LMFDB - Embedded newform 425.2.m.b.26.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

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([0, 1]))

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

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

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, degree $4$, 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			26.6
Character	$\chi$	$=$	425.26
Dual form			425.2.m.b.376.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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	$-0.166042\pi$
$3$	1.42916	+	0.591976i	0.825124	+	0.341778i	0.754971	−	0.655759i	$-0.227651\pi$
$3$	1.42916	+	0.591976i	0.825124	+	0.341778i	0.0701535	+	0.997536i	$0.477651\pi$
$4$		−	5.45623i		−	2.72811i
$5$		0			0
$5$		0			0
$6$	3.90247	−	1.61646i	1.59318	−	0.659915i
$7$	0.483886	+	1.16820i	0.182892	+	0.441540i	0.988560	−	0.150827i	$-0.0481937\pi$
$7$	0.483886	+	1.16820i	0.182892	+	0.441540i	−0.805668	+	0.592367i	$0.798194\pi$
$8$	−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	−0.323710	−	0.946156i	$-0.604930\pi$
$11$	0.386141	−	0.159945i	0.116426	−	0.0482252i	0.440136	+	0.897931i	$0.354930\pi$
$12$	3.22996	−	7.79781i	0.932408	−	2.25103i
$13$			5.66390i			1.57088i	0.618935	+	0.785442i	$0.287564\pi$
$13$			5.66390i			1.57088i	−0.618935	+	0.785442i	$0.712436\pi$
$14$	3.18991	+	1.32130i	0.852539	+	0.353133i
$15$		0			0
$16$	−14.8580			−3.71449
$17$	−1.27807	+	3.92002i	−0.309978	+	0.950744i
$17$	−1.27807	+	3.92002i	−0.309978	+	0.950744i
$18$	−1.65769			−0.390720
$19$	−0.0948539	+	0.0948539i	−0.0217610	+	0.0217610i	−0.717904	−	0.696143i	$-0.754898\pi$
$19$	−0.0948539	+	0.0948539i	−0.0217610	+	0.0217610i	0.696143	+	0.717904i	$0.254898\pi$
$20$		0			0
$21$			1.95600i			0.426833i
$22$	0.436747	−	1.05440i	0.0931148	−	0.224799i
$23$	6.30014	−	2.60960i	1.31367	−	0.544140i	0.387717	−	0.921778i	$-0.373264\pi$
$23$	6.30014	−	2.60960i	1.31367	−	0.544140i	0.925953	+	0.377638i	$0.123264\pi$
$24$	−5.58684	−	13.4878i	−1.14041	−	2.75319i
$25$		0			0
$26$	10.9361	+	10.9361i	2.14474	+	2.14474i
$27$	−2.13530	−	5.15508i	−0.410939	−	0.992095i
$28$	6.37399	−	2.64019i	1.20457	−	0.498949i
$29$	−0.126098	+	0.304427i	−0.0234158	+	0.0565307i	−0.935155	−	0.354239i	$-0.884740\pi$
$29$	−0.126098	+	0.304427i	−0.0234158	+	0.0565307i	0.911739	+	0.410770i	$0.134740\pi$
$30$		0			0
$31$	−0.559556	−	0.231776i	−0.100499	−	0.0416281i	0.331867	−	0.943326i	$-0.392321\pi$
$31$	−0.559556	−	0.231776i	−0.100499	−	0.0416281i	−0.432367	+	0.901698i	$0.642321\pi$
$32$	−15.3415	+	15.3415i	−2.71201	+	2.71201i
$33$	0.646540			0.112548
$34$	5.10115	+	10.0366i	0.874840	+	1.72127i
$35$		0			0
$36$	−2.34218	+	2.34218i	−0.390363	+	0.390363i
$37$	−8.16448	−	3.38184i	−1.34223	−	0.555970i	−0.408112	−	0.912932i	$-0.633813\pi$
$37$	−8.16448	−	3.38184i	−1.34223	−	0.555970i	−0.934119	+	0.356961i	$0.883813\pi$
$38$			0.366294i			0.0594207i
$39$	−3.35290	+	8.09461i	−0.536893	+	1.29617i
$40$		0			0
$41$	0.625194	+	1.50935i	0.0976389	+	0.235721i	0.965150	−	0.261696i	$-0.0842818\pi$
$41$	0.625194	+	1.50935i	0.0976389	+	0.235721i	−0.867511	+	0.497417i	$0.834282\pi$
$42$	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
$47$			5.06253i			0.738445i	0.929341	+	0.369223i	$0.120376\pi$
$47$			5.06253i			0.738445i	−0.929341	+	0.369223i	$0.879624\pi$
$48$	−21.2344	−	8.79557i	−3.06492	−	1.26953i
$49$	3.81919	−	3.81919i	0.545599	−	0.545599i
$50$		0			0
$51$	−4.14712	+	4.84573i	−0.580713	+	0.678538i
$52$	30.9036			4.28555
$53$	1.09104	−	1.09104i	0.149865	−	0.149865i	−0.628193	−	0.778058i	$-0.716205\pi$
$53$	1.09104	−	1.09104i	0.149865	−	0.149865i	0.778058	+	0.628193i	$0.216205\pi$
$54$	−14.0765	−	5.83068i	−1.91557	−	0.793455i
$55$		0			0
$56$	4.56673	−	11.0251i	0.610254	−	1.47328i
$57$	−0.191712	+	0.0794098i	−0.0253929	+	0.0105181i
$58$	0.344324	+	0.831272i	0.0452119	+	0.109151i
$59$	0.997758	+	0.997758i	0.129897	+	0.129897i	0.769066	−	0.639169i	$-0.220722\pi$
$59$	0.997758	+	0.997758i	0.129897	+	0.129897i	−0.639169	+	0.769066i	$0.720722\pi$
$60$		0			0
$61$	2.98684	+	7.21086i	0.382425	+	0.923256i	0.991496	+	0.130140i	$0.0415427\pi$
$61$	2.98684	+	7.21086i	0.382425	+	0.923256i	−0.609070	+	0.793116i	$0.708457\pi$
$62$	−1.52793	+	0.632889i	−0.194047	+	0.0803770i
$63$	0.293755	−	0.709187i	0.0370097	−	0.0893492i
$64$			29.5276i			3.69095i
$65$		0			0
$66$	1.24836	−	1.24836i	0.153662	−	0.153662i
$67$	−12.1014			−1.47842			−0.739209	−	0.673477i	$-0.764800\pi$
$67$	−12.1014			−1.47842			−0.739209	+	0.673477i	$0.764800\pi$
$68$	21.3885	+	6.97346i	2.59374	+	0.845656i
$69$	10.5487			1.26992
$70$		0			0
$71$	−4.45766	−	1.84642i	−0.529027	−	0.219130i	0.102150	−	0.994769i	$-0.467428\pi$
$71$	−4.45766	−	1.84642i	−0.529027	−	0.219130i	−0.631177	+	0.775639i	$0.717428\pi$
$72$			5.72934i			0.675209i
$73$	1.10994	−	2.67964i	0.129909	−	0.313628i	−0.845520	−	0.533944i	$-0.820709\pi$
$73$	1.10994	−	2.67964i	0.129909	−	0.313628i	0.975428	+	0.220317i	$0.0707091\pi$
$74$	−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
$78$	9.15545	+	22.1032i	1.03665	+	2.50270i
$79$	4.00751	−	1.65997i	0.450880	−	0.186761i	−0.145675	−	0.989332i	$-0.546535\pi$
$79$	4.00751	−	1.65997i	0.450880	−	0.186761i	0.596556	+	0.802572i	$0.296535\pi$
$80$		0			0
$81$		−	6.81023i		−	0.756693i
$82$	4.12145	+	1.70716i	0.455138	+	0.188524i
$83$	−3.10563	+	3.10563i	−0.340887	+	0.340887i	−0.856701	−	0.515814i	$-0.827490\pi$
$83$	−3.10563	+	3.10563i	−0.340887	+	0.340887i	0.515814	+	0.856701i	$0.327490\pi$
$84$	10.6724			1.16445
$85$		0			0
$86$	5.45443			0.588167
$87$	−0.360427	+	0.360427i	−0.0386418	+	0.0386418i
$88$	−3.64425	−	1.50950i	−0.388478	−	0.160913i
$89$		−	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
$92$	−14.2386	−	34.3750i	−1.48448	−	3.58384i
$93$	−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
$97$	−0.243150	+	0.587015i	−0.0246881	+	0.0596024i	−0.935743	−	0.352683i	$-0.885269\pi$
$97$	−0.243150	+	0.587015i	−0.0246881	+	0.0596024i	0.911055	+	0.412285i	$0.135269\pi$
$98$		−	14.7484i		−	1.48982i
$99$	−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	$0.379134\pi$
$102$	1.34889	+	17.3637i	0.133560	+	1.71926i
$103$	−13.5860			−1.33866			−0.669332	−	0.742963i	$-0.733420\pi$
$103$	−13.5860			−1.33866			−0.669332	+	0.742963i	$0.733420\pi$
$104$	37.7975	−	37.7975i	3.70635	−	3.70635i
$105$		0			0
$106$		−	4.21322i		−	0.409224i
$107$	3.54909	−	8.56826i	0.343103	−	0.828325i	−0.654295	−	0.756239i	$-0.727035\pi$
$107$	3.54909	−	8.56826i	0.343103	−	0.828325i	0.997398	−	0.0720853i	$-0.0229654\pi$
$108$	−28.1273	+	11.6507i	−2.70655	+	1.12109i
$109$	−6.01065	−	14.5110i	−0.575716	−	1.38990i	−0.896625	−	0.442791i	$-0.853988\pi$
$109$	−6.01065	−	14.5110i	−0.575716	−	1.38990i	0.320909	−	0.947110i	$-0.396012\pi$
$110$		0			0
$111$	−9.66635	−	9.66635i	−0.917489	−	0.917489i
$112$	−7.18956	−	17.3571i	−0.679350	−	1.64010i
$113$	1.15190	−	0.477131i	0.108361	−	0.0448847i	−0.327844	−	0.944732i	$-0.606322\pi$
$113$	1.15190	−	0.477131i	0.108361	−	0.0448847i	0.436205	+	0.899847i	$0.356322\pi$
$114$	−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
$118$	3.85301			0.354698
$119$	−5.19782	+	0.403791i	−0.476483	+	0.0370155i
$120$		0			0
$121$	−7.65465	+	7.65465i	−0.695877	+	0.695877i
$122$	19.6900	+	8.15588i	1.78265	+	0.738399i
$123$			2.52720i			0.227870i
$124$	−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	$0.0401412\pi$
$127$	12.5973	+	12.5973i	1.11783	+	1.11783i	0.125773	+	0.992059i	$0.459859\pi$
$128$	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	−0.831308	−	0.555812i	$-0.812407\pi$
$131$	1.71149	−	4.13191i	0.149534	−	0.361007i	0.980842	+	0.194805i	$0.0624075\pi$
$132$		−	3.52767i		−	0.307044i
$133$	−0.156707	−	0.0649102i	−0.0135882	−	0.00562843i
$134$	−23.3657	+	23.3657i	−2.01849	+	2.01849i
$135$		0			0
$136$	34.6889	−	17.6307i	2.97455	−	1.51182i
$137$	−9.04916			−0.773122			−0.386561	−	0.922264i	$-0.626337\pi$
$137$	−9.04916			−0.773122			−0.386561	+	0.922264i	$0.626337\pi$
$138$	20.3678	−	20.3678i	1.73382	−	1.73382i
$139$	4.34294	+	1.79890i	0.368363	+	0.152581i	0.559183	−	0.829044i	$-0.311115\pi$
$139$	4.34294	+	1.79890i	0.368363	+	0.152581i	−0.190820	+	0.981625i	$0.561115\pi$
$140$		0			0
$141$	−2.99689	+	7.23514i	−0.252384	+	0.609309i
$142$	−12.1721	+	5.04186i	−1.02146	+	0.423103i
$143$	0.905912	+	2.18707i	0.0757562	+	0.182892i
$144$	6.37804	+	6.37804i	0.531503	+	0.531503i
$145$		0			0
$146$	−3.03082	−	7.31704i	−0.250832	−	0.605562i
$147$	7.71910	−	3.19735i	0.636660	−	0.263713i
$148$	−18.4521	+	44.5472i	−1.51675	+	3.66176i
$149$		−	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	−0.638234	−	0.769843i	$-0.720335\pi$
$151$	1.61724	−	1.61724i	0.131609	−	0.131609i	0.769843	+	0.638234i	$0.220335\pi$
$152$	1.26600			0.102686
$153$	2.23137	−	1.13410i	0.180395	−	0.0916865i
$154$	1.44309			0.116288
$155$		0			0
$156$	44.1660	+	18.2942i	3.53611	+	1.46471i
$157$		−	19.1134i		−	1.52541i	−0.646745	−	0.762707i	$-0.723870\pi$
$157$		−	19.1134i		−	1.52541i	0.646745	−	0.762707i	$-0.276130\pi$
$158$	4.53272	−	10.9430i	0.360604	−	0.870575i
$159$	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
$163$	−7.01440	−	16.9343i	−0.549410	−	1.32639i	−0.917918	−	0.396769i	$-0.870131\pi$
$163$	−7.01440	−	16.9343i	−0.549410	−	1.32639i	0.368508	−	0.929625i	$-0.379869\pi$
$164$	8.23536	−	3.41120i	0.643074	−	0.266370i
$165$		0			0
$166$			11.9929i			0.930829i
$167$	18.6147	+	7.71045i	1.44045	+	0.596653i	0.959907	−	0.280320i	$-0.0904407\pi$
$167$	18.6147	+	7.71045i	1.44045	+	0.596653i	0.480540	+	0.876973i	$0.340441\pi$
$168$	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
$173$	−17.6594	−	7.31475i	−1.34262	−	0.556130i	−0.408389	−	0.912808i	$-0.633909\pi$
$173$	−17.6594	−	7.31475i	−1.34262	−	0.556130i	−0.934227	+	0.356678i	$0.883909\pi$
$174$			1.39185i			0.105516i
$175$		0			0
$176$	−5.73727	+	2.37646i	−0.432463	+	0.179132i
$177$	0.835303	+	2.01660i	0.0627852	+	0.151577i
$178$	−9.62914	−	9.62914i	−0.721735	−	0.721735i
$179$	14.0116	+	14.0116i	1.04727	+	1.04727i	0.998826	+	0.0484485i	$0.0154277\pi$
$179$	14.0116	+	14.0116i	1.04727	+	1.04727i	0.0484485	+	0.998826i	$0.484572\pi$
$180$		0			0
$181$	8.19070	−	3.39270i	0.608810	−	0.252177i	−0.0569098	−	0.998379i	$-0.518125\pi$
$181$	8.19070	−	3.39270i	0.608810	−	0.252177i	0.665719	+	0.746202i	$0.268125\pi$
$182$	−7.48374	+	18.0673i	−0.554731	+	1.33924i
$183$			12.0736i			0.892505i
$184$	−59.4583	−	24.6284i	−4.38332	−	1.81563i
$185$		0			0
$186$	−2.55831			−0.187584
$187$	0.133470	+	1.71810i	0.00976030	+	0.125640i
$188$	27.6223			2.01456
$189$	4.98894	−	4.98894i	0.362892	−	0.362892i
$190$		0			0
$191$		−	10.6081i		−	0.767576i	−0.923421	−	0.383788i	$-0.874619\pi$
$191$		−	10.6081i		−	0.767576i	0.923421	−	0.383788i	$-0.125381\pi$
$192$	−17.4797	+	42.1996i	−1.26149	+	3.04550i
$193$	8.98505	−	3.72173i	0.646758	−	0.267896i	−0.0350962	−	0.999384i	$-0.511174\pi$
$193$	8.98505	−	3.72173i	0.646758	−	0.267896i	0.681854	+	0.731488i	$0.261174\pi$
$194$	0.663947	+	1.60291i	0.0476686	+	0.115082i
$195$		0			0
$196$	−20.8384	−	20.8384i	−1.48846	−	1.48846i
$197$	9.10606	+	21.9840i	0.648780	+	1.56629i	0.814528	+	0.580125i	$0.196996\pi$
$197$	9.10606	+	21.9840i	0.648780	+	1.56629i	−0.165748	+	0.986168i	$0.553004\pi$
$198$	−0.640100	+	0.265138i	−0.0454899	+	0.0188426i
$199$	−5.05440	+	12.2024i	−0.358297	+	0.865006i	0.637243	+	0.770663i	$0.280075\pi$
$199$	−5.05440	+	12.2024i	−0.358297	+	0.865006i	−0.995540	+	0.0943427i	$0.969925\pi$
$200$		0			0
$201$	−17.2948	−	7.16372i	−1.21988	−	0.505290i
$202$	14.3848	−	14.3848i	1.01211	−	1.01211i
$203$	−0.416650			−0.0292431
$204$	26.4394	+	22.6276i	1.85113	+	1.58425i
$205$		0			0
$206$	−26.2322	+	26.2322i	−1.82768	+	1.82768i
$207$	−3.82466	−	1.58423i	−0.265832	−	0.110111i
$208$		−	84.1541i		−	5.83504i
$209$	−0.0214556	+	0.0517984i	−0.00148411	+	0.00358297i
$210$		0			0
$211$	−7.61020	−	18.3726i	−0.523907	−	1.26482i	−0.935458	−	0.353438i	$-0.885013\pi$
$211$	−7.61020	−	18.3726i	−0.523907	−	1.26482i	0.411551	−	0.911387i	$-0.364987\pi$
$212$	−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
$217$		−	0.765828i		−	0.0519878i
$218$	−39.6238	−	16.4127i	−2.68367	−	1.11161i
$219$	3.17256	−	3.17256i	0.214382	−	0.214382i
$220$		0			0
$221$	−22.2026	−	7.23888i	−1.49351	−	0.486940i
$222$	−37.3282			−2.50530
$223$	−4.49940	+	4.49940i	−0.301302	+	0.301302i	−0.841523	−	0.540221i	$-0.818341\pi$
$223$	−4.49940	+	4.49940i	−0.301302	+	0.301302i	0.540221	+	0.841523i	$0.318341\pi$
$224$	−25.3455	−	10.4984i	−1.69347	−	0.701456i
$225$		0			0
$226$	1.30286	−	3.14538i	0.0866648	−	0.209227i
$227$	−24.5160	+	10.1548i	−1.62718	+	0.674001i	−0.994912	−	0.100747i	$-0.967877\pi$
$227$	−24.5160	+	10.1548i	−1.62718	+	0.674001i	−0.632270	+	0.774748i	$0.717877\pi$
$228$	0.433278	+	1.04603i	0.0286946	+	0.0692748i
$229$	−10.9924	−	10.9924i	−0.726395	−	0.726395i	0.243504	−	0.969900i	$-0.421703\pi$
$229$	−10.9924	−	10.9924i	−0.726395	−	0.726395i	−0.969900	+	0.243504i	$0.921703\pi$
$230$		0			0
$231$	0.312851	+	0.755290i	0.0205841	+	0.0496944i
$232$	2.87306	−	1.19006i	0.188626	−	0.0781314i
$233$	1.45524	−	3.51327i	0.0953363	−	0.230162i	−0.869016	−	0.494784i	$-0.835247\pi$
$233$	1.45524	−	3.51327i	0.0953363	−	0.230162i	0.964352	+	0.264622i	$0.0852472\pi$
$234$		−	9.38897i		−	0.613776i
$235$		0			0
$236$	5.44399	−	5.44399i	0.354374	−	0.354374i
$237$	6.71002			0.435863
$238$	−9.25647	+	10.8158i	−0.600008	+	0.701082i
$239$	−5.80679			−0.375610			−0.187805	−	0.982206i	$-0.560137\pi$
$239$	−5.80679			−0.375610			−0.187805	+	0.982206i	$0.560137\pi$
$240$		0			0
$241$	8.06359	+	3.34005i	0.519421	+	0.215151i	0.626963	−	0.779049i	$-0.284298\pi$
$241$	8.06359	+	3.34005i	0.519421	+	0.215151i	−0.107541	+	0.994201i	$0.534298\pi$
$242$			29.5597i			1.90017i
$243$	−2.37441	+	5.73233i	−0.152319	+	0.367729i
$244$	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
$248$	2.18741	+	5.28087i	0.138901	+	0.335336i
$249$	−6.27689	+	2.59997i	−0.397781	+	0.164766i
$250$		0			0
$251$			15.2424i			0.962093i	0.876695	+	0.481047i	$0.159743\pi$
$251$			15.2424i			0.962093i	−0.876695	+	0.481047i	$0.840257\pi$
$252$	−3.86949	−	1.60279i	−0.243755	−	0.100967i
$253$	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	$0.399757\pi$
$258$	7.79524	+	3.22889i	0.485310	+	0.201022i
$259$		−	11.1742i		−	0.694331i
$260$		0			0
$261$	0.184810	−	0.0765508i	0.0114395	−	0.00473838i
$262$	−4.67342	−	11.2826i	−0.288725	−	0.697043i
$263$	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
$267$	2.95221	−	7.12726i	0.180672	−	0.436181i
$268$			66.0278i			4.03329i
$269$	20.9581	+	8.68112i	1.27784	+	0.529297i	0.915338	−	0.402687i	$-0.131924\pi$
$269$	20.9581	+	8.68112i	1.27784	+	0.529297i	0.362499	+	0.931984i	$0.381924\pi$
$270$		0			0
$271$	9.96764			0.605491			0.302745	−	0.953071i	$-0.402097\pi$
$271$	9.96764			0.605491			0.302745	+	0.953071i	$0.402097\pi$
$272$	18.9896	−	58.2435i	1.15141	−	3.53153i
$273$	−11.0786			−0.670506
$274$	−17.4724	+	17.4724i	−1.05555	+	1.05555i
$275$		0			0
$276$		−	57.5562i		−	3.46448i
$277$	4.48012	−	10.8160i	0.269184	−	0.649868i	−0.730261	−	0.683168i	$-0.760602\pi$
$277$	4.48012	−	10.8160i	0.269184	−	0.649868i	0.999445	+	0.0332998i	$0.0106016\pi$
$278$	11.8589	−	4.91210i	0.711247	−	0.294608i
$279$	0.140705	+	0.339693i	0.00842380	+	0.0203369i
$280$		0			0
$281$	−0.838071	−	0.838071i	−0.0499951	−	0.0499951i	0.681667	−	0.731662i	$-0.261255\pi$
$281$	−0.838071	−	0.838071i	−0.0499951	−	0.0499951i	−0.731662	+	0.681667i	$0.761255\pi$
$282$	8.18335	+	19.7564i	0.487311	+	1.17647i
$283$	−4.25986	+	1.76449i	−0.253222	+	0.104888i	−0.505684	−	0.862719i	$-0.668760\pi$
$283$	−4.25986	+	1.76449i	−0.253222	+	0.104888i	0.252462	+	0.967607i	$0.418760\pi$
$284$	−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
$288$	13.1712			0.776118
$289$	−13.7331	−	10.0201i	−0.807827	−	0.589420i
$290$		0			0
$291$	−0.694998	+	0.694998i	−0.0407415	+	0.0407415i
$292$	−14.6207	−	6.05609i	−0.855612	−	0.354406i
$293$		−	3.09527i		−	0.180828i	−0.995904	−	0.0904138i	$-0.971181\pi$
$293$		−	3.09527i		−	0.180828i	0.995904	−	0.0904138i	$-0.0288190\pi$
$294$	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
$302$		−	6.24524i		−	0.359373i
$303$	10.6473	+	4.41024i	0.611670	+	0.253362i
$304$	1.40934	−	1.40934i	0.0808310	−	0.0808310i
$305$		0			0
$306$	2.11864	−	6.49815i	0.121115	−	0.371475i
$307$	−11.8387			−0.675668			−0.337834	−	0.941206i	$-0.609694\pi$
$307$	−11.8387			−0.675668			−0.337834	+	0.941206i	$0.609694\pi$
$308$	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	−0.435674	−	0.900105i	$-0.643490\pi$
$311$	8.97392	−	21.6650i	0.508864	−	1.22851i	0.944538	−	0.328402i	$-0.106510\pi$
$312$	76.3938	−	31.6433i	4.32494	−	1.79145i
$313$	−10.5652	−	25.5068i	−0.597183	−	1.44173i	−0.876440	−	0.481511i	$-0.840088\pi$
$313$	−10.5652	−	25.5068i	−0.597183	−	1.44173i	0.279257	−	0.960216i	$-0.409912\pi$
$314$	−36.9047	−	36.9047i	−2.08265	−	2.08265i
$315$		0			0
$316$	−9.05715	−	21.8659i	−0.509505	−	1.23005i
$317$	29.4357	−	12.1926i	1.65327	−	0.684807i	0.655737	−	0.754989i	$-0.272358\pi$
$317$	29.4357	−	12.1926i	1.65327	−	0.684807i	0.997534	+	0.0701822i	$0.0223581\pi$
$318$	2.49412	−	6.02135i	0.139864	−	0.337660i
$319$			0.137720i			0.00771087i
$320$		0			0
$321$	10.1444	−	10.1444i	0.566206	−	0.566206i
$322$	23.5449			1.31211
$323$	−0.250599	−	0.493059i	−0.0139437	−	0.0274345i
$324$	−37.1582			−2.06434
$325$		0			0
$326$	−46.2409	−	19.1536i	−2.56104	−	1.06082i
$327$		−	24.2966i		−	1.34361i
$328$	5.90033	−	14.2447i	0.325791	−	0.786530i
$329$	−5.91406	+	2.44968i	−0.326053	+	0.135055i
$330$		0			0
$331$	18.4377	+	18.4377i	1.01343	+	1.01343i	0.999909	+	0.0135172i	$0.00430279\pi$
$331$	18.4377	+	18.4377i	1.01343	+	1.01343i	0.0135172	+	0.999909i	$0.495697\pi$
$332$	16.9450	+	16.9450i	0.929978	+	0.929978i
$333$	2.05303	+	4.95645i	0.112505	+	0.271612i
$334$	50.8294	−	21.0542i	2.78126	−	1.15204i
$335$		0			0
$336$		−	29.0621i		−	1.58547i
$337$	−15.2613	−	6.32145i	−0.831338	−	0.344351i	−0.0739055	−	0.997265i	$-0.523546\pi$
$337$	−15.2613	−	6.32145i	−0.831338	−	0.344351i	−0.757432	+	0.652914i	$0.773546\pi$
$338$	−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
$343$	14.4871	+	6.00074i	0.782229	+	0.324010i
$344$		−	18.8518i		−	1.01642i
$345$		0			0
$346$	−48.2208	+	19.9737i	−2.59237	+	1.07379i
$347$	7.77787	+	18.7774i	0.417538	+	1.00803i	0.983059	+	0.183292i	$0.0586753\pi$
$347$	7.77787	+	18.7774i	0.417538	+	1.00803i	−0.565521	+	0.824734i	$0.691325\pi$
$348$	1.96657	+	1.96657i	0.105419	+	0.105419i
$349$	3.45460	+	3.45460i	0.184921	+	0.184921i	0.793496	−	0.608575i	$-0.208259\pi$
$349$	3.45460	+	3.45460i	0.184921	+	0.184921i	−0.608575	+	0.793496i	$0.708259\pi$
$350$		0			0
$351$	29.1979	−	12.0941i	1.55847	−	0.645538i
$352$	−3.47018	+	8.37776i	−0.184961	+	0.446536i
$353$		−	22.6733i		−	1.20678i	−0.797447	−	0.603389i	$-0.793817\pi$
$353$		−	22.6733i		−	1.20678i	0.797447	−	0.603389i	$-0.206183\pi$
$354$	5.50655	+	2.28089i	0.292670	+	0.121228i
$355$		0			0
$356$	−27.2104			−1.44215
$357$	−7.66753	−	2.49990i	−0.405809	−	0.132309i
$358$	54.1080			2.85970
$359$	9.53237	−	9.53237i	0.503099	−	0.503099i	−0.409300	−	0.912400i	$-0.634227\pi$
$359$	9.53237	−	9.53237i	0.503099	−	0.503099i	0.912400	+	0.409300i	$0.134227\pi$
$360$		0			0
$361$			18.9820i			0.999053i
$362$	9.26413	−	22.3656i	0.486912	−	1.17551i
$363$	−15.4711	+	6.40833i	−0.812021	+	0.336350i
$364$	14.9538	+	36.1017i	0.783792	+	1.89224i
$365$		0			0
$366$	23.3121	+	23.3121i	1.21854	+	1.21854i
$367$	0.731262	+	1.76542i	0.0381715	+	0.0921543i	0.941816	−	0.336130i	$-0.109118\pi$
$367$	0.731262	+	1.76542i	0.0381715	+	0.0921543i	−0.903644	+	0.428284i	$0.859118\pi$
$368$	−93.6073	+	38.7734i	−4.87962	+	2.02120i
$369$	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
$373$	24.9357			1.29112			0.645562	−	0.763708i	$-0.276623\pi$
$373$	24.9357			1.29112			0.645562	+	0.763708i	$0.276623\pi$
$374$	3.57507	+	3.05966i	0.184863	+	0.158211i
$375$		0			0
$376$	33.7843	−	33.7843i	1.74229	−	1.74229i
$377$	−1.72425	−	0.714206i	−0.0888032	−	0.0367835i
$378$		−	19.2656i		−	0.990916i
$379$	−6.35332	+	15.3383i	−0.326348	+	0.787874i	0.672509	+	0.740089i	$0.265216\pi$
$379$	−6.35332	+	15.3383i	−0.326348	+	0.787874i	−0.998858	+	0.0477856i	$0.984784\pi$
$380$		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
$387$		−	1.21264i		−	0.0616420i
$388$	3.20289	+	1.32668i	0.162602	+	0.0673520i
$389$	15.7531	−	15.7531i	0.798715	−	0.798715i	−0.184178	−	0.982893i	$-0.558962\pi$
$389$	15.7531	−	15.7531i	0.798715	−	0.798715i	0.982893	+	0.184178i	$0.0589622\pi$
$390$		0			0
$391$	2.17765	+	28.0319i	0.110129	+	1.41764i
$392$	−50.9740			−2.57458
$393$	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
$397$	24.2702	−	10.0530i	1.21809	−	0.504548i	0.321285	−	0.946983i	$-0.395885\pi$
$397$	24.2702	−	10.0530i	1.21809	−	0.504548i	0.896801	+	0.442435i	$0.145885\pi$
$398$	13.8016	+	33.3200i	0.691812	+	1.67018i
$399$	−0.185534	−	0.185534i	−0.00928831	−	0.00928831i
$400$		0			0
$401$	14.6020	+	35.2524i	0.729191	+	1.76042i	0.645277	+	0.763949i	$0.276742\pi$
$401$	14.6020	+	35.2524i	0.729191	+	1.76042i	0.0839140	+	0.996473i	$0.473258\pi$
$402$	−47.2252	+	19.5613i	−2.35538	+	0.975630i
$403$	1.31276	−	3.16927i	0.0653930	−	0.157873i
$404$		−	40.6491i		−	2.02237i
$405$		0			0
$406$	−0.804481	+	0.804481i	−0.0399257	+	0.0399257i
$407$	−3.69355			−0.183082
$408$	60.0129	−	4.66208i	2.97108	−	0.230807i
$409$	−19.0995			−0.944411			−0.472206	−	0.881488i	$-0.656542\pi$
$409$	−19.0995			−0.944411			−0.472206	+	0.881488i	$0.656542\pi$
$410$		0			0
$411$	−12.9327	−	5.35689i	−0.637921	−	0.264236i
$412$			74.1281i			3.65203i
$413$	−0.682783	+	1.64838i	−0.0335976	+	0.0811117i
$414$	−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
$418$	0.0585868	+	0.141441i	0.00286558	+	0.00691811i
$419$	−30.9970	+	12.8394i	−1.51430	+	0.627244i	−0.976440	−	0.215790i	$-0.930767\pi$
$419$	−30.9970	+	12.8394i	−1.51430	+	0.627244i	−0.537860	+	0.843034i	$0.680767\pi$
$420$		0			0
$421$		−	18.9396i		−	0.923058i	−0.887125	−	0.461529i	$-0.847301\pi$
$421$		−	18.9396i		−	0.923058i	0.887125	−	0.461529i	$-0.152699\pi$
$422$	−50.1685	−	20.7805i	−2.44216	−	1.01158i
$423$	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
$428$	−46.7504	−	19.3646i	−2.25976	−	0.936025i
$429$			3.66194i			0.176800i
$430$		0			0
$431$	22.5308	−	9.33254i	1.08527	−	0.449533i	0.232914	−	0.972497i	$-0.425174\pi$
$431$	22.5308	−	9.33254i	1.08527	−	0.449533i	0.852354	+	0.522965i	$0.175174\pi$
$432$	31.7263	+	76.5940i	1.52643	+	3.68513i
$433$	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
$437$	−0.350062	+	0.845124i	−0.0167457	+	0.0404278i
$438$		−	12.2514i		−	0.585393i
$439$	2.97814	+	1.23359i	0.142139	+	0.0588759i	0.452619	−	0.891704i	$-0.350490\pi$
$439$	2.97814	+	1.23359i	0.142139	+	0.0588759i	−0.310480	+	0.950580i	$0.600490\pi$
$440$		0			0
$441$	−3.27891			−0.156138
$442$	−56.8466	+	28.8924i	−2.70392	+	1.37427i
$443$	17.5623			0.834412			0.417206	−	0.908812i	$-0.363009\pi$
$443$	17.5623			0.834412			0.417206	+	0.908812i	$0.363009\pi$
$444$	−52.7418	+	52.7418i	−2.50302	+	2.50302i
$445$		0			0
$446$			17.3752i			0.822739i
$447$	0.459344	−	1.10895i	0.0217262	−	0.0524517i
$448$	−34.4943	+	14.2880i	−1.62970	+	0.675045i
$449$	7.08856	+	17.1133i	0.334530	+	0.807626i	0.998221	+	0.0596199i	$0.0189889\pi$
$449$	7.08856	+	17.1133i	0.334530	+	0.807626i	−0.663691	+	0.748007i	$0.731011\pi$
$450$		0			0
$451$	0.482826	+	0.482826i	0.0227354	+	0.0227354i
$452$	−2.60333	−	6.28500i	−0.122451	−	0.295622i
$453$	3.26866	−	1.35392i	0.153575	−	0.0636128i
$454$	−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	$0.138219\pi$
$458$	−42.4488			−1.98350
$459$	22.9371	−	1.78186i	1.07061	−	0.0831700i
$460$		0			0
$461$	12.6921	−	12.6921i	0.591131	−	0.591131i	−0.346806	−	0.937937i	$-0.612734\pi$
$461$	12.6921	−	12.6921i	0.591131	−	0.591131i	0.937937	+	0.346806i	$0.112734\pi$
$462$	2.06240	+	0.854275i	0.0959516	+	0.0397445i
$463$			35.5792i			1.65350i	0.562567	+	0.826752i	$0.309814\pi$
$463$			35.5792i			1.65350i	−0.562567	+	0.826752i	$0.690186\pi$
$464$	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	0.999351	−	0.0360098i	$-0.0114647\pi$
$467$	20.8180	+	20.8180i	0.963342	+	0.963342i	−0.0360098	+	0.999351i	$0.511465\pi$
$468$	−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
$472$		−	13.3169i		−	0.612959i
$473$	0.771322	+	0.319492i	0.0354654	+	0.0146903i
$474$	12.9559	−	12.9559i	0.595086	−	0.595086i
$475$		0			0
$476$	2.20318	+	28.3605i	0.100982	+	1.29990i
$477$	−0.936692			−0.0428882
$478$	−11.2119	+	11.2119i	−0.512822	+	0.512822i
$479$	−15.4620	−	6.40457i	−0.706477	−	0.292632i	0.000368864	−	1.00000i	$-0.499883\pi$
$479$	−15.4620	−	6.40457i	−0.706477	−	0.292632i	−0.706846	+	0.707368i	$0.749883\pi$
$480$		0			0
$481$	19.1544	−	46.2428i	0.873365	−	2.10849i
$482$	22.0185	−	9.12036i	1.00292	−	0.415421i
$483$	5.10437	+	12.3230i	0.232257	+	0.560718i
$484$	41.7655	+	41.7655i	1.89843	+	1.89843i
$485$		0			0
$486$	6.48359	+	15.6528i	0.294102	+	0.710024i
$487$	21.6579	−	8.97101i	0.981415	−	0.406515i	0.166466	−	0.986047i	$-0.446765\pi$
$487$	21.6579	−	8.97101i	0.981415	−	0.406515i	0.814950	+	0.579532i	$0.196765\pi$
$488$	28.1886	−	68.0533i	1.27604	−	3.08063i
$489$		−	28.3541i		−	1.28222i
$490$		0			0
$491$	−18.0226	+	18.0226i	−0.813347	+	0.813347i	−0.985134	−	0.171787i	$-0.945046\pi$
$491$	−18.0226	+	18.0226i	−0.813347	+	0.813347i	0.171787	+	0.985134i	$0.445046\pi$
$492$	13.7890			0.621655
$493$	−1.03220	−	0.883386i	−0.0464878	−	0.0397857i
$494$	−2.07465			−0.0933431
$495$		0			0
$496$	8.31387	+	3.44372i	0.373304	+	0.154627i
$497$		−	6.10091i		−	0.273663i
$498$	−7.09951	+	17.1397i	−0.318136	+	0.768049i
$499$	26.5542	−	10.9991i	1.18873	−	0.492388i	0.301388	−	0.953502i	$-0.402550\pi$
$499$	26.5542	−	10.9991i	1.18873	−	0.492388i	0.887341	+	0.461114i	$0.152550\pi$
$500$		0			0
$501$	22.0389	+	22.0389i	0.984625	+	0.984625i
$502$	29.4306	+	29.4306i	1.31355	+	1.31355i
$503$	−0.00393607	−	0.00950252i	−0.000175501	−	0.000423697i	0.923792	−	0.382895i	$-0.125073\pi$
$503$	−0.00393607	−	0.00950252i	−0.000175501	−	0.000423697i	−0.923967	+	0.382472i	$0.875073\pi$
$504$	−6.69303	+	2.77235i	−0.298131	+	0.123490i
$505$		0			0
$506$		−	7.78261i		−	0.345979i
$507$	−27.2680	−	11.2948i	−1.21102	−	0.501619i
$508$	68.7339	−	68.7339i	3.04957	−	3.04957i
$509$	−26.8066			−1.18818			−0.594091	−	0.804398i	$-0.702488\pi$
$509$	−26.8066			−1.18818			−0.594091	+	0.804398i	$0.702488\pi$
$510$		0			0
$511$	3.66744			0.162238
$512$	29.6367	−	29.6367i	1.30977	−	1.30977i
$513$	0.691521	+	0.286437i	0.0305314	+	0.0126465i
$514$			39.6873i			1.75053i
$515$		0			0
$516$	15.5762	−	6.45189i	0.685705	−	0.284028i
$517$	0.809725	+	1.95485i	0.0356117	+	0.0859742i
$518$	−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	−0.167851	−	0.985812i	$-0.553683\pi$
$521$	9.37063	−	3.88144i	0.410535	−	0.170049i	0.578386	+	0.815763i	$0.303683\pi$
$522$	0.209030	−	0.504644i	0.00914902	−	0.0220877i
$523$			16.7568i			0.732724i	0.930472	+	0.366362i	$0.119397\pi$
$523$			16.7568i			0.732724i	−0.930472	+	0.366362i	$0.880603\pi$
$524$	−22.5446	−	9.33830i	−0.984867	−	0.407945i
$525$		0			0
$526$	51.9587			2.26551
$527$	1.62372	−	1.89724i	0.0707303	−	0.0826452i
$528$	−9.60627			−0.418059
$529$	16.6183	−	16.6183i	0.722534	−	0.722534i
$530$		0			0
$531$		−	0.856609i		−	0.0371736i
$532$	−0.354165	+	0.855030i	−0.0153550	+	0.0370702i
$533$	−8.54882	+	3.54104i	−0.370291	+	0.153379i
$534$	−8.06133	−	19.4618i	−0.348848	−	0.842193i
$535$		0			0
$536$	80.7572	+	80.7572i	3.48818	+	3.48818i
$537$	11.7302	+	28.3193i	0.506196	+	1.22207i
$538$	57.2283	−	23.7048i	2.46729	−	1.02198i
$539$	0.863887	−	2.08561i	0.0372102	−	0.0898335i
$540$		0			0
$541$	−16.7559	−	6.94050i	−0.720390	−	0.298395i	−0.00779397	−	0.999970i	$-0.502481\pi$
$541$	−16.7559	−	6.94050i	−0.720390	−	0.298395i	−0.712596	+	0.701574i	$0.752481\pi$
$542$	19.2458	−	19.2458i	0.826679	−	0.826679i
$543$	13.7142			0.588532
$544$	−40.5313	−	79.7463i	−1.73776	−	3.41909i
$545$		0			0
$546$	−21.3909	+	21.3909i	−0.915444	+	0.915444i
$547$	−20.8574	−	8.63943i	−0.891799	−	0.369395i	−0.110738	−	0.993850i	$-0.535321\pi$
$547$	−20.8574	−	8.63943i	−0.891799	−	0.369395i	−0.781061	+	0.624454i	$0.785321\pi$
$548$			49.3743i			2.10916i
$549$	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
$557$		−	5.97545i		−	0.253188i	−0.991955	−	0.126594i	$-0.959595\pi$
$557$		−	5.97545i		−	0.253188i	0.991955	−	0.126594i	$-0.0404045\pi$
$558$	0.927568	+	0.384211i	0.0392671	+	0.0162650i
$559$	−8.00002	+	8.00002i	−0.338365	+	0.338365i
$560$		0			0
$561$	−0.826325	+	2.53445i	−0.0348875	+	0.107004i
$562$	−3.23635			−0.136517
$563$	2.52298	−	2.52298i	0.106331	−	0.106331i	−0.651940	−	0.758271i	$-0.726045\pi$
$563$	2.52298	−	2.52298i	0.106331	−	0.106331i	0.758271	+	0.651940i	$0.226045\pi$
$564$	39.4766	+	16.3517i	1.66226	+	0.688533i
$565$		0			0
$566$	−4.81814	+	11.6320i	−0.202521	+	0.488930i
$567$	7.95574	−	3.29538i	0.334110	−	0.138393i
$568$	17.4258	+	42.0696i	0.731171	+	1.76520i
$569$	31.1965	+	31.1965i	1.30783	+	1.30783i	0.922981	+	0.384846i	$0.125746\pi$
$569$	31.1965	+	31.1965i	1.30783	+	1.30783i	0.384846	+	0.922981i	$0.374254\pi$
$570$		0			0
$571$	−4.81154	−	11.6161i	−0.201357	−	0.486118i	0.790655	−	0.612262i	$-0.209740\pi$
$571$	−4.81154	−	11.6161i	−0.201357	−	0.486118i	−0.992012	+	0.126143i	$0.959740\pi$
$572$	11.9331	−	4.94287i	0.498949	−	0.206672i
$573$	6.27975	−	15.1606i	0.262340	−	0.633345i
$574$			5.64076i			0.235441i
$575$		0			0
$576$	12.6752	−	12.6752i	0.528135	−	0.528135i
$577$	−14.5344			−0.605075			−0.302538	−	0.953137i	$-0.597834\pi$
$577$	−14.5344			−0.605075			−0.302538	+	0.953137i	$0.597834\pi$
$578$	−45.8634	+	7.16904i	−1.90767	+	0.298193i
$579$	15.0442			0.625217
$580$		0			0
$581$	−5.13077	−	2.12524i	−0.212860	−	0.0881697i
$582$			2.68385i			0.111249i
$583$	0.246788	−	0.595800i	0.0102209	−	0.0246755i
$584$	−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	0.506209	−	0.862411i	$-0.331046\pi$
$587$	−8.63007	−	8.63007i	−0.356201	−	0.356201i	−0.862411	+	0.506209i	$0.831046\pi$
$588$	−17.4455	−	42.1172i	−0.719440	−	1.73688i
$589$	0.0750609	−	0.0310912i	0.00309283	−	0.00128109i
$590$		0			0
$591$			36.8091i			1.51412i
$592$	121.308	+	50.2472i	4.98571	+	2.06515i
$593$	−8.08169	+	8.08169i	−0.331875	+	0.331875i	−0.853298	−	0.521423i	$-0.825401\pi$
$593$	−8.08169	+	8.08169i	−0.331875	+	0.331875i	0.521423	+	0.853298i	$0.325401\pi$
$594$	−6.36810			−0.261286
$595$		0			0
$596$	−4.23376			−0.173421
$597$	−14.4471	+	14.4471i	−0.591279	+	0.591279i
$598$	97.4374	+	40.3599i	3.98451	+	1.65044i
$599$			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	−0.583672	−	0.811989i	$-0.698385\pi$
$601$	−10.3510	+	4.28754i	−0.422228	+	0.174893i	0.161444	+	0.986882i	$0.448385\pi$
$602$	2.63932	+	6.37189i	0.107571	+	0.259699i
$603$	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
$607$	15.3256	−	36.9992i	0.622046	−	1.50175i	−0.227252	−	0.973836i	$-0.572974\pi$
$607$	15.3256	−	36.9992i	0.622046	−	1.50175i	0.849297	−	0.527915i	$-0.177026\pi$
$608$		−	2.91039i		−	0.118032i
$609$	−0.595458	−	0.246647i	−0.0241292	−	0.00999463i
$610$		0			0
$611$	−28.6737			−1.16001
$612$	−6.18790	−	12.1749i	−0.250131	−	0.492139i
$613$	−29.1043			−1.17551			−0.587755	−	0.809039i	$-0.699988\pi$
$613$	−29.1043			−1.17551			−0.587755	+	0.809039i	$0.699988\pi$
$614$	−22.8585	+	22.8585i	−0.922493	+	0.922493i
$615$		0			0
$616$		−	4.98765i		−	0.200958i
$617$	−6.30101	+	15.2120i	−0.253669	+	0.612411i	−0.998495	−	0.0548478i	$-0.982533\pi$
$617$	−6.30101	+	15.2120i	−0.253669	+	0.612411i	0.744826	+	0.667259i	$0.232533\pi$
$618$	−53.0188	+	21.9611i	−2.13273	+	0.883405i
$619$	2.91366	+	7.03419i	0.117110	+	0.282728i	0.971555	−	0.236813i	$-0.0761029\pi$
$619$	2.91366	+	7.03419i	0.117110	+	0.282728i	−0.854445	+	0.519541i	$0.826103\pi$
$620$		0			0
$621$	−26.9054	−	26.9054i	−1.07968	−	1.07968i
$622$	−24.5043	−	59.1585i	−0.982532	−	2.37204i
$623$	5.82588	−	2.41316i	0.233409	−	0.0966811i
$624$	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
$628$	−104.287			−4.16150
$629$	23.6916	−	27.6826i	0.944648	−	1.10378i
$630$		0			0
$631$	−26.3010	+	26.3010i	−1.04703	+	1.04703i	−0.0481871	+	0.998838i	$0.515344\pi$
$631$	−26.3010	+	26.3010i	−1.04703	+	1.04703i	−0.998838	+	0.0481871i	$0.984656\pi$
$632$	−37.8213	−	15.6661i	−1.50445	−	0.623165i
$633$		−	30.7624i		−	1.22270i
$634$	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	−0.845337	−	0.534233i	$-0.820600\pi$
$641$	3.29555	−	7.95617i	0.130167	−	0.314250i	0.975504	+	0.219983i	$0.0706003\pi$
$642$		−	39.1743i		−	1.54609i
$643$	−17.6673	−	7.31804i	−0.696731	−	0.288595i	0.00607035	−	0.999982i	$-0.498068\pi$
$643$	−17.6673	−	7.31804i	−0.696731	−	0.288595i	−0.702801	+	0.711386i	$0.748068\pi$
$644$	33.2672	−	33.2672i	1.31091	−	1.31091i
$645$		0			0
$646$	−1.43588	−	0.468150i	−0.0564939	−	0.0184191i
$647$	25.5972			1.00633			0.503164	−	0.864191i	$-0.332169\pi$
$647$	25.5972			1.00633			0.503164	+	0.864191i	$0.332169\pi$
$648$	−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
$652$	−92.3972	+	38.2722i	−3.61855	+	1.49885i
$653$	−3.31942	−	8.01379i	−0.129899	−	0.313604i	0.845527	−	0.533933i	$-0.179287\pi$
$653$	−3.31942	−	8.01379i	−0.129899	−	0.313604i	−0.975425	+	0.220330i	$0.929287\pi$
$654$	−46.9127	−	46.9127i	−1.83443	−	1.83443i
$655$		0			0
$656$	−9.28911	−	22.4259i	−0.362679	−	0.875584i
$657$	−1.62674	+	0.673818i	−0.0634652	+	0.0262881i
$658$	−6.68913	+	16.1490i	−0.260770	+	0.629553i
$659$			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	−0.565853	−	0.824506i	$-0.691453\pi$
$661$	6.64994	−	6.64994i	0.258653	−	0.258653i	0.824506	+	0.565853i	$0.191453\pi$
$662$	71.2001			2.76727
$663$	−27.4458	−	23.4889i	−1.06590	−	0.912234i
$664$	41.4502			1.60858
$665$		0			0
$666$	13.5341	+	5.60602i	0.524437	+	0.217229i
$667$			2.24700i			0.0870041i
$668$	42.0700	−	101.566i	1.62774	−	3.92970i
$669$	−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
$673$	1.74487	+	4.21250i	0.0672599	+	0.162380i	0.953935	−	0.300013i	$-0.0969910\pi$
$673$	1.74487	+	4.21250i	0.0672599	+	0.162380i	−0.886675	+	0.462393i	$0.846991\pi$
$674$	−41.6727	+	17.2614i	−1.60517	+	0.664885i
$675$		0			0
$676$			104.104i			4.00399i
$677$	−32.8914	−	13.6240i	−1.26412	−	0.523615i	−0.352947	−	0.935643i	$-0.614820\pi$
$677$	−32.8914	−	13.6240i	−1.26412	−	0.523615i	−0.911171	+	0.412029i	$0.864820\pi$
$678$	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
$683$	11.0606	+	4.58144i	0.423222	+	0.175304i	0.584121	−	0.811667i	$-0.301439\pi$
$683$	11.0606	+	4.58144i	0.423222	+	0.175304i	−0.160899	+	0.986971i	$0.551439\pi$
$684$		−	0.444329i		−	0.0169894i
$685$		0			0
$686$	39.5585	−	16.3857i	1.51035	−	0.625608i
$687$	−9.20259	−	22.2170i	−0.351101	−	0.847632i
$688$	−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	0.0139574	−	0.999903i	$-0.495557\pi$
$691$	19.2122	−	7.95793i	0.730865	−	0.302734i	0.716907	+	0.697169i	$0.245557\pi$
$692$	−39.9109	+	96.3535i	−1.51719	+	3.66281i
$693$		−	0.320831i		−	0.0121874i
$694$	51.2739	+	21.2383i	1.94633	+	0.806196i
$695$		0			0
$696$	4.81055			0.182343
$697$	−6.71572	+	0.521709i	−0.254376	+	0.0197611i
$698$	13.3405			0.504946
$699$	4.15955	−	4.15955i	0.157328	−	0.157328i
$700$		0			0
$701$			13.1645i			0.497215i	0.968604	+	0.248607i	$0.0799729\pi$
$701$			13.1645i			0.497215i	−0.968604	+	0.248607i	$0.920027\pi$
$702$	33.0244	−	79.7279i	1.24643	−	3.00914i
$703$	1.09521	−	0.453652i	0.0413067	−	0.0171098i
$704$	4.72279	+	11.4018i	0.177997	+	0.429723i
$705$		0			0
$706$	−43.7783	−	43.7783i	−1.64762	−	1.64762i
$707$	3.60497	+	8.70316i	0.135579	+	0.327316i
$708$	11.0030	−	4.55761i	0.413519	−	0.171285i
$709$	7.77328	−	18.7664i	0.291932	−	0.704785i	−0.708067	−	0.706145i	$-0.750433\pi$
$709$	7.77328	−	18.7664i	0.291932	−	0.704785i	0.999999	+	0.00135939i	$0.000432708\pi$
$710$		0			0
$711$	−2.43286	−	1.00772i	−0.0912394	−	0.0377926i
$712$	−33.2805	+	33.2805i	−1.24724	+	1.24724i
$713$	−4.13012			−0.154674
$714$	−19.6316	+	9.97783i	−0.734695	+	0.373411i
$715$		0			0
$716$	76.4504	−	76.4504i	2.85708	−	2.85708i
$717$	−8.29881	−	3.43748i	−0.309925	−	0.128375i
$718$		−	36.8108i		−	1.37377i
$719$	−11.1535	+	26.9270i	−0.415957	+	1.00421i	0.567550	+	0.823339i	$0.307891\pi$
$719$	−11.1535	+	26.9270i	−0.415957	+	1.00421i	−0.983507	+	0.180870i	$0.942109\pi$
$720$		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
$727$			18.9928i			0.704402i	0.935924	+	0.352201i	$0.114567\pi$
$727$			18.9928i			0.704402i	−0.935924	+	0.352201i	$0.885433\pi$
$728$	62.4448	+	25.8655i	2.31436	+	0.958639i
$729$	−21.2335	+	21.2335i	−0.786426	+	0.786426i
$730$		0			0
$731$	−7.34207	+	3.73163i	−0.271556	+	0.138019i
$732$	65.8762			2.43486
$733$	−23.0263	+	23.0263i	−0.850494	+	0.850494i	−0.990194	−	0.139700i	$-0.955386\pi$
$733$	−23.0263	+	23.0263i	−0.850494	+	0.850494i	0.139700	+	0.990194i	$0.455386\pi$
$734$	4.82068	+	1.99679i	0.177934	+	0.0737029i
$735$		0			0
$736$	−56.6182	+	136.688i	−2.08698	+	5.03840i
$737$	−4.67283	+	1.93555i	−0.172126	+	0.0712970i
$738$	−1.03637	−	2.50203i	−0.0381495	−	0.0921010i
$739$	−21.7401	−	21.7401i	−0.799723	−	0.799723i	0.183329	−	0.983052i	$-0.441313\pi$
$739$	−21.7401	−	21.7401i	−0.799723	−	0.799723i	−0.983052	+	0.183329i	$0.941313\pi$
$740$		0			0
$741$	−0.449770	−	1.08584i	−0.0165227	−	0.0398893i
$742$	4.92190	−	2.03872i	0.180688	−	0.0748436i
$743$	3.74040	−	9.03012i	0.137222	−	0.331283i	−0.840298	−	0.542124i	$-0.817620\pi$
$743$	3.74040	−	9.03012i	0.137222	−	0.331283i	0.977520	+	0.210841i	$0.0676202\pi$
$744$			8.84209i			0.324167i
$745$		0			0
$746$	48.1467	−	48.1467i	1.76278	−	1.76278i
$747$	2.66629			0.0975543
$748$	9.37435	−	0.728243i	0.342760	−	0.0266272i
$749$	11.7268			0.428489
$750$		0			0
$751$	11.9895	+	4.96623i	0.437504	+	0.181220i	0.590554	−	0.806998i	$-0.298909\pi$
$751$	11.9895	+	4.96623i	0.437504	+	0.181220i	−0.153050	+	0.988219i	$0.548909\pi$
$752$		−	75.2189i		−	2.74295i
$753$	−9.02315	+	21.7838i	−0.328822	+	0.793846i
$754$	−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	0.0839060	−	0.996474i	$-0.473260\pi$
$757$	−25.1081	−	25.1081i	−0.912568	−	0.912568i	−0.996474	+	0.0839060i	$0.973260\pi$
$758$	17.3484	+	41.8828i	0.630124	+	1.52125i
$759$	4.07329	−	1.68721i	0.147851	−	0.0612419i
$760$		0			0
$761$			23.6745i			0.858200i	0.903257	+	0.429100i	$0.141169\pi$
$761$			23.6745i			0.858200i	−0.903257	+	0.429100i	$0.858831\pi$
$762$	69.5237	+	28.7977i	2.51858	+	1.04323i
$763$	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
$768$	60.9140	+	25.2314i	2.19805	+	0.910461i
$769$		−	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
$772$	−20.3066	−	49.0245i	−0.730851	−	1.76443i
$773$	−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
$777$	6.61486	−	15.9697i	0.237307	−	0.572909i
$778$		−	60.8333i		−	2.18098i
$779$	−0.202470	−	0.0838658i	−0.00725424	−	0.00300480i
$780$		0			0
$781$	−2.01661			−0.0721600
$782$	58.3296	+	49.9203i	2.08586	+	1.78514i
$783$	1.83860			0.0657063
$784$	−56.7455	+	56.7455i	−2.02662	+	2.02662i
$785$		0			0
$786$		−	18.8912i		−	0.673827i
$787$	−14.4822	+	34.9631i	−0.516234	+	1.24630i	0.423967	+	0.905678i	$0.360637\pi$
$787$	−14.4822	+	34.9631i	−0.516234	+	1.24630i	−0.940201	+	0.340621i	$0.889363\pi$
$788$	119.950	−	49.6847i	4.27303	−	1.76995i
$789$	11.2643	+	27.1944i	0.401019	+	0.968145i
$790$		0			0
$791$	1.11477	+	1.11477i	0.0396367	+	0.0396367i
$792$	0.916378	+	2.21233i	0.0325621	+	0.0786118i
$793$	−40.8416	+	16.9172i	−1.45033	+	0.600746i
$794$	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	$0.292185\pi$
$798$	−0.716469			−0.0253627
$799$	−19.8452	−	6.47028i	−0.702072	−	0.228902i
$800$		0			0
$801$	−2.14077	+	2.14077i	−0.0756404	+	0.0756404i
$802$	96.2606	+	39.8724i	3.39908	+	1.40795i
$803$		−	1.21225i		−	0.0427793i
$804$	−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	−0.945605	−	0.325317i	$-0.894529\pi$
$809$	−14.4204	−	34.8140i	−0.506995	−	1.22399i	0.438610	−	0.898678i	$-0.355471\pi$
$810$		0			0
$811$	−2.63137	+	6.35270i	−0.0924001	+	0.223073i	−0.963322	−	0.268348i	$-0.913522\pi$
$811$	−2.63137	+	6.35270i	−0.0924001	+	0.223073i	0.870922	+	0.491421i	$0.163522\pi$
$812$			2.27334i			0.0797785i
$813$	14.2453	+	5.90060i	0.499605	+	0.206943i
$814$	−7.13162	+	7.13162i	−0.249963	+	0.249963i
$815$		0			0
$816$	61.6178	−	71.9977i	2.15706	−	2.52042i
$817$	−0.267954			−0.00937452
$818$	−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	−0.685569	−	0.728008i	$-0.740446\pi$
$821$	8.99652	−	21.7195i	0.313981	−	0.758017i	0.999550	−	0.0300089i	$-0.00955356\pi$
$822$	−35.3141	+	14.6276i	−1.23172	+	0.510195i
$823$	−20.9981	−	50.6939i	−0.731948	−	1.76708i	−0.635995	−	0.771693i	$-0.719410\pi$
$823$	−20.9981	−	50.6939i	−0.731948	−	1.76708i	−0.0959532	−	0.995386i	$-0.530590\pi$
$824$	90.6645	+	90.6645i	3.15845	+	3.15845i
$825$		0			0
$826$	1.86441	+	4.50110i	0.0648713	+	0.156613i
$827$	16.2768	−	6.74207i	0.566000	−	0.234445i	−0.0812877	−	0.996691i	$-0.525903\pi$
$827$	16.2768	−	6.74207i	0.566000	−	0.234445i	0.647288	+	0.762246i	$0.275903\pi$
$828$	−8.64390	+	20.8682i	−0.300396	+	0.725220i
$829$			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
$832$	−167.242			−5.79806
$833$	10.0901	+	19.8525i	0.349601	+	0.687849i
$834$	19.8560			0.687558
$835$		0			0
$836$	0.282624	+	0.117067i	0.00977475	+	0.00404883i
$837$			3.37946i			0.116811i
$838$	−35.0593	+	84.6406i	−1.21110	+	2.92386i
$839$	39.1157	−	16.2022i	1.35042	−	0.559364i	0.414013	−	0.910271i	$-0.364127\pi$
$839$	39.1157	−	16.2022i	1.35042	−	0.559364i	0.936410	+	0.350907i	$0.114127\pi$
$840$		0			0
$841$	20.4293	+	20.4293i	0.704459	+	0.704459i
$842$	−36.5691	−	36.5691i	−1.26026	−	1.26026i
$843$	−0.701617	−	1.69385i	−0.0241650	−	0.0583394i
$844$	−100.245	+	41.5230i	−3.45059	+	1.42928i
$845$		0			0
$846$		−	8.39207i		−	0.288525i
$847$	−12.6462	−	5.23822i	−0.434528	−	0.179987i
$848$	−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
$853$	−30.6477	−	12.6947i	−1.04936	−	0.434659i	−0.209696	−	0.977767i	$-0.567247\pi$
$853$	−30.6477	−	12.6947i	−1.04936	−	0.434659i	−0.839663	+	0.543108i	$0.817247\pi$
$854$			26.9485i			0.922159i
$855$		0			0
$856$	−80.8639	+	33.4949i	−2.76387	+	1.14483i
$857$	5.88221	+	14.2009i	0.200932	+	0.485094i	0.991939	−	0.126713i	$-0.0404428\pi$
$857$	5.88221	+	14.2009i	0.200932	+	0.485094i	−0.791007	+	0.611807i	$0.790443\pi$
$858$	7.07059	+	7.07059i	0.241386	+	0.241386i
$859$	−30.2680	−	30.2680i	−1.03273	−	1.03273i	−0.999446	−	0.0332837i	$-0.989404\pi$
$859$	−30.2680	−	30.2680i	−1.03273	−	1.03273i	−0.0332837	−	0.999446i	$-0.510596\pi$
$860$		0			0
$861$	−2.95228	+	1.22288i	−0.100614	+	0.0416755i
$862$	25.4835	−	61.5227i	0.867972	−	2.09547i
$863$		−	31.3841i		−	1.06833i	−0.845382	−	0.534163i	$-0.820627\pi$
$863$		−	31.3841i		−	1.06833i	0.845382	−	0.534163i	$-0.179373\pi$
$864$	111.845	+	46.3277i	3.80505	+	1.57610i
$865$		0			0
$866$	26.4630			0.899250
$867$	−13.6950	−	22.4500i	−0.465107	−	0.762441i
$868$	−4.17853			−0.141829
$869$	1.28196	−	1.28196i	0.0434876	−	0.0434876i
$870$		0			0
$871$		−	68.5410i		−	2.32242i
$872$	−56.7262	+	136.949i	−1.92099	+	4.63768i
$873$	0.356362	−	0.147610i	0.0120610	−	0.00499585i
$874$	0.955882	+	2.30770i	0.0323332	+	0.0780592i
$875$		0			0
$876$	−17.3102	−	17.3102i	−0.584858	−	0.584858i
$877$	11.1890	+	27.0128i	0.377827	+	0.912156i	0.992373	+	0.123274i	$0.0393395\pi$
$877$	11.1890	+	27.0128i	0.377827	+	0.912156i	−0.614545	+	0.788882i	$0.710661\pi$
$878$	8.13214	−	3.36844i	0.274447	−	0.113679i
$879$	1.83233	−	4.42363i	0.0618028	−	0.149205i
$880$		0			0
$881$	−21.1976	−	8.78032i	−0.714164	−	0.295816i	−0.00413755	−	0.999991i	$-0.501317\pi$
$881$	−21.1976	−	8.78032i	−0.714164	−	0.295816i	−0.710026	+	0.704175i	$0.751317\pi$
$882$	−6.33102	+	6.33102i	−0.213176	+	0.213176i
$883$	−21.1206			−0.710766			−0.355383	−	0.934721i	$-0.615649\pi$
$883$	−21.1206			−0.710766			−0.355383	+	0.934721i	$0.615649\pi$
$884$	−39.4970	+	121.142i	−1.32843	+	4.07446i
$885$		0			0
$886$	33.9099	−	33.9099i	1.13923	−	1.13923i
$887$	16.6051	+	6.87805i	0.557544	+	0.230942i	0.643619	−	0.765346i	$-0.277432\pi$
$887$	16.6051	+	6.87805i	0.557544	+	0.230942i	−0.0860744	+	0.996289i	$0.527432\pi$
$888$			129.015i			4.32945i
$889$	−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
$897$			59.7469i			1.99489i
$898$	46.7297	+	19.3561i	1.55939	+	0.645921i
$899$	0.141118	−	0.141118i	0.00470654	−	0.00470654i
$900$		0			0
$901$	2.88246	+	5.67130i	0.0960286	+	0.188939i
$902$	1.86451			0.0620815
$903$	−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
$907$	−51.6439	+	21.3916i	−1.71481	+	0.710297i	−0.714870	+	0.699257i	$0.753514\pi$
$907$	−51.6439	+	21.3916i	−1.71481	+	0.710297i	−0.999939	+	0.0110397i	$0.996486\pi$
$908$	55.4072	+	133.765i	1.83875	+	4.43914i
$909$	−3.19805	−	3.19805i	−0.106073	−	0.106073i
$910$		0			0
$911$	0.214803	+	0.518579i	0.00711673	+	0.0171813i	0.927398	−	0.374076i	$-0.122040\pi$
$911$	0.214803	+	0.518579i	0.00711673	+	0.0171813i	−0.920281	+	0.391258i	$0.872040\pi$
$912$	2.84846	−	1.17987i	0.0943218	−	0.0390694i
$913$	−0.702481	+	1.69594i	−0.0232487	+	0.0561274i
$914$		−	40.1610i		−	1.32841i
$915$		0			0
$916$	−59.9768	+	59.9768i	−1.98169	+	1.98169i
$917$	5.65508			0.186747
$918$	40.8471	−	47.7281i	1.34816	−	1.57526i
$919$	4.29583			0.141706			0.0708531	−	0.997487i	$-0.477428\pi$
$919$	4.29583			0.141706			0.0708531	+	0.997487i	$0.477428\pi$
$920$		0			0
$921$	−16.9193	−	7.00821i	−0.557510	−	0.230928i
$922$		−	49.0127i		−	1.61415i
$923$	10.4580	−	25.2477i	0.344228	−	0.831040i
$924$	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
$928$	−2.73583	−	6.60488i	−0.0898081	−	0.216816i
$929$	8.82633	−	3.65598i	0.289582	−	0.119949i	−0.233163	−	0.972438i	$-0.574908\pi$
$929$	8.82633	−	3.65598i	0.289582	−	0.119949i	0.522746	+	0.852489i	$0.324908\pi$
$930$		0			0
$931$			0.724531i			0.0237455i
$932$	−19.1692	−	7.94015i	−0.627908	−	0.260088i
$933$	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	$-0.114344\pi$
$938$	−38.6023	−	15.9896i	−1.26041	−	0.522078i
$939$		−	42.7075i		−	1.39371i
$940$		0			0
$941$	−27.2017	+	11.2673i	−0.886751	+	0.367304i	−0.779111	−	0.626885i	$-0.784329\pi$
$941$	−27.2017	+	11.2673i	−0.886751	+	0.367304i	−0.107640	+	0.994190i	$0.534329\pi$
$942$	−30.8959	−	74.5894i	−1.00664	−	2.43025i
$943$	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
$947$	12.0899	−	29.1876i	0.392869	−	0.948469i	−0.596443	−	0.802655i	$-0.703420\pi$
$947$	12.0899	−	29.1876i	0.392869	−	0.948469i	0.989312	−	0.145814i	$-0.0465801\pi$
$948$		−	36.6114i		−	1.18908i
$949$	15.1772	+	6.28660i	0.492673	+	0.204072i
$950$		0			0
$951$	49.2859			1.59821
$952$	37.3818	+	31.9925i	1.21155	+	1.03688i
$953$	18.4486			0.597610			0.298805	−	0.954314i	$-0.403412\pi$
$953$	18.4486			0.597610			0.298805	+	0.954314i	$0.403412\pi$
$954$	−1.80859	+	1.80859i	−0.0585554	+	0.0585554i
$955$		0			0
$956$			31.6832i			1.02471i
$957$	−0.0815272	+	0.196824i	−0.00263540	+	0.00636242i
$958$	−42.2207	+	17.4884i	−1.36409	+	0.565024i
$959$	−4.37876	−	10.5713i	−0.141398	−	0.341364i
$960$		0			0
$961$	−21.6609	−	21.6609i	−0.698740	−	0.698740i
$962$	−52.3032	−	126.271i	−1.68632	−	4.07114i
$963$	−5.20157	+	2.15456i	−0.167618	+	0.0694298i
$964$	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	$0.461591\pi$
$968$	102.165			3.28371
$969$	−0.0662656	−	0.853007i	−0.00212876	−	0.0274025i
$970$		0			0
$971$	−37.1678	+	37.1678i	−1.19277	+	1.19277i	−0.216486	+	0.976286i	$0.569459\pi$
$971$	−37.1678	+	37.1678i	−1.19277	+	1.19277i	−0.976286	+	0.216486i	$0.930541\pi$
$972$	31.2769	+	12.9553i	1.00321	+	0.415542i
$973$			5.94390i			0.190553i
$974$	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	0.201747	−	0.979438i	$-0.435338\pi$
$977$	−24.3083	−	24.3083i	−0.777691	−	0.777691i	−0.979438	+	0.201747i	$0.935338\pi$
$978$	−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
$982$			69.5971i			2.22093i
$983$	−26.5414	−	10.9938i	−0.846539	−	0.350648i	−0.0831107	−	0.996540i	$-0.526486\pi$
$983$	−26.5414	−	10.9938i	−0.846539	−	0.350648i	−0.763429	+	0.645892i	$0.776486\pi$
$984$	16.8650	−	16.8650i	0.537637	−	0.537637i
$985$		0			0
$986$	−3.69867	+	0.287330i	−0.117790	+	0.00915045i
$987$	−9.90228			−0.315193
$988$	−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	0.310003	+	0.950736i	$0.399670\pi$
$991$	−18.3049	+	44.1919i	−0.581474	+	1.40380i	−0.891477	+	0.453066i	$0.850330\pi$
$992$	12.1402	−	5.02863i	0.385451	−	0.159659i
$993$	15.4357	+	37.2650i	0.489836	+	1.18257i
$994$	−11.7798	−	11.7798i	−0.373634	−	0.373634i
$995$		0			0
$996$	14.1860	+	34.2481i	0.449502	+	1.08519i
$997$	−7.21729	+	2.98950i	−0.228574	+	0.0946783i	−0.494031	−	0.869444i	$-0.664477\pi$
$997$	−7.21729	+	2.98950i	−0.228574	+	0.0946783i	0.265457	+	0.964123i	$0.414477\pi$
$998$	30.0343	−	72.5091i	0.950718	−	2.29524i
$999$			49.3097i			1.56009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.b.26.6		24
5.2	odd	4		425.2.n.c.349.6		24
5.3	odd	4		425.2.n.f.349.1		24
5.4	even	2		85.2.l.a.26.1	✓	24
15.14	odd	2		765.2.be.b.451.6		24
17.2	even	8	inner	425.2.m.b.376.6		24
17.6	odd	16		7225.2.a.bq.1.12		12
17.11	odd	16		7225.2.a.bs.1.12		12
85.2	odd	8		425.2.n.f.274.1		24
85.19	even	8		85.2.l.a.36.1	yes	24
85.24	odd	16		1445.2.d.j.866.23		24
85.44	odd	16		1445.2.d.j.866.24		24
85.53	odd	8		425.2.n.c.274.6		24
85.74	odd	16		1445.2.a.q.1.1		12
85.79	odd	16		1445.2.a.p.1.1		12
255.104	odd	8		765.2.be.b.631.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.1	✓	24	5.4	even	2
85.2.l.a.36.1	yes	24	85.19	even	8
425.2.m.b.26.6		24	1.1	even	1	trivial
425.2.m.b.376.6		24	17.2	even	8	inner
425.2.n.c.274.6		24	85.53	odd	8
425.2.n.c.349.6		24	5.2	odd	4
425.2.n.f.274.1		24	85.2	odd	8
425.2.n.f.349.1		24	5.3	odd	4
765.2.be.b.451.6		24	15.14	odd	2
765.2.be.b.631.6		24	255.104	odd	8
1445.2.a.p.1.1		12	85.79	odd	16
1445.2.a.q.1.1		12	85.74	odd	16
1445.2.d.j.866.23		24	85.24	odd	16
1445.2.d.j.866.24		24	85.44	odd	16
7225.2.a.bq.1.12		12	17.6	odd	16
7225.2.a.bs.1.12		12	17.11	odd	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.m (of order \(8\), degree \(4\), minimal)

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

Introduction

L-functions

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