LMFDB - Embedded newform 105.4.s.a.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(26,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("105.26");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.s (of order $6$, 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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Character	$\chi$	$=$	105.101
Dual form			105.4.s.a.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.56345 + 2.63471i) q^{2} +(-4.97118 + 1.51242i) q^{3} +(9.88336 - 17.1185i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(18.7009 - 19.9994i) q^{6} +(12.9395 + 13.2503i) q^{7} +62.0037i q^{8} +(22.4252 - 15.0370i) q^{9} +O(q^{10})$	\(q+(-4.56345 + 2.63471i) q^{2} +(-4.97118 + 1.51242i) q^{3} +(9.88336 - 17.1185i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(18.7009 - 19.9994i) q^{6} +(12.9395 + 13.2503i) q^{7} +62.0037i q^{8} +(22.4252 - 15.0370i) q^{9} +(22.8172 + 13.1735i) q^{10} +(4.67930 + 2.70159i) q^{11} +(-23.2416 + 100.047i) q^{12} +11.1476i q^{13} +(-93.9592 - 26.3752i) q^{14} +(18.9769 + 17.7448i) q^{15} +(-84.2948 - 146.003i) q^{16} +(49.0554 - 84.9664i) q^{17} +(-62.7181 + 127.704i) q^{18} +(-38.3523 + 22.1427i) q^{19} -98.8336 q^{20} +(-84.3644 - 46.2996i) q^{21} -28.4716 q^{22} +(-161.199 + 93.0682i) q^{23} +(-93.7755 - 308.232i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-29.3705 - 50.8713i) q^{26} +(-88.7374 + 108.668i) q^{27} +(354.710 - 90.5469i) q^{28} +210.853i q^{29} +(-133.352 - 30.9788i) q^{30} +(143.496 + 82.8476i) q^{31} +(339.775 + 196.169i) q^{32} +(-27.3476 - 6.35305i) q^{33} +516.986i q^{34} +(25.0267 - 89.1553i) q^{35} +(-35.7741 - 532.501i) q^{36} +(37.5633 + 65.0615i) q^{37} +(116.679 - 202.094i) q^{38} +(-16.8598 - 55.4165i) q^{39} +(268.484 - 155.009i) q^{40} -149.096 q^{41} +(506.978 - 10.9897i) q^{42} -415.711 q^{43} +(92.4944 - 53.4017i) q^{44} +(-121.175 - 59.5115i) q^{45} +(490.415 - 849.424i) q^{46} +(276.394 + 478.728i) q^{47} +(639.861 + 598.317i) q^{48} +(-8.13985 + 342.903i) q^{49} -131.735i q^{50} +(-115.358 + 496.575i) q^{51} +(190.829 + 110.175i) q^{52} +(116.966 + 67.5305i) q^{53} +(118.641 - 729.696i) q^{54} -27.0159i q^{55} +(-821.567 + 802.296i) q^{56} +(157.167 - 168.080i) q^{57} +(-555.537 - 962.218i) q^{58} +(284.964 - 493.573i) q^{59} +(491.319 - 149.478i) q^{60} +(-403.866 + 233.172i) q^{61} -873.116 q^{62} +(489.414 + 102.569i) q^{63} -718.677 q^{64} +(48.2703 - 27.8689i) q^{65} +(141.538 - 43.0610i) q^{66} +(-379.212 + 656.814i) q^{67} +(-969.664 - 1679.51i) q^{68} +(660.590 - 706.458i) q^{69} +(120.690 + 472.793i) q^{70} +113.113i q^{71} +(932.349 + 1390.45i) q^{72} +(-590.839 - 341.121i) q^{73} +(-342.836 - 197.936i) q^{74} +(29.3949 - 126.534i) q^{75} +875.377i q^{76} +(24.7508 + 96.9592i) q^{77} +(222.945 + 208.470i) q^{78} +(649.347 + 1124.70i) q^{79} +(-421.474 + 730.014i) q^{80} +(276.778 - 674.414i) q^{81} +(680.391 - 392.824i) q^{82} -143.614 q^{83} +(-1626.38 + 986.595i) q^{84} -490.554 q^{85} +(1897.07 - 1095.28i) q^{86} +(-318.898 - 1048.19i) q^{87} +(-167.509 + 290.134i) q^{88} +(103.214 + 178.771i) q^{89} +(709.771 - 47.6834i) q^{90} +(-147.708 + 144.244i) q^{91} +3679.31i q^{92} +(-838.645 - 194.824i) q^{93} +(-2522.61 - 1456.43i) q^{94} +(191.761 + 110.714i) q^{95} +(-1985.77 - 461.310i) q^{96} -1044.15i q^{97} +(-866.304 - 1586.27i) q^{98} +(145.558 - 9.77878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9}+O(q^{10}) $ 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9} + 36 q^{11} + 246 q^{12} + 18 q^{14} + 20 q^{15} - 376 q^{16} - 72 q^{17} - 442 q^{18} - 198 q^{19} - 640 q^{20} - 218 q^{21} + 204 q^{22} + 72 q^{23} - 50 q^{24} - 400 q^{25} - 312 q^{26} + 508 q^{27} + 350 q^{28} + 40 q^{30} + 510 q^{31} + 810 q^{32} + 290 q^{33} - 70 q^{35} - 612 q^{36} - 658 q^{37} - 192 q^{38} - 648 q^{39} - 1404 q^{41} + 1892 q^{42} + 332 q^{43} + 2034 q^{44} - 490 q^{45} - 468 q^{46} + 408 q^{47} + 2810 q^{48} + 980 q^{49} - 888 q^{51} + 3378 q^{52} + 1152 q^{53} + 2714 q^{54} - 3354 q^{56} - 816 q^{57} - 1080 q^{58} - 48 q^{59} - 420 q^{60} - 1662 q^{61} - 2076 q^{62} + 874 q^{63} - 1952 q^{64} + 870 q^{65} - 1892 q^{66} - 1298 q^{67} + 1182 q^{68} + 2450 q^{69} - 450 q^{70} - 2708 q^{72} + 378 q^{73} + 2898 q^{74} - 50 q^{75} - 3528 q^{77} - 1896 q^{78} - 326 q^{79} - 1880 q^{80} - 3308 q^{81} - 2916 q^{82} - 1536 q^{83} + 1380 q^{84} + 720 q^{85} + 5202 q^{86} - 1090 q^{87} + 1668 q^{88} - 1590 q^{89} + 910 q^{90} + 2082 q^{91} - 4950 q^{93} - 1152 q^{94} + 990 q^{95} + 7416 q^{96} - 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9 + 36 * q^11 + 246 * q^12 + 18 * q^14 + 20 * q^15 - 376 * q^16 - 72 * q^17 - 442 * q^18 - 198 * q^19 - 640 * q^20 - 218 * q^21 + 204 * q^22 + 72 * q^23 - 50 * q^24 - 400 * q^25 - 312 * q^26 + 508 * q^27 + 350 * q^28 + 40 * q^30 + 510 * q^31 + 810 * q^32 + 290 * q^33 - 70 * q^35 - 612 * q^36 - 658 * q^37 - 192 * q^38 - 648 * q^39 - 1404 * q^41 + 1892 * q^42 + 332 * q^43 + 2034 * q^44 - 490 * q^45 - 468 * q^46 + 408 * q^47 + 2810 * q^48 + 980 * q^49 - 888 * q^51 + 3378 * q^52 + 1152 * q^53 + 2714 * q^54 - 3354 * q^56 - 816 * q^57 - 1080 * q^58 - 48 * q^59 - 420 * q^60 - 1662 * q^61 - 2076 * q^62 + 874 * q^63 - 1952 * q^64 + 870 * q^65 - 1892 * q^66 - 1298 * q^67 + 1182 * q^68 + 2450 * q^69 - 450 * q^70 - 2708 * q^72 + 378 * q^73 + 2898 * q^74 - 50 * q^75 - 3528 * q^77 - 1896 * q^78 - 326 * q^79 - 1880 * q^80 - 3308 * q^81 - 2916 * q^82 - 1536 * q^83 + 1380 * q^84 + 720 * q^85 + 5202 * q^86 - 1090 * q^87 + 1668 * q^88 - 1590 * q^89 + 910 * q^90 + 2082 * q^91 - 4950 * q^93 - 1152 * q^94 + 990 * q^95 + 7416 * q^96 - 7830 * q^98 + 3128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−4.56345	+	2.63471i	−1.61342	+	0.931510i	−0.624853	+	0.780743i	$0.714841\pi$
$2$	−4.56345	+	2.63471i	−1.61342	+	0.931510i	−0.988569	+	0.150767i	$0.951826\pi$
$3$	−4.97118	+	1.51242i	−0.956703	+	0.291065i
$3$	−4.97118	+	1.51242i	−0.956703	+	0.291065i
$4$	9.88336	−	17.1185i	1.23542	−	2.13981i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	18.7009	−	19.9994i	1.27244	−	1.36079i
$7$	12.9395	+	13.2503i	0.698666	+	0.715448i
$7$	12.9395	+	13.2503i	0.698666	+	0.715448i
$8$			62.0037i			2.74020i
$9$	22.4252	−	15.0370i	0.830563	−	0.556925i
$10$	22.8172	+	13.1735i	0.721544	+	0.416584i
$11$	4.67930	+	2.70159i	0.128260	+	0.0740510i	0.562757	−	0.826622i	$-0.309741\pi$
$11$	4.67930	+	2.70159i	0.128260	+	0.0740510i	−0.434497	+	0.900673i	$0.643074\pi$
$12$	−23.2416	+	100.047i	−0.559107	+	2.40675i
$13$			11.1476i			0.237829i	0.992905	+	0.118914i	$0.0379414\pi$
$13$			11.1476i			0.237829i	−0.992905	+	0.118914i	$0.962059\pi$
$14$	−93.9592	−	26.3752i	−1.79369	−	0.503505i
$15$	18.9769	+	17.7448i	0.326654	+	0.305446i
$16$	−84.2948	−	146.003i	−1.31711	−	2.28129i
$17$	49.0554	−	84.9664i	0.699864	−	1.21220i	−0.268650	−	0.963238i	$-0.586577\pi$
$17$	49.0554	−	84.9664i	0.699864	−	1.21220i	0.968513	−	0.248961i	$-0.0800892\pi$
$18$	−62.7181	+	127.704i	−0.821267	+	1.67223i
$19$	−38.3523	+	22.1427i	−0.463085	+	0.267362i	−0.713341	−	0.700818i	$-0.752819\pi$
$19$	−38.3523	+	22.1427i	−0.463085	+	0.267362i	0.250255	+	0.968180i	$0.419485\pi$
$20$	−98.8336			−1.10499
$21$	−84.3644	−	46.2996i	−0.876658	−	0.481114i
$22$	−28.4716			−0.275917
$23$	−161.199	+	93.0682i	−1.46140	+	0.843742i	−0.999076	−	0.0429674i	$-0.986319\pi$
$23$	−161.199	+	93.0682i	−1.46140	+	0.843742i	−0.462327	+	0.886709i	$0.652986\pi$
$24$	−93.7755	−	308.232i	−0.797577	−	2.62156i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−29.3705	−	50.8713i	−0.221540	−	0.383718i
$27$	−88.7374	+	108.668i	−0.632501	+	0.774560i
$28$	354.710	−	90.5469i	2.39407	−	0.611134i
$29$			210.853i			1.35015i	0.737747	+	0.675077i	$0.235890\pi$
$29$			210.853i			1.35015i	−0.737747	+	0.675077i	$0.764110\pi$
$30$	−133.352	−	30.9788i	−0.811557	−	0.188531i
$31$	143.496	+	82.8476i	0.831377	+	0.479996i	0.854324	−	0.519741i	$-0.173972\pi$
$31$	143.496	+	82.8476i	0.831377	+	0.479996i	−0.0229470	+	0.999737i	$0.507305\pi$
$32$	339.775	+	196.169i	1.87701	+	1.08369i
$33$	−27.3476	−	6.35305i	−0.144261	−	0.0335128i
$34$			516.986i			2.60772i
$35$	25.0267	−	89.1553i	0.120865	−	0.430571i
$36$	−35.7741	−	532.501i	−0.165621	−	2.46528i
$37$	37.5633	+	65.0615i	0.166902	+	0.289082i	0.937329	−	0.348446i	$-0.113290\pi$
$37$	37.5633	+	65.0615i	0.166902	+	0.289082i	−0.770427	+	0.637528i	$0.779957\pi$
$38$	116.679	−	202.094i	0.498101	−	0.862736i
$39$	−16.8598	−	55.4165i	−0.0692236	−	0.227532i
$40$	268.484	−	155.009i	1.06128	−	0.612728i
$41$	−149.096			−0.567924			−0.283962	−	0.958836i	$-0.591649\pi$
$41$	−149.096			−0.567924			−0.283962	+	0.958836i	$0.591649\pi$
$42$	506.978	−	10.9897i	1.86258	−	0.0403750i
$43$	−415.711			−1.47431			−0.737155	−	0.675724i	$-0.763831\pi$
$43$	−415.711			−1.47431			−0.737155	+	0.675724i	$0.763831\pi$
$44$	92.4944	−	53.4017i	0.316910	−	0.182968i
$45$	−121.175	−	59.5115i	−0.401416	−	0.197143i
$46$	490.415	−	849.424i	1.57191	−	2.72262i
$47$	276.394	+	478.728i	0.857790	+	1.48574i	0.874032	+	0.485868i	$0.161496\pi$
$47$	276.394	+	478.728i	0.857790	+	1.48574i	−0.0162420	+	0.999868i	$0.505170\pi$
$48$	639.861	+	598.317i	1.92408	+	1.79916i
$49$	−8.13985	+	342.903i	−0.0237313	+	0.999718i
$50$		−	131.735i		−	0.372604i
$51$	−115.358	+	496.575i	−0.316733	+	1.36342i
$52$	190.829	+	110.175i	0.508909	+	0.293819i
$53$	116.966	+	67.5305i	0.303142	+	0.175019i	0.643854	−	0.765149i	$-0.277335\pi$
$53$	116.966	+	67.5305i	0.303142	+	0.175019i	−0.340711	+	0.940168i	$0.610668\pi$
$54$	118.641	−	729.696i	0.298980	−	1.83887i
$55$		−	27.0159i		−	0.0662332i
$56$	−821.567	+	802.296i	−1.96047	+	1.91449i
$57$	157.167	−	168.080i	0.365215	−	0.390574i
$58$	−555.537	−	962.218i	−1.25768	−	2.17837i
$59$	284.964	−	493.573i	0.628800	−	1.08911i	−0.358993	−	0.933340i	$-0.616880\pi$
$59$	284.964	−	493.573i	0.628800	−	1.08911i	0.987793	−	0.155773i	$-0.0497868\pi$
$60$	491.319	−	149.478i	1.05715	−	0.321625i
$61$	−403.866	+	233.172i	−0.847700	+	0.489420i	−0.859874	−	0.510506i	$-0.829458\pi$
$61$	−403.866	+	233.172i	−0.847700	+	0.489420i	0.0121743	+	0.999926i	$0.496125\pi$
$62$	−873.116			−1.78848
$63$	489.414	+	102.569i	0.978737	+	0.205119i
$64$	−718.677			−1.40367
$65$	48.2703	−	27.8689i	0.0921107	−	0.0531802i
$66$	141.538	−	43.0610i	0.263971	−	0.0803097i
$67$	−379.212	+	656.814i	−0.691464	+	1.19765i	0.279894	+	0.960031i	$0.409701\pi$
$67$	−379.212	+	656.814i	−0.691464	+	1.19765i	−0.971358	+	0.237620i	$0.923633\pi$
$68$	−969.664	−	1679.51i	−1.72925	−	2.99515i
$69$	660.590	−	706.458i	1.15255	−	1.23257i
$70$	120.690	+	472.793i	0.206075	+	0.807280i
$71$			113.113i			0.189072i	0.995521	+	0.0945359i	$0.0301367\pi$
$71$			113.113i			0.189072i	−0.995521	+	0.0945359i	$0.969863\pi$
$72$	932.349	+	1390.45i	1.52609	+	2.27591i
$73$	−590.839	−	341.121i	−0.947295	−	0.546921i	−0.0550552	−	0.998483i	$-0.517533\pi$
$73$	−590.839	−	341.121i	−0.947295	−	0.546921i	−0.892240	+	0.451562i	$0.850867\pi$
$74$	−342.836	−	197.936i	−0.538566	−	0.310941i
$75$	29.3949	−	126.534i	0.0452564	−	0.194812i
$76$			875.377i			1.32122i
$77$	24.7508	+	96.9592i	0.0366314	+	0.143500i
$78$	222.945	+	208.470i	0.323635	+	0.302622i
$79$	649.347	+	1124.70i	0.924776	+	1.60176i	0.791921	+	0.610623i	$0.209081\pi$
$79$	649.347	+	1124.70i	0.924776	+	1.60176i	0.132855	+	0.991135i	$0.457586\pi$
$80$	−421.474	+	730.014i	−0.589028	+	1.02023i
$81$	276.778	−	674.414i	0.379668	−	0.925123i
$82$	680.391	−	392.824i	0.916300	−	0.529026i
$83$	−143.614			−0.189924			−0.0949620	−	0.995481i	$-0.530273\pi$
$83$	−143.614			−0.189924			−0.0949620	+	0.995481i	$0.530273\pi$
$84$	−1626.38	+	986.595i	−2.11253	+	1.28150i
$85$	−490.554			−0.625977
$86$	1897.07	−	1095.28i	2.37868	−	1.37333i
$87$	−318.898	−	1048.19i	−0.392982	−	1.29170i
$88$	−167.509	+	290.134i	−0.202915	+	0.351459i
$89$	103.214	+	178.771i	0.122928	+	0.212918i	0.920921	−	0.389749i	$-0.127438\pi$
$89$	103.214	+	178.771i	0.122928	+	0.212918i	−0.797993	+	0.602667i	$0.794105\pi$
$90$	709.771	−	47.6834i	0.831294	−	0.0558474i
$91$	−147.708	+	144.244i	−0.170154	+	0.166163i
$92$			3679.31i			4.16950i
$93$	−838.645	−	194.824i	−0.935091	−	0.217229i
$94$	−2522.61	−	1456.43i	−2.76795	−	1.59808i
$95$	191.761	+	110.714i	0.207098	+	0.119568i
$96$	−1985.77	−	461.310i	−2.11117	−	0.490440i
$97$		−	1044.15i		−	1.09296i	−0.837472	−	0.546480i	$-0.815967\pi$
$97$		−	1044.15i		−	1.09296i	0.837472	−	0.546480i	$-0.184033\pi$
$98$	−866.304	−	1586.27i	−0.892959	−	1.63507i
$99$	145.558	−	9.77878i	0.147769	−	0.00992732i
$100$	247.084	+	427.962i	0.247084	+	0.427962i
$101$	−305.238	+	528.688i	−0.300716	+	0.520856i	−0.976298	−	0.216429i	$-0.930559\pi$
$101$	−305.238	+	528.688i	−0.300716	+	0.520856i	0.675582	+	0.737285i	$0.263892\pi$
$102$	−781.899	−	2570.03i	−0.759015	−	2.49481i
$103$	984.662	−	568.495i	0.941957	−	0.543839i	0.0513839	−	0.998679i	$-0.483637\pi$
$103$	984.662	−	568.495i	0.941957	−	0.543839i	0.890573	+	0.454840i	$0.150303\pi$
$104$	−691.190			−0.651700
$105$	10.4278	+	481.057i	0.00969192	+	0.447109i
$106$	−711.692			−0.652129
$107$	311.996	−	180.131i	0.281886	−	0.162747i	−0.352391	−	0.935853i	$-0.614631\pi$
$107$	311.996	−	180.131i	0.281886	−	0.162747i	0.634277	+	0.773106i	$0.281298\pi$
$108$	983.204	+	2593.05i	0.876007	+	2.31034i
$109$	−134.943	+	233.729i	−0.118580	+	0.205387i	−0.919205	−	0.393779i	$-0.871168\pi$
$109$	−134.943	+	233.729i	−0.118580	+	0.205387i	0.800625	+	0.599166i	$0.204501\pi$
$110$	71.1791	+	123.286i	0.0616969	+	0.106862i
$111$	−285.134	−	266.621i	−0.243817	−	0.227987i
$112$	843.848	−	3006.13i	0.711930	−	2.53618i
$113$			1022.67i			0.851371i	0.904871	+	0.425686i	$0.139967\pi$
$113$			1022.67i			0.851371i	−0.904871	+	0.425686i	$0.860033\pi$
$114$	−274.382	+	1181.11i	−0.225423	+	0.970363i
$115$	805.994	+	465.341i	0.653560	+	0.377333i
$116$	3609.49	+	2083.94i	2.88907	+	1.66801i
$117$	167.626	+	249.986i	0.132453	+	0.197532i
$118$			3003.19i			2.34293i
$119$	1760.58	−	449.424i	1.35624	−	0.346207i
$120$	−1100.24	+	1176.64i	−0.836983	+	0.895099i
$121$	−650.903	−	1127.40i	−0.489033	−	0.847030i
$122$	1228.68	−	2128.13i	0.911798	−	1.57928i
$123$	741.182	−	225.495i	0.543334	−	0.165303i
$124$	2836.45	−	1637.63i	2.05420	−	1.18599i
$125$	125.000			0.0894427
$126$	−2503.66	+	821.394i	−1.77019	+	0.580759i
$127$	75.8307			0.0529834			0.0264917	−	0.999649i	$-0.491566\pi$
$127$	75.8307			0.0529834			0.0264917	+	0.999649i	$0.491566\pi$
$128$	561.442	−	324.149i	0.387695	−	0.223836i
$129$	2066.57	−	628.728i	1.41048	−	0.429120i
$130$	−146.853	+	254.356i	−0.0990757	+	0.171604i
$131$	581.287	+	1006.82i	0.387689	+	0.671498i	0.992138	−	0.125146i	$-0.0399400\pi$
$131$	581.287	+	1006.82i	0.387689	+	0.671498i	−0.604449	+	0.796644i	$0.706607\pi$
$132$	−379.040	+	405.359i	−0.249934	+	0.267288i
$133$	−789.655	−	221.664i	−0.514826	−	0.144516i
$134$		−	3996.45i		−	2.57642i
$135$	692.389	+	112.575i	0.441417	+	0.0717696i
$136$	5268.24	+	3041.62i	3.32167	+	1.91777i
$137$	−468.389	−	270.425i	−0.292096	−	0.168642i	0.346791	−	0.937943i	$-0.387271\pi$
$137$	−468.389	−	270.425i	−0.292096	−	0.168642i	−0.638887	+	0.769301i	$0.720605\pi$
$138$	−1153.26	+	4964.35i	−0.711389	+	3.06227i
$139$			964.096i			0.588299i	0.955759	+	0.294149i	$0.0950364\pi$
$139$			964.096i			0.588299i	−0.955759	+	0.294149i	$0.904964\pi$
$140$	−1278.86	−	1309.57i	−0.772021	−	0.790565i
$141$	−2098.04	−	1961.82i	−1.25310	−	1.17174i
$142$	−298.021	−	516.187i	−0.176122	−	0.305053i
$143$	−30.1162	+	52.1627i	−0.0176115	+	0.0305040i
$144$	−4085.77	−	2006.60i	−2.36445	−	1.16123i
$145$	913.022	−	527.133i	0.522913	−	0.301904i
$146$	3595.02			2.03785
$147$	−478.148	−	1716.94i	−0.268279	−	0.963341i
$148$	1485.01			0.824775
$149$	−1773.64	+	1024.01i	−0.975184	+	0.563023i	−0.900813	−	0.434208i	$-0.857028\pi$
$149$	−1773.64	+	1024.01i	−0.975184	+	0.563023i	−0.0743716	+	0.997231i	$0.523695\pi$
$150$	199.239	+	654.880i	0.108452	+	0.356471i
$151$	−714.656	+	1237.82i	−0.385151	+	0.667102i	−0.991790	−	0.127876i	$-0.959184\pi$
$151$	−714.656	+	1237.82i	−0.385151	+	0.667102i	0.606639	+	0.794978i	$0.292517\pi$
$152$	−1372.93	−	2377.98i	−0.732627	−	1.26895i
$153$	−177.563	−	2643.03i	−0.0938240	−	1.39658i
$154$	−368.408	−	377.257i	−0.192774	−	0.197404i
$155$		−	828.476i		−	0.429321i
$156$	−1115.28	−	259.088i	−0.572395	−	0.132972i
$157$	−512.548	−	295.920i	−0.260546	−	0.150427i	0.364037	−	0.931384i	$-0.381398\pi$
$157$	−512.548	−	295.920i	−0.260546	−	0.150427i	−0.624584	+	0.780958i	$0.714731\pi$
$158$	−5926.52	−	3421.68i	−2.98411	−	1.72288i
$159$	−683.594	−	158.804i	−0.340959	−	0.0792075i
$160$		−	1961.69i		−	0.969283i
$161$	−3319.01	−	931.676i	−1.62469	−	0.456064i
$162$	513.822	+	3806.88i	0.249196	+	1.84628i
$163$	855.184	+	1481.22i	0.410940	+	0.711769i	0.994993	−	0.0999469i	$-0.0318673\pi$
$163$	855.184	+	1481.22i	0.410940	+	0.711769i	−0.584053	+	0.811716i	$0.698534\pi$
$164$	−1473.57	+	2552.30i	−0.701624	+	1.21525i
$165$	40.8594	+	134.301i	0.0192782	+	0.0633656i
$166$	655.375	−	378.381i	0.306428	−	0.176916i
$167$	1174.71			0.544321			0.272161	−	0.962252i	$-0.412262\pi$
$167$	1174.71			0.544321			0.272161	+	0.962252i	$0.412262\pi$
$168$	2870.75	−	5230.91i	1.31835	−	2.40222i
$169$	2072.73			0.943437
$170$	2238.62	−	1292.47i	1.00997	−	0.583104i
$171$	−527.098	+	1073.26i	−0.235720	+	0.479965i
$172$	−4108.62	+	7116.34i	−1.82139	+	3.15474i
$173$	48.7109	+	84.3698i	0.0214071	+	0.0370781i	0.876530	−	0.481346i	$-0.159852\pi$
$173$	48.7109	+	84.3698i	0.0214071	+	0.0370781i	−0.855123	+	0.518424i	$0.826519\pi$
$174$	4216.95	+	3943.15i	1.83727	+	1.71799i
$175$	−448.620	+	114.519i	−0.193786	+	0.0494677i
$176$		−	910.921i		−	0.390132i
$177$	−670.120	+	2884.62i	−0.284572	+	1.22498i
$178$	−942.019	−	543.875i	−0.396670	−	0.229018i
$179$	414.659	+	239.403i	0.173146	+	0.0999656i	0.584068	−	0.811705i	$-0.301460\pi$
$179$	414.659	+	239.403i	0.173146	+	0.0999656i	−0.410923	+	0.911670i	$0.634793\pi$
$180$	−2216.36	+	1486.16i	−0.917766	+	0.615399i
$181$			1065.15i			0.437415i	0.975790	+	0.218707i	$0.0701840\pi$
$181$			1065.15i			0.437415i	−0.975790	+	0.218707i	$0.929816\pi$
$182$	294.019	−	1047.42i	0.119748	−	0.426591i
$183$	1655.03	−	1769.95i	0.668544	−	0.714965i
$184$	−5770.58	−	9994.93i	−2.31203	−	4.00454i
$185$	187.816	−	325.308i	0.0746407	−	0.129282i
$186$	4340.42	−	1320.52i	1.71105	−	0.520564i
$187$	459.090	−	265.056i	0.179529	−	0.103651i
$188$	10926.8			4.23893
$189$	−2588.09	+	230.309i	−0.996064	+	0.0886375i
$190$	−1166.79			−0.445515
$191$	−3166.69	+	1828.29i	−1.19965	+	0.692619i	−0.960477	−	0.278358i	$-0.910210\pi$
$191$	−3166.69	+	1828.29i	−1.19965	+	0.692619i	−0.239174	+	0.970977i	$0.576876\pi$
$192$	3572.67	−	1086.94i	1.34289	−	0.408558i
$193$	363.262	−	629.189i	0.135483	−	0.234663i	−0.790299	−	0.612721i	$-0.790075\pi$
$193$	363.262	−	629.189i	0.135483	−	0.234663i	0.925782	+	0.378058i	$0.123408\pi$
$194$	2751.02	+	4764.91i	1.01810	+	1.76341i
$195$	−197.811	+	211.546i	−0.0726438	+	0.0776878i
$196$	5789.54	+	3528.38i	2.10989	+	1.28585i
$197$			728.422i			0.263441i	0.991287	+	0.131721i	$0.0420501\pi$
$197$			728.422i			0.263441i	−0.991287	+	0.131721i	$0.957950\pi$
$198$	−638.482	+	428.128i	−0.229166	+	0.153665i
$199$	239.450	+	138.247i	0.0852974	+	0.0492465i	0.542042	−	0.840351i	$-0.317651\pi$
$199$	239.450	+	138.247i	0.0852974	+	0.0492465i	−0.456745	+	0.889598i	$0.650985\pi$
$200$	−1342.42	−	775.047i	−0.474617	−	0.274020i
$201$	891.752	−	3838.66i	0.312932	−	1.34706i
$202$		−	3216.85i		−	1.12048i
$203$	−2793.87	+	2728.33i	−0.965965	+	0.943307i
$204$	7360.49	+	6882.59i	2.52616	+	2.36215i
$205$	372.740	+	645.604i	0.126992	+	0.219956i
$206$	−2995.63	+	5188.59i	−1.01318	+	1.75488i
$207$	−2215.45	+	4511.02i	−0.743886	+	1.51467i
$208$	1627.57	−	939.681i	0.542558	−	0.313246i
$209$	−239.282			−0.0791938
$210$	−1315.03	−	2167.81i	−0.432123	−	0.712347i
$211$	−2684.64			−0.875917			−0.437959	−	0.898995i	$-0.644298\pi$
$211$	−2684.64			−0.875917			−0.437959	+	0.898995i	$0.644298\pi$
$212$	2312.04	−	1334.86i	0.749016	−	0.432445i
$213$	−171.075	−	562.307i	−0.0550321	−	0.180886i
$214$	−949.184	+	1644.03i	−0.303200	+	0.525158i
$215$	1039.28	+	1800.08i	0.329666	+	0.570998i
$216$	−6737.81	−	5502.05i	−2.12245	−	1.73318i
$217$	759.012	+	2973.37i	0.237443	+	0.930164i
$218$		−	1422.14i		−	0.441834i
$219$	3453.08	+	802.178i	1.06547	+	0.247517i
$220$	−462.472	−	267.008i	−0.141727	−	0.0818259i
$221$	947.168	+	546.848i	0.288296	+	0.166448i
$222$	2003.66	+	465.466i	0.605752	+	0.140721i
$223$		−	4590.36i		−	1.37845i	−0.724550	−	0.689223i	$-0.757952\pi$
$223$		−	4590.36i		−	1.37845i	0.724550	−	0.689223i	$-0.242048\pi$
$224$	1797.21	+	7040.44i	0.536078	+	2.10004i
$225$	45.2454	+	673.482i	0.0134060	+	0.199550i
$226$	−2694.44	−	4666.91i	−0.793060	−	1.37362i
$227$	1269.31	−	2198.52i	0.371134	−	0.642822i	−0.618607	−	0.785701i	$-0.712302\pi$
$227$	1269.31	−	2198.52i	0.371134	−	0.642822i	0.989740	+	0.142878i	$0.0456358\pi$
$228$	−1323.94	−	4351.65i	−0.384560	−	1.26401i
$229$	1878.77	−	1084.71i	0.542151	−	0.313011i	−0.203799	−	0.979013i	$-0.565329\pi$
$229$	1878.77	−	1084.71i	0.542151	−	0.313011i	0.745950	+	0.666002i	$0.231996\pi$
$230$	−4904.15			−1.40596
$231$	−269.683	−	444.568i	−0.0768133	−	0.126625i
$232$	−13073.7			−3.69970
$233$	−41.1861	+	23.7788i	−0.0115802	+	0.00668584i	−0.505779	−	0.862663i	$-0.668795\pi$
$233$	−41.1861	+	23.7788i	−0.0115802	+	0.00668584i	0.494199	+	0.869349i	$0.335462\pi$
$234$	−1423.59	−	699.153i	−0.397705	−	0.195321i
$235$	1381.97	−	2393.64i	0.383615	−	0.664441i
$236$	−5632.81	−	9756.31i	−1.55366	−	2.69103i
$237$	−4929.04	−	4609.01i	−1.35095	−	1.26324i
$238$	−6850.21	+	6689.53i	−1.86569	+	1.82192i
$239$		−	5902.02i		−	1.59736i	−0.601754	−	0.798682i	$-0.705531\pi$
$239$		−	5902.02i		−	1.59736i	0.601754	−	0.798682i	$-0.294469\pi$
$240$	991.135	−	4266.47i	0.266573	−	1.14750i
$241$	110.889	+	64.0217i	0.0296389	+	0.0171120i	0.514746	−	0.857343i	$-0.327886\pi$
$241$	110.889	+	64.0217i	0.0296389	+	0.0171120i	−0.485107	+	0.874455i	$0.661219\pi$
$242$	5940.72	+	3429.88i	1.57803	+	0.911078i
$243$	−355.917	+	3771.24i	−0.0939592	+	0.995576i
$244$			9218.09i			2.41856i
$245$	1505.16	−	822.012i	0.392496	−	0.214353i
$246$	−2788.23	+	2981.83i	−0.722647	+	0.772824i
$247$	−246.837	−	427.534i	−0.0635865	−	0.110135i
$248$	−5136.86	+	8897.30i	−1.31529	+	2.27814i
$249$	713.931	−	217.204i	0.181701	−	0.0552802i
$250$	−570.431	+	329.338i	−0.144309	+	0.0833168i
$251$	549.963			0.138300			0.0691501	−	0.997606i	$-0.477971\pi$
$251$	549.963			0.138300			0.0691501	+	0.997606i	$0.477971\pi$
$252$	6592.89	−	7364.30i	1.64807	−	1.84090i
$253$	−1005.73			−0.249920
$254$	−346.049	+	199.792i	−0.0854845	+	0.0493545i
$255$	2438.63	−	741.922i	0.598874	−	0.182200i
$256$	1166.63	−	2020.67i	0.284822	−	0.493327i
$257$	1683.67	+	2916.19i	0.408654	+	0.707810i	0.994739	−	0.102440i	$-0.0326648\pi$
$257$	1683.67	+	2916.19i	0.408654	+	0.707810i	−0.586085	+	0.810250i	$0.699331\pi$
$258$	−7774.18	+	8313.98i	−1.87597	+	2.00622i
$259$	−376.034	+	1339.59i	−0.0902147	+	0.321382i
$260$		−	1101.75i		−	0.262799i
$261$	3170.60	+	4728.42i	0.751935	+	1.12139i
$262$	−5305.35	−	3063.04i	−1.25101	−	0.722273i
$263$	2144.95	+	1238.39i	0.502902	+	0.290350i	0.729911	−	0.683542i	$-0.239561\pi$
$263$	2144.95	+	1238.39i	0.502902	+	0.290350i	−0.227009	+	0.973893i	$0.572895\pi$
$264$	393.913	−	1695.65i	0.0918320	−	0.395303i
$265$		−	675.305i		−	0.156542i
$266$	4187.57	−	1068.96i	0.965249	−	0.246399i
$267$	−783.469	−	732.601i	−0.179579	−	0.167919i
$268$	7495.77	+	12983.1i	1.70850	+	2.95920i
$269$	−582.167	+	1008.34i	−0.131953	+	0.228549i	−0.924429	−	0.381353i	$-0.875458\pi$
$269$	−582.167	+	1008.34i	−0.131953	+	0.228549i	0.792476	+	0.609903i	$0.208791\pi$
$270$	−3456.28	+	1310.51i	−0.779046	+	0.295390i
$271$	5367.38	−	3098.86i	1.20312	−	0.694621i	0.241871	−	0.970308i	$-0.422239\pi$
$271$	5367.38	−	3098.86i	1.20312	−	0.694621i	0.961247	+	0.275687i	$0.0889054\pi$
$272$	−16540.5			−3.68718
$273$	516.127	−	940.457i	0.114423	−	0.208495i
$274$	2849.96			0.628366
$275$	−116.982	+	67.5398i	−0.0256520	+	0.0148102i
$276$	−5564.65	−	18290.5i	−1.21360	−	3.98898i
$277$	1755.17	−	3040.04i	0.380714	−	0.659416i	−0.610451	−	0.792054i	$-0.709012\pi$
$277$	1755.17	−	3040.04i	0.380714	−	0.659416i	0.991164	+	0.132639i	$0.0423450\pi$
$278$	−2540.11	−	4399.60i	−0.548006	−	0.949174i
$279$	4463.71	−	299.878i	0.957832	−	0.0643484i
$280$	5527.96	+	1551.75i	1.17985	+	0.331196i
$281$		−	1889.29i		−	0.401088i	−0.979685	−	0.200544i	$-0.935729\pi$
$281$		−	1889.29i		−	0.401088i	0.979685	−	0.200544i	$-0.0642709\pi$
$282$	14743.1	+	3424.93i	3.11326	+	0.723234i
$283$	−4555.91	−	2630.36i	−0.956964	−	0.552504i	−0.0617270	−	0.998093i	$-0.519661\pi$
$283$	−4555.91	−	2630.36i	−0.956964	−	0.552504i	−0.895237	+	0.445589i	$0.852994\pi$
$284$	1936.33	+	1117.94i	0.404578	+	0.233583i
$285$	−1120.72	−	260.353i	−0.232933	−	0.0541122i
$286$		−	317.389i		−	0.0656210i
$287$	−1929.22	−	1975.56i	−0.396789	−	0.406320i
$288$	10569.3	−	710.060i	2.16251	−	0.145280i
$289$	−2356.36	−	4081.34i	−0.479618	−	0.830723i
$290$	−2777.68	+	4811.09i	−0.562452	+	0.974196i
$291$	1579.19	+	5190.64i	0.318122	+	1.04564i
$292$	−11679.0	+	6742.85i	−2.34061	+	1.35135i
$293$	1097.04			0.218737			0.109368	−	0.994001i	$-0.465117\pi$
$293$	1097.04			0.218737			0.109368	+	0.994001i	$0.465117\pi$
$294$	6705.65	+	6575.40i	1.33021	+	1.30437i
$295$	−2849.64			−0.562416
$296$	−4034.06	+	2329.06i	−0.792145	+	0.457345i
$297$	−708.805	+	268.756i	−0.138482	+	0.0525078i
$298$	5395.95	−	9346.06i	1.04892	−	1.81679i
$299$	−1037.48	−	1796.97i	−0.200666	−	0.347564i
$300$	−1875.56	−	1753.78i	−0.360951	−	0.337515i
$301$	−5379.08	−	5508.29i	−1.03005	−	1.05479i
$302$		−	7531.63i		−	1.43509i
$303$	717.796	−	3089.85i	0.136093	−	0.585832i
$304$	6465.79	+	3733.03i	1.21986	+	0.704289i
$305$	2019.33	+	1165.86i	0.379103	+	0.218875i
$306$	7773.92	+	11593.5i	1.45230	+	2.16587i
$307$		−	749.028i		−	0.139248i	−0.997573	−	0.0696242i	$-0.977820\pi$
$307$		−	749.028i		−	0.139248i	0.997573	−	0.0696242i	$-0.0221800\pi$
$308$	1904.42	+	534.587i	0.352319	+	0.0988991i
$309$	−4035.13	+	4315.31i	−0.742881	+	0.794463i
$310$	2182.79	+	3780.71i	0.399917	+	0.692676i
$311$	2264.03	−	3921.41i	0.412801	−	0.714992i	−0.582394	−	0.812907i	$-0.697884\pi$
$311$	2264.03	−	3921.41i	0.412801	−	0.714992i	0.995195	+	0.0979145i	$0.0312172\pi$
$312$	3436.03	−	1045.37i	0.623483	−	0.189687i
$313$	8795.49	−	5078.08i	1.58834	−	0.917029i	0.594760	−	0.803904i	$-0.297247\pi$
$313$	8795.49	−	5078.08i	1.58834	−	0.917029i	0.993581	−	0.113125i	$-0.0360861\pi$
$314$	3118.65			0.560495
$315$	−779.398	−	2375.65i	−0.139410	−	0.424929i
$316$	25670.9			4.56995
$317$	−264.996	+	152.995i	−0.0469516	+	0.0271075i	−0.523292	−	0.852153i	$-0.675296\pi$
$317$	−264.996	+	152.995i	−0.0469516	+	0.0271075i	0.476340	+	0.879261i	$0.341963\pi$
$318$	3537.95	−	1076.38i	0.623894	−	0.189812i
$319$	−569.640	+	986.645i	−0.0999803	+	0.173171i
$320$	1796.69	+	3111.96i	0.313869	+	0.543637i
$321$	−1278.55	+	1367.33i	−0.222311	+	0.237747i
$322$	17600.8	−	4492.96i	3.04613	−	0.777587i
$323$			4344.88i			0.748469i
$324$	−8809.45	−	11403.5i	−1.51054	−	1.95533i
$325$	−241.352	−	139.344i	−0.0411932	−	0.0237829i
$326$	−7805.17	−	4506.32i	−1.32604	−	0.765589i
$327$	317.332	−	1366.00i	0.0536651	−	0.231008i
$328$		−	9244.50i		−	1.55623i
$329$	−2766.89	+	9856.78i	−0.463658	+	1.65174i
$330$	−540.303	−	505.223i	−0.0901295	−	0.0842776i
$331$	2602.71	+	4508.02i	0.432198	+	0.748590i	0.997062	−	0.0765945i	$-0.0244047\pi$
$331$	2602.71	+	4508.02i	0.432198	+	0.748590i	−0.564864	+	0.825184i	$0.691071\pi$
$332$	−1419.39	+	2458.46i	−0.234636	+	0.406402i
$333$	1820.69	+	894.178i	0.299620	+	0.147149i
$334$	−5360.72	+	3095.01i	−0.878219	+	0.507040i
$335$	3792.12			0.618464
$336$	351.605	+	16220.3i	0.0570881	+	2.63359i
$337$	5139.75			0.830801			0.415401	−	0.909639i	$-0.363641\pi$
$337$	5139.75			0.830801			0.415401	+	0.909639i	$0.363641\pi$
$338$	−9458.80	+	5461.04i	−1.52216	+	0.878821i
$339$	−1546.71	−	5083.89i	−0.247804	−	0.814510i
$340$	−4848.32	+	8397.54i	−0.773345	+	1.33947i
$341$	447.641	+	775.337i	0.0710883	+	0.123129i
$342$	−422.335	−	6286.50i	−0.0667757	−	0.993962i
$343$	−4648.89	+	4329.14i	−0.731827	+	0.681491i
$344$		−	25775.6i		−	4.03991i
$345$	−4710.53	−	1094.29i	−0.735091	−	0.170767i
$346$	−444.580	−	256.678i	−0.0690773	−	0.0398818i
$347$	7067.55	+	4080.45i	1.09339	+	0.631268i	0.934477	−	0.356025i	$-0.115868\pi$
$347$	7067.55	+	4080.45i	1.09339	+	0.631268i	0.158912	+	0.987293i	$0.449201\pi$
$348$	−21095.2	−	4900.58i	−3.24949	−	0.754881i
$349$		−	3643.63i		−	0.558852i	−0.960167	−	0.279426i	$-0.909856\pi$
$349$		−	3643.63i		−	0.558852i	0.960167	−	0.279426i	$-0.0901441\pi$
$350$	1745.53	−	1704.59i	0.266579	−	0.260326i
$351$	−1211.38	−	989.205i	−0.184213	−	0.150427i
$352$	1059.94	+	1835.87i	0.160497	+	0.277989i
$353$	4242.75	−	7348.66i	0.639714	−	1.10802i	−0.345782	−	0.938315i	$-0.612386\pi$
$353$	4242.75	−	7348.66i	0.639714	−	1.10802i	0.985495	−	0.169702i	$-0.0542805\pi$
$354$	−4542.08	−	14929.4i	−0.681945	−	2.24149i
$355$	489.796	−	282.784i	0.0732272	−	0.0422777i
$356$	4080.39			0.607472
$357$	−8072.44	+	4896.90i	−1.19675	+	0.725970i
$358$	−2523.03			−0.372476
$359$	−5221.87	+	3014.85i	−0.767687	+	0.443225i	−0.832049	−	0.554702i	$-0.812832\pi$
$359$	−5221.87	+	3014.85i	−0.767687	+	0.443225i	0.0643616	+	0.997927i	$0.479499\pi$
$360$	3689.93	−	7513.30i	0.540213	−	1.09996i
$361$	−2448.90	+	4241.62i	−0.357035	+	0.618402i
$362$	−2806.36	−	4860.76i	−0.407456	−	0.705735i
$363$	4940.85	+	4620.05i	0.714400	+	0.668016i
$364$	1009.38	+	3954.15i	0.145345	+	0.569379i
$365$			3411.21i			0.489181i
$366$	−2889.35	+	12437.6i	−0.412647	+	1.77630i
$367$	3746.73	+	2163.18i	0.532910	+	0.307676i	0.742201	−	0.670178i	$-0.233782\pi$
$367$	3746.73	+	2163.18i	0.532910	+	0.307676i	−0.209291	+	0.977853i	$0.567116\pi$
$368$	27176.5	+	15690.3i	3.84965	+	2.22260i
$369$	−3343.50	+	2241.95i	−0.471696	+	0.316291i
$370$			1979.36i			0.278114i
$371$	618.684	+	2423.64i	0.0865781	+	0.339163i
$372$	−11623.7	+	12430.8i	−1.62006	+	1.73255i
$373$	−4580.70	−	7934.01i	−0.635871	−	1.10136i	−0.986330	−	0.164782i	$-0.947308\pi$
$373$	−4580.70	−	7934.01i	−0.635871	−	1.10136i	0.350459	−	0.936578i	$-0.386025\pi$
$374$	−1396.69	+	2419.13i	−0.193104	+	0.334466i
$375$	−621.397	+	189.052i	−0.0855701	+	0.0260336i
$376$	−29682.9	+	17137.4i	−4.07122	+	2.35052i
$377$	−2350.50			−0.321106
$378$	11203.8	−	7869.87i	1.52450	−	1.07085i
$379$	9768.98			1.32401			0.662004	−	0.749501i	$-0.269706\pi$
$379$	9768.98			1.32401			0.662004	+	0.749501i	$0.269706\pi$
$380$	3790.49	−	2188.44i	0.511706	−	0.295434i
$381$	−376.968	+	114.688i	−0.0506894	+	0.0154216i
$382$	9634.00	−	16686.6i	1.29036	−	2.23497i
$383$	3631.52	+	6289.98i	0.484497	+	0.839173i	0.999841	−	0.0178102i	$-0.00566945\pi$
$383$	3631.52	+	6289.98i	0.484497	+	0.839173i	−0.515345	+	0.856983i	$0.672336\pi$
$384$	−2300.78	+	2460.54i	−0.305758	+	0.326989i
$385$	357.969	−	349.572i	0.0473864	−	0.0462749i
$386$			3828.36i			0.504815i
$387$	−9322.40	+	6251.04i	−1.22451	+	0.821081i
$388$	−17874.2	−	10319.7i	−2.33873	−	1.35027i
$389$	−4946.69	−	2855.97i	−0.644749	−	0.372246i	0.141693	−	0.989911i	$-0.454746\pi$
$389$	−4946.69	−	2855.97i	−0.644749	−	0.372246i	−0.786441	+	0.617665i	$0.788079\pi$
$390$	345.338	−	1486.55i	0.0448381	−	0.193012i
$391$			18262.0i			2.36202i
$392$	−21261.3	−	504.701i	−2.73943	−	0.0650287i
$393$	−4412.41	−	4125.93i	−0.566353	−	0.529581i
$394$	−1919.18	−	3324.11i	−0.245398	−	0.425042i
$395$	3246.74	−	5623.51i	0.413572	−	0.716328i
$396$	1271.20	−	2588.38i	0.161314	−	0.328462i
$397$	−11800.7	+	6813.14i	−1.49184	+	0.861314i	−0.999956	−	0.00934699i	$-0.997025\pi$
$397$	−11800.7	+	6813.14i	−1.49184	+	0.861314i	−0.491883	+	0.870661i	$0.663691\pi$
$398$	−1456.96			−0.183494
$399$	4260.76	−	92.3601i	0.534599	−	0.0115884i
$400$	4214.74			0.526842
$401$	6146.26	−	3548.54i	0.765410	−	0.441910i	−0.0658246	−	0.997831i	$-0.520968\pi$
$401$	6146.26	−	3548.54i	0.765410	−	0.441910i	0.831235	+	0.555921i	$0.187634\pi$
$402$	6044.30	+	19867.0i	0.749906	+	2.46487i
$403$	−923.548	+	1599.63i	−0.114157	+	0.197725i
$404$	6033.56	+	10450.4i	0.743021	+	1.28695i
$405$	−3612.25	+	487.551i	−0.443195	+	0.0598188i
$406$	5561.30	−	19811.6i	0.679810	−	2.42176i
$407$			405.923i			0.0494370i
$408$	−30789.5	−	7152.65i	−3.73605	−	0.867914i
$409$	−738.997	−	426.660i	−0.0893424	−	0.0515818i	0.454663	−	0.890663i	$-0.349760\pi$
$409$	−738.997	−	426.660i	−0.0893424	−	0.0515818i	−0.544006	+	0.839082i	$0.683093\pi$
$410$	−3401.96	−	1964.12i	−0.409782	−	0.236588i
$411$	2737.44	+	635.928i	0.328535	+	0.0763213i
$412$		−	22474.6i		−	2.68748i
$413$	10227.3	−	2610.72i	1.21852	−	0.311053i
$414$	−1775.12	−	26422.8i	−0.210731	−	3.13674i
$415$	359.035	+	621.867i	0.0424683	+	0.0735573i
$416$	−2186.81	+	3787.66i	−0.257733	+	0.446407i
$417$	−1458.12	−	4792.69i	−0.171233	−	0.562828i
$418$	1091.95	−	630.439i	0.127773	−	0.0737698i
$419$	−16414.9			−1.91389			−0.956947	−	0.290263i	$-0.906257\pi$
$419$	−16414.9			−1.91389			−0.956947	+	0.290263i	$0.906257\pi$
$420$	8338.04	+	4575.96i	0.968701	+	0.531628i
$421$	91.0902			0.0105450			0.00527252	−	0.999986i	$-0.498322\pi$
$421$	91.0902			0.0105450			0.00527252	+	0.999986i	$0.498322\pi$
$422$	12251.2	−	7073.25i	1.41322	−	0.815925i
$423$	13396.8	+	6579.43i	1.53989	+	0.756272i
$424$	−4187.14	+	7252.34i	−0.479589	+	0.830672i
$425$	1226.38	+	2124.16i	0.139973	+	0.242440i
$426$	2262.20	+	2115.33i	0.257287	+	0.240582i
$427$	−8315.40	−	2334.21i	−0.942413	−	0.264544i
$428$		−	7121.19i		−	0.804243i
$429$	70.8210	−	304.858i	0.00797032	−	0.0343093i
$430$	−9485.37	−	5476.38i	−1.06378	−	0.614174i
$431$	−9266.32	−	5349.91i	−1.03560	−	0.597903i	−0.117015	−	0.993130i	$-0.537333\pi$
$431$	−9266.32	−	5349.91i	−1.03560	−	0.597903i	−0.918583	+	0.395227i	$0.870666\pi$
$432$	23345.9	+	3795.79i	2.60007	+	0.422743i
$433$			6880.53i			0.763642i	0.924236	+	0.381821i	$0.124703\pi$
$433$			6880.53i			0.763642i	−0.924236	+	0.381821i	$0.875297\pi$
$434$	−11297.7	−	11569.0i	−1.24955	−	1.27957i
$435$	−3741.55	+	4001.34i	−0.412399	+	0.441034i
$436$	2667.39	+	4620.05i	0.292992	+	0.507477i
$437$	4121.56	−	7138.76i	0.451170	−	0.781449i
$438$	−17871.5	+	5437.17i	−1.94962	+	0.593146i
$439$	−785.949	+	453.768i	−0.0854471	+	0.0493329i	−0.542115	−	0.840304i	$-0.682376\pi$
$439$	−785.949	+	453.768i	−0.0854471	+	0.0493329i	0.456668	+	0.889637i	$0.349043\pi$
$440$	1675.09			0.181493
$441$	4973.70	+	7812.07i	0.537058	+	0.843545i
$442$	−5763.13			−0.620191
$443$	−2511.71	+	1450.14i	−0.269379	+	0.155526i	−0.628605	−	0.777724i	$-0.716374\pi$
$443$	−2511.71	+	1450.14i	−0.269379	+	0.155526i	0.359226	+	0.933250i	$0.383041\pi$
$444$	−7382.23	+	2245.95i	−0.789065	+	0.240063i
$445$	516.068	−	893.855i	0.0549752	−	0.0952198i
$446$	12094.3	+	20947.9i	1.28404	+	2.22401i
$447$	7268.36	−	7773.04i	0.769086	−	0.822488i
$448$	−9299.30	−	9522.67i	−0.980693	−	1.00425i
$449$			11022.1i			1.15850i	0.815151	+	0.579249i	$0.196654\pi$
$449$			11022.1i			1.15850i	−0.815151	+	0.579249i	$0.803346\pi$
$450$	−1980.90	−	2954.19i	−0.207513	−	0.309471i
$451$	−697.664	−	402.797i	−0.0728419	−	0.0420553i
$452$	17506.6	+	10107.4i	1.82177	+	1.05180i
$453$	1680.58	−	7234.28i	0.174306	−	0.750323i
$454$			13377.1i			1.38286i
$455$	993.863	+	278.987i	0.102402	+	0.0287453i
$456$	10421.6	+	9744.94i	1.07025	+	1.00076i
$457$	907.562	+	1571.94i	0.0928971	+	0.160902i	0.908729	−	0.417387i	$-0.137054\pi$
$457$	907.562	+	1571.94i	0.0928971	+	0.160902i	−0.815832	+	0.578289i	$0.803721\pi$
$458$	−5715.77	+	9900.01i	−0.583145	+	1.01004i
$459$	4880.06	+	12870.4i	0.496257	+	1.30880i
$460$	15931.9	−	9198.27i	1.61484	−	0.932329i
$461$	−5247.54			−0.530157			−0.265078	−	0.964227i	$-0.585398\pi$
$461$	−5247.54			−0.530157			−0.265078	+	0.964227i	$0.585398\pi$
$462$	2401.99	+	1318.23i	0.241885	+	0.132748i
$463$	11225.9			1.12681			0.563404	−	0.826181i	$-0.309491\pi$
$463$	11225.9			1.12681			0.563404	+	0.826181i	$0.309491\pi$
$464$	30785.2	−	17773.8i	3.08010	−	1.77830i
$465$	1253.00	+	4118.50i	0.124960	+	0.410733i
$466$	125.300	−	217.027i	0.0124559	−	0.0215742i
$467$	−4608.69	−	7982.48i	−0.456669	−	0.790974i	0.542113	−	0.840305i	$-0.317624\pi$
$467$	−4608.69	−	7982.48i	−0.456669	−	0.790974i	−0.998782	+	0.0493311i	$0.984291\pi$
$468$	5936.09	−	398.794i	0.586316	−	0.0393895i
$469$	−13609.8	+	3474.17i	−1.33996	+	0.342052i
$470$			14564.3i			1.42937i
$471$	2995.52	+	695.883i	0.293050	+	0.0680777i
$472$	30603.3	+	17668.9i	2.98439	+	1.72304i
$473$	−1945.24	−	1123.08i	−0.189095	−	0.109174i
$474$	34636.8	+	8046.40i	3.35637	+	0.779712i
$475$		−	1107.14i		−	0.106945i
$476$	9707.00	−	34580.3i	0.934705	−	3.32980i
$477$	3638.44	−	244.436i	0.349251	−	0.0234632i
$478$	15550.1	+	26933.5i	1.48796	+	2.57722i
$479$	−5002.73	+	8664.97i	−0.477203	+	0.826540i	−0.999659	−	0.0261264i	$-0.991683\pi$
$479$	−5002.73	+	8664.97i	−0.477203	+	0.826540i	0.522455	+	0.852667i	$0.325016\pi$
$480$	2966.90	+	9751.92i	0.282124	+	0.927317i
$481$	−725.277	+	418.739i	−0.0687521	+	0.0396941i
$482$	−674.713			−0.0637601
$483$	17908.5	−	388.200i	1.68709	−	0.0365708i
$484$	−25732.4			−2.41664
$485$	−4521.29	+	2610.37i	−0.423302	+	0.244393i
$486$	−8311.90	−	18147.6i	−0.775793	−	1.69381i
$487$	−8507.45	+	14735.3i	−0.791600	+	1.37109i	0.133376	+	0.991066i	$0.457418\pi$
$487$	−8507.45	+	14735.3i	−0.791600	+	1.37109i	−0.924976	+	0.380026i	$0.875915\pi$
$488$	−14457.5	−	25041.2i	−1.34111	−	2.32287i
$489$	−6491.50	−	6070.02i	−0.600318	−	0.561341i
$490$	−4702.98	+	7716.88i	−0.433590	+	0.711455i
$491$		−	6956.50i		−	0.639394i	−0.947520	−	0.319697i	$-0.896419\pi$
$491$		−	6956.50i		−	0.639394i	0.947520	−	0.319697i	$-0.103581\pi$
$492$	3465.23	−	14916.6i	0.317530	−	1.36685i
$493$	17915.5	+	10343.5i	1.63666	+	0.944924i
$494$	2252.85	+	1300.69i	0.205184	+	0.118463i
$495$	−406.238	−	605.838i	−0.0368870	−	0.0550109i
$496$		−	27934.5i		−	2.52882i
$497$	−1498.78	+	1463.63i	−0.135271	+	0.132098i
$498$	−2685.72	+	2872.20i	−0.241666	+	0.258447i
$499$	−6545.11	−	11336.5i	−0.587173	−	1.01701i	−0.994601	−	0.103776i	$-0.966907\pi$
$499$	−6545.11	−	11336.5i	−0.587173	−	1.01701i	0.407428	−	0.913238i	$-0.366426\pi$
$500$	1235.42	−	2139.81i	0.110499	−	0.191390i
$501$	−5839.68	+	1776.65i	−0.520754	+	0.158433i
$502$	−2509.73	+	1448.99i	−0.223137	+	0.128828i
$503$	−10133.9			−0.898310			−0.449155	−	0.893454i	$-0.648275\pi$
$503$	−10133.9			−0.898310			−0.449155	+	0.893454i	$0.648275\pi$
$504$	−6359.68	+	30345.5i	−0.562069	+	2.68194i
$505$	3052.38			0.268969
$506$	4589.60	−	2649.80i	0.403226	−	0.232803i
$507$	−10303.9	+	3134.84i	−0.902590	+	0.274601i
$508$	749.462	−	1298.11i	0.0654567	−	0.113374i
$509$	−7484.28	−	12963.2i	−0.651739	−	1.12884i	−0.982701	−	0.185200i	$-0.940707\pi$
$509$	−7484.28	−	12963.2i	−0.651739	−	1.12884i	0.330962	−	0.943644i	$-0.392627\pi$
$510$	−9173.81	+	9810.80i	−0.796516	+	0.851822i
$511$	−3125.20	−	12242.7i	−0.270549	−	1.05986i
$512$			17481.3i			1.50893i
$513$	997.084	−	6132.54i	0.0858135	−	0.527794i
$514$	−15366.6	−	8871.93i	−1.31866	−	0.761331i
$515$	−4923.31	−	2842.47i	−0.421256	−	0.243212i
$516$	9661.81	−	41590.5i	0.824297	−	3.54830i
$517$			2986.81i			0.254081i
$518$	−1813.41	−	7103.87i	−0.153816	−	0.602560i
$519$	−369.753	−	345.746i	−0.0312724	−	0.0292419i
$520$	1727.98	+	2992.94i	0.145724	+	0.252402i
$521$	−2464.79	+	4269.14i	−0.207264	+	0.358991i	−0.950852	−	0.309647i	$-0.899789\pi$
$521$	−2464.79	+	4269.14i	−0.207264	+	0.358991i	0.743588	+	0.668638i	$0.233122\pi$
$522$	−26926.9	−	13224.3i	−2.25777	−	1.10884i
$523$	−10711.8	+	6184.48i	−0.895595	+	0.517072i	−0.875768	−	0.482732i	$-0.839645\pi$
$523$	−10711.8	+	6184.48i	−0.895595	+	0.517072i	−0.0198263	+	0.999803i	$0.506311\pi$
$524$	22980.3			1.91584
$525$	2056.97	−	1247.80i	0.170997	−	0.103730i
$526$	−13051.1			−1.08186
$527$	14078.5	−	8128.24i	1.16370	−	0.671863i
$528$	1377.69	+	4528.35i	0.113554	+	0.373241i
$529$	11239.9	−	19468.1i	0.923801	−	1.60007i
$530$	1779.23	+	3081.72i	0.145820	+	0.252568i
$531$	−1031.47	−	15353.5i	−0.0842972	−	1.25477i
$532$	−11599.0	+	11326.9i	−0.945263	+	0.923091i
$533$		−	1662.05i		−	0.135069i
$534$	5505.51	+	1278.97i	0.446155	+	0.103645i
$535$	−1559.98	−	900.654i	−0.126063	−	0.0727826i
$536$	−40724.9	−	23512.5i	−3.28181	−	1.89475i
$537$	−2423.42	−	562.979i	−0.194745	−	0.0452409i
$538$		−	6135.36i		−	0.491662i
$539$	−964.475	+	1582.56i	−0.0770739	+	0.126467i
$540$	8770.24	−	10740.0i	0.698909	−	0.855884i
$541$	−5162.10	−	8941.03i	−0.410233	−	0.710545i	0.584682	−	0.811263i	$-0.301219\pi$
$541$	−5162.10	−	8941.03i	−0.410233	−	0.710545i	−0.994915	+	0.100718i	$0.967886\pi$
$542$	−16329.2	+	28283.0i	−1.29409	+	2.24143i
$543$	−1610.95	−	5295.05i	−0.127316	−	0.418476i
$544$	33335.6	−	19246.3i	2.62730	−	1.51687i
$545$	1349.43			0.106061
$546$	122.508	+	5651.57i	0.00960233	+	0.442976i
$547$	17996.8			1.40674			0.703371	−	0.710823i	$-0.251677\pi$
$547$	17996.8			1.40674			0.703371	+	0.710823i	$0.251677\pi$
$548$	−9258.52	+	5345.41i	−0.721723	+	0.416687i
$549$	−5550.56	+	11301.8i	−0.431497	+	0.878599i
$550$	355.895	−	616.429i	0.0275917	−	0.0477902i
$551$	−4668.86	−	8086.70i	−0.360980	−	0.625236i
$552$	43803.1	+	40959.1i	3.37750	+	3.15821i
$553$	−6500.41	+	23157.1i	−0.499865	+	1.78072i
$554$			18497.4i			1.41855i
$555$	−441.668	+	1901.22i	−0.0337797	+	0.145409i
$556$	16503.9	+	9528.51i	1.25885	+	0.726796i
$557$	16846.3	+	9726.22i	1.28151	+	0.739880i	0.977124	−	0.212669i	$-0.0682157\pi$
$557$	16846.3	+	9726.22i	1.28151	+	0.739880i	0.304385	+	0.952549i	$0.401549\pi$
$558$	−19579.8	+	13129.0i	−1.48545	+	0.996051i
$559$		−	4634.16i		−	0.350634i
$560$	−15126.5	+	3861.36i	−1.14145	+	0.291379i
$561$	−1881.34	+	2011.97i	−0.141587	+	0.151418i
$562$	4977.73	+	8621.68i	0.373617	+	0.647124i
$563$	4845.31	−	8392.33i	0.362710	−	0.628232i	−0.625696	−	0.780067i	$-0.715185\pi$
$563$	4845.31	−	8392.33i	0.362710	−	0.628232i	0.988406	+	0.151835i	$0.0485183\pi$
$564$	−54319.0	+	16525.9i	−4.05539	+	1.23380i
$565$	4428.30	−	2556.68i	0.329735	−	0.190372i
$566$	27720.9			2.05865
$567$	12517.5	−	5059.18i	0.927138	−	0.374719i
$568$	−7013.46			−0.518095
$569$	11906.3	−	6874.13i	0.877223	−	0.506465i	0.00748111	−	0.999972i	$-0.497619\pi$
$569$	11906.3	−	6874.13i	0.877223	−	0.506465i	0.869742	+	0.493507i	$0.164285\pi$
$570$	5800.32	−	1764.67i	0.426226	−	0.129674i
$571$	−6964.40	+	12062.7i	−0.510422	+	0.884077i	0.489505	+	0.872001i	$0.337178\pi$
$571$	−6964.40	+	12062.7i	−0.510422	+	0.884077i	−0.999927	+	0.0120766i	$0.996156\pi$
$572$	595.298	+	1031.09i	0.0435151	+	0.0753704i
$573$	12977.0	−	13878.1i	0.946113	−	1.01181i
$574$	14008.9	+	3932.44i	1.01868	+	0.285952i
$575$		−	4653.41i		−	0.337497i
$576$	−16116.5	+	10806.7i	−1.16583	+	0.781737i
$577$	−1032.28	−	595.988i	−0.0744791	−	0.0430005i	0.462298	−	0.886725i	$-0.347025\pi$
$577$	−1032.28	−	595.988i	−0.0744791	−	0.0430005i	−0.536777	+	0.843724i	$0.680358\pi$
$578$	21506.3	+	12416.7i	1.54765	+	0.893538i
$579$	−854.245	+	3677.21i	−0.0613147	+	0.263937i
$580$		−	20839.4i		−	1.49191i
$581$	−1858.29	−	1902.93i	−0.132694	−	0.135881i
$582$	−20882.4	−	19526.5i	−1.48729	−	1.39072i
$583$	364.880	+	631.990i	0.0259207	+	0.0448960i
$584$	21150.8	−	36634.2i	1.49867	−	2.59578i
$585$	663.407	−	1350.81i	0.0468863	−	0.0954683i
$586$	−5006.30	+	2890.39i	−0.352915	+	0.203756i
$587$	4276.32			0.300686			0.150343	−	0.988634i	$-0.451962\pi$
$587$	4276.32			0.300686			0.150343	+	0.988634i	$0.451962\pi$
$588$	−34117.2	−	8784.00i	−2.39281	−	0.616065i
$589$	−7337.88			−0.513331
$590$	13004.2	−	7507.97i	0.907414	−	0.523896i
$591$	−1101.68	−	3621.11i	−0.0766784	−	0.252035i
$592$	6332.78	−	10968.7i	0.439655	−	0.761504i
$593$	−1930.62	−	3343.93i	−0.133695	−	0.231566i	0.791403	−	0.611294i	$-0.209351\pi$
$593$	−1930.62	−	3343.93i	−0.133695	−	0.231566i	−0.925098	+	0.379728i	$0.876018\pi$
$594$	2526.50	−	3093.95i	0.174518	−	0.213714i
$595$	−6347.51	−	6499.98i	−0.437349	−	0.447854i
$596$			40482.8i			2.78228i
$597$	−1399.44	−	325.100i	−0.0959382	−	0.0222872i
$598$	9469.00	+	5466.93i	0.647519	+	0.373845i
$599$	−6544.71	−	3778.59i	−0.446427	−	0.257745i	0.259893	−	0.965637i	$-0.416313\pi$
$599$	−6544.71	−	3778.59i	−0.446427	−	0.257745i	−0.706320	+	0.707893i	$0.749646\pi$
$600$	7845.60	+	1822.59i	0.533826	+	0.124012i
$601$			8854.35i			0.600959i	0.953788	+	0.300479i	$0.0971467\pi$
$601$			8854.35i			0.600959i	−0.953788	+	0.300479i	$0.902853\pi$
$602$	39059.9	+	10964.5i	2.64446	+	0.742323i
$603$	1372.61	+	20431.4i	0.0926980	+	1.37982i
$604$	14126.4	+	24467.6i	0.951648	+	1.64830i
$605$	−3254.51	+	5636.98i	−0.218702	+	0.378803i
$606$	4865.22	+	15991.5i	0.326132	+	1.07197i
$607$	11680.8	−	6743.90i	0.781068	−	0.450950i	−0.0557409	−	0.998445i	$-0.517752\pi$
$607$	11680.8	−	6743.90i	0.781068	−	0.450950i	0.836809	+	0.547496i	$0.184419\pi$
$608$	−17374.9			−1.15895
$609$	9762.42	−	17788.5i	0.649578	−	1.18362i
$610$	−12286.8			−0.815537
$611$	−5336.64	+	3081.11i	−0.353351	+	0.204007i
$612$	−46999.6	−	23082.5i	−3.10433	−	1.52460i
$613$	9641.06	−	16698.8i	0.635234	−	1.10026i	−0.351231	−	0.936289i	$-0.614237\pi$
$613$	9641.06	−	16698.8i	0.635234	−	1.10026i	0.986465	−	0.163969i	$-0.0524298\pi$
$614$	1973.47	+	3418.15i	0.129711	+	0.224666i
$615$	−2829.38	−	2645.67i	−0.185515	−	0.173470i
$616$	−6011.83	+	1534.64i	−0.393220	+	0.100377i
$617$		−	20155.9i		−	1.31515i	−0.753390	−	0.657574i	$-0.771583\pi$
$617$		−	20155.9i		−	1.31515i	0.753390	−	0.657574i	$-0.228417\pi$
$618$	7044.51	−	30324.0i	0.458530	−	1.97381i
$619$	4448.02	+	2568.06i	0.288822	+	0.166752i	0.637411	−	0.770524i	$-0.280006\pi$
$619$	4448.02	+	2568.06i	0.288822	+	0.166752i	−0.348588	+	0.937276i	$0.613339\pi$
$620$	−14182.3	−	8188.13i	−0.918666	−	0.530392i
$621$	4190.85	−	25775.7i	0.270810	−	1.66561i
$622$			23860.2i			1.53811i
$623$	−1033.24	+	3680.81i	−0.0664459	+	0.236707i
$624$	−6669.77	+	7132.89i	−0.427892	+	0.457603i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−26758.5	+	46347.1i	−1.70844	+	2.95911i
$627$	1189.51	−	361.895i	0.0757650	−	0.0230505i
$628$	−10131.4	+	5849.37i	−0.643769	+	0.371680i
$629$	7370.73			0.467234
$630$	9815.88	+	8787.67i	0.620753	+	0.555729i
$631$	22640.5			1.42837			0.714186	−	0.699956i	$-0.246797\pi$
$631$	22640.5			1.42837			0.714186	+	0.699956i	$0.246797\pi$
$632$	−69735.8	+	40262.0i	−4.38915	+	2.53407i
$633$	13345.8	−	4060.30i	0.837993	−	0.254949i
$634$	806.196	−	1396.37i	0.0505018	−	0.0874717i
$635$	−189.577	−	328.357i	−0.0118474	−	0.0205204i
$636$	−9474.69	+	10132.6i	−0.590717	+	0.631734i
$637$	−3822.53	−	90.7394i	−0.237762	−	0.00564400i
$638$		−	6003.34i		−	0.372530i
$639$	1700.89	+	2536.59i	0.105299	+	0.157036i
$640$	−2807.21	−	1620.74i	−0.173382	−	0.100102i
$641$	20595.2	+	11890.6i	1.26905	+	0.732687i	0.974808	−	0.223044i	$-0.0715994\pi$
$641$	20595.2	+	11890.6i	1.26905	+	0.732687i	0.294242	+	0.955731i	$0.404933\pi$
$642$	2232.09	−	9608.35i	0.137218	−	0.590672i
$643$			3632.10i			0.222762i	0.993778	+	0.111381i	$0.0355274\pi$
$643$			3632.10i			0.222762i	−0.993778	+	0.111381i	$0.964473\pi$
$644$	−48751.9	+	47608.3i	−2.98306	+	2.91309i
$645$	−7888.91	−	7376.70i	−0.481590	−	0.450321i
$646$	−11447.5	−	19827.6i	−0.697206	−	1.20760i
$647$	10275.1	−	17797.0i	0.624352	−	1.08141i	−0.364314	−	0.931276i	$-0.618696\pi$
$647$	10275.1	−	17797.0i	0.624352	−	1.08141i	0.988666	−	0.150133i	$-0.0479703\pi$
$648$	41816.2	+	17161.3i	2.53502	+	1.04037i
$649$	2666.87	−	1539.72i	0.161300	−	0.0931265i
$650$	1468.53			0.0886160
$651$	−8270.16	−	13633.2i	−0.497900	−	0.820779i
$652$	33808.4			2.03073
$653$	25694.2	−	14834.5i	1.53980	−	0.889005i	0.540952	−	0.841053i	$-0.318064\pi$
$653$	25694.2	−	14834.5i	1.53980	−	0.889005i	0.998850	−	0.0479520i	$-0.0152694\pi$
$654$	2150.87	+	7069.73i	0.128602	+	0.422704i
$655$	2906.44	−	5034.10i	0.173380	−	0.300303i
$656$	12568.0	+	21768.4i	0.748016	+	1.29560i
$657$	−18379.1	+	1234.73i	−1.09138	+	0.0733205i
$658$	−13343.2	−	52270.8i	−0.790534	−	3.09685i
$659$			3586.12i			0.211981i	0.994367	+	0.105990i	$0.0338013\pi$
$659$			3586.12i			0.211981i	−0.994367	+	0.105990i	$0.966199\pi$
$660$	2702.86	+	627.895i	0.159407	+	0.0370315i
$661$	7982.52	+	4608.71i	0.469718	+	0.271192i	0.716122	−	0.697975i	$-0.245915\pi$
$661$	7982.52	+	4608.71i	0.469718	+	0.271192i	−0.246403	+	0.969167i	$0.579249\pi$
$662$	−23754.6	−	13714.7i	−1.39464	−	0.805194i
$663$	−5535.60	−	1285.96i	−0.324261	−	0.0753283i
$664$		−	8904.61i		−	0.520431i
$665$	1014.31	+	3973.47i	0.0591476	+	0.231706i
$666$	−10664.5	+	716.457i	−0.620484	+	0.0416849i
$667$	−19623.7	−	33989.3i	−1.13918	−	1.97312i
$668$	11610.1	−	20109.2i	0.672465	−	1.16474i
$669$	6942.54	+	22819.5i	0.401217	+	1.31876i
$670$	−17305.1	+	9991.12i	−0.997844	+	0.576105i
$671$	−2519.74			−0.144968
$672$	−19582.4	−	32281.1i	−1.12412	−	1.85308i
$673$	−21777.5			−1.24734			−0.623670	−	0.781688i	$-0.714359\pi$
$673$	−21777.5			−1.24734			−0.623670	+	0.781688i	$0.714359\pi$
$674$	−23455.0	+	13541.7i	−1.34043	+	0.773899i
$675$	−1243.51	−	3279.57i	−0.0709076	−	0.187008i
$676$	20485.6	−	35482.0i	1.16554	−	2.01878i
$677$	13892.5	+	24062.5i	0.788674	+	1.36602i	0.926779	+	0.375606i	$0.122565\pi$
$677$	13892.5	+	24062.5i	0.788674	+	1.36602i	−0.138105	+	0.990418i	$0.544101\pi$
$678$	20452.9	+	19124.9i	1.15854	+	1.08332i
$679$	13835.3	−	13510.7i	0.781956	−	0.763614i
$680$		−	30416.2i		−	1.71530i
$681$	−2984.91	+	12848.9i	−0.167962	+	0.723014i
$682$	−4085.57	−	2358.81i	−0.229391	−	0.132439i
$683$	−30200.7	−	17436.4i	−1.69194	−	0.976844i	−0.952948	−	0.303134i	$-0.901967\pi$
$683$	−30200.7	−	17436.4i	−1.69194	−	0.976844i	−0.738996	−	0.673710i	$-0.764700\pi$
$684$	13163.0	+	19630.5i	0.735820	+	1.09736i
$685$			2704.25i			0.150838i
$686$	9808.96	−	32004.2i	0.545930	−	1.78124i
$687$	−7699.16	+	8233.75i	−0.427571	+	0.457259i
$688$	35042.3	+	60695.0i	1.94182	+	3.36334i
$689$	−752.800	+	1303.89i	−0.0416247	+	0.0720960i
$690$	24379.4	−	7417.12i	1.34508	−	0.409225i
$691$	−16443.9	+	9493.88i	−0.905289	+	0.522669i	−0.878912	−	0.476983i	$-0.841730\pi$
$691$	−16443.9	+	9493.88i	−0.905289	+	0.522669i	−0.0263765	+	0.999652i	$0.508397\pi$
$692$	1925.71			0.105787
$693$	2013.02	+	1802.15i	0.110344	+	0.0987851i
$694$	−43003.2			−2.35213
$695$	4174.66	−	2410.24i	0.227847	−	0.131548i
$696$	64991.6	−	19772.9i	3.53951	−	1.07685i
$697$	−7313.96	+	12668.1i	−0.397469	+	0.688437i
$698$	9599.91	+	16627.5i	0.520576	+	0.901663i
$699$	168.780	−	180.499i	0.00913282	−	0.00976696i
$700$	−2473.48	+	8811.54i	−0.133555	+	0.475778i
$701$		−	12203.2i		−	0.657499i	−0.944417	−	0.328749i	$-0.893373\pi$
$701$		−	12203.2i		−	0.657499i	0.944417	−	0.328749i	$-0.106627\pi$
$702$	8134.33	+	1322.55i	0.437337	+	0.0711062i
$703$	−2881.27	−	1663.50i	−0.154579	−	0.0892465i
$704$	−3362.90	−	1941.57i	−0.180034	−	0.103943i
$705$	−3249.83	+	13989.3i	−0.173611	+	0.747330i
$706$			44713.6i			2.38360i
$707$	−10954.9	+	2796.45i	−0.582745	+	0.148757i
$708$	42757.3	+	39981.2i	2.26966	+	2.12230i
$709$	5138.72	+	8900.52i	0.272198	+	0.471461i	0.969424	−	0.245390i	$-0.0789160\pi$
$709$	5138.72	+	8900.52i	0.272198	+	0.471461i	−0.697226	+	0.716851i	$0.745583\pi$
$710$	−1490.10	+	2580.94i	−0.0787642	+	0.136424i
$711$	31473.9	+	15457.4i	1.66014	+	0.815330i
$712$	−11084.5	+	6399.63i	−0.583439	+	0.336848i
$713$	−30841.9			−1.61997
$714$	23936.3	−	43615.2i	1.25461	−	2.28608i
$715$	301.162			0.0157522
$716$	8196.45	−	4732.22i	0.427815	−	0.246999i
$717$	8926.31	+	29340.0i	0.464936	+	1.52820i
$718$	15886.5	−	27516.2i	0.825736	−	1.43022i
$719$	−14256.3	−	24692.6i	−0.739458	−	1.28078i	−0.952740	−	0.303788i	$-0.901749\pi$
$719$	−14256.3	−	24692.6i	−0.739458	−	1.28078i	0.213282	−	0.976991i	$-0.431585\pi$
$720$	1525.58	+	22708.4i	0.0789653	+	1.17541i
$721$	20273.7	+	5691.02i	1.04720	+	0.293959i
$722$		−	25808.6i		−	1.33033i
$723$	−648.075	−	150.553i	−0.0333363	−	0.00774429i
$724$	18233.8	+	10527.3i	0.935985	+	0.540391i
$725$	−4565.11	−	2635.67i	−0.233854	−	0.135015i
$726$	−34719.8	−	8065.67i	−1.77489	−	0.412321i
$727$			18858.2i			0.962052i	0.876706	+	0.481026i	$0.159736\pi$
$727$			18858.2i			0.962052i	−0.876706	+	0.481026i	$0.840264\pi$
$728$	−8943.64	−	9158.46i	−0.455320	−	0.466257i
$729$	−3934.36	−	19285.8i	−0.199886	−	0.979819i
$730$	−8987.55	−	15566.9i	−0.455677	−	0.789255i
$731$	−20392.9	+	35321.5i	−1.03182	+	1.78716i
$732$	−13941.6	−	45824.7i	−0.703957	−	2.31384i
$733$	−25590.6	+	14774.7i	−1.28951	+	0.744499i	−0.978567	−	0.205929i	$-0.933978\pi$
$733$	−25590.6	+	14774.7i	−1.28951	+	0.744499i	−0.310943	+	0.950428i	$0.600645\pi$
$734$	−22797.4			−1.14641
$735$	−6239.22	+	6362.80i	−0.313111	+	0.319314i
$736$	−73028.5			−3.65743
$737$	−3548.89	+	2048.95i	−0.177375	+	0.102407i
$738$	9351.01	−	19040.2i	0.466417	−	0.949700i
$739$	−11576.9	+	20051.8i	−0.576270	+	0.998129i	0.419632	+	0.907694i	$0.362159\pi$
$739$	−11576.9	+	20051.8i	−0.576270	+	0.998129i	−0.995902	+	0.0904348i	$0.971174\pi$
$740$	−3712.51	−	6430.26i	−0.184425	−	0.319434i
$741$	1873.68	+	1752.03i	0.0928898	+	0.0868588i
$742$	−9208.92	−	9430.12i	−0.455620	−	0.466564i
$743$			1690.45i			0.0834677i	0.999129	+	0.0417339i	$0.0132882\pi$
$743$			1690.45i			0.0834677i	−0.999129	+	0.0417339i	$0.986712\pi$
$744$	12079.8	−	51999.1i	0.595251	−	2.56234i
$745$	8868.21	+	5120.07i	0.436116	+	0.251792i
$746$	41807.6	+	24137.6i	2.05185	+	1.18464i
$747$	−3220.57	+	2159.52i	−0.157744	+	0.105774i
$748$		−	10478.6i		−	0.512211i
$749$	6423.85	+	1803.23i	0.313381	+	0.0879688i
$750$	2337.62	−	2499.93i	0.113810	−	0.121713i
$751$	−3030.19	−	5248.44i	−0.147235	−	0.255018i	0.782970	−	0.622060i	$-0.213704\pi$
$751$	−3030.19	−	5248.44i	−0.147235	−	0.255018i	−0.930204	+	0.367042i	$0.880371\pi$
$752$	46597.1	−	80708.5i	2.25960	−	3.91374i
$753$	−2733.96	+	831.774i	−0.132312	+	0.0402543i
$754$	10726.4	−	6192.88i	0.518079	−	0.299113i
$755$	7146.56			0.344490
$756$	−21636.5	+	46580.5i	−1.04089	+	2.24089i
$757$	24942.2			1.19754			0.598770	−	0.800921i	$-0.295656\pi$
$757$	24942.2			1.19754			0.598770	+	0.800921i	$0.295656\pi$
$758$	−44580.2	+	25738.4i	−2.13618	+	1.23333i
$759$	4999.66	−	1521.08i	0.239099	−	0.0727429i
$760$	−6864.65	+	11889.9i	−0.327641	+	0.567491i
$761$	−1876.53	−	3250.25i	−0.0893880	−	0.154824i	0.817865	−	0.575411i	$-0.195158\pi$
$761$	−1876.53	−	3250.25i	−0.0893880	−	0.154824i	−0.907253	+	0.420586i	$0.861824\pi$
$762$	1418.10	−	1516.57i	0.0674180	−	0.0720992i
$763$	−4843.06	+	1236.29i	−0.229791	+	0.0586588i
$764$			72278.5i			3.42270i
$765$	−11000.8	+	7376.45i	−0.519913	+	0.348622i
$766$	−33144.5	−	19136.0i	−1.56340	−	0.902627i
$767$	5502.13	+	3176.66i	0.259023	+	0.149547i
$768$	−2743.44	+	11809.5i	−0.128900	+	0.554869i
$769$			11814.2i			0.554004i	0.960869	+	0.277002i	$0.0893409\pi$
$769$			11814.2i			0.554004i	−0.960869	+	0.277002i	$0.910659\pi$
$770$	−712.551	+	2538.40i	−0.0333488	+	0.118802i
$771$	−12780.3	−	11950.5i	−0.596980	−	0.558219i
$772$	−7180.51	−	12437.0i	−0.334757	−	0.579816i
$773$	−6630.05	+	11483.6i	−0.308494	+	0.534328i	−0.978033	−	0.208449i	$-0.933158\pi$
$773$	−6630.05	+	11483.6i	−0.308494	+	0.534328i	0.669539	+	0.742777i	$0.266492\pi$
$774$	26072.6	−	53088.1i	1.21080	−	2.46539i
$775$	−3587.41	+	2071.19i	−0.166275	+	0.0959991i
$776$	64741.1			2.99493
$777$	−156.681	−	7228.04i	−0.00723412	−	0.333725i
$778$	30098.6			1.38700
$779$	5718.17	−	3301.39i	0.262997	−	0.151841i
$780$	1666.31	+	5477.01i	0.0764917	+	0.251421i
$781$	−305.587	+	529.292i	−0.0140010	+	0.0242504i
$782$	−48115.0	−	83337.6i	−2.20024	−	3.81093i
$783$	−22913.0	−	18710.6i	−1.04578	−	0.853973i
$784$	50751.0	−	27716.5i	2.31191	−	1.26260i
$785$			2959.20i			0.134546i
$786$	31006.4	+	7203.03i	1.40708	+	0.326875i
$787$	−28716.8	−	16579.6i	−1.30069	−	0.750954i	−0.320168	−	0.947361i	$-0.603739\pi$
$787$	−28716.8	−	16579.6i	−1.30069	−	0.750954i	−0.980522	+	0.196407i	$0.937073\pi$
$788$	12469.5	+	7199.25i	0.563714	+	0.325460i
$789$	−12535.9	−	2912.18i	−0.565638	−	0.131402i
$790$			34216.8i			1.54099i
$791$	−13550.7	+	13232.8i	−0.609112	+	0.594824i
$792$	606.321	+	9025.14i	0.0272029	+	0.404917i
$793$	−2599.30	−	4502.11i	−0.116398	−	0.201608i
$794$	35901.3	−	62182.8i	1.60464	−	2.77933i
$795$	1021.34	+	3357.06i	0.0455639	+	0.149764i
$796$	4733.15	−	2732.68i	0.210756	−	0.121680i
$797$	9453.43			0.420148			0.210074	−	0.977686i	$-0.432630\pi$
$797$	9453.43			0.420148			0.210074	+	0.977686i	$0.432630\pi$
$798$	−19200.4	+	11647.3i	−0.851739	+	0.516681i
$799$	54234.4			2.40134
$800$	−8494.37	+	4904.23i	−0.375402	+	0.216738i
$801$	5002.76	+	2456.96i	0.220679	+	0.108380i
$802$	−18698.7	+	32387.2i	−0.823286	+	1.42597i
$803$	−1843.14	−	3192.42i	−0.0810001	−	0.140296i
$804$	−56898.6	−	53204.4i	−2.49585	−	2.33380i
$805$	4263.25	+	16700.9i	0.186658	+	0.731218i
$806$		−	9733.11i		−	0.425353i
$807$	1369.02	−	5893.13i	0.0597172	−	0.257061i
$808$	−32780.6	−	18925.9i	−1.42725	−	0.824023i
$809$	13580.6	+	7840.76i	0.590196	+	0.340750i	0.765175	−	0.643823i	$-0.222653\pi$
$809$	13580.6	+	7840.76i	0.590196	+	0.340750i	−0.174979	+	0.984572i	$0.555986\pi$
$810$	15199.7	−	11742.1i	0.659339	−	0.509353i
$811$		−	34875.0i		−	1.51002i	−0.655713	−	0.755010i	$-0.727632\pi$
$811$		−	34875.0i		−	1.51002i	0.655713	−	0.755010i	$-0.272368\pi$
$812$	19092.1	+	74791.8i	0.825126	+	3.23236i
$813$	−21995.4	+	23522.7i	−0.948848	+	1.01473i
$814$	−1069.49	−	1852.41i	−0.0460510	−	0.0797627i
$815$	4275.92	−	7406.11i	0.183778	−	0.318313i
$816$	82225.5	−	25016.1i	3.52754	−	1.07321i
$817$	15943.5	−	9204.96i	0.682731	−	0.394175i
$818$	4496.49			0.192196
$819$	−1143.40	+	5455.78i	−0.0487833	+	0.232772i
$820$	14735.7			0.627552
$821$	27613.7	−	15942.8i	1.17384	−	0.677718i	0.219261	−	0.975666i	$-0.429636\pi$
$821$	27613.7	−	15942.8i	1.17384	−	0.677718i	0.954582	+	0.297948i	$0.0963022\pi$
$822$	−14167.6	+	4310.32i	−0.601160	+	0.182895i
$823$	1016.88	−	1761.29i	0.0430696	−	0.0745987i	−0.843687	−	0.536835i	$-0.819620\pi$
$823$	1016.88	−	1761.29i	0.0430696	−	0.0745987i	0.886757	+	0.462237i	$0.152953\pi$
$824$	35248.8	+	61052.7i	1.49023	+	2.58116i
$825$	479.392	−	512.679i	0.0202306	−	0.0216354i
$826$	−39793.1	+	38859.7i	−1.67625	+	1.63693i
$827$		−	7211.09i		−	0.303209i	−0.988441	−	0.151605i	$-0.951556\pi$
$827$		−	7211.09i		−	0.303209i	0.988441	−	0.151605i	$-0.0484441\pi$
$828$	55325.7	+	82509.2i	2.32210	+	3.46303i
$829$	−4723.78	−	2727.28i	−0.197906	−	0.114261i	0.397773	−	0.917484i	$-0.369783\pi$
$829$	−4723.78	−	2727.28i	−0.197906	−	0.114261i	−0.595678	+	0.803223i	$0.703117\pi$
$830$	−3276.88	−	1891.91i	−0.137039	−	0.0791193i
$831$	−4127.44	+	17767.1i	−0.172297	+	0.741678i
$832$		−	8011.49i		−	0.333832i
$833$	28736.0	+	17512.9i	1.19525	+	0.728434i
$834$	19281.4	+	18029.5i	0.800551	+	0.748573i
$835$	−2936.77	−	5086.63i	−0.121714	−	0.210815i
$836$	−2364.91	+	4096.15i	−0.0978376	+	0.169460i
$837$	−21736.3	+	8241.73i	−0.897632	+	0.340354i
$838$	74908.6	−	43248.5i	3.08792	−	1.78281i
$839$	−16033.1			−0.659744			−0.329872	−	0.944026i	$-0.607006\pi$
$839$	−16033.1			−0.659744			−0.329872	+	0.944026i	$0.607006\pi$
$840$	−29827.4	+	646.564i	−1.22517	+	0.0265578i
$841$	−20070.1			−0.822917
$842$	−415.685	+	239.996i	−0.0170136	+	0.00982281i
$843$	2857.40	+	9392.00i	0.116743	+	0.383722i
$844$	−26533.3	+	45957.0i	−1.08213	+	1.87430i
$845$	−5181.83	−	8975.19i	−0.210959	−	0.365392i
$846$	−78470.4	+	5271.75i	−3.18897	+	0.214239i
$847$	6515.98	−	23212.6i	0.264335	−	0.941669i
$848$		−	22769.9i		−	0.922076i
$849$	26626.4	+	6185.53i	1.07635	+	0.250043i
$850$	−11193.1	−	6462.33i	−0.451670	−	0.260772i
$851$	−12110.3	−	6991.89i	−0.487822	−	0.281644i
$852$	−11316.6	−	2628.94i	−0.455049	−	0.105711i
$853$			3439.64i			0.138067i	0.997614	+	0.0690334i	$0.0219915\pi$
$853$			3439.64i			0.138067i	−0.997614	+	0.0690334i	$0.978008\pi$
$854$	44096.9	−	11256.6i	1.76694	−	0.451046i
$855$	5965.08	−	400.742i	0.238598	−	0.0160294i
$856$	11168.8	+	19344.9i	0.445959	+	0.772424i
$857$	1123.79	−	1946.45i	0.0447932	−	0.0775841i	−0.842760	−	0.538290i	$-0.819070\pi$
$857$	1123.79	−	1946.45i	0.0447932	−	0.0775841i	0.887553	+	0.460706i	$0.152404\pi$
$858$	480.025	+	1577.80i	0.0191000	+	0.0627799i
$859$	−7923.41	+	4574.58i	−0.314718	+	0.181703i	−0.649036	−	0.760758i	$-0.724828\pi$
$859$	−7923.41	+	4574.58i	−0.314718	+	0.181703i	0.334318	+	0.942461i	$0.391494\pi$
$860$	41086.2			1.62910
$861$	12578.4	+	6903.08i	0.497875	+	0.273236i
$862$	56381.8			2.22781
$863$	−38668.7	+	22325.4i	−1.52526	+	0.880608i	−0.525707	+	0.850666i	$0.676199\pi$
$863$	−38668.7	+	22325.4i	−1.52526	+	0.880608i	−0.999552	+	0.0299427i	$0.990468\pi$
$864$	−51468.0	+	19515.0i	−2.02659	+	0.768420i
$865$	243.555	−	421.849i	0.00957354	−	0.0165819i
$866$	−18128.2	−	31398.9i	−0.711340	−	1.23208i
$867$	17886.6	+	16725.3i	0.700646	+	0.655155i
$868$	58401.2	+	16393.7i	2.28372	+	0.641060i
$869$			7017.09i			0.273922i
$870$	6531.98	−	28117.8i	0.254546	−	1.09573i
$871$	−7321.87	−	4227.28i	−0.284836	−	0.164450i
$872$	−14492.0	−	8366.98i	−0.562801	−	0.324933i
$873$	−15700.8	−	23415.2i	−0.608697	−	0.907772i
$874$			43436.4i			1.68108i
$875$	1617.43	+	1656.29i	0.0624906	+	0.0639916i
$876$	47860.2	−	51183.4i	1.84594	−	1.97412i
$877$	13965.8	+	24189.4i	0.537732	+	0.931379i	0.999026	+	0.0441316i	$0.0140521\pi$
$877$	13965.8	+	24189.4i	0.537732	+	0.931379i	−0.461294	+	0.887247i	$0.652615\pi$
$878$	2391.09	−	4141.49i	0.0919082	−	0.159190i
$879$	−5453.59	+	1659.19i	−0.209266	+	0.0636666i
$880$	−3944.40	+	2277.30i	−0.151098	+	0.0872362i
$881$	45748.3			1.74949			0.874744	−	0.484586i	$-0.161030\pi$
$881$	45748.3			1.74949			0.874744	+	0.484586i	$0.161030\pi$
$882$	−43279.7	−	22545.7i	−1.65227	−	0.860720i
$883$	−46042.8			−1.75477			−0.877387	−	0.479784i	$-0.840715\pi$
$883$	−46042.8			−1.75477			−0.877387	+	0.479784i	$0.840715\pi$
$884$	18722.4	−	10809.4i	0.712333	−	0.411266i
$885$	14166.1	−	4309.85i	0.538065	−	0.163699i
$886$	7641.36	−	13235.2i	0.289748	−	0.501858i
$887$	11333.5	+	19630.2i	0.429021	+	0.743086i	0.996786	−	0.0801046i	$-0.0255254\pi$
$887$	11333.5	+	19630.2i	0.429021	+	0.743086i	−0.567766	+	0.823190i	$0.692192\pi$
$888$	16531.5	−	17679.4i	0.624730	−	0.668109i
$889$	981.210	+	1004.78i	0.0370177	+	0.0379068i
$890$			5438.75i			0.204840i
$891$	3117.12	−	2408.04i	0.117203	−	0.0905415i
$892$	−78580.0	−	45368.2i	−2.94961	−	1.70296i
$893$	−21200.6	−	12240.2i	−0.794460	−	0.458682i
$894$	−12689.1	+	54621.8i	−0.474705	+	2.04343i
$895$		−	2394.03i		−	0.0894120i
$896$	11559.8	+	3244.95i	0.431012	+	0.120989i
$897$	7875.29	+	7363.96i	0.293142	+	0.274109i
$898$	−29040.0	−	50298.8i	−1.07915	−	1.86915i
$899$	−17468.7	+	30256.7i	−0.648068	+	1.12249i
$900$	11976.2	+	5881.73i	0.443562	+	0.217842i
$901$	11475.6	−	6625.47i	0.424317	−	0.244979i
$902$	4245.00			0.156700
$903$	35071.2	+	19247.3i	1.29247	+	0.709312i
$904$	−63409.5			−2.33293
$905$	4612.24	−	2662.88i	0.169410	−	0.0978089i
$906$	11391.0	+	37441.1i	0.417704	+	1.37295i
$907$	25268.1	−	43765.6i	0.925042	−	1.60222i	0.133549	−	0.991042i	$-0.457363\pi$
$907$	25268.1	−	43765.6i	0.925042	−	1.60222i	0.791493	−	0.611178i	$-0.209304\pi$
$908$	−25090.2	−	43457.5i	−0.917012	−	1.58831i
$909$	1104.85	+	16445.8i	0.0403141	+	0.600080i
$910$	−5270.49	+	1345.40i	−0.191995	+	0.0490105i
$911$		−	31066.4i		−	1.12983i	−0.825149	−	0.564915i	$-0.808909\pi$
$911$		−	31066.4i		−	1.12983i	0.825149	−	0.564915i	$-0.191091\pi$
$912$	−37788.5	−	8778.56i	−1.37204	−	0.318736i
$913$	−672.013	−	387.987i	−0.0243597	−	0.0140641i
$914$	−8283.22	−	4782.32i	−0.299764	−	0.173069i
$915$	−11801.7	−	2741.63i	−0.426396	−	0.0990551i
$916$		−	42882.2i		−	1.54680i
$917$	−5819.08	+	20729.9i	−0.209556	+	0.746524i
$918$	−56179.7	−	45876.0i	−2.01983	−	1.64938i
$919$	3177.67	+	5503.89i	0.114061	+	0.197559i	0.917404	−	0.397958i	$-0.130281\pi$
$919$	3177.67	+	5503.89i	0.114061	+	0.197559i	−0.803343	+	0.595516i	$0.796948\pi$
$920$	−28852.9	+	49974.7i	−1.03397	+	1.79089i
$921$	1132.84	+	3723.55i	0.0405303	+	0.133219i
$922$	23946.9	−	13825.7i	0.855366	−	0.493846i
$923$	−1260.94			−0.0449667
$924$	−10275.7	+	222.745i	−0.365851	+	0.00793050i
$925$	−1878.16			−0.0667607
$926$	−51228.9	+	29577.0i	−1.81802	+	1.04963i
$927$	13532.8	−	27554.9i	0.479477	−	0.976292i
$928$	−41362.9	+	71642.7i	−1.46315	+	2.53425i
$929$	−1646.90	−	2852.51i	−0.0581625	−	0.100740i	0.835478	−	0.549524i	$-0.185191\pi$
$929$	−1646.90	−	2852.51i	−0.0581625	−	0.100740i	−0.893641	+	0.448783i	$0.851857\pi$
$930$	−16569.0	−	15493.3i	−0.584215	−	0.546284i
$931$	−7280.63	−	13331.4i	−0.256297	−	0.469300i
$932$			940.058i			0.0330393i
$933$	−5324.07	+	22918.2i	−0.186819	+	0.804187i
$934$	42063.0	+	24285.1i	1.47360	+	0.850784i
$935$	−2295.45	−	1325.28i	−0.0802879	−	0.0463542i
$936$	−15500.1	+	10393.4i	−0.541277	+	0.362948i
$937$			28497.7i			0.993576i	0.867872	+	0.496788i	$0.165487\pi$
$937$			28497.7i			0.993576i	−0.867872	+	0.496788i	$0.834513\pi$
$938$	52954.0	−	51711.9i	1.84330	−	1.80006i
$939$	−36043.8	+	38546.5i	−1.25266	+	1.33963i
$940$	−27317.0	−	47314.4i	−0.947852	−	1.64173i
$941$	−11984.2	+	20757.3i	−0.415170	+	0.719096i	−0.995446	−	0.0953240i	$-0.969611\pi$
$941$	−11984.2	+	20757.3i	−0.415170	+	0.719096i	0.580276	+	0.814420i	$0.302945\pi$
$942$	−15503.3	+	4716.70i	−0.536228	+	0.163140i
$943$	24034.1	−	13876.1i	0.829966	−	0.479181i
$944$	−96084.0			−3.31278
$945$	7467.50	+	10631.0i	0.257056	+	0.365954i
$946$	11836.0			0.406787
$947$	−33526.8	+	19356.7i	−1.15045	+	0.664212i	−0.948997	−	0.315287i	$-0.897899\pi$
$947$	−33526.8	+	19356.7i	−1.15045	+	0.664212i	−0.201452	+	0.979498i	$0.564566\pi$
$948$	−127615.	+	38825.2i	−4.37208	+	1.33015i
$949$	3802.67	−	6586.41i	0.130074	−	0.225294i
$950$	2916.98	+	5052.35i	0.0996202	+	0.172547i
$951$	1085.95	−	1161.35i	0.0370287	−	0.0395998i
$952$	27865.9	+	109163.i	0.948677	+	3.71636i
$953$			15739.7i			0.535005i	0.963557	+	0.267502i	$0.0861983\pi$
$953$			15739.7i			0.535005i	−0.963557	+	0.267502i	$0.913802\pi$
$954$	−15959.8	+	10701.7i	−0.541634	+	0.363187i
$955$	15833.4	+	9141.43i	0.536500	+	0.309749i
$956$	−101034.	−	58331.8i	−3.41806	−	1.97342i
$957$	1339.56	−	5766.32i	0.0452475	−	0.194774i
$958$		−	52722.9i		−	1.77808i
$959$	−2477.51	−	9705.44i	−0.0834233	−	0.326804i
$960$	−13638.3	−	12752.8i	−0.458513	−	0.428743i
$961$	−1168.05	−	2023.13i	−0.0392083	−	0.0679108i
$962$	2206.51	−	3821.78i	0.0739508	−	0.128087i
$963$	4287.94	−	8730.94i	0.143486	−	0.292161i
$964$	2191.91	−	1265.50i	0.0732330	−	0.0422811i
$965$	−3632.62			−0.121180
$966$	−80701.5	+	48955.1i	−2.68792	+	1.63054i
$967$	−48618.0			−1.61681			−0.808403	−	0.588630i	$-0.799668\pi$
$967$	−48618.0			−1.61681			−0.808403	+	0.588630i	$0.799668\pi$
$968$	69902.8	−	40358.4i	2.32103	−	1.34005i
$969$	−6571.26	−	21599.1i	−0.217853	−	0.716062i
$970$	13755.1	−	23824.6i	0.455310	−	0.788619i
$971$	26214.6	+	45405.0i	0.866392	+	1.50063i	0.865658	+	0.500635i	$0.166900\pi$
$971$	26214.6	+	45405.0i	0.866392	+	1.50063i	0.000733428		1.00000i	$0.499767\pi$
$972$	61040.2	+	43365.3i	2.01427	+	1.43101i
$973$	−12774.5	+	12474.9i	−0.420897	+	0.411025i
$974$		−	89658.5i		−	2.94953i
$975$	1410.55	+	327.681i	0.0463320	+	0.0107633i
$976$	68087.5	+	39310.4i	2.23302	+	1.28924i
$977$	−22175.5	−	12803.0i	−0.726159	−	0.419248i	0.0908563	−	0.995864i	$-0.471040\pi$
$977$	−22175.5	−	12803.0i	−0.726159	−	0.419248i	−0.817015	+	0.576616i	$0.804373\pi$
$978$	45616.3	+	10597.0i	1.49146	+	0.346478i
$979$			1115.36i			0.0364118i
$980$	804.491	−	33890.4i	0.0262230	−	1.10468i
$981$	488.445	+	7270.55i	0.0158969	+	0.236627i
$982$	18328.4	+	31745.6i	0.595602	+	1.03161i
$983$	19400.9	−	33603.4i	0.629496	−	1.09032i	−0.358158	−	0.933661i	$-0.616595\pi$
$983$	19400.9	−	33603.4i	0.629496	−	1.09032i	0.987653	−	0.156657i	$-0.0500717\pi$
$984$	13981.5	+	45956.1i	0.452963	+	1.48885i
$985$	3154.16	−	1821.05i	0.102030	−	0.0589072i
$986$	−109008.			−3.52082
$987$	−1152.87	−	53184.5i	−0.0371797	−	1.71518i
$988$	−9758.32			−0.314224
$989$	67012.2	−	38689.5i	2.15456	−	1.24394i
$990$	3450.05	+	1694.39i	0.110757	+	0.0543951i
$991$	−12684.3	+	21969.9i	−0.406590	+	0.704234i	−0.994505	−	0.104688i	$-0.966616\pi$
$991$	−12684.3	+	21969.9i	−0.406590	+	0.704234i	0.587915	+	0.808923i	$0.299949\pi$
$992$	32504.3	+	56299.1i	1.04033	+	1.80191i
$993$	−19756.5	−	18473.8i	−0.631374	−	0.590380i
$994$	2983.39	−	10628.1i	0.0951986	−	0.339136i
$995$		−	1382.47i		−	0.0440474i
$996$	3337.83	−	14368.1i	0.106188	−	0.457100i
$997$	4197.90	+	2423.66i	0.133349	+	0.0769889i	0.565190	−	0.824961i	$-0.308803\pi$
$997$	4197.90	+	2423.66i	0.133349	+	0.0769889i	−0.431842	+	0.901949i	$0.642136\pi$
$998$	59736.5	+	34488.9i	1.89472	+	1.09391i
$999$	−10403.4	−	1691.47i	−0.329477	−	0.0535693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.s.a.101.2	yes	32
3.2	odd	2		105.4.s.b.101.15	yes	32
7.5	odd	6		105.4.s.b.26.15	yes	32
21.5	even	6	inner	105.4.s.a.26.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.s.a.26.2	✓	32	21.5	even	6	inner
105.4.s.a.101.2	yes	32	1.1	even	1	trivial
105.4.s.b.26.15	yes	32	7.5	odd	6
105.4.s.b.101.15	yes	32	3.2	odd	2

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.56345 + 2.63471i) q^{2} +(-4.97118 + 1.51242i) q^{3} +(9.88336 - 17.1185i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(18.7009 - 19.9994i) q^{6} +(12.9395 + 13.2503i) q^{7} +62.0037i q^{8} +(22.4252 - 15.0370i) q^{9} +O(q^{10})\)	\(q+(-4.56345 + 2.63471i) q^{2} +(-4.97118 + 1.51242i) q^{3} +(9.88336 - 17.1185i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(18.7009 - 19.9994i) q^{6} +(12.9395 + 13.2503i) q^{7} +62.0037i q^{8} +(22.4252 - 15.0370i) q^{9} +(22.8172 + 13.1735i) q^{10} +(4.67930 + 2.70159i) q^{11} +(-23.2416 + 100.047i) q^{12} +11.1476i q^{13} +(-93.9592 - 26.3752i) q^{14} +(18.9769 + 17.7448i) q^{15} +(-84.2948 - 146.003i) q^{16} +(49.0554 - 84.9664i) q^{17} +(-62.7181 + 127.704i) q^{18} +(-38.3523 + 22.1427i) q^{19} -98.8336 q^{20} +(-84.3644 - 46.2996i) q^{21} -28.4716 q^{22} +(-161.199 + 93.0682i) q^{23} +(-93.7755 - 308.232i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-29.3705 - 50.8713i) q^{26} +(-88.7374 + 108.668i) q^{27} +(354.710 - 90.5469i) q^{28} +210.853i q^{29} +(-133.352 - 30.9788i) q^{30} +(143.496 + 82.8476i) q^{31} +(339.775 + 196.169i) q^{32} +(-27.3476 - 6.35305i) q^{33} +516.986i q^{34} +(25.0267 - 89.1553i) q^{35} +(-35.7741 - 532.501i) q^{36} +(37.5633 + 65.0615i) q^{37} +(116.679 - 202.094i) q^{38} +(-16.8598 - 55.4165i) q^{39} +(268.484 - 155.009i) q^{40} -149.096 q^{41} +(506.978 - 10.9897i) q^{42} -415.711 q^{43} +(92.4944 - 53.4017i) q^{44} +(-121.175 - 59.5115i) q^{45} +(490.415 - 849.424i) q^{46} +(276.394 + 478.728i) q^{47} +(639.861 + 598.317i) q^{48} +(-8.13985 + 342.903i) q^{49} -131.735i q^{50} +(-115.358 + 496.575i) q^{51} +(190.829 + 110.175i) q^{52} +(116.966 + 67.5305i) q^{53} +(118.641 - 729.696i) q^{54} -27.0159i q^{55} +(-821.567 + 802.296i) q^{56} +(157.167 - 168.080i) q^{57} +(-555.537 - 962.218i) q^{58} +(284.964 - 493.573i) q^{59} +(491.319 - 149.478i) q^{60} +(-403.866 + 233.172i) q^{61} -873.116 q^{62} +(489.414 + 102.569i) q^{63} -718.677 q^{64} +(48.2703 - 27.8689i) q^{65} +(141.538 - 43.0610i) q^{66} +(-379.212 + 656.814i) q^{67} +(-969.664 - 1679.51i) q^{68} +(660.590 - 706.458i) q^{69} +(120.690 + 472.793i) q^{70} +113.113i q^{71} +(932.349 + 1390.45i) q^{72} +(-590.839 - 341.121i) q^{73} +(-342.836 - 197.936i) q^{74} +(29.3949 - 126.534i) q^{75} +875.377i q^{76} +(24.7508 + 96.9592i) q^{77} +(222.945 + 208.470i) q^{78} +(649.347 + 1124.70i) q^{79} +(-421.474 + 730.014i) q^{80} +(276.778 - 674.414i) q^{81} +(680.391 - 392.824i) q^{82} -143.614 q^{83} +(-1626.38 + 986.595i) q^{84} -490.554 q^{85} +(1897.07 - 1095.28i) q^{86} +(-318.898 - 1048.19i) q^{87} +(-167.509 + 290.134i) q^{88} +(103.214 + 178.771i) q^{89} +(709.771 - 47.6834i) q^{90} +(-147.708 + 144.244i) q^{91} +3679.31i q^{92} +(-838.645 - 194.824i) q^{93} +(-2522.61 - 1456.43i) q^{94} +(191.761 + 110.714i) q^{95} +(-1985.77 - 461.310i) q^{96} -1044.15i q^{97} +(-866.304 - 1586.27i) q^{98} +(145.558 - 9.77878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9}+O(q^{10}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9} + 36 q^{11} + 246 q^{12} + 18 q^{14} + 20 q^{15} - 376 q^{16} - 72 q^{17} - 442 q^{18} - 198 q^{19} - 640 q^{20} - 218 q^{21} + 204 q^{22} + 72 q^{23} - 50 q^{24} - 400 q^{25} - 312 q^{26} + 508 q^{27} + 350 q^{28} + 40 q^{30} + 510 q^{31} + 810 q^{32} + 290 q^{33} - 70 q^{35} - 612 q^{36} - 658 q^{37} - 192 q^{38} - 648 q^{39} - 1404 q^{41} + 1892 q^{42} + 332 q^{43} + 2034 q^{44} - 490 q^{45} - 468 q^{46} + 408 q^{47} + 2810 q^{48} + 980 q^{49} - 888 q^{51} + 3378 q^{52} + 1152 q^{53} + 2714 q^{54} - 3354 q^{56} - 816 q^{57} - 1080 q^{58} - 48 q^{59} - 420 q^{60} - 1662 q^{61} - 2076 q^{62} + 874 q^{63} - 1952 q^{64} + 870 q^{65} - 1892 q^{66} - 1298 q^{67} + 1182 q^{68} + 2450 q^{69} - 450 q^{70} - 2708 q^{72} + 378 q^{73} + 2898 q^{74} - 50 q^{75} - 3528 q^{77} - 1896 q^{78} - 326 q^{79} - 1880 q^{80} - 3308 q^{81} - 2916 q^{82} - 1536 q^{83} + 1380 q^{84} + 720 q^{85} + 5202 q^{86} - 1090 q^{87} + 1668 q^{88} - 1590 q^{89} + 910 q^{90} + 2082 q^{91} - 4950 q^{93} - 1152 q^{94} + 990 q^{95} + 7416 q^{96} - 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9 + 36 * q^11 + 246 * q^12 + 18 * q^14 + 20 * q^15 - 376 * q^16 - 72 * q^17 - 442 * q^18 - 198 * q^19 - 640 * q^20 - 218 * q^21 + 204 * q^22 + 72 * q^23 - 50 * q^24 - 400 * q^25 - 312 * q^26 + 508 * q^27 + 350 * q^28 + 40 * q^30 + 510 * q^31 + 810 * q^32 + 290 * q^33 - 70 * q^35 - 612 * q^36 - 658 * q^37 - 192 * q^38 - 648 * q^39 - 1404 * q^41 + 1892 * q^42 + 332 * q^43 + 2034 * q^44 - 490 * q^45 - 468 * q^46 + 408 * q^47 + 2810 * q^48 + 980 * q^49 - 888 * q^51 + 3378 * q^52 + 1152 * q^53 + 2714 * q^54 - 3354 * q^56 - 816 * q^57 - 1080 * q^58 - 48 * q^59 - 420 * q^60 - 1662 * q^61 - 2076 * q^62 + 874 * q^63 - 1952 * q^64 + 870 * q^65 - 1892 * q^66 - 1298 * q^67 + 1182 * q^68 + 2450 * q^69 - 450 * q^70 - 2708 * q^72 + 378 * q^73 + 2898 * q^74 - 50 * q^75 - 3528 * q^77 - 1896 * q^78 - 326 * q^79 - 1880 * q^80 - 3308 * q^81 - 2916 * q^82 - 1536 * q^83 + 1380 * q^84 + 720 * q^85 + 5202 * q^86 - 1090 * q^87 + 1668 * q^88 - 1590 * q^89 + 910 * q^90 + 2082 * q^91 - 4950 * q^93 - 1152 * q^94 + 990 * q^95 + 7416 * q^96 - 7830 * q^98 + 3128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more