LMFDB - Embedded newform 425.2.n.c.274.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(49,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("425.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.n (of order $8$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			274.6
Character	$\chi$	$=$	425.274
Dual form			425.2.n.c.349.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93083 - 1.93083i) q^{2} +(0.591976 + 1.42916i) q^{3} -5.45623i q^{4} +(3.90247 + 1.61646i) q^{6} +(-1.16820 - 0.483886i) q^{7} +(-6.67340 - 6.67340i) q^{8} +(0.429267 - 0.429267i) q^{9} +O(q^{10})$	\(q+(1.93083 - 1.93083i) q^{2} +(0.591976 + 1.42916i) q^{3} -5.45623i q^{4} +(3.90247 + 1.61646i) q^{6} +(-1.16820 - 0.483886i) q^{7} +(-6.67340 - 6.67340i) q^{8} +(0.429267 - 0.429267i) q^{9} +(0.386141 + 0.159945i) q^{11} +(7.79781 - 3.22996i) q^{12} +5.66390 q^{13} +(-3.18991 + 1.32130i) q^{14} -14.8580 q^{16} +(-3.92002 + 1.27807i) q^{17} -1.65769i q^{18} +(0.0948539 + 0.0948539i) q^{19} -1.95600i q^{21} +(1.05440 - 0.436747i) q^{22} +(-2.60960 + 6.30014i) q^{23} +(5.58684 - 13.4878i) q^{24} +(10.9361 - 10.9361i) q^{26} +(5.15508 + 2.13530i) q^{27} +(-2.64019 + 6.37399i) q^{28} +(0.126098 + 0.304427i) q^{29} +(-0.559556 + 0.231776i) q^{31} +(-15.3415 + 15.3415i) q^{32} +0.646540i q^{33} +(-5.10115 + 10.0366i) q^{34} +(-2.34218 - 2.34218i) q^{36} +(3.38184 + 8.16448i) q^{37} +0.366294 q^{38} +(3.35290 + 8.09461i) q^{39} +(0.625194 - 1.50935i) q^{41} +(-3.77670 - 3.77670i) q^{42} +(1.41246 + 1.41246i) q^{43} +(0.872696 - 2.10687i) q^{44} +(7.12581 + 17.2032i) q^{46} -5.06253 q^{47} +(-8.79557 - 21.2344i) q^{48} +(-3.81919 - 3.81919i) q^{49} +(-4.14712 - 4.84573i) q^{51} -30.9036i q^{52} +(-1.09104 + 1.09104i) q^{53} +(14.0765 - 5.83068i) q^{54} +(4.56673 + 11.0251i) q^{56} +(-0.0794098 + 0.191712i) q^{57} +(0.831272 + 0.344324i) q^{58} +(-0.997758 + 0.997758i) q^{59} +(2.98684 - 7.21086i) q^{61} +(-0.632889 + 1.52793i) q^{62} +(-0.709187 + 0.293755i) q^{63} +29.5276i q^{64} +(1.24836 + 1.24836i) q^{66} +12.1014i q^{67} +(6.97346 + 21.3885i) q^{68} -10.5487 q^{69} +(-4.45766 + 1.84642i) q^{71} -5.72934 q^{72} +(-2.67964 + 1.10994i) q^{73} +(22.2940 + 9.23447i) q^{74} +(0.517545 - 0.517545i) q^{76} +(-0.373696 - 0.373696i) q^{77} +(22.1032 + 9.15545i) q^{78} +(-4.00751 - 1.65997i) q^{79} +6.81023i q^{81} +(-1.70716 - 4.12145i) q^{82} +(3.10563 - 3.10563i) q^{83} -10.6724 q^{84} +5.45443 q^{86} +(-0.360427 + 0.360427i) q^{87} +(-1.50950 - 3.64425i) q^{88} -4.98704i q^{89} +(-6.61659 - 2.74068i) q^{91} +(34.3750 + 14.2386i) q^{92} +(-0.662488 - 0.662488i) q^{93} +(-9.77489 + 9.77489i) q^{94} +(-31.0071 - 12.8436i) q^{96} +(-0.587015 + 0.243150i) q^{97} -14.7484 q^{98} +(0.234417 - 0.0970985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9	$ 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} + 40 q^{12} + 16 q^{13} - 24 q^{16} + 8 q^{19} - 24 q^{22} + 8 q^{23} + 8 q^{24} + 16 q^{26} + 16 q^{27} - 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} - 16 q^{37} - 48 q^{38} - 8 q^{39} + 16 q^{41} - 24 q^{42} - 8 q^{43} - 16 q^{44} + 8 q^{46} - 64 q^{47} - 8 q^{48} - 56 q^{51} + 24 q^{53} + 32 q^{54} + 64 q^{56} + 16 q^{57} + 56 q^{58} - 32 q^{59} + 32 q^{61} - 32 q^{62} + 80 q^{63} + 96 q^{66} + 24 q^{68} - 96 q^{69} - 24 q^{71} - 24 q^{72} - 64 q^{73} + 64 q^{74} - 8 q^{76} + 24 q^{77} + 8 q^{78} - 16 q^{82} - 96 q^{83} + 64 q^{84} - 16 q^{86} + 48 q^{87} + 8 q^{88} - 24 q^{91} + 112 q^{92} - 64 q^{93} - 56 q^{94} - 168 q^{96} + 48 q^{97} + 120 q^{98} + 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 + 40 * q^12 + 16 * q^13 - 24 * q^16 + 8 * q^19 - 24 * q^22 + 8 * q^23 + 8 * q^24 + 16 * q^26 + 16 * q^27 - 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 + 16 * q^41 - 24 * q^42 - 8 * q^43 - 16 * q^44 + 8 * q^46 - 64 * q^47 - 8 * q^48 - 56 * q^51 + 24 * q^53 + 32 * q^54 + 64 * q^56 + 16 * q^57 + 56 * q^58 - 32 * q^59 + 32 * q^61 - 32 * q^62 + 80 * q^63 + 96 * q^66 + 24 * q^68 - 96 * q^69 - 24 * q^71 - 24 * q^72 - 64 * q^73 + 64 * q^74 - 8 * q^76 + 24 * q^77 + 8 * q^78 - 16 * q^82 - 96 * q^83 + 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 + 112 * q^92 - 64 * q^93 - 56 * q^94 - 168 * q^96 + 48 * q^97 + 120 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	1.93083	−	1.93083i	1.36530	−	1.36530i	0.498300	−	0.867005i	$-0.333958\pi$
$2$	1.93083	−	1.93083i	1.36530	−	1.36530i	0.867005	−	0.498300i	$-0.166042\pi$
$3$	0.591976	+	1.42916i	0.341778	+	0.825124i	0.997536	+	0.0701535i	$0.0223489\pi$
$3$	0.591976	+	1.42916i	0.341778	+	0.825124i	−0.655759	+	0.754971i	$0.727651\pi$
$4$		−	5.45623i		−	2.72811i
$5$		0			0
$5$		0			0
$6$	3.90247	+	1.61646i	1.59318	+	0.659915i
$7$	−1.16820	−	0.483886i	−0.441540	−	0.182892i	0.150827	−	0.988560i	$-0.451806\pi$
$7$	−1.16820	−	0.483886i	−0.441540	−	0.182892i	−0.592367	+	0.805668i	$0.701806\pi$
$8$	−6.67340	−	6.67340i	−2.35940	−	2.35940i
$9$	0.429267	−	0.429267i	0.143089	−	0.143089i
$10$		0			0
$11$	0.386141	+	0.159945i	0.116426	+	0.0482252i	0.440136	−	0.897931i	$-0.354930\pi$
$11$	0.386141	+	0.159945i	0.116426	+	0.0482252i	−0.323710	+	0.946156i	$0.604930\pi$
$12$	7.79781	−	3.22996i	2.25103	−	0.932408i
$13$	5.66390			1.57088			0.785442	−	0.618935i	$-0.212436\pi$
$13$	5.66390			1.57088			0.785442	+	0.618935i	$0.212436\pi$
$14$	−3.18991	+	1.32130i	−0.852539	+	0.353133i
$15$		0			0
$16$	−14.8580			−3.71449
$17$	−3.92002	+	1.27807i	−0.950744	+	0.309978i
$17$	−3.92002	+	1.27807i	−0.950744	+	0.309978i
$18$		−	1.65769i		−	0.390720i
$19$	0.0948539	+	0.0948539i	0.0217610	+	0.0217610i	0.717904	−	0.696143i	$-0.245102\pi$
$19$	0.0948539	+	0.0948539i	0.0217610	+	0.0217610i	−0.696143	+	0.717904i	$0.745102\pi$
$20$		0			0
$21$		−	1.95600i		−	0.426833i
$22$	1.05440	−	0.436747i	0.224799	−	0.0931148i
$23$	−2.60960	+	6.30014i	−0.544140	+	1.31367i	0.377638	+	0.925953i	$0.376736\pi$
$23$	−2.60960	+	6.30014i	−0.544140	+	1.31367i	−0.921778	+	0.387717i	$0.873264\pi$
$24$	5.58684	−	13.4878i	1.14041	−	2.75319i
$25$		0			0
$26$	10.9361	−	10.9361i	2.14474	−	2.14474i
$27$	5.15508	+	2.13530i	0.992095	+	0.410939i
$28$	−2.64019	+	6.37399i	−0.498949	+	1.20457i
$29$	0.126098	+	0.304427i	0.0234158	+	0.0565307i	0.935155	−	0.354239i	$-0.115260\pi$
$29$	0.126098	+	0.304427i	0.0234158	+	0.0565307i	−0.911739	+	0.410770i	$0.865260\pi$
$30$		0			0
$31$	−0.559556	+	0.231776i	−0.100499	+	0.0416281i	−0.432367	−	0.901698i	$-0.642321\pi$
$31$	−0.559556	+	0.231776i	−0.100499	+	0.0416281i	0.331867	+	0.943326i	$0.392321\pi$
$32$	−15.3415	+	15.3415i	−2.71201	+	2.71201i
$33$			0.646540i			0.112548i
$34$	−5.10115	+	10.0366i	−0.874840	+	1.72127i
$35$		0			0
$36$	−2.34218	−	2.34218i	−0.390363	−	0.390363i
$37$	3.38184	+	8.16448i	0.555970	+	1.34223i	0.912932	+	0.408112i	$0.133813\pi$
$37$	3.38184	+	8.16448i	0.555970	+	1.34223i	−0.356961	+	0.934119i	$0.616187\pi$
$38$	0.366294			0.0594207
$39$	3.35290	+	8.09461i	0.536893	+	1.29617i
$40$		0			0
$41$	0.625194	−	1.50935i	0.0976389	−	0.235721i	−0.867511	−	0.497417i	$-0.834282\pi$
$41$	0.625194	−	1.50935i	0.0976389	−	0.235721i	0.965150	+	0.261696i	$0.0842818\pi$
$42$	−3.77670	−	3.77670i	−0.582757	−	0.582757i
$43$	1.41246	+	1.41246i	0.215398	+	0.215398i	0.806556	−	0.591158i	$-0.201329\pi$
$43$	1.41246	+	1.41246i	0.215398	+	0.215398i	−0.591158	+	0.806556i	$0.701329\pi$
$44$	0.872696	−	2.10687i	0.131564	−	0.317623i
$45$		0			0
$46$	7.12581	+	17.2032i	1.05064	+	2.53648i
$47$	−5.06253			−0.738445			−0.369223	−	0.929341i	$-0.620376\pi$
$47$	−5.06253			−0.738445			−0.369223	+	0.929341i	$0.620376\pi$
$48$	−8.79557	−	21.2344i	−1.26953	−	3.06492i
$49$	−3.81919	−	3.81919i	−0.545599	−	0.545599i
$50$		0			0
$51$	−4.14712	−	4.84573i	−0.580713	−	0.678538i
$52$		−	30.9036i		−	4.28555i
$53$	−1.09104	+	1.09104i	−0.149865	+	0.149865i	−0.778058	−	0.628193i	$-0.783795\pi$
$53$	−1.09104	+	1.09104i	−0.149865	+	0.149865i	0.628193	+	0.778058i	$0.283795\pi$
$54$	14.0765	−	5.83068i	1.91557	−	0.793455i
$55$		0			0
$56$	4.56673	+	11.0251i	0.610254	+	1.47328i
$57$	−0.0794098	+	0.191712i	−0.0105181	+	0.0253929i
$58$	0.831272	+	0.344324i	0.109151	+	0.0452119i
$59$	−0.997758	+	0.997758i	−0.129897	+	0.129897i	−0.769066	−	0.639169i	$-0.779278\pi$
$59$	−0.997758	+	0.997758i	−0.129897	+	0.129897i	0.639169	+	0.769066i	$0.279278\pi$
$60$		0			0
$61$	2.98684	−	7.21086i	0.382425	−	0.923256i	−0.609070	−	0.793116i	$-0.708457\pi$
$61$	2.98684	−	7.21086i	0.382425	−	0.923256i	0.991496	−	0.130140i	$-0.0415427\pi$
$62$	−0.632889	+	1.52793i	−0.0803770	+	0.194047i
$63$	−0.709187	+	0.293755i	−0.0893492	+	0.0370097i
$64$			29.5276i			3.69095i
$65$		0			0
$66$	1.24836	+	1.24836i	0.153662	+	0.153662i
$67$			12.1014i			1.47842i	0.673477	+	0.739209i	$0.264800\pi$
$67$			12.1014i			1.47842i	−0.673477	+	0.739209i	$0.735200\pi$
$68$	6.97346	+	21.3885i	0.845656	+	2.59374i
$69$	−10.5487			−1.26992
$70$		0			0
$71$	−4.45766	+	1.84642i	−0.529027	+	0.219130i	−0.631177	−	0.775639i	$-0.717428\pi$
$71$	−4.45766	+	1.84642i	−0.529027	+	0.219130i	0.102150	+	0.994769i	$0.467428\pi$
$72$	−5.72934			−0.675209
$73$	−2.67964	+	1.10994i	−0.313628	+	0.129909i	−0.533944	−	0.845520i	$-0.679291\pi$
$73$	−2.67964	+	1.10994i	−0.313628	+	0.129909i	0.220317	+	0.975428i	$0.429291\pi$
$74$	22.2940	+	9.23447i	2.59162	+	1.07349i
$75$		0			0
$76$	0.517545	−	0.517545i	0.0593664	−	0.0593664i
$77$	−0.373696	−	0.373696i	−0.0425867	−	0.0425867i
$78$	22.1032	+	9.15545i	2.50270	+	1.03665i
$79$	−4.00751	−	1.65997i	−0.450880	−	0.186761i	0.145675	−	0.989332i	$-0.453465\pi$
$79$	−4.00751	−	1.65997i	−0.450880	−	0.186761i	−0.596556	+	0.802572i	$0.703465\pi$
$80$		0			0
$81$			6.81023i			0.756693i
$82$	−1.70716	−	4.12145i	−0.188524	−	0.455138i
$83$	3.10563	−	3.10563i	0.340887	−	0.340887i	−0.515814	−	0.856701i	$-0.672510\pi$
$83$	3.10563	−	3.10563i	0.340887	−	0.340887i	0.856701	+	0.515814i	$0.172510\pi$
$84$	−10.6724			−1.16445
$85$		0			0
$86$	5.45443			0.588167
$87$	−0.360427	+	0.360427i	−0.0386418	+	0.0386418i
$88$	−1.50950	−	3.64425i	−0.160913	−	0.388478i
$89$		−	4.98704i		−	0.528625i	−0.964437	−	0.264313i	$-0.914855\pi$
$89$		−	4.98704i		−	0.528625i	0.964437	−	0.264313i	$-0.0851451\pi$
$90$		0			0
$91$	−6.61659	−	2.74068i	−0.693608	−	0.287302i
$92$	34.3750	+	14.2386i	3.58384	+	1.48448i
$93$	−0.662488	−	0.662488i	−0.0686968	−	0.0686968i
$94$	−9.77489	+	9.77489i	−1.00820	+	1.00820i
$95$		0			0
$96$	−31.0071	−	12.8436i	−3.16465	−	1.31084i
$97$	−0.587015	+	0.243150i	−0.0596024	+	0.0246881i	−0.412285	−	0.911055i	$-0.635269\pi$
$97$	−0.587015	+	0.243150i	−0.0596024	+	0.0246881i	0.352683	+	0.935743i	$0.385269\pi$
$98$	−14.7484			−1.48982
$99$	0.234417	−	0.0970985i	0.0235598	−	0.00975877i
$100$		0			0
$101$	7.45004			0.741307			0.370653	−	0.928771i	$-0.379134\pi$
$101$	7.45004			0.741307			0.370653	+	0.928771i	$0.379134\pi$
$102$	−17.3637	−	1.34889i	−1.71926	−	0.133560i
$103$		−	13.5860i		−	1.33866i	−0.742963	−	0.669332i	$-0.766580\pi$
$103$		−	13.5860i		−	1.33866i	0.742963	−	0.669332i	$-0.233420\pi$
$104$	−37.7975	−	37.7975i	−3.70635	−	3.70635i
$105$		0			0
$106$			4.21322i			0.409224i
$107$	8.56826	−	3.54909i	0.828325	−	0.343103i	0.0720853	−	0.997398i	$-0.477035\pi$
$107$	8.56826	−	3.54909i	0.828325	−	0.343103i	0.756239	+	0.654295i	$0.227035\pi$
$108$	11.6507	−	28.1273i	1.12109	−	2.70655i
$109$	6.01065	−	14.5110i	0.575716	−	1.38990i	−0.320909	−	0.947110i	$-0.603988\pi$
$109$	6.01065	−	14.5110i	0.575716	−	1.38990i	0.896625	−	0.442791i	$-0.146012\pi$
$110$		0			0
$111$	−9.66635	+	9.66635i	−0.917489	+	0.917489i
$112$	17.3571	+	7.18956i	1.64010	+	0.679350i
$113$	−0.477131	+	1.15190i	−0.0448847	+	0.108361i	−0.944732	−	0.327844i	$-0.893678\pi$
$113$	−0.477131	+	1.15190i	−0.0448847	+	0.108361i	0.899847	+	0.436205i	$0.143678\pi$
$114$	0.216837	+	0.523492i	0.0203087	+	0.0490295i
$115$		0			0
$116$	1.66102	−	0.688019i	0.154222	−	0.0638809i
$117$	2.43133	−	2.43133i	0.224776	−	0.224776i
$118$			3.85301i			0.354698i
$119$	5.19782	+	0.403791i	0.476483	+	0.0370155i
$120$		0			0
$121$	−7.65465	−	7.65465i	−0.695877	−	0.695877i
$122$	−8.15588	−	19.6900i	−0.738399	−	1.78265i
$123$	2.52720			0.227870
$124$	1.26462	+	3.05307i	0.113566	+	0.274173i
$125$		0			0
$126$	−0.802130	+	1.93651i	−0.0714594	+	0.172518i
$127$	−12.5973	−	12.5973i	−1.11783	−	1.11783i	−0.992059	−	0.125773i	$-0.959859\pi$
$127$	−12.5973	−	12.5973i	−1.11783	−	1.11783i	−0.125773	−	0.992059i	$-0.540141\pi$
$128$	26.3300	+	26.3300i	2.32727	+	2.32727i
$129$	−1.18248	+	2.85476i	−0.104112	+	0.251348i
$130$		0			0
$131$	1.71149	+	4.13191i	0.149534	+	0.361007i	0.980842	−	0.194805i	$-0.0624075\pi$
$131$	1.71149	+	4.13191i	0.149534	+	0.361007i	−0.831308	+	0.555812i	$0.812407\pi$
$132$	3.52767			0.307044
$133$	−0.0649102	−	0.156707i	−0.00562843	−	0.0135882i
$134$	23.3657	+	23.3657i	2.01849	+	2.01849i
$135$		0			0
$136$	34.6889	+	17.6307i	2.97455	+	1.51182i
$137$			9.04916i			0.773122i	0.922264	+	0.386561i	$0.126337\pi$
$137$			9.04916i			0.773122i	−0.922264	+	0.386561i	$0.873663\pi$
$138$	−20.3678	+	20.3678i	−1.73382	+	1.73382i
$139$	−4.34294	+	1.79890i	−0.368363	+	0.152581i	−0.559183	−	0.829044i	$-0.688885\pi$
$139$	−4.34294	+	1.79890i	−0.368363	+	0.152581i	0.190820	+	0.981625i	$0.438885\pi$
$140$		0			0
$141$	−2.99689	−	7.23514i	−0.252384	−	0.609309i
$142$	−5.04186	+	12.1721i	−0.423103	+	1.02146i
$143$	2.18707	+	0.905912i	0.182892	+	0.0757562i
$144$	−6.37804	+	6.37804i	−0.531503	+	0.531503i
$145$		0			0
$146$	−3.03082	+	7.31704i	−0.250832	+	0.605562i
$147$	3.19735	−	7.71910i	0.263713	−	0.636660i
$148$	44.5472	−	18.4521i	3.66176	−	1.51675i
$149$		−	0.775949i		−	0.0635683i	−0.999495	−	0.0317841i	$-0.989881\pi$
$149$		−	0.775949i		−	0.0635683i	0.999495	−	0.0317841i	$-0.0101189\pi$
$150$		0			0
$151$	1.61724	+	1.61724i	0.131609	+	0.131609i	0.769843	−	0.638234i	$-0.220335\pi$
$151$	1.61724	+	1.61724i	0.131609	+	0.131609i	−0.638234	+	0.769843i	$0.720335\pi$
$152$		−	1.26600i		−	0.102686i
$153$	−1.13410	+	2.23137i	−0.0916865	+	0.180395i
$154$	−1.44309			−0.116288
$155$		0			0
$156$	44.1660	−	18.2942i	3.53611	−	1.46471i
$157$	19.1134			1.52541			0.762707	−	0.646745i	$-0.223870\pi$
$157$	19.1134			1.52541			0.762707	+	0.646745i	$0.223870\pi$
$158$	−10.9430	+	4.53272i	−0.870575	+	0.360604i
$159$	−2.20513	−	0.913395i	−0.174878	−	0.0724369i
$160$		0			0
$161$	6.09710	−	6.09710i	0.480519	−	0.480519i
$162$	13.1494	+	13.1494i	1.03312	+	1.03312i
$163$	−16.9343	−	7.01440i	−1.32639	−	0.549410i	−0.396769	−	0.917918i	$-0.629869\pi$
$163$	−16.9343	−	7.01440i	−1.32639	−	0.549410i	−0.929625	+	0.368508i	$0.879869\pi$
$164$	−8.23536	−	3.41120i	−0.643074	−	0.266370i
$165$		0			0
$166$		−	11.9929i		−	0.930829i
$167$	−7.71045	−	18.6147i	−0.596653	−	1.44045i	−0.876973	−	0.480540i	$-0.840441\pi$
$167$	−7.71045	−	18.6147i	−0.596653	−	1.44045i	0.280320	−	0.959907i	$-0.409559\pi$
$168$	−13.0531	+	13.0531i	−1.00707	+	1.00707i
$169$	19.0798			1.46768
$170$		0			0
$171$	0.0814353			0.00622751
$172$	7.70668	−	7.70668i	0.587629	−	0.587629i
$173$	−7.31475	−	17.6594i	−0.556130	−	1.34262i	−0.912808	−	0.408389i	$-0.866091\pi$
$173$	−7.31475	−	17.6594i	−0.556130	−	1.34262i	0.356678	−	0.934227i	$-0.383909\pi$
$174$			1.39185i			0.105516i
$175$		0			0
$176$	−5.73727	−	2.37646i	−0.432463	−	0.179132i
$177$	−2.01660	−	0.835303i	−0.151577	−	0.0627852i
$178$	−9.62914	−	9.62914i	−0.721735	−	0.721735i
$179$	−14.0116	+	14.0116i	−1.04727	+	1.04727i	−0.0484485	+	0.998826i	$0.515428\pi$
$179$	−14.0116	+	14.0116i	−1.04727	+	1.04727i	−0.998826	+	0.0484485i	$0.984572\pi$
$180$		0			0
$181$	8.19070	+	3.39270i	0.608810	+	0.252177i	0.665719	−	0.746202i	$-0.268125\pi$
$181$	8.19070	+	3.39270i	0.608810	+	0.252177i	−0.0569098	+	0.998379i	$0.518125\pi$
$182$	−18.0673	+	7.48374i	−1.33924	+	0.554731i
$183$	12.0736			0.892505
$184$	59.4583	−	24.6284i	4.38332	−	1.81563i
$185$		0			0
$186$	−2.55831			−0.187584
$187$	−1.71810	−	0.133470i	−0.125640	−	0.00976030i
$188$			27.6223i			2.01456i
$189$	−4.98894	−	4.98894i	−0.362892	−	0.362892i
$190$		0			0
$191$			10.6081i			0.767576i	0.923421	+	0.383788i	$0.125381\pi$
$191$			10.6081i			0.767576i	−0.923421	+	0.383788i	$0.874619\pi$
$192$	−42.1996	+	17.4797i	−3.04550	+	1.26149i
$193$	−3.72173	+	8.98505i	−0.267896	+	0.646758i	−0.999384	−	0.0350962i	$-0.988826\pi$
$193$	−3.72173	+	8.98505i	−0.267896	+	0.646758i	0.731488	+	0.681854i	$0.238826\pi$
$194$	−0.663947	+	1.60291i	−0.0476686	+	0.115082i
$195$		0			0
$196$	−20.8384	+	20.8384i	−1.48846	+	1.48846i
$197$	−21.9840	−	9.10606i	−1.56629	−	0.648780i	−0.580125	−	0.814528i	$-0.696996\pi$
$197$	−21.9840	−	9.10606i	−1.56629	−	0.648780i	−0.986168	+	0.165748i	$0.946996\pi$
$198$	0.265138	−	0.640100i	0.0188426	−	0.0454899i
$199$	5.05440	+	12.2024i	0.358297	+	0.865006i	0.995540	+	0.0943427i	$0.0300749\pi$
$199$	5.05440	+	12.2024i	0.358297	+	0.865006i	−0.637243	+	0.770663i	$0.719925\pi$
$200$		0			0
$201$	−17.2948	+	7.16372i	−1.21988	+	0.505290i
$202$	14.3848	−	14.3848i	1.01211	−	1.01211i
$203$		−	0.416650i		−	0.0292431i
$204$	−26.4394	+	22.6276i	−1.85113	+	1.58425i
$205$		0			0
$206$	−26.2322	−	26.2322i	−1.82768	−	1.82768i
$207$	1.58423	+	3.82466i	0.110111	+	0.265832i
$208$	−84.1541			−5.83504
$209$	0.0214556	+	0.0517984i	0.00148411	+	0.00358297i
$210$		0			0
$211$	−7.61020	+	18.3726i	−0.523907	+	1.26482i	0.411551	+	0.911387i	$0.364987\pi$
$211$	−7.61020	+	18.3726i	−0.523907	+	1.26482i	−0.935458	+	0.353438i	$0.885013\pi$
$212$	5.95294	+	5.95294i	0.408850	+	0.408850i
$213$	−5.27765	−	5.27765i	−0.361619	−	0.361619i
$214$	9.69117	−	23.3966i	0.662475	−	1.59936i
$215$		0			0
$216$	−20.1522	−	48.6516i	−1.37118	−	3.31032i
$217$	0.765828			0.0519878
$218$	−16.4127	−	39.6238i	−1.11161	−	2.68367i
$219$	−3.17256	−	3.17256i	−0.214382	−	0.214382i
$220$		0			0
$221$	−22.2026	+	7.23888i	−1.49351	+	0.486940i
$222$			37.3282i			2.50530i
$223$	4.49940	−	4.49940i	0.301302	−	0.301302i	−0.540221	−	0.841523i	$-0.681659\pi$
$223$	4.49940	−	4.49940i	0.301302	−	0.301302i	0.841523	+	0.540221i	$0.181659\pi$
$224$	25.3455	−	10.4984i	1.69347	−	0.701456i
$225$		0			0
$226$	1.30286	+	3.14538i	0.0866648	+	0.209227i
$227$	−10.1548	+	24.5160i	−0.674001	+	1.62718i	0.100747	+	0.994912i	$0.467877\pi$
$227$	−10.1548	+	24.5160i	−0.674001	+	1.62718i	−0.774748	+	0.632270i	$0.782123\pi$
$228$	1.04603	+	0.433278i	0.0692748	+	0.0286946i
$229$	10.9924	−	10.9924i	0.726395	−	0.726395i	−0.243504	−	0.969900i	$-0.578297\pi$
$229$	10.9924	−	10.9924i	0.726395	−	0.726395i	0.969900	+	0.243504i	$0.0782970\pi$
$230$		0			0
$231$	0.312851	−	0.755290i	0.0205841	−	0.0496944i
$232$	1.19006	−	2.87306i	0.0781314	−	0.188626i
$233$	−3.51327	+	1.45524i	−0.230162	+	0.0953363i	−0.494784	−	0.869016i	$-0.664753\pi$
$233$	−3.51327	+	1.45524i	−0.230162	+	0.0953363i	0.264622	+	0.964352i	$0.414753\pi$
$234$		−	9.38897i		−	0.613776i
$235$		0			0
$236$	5.44399	+	5.44399i	0.354374	+	0.354374i
$237$		−	6.71002i		−	0.435863i
$238$	10.8158	−	9.25647i	0.701082	−	0.600008i
$239$	5.80679			0.375610			0.187805	−	0.982206i	$-0.439863\pi$
$239$	5.80679			0.375610			0.187805	+	0.982206i	$0.439863\pi$
$240$		0			0
$241$	8.06359	−	3.34005i	0.519421	−	0.215151i	−0.107541	−	0.994201i	$-0.534298\pi$
$241$	8.06359	−	3.34005i	0.519421	−	0.215151i	0.626963	+	0.779049i	$0.284298\pi$
$242$	−29.5597			−1.90017
$243$	5.73233	−	2.37441i	0.367729	−	0.152319i
$244$	−39.3441	−	16.2969i	−2.51875	−	1.04330i
$245$		0			0
$246$	4.87960	−	4.87960i	0.311112	−	0.311112i
$247$	0.537243	+	0.537243i	0.0341840	+	0.0341840i
$248$	5.28087	+	2.18741i	0.335336	+	0.138901i
$249$	6.27689	+	2.59997i	0.397781	+	0.164766i
$250$		0			0
$251$		−	15.2424i		−	0.962093i	−0.876695	−	0.481047i	$-0.840257\pi$
$251$		−	15.2424i		−	0.962093i	0.876695	−	0.481047i	$-0.159743\pi$
$252$	1.60279	+	3.86949i	0.100967	+	0.243755i
$253$	−2.01535	+	2.01535i	−0.126704	+	0.126704i
$254$	−48.6467			−3.05236
$255$		0			0
$256$	42.6224			2.66390
$257$	−10.2772	+	10.2772i	−0.641077	+	0.641077i	−0.950820	−	0.309743i	$-0.899757\pi$
$257$	−10.2772	+	10.2772i	−0.641077	+	0.641077i	0.309743	+	0.950820i	$0.399757\pi$
$258$	3.22889	+	7.79524i	0.201022	+	0.485310i
$259$		−	11.1742i		−	0.694331i
$260$		0			0
$261$	0.184810	+	0.0765508i	0.0114395	+	0.00473838i
$262$	11.2826	+	4.67342i	0.697043	+	0.288725i
$263$	13.4550	+	13.4550i	0.829671	+	0.829671i	0.987471	−	0.157800i	$-0.0504401\pi$
$263$	13.4550	+	13.4550i	0.829671	+	0.829671i	−0.157800	+	0.987471i	$0.550440\pi$
$264$	4.31462	−	4.31462i	0.265546	−	0.265546i
$265$		0			0
$266$	−0.427906	−	0.177244i	−0.0262366	−	0.0108676i
$267$	7.12726	−	2.95221i	0.436181	−	0.180672i
$268$	66.0278			4.03329
$269$	−20.9581	+	8.68112i	−1.27784	+	0.529297i	−0.915338	−	0.402687i	$-0.868076\pi$
$269$	−20.9581	+	8.68112i	−1.27784	+	0.529297i	−0.362499	+	0.931984i	$0.618076\pi$
$270$		0			0
$271$	9.96764			0.605491			0.302745	−	0.953071i	$-0.402097\pi$
$271$	9.96764			0.605491			0.302745	+	0.953071i	$0.402097\pi$
$272$	58.2435	−	18.9896i	3.53153	−	1.15141i
$273$		−	11.0786i		−	0.670506i
$274$	17.4724	+	17.4724i	1.05555	+	1.05555i
$275$		0			0
$276$			57.5562i			3.46448i
$277$	10.8160	−	4.48012i	0.649868	−	0.269184i	−0.0332998	−	0.999445i	$-0.510602\pi$
$277$	10.8160	−	4.48012i	0.649868	−	0.269184i	0.683168	+	0.730261i	$0.260602\pi$
$278$	−4.91210	+	11.8589i	−0.294608	+	0.711247i
$279$	−0.140705	+	0.339693i	−0.00842380	+	0.0203369i
$280$		0			0
$281$	−0.838071	+	0.838071i	−0.0499951	+	0.0499951i	−0.731662	−	0.681667i	$-0.761255\pi$
$281$	−0.838071	+	0.838071i	−0.0499951	+	0.0499951i	0.681667	+	0.731662i	$0.261255\pi$
$282$	−19.7564	−	8.18335i	−1.17647	−	0.487311i
$283$	1.76449	−	4.25986i	0.104888	−	0.253222i	−0.862719	−	0.505684i	$-0.831240\pi$
$283$	1.76449	−	4.25986i	0.104888	−	0.253222i	0.967607	+	0.252462i	$0.0812402\pi$
$284$	10.0745	+	24.3220i	0.597812	+	1.44324i
$285$		0			0
$286$	5.97202	−	2.47369i	0.353133	−	0.146273i
$287$	−1.46071	+	1.46071i	−0.0862228	+	0.0862228i
$288$			13.1712i			0.776118i
$289$	13.7331	−	10.0201i	0.807827	−	0.589420i
$290$		0			0
$291$	−0.694998	−	0.694998i	−0.0407415	−	0.0407415i
$292$	6.05609	+	14.6207i	0.354406	+	0.855612i
$293$	−3.09527			−0.180828			−0.0904138	−	0.995904i	$-0.528819\pi$
$293$	−3.09527			−0.180828			−0.0904138	+	0.995904i	$0.528819\pi$
$294$	−8.73073	−	21.0778i	−0.509186	−	1.22928i
$295$		0			0
$296$	31.9165	−	77.0531i	1.85511	−	4.47862i
$297$	1.64906	+	1.64906i	0.0956879	+	0.0956879i
$298$	−1.49823	−	1.49823i	−0.0867900	−	0.0867900i
$299$	−14.7805	+	35.6834i	−0.854781	+	2.06362i
$300$		0			0
$301$	−0.966569	−	2.33350i	−0.0557121	−	0.134501i
$302$	6.24524			0.359373
$303$	4.41024	+	10.6473i	0.253362	+	0.611670i
$304$	−1.40934	−	1.40934i	−0.0808310	−	0.0808310i
$305$		0			0
$306$	2.11864	+	6.49815i	0.121115	+	0.371475i
$307$			11.8387i			0.675668i	0.941206	+	0.337834i	$0.109694\pi$
$307$			11.8387i			0.675668i	−0.941206	+	0.337834i	$0.890306\pi$
$308$	−2.03897	+	2.03897i	−0.116181	+	0.116181i
$309$	19.4165	−	8.04256i	1.10456	−	0.457525i
$310$		0			0
$311$	8.97392	+	21.6650i	0.508864	+	1.22851i	0.944538	+	0.328402i	$0.106510\pi$
$311$	8.97392	+	21.6650i	0.508864	+	1.22851i	−0.435674	+	0.900105i	$0.643490\pi$
$312$	31.6433	−	76.3938i	1.79145	−	4.32494i
$313$	−25.5068	−	10.5652i	−1.44173	−	0.597183i	−0.481511	−	0.876440i	$-0.659912\pi$
$313$	−25.5068	−	10.5652i	−1.44173	−	0.597183i	−0.960216	+	0.279257i	$0.909912\pi$
$314$	36.9047	−	36.9047i	2.08265	−	2.08265i
$315$		0			0
$316$	−9.05715	+	21.8659i	−0.509505	+	1.23005i
$317$	12.1926	−	29.4357i	0.684807	−	1.65327i	−0.0701822	−	0.997534i	$-0.522358\pi$
$317$	12.1926	−	29.4357i	0.684807	−	1.65327i	0.754989	−	0.655737i	$-0.227642\pi$
$318$	−6.02135	+	2.49412i	−0.337660	+	0.139864i
$319$			0.137720i			0.00771087i
$320$		0			0
$321$	10.1444	+	10.1444i	0.566206	+	0.566206i
$322$		−	23.5449i		−	1.31211i
$323$	−0.493059	−	0.250599i	−0.0274345	−	0.0139437i
$324$	37.1582			2.06434
$325$		0			0
$326$	−46.2409	+	19.1536i	−2.56104	+	1.06082i
$327$	24.2966			1.34361
$328$	−14.2447	+	5.90033i	−0.786530	+	0.325791i
$329$	5.91406	+	2.44968i	0.326053	+	0.135055i
$330$		0			0
$331$	18.4377	−	18.4377i	1.01343	−	1.01343i	0.0135172	−	0.999909i	$-0.495697\pi$
$331$	18.4377	−	18.4377i	1.01343	−	1.01343i	0.999909	−	0.0135172i	$-0.00430279\pi$
$332$	−16.9450	−	16.9450i	−0.929978	−	0.929978i
$333$	4.95645	+	2.05303i	0.271612	+	0.112505i
$334$	−50.8294	−	21.0542i	−2.78126	−	1.15204i
$335$		0			0
$336$			29.0621i			1.58547i
$337$	6.32145	+	15.2613i	0.344351	+	0.831338i	0.997265	+	0.0739055i	$0.0235463\pi$
$337$	6.32145	+	15.2613i	0.344351	+	0.831338i	−0.652914	+	0.757432i	$0.726454\pi$
$338$	36.8399	−	36.8399i	2.00383	−	2.00383i
$339$	−1.92869			−0.104752
$340$		0			0
$341$	−0.253139			−0.0137082
$342$	0.157238	−	0.157238i	0.00850245	−	0.00850245i
$343$	6.00074	+	14.4871i	0.324010	+	0.782229i
$344$		−	18.8518i		−	1.01642i
$345$		0			0
$346$	−48.2208	−	19.9737i	−2.59237	−	1.07379i
$347$	−18.7774	−	7.77787i	−1.00803	−	0.417538i	−0.183292	−	0.983059i	$-0.558675\pi$
$347$	−18.7774	−	7.77787i	−1.00803	−	0.417538i	−0.824734	+	0.565521i	$0.808675\pi$
$348$	1.96657	+	1.96657i	0.105419	+	0.105419i
$349$	−3.45460	+	3.45460i	−0.184921	+	0.184921i	−0.793496	−	0.608575i	$-0.791741\pi$
$349$	−3.45460	+	3.45460i	−0.184921	+	0.184921i	0.608575	+	0.793496i	$0.291741\pi$
$350$		0			0
$351$	29.1979	+	12.0941i	1.55847	+	0.645538i
$352$	−8.37776	+	3.47018i	−0.446536	+	0.184961i
$353$	−22.6733			−1.20678			−0.603389	−	0.797447i	$-0.706183\pi$
$353$	−22.6733			−1.20678			−0.603389	+	0.797447i	$0.706183\pi$
$354$	−5.50655	+	2.28089i	−0.292670	+	0.121228i
$355$		0			0
$356$	−27.2104			−1.44215
$357$	2.49990	+	7.66753i	0.132309	+	0.405809i
$358$			54.1080i			2.85970i
$359$	−9.53237	−	9.53237i	−0.503099	−	0.503099i	0.409300	−	0.912400i	$-0.365773\pi$
$359$	−9.53237	−	9.53237i	−0.503099	−	0.503099i	−0.912400	+	0.409300i	$0.865773\pi$
$360$		0			0
$361$		−	18.9820i		−	0.999053i
$362$	22.3656	−	9.26413i	1.17551	−	0.486912i
$363$	6.40833	−	15.4711i	0.336350	−	0.812021i
$364$	−14.9538	+	36.1017i	−0.783792	+	1.89224i
$365$		0			0
$366$	23.3121	−	23.3121i	1.21854	−	1.21854i
$367$	−1.76542	−	0.731262i	−0.0921543	−	0.0381715i	0.336130	−	0.941816i	$-0.390882\pi$
$367$	−1.76542	−	0.731262i	−0.0921543	−	0.0381715i	−0.428284	+	0.903644i	$0.640882\pi$
$368$	38.7734	−	93.6073i	2.02120	−	4.87962i
$369$	−0.379540	−	0.916289i	−0.0197580	−	0.0477001i
$370$		0			0
$371$	1.80249	−	0.746616i	0.0935806	−	0.0387624i
$372$	−3.61468	+	3.61468i	−0.187413	+	0.187413i
$373$			24.9357i			1.29112i	0.763708	+	0.645562i	$0.223377\pi$
$373$			24.9357i			1.29112i	−0.763708	+	0.645562i	$0.776623\pi$
$374$	−3.57507	+	3.05966i	−0.184863	+	0.158211i
$375$		0			0
$376$	33.7843	+	33.7843i	1.74229	+	1.74229i
$377$	0.714206	+	1.72425i	0.0367835	+	0.0888032i
$378$	−19.2656			−0.990916
$379$	6.35332	+	15.3383i	0.326348	+	0.787874i	0.998858	+	0.0477856i	$0.0152164\pi$
$379$	6.35332	+	15.3383i	0.326348	+	0.787874i	−0.672509	+	0.740089i	$0.734784\pi$
$380$		0			0
$381$	10.5462	−	25.4609i	0.540300	−	1.30440i
$382$	20.4825	+	20.4825i	1.04797	+	1.04797i
$383$	14.2058	+	14.2058i	0.725883	+	0.725883i	0.969797	−	0.243914i	$-0.0784315\pi$
$383$	14.2058	+	14.2058i	0.725883	+	0.725883i	−0.243914	+	0.969797i	$0.578432\pi$
$384$	−22.0430	+	53.2164i	−1.12488	+	2.71569i
$385$		0			0
$386$	10.1626	+	24.5347i	0.517262	+	1.24878i
$387$	1.21264			0.0616420
$388$	1.32668	+	3.20289i	0.0673520	+	0.162602i
$389$	−15.7531	−	15.7531i	−0.798715	−	0.798715i	0.184178	−	0.982893i	$-0.441038\pi$
$389$	−15.7531	−	15.7531i	−0.798715	−	0.798715i	−0.982893	+	0.184178i	$0.941038\pi$
$390$		0			0
$391$	2.17765	−	28.0319i	0.110129	−	1.41764i
$392$			50.9740i			2.57458i
$393$	−4.89198	+	4.89198i	−0.246768	+	0.246768i
$394$	−60.0296	+	24.8651i	−3.02425	+	1.25268i
$395$		0			0
$396$	−0.529792	−	1.27903i	−0.0266230	−	0.0642737i
$397$	10.0530	−	24.2702i	0.504548	−	1.21809i	−0.442435	−	0.896801i	$-0.645885\pi$
$397$	10.0530	−	24.2702i	0.504548	−	1.21809i	0.946983	−	0.321285i	$-0.104115\pi$
$398$	33.3200	+	13.8016i	1.67018	+	0.691812i
$399$	0.185534	−	0.185534i	0.00928831	−	0.00928831i
$400$		0			0
$401$	14.6020	−	35.2524i	0.729191	−	1.76042i	0.0839140	−	0.996473i	$-0.473258\pi$
$401$	14.6020	−	35.2524i	0.729191	−	1.76042i	0.645277	−	0.763949i	$-0.276742\pi$
$402$	−19.5613	+	47.2252i	−0.975630	+	2.35538i
$403$	−3.16927	+	1.31276i	−0.157873	+	0.0653930i
$404$		−	40.6491i		−	2.02237i
$405$		0			0
$406$	−0.804481	−	0.804481i	−0.0399257	−	0.0399257i
$407$			3.69355i			0.183082i
$408$	−4.66208	+	60.0129i	−0.230807	+	2.97108i
$409$	19.0995			0.944411			0.472206	−	0.881488i	$-0.343458\pi$
$409$	19.0995			0.944411			0.472206	+	0.881488i	$0.343458\pi$
$410$		0			0
$411$	−12.9327	+	5.35689i	−0.637921	+	0.264236i
$412$	−74.1281			−3.65203
$413$	1.64838	−	0.682783i	0.0811117	−	0.0335976i
$414$	10.4436	+	4.32590i	0.513277	+	0.212606i
$415$		0			0
$416$	−86.8926	+	86.8926i	−4.26026	+	4.26026i
$417$	−5.14183	−	5.14183i	−0.251796	−	0.251796i
$418$	0.141441	+	0.0585868i	0.00691811	+	0.00286558i
$419$	30.9970	+	12.8394i	1.51430	+	0.627244i	0.976440	−	0.215790i	$-0.0692327\pi$
$419$	30.9970	+	12.8394i	1.51430	+	0.627244i	0.537860	+	0.843034i	$0.319233\pi$
$420$		0			0
$421$			18.9396i			0.923058i	0.887125	+	0.461529i	$0.152699\pi$
$421$			18.9396i			0.923058i	−0.887125	+	0.461529i	$0.847301\pi$
$422$	20.7805	+	50.1685i	1.01158	+	2.44216i
$423$	−2.17317	+	2.17317i	−0.105663	+	0.105663i
$424$	14.5618			0.707186
$425$		0			0
$426$	−20.3805			−0.987440
$427$	−6.97847	+	6.97847i	−0.337712	+	0.337712i
$428$	−19.3646	−	46.7504i	−0.936025	−	2.25976i
$429$			3.66194i			0.176800i
$430$		0			0
$431$	22.5308	+	9.33254i	1.08527	+	0.449533i	0.852354	−	0.522965i	$-0.175174\pi$
$431$	22.5308	+	9.33254i	1.08527	+	0.449533i	0.232914	+	0.972497i	$0.425174\pi$
$432$	−76.5940	−	31.7263i	−3.68513	−	1.52643i
$433$	6.85275	+	6.85275i	0.329322	+	0.329322i	0.852329	−	0.523007i	$-0.175190\pi$
$433$	6.85275	+	6.85275i	0.329322	+	0.329322i	−0.523007	+	0.852329i	$0.675190\pi$
$434$	1.47869	−	1.47869i	0.0709792	−	0.0709792i
$435$		0			0
$436$	−79.1753	−	32.7955i	−3.79181	−	1.57062i
$437$	−0.845124	+	0.350062i	−0.0404278	+	0.0167457i
$438$	−12.2514			−0.585393
$439$	−2.97814	+	1.23359i	−0.142139	+	0.0588759i	−0.452619	−	0.891704i	$-0.649510\pi$
$439$	−2.97814	+	1.23359i	−0.142139	+	0.0588759i	0.310480	+	0.950580i	$0.399510\pi$
$440$		0			0
$441$	−3.27891			−0.156138
$442$	−28.8924	+	56.8466i	−1.37427	+	2.70392i
$443$			17.5623i			0.834412i	0.908812	+	0.417206i	$0.136991\pi$
$443$			17.5623i			0.834412i	−0.908812	+	0.417206i	$0.863009\pi$
$444$	52.7418	+	52.7418i	2.50302	+	2.50302i
$445$		0			0
$446$		−	17.3752i		−	0.822739i
$447$	1.10895	−	0.459344i	0.0524517	−	0.0217262i
$448$	14.2880	−	34.4943i	0.675045	−	1.62970i
$449$	−7.08856	+	17.1133i	−0.334530	+	0.807626i	0.663691	+	0.748007i	$0.268989\pi$
$449$	−7.08856	+	17.1133i	−0.334530	+	0.807626i	−0.998221	+	0.0596199i	$0.981011\pi$
$450$		0			0
$451$	0.482826	−	0.482826i	0.0227354	−	0.0227354i
$452$	6.28500	+	2.60333i	0.295622	+	0.122451i
$453$	−1.35392	+	3.26866i	−0.0636128	+	0.153575i
$454$	27.7289	+	66.9435i	1.30138	+	3.14182i
$455$		0			0
$456$	1.80931	−	0.749439i	0.0847285	−	0.0350957i
$457$	10.3999	−	10.3999i	0.486487	−	0.486487i	−0.420709	−	0.907196i	$-0.638219\pi$
$457$	10.3999	−	10.3999i	0.486487	−	0.486487i	0.907196	+	0.420709i	$0.138219\pi$
$458$		−	42.4488i		−	1.98350i
$459$	−22.9371	−	1.78186i	−1.07061	−	0.0831700i
$460$		0			0
$461$	12.6921	+	12.6921i	0.591131	+	0.591131i	0.937937	−	0.346806i	$-0.112734\pi$
$461$	12.6921	+	12.6921i	0.591131	+	0.591131i	−0.346806	+	0.937937i	$0.612734\pi$
$462$	−0.854275	−	2.06240i	−0.0397445	−	0.0959516i
$463$	35.5792			1.65350			0.826752	−	0.562567i	$-0.190186\pi$
$463$	35.5792			1.65350			0.826752	+	0.562567i	$0.190186\pi$
$464$	−1.87356	−	4.52317i	−0.0869778	−	0.209983i
$465$		0			0
$466$	−3.97371	+	9.59337i	−0.184078	+	0.444404i
$467$	−20.8180	−	20.8180i	−0.963342	−	0.963342i	0.0360098	−	0.999351i	$-0.488535\pi$
$467$	−20.8180	−	20.8180i	−0.963342	−	0.963342i	−0.999351	+	0.0360098i	$0.988535\pi$
$468$	−13.2659	−	13.2659i	−0.613215	−	0.613215i
$469$	5.85568	−	14.1369i	0.270390	−	0.652780i
$470$		0			0
$471$	11.3147	+	27.3160i	0.521352	+	1.25866i
$472$	13.3169			0.612959
$473$	0.319492	+	0.771322i	0.0146903	+	0.0354654i
$474$	−12.9559	−	12.9559i	−0.595086	−	0.595086i
$475$		0			0
$476$	2.20318	−	28.3605i	0.100982	−	1.29990i
$477$			0.936692i			0.0428882i
$478$	11.2119	−	11.2119i	0.512822	−	0.512822i
$479$	15.4620	−	6.40457i	0.706477	−	0.292632i	−0.000368864	−	1.00000i	$-0.500117\pi$
$479$	15.4620	−	6.40457i	0.706477	−	0.292632i	0.706846	+	0.707368i	$0.250117\pi$
$480$		0			0
$481$	19.1544	+	46.2428i	0.873365	+	2.10849i
$482$	9.12036	−	22.0185i	0.415421	−	1.00292i
$483$	12.3230	+	5.10437i	0.560718	+	0.232257i
$484$	−41.7655	+	41.7655i	−1.89843	+	1.89843i
$485$		0			0
$486$	6.48359	−	15.6528i	0.294102	−	0.710024i
$487$	8.97101	−	21.6579i	0.406515	−	0.981415i	−0.579532	−	0.814950i	$-0.696765\pi$
$487$	8.97101	−	21.6579i	0.406515	−	0.981415i	0.986047	−	0.166466i	$-0.0532355\pi$
$488$	−68.0533	+	28.1886i	−3.08063	+	1.27604i
$489$		−	28.3541i		−	1.28222i
$490$		0			0
$491$	−18.0226	−	18.0226i	−0.813347	−	0.813347i	0.171787	−	0.985134i	$-0.445046\pi$
$491$	−18.0226	−	18.0226i	−0.813347	−	0.813347i	−0.985134	+	0.171787i	$0.945046\pi$
$492$		−	13.7890i		−	0.621655i
$493$	−0.883386	−	1.03220i	−0.0397857	−	0.0464878i
$494$	2.07465			0.0933431
$495$		0			0
$496$	8.31387	−	3.44372i	0.373304	−	0.154627i
$497$	6.10091			0.273663
$498$	17.1397	−	7.09951i	0.768049	−	0.318136i
$499$	−26.5542	−	10.9991i	−1.18873	−	0.492388i	−0.301388	−	0.953502i	$-0.597450\pi$
$499$	−26.5542	−	10.9991i	−1.18873	−	0.492388i	−0.887341	+	0.461114i	$0.847450\pi$
$500$		0			0
$501$	22.0389	−	22.0389i	0.984625	−	0.984625i
$502$	−29.4306	−	29.4306i	−1.31355	−	1.31355i
$503$	−0.00950252	−	0.00393607i	−0.000423697	−	0.000175501i	0.382472	−	0.923967i	$-0.375073\pi$
$503$	−0.00950252	−	0.00393607i	−0.000423697	−	0.000175501i	−0.382895	+	0.923792i	$0.625073\pi$
$504$	6.69303	+	2.77235i	0.298131	+	0.123490i
$505$		0			0
$506$			7.78261i			0.345979i
$507$	11.2948	+	27.2680i	0.501619	+	1.21102i
$508$	−68.7339	+	68.7339i	−3.04957	+	3.04957i
$509$	26.8066			1.18818			0.594091	−	0.804398i	$-0.297512\pi$
$509$	26.8066			1.18818			0.594091	+	0.804398i	$0.297512\pi$
$510$		0			0
$511$	3.66744			0.162238
$512$	29.6367	−	29.6367i	1.30977	−	1.30977i
$513$	0.286437	+	0.691521i	0.0126465	+	0.0305314i
$514$			39.6873i			1.75053i
$515$		0			0
$516$	15.5762	+	6.45189i	0.685705	+	0.284028i
$517$	−1.95485	−	0.809725i	−0.0859742	−	0.0356117i
$518$	−21.5755	−	21.5755i	−0.947973	−	0.947973i
$519$	20.9078	−	20.9078i	0.917752	−	0.917752i
$520$		0			0
$521$	9.37063	+	3.88144i	0.410535	+	0.170049i	0.578386	−	0.815763i	$-0.303683\pi$
$521$	9.37063	+	3.88144i	0.410535	+	0.170049i	−0.167851	+	0.985812i	$0.553683\pi$
$522$	0.504644	−	0.209030i	0.0220877	−	0.00914902i
$523$	16.7568			0.732724			0.366362	−	0.930472i	$-0.380603\pi$
$523$	16.7568			0.732724			0.366362	+	0.930472i	$0.380603\pi$
$524$	22.5446	−	9.33830i	0.984867	−	0.407945i
$525$		0			0
$526$	51.9587			2.26551
$527$	1.89724	−	1.62372i	0.0826452	−	0.0707303i
$528$		−	9.60627i		−	0.418059i
$529$	−16.6183	−	16.6183i	−0.722534	−	0.722534i
$530$		0			0
$531$			0.856609i			0.0371736i
$532$	−0.855030	+	0.354165i	−0.0370702	+	0.0153550i
$533$	3.54104	−	8.54882i	0.153379	−	0.370291i
$534$	8.06133	−	19.4618i	0.348848	−	0.842193i
$535$		0			0
$536$	80.7572	−	80.7572i	3.48818	−	3.48818i
$537$	−28.3193	−	11.7302i	−1.22207	−	0.506196i
$538$	−23.7048	+	57.2283i	−1.02198	+	2.46729i
$539$	−0.863887	−	2.08561i	−0.0372102	−	0.0898335i
$540$		0			0
$541$	−16.7559	+	6.94050i	−0.720390	+	0.298395i	−0.712596	−	0.701574i	$-0.752481\pi$
$541$	−16.7559	+	6.94050i	−0.720390	+	0.298395i	−0.00779397	+	0.999970i	$0.502481\pi$
$542$	19.2458	−	19.2458i	0.826679	−	0.826679i
$543$			13.7142i			0.588532i
$544$	40.5313	−	79.7463i	1.73776	−	3.41909i
$545$		0			0
$546$	−21.3909	−	21.3909i	−0.915444	−	0.915444i
$547$	8.63943	+	20.8574i	0.369395	+	0.891799i	0.993850	+	0.110738i	$0.0353215\pi$
$547$	8.63943	+	20.8574i	0.369395	+	0.891799i	−0.624454	+	0.781061i	$0.714679\pi$
$548$	49.3743			2.10916
$549$	−1.81323	−	4.37753i	−0.0773869	−	0.186829i
$550$		0			0
$551$	−0.0169152	+	0.0408370i	−0.000720613	+	0.00173971i
$552$	70.3958	+	70.3958i	2.99624	+	2.99624i
$553$	3.87836	+	3.87836i	0.164925	+	0.164925i
$554$	12.2335	−	29.5342i	0.519750	−	1.25479i
$555$		0			0
$556$	9.81523	+	23.6960i	0.416258	+	1.00494i
$557$	5.97545			0.253188			0.126594	−	0.991955i	$-0.459595\pi$
$557$	5.97545			0.253188			0.126594	+	0.991955i	$0.459595\pi$
$558$	0.384211	+	0.927568i	0.0162650	+	0.0392671i
$559$	8.00002	+	8.00002i	0.338365	+	0.338365i
$560$		0			0
$561$	−0.826325	−	2.53445i	−0.0348875	−	0.107004i
$562$			3.23635i			0.136517i
$563$	−2.52298	+	2.52298i	−0.106331	+	0.106331i	−0.758271	−	0.651940i	$-0.773955\pi$
$563$	−2.52298	+	2.52298i	−0.106331	+	0.106331i	0.651940	+	0.758271i	$0.273955\pi$
$564$	−39.4766	+	16.3517i	−1.66226	+	0.688533i
$565$		0			0
$566$	−4.81814	−	11.6320i	−0.202521	−	0.488930i
$567$	3.29538	−	7.95574i	0.138393	−	0.334110i
$568$	42.0696	+	17.4258i	1.76520	+	0.731171i
$569$	−31.1965	+	31.1965i	−1.30783	+	1.30783i	−0.384846	+	0.922981i	$0.625746\pi$
$569$	−31.1965	+	31.1965i	−1.30783	+	1.30783i	−0.922981	+	0.384846i	$0.874254\pi$
$570$		0			0
$571$	−4.81154	+	11.6161i	−0.201357	+	0.486118i	−0.992012	−	0.126143i	$-0.959740\pi$
$571$	−4.81154	+	11.6161i	−0.201357	+	0.486118i	0.790655	+	0.612262i	$0.209740\pi$
$572$	4.94287	−	11.9331i	0.206672	−	0.498949i
$573$	−15.1606	+	6.27975i	−0.633345	+	0.262340i
$574$			5.64076i			0.235441i
$575$		0			0
$576$	12.6752	+	12.6752i	0.528135	+	0.528135i
$577$			14.5344i			0.605075i	0.953137	+	0.302538i	$0.0978338\pi$
$577$			14.5344i			0.605075i	−0.953137	+	0.302538i	$0.902166\pi$
$578$	7.16904	−	45.8634i	0.298193	−	1.90767i
$579$	−15.0442			−0.625217
$580$		0			0
$581$	−5.13077	+	2.12524i	−0.212860	+	0.0881697i
$582$	−2.68385			−0.111249
$583$	−0.595800	+	0.246788i	−0.0246755	+	0.0102209i
$584$	25.2894	+	10.4752i	1.04648	+	0.433467i
$585$		0			0
$586$	−5.97645	+	5.97645i	−0.246885	+	0.246885i
$587$	8.63007	+	8.63007i	0.356201	+	0.356201i	0.862411	−	0.506209i	$-0.168954\pi$
$587$	8.63007	+	8.63007i	0.356201	+	0.356201i	−0.506209	+	0.862411i	$0.668954\pi$
$588$	−42.1172	−	17.4455i	−1.73688	−	0.719440i
$589$	−0.0750609	−	0.0310912i	−0.00309283	−	0.00128109i
$590$		0			0
$591$		−	36.8091i		−	1.51412i
$592$	−50.2472	−	121.308i	−2.06515	−	4.98571i
$593$	8.08169	−	8.08169i	0.331875	−	0.331875i	−0.521423	−	0.853298i	$-0.674599\pi$
$593$	8.08169	−	8.08169i	0.331875	−	0.331875i	0.853298	+	0.521423i	$0.174599\pi$
$594$	6.36810			0.261286
$595$		0			0
$596$	−4.23376			−0.173421
$597$	−14.4471	+	14.4471i	−0.591279	+	0.591279i
$598$	40.3599	+	97.4374i	1.65044	+	3.98451i
$599$			27.2578i			1.11372i	0.830606	+	0.556861i	$0.187994\pi$
$599$			27.2578i			1.11372i	−0.830606	+	0.556861i	$0.812006\pi$
$600$		0			0
$601$	−10.3510	−	4.28754i	−0.422228	−	0.174893i	0.161444	−	0.986882i	$-0.448385\pi$
$601$	−10.3510	−	4.28754i	−0.422228	−	0.174893i	−0.583672	+	0.811989i	$0.698385\pi$
$602$	−6.37189	−	2.63932i	−0.259699	−	0.107571i
$603$	5.19472	+	5.19472i	0.211545	+	0.211545i
$604$	8.82403	−	8.82403i	0.359045	−	0.359045i
$605$		0			0
$606$	29.0735	+	12.0427i	1.18103	+	0.489199i
$607$	36.9992	−	15.3256i	1.50175	−	0.622046i	0.527915	−	0.849297i	$-0.322974\pi$
$607$	36.9992	−	15.3256i	1.50175	−	0.622046i	0.973836	+	0.227252i	$0.0729739\pi$
$608$	−2.91039			−0.118032
$609$	0.595458	−	0.246647i	0.0241292	−	0.00999463i
$610$		0			0
$611$	−28.6737			−1.16001
$612$	12.1749	+	6.18790i	0.492139	+	0.250131i
$613$		−	29.1043i		−	1.17551i	−0.809039	−	0.587755i	$-0.800012\pi$
$613$		−	29.1043i		−	1.17551i	0.809039	−	0.587755i	$-0.199988\pi$
$614$	22.8585	+	22.8585i	0.922493	+	0.922493i
$615$		0			0
$616$			4.98765i			0.200958i
$617$	−15.2120	+	6.30101i	−0.612411	+	0.253669i	−0.667259	−	0.744826i	$-0.732533\pi$
$617$	−15.2120	+	6.30101i	−0.612411	+	0.253669i	0.0548478	+	0.998495i	$0.482533\pi$
$618$	21.9611	−	53.0188i	0.883405	−	2.13273i
$619$	−2.91366	+	7.03419i	−0.117110	+	0.282728i	−0.971555	−	0.236813i	$-0.923897\pi$
$619$	−2.91366	+	7.03419i	−0.117110	+	0.282728i	0.854445	+	0.519541i	$0.173897\pi$
$620$		0			0
$621$	−26.9054	+	26.9054i	−1.07968	+	1.07968i
$622$	59.1585	+	24.5043i	2.37204	+	0.982532i
$623$	−2.41316	+	5.82588i	−0.0966811	+	0.233409i
$624$	−49.8172	−	120.269i	−1.99429	−	4.81463i
$625$		0			0
$626$	−69.6490	+	28.8496i	−2.78373	+	1.15306i
$627$	−0.0613268	+	0.0613268i	−0.00244916	+	0.00244916i
$628$		−	104.287i		−	4.16150i
$629$	−23.6916	−	27.6826i	−0.944648	−	1.10378i
$630$		0			0
$631$	−26.3010	−	26.3010i	−1.04703	−	1.04703i	−0.998838	−	0.0481871i	$-0.984656\pi$
$631$	−26.3010	−	26.3010i	−1.04703	−	1.04703i	−0.0481871	−	0.998838i	$-0.515344\pi$
$632$	15.6661	+	37.8213i	0.623165	+	1.50445i
$633$	−30.7624			−1.22270
$634$	−33.2934	−	80.3773i	−1.32225	−	3.19219i
$635$		0			0
$636$	−4.98369	+	12.0317i	−0.197616	+	0.477088i
$637$	−21.6315	−	21.6315i	−0.857073	−	0.857073i
$638$	0.265915	+	0.265915i	0.0105277	+	0.0105277i
$639$	−1.12092	+	2.70613i	−0.0443428	+	0.107053i
$640$		0			0
$641$	3.29555	+	7.95617i	0.130167	+	0.314250i	0.975504	−	0.219983i	$-0.0706003\pi$
$641$	3.29555	+	7.95617i	0.130167	+	0.314250i	−0.845337	+	0.534233i	$0.820600\pi$
$642$	39.1743			1.54609
$643$	−7.31804	−	17.6673i	−0.288595	−	0.696731i	0.711386	−	0.702801i	$-0.248068\pi$
$643$	−7.31804	−	17.6673i	−0.288595	−	0.696731i	−0.999982	+	0.00607035i	$0.998068\pi$
$644$	−33.2672	−	33.2672i	−1.31091	−	1.31091i
$645$		0			0
$646$	−1.43588	+	0.468150i	−0.0564939	+	0.0184191i
$647$		−	25.5972i		−	1.00633i	−0.864191	−	0.503164i	$-0.832169\pi$
$647$		−	25.5972i		−	1.00633i	0.864191	−	0.503164i	$-0.167831\pi$
$648$	45.4474	−	45.4474i	1.78534	−	1.78534i
$649$	−0.544861	+	0.225689i	−0.0213877	+	0.00885907i
$650$		0			0
$651$	0.453352	+	1.09449i	0.0177683	+	0.0428964i
$652$	−38.2722	+	92.3972i	−1.49885	+	3.61855i
$653$	−8.01379	−	3.31942i	−0.313604	−	0.129899i	0.220330	−	0.975425i	$-0.429287\pi$
$653$	−8.01379	−	3.31942i	−0.313604	−	0.129899i	−0.533933	+	0.845527i	$0.679287\pi$
$654$	46.9127	−	46.9127i	1.83443	−	1.83443i
$655$		0			0
$656$	−9.28911	+	22.4259i	−0.362679	+	0.875584i
$657$	−0.673818	+	1.62674i	−0.0262881	+	0.0634652i
$658$	16.1490	−	6.68913i	0.629553	−	0.260770i
$659$			36.0328i			1.40364i	0.712355	+	0.701819i	$0.247628\pi$
$659$			36.0328i			1.40364i	−0.712355	+	0.701819i	$0.752372\pi$
$660$		0			0
$661$	6.64994	+	6.64994i	0.258653	+	0.258653i	0.824506	−	0.565853i	$-0.191453\pi$
$661$	6.64994	+	6.64994i	0.258653	+	0.258653i	−0.565853	+	0.824506i	$0.691453\pi$
$662$		−	71.2001i		−	2.76727i
$663$	−23.4889	−	27.4458i	−0.912234	−	1.06590i
$664$	−41.4502			−1.60858
$665$		0			0
$666$	13.5341	−	5.60602i	0.524437	−	0.217229i
$667$	−2.24700			−0.0870041
$668$	−101.566	+	42.0700i	−3.92970	+	1.62774i
$669$	9.09389	+	3.76681i	0.351590	+	0.145633i
$670$		0			0
$671$	2.30668	−	2.30668i	0.0890484	−	0.0890484i
$672$	30.0078	+	30.0078i	1.15758	+	1.15758i
$673$	4.21250	+	1.74487i	0.162380	+	0.0672599i	0.462393	−	0.886675i	$-0.346991\pi$
$673$	4.21250	+	1.74487i	0.162380	+	0.0672599i	−0.300013	+	0.953935i	$0.596991\pi$
$674$	41.6727	+	17.2614i	1.60517	+	0.664885i
$675$		0			0
$676$		−	104.104i		−	4.00399i
$677$	13.6240	+	32.8914i	0.523615	+	1.26412i	0.935643	+	0.352947i	$0.114820\pi$
$677$	13.6240	+	32.8914i	0.523615	+	1.26412i	−0.412029	+	0.911171i	$0.635180\pi$
$678$	−3.72398	+	3.72398i	−0.143018	+	0.143018i
$679$	0.803410			0.0308321
$680$		0			0
$681$	−41.0486			−1.57299
$682$	−0.488769	+	0.488769i	−0.0187159	+	0.0187159i
$683$	4.58144	+	11.0606i	0.175304	+	0.423222i	0.986971	−	0.160899i	$-0.0514394\pi$
$683$	4.58144	+	11.0606i	0.175304	+	0.423222i	−0.811667	+	0.584121i	$0.801439\pi$
$684$		−	0.444329i		−	0.0169894i
$685$		0			0
$686$	39.5585	+	16.3857i	1.51035	+	0.625608i
$687$	22.2170	+	9.20259i	0.847632	+	0.351101i
$688$	−20.9862	−	20.9862i	−0.800093	−	0.800093i
$689$	−6.17953	+	6.17953i	−0.235421	+	0.235421i
$690$		0			0
$691$	19.2122	+	7.95793i	0.730865	+	0.302734i	0.716907	−	0.697169i	$-0.245557\pi$
$691$	19.2122	+	7.95793i	0.730865	+	0.302734i	0.0139574	+	0.999903i	$0.495557\pi$
$692$	−96.3535	+	39.9109i	−3.66281	+	1.51719i
$693$	−0.320831			−0.0121874
$694$	−51.2739	+	21.2383i	−1.94633	+	0.806196i
$695$		0			0
$696$	4.81055			0.182343
$697$	−0.521709	+	6.71572i	−0.0197611	+	0.254376i
$698$			13.3405i			0.504946i
$699$	−4.15955	−	4.15955i	−0.157328	−	0.157328i
$700$		0			0
$701$		−	13.1645i		−	0.497215i	−0.968604	−	0.248607i	$-0.920027\pi$
$701$		−	13.1645i		−	0.497215i	0.968604	−	0.248607i	$-0.0799729\pi$
$702$	79.7279	−	33.0244i	3.00914	−	1.24643i
$703$	−0.453652	+	1.09521i	−0.0171098	+	0.0413067i
$704$	−4.72279	+	11.4018i	−0.177997	+	0.429723i
$705$		0			0
$706$	−43.7783	+	43.7783i	−1.64762	+	1.64762i
$707$	−8.70316	−	3.60497i	−0.327316	−	0.135579i
$708$	−4.55761	+	11.0030i	−0.171285	+	0.413519i
$709$	−7.77328	−	18.7664i	−0.291932	−	0.704785i	0.708067	−	0.706145i	$-0.249567\pi$
$709$	−7.77328	−	18.7664i	−0.291932	−	0.704785i	−0.999999	+	0.00135939i	$0.999567\pi$
$710$		0			0
$711$	−2.43286	+	1.00772i	−0.0912394	+	0.0377926i
$712$	−33.2805	+	33.2805i	−1.24724	+	1.24724i
$713$		−	4.13012i		−	0.154674i
$714$	19.6316	+	9.97783i	0.734695	+	0.373411i
$715$		0			0
$716$	76.4504	+	76.4504i	2.85708	+	2.85708i
$717$	3.43748	+	8.29881i	0.128375	+	0.309925i
$718$	−36.8108			−1.37377
$719$	11.1535	+	26.9270i	0.415957	+	1.00421i	0.983507	+	0.180870i	$0.0578912\pi$
$719$	11.1535	+	26.9270i	0.415957	+	1.00421i	−0.567550	+	0.823339i	$0.692109\pi$
$720$		0			0
$721$	−6.57405	+	15.8712i	−0.244830	+	0.591073i
$722$	−36.6511	−	36.6511i	−1.36401	−	1.36401i
$723$	9.54690	+	9.54690i	0.355053	+	0.355053i
$724$	18.5113	−	44.6903i	0.687968	−	1.66090i
$725$		0			0
$726$	−17.4986	−	42.2454i	−0.649435	−	1.56788i
$727$	−18.9928			−0.704402			−0.352201	−	0.935924i	$-0.614567\pi$
$727$	−18.9928			−0.704402			−0.352201	+	0.935924i	$0.614567\pi$
$728$	25.8655	+	62.4448i	0.958639	+	2.31436i
$729$	21.2335	+	21.2335i	0.786426	+	0.786426i
$730$		0			0
$731$	−7.34207	−	3.73163i	−0.271556	−	0.138019i
$732$		−	65.8762i		−	2.43486i
$733$	23.0263	−	23.0263i	0.850494	−	0.850494i	−0.139700	−	0.990194i	$-0.544614\pi$
$733$	23.0263	−	23.0263i	0.850494	−	0.850494i	0.990194	+	0.139700i	$0.0446138\pi$
$734$	−4.82068	+	1.99679i	−0.177934	+	0.0737029i
$735$		0			0
$736$	−56.6182	−	136.688i	−2.08698	−	5.03840i
$737$	−1.93555	+	4.67283i	−0.0712970	+	0.172126i
$738$	−2.50203	−	1.03637i	−0.0921010	−	0.0381495i
$739$	21.7401	−	21.7401i	0.799723	−	0.799723i	−0.183329	−	0.983052i	$-0.558687\pi$
$739$	21.7401	−	21.7401i	0.799723	−	0.799723i	0.983052	+	0.183329i	$0.0586873\pi$
$740$		0			0
$741$	−0.449770	+	1.08584i	−0.0165227	+	0.0398893i
$742$	2.03872	−	4.92190i	0.0748436	−	0.180688i
$743$	−9.03012	+	3.74040i	−0.331283	+	0.137222i	−0.542124	−	0.840298i	$-0.682380\pi$
$743$	−9.03012	+	3.74040i	−0.331283	+	0.137222i	0.210841	+	0.977520i	$0.432380\pi$
$744$			8.84209i			0.324167i
$745$		0			0
$746$	48.1467	+	48.1467i	1.76278	+	1.76278i
$747$		−	2.66629i		−	0.0975543i
$748$	−0.728243	+	9.37435i	−0.0266272	+	0.342760i
$749$	−11.7268			−0.428489
$750$		0			0
$751$	11.9895	−	4.96623i	0.437504	−	0.181220i	−0.153050	−	0.988219i	$-0.548909\pi$
$751$	11.9895	−	4.96623i	0.437504	−	0.181220i	0.590554	+	0.806998i	$0.298909\pi$
$752$	75.2189			2.74295
$753$	21.7838	−	9.02315i	0.793846	−	0.328822i
$754$	4.70824	+	1.95022i	0.171464	+	0.0710227i
$755$		0			0
$756$	−27.2208	+	27.2208i	−0.990010	+	0.990010i
$757$	25.1081	+	25.1081i	0.912568	+	0.912568i	0.996474	−	0.0839060i	$-0.0267396\pi$
$757$	25.1081	+	25.1081i	0.912568	+	0.912568i	−0.0839060	+	0.996474i	$0.526740\pi$
$758$	41.8828	+	17.3484i	1.52125	+	0.630124i
$759$	−4.07329	−	1.68721i	−0.147851	−	0.0612419i
$760$		0			0
$761$		−	23.6745i		−	0.858200i	−0.903257	−	0.429100i	$-0.858831\pi$
$761$		−	23.6745i		−	0.858200i	0.903257	−	0.429100i	$-0.141169\pi$
$762$	−28.7977	−	69.5237i	−1.04323	−	2.51858i
$763$	−14.0433	+	14.0433i	−0.508402	+	0.508402i
$764$	57.8802			2.09403
$765$		0			0
$766$	54.8581			1.98210
$767$	−5.65120	+	5.65120i	−0.204053	+	0.204053i
$768$	25.2314	+	60.9140i	0.910461	+	2.19805i
$769$		−	5.83645i		−	0.210468i	−0.994447	−	0.105234i	$-0.966441\pi$
$769$		−	5.83645i		−	0.210468i	0.994447	−	0.105234i	$-0.0335591\pi$
$770$		0			0
$771$	−20.7717	−	8.60391i	−0.748074	−	0.309862i
$772$	49.0245	+	20.3066i	1.76443	+	0.730851i
$773$	−21.6507	−	21.6507i	−0.778721	−	0.778721i	0.200892	−	0.979613i	$-0.435616\pi$
$773$	−21.6507	−	21.6507i	−0.778721	−	0.778721i	−0.979613	+	0.200892i	$0.935616\pi$
$774$	2.34141	−	2.34141i	0.0841601	−	0.0841601i
$775$		0			0
$776$	5.54002	+	2.29475i	0.198875	+	0.0823768i
$777$	15.9697	−	6.61486i	0.572909	−	0.237307i
$778$	−60.8333			−2.18098
$779$	0.202470	−	0.0838658i	0.00725424	−	0.00300480i
$780$		0			0
$781$	−2.01661			−0.0721600
$782$	−49.9203	−	58.3296i	−1.78514	−	2.08586i
$783$			1.83860i			0.0657063i
$784$	56.7455	+	56.7455i	2.02662	+	2.02662i
$785$		0			0
$786$			18.8912i			0.673827i
$787$	−34.9631	+	14.4822i	−1.24630	+	0.516234i	−0.905678	−	0.423967i	$-0.860637\pi$
$787$	−34.9631	+	14.4822i	−1.24630	+	0.516234i	−0.340621	+	0.940201i	$0.610637\pi$
$788$	−49.6847	+	119.950i	−1.76995	+	4.27303i
$789$	−11.2643	+	27.1944i	−0.401019	+	0.968145i
$790$		0			0
$791$	1.11477	−	1.11477i	0.0396367	−	0.0396367i
$792$	−2.21233	−	0.916378i	−0.0786118	−	0.0325621i
$793$	16.9172	−	40.8416i	0.600746	−	1.45033i
$794$	−27.4509	−	66.2724i	−0.974197	−	2.35192i
$795$		0			0
$796$	66.5791	−	27.5780i	2.35984	−	0.977476i
$797$	−5.27565	+	5.27565i	−0.186873	+	0.186873i	−0.794343	−	0.607470i	$-0.792185\pi$
$797$	−5.27565	+	5.27565i	−0.186873	+	0.186873i	0.607470	+	0.794343i	$0.292185\pi$
$798$		−	0.716469i		−	0.0253627i
$799$	19.8452	−	6.47028i	0.702072	−	0.228902i
$800$		0			0
$801$	−2.14077	−	2.14077i	−0.0756404	−	0.0756404i
$802$	−39.8724	−	96.2606i	−1.40795	−	3.39908i
$803$	−1.21225			−0.0427793
$804$	39.0869	+	94.3641i	1.37849	+	3.32797i
$805$		0			0
$806$	−3.58462	+	8.65404i	−0.126263	+	0.304826i
$807$	−24.8134	−	24.8134i	−0.873472	−	0.873472i
$808$	−49.7171	−	49.7171i	−1.74904	−	1.74904i
$809$	14.4204	−	34.8140i	0.506995	−	1.22399i	−0.438610	−	0.898678i	$-0.644529\pi$
$809$	14.4204	−	34.8140i	0.506995	−	1.22399i	0.945605	−	0.325317i	$-0.105471\pi$
$810$		0			0
$811$	−2.63137	−	6.35270i	−0.0924001	−	0.223073i	0.870922	−	0.491421i	$-0.163522\pi$
$811$	−2.63137	−	6.35270i	−0.0924001	−	0.223073i	−0.963322	+	0.268348i	$0.913522\pi$
$812$	−2.27334			−0.0797785
$813$	5.90060	+	14.2453i	0.206943	+	0.499605i
$814$	7.13162	+	7.13162i	0.249963	+	0.249963i
$815$		0			0
$816$	61.6178	+	71.9977i	2.15706	+	2.52042i
$817$			0.267954i			0.00937452i
$818$	36.8780	−	36.8780i	1.28941	−	1.28941i
$819$	−4.01677	+	1.66380i	−0.140357	+	0.0581379i
$820$		0			0
$821$	8.99652	+	21.7195i	0.313981	+	0.758017i	0.999550	+	0.0300089i	$0.00955356\pi$
$821$	8.99652	+	21.7195i	0.313981	+	0.758017i	−0.685569	+	0.728008i	$0.740446\pi$
$822$	−14.6276	+	35.3141i	−0.510195	+	1.23172i
$823$	−50.6939	−	20.9981i	−1.76708	−	0.731948i	−0.995386	−	0.0959532i	$-0.969410\pi$
$823$	−50.6939	−	20.9981i	−1.76708	−	0.731948i	−0.771693	−	0.635995i	$-0.780590\pi$
$824$	−90.6645	+	90.6645i	−3.15845	+	3.15845i
$825$		0			0
$826$	1.86441	−	4.50110i	0.0648713	−	0.156613i
$827$	6.74207	−	16.2768i	0.234445	−	0.566000i	−0.762246	−	0.647288i	$-0.775903\pi$
$827$	6.74207	−	16.2768i	0.234445	−	0.566000i	0.996691	+	0.0812877i	$0.0259033\pi$
$828$	20.8682	−	8.64390i	0.725220	−	0.300396i
$829$			11.9207i			0.414022i	0.978339	+	0.207011i	$0.0663736\pi$
$829$			11.9207i			0.414022i	−0.978339	+	0.207011i	$0.933626\pi$
$830$		0			0
$831$	12.8056	+	12.8056i	0.444221	+	0.444221i
$832$			167.242i			5.79806i
$833$	19.8525	+	10.0901i	0.687849	+	0.349601i
$834$	−19.8560			−0.687558
$835$		0			0
$836$	0.282624	−	0.117067i	0.00977475	−	0.00404883i
$837$	−3.37946			−0.116811
$838$	84.6406	−	35.0593i	2.92386	−	1.21110i
$839$	−39.1157	−	16.2022i	−1.35042	−	0.559364i	−0.414013	−	0.910271i	$-0.635873\pi$
$839$	−39.1157	−	16.2022i	−1.35042	−	0.559364i	−0.936410	+	0.350907i	$0.885873\pi$
$840$		0			0
$841$	20.4293	−	20.4293i	0.704459	−	0.704459i
$842$	36.5691	+	36.5691i	1.26026	+	1.26026i
$843$	−1.69385	−	0.701617i	−0.0583394	−	0.0241650i
$844$	100.245	+	41.5230i	3.45059	+	1.42928i
$845$		0			0
$846$			8.39207i			0.288525i
$847$	5.23822	+	12.6462i	0.179987	+	0.434528i
$848$	16.2106	−	16.2106i	0.556674	−	0.556674i
$849$	7.13254			0.244788
$850$		0			0
$851$	−60.2626			−2.06578
$852$	−28.7961	+	28.7961i	−0.986538	+	0.986538i
$853$	−12.6947	−	30.6477i	−0.434659	−	1.04936i	−0.977767	−	0.209696i	$-0.932753\pi$
$853$	−12.6947	−	30.6477i	−0.434659	−	1.04936i	0.543108	−	0.839663i	$-0.317247\pi$
$854$			26.9485i			0.922159i
$855$		0			0
$856$	−80.8639	−	33.4949i	−2.76387	−	1.14483i
$857$	−14.2009	−	5.88221i	−0.485094	−	0.200932i	0.126713	−	0.991939i	$-0.459557\pi$
$857$	−14.2009	−	5.88221i	−0.485094	−	0.200932i	−0.611807	+	0.791007i	$0.709557\pi$
$858$	7.07059	+	7.07059i	0.241386	+	0.241386i
$859$	30.2680	−	30.2680i	1.03273	−	1.03273i	0.0332837	−	0.999446i	$-0.489404\pi$
$859$	30.2680	−	30.2680i	1.03273	−	1.03273i	0.999446	−	0.0332837i	$-0.0105965\pi$
$860$		0			0
$861$	−2.95228	−	1.22288i	−0.100614	−	0.0416755i
$862$	61.5227	−	25.4835i	2.09547	−	0.867972i
$863$	−31.3841			−1.06833			−0.534163	−	0.845382i	$-0.679373\pi$
$863$	−31.3841			−1.06833			−0.534163	+	0.845382i	$0.679373\pi$
$864$	−111.845	+	46.3277i	−3.80505	+	1.57610i
$865$		0			0
$866$	26.4630			0.899250
$867$	22.4500	+	13.6950i	0.762441	+	0.465107i
$868$		−	4.17853i		−	0.141829i
$869$	−1.28196	−	1.28196i	−0.0434876	−	0.0434876i
$870$		0			0
$871$			68.5410i			2.32242i
$872$	−136.949	+	56.7262i	−4.63768	+	1.92099i
$873$	−0.147610	+	0.356362i	−0.00499585	+	0.0120610i
$874$	−0.955882	+	2.30770i	−0.0323332	+	0.0780592i
$875$		0			0
$876$	−17.3102	+	17.3102i	−0.584858	+	0.584858i
$877$	−27.0128	−	11.1890i	−0.912156	−	0.377827i	−0.123274	−	0.992373i	$-0.539339\pi$
$877$	−27.0128	−	11.1890i	−0.912156	−	0.377827i	−0.788882	+	0.614545i	$0.789339\pi$
$878$	−3.36844	+	8.13214i	−0.113679	+	0.274447i
$879$	−1.83233	−	4.42363i	−0.0618028	−	0.149205i
$880$		0			0
$881$	−21.1976	+	8.78032i	−0.714164	+	0.295816i	−0.710026	−	0.704175i	$-0.751317\pi$
$881$	−21.1976	+	8.78032i	−0.714164	+	0.295816i	−0.00413755	+	0.999991i	$0.501317\pi$
$882$	−6.33102	+	6.33102i	−0.213176	+	0.213176i
$883$		−	21.1206i		−	0.710766i	−0.934721	−	0.355383i	$-0.884351\pi$
$883$		−	21.1206i		−	0.710766i	0.934721	−	0.355383i	$-0.115649\pi$
$884$	39.4970	+	121.142i	1.32843	+	4.07446i
$885$		0			0
$886$	33.9099	+	33.9099i	1.13923	+	1.13923i
$887$	−6.87805	−	16.6051i	−0.230942	−	0.557544i	0.765346	−	0.643619i	$-0.222568\pi$
$887$	−6.87805	−	16.6051i	−0.230942	−	0.557544i	−0.996289	+	0.0860744i	$0.972568\pi$
$888$	129.015			4.32945
$889$	8.62058	+	20.8119i	0.289125	+	0.698009i
$890$		0			0
$891$	−1.08926	+	2.62971i	−0.0364917	+	0.0880986i
$892$	−24.5498	−	24.5498i	−0.821987	−	0.821987i
$893$	−0.480200	−	0.480200i	−0.0160693	−	0.0160693i
$894$	1.25429	−	3.02812i	0.0419497	−	0.101275i
$895$		0			0
$896$	−18.0181	−	43.4995i	−0.601942	−	1.45322i
$897$	−59.7469			−1.99489
$898$	19.3561	+	46.7297i	0.645921	+	1.55939i
$899$	−0.141118	−	0.141118i	−0.00470654	−	0.00470654i
$900$		0			0
$901$	2.88246	−	5.67130i	0.0960286	−	0.188939i
$902$		−	1.86451i		−	0.0620815i
$903$	2.76276	−	2.76276i	0.0919388	−	0.0919388i
$904$	10.8711	−	4.50297i	0.361569	−	0.149767i
$905$		0			0
$906$	3.69703	+	8.92542i	0.122826	+	0.296527i
$907$	−21.3916	+	51.6439i	−0.710297	+	1.71481i	−0.0110397	+	0.999939i	$0.503514\pi$
$907$	−21.3916	+	51.6439i	−0.710297	+	1.71481i	−0.699257	+	0.714870i	$0.746486\pi$
$908$	133.765	+	55.4072i	4.43914	+	1.83875i
$909$	3.19805	−	3.19805i	0.106073	−	0.106073i
$910$		0			0
$911$	0.214803	−	0.518579i	0.00711673	−	0.0171813i	−0.920281	−	0.391258i	$-0.872040\pi$
$911$	0.214803	−	0.518579i	0.00711673	−	0.0171813i	0.927398	+	0.374076i	$0.122040\pi$
$912$	1.17987	−	2.84846i	0.0390694	−	0.0943218i
$913$	1.69594	−	0.702481i	0.0561274	−	0.0232487i
$914$		−	40.1610i		−	1.32841i
$915$		0			0
$916$	−59.9768	−	59.9768i	−1.98169	−	1.98169i
$917$		−	5.65508i		−	0.186747i
$918$	−47.7281	+	40.8471i	−1.57526	+	1.34816i
$919$	−4.29583			−0.141706			−0.0708531	−	0.997487i	$-0.522572\pi$
$919$	−4.29583			−0.141706			−0.0708531	+	0.997487i	$0.522572\pi$
$920$		0			0
$921$	−16.9193	+	7.00821i	−0.557510	+	0.230928i
$922$	49.0127			1.61415
$923$	−25.2477	+	10.4580i	−0.831040	+	0.344228i
$924$	−4.12104	−	1.70699i	−0.135572	−	0.0561558i
$925$		0			0
$926$	68.6974	−	68.6974i	2.25754	−	2.25754i
$927$	−5.83200	−	5.83200i	−0.191548	−	0.191548i
$928$	−6.60488	−	2.73583i	−0.216816	−	0.0898081i
$929$	−8.82633	−	3.65598i	−0.289582	−	0.119949i	0.233163	−	0.972438i	$-0.425092\pi$
$929$	−8.82633	−	3.65598i	−0.289582	−	0.119949i	−0.522746	+	0.852489i	$0.675092\pi$
$930$		0			0
$931$		−	0.724531i		−	0.0237455i
$932$	7.94015	+	19.1692i	0.260088	+	0.627908i
$933$	−25.6503	+	25.6503i	−0.839752	+	0.839752i
$934$	−80.3921			−2.63051
$935$		0			0
$936$	−32.4504			−1.06068
$937$	39.4176	−	39.4176i	1.28772	−	1.28772i	0.351546	−	0.936171i	$-0.385656\pi$
$937$	39.4176	−	39.4176i	1.28772	−	1.28772i	0.936171	−	0.351546i	$-0.114344\pi$
$938$	−15.9896	−	38.6023i	−0.522078	−	1.26041i
$939$		−	42.7075i		−	1.39371i
$940$		0			0
$941$	−27.2017	−	11.2673i	−0.886751	−	0.367304i	−0.107640	−	0.994190i	$-0.534329\pi$
$941$	−27.2017	−	11.2673i	−0.886751	−	0.367304i	−0.779111	+	0.626885i	$0.784329\pi$
$942$	74.5894	+	30.8959i	2.43025	+	1.00664i
$943$	7.87762	+	7.87762i	0.256530	+	0.256530i
$944$	14.8247	−	14.8247i	0.482501	−	0.482501i
$945$		0			0
$946$	2.10618	+	0.872408i	0.0684778	+	0.0283644i
$947$	29.1876	−	12.0899i	0.948469	−	0.392869i	0.145814	−	0.989312i	$-0.453420\pi$
$947$	29.1876	−	12.0899i	0.948469	−	0.392869i	0.802655	+	0.596443i	$0.203420\pi$
$948$	−36.6114			−1.18908
$949$	−15.1772	+	6.28660i	−0.492673	+	0.204072i
$950$		0			0
$951$	49.2859			1.59821
$952$	−31.9925	−	37.3818i	−1.03688	−	1.21155i
$953$			18.4486i			0.597610i	0.954314	+	0.298805i	$0.0965881\pi$
$953$			18.4486i			0.597610i	−0.954314	+	0.298805i	$0.903412\pi$
$954$	1.80859	+	1.80859i	0.0585554	+	0.0585554i
$955$		0			0
$956$		−	31.6832i		−	1.02471i
$957$	−0.196824	+	0.0815272i	−0.00636242	+	0.00263540i
$958$	17.4884	−	42.2207i	0.565024	−	1.36409i
$959$	4.37876	−	10.5713i	0.141398	−	0.341364i
$960$		0			0
$961$	−21.6609	+	21.6609i	−0.698740	+	0.698740i
$962$	126.271	+	52.3032i	4.07114	+	1.68632i
$963$	2.15456	−	5.20157i	0.0694298	−	0.167618i
$964$	−18.2241	−	43.9968i	−0.586957	−	1.41704i
$965$		0			0
$966$	33.6494	−	13.9380i	1.08265	−	0.448449i
$967$	−27.1273	+	27.1273i	−0.872354	+	0.872354i	−0.992729	−	0.120374i	$-0.961591\pi$
$967$	−27.1273	+	27.1273i	−0.872354	+	0.872354i	0.120374	+	0.992729i	$0.461591\pi$
$968$			102.165i			3.28371i
$969$	0.0662656	−	0.853007i	0.00212876	−	0.0274025i
$970$		0			0
$971$	−37.1678	−	37.1678i	−1.19277	−	1.19277i	−0.976286	−	0.216486i	$-0.930541\pi$
$971$	−37.1678	−	37.1678i	−1.19277	−	1.19277i	−0.216486	−	0.976286i	$-0.569459\pi$
$972$	−12.9553	−	31.2769i	−0.415542	−	1.00321i
$973$	5.94390			0.190553
$974$	−24.4963	−	59.1394i	−0.784913	−	1.89495i
$975$		0			0
$976$	−44.3783	+	107.139i	−1.42052	+	3.42943i
$977$	24.3083	+	24.3083i	0.777691	+	0.777691i	0.979438	−	0.201747i	$-0.0646618\pi$
$977$	24.3083	+	24.3083i	0.777691	+	0.777691i	−0.201747	+	0.979438i	$0.564662\pi$
$978$	−54.7470	−	54.7470i	−1.75061	−	1.75061i
$979$	0.797652	−	1.92570i	0.0254931	−	0.0615457i
$980$		0			0
$981$	−3.64891	−	8.80926i	−0.116501	−	0.281258i
$982$	−69.5971			−2.22093
$983$	−10.9938	−	26.5414i	−0.350648	−	0.846539i	−0.996540	−	0.0831107i	$-0.973514\pi$
$983$	−10.9938	−	26.5414i	−0.350648	−	0.846539i	0.645892	−	0.763429i	$-0.276486\pi$
$984$	−16.8650	−	16.8650i	−0.537637	−	0.537637i
$985$		0			0
$986$	−3.69867	−	0.287330i	−0.117790	−	0.00915045i
$987$			9.90228i			0.315193i
$988$	2.93132	−	2.93132i	0.0932578	−	0.0932578i
$989$	−12.5846	+	5.21272i	−0.400168	+	0.165755i
$990$		0			0
$991$	−18.3049	−	44.1919i	−0.581474	−	1.40380i	−0.891477	−	0.453066i	$-0.850330\pi$
$991$	−18.3049	−	44.1919i	−0.581474	−	1.40380i	0.310003	−	0.950736i	$-0.399670\pi$
$992$	5.02863	−	12.1402i	0.159659	−	0.385451i
$993$	37.2650	+	15.4357i	1.18257	+	0.489836i
$994$	11.7798	−	11.7798i	0.373634	−	0.373634i
$995$		0			0
$996$	14.1860	−	34.2481i	0.449502	−	1.08519i
$997$	−2.98950	+	7.21729i	−0.0946783	+	0.228574i	−0.964123	−	0.265457i	$-0.914477\pi$
$997$	−2.98950	+	7.21729i	−0.0946783	+	0.228574i	0.869444	+	0.494031i	$0.164477\pi$
$998$	−72.5091	+	30.0343i	−2.29524	+	0.950718i
$999$			49.3097i			1.56009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.c.274.6		24
5.2	odd	4		425.2.m.b.376.6		24
5.3	odd	4		85.2.l.a.36.1	yes	24
5.4	even	2		425.2.n.f.274.1		24
15.8	even	4		765.2.be.b.631.6		24
17.9	even	8		425.2.n.f.349.1		24
85.3	even	16		1445.2.a.q.1.1		12
85.9	even	8	inner	425.2.n.c.349.6		24
85.37	even	16		7225.2.a.bq.1.12		12
85.43	odd	8		85.2.l.a.26.1	✓	24
85.48	even	16		1445.2.a.p.1.1		12
85.63	even	16		1445.2.d.j.866.23		24
85.73	even	16		1445.2.d.j.866.24		24
85.77	odd	8		425.2.m.b.26.6		24
85.82	even	16		7225.2.a.bs.1.12		12
255.128	even	8		765.2.be.b.451.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.1	✓	24	85.43	odd	8
85.2.l.a.36.1	yes	24	5.3	odd	4
425.2.m.b.26.6		24	85.77	odd	8
425.2.m.b.376.6		24	5.2	odd	4
425.2.n.c.274.6		24	1.1	even	1	trivial
425.2.n.c.349.6		24	85.9	even	8	inner
425.2.n.f.274.1		24	5.4	even	2
425.2.n.f.349.1		24	17.9	even	8
765.2.be.b.451.6		24	255.128	even	8
765.2.be.b.631.6		24	15.8	even	4
1445.2.a.p.1.1		12	85.48	even	16
1445.2.a.q.1.1		12	85.3	even	16
1445.2.d.j.866.23		24	85.63	even	16
1445.2.d.j.866.24		24	85.73	even	16
7225.2.a.bq.1.12		12	85.37	even	16
7225.2.a.bs.1.12		12	85.82	even	16

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.93083 - 1.93083i) q^{2} +(0.591976 + 1.42916i) q^{3} -5.45623i q^{4} +(3.90247 + 1.61646i) q^{6} +(-1.16820 - 0.483886i) q^{7} +(-6.67340 - 6.67340i) q^{8} +(0.429267 - 0.429267i) q^{9} +O(q^{10})\)	\(q+(1.93083 - 1.93083i) q^{2} +(0.591976 + 1.42916i) q^{3} -5.45623i q^{4} +(3.90247 + 1.61646i) q^{6} +(-1.16820 - 0.483886i) q^{7} +(-6.67340 - 6.67340i) q^{8} +(0.429267 - 0.429267i) q^{9} +(0.386141 + 0.159945i) q^{11} +(7.79781 - 3.22996i) q^{12} +5.66390 q^{13} +(-3.18991 + 1.32130i) q^{14} -14.8580 q^{16} +(-3.92002 + 1.27807i) q^{17} -1.65769i q^{18} +(0.0948539 + 0.0948539i) q^{19} -1.95600i q^{21} +(1.05440 - 0.436747i) q^{22} +(-2.60960 + 6.30014i) q^{23} +(5.58684 - 13.4878i) q^{24} +(10.9361 - 10.9361i) q^{26} +(5.15508 + 2.13530i) q^{27} +(-2.64019 + 6.37399i) q^{28} +(0.126098 + 0.304427i) q^{29} +(-0.559556 + 0.231776i) q^{31} +(-15.3415 + 15.3415i) q^{32} +0.646540i q^{33} +(-5.10115 + 10.0366i) q^{34} +(-2.34218 - 2.34218i) q^{36} +(3.38184 + 8.16448i) q^{37} +0.366294 q^{38} +(3.35290 + 8.09461i) q^{39} +(0.625194 - 1.50935i) q^{41} +(-3.77670 - 3.77670i) q^{42} +(1.41246 + 1.41246i) q^{43} +(0.872696 - 2.10687i) q^{44} +(7.12581 + 17.2032i) q^{46} -5.06253 q^{47} +(-8.79557 - 21.2344i) q^{48} +(-3.81919 - 3.81919i) q^{49} +(-4.14712 - 4.84573i) q^{51} -30.9036i q^{52} +(-1.09104 + 1.09104i) q^{53} +(14.0765 - 5.83068i) q^{54} +(4.56673 + 11.0251i) q^{56} +(-0.0794098 + 0.191712i) q^{57} +(0.831272 + 0.344324i) q^{58} +(-0.997758 + 0.997758i) q^{59} +(2.98684 - 7.21086i) q^{61} +(-0.632889 + 1.52793i) q^{62} +(-0.709187 + 0.293755i) q^{63} +29.5276i q^{64} +(1.24836 + 1.24836i) q^{66} +12.1014i q^{67} +(6.97346 + 21.3885i) q^{68} -10.5487 q^{69} +(-4.45766 + 1.84642i) q^{71} -5.72934 q^{72} +(-2.67964 + 1.10994i) q^{73} +(22.2940 + 9.23447i) q^{74} +(0.517545 - 0.517545i) q^{76} +(-0.373696 - 0.373696i) q^{77} +(22.1032 + 9.15545i) q^{78} +(-4.00751 - 1.65997i) q^{79} +6.81023i q^{81} +(-1.70716 - 4.12145i) q^{82} +(3.10563 - 3.10563i) q^{83} -10.6724 q^{84} +5.45443 q^{86} +(-0.360427 + 0.360427i) q^{87} +(-1.50950 - 3.64425i) q^{88} -4.98704i q^{89} +(-6.61659 - 2.74068i) q^{91} +(34.3750 + 14.2386i) q^{92} +(-0.662488 - 0.662488i) q^{93} +(-9.77489 + 9.77489i) q^{94} +(-31.0071 - 12.8436i) q^{96} +(-0.587015 + 0.243150i) q^{97} -14.7484 q^{98} +(0.234417 - 0.0970985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9	\( 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} + 40 q^{12} + 16 q^{13} - 24 q^{16} + 8 q^{19} - 24 q^{22} + 8 q^{23} + 8 q^{24} + 16 q^{26} + 16 q^{27} - 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} - 16 q^{37} - 48 q^{38} - 8 q^{39} + 16 q^{41} - 24 q^{42} - 8 q^{43} - 16 q^{44} + 8 q^{46} - 64 q^{47} - 8 q^{48} - 56 q^{51} + 24 q^{53} + 32 q^{54} + 64 q^{56} + 16 q^{57} + 56 q^{58} - 32 q^{59} + 32 q^{61} - 32 q^{62} + 80 q^{63} + 96 q^{66} + 24 q^{68} - 96 q^{69} - 24 q^{71} - 24 q^{72} - 64 q^{73} + 64 q^{74} - 8 q^{76} + 24 q^{77} + 8 q^{78} - 16 q^{82} - 96 q^{83} + 64 q^{84} - 16 q^{86} + 48 q^{87} + 8 q^{88} - 24 q^{91} + 112 q^{92} - 64 q^{93} - 56 q^{94} - 168 q^{96} + 48 q^{97} + 120 q^{98} + 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 + 40 * q^12 + 16 * q^13 - 24 * q^16 + 8 * q^19 - 24 * q^22 + 8 * q^23 + 8 * q^24 + 16 * q^26 + 16 * q^27 - 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 + 16 * q^41 - 24 * q^42 - 8 * q^43 - 16 * q^44 + 8 * q^46 - 64 * q^47 - 8 * q^48 - 56 * q^51 + 24 * q^53 + 32 * q^54 + 64 * q^56 + 16 * q^57 + 56 * q^58 - 32 * q^59 + 32 * q^61 - 32 * q^62 + 80 * q^63 + 96 * q^66 + 24 * q^68 - 96 * q^69 - 24 * q^71 - 24 * q^72 - 64 * q^73 + 64 * q^74 - 8 * q^76 + 24 * q^77 + 8 * q^78 - 16 * q^82 - 96 * q^83 + 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 + 112 * q^92 - 64 * q^93 - 56 * q^94 - 168 * q^96 + 48 * q^97 + 120 * q^98 + 8 * q^99

Introduction

L-functions

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