LMFDB - Embedded newform 75.3.k.a.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(13,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			67.1
Character	$\chi$	$=$	75.67
Dual form			75.3.k.a.28.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47736 + 2.89947i) q^{2} +(0.270952 - 1.71073i) q^{3} +(-3.87323 - 5.33104i) q^{4} +(-3.93419 - 3.08579i) q^{5} +(4.55991 + 3.31297i) q^{6} +(-8.41509 - 8.41509i) q^{7} +(8.32297 - 1.31823i) q^{8} +(-2.85317 - 0.927051i) q^{9} +O(q^{10})$	\(q+(-1.47736 + 2.89947i) q^{2} +(0.270952 - 1.71073i) q^{3} +(-3.87323 - 5.33104i) q^{4} +(-3.93419 - 3.08579i) q^{5} +(4.55991 + 3.31297i) q^{6} +(-8.41509 - 8.41509i) q^{7} +(8.32297 - 1.31823i) q^{8} +(-2.85317 - 0.927051i) q^{9} +(14.7594 - 6.84828i) q^{10} +(4.07737 + 12.5489i) q^{11} +(-10.1694 + 5.18157i) q^{12} +(-2.42106 - 4.75160i) q^{13} +(36.8314 - 11.9672i) q^{14} +(-6.34493 + 5.89423i) q^{15} +(-0.328717 + 1.01169i) q^{16} +(0.874942 + 5.52417i) q^{17} +(6.90311 - 6.90311i) q^{18} +(2.03221 - 2.79710i) q^{19} +(-1.21246 + 32.9253i) q^{20} +(-16.6760 + 12.1158i) q^{21} +(-42.4088 - 6.71690i) q^{22} +(-34.7044 - 17.6828i) q^{23} -14.5955i q^{24} +(5.95576 + 24.2802i) q^{25} +17.3539 q^{26} +(-2.35900 + 4.62981i) q^{27} +(-12.2676 + 77.4547i) q^{28} +(-20.4329 - 28.1234i) q^{29} +(-7.71644 - 27.1048i) q^{30} +(6.74468 + 4.90030i) q^{31} +(21.3866 + 21.3866i) q^{32} +(22.5724 - 3.57512i) q^{33} +(-17.3098 - 5.62429i) q^{34} +(7.13936 + 59.0738i) q^{35} +(6.10883 + 18.8010i) q^{36} +(43.7136 - 22.2732i) q^{37} +(5.10782 + 10.0247i) q^{38} +(-8.78468 + 2.85432i) q^{39} +(-36.8120 - 20.4968i) q^{40} +(20.8683 - 64.2261i) q^{41} +(-10.4931 - 66.2510i) q^{42} +(-2.42347 + 2.42347i) q^{43} +(51.1059 - 70.3412i) q^{44} +(8.36423 + 12.4515i) q^{45} +(102.542 - 74.5008i) q^{46} +(-20.5685 - 3.25773i) q^{47} +(1.64165 + 0.836465i) q^{48} +92.6274i q^{49} +(-79.1986 - 18.6020i) q^{50} +9.68741 q^{51} +(-15.9537 + 31.3108i) q^{52} +(-6.91898 + 43.6847i) q^{53} +(-9.93891 - 13.6797i) q^{54} +(22.6820 - 61.9516i) q^{55} +(-81.1316 - 58.9455i) q^{56} +(-4.23445 - 4.23445i) q^{57} +(111.730 - 17.6963i) q^{58} +(10.2678 + 3.33622i) q^{59} +(55.9977 + 10.9954i) q^{60} +(10.8085 + 33.2652i) q^{61} +(-24.1726 + 12.3165i) q^{62} +(16.2085 + 31.8109i) q^{63} +(-97.6524 + 31.7292i) q^{64} +(-5.13754 + 26.1646i) q^{65} +(-22.9815 + 70.7299i) q^{66} +(-14.1735 - 89.4880i) q^{67} +(26.0607 - 26.0607i) q^{68} +(-39.6536 + 54.5786i) q^{69} +(-181.830 - 66.5726i) q^{70} +(-25.0754 + 18.2183i) q^{71} +(-24.9689 - 3.95469i) q^{72} +(-9.90535 - 5.04703i) q^{73} +159.652i q^{74} +(43.1505 - 3.60989i) q^{75} -22.7827 q^{76} +(71.2883 - 139.911i) q^{77} +(4.70209 - 29.6878i) q^{78} +(-69.0749 - 95.0734i) q^{79} +(4.41510 - 2.96582i) q^{80} +(7.28115 + 5.29007i) q^{81} +(155.392 + 155.392i) q^{82} +(-22.3462 + 3.53929i) q^{83} +(129.180 + 41.9731i) q^{84} +(13.6042 - 24.4330i) q^{85} +(-3.44646 - 10.6071i) q^{86} +(-53.6478 + 27.3349i) q^{87} +(50.4781 + 99.0689i) q^{88} +(25.3377 - 8.23270i) q^{89} +(-48.4597 + 5.85659i) q^{90} +(-19.6117 + 60.3586i) q^{91} +(40.1505 + 253.500i) q^{92} +(10.2106 - 10.2106i) q^{93} +(39.8327 - 54.8249i) q^{94} +(-16.6264 + 4.73335i) q^{95} +(42.3814 - 30.7919i) q^{96} +(169.907 + 26.9106i) q^{97} +(-268.571 - 136.844i) q^{98} -39.5840i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−1.47736	+	2.89947i	−0.738678	+	1.44974i	0.148791	+	0.988869i	$0.452462\pi$
$2$	−1.47736	+	2.89947i	−0.738678	+	1.44974i	−0.887469	+	0.460868i	$0.847538\pi$
$3$	0.270952	−	1.71073i	0.0903175	−	0.570242i
$3$	0.270952	−	1.71073i	0.0903175	−	0.570242i
$4$	−3.87323	−	5.33104i	−0.968307	−	1.33276i
$5$	−3.93419	−	3.08579i	−0.786839	−	0.617159i
$5$	−3.93419	−	3.08579i	−0.786839	−	0.617159i
$6$	4.55991	+	3.31297i	0.759985	+	0.552162i
$7$	−8.41509	−	8.41509i	−1.20216	−	1.20216i	−0.973510	−	0.228646i	$-0.926570\pi$
$7$	−8.41509	−	8.41509i	−1.20216	−	1.20216i	−0.228646	−	0.973510i	$-0.573430\pi$
$8$	8.32297	−	1.31823i	1.04037	−	0.164779i
$9$	−2.85317	−	0.927051i	−0.317019	−	0.103006i
$10$	14.7594	−	6.84828i	1.47594	−	0.684828i
$11$	4.07737	+	12.5489i	0.370670	+	1.14081i	0.946354	+	0.323133i	$0.104736\pi$
$11$	4.07737	+	12.5489i	0.370670	+	1.14081i	−0.575683	+	0.817673i	$0.695264\pi$
$12$	−10.1694	+	5.18157i	−0.847451	+	0.431798i
$13$	−2.42106	−	4.75160i	−0.186236	−	0.365508i	0.778945	−	0.627092i	$-0.215755\pi$
$13$	−2.42106	−	4.75160i	−0.186236	−	0.365508i	−0.965181	+	0.261584i	$0.915755\pi$
$14$	36.8314	−	11.9672i	2.63081	−	0.854803i
$15$	−6.34493	+	5.89423i	−0.422995	+	0.392948i
$16$	−0.328717	+	1.01169i	−0.0205448	+	0.0632305i
$17$	0.874942	+	5.52417i	0.0514672	+	0.324951i	0.999967	+	0.00817215i	$0.00260130\pi$
$17$	0.874942	+	5.52417i	0.0514672	+	0.324951i	−0.948499	+	0.316779i	$0.897399\pi$
$18$	6.90311	−	6.90311i	0.383506	−	0.383506i
$19$	2.03221	−	2.79710i	0.106959	−	0.147216i	−0.752182	−	0.658955i	$-0.770999\pi$
$19$	2.03221	−	2.79710i	0.106959	−	0.147216i	0.859141	+	0.511739i	$0.170999\pi$
$20$	−1.21246	+	32.9253i	−0.0606232	+	1.64627i
$21$	−16.6760	+	12.1158i	−0.794095	+	0.576944i
$22$	−42.4088	−	6.71690i	−1.92767	−	0.305313i
$23$	−34.7044	−	17.6828i	−1.50889	−	0.768817i	−0.512912	−	0.858441i	$-0.671433\pi$
$23$	−34.7044	−	17.6828i	−1.50889	−	0.768817i	−0.995976	+	0.0896248i	$0.971433\pi$
$24$		−	14.5955i		−	0.608146i
$25$	5.95576	+	24.2802i	0.238230	+	0.971209i
$26$	17.3539			0.667458
$27$	−2.35900	+	4.62981i	−0.0873705	+	0.171474i
$28$	−12.2676	+	77.4547i	−0.438129	+	2.76624i
$29$	−20.4329	−	28.1234i	−0.704582	−	0.969774i	−0.999897	−	0.0143737i	$-0.995425\pi$
$29$	−20.4329	−	28.1234i	−0.704582	−	0.969774i	0.295315	−	0.955400i	$-0.404575\pi$
$30$	−7.71644	−	27.1048i	−0.257215	−	0.903494i
$31$	6.74468	+	4.90030i	0.217570	+	0.158074i	0.691232	−	0.722633i	$-0.257068\pi$
$31$	6.74468	+	4.90030i	0.217570	+	0.158074i	−0.473662	+	0.880707i	$0.657068\pi$
$32$	21.3866	+	21.3866i	0.668332	+	0.668332i
$33$	22.5724	−	3.57512i	0.684013	−	0.108337i
$34$	−17.3098	−	5.62429i	−0.509111	−	0.165420i
$35$	7.13936	+	59.0738i	0.203982	+	1.68782i
$36$	6.10883	+	18.8010i	0.169690	+	0.522251i
$37$	43.7136	−	22.2732i	1.18145	−	0.601978i	0.250852	−	0.968025i	$-0.419289\pi$
$37$	43.7136	−	22.2732i	1.18145	−	0.601978i	0.930596	+	0.366047i	$0.119289\pi$
$38$	5.10782	+	10.0247i	0.134416	+	0.263807i
$39$	−8.78468	+	2.85432i	−0.225248	+	0.0731876i
$40$	−36.8120	−	20.4968i	−0.920299	−	0.512420i
$41$	20.8683	−	64.2261i	0.508984	−	1.56649i	−0.284985	−	0.958532i	$-0.591989\pi$
$41$	20.8683	−	64.2261i	0.508984	−	1.56649i	0.793969	−	0.607959i	$-0.208011\pi$
$42$	−10.4931	−	66.2510i	−0.249836	−	1.57741i
$43$	−2.42347	+	2.42347i	−0.0563598	+	0.0563598i	−0.734725	−	0.678365i	$-0.762689\pi$
$43$	−2.42347	+	2.42347i	−0.0563598	+	0.0563598i	0.678365	+	0.734725i	$0.262689\pi$
$44$	51.1059	−	70.3412i	1.16150	−	1.59866i
$45$	8.36423	+	12.4515i	0.185872	+	0.276700i
$46$	102.542	−	74.5008i	2.22916	−	1.61958i
$47$	−20.5685	−	3.25773i	−0.437627	−	0.0693133i	−0.0662664	−	0.997802i	$-0.521109\pi$
$47$	−20.5685	−	3.25773i	−0.437627	−	0.0693133i	−0.371361	+	0.928489i	$0.621109\pi$
$48$	1.64165	+	0.836465i	0.0342011	+	0.0174264i
$49$			92.6274i			1.89036i
$50$	−79.1986	−	18.6020i	−1.58397	−	0.372039i
$51$	9.68741			0.189949
$52$	−15.9537	+	31.3108i	−0.306801	+	0.602131i
$53$	−6.91898	+	43.6847i	−0.130547	+	0.824240i	0.832326	+	0.554286i	$0.187009\pi$
$53$	−6.91898	+	43.6847i	−0.130547	+	0.824240i	−0.962873	+	0.269954i	$0.912991\pi$
$54$	−9.93891	−	13.6797i	−0.184054	−	0.253328i
$55$	22.6820	−	61.9516i	0.412400	−	1.12639i
$56$	−81.1316	−	58.9455i	−1.44878	−	1.05260i
$57$	−4.23445	−	4.23445i	−0.0742885	−	0.0742885i
$58$	111.730	−	17.6963i	1.92638	−	0.305108i
$59$	10.2678	+	3.33622i	0.174031	+	0.0565460i	0.394736	−	0.918794i	$-0.370836\pi$
$59$	10.2678	+	3.33622i	0.174031	+	0.0565460i	−0.220705	+	0.975340i	$0.570836\pi$
$60$	55.9977	+	10.9954i	0.933295	+	0.183256i
$61$	10.8085	+	33.2652i	0.177189	+	0.545332i	0.999727	−	0.0233789i	$-0.00744242\pi$
$61$	10.8085	+	33.2652i	0.177189	+	0.545332i	−0.822538	+	0.568711i	$0.807442\pi$
$62$	−24.1726	+	12.3165i	−0.389880	+	0.198654i
$63$	16.2085	+	31.8109i	0.257277	+	0.504935i
$64$	−97.6524	+	31.7292i	−1.52582	+	0.495769i
$65$	−5.13754	+	26.1646i	−0.0790390	+	0.402533i
$66$	−22.9815	+	70.7299i	−0.348205	+	1.07167i
$67$	−14.1735	−	89.4880i	−0.211545	−	1.33564i	−0.833470	−	0.552565i	$-0.813649\pi$
$67$	−14.1735	−	89.4880i	−0.211545	−	1.33564i	0.621925	−	0.783077i	$-0.286351\pi$
$68$	26.0607	−	26.0607i	0.383246	−	0.383246i
$69$	−39.6536	+	54.5786i	−0.574690	+	0.790994i
$70$	−181.830	−	66.5726i	−2.59758	−	0.951038i
$71$	−25.0754	+	18.2183i	−0.353174	+	0.256596i	−0.750199	−	0.661212i	$-0.770043\pi$
$71$	−25.0754	+	18.2183i	−0.353174	+	0.256596i	0.397025	+	0.917808i	$0.370043\pi$
$72$	−24.9689	−	3.95469i	−0.346791	−	0.0549262i
$73$	−9.90535	−	5.04703i	−0.135690	−	0.0691374i	0.384828	−	0.922988i	$-0.374261\pi$
$73$	−9.90535	−	5.04703i	−0.135690	−	0.0691374i	−0.520517	+	0.853851i	$0.674261\pi$
$74$			159.652i			2.15746i
$75$	43.1505	−	3.60989i	0.575340	−	0.0481318i
$76$	−22.7827			−0.299772
$77$	71.2883	−	139.911i	0.925822	−	1.81703i
$78$	4.70209	−	29.6878i	0.0602831	−	0.380613i
$79$	−69.0749	−	95.0734i	−0.874366	−	1.20346i	−0.977950	−	0.208840i	$-0.933031\pi$
$79$	−69.0749	−	95.0734i	−0.874366	−	1.20346i	0.103584	−	0.994621i	$-0.466969\pi$
$80$	4.41510	−	2.96582i	0.0551887	−	0.0370728i
$81$	7.28115	+	5.29007i	0.0898908	+	0.0653095i
$82$	155.392	+	155.392i	1.89502	+	1.89502i
$83$	−22.3462	+	3.53929i	−0.269232	+	0.0426421i	−0.289590	−	0.957151i	$-0.593519\pi$
$83$	−22.3462	+	3.53929i	−0.269232	+	0.0426421i	0.0203589	+	0.999793i	$0.493519\pi$
$84$	129.180	+	41.9731i	1.53786	+	0.499680i
$85$	13.6042	−	24.4330i	0.160050	−	0.287447i
$86$	−3.44646	−	10.6071i	−0.0400751	−	0.123339i
$87$	−53.6478	+	27.3349i	−0.616642	+	0.314195i
$88$	50.4781	+	99.0689i	0.573615	+	1.12578i
$89$	25.3377	−	8.23270i	0.284693	−	0.0925023i	−0.163190	−	0.986595i	$-0.552178\pi$
$89$	25.3377	−	8.23270i	0.284693	−	0.0925023i	0.447883	+	0.894092i	$0.352178\pi$
$90$	−48.4597	+	5.85659i	−0.538441	+	0.0650733i
$91$	−19.6117	+	60.3586i	−0.215513	+	0.663281i
$92$	40.1505	+	253.500i	0.436418	+	2.75543i
$93$	10.2106	−	10.2106i	0.109791	−	0.109791i
$94$	39.8327	−	54.8249i	0.423752	−	0.583244i
$95$	−16.6264	+	4.73335i	−0.175015	+	0.0498248i
$96$	42.3814	−	30.7919i	0.441473	−	0.320749i
$97$	169.907	+	26.9106i	1.75162	+	0.277429i	0.948127	−	0.317891i	$-0.102975\pi$
$97$	169.907	+	26.9106i	1.75162	+	0.277429i	0.803489	+	0.595320i	$0.202975\pi$
$98$	−268.571	−	136.844i	−2.74052	−	1.39636i
$99$		−	39.5840i		−	0.399838i
$100$	106.371	−	125.793i	1.06371	−	1.25793i
$101$	53.6633			0.531320			0.265660	−	0.964067i	$-0.414410\pi$
$101$	53.6633			0.531320			0.265660	+	0.964067i	$0.414410\pi$
$102$	−14.3117	+	28.0884i	−0.140311	+	0.275376i
$103$	1.79109	−	11.3085i	0.0173892	−	0.109791i	−0.977467	−	0.211088i	$-0.932299\pi$
$103$	1.79109	−	11.3085i	0.0173892	−	0.109791i	0.994856	+	0.101297i	$0.0322992\pi$
$104$	−26.4141	−	36.3559i	−0.253982	−	0.349576i
$105$	102.994	+	3.79270i	0.980891	+	0.0361210i
$106$	−116.441	−	84.5992i	−1.09850	−	0.798106i
$107$	−123.048	−	123.048i	−1.14998	−	1.14998i	−0.986556	−	0.163426i	$-0.947745\pi$
$107$	−123.048	−	123.048i	−1.14998	−	1.14998i	−0.163426	−	0.986556i	$-0.552255\pi$
$108$	33.8186	−	5.35634i	0.313135	−	0.0495958i
$109$	−71.4191	−	23.2055i	−0.655221	−	0.212894i	−0.0375064	−	0.999296i	$-0.511941\pi$
$109$	−71.4191	−	23.2055i	−0.655221	−	0.212894i	−0.617715	+	0.786402i	$0.711941\pi$
$110$	146.118	+	157.290i	1.32834	+	1.42991i
$111$	−26.2590	−	80.8170i	−0.236568	−	0.728081i
$112$	11.2796	−	5.74726i	0.100711	−	0.0513148i
$113$	27.7020	+	54.3682i	0.245150	+	0.481135i	0.980491	−	0.196563i	$-0.0629780\pi$
$113$	27.7020	+	54.3682i	0.245150	+	0.481135i	−0.735341	+	0.677697i	$0.762978\pi$
$114$	18.5334	−	6.02188i	0.162574	−	0.0528235i
$115$	81.9685	+	176.658i	0.712769	+	1.53616i
$116$	−70.7860	+	217.857i	−0.610224	+	1.87808i
$117$	2.50272	+	15.8016i	0.0213908	+	0.135056i
$118$	−24.8425	+	24.8425i	−0.210530	+	0.210530i
$119$	39.1236	−	53.8491i	0.328770	−	0.452513i
$120$	−45.0387	+	57.4216i	−0.375323	+	0.478513i
$121$	−42.9579	+	31.2107i	−0.355024	+	0.257940i
$122$	−112.420	−	17.8055i	−0.921473	−	0.145947i
$123$	−104.219	−	53.1022i	−0.847309	−	0.431725i
$124$		−	54.9361i		−	0.443033i
$125$	51.4926	−	113.901i	0.411941	−	0.911210i
$126$	−116.180			−0.922067
$127$	−48.5097	+	95.2056i	−0.381966	+	0.749651i	−0.999314	−	0.0370399i	$-0.988207\pi$
$127$	−48.5097	+	95.2056i	−0.381966	+	0.749651i	0.617348	+	0.786690i	$0.288207\pi$
$128$	33.3438	−	210.524i	0.260498	−	1.64472i
$129$	3.48925	+	4.80254i	0.0270484	+	0.0372290i
$130$	−68.2737	−	53.5506i	−0.525182	−	0.411928i
$131$	−134.006	−	97.3611i	−1.02295	−	0.743214i	−0.0560617	−	0.998427i	$-0.517854\pi$
$131$	−134.006	−	97.3611i	−1.02295	−	0.743214i	−0.966885	+	0.255213i	$0.917854\pi$
$132$	−106.487	−	106.487i	−0.806722	−	0.806722i
$133$	−40.6391	+	6.43661i	−0.305557	+	0.0483955i
$134$	280.407	+	91.1098i	2.09259	+	0.679924i
$135$	23.5674	−	10.9352i	0.174573	−	0.0810011i
$136$	14.5642	+	44.8241i	0.107090	+	0.329589i
$137$	22.0971	−	11.2590i	0.161293	−	0.0821827i	−0.371481	−	0.928441i	$-0.621150\pi$
$137$	22.0971	−	11.2590i	0.161293	−	0.0821827i	0.532773	+	0.846258i	$0.321150\pi$
$138$	−99.6666	−	195.607i	−0.722221	−	1.41744i
$139$	−188.491	+	61.2443i	−1.35605	+	0.440606i	−0.894722	−	0.446624i	$-0.852626\pi$
$139$	−188.491	+	61.2443i	−1.35605	+	0.440606i	−0.461326	+	0.887231i	$0.652626\pi$
$140$	287.272	−	266.866i	2.05195	−	1.90619i
$141$	−11.1462	+	34.3044i	−0.0790508	+	0.243293i
$142$	−15.7783	−	99.6203i	−0.111115	−	0.701551i
$143$	49.7556	−	49.7556i	0.347941	−	0.347941i
$144$	1.87577	−	2.58178i	0.0130262	−	0.0179290i
$145$	−6.39625	+	173.695i	−0.0441120	+	1.19789i
$146$	29.2674	−	21.2640i	0.200462	−	0.145644i
$147$	158.460	+	25.0976i	1.07796	+	0.170732i
$148$	−288.052	−	146.770i	−1.94630	−	0.991687i
$149$		−	135.893i		−	0.912035i	−0.889971	−	0.456017i	$-0.849276\pi$
$149$		−	135.893i		−	0.912035i	0.889971	−	0.456017i	$-0.150724\pi$
$150$	−53.2819	+	130.447i	−0.355213	+	0.869646i
$151$	120.689			0.799264			0.399632	−	0.916676i	$-0.369138\pi$
$151$	120.689			0.799264			0.399632	+	0.916676i	$0.369138\pi$
$152$	13.2268	−	25.9591i	0.0870187	−	0.170784i
$153$	2.62483	−	16.5725i	0.0171557	−	0.108317i
$154$	300.351	+	413.397i	1.95033	+	2.68440i
$155$	−11.4136	−	40.0914i	−0.0736360	−	0.258654i
$156$	49.2415	+	35.7761i	0.315651	+	0.229334i
$157$	59.7667	+	59.7667i	0.380680	+	0.380680i	0.871347	−	0.490667i	$-0.163247\pi$
$157$	59.7667	+	59.7667i	0.380680	+	0.380680i	−0.490667	+	0.871347i	$0.663247\pi$
$158$	377.711	−	59.8235i	2.39058	−	0.378630i
$159$	72.8579	+	23.6730i	0.458226	+	0.148887i
$160$	−18.1444	−	150.134i	−0.113403	−	0.938337i
$161$	143.239	+	440.843i	0.889680	+	2.73815i
$162$	−26.0953	+	13.2962i	−0.161082	+	0.0820753i
$163$	−39.2824	−	77.0961i	−0.240997	−	0.472983i	0.738550	−	0.674198i	$-0.235511\pi$
$163$	−39.2824	−	77.0961i	−0.240997	−	0.472983i	−0.979547	+	0.201216i	$0.935511\pi$
$164$	−423.220	+	137.512i	−2.58061	+	0.838490i
$165$	−99.8364	−	55.5887i	−0.605069	−	0.336901i
$166$	22.7512	−	70.0211i	0.137056	−	0.421814i
$167$	12.0497	+	76.0789i	0.0721539	+	0.455562i	0.997141	+	0.0755634i	$0.0240755\pi$
$167$	12.0497	+	76.0789i	0.0721539	+	0.455562i	−0.924987	+	0.379999i	$0.875924\pi$
$168$	−122.822	+	122.822i	−0.731086	+	0.731086i
$169$	82.6195	−	113.716i	0.488873	−	0.672876i
$170$	50.7446	+	75.5414i	0.298498	+	0.444361i
$171$	−8.39131	+	6.09664i	−0.0490720	+	0.0356529i
$172$	22.3063	+	3.53297i	0.129688	+	0.0205405i
$173$	189.844	+	96.7302i	1.09736	+	0.559134i	0.906382	−	0.422460i	$-0.138833\pi$
$173$	189.844	+	96.7302i	1.09736	+	0.559134i	0.190981	+	0.981594i	$0.438833\pi$
$174$		−	195.934i		−	1.12606i
$175$	154.202	−	254.438i	0.881154	−	1.45393i
$176$	−14.0358			−0.0797491
$177$	8.48944	−	16.6615i	0.0479630	−	0.0941326i
$178$	−13.5622	+	85.6285i	−0.0761923	+	0.481059i
$179$	−49.0151	−	67.4634i	−0.273827	−	0.376891i	0.649850	−	0.760063i	$-0.274832\pi$
$179$	−49.0151	−	67.4634i	−0.273827	−	0.376891i	−0.923677	+	0.383172i	$0.874832\pi$
$180$	33.9828	−	92.8175i	0.188793	−	0.515653i
$181$	−148.561	−	107.936i	−0.820778	−	0.596330i	0.0961569	−	0.995366i	$-0.469345\pi$
$181$	−148.561	−	107.936i	−0.820778	−	0.596330i	−0.916935	+	0.399036i	$0.869345\pi$
$182$	−146.035	−	146.035i	−0.802389	−	0.802389i
$183$	59.8363	−	9.47714i	0.326974	−	0.0517877i
$184$	−312.154	−	101.425i	−1.69649	−	0.551222i
$185$	−240.708	−	47.2641i	−1.30113	−	0.255482i
$186$	14.5206	+	44.6899i	0.0780679	+	0.240268i
$187$	−65.7545	+	33.5036i	−0.351629	+	0.179164i
$188$	62.2993	+	122.269i	0.331379	+	0.650368i
$189$	58.8115	−	19.1090i	0.311172	−	0.101106i
$190$	10.8389	−	55.2007i	0.0570468	−	0.290530i
$191$	0.850722	−	2.61825i	0.00445404	−	0.0137081i	−0.948805	−	0.315863i	$-0.897706\pi$
$191$	0.850722	−	2.61825i	0.00445404	−	0.0137081i	0.953259	+	0.302155i	$0.0977060\pi$
$192$	27.8208	+	175.654i	0.144900	+	0.914863i
$193$	−156.688	+	156.688i	−0.811854	+	0.811854i	−0.984912	−	0.173057i	$-0.944635\pi$
$193$	−156.688	+	156.688i	−0.811854	+	0.811854i	0.173057	+	0.984912i	$0.444635\pi$
$194$	−329.039	+	452.884i	−1.69608	+	2.33445i
$195$	43.3685	+	15.8783i	0.222402	+	0.0814271i
$196$	493.800	−	358.767i	2.51939	−	1.83044i
$197$	−76.0984	−	12.0528i	−0.386286	−	0.0611817i	−0.0397288	−	0.999210i	$-0.512649\pi$
$197$	−76.0984	−	12.0528i	−0.386286	−	0.0611817i	−0.346557	+	0.938029i	$0.612649\pi$
$198$	114.773	+	58.4796i	0.579660	+	0.295351i
$199$			205.173i			1.03102i	0.856883	+	0.515511i	$0.172398\pi$
$199$			205.173i			1.03102i	−0.856883	+	0.515511i	$0.827602\pi$
$200$	81.5765	+	194.233i	0.407883	+	0.971163i
$201$	−156.930			−0.780745
$202$	−79.2798	+	155.595i	−0.392474	+	0.770274i
$203$	−64.7168	+	408.606i	−0.318802	+	2.01284i
$204$	−37.5215	−	51.6439i	−0.183929	−	0.253157i
$205$	−280.289	+	188.283i	−1.36726	+	0.918452i
$206$	30.1427	+	21.8999i	0.146324	+	0.106310i
$207$	82.6247	+	82.6247i	0.399153	+	0.399153i
$208$	5.60298	−	0.887426i	0.0269374	−	0.00426647i
$209$	43.3866	+	14.0971i	0.207591	+	0.0674505i
$210$	−163.155	+	293.024i	−0.776928	+	1.39535i
$211$	−108.709	−	334.571i	−0.515207	−	1.58564i	−0.782906	−	0.622140i	$-0.786263\pi$
$211$	−108.709	−	334.571i	−0.515207	−	1.58564i	0.267699	−	0.963503i	$-0.413737\pi$
$212$	259.684	−	132.315i	1.22492	−	0.624129i
$213$	24.3723	+	47.8334i	0.114424	+	0.224570i
$214$	538.560	−	174.989i	2.51664	−	0.817705i
$215$	17.0127	−	2.05607i	0.0791290	−	0.00956313i
$216$	−13.5308	+	41.6435i	−0.0626425	+	0.192794i
$217$	−15.5207	−	97.9936i	−0.0715238	−	0.451583i
$218$	172.795	−	172.795i	0.792638	−	0.792638i
$219$	−11.3180	+	15.5778i	−0.0516802	+	0.0711317i
$220$	−418.119	+	119.034i	−1.90054	+	0.541062i
$221$	24.1304	−	17.5317i	0.109187	−	0.0793291i
$222$	273.121	+	43.2580i	1.23027	+	0.194856i
$223$	301.977	+	153.865i	1.35416	+	0.689978i	0.972189	−	0.234197i	$-0.0752461\pi$
$223$	301.977	+	153.865i	1.35416	+	0.689978i	0.381969	+	0.924175i	$0.375246\pi$
$224$		−	359.941i		−	1.60688i
$225$	5.51622	−	74.7969i	0.0245165	−	0.332431i
$226$	−198.565			−0.878606
$227$	69.7971	−	136.985i	0.307476	−	0.603456i	−0.684625	−	0.728895i	$-0.740034\pi$
$227$	69.7971	−	136.985i	0.307476	−	0.603456i	0.992101	+	0.125439i	$0.0400340\pi$
$228$	−6.17303	+	38.9750i	−0.0270747	+	0.170943i
$229$	45.6600	+	62.8456i	0.199389	+	0.274435i	0.896990	−	0.442052i	$-0.145749\pi$
$229$	45.6600	+	62.8456i	0.199389	+	0.274435i	−0.697601	+	0.716486i	$0.745749\pi$
$230$	−633.312	−	23.3215i	−2.75353	−	0.101398i
$231$	−220.034	−	159.864i	−0.952528	−	0.692052i
$232$	−207.135	−	207.135i	−0.892825	−	0.892825i
$233$	−239.621	+	37.9522i	−1.02842	+	0.162885i	−0.647770	−	0.761836i	$-0.724298\pi$
$233$	−239.621	+	37.9522i	−1.02842	+	0.162885i	−0.380646	+	0.924721i	$0.624298\pi$
$234$	−49.5137	−	16.0880i	−0.211597	−	0.0687520i
$235$	70.8677	+	76.2866i	0.301565	+	0.324624i
$236$	−21.9841	−	67.6600i	−0.0931529	−	0.286695i
$237$	−181.361	+	92.4078i	−0.765235	+	0.389907i
$238$	98.3344	+	192.992i	0.413170	+	0.810891i
$239$	190.478	−	61.8902i	0.796981	−	0.258955i	0.117907	−	0.993025i	$-0.462382\pi$
$239$	190.478	−	61.8902i	0.796981	−	0.258955i	0.679074	+	0.734070i	$0.262382\pi$
$240$	−3.87743	−	8.35662i	−0.0161560	−	0.0348193i
$241$	−10.0363	+	30.8886i	−0.0416445	+	0.128169i	−0.969717	−	0.244230i	$-0.921465\pi$
$241$	−10.0363	+	30.8886i	−0.0416445	+	0.128169i	0.928073	+	0.372399i	$0.121465\pi$
$242$	−27.0306	−	170.665i	−0.111697	−	0.705225i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$	135.474	−	186.464i	0.555223	−	0.764199i
$245$	285.829	−	364.414i	1.16665	−	1.48741i
$246$	307.937	−	223.729i	1.25178	−	0.909469i
$247$	−18.2108	−	2.88431i	−0.0737281	−	0.0116774i
$248$	62.5956	+	31.8940i	0.252401	+	0.128605i
$249$			39.1872i			0.157379i
$250$	254.181	+	317.574i	1.01672	+	1.27030i
$251$	−51.5646			−0.205437			−0.102718	−	0.994710i	$-0.532754\pi$
$251$	−51.5646			−0.205437			−0.102718	+	0.994710i	$0.532754\pi$
$252$	106.806	−	209.619i	0.423834	−	0.831820i
$253$	80.3960	−	507.600i	0.317771	−	2.00632i
$254$	−204.380	−	281.305i	−0.804646	−	1.10750i
$255$	−38.1121	−	29.8933i	−0.149459	−	0.117229i
$256$	228.877	+	166.289i	0.894049	+	0.649565i
$257$	125.184	+	125.184i	0.487096	+	0.487096i	0.907389	−	0.420293i	$-0.138073\pi$
$257$	125.184	+	125.184i	0.487096	+	0.487096i	−0.420293	+	0.907389i	$0.638073\pi$
$258$	−19.0797	+	3.02193i	−0.0739523	+	0.0117129i
$259$	−555.285	−	180.423i	−2.14396	−	0.696613i
$260$	159.383	−	73.9531i	0.613013	−	0.284435i
$261$	32.2266	+	99.1832i	0.123474	+	0.380012i
$262$	480.270	−	244.710i	1.83309	−	0.934007i
$263$	197.754	+	388.114i	0.751916	+	1.47572i	0.875414	+	0.483374i	$0.160589\pi$
$263$	197.754	+	388.114i	0.751916	+	1.47572i	−0.123498	+	0.992345i	$0.539411\pi$
$264$	183.157	−	59.5113i	0.693776	−	0.225422i
$265$	162.023	−	150.514i	0.611406	−	0.567976i
$266$	41.3757	−	127.341i	0.155548	−	0.478727i
$267$	−7.21860	−	45.5765i	−0.0270360	−	0.170698i
$268$	−422.167	+	422.167i	−1.57525	+	1.57525i
$269$	110.459	−	152.033i	0.410627	−	0.565180i	−0.552744	−	0.833351i	$-0.686419\pi$
$269$	110.459	−	152.033i	0.410627	−	0.565180i	0.963371	+	0.268171i	$0.0864193\pi$
$270$	−3.11125	+	84.4882i	−0.0115231	+	0.312919i
$271$	−257.811	+	187.311i	−0.951332	+	0.691183i	−0.951122	−	0.308817i	$-0.900067\pi$
$271$	−257.811	+	187.311i	−0.951332	+	0.691183i	−0.000210513		1.00000i	$0.500067\pi$
$272$	−5.87634	−	0.930721i	−0.0216042	−	0.00342177i
$273$	97.9432	+	49.9046i	0.358766	+	0.182801i
$274$			80.7035i			0.294538i
$275$	−280.405	+	173.737i	−1.01966	+	0.631772i
$276$	444.548			1.61068
$277$	−10.1546	+	19.9296i	−0.0366593	+	0.0719480i	−0.908610	−	0.417646i	$-0.862855\pi$
$277$	−10.1546	+	19.9296i	−0.0366593	+	0.0719480i	0.871950	+	0.489594i	$0.162855\pi$
$278$	100.891	−	637.003i	0.362919	−	2.29138i
$279$	−14.7009	−	20.2341i	−0.0526914	−	0.0725235i
$280$	137.294	+	482.258i	0.490334	+	1.72235i
$281$	−54.7113	−	39.7501i	−0.194702	−	0.141459i	0.486163	−	0.873868i	$-0.338396\pi$
$281$	−54.7113	−	39.7501i	−0.194702	−	0.141459i	−0.680865	+	0.732409i	$0.738396\pi$
$282$	−82.9977	−	82.9977i	−0.294318	−	0.294318i
$283$	169.336	−	26.8201i	0.598359	−	0.0947708i	0.150095	−	0.988672i	$-0.452042\pi$
$283$	169.336	−	26.8201i	0.598359	−	0.0947708i	0.448265	+	0.893901i	$0.352042\pi$
$284$	194.245	+	63.1141i	0.683962	+	0.222233i
$285$	3.59250	+	29.7258i	0.0126053	+	0.104301i
$286$	70.7584	+	217.772i	0.247407	+	0.761440i
$287$	−716.077	+	364.860i	−2.49504	+	1.27129i
$288$	−41.1932	−	80.8462i	−0.143032	−	0.280716i
$289$	245.104	−	79.6393i	0.848112	−	0.275568i
$290$	−494.174	−	275.155i	−1.70405	−	0.948809i
$291$	92.0733	−	283.373i	0.316403	−	0.973789i
$292$	11.4598	+	72.3541i	0.0392458	+	0.247788i
$293$	−196.949	+	196.949i	−0.672180	+	0.672180i	−0.958218	−	0.286038i	$-0.907662\pi$
$293$	−196.949	+	196.949i	−0.672180	+	0.672180i	0.286038	+	0.958218i	$0.407662\pi$
$294$	−306.872	+	422.373i	−1.04378	+	1.43664i
$295$	−30.1007	−	44.8097i	−0.102036	−	0.151897i
$296$	334.466	−	243.004i	1.12995	−	0.820958i
$297$	−67.7173	−	10.7254i	−0.228004	−	0.0361124i
$298$	394.019	+	200.763i	1.32221	+	0.673700i
$299$			207.713i			0.694691i
$300$	−186.376	−	216.055i	−0.621254	−	0.720184i
$301$	40.7874			0.135506
$302$	−178.300	+	349.934i	−0.590398	+	1.15872i
$303$	14.5402	−	91.8033i	0.0479875	−	0.302981i
$304$	2.16177	+	2.97542i	0.00711109	+	0.00978758i
$305$	60.1268	−	164.225i	0.197137	−	0.538442i
$306$	44.1737	+	32.0941i	0.144359	+	0.104883i
$307$	224.021	+	224.021i	0.729709	+	0.729709i	0.970562	−	0.240853i	$-0.0774271\pi$
$307$	224.021	+	224.021i	0.729709	+	0.729709i	−0.240853	+	0.970562i	$0.577427\pi$
$308$	−1021.99	+	161.867i	−3.31814	+	0.525542i
$309$	−18.8605	−	6.12814i	−0.0610371	−	0.0198322i
$310$	133.106	+	26.1359i	0.429374	+	0.0843095i
$311$	−11.4037	−	35.0970i	−0.0366679	−	0.112852i	0.931047	−	0.364899i	$-0.118896\pi$
$311$	−11.4037	−	35.0970i	−0.0366679	−	0.112852i	−0.967715	+	0.252047i	$0.918896\pi$
$312$	−69.3520	+	35.3366i	−0.222282	+	0.113258i
$313$	−49.4635	−	97.0775i	−0.158030	−	0.310152i	0.798392	−	0.602137i	$-0.205684\pi$
$313$	−49.4635	−	97.0775i	−0.158030	−	0.310152i	−0.956423	+	0.291986i	$0.905684\pi$
$314$	−261.589	+	84.9954i	−0.833085	+	0.270686i
$315$	34.3946	−	175.166i	0.109189	−	0.556083i
$316$	−239.297	+	736.482i	−0.757270	+	2.33064i
$317$	−94.9910	−	599.750i	−0.299656	−	1.89195i	−0.433826	−	0.900997i	$-0.642837\pi$
$317$	−94.9910	−	599.750i	−0.299656	−	1.89195i	0.134170	−	0.990958i	$-0.457163\pi$
$318$	−176.276	+	176.276i	−0.554327	+	0.554327i
$319$	269.605	−	371.079i	0.845156	−	1.16326i
$320$	482.093	+	176.506i	1.50654	+	0.551582i
$321$	−243.842	+	177.161i	−0.759632	+	0.551905i
$322$	−1489.83	−	235.965i	−4.62679	−	0.732812i
$323$	17.2297	+	8.77899i	0.0533428	+	0.0271795i
$324$		−	59.3057i		−	0.183042i
$325$	100.951	−	87.0833i	0.310617	−	0.267949i
$326$	281.572			0.863719
$327$	−59.0494	+	115.891i	−0.180579	+	0.354407i
$328$	89.0218	−	562.062i	0.271408	−	1.71360i
$329$	145.672	+	200.500i	0.442771	+	0.609421i
$330$	308.672	−	207.349i	0.935369	−	0.628330i
$331$	462.408	+	335.959i	1.39700	+	1.01498i	0.995055	+	0.0993209i	$0.0316670\pi$
$331$	462.408	+	335.959i	1.39700	+	1.01498i	0.401949	+	0.915662i	$0.368333\pi$
$332$	105.420	+	105.420i	0.317530	+	0.317530i
$333$	−145.371	+	23.0244i	−0.436549	+	0.0691425i
$334$	−238.390	−	77.4577i	−0.713743	−	0.231909i
$335$	−220.380	+	395.799i	−0.657851	+	1.18149i
$336$	−6.77574	−	20.8536i	−0.0201659	−	0.0620643i
$337$	47.8283	−	24.3697i	0.141924	−	0.0723138i	−0.381587	−	0.924333i	$-0.624622\pi$
$337$	47.8283	−	24.3697i	0.141924	−	0.0723138i	0.523510	+	0.852019i	$0.324622\pi$
$338$	207.658	+	407.552i	0.614373	+	1.20578i
$339$	100.515	−	32.6593i	0.296505	−	0.0963402i
$340$	−182.946	+	22.1099i	−0.538076	+	0.0650291i
$341$	−33.9926	+	104.618i	−0.0996850	+	0.306799i
$342$	−5.28011	−	33.3373i	−0.0154389	−	0.0974775i
$343$	367.129	−	367.129i	1.07035	−	1.07035i
$344$	−16.9758	+	23.3652i	−0.0493482	+	0.0679220i
$345$	324.423	−	92.3596i	0.940357	−	0.267709i
$346$	−560.933	+	407.542i	−1.62119	+	1.17787i
$347$	295.559	+	46.8119i	0.851754	+	0.134905i	0.567022	−	0.823702i	$-0.308095\pi$
$347$	295.559	+	46.8119i	0.851754	+	0.134905i	0.284732	+	0.958607i	$0.408095\pi$
$348$	353.514	+	180.124i	1.01584	+	0.517599i
$349$		−	74.9026i		−	0.214621i	−0.994226	−	0.107310i	$-0.965776\pi$
$349$		−	74.9026i		−	0.214621i	0.994226	−	0.107310i	$-0.0342238\pi$
$350$	509.926	+	823.000i	1.45693	+	2.35143i
$351$	27.7103			0.0789467
$352$	−181.177	+	355.579i	−0.514706	+	1.01017i
$353$	94.6843	−	597.813i	0.268228	−	1.69352i	−0.374339	−	0.927292i	$-0.622130\pi$
$353$	94.6843	−	597.813i	0.268228	−	1.69352i	0.642566	−	0.766230i	$-0.277870\pi$
$354$	35.7676	+	49.2298i	0.101038	+	0.139067i
$355$	154.869	+	5.70301i	0.436252	+	0.0160648i
$356$	−142.027	−	103.189i	−0.398953	−	0.289856i
$357$	−81.5204	−	81.5204i	−0.228348	−	0.228348i
$358$	268.021	−	42.4504i	0.748662	−	0.118576i
$359$	225.117	+	73.1449i	0.627066	+	0.203746i	0.605275	−	0.796016i	$-0.293063\pi$
$359$	225.117	+	73.1449i	0.627066	+	0.203746i	0.0217912	+	0.999763i	$0.493063\pi$
$360$	86.0292	+	92.6074i	0.238970	+	0.257243i
$361$	107.861	+	331.963i	0.298785	+	0.919564i
$362$	532.434	−	271.289i	1.47081	−	0.749417i
$363$	41.7535	+	81.9458i	0.115023	+	0.225746i
$364$	397.735	−	129.232i	1.09268	−	0.355032i
$365$	23.3955	+	50.4218i	0.0640972	+	0.138142i
$366$	−60.9208	+	187.495i	−0.166450	+	0.512281i
$367$	−61.0015	−	385.148i	−0.166217	−	1.04945i	−0.919883	−	0.392193i	$-0.871716\pi$
$367$	−61.0015	−	385.148i	−0.166217	−	1.04945i	0.753666	−	0.657257i	$-0.228284\pi$
$368$	29.2974	−	29.2974i	0.0796125	−	0.0796125i
$369$	−119.082	+	163.902i	−0.322715	+	0.444179i
$370$	492.653	−	628.101i	1.33149	−	1.69757i
$371$	425.834	−	309.387i	1.14780	−	0.833927i
$372$	−93.9807	−	14.8851i	−0.252636	−	0.0400137i
$373$	−340.970	−	173.733i	−0.914128	−	0.465772i	−0.0673572	−	0.997729i	$-0.521457\pi$
$373$	−340.970	−	173.733i	−0.914128	−	0.465772i	−0.846771	+	0.531957i	$0.821457\pi$
$374$		−	240.150i		−	0.642113i
$375$	−180.902	−	118.952i	−0.482405	−	0.317204i
$376$	−175.485			−0.466716
$377$	−84.1621	+	165.177i	−0.223242	+	0.438137i
$378$	−31.4794	+	198.753i	−0.0832788	+	0.525802i
$379$	107.748	+	148.303i	0.284296	+	0.391300i	0.927151	−	0.374688i	$-0.122250\pi$
$379$	107.748	+	148.303i	0.284296	+	0.391300i	−0.642855	+	0.765988i	$0.722250\pi$
$380$	89.6315	+	70.3027i	0.235872	+	0.185007i
$381$	149.727	+	108.783i	0.392984	+	0.285520i
$382$	6.33473	+	6.33473i	0.0165831	+	0.0165831i
$383$	188.495	−	29.8547i	0.492154	−	0.0779495i	0.0945755	−	0.995518i	$-0.469851\pi$
$383$	188.495	−	29.8547i	0.492154	−	0.0779495i	0.397578	+	0.917568i	$0.369851\pi$
$384$	−351.115	−	114.084i	−0.914361	−	0.297094i
$385$	−712.199	+	330.457i	−1.84987	+	0.858329i
$386$	−222.829	−	685.796i	−0.577276	−	1.77667i
$387$	9.16125	−	4.66789i	0.0236725	−	0.0120617i
$388$	−514.626	−	1010.01i	−1.32636	−	2.60312i
$389$	542.117	−	176.145i	1.39362	−	0.452814i	0.486496	−	0.873683i	$-0.338275\pi$
$389$	542.117	−	176.145i	1.39362	−	0.452814i	0.907121	+	0.420869i	$0.138275\pi$
$390$	−110.109	+	102.288i	−0.282332	+	0.262277i
$391$	67.3183	−	207.184i	0.172170	−	0.529883i
$392$	122.104	+	770.936i	0.311490	+	1.96667i
$393$	−202.867	+	202.867i	−0.516202	+	0.516202i
$394$	147.371	−	202.839i	0.374038	−	0.514820i
$395$	−21.6230	+	587.188i	−0.0547418	+	1.48655i
$396$	−211.024	+	153.318i	−0.532888	+	0.387166i
$397$	501.500	+	79.4298i	1.26322	+	0.200075i	0.751880	−	0.659300i	$-0.229147\pi$
$397$	501.500	+	79.4298i	1.26322	+	0.200075i	0.511345	+	0.859375i	$0.329147\pi$
$398$	−594.895	−	303.114i	−1.49471	−	0.761593i
$399$			71.2665i			0.178613i
$400$	−26.5218	−	1.95596i	−0.0663044	−	0.00488991i
$401$	−308.251			−0.768707			−0.384353	−	0.923186i	$-0.625576\pi$
$401$	−308.251			−0.768707			−0.384353	+	0.923186i	$0.625576\pi$
$402$	231.841	−	455.014i	0.576719	−	1.13187i
$403$	6.95498	−	43.9120i	0.0172580	−	0.108963i
$404$	−207.850	−	286.081i	−0.514481	−	0.708122i
$405$	−12.3214	−	43.2803i	−0.0304232	−	0.106865i
$406$	−1089.13	−	791.300i	−2.68259	−	1.94902i
$407$	457.740	+	457.740i	1.12467	+	1.12467i
$408$	80.6280	−	12.7702i	0.197618	−	0.0312996i
$409$	−185.043	−	60.1242i	−0.452429	−	0.147003i	0.0739339	−	0.997263i	$-0.476445\pi$
$409$	−185.043	−	60.1242i	−0.452429	−	0.147003i	−0.526363	+	0.850260i	$0.676445\pi$
$410$	−131.835	−	1090.85i	−0.321548	−	2.66061i
$411$	−13.2739	−	40.8527i	−0.0322965	−	0.0993984i
$412$	−67.2234	+	34.2520i	−0.163164	+	0.0831360i
$413$	−58.3300	−	114.479i	−0.141235	−	0.277189i
$414$	−361.634	+	117.502i	−0.873513	+	0.283822i
$415$	98.8359	+	55.0316i	0.238159	+	0.132606i
$416$	49.8424	−	153.399i	0.119813	−	0.368748i
$417$	53.7003	+	339.050i	0.128778	+	0.813070i
$418$	−104.972	+	104.972i	−0.251128	+	0.251128i
$419$	−80.0039	+	110.116i	−0.190940	+	0.262807i	−0.893744	−	0.448577i	$-0.851931\pi$
$419$	−80.0039	+	110.116i	−0.190940	+	0.262807i	0.702804	+	0.711383i	$0.251931\pi$
$420$	−378.698	−	563.753i	−0.901663	−	1.34227i
$421$	−154.192	+	112.027i	−0.366251	+	0.266097i	−0.755655	−	0.654970i	$-0.772681\pi$
$421$	−154.192	+	112.027i	−0.366251	+	0.266097i	0.389403	+	0.921067i	$0.372681\pi$
$422$	1130.68	+	179.082i	2.67934	+	0.424365i
$423$	55.6653	+	28.3629i	0.131596	+	0.0670517i
$424$			372.707i			0.879027i
$425$	−128.917	+	54.1444i	−0.303334	+	0.127399i
$426$	−174.698			−0.410090
$427$	188.975	−	370.885i	0.442565	−	0.868582i
$428$	−179.381	+	1132.57i	−0.419115	+	2.64618i
$429$	−71.6368	−	98.5997i	−0.166986	−	0.229836i
$430$	−19.1723	+	52.3655i	−0.0445868	+	0.121780i
$431$	−60.7722	−	44.1536i	−0.141003	−	0.102445i	0.515048	−	0.857162i	$-0.327774\pi$
$431$	−60.7722	−	44.1536i	−0.141003	−	0.102445i	−0.656051	+	0.754717i	$0.727774\pi$
$432$	−3.90847	−	3.90847i	−0.00904739	−	0.00904739i
$433$	−528.704	+	83.7385i	−1.22103	+	0.193391i	−0.733483	−	0.679708i	$-0.762106\pi$
$433$	−528.704	+	83.7385i	−1.22103	+	0.193391i	−0.487542	+	0.873099i	$0.662106\pi$
$434$	307.059	+	99.7696i	0.707510	+	0.229884i
$435$	295.411	+	58.0052i	0.679106	+	0.133345i
$436$	152.913	+	470.618i	0.350718	+	1.07940i
$437$	−119.987	+	61.1366i	−0.274571	+	0.139901i
$438$	−28.4469	−	55.8301i	−0.0649472	−	0.127466i
$439$	−249.056	+	80.9230i	−0.567325	+	0.184335i	−0.578614	−	0.815601i	$-0.696406\pi$
$439$	−249.056	+	80.9230i	−0.567325	+	0.184335i	0.0112896	+	0.999936i	$0.496406\pi$
$440$	107.115	−	545.521i	0.243444	−	1.23982i
$441$	85.8703	−	264.282i	0.194717	−	0.599278i
$442$	15.1837	+	95.8659i	0.0343522	+	0.216891i
$443$	58.7297	−	58.7297i	0.132573	−	0.132573i	−0.637707	−	0.770279i	$-0.720117\pi$
$443$	58.7297	−	58.7297i	0.132573	−	0.132573i	0.770279	+	0.637707i	$0.220117\pi$
$444$	−329.131	+	453.010i	−0.741287	+	1.02029i
$445$	−125.088	−	45.7977i	−0.281096	−	0.102916i
$446$	−892.256	+	648.262i	−2.00057	+	1.45350i
$447$	−232.476	−	36.8206i	−0.520081	−	0.0823727i
$448$	1088.76	+	554.750i	2.43026	+	1.23828i
$449$			384.054i			0.855354i	0.903932	+	0.427677i	$0.140668\pi$
$449$			384.054i			0.855354i	−0.903932	+	0.427677i	$0.859332\pi$
$450$	208.722	+	126.496i	0.463827	+	0.281102i
$451$	891.053			1.97573
$452$	182.543	−	358.261i	0.403856	−	0.792612i
$453$	32.7009	−	206.465i	0.0721875	−	0.455774i
$454$	294.068	+	404.750i	0.647727	+	0.891519i
$455$	263.410	−	176.945i	0.578924	−	0.388890i
$456$	−40.8252	−	29.6612i	−0.0895288	−	0.0650465i
$457$	−94.4348	−	94.4348i	−0.206641	−	0.206641i	0.596197	−	0.802838i	$-0.296678\pi$
$457$	−94.4348	−	94.4348i	−0.206641	−	0.206641i	−0.802838	+	0.596197i	$0.796678\pi$
$458$	−249.675	+	39.5447i	−0.545142	+	0.0863421i
$459$	−27.6398	−	8.98072i	−0.0602175	−	0.0195658i
$460$	624.289	−	1121.21i	1.35715	−	2.43742i
$461$	−94.2275	−	290.002i	−0.204398	−	0.629072i	−0.999738	−	0.0229082i	$-0.992707\pi$
$461$	−94.2275	−	290.002i	−0.204398	−	0.629072i	0.795340	−	0.606164i	$-0.207293\pi$
$462$	788.590	−	401.807i	1.70691	−	0.869712i
$463$	−210.731	−	413.582i	−0.455142	−	0.893266i	−0.998552	−	0.0537985i	$-0.982867\pi$
$463$	−210.731	−	413.582i	−0.455142	−	0.893266i	0.543410	−	0.839467i	$-0.317133\pi$
$464$	35.1688	−	11.4270i	0.0757948	−	0.0246272i
$465$	−71.6780	+	8.66264i	−0.154146	+	0.0186293i
$466$	243.964	−	750.844i	0.523528	−	1.61125i
$467$	39.0701	+	246.679i	0.0836619	+	0.528221i	0.993553	+	0.113372i	$0.0361653\pi$
$467$	39.0701	+	246.679i	0.0836619	+	0.528221i	−0.909891	+	0.414848i	$0.863835\pi$
$468$	74.5452	−	74.5452i	0.159285	−	0.159285i
$469$	−633.778	+	872.320i	−1.35134	+	1.85996i
$470$	−325.888	+	92.7766i	−0.693378	+	0.197397i
$471$	118.438	−	86.0506i	0.251462	−	0.182698i
$472$	89.8567	+	14.2319i	0.190374	+	0.0301523i
$473$	−40.2932	−	20.5304i	−0.0851864	−	0.0434047i
$474$		−	662.370i		−	1.39740i
$475$	80.0177	+	32.6838i	0.168458	+	0.0688079i
$476$	−438.606			−0.921442
$477$	60.2390	−	118.226i	0.126287	−	0.247852i
$478$	−101.955	+	643.721i	−0.213296	+	1.34670i
$479$	−186.285	−	256.400i	−0.388904	−	0.535281i	0.569012	−	0.822329i	$-0.307326\pi$
$479$	−186.285	−	256.400i	−0.388904	−	0.535281i	−0.957916	+	0.287049i	$0.907326\pi$
$480$	−261.754	−	9.63901i	−0.545321	−	0.0200813i
$481$	−211.667	−	153.785i	−0.440055	−	0.319719i
$482$	−74.7335	−	74.7335i	−0.155049	−	0.155049i
$483$	792.972	−	125.594i	1.64176	−	0.260030i
$484$	332.771	+	108.124i	0.687544	+	0.223396i
$485$	−585.406	−	630.169i	−1.20702	−	1.29932i
$486$	15.6756	+	48.2445i	0.0322543	+	0.0992685i
$487$	−666.845	+	339.774i	−1.36929	+	0.697689i	−0.975188	−	0.221377i	$-0.928945\pi$
$487$	−666.845	+	339.774i	−1.36929	+	0.697689i	−0.394103	+	0.919066i	$0.628945\pi$
$488$	133.810	+	262.618i	0.274202	+	0.538151i
$489$	−142.534	+	46.3121i	−0.291481	+	0.0947078i
$490$	634.338	+	1367.12i	1.29457	+	2.79005i
$491$	137.008	−	421.669i	0.279040	−	0.858795i	−0.709083	−	0.705125i	$-0.750891\pi$
$491$	137.008	−	421.669i	0.279040	−	0.858795i	0.988122	−	0.153670i	$-0.0491093\pi$
$492$	120.574	+	761.272i	0.245069	+	1.54730i
$493$	137.481	−	137.481i	0.278866	−	0.278866i
$494$	35.2669	−	48.5407i	0.0713905	−	0.0982605i
$495$	−122.148	+	155.731i	−0.246763	+	0.314608i
$496$	−7.17467	+	5.21270i	−0.0144651	+	0.0105095i
$497$	364.320	+	57.7026i	0.733039	+	0.116102i
$498$	−113.622	−	57.8935i	−0.228157	−	0.116252i
$499$			362.284i			0.726020i	0.931785	+	0.363010i	$0.118251\pi$
$499$			362.284i			0.726020i	−0.931785	+	0.363010i	$0.881749\pi$
$500$	−806.655	+	166.656i	−1.61331	+	0.333313i
$501$	133.415			0.266297
$502$	76.1792	−	149.510i	0.151751	−	0.297829i
$503$	24.6146	−	155.411i	0.0489357	−	0.308968i	−0.951064	−	0.308993i	$-0.900008\pi$
$503$	24.6146	−	155.411i	0.0489357	−	0.308968i	1.00000		2.52957e-5i	$8.05188e-6\pi$
$504$	176.837	+	243.395i	0.350866	+	0.482926i
$505$	−211.122	−	165.594i	−0.418063	−	0.327909i
$506$	1353.00	+	983.012i	2.67391	+	1.94271i
$507$	−172.151	−	172.151i	−0.339548	−	0.339548i
$508$	695.434	−	110.146i	1.36896	−	0.216823i
$509$	−213.931	−	69.5105i	−0.420297	−	0.136563i	0.0912301	−	0.995830i	$-0.470920\pi$
$509$	−213.931	−	69.5105i	−0.420297	−	0.136563i	−0.511527	+	0.859267i	$0.670920\pi$
$510$	142.980	−	66.3420i	0.280353	−	0.130082i
$511$	40.8832	+	125.826i	0.0800063	+	0.246234i
$512$	−60.6145	+	30.8846i	−0.118388	+	0.0603215i
$513$	8.15604	+	16.0071i	0.0158987	+	0.0312030i
$514$	−547.908	+	178.026i	−1.06597	+	0.346354i
$515$	−41.9422	+	38.9629i	−0.0814412	+	0.0756562i
$516$	12.0879	−	37.2026i	0.0234261	−	0.0720982i
$517$	−42.9846	−	271.394i	−0.0831423	−	0.524940i
$518$	1343.48	−	1343.48i	2.59360	−	2.59360i
$519$	216.917	−	298.561i	0.417953	−	0.575263i
$520$	−8.26860	+	224.540i	−0.0159012	+	0.431807i
$521$	348.310	−	253.062i	0.668541	−	0.485724i	−0.200995	−	0.979592i	$-0.564418\pi$
$521$	348.310	−	253.062i	0.668541	−	0.485724i	0.869537	+	0.493868i	$0.164418\pi$
$522$	−335.189	−	53.0888i	−0.642125	−	0.101703i
$523$	−711.580	−	362.568i	−1.36057	−	0.693247i	−0.387098	−	0.922039i	$-0.626522\pi$
$523$	−711.580	−	362.568i	−1.36057	−	0.693247i	−0.973475	+	0.228792i	$0.926522\pi$
$524$			1091.49i			2.08300i
$525$	−393.493	−	332.738i	−0.749511	−	0.633787i
$526$	−1417.48			−2.69483
$527$	−21.1689	+	41.5462i	−0.0401686	+	0.0788354i
$528$	−3.80304	+	24.0115i	−0.00720273	+	0.0454763i
$529$	580.777	+	799.371i	1.09788	+	1.51110i
$530$	197.045	+	692.142i	0.371783	+	1.30593i
$531$	−26.2030	−	19.0376i	−0.0493465	−	0.0358523i
$532$	191.718	+	191.718i	0.360373	+	0.360373i
$533$	−355.700	+	56.3374i	−0.667356	+	0.105699i
$534$	142.812	+	46.4025i	0.267439	+	0.0868961i
$535$	104.394	+	863.796i	0.195129	+	1.61457i
$536$	−235.931	−	726.122i	−0.440170	−	1.35471i
$537$	−128.692	+	65.5720i	−0.239650	+	0.122108i
$538$	277.630	+	544.879i	0.516041	+	1.01279i
$539$	−1162.37	+	377.676i	−2.15653	+	0.700698i
$540$	−149.578	−	83.2844i	−0.276996	−	0.154230i
$541$	−25.5752	+	78.7125i	−0.0472740	+	0.145494i	−0.971907	−	0.235364i	$-0.924372\pi$
$541$	−25.5752	+	78.7125i	−0.0472740	+	0.145494i	0.924633	+	0.380859i	$0.124372\pi$
$542$	−162.224	−	1024.24i	−0.299306	−	1.88974i
$543$	−224.902	+	224.902i	−0.414183	+	0.414183i
$544$	−99.4313	+	136.855i	−0.182778	+	0.251572i
$545$	209.369	+	311.680i	0.384164	+	0.571889i
$546$	−289.394	+	210.257i	−0.530026	+	0.385086i
$547$	−270.040	−	42.7702i	−0.493675	−	0.0781904i	−0.0953670	−	0.995442i	$-0.530402\pi$
$547$	−270.040	−	42.7702i	−0.493675	−	0.0781904i	−0.398308	+	0.917252i	$0.630402\pi$
$548$	−145.609	−	74.1917i	−0.265711	−	0.135386i
$549$		−	104.931i		−	0.191132i
$550$	−89.4889	−	1069.70i	−0.162707	−	1.94491i
$551$	−120.188			−0.218127
$552$	−258.089	+	506.529i	−0.467553	+	0.917624i
$553$	−218.780	+	1381.32i	−0.395624	+	2.49787i
$554$	−42.7833	−	58.8862i	−0.0772262	−	0.106293i
$555$	−146.076	+	398.979i	−0.263201	+	0.718882i
$556$	1056.56	+	767.638i	1.90029	+	1.38064i
$557$	−514.795	−	514.795i	−0.924229	−	0.924229i	0.0730964	−	0.997325i	$-0.476712\pi$
$557$	−514.795	−	514.795i	−0.924229	−	0.924229i	−0.997325	+	0.0730964i	$0.976712\pi$
$558$	80.3866	−	12.7320i	0.144062	−	0.0228172i
$559$	17.3827	+	5.64799i	0.0310961	+	0.0101037i
$560$	−62.1111	−	12.1958i	−0.110913	−	0.0217782i
$561$	39.4992	+	121.566i	0.0704085	+	0.216695i
$562$	196.082	−	99.9089i	0.348901	−	0.177774i
$563$	−310.789	−	609.959i	−0.552024	−	1.08341i	−0.983436	−	0.181253i	$-0.941985\pi$
$563$	−310.789	−	609.959i	−0.552024	−	1.08341i	0.431413	−	0.902155i	$-0.358015\pi$
$564$	226.049	−	73.4479i	0.400797	−	0.130227i
$565$	58.7841	−	299.378i	0.104043	−	0.529872i
$566$	−172.405	+	530.607i	−0.304602	+	0.937469i
$567$	−16.7552	−	105.788i	−0.0295506	−	0.186575i
$568$	−184.686	+	184.686i	−0.325151	+	0.325151i
$569$	342.908	−	471.973i	0.602651	−	0.829478i	−0.393297	−	0.919412i	$-0.628666\pi$
$569$	342.908	−	471.973i	0.602651	−	0.829478i	0.995948	+	0.0899337i	$0.0286655\pi$
$570$	−91.4964	−	33.4991i	−0.160520	−	0.0587704i
$571$	−169.526	+	123.168i	−0.296893	+	0.215705i	−0.726252	−	0.687429i	$-0.758739\pi$
$571$	−169.526	+	123.168i	−0.296893	+	0.215705i	0.429359	+	0.903134i	$0.358739\pi$
$572$	−457.964	−	72.5344i	−0.800636	−	0.126808i
$573$	−4.24861	−	2.16477i	−0.00741467	−	0.00377796i
$574$		−	2615.27i		−	4.55623i
$575$	222.651	−	947.945i	0.387219	−	1.64860i
$576$	308.033			0.534780
$577$	360.693	−	707.899i	0.625117	−	1.22686i	−0.333657	−	0.942694i	$-0.608283\pi$
$577$	360.693	−	707.899i	0.625117	−	1.22686i	0.958775	−	0.284167i	$-0.0917172\pi$
$578$	−131.194	+	828.329i	−0.226980	+	1.43310i
$579$	225.595	+	310.505i	0.389629	+	0.536278i
$580$	950.747	−	638.660i	1.63922	−	1.10114i
$581$	217.829	+	158.262i	0.374921	+	0.272396i
$582$	685.606	+	685.606i	1.17802	+	1.17802i
$583$	−576.405	+	91.2935i	−0.988687	+	0.156593i
$584$	−89.0951	−	28.9488i	−0.152560	−	0.0495698i
$585$	38.9142	−	69.8893i	0.0665200	−	0.119469i
$586$	−280.084	−	862.011i	−0.477960	−	1.47101i
$587$	−764.440	+	389.502i	−1.30228	+	0.663546i	−0.961035	−	0.276427i	$-0.910850\pi$
$587$	−764.440	+	389.502i	−1.30228	+	0.663546i	−0.341248	+	0.939973i	$0.610850\pi$
$588$	−479.956	−	941.966i	−0.816251	−	1.60198i
$589$	27.4133	−	8.90712i	0.0465421	−	0.0151224i
$590$	174.394	−	21.0764i	0.295583	−	0.0357226i
$591$	−41.2381	+	126.918i	−0.0697768	+	0.214751i
$592$	8.16410	+	51.5461i	0.0137907	+	0.0870711i
$593$	108.078	−	108.078i	0.182256	−	0.182256i	−0.610082	−	0.792338i	$-0.708864\pi$
$593$	108.078	−	108.078i	0.182256	−	0.182256i	0.792338	+	0.610082i	$0.208864\pi$
$594$	131.140	−	180.499i	0.220775	−	0.303871i
$595$	−320.087	+	91.1252i	−0.537961	+	0.153152i
$596$	−724.452	+	526.345i	−1.21552	+	0.883129i
$597$	350.995	+	55.5922i	0.587932	+	0.0931193i
$598$	−602.257	−	306.865i	−1.00712	−	0.513153i
$599$		−	145.078i		−	0.242201i	−0.992640	−	0.121100i	$-0.961358\pi$
$599$		−	145.078i		−	0.242201i	0.992640	−	0.121100i	$-0.0386423\pi$
$600$	354.382	−	86.9273i	0.590637	−	0.144879i
$601$	1184.98			1.97169			0.985844	−	0.167667i	$-0.0536233\pi$
$601$	1184.98			1.97169			0.985844	+	0.167667i	$0.0536233\pi$
$602$	−60.2575	+	118.262i	−0.100096	+	0.196449i
$603$	−42.5205	+	268.464i	−0.0705149	+	0.445214i
$604$	−467.455	−	643.397i	−0.773932	−	1.06523i
$605$	265.314	+	9.77011i	0.438536	+	0.0161489i
$606$	244.700	+	177.785i	0.403795	+	0.293375i
$607$	102.290	+	102.290i	0.168517	+	0.168517i	0.786327	−	0.617810i	$-0.211980\pi$
$607$	102.290	+	102.290i	0.168517	+	0.168517i	−0.617810	+	0.786327i	$0.711980\pi$
$608$	103.283	−	16.3584i	0.169873	−	0.0269053i
$609$	681.477	+	221.425i	1.11901	+	0.363588i
$610$	387.337	+	416.954i	0.634978	+	0.683532i
$611$	34.3181	+	105.620i	0.0561672	+	0.172865i
$612$	−98.5152	+	50.1960i	−0.160973	+	0.0820196i
$613$	−248.535	−	487.778i	−0.405441	−	0.795723i	0.594524	−	0.804078i	$-0.297340\pi$
$613$	−248.535	−	487.778i	−0.405441	−	0.795723i	−0.999965	+	0.00835497i	$0.997340\pi$
$614$	−980.500	+	318.584i	−1.59691	+	0.518866i
$615$	246.155	+	530.513i	0.400252	+	0.862622i
$616$	408.896	−	1258.45i	0.663792	−	2.04294i
$617$	94.2919	+	595.335i	0.152823	+	0.964887i	0.938256	+	0.345941i	$0.112440\pi$
$617$	94.2919	+	595.335i	0.152823	+	0.964887i	−0.785433	+	0.618946i	$0.787560\pi$
$618$	45.6320	−	45.6320i	0.0738382	−	0.0738382i
$619$	485.546	−	668.297i	0.784404	−	1.07964i	−0.210379	−	0.977620i	$-0.567470\pi$
$619$	485.546	−	668.297i	0.784404	−	1.07964i	0.994782	−	0.102019i	$-0.0325303\pi$
$620$	−169.522	+	216.129i	−0.273422	+	0.348596i
$621$	163.736	−	118.961i	0.263665	−	0.191563i
$622$	118.610	+	18.7860i	0.190692	+	0.0302026i
$623$	−282.498	−	143.940i	−0.453447	−	0.231043i
$624$		−	9.82562i		−	0.0157462i
$625$	−554.058	+	289.214i	−0.886493	+	0.462743i
$626$	354.549			0.566372
$627$	35.8721	−	70.4029i	0.0572122	−	0.112285i
$628$	87.1287	−	550.109i	0.138740	−	0.875970i
$629$	161.288	+	221.993i	0.256419	+	0.352931i
$630$	457.077	+	358.509i	0.725518	+	0.569062i
$631$	−3.81305	−	2.77034i	−0.00604287	−	0.00439040i	0.584760	−	0.811207i	$-0.301189\pi$
$631$	−3.81305	−	2.77034i	−0.00604287	−	0.00439040i	−0.590803	+	0.806816i	$0.701189\pi$
$632$	−700.237	−	700.237i	−1.10797	−	1.10797i
$633$	−601.814	+	95.3179i	−0.950733	+	0.150581i
$634$	1879.29	+	610.620i	2.96419	+	0.963122i
$635$	484.631	−	224.866i	0.763199	−	0.354120i
$636$	−155.994	−	480.099i	−0.245273	−	0.754872i
$637$	440.129	−	224.257i	0.690940	−	0.352051i
$638$	677.632	+	1329.93i	1.06212	+	2.08453i
$639$	88.4336	−	28.7338i	0.138394	−	0.0449668i
$640$	−780.815	+	725.351i	−1.22002	+	1.13336i
$641$	−60.8707	+	187.341i	−0.0949621	+	0.292263i	−0.987244	−	0.159216i	$-0.949103\pi$
$641$	−60.8707	+	187.341i	−0.0949621	+	0.292263i	0.892282	+	0.451479i	$0.149103\pi$
$642$	−153.434	−	968.743i	−0.238994	−	1.50895i
$643$	734.954	−	734.954i	1.14301	−	1.14301i	0.155110	−	0.987897i	$-0.450427\pi$
$643$	734.954	−	734.954i	1.14301	−	1.14301i	0.987897	−	0.155110i	$-0.0495732\pi$
$644$	1795.36	−	2471.09i	2.78782	−	3.83710i
$645$	1.09226	−	29.6612i	0.00169343	−	0.0459864i
$646$	−50.9089	+	36.9875i	−0.0788063	+	0.0572562i
$647$	206.664	+	32.7324i	0.319419	+	0.0505910i	0.314085	−	0.949395i	$-0.398302\pi$
$647$	206.664	+	32.7324i	0.319419	+	0.0505910i	0.00533375	+	0.999986i	$0.498302\pi$
$648$	67.5744	+	34.4309i	0.104281	+	0.0531340i
$649$			142.452i			0.219495i
$650$	103.356	+	421.357i	0.159009	+	0.648241i
$651$	−171.846			−0.263972
$652$	−258.853	+	508.027i	−0.397013	+	0.779183i
$653$	−54.5546	+	344.444i	−0.0835446	+	0.527480i	0.910052	+	0.414494i	$0.136041\pi$
$653$	−54.5546	+	344.444i	−0.0835446	+	0.527480i	−0.993597	+	0.112986i	$0.963959\pi$
$654$	−248.786	−	342.424i	−0.380407	−	0.523585i
$655$	226.769	+	796.552i	0.346213	+	1.21611i
$656$	58.1170	+	42.2245i	0.0885930	+	0.0643666i
$657$	23.5828	+	23.5828i	0.0358947	+	0.0358947i
$658$	−796.552	+	126.161i	−1.21057	+	0.191735i
$659$	−384.080	−	124.795i	−0.582822	−	0.189370i	0.00274229	−	0.999996i	$-0.499127\pi$
$659$	−384.080	−	124.795i	−0.582822	−	0.189370i	−0.585564	+	0.810626i	$0.699127\pi$
$660$	90.3438	+	747.539i	0.136885	+	1.13264i
$661$	39.6572	+	122.052i	0.0599958	+	0.184648i	0.976563	−	0.215234i	$-0.0690513\pi$
$661$	39.6572	+	122.052i	0.0599958	+	0.184648i	−0.916567	+	0.399882i	$0.869051\pi$
$662$	−1657.25	+	844.410i	−2.50339	+	1.27554i
$663$	−23.4538	−	46.0307i	−0.0353753	−	0.0694279i
$664$	−181.321	+	58.9149i	−0.273074	+	0.0887273i
$665$	179.744	+	100.081i	0.270292	+	0.150498i
$666$	148.005	−	455.514i	0.222230	−	0.683954i
$667$	211.810	+	1337.32i	0.317557	+	2.00497i
$668$	358.908	−	358.908i	0.537288	−	0.537288i
$669$	345.043	−	474.910i	0.515759	−	0.709881i
$670$	−822.030	−	1223.72i	−1.22691	−	1.82645i
$671$	−373.370	+	271.269i	−0.556439	+	0.404276i
$672$	−615.760	−	97.5269i	−0.916310	−	0.145129i
$673$	767.789	+	391.208i	1.14085	+	0.581290i	0.919182	−	0.393834i	$-0.128851\pi$
$673$	767.789	+	391.208i	1.14085	+	0.581290i	0.221663	+	0.975123i	$0.428851\pi$
$674$			174.680i			0.259169i
$675$	−126.462	−	29.7031i	−0.187352	−	0.0440046i
$676$	−926.229			−1.37016
$677$	101.458	−	199.123i	0.149864	−	0.294126i	−0.803854	−	0.594827i	$-0.797221\pi$
$677$	101.458	−	199.123i	0.149864	−	0.294126i	0.953718	+	0.300701i	$0.0972207\pi$
$678$	−53.8016	+	339.690i	−0.0793534	+	0.501018i
$679$	−1203.33	−	1656.24i	−1.77220	−	2.43923i
$680$	81.0194	−	221.289i	0.119146	−	0.325425i
$681$	−215.431	−	156.520i	−0.316346	−	0.229839i
$682$	−253.119	−	253.119i	−0.371143	−	0.371143i
$683$	1133.41	−	179.515i	1.65946	−	0.262833i	0.744869	−	0.667210i	$-0.232512\pi$
$683$	1133.41	−	179.515i	1.65946	−	0.262833i	0.914592	+	0.404378i	$0.132512\pi$
$684$	65.0029	+	21.1207i	0.0950335	+	0.0308782i
$685$	−121.677	−	23.8919i	−0.177631	−	0.0348786i
$686$	522.100	+	1606.86i	0.761079	+	2.34236i
$687$	119.883	−	61.0836i	0.174503	−	0.0889135i
$688$	−1.65516	−	3.24843i	−0.00240575	−	0.00472156i
$689$	224.324	−	72.8872i	0.325579	−	0.105787i
$690$	−211.494	+	1077.10i	−0.306513	+	1.56102i
$691$	−63.2611	+	194.698i	−0.0915501	+	0.281762i	−0.986339	−	0.164727i	$-0.947326\pi$
$691$	−63.2611	+	194.698i	−0.0915501	+	0.281762i	0.894789	+	0.446489i	$0.147326\pi$
$692$	−219.635	−	1386.72i	−0.317392	−	2.00393i
$693$	−333.103	+	333.103i	−0.480667	+	0.480667i
$694$	−572.375	+	787.807i	−0.824748	+	1.13517i
$695$	930.546	+	340.696i	1.33891	+	0.490210i
$696$	−410.476	+	298.228i	−0.589764	+	0.428489i
$697$	373.054	+	59.0860i	0.535229	+	0.0847719i
$698$	217.178	+	110.658i	0.311144	+	0.158536i
$699$			420.209i			0.601158i
$700$	−1953.68	+	163.441i	−2.79097	+	0.233487i
$701$	−253.078			−0.361024			−0.180512	−	0.983573i	$-0.557775\pi$
$701$	−253.078			−0.361024			−0.180512	+	0.983573i	$0.557775\pi$
$702$	−40.9380	+	80.3453i	−0.0583162	+	0.114452i
$703$	26.5350	−	167.535i	0.0377454	−	0.238315i
$704$	−796.330	−	1096.05i	−1.13115	−	1.55690i
$705$	149.707	−	100.565i	0.212351	−	0.142646i
$706$	1593.46	+	1157.72i	2.25703	+	1.63983i
$707$	−451.582	−	451.582i	−0.638729	−	0.638729i
$708$	−121.704	+	19.2761i	−0.171899	+	0.0272261i
$709$	−402.374	−	130.739i	−0.567524	−	0.184400i	0.0111799	−	0.999938i	$-0.496441\pi$
$709$	−402.374	−	130.739i	−0.567524	−	0.184400i	−0.578704	+	0.815538i	$0.696441\pi$
$710$	−245.333	+	440.614i	−0.345539	+	0.620583i
$711$	108.944	+	335.296i	0.153227	+	0.471584i
$712$	200.032	−	101.921i	0.280944	−	0.143148i
$713$	−147.419	−	289.327i	−0.206759	−	0.405788i
$714$	356.801	−	115.932i	0.499721	−	0.162369i
$715$	−349.284	+	42.2127i	−0.488509	+	0.0590387i
$716$	−169.804	+	522.602i	−0.237156	+	0.729892i
$717$	−54.2666	−	342.626i	−0.0756856	−	0.477860i
$718$	−544.659	+	544.659i	−0.758578	+	0.758578i
$719$	−527.346	+	725.829i	−0.733443	+	1.00950i	0.265526	+	0.964104i	$0.414454\pi$
$719$	−527.346	+	725.829i	−0.733443	+	1.00950i	−0.998969	+	0.0453941i	$0.985546\pi$
$720$	−15.3465	+	4.36897i	−0.0213146	+	0.00606802i
$721$	−110.234	+	80.0899i	−0.152891	+	0.111082i
$722$	−1121.87	−	177.686i	−1.55383	−	0.246103i
$723$	50.1226	+	25.5388i	0.0693259	+	0.0353233i
$724$			1210.04i			1.67133i
$725$	561.150	−	663.611i	0.774000	−	0.915325i
$726$	−299.284			−0.412237
$727$	−481.786	+	945.559i	−0.662705	+	1.30063i	0.277730	+	0.960659i	$0.410418\pi$
$727$	−481.786	+	945.559i	−0.662705	+	1.30063i	−0.940435	+	0.339973i	$0.889582\pi$
$728$	−83.6612	+	528.216i	−0.114919	+	0.725571i
$729$	−15.8702	−	21.8435i	−0.0217698	−	0.0299636i
$730$	−180.760	−	6.65643i	−0.247617	−	0.00911840i
$731$	−15.5081	−	11.2673i	−0.0212148	−	0.0154135i
$732$	−282.283	−	282.283i	−0.385632	−	0.385632i
$733$	1128.18	−	178.685i	1.53912	−	0.243773i	0.671502	−	0.741003i	$-0.265650\pi$
$733$	1128.18	−	178.685i	1.53912	−	0.243773i	0.867619	+	0.497230i	$0.165650\pi$
$734$	1206.85	+	392.129i	1.64421	+	0.534235i
$735$	−545.967	−	587.714i	−0.742812	−	0.799611i
$736$	−364.035	−	1120.39i	−0.494613	−	1.52226i
$737$	1065.18	−	542.737i	1.44529	−	0.736414i
$738$	−299.303	−	587.416i	−0.405560	−	0.795957i
$739$	925.773	−	300.802i	1.25274	−	0.407039i	0.393837	−	0.919180i	$-0.371148\pi$
$739$	925.773	−	300.802i	1.25274	−	0.407039i	0.858901	+	0.512141i	$0.171148\pi$
$740$	680.351	+	1466.29i	0.919393	+	1.98147i
$741$	−9.86854	+	30.3723i	−0.0133179	+	0.0409882i
$742$	267.950	+	1691.77i	0.361119	+	2.28001i
$743$	497.687	−	497.687i	0.669835	−	0.669835i	−0.287843	−	0.957678i	$-0.592938\pi$
$743$	497.687	−	497.687i	0.669835	−	0.669835i	0.957678	+	0.287843i	$0.0929381\pi$
$744$	71.5224	−	98.4421i	0.0961322	−	0.132315i
$745$	−419.338	+	534.630i	−0.562870	+	0.717624i
$746$	1007.47	−	731.968i	1.35049	−	0.981190i
$747$	67.0387	+	10.6179i	0.0897439	+	0.0142140i
$748$	433.291	+	220.773i	0.579266	+	0.295151i
$749$			2070.92i			2.76491i
$750$	612.154	−	348.786i	0.816205	−	0.465049i
$751$	865.195			1.15206			0.576028	−	0.817430i	$-0.304602\pi$
$751$	865.195			1.15206			0.576028	+	0.817430i	$0.304602\pi$
$752$	10.0570	−	19.7380i	0.0133737	−	0.0262474i
$753$	−13.9715	+	88.2129i	−0.0185545	+	0.117149i
$754$	−354.590	−	488.052i	−0.470279	−	0.647283i
$755$	−474.813	−	372.421i	−0.628891	−	0.493272i
$756$	−329.661	−	239.513i	−0.436059	−	0.316816i
$757$	−751.354	−	751.354i	−0.992542	−	0.992542i	0.00743042	−	0.999972i	$-0.497635\pi$
$757$	−751.354	−	751.354i	−0.992542	−	0.992542i	−0.999972	+	0.00743042i	$0.997635\pi$
$758$	−589.182	+	93.3172i	−0.777284	+	0.123110i
$759$	−846.581	−	275.071i	−1.11539	−	0.362412i
$760$	−132.142	+	61.3130i	−0.173870	+	0.0806750i
$761$	51.2671	+	157.784i	0.0673681	+	0.207338i	0.979074	−	0.203507i	$-0.0652339\pi$
$761$	51.2671	+	157.784i	0.0673681	+	0.207338i	−0.911705	+	0.410845i	$0.865234\pi$
$762$	−536.613	+	273.418i	−0.704217	+	0.358816i
$763$	405.722	+	796.274i	0.531746	+	1.04361i
$764$	−17.2530	+	5.60585i	−0.0225825	+	0.00733750i
$765$	−61.4659	+	57.0998i	−0.0803476	+	0.0746402i
$766$	−191.911	+	590.642i	−0.250537	+	0.771073i
$767$	−9.00665	−	56.8658i	−0.0117427	−	0.0741405i
$768$	346.489	−	346.489i	0.451157	−	0.451157i
$769$	24.3300	−	33.4873i	0.0316385	−	0.0435466i	−0.792905	−	0.609346i	$-0.791432\pi$
$769$	24.3300	−	33.4873i	0.0316385	−	0.0435466i	0.824543	+	0.565799i	$0.191432\pi$
$770$	94.0209	−	2553.20i	0.122105	−	3.31585i
$771$	248.074	−	180.236i	0.321756	−	0.233769i
$772$	1442.20	+	228.422i	1.86813	+	0.295883i
$773$	−357.635	−	182.224i	−0.462659	−	0.235736i	0.207093	−	0.978321i	$-0.433600\pi$
$773$	−357.635	−	182.224i	−0.462659	−	0.235736i	−0.669752	+	0.742585i	$0.733600\pi$
$774$			33.4589i			0.0432286i
$775$	−78.8107	+	192.947i	−0.101691	+	0.248964i
$776$	1449.60			1.86805
$777$	−459.110	+	901.054i	−0.590875	+	1.15966i
$778$	−290.173	+	1832.08i	−0.372973	+	2.35486i
$779$	−137.238	−	188.892i	−0.176172	−	0.242480i
$780$	−83.3282	−	292.699i	−0.106831	−	0.375255i
$781$	−330.861	−	240.384i	−0.423637	−	0.307790i
$782$	501.273	+	501.273i	0.641013	+	0.641013i
$783$	178.407	−	28.2569i	0.227851	−	0.0360880i
$784$	−93.7101	−	30.4482i	−0.119528	−	0.0388370i
$785$	−50.7061	−	419.562i	−0.0645938	−	0.534474i
$786$	−288.501	−	887.916i	−0.367050	−	1.12966i
$787$	340.171	−	173.326i	0.432238	−	0.220236i	−0.224314	−	0.974517i	$-0.572014\pi$
$787$	340.171	−	173.326i	0.432238	−	0.220236i	0.656552	+	0.754281i	$0.272014\pi$
$788$	230.492	+	452.367i	0.292503	+	0.574069i
$789$	717.539	−	233.142i	0.909428	−	0.295491i
$790$	−1670.59	−	930.181i	−2.11467	−	1.17744i
$791$	224.399	−	690.628i	0.283690	−	0.873107i
$792$	−52.1807	−	329.456i	−0.0658848	−	0.415980i
$793$	131.895	−	131.895i	0.166324	−	0.166324i
$794$	−971.199	+	1336.74i	−1.22317	+	1.68355i
$795$	−213.587	−	317.958i	−0.268663	−	0.399948i
$796$	1093.79	−	794.683i	1.37410	−	0.998345i
$797$	−920.398	−	145.777i	−1.15483	−	0.182907i	−0.450497	−	0.892778i	$-0.648753\pi$
$797$	−920.398	−	145.777i	−1.15483	−	0.182907i	−0.704332	+	0.709871i	$0.748753\pi$
$798$	−206.635	−	105.286i	−0.258941	−	0.131937i
$799$		−	116.474i		−	0.145775i
$800$	−391.899	+	646.646i	−0.489873	+	0.808307i
$801$	−79.9248			−0.0997812
$802$	455.397	−	893.767i	0.567826	−	1.11442i
$803$	22.9466	−	144.879i	0.0285762	−	0.180423i
$804$	607.824	+	836.599i	0.756001	+	1.04055i
$805$	796.822	−	2176.37i	0.989841	−	2.70356i
$806$	117.047	+	85.0394i	0.145219	+	0.105508i
$807$	−230.158	−	230.158i	−0.285203	−	0.285203i
$808$	446.638	−	70.7406i	0.552770	−	0.0875502i
$809$	−558.221	−	181.377i	−0.690014	−	0.224199i	−0.0570397	−	0.998372i	$-0.518166\pi$
$809$	−558.221	−	181.377i	−0.690014	−	0.224199i	−0.632974	+	0.774173i	$0.718166\pi$
$810$	143.693	+	28.2148i	0.177399	+	0.0348330i
$811$	−485.365	−	1493.80i	−0.598477	−	1.84192i	−0.536598	−	0.843838i	$-0.680291\pi$
$811$	−485.365	−	1493.80i	−0.598477	−	1.84192i	−0.0618786	−	0.998084i	$-0.519709\pi$
$812$	2428.96	−	1237.61i	2.99132	−	1.52416i
$813$	250.583	+	491.796i	0.308220	+	0.604916i
$814$	−2003.45	+	650.960i	−2.46124	+	0.799705i
$815$	−83.3580	+	424.529i	−0.102280	+	0.520894i
$816$	−3.18442	+	9.80063i	−0.00390247	+	0.0120106i
$817$	1.85369	+	11.7037i	0.00226889	+	0.0143252i
$818$	447.704	−	447.704i	0.547315	−	0.547315i
$819$	111.911	−	154.032i	0.136643	−	0.188074i
$820$	2089.36	+	764.968i	2.54800	+	0.932888i
$821$	−538.579	+	391.301i	−0.656004	+	0.476615i	−0.865311	−	0.501235i	$-0.832879\pi$
$821$	−538.579	+	391.301i	−0.656004	+	0.476615i	0.209307	+	0.977850i	$0.432879\pi$
$822$	138.062	+	21.8668i	0.167958	+	0.0266020i
$823$	−382.678	−	194.984i	−0.464980	−	0.236919i	0.205773	−	0.978600i	$-0.434029\pi$
$823$	−382.678	−	194.984i	−0.464980	−	0.236919i	−0.670753	+	0.741681i	$0.734029\pi$
$824$		−	96.4815i		−	0.117089i
$825$	221.241	+	526.771i	0.268171	+	0.638511i
$826$	418.103			0.506179
$827$	132.332	−	259.716i	0.160014	−	0.314046i	−0.797054	−	0.603908i	$-0.793609\pi$
$827$	132.332	−	259.716i	0.160014	−	0.314046i	0.957068	+	0.289862i	$0.0936094\pi$
$828$	120.451	−	760.500i	0.145473	−	0.918478i
$829$	98.7979	+	135.984i	0.119177	+	0.164033i	0.864437	−	0.502740i	$-0.167675\pi$
$829$	98.7979	+	135.984i	0.119177	+	0.164033i	−0.745260	+	0.666774i	$0.767675\pi$
$830$	−305.578	+	205.271i	−0.368167	+	0.247314i
$831$	31.3427	+	22.7718i	0.0377168	+	0.0274029i
$832$	387.187	+	387.187i	0.465369	+	0.465369i
$833$	−511.689	+	81.0436i	−0.614273	+	0.0972913i
$834$	−1062.40	−	345.195i	−1.27386	−	0.413903i
$835$	187.358	−	336.492i	0.224381	−	0.402984i
$836$	−92.8935	−	285.897i	−0.111117	−	0.341982i
$837$	−38.5982	+	19.6668i	−0.0461149	+	0.0234967i
$838$	−201.084	−	394.650i	−0.239957	−	0.470942i
$839$	1080.48	−	351.069i	1.28782	−	0.418437i	0.416490	−	0.909140i	$-0.363260\pi$
$839$	1080.48	−	351.069i	1.28782	−	0.418437i	0.871327	+	0.490704i	$0.163260\pi$
$840$	862.212	−	104.203i	1.02644	−	0.124051i
$841$	−113.542	+	349.447i	−0.135008	+	0.415513i
$842$	−97.0229	−	612.579i	−0.115229	−	0.727528i
$843$	−82.8256	+	82.8256i	−0.0982511	+	0.0982511i
$844$	−1362.56	+	1875.40i	−1.61440	+	2.22203i
$845$	−675.945	+	192.434i	−0.799935	+	0.227733i
$846$	−164.475	+	119.498i	−0.194415	+	0.141251i
$847$	624.135	+	98.8533i	0.736878	+	0.116710i
$848$	−41.9209	−	21.3598i	−0.0494350	−	0.0251884i
$849$		−	296.954i		−	0.349769i
$850$	33.4661	−	453.782i	0.0393719	−	0.533861i
$851$	−1910.91			−2.24548
$852$	160.602	−	315.199i	0.188500	−	0.369952i
$853$	−76.5263	+	483.168i	−0.0897143	+	0.566434i	0.901354	+	0.433082i	$0.142574\pi$
$853$	−76.5263	+	483.168i	−0.0897143	+	0.566434i	−0.991069	+	0.133352i	$0.957426\pi$
$854$	796.187	+	1095.86i	0.932303	+	1.28320i
$855$	51.8260	+	1.90848i	0.0606152	+	0.00223213i
$856$	−1186.33	−	861.920i	−1.38590	−	1.00692i
$857$	1078.99	+	1078.99i	1.25903	+	1.25903i	0.951556	+	0.307476i	$0.0994844\pi$
$857$	1078.99	+	1078.99i	1.25903	+	1.25903i	0.307476	+	0.951556i	$0.400516\pi$
$858$	391.720	−	62.0424i	0.456550	−	0.0723105i
$859$	−506.443	−	164.553i	−0.589573	−	0.191564i	−0.000988196	−	1.00000i	$-0.500315\pi$
$859$	−506.443	−	164.553i	−0.589573	−	0.191564i	−0.588584	+	0.808436i	$0.700315\pi$
$860$	−76.8552	−	82.7319i	−0.0893665	−	0.0961999i
$861$	430.152	+	1323.87i	0.499596	+	1.53760i
$862$	217.804	−	110.977i	0.252673	−	0.128743i
$863$	512.895	+	1006.61i	0.594317	+	1.16641i	0.970778	+	0.239980i	$0.0771408\pi$
$863$	512.895	+	1006.61i	0.594317	+	1.16641i	−0.376461	+	0.926432i	$0.622859\pi$
$864$	−149.467	+	48.5648i	−0.172994	+	0.0562093i
$865$	−448.392	−	966.374i	−0.518373	−	1.11719i
$866$	538.286	−	1656.67i	0.621578	−	1.91302i
$867$	−69.8293	−	440.885i	−0.0805413	−	0.508518i
$868$	−462.293	+	462.293i	−0.532595	+	0.532595i
$869$	911.419	−	1254.46i	1.04881	−	1.44357i
$870$	−604.612	+	770.842i	−0.694956	+	0.886025i
$871$	−390.896	+	284.003i	−0.448790	+	0.326065i
$872$	−625.010	−	98.9918i	−0.716754	−	0.113523i
$873$	−459.825	−	234.293i	−0.526719	−	0.268377i
$874$		−	438.221i		−	0.501397i
$875$	−1391.80	+	525.174i	−1.59063	+	0.600199i
$876$	126.883			0.144844
$877$	369.645	−	725.469i	0.421488	−	0.827216i	−0.578446	−	0.815721i	$-0.696341\pi$
$877$	369.645	−	725.469i	0.421488	−	0.827216i	0.999934	−	0.0114959i	$-0.00365933\pi$
$878$	133.309	−	841.682i	0.151833	−	0.958636i
$879$	283.562	+	390.289i	0.322596	+	0.444015i
$880$	55.2197	+	43.3117i	0.0627497	+	0.0492178i
$881$	−682.855	−	496.124i	−0.775091	−	0.563137i	0.128410	−	0.991721i	$-0.459012\pi$
$881$	−682.855	−	496.124i	−0.775091	−	0.563137i	−0.903502	+	0.428584i	$0.859012\pi$
$882$	639.417	+	639.417i	0.724963	+	0.724963i
$883$	−187.945	+	29.7676i	−0.212849	+	0.0337119i	−0.261948	−	0.965082i	$-0.584365\pi$
$883$	−187.945	+	29.7676i	−0.212849	+	0.0337119i	0.0490994	+	0.998794i	$0.484365\pi$
$884$	−186.925	−	60.7355i	−0.211453	−	0.0687053i
$885$	−84.8130	+	39.3528i	−0.0958339	+	0.0444664i
$886$	83.5206	+	257.050i	0.0942671	+	0.290124i
$887$	822.953	−	419.315i	0.927793	−	0.472734i	0.0762913	−	0.997086i	$-0.475692\pi$
$887$	822.953	−	419.315i	0.927793	−	0.472734i	0.851502	+	0.524351i	$0.175692\pi$
$888$	−325.088	−	638.022i	−0.366091	−	0.718493i
$889$	1209.38	−	392.950i	1.36038	−	0.442014i
$890$	317.588	−	295.029i	0.356841	−	0.331493i
$891$	−36.6963	+	112.940i	−0.0411856	+	0.126756i
$892$	−349.366	−	2205.81i	−0.391665	−	2.47288i
$893$	−50.9118	+	50.9118i	−0.0570121	+	0.0570121i
$894$	450.210	−	619.661i	0.503591	−	0.693133i
$895$	−15.3435	+	416.665i	−0.0171436	+	0.465547i
$896$	−2052.17	+	1490.99i	−2.29037	+	1.66405i
$897$	355.340	+	56.2803i	0.396142	+	0.0627428i
$898$	−1113.55	−	567.385i	−1.24004	−	0.631831i
$899$		−	289.811i		−	0.322370i
$900$	−420.111	+	260.298i	−0.466790	+	0.289220i
$901$	−247.375			−0.274556
$902$	−1316.40	+	2583.58i	−1.45943	+	2.86428i
$903$	11.0515	−	69.7761i	0.0122386	−	0.0772715i
$904$	302.233	+	415.988i	0.334328	+	0.460163i
$905$	251.400	+	883.069i	0.277790	+	0.975766i
$906$	550.330	+	399.838i	0.607429	+	0.441323i
$907$	−357.878	−	357.878i	−0.394574	−	0.394574i	0.481740	−	0.876314i	$-0.340005\pi$
$907$	−357.878	−	357.878i	−0.394574	−	0.394574i	−0.876314	+	0.481740i	$0.840005\pi$
$908$	−1000.61	+	158.481i	−1.10199	+	0.174539i
$909$	−153.111	−	49.7486i	−0.168438	−	0.0547290i
$910$	123.896	+	1025.16i	0.136149	+	1.12655i
$911$	−387.669	−	1193.12i	−0.425542	−	1.30968i	−0.902474	−	0.430744i	$-0.858251\pi$
$911$	−387.669	−	1193.12i	−0.425542	−	1.30968i	0.476932	−	0.878940i	$-0.341749\pi$
$912$	5.67587	−	2.89200i	0.00622355	−	0.00317106i
$913$	−135.528	−	265.989i	−0.148442	−	0.291335i
$914$	413.325	−	134.297i	0.452215	−	0.146934i
$915$	−264.652	−	147.358i	−0.289237	−	0.161047i
$916$	158.181	−	486.830i	0.172686	−	0.531474i
$917$	308.370	+	1946.97i	0.336282	+	2.12320i
$918$	66.8732	−	66.8732i	0.0728466	−	0.0728466i
$919$	−83.0683	+	114.334i	−0.0903899	+	0.124411i	−0.851817	−	0.523840i	$-0.824499\pi$
$919$	−83.0683	+	114.334i	−0.0903899	+	0.124411i	0.761427	+	0.648251i	$0.224499\pi$
$920$	915.097	+	1362.27i	0.994671	+	1.48073i
$921$	443.937	−	322.539i	0.482016	−	0.350205i
$922$	980.061	+	155.226i	1.06297	+	0.168358i
$923$	147.275	+	75.0405i	0.159561	+	0.0813006i
$924$			1792.20i			1.93961i
$925$	801.145	+	928.722i	0.866103	+	1.00402i
$926$	1510.49			1.63120
$927$	−15.5939	+	30.6047i	−0.0168219	+	0.0330147i
$928$	164.475	−	1038.46i	0.177236	−	1.11903i
$929$	126.757	+	174.466i	0.136444	+	0.187799i	0.871771	−	0.489913i	$-0.162971\pi$
$929$	126.757	+	174.466i	0.136444	+	0.187799i	−0.735327	+	0.677712i	$0.762971\pi$
$930$	80.7768	−	220.626i	0.0868568	−	0.237233i
$931$	259.089	+	188.239i	0.278291	+	0.202190i
$932$	1130.43	+	1130.43i	1.21291	+	1.21291i
$933$	−63.1312	+	9.99901i	−0.0676648	+	0.0107170i
$934$	−772.960	−	251.150i	−0.827580	−	0.268897i
$935$	362.076	+	71.0952i	0.387247	+	0.0760377i
$936$	41.6602	+	128.217i	0.0445088	+	0.136984i
$937$	−949.778	+	483.936i	−1.01364	+	0.516474i	−0.880210	−	0.474584i	$-0.842598\pi$
$937$	−949.778	+	483.936i	−1.01364	+	0.516474i	−0.133428	+	0.991059i	$0.542598\pi$
$938$	−1592.95	−	3126.35i	−1.69825	−	3.33299i
$939$	−179.475	+	58.3151i	−0.191135	+	0.0621034i
$940$	132.200	−	673.274i	0.140639	−	0.716249i
$941$	−88.7313	+	273.087i	−0.0942947	+	0.290209i	−0.987069	−	0.160295i	$-0.948756\pi$
$941$	−88.7313	+	273.087i	−0.0942947	+	0.290209i	0.892775	+	0.450504i	$0.148756\pi$
$942$	74.5257	+	470.537i	0.0791143	+	0.499508i
$943$	−1859.92	+	1859.92i	−1.97234	+	1.97234i
$944$	−6.75042	+	9.29116i	−0.00715087	+	0.00984233i
$945$	−290.342	−	106.301i	−0.307240	−	0.112488i
$946$	119.055	−	86.4983i	0.125851	−	0.0914358i
$947$	−1209.21	−	191.521i	−1.27689	−	0.202239i	−0.519085	−	0.854722i	$-0.673727\pi$
$947$	−1209.21	−	191.521i	−1.27689	−	0.202239i	−0.757803	+	0.652483i	$0.773727\pi$
$948$	1195.08	+	608.924i	1.26063	+	0.642325i
$949$			59.2854i			0.0624715i
$950$	−212.980	+	183.724i	−0.224190	+	0.193393i
$951$	−1051.75			−1.10594
$952$	254.640	−	499.758i	0.267479	−	0.524956i
$953$	18.0977	−	114.265i	0.0189903	−	0.119900i	−0.976372	−	0.216096i	$-0.930668\pi$
$953$	18.0977	−	114.265i	0.0189903	−	0.119900i	0.995362	+	0.0961960i	$0.0306676\pi$
$954$	253.798	+	349.323i	0.266035	+	0.366166i
$955$	−11.4263	+	7.67556i	−0.0119647	+	0.00803723i
$956$	−1067.70	−	775.733i	−1.11685	−	0.811436i
$957$	−561.765	−	561.765i	−0.587006	−	0.587006i
$958$	1018.63	−	161.336i	1.06329	−	0.168409i
$959$	−280.695	−	91.2033i	−0.292695	−	0.0951025i
$960$	432.578	−	776.905i	0.450603	−	0.809276i
$961$	−275.488	−	847.863i	−0.286668	−	0.882272i
$962$	758.602	−	386.527i	0.788567	−	0.401795i
$963$	237.005	+	465.149i	0.246111	+	0.483021i
$964$	203.541	−	66.1346i	0.211143	−	0.0686044i
$965$	1099.95	−	132.934i	1.13984	−	0.137755i
$966$	−807.344	+	2484.75i	−0.835760	+	2.57220i
$967$	−178.061	−	1124.23i	−0.184137	−	1.16260i	−0.890580	−	0.454827i	$-0.849701\pi$
$967$	−178.061	−	1124.23i	−0.184137	−	1.16260i	0.706442	−	0.707771i	$-0.250299\pi$
$968$	−316.394	+	316.394i	−0.326854	+	0.326854i
$969$	19.6869	−	27.0967i	0.0203167	−	0.0279635i
$970$	2692.01	−	766.385i	2.77527	−	0.790087i
$971$	103.410	−	75.1321i	0.106499	−	0.0773760i	−0.533261	−	0.845951i	$-0.679034\pi$
$971$	103.410	−	75.1321i	0.106499	−	0.0773760i	0.639760	+	0.768575i	$0.279034\pi$
$972$	−101.456	−	16.0690i	−0.104378	−	0.0165319i
$973$	2101.54	+	1070.79i	2.15986	+	1.10050i
$974$		−	2435.47i		−	2.50048i
$975$	−121.623	−	196.294i	−0.124741	−	0.201328i
$976$	−37.2070			−0.0381219
$977$	−320.924	+	629.848i	−0.328479	+	0.644676i	−0.994896	−	0.100903i	$-0.967827\pi$
$977$	−320.924	+	629.848i	−0.328479	+	0.644676i	0.666418	+	0.745579i	$0.267827\pi$
$978$	76.2927	−	481.693i	0.0780089	−	0.492529i
$979$	206.622	+	284.391i	0.211054	+	0.290491i
$980$	−3049.79	−	112.307i	−3.11203	−	0.114599i
$981$	182.258	+	132.418i	0.185788	+	0.134983i
$982$	1020.21	+	1020.21i	1.03891	+	1.03891i
$983$	1467.14	−	232.373i	1.49252	−	0.236391i	0.643781	−	0.765210i	$-0.277365\pi$
$983$	1467.14	−	232.373i	1.49252	−	0.236391i	0.848735	+	0.528818i	$0.177365\pi$
$984$	−937.413	−	304.584i	−0.952655	−	0.309536i
$985$	262.193	+	282.242i	0.266186	+	0.286540i
$986$	195.514	+	601.731i	0.198290	+	0.610275i
$987$	382.470	−	194.878i	0.387508	−	0.197445i
$988$	55.1583	+	108.254i	0.0558283	+	0.109569i
$989$	126.959	−	41.2514i	0.128371	−	0.0417102i
$990$	−271.082	−	584.235i	−0.273820	−	0.590136i
$991$	−113.898	+	350.542i	−0.114932	+	0.353725i	−0.991933	−	0.126764i	$-0.959541\pi$
$991$	−113.898	+	350.542i	−0.114932	+	0.353725i	0.877001	+	0.480489i	$0.159541\pi$
$992$	39.4452	+	249.047i	0.0397633	+	0.251055i
$993$	700.025	−	700.025i	0.704960	−	0.704960i
$994$	−705.538	+	971.089i	−0.709796	+	0.976951i
$995$	633.123	−	807.192i	0.636304	−	0.811248i
$996$	208.909	−	151.781i	0.209748	−	0.152391i
$997$	322.809	+	51.1279i	0.323781	+	0.0512818i	0.316209	−	0.948690i	$-0.397590\pi$
$997$	322.809	+	51.1279i	0.323781	+	0.0512818i	0.00757147	+	0.999971i	$0.497590\pi$
$998$	−1050.43	−	535.222i	−1.05254	−	0.536295i
$999$			254.928i			0.255183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.67.1	yes	80
3.2	odd	2		225.3.r.b.217.10		80
5.2	odd	4		375.3.k.b.268.1		80
5.3	odd	4		375.3.k.c.268.10		80
5.4	even	2		375.3.k.a.232.10		80
25.3	odd	20	inner	75.3.k.a.28.1	✓	80
25.4	even	10		375.3.k.b.7.1		80
25.21	even	5		375.3.k.c.7.10		80
25.22	odd	20		375.3.k.a.118.10		80
75.53	even	20		225.3.r.b.28.10		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.28.1	✓	80	25.3	odd	20	inner
75.3.k.a.67.1	yes	80	1.1	even	1	trivial
225.3.r.b.28.10		80	75.53	even	20
225.3.r.b.217.10		80	3.2	odd	2
375.3.k.a.118.10		80	25.22	odd	20
375.3.k.a.232.10		80	5.4	even	2
375.3.k.b.7.1		80	25.4	even	10
375.3.k.b.268.1		80	5.2	odd	4
375.3.k.c.7.10		80	25.21	even	5
375.3.k.c.268.10		80	5.3	odd	4

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.47736 + 2.89947i) q^{2} +(0.270952 - 1.71073i) q^{3} +(-3.87323 - 5.33104i) q^{4} +(-3.93419 - 3.08579i) q^{5} +(4.55991 + 3.31297i) q^{6} +(-8.41509 - 8.41509i) q^{7} +(8.32297 - 1.31823i) q^{8} +(-2.85317 - 0.927051i) q^{9} +O(q^{10})\)	\(q+(-1.47736 + 2.89947i) q^{2} +(0.270952 - 1.71073i) q^{3} +(-3.87323 - 5.33104i) q^{4} +(-3.93419 - 3.08579i) q^{5} +(4.55991 + 3.31297i) q^{6} +(-8.41509 - 8.41509i) q^{7} +(8.32297 - 1.31823i) q^{8} +(-2.85317 - 0.927051i) q^{9} +(14.7594 - 6.84828i) q^{10} +(4.07737 + 12.5489i) q^{11} +(-10.1694 + 5.18157i) q^{12} +(-2.42106 - 4.75160i) q^{13} +(36.8314 - 11.9672i) q^{14} +(-6.34493 + 5.89423i) q^{15} +(-0.328717 + 1.01169i) q^{16} +(0.874942 + 5.52417i) q^{17} +(6.90311 - 6.90311i) q^{18} +(2.03221 - 2.79710i) q^{19} +(-1.21246 + 32.9253i) q^{20} +(-16.6760 + 12.1158i) q^{21} +(-42.4088 - 6.71690i) q^{22} +(-34.7044 - 17.6828i) q^{23} -14.5955i q^{24} +(5.95576 + 24.2802i) q^{25} +17.3539 q^{26} +(-2.35900 + 4.62981i) q^{27} +(-12.2676 + 77.4547i) q^{28} +(-20.4329 - 28.1234i) q^{29} +(-7.71644 - 27.1048i) q^{30} +(6.74468 + 4.90030i) q^{31} +(21.3866 + 21.3866i) q^{32} +(22.5724 - 3.57512i) q^{33} +(-17.3098 - 5.62429i) q^{34} +(7.13936 + 59.0738i) q^{35} +(6.10883 + 18.8010i) q^{36} +(43.7136 - 22.2732i) q^{37} +(5.10782 + 10.0247i) q^{38} +(-8.78468 + 2.85432i) q^{39} +(-36.8120 - 20.4968i) q^{40} +(20.8683 - 64.2261i) q^{41} +(-10.4931 - 66.2510i) q^{42} +(-2.42347 + 2.42347i) q^{43} +(51.1059 - 70.3412i) q^{44} +(8.36423 + 12.4515i) q^{45} +(102.542 - 74.5008i) q^{46} +(-20.5685 - 3.25773i) q^{47} +(1.64165 + 0.836465i) q^{48} +92.6274i q^{49} +(-79.1986 - 18.6020i) q^{50} +9.68741 q^{51} +(-15.9537 + 31.3108i) q^{52} +(-6.91898 + 43.6847i) q^{53} +(-9.93891 - 13.6797i) q^{54} +(22.6820 - 61.9516i) q^{55} +(-81.1316 - 58.9455i) q^{56} +(-4.23445 - 4.23445i) q^{57} +(111.730 - 17.6963i) q^{58} +(10.2678 + 3.33622i) q^{59} +(55.9977 + 10.9954i) q^{60} +(10.8085 + 33.2652i) q^{61} +(-24.1726 + 12.3165i) q^{62} +(16.2085 + 31.8109i) q^{63} +(-97.6524 + 31.7292i) q^{64} +(-5.13754 + 26.1646i) q^{65} +(-22.9815 + 70.7299i) q^{66} +(-14.1735 - 89.4880i) q^{67} +(26.0607 - 26.0607i) q^{68} +(-39.6536 + 54.5786i) q^{69} +(-181.830 - 66.5726i) q^{70} +(-25.0754 + 18.2183i) q^{71} +(-24.9689 - 3.95469i) q^{72} +(-9.90535 - 5.04703i) q^{73} +159.652i q^{74} +(43.1505 - 3.60989i) q^{75} -22.7827 q^{76} +(71.2883 - 139.911i) q^{77} +(4.70209 - 29.6878i) q^{78} +(-69.0749 - 95.0734i) q^{79} +(4.41510 - 2.96582i) q^{80} +(7.28115 + 5.29007i) q^{81} +(155.392 + 155.392i) q^{82} +(-22.3462 + 3.53929i) q^{83} +(129.180 + 41.9731i) q^{84} +(13.6042 - 24.4330i) q^{85} +(-3.44646 - 10.6071i) q^{86} +(-53.6478 + 27.3349i) q^{87} +(50.4781 + 99.0689i) q^{88} +(25.3377 - 8.23270i) q^{89} +(-48.4597 + 5.85659i) q^{90} +(-19.6117 + 60.3586i) q^{91} +(40.1505 + 253.500i) q^{92} +(10.2106 - 10.2106i) q^{93} +(39.8327 - 54.8249i) q^{94} +(-16.6264 + 4.73335i) q^{95} +(42.3814 - 30.7919i) q^{96} +(169.907 + 26.9106i) q^{97} +(-268.571 - 136.844i) q^{98} -39.5840i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

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