LMFDB - Embedded newform 525.2.q.g.299.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(299,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("525.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.q (of order $6$, degree $2$, not 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.11
Character	$\chi$	$=$	525.299
Dual form			525.2.q.g.374.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.442404 - 0.766266i) q^{2} +(1.02493 - 1.39625i) q^{3} +(0.608557 + 1.05405i) q^{4} +(-0.616465 - 1.40308i) q^{6} +(0.206062 - 2.63771i) q^{7} +2.84653 q^{8} +(-0.899028 - 2.86212i) q^{9} +O(q^{10})$	\(q+(0.442404 - 0.766266i) q^{2} +(1.02493 - 1.39625i) q^{3} +(0.608557 + 1.05405i) q^{4} +(-0.616465 - 1.40308i) q^{6} +(0.206062 - 2.63771i) q^{7} +2.84653 q^{8} +(-0.899028 - 2.86212i) q^{9} +(-1.25362 + 0.723775i) q^{11} +(2.09545 + 0.230634i) q^{12} +4.04326 q^{13} +(-1.93003 - 1.32483i) q^{14} +(0.0422021 - 0.0730962i) q^{16} +(-4.98592 + 2.87862i) q^{17} +(-2.59088 - 0.577320i) q^{18} +(0.356910 + 0.206062i) q^{19} +(-3.47171 - 2.99119i) q^{21} +1.28081i q^{22} +(3.65719 - 6.33444i) q^{23} +(2.91750 - 3.97447i) q^{24} +(1.78875 - 3.09821i) q^{26} +(-4.91768 - 1.67821i) q^{27} +(2.90569 - 1.38800i) q^{28} +1.82121i q^{29} +(2.30936 - 1.33331i) q^{31} +(2.80919 + 4.86566i) q^{32} +(-0.274300 + 2.49218i) q^{33} +5.09406i q^{34} +(2.46972 - 2.68939i) q^{36} +(5.06429 + 2.92387i) q^{37} +(0.315797 - 0.182325i) q^{38} +(4.14406 - 5.64540i) q^{39} -6.46287 q^{41} +(-3.82795 + 1.33694i) q^{42} +10.3583i q^{43} +(-1.52579 - 0.880917i) q^{44} +(-3.23592 - 5.60477i) q^{46} +(-9.41134 - 5.43364i) q^{47} +(-0.0588063 - 0.133843i) q^{48} +(-6.91508 - 1.08706i) q^{49} +(-1.09095 + 9.91198i) q^{51} +(2.46055 + 4.26180i) q^{52} +(0.697977 + 1.20893i) q^{53} +(-3.46156 + 3.02581i) q^{54} +(0.586561 - 7.50833i) q^{56} +(0.653522 - 0.287136i) q^{57} +(1.39554 + 0.805713i) q^{58} +(-0.583941 - 1.01142i) q^{59} +(3.58903 + 2.07213i) q^{61} -2.35944i q^{62} +(-7.73472 + 1.78160i) q^{63} +5.14000 q^{64} +(1.78832 + 1.31274i) q^{66} +(5.99309 - 3.46011i) q^{67} +(-6.06843 - 3.50361i) q^{68} +(-5.09609 - 11.5987i) q^{69} +13.3217i q^{71} +(-2.55911 - 8.14712i) q^{72} +(-1.57238 - 2.72344i) q^{73} +(4.48093 - 2.58707i) q^{74} +0.501602i q^{76} +(1.65079 + 3.45582i) q^{77} +(-2.49253 - 5.67300i) q^{78} +(-6.42216 + 11.1235i) q^{79} +(-7.38350 + 5.14626i) q^{81} +(-2.85920 + 4.95228i) q^{82} +11.5010i q^{83} +(1.04014 - 5.47967i) q^{84} +(7.93724 + 4.58257i) q^{86} +(2.54287 + 1.86662i) q^{87} +(-3.56845 + 2.06025i) q^{88} +(-3.90111 + 6.75692i) q^{89} +(0.833161 - 10.6650i) q^{91} +8.90244 q^{92} +(0.505303 - 4.59099i) q^{93} +(-8.32723 + 4.80773i) q^{94} +(9.67290 + 1.06464i) q^{96} -3.86099 q^{97} +(-3.89224 + 4.81787i) q^{98} +(3.19857 + 2.93731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 28 q^{4} + 14 q^{9}+O(q^{10}) $ 40 * q - 28 * q^4 + 14 * q^9	$ 40 q - 28 q^{4} + 14 q^{9} - 36 q^{16} - 18 q^{21} - 36 q^{24} + 84 q^{31} - 72 q^{36} - 16 q^{46} + 8 q^{49} + 42 q^{51} + 150 q^{54} - 180 q^{61} + 240 q^{64} + 12 q^{66} - 92 q^{79} + 58 q^{81} - 150 q^{84} - 60 q^{91} - 12 q^{94} + 270 q^{96} - 188 q^{99}+O(q^{100}) $ 40 * q - 28 * q^4 + 14 * q^9 - 36 * q^16 - 18 * q^21 - 36 * q^24 + 84 * q^31 - 72 * q^36 - 16 * q^46 + 8 * q^49 + 42 * q^51 + 150 * q^54 - 180 * q^61 + 240 * q^64 + 12 * q^66 - 92 * q^79 + 58 * q^81 - 150 * q^84 - 60 * q^91 - 12 * q^94 + 270 * q^96 - 188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.442404	−	0.766266i	0.312827	−	0.541832i	−0.666146	−	0.745821i	$-0.732057\pi$
$2$	0.442404	−	0.766266i	0.312827	−	0.541832i	0.978973	+	0.203989i	$0.0653907\pi$
$3$	1.02493	−	1.39625i	0.591745	−	0.806125i
$3$	1.02493	−	1.39625i	0.591745	−	0.806125i
$4$	0.608557	+	1.05405i	0.304279	+	0.527026i
$5$		0			0
$5$		0			0
$6$	−0.616465	−	1.40308i	−0.251671	−	0.572804i
$7$	0.206062	−	2.63771i	0.0778841	−	0.996962i
$7$	0.206062	−	2.63771i	0.0778841	−	0.996962i
$8$	2.84653			1.00640
$9$	−0.899028	−	2.86212i	−0.299676	−	0.954041i
$10$		0			0
$11$	−1.25362	+	0.723775i	−0.377979	+	0.218227i	−0.676939	−	0.736039i	$-0.736694\pi$
$11$	−1.25362	+	0.723775i	−0.377979	+	0.218227i	0.298959	+	0.954266i	$0.403360\pi$
$12$	2.09545	+	0.230634i	0.604904	+	0.0665783i
$13$	4.04326			1.12140			0.560699	−	0.828020i	$-0.310533\pi$
$13$	4.04326			1.12140			0.560699	+	0.828020i	$0.310533\pi$
$14$	−1.93003	−	1.32483i	−0.515822	−	0.354077i
$15$		0			0
$16$	0.0422021	−	0.0730962i	0.0105505	−	0.0182741i
$17$	−4.98592	+	2.87862i	−1.20926	+	0.698168i	−0.962598	−	0.270933i	$-0.912668\pi$
$17$	−4.98592	+	2.87862i	−1.20926	+	0.698168i	−0.246665	+	0.969101i	$0.579335\pi$
$18$	−2.59088	−	0.577320i	−0.610677	−	0.136076i
$19$	0.356910	+	0.206062i	0.0818807	+	0.0472738i	0.540381	−	0.841420i	$-0.318280\pi$
$19$	0.356910	+	0.206062i	0.0818807	+	0.0472738i	−0.458501	+	0.888694i	$0.651613\pi$
$20$		0			0
$21$	−3.47171	−	2.99119i	−0.757589	−	0.652732i
$22$			1.28081i			0.273069i
$23$	3.65719	−	6.33444i	0.762578	−	1.32082i	−0.178940	−	0.983860i	$-0.557267\pi$
$23$	3.65719	−	6.33444i	0.762578	−	1.32082i	0.941518	−	0.336963i	$-0.109400\pi$
$24$	2.91750	−	3.97447i	0.595532	−	0.811285i
$25$		0			0
$26$	1.78875	−	3.09821i	0.350803	−	0.607609i
$27$	−4.91768	−	1.67821i	−0.946408	−	0.322973i
$28$	2.90569	−	1.38800i	0.549124	−	0.262307i
$29$			1.82121i			0.338191i	0.985600	+	0.169095i	$0.0540846\pi$
$29$			1.82121i			0.338191i	−0.985600	+	0.169095i	$0.945915\pi$
$30$		0			0
$31$	2.30936	−	1.33331i	0.414772	−	0.239469i	−0.278066	−	0.960562i	$-0.589693\pi$
$31$	2.30936	−	1.33331i	0.414772	−	0.239469i	0.692838	+	0.721093i	$0.256360\pi$
$32$	2.80919	+	4.86566i	0.496599	+	0.860135i
$33$	−0.274300	+	2.49218i	−0.0477495	+	0.433833i
$34$			5.09406i			0.873623i
$35$		0			0
$36$	2.46972	−	2.68939i	0.411619	−	0.448231i
$37$	5.06429	+	2.92387i	0.832565	+	0.480682i	0.854730	−	0.519073i	$-0.173723\pi$
$37$	5.06429	+	2.92387i	0.832565	+	0.480682i	−0.0221652	+	0.999754i	$0.507056\pi$
$38$	0.315797	−	0.182325i	0.0512290	−	0.0295771i
$39$	4.14406	−	5.64540i	0.663581	−	0.903987i
$40$		0			0
$41$	−6.46287			−1.00933			−0.504665	−	0.863315i	$-0.668384\pi$
$41$	−6.46287			−1.00933			−0.504665	+	0.863315i	$0.668384\pi$
$42$	−3.82795	+	1.33694i	−0.590665	+	0.206294i
$43$			10.3583i			1.57963i	0.613345	+	0.789815i	$0.289823\pi$
$43$			10.3583i			1.57963i	−0.613345	+	0.789815i	$0.710177\pi$
$44$	−1.52579	−	0.880917i	−0.230022	−	0.132803i
$45$		0			0
$46$	−3.23592	−	5.60477i	−0.477110	−	0.826378i
$47$	−9.41134	−	5.43364i	−1.37279	−	0.792578i	−0.381507	−	0.924366i	$-0.624595\pi$
$47$	−9.41134	−	5.43364i	−1.37279	−	0.792578i	−0.991278	+	0.131788i	$0.957928\pi$
$48$	−0.0588063	−	0.133843i	−0.00848796	−	0.0193186i
$49$	−6.91508	−	1.08706i	−0.987868	−	0.155295i
$50$		0			0
$51$	−1.09095	+	9.91198i	−0.152764	+	1.38795i
$52$	2.46055	+	4.26180i	0.341217	+	0.591005i
$53$	0.697977	+	1.20893i	0.0958745	+	0.166059i	0.909973	−	0.414667i	$-0.136102\pi$
$53$	0.697977	+	1.20893i	0.0958745	+	0.166059i	−0.814099	+	0.580726i	$0.802769\pi$
$54$	−3.46156	+	3.02581i	−0.471059	+	0.411760i
$55$		0			0
$56$	0.586561	−	7.50833i	0.0783825	−	1.00334i
$57$	0.653522	−	0.287136i	0.0865611	−	0.0380320i
$58$	1.39554	+	0.805713i	0.183243	+	0.105795i
$59$	−0.583941	−	1.01142i	−0.0760227	−	0.131675i	0.825508	−	0.564391i	$-0.190889\pi$
$59$	−0.583941	−	1.01142i	−0.0760227	−	0.131675i	−0.901531	+	0.432715i	$0.857555\pi$
$60$		0			0
$61$	3.58903	+	2.07213i	0.459529	+	0.265309i	0.711846	−	0.702335i	$-0.247859\pi$
$61$	3.58903	+	2.07213i	0.459529	+	0.265309i	−0.252317	+	0.967645i	$0.581193\pi$
$62$		−	2.35944i		−	0.299649i
$63$	−7.73472	+	1.78160i	−0.974483	+	0.224461i
$64$	5.14000			0.642499
$65$		0			0
$66$	1.78832	+	1.31274i	0.220127	+	0.161587i
$67$	5.99309	−	3.46011i	0.732173	−	0.422720i	−0.0870436	−	0.996205i	$-0.527742\pi$
$67$	5.99309	−	3.46011i	0.732173	−	0.422720i	0.819217	+	0.573484i	$0.194409\pi$
$68$	−6.06843	−	3.50361i	−0.735906	−	0.424875i
$69$	−5.09609	−	11.5987i	−0.613497	−	1.39632i
$70$		0			0
$71$			13.3217i			1.58100i	0.612463	+	0.790499i	$0.290179\pi$
$71$			13.3217i			1.58100i	−0.612463	+	0.790499i	$0.709821\pi$
$72$	−2.55911	−	8.14712i	−0.301594	−	0.960147i
$73$	−1.57238	−	2.72344i	−0.184033	−	0.318755i	0.759217	−	0.650838i	$-0.225582\pi$
$73$	−1.57238	−	2.72344i	−0.184033	−	0.318755i	−0.943250	+	0.332082i	$0.892249\pi$
$74$	4.48093	−	2.58707i	0.520898	−	0.300740i
$75$		0			0
$76$			0.501602i			0.0575377i
$77$	1.65079	+	3.45582i	0.188125	+	0.393828i
$78$	−2.49253	−	5.67300i	−0.282223	−	0.642341i
$79$	−6.42216	+	11.1235i	−0.722550	+	1.25149i	0.237425	+	0.971406i	$0.423697\pi$
$79$	−6.42216	+	11.1235i	−0.722550	+	1.25149i	−0.959975	+	0.280087i	$0.909637\pi$
$80$		0			0
$81$	−7.38350	+	5.14626i	−0.820389	+	0.571806i
$82$	−2.85920	+	4.95228i	−0.315746	+	0.546888i
$83$			11.5010i			1.26240i	0.775620	+	0.631200i	$0.217437\pi$
$83$			11.5010i			1.26240i	−0.775620	+	0.631200i	$0.782563\pi$
$84$	1.04014	−	5.47967i	0.113488	−	0.597881i
$85$		0			0
$86$	7.93724	+	4.58257i	0.855894	+	0.494151i
$87$	2.54287	+	1.86662i	0.272624	+	0.200123i
$88$	−3.56845	+	2.06025i	−0.380399	+	0.219623i
$89$	−3.90111	+	6.75692i	−0.413517	+	0.716232i	−0.995271	−	0.0971324i	$-0.969033\pi$
$89$	−3.90111	+	6.75692i	−0.413517	+	0.716232i	0.581755	+	0.813364i	$0.302366\pi$
$90$		0			0
$91$	0.833161	−	10.6650i	0.0873390	−	1.11799i
$92$	8.90244			0.928144
$93$	0.505303	−	4.59099i	0.0523975	−	0.476063i
$94$	−8.32723	+	4.80773i	−0.858889	+	0.495880i
$95$		0			0
$96$	9.67290	+	1.06464i	0.987236	+	0.108659i
$97$	−3.86099			−0.392024			−0.196012	−	0.980601i	$-0.562799\pi$
$97$	−3.86099			−0.392024			−0.196012	+	0.980601i	$0.562799\pi$
$98$	−3.89224	+	4.81787i	−0.393176	+	0.486678i
$99$	3.19857	+	2.93731i	0.321468	+	0.295211i
$100$		0			0
$101$	6.61336	+	11.4547i	0.658054	+	1.13978i	0.981119	+	0.193406i	$0.0619535\pi$
$101$	6.61336	+	11.4547i	0.658054	+	1.13978i	−0.323065	+	0.946377i	$0.604713\pi$
$102$	7.11258	+	5.22106i	0.704250	+	0.516962i
$103$	8.49538	−	14.7144i	0.837075	−	1.44986i	−0.0552547	−	0.998472i	$-0.517597\pi$
$103$	8.49538	−	14.7144i	0.837075	−	1.44986i	0.892330	−	0.451384i	$-0.149070\pi$
$104$	11.5092			1.12857
$105$		0			0
$106$	1.23515			0.119968
$107$	6.47403	−	11.2134i	0.625868	−	1.08404i	−0.362504	−	0.931982i	$-0.618078\pi$
$107$	6.47403	−	11.2134i	0.625868	−	1.08404i	0.988372	−	0.152054i	$-0.0485886\pi$
$108$	−1.22376	−	6.20478i	−0.117757	−	0.597055i
$109$	3.63427	+	6.29474i	0.348100	+	0.602927i	0.985912	−	0.167265i	$-0.0534936\pi$
$109$	3.63427	+	6.29474i	0.348100	+	0.602927i	−0.637812	+	0.770192i	$0.720160\pi$
$110$		0			0
$111$	9.27301	−	4.07425i	0.880156	−	0.386711i
$112$	−0.184111	−	0.126380i	−0.0173968	−	0.0119417i
$113$	−4.78517			−0.450151			−0.225075	−	0.974341i	$-0.572263\pi$
$113$	−4.78517			−0.450151			−0.225075	+	0.974341i	$0.572263\pi$
$114$	0.0690985	−	0.627802i	0.00647167	−	0.0587990i
$115$		0			0
$116$	−1.91965	+	1.10831i	−0.178235	+	0.102904i
$117$	−3.63500	−	11.5723i	−0.336056	−	1.06986i
$118$	−1.03335			−0.0951278
$119$	6.56557	+	13.7446i	0.601865	+	1.25997i
$120$		0			0
$121$	−4.45230	+	7.71161i	−0.404754	+	0.701055i
$122$	3.17561	−	1.83344i	0.287506	−	0.165992i
$123$	−6.62400	+	9.02378i	−0.597266	+	0.813647i
$124$	2.81075	+	1.62279i	0.252413	+	0.145731i
$125$		0			0
$126$	−2.05669	+	6.71505i	−0.183224	+	0.598224i
$127$		−	9.16192i		−	0.812989i	−0.913653	−	0.406495i	$-0.866751\pi$
$127$		−	9.16192i		−	0.812989i	0.913653	−	0.406495i	$-0.133249\pi$
$128$	−3.34442	+	5.79271i	−0.295608	+	0.512008i
$129$	14.4628	+	10.6166i	1.27338	+	0.934738i
$130$		0			0
$131$	10.4220	−	18.0514i	0.910574	−	1.57716i	0.0973191	−	0.995253i	$-0.468973\pi$
$131$	10.4220	−	18.0514i	0.910574	−	1.57716i	0.813255	−	0.581907i	$-0.197693\pi$
$132$	−2.79382	+	1.22751i	−0.243170	+	0.106841i
$133$	0.617078	−	0.898964i	0.0535074	−	0.0779501i
$134$		−	6.12308i		−	0.528953i
$135$		0			0
$136$	−14.1926	+	8.19408i	−1.21700	+	0.702637i
$137$	4.73886	+	8.20795i	0.404868	+	0.701253i	0.994306	−	0.106561i	$-0.0339840\pi$
$137$	4.73886	+	8.20795i	0.404868	+	0.701253i	−0.589438	+	0.807814i	$0.700651\pi$
$138$	−11.1423	−	1.22636i	−0.948492	−	0.104395i
$139$			5.75447i			0.488088i	0.969764	+	0.244044i	$0.0784741\pi$
$139$			5.75447i			0.488088i	−0.969764	+	0.244044i	$0.921526\pi$
$140$		0			0
$141$	−17.2327	+	7.57147i	−1.45126	+	0.637633i
$142$	10.2080	+	5.89359i	0.856636	+	0.494579i
$143$	−5.06869	+	2.92641i	−0.423865	+	0.244719i
$144$	−0.247151	−	0.0550721i	−0.0205959	−	0.00458935i
$145$		0			0
$146$	−2.78251			−0.230282
$147$	−8.60530	+	8.54101i	−0.709753	+	0.704450i
$148$			7.11737i			0.585044i
$149$	−5.57080	−	3.21630i	−0.456378	−	0.263490i	0.254142	−	0.967167i	$-0.418207\pi$
$149$	−5.57080	−	3.21630i	−0.456378	−	0.263490i	−0.710520	+	0.703677i	$0.751540\pi$
$150$		0			0
$151$	−2.06002	−	3.56807i	−0.167642	−	0.290365i	0.769948	−	0.638107i	$-0.220282\pi$
$151$	−2.06002	−	3.56807i	−0.167642	−	0.290365i	−0.937591	+	0.347741i	$0.886949\pi$
$152$	1.01595	+	0.586561i	0.0824047	+	0.0475764i
$153$	12.7214	+	11.6824i	1.02847	+	0.944462i
$154$	3.37840	+	0.263925i	0.272239	+	0.0212677i
$155$		0			0
$156$	8.47244	+	0.932512i	0.678338	+	0.0746607i
$157$	0.619880	+	1.07366i	0.0494718	+	0.0856877i	0.889701	−	0.456544i	$-0.150913\pi$
$157$	0.619880	+	1.07366i	0.0494718	+	0.0856877i	−0.840229	+	0.542232i	$0.817580\pi$
$158$	5.68238	+	9.84218i	0.452066	+	0.783001i
$159$	2.40335	+	0.264523i	0.190598	+	0.0209780i
$160$		0			0
$161$	−15.9548	−	10.9519i	−1.25742	−	0.863132i
$162$	0.676913	+	7.93445i	0.0531833	+	0.623389i
$163$	−6.44585	−	3.72151i	−0.504878	−	0.291491i	0.225848	−	0.974163i	$-0.427485\pi$
$163$	−6.44585	−	3.72151i	−0.504878	−	0.291491i	−0.730726	+	0.682671i	$0.760818\pi$
$164$	−3.93302	−	6.81220i	−0.307118	−	0.531943i
$165$		0			0
$166$	8.81284	+	5.08809i	0.684009	+	0.394913i
$167$			2.50723i			0.194015i	0.995284	+	0.0970077i	$0.0309271\pi$
$167$			2.50723i			0.194015i	−0.995284	+	0.0970077i	$0.969073\pi$
$168$	−9.88232	−	8.51452i	−0.762438	−	0.656909i
$169$	3.34791			0.257532
$170$		0			0
$171$	0.268903	−	1.20677i	0.0205635	−	0.0922844i
$172$	−10.9182	+	6.30363i	−0.832506	+	0.480647i
$173$	−14.7654	−	8.52481i	−1.12259	−	0.648130i	−0.180532	−	0.983569i	$-0.557782\pi$
$173$	−14.7654	−	8.52481i	−1.12259	−	0.648130i	−0.942062	+	0.335440i	$0.891115\pi$
$174$	2.55531	−	1.12272i	0.193717	−	0.0851128i
$175$		0			0
$176$			0.122179i			0.00920962i
$177$	−2.01069	−	0.221305i	−0.151133	−	0.0166343i
$178$	3.45173	+	5.97858i	0.258718	+	0.448113i
$179$	−10.1751	+	5.87462i	−0.760525	+	0.439090i	−0.829484	−	0.558530i	$-0.811366\pi$
$179$	−10.1751	+	5.87462i	−0.760525	+	0.439090i	0.0689590	+	0.997619i	$0.478032\pi$
$180$		0			0
$181$		−	2.41221i		−	0.179298i	−0.995973	−	0.0896490i	$-0.971425\pi$
$181$		−	2.41221i		−	0.179298i	0.995973	−	0.0896490i	$-0.0285745\pi$
$182$	−7.80360	−	5.35664i	−0.578442	−	0.397061i
$183$	6.57173	−	2.88740i	0.485796	−	0.213442i
$184$	10.4103	−	18.0312i	0.767458	−	1.32928i
$185$		0			0
$186$	−3.29437	−	2.41827i	−0.241555	−	0.177316i
$187$	4.16695	−	7.21737i	0.304718	−	0.527786i
$188$		−	13.2267i		−	0.964658i
$189$	−5.44000	+	12.6256i	−0.395702	+	0.918379i
$190$		0			0
$191$	11.9159	+	6.87963i	0.862202	+	0.497793i	0.864749	−	0.502204i	$-0.167477\pi$
$191$	11.9159	+	6.87963i	0.862202	+	0.497793i	−0.00254675	+	0.999997i	$0.500811\pi$
$192$	5.26815	−	7.17672i	0.380196	−	0.517935i
$193$	7.97929	−	4.60685i	0.574362	−	0.331608i	−0.184528	−	0.982827i	$-0.559075\pi$
$193$	7.97929	−	4.60685i	0.574362	−	0.331608i	0.758890	+	0.651219i	$0.225742\pi$
$194$	−1.70812	+	2.95855i	−0.122636	+	0.212411i
$195$		0			0
$196$	−3.06240	−	7.95039i	−0.218743	−	0.567885i
$197$	−4.11728			−0.293344			−0.146672	−	0.989185i	$-0.546856\pi$
$197$	−4.11728			−0.293344			−0.146672	+	0.989185i	$0.546856\pi$
$198$	3.66582	−	1.15148i	0.260519	−	0.0818321i
$199$	−0.0694265	+	0.0400834i	−0.00492151	+	0.00284144i	−0.502459	−	0.864601i	$-0.667571\pi$
$199$	−0.0694265	+	0.0400834i	−0.00492151	+	0.00284144i	0.497537	+	0.867443i	$0.334238\pi$
$200$		0			0
$201$	1.31133	−	11.9142i	0.0924941	−	0.840366i
$202$	11.7031			0.823428
$203$	4.80384	+	0.375283i	0.337164	+	0.0263397i
$204$	−11.1116	+	4.88208i	−0.777971	+	0.341814i
$205$		0			0
$206$	−7.51679	−	13.0195i	−0.523719	−	0.907108i
$207$	−21.4179	−	4.77250i	−1.48865	−	0.331711i
$208$	0.170634	−	0.295547i	0.0118313	−	0.0204925i
$209$	−0.596570			−0.0412656
$210$		0			0
$211$	17.5804			1.21028			0.605141	−	0.796118i	$-0.293117\pi$
$211$	17.5804			1.21028			0.605141	+	0.796118i	$0.293117\pi$
$212$	−0.849517	+	1.47141i	−0.0583451	+	0.101057i
$213$	18.6005	+	13.6539i	1.27448	+	0.935548i
$214$	−5.72828	−	9.92167i	−0.391577	−	0.678231i
$215$		0			0
$216$	−13.9983	−	4.77709i	−0.952465	−	0.325040i
$217$	−3.04101	−	6.36616i	−0.206437	−	0.432163i
$218$	6.43127			0.435580
$219$	−5.41419	−	0.595909i	−0.365857	−	0.0402678i
$220$		0			0
$221$	−20.1593	+	11.6390i	−1.35606	+	0.782924i
$222$	0.980459	−	8.90807i	0.0658041	−	0.597870i
$223$	−27.4965			−1.84130			−0.920651	−	0.390387i	$-0.872341\pi$
$223$	−27.4965			−1.84130			−0.920651	+	0.390387i	$0.872341\pi$
$224$	13.4131	−	6.40721i	0.896199	−	0.428100i
$225$		0			0
$226$	−2.11698	+	3.66671i	−0.140819	+	0.243906i
$227$	10.7431	−	6.20253i	0.713044	−	0.411676i	−0.0991431	−	0.995073i	$-0.531610\pi$
$227$	10.7431	−	6.20253i	0.713044	−	0.411676i	0.812187	+	0.583397i	$0.198277\pi$
$228$	0.700361	+	0.514108i	0.0463826	+	0.0340476i
$229$	−23.5513	−	13.5973i	−1.55631	−	0.898538i	−0.997605	−	0.0691740i	$-0.977964\pi$
$229$	−23.5513	−	13.5973i	−1.55631	−	0.898538i	−0.558709	−	0.829364i	$-0.688703\pi$
$230$		0			0
$231$	6.51714	+	1.23707i	0.428796	+	0.0813931i
$232$			5.18414i			0.340355i
$233$	14.4675	−	25.0585i	0.947798	−	1.64163i	0.197749	−	0.980253i	$-0.436637\pi$
$233$	14.4675	−	25.0585i	0.947798	−	1.64163i	0.750049	−	0.661382i	$-0.230030\pi$
$234$	−10.4756	−	2.33425i	−0.684811	−	0.152595i
$235$		0			0
$236$	0.710723	−	1.23101i	0.0462641	−	0.0801318i
$237$	8.94892	+	20.3678i	0.581295	+	1.32303i
$238$	13.4367	+	1.04969i	0.870970	+	0.0680413i
$239$		−	19.2419i		−	1.24465i	−0.782757	−	0.622327i	$-0.786187\pi$
$239$		−	19.2419i		−	1.24465i	0.782757	−	0.622327i	$-0.213813\pi$
$240$		0			0
$241$	4.90603	−	2.83250i	0.316025	−	0.182457i	−0.333594	−	0.942717i	$-0.608262\pi$
$241$	4.90603	−	2.83250i	0.316025	−	0.182457i	0.649619	+	0.760260i	$0.274928\pi$
$242$	3.93943	+	6.82329i	0.253236	+	0.438618i
$243$	−0.382125	+	15.5838i	−0.0245133	+	0.999700i
$244$			5.04404i			0.322911i
$245$		0			0
$246$	3.98413	+	9.06791i	0.254019	+	0.578149i
$247$	1.44308	+	0.833161i	0.0918208	+	0.0530127i
$248$	6.57365	−	3.79530i	0.417427	−	0.241002i
$249$	16.0583	+	11.7878i	1.01765	+	0.747018i
$250$		0			0
$251$	6.55844			0.413965			0.206983	−	0.978345i	$-0.433636\pi$
$251$	6.55844			0.413965			0.206983	+	0.978345i	$0.433636\pi$
$252$	−6.58492	−	7.06859i	−0.414811	−	0.445279i
$253$			10.5879i			0.665659i
$254$	−7.02047	−	4.05327i	−0.440504	−	0.254325i
$255$		0			0
$256$	8.09917	+	14.0282i	0.506198	+	0.876761i
$257$	−7.56295	−	4.36647i	−0.471764	−	0.272373i	0.245214	−	0.969469i	$-0.421142\pi$
$257$	−7.56295	−	4.36647i	−0.471764	−	0.272373i	−0.716978	+	0.697096i	$0.754475\pi$
$258$	14.5335	−	6.38555i	0.904818	−	0.397547i
$259$	8.75590	−	12.7557i	0.544065	−	0.792598i
$260$		0			0
$261$	5.21254	−	1.63732i	0.322648	−	0.101348i
$262$	−9.22147	−	15.9721i	−0.569704	−	0.986757i
$263$	11.2709	+	19.5217i	0.694992	+	1.20376i	0.970183	+	0.242372i	$0.0779253\pi$
$263$	11.2709	+	19.5217i	0.694992	+	1.20376i	−0.275192	+	0.961389i	$0.588741\pi$
$264$	−0.780803	+	7.09407i	−0.0480551	+	0.436610i
$265$		0			0
$266$	−0.415848	−	0.870551i	−0.0254973	−	0.0533769i
$267$	5.43597	+	12.3723i	0.332676	+	0.757173i
$268$	7.29428	+	4.21135i	0.445569	+	0.257249i
$269$	−7.09460	−	12.2882i	−0.432565	−	0.749225i	0.564528	−	0.825414i	$-0.309058\pi$
$269$	−7.09460	−	12.2882i	−0.432565	−	0.749225i	−0.997093	+	0.0761890i	$0.975725\pi$
$270$		0			0
$271$	−11.0247	−	6.36513i	−0.669705	−	0.386654i	0.126260	−	0.991997i	$-0.459703\pi$
$271$	−11.0247	−	6.36513i	−0.669705	−	0.386654i	−0.795965	+	0.605343i	$0.793036\pi$
$272$			0.485936i			0.0294642i
$273$	−14.0370	−	12.0942i	−0.849558	−	0.731972i
$274$	8.38597			0.506615
$275$		0			0
$276$	9.12440	−	12.4300i	0.549224	−	0.748200i
$277$	−24.9564	+	14.4086i	−1.49948	+	0.865727i	−1.00000		0.000595725i	$-0.999810\pi$
$277$	−24.9564	+	14.4086i	−1.49948	+	0.865727i	−0.499484	+	0.866323i	$0.666477\pi$
$278$	4.40946	+	2.54580i	0.264462	+	0.152687i
$279$	−5.89226	−	5.41098i	−0.352761	−	0.323947i
$280$		0			0
$281$		−	13.4500i		−	0.802357i	−0.916000	−	0.401179i	$-0.868601\pi$
$281$		−	13.4500i		−	0.802357i	0.916000	−	0.401179i	$-0.131399\pi$
$282$	−1.82206	+	16.5545i	−0.108502	+	0.985806i
$283$	−7.03838	−	12.1908i	−0.418388	−	0.724670i	0.577389	−	0.816469i	$-0.304072\pi$
$283$	−7.03838	−	12.1908i	−0.418388	−	0.724670i	−0.995778	+	0.0917992i	$0.970738\pi$
$284$	−14.0418	+	8.10703i	−0.833227	+	0.481064i
$285$		0			0
$286$			5.17862i			0.306218i
$287$	−1.33175	+	17.0472i	−0.0786107	+	1.00626i
$288$	11.4006	−	12.4146i	0.671785	−	0.731538i
$289$	8.07292	−	13.9827i	0.474878	−	0.822512i
$290$		0			0
$291$	−3.95726	+	5.39091i	−0.231978	+	0.316021i
$292$	1.91377	−	3.31474i	0.111995	−	0.193981i
$293$		−	16.7139i		−	0.976436i	−0.872722	−	0.488218i	$-0.837647\pi$
$293$		−	16.7139i		−	0.976436i	0.872722	−	0.488218i	$-0.162353\pi$
$294$	2.73767	+	10.3725i	0.159664	+	0.604938i
$295$		0			0
$296$	14.4157	+	8.32289i	0.837893	+	0.483758i
$297$	7.37953	−	1.45546i	0.428204	−	0.0844544i
$298$	−4.92909	+	2.84581i	−0.285534	+	0.164853i
$299$	14.7870	−	25.6118i	0.855152	−	1.48117i
$300$		0			0
$301$	27.3223	+	2.13446i	1.57483	+	0.123028i
$302$	−3.64545			−0.209772
$303$	22.7718	+	2.50636i	1.30821	+	0.143987i
$304$	0.0301247	−	0.0173925i	0.00172777	−	0.000997528i
$305$		0			0
$306$	14.5798	−	4.57970i	0.833473	−	0.261804i
$307$	−9.72258			−0.554897			−0.277449	−	0.960741i	$-0.589489\pi$
$307$	−9.72258			−0.554897			−0.277449	+	0.960741i	$0.589489\pi$
$308$	−2.63802	+	3.84309i	−0.150315	+	0.218980i
$309$	−11.8378	−	26.9430i	−0.673431	−	1.53273i
$310$		0			0
$311$	−2.50723	−	4.34265i	−0.142172	−	0.246249i	0.786142	−	0.618046i	$-0.212075\pi$
$311$	−2.50723	−	4.34265i	−0.142172	−	0.246249i	−0.928314	+	0.371796i	$0.878742\pi$
$312$	11.7962	−	16.0698i	0.667828	−	0.909772i
$313$	8.86441	−	15.3536i	0.501046	−	0.867837i	−0.498953	−	0.866629i	$-0.666282\pi$
$313$	8.86441	−	15.3536i	0.501046	−	0.867837i	0.999999	−	0.00120811i	$-0.000384553\pi$
$314$	1.09695			0.0619045
$315$		0			0
$316$	−15.6330			−0.879426
$317$	2.10107	−	3.63917i	0.118008	−	0.204396i	−0.800970	−	0.598704i	$-0.795682\pi$
$317$	2.10107	−	3.63917i	0.118008	−	0.204396i	0.918978	+	0.394308i	$0.129016\pi$
$318$	1.26595	−	1.72458i	0.0709907	−	0.0967096i
$319$	−1.31815	−	2.28310i	−0.0738022	−	0.127829i
$320$		0			0
$321$	−9.02120	−	20.5323i	−0.503514	−	1.14600i
$322$	−15.4506	+	7.38049i	−0.861027	+	0.411299i
$323$	−2.37270			−0.132020
$324$	−9.91770	−	4.65080i	−0.550983	−	0.258378i
$325$		0			0
$326$	−5.70334	+	3.29282i	−0.315879	+	0.182373i
$327$	12.5139	+	1.37733i	0.692021	+	0.0761667i
$328$	−18.3967			−1.01579
$329$	−16.2717	+	23.7048i	−0.897089	+	1.30689i
$330$		0			0
$331$	0.680140	−	1.17804i	0.0373839	−	0.0647508i	−0.846728	−	0.532026i	$-0.821431\pi$
$331$	0.680140	−	1.17804i	0.0373839	−	0.0647508i	0.884112	+	0.467275i	$0.154764\pi$
$332$	−12.1227	+	6.99902i	−0.665317	+	0.384121i
$333$	3.81554	−	17.1233i	0.209090	−	0.938350i
$334$	1.92121	+	1.10921i	0.105124	+	0.0606933i
$335$		0			0
$336$	−0.365158	+	0.127534i	−0.0199210	+	0.00695756i
$337$		−	26.2620i		−	1.43058i	−0.698826	−	0.715292i	$-0.746294\pi$
$337$		−	26.2620i		−	1.43058i	0.698826	−	0.715292i	$-0.253706\pi$
$338$	1.48113	−	2.56539i	0.0805629	−	0.139539i
$339$	−4.90447	+	6.68129i	−0.266374	+	0.362878i
$340$		0			0
$341$	−1.93003	+	3.34291i	−0.104517	+	0.181029i
$342$	−0.805747	−	0.739933i	−0.0435698	−	0.0400110i
$343$	−4.29230	+	18.0160i	−0.231762	+	0.972772i
$344$			29.4853i			1.58974i
$345$		0			0
$346$	−13.0646	+	7.54283i	−0.702355	+	0.405505i
$347$	−3.13913	−	5.43714i	−0.168517	−	0.291881i	0.769381	−	0.638790i	$-0.220565\pi$
$347$	−3.13913	−	5.43714i	−0.168517	−	0.291881i	−0.937899	+	0.346909i	$0.887231\pi$
$348$	−0.420034	+	3.81626i	−0.0225162	+	0.204573i
$349$		−	4.99426i		−	0.267336i	−0.991026	−	0.133668i	$-0.957324\pi$
$349$		−	4.99426i		−	0.267336i	0.991026	−	0.133668i	$-0.0426756\pi$
$350$		0			0
$351$	−19.8834	−	6.78545i	−1.06130	−	0.362181i
$352$	−7.04329	−	4.06644i	−0.375408	−	0.216742i
$353$	0.682186	−	0.393860i	0.0363091	−	0.0209631i	−0.481736	−	0.876317i	$-0.659993\pi$
$353$	0.682186	−	0.393860i	0.0363091	−	0.0209631i	0.518045	+	0.855354i	$0.326660\pi$
$354$	−1.05912	+	1.44282i	−0.0562914	+	0.0766849i
$355$		0			0
$356$	−9.49619			−0.503297
$357$	25.9202	+	4.92011i	1.37184	+	0.260400i
$358$			10.3958i			0.549436i
$359$	21.9487	+	12.6721i	1.15841	+	0.668808i	0.950922	−	0.309430i	$-0.100138\pi$
$359$	21.9487	+	12.6721i	1.15841	+	0.668808i	0.207487	+	0.978238i	$0.433472\pi$
$360$		0			0
$361$	−9.41508	−	16.3074i	−0.495530	−	0.858284i
$362$	−1.84840	−	1.06717i	−0.0971495	−	0.0560893i
$363$	6.20403	+	14.1204i	0.325627	+	0.741129i
$364$	11.7484	−	5.61204i	0.615786	−	0.294151i
$365$		0			0
$366$	0.694845	−	6.31309i	0.0363201	−	0.329991i
$367$	0.912964	+	1.58130i	0.0476563	+	0.0825432i	0.888870	−	0.458160i	$-0.151491\pi$
$367$	0.912964	+	1.58130i	0.0476563	+	0.0825432i	−0.841213	+	0.540703i	$0.818158\pi$
$368$	−0.308683	−	0.534654i	−0.0160912	−	0.0278708i
$369$	5.81030	+	18.4975i	0.302472	+	0.962942i
$370$		0			0
$371$	3.33264	−	1.59195i	0.173022	−	0.0826499i
$372$	5.14664	−	2.26126i	0.266841	−	0.117241i
$373$	1.81882	+	1.05009i	0.0941748	+	0.0543718i	0.546348	−	0.837558i	$-0.316018\pi$
$373$	1.81882	+	1.05009i	0.0941748	+	0.0543718i	−0.452173	+	0.891930i	$0.649351\pi$
$374$	−3.68695	−	6.38599i	−0.190648	−	0.330212i
$375$		0			0
$376$	−26.7897	−	15.4670i	−1.38157	−	0.797651i
$377$			7.36363i			0.379246i
$378$	7.26792	+	9.75412i	0.373821	+	0.501698i
$379$	19.2106			0.986782			0.493391	−	0.869808i	$-0.335757\pi$
$379$	19.2106			0.986782			0.493391	+	0.869808i	$0.335757\pi$
$380$		0			0
$381$	−12.7923	−	9.39035i	−0.655371	−	0.481082i
$382$	10.5433	−	6.08716i	0.539440	−	0.311446i
$383$	−2.73720	−	1.58032i	−0.139864	−	0.0807506i	0.428435	−	0.903573i	$-0.359065\pi$
$383$	−2.73720	−	1.58032i	−0.139864	−	0.0807506i	−0.568299	+	0.822822i	$0.692398\pi$
$384$	4.66026	+	10.6068i	0.237818	+	0.541275i
$385$		0			0
$386$		−	8.15235i		−	0.414944i
$387$	29.6468	−	9.31242i	1.50703	−	0.473377i
$388$	−2.34963	−	4.06969i	−0.119285	−	0.206607i
$389$	9.77019	−	5.64082i	0.495368	−	0.286001i	−0.231430	−	0.972851i	$-0.574341\pi$
$389$	9.77019	−	5.64082i	0.495368	−	0.286001i	0.726799	+	0.686850i	$0.241007\pi$
$390$		0			0
$391$			42.1107i			2.12963i
$392$	−19.6840	−	3.09436i	−0.994191	−	0.156289i
$393$	−14.5225	−	33.0532i	−0.732561	−	1.66731i
$394$	−1.82150	+	3.15493i	−0.0917659	+	0.158943i
$395$		0			0
$396$	−1.14956	+	5.15898i	−0.0577677	+	0.259248i
$397$	−15.3087	+	26.5154i	−0.768319	+	1.33077i	0.170154	+	0.985417i	$0.445573\pi$
$397$	−15.3087	+	26.5154i	−0.768319	+	1.33077i	−0.938474	+	0.345351i	$0.887760\pi$
$398$			0.0709323i			0.00355551i
$399$	−0.622716	−	1.78297i	−0.0311748	−	0.0892603i
$400$		0			0
$401$	−20.4532	−	11.8087i	−1.02139	−	0.589697i	−0.106881	−	0.994272i	$-0.534086\pi$
$401$	−20.4532	−	11.8087i	−1.02139	−	0.589697i	−0.914505	+	0.404574i	$0.867420\pi$
$402$	−8.54934	−	6.27574i	−0.426403	−	0.313005i
$403$	9.33731	−	5.39090i	0.465125	−	0.268540i
$404$	−8.04922	+	13.9417i	−0.400464	+	0.693623i
$405$		0			0
$406$	2.41281	−	3.51500i	0.119746	−	0.174446i
$407$	−8.46491			−0.419590
$408$	−3.10543	+	28.2147i	−0.153742	+	1.39684i
$409$	11.1411	−	6.43231i	0.550891	−	0.318057i	−0.198590	−	0.980083i	$-0.563636\pi$
$409$	11.1411	−	6.43231i	0.550891	−	0.318057i	0.749481	+	0.662025i	$0.230303\pi$
$410$		0			0
$411$	16.3174	+	1.79596i	0.804876	+	0.0885880i
$412$	20.6797			1.01882
$413$	−2.78815	+	1.33186i	−0.137196	+	0.0655364i
$414$	−13.1324	+	14.3004i	−0.645420	+	0.702828i
$415$		0			0
$416$	11.3583	+	19.6731i	0.556885	+	0.964553i
$417$	8.03468	+	5.89794i	0.393460	+	0.288823i
$418$	−0.263925	+	0.457132i	−0.0129090	+	0.0223590i
$419$	−3.78089			−0.184708			−0.0923542	−	0.995726i	$-0.529439\pi$
$419$	−3.78089			−0.184708			−0.0923542	+	0.995726i	$0.529439\pi$
$420$		0			0
$421$	−2.43659			−0.118752			−0.0593759	−	0.998236i	$-0.518911\pi$
$421$	−2.43659			−0.118752			−0.0593759	+	0.998236i	$0.518911\pi$
$422$	7.77763	−	13.4712i	0.378609	−	0.655770i
$423$	−7.09069	+	31.8214i	−0.344761	+	1.54721i
$424$	1.98681	+	3.44126i	0.0964881	+	0.167122i
$425$		0			0
$426$	18.6914	−	8.21238i	0.905603	−	0.397891i
$427$	6.20525	−	9.03986i	0.300293	−	0.437470i
$428$	15.7593			0.761753
$429$	−1.10906	+	10.0765i	−0.0535461	+	0.486499i
$430$		0			0
$431$	26.4558	−	15.2743i	1.27433	−	0.735737i	0.298533	−	0.954399i	$-0.403503\pi$
$431$	26.4558	−	15.2743i	1.27433	−	0.735737i	0.975800	+	0.218663i	$0.0701695\pi$
$432$	−0.330208	+	0.288640i	−0.0158871	+	0.0138872i
$433$	−37.7749			−1.81534			−0.907672	−	0.419680i	$-0.862142\pi$
$433$	−37.7749			−1.81534			−0.907672	+	0.419680i	$0.862142\pi$
$434$	−6.22353	−	0.486191i	−0.298739	−	0.0233379i
$435$		0			0
$436$	−4.42332	+	7.66142i	−0.211839	+	0.366916i
$437$	2.61057	−	1.50722i	0.124881	−	0.0720999i
$438$	−2.85189	+	3.88508i	−0.136268	+	0.185636i
$439$	3.55267	+	2.05113i	0.169560	+	0.0978953i	0.582378	−	0.812918i	$-0.302122\pi$
$439$	3.55267	+	2.05113i	0.169560	+	0.0978953i	−0.412819	+	0.910813i	$0.635456\pi$
$440$		0			0
$441$	3.10553	+	20.7691i	0.147883	+	0.989005i
$442$			20.5966i			0.979679i
$443$	−13.1240	+	22.7315i	−0.623541	+	1.08001i	0.365280	+	0.930898i	$0.380973\pi$
$443$	−13.1240	+	22.7315i	−0.623541	+	1.08001i	−0.988821	+	0.149107i	$0.952360\pi$
$444$	9.93763	+	7.29482i	0.471619	+	0.346197i
$445$		0			0
$446$	−12.1646	+	21.0696i	−0.576009	+	0.997677i
$447$	−10.2005	+	4.48174i	−0.482465	+	0.211979i
$448$	1.05916	−	13.5578i	0.0500405	−	0.640548i
$449$		−	14.6382i		−	0.690821i	−0.938452	−	0.345411i	$-0.887740\pi$
$449$		−	14.6382i		−	0.690821i	0.938452	−	0.345411i	$-0.112260\pi$
$450$		0			0
$451$	8.10195	−	4.67766i	0.381506	−	0.220263i
$452$	−2.91205	−	5.04381i	−0.136971	−	0.237241i
$453$	−7.09330	−	0.780718i	−0.333272	−	0.0366813i
$454$		−	10.9761i		−	0.515134i
$455$		0			0
$456$	1.86027	−	0.817340i	0.0871151	−	0.0382754i
$457$	−25.2776	−	14.5940i	−1.18244	−	0.682679i	−0.225858	−	0.974160i	$-0.572519\pi$
$457$	−25.2776	−	14.5940i	−1.18244	−	0.682679i	−0.956577	+	0.291481i	$0.905852\pi$
$458$	−20.8384	+	12.0310i	−0.973714	+	0.562174i
$459$	29.3501	−	5.78870i	1.36995	−	0.270193i
$460$		0			0
$461$	15.8295			0.737255			0.368627	−	0.929577i	$-0.379828\pi$
$461$	15.8295			0.737255			0.368627	+	0.929577i	$0.379828\pi$
$462$	3.83113	−	4.44658i	0.178241	−	0.206874i
$463$		−	19.1466i		−	0.889816i	−0.895576	−	0.444908i	$-0.853236\pi$
$463$		−	19.1466i		−	0.889816i	0.895576	−	0.444908i	$-0.146764\pi$
$464$	0.133124	+	0.0768591i	0.00618012	+	0.00356809i
$465$		0			0
$466$	−12.8010	−	22.1719i	−0.592994	−	1.02710i
$467$	12.9081	+	7.45251i	0.597317	+	0.344861i	0.767985	−	0.640468i	$-0.221259\pi$
$467$	12.9081	+	7.45251i	0.597317	+	0.344861i	−0.170669	+	0.985328i	$0.554593\pi$
$468$	9.98570	−	10.8739i	0.461589	−	0.502645i
$469$	−7.89185	−	16.5211i	−0.364412	−	0.762872i
$470$		0			0
$471$	2.13444	+	0.234925i	0.0983497	+	0.0108248i
$472$	−1.66221	−	2.87903i	−0.0765092	−	0.132518i
$473$	−7.49710	−	12.9854i	−0.344717	−	0.597067i
$474$	19.5662	+	2.15354i	0.898705	+	0.0989152i
$475$		0			0
$476$	−10.4920	+	15.2848i	−0.480900	+	0.700579i
$477$	2.83261	−	3.08456i	0.129696	−	0.141232i
$478$	−14.7444	−	8.51269i	−0.674394	−	0.389362i
$479$	10.9530	+	18.9712i	0.500456	+	0.866815i	1.00000		0.000526656i	$0.000167640\pi$
$479$	10.9530	+	18.9712i	0.500456	+	0.866815i	−0.499544	+	0.866289i	$0.666499\pi$
$480$		0			0
$481$	20.4762	+	11.8220i	0.933636	+	0.539035i
$482$		−	5.01243i		−	0.228310i
$483$	−31.6443	+	11.0520i	−1.43986	+	0.502883i
$484$	−10.8379			−0.492632
$485$		0			0
$486$	11.7723	+	7.18714i	0.534001	+	0.326015i
$487$	10.7731	−	6.21983i	0.488174	−	0.281848i	−0.235642	−	0.971840i	$-0.575719\pi$
$487$	10.7731	−	6.21983i	0.488174	−	0.281848i	0.723817	+	0.689992i	$0.242386\pi$
$488$	10.2163	+	5.89838i	0.462470	+	0.267007i
$489$	−11.8027	+	5.18572i	−0.533737	+	0.234506i
$490$		0			0
$491$			23.2765i			1.05045i	0.850962	+	0.525227i	$0.176020\pi$
$491$			23.2765i			1.05045i	−0.850962	+	0.525227i	$0.823980\pi$
$492$	−13.5426	−	1.49056i	−0.610548	−	0.0671995i
$493$	−5.24259	−	9.08043i	−0.236114	−	0.408962i
$494$	1.27685	−	0.737187i	0.0574480	−	0.0331676i
$495$		0			0
$496$		−	0.225074i		−	0.0101061i
$497$	35.1389	+	2.74510i	1.57620	+	0.123135i
$498$	16.1368	−	7.08997i	0.723108	−	0.317709i
$499$	−13.2171	+	22.8927i	−0.591680	+	1.02482i	0.402327	+	0.915496i	$0.368202\pi$
$499$	−13.2171	+	22.8927i	−0.591680	+	1.02482i	−0.994006	+	0.109323i	$0.965132\pi$
$500$		0			0
$501$	3.50072	+	2.56974i	0.156401	+	0.114808i
$502$	2.90148	−	5.02551i	0.129499	−	0.224300i
$503$			17.4645i			0.778702i	0.921090	+	0.389351i	$0.127301\pi$
$503$			17.4645i			0.778702i	−0.921090	+	0.389351i	$0.872699\pi$
$504$	−22.0171	+	5.07139i	−0.980720	+	0.225898i
$505$		0			0
$506$	8.11319	+	4.68415i	0.360675	+	0.208236i
$507$	3.43139	−	4.67453i	0.152393	−	0.207603i
$508$	9.65714	−	5.57555i	0.428466	−	0.247375i
$509$	−1.20504	+	2.08719i	−0.0534124	+	0.0925129i	−0.891495	−	0.453030i	$-0.850343\pi$
$509$	−1.20504	+	2.08719i	−0.0534124	+	0.0925129i	0.838083	+	0.545543i	$0.183676\pi$
$510$		0			0
$511$	−7.50768	+	3.58630i	−0.332120	+	0.158648i
$512$	0.954733			0.0421937
$513$	−1.40935	−	1.61232i	−0.0622244	−	0.0711856i
$514$	−6.69176	+	3.86349i	−0.295161	+	0.170411i
$515$		0			0
$516$	−2.38898	+	21.7053i	−0.105169	+	0.955525i
$517$	15.7309			0.691846
$518$	−5.90059	−	12.3525i	−0.259257	−	0.542738i
$519$	−27.0363	+	11.8788i	−1.18676	+	0.521424i
$520$		0			0
$521$	15.7340	+	27.2520i	0.689317	+	1.19393i	0.972059	+	0.234736i	$0.0754226\pi$
$521$	15.7340	+	27.2520i	0.689317	+	1.19393i	−0.282742	+	0.959196i	$0.591244\pi$
$522$	1.05142	−	4.71855i	0.0460196	−	0.206525i
$523$	8.54828	−	14.8061i	0.373790	−	0.647424i	−0.616355	−	0.787469i	$-0.711391\pi$
$523$	8.54828	−	14.8061i	0.373790	−	0.647424i	0.990145	+	0.140045i	$0.0447246\pi$
$524$	25.3695			1.10827
$525$		0			0
$526$	19.9451			0.869649
$527$	−7.67617	+	13.2955i	−0.334379	+	0.579162i
$528$	0.170593	+	0.125226i	0.00742411	+	0.00544975i
$529$	−15.2501	−	26.4140i	−0.663049	−	1.14843i
$530$		0			0
$531$	−2.36982	+	2.58060i	−0.102841	+	0.111989i
$532$	1.32308	+	0.103361i	0.0573629	+	0.00448127i
$533$	−26.1310			−1.13186
$534$	11.8854	+	1.30815i	0.514331	+	0.0566094i
$535$		0			0
$536$	17.0595	−	9.84932i	0.736859	−	0.425426i
$537$	−2.22639	+	20.2281i	−0.0960759	+	0.872908i
$538$	−12.5547			−0.541272
$539$	9.45564	−	3.64220i	0.407283	−	0.156881i
$540$		0			0
$541$	10.8422	−	18.7792i	0.466142	−	0.807382i	−0.533110	−	0.846046i	$-0.678977\pi$
$541$	10.8422	−	18.7792i	0.466142	−	0.807382i	0.999252	+	0.0386641i	$0.0123102\pi$
$542$	−9.75478	+	5.63192i	−0.419004	+	0.241912i
$543$	−3.36805	−	2.47235i	−0.144537	−	0.106099i
$544$	−28.0128	−	16.1732i	−1.20104	−	0.693419i
$545$		0			0
$546$	−15.4774	+	5.40558i	−0.662371	+	0.231338i
$547$			9.42694i			0.403067i	0.979482	+	0.201533i	$0.0645925\pi$
$547$			9.42694i			0.403067i	−0.979482	+	0.201533i	$0.935408\pi$
$548$	−5.76774	+	9.99001i	−0.246386	+	0.426752i
$549$	2.70405	−	12.1352i	0.115406	−	0.517916i
$550$		0			0
$551$	−0.375283	+	0.650009i	−0.0159876	+	0.0276913i
$552$	−14.5062	−	33.0161i	−0.617424	−	1.40526i
$553$	28.0173	+	19.2320i	1.19142	+	0.817826i
$554$			25.4977i			1.08329i
$555$		0			0
$556$	−6.06551	+	3.50192i	−0.257235	+	0.148515i
$557$	−2.82874	−	4.89952i	−0.119858	−	0.207599i	0.799854	−	0.600195i	$-0.204910\pi$
$557$	−2.82874	−	4.89952i	−0.119858	−	0.207599i	−0.919711	+	0.392596i	$0.871577\pi$
$558$	−6.75301	+	2.12120i	−0.285878	+	0.0897977i
$559$			41.8814i			1.77139i
$560$		0			0
$561$	−5.80641	−	13.2154i	−0.245147	−	0.557956i
$562$	−10.3063	−	5.95032i	−0.434743	−	0.250999i
$563$	−6.32441	+	3.65140i	−0.266542	+	0.153888i	−0.627315	−	0.778765i	$-0.715846\pi$
$563$	−6.32441	+	3.65140i	−0.266542	+	0.153888i	0.360773	+	0.932654i	$0.382513\pi$
$564$	−18.4678	−	13.5565i	−0.777635	−	0.570831i
$565$		0			0
$566$	−12.4552			−0.523533
$567$	12.0529	+	20.5360i	0.506174	+	0.862431i
$568$			37.9207i			1.59112i
$569$	12.6704	+	7.31525i	0.531170	+	0.306671i	0.741493	−	0.670961i	$-0.234118\pi$
$569$	12.6704	+	7.31525i	0.531170	+	0.306671i	−0.210323	+	0.977632i	$0.567451\pi$
$570$		0			0
$571$	15.0693	+	26.1009i	0.630632	+	1.09229i	0.987423	+	0.158103i	$0.0505377\pi$
$571$	15.0693	+	26.1009i	0.630632	+	1.09229i	−0.356790	+	0.934184i	$0.616129\pi$
$572$	−6.16917	−	3.56177i	−0.257946	−	0.148925i
$573$	21.8187	−	9.58638i	0.911487	−	0.400477i
$574$	12.4735	+	8.56223i	0.520635	+	0.357380i
$575$		0			0
$576$	−4.62100	−	14.7113i	−0.192542	−	0.612971i
$577$	22.6632	+	39.2538i	0.943482	+	1.63416i	0.758762	+	0.651367i	$0.225804\pi$
$577$	22.6632	+	39.2538i	0.943482	+	1.63416i	0.184720	+	0.982791i	$0.440862\pi$
$578$	−7.14299	−	12.3720i	−0.297109	−	0.514608i
$579$	1.74593	−	15.8628i	0.0725582	−	0.659235i
$580$		0			0
$581$	30.3364	+	2.36992i	1.25856	+	0.0983208i
$582$	2.38017	+	5.41727i	0.0986611	+	0.224553i
$583$	−1.74999	−	1.01036i	−0.0724771	−	0.0418447i
$584$	−4.47583	−	7.75237i	−0.185211	−	0.320795i
$585$		0			0
$586$	−12.8073	−	7.39430i	−0.529065	−	0.305456i
$587$		−	27.9328i		−	1.15291i	−0.817129	−	0.576455i	$-0.804436\pi$
$587$		−	27.9328i		−	1.15291i	0.817129	−	0.576455i	$-0.195564\pi$
$588$	−14.2395	−	3.87274i	−0.587226	−	0.159709i
$589$	1.09897			0.0452825
$590$		0			0
$591$	−4.21993	+	5.74875i	−0.173585	+	0.236472i
$592$	0.427448	−	0.246787i	0.0175680	−	0.0101429i
$593$	25.5085	+	14.7273i	1.04751	+	0.604779i	0.921951	−	0.387307i	$-0.126595\pi$
$593$	25.5085	+	14.7273i	1.04751	+	0.604779i	0.125558	+	0.992086i	$0.459928\pi$
$594$	2.14947	−	6.29859i	0.0881937	−	0.258434i
$595$		0			0
$596$		−	7.82921i		−	0.320697i
$597$	−0.0151910	+	0.138020i	−0.000621726	+	0.00564876i
$598$	−13.0836	−	22.6615i	−0.535029	−	0.926698i
$599$	13.1940	−	7.61757i	0.539093	−	0.311245i	−0.205618	−	0.978632i	$-0.565921\pi$
$599$	13.1940	−	7.61757i	0.539093	−	0.311245i	0.744711	+	0.667387i	$0.232587\pi$
$600$		0			0
$601$			18.6064i			0.758970i	0.925198	+	0.379485i	$0.123899\pi$
$601$			18.6064i			0.758970i	−0.925198	+	0.379485i	$0.876101\pi$
$602$	13.7231	−	19.9919i	0.559310	−	0.814808i
$603$	−15.2912	−	14.0422i	−0.622707	−	0.571844i
$604$	2.50729	−	4.34275i	0.102020	−	0.176704i
$605$		0			0
$606$	11.9949	−	16.3405i	0.487259	−	0.663786i
$607$	9.55240	−	16.5452i	0.387720	−	0.671550i	−0.604423	−	0.796664i	$-0.706596\pi$
$607$	9.55240	−	16.5452i	0.387720	−	0.671550i	0.992142	+	0.125113i	$0.0399295\pi$
$608$			2.31547i			0.0939046i
$609$	5.44760	−	6.32273i	0.220748	−	0.256210i
$610$		0			0
$611$	−38.0525	−	21.9696i	−1.53944	−	0.888795i
$612$	−4.57208	+	20.5184i	−0.184815	+	0.829409i
$613$	−10.7916	+	6.23054i	−0.435869	+	0.251649i	−0.701844	−	0.712331i	$-0.747640\pi$
$613$	−10.7916	+	6.23054i	−0.435869	+	0.251649i	0.265975	+	0.963980i	$0.414306\pi$
$614$	−4.30131	+	7.45009i	−0.173587	+	0.300661i
$615$		0			0
$616$	4.69902	+	9.83710i	0.189329	+	0.396348i
$617$	19.4451			0.782829			0.391414	−	0.920214i	$-0.371986\pi$
$617$	19.4451			0.782829			0.391414	+	0.920214i	$0.371986\pi$
$618$	−25.8826	−	2.84875i	−1.04115	−	0.114593i
$619$	9.61812	−	5.55302i	0.386585	−	0.223195i	−0.294095	−	0.955776i	$-0.595018\pi$
$619$	9.61812	−	5.55302i	0.386585	−	0.223195i	0.680679	+	0.732582i	$0.261685\pi$
$620$		0			0
$621$	−28.6155	+	25.0132i	−1.14830	+	1.00375i
$622$	−4.43684			−0.177901
$623$	17.0189	+	11.6824i	0.681850	+	0.468044i
$624$	−0.237769	−	0.541163i	−0.00951837	−	0.0216639i
$625$		0			0
$626$	−7.84330	−	13.5850i	−0.313481	−	0.542966i
$627$	−0.611444	+	0.832961i	−0.0244187	+	0.0332653i
$628$	−0.754465	+	1.30677i	−0.0301064	+	0.0521459i
$629$	−33.6669			−1.34239
$630$		0			0
$631$	9.89504			0.393915			0.196958	−	0.980412i	$-0.436894\pi$
$631$	9.89504			0.393915			0.196958	+	0.980412i	$0.436894\pi$
$632$	−18.2809	+	31.6634i	−0.727174	+	1.25950i
$633$	18.0187	−	24.5466i	0.716178	−	0.975639i
$634$	−1.85905	−	3.21996i	−0.0738322	−	0.127881i
$635$		0			0
$636$	1.18375	+	2.69423i	0.0469389	+	0.106833i
$637$	−27.9594	−	4.39528i	−1.10779	−	0.174147i
$638$	−2.33262			−0.0923493
$639$	38.1284	−	11.9766i	1.50834	−	0.473787i
$640$		0			0
$641$	2.40816	−	1.39035i	0.0951166	−	0.0549156i	−0.451687	−	0.892176i	$-0.649178\pi$
$641$	2.40816	−	1.39035i	0.0951166	−	0.0549156i	0.546804	+	0.837261i	$0.315844\pi$
$642$	−19.7242	−	2.17093i	−0.778453	−	0.0856798i
$643$	37.8005			1.49071			0.745354	−	0.666669i	$-0.232281\pi$
$643$	37.8005			1.49071			0.745354	+	0.666669i	$0.232281\pi$
$644$	1.83445	−	23.4821i	0.0722876	−	0.925325i
$645$		0			0
$646$	−1.04969	+	1.81812i	−0.0412995	+	0.0715329i
$647$	−17.6163	+	10.1708i	−0.692569	+	0.399855i	−0.804574	−	0.593853i	$-0.797606\pi$
$647$	−17.6163	+	10.1708i	−0.692569	+	0.399855i	0.112005	+	0.993708i	$0.464273\pi$
$648$	−21.0173	+	14.6490i	−0.825639	+	0.575466i
$649$	1.46408	+	0.845285i	0.0574700	+	0.0331803i
$650$		0			0
$651$	−12.0056	−	2.27887i	−0.470536	−	0.0893161i
$652$		−	9.05901i		−	0.354778i
$653$	−12.4472	+	21.5592i	−0.487097	+	0.843677i	−0.999890	−	0.0148355i	$-0.995278\pi$
$653$	−12.4472	+	21.5592i	−0.487097	+	0.843677i	0.512793	+	0.858512i	$0.328611\pi$
$654$	6.59161	−	8.97966i	0.257753	−	0.351132i
$655$		0			0
$656$	−0.272747	+	0.472411i	−0.0106490	+	0.0184446i
$657$	−6.38122	+	6.94880i	−0.248955	+	0.271099i
$658$	10.9655	+	22.9556i	0.427480	+	0.894901i
$659$		−	29.3981i		−	1.14519i	−0.819840	−	0.572593i	$-0.805938\pi$
$659$		−	29.3981i		−	1.14519i	0.819840	−	0.572593i	$-0.194062\pi$
$660$		0			0
$661$	17.1948	−	9.92744i	0.668801	−	0.386133i	−0.126821	−	0.991926i	$-0.540477\pi$
$661$	17.1948	−	9.92744i	0.668801	−	0.386133i	0.795622	+	0.605793i	$0.207144\pi$
$662$	−0.601794	−	1.04234i	−0.0233894	−	0.0405116i
$663$	−4.41100	+	40.0767i	−0.171309	+	1.55645i
$664$			32.7380i			1.27048i
$665$		0			0
$666$	−11.4330	−	10.4991i	−0.443019	−	0.406833i
$667$	11.5364	+	6.66053i	0.446690	+	0.257897i
$668$	−2.64275	+	1.52579i	−0.102251	+	0.0590347i
$669$	−28.1821	+	38.3920i	−1.08958	+	1.48432i
$670$		0			0
$671$	−5.99903			−0.231590
$672$	4.80143	−	25.2950i	0.185219	−	0.975775i
$673$			17.4983i			0.674509i	0.941414	+	0.337255i	$0.109498\pi$
$673$			17.4983i			0.674509i	−0.941414	+	0.337255i	$0.890502\pi$
$674$	−20.1237	−	11.6184i	−0.775136	−	0.447525i
$675$		0			0
$676$	2.03740	+	3.52888i	0.0783614	+	0.135726i
$677$	3.78846	+	2.18727i	0.145602	+	0.0840635i	0.571031	−	0.820928i	$-0.306543\pi$
$677$	3.78846	+	2.18727i	0.145602	+	0.0840635i	−0.425429	+	0.904992i	$0.639877\pi$
$678$	2.94989	+	6.71396i	0.113290	+	0.257848i
$679$	−0.795603	+	10.1842i	−0.0305324	+	0.390834i
$680$		0			0
$681$	2.35066	−	21.3572i	0.0900776	−	0.818410i
$682$	1.70771	+	2.95783i	0.0653915	+	0.113261i
$683$	−14.7046	−	25.4692i	−0.562657	−	0.974550i	−0.997263	−	0.0739300i	$-0.976446\pi$
$683$	−14.7046	−	25.4692i	−0.562657	−	0.974550i	0.434606	−	0.900620i	$-0.356887\pi$
$684$	1.43565	−	0.450954i	0.0548933	−	0.0172426i
$685$		0			0
$686$	11.9061	+	11.2594i	0.454578	+	0.429886i
$687$	−43.1238	+	18.9471i	−1.64527	+	0.722878i
$688$	0.757154	+	0.437143i	0.0288662	+	0.0166659i
$689$	2.82210	+	4.88802i	0.107513	+	0.186219i
$690$		0			0
$691$	−43.6753	−	25.2160i	−1.66149	−	0.959260i	−0.972006	−	0.234956i	$-0.924505\pi$
$691$	−43.6753	−	25.2160i	−1.66149	−	0.959260i	−0.689481	−	0.724304i	$-0.742161\pi$
$692$		−	20.7513i		−	0.788848i
$693$	8.40689	−	7.83165i	0.319351	−	0.297500i
$694$	−5.55506			−0.210867
$695$		0			0
$696$	7.23835	+	5.31339i	0.274369	+	0.201404i
$697$	32.2233	−	18.6041i	1.22055	−	0.704682i
$698$	−3.82693	−	2.20948i	−0.144852	−	0.0836301i
$699$	−20.1597	−	45.8835i	−0.762509	−	1.73547i
$700$		0			0
$701$		−	19.8266i		−	0.748842i	−0.927259	−	0.374421i	$-0.877841\pi$
$701$		−	19.8266i		−	0.748842i	0.927259	−	0.374421i	$-0.122159\pi$
$702$	−13.9960	+	12.2341i	−0.528244	+	0.461747i
$703$	1.20500	+	2.08712i	0.0454473	+	0.0787171i
$704$	−6.44358	+	3.72020i	−0.242852	+	0.140210i
$705$		0			0
$706$		−	0.696982i		−	0.0262313i
$707$	31.5769	−	15.0838i	1.18757	−	0.567284i
$708$	−0.990353	−	2.25405i	−0.0372197	−	0.0847123i
$709$	−13.2605	+	22.9678i	−0.498008	+	0.862575i	−0.999997	−	0.00229888i	$-0.999268\pi$
$709$	−13.2605	+	22.9678i	−0.498008	+	0.862575i	0.501990	+	0.864874i	$0.332602\pi$
$710$		0			0
$711$	37.6106	+	8.38067i	1.41051	+	0.314300i
$712$	−11.1046	+	19.2338i	−0.416163	+	0.720816i
$713$		−	19.5046i		−	0.730455i
$714$	15.2373	−	17.6851i	0.570242	−	0.661848i
$715$		0			0
$716$	−12.3843	−	7.15008i	−0.462823	−	0.267211i
$717$	−26.8665	−	19.7216i	−1.00335	−	0.736518i
$718$	19.4204	−	11.2124i	0.724763	−	0.418442i
$719$	1.12519	−	1.94889i	0.0419627	−	0.0726815i	−0.844281	−	0.535900i	$-0.819972\pi$
$719$	1.12519	−	1.94889i	0.0419627	−	0.0726815i	0.886244	+	0.463219i	$0.153306\pi$
$720$		0			0
$721$	−37.0619	−	25.4405i	−1.38026	−	0.947453i
$722$	−16.6611			−0.620061
$723$	1.07347	−	9.75315i	0.0399229	−	0.362724i
$724$	2.54259	−	1.46797i	0.0944947	−	0.0545566i
$725$		0			0
$726$	13.5647	+	1.49298i	0.503432	+	0.0554098i
$727$	−6.85964			−0.254410			−0.127205	−	0.991876i	$-0.540601\pi$
$727$	−6.85964			−0.254410			−0.127205	+	0.991876i	$0.540601\pi$
$728$	2.37162	−	30.3581i	0.0878980	−	1.12515i
$729$	21.3672	+	16.5059i	0.791377	+	0.611328i
$730$		0			0
$731$	−29.8177	−	51.6458i	−1.10285	−	1.91019i
$732$	7.04274	+	5.16980i	0.260307	+	0.191081i
$733$	2.75930	−	4.77925i	0.101917	−	0.176526i	−0.810557	−	0.585659i	$-0.800836\pi$
$733$	2.75930	−	4.77925i	0.101917	−	0.176526i	0.912474	+	0.409134i	$0.134169\pi$
$734$	1.61560			0.0596327
$735$		0			0
$736$	41.0950			1.51478
$737$	−5.00869	+	8.67531i	−0.184498	+	0.319559i
$738$	16.7445	+	3.73114i	0.616375	+	0.137345i
$739$	5.01222	+	8.68142i	0.184378	+	0.319351i	0.943367	−	0.331752i	$-0.107640\pi$
$739$	5.01222	+	8.68142i	0.184378	+	0.319351i	−0.758989	+	0.651103i	$0.774306\pi$
$740$		0			0
$741$	2.64236	−	1.16096i	0.0970694	−	0.0426490i
$742$	0.254518	−	3.25798i	0.00934363	−	0.119604i
$743$	26.2588			0.963342			0.481671	−	0.876352i	$-0.340030\pi$
$743$	26.2588			0.963342			0.481671	+	0.876352i	$0.340030\pi$
$744$	1.43836	−	13.0684i	0.0527328	−	0.479110i
$745$		0			0
$746$	1.60930	−	0.929132i	0.0589208	−	0.0340180i
$747$	32.9173	−	10.3397i	1.20438	−	0.378311i
$748$	10.1433			0.370876
$749$	−28.2436	−	19.3873i	−1.03200	−	0.708396i
$750$		0			0
$751$	−5.68833	+	9.85247i	−0.207570	+	0.359522i	−0.950949	−	0.309349i	$-0.899889\pi$
$751$	−5.68833	+	9.85247i	−0.207570	+	0.359522i	0.743378	+	0.668871i	$0.233222\pi$
$752$	−0.794357	+	0.458622i	−0.0289672	+	0.0167242i
$753$	6.72196	−	9.15722i	0.244962	−	0.333708i
$754$	5.64251	+	3.25770i	0.205488	+	0.118639i
$755$		0			0
$756$	−16.6186	+	1.94937i	−0.604413	+	0.0708980i
$757$		−	20.1866i		−	0.733693i	−0.930281	−	0.366847i	$-0.880437\pi$
$757$		−	20.1866i		−	0.733693i	0.930281	−	0.366847i	$-0.119563\pi$
$758$	8.49884	−	14.7204i	0.308692	−	0.534670i
$759$	14.7834	+	10.8519i	0.536604	+	0.393900i
$760$		0			0
$761$	−2.04697	+	3.54546i	−0.0742026	+	0.128523i	−0.900739	−	0.434360i	$-0.856974\pi$
$761$	−2.04697	+	3.54546i	−0.0742026	+	0.128523i	0.826537	+	0.562883i	$0.190308\pi$
$762$	−12.8549	+	5.64801i	−0.465684	+	0.204606i
$763$	17.3526	−	8.28907i	0.628207	−	0.300084i
$764$			16.7466i			0.605871i
$765$		0			0
$766$	−2.42189	+	1.39828i	−0.0875066	+	0.0505219i
$767$	−2.36102	−	4.08941i	−0.0852516	−	0.147660i
$768$	27.8879	+	3.06946i	1.00632	+	0.110760i
$769$		−	8.66796i		−	0.312575i	−0.987712	−	0.156287i	$-0.950047\pi$
$769$		−	8.66796i		−	0.312575i	0.987712	−	0.156287i	$-0.0499526\pi$
$770$		0			0
$771$	−13.8482	+	6.08443i	−0.498730	+	0.219125i
$772$	9.71171	+	5.60706i	0.349532	+	0.201803i
$773$	38.3891	−	22.1640i	1.38076	−	0.797183i	0.388512	−	0.921444i	$-0.372989\pi$
$773$	38.3891	−	22.1640i	1.38076	−	0.797183i	0.992250	+	0.124261i	$0.0396560\pi$
$774$	5.98007	−	26.8372i	0.214949	−	0.964643i
$775$		0			0
$776$	−10.9904			−0.394533
$777$	−8.83590	−	25.2991i	−0.316986	−	0.907601i
$778$		−	9.98209i		−	0.357875i
$779$	−2.30666	−	1.33175i	−0.0826446	−	0.0477149i
$780$		0			0
$781$	−9.64194	−	16.7003i	−0.345016	−	0.597585i
$782$	32.2680	+	18.6299i	1.15390	+	0.666206i
$783$	3.05639	−	8.95615i	0.109226	−	0.320067i
$784$	−0.371291	+	0.459590i	−0.0132604	+	0.0164139i
$785$		0			0
$786$	−31.7524	−	3.49480i	−1.13257	−	0.124655i
$787$	12.5896	+	21.8059i	0.448772	+	0.777296i	0.998306	−	0.0581753i	$-0.0185282\pi$
$787$	12.5896	+	21.8059i	0.448772	+	0.777296i	−0.549535	+	0.835471i	$0.685195\pi$
$788$	−2.50560	−	4.33982i	−0.0892583	−	0.154600i
$789$	38.8091	+	4.27149i	1.38164	+	0.152069i
$790$		0			0
$791$	−0.986040	+	12.6219i	−0.0350596	+	0.448783i
$792$	9.10482	+	8.36114i	0.323526	+	0.297100i
$793$	14.5114	+	8.37815i	0.515314	+	0.297517i
$794$	13.5452	+	23.4610i	0.480702	+	0.832600i
$795$		0			0
$796$	−0.0845000	−	0.0487861i	−0.00299502	−	0.00172918i
$797$			48.5237i			1.71880i	0.511305	+	0.859400i	$0.329162\pi$
$797$			48.5237i			1.71880i	−0.511305	+	0.859400i	$0.670838\pi$
$798$	−1.64172	−	0.311628i	−0.0581164	−	0.0110315i
$799$	62.5656			2.21341
$800$		0			0
$801$	22.8463	+	5.09080i	0.807235	+	0.179874i
$802$	−18.0972	+	10.4484i	−0.639034	+	0.368947i
$803$	3.94232	+	2.27610i	0.139122	+	0.0803219i
$804$	13.3562	−	5.86829i	0.471039	−	0.206958i
$805$		0			0
$806$		−	9.53983i		−	0.336026i
$807$	−24.4289	−	2.68874i	−0.859937	−	0.0946483i
$808$	18.8251	+	32.6061i	0.662266	+	1.14708i
$809$	0.751275	−	0.433749i	0.0264134	−	0.0152498i	−0.486735	−	0.873550i	$-0.661812\pi$
$809$	0.751275	−	0.433749i	0.0264134	−	0.0152498i	0.513149	+	0.858300i	$0.328479\pi$
$810$		0			0
$811$		−	19.2304i		−	0.675271i	−0.941277	−	0.337636i	$-0.890373\pi$
$811$		−	19.2304i		−	0.675271i	0.941277	−	0.337636i	$-0.109627\pi$
$812$	2.52785	+	5.29188i	0.0887100	+	0.185709i
$813$	−20.1869	+	8.86946i	−0.707986	+	0.311065i
$814$	−3.74491	+	6.48637i	−0.131259	+	0.227347i
$815$		0			0
$816$	0.678488	+	0.498051i	0.0237518	+	0.0174353i
$817$	−2.13446	+	3.69699i	−0.0746751	+	0.129341i
$818$		−	11.3827i		−	0.397987i
$819$	−31.2734	+	7.20348i	−1.09278	+	0.251710i
$820$		0			0
$821$	−32.0917	−	18.5281i	−1.12001	−	0.646636i	−0.178604	−	0.983921i	$-0.557158\pi$
$821$	−32.0917	−	18.5281i	−1.12001	−	0.646636i	−0.941403	+	0.337285i	$0.890491\pi$
$822$	8.59505	−	11.7089i	0.299787	−	0.408395i
$823$	21.2677	−	12.2789i	0.741345	−	0.428016i	−0.0812133	−	0.996697i	$-0.525879\pi$
$823$	21.2677	−	12.2789i	0.741345	−	0.428016i	0.822558	+	0.568681i	$0.192546\pi$
$824$	24.1824	−	41.8851i	0.842432	−	1.45914i
$825$		0			0
$826$	−0.212934	+	2.72569i	−0.00740894	+	0.0948388i
$827$	−28.2836			−0.983518			−0.491759	−	0.870731i	$-0.663646\pi$
$827$	−28.2836			−0.983518			−0.491759	+	0.870731i	$0.663646\pi$
$828$	−8.00354	−	25.4799i	−0.278142	−	0.885487i
$829$	−41.6000	+	24.0178i	−1.44483	+	0.834171i	−0.998166	−	0.0605325i	$-0.980720\pi$
$829$	−41.6000	+	24.0178i	−1.44483	+	0.834171i	−0.446660	+	0.894704i	$0.647387\pi$
$830$		0			0
$831$	−5.46063	+	49.6132i	−0.189427	+	1.72106i
$832$	20.7823			0.720497
$833$	37.6073	−	14.4859i	1.30301	−	0.501906i
$834$	8.07397	−	3.54743i	0.279579	−	0.122837i
$835$		0			0
$836$	−0.363047	−	0.628816i	−0.0125562	−	0.0217480i
$837$	−13.5943	+	2.68118i	−0.469886	+	0.0926753i
$838$	−1.67268	+	2.89717i	−0.0577818	+	0.100081i
$839$	−26.6446			−0.919874			−0.459937	−	0.887952i	$-0.652128\pi$
$839$	−26.6446			−0.919874			−0.459937	+	0.887952i	$0.652128\pi$
$840$		0			0
$841$	25.6832			0.885627
$842$	−1.07796	+	1.86707i	−0.0371488	+	0.0643436i
$843$	−18.7795	−	13.7853i	−0.646801	−	0.474791i
$844$	10.6987	+	18.5306i	0.368263	+	0.637850i
$845$		0			0
$846$	21.2467	+	19.5113i	0.730478	+	0.670812i
$847$	19.4236	+	13.3330i	0.667402	+	0.458126i
$848$	0.117824			0.00404611
$849$	−24.2353	−	2.66744i	−0.831754	−	0.0915463i
$850$		0			0
$851$	37.0422	−	21.3863i	1.26979	−	0.733114i
$852$	−3.07244	+	27.9150i	−0.105260	+	0.956353i
$853$	−35.4466			−1.21367			−0.606834	−	0.794829i	$-0.707561\pi$
$853$	−35.4466			−1.21367			−0.606834	+	0.794829i	$0.707561\pi$
$854$	−4.18171	−	8.75415i	−0.143095	−	0.299561i
$855$		0			0
$856$	18.4285	−	31.9191i	0.629874	−	1.09097i
$857$	9.87394	−	5.70072i	0.337287	−	0.194733i	−0.321785	−	0.946813i	$-0.604283\pi$
$857$	9.87394	−	5.70072i	0.337287	−	0.194733i	0.659072	+	0.752080i	$0.270949\pi$
$858$	7.23065	+	5.30774i	0.246850	+	0.181203i
$859$	18.3838	+	10.6139i	0.627248	+	0.362142i	0.779686	−	0.626171i	$-0.215379\pi$
$859$	18.3838	+	10.6139i	0.627248	+	0.362142i	−0.152438	+	0.988313i	$0.548712\pi$
$860$		0			0
$861$	22.4372	+	19.3317i	0.764658	+	0.658822i
$862$		−	27.0296i		−	0.920633i
$863$	−0.702733	+	1.21717i	−0.0239213	+	0.0414329i	−0.877738	−	0.479140i	$-0.840948\pi$
$863$	−0.702733	+	1.21717i	−0.0239213	+	0.0414329i	0.853817	+	0.520573i	$0.174282\pi$
$864$	−5.64908	−	28.6422i	−0.192186	−	0.974427i
$865$		0			0
$866$	−16.7118	+	28.9456i	−0.567889	+	0.983612i
$867$	−11.2492	−	25.6031i	−0.382042	−	0.869528i
$868$	4.85964	−	7.07956i	0.164947	−	0.240296i
$869$		−	18.5928i		−	0.630718i
$870$		0			0
$871$	24.2316	−	13.9901i	0.821057	−	0.474037i
$872$	10.3451	+	17.9182i	0.350328	+	0.606786i
$873$	3.47114	+	11.0506i	0.117480	+	0.374007i
$874$		−	2.66719i		−	0.0902192i
$875$		0			0
$876$	−2.66673	−	6.06949i	−0.0901004	−	0.205069i
$877$	1.82900	+	1.05597i	0.0617610	+	0.0356577i	0.530563	−	0.847646i	$-0.321981\pi$
$877$	1.82900	+	1.05597i	0.0617610	+	0.0356577i	−0.468802	+	0.883304i	$0.655314\pi$
$878$	3.14343	−	1.81486i	0.106086	−	0.0612486i
$879$	−23.3368	−	17.1306i	−0.787130	−	0.577801i
$880$		0			0
$881$	35.9949			1.21270			0.606349	−	0.795199i	$-0.292634\pi$
$881$	35.9949			1.21270			0.606349	+	0.795199i	$0.292634\pi$
$882$	17.2886	+	6.80867i	0.582136	+	0.229260i
$883$			17.2298i			0.579828i	0.957053	+	0.289914i	$0.0936267\pi$
$883$			17.2298i			0.579828i	−0.957053	+	0.289914i	$0.906373\pi$
$884$	−24.5362	−	14.1660i	−0.825242	−	0.476454i
$885$		0			0
$886$	11.6122	+	20.1130i	0.390121	+	0.675709i
$887$	5.40675	+	3.12159i	0.181541	+	0.104813i	0.588016	−	0.808849i	$-0.299909\pi$
$887$	5.40675	+	3.12159i	0.181541	+	0.104813i	−0.406476	+	0.913662i	$0.633242\pi$
$888$	26.3959	−	11.5975i	0.885789	−	0.389186i
$889$	−24.1665	−	1.88792i	−0.810520	−	0.0633189i
$890$		0			0
$891$	5.53134	−	11.7954i	0.185307	−	0.395162i
$892$	−16.7332	−	28.9827i	−0.560269	−	0.970414i
$893$	−2.23933	−	3.87864i	−0.0749364	−	0.129794i
$894$	−1.07852	+	9.79900i	−0.0360711	+	0.327728i
$895$		0			0
$896$	14.5904	+	10.0153i	0.487430	+	0.334587i
$897$	−20.6048	−	46.8966i	−0.687974	−	1.56583i
$898$	−11.2168	−	6.47602i	−0.374309	−	0.216108i
$899$	2.42824	+	4.20583i	0.0809863	+	0.140272i
$900$		0			0
$901$	−6.96011	−	4.01842i	−0.231875	−	0.133873i
$902$		−	8.27767i		−	0.275616i
$903$	30.9837	−	35.9611i	1.03107	−	1.19671i
$904$	−13.6211			−0.453032
$905$		0			0
$906$	−3.73634	+	5.08996i	−0.124132	+	0.169103i
$907$	34.2738	−	19.7880i	1.13804	−	0.657049i	0.192097	−	0.981376i	$-0.438471\pi$
$907$	34.2738	−	19.7880i	1.13804	−	0.657049i	0.945945	+	0.324327i	$0.105138\pi$
$908$	13.0756	+	7.54918i	0.433928	+	0.250528i
$909$	26.8391	−	29.2263i	0.890197	−	0.969376i
$910$		0			0
$911$			24.4007i			0.808431i	0.914664	+	0.404215i	$0.132455\pi$
$911$			24.4007i			0.808431i	−0.914664	+	0.404215i	$0.867545\pi$
$912$	0.00659149	−	0.0598877i	0.000218266	−	0.00198308i
$913$	−8.32415	−	14.4178i	−0.275489	−	0.477161i
$914$	−22.3658	+	12.9129i	−0.739795	+	0.427121i
$915$		0			0
$916$		−	33.0990i		−	1.09362i
$917$	−45.4669	−	31.2100i	−1.50145	−	1.03064i
$918$	8.54892	−	25.0509i	0.282156	−	0.826804i
$919$	−10.5155	+	18.2133i	−0.346873	+	0.600802i	−0.985692	−	0.168555i	$-0.946090\pi$
$919$	−10.5155	+	18.2133i	−0.346873	+	0.600802i	0.638819	+	0.769357i	$0.279423\pi$
$920$		0			0
$921$	−9.96499	+	13.5752i	−0.328357	+	0.447317i
$922$	7.00305	−	12.1296i	0.230633	−	0.399468i
$923$			53.8632i			1.77293i
$924$	2.66212	+	7.62223i	0.0875773	+	0.250753i
$925$		0			0
$926$	−14.6714	−	8.47052i	−0.482131	−	0.278358i
$927$	−49.7521	−	11.0861i	−1.63407	−	0.364117i
$928$	−8.86140	+	5.11613i	−0.290890	+	0.167945i
$929$	−6.50741	+	11.2712i	−0.213501	+	0.369795i	−0.952808	−	0.303574i	$-0.901820\pi$
$929$	−6.50741	+	11.2712i	−0.213501	+	0.369795i	0.739307	+	0.673369i	$0.235153\pi$
$930$		0			0
$931$	−2.24405	−	1.81292i	−0.0735459	−	0.0594160i
$932$	35.2172			1.15358
$933$	−8.63317	−	0.950203i	−0.282637	−	0.0311082i
$934$	11.4212	−	6.59404i	0.373713	−	0.215764i
$935$		0			0
$936$	−10.3471	−	32.9409i	−0.338207	−	1.07671i
$937$	−29.9338			−0.977896			−0.488948	−	0.872313i	$-0.662619\pi$
$937$	−29.9338			−0.977896			−0.488948	+	0.872313i	$0.662619\pi$
$938$	−16.1509	−	1.26173i	−0.527346	−	0.0411970i
$939$	−12.3521	−	28.1133i	−0.403094	−	0.917444i
$940$		0			0
$941$	−3.58035	−	6.20135i	−0.116716	−	0.202158i	0.801748	−	0.597662i	$-0.203903\pi$
$941$	−3.58035	−	6.20135i	−0.116716	−	0.202158i	−0.918464	+	0.395504i	$0.870570\pi$
$942$	1.12430	−	1.53162i	0.0366317	−	0.0499028i
$943$	−23.6360	+	40.9387i	−0.769693	+	1.33315i
$944$	−0.0985743			−0.00320832
$945$		0			0
$946$	−13.2670			−0.431347
$947$	11.5521	−	20.0088i	0.375393	−	0.650200i	−0.614993	−	0.788533i	$-0.710841\pi$
$947$	11.5521	−	20.0088i	0.375393	−	0.650200i	0.990386	+	0.138333i	$0.0441743\pi$
$948$	−16.0228	+	21.8276i	−0.520396	+	0.708927i
$949$	−6.35754	−	11.0116i	−0.206374	−	0.357451i
$950$		0			0
$951$	−2.92773	−	6.66352i	−0.0949380	−	0.216079i
$952$	18.6891	+	39.1244i	0.605717	+	1.26803i
$953$	−42.4806			−1.37608			−0.688040	−	0.725672i	$-0.741529\pi$
$953$	−42.4806			−1.37608			−0.688040	+	0.725672i	$0.741529\pi$
$954$	−1.11044	−	3.53515i	−0.0359517	−	0.114455i
$955$		0			0
$956$	20.2820	−	11.7098i	0.655965	−	0.378722i
$957$	−4.53880	−	0.499559i	−0.146718	−	0.0161484i
$958$	19.3826			0.626225
$959$	22.6267	−	10.8084i	0.730655	−	0.349022i
$960$		0			0
$961$	−11.9446	+	20.6886i	−0.385309	+	0.667375i
$962$	18.1175	−	10.4602i	0.584133	−	0.337249i
$963$	−37.9143	−	8.44836i	−1.22177	−	0.272245i
$964$	5.97119	+	3.44747i	0.192319	+	0.111036i
$965$		0			0
$966$	−5.53079	+	29.1374i	−0.177950	+	0.937480i
$967$			2.04795i			0.0658575i	0.999458	+	0.0329288i	$0.0104834\pi$
$967$			2.04795i			0.0658575i	−0.999458	+	0.0329288i	$0.989517\pi$
$968$	−12.6736	+	21.9513i	−0.407345	+	0.705542i
$969$	−2.43185	+	3.31288i	−0.0781224	+	0.106425i
$970$		0			0
$971$	−29.0027	+	50.2341i	−0.930740	+	1.61209i	−0.148679	+	0.988885i	$0.547502\pi$
$971$	−29.0027	+	50.2341i	−0.930740	+	1.61209i	−0.782060	+	0.623203i	$0.785831\pi$
$972$	−16.6587	+	9.08084i	−0.534326	+	0.291268i
$973$	15.1786	+	1.18578i	0.486605	+	0.0380142i
$974$		−	11.0067i		−	0.352678i
$975$		0			0
$976$	0.302930	−	0.174897i	0.00969655	−	0.00559830i
$977$	−24.8661	−	43.0694i	−0.795538	−	1.37791i	−0.922497	−	0.386004i	$-0.873855\pi$
$977$	−24.8661	−	43.0694i	−0.795538	−	1.37791i	0.126960	−	0.991908i	$-0.459478\pi$
$978$	−1.24793	+	11.3382i	−0.0399044	+	0.362556i
$979$		−	11.2941i		−	0.360961i
$980$		0			0
$981$	14.7490	−	16.0609i	0.470900	−	0.512785i
$982$	17.8360	+	10.2976i	0.569170	+	0.328610i
$983$	12.0399	−	6.95123i	0.384013	−	0.221710i	−0.295550	−	0.955327i	$-0.595503\pi$
$983$	12.0399	−	6.95123i	0.384013	−	0.221710i	0.679563	+	0.733617i	$0.262170\pi$
$984$	−18.8554	+	25.6864i	−0.601089	+	0.818854i
$985$		0			0
$986$	−9.27737			−0.295452
$987$	16.4204	+	47.0152i	0.522666	+	1.49651i
$988$			2.02810i			0.0645226i
$989$	65.6142	+	37.8824i	2.08641	+	1.20459i
$990$		0			0
$991$	−4.79414	−	8.30370i	−0.152291	−	0.263776i	0.779778	−	0.626056i	$-0.215332\pi$
$991$	−4.79414	−	8.30370i	−0.152291	−	0.263776i	−0.932069	+	0.362280i	$0.881998\pi$
$992$	12.9748	+	7.49102i	0.411951	+	0.237840i
$993$	−0.947737	−	2.15705i	−0.0300755	−	0.0684521i
$994$	17.6491	−	25.7113i	0.559795	−	0.815514i
$995$		0			0
$996$	−2.65252	+	24.0998i	−0.0840484	+	0.763631i
$997$	11.8733	+	20.5651i	0.376030	+	0.651303i	0.990481	−	0.137652i	$-0.0439556\pi$
$997$	11.8733	+	20.5651i	0.376030	+	0.651303i	−0.614451	+	0.788955i	$0.710622\pi$
$998$	11.6946	+	20.2557i	0.370187	+	0.641182i
$999$	−19.9977	−	22.8776i	−0.632699	−	0.723817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.q.g.299.11		40
3.2	odd	2	inner	525.2.q.g.299.9		40
5.2	odd	4		525.2.t.i.26.6	yes	20
5.3	odd	4		525.2.t.h.26.5	✓	20
5.4	even	2	inner	525.2.q.g.299.10		40
7.3	odd	6	inner	525.2.q.g.374.12		40
15.2	even	4		525.2.t.i.26.5	yes	20
15.8	even	4		525.2.t.h.26.6	yes	20
15.14	odd	2	inner	525.2.q.g.299.12		40
21.17	even	6	inner	525.2.q.g.374.10		40
35.3	even	12		525.2.t.h.101.6	yes	20
35.17	even	12		525.2.t.i.101.5	yes	20
35.24	odd	6	inner	525.2.q.g.374.9		40
105.17	odd	12		525.2.t.i.101.6	yes	20
105.38	odd	12		525.2.t.h.101.5	yes	20
105.59	even	6	inner	525.2.q.g.374.11		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.q.g.299.9		40	3.2	odd	2	inner
525.2.q.g.299.10		40	5.4	even	2	inner
525.2.q.g.299.11		40	1.1	even	1	trivial
525.2.q.g.299.12		40	15.14	odd	2	inner
525.2.q.g.374.9		40	35.24	odd	6	inner
525.2.q.g.374.10		40	21.17	even	6	inner
525.2.q.g.374.11		40	105.59	even	6	inner
525.2.q.g.374.12		40	7.3	odd	6	inner
525.2.t.h.26.5	✓	20	5.3	odd	4
525.2.t.h.26.6	yes	20	15.8	even	4
525.2.t.h.101.5	yes	20	105.38	odd	12
525.2.t.h.101.6	yes	20	35.3	even	12
525.2.t.i.26.5	yes	20	15.2	even	4
525.2.t.i.26.6	yes	20	5.2	odd	4
525.2.t.i.101.5	yes	20	35.17	even	12
525.2.t.i.101.6	yes	20	105.17	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.442404 - 0.766266i) q^{2} +(1.02493 - 1.39625i) q^{3} +(0.608557 + 1.05405i) q^{4} +(-0.616465 - 1.40308i) q^{6} +(0.206062 - 2.63771i) q^{7} +2.84653 q^{8} +(-0.899028 - 2.86212i) q^{9} +O(q^{10})\)	\(q+(0.442404 - 0.766266i) q^{2} +(1.02493 - 1.39625i) q^{3} +(0.608557 + 1.05405i) q^{4} +(-0.616465 - 1.40308i) q^{6} +(0.206062 - 2.63771i) q^{7} +2.84653 q^{8} +(-0.899028 - 2.86212i) q^{9} +(-1.25362 + 0.723775i) q^{11} +(2.09545 + 0.230634i) q^{12} +4.04326 q^{13} +(-1.93003 - 1.32483i) q^{14} +(0.0422021 - 0.0730962i) q^{16} +(-4.98592 + 2.87862i) q^{17} +(-2.59088 - 0.577320i) q^{18} +(0.356910 + 0.206062i) q^{19} +(-3.47171 - 2.99119i) q^{21} +1.28081i q^{22} +(3.65719 - 6.33444i) q^{23} +(2.91750 - 3.97447i) q^{24} +(1.78875 - 3.09821i) q^{26} +(-4.91768 - 1.67821i) q^{27} +(2.90569 - 1.38800i) q^{28} +1.82121i q^{29} +(2.30936 - 1.33331i) q^{31} +(2.80919 + 4.86566i) q^{32} +(-0.274300 + 2.49218i) q^{33} +5.09406i q^{34} +(2.46972 - 2.68939i) q^{36} +(5.06429 + 2.92387i) q^{37} +(0.315797 - 0.182325i) q^{38} +(4.14406 - 5.64540i) q^{39} -6.46287 q^{41} +(-3.82795 + 1.33694i) q^{42} +10.3583i q^{43} +(-1.52579 - 0.880917i) q^{44} +(-3.23592 - 5.60477i) q^{46} +(-9.41134 - 5.43364i) q^{47} +(-0.0588063 - 0.133843i) q^{48} +(-6.91508 - 1.08706i) q^{49} +(-1.09095 + 9.91198i) q^{51} +(2.46055 + 4.26180i) q^{52} +(0.697977 + 1.20893i) q^{53} +(-3.46156 + 3.02581i) q^{54} +(0.586561 - 7.50833i) q^{56} +(0.653522 - 0.287136i) q^{57} +(1.39554 + 0.805713i) q^{58} +(-0.583941 - 1.01142i) q^{59} +(3.58903 + 2.07213i) q^{61} -2.35944i q^{62} +(-7.73472 + 1.78160i) q^{63} +5.14000 q^{64} +(1.78832 + 1.31274i) q^{66} +(5.99309 - 3.46011i) q^{67} +(-6.06843 - 3.50361i) q^{68} +(-5.09609 - 11.5987i) q^{69} +13.3217i q^{71} +(-2.55911 - 8.14712i) q^{72} +(-1.57238 - 2.72344i) q^{73} +(4.48093 - 2.58707i) q^{74} +0.501602i q^{76} +(1.65079 + 3.45582i) q^{77} +(-2.49253 - 5.67300i) q^{78} +(-6.42216 + 11.1235i) q^{79} +(-7.38350 + 5.14626i) q^{81} +(-2.85920 + 4.95228i) q^{82} +11.5010i q^{83} +(1.04014 - 5.47967i) q^{84} +(7.93724 + 4.58257i) q^{86} +(2.54287 + 1.86662i) q^{87} +(-3.56845 + 2.06025i) q^{88} +(-3.90111 + 6.75692i) q^{89} +(0.833161 - 10.6650i) q^{91} +8.90244 q^{92} +(0.505303 - 4.59099i) q^{93} +(-8.32723 + 4.80773i) q^{94} +(9.67290 + 1.06464i) q^{96} -3.86099 q^{97} +(-3.89224 + 4.81787i) q^{98} +(3.19857 + 2.93731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 28 q^{4} + 14 q^{9}+O(q^{10}) \) 40 * q - 28 * q^4 + 14 * q^9	\( 40 q - 28 q^{4} + 14 q^{9} - 36 q^{16} - 18 q^{21} - 36 q^{24} + 84 q^{31} - 72 q^{36} - 16 q^{46} + 8 q^{49} + 42 q^{51} + 150 q^{54} - 180 q^{61} + 240 q^{64} + 12 q^{66} - 92 q^{79} + 58 q^{81} - 150 q^{84} - 60 q^{91} - 12 q^{94} + 270 q^{96} - 188 q^{99}+O(q^{100}) \) 40 * q - 28 * q^4 + 14 * q^9 - 36 * q^16 - 18 * q^21 - 36 * q^24 + 84 * q^31 - 72 * q^36 - 16 * q^46 + 8 * q^49 + 42 * q^51 + 150 * q^54 - 180 * q^61 + 240 * q^64 + 12 * q^66 - 92 * q^79 + 58 * q^81 - 150 * q^84 - 60 * q^91 - 12 * q^94 + 270 * q^96 - 188 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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