LMFDB - Embedded newform 400.2.j.d.307.6

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			307.6
Root			$0.0376504 + 1.41371i$ of defining polynomial
Character	$\chi$	$=$	400.307
Dual form			400.2.j.d.43.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.558542 + 1.29924i) q^{2} -2.55161i q^{3} +(-1.37606 + 1.45136i) q^{4} +(3.31516 - 1.42518i) q^{6} +(-2.40368 - 2.40368i) q^{7} +(-2.65426 - 0.977191i) q^{8} -3.51070 q^{9} +O(q^{10})$	\(q+(0.558542 + 1.29924i) q^{2} -2.55161i q^{3} +(-1.37606 + 1.45136i) q^{4} +(3.31516 - 1.42518i) q^{6} +(-2.40368 - 2.40368i) q^{7} +(-2.65426 - 0.977191i) q^{8} -3.51070 q^{9} +(-2.67707 - 2.67707i) q^{11} +(3.70331 + 3.51117i) q^{12} +2.40164 q^{13} +(1.78040 - 4.46551i) q^{14} +(-0.212908 - 3.99433i) q^{16} +(0.0750544 + 0.0750544i) q^{17} +(-1.96087 - 4.56125i) q^{18} +(-2.67236 - 2.67236i) q^{19} +(-6.13324 + 6.13324i) q^{21} +(1.98291 - 4.97342i) q^{22} +(-2.12375 + 2.12375i) q^{23} +(-2.49341 + 6.77263i) q^{24} +(1.34141 + 3.12031i) q^{26} +1.30310i q^{27} +(6.79621 - 0.180999i) q^{28} +(3.95795 - 3.95795i) q^{29} +1.65367i q^{31} +(5.07068 - 2.50762i) q^{32} +(-6.83083 + 6.83083i) q^{33} +(-0.0555929 + 0.139435i) q^{34} +(4.83094 - 5.09530i) q^{36} +2.53082 q^{37} +(1.97942 - 4.96467i) q^{38} -6.12803i q^{39} -1.70882i q^{41} +(-11.3942 - 4.54289i) q^{42} +3.84601 q^{43} +(7.56921 - 0.201586i) q^{44} +(-3.94547 - 1.57306i) q^{46} +(2.15264 - 2.15264i) q^{47} +(-10.1920 + 0.543256i) q^{48} +4.55532i q^{49} +(0.191509 - 0.191509i) q^{51} +(-3.30480 + 3.48565i) q^{52} -1.29475i q^{53} +(-1.69305 + 0.727839i) q^{54} +(4.03113 + 8.72883i) q^{56} +(-6.81881 + 6.81881i) q^{57} +(7.35302 + 2.93166i) q^{58} +(-5.29614 + 5.29614i) q^{59} +(10.2413 + 10.2413i) q^{61} +(-2.14852 + 0.923645i) q^{62} +(8.43858 + 8.43858i) q^{63} +(6.09020 + 5.18744i) q^{64} +(-12.6902 - 5.05960i) q^{66} +10.6230 q^{67} +(-0.212211 + 0.00565167i) q^{68} +(5.41898 + 5.41898i) q^{69} +2.27322 q^{71} +(9.31831 + 3.43062i) q^{72} +(-9.99096 - 9.99096i) q^{73} +(1.41357 + 3.28815i) q^{74} +(7.55589 - 0.201231i) q^{76} +12.8696i q^{77} +(7.96180 - 3.42276i) q^{78} +8.70617 q^{79} -7.20709 q^{81} +(2.22017 - 0.954448i) q^{82} +11.1310i q^{83} +(-0.461838 - 17.3413i) q^{84} +(2.14816 + 4.99689i) q^{86} +(-10.0991 - 10.0991i) q^{87} +(4.48963 + 9.72165i) q^{88} -15.6390 q^{89} +(-5.77276 - 5.77276i) q^{91} +(-0.159920 - 6.00475i) q^{92} +4.21952 q^{93} +(3.99914 + 1.59446i) q^{94} +(-6.39846 - 12.9384i) q^{96} +(-5.00672 - 5.00672i) q^{97} +(-5.91846 + 2.54434i) q^{98} +(9.39839 + 9.39839i) 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 $

$2$	0.558542	+	1.29924i	0.394949	+	0.918703i
$2$	0.558542	+	1.29924i	0.394949	+	0.918703i
$3$		−	2.55161i		−	1.47317i	−0.676344	−	0.736586i	$-0.736437\pi$
$3$		−	2.55161i		−	1.47317i	0.676344	−	0.736586i	$-0.263563\pi$
$4$	−1.37606	+	1.45136i	−0.688031	+	0.725681i
$5$		0			0
$5$		0			0
$6$	3.31516	−	1.42518i	1.35341	−	0.581827i
$7$	−2.40368	−	2.40368i	−0.908504	−	0.908504i	0.0876474	−	0.996152i	$-0.472065\pi$
$7$	−2.40368	−	2.40368i	−0.908504	−	0.908504i	−0.996152	+	0.0876474i	$0.972065\pi$
$8$	−2.65426	−	0.977191i	−0.938423	−	0.345489i
$9$	−3.51070			−1.17023
$10$		0			0
$11$	−2.67707	−	2.67707i	−0.807167	−	0.807167i	0.177037	−	0.984204i	$-0.443349\pi$
$11$	−2.67707	−	2.67707i	−0.807167	−	0.807167i	−0.984204	+	0.177037i	$0.943349\pi$
$12$	3.70331	+	3.51117i	1.06905	+	1.01359i
$13$	2.40164			0.666094			0.333047	−	0.942910i	$-0.391923\pi$
$13$	2.40164			0.666094			0.333047	+	0.942910i	$0.391923\pi$
$14$	1.78040	−	4.46551i	0.475833	−	1.19346i
$15$		0			0
$16$	−0.212908	−	3.99433i	−0.0532269	−	0.998582i
$17$	0.0750544	+	0.0750544i	0.0182034	+	0.0182034i	0.716150	−	0.697947i	$-0.245903\pi$
$17$	0.0750544	+	0.0750544i	0.0182034	+	0.0182034i	−0.697947	+	0.716150i	$0.745903\pi$
$18$	−1.96087	−	4.56125i	−0.462182	−	1.07510i
$19$	−2.67236	−	2.67236i	−0.613081	−	0.613081i	0.330666	−	0.943748i	$-0.392726\pi$
$19$	−2.67236	−	2.67236i	−0.613081	−	0.613081i	−0.943748	+	0.330666i	$0.892726\pi$
$20$		0			0
$21$	−6.13324	+	6.13324i	−1.33838	+	1.33838i
$22$	1.98291	−	4.97342i	0.422757	−	1.06034i
$23$	−2.12375	+	2.12375i	−0.442833	+	0.442833i	−0.892963	−	0.450130i	$-0.851378\pi$
$23$	−2.12375	+	2.12375i	−0.442833	+	0.442833i	0.450130	+	0.892963i	$0.351378\pi$
$24$	−2.49341	+	6.77263i	−0.508965	+	1.38246i
$25$		0			0
$26$	1.34141	+	3.12031i	0.263073	+	0.611943i
$27$			1.30310i			0.250783i
$28$	6.79621	−	0.180999i	1.28436	−	0.0342056i
$29$	3.95795	−	3.95795i	0.734974	−	0.734974i	−0.236627	−	0.971601i	$-0.576042\pi$
$29$	3.95795	−	3.95795i	0.734974	−	0.734974i	0.971601	+	0.236627i	$0.0760419\pi$
$30$		0			0
$31$			1.65367i			0.297008i	0.988912	+	0.148504i	$0.0474458\pi$
$31$			1.65367i			0.297008i	−0.988912	+	0.148504i	$0.952554\pi$
$32$	5.07068	−	2.50762i	0.896379	−	0.443289i
$33$	−6.83083	+	6.83083i	−1.18909	+	1.18909i
$34$	−0.0555929	+	0.139435i	−0.00953410	+	0.0239129i
$35$		0			0
$36$	4.83094	−	5.09530i	0.805157	−	0.849216i
$37$	2.53082			0.416064			0.208032	−	0.978122i	$-0.433294\pi$
$37$	2.53082			0.416064			0.208032	+	0.978122i	$0.433294\pi$
$38$	1.97942	−	4.96467i	0.321104	−	0.805375i
$39$		−	6.12803i		−	0.981271i
$40$		0			0
$41$		−	1.70882i		−	0.266873i	−0.991057	−	0.133436i	$-0.957399\pi$
$41$		−	1.70882i		−	0.266873i	0.991057	−	0.133436i	$-0.0426012\pi$
$42$	−11.3942	−	4.54289i	−1.75817	−	0.700983i
$43$	3.84601			0.586510			0.293255	−	0.956034i	$-0.405261\pi$
$43$	3.84601			0.586510			0.293255	+	0.956034i	$0.405261\pi$
$44$	7.56921	−	0.201586i	1.14110	−	0.0303902i
$45$		0			0
$46$	−3.94547	−	1.57306i	−0.581728	−	0.231936i
$47$	2.15264	−	2.15264i	0.313995	−	0.313995i	−0.532460	−	0.846455i	$-0.678732\pi$
$47$	2.15264	−	2.15264i	0.313995	−	0.313995i	0.846455	+	0.532460i	$0.178732\pi$
$48$	−10.1920	+	0.543256i	−1.47108	+	0.0784123i
$49$			4.55532i			0.650760i
$50$		0			0
$51$	0.191509	−	0.191509i	0.0268167	−	0.0268167i
$52$	−3.30480	+	3.48565i	−0.458293	+	0.483372i
$53$		−	1.29475i		−	0.177848i	−0.996038	−	0.0889239i	$-0.971657\pi$
$53$		−	1.29475i		−	0.177848i	0.996038	−	0.0889239i	$-0.0283428\pi$
$54$	−1.69305	+	0.727839i	−0.230395	+	0.0990463i
$55$		0			0
$56$	4.03113	+	8.72883i	0.538683	+	1.16644i
$57$	−6.81881	+	6.81881i	−0.903174	+	0.903174i
$58$	7.35302	+	2.93166i	0.965499	+	0.384946i
$59$	−5.29614	+	5.29614i	−0.689499	+	0.689499i	−0.962121	−	0.272622i	$-0.912109\pi$
$59$	−5.29614	+	5.29614i	−0.689499	+	0.689499i	0.272622	+	0.962121i	$0.412109\pi$
$60$		0			0
$61$	10.2413	+	10.2413i	1.31126	+	1.31126i	0.920484	+	0.390780i	$0.127795\pi$
$61$	10.2413	+	10.2413i	1.31126	+	1.31126i	0.390780	+	0.920484i	$0.372205\pi$
$62$	−2.14852	+	0.923645i	−0.272862	+	0.117303i
$63$	8.43858	+	8.43858i	1.06316	+	1.06316i
$64$	6.09020	+	5.18744i	0.761274	+	0.648430i
$65$		0			0
$66$	−12.6902	−	5.05960i	−1.56206	−	0.622794i
$67$	10.6230			1.29780			0.648901	−	0.760873i	$-0.275229\pi$
$67$	10.6230			1.29780			0.648901	+	0.760873i	$0.275229\pi$
$68$	−0.212211	+	0.00565167i	−0.0257343	+	0.000685365i
$69$	5.41898	+	5.41898i	0.652369	+	0.652369i
$70$		0			0
$71$	2.27322			0.269781			0.134891	−	0.990860i	$-0.456932\pi$
$71$	2.27322			0.269781			0.134891	+	0.990860i	$0.456932\pi$
$72$	9.31831	+	3.43062i	1.09817	+	0.404303i
$73$	−9.99096	−	9.99096i	−1.16935	−	1.16935i	−0.982361	−	0.186992i	$-0.940126\pi$
$73$	−9.99096	−	9.99096i	−1.16935	−	1.16935i	−0.186992	−	0.982361i	$-0.559874\pi$
$74$	1.41357	+	3.28815i	0.164324	+	0.382240i
$75$		0			0
$76$	7.55589	−	0.201231i	0.866720	−	0.0230828i
$77$			12.8696i			1.46663i
$78$	7.96180	−	3.42276i	0.901496	−	0.387552i
$79$	8.70617			0.979520			0.489760	−	0.871857i	$-0.337084\pi$
$79$	8.70617			0.979520			0.489760	+	0.871857i	$0.337084\pi$
$80$		0			0
$81$	−7.20709			−0.800787
$82$	2.22017	−	0.954448i	0.245177	−	0.105401i
$83$			11.1310i			1.22178i	0.791715	+	0.610890i	$0.209188\pi$
$83$			11.1310i			1.22178i	−0.791715	+	0.610890i	$0.790812\pi$
$84$	−0.461838	−	17.3413i	−0.0503907	−	1.89209i
$85$		0			0
$86$	2.14816	+	4.99689i	0.231642	+	0.538829i
$87$	−10.0991	−	10.0991i	−1.08274	−	1.08274i
$88$	4.48963	+	9.72165i	0.478596	+	1.03633i
$89$	−15.6390			−1.65773			−0.828866	−	0.559447i	$-0.811014\pi$
$89$	−15.6390			−1.65773			−0.828866	+	0.559447i	$0.811014\pi$
$90$		0			0
$91$	−5.77276	−	5.77276i	−0.605149	−	0.605149i
$92$	−0.159920	−	6.00475i	−0.0166729	−	0.626038i
$93$	4.21952			0.437544
$94$	3.99914	+	1.59446i	0.412480	+	0.164456i
$95$		0			0
$96$	−6.39846	−	12.9384i	−0.653040	−	1.32052i
$97$	−5.00672	−	5.00672i	−0.508355	−	0.508355i	0.405666	−	0.914021i	$-0.367040\pi$
$97$	−5.00672	−	5.00672i	−0.508355	−	0.508355i	−0.914021	+	0.405666i	$0.867040\pi$
$98$	−5.91846	+	2.54434i	−0.597855	+	0.257017i
$99$	9.39839	+	9.39839i	0.944573	+	0.944573i
$100$		0			0
$101$	6.37101	−	6.37101i	0.633939	−	0.633939i	−0.315115	−	0.949054i	$-0.602043\pi$
$101$	6.37101	−	6.37101i	0.633939	−	0.633939i	0.949054	+	0.315115i	$0.102043\pi$
$102$	0.355783	+	0.141851i	0.0352278	+	0.0140454i
$103$	1.93695	−	1.93695i	0.190854	−	0.190854i	−0.605211	−	0.796065i	$-0.706911\pi$
$103$	1.93695	−	1.93695i	0.190854	−	0.190854i	0.796065	+	0.605211i	$0.206911\pi$
$104$	−6.37457	−	2.34686i	−0.625078	−	0.230128i
$105$		0			0
$106$	1.68220	−	0.723173i	0.163389	−	0.0702408i
$107$		−	6.97778i		−	0.674568i	−0.941403	−	0.337284i	$-0.890492\pi$
$107$		−	6.97778i		−	0.674568i	0.941403	−	0.337284i	$-0.109508\pi$
$108$	−1.89128	−	1.79315i	−0.181988	−	0.172546i
$109$	−0.277748	+	0.277748i	−0.0266034	+	0.0266034i	−0.720283	−	0.693680i	$-0.755988\pi$
$109$	−0.277748	+	0.277748i	−0.0266034	+	0.0266034i	0.693680	+	0.720283i	$0.255988\pi$
$110$		0			0
$111$		−	6.45766i		−	0.612934i
$112$	−9.08931	+	10.1128i	−0.858859	+	0.955573i
$113$	8.75577	−	8.75577i	0.823674	−	0.823674i	−0.162959	−	0.986633i	$-0.552104\pi$
$113$	8.75577	−	8.75577i	0.823674	−	0.823674i	0.986633	+	0.162959i	$0.0521038\pi$
$114$	−12.6679	−	5.05070i	−1.18646	−	0.473041i
$115$		0			0
$116$	0.298037	+	11.1908i	0.0276721	+	1.03904i
$117$	−8.43142			−0.779485
$118$	−9.83909	−	3.92286i	−0.905762	−	0.361128i
$119$		−	0.360813i		−	0.0330757i
$120$		0			0
$121$			3.33340i			0.303036i
$122$	−7.58574	+	19.0261i	−0.686780	+	1.72254i
$123$	−4.36024			−0.393149
$124$	−2.40008	−	2.27555i	−0.215533	−	0.204351i
$125$		0			0
$126$	−6.25046	+	15.6771i	−0.556836	+	1.39662i
$127$	−0.679502	+	0.679502i	−0.0602961	+	0.0602961i	−0.736612	−	0.676316i	$-0.763576\pi$
$127$	−0.679502	+	0.679502i	−0.0602961	+	0.0602961i	0.676316	+	0.736612i	$0.263576\pi$
$128$	−3.33811	+	10.8100i	−0.295050	+	0.955482i
$129$		−	9.81350i		−	0.864030i
$130$		0			0
$131$	−5.43859	+	5.43859i	−0.475172	+	0.475172i	−0.903584	−	0.428412i	$-0.859073\pi$
$131$	−5.43859	+	5.43859i	−0.475172	+	0.475172i	0.428412	+	0.903584i	$0.359073\pi$
$132$	−0.514367	−	19.3137i	−0.0447699	−	1.68104i
$133$			12.8470i			1.11397i
$134$	5.93337	+	13.8018i	0.512565	+	1.19229i
$135$		0			0
$136$	−0.125871	−	0.272557i	−0.0107934	−	0.0233715i
$137$	−7.47496	+	7.47496i	−0.638629	+	0.638629i	−0.950217	−	0.311588i	$-0.899139\pi$
$137$	−7.47496	+	7.47496i	−0.638629	+	0.638629i	0.311588	+	0.950217i	$0.399139\pi$
$138$	−4.01384	+	10.0673i	−0.341681	+	0.856986i
$139$	11.5307	−	11.5307i	0.978023	−	0.978023i	−0.0217404	−	0.999764i	$-0.506921\pi$
$139$	11.5307	−	11.5307i	0.978023	−	0.978023i	0.999764	+	0.0217404i	$0.00692074\pi$
$140$		0			0
$141$	−5.49270	−	5.49270i	−0.462568	−	0.462568i
$142$	1.26969	+	2.95346i	0.106550	+	0.247849i
$143$	−6.42935	−	6.42935i	−0.537649	−	0.537649i
$144$	0.747455	+	14.0229i	0.0622879	+	1.16857i
$145$		0			0
$146$	7.40031	−	18.5611i	0.612454	−	1.53612i
$147$	11.6234			0.958680
$148$	−3.48257	+	3.67314i	−0.286265	+	0.301930i
$149$	−5.51174	−	5.51174i	−0.451539	−	0.451539i	0.444326	−	0.895865i	$-0.353443\pi$
$149$	−5.51174	−	5.51174i	−0.451539	−	0.451539i	−0.895865	+	0.444326i	$0.853443\pi$
$150$		0			0
$151$	−4.13617			−0.336597			−0.168299	−	0.985736i	$-0.553827\pi$
$151$	−4.13617			−0.336597			−0.168299	+	0.985736i	$0.553827\pi$
$152$	4.48173	+	9.70454i	0.363516	+	0.787142i
$153$	−0.263494	−	0.263494i	−0.0213022	−	0.0213022i
$154$	−16.7207	+	7.18822i	−1.34740	+	0.579243i
$155$		0			0
$156$	8.89400	+	8.43255i	0.712090	+	0.675144i
$157$		−	20.2700i		−	1.61772i	−0.587999	−	0.808861i	$-0.700084\pi$
$157$		−	20.2700i		−	1.61772i	0.587999	−	0.808861i	$-0.299916\pi$
$158$	4.86276	+	11.3114i	0.386860	+	0.899889i
$159$	−3.30370			−0.262000
$160$		0			0
$161$	10.2096			0.804631
$162$	−4.02546	−	9.36375i	−0.316270	−	0.735686i
$163$		−	13.1835i		−	1.03262i	−0.856403	−	0.516308i	$-0.827306\pi$
$163$		−	13.1835i		−	1.03262i	0.856403	−	0.516308i	$-0.172694\pi$
$164$	2.48012	+	2.35144i	0.193665	+	0.183617i
$165$		0			0
$166$	−14.4618	+	6.21710i	−1.12245	+	0.482541i
$167$	11.8190	+	11.8190i	0.914585	+	0.914585i	0.996629	−	0.0820441i	$-0.0261448\pi$
$167$	11.8190	+	11.8190i	0.914585	+	0.914585i	−0.0820441	+	0.996629i	$0.526145\pi$
$168$	22.2726	−	10.2859i	1.71836	−	0.793572i
$169$	−7.23214			−0.556319
$170$		0			0
$171$	9.38185	+	9.38185i	0.717448	+	0.717448i
$172$	−5.29234	+	5.58195i	−0.403537	+	0.425620i
$173$	−15.5763			−1.18424			−0.592120	−	0.805849i	$-0.701709\pi$
$173$	−15.5763			−1.18424			−0.592120	+	0.805849i	$0.701709\pi$
$174$	7.48044	−	18.7620i	0.567091	−	1.42235i
$175$		0			0
$176$	−10.1231	+	11.2631i	−0.763060	+	0.848986i
$177$	13.5137	+	13.5137i	1.01575	+	1.01575i
$178$	−8.73505	−	20.3189i	−0.654719	−	1.52296i
$179$	15.5963	+	15.5963i	1.16572	+	1.16572i	0.983202	+	0.182523i	$0.0584265\pi$
$179$	15.5963	+	15.5963i	1.16572	+	1.16572i	0.182523	+	0.983202i	$0.441574\pi$
$180$		0			0
$181$	2.98705	−	2.98705i	0.222026	−	0.222026i	−0.587325	−	0.809351i	$-0.699819\pi$
$181$	2.98705	−	2.98705i	0.222026	−	0.222026i	0.809351	+	0.587325i	$0.199819\pi$
$182$	4.27588	−	10.7245i	0.316950	−	0.794955i
$183$	26.1318	−	26.1318i	1.93172	−	1.93172i
$184$	7.71230	−	3.56168i	0.568559	−	0.262571i
$185$		0			0
$186$	2.35678	+	5.48218i	0.172807	+	0.401973i
$187$		−	0.401852i		−	0.0293863i
$188$	0.162096	+	6.08643i	0.0118221	+	0.443899i
$189$	3.13224	−	3.13224i	0.227837	−	0.227837i
$190$		0			0
$191$		−	6.47168i		−	0.468274i	−0.972204	−	0.234137i	$-0.924774\pi$
$191$		−	6.47168i		−	0.468274i	0.972204	−	0.234137i	$-0.0752264\pi$
$192$	13.2363	−	15.5398i	0.955248	−	1.12149i
$193$	11.1131	−	11.1131i	0.799936	−	0.799936i	−0.183149	−	0.983085i	$-0.558629\pi$
$193$	11.1131	−	11.1131i	0.799936	−	0.799936i	0.983085	+	0.183149i	$0.0586292\pi$
$194$	3.70848	−	9.30141i	0.266253	−	0.667802i
$195$		0			0
$196$	−6.61142	−	6.26840i	−0.472244	−	0.447743i
$197$	25.0927			1.78778			0.893889	−	0.448288i	$-0.147966\pi$
$197$	25.0927			1.78778			0.893889	+	0.448288i	$0.147966\pi$
$198$	−6.96139	+	17.4602i	−0.494724	+	1.24084i
$199$		−	18.7579i		−	1.32972i	−0.746970	−	0.664858i	$-0.768492\pi$
$199$		−	18.7579i		−	1.32972i	0.746970	−	0.664858i	$-0.231508\pi$
$200$		0			0
$201$		−	27.1056i		−	1.91188i
$202$	11.8360	+	4.71901i	0.832775	+	0.332028i
$203$	−19.0273			−1.33545
$204$	0.0144208	+	0.541479i	0.00100966	+	0.0379111i
$205$		0			0
$206$	3.59844	+	1.43470i	0.250715	+	0.0999604i
$207$	7.45586	−	7.45586i	0.518218	−	0.518218i
$208$	−0.511327	−	9.59293i	−0.0354541	−	0.665150i
$209$			14.3082i			0.989718i
$210$		0			0
$211$	6.38863	−	6.38863i	0.439811	−	0.439811i	−0.452137	−	0.891948i	$-0.649338\pi$
$211$	6.38863	−	6.38863i	0.439811	−	0.439811i	0.891948	+	0.452137i	$0.149338\pi$
$212$	1.87915	+	1.78166i	0.129061	+	0.122365i
$213$		−	5.80036i		−	0.397434i
$214$	9.06583	−	3.89738i	0.619727	−	0.266420i
$215$		0			0
$216$	1.27338	−	3.45878i	0.0866427	−	0.235340i
$217$	3.97489	−	3.97489i	0.269833	−	0.269833i
$218$	−0.515996	−	0.205728i	−0.0349476	−	0.0139337i
$219$	−25.4930	+	25.4930i	−1.72266	+	1.72266i
$220$		0			0
$221$	0.180253	+	0.180253i	0.0121252	+	0.0121252i
$222$	8.39006	−	3.60687i	0.563104	−	0.242077i
$223$	−4.29779	−	4.29779i	−0.287801	−	0.287801i	0.548409	−	0.836210i	$-0.315234\pi$
$223$	−4.29779	−	4.29779i	−0.287801	−	0.287801i	−0.836210	+	0.548409i	$0.815234\pi$
$224$	−18.2158	−	6.16078i	−1.21709	−	0.411634i
$225$		0			0
$226$	16.2663	+	6.48541i	1.08202	+	0.431403i
$227$	−29.1029			−1.93163			−0.965813	−	0.259241i	$-0.916528\pi$
$227$	−29.1029			−1.93163			−0.965813	+	0.259241i	$0.916528\pi$
$228$	−0.513462	−	19.2797i	−0.0340049	−	1.27683i
$229$	18.3405	+	18.3405i	1.21198	+	1.21198i	0.970376	+	0.241600i	$0.0776721\pi$
$229$	18.3405	+	18.3405i	1.21198	+	1.21198i	0.241600	+	0.970376i	$0.422328\pi$
$230$		0			0
$231$	32.8382			2.16060
$232$	−14.3731	+	6.63776i	−0.943641	+	0.435790i
$233$	1.46663	+	1.46663i	0.0960824	+	0.0960824i	0.753514	−	0.657432i	$-0.228357\pi$
$233$	1.46663	+	1.46663i	0.0960824	+	0.0960824i	−0.657432	+	0.753514i	$0.728357\pi$
$234$	−4.70930	−	10.9545i	−0.307857	−	0.716116i
$235$		0			0
$236$	−0.398804	−	14.9744i	−0.0259600	−	0.974754i
$237$		−	22.2147i		−	1.44300i
$238$	0.468784	−	0.201529i	0.0303867	−	0.0130632i
$239$	−12.5432			−0.811352			−0.405676	−	0.914017i	$-0.632964\pi$
$239$	−12.5432			−0.811352			−0.405676	+	0.914017i	$0.632964\pi$
$240$		0			0
$241$	14.8870			0.958954			0.479477	−	0.877554i	$-0.340826\pi$
$241$	14.8870			0.958954			0.479477	+	0.877554i	$0.340826\pi$
$242$	−4.33089	+	1.86184i	−0.278400	+	0.119684i
$243$			22.2990i			1.43048i
$244$	−28.9565	+	0.771179i	−1.85375	+	0.0493697i
$245$		0			0
$246$	−2.43538	−	5.66501i	−0.155274	−	0.361188i
$247$	−6.41803	−	6.41803i	−0.408370	−	0.408370i
$248$	1.61595	−	4.38927i	0.102613	−	0.278719i
$249$	28.4018			1.79989
$250$		0			0
$251$	−5.38459	−	5.38459i	−0.339872	−	0.339872i	0.516447	−	0.856319i	$-0.327254\pi$
$251$	−5.38459	−	5.38459i	−0.339872	−	0.339872i	−0.856319	+	0.516447i	$0.827254\pi$
$252$	−23.8595	+	0.635433i	−1.50300	+	0.0400285i
$253$	11.3709			0.714880
$254$	−1.26237	−	0.503308i	−0.0792081	−	0.0315803i
$255$		0			0
$256$	−15.9093	+	1.70085i	−0.994334	+	0.106303i
$257$	3.88657	+	3.88657i	0.242437	+	0.242437i	0.817858	−	0.575420i	$-0.195162\pi$
$257$	3.88657	+	3.88657i	0.242437	+	0.242437i	−0.575420	+	0.817858i	$0.695162\pi$
$258$	12.7501	−	5.48125i	0.793787	−	0.341248i
$259$	−6.08327	−	6.08327i	−0.377996	−	0.377996i
$260$		0			0
$261$	−13.8952	+	13.8952i	−0.860090	+	0.860090i
$262$	−10.1037	−	4.02836i	−0.624210	−	0.248873i
$263$	−16.9658	+	16.9658i	−1.04615	+	1.04615i	−0.0472716	+	0.998882i	$0.515053\pi$
$263$	−16.9658	+	16.9658i	−1.04615	+	1.04615i	−0.998882	+	0.0472716i	$0.984947\pi$
$264$	24.8058	−	11.4558i	1.52669	−	0.705054i
$265$		0			0
$266$	−16.6913	+	7.17557i	−1.02341	+	0.439963i
$267$			39.9046i			2.44212i
$268$	−14.6179	+	15.4178i	−0.892928	+	0.941791i
$269$	−2.55482	+	2.55482i	−0.155770	+	0.155770i	−0.780689	−	0.624919i	$-0.785132\pi$
$269$	−2.55482	+	2.55482i	−0.155770	+	0.155770i	0.624919	+	0.780689i	$0.285132\pi$
$270$		0			0
$271$			3.33684i			0.202698i	0.994851	+	0.101349i	$0.0323159\pi$
$271$			3.33684i			0.202698i	−0.994851	+	0.101349i	$0.967684\pi$
$272$	0.283813	−	0.315772i	0.0172087	−	0.0191465i
$273$	−14.7298	+	14.7298i	−0.891488	+	0.891488i
$274$	−13.8869	−	5.53671i	−0.838937	−	0.334485i
$275$		0			0
$276$	−15.3218	+	0.408054i	−0.922262	+	0.0245620i
$277$	−4.60736			−0.276830			−0.138415	−	0.990374i	$-0.544201\pi$
$277$	−4.60736			−0.276830			−0.138415	+	0.990374i	$0.544201\pi$
$278$	21.4216	+	8.54081i	1.28478	+	0.512244i
$279$		−	5.80554i		−	0.347569i
$280$		0			0
$281$			22.1178i			1.31944i	0.751513	+	0.659718i	$0.229324\pi$
$281$			22.1178i			1.31944i	−0.751513	+	0.659718i	$0.770676\pi$
$282$	4.06844	−	10.2042i	0.242272	−	0.607654i
$283$	10.8629			0.645734			0.322867	−	0.946444i	$-0.395353\pi$
$283$	10.8629			0.645734			0.322867	+	0.946444i	$0.395353\pi$
$284$	−3.12809	+	3.29926i	−0.185618	+	0.195775i
$285$		0			0
$286$	4.76222	−	11.9443i	0.281596	−	0.706284i
$287$	−4.10745	+	4.10745i	−0.242455	+	0.242455i
$288$	−17.8017	+	8.80350i	−1.04897	+	0.518751i
$289$		−	16.9887i		−	0.999337i
$290$		0			0
$291$	−12.7752	+	12.7752i	−0.748895	+	0.748895i
$292$	28.2487	−	0.752328i	1.65313	−	0.0440267i
$293$		−	18.4067i		−	1.07533i	−0.843159	−	0.537665i	$-0.819307\pi$
$293$		−	18.4067i		−	1.07533i	0.843159	−	0.537665i	$-0.180693\pi$
$294$	6.49214	+	15.1016i	0.378630	+	0.880743i
$295$		0			0
$296$	−6.71746	−	2.47309i	−0.390444	−	0.143746i
$297$	3.48850	−	3.48850i	0.202423	−	0.202423i
$298$	4.08255	−	10.2396i	0.236496	−	0.593166i
$299$	−5.10048	+	5.10048i	−0.294968	+	0.294968i
$300$		0			0
$301$	−9.24455	−	9.24455i	−0.532847	−	0.532847i
$302$	−2.31023	−	5.37389i	−0.132939	−	0.309233i
$303$	−16.2563	−	16.2563i	−0.933900	−	0.933900i
$304$	−10.1053	+	11.2432i	−0.579580	+	0.644845i
$305$		0			0
$306$	0.195170	−	0.489514i	0.0111571	−	0.0279837i
$307$	6.60872			0.377180			0.188590	−	0.982056i	$-0.439608\pi$
$307$	6.60872			0.377180			0.188590	+	0.982056i	$0.439608\pi$
$308$	−18.6785	−	17.7094i	−1.06431	−	1.00909i
$309$	−4.94234	−	4.94234i	−0.281160	−	0.281160i
$310$		0			0
$311$	−0.606102			−0.0343689			−0.0171845	−	0.999852i	$-0.505470\pi$
$311$	−0.606102			−0.0343689			−0.0171845	+	0.999852i	$0.505470\pi$
$312$	−5.98826	+	16.2654i	−0.339018	+	0.920847i
$313$	19.3708	+	19.3708i	1.09490	+	1.09490i	0.994997	+	0.0999032i	$0.0318533\pi$
$313$	19.3708	+	19.3708i	1.09490	+	1.09490i	0.0999032	+	0.994997i	$0.468147\pi$
$314$	26.3357	−	11.3216i	1.48621	−	0.638918i
$315$		0			0
$316$	−11.9802	+	12.6358i	−0.673940	+	0.710820i
$317$			7.04328i			0.395590i	0.980243	+	0.197795i	$0.0633780\pi$
$317$			7.04328i			0.395590i	−0.980243	+	0.197795i	$0.936622\pi$
$318$	−1.84525	−	4.29230i	−0.103477	−	0.240700i
$319$	−21.1914			−1.18649
$320$		0			0
$321$	−17.8046			−0.993753
$322$	5.70250	+	13.2648i	0.317788	+	0.739217i
$323$		−	0.401145i		−	0.0223203i
$324$	9.91740	−	10.4601i	0.550967	−	0.581117i
$325$		0			0
$326$	17.1286	−	7.36356i	0.948667	−	0.407830i
$327$	0.708703	+	0.708703i	0.0391914	+	0.0391914i
$328$	−1.66984	+	4.53565i	−0.0922017	+	0.250440i
$329$	−10.3485			−0.570532
$330$		0			0
$331$	−13.2275	−	13.2275i	−0.727047	−	0.727047i	0.242983	−	0.970031i	$-0.421874\pi$
$331$	−13.2275	−	13.2275i	−0.727047	−	0.727047i	−0.970031	+	0.242983i	$0.921874\pi$
$332$	−16.1550	−	15.3169i	−0.886624	−	0.840623i
$333$	−8.88495			−0.486892
$334$	−8.75437	+	21.9572i	−0.479018	+	1.20145i
$335$		0			0
$336$	25.8040	+	23.1924i	1.40772	+	1.26525i
$337$	−7.73287	−	7.73287i	−0.421236	−	0.421236i	0.464393	−	0.885629i	$-0.346273\pi$
$337$	−7.73287	−	7.73287i	−0.421236	−	0.421236i	−0.885629	+	0.464393i	$0.846273\pi$
$338$	−4.03945	−	9.39631i	−0.219717	−	0.511092i
$339$	−22.3413	−	22.3413i	−1.21341	−	1.21341i
$340$		0			0
$341$	4.42699	−	4.42699i	0.239735	−	0.239735i
$342$	−6.94914	+	17.4295i	−0.375767	+	0.942477i
$343$	−5.87623	+	5.87623i	−0.317286	+	0.317286i
$344$	−10.2083	−	3.75828i	−0.550395	−	0.202633i
$345$		0			0
$346$	−8.69999	−	20.2373i	−0.467714	−	1.08797i
$347$			11.3945i			0.611691i	0.952081	+	0.305845i	$0.0989391\pi$
$347$			11.3945i			0.611691i	−0.952081	+	0.305845i	$0.901061\pi$
$348$	28.5546	−	0.760474i	1.53069	−	0.0407657i
$349$	12.0508	−	12.0508i	0.645066	−	0.645066i	−0.306730	−	0.951796i	$-0.599235\pi$
$349$	12.0508	−	12.0508i	0.645066	−	0.645066i	0.951796	+	0.306730i	$0.0992350\pi$
$350$		0			0
$351$			3.12958i			0.167045i
$352$	−20.2876	−	6.86150i	−1.08134	−	0.365719i
$353$	6.47876	−	6.47876i	0.344830	−	0.344830i	−0.513350	−	0.858179i	$-0.671596\pi$
$353$	6.47876	−	6.47876i	0.344830	−	0.344830i	0.858179	+	0.513350i	$0.171596\pi$
$354$	−10.0096	+	25.1055i	−0.532004	+	1.33434i
$355$		0			0
$356$	21.5203	−	22.6979i	1.14057	−	1.20299i
$357$	−0.920653			−0.0487261
$358$	−11.5522	+	28.9746i	−0.610553	+	1.53136i
$359$		−	3.25098i		−	0.171580i	−0.996313	−	0.0857902i	$-0.972659\pi$
$359$		−	3.25098i		−	0.171580i	0.996313	−	0.0857902i	$-0.0273415\pi$
$360$		0			0
$361$		−	4.71699i		−	0.248263i
$362$	5.54929	+	2.21251i	0.291664	+	0.116287i
$363$	8.50553			0.446424
$364$	16.3220	−	0.434694i	0.855507	−	0.0227841i
$365$		0			0
$366$	48.5472	+	19.3558i	2.53760	+	1.01174i
$367$	−12.7038	+	12.7038i	−0.663132	+	0.663132i	−0.956117	−	0.292985i	$-0.905351\pi$
$367$	−12.7038	+	12.7038i	−0.663132	+	0.663132i	0.292985	+	0.956117i	$0.405351\pi$
$368$	8.93513	+	8.03080i	0.465776	+	0.418635i
$369$			5.99916i			0.312304i
$370$		0			0
$371$	−3.11216	+	3.11216i	−0.161575	+	0.161575i
$372$	−5.80632	+	6.12405i	−0.301044	+	0.317517i
$373$			21.9761i			1.13788i	0.822379	+	0.568939i	$0.192646\pi$
$373$			21.9761i			1.13788i	−0.822379	+	0.568939i	$0.807354\pi$
$374$	0.522103	−	0.224451i	0.0269973	−	0.0116061i
$375$		0			0
$376$	−7.81721	+	3.61013i	−0.403142	+	0.186178i
$377$	9.50557	−	9.50557i	0.489562	−	0.489562i
$378$	5.81903	+	2.32005i	0.299299	+	0.119331i
$379$	17.0642	−	17.0642i	0.876527	−	0.876527i	−0.116646	−	0.993174i	$-0.537214\pi$
$379$	17.0642	−	17.0642i	0.876527	−	0.876527i	0.993174	+	0.116646i	$0.0372144\pi$
$380$		0			0
$381$	1.73382	+	1.73382i	0.0888264	+	0.0888264i
$382$	8.40828	−	3.61470i	0.430205	−	0.184944i
$383$	−0.228058	−	0.228058i	−0.0116532	−	0.0116532i	0.701256	−	0.712909i	$-0.252623\pi$
$383$	−0.228058	−	0.228058i	−0.0116532	−	0.0116532i	−0.712909	+	0.701256i	$0.752623\pi$
$384$	27.5830	+	8.51755i	1.40759	+	0.434659i
$385$		0			0
$386$	20.6457	+	8.23145i	1.05084	+	0.418970i
$387$	−13.5022			−0.686354
$388$	14.1561	−	0.377011i	0.718668	−	0.0191398i
$389$	14.3036	+	14.3036i	0.725221	+	0.725221i	0.969664	−	0.244443i	$-0.0786050\pi$
$389$	14.3036	+	14.3036i	0.725221	+	0.725221i	−0.244443	+	0.969664i	$0.578605\pi$
$390$		0			0
$391$	−0.318794			−0.0161221
$392$	4.45141	−	12.0910i	0.224830	−	0.610688i
$393$	13.8771	+	13.8771i	0.700009	+	0.700009i
$394$	14.0153	+	32.6015i	0.706081	+	1.64244i
$395$		0			0
$396$	−26.5732	+	0.707707i	−1.33535	+	0.0355636i
$397$		−	5.11618i		−	0.256774i	−0.991724	−	0.128387i	$-0.959020\pi$
$397$		−	5.11618i		−	0.256774i	0.991724	−	0.128387i	$-0.0409799\pi$
$398$	24.3711	−	10.4771i	1.22161	−	0.525170i
$399$	32.7804			1.64107
$400$		0			0
$401$	−16.2837			−0.813170			−0.406585	−	0.913613i	$-0.633281\pi$
$401$	−16.2837			−0.813170			−0.406585	+	0.913613i	$0.633281\pi$
$402$	35.2168	−	15.1396i	1.75645	−	0.755096i
$403$			3.97152i			0.197835i
$404$	0.479742	+	18.0135i	0.0238681	+	0.896207i
$405$		0			0
$406$	−10.6275	−	24.7210i	−0.527436	−	1.22688i
$407$	−6.77518	−	6.77518i	−0.335833	−	0.335833i
$408$	−0.695457	+	0.321175i	−0.0344303	+	0.0159005i
$409$	17.4256			0.861640			0.430820	−	0.902438i	$-0.358224\pi$
$409$	17.4256			0.861640			0.430820	+	0.902438i	$0.358224\pi$
$410$		0			0
$411$	19.0732	+	19.0732i	0.940810	+	0.940810i
$412$	0.145854	+	5.47659i	0.00718573	+	0.269812i
$413$	25.4604			1.25283
$414$	13.8514	+	5.52256i	0.680758	+	0.271419i
$415$		0			0
$416$	12.1779	−	6.02239i	0.597073	−	0.295272i
$417$	−29.4219	−	29.4219i	−1.44080	−	1.44080i
$418$	−18.5898	+	7.99172i	−0.909257	+	0.390888i
$419$	11.7257	+	11.7257i	0.572837	+	0.572837i	0.932920	−	0.360083i	$-0.117252\pi$
$419$	11.7257	+	11.7257i	0.572837	+	0.572837i	−0.360083	+	0.932920i	$0.617252\pi$
$420$		0			0
$421$	−23.5406	+	23.5406i	−1.14730	+	1.14730i	−0.160216	+	0.987082i	$0.551219\pi$
$421$	−23.5406	+	23.5406i	−1.14730	+	1.14730i	−0.987082	+	0.160216i	$0.948781\pi$
$422$	11.8687	+	4.73206i	0.577759	+	0.230353i
$423$	−7.55728	+	7.55728i	−0.367447	+	0.367447i
$424$	−1.26522	+	3.43661i	−0.0614445	+	0.166896i
$425$		0			0
$426$	7.53608	−	3.23974i	0.365124	−	0.156966i
$427$		−	49.2335i		−	2.38258i
$428$	10.1273	+	9.60186i	0.489521	+	0.464123i
$429$	−16.4052	+	16.4052i	−0.792049	+	0.792049i
$430$		0			0
$431$			35.0243i			1.68706i	0.537079	+	0.843532i	$0.319528\pi$
$431$			35.0243i			1.68706i	−0.537079	+	0.843532i	$0.680472\pi$
$432$	5.20503	−	0.277441i	0.250427	−	0.0133484i
$433$	−10.1094	+	10.1094i	−0.485828	+	0.485828i	−0.906987	−	0.421159i	$-0.861624\pi$
$433$	−10.1094	+	10.1094i	−0.485828	+	0.485828i	0.421159	+	0.906987i	$0.361624\pi$
$434$	7.38449	+	2.94420i	0.354467	+	0.141326i
$435$		0			0
$436$	−0.0209147	−	0.785311i	−0.00100163	−	0.0376096i
$437$	11.3509			0.542985
$438$	−47.3605	−	18.8827i	−2.26297	−	0.902250i
$439$			22.6071i			1.07898i	0.841993	+	0.539488i	$0.181382\pi$
$439$			22.6071i			1.07898i	−0.841993	+	0.539488i	$0.818618\pi$
$440$		0			0
$441$		−	15.9923i		−	0.761540i
$442$	−0.133514	+	0.334872i	−0.00635061	+	0.0159282i
$443$	10.9178			0.518721			0.259360	−	0.965781i	$-0.416488\pi$
$443$	10.9178			0.518721			0.259360	+	0.965781i	$0.416488\pi$
$444$	9.37241	+	8.88614i	0.444795	+	0.421717i
$445$		0			0
$446$	3.18337	−	7.98436i	0.150737	−	0.378071i
$447$	−14.0638	+	14.0638i	−0.665195	+	0.665195i
$448$	−2.16993	−	27.1078i	−0.102520	−	1.28072i
$449$		−	28.8112i		−	1.35969i	−0.733358	−	0.679843i	$-0.762048\pi$
$449$		−	28.8112i		−	1.35969i	0.733358	−	0.679843i	$-0.237952\pi$
$450$		0			0
$451$	−4.57463	+	4.57463i	−0.215411	+	0.215411i
$452$	0.659318	+	24.7563i	0.0310117	+	1.16444i
$453$			10.5539i			0.495865i
$454$	−16.2552	−	37.8117i	−0.762893	−	1.77459i
$455$		0			0
$456$	24.7622	−	11.4356i	1.15960	−	0.535522i
$457$	−19.1653	+	19.1653i	−0.896513	+	0.896513i	−0.995126	−	0.0986128i	$-0.968559\pi$
$457$	−19.1653	+	19.1653i	−0.896513	+	0.896513i	0.0986128	+	0.995126i	$0.468559\pi$
$458$	−13.5848	+	34.0727i	−0.634778	+	1.59211i
$459$	−0.0978038	+	0.0978038i	−0.00456509	+	0.00456509i
$460$		0			0
$461$	4.43227	+	4.43227i	0.206431	+	0.206431i	0.802749	−	0.596317i	$-0.203370\pi$
$461$	4.43227	+	4.43227i	0.206431	+	0.206431i	−0.596317	+	0.802749i	$0.703370\pi$
$462$	18.3415	+	42.6648i	0.853324	+	1.98495i
$463$	20.1518	+	20.1518i	0.936534	+	0.936534i	0.998103	−	0.0615691i	$-0.0196105\pi$
$463$	20.1518	+	20.1518i	0.936534	+	0.936534i	−0.0615691	+	0.998103i	$0.519610\pi$
$464$	−16.6521	−	14.9667i	−0.773052	−	0.694811i
$465$		0			0
$466$	−1.08634	+	2.72469i	−0.0503236	+	0.126219i
$467$	3.89858			0.180405			0.0902025	−	0.995923i	$-0.471249\pi$
$467$	3.89858			0.180405			0.0902025	+	0.995923i	$0.471249\pi$
$468$	11.6022	−	12.2371i	0.536310	−	0.565658i
$469$	−25.5342	−	25.5342i	−1.17906	−	1.17906i
$470$		0			0
$471$	−51.7211			−2.38318
$472$	19.2327	−	8.88200i	0.885256	−	0.408827i
$473$	−10.2960	−	10.2960i	−0.473412	−	0.473412i
$474$	28.8623	−	12.4079i	1.32569	−	0.569912i
$475$		0			0
$476$	0.523671	+	0.496501i	0.0240024	+	0.0227571i
$477$			4.54548i			0.208123i
$478$	−7.00590	−	16.2967i	−0.320443	−	0.745392i
$479$	−9.85299			−0.450194			−0.225097	−	0.974336i	$-0.572270\pi$
$479$	−9.85299			−0.450194			−0.225097	+	0.974336i	$0.572270\pi$
$480$		0			0
$481$	6.07811			0.277138
$482$	8.31500	+	19.3418i	0.378738	+	0.880994i
$483$		−	26.0510i		−	1.18536i
$484$	−4.83797	−	4.58696i	−0.219908	−	0.208498i
$485$		0			0
$486$	−28.9718	+	12.4549i	−1.31419	+	0.564966i
$487$	13.9164	+	13.9164i	0.630611	+	0.630611i	0.948221	−	0.317610i	$-0.102880\pi$
$487$	13.9164	+	13.9164i	0.630611	+	0.630611i	−0.317610	+	0.948221i	$0.602880\pi$
$488$	−17.1754	−	37.1908i	−0.777492	−	1.68355i
$489$	−33.6392			−1.52122
$490$		0			0
$491$	2.39213	+	2.39213i	0.107955	+	0.107955i	0.759021	−	0.651066i	$-0.225678\pi$
$491$	2.39213	+	2.39213i	0.107955	+	0.107955i	−0.651066	+	0.759021i	$0.725678\pi$
$492$	5.99996	−	6.32829i	0.270499	−	0.285301i
$493$	0.594124			0.0267580
$494$	4.75384	−	11.9233i	0.213885	−	0.536456i
$495$		0			0
$496$	6.60531	−	0.352079i	0.296587	−	0.0158088i
$497$	−5.46408	−	5.46408i	−0.245098	−	0.245098i
$498$	15.8636	+	36.9008i	0.710865	+	1.65357i
$499$	9.87034	+	9.87034i	0.441857	+	0.441857i	0.892636	−	0.450779i	$-0.148854\pi$
$499$	9.87034	+	9.87034i	0.441857	+	0.441857i	−0.450779	+	0.892636i	$0.648854\pi$
$500$		0			0
$501$	30.1575	−	30.1575i	1.34734	−	1.34734i
$502$	3.98837	−	10.0034i	0.178010	−	0.446474i
$503$	−9.29035	+	9.29035i	−0.414236	+	0.414236i	−0.883211	−	0.468975i	$-0.844623\pi$
$503$	−9.29035	+	9.29035i	−0.414236	+	0.414236i	0.468975	+	0.883211i	$0.344623\pi$
$504$	−14.1521	−	30.6443i	−0.630384	−	1.36501i
$505$		0			0
$506$	6.35110	+	14.7735i	0.282341	+	0.656763i
$507$			18.4536i			0.819553i
$508$	−0.0511671	−	1.92124i	−0.00227017	−	0.0852413i
$509$	6.53818	−	6.53818i	0.289800	−	0.289800i	−0.547201	−	0.837001i	$-0.684307\pi$
$509$	6.53818	−	6.53818i	0.289800	−	0.289800i	0.837001	+	0.547201i	$0.184307\pi$
$510$		0			0
$511$			48.0301i			2.12473i
$512$	−11.0958	−	19.7201i	−0.490372	−	0.871513i
$513$	3.48236	−	3.48236i	0.153750	−	0.153750i
$514$	−2.87878	+	7.22040i	−0.126978	+	0.318478i
$515$		0			0
$516$	14.2429	+	13.5040i	0.627011	+	0.594480i
$517$	−11.5255			−0.506893
$518$	4.50588	−	11.3014i	0.197977	−	0.496555i
$519$			39.7445i			1.74459i
$520$		0			0
$521$		−	14.2961i		−	0.626324i	−0.949700	−	0.313162i	$-0.898612\pi$
$521$		−	14.2961i		−	0.626324i	0.949700	−	0.313162i	$-0.101388\pi$
$522$	−25.8143	−	10.2922i	−1.12986	−	0.450476i
$523$	−16.0319			−0.701027			−0.350513	−	0.936558i	$-0.613993\pi$
$523$	−16.0319			−0.701027			−0.350513	+	0.936558i	$0.613993\pi$
$524$	−0.409530	−	15.3772i	−0.0178904	−	0.671756i
$525$		0			0
$526$	−31.5187	−	12.5665i	−1.37428	−	0.547928i
$527$	−0.124115	+	0.124115i	−0.00540655	+	0.00540655i
$528$	28.7389	+	25.8302i	1.25070	+	1.12412i
$529$			13.9794i			0.607798i
$530$		0			0
$531$	18.5932	−	18.5932i	0.806875	−	0.806875i
$532$	−18.6456	−	17.6782i	−0.808390	−	0.766448i
$533$		−	4.10397i		−	0.177762i
$534$	−51.8458	+	22.2884i	−2.24359	+	0.964514i
$535$		0			0
$536$	−28.1961	−	10.3807i	−1.21789	−	0.448376i
$537$	39.7957	−	39.7957i	1.71731	−	1.71731i
$538$	−4.74631	−	1.89236i	−0.204628	−	0.0815854i
$539$	12.1949	−	12.1949i	0.525271	−	0.525271i
$540$		0			0
$541$	−14.3926	−	14.3926i	−0.618785	−	0.618785i	0.326435	−	0.945220i	$-0.394153\pi$
$541$	−14.3926	−	14.3926i	−0.618785	−	0.618785i	−0.945220	+	0.326435i	$0.894153\pi$
$542$	−4.33536	+	1.86376i	−0.186220	+	0.0800555i
$543$	−7.62178	−	7.62178i	−0.327082	−	0.327082i
$544$	0.568785	+	0.192369i	0.0243865	+	0.00824777i
$545$		0			0
$546$	−27.3648	−	10.9104i	−1.17111	−	0.466921i
$547$	11.6741			0.499148			0.249574	−	0.968356i	$-0.419709\pi$
$547$	11.6741			0.499148			0.249574	+	0.968356i	$0.419709\pi$
$548$	−0.562871	−	21.1349i	−0.0240447	−	0.902838i
$549$	−35.9541	−	35.9541i	−1.53448	−	1.53448i
$550$		0			0
$551$	−21.1541			−0.901197
$552$	−9.08801	−	19.6788i	−0.386811	−	0.837584i
$553$	−20.9268	−	20.9268i	−0.889898	−	0.889898i
$554$	−2.57340	−	5.98608i	−0.109333	−	0.254324i
$555$		0			0
$556$	0.868274	+	32.6023i	0.0368230	+	1.38264i
$557$			39.6712i			1.68092i	0.541873	+	0.840460i	$0.317715\pi$
$557$			39.6712i			1.68092i	−0.541873	+	0.840460i	$0.682285\pi$
$558$	7.54281	−	3.24264i	0.319313	−	0.137272i
$559$	9.23671			0.390671
$560$		0			0
$561$	−1.02537			−0.0432911
$562$	−28.7364	+	12.3537i	−1.21217	+	0.521110i
$563$		−	12.4534i		−	0.524850i	−0.964952	−	0.262425i	$-0.915478\pi$
$563$		−	12.4534i		−	0.524850i	0.964952	−	0.262425i	$-0.0845222\pi$
$564$	15.5302	−	0.413605i	0.653939	−	0.0174159i
$565$		0			0
$566$	6.06740	+	14.1136i	0.255032	+	0.593238i
$567$	17.3235	+	17.3235i	0.727519	+	0.727519i
$568$	−6.03371	−	2.22137i	−0.253169	−	0.0932066i
$569$	5.62622			0.235863			0.117932	−	0.993022i	$-0.462374\pi$
$569$	5.62622			0.235863			0.117932	+	0.993022i	$0.462374\pi$
$570$		0			0
$571$	23.1808	+	23.1808i	0.970086	+	0.970086i	0.999565	−	0.0294797i	$-0.00938505\pi$
$571$	23.1808	+	23.1808i	0.970086	+	0.970086i	−0.0294797	+	0.999565i	$0.509385\pi$
$572$	18.1785	−	0.484136i	0.760081	−	0.0202427i
$573$	−16.5132			−0.689848
$574$	−7.63076	−	3.04239i	−0.318502	−	0.126987i
$575$		0			0
$576$	−21.3808	−	18.2115i	−0.890869	−	0.758814i
$577$	25.6307	+	25.6307i	1.06702	+	1.06702i	0.997587	+	0.0694322i	$0.0221187\pi$
$577$	25.6307	+	25.6307i	1.06702	+	1.06702i	0.0694322	+	0.997587i	$0.477881\pi$
$578$	22.0725	−	9.48892i	0.918094	−	0.394687i
$579$	−28.3562	−	28.3562i	−1.17844	−	1.17844i
$580$		0			0
$581$	26.7552	−	26.7552i	1.10999	−	1.10999i
$582$	−23.7335	−	9.46259i	−0.983787	−	0.392237i
$583$	−3.46614	+	3.46614i	−0.143553	+	0.143553i
$584$	16.7555	+	36.2817i	0.693349	+	1.50135i
$585$		0			0
$586$	23.9147	−	10.2809i	0.987908	−	0.424700i
$587$		−	25.5579i		−	1.05489i	−0.849590	−	0.527444i	$-0.823151\pi$
$587$		−	25.5579i		−	1.05489i	0.849590	−	0.527444i	$-0.176849\pi$
$588$	−15.9945	+	16.8697i	−0.659602	+	0.695696i
$589$	4.41920	−	4.41920i	0.182090	−	0.182090i
$590$		0			0
$591$		−	64.0266i		−	2.63370i
$592$	−0.538831	−	10.1089i	−0.0221458	−	0.415474i
$593$	−2.96607	+	2.96607i	−0.121802	+	0.121802i	−0.765380	−	0.643578i	$-0.777449\pi$
$593$	−2.96607	+	2.96607i	−0.121802	+	0.121802i	0.643578	+	0.765380i	$0.277449\pi$
$594$	6.48088	+	2.58393i	0.265914	+	0.106020i
$595$		0			0
$596$	15.5840	−	0.415039i	0.638347	−	0.0170007i
$597$	−47.8629			−1.95890
$598$	−9.47559	−	3.77793i	−0.387486	−	0.154491i
$599$			5.14724i			0.210311i	0.994456	+	0.105155i	$0.0335340\pi$
$599$			5.14724i			0.210311i	−0.994456	+	0.105155i	$0.966466\pi$
$600$		0			0
$601$			33.5619i			1.36902i	0.729005	+	0.684509i	$0.239983\pi$
$601$			33.5619i			1.36902i	−0.729005	+	0.684509i	$0.760017\pi$
$602$	6.84745	−	17.1744i	0.279081	−	0.699976i
$603$	−37.2940			−1.51873
$604$	5.69163	−	6.00309i	0.231589	−	0.244262i
$605$		0			0
$606$	12.0411	−	30.2007i	0.489134	−	1.22682i
$607$	−3.29572	+	3.29572i	−0.133769	+	0.133769i	−0.770821	−	0.637052i	$-0.780154\pi$
$607$	−3.29572	+	3.29572i	−0.133769	+	0.133769i	0.637052	+	0.770821i	$0.280154\pi$
$608$	−20.2519	−	6.84943i	−0.821325	−	0.277781i
$609$			48.5501i			1.96735i
$610$		0			0
$611$	5.16986	−	5.16986i	0.209150	−	0.209150i
$612$	0.745008	−	0.0198413i	0.0301152	−	0.000802037i
$613$			0.261903i			0.0105781i	0.999986	+	0.00528907i	$0.00168357\pi$
$613$			0.261903i			0.0105781i	−0.999986	+	0.00528907i	$0.998316\pi$
$614$	3.69125	+	8.58633i	0.148967	+	0.346516i
$615$		0			0
$616$	12.5761	−	34.1593i	0.506704	−	1.37632i
$617$	12.1529	−	12.1529i	0.489259	−	0.489259i	−0.418813	−	0.908072i	$-0.637554\pi$
$617$	12.1529	−	12.1529i	0.489259	−	0.489259i	0.908072	+	0.418813i	$0.137554\pi$
$618$	3.66080	−	9.18181i	0.147259	−	0.369347i
$619$	12.1134	−	12.1134i	0.486877	−	0.486877i	−0.420442	−	0.907319i	$-0.638125\pi$
$619$	12.1134	−	12.1134i	0.486877	−	0.486877i	0.907319	+	0.420442i	$0.138125\pi$
$620$		0			0
$621$	−2.76747	−	2.76747i	−0.111055	−	0.111055i
$622$	−0.338534	−	0.787474i	−0.0135740	−	0.0315748i
$623$	37.5911	+	37.5911i	1.50606	+	1.50606i
$624$	−24.4774	+	1.30470i	−0.979880	+	0.0522300i
$625$		0			0
$626$	−14.3479	+	35.9867i	−0.573459	+	1.43832i
$627$	36.5089			1.45802
$628$	29.4191	+	27.8928i	1.17395	+	1.11304i
$629$	0.189949	+	0.189949i	0.00757377	+	0.00757377i
$630$		0			0
$631$	49.8568			1.98477			0.992384	−	0.123179i	$-0.0393090\pi$
$631$	49.8568			1.98477			0.992384	+	0.123179i	$0.0393090\pi$
$632$	−23.1084	−	8.50759i	−0.919204	−	0.338414i
$633$	−16.3013	−	16.3013i	−0.647917	−	0.647917i
$634$	−9.15093	+	3.93397i	−0.363430	+	0.156238i
$635$		0			0
$636$	4.54609	−	4.79486i	0.180264	−	0.190129i
$637$			10.9402i			0.433467i
$638$	−11.8363	−	27.5328i	−0.468604	−	1.09003i
$639$	−7.98059			−0.315707
$640$		0			0
$641$	−4.10036			−0.161954			−0.0809772	−	0.996716i	$-0.525804\pi$
$641$	−4.10036			−0.161954			−0.0809772	+	0.996716i	$0.525804\pi$
$642$	−9.94459	−	23.1324i	−0.392482	−	0.912964i
$643$		−	18.7451i		−	0.739233i	−0.929184	−	0.369617i	$-0.879489\pi$
$643$		−	18.7451i		−	0.739233i	0.929184	−	0.369617i	$-0.120511\pi$
$644$	−14.0491	+	14.8179i	−0.553611	+	0.583906i
$645$		0			0
$646$	0.521184	−	0.224056i	0.0205057	−	0.00881537i
$647$	−5.46529	−	5.46529i	−0.214863	−	0.214863i	0.591467	−	0.806330i	$-0.298549\pi$
$647$	−5.46529	−	5.46529i	−0.214863	−	0.214863i	−0.806330	+	0.591467i	$0.798549\pi$
$648$	19.1295	+	7.04270i	0.751477	+	0.276663i
$649$	28.3563			1.11308
$650$		0			0
$651$	−10.1424	−	10.1424i	−0.397510	−	0.397510i
$652$	19.1341	+	18.1414i	0.749350	+	0.710471i
$653$	33.9219			1.32747			0.663733	−	0.747970i	$-0.268971\pi$
$653$	33.9219			1.32747			0.663733	+	0.747970i	$0.268971\pi$
$654$	−0.524937	+	1.31662i	−0.0205267	+	0.0514838i
$655$		0			0
$656$	−6.82559	+	0.363821i	−0.266495	+	0.0142048i
$657$	35.0753	+	35.0753i	1.36842	+	1.36842i
$658$	−5.78007	−	13.4452i	−0.225331	−	0.524149i
$659$	−26.4961	−	26.4961i	−1.03214	−	1.03214i	−0.999466	−	0.0326746i	$-0.989598\pi$
$659$	−26.4961	−	26.4961i	−1.03214	−	1.03214i	−0.0326746	−	0.999466i	$-0.510402\pi$
$660$		0			0
$661$	10.6974	−	10.6974i	0.416081	−	0.416081i	−0.467769	−	0.883851i	$-0.654942\pi$
$661$	10.6974	−	10.6974i	0.416081	−	0.416081i	0.883851	+	0.467769i	$0.154942\pi$
$662$	9.79759	−	24.5738i	0.380794	−	0.955087i
$663$	0.459936	−	0.459936i	0.0178624	−	0.0178624i
$664$	10.8771	−	29.5444i	0.422112	−	1.14655i
$665$		0			0
$666$	−4.96262	−	11.5437i	−0.192297	−	0.447309i
$667$			16.8114i			0.650941i
$668$	−33.4174	+	0.889984i	−1.29296	+	0.0344345i
$669$	−10.9663	+	10.9663i	−0.423980	+	0.423980i
$670$		0			0
$671$		−	54.8333i		−	2.11682i
$672$	−15.7199	+	46.4795i	−0.606408	+	1.79299i
$673$	6.70854	−	6.70854i	0.258595	−	0.258595i	−0.565887	−	0.824483i	$-0.691466\pi$
$673$	6.70854	−	6.70854i	0.258595	−	0.258595i	0.824483	+	0.565887i	$0.191466\pi$
$674$	5.72774	−	14.3660i	0.220624	−	0.553358i
$675$		0			0
$676$	9.95188	−	10.4965i	0.382764	−	0.403710i
$677$	−13.1970			−0.507200			−0.253600	−	0.967309i	$-0.581615\pi$
$677$	−13.1970			−0.507200			−0.253600	+	0.967309i	$0.581615\pi$
$678$	16.5482	−	41.5053i	0.635530	−	1.59400i
$679$			24.0691i			0.923686i
$680$		0			0
$681$			74.2591i			2.84561i
$682$	8.22440	+	3.27908i	0.314928	+	0.125562i
$683$	37.9089			1.45054			0.725272	−	0.688462i	$-0.241714\pi$
$683$	37.9089			1.45054			0.725272	+	0.688462i	$0.241714\pi$
$684$	−26.5265	+	0.706462i	−1.01427	+	0.0270122i
$685$		0			0
$686$	−10.9168	−	4.35252i	−0.416804	−	0.166180i
$687$	46.7978	−	46.7978i	1.78545	−	1.78545i
$688$	−0.818844	−	15.3622i	−0.0312181	−	0.585679i
$689$		−	3.10952i		−	0.118463i
$690$		0			0
$691$	20.8280	−	20.8280i	0.792335	−	0.792335i	−0.189538	−	0.981873i	$-0.560699\pi$
$691$	20.8280	−	20.8280i	0.792335	−	0.792335i	0.981873	+	0.189538i	$0.0606991\pi$
$692$	21.4339	−	22.6068i	0.814794	−	0.859382i
$693$		−	45.1813i		−	1.71630i
$694$	−14.8043	+	6.36433i	−0.561962	+	0.241586i
$695$		0			0
$696$	16.9370	+	36.6745i	0.641994	+	1.39015i
$697$	0.128255	−	0.128255i	0.00485799	−	0.00485799i
$698$	22.3878	+	8.92605i	0.847392	+	0.337856i
$699$	3.74227	−	3.74227i	0.141546	−	0.141546i
$700$		0			0
$701$	19.9053	+	19.9053i	0.751812	+	0.751812i	0.974817	−	0.223005i	$-0.0715868\pi$
$701$	19.9053	+	19.9053i	0.751812	+	0.751812i	−0.223005	+	0.974817i	$0.571587\pi$
$702$	−4.06609	+	1.74800i	−0.153465	+	0.0659741i
$703$	−6.76326	−	6.76326i	−0.255081	−	0.255081i
$704$	−2.41674	−	30.1910i	−0.0910844	−	1.13787i
$705$		0			0
$706$	12.0361	+	4.79882i	0.452986	+	0.180606i
$707$	−30.6277			−1.15187
$708$	−38.2089	+	1.01759i	−1.43598	+	0.0382435i
$709$	8.57112	+	8.57112i	0.321895	+	0.321895i	0.849494	−	0.527599i	$-0.176908\pi$
$709$	8.57112	+	8.57112i	0.321895	+	0.321895i	−0.527599	+	0.849494i	$0.676908\pi$
$710$		0			0
$711$	−30.5647			−1.14627
$712$	41.5100	+	15.2823i	1.55565	+	0.572729i
$713$	−3.51199	−	3.51199i	−0.131525	−	0.131525i
$714$	−0.514224	−	1.19615i	−0.0192443	−	0.0447649i
$715$		0			0
$716$	−44.0975	+	1.17442i	−1.64800	+	0.0438901i
$717$			32.0053i			1.19526i
$718$	4.22382	−	1.81581i	0.157631	−	0.0677655i
$719$	33.1900			1.23778			0.618889	−	0.785478i	$-0.287583\pi$
$719$	33.1900			1.23778			0.618889	+	0.785478i	$0.287583\pi$
$720$		0			0
$721$	−9.31162			−0.346783
$722$	6.12852	−	2.63464i	0.228080	−	0.0980511i
$723$		−	37.9857i		−	1.41270i
$724$	0.224927	+	8.44566i	0.00835936	+	0.313880i
$725$		0			0
$726$	4.75069	+	11.0507i	0.176315	+	0.410131i
$727$	−5.06503	−	5.06503i	−0.187852	−	0.187852i	0.606915	−	0.794767i	$-0.292407\pi$
$727$	−5.06503	−	5.06503i	−0.187852	−	0.187852i	−0.794767	+	0.606915i	$0.792407\pi$
$728$	9.68131	+	20.9635i	0.358813	+	0.776958i
$729$	35.2770			1.30655
$730$		0			0
$731$	0.288660	+	0.288660i	0.0106765	+	0.0106765i
$732$	1.96775	+	73.8856i	0.0727300	+	2.73089i
$733$	−43.0744			−1.59099			−0.795494	−	0.605961i	$-0.792789\pi$
$733$	−43.0744			−1.59099			−0.795494	+	0.605961i	$0.792789\pi$
$734$	−23.6009	−	9.40969i	−0.871124	−	0.347318i
$735$		0			0
$736$	−5.44332	+	16.0944i	−0.200643	+	0.593249i
$737$	−28.4384	−	28.4384i	−1.04754	−	1.04754i
$738$	−7.79436	+	3.35078i	−0.286914	+	0.123344i
$739$	−11.3838	−	11.3838i	−0.418762	−	0.418762i	0.466015	−	0.884777i	$-0.345689\pi$
$739$	−11.3838	−	11.3838i	−0.418762	−	0.418762i	−0.884777	+	0.466015i	$0.845689\pi$
$740$		0			0
$741$	−16.3763	+	16.3763i	−0.601599	+	0.601599i
$742$	−5.78173	−	2.30518i	−0.212254	−	0.0846258i
$743$	−1.54795	+	1.54795i	−0.0567888	+	0.0567888i	−0.734931	−	0.678142i	$-0.762785\pi$
$743$	−1.54795	+	1.54795i	−0.0567888	+	0.0567888i	0.678142	+	0.734931i	$0.262785\pi$
$744$	−11.1997	−	4.12328i	−0.410601	−	0.151167i
$745$		0			0
$746$	−28.5523	+	12.2746i	−1.04537	+	0.449404i
$747$		−	39.0774i		−	1.42977i
$748$	0.583233	+	0.552973i	0.0213251	+	0.0202187i
$749$	−16.7723	+	16.7723i	−0.612847	+	0.612847i
$750$		0			0
$751$		−	1.49244i		−	0.0544600i	−0.999629	−	0.0272300i	$-0.991331\pi$
$751$		−	1.49244i		−	0.0544600i	0.999629	−	0.0272300i	$-0.00866865\pi$
$752$	−9.05667	−	8.14005i	−0.330263	−	0.296837i
$753$	−13.7394	+	13.7394i	−0.500690	+	0.500690i
$754$	17.6593	+	7.04078i	0.643113	+	0.256410i
$755$		0			0
$756$	0.235861	+	8.85618i	0.00857817	+	0.322096i
$757$	22.7030			0.825154			0.412577	−	0.910923i	$-0.364629\pi$
$757$	22.7030			0.825154			0.412577	+	0.910923i	$0.364629\pi$
$758$	31.7015	+	12.6394i	1.15145	+	0.459085i
$759$		−	29.0140i		−	1.05314i
$760$		0			0
$761$		−	33.6599i		−	1.22017i	−0.792335	−	0.610086i	$-0.791135\pi$
$761$		−	33.6599i		−	1.22017i	0.792335	−	0.610086i	$-0.208865\pi$
$762$	−1.28424	+	3.22107i	−0.0465232	+	0.116687i
$763$	1.33523			0.0483386
$764$	9.39275	+	8.90543i	0.339818	+	0.322187i
$765$		0			0
$766$	0.168923	−	0.423683i	0.00610343	−	0.0153083i
$767$	−12.7194	+	12.7194i	−0.459271	+	0.459271i
$768$	4.33989	+	40.5944i	0.156602	+	1.46482i
$769$			10.1943i			0.367615i	0.982962	+	0.183808i	$0.0588423\pi$
$769$			10.1943i			0.367615i	−0.982962	+	0.183808i	$0.941158\pi$
$770$		0			0
$771$	9.91699	−	9.91699i	0.357152	−	0.357152i
$772$	0.836823	+	31.4213i	0.0301179	+	1.13088i
$773$			7.34419i			0.264152i	0.991240	+	0.132076i	$0.0421643\pi$
$773$			7.34419i			0.264152i	−0.991240	+	0.132076i	$0.957836\pi$
$774$	−7.54153	−	17.5426i	−0.271075	−	0.630556i
$775$		0			0
$776$	8.39662	+	18.1817i	0.301421	+	0.652684i
$777$	−15.5221	+	15.5221i	−0.556853	+	0.556853i
$778$	−10.5947	+	26.5730i	−0.379838	+	0.952688i
$779$	−4.56658	+	4.56658i	−0.163615	+	0.163615i
$780$		0			0
$781$	−6.08556	−	6.08556i	−0.217759	−	0.217759i
$782$	−0.178060	−	0.414191i	−0.00636741	−	0.0148114i
$783$	5.15763	+	5.15763i	0.184319	+	0.184319i
$784$	18.1954	−	0.969861i	0.649837	−	0.0346379i
$785$		0			0
$786$	−10.2788	+	25.7807i	−0.366633	+	0.919568i
$787$	−29.4359			−1.04928			−0.524638	−	0.851326i	$-0.675799\pi$
$787$	−29.4359			−1.04928			−0.524638	+	0.851326i	$0.675799\pi$
$788$	−34.5291	+	36.4186i	−1.23005	+	1.29736i
$789$	43.2900	+	43.2900i	1.54116	+	1.54116i
$790$		0			0
$791$	−42.0921			−1.49662
$792$	−15.7617	−	34.1298i	−0.560069	−	1.21275i
$793$	24.5959	+	24.5959i	0.873425	+	0.873425i
$794$	6.64715	−	2.85760i	0.235899	−	0.101412i
$795$		0			0
$796$	27.2246	+	25.8121i	0.964950	+	0.914886i
$797$		−	50.3934i		−	1.78503i	−0.451022	−	0.892513i	$-0.648940\pi$
$797$		−	50.3934i		−	1.78503i	0.451022	−	0.892513i	$-0.351060\pi$
$798$	18.3092	+	42.5897i	0.648140	+	1.50766i
$799$	0.323131			0.0114315
$800$		0			0
$801$	54.9039			1.93993
$802$	−9.09514	−	21.1565i	−0.321161	−	0.747062i
$803$			53.4930i			1.88773i
$804$	39.3401	+	37.2990i	1.38742	+	1.31544i
$805$		0			0
$806$	−5.15996	+	2.21826i	−0.181752	+	0.0781348i
$807$	6.51890	+	6.51890i	0.229476	+	0.229476i
$808$	−23.1360	+	10.6846i	−0.813922	+	0.375884i
$809$	27.1588			0.954851			0.477426	−	0.878672i	$-0.341570\pi$
$809$	27.1588			0.954851			0.477426	+	0.878672i	$0.341570\pi$
$810$		0			0
$811$	−11.5416	−	11.5416i	−0.405280	−	0.405280i	0.474809	−	0.880089i	$-0.342517\pi$
$811$	−11.5416	−	11.5416i	−0.405280	−	0.405280i	−0.880089	+	0.474809i	$0.842517\pi$
$812$	26.1827	−	27.6155i	0.918833	−	0.969113i
$813$	8.51429			0.298609
$814$	5.01838	−	12.5868i	0.175894	−	0.441168i
$815$		0			0
$816$	−0.805726	−	0.724178i	−0.0282060	−	0.0253513i
$817$	−10.2779	−	10.2779i	−0.359579	−	0.359579i
$818$	9.73292	+	22.6401i	0.340304	+	0.791591i
$819$	20.2664	+	20.2664i	0.708166	+	0.708166i
$820$		0			0
$821$	−20.2900	+	20.2900i	−0.708126	+	0.708126i	−0.966141	−	0.258015i	$-0.916932\pi$
$821$	−20.2900	+	20.2900i	−0.708126	+	0.708126i	0.258015	+	0.966141i	$0.416932\pi$
$822$	−14.1275	+	35.4338i	−0.492754	+	1.23590i
$823$	31.4540	−	31.4540i	1.09642	−	1.09642i	0.101592	−	0.994826i	$-0.467606\pi$
$823$	31.4540	−	31.4540i	1.09642	−	1.09642i	0.994826	−	0.101592i	$-0.0323936\pi$
$824$	−7.03395	+	3.24840i	−0.245039	+	0.113164i
$825$		0			0
$826$	14.2207	+	33.0793i	0.494802	+	1.15098i
$827$		−	15.3304i		−	0.533090i	−0.963822	−	0.266545i	$-0.914118\pi$
$827$		−	15.3304i		−	0.533090i	0.963822	−	0.266545i	$-0.0858822\pi$
$828$	0.561433	+	21.0809i	0.0195111	+	0.732611i
$829$	0.896046	−	0.896046i	0.0311210	−	0.0311210i	−0.691375	−	0.722496i	$-0.742995\pi$
$829$	0.896046	−	0.896046i	0.0311210	−	0.0311210i	0.722496	+	0.691375i	$0.242995\pi$
$830$		0			0
$831$			11.7562i			0.407817i
$832$	14.6264	+	12.4583i	0.507080	+	0.431915i
$833$	−0.341897	+	0.341897i	−0.0118460	+	0.0118460i
$834$	21.7928	−	54.6595i	0.754623	−	1.89270i
$835$		0			0
$836$	−20.7664	−	19.6889i	−0.718220	−	0.680956i
$837$	−2.15491			−0.0744845
$838$	−8.68522	+	21.7838i	−0.300026	+	0.752508i
$839$			48.1891i			1.66367i	0.555021	+	0.831837i	$0.312710\pi$
$839$			48.1891i			1.66367i	−0.555021	+	0.831837i	$0.687290\pi$
$840$		0			0
$841$		−	2.33080i		−	0.0803723i
$842$	−43.7333	−	17.4365i	−1.50715	−	0.600902i
$843$	56.4359			1.94376
$844$	0.481069	+	18.0634i	0.0165591	+	0.621767i
$845$		0			0
$846$	−14.0398	−	5.59768i	−0.482698	−	0.192452i
$847$	8.01241	−	8.01241i	0.275310	−	0.275310i
$848$	−5.17166	+	0.275662i	−0.177596	+	0.00946628i
$849$		−	27.7179i		−	0.951277i
$850$		0			0
$851$	−5.37484	+	5.37484i	−0.184247	+	0.184247i
$852$	8.41843	+	7.98166i	0.288411	+	0.273447i
$853$		−	13.7426i		−	0.470537i	−0.971930	−	0.235268i	$-0.924403\pi$
$853$		−	13.7426i		−	0.470537i	0.971930	−	0.235268i	$-0.0755969\pi$
$854$	63.9663	−	27.4990i	2.18888	−	0.940996i
$855$		0			0
$856$	−6.81862	+	18.5208i	−0.233056	+	0.633029i
$857$	−13.4366	+	13.4366i	−0.458986	+	0.458986i	−0.898323	−	0.439336i	$-0.855214\pi$
$857$	−13.4366	+	13.4366i	−0.458986	+	0.458986i	0.439336	+	0.898323i	$0.355214\pi$
$858$	−30.4773	−	12.1513i	−1.04048	−	0.414839i
$859$	−7.00719	+	7.00719i	−0.239082	+	0.239082i	−0.816470	−	0.577388i	$-0.804072\pi$
$859$	−7.00719	+	7.00719i	−0.239082	+	0.239082i	0.577388	+	0.816470i	$0.304072\pi$
$860$		0			0
$861$	10.4806	+	10.4806i	0.357178	+	0.357178i
$862$	−45.5051	+	19.5626i	−1.54991	+	0.666304i
$863$	−41.4708	−	41.4708i	−1.41168	−	1.41168i	−0.748123	−	0.663560i	$-0.769045\pi$
$863$	−41.4708	−	41.4708i	−1.41168	−	1.41168i	−0.663560	−	0.748123i	$-0.730955\pi$
$864$	3.26769	+	6.60763i	0.111169	+	0.224796i
$865$		0			0
$866$	−18.7811	−	7.48806i	−0.638209	−	0.254455i
$867$	−43.3486			−1.47219
$868$	0.299313	+	11.2387i	0.0101593	+	0.381466i
$869$	−23.3070	−	23.3070i	−0.790636	−	0.790636i
$870$		0			0
$871$	25.5125			0.864458
$872$	1.00863	−	0.465802i	0.0341564	−	0.0157741i
$873$	17.5771	+	17.5771i	0.594894	+	0.594894i
$874$	6.33993	+	14.7475i	0.214451	+	0.498842i
$875$		0			0
$876$	−1.91965	−	72.0796i	−0.0648588	−	2.43534i
$877$			5.34168i			0.180376i	0.995925	+	0.0901879i	$0.0287468\pi$
$877$			5.34168i			0.180376i	−0.995925	+	0.0901879i	$0.971253\pi$
$878$	−29.3721	+	12.6270i	−0.991259	+	0.426141i
$879$	−46.9666			−1.58414
$880$		0			0
$881$	−45.9723			−1.54885			−0.774423	−	0.632668i	$-0.781960\pi$
$881$	−45.9723			−1.54885			−0.774423	+	0.632668i	$0.781960\pi$
$882$	20.7779	−	8.93240i	0.699630	−	0.300769i
$883$			2.64739i			0.0890918i	0.999007	+	0.0445459i	$0.0141841\pi$
$883$			2.64739i			0.0890918i	−0.999007	+	0.0445459i	$0.985816\pi$
$884$	−0.509653	+	0.0135732i	−0.0171415	+	0.000456518i
$885$		0			0
$886$	6.09806	+	14.1849i	0.204868	+	0.476551i
$887$	−3.87171	−	3.87171i	−0.129999	−	0.129999i	0.639113	−	0.769113i	$-0.279301\pi$
$887$	−3.87171	−	3.87171i	−0.129999	−	0.129999i	−0.769113	+	0.639113i	$0.779301\pi$
$888$	−6.31037	+	17.1403i	−0.211762	+	0.575191i
$889$	3.26661			0.109558
$890$		0			0
$891$	19.2939	+	19.2939i	0.646369	+	0.646369i
$892$	12.1517	−	0.323627i	0.406868	−	0.0108358i
$893$	−11.5053			−0.385009
$894$	−26.1275	−	10.4171i	−0.873834	−	0.348399i
$895$		0			0
$896$	34.0076	−	17.9601i	1.13611	−	0.600005i
$897$	13.0144	+	13.0144i	0.434539	+	0.434539i
$898$	37.4328	−	16.0923i	1.24915	−	0.537006i
$899$	6.54516	+	6.54516i	0.218293	+	0.218293i
$900$		0			0
$901$	0.0971768	−	0.0971768i	0.00323743	−	0.00323743i
$902$	−8.49868	−	3.38843i	−0.282975	−	0.112822i
$903$	−23.5885	+	23.5885i	−0.784975	+	0.784975i
$904$	−31.7962	+	14.6840i	−1.05752	+	0.488384i
$905$		0			0
$906$	−13.7121	+	5.89479i	−0.455553	+	0.195841i
$907$		−	26.2062i		−	0.870163i	−0.900391	−	0.435081i	$-0.856720\pi$
$907$		−	26.2062i		−	0.870163i	0.900391	−	0.435081i	$-0.143280\pi$
$908$	40.0473	−	42.2388i	1.32902	−	1.40174i
$909$	−22.3667	+	22.3667i	−0.741856	+	0.741856i
$910$		0			0
$911$		−	24.2898i		−	0.804757i	−0.915473	−	0.402378i	$-0.868184\pi$
$911$		−	24.2898i		−	0.804757i	0.915473	−	0.402378i	$-0.131816\pi$
$912$	28.6884	+	25.7848i	0.949966	+	0.853820i
$913$	29.7983	−	29.7983i	0.986181	−	0.986181i
$914$	−35.6049	−	14.1957i	−1.17771	−	0.469553i
$915$		0			0
$916$	−51.8564	+	1.38106i	−1.71339	+	0.0456314i
$917$	26.1452			0.863391
$918$	−0.181698	−	0.0724433i	−0.00599694	−	0.00239099i
$919$		−	41.1294i		−	1.35673i	−0.734723	−	0.678367i	$-0.762688\pi$
$919$		−	41.1294i		−	1.35673i	0.734723	−	0.678367i	$-0.237312\pi$
$920$		0			0
$921$		−	16.8629i		−	0.555650i
$922$	−3.28298	+	8.23420i	−0.108119	+	0.271179i
$923$	5.45944			0.179700
$924$	−45.1874	+	47.6601i	−1.48656	+	1.56790i
$925$		0			0
$926$	−14.9265	+	37.4377i	−0.490514	+	1.23028i
$927$	−6.80006	+	6.80006i	−0.223343	+	0.223343i
$928$	10.1445	−	29.9946i	0.333009	−	0.984620i
$929$		−	43.4799i		−	1.42653i	−0.700894	−	0.713265i	$-0.747215\pi$
$929$		−	43.4799i		−	1.42653i	0.700894	−	0.713265i	$-0.252785\pi$
$930$		0			0
$931$	12.1734	−	12.1734i	0.398968	−	0.398968i
$932$	−4.14680	+	0.110439i	−0.135833	+	0.00361754i
$933$			1.54653i			0.0506313i
$934$	2.17752	+	5.06521i	0.0712507	+	0.165739i
$935$		0			0
$936$	22.3792	+	8.23911i	0.731487	+	0.269304i
$937$	13.0565	−	13.0565i	0.426537	−	0.426537i	−0.460910	−	0.887447i	$-0.652477\pi$
$937$	13.0565	−	13.0565i	0.426537	−	0.426537i	0.887447	+	0.460910i	$0.152477\pi$
$938$	18.9132	−	47.4370i	0.617537	−	1.54887i
$939$	49.4266	−	49.4266i	1.61298	−	1.61298i
$940$		0			0
$941$	−5.53494	−	5.53494i	−0.180434	−	0.180434i	0.611111	−	0.791545i	$-0.290723\pi$
$941$	−5.53494	−	5.53494i	−0.180434	−	0.180434i	−0.791545	+	0.611111i	$0.790723\pi$
$942$	−28.8884	−	67.1982i	−0.941235	−	2.18944i
$943$	3.62911	+	3.62911i	0.118180	+	0.118180i
$944$	22.2821	+	20.0270i	0.725222	+	0.651822i
$945$		0			0
$946$	7.62627	−	19.1278i	0.247951	−	0.621898i
$947$	31.6905			1.02980			0.514902	−	0.857249i	$-0.327828\pi$
$947$	31.6905			1.02980			0.514902	+	0.857249i	$0.327828\pi$
$948$	32.2416	+	30.5688i	1.04716	+	0.992830i
$949$	−23.9947	−	23.9947i	−0.778900	−	0.778900i
$950$		0			0
$951$	17.9717			0.582772
$952$	−0.352583	+	0.957692i	−0.0114273	+	0.0310390i
$953$	2.85543	+	2.85543i	0.0924965	+	0.0924965i	0.751841	−	0.659344i	$-0.229166\pi$
$953$	2.85543	+	2.85543i	0.0924965	+	0.0924965i	−0.659344	+	0.751841i	$0.729166\pi$
$954$	−5.90568	+	2.53884i	−0.191204	+	0.0821981i
$955$		0			0
$956$	17.2602	−	18.2047i	0.558235	−	0.588783i
$957$			54.0722i			1.74791i
$958$	−5.50331	−	12.8014i	−0.177804	−	0.413595i
$959$	35.9348			1.16039
$960$		0			0
$961$	28.2654			0.911786
$962$	3.39488	+	7.89694i	0.109455	+	0.254608i
$963$			24.4969i			0.789401i
$964$	−20.4854	+	21.6064i	−0.659790	+	0.695895i
$965$		0			0
$966$	33.8465	−	14.5506i	1.08899	−	0.468156i
$967$	40.1144	+	40.1144i	1.28999	+	1.28999i	0.934790	+	0.355202i	$0.115588\pi$
$967$	40.1144	+	40.1144i	1.28999	+	1.28999i	0.355202	+	0.934790i	$0.384412\pi$
$968$	3.25737	−	8.84771i	0.104696	−	0.284376i
$969$	−1.02356			−0.0328816
$970$		0			0
$971$	−17.3439	−	17.3439i	−0.556592	−	0.556592i	0.371743	−	0.928335i	$-0.378760\pi$
$971$	−17.3439	−	17.3439i	−0.556592	−	0.556592i	−0.928335	+	0.371743i	$0.878760\pi$
$972$	−32.3639	−	30.6848i	−1.03807	−	0.984214i
$973$	−55.4322			−1.77708
$974$	−10.3079	+	25.8536i	−0.330285	+	0.828404i
$975$		0			0
$976$	38.7267	−	43.0876i	1.23961	−	1.37920i
$977$	12.2234	+	12.2234i	0.391060	+	0.391060i	0.875065	−	0.484005i	$-0.160818\pi$
$977$	12.2234	+	12.2234i	0.391060	+	0.391060i	−0.484005	+	0.875065i	$0.660818\pi$
$978$	−18.7889	−	43.7055i	−0.600804	−	1.39755i
$979$	41.8667	+	41.8667i	1.33807	+	1.33807i
$980$		0			0
$981$	0.975089	−	0.975089i	0.0311322	−	0.0311322i
$982$	−1.77185	+	4.44406i	−0.0565421	+	0.141816i
$983$	−13.6091	+	13.6091i	−0.434063	+	0.434063i	−0.890008	−	0.455945i	$-0.849301\pi$
$983$	−13.6091	+	13.6091i	−0.434063	+	0.434063i	0.455945	+	0.890008i	$0.349301\pi$
$984$	11.5732	+	4.26079i	0.368940	+	0.135829i
$985$		0			0
$986$	0.331843	+	0.771911i	0.0105680	+	0.0245827i
$987$			26.4053i			0.840491i
$988$	18.1465	−	0.483284i	0.577317	−	0.0153753i
$989$	−8.16797	+	8.16797i	−0.259726	+	0.259726i
$990$		0			0
$991$			52.9400i			1.68169i	0.541273	+	0.840847i	$0.317942\pi$
$991$			52.9400i			1.68169i	−0.541273	+	0.840847i	$0.682058\pi$
$992$	4.14678	+	8.38525i	0.131660	+	0.266232i
$993$	−33.7513	+	33.7513i	−1.07107	+	1.07107i
$994$	4.04725	−	10.1511i	0.128371	−	0.321973i
$995$		0			0
$996$	−39.0827	+	41.2213i	−1.23838	+	1.30615i
$997$	−3.67381			−0.116351			−0.0581754	−	0.998306i	$-0.518528\pi$
$997$	−3.67381			−0.116351			−0.0581754	+	0.998306i	$0.518528\pi$
$998$	−7.31097	+	18.3370i	−0.231425	+	0.580446i
$999$			3.29792i			0.104342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.j.d.307.6		18
4.3	odd	2		1600.2.j.d.1007.8		18
5.2	odd	4		80.2.s.b.3.2	yes	18
5.3	odd	4		400.2.s.d.243.8		18
5.4	even	2		80.2.j.b.67.4	yes	18
15.2	even	4		720.2.z.g.163.8		18
15.14	odd	2		720.2.bd.g.307.6		18
16.5	even	4		1600.2.s.d.207.2		18
16.11	odd	4		400.2.s.d.107.8		18
20.3	even	4		1600.2.s.d.943.2		18
20.7	even	4		320.2.s.b.303.8		18
20.19	odd	2		320.2.j.b.47.2		18
40.19	odd	2		640.2.j.c.607.8		18
40.27	even	4		640.2.s.c.223.2		18
40.29	even	2		640.2.j.d.607.2		18
40.37	odd	4		640.2.s.d.223.8		18
80.19	odd	4		640.2.s.d.287.8		18
80.27	even	4		80.2.j.b.43.4	✓	18
80.29	even	4		640.2.s.c.287.2		18
80.37	odd	4		320.2.j.b.143.8		18
80.43	even	4	inner	400.2.j.d.43.6		18
80.53	odd	4		1600.2.j.d.143.2		18
80.59	odd	4		80.2.s.b.27.2	yes	18
80.67	even	4		640.2.j.d.543.8		18
80.69	even	4		320.2.s.b.207.8		18
80.77	odd	4		640.2.j.c.543.2		18
240.59	even	4		720.2.z.g.667.8		18
240.107	odd	4		720.2.bd.g.523.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.4	✓	18	80.27	even	4
80.2.j.b.67.4	yes	18	5.4	even	2
80.2.s.b.3.2	yes	18	5.2	odd	4
80.2.s.b.27.2	yes	18	80.59	odd	4
320.2.j.b.47.2		18	20.19	odd	2
320.2.j.b.143.8		18	80.37	odd	4
320.2.s.b.207.8		18	80.69	even	4
320.2.s.b.303.8		18	20.7	even	4
400.2.j.d.43.6		18	80.43	even	4	inner
400.2.j.d.307.6		18	1.1	even	1	trivial
400.2.s.d.107.8		18	16.11	odd	4
400.2.s.d.243.8		18	5.3	odd	4
640.2.j.c.543.2		18	80.77	odd	4
640.2.j.c.607.8		18	40.19	odd	2
640.2.j.d.543.8		18	80.67	even	4
640.2.j.d.607.2		18	40.29	even	2
640.2.s.c.223.2		18	40.27	even	4
640.2.s.c.287.2		18	80.29	even	4
640.2.s.d.223.8		18	40.37	odd	4
640.2.s.d.287.8		18	80.19	odd	4
720.2.z.g.163.8		18	15.2	even	4
720.2.z.g.667.8		18	240.59	even	4
720.2.bd.g.307.6		18	15.14	odd	2
720.2.bd.g.523.6		18	240.107	odd	4
1600.2.j.d.143.2		18	80.53	odd	4
1600.2.j.d.1007.8		18	4.3	odd	2
1600.2.s.d.207.2		18	16.5	even	4
1600.2.s.d.943.2		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)

\(f(q)\)	\(=\)	\(q+(0.558542 + 1.29924i) q^{2} -2.55161i q^{3} +(-1.37606 + 1.45136i) q^{4} +(3.31516 - 1.42518i) q^{6} +(-2.40368 - 2.40368i) q^{7} +(-2.65426 - 0.977191i) q^{8} -3.51070 q^{9} +O(q^{10})\)	\(q+(0.558542 + 1.29924i) q^{2} -2.55161i q^{3} +(-1.37606 + 1.45136i) q^{4} +(3.31516 - 1.42518i) q^{6} +(-2.40368 - 2.40368i) q^{7} +(-2.65426 - 0.977191i) q^{8} -3.51070 q^{9} +(-2.67707 - 2.67707i) q^{11} +(3.70331 + 3.51117i) q^{12} +2.40164 q^{13} +(1.78040 - 4.46551i) q^{14} +(-0.212908 - 3.99433i) q^{16} +(0.0750544 + 0.0750544i) q^{17} +(-1.96087 - 4.56125i) q^{18} +(-2.67236 - 2.67236i) q^{19} +(-6.13324 + 6.13324i) q^{21} +(1.98291 - 4.97342i) q^{22} +(-2.12375 + 2.12375i) q^{23} +(-2.49341 + 6.77263i) q^{24} +(1.34141 + 3.12031i) q^{26} +1.30310i q^{27} +(6.79621 - 0.180999i) q^{28} +(3.95795 - 3.95795i) q^{29} +1.65367i q^{31} +(5.07068 - 2.50762i) q^{32} +(-6.83083 + 6.83083i) q^{33} +(-0.0555929 + 0.139435i) q^{34} +(4.83094 - 5.09530i) q^{36} +2.53082 q^{37} +(1.97942 - 4.96467i) q^{38} -6.12803i q^{39} -1.70882i q^{41} +(-11.3942 - 4.54289i) q^{42} +3.84601 q^{43} +(7.56921 - 0.201586i) q^{44} +(-3.94547 - 1.57306i) q^{46} +(2.15264 - 2.15264i) q^{47} +(-10.1920 + 0.543256i) q^{48} +4.55532i q^{49} +(0.191509 - 0.191509i) q^{51} +(-3.30480 + 3.48565i) q^{52} -1.29475i q^{53} +(-1.69305 + 0.727839i) q^{54} +(4.03113 + 8.72883i) q^{56} +(-6.81881 + 6.81881i) q^{57} +(7.35302 + 2.93166i) q^{58} +(-5.29614 + 5.29614i) q^{59} +(10.2413 + 10.2413i) q^{61} +(-2.14852 + 0.923645i) q^{62} +(8.43858 + 8.43858i) q^{63} +(6.09020 + 5.18744i) q^{64} +(-12.6902 - 5.05960i) q^{66} +10.6230 q^{67} +(-0.212211 + 0.00565167i) q^{68} +(5.41898 + 5.41898i) q^{69} +2.27322 q^{71} +(9.31831 + 3.43062i) q^{72} +(-9.99096 - 9.99096i) q^{73} +(1.41357 + 3.28815i) q^{74} +(7.55589 - 0.201231i) q^{76} +12.8696i q^{77} +(7.96180 - 3.42276i) q^{78} +8.70617 q^{79} -7.20709 q^{81} +(2.22017 - 0.954448i) q^{82} +11.1310i q^{83} +(-0.461838 - 17.3413i) q^{84} +(2.14816 + 4.99689i) q^{86} +(-10.0991 - 10.0991i) q^{87} +(4.48963 + 9.72165i) q^{88} -15.6390 q^{89} +(-5.77276 - 5.77276i) q^{91} +(-0.159920 - 6.00475i) q^{92} +4.21952 q^{93} +(3.99914 + 1.59446i) q^{94} +(-6.39846 - 12.9384i) q^{96} +(-5.00672 - 5.00672i) q^{97} +(-5.91846 + 2.54434i) q^{98} +(9.39839 + 9.39839i) 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

Introduction

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