LMFDB - Embedded newform 35.4.f.b.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,4,Mod(13,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("35.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	35.f (of order $4$, 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:	$2.06506685020$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10654x^{12} + 22102125x^{8} + 5700572500x^{4} + 44626562500 $ x^16 + 10654x^12 + 22102125x^8 + 5700572500*x^4 + 44626562500
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.5
Root			$-6.68128 - 6.68128i$ of defining polynomial
Character	$\chi$	$=$	35.13
Dual form			35.4.f.b.27.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31781 - 1.31781i) q^{2} +(-6.68128 + 6.68128i) q^{3} +4.52674i q^{4} +(11.1616 + 0.646864i) q^{5} +17.6093i q^{6} +(-17.1776 + 6.92319i) q^{7} +(16.5079 + 16.5079i) q^{8} -62.2789i q^{9} +O(q^{10})$	\(q+(1.31781 - 1.31781i) q^{2} +(-6.68128 + 6.68128i) q^{3} +4.52674i q^{4} +(11.1616 + 0.646864i) q^{5} +17.6093i q^{6} +(-17.1776 + 6.92319i) q^{7} +(16.5079 + 16.5079i) q^{8} -62.2789i q^{9} +(15.5614 - 13.8565i) q^{10} +24.9919 q^{11} +(-30.2444 - 30.2444i) q^{12} +(8.80162 - 8.80162i) q^{13} +(-13.5134 + 31.7603i) q^{14} +(-78.8957 + 70.2519i) q^{15} +7.29465 q^{16} +(7.24755 + 7.24755i) q^{17} +(-82.0719 - 82.0719i) q^{18} +85.0979 q^{19} +(-2.92819 + 50.5258i) q^{20} +(68.5125 - 161.024i) q^{21} +(32.9346 - 32.9346i) q^{22} +(18.9131 + 18.9131i) q^{23} -220.588 q^{24} +(124.163 + 14.4401i) q^{25} -23.1978i q^{26} +(235.708 + 235.708i) q^{27} +(-31.3395 - 77.7585i) q^{28} -162.511i q^{29} +(-11.3909 + 196.549i) q^{30} +26.6139i q^{31} +(-122.450 + 122.450i) q^{32} +(-166.978 + 166.978i) q^{33} +19.1018 q^{34} +(-196.208 + 66.1624i) q^{35} +281.921 q^{36} +(-54.1514 + 54.1514i) q^{37} +(112.143 - 112.143i) q^{38} +117.612i q^{39} +(173.576 + 194.933i) q^{40} +137.076i q^{41} +(-121.913 - 302.486i) q^{42} +(-221.858 - 221.858i) q^{43} +113.132i q^{44} +(40.2860 - 695.133i) q^{45} +49.8478 q^{46} +(-229.976 - 229.976i) q^{47} +(-48.7375 + 48.7375i) q^{48} +(247.139 - 237.847i) q^{49} +(182.653 - 144.594i) q^{50} -96.8457 q^{51} +(39.8427 + 39.8427i) q^{52} +(154.172 + 154.172i) q^{53} +621.238 q^{54} +(278.950 + 16.1664i) q^{55} +(-397.853 - 169.278i) q^{56} +(-568.563 + 568.563i) q^{57} +(-214.160 - 214.160i) q^{58} -685.748 q^{59} +(-318.012 - 357.141i) q^{60} -23.6916i q^{61} +(35.0721 + 35.0721i) q^{62} +(431.169 + 1069.80i) q^{63} +381.090i q^{64} +(103.934 - 92.5469i) q^{65} +440.091i q^{66} +(602.716 - 602.716i) q^{67} +(-32.8078 + 32.8078i) q^{68} -252.727 q^{69} +(-171.376 + 345.755i) q^{70} +265.331 q^{71} +(1028.09 - 1028.09i) q^{72} +(609.073 - 609.073i) q^{73} +142.723i q^{74} +(-926.047 + 733.090i) q^{75} +385.216i q^{76} +(-429.300 + 173.024i) q^{77} +(154.991 + 154.991i) q^{78} +145.122i q^{79} +(81.4200 + 4.71865i) q^{80} -1468.13 q^{81} +(180.641 + 180.641i) q^{82} +(454.928 - 454.928i) q^{83} +(728.914 + 310.138i) q^{84} +(76.2061 + 85.5825i) q^{85} -584.735 q^{86} +(1085.78 + 1085.78i) q^{87} +(412.563 + 412.563i) q^{88} -209.235 q^{89} +(-862.965 - 969.144i) q^{90} +(-90.2554 + 212.126i) q^{91} +(-85.6148 + 85.6148i) q^{92} +(-177.815 - 177.815i) q^{93} -606.130 q^{94} +(949.830 + 55.0468i) q^{95} -1636.25i q^{96} +(-1012.24 - 1012.24i) q^{97} +(12.2446 - 639.121i) q^{98} -1556.47i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 32 q^{7} + 176 q^{8}+O(q^{10}) $ 16 * q + 4 * q^2 + 32 * q^7 + 176 * q^8	$ 16 q + 4 q^{2} + 32 q^{7} + 176 q^{8} - 152 q^{11} - 480 q^{15} - 504 q^{16} + 288 q^{18} + 328 q^{21} + 348 q^{22} - 72 q^{23} - 160 q^{25} - 528 q^{28} + 1780 q^{30} + 432 q^{32} + 160 q^{35} + 344 q^{36} - 256 q^{37} - 1300 q^{42} - 312 q^{43} - 1856 q^{46} - 20 q^{50} + 696 q^{51} + 1768 q^{53} + 1304 q^{56} - 3920 q^{57} - 4764 q^{58} - 2000 q^{60} + 2544 q^{63} - 1000 q^{65} + 4504 q^{67} - 180 q^{70} + 6368 q^{71} + 7848 q^{72} - 3016 q^{77} + 5340 q^{78} - 3088 q^{81} - 2280 q^{85} - 9336 q^{86} - 2048 q^{88} + 1608 q^{91} - 6328 q^{92} - 3960 q^{93} + 1240 q^{95} + 3308 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 + 32 * q^7 + 176 * q^8 - 152 * q^11 - 480 * q^15 - 504 * q^16 + 288 * q^18 + 328 * q^21 + 348 * q^22 - 72 * q^23 - 160 * q^25 - 528 * q^28 + 1780 * q^30 + 432 * q^32 + 160 * q^35 + 344 * q^36 - 256 * q^37 - 1300 * q^42 - 312 * q^43 - 1856 * q^46 - 20 * q^50 + 696 * q^51 + 1768 * q^53 + 1304 * q^56 - 3920 * q^57 - 4764 * q^58 - 2000 * q^60 + 2544 * q^63 - 1000 * q^65 + 4504 * q^67 - 180 * q^70 + 6368 * q^71 + 7848 * q^72 - 3016 * q^77 + 5340 * q^78 - 3088 * q^81 - 2280 * q^85 - 9336 * q^86 - 2048 * q^88 + 1608 * q^91 - 6328 * q^92 - 3960 * q^93 + 1240 * q^95 + 3308 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	1.31781	−	1.31781i	0.465917	−	0.465917i	−0.434672	−	0.900589i	$-0.643136\pi$
$2$	1.31781	−	1.31781i	0.465917	−	0.465917i	0.900589	+	0.434672i	$0.143136\pi$
$3$	−6.68128	+	6.68128i	−1.28581	+	1.28581i	−0.348506	+	0.937307i	$0.613311\pi$
$3$	−6.68128	+	6.68128i	−1.28581	+	1.28581i	−0.937307	+	0.348506i	$0.886689\pi$
$4$			4.52674i			0.565843i
$5$	11.1616	+	0.646864i	0.998325	+	0.0578573i
$5$	11.1616	+	0.646864i	0.998325	+	0.0578573i
$6$			17.6093i			1.19816i
$7$	−17.1776	+	6.92319i	−0.927502	+	0.373817i
$7$	−17.1776	+	6.92319i	−0.927502	+	0.373817i
$8$	16.5079	+	16.5079i	0.729553	+	0.729553i
$9$		−	62.2789i		−	2.30663i
$10$	15.5614	−	13.8565i	0.492093	−	0.438180i
$11$	24.9919			0.685031			0.342515	−	0.939512i	$-0.388721\pi$
$11$	24.9919			0.685031			0.342515	+	0.939512i	$0.388721\pi$
$12$	−30.2444	−	30.2444i	−0.727568	−	0.727568i
$13$	8.80162	−	8.80162i	0.187779	−	0.187779i	−0.606956	−	0.794735i	$-0.707610\pi$
$13$	8.80162	−	8.80162i	0.187779	−	0.187779i	0.794735	+	0.606956i	$0.207610\pi$
$14$	−13.5134	+	31.7603i	−0.257971	+	0.606307i
$15$	−78.8957	+	70.2519i	−1.35805	+	1.20926i
$16$	7.29465			0.113979
$17$	7.24755	+	7.24755i	0.103399	+	0.103399i	0.756914	−	0.653515i	$-0.226706\pi$
$17$	7.24755	+	7.24755i	0.103399	+	0.103399i	−0.653515	+	0.756914i	$0.726706\pi$
$18$	−82.0719	−	82.0719i	−1.07470	−	1.07470i
$19$	85.0979			1.02752			0.513758	−	0.857935i	$-0.328253\pi$
$19$	85.0979			1.02752			0.513758	+	0.857935i	$0.328253\pi$
$20$	−2.92819	+	50.5258i	−0.0327382	+	0.564895i
$21$	68.5125	−	161.024i	0.711936	−	1.67325i
$22$	32.9346	−	32.9346i	0.319167	−	0.319167i
$23$	18.9131	+	18.9131i	0.171463	+	0.171463i	0.787622	−	0.616159i	$-0.211312\pi$
$23$	18.9131	+	18.9131i	0.171463	+	0.171463i	−0.616159	+	0.787622i	$0.711312\pi$
$24$	−220.588			−1.87614
$25$	124.163	+	14.4401i	0.993305	+	0.115521i
$26$		−	23.1978i		−	0.174979i
$27$	235.708	+	235.708i	1.68008	+	1.68008i
$28$	−31.3395	−	77.7585i	−0.211522	−	0.524821i
$29$		−	162.511i		−	1.04061i	−0.853981	−	0.520304i	$-0.825819\pi$
$29$		−	162.511i		−	1.04061i	0.853981	−	0.520304i	$-0.174181\pi$
$30$	−11.3909	+	196.549i	−0.0693225	+	1.19616i
$31$			26.6139i			0.154194i	0.997024	+	0.0770968i	$0.0245651\pi$
$31$			26.6139i			0.154194i	−0.997024	+	0.0770968i	$0.975435\pi$
$32$	−122.450	+	122.450i	−0.676448	+	0.676448i
$33$	−166.978	+	166.978i	−0.880821	+	0.880821i
$34$	19.1018			0.0963510
$35$	−196.208	+	66.1624i	−0.947577	+	0.319528i
$36$	281.921			1.30519
$37$	−54.1514	+	54.1514i	−0.240607	+	0.240607i	−0.817101	−	0.576494i	$-0.804420\pi$
$37$	−54.1514	+	54.1514i	−0.240607	+	0.240607i	0.576494	+	0.817101i	$0.304420\pi$
$38$	112.143	−	112.143i	0.478737	−	0.478737i
$39$			117.612i			0.482898i
$40$	173.576	+	194.933i	0.686121	+	0.770541i
$41$			137.076i			0.522139i	0.965320	+	0.261069i	$0.0840752\pi$
$41$			137.076i			0.522139i	−0.965320	+	0.261069i	$0.915925\pi$
$42$	−121.913	−	302.486i	−0.447894	−	1.11130i
$43$	−221.858	−	221.858i	−0.786815	−	0.786815i	0.194155	−	0.980971i	$-0.437803\pi$
$43$	−221.858	−	221.858i	−0.786815	−	0.786815i	−0.980971	+	0.194155i	$0.937803\pi$
$44$			113.132i			0.387620i
$45$	40.2860	−	695.133i	0.133455	−	2.30276i
$46$	49.8478			0.159775
$47$	−229.976	−	229.976i	−0.713732	−	0.713732i	0.253582	−	0.967314i	$-0.418391\pi$
$47$	−229.976	−	229.976i	−0.713732	−	0.713732i	−0.967314	+	0.253582i	$0.918391\pi$
$48$	−48.7375	+	48.7375i	−0.146555	+	0.146555i
$49$	247.139	−	237.847i	0.720522	−	0.693432i
$50$	182.653	−	144.594i	0.516621	−	0.408974i
$51$	−96.8457			−0.265904
$52$	39.8427	+	39.8427i	0.106254	+	0.106254i
$53$	154.172	+	154.172i	0.399569	+	0.399569i	0.878081	−	0.478512i	$-0.158824\pi$
$53$	154.172	+	154.172i	0.399569	+	0.399569i	−0.478512	+	0.878081i	$0.658824\pi$
$54$	621.238			1.56555
$55$	278.950	+	16.1664i	0.683883	+	0.0396340i
$56$	−397.853	−	169.278i	−0.949381	−	0.403943i
$57$	−568.563	+	568.563i	−1.32119	+	1.32119i
$58$	−214.160	−	214.160i	−0.484837	−	0.484837i
$59$	−685.748			−1.51317			−0.756583	−	0.653898i	$-0.773133\pi$
$59$	−685.748			−1.51317			−0.756583	+	0.653898i	$0.773133\pi$
$60$	−318.012	−	357.141i	−0.684254	−	0.768444i
$61$		−	23.6916i		−	0.0497278i	−0.999691	−	0.0248639i	$-0.992085\pi$
$61$		−	23.6916i		−	0.0497278i	0.999691	−	0.0248639i	$-0.00791524\pi$
$62$	35.0721	+	35.0721i	0.0718414	+	0.0718414i
$63$	431.169	+	1069.80i	0.862256	+	2.13940i
$64$			381.090i			0.744316i
$65$	103.934	−	92.5469i	0.198329	−	0.176600i
$66$			440.091i			0.820779i
$67$	602.716	−	602.716i	1.09901	−	1.09901i	0.104480	−	0.994527i	$-0.466682\pi$
$67$	602.716	−	602.716i	1.09901	−	1.09901i	0.994527	−	0.104480i	$-0.0333179\pi$
$68$	−32.8078	+	32.8078i	−0.0585078	+	0.0585078i
$69$	−252.727			−0.440939
$70$	−171.376	+	345.755i	−0.292619	+	0.590366i
$71$	265.331			0.443506			0.221753	−	0.975103i	$-0.428822\pi$
$71$	265.331			0.443506			0.221753	+	0.975103i	$0.428822\pi$
$72$	1028.09	−	1028.09i	1.68281	−	1.68281i
$73$	609.073	−	609.073i	0.976528	−	0.976528i	−0.0232024	−	0.999731i	$-0.507386\pi$
$73$	609.073	−	609.073i	0.976528	−	0.976528i	0.999731	+	0.0232024i	$0.00738622\pi$
$74$			142.723i			0.224205i
$75$	−926.047	+	733.090i	−1.42574	+	1.12867i
$76$			385.216i			0.581413i
$77$	−429.300	+	173.024i	−0.635368	+	0.256076i
$78$	154.991	+	154.991i	0.224990	+	0.224990i
$79$			145.122i			0.206678i	0.994646	+	0.103339i	$0.0329526\pi$
$79$			145.122i			0.206678i	−0.994646	+	0.103339i	$0.967047\pi$
$80$	81.4200	+	4.71865i	0.113788	+	0.00659451i
$81$	−1468.13			−2.01390
$82$	180.641	+	180.641i	0.243273	+	0.243273i
$83$	454.928	−	454.928i	0.601625	−	0.601625i	−0.339119	−	0.940744i	$-0.610129\pi$
$83$	454.928	−	454.928i	0.601625	−	0.601625i	0.940744	+	0.339119i	$0.110129\pi$
$84$	728.914	+	310.138i	0.946798	+	0.402844i
$85$	76.2061	+	85.5825i	0.0972437	+	0.109208i
$86$	−584.735			−0.733181
$87$	1085.78	+	1085.78i	1.33803	+	1.33803i
$88$	412.563	+	412.563i	0.499766	+	0.499766i
$89$	−209.235			−0.249201			−0.124600	−	0.992207i	$-0.539765\pi$
$89$	−209.235			−0.249201			−0.124600	+	0.992207i	$0.539765\pi$
$90$	−862.965	−	969.144i	−1.01072	−	1.13508i
$91$	−90.2554	+	212.126i	−0.103971	+	0.244361i
$92$	−85.6148	+	85.6148i	−0.0970213	+	0.0970213i
$93$	−177.815	−	177.815i	−0.198264	−	0.198264i
$94$	−606.130			−0.665080
$95$	949.830	+	55.0468i	1.02579	+	0.0594493i
$96$		−	1636.25i		−	1.73957i
$97$	−1012.24	−	1012.24i	−1.05956	−	1.05956i	−0.998110	−	0.0614533i	$-0.980426\pi$
$97$	−1012.24	−	1012.24i	−1.05956	−	1.05956i	−0.0614533	−	0.998110i	$-0.519574\pi$
$98$	12.2446	−	639.121i	0.0126213	−	0.658785i
$99$		−	1556.47i		−	1.58011i
$100$	−65.3666	+	562.055i	−0.0653666	+	0.562055i
$101$			912.036i			0.898524i	0.893400	+	0.449262i	$0.148313\pi$
$101$			912.036i			0.898524i	−0.893400	+	0.449262i	$0.851687\pi$
$102$	−127.624	+	127.624i	−0.123889	+	0.123889i
$103$	594.521	−	594.521i	0.568737	−	0.568737i	−0.363038	−	0.931774i	$-0.618260\pi$
$103$	594.521	−	594.521i	0.568737	−	0.568737i	0.931774	+	0.363038i	$0.118260\pi$
$104$	290.593			0.273990
$105$	868.870	−	1752.97i	0.807553	−	1.62926i
$106$	406.339			0.372332
$107$	−435.539	+	435.539i	−0.393506	+	0.393506i	−0.875935	−	0.482429i	$-0.839755\pi$
$107$	−435.539	+	435.539i	−0.393506	+	0.393506i	0.482429	+	0.875935i	$0.339755\pi$
$108$	−1066.99	+	1066.99i	−0.950660	+	0.950660i
$109$			1023.24i			0.899165i	0.893239	+	0.449582i	$0.148427\pi$
$109$			1023.24i			0.899165i	−0.893239	+	0.449582i	$0.851573\pi$
$110$	388.908	−	346.299i	0.337099	−	0.300167i
$111$		−	723.602i		−	0.618750i
$112$	−125.304	+	50.5022i	−0.105716	+	0.0426072i
$113$	678.584	+	678.584i	0.564919	+	0.564919i	0.930701	−	0.365782i	$-0.119198\pi$
$113$	678.584	+	678.584i	0.564919	+	0.564919i	−0.365782	+	0.930701i	$0.619198\pi$
$114$			1498.52i			1.23113i
$115$	198.866	+	223.335i	0.161256	+	0.181096i
$116$	735.648			0.588821
$117$	−548.156	−	548.156i	−0.433137	−	0.433137i
$118$	−903.687	+	903.687i	−0.705009	+	0.705009i
$119$	−174.671	−	74.3192i	−0.134556	−	0.0572507i
$120$	−2462.11	−	142.690i	−1.87299	−	0.108548i
$121$	−706.405			−0.530733
$122$	−31.2210	−	31.2210i	−0.0231690	−	0.0231690i
$123$	−915.844	−	915.844i	−0.671373	−	0.671373i
$124$	−120.474			−0.0872494
$125$	1376.52	+	241.491i	0.984957	+	0.172797i
$126$	1978.00	+	841.598i	1.39852	+	0.595044i
$127$	−2.16418	+	2.16418i	−0.00151212	+	0.00151212i	−0.707862	−	0.706350i	$-0.750340\pi$
$127$	−2.16418	+	2.16418i	−0.00151212	+	0.00151212i	0.706350	+	0.707862i	$0.250340\pi$
$128$	−477.397	−	477.397i	−0.329659	−	0.329659i
$129$	2964.59			2.02339
$130$	15.0058	−	258.925i	0.0101238	−	0.174686i
$131$			1996.71i			1.33170i	0.746085	+	0.665851i	$0.231931\pi$
$131$			1996.71i			1.33170i	−0.746085	+	0.665851i	$0.768069\pi$
$132$	−755.866	−	755.866i	−0.498406	−	0.498406i
$133$	−1461.78	+	589.149i	−0.953023	+	0.384103i
$134$		−	1588.53i		−	1.02409i
$135$	2478.41	+	2783.36i	1.58006	+	1.77447i
$136$			239.283i			0.150870i
$137$	1.36186	−	1.36186i	0.000849278	−	0.000849278i	−0.706682	−	0.707531i	$-0.749809\pi$
$137$	1.36186	−	1.36186i	0.000849278	−	0.000849278i	0.707531	+	0.706682i	$0.249809\pi$
$138$	−333.047	+	333.047i	−0.205441	+	0.205441i
$139$	−2121.99			−1.29486			−0.647428	−	0.762126i	$-0.724156\pi$
$139$	−2121.99			−1.29486			−0.647428	+	0.762126i	$0.724156\pi$
$140$	−299.500	−	888.183i	−0.180803	−	0.536180i
$141$	3073.06			1.83545
$142$	349.656	−	349.656i	0.206637	−	0.206637i
$143$	219.969	−	219.969i	0.128635	−	0.128635i
$144$		−	454.303i		−	0.262907i
$145$	105.123	−	1813.89i	0.0602068	−	1.03886i
$146$		−	1605.29i		−	0.909962i
$147$	−62.0797	+	3240.33i	−0.0348316	+	1.81808i
$148$	−245.130	−	245.130i	−0.136146	−	0.136146i
$149$		−	2011.15i		−	1.10577i	−0.833257	−	0.552886i	$-0.813526\pi$
$149$		−	2011.15i		−	1.10577i	0.833257	−	0.552886i	$-0.186474\pi$
$150$	−254.281	+	2186.43i	−0.138413	+	1.19014i
$151$	−300.663			−0.162037			−0.0810185	−	0.996713i	$-0.525817\pi$
$151$	−300.663			−0.162037			−0.0810185	+	0.996713i	$0.525817\pi$
$152$	1404.79	+	1404.79i	0.749627	+	0.749627i
$153$	451.369	−	451.369i	0.238504	−	0.238504i
$154$	−337.725	+	793.750i	−0.176718	+	0.415339i
$155$	−17.2156	+	297.054i	−0.00892123	+	0.153935i
$156$	−532.400			−0.273244
$157$	−1672.49	−	1672.49i	−0.850184	−	0.850184i	0.139971	−	0.990156i	$-0.455299\pi$
$157$	−1672.49	−	1672.49i	−0.850184	−	0.850184i	−0.990156	+	0.139971i	$0.955299\pi$
$158$	191.244	+	191.244i	0.0962947	+	0.0962947i
$159$	−2060.13			−1.02754
$160$	−1445.95	+	1287.53i	−0.714452	+	0.636177i
$161$	−455.820	−	193.942i	−0.223128	−	0.0949367i
$162$	−1934.72	+	1934.72i	−0.938310	+	0.938310i
$163$	−2459.41	−	2459.41i	−1.18181	−	1.18181i	−0.979274	−	0.202539i	$-0.935081\pi$
$163$	−2459.41	−	2459.41i	−1.18181	−	1.18181i	−0.202539	−	0.979274i	$-0.564919\pi$
$164$	−620.508			−0.295449
$165$	−1971.75	+	1755.73i	−0.930308	+	0.828384i
$166$		−	1199.02i		−	0.560614i
$167$	2190.81	+	2190.81i	1.01515	+	1.01515i	0.999883	+	0.0152650i	$0.00485918\pi$
$167$	2190.81	+	2190.81i	1.01515	+	1.01515i	0.0152650	+	0.999883i	$0.495141\pi$
$168$	3789.16	−	1527.17i	1.74012	−	0.701331i
$169$			2042.06i			0.929478i
$170$	213.207	+	12.3563i	0.0961896	+	0.00557461i
$171$		−	5299.81i		−	2.37010i
$172$	1004.30	−	1004.30i	0.445214	−	0.445214i
$173$	−543.389	+	543.389i	−0.238804	+	0.238804i	−0.816355	−	0.577551i	$-0.804009\pi$
$173$	−543.389	+	543.389i	−0.238804	+	0.238804i	0.577551	+	0.816355i	$0.304009\pi$
$174$	2861.72			1.24682
$175$	−2232.79	+	611.559i	−0.964477	+	0.264169i
$176$	182.307			0.0780790
$177$	4581.67	−	4581.67i	1.94565	−	1.94565i
$178$	−275.732	+	275.732i	−0.116107	+	0.116107i
$179$		−	3217.81i		−	1.34363i	−0.740717	−	0.671817i	$-0.765514\pi$
$179$		−	3217.81i		−	1.34363i	0.740717	−	0.671817i	$-0.234486\pi$
$180$	3146.69	+	182.364i	1.30300	+	0.0755147i
$181$		−	1653.80i		−	0.679148i	−0.940579	−	0.339574i	$-0.889717\pi$
$181$		−	1653.80i		−	0.679148i	0.940579	−	0.339574i	$-0.110283\pi$
$182$	160.603	+	398.482i	0.0654102	+	0.162294i
$183$	158.290	+	158.290i	0.0639406	+	0.0639406i
$184$			624.431i			0.250183i
$185$	−639.446	+	569.389i	−0.254124	+	0.226283i
$186$	−468.653			−0.184749
$187$	181.130	+	181.130i	0.0708317	+	0.0708317i
$188$	1041.04	−	1041.04i	0.403860	−	0.403860i
$189$	−5680.75	−	2417.05i	−2.18632	−	0.930234i
$190$	1324.24	−	1179.16i	0.505633	−	0.450237i
$191$	−2252.81			−0.853442			−0.426721	−	0.904383i	$-0.640331\pi$
$191$	−2252.81			−0.853442			−0.426721	+	0.904383i	$0.640331\pi$
$192$	−2546.17	−	2546.17i	−0.957051	−	0.957051i
$193$	2201.68	+	2201.68i	0.821141	+	0.821141i	0.986272	−	0.165131i	$-0.0528046\pi$
$193$	2201.68	+	2201.68i	0.821141	+	0.821141i	−0.165131	+	0.986272i	$0.552805\pi$
$194$	−2667.89			−0.987337
$195$	−76.0791	+	1312.74i	−0.0279392	+	0.482089i
$196$	1076.67	+	1118.73i	0.392374	+	0.407702i
$197$	−3634.93	+	3634.93i	−1.31461	+	1.31461i	−0.396630	+	0.917978i	$0.629821\pi$
$197$	−3634.93	+	3634.93i	−1.31461	+	1.31461i	−0.917978	+	0.396630i	$0.870179\pi$
$198$	−2051.13	−	2051.13i	−0.736200	−	0.736200i
$199$	4951.46			1.76382			0.881908	−	0.471421i	$-0.156259\pi$
$199$	4951.46			1.76382			0.881908	+	0.471421i	$0.156259\pi$
$200$	1811.30	+	2288.05i	0.640390	+	0.808947i
$201$			8053.83i			2.82623i
$202$	1201.89	+	1201.89i	0.418638	+	0.418638i
$203$	1125.10	+	2791.56i	0.388997	+	0.965166i
$204$		−	438.396i		−	0.150460i
$205$	−88.6697	+	1529.99i	−0.0302096	+	0.521264i
$206$		−	1566.93i		−	0.529968i
$207$	1177.89	−	1177.89i	0.395502	−	0.395502i
$208$	64.2047	−	64.2047i	0.0214029	−	0.0214029i
$209$	2126.76			0.703880
$210$	−1165.08	−	3455.09i	−0.382847	−	1.13535i
$211$	148.487			0.0484469			0.0242234	−	0.999707i	$-0.492289\pi$
$211$	148.487			0.0484469			0.0242234	+	0.999707i	$0.492289\pi$
$212$	−697.897	+	697.897i	−0.226093	+	0.226093i
$213$	−1772.75	+	1772.75i	−0.570266	+	0.570266i
$214$			1147.92i			0.366682i
$215$	−2332.78	−	2619.81i	−0.739974	−	0.831020i
$216$			7782.09i			2.45141i
$217$	−184.253	−	457.163i	−0.0576402	−	0.143015i
$218$	1348.44	+	1348.44i	0.418936	+	0.418936i
$219$			8138.77i			2.51126i
$220$	−73.1810	+	1262.73i	−0.0224266	+	0.386971i
$221$	127.580			0.0388325
$222$	−953.571	−	953.571i	−0.288286	−	0.288286i
$223$	−3171.97	+	3171.97i	−0.952515	+	0.952515i	−0.998923	−	0.0464080i	$-0.985223\pi$
$223$	−3171.97	+	3171.97i	−0.952515	+	0.952515i	0.0464080	+	0.998923i	$0.485223\pi$
$224$	1255.65	−	2951.14i	0.374539	−	0.880275i
$225$	899.314	−	7732.75i	0.266463	−	2.29118i
$226$	1788.49			0.526410
$227$	−2955.01	−	2955.01i	−0.864013	−	0.864013i	0.127789	−	0.991801i	$-0.459212\pi$
$227$	−2955.01	−	2955.01i	−0.864013	−	0.864013i	−0.991801	+	0.127789i	$0.959212\pi$
$228$	−2573.74	−	2573.74i	−0.747587	−	0.747587i
$229$	5785.89			1.66962			0.834809	−	0.550539i	$-0.185578\pi$
$229$	5785.89			1.66962			0.834809	+	0.550539i	$0.185578\pi$
$230$	556.382	+	32.2448i	0.159508	+	0.00924417i
$231$	1712.26	−	4024.29i	0.487698	−	1.14623i
$232$	2682.72	−	2682.72i	0.759178	−	0.759178i
$233$	3092.94	+	3092.94i	0.869636	+	0.869636i	0.992432	−	0.122796i	$-0.0391862\pi$
$233$	3092.94	+	3092.94i	0.869636	+	0.869636i	−0.122796	+	0.992432i	$0.539186\pi$
$234$	−1444.73			−0.403612
$235$	−2418.14	−	2715.66i	−0.671242	−	0.753831i
$236$		−	3104.20i		−	0.856214i
$237$	−969.603	−	969.603i	−0.265749	−	0.265749i
$238$	−328.123	+	132.245i	−0.0893658	+	0.0360176i
$239$		−	1703.12i		−	0.460946i	−0.973079	−	0.230473i	$-0.925973\pi$
$239$		−	1703.12i		−	0.460946i	0.973079	−	0.230473i	$-0.0740273\pi$
$240$	−575.516	+	512.463i	−0.154789	+	0.137831i
$241$			2017.99i			0.539378i	0.962947	+	0.269689i	$0.0869209\pi$
$241$			2017.99i			0.539378i	−0.962947	+	0.269689i	$0.913079\pi$
$242$	−930.909	+	930.909i	−0.247277	+	0.247277i
$243$	3444.88	−	3444.88i	0.909421	−	0.909421i
$244$	107.246			0.0281381
$245$	2912.32	−	2494.89i	0.759435	−	0.650583i
$246$	−2413.82			−0.625608
$247$	749.000	−	749.000i	0.192946	−	0.192946i
$248$	−439.340	+	439.340i	−0.112492	+	0.112492i
$249$			6079.00i			1.54715i
$250$	2132.23	−	1495.75i	0.539417	−	0.378399i
$251$		−	841.491i		−	0.211611i	−0.994387	−	0.105806i	$-0.966258\pi$
$251$		−	841.491i		−	0.211611i	0.994387	−	0.105806i	$-0.0337422\pi$
$252$	−4842.72	+	1951.79i	−1.21057	+	0.487902i
$253$	472.674	+	472.674i	0.117458	+	0.117458i
$254$			5.70395i			0.00140905i
$255$	−1080.95	−	62.6461i	−0.265459	−	0.0153845i
$256$	−4306.96			−1.05150
$257$	2421.89	+	2421.89i	0.587833	+	0.587833i	0.937044	−	0.349211i	$-0.113550\pi$
$257$	2421.89	+	2421.89i	0.587833	+	0.587833i	−0.349211	+	0.937044i	$0.613550\pi$
$258$	3906.78	−	3906.78i	0.942733	−	0.942733i
$259$	555.290	−	1305.09i	0.133220	−	0.313106i
$260$	418.936	+	470.482i	0.0999281	+	0.112223i
$261$	−10121.0			−2.40029
$262$	2631.28	+	2631.28i	0.620462	+	0.620462i
$263$	−3472.86	−	3472.86i	−0.814242	−	0.814242i	0.171025	−	0.985267i	$-0.445292\pi$
$263$	−3472.86	−	3472.86i	−0.814242	−	0.814242i	−0.985267	+	0.171025i	$0.945292\pi$
$264$	−5512.90			−1.28521
$265$	1621.08	+	1820.54i	0.375782	+	0.422017i
$266$	−1149.96	+	2702.73i	−0.265070	+	0.622990i
$267$	1397.96	−	1397.96i	0.320425	−	0.320425i
$268$	2728.34	+	2728.34i	0.621865	+	0.621865i
$269$	−3166.14			−0.717631			−0.358816	−	0.933408i	$-0.616819\pi$
$269$	−3166.14			−0.717631			−0.358816	+	0.933408i	$0.616819\pi$
$270$	6934.02	+	401.857i	1.56293	+	0.0905787i
$271$		−	5813.58i		−	1.30314i	−0.758590	−	0.651568i	$-0.774111\pi$
$271$		−	5813.58i		−	1.30314i	0.758590	−	0.651568i	$-0.225889\pi$
$272$	52.8683	+	52.8683i	0.0117853	+	0.0117853i
$273$	−814.251	−	2020.29i	−0.180515	−	0.447889i
$274$		−	3.58934i		−	0.000791386i
$275$	3103.07	+	360.885i	0.680445	+	0.0791353i
$276$		−	1144.03i		−	0.249502i
$277$	−844.503	+	844.503i	−0.183181	+	0.183181i	−0.792741	−	0.609559i	$-0.791346\pi$
$277$	−844.503	+	844.503i	−0.183181	+	0.183181i	0.609559	+	0.792741i	$0.291346\pi$
$278$	−2796.39	+	2796.39i	−0.603296	+	0.603296i
$279$	1657.49			0.355667
$280$	−4331.18	−	2146.78i	−0.924420	−	0.458195i
$281$	−4548.77			−0.965683			−0.482842	−	0.875708i	$-0.660395\pi$
$281$	−4548.77			−0.965683			−0.482842	+	0.875708i	$0.660395\pi$
$282$	4049.72	−	4049.72i	0.855168	−	0.855168i
$283$	4334.44	−	4334.44i	0.910445	−	0.910445i	−0.0858623	−	0.996307i	$-0.527365\pi$
$283$	4334.44	−	4334.44i	0.910445	−	0.910445i	0.996307	+	0.0858623i	$0.0273645\pi$
$284$			1201.08i			0.250955i
$285$	−6713.86	+	5978.29i	−1.39542	+	1.24254i
$286$		−	579.756i		−	0.119866i
$287$	−949.004	−	2354.64i	−0.195184	−	0.484285i
$288$	7626.06	+	7626.06i	1.56031	+	1.56031i
$289$		−	4807.95i		−	0.978617i
$290$	−2251.83	−	2528.90i	−0.455973	−	0.512076i
$291$	13526.1			2.72480
$292$	2757.12	+	2757.12i	0.552562	+	0.552562i
$293$	−3204.15	+	3204.15i	−0.638869	+	0.638869i	−0.950276	−	0.311408i	$-0.899199\pi$
$293$	−3204.15	+	3204.15i	−0.638869	+	0.638869i	0.311408	+	0.950276i	$0.399199\pi$
$294$	4188.33	+	4351.95i	0.830845	+	0.863303i
$295$	−7654.05	−	443.586i	−1.51063	−	0.0875477i
$296$	−1787.85			−0.351070
$297$	5890.80	+	5890.80i	1.15090	+	1.15090i
$298$	−2650.32	−	2650.32i	−0.515198	−	0.515198i
$299$	332.932			0.0643945
$300$	−3318.51	−	4191.98i	−0.638648	−	0.806746i
$301$	5346.95	+	2275.02i	1.02390	+	0.435648i
$302$	−396.217	+	396.217i	−0.0754958	+	0.0754958i
$303$	−6093.56	−	6093.56i	−1.15533	−	1.15533i
$304$	620.759			0.117115
$305$	15.3252	−	264.436i	0.00287712	−	0.0496445i
$306$		−	1189.64i		−	0.222246i
$307$	189.516	+	189.516i	0.0352321	+	0.0352321i	0.724503	−	0.689271i	$-0.242069\pi$
$307$	189.516	+	189.516i	0.0352321	+	0.0352321i	−0.689271	+	0.724503i	$0.742069\pi$
$308$	−783.233	−	1943.33i	−0.144899	−	0.359518i
$309$			7944.32i			1.46258i
$310$	368.775	+	414.149i	0.0675645	+	0.0758776i
$311$			9876.93i			1.80087i	0.434994	+	0.900433i	$0.356750\pi$
$311$			9876.93i			1.80087i	−0.434994	+	0.900433i	$0.643250\pi$
$312$	−1941.53	+	1941.53i	−0.352300	+	0.352300i
$313$	3725.02	−	3725.02i	0.672686	−	0.672686i	−0.285649	−	0.958334i	$-0.592209\pi$
$313$	3725.02	−	3725.02i	0.672686	−	0.672686i	0.958334	+	0.285649i	$0.0922091\pi$
$314$	−4408.04			−0.792230
$315$	4120.52	+	12219.6i	0.737032	+	2.18571i
$316$	−656.932			−0.116947
$317$	3053.99	−	3053.99i	0.541101	−	0.541101i	−0.382750	−	0.923852i	$-0.625023\pi$
$317$	3053.99	−	3053.99i	0.541101	−	0.541101i	0.923852	+	0.382750i	$0.125023\pi$
$318$	−2714.87	+	2714.87i	−0.478749	+	0.478749i
$319$		−	4061.47i		−	0.712848i
$320$	−246.513	+	4253.58i	−0.0430641	+	0.743069i
$321$		−	5819.91i		−	1.01195i
$322$	−856.265	+	345.106i	−0.148192	+	0.0597267i
$323$	616.751	+	616.751i	0.106244	+	0.106244i
$324$		−	6645.86i		−	1.13955i
$325$	1219.93	−	965.741i	0.208215	−	0.164830i
$326$	−6482.07			−1.10125
$327$	−6836.57	−	6836.57i	−1.15616	−	1.15616i
$328$	−2262.84	+	2262.84i	−0.380928	+	0.380928i
$329$	5542.60	+	2358.26i	0.928794	+	0.395183i
$330$	−284.679	+	4912.12i	−0.0474881	+	0.819404i
$331$	6883.48			1.14305			0.571526	−	0.820584i	$-0.306352\pi$
$331$	6883.48			1.14305			0.571526	+	0.820584i	$0.306352\pi$
$332$	2059.34	+	2059.34i	0.340425	+	0.340425i
$333$	3372.49	+	3372.49i	0.554990	+	0.554990i
$334$	5774.15			0.945950
$335$	7117.16	−	6337.41i	1.16075	−	1.03358i
$336$	499.774	−	1174.61i	0.0811456	−	0.190715i
$337$	−506.829	+	506.829i	−0.0819251	+	0.0819251i	−0.746882	−	0.664957i	$-0.768450\pi$
$337$	−506.829	+	506.829i	−0.0819251	+	0.0819251i	0.664957	+	0.746882i	$0.268450\pi$
$338$	2691.05	+	2691.05i	0.433059	+	0.433059i
$339$	−9067.61			−1.45276
$340$	−387.410	+	344.966i	−0.0617949	+	0.0550247i
$341$			665.132i			0.105627i
$342$	−6984.15	−	6984.15i	−1.10427	−	1.10427i
$343$	−2598.59	+	5796.63i	−0.409069	+	0.912504i
$344$		−	7324.82i		−	1.14805i
$345$	−2820.84	−	163.480i	−0.440200	−	0.0255116i
$346$			1432.17i			0.222526i
$347$	−1458.26	+	1458.26i	−0.225601	+	0.225601i	−0.810852	−	0.585251i	$-0.800996\pi$
$347$	−1458.26	+	1458.26i	−0.225601	+	0.225601i	0.585251	+	0.810852i	$0.300996\pi$
$348$	−4915.07	+	4915.07i	−0.757113	+	0.757113i
$349$	−10334.5			−1.58508			−0.792542	−	0.609817i	$-0.791243\pi$
$349$	−10334.5			−1.58508			−0.792542	+	0.609817i	$0.791243\pi$
$350$	−2136.48	+	3748.32i	−0.326285	+	0.572446i
$351$	4149.23			0.630967
$352$	−3060.26	+	3060.26i	−0.463388	+	0.463388i
$353$	5534.44	−	5534.44i	0.834471	−	0.834471i	−0.153654	−	0.988125i	$-0.549104\pi$
$353$	5534.44	−	5534.44i	0.834471	−	0.834471i	0.988125	+	0.153654i	$0.0491040\pi$
$354$		−	12075.6i		−	1.81302i
$355$	2961.52	+	171.633i	0.442763	+	0.0256601i
$356$		−	947.153i		−	0.141008i
$357$	1663.58	−	670.481i	0.246627	−	0.0993995i
$358$	−4240.47	−	4240.47i	−0.626022	−	0.626022i
$359$		−	28.9268i		−	0.00425263i	−0.999998	−	0.00212632i	$-0.999323\pi$
$359$		−	28.9268i		−	0.00425263i	0.999998	−	0.00212632i	$-0.000676828\pi$
$360$	12140.2	−	10810.1i	1.77735	−	1.58262i
$361$	382.654			0.0557886
$362$	−2179.39	−	2179.39i	−0.316427	−	0.316427i
$363$	4719.69	−	4719.69i	0.682423	−	0.682423i
$364$	−960.240	−	408.563i	−0.138270	−	0.0588311i
$365$	7192.22	−	6404.25i	1.03139	−	0.918393i
$366$	417.193			0.0595820
$367$	−703.106	−	703.106i	−0.100005	−	0.100005i	0.655334	−	0.755339i	$-0.272528\pi$
$367$	−703.106	−	703.106i	−0.100005	−	0.100005i	−0.755339	+	0.655334i	$0.772528\pi$
$368$	137.964	+	137.964i	0.0195432	+	0.0195432i
$369$	8536.95			1.20438
$370$	−92.3223	+	1593.02i	−0.0129719	+	0.223830i
$371$	−3715.66	−	1580.94i	−0.519967	−	0.221235i
$372$	804.923	−	804.923i	0.112186	−	0.112186i
$373$	2472.73	+	2472.73i	0.343252	+	0.343252i	0.857588	−	0.514337i	$-0.171962\pi$
$373$	2472.73	+	2472.73i	0.343252	+	0.343252i	−0.514337	+	0.857588i	$0.671962\pi$
$374$	477.390			0.0660034
$375$	−10810.4	+	7583.44i	−1.48866	+	1.04429i
$376$		−	7592.83i		−	1.04141i
$377$	−1430.37	−	1430.37i	−0.195405	−	0.195405i
$378$	−10671.4	+	4300.95i	−1.45205	+	0.585230i
$379$			4711.22i			0.638521i	0.947667	+	0.319260i	$0.103434\pi$
$379$			4711.22i			0.638521i	−0.947667	+	0.319260i	$0.896566\pi$
$380$	−249.183	+	4299.64i	−0.0336390	+	0.580439i
$381$		−	28.9189i		−	0.00388861i
$382$	−2968.78	+	2968.78i	−0.397633	+	0.397633i
$383$	−6945.43	+	6945.43i	−0.926618	+	0.926618i	−0.997486	−	0.0708675i	$-0.977423\pi$
$383$	−6945.43	+	6945.43i	−0.926618	+	0.926618i	0.0708675	+	0.997486i	$0.477423\pi$
$384$	6379.24			0.847758
$385$	−4903.61	+	1653.52i	−0.649119	+	0.218887i
$386$	5802.79			0.765167
$387$	−13817.1	+	13817.1i	−1.81489	+	1.81489i
$388$	4582.16	−	4582.16i	0.599546	−	0.599546i
$389$			3515.63i			0.458226i	0.973400	+	0.229113i	$0.0735825\pi$
$389$			3515.63i			0.458226i	−0.973400	+	0.229113i	$0.926418\pi$
$390$	1629.69	+	1830.20i	0.211596	+	0.237631i
$391$			274.147i			0.0354584i
$392$	8006.10	+	153.385i	1.03155	+	0.0197630i
$393$	−13340.5	−	13340.5i	−1.71232	−	1.71232i
$394$			9580.30i			1.22500i
$395$	−93.8745	+	1619.80i	−0.0119578	+	0.206332i
$396$	7045.73			0.894094
$397$	−2998.00	−	2998.00i	−0.379005	−	0.379005i	0.491738	−	0.870743i	$-0.336362\pi$
$397$	−2998.00	−	2998.00i	−0.379005	−	0.379005i	−0.870743	+	0.491738i	$0.836362\pi$
$398$	6525.09	−	6525.09i	0.821792	−	0.821792i
$399$	5830.27	−	13702.8i	0.731525	−	1.71929i
$400$	905.726	+	105.335i	0.113216	+	0.0131669i
$401$	9037.21			1.12543			0.562714	−	0.826652i	$-0.309757\pi$
$401$	9037.21			1.12543			0.562714	+	0.826652i	$0.309757\pi$
$402$	10613.4	+	10613.4i	1.31679	+	1.31679i
$403$	234.246	+	234.246i	0.0289544	+	0.0289544i
$404$	−4128.55			−0.508424
$405$	−16386.7	−	949.683i	−2.01053	−	0.116519i
$406$	5161.41	+	2196.08i	0.630927	+	0.268447i
$407$	−1353.35	+	1353.35i	−0.164823	+	0.164823i
$408$	−1598.72	−	1598.72i	−0.193991	−	0.193991i
$409$	−10974.7			−1.32681			−0.663406	−	0.748259i	$-0.730890\pi$
$409$	−10974.7			−1.32681			−0.663406	+	0.748259i	$0.730890\pi$
$410$	1899.39	+	2133.09i	0.228791	+	0.256941i
$411$			18.1979i			0.00218403i
$412$	2691.24	+	2691.24i	0.321816	+	0.321816i
$413$	11779.5	−	4747.56i	1.40346	−	0.565647i
$414$		−	3104.47i		−	0.368542i
$415$	5372.01	−	4783.45i	0.635425	−	0.565808i
$416$			2155.52i			0.254046i
$417$	14177.6	−	14177.6i	1.66494	−	1.66494i
$418$	2802.67	−	2802.67i	0.327950	−	0.327950i
$419$	−6134.21			−0.715216			−0.357608	−	0.933872i	$-0.616408\pi$
$419$	−6134.21			−0.715216			−0.357608	+	0.933872i	$0.616408\pi$
$420$	7935.24	+	3933.15i	0.921905	+	0.456948i
$421$	2593.11			0.300192			0.150096	−	0.988671i	$-0.452042\pi$
$421$	2593.11			0.300192			0.150096	+	0.988671i	$0.452042\pi$
$422$	195.678	−	195.678i	0.0225722	−	0.0225722i
$423$	−14322.6	+	14322.6i	−1.64631	+	1.64631i
$424$			5090.11i			0.583013i
$425$	795.223	+	1004.53i	0.0907623	+	0.114652i
$426$			4672.29i			0.531393i
$427$	164.021	+	406.964i	0.0185891	+	0.0461227i
$428$	−1971.57	−	1971.57i	−0.222662	−	0.222662i
$429$			2939.35i			0.330800i
$430$	−6526.58	−	378.244i	−0.731953	−	0.0424199i
$431$	−10409.7			−1.16339			−0.581693	−	0.813408i	$-0.697610\pi$
$431$	−10409.7			−1.16339			−0.581693	+	0.813408i	$0.697610\pi$
$432$	1719.41	+	1719.41i	0.191493	+	0.191493i
$433$	−5550.33	+	5550.33i	−0.616009	+	0.616009i	−0.944505	−	0.328496i	$-0.893458\pi$
$433$	−5550.33	+	5550.33i	−0.616009	+	0.616009i	0.328496	+	0.944505i	$0.393458\pi$
$434$	−845.266	−	359.644i	−0.0934886	−	0.0397775i
$435$	11416.7	+	12821.5i	1.25837	+	1.41320i
$436$	−4631.96			−0.508786
$437$	1609.47	+	1609.47i	0.176181	+	0.176181i
$438$	10725.4	+	10725.4i	1.17004	+	1.17004i
$439$	5255.37			0.571356			0.285678	−	0.958326i	$-0.407781\pi$
$439$	5255.37			0.571356			0.285678	+	0.958326i	$0.407781\pi$
$440$	4338.00	+	4871.75i	0.470014	+	0.527844i
$441$	−14812.9	−	15391.5i	−1.59949	−	1.66197i
$442$	168.127	−	168.127i	0.0180927	−	0.0180927i
$443$	−3048.77	−	3048.77i	−0.326979	−	0.326979i	0.524458	−	0.851436i	$-0.324268\pi$
$443$	−3048.77	−	3048.77i	−0.326979	−	0.326979i	−0.851436	+	0.524458i	$0.824268\pi$
$444$	3275.56			0.350115
$445$	−2335.40	−	135.347i	−0.248783	−	0.0144181i
$446$			8360.12i			0.887585i
$447$	13437.1	+	13437.1i	1.42182	+	1.42182i
$448$	−2638.36	−	6546.20i	−0.278238	−	0.690355i
$449$			6234.57i			0.655295i	0.944800	+	0.327648i	$0.106256\pi$
$449$			6234.57i			0.655295i	−0.944800	+	0.327648i	$0.893744\pi$
$450$	−9005.18	−	11375.4i	−0.943352	−	1.19165i
$451$			3425.79i			0.357681i
$452$	−3071.78	+	3071.78i	−0.319655	+	0.319655i
$453$	2008.81	−	2008.81i	0.208349	−	0.208349i
$454$	−7788.29			−0.805116
$455$	−1144.61	+	2309.28i	−0.117935	+	0.237936i
$456$	−18771.5			−1.92776
$457$	−2938.32	+	2938.32i	−0.300763	+	0.300763i	−0.841312	−	0.540549i	$-0.818216\pi$
$457$	−2938.32	+	2938.32i	−0.300763	+	0.300763i	0.540549	+	0.841312i	$0.318216\pi$
$458$	7624.72	−	7624.72i	0.777903	−	0.777903i
$459$			3416.61i			0.347438i
$460$	−1010.98	+	900.218i	−0.102472	+	0.0912453i
$461$		−	11965.0i		−	1.20882i	−0.796672	−	0.604411i	$-0.793408\pi$
$461$		−	11965.0i		−	1.20882i	0.796672	−	0.604411i	$-0.206592\pi$
$462$	−3046.83	−	7559.69i	−0.306821	−	0.761274i
$463$	4892.04	+	4892.04i	0.491042	+	0.491042i	0.908634	−	0.417592i	$-0.137126\pi$
$463$	4892.04	+	4892.04i	0.491042	+	0.491042i	−0.417592	+	0.908634i	$0.637126\pi$
$464$		−	1185.46i		−	0.118607i
$465$	−1869.68	−	2099.72i	−0.186461	−	0.209403i
$466$	8151.82			0.810356
$467$	−6801.21	−	6801.21i	−0.673924	−	0.673924i	0.284694	−	0.958618i	$-0.408108\pi$
$467$	−6801.21	−	6801.21i	−0.673924	−	0.673924i	−0.958618	+	0.284694i	$0.908108\pi$
$468$	2481.36	−	2481.36i	0.245087	−	0.245087i
$469$	−6180.49	+	14525.9i	−0.608504	+	1.43016i
$470$	−6765.38	−	392.084i	−0.663966	−	0.0384797i
$471$	22348.7			2.18635
$472$	−11320.2	−	11320.2i	−1.10393	−	1.10393i
$473$	−5544.66	−	5544.66i	−0.538993	−	0.538993i
$474$	−2555.51			−0.247634
$475$	10566.0	+	1228.82i	1.02064	+	0.118699i
$476$	336.424	−	790.693i	0.0323949	−	0.0761373i
$477$	9601.66	−	9601.66i	0.921656	−	0.921656i
$478$	−2244.40	−	2244.40i	−0.214762	−	0.214762i
$479$	7411.56			0.706978			0.353489	−	0.935439i	$-0.384995\pi$
$479$	7411.56			0.706978			0.353489	+	0.935439i	$0.384995\pi$
$480$	1058.43	−	18263.2i	0.100647	−	1.73666i
$481$			953.241i			0.0903619i
$482$	2659.33	+	2659.33i	0.251305	+	0.251305i
$483$	4341.25	−	1749.68i	0.408972	−	0.164831i
$484$		−	3197.72i		−	0.300311i
$485$	−10643.5	−	11953.0i	−0.996485	−	1.11909i
$486$		−	9079.42i		−	0.847430i
$487$	−2511.31	+	2511.31i	−0.233672	+	0.233672i	−0.814224	−	0.580551i	$-0.802837\pi$
$487$	−2511.31	+	2511.31i	−0.233672	+	0.233672i	0.580551	+	0.814224i	$0.302837\pi$
$488$	391.098	−	391.098i	0.0362791	−	0.0362791i
$489$	32863.9			3.03918
$490$	550.094	−	7125.70i	0.0507157	−	0.656951i
$491$	3326.90			0.305786			0.152893	−	0.988243i	$-0.451141\pi$
$491$	3326.90			0.305786			0.152893	+	0.988243i	$0.451141\pi$
$492$	4145.79	−	4145.79i	0.379891	−	0.379891i
$493$	1177.81	−	1177.81i	0.107598	−	0.107598i
$494$		−	1974.08i		−	0.179794i
$495$	1006.82	−	17372.7i	0.0914210	−	1.57746i
$496$			194.139i			0.0175748i
$497$	−4557.74	+	1836.93i	−0.411353	+	0.165790i
$498$	8010.98	+	8010.98i	0.720845	+	0.720845i
$499$		−	19064.3i		−	1.71029i	−0.518390	−	0.855144i	$-0.673469\pi$
$499$		−	19064.3i		−	1.71029i	0.518390	−	0.855144i	$-0.326531\pi$
$500$	−1093.17	+	6231.15i	−0.0977761	+	0.557331i
$501$	−29274.8			−2.61058
$502$	−1108.93	−	1108.93i	−0.0985933	−	0.0985933i
$503$	−8758.73	+	8758.73i	−0.776407	+	0.776407i	−0.979218	−	0.202811i	$-0.934992\pi$
$503$	−8758.73	+	8758.73i	−0.776407	+	0.776407i	0.202811	+	0.979218i	$0.434992\pi$
$504$	−10542.5	+	24777.9i	−0.931745	+	2.18987i
$505$	−589.963	+	10179.8i	−0.0519862	+	0.897019i
$506$	1245.79			0.109451
$507$	−13643.6	−	13643.6i	−1.19513	−	1.19513i
$508$	−9.79667	−	9.79667i	−0.000855624	−	0.000855624i
$509$	−527.195			−0.0459087			−0.0229543	−	0.999737i	$-0.507307\pi$
$509$	−527.195			−0.0459087			−0.0229543	+	0.999737i	$0.507307\pi$
$510$	−1507.05	+	1341.94i	−0.130850	+	0.116514i
$511$	−6245.67	+	14679.1i	−0.540690	+	1.27078i
$512$	−1856.58	+	1856.58i	−0.160254	+	0.160254i
$513$	20058.3	+	20058.3i	1.72631	+	1.72631i
$514$	6383.18			0.547763
$515$	7020.39	−	6251.24i	0.600690	−	0.534878i
$516$			13419.9i			1.14492i
$517$	−5747.53	−	5747.53i	−0.488929	−	0.488929i
$518$	−988.097	−	2451.63i	−0.0838118	−	0.207951i
$519$		−	7261.07i		−	0.614115i
$520$	3243.48	+	187.974i	0.273531	+	0.0158523i
$521$			9334.16i			0.784908i	0.919772	+	0.392454i	$0.128374\pi$
$521$			9334.16i			0.784908i	−0.919772	+	0.392454i	$0.871626\pi$
$522$	−13337.6	+	13337.6i	−1.11834	+	1.11834i
$523$	2029.57	−	2029.57i	0.169688	−	0.169688i	−0.617154	−	0.786842i	$-0.711715\pi$
$523$	2029.57	−	2029.57i	0.169688	−	0.169688i	0.786842	+	0.617154i	$0.211715\pi$
$524$	−9038.57			−0.753534
$525$	10831.9	−	19003.9i	0.900465	−	1.57981i
$526$	−9153.15			−0.758738
$527$	−192.886	+	192.886i	−0.0159435	+	0.0159435i
$528$	−1218.04	+	1218.04i	−0.100395	+	0.100395i
$529$		−	11451.6i		−	0.941201i
$530$	4535.40	+	262.846i	0.371708	+	0.0215421i
$531$			42707.6i			3.49031i
$532$	−2666.93	−	6617.09i	−0.217342	−	0.539262i
$533$	1206.49	+	1206.49i	0.0980469	+	0.0980469i
$534$		−	3684.49i		−	0.298583i
$535$	−5143.05	+	4579.58i	−0.415614	+	0.370079i
$536$	19899.1			1.60357
$537$	21499.1	+	21499.1i	1.72766	+	1.72766i
$538$	−4172.37	+	4172.37i	−0.334357	+	0.334357i
$539$	6176.47	−	5944.26i	0.493580	−	0.475023i
$540$	−12599.5	+	11219.1i	−1.00407	+	0.894065i
$541$	−24171.1			−1.92088			−0.960439	−	0.278491i	$-0.910166\pi$
$541$	−24171.1			−1.92088			−0.960439	+	0.278491i	$0.910166\pi$
$542$	−7661.21	−	7661.21i	−0.607153	−	0.607153i
$543$	11049.5	+	11049.5i	0.873257	+	0.873257i
$544$	−1774.93			−0.139888
$545$	−661.900	+	11421.0i	−0.0520232	+	0.897658i
$546$	−3735.40	−	1589.34i	−0.292784	−	0.124574i
$547$	5768.43	−	5768.43i	0.450896	−	0.450896i	−0.444756	−	0.895652i	$-0.646710\pi$
$547$	5768.43	−	5768.43i	0.450896	−	0.450896i	0.895652	+	0.444756i	$0.146710\pi$
$548$	6.16477	+	6.16477i	0.000480558	+	0.000480558i
$549$	−1475.49			−0.114703
$550$	4564.84	−	3613.69i	0.353901	−	0.280160i
$551$		−	13829.4i		−	1.06924i
$552$	−4172.00	−	4172.00i	−0.321688	−	0.321688i
$553$	−1004.71	−	2492.85i	−0.0772597	−	0.191694i
$554$			2225.79i			0.170695i
$555$	468.072	−	8076.56i	0.0357992	−	0.617713i
$556$		−	9605.72i		−	0.732686i
$557$	10847.0	−	10847.0i	0.825135	−	0.825135i	−0.161704	−	0.986839i	$-0.551699\pi$
$557$	10847.0	−	10847.0i	0.825135	−	0.825135i	0.986839	+	0.161704i	$0.0516990\pi$
$558$	2184.26	−	2184.26i	0.165711	−	0.165711i
$559$	−3905.43			−0.295495
$560$	−1431.27	+	482.631i	−0.108004	+	0.0364194i
$561$	−2420.36			−0.182153
$562$	−5994.43	+	5994.43i	−0.449928	+	0.449928i
$563$	−5379.59	+	5379.59i	−0.402705	+	0.402705i	−0.879185	−	0.476480i	$-0.841912\pi$
$563$	−5379.59	+	5379.59i	−0.402705	+	0.402705i	0.476480	+	0.879185i	$0.341912\pi$
$564$			13911.0i			1.03858i
$565$	7135.14	+	8013.04i	0.531288	+	0.596657i
$566$		−	11424.0i		−	0.848383i
$567$	25219.0	−	10164.2i	1.86790	−	0.752830i
$568$	4380.05	+	4380.05i	0.323561	+	0.323561i
$569$			2968.05i			0.218677i	0.994005	+	0.109339i	$0.0348733\pi$
$569$			2968.05i			0.218677i	−0.994005	+	0.109339i	$0.965127\pi$
$570$	−969.338	+	16725.9i	−0.0712300	+	1.22907i
$571$	7018.62			0.514396			0.257198	−	0.966359i	$-0.417201\pi$
$571$	7018.62			0.514396			0.257198	+	0.966359i	$0.417201\pi$
$572$	995.744	+	995.744i	0.0727870	+	0.0727870i
$573$	15051.6	−	15051.6i	1.09737	−	1.09737i
$574$	−4353.58	−	1852.36i	−0.316576	−	0.134697i
$575$	2075.20	+	2621.42i	0.150508	+	0.190123i
$576$	23733.9			1.71686
$577$	172.987	+	172.987i	0.0124810	+	0.0124810i	0.713320	−	0.700839i	$-0.247191\pi$
$577$	172.987	+	172.987i	0.0124810	+	0.0124810i	−0.700839	+	0.713320i	$0.747191\pi$
$578$	−6335.97	−	6335.97i	−0.455954	−	0.455954i
$579$	−29420.0			−2.11167
$580$	8211.01	+	475.864i	0.587834	+	0.0340676i
$581$	−4665.01	+	10964.1i	−0.333111	+	0.782906i
$582$	17824.9	−	17824.9i	1.26953	−	1.26953i
$583$	3853.05	+	3853.05i	0.273717	+	0.273717i
$584$	20109.0			1.42486
$585$	−5763.72	−	6472.88i	−0.407351	−	0.457471i
$586$			8444.94i			0.595319i
$587$	1167.08	+	1167.08i	0.0820620	+	0.0820620i	0.746946	−	0.664884i	$-0.231519\pi$
$587$	1167.08	+	1167.08i	0.0820620	+	0.0820620i	−0.664884	+	0.746946i	$0.731519\pi$
$588$	−14668.1	−	281.019i	−1.02875	−	0.0197092i
$589$			2264.79i			0.158436i
$590$	−10671.2	+	9502.04i	−0.744618	+	0.663038i
$591$		−	48571.9i		−	3.38068i
$592$	−395.016	+	395.016i	−0.0274241	+	0.0274241i
$593$	7315.54	−	7315.54i	0.506599	−	0.506599i	−0.406882	−	0.913481i	$-0.633384\pi$
$593$	7315.54	−	7315.54i	0.506599	−	0.506599i	0.913481	+	0.406882i	$0.133384\pi$
$594$	15525.9			1.07245
$595$	−1901.54	−	942.511i	−0.131018	−	0.0649398i
$596$	9103.98			0.625694
$597$	−33082.1	+	33082.1i	−2.26794	+	2.26794i
$598$	438.742	−	438.742i	0.0300025	−	0.0300025i
$599$			27137.0i			1.85107i	0.378668	+	0.925533i	$0.376382\pi$
$599$			27137.0i			1.85107i	−0.378668	+	0.925533i	$0.623618\pi$
$600$	−27388.8	−	3185.31i	−1.86358	−	0.216733i
$601$		−	14268.6i		−	0.968436i	−0.874947	−	0.484218i	$-0.839104\pi$
$601$		−	14268.6i		−	0.968436i	0.874947	−	0.484218i	$-0.160896\pi$
$602$	10044.3	−	4048.23i	0.680027	−	0.274076i
$603$	−37536.5	−	37536.5i	−2.53500	−	2.53500i
$604$		−	1361.02i		−	0.0916875i
$605$	−7884.62	−	456.948i	−0.529844	−	0.0307068i
$606$	−16060.3			−1.07658
$607$	16609.9	+	16609.9i	1.11067	+	1.11067i	0.993060	+	0.117606i	$0.0375221\pi$
$607$	16609.9	+	16609.9i	1.11067	+	1.11067i	0.117606	+	0.993060i	$0.462478\pi$
$608$	−10420.3	+	10420.3i	−0.695061	+	0.695061i
$609$	−26168.2	−	11134.1i	−1.74120	−	0.740846i
$610$	−328.281	−	368.673i	−0.0217897	−	0.0244707i
$611$	−4048.32			−0.268048
$612$	2043.23	+	2043.23i	0.134956	+	0.134956i
$613$	10690.3	+	10690.3i	0.704365	+	0.704365i	0.965344	−	0.260979i	$-0.0840454\pi$
$613$	10690.3	+	10690.3i	0.704365	+	0.704365i	−0.260979	+	0.965344i	$0.584045\pi$
$614$	499.493			0.0328305
$615$	−9629.86	−	10814.7i	−0.631404	−	0.709092i
$616$	−9943.10	−	4230.59i	−0.650355	−	0.276713i
$617$	−7458.41	+	7458.41i	−0.486652	+	0.486652i	−0.907248	−	0.420596i	$-0.861821\pi$
$617$	−7458.41	+	7458.41i	−0.486652	+	0.486652i	0.420596	+	0.907248i	$0.361821\pi$
$618$	10469.1	+	10469.1i	0.681439	+	0.681439i
$619$	22077.4			1.43354			0.716772	−	0.697307i	$-0.245619\pi$
$619$	22077.4			1.43354			0.716772	+	0.697307i	$0.245619\pi$
$620$	−1344.69	−	77.9306i	−0.0871032	−	0.00504801i
$621$			8915.95i			0.576143i
$622$	13015.9	+	13015.9i	0.839054	+	0.839054i
$623$	3594.15	−	1448.57i	0.231134	−	0.0931555i
$624$			857.939i			0.0550402i
$625$	15208.0	+	3585.86i	0.973310	+	0.229495i
$626$		−	9817.75i		−	0.626831i
$627$	−14209.5	+	14209.5i	−0.905058	+	0.905058i
$628$	7570.91	−	7570.91i	0.481071	−	0.481071i
$629$	−784.930			−0.0497571
$630$	21533.2	+	10673.1i	1.36175	+	0.674962i
$631$	17501.0			1.10413			0.552064	−	0.833802i	$-0.313840\pi$
$631$	17501.0			1.10413			0.552064	+	0.833802i	$0.313840\pi$
$632$	−2395.66	+	2395.66i	−0.150782	+	0.150782i
$633$	−992.085	+	992.085i	−0.0622936	+	0.0622936i
$634$		−	8049.17i		−	0.504217i
$635$	−25.5556	+	22.7558i	−0.00159708	+	0.00142210i
$636$		−	9325.69i		−	0.581427i
$637$	81.7811	−	4268.67i	0.00508679	−	0.265511i
$638$	−5352.25	−	5352.25i	−0.332128	−	0.332128i
$639$		−	16524.5i		−	1.02300i
$640$	−5019.71	−	5637.33i	−0.310033	−	0.348180i
$641$	18131.1			1.11721			0.558607	−	0.829433i	$-0.311336\pi$
$641$	18131.1			1.11721			0.558607	+	0.829433i	$0.311336\pi$
$642$	−7669.55	−	7669.55i	−0.471484	−	0.471484i
$643$	4575.87	−	4575.87i	0.280645	−	0.280645i	−0.552721	−	0.833366i	$-0.686411\pi$
$643$	4575.87	−	4575.87i	0.280645	−	0.280645i	0.833366	+	0.552721i	$0.186411\pi$
$644$	877.928	−	2063.38i	0.0537193	−	0.126256i
$645$	33089.6	+	1917.69i	2.02000	+	0.117068i
$646$	1625.52			0.0990021
$647$	−367.147	−	367.147i	−0.0223092	−	0.0223092i	0.695864	−	0.718173i	$-0.255022\pi$
$647$	−367.147	−	367.147i	−0.0223092	−	0.0223092i	−0.718173	+	0.695864i	$0.755022\pi$
$648$	−24235.8	−	24235.8i	−1.46925	−	1.46925i
$649$	−17138.1			−1.03656
$650$	334.978	−	2880.31i	0.0202137	−	0.173808i
$651$	4285.48	+	1823.39i	0.258005	+	0.109776i
$652$	11133.1	−	11133.1i	0.668721	−	0.668721i
$653$	−6356.95	−	6356.95i	−0.380960	−	0.380960i	0.490488	−	0.871448i	$-0.336819\pi$
$653$	−6356.95	−	6356.95i	−0.380960	−	0.380960i	−0.871448	+	0.490488i	$0.836819\pi$
$654$	−18018.6			−1.07735
$655$	−1291.60	+	22286.5i	−0.0770487	+	1.32947i
$656$			999.922i			0.0595128i
$657$	−37932.4	−	37932.4i	−2.25249	−	2.25249i
$658$	10411.8	−	4196.35i	0.616863	−	0.248618i
$659$			14558.0i			0.860546i	0.902699	+	0.430273i	$0.141583\pi$
$659$			14558.0i			0.860546i	−0.902699	+	0.430273i	$0.858417\pi$
$660$	−7947.73	−	8925.62i	−0.468735	−	0.526408i
$661$			22883.5i			1.34655i	0.739394	+	0.673273i	$0.235112\pi$
$661$			22883.5i			1.34655i	−0.739394	+	0.673273i	$0.764888\pi$
$662$	9071.13	−	9071.13i	0.532567	−	0.532567i
$663$	−852.400	+	852.400i	−0.0499313	+	0.0499313i
$664$	15019.8			0.877834
$665$	−16696.9	+	5630.28i	−0.973650	+	0.328320i
$666$	8888.63			0.517158
$667$	3073.60	−	3073.60i	0.178426	−	0.178426i
$668$	−9917.22	+	9917.22i	−0.574415	+	0.574415i
$669$		−	42385.6i		−	2.44951i
$670$	1027.57	−	17730.6i	0.0592512	−	1.02238i
$671$		−	592.097i		−	0.0340651i
$672$	11328.0	+	28106.8i	0.650281	+	1.61346i
$673$	−19499.1	−	19499.1i	−1.11684	−	1.11684i	−0.992202	−	0.124641i	$-0.960222\pi$
$673$	−19499.1	−	19499.1i	−1.11684	−	1.11684i	−0.124641	−	0.992202i	$-0.539778\pi$
$674$			1335.81i			0.0763406i
$675$	25862.6	+	32669.9i	1.47475	+	1.86291i
$676$	−9243.89			−0.525938
$677$	2638.87	+	2638.87i	0.149808	+	0.149808i	0.778032	−	0.628224i	$-0.216218\pi$
$677$	2638.87	+	2638.87i	0.149808	+	0.149808i	−0.628224	+	0.778032i	$0.716218\pi$
$678$	−11949.4	+	11949.4i	−0.676865	+	0.676865i
$679$	24395.8	+	10379.9i	1.37883	+	0.586665i
$680$	−154.784	+	2670.79i	−0.00872896	+	0.150618i
$681$	39486.5			2.22192
$682$	876.519	+	876.519i	0.0492136	+	0.0492136i
$683$	11485.3	+	11485.3i	0.643447	+	0.643447i	0.951401	−	0.307954i	$-0.0996443\pi$
$683$	11485.3	+	11485.3i	0.643447	+	0.643447i	−0.307954	+	0.951401i	$0.599644\pi$
$684$	23990.9			1.34110
$685$	16.0814	−	14.3196i	0.000896993	−	0.000798719i
$686$	4214.42	+	11063.3i	0.234559	+	0.615743i
$687$	−38657.2	+	38657.2i	−2.14682	+	2.14682i
$688$	−1618.38	−	1618.38i	−0.0896803	−	0.0896803i
$689$	2713.93			0.150062
$690$	−3932.78	+	3501.91i	−0.216983	+	0.193211i
$691$		−	13142.5i		−	0.723540i	−0.932267	−	0.361770i	$-0.882173\pi$
$691$		−	13142.5i		−	0.723540i	0.932267	−	0.361770i	$-0.117827\pi$
$692$	−2459.78	−	2459.78i	−0.135126	−	0.135126i
$693$	10775.7	+	26736.4i	0.590672	+	1.46556i
$694$			3843.43i			0.210223i
$695$	−23684.9	−	1372.64i	−1.29269	−	0.0749169i
$696$			35848.0i			1.95232i
$697$	−993.466	+	993.466i	−0.0539888	+	0.0539888i
$698$	−13619.0	+	13619.0i	−0.738517	+	0.738517i
$699$	−41329.6			−2.23638
$700$	−2768.37	−	10107.3i	−0.149478	−	0.545742i
$701$	−13075.3			−0.704488			−0.352244	−	0.935908i	$-0.614581\pi$
$701$	−13075.3			−0.704488			−0.352244	+	0.935908i	$0.614581\pi$
$702$	5467.91	−	5467.91i	0.293978	−	0.293978i
$703$	−4608.17	+	4608.17i	−0.247227	+	0.247227i
$704$			9524.15i			0.509879i
$705$	34300.3	+	1987.86i	1.83238	+	0.106194i
$706$		−	14586.7i		−	0.777588i
$707$	−6314.19	−	15666.6i	−0.335884	−	0.833383i
$708$	20740.0	+	20740.0i	1.10093	+	1.10093i
$709$		−	6813.33i		−	0.360903i	−0.983584	−	0.180451i	$-0.942244\pi$
$709$		−	6813.33i		−	0.360903i	0.983584	−	0.180451i	$-0.0577558\pi$
$710$	4128.90	−	3676.54i	0.218246	−	0.194335i
$711$	9038.07			0.476729
$712$	−3454.03	−	3454.03i	−0.181805	−	0.181805i
$713$	−503.352	+	503.352i	−0.0264385	+	0.0264385i
$714$	1308.71	−	3075.85i	0.0685957	−	0.161220i
$715$	2597.50	−	2312.92i	0.135862	−	0.120977i
$716$	14566.2			0.760286
$717$	11379.0	+	11379.0i	0.592689	+	0.592689i
$718$	−38.1200	−	38.1200i	−0.00198137	−	0.00198137i
$719$	−11781.0			−0.611066			−0.305533	−	0.952182i	$-0.598835\pi$
$719$	−11781.0			−0.611066			−0.305533	+	0.952182i	$0.598835\pi$
$720$	293.872	−	5070.75i	0.0152111	−	0.262466i
$721$	−6096.45	+	14328.4i	−0.314901	+	0.740108i
$722$	504.266	−	504.266i	0.0259929	−	0.0259929i
$723$	−13482.7	−	13482.7i	−0.693539	−	0.693539i
$724$	7486.32			0.384291
$725$	2346.68	−	20177.9i	0.120212	−	1.03364i
$726$		−	12439.3i		−	0.635904i
$727$	11932.2	+	11932.2i	0.608722	+	0.608722i	0.942612	−	0.333890i	$-0.108361\pi$
$727$	11932.2	+	11932.2i	0.608722	+	0.608722i	−0.333890	+	0.942612i	$0.608361\pi$
$728$	−4991.68	+	2011.83i	−0.254126	+	0.102422i
$729$			6392.84i			0.324790i
$730$	1038.40	−	17917.6i	0.0526480	−	0.908438i
$731$		−	3215.86i		−	0.162712i
$732$	−716.538	+	716.538i	−0.0361804	+	0.0361804i
$733$	−23699.4	+	23699.4i	−1.19421	+	1.19421i	−0.218341	+	0.975872i	$0.570065\pi$
$733$	−23699.4	+	23699.4i	−1.19421	+	1.19421i	−0.975872	+	0.218341i	$0.929935\pi$
$734$	−1853.12			−0.0931881
$735$	−2788.96	+	36127.1i	−0.139962	+	1.81302i
$736$	−4631.83			−0.231972
$737$	15063.0	−	15063.0i	0.752854	−	0.752854i
$738$	11250.1	−	11250.1i	0.561141	−	0.561141i
$739$		−	25417.1i		−	1.26520i	−0.774479	−	0.632599i	$-0.781988\pi$
$739$		−	25417.1i		−	1.26520i	0.774479	−	0.632599i	$-0.218012\pi$
$740$	−2577.48	−	2894.61i	−0.128040	−	0.143794i
$741$			10008.6i			0.496185i
$742$	−6979.93	+	2813.16i	−0.345339	+	0.139184i
$743$	6699.21	+	6699.21i	0.330781	+	0.330781i	0.852883	−	0.522102i	$-0.174852\pi$
$743$	6699.21	+	6699.21i	0.330781	+	0.330781i	−0.522102	+	0.852883i	$0.674852\pi$
$744$		−	5870.70i		−	0.289288i
$745$	1300.94	−	22447.7i	0.0639771	−	1.10392i
$746$	6517.18			0.319854
$747$	−28332.4	−	28332.4i	−1.38772	−	1.38772i
$748$	−819.929	+	819.929i	−0.0400796	+	0.0400796i
$749$	4466.19	−	10496.8i	0.217878	−	0.512077i
$750$	−4252.50	+	24239.6i	−0.207039	+	1.18014i
$751$	−13367.6			−0.649521			−0.324761	−	0.945796i	$-0.605284\pi$
$751$	−13367.6			−0.649521			−0.324761	+	0.945796i	$0.605284\pi$
$752$	−1677.59	−	1677.59i	−0.0813504	−	0.0813504i
$753$	5622.24	+	5622.24i	0.272093	+	0.272093i
$754$	−3769.90			−0.182085
$755$	−3355.88	−	194.488i	−0.161766	−	0.00937503i
$756$	10941.3	−	25715.3i	0.526366	−	1.23711i
$757$	6207.76	−	6207.76i	0.298051	−	0.298051i	−0.542199	−	0.840250i	$-0.682408\pi$
$757$	6207.76	−	6207.76i	0.298051	−	0.298051i	0.840250	+	0.542199i	$0.182408\pi$
$758$	6208.51	+	6208.51i	0.297498	+	0.297498i
$759$	−6316.14			−0.302057
$760$	14771.0	+	16588.4i	0.705000	+	0.791742i
$761$		−	9524.31i		−	0.453687i	−0.973931	−	0.226844i	$-0.927159\pi$
$761$		−	9524.31i		−	0.453687i	0.973931	−	0.226844i	$-0.0728406\pi$
$762$	−38.1097	−	38.1097i	−0.00181177	−	0.00181177i
$763$	−7084.11	−	17576.8i	−0.336123	−	0.833977i
$764$		−	10197.9i		−	0.482914i
$765$	5329.98	−	4746.03i	0.251903	−	0.224305i
$766$			18305.5i			0.863454i
$767$	−6035.69	+	6035.69i	−0.284141	+	0.284141i
$768$	28776.0	−	28776.0i	1.35204	−	1.35204i
$769$	−4045.49			−0.189706			−0.0948532	−	0.995491i	$-0.530238\pi$
$769$	−4045.49			−0.189706			−0.0948532	+	0.995491i	$0.530238\pi$
$770$	−4283.00	+	8641.06i	−0.200453	+	0.404419i
$771$	−32362.6			−1.51169
$772$	−9966.43	+	9966.43i	−0.464637	+	0.464637i
$773$	3452.33	−	3452.33i	0.160636	−	0.160636i	−0.622213	−	0.782848i	$-0.713766\pi$
$773$	3452.33	−	3452.33i	0.160636	−	0.160636i	0.782848	+	0.622213i	$0.213766\pi$
$774$			36416.7i			1.69118i
$775$	−384.308	+	3304.47i	−0.0178126	+	0.153161i
$776$		−	33420.0i		−	1.54601i
$777$	5009.63	+	12429.7i	0.231299	+	0.573892i
$778$	4632.95	+	4632.95i	0.213495	+	0.213495i
$779$			11664.9i			0.536506i
$780$	−5942.44	−	344.391i	−0.272787	−	0.0158092i
$781$	6631.11			0.303815
$782$	361.274	+	361.274i	0.0165206	+	0.0165206i
$783$	38305.3	−	38305.3i	1.74830	−	1.74830i
$784$	1802.79	−	1735.01i	0.0821242	−	0.0790366i
$785$	−17585.8	−	19749.5i	−0.799570	−	0.897949i
$786$	−35160.7			−1.59560
$787$	24964.1	+	24964.1i	1.13072	+	1.13072i	0.990058	+	0.140657i	$0.0449214\pi$
$787$	24964.1	+	24964.1i	1.13072	+	1.13072i	0.140657	+	0.990058i	$0.455079\pi$
$788$	−16454.4	−	16454.4i	−0.743862	−	0.743862i
$789$	46406.3			2.09393
$790$	2010.88	+	2258.30i	0.0905620	+	0.101705i
$791$	−16354.4	−	6958.47i	−0.735140	−	0.312787i
$792$	25694.0	−	25694.0i	1.15277	−	1.15277i
$793$	−208.524	−	208.524i	−0.00933785	−	0.00933785i
$794$	−7901.59			−0.353170
$795$	−22994.4	−	1332.63i	−1.02582	−	0.0594508i
$796$			22414.0i			0.998043i
$797$	3736.59	+	3736.59i	0.166069	+	0.166069i	0.785249	−	0.619180i	$-0.212535\pi$
$797$	3736.59	+	3736.59i	0.166069	+	0.166069i	−0.619180	+	0.785249i	$0.712535\pi$
$798$	−10374.5	−	25740.9i	−0.460218	−	1.14188i
$799$		−	3333.52i		−	0.147599i
$800$	−16972.0	+	13435.6i	−0.750063	+	0.593775i
$801$			13030.9i			0.574813i
$802$	11909.3	−	11909.3i	0.524356	−	0.524356i
$803$	15221.9	−	15221.9i	0.668952	−	0.668952i
$804$	−36457.6			−1.59920
$805$	−4962.24	−	2459.56i	−0.217262	−	0.107687i
$806$	617.384			0.0269807
$807$	21153.8	−	21153.8i	0.922739	−	0.922739i
$808$	−15055.8	+	15055.8i	−0.655521	+	0.655521i
$809$			29612.2i			1.28691i	0.765484	+	0.643455i	$0.222500\pi$
$809$			29612.2i			1.28691i	−0.765484	+	0.643455i	$0.777500\pi$
$810$	−22846.1	+	20343.1i	−0.991027	+	0.882450i
$811$		−	13678.2i		−	0.592241i	−0.955151	−	0.296121i	$-0.904307\pi$
$811$		−	13678.2i		−	0.592241i	0.955151	−	0.296121i	$-0.0956931\pi$
$812$	−12636.7	+	5093.03i	−0.546133	+	0.220111i
$813$	38842.2	+	38842.2i	1.67559	+	1.67559i
$814$			3566.91i			0.153588i
$815$	−25860.0	−	29041.8i	−1.11146	−	1.24821i
$816$	−706.455			−0.0303075
$817$	−18879.7	−	18879.7i	−0.808465	−	0.808465i
$818$	−14462.7	+	14462.7i	−0.618184	+	0.618184i
$819$	13211.0	+	5621.01i	0.563649	+	0.239822i
$820$	−6925.87	−	401.385i	−0.294954	−	0.0170939i
$821$	−7174.41			−0.304980			−0.152490	−	0.988305i	$-0.548729\pi$
$821$	−7174.41			−0.304980			−0.152490	+	0.988305i	$0.548729\pi$
$822$	23.9814	+	23.9814i	0.00101757	+	0.00101757i
$823$	2598.49	+	2598.49i	0.110058	+	0.110058i	0.759991	−	0.649933i	$-0.225203\pi$
$823$	2598.49	+	2598.49i	0.110058	+	0.110058i	−0.649933	+	0.759991i	$0.725203\pi$
$824$	19628.6			0.829847
$825$	−23143.7	+	18321.3i	−0.976677	+	0.773171i
$826$	9266.76	−	21779.5i	0.390353	−	0.917442i
$827$	25938.0	−	25938.0i	1.09063	−	1.09063i	0.0951702	−	0.995461i	$-0.469660\pi$
$827$	25938.0	−	25938.0i	1.09063	−	1.09063i	0.995461	−	0.0951702i	$-0.0303395\pi$
$828$	5332.00	+	5332.00i	0.223792	+	0.223792i
$829$	−18263.9			−0.765176			−0.382588	−	0.923919i	$-0.624967\pi$
$829$	−18263.9			−0.765176			−0.382588	+	0.923919i	$0.624967\pi$
$830$	775.603	−	13383.0i	0.0324356	−	0.559675i
$831$		−	11284.7i		−	0.471074i
$832$	3354.21	+	3354.21i	0.139767	+	0.139767i
$833$	3514.96	+	67.3412i	0.146202	+	0.00280100i
$834$		−	37366.9i		−	1.55145i
$835$	23035.8	+	25870.1i	0.954714	+	1.07218i
$836$			9627.29i			0.398286i
$837$	−6273.12	+	6273.12i	−0.259057	+	0.259057i
$838$	−8083.73	+	8083.73i	−0.333231	+	0.333231i
$839$	24855.3			1.02277			0.511383	−	0.859353i	$-0.329134\pi$
$839$	24855.3			1.02277			0.511383	+	0.859353i	$0.329134\pi$
$840$	43281.0	−	14594.6i	1.77778	−	0.599478i
$841$	−2020.98			−0.0828645
$842$	3417.24	−	3417.24i	0.139864	−	0.139864i
$843$	30391.6	−	30391.6i	1.24169	−	1.24169i
$844$			672.164i			0.0274133i
$845$	−1320.94	+	22792.7i	−0.0537771	+	0.927921i
$846$			37749.1i			1.53409i
$847$	12134.3	−	4890.58i	0.492256	−	0.198397i
$848$	1124.63	+	1124.63i	0.0455424	+	0.0455424i
$849$			57919.2i			2.34132i
$850$	2371.74	+	275.832i	0.0957059	+	0.0111305i
$851$	−2048.34			−0.0825104
$852$	−8024.77	−	8024.77i	−0.322681	−	0.322681i
$853$	−10701.3	+	10701.3i	−0.429551	+	0.429551i	−0.888475	−	0.458924i	$-0.848235\pi$
$853$	−10701.3	+	10701.3i	−0.429551	+	0.429551i	0.458924	+	0.888475i	$0.348235\pi$
$854$	752.451	+	320.153i	0.0301503	+	0.0128284i
$855$	3428.26	−	59154.4i	0.137127	−	2.36613i
$856$	−14379.7			−0.574166
$857$	16707.0	+	16707.0i	0.665927	+	0.665927i	0.956771	−	0.290844i	$-0.0939359\pi$
$857$	16707.0	+	16707.0i	0.665927	+	0.665927i	−0.290844	+	0.956771i	$0.593936\pi$
$858$	3873.51	+	3873.51i	0.154125	+	0.154125i
$859$	−26662.8			−1.05905			−0.529524	−	0.848295i	$-0.677630\pi$
$859$	−26662.8			−1.05905			−0.529524	+	0.848295i	$0.677630\pi$
$860$	11859.2	−	10559.9i	0.470227	−	0.418709i
$861$	22072.5	+	9391.42i	0.873670	+	0.371729i
$862$	−13718.1	+	13718.1i	−0.542041	+	0.542041i
$863$	26487.1	+	26487.1i	1.04477	+	1.04477i	0.998950	+	0.0458157i	$0.0145887\pi$
$863$	26487.1	+	26487.1i	1.04477	+	1.04477i	0.0458157	+	0.998950i	$0.485411\pi$
$864$	−57725.0			−2.27297
$865$	−6416.60	+	5713.60i	−0.252221	+	0.224588i
$866$			14628.6i			0.574018i
$867$	32123.2	+	32123.2i	1.25832	+	1.25832i
$868$	2069.46	−	834.067i	0.0809240	−	0.0326153i
$869$			3626.88i			0.141581i
$870$	31941.4	+	1851.14i	1.24473	+	0.0721376i
$871$		−	10609.8i		−	0.412742i
$872$	−16891.6	+	16891.6i	−0.655988	+	0.655988i
$873$	−63041.4	+	63041.4i	−2.44402	+	2.44402i
$874$	4241.95			0.164172
$875$	−25317.2	+	5381.67i	−0.978145	+	0.207924i
$876$	−36842.1			−1.42098
$877$	−21275.9	+	21275.9i	−0.819199	+	0.819199i	−0.985992	−	0.166793i	$-0.946659\pi$
$877$	−21275.9	+	21275.9i	−0.819199	+	0.819199i	0.166793	+	0.985992i	$0.446659\pi$
$878$	6925.59	−	6925.59i	0.266204	−	0.266204i
$879$		−	42815.6i		−	1.64293i
$880$	2034.84	+	117.928i	0.0779482	+	0.00451744i
$881$			30534.2i			1.16768i	0.811870	+	0.583839i	$0.198450\pi$
$881$			30534.2i			1.16768i	−0.811870	+	0.583839i	$0.801550\pi$
$882$	−39803.7	−	762.578i	−1.51957	−	0.0291126i
$883$	5071.07	+	5071.07i	0.193268	+	0.193268i	0.797106	−	0.603839i	$-0.206363\pi$
$883$	5071.07	+	5071.07i	0.193268	+	0.193268i	−0.603839	+	0.797106i	$0.706363\pi$
$884$			577.524i			0.0219731i
$885$	54102.5	−	48175.1i	2.05496	−	1.82982i
$886$	−8035.41			−0.304690
$887$	22739.1	+	22739.1i	0.860770	+	0.860770i	0.991428	−	0.130658i	$-0.0417088\pi$
$887$	22739.1	+	22739.1i	0.860770	+	0.860770i	−0.130658	+	0.991428i	$0.541709\pi$
$888$	11945.1	−	11945.1i	0.451411	−	0.451411i
$889$	22.1923	−	52.1583i	0.000837240	−	0.00196775i
$890$	−3255.98	+	2899.26i	−0.122630	+	0.109195i
$891$	−36691.4			−1.37958
$892$	−14358.7	−	14358.7i	−0.538974	−	0.538974i
$893$	−19570.5	−	19570.5i	−0.733371	−	0.733371i
$894$	35415.1			1.32490
$895$	2081.49	−	35916.0i	0.0777391	−	1.34138i
$896$	11505.6	+	4895.42i	0.428991	+	0.182527i
$897$	−2224.41	+	2224.41i	−0.0827993	+	0.0827993i
$898$	8215.99	+	8215.99i	0.305313	+	0.305313i
$899$	4325.07			0.160455
$900$	35004.2	+	4070.96i	1.29645	+	0.150776i
$901$			2234.74i			0.0826303i
$902$	4514.55	+	4514.55i	0.166650	+	0.166650i
$903$	−50924.5	+	20524.4i	−1.87670	+	0.756379i
$904$			22404.0i			0.824276i
$905$	1069.78	−	18459.1i	0.0392937	−	0.678011i
$906$		−	5294.47i		−	0.194147i
$907$	6730.54	−	6730.54i	0.246399	−	0.246399i	−0.573092	−	0.819491i	$-0.694256\pi$
$907$	6730.54	−	6730.54i	0.246399	−	0.246399i	0.819491	+	0.573092i	$0.194256\pi$
$908$	13376.6	−	13376.6i	0.488895	−	0.488895i
$909$	56800.6			2.07256
$910$	1534.82	+	4551.59i	0.0559107	+	0.165806i
$911$	22469.7			0.817185			0.408593	−	0.912717i	$-0.366020\pi$
$911$	22469.7			0.817185			0.408593	+	0.912717i	$0.366020\pi$
$912$	−4147.46	+	4147.46i	−0.150588	+	0.150588i
$913$	11369.5	−	11369.5i	0.412131	−	0.412131i
$914$			7744.30i			0.280261i
$915$	1664.38	+	1869.16i	0.0601341	+	0.0675330i
$916$			26191.3i			0.944742i
$917$	−13823.6	−	34298.6i	−0.497813	−	1.23516i
$918$	4502.45	+	4502.45i	0.161877	+	0.161877i
$919$		−	5854.64i		−	0.210149i	−0.994464	−	0.105074i	$-0.966492\pi$
$919$		−	5854.64i		−	0.210149i	0.994464	−	0.105074i	$-0.0335081\pi$
$920$	−403.922	+	6969.66i	−0.0144749	+	0.249764i
$921$	−2532.42			−0.0906037
$922$	−15767.7	−	15767.7i	−0.563211	−	0.563211i
$923$	2335.34	−	2335.34i	0.0832813	−	0.0832813i
$924$	18216.9	+	7750.95i	0.648586	+	0.275960i
$925$	−7505.57	+	5941.66i	−0.266791	+	0.211201i
$926$	12893.6			0.457569
$927$	−37026.1	−	37026.1i	−1.31186	−	1.31186i
$928$	19899.6	+	19899.6i	0.703917	+	0.703917i
$929$	30810.8			1.08813			0.544064	−	0.839044i	$-0.316885\pi$
$929$	30810.8			1.08813			0.544064	+	0.839044i	$0.316885\pi$
$930$	−5230.93	−	303.155i	−0.184440	−	0.0106891i
$931$	21031.0	−	20240.3i	0.740347	−	0.712513i
$932$	−14000.9	+	14000.9i	−0.492077	+	0.492077i
$933$	−65990.5	−	65990.5i	−2.31558	−	2.31558i
$934$	−17925.4			−0.627985
$935$	1904.54	+	2138.87i	0.0666149	+	0.0748112i
$936$		−	18097.8i		−	0.631992i
$937$	−35445.3	−	35445.3i	−1.23580	−	1.23580i	−0.961701	−	0.274101i	$-0.911620\pi$
$937$	−35445.3	−	35445.3i	−1.23580	−	1.23580i	−0.274101	−	0.961701i	$-0.588380\pi$
$938$	10997.7	+	27287.2i	0.382823	+	0.949848i
$939$			49775.8i			1.72990i
$940$	12293.1	−	10946.3i	0.426550	−	0.379818i
$941$		−	17873.9i		−	0.619207i	−0.950866	−	0.309604i	$-0.899804\pi$
$941$		−	17873.9i		−	0.619207i	0.950866	−	0.309604i	$-0.100196\pi$
$942$	29451.4	−	29451.4i	1.01866	−	1.01866i
$943$	−2592.53	+	2592.53i	−0.0895276	+	0.0895276i
$944$	−5002.29			−0.172469
$945$	−61842.8	−	30652.8i	−2.12883	−	1.05517i
$946$	−14613.6			−0.502252
$947$	33334.2	−	33334.2i	1.14384	−	1.14384i	0.156097	−	0.987742i	$-0.450109\pi$
$947$	33334.2	−	33334.2i	1.14384	−	1.14384i	0.987742	−	0.156097i	$-0.0498913\pi$
$948$	4389.14	−	4389.14i	0.150372	−	0.150372i
$949$		−	10721.7i		−	0.366744i
$950$	15543.4	−	12304.7i	0.530836	−	0.420228i
$951$			40809.1i			1.39151i
$952$	−1656.60	−	4110.31i	−0.0563980	−	0.139933i
$953$	−9789.22	−	9789.22i	−0.332743	−	0.332743i	0.520884	−	0.853627i	$-0.325602\pi$
$953$	−9789.22	−	9789.22i	−0.332743	−	0.332743i	−0.853627	+	0.520884i	$0.825602\pi$
$954$		−	25306.4i		−	0.858830i
$955$	−25145.0	−	1457.26i	−0.852013	−	0.0493779i
$956$	7709.61			0.260823
$957$	27135.8	+	27135.8i	0.916589	+	0.916589i
$958$	9767.04	−	9767.04i	0.329393	−	0.329393i
$959$	−13.9650	+	32.8218i	−0.000470233	+	0.00110518i
$960$	−26772.3	−	30066.3i	−0.900075	−	1.01082i
$961$	29082.7			0.976224
$962$	1256.19	+	1256.19i	0.0421011	+	0.0421011i
$963$	27124.9	+	27124.9i	0.907671	+	0.907671i
$964$	−9134.92			−0.305203
$965$	23150.1	+	25998.5i	0.772256	+	0.867275i
$966$	3415.20	−	8026.69i	0.113750	−	0.267344i
$967$	−15607.2	+	15607.2i	−0.519021	+	0.519021i	−0.917275	−	0.398254i	$-0.869616\pi$
$967$	−15607.2	+	15607.2i	−0.519021	+	0.519021i	0.398254	+	0.917275i	$0.369616\pi$
$968$	−11661.3	−	11661.3i	−0.387197	−	0.387197i
$969$	−8241.37			−0.273221
$970$	−29778.0	−	1725.76i	−0.985683	−	0.0571247i
$971$		−	25905.8i		−	0.856186i	−0.903735	−	0.428093i	$-0.859186\pi$
$971$		−	25905.8i		−	0.856186i	0.903735	−	0.428093i	$-0.140814\pi$
$972$	15594.1	+	15594.1i	0.514590	+	0.514590i
$973$	36450.7	−	14691.0i	1.20098	−	0.484040i
$974$			6618.87i			0.217744i
$975$	−1698.33	+	14603.1i	−0.0557848	+	0.479665i
$976$		−	172.822i		−	0.00566792i
$977$	−15017.6	+	15017.6i	−0.491766	+	0.491766i	−0.908862	−	0.417097i	$-0.863048\pi$
$977$	−15017.6	+	15017.6i	−0.491766	+	0.491766i	0.417097	+	0.908862i	$0.363048\pi$
$978$	43308.5	−	43308.5i	1.41601	−	1.41601i
$979$	−5229.18			−0.170710
$980$	11293.7	+	13183.3i	0.368128	+	0.429721i
$981$	63726.5			2.07404
$982$	4384.23	−	4384.23i	0.142471	−	0.142471i
$983$	−11521.7	+	11521.7i	−0.373841	+	0.373841i	−0.868874	−	0.495033i	$-0.835156\pi$
$983$	−11521.7	+	11521.7i	−0.373841	+	0.373841i	0.495033	+	0.868874i	$0.335156\pi$
$984$		−	30237.3i		−	0.979603i
$985$	−42923.0	+	38220.4i	−1.38847	+	1.23635i
$986$		−	3104.26i		−	0.100264i
$987$	−52787.8	+	21275.4i	−1.70239	+	0.686123i
$988$	3390.53	+	3390.53i	0.109177	+	0.109177i
$989$		−	8392.05i		−	0.269820i
$990$	−21567.1	−	24220.7i	−0.692372	−	0.777562i
$991$	−57443.2			−1.84132			−0.920658	−	0.390369i	$-0.872347\pi$
$991$	−57443.2			−1.84132			−0.920658	+	0.390369i	$0.872347\pi$
$992$	−3258.88	−	3258.88i	−0.104304	−	0.104304i
$993$	−45990.4	+	45990.4i	−1.46975	+	1.46975i
$994$	−3585.51	+	8426.97i	−0.114412	+	0.268901i
$995$	55266.2	+	3202.92i	1.76086	+	0.102050i
$996$	−27518.1			−0.875445
$997$	15928.4	+	15928.4i	0.505975	+	0.505975i	0.913289	−	0.407313i	$-0.133534\pi$
$997$	15928.4	+	15928.4i	0.505975	+	0.505975i	−0.407313	+	0.913289i	$0.633534\pi$
$998$	−25123.1	−	25123.1i	−0.796852	−	0.796852i
$999$	−25527.9			−0.808475

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.4.f.b.13.5	✓	16
5.2	odd	4	inner	35.4.f.b.27.6	yes	16
5.3	odd	4		175.4.f.g.132.3		16
5.4	even	2		175.4.f.g.118.4		16
7.2	even	3		245.4.l.b.178.3		32
7.3	odd	6		245.4.l.b.68.5		32
7.4	even	3		245.4.l.b.68.6		32
7.5	odd	6		245.4.l.b.178.4		32
7.6	odd	2	inner	35.4.f.b.13.6	yes	16
35.2	odd	12		245.4.l.b.227.5		32
35.12	even	12		245.4.l.b.227.6		32
35.13	even	4		175.4.f.g.132.4		16
35.17	even	12		245.4.l.b.117.3		32
35.27	even	4	inner	35.4.f.b.27.5	yes	16
35.32	odd	12		245.4.l.b.117.4		32
35.34	odd	2		175.4.f.g.118.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.f.b.13.5	✓	16	1.1	even	1	trivial
35.4.f.b.13.6	yes	16	7.6	odd	2	inner
35.4.f.b.27.5	yes	16	35.27	even	4	inner
35.4.f.b.27.6	yes	16	5.2	odd	4	inner
175.4.f.g.118.3		16	35.34	odd	2
175.4.f.g.118.4		16	5.4	even	2
175.4.f.g.132.3		16	5.3	odd	4
175.4.f.g.132.4		16	35.13	even	4
245.4.l.b.68.5		32	7.3	odd	6
245.4.l.b.68.6		32	7.4	even	3
245.4.l.b.117.3		32	35.17	even	12
245.4.l.b.117.4		32	35.32	odd	12
245.4.l.b.178.3		32	7.2	even	3
245.4.l.b.178.4		32	7.5	odd	6
245.4.l.b.227.5		32	35.2	odd	12
245.4.l.b.227.6		32	35.12	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	35.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31781 - 1.31781i) q^{2} +(-6.68128 + 6.68128i) q^{3} +4.52674i q^{4} +(11.1616 + 0.646864i) q^{5} +17.6093i q^{6} +(-17.1776 + 6.92319i) q^{7} +(16.5079 + 16.5079i) q^{8} -62.2789i q^{9} +O(q^{10})\)	\(q+(1.31781 - 1.31781i) q^{2} +(-6.68128 + 6.68128i) q^{3} +4.52674i q^{4} +(11.1616 + 0.646864i) q^{5} +17.6093i q^{6} +(-17.1776 + 6.92319i) q^{7} +(16.5079 + 16.5079i) q^{8} -62.2789i q^{9} +(15.5614 - 13.8565i) q^{10} +24.9919 q^{11} +(-30.2444 - 30.2444i) q^{12} +(8.80162 - 8.80162i) q^{13} +(-13.5134 + 31.7603i) q^{14} +(-78.8957 + 70.2519i) q^{15} +7.29465 q^{16} +(7.24755 + 7.24755i) q^{17} +(-82.0719 - 82.0719i) q^{18} +85.0979 q^{19} +(-2.92819 + 50.5258i) q^{20} +(68.5125 - 161.024i) q^{21} +(32.9346 - 32.9346i) q^{22} +(18.9131 + 18.9131i) q^{23} -220.588 q^{24} +(124.163 + 14.4401i) q^{25} -23.1978i q^{26} +(235.708 + 235.708i) q^{27} +(-31.3395 - 77.7585i) q^{28} -162.511i q^{29} +(-11.3909 + 196.549i) q^{30} +26.6139i q^{31} +(-122.450 + 122.450i) q^{32} +(-166.978 + 166.978i) q^{33} +19.1018 q^{34} +(-196.208 + 66.1624i) q^{35} +281.921 q^{36} +(-54.1514 + 54.1514i) q^{37} +(112.143 - 112.143i) q^{38} +117.612i q^{39} +(173.576 + 194.933i) q^{40} +137.076i q^{41} +(-121.913 - 302.486i) q^{42} +(-221.858 - 221.858i) q^{43} +113.132i q^{44} +(40.2860 - 695.133i) q^{45} +49.8478 q^{46} +(-229.976 - 229.976i) q^{47} +(-48.7375 + 48.7375i) q^{48} +(247.139 - 237.847i) q^{49} +(182.653 - 144.594i) q^{50} -96.8457 q^{51} +(39.8427 + 39.8427i) q^{52} +(154.172 + 154.172i) q^{53} +621.238 q^{54} +(278.950 + 16.1664i) q^{55} +(-397.853 - 169.278i) q^{56} +(-568.563 + 568.563i) q^{57} +(-214.160 - 214.160i) q^{58} -685.748 q^{59} +(-318.012 - 357.141i) q^{60} -23.6916i q^{61} +(35.0721 + 35.0721i) q^{62} +(431.169 + 1069.80i) q^{63} +381.090i q^{64} +(103.934 - 92.5469i) q^{65} +440.091i q^{66} +(602.716 - 602.716i) q^{67} +(-32.8078 + 32.8078i) q^{68} -252.727 q^{69} +(-171.376 + 345.755i) q^{70} +265.331 q^{71} +(1028.09 - 1028.09i) q^{72} +(609.073 - 609.073i) q^{73} +142.723i q^{74} +(-926.047 + 733.090i) q^{75} +385.216i q^{76} +(-429.300 + 173.024i) q^{77} +(154.991 + 154.991i) q^{78} +145.122i q^{79} +(81.4200 + 4.71865i) q^{80} -1468.13 q^{81} +(180.641 + 180.641i) q^{82} +(454.928 - 454.928i) q^{83} +(728.914 + 310.138i) q^{84} +(76.2061 + 85.5825i) q^{85} -584.735 q^{86} +(1085.78 + 1085.78i) q^{87} +(412.563 + 412.563i) q^{88} -209.235 q^{89} +(-862.965 - 969.144i) q^{90} +(-90.2554 + 212.126i) q^{91} +(-85.6148 + 85.6148i) q^{92} +(-177.815 - 177.815i) q^{93} -606.130 q^{94} +(949.830 + 55.0468i) q^{95} -1636.25i q^{96} +(-1012.24 - 1012.24i) q^{97} +(12.2446 - 639.121i) q^{98} -1556.47i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 32 q^{7} + 176 q^{8}+O(q^{10}) \) 16 * q + 4 * q^2 + 32 * q^7 + 176 * q^8	\( 16 q + 4 q^{2} + 32 q^{7} + 176 q^{8} - 152 q^{11} - 480 q^{15} - 504 q^{16} + 288 q^{18} + 328 q^{21} + 348 q^{22} - 72 q^{23} - 160 q^{25} - 528 q^{28} + 1780 q^{30} + 432 q^{32} + 160 q^{35} + 344 q^{36} - 256 q^{37} - 1300 q^{42} - 312 q^{43} - 1856 q^{46} - 20 q^{50} + 696 q^{51} + 1768 q^{53} + 1304 q^{56} - 3920 q^{57} - 4764 q^{58} - 2000 q^{60} + 2544 q^{63} - 1000 q^{65} + 4504 q^{67} - 180 q^{70} + 6368 q^{71} + 7848 q^{72} - 3016 q^{77} + 5340 q^{78} - 3088 q^{81} - 2280 q^{85} - 9336 q^{86} - 2048 q^{88} + 1608 q^{91} - 6328 q^{92} - 3960 q^{93} + 1240 q^{95} + 3308 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 + 32 * q^7 + 176 * q^8 - 152 * q^11 - 480 * q^15 - 504 * q^16 + 288 * q^18 + 328 * q^21 + 348 * q^22 - 72 * q^23 - 160 * q^25 - 528 * q^28 + 1780 * q^30 + 432 * q^32 + 160 * q^35 + 344 * q^36 - 256 * q^37 - 1300 * q^42 - 312 * q^43 - 1856 * q^46 - 20 * q^50 + 696 * q^51 + 1768 * q^53 + 1304 * q^56 - 3920 * q^57 - 4764 * q^58 - 2000 * q^60 + 2544 * q^63 - 1000 * q^65 + 4504 * q^67 - 180 * q^70 + 6368 * q^71 + 7848 * q^72 - 3016 * q^77 + 5340 * q^78 - 3088 * q^81 - 2280 * q^85 - 9336 * q^86 - 2048 * q^88 + 1608 * q^91 - 6328 * q^92 - 3960 * q^93 + 1240 * q^95 + 3308 * q^98

Introduction

L-functions

Modular forms

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