LMFDB - Embedded newform 525.2.q.g.299.12

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			299.12
Character	$\chi$	$=$	525.299
Dual form			525.2.q.g.374.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.442404 - 0.766266i) q^{2} +(1.72165 - 0.189492i) q^{3} +(0.608557 + 1.05405i) q^{4} +(0.616465 - 1.40308i) q^{6} +(-0.206062 + 2.63771i) q^{7} +2.84653 q^{8} +(2.92819 - 0.652481i) q^{9} +O(q^{10})$	\(q+(0.442404 - 0.766266i) q^{2} +(1.72165 - 0.189492i) q^{3} +(0.608557 + 1.05405i) q^{4} +(0.616465 - 1.40308i) q^{6} +(-0.206062 + 2.63771i) q^{7} +2.84653 q^{8} +(2.92819 - 0.652481i) q^{9} +(1.25362 - 0.723775i) q^{11} +(1.24746 + 1.69940i) q^{12} -4.04326 q^{13} +(1.93003 + 1.32483i) q^{14} +(0.0422021 - 0.0730962i) q^{16} +(-4.98592 + 2.87862i) q^{17} +(0.795467 - 2.53243i) q^{18} +(0.356910 + 0.206062i) q^{19} +(0.145060 + 4.58028i) q^{21} -1.28081i q^{22} +(3.65719 - 6.33444i) q^{23} +(4.90074 - 0.539396i) 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} +(2.02114 - 1.48364i) q^{33} +5.09406i q^{34} +(2.46972 + 2.68939i) q^{36} +(-5.06429 - 2.92387i) q^{37} +(0.315797 - 0.182325i) q^{38} +(-6.96109 + 0.766166i) q^{39} +6.46287 q^{41} +(3.57389 + 1.91518i) 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} +(-8.03855 + 5.90078i) q^{51} +(-2.46055 - 4.26180i) q^{52} +(0.697977 + 1.20893i) q^{53} +(0.889643 - 4.51070i) 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} +(1.11767 + 7.85817i) q^{63} +5.14000 q^{64} +(-0.242703 - 2.20510i) q^{66} +(-5.99309 + 3.46011i) q^{67} +(-6.06843 - 3.50361i) q^{68} +(5.09609 - 11.5987i) q^{69} -13.3217i q^{71} +(8.33517 - 1.85731i) 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} +(8.14854 - 3.82117i) q^{81} +(2.85920 - 4.95228i) q^{82} +11.5010i q^{83} +(-4.73957 + 2.94026i) q^{84} +(-7.93724 - 4.58257i) q^{86} +(-0.345106 - 3.13550i) q^{87} +(3.56845 - 2.06025i) q^{88} +(3.90111 - 6.75692i) q^{89} +(0.833161 - 10.6650i) q^{91} +8.90244 q^{92} +(3.72326 - 2.73310i) q^{93} +(-8.32723 + 4.80773i) q^{94} +(5.75846 + 7.84466i) 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	$0.0653907\pi$
$3$	1.72165	−	0.189492i	0.993997	−	0.109403i
$3$	1.72165	−	0.189492i	0.993997	−	0.109403i
$4$	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
$9$	2.92819	−	0.652481i	0.976062	−	0.217494i
$10$		0			0
$11$	1.25362	−	0.723775i	0.377979	−	0.218227i	−0.298959	−	0.954266i	$-0.596640\pi$
$11$	1.25362	−	0.723775i	0.377979	−	0.218227i	0.676939	+	0.736039i	$0.263306\pi$
$12$	1.24746	+	1.69940i	0.360111	+	0.490573i
$13$	−4.04326			−1.12140			−0.560699	−	0.828020i	$-0.689467\pi$
$13$	−4.04326			−1.12140			−0.560699	+	0.828020i	$0.689467\pi$
$14$	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	$0.579335\pi$
$18$	0.795467	−	2.53243i	0.187493	−	0.596900i
$19$	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
$21$	0.145060	+	4.58028i	0.0316546	+	0.999499i
$22$		−	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	$-0.109400\pi$
$24$	4.90074	−	0.539396i	1.00036	−	0.110104i
$25$		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	$-0.945915\pi$
$29$		−	1.82121i		−	0.338191i	0.985600	−	0.169095i	$-0.0540846\pi$
$30$		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
$33$	2.02114	−	1.48364i	0.351836	−	0.258269i
$34$			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	0.0221652	−	0.999754i	$-0.492944\pi$
$37$	−5.06429	−	2.92387i	−0.832565	−	0.480682i	−0.854730	+	0.519073i	$0.826277\pi$
$38$	0.315797	−	0.182325i	0.0512290	−	0.0295771i
$39$	−6.96109	+	0.766166i	−1.11467	+	0.122685i
$40$		0			0
$41$	6.46287			1.00933			0.504665	−	0.863315i	$-0.331616\pi$
$41$	6.46287			1.00933			0.504665	+	0.863315i	$0.331616\pi$
$42$	3.57389	+	1.91518i	0.551463	+	0.295519i
$43$		−	10.3583i		−	1.57963i	−0.613345	−	0.789815i	$-0.710177\pi$
$43$		−	10.3583i		−	1.57963i	0.613345	−	0.789815i	$-0.289823\pi$
$44$	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
$51$	−8.03855	+	5.90078i	−1.12562	+	0.826275i
$52$	−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	$0.802769\pi$
$54$	0.889643	−	4.51070i	0.121065	−	0.613829i
$55$		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	0.901531	−	0.432715i	$-0.142445\pi$
$59$	0.583941	+	1.01142i	0.0760227	+	0.131675i	−0.825508	+	0.564391i	$0.809111\pi$
$60$		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
$63$	1.11767	+	7.85817i	0.140813	+	0.990036i
$64$	5.14000			0.642499
$65$		0			0
$66$	−0.242703	−	2.20510i	−0.0298747	−	0.271429i
$67$	−5.99309	+	3.46011i	−0.732173	+	0.422720i	−0.819217	−	0.573484i	$-0.805591\pi$
$67$	−5.99309	+	3.46011i	−0.732173	+	0.422720i	0.0870436	+	0.996205i	$0.472258\pi$
$68$	−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	$-0.709821\pi$
$71$		−	13.3217i		−	1.58100i	0.612463	−	0.790499i	$-0.290179\pi$
$72$	8.33517	−	1.85731i	0.982309	−	0.218886i
$73$	1.57238	+	2.72344i	0.184033	+	0.318755i	0.943250	−	0.332082i	$-0.107751\pi$
$73$	1.57238	+	2.72344i	0.184033	+	0.318755i	−0.759217	+	0.650838i	$0.774418\pi$
$74$	−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
$81$	8.14854	−	3.82117i	0.905393	−	0.424574i
$82$	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	$0.782563\pi$
$84$	−4.73957	+	2.94026i	−0.517130	+	0.320809i
$85$		0			0
$86$	−7.93724	−	4.58257i	−0.855894	−	0.494151i
$87$	−0.345106	−	3.13550i	−0.0369993	−	0.336161i
$88$	3.56845	−	2.06025i	0.380399	−	0.219623i
$89$	3.90111	−	6.75692i	0.413517	−	0.716232i	−0.581755	−	0.813364i	$-0.697634\pi$
$89$	3.90111	−	6.75692i	0.413517	−	0.716232i	0.995271	+	0.0971324i	$0.0309670\pi$
$90$		0			0
$91$	0.833161	−	10.6650i	0.0873390	−	1.11799i
$92$	8.90244			0.928144
$93$	3.72326	−	2.73310i	0.386084	−	0.283409i
$94$	−8.32723	+	4.80773i	−0.858889	+	0.495880i
$95$		0			0
$96$	5.75846	+	7.84466i	0.587720	+	0.800642i
$97$	3.86099			0.392024			0.196012	−	0.980601i	$-0.437201\pi$
$97$	3.86099			0.392024			0.196012	+	0.980601i	$0.437201\pi$
$98$	−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	$-0.938046\pi$
$101$	−6.61336	−	11.4547i	−0.658054	−	1.13978i	0.323065	−	0.946377i	$-0.395287\pi$
$102$	0.965285	+	8.77020i	0.0955774	+	0.868379i
$103$	−8.49538	+	14.7144i	−0.837075	+	1.44986i	0.0552547	+	0.998472i	$0.482403\pi$
$103$	−8.49538	+	14.7144i	−0.837075	+	1.44986i	−0.892330	+	0.451384i	$0.850930\pi$
$104$	−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	$-0.0485886\pi$
$108$	4.76162	+	4.16220i	0.458187	+	0.400508i
$109$	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	$0.572263\pi$
$114$	0.509143	−	0.373742i	0.0476856	−	0.0350041i
$115$		0			0
$116$	1.91965	−	1.10831i	0.178235	−	0.102904i
$117$	−11.8394	+	2.63815i	−1.09455	+	0.243897i
$118$	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
$123$	11.1268	−	1.22466i	1.00327	−	0.110424i
$124$	2.81075	+	1.62279i	0.252413	+	0.145731i
$125$		0			0
$126$	6.51591	+	2.62005i	0.580484	+	0.233413i
$127$			9.16192i			0.812989i	0.913653	+	0.406495i	$0.133249\pi$
$127$			9.16192i			0.812989i	−0.913653	+	0.406495i	$0.866751\pi$
$128$	−3.34442	+	5.79271i	−0.295608	+	0.512008i
$129$	−1.96282	−	17.8335i	−0.172817	−	1.57015i
$130$		0			0
$131$	−10.4220	+	18.0514i	−0.910574	+	1.57716i	−0.0973191	+	0.995253i	$0.531027\pi$
$131$	−10.4220	+	18.0514i	−0.910574	+	1.57716i	−0.813255	+	0.581907i	$0.802307\pi$
$132$	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	$0.700651\pi$
$138$	−6.63319	−	9.03629i	−0.564654	−	0.769220i
$139$			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
$144$	0.0758818	−	0.241575i	0.00632348	−	0.0201313i
$145$		0			0
$146$	2.78251			0.230282
$147$	−12.1114	−	0.561195i	−0.998928	−	0.0462866i
$148$		−	7.11737i		−	0.585044i
$149$	5.57080	+	3.21630i	0.456378	+	0.263490i	0.710520	−	0.703677i	$-0.248460\pi$
$149$	5.57080	+	3.21630i	0.456378	+	0.263490i	−0.254142	+	0.967167i	$0.581793\pi$
$150$		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
$156$	−5.04380	−	6.87109i	−0.403827	−	0.550128i
$157$	−0.619880	−	1.07366i	−0.0494718	−	0.0856877i	0.840229	−	0.542232i	$-0.182420\pi$
$157$	−0.619880	−	1.07366i	−0.0494718	−	0.0856877i	−0.889701	+	0.456544i	$0.849087\pi$
$158$	5.68238	+	9.84218i	0.452066	+	0.783001i
$159$	1.43076	+	1.94910i	0.113466	+	0.154574i
$160$		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	0.730726	−	0.682671i	$-0.239182\pi$
$163$	6.44585	+	3.72151i	0.504878	+	0.291491i	−0.225848	+	0.974163i	$0.572515\pi$
$164$	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	$0.969073\pi$
$168$	0.412917	+	13.0379i	0.0318572	+	1.00590i
$169$	3.34791			0.257532
$170$		0			0
$171$	1.17955	+	0.370511i	0.0902023	+	0.0283337i
$172$	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
$177$	1.19700	+	1.63066i	0.0899721	+	0.122568i
$178$	−3.45173	−	5.97858i	−0.258718	−	0.448113i
$179$	10.1751	−	5.87462i	0.760525	−	0.439090i	−0.0689590	−	0.997619i	$-0.521968\pi$
$179$	10.1751	−	5.87462i	0.760525	−	0.439090i	0.829484	+	0.558530i	$0.188634\pi$
$180$		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
$186$	−0.447096	−	4.06214i	−0.0327827	−	0.297851i
$187$	−4.16695	+	7.21737i	−0.304718	+	0.527786i
$188$		−	13.2267i		−	0.964658i
$189$	3.41331	+	13.3173i	0.248281	+	0.968688i
$190$		0			0
$191$	−11.9159	−	6.87963i	−0.862202	−	0.497793i	0.00254675	−	0.999997i	$-0.499189\pi$
$191$	−11.9159	−	6.87963i	−0.862202	−	0.497793i	−0.864749	+	0.502204i	$0.832523\pi$
$192$	8.84929	−	0.973990i	0.638643	−	0.0702917i
$193$	−7.97929	+	4.60685i	−0.574362	+	0.331608i	−0.758890	−	0.651219i	$-0.774258\pi$
$193$	−7.97929	+	4.60685i	−0.574362	+	0.331608i	0.184528	+	0.982827i	$0.440925\pi$
$194$	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	$0.546856\pi$
$198$	−0.835701	−	3.75043i	−0.0593907	−	0.266532i
$199$	−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
$201$	−9.66237	+	7.09277i	−0.681531	+	0.500285i
$202$	−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
$207$	6.57584	−	20.9347i	0.457052	−	1.45506i
$208$	−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
$213$	−2.52437	−	22.9354i	−0.172967	−	1.57151i
$214$	−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
$219$	3.22317	+	4.39088i	0.217802	+	0.296708i
$220$		0			0
$221$	20.1593	−	11.6390i	1.35606	−	0.782924i
$222$	−7.22438	+	5.30313i	−0.484869	+	0.355923i
$223$	27.4965			1.84130			0.920651	−	0.390387i	$-0.127659\pi$
$223$	27.4965			1.84130			0.920651	+	0.390387i	$0.127659\pi$
$224$	−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	$0.198277\pi$
$228$	0.0950497	+	0.863584i	0.00629482	+	0.0571923i
$229$	−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
$231$	3.49694	+	5.63692i	0.230082	+	0.370882i
$232$		−	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	$-0.230030\pi$
$234$	−3.21628	+	10.2393i	−0.210255	+	0.669362i
$235$		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	$0.213813\pi$
$239$			19.2419i			1.24465i	−0.782757	+	0.622327i	$0.786187\pi$
$240$		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
$243$	13.3049	−	8.12282i	0.853508	−	0.521079i
$244$			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
$249$	2.17935	+	19.8008i	0.138111	+	1.25482i
$250$		0			0
$251$	−6.55844			−0.413965			−0.206983	−	0.978345i	$-0.566364\pi$
$251$	−6.55844			−0.413965			−0.206983	+	0.978345i	$0.566364\pi$
$252$	−7.60275	+	5.96023i	−0.478928	+	0.375459i
$253$		−	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
$261$	−1.18831	−	5.33285i	−0.0735544	−	0.330095i
$262$	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	$0.588741\pi$
$264$	5.75324	−	4.22323i	0.354088	−	0.259922i
$265$		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	0.997093	−	0.0761890i	$-0.0242752\pi$
$269$	7.09460	+	12.2882i	0.432565	+	0.749225i	−0.564528	+	0.825414i	$0.690942\pi$
$270$		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
$273$	−0.586513	−	18.5192i	−0.0354974	−	1.12084i
$274$	8.38597			0.506615
$275$		0			0
$276$	15.3269	−	1.68695i	0.922573	−	0.101542i
$277$	24.9564	−	14.4086i	1.49948	−	0.865727i	0.499484	−	0.866323i	$-0.333523\pi$
$277$	24.9564	−	14.4086i	1.49948	−	0.865727i	1.00000		0.000595725i	$0.000189625\pi$
$278$	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	$0.131399\pi$
$281$			13.4500i			0.802357i	−0.916000	+	0.401179i	$0.868601\pi$
$282$	−13.4256	+	9.85520i	−0.799482	+	0.586868i
$283$	7.03838	+	12.1908i	0.418388	+	0.724670i	0.995778	−	0.0917992i	$-0.0292618\pi$
$283$	7.03838	+	12.1908i	0.418388	+	0.724670i	−0.577389	+	0.816469i	$0.695928\pi$
$284$	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
$291$	6.64729	−	0.731629i	0.389671	−	0.0428888i
$292$	−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	$-0.162353\pi$
$294$	−5.78814	+	9.03225i	−0.337571	+	0.526772i
$295$		0			0
$296$	−14.4157	−	8.32289i	−0.837893	−	0.483758i
$297$	4.95023	−	5.66313i	0.287242	−	0.328608i
$298$	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
$303$	−13.5565	−	18.4678i	−0.778800	−	1.06095i
$304$	0.0301247	−	0.0173925i	0.00172777	−	0.000997528i
$305$		0			0
$306$	3.32377	+	14.9163i	0.190007	+	0.852710i
$307$	9.72258			0.554897			0.277449	−	0.960741i	$-0.410511\pi$
$307$	9.72258			0.554897			0.277449	+	0.960741i	$0.410511\pi$
$308$	−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	0.928314	−	0.371796i	$-0.121258\pi$
$311$	2.50723	+	4.34265i	0.142172	+	0.246249i	−0.786142	+	0.618046i	$0.787925\pi$
$312$	−19.8149	+	2.18091i	−1.12180	+	0.123470i
$313$	−8.86441	+	15.3536i	−0.501046	+	0.867837i	0.498953	+	0.866629i	$0.333718\pi$
$313$	−8.86441	+	15.3536i	−0.501046	+	0.867837i	−0.999999	+	0.00120811i	$0.999615\pi$
$314$	−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	$0.129016\pi$
$318$	2.12650	−	0.234052i	0.119248	−	0.0131250i
$319$	−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
$324$	8.98656	+	6.26358i	0.499253	+	0.347977i
$325$		0			0
$326$	5.70334	−	3.29282i	0.315879	−	0.182373i
$327$	7.44977	+	10.1487i	0.411973	+	0.561225i
$328$	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
$333$	−16.7370	−	5.25728i	−0.917180	−	0.288097i
$334$	1.92121	+	1.10921i	0.105124	+	0.0606933i
$335$		0			0
$336$	0.340923	+	0.182694i	0.0185989	+	0.00996679i
$337$			26.2620i			1.43058i	0.698826	+	0.715292i	$0.253706\pi$
$337$			26.2620i			1.43058i	−0.698826	+	0.715292i	$0.746294\pi$
$338$	1.48113	−	2.56539i	0.0805629	−	0.139539i
$339$	−8.23840	+	0.906753i	−0.447449	+	0.0492480i
$340$		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	$0.887231\pi$
$348$	3.09496	−	2.27189i	0.165907	−	0.121786i
$349$		−	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	$0.326660\pi$
$354$	1.77907	−	0.195812i	0.0945568	−	0.0104073i
$355$		0			0
$356$	9.49619			0.503297
$357$	−13.9081	−	22.4193i	−0.736097	−	1.18656i
$358$		−	10.3958i		−	0.549436i
$359$	−21.9487	−	12.6721i	−1.15841	−	0.668808i	−0.207487	−	0.978238i	$-0.566528\pi$
$359$	−21.9487	−	12.6721i	−1.15841	−	0.668808i	−0.950922	+	0.309430i	$0.899862\pi$
$360$		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
$366$	5.11987	−	3.75830i	0.267620	−	0.196449i
$367$	−0.912964	−	1.58130i	−0.0476563	−	0.0825432i	0.841213	−	0.540703i	$-0.181842\pi$
$367$	−0.912964	−	1.58130i	−0.0476563	−	0.0825432i	−0.888870	+	0.458160i	$0.848509\pi$
$368$	−0.308683	−	0.534654i	−0.0160912	−	0.0278708i
$369$	18.9245	−	4.21690i	0.985169	−	0.219523i
$370$		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	0.452173	−	0.891930i	$-0.350649\pi$
$373$	−1.81882	−	1.05009i	−0.0941748	−	0.0543718i	−0.546348	+	0.837558i	$0.683982\pi$
$374$	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
$378$	11.7146	+	3.27611i	0.602535	+	0.168505i
$379$	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
$381$	1.73611	+	15.7737i	0.0889439	+	0.808109i
$382$	−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
$387$	−6.75861	−	30.3311i	−0.343559	−	1.54182i
$388$	2.34963	+	4.06969i	0.119285	+	0.206607i
$389$	−9.77019	+	5.64082i	−0.495368	+	0.286001i	−0.726799	−	0.686850i	$-0.758993\pi$
$389$	−9.77019	+	5.64082i	−0.495368	+	0.286001i	0.231430	+	0.972851i	$0.425659\pi$
$390$		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
$396$	5.04259	+	1.58394i	0.253400	+	0.0795959i
$397$	15.3087	−	26.5154i	0.768319	−	1.33077i	−0.170154	−	0.985417i	$-0.554427\pi$
$397$	15.3087	−	26.5154i	0.768319	−	1.33077i	0.938474	−	0.345351i	$-0.112240\pi$
$398$			0.0709323i			0.00355551i
$399$	−0.892048	+	1.66464i	−0.0446582	+	0.0833361i
$400$		0			0
$401$	20.4532	+	11.8087i	1.02139	+	0.589697i	0.914505	−	0.404574i	$-0.132580\pi$
$401$	20.4532	+	11.8087i	1.02139	+	0.589697i	0.106881	+	0.994272i	$0.465914\pi$
$402$	1.16028	+	10.5418i	0.0578693	+	0.525778i
$403$	−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
$408$	−22.8820	+	16.7968i	−1.13283	+	0.831563i
$409$	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
$411$	9.71403	+	13.2333i	0.479158	+	0.652749i
$412$	−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
$417$	1.09043	+	9.90720i	0.0533985	+	0.485158i
$418$	0.263925	−	0.457132i	0.0129090	−	0.0223590i
$419$	3.78089			0.184708			0.0923542	−	0.995726i	$-0.470561\pi$
$419$	3.78089			0.184708			0.0923542	+	0.995726i	$0.470561\pi$
$420$		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
$423$	−31.1035	−	9.76999i	−1.51230	−	0.475033i
$424$	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
$429$	−8.17200	+	5.99874i	−0.394548	+	0.289622i
$430$		0			0
$431$	−26.4558	+	15.2743i	−1.27433	+	0.735737i	−0.975800	−	0.218663i	$-0.929830\pi$
$431$	−26.4558	+	15.2743i	−1.27433	+	0.735737i	−0.298533	+	0.954399i	$0.596497\pi$
$432$	0.0848655	−	0.430288i	0.00408309	−	0.0207023i
$433$	37.7749			1.81534			0.907672	−	0.419680i	$-0.137858\pi$
$433$	37.7749			1.81534			0.907672	+	0.419680i	$0.137858\pi$
$434$	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
$438$	4.79052	−	0.527265i	0.228900	−	0.0251937i
$439$	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
$441$	−20.9579	+	1.32883i	−0.997996	+	0.0632775i
$442$		−	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	$0.952360\pi$
$444$	−1.34869	−	12.2537i	−0.0640059	−	0.581533i
$445$		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	$0.112260\pi$
$449$			14.6382i			0.690821i	−0.938452	+	0.345411i	$0.887740\pi$
$450$		0			0
$451$	8.10195	−	4.67766i	0.381506	−	0.220263i
$452$	−2.91205	−	5.04381i	−0.136971	−	0.237241i
$453$	−4.22277	−	5.75262i	−0.198403	−	0.270282i
$454$		−	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	0.956577	−	0.291481i	$-0.0941480\pi$
$457$	25.2776	+	14.5940i	1.18244	+	0.682679i	0.225858	+	0.974160i	$0.427481\pi$
$458$	−20.8384	+	12.0310i	−0.973714	+	0.562174i
$459$	−19.6882	+	22.5236i	−0.918967	+	1.05131i
$460$		0			0
$461$	−15.8295			−0.737255			−0.368627	−	0.929577i	$-0.620172\pi$
$461$	−15.8295			−0.737255			−0.368627	+	0.929577i	$0.620172\pi$
$462$	5.86644	−	0.185793i	0.272932	−	0.00864388i
$463$			19.1466i			0.889816i	0.895576	+	0.444908i	$0.146764\pi$
$463$			19.1466i			0.889816i	−0.895576	+	0.444908i	$0.853236\pi$
$464$	−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
$471$	−1.27067	−	1.73102i	−0.0585494	−	0.0797610i
$472$	1.66221	+	2.87903i	0.0765092	+	0.132518i
$473$	−7.49710	−	12.9854i	−0.344717	−	0.597067i
$474$	11.6481	+	15.8681i	0.535016	+	0.728844i
$475$		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	$-0.999832\pi$
$479$	−10.9530	−	18.9712i	−0.500456	−	0.866815i	0.499544	−	0.866289i	$-0.333501\pi$
$480$		0			0
$481$	20.4762	+	11.8220i	0.933636	+	0.539035i
$482$		−	5.01243i		−	0.228310i
$483$	29.5440	+	15.8321i	1.34430	+	0.720385i
$484$	−10.8379			−0.492632
$485$		0			0
$486$	−0.338108	−	13.7887i	−0.0153369	−	0.625466i
$487$	−10.7731	+	6.21983i	−0.488174	+	0.281848i	−0.723817	−	0.689992i	$-0.757614\pi$
$487$	−10.7731	+	6.21983i	−0.488174	+	0.281848i	0.235642	+	0.971840i	$0.424281\pi$
$488$	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	$-0.823980\pi$
$491$		−	23.2765i		−	1.05045i	0.850962	−	0.525227i	$-0.176020\pi$
$492$	8.06217	+	10.9830i	0.363470	+	0.495150i
$493$	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
$501$	0.475101	+	4.31659i	0.0212260	+	0.192851i
$502$	−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	$0.872699\pi$
$504$	3.18148	+	22.3685i	0.141714	+	0.996373i
$505$		0			0
$506$	−8.11319	−	4.68415i	−0.360675	−	0.208236i
$507$	5.76395	−	0.634404i	0.255986	−	0.0281749i
$508$	−9.65714	+	5.57555i	−0.428466	+	0.247375i
$509$	1.20504	−	2.08719i	0.0534124	−	0.0925129i	−0.838083	−	0.545543i	$-0.816324\pi$
$509$	1.20504	−	2.08719i	0.0534124	−	0.0925129i	0.891495	+	0.453030i	$0.149657\pi$
$510$		0			0
$511$	−7.50768	+	3.58630i	−0.332120	+	0.158648i
$512$	0.954733			0.0421937
$513$	2.10098	+	0.414376i	0.0927607	+	0.0182951i
$514$	−6.69176	+	3.86349i	−0.295161	+	0.170411i
$515$		0			0
$516$	17.6029	−	12.9216i	0.774924	−	0.568841i
$517$	−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	$-0.924577\pi$
$521$	−15.7340	−	27.2520i	−0.689317	−	1.19393i	0.282742	−	0.959196i	$-0.408756\pi$
$522$	−4.61210	−	1.44872i	−0.201866	−	0.0634086i
$523$	−8.54828	+	14.8061i	−0.373790	+	0.647424i	−0.990145	−	0.140045i	$-0.955275\pi$
$523$	−8.54828	+	14.8061i	−0.373790	+	0.647424i	0.616355	+	0.787469i	$0.288609\pi$
$524$	−25.3695			−1.10827
$525$		0			0
$526$	19.9451			0.869649
$527$	−7.67617	+	13.2955i	−0.334379	+	0.579162i
$528$	−0.0231521	−	0.210351i	−0.00100756	−	0.00915434i
$529$	−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
$534$	−7.07558	−	9.63896i	−0.306190	−	0.417119i
$535$		0			0
$536$	−17.0595	+	9.84932i	−0.736859	+	0.425426i
$537$	16.4049	−	12.0422i	0.707922	−	0.519658i
$538$	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
$543$	−0.457095	−	4.15299i	−0.0196158	−	0.178222i
$544$	−28.0128	−	16.1732i	−1.20104	−	0.693419i
$545$		0			0
$546$	−14.4501	−	7.74356i	−0.618409	−	0.331394i
$547$		−	9.42694i		−	0.403067i	−0.979482	−	0.201533i	$-0.935408\pi$
$547$		−	9.42694i		−	0.403067i	0.979482	−	0.201533i	$-0.0645925\pi$
$548$	−5.76774	+	9.99001i	−0.246386	+	0.426752i
$549$	11.8614	+	3.72580i	0.506231	+	0.159013i
$550$		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	$0.871577\pi$
$558$	−1.53949	−	6.90888i	−0.0651718	−	0.292476i
$559$			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	$0.382513\pi$
$564$	−2.50636	−	22.7718i	−0.105537	−	0.958868i
$565$		0			0
$566$	12.4552			0.523533
$567$	8.40005	+	22.2809i	0.352769	+	0.935710i
$568$		−	37.9207i		−	1.59112i
$569$	−12.6704	−	7.31525i	−0.531170	−	0.306671i	0.210323	−	0.977632i	$-0.432549\pi$
$569$	−12.6704	−	7.31525i	−0.531170	−	0.306671i	−0.741493	+	0.670961i	$0.765882\pi$
$570$		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
$576$	15.0509	−	3.35375i	0.627119	−	0.139739i
$577$	−22.6632	−	39.2538i	−0.943482	−	1.63416i	−0.758762	−	0.651367i	$-0.774196\pi$
$577$	−22.6632	−	39.2538i	−0.943482	−	1.63416i	−0.184720	−	0.982791i	$-0.559138\pi$
$578$	−7.14299	−	12.3720i	−0.297109	−	0.514608i
$579$	−12.8646	+	9.44341i	−0.534635	+	0.392455i
$580$		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	$-0.195564\pi$
$588$	−6.77893	−	13.1075i	−0.279558	−	0.540545i
$589$	1.09897			0.0452825
$590$		0			0
$591$	−7.08853	+	0.780193i	−0.291583	+	0.0320928i
$592$	−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
$597$	−0.111933	+	0.0821656i	−0.00458111	+	0.00336281i
$598$	13.0836	+	22.6615i	0.535029	+	0.926698i
$599$	−13.1940	+	7.61757i	−0.539093	+	0.311245i	−0.744711	−	0.667387i	$-0.767413\pi$
$599$	−13.1940	+	7.61757i	−0.539093	+	0.311245i	0.205618	+	0.978632i	$0.434079\pi$
$600$		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
$606$	−20.1487	+	2.21765i	−0.818486	+	0.0900859i
$607$	−9.55240	+	16.5452i	−0.387720	+	0.671550i	−0.992142	−	0.125113i	$-0.960071\pi$
$607$	−9.55240	+	16.5452i	−0.387720	+	0.671550i	0.604423	+	0.796664i	$0.293404\pi$
$608$			2.31547i			0.0939046i
$609$	8.34167	−	0.264185i	0.338022	−	0.0107053i
$610$		0			0
$611$	38.0525	+	21.9696i	1.53944	+	0.888795i
$612$	−20.0555	−	6.29969i	−0.810697	−	0.254650i
$613$	10.7916	−	6.23054i	0.435869	−	0.251649i	−0.265975	−	0.963980i	$-0.585694\pi$
$613$	10.7916	−	6.23054i	0.435869	−	0.251649i	0.701844	+	0.712331i	$0.252360\pi$
$614$	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	$0.371986\pi$
$618$	15.4084	+	20.9906i	0.619816	+	0.844367i
$619$	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
$621$	7.35435	−	37.2883i	0.295120	−	1.49633i
$622$	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
$627$	1.02709	−	0.113045i	0.0410179	−	0.00451460i
$628$	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
$633$	30.2673	−	3.33135i	1.20302	−	0.132409i
$634$	−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
$639$	−8.69217	−	39.0085i	−0.343857	−	1.54315i
$640$		0			0
$641$	−2.40816	+	1.39035i	−0.0951166	+	0.0549156i	−0.546804	−	0.837261i	$-0.684156\pi$
$641$	−2.40816	+	1.39035i	−0.0951166	+	0.0549156i	0.451687	+	0.892176i	$0.350822\pi$
$642$	−11.7422	−	15.9962i	−0.463427	−	0.631320i
$643$	−37.8005			−1.49071			−0.745354	−	0.666669i	$-0.767719\pi$
$643$	−37.8005			−1.49071			−0.745354	+	0.666669i	$0.767719\pi$
$644$	−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	$0.464273\pi$
$648$	23.1951	−	10.8771i	0.911188	−	0.427292i
$649$	1.46408	+	0.845285i	0.0574700	+	0.0331803i
$650$		0			0
$651$	6.44191	+	10.3841i	0.252478	+	0.406984i
$652$			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	$0.328611\pi$
$654$	11.0724	−	1.21868i	0.432966	−	0.0476540i
$655$		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	$0.194062\pi$
$659$			29.3981i			1.14519i	−0.819840	+	0.572593i	$0.805938\pi$
$660$		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
$663$	32.5019	−	23.8584i	1.26227	−	0.926583i
$664$			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
$669$	47.3395	−	5.21038i	1.83025	−	0.201445i
$670$		0			0
$671$	5.99903			0.231590
$672$	−21.8786	+	13.5727i	−0.843984	+	0.523577i
$673$		−	17.4983i		−	0.674509i	−0.941414	−	0.337255i	$-0.890502\pi$
$673$		−	17.4983i		−	0.674509i	0.941414	−	0.337255i	$-0.109498\pi$
$674$	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
$681$	17.3206	−	12.7143i	0.663725	−	0.487215i
$682$	−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	$-0.356887\pi$
$684$	0.327285	+	1.46878i	0.0125141	+	0.0561603i
$685$		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
$693$	7.08868	+	9.04218i	0.269277	+	0.343484i
$694$	−5.55506			−0.210867
$695$		0			0
$696$	−0.982355	−	8.92530i	−0.0372361	−	0.338312i
$697$	−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	$0.122159\pi$
$701$			19.8266i			0.748842i	−0.927259	+	0.374421i	$0.877841\pi$
$702$	−3.59705	+	18.2379i	−0.135762	+	0.688346i
$703$	−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
$711$	−11.5474	+	36.7620i	−0.433062	+	1.37868i
$712$	11.1046	−	19.2338i	0.416163	−	0.720816i
$713$		−	19.5046i		−	0.730455i
$714$	−23.3322	+	0.738942i	−0.873186	+	0.0276542i
$715$		0			0
$716$	12.3843	+	7.15008i	0.462823	+	0.267211i
$717$	3.64619	+	33.1279i	0.136170	+	1.23718i
$718$	−19.4204	+	11.2124i	−0.724763	+	0.418442i
$719$	−1.12519	+	1.94889i	−0.0419627	+	0.0726815i	−0.886244	−	0.463219i	$-0.846694\pi$
$719$	−1.12519	+	1.94889i	−0.0419627	+	0.0726815i	0.844281	+	0.535900i	$0.180028\pi$
$720$		0			0
$721$	−37.0619	−	25.4405i	−1.38026	−	0.947453i
$722$	−16.6611			−0.620061
$723$	7.90974	−	5.80623i	0.294167	−	0.215936i
$724$	2.54259	−	1.46797i	0.0944947	−	0.0545566i
$725$		0			0
$726$	8.07530	+	11.0009i	0.299702	+	0.408280i
$727$	6.85964			0.254410			0.127205	−	0.991876i	$-0.459399\pi$
$727$	6.85964			0.254410			0.127205	+	0.991876i	$0.459399\pi$
$728$	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
$732$	0.955807	+	8.68409i	0.0353276	+	0.320973i
$733$	−2.75930	+	4.77925i	−0.101917	+	0.176526i	−0.912474	−	0.409134i	$-0.865831\pi$
$733$	−2.75930	+	4.77925i	−0.101917	+	0.176526i	0.810557	+	0.585659i	$0.199164\pi$
$734$	−1.61560			−0.0596327
$735$		0			0
$736$	41.0950			1.51478
$737$	−5.00869	+	8.67531i	−0.184498	+	0.319559i
$738$	5.14100	−	16.3668i	0.189243	−	0.602469i
$739$	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	$0.340030\pi$
$744$	10.5984	−	7.77985i	0.388555	−	0.285223i
$745$		0			0
$746$	−1.60930	+	0.929132i	−0.0589208	+	0.0340180i
$747$	7.50419	+	33.6771i	0.274564	+	1.23218i
$748$	−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
$753$	−11.2914	+	1.24277i	−0.411480	+	0.0452892i
$754$	5.64251	+	3.25770i	0.205488	+	0.118639i
$755$		0			0
$756$	−11.9599	+	11.7021i	−0.434977	+	0.425602i
$757$			20.1866i			0.733693i	0.930281	+	0.366847i	$0.119563\pi$
$757$			20.1866i			0.733693i	−0.930281	+	0.366847i	$0.880437\pi$
$758$	8.49884	−	14.7204i	0.308692	−	0.534670i
$759$	−2.00634	−	18.2288i	−0.0728254	−	0.661663i
$760$		0			0
$761$	2.04697	−	3.54546i	0.0742026	−	0.128523i	−0.826537	−	0.562883i	$-0.809692\pi$
$761$	2.04697	−	3.54546i	0.0742026	−	0.128523i	0.900739	+	0.434360i	$0.143026\pi$
$762$	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
$768$	16.6022	+	22.6169i	0.599080	+	0.816118i
$769$		−	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	$0.0396560\pi$
$774$	−26.2317	−	8.23971i	−0.942880	−	0.296170i
$775$		0			0
$776$	10.9904			0.394533
$777$	12.6575	−	23.6200i	0.454086	−	0.847363i
$778$			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
$786$	18.9028	+	25.7510i	0.674239	+	0.918506i
$787$	−12.5896	−	21.8059i	−0.448772	−	0.777296i	0.549535	−	0.835471i	$-0.314805\pi$
$787$	−12.5896	−	21.8059i	−0.448772	−	0.777296i	−0.998306	+	0.0581753i	$0.981472\pi$
$788$	−2.50560	−	4.33982i	−0.0892583	−	0.154600i
$789$	23.1038	+	31.4739i	0.822516	+	1.12050i
$790$		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	$0.670838\pi$
$798$	0.880910	+	1.41999i	0.0311839	+	0.0502670i
$799$	62.5656			2.21341
$800$		0			0
$801$	7.01441	−	22.3309i	0.247842	−	0.789024i
$802$	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
$807$	14.5430	+	19.8117i	0.511936	+	0.697403i
$808$	−18.8251	−	32.6061i	−0.662266	−	1.14708i
$809$	−0.751275	+	0.433749i	−0.0264134	+	0.0152498i	−0.513149	−	0.858300i	$-0.671521\pi$
$809$	−0.751275	+	0.433749i	−0.0264134	+	0.0152498i	0.486735	+	0.873550i	$0.338188\pi$
$810$		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
$816$	0.0920811	+	0.836613i	0.00322348	+	0.0292873i
$817$	2.13446	−	3.69699i	0.0746751	−	0.129341i
$818$		−	11.3827i		−	0.397987i
$819$	−4.51903	−	31.7726i	−0.157908	−	1.11022i
$820$		0			0
$821$	32.0917	+	18.5281i	1.12001	+	0.646636i	0.941403	−	0.337285i	$-0.109509\pi$
$821$	32.0917	+	18.5281i	1.12001	+	0.646636i	0.178604	+	0.983921i	$0.442842\pi$
$822$	14.4377	−	1.58908i	0.503574	−	0.0554254i
$823$	−21.2677	+	12.2789i	−0.741345	+	0.428016i	−0.822558	−	0.568681i	$-0.807454\pi$
$823$	−21.2677	+	12.2789i	−0.741345	+	0.428016i	0.0812133	+	0.996697i	$0.474121\pi$
$824$	−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	$0.663646\pi$
$828$	26.0680	−	5.80867i	0.905926	−	0.201865i
$829$	−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
$831$	40.2359	−	29.5356i	1.39577	−	1.02458i
$832$	−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
$837$	9.11910	−	10.4324i	0.315202	−	0.360596i
$838$	1.67268	−	2.89717i	0.0577818	−	0.100081i
$839$	26.6446			0.919874			0.459937	−	0.887952i	$-0.347872\pi$
$839$	26.6446			0.919874			0.459937	+	0.887952i	$0.347872\pi$
$840$		0			0
$841$	25.6832			0.885627
$842$	−1.07796	+	1.86707i	−0.0371488	+	0.0643436i
$843$	2.54867	+	23.1562i	0.0877807	+	0.797541i
$844$	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
$849$	14.4277	+	19.6547i	0.495158	+	0.674547i
$850$		0			0
$851$	−37.0422	+	21.3863i	−1.26979	+	0.733114i
$852$	22.6389	−	16.6183i	0.775596	−	0.569334i
$853$	35.4466			1.21367			0.606834	−	0.794829i	$-0.292439\pi$
$853$	35.4466			1.21367			0.606834	+	0.794829i	$0.292439\pi$
$854$	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	$0.270949\pi$
$858$	0.981310	+	8.91580i	0.0335014	+	0.304380i
$859$	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
$861$	0.937501	+	29.6017i	0.0319500	+	1.00882i
$862$			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	$0.174282\pi$
$864$	21.9803	+	19.2133i	0.747785	+	0.653651i
$865$		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
$873$	11.3057	−	2.51922i	0.382640	−	0.0852628i
$874$		−	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	0.468802	−	0.883304i	$-0.344686\pi$
$877$	−1.82900	−	1.05597i	−0.0617610	−	0.0356577i	−0.530563	+	0.847646i	$0.678019\pi$
$878$	3.14343	−	1.81486i	0.106086	−	0.0612486i
$879$	−3.16716	−	28.7755i	−0.106826	−	0.970575i
$880$		0			0
$881$	−35.9949			−1.21270			−0.606349	−	0.795199i	$-0.707366\pi$
$881$	−35.9949			−1.21270			−0.606349	+	0.795199i	$0.707366\pi$
$882$	−8.25363	+	16.6472i	−0.277914	+	0.560541i
$883$		−	17.2298i		−	0.579828i	−0.957053	−	0.289914i	$-0.906373\pi$
$883$		−	17.2298i		−	0.579828i	0.957053	−	0.289914i	$-0.0936267\pi$
$884$	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
$891$	7.44947	−	10.6880i	0.249567	−	0.358061i
$892$	16.7332	+	28.9827i	0.560269	+	0.970414i
$893$	−2.23933	−	3.87864i	−0.0749364	−	0.129794i
$894$	7.94693	−	5.83353i	0.265785	−	0.195102i
$895$		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
$903$	47.4440	−	1.50257i	1.57884	−	0.0500026i
$904$	−13.6211			−0.453032
$905$		0			0
$906$	−6.27621	+	0.690786i	−0.208513	+	0.0229498i
$907$	−34.2738	+	19.7880i	−1.13804	+	0.657049i	−0.945945	−	0.324327i	$-0.894862\pi$
$907$	−34.2738	+	19.7880i	−1.13804	+	0.657049i	−0.192097	+	0.981376i	$0.561529\pi$
$908$	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	$-0.867545\pi$
$911$		−	24.4007i		−	0.808431i	0.914664	−	0.404215i	$-0.132455\pi$
$912$	0.0485685	−	0.0356523i	0.00160827	−	0.00118056i
$913$	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
$921$	16.7389	−	1.84236i	0.551566	−	0.0607077i
$922$	−7.00305	+	12.1296i	−0.230633	+	0.399468i
$923$			53.8632i			1.77293i
$924$	−3.81352	+	7.11635i	−0.125455	+	0.234111i
$925$		0			0
$926$	14.6714	+	8.47052i	0.482131	+	0.278358i
$927$	−15.2752	+	48.6297i	−0.501702	+	1.59721i
$928$	8.86140	−	5.11613i	0.290890	−	0.167945i
$929$	6.50741	−	11.2712i	0.213501	−	0.369795i	−0.739307	−	0.673369i	$-0.764847\pi$
$929$	6.50741	−	11.2712i	0.213501	−	0.369795i	0.952808	+	0.303574i	$0.0981799\pi$
$930$		0			0
$931$	−2.24405	−	1.81292i	−0.0735459	−	0.0594160i
$932$	35.2172			1.15358
$933$	5.13949	+	7.00144i	0.168259	+	0.229217i
$934$	11.4212	−	6.59404i	0.373713	−	0.215764i
$935$		0			0
$936$	−33.7012	+	7.50956i	−1.10156	+	0.245458i
$937$	29.9338			0.977896			0.488948	−	0.872313i	$-0.337381\pi$
$937$	29.9338			0.977896			0.488948	+	0.872313i	$0.337381\pi$
$938$	−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	0.918464	−	0.395504i	$-0.129430\pi$
$941$	3.58035	+	6.20135i	0.116716	+	0.202158i	−0.801748	+	0.597662i	$0.796097\pi$
$942$	−1.88857	+	0.207864i	−0.0615329	+	0.00677257i
$943$	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	$0.0441743\pi$
$948$	−26.9146	+	2.96234i	−0.874147	+	0.0962122i
$949$	−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	$0.741529\pi$
$954$	3.61675	−	0.805912i	0.117097	−	0.0260924i
$955$		0			0
$956$	−20.2820	+	11.7098i	−0.655965	+	0.378722i
$957$	−2.70203	−	3.68093i	−0.0873442	−	0.118988i
$958$	−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
$963$	11.6407	−	37.0590i	0.375115	−	1.19421i
$964$	5.97119	+	3.44747i	0.192319	+	0.111036i
$965$		0			0
$966$	25.2020	−	15.6344i	0.810861	−	0.503029i
$967$		−	2.04795i		−	0.0658575i	−0.999458	−	0.0329288i	$-0.989517\pi$
$967$		−	2.04795i		−	0.0658575i	0.999458	−	0.0329288i	$-0.0104834\pi$
$968$	−12.6736	+	21.9513i	−0.407345	+	0.705542i
$969$	−4.08496	+	0.449608i	−0.131228	+	0.0144435i
$970$		0			0
$971$	29.0027	−	50.2341i	0.930740	−	1.61209i	0.148679	−	0.988885i	$-0.452498\pi$
$971$	29.0027	−	50.2341i	0.930740	−	1.61209i	0.782060	−	0.623203i	$-0.214169\pi$
$972$	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	$-0.459478\pi$
$978$	9.19521	−	6.74984i	0.294030	−	0.215836i
$979$		−	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	$0.262170\pi$
$984$	31.6728	−	3.48604i	1.00969	−	0.111131i
$985$		0			0
$986$	9.27737			0.295452
$987$	23.5224	−	43.8948i	0.748726	−	1.39719i
$988$		−	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
$996$	−19.5448	+	14.3470i	−0.619299	+	0.454603i
$997$	−11.8733	−	20.5651i	−0.376030	−	0.651303i	0.614451	−	0.788955i	$-0.289378\pi$
$997$	−11.8733	−	20.5651i	−0.376030	−	0.651303i	−0.990481	+	0.137652i	$0.956044\pi$
$998$	11.6946	+	20.2557i	0.370187	+	0.641182i
$999$	−29.8115	−	5.87970i	−0.943193	−	0.186025i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.442404 - 0.766266i) q^{2} +(1.72165 - 0.189492i) q^{3} +(0.608557 + 1.05405i) q^{4} +(0.616465 - 1.40308i) q^{6} +(-0.206062 + 2.63771i) q^{7} +2.84653 q^{8} +(2.92819 - 0.652481i) q^{9} +O(q^{10})\)	\(q+(0.442404 - 0.766266i) q^{2} +(1.72165 - 0.189492i) q^{3} +(0.608557 + 1.05405i) q^{4} +(0.616465 - 1.40308i) q^{6} +(-0.206062 + 2.63771i) q^{7} +2.84653 q^{8} +(2.92819 - 0.652481i) q^{9} +(1.25362 - 0.723775i) q^{11} +(1.24746 + 1.69940i) q^{12} -4.04326 q^{13} +(1.93003 + 1.32483i) q^{14} +(0.0422021 - 0.0730962i) q^{16} +(-4.98592 + 2.87862i) q^{17} +(0.795467 - 2.53243i) q^{18} +(0.356910 + 0.206062i) q^{19} +(0.145060 + 4.58028i) q^{21} -1.28081i q^{22} +(3.65719 - 6.33444i) q^{23} +(4.90074 - 0.539396i) 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} +(2.02114 - 1.48364i) q^{33} +5.09406i q^{34} +(2.46972 + 2.68939i) q^{36} +(-5.06429 - 2.92387i) q^{37} +(0.315797 - 0.182325i) q^{38} +(-6.96109 + 0.766166i) q^{39} +6.46287 q^{41} +(3.57389 + 1.91518i) 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} +(-8.03855 + 5.90078i) q^{51} +(-2.46055 - 4.26180i) q^{52} +(0.697977 + 1.20893i) q^{53} +(0.889643 - 4.51070i) 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} +(1.11767 + 7.85817i) q^{63} +5.14000 q^{64} +(-0.242703 - 2.20510i) q^{66} +(-5.99309 + 3.46011i) q^{67} +(-6.06843 - 3.50361i) q^{68} +(5.09609 - 11.5987i) q^{69} -13.3217i q^{71} +(8.33517 - 1.85731i) 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} +(8.14854 - 3.82117i) q^{81} +(2.85920 - 4.95228i) q^{82} +11.5010i q^{83} +(-4.73957 + 2.94026i) q^{84} +(-7.93724 - 4.58257i) q^{86} +(-0.345106 - 3.13550i) q^{87} +(3.56845 - 2.06025i) q^{88} +(3.90111 - 6.75692i) q^{89} +(0.833161 - 10.6650i) q^{91} +8.90244 q^{92} +(3.72326 - 2.73310i) q^{93} +(-8.32723 + 4.80773i) q^{94} +(5.75846 + 7.84466i) 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

Fields

Representations

Groups

Database

Properties

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