LMFDB - Embedded newform 175.4.f.g.118.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(118,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, 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("175.118");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.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:	$10.3253342510$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			118.4
Root			$-6.68128 - 6.68128i$ of defining polynomial
Character	$\chi$	$=$	175.118
Dual form			175.4.f.g.132.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31781 + 1.31781i) q^{2} +(6.68128 - 6.68128i) q^{3} +4.52674i q^{4} +17.6093i q^{6} +(17.1776 - 6.92319i) q^{7} +(-16.5079 - 16.5079i) q^{8} -62.2789i q^{9} +O(q^{10})$	\(q+(-1.31781 + 1.31781i) q^{2} +(6.68128 - 6.68128i) q^{3} +4.52674i q^{4} +17.6093i q^{6} +(17.1776 - 6.92319i) q^{7} +(-16.5079 - 16.5079i) q^{8} -62.2789i q^{9} +24.9919 q^{11} +(30.2444 + 30.2444i) q^{12} +(-8.80162 + 8.80162i) q^{13} +(-13.5134 + 31.7603i) q^{14} +7.29465 q^{16} +(-7.24755 - 7.24755i) q^{17} +(82.0719 + 82.0719i) q^{18} +85.0979 q^{19} +(68.5125 - 161.024i) q^{21} +(-32.9346 + 32.9346i) q^{22} +(-18.9131 - 18.9131i) q^{23} -220.588 q^{24} -23.1978i q^{26} +(-235.708 - 235.708i) q^{27} +(31.3395 + 77.7585i) q^{28} -162.511i q^{29} +26.6139i q^{31} +(122.450 - 122.450i) q^{32} +(166.978 - 166.978i) q^{33} +19.1018 q^{34} +281.921 q^{36} +(54.1514 - 54.1514i) q^{37} +(-112.143 + 112.143i) q^{38} +117.612i q^{39} +137.076i q^{41} +(121.913 + 302.486i) q^{42} +(221.858 + 221.858i) q^{43} +113.132i q^{44} +49.8478 q^{46} +(229.976 + 229.976i) q^{47} +(48.7375 - 48.7375i) q^{48} +(247.139 - 237.847i) q^{49} -96.8457 q^{51} +(-39.8427 - 39.8427i) q^{52} +(-154.172 - 154.172i) q^{53} +621.238 q^{54} +(-397.853 - 169.278i) q^{56} +(568.563 - 568.563i) q^{57} +(214.160 + 214.160i) q^{58} -685.748 q^{59} -23.6916i q^{61} +(-35.0721 - 35.0721i) q^{62} +(-431.169 - 1069.80i) q^{63} +381.090i q^{64} +440.091i q^{66} +(-602.716 + 602.716i) q^{67} +(32.8078 - 32.8078i) q^{68} -252.727 q^{69} +265.331 q^{71} +(-1028.09 + 1028.09i) q^{72} +(-609.073 + 609.073i) q^{73} +142.723i q^{74} +385.216i q^{76} +(429.300 - 173.024i) q^{77} +(-154.991 - 154.991i) q^{78} +145.122i q^{79} -1468.13 q^{81} +(-180.641 - 180.641i) q^{82} +(-454.928 + 454.928i) q^{83} +(728.914 + 310.138i) q^{84} -584.735 q^{86} +(-1085.78 - 1085.78i) q^{87} +(-412.563 - 412.563i) q^{88} -209.235 q^{89} +(-90.2554 + 212.126i) q^{91} +(85.6148 - 85.6148i) q^{92} +(177.815 + 177.815i) q^{93} -606.130 q^{94} -1636.25i q^{96} +(1012.24 + 1012.24i) q^{97} +(-12.2446 + 639.121i) q^{98} -1556.47i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 504 q^{16} - 288 q^{18} + 328 q^{21} - 348 q^{22} + 72 q^{23} + 528 q^{28} - 432 q^{32} + 344 q^{36} + 256 q^{37} + 1300 q^{42} + 312 q^{43} - 1856 q^{46} + 696 q^{51} - 1768 q^{53} + 1304 q^{56} + 3920 q^{57} + 4764 q^{58} - 2544 q^{63} - 4504 q^{67} + 6368 q^{71} - 7848 q^{72} + 3016 q^{77} - 5340 q^{78} - 3088 q^{81} - 9336 q^{86} + 2048 q^{88} + 1608 q^{91} + 6328 q^{92} + 3960 q^{93} - 3308 q^{98}+O(q^{100}) $ 16 * q - 4 * q^2 - 32 * q^7 - 176 * q^8 - 152 * q^11 - 504 * q^16 - 288 * q^18 + 328 * q^21 - 348 * q^22 + 72 * q^23 + 528 * q^28 - 432 * q^32 + 344 * q^36 + 256 * q^37 + 1300 * q^42 + 312 * q^43 - 1856 * q^46 + 696 * q^51 - 1768 * q^53 + 1304 * q^56 + 3920 * q^57 + 4764 * q^58 - 2544 * q^63 - 4504 * q^67 + 6368 * q^71 - 7848 * q^72 + 3016 * q^77 - 5340 * q^78 - 3088 * q^81 - 9336 * q^86 + 2048 * q^88 + 1608 * q^91 + 6328 * q^92 + 3960 * q^93 - 3308 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.31781	+	1.31781i	−0.465917	+	0.465917i	−0.900589	−	0.434672i	$-0.856864\pi$
$2$	−1.31781	+	1.31781i	−0.465917	+	0.465917i	0.434672	+	0.900589i	$0.356864\pi$
$3$	6.68128	−	6.68128i	1.28581	−	1.28581i	0.348506	−	0.937307i	$-0.386689\pi$
$3$	6.68128	−	6.68128i	1.28581	−	1.28581i	0.937307	−	0.348506i	$-0.113311\pi$
$4$			4.52674i			0.565843i
$5$		0			0
$5$		0			0
$6$			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
$10$		0			0
$11$	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	−0.794735	−	0.606956i	$-0.792390\pi$
$13$	−8.80162	+	8.80162i	−0.187779	+	0.187779i	0.606956	+	0.794735i	$0.292390\pi$
$14$	−13.5134	+	31.7603i	−0.257971	+	0.606307i
$15$		0			0
$16$	7.29465			0.113979
$17$	−7.24755	−	7.24755i	−0.103399	−	0.103399i	0.653515	−	0.756914i	$-0.273294\pi$
$17$	−7.24755	−	7.24755i	−0.103399	−	0.103399i	−0.756914	+	0.653515i	$0.773294\pi$
$18$	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	$0.328253\pi$
$20$		0			0
$21$	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	0.616159	−	0.787622i	$-0.288688\pi$
$23$	−18.9131	−	18.9131i	−0.171463	−	0.171463i	−0.787622	+	0.616159i	$0.788688\pi$
$24$	−220.588			−1.87614
$25$		0			0
$26$		−	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	$-0.174181\pi$
$30$		0			0
$31$			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
$35$		0			0
$36$	281.921			1.30519
$37$	54.1514	−	54.1514i	0.240607	−	0.240607i	−0.576494	−	0.817101i	$-0.695580\pi$
$37$	54.1514	−	54.1514i	0.240607	−	0.240607i	0.817101	+	0.576494i	$0.195580\pi$
$38$	−112.143	+	112.143i	−0.478737	+	0.478737i
$39$			117.612i			0.482898i
$40$		0			0
$41$			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	0.980971	−	0.194155i	$-0.0621966\pi$
$43$	221.858	+	221.858i	0.786815	+	0.786815i	−0.194155	+	0.980971i	$0.562197\pi$
$44$			113.132i			0.387620i
$45$		0			0
$46$	49.8478			0.159775
$47$	229.976	+	229.976i	0.713732	+	0.713732i	0.967314	−	0.253582i	$-0.0816086\pi$
$47$	229.976	+	229.976i	0.713732	+	0.713732i	−0.253582	+	0.967314i	$0.581609\pi$
$48$	48.7375	−	48.7375i	0.146555	−	0.146555i
$49$	247.139	−	237.847i	0.720522	−	0.693432i
$50$		0			0
$51$	−96.8457			−0.265904
$52$	−39.8427	−	39.8427i	−0.106254	−	0.106254i
$53$	−154.172	−	154.172i	−0.399569	−	0.399569i	0.478512	−	0.878081i	$-0.341176\pi$
$53$	−154.172	−	154.172i	−0.399569	−	0.399569i	−0.878081	+	0.478512i	$0.841176\pi$
$54$	621.238			1.56555
$55$		0			0
$56$	−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	$0.773133\pi$
$60$		0			0
$61$		−	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
$65$		0			0
$66$			440.091i			0.820779i
$67$	−602.716	+	602.716i	−1.09901	+	1.09901i	−0.104480	+	0.994527i	$0.533318\pi$
$67$	−602.716	+	602.716i	−1.09901	+	1.09901i	−0.994527	+	0.104480i	$0.966682\pi$
$68$	32.8078	−	32.8078i	0.0585078	−	0.0585078i
$69$	−252.727			−0.440939
$70$		0			0
$71$	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	−0.999731	−	0.0232024i	$-0.992614\pi$
$73$	−609.073	+	609.073i	−0.976528	+	0.976528i	0.0232024	+	0.999731i	$0.492614\pi$
$74$			142.723i			0.224205i
$75$		0			0
$76$			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	$0.967047\pi$
$80$		0			0
$81$	−1468.13			−2.01390
$82$	−180.641	−	180.641i	−0.243273	−	0.243273i
$83$	−454.928	+	454.928i	−0.601625	+	0.601625i	−0.940744	−	0.339119i	$-0.889871\pi$
$83$	−454.928	+	454.928i	−0.601625	+	0.601625i	0.339119	+	0.940744i	$0.389871\pi$
$84$	728.914	+	310.138i	0.946798	+	0.402844i
$85$		0			0
$86$	−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	$0.539765\pi$
$90$		0			0
$91$	−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
$95$		0			0
$96$		−	1636.25i		−	1.73957i
$97$	1012.24	+	1012.24i	1.05956	+	1.05956i	0.998110	+	0.0614533i	$0.0195735\pi$
$97$	1012.24	+	1012.24i	1.05956	+	1.05956i	0.0614533	+	0.998110i	$0.480426\pi$
$98$	−12.2446	+	639.121i	−0.0126213	+	0.658785i
$99$		−	1556.47i		−	1.58011i
$100$		0			0
$101$			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	−0.931774	−	0.363038i	$-0.881740\pi$
$103$	−594.521	+	594.521i	−0.568737	+	0.568737i	0.363038	+	0.931774i	$0.381740\pi$
$104$	290.593			0.273990
$105$		0			0
$106$	406.339			0.372332
$107$	435.539	−	435.539i	0.393506	−	0.393506i	−0.482429	−	0.875935i	$-0.660245\pi$
$107$	435.539	−	435.539i	0.393506	−	0.393506i	0.875935	+	0.482429i	$0.160245\pi$
$108$	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	$0.851573\pi$
$110$		0			0
$111$		−	723.602i		−	0.618750i
$112$	125.304	−	50.5022i	0.105716	−	0.0426072i
$113$	−678.584	−	678.584i	−0.564919	−	0.564919i	0.365782	−	0.930701i	$-0.380802\pi$
$113$	−678.584	−	678.584i	−0.564919	−	0.564919i	−0.930701	+	0.365782i	$0.880802\pi$
$114$			1498.52i			1.23113i
$115$		0			0
$116$	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
$120$		0			0
$121$	−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
$125$		0			0
$126$	1978.00	+	841.598i	1.39852	+	0.595044i
$127$	2.16418	−	2.16418i	0.00151212	−	0.00151212i	−0.706350	−	0.707862i	$-0.749660\pi$
$127$	2.16418	−	2.16418i	0.00151212	−	0.00151212i	0.707862	+	0.706350i	$0.249660\pi$
$128$	477.397	+	477.397i	0.329659	+	0.329659i
$129$	2964.59			2.02339
$130$		0			0
$131$			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
$135$		0			0
$136$			239.283i			0.150870i
$137$	−1.36186	+	1.36186i	−0.000849278	+	0.000849278i	−0.707531	−	0.706682i	$-0.750191\pi$
$137$	−1.36186	+	1.36186i	−0.000849278	+	0.000849278i	0.706682	+	0.707531i	$0.250191\pi$
$138$	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	$0.724156\pi$
$140$		0			0
$141$	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
$145$		0			0
$146$		−	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	$-0.186474\pi$
$150$		0			0
$151$	−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
$155$		0			0
$156$	−532.400			−0.273244
$157$	1672.49	+	1672.49i	0.850184	+	0.850184i	0.990156	−	0.139971i	$-0.0447011\pi$
$157$	1672.49	+	1672.49i	0.850184	+	0.850184i	−0.139971	+	0.990156i	$0.544701\pi$
$158$	−191.244	−	191.244i	−0.0962947	−	0.0962947i
$159$	−2060.13			−1.02754
$160$		0			0
$161$	−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	$0.0649192\pi$
$163$	2459.41	+	2459.41i	1.18181	+	1.18181i	0.202539	+	0.979274i	$0.435081\pi$
$164$	−620.508			−0.295449
$165$		0			0
$166$		−	1199.02i		−	0.560614i
$167$	−2190.81	−	2190.81i	−1.01515	−	1.01515i	−0.999883	−	0.0152650i	$-0.995141\pi$
$167$	−2190.81	−	2190.81i	−1.01515	−	1.01515i	−0.0152650	−	0.999883i	$-0.504859\pi$
$168$	−3789.16	+	1527.17i	−1.74012	+	0.701331i
$169$			2042.06i			0.929478i
$170$		0			0
$171$		−	5299.81i		−	2.37010i
$172$	−1004.30	+	1004.30i	−0.445214	+	0.445214i
$173$	543.389	−	543.389i	0.238804	−	0.238804i	−0.577551	−	0.816355i	$-0.695991\pi$
$173$	543.389	−	543.389i	0.238804	−	0.238804i	0.816355	+	0.577551i	$0.195991\pi$
$174$	2861.72			1.24682
$175$		0			0
$176$	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	$-0.234486\pi$
$180$		0			0
$181$		−	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
$185$		0			0
$186$	−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
$190$		0			0
$191$	−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	0.165131	−	0.986272i	$-0.447195\pi$
$193$	−2201.68	−	2201.68i	−0.821141	−	0.821141i	−0.986272	+	0.165131i	$0.947195\pi$
$194$	−2667.89			−0.987337
$195$		0			0
$196$	1076.67	+	1118.73i	0.392374	+	0.407702i
$197$	3634.93	−	3634.93i	1.31461	−	1.31461i	0.396630	−	0.917978i	$-0.370179\pi$
$197$	3634.93	−	3634.93i	1.31461	−	1.31461i	0.917978	−	0.396630i	$-0.129821\pi$
$198$	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	$0.156259\pi$
$200$		0			0
$201$			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
$205$		0			0
$206$		−	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
$210$		0			0
$211$	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
$215$		0			0
$216$			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
$220$		0			0
$221$	127.580			0.0388325
$222$	953.571	+	953.571i	0.288286	+	0.288286i
$223$	3171.97	−	3171.97i	0.952515	−	0.952515i	−0.0464080	−	0.998923i	$-0.514777\pi$
$223$	3171.97	−	3171.97i	0.952515	−	0.952515i	0.998923	+	0.0464080i	$0.0147774\pi$
$224$	1255.65	−	2951.14i	0.374539	−	0.880275i
$225$		0			0
$226$	1788.49			0.526410
$227$	2955.01	+	2955.01i	0.864013	+	0.864013i	0.991801	−	0.127789i	$-0.0407880\pi$
$227$	2955.01	+	2955.01i	0.864013	+	0.864013i	−0.127789	+	0.991801i	$0.540788\pi$
$228$	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	$0.185578\pi$
$230$		0			0
$231$	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	0.122796	−	0.992432i	$-0.460814\pi$
$233$	−3092.94	−	3092.94i	−0.869636	−	0.869636i	−0.992432	+	0.122796i	$0.960814\pi$
$234$	−1444.73			−0.403612
$235$		0			0
$236$		−	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	$-0.0740273\pi$
$240$		0			0
$241$			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
$245$		0			0
$246$	−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
$250$		0			0
$251$		−	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
$255$		0			0
$256$	−4306.96			−1.05150
$257$	−2421.89	−	2421.89i	−0.587833	−	0.587833i	0.349211	−	0.937044i	$-0.386450\pi$
$257$	−2421.89	−	2421.89i	−0.587833	−	0.587833i	−0.937044	+	0.349211i	$0.886450\pi$
$258$	−3906.78	+	3906.78i	−0.942733	+	0.942733i
$259$	555.290	−	1305.09i	0.133220	−	0.313106i
$260$		0			0
$261$	−10121.0			−2.40029
$262$	−2631.28	−	2631.28i	−0.620462	−	0.620462i
$263$	3472.86	+	3472.86i	0.814242	+	0.814242i	0.985267	−	0.171025i	$-0.0547078\pi$
$263$	3472.86	+	3472.86i	0.814242	+	0.814242i	−0.171025	+	0.985267i	$0.554708\pi$
$264$	−5512.90			−1.28521
$265$		0			0
$266$	−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	$0.616819\pi$
$270$		0			0
$271$		−	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
$275$		0			0
$276$		−	1144.03i		−	0.249502i
$277$	844.503	−	844.503i	0.183181	−	0.183181i	−0.609559	−	0.792741i	$-0.708654\pi$
$277$	844.503	−	844.503i	0.183181	−	0.183181i	0.792741	+	0.609559i	$0.208654\pi$
$278$	2796.39	−	2796.39i	0.603296	−	0.603296i
$279$	1657.49			0.355667
$280$		0			0
$281$	−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	−0.996307	−	0.0858623i	$-0.972635\pi$
$283$	−4334.44	+	4334.44i	−0.910445	+	0.910445i	0.0858623	+	0.996307i	$0.472635\pi$
$284$			1201.08i			0.250955i
$285$		0			0
$286$		−	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
$290$		0			0
$291$	13526.1			2.72480
$292$	−2757.12	−	2757.12i	−0.552562	−	0.552562i
$293$	3204.15	−	3204.15i	0.638869	−	0.638869i	−0.311408	−	0.950276i	$-0.600801\pi$
$293$	3204.15	−	3204.15i	0.638869	−	0.638869i	0.950276	+	0.311408i	$0.100801\pi$
$294$	4188.33	+	4351.95i	0.830845	+	0.863303i
$295$		0			0
$296$	−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
$300$		0			0
$301$	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
$305$		0			0
$306$		−	1189.64i		−	0.222246i
$307$	−189.516	−	189.516i	−0.0352321	−	0.0352321i	0.689271	−	0.724503i	$-0.257931\pi$
$307$	−189.516	−	189.516i	−0.0352321	−	0.0352321i	−0.724503	+	0.689271i	$0.757931\pi$
$308$	783.233	+	1943.33i	0.144899	+	0.359518i
$309$			7944.32i			1.46258i
$310$		0			0
$311$			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	−0.958334	−	0.285649i	$-0.907791\pi$
$313$	−3725.02	+	3725.02i	−0.672686	+	0.672686i	0.285649	+	0.958334i	$0.407791\pi$
$314$	−4408.04			−0.792230
$315$		0			0
$316$	−656.932			−0.116947
$317$	−3053.99	+	3053.99i	−0.541101	+	0.541101i	−0.923852	−	0.382750i	$-0.874977\pi$
$317$	−3053.99	+	3053.99i	−0.541101	+	0.541101i	0.382750	+	0.923852i	$0.374977\pi$
$318$	2714.87	−	2714.87i	0.478749	−	0.478749i
$319$		−	4061.47i		−	0.712848i
$320$		0			0
$321$		−	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
$325$		0			0
$326$	−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
$330$		0			0
$331$	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
$335$		0			0
$336$	499.774	−	1174.61i	0.0811456	−	0.190715i
$337$	506.829	−	506.829i	0.0819251	−	0.0819251i	−0.664957	−	0.746882i	$-0.731550\pi$
$337$	506.829	−	506.829i	0.0819251	−	0.0819251i	0.746882	+	0.664957i	$0.231550\pi$
$338$	−2691.05	−	2691.05i	−0.433059	−	0.433059i
$339$	−9067.61			−1.45276
$340$		0			0
$341$			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
$345$		0			0
$346$			1432.17i			0.222526i
$347$	1458.26	−	1458.26i	0.225601	−	0.225601i	−0.585251	−	0.810852i	$-0.699004\pi$
$347$	1458.26	−	1458.26i	0.225601	−	0.225601i	0.810852	+	0.585251i	$0.199004\pi$
$348$	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	$0.791243\pi$
$350$		0			0
$351$	4149.23			0.630967
$352$	3060.26	−	3060.26i	0.463388	−	0.463388i
$353$	−5534.44	+	5534.44i	−0.834471	+	0.834471i	−0.988125	−	0.153654i	$-0.950896\pi$
$353$	−5534.44	+	5534.44i	−0.834471	+	0.834471i	0.153654	+	0.988125i	$0.450896\pi$
$354$		−	12075.6i		−	1.81302i
$355$		0			0
$356$		−	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	$-0.000676828\pi$
$360$		0			0
$361$	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
$365$		0			0
$366$	417.193			0.0595820
$367$	703.106	+	703.106i	0.100005	+	0.100005i	0.755339	−	0.655334i	$-0.227472\pi$
$367$	703.106	+	703.106i	0.100005	+	0.100005i	−0.655334	+	0.755339i	$0.727472\pi$
$368$	−137.964	−	137.964i	−0.0195432	−	0.0195432i
$369$	8536.95			1.20438
$370$		0			0
$371$	−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	0.514337	−	0.857588i	$-0.328038\pi$
$373$	−2472.73	−	2472.73i	−0.343252	−	0.343252i	−0.857588	+	0.514337i	$0.828038\pi$
$374$	477.390			0.0660034
$375$		0			0
$376$		−	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	$0.896566\pi$
$380$		0			0
$381$		−	28.9189i		−	0.00388861i
$382$	2968.78	−	2968.78i	0.397633	−	0.397633i
$383$	6945.43	−	6945.43i	0.926618	−	0.926618i	−0.0708675	−	0.997486i	$-0.522577\pi$
$383$	6945.43	−	6945.43i	0.926618	−	0.926618i	0.997486	+	0.0708675i	$0.0225768\pi$
$384$	6379.24			0.847758
$385$		0			0
$386$	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	$0.926418\pi$
$390$		0			0
$391$			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
$395$		0			0
$396$	7045.73			0.894094
$397$	2998.00	+	2998.00i	0.379005	+	0.379005i	0.870743	−	0.491738i	$-0.163638\pi$
$397$	2998.00	+	2998.00i	0.379005	+	0.379005i	−0.491738	+	0.870743i	$0.663638\pi$
$398$	−6525.09	+	6525.09i	−0.821792	+	0.821792i
$399$	5830.27	−	13702.8i	0.731525	−	1.71929i
$400$		0			0
$401$	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
$405$		0			0
$406$	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	$0.730890\pi$
$410$		0			0
$411$			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
$415$		0			0
$416$			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	$0.616408\pi$
$420$		0			0
$421$	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
$425$		0			0
$426$			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
$430$		0			0
$431$	−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	−0.328496	−	0.944505i	$-0.606542\pi$
$433$	5550.33	−	5550.33i	0.616009	−	0.616009i	0.944505	+	0.328496i	$0.106542\pi$
$434$	−845.266	−	359.644i	−0.0934886	−	0.0397775i
$435$		0			0
$436$	−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	$0.407781\pi$
$440$		0			0
$441$	−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	0.851436	−	0.524458i	$-0.175732\pi$
$443$	3048.77	+	3048.77i	0.326979	+	0.326979i	−0.524458	+	0.851436i	$0.675732\pi$
$444$	3275.56			0.350115
$445$		0			0
$446$			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	$0.893744\pi$
$450$		0			0
$451$			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
$455$		0			0
$456$	−18771.5			−1.92776
$457$	2938.32	−	2938.32i	0.300763	−	0.300763i	−0.540549	−	0.841312i	$-0.681784\pi$
$457$	2938.32	−	2938.32i	0.300763	−	0.300763i	0.841312	+	0.540549i	$0.181784\pi$
$458$	−7624.72	+	7624.72i	−0.777903	+	0.777903i
$459$			3416.61i			0.347438i
$460$		0			0
$461$		−	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	0.417592	−	0.908634i	$-0.362874\pi$
$463$	−4892.04	−	4892.04i	−0.491042	−	0.491042i	−0.908634	+	0.417592i	$0.862874\pi$
$464$		−	1185.46i		−	0.118607i
$465$		0			0
$466$	8151.82			0.810356
$467$	6801.21	+	6801.21i	0.673924	+	0.673924i	0.958618	−	0.284694i	$-0.0918921\pi$
$467$	6801.21	+	6801.21i	0.673924	+	0.673924i	−0.284694	+	0.958618i	$0.591892\pi$
$468$	−2481.36	+	2481.36i	−0.245087	+	0.245087i
$469$	−6180.49	+	14525.9i	−0.608504	+	1.43016i
$470$		0			0
$471$	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
$475$		0			0
$476$	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	$0.384995\pi$
$480$		0			0
$481$			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
$485$		0			0
$486$		−	9079.42i		−	0.847430i
$487$	2511.31	−	2511.31i	0.233672	−	0.233672i	−0.580551	−	0.814224i	$-0.697163\pi$
$487$	2511.31	−	2511.31i	0.233672	−	0.233672i	0.814224	+	0.580551i	$0.197163\pi$
$488$	−391.098	+	391.098i	−0.0362791	+	0.0362791i
$489$	32863.9			3.03918
$490$		0			0
$491$	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
$495$		0			0
$496$			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	$-0.326531\pi$
$500$		0			0
$501$	−29274.8			−2.61058
$502$	1108.93	+	1108.93i	0.0985933	+	0.0985933i
$503$	8758.73	−	8758.73i	0.776407	−	0.776407i	−0.202811	−	0.979218i	$-0.565008\pi$
$503$	8758.73	−	8758.73i	0.776407	−	0.776407i	0.979218	+	0.202811i	$0.0650077\pi$
$504$	−10542.5	+	24777.9i	−0.931745	+	2.18987i
$505$		0			0
$506$	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	$0.507307\pi$
$510$		0			0
$511$	−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
$515$		0			0
$516$			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
$520$		0			0
$521$			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	−0.786842	−	0.617154i	$-0.788285\pi$
$523$	−2029.57	+	2029.57i	−0.169688	+	0.169688i	0.617154	+	0.786842i	$0.288285\pi$
$524$	−9038.57			−0.753534
$525$		0			0
$526$	−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
$530$		0			0
$531$			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
$535$		0			0
$536$	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
$540$		0			0
$541$	−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
$545$		0			0
$546$	−3735.40	−	1589.34i	−0.292784	−	0.124574i
$547$	−5768.43	+	5768.43i	−0.450896	+	0.450896i	−0.895652	−	0.444756i	$-0.853290\pi$
$547$	−5768.43	+	5768.43i	−0.450896	+	0.450896i	0.444756	+	0.895652i	$0.353290\pi$
$548$	−6.16477	−	6.16477i	−0.000480558	−	0.000480558i
$549$	−1475.49			−0.114703
$550$		0			0
$551$		−	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
$555$		0			0
$556$		−	9605.72i		−	0.732686i
$557$	−10847.0	+	10847.0i	−0.825135	+	0.825135i	−0.986839	−	0.161704i	$-0.948301\pi$
$557$	−10847.0	+	10847.0i	−0.825135	+	0.825135i	0.161704	+	0.986839i	$0.448301\pi$
$558$	−2184.26	+	2184.26i	−0.165711	+	0.165711i
$559$	−3905.43			−0.295495
$560$		0			0
$561$	−2420.36			−0.182153
$562$	5994.43	−	5994.43i	0.449928	−	0.449928i
$563$	5379.59	−	5379.59i	0.402705	−	0.402705i	−0.476480	−	0.879185i	$-0.658088\pi$
$563$	5379.59	−	5379.59i	0.402705	−	0.402705i	0.879185	+	0.476480i	$0.158088\pi$
$564$			13911.0i			1.03858i
$565$		0			0
$566$		−	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	$0.965127\pi$
$570$		0			0
$571$	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
$575$		0			0
$576$	23733.9			1.71686
$577$	−172.987	−	172.987i	−0.0124810	−	0.0124810i	0.700839	−	0.713320i	$-0.252809\pi$
$577$	−172.987	−	172.987i	−0.0124810	−	0.0124810i	−0.713320	+	0.700839i	$0.752809\pi$
$578$	6335.97	+	6335.97i	0.455954	+	0.455954i
$579$	−29420.0			−2.11167
$580$		0			0
$581$	−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
$585$		0			0
$586$			8444.94i			0.595319i
$587$	−1167.08	−	1167.08i	−0.0820620	−	0.0820620i	0.664884	−	0.746946i	$-0.268481\pi$
$587$	−1167.08	−	1167.08i	−0.0820620	−	0.0820620i	−0.746946	+	0.664884i	$0.768481\pi$
$588$	14668.1	+	281.019i	1.02875	+	0.0197092i
$589$			2264.79i			0.158436i
$590$		0			0
$591$		−	48571.9i		−	3.38068i
$592$	395.016	−	395.016i	0.0274241	−	0.0274241i
$593$	−7315.54	+	7315.54i	−0.506599	+	0.506599i	−0.913481	−	0.406882i	$-0.866616\pi$
$593$	−7315.54	+	7315.54i	−0.506599	+	0.506599i	0.406882	+	0.913481i	$0.366616\pi$
$594$	15525.9			1.07245
$595$		0			0
$596$	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	$0.623618\pi$
$600$		0			0
$601$		−	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
$605$		0			0
$606$	−16060.3			−1.07658
$607$	−16609.9	−	16609.9i	−1.11067	−	1.11067i	−0.993060	−	0.117606i	$-0.962478\pi$
$607$	−16609.9	−	16609.9i	−1.11067	−	1.11067i	−0.117606	−	0.993060i	$-0.537522\pi$
$608$	10420.3	−	10420.3i	0.695061	−	0.695061i
$609$	−26168.2	−	11134.1i	−1.74120	−	0.740846i
$610$		0			0
$611$	−4048.32			−0.268048
$612$	−2043.23	−	2043.23i	−0.134956	−	0.134956i
$613$	−10690.3	−	10690.3i	−0.704365	−	0.704365i	0.260979	−	0.965344i	$-0.415955\pi$
$613$	−10690.3	−	10690.3i	−0.704365	−	0.704365i	−0.965344	+	0.260979i	$0.915955\pi$
$614$	499.493			0.0328305
$615$		0			0
$616$	−9943.10	−	4230.59i	−0.650355	−	0.276713i
$617$	7458.41	−	7458.41i	0.486652	−	0.486652i	−0.420596	−	0.907248i	$-0.638179\pi$
$617$	7458.41	−	7458.41i	0.486652	−	0.486652i	0.907248	+	0.420596i	$0.138179\pi$
$618$	−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	$0.245619\pi$
$620$		0			0
$621$			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
$625$		0			0
$626$		−	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
$630$		0			0
$631$	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
$635$		0			0
$636$		−	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
$640$		0			0
$641$	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	−0.833366	−	0.552721i	$-0.813589\pi$
$643$	−4575.87	+	4575.87i	−0.280645	+	0.280645i	0.552721	+	0.833366i	$0.313589\pi$
$644$	877.928	−	2063.38i	0.0537193	−	0.126256i
$645$		0			0
$646$	1625.52			0.0990021
$647$	367.147	+	367.147i	0.0223092	+	0.0223092i	0.718173	−	0.695864i	$-0.244978\pi$
$647$	367.147	+	367.147i	0.0223092	+	0.0223092i	−0.695864	+	0.718173i	$0.744978\pi$
$648$	24235.8	+	24235.8i	1.46925	+	1.46925i
$649$	−17138.1			−1.03656
$650$		0			0
$651$	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	0.871448	−	0.490488i	$-0.163181\pi$
$653$	6356.95	+	6356.95i	0.380960	+	0.380960i	−0.490488	+	0.871448i	$0.663181\pi$
$654$	−18018.6			−1.07735
$655$		0			0
$656$			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	$0.858417\pi$
$660$		0			0
$661$			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
$665$		0			0
$666$	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
$670$		0			0
$671$		−	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	$0.0397778\pi$
$673$	19499.1	+	19499.1i	1.11684	+	1.11684i	0.124641	+	0.992202i	$0.460222\pi$
$674$			1335.81i			0.0763406i
$675$		0			0
$676$	−9243.89			−0.525938
$677$	−2638.87	−	2638.87i	−0.149808	−	0.149808i	0.628224	−	0.778032i	$-0.283782\pi$
$677$	−2638.87	−	2638.87i	−0.149808	−	0.149808i	−0.778032	+	0.628224i	$0.783782\pi$
$678$	11949.4	−	11949.4i	0.676865	−	0.676865i
$679$	24395.8	+	10379.9i	1.37883	+	0.586665i
$680$		0			0
$681$	39486.5			2.22192
$682$	−876.519	−	876.519i	−0.0492136	−	0.0492136i
$683$	−11485.3	−	11485.3i	−0.643447	−	0.643447i	0.307954	−	0.951401i	$-0.400356\pi$
$683$	−11485.3	−	11485.3i	−0.643447	−	0.643447i	−0.951401	+	0.307954i	$0.900356\pi$
$684$	23990.9			1.34110
$685$		0			0
$686$	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
$690$		0			0
$691$		−	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
$695$		0			0
$696$			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
$700$		0			0
$701$	−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
$705$		0			0
$706$		−	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	$-0.0577558\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$	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	$0.598835\pi$
$720$		0			0
$721$	−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
$725$		0			0
$726$		−	12439.3i		−	0.635904i
$727$	−11932.2	−	11932.2i	−0.608722	−	0.608722i	0.333890	−	0.942612i	$-0.391639\pi$
$727$	−11932.2	−	11932.2i	−0.608722	−	0.608722i	−0.942612	+	0.333890i	$0.891639\pi$
$728$	4991.68	−	2011.83i	0.254126	−	0.102422i
$729$			6392.84i			0.324790i
$730$		0			0
$731$		−	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	$-0.429935\pi$
$733$	23699.4	−	23699.4i	1.19421	−	1.19421i	0.975872	−	0.218341i	$-0.0700646\pi$
$734$	−1853.12			−0.0931881
$735$		0			0
$736$	−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	$-0.218012\pi$
$740$		0			0
$741$			10008.6i			0.496185i
$742$	6979.93	−	2813.16i	0.345339	−	0.139184i
$743$	−6699.21	−	6699.21i	−0.330781	−	0.330781i	0.522102	−	0.852883i	$-0.325148\pi$
$743$	−6699.21	−	6699.21i	−0.330781	−	0.330781i	−0.852883	+	0.522102i	$0.825148\pi$
$744$		−	5870.70i		−	0.289288i
$745$		0			0
$746$	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
$750$		0			0
$751$	−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
$755$		0			0
$756$	10941.3	−	25715.3i	0.526366	−	1.23711i
$757$	−6207.76	+	6207.76i	−0.298051	+	0.298051i	−0.840250	−	0.542199i	$-0.817592\pi$
$757$	−6207.76	+	6207.76i	−0.298051	+	0.298051i	0.542199	+	0.840250i	$0.317592\pi$
$758$	−6208.51	−	6208.51i	−0.297498	−	0.297498i
$759$	−6316.14			−0.302057
$760$		0			0
$761$		−	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
$765$		0			0
$766$			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	$0.530238\pi$
$770$		0			0
$771$	−32362.6			−1.51169
$772$	9966.43	−	9966.43i	0.464637	−	0.464637i
$773$	−3452.33	+	3452.33i	−0.160636	+	0.160636i	−0.782848	−	0.622213i	$-0.786234\pi$
$773$	−3452.33	+	3452.33i	−0.160636	+	0.160636i	0.622213	+	0.782848i	$0.286234\pi$
$774$			36416.7i			1.69118i
$775$		0			0
$776$		−	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
$780$		0			0
$781$	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
$785$		0			0
$786$	−35160.7			−1.59560
$787$	−24964.1	−	24964.1i	−1.13072	−	1.13072i	−0.990058	−	0.140657i	$-0.955079\pi$
$787$	−24964.1	−	24964.1i	−1.13072	−	1.13072i	−0.140657	−	0.990058i	$-0.544921\pi$
$788$	16454.4	+	16454.4i	0.743862	+	0.743862i
$789$	46406.3			2.09393
$790$		0			0
$791$	−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
$795$		0			0
$796$			22414.0i			0.998043i
$797$	−3736.59	−	3736.59i	−0.166069	−	0.166069i	0.619180	−	0.785249i	$-0.287465\pi$
$797$	−3736.59	−	3736.59i	−0.166069	−	0.166069i	−0.785249	+	0.619180i	$0.787465\pi$
$798$	10374.5	+	25740.9i	0.460218	+	1.14188i
$799$		−	3333.52i		−	0.147599i
$800$		0			0
$801$			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
$805$		0			0
$806$	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	$0.777500\pi$
$810$		0			0
$811$		−	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
$815$		0			0
$816$	−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
$820$		0			0
$821$	−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	0.649933	−	0.759991i	$-0.274797\pi$
$823$	−2598.49	−	2598.49i	−0.110058	−	0.110058i	−0.759991	+	0.649933i	$0.774797\pi$
$824$	19628.6			0.829847
$825$		0			0
$826$	9266.76	−	21779.5i	0.390353	−	0.917442i
$827$	−25938.0	+	25938.0i	−1.09063	+	1.09063i	−0.0951702	+	0.995461i	$0.530340\pi$
$827$	−25938.0	+	25938.0i	−1.09063	+	1.09063i	−0.995461	+	0.0951702i	$0.969660\pi$
$828$	−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	$0.624967\pi$
$830$		0			0
$831$		−	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
$835$		0			0
$836$			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	$0.329134\pi$
$840$		0			0
$841$	−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
$845$		0			0
$846$			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
$850$		0			0
$851$	−2048.34			−0.0825104
$852$	8024.77	+	8024.77i	0.322681	+	0.322681i
$853$	10701.3	−	10701.3i	0.429551	−	0.429551i	−0.458924	−	0.888475i	$-0.651765\pi$
$853$	10701.3	−	10701.3i	0.429551	−	0.429551i	0.888475	+	0.458924i	$0.151765\pi$
$854$	752.451	+	320.153i	0.0301503	+	0.0128284i
$855$		0			0
$856$	−14379.7			−0.574166
$857$	−16707.0	−	16707.0i	−0.665927	−	0.665927i	0.290844	−	0.956771i	$-0.406064\pi$
$857$	−16707.0	−	16707.0i	−0.665927	−	0.665927i	−0.956771	+	0.290844i	$0.906064\pi$
$858$	−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	$0.677630\pi$
$860$		0			0
$861$	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	$-0.985411\pi$
$863$	−26487.1	−	26487.1i	−1.04477	−	1.04477i	−0.0458157	−	0.998950i	$-0.514589\pi$
$864$	−57725.0			−2.27297
$865$		0			0
$866$			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
$870$		0			0
$871$		−	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
$875$		0			0
$876$	−36842.1			−1.42098
$877$	21275.9	−	21275.9i	0.819199	−	0.819199i	−0.166793	−	0.985992i	$-0.553341\pi$
$877$	21275.9	−	21275.9i	0.819199	−	0.819199i	0.985992	+	0.166793i	$0.0533412\pi$
$878$	−6925.59	+	6925.59i	−0.266204	+	0.266204i
$879$		−	42815.6i		−	1.64293i
$880$		0			0
$881$			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	0.603839	−	0.797106i	$-0.293637\pi$
$883$	−5071.07	−	5071.07i	−0.193268	−	0.193268i	−0.797106	+	0.603839i	$0.793637\pi$
$884$			577.524i			0.0219731i
$885$		0			0
$886$	−8035.41			−0.304690
$887$	−22739.1	−	22739.1i	−0.860770	−	0.860770i	0.130658	−	0.991428i	$-0.458291\pi$
$887$	−22739.1	−	22739.1i	−0.860770	−	0.860770i	−0.991428	+	0.130658i	$0.958291\pi$
$888$	−11945.1	+	11945.1i	−0.451411	+	0.451411i
$889$	22.1923	−	52.1583i	0.000837240	−	0.00196775i
$890$		0			0
$891$	−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
$895$		0			0
$896$	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
$900$		0			0
$901$			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
$905$		0			0
$906$		−	5294.47i		−	0.194147i
$907$	−6730.54	+	6730.54i	−0.246399	+	0.246399i	−0.819491	−	0.573092i	$-0.805744\pi$
$907$	−6730.54	+	6730.54i	−0.246399	+	0.246399i	0.573092	+	0.819491i	$0.305744\pi$
$908$	−13376.6	+	13376.6i	−0.488895	+	0.488895i
$909$	56800.6			2.07256
$910$		0			0
$911$	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
$915$		0			0
$916$			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	$-0.0335081\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$	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	$0.316885\pi$
$930$		0			0
$931$	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
$935$		0			0
$936$		−	18097.8i		−	0.631992i
$937$	35445.3	+	35445.3i	1.23580	+	1.23580i	0.961701	+	0.274101i	$0.0883801\pi$
$937$	35445.3	+	35445.3i	1.23580	+	1.23580i	0.274101	+	0.961701i	$0.411620\pi$
$938$	−10997.7	−	27287.2i	−0.382823	−	0.949848i
$939$			49775.8i			1.72990i
$940$		0			0
$941$		−	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
$945$		0			0
$946$	−14613.6			−0.502252
$947$	−33334.2	+	33334.2i	−1.14384	+	1.14384i	−0.156097	+	0.987742i	$0.549891\pi$
$947$	−33334.2	+	33334.2i	−1.14384	+	1.14384i	−0.987742	+	0.156097i	$0.950109\pi$
$948$	−4389.14	+	4389.14i	−0.150372	+	0.150372i
$949$		−	10721.7i		−	0.366744i
$950$		0			0
$951$			40809.1i			1.39151i
$952$	1656.60	+	4110.31i	0.0563980	+	0.139933i
$953$	9789.22	+	9789.22i	0.332743	+	0.332743i	0.853627	−	0.520884i	$-0.174398\pi$
$953$	9789.22	+	9789.22i	0.332743	+	0.332743i	−0.520884	+	0.853627i	$0.674398\pi$
$954$		−	25306.4i		−	0.858830i
$955$		0			0
$956$	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
$960$		0			0
$961$	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
$965$		0			0
$966$	3415.20	−	8026.69i	0.113750	−	0.267344i
$967$	15607.2	−	15607.2i	0.519021	−	0.519021i	−0.398254	−	0.917275i	$-0.630384\pi$
$967$	15607.2	−	15607.2i	0.519021	−	0.519021i	0.917275	+	0.398254i	$0.130384\pi$
$968$	11661.3	+	11661.3i	0.387197	+	0.387197i
$969$	−8241.37			−0.273221
$970$		0			0
$971$		−	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
$975$		0			0
$976$		−	172.822i		−	0.00566792i
$977$	15017.6	−	15017.6i	0.491766	−	0.491766i	−0.417097	−	0.908862i	$-0.636952\pi$
$977$	15017.6	−	15017.6i	0.491766	−	0.491766i	0.908862	+	0.417097i	$0.136952\pi$
$978$	−43308.5	+	43308.5i	−1.41601	+	1.41601i
$979$	−5229.18			−0.170710
$980$		0			0
$981$	63726.5			2.07404
$982$	−4384.23	+	4384.23i	−0.142471	+	0.142471i
$983$	11521.7	−	11521.7i	0.373841	−	0.373841i	−0.495033	−	0.868874i	$-0.664844\pi$
$983$	11521.7	−	11521.7i	0.373841	−	0.373841i	0.868874	+	0.495033i	$0.164844\pi$
$984$		−	30237.3i		−	0.979603i
$985$		0			0
$986$		−	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
$990$		0			0
$991$	−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
$995$		0			0
$996$	−27518.1			−0.875445
$997$	−15928.4	−	15928.4i	−0.505975	−	0.505975i	0.407313	−	0.913289i	$-0.366466\pi$
$997$	−15928.4	−	15928.4i	−0.505975	−	0.505975i	−0.913289	+	0.407313i	$0.866466\pi$
$998$	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	175.4.f.g.118.4		16
5.2	odd	4	inner	175.4.f.g.132.3		16
5.3	odd	4		35.4.f.b.27.6	yes	16
5.4	even	2		35.4.f.b.13.5	✓	16
7.6	odd	2	inner	175.4.f.g.118.3		16
35.3	even	12		245.4.l.b.117.3		32
35.4	even	6		245.4.l.b.68.6		32
35.9	even	6		245.4.l.b.178.3		32
35.13	even	4		35.4.f.b.27.5	yes	16
35.18	odd	12		245.4.l.b.117.4		32
35.19	odd	6		245.4.l.b.178.4		32
35.23	odd	12		245.4.l.b.227.5		32
35.24	odd	6		245.4.l.b.68.5		32
35.27	even	4	inner	175.4.f.g.132.4		16
35.33	even	12		245.4.l.b.227.6		32
35.34	odd	2		35.4.f.b.13.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.f.b.13.5	✓	16	5.4	even	2
35.4.f.b.13.6	yes	16	35.34	odd	2
35.4.f.b.27.5	yes	16	35.13	even	4
35.4.f.b.27.6	yes	16	5.3	odd	4
175.4.f.g.118.3		16	7.6	odd	2	inner
175.4.f.g.118.4		16	1.1	even	1	trivial
175.4.f.g.132.3		16	5.2	odd	4	inner
175.4.f.g.132.4		16	35.27	even	4	inner
245.4.l.b.68.5		32	35.24	odd	6
245.4.l.b.68.6		32	35.4	even	6
245.4.l.b.117.3		32	35.3	even	12
245.4.l.b.117.4		32	35.18	odd	12
245.4.l.b.178.3		32	35.9	even	6
245.4.l.b.178.4		32	35.19	odd	6
245.4.l.b.227.5		32	35.23	odd	12
245.4.l.b.227.6		32	35.33	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31781 + 1.31781i) q^{2} +(6.68128 - 6.68128i) q^{3} +4.52674i q^{4} +17.6093i q^{6} +(17.1776 - 6.92319i) q^{7} +(-16.5079 - 16.5079i) q^{8} -62.2789i q^{9} +O(q^{10})\)	\(q+(-1.31781 + 1.31781i) q^{2} +(6.68128 - 6.68128i) q^{3} +4.52674i q^{4} +17.6093i q^{6} +(17.1776 - 6.92319i) q^{7} +(-16.5079 - 16.5079i) q^{8} -62.2789i q^{9} +24.9919 q^{11} +(30.2444 + 30.2444i) q^{12} +(-8.80162 + 8.80162i) q^{13} +(-13.5134 + 31.7603i) q^{14} +7.29465 q^{16} +(-7.24755 - 7.24755i) q^{17} +(82.0719 + 82.0719i) q^{18} +85.0979 q^{19} +(68.5125 - 161.024i) q^{21} +(-32.9346 + 32.9346i) q^{22} +(-18.9131 - 18.9131i) q^{23} -220.588 q^{24} -23.1978i q^{26} +(-235.708 - 235.708i) q^{27} +(31.3395 + 77.7585i) q^{28} -162.511i q^{29} +26.6139i q^{31} +(122.450 - 122.450i) q^{32} +(166.978 - 166.978i) q^{33} +19.1018 q^{34} +281.921 q^{36} +(54.1514 - 54.1514i) q^{37} +(-112.143 + 112.143i) q^{38} +117.612i q^{39} +137.076i q^{41} +(121.913 + 302.486i) q^{42} +(221.858 + 221.858i) q^{43} +113.132i q^{44} +49.8478 q^{46} +(229.976 + 229.976i) q^{47} +(48.7375 - 48.7375i) q^{48} +(247.139 - 237.847i) q^{49} -96.8457 q^{51} +(-39.8427 - 39.8427i) q^{52} +(-154.172 - 154.172i) q^{53} +621.238 q^{54} +(-397.853 - 169.278i) q^{56} +(568.563 - 568.563i) q^{57} +(214.160 + 214.160i) q^{58} -685.748 q^{59} -23.6916i q^{61} +(-35.0721 - 35.0721i) q^{62} +(-431.169 - 1069.80i) q^{63} +381.090i q^{64} +440.091i q^{66} +(-602.716 + 602.716i) q^{67} +(32.8078 - 32.8078i) q^{68} -252.727 q^{69} +265.331 q^{71} +(-1028.09 + 1028.09i) q^{72} +(-609.073 + 609.073i) q^{73} +142.723i q^{74} +385.216i q^{76} +(429.300 - 173.024i) q^{77} +(-154.991 - 154.991i) q^{78} +145.122i q^{79} -1468.13 q^{81} +(-180.641 - 180.641i) q^{82} +(-454.928 + 454.928i) q^{83} +(728.914 + 310.138i) q^{84} -584.735 q^{86} +(-1085.78 - 1085.78i) q^{87} +(-412.563 - 412.563i) q^{88} -209.235 q^{89} +(-90.2554 + 212.126i) q^{91} +(85.6148 - 85.6148i) q^{92} +(177.815 + 177.815i) q^{93} -606.130 q^{94} -1636.25i q^{96} +(1012.24 + 1012.24i) q^{97} +(-12.2446 + 639.121i) q^{98} -1556.47i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 32 q^{7} - 176 q^{8}+O(q^{10}) \) 16 * q - 4 * q^2 - 32 * q^7 - 176 * q^8	\( 16 q - 4 q^{2} - 32 q^{7} - 176 q^{8} - 152 q^{11} - 504 q^{16} - 288 q^{18} + 328 q^{21} - 348 q^{22} + 72 q^{23} + 528 q^{28} - 432 q^{32} + 344 q^{36} + 256 q^{37} + 1300 q^{42} + 312 q^{43} - 1856 q^{46} + 696 q^{51} - 1768 q^{53} + 1304 q^{56} + 3920 q^{57} + 4764 q^{58} - 2544 q^{63} - 4504 q^{67} + 6368 q^{71} - 7848 q^{72} + 3016 q^{77} - 5340 q^{78} - 3088 q^{81} - 9336 q^{86} + 2048 q^{88} + 1608 q^{91} + 6328 q^{92} + 3960 q^{93} - 3308 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 - 32 * q^7 - 176 * q^8 - 152 * q^11 - 504 * q^16 - 288 * q^18 + 328 * q^21 - 348 * q^22 + 72 * q^23 + 528 * q^28 - 432 * q^32 + 344 * q^36 + 256 * q^37 + 1300 * q^42 + 312 * q^43 - 1856 * q^46 + 696 * q^51 - 1768 * q^53 + 1304 * q^56 + 3920 * q^57 + 4764 * q^58 - 2544 * q^63 - 4504 * q^67 + 6368 * q^71 - 7848 * q^72 + 3016 * q^77 - 5340 * q^78 - 3088 * q^81 - 9336 * q^86 + 2048 * q^88 + 1608 * q^91 + 6328 * q^92 + 3960 * q^93 - 3308 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more