LMFDB - Embedded newform 400.2.j.d.43.4

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			43.4
Root			$-1.08900 - 0.902261i$ of defining polynomial
Character	$\chi$	$=$	400.43
Dual form			400.2.j.d.307.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0660953 + 1.41267i) q^{2} +0.496487i q^{3} +(-1.99126 + 0.186742i) q^{4} +(-0.701372 + 0.0328155i) q^{6} +(-1.55426 + 1.55426i) q^{7} +(-0.395417 - 2.80065i) q^{8} +2.75350 q^{9} +O(q^{10})$	\(q+(0.0660953 + 1.41267i) q^{2} +0.496487i q^{3} +(-1.99126 + 0.186742i) q^{4} +(-0.701372 + 0.0328155i) q^{6} +(-1.55426 + 1.55426i) q^{7} +(-0.395417 - 2.80065i) q^{8} +2.75350 q^{9} +(-4.19607 + 4.19607i) q^{11} +(-0.0927148 - 0.988637i) q^{12} -5.09530 q^{13} +(-2.29838 - 2.09292i) q^{14} +(3.93026 - 0.743703i) q^{16} +(-0.213542 + 0.213542i) q^{17} +(0.181993 + 3.88978i) q^{18} +(-0.844754 + 0.844754i) q^{19} +(-0.771668 - 0.771668i) q^{21} +(-6.20499 - 5.65031i) q^{22} +(-1.70744 - 1.70744i) q^{23} +(1.39049 - 0.196320i) q^{24} +(-0.336775 - 7.19797i) q^{26} +2.85654i q^{27} +(2.80469 - 3.38518i) q^{28} +(-2.24750 - 2.24750i) q^{29} +0.818209i q^{31} +(1.31038 + 5.50299i) q^{32} +(-2.08329 - 2.08329i) q^{33} +(-0.315778 - 0.287550i) q^{34} +(-5.48294 + 0.514193i) q^{36} +5.12639 q^{37} +(-1.24919 - 1.13752i) q^{38} -2.52975i q^{39} +3.34727i q^{41} +(1.03911 - 1.14111i) q^{42} +4.49131 q^{43} +(7.57189 - 9.13905i) q^{44} +(2.29920 - 2.52490i) q^{46} +(4.29355 + 4.29355i) q^{47} +(0.369239 + 1.95132i) q^{48} +2.16858i q^{49} +(-0.106021 - 0.106021i) q^{51} +(10.1461 - 0.951504i) q^{52} +1.00653i q^{53} +(-4.03534 + 0.188804i) q^{54} +(4.96751 + 3.73835i) q^{56} +(-0.419410 - 0.419410i) q^{57} +(3.02642 - 3.32352i) q^{58} +(7.65005 + 7.65005i) q^{59} +(-1.90291 + 1.90291i) q^{61} +(-1.15586 + 0.0540798i) q^{62} +(-4.27964 + 4.27964i) q^{63} +(-7.68729 + 2.21485i) q^{64} +(2.80531 - 3.08070i) q^{66} -11.0221 q^{67} +(0.385341 - 0.465096i) q^{68} +(0.847724 - 0.847724i) q^{69} -10.5331 q^{71} +(-1.08878 - 7.71159i) q^{72} +(2.70854 - 2.70854i) q^{73} +(0.338831 + 7.24189i) q^{74} +(1.52438 - 1.83988i) q^{76} -13.0435i q^{77} +(3.57370 - 0.167205i) q^{78} +8.32010 q^{79} +6.84226 q^{81} +(-4.72858 + 0.221239i) q^{82} +9.17237i q^{83} +(1.68070 + 1.39249i) q^{84} +(0.296855 + 6.34474i) q^{86} +(1.11585 - 1.11585i) q^{87} +(13.4109 + 10.0925i) q^{88} +4.25101 q^{89} +(7.91940 - 7.91940i) q^{91} +(3.71882 + 3.08112i) q^{92} -0.406230 q^{93} +(-5.78157 + 6.34914i) q^{94} +(-2.73217 + 0.650586i) q^{96} +(7.16000 - 7.16000i) q^{97} +(-3.06348 + 0.143333i) q^{98} +(-11.5539 + 11.5539i) 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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.0660953	+	1.41267i	0.0467365	+	0.998907i
$2$	0.0660953	+	1.41267i	0.0467365	+	0.998907i
$3$			0.496487i			0.286647i	0.989676	+	0.143324i	$0.0457790\pi$
$3$			0.496487i			0.286647i	−0.989676	+	0.143324i	$0.954221\pi$
$4$	−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	$0.386356\pi$
$8$	−0.395417	−	2.80065i	−0.139801	−	0.990180i
$9$	2.75350			0.917833
$10$		0			0
$11$	−4.19607	+	4.19607i	−1.26516	+	1.26516i	−0.316604	+	0.948558i	$0.602543\pi$
$11$	−4.19607	+	4.19607i	−1.26516	+	1.26516i	−0.948558	+	0.316604i	$0.897457\pi$
$12$	−0.0927148	−	0.988637i	−0.0267645	−	0.285395i
$13$	−5.09530			−1.41318			−0.706591	−	0.707622i	$-0.749768\pi$
$13$	−5.09530			−1.41318			−0.706591	+	0.707622i	$0.749768\pi$
$14$	−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	$0.261660\pi$
$18$	0.181993	+	3.88978i	0.0428963	+	0.916830i
$19$	−0.844754	+	0.844754i	−0.193800	+	0.193800i	−0.797336	−	0.603536i	$-0.793758\pi$
$19$	−0.844754	+	0.844754i	−0.193800	+	0.193800i	0.603536	+	0.797336i	$0.293758\pi$
$20$		0			0
$21$	−0.771668	−	0.771668i	−0.168392	−	0.168392i
$22$	−6.20499	−	5.65031i	−1.32291	−	1.20465i
$23$	−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
$27$			2.85654i			0.549741i
$28$	2.80469	−	3.38518i	0.530036	−	0.639738i
$29$	−2.24750	−	2.24750i	−0.417350	−	0.417350i	0.466939	−	0.884289i	$-0.345357\pi$
$29$	−2.24750	−	2.24750i	−0.417350	−	0.417350i	−0.884289	+	0.466939i	$0.845357\pi$
$30$		0			0
$31$			0.818209i			0.146955i	0.997297	+	0.0734773i	$0.0234097\pi$
$31$			0.818209i			0.146955i	−0.997297	+	0.0734773i	$0.976590\pi$
$32$	1.31038	+	5.50299i	0.231644	+	0.972801i
$33$	−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
$37$	5.12639			0.842774			0.421387	−	0.906881i	$-0.361543\pi$
$37$	5.12639			0.842774			0.421387	+	0.906881i	$0.361543\pi$
$38$	−1.24919	−	1.13752i	−0.202646	−	0.184531i
$39$		−	2.52975i		−	0.405084i
$40$		0			0
$41$			3.34727i			0.522756i	0.965237	+	0.261378i	$0.0841769\pi$
$41$			3.34727i			0.522756i	−0.965237	+	0.261378i	$0.915823\pi$
$42$	1.03911	−	1.14111i	0.160338	−	0.176078i
$43$	4.49131			0.684919			0.342460	−	0.939533i	$-0.388740\pi$
$43$	4.49131			0.684919			0.342460	+	0.939533i	$0.388740\pi$
$44$	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	0.947130	−	0.320851i	$-0.103969\pi$
$47$	4.29355	+	4.29355i	0.626278	+	0.626278i	−0.320851	+	0.947130i	$0.603969\pi$
$48$	0.369239	+	1.95132i	0.0532951	+	0.281649i
$49$			2.16858i			0.309797i
$50$		0			0
$51$	−0.106021	−	0.106021i	−0.0148459	−	0.0148459i
$52$	10.1461	−	0.951504i	1.40701	−	0.131950i
$53$			1.00653i			0.138258i	0.997608	+	0.0691291i	$0.0220220\pi$
$53$			1.00653i			0.138258i	−0.997608	+	0.0691291i	$0.977978\pi$
$54$	−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
$58$	3.02642	−	3.32352i	0.397388	−	0.436399i
$59$	7.65005	+	7.65005i	0.995952	+	0.995952i	0.999992	−	0.00404030i	$-0.00128607\pi$
$59$	7.65005	+	7.65005i	0.995952	+	0.995952i	−0.00404030	+	0.999992i	$0.501286\pi$
$60$		0			0
$61$	−1.90291	+	1.90291i	−0.243643	+	0.243643i	−0.818355	−	0.574712i	$-0.805114\pi$
$61$	−1.90291	+	1.90291i	−0.243643	+	0.243643i	0.574712	+	0.818355i	$0.305114\pi$
$62$	−1.15586	+	0.0540798i	−0.146794	+	0.00686814i
$63$	−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
$67$	−11.0221			−1.34656			−0.673280	−	0.739387i	$-0.735115\pi$
$67$	−11.0221			−1.34656			−0.673280	+	0.739387i	$0.735115\pi$
$68$	0.385341	−	0.465096i	0.0467295	−	0.0564012i
$69$	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	$0.714912\pi$
$72$	−1.08878	−	7.71159i	−0.128314	−	0.908820i
$73$	2.70854	−	2.70854i	0.317010	−	0.317010i	−0.530607	−	0.847618i	$-0.678036\pi$
$73$	2.70854	−	2.70854i	0.317010	−	0.317010i	0.847618	+	0.530607i	$0.178036\pi$
$74$	0.338831	+	7.24189i	0.0393883	+	0.841853i
$75$		0			0
$76$	1.52438	−	1.83988i	0.174858	−	0.211048i
$77$		−	13.0435i		−	1.48645i
$78$	3.57370	−	0.167205i	0.404642	−	0.0189322i
$79$	8.32010			0.936085			0.468042	−	0.883706i	$-0.344959\pi$
$79$	8.32010			0.936085			0.468042	+	0.883706i	$0.344959\pi$
$80$		0			0
$81$	6.84226			0.760252
$82$	−4.72858	+	0.221239i	−0.522185	+	0.0244317i
$83$			9.17237i			1.00680i	0.864054	+	0.503399i	$0.167917\pi$
$83$			9.17237i			1.00680i	−0.864054	+	0.503399i	$0.832083\pi$
$84$	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
$88$	13.4109	+	10.0925i	1.42961	+	1.07587i
$89$	4.25101			0.450606			0.225303	−	0.974289i	$-0.427663\pi$
$89$	4.25101			0.450606			0.225303	+	0.974289i	$0.427663\pi$
$90$		0			0
$91$	7.91940	−	7.91940i	0.830178	−	0.830178i
$92$	3.71882	+	3.08112i	0.387714	+	0.321229i
$93$	−0.406230			−0.0421241
$94$	−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	$0.0781417\pi$
$98$	−3.06348	+	0.143333i	−0.309458	+	0.0144788i
$99$	−11.5539	+	11.5539i	−1.16121	+	1.16121i
$100$		0			0
$101$	8.38846	+	8.38846i	0.834683	+	0.834683i	0.988153	−	0.153470i	$-0.0490448\pi$
$101$	8.38846	+	8.38846i	0.834683	+	0.834683i	−0.153470	+	0.988153i	$0.549045\pi$
$102$	0.142765	−	0.156780i	0.0141358	−	0.0155235i
$103$	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
$107$			8.97973i			0.868103i	0.900888	+	0.434052i	$0.142916\pi$
$107$			8.97973i			0.868103i	−0.900888	+	0.434052i	$0.857084\pi$
$108$	−0.533435	−	5.68812i	−0.0513298	−	0.547340i
$109$	−10.9081	−	10.9081i	−1.04481	−	1.04481i	−0.998948	−	0.0458592i	$-0.985397\pi$
$109$	−10.9081	−	10.9081i	−1.04481	−	1.04481i	−0.0458592	−	0.998948i	$-0.514603\pi$
$110$		0			0
$111$			2.54519i			0.241579i
$112$	−4.95272	+	7.26453i	−0.467988	+	0.686433i
$113$	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
$117$	−14.0299			−1.29707
$118$	−10.3013	+	11.3126i	−0.948316	+	1.04141i
$119$		−	0.663798i		−	0.0608503i
$120$		0			0
$121$		−	24.2140i		−	2.20127i
$122$	−2.81396	−	2.56241i	−0.254764	−	0.231990i
$123$	−1.66188			−0.149846
$124$	−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	0.740009	−	0.672597i	$-0.234821\pi$
$127$	0.759686	+	0.759686i	0.0674112	+	0.0674112i	−0.672597	+	0.740009i	$0.734821\pi$
$128$	−3.63694	−	10.7132i	−0.321463	−	0.946922i
$129$			2.22988i			0.196330i
$130$		0			0
$131$	7.59995	+	7.59995i	0.664010	+	0.664010i	0.956323	−	0.292312i	$-0.0944247\pi$
$131$	7.59995	+	7.59995i	0.664010	+	0.664010i	−0.292312	+	0.956323i	$0.594425\pi$
$132$	4.53742	+	3.75935i	0.394932	+	0.327209i
$133$		−	2.62593i		−	0.227697i
$134$	−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	$0.0307448\pi$
$137$	12.7789	+	12.7789i	1.09178	+	1.09178i	0.0964376	+	0.995339i	$0.469255\pi$
$138$	1.25358	+	1.14152i	0.106712	+	0.0971728i
$139$	−7.74227	−	7.74227i	−0.656691	−	0.656691i	0.297905	−	0.954596i	$-0.403712\pi$
$139$	−7.74227	−	7.74227i	−0.656691	−	0.656691i	−0.954596	+	0.297905i	$0.903712\pi$
$140$		0			0
$141$	−2.13169	+	2.13169i	−0.179521	+	0.179521i
$142$	−0.696191	−	14.8798i	−0.0584230	−	1.24869i
$143$	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
$147$	−1.07667			−0.0888024
$148$	−10.2080	+	0.957310i	−0.839092	+	0.0786904i
$149$	−9.57165	+	9.57165i	−0.784140	+	0.784140i	−0.980527	−	0.196386i	$-0.937079\pi$
$149$	−9.57165	+	9.57165i	−0.784140	+	0.784140i	0.196386	+	0.980527i	$0.437079\pi$
$150$		0			0
$151$	−9.68791			−0.788391			−0.394195	−	0.919027i	$-0.628977\pi$
$151$	−9.68791			−0.788391			−0.394195	+	0.919027i	$0.628977\pi$
$152$	2.69989	+	2.03183i	0.218990	+	0.164803i
$153$	−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
$157$		−	9.97637i		−	0.796201i	−0.917342	−	0.398101i	$-0.869669\pi$
$157$		−	9.97637i		−	0.796201i	0.917342	−	0.398101i	$-0.130331\pi$
$158$	0.549920	+	11.7535i	0.0437493	+	0.935062i
$159$	−0.499732			−0.0396313
$160$		0			0
$161$	5.30761			0.418298
$162$	0.452242	+	9.66585i	0.0355315	+	0.759421i
$163$		−	9.48267i		−	0.742740i	−0.928485	−	0.371370i	$-0.878888\pi$
$163$		−	9.48267i		−	0.742740i	0.928485	−	0.371370i	$-0.121112\pi$
$164$	−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	$0.0773180\pi$
$168$	−1.85604	+	2.46630i	−0.143197	+	0.190279i
$169$	12.9621			0.997082
$170$		0			0
$171$	−2.32603	+	2.32603i	−0.177876	+	0.177876i
$172$	−8.94339	+	0.838715i	−0.681927	+	0.0639514i
$173$	−8.94716			−0.680240			−0.340120	−	0.940382i	$-0.610468\pi$
$173$	−8.94716			−0.680240			−0.340120	+	0.940382i	$0.610468\pi$
$174$	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
$178$	0.280972	+	6.00526i	0.0210597	+	0.450114i
$179$	3.02430	−	3.02430i	0.226047	−	0.226047i	−0.584992	−	0.811039i	$-0.698902\pi$
$179$	3.02430	−	3.02430i	0.226047	−	0.226047i	0.811039	+	0.584992i	$0.198902\pi$
$180$		0			0
$181$	−1.54845	−	1.54845i	−0.115095	−	0.115095i	0.647213	−	0.762309i	$-0.275934\pi$
$181$	−1.54845	−	1.54845i	−0.115095	−	0.115095i	−0.762309	+	0.647213i	$0.775934\pi$
$182$	11.7109	+	10.6640i	0.868071	+	0.790472i
$183$	−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
$187$		−	1.79208i		−	0.131050i
$188$	−9.35136	−	7.74779i	−0.682018	−	0.565066i
$189$	−4.43979	−	4.43979i	−0.322947	−	0.322947i
$190$		0			0
$191$		−	20.1005i		−	1.45442i	−0.686415	−	0.727210i	$-0.740817\pi$
$191$		−	20.1005i		−	1.45442i	0.686415	−	0.727210i	$-0.259183\pi$
$192$	−1.09964	−	3.81664i	−0.0793600	−	0.275442i
$193$	−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
$197$	1.11758			0.0796246			0.0398123	−	0.999207i	$-0.487324\pi$
$197$	1.11758			0.0796246			0.0398123	+	0.999207i	$0.487324\pi$
$198$	−17.0854	−	15.5581i	−1.21421	−	1.10567i
$199$		−	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
$202$	−11.2957	+	12.4046i	−0.794761	+	0.872781i
$203$	6.98637			0.490347
$204$	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
$208$	−20.0258	+	3.78939i	−1.38854	+	0.262747i
$209$		−	7.08929i		−	0.490376i
$210$		0			0
$211$	0.411613	+	0.411613i	0.0283366	+	0.0283366i	0.721133	−	0.692797i	$-0.243622\pi$
$211$	0.411613	+	0.411613i	0.0283366	+	0.0283366i	−0.692797	+	0.721133i	$0.743622\pi$
$212$	−0.187962	−	2.00427i	−0.0129093	−	0.137654i
$213$		−	5.22957i		−	0.358324i
$214$	−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
$218$	14.6886	−	16.1305i	0.994835	−	1.09250i
$219$	1.34475	+	1.34475i	0.0908701	+	0.0908701i
$220$		0			0
$221$	1.08806	−	1.08806i	0.0731909	−	0.0731909i
$222$	−3.59551	+	0.168225i	−0.241315	+	0.0112905i
$223$	−16.7466	+	16.7466i	−1.12143	+	1.12143i	−0.129908	+	0.991526i	$0.541468\pi$
$223$	−16.7466	+	16.7466i	−1.12143	+	1.12143i	−0.991526	+	0.129908i	$0.958532\pi$
$224$	−10.5897	−	6.51639i	−0.707555	−	0.435395i
$225$		0			0
$226$	−5.78600	+	6.35401i	−0.384879	+	0.422662i
$227$	−13.7807			−0.914659			−0.457330	−	0.889297i	$-0.651194\pi$
$227$	−13.7807			−0.914659			−0.457330	+	0.889297i	$0.651194\pi$
$228$	0.913476	+	0.756833i	0.0604964	+	0.0501225i
$229$	7.90971	−	7.90971i	0.522688	−	0.522688i	−0.395694	−	0.918382i	$-0.629496\pi$
$229$	7.90971	−	7.90971i	0.522688	−	0.522688i	0.918382	+	0.395694i	$0.129496\pi$
$230$		0			0
$231$	6.47594			0.426086
$232$	−5.40576	+	7.18315i	−0.354905	+	0.471597i
$233$	−1.67997	+	1.67997i	−0.110058	+	0.110058i	−0.759991	−	0.649933i	$-0.774797\pi$
$233$	−1.67997	+	1.67997i	−0.110058	+	0.110058i	0.649933	+	0.759991i	$0.274797\pi$
$234$	−0.927311	−	19.8196i	−0.0606202	−	1.29565i
$235$		0			0
$236$	−16.6618	−	13.8047i	−1.08459	−	0.898608i
$237$			4.13083i			0.268326i
$238$	0.937727	−	0.0438740i	0.0607838	−	0.00284393i
$239$	−11.7685			−0.761241			−0.380620	−	0.924731i	$-0.624290\pi$
$239$	−11.7685			−0.761241			−0.380620	+	0.924731i	$0.624290\pi$
$240$		0			0
$241$	−13.2730			−0.854991			−0.427495	−	0.904018i	$-0.640604\pi$
$241$	−13.2730			−0.854991			−0.427495	+	0.904018i	$0.640604\pi$
$242$	34.2063	−	1.60043i	2.19886	−	0.102880i
$243$			11.9667i			0.767665i
$244$	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
$248$	2.29152	−	0.323534i	0.145511	−	0.0205444i
$249$	−4.55396			−0.288596
$250$		0			0
$251$	10.3795	−	10.3795i	0.655149	−	0.655149i	−0.299079	−	0.954228i	$-0.596679\pi$
$251$	10.3795	−	10.3795i	0.655149	−	0.655149i	0.954228	+	0.299079i	$0.0966795\pi$
$252$	7.72271	−	9.32108i	0.486485	−	0.587173i
$253$	14.3291			0.900863
$254$	−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	$0.892567\pi$
$258$	−3.15008	+	0.147385i	−0.196116	+	0.00917577i
$259$	−7.96772	+	7.96772i	−0.495090	+	0.495090i
$260$		0			0
$261$	−6.18848	−	6.18848i	−0.383058	−	0.383058i
$262$	−10.2339	+	11.2385i	−0.632251	+	0.694318i
$263$	−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
$267$			2.11057i			0.129165i
$268$	21.9478	−	2.05828i	1.34068	−	0.125729i
$269$	6.61443	+	6.61443i	0.403289	+	0.403289i	0.879390	−	0.476101i	$-0.157950\pi$
$269$	6.61443	+	6.61443i	0.403289	+	0.403289i	−0.476101	+	0.879390i	$0.657950\pi$
$270$		0			0
$271$			10.6219i			0.645237i	0.946529	+	0.322619i	$0.104563\pi$
$271$			10.6219i			0.645237i	−0.946529	+	0.322619i	$0.895437\pi$
$272$	−0.680463	+	0.998087i	−0.0412592	+	0.0605179i
$273$	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
$277$	8.28511			0.497804			0.248902	−	0.968529i	$-0.419930\pi$
$277$	8.28511			0.497804			0.248902	+	0.968529i	$0.419930\pi$
$278$	10.4255	−	11.4490i	0.625282	−	0.686665i
$279$			2.25294i			0.134880i
$280$		0			0
$281$			21.0176i			1.25380i	0.779098	+	0.626902i	$0.215677\pi$
$281$			21.0176i			1.25380i	−0.779098	+	0.626902i	$0.784323\pi$
$282$	−3.15227	−	2.87048i	−0.187715	−	0.170934i
$283$	−14.4748			−0.860436			−0.430218	−	0.902725i	$-0.641563\pi$
$283$	−14.4748			−0.860436			−0.430218	+	0.902725i	$0.641563\pi$
$284$	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
$288$	3.60812	+	15.1525i	0.212611	+	0.892869i
$289$			16.9088i			0.994635i
$290$		0			0
$291$	3.55485	+	3.55485i	0.208389	+	0.208389i
$292$	−4.88761	+	5.89921i	−0.286026	+	0.345225i
$293$			11.9165i			0.696171i	0.937463	+	0.348086i	$0.113168\pi$
$293$			11.9165i			0.696171i	−0.937463	+	0.348086i	$0.886832\pi$
$294$	−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
$298$	−14.1542	−	12.8889i	−0.819931	−	0.746635i
$299$	8.69993	+	8.69993i	0.503130	+	0.503130i
$300$		0			0
$301$	−6.98065	+	6.98065i	−0.402358	+	0.402358i
$302$	−0.640325	−	13.6858i	−0.0368466	−	0.787529i
$303$	−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
$307$	25.4511			1.45257			0.726287	−	0.687392i	$-0.241245\pi$
$307$	25.4511			1.45257			0.726287	+	0.687392i	$0.241245\pi$
$308$	2.43577	+	25.9731i	0.138791	+	1.47995i
$309$	−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	$0.291596\pi$
$312$	−7.08495	+	1.00031i	−0.401106	+	0.0566312i
$313$	18.7965	−	18.7965i	1.06244	−	1.06244i	0.0645277	−	0.997916i	$-0.479446\pi$
$313$	18.7965	−	18.7965i	1.06244	−	1.06244i	0.997916	−	0.0645277i	$-0.0205541\pi$
$314$	14.0933	−	0.659392i	0.795331	−	0.0372116i
$315$		0			0
$316$	−16.5675	+	1.55371i	−0.931995	+	0.0874029i
$317$			16.2531i			0.912864i	0.889758	+	0.456432i	$0.150873\pi$
$317$			16.2531i			0.912864i	−0.889758	+	0.456432i	$0.849127\pi$
$318$	−0.0330299	−	0.705955i	−0.00185223	−	0.0395880i
$319$	18.8613			1.05603
$320$		0			0
$321$	−4.45832			−0.248839
$322$	0.350808	+	7.49789i	0.0195498	+	0.417841i
$323$		−	0.360781i		−	0.0200744i
$324$	−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
$328$	9.37453	−	1.32357i	0.517622	−	0.0730818i
$329$	−13.3465			−0.735818
$330$		0			0
$331$	−8.71558	+	8.71558i	−0.479052	+	0.479052i	−0.904828	−	0.425777i	$-0.860001\pi$
$331$	−8.71558	+	8.71558i	−0.479052	+	0.479052i	0.425777	+	0.904828i	$0.360001\pi$
$332$	−1.71286	−	18.2646i	−0.0940055	−	1.00240i
$333$	14.1155			0.773526
$334$	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	$0.250499\pi$
$338$	0.856732	+	18.3111i	0.0466001	+	0.995993i
$339$	−2.13333	+	2.13333i	−0.115866	+	0.115866i
$340$		0			0
$341$	−3.43326	−	3.43326i	−0.185921	−	0.185921i
$342$	−3.43965	−	3.13217i	−0.185995	−	0.169368i
$343$	−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
$347$		−	35.7094i		−	1.91698i	−0.285124	−	0.958491i	$-0.592035\pi$
$347$		−	35.7094i		−	1.91698i	0.285124	−	0.958491i	$-0.407965\pi$
$348$	−2.01358	+	2.43033i	−0.107939	+	0.130280i
$349$	0.274452	+	0.274452i	0.0146911	+	0.0146911i	0.714414	−	0.699723i	$-0.246693\pi$
$349$	0.274452	+	0.274452i	0.0146911	+	0.0146911i	−0.699723	+	0.714414i	$0.746693\pi$
$350$		0			0
$351$		−	14.5549i		−	0.776884i
$352$	−28.5894	−	17.5925i	−1.52382	−	0.937683i
$353$	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
$357$	0.329567			0.0174426
$358$	4.47222	+	4.07244i	0.236364	+	0.215235i
$359$			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
$362$	2.08510	−	2.28979i	0.109591	−	0.120349i
$363$	12.0219			0.630988
$364$	−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	0.968517	−	0.248949i	$-0.0800852\pi$
$367$	13.7849	+	13.7849i	0.719568	+	0.719568i	−0.248949	+	0.968517i	$0.580085\pi$
$368$	−7.98052	−	5.44086i	−0.416013	−	0.283624i
$369$			9.21671i			0.479803i
$370$		0			0
$371$	−1.56441	−	1.56441i	−0.0812202	−	0.0812202i
$372$	0.808911	−	0.0758601i	0.0419401	−	0.00393316i
$373$			21.4003i			1.10806i	0.832496	+	0.554031i	$0.186911\pi$
$373$			21.4003i			1.10806i	−0.832496	+	0.554031i	$0.813089\pi$
$374$	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
$378$	5.97851	−	6.56540i	0.307501	−	0.337688i
$379$	−11.3922	−	11.3922i	−0.585180	−	0.585180i	0.351142	−	0.936322i	$-0.385793\pi$
$379$	−11.3922	−	11.3922i	−0.585180	−	0.585180i	−0.936322	+	0.351142i	$0.885793\pi$
$380$		0			0
$381$	−0.377174	+	0.377174i	−0.0193232	+	0.0193232i
$382$	28.3953	−	1.32855i	1.45283	−	0.0679744i
$383$	4.42635	−	4.42635i	0.226176	−	0.226176i	−0.584917	−	0.811093i	$-0.698873\pi$
$383$	4.42635	−	4.42635i	0.226176	−	0.226176i	0.811093	+	0.584917i	$0.198873\pi$
$384$	5.31897	−	1.80570i	0.271432	−	0.0921465i
$385$		0			0
$386$	5.15041	−	5.65602i	0.262149	−	0.287884i
$387$	12.3668			0.628642
$388$	−12.9204	+	15.5945i	−0.655932	+	0.791691i
$389$	−12.3502	+	12.3502i	−0.626180	+	0.626180i	−0.947105	−	0.320924i	$-0.896006\pi$
$389$	−12.3502	+	12.3502i	−0.626180	+	0.626180i	0.320924	+	0.947105i	$0.396006\pi$
$390$		0			0
$391$	0.729222			0.0368784
$392$	6.07343	−	0.857493i	0.306755	−	0.0433099i
$393$	−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
$397$			17.9832i			0.902551i	0.892385	+	0.451275i	$0.149031\pi$
$397$			17.9832i			0.902551i	−0.892385	+	0.451275i	$0.850969\pi$
$398$	36.1403	−	1.69092i	1.81155	−	0.0847580i
$399$	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	$0.427317\pi$
$402$	7.73057	−	0.361695i	0.385566	−	0.0180397i
$403$		−	4.16902i		−	0.207674i
$404$	−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
$408$	−0.255005	+	0.338850i	−0.0126246	+	0.0167756i
$409$	30.0616			1.48645			0.743226	−	0.669040i	$-0.233295\pi$
$409$	30.0616			1.48645			0.743226	+	0.669040i	$0.233295\pi$
$410$		0			0
$411$	−6.34457	+	6.34457i	−0.312955	+	0.312955i
$412$	−11.2489	−	9.31995i	−0.554194	−	0.459161i
$413$	−23.7803			−1.17015
$414$	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
$418$	10.0148	−	0.468569i	0.489840	−	0.0229184i
$419$	15.3986	−	15.3986i	0.752271	−	0.752271i	−0.222631	−	0.974903i	$-0.571465\pi$
$419$	15.3986	−	15.3986i	0.752271	−	0.752271i	0.974903	+	0.222631i	$0.0714646\pi$
$420$		0			0
$421$	−3.86468	−	3.86468i	−0.188353	−	0.188353i	0.606631	−	0.794984i	$-0.292521\pi$
$421$	−3.86468	−	3.86468i	−0.188353	−	0.188353i	−0.794984	+	0.606631i	$0.792521\pi$
$422$	−0.554267	+	0.608679i	−0.0269813	+	0.0296300i
$423$	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
$427$		−	5.91523i		−	0.286258i
$428$	−1.67689	−	17.8810i	−0.0810555	−	0.864311i
$429$	10.6150	+	10.6150i	0.512497	+	0.512497i
$430$		0			0
$431$			27.2692i			1.31351i	0.754103	+	0.656756i	$0.228072\pi$
$431$			27.2692i			1.31351i	−0.754103	+	0.656756i	$0.771928\pi$
$432$	2.12442	+	11.2269i	0.102211	+	0.540156i
$433$	−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
$437$	2.88474			0.137996
$438$	−1.81081	+	1.98857i	−0.0865238	+	0.0950177i
$439$			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
$442$	1.60899	+	1.46515i	0.0765316	+	0.0696903i
$443$	−27.7051			−1.31631			−0.658153	−	0.752884i	$-0.728662\pi$
$443$	−27.7051			−1.31631			−0.658153	+	0.752884i	$0.728662\pi$
$444$	−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
$448$	8.50557	−	15.3905i	0.401851	−	0.727131i
$449$		−	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
$452$	−9.35853	−	7.75373i	−0.440188	−	0.364705i
$453$		−	4.80992i		−	0.225990i
$454$	−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	0.693957	−	0.720017i	$-0.255866\pi$
$457$	−0.557108	−	0.557108i	−0.0260604	−	0.0260604i	−0.720017	+	0.693957i	$0.755866\pi$
$458$	11.6966	+	10.6510i	0.546546	+	0.497689i
$459$	−0.609992	−	0.609992i	−0.0284720	−	0.0284720i
$460$		0			0
$461$	−12.5791	+	12.5791i	−0.585865	+	0.585865i	−0.936509	−	0.350644i	$-0.885963\pi$
$461$	−12.5791	+	12.5791i	−0.585865	+	0.585865i	0.350644	+	0.936509i	$0.385963\pi$
$462$	0.428030	+	9.14836i	0.0199137	+	0.425620i
$463$	−3.29549	+	3.29549i	−0.153154	+	0.153154i	−0.779525	−	0.626371i	$-0.784540\pi$
$463$	−3.29549	+	3.29549i	−0.153154	+	0.153154i	0.626371	+	0.779525i	$0.284540\pi$
$464$	−10.5047	−	7.16177i	−0.487669	−	0.332477i
$465$		0			0
$466$	−2.48427	−	2.26220i	−0.115082	−	0.104794i
$467$	−10.1995			−0.471979			−0.235989	−	0.971756i	$-0.575833\pi$
$467$	−10.1995			−0.471979			−0.235989	+	0.971756i	$0.575833\pi$
$468$	27.9372	−	2.61997i	1.29140	−	0.121108i
$469$	17.1311	−	17.1311i	0.791042	−	0.791042i
$470$		0			0
$471$	4.95314			0.228229
$472$	18.4002	−	24.4501i	0.846936	−	1.12541i
$473$	−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
$477$			2.77149i			0.126898i
$478$	−0.777843	−	16.6250i	−0.0355777	−	0.760409i
$479$	−5.65795			−0.258518			−0.129259	−	0.991611i	$-0.541260\pi$
$479$	−5.65795			−0.258518			−0.129259	+	0.991611i	$0.541260\pi$
$480$		0			0
$481$	−26.1205			−1.19099
$482$	−0.877285	−	18.7504i	−0.0399592	−	0.854057i
$483$			2.63516i			0.119904i
$484$	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	$0.0319321\pi$
$488$	6.08184	+	4.57695i	0.275312	+	0.207189i
$489$	4.70802			0.212904
$490$		0			0
$491$	−4.21405	+	4.21405i	−0.190177	+	0.190177i	−0.795773	−	0.605595i	$-0.792935\pi$
$491$	−4.21405	+	4.21405i	−0.190177	+	0.190177i	0.605595	+	0.795773i	$0.292935\pi$
$492$	3.30923	−	0.310341i	0.149192	−	0.0139913i
$493$	0.959871			0.0432304
$494$	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
$498$	−0.300996	−	6.43324i	−0.0134879	−	0.288280i
$499$	16.8862	−	16.8862i	0.755928	−	0.755928i	−0.219650	−	0.975579i	$-0.570492\pi$
$499$	16.8862	−	16.8862i	0.755928	−	0.755928i	0.975579	+	0.219650i	$0.0704917\pi$
$500$		0			0
$501$	4.68450	+	4.68450i	0.209288	+	0.209288i
$502$	15.3488	+	13.9768i	0.685053	+	0.623814i
$503$	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
$507$			6.43550i			0.285811i
$508$	−1.65460	−	1.37087i	−0.0734110	−	0.0608225i
$509$	20.6309	+	20.6309i	0.914448	+	0.914448i	0.996618	−	0.0821701i	$-0.0261851\pi$
$509$	20.6309	+	20.6309i	0.914448	+	0.914448i	−0.0821701	+	0.996618i	$0.526185\pi$
$510$		0			0
$511$			8.41952i			0.372458i
$512$	9.24271	+	20.6536i	0.408474	+	0.912770i
$513$	−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
$517$	−36.0320			−1.58469
$518$	−11.7824	−	10.7291i	−0.517688	−	0.471411i
$519$		−	4.44215i		−	0.194989i
$520$		0			0
$521$		−	19.0433i		−	0.834300i	−0.908838	−	0.417150i	$-0.863029\pi$
$521$		−	19.0433i		−	0.834300i	0.908838	−	0.417150i	$-0.136971\pi$
$522$	8.33325	−	9.15131i	0.364736	−	0.400542i
$523$	19.1782			0.838603			0.419301	−	0.907847i	$-0.362275\pi$
$523$	19.1782			0.838603			0.419301	+	0.907847i	$0.362275\pi$
$524$	−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
$528$	−9.73723	−	6.63853i	−0.423759	−	0.288905i
$529$		−	17.1693i		−	0.746490i
$530$		0			0
$531$	21.0644	+	21.0644i	0.914118	+	0.914118i
$532$	0.490369	+	5.22891i	0.0212602	+	0.226702i
$533$		−	17.0553i		−	0.738749i
$534$	−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
$538$	−8.90681	+	9.78118i	−0.384000	+	0.421697i
$539$	−9.09950	−	9.09950i	−0.391943	−	0.391943i
$540$		0			0
$541$	14.5231	−	14.5231i	0.624398	−	0.624398i	−0.322255	−	0.946653i	$-0.604441\pi$
$541$	14.5231	−	14.5231i	0.624398	−	0.624398i	0.946653	+	0.322255i	$0.104441\pi$
$542$	−15.0053	+	0.702061i	−0.644532	+	0.0301561i
$543$	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
$547$	9.97058			0.426311			0.213156	−	0.977018i	$-0.431626\pi$
$547$	9.97058			0.426311			0.213156	+	0.977018i	$0.431626\pi$
$548$	−27.8325	−	23.0598i	−1.18895	−	0.985067i
$549$	−5.23967	+	5.23967i	−0.223624	+	0.223624i
$550$		0			0
$551$	3.79716			0.161765
$552$	−2.70938	−	2.03897i	−0.115319	−	0.0867845i
$553$	−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
$557$			11.4424i			0.484831i	0.970173	+	0.242416i	$0.0779397\pi$
$557$			11.4424i			0.484831i	−0.970173	+	0.242416i	$0.922060\pi$
$558$	−3.18265	+	0.148909i	−0.134732	+	0.00630381i
$559$	−22.8846			−0.967915
$560$		0			0
$561$	0.889743			0.0375650
$562$	−29.6909	+	1.38916i	−1.25243	+	0.0585984i
$563$		−	47.0585i		−	1.98328i	−0.129034	−	0.991640i	$-0.541188\pi$
$563$		−	47.0585i		−	1.98328i	0.129034	−	0.991640i	$-0.458812\pi$
$564$	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
$568$	4.16498	+	29.4996i	0.174759	+	1.23778i
$569$	−41.4684			−1.73845			−0.869224	−	0.494419i	$-0.835381\pi$
$569$	−41.4684			−1.73845			−0.869224	+	0.494419i	$0.835381\pi$
$570$		0			0
$571$	16.1745	−	16.1745i	0.676881	−	0.676881i	−0.282412	−	0.959293i	$-0.591135\pi$
$571$	16.1745	−	16.1745i	0.676881	−	0.676881i	0.959293	+	0.282412i	$0.0911347\pi$
$572$	−38.5811	+	46.5662i	−1.61316	+	1.94703i
$573$	9.97963			0.416905
$574$	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	$0.450744\pi$
$578$	−23.8865	+	1.11759i	−0.993548	+	0.0464857i
$579$	1.89898	−	1.89898i	0.0789189	−	0.0789189i
$580$		0			0
$581$	−14.2562	−	14.2562i	−0.591447	−	0.591447i
$582$	−4.78686	+	5.25678i	−0.198422	+	0.217900i
$583$	−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
$587$			29.1190i			1.20187i	0.799298	+	0.600935i	$0.205205\pi$
$587$			29.1190i			1.20187i	−0.799298	+	0.600935i	$0.794795\pi$
$588$	2.14394	−	0.201059i	0.0884145	−	0.00829155i
$589$	−0.691185	−	0.691185i	−0.0284798	−	0.0284798i
$590$		0			0
$591$			0.554866i			0.0228242i
$592$	20.1480	−	3.81251i	0.828079	−	0.156693i
$593$	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
$597$	12.7016			0.519843
$598$	−11.7151	+	12.8651i	−0.479066	+	0.526095i
$599$			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	$0.0949474\pi$
$601$			14.4092i			0.587765i	−0.955842	+	0.293882i	$0.905053\pi$
$602$	−10.3227	−	9.39996i	−0.420723	−	0.383114i
$603$	−30.3493			−1.23592
$604$	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	0.424461	−	0.905446i	$-0.360464\pi$
$607$	−11.8502	−	11.8502i	−0.480985	−	0.480985i	−0.905446	+	0.424461i	$0.860464\pi$
$608$	−5.75562	−	3.54173i	−0.233421	−	0.143636i
$609$			3.46864i			0.140557i
$610$		0			0
$611$	−21.8769	−	21.8769i	−0.885045	−	0.885045i
$612$	1.06104	−	1.28064i	0.0428899	−	0.0517669i
$613$		−	16.8256i		−	0.679579i	−0.940502	−	0.339789i	$-0.889644\pi$
$613$		−	16.8256i		−	0.679579i	0.940502	−	0.339789i	$-0.110356\pi$
$614$	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	0.0906720	−	0.995881i	$-0.471098\pi$
$617$	−22.4849	−	22.4849i	−0.905209	−	0.905209i	−0.995881	+	0.0906720i	$0.971098\pi$
$618$	−3.79191	−	3.45295i	−0.152533	−	0.138898i
$619$	14.1269	+	14.1269i	0.567809	+	0.567809i	0.931514	−	0.363705i	$-0.118488\pi$
$619$	14.1269	+	14.1269i	0.567809	+	0.567809i	−0.363705	+	0.931514i	$0.618488\pi$
$620$		0			0
$621$	4.87738	−	4.87738i	0.195723	−	0.195723i
$622$	1.41956	+	30.3406i	0.0569193	+	1.21655i
$623$	−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
$627$	3.51974			0.140565
$628$	1.86300	+	19.8656i	0.0743419	+	0.792723i
$629$	−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	$0.735958\pi$
$632$	−3.28991	−	23.3017i	−0.130866	−	0.926892i
$633$	−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
$637$		−	11.0496i		−	0.437799i
$638$	1.24664	+	26.6448i	0.0493551	+	1.05488i
$639$	−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	$0.378585\pi$
$642$	−0.294674	−	6.29813i	−0.0116299	−	0.248567i
$643$			16.4916i			0.650364i	0.945652	+	0.325182i	$0.105426\pi$
$643$			16.4916i			0.650364i	−0.945652	+	0.325182i	$0.894574\pi$
$644$	−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	$0.247196\pi$
$648$	−2.70555	−	19.1628i	−0.106284	−	0.752786i
$649$	−64.2002			−2.52008
$650$		0			0
$651$	0.631386	−	0.631386i	0.0247460	−	0.0247460i
$652$	1.77081	+	18.8825i	0.0693502	+	0.739495i
$653$	17.0751			0.668200			0.334100	−	0.942538i	$-0.391568\pi$
$653$	17.0751			0.668200			0.334100	+	0.942538i	$0.391568\pi$
$654$	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
$658$	−0.882144	−	18.8542i	−0.0343895	−	0.735014i
$659$	7.42245	−	7.42245i	0.289138	−	0.289138i	−0.547601	−	0.836739i	$-0.684459\pi$
$659$	7.42245	−	7.42245i	0.289138	−	0.289138i	0.836739	+	0.547601i	$0.184459\pi$
$660$		0			0
$661$	31.7614	+	31.7614i	1.23538	+	1.23538i	0.961870	+	0.273507i	$0.0881837\pi$
$661$	31.7614	+	31.7614i	1.23538	+	1.23538i	0.273507	+	0.961870i	$0.411816\pi$
$662$	−12.8883	−	11.7362i	−0.500917	−	0.456139i
$663$	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
$667$			7.67495i			0.297175i
$668$	−17.0262	+	20.5501i	−0.658762	+	0.795107i
$669$	−8.31446	−	8.31446i	−0.321456	−	0.321456i
$670$		0			0
$671$		−	15.9695i		−	0.616496i
$672$	3.23531	−	5.25766i	0.124805	−	0.202819i
$673$	−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
$677$	25.2618			0.970890			0.485445	−	0.874267i	$-0.338658\pi$
$677$	25.2618			0.970890			0.485445	+	0.874267i	$0.338658\pi$
$678$	−3.15468	−	2.87268i	−0.121155	−	0.110325i
$679$			22.2569i			0.854143i
$680$		0			0
$681$		−	6.84196i		−	0.262184i
$682$	4.62313	−	5.07698i	0.177029	−	0.194408i
$683$	8.20306			0.313881			0.156941	−	0.987608i	$-0.449837\pi$
$683$	8.20306			0.313881			0.156941	+	0.987608i	$0.449837\pi$
$684$	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
$688$	17.6520	−	3.34020i	0.672977	−	0.127344i
$689$		−	5.12859i		−	0.195384i
$690$		0			0
$691$	−7.89158	−	7.89158i	−0.300210	−	0.300210i	0.540886	−	0.841096i	$-0.318089\pi$
$691$	−7.89158	−	7.89158i	−0.300210	−	0.300210i	−0.841096	+	0.540886i	$0.818089\pi$
$692$	17.8162	−	1.67081i	0.677268	−	0.0635145i
$693$		−	35.9153i		−	1.36431i
$694$	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
$698$	−0.369570	+	0.405850i	−0.0139884	+	0.0153616i
$699$	−0.834083	−	0.834083i	−0.0315479	−	0.0315479i
$700$		0			0
$701$	1.50228	−	1.50228i	0.0567405	−	0.0567405i	−0.678167	−	0.734908i	$-0.737225\pi$
$701$	1.50228	−	1.50228i	0.0567405	−	0.0567405i	0.734908	+	0.678167i	$0.237225\pi$
$702$	20.5613	−	0.962012i	0.776036	−	0.0363088i
$703$	−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
$707$	−26.0756			−0.980675
$708$	6.85385	−	8.27239i	0.257583	−	0.310896i
$709$	36.0738	−	36.0738i	1.35478	−	1.35478i	0.474551	−	0.880228i	$-0.342610\pi$
$709$	36.0738	−	36.0738i	1.35478	−	1.35478i	0.880228	−	0.474551i	$-0.157390\pi$
$710$		0			0
$711$	22.9094			0.859170
$712$	−1.68092	−	11.9056i	−0.0629952	−	0.446181i
$713$	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
$717$		−	5.84291i		−	0.218207i
$718$	−1.08604	+	0.0508132i	−0.0405307	+	0.00189633i
$719$	35.0340			1.30655			0.653274	−	0.757121i	$-0.273395\pi$
$719$	35.0340			1.30655			0.653274	+	0.757121i	$0.273395\pi$
$720$		0			0
$721$	−16.0548			−0.597911
$722$	−24.8245	+	1.16148i	−0.923873	+	0.0432258i
$723$		−	6.58989i		−	0.245081i
$724$	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	$0.482315\pi$
$728$	−25.3109	−	19.0480i	−0.938085	−	0.705966i
$729$	14.5855			0.540203
$730$		0			0
$731$	−0.959085	+	0.959085i	−0.0354731	+	0.0354731i
$732$	2.05772	+	1.70486i	0.0760555	+	0.0630135i
$733$	7.37554			0.272422			0.136211	−	0.990680i	$-0.456508\pi$
$733$	7.37554			0.272422			0.136211	+	0.990680i	$0.456508\pi$
$734$	−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
$738$	−13.0202	+	0.609181i	−0.479278	+	0.0224243i
$739$	−5.55025	+	5.55025i	−0.204169	+	0.204169i	−0.801784	−	0.597614i	$-0.796115\pi$
$739$	−5.55025	+	5.55025i	−0.204169	+	0.204169i	0.597614	+	0.801784i	$0.296115\pi$
$740$		0			0
$741$	2.13702	+	2.13702i	0.0785053	+	0.0785053i
$742$	2.10659	−	2.31339i	0.0773355	−	0.0849274i
$743$	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
$747$			25.2561i			0.924073i
$748$	0.334655	+	3.56849i	0.0122362	+	0.130477i
$749$	−13.9568	−	13.9568i	−0.509970	−	0.509970i
$750$		0			0
$751$			3.93385i			0.143548i	0.997421	+	0.0717742i	$0.0228661\pi$
$751$			3.93385i			0.143548i	−0.997421	+	0.0717742i	$0.977134\pi$
$752$	20.0679	+	13.6816i	0.731799	+	0.498917i
$753$	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
$757$	21.8327			0.793525			0.396762	−	0.917921i	$-0.370134\pi$
$757$	21.8327			0.793525			0.396762	+	0.917921i	$0.370134\pi$
$758$	15.3405	−	16.8464i	0.557191	−	0.611890i
$759$			7.11421i			0.258230i
$760$		0			0
$761$		−	4.27291i		−	0.154893i	−0.996997	−	0.0774464i	$-0.975323\pi$
$761$		−	4.27291i		−	0.154893i	0.996997	−	0.0774464i	$-0.0246767\pi$
$762$	−0.557752	−	0.507893i	−0.0202052	−	0.0183990i
$763$	33.9080			1.22755
$764$	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
$768$	2.90241	+	7.39459i	0.104732	+	0.266829i
$769$		−	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
$772$	8.33049	+	6.90198i	0.299821	+	0.248408i
$773$			15.0077i			0.539791i	0.962890	+	0.269895i	$0.0869891\pi$
$773$			15.0077i			0.539791i	−0.962890	+	0.269895i	$0.913011\pi$
$774$	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
$778$	−18.2630	−	16.6305i	−0.654762	−	0.596231i
$779$	−2.82762	−	2.82762i	−0.101310	−	0.101310i
$780$		0			0
$781$	44.1977	−	44.1977i	1.58152	−	1.58152i
$782$	0.0481982	+	1.03015i	0.00172356	+	0.0368381i
$783$	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
$787$	42.9223			1.53001			0.765007	−	0.644022i	$-0.222736\pi$
$787$	42.9223			1.53001			0.765007	+	0.644022i	$0.222736\pi$
$788$	−2.22540	+	0.208699i	−0.0792767	+	0.00743461i
$789$	6.98118	−	6.98118i	0.248536	−	0.248536i
$790$		0			0
$791$	−13.3568			−0.474912
$792$	36.9270	+	27.7898i	1.31214	+	0.987466i
$793$	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
$797$			0.280831i			0.00994753i	0.999988	+	0.00497377i	$0.00158321\pi$
$797$			0.280831i			0.00994753i	−0.999988	+	0.00497377i	$0.998417\pi$
$798$	0.0861711	+	1.84175i	0.00305042	+	0.0651973i
$799$	−1.83371			−0.0648719
$800$		0			0
$801$	11.7052			0.413581
$802$	0.599200	+	12.8068i	0.0211585	+	0.452225i
$803$			22.7304i			0.802139i
$804$	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
$808$	20.1762	−	26.8101i	0.709797	−	0.943176i
$809$	16.5787			0.582876			0.291438	−	0.956590i	$-0.405866\pi$
$809$	16.5787			0.582876			0.291438	+	0.956590i	$0.405866\pi$
$810$		0			0
$811$	7.25384	−	7.25384i	0.254717	−	0.254717i	−0.568184	−	0.822901i	$-0.692354\pi$
$811$	7.25384	−	7.25384i	0.254717	−	0.254717i	0.822901	+	0.568184i	$0.192354\pi$
$812$	−13.9117	+	1.30465i	−0.488205	+	0.0457841i
$813$	−5.27366			−0.184955
$814$	−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
$818$	1.98693	+	42.4671i	0.0694715	+	1.48483i
$819$	21.8061	−	21.8061i	0.761965	−	0.761965i
$820$		0			0
$821$	−15.3525	−	15.3525i	−0.535806	−	0.535806i	0.386489	−	0.922294i	$-0.373688\pi$
$821$	−15.3525	−	15.3525i	−0.535806	−	0.535806i	−0.922294	+	0.386489i	$0.873688\pi$
$822$	−9.38212	−	8.54343i	−0.327239	−	0.297986i
$823$	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
$827$		−	39.4186i		−	1.37072i	−0.728205	−	0.685359i	$-0.759645\pi$
$827$		−	39.4186i		−	1.37072i	0.728205	−	0.685359i	$-0.240355\pi$
$828$	10.2398	+	8.48386i	0.355857	+	0.294834i
$829$	20.7102	+	20.7102i	0.719296	+	0.719296i	0.968461	−	0.249165i	$-0.0801561\pi$
$829$	20.7102	+	20.7102i	0.719296	+	0.719296i	−0.249165	+	0.968461i	$0.580156\pi$
$830$		0			0
$831$			4.11345i			0.142694i
$832$	39.1690	−	11.2853i	1.35794	−	0.391248i
$833$	−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
$837$	−2.33725			−0.0807870
$838$	22.7709	+	20.7354i	0.786608	+	0.716291i
$839$			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
$842$	5.20408	−	5.71495i	0.179344	−	0.196950i
$843$	−10.4350			−0.359399
$844$	−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
$848$	0.748562	+	3.95594i	0.0257057	+	0.135847i
$849$		−	7.18654i		−	0.246642i
$850$		0			0
$851$	−8.75302	−	8.75302i	−0.300050	−	0.300050i
$852$	0.976577	+	10.4134i	0.0334570	+	0.356759i
$853$			26.5538i			0.909185i	0.890700	+	0.454592i	$0.150215\pi$
$853$			26.5538i			0.909185i	−0.890700	+	0.454592i	$0.849785\pi$
$854$	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	0.258153	−	0.966104i	$-0.416886\pi$
$857$	−20.7249	−	20.7249i	−0.707951	−	0.707951i	−0.966104	+	0.258153i	$0.916886\pi$
$858$	−14.2939	+	15.6971i	−0.487985	+	0.535890i
$859$	−35.9248	−	35.9248i	−1.22574	−	1.22574i	−0.965561	−	0.260176i	$-0.916219\pi$
$859$	−35.9248	−	35.9248i	−1.22574	−	1.22574i	−0.260176	−	0.965561i	$-0.583781\pi$
$860$		0			0
$861$	2.58298	−	2.58298i	0.0880278	−	0.0880278i
$862$	−38.5224	+	1.80237i	−1.31208	+	0.0613889i
$863$	9.19232	−	9.19232i	0.312910	−	0.312910i	−0.533126	−	0.846036i	$-0.678983\pi$
$863$	9.19232	−	9.19232i	0.312910	−	0.312910i	0.846036	+	0.533126i	$0.178983\pi$
$864$	−15.7195	+	3.74314i	−0.534789	+	0.127344i
$865$		0			0
$866$	25.7781	−	28.3087i	0.875976	−	0.961969i
$867$	−8.39500			−0.285109
$868$	2.76978	+	2.29482i	0.0940125	+	0.0778913i
$869$	−34.9117	+	34.9117i	−1.18430	+	1.18430i
$870$		0			0
$871$	56.1608			1.90293
$872$	−26.2365	+	34.8630i	−0.888482	+	1.18061i
$873$	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
$877$		−	17.9106i		−	0.604799i	−0.953181	−	0.302399i	$-0.902212\pi$
$877$		−	17.9106i		−	0.604799i	0.953181	−	0.302399i	$-0.0977877\pi$
$878$	−42.6619	+	1.99605i	−1.43977	+	0.0673633i
$879$	−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	$0.467690\pi$
$882$	−8.43530	+	0.394667i	−0.284031	+	0.0132891i
$883$		−	19.8374i		−	0.667580i	−0.942647	−	0.333790i	$-0.891672\pi$
$883$		−	19.8374i		−	0.667580i	0.942647	−	0.333790i	$-0.108328\pi$
$884$	−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	$0.360858\pi$
$888$	7.12819	−	1.00641i	0.239206	−	0.0337729i
$889$	−2.36149			−0.0792019
$890$		0			0
$891$	−28.7106	+	28.7106i	−0.961842	+	0.961842i
$892$	30.2196	−	36.4741i	1.01183	−	1.22124i
$893$	−7.25398			−0.242745
$894$	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
$898$	13.8203	−	0.646620i	0.461191	−	0.0215780i
$899$	1.83892	−	1.83892i	0.0613315	−	0.0613315i
$900$		0			0
$901$	−0.214938	−	0.214938i	−0.00716061	−	0.00716061i
$902$	18.9131	−	20.7698i	0.629738	−	0.691558i
$903$	−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
$907$		−	39.0417i		−	1.29636i	−0.761487	−	0.648180i	$-0.775531\pi$
$907$		−	39.0417i		−	1.29636i	0.761487	−	0.648180i	$-0.224469\pi$
$908$	27.4411	−	2.57343i	0.910663	−	0.0854024i
$909$	23.0976	+	23.0976i	0.766100	+	0.766100i
$910$		0			0
$911$		−	14.0166i		−	0.464392i	−0.972669	−	0.232196i	$-0.925409\pi$
$911$		−	14.0166i		−	0.464392i	0.972669	−	0.232196i	$-0.0745911\pi$
$912$	−1.96030	−	1.33647i	−0.0649121	−	0.0442550i
$913$	−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
$917$	−23.6245			−0.780150
$918$	0.821399	−	0.902034i	0.0271102	−	0.0297716i
$919$			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
$922$	−18.6015	−	16.9386i	−0.612606	−	0.557844i
$923$	53.6695			1.76655
$924$	−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
$928$	9.42289	−	15.3130i	0.309322	−	0.502675i
$929$			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
$932$	3.03154	−	3.65898i	0.0993013	−	0.119854i
$933$			10.6633i			0.349101i
$934$	−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	0.398963	−	0.916967i	$-0.369370\pi$
$937$	−15.8564	−	15.8564i	−0.518005	−	0.518005i	−0.916967	+	0.398963i	$0.869370\pi$
$938$	25.3329	+	23.0683i	0.827148	+	0.753207i
$939$	9.33225	+	9.33225i	0.304546	+	0.304546i
$940$		0			0
$941$	15.7073	−	15.7073i	0.512044	−	0.512044i	−0.403108	−	0.915152i	$-0.632070\pi$
$941$	15.7073	−	15.7073i	0.512044	−	0.512044i	0.915152	+	0.403108i	$0.132070\pi$
$942$	0.327380	+	6.99715i	0.0106666	+	0.227979i
$943$	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
$947$	33.6925			1.09486			0.547430	−	0.836852i	$-0.315606\pi$
$947$	33.6925			1.09486			0.547430	+	0.836852i	$0.315606\pi$
$948$	−0.771397	−	8.22556i	−0.0250538	−	0.267154i
$949$	−13.8008	+	13.8008i	−0.447993	+	0.447993i
$950$		0			0
$951$	−8.06945			−0.261670
$952$	−1.85907	+	0.262477i	−0.0602527	+	0.00850693i
$953$	−33.5702	+	33.5702i	−1.08745	+	1.08745i	−0.0916550	+	0.995791i	$0.529216\pi$
$953$	−33.5702	+	33.5702i	−1.08745	+	1.08745i	−0.995791	+	0.0916550i	$0.970784\pi$
$954$	−3.91520	+	0.183183i	−0.126759	+	0.00593076i
$955$		0			0
$956$	23.4342	−	2.19767i	0.757915	−	0.0710776i
$957$			9.36440i			0.302708i
$958$	−0.373964	−	7.99281i	−0.0120822	−	0.258236i
$959$	−39.7234			−1.28274
$960$		0			0
$961$	30.3305			0.978404
$962$	−1.72644	−	36.8996i	−0.0556628	−	1.18969i
$963$			24.7257i			0.796774i
$964$	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	$0.475787\pi$
$968$	−67.8149	+	9.57461i	−2.17965	+	0.307740i
$969$	0.179123			0.00575427
$970$		0			0
$971$	−35.7115	+	35.7115i	−1.14604	+	1.14604i	−0.158713	+	0.987325i	$0.550734\pi$
$971$	−35.7115	+	35.7115i	−1.14604	+	1.14604i	−0.987325	+	0.158713i	$0.949266\pi$
$972$	−2.23468	−	23.8289i	−0.0716775	−	0.764312i
$973$	24.0669			0.771551
$974$	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	$0.301555\pi$
$978$	0.311178	+	6.65088i	0.00995039	+	0.212672i
$979$	−17.8375	+	17.8375i	−0.570090	+	0.570090i
$980$		0			0
$981$	−30.0355	−	30.0355i	−0.958959	−	0.958959i
$982$	−6.23158	−	5.67452i	−0.198858	−	0.181081i
$983$	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
$987$		−	6.62639i		−	0.210920i
$988$	−7.76715	+	9.37472i	−0.247106	+	0.298250i
$989$	−7.66866	−	7.66866i	−0.243849	−	0.243849i
$990$		0			0
$991$			40.6040i			1.28983i	0.764255	+	0.644914i	$0.223107\pi$
$991$			40.6040i			1.28983i	−0.764255	+	0.644914i	$0.776893\pi$
$992$	−4.50260	+	1.07216i	−0.142958	+	0.0340412i
$993$	−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
$997$	54.9087			1.73898			0.869488	−	0.493953i	$-0.164449\pi$
$997$	54.9087			1.73898			0.869488	+	0.493953i	$0.164449\pi$
$998$	24.9706	+	22.7384i	0.790431	+	0.719773i
$999$			14.6437i			0.463308i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.6	✓	18	5.4	even	2
80.2.j.b.67.6	yes	18	80.3	even	4
80.2.s.b.3.9	yes	18	80.19	odd	4
80.2.s.b.27.9	yes	18	5.3	odd	4
320.2.j.b.47.4		18	80.13	odd	4
320.2.j.b.143.6		18	20.19	odd	2
320.2.s.b.207.6		18	20.3	even	4
320.2.s.b.303.6		18	80.29	even	4
400.2.j.d.43.4		18	1.1	even	1	trivial
400.2.j.d.307.4		18	80.67	even	4	inner
400.2.s.d.107.1		18	5.2	odd	4
400.2.s.d.243.1		18	16.3	odd	4
640.2.j.c.543.4		18	40.19	odd	2
640.2.j.c.607.6		18	80.53	odd	4
640.2.j.d.543.6		18	40.29	even	2
640.2.j.d.607.4		18	80.43	even	4
640.2.s.c.223.4		18	80.69	even	4
640.2.s.c.287.4		18	40.3	even	4
640.2.s.d.223.6		18	80.59	odd	4
640.2.s.d.287.6		18	40.13	odd	4
720.2.z.g.163.1		18	240.179	even	4
720.2.z.g.667.1		18	15.8	even	4
720.2.bd.g.307.4		18	240.83	odd	4
720.2.bd.g.523.4		18	15.14	odd	2
1600.2.j.d.143.4		18	4.3	odd	2
1600.2.j.d.1007.6		18	80.77	odd	4
1600.2.s.d.207.4		18	20.7	even	4
1600.2.s.d.943.4		18	16.13	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)

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