LMFDB - Embedded newform 175.4.f.g.132.4

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			132.4
Root			$-6.68128 + 6.68128i$ of defining polynomial
Character	$\chi$	$=$	175.132
Dual form			175.4.f.g.118.4

$q$-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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

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

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	0.434672	−	0.900589i	$-0.356864\pi$
$2$	−1.31781	−	1.31781i	−0.465917	−	0.465917i	−0.900589	+	0.434672i	$0.856864\pi$
$3$	6.68128	+	6.68128i	1.28581	+	1.28581i	0.937307	+	0.348506i	$0.113311\pi$
$3$	6.68128	+	6.68128i	1.28581	+	1.28581i	0.348506	+	0.937307i	$0.386689\pi$
$4$		−	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	0.606956	−	0.794735i	$-0.292390\pi$
$13$	−8.80162	−	8.80162i	−0.187779	−	0.187779i	−0.794735	+	0.606956i	$0.792390\pi$
$14$	−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	−0.756914	−	0.653515i	$-0.773294\pi$
$17$	−7.24755	+	7.24755i	−0.103399	+	0.103399i	0.653515	+	0.756914i	$0.273294\pi$
$18$	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	−0.787622	−	0.616159i	$-0.788688\pi$
$23$	−18.9131	+	18.9131i	−0.171463	+	0.171463i	0.616159	+	0.787622i	$0.288688\pi$
$24$	−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	$0.174181\pi$
$29$			162.511i			1.04061i	−0.853981	+	0.520304i	$0.825819\pi$
$30$		0			0
$31$		−	26.6139i		−	0.154194i	−0.997024	−	0.0770968i	$-0.975435\pi$
$31$		−	26.6139i		−	0.154194i	0.997024	−	0.0770968i	$-0.0245651\pi$
$32$	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	0.817101	−	0.576494i	$-0.195580\pi$
$37$	54.1514	+	54.1514i	0.240607	+	0.240607i	−0.576494	+	0.817101i	$0.695580\pi$
$38$	−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	$-0.915925\pi$
$41$		−	137.076i		−	0.522139i	0.965320	−	0.261069i	$-0.0840752\pi$
$42$	121.913	−	302.486i	0.447894	−	1.11130i
$43$	221.858	−	221.858i	0.786815	−	0.786815i	−0.194155	−	0.980971i	$-0.562197\pi$
$43$	221.858	−	221.858i	0.786815	−	0.786815i	0.980971	+	0.194155i	$0.0621966\pi$
$44$		−	113.132i		−	0.387620i
$45$		0			0
$46$	49.8478			0.159775
$47$	229.976	−	229.976i	0.713732	−	0.713732i	−0.253582	−	0.967314i	$-0.581609\pi$
$47$	229.976	−	229.976i	0.713732	−	0.713732i	0.967314	+	0.253582i	$0.0816086\pi$
$48$	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	−0.878081	−	0.478512i	$-0.841176\pi$
$53$	−154.172	+	154.172i	−0.399569	+	0.399569i	0.478512	+	0.878081i	$0.341176\pi$
$54$	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	$0.00791524\pi$
$61$			23.6916i			0.0497278i	−0.999691	+	0.0248639i	$0.992085\pi$
$62$	−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	−0.994527	−	0.104480i	$-0.966682\pi$
$67$	−602.716	−	602.716i	−1.09901	−	1.09901i	−0.104480	−	0.994527i	$-0.533318\pi$
$68$	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	0.0232024	−	0.999731i	$-0.492614\pi$
$73$	−609.073	−	609.073i	−0.976528	−	0.976528i	−0.999731	+	0.0232024i	$0.992614\pi$
$74$		−	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	$-0.967047\pi$
$79$		−	145.122i		−	0.206678i	0.994646	−	0.103339i	$-0.0329526\pi$
$80$		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	0.339119	−	0.940744i	$-0.389871\pi$
$83$	−454.928	−	454.928i	−0.601625	−	0.601625i	−0.940744	+	0.339119i	$0.889871\pi$
$84$	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	0.0614533	−	0.998110i	$-0.480426\pi$
$97$	1012.24	−	1012.24i	1.05956	−	1.05956i	0.998110	−	0.0614533i	$-0.0195735\pi$
$98$	−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	$-0.851687\pi$
$101$		−	912.036i		−	0.898524i	0.893400	−	0.449262i	$-0.148313\pi$
$102$	127.624	+	127.624i	0.123889	+	0.123889i
$103$	−594.521	−	594.521i	−0.568737	−	0.568737i	0.363038	−	0.931774i	$-0.381740\pi$
$103$	−594.521	−	594.521i	−0.568737	−	0.568737i	−0.931774	+	0.363038i	$0.881740\pi$
$104$	290.593			0.273990
$105$		0			0
$106$	406.339			0.372332
$107$	435.539	+	435.539i	0.393506	+	0.393506i	0.875935	−	0.482429i	$-0.160245\pi$
$107$	435.539	+	435.539i	0.393506	+	0.393506i	−0.482429	+	0.875935i	$0.660245\pi$
$108$	1066.99	+	1066.99i	0.950660	+	0.950660i
$109$		−	1023.24i		−	0.899165i	−0.893239	−	0.449582i	$-0.851573\pi$
$109$		−	1023.24i		−	0.899165i	0.893239	−	0.449582i	$-0.148427\pi$
$110$		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	−0.930701	−	0.365782i	$-0.880802\pi$
$113$	−678.584	+	678.584i	−0.564919	+	0.564919i	0.365782	+	0.930701i	$0.380802\pi$
$114$		−	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	0.707862	−	0.706350i	$-0.249660\pi$
$127$	2.16418	+	2.16418i	0.00151212	+	0.00151212i	−0.706350	+	0.707862i	$0.749660\pi$
$128$	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	$-0.768069\pi$
$131$		−	1996.71i		−	1.33170i	0.746085	−	0.665851i	$-0.231931\pi$
$132$	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	0.706682	−	0.707531i	$-0.250191\pi$
$137$	−1.36186	−	1.36186i	−0.000849278	−	0.000849278i	−0.707531	+	0.706682i	$0.750191\pi$
$138$	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	$0.186474\pi$
$149$			2011.15i			1.10577i	−0.833257	+	0.552886i	$0.813526\pi$
$150$		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	−0.139971	−	0.990156i	$-0.544701\pi$
$157$	1672.49	−	1672.49i	0.850184	−	0.850184i	0.990156	+	0.139971i	$0.0447011\pi$
$158$	−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	0.202539	−	0.979274i	$-0.435081\pi$
$163$	2459.41	−	2459.41i	1.18181	−	1.18181i	0.979274	−	0.202539i	$-0.0649192\pi$
$164$	−620.508			−0.295449
$165$		0			0
$166$			1199.02i			0.560614i
$167$	−2190.81	+	2190.81i	−1.01515	+	1.01515i	−0.0152650	+	0.999883i	$0.504859\pi$
$167$	−2190.81	+	2190.81i	−1.01515	+	1.01515i	−0.999883	+	0.0152650i	$0.995141\pi$
$168$	−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	0.816355	−	0.577551i	$-0.195991\pi$
$173$	543.389	+	543.389i	0.238804	+	0.238804i	−0.577551	+	0.816355i	$0.695991\pi$
$174$	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	$0.234486\pi$
$179$			3217.81i			1.34363i	−0.740717	+	0.671817i	$0.765514\pi$
$180$		0			0
$181$			1653.80i			0.679148i	0.940579	+	0.339574i	$0.110283\pi$
$181$			1653.80i			0.679148i	−0.940579	+	0.339574i	$0.889717\pi$
$182$	−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	−0.986272	−	0.165131i	$-0.947195\pi$
$193$	−2201.68	+	2201.68i	−0.821141	+	0.821141i	0.165131	+	0.986272i	$0.447195\pi$
$194$	−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	0.917978	+	0.396630i	$0.129821\pi$
$197$	3634.93	+	3634.93i	1.31461	+	1.31461i	0.396630	+	0.917978i	$0.370179\pi$
$198$	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	0.998923	−	0.0464080i	$-0.0147774\pi$
$223$	3171.97	+	3171.97i	0.952515	+	0.952515i	−0.0464080	+	0.998923i	$0.514777\pi$
$224$	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	−0.127789	−	0.991801i	$-0.540788\pi$
$227$	2955.01	−	2955.01i	0.864013	−	0.864013i	0.991801	+	0.127789i	$0.0407880\pi$
$228$	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	−0.992432	−	0.122796i	$-0.960814\pi$
$233$	−3092.94	+	3092.94i	−0.869636	+	0.869636i	0.122796	+	0.992432i	$0.460814\pi$
$234$	−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	$0.0740273\pi$
$239$			1703.12i			0.460946i	−0.973079	+	0.230473i	$0.925973\pi$
$240$		0			0
$241$		−	2017.99i		−	0.539378i	−0.962947	−	0.269689i	$-0.913079\pi$
$241$		−	2017.99i		−	0.539378i	0.962947	−	0.269689i	$-0.0869209\pi$
$242$	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	$0.0337422\pi$
$251$			841.491i			0.211611i	−0.994387	+	0.105806i	$0.966258\pi$
$252$	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	−0.937044	−	0.349211i	$-0.886450\pi$
$257$	−2421.89	+	2421.89i	−0.587833	+	0.587833i	0.349211	+	0.937044i	$0.386450\pi$
$258$	−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	−0.171025	−	0.985267i	$-0.554708\pi$
$263$	3472.86	−	3472.86i	0.814242	−	0.814242i	0.985267	+	0.171025i	$0.0547078\pi$
$264$	−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	$0.225889\pi$
$271$			5813.58i			1.30314i	−0.758590	+	0.651568i	$0.774111\pi$
$272$	−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	0.792741	−	0.609559i	$-0.208654\pi$
$277$	844.503	+	844.503i	0.183181	+	0.183181i	−0.609559	+	0.792741i	$0.708654\pi$
$278$	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	0.0858623	−	0.996307i	$-0.472635\pi$
$283$	−4334.44	−	4334.44i	−0.910445	−	0.910445i	−0.996307	+	0.0858623i	$0.972635\pi$
$284$		−	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	0.950276	−	0.311408i	$-0.100801\pi$
$293$	3204.15	+	3204.15i	0.638869	+	0.638869i	−0.311408	+	0.950276i	$0.600801\pi$
$294$	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	−0.724503	−	0.689271i	$-0.757931\pi$
$307$	−189.516	+	189.516i	−0.0352321	+	0.0352321i	0.689271	+	0.724503i	$0.257931\pi$
$308$	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	$-0.643250\pi$
$311$		−	9876.93i		−	1.80087i	0.434994	−	0.900433i	$-0.356750\pi$
$312$	1941.53	+	1941.53i	0.352300	+	0.352300i
$313$	−3725.02	−	3725.02i	−0.672686	−	0.672686i	0.285649	−	0.958334i	$-0.407791\pi$
$313$	−3725.02	−	3725.02i	−0.672686	−	0.672686i	−0.958334	+	0.285649i	$0.907791\pi$
$314$	−4408.04			−0.792230
$315$		0			0
$316$	−656.932			−0.116947
$317$	−3053.99	−	3053.99i	−0.541101	−	0.541101i	0.382750	−	0.923852i	$-0.374977\pi$
$317$	−3053.99	−	3053.99i	−0.541101	−	0.541101i	−0.923852	+	0.382750i	$0.874977\pi$
$318$	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	0.746882	−	0.664957i	$-0.231550\pi$
$337$	506.829	+	506.829i	0.0819251	+	0.0819251i	−0.664957	+	0.746882i	$0.731550\pi$
$338$	−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	0.810852	−	0.585251i	$-0.199004\pi$
$347$	1458.26	+	1458.26i	0.225601	+	0.225601i	−0.585251	+	0.810852i	$0.699004\pi$
$348$	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	0.153654	−	0.988125i	$-0.450896\pi$
$353$	−5534.44	−	5534.44i	−0.834471	−	0.834471i	−0.988125	+	0.153654i	$0.950896\pi$
$354$			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	$0.000676828\pi$
$359$			28.9268i			0.00425263i	−0.999998	+	0.00212632i	$0.999323\pi$
$360$		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	−0.655334	−	0.755339i	$-0.727472\pi$
$367$	703.106	−	703.106i	0.100005	−	0.100005i	0.755339	+	0.655334i	$0.227472\pi$
$368$	−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	−0.857588	−	0.514337i	$-0.828038\pi$
$373$	−2472.73	+	2472.73i	−0.343252	+	0.343252i	0.514337	+	0.857588i	$0.328038\pi$
$374$	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	$-0.896566\pi$
$379$		−	4711.22i		−	0.638521i	0.947667	−	0.319260i	$-0.103434\pi$
$380$		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	0.997486	−	0.0708675i	$-0.0225768\pi$
$383$	6945.43	+	6945.43i	0.926618	+	0.926618i	−0.0708675	+	0.997486i	$0.522577\pi$
$384$	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	$-0.926418\pi$
$389$		−	3515.63i		−	0.458226i	0.973400	−	0.229113i	$-0.0735825\pi$
$390$		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	−0.491738	−	0.870743i	$-0.663638\pi$
$397$	2998.00	−	2998.00i	0.379005	−	0.379005i	0.870743	+	0.491738i	$0.163638\pi$
$398$	−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	0.944505	−	0.328496i	$-0.106542\pi$
$433$	5550.33	+	5550.33i	0.616009	+	0.616009i	−0.328496	+	0.944505i	$0.606542\pi$
$434$	−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	−0.524458	−	0.851436i	$-0.675732\pi$
$443$	3048.77	−	3048.77i	0.326979	−	0.326979i	0.851436	+	0.524458i	$0.175732\pi$
$444$	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	$-0.893744\pi$
$449$		−	6234.57i		−	0.655295i	0.944800	−	0.327648i	$-0.106256\pi$
$450$		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	0.841312	−	0.540549i	$-0.181784\pi$
$457$	2938.32	+	2938.32i	0.300763	+	0.300763i	−0.540549	+	0.841312i	$0.681784\pi$
$458$	−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	$0.206592\pi$
$461$			11965.0i			1.20882i	−0.796672	+	0.604411i	$0.793408\pi$
$462$	3046.83	−	7559.69i	0.306821	−	0.761274i
$463$	−4892.04	+	4892.04i	−0.491042	+	0.491042i	−0.908634	−	0.417592i	$-0.862874\pi$
$463$	−4892.04	+	4892.04i	−0.491042	+	0.491042i	0.417592	+	0.908634i	$0.362874\pi$
$464$			1185.46i			0.118607i
$465$		0			0
$466$	8151.82			0.810356
$467$	6801.21	−	6801.21i	0.673924	−	0.673924i	−0.284694	−	0.958618i	$-0.591892\pi$
$467$	6801.21	−	6801.21i	0.673924	−	0.673924i	0.958618	+	0.284694i	$0.0918921\pi$
$468$	−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	0.814224	−	0.580551i	$-0.197163\pi$
$487$	2511.31	+	2511.31i	0.233672	+	0.233672i	−0.580551	+	0.814224i	$0.697163\pi$
$488$	−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	$0.326531\pi$
$499$			19064.3i			1.71029i	−0.518390	+	0.855144i	$0.673469\pi$
$500$		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	0.979218	−	0.202811i	$-0.0650077\pi$
$503$	8758.73	+	8758.73i	0.776407	+	0.776407i	−0.202811	+	0.979218i	$0.565008\pi$
$504$	−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	$-0.871626\pi$
$521$		−	9334.16i		−	0.784908i	0.919772	−	0.392454i	$-0.128374\pi$
$522$	13337.6	+	13337.6i	1.11834	+	1.11834i
$523$	−2029.57	−	2029.57i	−0.169688	−	0.169688i	0.617154	−	0.786842i	$-0.288285\pi$
$523$	−2029.57	−	2029.57i	−0.169688	−	0.169688i	−0.786842	+	0.617154i	$0.788285\pi$
$524$	−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	0.444756	−	0.895652i	$-0.353290\pi$
$547$	−5768.43	−	5768.43i	−0.450896	−	0.450896i	−0.895652	+	0.444756i	$0.853290\pi$
$548$	−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	0.161704	−	0.986839i	$-0.448301\pi$
$557$	−10847.0	−	10847.0i	−0.825135	−	0.825135i	−0.986839	+	0.161704i	$0.948301\pi$
$558$	−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	0.879185	−	0.476480i	$-0.158088\pi$
$563$	5379.59	+	5379.59i	0.402705	+	0.402705i	−0.476480	+	0.879185i	$0.658088\pi$
$564$		−	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	$-0.965127\pi$
$569$		−	2968.05i		−	0.218677i	0.994005	−	0.109339i	$-0.0348733\pi$
$570$		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	−0.713320	−	0.700839i	$-0.752809\pi$
$577$	−172.987	+	172.987i	−0.0124810	+	0.0124810i	0.700839	+	0.713320i	$0.252809\pi$
$578$	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	−0.746946	−	0.664884i	$-0.768481\pi$
$587$	−1167.08	+	1167.08i	−0.0820620	+	0.0820620i	0.664884	+	0.746946i	$0.268481\pi$
$588$	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	0.406882	−	0.913481i	$-0.366616\pi$
$593$	−7315.54	−	7315.54i	−0.506599	−	0.506599i	−0.913481	+	0.406882i	$0.866616\pi$
$594$	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	$-0.623618\pi$
$599$		−	27137.0i		−	1.85107i	0.378668	−	0.925533i	$-0.376382\pi$
$600$		0			0
$601$			14268.6i			0.968436i	0.874947	+	0.484218i	$0.160896\pi$
$601$			14268.6i			0.968436i	−0.874947	+	0.484218i	$0.839104\pi$
$602$	−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	−0.117606	+	0.993060i	$0.537522\pi$
$607$	−16609.9	+	16609.9i	−1.11067	+	1.11067i	−0.993060	+	0.117606i	$0.962478\pi$
$608$	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	−0.965344	−	0.260979i	$-0.915955\pi$
$613$	−10690.3	+	10690.3i	−0.704365	+	0.704365i	0.260979	+	0.965344i	$0.415955\pi$
$614$	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	0.907248	−	0.420596i	$-0.138179\pi$
$617$	7458.41	+	7458.41i	0.486652	+	0.486652i	−0.420596	+	0.907248i	$0.638179\pi$
$618$	−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	0.552721	−	0.833366i	$-0.313589\pi$
$643$	−4575.87	−	4575.87i	−0.280645	−	0.280645i	−0.833366	+	0.552721i	$0.813589\pi$
$644$	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	−0.695864	−	0.718173i	$-0.744978\pi$
$647$	367.147	−	367.147i	0.0223092	−	0.0223092i	0.718173	+	0.695864i	$0.244978\pi$
$648$	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	−0.490488	−	0.871448i	$-0.663181\pi$
$653$	6356.95	−	6356.95i	0.380960	−	0.380960i	0.871448	+	0.490488i	$0.163181\pi$
$654$	−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	$-0.858417\pi$
$659$		−	14558.0i		−	0.860546i	0.902699	−	0.430273i	$-0.141583\pi$
$660$		0			0
$661$		−	22883.5i		−	1.34655i	−0.739394	−	0.673273i	$-0.764888\pi$
$661$		−	22883.5i		−	1.34655i	0.739394	−	0.673273i	$-0.235112\pi$
$662$	−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	0.124641	−	0.992202i	$-0.460222\pi$
$673$	19499.1	−	19499.1i	1.11684	−	1.11684i	0.992202	−	0.124641i	$-0.0397778\pi$
$674$		−	1335.81i		−	0.0763406i
$675$		0			0
$676$	−9243.89			−0.525938
$677$	−2638.87	+	2638.87i	−0.149808	+	0.149808i	−0.778032	−	0.628224i	$-0.783782\pi$
$677$	−2638.87	+	2638.87i	−0.149808	+	0.149808i	0.628224	+	0.778032i	$0.283782\pi$
$678$	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	−0.951401	−	0.307954i	$-0.900356\pi$
$683$	−11485.3	+	11485.3i	−0.643447	+	0.643447i	0.307954	+	0.951401i	$0.400356\pi$
$684$	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	$0.117827\pi$
$691$			13142.5i			0.723540i	−0.932267	+	0.361770i	$0.882173\pi$
$692$	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	$0.0577558\pi$
$709$			6813.33i			0.360903i	−0.983584	+	0.180451i	$0.942244\pi$
$710$		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	−0.942612	−	0.333890i	$-0.891639\pi$
$727$	−11932.2	+	11932.2i	−0.608722	+	0.608722i	0.333890	+	0.942612i	$0.391639\pi$
$728$	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	0.975872	+	0.218341i	$0.0700646\pi$
$733$	23699.4	+	23699.4i	1.19421	+	1.19421i	0.218341	+	0.975872i	$0.429935\pi$
$734$	−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	$0.218012\pi$
$739$			25417.1i			1.26520i	−0.774479	+	0.632599i	$0.781988\pi$
$740$		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	−0.852883	−	0.522102i	$-0.825148\pi$
$743$	−6699.21	+	6699.21i	−0.330781	+	0.330781i	0.522102	+	0.852883i	$0.325148\pi$
$744$			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	0.542199	−	0.840250i	$-0.317592\pi$
$757$	−6207.76	−	6207.76i	−0.298051	−	0.298051i	−0.840250	+	0.542199i	$0.817592\pi$
$758$	−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	$0.0728406\pi$
$761$			9524.31i			0.453687i	−0.973931	+	0.226844i	$0.927159\pi$
$762$	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	0.622213	−	0.782848i	$-0.286234\pi$
$773$	−3452.33	−	3452.33i	−0.160636	−	0.160636i	−0.782848	+	0.622213i	$0.786234\pi$
$774$		−	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	−0.140657	+	0.990058i	$0.544921\pi$
$787$	−24964.1	+	24964.1i	−1.13072	+	1.13072i	−0.990058	+	0.140657i	$0.955079\pi$
$788$	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	−0.785249	−	0.619180i	$-0.787465\pi$
$797$	−3736.59	+	3736.59i	−0.166069	+	0.166069i	0.619180	+	0.785249i	$0.287465\pi$
$798$	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	$-0.777500\pi$
$809$		−	29612.2i		−	1.28691i	0.765484	−	0.643455i	$-0.222500\pi$
$810$		0			0
$811$			13678.2i			0.592241i	0.955151	+	0.296121i	$0.0956931\pi$
$811$			13678.2i			0.592241i	−0.955151	+	0.296121i	$0.904307\pi$
$812$	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	−0.759991	−	0.649933i	$-0.774797\pi$
$823$	−2598.49	+	2598.49i	−0.110058	+	0.110058i	0.649933	+	0.759991i	$0.274797\pi$
$824$	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	−0.995461	−	0.0951702i	$-0.969660\pi$
$827$	−25938.0	−	25938.0i	−1.09063	−	1.09063i	−0.0951702	−	0.995461i	$-0.530340\pi$
$828$	−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	0.888475	−	0.458924i	$-0.151765\pi$
$853$	10701.3	+	10701.3i	0.429551	+	0.429551i	−0.458924	+	0.888475i	$0.651765\pi$
$854$	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	−0.956771	−	0.290844i	$-0.906064\pi$
$857$	−16707.0	+	16707.0i	−0.665927	+	0.665927i	0.290844	+	0.956771i	$0.406064\pi$
$858$	−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	−0.0458157	+	0.998950i	$0.514589\pi$
$863$	−26487.1	+	26487.1i	−1.04477	+	1.04477i	−0.998950	+	0.0458157i	$0.985411\pi$
$864$	−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	0.985992	−	0.166793i	$-0.0533412\pi$
$877$	21275.9	+	21275.9i	0.819199	+	0.819199i	−0.166793	+	0.985992i	$0.553341\pi$
$878$	−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	$-0.801550\pi$
$881$		−	30534.2i		−	1.16768i	0.811870	−	0.583839i	$-0.198450\pi$
$882$	39803.7	−	762.578i	1.51957	−	0.0291126i
$883$	−5071.07	+	5071.07i	−0.193268	+	0.193268i	−0.797106	−	0.603839i	$-0.793637\pi$
$883$	−5071.07	+	5071.07i	−0.193268	+	0.193268i	0.603839	+	0.797106i	$0.293637\pi$
$884$		−	577.524i		−	0.0219731i
$885$		0			0
$886$	−8035.41			−0.304690
$887$	−22739.1	+	22739.1i	−0.860770	+	0.860770i	−0.991428	−	0.130658i	$-0.958291\pi$
$887$	−22739.1	+	22739.1i	−0.860770	+	0.860770i	0.130658	+	0.991428i	$0.458291\pi$
$888$	−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	0.573092	−	0.819491i	$-0.305744\pi$
$907$	−6730.54	−	6730.54i	−0.246399	−	0.246399i	−0.819491	+	0.573092i	$0.805744\pi$
$908$	−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	$0.0335081\pi$
$919$			5854.64i			0.210149i	−0.994464	+	0.105074i	$0.966492\pi$
$920$		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	0.274101	−	0.961701i	$-0.411620\pi$
$937$	35445.3	−	35445.3i	1.23580	−	1.23580i	0.961701	−	0.274101i	$-0.0883801\pi$
$938$	−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	$0.100196\pi$
$941$			17873.9i			0.619207i	−0.950866	+	0.309604i	$0.899804\pi$
$942$	−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	−0.987742	−	0.156097i	$-0.950109\pi$
$947$	−33334.2	−	33334.2i	−1.14384	−	1.14384i	−0.156097	−	0.987742i	$-0.549891\pi$
$948$	−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	−0.520884	−	0.853627i	$-0.674398\pi$
$953$	9789.22	−	9789.22i	0.332743	−	0.332743i	0.853627	+	0.520884i	$0.174398\pi$
$954$			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	0.917275	−	0.398254i	$-0.130384\pi$
$967$	15607.2	+	15607.2i	0.519021	+	0.519021i	−0.398254	+	0.917275i	$0.630384\pi$
$968$	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	$0.140814\pi$
$971$			25905.8i			0.856186i	−0.903735	+	0.428093i	$0.859186\pi$
$972$	−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	0.908862	−	0.417097i	$-0.136952\pi$
$977$	15017.6	+	15017.6i	0.491766	+	0.491766i	−0.417097	+	0.908862i	$0.636952\pi$
$978$	−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	0.868874	−	0.495033i	$-0.164844\pi$
$983$	11521.7	+	11521.7i	0.373841	+	0.373841i	−0.495033	+	0.868874i	$0.664844\pi$
$984$			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	−0.913289	−	0.407313i	$-0.866466\pi$
$997$	−15928.4	+	15928.4i	−0.505975	+	0.505975i	0.407313	+	0.913289i	$0.366466\pi$
$998$	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.132.4		16
5.2	odd	4		35.4.f.b.13.6	yes	16
5.3	odd	4	inner	175.4.f.g.118.3		16
5.4	even	2		35.4.f.b.27.5	yes	16
7.6	odd	2	inner	175.4.f.g.132.3		16
35.2	odd	12		245.4.l.b.178.4		32
35.4	even	6		245.4.l.b.117.3		32
35.9	even	6		245.4.l.b.227.6		32
35.12	even	12		245.4.l.b.178.3		32
35.13	even	4	inner	175.4.f.g.118.4		16
35.17	even	12		245.4.l.b.68.6		32
35.19	odd	6		245.4.l.b.227.5		32
35.24	odd	6		245.4.l.b.117.4		32
35.27	even	4		35.4.f.b.13.5	✓	16
35.32	odd	12		245.4.l.b.68.5		32
35.34	odd	2		35.4.f.b.27.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.f.b.13.5	✓	16	35.27	even	4
35.4.f.b.13.6	yes	16	5.2	odd	4
35.4.f.b.27.5	yes	16	5.4	even	2
35.4.f.b.27.6	yes	16	35.34	odd	2
175.4.f.g.118.3		16	5.3	odd	4	inner
175.4.f.g.118.4		16	35.13	even	4	inner
175.4.f.g.132.3		16	7.6	odd	2	inner
175.4.f.g.132.4		16	1.1	even	1	trivial
245.4.l.b.68.5		32	35.32	odd	12
245.4.l.b.68.6		32	35.17	even	12
245.4.l.b.117.3		32	35.4	even	6
245.4.l.b.117.4		32	35.24	odd	6
245.4.l.b.178.3		32	35.12	even	12
245.4.l.b.178.4		32	35.2	odd	12
245.4.l.b.227.5		32	35.19	odd	6
245.4.l.b.227.6		32	35.9	even	6

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

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