LMFDB - Embedded newform 400.2.s.d.243.1

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			243.1
Root			$-1.08900 + 0.902261i$ of defining polynomial
Character	$\chi$	$=$	400.243
Dual form			400.2.s.d.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41267 - 0.0660953i) q^{2} +0.496487 q^{3} +(1.99126 + 0.186742i) q^{4} +(-0.701372 - 0.0328155i) q^{6} +(-1.55426 + 1.55426i) q^{7} +(-2.80065 - 0.395417i) q^{8} -2.75350 q^{9} +O(q^{10})$	\(q+(-1.41267 - 0.0660953i) q^{2} +0.496487 q^{3} +(1.99126 + 0.186742i) q^{4} +(-0.701372 - 0.0328155i) q^{6} +(-1.55426 + 1.55426i) q^{7} +(-2.80065 - 0.395417i) q^{8} -2.75350 q^{9} +(-4.19607 - 4.19607i) q^{11} +(0.988637 + 0.0927148i) q^{12} -5.09530i q^{13} +(2.29838 - 2.09292i) q^{14} +(3.93026 + 0.743703i) q^{16} +(-0.213542 + 0.213542i) q^{17} +(3.88978 + 0.181993i) q^{18} +(0.844754 + 0.844754i) q^{19} +(-0.771668 + 0.771668i) q^{21} +(5.65031 + 6.20499i) q^{22} +(-1.70744 - 1.70744i) q^{23} +(-1.39049 - 0.196320i) q^{24} +(-0.336775 + 7.19797i) q^{26} -2.85654 q^{27} +(-3.38518 + 2.80469i) q^{28} +(2.24750 - 2.24750i) q^{29} -0.818209i q^{31} +(-5.50299 - 1.31038i) q^{32} +(-2.08329 - 2.08329i) q^{33} +(0.315778 - 0.287550i) q^{34} +(-5.48294 - 0.514193i) q^{36} -5.12639i q^{37} +(-1.13752 - 1.24919i) q^{38} -2.52975i q^{39} -3.34727i q^{41} +(1.14111 - 1.03911i) q^{42} +4.49131i q^{43} +(-7.57189 - 9.13905i) q^{44} +(2.29920 + 2.52490i) q^{46} +(-4.29355 - 4.29355i) q^{47} +(1.95132 + 0.369239i) q^{48} +2.16858i q^{49} +(-0.106021 + 0.106021i) q^{51} +(0.951504 - 10.1461i) q^{52} +1.00653 q^{53} +(4.03534 + 0.188804i) q^{54} +(4.96751 - 3.73835i) q^{56} +(0.419410 + 0.419410i) q^{57} +(-3.32352 + 3.02642i) q^{58} +(-7.65005 + 7.65005i) q^{59} +(-1.90291 - 1.90291i) q^{61} +(-0.0540798 + 1.15586i) q^{62} +(4.27964 - 4.27964i) q^{63} +(7.68729 + 2.21485i) q^{64} +(2.80531 + 3.08070i) q^{66} +11.0221i q^{67} +(-0.465096 + 0.385341i) q^{68} +(-0.847724 - 0.847724i) q^{69} -10.5331 q^{71} +(7.71159 + 1.08878i) q^{72} +(-2.70854 + 2.70854i) q^{73} +(-0.338831 + 7.24189i) q^{74} +(1.52438 + 1.83988i) q^{76} +13.0435 q^{77} +(-0.167205 + 3.57370i) q^{78} -8.32010 q^{79} +6.84226 q^{81} +(-0.221239 + 4.72858i) q^{82} +9.17237 q^{83} +(-1.68070 + 1.39249i) q^{84} +(0.296855 - 6.34474i) q^{86} +(1.11585 - 1.11585i) q^{87} +(10.0925 + 13.4109i) q^{88} -4.25101 q^{89} +(7.91940 + 7.91940i) q^{91} +(-3.08112 - 3.71882i) q^{92} -0.406230i q^{93} +(5.78157 + 6.34914i) q^{94} +(-2.73217 - 0.650586i) q^{96} +(7.16000 - 7.16000i) q^{97} +(0.143333 - 3.06348i) q^{98} +(11.5539 + 11.5539i) 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 $

$2$	−1.41267	−	0.0660953i	−0.998907	−	0.0467365i
$2$	−1.41267	−	0.0660953i	−0.998907	−	0.0467365i
$3$	0.496487			0.286647			0.143324	−	0.989676i	$-0.454221\pi$
$3$	0.496487			0.286647			0.143324	+	0.989676i	$0.454221\pi$
$4$	1.99126	+	0.186742i	0.995631	+	0.0933708i
$5$		0			0
$5$		0			0
$6$	−0.701372	−	0.0328155i	−0.286334	−	0.0133969i
$7$	−1.55426	+	1.55426i	−0.587453	+	0.587453i	−0.936941	−	0.349488i	$-0.886356\pi$
$7$	−1.55426	+	1.55426i	−0.587453	+	0.587453i	0.349488	+	0.936941i	$0.386356\pi$
$8$	−2.80065	−	0.395417i	−0.990180	−	0.139801i
$9$	−2.75350			−0.917833
$10$		0			0
$11$	−4.19607	−	4.19607i	−1.26516	−	1.26516i	−0.948558	−	0.316604i	$-0.897457\pi$
$11$	−4.19607	−	4.19607i	−1.26516	−	1.26516i	−0.316604	−	0.948558i	$-0.602543\pi$
$12$	0.988637	+	0.0927148i	0.285395	+	0.0267645i
$13$		−	5.09530i		−	1.41318i	−0.707622	−	0.706591i	$-0.750232\pi$
$13$		−	5.09530i		−	1.41318i	0.707622	−	0.706591i	$-0.249768\pi$
$14$	2.29838	−	2.09292i	0.614267	−	0.559356i
$15$		0			0
$16$	3.93026	+	0.743703i	0.982564	+	0.185926i
$17$	−0.213542	+	0.213542i	−0.0517916	+	0.0517916i	−0.732528	−	0.680737i	$-0.761660\pi$
$17$	−0.213542	+	0.213542i	−0.0517916	+	0.0517916i	0.680737	+	0.732528i	$0.261660\pi$
$18$	3.88978	+	0.181993i	0.916830	+	0.0428963i
$19$	0.844754	+	0.844754i	0.193800	+	0.193800i	0.797336	−	0.603536i	$-0.206242\pi$
$19$	0.844754	+	0.844754i	0.193800	+	0.193800i	−0.603536	+	0.797336i	$0.706242\pi$
$20$		0			0
$21$	−0.771668	+	0.771668i	−0.168392	+	0.168392i
$22$	5.65031	+	6.20499i	1.20465	+	1.32291i
$23$	−1.70744	−	1.70744i	−0.356027	−	0.356027i	0.506319	−	0.862346i	$-0.331006\pi$
$23$	−1.70744	−	1.70744i	−0.356027	−	0.356027i	−0.862346	+	0.506319i	$0.831006\pi$
$24$	−1.39049	−	0.196320i	−0.283832	−	0.0400736i
$25$		0			0
$26$	−0.336775	+	7.19797i	−0.0660471	+	1.41164i
$27$	−2.85654			−0.549741
$28$	−3.38518	+	2.80469i	−0.639738	+	0.530036i
$29$	2.24750	−	2.24750i	0.417350	−	0.417350i	−0.466939	−	0.884289i	$-0.654643\pi$
$29$	2.24750	−	2.24750i	0.417350	−	0.417350i	0.884289	+	0.466939i	$0.154643\pi$
$30$		0			0
$31$		−	0.818209i		−	0.146955i	−0.997297	−	0.0734773i	$-0.976590\pi$
$31$		−	0.818209i		−	0.146955i	0.997297	−	0.0734773i	$-0.0234097\pi$
$32$	−5.50299	−	1.31038i	−0.972801	−	0.231644i
$33$	−2.08329	−	2.08329i	−0.362655	−	0.362655i
$34$	0.315778	−	0.287550i	0.0541556	−	0.0493144i
$35$		0			0
$36$	−5.48294	−	0.514193i	−0.913824	−	0.0856988i
$37$		−	5.12639i		−	0.842774i	−0.906881	−	0.421387i	$-0.861543\pi$
$37$		−	5.12639i		−	0.842774i	0.906881	−	0.421387i	$-0.138457\pi$
$38$	−1.13752	−	1.24919i	−0.184531	−	0.202646i
$39$		−	2.52975i		−	0.405084i
$40$		0			0
$41$		−	3.34727i		−	0.522756i	−0.965237	−	0.261378i	$-0.915823\pi$
$41$		−	3.34727i		−	0.522756i	0.965237	−	0.261378i	$-0.0841769\pi$
$42$	1.14111	−	1.03911i	0.176078	−	0.160338i
$43$			4.49131i			0.684919i	0.939533	+	0.342460i	$0.111260\pi$
$43$			4.49131i			0.684919i	−0.939533	+	0.342460i	$0.888740\pi$
$44$	−7.57189	−	9.13905i	−1.14151	−	1.37776i
$45$		0			0
$46$	2.29920	+	2.52490i	0.338998	+	0.372277i
$47$	−4.29355	−	4.29355i	−0.626278	−	0.626278i	0.320851	−	0.947130i	$-0.396031\pi$
$47$	−4.29355	−	4.29355i	−0.626278	−	0.626278i	−0.947130	+	0.320851i	$0.896031\pi$
$48$	1.95132	+	0.369239i	0.281649	+	0.0532951i
$49$			2.16858i			0.309797i
$50$		0			0
$51$	−0.106021	+	0.106021i	−0.0148459	+	0.0148459i
$52$	0.951504	−	10.1461i	0.131950	−	1.40701i
$53$	1.00653			0.138258			0.0691291	−	0.997608i	$-0.477978\pi$
$53$	1.00653			0.138258			0.0691291	+	0.997608i	$0.477978\pi$
$54$	4.03534	+	0.188804i	0.549141	+	0.0256930i
$55$		0			0
$56$	4.96751	−	3.73835i	0.663811	−	0.499558i
$57$	0.419410	+	0.419410i	0.0555521	+	0.0555521i
$58$	−3.32352	+	3.02642i	−0.436399	+	0.397388i
$59$	−7.65005	+	7.65005i	−0.995952	+	0.995952i	−0.999992	−	0.00404030i	$-0.998714\pi$
$59$	−7.65005	+	7.65005i	−0.995952	+	0.995952i	0.00404030	+	0.999992i	$0.498714\pi$
$60$		0			0
$61$	−1.90291	−	1.90291i	−0.243643	−	0.243643i	0.574712	−	0.818355i	$-0.305114\pi$
$61$	−1.90291	−	1.90291i	−0.243643	−	0.243643i	−0.818355	+	0.574712i	$0.805114\pi$
$62$	−0.0540798	+	1.15586i	−0.00686814	+	0.146794i
$63$	4.27964	−	4.27964i	0.539184	−	0.539184i
$64$	7.68729	+	2.21485i	0.960911	+	0.276856i
$65$		0			0
$66$	2.80531	+	3.08070i	0.345310	+	0.379208i
$67$			11.0221i			1.34656i	0.739387	+	0.673280i	$0.235115\pi$
$67$			11.0221i			1.34656i	−0.739387	+	0.673280i	$0.764885\pi$
$68$	−0.465096	+	0.385341i	−0.0564012	+	0.0467295i
$69$	−0.847724	−	0.847724i	−0.102054	−	0.102054i
$70$		0			0
$71$	−10.5331			−1.25005			−0.625027	−	0.780604i	$-0.714912\pi$
$71$	−10.5331			−1.25005			−0.625027	+	0.780604i	$0.714912\pi$
$72$	7.71159	+	1.08878i	0.908820	+	0.128314i
$73$	−2.70854	+	2.70854i	−0.317010	+	0.317010i	−0.847618	−	0.530607i	$-0.821964\pi$
$73$	−2.70854	+	2.70854i	−0.317010	+	0.317010i	0.530607	+	0.847618i	$0.321964\pi$
$74$	−0.338831	+	7.24189i	−0.0393883	+	0.841853i
$75$		0			0
$76$	1.52438	+	1.83988i	0.174858	+	0.211048i
$77$	13.0435			1.48645
$78$	−0.167205	+	3.57370i	−0.0189322	+	0.404642i
$79$	−8.32010			−0.936085			−0.468042	−	0.883706i	$-0.655041\pi$
$79$	−8.32010			−0.936085			−0.468042	+	0.883706i	$0.655041\pi$
$80$		0			0
$81$	6.84226			0.760252
$82$	−0.221239	+	4.72858i	−0.0244317	+	0.522185i
$83$	9.17237			1.00680			0.503399	−	0.864054i	$-0.332083\pi$
$83$	9.17237			1.00680			0.503399	+	0.864054i	$0.332083\pi$
$84$	−1.68070	+	1.39249i	−0.183379	+	0.151933i
$85$		0			0
$86$	0.296855	−	6.34474i	0.0320107	−	0.684171i
$87$	1.11585	−	1.11585i	0.119632	−	0.119632i
$88$	10.0925	+	13.4109i	1.07587	+	1.42961i
$89$	−4.25101			−0.450606			−0.225303	−	0.974289i	$-0.572337\pi$
$89$	−4.25101			−0.450606			−0.225303	+	0.974289i	$0.572337\pi$
$90$		0			0
$91$	7.91940	+	7.91940i	0.830178	+	0.830178i
$92$	−3.08112	−	3.71882i	−0.321229	−	0.387714i
$93$		−	0.406230i		−	0.0421241i
$94$	5.78157	+	6.34914i	0.596324	+	0.654864i
$95$		0			0
$96$	−2.73217	−	0.650586i	−0.278850	−	0.0664001i
$97$	7.16000	−	7.16000i	0.726987	−	0.726987i	−0.243031	−	0.970019i	$-0.578142\pi$
$97$	7.16000	−	7.16000i	0.726987	−	0.726987i	0.970019	+	0.243031i	$0.0781417\pi$
$98$	0.143333	−	3.06348i	0.0144788	−	0.309458i
$99$	11.5539	+	11.5539i	1.16121	+	1.16121i
$100$		0			0
$101$	8.38846	−	8.38846i	0.834683	−	0.834683i	−0.153470	−	0.988153i	$-0.549045\pi$
$101$	8.38846	−	8.38846i	0.834683	−	0.834683i	0.988153	+	0.153470i	$0.0490448\pi$
$102$	0.156780	−	0.142765i	0.0155235	−	0.0141358i
$103$	5.16478	+	5.16478i	0.508901	+	0.508901i	0.914189	−	0.405288i	$-0.132829\pi$
$103$	5.16478	+	5.16478i	0.508901	+	0.508901i	−0.405288	+	0.914189i	$0.632829\pi$
$104$	−2.01477	+	14.2702i	−0.197564	+	1.39930i
$105$		0			0
$106$	−1.42190	−	0.0665272i	−0.138107	−	0.00646169i
$107$	−8.97973			−0.868103			−0.434052	−	0.900888i	$-0.642916\pi$
$107$	−8.97973			−0.868103			−0.434052	+	0.900888i	$0.642916\pi$
$108$	−5.68812	−	0.533435i	−0.547340	−	0.0513298i
$109$	10.9081	−	10.9081i	1.04481	−	1.04481i	0.0458592	−	0.998948i	$-0.485397\pi$
$109$	10.9081	−	10.9081i	1.04481	−	1.04481i	0.998948	−	0.0458592i	$-0.0146025\pi$
$110$		0			0
$111$		−	2.54519i		−	0.241579i
$112$	−7.26453	+	4.95272i	−0.686433	+	0.467988i
$113$	4.29684	+	4.29684i	0.404212	+	0.404212i	0.879715	−	0.475502i	$-0.157734\pi$
$113$	4.29684	+	4.29684i	0.404212	+	0.404212i	−0.475502	+	0.879715i	$0.657734\pi$
$114$	−0.564765	−	0.620208i	−0.0528951	−	0.0580878i
$115$		0			0
$116$	4.89506	−	4.05566i	0.454495	−	0.376558i
$117$			14.0299i			1.29707i
$118$	11.3126	−	10.3013i	1.04141	−	0.948316i
$119$		−	0.663798i		−	0.0608503i
$120$		0			0
$121$			24.2140i			2.20127i
$122$	2.56241	+	2.81396i	0.231990	+	0.254764i
$123$		−	1.66188i		−	0.149846i
$124$	0.152794	−	1.62927i	0.0137213	−	0.146313i
$125$		0			0
$126$	−6.32858	+	5.76285i	−0.563795	+	0.513396i
$127$	−0.759686	−	0.759686i	−0.0674112	−	0.0674112i	0.672597	−	0.740009i	$-0.265179\pi$
$127$	−0.759686	−	0.759686i	−0.0674112	−	0.0674112i	−0.740009	+	0.672597i	$0.765179\pi$
$128$	−10.7132	−	3.63694i	−0.946922	−	0.321463i
$129$			2.22988i			0.196330i
$130$		0			0
$131$	7.59995	−	7.59995i	0.664010	−	0.664010i	−0.292312	−	0.956323i	$-0.594425\pi$
$131$	7.59995	−	7.59995i	0.664010	−	0.664010i	0.956323	+	0.292312i	$0.0944247\pi$
$132$	−3.75935	−	4.53742i	−0.327209	−	0.394932i
$133$	−2.62593			−0.227697
$134$	0.728507	−	15.5705i	0.0629335	−	1.34509i
$135$		0			0
$136$	0.682495	−	0.513619i	0.0585235	−	0.0440425i
$137$	−12.7789	−	12.7789i	−1.09178	−	1.09178i	−0.995339	−	0.0964376i	$-0.969255\pi$
$137$	−12.7789	−	12.7789i	−1.09178	−	1.09178i	−0.0964376	−	0.995339i	$-0.530745\pi$
$138$	1.14152	+	1.25358i	0.0971728	+	0.106712i
$139$	7.74227	−	7.74227i	0.656691	−	0.656691i	−0.297905	−	0.954596i	$-0.596288\pi$
$139$	7.74227	−	7.74227i	0.656691	−	0.656691i	0.954596	+	0.297905i	$0.0962877\pi$
$140$		0			0
$141$	−2.13169	−	2.13169i	−0.179521	−	0.179521i
$142$	14.8798	+	0.696191i	1.24869	+	0.0584230i
$143$	−21.3802	+	21.3802i	−1.78790	+	1.78790i
$144$	−10.8220	−	2.04779i	−0.901830	−	0.170649i
$145$		0			0
$146$	4.00529	−	3.64724i	0.331480	−	0.301848i
$147$			1.07667i			0.0888024i
$148$	0.957310	−	10.2080i	0.0786904	−	0.839092i
$149$	9.57165	+	9.57165i	0.784140	+	0.784140i	0.980527	−	0.196386i	$-0.0629207\pi$
$149$	9.57165	+	9.57165i	0.784140	+	0.784140i	−0.196386	+	0.980527i	$0.562921\pi$
$150$		0			0
$151$	−9.68791			−0.788391			−0.394195	−	0.919027i	$-0.628977\pi$
$151$	−9.68791			−0.788391			−0.394195	+	0.919027i	$0.628977\pi$
$152$	−2.03183	−	2.69989i	−0.164803	−	0.218990i
$153$	0.587989	−	0.587989i	0.0475361	−	0.0475361i
$154$	−18.4262	−	0.862116i	−1.48482	−	0.0694713i
$155$		0			0
$156$	0.472410	−	5.03740i	0.0378230	−	0.403315i
$157$	9.97637			0.796201			0.398101	−	0.917342i	$-0.369669\pi$
$157$	9.97637			0.796201			0.398101	+	0.917342i	$0.369669\pi$
$158$	11.7535	+	0.549920i	0.935062	+	0.0437493i
$159$	0.499732			0.0396313
$160$		0			0
$161$	5.30761			0.418298
$162$	−9.66585	−	0.452242i	−0.759421	−	0.0355315i
$163$	−9.48267			−0.742740			−0.371370	−	0.928485i	$-0.621112\pi$
$163$	−9.48267			−0.742740			−0.371370	+	0.928485i	$0.621112\pi$
$164$	0.625074	−	6.66529i	0.0488101	−	0.520472i
$165$		0			0
$166$	−12.9575	−	0.606250i	−1.00570	−	0.0470542i
$167$	9.43528	−	9.43528i	0.730124	−	0.730124i	−0.240520	−	0.970644i	$-0.577318\pi$
$167$	9.43528	−	9.43528i	0.730124	−	0.730124i	0.970644	+	0.240520i	$0.0773180\pi$
$168$	2.46630	−	1.85604i	0.190279	−	0.143197i
$169$	−12.9621			−0.997082
$170$		0			0
$171$	−2.32603	−	2.32603i	−0.177876	−	0.177876i
$172$	−0.838715	+	8.94339i	−0.0639514	+	0.681927i
$173$		−	8.94716i		−	0.680240i	−0.940382	−	0.340120i	$-0.889532\pi$
$173$		−	8.94716i		−	0.680240i	0.940382	−	0.340120i	$-0.110468\pi$
$174$	−1.65008	+	1.50258i	−0.125093	+	0.113910i
$175$		0			0
$176$	−13.3710	−	19.6122i	−1.00788	−	1.47833i
$177$	−3.79815	+	3.79815i	−0.285487	+	0.285487i
$178$	6.00526	+	0.280972i	0.450114	+	0.0210597i
$179$	−3.02430	−	3.02430i	−0.226047	−	0.226047i	0.584992	−	0.811039i	$-0.301098\pi$
$179$	−3.02430	−	3.02430i	−0.226047	−	0.226047i	−0.811039	+	0.584992i	$0.801098\pi$
$180$		0			0
$181$	−1.54845	+	1.54845i	−0.115095	+	0.115095i	−0.762309	−	0.647213i	$-0.775934\pi$
$181$	−1.54845	+	1.54845i	−0.115095	+	0.115095i	0.647213	+	0.762309i	$0.275934\pi$
$182$	−10.6640	−	11.7109i	−0.790472	−	0.868071i
$183$	−0.944773	−	0.944773i	−0.0698396	−	0.0698396i
$184$	4.10680	+	5.45710i	0.302757	+	0.402303i
$185$		0			0
$186$	−0.0268499	+	0.573869i	−0.00196873	+	0.0420781i
$187$	1.79208			0.131050
$188$	−7.74779	−	9.35136i	−0.565066	−	0.682018i
$189$	4.43979	−	4.43979i	0.322947	−	0.322947i
$190$		0			0
$191$			20.1005i			1.45442i	0.686415	+	0.727210i	$0.259183\pi$
$191$			20.1005i			1.45442i	−0.686415	+	0.727210i	$0.740817\pi$
$192$	3.81664	+	1.09964i	0.275442	+	0.0793600i
$193$	−3.82483	−	3.82483i	−0.275317	−	0.275317i	0.555919	−	0.831236i	$-0.312366\pi$
$193$	−3.82483	−	3.82483i	−0.275317	−	0.275317i	−0.831236	+	0.555919i	$0.812366\pi$
$194$	−10.5879	+	9.64146i	−0.760170	+	0.692216i
$195$		0			0
$196$	−0.404964	+	4.31821i	−0.0289260	+	0.308444i
$197$		−	1.11758i		−	0.0796246i	−0.999207	−	0.0398123i	$-0.987324\pi$
$197$		−	1.11758i		−	0.0796246i	0.999207	−	0.0398123i	$-0.0126760\pi$
$198$	−15.5581	−	17.0854i	−1.10567	−	1.21421i
$199$		−	25.5830i		−	1.81353i	−0.421635	−	0.906766i	$-0.638544\pi$
$199$		−	25.5830i		−	1.81353i	0.421635	−	0.906766i	$-0.361456\pi$
$200$		0			0
$201$			5.47232i			0.385988i
$202$	−12.4046	+	11.2957i	−0.872781	+	0.794761i
$203$			6.98637i			0.490347i
$204$	−0.230914	+	0.191317i	−0.0161672	+	0.0133949i
$205$		0			0
$206$	−6.95475	−	7.63749i	−0.484560	−	0.532129i
$207$	4.70145	+	4.70145i	0.326773	+	0.326773i
$208$	3.78939	−	20.0258i	0.262747	−	1.38854i
$209$		−	7.08929i		−	0.490376i
$210$		0			0
$211$	0.411613	−	0.411613i	0.0283366	−	0.0283366i	−0.692797	−	0.721133i	$-0.743622\pi$
$211$	0.411613	−	0.411613i	0.0283366	−	0.0283366i	0.721133	+	0.692797i	$0.243622\pi$
$212$	2.00427	+	0.187962i	0.137654	+	0.0129093i
$213$	−5.22957			−0.358324
$214$	12.6854	+	0.593518i	0.867155	+	0.0405721i
$215$		0			0
$216$	8.00017	+	1.12952i	0.544343	+	0.0768544i
$217$	1.27171	+	1.27171i	0.0863290	+	0.0863290i
$218$	−16.1305	+	14.6886i	−1.09250	+	0.994835i
$219$	−1.34475	+	1.34475i	−0.0908701	+	0.0908701i
$220$		0			0
$221$	1.08806	+	1.08806i	0.0731909	+	0.0731909i
$222$	−0.168225	+	3.59551i	−0.0112905	+	0.241315i
$223$	16.7466	−	16.7466i	1.12143	−	1.12143i	0.129908	−	0.991526i	$-0.458532\pi$
$223$	16.7466	−	16.7466i	1.12143	−	1.12143i	0.991526	−	0.129908i	$-0.0414682\pi$
$224$	10.5897	−	6.51639i	0.707555	−	0.435395i
$225$		0			0
$226$	−5.78600	−	6.35401i	−0.384879	−	0.422662i
$227$			13.7807i			0.914659i	0.889297	+	0.457330i	$0.151194\pi$
$227$			13.7807i			0.914659i	−0.889297	+	0.457330i	$0.848806\pi$
$228$	0.756833	+	0.913476i	0.0501225	+	0.0604964i
$229$	−7.90971	−	7.90971i	−0.522688	−	0.522688i	0.395694	−	0.918382i	$-0.370504\pi$
$229$	−7.90971	−	7.90971i	−0.522688	−	0.522688i	−0.918382	+	0.395694i	$0.870504\pi$
$230$		0			0
$231$	6.47594			0.426086
$232$	−7.18315	+	5.40576i	−0.471597	+	0.354905i
$233$	1.67997	−	1.67997i	0.110058	−	0.110058i	−0.649933	−	0.759991i	$-0.725203\pi$
$233$	1.67997	−	1.67997i	0.110058	−	0.110058i	0.759991	+	0.649933i	$0.225203\pi$
$234$	0.927311	−	19.8196i	0.0606202	−	1.29565i
$235$		0			0
$236$	−16.6618	+	13.8047i	−1.08459	+	0.898608i
$237$	−4.13083			−0.268326
$238$	−0.0438740	+	0.937727i	−0.00284393	+	0.0607838i
$239$	11.7685			0.761241			0.380620	−	0.924731i	$-0.375710\pi$
$239$	11.7685			0.761241			0.380620	+	0.924731i	$0.375710\pi$
$240$		0			0
$241$	−13.2730			−0.854991			−0.427495	−	0.904018i	$-0.640604\pi$
$241$	−13.2730			−0.854991			−0.427495	+	0.904018i	$0.640604\pi$
$242$	1.60043	−	34.2063i	0.102880	−	2.19886i
$243$	11.9667			0.767665
$244$	−3.43385	−	4.14455i	−0.219830	−	0.265328i
$245$		0			0
$246$	−0.109842	+	2.34768i	−0.00700329	+	0.149683i
$247$	4.30427	−	4.30427i	0.273874	−	0.273874i
$248$	−0.323534	+	2.29152i	−0.0205444	+	0.145511i
$249$	4.55396			0.288596
$250$		0			0
$251$	10.3795	+	10.3795i	0.655149	+	0.655149i	0.954228	−	0.299079i	$-0.0966795\pi$
$251$	10.3795	+	10.3795i	0.655149	+	0.655149i	−0.299079	+	0.954228i	$0.596679\pi$
$252$	9.32108	−	7.72271i	0.587173	−	0.486485i
$253$			14.3291i			0.900863i
$254$	1.02297	+	1.12340i	0.0641870	+	0.0704881i
$255$		0			0
$256$	14.8938	+	5.84588i	0.930863	+	0.365368i
$257$	−20.4353	+	20.4353i	−1.27472	+	1.27472i	−0.331140	+	0.943582i	$0.607433\pi$
$257$	−20.4353	+	20.4353i	−1.27472	+	1.27472i	−0.943582	+	0.331140i	$0.892567\pi$
$258$	0.147385	−	3.15008i	0.00917577	−	0.196116i
$259$	7.96772	+	7.96772i	0.495090	+	0.495090i
$260$		0			0
$261$	−6.18848	+	6.18848i	−0.383058	+	0.383058i
$262$	−11.2385	+	10.2339i	−0.694318	+	0.632251i
$263$	−14.0611	−	14.0611i	−0.867047	−	0.867047i	0.125098	−	0.992144i	$-0.460076\pi$
$263$	−14.0611	−	14.0611i	−0.867047	−	0.867047i	−0.992144	+	0.125098i	$0.960076\pi$
$264$	5.01081	+	6.65835i	0.308394	+	0.409793i
$265$		0			0
$266$	3.70956	+	0.173561i	0.227448	+	0.0106417i
$267$	−2.11057			−0.129165
$268$	−2.05828	+	21.9478i	−0.125729	+	1.34068i
$269$	−6.61443	+	6.61443i	−0.403289	+	0.403289i	−0.879390	−	0.476101i	$-0.842050\pi$
$269$	−6.61443	+	6.61443i	−0.403289	+	0.403289i	0.476101	+	0.879390i	$0.342050\pi$
$270$		0			0
$271$		−	10.6219i		−	0.645237i	−0.946529	−	0.322619i	$-0.895437\pi$
$271$		−	10.6219i		−	0.645237i	0.946529	−	0.322619i	$-0.104563\pi$
$272$	−0.998087	+	0.680463i	−0.0605179	+	0.0412592i
$273$	3.93188	+	3.93188i	0.237968	+	0.237968i
$274$	17.2077	+	18.8970i	1.03956	+	1.14161i
$275$		0			0
$276$	−1.52974	−	1.84635i	−0.0920793	−	0.111137i
$277$		−	8.28511i		−	0.497804i	−0.968529	−	0.248902i	$-0.919930\pi$
$277$		−	8.28511i		−	0.497804i	0.968529	−	0.248902i	$-0.0800697\pi$
$278$	−11.4490	+	10.4255i	−0.686665	+	0.625282i
$279$			2.25294i			0.134880i
$280$		0			0
$281$		−	21.0176i		−	1.25380i	−0.779098	−	0.626902i	$-0.784323\pi$
$281$		−	21.0176i		−	1.25380i	0.779098	−	0.626902i	$-0.215677\pi$
$282$	2.87048	+	3.15227i	0.170934	+	0.187715i
$283$		−	14.4748i		−	0.860436i	−0.902725	−	0.430218i	$-0.858437\pi$
$283$		−	14.4748i		−	0.860436i	0.902725	−	0.430218i	$-0.141563\pi$
$284$	−20.9742	−	1.96697i	−1.24459	−	0.116718i
$285$		0			0
$286$	31.6163	−	28.7900i	1.86951	−	1.70239i
$287$	5.20251	+	5.20251i	0.307095	+	0.307095i
$288$	15.1525	+	3.60812i	0.892869	+	0.212611i
$289$			16.9088i			0.994635i
$290$		0			0
$291$	3.55485	−	3.55485i	0.208389	−	0.208389i
$292$	−5.89921	+	4.88761i	−0.345225	+	0.286026i
$293$	11.9165			0.696171			0.348086	−	0.937463i	$-0.386832\pi$
$293$	11.9165			0.696171			0.348086	+	0.937463i	$0.386832\pi$
$294$	0.0711630	−	1.52098i	0.00415031	−	0.0887054i
$295$		0			0
$296$	−2.02706	+	14.3572i	−0.117821	+	0.834497i
$297$	11.9862	+	11.9862i	0.695512	+	0.695512i
$298$	−12.8889	−	14.1542i	−0.746635	−	0.819931i
$299$	−8.69993	+	8.69993i	−0.503130	+	0.503130i
$300$		0			0
$301$	−6.98065	−	6.98065i	−0.402358	−	0.402358i
$302$	13.6858	+	0.640325i	0.787529	+	0.0368466i
$303$	4.16477	−	4.16477i	0.239260	−	0.239260i
$304$	2.69185	+	3.94834i	0.154388	+	0.226453i
$305$		0			0
$306$	−0.869496	+	0.791769i	−0.0497058	+	0.0452624i
$307$		−	25.4511i		−	1.45257i	−0.687392	−	0.726287i	$-0.741245\pi$
$307$		−	25.4511i		−	1.45257i	0.687392	−	0.726287i	$-0.258755\pi$
$308$	25.9731	+	2.43577i	1.47995	+	0.138791i
$309$	2.56425	+	2.56425i	0.145875	+	0.145875i
$310$		0			0
$311$	21.4775			1.21788			0.608939	−	0.793217i	$-0.291596\pi$
$311$	21.4775			1.21788			0.608939	+	0.793217i	$0.291596\pi$
$312$	−1.00031	+	7.08495i	−0.0566312	+	0.401106i
$313$	−18.7965	+	18.7965i	−1.06244	+	1.06244i	−0.0645277	+	0.997916i	$0.520554\pi$
$313$	−18.7965	+	18.7965i	−1.06244	+	1.06244i	−0.997916	+	0.0645277i	$0.979446\pi$
$314$	−14.0933	−	0.659392i	−0.795331	−	0.0372116i
$315$		0			0
$316$	−16.5675	−	1.55371i	−0.931995	−	0.0874029i
$317$	−16.2531			−0.912864			−0.456432	−	0.889758i	$-0.650873\pi$
$317$	−16.2531			−0.912864			−0.456432	+	0.889758i	$0.650873\pi$
$318$	−0.705955	−	0.0330299i	−0.0395880	−	0.00185223i
$319$	−18.8613			−1.05603
$320$		0			0
$321$	−4.45832			−0.248839
$322$	−7.49789	−	0.350808i	−0.417841	−	0.0195498i
$323$	−0.360781			−0.0200744
$324$	13.6247	+	1.27773i	0.756930	+	0.0709853i
$325$		0			0
$326$	13.3959	+	0.626760i	0.741928	+	0.0347130i
$327$	5.41574	−	5.41574i	0.299491	−	0.299491i
$328$	−1.32357	+	9.37453i	−0.0730818	+	0.517622i
$329$	13.3465			0.735818
$330$		0			0
$331$	−8.71558	−	8.71558i	−0.479052	−	0.479052i	0.425777	−	0.904828i	$-0.360001\pi$
$331$	−8.71558	−	8.71558i	−0.479052	−	0.479052i	−0.904828	+	0.425777i	$0.860001\pi$
$332$	18.2646	+	1.71286i	1.00240	+	0.0940055i
$333$			14.1155i			0.773526i
$334$	−13.9526	+	12.7053i	−0.763450	+	0.695203i
$335$		0			0
$336$	−3.60674	+	2.45896i	−0.196764	+	0.134147i
$337$	−0.0406874	+	0.0406874i	−0.00221638	+	0.00221638i	−0.708214	−	0.705998i	$-0.750499\pi$
$337$	−0.0406874	+	0.0406874i	−0.00221638	+	0.00221638i	0.705998	+	0.708214i	$0.250499\pi$
$338$	18.3111	+	0.856732i	0.995993	+	0.0466001i
$339$	2.13333	+	2.13333i	0.115866	+	0.115866i
$340$		0			0
$341$	−3.43326	+	3.43326i	−0.185921	+	0.185921i
$342$	3.13217	+	3.43965i	0.169368	+	0.185995i
$343$	−14.2503	−	14.2503i	−0.769445	−	0.769445i
$344$	1.77594	−	12.5786i	0.0957524	−	0.678193i
$345$		0			0
$346$	−0.591366	+	12.6394i	−0.0317920	+	0.679497i
$347$	35.7094			1.91698			0.958491	−	0.285124i	$-0.0920348\pi$
$347$	35.7094			1.91698			0.958491	+	0.285124i	$0.0920348\pi$
$348$	2.43033	−	2.01358i	0.130280	−	0.107939i
$349$	−0.274452	+	0.274452i	−0.0146911	+	0.0146911i	−0.714414	−	0.699723i	$-0.753307\pi$
$349$	−0.274452	+	0.274452i	−0.0146911	+	0.0146911i	0.699723	+	0.714414i	$0.253307\pi$
$350$		0			0
$351$			14.5549i			0.776884i
$352$	17.5925	+	28.5894i	0.937683	+	1.52382i
$353$	15.6215	+	15.6215i	0.831446	+	0.831446i	0.987715	−	0.156268i	$-0.0499464\pi$
$353$	15.6215	+	15.6215i	0.831446	+	0.831446i	−0.156268	+	0.987715i	$0.549946\pi$
$354$	5.61657	−	5.11449i	0.298517	−	0.271832i
$355$		0			0
$356$	−8.46487	−	0.793840i	−0.448637	−	0.0420734i
$357$		−	0.329567i		−	0.0174426i
$358$	4.07244	+	4.47222i	0.215235	+	0.236364i
$359$			0.768787i			0.0405750i	0.999794	+	0.0202875i	$0.00645816\pi$
$359$			0.768787i			0.0405750i	−0.999794	+	0.0202875i	$0.993542\pi$
$360$		0			0
$361$		−	17.5728i		−	0.924883i
$362$	2.28979	−	2.08510i	0.120349	−	0.109591i
$363$			12.0219i			0.630988i
$364$	14.2907	+	17.2485i	0.749037	+	0.904066i
$365$		0			0
$366$	1.27221	+	1.39710i	0.0664992	+	0.0730273i
$367$	−13.7849	−	13.7849i	−0.719568	−	0.719568i	0.248949	−	0.968517i	$-0.419915\pi$
$367$	−13.7849	−	13.7849i	−0.719568	−	0.719568i	−0.968517	+	0.248949i	$0.919915\pi$
$368$	−5.44086	−	7.98052i	−0.283624	−	0.416013i
$369$			9.21671i			0.479803i
$370$		0			0
$371$	−1.56441	+	1.56441i	−0.0812202	+	0.0812202i
$372$	0.0758601	−	0.808911i	0.00393316	−	0.0419401i
$373$	21.4003			1.10806			0.554031	−	0.832496i	$-0.313089\pi$
$373$	21.4003			1.10806			0.554031	+	0.832496i	$0.313089\pi$
$374$	−2.53161	−	0.118448i	−0.130906	−	0.00612479i
$375$		0			0
$376$	10.3270	+	13.7225i	0.532573	+	0.707682i
$377$	−11.4517	−	11.4517i	−0.589791	−	0.589791i
$378$	−6.56540	+	5.97851i	−0.337688	+	0.307501i
$379$	11.3922	−	11.3922i	0.585180	−	0.585180i	−0.351142	−	0.936322i	$-0.614207\pi$
$379$	11.3922	−	11.3922i	0.585180	−	0.585180i	0.936322	+	0.351142i	$0.114207\pi$
$380$		0			0
$381$	−0.377174	−	0.377174i	−0.0193232	−	0.0193232i
$382$	1.32855	−	28.3953i	0.0679744	−	1.45283i
$383$	−4.42635	+	4.42635i	−0.226176	+	0.226176i	−0.811093	−	0.584917i	$-0.801127\pi$
$383$	−4.42635	+	4.42635i	−0.226176	+	0.226176i	0.584917	+	0.811093i	$0.301127\pi$
$384$	−5.31897	−	1.80570i	−0.271432	−	0.0921465i
$385$		0			0
$386$	5.15041	+	5.65602i	0.262149	+	0.287884i
$387$		−	12.3668i		−	0.628642i
$388$	15.5945	−	12.9204i	0.791691	−	0.655932i
$389$	12.3502	+	12.3502i	0.626180	+	0.626180i	0.947105	−	0.320924i	$-0.103994\pi$
$389$	12.3502	+	12.3502i	0.626180	+	0.626180i	−0.320924	+	0.947105i	$0.603994\pi$
$390$		0			0
$391$	0.729222			0.0368784
$392$	0.857493	−	6.07343i	0.0433099	−	0.306755i
$393$	3.77328	−	3.77328i	0.190337	−	0.190337i
$394$	−0.0738671	+	1.57878i	−0.00372137	+	0.0795376i
$395$		0			0
$396$	20.8492	+	25.1644i	1.04771	+	1.26456i
$397$	−17.9832			−0.902551			−0.451275	−	0.892385i	$-0.649031\pi$
$397$	−17.9832			−0.902551			−0.451275	+	0.892385i	$0.649031\pi$
$398$	−1.69092	+	36.1403i	−0.0847580	+	1.81155i
$399$	−1.30374			−0.0652686
$400$		0			0
$401$	9.06570			0.452720			0.226360	−	0.974044i	$-0.427317\pi$
$401$	9.06570			0.452720			0.226360	+	0.974044i	$0.427317\pi$
$402$	0.361695	−	7.73057i	0.0180397	−	0.385566i
$403$	−4.16902			−0.207674
$404$	18.2701	−	15.1372i	0.908972	−	0.753102i
$405$		0			0
$406$	0.461766	−	9.86942i	0.0229171	−	0.489811i
$407$	−21.5107	+	21.5107i	−1.06625	+	1.06625i
$408$	0.338850	−	0.255005i	0.0167756	−	0.0126246i
$409$	−30.0616			−1.48645			−0.743226	−	0.669040i	$-0.766705\pi$
$409$	−30.0616			−1.48645			−0.743226	+	0.669040i	$0.766705\pi$
$410$		0			0
$411$	−6.34457	−	6.34457i	−0.312955	−	0.312955i
$412$	9.31995	+	11.2489i	0.459161	+	0.554194i
$413$		−	23.7803i		−	1.17015i
$414$	−6.33084	−	6.95233i	−0.311144	−	0.341688i
$415$		0			0
$416$	−6.67676	+	28.0394i	−0.327355	+	1.37474i
$417$	3.84394	−	3.84394i	0.188239	−	0.188239i
$418$	−0.468569	+	10.0148i	−0.0229184	+	0.489840i
$419$	−15.3986	−	15.3986i	−0.752271	−	0.752271i	0.222631	−	0.974903i	$-0.428535\pi$
$419$	−15.3986	−	15.3986i	−0.752271	−	0.752271i	−0.974903	+	0.222631i	$0.928535\pi$
$420$		0			0
$421$	−3.86468	+	3.86468i	−0.188353	+	0.188353i	−0.794984	−	0.606631i	$-0.792521\pi$
$421$	−3.86468	+	3.86468i	−0.188353	+	0.188353i	0.606631	+	0.794984i	$0.292521\pi$
$422$	−0.608679	+	0.554267i	−0.0296300	+	0.0269813i
$423$	11.8223	+	11.8223i	0.574819	+	0.574819i
$424$	−2.81895	−	0.398001i	−0.136900	−	0.0193286i
$425$		0			0
$426$	7.38764	+	0.345650i	0.357933	+	0.0167468i
$427$	5.91523			0.286258
$428$	−17.8810	−	1.67689i	−0.864311	−	0.0810555i
$429$	−10.6150	+	10.6150i	−0.512497	+	0.512497i
$430$		0			0
$431$		−	27.2692i		−	1.31351i	−0.754103	−	0.656756i	$-0.771928\pi$
$431$		−	27.2692i		−	1.31351i	0.754103	−	0.656756i	$-0.228072\pi$
$432$	−11.2269	−	2.12442i	−0.540156	−	0.102211i
$433$	−19.1435	−	19.1435i	−0.919978	−	0.919978i	0.0770497	−	0.997027i	$-0.475450\pi$
$433$	−19.1435	−	19.1435i	−0.919978	−	0.919978i	−0.997027	+	0.0770497i	$0.975450\pi$
$434$	−1.71244	−	1.88055i	−0.0821999	−	0.0902694i
$435$		0			0
$436$	23.7579	−	19.6839i	1.13780	−	0.942688i
$437$		−	2.88474i		−	0.137996i
$438$	1.98857	−	1.81081i	0.0950177	−	0.0865238i
$439$			30.1995i			1.44134i	0.693276	+	0.720672i	$0.256167\pi$
$439$			30.1995i			1.44134i	−0.693276	+	0.720672i	$0.743833\pi$
$440$		0			0
$441$		−	5.97118i		−	0.284342i
$442$	−1.46515	−	1.60899i	−0.0696903	−	0.0765316i
$443$		−	27.7051i		−	1.31631i	−0.752884	−	0.658153i	$-0.771338\pi$
$443$		−	27.7051i		−	1.31631i	0.752884	−	0.658153i	$-0.228662\pi$
$444$	0.475292	−	5.06814i	0.0225564	−	0.240523i
$445$		0			0
$446$	−24.7642	+	22.5505i	−1.17262	+	1.06780i
$447$	4.75220	+	4.75220i	0.224772	+	0.224772i
$448$	−15.3905	+	8.50557i	−0.727131	+	0.401851i
$449$		−	9.78315i		−	0.461695i	−0.972990	−	0.230848i	$-0.925850\pi$
$449$		−	9.78315i		−	0.461695i	0.972990	−	0.230848i	$-0.0741499\pi$
$450$		0			0
$451$	−14.0454	+	14.0454i	−0.661371	+	0.661371i
$452$	7.75373	+	9.35853i	0.364705	+	0.440188i
$453$	−4.80992			−0.225990
$454$	0.910842	−	19.4676i	0.0427479	−	0.913660i
$455$		0			0
$456$	−1.00878	−	1.34046i	−0.0472404	−	0.0627729i
$457$	0.557108	+	0.557108i	0.0260604	+	0.0260604i	0.720017	−	0.693957i	$-0.244134\pi$
$457$	0.557108	+	0.557108i	0.0260604	+	0.0260604i	−0.693957	+	0.720017i	$0.744134\pi$
$458$	10.6510	+	11.6966i	0.497689	+	0.546546i
$459$	0.609992	−	0.609992i	0.0284720	−	0.0284720i
$460$		0			0
$461$	−12.5791	−	12.5791i	−0.585865	−	0.585865i	0.350644	−	0.936509i	$-0.385963\pi$
$461$	−12.5791	−	12.5791i	−0.585865	−	0.585865i	−0.936509	+	0.350644i	$0.885963\pi$
$462$	−9.14836	−	0.428030i	−0.425620	−	0.0199137i
$463$	3.29549	−	3.29549i	0.153154	−	0.153154i	−0.626371	−	0.779525i	$-0.715460\pi$
$463$	3.29549	−	3.29549i	0.153154	−	0.153154i	0.779525	+	0.626371i	$0.215460\pi$
$464$	10.5047	−	7.16177i	0.487669	−	0.332477i
$465$		0			0
$466$	−2.48427	+	2.26220i	−0.115082	+	0.104794i
$467$			10.1995i			0.471979i	0.971756	+	0.235989i	$0.0758331\pi$
$467$			10.1995i			0.471979i	−0.971756	+	0.235989i	$0.924167\pi$
$468$	−2.61997	+	27.9372i	−0.121108	+	1.29140i
$469$	−17.1311	−	17.1311i	−0.791042	−	0.791042i
$470$		0			0
$471$	4.95314			0.228229
$472$	24.4501	−	18.4002i	1.12541	−	0.846936i
$473$	18.8459	−	18.8459i	0.866534	−	0.866534i
$474$	5.83549	+	0.273028i	0.268033	+	0.0125406i
$475$		0			0
$476$	0.123959	−	1.32180i	0.00568164	−	0.0605845i
$477$	−2.77149			−0.126898
$478$	−16.6250	−	0.777843i	−0.760409	−	0.0355777i
$479$	5.65795			0.258518			0.129259	−	0.991611i	$-0.458740\pi$
$479$	5.65795			0.258518			0.129259	+	0.991611i	$0.458740\pi$
$480$		0			0
$481$	−26.1205			−1.19099
$482$	18.7504	+	0.877285i	0.854057	+	0.0399592i
$483$	2.63516			0.119904
$484$	−4.52175	+	48.2164i	−0.205534	+	2.19165i
$485$		0			0
$486$	−16.9050	−	0.790944i	−0.766826	−	0.0358780i
$487$	19.7470	−	19.7470i	0.894823	−	0.894823i	−0.100149	−	0.994972i	$-0.531932\pi$
$487$	19.7470	−	19.7470i	0.894823	−	0.894823i	0.994972	+	0.100149i	$0.0319321\pi$
$488$	4.57695	+	6.08184i	0.207189	+	0.275312i
$489$	−4.70802			−0.212904
$490$		0			0
$491$	−4.21405	−	4.21405i	−0.190177	−	0.190177i	0.605595	−	0.795773i	$-0.292935\pi$
$491$	−4.21405	−	4.21405i	−0.190177	−	0.190177i	−0.795773	+	0.605595i	$0.792935\pi$
$492$	0.310341	−	3.30923i	0.0139913	−	0.149192i
$493$			0.959871i			0.0432304i
$494$	−6.36500	+	5.79602i	−0.286375	+	0.260775i
$495$		0			0
$496$	0.608504	−	3.21577i	0.0273226	−	0.144392i
$497$	16.3712	−	16.3712i	0.734348	−	0.734348i
$498$	−6.43324	−	0.300996i	−0.288280	−	0.0134879i
$499$	−16.8862	−	16.8862i	−0.755928	−	0.755928i	0.219650	−	0.975579i	$-0.429508\pi$
$499$	−16.8862	−	16.8862i	−0.755928	−	0.755928i	−0.975579	+	0.219650i	$0.929508\pi$
$500$		0			0
$501$	4.68450	−	4.68450i	0.209288	−	0.209288i
$502$	−13.9768	−	15.3488i	−0.623814	−	0.685053i
$503$	20.3714	+	20.3714i	0.908317	+	0.908317i	0.996136	−	0.0878190i	$-0.0279897\pi$
$503$	20.3714	+	20.3714i	0.908317	+	0.908317i	−0.0878190	+	0.996136i	$0.527990\pi$
$504$	−13.6780	+	10.2935i	−0.609268	+	0.458511i
$505$		0			0
$506$	0.947086	−	20.2423i	0.0421031	−	0.899878i
$507$	−6.43550			−0.285811
$508$	−1.37087	−	1.65460i	−0.0608225	−	0.0734110i
$509$	−20.6309	+	20.6309i	−0.914448	+	0.914448i	−0.996618	−	0.0821701i	$-0.973815\pi$
$509$	−20.6309	+	20.6309i	−0.914448	+	0.914448i	0.0821701	+	0.996618i	$0.473815\pi$
$510$		0			0
$511$		−	8.41952i		−	0.372458i
$512$	−20.6536	−	9.24271i	−0.912770	−	0.408474i
$513$	−2.41307	−	2.41307i	−0.106540	−	0.106540i
$514$	30.2190	−	27.5177i	1.33290	−	1.21375i
$515$		0			0
$516$	−0.416411	+	4.44028i	−0.0183315	+	0.195472i
$517$			36.0320i			1.58469i
$518$	−10.7291	−	11.7824i	−0.471411	−	0.517688i
$519$		−	4.44215i		−	0.194989i
$520$		0			0
$521$			19.0433i			0.834300i	0.908838	+	0.417150i	$0.136971\pi$
$521$			19.0433i			0.834300i	−0.908838	+	0.417150i	$0.863029\pi$
$522$	9.15131	−	8.33325i	0.400542	−	0.364736i
$523$			19.1782i			0.838603i	0.907847	+	0.419301i	$0.137725\pi$
$523$			19.1782i			0.838603i	−0.907847	+	0.419301i	$0.862275\pi$
$524$	16.5527	−	13.7143i	0.723109	−	0.599110i
$525$		0			0
$526$	18.9343	+	20.7931i	0.825577	+	0.906622i
$527$	0.174722	+	0.174722i	0.00761101	+	0.00761101i
$528$	−6.63853	−	9.73723i	−0.288905	−	0.423759i
$529$		−	17.1693i		−	0.746490i
$530$		0			0
$531$	21.0644	−	21.0644i	0.914118	−	0.914118i
$532$	−5.22891	−	0.490369i	−0.226702	−	0.0212602i
$533$	−17.0553			−0.738749
$534$	2.98154	+	0.139499i	0.129024	+	0.00603671i
$535$		0			0
$536$	4.35831	−	30.8690i	0.188251	−	1.33334i
$537$	−1.50153	−	1.50153i	−0.0647957	−	0.0647957i
$538$	9.78118	−	8.90681i	0.421697	−	0.384000i
$539$	9.09950	−	9.09950i	0.391943	−	0.391943i
$540$		0			0
$541$	14.5231	+	14.5231i	0.624398	+	0.624398i	0.946653	−	0.322255i	$-0.104441\pi$
$541$	14.5231	+	14.5231i	0.624398	+	0.624398i	−0.322255	+	0.946653i	$0.604441\pi$
$542$	−0.702061	+	15.0053i	−0.0301561	+	0.644532i
$543$	−0.768787	+	0.768787i	−0.0329918	+	0.0329918i
$544$	1.45494	−	0.895300i	0.0623801	−	0.0383857i
$545$		0			0
$546$	−5.29456	−	5.81432i	−0.226586	−	0.248830i
$547$		−	9.97058i		−	0.426311i	−0.977018	−	0.213156i	$-0.931626\pi$
$547$		−	9.97058i		−	0.426311i	0.977018	−	0.213156i	$-0.0683742\pi$
$548$	−23.0598	−	27.8325i	−0.985067	−	1.18895i
$549$	5.23967	+	5.23967i	0.223624	+	0.223624i
$550$		0			0
$551$	3.79716			0.161765
$552$	2.03897	+	2.70938i	0.0867845	+	0.115319i
$553$	12.9316	−	12.9316i	0.549906	−	0.549906i
$554$	−0.547607	+	11.7041i	−0.0232656	+	0.497260i
$555$		0			0
$556$	16.8627	−	13.9711i	0.715138	−	0.592506i
$557$	−11.4424			−0.484831			−0.242416	−	0.970173i	$-0.577940\pi$
$557$	−11.4424			−0.484831			−0.242416	+	0.970173i	$0.577940\pi$
$558$	0.148909	−	3.18265i	0.00630381	−	0.134732i
$559$	22.8846			0.967915
$560$		0			0
$561$	0.889743			0.0375650
$562$	−1.38916	+	29.6909i	−0.0585984	+	1.25243i
$563$	−47.0585			−1.98328			−0.991640	−	0.129034i	$-0.958812\pi$
$563$	−47.0585			−1.98328			−0.991640	+	0.129034i	$0.958812\pi$
$564$	−3.84668	−	4.64283i	−0.161975	−	0.195499i
$565$		0			0
$566$	−0.956715	+	20.4481i	−0.0402137	+	0.859496i
$567$	−10.6346	+	10.6346i	−0.446612	+	0.446612i
$568$	29.4996	+	4.16498i	1.23778	+	0.174759i
$569$	41.4684			1.73845			0.869224	−	0.494419i	$-0.164619\pi$
$569$	41.4684			1.73845			0.869224	+	0.494419i	$0.164619\pi$
$570$		0			0
$571$	16.1745	+	16.1745i	0.676881	+	0.676881i	0.959293	−	0.282412i	$-0.0911347\pi$
$571$	16.1745	+	16.1745i	0.676881	+	0.676881i	−0.282412	+	0.959293i	$0.591135\pi$
$572$	−46.5662	+	38.5811i	−1.94703	+	1.61316i
$573$			9.97963i			0.416905i
$574$	−7.00556	−	7.69329i	−0.292407	−	0.321112i
$575$		0			0
$576$	−21.1670	−	6.09859i	−0.881957	−	0.254108i
$577$	−20.0316	+	20.0316i	−0.833926	+	0.833926i	−0.988051	−	0.154125i	$-0.950744\pi$
$577$	−20.0316	+	20.0316i	−0.833926	+	0.833926i	0.154125	+	0.988051i	$0.450744\pi$
$578$	1.11759	−	23.8865i	0.0464857	−	0.993548i
$579$	−1.89898	−	1.89898i	−0.0789189	−	0.0789189i
$580$		0			0
$581$	−14.2562	+	14.2562i	−0.591447	+	0.591447i
$582$	−5.25678	+	4.78686i	−0.217900	+	0.198422i
$583$	−4.22349	−	4.22349i	−0.174919	−	0.174919i
$584$	8.65667	−	6.51467i	0.358215	−	0.269579i
$585$		0			0
$586$	−16.8341	−	0.787627i	−0.695411	−	0.0325366i
$587$	−29.1190			−1.20187			−0.600935	−	0.799298i	$-0.705205\pi$
$587$	−29.1190			−1.20187			−0.600935	+	0.799298i	$0.705205\pi$
$588$	−0.201059	+	2.14394i	−0.00829155	+	0.0884145i
$589$	0.691185	−	0.691185i	0.0284798	−	0.0284798i
$590$		0			0
$591$		−	0.554866i		−	0.0228242i
$592$	3.81251	−	20.1480i	0.156693	−	0.828079i
$593$	10.3431	+	10.3431i	0.424740	+	0.424740i	0.886832	−	0.462092i	$-0.152901\pi$
$593$	10.3431	+	10.3431i	0.424740	+	0.424740i	−0.462092	+	0.886832i	$0.652901\pi$
$594$	−16.1403	−	17.7248i	−0.662246	−	0.727258i
$595$		0			0
$596$	17.2722	+	20.8471i	0.707499	+	0.853930i
$597$		−	12.7016i		−	0.519843i
$598$	12.8651	−	11.7151i	0.526095	−	0.479066i
$599$			2.59479i			0.106020i	0.998594	+	0.0530101i	$0.0168816\pi$
$599$			2.59479i			0.106020i	−0.998594	+	0.0530101i	$0.983118\pi$
$600$		0			0
$601$		−	14.4092i		−	0.587765i	−0.955842	−	0.293882i	$-0.905053\pi$
$601$		−	14.4092i		−	0.587765i	0.955842	−	0.293882i	$-0.0949474\pi$
$602$	9.39996	+	10.3227i	0.383114	+	0.420723i
$603$		−	30.3493i		−	1.23592i
$604$	−19.2912	−	1.80913i	−0.784946	−	0.0736126i
$605$		0			0
$606$	−6.15870	+	5.60816i	−0.250180	+	0.227816i
$607$	11.8502	+	11.8502i	0.480985	+	0.480985i	0.905446	−	0.424461i	$-0.139536\pi$
$607$	11.8502	+	11.8502i	0.480985	+	0.480985i	−0.424461	+	0.905446i	$0.639536\pi$
$608$	−3.54173	−	5.75562i	−0.143636	−	0.233421i
$609$			3.46864i			0.140557i
$610$		0			0
$611$	−21.8769	+	21.8769i	−0.885045	+	0.885045i
$612$	1.28064	−	1.06104i	0.0517669	−	0.0428899i
$613$	−16.8256			−0.679579			−0.339789	−	0.940502i	$-0.610356\pi$
$613$	−16.8256			−0.679579			−0.339789	+	0.940502i	$0.610356\pi$
$614$	−1.68220	+	35.9540i	−0.0678881	+	1.45099i
$615$		0			0
$616$	−36.5304	−	5.15763i	−1.47185	−	0.207807i
$617$	22.4849	+	22.4849i	0.905209	+	0.905209i	0.995881	−	0.0906720i	$-0.0289015\pi$
$617$	22.4849	+	22.4849i	0.905209	+	0.905209i	−0.0906720	+	0.995881i	$0.528902\pi$
$618$	−3.45295	−	3.79191i	−0.138898	−	0.152533i
$619$	−14.1269	+	14.1269i	−0.567809	+	0.567809i	−0.931514	−	0.363705i	$-0.881512\pi$
$619$	−14.1269	+	14.1269i	−0.567809	+	0.567809i	0.363705	+	0.931514i	$0.381512\pi$
$620$		0			0
$621$	4.87738	+	4.87738i	0.195723	+	0.195723i
$622$	−30.3406	−	1.41956i	−1.21655	−	0.0569193i
$623$	6.60715	−	6.60715i	0.264710	−	0.264710i
$624$	1.88138	−	9.94257i	0.0753156	−	0.398021i
$625$		0			0
$626$	27.7956	−	25.3109i	1.11094	−	1.01163i
$627$		−	3.51974i		−	0.140565i
$628$	19.8656	+	1.86300i	0.792723	+	0.0743419i
$629$	1.09470	+	1.09470i	0.0436486	+	0.0436486i
$630$		0			0
$631$	−33.9235			−1.35047			−0.675236	−	0.737601i	$-0.735958\pi$
$631$	−33.9235			−1.35047			−0.675236	+	0.737601i	$0.735958\pi$
$632$	23.3017	+	3.28991i	0.926892	+	0.130866i
$633$	0.204361	−	0.204361i	0.00812261	−	0.00812261i
$634$	22.9602	+	1.07425i	0.911867	+	0.0426640i
$635$		0			0
$636$	0.995097	+	0.0933206i	0.0394582	+	0.00370040i
$637$	11.0496			0.437799
$638$	26.6448	+	1.24664i	1.05488	+	0.0493551i
$639$	29.0030			1.14734
$640$		0			0
$641$	18.8495			0.744509			0.372254	−	0.928131i	$-0.378585\pi$
$641$	18.8495			0.744509			0.372254	+	0.928131i	$0.378585\pi$
$642$	6.29813	+	0.294674i	0.248567	+	0.0116299i
$643$	16.4916			0.650364			0.325182	−	0.945652i	$-0.394574\pi$
$643$	16.4916			0.650364			0.325182	+	0.945652i	$0.394574\pi$
$644$	10.5688	+	0.991150i	0.416471	+	0.0390568i
$645$		0			0
$646$	0.509664	+	0.0238459i	0.0200525	+	0.000938206i
$647$	0.316870	−	0.316870i	0.0124574	−	0.0124574i	−0.700851	−	0.713308i	$-0.747196\pi$
$647$	0.316870	−	0.316870i	0.0124574	−	0.0124574i	0.713308	+	0.700851i	$0.247196\pi$
$648$	−19.1628	−	2.70555i	−0.752786	−	0.106284i
$649$	64.2002			2.52008
$650$		0			0
$651$	0.631386	+	0.631386i	0.0247460	+	0.0247460i
$652$	−18.8825	−	1.77081i	−0.739495	−	0.0693502i
$653$			17.0751i			0.668200i	0.942538	+	0.334100i	$0.108432\pi$
$653$			17.0751i			0.668200i	−0.942538	+	0.334100i	$0.891568\pi$
$654$	−8.00859	+	7.29268i	−0.313161	+	0.285167i
$655$		0			0
$656$	2.48937	−	13.1556i	0.0971937	−	0.513641i
$657$	7.45796	−	7.45796i	0.290963	−	0.290963i
$658$	−18.8542	−	0.882144i	−0.735014	−	0.0343895i
$659$	−7.42245	−	7.42245i	−0.289138	−	0.289138i	0.547601	−	0.836739i	$-0.315541\pi$
$659$	−7.42245	−	7.42245i	−0.289138	−	0.289138i	−0.836739	+	0.547601i	$0.815541\pi$
$660$		0			0
$661$	31.7614	−	31.7614i	1.23538	−	1.23538i	0.273507	−	0.961870i	$-0.411816\pi$
$661$	31.7614	−	31.7614i	1.23538	−	1.23538i	0.961870	−	0.273507i	$-0.0881837\pi$
$662$	11.7362	+	12.8883i	0.456139	+	0.500917i
$663$	0.540209	+	0.540209i	0.0209800	+	0.0209800i
$664$	−25.6886	−	3.62691i	−0.996911	−	0.140751i
$665$		0			0
$666$	0.932970	−	19.9406i	0.0361519	−	0.772681i
$667$	−7.67495			−0.297175
$668$	20.5501	−	17.0262i	0.795107	−	0.658762i
$669$	8.31446	−	8.31446i	0.321456	−	0.321456i
$670$		0			0
$671$			15.9695i			0.616496i
$672$	5.25766	−	3.23531i	0.202819	−	0.124805i
$673$	−4.14672	−	4.14672i	−0.159844	−	0.159844i	0.622653	−	0.782498i	$-0.286055\pi$
$673$	−4.14672	−	4.14672i	−0.159844	−	0.159844i	−0.782498	+	0.622653i	$0.786055\pi$
$674$	0.0601670	−	0.0547885i	0.00231755	−	0.00211037i
$675$		0			0
$676$	−25.8109	−	2.42056i	−0.992727	−	0.0930983i
$677$		−	25.2618i		−	0.970890i	−0.874267	−	0.485445i	$-0.838658\pi$
$677$		−	25.2618i		−	0.970890i	0.874267	−	0.485445i	$-0.161342\pi$
$678$	−2.87268	−	3.15468i	−0.110325	−	0.121155i
$679$			22.2569i			0.854143i
$680$		0			0
$681$			6.84196i			0.262184i
$682$	5.07698	−	4.62313i	0.194408	−	0.177029i
$683$			8.20306i			0.313881i	0.987608	+	0.156941i	$0.0501631\pi$
$683$			8.20306i			0.313881i	−0.987608	+	0.156941i	$0.949837\pi$
$684$	−4.19737	−	5.06610i	−0.160490	−	0.193707i
$685$		0			0
$686$	19.1891	+	21.0728i	0.732643	+	0.804565i
$687$	−3.92707	−	3.92707i	−0.149827	−	0.149827i
$688$	−3.34020	+	17.6520i	−0.127344	+	0.672977i
$689$		−	5.12859i		−	0.195384i
$690$		0			0
$691$	−7.89158	+	7.89158i	−0.300210	+	0.300210i	−0.841096	−	0.540886i	$-0.818089\pi$
$691$	−7.89158	+	7.89158i	−0.300210	+	0.300210i	0.540886	+	0.841096i	$0.318089\pi$
$692$	1.67081	−	17.8162i	0.0635145	−	0.677268i
$693$	−35.9153			−1.36431
$694$	−50.4455	−	2.36022i	−1.91489	−	0.0895929i
$695$		0			0
$696$	−3.56635	+	2.68389i	−0.135182	+	0.101733i
$697$	0.714783	+	0.714783i	0.0270744	+	0.0270744i
$698$	0.405850	−	0.369570i	0.0153616	−	0.0139884i
$699$	0.834083	−	0.834083i	0.0315479	−	0.0315479i
$700$		0			0
$701$	1.50228	+	1.50228i	0.0567405	+	0.0567405i	0.734908	−	0.678167i	$-0.237225\pi$
$701$	1.50228	+	1.50228i	0.0567405	+	0.0567405i	−0.678167	+	0.734908i	$0.737225\pi$
$702$	0.962012	−	20.5613i	0.0363088	−	0.776036i
$703$	4.33054	−	4.33054i	0.163329	−	0.163329i
$704$	−22.9627	−	41.5501i	−0.865441	−	1.56598i
$705$		0			0
$706$	−21.0354	−	23.1004i	−0.791679	−	0.869397i
$707$			26.0756i			0.980675i
$708$	−8.27239	+	6.85385i	−0.310896	+	0.257583i
$709$	−36.0738	−	36.0738i	−1.35478	−	1.35478i	−0.880228	−	0.474551i	$-0.842610\pi$
$709$	−36.0738	−	36.0738i	−1.35478	−	1.35478i	−0.474551	−	0.880228i	$-0.657390\pi$
$710$		0			0
$711$	22.9094			0.859170
$712$	11.9056	+	1.68092i	0.446181	+	0.0629952i
$713$	−1.39704	+	1.39704i	−0.0523197	+	0.0523197i
$714$	−0.0217829	+	0.465570i	−0.000815203	+	0.0174235i
$715$		0			0
$716$	−5.45741	−	6.58694i	−0.203953	−	0.246165i
$717$	5.84291			0.218207
$718$	0.0508132	−	1.08604i	0.00189633	−	0.0405307i
$719$	−35.0340			−1.30655			−0.653274	−	0.757121i	$-0.726605\pi$
$719$	−35.0340			−1.30655			−0.653274	+	0.757121i	$0.726605\pi$
$720$		0			0
$721$	−16.0548			−0.597911
$722$	−1.16148	+	24.8245i	−0.0432258	+	0.923873i
$723$	−6.58989			−0.245081
$724$	−3.37253	+	2.79421i	−0.125339	+	0.103846i
$725$		0			0
$726$	0.794593	−	16.9830i	0.0294901	−	0.630298i
$727$	−25.4241	+	25.4241i	−0.942928	+	0.942928i	−0.998457	−	0.0555295i	$-0.982315\pi$
$727$	−25.4241	+	25.4241i	−0.942928	+	0.942928i	0.0555295	+	0.998457i	$0.482315\pi$
$728$	−19.0480	−	25.3109i	−0.705966	−	0.938085i
$729$	−14.5855			−0.540203
$730$		0			0
$731$	−0.959085	−	0.959085i	−0.0354731	−	0.0354731i
$732$	−1.70486	−	2.05772i	−0.0630135	−	0.0760555i
$733$			7.37554i			0.272422i	0.990680	+	0.136211i	$0.0434925\pi$
$733$			7.37554i			0.272422i	−0.990680	+	0.136211i	$0.956508\pi$
$734$	18.5624	+	20.3847i	0.685151	+	0.752411i
$735$		0			0
$736$	7.15865	+	11.6334i	0.263871	+	0.428814i
$737$	46.2494	−	46.2494i	1.70362	−	1.70362i
$738$	0.609181	−	13.0202i	0.0224243	−	0.479278i
$739$	5.55025	+	5.55025i	0.204169	+	0.204169i	0.801784	−	0.597614i	$-0.203885\pi$
$739$	5.55025	+	5.55025i	0.204169	+	0.204169i	−0.597614	+	0.801784i	$0.703885\pi$
$740$		0			0
$741$	2.13702	−	2.13702i	0.0785053	−	0.0785053i
$742$	2.31339	−	2.10659i	0.0849274	−	0.0773355i
$743$	6.78835	+	6.78835i	0.249040	+	0.249040i	0.820577	−	0.571536i	$-0.193652\pi$
$743$	6.78835	+	6.78835i	0.249040	+	0.249040i	−0.571536	+	0.820577i	$0.693652\pi$
$744$	−0.160630	+	1.13771i	−0.00588899	+	0.0417104i
$745$		0			0
$746$	−30.2315	−	1.41446i	−1.10685	−	0.0517869i
$747$	−25.2561			−0.924073
$748$	3.56849	+	0.334655i	0.130477	+	0.0122362i
$749$	13.9568	−	13.9568i	0.509970	−	0.509970i
$750$		0			0
$751$		−	3.93385i		−	0.143548i	−0.997421	−	0.0717742i	$-0.977134\pi$
$751$		−	3.93385i		−	0.143548i	0.997421	−	0.0717742i	$-0.0228661\pi$
$752$	−13.6816	−	20.0679i	−0.498917	−	0.731799i
$753$	5.15330	+	5.15330i	0.187797	+	0.187797i
$754$	15.4205	+	16.9343i	0.561582	+	0.616711i
$755$		0			0
$756$	9.66989	−	8.01170i	0.351690	−	0.291383i
$757$		−	21.8327i		−	0.793525i	−0.917921	−	0.396762i	$-0.870134\pi$
$757$		−	21.8327i		−	0.793525i	0.917921	−	0.396762i	$-0.129866\pi$
$758$	−16.8464	+	15.3405i	−0.611890	+	0.557191i
$759$			7.11421i			0.258230i
$760$		0			0
$761$			4.27291i			0.154893i	0.996997	+	0.0774464i	$0.0246767\pi$
$761$			4.27291i			0.154893i	−0.996997	+	0.0774464i	$0.975323\pi$
$762$	0.507893	+	0.557752i	0.0183990	+	0.0202052i
$763$			33.9080i			1.22755i
$764$	−3.75359	+	40.0253i	−0.135800	+	1.44807i
$765$		0			0
$766$	6.54552	−	5.96040i	0.236499	−	0.215358i
$767$	38.9793	+	38.9793i	1.40746	+	1.40746i
$768$	7.39459	+	2.90241i	0.266829	+	0.104732i
$769$		−	26.1800i		−	0.944074i	−0.881579	−	0.472037i	$-0.843519\pi$
$769$		−	26.1800i		−	0.944074i	0.881579	−	0.472037i	$-0.156481\pi$
$770$		0			0
$771$	−10.1459	+	10.1459i	−0.365395	+	0.365395i
$772$	−6.90198	−	8.33049i	−0.248408	−	0.299821i
$773$	15.0077			0.539791			0.269895	−	0.962890i	$-0.413011\pi$
$773$	15.0077			0.539791			0.269895	+	0.962890i	$0.413011\pi$
$774$	−0.817390	+	17.4702i	−0.0293805	+	0.627955i
$775$		0			0
$776$	−22.8838	+	17.2215i	−0.821482	+	0.618215i
$777$	3.95587	+	3.95587i	0.141916	+	0.141916i
$778$	−16.6305	−	18.2630i	−0.596231	−	0.654762i
$779$	2.82762	−	2.82762i	0.101310	−	0.101310i
$780$		0			0
$781$	44.1977	+	44.1977i	1.58152	+	1.58152i
$782$	−1.03015	−	0.0481982i	−0.0368381	−	0.00172356i
$783$	−6.42007	+	6.42007i	−0.229434	+	0.229434i
$784$	−1.61278	+	8.52307i	−0.0575992	+	0.304395i
$785$		0			0
$786$	−5.57978	+	5.08099i	−0.199024	+	0.181233i
$787$		−	42.9223i		−	1.53001i	−0.644022	−	0.765007i	$-0.722736\pi$
$787$		−	42.9223i		−	1.53001i	0.644022	−	0.765007i	$-0.277264\pi$
$788$	0.208699	−	2.22540i	0.00743461	−	0.0792767i
$789$	−6.98118	−	6.98118i	−0.248536	−	0.248536i
$790$		0			0
$791$	−13.3568			−0.474912
$792$	−27.7898	−	36.9270i	−0.987466	−	1.31214i
$793$	−9.69591	+	9.69591i	−0.344312	+	0.344312i
$794$	25.4043	+	1.18861i	0.901565	+	0.0421820i
$795$		0			0
$796$	4.77741	−	50.9425i	0.169331	−	1.80561i
$797$	−0.280831			−0.00994753			−0.00497377	−	0.999988i	$-0.501583\pi$
$797$	−0.280831			−0.00994753			−0.00497377	+	0.999988i	$0.501583\pi$
$798$	1.84175	+	0.0861711i	0.0651973	+	0.00305042i
$799$	1.83371			0.0648719
$800$		0			0
$801$	11.7052			0.413581
$802$	−12.8068	−	0.599200i	−0.452225	−	0.0211585i
$803$	22.7304			0.802139
$804$	−1.02191	+	10.8968i	−0.0360400	+	0.384301i
$805$		0			0
$806$	5.88944	+	0.275553i	0.207447	+	0.00970593i
$807$	−3.28398	+	3.28398i	−0.115602	+	0.115602i
$808$	−26.8101	+	20.1762i	−0.943176	+	0.709797i
$809$	−16.5787			−0.582876			−0.291438	−	0.956590i	$-0.594134\pi$
$809$	−16.5787			−0.582876			−0.291438	+	0.956590i	$0.594134\pi$
$810$		0			0
$811$	7.25384	+	7.25384i	0.254717	+	0.254717i	0.822901	−	0.568184i	$-0.192354\pi$
$811$	7.25384	+	7.25384i	0.254717	+	0.254717i	−0.568184	+	0.822901i	$0.692354\pi$
$812$	−1.30465	+	13.9117i	−0.0457841	+	0.488205i
$813$		−	5.27366i		−	0.184955i
$814$	31.8092	−	28.9657i	1.11491	−	1.01525i
$815$		0			0
$816$	−0.495538	+	0.337841i	−0.0173473	+	0.0118268i
$817$	−3.79405	+	3.79405i	−0.132737	+	0.132737i
$818$	42.4671	+	1.98693i	1.48483	+	0.0694715i
$819$	−21.8061	−	21.8061i	−0.761965	−	0.761965i
$820$		0			0
$821$	−15.3525	+	15.3525i	−0.535806	+	0.535806i	−0.922294	−	0.386489i	$-0.873688\pi$
$821$	−15.3525	+	15.3525i	−0.535806	+	0.535806i	0.386489	+	0.922294i	$0.373688\pi$
$822$	8.54343	+	9.38212i	0.297986	+	0.327239i
$823$	26.7794	+	26.7794i	0.933472	+	0.933472i	0.997921	−	0.0644492i	$-0.0205290\pi$
$823$	26.7794	+	26.7794i	0.933472	+	0.933472i	−0.0644492	+	0.997921i	$0.520529\pi$
$824$	−12.4225	−	16.5070i	−0.432758	−	0.575048i
$825$		0			0
$826$	−1.57176	+	33.5936i	−0.0546887	+	1.16887i
$827$	39.4186			1.37072			0.685359	−	0.728205i	$-0.259645\pi$
$827$	39.4186			1.37072			0.685359	+	0.728205i	$0.259645\pi$
$828$	8.48386	+	10.2398i	0.294834	+	0.355857i
$829$	−20.7102	+	20.7102i	−0.719296	+	0.719296i	−0.968461	−	0.249165i	$-0.919844\pi$
$829$	−20.7102	+	20.7102i	−0.719296	+	0.719296i	0.249165	+	0.968461i	$0.419844\pi$
$830$		0			0
$831$		−	4.11345i		−	0.142694i
$832$	11.2853	−	39.1690i	0.391248	−	1.35794i
$833$	−0.463083	−	0.463083i	−0.0160449	−	0.0160449i
$834$	−5.68428	+	5.17615i	−0.196830	+	0.179235i
$835$		0			0
$836$	1.32386	−	14.1166i	0.0457868	−	0.488234i
$837$			2.33725i			0.0807870i
$838$	20.7354	+	22.7709i	0.716291	+	0.786608i
$839$			31.8706i			1.10029i	0.835068	+	0.550147i	$0.185428\pi$
$839$			31.8706i			1.10029i	−0.835068	+	0.550147i	$0.814572\pi$
$840$		0			0
$841$			18.8975i			0.651638i
$842$	5.71495	−	5.20408i	0.196950	−	0.179344i
$843$		−	10.4350i		−	0.359399i
$844$	0.896495	−	0.742765i	0.0308586	−	0.0255670i
$845$		0			0
$846$	−15.9196	−	17.4824i	−0.547326	−	0.601056i
$847$	−37.6347	−	37.6347i	−1.29314	−	1.29314i
$848$	3.95594	+	0.748562i	0.135847	+	0.0257057i
$849$		−	7.18654i		−	0.246642i
$850$		0			0
$851$	−8.75302	+	8.75302i	−0.300050	+	0.300050i
$852$	−10.4134	−	0.976577i	−0.356759	−	0.0334570i
$853$	26.5538			0.909185			0.454592	−	0.890700i	$-0.349785\pi$
$853$	26.5538			0.909185			0.454592	+	0.890700i	$0.349785\pi$
$854$	−8.35626	−	0.390969i	−0.285945	−	0.0133787i
$855$		0			0
$856$	25.1491	+	3.55074i	0.859578	+	0.121362i
$857$	20.7249	+	20.7249i	0.707951	+	0.707951i	0.966104	−	0.258153i	$-0.0831140\pi$
$857$	20.7249	+	20.7249i	0.707951	+	0.707951i	−0.258153	+	0.966104i	$0.583114\pi$
$858$	15.6971	−	14.2939i	0.535890	−	0.487985i
$859$	35.9248	−	35.9248i	1.22574	−	1.22574i	0.260176	−	0.965561i	$-0.416219\pi$
$859$	35.9248	−	35.9248i	1.22574	−	1.22574i	0.965561	−	0.260176i	$-0.0837807\pi$
$860$		0			0
$861$	2.58298	+	2.58298i	0.0880278	+	0.0880278i
$862$	−1.80237	+	38.5224i	−0.0613889	+	1.31208i
$863$	−9.19232	+	9.19232i	−0.312910	+	0.312910i	−0.846036	−	0.533126i	$-0.821017\pi$
$863$	−9.19232	+	9.19232i	−0.312910	+	0.312910i	0.533126	+	0.846036i	$0.321017\pi$
$864$	15.7195	+	3.74314i	0.534789	+	0.127344i
$865$		0			0
$866$	25.7781	+	28.3087i	0.875976	+	0.961969i
$867$			8.39500i			0.285109i
$868$	2.29482	+	2.76978i	0.0778913	+	0.0940125i
$869$	34.9117	+	34.9117i	1.18430	+	1.18430i
$870$		0			0
$871$	56.1608			1.90293
$872$	−34.8630	+	26.2365i	−1.18061	+	0.888482i
$873$	−19.7151	+	19.7151i	−0.667253	+	0.667253i
$874$	−0.190668	+	4.07518i	−0.00644943	+	0.137845i
$875$		0			0
$876$	−2.92888	+	2.42664i	−0.0989577	+	0.0819885i
$877$	17.9106			0.604799			0.302399	−	0.953181i	$-0.402212\pi$
$877$	17.9106			0.604799			0.302399	+	0.953181i	$0.402212\pi$
$878$	1.99605	−	42.6619i	0.0673633	−	1.43977i
$879$	5.91641			0.199556
$880$		0			0
$881$	6.01537			0.202663			0.101332	−	0.994853i	$-0.467690\pi$
$881$	6.01537			0.202663			0.101332	+	0.994853i	$0.467690\pi$
$882$	−0.394667	+	8.43530i	−0.0132891	+	0.284031i
$883$	−19.8374			−0.667580			−0.333790	−	0.942647i	$-0.608328\pi$
$883$	−19.8374			−0.667580			−0.333790	+	0.942647i	$0.608328\pi$
$884$	1.96343	+	2.36980i	0.0660373	+	0.0797051i
$885$		0			0
$886$	−1.83117	+	39.1381i	−0.0615195	+	1.31487i
$887$	−14.3740	+	14.3740i	−0.482632	+	0.482632i	−0.905971	−	0.423339i	$-0.860858\pi$
$887$	−14.3740	+	14.3740i	−0.482632	+	0.482632i	0.423339	+	0.905971i	$0.360858\pi$
$888$	−1.00641	+	7.12819i	−0.0337729	+	0.239206i
$889$	2.36149			0.0792019
$890$		0			0
$891$	−28.7106	−	28.7106i	−0.961842	−	0.961842i
$892$	36.4741	−	30.2196i	1.22124	−	1.01183i
$893$		−	7.25398i		−	0.242745i
$894$	−6.39919	−	7.02739i	−0.214021	−	0.235031i
$895$		0			0
$896$	22.3038	−	10.9983i	0.745117	−	0.367428i
$897$	−4.31941	+	4.31941i	−0.144221	+	0.144221i
$898$	−0.646620	+	13.8203i	−0.0215780	+	0.461191i
$899$	−1.83892	−	1.83892i	−0.0613315	−	0.0613315i
$900$		0			0
$901$	−0.214938	+	0.214938i	−0.00716061	+	0.00716061i
$902$	20.7698	−	18.9131i	0.691558	−	0.629738i
$903$	−3.46580	−	3.46580i	−0.115335	−	0.115335i
$904$	−10.3349	−	13.7330i	−0.343734	−	0.456752i
$905$		0			0
$906$	6.79482	+	0.317913i	0.225743	+	0.0105620i
$907$	39.0417			1.29636			0.648180	−	0.761487i	$-0.275531\pi$
$907$	39.0417			1.29636			0.648180	+	0.761487i	$0.275531\pi$
$908$	−2.57343	+	27.4411i	−0.0854024	+	0.910663i
$909$	−23.0976	+	23.0976i	−0.766100	+	0.766100i
$910$		0			0
$911$			14.0166i			0.464392i	0.972669	+	0.232196i	$0.0745911\pi$
$911$			14.0166i			0.464392i	−0.972669	+	0.232196i	$0.925409\pi$
$912$	1.33647	+	1.96030i	0.0442550	+	0.0649121i
$913$	−38.4879	−	38.4879i	−1.27376	−	1.27376i
$914$	−0.750187	−	0.823831i	−0.0248140	−	0.0272499i
$915$		0			0
$916$	−14.2732	−	17.2274i	−0.471601	−	0.569209i
$917$			23.6245i			0.780150i
$918$	−0.902034	+	0.821399i	−0.0297716	+	0.0271102i
$919$			8.15149i			0.268893i	0.990921	+	0.134446i	$0.0429256\pi$
$919$			8.15149i			0.268893i	−0.990921	+	0.134446i	$0.957074\pi$
$920$		0			0
$921$		−	12.6362i		−	0.416376i
$922$	16.9386	+	18.6015i	0.557844	+	0.612606i
$923$			53.6695i			1.76655i
$924$	12.8953	+	1.20933i	0.424224	+	0.0397840i
$925$		0			0
$926$	−4.87325	+	4.43762i	−0.160145	+	0.145829i
$927$	−14.2212	−	14.2212i	−0.467086	−	0.467086i
$928$	−15.3130	+	9.42289i	−0.502675	+	0.309322i
$929$			13.4779i			0.442196i	0.975252	+	0.221098i	$0.0709641\pi$
$929$			13.4779i			0.442196i	−0.975252	+	0.221098i	$0.929036\pi$
$930$		0			0
$931$	−1.83192	+	1.83192i	−0.0600386	+	0.0600386i
$932$	3.65898	−	3.03154i	0.119854	−	0.0993013i
$933$	10.6633			0.349101
$934$	0.674142	−	14.4086i	0.0220586	−	0.471463i
$935$		0			0
$936$	5.54766	−	39.2929i	0.181331	−	1.28433i
$937$	15.8564	+	15.8564i	0.518005	+	0.518005i	0.916967	−	0.398963i	$-0.130630\pi$
$937$	15.8564	+	15.8564i	0.518005	+	0.518005i	−0.398963	+	0.916967i	$0.630630\pi$
$938$	23.0683	+	25.3329i	0.753207	+	0.827148i
$939$	−9.33225	+	9.33225i	−0.304546	+	0.304546i
$940$		0			0
$941$	15.7073	+	15.7073i	0.512044	+	0.512044i	0.915152	−	0.403108i	$-0.132070\pi$
$941$	15.7073	+	15.7073i	0.512044	+	0.512044i	−0.403108	+	0.915152i	$0.632070\pi$
$942$	−6.99715	−	0.327380i	−0.227979	−	0.0106666i
$943$	−5.71527	+	5.71527i	−0.186115	+	0.186115i
$944$	−35.7560	+	24.3773i	−1.16376	+	0.793413i
$945$		0			0
$946$	−27.8686	+	25.3773i	−0.906085	+	0.825088i
$947$		−	33.6925i		−	1.09486i	−0.836852	−	0.547430i	$-0.815606\pi$
$947$		−	33.6925i		−	1.09486i	0.836852	−	0.547430i	$-0.184394\pi$
$948$	−8.22556	−	0.771397i	−0.267154	−	0.0250538i
$949$	13.8008	+	13.8008i	0.447993	+	0.447993i
$950$		0			0
$951$	−8.06945			−0.261670
$952$	−0.262477	+	1.85907i	−0.00850693	+	0.0602527i
$953$	33.5702	−	33.5702i	1.08745	−	1.08745i	0.0916550	−	0.995791i	$-0.470784\pi$
$953$	33.5702	−	33.5702i	1.08745	−	1.08745i	0.995791	−	0.0916550i	$-0.0292157\pi$
$954$	3.91520	+	0.183183i	0.126759	+	0.00593076i
$955$		0			0
$956$	23.4342	+	2.19767i	0.757915	+	0.0710776i
$957$	−9.36440			−0.302708
$958$	−7.99281	−	0.373964i	−0.258236	−	0.0120822i
$959$	39.7234			1.28274
$960$		0			0
$961$	30.3305			0.978404
$962$	36.8996	+	1.72644i	1.18969	+	0.0556628i
$963$	24.7257			0.796774
$964$	−26.4301	−	2.47863i	−0.851256	−	0.0798311i
$965$		0			0
$966$	−3.72261	−	0.174172i	−0.119773	−	0.00560388i
$967$	−28.6436	+	28.6436i	−0.921115	+	0.921115i	−0.997108	−	0.0759933i	$-0.975787\pi$
$967$	−28.6436	+	28.6436i	−0.921115	+	0.921115i	0.0759933	+	0.997108i	$0.475787\pi$
$968$	9.57461	−	67.8149i	0.307740	−	2.17965i
$969$	−0.179123			−0.00575427
$970$		0			0
$971$	−35.7115	−	35.7115i	−1.14604	−	1.14604i	−0.987325	−	0.158713i	$-0.949266\pi$
$971$	−35.7115	−	35.7115i	−1.14604	−	1.14604i	−0.158713	−	0.987325i	$-0.550734\pi$
$972$	23.8289	+	2.23468i	0.764312	+	0.0716775i
$973$			24.0669i			0.771551i
$974$	−29.2012	+	26.5908i	−0.935666	+	0.852024i
$975$		0			0
$976$	−6.06373	−	8.89414i	−0.194095	−	0.284694i
$977$	−7.12822	+	7.12822i	−0.228052	+	0.228052i	−0.811879	−	0.583826i	$-0.801555\pi$
$977$	−7.12822	+	7.12822i	−0.228052	+	0.228052i	0.583826	+	0.811879i	$0.301555\pi$
$978$	6.65088	+	0.311178i	0.212672	+	0.00995039i
$979$	17.8375	+	17.8375i	0.570090	+	0.570090i
$980$		0			0
$981$	−30.0355	+	30.0355i	−0.958959	+	0.958959i
$982$	5.67452	+	6.23158i	0.181081	+	0.198858i
$983$	23.9941	+	23.9941i	0.765292	+	0.765292i	0.977274	−	0.211982i	$-0.0679918\pi$
$983$	23.9941	+	23.9941i	0.765292	+	0.765292i	−0.211982	+	0.977274i	$0.567992\pi$
$984$	−0.657134	+	4.65434i	−0.0209487	+	0.148375i
$985$		0			0
$986$	0.0634430	−	1.35598i	0.00202044	−	0.0431832i
$987$	6.62639			0.210920
$988$	9.37472	−	7.76715i	0.298250	−	0.247106i
$989$	7.66866	−	7.66866i	0.243849	−	0.243849i
$990$		0			0
$991$		−	40.6040i		−	1.28983i	−0.764255	−	0.644914i	$-0.776893\pi$
$991$		−	40.6040i		−	1.28983i	0.764255	−	0.644914i	$-0.223107\pi$
$992$	−1.07216	+	4.50260i	−0.0340412	+	0.142958i
$993$	−4.32718	−	4.32718i	−0.137319	−	0.137319i
$994$	−24.2091	+	22.0450i	−0.767866	+	0.699225i
$995$		0			0
$996$	9.06814	+	0.850414i	0.287335	+	0.0269464i
$997$		−	54.9087i		−	1.73898i	−0.493953	−	0.869488i	$-0.664449\pi$
$997$		−	54.9087i		−	1.73898i	0.493953	−	0.869488i	$-0.335551\pi$
$998$	22.7384	+	24.9706i	0.719773	+	0.790431i
$999$			14.6437i			0.463308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.s.d.243.1		18
4.3	odd	2		1600.2.s.d.943.4		18
5.2	odd	4		400.2.j.d.307.4		18
5.3	odd	4		80.2.j.b.67.6	yes	18
5.4	even	2		80.2.s.b.3.9	yes	18
15.8	even	4		720.2.bd.g.307.4		18
15.14	odd	2		720.2.z.g.163.1		18
16.5	even	4		1600.2.j.d.143.4		18
16.11	odd	4		400.2.j.d.43.4		18
20.3	even	4		320.2.j.b.47.4		18
20.7	even	4		1600.2.j.d.1007.6		18
20.19	odd	2		320.2.s.b.303.6		18
40.3	even	4		640.2.j.c.607.6		18
40.13	odd	4		640.2.j.d.607.4		18
40.19	odd	2		640.2.s.c.223.4		18
40.29	even	2		640.2.s.d.223.6		18
80.3	even	4		640.2.s.d.287.6		18
80.13	odd	4		640.2.s.c.287.4		18
80.19	odd	4		640.2.j.d.543.6		18
80.27	even	4	inner	400.2.s.d.107.1		18
80.29	even	4		640.2.j.c.543.4		18
80.37	odd	4		1600.2.s.d.207.4		18
80.43	even	4		80.2.s.b.27.9	yes	18
80.53	odd	4		320.2.s.b.207.6		18
80.59	odd	4		80.2.j.b.43.6	✓	18
80.69	even	4		320.2.j.b.143.6		18
240.59	even	4		720.2.bd.g.523.4		18
240.203	odd	4		720.2.z.g.667.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.6	✓	18	80.59	odd	4
80.2.j.b.67.6	yes	18	5.3	odd	4
80.2.s.b.3.9	yes	18	5.4	even	2
80.2.s.b.27.9	yes	18	80.43	even	4
320.2.j.b.47.4		18	20.3	even	4
320.2.j.b.143.6		18	80.69	even	4
320.2.s.b.207.6		18	80.53	odd	4
320.2.s.b.303.6		18	20.19	odd	2
400.2.j.d.43.4		18	16.11	odd	4
400.2.j.d.307.4		18	5.2	odd	4
400.2.s.d.107.1		18	80.27	even	4	inner
400.2.s.d.243.1		18	1.1	even	1	trivial
640.2.j.c.543.4		18	80.29	even	4
640.2.j.c.607.6		18	40.3	even	4
640.2.j.d.543.6		18	80.19	odd	4
640.2.j.d.607.4		18	40.13	odd	4
640.2.s.c.223.4		18	40.19	odd	2
640.2.s.c.287.4		18	80.13	odd	4
640.2.s.d.223.6		18	40.29	even	2
640.2.s.d.287.6		18	80.3	even	4
720.2.z.g.163.1		18	15.14	odd	2
720.2.z.g.667.1		18	240.203	odd	4
720.2.bd.g.307.4		18	15.8	even	4
720.2.bd.g.523.4		18	240.59	even	4
1600.2.j.d.143.4		18	16.5	even	4
1600.2.j.d.1007.6		18	20.7	even	4
1600.2.s.d.207.4		18	80.37	odd	4
1600.2.s.d.943.4		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)

\(f(q)\)	\(=\)	\(q+(-1.41267 - 0.0660953i) q^{2} +0.496487 q^{3} +(1.99126 + 0.186742i) q^{4} +(-0.701372 - 0.0328155i) q^{6} +(-1.55426 + 1.55426i) q^{7} +(-2.80065 - 0.395417i) q^{8} -2.75350 q^{9} +O(q^{10})\)	\(q+(-1.41267 - 0.0660953i) q^{2} +0.496487 q^{3} +(1.99126 + 0.186742i) q^{4} +(-0.701372 - 0.0328155i) q^{6} +(-1.55426 + 1.55426i) q^{7} +(-2.80065 - 0.395417i) q^{8} -2.75350 q^{9} +(-4.19607 - 4.19607i) q^{11} +(0.988637 + 0.0927148i) q^{12} -5.09530i q^{13} +(2.29838 - 2.09292i) q^{14} +(3.93026 + 0.743703i) q^{16} +(-0.213542 + 0.213542i) q^{17} +(3.88978 + 0.181993i) q^{18} +(0.844754 + 0.844754i) q^{19} +(-0.771668 + 0.771668i) q^{21} +(5.65031 + 6.20499i) q^{22} +(-1.70744 - 1.70744i) q^{23} +(-1.39049 - 0.196320i) q^{24} +(-0.336775 + 7.19797i) q^{26} -2.85654 q^{27} +(-3.38518 + 2.80469i) q^{28} +(2.24750 - 2.24750i) q^{29} -0.818209i q^{31} +(-5.50299 - 1.31038i) q^{32} +(-2.08329 - 2.08329i) q^{33} +(0.315778 - 0.287550i) q^{34} +(-5.48294 - 0.514193i) q^{36} -5.12639i q^{37} +(-1.13752 - 1.24919i) q^{38} -2.52975i q^{39} -3.34727i q^{41} +(1.14111 - 1.03911i) q^{42} +4.49131i q^{43} +(-7.57189 - 9.13905i) q^{44} +(2.29920 + 2.52490i) q^{46} +(-4.29355 - 4.29355i) q^{47} +(1.95132 + 0.369239i) q^{48} +2.16858i q^{49} +(-0.106021 + 0.106021i) q^{51} +(0.951504 - 10.1461i) q^{52} +1.00653 q^{53} +(4.03534 + 0.188804i) q^{54} +(4.96751 - 3.73835i) q^{56} +(0.419410 + 0.419410i) q^{57} +(-3.32352 + 3.02642i) q^{58} +(-7.65005 + 7.65005i) q^{59} +(-1.90291 - 1.90291i) q^{61} +(-0.0540798 + 1.15586i) q^{62} +(4.27964 - 4.27964i) q^{63} +(7.68729 + 2.21485i) q^{64} +(2.80531 + 3.08070i) q^{66} +11.0221i q^{67} +(-0.465096 + 0.385341i) q^{68} +(-0.847724 - 0.847724i) q^{69} -10.5331 q^{71} +(7.71159 + 1.08878i) q^{72} +(-2.70854 + 2.70854i) q^{73} +(-0.338831 + 7.24189i) q^{74} +(1.52438 + 1.83988i) q^{76} +13.0435 q^{77} +(-0.167205 + 3.57370i) q^{78} -8.32010 q^{79} +6.84226 q^{81} +(-0.221239 + 4.72858i) q^{82} +9.17237 q^{83} +(-1.68070 + 1.39249i) q^{84} +(0.296855 - 6.34474i) q^{86} +(1.11585 - 1.11585i) q^{87} +(10.0925 + 13.4109i) q^{88} -4.25101 q^{89} +(7.91940 + 7.91940i) q^{91} +(-3.08112 - 3.71882i) q^{92} -0.406230i q^{93} +(5.78157 + 6.34914i) q^{94} +(-2.73217 - 0.650586i) q^{96} +(7.16000 - 7.16000i) q^{97} +(0.143333 - 3.06348i) q^{98} +(11.5539 + 11.5539i) 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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