0605i	0.459313	−	0.123073i
$229$	−172.294	+	99.4742i	−0.752377	+	0.434385i	−0.826552	−	0.562860i	$-0.809701\pi$
$229$	−172.294	+	99.4742i	−0.752377	+	0.434385i	0.0741751	+	0.997245i	$0.476368\pi$
$230$	113.900	+	112.233i	0.495216	+	0.487971i
$231$	−45.5080	−	123.869i	−0.197005	−	0.536231i
$232$	70.8709	−	70.8709i	0.305478	−	0.305478i
$233$	51.9234	−	193.781i	0.222847	−	0.831677i	−0.760408	−	0.649445i	$-0.775001\pi$
$233$	51.9234	−	193.781i	0.222847	−	0.831677i	0.983256	−	0.182232i	$-0.0583322\pi$
$234$	21.4933	+	12.4092i	0.0918519	+	0.0530307i
$235$	228.849	−	403.210i	0.973825	−	1.71579i
$236$	45.9667	+	79.6167i	0.194774	+	0.337359i
$237$	−36.6264	+	36.6264i	−0.154542	+	0.154542i
$238$	10.7841	+	15.3029i	0.0453114	+	0.0642980i
$239$		−	118.152i		−	0.494360i	−0.968970	−	0.247180i	$-0.920496\pi$
$239$		−	118.152i		−	0.494360i	0.968970	−	0.247180i	$-0.0795039\pi$
$240$	29.8716	−	17.5411i	0.124465	−	0.0730879i
$241$	10.9226	−	18.9185i	0.0453219	−	0.0784999i	−0.842475	−	0.538736i	$-0.818902\pi$
$241$	10.9226	−	18.9185i	0.0453219	−	0.0784999i	0.887796	+	0.460236i	$0.152235\pi$
$242$	−0.927301	−	3.46073i	−0.00383182	−	0.0143006i
$243$	−4.03459	+	15.0573i	−0.0166032	+	0.0619642i
$244$			186.819i			0.765650i
$245$	202.557	+	137.825i	0.826763	+	0.562551i
$246$	−185.837			−0.755435
$247$	176.844	+	47.3852i	0.715967	+	0.191843i
$248$	38.8491	−	10.4096i	0.156650	−	0.0419742i
$249$	89.6390	+	51.7531i	0.359996	+	0.207844i
$250$	−151.102	+	91.7506i	−0.604408	+	0.367003i
$251$	−198.472			−0.790724			−0.395362	−	0.918525i	$-0.629381\pi$
$251$	−198.472			−0.790724			−0.395362	+	0.918525i	$0.629381\pi$
$252$	34.3316	−	24.1938i	0.136237	−	0.0960072i
$253$	−174.044	−	174.044i	−0.687920	−	0.687920i
$254$	−44.0499	+	25.4322i	−0.173425	+	0.100127i
$255$	−15.7878	+	4.35525i	−0.0619129	+	0.0170794i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−52.6213	−	14.0998i	−0.204752	−	0.0548632i	0.154985	−	0.987917i	$-0.450467\pi$
$257$	−52.6213	−	14.0998i	−0.204752	−	0.0548632i	−0.359737	+	0.933054i	$0.617134\pi$
$258$	−13.5702	−	13.5702i	−0.0525976	−	0.0525976i
$259$	91.5234	−	33.6246i	0.353372	−	0.129825i
$260$	58.4959	−	0.431030i	0.224984	−	0.00165781i
$261$	53.1532	+	92.0640i	0.203652	+	0.352736i
$262$	−31.7820	−	118.612i	−0.121305	−	0.452718i
$263$	−185.719	+	49.7632i	−0.706154	+	0.189214i	−0.593986	−	0.804476i	$-0.702446\pi$
$263$	−185.719	+	49.7632i	−0.706154	+	0.189214i	−0.112169	+	0.993689i	$0.535780\pi$
$264$	−46.1779	+	26.6608i	−0.174916	+	0.100988i
$265$	2.80418	+	380.560i	0.0105818	+	1.43608i
$266$	198.438	−	237.942i	0.746007	−	0.894519i
$267$	−101.392	+	101.392i	−0.379747	+	0.379747i
$268$	12.9593	−	48.3648i	0.0483557	−	0.180466i
$269$	168.301	+	97.1687i	0.625655	+	0.361222i	0.779067	−	0.626940i	$-0.215693\pi$
$269$	168.301	+	97.1687i	0.625655	+	0.361222i	−0.153413	+	0.988162i	$0.549026\pi$
$270$	9.77087	+	35.4193i	0.0361884	+	0.131183i
$271$	−211.981	−	367.162i	−0.782218	−	1.35484i	−0.930647	−	0.365918i	$-0.880755\pi$
$271$	−211.981	−	367.162i	−0.782218	−	1.35484i	0.148429	−	0.988923i	$-0.452578\pi$
$272$	5.34887	−	5.34887i	0.0196649	−	0.0196649i
$273$	70.6356	−	6.39442i	0.258738	−	0.0234228i
$274$		−	33.2317i		−	0.121284i
$275$	233.620	−	139.511i	0.849528	−	0.507312i
$276$	39.1684	−	67.8417i	0.141915	−	0.245803i
$277$	91.1582	+	340.207i	0.329091	+	1.22818i	0.910135	+	0.414312i	$0.135978\pi$
$277$	91.1582	+	340.207i	0.329091	+	1.22818i	−0.581044	+	0.813872i	$0.697356\pi$
$278$	45.0300	−	168.054i	0.161978	−	0.604512i
$279$			42.6593i			0.152901i
$280$	40.9033	−	90.1494i	0.146083	−	0.321962i
$281$	358.294			1.27507			0.637534	−	0.770422i	$-0.279954\pi$
$281$	358.294			1.27507			0.637534	+	0.770422i	$0.279954\pi$
$282$	−219.391	−	58.7856i	−0.777982	−	0.208460i
$283$	−529.966	+	142.004i	−1.87267	+	0.501781i	−0.872765	+	0.488141i	$0.837675\pi$
$283$	−529.966	+	142.004i	−1.87267	+	0.501781i	−0.999907	+	0.0136400i	$0.995658\pi$
$284$	7.11606	+	4.10846i	0.0250566	+	0.0144664i
$285$	137.248	+	233.726i	0.481572	+	0.820091i
$286$	−90.0430			−0.314836
$287$	−434.110	+	305.921i	−1.51258	+	1.06593i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$	247.184	−	142.712i	0.855309	−	0.493813i
$290$	217.914	+	123.681i	0.751428	+	0.426486i
$291$	73.5578	−	127.406i	0.252776	−	0.437821i
$292$	189.028	+	50.6498i	0.647355	+	0.173458i
$293$	−90.1783	−	90.1783i	−0.307776	−	0.307776i	0.536270	−	0.844046i	$-0.319833\pi$
$293$	−90.1783	−	90.1783i	−0.307776	−	0.307776i	−0.844046	+	0.536270i	$0.819833\pi$
$294$	40.3703	−	113.032i	0.137314	−	0.384463i
$295$	−161.315	+	163.710i	−0.546831	+	0.554949i
$296$	−19.6989	−	34.1195i	−0.0665504	−	0.115269i
$297$	−14.6378	−	54.6290i	−0.0492855	−	0.183936i
$298$	−51.9572	+	13.9219i	−0.174353	+	0.0467178i
$299$	114.563	−	66.1428i	0.383153	−	0.221213i
$300$	62.1330	+	60.3282i	0.207110	+	0.201094i
$301$	−54.0385	−	9.36058i	−0.179530	−	0.0310983i
$302$	−164.464	+	164.464i	−0.544582	+	0.544582i
$303$	12.4572	−	46.4909i	0.0411128	−	0.153435i
$304$	−108.418	−	62.5949i	−0.356637	−	0.205904i
$305$	−450.229	+	124.201i	−1.47616	+	0.407218i
$306$	4.01165	+	6.94838i	0.0131100	+	0.0227071i
$307$	201.844	−	201.844i	0.657473	−	0.657473i	−0.297309	−	0.954781i	$-0.596089\pi$
$307$	201.844	−	201.844i	0.657473	−	0.657473i	0.954781	+	0.297309i	$0.0960890\pi$
$308$	−63.9817	+	138.296i	−0.207733	+	0.449013i
$309$		−	248.477i		−	0.804133i
$310$	50.9147	+	86.7051i	0.164241	+	0.279694i
$311$	−232.134	+	402.068i	−0.746412	+	1.29282i	0.203121	+	0.979154i	$0.434892\pi$
$311$	−232.134	+	402.068i	−0.746412	+	1.29282i	−0.949532	+	0.313669i	$0.898442\pi$
$312$	−7.41718	−	27.6813i	−0.0237730	−	0.0887221i
$313$	32.4320	−	121.038i	0.103616	−	0.386702i	−0.894568	−	0.446932i	$-0.852517\pi$
$313$	32.4320	−	121.038i	0.103616	−	0.386702i	0.998185	+	0.0602298i	$0.0191833\pi$
$314$			0.378921i			0.00120676i
$315$	81.1311	+	66.6539i	0.257559	+	0.211600i
$316$	59.8107			0.189274
$317$	−68.5329	−	18.3633i	−0.216192	−	0.0579285i	0.149097	−	0.988823i	$-0.452363\pi$
$317$	−68.5329	−	18.3633i	−0.216192	−	0.0579285i	−0.365289	+	0.930894i	$0.619030\pi$
$318$	180.088	−	48.2544i	0.566314	−	0.151743i
$319$	−334.015	−	192.844i	−1.04707	−	0.604526i
$320$	−38.7123	−	10.0678i	−0.120976	−	0.0314618i
$321$	220.780			0.687789
$322$	−20.1834	−	222.954i	−0.0626813	−	0.692405i
$323$	41.8515	+	41.8515i	0.129571	+	0.129571i
$324$	15.5885	−	9.00000i	0.0481125	−	0.0277778i
$325$	39.9282	+	140.687i	0.122856	+	0.432884i
$326$	164.571	−	285.045i	0.504819	−	0.874372i
$327$	−115.340	−	30.9053i	−0.352723	−	0.0945117i
$328$	151.735	+	151.735i	0.462607	+	0.462607i
$329$	−609.262	+	223.835i	−1.85186	+	0.680351i
$330$	−94.9522	−	93.5631i	−0.287734	−	0.283525i
$331$	319.578	+	553.526i	0.965493	+	1.67228i	0.708285	+	0.705927i	$0.249469\pi$
$331$	319.578	+	553.526i	0.965493	+	1.67228i	0.257208	+	0.966356i	$0.417197\pi$
$332$	−30.9337	−	115.446i	−0.0931738	−	0.347729i
$333$	40.3638	−	10.8155i	0.121213	−	0.0324788i
$334$	−21.0171	+	12.1342i	−0.0629255	+	0.0363300i
$335$	125.174	−	0.922351i	0.373654	−	0.00275329i
$336$	−47.7858	−	8.27749i	−0.142220	−	0.0246354i
$337$	−257.177	+	257.177i	−0.763138	+	0.763138i	−0.976888	−	0.213751i	$-0.931432\pi$
$337$	−257.177	+	257.177i	−0.763138	+	0.763138i	0.213751	+	0.976888i	$0.431432\pi$
$338$	−49.3331	+	184.114i	−0.145956	+	0.544715i
$339$	−283.710	−	163.800i	−0.836902	−	0.483186i
$340$	16.4467	+	9.33462i	0.0483727	+	0.0274548i
$341$	−77.3856	−	134.036i	−0.226937	−	0.393067i
$342$	93.8924	−	93.8924i	0.274539	−	0.274539i
$343$	−91.7673	−	330.496i	−0.267543	−	0.963546i
$344$			22.1600i			0.0644187i
$345$	189.537	+	49.2924i	0.549384	+	0.142877i
$346$	−177.291	+	307.077i	−0.512402	+	0.887507i
$347$	−5.83564	−	21.7789i	−0.0168174	−	0.0627635i	0.957007	−	0.290064i	$-0.0936766\pi$
$347$	−5.83564	−	21.7789i	−0.0168174	−	0.0627635i	−0.973825	+	0.227301i	$0.927010\pi$
$348$	31.7706	−	118.569i	0.0912947	−	0.340716i
$349$		−	262.235i		−	0.751390i	−0.926743	−	0.375695i	$-0.877404\pi$
$349$		−	262.235i		−	0.751390i	0.926743	−	0.375695i	$-0.122596\pi$
$350$	244.452	+	38.6427i	0.698434	+	0.110408i
$351$	30.3962			0.0865988
$352$	59.4726	+	15.9356i	0.168956	+	0.0452717i
$353$	112.727	−	30.2052i	0.319341	−	0.0855671i	−0.0955880	−	0.995421i	$-0.530473\pi$
$353$	112.727	−	30.2052i	0.319341	−	0.0855671i	0.414929	+	0.909854i	$0.363806\pi$
$354$	97.5101	+	56.2975i	0.275452	+	0.159032i
$355$	−5.17039	+	19.8810i	−0.0145645	+	0.0560028i
$356$	165.573			0.465093
$357$	20.8094	+	9.62732i	0.0582896	+	0.0269673i
$358$	51.0392	+	51.0392i	0.142567	+	0.142567i
$359$	−189.185	+	109.226i	−0.526979	+	0.304251i	−0.739785	−	0.672843i	$-0.765073\pi$
$359$	−189.185	+	109.226i	−0.526979	+	0.304251i	0.212806	+	0.977094i	$0.431740\pi$
$360$	20.9419	−	36.8977i	0.0581719	−	0.102493i
$361$	309.266	−	535.664i	0.856692	−	1.48383i
$362$	250.006	+	66.9889i	0.690624	+	0.185052i
$363$	−3.10281	−	3.10281i	−0.00854768	−	0.00854768i
$364$	−62.8947	−	52.4527i	−0.172788	−	0.144101i
$365$	3.60489	+	489.226i	0.00987641	+	1.34035i
$366$	114.403	+	198.151i	0.312575	+	0.541396i
$367$	56.9224	+	212.437i	0.155102	+	0.578848i	0.999097	+	0.0424967i	$0.0135312\pi$
$367$	56.9224	+	212.437i	0.155102	+	0.578848i	−0.843995	+	0.536352i	$0.819802\pi$
$368$	−87.3734	+	23.4116i	−0.237428	+	0.0636186i
$369$	−197.110	+	113.801i	−0.534173	+	0.308405i
$370$	69.1311	−	70.1574i	0.186841	−	0.189615i
$371$	341.244	−	409.178i	0.919796	−	1.10291i
$372$	34.8312	−	34.8312i	0.0936322	−	0.0936322i
$373$	−164.238	+	612.944i	−0.440316	+	1.64328i	0.287700	+	0.957721i	$0.407109\pi$
$373$	−164.238	+	612.944i	−0.440316	+	1.64328i	−0.728016	+	0.685560i	$0.759557\pi$
$374$	−25.2093	−	14.5546i	−0.0674045	−	0.0389160i
$375$	−104.082	+	189.847i	−0.277553	+	0.506259i
$376$	131.134	+	227.130i	0.348760	+	0.604069i
$377$	146.575	−	146.575i	0.388793	−	0.388793i
$378$	21.5986	−	46.6851i	0.0571390	−	0.123506i
$379$		−	311.145i		−	0.820964i	−0.911869	−	0.410482i	$-0.865360\pi$
$379$		−	311.145i		−	0.820964i	0.911869	−	0.410482i	$-0.134640\pi$
$380$	78.7741	−	302.899i	0.207300	−	0.797103i
$381$	−31.1480	+	53.9499i	−0.0817533	+	0.141601i
$382$	49.9592	+	186.450i	0.130783	+	0.488090i
$383$	80.4180	−	300.124i	0.209969	−	0.783614i	−0.777909	−	0.628377i	$-0.783719\pi$
$383$	80.4180	−	300.124i	0.209969	−	0.783614i	0.987877	−	0.155236i	$-0.0496139\pi$
$384$			19.5959i			0.0510310i
$385$	−375.827	−	62.2523i	−0.976175	−	0.161694i
$386$	85.1181			0.220513
$387$	−22.7034	−	6.08335i	−0.0586650	−	0.0157192i
$388$	−164.086	+	43.9667i	−0.422902	+	0.113316i
$389$	−649.129	−	374.775i	−1.66871	−	0.963431i	−0.968334	−	0.249657i	$-0.919682\pi$
$389$	−649.129	−	374.775i	−1.66871	−	0.963431i	−0.700377	−	0.713774i	$-0.746985\pi$
$390$	61.7803	−	36.2785i	0.158411	−	0.0930217i
$391$	42.7654			0.109374
$392$	−125.252	+	59.3281i	−0.319522	+	0.151347i
$393$	−106.345	−	106.345i	−0.270597	−	0.270597i
$394$	−278.426	+	160.750i	−0.706666	+	0.407994i
$395$	39.7635	+	144.143i	0.100667	+	0.364918i
$396$	−32.6527	+	56.5561i	−0.0824563	+	0.142819i
$397$	−452.948	−	121.367i	−1.14093	−	0.305711i	−0.361604	−	0.932332i	$-0.617771\pi$
$397$	−452.948	−	121.367i	−1.14093	−	0.305711i	−0.779324	+	0.626621i	$0.784437\pi$
$398$	−226.058	−	226.058i	−0.567986	−	0.567986i
$399$	64.7661	−	373.894i	0.162321	−	0.937077i
$400$	−1.47363	−	99.9891i	−0.00368408	−	0.249973i
$401$	156.647	+	271.320i	0.390640	+	0.676609i	0.992534	−	0.121967i	$-0.0389203\pi$
$401$	156.647	+	271.320i	0.390640	+	0.676609i	−0.601894	+	0.798576i	$0.705587\pi$
$402$	−15.8719	−	59.2346i	−0.0394822	−	0.147350i
$403$	80.3477	−	21.5291i	0.199374	−	0.0534221i
$404$	−48.1309	+	27.7884i	−0.119136	+	0.0687831i
$405$	32.0534	+	31.5845i	0.0791442	+	0.0779864i
$406$	−120.971	−	329.274i	−0.297959	−	0.811021i
$407$	−107.204	+	107.204i	−0.263400	+	0.263400i
$408$	2.39783	−	8.94883i	0.00587704	−	0.0219334i
$409$	368.604	+	212.814i	0.901233	+	0.520327i	0.877600	−	0.479393i	$-0.159143\pi$
$409$	368.604	+	212.814i	0.901233	+	0.520327i	0.0236332	+	0.999721i	$0.492477\pi$
$410$	−264.802	+	466.556i	−0.645859	+	1.13794i
$411$	−20.3502	−	35.2476i	−0.0495139	−	0.0857605i
$412$	−202.881	+	202.881i	−0.492429	+	0.492429i
$413$	320.457	−	29.0099i	0.775924	−	0.0702420i
$414$		−	95.9427i		−	0.231746i
$415$	257.658	−	151.301i	0.620862	−	0.364581i
$416$	−16.5456	+	28.6578i	−0.0397730	+	0.0688889i
$417$	−55.1503	−	205.824i	−0.132255	−	0.493582i
$418$	−124.686	+	465.335i	−0.298292	+	1.11324i
$419$			804.373i			1.91975i	0.280437	+	0.959873i	$0.409521\pi$
$419$			804.373i			1.91975i	−0.280437	+	0.959873i	$0.590479\pi$
$420$	−11.8205	−	120.666i	−0.0281441	−	0.287300i
$421$	−184.978			−0.439379			−0.219689	−	0.975570i	$-0.570504\pi$
$421$	−184.978			−0.439379			−0.219689	+	0.975570i	$0.570504\pi$
$422$	−437.589	−	117.252i	−1.03694	−	0.277847i
$423$	−268.698	+	71.9973i	−0.635219	+	0.170206i
$424$	−186.441	−	107.642i	−0.439718	−	0.253872i
$425$	−11.5621	+	45.8422i	−0.0272049	+	0.107864i
$426$	10.0636			0.0236235
$427$	593.433	+	274.548i	1.38977	+	0.642969i
$428$	−180.266	−	180.266i	−0.421183	−	0.421183i
$429$	−95.5051	+	55.1399i	−0.222622	+	0.128531i
$430$	−53.4052	+	14.7325i	−0.124198	+	0.0342616i
$431$	−334.095	+	578.669i	−0.775162	+	1.34262i	0.159542	+	0.987191i	$0.448998\pi$
$431$	−334.095	+	578.669i	−0.775162	+	1.34262i	−0.934704	+	0.355428i	$0.884335\pi$
$432$	−20.0764	−	5.37945i	−0.0464731	−	0.0124524i
$433$	283.514	+	283.514i	0.654767	+	0.654767i	0.954137	−	0.299370i	$-0.0967765\pi$
$433$	283.514	+	283.514i	0.654767	+	0.654767i	−0.299370	+	0.954137i	$0.596776\pi$
$434$	24.0262	−	138.703i	0.0553599	−	0.319592i
$435$	306.872	−	2.26120i	0.705452	−	0.00519816i
$436$	68.9409	+	119.409i	0.158121	+	0.273874i
$437$	−183.181	−	683.642i	−0.419179	−	1.56440i
$438$	231.511	−	62.0331i	0.528563	−	0.141628i
$439$	533.804	−	308.192i	1.21595	−	0.702032i	0.251904	−	0.967752i	$-0.418943\pi$
$439$	533.804	−	308.192i	1.21595	−	0.702032i	0.964050	+	0.265721i	$0.0856099\pi$
$440$	1.13418	+	153.922i	0.00257769	+	0.349823i
$441$	−26.3986	−	144.610i	−0.0598607	−	0.327914i
$442$	11.0625	−	11.0625i	0.0250283	−	0.0250283i
$443$	−156.996	+	585.918i	−0.354393	+	1.32261i	0.526853	+	0.849956i	$0.323372\pi$
$443$	−156.996	+	585.918i	−0.354393	+	1.32261i	−0.881246	+	0.472657i	$0.843295\pi$
$444$	−41.7877	−	24.1261i	−0.0941164	−	0.0543381i
$445$	110.077	+	399.028i	0.247364	+	0.896693i
$446$	−134.141	−	232.339i	−0.300764	−	0.520939i
$447$	−46.5836	+	46.5836i	−0.104214	+	0.104214i
$448$	32.2584	+	45.7755i	0.0720054	+	0.102177i
$449$			794.202i			1.76882i	0.466707	+	0.884412i	$0.345440\pi$
$449$			794.202i			1.76882i	−0.466707	+	0.884412i	$0.654560\pi$
$450$	102.845	+	25.9392i	0.228545	+	0.0576426i
$451$	412.881	−	715.130i	0.915478	−	1.58565i
$452$	97.9060	+	365.390i	0.216606	+	0.808385i
$453$	−73.7271	+	275.153i	−0.162753	+	0.607403i
$454$			10.7191i			0.0236103i
$455$	84.5961	−	186.447i	0.185926	−	0.409773i
$456$	−153.326			−0.336240
$457$	−468.412	−	125.511i	−1.02497	−	0.274640i	−0.293099	−	0.956082i	$-0.594687\pi$
$457$	−468.412	−	125.511i	−1.02497	−	0.274640i	−0.731872	+	0.681442i	$0.761353\pi$
$458$	271.769	−	72.8202i	0.593381	−	0.158996i
$459$	8.50999	+	4.91325i	0.0185403	+	0.0107042i
$460$	−114.509	−	195.004i	−0.248934	−	0.423921i
$461$	259.108			0.562057			0.281028	−	0.959699i	$-0.409324\pi$
$461$	259.108			0.562057			0.281028	+	0.959699i	$0.409324\pi$
$462$	16.8258	+	185.866i	0.0364196	+	0.402307i
$463$	−529.834	−	529.834i	−1.14435	−	1.14435i	−0.987645	−	0.156705i	$-0.949913\pi$
$463$	−529.834	−	529.834i	−1.14435	−	1.14435i	−0.156705	−	0.987645i	$-0.550087\pi$
$464$	−122.752	+	70.8709i	−0.264552	+	0.152739i
$465$	107.099	+	60.7859i	0.230321	+	0.130722i
$466$	−141.857	+	245.704i	−0.304415	+	0.527262i
$467$	−100.756	−	26.9974i	−0.215751	−	0.0578103i	0.149324	−	0.988788i	$-0.452290\pi$
$467$	−100.756	−	26.9974i	−0.215751	−	0.0578103i	−0.365075	+	0.930978i	$0.618957\pi$
$468$	−24.8184	−	24.8184i	−0.0530307	−	0.0530307i
$469$	−134.587	−	112.242i	−0.286966	−	0.239323i
$470$	−460.199	+	467.031i	−0.979146	+	0.993683i
$471$	0.232041	+	0.401907i	0.000492656	+	0.000853306i
$472$	−33.6500	−	125.583i	−0.0712923	−	0.266067i
$473$	82.3696	−	22.0709i	0.174143	−	0.0466614i
$474$	63.4388	−	36.6264i	0.133837	−	0.0772709i
$475$	782.352	−	11.5302i	1.64706	−	0.0242742i
$476$	−9.13012	−	24.8515i	−0.0191809	−	0.0522089i
$477$	161.462	−	161.462i	0.338495	−	0.338495i
$478$	−43.2467	+	161.399i	−0.0904742	+	0.337654i
$479$	352.830	+	203.707i	0.736598	+	0.425275i	0.820831	−	0.571171i	$-0.193511\pi$
$479$	352.830	+	203.707i	0.736598	+	0.425275i	−0.0842332	+	0.996446i	$0.526844\pi$
$480$	−47.2258	+	13.0278i	−0.0983871	+	0.0271413i
$481$	−40.7412	−	70.5659i	−0.0847011	−	0.146707i
$482$	−21.8452	+	21.8452i	−0.0453219	+	0.0453219i
$483$	−157.939	−	224.119i	−0.326996	−	0.464015i
$484$			5.06687i			0.0104687i
$485$	−215.047	−	366.214i	−0.443396	−	0.755081i
$486$	11.0227	−	19.0919i	0.0226805	−	0.0392837i
$487$	210.150	+	784.291i	0.431520	+	1.61045i	0.749259	+	0.662277i	$0.230410\pi$
$487$	210.150	+	784.291i	0.431520	+	1.61045i	−0.317739	+	0.948178i	$0.602924\pi$
$488$	68.3804	−	255.199i	0.140124	−	0.522949i
$489$		−	403.115i		−	0.824366i
$490$	−226.250	−	262.413i	−0.461735	−	0.535538i
$491$	334.632			0.681531			0.340766	−	0.940148i	$-0.389314\pi$
$491$	334.632			0.681531			0.340766	+	0.940148i	$0.389314\pi$
$492$	253.858	+	68.0211i	0.515972	+	0.138254i
$493$	64.7289	−	17.3441i	0.131296	−	0.0351807i
$494$	−224.229	−	129.459i	−0.453905	−	0.262062i
$495$	−158.008	−	41.0926i	−0.319207	−	0.0830153i
$496$	−56.8791			−0.114676
$497$	23.5083	−	16.5665i	0.0473005	−	0.0333331i
$498$	−103.506	−	103.506i	−0.207844	−	0.207844i
$499$	313.315	−	180.893i	0.627886	−	0.362510i	−0.152047	−	0.988373i	$-0.548587\pi$
$499$	313.315	−	180.893i	0.627886	−	0.362510i	0.779933	+	0.625863i	$0.215253\pi$
$500$	239.992	−	70.0265i	0.479985	−	0.140053i
$501$	−14.8613	+	25.7406i	−0.0296634	+	0.0513784i
$502$	271.118	+	72.6457i	0.540075	+	0.144713i
$503$	−319.003	−	319.003i	−0.634200	−	0.634200i	0.314918	−	0.949119i	$-0.398023\pi$
$503$	−319.003	−	319.003i	−0.634200	−	0.634200i	−0.949119	+	0.314918i	$0.898023\pi$
$504$	−55.7534	+	20.4831i	−0.110622	+	0.0406411i
$505$	−98.9680	−	97.5201i	−0.195976	−	0.193109i
$506$	174.044	+	301.453i	0.343960	+	0.595756i
$507$	60.4204	+	225.492i	0.119172	+	0.444758i
$508$	69.4822	−	18.6177i	0.136776	−	0.0366490i
$509$	116.748	−	67.4044i	0.229367	−	0.132425i	−0.380913	−	0.924611i	$-0.624390\pi$
$509$	116.748	−	67.4044i	0.229367	−	0.132425i	0.610280	+	0.792186i	$0.291057\pi$
$510$	23.1606	−	0.170660i	0.0454130	−	0.000334628i
$511$	438.684	−	526.016i	0.858482	−	1.02938i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	42.0908	−	157.085i	0.0820484	−	0.306209i
$514$	66.7212	+	38.5215i	0.129808	+	0.0749445i
$515$	−623.819	−	354.059i	−1.21130	−	0.687493i
$516$	13.5702	+	23.5043i	0.0262988	+	0.0455509i
$517$	713.644	−	713.644i	1.38036	−	1.38036i
$518$	−137.331	+	12.4321i	−0.265117	+	0.0240002i
$519$			434.273i			0.836749i
$520$	−80.0646	−	20.8222i	−0.153970	−	0.0400427i
$521$	−299.369	+	518.522i	−0.574605	+	0.995244i	0.421480	+	0.906838i	$0.361511\pi$
$521$	−299.369	+	518.522i	−0.574605	+	0.995244i	−0.996084	+	0.0884066i	$0.971823\pi$
$522$	−38.9108	−	145.217i	−0.0745418	−	0.278194i
$523$	159.082	−	593.701i	0.304172	−	1.13518i	−0.629484	−	0.777013i	$-0.716734\pi$
$523$	159.082	−	593.701i	0.304172	−	1.13518i	0.933656	−	0.358171i	$-0.116600\pi$
$524$			173.660i			0.331413i
$525$	282.944	−	108.709i	0.538941	−	0.207064i
$526$	271.911			0.516941
$527$	25.9748	+	6.95994i	0.0492881	+	0.0132067i
$528$	72.8387	−	19.5171i	0.137952	−	0.0369642i
$529$	15.2520	+	8.80574i	0.0288317	+	0.0166460i
$530$	135.464	−	520.881i	0.255593	−	0.982794i
$531$	137.900			0.259699
$532$	−358.164	+	252.402i	−0.673241	+	0.474439i
$533$	313.819	+	313.819i	0.588778	+	0.588778i
$534$	175.617	−	101.392i	0.328871	−	0.189874i
$535$	314.593	−	554.284i	0.588025	−	1.03604i
$536$	−35.4055	+	61.3242i	−0.0660551	+	0.114411i
$537$	85.3902	+	22.8802i	0.159013	+	0.0426075i
$538$	−194.337	−	194.337i	−0.361222	−	0.361222i
$539$	345.273	+	406.478i	0.640581	+	0.754134i
$540$	−0.382871	−	51.9601i	−0.000709020	−	0.0962224i
$541$	−384.127	−	665.328i	−0.710032	−	1.22981i	−0.964845	−	0.262821i	$-0.915347\pi$
$541$	−384.127	−	665.328i	−0.710032	−	1.22981i	0.254813	−	0.966990i	$-0.417986\pi$
$542$	155.181	+	579.143i	0.286312	+	1.06853i
$543$	306.193	−	82.0443i	0.563892	−	0.151094i
$544$	−9.26451	+	5.34887i	−0.0170303	+	0.00983247i
$545$	−241.940	+	245.532i	−0.443927	+	0.450518i
$546$	−98.8305	−	17.1195i	−0.181008	−	0.0313544i
$547$	83.3079	−	83.3079i	0.152300	−	0.152300i	−0.626845	−	0.779144i	$-0.715654\pi$
$547$	83.3079	−	83.3079i	0.152300	−	0.152300i	0.779144	+	0.626845i	$0.215654\pi$
$548$	−12.1637	+	45.3954i	−0.0221965	+	0.0828383i
$549$	242.685	+	140.114i	0.442048	+	0.255217i
$550$	−370.195	+	105.064i	−0.673083	+	0.191026i
$551$	−554.520	−	960.457i	−1.00639	−	1.74312i
$552$	−78.3369	+	78.3369i	−0.141915	+	0.141915i
$553$	87.8975	−	189.990i	0.158947	−	0.343562i
$554$		−	498.097i		−	0.899093i
$555$	30.3621	−	116.747i	0.0547065	−	0.210355i
$556$	−123.024	+	213.084i	−0.221267	+	0.383245i
$557$	157.183	+	586.616i	0.282196	+	1.05317i	0.950864	+	0.309610i	$0.100198\pi$
$557$	157.183	+	586.616i	0.282196	+	1.05317i	−0.668667	+	0.743562i	$0.733135\pi$
$558$	15.6144	−	58.2737i	0.0279828	−	0.104433i
$559$			45.8313i			0.0819881i
$560$	−88.8719	+	108.175i	−0.158700	+	0.193169i
$561$	−35.6513			−0.0635495
$562$	−489.439	−	131.145i	−0.870888	−	0.233354i
$563$	578.669	−	155.054i	1.02783	−	0.275406i	0.294769	−	0.955569i	$-0.404757\pi$
$563$	578.669	−	155.054i	1.02783	−	0.275406i	0.733062	+	0.680162i	$0.238091\pi$
$564$	278.176	+	160.605i	0.493221	+	0.284761i
$565$	−815.493	+	478.871i	−1.44335	+	0.847560i
$566$	775.924			1.37089
$567$	−5.67997	−	62.7434i	−0.0100176	−	0.110659i
$568$	−8.21692	−	8.21692i	−0.0144664	−	0.0144664i
$569$	520.684	−	300.617i	0.915086	−	0.528325i	0.0330217	−	0.999455i	$-0.489487\pi$
$569$	520.684	−	300.617i	0.915086	−	0.528325i	0.882064	+	0.471130i	$0.156154\pi$
$570$	−101.934	−	369.512i	−0.178832	−	0.648267i
$571$	−175.699	+	304.320i	−0.307705	+	0.532960i	−0.977860	−	0.209261i	$-0.932894\pi$
$571$	−175.699	+	304.320i	−0.307705	+	0.532960i	0.670155	+	0.742221i	$0.266228\pi$
$572$	123.001	+	32.9580i	0.215037	+	0.0576189i
$573$	167.167	+	167.167i	0.291740	+	0.291740i
$574$	704.980	−	259.001i	1.22819	−	0.451221i
$575$	393.827	−	405.609i	0.684916	−	0.705406i
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−222.552	−	830.576i	−0.385705	−	1.43947i	−0.837052	−	0.547123i	$-0.815723\pi$
$577$	−222.552	−	830.576i	−0.385705	−	1.43947i	0.451346	−	0.892349i	$-0.350944\pi$
$578$	−389.896	+	104.472i	−0.674561	+	0.180748i
$579$	90.2814	−	52.1240i	0.155926	−	0.0900241i
$580$	−252.406	−	248.713i	−0.435183	−	0.428816i
$581$	−412.177	−	71.3976i	−0.709427	−	0.122887i
$582$	−147.116	+	147.116i	−0.252776	+	0.252776i
$583$	−214.417	+	800.215i	−0.367782	+	1.37258i
$584$	−239.677	−	138.378i	−0.410407	−	0.236948i
$585$	43.3120	−	76.3117i	0.0740376	−	0.130447i
$586$	90.1783	+	156.193i	0.153888	+	0.266542i
$587$	601.442	−	601.442i	1.02460	−	1.02460i	0.0249132	−	0.999690i	$-0.492069\pi$
$587$	601.442	−	601.442i	1.02460	−	1.02460i	0.999690	−	0.0249132i	$-0.00793095\pi$
$588$	−96.5194	+	139.628i	−0.164149	+	0.237463i
$589$		−	445.043i		−	0.755590i
$590$	280.282	−	164.587i	0.475055	−	0.278960i
$591$	−196.877	+	341.001i	−0.333126	+	0.576990i
$592$	14.4206	+	53.8184i	0.0243591	+	0.0909095i
$593$	50.6955	−	189.198i	0.0854898	−	0.319052i	−0.909917	−	0.414791i	$-0.863855\pi$
$593$	50.6955	−	189.198i	0.0854898	−	0.319052i	0.995407	+	0.0957387i	$0.0305213\pi$
$594$			79.9825i			0.134651i
$595$	53.8216	−	38.5252i	0.0904565	−	0.0647483i
$596$	76.0707			0.127635
$597$	−378.203	−	101.339i	−0.633506	−	0.169747i
$598$	−180.706	+	48.4199i	−0.302183	+	0.0809697i
$599$	273.403	+	157.849i	0.456432	+	0.263521i	0.710543	−	0.703654i	$-0.248449\pi$
$599$	273.403	+	157.849i	0.456432	+	0.263521i	−0.254111	+	0.967175i	$0.581783\pi$
$600$	−62.7936	−	105.152i	−0.104656	−	0.175253i
$601$	−956.156			−1.59094			−0.795470	−	0.605992i	$-0.792776\pi$
$601$	−956.156			−1.59094			−0.795470	+	0.605992i	$0.792776\pi$
$602$	70.3918	+	32.5663i	0.116930	+	0.0540968i
$603$	−53.1083	−	53.1083i	−0.0880734	−	0.0880734i
$604$	284.860	−	164.464i	0.471622	−	0.272291i
$605$	−12.2111	+	3.36857i	−0.0201836	+	0.00556788i
$606$	−34.0337	+	58.9480i	−0.0561612	+	0.0972740i
$607$	562.393	+	150.693i	0.926513	+	0.248258i	0.690367	−	0.723459i	$-0.257449\pi$
$607$	562.393	+	150.693i	0.926513	+	0.248258i	0.236146	+	0.971718i	$0.424116\pi$
$608$	125.190	+	125.190i	0.205904	+	0.205904i
$609$	−329.948	−	275.169i	−0.541787	−	0.451837i
$610$	660.486	−	4.86682i	1.08276	−	0.00797840i
$611$	271.210	+	469.750i	0.443879	+	0.768822i
$612$	−2.93673	−	10.9600i	−0.00479858	−	0.0179085i
$613$	659.677	−	176.760i	1.07614	−	0.288352i	0.323129	−	0.946355i	$-0.395265\pi$
$613$	659.677	−	176.760i	1.07614	−	0.288352i	0.753016	+	0.658003i	$0.228598\pi$
$614$	−349.604	+	201.844i	−0.569388	+	0.328736i
$615$	4.84125	+	657.015i	0.00787195	+	1.06832i
$616$	138.020	−	165.497i	0.224059	−	0.268664i
$617$	709.720	−	709.720i	1.15027	−	1.15027i	0.163777	−	0.986497i	$-0.447632\pi$
$617$	709.720	−	709.720i	1.15027	−	1.15027i	0.986497	−	0.163777i	$-0.0523679\pi$
$618$	−90.9490	+	339.426i	−0.147167	+	0.549233i
$619$	286.349	+	165.324i	0.462599	+	0.267082i	0.713137	−	0.701025i	$-0.247274\pi$
$619$	286.349	+	165.324i	0.462599	+	0.267082i	−0.250537	+	0.968107i	$0.580607\pi$
$620$	−37.8145	−	137.077i	−0.0609912	−	0.221093i
$621$	−58.7526	−	101.763i	−0.0946097	−	0.163869i
$622$	464.268	−	464.268i	0.746412	−	0.746412i
$623$	243.326	−	525.947i	0.390571	−	0.844216i
$624$			40.5282i			0.0649491i
$625$	328.315	+	531.822i	0.525304	+	0.850915i
$626$	−88.6058	+	153.470i	−0.141543	+	0.245159i
$627$	152.709	+	569.917i	0.243555	+	0.908958i
$628$	0.138695	−	0.517616i	0.000220852	−	0.000824230i
$629$		−	26.3417i		−	0.0418787i
$630$	−86.4301	−	120.747i	−0.137191	−	0.191662i
$631$	−786.255			−1.24605			−0.623023	−	0.782203i	$-0.714096\pi$
$631$	−786.255			−1.24605			−0.623023	+	0.782203i	$0.714096\pi$
$632$	−81.7029	−	21.8922i	−0.129277	−	0.0346396i
$633$	−535.935	+	143.603i	−0.846658	+	0.226861i
$634$	86.8962	+	50.1696i	0.137060	+	0.0791318i
$635$	91.0616	+	155.073i	0.143404	+	0.244210i
$636$	−263.667			−0.414571
$637$	−259.047	+	122.702i	−0.406667	+	0.192625i
$638$	385.688	+	385.688i	0.604526	+	0.604526i
$639$	10.6741	−	6.16269i	0.0167044	−	0.00964427i
$640$	49.1969	+	27.9225i	0.0768701	+	0.0436290i
$641$	−184.010	+	318.714i	−0.287067	+	0.497214i	−0.973108	−	0.230348i	$-0.926013\pi$
$641$	−184.010	+	318.714i	−0.287067	+	0.497214i	0.686042	+	0.727562i	$0.259347\pi$
$642$	−301.592	−	80.8112i	−0.469769	−	0.125874i
$643$	569.132	+	569.132i	0.885119	+	0.885119i	0.994049	−	0.108930i	$-0.0347425\pi$
$643$	569.132	+	569.132i	0.885119	+	0.885119i	−0.108930	+	0.994049i	$0.534743\pi$
$644$	−54.0360	+	311.949i	−0.0839068	+	0.484393i
$645$	−47.6230	+	48.3301i	−0.0738342	+	0.0749303i
$646$	−41.8515	−	72.4889i	−0.0647856	−	0.112212i
$647$	0.849457	+	3.17022i	0.00131292	+	0.00489987i	0.966579	−	0.256368i	$-0.0825260\pi$
$647$	0.849457	+	3.17022i	0.00131292	+	0.00489987i	−0.965266	+	0.261268i	$0.915859\pi$
$648$	−24.5885	+	6.58846i	−0.0379452	+	0.0101674i
$649$	−433.283	+	250.156i	−0.667617	+	0.385449i
$650$	−3.04776	−	206.797i	−0.00468886	−	0.318150i
$651$	−59.4542	−	161.830i	−0.0913275	−	0.248586i
$652$	−329.142	+	329.142i	−0.504819	+	0.504819i
$653$	−120.224	+	448.682i	−0.184110	+	0.687108i	0.810709	+	0.585449i	$0.199082\pi$
$653$	−120.224	+	448.682i	−0.184110	+	0.687108i	−0.994819	+	0.101659i	$0.967585\pi$
$654$	146.246	+	84.4350i	0.223617	+	0.129105i
$655$	−418.518	+	115.453i	−0.638959	+	0.176265i
$656$	−151.735	−	262.813i	−0.231304	−	0.400630i
$657$	207.567	−	207.567i	0.315931	−	0.315931i
$658$	914.197	−	82.7594i	1.38936	−	0.125774i
$659$			591.441i			0.897482i	0.893662	+	0.448741i	$0.148127\pi$
$659$			591.441i			0.897482i	−0.893662	+	0.448741i	$0.851873\pi$
$660$	95.4607	+	162.565i	0.144637	+	0.246310i
$661$	−251.099	+	434.916i	−0.379878	+	0.657967i	−0.991044	−	0.133535i	$-0.957367\pi$
$661$	−251.099	+	434.916i	−0.379878	+	0.657967i	0.611166	+	0.791502i	$0.290701\pi$
$662$	−233.947	−	873.104i	−0.353395	−	1.31889i
$663$	4.95919	−	18.5080i	0.00747993	−	0.0279155i
$664$			169.025i			0.254556i
$665$	−846.399	−	695.367i	−1.27278	−	1.04566i
$666$	−59.0967			−0.0887338
$667$	−774.029	−	207.400i	−1.16046	−	0.310945i
$668$	33.1513	−	8.88288i	0.0496278	−	0.0132977i
$669$	−284.556	−	164.288i	−0.425345	−	0.245573i
$670$	−171.328	−	44.5569i	−0.255714	−	0.0665029i
$671$	−1016.69			−1.51518
$672$	62.2469	+	28.7981i	0.0926292	+	0.0428543i
$673$	−145.430	−	145.430i	−0.216092	−	0.216092i	0.590757	−	0.806849i	$-0.298829\pi$
$673$	−145.430	−	145.430i	−0.216092	−	0.216092i	−0.806849	+	0.590757i	$0.798829\pi$
$674$	445.444	−	257.177i	0.660897	−	0.381569i
$675$	124.968	−	35.4670i	0.185138	−	0.0525437i
$676$	134.780	−	233.447i	0.199379	−	0.345335i
$677$	475.760	+	127.480i	0.702747	+	0.188301i	0.592461	−	0.805599i	$-0.298156\pi$
$677$	475.760	+	127.480i	0.702747	+	0.188301i	0.110287	+	0.993900i	$0.464823\pi$
$678$	327.600	+	327.600i	0.483186	+	0.483186i
$679$	−101.479	+	585.836i	−0.149453	+	0.862793i
$680$	−19.0499	−	18.7712i	−0.0280146	−	0.0276048i
$681$	6.56408	+	11.3693i	0.00963888	+	0.0166950i
$682$	56.6502	+	211.421i	0.0830648	+	0.310002i
$683$	−1070.02	+	286.711i	−1.56665	+	0.419782i	−0.934760	−	0.355279i	$-0.884386\pi$
$683$	−1070.02	+	286.711i	−1.56665	+	0.419782i	−0.631887	+	0.775061i	$0.717719\pi$
$684$	−162.626	+	93.8924i	−0.237758	+	0.137270i
$685$	−117.489	+	0.865722i	−0.171516	+	0.00126383i
$686$	4.38646	+	485.055i	0.00639426	+	0.707078i
$687$	243.661	−	243.661i	0.354674	−	0.354674i
$688$	8.11113	−	30.2712i	0.0117894	−	0.0439988i
$689$	−385.596	−	222.624i	−0.559646	−	0.323112i
$690$	−240.871	−	136.710i	−0.349088	−	0.198131i
$691$	551.244	+	954.783i	0.797748	+	1.38174i	0.921079	+	0.389375i	$0.127309\pi$
$691$	551.244	+	954.783i	0.797748	+	1.38174i	−0.123331	+	0.992366i	$0.539358\pi$
$692$	354.582	−	354.582i	0.512402	−	0.512402i
$693$	131.666	+	186.837i	0.189994	+	0.269606i
$694$			31.8866i			0.0459460i
$695$	−595.319	−	154.823i	−0.856574	−	0.222767i
$696$	−86.7988	+	150.340i	−0.124711	+	0.216006i
$697$	37.1338	+	138.585i	0.0532766	+	0.198831i
$698$	−95.9847	+	358.220i	−0.137514	+	0.513209i
$699$			347.478i			0.497108i
$700$	−319.783	−	142.263i	−0.456833	−	0.203232i
$701$	−869.635			−1.24056			−0.620282	−	0.784379i	$-0.712982\pi$
$701$	−869.635			−1.24056			−0.620282	+	0.784379i	$0.712982\pi$
$702$	−41.5220	−	11.1258i	−0.0591481	−	0.0158487i
$703$	−421.095	+	112.832i	−0.598997	+	0.160501i
$704$	−75.4082	−	43.5369i	−0.107114	−	0.0618422i
$705$	−202.117	+	777.174i	−0.286691	+	1.10237i
$706$	−165.044			−0.233774
$707$	17.5374	+	193.726i	0.0248054	+	0.274012i
$708$	−112.595	−	112.595i	−0.159032	−	0.159032i
$709$	−1104.74	+	637.824i	−1.55817	+	0.899610i	−0.560739	+	0.827993i	$0.689483\pi$
$709$	−1104.74	+	637.824i	−1.55817	+	0.899610i	−0.997432	+	0.0716178i	$0.977184\pi$
$710$	14.3398	−	25.2654i	0.0201969	−	0.0355851i
$711$	44.8580	−	77.6964i	0.0630915	−	0.109278i
$712$	−226.177	−	60.6040i	−0.317665	−	0.0851180i
$713$	−227.380	−	227.380i	−0.318907	−	0.318907i
$714$	−24.9023	−	20.7679i	−0.0348772	−	0.0290867i
$715$	2.34572	+	318.342i	0.00328072	+	0.445233i
$716$	−51.0392	−	88.4024i	−0.0712837	−	0.123467i
$717$	52.9661	+	197.672i	0.0738719	+	0.275694i
$718$	298.412	−	79.9592i	0.415615	−	0.111364i
$719$	477.496	−	275.682i	0.664111	−	0.383425i	−0.129731	−	0.991549i	$-0.541411\pi$
$719$	477.496	−	275.682i	0.664111	−	0.383425i	0.793841	+	0.608125i	$0.208078\pi$
$720$	−42.1126	+	42.7379i	−0.0584898	+	0.0593581i
$721$	346.303	+	942.608i	0.480309	+	1.30736i
$722$	−618.532	+	618.532i	−0.856692	+	0.856692i
$723$	−9.79292	+	36.5477i	−0.0135448	+	0.0505501i
$724$	−316.995	−	183.017i	−0.437838	−	0.252786i
$725$	431.589	−	773.644i	0.595296	−	1.06710i
$726$	3.10281	+	5.37422i	0.00427384	+	0.00740251i
$727$	380.507	−	380.507i	0.523393	−	0.523393i	−0.395202	−	0.918594i	$-0.629325\pi$
$727$	380.507	−	380.507i	0.523393	−	0.523393i	0.918594	+	0.395202i	$0.129325\pi$
$728$	66.7168	+	94.6728i	0.0916439	+	0.130045i
$729$		−	27.0000i		−	0.0370370i
$730$	174.145	−	669.615i	0.238555	−	0.917281i
$731$	−7.40819	+	12.8314i	−0.0101343	+	0.0175532i
$732$	−83.7485	−	312.554i	−0.114411	−	0.426986i
$733$	−44.1289	+	164.691i	−0.0602031	+	0.224681i	−0.989472	−	0.144722i	$-0.953771\pi$
$733$	−44.1289	+	164.691i	−0.0602031	+	0.224681i	0.929269	+	0.369403i	$0.120438\pi$
$734$		−	311.030i		−	0.423746i
$735$	−400.669	−	139.782i	−0.545128	−	0.190180i
$736$	127.924			0.173809
$737$	263.207	+	70.5261i	0.357133	+	0.0956935i
$738$	310.911	−	83.3084i	0.421289	−	0.112884i
$739$	−199.580	−	115.227i	−0.270067	−	0.155923i	0.358851	−	0.933395i	$-0.383169\pi$
$739$	−199.580	−	115.227i	−0.270067	−	0.155923i	−0.628918	+	0.777471i	$0.716502\pi$
$740$	−120.114	+	70.5331i	−0.162317	+	0.0953150i
$741$	−317.108			−0.427946
$742$	−615.918	+	434.043i	−0.830078	+	0.584964i
$743$	−944.117	−	944.117i	−1.27068	−	1.27068i	−0.945731	−	0.324952i	$-0.894652\pi$
$743$	−944.117	−	944.117i	−1.27068	−	1.27068i	−0.324952	−	0.945731i	$-0.605348\pi$
$744$	−60.3294	+	34.8312i	−0.0810878	+	0.0468161i
$745$	50.5736	+	183.329i	0.0678840	+	0.246079i
$746$	448.706	−	777.182i	0.601483	−	1.04180i
$747$	−173.169	−	46.4006i	−0.231820	−	0.0621159i
$748$	29.1092	+	29.1092i	0.0389160	+	0.0389160i
$749$	−837.539	+	307.701i	−1.11821	+	0.410816i
$750$	211.668	−	221.239i	0.282224	−	0.294985i
$751$	147.067	+	254.727i	0.195828	+	0.339184i	0.947172	−	0.320727i	$-0.103927\pi$
$751$	147.067	+	254.727i	0.195828	+	0.339184i	−0.751344	+	0.659911i	$0.770594\pi$
$752$	−95.9965	−	358.264i	−0.127655	−	0.476414i
$753$	332.050	−	88.9725i	0.440969	−	0.118157i
$754$	−253.875	+	146.575i	−0.336705	+	0.194397i
$755$	585.736	+	577.167i	0.775809	+	0.764460i
$756$	−46.5921	+	55.8675i	−0.0616298	+	0.0738988i
$757$	−521.238	+	521.238i	−0.688557	+	0.688557i	−0.961913	−	0.273356i	$-0.911866\pi$
$757$	−521.238	+	521.238i	−0.688557	+	0.688557i	0.273356	+	0.961913i	$0.411866\pi$
$758$	−113.887	+	425.033i	−0.150247	+	0.560729i
$759$	369.203	+	213.159i	0.486433	+	0.280842i
$760$	−218.476	+	384.934i	−0.287469	+	0.506493i
$761$	237.263	+	410.952i	0.311779	+	0.540016i	0.978747	−	0.205069i	$-0.0657420\pi$
$761$	237.263	+	410.952i	0.311779	+	0.540016i	−0.666969	+	0.745086i	$0.732409\pi$
$762$	62.2960	−	62.2960i	0.0817533	−	0.0817533i
$763$	480.621	−	43.5091i	0.629909	−	0.0570237i
$764$		−	272.982i		−	0.357307i
$765$	24.4611	−	14.3640i	0.0319752	−	0.0187764i
$766$	−219.706	+	380.542i	−0.286823	+	0.496791i
$767$	−69.5948	−	259.731i	−0.0907364	−	0.338633i
$768$	7.17260	−	26.7685i	0.00933933	−	0.0348548i
$769$			915.355i			1.19032i	0.803608	+	0.595159i	$0.202911\pi$
$769$			915.355i			1.19032i	−0.803608	+	0.595159i	$0.797089\pi$
$770$	490.604	+	222.601i	0.637148	+	0.289092i
$771$	94.3580			0.122384
$772$	−116.273	−	31.1554i	−0.150613	−	0.0403567i
$773$	591.497	−	158.491i	0.765197	−	0.205034i	0.144948	−	0.989439i	$-0.453698\pi$
$773$	591.497	−	158.491i	0.765197	−	0.205034i	0.620248	+	0.784405i	$0.287032\pi$
$774$	28.7867	+	16.6200i	0.0371921	+	0.0214729i
$775$	305.214	−	182.265i	0.393825	−	0.235180i
$776$	240.239			0.309586
$777$	−138.048	+	97.2838i	−0.177668	+	0.125204i
$778$	749.549	+	749.549i	0.963431	+	0.963431i
$779$	2056.35	−	1187.23i	2.63973	−	1.52405i
$780$	−97.6723	+	26.9441i	−0.125221	+	0.0345437i
$781$	−22.3587	+	38.7264i	−0.0286283	+	0.0495857i
$782$	−58.4186	−	15.6532i	−0.0747041	−	0.0200169i
$783$	−130.198	−	130.198i	−0.166281	−	0.166281i
$784$	192.814	−	35.1981i	0.245936	−	0.0448955i
$785$	1.33965	−	0.00987130i	0.00170656	−	1.25749e-5i
$786$	106.345	+	184.194i	0.135299	+	0.234344i
$787$	33.2528	+	124.101i	0.0422526	+	0.157689i	0.983829	−	0.179111i	$-0.0573221\pi$
$787$	33.2528	+	124.101i	0.0422526	+	0.157689i	−0.941576	+	0.336800i	$0.890655\pi$
$788$	439.176	−	117.677i	0.557330	−	0.149336i
$789$	288.405	−	166.511i	0.365532	−	0.211040i
$790$	−1.55813	−	211.457i	−0.00197232	−	0.267667i
$791$	1304.55	+	225.975i	1.64924	+	0.285683i
$792$	65.3054	−	65.3054i	0.0824563	−	0.0824563i
$793$	141.424	−	527.802i	0.178341	−	0.665577i
$794$	574.316	+	331.581i	0.723319	+	0.417609i
$795$	−175.292	−	635.432i	−0.220493	−	0.799286i
$796$	226.058	+	391.545i	0.283993	+	0.491890i
$797$	280.474	−	280.474i	0.351912	−	0.351912i	−0.508909	−	0.860821i	$-0.669951\pi$
$797$	280.474	−	280.474i	0.351912	−	0.351912i	0.860821	+	0.508909i	$0.169951\pi$
$798$	−225.327	+	487.042i	−0.282364	+	0.610329i
$799$			175.354i			0.219467i
$800$	−34.5855	+	137.127i	−0.0432319	+	0.171409i
$801$	124.180	−	215.086i	0.155031	−	0.268522i
$802$	−114.673	−	427.967i	−0.142984	−	0.533625i
$803$	−275.642	+	1028.71i	−0.343266	+	1.28108i
$804$			86.7255i			0.107867i
$805$	−787.716	+	77.1653i	−0.978529	+	0.0958575i
$806$	−117.637			−0.145952
$807$	−325.133	−	87.1191i	−0.402891	−	0.107954i
$808$	75.9192	−	20.3425i	0.0939595	−	0.0251764i
$809$	138.409	+	79.9106i	0.171087	+	0.0987770i	0.583098	−	0.812402i	$-0.301840\pi$
$809$	138.409	+	79.9106i	0.171087	+	0.0987770i	−0.412011	+	0.911179i	$0.635174\pi$
$810$	−32.2250	−	54.8776i	−0.0397840	−	0.0677501i
$811$	−651.825			−0.803730			−0.401865	−	0.915699i	$-0.631638\pi$
$811$	−651.825			−0.803730			−0.401865	+	0.915699i	$0.631638\pi$
$812$	44.7271	+	494.076i	0.0550827	+	0.608468i
$813$	519.245	+	519.245i	0.638678	+	0.638678i
$814$	185.682	−	107.204i	0.228111	−	0.131700i
$815$	−1012.05	−	574.405i	−1.24178	−	0.704791i
$816$	−6.55100	+	11.3467i	−0.00802818	+	0.0139052i
$817$	236.853	+	63.4645i	0.289905	+	0.0776799i
$818$	−425.628	−	425.628i	−0.520327	−	0.520327i
$819$	−115.309	+	42.3631i	−0.140793	+	0.0517254i
$820$	532.498	−	540.403i	0.649387	−	0.659029i
$821$	−105.062	−	181.974i	−0.127969	−	0.221649i	0.794921	−	0.606713i	$-0.207512\pi$
$821$	−105.062	−	181.974i	−0.127969	−	0.221649i	−0.922890	+	0.385065i	$0.874179\pi$
$822$	14.8974	+	55.5978i	0.0181233	+	0.0676372i
$823$	−377.850	+	101.245i	−0.459113	+	0.123019i	−0.480960	−	0.876742i	$-0.659712\pi$
$823$	−377.850	+	101.245i	−0.459113	+	0.123019i	0.0218473	+	0.999761i	$0.493045\pi$
$824$	351.400	−	202.881i	0.426456	−	0.246215i
$825$	−328.313	+	338.135i	−0.397955	+	0.409861i
$826$	−448.370	−	77.6670i	−0.542821	−	0.0940278i
$827$	295.979	−	295.979i	0.357895	−	0.357895i	−0.505142	−	0.863036i	$-0.668560\pi$
$827$	295.979	−	295.979i	0.357895	−	0.357895i	0.863036	+	0.505142i	$0.168560\pi$
$828$	−35.1174	+	131.060i	−0.0424124	+	0.158285i
$829$	−751.209	−	433.711i	−0.906163	−	0.523174i	−0.0269687	−	0.999636i	$-0.508585\pi$
$829$	−751.209	−	433.711i	−0.906163	−	0.523174i	−0.879195	+	0.476463i	$0.841919\pi$
$830$	−407.347	+	112.372i	−0.490779	+	0.135388i
$831$	−305.021	−	528.312i	−0.367053	−	0.635755i
$832$	33.0912	−	33.0912i	0.0397730	−	0.0397730i
$833$	−92.3588	−	7.51957i	−0.110875	−	0.00902710i
$834$			301.347i			0.361327i
$835$	43.4474	+	73.9886i	0.0520328	+	0.0886091i
$836$	340.649	−	590.021i	0.407475	−	0.705767i
$837$	−19.1236	−	71.3704i	−0.0228478	−	0.0852693i
$838$	294.421	−	1098.79i	0.351338	−	1.31121i
$839$			144.284i			0.171971i	0.996296	+	0.0859854i	$0.0274039\pi$
$839$			144.284i			0.171971i	−0.996296	+	0.0859854i	$0.972596\pi$
$840$	−28.0197	+	169.159i	−0.0333567	+	0.201380i
$841$	−414.671			−0.493069
$842$	252.685	+	67.7068i	0.300101	+	0.0804119i
$843$	−599.438	+	160.619i	−0.711077	+	0.190533i
$844$	554.840	+	320.337i	0.657394	+	0.379547i
$845$	652.207	+	169.618i	0.771843	+	0.200731i
$846$	393.401			0.465013
$847$	16.0950	+	7.44624i	0.0190024	+	0.00879131i
$848$	215.283	+	215.283i	0.253872	+	0.253872i
$849$	822.992	−	475.155i	0.969366	−	0.559664i
$850$	32.5735	−	58.3895i	0.0383218	−	0.0686936i
$851$	−157.497	+	272.793i	−0.185073	+	0.320556i
$852$	−13.7472	−	3.68354i	−0.0161352	−	0.00432341i
$853$	−1075.27	−	1075.27i	−1.26057	−	1.26057i	−0.950818	−	0.309751i	$-0.899754\pi$
$853$	−1075.27	−	1075.27i	−1.26057	−	1.26057i	−0.309751	−	0.950818i	$-0.600246\pi$
$854$	−710.154	−	592.251i	−0.831562	−	0.693502i
$855$	−334.397	−	329.505i	−0.391107	−	0.385386i
$856$	180.266	+	312.231i	0.210592	+	0.364755i
$857$	−134.657	−	502.546i	−0.157126	−	0.586402i	−0.998914	−	0.0465935i	$-0.985163\pi$
$857$	−134.657	−	502.546i	−0.157126	−	0.586402i	0.841788	−	0.539808i	$-0.181503\pi$
$858$	150.645	−	40.3652i	0.175577	−	0.0470457i
$859$	−344.151	+	198.695i	−0.400641	+	0.231310i	−0.686761	−	0.726884i	$-0.740968\pi$
$859$	−344.151	+	198.695i	−0.400641	+	0.231310i	0.286119	+	0.958194i	$0.407635\pi$
$860$	78.3454	−	0.577292i	0.0910993	−	0.000671270i
$861$	589.139	−	706.422i	0.684250	−	0.820467i
$862$	668.189	−	668.189i	0.775162	−	0.775162i
$863$	119.433	−	445.731i	0.138393	−	0.516490i	−0.861568	−	0.507643i	$-0.830517\pi$
$863$	119.433	−	445.731i	0.138393	−	0.516490i	0.999961	−	0.00884760i	$-0.00281632\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$	1090.27	+	618.802i	1.26043	+	0.715378i
$866$	−283.514	−	491.061i	−0.327384	−	0.567045i
$867$	−349.571	+	349.571i	−0.403196	+	0.403196i
$868$	−83.5892	+	180.678i	−0.0963009	+	0.208154i
$869$			325.497i			0.374565i
$870$	−420.022	−	109.234i	−0.482784	−	0.125556i
$871$	−73.2256	+	126.831i	−0.0840708	+	0.145615i
$872$	−50.4682	−	188.350i	−0.0578764	−	0.215998i
$873$	−65.9501	+	246.129i	−0.0755442	+	0.281935i
$874$			1000.92i			1.14522i
$875$	130.251	−	865.251i	0.148858	−	0.988859i
$876$	−338.955			−0.386935
$877$	−437.235	−	117.157i	−0.498558	−	0.133588i	0.000772786	−	1.00000i	$-0.499754\pi$
$877$	−437.235	−	117.157i	−0.498558	−	0.133588i	−0.499331	+	0.866412i	$0.666421\pi$
$878$	−841.996	+	225.612i	−0.958993	+	0.256961i
$879$	191.297	+	110.445i	0.217630	+	0.125649i
$880$	54.7901	−	210.677i	0.0622615	−	0.239405i
$881$	−810.821			−0.920342			−0.460171	−	0.887830i	$-0.652212\pi$
$881$	−810.821			−0.920342			−0.460171	+	0.887830i	$0.652212\pi$
$882$	−16.8699	+	207.204i	−0.0191269	+	0.234925i
$883$	−270.938	−	270.938i	−0.306839	−	0.306839i	0.536843	−	0.843682i	$-0.319617\pi$
$883$	−270.938	−	270.938i	−0.306839	−	0.306839i	−0.843682	+	0.536843i	$0.819617\pi$
$884$	−19.1608	+	11.0625i	−0.0216752	+	0.0125142i
$885$	196.496	−	346.208i	0.222029	−	0.391195i
$886$	428.922	−	742.914i	0.484110	−	0.838503i
$887$	784.980	+	210.335i	0.884983	+	0.237130i	0.672556	−	0.740047i	$-0.265197\pi$
$887$	784.980	+	210.335i	0.884983	+	0.237130i	0.212427	+	0.977177i	$0.431863\pi$
$888$	48.2523	+	48.2523i	0.0543381	+	0.0543381i
$889$	42.9712	−	248.072i	0.0483365	−	0.279046i
$890$	−4.31336	−	585.374i	−0.00484647	−	0.657723i
$891$	48.9791	+	84.8342i	0.0549709	+	0.0952124i
$892$	98.1978	+	366.479i	0.110087	+	0.410851i
$893$	2803.19	−	751.112i	3.13907	−	0.841110i
$894$	80.6851	−	46.5836i	0.0902518	−	0.0521069i
$895$	179.116	−	181.775i	0.200130	−	0.203101i
$896$	−27.3108	−	74.3379i	−0.0304808	−	0.0829664i
$897$	−162.016	+	162.016i	−0.180620	+	0.180620i
$898$	290.698	−	1084.90i	0.323717	−	1.20813i
$899$	−436.376	−	251.942i	−0.485402	−	0.280247i
$900$	−130.995	−	73.0776i	−0.145550	−	0.0811973i
$901$	−71.9700	−	124.656i	−0.0798779	−	0.138353i
$902$	−825.761	+	825.761i	−0.915478	+	0.915478i
$903$	94.6044	−	8.56424i	0.104767	−	0.00948421i
$904$		−	534.968i		−	0.591779i
$905$	230.322	−	885.625i	0.254500	−	0.978592i
$906$	201.426	−	348.880i	0.222325	−	0.385078i
$907$	−102.583	−	382.844i	−0.113101	−	0.422099i	0.886037	−	0.463615i	$-0.153448\pi$
$907$	−102.583	−	382.844i	−0.113101	−	0.422099i	−0.999138	+	0.0415160i	$0.986781\pi$
$908$	3.92346	−	14.6425i	0.00432099	−	0.0161262i
$909$			83.3651i			0.0917108i
$910$	−183.805	+	223.727i	−0.201983	+	0.245854i
$911$	55.2945			0.0606965			0.0303482	−	0.999539i	$-0.490338\pi$
$911$	55.2945			0.0606965			0.0303482	+	0.999539i	$0.490338\pi$
$912$	209.447	+	56.1211i	0.229657	+	0.0615363i
$913$	628.272	−	168.345i	0.688140	−	0.184386i
$914$	593.922	+	342.901i	0.649806	+	0.375166i
$915$	697.571	−	409.625i	0.762372	−	0.447678i
$916$	−397.897			−0.434385
$917$	551.635	+	255.210i	0.601565	+	0.278310i
$918$	−9.82649	−	9.82649i	−0.0107042	−	0.0107042i
$919$	−640.844	+	369.991i	−0.697327	+	0.402602i	−0.806351	−	0.591437i	$-0.798561\pi$
$919$	−640.844	+	369.991i	−0.697327	+	0.402602i	0.109024	+	0.994039i	$0.465227\pi$
$920$	85.0465	+	308.293i	0.0924419	+	0.335101i
$921$	−247.208	+	428.176i	−0.268412	+	0.464904i
$922$	−353.948	−	94.8402i	−0.383892	−	0.102864i
$923$	−16.9942	−	16.9942i	−0.0184119	−	0.0184119i
$924$	45.0470	−	260.056i	0.0487522	−	0.281446i
$925$	−249.838	−	242.581i	−0.270095	−	0.262250i
$926$	529.834	+	917.700i	0.572175	+	0.991037i
$927$	111.389	+	415.711i	0.120161	+	0.448447i
$928$	193.623	−	51.8811i	0.208645	−	0.0559064i
$929$	77.9485	−	45.0036i	0.0839058	−	0.0484430i	−0.457460	−	0.889230i	$-0.651241\pi$
$929$	77.9485	−	45.0036i	0.0839058	−	0.0484430i	0.541366	+	0.840787i	$0.317907\pi$
$930$	−124.051	−	122.236i	−0.133388	−	0.131437i
$931$	275.403	+	1508.64i	0.295814	+	1.62046i
$932$	283.715	−	283.715i	0.304415	−	0.304415i
$933$	208.126	−	776.736i	0.223071	−	0.832514i
$934$	127.753	+	73.7583i	0.136781	+	0.0789703i
$935$	−50.8001	+	89.5050i	−0.0543316	+	0.0957272i
$936$	24.8184	+	42.9867i	0.0265154	+	0.0459260i
$937$	172.515	−	172.515i	0.184115	−	0.184115i	−0.609031	−	0.793146i	$-0.708442\pi$
$937$	172.515	−	172.515i	0.184115	−	0.184115i	0.793146	+	0.609031i	$0.208442\pi$
$938$	142.766	+	202.588i	0.152202	+	0.215979i
$939$			217.039i			0.231138i
$940$	799.588	−	469.532i	0.850626	−	0.499502i
$941$	−703.886	+	1219.17i	−0.748019	+	1.29561i	0.200751	+	0.979642i	$0.435662\pi$
$941$	−703.886	+	1219.17i	−0.748019	+	1.29561i	−0.948771	+	0.315965i	$0.897672\pi$
$942$	−0.169866	−	0.633948i	−0.000180325	−	0.000672981i
$943$	444.046	−	1657.20i	0.470887	−	1.75737i
$944$			183.867i			0.194774i
$945$	−165.615	−	75.1442i	−0.175254	−	0.0795176i
$946$	−120.597			−0.127481
$947$	−1473.70	−	394.876i	−1.55617	−	0.416976i	−0.624724	−	0.780845i	$-0.714789\pi$
$947$	−1473.70	−	394.876i	−1.55617	−	0.416976i	−0.931450	+	0.363870i	$0.881455\pi$
$948$	−100.065	+	26.8124i	−0.105554	+	0.0282831i
$949$	−495.701	−	286.193i	−0.522340	−	0.301573i
$950$	−1072.93	−	270.610i	−1.12940	−	0.284853i
$951$	122.890			0.129222
$952$	3.37571	+	37.2896i	0.00354591	+	0.0391697i
$953$	911.207	+	911.207i	0.956146	+	0.956146i	0.999078	−	0.0429317i	$-0.0136698\pi$
$953$	911.207	+	911.207i	0.956146	+	0.956146i	−0.0429317	+	0.999078i	$0.513670\pi$
$954$	−279.661	+	161.462i	−0.293146	+	0.169248i
$955$	657.882	−	181.485i	0.688882	−	0.190037i
$956$	118.152	−	204.645i	0.123590	−	0.214064i
$957$	645.268	+	172.899i	0.674261	+	0.180668i
$958$	−407.413	−	407.413i	−0.425275	−	0.425275i
$959$	126.324	+	105.351i	0.131724	+	0.109855i
$960$	69.2802	−	0.510494i	0.0721668	−	0.000531765i
$961$	379.399	+	657.139i	0.394796	+	0.683807i
$962$	29.8247	+	111.307i	0.0310028	+	0.115704i
$963$	−369.373	+	98.9731i	−0.383565	+	0.102776i
$964$	37.8370	−	21.8452i	0.0392500	−	0.0226610i
$965$	−2.21742	−	300.930i	−0.00229784	−	0.311844i
$966$	133.715	+	363.962i	0.138422	+	0.376772i
$967$	181.527	−	181.527i	0.187722	−	0.187722i	−0.606989	−	0.794711i	$-0.707623\pi$
$967$	181.527	−	181.527i	0.187722	−	0.187722i	0.794711	+	0.606989i	$0.207623\pi$
$968$	1.85460	−	6.92147i	0.00191591	−	0.00715028i
$969$	−88.7804	−	51.2574i	−0.0916207	−	0.0528972i
$970$	159.716	+	578.971i	0.164656	+	0.596877i
$971$	−440.240	−	762.518i	−0.453388	−	0.785292i	0.545206	−	0.838302i	$-0.316452\pi$
$971$	−440.240	−	762.518i	−0.453388	−	0.785292i	−0.998594	+	0.0530107i	$0.983118\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	496.071	+	703.937i	0.509837	+	0.723471i
$974$		−	1148.28i		−	1.17893i
$975$	−129.870	−	217.475i	−0.133200	−	0.223052i
$976$	−186.819	+	323.579i	−0.191413	+	0.331536i
$977$	87.3479	+	325.987i	0.0894042	+	0.333661i	0.996112	−	0.0880989i	$-0.0280792\pi$
$977$	87.3479	+	325.987i	0.0894042	+	0.333661i	−0.906708	+	0.421760i	$0.861412\pi$
$978$	−147.550	+	550.665i	−0.150869	+	0.563053i
$979$			901.069i			0.920397i
$980$	213.014	+	441.277i	0.217361	+	0.450282i
$981$	206.823			0.210828
$982$	−457.115	−	122.484i	−0.465494	−	0.124729i
$983$	596.713	−	159.889i	0.607033	−	0.162654i	0.0578068	−	0.998328i	$-0.481589\pi$
$983$	596.713	−	159.889i	0.607033	−	0.162654i	0.549226	+	0.835674i	$0.314923\pi$
$984$	−321.879	−	185.837i	−0.327113	−	0.188859i
$985$	575.573	+	980.172i	0.584338	+	0.995098i
$986$	−94.7697			−0.0961154
$987$	918.973	−	647.609i	0.931077	−	0.656138i
$988$	258.917	+	258.917i	0.262062	+	0.262062i
$989$	153.437	−	88.5871i	0.155144	−	0.0895724i
$990$	200.801	+	113.968i	0.202830	+	0.115119i
$991$	821.382	−	1422.68i	0.828841	−	1.43560i	−0.0701063	−	0.997540i	$-0.522334\pi$
$991$	821.382	−	1422.68i	0.828841	−	1.43560i	0.898948	−	0.438056i	$-0.144333\pi$
$992$	77.6982	+	20.8192i	0.0783248	+	0.0209871i
$993$	−782.804	−	782.804i	−0.788322	−	0.788322i
$994$	−38.1768	+	14.0257i	−0.0384072	+	0.0141103i
$995$	−793.326	+	805.104i	−0.797313	+	0.809150i
$996$	103.506	+	179.278i	0.103922	+	0.179998i
$997$	−271.146	−	1011.93i	−0.271961	−	1.01497i	−0.957850	−	0.287268i	$-0.907253\pi$
$997$	−271.146	−	1011.93i	−0.271961	−	1.01497i	0.685889	−	0.727706i	$-0.259414\pi$
$998$	−494.208	+	132.423i	−0.495198	+	0.132688i
$999$	−62.6815	+	36.1892i	−0.0627443	+	0.0362254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.v.a.193.2	yes	32
5.2	odd	4	inner	210.3.v.a.67.8	yes	32
7.2	even	3	inner	210.3.v.a.163.8	yes	32
35.2	odd	12	inner	210.3.v.a.37.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.v.a.37.2	✓	32	35.2	odd	12	inner
210.3.v.a.67.8	yes	32	5.2	odd	4	inner
210.3.v.a.163.8	yes	32	7.2	even	3	inner
210.3.v.a.193.2	yes	32	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.25847 + 4.83903i) q^{5} +2.44949 q^{6} +(5.72194 - 4.03230i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(-1.36603 - 0.366025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.25847 + 4.83903i) q^{5} +2.44949 q^{6} +(5.72194 - 4.03230i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(3.49032 - 6.14961i) q^{10} +(-5.44212 + 9.42602i) q^{11} +(-3.34607 - 0.896575i) q^{12} +(-4.13640 - 4.13640i) q^{13} +(-9.29223 + 3.41385i) q^{14} +(-0.0638118 - 8.66002i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-0.489455 - 1.82667i) q^{17} +(-4.09808 + 1.09808i) q^{18} +(-27.1044 + 15.6487i) q^{19} +(-7.01877 + 7.12298i) q^{20} +(-7.76535 + 9.31124i) q^{21} +(10.8842 - 10.8842i) q^{22} +(-5.85291 + 21.8434i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-21.8325 - 12.1796i) q^{25} +(4.13640 + 7.16445i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(13.9430 - 1.26221i) q^{28} +35.4354i q^{29} +(-3.08262 + 11.8532i) q^{30} +(-7.10988 + 12.3147i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(4.87927 - 18.2097i) q^{33} +2.67443i q^{34} +(12.3115 + 32.7632i) q^{35} +6.00000 q^{36} +(13.4546 + 3.60515i) q^{37} +(42.7531 - 11.4557i) q^{38} +(8.77462 + 5.06603i) q^{39} +(12.1950 - 7.16112i) q^{40} -75.8676 q^{41} +(14.0158 - 9.87708i) q^{42} +(-5.54001 - 5.54001i) q^{43} +(-18.8520 + 10.8842i) q^{44} +(3.98894 + 14.4599i) q^{45} +(15.9904 - 27.6963i) q^{46} +(-89.5659 - 23.9991i) q^{47} +(-4.89898 - 4.89898i) q^{48} +(16.4811 - 46.1451i) q^{49} +(25.3657 + 24.6289i) q^{50} +(1.63775 + 2.83666i) q^{51} +(-3.02805 - 11.3008i) q^{52} +(73.5205 - 19.6998i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-38.7641 - 38.1970i) q^{55} +(-19.5085 - 3.37927i) q^{56} +(38.3314 - 38.3314i) q^{57} +(12.9703 - 48.4057i) q^{58} +(39.8083 + 22.9834i) q^{59} +(8.54949 - 15.0634i) q^{60} +(46.7047 + 80.8948i) q^{61} +(14.2198 - 14.2198i) q^{62} +(8.81757 - 19.0591i) q^{63} +8.00000i q^{64} +(25.2217 - 14.8106i) q^{65} +(-13.3304 + 23.0889i) q^{66} +(-6.47966 - 24.1824i) q^{67} +(0.978910 - 3.65334i) q^{68} -39.1684i q^{69} +(-4.82571 - 49.2617i) q^{70} +4.10846 q^{71} +(-8.19615 - 2.19615i) q^{72} +(94.5138 - 25.3249i) q^{73} +(-17.0598 - 9.84945i) q^{74} +(41.9864 + 10.5896i) q^{75} -62.5949 q^{76} +(6.86912 + 75.8794i) q^{77} +(-10.1321 - 10.1321i) q^{78} +(25.8988 - 14.9527i) q^{79} +(-19.2799 + 5.31859i) q^{80} +(4.50000 - 7.79423i) q^{81} +(103.637 + 27.7695i) q^{82} +(-42.2562 - 42.2562i) q^{83} +(-22.7612 + 8.36220i) q^{84} +(9.45529 - 0.0696718i) q^{85} +(5.54001 + 9.59557i) q^{86} +(-15.8853 - 59.2847i) q^{87} +(29.7363 - 7.96781i) q^{88} +(71.6953 - 41.3933i) q^{89} +(-0.156306 - 21.2126i) q^{90} +(-40.3474 - 6.98900i) q^{91} +(-31.9809 + 31.9809i) q^{92} +(6.37455 - 23.7901i) q^{93} +(113.565 + 65.5668i) q^{94} +(-41.6146 - 150.853i) q^{95} +(4.89898 + 8.48528i) q^{96} +(-60.0597 + 60.0597i) q^{97} +(-39.4039 + 57.0029i) q^{98} +32.6527i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 8 q^{7} - 64 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 8 * q^7 - 64 * q^8	\( 32 q - 16 q^{2} - 8 q^{7} - 64 q^{8} + 4 q^{10} - 32 q^{11} - 32 q^{13} + 64 q^{16} - 56 q^{17} - 48 q^{18} - 16 q^{20} - 48 q^{21} + 64 q^{22} - 48 q^{23} + 68 q^{25} + 32 q^{26} + 40 q^{28} + 12 q^{30} + 160 q^{31} + 64 q^{32} + 12 q^{33} + 152 q^{35} + 192 q^{36} + 44 q^{37} - 64 q^{38} + 8 q^{40} - 80 q^{41} - 48 q^{42} - 184 q^{43} - 12 q^{45} - 96 q^{46} - 228 q^{47} - 96 q^{50} + 192 q^{51} + 32 q^{52} + 48 q^{53} + 104 q^{55} + 32 q^{56} + 144 q^{57} - 112 q^{58} + 24 q^{60} + 216 q^{61} - 320 q^{62} + 84 q^{63} - 384 q^{65} + 24 q^{66} + 112 q^{68} - 24 q^{70} + 368 q^{71} - 96 q^{72} + 52 q^{73} + 48 q^{75} + 256 q^{76} - 836 q^{77} - 240 q^{78} + 144 q^{81} + 40 q^{82} - 736 q^{83} - 72 q^{85} + 184 q^{86} - 72 q^{87} + 64 q^{88} + 24 q^{90} + 216 q^{91} + 192 q^{92} - 216 q^{93} + 272 q^{95} - 408 q^{97} + 200 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 8 * q^7 - 64 * q^8 + 4 * q^10 - 32 * q^11 - 32 * q^13 + 64 * q^16 - 56 * q^17 - 48 * q^18 - 16 * q^20 - 48 * q^21 + 64 * q^22 - 48 * q^23 + 68 * q^25 + 32 * q^26 + 40 * q^28 + 12 * q^30 + 160 * q^31 + 64 * q^32 + 12 * q^33 + 152 * q^35 + 192 * q^36 + 44 * q^37 - 64 * q^38 + 8 * q^40 - 80 * q^41 - 48 * q^42 - 184 * q^43 - 12 * q^45 - 96 * q^46 - 228 * q^47 - 96 * q^50 + 192 * q^51 + 32 * q^52 + 48 * q^53 + 104 * q^55 + 32 * q^56 + 144 * q^57 - 112 * q^58 + 24 * q^60 + 216 * q^61 - 320 * q^62 + 84 * q^63 - 384 * q^65 + 24 * q^66 + 112 * q^68 - 24 * q^70 + 368 * q^71 - 96 * q^72 + 52 * q^73 + 48 * q^75 + 256 * q^76 - 836 * q^77 - 240 * q^78 + 144 * q^81 + 40 * q^82 - 736 * q^83 - 72 * q^85 + 184 * q^86 - 72 * q^87 + 64 * q^88 + 24 * q^90 + 216 * q^91 + 192 * q^92 - 216 * q^93 + 272 * q^95 - 408 * q^97 + 200 * q^98

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