LMFDB - Embedded newform 400.2.s.d.243.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(107,400)]

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, 1]))

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

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

chi := DirichletCharacter("400.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.s (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			243.9
Root			$-0.480367 + 1.33013i$ of defining polynomial
Character	$\chi$	$=$	400.243
Dual form			400.2.s.d.107.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.38031	−	0.307817i	0.976025	−	0.217659i
$2$	1.38031	−	0.307817i	0.976025	−	0.217659i
$3$	−2.85601			−1.64892			−0.824458	−	0.565923i	$-0.808520\pi$
$3$	−2.85601			−1.64892			−0.824458	+	0.565923i	$0.808520\pi$
$4$	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	−0.615046	−	0.788491i	$-0.710862\pi$
$7$	0.458895	−	0.458895i	0.173446	−	0.173446i	0.788491	+	0.615046i	$0.210862\pi$
$8$	2.23747	−	1.73024i	0.791066	−	0.611731i
$9$	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	$0.783503\pi$
$12$	−5.17080	+	2.42693i	−1.49268	+	0.700594i
$13$		−	4.52109i		−	1.25393i	−0.779049	−	0.626963i	$-0.784298\pi$
$13$		−	4.52109i		−	1.25393i	0.779049	−	0.626963i	$-0.215702\pi$
$14$	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	−0.217379	−	0.976087i	$-0.569751\pi$
$17$	3.12823	−	3.12823i	0.758708	−	0.758708i	0.976087	+	0.217379i	$0.0697508\pi$
$18$	7.11794	−	1.58734i	1.67772	−	0.374140i
$19$	−4.04508	−	4.04508i	−0.928005	−	0.928005i	0.0695721	−	0.997577i	$-0.477837\pi$
$19$	−4.04508	−	4.04508i	−0.928005	−	0.928005i	−0.997577	+	0.0695721i	$0.977837\pi$
$20$		0			0
$21$	−1.31061	+	1.31061i	−0.285998	+	0.285998i
$22$	−0.831845	−	0.528484i	−0.177350	−	0.112673i
$23$	1.80660	+	1.80660i	0.376701	+	0.376701i	0.869911	−	0.493209i	$-0.164176\pi$
$23$	1.80660	+	1.80660i	0.376701	+	0.376701i	−0.493209	+	0.869911i	$0.664176\pi$
$24$	−6.39024	+	4.94157i	−1.30440	+	1.00869i
$25$		0			0
$26$	−1.39167	−	6.24050i	−0.272928	−	1.22386i
$27$	−6.15978			−1.18545
$28$	0.440876	−	1.22078i	0.0833177	−	0.230706i
$29$	3.83926	−	3.83926i	0.712932	−	0.712932i	−0.254215	−	0.967148i	$-0.581817\pi$
$29$	3.83926	−	3.83926i	0.712932	−	0.712932i	0.967148	+	0.254215i	$0.0818172\pi$
$30$		0			0
$31$			0.139949i			0.0251356i	0.999921	+	0.0125678i	$0.00400057\pi$
$31$			0.139949i			0.0251356i	−0.999921	+	0.0125678i	$0.995999\pi$
$32$	2.58065	−	5.03391i	0.456199	−	0.889878i
$33$	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
$37$			5.84330i			0.960633i	0.877095	+	0.480317i	$0.159478\pi$
$37$			5.84330i			0.960633i	−0.877095	+	0.480317i	$0.840522\pi$
$38$	−6.82860	−	4.33831i	−1.10774	−	0.703767i
$39$			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	$0.884208\pi$
$42$	−1.40561	+	2.21247i	−0.216891	+	0.341391i
$43$			7.49928i			1.14363i	0.820383	+	0.571815i	$0.193760\pi$
$43$			7.49928i			1.14363i	−0.820383	+	0.571815i	$0.806240\pi$
$44$	−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	$-0.390459\pi$
$47$	−4.14073	−	4.14073i	−0.603987	−	0.603987i	−0.941368	+	0.337381i	$0.890459\pi$
$48$	−7.29940	+	8.78790i	−1.05358	+	1.26842i
$49$			6.57883i			0.939833i
$50$		0			0
$51$	−8.93426	+	8.93426i	−1.25105	+	1.25105i
$52$	−3.84186	−	8.18543i	−0.532770	−	1.13511i
$53$	−2.75773			−0.378803			−0.189402	−	0.981900i	$-0.560655\pi$
$53$	−2.75773			−0.378803			−0.189402	+	0.981900i	$0.560655\pi$
$54$	−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
$58$	4.11757	−	6.48115i	0.540663	−	0.851016i
$59$	3.62521	−	3.62521i	0.471962	−	0.471962i	−0.430587	−	0.902549i	$-0.641694\pi$
$59$	3.62521	−	3.62521i	0.471962	−	0.471962i	0.902549	+	0.430587i	$0.141694\pi$
$60$		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	$0.640419\pi$
$62$	0.0430787	+	0.193173i	0.00547100	+	0.0245330i
$63$	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
$67$			3.32677i			0.406430i	0.979134	+	0.203215i	$0.0651390\pi$
$67$			3.32677i			0.406430i	−0.979134	+	0.203215i	$0.934861\pi$
$68$	3.00540	−	8.32192i	0.364459	−	1.00918i
$69$	−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	$0.474084\pi$
$72$	11.5382	−	8.92244i	1.35978	−	1.05152i
$73$	−2.55028	+	2.55028i	−0.298488	+	0.298488i	−0.840422	−	0.541933i	$-0.817693\pi$
$73$	−2.55028	+	2.55028i	−0.298488	+	0.298488i	0.541933	+	0.840422i	$0.317693\pi$
$74$	1.79867	+	8.06556i	0.209091	+	0.937602i
$75$		0			0
$76$	−10.7610	−	3.88625i	−1.23437	−	0.445783i
$77$	−0.452252			−0.0515389
$78$	3.97461	+	17.8229i	0.450036	+	2.01805i
$79$	3.86426			0.434763			0.217382	−	0.976087i	$-0.430248\pi$
$79$	3.86426			0.434763			0.217382	+	0.976087i	$0.430248\pi$
$80$		0			0
$81$	2.12204			0.235782
$82$	1.40256	+	6.28934i	0.154887	+	0.694541i
$83$	−14.4698			−1.58827			−0.794133	−	0.607744i	$-0.792075\pi$
$83$	−14.4698			−1.58827			−0.794133	+	0.607744i	$0.792075\pi$
$84$	−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
$88$	−1.95514	−	0.249948i	−0.208419	−	0.0266445i
$89$	3.35011			0.355111			0.177556	−	0.984111i	$-0.443181\pi$
$89$	3.35011			0.355111			0.177556	+	0.984111i	$0.443181\pi$
$90$		0			0
$91$	−2.07470	−	2.07470i	−0.217488	−	0.217488i
$92$	4.80602	+	1.73566i	0.501062	+	0.180955i
$93$		−	0.399696i		−	0.0414466i
$94$	−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	−0.409240	−	0.912427i	$-0.634206\pi$
$97$	4.95582	−	4.95582i	0.503187	−	0.503187i	0.912427	+	0.409240i	$0.134206\pi$
$98$	2.02507	+	9.08081i	0.204563	+	0.917300i
$99$	−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	$0.291446\pi$
$102$	−9.58191	+	15.0821i	−0.948751	+	1.49335i
$103$	11.6655	+	11.6655i	1.14944	+	1.14944i	0.986664	+	0.162773i	$0.0520437\pi$
$103$	11.6655	+	11.6655i	1.14944	+	1.14944i	0.162773	+	0.986664i	$0.447956\pi$
$104$	−7.82256	−	10.1158i	−0.767065	−	0.991938i
$105$		0			0
$106$	−3.80651	+	0.848874i	−0.369721	+	0.0824500i
$107$	15.3106			1.48013			0.740067	−	0.672534i	$-0.234794\pi$
$107$	15.3106			1.48013			0.740067	+	0.672534i	$0.234794\pi$
$108$	−11.1523	+	5.23435i	−1.07313	+	0.503676i
$109$	−12.4798	+	12.4798i	−1.19535	+	1.19535i	−0.219803	+	0.975544i	$0.570542\pi$
$109$	−12.4798	+	12.4798i	−1.19535	+	1.19535i	−0.975544	+	0.219803i	$0.929458\pi$
$110$		0			0
$111$		−	16.6885i		−	1.58400i
$112$	−0.239168	−	2.58486i	−0.0225993	−	0.244246i
$113$	−2.53557	−	2.53557i	−0.238526	−	0.238526i	0.577713	−	0.816240i	$-0.303945\pi$
$113$	−2.53557	−	2.53557i	−0.238526	−	0.238526i	−0.816240	+	0.577713i	$0.803945\pi$
$114$	19.5025	+	12.3903i	1.82658	+	1.16045i
$115$		0			0
$116$	3.68851	−	10.2134i	0.342470	−	0.948293i
$117$		−	23.3143i		−	2.15541i
$118$	3.88800	−	6.11980i	0.357919	−	0.563373i
$119$		−	2.87106i		−	0.263189i
$120$		0			0
$121$		−	10.5144i		−	0.955852i
$122$	6.29301	+	3.99805i	0.569743	+	0.361966i
$123$		−	13.0133i		−	1.17337i
$124$	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	$-0.262302\pi$
$127$	−0.615790	−	0.615790i	−0.0546426	−	0.0546426i	−0.733900	+	0.679257i	$0.762302\pi$
$128$	0.394630	−	11.3068i	0.0348807	−	0.999391i
$129$		−	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	$0.0490268\pi$
$132$	3.74388	+	1.35208i	0.325863	+	0.117683i
$133$	−3.71253			−0.321917
$134$	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	$-0.321811\pi$
$137$	−3.70277	−	3.70277i	−0.316349	−	0.316349i	−0.847363	+	0.531014i	$0.821811\pi$
$138$	−8.71013	−	5.53368i	−0.741456	−	0.471058i
$139$	−5.46761	+	5.46761i	−0.463756	+	0.463756i	−0.899885	−	0.436128i	$-0.856349\pi$
$139$	−5.46761	+	5.46761i	−0.463756	+	0.463756i	0.436128	+	0.899885i	$0.356349\pi$
$140$		0			0
$141$	11.8260	+	11.8260i	0.995925	+	0.995925i
$142$	1.89179	−	0.421880i	0.158755	−	0.0354034i
$143$	−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
$147$		−	18.7892i		−	1.54971i
$148$	4.96542	+	10.5793i	0.408155	+	0.869612i
$149$	−4.21561	−	4.21561i	−0.345356	−	0.345356i	0.513021	−	0.858376i	$-0.328526\pi$
$149$	−4.21561	−	4.21561i	−0.345356	−	0.345356i	−0.858376	+	0.513021i	$0.828526\pi$
$150$		0			0
$151$	12.4417			1.01249			0.506244	−	0.862390i	$-0.331034\pi$
$151$	12.4417			1.01249			0.506244	+	0.862390i	$0.331034\pi$
$152$	−16.0497	−	2.05181i	−1.30180	−	0.166424i
$153$	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
$157$	−7.50500			−0.598964			−0.299482	−	0.954102i	$-0.596814\pi$
$157$	−7.50500			−0.598964			−0.299482	+	0.954102i	$0.596814\pi$
$158$	5.33387	−	1.18948i	0.424340	−	0.0946302i
$159$	7.87609			0.624615
$160$		0			0
$161$	1.65807			0.130675
$162$	2.92907	−	0.653199i	0.230129	−	0.0513202i
$163$	23.7284			1.85855			0.929277	−	0.369383i	$-0.120431\pi$
$163$	23.7284			1.85855			0.929277	+	0.369383i	$0.120431\pi$
$164$	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	−0.691343	−	0.722526i	$-0.742981\pi$
$167$	0.402976	−	0.402976i	0.0311832	−	0.0311832i	0.722526	+	0.691343i	$0.242981\pi$
$168$	−0.664788	+	5.20010i	−0.0512895	+	0.401197i
$169$	−7.44028			−0.572330
$170$		0			0
$171$	−20.8596	−	20.8596i	−1.59517	−	1.59517i
$172$	6.37261	+	13.5774i	0.485907	+	1.03527i
$173$			15.4500i			1.17464i	0.809355	+	0.587320i	$0.199817\pi$
$173$			15.4500i			1.17464i	−0.809355	+	0.587320i	$0.800183\pi$
$174$	−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
$178$	4.62419	−	1.03122i	0.346597	−	0.0772932i
$179$	−5.20444	−	5.20444i	−0.388998	−	0.388998i	0.485332	−	0.874330i	$-0.338699\pi$
$179$	−5.20444	−	5.20444i	−0.388998	−	0.388998i	−0.874330	+	0.485332i	$0.838699\pi$
$180$		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	$0.408537\pi$
$182$	−3.50236	−	2.22510i	−0.259612	−	0.164936i
$183$	−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
$187$	−3.08295			−0.225448
$188$	−11.0154	−	3.97814i	−0.803382	−	0.290136i
$189$	−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	$0.815933\pi$
$192$	−5.74791	+	22.1132i	−0.414820	+	1.59589i
$193$	−4.19166	−	4.19166i	−0.301722	−	0.301722i	0.539965	−	0.841687i	$-0.318437\pi$
$193$	−4.19166	−	4.19166i	−0.301722	−	0.301722i	−0.841687	+	0.539965i	$0.818437\pi$
$194$	5.31507	−	8.36604i	0.381600	−	0.600647i
$195$		0			0
$196$	5.59045	+	11.9110i	0.399318	+	0.850783i
$197$		−	4.03184i		−	0.287256i	−0.989632	−	0.143628i	$-0.954123\pi$
$197$		−	4.03184i		−	0.287256i	0.989632	−	0.143628i	$-0.0458769\pi$
$198$	−4.28964	−	2.72527i	−0.304852	−	0.193677i
$199$			5.43055i			0.384961i	0.981301	+	0.192481i	$0.0616533\pi$
$199$			5.43055i			0.384961i	−0.981301	+	0.192481i	$0.938347\pi$
$200$		0			0
$201$		−	9.50129i		−	0.670169i
$202$	−1.97914	+	3.11520i	−0.139252	+	0.219185i
$203$		−	3.52363i		−	0.247310i
$204$	−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
$208$	−13.9114	−	11.5550i	−0.964579	−	0.801197i
$209$			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	$0.199739\pi$
$212$	−4.99286	+	2.34342i	−0.342911	+	0.160946i
$213$	−3.91432			−0.268205
$214$	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
$218$	−13.3845	+	21.0674i	−0.906511	+	1.42687i
$219$	7.28363	−	7.28363i	0.492182	−	0.492182i
$220$		0			0
$221$	−14.1430	−	14.1430i	−0.951363	−	0.951363i
$222$	−5.13700	−	23.0353i	−0.344773	−	1.54603i
$223$	−8.17319	+	8.17319i	−0.547317	+	0.547317i	−0.925664	−	0.378347i	$-0.876493\pi$
$223$	−8.17319	+	8.17319i	−0.547317	+	0.547317i	0.378347	+	0.925664i	$0.376493\pi$
$224$	−1.12579	−	3.49428i	−0.0752199	−	0.233471i
$225$		0			0
$226$	−4.28035	−	2.71937i	−0.284725	−	0.180890i
$227$		−	1.54068i		−	0.102258i	−0.998692	−	0.0511292i	$-0.983718\pi$
$227$		−	1.54068i		−	0.102258i	0.998692	−	0.0511292i	$-0.0162820\pi$
$228$	30.7334	+	11.0992i	2.03537	+	0.735060i
$229$	17.5646	+	17.5646i	1.16070	+	1.16070i	0.984322	+	0.176378i	$0.0564382\pi$
$229$	17.5646	+	17.5646i	1.16070	+	1.16070i	0.176378	+	0.984322i	$0.443562\pi$
$230$		0			0
$231$	1.29164			0.0849834
$232$	1.94741	−	15.2331i	0.127854	−	1.00010i
$233$	9.99018	−	9.99018i	0.654479	−	0.654479i	−0.299590	−	0.954068i	$-0.596850\pi$
$233$	9.99018	−	9.99018i	0.654479	−	0.654479i	0.954068	+	0.299590i	$0.0968498\pi$
$234$	−7.17652	−	32.1809i	−0.469144	−	2.10373i
$235$		0			0
$236$	3.48286	−	9.64399i	0.226715	−	0.627771i
$237$	−11.0364			−0.716889
$238$	−0.883759	−	3.96294i	−0.0572856	−	0.256879i
$239$	−26.2762			−1.69967			−0.849833	−	0.527052i	$-0.823297\pi$
$239$	−26.2762			−1.69967			−0.849833	+	0.527052i	$0.823297\pi$
$240$		0			0
$241$	−0.113242			−0.00729456			−0.00364728	−	0.999993i	$-0.501161\pi$
$241$	−0.113242			−0.00729456			−0.00364728	+	0.999993i	$0.501161\pi$
$242$	−3.23650	−	14.5131i	−0.208050	−	0.932935i
$243$	12.4188			0.796665
$244$	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
$248$	0.242145	+	0.313133i	0.0153762	+	0.0198840i
$249$	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	$0.421757\pi$
$252$	2.27350	−	6.29529i	0.143217	−	0.396566i
$253$		−	1.78045i		−	0.111936i
$254$	−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	−0.683077	−	0.730347i	$-0.739358\pi$
$257$	0.757800	−	0.757800i	0.0472703	−	0.0472703i	0.730347	+	0.683077i	$0.239358\pi$
$258$	−6.59282	−	29.5634i	−0.410451	−	1.84054i
$259$	2.68146	+	2.68146i	0.166618	+	0.166618i
$260$		0			0
$261$	19.7982	−	19.7982i	1.22548	−	1.22548i
$262$	10.2467	−	16.1286i	0.633044	−	0.996425i
$263$	−5.73017	−	5.73017i	−0.353338	−	0.353338i	0.508012	−	0.861350i	$-0.330380\pi$
$263$	−5.73017	−	5.73017i	−0.353338	−	0.353338i	−0.861350	+	0.508012i	$0.830380\pi$
$264$	5.58389	+	0.713852i	0.343665	+	0.0439346i
$265$		0			0
$266$	−5.12443	+	1.14278i	−0.314199	+	0.0700682i
$267$	−9.56795			−0.585549
$268$	2.82697	+	6.02311i	0.172685	+	0.367920i
$269$	−9.78879	+	9.78879i	−0.596833	+	0.596833i	−0.939468	−	0.342635i	$-0.888680\pi$
$269$	−9.78879	+	9.78879i	−0.596833	+	0.596833i	0.342635	+	0.939468i	$0.388680\pi$
$270$		0			0
$271$			4.10159i			0.249154i	0.992210	+	0.124577i	$0.0397574\pi$
$271$			4.10159i			0.249154i	−0.992210	+	0.124577i	$0.960243\pi$
$272$	−1.63038	−	17.6207i	−0.0988565	−	1.06841i
$273$	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
$277$			24.6755i			1.48261i	0.671169	+	0.741305i	$0.265793\pi$
$277$			24.6755i			1.48261i	−0.671169	+	0.741305i	$0.734207\pi$
$278$	−5.86396	+	9.23000i	−0.351697	+	0.553578i
$279$			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	$-0.249494\pi$
$282$	19.9637	+	12.6832i	1.18882	+	0.755275i
$283$		−	13.0492i		−	0.775694i	−0.921724	−	0.387847i	$-0.873219\pi$
$283$		−	13.0492i		−	0.775694i	0.921724	−	0.387847i	$-0.126781\pi$
$284$	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
$288$	13.3078	−	25.9588i	0.784172	−	1.52963i
$289$		−	2.57168i		−	0.151275i
$290$		0			0
$291$	−14.1539	+	14.1539i	−0.829714	+	0.829714i
$292$	−2.45015	+	6.78442i	−0.143384	+	0.397028i
$293$	31.6731			1.85036			0.925181	−	0.379526i	$-0.123913\pi$
$293$	31.6731			1.85036			0.925181	+	0.379526i	$0.123913\pi$
$294$	−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
$298$	−7.11646	−	4.52120i	−0.412246	−	0.261906i
$299$	8.16779	−	8.16779i	0.472355	−	0.472355i
$300$		0			0
$301$	3.44138	+	3.44138i	0.198358	+	0.198358i
$302$	17.1733	−	3.82975i	0.988213	−	0.220377i
$303$	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
$307$		−	27.3597i		−	1.56150i	−0.624843	−	0.780751i	$-0.714837\pi$
$307$		−	27.3597i		−	1.56150i	0.624843	−	0.780751i	$-0.285163\pi$
$308$	−0.818802	+	0.384307i	−0.0466556	+	0.0218979i
$309$	−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	$0.647929\pi$
$312$	22.3413	+	28.8909i	1.26483	+	1.63562i
$313$	−13.8388	+	13.8388i	−0.782217	+	0.782217i	−0.980205	−	0.197988i	$-0.936559\pi$
$313$	−13.8388	+	13.8388i	−0.782217	+	0.782217i	0.197988	+	0.980205i	$0.436559\pi$
$314$	−10.3592	+	2.31016i	−0.584604	+	0.130370i
$315$		0			0
$316$	6.99624	−	3.28371i	0.393569	−	0.184723i
$317$	35.0092			1.96631			0.983156	−	0.182766i	$-0.0585051\pi$
$317$	35.0092			1.96631			0.983156	+	0.182766i	$0.0585051\pi$
$318$	10.8714	−	2.42439i	0.609639	−	0.135953i
$319$	−3.78369			−0.211846
$320$		0			0
$321$	−43.7272			−2.44062
$322$	2.28865	−	0.510383i	0.127542	−	0.0284425i
$323$	−25.3079			−1.40817
$324$	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
$328$	7.88378	+	10.1950i	0.435309	+	0.562924i
$329$	−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	$0.523184\pi$
$332$	−26.1975	+	12.2959i	−1.43778	+	0.674825i
$333$			30.1326i			1.65126i
$334$	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	−0.981457	−	0.191680i	$-0.938606\pi$
$337$	−14.4984	+	14.4984i	−0.789777	+	0.789777i	0.191680	+	0.981457i	$0.438606\pi$
$338$	−10.2699	+	2.29024i	−0.558608	+	0.124573i
$339$	7.24160	+	7.24160i	0.393310	+	0.393310i
$340$		0			0
$341$	0.0689618	−	0.0689618i	0.00373449	−	0.00373449i
$342$	−35.2136	−	22.3717i	−1.90413	−	1.20972i
$343$	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
$347$	16.7705			0.900286			0.450143	−	0.892956i	$-0.351373\pi$
$347$	16.7705			0.900286			0.450143	+	0.892956i	$0.351373\pi$
$348$	−10.5344	+	29.1696i	−0.564704	+	1.56366i
$349$	−1.86337	+	1.86337i	−0.0997439	+	0.0997439i	−0.755218	−	0.655474i	$-0.772469\pi$
$349$	−1.86337	+	1.86337i	−0.0997439	+	0.0997439i	0.655474	+	0.755218i	$0.272469\pi$
$350$		0			0
$351$			27.8489i			1.48647i
$352$	−3.75217	+	1.20888i	−0.199991	+	0.0644333i
$353$	−24.1362	−	24.1362i	−1.28464	−	1.28464i	−0.937998	−	0.346642i	$-0.887322\pi$
$353$	−24.1362	−	24.1362i	−1.28464	−	1.28464i	−0.346642	−	0.937998i	$-0.612678\pi$
$354$	−11.1042	+	17.4782i	−0.590179	+	0.928955i
$355$		0			0
$356$	6.06537	−	2.84680i	0.321464	−	0.150880i
$357$			8.19976i			0.433978i
$358$	−8.78574	−	5.58171i	−0.464341	−	0.295003i
$359$		−	12.2500i		−	0.646532i	−0.946308	−	0.323266i	$-0.895219\pi$
$359$		−	12.2500i		−	0.646532i	0.946308	−	0.323266i	$-0.104781\pi$
$360$		0			0
$361$			13.7253i			0.722386i
$362$	−9.74814	+	15.3438i	−0.512351	+	0.806451i
$363$			30.0291i			1.57612i
$364$	−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	$-0.218071\pi$
$367$	2.71307	+	2.71307i	0.141621	+	0.141621i	−0.632742	+	0.774363i	$0.718071\pi$
$368$	10.1762	−	0.941567i	0.530470	−	0.0490826i
$369$			23.4967i			1.22319i
$370$		0			0
$371$	−1.26551	+	1.26551i	−0.0657018	+	0.0657018i
$372$	−0.339647	−	0.723649i	−0.0176099	−	0.0375195i
$373$	−16.4846			−0.853541			−0.426771	−	0.904360i	$-0.640349\pi$
$373$	−16.4846			−0.853541			−0.426771	+	0.904360i	$0.640349\pi$
$374$	−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
$378$	−3.03160	+	4.77180i	−0.155929	+	0.245435i
$379$	13.7716	−	13.7716i	0.707401	−	0.707401i	−0.258587	−	0.965988i	$-0.583257\pi$
$379$	13.7716	−	13.7716i	0.707401	−	0.707401i	0.965988	+	0.258587i	$0.0832568\pi$
$380$		0			0
$381$	1.75870	+	1.75870i	0.0901011	+	0.0901011i
$382$	4.65034	+	20.8530i	0.237932	+	1.06693i
$383$	11.5530	−	11.5530i	0.590332	−	0.590332i	−0.347389	−	0.937721i	$-0.612932\pi$
$383$	11.5530	−	11.5530i	0.590332	−	0.590332i	0.937721	+	0.347389i	$0.112932\pi$
$384$	−1.12707	+	32.2924i	−0.0575153	+	1.64791i
$385$		0			0
$386$	−7.07604	−	4.49552i	−0.360161	−	0.228816i
$387$			38.6722i			1.96582i
$388$	4.76123	−	13.1838i	0.241715	−	0.669305i
$389$	15.7728	+	15.7728i	0.799712	+	0.799712i	0.983050	−	0.183338i	$-0.0586903\pi$
$389$	15.7728	+	15.7728i	0.799712	+	0.799712i	−0.183338	+	0.983050i	$0.558690\pi$
$390$		0			0
$391$	11.3029			0.571612
$392$	11.3829	+	14.7200i	0.574925	+	0.743470i
$393$	−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
$397$	−29.9558			−1.50344			−0.751720	−	0.659483i	$-0.770775\pi$
$397$	−29.9558			−1.50344			−0.751720	+	0.659483i	$0.770775\pi$
$398$	1.67161	+	7.49583i	0.0837904	+	0.375732i
$399$	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	$0.334258\pi$
$402$	−2.92465	−	13.1147i	−0.145868	−	0.654102i
$403$	0.632724			0.0315182
$404$	−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
$408$	−4.53179	+	35.4485i	−0.224357	+	1.75496i
$409$	−5.89856			−0.291665			−0.145832	−	0.989309i	$-0.546586\pi$
$409$	−5.89856			−0.291665			−0.145832	+	0.989309i	$0.546586\pi$
$410$		0			0
$411$	10.5751	+	10.5751i	0.521634	+	0.521634i
$412$	31.0333	+	11.2075i	1.52890	+	0.552152i
$413$		−	3.32717i		−	0.163720i
$414$	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
$418$	1.22712	+	5.50264i	0.0600204	+	0.269143i
$419$	−8.24430	−	8.24430i	−0.402760	−	0.402760i	0.476444	−	0.879205i	$-0.341925\pi$
$419$	−8.24430	−	8.24430i	−0.402760	−	0.402760i	−0.879205	+	0.476444i	$0.841925\pi$
$420$		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	$0.451653\pi$
$422$	3.46436	−	5.45297i	0.168642	−	0.265447i
$423$	−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
$427$	3.42135			0.165571
$428$	27.7198	−	13.0104i	1.33989	−	0.628881i
$429$	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	$-0.282226\pi$
$432$	−15.7432	+	18.9536i	−0.757445	+	0.911904i
$433$	20.3383	+	20.3383i	0.977396	+	0.977396i	0.999750	−	0.0223540i	$-0.00711609\pi$
$433$	20.3383	+	20.3383i	0.977396	+	0.977396i	−0.0223540	+	0.999750i	$0.507116\pi$
$434$	0.108415	+	0.0688775i	0.00520407	+	0.00330623i
$435$		0			0
$436$	−11.9898	+	33.1995i	−0.574206	+	1.58997i
$437$		−	14.6156i		−	0.699161i
$438$	7.81163	−	12.2957i	0.373254	−	0.587510i
$439$			35.4180i			1.69041i	0.534444	+	0.845204i	$0.320521\pi$
$439$			35.4180i			1.69041i	−0.534444	+	0.845204i	$0.679479\pi$
$440$		0			0
$441$			33.9256i			1.61550i
$442$	−23.8752	−	15.1683i	−1.13563	−	0.721481i
$443$			3.03787i			0.144333i	0.997393	+	0.0721667i	$0.0229913\pi$
$443$			3.03787i			0.144333i	−0.997393	+	0.0721667i	$0.977009\pi$
$444$	−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
$448$	−2.62953	−	4.47664i	−0.124234	−	0.211502i
$449$			8.65559i			0.408483i	0.978921	+	0.204241i	$0.0654727\pi$
$449$			8.65559i			0.408483i	−0.978921	+	0.204241i	$0.934527\pi$
$450$		0			0
$451$	2.24526	−	2.24526i	0.105725	−	0.105725i
$452$	−6.74527	−	2.43601i	−0.317271	−	0.114580i
$453$	−35.5335			−1.66951
$454$	−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	$-0.398021\pi$
$457$	−13.5575	−	13.5575i	−0.634193	−	0.634193i	−0.949117	+	0.314924i	$0.898021\pi$
$458$	29.6512	+	18.8379i	1.38551	+	0.880236i
$459$	−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	$0.762550\pi$
$462$	1.78286	−	0.397587i	0.0829459	−	0.0184974i
$463$	−21.1815	+	21.1815i	−0.984390	+	0.984390i	−0.999880	−	0.0154904i	$-0.995069\pi$
$463$	−21.1815	+	21.1815i	−0.984390	+	0.984390i	0.0154904	+	0.999880i	$0.495069\pi$
$464$	−2.00096	−	21.6258i	−0.0928921	−	1.00395i
$465$		0			0
$466$	10.7144	−	16.8647i	0.496334	−	0.781241i
$467$			24.8448i			1.14968i	0.818266	+	0.574840i	$0.194936\pi$
$467$			24.8448i			1.14968i	−0.818266	+	0.574840i	$0.805064\pi$
$468$	−19.8116	−	42.2105i	−0.915792	−	1.95118i
$469$	1.52664	+	1.52664i	0.0704936	+	0.0704936i
$470$		0			0
$471$	21.4343			0.987642
$472$	1.83884	−	14.3838i	0.0846394	−	0.662066i
$473$	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
$477$	−14.2210			−0.651135
$478$	−36.2692	+	8.08825i	−1.65892	+	0.369948i
$479$	23.5766			1.07724			0.538621	−	0.842548i	$-0.318946\pi$
$479$	23.5766			1.07724			0.538621	+	0.842548i	$0.318946\pi$
$480$		0			0
$481$	26.4181			1.20456
$482$	−0.156309	+	0.0348578i	−0.00711967	+	0.00158773i
$483$	−4.73547			−0.215471
$484$	−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	−0.645001	−	0.764182i	$-0.723143\pi$
$487$	2.63011	−	2.63011i	0.119182	−	0.119182i	0.764182	+	0.645001i	$0.223143\pi$
$488$	14.7909	+	1.89089i	0.669552	+	0.0855964i
$489$	−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	$0.953411\pi$
$492$	−11.0582	−	23.5606i	−0.498544	−	1.06219i
$493$		−	24.0202i		−	1.08182i
$494$	−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
$498$	57.0424	−	12.7208i	2.55613	−	0.570032i
$499$	9.69342	+	9.69342i	0.433937	+	0.433937i	0.889965	−	0.456028i	$-0.150728\pi$
$499$	9.69342	+	9.69342i	0.433937	+	0.433937i	−0.456028	+	0.889965i	$0.650728\pi$
$500$		0			0
$501$	−1.15090	+	1.15090i	−0.0514185	+	0.0514185i
$502$	32.4491	+	20.6154i	1.44827	+	0.920110i
$503$	13.0434	+	13.0434i	0.581577	+	0.581577i	0.935336	−	0.353759i	$-0.115097\pi$
$503$	13.0434	+	13.0434i	0.581577	+	0.581577i	−0.353759	+	0.935336i	$0.615097\pi$
$504$	1.20034	−	9.38926i	0.0534672	−	0.418231i
$505$		0			0
$506$	−0.548051	−	2.45756i	−0.0243638	−	0.109252i
$507$	21.2495			0.943724
$508$	−1.63816	−	0.591611i	−0.0726817	−	0.0262485i
$509$	25.8539	−	25.8539i	1.14595	−	1.14595i	0.158611	−	0.987341i	$-0.449298\pi$
$509$	25.8539	−	25.8539i	1.14595	−	1.14595i	0.987341	−	0.158611i	$-0.0507016\pi$
$510$		0			0
$511$			2.34062i			0.103543i
$512$	−8.89365	−	20.8063i	−0.393047	−	0.919518i
$513$	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
$517$			4.08080i			0.179473i
$518$	4.52664	+	2.87584i	0.198889	+	0.126357i
$519$		−	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	$0.815088\pi$
$522$	21.2334	−	33.4218i	0.929361	−	1.46283i
$523$		−	40.3434i		−	1.76410i	−0.471160	−	0.882048i	$-0.656165\pi$
$523$		−	40.3434i		−	1.76410i	0.471160	−	0.882048i	$-0.343835\pi$
$524$	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
$528$	7.92723	−	0.733479i	0.344988	−	0.0319206i
$529$		−	16.4724i		−	0.716192i
$530$		0			0
$531$	18.6944	−	18.6944i	0.811267	−	0.811267i
$532$	−6.72153	+	3.15477i	−0.291415	+	0.136777i
$533$	20.6003			0.892296
$534$	−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
$538$	−10.4984	+	16.5247i	−0.452618	+	0.712430i
$539$	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	$-0.521035\pi$
$542$	1.26254	+	5.66146i	0.0542307	+	0.243181i
$543$	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
$547$			19.0254i			0.813465i	0.913547	+	0.406733i	$0.133332\pi$
$547$			19.0254i			0.813465i	−0.913547	+	0.406733i	$0.866668\pi$
$548$	−9.85034	−	3.55738i	−0.420786	−	0.151964i
$549$	19.2235	+	19.2235i	0.820440	+	0.820440i
$550$		0			0
$551$	−31.0602			−1.32321
$552$	−20.4720	−	2.61717i	−0.871346	−	0.111394i
$553$	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
$557$	−30.9517			−1.31146			−0.655732	−	0.754993i	$-0.727640\pi$
$557$	−30.9517			−1.31146			−0.655732	+	0.754993i	$0.727640\pi$
$558$	0.222148	+	0.996151i	0.00940425	+	0.0421704i
$559$	33.9050			1.43403
$560$		0			0
$561$	8.80494			0.371745
$562$	−7.28565	−	32.6702i	−0.307327	−	1.37811i
$563$	−3.50238			−0.147608			−0.0738039	−	0.997273i	$-0.523514\pi$
$563$	−3.50238			−0.147608			−0.0738039	+	0.997273i	$0.523514\pi$
$564$	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
$568$	3.06658	−	2.37138i	0.128671	−	0.0995011i
$569$	0.525780			0.0220418			0.0110209	−	0.999939i	$-0.496492\pi$
$569$	0.525780			0.0220418			0.0110209	+	0.999939i	$0.496492\pi$
$570$		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	$0.858016\pi$
$572$	−2.14035	+	5.92660i	−0.0894926	+	0.247804i
$573$		−	43.1472i		−	1.80250i
$574$	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	−0.643509	−	0.765438i	$-0.722522\pi$
$577$	2.92884	−	2.92884i	0.121929	−	0.121929i	0.765438	+	0.643509i	$0.222522\pi$
$578$	−0.791607	−	3.54971i	−0.0329265	−	0.147649i
$579$	11.9714	+	11.9714i	0.497515	+	0.497515i
$580$		0			0
$581$	−6.64011	+	6.64011i	−0.275478	+	0.275478i
$582$	−15.1799	+	23.8935i	−0.629227	+	0.990416i
$583$	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
$587$	−23.1574			−0.955809			−0.477905	−	0.878412i	$-0.658604\pi$
$587$	−23.1574			−0.955809			−0.477905	+	0.878412i	$0.658604\pi$
$588$	−15.9664	−	34.0178i	−0.658442	−	1.40287i
$589$	0.566106	−	0.566106i	0.0233260	−	0.0233260i
$590$		0			0
$591$			11.5150i			0.473662i
$592$	17.9798	+	14.9343i	0.738964	+	0.613798i
$593$	13.9325	+	13.9325i	0.572141	+	0.572141i	0.932726	−	0.360585i	$-0.117423\pi$
$593$	13.9325	+	13.9325i	0.572141	+	0.572141i	−0.360585	+	0.932726i	$0.617423\pi$
$594$	5.12398	+	3.25534i	0.210240	+	0.133568i
$595$		0			0
$596$	−11.2146	−	4.05008i	−0.459368	−	0.165898i
$597$		−	15.5097i		−	0.634769i
$598$	8.75988	−	13.7882i	0.358218	−	0.563843i
$599$		−	33.5311i		−	1.37004i	−0.728523	−	0.685021i	$-0.759793\pi$
$599$		−	33.5311i		−	1.37004i	0.728523	−	0.685021i	$-0.240207\pi$
$600$		0			0
$601$		−	19.4164i		−	0.792011i	−0.918248	−	0.396005i	$-0.870396\pi$
$601$		−	19.4164i		−	0.792011i	0.918248	−	0.396005i	$-0.129604\pi$
$602$	5.80948	+	3.69085i	0.236777	+	0.150428i
$603$			17.1554i			0.698623i
$604$	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	$-0.338044\pi$
$607$	−9.51495	−	9.51495i	−0.386200	−	0.386200i	−0.873330	+	0.487130i	$0.838044\pi$
$608$	−30.8015	+	9.92363i	−1.24917	+	0.402456i
$609$			10.0635i			0.407794i
$610$		0			0
$611$	−18.7206	+	18.7206i	−0.757355	+	0.757355i
$612$	15.4982	−	42.9143i	0.626478	−	1.73471i
$613$	9.37947			0.378833			0.189417	−	0.981897i	$-0.439340\pi$
$613$	9.37947			0.378833			0.189417	+	0.981897i	$0.439340\pi$
$614$	−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	$-0.282202\pi$
$617$	−3.54768	−	3.54768i	−0.142824	−	0.142824i	−0.774904	+	0.632079i	$0.782202\pi$
$618$	−56.2428	−	35.7319i	−2.26242	−	1.43735i
$619$	−24.6158	+	24.6158i	−0.989392	+	0.989392i	−0.999944	−	0.0105527i	$-0.996641\pi$
$619$	−24.6158	+	24.6158i	−0.989392	+	0.989392i	0.0105527	+	0.999944i	$0.496641\pi$
$620$		0			0
$621$	−11.1282	−	11.1282i	−0.446561	−	0.446561i
$622$	−21.8194	+	4.86585i	−0.874877	+	0.195103i
$623$	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
$627$		−	11.3856i		−	0.454695i
$628$	−13.5878	+	6.37747i	−0.542211	+	0.254489i
$629$	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	$0.695032\pi$
$632$	8.64618	−	6.68608i	0.343927	−	0.265958i
$633$	−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
$637$	29.7435			1.17848
$638$	−5.22265	+	1.16468i	−0.206767	+	0.0461102i
$639$	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	$0.606926\pi$
$642$	−60.3570	+	13.4600i	−2.38210	+	0.531223i
$643$	5.22468			0.206041			0.103021	−	0.994679i	$-0.467149\pi$
$643$	5.22468			0.206041			0.103021	+	0.994679i	$0.467149\pi$
$644$	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	−0.990418	−	0.138100i	$-0.955900\pi$
$647$	−21.6797	+	21.6797i	−0.852318	+	0.852318i	0.138100	+	0.990418i	$0.455900\pi$
$648$	4.74801	−	3.67163i	0.186519	−	0.144235i
$649$	−3.57273			−0.140242
$650$		0			0
$651$	−0.183418	−	0.183418i	−0.00718874	−	0.00718874i
$652$	42.9603	−	20.1636i	1.68245	−	0.789666i
$653$		−	22.7642i		−	0.890833i	−0.895323	−	0.445417i	$-0.853056\pi$
$653$		−	22.7642i		−	0.890833i	0.895323	−	0.445417i	$-0.146944\pi$
$654$	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
$658$	−5.24560	+	1.16980i	−0.204495	+	0.0456036i
$659$	1.66201	+	1.66201i	0.0647427	+	0.0647427i	0.738737	−	0.673994i	$-0.235423\pi$
$659$	1.66201	+	1.66201i	0.0647427	+	0.0647427i	−0.673994	+	0.738737i	$0.735423\pi$
$660$		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	$0.299471\pi$
$662$	28.3963	+	18.0406i	1.10365	+	0.701168i
$663$	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
$667$	13.8720			0.537125
$668$	0.387153	−	1.07202i	0.0149794	−	0.0414777i
$669$	23.3427	−	23.3427i	0.902481	−	0.902481i
$670$		0			0
$671$		−	3.67386i		−	0.141828i
$672$	3.21526	+	9.97969i	0.124031	+	0.384975i
$673$	−0.278251	−	0.278251i	−0.0107258	−	0.0107258i	0.701724	−	0.712449i	$-0.252414\pi$
$673$	−0.278251	−	0.278251i	−0.0107258	−	0.0107258i	−0.712449	+	0.701724i	$0.752414\pi$
$674$	−15.5494	+	24.4751i	−0.598940	+	0.942744i
$675$		0			0
$676$	−13.4706	+	6.32248i	−0.518101	+	0.243172i
$677$			26.3591i			1.01306i	0.862222	+	0.506531i	$0.169072\pi$
$677$			26.3591i			1.01306i	−0.862222	+	0.506531i	$0.830928\pi$
$678$	12.2247	+	7.76655i	0.469488	+	0.298273i
$679$		−	4.54840i		−	0.174551i
$680$		0			0
$681$			4.40019i			0.168616i
$682$	0.0739609	−	0.116416i	0.00283211	−	0.00445780i
$683$			2.83023i			0.108296i	0.998533	+	0.0541479i	$0.0172442\pi$
$683$			2.83023i			0.108296i	−0.998533	+	0.0541479i	$0.982756\pi$
$684$	−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
$688$	23.0752	+	19.1667i	0.879734	+	0.730724i
$689$			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	$0.0464884\pi$
$692$	13.1288	+	27.9721i	0.499083	+	1.06334i
$693$	−2.33217			−0.0885917
$694$	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
$698$	−1.99845	+	3.14560i	−0.0756423	+	0.119063i
$699$	−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	$0.607328\pi$
$702$	8.57237	+	38.4401i	0.323543	+	1.45083i
$703$	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
$707$			1.69365i			0.0636965i
$708$	−9.94708	+	27.5433i	−0.373834	+	1.03514i
$709$	−25.3577	−	25.3577i	−0.952329	−	0.952329i	0.0465856	−	0.998914i	$-0.485166\pi$
$709$	−25.3577	−	25.3577i	−0.952329	−	0.952329i	−0.998914	+	0.0465856i	$0.985166\pi$
$710$		0			0
$711$	19.9271			0.747326
$712$	7.49579	−	5.79648i	0.280916	−	0.217232i
$713$	−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
$717$	75.0450			2.80261
$718$	−3.77076	−	16.9088i	−0.140724	−	0.631031i
$719$	−41.3374			−1.54163			−0.770813	−	0.637061i	$-0.780150\pi$
$719$	−41.3374			−1.54163			−0.770813	+	0.637061i	$0.780150\pi$
$720$		0			0
$721$	10.7065			0.398730
$722$	4.22489	+	18.9452i	0.157234	+	0.705067i
$723$	0.323420			0.0120281
$724$	−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	−0.122300	−	0.992493i	$-0.539027\pi$
$727$	23.4630	−	23.4630i	0.870193	−	0.870193i	0.992493	+	0.122300i	$0.0390271\pi$
$728$	−8.23182	−	1.05237i	−0.305092	−	0.0390033i
$729$	−41.8342			−1.54942
$730$		0			0
$731$	23.4595	+	23.4595i	0.867681	+	0.867681i
$732$	−28.3229	−	10.2286i	−1.04684	−	0.378061i
$733$			15.1628i			0.560051i	0.959993	+	0.280025i	$0.0903429\pi$
$733$			15.1628i			0.560051i	−0.959993	+	0.280025i	$0.909657\pi$
$734$	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
$738$	7.23269	+	32.4327i	0.266239	+	1.19387i
$739$	0.974343	+	0.974343i	0.0358418	+	0.0358418i	0.724801	−	0.688959i	$-0.241932\pi$
$739$	0.974343	+	0.974343i	0.0358418	+	0.0358418i	−0.688959	+	0.724801i	$0.741932\pi$
$740$		0			0
$741$	52.2312	−	52.2312i	1.91876	−	1.91876i
$742$	−1.35724	+	2.13633i	−0.0498260	+	0.0784272i
$743$	−29.0897	−	29.0897i	−1.06720	−	1.06720i	−0.997573	−	0.0696259i	$-0.977819\pi$
$743$	−29.0897	−	29.0897i	−1.06720	−	1.06720i	−0.0696259	−	0.997573i	$-0.522181\pi$
$744$	−0.691569	−	0.894310i	−0.0253541	−	0.0327870i
$745$		0			0
$746$	−22.7538	+	5.07424i	−0.833078	+	0.185781i
$747$	−74.6176			−2.73011
$748$	−5.58168	+	2.61978i	−0.204087	+	0.0957887i
$749$	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	$-0.0453193\pi$
$752$	−23.3239	+	2.15808i	−0.850534	+	0.0786970i
$753$	−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
$757$			1.42073i			0.0516372i	0.999667	+	0.0258186i	$0.00821923\pi$
$757$			1.42073i			0.0516372i	−0.999667	+	0.0258186i	$0.991781\pi$
$758$	14.7699	−	23.2482i	0.536469	−	0.844413i
$759$			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	$-0.160620\pi$
$762$	2.96891	+	1.88619i	0.107552	+	0.0683295i
$763$			11.4538i			0.414656i
$764$	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
$768$	8.38443	+	44.9203i	0.302547	+	1.62092i
$769$		−	45.8210i		−	1.65235i	−0.563415	−	0.826174i	$-0.690513\pi$
$769$		−	45.8210i		−	1.65235i	0.563415	−	0.826174i	$-0.309487\pi$
$770$		0			0
$771$	−2.16428	+	2.16428i	−0.0779447	+	0.0779447i
$772$	−11.1509	−	4.02707i	−0.401330	−	0.144937i
$773$	18.5473			0.667101			0.333550	−	0.942732i	$-0.391753\pi$
$773$	18.5473			0.667101			0.333550	+	0.942732i	$0.391753\pi$
$774$	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
$778$	26.6264	+	16.9162i	0.954603	+	0.606474i
$779$	18.4313	−	18.4313i	0.660370	−	0.660370i
$780$		0			0
$781$	−0.675359	−	0.675359i	−0.0241662	−	0.0241662i
$782$	15.6015	−	3.47922i	0.557908	−	0.124417i
$783$	−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
$787$		−	21.3016i		−	0.759319i	−0.925126	−	0.379659i	$-0.876041\pi$
$787$		−	21.3016i		−	0.759319i	0.925126	−	0.379659i	$-0.123959\pi$
$788$	−3.42610	−	7.29963i	−0.122050	−	0.260039i
$789$	16.3654	+	16.3654i	0.582624	+	0.582624i
$790$		0			0
$791$	−2.32712			−0.0827427
$792$	−10.0822	−	1.28892i	−0.358256	−	0.0458000i
$793$	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
$797$	2.35457			0.0834033			0.0417016	−	0.999130i	$-0.486722\pi$
$797$	2.35457			0.0834033			0.0417016	+	0.999130i	$0.486722\pi$
$798$	14.6354	−	3.26378i	0.518088	−	0.115537i
$799$	−25.9063			−0.916500
$800$		0			0
$801$	17.2758			0.610410
$802$	27.5014	−	6.13297i	0.971108	−	0.216563i
$803$	2.51337			0.0886949
$804$	−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
$808$	−0.936037	+	7.32187i	−0.0329297	+	0.257582i
$809$	23.9476			0.841952			0.420976	−	0.907072i	$-0.361688\pi$
$809$	23.9476			0.841952			0.420976	+	0.907072i	$0.361688\pi$
$810$		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	$0.760514\pi$
$812$	−2.99425	−	6.37952i	−0.105078	−	0.223877i
$813$		−	11.7142i		−	0.410834i
$814$	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
$818$	−8.14182	+	1.81567i	−0.284672	+	0.0634836i
$819$	−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	$-0.106400\pi$
$822$	17.8522	+	11.3417i	0.622666	+	0.395589i
$823$	−26.3978	−	26.3978i	−0.920170	−	0.920170i	0.0768712	−	0.997041i	$-0.475507\pi$
$823$	−26.3978	−	26.3978i	−0.920170	−	0.920170i	−0.997041	+	0.0768712i	$0.975507\pi$
$824$	46.2853	+	5.91718i	1.61243	+	0.206135i
$825$		0			0
$826$	−1.02416	−	4.59252i	−0.0356351	−	0.159794i
$827$	1.99830			0.0694878			0.0347439	−	0.999396i	$-0.488938\pi$
$827$	1.99830			0.0694878			0.0347439	+	0.999396i	$0.488938\pi$
$828$	24.7836	+	8.95041i	0.861288	+	0.311048i
$829$	13.0376	−	13.0376i	0.452813	−	0.452813i	−0.443474	−	0.896287i	$-0.646254\pi$
$829$	13.0376	−	13.0376i	0.452813	−	0.452813i	0.896287	+	0.443474i	$0.146254\pi$
$830$		0			0
$831$		−	70.4735i		−	2.44470i
$832$	−35.0055	−	9.09901i	−1.21360	−	0.315451i
$833$	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
$837$		−	0.862057i		−	0.0297971i
$838$	−13.9174	−	8.84194i	−0.480769	−	0.305440i
$839$			15.4102i			0.532018i	0.963971	+	0.266009i	$0.0857050\pi$
$839$			15.4102i			0.532018i	−0.963971	+	0.266009i	$0.914295\pi$
$840$		0			0
$841$		−	0.479815i		−	0.0165453i
$842$	−18.4228	+	28.9979i	−0.634891	+	0.999333i
$843$			67.5983i			2.32821i
$844$	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
$848$	−7.04822	+	8.48550i	−0.242037	+	0.291393i
$849$			37.2686i			1.27906i
$850$		0			0
$851$	−10.5565	+	10.5565i	−0.361872	+	0.361872i
$852$	−7.08686	+	3.32624i	−0.242792	+	0.113955i
$853$	−7.96419			−0.272689			−0.136344	−	0.990662i	$-0.543535\pi$
$853$	−7.96419			−0.272689			−0.136344	+	0.990662i	$0.543535\pi$
$854$	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	$-0.208719\pi$
$857$	5.35407	+	5.35407i	0.182891	+	0.182891i	−0.609723	+	0.792615i	$0.708719\pi$
$858$	6.82393	−	10.7410i	0.232965	−	0.366692i
$859$	−35.0058	+	35.0058i	−1.19438	+	1.19438i	−0.218559	+	0.975824i	$0.570136\pi$
$859$	−35.0058	+	35.0058i	−1.19438	+	1.19438i	−0.975824	+	0.218559i	$0.929864\pi$
$860$		0			0
$861$	−5.97175	−	5.97175i	−0.203517	−	0.203517i
$862$	−9.90457	−	44.4140i	−0.337351	−	1.51275i
$863$	−36.7138	+	36.7138i	−1.24975	+	1.24975i	−0.293923	+	0.955829i	$0.594961\pi$
$863$	−36.7138	+	36.7138i	−1.24975	+	1.24975i	−0.955829	+	0.293923i	$0.905039\pi$
$864$	−15.8962	+	31.0078i	−0.540801	+	1.05491i
$865$		0			0
$866$	34.3336	+	21.8126i	1.16670	+	0.741224i
$867$			7.34475i			0.249441i
$868$	0.170847	+	0.0617003i	0.00579893	+	0.00209424i
$869$	−1.90416	−	1.90416i	−0.0645943	−	0.0645943i
$870$		0			0
$871$	15.0406			0.509633
$872$	−6.33022	+	49.5162i	−0.214368	+	1.67683i
$873$	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
$877$	14.3410			0.484262			0.242131	−	0.970244i	$-0.422154\pi$
$877$	14.3410			0.484262			0.242131	+	0.970244i	$0.422154\pi$
$878$	10.9022	+	48.8877i	0.367933	+	1.64988i
$879$	−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	$0.573796\pi$
$882$	10.4429	+	46.8277i	0.351629	+	1.57677i
$883$	−6.12563			−0.206144			−0.103072	−	0.994674i	$-0.532867\pi$
$883$	−6.12563			−0.206144			−0.103072	+	0.994674i	$0.532867\pi$
$884$	−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	−0.990964	−	0.134130i	$-0.957176\pi$
$887$	−25.5187	+	25.5187i	−0.856834	+	0.856834i	0.134130	+	0.990964i	$0.457176\pi$
$888$	−28.8751	−	37.3401i	−0.968984	−	1.25305i
$889$	−0.565166			−0.0189551
$890$		0			0
$891$	−1.04566	−	1.04566i	−0.0350310	−	0.0350310i
$892$	−7.85227	+	21.7428i	−0.262913	+	0.728003i
$893$			33.4992i			1.12101i
$894$	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
$898$	2.66433	+	11.9474i	0.0889100	+	0.398689i
$899$	0.537302	+	0.537302i	0.0179200	+	0.0179200i
$900$		0			0
$901$	−8.62682	+	8.62682i	−0.287401	+	0.287401i
$902$	2.40802	−	3.79028i	0.0801784	−	0.126203i
$903$	−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
$907$	−32.1815			−1.06857			−0.534284	−	0.845305i	$-0.679419\pi$
$907$	−32.1815			−1.06857			−0.534284	+	0.845305i	$0.679419\pi$
$908$	−1.30921	−	2.78940i	−0.0434477	−	0.0925694i
$909$	−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	$0.778974\pi$
$912$	65.0744	−	6.02111i	2.15483	−	0.199379i
$913$	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
$917$		−	8.76867i		−	0.289567i
$918$	−20.6661	+	32.5289i	−0.682082	+	1.07361i
$919$		−	19.1924i		−	0.633099i	−0.948576	−	0.316550i	$-0.897476\pi$
$919$		−	19.1924i		−	0.633099i	0.948576	−	0.316550i	$-0.102524\pi$
$920$		0			0
$921$			78.1395i			2.57479i
$922$	−2.02038	−	1.28358i	−0.0665378	−	0.0422725i
$923$		−	6.19641i		−	0.203957i
$924$	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
$928$	−9.41870	−	29.2343i	−0.309184	−	0.959662i
$929$			16.8576i			0.553081i	0.961002	+	0.276541i	$0.0891880\pi$
$929$			16.8576i			0.553081i	−0.961002	+	0.276541i	$0.910812\pi$
$930$		0			0
$931$	26.6119	−	26.6119i	0.872170	−	0.872170i
$932$	9.59792	−	26.5765i	0.314390	−	0.870542i
$933$	45.1467			1.47804
$934$	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	$-0.436622\pi$
$937$	−23.9511	−	23.9511i	−0.782449	−	0.782449i	−0.980243	+	0.197795i	$0.936622\pi$
$938$	2.57715	+	1.63730i	0.0841470	+	0.0534599i
$939$	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	$0.643467\pi$
$942$	29.5860	−	6.59784i	0.963963	−	0.214969i
$943$	−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
$947$			20.2943i			0.659477i	0.944072	+	0.329738i	$0.106961\pi$
$947$			20.2943i			0.659477i	−0.944072	+	0.329738i	$0.893039\pi$
$948$	−19.9813	+	9.37829i	−0.648963	+	0.304593i
$949$	11.5301	+	11.5301i	0.374282	+	0.374282i
$950$		0			0
$951$	−99.9866			−3.24229
$952$	−4.96761	−	6.42391i	−0.161001	−	0.208200i
$953$	−10.9257	+	10.9257i	−0.353919	+	0.353919i	−0.861565	−	0.507647i	$-0.830516\pi$
$953$	−10.9257	+	10.9257i	−0.353919	+	0.353919i	0.507647	+	0.861565i	$0.330516\pi$
$954$	−19.6293	+	4.37746i	−0.635524	+	0.141725i
$955$		0			0
$956$	−47.5730	+	22.3285i	−1.53862	+	0.722157i
$957$	10.8062			0.349316
$958$	32.5429	−	7.25726i	1.05141	−	0.234471i
$959$	−3.39836			−0.109739
$960$		0			0
$961$	30.9804			0.999368
$962$	36.4651	−	8.13193i	1.17568	−	0.262184i
$963$	78.9535			2.54424
$964$	−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	−0.858586	−	0.512669i	$-0.828657\pi$
$967$	−10.7569	+	10.7569i	−0.345918	+	0.345918i	0.512669	+	0.858586i	$0.328657\pi$
$968$	−18.1923	−	23.5256i	−0.584724	−	0.756142i
$969$	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	$0.889858\pi$
$972$	22.4842	−	10.5530i	0.721180	−	0.338488i
$973$			5.01811i			0.160873i
$974$	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	−0.145107	−	0.989416i	$-0.546353\pi$
$977$	26.3906	−	26.3906i	0.844309	−	0.844309i	0.989416	+	0.145107i	$0.0463526\pi$
$978$	−93.5415	+	20.8603i	−2.99113	+	0.667039i
$979$	−1.65081	−	1.65081i	−0.0527602	−	0.0527602i
$980$		0			0
$981$	−64.3556	+	64.3556i	−2.05472	+	2.05472i
$982$	−31.5509	−	20.0448i	−1.00683	−	0.639655i
$983$	4.87875	+	4.87875i	0.155608	+	0.155608i	0.780617	−	0.625009i	$-0.214905\pi$
$983$	4.87875	+	4.87875i	0.155608	+	0.155608i	−0.625009	+	0.780617i	$0.714905\pi$
$984$	−22.5161	−	29.1170i	−0.717788	−	0.928215i
$985$		0			0
$986$	−7.39381	−	33.1553i	−0.235467	−	1.05588i
$987$	10.8537			0.345478
$988$	−17.5701	+	48.6513i	−0.558979	+	1.54781i
$989$	−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	$0.575224\pi$
$992$	0.704492	+	0.361160i	0.0223677	+	0.0114668i
$993$	−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
$997$			39.1082i			1.23857i	0.785167	+	0.619284i	$0.212577\pi$
$997$			39.1082i			1.23857i	−0.785167	+	0.619284i	$0.787423\pi$
$998$	16.3637	+	10.3961i	0.517984	+	0.329083i
$999$		−	35.9935i		−	1.13878i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.5	✓	18	80.59	odd	4
80.2.j.b.67.5	yes	18	5.3	odd	4
80.2.s.b.3.1	yes	18	5.4	even	2
80.2.s.b.27.1	yes	18	80.43	even	4
320.2.j.b.47.9		18	20.3	even	4
320.2.j.b.143.1		18	80.69	even	4
320.2.s.b.207.1		18	80.53	odd	4
320.2.s.b.303.1		18	20.19	odd	2
400.2.j.d.43.5		18	16.11	odd	4
400.2.j.d.307.5		18	5.2	odd	4
400.2.s.d.107.9		18	80.27	even	4	inner
400.2.s.d.243.9		18	1.1	even	1	trivial
640.2.j.c.543.9		18	80.29	even	4
640.2.j.c.607.1		18	40.3	even	4
640.2.j.d.543.1		18	80.19	odd	4
640.2.j.d.607.9		18	40.13	odd	4
640.2.s.c.223.9		18	40.19	odd	2
640.2.s.c.287.9		18	80.13	odd	4
640.2.s.d.223.1		18	40.29	even	2
640.2.s.d.287.1		18	80.3	even	4
720.2.z.g.163.9		18	15.14	odd	2
720.2.z.g.667.9		18	240.203	odd	4
720.2.bd.g.307.5		18	15.8	even	4
720.2.bd.g.523.5		18	240.59	even	4
1600.2.j.d.143.9		18	16.5	even	4
1600.2.j.d.1007.1		18	20.7	even	4
1600.2.s.d.207.9		18	80.37	odd	4
1600.2.s.d.943.9		18	4.3	odd	2

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.s (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

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