LMFDB - Embedded newform 400.2.j.d.307.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(43,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("400.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.j (of order $4$, degree $2$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.5
Root			$-0.480367 + 1.33013i$ of defining polynomial
Character	$\chi$	$=$	400.307
Dual form			400.2.j.d.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.307817 + 1.38031i) q^{2} +2.85601i q^{3} +(-1.81050 + 0.849763i) q^{4} +(-3.94217 + 0.879127i) q^{6} +(0.458895 + 0.458895i) q^{7} +(-1.73024 - 2.23747i) q^{8} -5.15678 q^{9} +O(q^{10})$	\(q+(0.307817 + 1.38031i) q^{2} +2.85601i q^{3} +(-1.81050 + 0.849763i) q^{4} +(-3.94217 + 0.879127i) q^{6} +(0.458895 + 0.458895i) q^{7} +(-1.73024 - 2.23747i) q^{8} -5.15678 q^{9} +(-0.492763 - 0.492763i) q^{11} +(-2.42693 - 5.17080i) q^{12} -4.52109 q^{13} +(-0.492160 + 0.774671i) q^{14} +(2.55581 - 3.07699i) q^{16} +(3.12823 + 3.12823i) q^{17} +(-1.58734 - 7.11794i) q^{18} +(4.04508 + 4.04508i) q^{19} +(-1.31061 + 1.31061i) q^{21} +(0.528484 - 0.831845i) q^{22} +(1.80660 - 1.80660i) q^{23} +(6.39024 - 4.94157i) q^{24} +(-1.39167 - 6.24050i) q^{26} -6.15978i q^{27} +(-1.22078 - 0.440876i) q^{28} +(-3.83926 + 3.83926i) q^{29} +0.139949i q^{31} +(5.03391 + 2.58065i) q^{32} +(1.40733 - 1.40733i) q^{33} +(-3.35500 + 5.28085i) q^{34} +(9.33634 - 4.38204i) q^{36} -5.84330 q^{37} +(-4.33831 + 6.82860i) q^{38} -12.9123i q^{39} +4.55648i q^{41} +(-2.21247 - 1.40561i) q^{42} +7.49928 q^{43} +(1.31088 + 0.473414i) q^{44} +(3.04976 + 1.93756i) q^{46} +(4.14073 - 4.14073i) q^{47} +(8.78790 + 7.29940i) q^{48} -6.57883i q^{49} +(-8.93426 + 8.93426i) q^{51} +(8.18543 - 3.84186i) q^{52} +2.75773i q^{53} +(8.50239 - 1.89608i) q^{54} +(0.232768 - 1.82076i) q^{56} +(-11.5528 + 11.5528i) q^{57} +(-6.48115 - 4.11757i) q^{58} +(-3.62521 + 3.62521i) q^{59} +(3.72781 + 3.72781i) q^{61} +(-0.193173 + 0.0430787i) q^{62} +(-2.36642 - 2.36642i) q^{63} +(-2.01257 + 7.74271i) q^{64} +(2.37576 + 1.50935i) q^{66} -3.32677 q^{67} +(-8.32192 - 3.00540i) q^{68} +(5.15965 + 5.15965i) q^{69} +1.37056 q^{71} +(8.92244 + 11.5382i) q^{72} +(2.55028 + 2.55028i) q^{73} +(-1.79867 - 8.06556i) q^{74} +(-10.7610 - 3.88625i) q^{76} -0.452252i q^{77} +(17.8229 - 3.97461i) q^{78} -3.86426 q^{79} +2.12204 q^{81} +(-6.28934 + 1.40256i) q^{82} +14.4698i q^{83} +(1.25915 - 3.48655i) q^{84} +(2.30840 + 10.3513i) q^{86} +(-10.9650 - 10.9650i) q^{87} +(-0.249948 + 1.95514i) q^{88} -3.35011 q^{89} +(-2.07470 - 2.07470i) q^{91} +(-1.73566 + 4.80602i) q^{92} -0.399696 q^{93} +(6.99006 + 4.44089i) q^{94} +(-7.37035 + 14.3769i) q^{96} +(4.95582 + 4.95582i) q^{97} +(9.08081 - 2.02507i) q^{98} +(2.54107 + 2.54107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9}+O(q^{10}) $ 18 * q + 4 * q^2 - 4 * q^4 - 8 * q^6 - 2 * q^7 + 4 * q^8 - 10 * q^9	$ 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9} - 2 q^{11} - 4 q^{12} + 12 q^{14} + 6 q^{17} - 16 q^{18} + 2 q^{19} - 16 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 16 q^{26} + 4 q^{28} - 14 q^{29} + 4 q^{32} + 8 q^{33} - 28 q^{34} - 4 q^{36} - 8 q^{37} - 16 q^{38} - 28 q^{42} + 44 q^{43} + 44 q^{44} + 12 q^{46} + 38 q^{47} - 60 q^{48} + 8 q^{51} + 40 q^{52} - 4 q^{54} + 20 q^{56} - 24 q^{57} + 20 q^{58} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 16 q^{64} + 4 q^{66} - 12 q^{67} - 36 q^{68} + 32 q^{69} + 24 q^{71} + 36 q^{72} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 84 q^{78} + 16 q^{79} + 2 q^{81} + 28 q^{82} - 24 q^{84} - 36 q^{86} - 24 q^{87} + 96 q^{88} - 12 q^{89} - 52 q^{92} - 16 q^{93} + 28 q^{94} - 40 q^{96} - 18 q^{97} - 32 q^{98} - 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^2 - 4 * q^4 - 8 * q^6 - 2 * q^7 + 4 * q^8 - 10 * q^9 - 2 * q^11 - 4 * q^12 + 12 * q^14 + 6 * q^17 - 16 * q^18 + 2 * q^19 - 16 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 16 * q^26 + 4 * q^28 - 14 * q^29 + 4 * q^32 + 8 * q^33 - 28 * q^34 - 4 * q^36 - 8 * q^37 - 16 * q^38 - 28 * q^42 + 44 * q^43 + 44 * q^44 + 12 * q^46 + 38 * q^47 - 60 * q^48 + 8 * q^51 + 40 * q^52 - 4 * q^54 + 20 * q^56 - 24 * q^57 + 20 * q^58 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 16 * q^64 + 4 * q^66 - 12 * q^67 - 36 * q^68 + 32 * q^69 + 24 * q^71 + 36 * q^72 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 84 * q^78 + 16 * q^79 + 2 * q^81 + 28 * q^82 - 24 * q^84 - 36 * q^86 - 24 * q^87 + 96 * q^88 - 12 * q^89 - 52 * q^92 - 16 * q^93 + 28 * q^94 - 40 * q^96 - 18 * q^97 - 32 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.307817	+	1.38031i	0.217659	+	0.976025i
$2$	0.307817	+	1.38031i	0.217659	+	0.976025i
$3$			2.85601i			1.64892i	0.565923	+	0.824458i	$0.308520\pi$
$3$			2.85601i			1.64892i	−0.565923	+	0.824458i	$0.691480\pi$
$4$	−1.81050	+	0.849763i	−0.905249	+	0.424882i
$5$		0			0
$5$		0			0
$6$	−3.94217	+	0.879127i	−1.60938	+	0.358902i
$7$	0.458895	+	0.458895i	0.173446	+	0.173446i	0.788491	−	0.615046i	$-0.210862\pi$
$7$	0.458895	+	0.458895i	0.173446	+	0.173446i	−0.615046	+	0.788491i	$0.710862\pi$
$8$	−1.73024	−	2.23747i	−0.611731	−	0.791066i
$9$	−5.15678			−1.71893
$10$		0			0
$11$	−0.492763	−	0.492763i	−0.148574	−	0.148574i	0.628907	−	0.777481i	$-0.283503\pi$
$11$	−0.492763	−	0.492763i	−0.148574	−	0.148574i	−0.777481	+	0.628907i	$0.783503\pi$
$12$	−2.42693	−	5.17080i	−0.700594	−	1.49268i
$13$	−4.52109			−1.25393			−0.626963	−	0.779049i	$-0.715702\pi$
$13$	−4.52109			−1.25393			−0.626963	+	0.779049i	$0.715702\pi$
$14$	−0.492160	+	0.774671i	−0.131535	+	0.207040i
$15$		0			0
$16$	2.55581	−	3.07699i	0.638951	−	0.769247i
$17$	3.12823	+	3.12823i	0.758708	+	0.758708i	0.976087	−	0.217379i	$-0.0697508\pi$
$17$	3.12823	+	3.12823i	0.758708	+	0.758708i	−0.217379	+	0.976087i	$0.569751\pi$
$18$	−1.58734	−	7.11794i	−0.374140	−	1.67772i
$19$	4.04508	+	4.04508i	0.928005	+	0.928005i	0.997577	−	0.0695721i	$-0.0221634\pi$
$19$	4.04508	+	4.04508i	0.928005	+	0.928005i	−0.0695721	+	0.997577i	$0.522163\pi$
$20$		0			0
$21$	−1.31061	+	1.31061i	−0.285998	+	0.285998i
$22$	0.528484	−	0.831845i	0.112673	−	0.177350i
$23$	1.80660	−	1.80660i	0.376701	−	0.376701i	−0.493209	−	0.869911i	$-0.664176\pi$
$23$	1.80660	−	1.80660i	0.376701	−	0.376701i	0.869911	+	0.493209i	$0.164176\pi$
$24$	6.39024	−	4.94157i	1.30440	−	1.00869i
$25$		0			0
$26$	−1.39167	−	6.24050i	−0.272928	−	1.22386i
$27$		−	6.15978i		−	1.18545i
$28$	−1.22078	−	0.440876i	−0.230706	−	0.0833177i
$29$	−3.83926	+	3.83926i	−0.712932	+	0.712932i	−0.967148	−	0.254215i	$-0.918183\pi$
$29$	−3.83926	+	3.83926i	−0.712932	+	0.712932i	0.254215	+	0.967148i	$0.418183\pi$
$30$		0			0
$31$			0.139949i			0.0251356i	0.999921	+	0.0125678i	$0.00400057\pi$
$31$			0.139949i			0.0251356i	−0.999921	+	0.0125678i	$0.995999\pi$
$32$	5.03391	+	2.58065i	0.889878	+	0.456199i
$33$	1.40733	−	1.40733i	0.244985	−	0.244985i
$34$	−3.35500	+	5.28085i	−0.575378	+	0.905658i
$35$		0			0
$36$	9.33634	−	4.38204i	1.55606	−	0.730340i
$37$	−5.84330			−0.960633			−0.480317	−	0.877095i	$-0.659478\pi$
$37$	−5.84330			−0.960633			−0.480317	+	0.877095i	$0.659478\pi$
$38$	−4.33831	+	6.82860i	−0.703767	+	1.10774i
$39$		−	12.9123i		−	2.06762i
$40$		0			0
$41$			4.55648i			0.711602i	0.934562	+	0.355801i	$0.115792\pi$
$41$			4.55648i			0.711602i	−0.934562	+	0.355801i	$0.884208\pi$
$42$	−2.21247	−	1.40561i	−0.341391	−	0.216891i
$43$	7.49928			1.14363			0.571815	−	0.820383i	$-0.306240\pi$
$43$	7.49928			1.14363			0.571815	+	0.820383i	$0.306240\pi$
$44$	1.31088	+	0.473414i	0.197622	+	0.0713699i
$45$		0			0
$46$	3.04976	+	1.93756i	0.449662	+	0.285677i
$47$	4.14073	−	4.14073i	0.603987	−	0.603987i	−0.337381	−	0.941368i	$-0.609541\pi$
$47$	4.14073	−	4.14073i	0.603987	−	0.603987i	0.941368	+	0.337381i	$0.109541\pi$
$48$	8.78790	+	7.29940i	1.26842	+	1.05358i
$49$		−	6.57883i		−	0.939833i
$50$		0			0
$51$	−8.93426	+	8.93426i	−1.25105	+	1.25105i
$52$	8.18543	−	3.84186i	1.13511	−	0.532770i
$53$			2.75773i			0.378803i	0.981900	+	0.189402i	$0.0606548\pi$
$53$			2.75773i			0.378803i	−0.981900	+	0.189402i	$0.939345\pi$
$54$	8.50239	−	1.89608i	1.15703	−	0.258024i
$55$		0			0
$56$	0.232768	−	1.82076i	0.0311050	−	0.243309i
$57$	−11.5528	+	11.5528i	−1.53020	+	1.53020i
$58$	−6.48115	−	4.11757i	−0.851016	−	0.540663i
$59$	−3.62521	+	3.62521i	−0.471962	+	0.471962i	−0.902549	−	0.430587i	$-0.858306\pi$
$59$	−3.62521	+	3.62521i	−0.471962	+	0.471962i	0.430587	+	0.902549i	$0.358306\pi$
$60$		0			0
$61$	3.72781	+	3.72781i	0.477298	+	0.477298i	0.904266	−	0.426969i	$-0.140419\pi$
$61$	3.72781	+	3.72781i	0.477298	+	0.477298i	−0.426969	+	0.904266i	$0.640419\pi$
$62$	−0.193173	+	0.0430787i	−0.0245330	+	0.00547100i
$63$	−2.36642	−	2.36642i	−0.298141	−	0.298141i
$64$	−2.01257	+	7.74271i	−0.251571	+	0.967839i
$65$		0			0
$66$	2.37576	+	1.50935i	0.292435	+	0.185789i
$67$	−3.32677			−0.406430			−0.203215	−	0.979134i	$-0.565139\pi$
$67$	−3.32677			−0.406430			−0.203215	+	0.979134i	$0.565139\pi$
$68$	−8.32192	−	3.00540i	−1.00918	−	0.364459i
$69$	5.15965	+	5.15965i	0.621149	+	0.621149i
$70$		0			0
$71$	1.37056			0.162655			0.0813275	−	0.996687i	$-0.474084\pi$
$71$	1.37056			0.162655			0.0813275	+	0.996687i	$0.474084\pi$
$72$	8.92244	+	11.5382i	1.05152	+	1.35978i
$73$	2.55028	+	2.55028i	0.298488	+	0.298488i	0.840422	−	0.541933i	$-0.182307\pi$
$73$	2.55028	+	2.55028i	0.298488	+	0.298488i	−0.541933	+	0.840422i	$0.682307\pi$
$74$	−1.79867	−	8.06556i	−0.209091	−	0.937602i
$75$		0			0
$76$	−10.7610	−	3.88625i	−1.23437	−	0.445783i
$77$		−	0.452252i		−	0.0515389i
$78$	17.8229	−	3.97461i	2.01805	−	0.450036i
$79$	−3.86426			−0.434763			−0.217382	−	0.976087i	$-0.569752\pi$
$79$	−3.86426			−0.434763			−0.217382	+	0.976087i	$0.569752\pi$
$80$		0			0
$81$	2.12204			0.235782
$82$	−6.28934	+	1.40256i	−0.694541	+	0.154887i
$83$			14.4698i			1.58827i	0.607744	+	0.794133i	$0.292075\pi$
$83$			14.4698i			1.58827i	−0.607744	+	0.794133i	$0.707925\pi$
$84$	1.25915	−	3.48655i	0.137384	−	0.380414i
$85$		0			0
$86$	2.30840	+	10.3513i	0.248922	+	1.11621i
$87$	−10.9650	−	10.9650i	−1.17557	−	1.17557i
$88$	−0.249948	+	1.95514i	−0.0266445	+	0.208419i
$89$	−3.35011			−0.355111			−0.177556	−	0.984111i	$-0.556819\pi$
$89$	−3.35011			−0.355111			−0.177556	+	0.984111i	$0.556819\pi$
$90$		0			0
$91$	−2.07470	−	2.07470i	−0.217488	−	0.217488i
$92$	−1.73566	+	4.80602i	−0.180955	+	0.501062i
$93$	−0.399696			−0.0414466
$94$	6.99006	+	4.44089i	0.720970	+	0.458043i
$95$		0			0
$96$	−7.37035	+	14.3769i	−0.752234	+	1.46733i
$97$	4.95582	+	4.95582i	0.503187	+	0.503187i	0.912427	−	0.409240i	$-0.134206\pi$
$97$	4.95582	+	4.95582i	0.503187	+	0.503187i	−0.409240	+	0.912427i	$0.634206\pi$
$98$	9.08081	−	2.02507i	0.917300	−	0.204563i
$99$	2.54107	+	2.54107i	0.255387	+	0.255387i
$100$		0			0
$101$	−1.84536	+	1.84536i	−0.183621	+	0.183621i	−0.792931	−	0.609311i	$-0.791446\pi$
$101$	−1.84536	+	1.84536i	−0.183621	+	0.183621i	0.609311	+	0.792931i	$0.291446\pi$
$102$	−15.0821	−	9.58191i	−1.49335	−	0.948751i
$103$	11.6655	−	11.6655i	1.14944	−	1.14944i	0.162773	−	0.986664i	$-0.447956\pi$
$103$	11.6655	−	11.6655i	1.14944	−	1.14944i	0.986664	−	0.162773i	$-0.0520437\pi$
$104$	7.82256	+	10.1158i	0.767065	+	0.991938i
$105$		0			0
$106$	−3.80651	+	0.848874i	−0.369721	+	0.0824500i
$107$			15.3106i			1.48013i	0.672534	+	0.740067i	$0.265206\pi$
$107$			15.3106i			1.48013i	−0.672534	+	0.740067i	$0.734794\pi$
$108$	5.23435	+	11.1523i	0.503676	+	1.07313i
$109$	12.4798	−	12.4798i	1.19535	−	1.19535i	0.219803	−	0.975544i	$-0.429458\pi$
$109$	12.4798	−	12.4798i	1.19535	−	1.19535i	0.975544	−	0.219803i	$-0.0705416\pi$
$110$		0			0
$111$		−	16.6885i		−	1.58400i
$112$	2.58486	−	0.239168i	0.244246	−	0.0225993i
$113$	−2.53557	+	2.53557i	−0.238526	+	0.238526i	−0.816240	−	0.577713i	$-0.803945\pi$
$113$	−2.53557	+	2.53557i	−0.238526	+	0.238526i	0.577713	+	0.816240i	$0.303945\pi$
$114$	−19.5025	−	12.3903i	−1.82658	−	1.16045i
$115$		0			0
$116$	3.68851	−	10.2134i	0.342470	−	0.948293i
$117$	23.3143			2.15541
$118$	−6.11980	−	3.88800i	−0.563373	−	0.357919i
$119$			2.87106i			0.263189i
$120$		0			0
$121$		−	10.5144i		−	0.955852i
$122$	−3.99805	+	6.29301i	−0.361966	+	0.569743i
$123$	−13.0133			−1.17337
$124$	−0.118924	−	0.253378i	−0.0106797	−	0.0227540i
$125$		0			0
$126$	2.53796	−	3.99481i	0.226100	−	0.355886i
$127$	0.615790	−	0.615790i	0.0546426	−	0.0546426i	−0.679257	−	0.733900i	$-0.737698\pi$
$127$	0.615790	−	0.615790i	0.0546426	−	0.0546426i	0.733900	+	0.679257i	$0.237698\pi$
$128$	−11.3068	−	0.394630i	−0.999391	−	0.0348807i
$129$			21.4180i			1.88575i
$130$		0			0
$131$	9.55413	−	9.55413i	0.834748	−	0.834748i	−0.153414	−	0.988162i	$-0.549027\pi$
$131$	9.55413	−	9.55413i	0.834748	−	0.834748i	0.988162	+	0.153414i	$0.0490268\pi$
$132$	−1.35208	+	3.74388i	−0.117683	+	0.325863i
$133$			3.71253i			0.321917i
$134$	−1.02404	−	4.59197i	−0.0884632	−	0.396686i
$135$		0			0
$136$	1.58676	−	12.4119i	0.136063	−	1.06431i
$137$	3.70277	−	3.70277i	0.316349	−	0.316349i	−0.531014	−	0.847363i	$-0.678189\pi$
$137$	3.70277	−	3.70277i	0.316349	−	0.316349i	0.847363	+	0.531014i	$0.178189\pi$
$138$	−5.53368	+	8.71013i	−0.471058	+	0.741456i
$139$	5.46761	−	5.46761i	0.463756	−	0.463756i	−0.436128	−	0.899885i	$-0.643651\pi$
$139$	5.46761	−	5.46761i	0.463756	−	0.463756i	0.899885	+	0.436128i	$0.143651\pi$
$140$		0			0
$141$	11.8260	+	11.8260i	0.995925	+	0.995925i
$142$	0.421880	+	1.89179i	0.0354034	+	0.158755i
$143$	2.22783	+	2.22783i	0.186300	+	0.186300i
$144$	−13.1797	+	15.8674i	−1.09831	+	1.32228i
$145$		0			0
$146$	−2.73516	+	4.30520i	−0.226363	+	0.356301i
$147$	18.7892			1.54971
$148$	10.5793	−	4.96542i	0.869612	−	0.408155i
$149$	4.21561	+	4.21561i	0.345356	+	0.345356i	0.858376	−	0.513021i	$-0.171474\pi$
$149$	4.21561	+	4.21561i	0.345356	+	0.345356i	−0.513021	+	0.858376i	$0.671474\pi$
$150$		0			0
$151$	12.4417			1.01249			0.506244	−	0.862390i	$-0.331034\pi$
$151$	12.4417			1.01249			0.506244	+	0.862390i	$0.331034\pi$
$152$	2.05181	−	16.0497i	0.166424	−	1.30180i
$153$	−16.1316	−	16.1316i	−1.30416	−	1.30416i
$154$	0.624247	−	0.139211i	0.0503033	−	0.0112179i
$155$		0			0
$156$	10.9724	+	23.3777i	0.878493	+	1.87171i
$157$		−	7.50500i		−	0.598964i	−0.954102	−	0.299482i	$-0.903186\pi$
$157$		−	7.50500i		−	0.598964i	0.954102	−	0.299482i	$-0.0968138\pi$
$158$	−1.18948	−	5.33387i	−0.0946302	−	0.424340i
$159$	−7.87609			−0.624615
$160$		0			0
$161$	1.65807			0.130675
$162$	0.653199	+	2.92907i	0.0513202	+	0.230129i
$163$		−	23.7284i		−	1.85855i	−0.369383	−	0.929277i	$-0.620431\pi$
$163$		−	23.7284i		−	1.85855i	0.369383	−	0.929277i	$-0.379569\pi$
$164$	−3.87193	−	8.24949i	−0.302347	−	0.644177i
$165$		0			0
$166$	−19.9728	+	4.45404i	−1.55019	+	0.345701i
$167$	0.402976	+	0.402976i	0.0311832	+	0.0311832i	0.722526	−	0.691343i	$-0.242981\pi$
$167$	0.402976	+	0.402976i	0.0311832	+	0.0311832i	−0.691343	+	0.722526i	$0.742981\pi$
$168$	5.20010	+	0.664788i	0.401197	+	0.0512895i
$169$	7.44028			0.572330
$170$		0			0
$171$	−20.8596	−	20.8596i	−1.59517	−	1.59517i
$172$	−13.5774	+	6.37261i	−1.03527	+	0.485907i
$173$	15.4500			1.17464			0.587320	−	0.809355i	$-0.300183\pi$
$173$	15.4500			1.17464			0.587320	+	0.809355i	$0.300183\pi$
$174$	11.7598	−	18.5102i	0.891509	−	1.40325i
$175$		0			0
$176$	−2.77563	+	0.256820i	−0.209221	+	0.0193585i
$177$	−10.3536	−	10.3536i	−0.778225	−	0.778225i
$178$	−1.03122	−	4.62419i	−0.0772932	−	0.346597i
$179$	5.20444	+	5.20444i	0.388998	+	0.388998i	0.874330	−	0.485332i	$-0.161301\pi$
$179$	5.20444	+	5.20444i	0.388998	+	0.388998i	−0.485332	+	0.874330i	$0.661301\pi$
$180$		0			0
$181$	−9.08925	+	9.08925i	−0.675599	+	0.675599i	−0.959001	−	0.283402i	$-0.908537\pi$
$181$	−9.08925	+	9.08925i	−0.675599	+	0.675599i	0.283402	+	0.959001i	$0.408537\pi$
$182$	2.22510	−	3.50236i	0.164936	−	0.259612i
$183$	−10.6467	+	10.6467i	−0.787024	+	0.787024i
$184$	−7.16804	−	0.916372i	−0.528435	−	0.0675559i
$185$		0			0
$186$	−0.123033	−	0.551704i	−0.00902123	−	0.0404529i
$187$		−	3.08295i		−	0.225448i
$188$	−3.97814	+	11.0154i	−0.290136	+	0.803382i
$189$	2.82669	−	2.82669i	0.205611	−	0.205611i
$190$		0			0
$191$			15.1075i			1.09314i	0.837413	+	0.546571i	$0.184067\pi$
$191$			15.1075i			1.09314i	−0.837413	+	0.546571i	$0.815933\pi$
$192$	−22.1132	−	5.74791i	−1.59589	−	0.414820i
$193$	−4.19166	+	4.19166i	−0.301722	+	0.301722i	−0.841687	−	0.539965i	$-0.818437\pi$
$193$	−4.19166	+	4.19166i	−0.301722	+	0.301722i	0.539965	+	0.841687i	$0.318437\pi$
$194$	−5.31507	+	8.36604i	−0.381600	+	0.600647i
$195$		0			0
$196$	5.59045	+	11.9110i	0.399318	+	0.850783i
$197$	4.03184			0.287256			0.143628	−	0.989632i	$-0.454123\pi$
$197$	4.03184			0.287256			0.143628	+	0.989632i	$0.454123\pi$
$198$	−2.72527	+	4.28964i	−0.193677	+	0.304852i
$199$		−	5.43055i		−	0.384961i	−0.981301	−	0.192481i	$-0.938347\pi$
$199$		−	5.43055i		−	0.384961i	0.981301	−	0.192481i	$-0.0616533\pi$
$200$		0			0
$201$		−	9.50129i		−	0.670169i
$202$	−3.11520	−	1.97914i	−0.219185	−	0.139252i
$203$	−3.52363			−0.247310
$204$	8.58345	−	23.7675i	0.600962	−	1.66405i
$205$		0			0
$206$	19.6928	+	12.5111i	1.37206	+	0.871693i
$207$	−9.31622	+	9.31622i	−0.647522	+	0.647522i
$208$	−11.5550	+	13.9114i	−0.801197	+	0.964579i
$209$		−	3.98653i		−	0.275754i
$210$		0			0
$211$	3.23020	−	3.23020i	0.222376	−	0.222376i	−0.587122	−	0.809498i	$-0.699739\pi$
$211$	3.23020	−	3.23020i	0.222376	−	0.222376i	0.809498	+	0.587122i	$0.199739\pi$
$212$	−2.34342	−	4.99286i	−0.160946	−	0.342911i
$213$			3.91432i			0.268205i
$214$	−21.1334	+	4.71286i	−1.44465	+	0.322165i
$215$		0			0
$216$	−13.7823	+	10.6579i	−0.937770	+	0.725176i
$217$	−0.0642220	+	0.0642220i	−0.00435967	+	0.00435967i
$218$	21.0674	+	13.3845i	1.42687	+	0.906511i
$219$	−7.28363	+	7.28363i	−0.492182	+	0.492182i
$220$		0			0
$221$	−14.1430	−	14.1430i	−0.951363	−	0.951363i
$222$	23.0353	−	5.13700i	1.54603	−	0.344773i
$223$	8.17319	+	8.17319i	0.547317	+	0.547317i	0.925664	−	0.378347i	$-0.123507\pi$
$223$	8.17319	+	8.17319i	0.547317	+	0.547317i	−0.378347	+	0.925664i	$0.623507\pi$
$224$	1.12579	+	3.49428i	0.0752199	+	0.233471i
$225$		0			0
$226$	−4.28035	−	2.71937i	−0.284725	−	0.180890i
$227$	1.54068			0.102258			0.0511292	−	0.998692i	$-0.483718\pi$
$227$	1.54068			0.102258			0.0511292	+	0.998692i	$0.483718\pi$
$228$	11.0992	−	30.7334i	0.735060	−	2.03537i
$229$	−17.5646	−	17.5646i	−1.16070	−	1.16070i	−0.984322	−	0.176378i	$-0.943562\pi$
$229$	−17.5646	−	17.5646i	−1.16070	−	1.16070i	−0.176378	−	0.984322i	$-0.556438\pi$
$230$		0			0
$231$	1.29164			0.0849834
$232$	15.2331	+	1.94741i	1.00010	+	0.127854i
$233$	−9.99018	−	9.99018i	−0.654479	−	0.654479i	0.299590	−	0.954068i	$-0.403150\pi$
$233$	−9.99018	−	9.99018i	−0.654479	−	0.654479i	−0.954068	+	0.299590i	$0.903150\pi$
$234$	7.17652	+	32.1809i	0.469144	+	2.10373i
$235$		0			0
$236$	3.48286	−	9.64399i	0.226715	−	0.627771i
$237$		−	11.0364i		−	0.716889i
$238$	−3.96294	+	0.883759i	−0.256879	+	0.0572856i
$239$	26.2762			1.69967			0.849833	−	0.527052i	$-0.176703\pi$
$239$	26.2762			1.69967			0.849833	+	0.527052i	$0.176703\pi$
$240$		0			0
$241$	−0.113242			−0.00729456			−0.00364728	−	0.999993i	$-0.501161\pi$
$241$	−0.113242			−0.00729456			−0.00364728	+	0.999993i	$0.501161\pi$
$242$	14.5131	−	3.23650i	0.932935	−	0.208050i
$243$		−	12.4188i		−	0.796665i
$244$	−9.91696	−	3.58144i	−0.634868	−	0.229278i
$245$		0			0
$246$	−4.00572	−	17.9624i	−0.255395	−	1.14524i
$247$	−18.2882	−	18.2882i	−1.16365	−	1.16365i
$248$	0.313133	−	0.242145i	0.0198840	−	0.0153762i
$249$	−41.3258			−2.61892
$250$		0			0
$251$	19.2220	+	19.2220i	1.21328	+	1.21328i	0.969941	+	0.243339i	$0.0782427\pi$
$251$	19.2220	+	19.2220i	1.21328	+	1.21328i	0.243339	+	0.969941i	$0.421757\pi$
$252$	6.29529	+	2.27350i	0.396566	+	0.143217i
$253$	−1.78045			−0.111936
$254$	1.03953	+	0.660430i	0.0652260	+	0.0414390i
$255$		0			0
$256$	−2.93572	−	15.7284i	−0.183482	−	0.983023i
$257$	0.757800	+	0.757800i	0.0472703	+	0.0472703i	0.730347	−	0.683077i	$-0.239358\pi$
$257$	0.757800	+	0.757800i	0.0472703	+	0.0472703i	−0.683077	+	0.730347i	$0.739358\pi$
$258$	−29.5634	+	6.59282i	−1.84054	+	0.410451i
$259$	−2.68146	−	2.68146i	−0.166618	−	0.166618i
$260$		0			0
$261$	19.7982	−	19.7982i	1.22548	−	1.22548i
$262$	16.1286	+	10.2467i	0.996425	+	0.633044i
$263$	−5.73017	+	5.73017i	−0.353338	+	0.353338i	−0.861350	−	0.508012i	$-0.830380\pi$
$263$	−5.73017	+	5.73017i	−0.353338	+	0.353338i	0.508012	+	0.861350i	$0.330380\pi$
$264$	−5.58389	−	0.713852i	−0.343665	−	0.0439346i
$265$		0			0
$266$	−5.12443	+	1.14278i	−0.314199	+	0.0700682i
$267$		−	9.56795i		−	0.585549i
$268$	6.02311	−	2.82697i	0.367920	−	0.172685i
$269$	9.78879	−	9.78879i	0.596833	−	0.596833i	−0.342635	−	0.939468i	$-0.611320\pi$
$269$	9.78879	−	9.78879i	0.596833	−	0.596833i	0.939468	+	0.342635i	$0.111320\pi$
$270$		0			0
$271$			4.10159i			0.249154i	0.992210	+	0.124577i	$0.0397574\pi$
$271$			4.10159i			0.249154i	−0.992210	+	0.124577i	$0.960243\pi$
$272$	17.6207	−	1.63038i	1.06841	−	0.0988565i
$273$	5.92537	−	5.92537i	0.358620	−	0.358620i
$274$	6.25074	+	3.97119i	0.377621	+	0.239908i
$275$		0			0
$276$	−13.7260	−	4.95706i	−0.826209	−	0.298380i
$277$	−24.6755			−1.48261			−0.741305	−	0.671169i	$-0.765793\pi$
$277$	−24.6755			−1.48261			−0.741305	+	0.671169i	$0.765793\pi$
$278$	9.23000	+	5.86396i	0.553578	+	0.351697i
$279$		−	0.721688i		−	0.0432063i
$280$		0			0
$281$		−	23.6688i		−	1.41196i	−0.708230	−	0.705981i	$-0.750506\pi$
$281$		−	23.6688i		−	1.41196i	0.708230	−	0.705981i	$-0.249494\pi$
$282$	−12.6832	+	19.9637i	−0.755275	+	1.18882i
$283$	−13.0492			−0.775694			−0.387847	−	0.921724i	$-0.626781\pi$
$283$	−13.0492			−0.775694			−0.387847	+	0.921724i	$0.626781\pi$
$284$	−2.48139	+	1.16465i	−0.147243	+	0.0691091i
$285$		0			0
$286$	−2.38932	+	3.76085i	−0.141284	+	0.222384i
$287$	−2.09094	+	2.09094i	−0.123424	+	0.123424i
$288$	−25.9588	−	13.3078i	−1.52963	−	0.784172i
$289$			2.57168i			0.151275i
$290$		0			0
$291$	−14.1539	+	14.1539i	−0.829714	+	0.829714i
$292$	−6.78442	−	2.45015i	−0.397028	−	0.143384i
$293$		−	31.6731i		−	1.85036i	−0.379526	−	0.925181i	$-0.623913\pi$
$293$		−	31.6731i		−	1.85036i	0.379526	−	0.925181i	$-0.376087\pi$
$294$	5.78363	+	25.9349i	0.337308	+	1.51255i
$295$		0			0
$296$	10.1103	+	13.0742i	0.587649	+	0.759924i
$297$	−3.03531	+	3.03531i	−0.176127	+	0.176127i
$298$	−4.52120	+	7.11646i	−0.261906	+	0.412246i
$299$	−8.16779	+	8.16779i	−0.472355	+	0.472355i
$300$		0			0
$301$	3.44138	+	3.44138i	0.198358	+	0.198358i
$302$	3.82975	+	17.1733i	0.220377	+	0.988213i
$303$	−5.27037	−	5.27037i	−0.302775	−	0.302775i
$304$	22.7851	−	2.10823i	1.30682	−	0.120915i
$305$		0			0
$306$	17.3010	−	27.2322i	0.989033	−	1.55676i
$307$	27.3597			1.56150			0.780751	−	0.624843i	$-0.214837\pi$
$307$	27.3597			1.56150			0.780751	+	0.624843i	$0.214837\pi$
$308$	0.384307	+	0.818802i	0.0218979	+	0.0466556i
$309$	33.3168	+	33.3168i	1.89532	+	1.89532i
$310$		0			0
$311$	−15.8076			−0.896368			−0.448184	−	0.893941i	$-0.647929\pi$
$311$	−15.8076			−0.896368			−0.448184	+	0.893941i	$0.647929\pi$
$312$	−28.8909	+	22.3413i	−1.63562	+	1.26483i
$313$	13.8388	+	13.8388i	0.782217	+	0.782217i	0.980205	−	0.197988i	$-0.0634406\pi$
$313$	13.8388	+	13.8388i	0.782217	+	0.782217i	−0.197988	+	0.980205i	$0.563441\pi$
$314$	10.3592	−	2.31016i	0.584604	−	0.130370i
$315$		0			0
$316$	6.99624	−	3.28371i	0.393569	−	0.184723i
$317$			35.0092i			1.96631i	0.182766	+	0.983156i	$0.441495\pi$
$317$			35.0092i			1.96631i	−0.182766	+	0.983156i	$0.558505\pi$
$318$	−2.42439	−	10.8714i	−0.135953	−	0.609639i
$319$	3.78369			0.211846
$320$		0			0
$321$	−43.7272			−2.44062
$322$	0.510383	+	2.28865i	0.0284425	+	0.127542i
$323$			25.3079i			1.40817i
$324$	−3.84195	+	1.80323i	−0.213442	+	0.100180i
$325$		0			0
$326$	32.7525	−	7.30401i	1.81400	−	0.404532i
$327$	35.6424	+	35.6424i	1.97103	+	1.97103i
$328$	10.1950	−	7.88378i	0.562924	−	0.435309i
$329$	3.80032			0.209518
$330$		0			0
$331$	16.8212	+	16.8212i	0.924578	+	0.924578i	0.997349	−	0.0727709i	$-0.0231842\pi$
$331$	16.8212	+	16.8212i	0.924578	+	0.924578i	−0.0727709	+	0.997349i	$0.523184\pi$
$332$	−12.2959	−	26.1975i	−0.674825	−	1.43778i
$333$	30.1326			1.65126
$334$	−0.432188	+	0.680273i	−0.0236483	+	0.0372229i
$335$		0			0
$336$	0.683066	+	7.38238i	0.0372643	+	0.402742i
$337$	−14.4984	−	14.4984i	−0.789777	−	0.789777i	0.191680	−	0.981457i	$-0.438606\pi$
$337$	−14.4984	−	14.4984i	−0.789777	−	0.789777i	−0.981457	+	0.191680i	$0.938606\pi$
$338$	2.29024	+	10.2699i	0.124573	+	0.558608i
$339$	−7.24160	−	7.24160i	−0.393310	−	0.393310i
$340$		0			0
$341$	0.0689618	−	0.0689618i	0.00373449	−	0.00373449i
$342$	22.3717	−	35.2136i	1.20972	−	1.90413i
$343$	6.23125	−	6.23125i	0.336456	−	0.336456i
$344$	−12.9755	−	16.7794i	−0.699593	−	0.904687i
$345$		0			0
$346$	4.75576	+	21.3257i	0.255671	+	1.14648i
$347$			16.7705i			0.900286i	0.892956	+	0.450143i	$0.148627\pi$
$347$			16.7705i			0.900286i	−0.892956	+	0.450143i	$0.851373\pi$
$348$	29.1696	+	10.5344i	1.56366	+	0.564704i
$349$	1.86337	−	1.86337i	0.0997439	−	0.0997439i	−0.655474	−	0.755218i	$-0.727531\pi$
$349$	1.86337	−	1.86337i	0.0997439	−	0.0997439i	0.755218	+	0.655474i	$0.227531\pi$
$350$		0			0
$351$			27.8489i			1.48647i
$352$	−1.20888	−	3.75217i	−0.0644333	−	0.199991i
$353$	−24.1362	+	24.1362i	−1.28464	+	1.28464i	−0.346642	+	0.937998i	$0.612678\pi$
$353$	−24.1362	+	24.1362i	−1.28464	+	1.28464i	−0.937998	+	0.346642i	$0.887322\pi$
$354$	11.1042	−	17.4782i	0.590179	−	0.928955i
$355$		0			0
$356$	6.06537	−	2.84680i	0.321464	−	0.150880i
$357$	−8.19976			−0.433978
$358$	−5.58171	+	8.78574i	−0.295003	+	0.464341i
$359$			12.2500i			0.646532i	0.946308	+	0.323266i	$0.104781\pi$
$359$			12.2500i			0.646532i	−0.946308	+	0.323266i	$0.895219\pi$
$360$		0			0
$361$			13.7253i			0.722386i
$362$	−15.3438	−	9.74814i	−0.806451	−	0.512351i
$363$	30.0291			1.57612
$364$	5.51926	+	1.99324i	0.289288	+	0.104474i
$365$		0			0
$366$	−17.9729	−	11.4185i	−0.939458	−	0.596852i
$367$	−2.71307	+	2.71307i	−0.141621	+	0.141621i	−0.774363	−	0.632742i	$-0.781929\pi$
$367$	−2.71307	+	2.71307i	−0.141621	+	0.141621i	0.632742	+	0.774363i	$0.281929\pi$
$368$	−0.941567	−	10.1762i	−0.0490826	−	0.530470i
$369$		−	23.4967i		−	1.22319i
$370$		0			0
$371$	−1.26551	+	1.26551i	−0.0657018	+	0.0657018i
$372$	0.723649	−	0.339647i	0.0375195	−	0.0176099i
$373$			16.4846i			0.853541i	0.904360	+	0.426771i	$0.140349\pi$
$373$			16.4846i			0.853541i	−0.904360	+	0.426771i	$0.859651\pi$
$374$	4.25542	−	0.948984i	0.220043	−	0.0490708i
$375$		0			0
$376$	−16.4292	−	2.10033i	−0.847272	−	0.108316i
$377$	17.3576	−	17.3576i	0.893964	−	0.893964i
$378$	4.77180	+	3.03160i	0.245435	+	0.155929i
$379$	−13.7716	+	13.7716i	−0.707401	+	0.707401i	−0.965988	−	0.258587i	$-0.916743\pi$
$379$	−13.7716	+	13.7716i	−0.707401	+	0.707401i	0.258587	+	0.965988i	$0.416743\pi$
$380$		0			0
$381$	1.75870	+	1.75870i	0.0901011	+	0.0901011i
$382$	−20.8530	+	4.65034i	−1.06693	+	0.237932i
$383$	−11.5530	−	11.5530i	−0.590332	−	0.590332i	0.347389	−	0.937721i	$-0.387068\pi$
$383$	−11.5530	−	11.5530i	−0.590332	−	0.590332i	−0.937721	+	0.347389i	$0.887068\pi$
$384$	1.12707	−	32.2924i	0.0575153	−	1.64791i
$385$		0			0
$386$	−7.07604	−	4.49552i	−0.360161	−	0.228816i
$387$	−38.6722			−1.96582
$388$	−13.1838	−	4.76123i	−0.669305	−	0.241715i
$389$	−15.7728	−	15.7728i	−0.799712	−	0.799712i	0.183338	−	0.983050i	$-0.441310\pi$
$389$	−15.7728	−	15.7728i	−0.799712	−	0.799712i	−0.983050	+	0.183338i	$0.941310\pi$
$390$		0			0
$391$	11.3029			0.571612
$392$	−14.7200	+	11.3829i	−0.743470	+	0.574925i
$393$	27.2867	+	27.2867i	1.37643	+	1.37643i
$394$	1.24107	+	5.56517i	0.0625240	+	0.280369i
$395$		0			0
$396$	−6.75991	−	2.44129i	−0.339698	−	0.122680i
$397$		−	29.9558i		−	1.50344i	−0.659483	−	0.751720i	$-0.729225\pi$
$397$		−	29.9558i		−	1.50344i	0.659483	−	0.751720i	$-0.270775\pi$
$398$	7.49583	−	1.67161i	0.375732	−	0.0837904i
$399$	−10.6030			−0.530815
$400$		0			0
$401$	19.9241			0.994963			0.497481	−	0.867475i	$-0.334258\pi$
$401$	19.9241			0.994963			0.497481	+	0.867475i	$0.334258\pi$
$402$	13.1147	−	2.92465i	0.654102	−	0.145868i
$403$		−	0.632724i		−	0.0315182i
$404$	1.77291	−	4.90915i	0.0882054	−	0.244239i
$405$		0			0
$406$	−1.08463	−	4.86369i	−0.0538294	−	0.241381i
$407$	2.87936	+	2.87936i	0.142725	+	0.142725i
$408$	35.4485	+	4.53179i	1.75496	+	0.224357i
$409$	5.89856			0.291665			0.145832	−	0.989309i	$-0.453414\pi$
$409$	5.89856			0.291665			0.145832	+	0.989309i	$0.453414\pi$
$410$		0			0
$411$	10.5751	+	10.5751i	0.521634	+	0.521634i
$412$	−11.2075	+	31.0333i	−0.552152	+	1.52890i
$413$	−3.32717			−0.163720
$414$	−15.7269	−	9.99156i	−0.772936	−	0.491058i
$415$		0			0
$416$	−22.7588	−	11.6674i	−1.11584	−	0.572039i
$417$	15.6155	+	15.6155i	0.764696	+	0.764696i
$418$	5.50264	−	1.22712i	0.269143	−	0.0600204i
$419$	8.24430	+	8.24430i	0.402760	+	0.402760i	0.879205	−	0.476444i	$-0.158075\pi$
$419$	8.24430	+	8.24430i	0.402760	+	0.402760i	−0.476444	+	0.879205i	$0.658075\pi$
$420$		0			0
$421$	−17.1776	+	17.1776i	−0.837184	+	0.837184i	−0.988487	−	0.151304i	$-0.951653\pi$
$421$	−17.1776	+	17.1776i	−0.837184	+	0.837184i	0.151304	+	0.988487i	$0.451653\pi$
$422$	5.45297	+	3.46436i	0.265447	+	0.168642i
$423$	−21.3528	+	21.3528i	−1.03821	+	1.03821i
$424$	6.17034	−	4.77152i	0.299658	−	0.231725i
$425$		0			0
$426$	−5.40296	+	1.20489i	−0.261774	+	0.0583772i
$427$			3.42135i			0.165571i
$428$	−13.0104	−	27.7198i	−0.628881	−	1.33989i
$429$	−6.36269	+	6.36269i	−0.307194	+	0.307194i
$430$		0			0
$431$		−	32.1769i		−	1.54990i	−0.632020	−	0.774952i	$-0.717774\pi$
$431$		−	32.1769i		−	1.54990i	0.632020	−	0.774952i	$-0.282226\pi$
$432$	−18.9536	−	15.7432i	−0.911904	−	0.757445i
$433$	20.3383	−	20.3383i	0.977396	−	0.977396i	−0.0223540	−	0.999750i	$-0.507116\pi$
$433$	20.3383	−	20.3383i	0.977396	−	0.977396i	0.999750	+	0.0223540i	$0.00711609\pi$
$434$	−0.108415	−	0.0688775i	−0.00520407	−	0.00330623i
$435$		0			0
$436$	−11.9898	+	33.1995i	−0.574206	+	1.58997i
$437$	14.6156			0.699161
$438$	−12.2957	−	7.81163i	−0.587510	−	0.373254i
$439$		−	35.4180i		−	1.69041i	−0.534444	−	0.845204i	$-0.679479\pi$
$439$		−	35.4180i		−	1.69041i	0.534444	−	0.845204i	$-0.320521\pi$
$440$		0			0
$441$			33.9256i			1.61550i
$442$	15.1683	−	23.8752i	0.721481	−	1.13563i
$443$	3.03787			0.144333			0.0721667	−	0.997393i	$-0.477009\pi$
$443$	3.03787			0.144333			0.0721667	+	0.997393i	$0.477009\pi$
$444$	14.1813	+	30.2145i	0.673014	+	1.43392i
$445$		0			0
$446$	−8.76567	+	13.7974i	−0.415067	+	0.653324i
$447$	−12.0398	+	12.0398i	−0.569463	+	0.569463i
$448$	−4.47664	+	2.62953i	−0.211502	+	0.124234i
$449$		−	8.65559i		−	0.408483i	−0.978921	−	0.204241i	$-0.934527\pi$
$449$		−	8.65559i		−	0.408483i	0.978921	−	0.204241i	$-0.0654727\pi$
$450$		0			0
$451$	2.24526	−	2.24526i	0.105725	−	0.105725i
$452$	2.43601	−	6.74527i	0.114580	−	0.317271i
$453$			35.5335i			1.66951i
$454$	0.474247	+	2.12661i	0.0222575	+	0.0998068i
$455$		0			0
$456$	45.8381	+	5.86000i	2.14656	+	0.274420i
$457$	13.5575	−	13.5575i	0.634193	−	0.634193i	−0.314924	−	0.949117i	$-0.601979\pi$
$457$	13.5575	−	13.5575i	0.634193	−	0.634193i	0.949117	+	0.314924i	$0.101979\pi$
$458$	18.8379	−	29.6512i	0.880236	−	1.38551i
$459$	19.2692	−	19.2692i	0.899411	−	0.899411i
$460$		0			0
$461$	−1.19682	−	1.19682i	−0.0557416	−	0.0557416i	0.678687	−	0.734428i	$-0.262550\pi$
$461$	−1.19682	−	1.19682i	−0.0557416	−	0.0557416i	−0.734428	+	0.678687i	$0.762550\pi$
$462$	0.397587	+	1.78286i	0.0184974	+	0.0829459i
$463$	21.1815	+	21.1815i	0.984390	+	0.984390i	0.999880	−	0.0154904i	$-0.00493096\pi$
$463$	21.1815	+	21.1815i	0.984390	+	0.984390i	−0.0154904	+	0.999880i	$0.504931\pi$
$464$	2.00096	+	21.6258i	0.0928921	+	1.00395i
$465$		0			0
$466$	10.7144	−	16.8647i	0.496334	−	0.781241i
$467$	−24.8448			−1.14968			−0.574840	−	0.818266i	$-0.694936\pi$
$467$	−24.8448			−1.14968			−0.574840	+	0.818266i	$0.694936\pi$
$468$	−42.2105	+	19.8116i	−1.95118	+	0.915792i
$469$	−1.52664	−	1.52664i	−0.0704936	−	0.0704936i
$470$		0			0
$471$	21.4343			0.987642
$472$	14.3838	+	1.83884i	0.662066	+	0.0846394i
$473$	−3.69537	−	3.69537i	−0.169913	−	0.169913i
$474$	15.2336	−	3.39717i	0.699701	−	0.156037i
$475$		0			0
$476$	−2.43972	−	5.19804i	−0.111824	−	0.238252i
$477$		−	14.2210i		−	0.651135i
$478$	8.08825	+	36.2692i	0.369948	+	1.65892i
$479$	−23.5766			−1.07724			−0.538621	−	0.842548i	$-0.681054\pi$
$479$	−23.5766			−1.07724			−0.538621	+	0.842548i	$0.681054\pi$
$480$		0			0
$481$	26.4181			1.20456
$482$	−0.0348578	−	0.156309i	−0.00158773	−	0.00711967i
$483$			4.73547i			0.215471i
$484$	8.93472	+	19.0362i	0.406124	+	0.865284i
$485$		0			0
$486$	17.1417	−	3.82271i	0.777565	−	0.173401i
$487$	2.63011	+	2.63011i	0.119182	+	0.119182i	0.764182	−	0.645001i	$-0.223143\pi$
$487$	2.63011	+	2.63011i	0.119182	+	0.119182i	−0.645001	+	0.764182i	$0.723143\pi$
$488$	1.89089	−	14.7909i	0.0855964	−	0.669552i
$489$	67.7686			3.06460
$490$		0			0
$491$	−18.6899	−	18.6899i	−0.843465	−	0.843465i	0.145843	−	0.989308i	$-0.453411\pi$
$491$	−18.6899	−	18.6899i	−0.843465	−	0.843465i	−0.989308	+	0.145843i	$0.953411\pi$
$492$	23.5606	−	11.0582i	1.06219	−	0.498544i
$493$	−24.0202			−1.08182
$494$	19.6139	−	30.8727i	0.882472	−	1.38903i
$495$		0			0
$496$	0.430623	+	0.357683i	0.0193355	+	0.0160605i
$497$	0.628940	+	0.628940i	0.0282118	+	0.0282118i
$498$	−12.7208	−	57.0424i	−0.570032	−	2.55613i
$499$	−9.69342	−	9.69342i	−0.433937	−	0.433937i	0.456028	−	0.889965i	$-0.349272\pi$
$499$	−9.69342	−	9.69342i	−0.433937	−	0.433937i	−0.889965	+	0.456028i	$0.849272\pi$
$500$		0			0
$501$	−1.15090	+	1.15090i	−0.0514185	+	0.0514185i
$502$	−20.6154	+	32.4491i	−0.920110	+	1.44827i
$503$	13.0434	−	13.0434i	0.581577	−	0.581577i	−0.353759	−	0.935336i	$-0.615097\pi$
$503$	13.0434	−	13.0434i	0.581577	−	0.581577i	0.935336	+	0.353759i	$0.115097\pi$
$504$	−1.20034	+	9.38926i	−0.0534672	+	0.418231i
$505$		0			0
$506$	−0.548051	−	2.45756i	−0.0243638	−	0.109252i
$507$			21.2495i			0.943724i
$508$	−0.591611	+	1.63816i	−0.0262485	+	0.0726817i
$509$	−25.8539	+	25.8539i	−1.14595	+	1.14595i	−0.158611	+	0.987341i	$0.550702\pi$
$509$	−25.8539	+	25.8539i	−1.14595	+	1.14595i	−0.987341	+	0.158611i	$0.949298\pi$
$510$		0			0
$511$			2.34062i			0.103543i
$512$	20.8063	−	8.89365i	0.919518	−	0.393047i
$513$	24.9168	−	24.9168i	1.10010	−	1.10010i
$514$	−0.812734	+	1.27926i	−0.0358481	+	0.0564258i
$515$		0			0
$516$	−18.2002	−	38.7773i	−0.801221	−	1.70707i
$517$	−4.08080			−0.179473
$518$	2.87584	−	4.52664i	0.126357	−	0.198889i
$519$			44.1252i			1.93688i
$520$		0			0
$521$			25.0528i			1.09758i	0.835959	+	0.548792i	$0.184912\pi$
$521$			25.0528i			1.09758i	−0.835959	+	0.548792i	$0.815088\pi$
$522$	33.4218	+	21.2334i	1.46283	+	0.929361i
$523$	−40.3434			−1.76410			−0.882048	−	0.471160i	$-0.843835\pi$
$523$	−40.3434			−1.76410			−0.882048	+	0.471160i	$0.843835\pi$
$524$	−9.17898	+	25.4165i	−0.400986	+	1.11032i
$525$		0			0
$526$	−9.67325	−	6.14556i	−0.421774	−	0.267959i
$527$	−0.437794	+	0.437794i	−0.0190706	+	0.0190706i
$528$	−0.733479	−	7.92723i	−0.0319206	−	0.344988i
$529$			16.4724i			0.716192i
$530$		0			0
$531$	18.6944	−	18.6944i	0.811267	−	0.811267i
$532$	−3.15477	−	6.72153i	−0.136777	−	0.291415i
$533$		−	20.6003i		−	0.892296i
$534$	13.2067	−	2.94517i	0.571510	−	0.127450i
$535$		0			0
$536$	5.75610	+	7.44356i	0.248626	+	0.321513i
$537$	−14.8639	+	14.8639i	−0.641425	+	0.641425i
$538$	16.5247	+	10.4984i	0.712430	+	0.452618i
$539$	−3.24180	+	3.24180i	−0.139634	+	0.139634i
$540$		0			0
$541$	−24.7446	−	24.7446i	−1.06385	−	1.06385i	−0.997817	−	0.0660360i	$-0.978965\pi$
$541$	−24.7446	−	24.7446i	−1.06385	−	1.06385i	−0.0660360	−	0.997817i	$-0.521035\pi$
$542$	−5.66146	+	1.26254i	−0.243181	+	0.0542307i
$543$	−25.9590	−	25.9590i	−1.11401	−	1.11401i
$544$	7.67437	+	23.8201i	0.329036	+	1.02128i
$545$		0			0
$546$	10.0028	+	6.35491i	0.428079	+	0.271965i
$547$	−19.0254			−0.813465			−0.406733	−	0.913547i	$-0.633332\pi$
$547$	−19.0254			−0.813465			−0.406733	+	0.913547i	$0.633332\pi$
$548$	−3.55738	+	9.85034i	−0.151964	+	0.420786i
$549$	−19.2235	−	19.2235i	−0.820440	−	0.820440i
$550$		0			0
$551$	−31.0602			−1.32321
$552$	2.61717	−	20.4720i	0.111394	−	0.871346i
$553$	−1.77329	−	1.77329i	−0.0754079	−	0.0754079i
$554$	−7.59554	−	34.0598i	−0.322704	−	1.44706i
$555$		0			0
$556$	−5.25292	+	14.5453i	−0.222773	+	0.616856i
$557$		−	30.9517i		−	1.31146i	−0.754993	−	0.655732i	$-0.772360\pi$
$557$		−	30.9517i		−	1.31146i	0.754993	−	0.655732i	$-0.227640\pi$
$558$	0.996151	−	0.222148i	0.0421704	−	0.00940425i
$559$	−33.9050			−1.43403
$560$		0			0
$561$	8.80494			0.371745
$562$	32.6702	−	7.28565i	1.37811	−	0.307327i
$563$			3.50238i			0.147608i	0.997273	+	0.0738039i	$0.0235139\pi$
$563$			3.50238i			0.147608i	−0.997273	+	0.0738039i	$0.976486\pi$
$564$	−31.4601	−	11.3616i	−1.32471	−	0.478410i
$565$		0			0
$566$	−4.01676	−	18.0119i	−0.168837	−	0.757097i
$567$	0.973793	+	0.973793i	0.0408955	+	0.0408955i
$568$	−2.37138	−	3.06658i	−0.0995011	−	0.128671i
$569$	−0.525780			−0.0220418			−0.0110209	−	0.999939i	$-0.503508\pi$
$569$	−0.525780			−0.0220418			−0.0110209	+	0.999939i	$0.503508\pi$
$570$		0			0
$571$	−11.2487	−	11.2487i	−0.470743	−	0.470743i	0.431412	−	0.902155i	$-0.358016\pi$
$571$	−11.2487	−	11.2487i	−0.470743	−	0.470743i	−0.902155	+	0.431412i	$0.858016\pi$
$572$	−5.92660	−	2.14035i	−0.247804	−	0.0894926i
$573$	−43.1472			−1.80250
$574$	−3.52977	−	2.24252i	−0.147330	−	0.0936008i
$575$		0			0
$576$	10.3784	−	39.9275i	0.432432	−	1.66364i
$577$	2.92884	+	2.92884i	0.121929	+	0.121929i	0.765438	−	0.643509i	$-0.222522\pi$
$577$	2.92884	+	2.92884i	0.121929	+	0.121929i	−0.643509	+	0.765438i	$0.722522\pi$
$578$	−3.54971	+	0.791607i	−0.147649	+	0.0329265i
$579$	−11.9714	−	11.9714i	−0.497515	−	0.497515i
$580$		0			0
$581$	−6.64011	+	6.64011i	−0.275478	+	0.275478i
$582$	−23.8935	−	15.1799i	−0.990416	−	0.629227i
$583$	1.35891	−	1.35891i	0.0562801	−	0.0562801i
$584$	1.29360	−	10.1188i	0.0535295	−	0.418718i
$585$		0			0
$586$	43.7186	−	9.74951i	1.80600	−	0.402748i
$587$		−	23.1574i		−	0.955809i	−0.878412	−	0.477905i	$-0.841396\pi$
$587$		−	23.1574i		−	0.955809i	0.878412	−	0.477905i	$-0.158604\pi$
$588$	−34.0178	+	15.9664i	−1.40287	+	0.658442i
$589$	−0.566106	+	0.566106i	−0.0233260	+	0.0233260i
$590$		0			0
$591$			11.5150i			0.473662i
$592$	−14.9343	+	17.9798i	−0.613798	+	0.738964i
$593$	13.9325	−	13.9325i	0.572141	−	0.572141i	−0.360585	−	0.932726i	$-0.617423\pi$
$593$	13.9325	−	13.9325i	0.572141	−	0.572141i	0.932726	+	0.360585i	$0.117423\pi$
$594$	−5.12398	−	3.25534i	−0.210240	−	0.133568i
$595$		0			0
$596$	−11.2146	−	4.05008i	−0.459368	−	0.165898i
$597$	15.5097			0.634769
$598$	−13.7882	−	8.75988i	−0.563843	−	0.358218i
$599$			33.5311i			1.37004i	0.728523	+	0.685021i	$0.240207\pi$
$599$			33.5311i			1.37004i	−0.728523	+	0.685021i	$0.759793\pi$
$600$		0			0
$601$		−	19.4164i		−	0.792011i	−0.918248	−	0.396005i	$-0.870396\pi$
$601$		−	19.4164i		−	0.792011i	0.918248	−	0.396005i	$-0.129604\pi$
$602$	−3.69085	+	5.80948i	−0.150428	+	0.236777i
$603$	17.1554			0.698623
$604$	−22.5256	+	10.5725i	−0.916554	+	0.430187i
$605$		0			0
$606$	5.65243	−	8.89705i	0.229614	−	0.361418i
$607$	9.51495	−	9.51495i	0.386200	−	0.386200i	−0.487130	−	0.873330i	$-0.661956\pi$
$607$	9.51495	−	9.51495i	0.386200	−	0.386200i	0.873330	+	0.487130i	$0.161956\pi$
$608$	9.92363	+	30.8015i	0.402456	+	1.24917i
$609$		−	10.0635i		−	0.407794i
$610$		0			0
$611$	−18.7206	+	18.7206i	−0.757355	+	0.757355i
$612$	42.9143	+	15.4982i	1.73471	+	0.626478i
$613$		−	9.37947i		−	0.378833i	−0.981897	−	0.189417i	$-0.939340\pi$
$613$		−	9.37947i		−	0.378833i	0.981897	−	0.189417i	$-0.0606597\pi$
$614$	8.42177	+	37.7648i	0.339875	+	1.52406i
$615$		0			0
$616$	−1.01190	+	0.782503i	−0.0407707	+	0.0315280i
$617$	3.54768	−	3.54768i	0.142824	−	0.142824i	−0.632079	−	0.774904i	$-0.717798\pi$
$617$	3.54768	−	3.54768i	0.142824	−	0.142824i	0.774904	+	0.632079i	$0.217798\pi$
$618$	−35.7319	+	56.2428i	−1.43735	+	2.26242i
$619$	24.6158	−	24.6158i	0.989392	−	0.989392i	−0.0105527	−	0.999944i	$-0.503359\pi$
$619$	24.6158	−	24.6158i	0.989392	−	0.989392i	0.999944	+	0.0105527i	$0.00335910\pi$
$620$		0			0
$621$	−11.1282	−	11.1282i	−0.446561	−	0.446561i
$622$	−4.86585	−	21.8194i	−0.195103	−	0.874877i
$623$	−1.53735	−	1.53735i	−0.0615926	−	0.0615926i
$624$	−39.7309	−	33.0013i	−1.59051	−	1.32111i
$625$		0			0
$626$	−14.8420	+	23.3617i	−0.593206	+	0.933720i
$627$	11.3856			0.454695
$628$	6.37747	+	13.5878i	0.254489	+	0.542211i
$629$	−18.2792	−	18.2792i	−0.728840	−	0.728840i
$630$		0			0
$631$	−28.8921			−1.15018			−0.575088	−	0.818092i	$-0.695032\pi$
$631$	−28.8921			−1.15018			−0.575088	+	0.818092i	$0.695032\pi$
$632$	6.68608	+	8.64618i	0.265958	+	0.343927i
$633$	9.22547	+	9.22547i	0.366679	+	0.366679i
$634$	−48.3235	+	10.7764i	−1.91917	+	0.427986i
$635$		0			0
$636$	14.2596	−	6.69281i	0.565432	−	0.265387i
$637$			29.7435i			1.17848i
$638$	1.16468	+	5.22265i	0.0461102	+	0.206767i
$639$	−7.06765			−0.279592
$640$		0			0
$641$	−16.6914			−0.659271			−0.329636	−	0.944108i	$-0.606926\pi$
$641$	−16.6914			−0.659271			−0.329636	+	0.944108i	$0.606926\pi$
$642$	−13.4600	−	60.3570i	−0.531223	−	2.38210i
$643$		−	5.22468i		−	0.206041i	−0.994679	−	0.103021i	$-0.967149\pi$
$643$		−	5.22468i		−	0.206041i	0.994679	−	0.103021i	$-0.0328507\pi$
$644$	−3.00194	+	1.40897i	−0.118293	+	0.0555212i
$645$		0			0
$646$	−34.9327	+	7.79019i	−1.37441	+	0.306501i
$647$	−21.6797	−	21.6797i	−0.852318	−	0.852318i	0.138100	−	0.990418i	$-0.455900\pi$
$647$	−21.6797	−	21.6797i	−0.852318	−	0.852318i	−0.990418	+	0.138100i	$0.955900\pi$
$648$	−3.67163	−	4.74801i	−0.144235	−	0.186519i
$649$	3.57273			0.140242
$650$		0			0
$651$	−0.183418	−	0.183418i	−0.00718874	−	0.00718874i
$652$	20.1636	+	42.9603i	0.789666	+	1.68245i
$653$	−22.7642			−0.890833			−0.445417	−	0.895323i	$-0.646944\pi$
$653$	−22.7642			−0.890833			−0.445417	+	0.895323i	$0.646944\pi$
$654$	−38.2261	+	60.1688i	−1.49476	+	2.35279i
$655$		0			0
$656$	14.0202	+	11.6455i	0.547398	+	0.454679i
$657$	−13.1513	−	13.1513i	−0.513079	−	0.513079i
$658$	1.16980	+	5.24560i	0.0456036	+	0.204495i
$659$	−1.66201	−	1.66201i	−0.0647427	−	0.0647427i	0.673994	−	0.738737i	$-0.264577\pi$
$659$	−1.66201	−	1.66201i	−0.0647427	−	0.0647427i	−0.738737	+	0.673994i	$0.764577\pi$
$660$		0			0
$661$	−5.62818	+	5.62818i	−0.218911	+	0.218911i	−0.808039	−	0.589129i	$-0.799471\pi$
$661$	−5.62818	+	5.62818i	−0.218911	+	0.218911i	0.589129	+	0.808039i	$0.299471\pi$
$662$	−18.0406	+	28.3963i	−0.701168	+	1.10365i
$663$	40.3926	−	40.3926i	1.56872	−	1.56872i
$664$	32.3758	−	25.0362i	1.25642	−	0.971591i
$665$		0			0
$666$	9.27532	+	41.5923i	0.359411	+	1.61167i
$667$			13.8720i			0.537125i
$668$	−1.07202	−	0.387153i	−0.0414777	−	0.0149794i
$669$	−23.3427	+	23.3427i	−0.902481	+	0.902481i
$670$		0			0
$671$		−	3.67386i		−	0.141828i
$672$	−9.97969	+	3.21526i	−0.384975	+	0.124031i
$673$	−0.278251	+	0.278251i	−0.0107258	+	0.0107258i	−0.712449	−	0.701724i	$-0.752414\pi$
$673$	−0.278251	+	0.278251i	−0.0107258	+	0.0107258i	0.701724	+	0.712449i	$0.252414\pi$
$674$	15.5494	−	24.4751i	0.598940	−	0.942744i
$675$		0			0
$676$	−13.4706	+	6.32248i	−0.518101	+	0.243172i
$677$	−26.3591			−1.01306			−0.506531	−	0.862222i	$-0.669072\pi$
$677$	−26.3591			−1.01306			−0.506531	+	0.862222i	$0.669072\pi$
$678$	7.76655	−	12.2247i	0.298273	−	0.469488i
$679$			4.54840i			0.174551i
$680$		0			0
$681$			4.40019i			0.168616i
$682$	0.116416	+	0.0739609i	0.00445780	+	0.00283211i
$683$	2.83023			0.108296			0.0541479	−	0.998533i	$-0.482756\pi$
$683$	2.83023			0.108296			0.0541479	+	0.998533i	$0.482756\pi$
$684$	55.4919	+	20.0405i	2.12179	+	0.766269i
$685$		0			0
$686$	10.5191	+	6.68296i	0.401622	+	0.255157i
$687$	50.1646	−	50.1646i	1.91390	−	1.91390i
$688$	19.1667	−	23.0752i	0.730724	−	0.879734i
$689$		−	12.4679i		−	0.474991i
$690$		0			0
$691$	22.1815	−	22.1815i	0.843825	−	0.843825i	−0.145529	−	0.989354i	$-0.546488\pi$
$691$	22.1815	−	22.1815i	0.843825	−	0.843825i	0.989354	+	0.145529i	$0.0464884\pi$
$692$	−27.9721	+	13.1288i	−1.06334	+	0.499083i
$693$			2.33217i			0.0885917i
$694$	−23.1484	+	5.16223i	−0.878702	+	0.195956i
$695$		0			0
$696$	−5.56183	+	43.5057i	−0.210821	+	1.64908i
$697$	−14.2537	+	14.2537i	−0.539898	+	0.539898i
$698$	3.14560	+	1.99845i	0.119063	+	0.0756423i
$699$	28.5320	−	28.5320i	1.07918	−	1.07918i
$700$		0			0
$701$	16.2264	+	16.2264i	0.612864	+	0.612864i	0.943691	−	0.330828i	$-0.107328\pi$
$701$	16.2264	+	16.2264i	0.612864	+	0.612864i	−0.330828	+	0.943691i	$0.607328\pi$
$702$	−38.4401	+	8.57237i	−1.45083	+	0.323543i
$703$	−23.6366	−	23.6366i	−0.891472	−	0.891472i
$704$	4.80704	−	2.82360i	0.181172	−	0.106418i
$705$		0			0
$706$	−40.7449	−	25.8858i	−1.53345	−	0.974226i
$707$	−1.69365			−0.0636965
$708$	27.5433	+	9.94708i	1.03514	+	0.373834i
$709$	25.3577	+	25.3577i	0.952329	+	0.952329i	0.998914	−	0.0465856i	$-0.0148340\pi$
$709$	25.3577	+	25.3577i	0.952329	+	0.952329i	−0.0465856	+	0.998914i	$0.514834\pi$
$710$		0			0
$711$	19.9271			0.747326
$712$	5.79648	+	7.49579i	0.217232	+	0.280916i
$713$	0.252832	+	0.252832i	0.00946863	+	0.00946863i
$714$	−2.52402	−	11.3182i	−0.0944592	−	0.423573i
$715$		0			0
$716$	−13.8452	−	5.00009i	−0.517418	−	0.186862i
$717$			75.0450i			2.80261i
$718$	−16.9088	+	3.77076i	−0.631031	+	0.140724i
$719$	41.3374			1.54163			0.770813	−	0.637061i	$-0.219850\pi$
$719$	41.3374			1.54163			0.770813	+	0.637061i	$0.219850\pi$
$720$		0			0
$721$	10.7065			0.398730
$722$	−18.9452	+	4.22489i	−0.705067	+	0.157234i
$723$		−	0.323420i		−	0.0120281i
$724$	8.73236	−	24.1798i	0.324536	−	0.898635i
$725$		0			0
$726$	9.24346	+	41.4494i	0.343057	+	1.53833i
$727$	23.4630	+	23.4630i	0.870193	+	0.870193i	0.992493	−	0.122300i	$-0.0390271\pi$
$727$	23.4630	+	23.4630i	0.870193	+	0.870193i	−0.122300	+	0.992493i	$0.539027\pi$
$728$	−1.05237	+	8.23182i	−0.0390033	+	0.305092i
$729$	41.8342			1.54942
$730$		0			0
$731$	23.4595	+	23.4595i	0.867681	+	0.867681i
$732$	10.2286	−	28.3229i	0.378061	−	1.04684i
$733$	15.1628			0.560051			0.280025	−	0.959993i	$-0.409657\pi$
$733$	15.1628			0.560051			0.280025	+	0.959993i	$0.409657\pi$
$734$	−4.58000	−	2.90975i	−0.169051	−	0.107401i
$735$		0			0
$736$	13.7564	−	4.43205i	0.507069	−	0.163368i
$737$	1.63931	+	1.63931i	0.0603848	+	0.0603848i
$738$	32.4327	−	7.23269i	1.19387	−	0.266239i
$739$	−0.974343	−	0.974343i	−0.0358418	−	0.0358418i	0.688959	−	0.724801i	$-0.258068\pi$
$739$	−0.974343	−	0.974343i	−0.0358418	−	0.0358418i	−0.724801	+	0.688959i	$0.758068\pi$
$740$		0			0
$741$	52.2312	−	52.2312i	1.91876	−	1.91876i
$742$	−2.13633	−	1.35724i	−0.0784272	−	0.0498260i
$743$	−29.0897	+	29.0897i	−1.06720	+	1.06720i	−0.0696259	+	0.997573i	$0.522181\pi$
$743$	−29.0897	+	29.0897i	−1.06720	+	1.06720i	−0.997573	+	0.0696259i	$0.977819\pi$
$744$	0.691569	+	0.894310i	0.0253541	+	0.0327870i
$745$		0			0
$746$	−22.7538	+	5.07424i	−0.833078	+	0.185781i
$747$		−	74.6176i		−	2.73011i
$748$	2.61978	+	5.58168i	0.0957887	+	0.204087i
$749$	−7.02596	+	7.02596i	−0.256723	+	0.256723i
$750$		0			0
$751$		−	7.77705i		−	0.283789i	−0.989882	−	0.141894i	$-0.954681\pi$
$751$		−	7.77705i		−	0.283789i	0.989882	−	0.141894i	$-0.0453193\pi$
$752$	−2.15808	−	23.3239i	−0.0786970	−	0.850534i
$753$	−54.8981	+	54.8981i	−2.00060	+	2.00060i
$754$	29.3019	+	18.6159i	1.06711	+	0.677952i
$755$		0			0
$756$	−2.71570	+	7.51973i	−0.0987690	+	0.273490i
$757$	−1.42073			−0.0516372			−0.0258186	−	0.999667i	$-0.508219\pi$
$757$	−1.42073			−0.0516372			−0.0258186	+	0.999667i	$0.508219\pi$
$758$	−23.2482	−	14.7699i	−0.844413	−	0.536469i
$759$		−	5.08497i		−	0.184573i
$760$		0			0
$761$		−	26.6737i		−	0.966921i	−0.875366	−	0.483460i	$-0.839380\pi$
$761$		−	26.6737i		−	0.966921i	0.875366	−	0.483460i	$-0.160620\pi$
$762$	−1.88619	+	2.96891i	−0.0683295	+	0.107552i
$763$	11.4538			0.414656
$764$	−12.8378	−	27.3521i	−0.464456	−	0.989565i
$765$		0			0
$766$	12.3905	−	19.5029i	0.447687	−	0.704669i
$767$	16.3899	−	16.3899i	0.591805	−	0.591805i
$768$	44.9203	−	8.38443i	1.62092	−	0.302547i
$769$			45.8210i			1.65235i	0.563415	+	0.826174i	$0.309487\pi$
$769$			45.8210i			1.65235i	−0.563415	+	0.826174i	$0.690513\pi$
$770$		0			0
$771$	−2.16428	+	2.16428i	−0.0779447	+	0.0779447i
$772$	4.02707	−	11.1509i	0.144937	−	0.401330i
$773$		−	18.5473i		−	0.667101i	−0.942732	−	0.333550i	$-0.891753\pi$
$773$		−	18.5473i		−	0.667101i	0.942732	−	0.333550i	$-0.108247\pi$
$774$	−11.9039	−	53.3795i	−0.427878	−	1.91869i
$775$		0			0
$776$	2.51378	−	19.6633i	0.0902393	−	0.705870i
$777$	7.65827	−	7.65827i	0.274739	−	0.274739i
$778$	16.9162	−	26.6264i	0.606474	−	0.954603i
$779$	−18.4313	+	18.4313i	−0.660370	+	0.660370i
$780$		0			0
$781$	−0.675359	−	0.675359i	−0.0241662	−	0.0241662i
$782$	3.47922	+	15.6015i	0.124417	+	0.557908i
$783$	23.6490	+	23.6490i	0.845146	+	0.845146i
$784$	−20.2430	−	16.8142i	−0.722964	−	0.600508i
$785$		0			0
$786$	−29.2647	+	46.0633i	−1.04384	+	1.64302i
$787$	21.3016			0.759319			0.379659	−	0.925126i	$-0.376041\pi$
$787$	21.3016			0.759319			0.379659	+	0.925126i	$0.376041\pi$
$788$	−7.29963	+	3.42610i	−0.260039	+	0.122050i
$789$	−16.3654	−	16.3654i	−0.582624	−	0.582624i
$790$		0			0
$791$	−2.32712			−0.0827427
$792$	1.28892	−	10.0822i	0.0458000	−	0.358256i
$793$	−16.8538	−	16.8538i	−0.598496	−	0.598496i
$794$	41.3482	−	9.22090i	1.46739	−	0.327237i
$795$		0			0
$796$	4.61468	+	9.83200i	0.163563	+	0.348486i
$797$			2.35457i			0.0834033i	0.999130	+	0.0417016i	$0.0132779\pi$
$797$			2.35457i			0.0834033i	−0.999130	+	0.0417016i	$0.986722\pi$
$798$	−3.26378	−	14.6354i	−0.115537	−	0.518088i
$799$	25.9063			0.916500
$800$		0			0
$801$	17.2758			0.610410
$802$	6.13297	+	27.5014i	0.216563	+	0.971108i
$803$		−	2.51337i		−	0.0886949i
$804$	8.07384	+	17.2021i	0.284742	+	0.606670i
$805$		0			0
$806$	0.873354	−	0.194763i	0.0307626	−	0.00686023i
$807$	27.9569	+	27.9569i	0.984128	+	0.984128i
$808$	7.32187	+	0.936037i	0.257582	+	0.0329297i
$809$	−23.9476			−0.841952			−0.420976	−	0.907072i	$-0.638312\pi$
$809$	−23.9476			−0.841952			−0.420976	+	0.907072i	$0.638312\pi$
$810$		0			0
$811$	−1.33006	−	1.33006i	−0.0467048	−	0.0467048i	0.683369	−	0.730073i	$-0.260514\pi$
$811$	−1.33006	−	1.33006i	−0.0467048	−	0.0467048i	−0.730073	+	0.683369i	$0.760514\pi$
$812$	6.37952	−	2.99425i	0.223877	−	0.105078i
$813$	−11.7142			−0.410834
$814$	−3.08809	+	4.86072i	−0.108238	+	0.170368i
$815$		0			0
$816$	4.65638	+	50.3248i	0.163006	+	1.76172i
$817$	30.3352	+	30.3352i	1.06129	+	1.06129i
$818$	1.81567	+	8.14182i	0.0634836	+	0.284672i
$819$	10.6988	+	10.6988i	0.373846	+	0.373846i
$820$		0			0
$821$	36.4676	−	36.4676i	1.27273	−	1.27273i	0.328076	−	0.944651i	$-0.393600\pi$
$821$	36.4676	−	36.4676i	1.27273	−	1.27273i	0.944651	−	0.328076i	$-0.106400\pi$
$822$	−11.3417	+	17.8522i	−0.395589	+	0.622666i
$823$	−26.3978	+	26.3978i	−0.920170	+	0.920170i	−0.997041	−	0.0768712i	$-0.975507\pi$
$823$	−26.3978	+	26.3978i	−0.920170	+	0.920170i	0.0768712	+	0.997041i	$0.475507\pi$
$824$	−46.2853	−	5.91718i	−1.61243	−	0.206135i
$825$		0			0
$826$	−1.02416	−	4.59252i	−0.0356351	−	0.159794i
$827$			1.99830i			0.0694878i	0.999396	+	0.0347439i	$0.0110616\pi$
$827$			1.99830i			0.0694878i	−0.999396	+	0.0347439i	$0.988938\pi$
$828$	8.95041	−	24.7836i	0.311048	−	0.861288i
$829$	−13.0376	+	13.0376i	−0.452813	+	0.452813i	−0.896287	−	0.443474i	$-0.853746\pi$
$829$	−13.0376	+	13.0376i	−0.452813	+	0.452813i	0.443474	+	0.896287i	$0.353746\pi$
$830$		0			0
$831$		−	70.4735i		−	2.44470i
$832$	9.09901	−	35.0055i	0.315451	−	1.21360i
$833$	20.5801	−	20.5801i	0.713059	−	0.713059i
$834$	−16.7475	+	26.3609i	−0.579919	+	0.912805i
$835$		0			0
$836$	3.38761	+	7.21760i	0.117163	+	0.249626i
$837$	0.862057			0.0297971
$838$	−8.84194	+	13.9174i	−0.305440	+	0.480769i
$839$		−	15.4102i		−	0.532018i	−0.963971	−	0.266009i	$-0.914295\pi$
$839$		−	15.4102i		−	0.532018i	0.963971	−	0.266009i	$-0.0857050\pi$
$840$		0			0
$841$		−	0.479815i		−	0.0165453i
$842$	−28.9979	−	18.4228i	−0.999333	−	0.634891i
$843$	67.5983			2.32821
$844$	−3.10336	+	8.59317i	−0.106822	+	0.295789i
$845$		0			0
$846$	−36.0462	−	22.9007i	−1.23929	−	0.787343i
$847$	4.82499	−	4.82499i	0.165789	−	0.165789i
$848$	8.48550	+	7.04822i	0.291393	+	0.242037i
$849$		−	37.2686i		−	1.27906i
$850$		0			0
$851$	−10.5565	+	10.5565i	−0.361872	+	0.361872i
$852$	−3.32624	−	7.08686i	−0.113955	−	0.242792i
$853$			7.96419i			0.272689i	0.990662	+	0.136344i	$0.0435353\pi$
$853$			7.96419i			0.272689i	−0.990662	+	0.136344i	$0.956465\pi$
$854$	−4.72251	+	1.05315i	−0.161601	+	0.0360380i
$855$		0			0
$856$	34.2571	−	26.4910i	1.17088	−	0.905443i
$857$	−5.35407	+	5.35407i	−0.182891	+	0.182891i	−0.792615	−	0.609723i	$-0.791281\pi$
$857$	−5.35407	+	5.35407i	−0.182891	+	0.182891i	0.609723	+	0.792615i	$0.291281\pi$
$858$	−10.7410	−	6.82393i	−0.366692	−	0.232965i
$859$	35.0058	−	35.0058i	1.19438	−	1.19438i	0.218559	−	0.975824i	$-0.429864\pi$
$859$	35.0058	−	35.0058i	1.19438	−	1.19438i	0.975824	−	0.218559i	$-0.0701355\pi$
$860$		0			0
$861$	−5.97175	−	5.97175i	−0.203517	−	0.203517i
$862$	44.4140	−	9.90457i	1.51275	−	0.337351i
$863$	36.7138	+	36.7138i	1.24975	+	1.24975i	0.955829	+	0.293923i	$0.0949610\pi$
$863$	36.7138	+	36.7138i	1.24975	+	1.24975i	0.293923	+	0.955829i	$0.405039\pi$
$864$	15.8962	−	31.0078i	0.540801	−	1.05491i
$865$		0			0
$866$	34.3336	+	21.8126i	1.16670	+	0.741224i
$867$	−7.34475			−0.249441
$868$	0.0617003	−	0.170847i	0.00209424	−	0.00579893i
$869$	1.90416	+	1.90416i	0.0645943	+	0.0645943i
$870$		0			0
$871$	15.0406			0.509633
$872$	−49.5162	−	6.33022i	−1.67683	−	0.214368i
$873$	−25.5561	−	25.5561i	−0.864942	−	0.864942i
$874$	4.49894	+	20.1741i	0.152179	+	0.682399i
$875$		0			0
$876$	6.99764	−	19.3764i	0.236428	−	0.654667i
$877$			14.3410i			0.484262i	0.970244	+	0.242131i	$0.0778463\pi$
$877$			14.3410i			0.484262i	−0.970244	+	0.242131i	$0.922154\pi$
$878$	48.8877	−	10.9022i	1.64988	−	0.367933i
$879$	90.4586			3.05109
$880$		0			0
$881$	−13.6397			−0.459533			−0.229767	−	0.973246i	$-0.573796\pi$
$881$	−13.6397			−0.459533			−0.229767	+	0.973246i	$0.573796\pi$
$882$	−46.8277	+	10.4429i	−1.57677	+	0.351629i
$883$			6.12563i			0.206144i	0.994674	+	0.103072i	$0.0328672\pi$
$883$			6.12563i			0.206144i	−0.994674	+	0.103072i	$0.967133\pi$
$884$	37.6242	+	13.5877i	1.26544	+	0.457004i
$885$		0			0
$886$	0.935105	+	4.19319i	0.0314155	+	0.140873i
$887$	−25.5187	−	25.5187i	−0.856834	−	0.856834i	0.134130	−	0.990964i	$-0.457176\pi$
$887$	−25.5187	−	25.5187i	−0.856834	−	0.856834i	−0.990964	+	0.134130i	$0.957176\pi$
$888$	−37.3401	+	28.8751i	−1.25305	+	0.968984i
$889$	0.565166			0.0189551
$890$		0			0
$891$	−1.04566	−	1.04566i	−0.0350310	−	0.0350310i
$892$	−21.7428	−	7.85227i	−0.728003	−	0.262913i
$893$	33.4992			1.12101
$894$	−20.3247	−	12.9126i	−0.679759	−	0.431861i
$895$		0			0
$896$	−5.00755	−	5.36973i	−0.167290	−	0.179390i
$897$	−23.3273	−	23.3273i	−0.778875	−	0.778875i
$898$	11.9474	−	2.66433i	0.398689	−	0.0889100i
$899$	−0.537302	−	0.537302i	−0.0179200	−	0.0179200i
$900$		0			0
$901$	−8.62682	+	8.62682i	−0.287401	+	0.287401i
$902$	3.79028	+	2.40802i	0.126203	+	0.0801784i
$903$	−9.82861	+	9.82861i	−0.327076	+	0.327076i
$904$	10.0604	+	1.28613i	0.334604	+	0.0427762i
$905$		0			0
$906$	−49.0471	+	10.9378i	−1.62948	+	0.363384i
$907$		−	32.1815i		−	1.06857i	−0.845305	−	0.534284i	$-0.820581\pi$
$907$		−	32.1815i		−	1.06857i	0.845305	−	0.534284i	$-0.179419\pi$
$908$	−2.78940	+	1.30921i	−0.0925694	+	0.0434477i
$909$	9.51614	−	9.51614i	0.315630	−	0.315630i
$910$		0			0
$911$			38.6282i			1.27981i	0.768455	+	0.639904i	$0.221026\pi$
$911$			38.6282i			1.27981i	−0.768455	+	0.639904i	$0.778974\pi$
$912$	6.02111	+	65.0744i	0.199379	+	2.15483i
$913$	7.13018	−	7.13018i	0.235974	−	0.235974i
$914$	22.8868	+	14.5403i	0.757027	+	0.480950i
$915$		0			0
$916$	46.7264	+	16.8749i	1.54388	+	0.557563i
$917$	8.76867			0.289567
$918$	32.5289	+	20.6661i	1.07361	+	0.682082i
$919$			19.1924i			0.633099i	0.948576	+	0.316550i	$0.102524\pi$
$919$			19.1924i			0.633099i	−0.948576	+	0.316550i	$0.897476\pi$
$920$		0			0
$921$			78.1395i			2.57479i
$922$	1.28358	−	2.02038i	0.0422725	−	0.0665378i
$923$	−6.19641			−0.203957
$924$	−2.33850	+	1.09758i	−0.0769312	+	0.0361079i
$925$		0			0
$926$	−22.7170	+	35.7571i	−0.746527	+	1.17505i
$927$	−60.1564	+	60.1564i	−1.97580	+	1.97580i
$928$	−29.2343	+	9.41870i	−0.959662	+	0.309184i
$929$		−	16.8576i		−	0.553081i	−0.961002	−	0.276541i	$-0.910812\pi$
$929$		−	16.8576i		−	0.553081i	0.961002	−	0.276541i	$-0.0891880\pi$
$930$		0			0
$931$	26.6119	−	26.6119i	0.872170	−	0.872170i
$932$	26.5765	+	9.59792i	0.870542	+	0.314390i
$933$		−	45.1467i		−	1.47804i
$934$	−7.64764	−	34.2935i	−0.250239	−	1.12212i
$935$		0			0
$936$	−40.3392	−	52.1651i	−1.31853	−	1.70507i
$937$	23.9511	−	23.9511i	0.782449	−	0.782449i	−0.197795	−	0.980243i	$-0.563378\pi$
$937$	23.9511	−	23.9511i	0.782449	−	0.782449i	0.980243	+	0.197795i	$0.0633779\pi$
$938$	1.63730	−	2.57715i	0.0534599	−	0.0841470i
$939$	−39.5238	+	39.5238i	−1.28981	+	1.28981i
$940$		0			0
$941$	14.2496	+	14.2496i	0.464525	+	0.464525i	0.900135	−	0.435610i	$-0.143467\pi$
$941$	14.2496	+	14.2496i	0.464525	+	0.464525i	−0.435610	+	0.900135i	$0.643467\pi$
$942$	6.59784	+	29.5860i	0.214969	+	0.963963i
$943$	8.23171	+	8.23171i	0.268061	+	0.268061i
$944$	1.88940	+	20.4200i	0.0614946	+	0.664616i
$945$		0			0
$946$	3.96325	−	6.23824i	0.128856	−	0.202823i
$947$	−20.2943			−0.659477			−0.329738	−	0.944072i	$-0.606961\pi$
$947$	−20.2943			−0.659477			−0.329738	+	0.944072i	$0.606961\pi$
$948$	9.37829	+	19.9813i	0.304593	+	0.648963i
$949$	−11.5301	−	11.5301i	−0.374282	−	0.374282i
$950$		0			0
$951$	−99.9866			−3.24229
$952$	6.42391	−	4.96761i	0.208200	−	0.161001i
$953$	10.9257	+	10.9257i	0.353919	+	0.353919i	0.861565	−	0.507647i	$-0.169484\pi$
$953$	10.9257	+	10.9257i	0.353919	+	0.353919i	−0.507647	+	0.861565i	$0.669484\pi$
$954$	19.6293	−	4.37746i	0.635524	−	0.141725i
$955$		0			0
$956$	−47.5730	+	22.3285i	−1.53862	+	0.722157i
$957$			10.8062i			0.349316i
$958$	−7.25726	−	32.5429i	−0.234471	−	1.05141i
$959$	3.39836			0.109739
$960$		0			0
$961$	30.9804			0.999368
$962$	8.13193	+	36.4651i	0.262184	+	1.17568i
$963$		−	78.9535i		−	2.54424i
$964$	0.205024	−	0.0962289i	0.00660339	−	0.00309932i
$965$		0			0
$966$	−6.53641	+	1.45766i	−0.210305	+	0.0468993i
$967$	−10.7569	−	10.7569i	−0.345918	−	0.345918i	0.512669	−	0.858586i	$-0.328657\pi$
$967$	−10.7569	−	10.7569i	−0.345918	−	0.345918i	−0.858586	+	0.512669i	$0.828657\pi$
$968$	−23.5256	+	18.1923i	−0.756142	+	0.584724i
$969$	−72.2796			−2.32195
$970$		0			0
$971$	−18.7456	−	18.7456i	−0.601574	−	0.601574i	0.339156	−	0.940730i	$-0.389858\pi$
$971$	−18.7456	−	18.7456i	−0.601574	−	0.601574i	−0.940730	+	0.339156i	$0.889858\pi$
$972$	10.5530	+	22.4842i	0.338488	+	0.721180i
$973$	5.01811			0.160873
$974$	−2.82077	+	4.43995i	−0.0903832	+	0.142265i
$975$		0			0
$976$	20.9980	−	1.94287i	0.672130	−	0.0621899i
$977$	26.3906	+	26.3906i	0.844309	+	0.844309i	0.989416	−	0.145107i	$-0.0463526\pi$
$977$	26.3906	+	26.3906i	0.844309	+	0.844309i	−0.145107	+	0.989416i	$0.546353\pi$
$978$	20.8603	+	93.5415i	0.667039	+	2.99113i
$979$	1.65081	+	1.65081i	0.0527602	+	0.0527602i
$980$		0			0
$981$	−64.3556	+	64.3556i	−2.05472	+	2.05472i
$982$	20.0448	−	31.5509i	0.639655	−	1.00683i
$983$	4.87875	−	4.87875i	0.155608	−	0.155608i	−0.625009	−	0.780617i	$-0.714905\pi$
$983$	4.87875	−	4.87875i	0.155608	−	0.155608i	0.780617	+	0.625009i	$0.214905\pi$
$984$	22.5161	+	29.1170i	0.717788	+	0.928215i
$985$		0			0
$986$	−7.39381	−	33.1553i	−0.235467	−	1.05588i
$987$			10.8537i			0.345478i
$988$	48.6513	+	17.5701i	1.54781	+	0.558979i
$989$	13.5482	−	13.5482i	0.430807	−	0.430807i
$990$		0			0
$991$			61.2103i			1.94441i	0.234130	+	0.972205i	$0.424776\pi$
$991$			61.2103i			1.94441i	−0.234130	+	0.972205i	$0.575224\pi$
$992$	−0.361160	+	0.704492i	−0.0114668	+	0.0223677i
$993$	−48.0415	+	48.0415i	−1.52455	+	1.52455i
$994$	−0.674533	+	1.06173i	−0.0213949	+	0.0336760i
$995$		0			0
$996$	74.8204	−	35.1172i	2.37077	−	1.11273i
$997$	−39.1082			−1.23857			−0.619284	−	0.785167i	$-0.712577\pi$
$997$	−39.1082			−1.23857			−0.619284	+	0.785167i	$0.712577\pi$
$998$	10.3961	−	16.3637i	0.329083	−	0.517984i
$999$			35.9935i			1.13878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.j.d.307.5		18
4.3	odd	2		1600.2.j.d.1007.1		18
5.2	odd	4		80.2.s.b.3.1	yes	18
5.3	odd	4		400.2.s.d.243.9		18
5.4	even	2		80.2.j.b.67.5	yes	18
15.2	even	4		720.2.z.g.163.9		18
15.14	odd	2		720.2.bd.g.307.5		18
16.5	even	4		1600.2.s.d.207.9		18
16.11	odd	4		400.2.s.d.107.9		18
20.3	even	4		1600.2.s.d.943.9		18
20.7	even	4		320.2.s.b.303.1		18
20.19	odd	2		320.2.j.b.47.9		18
40.19	odd	2		640.2.j.c.607.1		18
40.27	even	4		640.2.s.c.223.9		18
40.29	even	2		640.2.j.d.607.9		18
40.37	odd	4		640.2.s.d.223.1		18
80.19	odd	4		640.2.s.d.287.1		18
80.27	even	4		80.2.j.b.43.5	✓	18
80.29	even	4		640.2.s.c.287.9		18
80.37	odd	4		320.2.j.b.143.1		18
80.43	even	4	inner	400.2.j.d.43.5		18
80.53	odd	4		1600.2.j.d.143.9		18
80.59	odd	4		80.2.s.b.27.1	yes	18
80.67	even	4		640.2.j.d.543.1		18
80.69	even	4		320.2.s.b.207.1		18
80.77	odd	4		640.2.j.c.543.9		18
240.59	even	4		720.2.z.g.667.9		18
240.107	odd	4		720.2.bd.g.523.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.5	✓	18	80.27	even	4
80.2.j.b.67.5	yes	18	5.4	even	2
80.2.s.b.3.1	yes	18	5.2	odd	4
80.2.s.b.27.1	yes	18	80.59	odd	4
320.2.j.b.47.9		18	20.19	odd	2
320.2.j.b.143.1		18	80.37	odd	4
320.2.s.b.207.1		18	80.69	even	4
320.2.s.b.303.1		18	20.7	even	4
400.2.j.d.43.5		18	80.43	even	4	inner
400.2.j.d.307.5		18	1.1	even	1	trivial
400.2.s.d.107.9		18	16.11	odd	4
400.2.s.d.243.9		18	5.3	odd	4
640.2.j.c.543.9		18	80.77	odd	4
640.2.j.c.607.1		18	40.19	odd	2
640.2.j.d.543.1		18	80.67	even	4
640.2.j.d.607.9		18	40.29	even	2
640.2.s.c.223.9		18	40.27	even	4
640.2.s.c.287.9		18	80.29	even	4
640.2.s.d.223.1		18	40.37	odd	4
640.2.s.d.287.1		18	80.19	odd	4
720.2.z.g.163.9		18	15.2	even	4
720.2.z.g.667.9		18	240.59	even	4
720.2.bd.g.307.5		18	15.14	odd	2
720.2.bd.g.523.5		18	240.107	odd	4
1600.2.j.d.143.9		18	80.53	odd	4
1600.2.j.d.1007.1		18	4.3	odd	2
1600.2.s.d.207.9		18	16.5	even	4
1600.2.s.d.943.9		18	20.3	even	4

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.307817 + 1.38031i) q^{2} +2.85601i q^{3} +(-1.81050 + 0.849763i) q^{4} +(-3.94217 + 0.879127i) q^{6} +(0.458895 + 0.458895i) q^{7} +(-1.73024 - 2.23747i) q^{8} -5.15678 q^{9} +O(q^{10})\)	\(q+(0.307817 + 1.38031i) q^{2} +2.85601i q^{3} +(-1.81050 + 0.849763i) q^{4} +(-3.94217 + 0.879127i) q^{6} +(0.458895 + 0.458895i) q^{7} +(-1.73024 - 2.23747i) q^{8} -5.15678 q^{9} +(-0.492763 - 0.492763i) q^{11} +(-2.42693 - 5.17080i) q^{12} -4.52109 q^{13} +(-0.492160 + 0.774671i) q^{14} +(2.55581 - 3.07699i) q^{16} +(3.12823 + 3.12823i) q^{17} +(-1.58734 - 7.11794i) q^{18} +(4.04508 + 4.04508i) q^{19} +(-1.31061 + 1.31061i) q^{21} +(0.528484 - 0.831845i) q^{22} +(1.80660 - 1.80660i) q^{23} +(6.39024 - 4.94157i) q^{24} +(-1.39167 - 6.24050i) q^{26} -6.15978i q^{27} +(-1.22078 - 0.440876i) q^{28} +(-3.83926 + 3.83926i) q^{29} +0.139949i q^{31} +(5.03391 + 2.58065i) q^{32} +(1.40733 - 1.40733i) q^{33} +(-3.35500 + 5.28085i) q^{34} +(9.33634 - 4.38204i) q^{36} -5.84330 q^{37} +(-4.33831 + 6.82860i) q^{38} -12.9123i q^{39} +4.55648i q^{41} +(-2.21247 - 1.40561i) q^{42} +7.49928 q^{43} +(1.31088 + 0.473414i) q^{44} +(3.04976 + 1.93756i) q^{46} +(4.14073 - 4.14073i) q^{47} +(8.78790 + 7.29940i) q^{48} -6.57883i q^{49} +(-8.93426 + 8.93426i) q^{51} +(8.18543 - 3.84186i) q^{52} +2.75773i q^{53} +(8.50239 - 1.89608i) q^{54} +(0.232768 - 1.82076i) q^{56} +(-11.5528 + 11.5528i) q^{57} +(-6.48115 - 4.11757i) q^{58} +(-3.62521 + 3.62521i) q^{59} +(3.72781 + 3.72781i) q^{61} +(-0.193173 + 0.0430787i) q^{62} +(-2.36642 - 2.36642i) q^{63} +(-2.01257 + 7.74271i) q^{64} +(2.37576 + 1.50935i) q^{66} -3.32677 q^{67} +(-8.32192 - 3.00540i) q^{68} +(5.15965 + 5.15965i) q^{69} +1.37056 q^{71} +(8.92244 + 11.5382i) q^{72} +(2.55028 + 2.55028i) q^{73} +(-1.79867 - 8.06556i) q^{74} +(-10.7610 - 3.88625i) q^{76} -0.452252i q^{77} +(17.8229 - 3.97461i) q^{78} -3.86426 q^{79} +2.12204 q^{81} +(-6.28934 + 1.40256i) q^{82} +14.4698i q^{83} +(1.25915 - 3.48655i) q^{84} +(2.30840 + 10.3513i) q^{86} +(-10.9650 - 10.9650i) q^{87} +(-0.249948 + 1.95514i) q^{88} -3.35011 q^{89} +(-2.07470 - 2.07470i) q^{91} +(-1.73566 + 4.80602i) q^{92} -0.399696 q^{93} +(6.99006 + 4.44089i) q^{94} +(-7.37035 + 14.3769i) q^{96} +(4.95582 + 4.95582i) q^{97} +(9.08081 - 2.02507i) q^{98} +(2.54107 + 2.54107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9}+O(q^{10}) \) 18 * q + 4 * q^2 - 4 * q^4 - 8 * q^6 - 2 * q^7 + 4 * q^8 - 10 * q^9	\( 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9} - 2 q^{11} - 4 q^{12} + 12 q^{14} + 6 q^{17} - 16 q^{18} + 2 q^{19} - 16 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 16 q^{26} + 4 q^{28} - 14 q^{29} + 4 q^{32} + 8 q^{33} - 28 q^{34} - 4 q^{36} - 8 q^{37} - 16 q^{38} - 28 q^{42} + 44 q^{43} + 44 q^{44} + 12 q^{46} + 38 q^{47} - 60 q^{48} + 8 q^{51} + 40 q^{52} - 4 q^{54} + 20 q^{56} - 24 q^{57} + 20 q^{58} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 16 q^{64} + 4 q^{66} - 12 q^{67} - 36 q^{68} + 32 q^{69} + 24 q^{71} + 36 q^{72} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 84 q^{78} + 16 q^{79} + 2 q^{81} + 28 q^{82} - 24 q^{84} - 36 q^{86} - 24 q^{87} + 96 q^{88} - 12 q^{89} - 52 q^{92} - 16 q^{93} + 28 q^{94} - 40 q^{96} - 18 q^{97} - 32 q^{98} - 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 - 4 * q^4 - 8 * q^6 - 2 * q^7 + 4 * q^8 - 10 * q^9 - 2 * q^11 - 4 * q^12 + 12 * q^14 + 6 * q^17 - 16 * q^18 + 2 * q^19 - 16 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 16 * q^26 + 4 * q^28 - 14 * q^29 + 4 * q^32 + 8 * q^33 - 28 * q^34 - 4 * q^36 - 8 * q^37 - 16 * q^38 - 28 * q^42 + 44 * q^43 + 44 * q^44 + 12 * q^46 + 38 * q^47 - 60 * q^48 + 8 * q^51 + 40 * q^52 - 4 * q^54 + 20 * q^56 - 24 * q^57 + 20 * q^58 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 16 * q^64 + 4 * q^66 - 12 * q^67 - 36 * q^68 + 32 * q^69 + 24 * q^71 + 36 * q^72 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 84 * q^78 + 16 * q^79 + 2 * q^81 + 28 * q^82 - 24 * q^84 - 36 * q^86 - 24 * q^87 + 96 * q^88 - 12 * q^89 - 52 * q^92 - 16 * q^93 + 28 * q^94 - 40 * q^96 - 18 * q^97 - 32 * q^98 - 22 * q^99

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