LMFDB - Embedded newform 625.2.e.k.499.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(124,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("625.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.e (of order $10$, degree $4$, 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			499.3
Character	$\chi$	$=$	625.499
Dual form			625.2.e.k.124.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.60102 + 0.520202i) q^{2} +(-0.417528 - 0.574677i) q^{3} +(0.674615 - 0.490137i) q^{4} +(0.967418 + 0.702870i) q^{6} -4.59110i q^{7} +(1.15387 - 1.58816i) q^{8} +(0.771126 - 2.37328i) q^{9} +O(q^{10})$	\(q+(-1.60102 + 0.520202i) q^{2} +(-0.417528 - 0.574677i) q^{3} +(0.674615 - 0.490137i) q^{4} +(0.967418 + 0.702870i) q^{6} -4.59110i q^{7} +(1.15387 - 1.58816i) q^{8} +(0.771126 - 2.37328i) q^{9} +(1.20974 + 3.72319i) q^{11} +(-0.563341 - 0.183041i) q^{12} +(0.544898 + 0.177048i) q^{13} +(2.38830 + 7.35044i) q^{14} +(-1.53656 + 4.72903i) q^{16} +(-0.136725 + 0.188186i) q^{17} +4.20081i q^{18} +(-4.49012 - 3.26227i) q^{19} +(-2.63840 + 1.91691i) q^{21} +(-3.87362 - 5.33158i) q^{22} +(-4.69124 + 1.52428i) q^{23} -1.39445 q^{24} -0.964492 q^{26} +(-3.71256 + 1.20628i) q^{27} +(-2.25027 - 3.09723i) q^{28} +(3.34174 - 2.42792i) q^{29} +(2.82777 + 2.05449i) q^{31} -4.44444i q^{32} +(1.63453 - 2.24974i) q^{33} +(0.121005 - 0.372415i) q^{34} +(-0.643019 - 1.97901i) q^{36} +(-5.15138 - 1.67378i) q^{37} +(8.88581 + 2.88717i) q^{38} +(-0.125764 - 0.387063i) q^{39} +(3.22079 - 9.91257i) q^{41} +(3.22695 - 4.44152i) q^{42} -1.38833i q^{43} +(2.64098 + 1.91878i) q^{44} +(6.71783 - 4.88079i) q^{46} +(-0.541008 - 0.744634i) q^{47} +(3.35922 - 1.09148i) q^{48} -14.0782 q^{49} +0.165233 q^{51} +(0.454374 - 0.147635i) q^{52} +(0.723668 + 0.996044i) q^{53} +(5.31636 - 3.86256i) q^{54} +(-7.29141 - 5.29752i) q^{56} +3.94246i q^{57} +(-4.08718 + 5.62552i) q^{58} +(-1.39299 + 4.28718i) q^{59} +(-3.60276 - 11.0881i) q^{61} +(-5.59606 - 1.81827i) q^{62} +(-10.8960 - 3.54032i) q^{63} +(-0.761103 - 2.34244i) q^{64} +(-1.44660 + 4.45216i) q^{66} +(-1.73660 + 2.39022i) q^{67} +0.193968i q^{68} +(2.83469 + 2.05952i) q^{69} +(-2.59331 + 1.88415i) q^{71} +(-2.87938 - 3.96312i) q^{72} +(-9.78847 + 3.18047i) q^{73} +9.11816 q^{74} -4.62806 q^{76} +(17.0935 - 5.55402i) q^{77} +(0.402702 + 0.554272i) q^{78} +(-7.77877 + 5.65161i) q^{79} +(-3.81318 - 2.77044i) q^{81} +17.5457i q^{82} +(6.16199 - 8.48125i) q^{83} +(-0.840358 + 2.58636i) q^{84} +(0.722211 + 2.22274i) q^{86} +(-2.79054 - 0.906701i) q^{87} +(7.30889 + 2.37480i) q^{88} +(-2.24293 - 6.90303i) q^{89} +(0.812846 - 2.50168i) q^{91} +(-2.41768 + 3.32765i) q^{92} -2.48286i q^{93} +(1.25352 + 0.910739i) q^{94} +(-2.55412 + 1.85568i) q^{96} +(4.89020 + 6.73079i) q^{97} +(22.5395 - 7.32353i) q^{98} +9.76903 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 - 6 * q^6 - 6 * q^9	$ 32 q + 16 q^{4} - 6 q^{6} - 6 q^{9} + 4 q^{11} - 18 q^{14} - 28 q^{16} + 14 q^{21} - 20 q^{24} + 44 q^{26} + 20 q^{29} + 34 q^{31} + 2 q^{34} - 8 q^{36} + 18 q^{39} + 24 q^{41} - 98 q^{44} - 66 q^{46} + 16 q^{49} - 56 q^{51} + 60 q^{54} - 70 q^{56} - 40 q^{59} - 46 q^{61} + 56 q^{64} - 52 q^{66} - 12 q^{69} + 44 q^{71} + 72 q^{74} - 40 q^{76} - 150 q^{79} + 22 q^{81} + 62 q^{84} + 34 q^{86} - 10 q^{89} + 44 q^{91} + 102 q^{94} - 56 q^{96} + 88 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 - 6 * q^6 - 6 * q^9 + 4 * q^11 - 18 * q^14 - 28 * q^16 + 14 * q^21 - 20 * q^24 + 44 * q^26 + 20 * q^29 + 34 * q^31 + 2 * q^34 - 8 * q^36 + 18 * q^39 + 24 * q^41 - 98 * q^44 - 66 * q^46 + 16 * q^49 - 56 * q^51 + 60 * q^54 - 70 * q^56 - 40 * q^59 - 46 * q^61 + 56 * q^64 - 52 * q^66 - 12 * q^69 + 44 * q^71 + 72 * q^74 - 40 * q^76 - 150 * q^79 + 22 * q^81 + 62 * q^84 + 34 * q^86 - 10 * q^89 + 44 * q^91 + 102 * q^94 - 56 * q^96 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	−1.60102	+	0.520202i	−1.13209	+	0.367839i	−0.814370	−	0.580346i	$-0.802917\pi$
$2$	−1.60102	+	0.520202i	−1.13209	+	0.367839i	−0.317721	+	0.948184i	$0.602917\pi$
$3$	−0.417528	−	0.574677i	−0.241060	−	0.331790i	0.671295	−	0.741190i	$-0.265738\pi$
$3$	−0.417528	−	0.574677i	−0.241060	−	0.331790i	−0.912355	+	0.409400i	$0.865738\pi$
$4$	0.674615	−	0.490137i	0.337308	−	0.245068i
$5$		0			0
$5$		0			0
$6$	0.967418	+	0.702870i	0.394947	+	0.286946i
$7$		−	4.59110i		−	1.73527i	−0.497198	−	0.867637i	$-0.665638\pi$
$7$		−	4.59110i		−	1.73527i	0.497198	−	0.867637i	$-0.334362\pi$
$8$	1.15387	−	1.58816i	0.407953	−	0.561500i
$9$	0.771126	−	2.37328i	0.257042	−	0.791094i
$10$		0			0
$11$	1.20974	+	3.72319i	0.364749	+	1.12258i	0.950138	+	0.311830i	$0.100942\pi$
$11$	1.20974	+	3.72319i	0.364749	+	1.12258i	−0.585389	+	0.810753i	$0.699058\pi$
$12$	−0.563341	−	0.183041i	−0.162623	−	0.0528393i
$13$	0.544898	+	0.177048i	0.151127	+	0.0491043i	0.383604	−	0.923498i	$-0.374683\pi$
$13$	0.544898	+	0.177048i	0.151127	+	0.0491043i	−0.232476	+	0.972602i	$0.574683\pi$
$14$	2.38830	+	7.35044i	0.638301	+	1.96449i
$15$		0			0
$16$	−1.53656	+	4.72903i	−0.384139	+	1.18226i
$17$	−0.136725	+	0.188186i	−0.0331608	+	0.0456419i	−0.825275	−	0.564730i	$-0.808980\pi$
$17$	−0.136725	+	0.188186i	−0.0331608	+	0.0456419i	0.792115	+	0.610372i	$0.208980\pi$
$18$			4.20081i			0.990140i
$19$	−4.49012	−	3.26227i	−1.03010	−	0.748415i	−0.0617752	−	0.998090i	$-0.519676\pi$
$19$	−4.49012	−	3.26227i	−1.03010	−	0.748415i	−0.968330	+	0.249675i	$0.919676\pi$
$20$		0			0
$21$	−2.63840	+	1.91691i	−0.575747	+	0.418305i
$22$	−3.87362	−	5.33158i	−0.825858	−	1.13670i
$23$	−4.69124	+	1.52428i	−0.978192	+	0.317834i	−0.754118	−	0.656738i	$-0.771936\pi$
$23$	−4.69124	+	1.52428i	−0.978192	+	0.317834i	−0.224073	+	0.974572i	$0.571936\pi$
$24$	−1.39445			−0.284641
$25$		0			0
$26$	−0.964492			−0.189152
$27$	−3.71256	+	1.20628i	−0.714482	+	0.232149i
$28$	−2.25027	−	3.09723i	−0.425261	−	0.585321i
$29$	3.34174	−	2.42792i	0.620546	−	0.450853i	−0.232566	−	0.972581i	$-0.574712\pi$
$29$	3.34174	−	2.42792i	0.620546	−	0.450853i	0.853112	+	0.521727i	$0.174712\pi$
$30$		0			0
$31$	2.82777	+	2.05449i	0.507882	+	0.368998i	0.812020	−	0.583630i	$-0.198368\pi$
$31$	2.82777	+	2.05449i	0.507882	+	0.368998i	−0.304138	+	0.952628i	$0.598368\pi$
$32$		−	4.44444i		−	0.785674i
$33$	1.63453	−	2.24974i	0.284536	−	0.391630i
$34$	0.121005	−	0.372415i	0.0207522	−	0.0638686i
$35$		0			0
$36$	−0.643019	−	1.97901i	−0.107170	−	0.329835i
$37$	−5.15138	−	1.67378i	−0.846882	−	0.275169i	−0.146742	−	0.989175i	$-0.546879\pi$
$37$	−5.15138	−	1.67378i	−0.846882	−	0.275169i	−0.700139	+	0.714006i	$0.746879\pi$
$38$	8.88581	+	2.88717i	1.44147	+	0.468361i
$39$	−0.125764	−	0.387063i	−0.0201384	−	0.0619797i
$40$		0			0
$41$	3.22079	−	9.91257i	0.503003	−	1.54808i	−0.301100	−	0.953593i	$-0.597354\pi$
$41$	3.22079	−	9.91257i	0.503003	−	1.54808i	0.804103	−	0.594491i	$-0.202646\pi$
$42$	3.22695	−	4.44152i	0.497929	−	0.685341i
$43$		−	1.38833i		−	0.211718i	−0.994381	−	0.105859i	$-0.966241\pi$
$43$		−	1.38833i		−	0.211718i	0.994381	−	0.105859i	$-0.0337592\pi$
$44$	2.64098	+	1.91878i	0.398142	+	0.289267i
$45$		0			0
$46$	6.71783	−	4.88079i	0.990491	−	0.719634i
$47$	−0.541008	−	0.744634i	−0.0789142	−	0.108616i	0.767735	−	0.640767i	$-0.221384\pi$
$47$	−0.541008	−	0.744634i	−0.0789142	−	0.108616i	−0.846649	+	0.532151i	$0.821384\pi$
$48$	3.35922	−	1.09148i	0.484862	−	0.157541i
$49$	−14.0782			−2.01118
$50$		0			0
$51$	0.165233			0.0231373
$52$	0.454374	−	0.147635i	0.0630103	−	0.0204733i
$53$	0.723668	+	0.996044i	0.0994034	+	0.136817i	0.855821	−	0.517272i	$-0.173052\pi$
$53$	0.723668	+	0.996044i	0.0994034	+	0.136817i	−0.756418	+	0.654089i	$0.773052\pi$
$54$	5.31636	−	3.86256i	0.723466	−	0.525628i
$55$		0			0
$56$	−7.29141	−	5.29752i	−0.974356	−	0.707911i
$57$			3.94246i			0.522191i
$58$	−4.08718	+	5.62552i	−0.536673	+	0.738668i
$59$	−1.39299	+	4.28718i	−0.181352	+	0.558143i	−0.999866	−	0.0163426i	$-0.994798\pi$
$59$	−1.39299	+	4.28718i	−0.181352	+	0.558143i	0.818515	+	0.574485i	$0.194798\pi$
$60$		0			0
$61$	−3.60276	−	11.0881i	−0.461286	−	1.41969i	−0.863594	−	0.504187i	$-0.831792\pi$
$61$	−3.60276	−	11.0881i	−0.461286	−	1.41969i	0.402309	−	0.915504i	$-0.368208\pi$
$62$	−5.59606	−	1.81827i	−0.710700	−	0.230921i
$63$	−10.8960	−	3.54032i	−1.37277	−	0.446038i
$64$	−0.761103	−	2.34244i	−0.0951379	−	0.292804i
$65$		0			0
$66$	−1.44660	+	4.45216i	−0.178064	+	0.548023i
$67$	−1.73660	+	2.39022i	−0.212159	+	0.292012i	−0.901812	−	0.432128i	$-0.857763\pi$
$67$	−1.73660	+	2.39022i	−0.212159	+	0.292012i	0.689653	+	0.724140i	$0.257763\pi$
$68$			0.193968i			0.0235220i
$69$	2.83469	+	2.05952i	0.341257	+	0.247938i
$70$		0			0
$71$	−2.59331	+	1.88415i	−0.307770	+	0.223608i	−0.730939	−	0.682443i	$-0.760918\pi$
$71$	−2.59331	+	1.88415i	−0.307770	+	0.223608i	0.423169	+	0.906051i	$0.360918\pi$
$72$	−2.87938	−	3.96312i	−0.339338	−	0.467058i
$73$	−9.78847	+	3.18047i	−1.14565	+	0.372245i	−0.819504	−	0.573073i	$-0.805751\pi$
$73$	−9.78847	+	3.18047i	−1.14565	+	0.372245i	−0.326149	+	0.945318i	$0.605751\pi$
$74$	9.11816			1.05996
$75$		0			0
$76$	−4.62806			−0.530875
$77$	17.0935	−	5.55402i	1.94799	−	0.632940i
$78$	0.402702	+	0.554272i	0.0455970	+	0.0627589i
$79$	−7.77877	+	5.65161i	−0.875180	+	0.635856i	−0.931972	−	0.362531i	$-0.881913\pi$
$79$	−7.77877	+	5.65161i	−0.875180	+	0.635856i	0.0567919	+	0.998386i	$0.481913\pi$
$80$		0			0
$81$	−3.81318	−	2.77044i	−0.423687	−	0.307827i
$82$			17.5457i			1.93759i
$83$	6.16199	−	8.48125i	0.676366	−	0.930938i	−0.323517	−	0.946222i	$-0.604865\pi$
$83$	6.16199	−	8.48125i	0.676366	−	0.930938i	0.999883	+	0.0152844i	$0.00486536\pi$
$84$	−0.840358	+	2.58636i	−0.0916906	+	0.282195i
$85$		0			0
$86$	0.722211	+	2.22274i	0.0778780	+	0.239684i
$87$	−2.79054	−	0.906701i	−0.299177	−	0.0972086i
$88$	7.30889	+	2.37480i	0.779130	+	0.253155i
$89$	−2.24293	−	6.90303i	−0.237750	−	0.731720i	−0.996745	−	0.0806230i	$-0.974309\pi$
$89$	−2.24293	−	6.90303i	−0.237750	−	0.731720i	0.758994	−	0.651097i	$-0.225691\pi$
$90$		0			0
$91$	0.812846	−	2.50168i	0.0852094	−	0.262248i
$92$	−2.41768	+	3.32765i	−0.252061	+	0.346932i
$93$		−	2.48286i		−	0.257461i
$94$	1.25352	+	0.910739i	0.129291	+	0.0939356i
$95$		0			0
$96$	−2.55412	+	1.85568i	−0.260679	+	0.189394i
$97$	4.89020	+	6.73079i	0.496525	+	0.683408i	0.981575	−	0.191079i	$-0.0611985\pi$
$97$	4.89020	+	6.73079i	0.496525	+	0.683408i	−0.485050	+	0.874487i	$0.661199\pi$
$98$	22.5395	−	7.32353i	2.27683	−	0.739788i
$99$	9.76903			0.981824
$100$		0			0
$101$	−3.56513			−0.354744			−0.177372	−	0.984144i	$-0.556760\pi$
$101$	−3.56513			−0.354744			−0.177372	+	0.984144i	$0.556760\pi$
$102$	−0.264541	+	0.0859547i	−0.0261935	+	0.00851078i
$103$	−0.234716	−	0.323059i	−0.0231273	−	0.0318320i	0.797297	−	0.603587i	$-0.206263\pi$
$103$	−0.234716	−	0.323059i	−0.0231273	−	0.0318320i	−0.820424	+	0.571756i	$0.806263\pi$
$104$	0.909920	−	0.661095i	0.0892250	−	0.0648257i
$105$		0			0
$106$	−1.67675	−	1.21823i	−0.162860	−	0.118325i
$107$		−	1.64372i		−	0.158904i	−0.996839	−	0.0794522i	$-0.974683\pi$
$107$		−	1.64372i		−	0.158904i	0.996839	−	0.0794522i	$-0.0253171\pi$
$108$	−1.91331	+	2.63344i	−0.184108	+	0.253403i
$109$	−0.0231501	+	0.0712488i	−0.00221738	+	0.00682440i	−0.952159	−	0.305603i	$-0.901142\pi$
$109$	−0.0231501	+	0.0712488i	−0.00221738	+	0.00682440i	0.949942	+	0.312427i	$0.101142\pi$
$110$		0			0
$111$	1.18896	+	3.65923i	0.112851	+	0.347319i
$112$	21.7115	+	7.05449i	2.05154	+	0.666587i
$113$	−13.4411	−	4.36729i	−1.26444	−	0.410840i	−0.401363	−	0.915919i	$-0.631463\pi$
$113$	−13.4411	−	4.36729i	−1.26444	−	0.410840i	−0.863073	+	0.505079i	$0.831463\pi$
$114$	−2.05088	−	6.31195i	−0.192082	−	0.591168i
$115$		0			0
$116$	1.06438	−	3.27582i	0.0988251	−	0.304152i
$117$	0.840370	−	1.15667i	0.0776922	−	0.106934i
$118$		−	7.58848i		−	0.698576i
$119$	0.863983	+	0.627721i	0.0792012	+	0.0575431i
$120$		0			0
$121$	−3.49946	+	2.54251i	−0.318133	+	0.231137i
$122$	11.5362	+	15.8782i	1.04443	+	1.43754i
$123$	−7.04130	+	2.28786i	−0.634892	+	0.206289i
$124$	2.91464			0.261742
$125$		0			0
$126$	19.2864			1.71817
$127$	−11.2343	+	3.65025i	−0.996883	+	0.323907i	−0.761619	−	0.648025i	$-0.775595\pi$
$127$	−11.2343	+	3.65025i	−0.996883	+	0.323907i	−0.235264	+	0.971932i	$0.575595\pi$
$128$	7.66184	+	10.5456i	0.677217	+	0.932109i
$129$	−0.797840	+	0.579665i	−0.0702459	+	0.0510366i
$130$		0			0
$131$	13.5407	+	9.83791i	1.18306	+	0.859542i	0.992513	−	0.122136i	$-0.0389744\pi$
$131$	13.5407	+	9.83791i	1.18306	+	0.859542i	0.190545	+	0.981678i	$0.438974\pi$
$132$		−	2.31885i		−	0.201830i
$133$	−14.9774	+	20.6146i	−1.29871	+	1.78751i
$134$	1.53692	−	4.73017i	0.132770	−	0.408624i
$135$		0			0
$136$	0.141107	+	0.434284i	0.0120999	+	0.0372395i
$137$	9.91204	+	3.22062i	0.846843	+	0.275156i	0.700123	−	0.714022i	$-0.253128\pi$
$137$	9.91204	+	3.22062i	0.846843	+	0.275156i	0.146720	+	0.989178i	$0.453128\pi$
$138$	−5.60976	−	1.82272i	−0.477535	−	0.155160i
$139$	−2.05803	−	6.33397i	−0.174560	−	0.537241i	0.825053	−	0.565055i	$-0.191145\pi$
$139$	−2.05803	−	6.33397i	−0.174560	−	0.537241i	−0.999613	+	0.0278147i	$0.991145\pi$
$140$		0			0
$141$	−0.202038	+	0.621811i	−0.0170147	+	0.0523659i
$142$	3.17180	−	4.36561i	0.266172	−	0.366354i
$143$			2.24294i			0.187564i
$144$	10.0385	+	7.29336i	0.836538	+	0.607780i
$145$		0			0
$146$	14.0170	−	10.1840i	1.16006	−	0.842831i
$147$	5.87805	+	8.09044i	0.484814	+	0.667289i
$148$	−4.29558	+	1.39572i	−0.353095	+	0.114727i
$149$	12.0316			0.985667			0.492834	−	0.870124i	$-0.335961\pi$
$149$	12.0316			0.985667			0.492834	+	0.870124i	$0.335961\pi$
$150$		0			0
$151$	−1.54218			−0.125501			−0.0627505	−	0.998029i	$-0.519987\pi$
$151$	−1.54218			−0.125501			−0.0627505	+	0.998029i	$0.519987\pi$
$152$	−10.3620	+	3.36682i	−0.840469	+	0.273085i
$153$	0.341187	+	0.469603i	0.0275833	+	0.0379652i
$154$	−24.4778	+	17.7842i	−1.97248	+	1.43309i
$155$		0			0
$156$	−0.274556	−	0.199477i	−0.0219821	−	0.0159709i
$157$		−	9.82482i		−	0.784106i	−0.919943	−	0.392053i	$-0.871765\pi$
$157$		−	9.82482i		−	0.784106i	0.919943	−	0.392053i	$-0.128235\pi$
$158$	9.51397	−	13.0949i	0.756891	−	1.04177i
$159$	0.270252	−	0.831751i	0.0214324	−	0.0659622i
$160$		0			0
$161$	6.99812	+	21.5380i	0.551529	+	1.69743i
$162$	7.54617	+	2.45190i	0.592883	+	0.192639i
$163$	5.30792	+	1.72465i	0.415748	+	0.135085i	0.509419	−	0.860518i	$-0.329860\pi$
$163$	5.30792	+	1.72465i	0.415748	+	0.135085i	−0.0936712	+	0.995603i	$0.529860\pi$
$164$	−2.68572	−	8.26580i	−0.209720	−	0.645450i
$165$		0			0
$166$	−5.45349	+	16.7841i	−0.423273	+	1.30270i
$167$	−12.8494	+	17.6857i	−0.994318	+	1.36856i	−0.0655703	+	0.997848i	$0.520887\pi$
$167$	−12.8494	+	17.6857i	−0.994318	+	1.36856i	−0.928747	+	0.370713i	$0.879113\pi$
$168$			6.40207i			0.493930i
$169$	−10.2517	−	7.44826i	−0.788589	−	0.572943i
$170$		0			0
$171$	−11.2047	+	8.14071i	−0.856847	+	0.622536i
$172$	−0.680470	−	0.936586i	−0.0518853	−	0.0714140i
$173$	22.2914	−	7.24291i	1.69478	−	0.550668i	0.707096	−	0.707117i	$-0.250005\pi$
$173$	22.2914	−	7.24291i	1.69478	−	0.550668i	0.987686	+	0.156449i	$0.0500047\pi$
$174$	4.93937			0.374453
$175$		0			0
$176$	−19.4659			−1.46730
$177$	3.04535	−	0.989495i	0.228903	−	0.0743750i
$178$	7.18195	+	9.88511i	0.538310	+	0.740920i
$179$	−5.11196	+	3.71406i	−0.382086	+	0.277602i	−0.762205	−	0.647336i	$-0.775883\pi$
$179$	−5.11196	+	3.71406i	−0.382086	+	0.277602i	0.380119	+	0.924938i	$0.375883\pi$
$180$		0			0
$181$	10.7904	+	7.83972i	0.802047	+	0.582722i	0.911514	−	0.411269i	$-0.134914\pi$
$181$	10.7904	+	7.83972i	0.802047	+	0.582722i	−0.109467	+	0.993990i	$0.534914\pi$
$182$			4.42808i			0.328231i
$183$	−4.86786	+	6.70003i	−0.359842	+	0.495280i
$184$	−2.99227	+	9.20926i	−0.220593	+	0.678916i
$185$		0			0
$186$	1.29159	+	3.97511i	0.0947040	+	0.291469i
$187$	−0.866054	−	0.281398i	−0.0633322	−	0.0205779i
$188$	−0.729945	−	0.237174i	−0.0532367	−	0.0172977i
$189$	5.53817	+	17.0447i	0.402843	+	1.23982i
$190$		0			0
$191$	−0.859323	+	2.64472i	−0.0621784	+	0.191365i	−0.977320	−	0.211766i	$-0.932078\pi$
$191$	−0.859323	+	2.64472i	−0.0621784	+	0.191365i	0.915142	+	0.403132i	$0.132078\pi$
$192$	−1.02836	+	1.41542i	−0.0742157	+	0.102149i
$193$		−	22.5667i		−	1.62438i	−0.583391	−	0.812192i	$-0.698274\pi$
$193$		−	22.5667i		−	1.62438i	0.583391	−	0.812192i	$-0.301726\pi$
$194$	−11.3307	−	8.23222i	−0.813495	−	0.591039i
$195$		0			0
$196$	−9.49739	+	6.90026i	−0.678385	+	0.492876i
$197$	−0.747558	−	1.02892i	−0.0532613	−	0.0733079i	0.781556	−	0.623836i	$-0.214427\pi$
$197$	−0.747558	−	1.02892i	−0.0532613	−	0.0733079i	−0.834817	+	0.550528i	$0.814427\pi$
$198$	−15.6404	+	5.08187i	−1.11151	+	0.361153i
$199$	8.62648			0.611515			0.305757	−	0.952109i	$-0.401090\pi$
$199$	8.62648			0.611515			0.305757	+	0.952109i	$0.401090\pi$
$200$		0			0
$201$	2.09868			0.148030
$202$	5.70784	−	1.85459i	0.401602	−	0.130488i
$203$	−11.1468	−	15.3423i	−0.782354	−	1.07682i
$204$	0.111469	−	0.0809868i	0.00780438	−	0.00567021i
$205$		0			0
$206$	0.543841	+	0.395124i	0.0378912	+	0.0275296i
$207$			12.3091i			0.855538i
$208$	−1.67453	+	2.30480i	−0.116108	+	0.159809i
$209$	6.71415	−	20.6640i	0.464428	−	1.42936i
$210$		0			0
$211$	−6.49912	−	20.0022i	−0.447418	−	1.37701i	−0.879810	−	0.475325i	$-0.842330\pi$
$211$	−6.49912	−	20.0022i	−0.447418	−	1.37701i	0.432392	−	0.901686i	$-0.357670\pi$
$212$	0.976395	+	0.317250i	0.0670591	+	0.0217888i
$213$	2.16556	+	0.703633i	0.148382	+	0.0482121i
$214$	0.855067	+	2.63162i	0.0584511	+	0.179894i
$215$		0			0
$216$	−2.36803	+	7.28803i	−0.161124	+	0.495888i
$217$	9.43239	−	12.9826i	0.640313	−	0.881315i
$218$		−	0.126113i		−	0.00854148i
$219$	5.91470	+	4.29728i	0.399678	+	0.290383i
$220$		0			0
$221$	−0.107819	+	0.0783354i	−0.00725272	+	0.00526941i
$222$	−3.80708	−	5.24000i	−0.255515	−	0.351686i
$223$	−6.02530	+	1.95774i	−0.403484	+	0.131100i	−0.503726	−	0.863863i	$-0.668038\pi$
$223$	−6.02530	+	1.95774i	−0.403484	+	0.131100i	0.100243	+	0.994963i	$0.468038\pi$
$224$	−20.4049			−1.36336
$225$		0			0
$226$	23.7914			1.58258
$227$	10.7112	−	3.48028i	0.710926	−	0.230994i	0.0688416	−	0.997628i	$-0.478070\pi$
$227$	10.7112	−	3.48028i	0.710926	−	0.230994i	0.642085	+	0.766634i	$0.278070\pi$
$228$	1.93234	+	2.65964i	0.127973	+	0.176139i
$229$	12.1683	−	8.84079i	0.804104	−	0.584216i	−0.108011	−	0.994150i	$-0.534448\pi$
$229$	12.1683	−	8.84079i	0.804104	−	0.584216i	0.912115	+	0.409934i	$0.134448\pi$
$230$		0			0
$231$	−10.3288	−	7.50431i	−0.679585	−	0.493747i
$232$		−	8.10872i		−	0.532363i
$233$	4.60088	−	6.33257i	0.301414	−	0.414861i	−0.631266	−	0.775567i	$-0.717464\pi$
$233$	4.60088	−	6.33257i	0.301414	−	0.414861i	0.932680	+	0.360706i	$0.117464\pi$
$234$	−0.743745	+	2.28901i	−0.0486201	+	0.149637i
$235$		0			0
$236$	1.16157	+	3.57495i	0.0756119	+	0.232709i
$237$	6.49570	+	2.11058i	0.421941	+	0.137097i
$238$	−1.70979	−	0.555546i	−0.110830	−	0.0360107i
$239$	−2.70046	−	8.31115i	−0.174678	−	0.537603i	0.824941	−	0.565219i	$-0.191208\pi$
$239$	−2.70046	−	8.31115i	−0.174678	−	0.537603i	−0.999619	+	0.0276159i	$0.991208\pi$
$240$		0			0
$241$	−0.185686	+	0.571482i	−0.0119611	+	0.0368124i	−0.956859	−	0.290553i	$-0.906161\pi$
$241$	−0.185686	+	0.571482i	−0.0119611	+	0.0368124i	0.944898	+	0.327365i	$0.106161\pi$
$242$	4.28008	−	5.89102i	0.275134	−	0.378689i
$243$			15.0589i			0.966031i
$244$	−7.86518	−	5.71439i	−0.503517	−	0.365826i
$245$		0			0
$246$	10.0831	−	7.32580i	0.642875	−	0.467076i
$247$	−1.86908	−	2.57257i	−0.118927	−	0.163689i
$248$	6.52573	−	2.12034i	0.414384	−	0.134642i
$249$	−7.44678			−0.471921
$250$		0			0
$251$	−14.1908			−0.895712			−0.447856	−	0.894106i	$-0.647812\pi$
$251$	−14.1908			−0.895712			−0.447856	+	0.894106i	$0.647812\pi$
$252$	−9.08584	+	2.95217i	−0.572354	+	0.185969i
$253$	−11.3503	−	15.6224i	−0.713589	−	0.982171i
$254$	16.0875	−	11.6882i	1.00942	−	0.733384i
$255$		0			0
$256$	−13.7674	−	10.0026i	−0.860463	−	0.625163i
$257$		−	17.6859i		−	1.10322i	−0.834103	−	0.551609i	$-0.814014\pi$
$257$		−	17.6859i		−	1.10322i	0.834103	−	0.551609i	$-0.185986\pi$
$258$	0.975813	−	1.34309i	0.0607515	−	0.0836173i
$259$	−7.68452	+	23.6505i	−0.477493	+	1.46957i
$260$		0			0
$261$	−3.18523	−	9.80313i	−0.197161	−	0.606799i
$262$	−26.7967	−	8.70676i	−1.65550	−	0.537906i
$263$	23.1438	+	7.51987i	1.42711	+	0.463695i	0.917852	−	0.396922i	$-0.129922\pi$
$263$	23.1438	+	7.51987i	1.42711	+	0.463695i	0.509254	+	0.860617i	$0.329922\pi$
$264$	−1.68692	−	5.19180i	−0.103823	−	0.319533i
$265$		0			0
$266$	13.2553	−	40.7957i	0.812736	−	2.50134i
$267$	−3.03053	+	4.17117i	−0.185466	+	0.255271i
$268$			2.46365i			0.150491i
$269$	24.2558	+	17.6229i	1.47890	+	1.07449i	0.977908	+	0.209037i	$0.0670330\pi$
$269$	24.2558	+	17.6229i	1.47890	+	1.07449i	0.500996	+	0.865449i	$0.332967\pi$
$270$		0			0
$271$	22.4083	−	16.2806i	1.36121	−	0.988974i	0.362838	−	0.931852i	$-0.381808\pi$
$271$	22.4083	−	16.2806i	1.36121	−	0.988974i	0.998367	−	0.0571213i	$-0.0181922\pi$
$272$	−0.679854	−	0.935738i	−0.0412222	−	0.0567375i
$273$	−1.77705	+	0.577397i	−0.107552	+	0.0349457i
$274$	−17.5447			−1.05992
$275$		0			0
$276$	2.92177			0.175870
$277$	−2.18179	+	0.708908i	−0.131091	+	0.0425941i	−0.373828	−	0.927498i	$-0.621955\pi$
$277$	−2.18179	+	0.708908i	−0.131091	+	0.0425941i	0.242737	+	0.970092i	$0.421955\pi$
$278$	6.58990	+	9.07021i	0.395236	+	0.543995i
$279$	7.05646	−	5.12682i	0.422459	−	0.306934i
$280$		0			0
$281$	1.30922	+	0.951204i	0.0781015	+	0.0567441i	0.626151	−	0.779702i	$-0.284629\pi$
$281$	1.30922	+	0.951204i	0.0781015	+	0.0567441i	−0.548049	+	0.836446i	$0.684629\pi$
$282$		−	1.10063i		−	0.0655416i
$283$	7.63662	−	10.5109i	0.453950	−	0.624808i	−0.519291	−	0.854598i	$-0.673804\pi$
$283$	7.63662	−	10.5109i	0.453950	−	0.624808i	0.973240	+	0.229789i	$0.0738037\pi$
$284$	−0.825997	+	2.54216i	−0.0490139	+	0.150849i
$285$		0			0
$286$	−1.16678	−	3.59098i	−0.0689932	−	0.212339i
$287$	−45.5096	−	14.7870i	−2.68635	−	0.872848i
$288$	−10.5479	−	3.42723i	−0.621542	−	0.201951i
$289$	5.23657	+	16.1165i	0.308033	+	0.948029i
$290$		0			0
$291$	1.82624	−	5.62058i	0.107056	−	0.329484i
$292$	−5.04459	+	6.94328i	−0.295212	+	0.406325i
$293$			11.7009i			0.683572i	0.939778	+	0.341786i	$0.111032\pi$
$293$			11.7009i			0.683572i	−0.939778	+	0.341786i	$0.888968\pi$
$294$	−13.6195	−	9.89517i	−0.794308	−	0.577098i
$295$		0			0
$296$	−8.60224	+	6.24990i	−0.499995	+	0.363268i
$297$	−8.98244	−	12.3633i	−0.521214	−	0.717389i
$298$	−19.2628	+	6.25887i	−1.11586	+	0.362566i
$299$	−2.82612			−0.163439
$300$		0			0
$301$	−6.37395			−0.367388
$302$	2.46906	−	0.802247i	0.142079	−	0.0461641i
$303$	1.48854	+	2.04880i	0.0855144	+	0.117701i
$304$	22.3267	−	16.2213i	1.28052	−	0.930355i
$305$		0			0
$306$	−0.790535	−	0.574358i	−0.0451919	−	0.0328338i
$307$			26.5673i			1.51628i	0.652094	+	0.758138i	$0.273891\pi$
$307$			26.5673i			1.51628i	−0.652094	+	0.758138i	$0.726109\pi$
$308$	8.80933	−	12.1250i	0.501958	−	0.690886i
$309$	−0.0876543	+	0.269772i	−0.00498648	+	0.0153468i
$310$		0			0
$311$	−4.16895	−	12.8307i	−0.236399	−	0.727563i	−0.996933	−	0.0782636i	$-0.975062\pi$
$311$	−4.16895	−	12.8307i	−0.236399	−	0.727563i	0.760533	−	0.649299i	$-0.224938\pi$
$312$	−0.759833	−	0.246885i	−0.0430171	−	0.0139771i
$313$	−16.1626	−	5.25155i	−0.913564	−	0.296835i	−0.185740	−	0.982599i	$-0.559468\pi$
$313$	−16.1626	−	5.25155i	−0.913564	−	0.296835i	−0.727824	+	0.685764i	$0.759468\pi$
$314$	5.11089	+	15.7297i	0.288424	+	0.887679i
$315$		0			0
$316$	−2.47762	+	7.62532i	−0.139377	+	0.428958i
$317$	9.87237	−	13.5882i	0.554488	−	0.763187i	−0.436125	−	0.899886i	$-0.643649\pi$
$317$	9.87237	−	13.5882i	0.554488	−	0.763187i	0.990613	+	0.136699i	$0.0436495\pi$
$318$			1.47224i			0.0825588i
$319$	13.0822	+	9.50479i	0.732464	+	0.532166i
$320$		0			0
$321$	−0.944608	+	0.686298i	−0.0527229	+	0.0383054i
$322$	−22.4082	−	30.8423i	−1.24876	−	1.71877i
$323$	1.22783	−	0.398945i	0.0683182	−	0.0221979i
$324$	−3.93033			−0.218351
$325$		0			0
$326$	−9.39524			−0.520354
$327$	0.0506109	−	0.0164445i	0.00279879	−	0.000909382i
$328$	−12.0264	−	16.5529i	−0.664047	−	0.913982i
$329$	−3.41869	+	2.48383i	−0.188479	+	0.136938i
$330$		0			0
$331$	−10.3832	−	7.54386i	−0.570714	−	0.414648i	0.264650	−	0.964344i	$-0.414743\pi$
$331$	−10.3832	−	7.54386i	−0.570714	−	0.414648i	−0.835365	+	0.549696i	$0.814743\pi$
$332$		−	8.74180i		−	0.479768i
$333$	−7.94473	+	10.9350i	−0.435368	+	0.599233i
$334$	11.3720	−	34.9994i	0.622249	−	1.91508i
$335$		0			0
$336$	−5.01109	−	15.4225i	−0.273377	−	0.841369i
$337$	20.1980	+	6.56274i	1.10026	+	0.357495i	0.802202	−	0.597053i	$-0.203662\pi$
$337$	20.1980	+	6.56274i	1.10026	+	0.357495i	0.298056	+	0.954548i	$0.403662\pi$
$338$	20.2877	+	6.59187i	1.10350	+	0.358550i
$339$	3.10226	+	9.54778i	0.168492	+	0.518564i
$340$		0			0
$341$	−4.22841	+	13.0137i	−0.228981	+	0.704731i
$342$	13.7042	−	18.8622i	0.741036	−	1.01995i
$343$			32.4969i			1.75467i
$344$	−2.20489	−	1.60194i	−0.118879	−	0.0863710i
$345$		0			0
$346$	−31.9211	+	23.1921i	−1.71609	+	1.24681i
$347$	−16.8272	−	23.1606i	−0.903331	−	1.24333i	−0.969393	−	0.245513i	$-0.921044\pi$
$347$	−16.8272	−	23.1606i	−0.903331	−	1.24333i	0.0660623	−	0.997815i	$-0.478956\pi$
$348$	−2.32695	+	0.756071i	−0.124738	+	0.0405297i
$349$	−19.9124			−1.06588			−0.532942	−	0.846152i	$-0.678914\pi$
$349$	−19.9124			−1.06588			−0.532942	+	0.846152i	$0.678914\pi$
$350$		0			0
$351$	−2.23654			−0.119377
$352$	16.5475	−	5.37660i	0.881984	−	0.286574i
$353$	14.5133	+	19.9759i	0.772467	+	1.06321i	0.996074	+	0.0885298i	$0.0282168\pi$
$353$	14.5133	+	19.9759i	0.772467	+	1.06321i	−0.223607	+	0.974679i	$0.571783\pi$
$354$	−4.36093	+	3.16840i	−0.231781	+	0.168399i
$355$		0			0
$356$	−4.89655	−	3.55755i	−0.259516	−	0.188550i
$357$		−	0.758602i		−	0.0401495i
$358$	6.25228	−	8.60552i	0.330443	−	0.454816i
$359$	−6.64419	+	20.4487i	−0.350667	+	1.07924i	0.607812	+	0.794081i	$0.292047\pi$
$359$	−6.64419	+	20.4487i	−0.350667	+	1.07924i	−0.958479	+	0.285162i	$0.907953\pi$
$360$		0			0
$361$	3.64751	+	11.2259i	0.191974	+	0.590835i
$362$	−21.3539	−	6.93832i	−1.12234	−	0.364670i
$363$	2.92224	+	0.949494i	0.153378	+	0.0498355i
$364$	−0.677808	−	2.08608i	−0.0355268	−	0.109340i
$365$		0			0
$366$	4.30816	−	13.2591i	0.225191	−	0.693066i
$367$	−0.672327	+	0.925379i	−0.0350952	+	0.0483044i	−0.826204	−	0.563371i	$-0.809504\pi$
$367$	−0.672327	+	0.925379i	−0.0350952	+	0.0483044i	0.791109	+	0.611675i	$0.209504\pi$
$368$		−	24.5272i		−	1.27857i
$369$	−21.0417	−	15.2877i	−1.09539	−	0.795845i
$370$		0			0
$371$	4.57294	−	3.32244i	0.237415	−	0.172492i
$372$	−1.21694	−	1.67498i	−0.0630955	−	0.0868435i
$373$	10.9747	−	3.56590i	0.568250	−	0.184636i	−0.0107800	−	0.999942i	$-0.503431\pi$
$373$	10.9747	−	3.56590i	0.568250	−	0.184636i	0.579030	+	0.815306i	$0.303431\pi$
$374$	1.53295			0.0792671
$375$		0			0
$376$	−1.80685			−0.0931812
$377$	2.25077	−	0.731318i	0.115920	−	0.0376648i
$378$	−17.7334	−	24.4080i	−0.912110	−	1.25541i
$379$	17.0745	−	12.4054i	0.877059	−	0.637221i	−0.0554129	−	0.998464i	$-0.517648\pi$
$379$	17.0745	−	12.4054i	0.877059	−	0.637221i	0.932472	+	0.361243i	$0.117648\pi$
$380$		0			0
$381$	6.78835	+	4.93202i	0.347778	+	0.252675i
$382$		−	4.68127i		−	0.239515i
$383$	0.504395	−	0.694241i	0.0257734	−	0.0354740i	−0.795936	−	0.605381i	$-0.793021\pi$
$383$	0.504395	−	0.694241i	0.0257734	−	0.0354740i	0.821709	+	0.569907i	$0.193021\pi$
$384$	2.86130	−	8.80617i	0.146015	−	0.449388i
$385$		0			0
$386$	11.7392	+	36.1296i	0.597511	+	1.83895i
$387$	−3.29489	−	1.07057i	−0.167489	−	0.0544204i
$388$	6.59801	+	2.14382i	0.334963	+	0.108836i
$389$	10.4864	+	32.2738i	0.531681	+	1.63634i	0.750714	+	0.660627i	$0.229710\pi$
$389$	10.4864	+	32.2738i	0.531681	+	1.63634i	−0.219034	+	0.975717i	$0.570290\pi$
$390$		0			0
$391$	0.354564	−	1.09124i	0.0179311	−	0.0551862i
$392$	−16.2444	+	22.3585i	−0.820466	+	1.12927i
$393$		−	11.8891i		−	0.599728i
$394$	1.73210	+	1.25845i	0.0872621	+	0.0633996i
$395$		0			0
$396$	6.59034	−	4.78816i	0.331177	−	0.240614i
$397$	15.7695	+	21.7048i	0.791446	+	1.08933i	0.993926	+	0.110046i	$0.0350999\pi$
$397$	15.7695	+	21.7048i	0.791446	+	1.08933i	−0.202480	+	0.979286i	$0.564900\pi$
$398$	−13.8112	+	4.48751i	−0.692290	+	0.224939i
$399$	18.1002			0.906145
$400$		0			0
$401$	3.79757			0.189642			0.0948208	−	0.995494i	$-0.469772\pi$
$401$	3.79757			0.189642			0.0948208	+	0.995494i	$0.469772\pi$
$402$	−3.36003	+	1.09174i	−0.167583	+	0.0544510i
$403$	1.17710	+	1.62014i	0.0586355	+	0.0807049i
$404$	−2.40509	+	1.74740i	−0.119658	+	0.0869365i
$405$		0			0
$406$	25.8274	+	18.7647i	1.28179	+	0.931276i
$407$		−	21.2044i		−	1.05106i
$408$	0.190657	−	0.262417i	0.00943892	−	0.0129916i
$409$	4.38043	−	13.4816i	0.216598	−	0.666621i	−0.782438	−	0.622728i	$-0.786024\pi$
$409$	4.38043	−	13.4816i	0.216598	−	0.666621i	0.999036	−	0.0438924i	$-0.0139759\pi$
$410$		0			0
$411$	−2.28773	−	7.04092i	−0.112846	−	0.347303i
$412$	−0.316686	−	0.102898i	−0.0156020	−	0.00506940i
$413$	19.6829	+	6.39535i	0.968531	+	0.314695i
$414$	−6.40320	−	19.7070i	−0.314700	−	0.968547i
$415$		0			0
$416$	0.786879	−	2.42177i	0.0385799	−	0.118737i
$417$	−2.78071	+	3.82731i	−0.136172	+	0.187424i
$418$			36.5762i			1.78900i
$419$	−15.8542	−	11.5187i	−0.774528	−	0.562727i	0.128804	−	0.991670i	$-0.458886\pi$
$419$	−15.8542	−	11.5187i	−0.774528	−	0.562727i	−0.903332	+	0.428943i	$0.858886\pi$
$420$		0			0
$421$	20.8597	−	15.1555i	1.01664	−	0.738632i	0.0510485	−	0.998696i	$-0.483744\pi$
$421$	20.8597	−	15.1555i	1.01664	−	0.738632i	0.965591	+	0.260064i	$0.0837437\pi$
$422$	20.8104	+	28.6431i	1.01304	+	1.39432i
$423$	−2.18441	+	0.709759i	−0.106210	+	0.0345096i
$424$	2.41689			0.117375
$425$		0			0
$426$	−3.83313			−0.185716
$427$	−50.9068	+	16.5406i	−2.46355	+	0.800457i
$428$	−0.805647	−	1.10888i	−0.0389424	−	0.0535996i
$429$	1.28896	−	0.936488i	0.0622318	−	0.0452141i
$430$		0			0
$431$	−7.62525	−	5.54007i	−0.367296	−	0.266856i	0.388793	−	0.921325i	$-0.372892\pi$
$431$	−7.62525	−	5.54007i	−0.367296	−	0.266856i	−0.756089	+	0.654469i	$0.772892\pi$
$432$		−	19.4103i		−	0.933881i
$433$	1.02957	−	1.41708i	0.0494780	−	0.0681006i	−0.783561	−	0.621315i	$-0.786599\pi$
$433$	1.02957	−	1.41708i	0.0494780	−	0.0681006i	0.833039	+	0.553214i	$0.186599\pi$
$434$	−8.34787	+	25.6921i	−0.400710	+	1.23326i
$435$		0			0
$436$	0.0193042	+	0.0594123i	0.000924504	+	0.00284533i
$437$	26.0369	+	8.45989i	1.24551	+	0.404691i
$438$	−11.7050	−	3.80318i	−0.559286	−	0.181723i
$439$	−8.67814	−	26.7086i	−0.414185	−	1.27473i	−0.912978	−	0.408009i	$-0.866223\pi$
$439$	−8.67814	−	26.7086i	−0.414185	−	1.27473i	0.498793	−	0.866721i	$-0.333777\pi$
$440$		0			0
$441$	−10.8561	+	33.4116i	−0.516957	+	1.59103i
$442$	0.131871	−	0.181504i	0.00627244	−	0.00863328i
$443$		−	29.9110i		−	1.42111i	−0.703640	−	0.710557i	$-0.748443\pi$
$443$		−	29.9110i		−	1.42111i	0.703640	−	0.710557i	$-0.251557\pi$
$444$	2.59561	+	1.88582i	0.123182	+	0.0894972i
$445$		0			0
$446$	8.62819	−	6.26875i	0.408557	−	0.296834i
$447$	−5.02352	−	6.91429i	−0.237605	−	0.327035i
$448$	−10.7544	+	3.49431i	−0.508096	+	0.165090i
$449$	−6.29974			−0.297303			−0.148652	−	0.988890i	$-0.547493\pi$
$449$	−6.29974			−0.297303			−0.148652	+	0.988890i	$0.547493\pi$
$450$		0			0
$451$	40.8026			1.92132
$452$	−11.2082	+	3.64175i	−0.527188	+	0.171294i
$453$	0.643904	+	0.886258i	0.0302532	+	0.0416400i
$454$	−15.3384	+	11.1440i	−0.719865	+	0.523012i
$455$		0			0
$456$	6.26126	+	4.54907i	0.293210	+	0.213030i
$457$		−	19.1809i		−	0.897243i	−0.893722	−	0.448622i	$-0.851915\pi$
$457$		−	19.1809i		−	0.897243i	0.893722	−	0.448622i	$-0.148085\pi$
$458$	−14.8827	+	20.4842i	−0.695422	+	0.957166i
$459$	0.280595	−	0.863583i	0.0130971	−	0.0403086i
$460$		0			0
$461$	2.18509	+	6.72502i	0.101770	+	0.313215i	0.988959	−	0.148191i	$-0.0473450\pi$
$461$	2.18509	+	6.72502i	0.101770	+	0.313215i	−0.887189	+	0.461406i	$0.847345\pi$
$462$	20.4403	+	6.64147i	0.950971	+	0.308989i
$463$	−9.14766	−	2.97225i	−0.425128	−	0.138132i	0.0886360	−	0.996064i	$-0.471749\pi$
$463$	−9.14766	−	2.97225i	−0.425128	−	0.138132i	−0.513764	+	0.857932i	$0.671749\pi$
$464$	6.34693	+	19.5339i	0.294649	+	0.906836i
$465$		0			0
$466$	−4.07188	+	12.5320i	−0.188626	+	0.580531i
$467$	11.2984	−	15.5509i	0.522828	−	0.719611i	−0.463188	−	0.886260i	$-0.653295\pi$
$467$	11.2984	−	15.5509i	0.522828	−	0.719611i	0.986016	+	0.166649i	$0.0532947\pi$
$468$		−	1.19220i		−	0.0551096i
$469$	10.9737	+	7.97289i	0.506720	+	0.368154i
$470$		0			0
$471$	−5.64610	+	4.10213i	−0.260159	+	0.189016i
$472$	5.20140	+	7.15912i	0.239414	+	0.329525i
$473$	5.16900	−	1.67951i	0.237671	−	0.0772239i
$474$	−11.4977			−0.528105
$475$		0			0
$476$	0.890525			0.0408172
$477$	2.92193	−	0.949393i	0.133786	−	0.0434697i
$478$	8.64696	+	11.9015i	0.395503	+	0.544363i
$479$	−30.7423	+	22.3356i	−1.40465	+	1.02054i	−0.410579	+	0.911825i	$0.634673\pi$
$479$	−30.7423	+	22.3356i	−1.40465	+	1.02054i	−0.994073	+	0.108714i	$0.965327\pi$
$480$		0			0
$481$	−2.51063	−	1.82408i	−0.114475	−	0.0831710i
$482$		−	1.01155i		−	0.0460747i
$483$	9.45549	−	13.0144i	0.430240	−	0.592174i
$484$	−1.11461	+	3.43043i	−0.0506642	+	0.155928i
$485$		0			0
$486$	−7.83369	−	24.1096i	−0.355344	−	1.09364i
$487$	15.9292	+	5.17572i	0.721823	+	0.234534i	0.646813	−	0.762648i	$-0.276101\pi$
$487$	15.9292	+	5.17572i	0.721823	+	0.234534i	0.0750094	+	0.997183i	$0.476101\pi$
$488$	−21.7669	−	7.07248i	−0.985339	−	0.320156i
$489$	−1.22509	−	3.77043i	−0.0554003	−	0.170505i
$490$		0			0
$491$	−2.76587	+	8.51248i	−0.124822	+	0.384163i	−0.993869	−	0.110567i	$-0.964733\pi$
$491$	−2.76587	+	8.51248i	−0.124822	+	0.384163i	0.869047	+	0.494730i	$0.164733\pi$
$492$	−3.62880	+	4.99462i	−0.163599	+	0.225175i
$493$			0.960829i			0.0432736i
$494$	4.33069	+	3.14643i	0.194847	+	0.141565i
$495$		0			0
$496$	−14.0608	+	10.2158i	−0.631348	+	0.458701i
$497$	8.65034	+	11.9062i	0.388021	+	0.534065i
$498$	11.9224	−	3.87383i	0.534257	−	0.173591i
$499$	36.3310			1.62640			0.813200	−	0.581985i	$-0.197724\pi$
$499$	36.3310			1.62640			0.813200	+	0.581985i	$0.197724\pi$
$500$		0			0
$501$	15.5286			0.693765
$502$	22.7197	−	7.38206i	1.01403	−	0.329478i
$503$	−7.22652	−	9.94645i	−0.322215	−	0.443490i	0.616927	−	0.787020i	$-0.288377\pi$
$503$	−7.22652	−	9.94645i	−0.322215	−	0.443490i	−0.939142	+	0.343530i	$0.888377\pi$
$504$	−18.1951	+	13.2195i	−0.810475	+	0.588844i
$505$		0			0
$506$	26.2989	+	19.1073i	1.16913	+	0.849422i
$507$			9.00125i			0.399759i
$508$	−5.78971	+	7.96886i	−0.256877	+	0.353561i
$509$	9.61945	−	29.6056i	0.426375	−	1.31225i	−0.475297	−	0.879825i	$-0.657659\pi$
$509$	9.61945	−	29.6056i	0.426375	−	1.31225i	0.901672	−	0.432421i	$-0.142341\pi$
$510$		0			0
$511$	14.6018	+	44.9399i	0.645948	+	1.98802i
$512$	2.45102	+	0.796386i	0.108321	+	0.0351956i
$513$	20.6051	+	6.69499i	0.909736	+	0.295591i
$514$	9.20026	+	28.3155i	0.405806	+	1.24894i
$515$		0			0
$516$	−0.254120	+	0.782101i	−0.0111870	+	0.0344301i
$517$	2.11793	−	2.91508i	0.0931466	−	0.128205i
$518$		−	41.8624i		−	1.83933i
$519$	−13.4696	−	9.78624i	−0.591250	−	0.429568i
$520$		0			0
$521$	−13.1198	+	9.53206i	−0.574787	+	0.417607i	−0.836841	−	0.547446i	$-0.815600\pi$
$521$	−13.1198	+	9.53206i	−0.574787	+	0.417607i	0.262054	+	0.965053i	$0.415600\pi$
$522$	10.1992	+	14.0380i	0.446408	+	0.614428i
$523$	29.0958	−	9.45381i	1.27227	−	0.413386i	0.406420	−	0.913686i	$-0.366777\pi$
$523$	29.0958	−	9.45381i	1.27227	−	0.413386i	0.865852	+	0.500300i	$0.166777\pi$
$524$	13.9567			0.609701
$525$		0			0
$526$	−40.9655			−1.78618
$527$	−0.773255	+	0.251246i	−0.0336835	+	0.0109444i
$528$	8.12755	+	11.1866i	0.353706	+	0.486835i
$529$	1.07695	−	0.782451i	0.0468240	−	0.0340196i
$530$		0			0
$531$	9.10051	+	6.61191i	0.394928	+	0.286932i
$532$			21.2479i			0.921214i
$533$	3.51000	−	4.83110i	0.152035	−	0.209258i
$534$	2.68208	−	8.25461i	0.116065	−	0.357212i
$535$		0			0
$536$	1.79225	+	5.51599i	0.0774135	+	0.238254i
$537$	4.26877	+	1.38701i	0.184211	+	0.0598538i
$538$	−48.0015	−	15.5966i	−2.06949	−	0.672419i
$539$	−17.0310	−	52.4159i	−0.733575	−	2.25771i
$540$		0			0
$541$	5.65545	−	17.4057i	0.243147	−	0.748329i	−0.752789	−	0.658262i	$-0.771292\pi$
$541$	5.65545	−	17.4057i	0.243147	−	0.748329i	0.995936	−	0.0900672i	$-0.0287082\pi$
$542$	−27.4069	+	37.7223i	−1.17723	+	1.62031i
$543$		−	9.47432i		−	0.406582i
$544$	0.836383	+	0.607668i	0.0358596	+	0.0260536i
$545$		0			0
$546$	2.54472	−	1.84885i	0.108904	−	0.0791233i
$547$	−3.85354	−	5.30394i	−0.164765	−	0.226780i	0.718649	−	0.695373i	$-0.244761\pi$
$547$	−3.85354	−	5.30394i	−0.164765	−	0.226780i	−0.883414	+	0.468593i	$0.844761\pi$
$548$	8.26536	−	2.68558i	0.353078	−	0.114722i
$549$	−29.0935			−1.24168
$550$		0			0
$551$	−22.9254			−0.976653
$552$	6.54171	−	2.12553i	0.278434	−	0.0904686i
$553$	25.9471	+	35.7131i	1.10338	+	1.51868i
$554$	3.12432	−	2.26995i	0.132739	−	0.0964409i
$555$		0			0
$556$	−4.49289	−	3.26428i	−0.190541	−	0.138436i
$557$			35.5383i			1.50581i	0.658131	+	0.752904i	$0.271347\pi$
$557$			35.5383i			1.50581i	−0.658131	+	0.752904i	$0.728653\pi$
$558$	−8.63054	+	11.8789i	−0.365360	+	0.502875i
$559$	0.245800	−	0.756496i	0.0103963	−	0.0319964i
$560$		0			0
$561$	0.199888	+	0.615193i	0.00843930	+	0.0259735i
$562$	−2.59090	−	0.841836i	−0.109291	−	0.0355107i
$563$	36.3760	+	11.8193i	1.53306	+	0.498123i	0.949453	−	0.313911i	$-0.101639\pi$
$563$	36.3760	+	11.8193i	1.53306	+	0.498123i	0.583611	+	0.812033i	$0.301639\pi$
$564$	0.168474	+	0.518509i	0.00709403	+	0.0218332i
$565$		0			0
$566$	−6.75857	+	20.8007i	−0.284084	+	0.874320i
$567$	−12.7194	+	17.5067i	−0.534164	+	0.735213i
$568$			6.29266i			0.264034i
$569$	6.11534	+	4.44305i	0.256368	+	0.186262i	0.708544	−	0.705666i	$-0.249352\pi$
$569$	6.11534	+	4.44305i	0.256368	+	0.186262i	−0.452176	+	0.891929i	$0.649352\pi$
$570$		0			0
$571$	−18.6286	+	13.5345i	−0.779583	+	0.566400i	−0.904854	−	0.425723i	$-0.860020\pi$
$571$	−18.6286	+	13.5345i	−0.779583	+	0.566400i	0.125271	+	0.992123i	$0.460020\pi$
$572$	1.09935	+	1.51312i	0.0459659	+	0.0632667i
$573$	1.87865	−	0.610412i	0.0784819	−	0.0255003i
$574$	80.5540			3.36226
$575$		0			0
$576$	−6.14617			−0.256090
$577$	21.2245	−	6.89626i	0.883587	−	0.287095i	0.168141	−	0.985763i	$-0.446223\pi$
$577$	21.2245	−	6.89626i	0.883587	−	0.287095i	0.715446	+	0.698668i	$0.246223\pi$
$578$	−16.7677	−	23.0787i	−0.697444	−	0.959949i
$579$	−12.9685	+	9.42220i	−0.538954	+	0.391573i
$580$		0			0
$581$	−38.9383	−	28.2903i	−1.61543	−	1.17368i
$582$			9.94866i			0.412385i
$583$	−2.83301	+	3.89930i	−0.117331	+	0.161493i
$584$	−6.24349	+	19.2155i	−0.258358	+	0.795143i
$585$		0			0
$586$	−6.08682	−	18.7333i	−0.251444	−	0.773866i
$587$	20.0470	+	6.51365i	0.827426	+	0.268847i	0.691961	−	0.721935i	$-0.256747\pi$
$587$	20.0470	+	6.51365i	0.827426	+	0.268847i	0.135465	+	0.990782i	$0.456747\pi$
$588$	7.93085	+	2.57689i	0.327063	+	0.106269i
$589$	−5.99472	−	18.4499i	−0.247008	−	0.760213i
$590$		0			0
$591$	−0.279174	+	0.859209i	−0.0114837	+	0.0353431i
$592$	15.8308	−	21.7892i	0.650641	−	0.895530i
$593$			34.3547i			1.41078i	0.708819	+	0.705390i	$0.249228\pi$
$593$			34.3547i			1.41078i	−0.708819	+	0.705390i	$0.750772\pi$
$594$	20.8124	+	15.1211i	0.853945	+	0.620427i
$595$		0			0
$596$	8.11670	−	5.89713i	0.332473	−	0.241556i
$597$	−3.60179	−	4.95744i	−0.147412	−	0.202895i
$598$	4.52467	−	1.47015i	0.185027	−	0.0601190i
$599$	−0.498231			−0.0203572			−0.0101786	−	0.999948i	$-0.503240\pi$
$599$	−0.498231			−0.0203572			−0.0101786	+	0.999948i	$0.503240\pi$
$600$		0			0
$601$	27.8635			1.13657			0.568287	−	0.822830i	$-0.307606\pi$
$601$	27.8635			1.13657			0.568287	+	0.822830i	$0.307606\pi$
$602$	10.2048	−	3.31574i	0.415917	−	0.135140i
$603$	4.33353	+	5.96459i	0.176475	+	0.242897i
$604$	−1.04038	+	0.755880i	−0.0423325	+	0.0307563i
$605$		0			0
$606$	−3.44897	−	2.50582i	−0.140105	−	0.101792i
$607$			14.1000i			0.572303i	0.958184	+	0.286152i	$0.0923761\pi$
$607$			14.1000i			0.572303i	−0.958184	+	0.286152i	$0.907624\pi$
$608$	−14.4989	+	19.9561i	−0.588010	+	0.809326i
$609$	−4.16276	+	12.8117i	−0.168684	+	0.519155i
$610$		0			0
$611$	−0.162958	−	0.501534i	−0.00659258	−	0.0202899i
$612$	0.460340	+	0.149573i	0.0186081	+	0.00604615i
$613$	−30.2680	−	9.83468i	−1.22251	−	0.397219i	−0.374518	−	0.927220i	$-0.622192\pi$
$613$	−30.2680	−	9.83468i	−1.22251	−	0.397219i	−0.847997	+	0.530001i	$0.822192\pi$
$614$	−13.8204	−	42.5348i	−0.557745	−	1.71656i
$615$		0			0
$616$	10.9030	−	33.5559i	0.439293	−	1.35200i
$617$	19.9649	−	27.4793i	0.803755	−	1.10627i	−0.188502	−	0.982073i	$-0.560363\pi$
$617$	19.9649	−	27.4793i	0.803755	−	1.10627i	0.992257	−	0.124201i	$-0.0396367\pi$
$618$		−	0.477508i		−	0.0192082i
$619$	0.912910	+	0.663268i	0.0366929	+	0.0266590i	0.605981	−	0.795479i	$-0.292781\pi$
$619$	0.912910	+	0.663268i	0.0366929	+	0.0266590i	−0.569288	+	0.822138i	$0.692781\pi$
$620$		0			0
$621$	15.5778	−	11.3179i	0.625116	−	0.454173i
$622$	13.3491	+	18.3735i	0.535251	+	0.736710i
$623$	−31.6925	+	10.2975i	−1.26974	+	0.412562i
$624$	2.02368			0.0810119
$625$		0			0
$626$	28.6085			1.14343
$627$	−14.6785	+	4.76933i	−0.586203	+	0.190469i
$628$	−4.81550	−	6.62797i	−0.192159	−	0.264485i
$629$	1.01931	−	0.740571i	0.0406425	−	0.0295285i
$630$		0			0
$631$	−26.5197	−	19.2677i	−1.05573	−	0.767034i	−0.0824380	−	0.996596i	$-0.526271\pi$
$631$	−26.5197	−	19.2677i	−1.05573	−	0.767034i	−0.973294	+	0.229562i	$0.926271\pi$
$632$			18.8751i			0.750813i
$633$	−8.78127	+	12.0864i	−0.349024	+	0.480391i
$634$	−8.73726	+	26.8905i	−0.347001	+	1.06796i
$635$		0			0
$636$	−0.225355	−	0.693573i	−0.00893593	−	0.0275020i
$637$	−7.67120	−	2.49252i	−0.303944	−	0.0987574i
$638$	−25.8893	−	8.41194i	−1.02497	−	0.333032i
$639$	2.47185	+	7.60758i	0.0977850	+	0.300951i
$640$		0			0
$641$	9.39802	−	28.9241i	0.371199	−	1.14243i	−0.574808	−	0.818288i	$-0.694923\pi$
$641$	9.39802	−	28.9241i	0.371199	−	1.14243i	0.946007	−	0.324146i	$-0.105077\pi$
$642$	1.15532	−	1.59016i	0.0455969	−	0.0627587i
$643$			1.06932i			0.0421700i	0.999778	+	0.0210850i	$0.00671206\pi$
$643$			1.06932i			0.0421700i	−0.999778	+	0.0210850i	$0.993288\pi$
$644$	15.2776	+	11.0998i	0.602022	+	0.437394i
$645$		0			0
$646$	−1.75824	+	1.27744i	−0.0691771	+	0.0502601i
$647$	17.9674	+	24.7300i	0.706372	+	0.972237i	0.999868	+	0.0162768i	$0.00518131\pi$
$647$	17.9674	+	24.7300i	0.706372	+	0.972237i	−0.293496	+	0.955960i	$0.594819\pi$
$648$	−8.79981	+	2.85923i	−0.345689	+	0.112321i
$649$	−17.6471			−0.692709
$650$		0			0
$651$	−11.3991			−0.446765
$652$	4.42611	−	1.43813i	0.173340	−	0.0563216i
$653$	19.6027	+	26.9808i	0.767114	+	1.05584i	0.996589	+	0.0825273i	$0.0262992\pi$
$653$	19.6027	+	26.9808i	0.767114	+	1.05584i	−0.229475	+	0.973315i	$0.573701\pi$
$654$	−0.0724745	+	0.0526558i	−0.00283398	+	0.00205901i
$655$		0			0
$656$	41.9280	+	30.4624i	1.63701	+	1.18936i
$657$			25.6833i			1.00200i
$658$	4.18130	−	5.75506i	0.163004	−	0.224356i
$659$	3.12572	−	9.61998i	0.121761	−	0.374741i	−0.871536	−	0.490331i	$-0.836876\pi$
$659$	3.12572	−	9.61998i	0.121761	−	0.374741i	0.993297	+	0.115590i	$0.0368758\pi$
$660$		0			0
$661$	−9.52955	−	29.3290i	−0.370657	−	1.14076i	−0.946362	−	0.323107i	$-0.895273\pi$
$661$	−9.52955	−	29.3290i	−0.370657	−	1.14076i	0.575706	−	0.817657i	$-0.304727\pi$
$662$	20.5481	+	6.67648i	0.798624	+	0.259489i
$663$	0.0900351	+	0.0292542i	0.00349667	+	0.00113614i
$664$	−6.35948	−	19.5725i	−0.246796	−	0.759558i
$665$		0			0
$666$	7.03125	−	21.6400i	0.272455	−	0.838532i
$667$	−11.9761	+	16.4837i	−0.463717	+	0.638251i
$668$			18.2290i			0.705302i
$669$	3.64079	+	2.64519i	0.140761	+	0.102269i
$670$		0			0
$671$	36.9248	−	26.8275i	1.42547	−	1.03566i
$672$	8.51961	+	11.7262i	0.328651	+	0.452349i
$673$	29.3163	−	9.52544i	1.13006	−	0.367179i	0.316461	−	0.948606i	$-0.397505\pi$
$673$	29.3163	−	9.52544i	1.13006	−	0.367179i	0.813599	+	0.581427i	$0.197505\pi$
$674$	−35.7514			−1.37709
$675$		0			0
$676$	−10.5666			−0.406407
$677$	39.2331	−	12.7476i	1.50785	−	0.489930i	0.565553	−	0.824712i	$-0.308663\pi$
$677$	39.2331	−	12.7476i	1.50785	−	0.489930i	0.942296	+	0.334782i	$0.108663\pi$
$678$	−9.93356	−	13.6724i	−0.381496	−	0.525084i
$679$	30.9017	−	22.4514i	1.18590	−	0.861607i
$680$		0			0
$681$	−6.47225	−	4.70237i	−0.248017	−	0.180195i
$682$		−	23.0348i		−	0.882048i
$683$	13.1379	−	18.0827i	0.502706	−	0.691915i	−0.479962	−	0.877289i	$-0.659350\pi$
$683$	13.1379	−	18.0827i	0.502706	−	0.691915i	0.982668	+	0.185374i	$0.0593496\pi$
$684$	−3.56882	+	10.9837i	−0.136457	+	0.419972i
$685$		0			0
$686$	−16.9050	−	52.0282i	−0.645435	−	1.98644i
$687$	−10.1612	−	3.30157i	−0.387674	−	0.125963i
$688$	6.56544	+	2.13324i	0.250305	+	0.0813291i
$689$	0.217978	+	0.670866i	0.00830428	+	0.0255580i
$690$		0			0
$691$	2.83956	−	8.73927i	0.108022	−	0.332457i	−0.882406	−	0.470489i	$-0.844078\pi$
$691$	2.83956	−	8.73927i	0.108022	−	0.332457i	0.990428	+	0.138032i	$0.0440776\pi$
$692$	11.4881	−	15.8120i	0.436712	−	0.601082i
$693$		−	44.8506i		−	1.70373i
$694$	38.9889	+	28.3271i	1.48000	+	1.07528i
$695$		0			0
$696$	−4.65990	+	3.38561i	−0.176633	+	0.128331i
$697$	1.42505	+	1.96141i	0.0539775	+	0.0742937i
$698$	31.8801	−	10.3585i	1.20668	−	0.392073i
$699$	−5.56018			−0.210305
$700$		0			0
$701$	−35.9929			−1.35943			−0.679717	−	0.733475i	$-0.737897\pi$
$701$	−35.9929			−1.35943			−0.679717	+	0.733475i	$0.737897\pi$
$702$	3.58073	−	1.16345i	0.135146	−	0.0439116i
$703$	17.6700	+	24.3207i	0.666437	+	0.917271i
$704$	7.80059	−	5.66746i	0.293996	−	0.213600i
$705$		0			0
$706$	−33.6276	−	24.4319i	−1.26559	−	0.919506i
$707$			16.3679i			0.615578i
$708$	1.56945	−	2.16017i	0.0589837	−	0.0811841i
$709$	−6.25640	+	19.2552i	−0.234964	+	0.723145i	0.762162	+	0.647386i	$0.224138\pi$
$709$	−6.25640	+	19.2552i	−0.234964	+	0.723145i	−0.997126	+	0.0757586i	$0.975862\pi$
$710$		0			0
$711$	7.41445	+	22.8193i	0.278063	+	0.855791i
$712$	−13.5512	−	4.40304i	−0.507852	−	0.165011i
$713$	−16.3974	−	5.32783i	−0.614086	−	0.199529i
$714$	0.394627	+	1.21454i	0.0147685	+	0.0454529i
$715$		0			0
$716$	−1.62821	+	5.01112i	−0.0608491	+	0.187274i
$717$	−3.64871	+	5.02202i	−0.136264	+	0.187551i
$718$		−	36.1951i		−	1.35079i
$719$	−29.9551	−	21.7637i	−1.11714	−	0.811647i	−0.133364	−	0.991067i	$-0.542578\pi$
$719$	−29.9551	−	21.7637i	−1.11714	−	0.811647i	−0.983773	+	0.179420i	$0.942578\pi$
$720$		0			0
$721$	−1.48320	+	1.07761i	−0.0552372	+	0.0401322i
$722$	−11.6794	−	16.0754i	−0.434664	−	0.598264i
$723$	0.405947	−	0.131900i	0.0150973	−	0.00490542i
$724$	11.1219			0.413343
$725$		0			0
$726$	−5.17249			−0.191969
$727$	−11.4878	+	3.73261i	−0.426059	+	0.138435i	−0.514195	−	0.857673i	$-0.671909\pi$
$727$	−11.4878	+	3.73261i	−0.426059	+	0.138435i	0.0881356	+	0.996108i	$0.471909\pi$
$728$	−3.03516	−	4.17754i	−0.112490	−	0.154830i
$729$	−2.78552	+	2.02380i	−0.103167	+	0.0749555i
$730$		0			0
$731$	0.261264	+	0.189820i	0.00966320	+	0.00702073i
$732$			6.90586i			0.255248i
$733$	26.2221	−	36.0916i	0.968534	−	1.33307i	0.0257496	−	0.999668i	$-0.491803\pi$
$733$	26.2221	−	36.0916i	0.968534	−	1.33307i	0.942784	−	0.333404i	$-0.108197\pi$
$734$	0.595024	−	1.83130i	0.0219627	−	0.0675943i
$735$		0			0
$736$	6.77456	+	20.8500i	0.249714	+	0.768540i
$737$	−11.0001	−	3.57413i	−0.405192	−	0.131655i
$738$	41.6408	+	13.5299i	1.53282	+	0.498043i
$739$	4.52596	+	13.9295i	0.166490	+	0.512404i	0.999143	−	0.0413910i	$-0.0131789\pi$
$739$	4.52596	+	13.9295i	0.166490	+	0.512404i	−0.832653	+	0.553795i	$0.813179\pi$
$740$		0			0
$741$	−0.698004	+	2.14824i	−0.0256418	+	0.0789174i
$742$	−5.59302	+	7.69813i	−0.205326	+	0.282607i
$743$			24.4397i			0.896604i	0.893882	+	0.448302i	$0.147971\pi$
$743$			24.4397i			0.896604i	−0.893882	+	0.448302i	$0.852029\pi$
$744$	−3.94318	−	2.86489i	−0.144564	−	0.105032i
$745$		0			0
$746$	−15.7157	+	11.4182i	−0.575394	+	0.418048i
$747$	−15.3767	−	21.1642i	−0.562605	−	0.774359i
$748$	−0.722177	+	0.234650i	−0.0264054	+	0.00857964i
$749$	−7.54648			−0.275743
$750$		0			0
$751$	31.2863			1.14165			0.570826	−	0.821071i	$-0.306623\pi$
$751$	31.2863			1.14165			0.570826	+	0.821071i	$0.306623\pi$
$752$	4.35269	−	1.41427i	0.158726	−	0.0515733i
$753$	5.92503	+	8.15510i	0.215920	+	0.297189i
$754$	−3.22308	+	2.34171i	−0.117378	+	0.0852800i
$755$		0			0
$756$	12.0904	+	8.78418i	0.439723	+	0.319478i
$757$			11.3251i			0.411617i	0.978592	+	0.205808i	$0.0659824\pi$
$757$			11.3251i			0.411617i	−0.978592	+	0.205808i	$0.934018\pi$
$758$	−20.8833	+	28.7434i	−0.758516	+	1.04401i
$759$	−4.23876	+	13.0456i	−0.153857	+	0.473524i
$760$		0			0
$761$	−12.7728	−	39.3108i	−0.463015	−	1.42501i	−0.861462	−	0.507822i	$-0.830451\pi$
$761$	−12.7728	−	39.3108i	−0.463015	−	1.42501i	0.398447	−	0.917191i	$-0.369549\pi$
$762$	−13.4339	−	4.36494i	−0.486659	−	0.158125i
$763$	0.327111	+	0.106285i	0.0118422	+	0.00384776i
$764$	0.716564	+	2.20536i	0.0259244	+	0.0797870i
$765$		0			0
$766$	−0.446401	+	1.37388i	−0.0161291	+	0.0496403i
$767$	−1.51807	+	2.08945i	−0.0548144	+	0.0754455i
$768$			12.0882i			0.436195i
$769$	18.3235	+	13.3128i	0.660762	+	0.480072i	0.866920	−	0.498447i	$-0.166096\pi$
$769$	18.3235	+	13.3128i	0.660762	+	0.480072i	−0.206158	+	0.978519i	$0.566096\pi$
$770$		0			0
$771$	−10.1637	+	7.38436i	−0.366037	+	0.265941i
$772$	−11.0607	−	15.2238i	−0.398085	−	0.547917i
$773$	−16.0292	+	5.20820i	−0.576530	+	0.187326i	−0.582746	−	0.812655i	$-0.698022\pi$
$773$	−16.0292	+	5.20820i	−0.576530	+	0.187326i	0.00621531	+	0.999981i	$0.498022\pi$
$774$	5.83210			0.209630
$775$		0			0
$776$	16.3322			0.586292
$777$	16.7999	−	5.45862i	0.602694	−	0.195827i
$778$	−33.5778	−	46.2158i	−1.20382	−	1.65692i
$779$	−46.7992	+	34.0016i	−1.67675	+	1.21823i
$780$		0			0
$781$	−10.1523	−	7.37606i	−0.363277	−	0.263936i
$782$			1.93153i			0.0690715i
$783$	−9.47766	+	13.0449i	−0.338704	+	0.466186i
$784$	21.6320	−	66.5765i	0.772572	−	2.37773i
$785$		0			0
$786$	6.18476	+	19.0347i	0.220603	+	0.678947i
$787$	−19.1245	−	6.21393i	−0.681716	−	0.221503i	−0.0523693	−	0.998628i	$-0.516677\pi$
$787$	−19.1245	−	6.21393i	−0.681716	−	0.221503i	−0.629346	+	0.777125i	$0.716677\pi$
$788$	−1.00863	−	0.327723i	−0.0359309	−	0.0116746i
$789$	−5.34166	−	16.4400i	−0.190168	−	0.585278i
$790$		0			0
$791$	−20.0507	+	61.7097i	−0.712920	+	2.19414i
$792$	11.2722	−	15.5148i	0.400539	−	0.551294i
$793$		−	6.67976i		−	0.237205i
$794$	−36.5381	−	26.5465i	−1.29669	−	0.942099i
$795$		0			0
$796$	5.81955	−	4.22815i	0.206269	−	0.149863i
$797$	−31.8419	−	43.8266i	−1.12790	−	1.55242i	−0.792000	−	0.610521i	$-0.790960\pi$
$797$	−31.8419	−	43.8266i	−1.12790	−	1.55242i	−0.335898	−	0.941898i	$-0.609040\pi$
$798$	−28.9788	+	9.41579i	−1.02584	+	0.333315i
$799$	0.214100			0.00757430
$800$		0			0
$801$	−18.1124			−0.639971
$802$	−6.07998	+	1.97550i	−0.214691	+	0.0697575i
$803$	−23.6829	−	32.5967i	−0.835752	−	1.15031i
$804$	1.41580	−	1.02864i	0.0499315	−	0.0362774i
$805$		0			0
$806$	−2.72736	−	1.98154i	−0.0960671	−	0.0697969i
$807$		−	21.2973i		−	0.749701i
$808$	−4.11368	+	5.66200i	−0.144719	+	0.199189i
$809$	−4.73927	+	14.5860i	−0.166624	+	0.512815i	−0.999152	−	0.0411669i	$-0.986892\pi$
$809$	−4.73927	+	14.5860i	−0.166624	+	0.512815i	0.832528	+	0.553982i	$0.186892\pi$
$810$		0			0
$811$	3.57428	+	11.0005i	0.125510	+	0.386279i	0.993994	−	0.109438i	$-0.0349051\pi$
$811$	3.57428	+	11.0005i	0.125510	+	0.386279i	−0.868484	+	0.495717i	$0.834905\pi$
$812$	−15.0396	−	4.88667i	−0.527788	−	0.171489i
$813$	−18.7121	−	6.07994i	−0.656263	−	0.213233i
$814$	11.0306	+	33.9486i	0.386621	+	1.18990i
$815$		0			0
$816$	−0.253890	+	0.781393i	−0.00888793	+	0.0273542i
$817$	−4.52909	+	6.23376i	−0.158453	+	0.218092i
$818$			23.8630i			0.834349i
$819$	−5.31039	−	3.85822i	−0.185560	−	0.134817i
$820$		0			0
$821$	−26.9949	+	19.6129i	−0.942128	+	0.684496i	−0.948932	−	0.315480i	$-0.897834\pi$
$821$	−26.9949	+	19.6129i	−0.942128	+	0.684496i	0.00680360	+	0.999977i	$0.497834\pi$
$822$	7.32541	+	10.0826i	0.255503	+	0.351670i
$823$	−28.5146	+	9.26497i	−0.993958	+	0.322956i	−0.760449	−	0.649398i	$-0.775021\pi$
$823$	−28.5146	+	9.26497i	−0.993958	+	0.322956i	−0.233509	+	0.972355i	$0.575021\pi$
$824$	−0.783901			−0.0273085
$825$		0			0
$826$	−34.8395			−1.21222
$827$	−23.5130	+	7.63982i	−0.817626	+	0.265663i	−0.687824	−	0.725877i	$-0.741434\pi$
$827$	−23.5130	+	7.63982i	−0.817626	+	0.265663i	−0.129801	+	0.991540i	$0.541434\pi$
$828$	6.03312	+	8.30388i	0.209665	+	0.288580i
$829$	−0.171031	+	0.124261i	−0.00594015	+	0.00431577i	−0.590751	−	0.806854i	$-0.701169\pi$
$829$	−0.171031	+	0.124261i	−0.00594015	+	0.00431577i	0.584811	+	0.811169i	$0.301169\pi$
$830$		0			0
$831$	1.31835	+	0.957839i	0.0457331	+	0.0332271i
$832$		−	1.41114i		−	0.0489225i
$833$	1.92485	−	2.64933i	0.0666922	−	0.0917939i
$834$	2.46098	−	7.57413i	0.0852169	−	0.262271i
$835$		0			0
$836$	−5.59873	−	17.2311i	−0.193636	−	0.595951i
$837$	−12.9766	−	4.21634i	−0.448535	−	0.145738i
$838$	31.3749	+	10.1943i	1.08383	+	0.352157i
$839$	1.70489	+	5.24712i	0.0588594	+	0.181151i	0.976163	−	0.217037i	$-0.0696393\pi$
$839$	1.70489	+	5.24712i	0.0588594	+	0.181151i	−0.917304	+	0.398188i	$0.869639\pi$
$840$		0			0
$841$	−3.68903	+	11.3537i	−0.127208	+	0.391506i
$842$	−25.5129	+	35.1154i	−0.879231	+	1.21016i
$843$		−	1.14953i		−	0.0395920i
$844$	−14.1882	−	10.3084i	−0.488379	−	0.354828i
$845$		0			0
$846$	3.12807	−	2.27267i	0.107545	−	0.0781361i
$847$	11.6729	+	16.0664i	0.401086	+	0.552047i
$848$	−5.82228	+	1.89177i	−0.199938	+	0.0649638i
$849$	−9.22888			−0.316734
$850$		0			0
$851$	26.7177			0.915871
$852$	1.80580	−	0.586739i	0.0618656	−	0.0201013i
$853$	−0.904870	−	1.24545i	−0.0309822	−	0.0426433i	0.793245	−	0.608903i	$-0.208390\pi$
$853$	−0.904870	−	1.24545i	−0.0309822	−	0.0426433i	−0.824227	+	0.566259i	$0.808390\pi$
$854$	72.8983	−	52.9637i	2.49453	−	1.81238i
$855$		0			0
$856$	−2.61049	−	1.89663i	−0.0892247	−	0.0648255i
$857$		−	45.3407i		−	1.54881i	−0.632691	−	0.774404i	$-0.718050\pi$
$857$		−	45.3407i		−	1.54881i	0.632691	−	0.774404i	$-0.281950\pi$
$858$	−1.57649	+	2.16986i	−0.0538206	+	0.0740777i
$859$	6.73547	−	20.7296i	0.229811	−	0.707286i	−0.767956	−	0.640502i	$-0.778726\pi$
$859$	6.73547	−	20.7296i	0.229811	−	0.707286i	0.997767	−	0.0667839i	$-0.0212738\pi$
$860$		0			0
$861$	10.5038	+	32.3273i	0.357968	+	1.10171i
$862$	15.0901	+	4.90308i	0.513972	+	0.167000i
$863$	12.1623	+	3.95176i	0.414008	+	0.134519i	0.508613	−	0.860996i	$-0.330159\pi$
$863$	12.1623	+	3.95176i	0.414008	+	0.134519i	−0.0946043	+	0.995515i	$0.530159\pi$
$864$	5.36126	+	16.5003i	0.182394	+	0.561350i
$865$		0			0
$866$	−0.911192	+	2.80436i	−0.0309636	+	0.0952960i
$867$	7.07538	−	9.73842i	0.240292	−	0.330734i
$868$		−	13.3814i		−	0.454194i
$869$	−30.4522	−	22.1248i	−1.03302	−	0.750534i
$870$		0			0
$871$	−1.36945	+	0.994964i	−0.0464021	+	0.0337131i
$872$	0.0864424	+	0.118978i	0.00292731	+	0.00402909i
$873$	19.7450	−	6.41555i	0.668268	−	0.217133i
$874$	−46.0863			−1.55889
$875$		0			0
$876$	6.09640			0.205978
$877$	−9.08583	+	2.95216i	−0.306807	+	0.0996875i	−0.458374	−	0.888759i	$-0.651568\pi$
$877$	−9.08583	+	2.95216i	−0.306807	+	0.0996875i	0.151567	+	0.988447i	$0.451568\pi$
$878$	27.7877	+	38.2465i	0.937790	+	1.29076i
$879$	6.72423	−	4.88544i	0.226803	−	0.164782i
$880$		0			0
$881$	31.6595	+	23.0020i	1.06664	+	0.774956i	0.975305	−	0.220864i	$-0.0708877\pi$
$881$	31.6595	+	23.0020i	1.06664	+	0.774956i	0.0913314	+	0.995821i	$0.470888\pi$
$882$		−	59.1400i		−	1.99135i
$883$	20.5874	−	28.3361i	0.692821	−	0.953586i	−0.307177	−	0.951652i	$-0.599384\pi$
$883$	20.5874	−	28.3361i	0.692821	−	0.953586i	0.999998	−	0.00193394i	$-0.000615594\pi$
$884$	−0.0343416	+	0.105692i	−0.00115503	+	0.00355482i
$885$		0			0
$886$	15.5598	+	47.8880i	0.522741	+	1.60883i
$887$	34.4699	+	11.2000i	1.15739	+	0.376058i	0.823921	−	0.566705i	$-0.191782\pi$
$887$	34.4699	+	11.2000i	1.15739	+	0.376058i	0.333465	+	0.942762i	$0.391782\pi$
$888$	7.18335	+	2.33401i	0.241057	+	0.0783243i
$889$	16.7587	+	51.5779i	0.562068	+	1.72987i
$890$		0			0
$891$	5.70191	−	17.5487i	0.191021	−	0.587903i
$892$	−3.10520	+	4.27394i	−0.103970	+	0.143102i
$893$			5.10841i			0.170946i
$894$	11.6396	+	8.45665i	0.389286	+	0.282833i
$895$		0			0
$896$	48.4160	−	35.1763i	1.61747	−	1.17516i
$897$	1.17998	+	1.62411i	0.0393985	+	0.0542273i
$898$	10.0860	−	3.27714i	0.336574	−	0.109360i
$899$	14.4378			0.481528
$900$		0			0
$901$	−0.286386			−0.00954089
$902$	−65.3258	+	21.2256i	−2.17511	+	0.706736i
$903$	2.66130	+	3.66297i	0.0885625	+	0.121896i
$904$	−22.4452	+	16.3074i	−0.746517	+	0.542377i
$905$		0			0
$906$	−1.49194	−	1.08395i	−0.0495662	−	0.0360120i
$907$		−	40.8532i		−	1.35651i	−0.734827	−	0.678255i	$-0.762737\pi$
$907$		−	40.8532i		−	1.35651i	0.734827	−	0.678255i	$-0.237263\pi$
$908$	5.52012	−	7.59779i	0.183192	−	0.252142i
$909$	−2.74917	+	8.46106i	−0.0911841	+	0.280636i
$910$		0			0
$911$	3.93897	+	12.1229i	0.130504	+	0.401650i	0.994864	−	0.101224i	$-0.0322759\pi$
$911$	3.93897	+	12.1229i	0.130504	+	0.401650i	−0.864360	+	0.502874i	$0.832276\pi$
$912$	−18.6440	−	6.05781i	−0.617365	−	0.200594i
$913$	39.0316	+	12.6821i	1.29176	+	0.419718i
$914$	9.97794	+	30.7089i	0.330041	+	1.01576i
$915$		0			0
$916$	3.87573	−	11.9283i	0.128058	−	0.394121i
$917$	45.1669	−	62.1669i	1.49154	−	2.05293i
$918$			1.52858i			0.0504506i
$919$	7.82486	+	5.68509i	0.258118	+	0.187534i	0.709317	−	0.704890i	$-0.249003\pi$
$919$	7.82486	+	5.68509i	0.258118	+	0.187534i	−0.451199	+	0.892423i	$0.649003\pi$
$920$		0			0
$921$	15.2676	−	11.0926i	0.503086	−	0.365513i
$922$	−6.99674	−	9.63019i	−0.230425	−	0.317153i
$923$	−1.74668	+	0.567529i	−0.0574925	+	0.0186805i
$924$	−10.6461			−0.350231
$925$		0			0
$926$	16.1917			0.532094
$927$	−0.947706	+	0.307928i	−0.0311268	+	0.0101137i
$928$	−10.7907	−	14.8522i	−0.354223	−	0.487547i
$929$	8.83405	−	6.41831i	0.289836	−	0.210578i	−0.433360	−	0.901221i	$-0.642672\pi$
$929$	8.83405	−	6.41831i	0.289836	−	0.210578i	0.723196	+	0.690643i	$0.242672\pi$
$930$		0			0
$931$	63.2130	+	45.9269i	2.07172	+	1.50519i
$932$		−	6.52711i		−	0.213803i
$933$	−5.63287	+	7.75297i	−0.184412	+	0.253821i
$934$	−9.99933	+	30.7748i	−0.327188	+	1.00698i
$935$		0			0
$936$	−0.867303	−	2.66928i	−0.0283487	−	0.0872483i
$937$	15.1661	+	4.92778i	0.495456	+	0.160984i	0.546078	−	0.837734i	$-0.316120\pi$
$937$	15.1661	+	4.92778i	0.495456	+	0.160984i	−0.0506216	+	0.998718i	$0.516120\pi$
$938$	−21.7167	−	7.05618i	−0.709075	−	0.230392i
$939$	3.73039	+	11.4809i	0.121737	+	0.374667i
$940$		0			0
$941$	1.83155	−	5.63692i	0.0597067	−	0.183758i	−0.916755	−	0.399451i	$-0.869201\pi$
$941$	1.83155	−	5.63692i	0.0597067	−	0.183758i	0.976461	+	0.215692i	$0.0692009\pi$
$942$	6.90557	−	9.50470i	0.224996	−	0.309680i
$943$			51.4117i			1.67419i
$944$	−18.1338	−	13.1750i	−0.590205	−	0.428809i
$945$		0			0
$946$	−7.40197	+	5.37785i	−0.240659	+	0.174849i
$947$	0.582132	+	0.801236i	0.0189168	+	0.0260367i	0.818371	−	0.574691i	$-0.194878\pi$
$947$	0.582132	+	0.801236i	0.0189168	+	0.0260367i	−0.799454	+	0.600727i	$0.794878\pi$
$948$	5.41657	−	1.75995i	0.175922	−	0.0571606i
$949$	−5.89681			−0.191418
$950$		0			0
$951$	−11.9308			−0.386882
$952$	1.99384	−	0.647839i	0.0646208	−	0.0209966i
$953$	−31.5049	−	43.3627i	−1.02054	−	1.40466i	−0.911823	−	0.410584i	$-0.865325\pi$
$953$	−31.5049	−	43.3627i	−1.02054	−	1.40466i	−0.108720	−	0.994072i	$-0.534675\pi$
$954$	−4.18419	+	3.03999i	−0.135468	+	0.0984234i
$955$		0			0
$956$	−5.89537	−	4.28324i	−0.190670	−	0.138530i
$957$		−	11.4866i		−	0.371308i
$958$	37.6000	−	51.7519i	1.21480	−	1.67203i
$959$	14.7862	−	45.5072i	0.477471	−	1.46950i
$960$		0			0
$961$	−5.80420	−	17.8635i	−0.187232	−	0.576242i
$962$	4.96846	+	1.61435i	0.160190	+	0.0520488i
$963$	−3.90101	−	1.26751i	−0.125708	−	0.0408451i
$964$	0.154838	+	0.476542i	0.00498699	+	0.0153484i
$965$		0			0
$966$	−8.36831	+	25.7550i	−0.269246	+	0.828654i
$967$	−17.4778	+	24.0561i	−0.562047	+	0.773592i	−0.991585	−	0.129457i	$-0.958677\pi$
$967$	−17.4778	+	24.0561i	−0.562047	+	0.773592i	0.429538	+	0.903049i	$0.358677\pi$
$968$			8.49141i			0.272924i
$969$	−0.741917	−	0.539034i	−0.0238338	−	0.0173163i
$970$		0			0
$971$	−49.0399	+	35.6296i	−1.57376	+	1.14341i	−0.650330	+	0.759652i	$0.725369\pi$
$971$	−49.0399	+	35.6296i	−1.57376	+	1.14341i	−0.923435	+	0.383755i	$0.874631\pi$
$972$	7.38094	+	10.1590i	0.236744	+	0.325850i
$973$	−29.0799	+	9.44864i	−0.932260	+	0.302910i
$974$	−28.1954			−0.903440
$975$		0			0
$976$	57.9720			1.85564
$977$	−42.3343	+	13.7553i	−1.35440	+	0.440070i	−0.894168	−	0.447731i	$-0.852232\pi$
$977$	−42.3343	+	13.7553i	−1.35440	+	0.440070i	−0.460227	+	0.887801i	$0.652232\pi$
$978$	3.92277	+	5.39923i	0.125436	+	0.172648i
$979$	22.9879	−	16.7017i	0.734697	−	0.533789i
$980$		0			0
$981$	0.151242	+	0.109884i	0.00482878	+	0.00350831i
$982$		−	15.0675i		−	0.480822i
$983$	−22.4769	+	30.9369i	−0.716903	+	0.986732i	0.282718	+	0.959203i	$0.408764\pi$
$983$	−22.4769	+	30.9369i	−0.716903	+	0.986732i	−0.999621	+	0.0275293i	$0.991236\pi$
$984$	−4.49123	+	13.8226i	−0.143175	+	0.440648i
$985$		0			0
$986$	−0.499825	−	1.53830i	−0.0159177	−	0.0489896i
$987$	2.85480	+	0.927580i	0.0908692	+	0.0295252i
$988$	−2.52182	−	0.819389i	−0.0802298	−	0.0260682i
$989$	2.11619	+	6.51298i	0.0672911	+	0.207101i
$990$		0			0
$991$	7.01721	−	21.5968i	0.222909	−	0.686044i	−0.775588	−	0.631239i	$-0.782547\pi$
$991$	7.01721	−	21.5968i	0.222909	−	0.686044i	0.998497	−	0.0548043i	$-0.0174535\pi$
$992$	9.13108	−	12.5678i	0.289912	−	0.399030i
$993$			9.11678i			0.289312i
$994$	−20.0430	−	14.5621i	−0.635725	−	0.461881i
$995$		0			0
$996$	−5.02371	+	3.64994i	−0.159182	+	0.115653i
$997$	−12.1251	−	16.6887i	−0.384005	−	0.528538i	0.572635	−	0.819811i	$-0.305921\pi$
$997$	−12.1251	−	16.6887i	−0.384005	−	0.528538i	−0.956640	+	0.291273i	$0.905921\pi$
$998$	−58.1666	+	18.8995i	−1.84123	+	0.598253i
$999$	21.1439			0.668962

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.e.k.499.3		32
5.2	odd	4		625.2.d.n.126.1		16
5.3	odd	4		625.2.d.p.126.4		16
5.4	even	2	inner	625.2.e.k.499.6		32
25.2	odd	20		625.2.a.g.1.2	yes	8
25.3	odd	20		625.2.d.p.501.4		16
25.4	even	10	inner	625.2.e.k.124.3		32
25.6	even	5		625.2.e.j.249.6		32
25.8	odd	20		625.2.d.q.376.1		16
25.9	even	10		625.2.e.j.374.6		32
25.11	even	5		625.2.b.d.624.12		16
25.12	odd	20		625.2.d.m.251.4		16
25.13	odd	20		625.2.d.q.251.1		16
25.14	even	10		625.2.b.d.624.5		16
25.16	even	5		625.2.e.j.374.3		32
25.17	odd	20		625.2.d.m.376.4		16
25.19	even	10		625.2.e.j.249.3		32
25.21	even	5	inner	625.2.e.k.124.6		32
25.22	odd	20		625.2.d.n.501.1		16
25.23	odd	20		625.2.a.e.1.7	✓	8
75.2	even	20		5625.2.a.s.1.7		8
75.23	even	20		5625.2.a.be.1.2		8
100.23	even	20		10000.2.a.bn.1.4		8
100.27	even	20		10000.2.a.be.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.7	✓	8	25.23	odd	20
625.2.a.g.1.2	yes	8	25.2	odd	20
625.2.b.d.624.5		16	25.14	even	10
625.2.b.d.624.12		16	25.11	even	5
625.2.d.m.251.4		16	25.12	odd	20
625.2.d.m.376.4		16	25.17	odd	20
625.2.d.n.126.1		16	5.2	odd	4
625.2.d.n.501.1		16	25.22	odd	20
625.2.d.p.126.4		16	5.3	odd	4
625.2.d.p.501.4		16	25.3	odd	20
625.2.d.q.251.1		16	25.13	odd	20
625.2.d.q.376.1		16	25.8	odd	20
625.2.e.j.249.3		32	25.19	even	10
625.2.e.j.249.6		32	25.6	even	5
625.2.e.j.374.3		32	25.16	even	5
625.2.e.j.374.6		32	25.9	even	10
625.2.e.k.124.3		32	25.4	even	10	inner
625.2.e.k.124.6		32	25.21	even	5	inner
625.2.e.k.499.3		32	1.1	even	1	trivial
625.2.e.k.499.6		32	5.4	even	2	inner
5625.2.a.s.1.7		8	75.2	even	20
5625.2.a.be.1.2		8	75.23	even	20
10000.2.a.be.1.5		8	100.27	even	20
10000.2.a.bn.1.4		8	100.23	even	20

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.60102 + 0.520202i) q^{2} +(-0.417528 - 0.574677i) q^{3} +(0.674615 - 0.490137i) q^{4} +(0.967418 + 0.702870i) q^{6} -4.59110i q^{7} +(1.15387 - 1.58816i) q^{8} +(0.771126 - 2.37328i) q^{9} +O(q^{10})\)	\(q+(-1.60102 + 0.520202i) q^{2} +(-0.417528 - 0.574677i) q^{3} +(0.674615 - 0.490137i) q^{4} +(0.967418 + 0.702870i) q^{6} -4.59110i q^{7} +(1.15387 - 1.58816i) q^{8} +(0.771126 - 2.37328i) q^{9} +(1.20974 + 3.72319i) q^{11} +(-0.563341 - 0.183041i) q^{12} +(0.544898 + 0.177048i) q^{13} +(2.38830 + 7.35044i) q^{14} +(-1.53656 + 4.72903i) q^{16} +(-0.136725 + 0.188186i) q^{17} +4.20081i q^{18} +(-4.49012 - 3.26227i) q^{19} +(-2.63840 + 1.91691i) q^{21} +(-3.87362 - 5.33158i) q^{22} +(-4.69124 + 1.52428i) q^{23} -1.39445 q^{24} -0.964492 q^{26} +(-3.71256 + 1.20628i) q^{27} +(-2.25027 - 3.09723i) q^{28} +(3.34174 - 2.42792i) q^{29} +(2.82777 + 2.05449i) q^{31} -4.44444i q^{32} +(1.63453 - 2.24974i) q^{33} +(0.121005 - 0.372415i) q^{34} +(-0.643019 - 1.97901i) q^{36} +(-5.15138 - 1.67378i) q^{37} +(8.88581 + 2.88717i) q^{38} +(-0.125764 - 0.387063i) q^{39} +(3.22079 - 9.91257i) q^{41} +(3.22695 - 4.44152i) q^{42} -1.38833i q^{43} +(2.64098 + 1.91878i) q^{44} +(6.71783 - 4.88079i) q^{46} +(-0.541008 - 0.744634i) q^{47} +(3.35922 - 1.09148i) q^{48} -14.0782 q^{49} +0.165233 q^{51} +(0.454374 - 0.147635i) q^{52} +(0.723668 + 0.996044i) q^{53} +(5.31636 - 3.86256i) q^{54} +(-7.29141 - 5.29752i) q^{56} +3.94246i q^{57} +(-4.08718 + 5.62552i) q^{58} +(-1.39299 + 4.28718i) q^{59} +(-3.60276 - 11.0881i) q^{61} +(-5.59606 - 1.81827i) q^{62} +(-10.8960 - 3.54032i) q^{63} +(-0.761103 - 2.34244i) q^{64} +(-1.44660 + 4.45216i) q^{66} +(-1.73660 + 2.39022i) q^{67} +0.193968i q^{68} +(2.83469 + 2.05952i) q^{69} +(-2.59331 + 1.88415i) q^{71} +(-2.87938 - 3.96312i) q^{72} +(-9.78847 + 3.18047i) q^{73} +9.11816 q^{74} -4.62806 q^{76} +(17.0935 - 5.55402i) q^{77} +(0.402702 + 0.554272i) q^{78} +(-7.77877 + 5.65161i) q^{79} +(-3.81318 - 2.77044i) q^{81} +17.5457i q^{82} +(6.16199 - 8.48125i) q^{83} +(-0.840358 + 2.58636i) q^{84} +(0.722211 + 2.22274i) q^{86} +(-2.79054 - 0.906701i) q^{87} +(7.30889 + 2.37480i) q^{88} +(-2.24293 - 6.90303i) q^{89} +(0.812846 - 2.50168i) q^{91} +(-2.41768 + 3.32765i) q^{92} -2.48286i q^{93} +(1.25352 + 0.910739i) q^{94} +(-2.55412 + 1.85568i) q^{96} +(4.89020 + 6.73079i) q^{97} +(22.5395 - 7.32353i) q^{98} +9.76903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 - 6 * q^6 - 6 * q^9	\( 32 q + 16 q^{4} - 6 q^{6} - 6 q^{9} + 4 q^{11} - 18 q^{14} - 28 q^{16} + 14 q^{21} - 20 q^{24} + 44 q^{26} + 20 q^{29} + 34 q^{31} + 2 q^{34} - 8 q^{36} + 18 q^{39} + 24 q^{41} - 98 q^{44} - 66 q^{46} + 16 q^{49} - 56 q^{51} + 60 q^{54} - 70 q^{56} - 40 q^{59} - 46 q^{61} + 56 q^{64} - 52 q^{66} - 12 q^{69} + 44 q^{71} + 72 q^{74} - 40 q^{76} - 150 q^{79} + 22 q^{81} + 62 q^{84} + 34 q^{86} - 10 q^{89} + 44 q^{91} + 102 q^{94} - 56 q^{96} + 88 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 - 6 * q^6 - 6 * q^9 + 4 * q^11 - 18 * q^14 - 28 * q^16 + 14 * q^21 - 20 * q^24 + 44 * q^26 + 20 * q^29 + 34 * q^31 + 2 * q^34 - 8 * q^36 + 18 * q^39 + 24 * q^41 - 98 * q^44 - 66 * q^46 + 16 * q^49 - 56 * q^51 + 60 * q^54 - 70 * q^56 - 40 * q^59 - 46 * q^61 + 56 * q^64 - 52 * q^66 - 12 * q^69 + 44 * q^71 + 72 * q^74 - 40 * q^76 - 150 * q^79 + 22 * q^81 + 62 * q^84 + 34 * q^86 - 10 * q^89 + 44 * q^91 + 102 * q^94 - 56 * q^96 + 88 * q^99

Introduction

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