LMFDB - Embedded newform 925.2.f.f.43.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(43,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("925.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.15
Character	$\chi$	$=$	925.43
Dual form			925.2.f.f.882.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.715481i q^{2} +(-0.0427756 + 0.0427756i) q^{3} +1.48809 q^{4} +(-0.0306051 - 0.0306051i) q^{6} +(0.0275714 - 0.0275714i) q^{7} +2.49566i q^{8} +2.99634i q^{9} +5.26598i q^{11} +(-0.0636538 + 0.0636538i) q^{12} -4.18897i q^{13} +(0.0197268 + 0.0197268i) q^{14} +1.19058 q^{16} -0.926314 q^{17} -2.14382 q^{18} +(-4.88259 + 4.88259i) q^{19} +0.00235876i q^{21} -3.76771 q^{22} -2.22938i q^{23} +(-0.106753 - 0.106753i) q^{24} +2.99713 q^{26} +(-0.256497 - 0.256497i) q^{27} +(0.0410286 - 0.0410286i) q^{28} +(-0.240739 - 0.240739i) q^{29} +(4.46100 - 4.46100i) q^{31} +5.84315i q^{32} +(-0.225255 - 0.225255i) q^{33} -0.662760i q^{34} +4.45882i q^{36} +(1.61350 + 5.86486i) q^{37} +(-3.49340 - 3.49340i) q^{38} +(0.179186 + 0.179186i) q^{39} -2.57150i q^{41} -0.00168765 q^{42} -2.51937i q^{43} +7.83623i q^{44} +1.59508 q^{46} +(-5.85521 + 5.85521i) q^{47} +(-0.0509276 + 0.0509276i) q^{48} +6.99848i q^{49} +(0.0396236 - 0.0396236i) q^{51} -6.23356i q^{52} +(9.82144 + 9.82144i) q^{53} +(0.183519 - 0.183519i) q^{54} +(0.0688088 + 0.0688088i) q^{56} -0.417712i q^{57} +(0.172244 - 0.172244i) q^{58} +(2.74050 - 2.74050i) q^{59} +(8.05038 - 8.05038i) q^{61} +(3.19176 + 3.19176i) q^{62} +(0.0826132 + 0.0826132i) q^{63} -1.79951 q^{64} +(0.161166 - 0.161166i) q^{66} +(-7.34282 - 7.34282i) q^{67} -1.37844 q^{68} +(0.0953629 + 0.0953629i) q^{69} +5.42263 q^{71} -7.47785 q^{72} +(9.24390 - 9.24390i) q^{73} +(-4.19620 + 1.15443i) q^{74} +(-7.26572 + 7.26572i) q^{76} +(0.145190 + 0.145190i) q^{77} +(-0.128204 + 0.128204i) q^{78} +(-2.23842 + 2.23842i) q^{79} -8.96708 q^{81} +1.83986 q^{82} +(5.68166 + 5.68166i) q^{83} +0.00351005i q^{84} +1.80256 q^{86} +0.0205955 q^{87} -13.1421 q^{88} +(5.42270 + 5.42270i) q^{89} +(-0.115496 - 0.115496i) q^{91} -3.31751i q^{92} +0.381644i q^{93} +(-4.18929 - 4.18929i) q^{94} +(-0.249945 - 0.249945i) q^{96} -6.18329 q^{97} -5.00728 q^{98} -15.7787 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 40 q^{4} + 8 q^{14} + 64 q^{16} + 12 q^{19} - 52 q^{24} - 16 q^{26} + 20 q^{31} + 32 q^{39} - 24 q^{46} - 36 q^{51} - 116 q^{54} - 28 q^{56} + 28 q^{59} - 20 q^{61} - 24 q^{64} - 76 q^{66} + 68 q^{69}+ \cdots - 48 q^{99}+O(q^{100}) $ 48 * q - 40 * q^4 + 8 * q^14 + 64 * q^16 + 12 * q^19 - 52 * q^24 - 16 * q^26 + 20 * q^31 + 32 * q^39 - 24 * q^46 - 36 * q^51 - 116 * q^54 - 28 * q^56 + 28 * q^59 - 20 * q^61 - 24 * q^64 - 76 * q^66 + 68 * q^69 + 48 * q^71 - 72 * q^74 - 100 * q^76 + 80 * q^79 - 80 * q^81 - 176 * q^86 + 32 * q^89 + 12 * q^91 - 44 * q^94 + 36 * q^96 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$			0.715481i			0.505921i	0.967477	+	0.252961i	$0.0814044\pi$
$2$			0.715481i			0.505921i	−0.967477	+	0.252961i	$0.918596\pi$
$3$	−0.0427756	+	0.0427756i	−0.0246965	+	0.0246965i	−0.719347	−	0.694651i	$-0.755559\pi$
$3$	−0.0427756	+	0.0427756i	−0.0246965	+	0.0246965i	0.694651	+	0.719347i	$0.255559\pi$
$4$	1.48809			0.744043
$5$		0			0
$5$		0			0
$6$	−0.0306051	−	0.0306051i	−0.0124945	−	0.0124945i
$7$	0.0275714	−	0.0275714i	0.0104210	−	0.0104210i	−0.701877	−	0.712298i	$-0.747654\pi$
$7$	0.0275714	−	0.0275714i	0.0104210	−	0.0104210i	0.712298	+	0.701877i	$0.247654\pi$
$8$			2.49566i			0.882349i
$9$			2.99634i			0.998780i
$10$		0			0
$11$			5.26598i			1.58775i	0.608080	+	0.793876i	$0.291940\pi$
$11$			5.26598i			1.58775i	−0.608080	+	0.793876i	$0.708060\pi$
$12$	−0.0636538	+	0.0636538i	−0.0183753	+	0.0183753i
$13$		−	4.18897i		−	1.16181i	−0.813971	−	0.580906i	$-0.802698\pi$
$13$		−	4.18897i		−	1.16181i	0.813971	−	0.580906i	$-0.197302\pi$
$14$	0.0197268	+	0.0197268i	0.00527221	+	0.00527221i
$15$		0			0
$16$	1.19058			0.297644
$17$	−0.926314			−0.224664			−0.112332	−	0.993671i	$-0.535832\pi$
$17$	−0.926314			−0.224664			−0.112332	+	0.993671i	$0.535832\pi$
$18$	−2.14382			−0.505304
$19$	−4.88259	+	4.88259i	−1.12014	+	1.12014i	−0.128424	+	0.991719i	$0.540992\pi$
$19$	−4.88259	+	4.88259i	−1.12014	+	1.12014i	−0.991719	+	0.128424i	$0.959008\pi$
$20$		0			0
$21$			0.00235876i			0.000514725i
$22$	−3.76771			−0.803278
$23$		−	2.22938i		−	0.464857i	−0.972613	−	0.232429i	$-0.925333\pi$
$23$		−	2.22938i		−	0.464857i	0.972613	−	0.232429i	$-0.0746672\pi$
$24$	−0.106753	−	0.106753i	−0.0217909	−	0.0217909i
$25$		0			0
$26$	2.99713			0.587786
$27$	−0.256497	−	0.256497i	−0.0493629	−	0.0493629i
$28$	0.0410286	−	0.0410286i	0.00775368	−	0.00775368i
$29$	−0.240739	−	0.240739i	−0.0447041	−	0.0447041i	0.684401	−	0.729105i	$-0.260064\pi$
$29$	−0.240739	−	0.240739i	−0.0447041	−	0.0447041i	−0.729105	+	0.684401i	$0.760064\pi$
$30$		0			0
$31$	4.46100	−	4.46100i	0.801220	−	0.801220i	−0.182066	−	0.983286i	$-0.558279\pi$
$31$	4.46100	−	4.46100i	0.801220	−	0.801220i	0.983286	+	0.182066i	$0.0582786\pi$
$32$			5.84315i			1.03293i
$33$	−0.225255	−	0.225255i	−0.0392119	−	0.0392119i
$34$		−	0.662760i		−	0.113662i
$35$		0			0
$36$			4.45882i			0.743136i
$37$	1.61350	+	5.86486i	0.265257	+	0.964178i
$37$	1.61350	+	5.86486i	0.265257	+	0.964178i
$38$	−3.49340	−	3.49340i	−0.566705	−	0.566705i
$39$	0.179186	+	0.179186i	0.0286927	+	0.0286927i
$40$		0			0
$41$		−	2.57150i		−	0.401601i	−0.979632	−	0.200801i	$-0.935646\pi$
$41$		−	2.57150i		−	0.401601i	0.979632	−	0.200801i	$-0.0643543\pi$
$42$	−0.00168765			−0.000260410
$43$		−	2.51937i		−	0.384200i	−0.981375	−	0.192100i	$-0.938470\pi$
$43$		−	2.51937i		−	0.384200i	0.981375	−	0.192100i	$-0.0615298\pi$
$44$			7.83623i			1.18136i
$45$		0			0
$46$	1.59508			0.235181
$47$	−5.85521	+	5.85521i	−0.854070	+	0.854070i	−0.990632	−	0.136562i	$-0.956395\pi$
$47$	−5.85521	+	5.85521i	−0.854070	+	0.854070i	0.136562	+	0.990632i	$0.456395\pi$
$48$	−0.0509276	+	0.0509276i	−0.00735077	+	0.00735077i
$49$			6.99848i			0.999783i
$50$		0			0
$51$	0.0396236	−	0.0396236i	0.00554842	−	0.00554842i
$52$		−	6.23356i		−	0.864439i
$53$	9.82144	+	9.82144i	1.34908	+	1.34908i	0.886663	+	0.462416i	$0.153017\pi$
$53$	9.82144	+	9.82144i	1.34908	+	1.34908i	0.462416	+	0.886663i	$0.346983\pi$
$54$	0.183519	−	0.183519i	0.0249737	−	0.0249737i
$55$		0			0
$56$	0.0688088	+	0.0688088i	0.00919496	+	0.00919496i
$57$		−	0.417712i		−	0.0553273i
$58$	0.172244	−	0.172244i	0.0226168	−	0.0226168i
$59$	2.74050	−	2.74050i	0.356783	−	0.356783i	−0.505843	−	0.862626i	$-0.668818\pi$
$59$	2.74050	−	2.74050i	0.356783	−	0.356783i	0.862626	+	0.505843i	$0.168818\pi$
$60$		0			0
$61$	8.05038	−	8.05038i	1.03075	−	1.03075i	0.0312335	−	0.999512i	$-0.490056\pi$
$61$	8.05038	−	8.05038i	1.03075	−	1.03075i	0.999512	−	0.0312335i	$-0.00994355\pi$
$62$	3.19176	+	3.19176i	0.405354	+	0.405354i
$63$	0.0826132	+	0.0826132i	0.0104083	+	0.0104083i
$64$	−1.79951			−0.224939
$65$		0			0
$66$	0.161166	−	0.161166i	0.0198382	−	0.0198382i
$67$	−7.34282	−	7.34282i	−0.897068	−	0.897068i	0.0981075	−	0.995176i	$-0.468721\pi$
$67$	−7.34282	−	7.34282i	−0.897068	−	0.897068i	−0.995176	+	0.0981075i	$0.968721\pi$
$68$	−1.37844			−0.167160
$69$	0.0953629	+	0.0953629i	0.0114803	+	0.0114803i
$70$		0			0
$71$	5.42263			0.643548			0.321774	−	0.946817i	$-0.395721\pi$
$71$	5.42263			0.643548			0.321774	+	0.946817i	$0.395721\pi$
$72$	−7.47785			−0.881273
$73$	9.24390	−	9.24390i	1.08192	−	1.08192i	0.0855854	−	0.996331i	$-0.472724\pi$
$73$	9.24390	−	9.24390i	1.08192	−	1.08192i	0.996331	−	0.0855854i	$-0.0272761\pi$
$74$	−4.19620	+	1.15443i	−0.487798	+	0.134199i
$75$		0			0
$76$	−7.26572	+	7.26572i	−0.833435	+	0.833435i
$77$	0.145190	+	0.145190i	0.0165460	+	0.0165460i
$78$	−0.128204	+	0.128204i	−0.0145163	+	0.0145163i
$79$	−2.23842	+	2.23842i	−0.251842	+	0.251842i	−0.821726	−	0.569883i	$-0.806988\pi$
$79$	−2.23842	+	2.23842i	−0.251842	+	0.251842i	0.569883	+	0.821726i	$0.306988\pi$
$80$		0			0
$81$	−8.96708			−0.996342
$82$	1.83986			0.203179
$83$	5.68166	+	5.68166i	0.623643	+	0.623643i	0.946461	−	0.322818i	$-0.104630\pi$
$83$	5.68166	+	5.68166i	0.623643	+	0.623643i	−0.322818	+	0.946461i	$0.604630\pi$
$84$			0.00351005i			0.000382977i
$85$		0			0
$86$	1.80256			0.194375
$87$	0.0205955			0.00220807
$88$	−13.1421			−1.40095
$89$	5.42270	+	5.42270i	0.574805	+	0.574805i	0.933467	−	0.358662i	$-0.116767\pi$
$89$	5.42270	+	5.42270i	0.574805	+	0.574805i	−0.358662	+	0.933467i	$0.616767\pi$
$90$		0			0
$91$	−0.115496	−	0.115496i	−0.0121072	−	0.0121072i
$92$		−	3.31751i		−	0.345874i
$93$			0.381644i			0.0395747i
$94$	−4.18929	−	4.18929i	−0.432092	−	0.432092i
$95$		0			0
$96$	−0.249945	−	0.249945i	−0.0255099	−	0.0255099i
$97$	−6.18329			−0.627818			−0.313909	−	0.949453i	$-0.601639\pi$
$97$	−6.18329			−0.627818			−0.313909	+	0.949453i	$0.601639\pi$
$98$	−5.00728			−0.505812
$99$	−15.7787			−1.58582
$100$		0			0
$101$		−	6.08887i		−	0.605865i	−0.953012	−	0.302932i	$-0.902034\pi$
$101$		−	6.08887i		−	0.605865i	0.953012	−	0.302932i	$-0.0979656\pi$
$102$	0.0283500	+	0.0283500i	0.00280706	+	0.00280706i
$103$	−12.3217			−1.21409			−0.607047	−	0.794666i	$-0.707646\pi$
$103$	−12.3217			−1.21409			−0.607047	+	0.794666i	$0.707646\pi$
$104$	10.4543			1.02512
$105$		0			0
$106$	−7.02706	+	7.02706i	−0.682528	+	0.682528i
$107$	−7.63887	+	7.63887i	−0.738477	+	0.738477i	−0.972283	−	0.233806i	$-0.924882\pi$
$107$	−7.63887	+	7.63887i	−0.738477	+	0.738477i	0.233806	+	0.972283i	$0.424882\pi$
$108$	−0.381690	−	0.381690i	−0.0367281	−	0.0367281i
$109$	9.60192	−	9.60192i	0.919697	−	0.919697i	−0.0773097	−	0.997007i	$-0.524633\pi$
$109$	9.60192	−	9.60192i	0.919697	−	0.919697i	0.997007	+	0.0773097i	$0.0246330\pi$
$110$		0			0
$111$	−0.319891	−	0.181855i	−0.0303627	−	0.0172609i
$112$	0.0328258	−	0.0328258i	0.00310175	−	0.00310175i
$113$	−14.1139			−1.32773			−0.663863	−	0.747854i	$-0.731084\pi$
$113$	−14.1139			−1.32773			−0.663863	+	0.747854i	$0.731084\pi$
$114$	0.298865			0.0279913
$115$		0			0
$116$	−0.358241	−	0.358241i	−0.0332618	−	0.0332618i
$117$	12.5516			1.16040
$118$	1.96078	+	1.96078i	0.180504	+	0.180504i
$119$	−0.0255397	+	0.0255397i	−0.00234122	+	0.00234122i
$120$		0			0
$121$	−16.7305			−1.52096
$122$	5.75989	+	5.75989i	0.521476	+	0.521476i
$123$	0.109998	+	0.109998i	0.00991815	+	0.00991815i
$124$	6.63836	−	6.63836i	0.596142	−	0.596142i
$125$		0			0
$126$	−0.0591082	+	0.0591082i	−0.00526578	+	0.00526578i
$127$	1.17651	−	1.17651i	0.104399	−	0.104399i	−0.652978	−	0.757377i	$-0.726481\pi$
$127$	1.17651	−	1.17651i	0.104399	−	0.104399i	0.757377	+	0.652978i	$0.226481\pi$
$128$			10.3988i			0.919132i
$129$	0.107768	+	0.107768i	0.00948840	+	0.00948840i
$130$		0			0
$131$	14.6623	−	14.6623i	1.28105	−	1.28105i	0.340978	−	0.940071i	$-0.389242\pi$
$131$	14.6623	−	14.6623i	1.28105	−	1.28105i	0.940071	−	0.340978i	$-0.110758\pi$
$132$	−0.335200	−	0.335200i	−0.0291754	−	0.0291754i
$133$			0.269240i			0.0233460i
$134$	5.25365	−	5.25365i	0.453846	−	0.453846i
$135$		0			0
$136$		−	2.31176i		−	0.198232i
$137$	10.8942	−	10.8942i	0.930757	−	0.930757i	−0.0669964	−	0.997753i	$-0.521342\pi$
$137$	10.8942	−	10.8942i	0.930757	−	0.930757i	0.997753	+	0.0669964i	$0.0213416\pi$
$138$	−0.0682304	+	0.0682304i	−0.00580815	+	0.00580815i
$139$	5.55120			0.470846			0.235423	−	0.971893i	$-0.424352\pi$
$139$	5.55120			0.470846			0.235423	+	0.971893i	$0.424352\pi$
$140$		0			0
$141$		−	0.500920i		−	0.0421851i
$142$			3.87979i			0.325585i
$143$	22.0590			1.84467
$144$			3.56737i			0.297281i
$145$		0			0
$146$	6.61383	+	6.61383i	0.547365	+	0.547365i
$147$	−0.299364	−	0.299364i	−0.0246911	−	0.0246911i
$148$	2.40102	+	8.72743i	0.197363	+	0.717390i
$149$		−	11.1081i		−	0.910014i	−0.890488	−	0.455007i	$-0.849637\pi$
$149$		−	11.1081i		−	0.910014i	0.890488	−	0.455007i	$-0.150363\pi$
$150$		0			0
$151$			14.0367i			1.14229i	0.820850	+	0.571144i	$0.193500\pi$
$151$			14.0367i			1.14229i	−0.820850	+	0.571144i	$0.806500\pi$
$152$	−12.1853	−	12.1853i	−0.988358	−	0.988358i
$153$		−	2.77555i		−	0.224390i
$154$	−0.103881	+	0.103881i	−0.00837096	+	0.00837096i
$155$		0			0
$156$	0.266644	+	0.266644i	0.0213486	+	0.0213486i
$157$	1.50319	−	1.50319i	0.119967	−	0.119967i	−0.644574	−	0.764542i	$-0.722965\pi$
$157$	1.50319	−	1.50319i	0.119967	−	0.119967i	0.764542	+	0.644574i	$0.222965\pi$
$158$	−1.60155	−	1.60155i	−0.127412	−	0.127412i
$159$	−0.840236			−0.0666351
$160$		0			0
$161$	−0.0614669	−	0.0614669i	−0.00484427	−	0.00484427i
$162$		−	6.41577i		−	0.504071i
$163$	22.1630			1.73594			0.867970	−	0.496617i	$-0.165425\pi$
$163$	22.1630			1.73594			0.867970	+	0.496617i	$0.165425\pi$
$164$		−	3.82662i		−	0.298809i
$165$		0			0
$166$	−4.06512	+	4.06512i	−0.315514	+	0.315514i
$167$	13.4294			1.03920			0.519599	−	0.854410i	$-0.326081\pi$
$167$	13.4294			1.03920			0.519599	+	0.854410i	$0.326081\pi$
$168$	−0.00588667			−0.000454167
$169$	−4.54750			−0.349808
$170$		0			0
$171$	−14.6299	−	14.6299i	−1.11878	−	1.11878i
$172$		−	3.74904i		−	0.285862i
$173$	−0.347222	+	0.347222i	−0.0263988	+	0.0263988i	−0.720183	−	0.693784i	$-0.755942\pi$
$173$	−0.347222	+	0.347222i	−0.0263988	+	0.0263988i	0.693784	+	0.720183i	$0.255942\pi$
$174$			0.0147357i			0.00111711i
$175$		0			0
$176$			6.26955i			0.472585i
$177$			0.234453i			0.0176226i
$178$	−3.87984	+	3.87984i	−0.290806	+	0.290806i
$179$	−4.95444	−	4.95444i	−0.370312	−	0.370312i	0.497279	−	0.867591i	$-0.334333\pi$
$179$	−4.95444	−	4.95444i	−0.370312	−	0.370312i	−0.867591	+	0.497279i	$0.834333\pi$
$180$		0			0
$181$	−8.10979			−0.602796			−0.301398	−	0.953498i	$-0.597453\pi$
$181$	−8.10979			−0.602796			−0.301398	+	0.953498i	$0.597453\pi$
$182$	0.0826350	−	0.0826350i	0.00612531	−	0.00612531i
$183$			0.688720i			0.0509116i
$184$	5.56376			0.410166
$185$		0			0
$186$	−0.273059			−0.0200217
$187$		−	4.87795i		−	0.356711i
$188$	−8.71306	+	8.71306i	−0.635465	+	0.635465i
$189$	−0.0141440			−0.00102882
$190$		0			0
$191$	−2.19329	−	2.19329i	−0.158701	−	0.158701i	0.623290	−	0.781991i	$-0.285796\pi$
$191$	−2.19329	−	2.19329i	−0.158701	−	0.158701i	−0.781991	+	0.623290i	$0.785796\pi$
$192$	0.0769753	−	0.0769753i	0.00555521	−	0.00555521i
$193$		−	14.0361i		−	1.01034i	−0.863021	−	0.505169i	$-0.831430\pi$
$193$		−	14.0361i		−	1.01034i	0.863021	−	0.505169i	$-0.168570\pi$
$194$		−	4.42402i		−	0.317626i
$195$		0			0
$196$			10.4143i			0.743882i
$197$	15.1249	−	15.1249i	1.07761	−	1.07761i	0.0808819	−	0.996724i	$-0.474226\pi$
$197$	15.1249	−	15.1249i	1.07761	−	1.07761i	0.996724	−	0.0808819i	$-0.0257736\pi$
$198$		−	11.2893i		−	0.802298i
$199$	5.62952	+	5.62952i	0.399066	+	0.399066i	0.877904	−	0.478837i	$-0.158942\pi$
$199$	5.62952	+	5.62952i	0.399066	+	0.399066i	−0.478837	+	0.877904i	$0.658942\pi$
$200$		0			0
$201$	0.628187			0.0443089
$202$	4.35647			0.306520
$203$	−0.0132750			−0.000931723
$204$	0.0589634	−	0.0589634i	0.00412826	−	0.00412826i
$205$		0			0
$206$		−	8.81595i		−	0.614236i
$207$	6.67997			0.464290
$208$		−	4.98729i		−	0.345807i
$209$	−25.7116	−	25.7116i	−1.77851	−	1.77851i
$210$		0			0
$211$	−3.08351			−0.212277			−0.106139	−	0.994351i	$-0.533849\pi$
$211$	−3.08351			−0.212277			−0.106139	+	0.994351i	$0.533849\pi$
$212$	14.6152	+	14.6152i	1.00377	+	1.00377i
$213$	−0.231956	+	0.231956i	−0.0158934	+	0.0158934i
$214$	−5.46547	−	5.46547i	−0.373612	−	0.373612i
$215$		0			0
$216$	0.640130	−	0.640130i	0.0435553	−	0.0435553i
$217$		−	0.245992i		−	0.0166990i
$218$	6.86999	+	6.86999i	0.465295	+	0.465295i
$219$			0.790827i			0.0534391i
$220$		0			0
$221$			3.88030i			0.261017i
$222$	0.130114	−	0.228876i	0.00873266	−	0.0153612i
$223$	−14.6332	−	14.6332i	−0.979913	−	0.979913i	0.0198893	−	0.999802i	$-0.493669\pi$
$223$	−14.6332	−	14.6332i	−0.979913	−	0.979913i	−0.999802	+	0.0198893i	$0.993669\pi$
$224$	0.161104	+	0.161104i	0.0107642	+	0.0107642i
$225$		0			0
$226$		−	10.0982i		−	0.671726i
$227$	−2.03489			−0.135060			−0.0675301	−	0.997717i	$-0.521512\pi$
$227$	−2.03489			−0.135060			−0.0675301	+	0.997717i	$0.521512\pi$
$228$		−	0.621591i		−	0.0411659i
$229$		−	4.75926i		−	0.314501i	−0.987559	−	0.157250i	$-0.949737\pi$
$229$		−	4.75926i		−	0.314501i	0.987559	−	0.157250i	$-0.0502630\pi$
$230$		0			0
$231$	−0.0124212			−0.000817255
$232$	0.600803	−	0.600803i	0.0394447	−	0.0394447i
$233$	−0.227731	+	0.227731i	−0.0149192	+	0.0149192i	−0.714527	−	0.699608i	$-0.753358\pi$
$233$	−0.227731	+	0.227731i	−0.0149192	+	0.0149192i	0.699608	+	0.714527i	$0.253358\pi$
$234$			8.98043i			0.587069i
$235$		0			0
$236$	4.07811	−	4.07811i	0.265462	−	0.265462i
$237$		−	0.191500i		−	0.0124392i
$238$	−0.0182732	−	0.0182732i	−0.00118448	−	0.00118448i
$239$	6.93429	−	6.93429i	0.448542	−	0.448542i	−0.446328	−	0.894869i	$-0.647268\pi$
$239$	6.93429	−	6.93429i	0.448542	−	0.448542i	0.894869	+	0.446328i	$0.147268\pi$
$240$		0			0
$241$	−10.4973	−	10.4973i	−0.676192	−	0.676192i	0.282944	−	0.959136i	$-0.408689\pi$
$241$	−10.4973	−	10.4973i	−0.676192	−	0.676192i	−0.959136	+	0.282944i	$0.908689\pi$
$242$		−	11.9704i		−	0.769485i
$243$	1.15306	−	1.15306i	0.0739691	−	0.0739691i
$244$	11.9797	−	11.9797i	0.766920	−	0.766920i
$245$		0			0
$246$	−0.0787012	+	0.0787012i	−0.00501780	+	0.00501780i
$247$	20.4531	+	20.4531i	1.30140	+	1.30140i
$248$	11.1331	+	11.1331i	0.706956	+	0.706956i
$249$	−0.486073			−0.0308036
$250$		0			0
$251$	5.00819	−	5.00819i	0.316114	−	0.316114i	−0.531158	−	0.847273i	$-0.678243\pi$
$251$	5.00819	−	5.00819i	0.316114	−	0.316114i	0.847273	+	0.531158i	$0.178243\pi$
$252$	0.122936	+	0.122936i	0.00774422	+	0.00774422i
$253$	11.7398			0.738078
$254$	0.841772	+	0.841772i	0.0528175	+	0.0528175i
$255$		0			0
$256$	−11.0392			−0.689948
$257$	−3.32518			−0.207419			−0.103710	−	0.994608i	$-0.533071\pi$
$257$	−3.32518			−0.207419			−0.103710	+	0.994608i	$0.533071\pi$
$258$	−0.0771056	+	0.0771056i	−0.00480039	+	0.00480039i
$259$	0.206189	+	0.117216i	0.0128119	+	0.00728345i
$260$		0			0
$261$	0.721336	−	0.721336i	0.0446496	−	0.0446496i
$262$	10.4906	+	10.4906i	0.648110	+	0.648110i
$263$	8.70082	−	8.70082i	0.536516	−	0.536516i	−0.385988	−	0.922504i	$-0.626139\pi$
$263$	8.70082	−	8.70082i	0.536516	−	0.536516i	0.922504	+	0.385988i	$0.126139\pi$
$264$	0.562161	−	0.562161i	0.0345986	−	0.0345986i
$265$		0			0
$266$	−0.192636			−0.0118113
$267$	−0.463919			−0.0283914
$268$	−10.9268	−	10.9268i	−0.667458	−	0.667458i
$269$		−	14.5304i		−	0.885932i	−0.896538	−	0.442966i	$-0.853926\pi$
$269$		−	14.5304i		−	0.885932i	0.896538	−	0.442966i	$-0.146074\pi$
$270$		0			0
$271$	14.6118			0.887605			0.443802	−	0.896125i	$-0.353629\pi$
$271$	14.6118			0.887605			0.443802	+	0.896125i	$0.353629\pi$
$272$	−1.10285			−0.0668699
$273$	0.00988080			0.000598013
$274$	7.79461	+	7.79461i	0.470890	+	0.470890i
$275$		0			0
$276$	0.141908	+	0.141908i	0.00854188	+	0.00854188i
$277$			1.60224i			0.0962691i	0.998841	+	0.0481346i	$0.0153276\pi$
$277$			1.60224i			0.0962691i	−0.998841	+	0.0481346i	$0.984672\pi$
$278$			3.97178i			0.238211i
$279$	13.3667	+	13.3667i	0.800243	+	0.800243i
$280$		0			0
$281$	13.1357	+	13.1357i	0.783609	+	0.783609i	0.980438	−	0.196829i	$-0.0630642\pi$
$281$	13.1357	+	13.1357i	0.783609	+	0.783609i	−0.196829	+	0.980438i	$0.563064\pi$
$282$	0.358399			0.0213423
$283$	−19.4089			−1.15374			−0.576868	−	0.816837i	$-0.695725\pi$
$283$	−19.4089			−1.15374			−0.576868	+	0.816837i	$0.695725\pi$
$284$	8.06935			0.478828
$285$		0			0
$286$			15.7828i			0.933258i
$287$	−0.0708998	−	0.0708998i	−0.00418509	−	0.00418509i
$288$	−17.5081			−1.03167
$289$	−16.1419			−0.949526
$290$		0			0
$291$	0.264494	−	0.264494i	0.0155049	−	0.0155049i
$292$	13.7557	−	13.7557i	0.804993	−	0.804993i
$293$	18.7278	+	18.7278i	1.09409	+	1.09409i	0.995087	+	0.0990018i	$0.0315650\pi$
$293$	18.7278	+	18.7278i	1.09409	+	1.09409i	0.0990018	+	0.995087i	$0.468435\pi$
$294$	0.214189	−	0.214189i	0.0124918	−	0.0124918i
$295$		0			0
$296$	−14.6367	+	4.02674i	−0.850741	+	0.234049i
$297$	1.35071	−	1.35071i	0.0783760	−	0.0783760i
$298$	7.94766			0.460396
$299$	−9.33880			−0.540077
$300$		0			0
$301$	−0.0694624	−	0.0694624i	−0.00400375	−	0.00400375i
$302$	−10.0430			−0.577908
$303$	0.260455	+	0.260455i	0.0149627	+	0.0149627i
$304$	−5.81310	+	5.81310i	−0.333404	+	0.333404i
$305$		0			0
$306$	1.98585			0.113524
$307$	−17.3114	−	17.3114i	−0.988014	−	0.988014i	0.0119148	−	0.999929i	$-0.496207\pi$
$307$	−17.3114	−	17.3114i	−0.988014	−	0.988014i	−0.999929	+	0.0119148i	$0.996207\pi$
$308$	0.216056	+	0.216056i	0.0123109	+	0.0123109i
$309$	0.527068	−	0.527068i	0.0299839	−	0.0299839i
$310$		0			0
$311$	0.429170	−	0.429170i	0.0243360	−	0.0243360i	−0.694834	−	0.719170i	$-0.744522\pi$
$311$	0.429170	−	0.429170i	0.0243360	−	0.0243360i	0.719170	+	0.694834i	$0.244522\pi$
$312$	−0.447187	+	0.447187i	−0.0253170	+	0.0253170i
$313$			14.4025i			0.814077i	0.913411	+	0.407039i	$0.133439\pi$
$313$			14.4025i			0.814077i	−0.913411	+	0.407039i	$0.866561\pi$
$314$	1.07550	+	1.07550i	0.0606940	+	0.0606940i
$315$		0			0
$316$	−3.33097	+	3.33097i	−0.187381	+	0.187381i
$317$	−13.8484	−	13.8484i	−0.777805	−	0.777805i	0.201652	−	0.979457i	$-0.435369\pi$
$317$	−13.8484	−	13.8484i	−0.777805	−	0.777805i	−0.979457	+	0.201652i	$0.935369\pi$
$318$		−	0.601173i		−	0.0337121i
$319$	1.26773	−	1.26773i	0.0709791	−	0.0709791i
$320$		0			0
$321$		−	0.653515i		−	0.0364756i
$322$	0.0439784	−	0.0439784i	0.00245082	−	0.00245082i
$323$	4.52281	−	4.52281i	0.251656	−	0.251656i
$324$	−13.3438			−0.741322
$325$		0			0
$326$			15.8572i			0.878249i
$327$			0.821456i			0.0454266i
$328$	6.41760			0.354352
$329$			0.322872i			0.0178005i
$330$		0			0
$331$	−7.97242	−	7.97242i	−0.438204	−	0.438204i	0.453203	−	0.891407i	$-0.350281\pi$
$331$	−7.97242	−	7.97242i	−0.438204	−	0.438204i	−0.891407	+	0.453203i	$0.850281\pi$
$332$	8.45480	+	8.45480i	0.464017	+	0.464017i
$333$	−17.5731	+	4.83458i	−0.963002	+	0.264933i
$334$			9.60848i			0.525753i
$335$		0			0
$336$			0.00280829i			0.000153205i
$337$	−4.31604	−	4.31604i	−0.235110	−	0.235110i	0.579712	−	0.814822i	$-0.303165\pi$
$337$	−4.31604	−	4.31604i	−0.235110	−	0.235110i	−0.814822	+	0.579712i	$0.803165\pi$
$338$		−	3.25365i		−	0.176975i
$339$	0.603732	−	0.603732i	0.0327902	−	0.0327902i
$340$		0			0
$341$	23.4915	+	23.4915i	1.27214	+	1.27214i
$342$	10.4674	−	10.4674i	0.566013	−	0.566013i
$343$	0.385957	+	0.385957i	0.0208397	+	0.0208397i
$344$	6.28749			0.338999
$345$		0			0
$346$	−0.248431	−	0.248431i	−0.0133557	−	0.0133557i
$347$			31.5847i			1.69555i	0.530353	+	0.847777i	$0.322060\pi$
$347$			31.5847i			1.69555i	−0.530353	+	0.847777i	$0.677940\pi$
$348$	0.0306479			0.00164290
$349$		−	31.4804i		−	1.68511i	−0.538614	−	0.842553i	$-0.681052\pi$
$349$		−	31.4804i		−	1.68511i	0.538614	−	0.842553i	$-0.318948\pi$
$350$		0			0
$351$	−1.07446	+	1.07446i	−0.0573504	+	0.0573504i
$352$	−30.7699			−1.64004
$353$	−4.40596			−0.234506			−0.117253	−	0.993102i	$-0.537409\pi$
$353$	−4.40596			−0.234506			−0.117253	+	0.993102i	$0.537409\pi$
$354$	−0.167747			−0.00891565
$355$		0			0
$356$	8.06945	+	8.06945i	0.427680	+	0.427680i
$357$		−	0.00218496i		−	0.000115640i
$358$	3.54481	−	3.54481i	0.187349	−	0.187349i
$359$			26.2092i			1.38327i	0.722249	+	0.691634i	$0.243109\pi$
$359$			26.2092i			1.38327i	−0.722249	+	0.691634i	$0.756891\pi$
$360$		0			0
$361$		−	28.6794i		−	1.50944i
$362$		−	5.80240i		−	0.304967i
$363$	0.715658	−	0.715658i	0.0375623	−	0.0375623i
$364$	−0.171868	−	0.171868i	−0.00900832	−	0.00900832i
$365$		0			0
$366$	−0.492766			−0.0257573
$367$	−6.54048	+	6.54048i	−0.341410	+	0.341410i	−0.856897	−	0.515487i	$-0.827611\pi$
$367$	−6.54048	+	6.54048i	−0.341410	+	0.341410i	0.515487	+	0.856897i	$0.327611\pi$
$368$		−	2.65424i		−	0.138362i
$369$	7.70510			0.401111
$370$		0			0
$371$	0.541581			0.0281175
$372$			0.567920i			0.0294453i
$373$	11.2619	−	11.2619i	0.583119	−	0.583119i	−0.352640	−	0.935759i	$-0.614716\pi$
$373$	11.2619	−	11.2619i	0.583119	−	0.583119i	0.935759	+	0.352640i	$0.114716\pi$
$374$	3.49008			0.180468
$375$		0			0
$376$	−14.6126	−	14.6126i	−0.753587	−	0.753587i
$377$	−1.00845	+	1.00845i	−0.0519378	+	0.0519378i
$378$		−	0.0101197i		−	0.000520503i
$379$			29.9982i			1.54090i	0.637498	+	0.770452i	$0.279970\pi$
$379$			29.9982i			1.54090i	−0.637498	+	0.770452i	$0.720030\pi$
$380$		0			0
$381$			0.100652i			0.00515656i
$382$	1.56926	−	1.56926i	0.0802903	−	0.0802903i
$383$			32.1226i			1.64139i	0.571366	+	0.820695i	$0.306414\pi$
$383$			32.1226i			1.64139i	−0.571366	+	0.820695i	$0.693586\pi$
$384$	−0.444815	−	0.444815i	−0.0226994	−	0.0226994i
$385$		0			0
$386$	10.0425			0.511151
$387$	7.54889			0.383731
$388$	−9.20127			−0.467124
$389$	1.67677	−	1.67677i	0.0850155	−	0.0850155i	−0.663320	−	0.748336i	$-0.730853\pi$
$389$	1.67677	−	1.67677i	0.0850155	−	0.0850155i	0.748336	+	0.663320i	$0.230853\pi$
$390$		0			0
$391$			2.06510i			0.104437i
$392$	−17.4658			−0.882157
$393$			1.25438i			0.0632749i
$394$	10.8216	+	10.8216i	0.545184	+	0.545184i
$395$		0			0
$396$	−23.4800			−1.17992
$397$	15.7557	+	15.7557i	0.790757	+	0.790757i	0.981617	−	0.190861i	$-0.0611278\pi$
$397$	15.7557	+	15.7557i	0.790757	+	0.790757i	−0.190861	+	0.981617i	$0.561128\pi$
$398$	−4.02782	+	4.02782i	−0.201896	+	0.201896i
$399$	−0.0115169	−	0.0115169i	−0.000576565	−	0.000576565i
$400$		0			0
$401$	−4.22356	+	4.22356i	−0.210915	+	0.210915i	−0.804656	−	0.593741i	$-0.797650\pi$
$401$	−4.22356	+	4.22356i	−0.210915	+	0.210915i	0.593741	+	0.804656i	$0.297650\pi$
$402$			0.449456i			0.0224168i
$403$	−18.6870	−	18.6870i	−0.930867	−	0.930867i
$404$		−	9.06076i		−	0.450790i
$405$		0			0
$406$		−	0.00949802i		−	0.000471379i
$407$	−30.8842	+	8.49663i	−1.53088	+	0.421162i
$408$	0.0988871	+	0.0988871i	0.00489564	+	0.00489564i
$409$	0.710984	+	0.710984i	0.0351559	+	0.0351559i	0.724466	−	0.689310i	$-0.242086\pi$
$409$	0.710984	+	0.710984i	0.0351559	+	0.0351559i	−0.689310	+	0.724466i	$0.742086\pi$
$410$		0			0
$411$			0.932015i			0.0459729i
$412$	−18.3358			−0.903338
$413$		−	0.151119i		−	0.00743608i
$414$			4.77939i			0.234894i
$415$		0			0
$416$	24.4768			1.20008
$417$	−0.237456	+	0.237456i	−0.0116283	+	0.0116283i
$418$	18.3962	−	18.3962i	0.899787	−	0.899787i
$419$			22.7576i			1.11178i	0.831256	+	0.555890i	$0.187622\pi$
$419$			22.7576i			1.11178i	−0.831256	+	0.555890i	$0.812378\pi$
$420$		0			0
$421$	4.90424	−	4.90424i	0.239018	−	0.239018i	−0.577425	−	0.816443i	$-0.695943\pi$
$421$	4.90424	−	4.90424i	0.239018	−	0.239018i	0.816443	+	0.577425i	$0.195943\pi$
$422$		−	2.20619i		−	0.107396i
$423$	−17.5442	−	17.5442i	−0.853028	−	0.853028i
$424$	−24.5110	+	24.5110i	−1.19036	+	1.19036i
$425$		0			0
$426$	−0.165960	−	0.165960i	−0.00804081	−	0.00804081i
$427$		−	0.443920i		−	0.0214828i
$428$	−11.3673	+	11.3673i	−0.549459	+	0.549459i
$429$	−0.943589	+	0.943589i	−0.0455569	+	0.0455569i
$430$		0			0
$431$	−7.09872	+	7.09872i	−0.341933	+	0.341933i	−0.857094	−	0.515160i	$-0.827732\pi$
$431$	−7.09872	+	7.09872i	−0.341933	+	0.341933i	0.515160	+	0.857094i	$0.327732\pi$
$432$	−0.305379	−	0.305379i	−0.0146926	−	0.0146926i
$433$	−9.41111	−	9.41111i	−0.452269	−	0.452269i	0.443838	−	0.896107i	$-0.353617\pi$
$433$	−9.41111	−	9.41111i	−0.452269	−	0.452269i	−0.896107	+	0.443838i	$0.853617\pi$
$434$	0.176003			0.00844839
$435$		0			0
$436$	14.2885	−	14.2885i	0.684295	−	0.684295i
$437$	10.8851	+	10.8851i	0.520707	+	0.520707i
$438$	−0.565821			−0.0270360
$439$	20.2500	+	20.2500i	0.966482	+	0.966482i	0.999456	−	0.0329741i	$-0.0104979\pi$
$439$	20.2500	+	20.2500i	0.966482	+	0.966482i	−0.0329741	+	0.999456i	$0.510498\pi$
$440$		0			0
$441$	−20.9698			−0.998563
$442$	−2.77628			−0.132054
$443$	−13.9273	+	13.9273i	−0.661705	+	0.661705i	−0.955782	−	0.294077i	$-0.904988\pi$
$443$	−13.9273	+	13.9273i	−0.661705	+	0.661705i	0.294077	+	0.955782i	$0.404988\pi$
$444$	−0.476026	−	0.270616i	−0.0225912	−	0.0128429i
$445$		0			0
$446$	10.4698	−	10.4698i	0.495759	−	0.495759i
$447$	0.475157	+	0.475157i	0.0224742	+	0.0224742i
$448$	−0.0496151	+	0.0496151i	−0.00234409	+	0.00234409i
$449$	19.0153	−	19.0153i	0.897387	−	0.897387i	−0.0978171	−	0.995204i	$-0.531186\pi$
$449$	19.0153	−	19.0153i	0.897387	−	0.897387i	0.995204	+	0.0978171i	$0.0311860\pi$
$450$		0			0
$451$	13.5415			0.637643
$452$	−21.0028			−0.987886
$453$	−0.600427	−	0.600427i	−0.0282105	−	0.0282105i
$454$		−	1.45592i		−	0.0683299i
$455$		0			0
$456$	1.04247			0.0488180
$457$	39.1978			1.83359			0.916797	−	0.399353i	$-0.130765\pi$
$457$	39.1978			1.83359			0.916797	+	0.399353i	$0.130765\pi$
$458$	3.40516			0.159113
$459$	0.237597	+	0.237597i	0.0110901	+	0.0110901i
$460$		0			0
$461$	−16.5174	−	16.5174i	−0.769291	−	0.769291i	0.208691	−	0.977982i	$-0.433080\pi$
$461$	−16.5174	−	16.5174i	−0.769291	−	0.769291i	−0.977982	+	0.208691i	$0.933080\pi$
$462$		−	0.00888713i		−	0.000413467i
$463$			9.95672i			0.462728i	0.972867	+	0.231364i	$0.0743188\pi$
$463$			9.95672i			0.462728i	−0.972867	+	0.231364i	$0.925681\pi$
$464$	−0.286618	−	0.286618i	−0.0133059	−	0.0133059i
$465$		0			0
$466$	−0.162937	−	0.162937i	−0.00754792	−	0.00754792i
$467$	−35.9730			−1.66463			−0.832315	−	0.554302i	$-0.812985\pi$
$467$	−35.9730			−1.66463			−0.832315	+	0.554302i	$0.812985\pi$
$468$	18.6779			0.863384
$469$	−0.404903			−0.0186967
$470$		0			0
$471$			0.128599i			0.00592555i
$472$	6.83937	+	6.83937i	0.314807	+	0.314807i
$473$	13.2669			0.610015
$474$	0.137014			0.00629328
$475$		0			0
$476$	−0.0380053	+	0.0380053i	−0.00174197	+	0.00174197i
$477$	−29.4284	+	29.4284i	−1.34743	+	1.34743i
$478$	4.96135	+	4.96135i	0.226927	+	0.226927i
$479$	−12.3944	+	12.3944i	−0.566314	+	0.566314i	−0.931094	−	0.364780i	$-0.881144\pi$
$479$	−12.3944	+	12.3944i	−0.566314	+	0.566314i	0.364780	+	0.931094i	$0.381144\pi$
$480$		0			0
$481$	24.5678	−	6.75889i	1.12019	−	0.308179i
$482$	7.51064	−	7.51064i	0.342100	−	0.342100i
$483$	0.00525857			0.000239273
$484$	−24.8965			−1.13166
$485$		0			0
$486$	0.824995	+	0.824995i	0.0374225	+	0.0374225i
$487$	−30.4671			−1.38059			−0.690297	−	0.723526i	$-0.742520\pi$
$487$	−30.4671			−1.38059			−0.690297	+	0.723526i	$0.742520\pi$
$488$	20.0910	+	20.0910i	0.909477	+	0.909477i
$489$	−0.948036	+	0.948036i	−0.0428716	+	0.0428716i
$490$		0			0
$491$	18.9414			0.854816			0.427408	−	0.904059i	$-0.359427\pi$
$491$	18.9414			0.854816			0.427408	+	0.904059i	$0.359427\pi$
$492$	0.163686	+	0.163686i	0.00737953	+	0.00737953i
$493$	0.223000	+	0.223000i	0.0100434	+	0.0100434i
$494$	−14.6338	+	14.6338i	−0.658405	+	0.658405i
$495$		0			0
$496$	5.31117	−	5.31117i	0.238478	−	0.238478i
$497$	0.149509	−	0.149509i	0.00670641	−	0.00670641i
$498$		−	0.347776i		−	0.0155842i
$499$	−13.6341	−	13.6341i	−0.610347	−	0.610347i	0.332689	−	0.943037i	$-0.392044\pi$
$499$	−13.6341	−	13.6341i	−0.610347	−	0.610347i	−0.943037	+	0.332689i	$0.892044\pi$
$500$		0			0
$501$	−0.574451	+	0.574451i	−0.0256646	+	0.0256646i
$502$	3.58327	+	3.58327i	0.159929	+	0.159929i
$503$		−	18.0628i		−	0.805378i	−0.915337	−	0.402689i	$-0.868076\pi$
$503$		−	18.0628i		−	0.805378i	0.915337	−	0.402689i	$-0.131924\pi$
$504$	−0.206174	+	0.206174i	−0.00918374	+	0.00918374i
$505$		0			0
$506$			8.39964i			0.373409i
$507$	0.194522	−	0.194522i	0.00863903	−	0.00863903i
$508$	1.75075	−	1.75075i	0.0776771	−	0.0776771i
$509$	−40.5243			−1.79621			−0.898104	−	0.439783i	$-0.855055\pi$
$509$	−40.5243			−1.79621			−0.898104	+	0.439783i	$0.855055\pi$
$510$		0			0
$511$		−	0.509734i		−	0.0225493i
$512$			12.8993i			0.570073i
$513$	2.50474			0.110587
$514$		−	2.37910i		−	0.104938i
$515$		0			0
$516$	0.160367	+	0.160367i	0.00705978	+	0.00705978i
$517$	−30.8334	−	30.8334i	−1.35605	−	1.35605i
$518$	−0.0838659	+	0.147524i	−0.00368485	+	0.00648183i
$519$		−	0.0297053i		−	0.00130392i
$520$		0			0
$521$			18.1840i			0.796654i	0.917243	+	0.398327i	$0.130409\pi$
$521$			18.1840i			0.796654i	−0.917243	+	0.398327i	$0.869591\pi$
$522$	0.516103	+	0.516103i	0.0225892	+	0.0225892i
$523$		−	19.1713i		−	0.838300i	−0.907917	−	0.419150i	$-0.862328\pi$
$523$		−	19.1713i		−	0.838300i	0.907917	−	0.419150i	$-0.137672\pi$
$524$	21.8187	−	21.8187i	0.953156	−	0.953156i
$525$		0			0
$526$	6.22527	+	6.22527i	0.271435	+	0.271435i
$527$	−4.13229	+	4.13229i	−0.180005	+	0.180005i
$528$	−0.268184	−	0.268184i	−0.0116712	−	0.0116712i
$529$	18.0299			0.783908
$530$		0			0
$531$	8.21148	+	8.21148i	0.356348	+	0.356348i
$532$			0.400652i			0.0173705i
$533$	−10.7720			−0.466585
$534$		−	0.331925i		−	0.0143638i
$535$		0			0
$536$	18.3252	−	18.3252i	0.791527	−	0.791527i
$537$	0.423858			0.0182908
$538$	10.3962			0.448212
$539$	−36.8538			−1.58741
$540$		0			0
$541$	7.46366	+	7.46366i	0.320888	+	0.320888i	0.849108	−	0.528220i	$-0.177140\pi$
$541$	7.46366	+	7.46366i	0.320888	+	0.320888i	−0.528220	+	0.849108i	$0.677140\pi$
$542$			10.4545i			0.449058i
$543$	0.346901	−	0.346901i	0.0148870	−	0.0148870i
$544$		−	5.41259i		−	0.232063i
$545$		0			0
$546$			0.00706953i			0.000302548i
$547$			14.0903i			0.602458i	0.953552	+	0.301229i	$0.0973969\pi$
$547$			14.0903i			0.602458i	−0.953552	+	0.301229i	$0.902603\pi$
$548$	16.2116	−	16.2116i	0.692523	−	0.692523i
$549$	24.1217	+	24.1217i	1.02949	+	1.02949i
$550$		0			0
$551$	2.35086			0.100150
$552$	−0.237993	+	0.237993i	−0.0101297	+	0.0101297i
$553$			0.123433i			0.00524889i
$554$	−1.14637			−0.0487046
$555$		0			0
$556$	8.26066			0.350330
$557$		−	26.7903i		−	1.13514i	−0.823325	−	0.567571i	$-0.807883\pi$
$557$		−	26.7903i		−	1.13514i	0.823325	−	0.567571i	$-0.192117\pi$
$558$	−9.56361	+	9.56361i	−0.404860	+	0.404860i
$559$	−10.5536			−0.446368
$560$		0			0
$561$	0.208657	+	0.208657i	0.00880951	+	0.00880951i
$562$	−9.39834	+	9.39834i	−0.396445	+	0.396445i
$563$		−	33.0658i		−	1.39356i	−0.717287	−	0.696778i	$-0.754616\pi$
$563$		−	33.0658i		−	1.39356i	0.717287	−	0.696778i	$-0.245384\pi$
$564$		−	0.745412i		−	0.0313875i
$565$		0			0
$566$		−	13.8867i		−	0.583700i
$567$	−0.247235	+	0.247235i	−0.0103829	+	0.0103829i
$568$			13.5330i			0.567834i
$569$	7.57201	+	7.57201i	0.317435	+	0.317435i	0.847781	−	0.530346i	$-0.177938\pi$
$569$	7.57201	+	7.57201i	0.317435	+	0.317435i	−0.530346	+	0.847781i	$0.677938\pi$
$570$		0			0
$571$	−27.8328			−1.16477			−0.582383	−	0.812915i	$-0.697880\pi$
$571$	−27.8328			−1.16477			−0.582383	+	0.812915i	$0.697880\pi$
$572$	32.8258			1.37251
$573$	0.187639			0.00783872
$574$	0.0507275	−	0.0507275i	0.00211732	−	0.00211732i
$575$		0			0
$576$		−	5.39196i		−	0.224665i
$577$	8.46185			0.352271			0.176136	−	0.984366i	$-0.443640\pi$
$577$	8.46185			0.352271			0.176136	+	0.984366i	$0.443640\pi$
$578$		−	11.5493i		−	0.480386i
$579$	0.600401	+	0.600401i	0.0249518	+	0.0249518i
$580$		0			0
$581$	0.313302			0.0129980
$582$	0.189240	+	0.189240i	0.00784426	+	0.00784426i
$583$	−51.7195	+	51.7195i	−2.14200	+	2.14200i
$584$	23.0696	+	23.0696i	0.954628	+	0.954628i
$585$		0			0
$586$	−13.3994	+	13.3994i	−0.553523	+	0.553523i
$587$		−	3.25054i		−	0.134164i	−0.997747	−	0.0670821i	$-0.978631\pi$
$587$		−	3.25054i		−	0.134164i	0.997747	−	0.0670821i	$-0.0213690\pi$
$588$	−0.445480	−	0.445480i	−0.0183713	−	0.0183713i
$589$			43.5625i			1.79496i
$590$		0			0
$591$			1.29395i			0.0532262i
$592$	1.92099	+	6.98257i	0.0789522	+	0.286982i
$593$	32.5909	+	32.5909i	1.33835	+	1.33835i	0.897660	+	0.440689i	$0.145266\pi$
$593$	32.5909	+	32.5909i	1.33835	+	1.33835i	0.440689	+	0.897660i	$0.354734\pi$
$594$	0.966406	+	0.966406i	0.0396521	+	0.0396521i
$595$		0			0
$596$		−	16.5299i		−	0.677090i
$597$	−0.481612			−0.0197111
$598$		−	6.68173i		−	0.273236i
$599$		−	9.55942i		−	0.390587i	−0.980745	−	0.195294i	$-0.937434\pi$
$599$		−	9.55942i		−	0.390587i	0.980745	−	0.195294i	$-0.0625660\pi$
$600$		0			0
$601$	−28.6006			−1.16664			−0.583321	−	0.812242i	$-0.698247\pi$
$601$	−28.6006			−1.16664			−0.583321	+	0.812242i	$0.698247\pi$
$602$	0.0496991	−	0.0496991i	0.00202558	−	0.00202558i
$603$	22.0016	−	22.0016i	0.895974	−	0.895974i
$604$			20.8878i			0.849911i
$605$		0			0
$606$	−0.186351	+	0.186351i	−0.00756997	+	0.00756997i
$607$			4.13460i			0.167818i	0.996473	+	0.0839090i	$0.0267405\pi$
$607$			4.13460i			0.167818i	−0.996473	+	0.0839090i	$0.973259\pi$
$608$	−28.5297	−	28.5297i	−1.15703	−	1.15703i
$609$	0.000567847	0	0.000567847i	2.30103e−5	0	2.30103e-5i
$610$		0			0
$611$	24.5273	+	24.5273i	0.992269	+	0.992269i
$612$		−	4.13026i		−	0.166956i
$613$	−3.45702	+	3.45702i	−0.139628	+	0.139628i	−0.773466	−	0.633838i	$-0.781479\pi$
$613$	−3.45702	+	3.45702i	−0.139628	+	0.139628i	0.633838	+	0.773466i	$0.281479\pi$
$614$	12.3860	−	12.3860i	0.499858	−	0.499858i
$615$		0			0
$616$	−0.362345	+	0.362345i	−0.0145993	+	0.0145993i
$617$	−13.5894	−	13.5894i	−0.547087	−	0.547087i	0.378510	−	0.925597i	$-0.376437\pi$
$617$	−13.5894	−	13.5894i	−0.547087	−	0.547087i	−0.925597	+	0.378510i	$0.876437\pi$
$618$	0.377107	+	0.377107i	0.0151695	+	0.0151695i
$619$	37.7003			1.51530			0.757651	−	0.652660i	$-0.226347\pi$
$619$	37.7003			1.51530			0.757651	+	0.652660i	$0.226347\pi$
$620$		0			0
$621$	−0.571829	+	0.571829i	−0.0229467	+	0.0229467i
$622$	0.307063	+	0.307063i	0.0123121	+	0.0123121i
$623$	0.299023			0.0119801
$624$	0.213335	+	0.213335i	0.00854022	+	0.00854022i
$625$		0			0
$626$	−10.3047			−0.411859
$627$	2.19966			0.0878460
$628$	2.23687	−	2.23687i	0.0892609	−	0.0892609i
$629$	−1.49460	−	5.43270i	−0.0595937	−	0.216616i
$630$		0			0
$631$	8.07494	−	8.07494i	0.321458	−	0.321458i	−0.527868	−	0.849326i	$-0.677008\pi$
$631$	8.07494	−	8.07494i	0.321458	−	0.321458i	0.849326	+	0.527868i	$0.177008\pi$
$632$	−5.58634	−	5.58634i	−0.222213	−	0.222213i
$633$	0.131899	−	0.131899i	0.00524251	−	0.00524251i
$634$	9.90829	−	9.90829i	0.393508	−	0.393508i
$635$		0			0
$636$	−1.25034			−0.0495794
$637$	29.3164			1.16156
$638$	0.907035	+	0.907035i	0.0359098	+	0.0359098i
$639$			16.2480i			0.642763i
$640$		0			0
$641$	−5.92418			−0.233991			−0.116995	−	0.993132i	$-0.537326\pi$
$641$	−5.92418			−0.233991			−0.116995	+	0.993132i	$0.537326\pi$
$642$	0.467577			0.0184538
$643$	20.1006			0.792689			0.396344	−	0.918102i	$-0.370279\pi$
$643$	20.1006			0.792689			0.396344	+	0.918102i	$0.370279\pi$
$644$	−0.0914682	−	0.0914682i	−0.00360435	−	0.00360435i
$645$		0			0
$646$	3.23599	+	3.23599i	0.127318	+	0.127318i
$647$			19.4845i			0.766016i	0.923745	+	0.383008i	$0.125112\pi$
$647$			19.4845i			0.766016i	−0.923745	+	0.383008i	$0.874888\pi$
$648$		−	22.3788i		−	0.879121i
$649$	14.4314	+	14.4314i	0.566483	+	0.566483i
$650$		0			0
$651$	0.0105225	+	0.0105225i	0.000412408	+	0.000412408i
$652$	32.9805			1.29161
$653$	−37.6994			−1.47529			−0.737646	−	0.675187i	$-0.764063\pi$
$653$	−37.6994			−1.47529			−0.737646	+	0.675187i	$0.764063\pi$
$654$	−0.587736			−0.0229823
$655$		0			0
$656$		−	3.06157i		−	0.119534i
$657$	27.6979	+	27.6979i	1.08060	+	1.08060i
$658$	−0.231009			−0.00900566
$659$	−49.3851			−1.92377			−0.961885	−	0.273455i	$-0.911833\pi$
$659$	−49.3851			−1.92377			−0.961885	+	0.273455i	$0.911833\pi$
$660$		0			0
$661$	−15.0011	+	15.0011i	−0.583475	+	0.583475i	−0.935856	−	0.352382i	$-0.885372\pi$
$661$	−15.0011	+	15.0011i	−0.583475	+	0.583475i	0.352382	+	0.935856i	$0.385372\pi$
$662$	5.70412	−	5.70412i	0.221697	−	0.221697i
$663$	−0.165982	−	0.165982i	−0.00644622	−	0.00644622i
$664$	−14.1795	+	14.1795i	−0.550271	+	0.550271i
$665$		0			0
$666$	−3.45905	−	12.5732i	−0.134036	−	0.487203i
$667$	−0.536698	+	0.536698i	−0.0207810	+	0.0207810i
$668$	19.9841			0.773209
$669$	1.25189			0.0484009
$670$		0			0
$671$	42.3931	+	42.3931i	1.63657	+	1.63657i
$672$	−0.0137826			−0.000531676
$673$	12.7892	+	12.7892i	0.492986	+	0.492986i	0.909246	−	0.416260i	$-0.136659\pi$
$673$	12.7892	+	12.7892i	0.492986	+	0.492986i	−0.416260	+	0.909246i	$0.636659\pi$
$674$	3.08805	−	3.08805i	0.118947	−	0.118947i
$675$		0			0
$676$	−6.76708			−0.260272
$677$	−22.1825	−	22.1825i	−0.852544	−	0.852544i	0.137902	−	0.990446i	$-0.455964\pi$
$677$	−22.1825	−	22.1825i	−0.852544	−	0.852544i	−0.990446	+	0.137902i	$0.955964\pi$
$678$	0.431959	+	0.431959i	0.0165893	+	0.0165893i
$679$	−0.170482	+	0.170482i	−0.00654249	+	0.00654249i
$680$		0			0
$681$	0.0870436	−	0.0870436i	0.00333552	−	0.00333552i
$682$	−16.8078	+	16.8078i	−0.643602	+	0.643602i
$683$			29.6316i			1.13382i	0.823779	+	0.566912i	$0.191862\pi$
$683$			29.6316i			1.13382i	−0.823779	+	0.566912i	$0.808138\pi$
$684$	−21.7706	−	21.7706i	−0.832419	−	0.832419i
$685$		0			0
$686$	−0.276145	+	0.276145i	−0.0105433	+	0.0105433i
$687$	0.203580	+	0.203580i	0.00776707	+	0.00776707i
$688$		−	2.99950i		−	0.114355i
$689$	41.1418	−	41.1418i	1.56738	−	1.56738i
$690$		0			0
$691$			25.5929i			0.973602i	0.873513	+	0.486801i	$0.161836\pi$
$691$			25.5929i			0.973602i	−0.873513	+	0.486801i	$0.838164\pi$
$692$	−0.516696	+	0.516696i	−0.0196419	+	0.0196419i
$693$	−0.435039	+	0.435039i	−0.0165258	+	0.0165258i
$694$	−22.5982			−0.857817
$695$		0			0
$696$			0.0513994i			0.00194829i
$697$			2.38202i			0.0902254i
$698$	22.5236			0.852531
$699$		−	0.0194827i		−	0.000736902i
$700$		0			0
$701$	−13.1318	−	13.1318i	−0.495982	−	0.495982i	0.414202	−	0.910185i	$-0.364061\pi$
$701$	−13.1318	−	13.1318i	−0.495982	−	0.495982i	−0.910185	+	0.414202i	$0.864061\pi$
$702$	−0.768756	−	0.768756i	−0.0290148	−	0.0290148i
$703$	−36.5138	−	20.7577i	−1.37714	−	0.782891i
$704$		−	9.47620i		−	0.357148i
$705$		0			0
$706$		−	3.15238i		−	0.118641i
$707$	−0.167878	−	0.167878i	−0.00631372	−	0.00631372i
$708$			0.348887i			0.0131120i
$709$	28.9060	−	28.9060i	1.08559	−	1.08559i	0.0896090	−	0.995977i	$-0.471438\pi$
$709$	28.9060	−	28.9060i	1.08559	−	1.08559i	0.995977	−	0.0896090i	$-0.0285617\pi$
$710$		0			0
$711$	−6.70707	−	6.70707i	−0.251535	−	0.251535i
$712$	−13.5332	+	13.5332i	−0.507179	+	0.507179i
$713$	−9.94525	−	9.94525i	−0.372453	−	0.372453i
$714$	0.00156329			5.85048e−5
$715$		0			0
$716$	−7.37263	−	7.37263i	−0.275528	−	0.275528i
$717$			0.593237i			0.0221548i
$718$	−18.7522			−0.699825
$719$		−	33.9623i		−	1.26658i	−0.773915	−	0.633289i	$-0.781704\pi$
$719$		−	33.9623i		−	1.26658i	0.773915	−	0.633289i	$-0.218296\pi$
$720$		0			0
$721$	−0.339726	+	0.339726i	−0.0126521	+	0.0126521i
$722$	20.5196			0.763660
$723$	0.898059			0.0333992
$724$	−12.0681			−0.448506
$725$		0			0
$726$	0.512040	+	0.512040i	0.0190036	+	0.0190036i
$727$		−	43.4312i		−	1.61078i	−0.592749	−	0.805388i	$-0.701957\pi$
$727$		−	43.4312i		−	1.61078i	0.592749	−	0.805388i	$-0.298043\pi$
$728$	0.288238	−	0.288238i	0.0106828	−	0.0106828i
$729$		−	26.8026i		−	0.992688i
$730$		0			0
$731$			2.33373i			0.0863160i
$732$			1.02487i			0.0378805i
$733$	−26.7771	+	26.7771i	−0.989033	+	0.989033i	−0.999941	−	0.0109070i	$-0.996528\pi$
$733$	−26.7771	+	26.7771i	−0.989033	+	0.989033i	0.0109070	+	0.999941i	$0.496528\pi$
$734$	−4.67959	−	4.67959i	−0.172727	−	0.172727i
$735$		0			0
$736$	13.0266			0.480166
$737$	38.6671	−	38.6671i	1.42432	−	1.42432i
$738$			5.51285i			0.202931i
$739$	−17.1319			−0.630209			−0.315104	−	0.949057i	$-0.602040\pi$
$739$	−17.1319			−0.630209			−0.315104	+	0.949057i	$0.602040\pi$
$740$		0			0
$741$	−1.74978			−0.0642799
$742$			0.387491i			0.0142252i
$743$	0.820989	−	0.820989i	0.0301192	−	0.0301192i	−0.691887	−	0.722006i	$-0.743220\pi$
$743$	0.820989	−	0.820989i	0.0301192	−	0.0301192i	0.722006	+	0.691887i	$0.243220\pi$
$744$	−0.952454			−0.0349187
$745$		0			0
$746$	8.05768	+	8.05768i	0.295013	+	0.295013i
$747$	−17.0242	+	17.0242i	−0.622882	+	0.622882i
$748$		−	7.25881i		−	0.265408i
$749$			0.421228i			0.0153913i
$750$		0			0
$751$			1.31114i			0.0478442i	0.999714	+	0.0239221i	$0.00761537\pi$
$751$			1.31114i			0.0478442i	−0.999714	+	0.0239221i	$0.992385\pi$
$752$	−6.97107	+	6.97107i	−0.254209	+	0.254209i
$753$			0.428457i			0.0156138i
$754$	−0.721527	−	0.721527i	−0.0262765	−	0.0262765i
$755$		0			0
$756$	−0.0210474			−0.000765488
$757$	43.3288			1.57481			0.787406	−	0.616435i	$-0.211424\pi$
$757$	43.3288			1.57481			0.787406	+	0.616435i	$0.211424\pi$
$758$	−21.4632			−0.779577
$759$	−0.502179	+	0.502179i	−0.0182279	+	0.0182279i
$760$		0			0
$761$			26.7584i			0.969990i	0.874517	+	0.484995i	$0.161179\pi$
$761$			26.7584i			0.969990i	−0.874517	+	0.484995i	$0.838821\pi$
$762$	−0.0720146			−0.00260881
$763$		−	0.529476i		−	0.0191683i
$764$	−3.26381	−	3.26381i	−0.118080	−	0.118080i
$765$		0			0
$766$	−22.9831			−0.830415
$767$	−11.4799	−	11.4799i	−0.414515	−	0.414515i
$768$	0.472207	−	0.472207i	0.0170393	−	0.0170393i
$769$	−22.8580	−	22.8580i	−0.824282	−	0.824282i	0.162437	−	0.986719i	$-0.448064\pi$
$769$	−22.8580	−	22.8580i	−0.824282	−	0.824282i	−0.986719	+	0.162437i	$0.948064\pi$
$770$		0			0
$771$	0.142237	−	0.142237i	0.00512253	−	0.00512253i
$772$		−	20.8869i		−	0.751735i
$773$	10.0121	+	10.0121i	0.360109	+	0.360109i	0.863853	−	0.503744i	$-0.168045\pi$
$773$	10.0121	+	10.0121i	0.360109	+	0.360109i	−0.503744	+	0.863853i	$0.668045\pi$
$774$			5.40108i			0.194138i
$775$		0			0
$776$		−	15.4314i		−	0.553954i
$777$	−0.0138338	+	0.00380586i	−0.000496286	+	0.000136534i
$778$	1.19970	+	1.19970i	0.0430112	+	0.0430112i
$779$	12.5556	+	12.5556i	0.449851	+	0.449851i
$780$		0			0
$781$			28.5555i			1.02179i
$782$	−1.47754			−0.0528368
$783$			0.123498i			0.00441345i
$784$			8.33222i			0.297579i
$785$		0			0
$786$	−0.897482			−0.0320121
$787$	−0.222957	+	0.222957i	−0.00794755	+	0.00794755i	−0.711069	−	0.703122i	$-0.751789\pi$
$787$	−0.222957	+	0.222957i	−0.00794755	+	0.00794755i	0.703122	+	0.711069i	$0.251789\pi$
$788$	22.5072	−	22.5072i	0.801785	−	0.801785i
$789$			0.744366i			0.0265001i
$790$		0			0
$791$	−0.389140	+	0.389140i	−0.0138362	+	0.0138362i
$792$		−	39.3782i		−	1.39924i
$793$	−33.7228	−	33.7228i	−1.19753	−	1.19753i
$794$	−11.2729	+	11.2729i	−0.400061	+	0.400061i
$795$		0			0
$796$	8.37722	+	8.37722i	0.296923	+	0.296923i
$797$			21.5306i			0.762653i	0.924440	+	0.381326i	$0.124533\pi$
$797$			21.5306i			0.762653i	−0.924440	+	0.381326i	$0.875467\pi$
$798$	0.00824011	−	0.00824011i	0.000291697	−	0.000291697i
$799$	5.42376	−	5.42376i	0.191879	−	0.191879i
$800$		0			0
$801$	−16.2483	+	16.2483i	−0.574104	+	0.574104i
$802$	−3.02188	−	3.02188i	−0.106706	−	0.106706i
$803$	48.6782	+	48.6782i	1.71781	+	1.71781i
$804$	0.934797			0.0329678
$805$		0			0
$806$	13.3702	−	13.3702i	0.470946	−	0.470946i
$807$	0.621545	+	0.621545i	0.0218794	+	0.0218794i
$808$	15.1957			0.534584
$809$	19.6304	+	19.6304i	0.690170	+	0.690170i	0.962269	−	0.272100i	$-0.0877180\pi$
$809$	19.6304	+	19.6304i	0.690170	+	0.690170i	−0.272100	+	0.962269i	$0.587718\pi$
$810$		0			0
$811$	41.8784			1.47055			0.735275	−	0.677768i	$-0.237053\pi$
$811$	41.8784			1.47055			0.735275	+	0.677768i	$0.237053\pi$
$812$	−0.0197544			−0.000693243
$813$	−0.625029	+	0.625029i	−0.0219207	+	0.0219207i
$814$	−6.07918	−	22.0971i	−0.213075	−	0.774503i
$815$		0			0
$816$	0.0471750	−	0.0471750i	0.00165145	−	0.00165145i
$817$	12.3011	+	12.3011i	0.430359	+	0.430359i
$818$	−0.508695	+	0.508695i	−0.0177861	+	0.0177861i
$819$	0.346065	−	0.346065i	0.0120925	−	0.0120925i
$820$		0			0
$821$	−53.4952			−1.86699			−0.933497	−	0.358584i	$-0.883260\pi$
$821$	−53.4952			−1.86699			−0.933497	+	0.358584i	$0.883260\pi$
$822$	−0.666839			−0.0232587
$823$	20.9538	+	20.9538i	0.730404	+	0.730404i	0.970700	−	0.240296i	$-0.0772444\pi$
$823$	20.9538	+	20.9538i	0.730404	+	0.730404i	−0.240296	+	0.970700i	$0.577244\pi$
$824$		−	30.7508i		−	1.07125i
$825$		0			0
$826$	0.108123			0.00376207
$827$	37.2295			1.29460			0.647299	−	0.762236i	$-0.275899\pi$
$827$	37.2295			1.29460			0.647299	+	0.762236i	$0.275899\pi$
$828$	9.94038			0.345452
$829$	12.8198	+	12.8198i	0.445249	+	0.445249i	0.893771	−	0.448523i	$-0.148050\pi$
$829$	12.8198	+	12.8198i	0.445249	+	0.445249i	−0.448523	+	0.893771i	$0.648050\pi$
$830$		0			0
$831$	−0.0685367	−	0.0685367i	−0.00237751	−	0.00237751i
$832$			7.53812i			0.261337i
$833$		−	6.48279i		−	0.224615i
$834$	−0.169895	−	0.169895i	−0.00588299	−	0.00588299i
$835$		0			0
$836$	−38.2611	−	38.2611i	−1.32329	−	1.32329i
$837$	−2.28847			−0.0791011
$838$	−16.2826			−0.562474
$839$	35.5391			1.22695			0.613473	−	0.789715i	$-0.289772\pi$
$839$	35.5391			1.22695			0.613473	+	0.789715i	$0.289772\pi$
$840$		0			0
$841$		−	28.8841i		−	0.996003i
$842$	3.50889	+	3.50889i	0.120924	+	0.120924i
$843$	−1.12377			−0.0387048
$844$	−4.58853			−0.157944
$845$		0			0
$846$	12.5525	−	12.5525i	0.431565	−	0.431565i
$847$	−0.461283	+	0.461283i	−0.0158499	+	0.0158499i
$848$	11.6932	+	11.6932i	0.401545	+	0.401545i
$849$	0.830225	−	0.830225i	0.0284933	−	0.0284933i
$850$		0			0
$851$	13.0750	−	3.59709i	0.448205	−	0.123307i
$852$	−0.345171	+	0.345171i	−0.0118254	+	0.0118254i
$853$	45.8043			1.56831			0.784155	−	0.620565i	$-0.213097\pi$
$853$	45.8043			1.56831			0.784155	+	0.620565i	$0.213097\pi$
$854$	0.317616			0.0108686
$855$		0			0
$856$	−19.0640	−	19.0640i	−0.651595	−	0.651595i
$857$	9.27829			0.316940			0.158470	−	0.987364i	$-0.449344\pi$
$857$	9.27829			0.316940			0.158470	+	0.987364i	$0.449344\pi$
$858$	−0.675120	−	0.675120i	−0.0230482	−	0.0230482i
$859$	28.7601	−	28.7601i	0.981280	−	0.981280i	−0.0185476	−	0.999828i	$-0.505904\pi$
$859$	28.7601	−	28.7601i	0.981280	−	0.981280i	0.999828	+	0.0185476i	$0.00590421\pi$
$860$		0			0
$861$	0.00606557			0.000206714
$862$	−5.07900	−	5.07900i	−0.172991	−	0.172991i
$863$	14.4607	+	14.4607i	0.492247	+	0.492247i	0.909013	−	0.416767i	$-0.136837\pi$
$863$	14.4607	+	14.4607i	0.492247	+	0.492247i	−0.416767	+	0.909013i	$0.636837\pi$
$864$	1.49875	−	1.49875i	0.0509886	−	0.0509886i
$865$		0			0
$866$	6.73347	−	6.73347i	0.228813	−	0.228813i
$867$	0.690481	−	0.690481i	0.0234500	−	0.0234500i
$868$		−	0.366057i		−	0.0124248i
$869$	−11.7875	−	11.7875i	−0.399863	−	0.399863i
$870$		0			0
$871$	−30.7589	+	30.7589i	−1.04223	+	1.04223i
$872$	23.9631	+	23.9631i	0.811494	+	0.811494i
$873$		−	18.5272i		−	0.627052i
$874$	−7.78811	+	7.78811i	−0.263437	+	0.263437i
$875$		0			0
$876$			1.17682i			0.0397610i
$877$	37.4481	−	37.4481i	1.26453	−	1.26453i	0.315658	−	0.948873i	$-0.397775\pi$
$877$	37.4481	−	37.4481i	1.26453	−	1.26453i	0.948873	−	0.315658i	$-0.102225\pi$
$878$	−14.4885	+	14.4885i	−0.488964	+	0.488964i
$879$	−1.60219			−0.0540404
$880$		0			0
$881$		−	8.89349i		−	0.299629i	−0.988714	−	0.149815i	$-0.952132\pi$
$881$		−	8.89349i		−	0.299629i	0.988714	−	0.149815i	$-0.0478677\pi$
$882$		−	15.0035i		−	0.505195i
$883$	36.5732			1.23078			0.615392	−	0.788221i	$-0.288998\pi$
$883$	36.5732			1.23078			0.615392	+	0.788221i	$0.288998\pi$
$884$			5.77423i			0.194208i
$885$		0			0
$886$	−9.96470	−	9.96470i	−0.334771	−	0.334771i
$887$	10.0384	+	10.0384i	0.337056	+	0.337056i	0.855258	−	0.518202i	$-0.173399\pi$
$887$	10.0384	+	10.0384i	0.337056	+	0.337056i	−0.518202	+	0.855258i	$0.673399\pi$
$888$	0.453848	−	0.798340i	0.0152301	−	0.0267905i
$889$		−	0.0648761i		−	0.00217587i
$890$		0			0
$891$		−	47.2204i		−	1.58194i
$892$	−21.7755	−	21.7755i	−0.729098	−	0.729098i
$893$		−	57.1772i		−	1.91336i
$894$	−0.339966	+	0.339966i	−0.0113702	+	0.0113702i
$895$		0			0
$896$	0.286709	+	0.286709i	0.00957827	+	0.00957827i
$897$	0.399473	−	0.399473i	0.0133380	−	0.0133380i
$898$	13.6051	+	13.6051i	0.454008	+	0.454008i
$899$	−2.14788			−0.0716357
$900$		0			0
$901$	−9.09774	−	9.09774i	−0.303090	−	0.303090i
$902$			9.68867i			0.322597i
$903$	0.00594260			0.000197757
$904$		−	35.2236i		−	1.17152i
$905$		0			0
$906$	0.429594	−	0.429594i	0.0142723	−	0.0142723i
$907$	10.8933			0.361706			0.180853	−	0.983510i	$-0.442114\pi$
$907$	10.8933			0.361706			0.180853	+	0.983510i	$0.442114\pi$
$908$	−3.02809			−0.100491
$909$	18.2443			0.605126
$910$		0			0
$911$	−3.61681	−	3.61681i	−0.119830	−	0.119830i	0.644649	−	0.764479i	$-0.277004\pi$
$911$	−3.61681	−	3.61681i	−0.119830	−	0.119830i	−0.764479	+	0.644649i	$0.777004\pi$
$912$		−	0.497318i		−	0.0164678i
$913$	−29.9195	+	29.9195i	−0.990190	+	0.990190i
$914$			28.0453i			0.927655i
$915$		0			0
$916$		−	7.08219i		−	0.234002i
$917$		−	0.808518i		−	0.0266996i
$918$	−0.169996	+	0.169996i	−0.00561070	+	0.00561070i
$919$	26.7850	+	26.7850i	0.883555	+	0.883555i	0.993894	−	0.110339i	$-0.0351938\pi$
$919$	26.7850	+	26.7850i	0.883555	+	0.883555i	−0.110339	+	0.993894i	$0.535194\pi$
$920$		0			0
$921$	1.48101			0.0488010
$922$	11.8179	−	11.8179i	0.389201	−	0.389201i
$923$		−	22.7153i		−	0.747682i
$924$	−0.0184838			−0.000608073
$925$		0			0
$926$	−7.12384			−0.234104
$927$		−	36.9200i		−	1.21261i
$928$	1.40668	−	1.40668i	0.0461764	−	0.0461764i
$929$	22.1681			0.727313			0.363657	−	0.931533i	$-0.381528\pi$
$929$	22.1681			0.727313			0.363657	+	0.931533i	$0.381528\pi$
$930$		0			0
$931$	−34.1707	−	34.1707i	−1.11990	−	1.11990i
$932$	−0.338884	+	0.338884i	−0.0111005	+	0.0111005i
$933$			0.0367160i			0.00120203i
$934$		−	25.7380i		−	0.842173i
$935$		0			0
$936$			31.3245i			1.02387i
$937$	−17.7996	+	17.7996i	−0.581488	+	0.581488i	−0.935312	−	0.353824i	$-0.884881\pi$
$937$	−17.7996	+	17.7996i	−0.581488	+	0.581488i	0.353824	+	0.935312i	$0.384881\pi$
$938$		−	0.289701i		−	0.00945906i
$939$	−0.616076	−	0.616076i	−0.0201049	−	0.0201049i
$940$		0			0
$941$	−26.7051			−0.870562			−0.435281	−	0.900295i	$-0.643351\pi$
$941$	−26.7051			−0.870562			−0.435281	+	0.900295i	$0.643351\pi$
$942$	−0.0920104			−0.00299786
$943$	−5.73285			−0.186687
$944$	3.26278	−	3.26278i	0.106194	−	0.106194i
$945$		0			0
$946$			9.49224i			0.308619i
$947$	−13.8301			−0.449417			−0.224709	−	0.974426i	$-0.572143\pi$
$947$	−13.8301			−0.449417			−0.224709	+	0.974426i	$0.572143\pi$
$948$		−	0.284968i		−	0.00925534i
$949$	−38.7224	−	38.7224i	−1.25698	−	1.25698i
$950$		0			0
$951$	1.18475			0.0384181
$952$	−0.0637385	−	0.0637385i	−0.00206578	−	0.00206578i
$953$	−31.5118	+	31.5118i	−1.02077	+	1.02077i	−0.0209884	+	0.999780i	$0.506681\pi$
$953$	−31.5118	+	31.5118i	−1.02077	+	1.02077i	−0.999780	+	0.0209884i	$0.993319\pi$
$954$	−21.0555	−	21.0555i	−0.681696	−	0.681696i
$955$		0			0
$956$	10.3188	−	10.3188i	0.333734	−	0.333734i
$957$			0.108456i			0.00350587i
$958$	−8.86796	−	8.86796i	−0.286511	−	0.286511i
$959$		−	0.600738i		−	0.0193988i
$960$		0			0
$961$		−	8.80111i		−	0.283907i
$962$	4.83586	+	17.5778i	0.155914	+	0.566730i
$963$	−22.8887	−	22.8887i	−0.737577	−	0.737577i
$964$	−15.6209	−	15.6209i	−0.503116	−	0.503116i
$965$		0			0
$966$			0.00376241i			0.000121054i
$967$	−3.80622			−0.122400			−0.0612000	−	0.998126i	$-0.519493\pi$
$967$	−3.80622			−0.122400			−0.0612000	+	0.998126i	$0.519493\pi$
$968$		−	41.7537i		−	1.34201i
$969$			0.386932i			0.0124300i
$970$		0			0
$971$	13.2020			0.423671			0.211836	−	0.977305i	$-0.432056\pi$
$971$	13.2020			0.423671			0.211836	+	0.977305i	$0.432056\pi$
$972$	1.71586	−	1.71586i	0.0550362	−	0.0550362i
$973$	0.153054	−	0.153054i	0.00490669	−	0.00490669i
$974$		−	21.7986i		−	0.698472i
$975$		0			0
$976$	9.58459	−	9.58459i	0.306795	−	0.306795i
$977$		−	31.9696i		−	1.02280i	−0.859344	−	0.511398i	$-0.829128\pi$
$977$		−	31.9696i		−	1.02280i	0.859344	−	0.511398i	$-0.170872\pi$
$978$	−0.678301	−	0.678301i	−0.0216897	−	0.0216897i
$979$	−28.5558	+	28.5558i	−0.912648	+	0.912648i
$980$		0			0
$981$	28.7706	+	28.7706i	0.918576	+	0.918576i
$982$			13.5522i			0.432470i
$983$	−27.7372	+	27.7372i	−0.884678	+	0.884678i	−0.994006	−	0.109327i	$-0.965130\pi$
$983$	−27.7372	+	27.7372i	−0.884678	+	0.884678i	0.109327	+	0.994006i	$0.465130\pi$
$984$	−0.274517	+	0.274517i	−0.00875127	+	0.00875127i
$985$		0			0
$986$	−0.159552	+	0.159552i	−0.00508118	+	0.00508118i
$987$	−0.0138110	−	0.0138110i	−0.000439611	−	0.000439611i
$988$	30.4359	+	30.4359i	0.968296	+	0.968296i
$989$	−5.61662			−0.178598
$990$		0			0
$991$	−28.8618	+	28.8618i	−0.916825	+	0.916825i	−0.996797	−	0.0799719i	$-0.974517\pi$
$991$	−28.8618	+	28.8618i	−0.916825	+	0.916825i	0.0799719	+	0.996797i	$0.474517\pi$
$992$	26.0663	+	26.0663i	0.827607	+	0.827607i
$993$	0.682051			0.0216442
$994$	0.106971	+	0.106971i	0.00339292	+	0.00339292i
$995$		0			0
$996$	−0.723318			−0.0229192
$997$	−0.533402			−0.0168930			−0.00844651	−	0.999964i	$-0.502689\pi$
$997$	−0.533402			−0.0168930			−0.00844651	+	0.999964i	$0.502689\pi$
$998$	9.75496	−	9.75496i	0.308788	−	0.308788i
$999$	1.09046	−	1.91818i	0.0345007	−	0.0606885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.f.f.43.15	yes	48
5.2	odd	4		925.2.k.f.857.10	yes	48
5.3	odd	4		925.2.k.f.857.15	yes	48
5.4	even	2	inner	925.2.f.f.43.10	✓	48
37.31	odd	4		925.2.k.f.68.10	yes	48
185.68	even	4	inner	925.2.f.f.882.15	yes	48
185.142	even	4	inner	925.2.f.f.882.10	yes	48
185.179	odd	4		925.2.k.f.68.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.f.f.43.10	✓	48	5.4	even	2	inner
925.2.f.f.43.15	yes	48	1.1	even	1	trivial
925.2.f.f.882.10	yes	48	185.142	even	4	inner
925.2.f.f.882.15	yes	48	185.68	even	4	inner
925.2.k.f.68.10	yes	48	37.31	odd	4
925.2.k.f.68.15	yes	48	185.179	odd	4
925.2.k.f.857.10	yes	48	5.2	odd	4
925.2.k.f.857.15	yes	48	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.715481i q^{2} +(-0.0427756 + 0.0427756i) q^{3} +1.48809 q^{4} +(-0.0306051 - 0.0306051i) q^{6} +(0.0275714 - 0.0275714i) q^{7} +2.49566i q^{8} +2.99634i q^{9} +5.26598i q^{11} +(-0.0636538 + 0.0636538i) q^{12} -4.18897i q^{13} +(0.0197268 + 0.0197268i) q^{14} +1.19058 q^{16} -0.926314 q^{17} -2.14382 q^{18} +(-4.88259 + 4.88259i) q^{19} +0.00235876i q^{21} -3.76771 q^{22} -2.22938i q^{23} +(-0.106753 - 0.106753i) q^{24} +2.99713 q^{26} +(-0.256497 - 0.256497i) q^{27} +(0.0410286 - 0.0410286i) q^{28} +(-0.240739 - 0.240739i) q^{29} +(4.46100 - 4.46100i) q^{31} +5.84315i q^{32} +(-0.225255 - 0.225255i) q^{33} -0.662760i q^{34} +4.45882i q^{36} +(1.61350 + 5.86486i) q^{37} +(-3.49340 - 3.49340i) q^{38} +(0.179186 + 0.179186i) q^{39} -2.57150i q^{41} -0.00168765 q^{42} -2.51937i q^{43} +7.83623i q^{44} +1.59508 q^{46} +(-5.85521 + 5.85521i) q^{47} +(-0.0509276 + 0.0509276i) q^{48} +6.99848i q^{49} +(0.0396236 - 0.0396236i) q^{51} -6.23356i q^{52} +(9.82144 + 9.82144i) q^{53} +(0.183519 - 0.183519i) q^{54} +(0.0688088 + 0.0688088i) q^{56} -0.417712i q^{57} +(0.172244 - 0.172244i) q^{58} +(2.74050 - 2.74050i) q^{59} +(8.05038 - 8.05038i) q^{61} +(3.19176 + 3.19176i) q^{62} +(0.0826132 + 0.0826132i) q^{63} -1.79951 q^{64} +(0.161166 - 0.161166i) q^{66} +(-7.34282 - 7.34282i) q^{67} -1.37844 q^{68} +(0.0953629 + 0.0953629i) q^{69} +5.42263 q^{71} -7.47785 q^{72} +(9.24390 - 9.24390i) q^{73} +(-4.19620 + 1.15443i) q^{74} +(-7.26572 + 7.26572i) q^{76} +(0.145190 + 0.145190i) q^{77} +(-0.128204 + 0.128204i) q^{78} +(-2.23842 + 2.23842i) q^{79} -8.96708 q^{81} +1.83986 q^{82} +(5.68166 + 5.68166i) q^{83} +0.00351005i q^{84} +1.80256 q^{86} +0.0205955 q^{87} -13.1421 q^{88} +(5.42270 + 5.42270i) q^{89} +(-0.115496 - 0.115496i) q^{91} -3.31751i q^{92} +0.381644i q^{93} +(-4.18929 - 4.18929i) q^{94} +(-0.249945 - 0.249945i) q^{96} -6.18329 q^{97} -5.00728 q^{98} -15.7787 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 40 q^{4} + 8 q^{14} + 64 q^{16} + 12 q^{19} - 52 q^{24} - 16 q^{26} + 20 q^{31} + 32 q^{39} - 24 q^{46} - 36 q^{51} - 116 q^{54} - 28 q^{56} + 28 q^{59} - 20 q^{61} - 24 q^{64} - 76 q^{66} + 68 q^{69}+ \cdots - 48 q^{99}+O(q^{100}) \) 48 * q - 40 * q^4 + 8 * q^14 + 64 * q^16 + 12 * q^19 - 52 * q^24 - 16 * q^26 + 20 * q^31 + 32 * q^39 - 24 * q^46 - 36 * q^51 - 116 * q^54 - 28 * q^56 + 28 * q^59 - 20 * q^61 - 24 * q^64 - 76 * q^66 + 68 * q^69 + 48 * q^71 - 72 * q^74 - 100 * q^76 + 80 * q^79 - 80 * q^81 - 176 * q^86 + 32 * q^89 + 12 * q^91 - 44 * q^94 + 36 * q^96 - 48 * q^99

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