LMFDB - Embedded newform 99.4.e.b.34.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,4,Mod(34,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("99.34");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	99.e (of order $3$, degree $2$, 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:	$5.84118909057$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			34.8
Character	$\chi$	$=$	99.34
Dual form			99.4.e.b.67.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0391684 + 0.0678417i) q^{2} +(1.19695 + 5.05641i) q^{3} +(3.99693 + 6.92289i) q^{4} +(4.72166 + 8.17816i) q^{5} +(-0.389918 - 0.116849i) q^{6} +(7.37292 - 12.7703i) q^{7} -1.25291 q^{8} +(-24.1346 + 12.1045i) q^{9} +O(q^{10})$	\(q+(-0.0391684 + 0.0678417i) q^{2} +(1.19695 + 5.05641i) q^{3} +(3.99693 + 6.92289i) q^{4} +(4.72166 + 8.17816i) q^{5} +(-0.389918 - 0.116849i) q^{6} +(7.37292 - 12.7703i) q^{7} -1.25291 q^{8} +(-24.1346 + 12.1045i) q^{9} -0.739761 q^{10} +(-5.50000 + 9.52628i) q^{11} +(-30.2209 + 28.4965i) q^{12} +(-22.6500 - 39.2309i) q^{13} +(0.577571 + 1.00038i) q^{14} +(-35.7006 + 33.6635i) q^{15} +(-31.9264 + 55.2981i) q^{16} +58.6625 q^{17} +(0.124125 - 2.11145i) q^{18} +29.7175 q^{19} +(-37.7443 + 65.3751i) q^{20} +(73.3967 + 21.9952i) q^{21} +(-0.430853 - 0.746259i) q^{22} +(46.5441 + 80.6168i) q^{23} +(-1.49967 - 6.33522i) q^{24} +(17.9118 - 31.0241i) q^{25} +3.54865 q^{26} +(-90.0933 - 107.546i) q^{27} +117.876 q^{28} +(-74.4806 + 129.004i) q^{29} +(-0.885454 - 3.74054i) q^{30} +(-83.7650 - 145.085i) q^{31} +(-7.51265 - 13.0123i) q^{32} +(-54.7520 - 16.4078i) q^{33} +(-2.29772 + 3.97977i) q^{34} +139.250 q^{35} +(-180.263 - 118.700i) q^{36} +203.342 q^{37} +(-1.16399 + 2.01609i) q^{38} +(171.257 - 161.485i) q^{39} +(-5.91582 - 10.2465i) q^{40} +(27.7626 + 48.0863i) q^{41} +(-4.36702 + 4.11784i) q^{42} +(199.070 - 344.799i) q^{43} -87.9325 q^{44} +(-212.948 - 140.224i) q^{45} -7.29224 q^{46} +(58.3498 - 101.065i) q^{47} +(-317.824 - 95.2441i) q^{48} +(62.7802 + 108.739i) q^{49} +(1.40315 + 2.43033i) q^{50} +(70.2159 + 296.622i) q^{51} +(181.061 - 313.606i) q^{52} +3.72895 q^{53} +(10.8249 - 1.89967i) q^{54} -103.877 q^{55} +(-9.23759 + 16.0000i) q^{56} +(35.5703 + 150.264i) q^{57} +(-5.83458 - 10.1058i) q^{58} +(128.992 + 223.421i) q^{59} +(-375.742 - 112.600i) q^{60} +(382.194 - 661.980i) q^{61} +13.1238 q^{62} +(-23.3648 + 397.451i) q^{63} -509.645 q^{64} +(213.891 - 370.470i) q^{65} +(3.25768 - 3.07180i) q^{66} +(-4.13528 - 7.16252i) q^{67} +(234.470 + 406.114i) q^{68} +(-351.921 + 331.840i) q^{69} +(-5.45419 + 9.44694i) q^{70} +1033.26 q^{71} +(30.2385 - 15.1659i) q^{72} -160.724 q^{73} +(-7.96459 + 13.7951i) q^{74} +(178.310 + 53.4351i) q^{75} +(118.779 + 205.731i) q^{76} +(81.1021 + 140.473i) q^{77} +(4.24755 + 17.9435i) q^{78} +(-325.793 + 564.290i) q^{79} -602.983 q^{80} +(435.961 - 584.276i) q^{81} -4.34967 q^{82} +(-561.606 + 972.729i) q^{83} +(141.091 + 596.031i) q^{84} +(276.985 + 479.752i) q^{85} +(15.5945 + 27.0105i) q^{86} +(-741.448 - 222.194i) q^{87} +(6.89100 - 11.9356i) q^{88} -1141.06 q^{89} +(17.8539 - 8.95444i) q^{90} -667.985 q^{91} +(-372.067 + 644.440i) q^{92} +(633.349 - 597.210i) q^{93} +(4.57094 + 7.91711i) q^{94} +(140.316 + 243.035i) q^{95} +(56.8033 - 53.5621i) q^{96} +(135.221 - 234.210i) q^{97} -9.83601 q^{98} +(17.4295 - 296.488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 6 q^{3} - 32 q^{4} + 2 q^{5} + 57 q^{6} + 8 q^{7} - 6 q^{8} - 54 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 6 * q^3 - 32 * q^4 + 2 * q^5 + 57 * q^6 + 8 * q^7 - 6 * q^8 - 54 * q^9	\( 24 q - 4 q^{2} + 6 q^{3} - 32 q^{4} + 2 q^{5} + 57 q^{6} + 8 q^{7} - 6 q^{8} - 54 q^{9} - 272 q^{10} - 132 q^{11} + 21 q^{12} + 62 q^{13} + 179 q^{14} - 24 q^{15} - 128 q^{16} - 160 q^{17} + 63 q^{18} - 128 q^{19} + 67 q^{20} - 48 q^{21} - 44 q^{22} + 280 q^{23} - 513 q^{24} + 112 q^{25} - 100 q^{26} + 756 q^{27} - 1158 q^{28} + 60 q^{29} + 618 q^{30} + 704 q^{31} - 755 q^{32} + 66 q^{33} + 778 q^{34} - 448 q^{35} + 1089 q^{36} - 1760 q^{37} - 171 q^{38} + 636 q^{39} + 1695 q^{40} + 374 q^{41} - 1041 q^{42} + 826 q^{43} + 704 q^{44} - 846 q^{45} - 1912 q^{46} + 214 q^{47} + 3009 q^{48} + 462 q^{49} - 1019 q^{50} + 372 q^{51} + 834 q^{52} - 756 q^{53} - 1026 q^{54} - 44 q^{55} + 750 q^{56} + 2574 q^{57} + 867 q^{58} + 748 q^{59} - 5061 q^{60} + 2662 q^{61} - 1258 q^{62} - 828 q^{63} - 306 q^{64} + 416 q^{65} + 330 q^{66} + 2430 q^{67} + 895 q^{68} - 1920 q^{69} + 136 q^{70} - 1224 q^{71} - 5166 q^{72} - 1696 q^{73} - 93 q^{74} + 4314 q^{75} + 934 q^{76} + 88 q^{77} - 2481 q^{78} + 1770 q^{79} - 4262 q^{80} - 1566 q^{81} - 3590 q^{82} - 156 q^{83} + 6114 q^{84} + 1414 q^{85} - 3576 q^{86} - 1980 q^{87} + 33 q^{88} - 504 q^{89} + 405 q^{90} - 5004 q^{91} + 3821 q^{92} + 7098 q^{93} + 4046 q^{94} + 510 q^{95} - 9939 q^{96} + 2436 q^{97} + 2448 q^{98} - 594 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 6 * q^3 - 32 * q^4 + 2 * q^5 + 57 * q^6 + 8 * q^7 - 6 * q^8 - 54 * q^9 - 272 * q^10 - 132 * q^11 + 21 * q^12 + 62 * q^13 + 179 * q^14 - 24 * q^15 - 128 * q^16 - 160 * q^17 + 63 * q^18 - 128 * q^19 + 67 * q^20 - 48 * q^21 - 44 * q^22 + 280 * q^23 - 513 * q^24 + 112 * q^25 - 100 * q^26 + 756 * q^27 - 1158 * q^28 + 60 * q^29 + 618 * q^30 + 704 * q^31 - 755 * q^32 + 66 * q^33 + 778 * q^34 - 448 * q^35 + 1089 * q^36 - 1760 * q^37 - 171 * q^38 + 636 * q^39 + 1695 * q^40 + 374 * q^41 - 1041 * q^42 + 826 * q^43 + 704 * q^44 - 846 * q^45 - 1912 * q^46 + 214 * q^47 + 3009 * q^48 + 462 * q^49 - 1019 * q^50 + 372 * q^51 + 834 * q^52 - 756 * q^53 - 1026 * q^54 - 44 * q^55 + 750 * q^56 + 2574 * q^57 + 867 * q^58 + 748 * q^59 - 5061 * q^60 + 2662 * q^61 - 1258 * q^62 - 828 * q^63 - 306 * q^64 + 416 * q^65 + 330 * q^66 + 2430 * q^67 + 895 * q^68 - 1920 * q^69 + 136 * q^70 - 1224 * q^71 - 5166 * q^72 - 1696 * q^73 - 93 * q^74 + 4314 * q^75 + 934 * q^76 + 88 * q^77 - 2481 * q^78 + 1770 * q^79 - 4262 * q^80 - 1566 * q^81 - 3590 * q^82 - 156 * q^83 + 6114 * q^84 + 1414 * q^85 - 3576 * q^86 - 1980 * q^87 + 33 * q^88 - 504 * q^89 + 405 * q^90 - 5004 * q^91 + 3821 * q^92 + 7098 * q^93 + 4046 * q^94 + 510 * q^95 - 9939 * q^96 + 2436 * q^97 + 2448 * q^98 - 594 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.0391684	+	0.0678417i	−0.0138481	+	0.0239857i	−0.872866	−	0.487959i	$-0.837741\pi$
$2$	−0.0391684	+	0.0678417i	−0.0138481	+	0.0239857i	0.859018	+	0.511945i	$0.171075\pi$
$3$	1.19695	+	5.05641i	0.230353	+	0.973107i
$3$	1.19695	+	5.05641i	0.230353	+	0.973107i
$4$	3.99693	+	6.92289i	0.499616	+	0.865361i
$5$	4.72166	+	8.17816i	0.422319	+	0.731477i	0.996166	−	0.0874852i	$-0.0278830\pi$
$5$	4.72166	+	8.17816i	0.422319	+	0.731477i	−0.573847	+	0.818962i	$0.694550\pi$
$6$	−0.389918	−	0.116849i	−0.0265306	−	0.00795056i
$7$	7.37292	−	12.7703i	0.398100	−	0.689529i	−0.595391	−	0.803436i	$-0.703003\pi$
$7$	7.37292	−	12.7703i	0.398100	−	0.689529i	0.993492	+	0.113906i	$0.0363364\pi$
$8$	−1.25291			−0.0553713
$9$	−24.1346	+	12.1045i	−0.893875	+	0.448315i
$10$	−0.739761			−0.0233933
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$12$	−30.2209	+	28.4965i	−0.727001	+	0.685518i
$13$	−22.6500	−	39.2309i	−0.483229	−	0.836977i	0.516586	−	0.856235i	$-0.327203\pi$
$13$	−22.6500	−	39.2309i	−0.483229	−	0.836977i	−0.999815	+	0.0192588i	$0.993869\pi$
$14$	0.577571	+	1.00038i	0.0110259	+	0.0190974i
$15$	−35.7006	+	33.6635i	−0.614524	+	0.579459i
$16$	−31.9264	+	55.2981i	−0.498850	+	0.864033i
$17$	58.6625			0.836927			0.418463	−	0.908234i	$-0.362569\pi$
$17$	58.6625			0.836927			0.418463	+	0.908234i	$0.362569\pi$
$18$	0.124125	−	2.11145i	0.00162536	−	0.0276485i
$19$	29.7175			0.358824			0.179412	−	0.983774i	$-0.442580\pi$
$19$	29.7175			0.358824			0.179412	+	0.983774i	$0.442580\pi$
$20$	−37.7443	+	65.3751i	−0.421995	+	0.730916i
$21$	73.3967	+	21.9952i	0.762689	+	0.228559i
$22$	−0.430853	−	0.746259i	−0.00417537	−	0.00723195i
$23$	46.5441	+	80.6168i	0.421962	+	0.730859i	0.996131	−	0.0878772i	$-0.0280083\pi$
$23$	46.5441	+	80.6168i	0.421962	+	0.730859i	−0.574170	+	0.818736i	$0.694675\pi$
$24$	−1.49967	−	6.33522i	−0.0127549	−	0.0538822i
$25$	17.9118	−	31.0241i	0.143294	−	0.248193i
$26$	3.54865			0.0267672
$27$	−90.0933	−	107.546i	−0.642165	−	0.766566i
$28$	117.876			0.795589
$29$	−74.4806	+	129.004i	−0.476921	+	0.826051i	−0.999650	−	0.0264474i	$-0.991581\pi$
$29$	−74.4806	+	129.004i	−0.476921	+	0.826051i	0.522729	+	0.852499i	$0.324914\pi$
$30$	−0.885454	−	3.74054i	−0.00538870	−	0.0227642i
$31$	−83.7650	−	145.085i	−0.485311	−	0.840583i	0.514547	−	0.857462i	$-0.327960\pi$
$31$	−83.7650	−	145.085i	−0.485311	−	0.840583i	−0.999858	+	0.0168794i	$0.994627\pi$
$32$	−7.51265	−	13.0123i	−0.0415019	−	0.0718834i
$33$	−54.7520	−	16.4078i	−0.288821	−	0.0865526i
$34$	−2.29772	+	3.97977i	−0.0115899	+	0.0200742i
$35$	139.250			0.672500
$36$	−180.263	−	118.700i	−0.834550	−	0.549539i
$37$	203.342			0.903492			0.451746	−	0.892146i	$-0.350801\pi$
$37$	203.342			0.903492			0.451746	+	0.892146i	$0.350801\pi$
$38$	−1.16399	+	2.01609i	−0.00496905	+	0.00860664i
$39$	171.257	−	161.485i	0.703155	−	0.663033i
$40$	−5.91582	−	10.2465i	−0.0233843	−	0.0405028i
$41$	27.7626	+	48.0863i	0.105751	+	0.183166i	0.914045	−	0.405613i	$-0.132942\pi$
$41$	27.7626	+	48.0863i	0.105751	+	0.183166i	−0.808294	+	0.588779i	$0.799609\pi$
$42$	−4.36702	+	4.11784i	−0.0160440	+	0.0151285i
$43$	199.070	−	344.799i	0.705997	−	1.22282i	−0.260333	−	0.965519i	$-0.583832\pi$
$43$	199.070	−	344.799i	0.705997	−	1.22282i	0.966330	−	0.257304i	$-0.0828342\pi$
$44$	−87.9325			−0.301280
$45$	−212.948	−	140.224i	−0.705433	−	0.464518i
$46$	−7.29224			−0.0233735
$47$	58.3498	−	101.065i	0.181089	−	0.313656i	−0.761162	−	0.648561i	$-0.775371\pi$
$47$	58.3498	−	101.065i	0.181089	−	0.313656i	0.942252	+	0.334905i	$0.108704\pi$
$48$	−317.824	−	95.2441i	−0.955708	−	0.286402i
$49$	62.7802	+	108.739i	0.183033	+	0.317022i
$50$	1.40315	+	2.43033i	0.00396871	+	0.00687401i
$51$	70.2159	+	296.622i	0.192788	+	0.814419i
$52$	181.061	−	313.606i	0.482858	−	0.836335i
$53$	3.72895			0.00966435			0.00483218	−	0.999988i	$-0.498462\pi$
$53$	3.72895			0.00966435			0.00483218	+	0.999988i	$0.498462\pi$
$54$	10.8249	−	1.89967i	0.0272794	−	0.00478726i
$55$	−103.877			−0.254668
$56$	−9.23759	+	16.0000i	−0.0220433	+	0.0381801i
$57$	35.5703	+	150.264i	0.0826561	+	0.349175i
$58$	−5.83458	−	10.1058i	−0.0132089	−	0.0228785i
$59$	128.992	+	223.421i	0.284633	+	0.492999i	0.972520	−	0.232819i	$-0.0747949\pi$
$59$	128.992	+	223.421i	0.284633	+	0.492999i	−0.687887	+	0.725818i	$0.741462\pi$
$60$	−375.742	−	112.600i	−0.808467	−	0.242278i
$61$	382.194	−	661.980i	0.802213	−	1.38947i	−0.115944	−	0.993256i	$-0.536989\pi$
$61$	382.194	−	661.980i	0.802213	−	1.38947i	0.918157	−	0.396217i	$-0.129677\pi$
$62$	13.1238			0.0268826
$63$	−23.3648	+	397.451i	−0.0467252	+	0.794828i
$64$	−509.645			−0.995400
$65$	213.891	−	370.470i	0.408153	−	0.706941i
$66$	3.25768	−	3.07180i	0.00607566	−	0.00572898i
$67$	−4.13528	−	7.16252i	−0.00754038	−	0.0130603i	0.862231	−	0.506516i	$-0.169067\pi$
$67$	−4.13528	−	7.16252i	−0.00754038	−	0.0130603i	−0.869771	+	0.493456i	$0.835734\pi$
$68$	234.470	+	406.114i	0.418142	+	0.724244i
$69$	−351.921	+	331.840i	−0.614004	+	0.578969i
$70$	−5.45419	+	9.44694i	−0.00931287	+	0.0161304i
$71$	1033.26			1.72712			0.863559	−	0.504247i	$-0.168230\pi$
$71$	1033.26			1.72712			0.863559	+	0.504247i	$0.168230\pi$
$72$	30.2385	−	15.1659i	0.0494950	−	0.0248238i
$73$	−160.724			−0.257689			−0.128844	−	0.991665i	$-0.541127\pi$
$73$	−160.724			−0.257689			−0.128844	+	0.991665i	$0.541127\pi$
$74$	−7.96459	+	13.7951i	−0.0125117	+	0.0216709i
$75$	178.310	+	53.4351i	0.274526	+	0.0822687i
$76$	118.779	+	205.731i	0.179275	+	0.310513i
$77$	81.1021	+	140.473i	0.120032	+	0.207901i
$78$	4.24755	+	17.9435i	0.00616590	+	0.0260474i
$79$	−325.793	+	564.290i	−0.463982	+	0.803640i	−0.999155	−	0.0411024i	$-0.986913\pi$
$79$	−325.793	+	564.290i	−0.463982	+	0.803640i	0.535173	+	0.844742i	$0.320246\pi$
$80$	−602.983			−0.842694
$81$	435.961	−	584.276i	0.598027	−	0.801476i
$82$	−4.34967			−0.00585782
$83$	−561.606	+	972.729i	−0.742701	+	1.28640i	0.208560	+	0.978010i	$0.433122\pi$
$83$	−561.606	+	972.729i	−0.742701	+	1.28640i	−0.951261	+	0.308387i	$0.900211\pi$
$84$	141.091	+	596.031i	0.183266	+	0.774194i
$85$	276.985	+	479.752i	0.353450	+	0.612193i
$86$	15.5945	+	27.0105i	0.0195535	+	0.0338676i
$87$	−741.448	−	222.194i	−0.913697	−	0.273812i
$88$	6.89100	−	11.9356i	0.00834753	−	0.0144584i
$89$	−1141.06			−1.35902			−0.679509	−	0.733667i	$-0.737807\pi$
$89$	−1141.06			−1.35902			−0.679509	+	0.733667i	$0.737807\pi$
$90$	17.8539	−	8.95444i	0.0209107	−	0.0104876i
$91$	−667.985			−0.769493
$92$	−372.067	+	644.440i	−0.421638	+	0.730299i
$93$	633.349	−	597.210i	0.706185	−	0.665890i
$94$	4.57094	+	7.91711i	0.00501550	+	0.00868710i
$95$	140.316	+	243.035i	0.151538	+	0.262472i
$96$	56.8033	−	53.5621i	0.0603902	−	0.0569443i
$97$	135.221	−	234.210i	0.141542	−	0.245159i	−0.786535	−	0.617545i	$-0.788127\pi$
$97$	135.221	−	234.210i	0.141542	−	0.245159i	0.928078	+	0.372387i	$0.121461\pi$
$98$	−9.83601			−0.0101386
$99$	17.4295	−	296.488i	0.0176943	−	0.300992i
$100$	286.368			0.286368
$101$	902.733	−	1563.58i	0.889360	−	1.54042i	0.0487261	−	0.998812i	$-0.484484\pi$
$101$	902.733	−	1563.58i	0.889360	−	1.54042i	0.840634	−	0.541604i	$-0.182183\pi$
$102$	−22.8736	−	6.85465i	−0.0222041	−	0.00665403i
$103$	839.534	+	1454.11i	0.803123	+	1.39105i	0.917551	+	0.397619i	$0.130163\pi$
$103$	839.534	+	1454.11i	0.803123	+	1.39105i	−0.114427	+	0.993432i	$0.536503\pi$
$104$	28.3784	+	49.1527i	0.0267570	+	0.0463445i
$105$	166.675	+	704.104i	0.154912	+	0.654415i
$106$	−0.146057	+	0.252978i	−0.000133833	+	0.000231806i
$107$	−378.360			−0.341845			−0.170922	−	0.985284i	$-0.554675\pi$
$107$	−378.360			−0.341845			−0.170922	+	0.985284i	$0.554675\pi$
$108$	384.434	−	1053.56i	0.342520	−	0.938694i
$109$	−1904.42			−1.67349			−0.836744	−	0.547594i	$-0.815544\pi$
$109$	−1904.42			−1.67349			−0.836744	+	0.547594i	$0.815544\pi$
$110$	4.06868	−	7.04717i	0.00352667	−	0.00610837i
$111$	243.390	+	1028.18i	0.208122	+	0.879195i
$112$	470.781	+	815.417i	0.397184	+	0.687943i
$113$	−967.208	−	1675.25i	−0.805197	−	1.39464i	−0.916158	−	0.400817i	$-0.868726\pi$
$113$	−967.208	−	1675.25i	−0.805197	−	1.39464i	0.110961	−	0.993825i	$-0.464607\pi$
$114$	−11.5874	−	3.47246i	−0.00951982	−	0.00285285i
$115$	−439.532	+	761.291i	−0.356405	+	0.617311i
$116$	−1190.78			−0.953110
$117$	1021.52	+	672.657i	0.807176	+	0.531514i
$118$	−20.2097			−0.0157665
$119$	432.514	−	749.136i	0.333181	−	0.577086i
$120$	44.7296	−	42.1773i	0.0340270	−	0.0320854i
$121$	−60.5000	−	104.789i	−0.0454545	−	0.0787296i
$122$	29.9399	+	51.8574i	0.0222183	+	0.0384832i
$123$	−209.914	+	197.936i	−0.153880	+	0.145100i
$124$	669.606	−	1159.79i	0.484939	−	0.839938i
$125$	1518.71			1.08670
$126$	−26.0486	−	17.1526i	−0.0184174	−	0.0121276i
$127$	−24.0310			−0.0167906			−0.00839529	−	0.999965i	$-0.502672\pi$
$127$	−24.0310			−0.0167906			−0.00839529	+	0.999965i	$0.502672\pi$
$128$	80.0632	−	138.673i	0.0552863	−	0.0957587i
$129$	1981.72	+	593.873i	1.35257	+	0.405331i
$130$	16.7556	+	29.0215i	0.0113043	+	0.0195796i
$131$	−1375.52	−	2382.48i	−0.917405	−	1.58899i	−0.803342	−	0.595518i	$-0.796947\pi$
$131$	−1375.52	−	2382.48i	−0.917405	−	1.58899i	−0.114063	−	0.993473i	$-0.536387\pi$
$132$	−105.251	−	444.623i	−0.0694006	−	0.293178i
$133$	219.105	−	379.501i	0.142848	−	0.247420i
$134$	0.647890			0.000417681
$135$	454.140	−	1244.60i	0.289527	−	0.793464i
$136$	−73.4988			−0.0463417
$137$	−87.6219	+	151.766i	−0.0546426	+	0.0946438i	−0.892053	−	0.451931i	$-0.850735\pi$
$137$	−87.6219	+	151.766i	−0.0546426	+	0.0946438i	0.837410	+	0.546575i	$0.184069\pi$
$138$	−8.72842	−	36.8726i	−0.00538415	−	0.0227449i
$139$	461.421	+	799.204i	0.281563	+	0.487681i	0.971770	−	0.235931i	$-0.0758139\pi$
$139$	461.421	+	799.204i	0.281563	+	0.487681i	−0.690207	+	0.723612i	$0.742481\pi$
$140$	556.572	+	964.010i	0.335992	+	0.581955i
$141$	580.868	+	174.072i	0.346935	+	0.103968i
$142$	−40.4712	+	70.0981i	−0.0239174	+	0.0414261i
$143$	498.299			0.291398
$144$	101.175	−	1721.05i	0.0585502	−	0.995980i
$145$	−1406.69			−0.805650
$146$	6.29530	−	10.9038i	0.00356851	−	0.00618084i
$147$	−474.682	+	447.597i	−0.266334	+	0.251137i
$148$	812.744	+	1407.71i	0.451400	+	0.781847i
$149$	−1381.77	−	2393.30i	−0.759727	−	1.31589i	−0.942990	−	0.332822i	$-0.891999\pi$
$149$	−1381.77	−	2393.30i	−0.759727	−	1.31589i	0.183262	−	0.983064i	$-0.441334\pi$
$150$	−10.6093	+	10.0039i	−0.00577494	+	0.00544543i
$151$	236.463	−	409.565i	0.127438	−	0.220728i	−0.795246	−	0.606287i	$-0.792658\pi$
$151$	236.463	−	409.565i	0.127438	−	0.220728i	0.922683	+	0.385559i	$0.125991\pi$
$152$	−37.2333			−0.0198686
$153$	−1415.80	+	710.082i	−0.748108	+	0.375207i
$154$	−12.7066			−0.00664886
$155$	791.020	−	1370.09i	0.409911	−	0.709988i
$156$	1802.44	+	540.148i	0.925071	+	0.277221i
$157$	−1309.21	−	2267.62i	−0.665520	−	1.15271i	−0.979144	−	0.203167i	$-0.934877\pi$
$157$	−1309.21	−	2267.62i	−0.665520	−	1.15271i	0.313624	−	0.949547i	$-0.398457\pi$
$158$	−25.5216	−	44.2047i	−0.0128506	−	0.0222578i
$159$	4.46336	+	18.8551i	0.00222621	+	0.00940445i
$160$	70.9444	−	122.879i	0.0350540	−	0.0607154i
$161$	1372.66			0.671932
$162$	22.5624	+	52.4615i	0.0109424	+	0.0254430i
$163$	−3111.19			−1.49501			−0.747506	−	0.664255i	$-0.768749\pi$
$163$	−3111.19			−1.49501			−0.747506	+	0.664255i	$0.768749\pi$
$164$	−221.931	+	384.395i	−0.105670	+	0.183026i
$165$	−124.335	−	525.243i	−0.0586633	−	0.247819i
$166$	−43.9944	−	76.2006i	−0.0205701	−	0.0356284i
$167$	891.988	+	1544.97i	0.413318	+	0.715887i	0.995250	−	0.0973497i	$-0.0310365\pi$
$167$	891.988	+	1544.97i	0.413318	+	0.715887i	−0.581932	+	0.813237i	$0.697703\pi$
$168$	−91.9594	−	27.5580i	−0.0422311	−	0.0126556i
$169$	72.4574	−	125.500i	0.0329801	−	0.0571233i
$170$	−43.3962			−0.0195785
$171$	−717.221	+	359.716i	−0.320744	+	0.160867i
$172$	3182.68			1.41091
$173$	−683.114	+	1183.19i	−0.300209	+	0.519978i	−0.976183	−	0.216948i	$-0.930390\pi$
$173$	−683.114	+	1183.19i	−0.300209	+	0.519978i	0.675974	+	0.736926i	$0.263723\pi$
$174$	44.1154	−	41.5981i	0.0192206	−	0.0181238i
$175$	−264.124	−	457.476i	−0.114091	−	0.197611i
$176$	−351.190	−	608.279i	−0.150409	−	0.260516i
$177$	−975.312	+	919.661i	−0.414175	+	0.390542i
$178$	44.6937	−	77.4118i	0.0188199	−	0.0325970i
$179$	−1191.29			−0.497438			−0.248719	−	0.968576i	$-0.580010\pi$
$179$	−1191.29			−0.497438			−0.248719	+	0.968576i	$0.580010\pi$
$180$	119.612	−	2034.68i	0.0495297	−	0.842535i
$181$	−4079.25			−1.67518			−0.837592	−	0.546296i	$-0.816037\pi$
$181$	−4079.25			−1.67518			−0.837592	+	0.546296i	$0.816037\pi$
$182$	26.1639	−	45.3173i	0.0106560	−	0.0184568i
$183$	3804.71	+	1140.18i	1.53690	+	0.460570i
$184$	−58.3155	−	101.005i	−0.0233646	−	0.0404686i
$185$	960.113	+	1662.96i	0.381562	+	0.660884i
$186$	15.7085	+	66.3592i	0.00619247	+	0.0261596i
$187$	−322.644	+	558.836i	−0.126171	+	0.218535i
$188$	932.881			0.361901
$189$	−2037.64	+	357.586i	−0.784216	+	0.137622i
$190$	−21.9838			−0.00839408
$191$	−145.069	+	251.268i	−0.0549574	+	0.0951889i	−0.892195	−	0.451650i	$-0.850836\pi$
$191$	−145.069	+	251.268i	−0.0549574	+	0.0951889i	0.837238	+	0.546839i	$0.184169\pi$
$192$	−610.018	−	2576.98i	−0.229293	−	0.968631i
$193$	1760.01	+	3048.43i	0.656417	+	1.13695i	0.981536	+	0.191275i	$0.0612622\pi$
$193$	1760.01	+	3048.43i	0.656417	+	1.13695i	−0.325119	+	0.945673i	$0.605404\pi$
$194$	10.5928	+	18.3472i	0.00392019	+	0.00678997i
$195$	2129.27	+	638.089i	0.781949	+	0.234331i
$196$	−501.857	+	869.241i	−0.182892	+	0.316779i
$197$	−3541.38			−1.28077			−0.640387	−	0.768052i	$-0.721226\pi$
$197$	−3541.38			−1.28077			−0.640387	+	0.768052i	$0.721226\pi$
$198$	19.4316	+	12.7954i	0.00697445	+	0.00459258i
$199$	2678.64			0.954189			0.477094	−	0.878852i	$-0.341690\pi$
$199$	2678.64			0.954189			0.477094	+	0.878852i	$0.341690\pi$
$200$	−22.4418	+	38.8703i	−0.00793438	+	0.0137427i
$201$	31.2670	−	29.4829i	0.0109721	−	0.0103461i
$202$	70.7173	+	122.486i	0.0246319	+	0.0426638i
$203$	1098.28	+	1902.28i	0.379725	+	0.657702i
$204$	−1772.83	+	1671.68i	−0.608447	+	0.573729i
$205$	−262.172	+	454.095i	−0.0893213	+	0.154709i
$206$	−131.533			−0.0444870
$207$	−2099.15	−	1382.26i	−0.704837	−	0.464125i
$208$	2892.53			0.964234
$209$	−163.446	+	283.097i	−0.0540948	+	0.0936950i
$210$	−54.2960	−	16.2712i	−0.0178418	−	0.00534675i
$211$	1485.93	+	2573.70i	0.484813	+	0.839720i	0.999848	−	0.0174490i	$-0.00555446\pi$
$211$	1485.93	+	2573.70i	0.484813	+	0.839720i	−0.515035	+	0.857169i	$0.672221\pi$
$212$	14.9044	+	25.8151i	0.00482847	+	0.00836316i
$213$	1236.76	+	5224.59i	0.397846	+	1.68067i
$214$	14.8198	−	25.6686i	0.00473391	−	0.00819938i
$215$	3759.77			1.19262
$216$	112.879	+	134.746i	0.0355575	+	0.0424457i
$217$	−2470.37			−0.772809
$218$	74.5931	−	129.199i	0.0231747	−	0.0401397i
$219$	−192.378	−	812.686i	−0.0593593	−	0.250759i
$220$	−415.188	−	719.126i	−0.127236	−	0.220379i
$221$	−1328.70	−	2301.38i	−0.404427	−	0.700488i
$222$	−79.2868	−	23.7603i	−0.0239702	−	0.00718327i
$223$	−942.217	+	1631.97i	−0.282939	+	0.490065i	−0.972107	−	0.234536i	$-0.924643\pi$
$223$	−942.217	+	1631.97i	−0.282939	+	0.490065i	0.689168	+	0.724602i	$0.257976\pi$
$224$	−221.560			−0.0660876
$225$	−56.7624	+	965.568i	−0.0168185	+	0.286094i
$226$	151.536			0.0446019
$227$	−1361.33	+	2357.89i	−0.398038	+	0.689422i	−0.993484	−	0.113974i	$-0.963642\pi$
$227$	−1361.33	+	2357.89i	−0.398038	+	0.689422i	0.595446	+	0.803395i	$0.296975\pi$
$228$	−898.089	+	846.844i	−0.260866	+	0.245981i
$229$	−1290.22	−	2234.73i	−0.372316	−	0.644870i	0.617605	−	0.786488i	$-0.288103\pi$
$229$	−1290.22	−	2234.73i	−0.372316	−	0.644870i	−0.989921	+	0.141618i	$0.954770\pi$
$230$	−34.4315	−	59.6371i	−0.00987107	−	0.0170972i
$231$	−613.214	+	578.224i	−0.174660	+	0.164694i
$232$	93.3175	−	161.631i	0.0264077	−	0.0457395i
$233$	−1821.74			−0.512216			−0.256108	−	0.966648i	$-0.582440\pi$
$233$	−1821.74			−0.512216			−0.256108	+	0.966648i	$0.582440\pi$
$234$	−85.6455	+	42.9547i	−0.0239266	+	0.0120002i
$235$	1102.03			0.305910
$236$	−1031.15	+	1786.00i	−0.284415	+	0.492621i
$237$	−3243.24	−	971.919i	−0.888907	−	0.266384i
$238$	33.8818	+	58.6850i	0.00922785	+	0.0159831i
$239$	2100.88	+	3638.83i	0.568597	+	0.984840i	0.996705	+	0.0811118i	$0.0258471\pi$
$239$	2100.88	+	3638.83i	0.568597	+	0.984840i	−0.428108	+	0.903728i	$0.640820\pi$
$240$	−721.738	−	3048.93i	−0.194117	−	0.820031i
$241$	2962.33	−	5130.90i	0.791785	−	1.37141i	−0.133076	−	0.991106i	$-0.542485\pi$
$241$	2962.33	−	5130.90i	0.791785	−	1.37141i	0.924861	−	0.380306i	$-0.124181\pi$
$242$	9.47876			0.00251784
$243$	3476.16	+	1505.05i	0.917679	+	0.397322i
$244$	6110.42			1.60319
$245$	−592.854	+	1026.85i	−0.154596	+	0.267769i
$246$	−5.20633	−	21.9938i	−0.00134936	−	0.00570029i
$247$	−673.101	−	1165.84i	−0.173394	−	0.300328i
$248$	104.950	+	181.779i	0.0268723	+	0.0465441i
$249$	−5590.73	−	1675.40i	−1.42289	−	0.426403i
$250$	−59.4855	+	103.032i	−0.0150488	+	0.0260652i
$251$	−3024.65			−0.760614			−0.380307	−	0.924860i	$-0.624182\pi$
$251$	−3024.65			−0.760614			−0.380307	+	0.924860i	$0.624182\pi$
$252$	−2844.90	+	1426.83i	−0.711158	+	0.356675i
$253$	−1023.97			−0.254453
$254$	0.941256	−	1.63030i	0.000232518	−	0.000402733i
$255$	−2094.29	+	1974.79i	−0.514311	+	0.484965i
$256$	−2032.31	−	3520.06i	−0.496169	−	0.859390i
$257$	558.674	+	967.651i	0.135600	+	0.234865i	0.925826	−	0.377949i	$-0.123371\pi$
$257$	558.674	+	967.651i	0.135600	+	0.234865i	−0.790227	+	0.612815i	$0.790037\pi$
$258$	−117.910	+	111.182i	−0.0284526	+	0.0268291i
$259$	1499.22	−	2596.73i	0.359680	−	0.622985i
$260$	3419.63			0.815679
$261$	236.029	−	4015.02i	0.0559764	−	0.952198i
$262$	215.508			0.0508174
$263$	2765.49	−	4789.96i	0.648392	−	1.12305i	−0.335114	−	0.942177i	$-0.608775\pi$
$263$	2765.49	−	4789.96i	0.648392	−	1.12305i	0.983507	−	0.180871i	$-0.0578917\pi$
$264$	68.5993	+	20.5575i	0.0159924	+	0.00479253i
$265$	17.6069	+	30.4960i	0.00408144	+	0.00706925i
$266$	17.1640	+	29.7289i	0.00395636	+	0.00685261i
$267$	−1365.79	−	5769.70i	−0.313053	−	1.32247i
$268$	33.0569	−	57.2562i	0.00753460	−	0.0130503i
$269$	2304.66			0.522371			0.261186	−	0.965289i	$-0.415887\pi$
$269$	2304.66			0.522371			0.261186	+	0.965289i	$0.415887\pi$
$270$	66.6475	+	79.5585i	0.0150224	+	0.0179325i
$271$	−648.267			−0.145312			−0.0726558	−	0.997357i	$-0.523147\pi$
$271$	−648.267			−0.145312			−0.0726558	+	0.997357i	$0.523147\pi$
$272$	−1872.88	+	3243.93i	−0.417501	+	0.723132i
$273$	−799.543	−	3377.61i	−0.177255	−	0.748800i
$274$	−6.86402	−	11.8888i	−0.00151340	−	0.00262128i
$275$	197.029	+	341.265i	0.0432048	+	0.0748329i
$276$	−3703.90	−	1109.97i	−0.807784	−	0.242073i
$277$	2400.17	−	4157.22i	0.520622	−	0.901744i	−0.479090	−	0.877766i	$-0.659033\pi$
$277$	2400.17	−	4157.22i	0.520622	−	0.901744i	0.999712	−	0.0239785i	$-0.00763333\pi$
$278$	−72.2925			−0.0155965
$279$	3777.82	+	2487.64i	0.810654	+	0.533804i
$280$	−174.467			−0.0372372
$281$	2019.33	−	3497.58i	0.428694	−	0.742519i	−0.568064	−	0.822985i	$-0.692307\pi$
$281$	2019.33	−	3497.58i	0.428694	−	0.742519i	0.996757	+	0.0804653i	$0.0256406\pi$
$282$	−34.5610	+	32.5889i	−0.00729814	+	0.00688171i
$283$	−638.509	−	1105.93i	−0.134118	−	0.232299i	0.791142	−	0.611632i	$-0.209487\pi$
$283$	−638.509	−	1105.93i	−0.134118	−	0.232299i	−0.925260	+	0.379333i	$0.876153\pi$
$284$	4129.87	+	7153.14i	0.862897	+	1.49458i
$285$	−1060.93	+	1000.40i	−0.220506	+	0.207924i
$286$	−19.5176	+	33.8055i	−0.00403531	+	0.00698937i
$287$	818.766			0.168398
$288$	338.822	+	223.110i	0.0693240	+	0.0456489i
$289$	−1471.71			−0.299554
$290$	55.0978	−	95.4323i	0.0111567	−	0.0193241i
$291$	1346.11	+	403.397i	0.271170	+	0.0812630i
$292$	−642.402	−	1112.67i	−0.128746	−	0.222994i
$293$	1098.88	+	1903.31i	0.219103	+	0.379498i	0.954534	−	0.298102i	$-0.0963536\pi$
$293$	1098.88	+	1903.31i	0.219103	+	0.379498i	−0.735431	+	0.677600i	$0.763020\pi$
$294$	−11.7732	−	49.7349i	−0.00233546	−	0.00986599i
$295$	−1218.12	+	2109.84i	−0.240412	+	0.416405i
$296$	−254.769			−0.0500275
$297$	1520.03	−	266.750i	0.296973	−	0.0521158i
$298$	216.488			0.0420832
$299$	2108.45	−	3651.94i	0.407808	−	0.706344i
$300$	342.768	+	1448.00i	0.0659657	+	0.278667i
$301$	−2935.45	−	5084.35i	−0.562115	−	0.973612i
$302$	18.5237	+	32.0841i	0.00352954	+	0.00611335i
$303$	8986.63	+	2693.07i	1.70386	+	0.510604i
$304$	−948.773	+	1643.32i	−0.178999	+	0.310036i
$305$	7218.37			1.35516
$306$	7.28147	−	123.863i	0.00136031	−	0.0231398i
$307$	7542.25			1.40215			0.701073	−	0.713089i	$-0.252705\pi$
$307$	7542.25			1.40215			0.701073	+	0.713089i	$0.252705\pi$
$308$	−648.319	+	1122.92i	−0.119940	+	0.207741i
$309$	−6347.73	+	5985.53i	−1.16864	+	1.10196i
$310$	61.9660	+	107.328i	0.0113530	+	0.0196640i
$311$	1421.35	+	2461.86i	0.259156	+	0.448871i	0.966016	−	0.258482i	$-0.0832223\pi$
$311$	1421.35	+	2461.86i	0.259156	+	0.448871i	−0.706860	+	0.707353i	$0.749889\pi$
$312$	−214.569	+	202.326i	−0.0389346	+	0.0367130i
$313$	5077.22	−	8794.00i	0.916873	−	1.58807i	0.112737	−	0.993625i	$-0.464038\pi$
$313$	5077.22	−	8794.00i	0.916873	−	1.58807i	0.804136	−	0.594445i	$-0.202628\pi$
$314$	205.119			0.0368648
$315$	−3360.74	+	1685.55i	−0.601131	+	0.301492i
$316$	−5208.69			−0.927252
$317$	−918.635	+	1591.12i	−0.162762	+	0.281913i	−0.935858	−	0.352376i	$-0.885374\pi$
$317$	−918.635	+	1591.12i	−0.162762	+	0.281913i	0.773096	+	0.634289i	$0.218707\pi$
$318$	−1.45399	−	0.435724i	−0.000256401	−	7.68370e-5i
$319$	−819.287	−	1419.05i	−0.143797	−	0.249064i
$320$	−2406.37	−	4167.96i	−0.420376	−	0.728113i
$321$	−452.876	−	1913.14i	−0.0787448	−	0.332652i
$322$	−53.7651	+	93.1238i	−0.00930500	+	0.0161167i
$323$	1743.30			0.300310
$324$	5787.39	+	682.800i	0.992350	+	0.117078i
$325$	−1622.80			−0.276975
$326$	121.860	−	211.068i	0.0207031	−	0.0358589i
$327$	−2279.49	−	9629.53i	−0.385492	−	1.62848i
$328$	−34.7841	−	60.2477i	−0.00585557	−	0.0101421i
$329$	−860.417	−	1490.29i	−0.144183	−	0.249733i
$330$	40.5034	+	12.1379i	0.00675648	+	0.00202475i
$331$	−2666.62	+	4618.72i	−0.442812	+	0.766973i	−0.997897	−	0.0648210i	$-0.979352\pi$
$331$	−2666.62	+	4618.72i	−0.442812	+	0.766973i	0.555085	+	0.831794i	$0.312686\pi$
$332$	−8978.80			−1.48426
$333$	−4907.59	+	2461.36i	−0.807610	+	0.405050i
$334$	−139.751			−0.0228947
$335$	39.0509	−	67.6381i	0.00636888	−	0.0110312i
$336$	−3559.58	+	3356.47i	−0.577950	+	0.544972i
$337$	157.385	+	272.598i	0.0254400	+	0.0440634i	0.878465	−	0.477806i	$-0.158568\pi$
$337$	157.385	+	272.598i	0.0254400	+	0.0440634i	−0.853025	+	0.521870i	$0.825235\pi$
$338$	5.67608	+	9.83126i	0.000913427	+	0.00158210i
$339$	7313.07	−	6895.79i	1.17166	−	1.10480i
$340$	−2214.18	+	3835.07i	−0.353179	+	0.611723i
$341$	1842.83			0.292653
$342$	3.68868	−	62.7470i	0.000583219	−	0.00992097i
$343$	6909.31			1.08766
$344$	−249.416	+	432.002i	−0.0390920	+	0.0677092i
$345$	−4375.50	−	1311.23i	−0.682808	−	0.204621i
$346$	−53.5130	−	92.6873i	−0.00831468	−	0.0144014i
$347$	−4900.31	−	8487.58i	−0.758105	−	1.31308i	−0.943816	−	0.330471i	$-0.892792\pi$
$347$	−4900.31	−	8487.58i	−0.758105	−	1.31308i	0.185711	−	0.982604i	$-0.440541\pi$
$348$	−1425.30	−	6021.06i	−0.219551	−	0.927479i
$349$	−3181.28	+	5510.13i	−0.487936	+	0.845131i	−0.999904	−	0.0138742i	$-0.995584\pi$
$349$	−3181.28	+	5510.13i	−0.487936	+	0.845131i	0.511967	+	0.859005i	$0.328917\pi$
$350$	41.3813			0.00631977
$351$	−2178.53	+	5970.36i	−0.331285	+	0.907904i
$352$	165.278			0.0250266
$353$	−4135.51	+	7162.91i	−0.623544	+	1.08001i	0.365277	+	0.930899i	$0.380974\pi$
$353$	−4135.51	+	7162.91i	−0.623544	+	1.08001i	−0.988821	+	0.149111i	$0.952359\pi$
$354$	−24.1899	−	102.188i	−0.00363186	−	0.0153425i
$355$	4878.71	+	8450.17i	0.729394	+	1.26335i
$356$	−4560.76	−	7899.47i	−0.678988	−	1.17604i
$357$	4305.64	+	1290.29i	0.638315	+	0.191287i
$358$	46.6610	−	80.8193i	0.00688858	−	0.0119314i
$359$	−9012.63			−1.32498			−0.662491	−	0.749070i	$-0.730501\pi$
$359$	−9012.63			−1.32498			−0.662491	+	0.749070i	$0.730501\pi$
$360$	266.805	+	175.687i	0.0390607	+	0.0257209i
$361$	−5975.87			−0.871245
$362$	159.778	−	276.743i	0.0231982	−	0.0401804i
$363$	457.442	−	431.340i	0.0661418	−	0.0623677i
$364$	−2669.89	−	4624.39i	−0.384452	−	0.665890i
$365$	−758.884	−	1314.43i	−0.108827	−	0.188494i
$366$	−226.376	+	213.459i	−0.0323302	+	0.0304855i
$367$	−1887.71	+	3269.61i	−0.268495	+	0.465048i	−0.968473	−	0.249117i	$-0.919860\pi$
$367$	−1887.71	+	3269.61i	−0.268495	+	0.465048i	0.699978	+	0.714164i	$0.253193\pi$
$368$	−5943.94			−0.841982
$369$	−1252.10	−	824.492i	−0.176645	−	0.116318i
$370$	−150.424			−0.0211357
$371$	27.4932	−	47.6197i	0.00384738	−	0.00666386i
$372$	6665.87	+	1997.60i	0.929057	+	0.278415i
$373$	6627.73	+	11479.6i	0.920029	+	1.59354i	0.799367	+	0.600843i	$0.205168\pi$
$373$	6627.73	+	11479.6i	0.920029	+	1.59354i	0.120662	+	0.992694i	$0.461498\pi$
$374$	−25.2749	−	43.7774i	−0.00349448	−	0.00605261i
$375$	1817.81	+	7679.22i	0.250324	+	1.05748i
$376$	−73.1070	+	126.625i	−0.0100271	+	0.0173675i
$377$	6747.94			0.921848
$378$	55.5521	−	152.243i	0.00755897	−	0.0207157i
$379$	2567.88			0.348029			0.174014	−	0.984743i	$-0.444326\pi$
$379$	2567.88			0.348029			0.174014	+	0.984743i	$0.444326\pi$
$380$	−1121.67	+	1942.79i	−0.151422	+	0.262271i
$381$	−28.7638	−	121.511i	−0.00386775	−	0.0163390i
$382$	−11.3643	−	19.6835i	−0.00152211	−	0.00263638i
$383$	6809.92	+	11795.1i	0.908540	+	1.57364i	0.816094	+	0.577919i	$0.196135\pi$
$383$	6809.92	+	11795.1i	0.908540	+	1.57364i	0.0924458	+	0.995718i	$0.470532\pi$
$384$	797.022	+	238.848i	0.105919	+	0.0317413i
$385$	−765.874	+	1326.53i	−0.101383	+	0.175601i
$386$	−275.748			−0.0363606
$387$	−630.853	+	10731.2i	−0.0828632	+	1.40956i
$388$	2161.88			0.282868
$389$	1366.51	−	2366.86i	0.178110	−	0.308495i	−0.763123	−	0.646253i	$-0.776335\pi$
$389$	1366.51	−	2366.86i	0.178110	−	0.308495i	0.941233	+	0.337758i	$0.109668\pi$
$390$	−126.689	+	119.460i	−0.0164491	+	0.0155105i
$391$	2730.40	+	4729.19i	0.353151	+	0.611676i
$392$	−78.6579	−	136.239i	−0.0101348	−	0.0175539i
$393$	10400.4	−	9806.91i	1.33493	−	1.25876i
$394$	138.710	−	240.253i	0.0177363	−	0.0307202i
$395$	−6153.14			−0.783792
$396$	2122.22	−	1064.38i	0.269307	−	0.135068i
$397$	8924.95			1.12829			0.564144	−	0.825676i	$-0.309206\pi$
$397$	8924.95			1.12829			0.564144	+	0.825676i	$0.309206\pi$
$398$	−104.918	+	181.723i	−0.0132137	+	0.0228868i
$399$	2181.17	+	653.642i	0.273672	+	0.0820126i
$400$	1143.72	+	1980.97i	0.142964	+	0.247622i
$401$	−1558.67	−	2699.70i	−0.194105	−	0.336200i	0.752501	−	0.658591i	$-0.228847\pi$
$401$	−1558.67	−	2699.70i	−0.194105	−	0.336200i	−0.946607	+	0.322390i	$0.895514\pi$
$402$	0.775490	+	3.27600i	9.62138e−5	+	0.000406448i
$403$	−3794.55	+	6572.35i	−0.469032	+	0.812388i
$404$	14432.7			1.77736
$405$	6836.77	+	806.607i	0.838819	+	0.0989645i
$406$	−172.071			−0.0210339
$407$	−1118.38	+	1937.09i	−0.136207	+	0.235917i
$408$	−87.9742	−	371.640i	−0.0106749	−	0.0450954i
$409$	−4189.20	−	7255.91i	−0.506461	−	0.877217i	−0.999972	−	0.00747708i	$-0.997620\pi$
$409$	−4189.20	−	7255.91i	−0.506461	−	0.877217i	0.493511	−	0.869740i	$-0.335713\pi$
$410$	−20.5377	−	35.5723i	−0.00247387	−	0.00428486i
$411$	−872.268	−	261.397i	−0.104686	−	0.0313717i
$412$	−6711.12	+	11624.0i	−0.802507	+	1.38998i
$413$	3804.19			0.453250
$414$	175.996	−	88.2690i	0.0208930	−	0.0104787i
$415$	−10606.9			−1.25463
$416$	−340.323	+	589.456i	−0.0401098	+	0.0694722i
$417$	−3488.81	+	3289.74i	−0.409707	+	0.386329i
$418$	−12.8039	−	22.1770i	−0.00149822	−	0.00259500i
$419$	−5225.34	−	9050.55i	−0.609247	−	1.05525i	−0.991365	−	0.131133i	$-0.958138\pi$
$419$	−5225.34	−	9050.55i	−0.609247	−	1.05525i	0.382118	−	0.924114i	$-0.375195\pi$
$420$	−4208.25	+	3968.13i	−0.488908	+	0.461011i
$421$	−5937.34	+	10283.8i	−0.687335	+	1.19050i	0.285362	+	0.958420i	$0.407886\pi$
$421$	−5937.34	+	10283.8i	−0.687335	+	1.19050i	−0.972697	+	0.232079i	$0.925447\pi$
$422$	−232.806			−0.0268550
$423$	−184.911	+	3145.46i	−0.0212545	+	0.361555i
$424$	−4.67203			−0.000535128
$425$	1050.75	−	1819.95i	0.119927	−	0.207719i
$426$	−402.887	−	120.735i	−0.0458214	−	0.0137316i
$427$	−5635.77	−	9761.45i	−0.638722	−	1.10630i
$428$	−1512.28	−	2619.34i	−0.170791	−	0.295819i
$429$	596.438	+	2519.61i	0.0671242	+	0.283561i
$430$	−147.264	+	255.069i	−0.0165156	+	0.0286058i
$431$	−15521.2			−1.73464			−0.867322	−	0.497747i	$-0.834161\pi$
$431$	−15521.2			−1.73464			−0.867322	+	0.497747i	$0.834161\pi$
$432$	8823.46	−	1548.43i	0.982682	−	0.172451i
$433$	2509.27			0.278494			0.139247	−	0.990258i	$-0.455532\pi$
$433$	2509.27			0.278494			0.139247	+	0.990258i	$0.455532\pi$
$434$	96.7604	−	167.594i	0.0107020	−	0.0185363i
$435$	−1683.73	−	7112.81i	−0.185584	−	0.783984i
$436$	−7611.83	−	13184.1i	−0.836102	−	1.44817i
$437$	1383.18	+	2395.73i	0.151410	+	0.262250i
$438$	62.6691	+	18.7804i	0.00683664	+	0.00204877i
$439$	3657.68	−	6335.30i	0.397658	−	0.688763i	−0.595779	−	0.803149i	$-0.703156\pi$
$439$	3657.68	−	6335.30i	0.397658	−	0.688763i	0.993436	+	0.114385i	$0.0364898\pi$
$440$	130.148			0.0141013
$441$	−2831.41	−	1864.44i	−0.305734	−	0.201322i
$442$	208.173			0.0224022
$443$	1854.79	−	3212.59i	0.198925	−	0.344548i	−0.749255	−	0.662281i	$-0.769588\pi$
$443$	1854.79	−	3212.59i	0.198925	−	0.344548i	0.948180	+	0.317733i	$0.102922\pi$
$444$	−6145.17	+	5794.53i	−0.656840	+	0.619361i
$445$	−5387.73	−	9331.82i	−0.573939	−	0.994091i
$446$	−73.8103	−	127.843i	−0.00783636	−	0.0135730i
$447$	10447.6	−	9851.48i	1.10549	−	1.04241i
$448$	−3757.57	+	6508.30i	−0.396269	+	0.686358i
$449$	9350.80			0.982832			0.491416	−	0.870925i	$-0.336480\pi$
$449$	9350.80			0.982832			0.491416	+	0.870925i	$0.336480\pi$
$450$	−63.2825	−	41.6706i	−0.00662926	−	0.00436527i
$451$	−610.778			−0.0637703
$452$	7731.73	−	13391.7i	0.804579	−	1.39357i
$453$	2353.97	+	705.425i	0.244148	+	0.0731651i
$454$	−106.642	−	184.710i	−0.0110242	−	0.0190944i
$455$	−3154.00	−	5462.89i	−0.324971	−	0.562867i
$456$	−44.5663	−	188.267i	−0.00457677	−	0.0193342i
$457$	−326.568	+	565.632i	−0.0334272	+	0.0578975i	−0.882255	−	0.470772i	$-0.843976\pi$
$457$	−326.568	+	565.632i	−0.0334272	+	0.0578975i	0.848828	+	0.528669i	$0.177309\pi$
$458$	202.144			0.0206235
$459$	−5285.10	−	6308.94i	−0.537445	−	0.641560i
$460$	−7027.11			−0.712262
$461$	4003.65	−	6934.53i	0.404487	−	0.700593i	−0.589774	−	0.807568i	$-0.700783\pi$
$461$	4003.65	−	6934.53i	0.404487	−	0.700593i	0.994262	+	0.106975i	$0.0341166\pi$
$462$	−15.2091	−	64.2496i	−0.00153158	−	0.00647005i
$463$	4729.05	+	8190.95i	0.474681	+	0.822172i	0.999580	−	0.0289927i	$-0.00922997\pi$
$463$	4729.05	+	8190.95i	0.474681	+	0.822172i	−0.524898	+	0.851165i	$0.675897\pi$
$464$	−4755.79	−	8237.28i	−0.475824	−	0.824151i
$465$	7874.54	+	2359.80i	0.785318	+	0.235340i
$466$	71.3548	−	123.590i	0.00709323	−	0.0122858i
$467$	−5785.61			−0.573289			−0.286645	−	0.958037i	$-0.592540\pi$
$467$	−5785.61			−0.573289			−0.286645	+	0.958037i	$0.592540\pi$
$468$	−573.782	+	9760.43i	−0.0566732	+	0.964052i
$469$	−121.956			−0.0120073
$470$	−43.1649	+	74.7638i	−0.00423628	+	0.00733744i
$471$	9898.99	−	9334.15i	0.968411	−	0.913153i
$472$	−161.615	−	279.926i	−0.0157605	−	0.0272980i
$473$	2189.77	+	3792.79i	0.212866	+	0.368695i
$474$	192.969	−	181.958i	0.0186991	−	0.0176321i
$475$	532.293	−	921.959i	0.0514174	−	0.0890576i
$476$	6914.91			0.665850
$477$	−89.9969	+	45.1371i	−0.00863873	+	0.00433268i
$478$	−329.153			−0.0314960
$479$	−5783.07	+	10016.6i	−0.551639	+	0.955467i	0.446517	+	0.894775i	$0.352664\pi$
$479$	−5783.07	+	10016.6i	−0.551639	+	0.955467i	−0.998157	+	0.0606920i	$0.980669\pi$
$480$	706.245	+	211.644i	0.0671574	+	0.0201254i
$481$	−4605.69	−	7977.29i	−0.436593	−	0.756202i
$482$	232.059	+	401.938i	0.0219295	+	0.0379830i
$483$	1643.01	+	6940.75i	0.154781	+	0.653862i
$484$	483.629	−	837.670i	0.0454197	−	0.0786692i
$485$	2553.87			0.239104
$486$	−238.261	+	176.878i	−0.0222382	+	0.0165090i
$487$	7377.00			0.686415			0.343207	−	0.939260i	$-0.388487\pi$
$487$	7377.00			0.686415			0.343207	+	0.939260i	$0.388487\pi$
$488$	−478.855	+	829.401i	−0.0444195	+	0.0769369i
$489$	−3723.93	−	15731.5i	−0.344380	−	1.45481i
$490$	−46.4423	−	80.4405i	−0.00428174	−	0.00741619i
$491$	−2202.33	−	3814.54i	−0.202423	−	0.350607i	0.746886	−	0.664953i	$-0.231548\pi$
$491$	−2202.33	−	3814.54i	−0.202423	−	0.350607i	−0.949309	+	0.314346i	$0.898215\pi$
$492$	−2209.30	−	662.073i	−0.202445	−	0.0606678i
$493$	−4369.22	+	7567.72i	−0.399148	+	0.691345i
$494$	105.457			0.00960474
$495$	2507.02	−	1257.38i	0.227641	−	0.114171i
$496$	10697.2			0.968389
$497$	7618.14	−	13195.0i	0.687566	−	1.19090i
$498$	332.643	−	313.662i	0.0299319	−	0.0282239i
$499$	−1145.73	−	1984.47i	−0.102786	−	0.178030i	0.810046	−	0.586367i	$-0.199442\pi$
$499$	−1145.73	−	1984.47i	−0.102786	−	0.178030i	−0.912831	+	0.408337i	$0.866109\pi$
$500$	6070.18	+	10513.9i	0.542933	+	0.940388i
$501$	−6744.33	+	6359.50i	−0.601426	+	0.567109i
$502$	118.471	−	205.197i	0.0105331	−	0.0182438i
$503$	−11301.7			−1.00183			−0.500914	−	0.865497i	$-0.667003\pi$
$503$	−11301.7			−1.00183			−0.500914	+	0.865497i	$0.667003\pi$
$504$	29.2739	−	497.970i	0.00258723	−	0.0440106i
$505$	17049.6			1.50237
$506$	40.1073	−	69.4679i	0.00352369	−	0.00610321i
$507$	721.307	+	216.158i	0.0631841	+	0.0189347i
$508$	−96.0502	−	166.364i	−0.00838885	−	0.0145299i
$509$	8232.74	+	14259.5i	0.716916	+	1.24173i	0.962216	+	0.272287i	$0.0877800\pi$
$509$	8232.74	+	14259.5i	0.716916	+	1.24173i	−0.245301	+	0.969447i	$0.578887\pi$
$510$	−51.9430	−	219.429i	−0.00450995	−	0.0190519i
$511$	−1185.00	+	2052.49i	−0.102586	+	0.177684i
$512$	1599.42			0.138057
$513$	−2677.35	−	3196.01i	−0.230425	−	0.275063i
$514$	−87.5294			−0.00751120
$515$	−7927.99	+	13731.7i	−0.678348	+	1.17493i
$516$	3809.49	+	16092.9i	0.325007	+	1.37297i
$517$	641.848	+	1111.71i	0.0546005	+	0.0945708i
$518$	117.444	+	203.420i	0.00996180	+	0.0172543i
$519$	−6800.34	−	2037.90i	−0.575148	−	0.172358i
$520$	−267.986	+	464.166i	−0.0225999	+	0.0391442i
$521$	−12355.4			−1.03896			−0.519481	−	0.854482i	$-0.673875\pi$
$521$	−12355.4			−1.03896			−0.519481	+	0.854482i	$0.673875\pi$
$522$	263.141	+	173.275i	0.0220639	+	0.0145288i
$523$	18491.9			1.54607			0.773033	−	0.634366i	$-0.218739\pi$
$523$	18491.9			1.54607			0.773033	+	0.634366i	$0.218739\pi$
$524$	10995.7	−	19045.2i	0.916701	−	1.58777i
$525$	1997.05	−	1883.09i	0.166016	−	0.156543i
$526$	216.639	+	375.231i	0.0179580	+	0.0311042i
$527$	−4913.87	−	8511.07i	−0.406170	−	0.703506i
$528$	2655.36	−	2503.84i	0.218863	−	0.206374i
$529$	1750.79	−	3032.46i	0.143897	−	0.249236i
$530$	−2.75853			−0.000226081
$531$	−5817.58	−	3830.80i	−0.475445	−	0.313074i
$532$	3502.99			0.285477
$533$	1257.65	−	2178.31i	0.102204	−	0.177022i
$534$	444.922	+	133.332i	0.0360555	+	0.0108050i
$535$	−1786.49	−	3094.29i	−0.144367	−	0.250052i
$536$	5.18113	+	8.97399i	0.000417520	+	0.000723166i
$537$	−1425.91	−	6023.67i	−0.114586	−	0.484060i
$538$	−90.2700	+	156.352i	−0.00723386	+	0.0125294i
$539$	−1381.17			−0.110373
$540$	10431.4	−	1830.60i	0.831286	−	0.145882i
$541$	−681.711			−0.0541757			−0.0270878	−	0.999633i	$-0.508623\pi$
$541$	−681.711			−0.0541757			−0.0270878	+	0.999633i	$0.508623\pi$
$542$	25.3916	−	43.9796i	0.00201229	−	0.00348539i
$543$	−4882.65	−	20626.4i	−0.385883	−	1.63013i
$544$	−440.711	−	763.334i	−0.0347341	−	0.0601611i
$545$	−8992.03	−	15574.6i	−0.706745	−	1.22412i
$546$	260.460	+	78.0533i	0.0204151	+	0.00611790i
$547$	1823.33	−	3158.09i	0.142523	−	0.246856i	−0.785923	−	0.618324i	$-0.787812\pi$
$547$	1823.33	−	3158.09i	0.142523	−	0.246856i	0.928446	+	0.371468i	$0.121145\pi$
$548$	−1400.87			−0.109201
$549$	−1211.17	+	20602.9i	−0.0941560	+	1.60166i
$550$	−30.8693			−0.00239322
$551$	−2213.38	+	3833.69i	−0.171131	+	0.296407i
$552$	440.925	−	415.766i	0.0339982	−	0.0320583i
$553$	4804.09	+	8320.92i	0.369422	+	0.639858i
$554$	188.022	+	325.663i	0.0144193	+	0.0249749i
$555$	−7259.43	+	6845.21i	−0.555217	+	0.523537i
$556$	−3688.54	+	6388.73i	−0.281347	+	0.487307i
$557$	−1472.43			−0.112009			−0.0560045	−	0.998431i	$-0.517836\pi$
$557$	−1472.43			−0.112009			−0.0560045	+	0.998431i	$0.517836\pi$
$558$	−316.737	+	158.857i	−0.0240297	+	0.0120519i
$559$	−18035.7			−1.36463
$560$	−4445.74	+	7700.25i	−0.335476	+	0.581062i
$561$	−3211.89	−	962.525i	−0.241722	−	0.0724382i
$562$	158.188	+	273.989i	0.0118732	+	0.0205650i
$563$	1418.50	+	2456.91i	0.106186	+	0.183919i	0.914222	−	0.405214i	$-0.132803\pi$
$563$	1418.50	+	2456.91i	0.106186	+	0.183919i	−0.808036	+	0.589133i	$0.799469\pi$
$564$	1116.61	+	4717.03i	0.0833648	+	0.352168i
$565$	9133.66	−	15820.0i	0.680099	−	1.17797i
$566$	100.038			0.00742914
$567$	−4247.05	−	9875.16i	−0.314567	−	0.731425i
$568$	−1294.58			−0.0956327
$569$	−11838.8	+	20505.4i	−0.872248	+	1.51078i	−0.0125824	+	0.999921i	$0.504005\pi$
$569$	−11838.8	+	20505.4i	−0.872248	+	1.51078i	−0.859666	+	0.510857i	$0.829328\pi$
$570$	−26.3135	−	111.159i	−0.00193360	−	0.00816834i
$571$	7429.85	+	12868.9i	0.544535	+	0.943162i	0.998636	+	0.0522118i	$0.0166271\pi$
$571$	7429.85	+	12868.9i	0.544535	+	0.943162i	−0.454101	+	0.890950i	$0.650040\pi$
$572$	1991.67	+	3449.67i	0.145587	+	0.252164i
$573$	−1444.15	−	432.777i	−0.105289	−	0.0315524i
$574$	−32.0698	+	55.5465i	−0.00233200	+	0.00403914i
$575$	3334.75			0.241859
$576$	12300.1	−	6169.01i	0.889764	−	0.446253i
$577$	−18601.1			−1.34207			−0.671033	−	0.741427i	$-0.734149\pi$
$577$	−18601.1			−1.34207			−0.671033	+	0.741427i	$0.734149\pi$
$578$	57.6444	−	99.8431i	0.00414826	−	0.00718499i
$579$	−13307.5	+	12548.2i	−0.955165	+	0.900663i
$580$	−5622.45	−	9738.36i	−0.402516	−	0.697178i
$581$	8281.34	+	14343.7i	0.591339	+	1.02423i
$582$	−80.0922	+	75.5221i	−0.00570435	+	0.00537886i
$583$	−20.5092	+	35.5230i	−0.00145696	+	0.00252352i
$584$	201.372			0.0142686
$585$	−677.821	+	11530.2i	−0.0479051	+	0.814899i
$586$	−172.165			−0.0121367
$587$	−9744.27	+	16877.6i	−0.685160	+	1.18673i	0.288226	+	0.957562i	$0.406935\pi$
$587$	−9744.27	+	16877.6i	−0.685160	+	1.18673i	−0.973386	+	0.229170i	$0.926399\pi$
$588$	−4995.94	−	1497.16i	−0.350389	−	0.105003i
$589$	−2489.29	−	4311.57i	−0.174141	−	0.301622i
$590$	−95.4233	−	165.278i	−0.00665850	−	0.0115329i
$591$	−4238.84	−	17906.7i	−0.295030	−	1.24633i
$592$	−6491.97	+	11244.4i	−0.450707	+	0.780647i
$593$	9066.15			0.627828			0.313914	−	0.949451i	$-0.398360\pi$
$593$	9066.15			0.627828			0.313914	+	0.949451i	$0.398360\pi$
$594$	−41.4404	+	113.569i	−0.00286249	+	0.00784480i
$595$	8168.74			0.562833
$596$	11045.7	−	19131.7i	0.759145	−	1.31488i
$597$	3206.19	+	13544.3i	0.219800	+	0.928528i
$598$	165.169	+	286.081i	0.0112948	+	0.0195631i
$599$	12404.7	+	21485.5i	0.846145	+	1.46557i	0.884623	+	0.466307i	$0.154416\pi$
$599$	12404.7	+	21485.5i	0.846145	+	1.46557i	−0.0384780	+	0.999259i	$0.512251\pi$
$600$	−223.406	−	66.9493i	−0.0152009	−	0.00455532i
$601$	7025.79	−	12169.0i	0.476852	−	0.825931i	−0.522796	−	0.852458i	$-0.675111\pi$
$601$	7025.79	−	12169.0i	0.476852	−	0.825931i	0.999648	+	0.0265262i	$0.00844455\pi$
$602$	459.908			0.0311370
$603$	186.502	+	122.809i	0.0125953	+	0.00829383i
$604$	3780.50			0.254679
$605$	571.321	−	989.558i	0.0383926	−	0.0664979i
$606$	−534.695	+	504.185i	−0.0358424	+	0.0337972i
$607$	7782.77	+	13480.2i	0.520417	+	0.901388i	0.999718	+	0.0237380i	$0.00755674\pi$
$607$	7782.77	+	13480.2i	0.520417	+	0.901388i	−0.479301	+	0.877650i	$0.659110\pi$
$608$	−223.257	−	386.693i	−0.0148919	−	0.0257935i
$609$	−8304.11	+	7830.28i	−0.552544	+	0.521016i
$610$	−282.732	+	489.707i	−0.0187664	+	0.0325043i
$611$	−5286.49			−0.350030
$612$	−10574.7	−	6963.27i	−0.698457	−	0.459924i
$613$	−24858.8			−1.63791			−0.818953	−	0.573860i	$-0.805445\pi$
$613$	−24858.8			−1.63791			−0.818953	+	0.573860i	$0.805445\pi$
$614$	−295.418	+	511.679i	−0.0194171	+	0.0336314i
$615$	−2609.90	−	782.121i	−0.171124	−	0.0512816i
$616$	−101.613	−	176.000i	−0.00664631	−	0.0115117i
$617$	4249.00	+	7359.48i	0.277242	+	0.480197i	0.970698	−	0.240302i	$-0.0772463\pi$
$617$	4249.00	+	7359.48i	0.277242	+	0.480197i	−0.693456	+	0.720499i	$0.743913\pi$
$618$	−157.438	−	665.084i	−0.0102477	−	0.0432906i
$619$	6442.52	−	11158.8i	0.418331	−	0.724570i	−0.577441	−	0.816432i	$-0.695949\pi$
$619$	6442.52	−	11158.8i	0.418331	−	0.724570i	0.995772	+	0.0918624i	$0.0292820\pi$
$620$	12646.6			0.819194
$621$	4476.72	−	12268.7i	0.289283	−	0.792794i
$622$	−222.689			−0.0143553
$623$	−8412.98	+	14571.7i	−0.541025	+	0.937083i
$624$	3462.20	+	14625.8i	0.222114	+	0.938303i
$625$	4931.87	+	8542.24i	0.315639	+	0.546704i
$626$	397.733	+	688.894i	0.0253939	+	0.0439836i
$627$	−1627.09	−	487.600i	−0.103636	−	0.0310572i
$628$	10465.7	−	18127.1i	0.665009	−	1.15183i
$629$	11928.6			0.756157
$630$	17.2843	−	294.019i	0.00109305	−	0.0185936i
$631$	−1589.42			−0.100275			−0.0501377	−	0.998742i	$-0.515966\pi$
$631$	−1589.42			−0.100275			−0.0501377	+	0.998742i	$0.515966\pi$
$632$	408.189	−	707.004i	0.0256913	−	0.0444986i
$633$	−11235.1	+	10594.0i	−0.705460	+	0.665206i
$634$	−71.9630	−	124.643i	−0.00450791	−	0.00780793i
$635$	−113.466	−	196.529i	−0.00709098	−	0.0122819i
$636$	−112.692	+	106.262i	−0.00702600	+	0.00662509i
$637$	2843.94	−	4925.85i	0.176893	−	0.306388i
$638$	128.361			0.00796528
$639$	−24937.4	+	12507.1i	−1.54383	+	0.774294i
$640$	1512.13			0.0933938
$641$	−11763.3	+	20374.6i	−0.724839	+	1.25546i	0.234202	+	0.972188i	$0.424752\pi$
$641$	−11763.3	+	20374.6i	−0.724839	+	1.25546i	−0.959040	+	0.283270i	$0.908581\pi$
$642$	147.529	+	44.2109i	0.00906934	+	0.00271786i
$643$	3590.24	+	6218.47i	0.220195	+	0.381388i	0.954867	−	0.297034i	$-0.0959974\pi$
$643$	3590.24	+	6218.47i	0.220195	+	0.381388i	−0.734672	+	0.678422i	$0.762664\pi$
$644$	5486.44	+	9502.80i	0.335708	+	0.581464i
$645$	4500.24	+	19010.9i	0.274724	+	1.16055i
$646$	−68.2825	+	118.269i	−0.00415873	+	0.00720313i
$647$	24325.3			1.47810			0.739048	−	0.673653i	$-0.235276\pi$
$647$	24325.3			1.47810			0.739048	+	0.673653i	$0.235276\pi$
$648$	−546.220	+	732.045i	−0.0331135	+	0.0443788i
$649$	−2837.83			−0.171640
$650$	63.5627	−	110.094i	0.00383559	−	0.00664344i
$651$	−2956.90	−	12491.2i	−0.178018	−	0.752026i
$652$	−12435.2	−	21538.4i	−0.746933	−	1.29373i
$653$	−942.338	−	1632.18i	−0.0564725	−	0.0978132i	0.836407	−	0.548109i	$-0.184652\pi$
$653$	−942.338	−	1632.18i	−0.0564725	−	0.0978132i	−0.892880	+	0.450295i	$0.851319\pi$
$654$	742.567	+	222.529i	0.0443986	+	0.0133052i
$655$	12989.5	−	22498.5i	0.774874	−	1.34212i
$656$	−3545.44			−0.211016
$657$	3879.01	−	1945.48i	0.230342	−	0.115526i
$658$	134.805			0.00798668
$659$	14179.8	−	24560.1i	0.838188	−	1.45178i	−0.0532210	−	0.998583i	$-0.516949\pi$
$659$	14179.8	−	24560.1i	0.838188	−	1.45178i	0.891409	−	0.453201i	$-0.149718\pi$
$660$	3139.24	−	2960.12i	0.185144	−	0.174579i
$661$	4910.44	+	8505.12i	0.288947	+	0.500470i	0.973559	−	0.228437i	$-0.0733616\pi$
$661$	4910.44	+	8505.12i	0.288947	+	0.500470i	−0.684612	+	0.728908i	$0.740028\pi$
$662$	−208.895	−	361.816i	−0.0122642	−	0.0212423i
$663$	10046.4	−	9473.12i	0.588489	−	0.554910i
$664$	703.641	−	1218.74i	0.0411243	−	0.0712294i
$665$	4138.16			0.241310
$666$	25.2398	−	429.346i	0.00146850	−	0.0249802i
$667$	−13866.5			−0.804970
$668$	−7130.43	+	12350.3i	−0.413001	+	0.715338i
$669$	−9379.68	−	2810.86i	−0.542062	−	0.162443i
$670$	3.05912	+	5.29855i	0.000176394	+	0.000305524i
$671$	4204.14	+	7281.78i	0.241876	+	0.418942i
$672$	−265.196	−	1120.30i	−0.0152235	−	0.0643104i
$673$	8811.48	−	15261.9i	0.504692	−	0.874151i	−0.495294	−	0.868726i	$-0.664940\pi$
$673$	8811.48	−	15261.9i	0.504692	−	0.874151i	0.999985	−	0.00542582i	$-0.00172710\pi$
$674$	−24.6580			−0.00140919
$675$	−4950.25	+	868.720i	−0.282275	+	0.0495363i
$676$	1158.43			0.0659097
$677$	−709.341	+	1228.61i	−0.0402691	+	0.0697481i	−0.885457	−	0.464720i	$-0.846155\pi$
$677$	−709.341	+	1228.61i	−0.0402691	+	0.0697481i	0.845188	+	0.534468i	$0.179488\pi$
$678$	181.380	+	766.229i	0.0102742	+	0.0434024i
$679$	−1993.95	−	3453.61i	−0.112696	−	0.195195i
$680$	−347.037	−	601.085i	−0.0195710	−	0.0338979i
$681$	−13551.9	−	4061.17i	−0.762570	−	0.228523i
$682$	−72.1807	+	125.021i	−0.00405270	+	0.00701949i
$683$	−17878.5			−1.00161			−0.500807	−	0.865559i	$-0.666963\pi$
$683$	−17878.5			−1.00161			−0.500807	+	0.865559i	$0.666963\pi$
$684$	−5356.96	−	3527.48i	−0.299457	−	0.197188i
$685$	−1654.88			−0.0923064
$686$	−270.627	+	468.740i	−0.0150621	+	0.0260883i
$687$	9755.41	−	9198.76i	0.541764	−	0.510851i
$688$	12711.2	+	22016.4i	0.704373	+	1.22001i
$689$	−84.4606	−	146.290i	−0.00467009	−	0.00808884i
$690$	260.337	−	245.482i	0.0143636	−	0.0135440i
$691$	2561.93	−	4437.40i	0.141043	−	0.244293i	−0.786847	−	0.617148i	$-0.788288\pi$
$691$	2561.93	−	4437.40i	0.141043	−	0.244293i	0.927890	+	0.372855i	$0.121621\pi$
$692$	−10921.4			−0.599958
$693$	−3657.73	−	2408.56i	−0.200499	−	0.132026i
$694$	767.749			0.0419933
$695$	−4357.35	+	7547.15i	−0.237818	+	0.411913i
$696$	928.967	+	278.388i	0.0505925	+	0.0151613i
$697$	1628.63	+	2820.86i	0.0885059	+	0.153297i
$698$	−249.211	−	431.646i	−0.0135140	−	0.0234070i
$699$	−2180.53	−	9211.48i	−0.117990	−	0.498441i
$700$	2111.37	−	3657.00i	0.114003	−	0.197459i
$701$	11937.9			0.643205			0.321602	−	0.946875i	$-0.395779\pi$
$701$	11937.9			0.643205			0.321602	+	0.946875i	$0.395779\pi$
$702$	−319.710	−	381.645i	−0.0171890	−	0.0205189i
$703$	6042.82			0.324195
$704$	2803.05	−	4855.02i	0.150062	−	0.259915i
$705$	1319.08	+	5572.34i	0.0704670	+	0.297683i
$706$	−323.963	−	561.120i	−0.0172698	−	0.0299122i
$707$	−13311.6	−	23056.3i	−0.708108	−	1.22648i
$708$	−10265.0	−	3076.16i	−0.544888	−	0.163290i
$709$	2363.49	−	4093.68i	0.125194	−	0.216842i	−0.796615	−	0.604487i	$-0.793378\pi$
$709$	2363.49	−	4093.68i	0.125194	−	0.216842i	0.921809	+	0.387645i	$0.126711\pi$
$710$	−764.365			−0.0404030
$711$	1032.44	−	17562.5i	0.0544577	−	0.926364i
$712$	1429.65			0.0752506
$713$	7797.54	−	13505.7i	0.409565	−	0.709388i
$714$	−256.181	+	241.563i	−0.0134276	+	0.0126614i
$715$	2352.80	+	4075.17i	0.123063	+	0.213151i
$716$	−4761.51	−	8247.18i	−0.248528	−	0.430463i
$717$	−15884.8	+	14978.4i	−0.827377	+	0.780166i
$718$	353.010	−	611.432i	0.0183485	−	0.0317805i
$719$	7725.36			0.400705			0.200353	−	0.979724i	$-0.435791\pi$
$719$	7725.36			0.400705			0.200353	+	0.979724i	$0.435791\pi$
$720$	14552.8	−	7298.81i	0.753263	−	0.377793i
$721$	24759.2			1.27889
$722$	234.065	−	405.413i	0.0120651	−	0.0208974i
$723$	29489.7	+	8837.33i	1.51692	+	0.454584i
$724$	−16304.5	−	28240.2i	−0.836949	−	1.44964i
$725$	2668.16	+	4621.39i	0.136680	+	0.236737i
$726$	11.3456	+	47.9285i	0.000579991	+	0.00245013i
$727$	−2448.69	+	4241.26i	−0.124920	+	0.216368i	−0.921702	−	0.387899i	$-0.873201\pi$
$727$	−2448.69	+	4241.26i	−0.124920	+	0.216368i	0.796781	+	0.604268i	$0.206534\pi$
$728$	836.925			0.0426078
$729$	−3449.39	+	19378.4i	−0.175247	+	0.984524i
$730$	118.897			0.00602819
$731$	11677.9	−	20226.8i	0.590868	−	1.02341i
$732$	7313.85	+	30896.8i	0.369300	+	1.56008i
$733$	10552.0	+	18276.7i	0.531717	+	0.920961i	0.999315	+	0.0370198i	$0.0117865\pi$
$733$	10552.0	+	18276.7i	0.531717	+	0.920961i	−0.467597	+	0.883942i	$0.654880\pi$
$734$	−147.877	−	256.131i	−0.00743632	−	0.0128801i
$735$	−5901.81	−	1768.63i	−0.296179	−	0.0887576i
$736$	699.339	−	1211.29i	0.0350244	−	0.0606641i
$737$	90.9763			0.00454702
$738$	104.978	−	52.6507i	0.00523616	−	0.00262615i
$739$	−12852.5			−0.639768			−0.319884	−	0.947457i	$-0.603644\pi$
$739$	−12852.5			−0.639768			−0.319884	+	0.947457i	$0.603644\pi$
$740$	−7675.01	+	13293.5i	−0.381269	+	0.660377i
$741$	5089.33	−	4798.93i	0.252309	−	0.237912i
$742$	2.15373	+	3.73038i	0.000106558	+	0.000184564i
$743$	−17351.6	−	30053.8i	−0.856754	−	1.48394i	−0.875008	−	0.484108i	$-0.839144\pi$
$743$	−17351.6	−	30053.8i	−0.856754	−	1.48394i	0.0182546	−	0.999833i	$-0.494189\pi$
$744$	−793.528	+	748.249i	−0.0391023	+	0.0368712i
$745$	13048.6	−	22600.8i	0.641694	−	1.11145i
$746$	−1038.39			−0.0509627
$747$	1779.73	−	30274.4i	0.0871712	−	1.48284i
$748$	−5158.34			−0.252149
$749$	−2789.61	+	4831.75i	−0.136088	+	0.235712i
$750$	−592.172	−	177.459i	−0.0288308	−	0.00863987i
$751$	4892.76	+	8474.51i	0.237735	+	0.411770i	0.960064	−	0.279780i	$-0.0902615\pi$
$751$	4892.76	+	8474.51i	0.237735	+	0.411770i	−0.722329	+	0.691550i	$0.756928\pi$
$752$	3725.80	+	6453.27i	0.180673	+	0.312934i
$753$	−3620.34	−	15293.9i	−0.175209	−	0.740159i
$754$	−264.306	+	457.792i	−0.0127659	+	0.0221111i
$755$	4465.99			0.215277
$756$	−10619.9	−	12677.1i	−0.510900	−	0.609872i
$757$	−3760.04			−0.180530			−0.0902648	−	0.995918i	$-0.528771\pi$
$757$	−3760.04			−0.180530			−0.0902648	+	0.995918i	$0.528771\pi$
$758$	−100.580	+	174.209i	−0.00481955	+	0.00834770i
$759$	−1225.64	−	5177.62i	−0.0586138	−	0.247610i
$760$	−175.803	−	304.500i	−0.00839086	−	0.0145334i
$761$	−244.617	−	423.688i	−0.0116522	−	0.0201823i	0.860140	−	0.510057i	$-0.170376\pi$
$761$	−244.617	−	423.688i	−0.0116522	−	0.0201823i	−0.871793	+	0.489875i	$0.837042\pi$
$762$	9.37012	+	2.80799i	0.000445464	+	0.000133495i
$763$	−14041.1	+	24319.9i	−0.666216	+	1.15392i
$764$	−2319.33			−0.109830
$765$	−12492.1	−	8225.87i	−0.590395	−	0.388767i
$766$	−1066.94			−0.0503263
$767$	5843.34	−	10121.0i	0.275086	−	0.476462i
$768$	15366.3	−	14489.5i	0.721985	−	0.680788i
$769$	−5195.69	−	8999.20i	−0.243643	−	0.422002i	0.718106	−	0.695933i	$-0.245009\pi$
$769$	−5195.69	−	8999.20i	−0.243643	−	0.422002i	−0.961749	+	0.273932i	$0.911676\pi$
$770$	−59.9961	−	103.916i	−0.00280794	−	0.00486349i
$771$	−4224.14	+	3983.11i	−0.197314	+	0.186055i
$772$	−14069.3	+	24368.8i	−0.655914	+	1.13608i
$773$	−8754.87			−0.407362			−0.203681	−	0.979037i	$-0.565291\pi$
$773$	−8754.87			−0.407362			−0.203681	+	0.979037i	$0.565291\pi$
$774$	−703.317	−	463.124i	−0.0326617	−	0.0215073i
$775$	−6001.51			−0.278169
$776$	−169.419	+	293.443i	−0.00783738	+	0.0135747i
$777$	14924.6	+	4472.55i	0.689084	+	0.206501i
$778$	107.048	+	185.412i	0.00493298	+	0.00854416i
$779$	825.037	+	1429.01i	0.0379461	+	0.0657246i
$780$	4093.12	+	17291.1i	0.187894	+	0.793744i
$781$	−5682.93	+	9843.12i	−0.260373	+	0.450979i
$782$	−427.781			−0.0195619
$783$	20584.1	−	3612.31i	0.939485	−	0.164870i
$784$	−8017.38			−0.365223
$785$	12363.3	−	21413.9i	0.562123	−	0.973625i
$786$	257.952	+	1089.70i	0.0117059	+	0.0494507i
$787$	−9897.10	−	17142.3i	−0.448277	−	0.776438i	0.549997	−	0.835166i	$-0.314629\pi$
$787$	−9897.10	−	17142.3i	−0.448277	−	0.776438i	−0.998274	+	0.0587286i	$0.981295\pi$
$788$	−14154.6	−	24516.5i	−0.639896	−	1.10833i
$789$	27530.2	+	8250.11i	1.24221	+	0.372258i
$790$	241.009	−	417.439i	0.0108541	−	0.0187998i
$791$	−28524.6			−1.28220
$792$	−21.8376	+	371.473i	−0.000979753	+	0.0166663i
$793$	−34626.8			−1.55061
$794$	−349.576	+	605.484i	−0.0156247	+	0.0270627i
$795$	−133.126	+	125.530i	−0.00593897	+	0.00560010i
$796$	10706.3	+	18543.9i	0.476728	+	0.825718i
$797$	16441.5	+	28477.6i	0.730727	+	1.26566i	0.956573	+	0.291493i	$0.0941520\pi$
$797$	16441.5	+	28477.6i	0.730727	+	1.26566i	−0.225846	+	0.974163i	$0.572515\pi$
$798$	−129.777	+	122.372i	−0.00575697	+	0.00542847i
$799$	3422.95	−	5928.72i	0.151559	−	0.262507i
$800$	−538.259			−0.0237879
$801$	27539.2	−	13812.0i	1.21479	−	0.609269i
$802$	244.203			0.0107520
$803$	883.981	−	1531.10i	0.0388481	−	0.0672868i
$804$	329.079	+	98.6167i	0.0144350	+	0.00432580i
$805$	6481.26	+	11225.9i	0.283769	+	0.491503i
$806$	−297.253	−	514.857i	−0.0129904	−	0.0225001i
$807$	2758.56	+	11653.3i	0.120329	+	0.508323i
$808$	−1131.04	+	1959.02i	−0.0492450	+	0.0852948i
$809$	17378.6			0.755250			0.377625	−	0.925959i	$-0.376741\pi$
$809$	17378.6			0.755250			0.377625	+	0.925959i	$0.376741\pi$
$810$	−322.507	+	432.225i	−0.0139898	+	0.0187492i
$811$	41157.1			1.78203			0.891013	−	0.453978i	$-0.149996\pi$
$811$	41157.1			1.78203			0.891013	+	0.453978i	$0.149996\pi$
$812$	−8779.49	+	15206.5i	−0.379433	+	0.657198i
$813$	−775.941	−	3277.91i	−0.0334729	−	0.141404i
$814$	−87.6104	−	151.746i	−0.00377241	−	0.00653401i
$815$	−14690.0	−	25443.8i	−0.631372	−	1.09357i
$816$	−18644.4	−	5587.26i	−0.799858	−	0.239698i
$817$	5915.86	−	10246.6i	0.253329	−	0.438779i
$818$	656.338			0.0280542
$819$	16121.6	−	8085.64i	0.687831	−	0.344976i
$820$	−4191.53			−0.178506
$821$	−15996.5	+	27706.8i	−0.680004	+	1.17780i	0.294976	+	0.955505i	$0.404688\pi$
$821$	−15996.5	+	27706.8i	−0.680004	+	1.17780i	−0.974979	+	0.222296i	$0.928645\pi$
$822$	51.8990	−	48.9376i	0.00220217	−	0.00207652i
$823$	11753.3	+	20357.3i	0.497805	+	0.862223i	0.999997	−	0.00253315i	$-0.000806329\pi$
$823$	11753.3	+	20357.3i	0.497805	+	0.862223i	−0.502192	+	0.864756i	$0.667473\pi$
$824$	−1051.86	−	1821.87i	−0.0444700	−	0.0770242i
$825$	−1489.74	+	1404.74i	−0.0628681	+	0.0592809i
$826$	−149.004	+	258.083i	−0.00627666	+	0.0108715i
$827$	−21490.1			−0.903608			−0.451804	−	0.892117i	$-0.649219\pi$
$827$	−21490.1			−0.903608			−0.451804	+	0.892117i	$0.649219\pi$
$828$	1179.08	−	20057.0i	0.0494878	−	0.841823i
$829$	−21194.9			−0.887971			−0.443985	−	0.896034i	$-0.646436\pi$
$829$	−21194.9			−0.887971			−0.443985	+	0.896034i	$0.646436\pi$
$830$	415.454	−	719.587i	0.0173742	−	0.0300930i
$831$	23893.5	+	7160.29i	0.997420	+	0.298902i
$832$	11543.4	+	19993.8i	0.481006	+	0.833127i
$833$	3682.85	+	6378.88i	0.153185	+	0.265324i
$834$	−86.5303	−	365.541i	−0.00359268	−	0.0151770i
$835$	−8423.33	+	14589.6i	−0.349104	+	0.604665i
$836$	−2613.14			−0.108107
$837$	−8056.70	+	22079.8i	−0.332713	+	0.911816i
$838$	818.673			0.0337477
$839$	3174.45	−	5498.31i	0.130625	−	0.226249i	−0.793293	−	0.608840i	$-0.791635\pi$
$839$	3174.45	−	5498.31i	0.130625	−	0.226249i	0.923918	+	0.382592i	$0.124968\pi$
$840$	−208.828	−	882.178i	−0.00857768	−	0.0362358i
$841$	1099.77	+	1904.85i	0.0450927	+	0.0781029i
$842$	−465.112	−	805.598i	−0.0190366	−	0.0329724i
$843$	20102.2	+	6024.14i	0.821302	+	0.246124i
$844$	−11878.3	+	20573.8i	−0.484441	+	0.839076i
$845$	1368.48			0.0557125
$846$	−206.151	−	135.747i	−0.00837779	−	0.00551666i
$847$	−1784.25			−0.0723818
$848$	−119.052	+	206.204i	−0.00482106	+	0.00835032i
$849$	4827.78	−	4552.30i	0.195158	−	0.184022i
$850$	82.3124	+	142.569i	0.00332152	+	0.00575304i
$851$	9464.38	+	16392.8i	0.381239	+	0.660326i
$852$	−31226.0	+	29444.3i	−1.25562	+	1.18397i
$853$	−4967.70	+	8604.30i	−0.199403	+	0.345376i	−0.948335	−	0.317271i	$-0.897234\pi$
$853$	−4967.70	+	8604.30i	−0.199403	+	0.345376i	0.748932	+	0.662647i	$0.230567\pi$
$854$	882.977			0.0353804
$855$	−6328.30	−	4167.09i	−0.253127	−	0.166680i
$856$	474.050			0.0189284
$857$	4624.66	−	8010.15i	0.184335	−	0.319278i	−0.759017	−	0.651071i	$-0.774320\pi$
$857$	4624.66	−	8010.15i	0.184335	−	0.319278i	0.943352	+	0.331793i	$0.107653\pi$
$858$	−194.296	−	58.2257i	−0.00773095	−	0.00231678i
$859$	11268.6	+	19517.8i	0.447589	+	0.775248i	0.998229	−	0.0594958i	$-0.0189493\pi$
$859$	11268.6	+	19517.8i	0.447589	+	0.775248i	−0.550639	+	0.834743i	$0.685616\pi$
$860$	15027.5	+	26028.4i	0.595854	+	1.03205i
$861$	980.020	+	4140.02i	0.0387909	+	0.163869i
$862$	607.942	−	1052.99i	0.0240216	−	0.0416066i
$863$	−23882.1			−0.942011			−0.471005	−	0.882130i	$-0.656109\pi$
$863$	−23882.1			−0.942011			−0.471005	+	0.882130i	$0.656109\pi$
$864$	−722.583	+	1980.28i	−0.0284523	+	0.0779750i
$865$	−12901.7			−0.507136
$866$	−98.2842	+	170.233i	−0.00385662	+	0.00667986i
$867$	−1761.55	−	7441.56i	−0.0690029	−	0.291498i
$868$	−9873.89	−	17102.1i	−0.386108	−	0.668759i
$869$	−3583.72	−	6207.19i	−0.139896	−	0.242307i
$870$	548.494	+	164.370i	0.0213744	+	0.00640537i
$871$	−187.328	+	324.462i	−0.00728745	+	0.0126222i
$872$	2386.06			0.0926632
$873$	−428.515	+	7289.35i	−0.0166129	+	0.282597i
$874$	−216.707			−0.00838699
$875$	11197.3	−	19394.3i	0.432615	−	0.749312i
$876$	4857.21	−	4580.06i	0.187340	−	0.176651i
$877$	−742.694	−	1286.38i	−0.0285963	−	0.0495303i	0.851373	−	0.524561i	$-0.175770\pi$
$877$	−742.694	−	1286.38i	−0.0285963	−	0.0495303i	−0.879969	+	0.475030i	$0.842437\pi$
$878$	286.531	+	496.287i	0.0110136	+	0.0190762i
$879$	−8308.65	+	7834.55i	−0.318821	+	0.300629i
$880$	3316.40	−	5744.18i	0.127041	−	0.220041i
$881$	14837.2			0.567397			0.283699	−	0.958914i	$-0.408438\pi$
$881$	14837.2			0.567397			0.283699	+	0.958914i	$0.408438\pi$
$882$	237.389	−	119.060i	0.00906268	−	0.00454531i
$883$	−32949.0			−1.25575			−0.627873	−	0.778316i	$-0.716074\pi$
$883$	−32949.0			−1.25575			−0.627873	+	0.778316i	$0.716074\pi$
$884$	10621.5	−	18397.0i	0.404117	−	0.699951i
$885$	−12126.2	−	3633.93i	−0.460586	−	0.138026i
$886$	145.298	+	251.664i	0.00550947	+	0.00954269i
$887$	15372.6	+	26626.1i	0.581917	+	1.00791i	0.995252	+	0.0973303i	$0.0310303\pi$
$887$	15372.6	+	26626.1i	0.581917	+	1.00791i	−0.413336	+	0.910579i	$0.635636\pi$
$888$	−304.945	−	1288.22i	−0.0115240	−	0.0486821i
$889$	−177.178	+	306.882i	−0.00668433	+	0.0115776i
$890$	844.115			0.0317919
$891$	3168.19	+	7366.61i	0.119123	+	0.276982i
$892$	−15063.9			−0.565445
$893$	1734.01	−	3003.40i	0.0649793	−	0.112547i
$894$	259.124	+	1094.65i	0.00969397	+	0.0409515i
$895$	−5624.88	−	9742.58i	−0.210077	−	0.363864i
$896$	−1180.60	−	2044.86i	−0.0440190	−	0.0762431i
$897$	20989.4	+	6290.00i	0.781288	+	0.234133i
$898$	−366.256	+	634.374i	−0.0136104	+	0.0235739i
$899$	24955.5			0.925820
$900$	−6911.40	+	3466.35i	−0.255978	+	0.128383i
$901$	218.750			0.00808836
$902$	23.9232	−	41.4362i	0.000883100	−	0.00152957i
$903$	22195.0	−	20928.6i	0.817944	−	0.771272i
$904$	1211.82	+	2098.94i	0.0445848	+	0.0772231i
$905$	−19260.9	−	33360.8i	−0.707461	−	1.22536i
$906$	−140.058	+	132.067i	−0.00513590	+	0.00484285i
$907$	−16924.9	+	29314.8i	−0.619606	+	1.07319i	0.369951	+	0.929051i	$0.379374\pi$
$907$	−16924.9	+	29314.8i	−0.619606	+	1.07319i	−0.989558	+	0.144138i	$0.953959\pi$
$908$	−21764.6			−0.795465
$909$	−2860.76	+	48663.6i	−0.104385	+	1.77565i
$910$	494.149			0.0180010
$911$	−9915.58	+	17174.3i	−0.360612	+	0.624599i	−0.988062	−	0.154058i	$-0.950766\pi$
$911$	−9915.58	+	17174.3i	−0.360612	+	0.624599i	0.627449	+	0.778657i	$0.284099\pi$
$912$	−9444.95	−	2830.42i	−0.342931	−	0.102768i
$913$	−6177.66	−	10700.0i	−0.223933	−	0.387863i
$914$	−25.5823	−	44.3099i	−0.000925807	−	0.00160354i
$915$	8640.01	+	36499.1i	0.312164	+	1.31871i
$916$	10313.9	−	17864.2i	0.372031	−	0.644376i
$917$	−40566.5			−1.46088
$918$	635.018	−	111.439i	0.0228308	−	0.00400658i
$919$	−39260.6			−1.40923			−0.704617	−	0.709588i	$-0.748881\pi$
$919$	−39260.6			−1.40923			−0.704617	+	0.709588i	$0.748881\pi$
$920$	550.693	−	953.828i	0.0197346	−	0.0341813i
$921$	9027.67	+	38136.7i	0.322988	+	1.36444i
$922$	313.633	+	543.229i	0.0112028	+	0.0194038i
$923$	−23403.3	−	40535.7i	−0.834593	−	1.44556i
$924$	−6453.96	−	1934.09i	−0.229783	−	0.0688603i
$925$	3642.21	−	6308.50i	0.129465	−	0.224240i
$926$	−740.917			−0.0262938
$927$	−37863.2	−	24932.4i	−1.34152	−	0.883373i
$928$	2238.19			0.0791725
$929$	28179.0	−	48807.5i	0.995181	−	1.72370i	0.412677	−	0.910878i	$-0.364594\pi$
$929$	28179.0	−	48807.5i	0.995181	−	1.72370i	0.582505	−	0.812827i	$-0.302073\pi$
$930$	−468.526	+	441.792i	−0.0165200	+	0.0155774i
$931$	1865.67	+	3231.44i	0.0656766	+	0.113755i
$932$	−7281.38	−	12611.7i	−0.255911	−	0.443252i
$933$	−10746.9	+	10133.7i	−0.377103	+	0.355585i
$934$	226.613	−	392.506i	0.00793899	−	0.0137507i
$935$	−6093.67			−0.213138
$936$	−1279.87	−	842.777i	−0.0446943	−	0.0294306i
$937$	28800.1			1.00412			0.502059	−	0.864833i	$-0.332576\pi$
$937$	28800.1			1.00412			0.502059	+	0.864833i	$0.332576\pi$
$938$	4.77684	−	8.27373i	0.000166279	−	0.000288003i
$939$	50543.2	+	15146.6i	1.75657	+	0.526400i
$940$	4404.75	+	7629.26i	0.152837	+	0.264722i
$941$	11124.4	+	19267.9i	0.385381	+	0.667499i	0.991822	−	0.127629i	$-0.0407367\pi$
$941$	11124.4	+	19267.9i	0.385381	+	0.667499i	−0.606441	+	0.795129i	$0.707403\pi$
$942$	245.517	+	1037.17i	0.00849190	+	0.0358734i
$943$	−2584.38	+	4476.27i	−0.0892459	+	0.154578i
$944$	−16473.0			−0.567956
$945$	−12545.5	−	14975.8i	−0.431856	−	0.515516i
$946$	−343.079			−0.0117912
$947$	3147.42	−	5451.49i	0.108001	−	0.187064i	−0.806959	−	0.590607i	$-0.798888\pi$
$947$	3147.42	−	5451.49i	0.108001	−	0.187064i	0.914961	+	0.403543i	$0.132222\pi$
$948$	−6234.52	−	26337.3i	−0.213595	−	0.902315i
$949$	3640.39	+	6305.34i	0.124523	+	0.215680i
$950$	41.6982	+	72.2233i	0.00142407	+	0.00246656i
$951$	−9144.93	−	2740.51i	−0.311824	−	0.0934460i
$952$	−541.900	+	938.599i	−0.0184486	+	0.0319540i
$953$	34863.0			1.18502			0.592510	−	0.805563i	$-0.298137\pi$
$953$	34863.0			1.18502			0.592510	+	0.805563i	$0.298137\pi$
$954$	0.462855	−	7.87349i	1.57081e−5	−	0.000267205i
$955$	−2739.88			−0.0928380
$956$	−16794.2	+	29088.3i	−0.568161	+	0.984084i
$957$	6194.64	−	5841.18i	0.209242	−	0.197302i
$958$	−453.027	−	784.666i	−0.0152783	−	0.0264629i
$959$	1292.06	+	2237.91i	0.0435065	+	0.0753554i
$960$	18194.6	−	17156.4i	0.611697	−	0.576794i
$961$	862.356	−	1493.64i	0.0289469	−	0.0501374i
$962$	721.591			0.0241840
$963$	9131.57	−	4579.86i	0.305567	−	0.153254i
$964$	47360.9			1.58236
$965$	−16620.4	+	28787.4i	−0.554434	+	0.960308i
$966$	−535.227	−	160.394i	−0.0178267	−	0.00534223i
$967$	−1497.47	−	2593.69i	−0.0497987	−	0.0862540i	0.840052	−	0.542507i	$-0.182525\pi$
$967$	−1497.47	−	2593.69i	−0.0497987	−	0.0862540i	−0.889850	+	0.456253i	$0.849191\pi$
$968$	75.8010	+	131.291i	0.00251688	+	0.00435936i
$969$	2086.64	+	8814.87i	0.0691771	+	0.292234i
$970$	−100.031	+	173.259i	−0.00331114	+	0.00573506i
$971$	14802.4			0.489220			0.244610	−	0.969622i	$-0.421340\pi$
$971$	14802.4			0.489220			0.244610	+	0.969622i	$0.421340\pi$
$972$	3474.67	+	30080.7i	0.114661	+	0.992633i
$973$	13608.1			0.448360
$974$	−288.946	+	500.468i	−0.00950556	+	0.0164641i
$975$	−1942.41	−	8205.57i	−0.0638020	−	0.269527i
$976$	24404.2	+	42269.2i	0.800367	+	1.38628i
$977$	−24365.4	−	42202.2i	−0.797870	−	1.38195i	−0.921001	−	0.389561i	$-0.872627\pi$
$977$	−24365.4	−	42202.2i	−0.797870	−	1.38195i	0.123130	−	0.992391i	$-0.460707\pi$
$978$	1213.11	+	363.539i	0.0396635	+	0.0118862i
$979$	6275.86	−	10870.1i	0.204880	−	0.354862i
$980$	−9478.39			−0.308955
$981$	45962.4	−	23052.1i	1.49589	−	0.750250i
$982$	345.047			0.0112127
$983$	17385.7	−	30112.9i	0.564108	−	0.977064i	−0.433024	−	0.901382i	$-0.642554\pi$
$983$	17385.7	−	30112.9i	0.564108	−	0.977064i	0.997132	−	0.0756813i	$-0.0241132\pi$
$984$	263.003	−	247.996i	0.00852055	−	0.00803437i
$985$	−16721.2	−	28961.9i	−0.540895	−	0.936857i
$986$	−342.271	−	592.831i	−0.0110549	−	0.0191477i
$987$	6505.63	−	6134.42i	0.209804	−	0.197832i
$988$	5380.68	−	9319.61i	0.173261	−	0.300097i
$989$	37062.1			1.19162
$990$	−12.8937	+	219.330i	−0.000413927	+	0.00704118i
$991$	1085.07			0.0347813			0.0173907	−	0.999849i	$-0.494464\pi$
$991$	1085.07			0.0347813			0.0173907	+	0.999849i	$0.494464\pi$
$992$	−1258.59	+	2179.95i	−0.0402826	+	0.0697716i
$993$	−26546.0	−	7955.17i	−0.848349	−	0.254229i
$994$	596.781	+	1033.65i	0.0190430	+	0.0329834i
$995$	12647.6	+	21906.3i	0.402972	+	0.697967i
$996$	−10747.1	−	45400.5i	−0.341904	−	1.44435i
$997$	2608.67	−	4518.35i	0.0828660	−	0.143528i	−0.821614	−	0.570044i	$-0.806926\pi$
$997$	2608.67	−	4518.35i	0.0828660	−	0.143528i	0.904480	+	0.426516i	$0.140259\pi$
$998$	179.506			0.00569357
$999$	−18319.8	−	21868.7i	−0.580192	−	0.692587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.4.e.b.34.8	✓	24
3.2	odd	2		297.4.e.b.100.5		24
9.2	odd	6		891.4.a.k.1.8		12
9.4	even	3	inner	99.4.e.b.67.8	yes	24
9.5	odd	6		297.4.e.b.199.5		24
9.7	even	3		891.4.a.l.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.4.e.b.34.8	✓	24	1.1	even	1	trivial
99.4.e.b.67.8	yes	24	9.4	even	3	inner
297.4.e.b.100.5		24	3.2	odd	2
297.4.e.b.199.5		24	9.5	odd	6
891.4.a.k.1.8		12	9.2	odd	6
891.4.a.l.1.5		12	9.7	even	3

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	99.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0391684 + 0.0678417i) q^{2} +(1.19695 + 5.05641i) q^{3} +(3.99693 + 6.92289i) q^{4} +(4.72166 + 8.17816i) q^{5} +(-0.389918 - 0.116849i) q^{6} +(7.37292 - 12.7703i) q^{7} -1.25291 q^{8} +(-24.1346 + 12.1045i) q^{9} +O(q^{10})\)	\(q+(-0.0391684 + 0.0678417i) q^{2} +(1.19695 + 5.05641i) q^{3} +(3.99693 + 6.92289i) q^{4} +(4.72166 + 8.17816i) q^{5} +(-0.389918 - 0.116849i) q^{6} +(7.37292 - 12.7703i) q^{7} -1.25291 q^{8} +(-24.1346 + 12.1045i) q^{9} -0.739761 q^{10} +(-5.50000 + 9.52628i) q^{11} +(-30.2209 + 28.4965i) q^{12} +(-22.6500 - 39.2309i) q^{13} +(0.577571 + 1.00038i) q^{14} +(-35.7006 + 33.6635i) q^{15} +(-31.9264 + 55.2981i) q^{16} +58.6625 q^{17} +(0.124125 - 2.11145i) q^{18} +29.7175 q^{19} +(-37.7443 + 65.3751i) q^{20} +(73.3967 + 21.9952i) q^{21} +(-0.430853 - 0.746259i) q^{22} +(46.5441 + 80.6168i) q^{23} +(-1.49967 - 6.33522i) q^{24} +(17.9118 - 31.0241i) q^{25} +3.54865 q^{26} +(-90.0933 - 107.546i) q^{27} +117.876 q^{28} +(-74.4806 + 129.004i) q^{29} +(-0.885454 - 3.74054i) q^{30} +(-83.7650 - 145.085i) q^{31} +(-7.51265 - 13.0123i) q^{32} +(-54.7520 - 16.4078i) q^{33} +(-2.29772 + 3.97977i) q^{34} +139.250 q^{35} +(-180.263 - 118.700i) q^{36} +203.342 q^{37} +(-1.16399 + 2.01609i) q^{38} +(171.257 - 161.485i) q^{39} +(-5.91582 - 10.2465i) q^{40} +(27.7626 + 48.0863i) q^{41} +(-4.36702 + 4.11784i) q^{42} +(199.070 - 344.799i) q^{43} -87.9325 q^{44} +(-212.948 - 140.224i) q^{45} -7.29224 q^{46} +(58.3498 - 101.065i) q^{47} +(-317.824 - 95.2441i) q^{48} +(62.7802 + 108.739i) q^{49} +(1.40315 + 2.43033i) q^{50} +(70.2159 + 296.622i) q^{51} +(181.061 - 313.606i) q^{52} +3.72895 q^{53} +(10.8249 - 1.89967i) q^{54} -103.877 q^{55} +(-9.23759 + 16.0000i) q^{56} +(35.5703 + 150.264i) q^{57} +(-5.83458 - 10.1058i) q^{58} +(128.992 + 223.421i) q^{59} +(-375.742 - 112.600i) q^{60} +(382.194 - 661.980i) q^{61} +13.1238 q^{62} +(-23.3648 + 397.451i) q^{63} -509.645 q^{64} +(213.891 - 370.470i) q^{65} +(3.25768 - 3.07180i) q^{66} +(-4.13528 - 7.16252i) q^{67} +(234.470 + 406.114i) q^{68} +(-351.921 + 331.840i) q^{69} +(-5.45419 + 9.44694i) q^{70} +1033.26 q^{71} +(30.2385 - 15.1659i) q^{72} -160.724 q^{73} +(-7.96459 + 13.7951i) q^{74} +(178.310 + 53.4351i) q^{75} +(118.779 + 205.731i) q^{76} +(81.1021 + 140.473i) q^{77} +(4.24755 + 17.9435i) q^{78} +(-325.793 + 564.290i) q^{79} -602.983 q^{80} +(435.961 - 584.276i) q^{81} -4.34967 q^{82} +(-561.606 + 972.729i) q^{83} +(141.091 + 596.031i) q^{84} +(276.985 + 479.752i) q^{85} +(15.5945 + 27.0105i) q^{86} +(-741.448 - 222.194i) q^{87} +(6.89100 - 11.9356i) q^{88} -1141.06 q^{89} +(17.8539 - 8.95444i) q^{90} -667.985 q^{91} +(-372.067 + 644.440i) q^{92} +(633.349 - 597.210i) q^{93} +(4.57094 + 7.91711i) q^{94} +(140.316 + 243.035i) q^{95} +(56.8033 - 53.5621i) q^{96} +(135.221 - 234.210i) q^{97} -9.83601 q^{98} +(17.4295 - 296.488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 6 q^{3} - 32 q^{4} + 2 q^{5} + 57 q^{6} + 8 q^{7} - 6 q^{8} - 54 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 6 * q^3 - 32 * q^4 + 2 * q^5 + 57 * q^6 + 8 * q^7 - 6 * q^8 - 54 * q^9	\( 24 q - 4 q^{2} + 6 q^{3} - 32 q^{4} + 2 q^{5} + 57 q^{6} + 8 q^{7} - 6 q^{8} - 54 q^{9} - 272 q^{10} - 132 q^{11} + 21 q^{12} + 62 q^{13} + 179 q^{14} - 24 q^{15} - 128 q^{16} - 160 q^{17} + 63 q^{18} - 128 q^{19} + 67 q^{20} - 48 q^{21} - 44 q^{22} + 280 q^{23} - 513 q^{24} + 112 q^{25} - 100 q^{26} + 756 q^{27} - 1158 q^{28} + 60 q^{29} + 618 q^{30} + 704 q^{31} - 755 q^{32} + 66 q^{33} + 778 q^{34} - 448 q^{35} + 1089 q^{36} - 1760 q^{37} - 171 q^{38} + 636 q^{39} + 1695 q^{40} + 374 q^{41} - 1041 q^{42} + 826 q^{43} + 704 q^{44} - 846 q^{45} - 1912 q^{46} + 214 q^{47} + 3009 q^{48} + 462 q^{49} - 1019 q^{50} + 372 q^{51} + 834 q^{52} - 756 q^{53} - 1026 q^{54} - 44 q^{55} + 750 q^{56} + 2574 q^{57} + 867 q^{58} + 748 q^{59} - 5061 q^{60} + 2662 q^{61} - 1258 q^{62} - 828 q^{63} - 306 q^{64} + 416 q^{65} + 330 q^{66} + 2430 q^{67} + 895 q^{68} - 1920 q^{69} + 136 q^{70} - 1224 q^{71} - 5166 q^{72} - 1696 q^{73} - 93 q^{74} + 4314 q^{75} + 934 q^{76} + 88 q^{77} - 2481 q^{78} + 1770 q^{79} - 4262 q^{80} - 1566 q^{81} - 3590 q^{82} - 156 q^{83} + 6114 q^{84} + 1414 q^{85} - 3576 q^{86} - 1980 q^{87} + 33 q^{88} - 504 q^{89} + 405 q^{90} - 5004 q^{91} + 3821 q^{92} + 7098 q^{93} + 4046 q^{94} + 510 q^{95} - 9939 q^{96} + 2436 q^{97} + 2448 q^{98} - 594 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 6 * q^3 - 32 * q^4 + 2 * q^5 + 57 * q^6 + 8 * q^7 - 6 * q^8 - 54 * q^9 - 272 * q^10 - 132 * q^11 + 21 * q^12 + 62 * q^13 + 179 * q^14 - 24 * q^15 - 128 * q^16 - 160 * q^17 + 63 * q^18 - 128 * q^19 + 67 * q^20 - 48 * q^21 - 44 * q^22 + 280 * q^23 - 513 * q^24 + 112 * q^25 - 100 * q^26 + 756 * q^27 - 1158 * q^28 + 60 * q^29 + 618 * q^30 + 704 * q^31 - 755 * q^32 + 66 * q^33 + 778 * q^34 - 448 * q^35 + 1089 * q^36 - 1760 * q^37 - 171 * q^38 + 636 * q^39 + 1695 * q^40 + 374 * q^41 - 1041 * q^42 + 826 * q^43 + 704 * q^44 - 846 * q^45 - 1912 * q^46 + 214 * q^47 + 3009 * q^48 + 462 * q^49 - 1019 * q^50 + 372 * q^51 + 834 * q^52 - 756 * q^53 - 1026 * q^54 - 44 * q^55 + 750 * q^56 + 2574 * q^57 + 867 * q^58 + 748 * q^59 - 5061 * q^60 + 2662 * q^61 - 1258 * q^62 - 828 * q^63 - 306 * q^64 + 416 * q^65 + 330 * q^66 + 2430 * q^67 + 895 * q^68 - 1920 * q^69 + 136 * q^70 - 1224 * q^71 - 5166 * q^72 - 1696 * q^73 - 93 * q^74 + 4314 * q^75 + 934 * q^76 + 88 * q^77 - 2481 * q^78 + 1770 * q^79 - 4262 * q^80 - 1566 * q^81 - 3590 * q^82 - 156 * q^83 + 6114 * q^84 + 1414 * q^85 - 3576 * q^86 - 1980 * q^87 + 33 * q^88 - 504 * q^89 + 405 * q^90 - 5004 * q^91 + 3821 * q^92 + 7098 * q^93 + 4046 * q^94 + 510 * q^95 - 9939 * q^96 + 2436 * q^97 + 2448 * q^98 - 594 * q^99

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