LMFDB - Embedded newform 400.2.j.d.307.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("400.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			307.9
Root			$0.235136 - 1.39453i$ of defining polynomial
Character	$\chi$	$=$	400.307
Dual form			400.2.j.d.43.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34716 - 0.430311i) q^{2} -2.96561i q^{3} +(1.62967 - 1.15939i) q^{4} +(-1.27613 - 3.99515i) q^{6} +(0.115101 + 0.115101i) q^{7} +(1.69652 - 2.26315i) q^{8} -5.79486 q^{9} +O(q^{10})$	\(q+(1.34716 - 0.430311i) q^{2} -2.96561i q^{3} +(1.62967 - 1.15939i) q^{4} +(-1.27613 - 3.99515i) q^{6} +(0.115101 + 0.115101i) q^{7} +(1.69652 - 2.26315i) q^{8} -5.79486 q^{9} +(2.95966 + 2.95966i) q^{11} +(-3.43831 - 4.83296i) q^{12} -1.55822 q^{13} +(0.204588 + 0.105530i) q^{14} +(1.31162 - 3.77884i) q^{16} +(-0.299668 - 0.299668i) q^{17} +(-7.80658 + 2.49359i) q^{18} +(2.26261 + 2.26261i) q^{19} +(0.341344 - 0.341344i) q^{21} +(5.26071 + 2.71356i) q^{22} +(-4.14573 + 4.14573i) q^{23} +(-6.71162 - 5.03121i) q^{24} +(-2.09917 + 0.670518i) q^{26} +8.28846i q^{27} +(0.321023 + 0.0541288i) q^{28} +(-0.289656 + 0.289656i) q^{29} +4.18508i q^{31} +(0.140879 - 5.65510i) q^{32} +(8.77721 - 8.77721i) q^{33} +(-0.532650 - 0.274749i) q^{34} +(-9.44368 + 6.71851i) q^{36} -1.63643 q^{37} +(4.02172 + 2.07447i) q^{38} +4.62107i q^{39} -7.61648i q^{41} +(0.312960 - 0.606729i) q^{42} +6.72651 q^{43} +(8.25467 + 1.39185i) q^{44} +(-3.80100 + 7.36890i) q^{46} +(4.38366 - 4.38366i) q^{47} +(-11.2066 - 3.88975i) q^{48} -6.97350i q^{49} +(-0.888698 + 0.888698i) q^{51} +(-2.53938 + 1.80659i) q^{52} +11.4324i q^{53} +(3.56661 + 11.1659i) q^{54} +(0.455760 - 0.0652196i) q^{56} +(6.71003 - 6.71003i) q^{57} +(-0.265570 + 0.514854i) q^{58} +(-1.63497 + 1.63497i) q^{59} +(-1.23034 - 1.23034i) q^{61} +(1.80089 + 5.63796i) q^{62} +(-0.666993 - 0.666993i) q^{63} +(-2.24366 - 7.67893i) q^{64} +(8.04736 - 15.6012i) q^{66} -2.49337 q^{67} +(-0.835791 - 0.140926i) q^{68} +(12.2946 + 12.2946i) q^{69} +8.00096 q^{71} +(-9.83107 + 13.1146i) q^{72} +(-1.12102 - 1.12102i) q^{73} +(-2.20453 + 0.704173i) q^{74} +(6.31056 + 1.06405i) q^{76} +0.681319i q^{77} +(1.98850 + 6.22531i) q^{78} -3.62218 q^{79} +7.19579 q^{81} +(-3.27745 - 10.2606i) q^{82} +1.62629i q^{83} +(0.160525 - 0.952029i) q^{84} +(9.06167 - 2.89449i) q^{86} +(0.859007 + 0.859007i) q^{87} +(11.7193 - 1.67703i) q^{88} +15.7149 q^{89} +(-0.179352 - 0.179352i) q^{91} +(-1.94962 + 11.5627i) q^{92} +12.4113 q^{93} +(4.01915 - 7.79182i) q^{94} +(-16.7708 - 0.417792i) q^{96} +(-9.69217 - 9.69217i) q^{97} +(-3.00077 - 9.39441i) q^{98} +(-17.1508 - 17.1508i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9}+O(q^{10}) $ 18 * q + 4 * q^2 - 4 * q^4 - 8 * q^6 - 2 * q^7 + 4 * q^8 - 10 * q^9	$ 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9} - 2 q^{11} - 4 q^{12} + 12 q^{14} + 6 q^{17} - 16 q^{18} + 2 q^{19} - 16 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 16 q^{26} + 4 q^{28} - 14 q^{29} + 4 q^{32} + 8 q^{33} - 28 q^{34} - 4 q^{36} - 8 q^{37} - 16 q^{38} - 28 q^{42} + 44 q^{43} + 44 q^{44} + 12 q^{46} + 38 q^{47} - 60 q^{48} + 8 q^{51} + 40 q^{52} - 4 q^{54} + 20 q^{56} - 24 q^{57} + 20 q^{58} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 16 q^{64} + 4 q^{66} - 12 q^{67} - 36 q^{68} + 32 q^{69} + 24 q^{71} + 36 q^{72} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 84 q^{78} + 16 q^{79} + 2 q^{81} + 28 q^{82} - 24 q^{84} - 36 q^{86} - 24 q^{87} + 96 q^{88} - 12 q^{89} - 52 q^{92} - 16 q^{93} + 28 q^{94} - 40 q^{96} - 18 q^{97} - 32 q^{98} - 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^2 - 4 * q^4 - 8 * q^6 - 2 * q^7 + 4 * q^8 - 10 * q^9 - 2 * q^11 - 4 * q^12 + 12 * q^14 + 6 * q^17 - 16 * q^18 + 2 * q^19 - 16 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 16 * q^26 + 4 * q^28 - 14 * q^29 + 4 * q^32 + 8 * q^33 - 28 * q^34 - 4 * q^36 - 8 * q^37 - 16 * q^38 - 28 * q^42 + 44 * q^43 + 44 * q^44 + 12 * q^46 + 38 * q^47 - 60 * q^48 + 8 * q^51 + 40 * q^52 - 4 * q^54 + 20 * q^56 - 24 * q^57 + 20 * q^58 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 16 * q^64 + 4 * q^66 - 12 * q^67 - 36 * q^68 + 32 * q^69 + 24 * q^71 + 36 * q^72 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 84 * q^78 + 16 * q^79 + 2 * q^81 + 28 * q^82 - 24 * q^84 - 36 * q^86 - 24 * q^87 + 96 * q^88 - 12 * q^89 - 52 * q^92 - 16 * q^93 + 28 * q^94 - 40 * q^96 - 18 * q^97 - 32 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.34716	−	0.430311i	0.952584	−	0.304276i
$2$	1.34716	−	0.430311i	0.952584	−	0.304276i
$3$		−	2.96561i		−	1.71220i	−0.516813	−	0.856099i	$-0.672882\pi$
$3$		−	2.96561i		−	1.71220i	0.516813	−	0.856099i	$-0.327118\pi$
$4$	1.62967	−	1.15939i	0.814833	−	0.579696i
$5$		0			0
$5$		0			0
$6$	−1.27613	−	3.99515i	−0.520980	−	1.63101i
$7$	0.115101	+	0.115101i	0.0435040	+	0.0435040i	0.728524	−	0.685020i	$-0.240207\pi$
$7$	0.115101	+	0.115101i	0.0435040	+	0.0435040i	−0.685020	+	0.728524i	$0.740207\pi$
$8$	1.69652	−	2.26315i	0.599809	−	0.800143i
$9$	−5.79486			−1.93162
$10$		0			0
$11$	2.95966	+	2.95966i	0.892372	+	0.892372i	0.994746	−	0.102374i	$-0.0326439\pi$
$11$	2.95966	+	2.95966i	0.892372	+	0.892372i	−0.102374	+	0.994746i	$0.532644\pi$
$12$	−3.43831	−	4.83296i	−0.992554	−	1.39515i
$13$	−1.55822			−0.432172			−0.216086	−	0.976374i	$-0.569329\pi$
$13$	−1.55822			−0.432172			−0.216086	+	0.976374i	$0.569329\pi$
$14$	0.204588	+	0.105530i	0.0546784	+	0.0282040i
$15$		0			0
$16$	1.31162	−	3.77884i	0.327905	−	0.944711i
$17$	−0.299668	−	0.299668i	−0.0726801	−	0.0726801i	0.669832	−	0.742512i	$-0.266366\pi$
$17$	−0.299668	−	0.299668i	−0.0726801	−	0.0726801i	−0.742512	+	0.669832i	$0.766366\pi$
$18$	−7.80658	+	2.49359i	−1.84003	+	0.587745i
$19$	2.26261	+	2.26261i	0.519079	+	0.519079i	0.917293	−	0.398214i	$-0.130370\pi$
$19$	2.26261	+	2.26261i	0.519079	+	0.519079i	−0.398214	+	0.917293i	$0.630370\pi$
$20$		0			0
$21$	0.341344	−	0.341344i	0.0744874	−	0.0744874i
$22$	5.26071	+	2.71356i	1.12159	+	0.578532i
$23$	−4.14573	+	4.14573i	−0.864444	+	0.864444i	−0.991851	−	0.127406i	$-0.959335\pi$
$23$	−4.14573	+	4.14573i	−0.864444	+	0.864444i	0.127406	+	0.991851i	$0.459335\pi$
$24$	−6.71162	−	5.03121i	−1.37000	−	1.02699i
$25$		0			0
$26$	−2.09917	+	0.670518i	−0.411680	+	0.131499i
$27$			8.28846i			1.59511i
$28$	0.321023	+	0.0541288i	0.0606676	+	0.0102294i
$29$	−0.289656	+	0.289656i	−0.0537878	+	0.0537878i	−0.733489	−	0.679701i	$-0.762109\pi$
$29$	−0.289656	+	0.289656i	−0.0537878	+	0.0537878i	0.679701	+	0.733489i	$0.262109\pi$
$30$		0			0
$31$			4.18508i			0.751663i	0.926688	+	0.375832i	$0.122643\pi$
$31$			4.18508i			0.751663i	−0.926688	+	0.375832i	$0.877357\pi$
$32$	0.140879	−	5.65510i	0.0249041	−	0.999690i
$33$	8.77721	−	8.77721i	1.52792	−	1.52792i
$34$	−0.532650	−	0.274749i	−0.0913487	−	0.0471191i
$35$		0			0
$36$	−9.44368	+	6.71851i	−1.57395	+	1.11975i
$37$	−1.63643			−0.269027			−0.134514	−	0.990912i	$-0.542947\pi$
$37$	−1.63643			−0.269027			−0.134514	+	0.990912i	$0.542947\pi$
$38$	4.02172	+	2.07447i	0.652410	+	0.336523i
$39$			4.62107i			0.739964i
$40$		0			0
$41$		−	7.61648i		−	1.18949i	−0.803913	−	0.594747i	$-0.797252\pi$
$41$		−	7.61648i		−	1.18949i	0.803913	−	0.594747i	$-0.202748\pi$
$42$	0.312960	−	0.606729i	0.0482908	−	0.0936203i
$43$	6.72651			1.02578			0.512892	−	0.858453i	$-0.328574\pi$
$43$	6.72651			1.02578			0.512892	+	0.858453i	$0.328574\pi$
$44$	8.25467	+	1.39185i	1.24444	+	0.209829i
$45$		0			0
$46$	−3.80100	+	7.36890i	−0.560427	+	1.08649i
$47$	4.38366	−	4.38366i	0.639423	−	0.639423i	−0.310990	−	0.950413i	$-0.600661\pi$
$47$	4.38366	−	4.38366i	0.639423	−	0.639423i	0.950413	+	0.310990i	$0.100661\pi$
$48$	−11.2066	−	3.88975i	−1.61753	−	0.561437i
$49$		−	6.97350i		−	0.996215i
$50$		0			0
$51$	−0.888698	+	0.888698i	−0.124443	+	0.124443i
$52$	−2.53938	+	1.80659i	−0.352148	+	0.250529i
$53$			11.4324i			1.57036i	0.619265	+	0.785182i	$0.287431\pi$
$53$			11.4324i			1.57036i	−0.619265	+	0.785182i	$0.712569\pi$
$54$	3.56661	+	11.1659i	0.485355	+	1.51948i
$55$		0			0
$56$	0.455760	−	0.0652196i	0.0609035	−	0.00871533i
$57$	6.71003	−	6.71003i	0.888766	−	0.888766i
$58$	−0.265570	+	0.514854i	−0.0348711	+	0.0676037i
$59$	−1.63497	+	1.63497i	−0.212855	+	0.212855i	−0.805479	−	0.592624i	$-0.798092\pi$
$59$	−1.63497	+	1.63497i	−0.212855	+	0.212855i	0.592624	+	0.805479i	$0.298092\pi$
$60$		0			0
$61$	−1.23034	−	1.23034i	−0.157528	−	0.157528i	0.623942	−	0.781471i	$-0.285530\pi$
$61$	−1.23034	−	1.23034i	−0.157528	−	0.157528i	−0.781471	+	0.623942i	$0.785530\pi$
$62$	1.80089	+	5.63796i	0.228713	+	0.716022i
$63$	−0.666993	−	0.666993i	−0.0840332	−	0.0840332i
$64$	−2.24366	−	7.67893i	−0.280458	−	0.959866i
$65$		0			0
$66$	8.04736	−	15.6012i	0.990561	−	1.92038i
$67$	−2.49337			−0.304614			−0.152307	−	0.988333i	$-0.548670\pi$
$67$	−2.49337			−0.304614			−0.152307	+	0.988333i	$0.548670\pi$
$68$	−0.835791	−	0.140926i	−0.101354	−	0.0170897i
$69$	12.2946	+	12.2946i	1.48010	+	1.48010i
$70$		0			0
$71$	8.00096			0.949540			0.474770	−	0.880110i	$-0.342531\pi$
$71$	8.00096			0.949540			0.474770	+	0.880110i	$0.342531\pi$
$72$	−9.83107	+	13.1146i	−1.15860	+	1.54557i
$73$	−1.12102	−	1.12102i	−0.131205	−	0.131205i	0.638454	−	0.769660i	$-0.279574\pi$
$73$	−1.12102	−	1.12102i	−0.131205	−	0.131205i	−0.769660	+	0.638454i	$0.779574\pi$
$74$	−2.20453	+	0.704173i	−0.256271	+	0.0818584i
$75$		0			0
$76$	6.31056	+	1.06405i	0.723871	+	0.122054i
$77$			0.681319i			0.0776435i
$78$	1.98850	+	6.22531i	0.225153	+	0.704878i
$79$	−3.62218			−0.407527			−0.203763	−	0.979020i	$-0.565317\pi$
$79$	−3.62218			−0.407527			−0.203763	+	0.979020i	$0.565317\pi$
$80$		0			0
$81$	7.19579			0.799532
$82$	−3.27745	−	10.2606i	−0.361934	−	1.13309i
$83$			1.62629i			0.178509i	0.996009	+	0.0892545i	$0.0284484\pi$
$83$			1.62629i			0.178509i	−0.996009	+	0.0892545i	$0.971552\pi$
$84$	0.160525	−	0.952029i	0.0175147	−	0.103875i
$85$		0			0
$86$	9.06167	−	2.89449i	0.977145	−	0.312121i
$87$	0.859007	+	0.859007i	0.0920953	+	0.0920953i
$88$	11.7193	−	1.67703i	1.24928	−	0.178772i
$89$	15.7149			1.66577			0.832887	−	0.553443i	$-0.186686\pi$
$89$	15.7149			1.66577			0.832887	+	0.553443i	$0.186686\pi$
$90$		0			0
$91$	−0.179352	−	0.179352i	−0.0188012	−	0.0188012i
$92$	−1.94962	+	11.5627i	−0.203262	+	1.20549i
$93$	12.4113			1.28700
$94$	4.01915	−	7.79182i	0.414543	−	0.803665i
$95$		0			0
$96$	−16.7708	−	0.417792i	−1.71167	−	0.0426407i
$97$	−9.69217	−	9.69217i	−0.984091	−	0.984091i	0.0157848	−	0.999875i	$-0.494975\pi$
$97$	−9.69217	−	9.69217i	−0.984091	−	0.984091i	−0.999875	+	0.0157848i	$0.994975\pi$
$98$	−3.00077	−	9.39441i	−0.303124	−	0.948978i
$99$	−17.1508	−	17.1508i	−1.72372	−	1.72372i
$100$		0			0
$101$	−12.8067	+	12.8067i	−1.27432	+	1.27432i	−0.330516	+	0.943800i	$0.607223\pi$
$101$	−12.8067	+	12.8067i	−1.27432	+	1.27432i	−0.943800	+	0.330516i	$0.892777\pi$
$102$	−0.814800	+	1.57963i	−0.0806772	+	0.156407i
$103$	4.33738	−	4.33738i	0.427375	−	0.427375i	−0.460358	−	0.887733i	$-0.652279\pi$
$103$	4.33738	−	4.33738i	0.427375	−	0.427375i	0.887733	+	0.460358i	$0.152279\pi$
$104$	−2.64354	+	3.52648i	−0.259221	+	0.345800i
$105$		0			0
$106$	4.91950	+	15.4013i	0.477824	+	1.49590i
$107$			11.9807i			1.15822i	0.815251	+	0.579108i	$0.196599\pi$
$107$			11.9807i			1.15822i	−0.815251	+	0.579108i	$0.803401\pi$
$108$	9.60958	+	13.5074i	0.924682	+	1.29975i
$109$	−4.01503	+	4.01503i	−0.384570	+	0.384570i	−0.872746	−	0.488175i	$-0.837663\pi$
$109$	−4.01503	+	4.01503i	−0.384570	+	0.384570i	0.488175	+	0.872746i	$0.337663\pi$
$110$		0			0
$111$			4.85301i			0.460628i
$112$	0.585916	−	0.283980i	0.0553639	−	0.0268336i
$113$	−6.47754	+	6.47754i	−0.609356	+	0.609356i	−0.942778	−	0.333422i	$-0.891797\pi$
$113$	−6.47754	+	6.47754i	−0.609356	+	0.609356i	0.333422	+	0.942778i	$0.391797\pi$
$114$	6.15207	−	11.9269i	0.576194	−	1.11705i
$115$		0			0
$116$	−0.136217	+	0.807867i	−0.0126475	+	0.0750086i
$117$	9.02966			0.834792
$118$	−1.49902	+	2.90611i	−0.137996	+	0.267529i
$119$		−	0.0689840i		−	0.00632375i
$120$		0			0
$121$			6.51921i			0.592655i
$122$	−2.18688	−	1.12803i	−0.197991	−	0.102127i
$123$	−22.5875			−2.03665
$124$	4.85215	+	6.82028i	0.435736	+	0.612480i
$125$		0			0
$126$	−1.18556	−	0.611530i	−0.105618	−	0.0544794i
$127$	−12.2756	+	12.2756i	−1.08928	+	1.08928i	−0.0936781	+	0.995603i	$0.529862\pi$
$127$	−12.2756	+	12.2756i	−1.08928	+	1.08928i	−0.995603	+	0.0936781i	$0.970138\pi$
$128$	−6.32690	−	9.37925i	−0.559224	−	0.829017i
$129$		−	19.9482i		−	1.75634i
$130$		0			0
$131$	7.99562	−	7.99562i	0.698581	−	0.698581i	−0.265524	−	0.964104i	$-0.585545\pi$
$131$	7.99562	−	7.99562i	0.698581	−	0.698581i	0.964104	+	0.265524i	$0.0855448\pi$
$132$	4.12768	−	24.4802i	0.359269	−	2.13072i
$133$			0.520857i			0.0451641i
$134$	−3.35896	+	1.07292i	−0.290170	+	0.0926865i
$135$		0			0
$136$	−1.18658	+	0.169801i	−0.101749	+	0.0145603i
$137$	−3.08551	+	3.08551i	−0.263613	+	0.263613i	−0.826520	−	0.562907i	$-0.809683\pi$
$137$	−3.08551	+	3.08551i	−0.263613	+	0.263613i	0.562907	+	0.826520i	$0.309683\pi$
$138$	21.8533	+	11.2723i	1.86028	+	0.959561i
$139$	−12.2206	+	12.2206i	−1.03654	+	1.03654i	−0.0372284	+	0.999307i	$0.511853\pi$
$139$	−12.2206	+	12.2206i	−1.03654	+	1.03654i	−0.999307	+	0.0372284i	$0.988147\pi$
$140$		0			0
$141$	−13.0002	−	13.0002i	−1.09482	−	1.09482i
$142$	10.7786	−	3.44290i	0.904516	−	0.288922i
$143$	−4.61180	−	4.61180i	−0.385658	−	0.385658i
$144$	−7.60064	+	21.8979i	−0.633386	+	1.82482i
$145$		0			0
$146$	−1.99258	−	1.02780i	−0.164907	−	0.0850616i
$147$	−20.6807			−1.70572
$148$	−2.66683	+	1.89726i	−0.219212	+	0.155954i
$149$	−2.59172	−	2.59172i	−0.212322	−	0.212322i	0.592931	−	0.805253i	$-0.297971\pi$
$149$	−2.59172	−	2.59172i	−0.212322	−	0.212322i	−0.805253	+	0.592931i	$0.797971\pi$
$150$		0			0
$151$	−16.9594			−1.38014			−0.690068	−	0.723745i	$-0.742419\pi$
$151$	−16.9594			−1.38014			−0.690068	+	0.723745i	$0.742419\pi$
$152$	8.95919	−	1.28207i	0.726686	−	0.103989i
$153$	1.73653	+	1.73653i	0.140390	+	0.140390i
$154$	0.293179	+	0.917844i	0.0236250	+	0.0739620i
$155$		0			0
$156$	5.35764	+	7.53080i	0.428954	+	0.602947i
$157$		−	8.55235i		−	0.682552i	−0.939963	−	0.341276i	$-0.889141\pi$
$157$		−	8.55235i		−	0.682552i	0.939963	−	0.341276i	$-0.110859\pi$
$158$	−4.87964	+	1.55866i	−0.388203	+	0.124000i
$159$	33.9041			2.68877
$160$		0			0
$161$	−0.954354			−0.0752136
$162$	9.69386	−	3.09643i	0.761622	−	0.243278i
$163$		−	3.57797i		−	0.280248i	−0.990134	−	0.140124i	$-0.955250\pi$
$163$		−	3.57797i		−	0.280248i	0.990134	−	0.140124i	$-0.0447501\pi$
$164$	−8.83049	−	12.4123i	−0.689545	−	0.969238i
$165$		0			0
$166$	0.699812	+	2.19087i	0.0543159	+	0.170045i
$167$	−0.482874	−	0.482874i	−0.0373659	−	0.0373659i	0.688177	−	0.725543i	$-0.258411\pi$
$167$	−0.482874	−	0.482874i	−0.0373659	−	0.0373659i	−0.725543	+	0.688177i	$0.758411\pi$
$168$	−0.193416	−	1.35161i	−0.0149224	−	0.104279i
$169$	−10.5720			−0.813227
$170$		0			0
$171$	−13.1115	−	13.1115i	−1.00266	−	1.00266i
$172$	10.9620	−	7.79867i	0.835842	−	0.594643i
$173$	−11.8189			−0.898576			−0.449288	−	0.893387i	$-0.648322\pi$
$173$	−11.8189			−0.898576			−0.449288	+	0.893387i	$0.648322\pi$
$174$	1.52686	+	0.787578i	0.115751	+	0.0597061i
$175$		0			0
$176$	15.0661	−	7.30216i	1.13565	−	0.550421i
$177$	4.84870	+	4.84870i	0.364451	+	0.364451i
$178$	21.1704	−	6.76228i	1.58679	−	0.506855i
$179$	4.71524	+	4.71524i	0.352433	+	0.352433i	0.861014	−	0.508581i	$-0.169830\pi$
$179$	4.71524	+	4.71524i	0.352433	+	0.352433i	−0.508581	+	0.861014i	$0.669830\pi$
$180$		0			0
$181$	13.1843	−	13.1843i	0.979983	−	0.979983i	−0.0198205	−	0.999804i	$-0.506309\pi$
$181$	13.1843	−	13.1843i	0.979983	−	0.979983i	0.999804	+	0.0198205i	$0.00630948\pi$
$182$	−0.318793	−	0.164439i	−0.0236305	−	0.0121890i
$183$	−3.64870	+	3.64870i	−0.269720	+	0.269720i
$184$	2.34910	+	16.4157i	0.173178	+	1.21018i
$185$		0			0
$186$	16.7200	−	5.34073i	1.22597	−	0.391601i
$187$		−	1.77383i		−	0.129715i
$188$	2.06152	−	12.2263i	0.150352	−	0.891694i
$189$	−0.954008	+	0.954008i	−0.0693939	+	0.0693939i
$190$		0			0
$191$			13.9872i			1.01208i	0.862510	+	0.506040i	$0.168891\pi$
$191$			13.9872i			1.01208i	−0.862510	+	0.506040i	$0.831109\pi$
$192$	−22.7727	+	6.65384i	−1.64348	+	0.480199i
$193$	−3.88875	+	3.88875i	−0.279919	+	0.279919i	−0.833076	−	0.553158i	$-0.813423\pi$
$193$	−3.88875	+	3.88875i	−0.279919	+	0.279919i	0.553158	+	0.833076i	$0.313423\pi$
$194$	−17.2275	−	8.88623i	−1.23686	−	0.637994i
$195$		0			0
$196$	−8.08503	−	11.3645i	−0.577502	−	0.811748i
$197$	22.3277			1.59078			0.795391	−	0.606097i	$-0.207266\pi$
$197$	22.3277			1.59078			0.795391	+	0.606097i	$0.207266\pi$
$198$	−30.4850	−	15.7247i	−2.16648	−	1.11750i
$199$		−	9.83847i		−	0.697431i	−0.937229	−	0.348715i	$-0.886618\pi$
$199$		−	9.83847i		−	0.697431i	0.937229	−	0.348715i	$-0.113382\pi$
$200$		0			0
$201$			7.39437i			0.521559i
$202$	−11.7418	+	22.7635i	−0.826150	+	1.60164i
$203$	−0.0666793			−0.00467997
$204$	−0.417931	+	2.47863i	−0.0292610	+	0.173539i
$205$		0			0
$206$	3.97671	−	7.70955i	0.277071	−	0.537150i
$207$	24.0239	−	24.0239i	1.66978	−	1.66978i
$208$	−2.04379	+	5.88827i	−0.141711	+	0.408278i
$209$			13.3931i			0.926423i
$210$		0			0
$211$	11.0531	−	11.0531i	0.760925	−	0.760925i	−0.215565	−	0.976490i	$-0.569159\pi$
$211$	11.0531	−	11.0531i	0.760925	−	0.760925i	0.976490	+	0.215565i	$0.0691592\pi$
$212$	13.2547	+	18.6310i	0.910334	+	1.27958i
$213$		−	23.7278i		−	1.62580i
$214$	5.15541	+	16.1398i	0.352417	+	1.10330i
$215$		0			0
$216$	18.7580	+	14.0615i	1.27632	+	0.956764i
$217$	−0.481706	+	0.481706i	−0.0327004	+	0.0327004i
$218$	−3.68117	+	7.13659i	−0.249320	+	0.483351i
$219$	−3.32451	+	3.32451i	−0.224650	+	0.224650i
$220$		0			0
$221$	0.466948	+	0.466948i	0.0314103	+	0.0314103i
$222$	2.08830	+	6.53777i	0.140158	+	0.438787i
$223$	5.93975	+	5.93975i	0.397755	+	0.397755i	0.877440	−	0.479686i	$-0.159249\pi$
$223$	5.93975	+	5.93975i	0.397755	+	0.397755i	−0.479686	+	0.877440i	$0.659249\pi$
$224$	0.667122	−	0.634691i	0.0445740	−	0.0424071i
$225$		0			0
$226$	−5.93891	+	11.5136i	−0.395051	+	0.765875i
$227$	23.2105			1.54054			0.770269	−	0.637720i	$-0.220122\pi$
$227$	23.2105			1.54054			0.770269	+	0.637720i	$0.220122\pi$
$228$	3.15555	−	18.7147i	0.208981	−	1.23941i
$229$	−5.59944	−	5.59944i	−0.370021	−	0.370021i	0.497464	−	0.867485i	$-0.334265\pi$
$229$	−5.59944	−	5.59944i	−0.370021	−	0.370021i	−0.867485	+	0.497464i	$0.834265\pi$
$230$		0			0
$231$	2.02053			0.132941
$232$	0.164128	+	1.14694i	0.0107755	+	0.0753003i
$233$	3.01998	+	3.01998i	0.197845	+	0.197845i	0.799076	−	0.601230i	$-0.205323\pi$
$233$	3.01998	+	3.01998i	0.197845	+	0.197845i	−0.601230	+	0.799076i	$0.705323\pi$
$234$	12.1644	−	3.88556i	0.795209	−	0.254007i
$235$		0			0
$236$	−0.768884	+	4.56004i	−0.0500501	+	0.296833i
$237$			10.7420i			0.697766i
$238$	−0.0296846	−	0.0929323i	−0.00192416	−	0.00602391i
$239$	0.00138865			8.98241e−5			4.49120e−5	−	1.00000i	$-0.499986\pi$
$239$	0.00138865			8.98241e−5			4.49120e−5		1.00000i	$0.499986\pi$
$240$		0			0
$241$	−12.8578			−0.828245			−0.414123	−	0.910221i	$-0.635912\pi$
$241$	−12.8578			−0.828245			−0.414123	+	0.910221i	$0.635912\pi$
$242$	2.80529	+	8.78240i	0.180331	+	0.564554i
$243$			3.52546i			0.226158i
$244$	−3.43148	−	0.578593i	−0.219678	−	0.0370407i
$245$		0			0
$246$	−30.4289	+	9.71965i	−1.94008	+	0.619702i
$247$	−3.52565	−	3.52565i	−0.224332	−	0.224332i
$248$	9.47146	+	7.10006i	0.601438	+	0.450854i
$249$	4.82296			0.305643
$250$		0			0
$251$	−9.14111	−	9.14111i	−0.576982	−	0.576982i	0.357089	−	0.934071i	$-0.383769\pi$
$251$	−9.14111	−	9.14111i	−0.576982	−	0.576982i	−0.934071	+	0.357089i	$0.883769\pi$
$252$	−1.86028	−	0.313668i	−0.117187	−	0.0197593i
$253$	−24.5399			−1.54281
$254$	−11.2548	+	21.8194i	−0.706190	+	1.36907i
$255$		0			0
$256$	−12.5593	−	9.91280i	−0.784957	−	0.619550i
$257$	−21.2733	−	21.2733i	−1.32699	−	1.32699i	−0.907980	−	0.419013i	$-0.862376\pi$
$257$	−21.2733	−	21.2733i	−1.32699	−	1.32699i	−0.419013	−	0.907980i	$-0.637624\pi$
$258$	−8.58394	−	26.8734i	−0.534413	−	1.67306i
$259$	−0.188354	−	0.188354i	−0.0117038	−	0.0117038i
$260$		0			0
$261$	1.67851	−	1.67851i	0.103897	−	0.103897i
$262$	7.33076	−	14.2120i	0.452896	−	0.878018i
$263$	16.7214	−	16.7214i	1.03108	−	1.03108i	0.0315818	−	0.999501i	$-0.489946\pi$
$263$	16.7214	−	16.7214i	1.03108	−	1.03108i	0.999501	−	0.0315818i	$-0.0100545\pi$
$264$	−4.97343	−	34.7548i	−0.306094	−	2.13901i
$265$		0			0
$266$	0.224131	+	0.701677i	0.0137423	+	0.0430226i
$267$		−	46.6043i		−	2.85213i
$268$	−4.06336	+	2.89079i	−0.248209	+	0.176583i
$269$	−15.9096	+	15.9096i	−0.970026	+	0.970026i	−0.999564	−	0.0295378i	$-0.990596\pi$
$269$	−15.9096	+	15.9096i	−0.970026	+	0.970026i	0.0295378	+	0.999564i	$0.490596\pi$
$270$		0			0
$271$		−	12.3601i		−	0.750824i	−0.926858	−	0.375412i	$-0.877501\pi$
$271$		−	12.3601i		−	0.750824i	0.926858	−	0.375412i	$-0.122499\pi$
$272$	−1.52545	+	0.739348i	−0.0924938	+	0.0448295i
$273$	−0.531889	+	0.531889i	−0.0321914	+	0.0321914i
$274$	−2.82894	+	5.48440i	−0.170902	+	0.331324i
$275$		0			0
$276$	34.2904	+	5.78183i	2.06404	+	0.348025i
$277$	−21.0270			−1.26339			−0.631695	−	0.775217i	$-0.717641\pi$
$277$	−21.0270			−1.26339			−0.631695	+	0.775217i	$0.717641\pi$
$278$	−11.2044	+	21.7217i	−0.671994	+	1.30278i
$279$		−	24.2520i		−	1.45193i
$280$		0			0
$281$		−	10.6807i		−	0.637158i	−0.947896	−	0.318579i	$-0.896794\pi$
$281$		−	10.6807i		−	0.637158i	0.947896	−	0.318579i	$-0.103206\pi$
$282$	−23.1075	−	11.9192i	−1.37603	−	0.709780i
$283$	−12.5946			−0.748673			−0.374336	−	0.927293i	$-0.622129\pi$
$283$	−12.5946			−0.748673			−0.374336	+	0.927293i	$0.622129\pi$
$284$	13.0389	−	9.27626i	0.773716	−	0.550445i
$285$		0			0
$286$	−8.19733	−	4.22832i	−0.484718	−	0.250026i
$287$	0.876663	−	0.876663i	0.0517478	−	0.0517478i
$288$	−0.816372	+	32.7705i	−0.0481052	+	1.93102i
$289$		−	16.8204i		−	0.989435i
$290$		0			0
$291$	−28.7432	+	28.7432i	−1.68496	+	1.68496i
$292$	−3.12659	−	0.527185i	−0.182970	−	0.0308512i
$293$			3.43132i			0.200460i	0.994964	+	0.100230i	$0.0319579\pi$
$293$			3.43132i			0.200460i	−0.994964	+	0.100230i	$0.968042\pi$
$294$	−27.8602	+	8.89913i	−1.62484	+	0.519008i
$295$		0			0
$296$	−2.77623	+	3.70348i	−0.161365	+	0.215260i
$297$	−24.5310	+	24.5310i	−1.42344	+	1.42344i
$298$	−4.60670	−	2.37621i	−0.266859	−	0.137650i
$299$	6.45996	−	6.45996i	0.373589	−	0.373589i
$300$		0			0
$301$	0.774227	+	0.774227i	0.0446257	+	0.0446257i
$302$	−22.8470	+	7.29781i	−1.31470	+	0.419942i
$303$	37.9798	+	37.9798i	2.18188	+	2.18188i
$304$	11.5177	−	5.58238i	0.660588	−	0.320171i
$305$		0			0
$306$	3.08663	+	1.59213i	0.176451	+	0.0910162i
$307$	11.8104			0.674053			0.337027	−	0.941495i	$-0.390579\pi$
$307$	11.8104			0.674053			0.337027	+	0.941495i	$0.390579\pi$
$308$	0.789916	+	1.11032i	0.0450097	+	0.0632665i
$309$	−12.8630	−	12.8630i	−0.731750	−	0.731750i
$310$		0			0
$311$	22.6262			1.28301			0.641506	−	0.767118i	$-0.278310\pi$
$311$	22.6262			1.28301			0.641506	+	0.767118i	$0.278310\pi$
$312$	10.4582	+	7.83973i	0.592077	+	0.443837i
$313$	7.08945	+	7.08945i	0.400719	+	0.400719i	0.878486	−	0.477767i	$-0.158554\pi$
$313$	7.08945	+	7.08945i	0.400719	+	0.400719i	−0.477767	+	0.878486i	$0.658554\pi$
$314$	−3.68017	−	11.5214i	−0.207684	−	0.650188i
$315$		0			0
$316$	−5.90294	+	4.19952i	−0.332066	+	0.236242i
$317$			25.1265i			1.41124i	0.708589	+	0.705621i	$0.249332\pi$
$317$			25.1265i			1.41124i	−0.708589	+	0.705621i	$0.750668\pi$
$318$	45.6742	−	14.5893i	2.56128	−	0.818128i
$319$	−1.71457			−0.0959974
$320$		0			0
$321$	35.5300			1.98309
$322$	−1.28566	+	0.410669i	−0.0716473	+	0.0228857i
$323$		−	1.35606i		−	0.0754535i
$324$	11.7267	−	8.34274i	0.651485	−	0.463486i
$325$		0			0
$326$	−1.53964	−	4.82008i	−0.0852726	−	0.266960i
$327$	11.9070	+	11.9070i	0.658460	+	0.658460i
$328$	−17.2372	−	12.9215i	−0.951765	−	0.713469i
$329$	1.00913			0.0556349
$330$		0			0
$331$	5.80829	+	5.80829i	0.319253	+	0.319253i	0.848480	−	0.529227i	$-0.177518\pi$
$331$	5.80829	+	5.80829i	0.319253	+	0.319253i	−0.529227	+	0.848480i	$0.677518\pi$
$332$	1.88551	+	2.65032i	0.103481	+	0.145455i
$333$	9.48287			0.519658
$334$	−0.858293	−	0.442721i	−0.0469637	−	0.0242246i
$335$		0			0
$336$	−0.842174	−	1.73760i	−0.0459443	−	0.0947939i
$337$	7.41679	+	7.41679i	0.404019	+	0.404019i	0.879647	−	0.475628i	$-0.157779\pi$
$337$	7.41679	+	7.41679i	0.404019	+	0.404019i	−0.475628	+	0.879647i	$0.657779\pi$
$338$	−14.2421	+	4.54923i	−0.774667	+	0.247445i
$339$	19.2099	+	19.2099i	1.04334	+	1.04334i
$340$		0			0
$341$	−12.3864	+	12.3864i	−0.670763	+	0.670763i
$342$	−23.3053	−	12.0213i	−1.26021	−	0.650035i
$343$	1.60836	−	1.60836i	0.0868434	−	0.0868434i
$344$	11.4116	−	15.2231i	0.615274	−	0.820774i
$345$		0			0
$346$	−15.9220	+	5.08581i	−0.855970	+	0.273415i
$347$			18.2493i			0.979673i	0.871814	+	0.489837i	$0.162944\pi$
$347$			18.2493i			0.979673i	−0.871814	+	0.489837i	$0.837056\pi$
$348$	2.39582	+	0.403968i	0.128430	+	0.0216549i
$349$	19.4413	−	19.4413i	1.04067	−	1.04067i	0.0415330	−	0.999137i	$-0.486776\pi$
$349$	19.4413	−	19.4413i	1.04067	−	1.04067i	0.999137	−	0.0415330i	$-0.0132242\pi$
$350$		0			0
$351$		−	12.9152i		−	0.689364i
$352$	17.1541	−	16.3202i	0.914319	−	0.869871i
$353$	1.13598	−	1.13598i	0.0604622	−	0.0604622i	−0.676229	−	0.736691i	$-0.736387\pi$
$353$	1.13598	−	1.13598i	0.0604622	−	0.0604622i	0.736691	+	0.676229i	$0.236387\pi$
$354$	8.61841	+	4.44551i	0.458063	+	0.236276i
$355$		0			0
$356$	25.6100	−	18.2197i	1.35733	−	0.965643i
$357$	−0.204580			−0.0108275
$358$	8.38118	+	4.32315i	0.442959	+	0.228485i
$359$			28.4140i			1.49963i	0.661645	+	0.749817i	$0.269859\pi$
$359$			28.4140i			1.49963i	−0.661645	+	0.749817i	$0.730141\pi$
$360$		0			0
$361$		−	8.76116i		−	0.461114i
$362$	12.0880	−	23.4347i	0.635331	−	1.23170i
$363$	19.3334			1.01474
$364$	−0.500224	−	0.0843445i	−0.0262189	−	0.00442085i
$365$		0			0
$366$	−3.34530	+	6.48545i	−0.174861	+	0.339000i
$367$	−2.29692	+	2.29692i	−0.119898	+	0.119898i	−0.764510	−	0.644612i	$-0.777019\pi$
$367$	−2.29692	+	2.29692i	−0.119898	+	0.119898i	0.644612	+	0.764510i	$0.277019\pi$
$368$	10.2285	+	21.1037i	0.533195	+	1.10011i
$369$			44.1364i			2.29765i
$370$		0			0
$371$	−1.31588	+	1.31588i	−0.0683172	+	0.0683172i
$372$	20.2263	−	14.3896i	1.04869	−	0.746066i
$373$		−	18.0787i		−	0.936081i	−0.883707	−	0.468040i	$-0.844960\pi$
$373$		−	18.0787i		−	0.936081i	0.883707	−	0.468040i	$-0.155040\pi$
$374$	−0.763298	−	2.38963i	−0.0394692	−	0.123565i
$375$		0			0
$376$	−2.48392	−	17.3578i	−0.128098	−	0.895162i
$377$	0.451348	−	0.451348i	0.0232456	−	0.0232456i
$378$	−0.874679	+	1.69572i	−0.0449886	+	0.0872184i
$379$	2.79031	−	2.79031i	0.143328	−	0.143328i	−0.631802	−	0.775130i	$-0.717684\pi$
$379$	2.79031	−	2.79031i	0.143328	−	0.143328i	0.775130	+	0.631802i	$0.217684\pi$
$380$		0			0
$381$	36.4046	+	36.4046i	1.86506	+	1.86506i
$382$	6.01885	+	18.8430i	0.307951	+	0.964090i
$383$	−8.12206	−	8.12206i	−0.415018	−	0.415018i	0.468464	−	0.883482i	$-0.344807\pi$
$383$	−8.12206	−	8.12206i	−0.415018	−	0.415018i	−0.883482	+	0.468464i	$0.844807\pi$
$384$	−27.8152	+	18.7631i	−1.41944	+	0.957501i
$385$		0			0
$386$	−3.56539	+	6.91213i	−0.181474	+	0.351818i
$387$	−38.9792			−1.98142
$388$	−27.0320	−	4.55796i	−1.37234	−	0.231396i
$389$	14.4341	+	14.4341i	0.731839	+	0.731839i	0.970984	−	0.239145i	$-0.0768670\pi$
$389$	14.4341	+	14.4341i	0.731839	+	0.731839i	−0.239145	+	0.970984i	$0.576867\pi$
$390$		0			0
$391$	2.48468			0.125656
$392$	−15.7821	−	11.8307i	−0.797114	−	0.597539i
$393$	−23.7119	−	23.7119i	−1.19611	−	1.19611i
$394$	30.0789	−	9.60785i	1.51535	−	0.484036i
$395$		0			0
$396$	−47.8346	−	8.06556i	−2.40378	−	0.405310i
$397$			35.1624i			1.76475i	0.470549	+	0.882374i	$0.344056\pi$
$397$			35.1624i			1.76475i	−0.470549	+	0.882374i	$0.655944\pi$
$398$	−4.23360	−	13.2540i	−0.212211	−	0.664362i
$399$	1.54466			0.0773298
$400$		0			0
$401$	−23.5164			−1.17435			−0.587176	−	0.809459i	$-0.699760\pi$
$401$	−23.5164			−1.17435			−0.587176	+	0.809459i	$0.699760\pi$
$402$	3.18188	+	9.96138i	0.158698	+	0.496828i
$403$		−	6.52128i		−	0.324848i
$404$	−6.02265	+	35.7187i	−0.299638	+	1.77707i
$405$		0			0
$406$	−0.0898275	+	0.0286928i	−0.00445806	+	0.00142400i
$407$	−4.84328	−	4.84328i	−0.240072	−	0.240072i
$408$	0.503563	+	3.51895i	0.0249301	+	0.174214i
$409$	−23.2595			−1.15011			−0.575054	−	0.818115i	$-0.695019\pi$
$409$	−23.2595			−1.15011			−0.575054	+	0.818115i	$0.695019\pi$
$410$		0			0
$411$	9.15043	+	9.15043i	0.451357	+	0.451357i
$412$	2.03975	−	12.0972i	0.100491	−	0.595986i
$413$	−0.376374			−0.0185201
$414$	22.0262	−	42.7017i	1.08253	−	2.09868i
$415$		0			0
$416$	−0.219520	+	8.81188i	−0.0107628	+	0.432038i
$417$	36.2415	+	36.2415i	1.77475	+	1.77475i
$418$	5.76322	+	18.0427i	0.281888	+	0.882496i
$419$	−6.63975	−	6.63975i	−0.324373	−	0.324373i	0.526069	−	0.850442i	$-0.323665\pi$
$419$	−6.63975	−	6.63975i	−0.324373	−	0.324373i	−0.850442	+	0.526069i	$0.823665\pi$
$420$		0			0
$421$	7.28216	−	7.28216i	0.354911	−	0.354911i	−0.507022	−	0.861933i	$-0.669254\pi$
$421$	7.28216	−	7.28216i	0.354911	−	0.354911i	0.861933	+	0.507022i	$0.169254\pi$
$422$	10.1340	−	19.6465i	0.493314	−	0.956376i
$423$	−25.4027	+	25.4027i	−1.23512	+	1.23512i
$424$	25.8733	+	19.3953i	1.25652	+	0.941919i
$425$		0			0
$426$	−10.2103	−	31.9650i	−0.494691	−	1.54871i
$427$		−	0.283225i		−	0.0137062i
$428$	13.8903	+	19.5245i	0.671413	+	0.943751i
$429$	−13.6768	+	13.6768i	−0.660323	+	0.660323i
$430$		0			0
$431$			11.7250i			0.564771i	0.959301	+	0.282386i	$0.0911258\pi$
$431$			11.7250i			0.564771i	−0.959301	+	0.282386i	$0.908874\pi$
$432$	31.3208	+	10.8713i	1.50692	+	0.523045i
$433$	20.8827	−	20.8827i	1.00356	−	1.00356i	0.00356603	−	0.999994i	$-0.498865\pi$
$433$	20.8827	−	20.8827i	1.00356	−	1.00356i	0.999994	−	0.00356603i	$-0.00113511\pi$
$434$	−0.441651	+	0.856218i	−0.0211999	+	0.0410998i
$435$		0			0
$436$	−1.88816	+	11.1982i	−0.0904265	+	0.536294i
$437$	−18.7604			−0.897430
$438$	−3.04807	+	5.90921i	−0.145642	+	0.282353i
$439$		−	7.53661i		−	0.359703i	−0.983694	−	0.179851i	$-0.942438\pi$
$439$		−	7.53661i		−	0.359703i	0.983694	−	0.179851i	$-0.0575617\pi$
$440$		0			0
$441$			40.4105i			1.92431i
$442$	0.829985	+	0.428120i	0.0394784	+	0.0203636i
$443$	25.7280			1.22237			0.611187	−	0.791486i	$-0.290692\pi$
$443$	25.7280			1.22237			0.611187	+	0.791486i	$0.290692\pi$
$444$	5.62655	+	7.90879i	0.267024	+	0.375334i
$445$		0			0
$446$	10.5577	+	5.44584i	0.499922	+	0.257868i
$447$	−7.68604	+	7.68604i	−0.363537	+	0.363537i
$448$	0.625604	−	1.14210i	0.0295570	−	0.0539591i
$449$			2.33824i			0.110348i	0.998477	+	0.0551741i	$0.0175714\pi$
$449$			2.33824i			0.110348i	−0.998477	+	0.0551741i	$0.982429\pi$
$450$		0			0
$451$	22.5422	−	22.5422i	1.06147	−	1.06147i
$452$	−3.04621	+	18.0662i	−0.143282	+	0.849765i
$453$			50.2950i			2.36306i
$454$	31.2682	−	9.98774i	1.46749	−	0.468748i
$455$		0			0
$456$	−3.80211	−	26.5695i	−0.178050	−	1.24423i
$457$	10.4561	−	10.4561i	0.489115	−	0.489115i	−0.418912	−	0.908027i	$-0.637588\pi$
$457$	10.4561	−	10.4561i	0.489115	−	0.489115i	0.908027	+	0.418912i	$0.137588\pi$
$458$	−9.95282	−	5.13383i	−0.465065	−	0.239888i
$459$	2.48378	−	2.48378i	0.115933	−	0.115933i
$460$		0			0
$461$	15.6903	+	15.6903i	0.730769	+	0.730769i	0.970772	−	0.240003i	$-0.0771484\pi$
$461$	15.6903	+	15.6903i	0.730769	+	0.730769i	−0.240003	+	0.970772i	$0.577148\pi$
$462$	2.72197	−	0.869455i	0.126637	−	0.0404507i
$463$	−19.6332	−	19.6332i	−0.912434	−	0.912434i	0.0840297	−	0.996463i	$-0.473221\pi$
$463$	−19.6332	−	19.6332i	−0.912434	−	0.912434i	−0.996463	+	0.0840297i	$0.973221\pi$
$464$	0.714647	+	1.47448i	0.0331766	+	0.0684511i
$465$		0			0
$466$	5.36791	+	2.76886i	0.248664	+	0.128265i
$467$	24.4862			1.13309			0.566543	−	0.824032i	$-0.308281\pi$
$467$	24.4862			1.13309			0.566543	+	0.824032i	$0.308281\pi$
$468$	14.7153	−	10.4689i	0.680216	−	0.483926i
$469$	−0.286989	−	0.286989i	−0.0132519	−	0.0132519i
$470$		0			0
$471$	−25.3630			−1.16866
$472$	0.926426	+	6.47395i	0.0426422	+	0.297987i
$473$	19.9082	+	19.9082i	0.915380	+	0.915380i
$474$	4.62239	+	14.4711i	0.212313	+	0.664681i
$475$		0			0
$476$	−0.0799795	−	0.112421i	−0.00366586	−	0.00515280i
$477$		−	66.2493i		−	3.03335i
$478$	0.00187073		0.000597550i	8.55650e−5		2.73313e-5i
$479$	−37.0609			−1.69335			−0.846677	−	0.532108i	$-0.821400\pi$
$479$	−37.0609			−1.69335			−0.846677	+	0.532108i	$0.821400\pi$
$480$		0			0
$481$	2.54991			0.116266
$482$	−17.3215	+	5.53286i	−0.788973	+	0.252015i
$483$			2.83024i			0.128781i
$484$	7.55832	+	10.6241i	0.343560	+	0.482915i
$485$		0			0
$486$	1.51704	+	4.74935i	0.0688145	+	0.215435i
$487$	−20.1912	−	20.1912i	−0.914950	−	0.914950i	0.0817061	−	0.996656i	$-0.473963\pi$
$487$	−20.1912	−	20.1912i	−0.914950	−	0.914950i	−0.996656	+	0.0817061i	$0.973963\pi$
$488$	−4.87172	+	0.697145i	−0.220532	+	0.0315583i
$489$	−10.6109			−0.479840
$490$		0			0
$491$	−7.45822	−	7.45822i	−0.336585	−	0.336585i	0.518496	−	0.855080i	$-0.326492\pi$
$491$	−7.45822	−	7.45822i	−0.336585	−	0.336585i	−0.855080	+	0.518496i	$0.826492\pi$
$492$	−36.8101	+	26.1878i	−1.65953	+	1.18064i
$493$	0.173601			0.00781860
$494$	−6.26673	−	3.23248i	−0.281953	−	0.145436i
$495$		0			0
$496$	15.8148	+	5.48923i	0.710104	+	0.246474i
$497$	0.920917	+	0.920917i	0.0413088	+	0.0413088i
$498$	6.49728	−	2.07537i	0.291150	−	0.0929996i
$499$	−8.17420	−	8.17420i	−0.365927	−	0.365927i	0.500062	−	0.865990i	$-0.333311\pi$
$499$	−8.17420	−	8.17420i	−0.365927	−	0.365927i	−0.865990	+	0.500062i	$0.833311\pi$
$500$		0			0
$501$	−1.43202	+	1.43202i	−0.0639778	+	0.0639778i
$502$	−16.2480	−	8.38100i	−0.725185	−	0.374062i
$503$	29.2327	−	29.2327i	1.30342	−	1.30342i	0.377348	−	0.926072i	$-0.376836\pi$
$503$	29.2327	−	29.2327i	1.30342	−	1.30342i	0.926072	−	0.377348i	$-0.123164\pi$
$504$	−2.64107	+	0.377938i	−0.117642	+	0.0168347i
$505$		0			0
$506$	−33.0591	+	10.5598i	−1.46966	+	0.469440i
$507$			31.3523i			1.39241i
$508$	−5.77287	+	34.2373i	−0.256130	+	1.51903i
$509$	20.0340	−	20.0340i	0.887992	−	0.887992i	−0.106338	−	0.994330i	$-0.533912\pi$
$509$	20.0340	−	20.0340i	0.887992	−	0.887992i	0.994330	+	0.106338i	$0.0339125\pi$
$510$		0			0
$511$		−	0.258061i		−	0.0114159i
$512$	−21.1850	−	7.94969i	−0.936252	−	0.351330i
$513$	−18.7536	+	18.7536i	−0.827991	+	0.827991i
$514$	−37.8126	−	19.5044i	−1.66784	−	0.860301i
$515$		0			0
$516$	−23.1278	−	32.5089i	−1.01815	−	1.43113i
$517$	25.9483			1.14121
$518$	−0.334794	−	0.172692i	−0.0147100	−	0.00758765i
$519$			35.0504i			1.53854i
$520$		0			0
$521$			5.89264i			0.258161i	0.991634	+	0.129081i	$0.0412026\pi$
$521$			5.89264i			0.258161i	−0.991634	+	0.129081i	$0.958797\pi$
$522$	1.53894	−	2.98351i	0.0673576	−	0.130585i
$523$	24.6537			1.07803			0.539015	−	0.842296i	$-0.318797\pi$
$523$	24.6537			1.07803			0.539015	+	0.842296i	$0.318797\pi$
$524$	3.76012	−	22.3003i	0.164262	−	0.974191i
$525$		0			0
$526$	15.3309	−	29.7217i	0.668460	−	1.29593i
$527$	1.25413	−	1.25413i	0.0546309	−	0.0546309i
$528$	−21.6554	−	44.6801i	−0.942429	−	1.94445i
$529$		−	11.3742i		−	0.494528i
$530$		0			0
$531$	9.47444	−	9.47444i	0.411156	−	0.411156i
$532$	0.603878	+	0.848823i	0.0261814	+	0.0368012i
$533$			11.8681i			0.514066i
$534$	−20.0543	−	62.7833i	−0.867835	−	2.71690i
$535$		0			0
$536$	−4.23004	+	5.64286i	−0.182710	+	0.243735i
$537$	13.9836	−	13.9836i	0.603435	−	0.603435i
$538$	−14.5867	+	28.2788i	−0.628876	+	1.21919i
$539$	20.6392	−	20.6392i	0.888994	−	0.888994i
$540$		0			0
$541$	−27.1762	−	27.1762i	−1.16840	−	1.16840i	−0.982585	−	0.185812i	$-0.940508\pi$
$541$	−27.1762	−	27.1762i	−1.16840	−	1.16840i	−0.185812	−	0.982585i	$-0.559492\pi$
$542$	−5.31869	−	16.6510i	−0.228457	−	0.715223i
$543$	−39.0996	−	39.0996i	−1.67792	−	1.67792i
$544$	−1.73687	+	1.65243i	−0.0744676	+	0.0708475i
$545$		0			0
$546$	−0.487661	+	0.945416i	−0.0208700	+	0.0404601i
$547$	−3.69225			−0.157869			−0.0789347	−	0.996880i	$-0.525152\pi$
$547$	−3.69225			−0.157869			−0.0789347	+	0.996880i	$0.525152\pi$
$548$	−1.45103	+	8.60567i	−0.0619850	+	0.367616i
$549$	7.12962	+	7.12962i	0.304285	+	0.304285i
$550$		0			0
$551$	−1.31076			−0.0558402
$552$	48.6826	−	6.96651i	2.07207	−	0.296514i
$553$	−0.416915	−	0.416915i	−0.0177290	−	0.0177290i
$554$	−28.3267	+	9.04815i	−1.20349	+	0.384419i
$555$		0			0
$556$	−5.74700	+	34.0839i	−0.243727	+	1.44548i
$557$		−	12.2117i		−	0.517426i	−0.965954	−	0.258713i	$-0.916702\pi$
$557$		−	12.2117i		−	0.517426i	0.965954	−	0.258713i	$-0.0832984\pi$
$558$	−10.4359	−	32.6712i	−0.441786	−	1.38308i
$559$	−10.4814			−0.443315
$560$		0			0
$561$	−5.26049			−0.222098
$562$	−4.59603	−	14.3886i	−0.193872	−	0.606947i
$563$		−	12.2211i		−	0.515057i	−0.966271	−	0.257528i	$-0.917092\pi$
$563$		−	12.2211i		−	0.515057i	0.966271	−	0.257528i	$-0.0829081\pi$
$564$	−36.2584	−	6.11366i	−1.52676	−	0.257432i
$565$		0			0
$566$	−16.9669	+	5.41960i	−0.713174	+	0.227803i
$567$	0.828241	+	0.828241i	0.0347829	+	0.0347829i
$568$	13.5738	−	18.1074i	0.569543	−	0.759768i
$569$	30.9592			1.29788			0.648938	−	0.760841i	$-0.275213\pi$
$569$	30.9592			1.29788			0.648938	+	0.760841i	$0.275213\pi$
$570$		0			0
$571$	30.1508	+	30.1508i	1.26177	+	1.26177i	0.950233	+	0.311539i	$0.100844\pi$
$571$	30.1508	+	30.1508i	1.26177	+	1.26177i	0.311539	+	0.950233i	$0.399156\pi$
$572$	−12.8626	−	2.16881i	−0.537812	−	0.0906823i
$573$	41.4806			1.73288
$574$	0.803765	−	1.55824i	0.0335485	−	0.0650397i
$575$		0			0
$576$	13.0017	+	44.4983i	0.541738	+	1.85410i
$577$	−1.98215	−	1.98215i	−0.0825181	−	0.0825181i	0.664643	−	0.747161i	$-0.268584\pi$
$577$	−1.98215	−	1.98215i	−0.0825181	−	0.0825181i	−0.747161	+	0.664643i	$0.768584\pi$
$578$	−7.23800	−	22.6597i	−0.301061	−	0.942520i
$579$	11.5325	+	11.5325i	0.479276	+	0.479276i
$580$		0			0
$581$	−0.187188	+	0.187188i	−0.00776586	+	0.00776586i
$582$	−26.3531	+	51.0901i	−1.09237	+	2.11775i
$583$	−33.8361	+	33.8361i	−1.40135	+	1.40135i
$584$	−4.43886	+	0.635204i	−0.183681	+	0.0262849i
$585$		0			0
$586$	1.47653	+	4.62253i	0.0609951	+	0.190955i
$587$		−	26.9680i		−	1.11309i	−0.830818	−	0.556544i	$-0.812127\pi$
$587$		−	26.9680i		−	1.11309i	0.830818	−	0.556544i	$-0.187873\pi$
$588$	−33.7026	+	23.9771i	−1.38987	+	0.988797i
$589$	−9.46923	+	9.46923i	−0.390173	+	0.390173i
$590$		0			0
$591$		−	66.2153i		−	2.72373i
$592$	−2.14637	+	6.18381i	−0.0882152	+	0.254153i
$593$	−16.6701	+	16.6701i	−0.684560	+	0.684560i	−0.961024	−	0.276464i	$-0.910837\pi$
$593$	−16.6701	+	16.6701i	−0.684560	+	0.684560i	0.276464	+	0.961024i	$0.410837\pi$
$594$	−22.4912	+	43.6032i	−0.922825	+	1.78906i
$595$		0			0
$596$	−7.22846	−	1.21882i	−0.296089	−	0.0499247i
$597$	−29.1771			−1.19414
$598$	5.92279	−	11.4824i	0.242201	−	0.469549i
$599$		−	28.8376i		−	1.17827i	−0.808033	−	0.589137i	$-0.799468\pi$
$599$		−	28.8376i		−	1.17827i	0.808033	−	0.589137i	$-0.200532\pi$
$600$		0			0
$601$			1.91377i			0.0780642i	0.999238	+	0.0390321i	$0.0124275\pi$
$601$			1.91377i			0.0780642i	−0.999238	+	0.0390321i	$0.987573\pi$
$602$	1.37616	+	0.709847i	0.0560882	+	0.0289312i
$603$	14.4487			0.588397
$604$	−27.6381	+	19.6626i	−1.12458	+	0.800059i
$605$		0			0
$606$	67.5078	+	34.8216i	2.74232	+	1.41453i
$607$	−7.89049	+	7.89049i	−0.320265	+	0.320265i	−0.848869	−	0.528604i	$-0.822716\pi$
$607$	−7.89049	+	7.89049i	−0.320265	+	0.320265i	0.528604	+	0.848869i	$0.322716\pi$
$608$	13.1141	−	12.4766i	0.531845	−	0.505991i
$609$			0.197745i			0.00801303i
$610$		0			0
$611$	−6.83071	+	6.83071i	−0.276341	+	0.276341i
$612$	4.84329	+	0.816643i	0.195778	+	0.0330109i
$613$		−	40.1035i		−	1.61976i	−0.586592	−	0.809882i	$-0.699531\pi$
$613$		−	40.1035i		−	1.61976i	0.586592	−	0.809882i	$-0.300469\pi$
$614$	15.9104	−	5.08213i	0.642092	−	0.205098i
$615$		0			0
$616$	1.54193	+	1.15587i	0.0621259	+	0.0465713i
$617$	14.5821	−	14.5821i	0.587052	−	0.587052i	−0.349780	−	0.936832i	$-0.613744\pi$
$617$	14.5821	−	14.5821i	0.587052	−	0.587052i	0.936832	+	0.349780i	$0.113744\pi$
$618$	−22.8635	−	11.7934i	−0.919707	−	0.474399i
$619$	4.01752	−	4.01752i	0.161478	−	0.161478i	−0.621743	−	0.783221i	$-0.713575\pi$
$619$	4.01752	−	4.01752i	0.161478	−	0.161478i	0.783221	+	0.621743i	$0.213575\pi$
$620$		0			0
$621$	−34.3617	−	34.3617i	−1.37889	−	1.37889i
$622$	30.4810	−	9.73628i	1.22218	−	0.390389i
$623$	1.80880	+	1.80880i	0.0724679	+	0.0724679i
$624$	17.4623	+	6.06108i	0.699052	+	0.242638i
$625$		0			0
$626$	12.6013	+	6.49993i	0.503648	+	0.259790i
$627$	39.7189			1.58622
$628$	−9.91553	−	13.9375i	−0.395673	−	0.556166i
$629$	0.490385	+	0.490385i	0.0195529	+	0.0195529i
$630$		0			0
$631$	−26.9309			−1.07210			−0.536052	−	0.844185i	$-0.680085\pi$
$631$	−26.9309			−1.07210			−0.536052	+	0.844185i	$0.680085\pi$
$632$	−6.14508	+	8.19752i	−0.244438	+	0.326080i
$633$	−32.7791	−	32.7791i	−1.30285	−	1.30285i
$634$	10.8122	+	33.8493i	0.429407	+	1.34433i
$635$		0			0
$636$	55.2524	−	39.3082i	2.19090	−	1.55867i
$637$			10.8662i			0.430536i
$638$	−2.30979	+	0.737797i	−0.0914456	+	0.0292097i
$639$	−46.3644			−1.83415
$640$		0			0
$641$	18.6880			0.738131			0.369065	−	0.929403i	$-0.379678\pi$
$641$	18.6880			0.738131			0.369065	+	0.929403i	$0.379678\pi$
$642$	47.8645	−	15.2890i	1.88906	−	0.603407i
$643$			29.6249i			1.16829i	0.811648	+	0.584146i	$0.198571\pi$
$643$			29.6249i			1.16829i	−0.811648	+	0.584146i	$0.801429\pi$
$644$	−1.55528	+	1.10647i	−0.0612865	+	0.0436011i
$645$		0			0
$646$	−0.583529	−	1.82683i	−0.0229586	−	0.0718758i
$647$	5.04426	+	5.04426i	0.198310	+	0.198310i	0.799275	−	0.600965i	$-0.205217\pi$
$647$	5.04426	+	5.04426i	0.198310	+	0.198310i	−0.600965	+	0.799275i	$0.705217\pi$
$648$	12.2078	−	16.2851i	0.479567	−	0.639740i
$649$	−9.67794			−0.379893
$650$		0			0
$651$	1.42855	+	1.42855i	0.0559895	+	0.0559895i
$652$	−4.14827	−	5.83089i	−0.162459	−	0.228355i
$653$	−3.04934			−0.119330			−0.0596649	−	0.998218i	$-0.519003\pi$
$653$	−3.04934			−0.119330			−0.0596649	+	0.998218i	$0.519003\pi$
$654$	21.1644	+	10.9169i	0.827592	+	0.426885i
$655$		0			0
$656$	−28.7815	−	9.98991i	−1.12373	−	0.390040i
$657$	6.49615	+	6.49615i	0.253439	+	0.253439i
$658$	1.35945	−	0.434238i	0.0529970	−	0.0169284i
$659$	−22.0441	−	22.0441i	−0.858718	−	0.858718i	0.132469	−	0.991187i	$-0.457709\pi$
$659$	−22.0441	−	22.0441i	−0.858718	−	0.858718i	−0.991187	+	0.132469i	$0.957709\pi$
$660$		0			0
$661$	8.09788	−	8.09788i	0.314971	−	0.314971i	−0.531861	−	0.846832i	$-0.678507\pi$
$661$	8.09788	−	8.09788i	0.314971	−	0.314971i	0.846832	+	0.531861i	$0.178507\pi$
$662$	10.3241	+	5.32531i	0.401256	+	0.206974i
$663$	1.38479	−	1.38479i	0.0537807	−	0.0537807i
$664$	3.68054	+	2.75904i	0.142833	+	0.107071i
$665$		0			0
$666$	12.7749	−	4.08058i	0.495018	−	0.158119i
$667$		−	2.40167i		−	0.0929931i
$668$	−1.34676	−	0.227083i	−0.0521078	−	0.00878609i
$669$	17.6150	−	17.6150i	0.681035	−	0.681035i
$670$		0			0
$671$		−	7.28276i		−	0.281148i
$672$	−1.88225	−	1.97842i	−0.0726093	−	0.0763194i
$673$	27.1768	−	27.1768i	1.04759	−	1.04759i	0.0487786	−	0.998810i	$-0.484467\pi$
$673$	27.1768	−	27.1768i	1.04759	−	1.04759i	0.998810	−	0.0487786i	$-0.0155329\pi$
$674$	13.1831	+	6.80006i	0.507795	+	0.261929i
$675$		0			0
$676$	−17.2287	+	12.2570i	−0.662644	+	0.471425i
$677$	−28.6501			−1.10111			−0.550557	−	0.834798i	$-0.685585\pi$
$677$	−28.6501			−1.10111			−0.550557	+	0.834798i	$0.685585\pi$
$678$	34.1450	+	17.6125i	1.31133	+	0.676405i
$679$		−	2.23115i		−	0.0856238i
$680$		0			0
$681$		−	68.8334i		−	2.63770i
$682$	−11.3565	+	22.0165i	−0.434861	+	0.843055i
$683$	−30.8472			−1.18034			−0.590168	−	0.807281i	$-0.700938\pi$
$683$	−30.8472			−1.18034			−0.590168	+	0.807281i	$0.700938\pi$
$684$	−36.5688	−	6.16599i	−1.39824	−	0.235763i
$685$		0			0
$686$	1.47462	−	2.85881i	0.0563013	−	0.109150i
$687$	−16.6058	+	16.6058i	−0.633549	+	0.633549i
$688$	8.82261	−	25.4184i	0.336359	−	0.969069i
$689$		−	17.8142i		−	0.678668i
$690$		0			0
$691$	0.253186	−	0.253186i	0.00963164	−	0.00963164i	−0.702275	−	0.711906i	$-0.747832\pi$
$691$	0.253186	−	0.253186i	0.00963164	−	0.00963164i	0.711906	+	0.702275i	$0.247832\pi$
$692$	−19.2609	+	13.7028i	−0.732189	+	0.520901i
$693$		−	3.94815i		−	0.149978i
$694$	7.85286	+	24.5847i	0.298091	+	0.933221i
$695$		0			0
$696$	3.40138	−	0.486740i	0.128929	−	0.0184498i
$697$	−2.28241	+	2.28241i	−0.0864525	+	0.0864525i
$698$	17.8247	−	34.5563i	0.674675	−	1.30798i
$699$	8.95608	−	8.95608i	0.338750	−	0.338750i
$700$		0			0
$701$	10.5238	+	10.5238i	0.397479	+	0.397479i	0.877343	−	0.479864i	$-0.159314\pi$
$701$	10.5238	+	10.5238i	0.397479	+	0.397479i	−0.479864	+	0.877343i	$0.659314\pi$
$702$	−5.55756	−	17.3989i	−0.209757	−	0.656677i
$703$	−3.70261	−	3.70261i	−0.139646	−	0.139646i
$704$	16.0866	−	29.3675i	0.606285	−	1.10683i
$705$		0			0
$706$	1.04152	−	2.01917i	0.0391982	−	0.0759925i
$707$	−2.94813			−0.110876
$708$	13.5233	+	2.28021i	0.508237	+	0.0856956i
$709$	−1.58968	−	1.58968i	−0.0597015	−	0.0597015i	0.676626	−	0.736327i	$-0.263442\pi$
$709$	−1.58968	−	1.58968i	−0.0597015	−	0.0597015i	−0.736327	+	0.676626i	$0.763442\pi$
$710$		0			0
$711$	20.9900			0.787186
$712$	26.6606	−	35.5651i	0.999147	−	1.33286i
$713$	−17.3502	−	17.3502i	−0.649771	−	0.649771i
$714$	−0.275601	+	0.0880329i	−0.0103141	+	0.00329455i
$715$		0			0
$716$	13.1511	+	2.21745i	0.491478	+	0.0828699i
$717$		−	0.00411819i		−	0.000153797i
$718$	12.2269	+	38.2781i	0.456302	+	1.42853i
$719$	22.8919			0.853722			0.426861	−	0.904317i	$-0.359619\pi$
$719$	22.8919			0.853722			0.426861	+	0.904317i	$0.359619\pi$
$720$		0			0
$721$	0.998472			0.0371850
$722$	−3.77002	−	11.8027i	−0.140306	−	0.439249i
$723$			38.1313i			1.41812i
$724$	6.20023	−	36.7718i	0.230430	−	1.36661i
$725$		0			0
$726$	26.0452	−	8.31939i	0.966628	−	0.308762i
$727$	−20.1893	−	20.1893i	−0.748780	−	0.748780i	0.225470	−	0.974250i	$-0.427608\pi$
$727$	−20.1893	−	20.1893i	−0.748780	−	0.748780i	−0.974250	+	0.225470i	$0.927608\pi$
$728$	−0.710175	+	0.101626i	−0.0263208	+	0.00376653i
$729$	32.0425			1.18676
$730$		0			0
$731$	−2.01572	−	2.01572i	−0.0745540	−	0.0745540i
$732$	−1.71588	+	10.1764i	−0.0634209	+	0.376132i
$733$	14.3253			0.529118			0.264559	−	0.964370i	$-0.414774\pi$
$733$	14.3253			0.529118			0.264559	+	0.964370i	$0.414774\pi$
$734$	−2.10592	+	4.08270i	−0.0777311	+	0.150695i
$735$		0			0
$736$	22.8605	+	24.0286i	0.842648	+	0.885705i
$737$	−7.37954	−	7.37954i	−0.271829	−	0.271829i
$738$	18.9924	+	59.4587i	0.699119	+	2.18870i
$739$	32.3401	+	32.3401i	1.18965	+	1.18965i	0.977164	+	0.212487i	$0.0681564\pi$
$739$	32.3401	+	32.3401i	1.18965	+	1.18965i	0.212487	+	0.977164i	$0.431844\pi$
$740$		0			0
$741$	−10.4557	+	10.4557i	−0.384100	+	0.384100i
$742$	−1.20646	+	2.33894i	−0.0442906	+	0.0858651i
$743$	6.06842	−	6.06842i	0.222629	−	0.222629i	−0.586976	−	0.809605i	$-0.699682\pi$
$743$	6.06842	−	6.06842i	0.222629	−	0.222629i	0.809605	+	0.586976i	$0.199682\pi$
$744$	21.0560	−	28.0887i	0.771952	−	1.02978i
$745$		0			0
$746$	−7.77947	−	24.3549i	−0.284827	−	0.891696i
$747$		−	9.42414i		−	0.344811i
$748$	−2.05657	−	2.89075i	−0.0751955	−	0.105696i
$749$	−1.37898	+	1.37898i	−0.0503870	+	0.0503870i
$750$		0			0
$751$			49.6431i			1.81150i	0.423810	+	0.905751i	$0.360692\pi$
$751$			49.6431i			1.81150i	−0.423810	+	0.905751i	$0.639308\pi$
$752$	−10.8155	−	22.3149i	−0.394400	−	0.813740i
$753$	−27.1090	+	27.1090i	−0.987907	+	0.987907i
$754$	0.413816	−	0.802256i	0.0150703	−	0.0292164i
$755$		0			0
$756$	−0.448644	+	2.66078i	−0.0163170	+	0.0967718i
$757$	9.18443			0.333814			0.166907	−	0.985973i	$-0.446622\pi$
$757$	9.18443			0.333814			0.166907	+	0.985973i	$0.446622\pi$
$758$	2.55828	−	4.95968i	0.0929211	−	0.180144i
$759$			72.7759i			2.64160i
$760$		0			0
$761$		−	4.75310i		−	0.172300i	−0.996282	−	0.0861499i	$-0.972544\pi$
$761$		−	4.75310i		−	0.172300i	0.996282	−	0.0861499i	$-0.0274564\pi$
$762$	64.7080	+	33.3774i	2.34412	+	1.20914i
$763$	−0.924267			−0.0334607
$764$	16.2167	+	22.7945i	0.586698	+	0.824675i
$765$		0			0
$766$	−14.4367	−	7.44668i	−0.521619	−	0.269060i
$767$	2.54765	−	2.54765i	0.0919902	−	0.0919902i
$768$	−29.3975	+	37.2461i	−1.06079	+	1.34400i
$769$			19.4153i			0.700135i	0.936724	+	0.350067i	$0.113841\pi$
$769$			19.4153i			0.700135i	−0.936724	+	0.350067i	$0.886159\pi$
$770$		0			0
$771$	−63.0884	+	63.0884i	−2.27207	+	2.27207i
$772$	−1.82877	+	10.8460i	−0.0658190	+	0.390355i
$773$			26.0890i			0.938356i	0.883104	+	0.469178i	$0.155450\pi$
$773$			26.0890i			0.938356i	−0.883104	+	0.469178i	$0.844550\pi$
$774$	−52.5111	+	16.7732i	−1.88747	+	0.602899i
$775$		0			0
$776$	−38.3777	+	5.49187i	−1.37768	+	0.197147i
$777$	−0.558586	+	0.558586i	−0.0200392	+	0.0200392i
$778$	25.6562	+	13.2339i	0.919819	+	0.474458i
$779$	17.2331	−	17.2331i	0.617442	−	0.617442i
$780$		0			0
$781$	23.6802	+	23.6802i	0.847343	+	0.847343i
$782$	3.34726	−	1.06919i	0.119698	−	0.0382340i
$783$	−2.40080	−	2.40080i	−0.0857977	−	0.0857977i
$784$	−26.3518	−	9.14657i	−0.941135	−	0.326663i
$785$		0			0
$786$	−42.1472	−	21.7402i	−1.50334	−	0.775447i
$787$	14.2339			0.507384			0.253692	−	0.967285i	$-0.418355\pi$
$787$	14.2339			0.507384			0.253692	+	0.967285i	$0.418355\pi$
$788$	36.3867	−	25.8866i	1.29622	−	0.922170i
$789$	−49.5891	−	49.5891i	−1.76542	−	1.76542i
$790$		0			0
$791$	−1.49114			−0.0530189
$792$	−67.9115	+	9.71817i	−2.41313	+	0.345320i
$793$	1.91713	+	1.91713i	0.0680794	+	0.0680794i
$794$	15.1307	+	47.3692i	0.536970	+	1.68107i
$795$		0			0
$796$	−11.4067	−	16.0334i	−0.404298	−	0.568289i
$797$		−	19.8283i		−	0.702353i	−0.936309	−	0.351176i	$-0.885782\pi$
$797$		−	19.8283i		−	0.702353i	0.936309	−	0.351176i	$-0.114218\pi$
$798$	2.08090	−	0.664684i	0.0736631	−	0.0235296i
$799$	−2.62729			−0.0929467
$800$		0			0
$801$	−91.0655			−3.21764
$802$	−31.6803	+	10.1194i	−1.11867	+	0.357327i
$803$		−	6.63568i		−	0.234168i
$804$	8.57298	+	12.0503i	0.302346	+	0.424983i
$805$		0			0
$806$	−2.80618	−	8.78518i	−0.0988433	−	0.309445i
$807$	47.1817	+	47.1817i	1.66088	+	1.66088i
$808$	7.25667	+	50.7103i	0.255289	+	1.78398i
$809$	−21.3864			−0.751907			−0.375954	−	0.926639i	$-0.622685\pi$
$809$	−21.3864			−0.751907			−0.375954	+	0.926639i	$0.622685\pi$
$810$		0			0
$811$	−9.90624	−	9.90624i	−0.347855	−	0.347855i	0.511455	−	0.859310i	$-0.329107\pi$
$811$	−9.90624	−	9.90624i	−0.347855	−	0.347855i	−0.859310	+	0.511455i	$0.829107\pi$
$812$	−0.108665	+	0.0773075i	−0.00381339	+	0.00271296i
$813$	−36.6553			−1.28556
$814$	−8.60877	−	4.44054i	−0.301737	−	0.155641i
$815$		0			0
$816$	2.19262	+	4.52388i	0.0767570	+	0.158368i
$817$	15.2195	+	15.2195i	0.532463	+	0.532463i
$818$	−31.3342	+	10.0088i	−1.09557	+	0.349950i
$819$	1.03932	+	1.03932i	0.0363168	+	0.0363168i
$820$		0			0
$821$	22.6209	−	22.6209i	0.789474	−	0.789474i	−0.191934	−	0.981408i	$-0.561476\pi$
$821$	22.6209	−	22.6209i	0.789474	−	0.789474i	0.981408	+	0.191934i	$0.0614759\pi$
$822$	16.2646	+	8.38954i	0.567293	+	0.292619i
$823$	−4.89892	+	4.89892i	−0.170766	+	0.170766i	−0.787316	−	0.616550i	$-0.788530\pi$
$823$	−4.89892	+	4.89892i	−0.170766	+	0.170766i	0.616550	+	0.787316i	$0.288530\pi$
$824$	−2.45769	−	17.1746i	−0.0856177	−	0.598304i
$825$		0			0
$826$	−0.507034	+	0.161958i	−0.0176420	+	0.00563523i
$827$		−	1.05434i		−	0.0366630i	−0.999832	−	0.0183315i	$-0.994165\pi$
$827$		−	1.05434i		−	0.0366630i	0.999832	−	0.0183315i	$-0.00583542\pi$
$828$	11.2978	−	67.0041i	0.392625	−	2.32855i
$829$	−11.7754	+	11.7754i	−0.408978	+	0.408978i	−0.881382	−	0.472404i	$-0.843386\pi$
$829$	−11.7754	+	11.7754i	−0.408978	+	0.408978i	0.472404	+	0.881382i	$0.343386\pi$
$830$		0			0
$831$			62.3580i			2.16317i
$832$	3.49612	+	11.9655i	0.121206	+	0.414828i
$833$	−2.08973	+	2.08973i	−0.0724050	+	0.0724050i
$834$	64.4181	+	33.2279i	2.23061	+	1.15059i
$835$		0			0
$836$	15.5279	+	21.8263i	0.537044	+	0.754880i
$837$	−34.6879			−1.19899
$838$	−11.8019	−	6.08763i	−0.407691	−	0.210294i
$839$		−	41.1678i		−	1.42127i	−0.703560	−	0.710636i	$-0.748407\pi$
$839$		−	41.1678i		−	1.42127i	0.703560	−	0.710636i	$-0.251593\pi$
$840$		0			0
$841$			28.8322i			0.994214i
$842$	6.67662	−	12.9438i	0.230092	−	0.446073i
$843$	−31.6749			−1.09094
$844$	5.19796	−	30.8277i	0.178921	−	1.06113i
$845$		0			0
$846$	−23.2904	+	45.1525i	−0.800740	+	1.55237i
$847$	−0.750366	+	0.750366i	−0.0257829	+	0.0257829i
$848$	43.2013	+	14.9950i	1.48354	+	0.514930i
$849$			37.3508i			1.28188i
$850$		0			0
$851$	6.78419	−	6.78419i	0.232559	−	0.232559i
$852$	−27.5098	−	38.6683i	−0.942470	−	1.32475i
$853$			11.7179i			0.401212i	0.979672	+	0.200606i	$0.0642911\pi$
$853$			11.7179i			0.401212i	−0.979672	+	0.200606i	$0.935709\pi$
$854$	−0.121875	−	0.381549i	−0.00417047	−	0.0130563i
$855$		0			0
$856$	27.1140	+	20.3254i	0.926738	+	0.694708i
$857$	−12.2154	+	12.2154i	−0.417270	+	0.417270i	−0.884262	−	0.466992i	$-0.845338\pi$
$857$	−12.2154	+	12.2154i	−0.417270	+	0.417270i	0.466992	+	0.884262i	$0.345338\pi$
$858$	−12.5395	+	24.3101i	−0.428093	+	0.829933i
$859$	−17.2170	+	17.2170i	−0.587436	+	0.587436i	−0.936936	−	0.349500i	$-0.886351\pi$
$859$	−17.2170	+	17.2170i	−0.587436	+	0.587436i	0.349500	+	0.936936i	$0.386351\pi$
$860$		0			0
$861$	−2.59984	−	2.59984i	−0.0886024	−	0.0886024i
$862$	5.04537	+	15.7954i	0.171846	+	0.537992i
$863$	−11.1929	−	11.1929i	−0.381011	−	0.381011i	0.490455	−	0.871466i	$-0.336831\pi$
$863$	−11.1929	−	11.1929i	−0.381011	−	0.381011i	−0.871466	+	0.490455i	$0.836831\pi$
$864$	46.8721	+	1.16767i	1.59462	+	0.0397249i
$865$		0			0
$866$	19.1463	−	37.1184i	0.650616	−	1.26133i
$867$	−49.8828			−1.69411
$868$	−0.226533	+	1.34351i	−0.00768905	+	0.0456016i
$869$	−10.7204	−	10.7204i	−0.363665	−	0.363665i
$870$		0			0
$871$	3.88522			0.131646
$872$	2.27504	+	15.8982i	0.0770425	+	0.538380i
$873$	56.1647	+	56.1647i	1.90089	+	1.90089i
$874$	−25.2732	+	8.07279i	−0.854878	+	0.273066i
$875$		0			0
$876$	−1.56343	+	9.27225i	−0.0528233	+	0.313280i
$877$		−	43.1739i		−	1.45788i	−0.684578	−	0.728940i	$-0.740013\pi$
$877$		−	43.1739i		−	1.45788i	0.684578	−	0.728940i	$-0.259987\pi$
$878$	−3.24308	−	10.1530i	−0.109449	−	0.342647i
$879$	10.1760			0.343227
$880$		0			0
$881$	−33.4204			−1.12596			−0.562981	−	0.826470i	$-0.690346\pi$
$881$	−33.4204			−1.12596			−0.562981	+	0.826470i	$0.690346\pi$
$882$	17.3891	+	54.4392i	0.585520	+	1.83306i
$883$			2.00362i			0.0674270i	0.999432	+	0.0337135i	$0.0107334\pi$
$883$			2.00362i			0.0674270i	−0.999432	+	0.0337135i	$0.989267\pi$
$884$	1.30234	+	0.219593i	0.0438026	+	0.00738571i
$885$		0			0
$886$	34.6597	−	11.0710i	1.16441	−	0.371939i
$887$	16.1765	+	16.1765i	0.543154	+	0.543154i	0.924452	−	0.381298i	$-0.124523\pi$
$887$	16.1765	+	16.1765i	0.543154	+	0.543154i	−0.381298	+	0.924452i	$0.624523\pi$
$888$	10.9831	+	8.23322i	0.368568	+	0.276289i
$889$	−2.82586			−0.0947762
$890$		0			0
$891$	21.2971	+	21.2971i	0.713480	+	0.713480i
$892$	16.5663	+	2.79330i	0.554681	+	0.0935266i
$893$	19.8371			0.663822
$894$	−7.04692	+	13.6617i	−0.235684	+	0.456915i
$895$		0			0
$896$	0.351329	−	1.80779i	0.0117371	−	0.0603940i
$897$	−19.1577	−	19.1577i	−0.639658	−	0.639658i
$898$	1.00617	+	3.14997i	0.0335763	+	0.105116i
$899$	−1.21223	−	1.21223i	−0.0404303	−	0.0404303i
$900$		0			0
$901$	3.42593	−	3.42593i	0.114134	−	0.114134i
$902$	20.6677	−	40.0680i	0.688161	−	1.33412i
$903$	2.29606	−	2.29606i	0.0764080	−	0.0764080i
$904$	3.67037	+	25.6489i	0.122075	+	0.853070i
$905$		0			0
$906$	21.6425	+	67.7552i	0.719023	+	2.25102i
$907$			29.7116i			0.986559i	0.869871	+	0.493279i	$0.164202\pi$
$907$			29.7116i			0.986559i	−0.869871	+	0.493279i	$0.835798\pi$
$908$	37.8254	−	26.9101i	1.25528	−	0.893044i
$909$	74.2131	−	74.2131i	2.46149	−	2.46149i
$910$		0			0
$911$		−	44.6931i		−	1.48075i	−0.672195	−	0.740374i	$-0.734648\pi$
$911$		−	44.6931i		−	1.48075i	0.672195	−	0.740374i	$-0.265352\pi$
$912$	−16.5552	−	34.1572i	−0.548196	−	1.13106i
$913$	−4.81328	+	4.81328i	−0.159296	+	0.159296i
$914$	9.58663	−	18.5854i	0.317097	−	0.614749i
$915$		0			0
$916$	−15.6172	−	2.63326i	−0.516005	−	0.0870055i
$917$	1.84061			0.0607821
$918$	2.27725	−	4.41485i	0.0751604	−	0.145712i
$919$		−	40.1278i		−	1.32369i	−0.749639	−	0.661847i	$-0.769773\pi$
$919$		−	40.1278i		−	1.32369i	0.749639	−	0.661847i	$-0.230227\pi$
$920$		0			0
$921$		−	35.0250i		−	1.15411i
$922$	27.8890	+	14.3856i	0.918474	+	0.473764i
$923$	−12.4673			−0.410365
$924$	3.29279	−	2.34259i	0.108325	−	0.0770654i
$925$		0			0
$926$	−34.8974	−	18.0007i	−1.14680	−	0.591538i
$927$	−25.1345	+	25.1345i	−0.825525	+	0.825525i
$928$	1.59723	+	1.67884i	0.0524316	+	0.0551106i
$929$			27.7519i			0.910512i	0.890361	+	0.455256i	$0.150452\pi$
$929$			27.7519i			0.910512i	−0.890361	+	0.455256i	$0.849548\pi$
$930$		0			0
$931$	15.7783	−	15.7783i	0.517114	−	0.517114i
$932$	8.42289	+	1.42021i	0.275901	+	0.0465206i
$933$		−	67.1004i		−	2.19677i
$934$	32.9867	−	10.5367i	1.07936	−	0.344770i
$935$		0			0
$936$	15.3190	−	20.4354i	0.500716	−	0.667953i
$937$	−17.2805	+	17.2805i	−0.564531	+	0.564531i	−0.930591	−	0.366060i	$-0.880706\pi$
$937$	−17.2805	+	17.2805i	−0.564531	+	0.564531i	0.366060	+	0.930591i	$0.380706\pi$
$938$	−0.510114	−	0.263125i	−0.0166558	−	0.00859133i
$939$	21.0245	−	21.0245i	0.686110	−	0.686110i
$940$		0			0
$941$	−4.81532	−	4.81532i	−0.156975	−	0.156975i	0.624250	−	0.781225i	$-0.285405\pi$
$941$	−4.81532	−	4.81532i	−0.156975	−	0.156975i	−0.781225	+	0.624250i	$0.785405\pi$
$942$	−34.1679	+	10.9140i	−1.11325	+	0.355596i
$943$	31.5759	+	31.5759i	1.02825	+	1.02825i
$944$	4.03385	+	8.32277i	0.131291	+	0.270883i
$945$		0			0
$946$	35.3862	+	18.2528i	1.15050	+	0.593449i
$947$	−3.37347			−0.109623			−0.0548115	−	0.998497i	$-0.517456\pi$
$947$	−3.37347			−0.109623			−0.0548115	+	0.998497i	$0.517456\pi$
$948$	12.4542	+	17.5058i	0.404492	+	0.568563i
$949$	1.74680	+	1.74680i	0.0567034	+	0.0567034i
$950$		0			0
$951$	74.5153			2.41632
$952$	−0.156121	−	0.117032i	−0.00505991	−	0.00379304i
$953$	14.3663	+	14.3663i	0.465369	+	0.465369i	0.900410	−	0.435041i	$-0.143266\pi$
$953$	14.3663	+	14.3663i	0.465369	+	0.465369i	−0.435041	+	0.900410i	$0.643266\pi$
$954$	−28.5078	−	89.2482i	−0.922973	−	2.88952i
$955$		0			0
$956$	0.00226303	−	0.00160999i	7.31916e−5	−	5.20707e-5i
$957$			5.08475i			0.164366i
$958$	−49.9268	+	15.9477i	−1.61306	+	0.515246i
$959$	−0.710289			−0.0229364
$960$		0			0
$961$	13.4851			0.435003
$962$	3.43514	−	1.09726i	0.110753	−	0.0353769i
$963$		−	69.4263i		−	2.23723i
$964$	−20.9539	+	14.9073i	−0.674881	+	0.480131i
$965$		0			0
$966$	1.21788	+	3.81278i	0.0391848	+	0.122674i
$967$	11.8576	+	11.8576i	0.381315	+	0.381315i	0.871576	−	0.490260i	$-0.163098\pi$
$967$	11.8576	+	11.8576i	0.381315	+	0.381315i	−0.490260	+	0.871576i	$0.663098\pi$
$968$	14.7539	+	11.0599i	0.474209	+	0.355480i
$969$	−4.02156			−0.129191
$970$		0			0
$971$	−14.6082	−	14.6082i	−0.468799	−	0.468799i	0.432726	−	0.901525i	$-0.357552\pi$
$971$	−14.6082	−	14.6082i	−0.468799	−	0.468799i	−0.901525	+	0.432726i	$0.857552\pi$
$972$	4.08739	+	5.74532i	0.131103	+	0.184281i
$973$	−2.81319			−0.0901869
$974$	−35.8892	−	18.5122i	−1.14996	−	0.593170i
$975$		0			0
$976$	−6.26298	+	3.03552i	−0.200473	+	0.0971645i
$977$	−12.9249	−	12.9249i	−0.413504	−	0.413504i	0.469454	−	0.882957i	$-0.344451\pi$
$977$	−12.9249	−	12.9249i	−0.413504	−	0.413504i	−0.882957	+	0.469454i	$0.844451\pi$
$978$	−14.2945	+	4.56597i	−0.457088	+	0.146004i
$979$	46.5108	+	46.5108i	1.48649	+	1.48649i
$980$		0			0
$981$	23.2665	−	23.2665i	0.742843	−	0.742843i
$982$	−13.2567	−	6.83804i	−0.423040	−	0.218211i
$983$	0.133323	−	0.133323i	0.00425235	−	0.00425235i	−0.704977	−	0.709230i	$-0.749043\pi$
$983$	0.133323	−	0.133323i	0.00425235	−	0.00425235i	0.709230	+	0.704977i	$0.249043\pi$
$984$	−38.3201	+	51.1189i	−1.22160	+	1.62961i
$985$		0			0
$986$	0.233868	−	0.0747024i	0.00744787	−	0.00237901i
$987$		−	2.99268i		−	0.0952580i
$988$	−9.83324	−	1.65802i	−0.312837	−	0.0527485i
$989$	−27.8863	+	27.8863i	−0.886733	+	0.886733i
$990$		0			0
$991$		−	47.9032i		−	1.52170i	−0.648930	−	0.760848i	$-0.724783\pi$
$991$		−	47.9032i		−	1.52170i	0.648930	−	0.760848i	$-0.275217\pi$
$992$	23.6671	+	0.589589i	0.751430	+	0.0187195i
$993$	17.2251	−	17.2251i	0.546624	−	0.546624i
$994$	1.63690	+	0.844340i	0.0519194	+	0.0267808i
$995$		0			0
$996$	7.85981	−	5.59170i	0.249048	−	0.177180i
$997$	54.9379			1.73990			0.869951	−	0.493138i	$-0.164150\pi$
$997$	54.9379			1.73990			0.869951	+	0.493138i	$0.164150\pi$
$998$	−14.5294	−	7.49449i	−0.459919	−	0.237234i
$999$		−	13.5635i		−	0.429129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.j.d.307.9		18
4.3	odd	2		1600.2.j.d.1007.9		18
5.2	odd	4		80.2.s.b.3.5	yes	18
5.3	odd	4		400.2.s.d.243.5		18
5.4	even	2		80.2.j.b.67.1	yes	18
15.2	even	4		720.2.z.g.163.5		18
15.14	odd	2		720.2.bd.g.307.9		18
16.5	even	4		1600.2.s.d.207.1		18
16.11	odd	4		400.2.s.d.107.5		18
20.3	even	4		1600.2.s.d.943.1		18
20.7	even	4		320.2.s.b.303.9		18
20.19	odd	2		320.2.j.b.47.1		18
40.19	odd	2		640.2.j.c.607.9		18
40.27	even	4		640.2.s.c.223.1		18
40.29	even	2		640.2.j.d.607.1		18
40.37	odd	4		640.2.s.d.223.9		18
80.19	odd	4		640.2.s.d.287.9		18
80.27	even	4		80.2.j.b.43.1	✓	18
80.29	even	4		640.2.s.c.287.1		18
80.37	odd	4		320.2.j.b.143.9		18
80.43	even	4	inner	400.2.j.d.43.9		18
80.53	odd	4		1600.2.j.d.143.1		18
80.59	odd	4		80.2.s.b.27.5	yes	18
80.67	even	4		640.2.j.d.543.9		18
80.69	even	4		320.2.s.b.207.9		18
80.77	odd	4		640.2.j.c.543.1		18
240.59	even	4		720.2.z.g.667.5		18
240.107	odd	4		720.2.bd.g.523.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.1	✓	18	80.27	even	4
80.2.j.b.67.1	yes	18	5.4	even	2
80.2.s.b.3.5	yes	18	5.2	odd	4
80.2.s.b.27.5	yes	18	80.59	odd	4
320.2.j.b.47.1		18	20.19	odd	2
320.2.j.b.143.9		18	80.37	odd	4
320.2.s.b.207.9		18	80.69	even	4
320.2.s.b.303.9		18	20.7	even	4
400.2.j.d.43.9		18	80.43	even	4	inner
400.2.j.d.307.9		18	1.1	even	1	trivial
400.2.s.d.107.5		18	16.11	odd	4
400.2.s.d.243.5		18	5.3	odd	4
640.2.j.c.543.1		18	80.77	odd	4
640.2.j.c.607.9		18	40.19	odd	2
640.2.j.d.543.9		18	80.67	even	4
640.2.j.d.607.1		18	40.29	even	2
640.2.s.c.223.1		18	40.27	even	4
640.2.s.c.287.1		18	80.29	even	4
640.2.s.d.223.9		18	40.37	odd	4
640.2.s.d.287.9		18	80.19	odd	4
720.2.z.g.163.5		18	15.2	even	4
720.2.z.g.667.5		18	240.59	even	4
720.2.bd.g.307.9		18	15.14	odd	2
720.2.bd.g.523.9		18	240.107	odd	4
1600.2.j.d.143.1		18	80.53	odd	4
1600.2.j.d.1007.9		18	4.3	odd	2
1600.2.s.d.207.1		18	16.5	even	4
1600.2.s.d.943.1		18	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.34716 - 0.430311i) q^{2} -2.96561i q^{3} +(1.62967 - 1.15939i) q^{4} +(-1.27613 - 3.99515i) q^{6} +(0.115101 + 0.115101i) q^{7} +(1.69652 - 2.26315i) q^{8} -5.79486 q^{9} +O(q^{10})\)	\(q+(1.34716 - 0.430311i) q^{2} -2.96561i q^{3} +(1.62967 - 1.15939i) q^{4} +(-1.27613 - 3.99515i) q^{6} +(0.115101 + 0.115101i) q^{7} +(1.69652 - 2.26315i) q^{8} -5.79486 q^{9} +(2.95966 + 2.95966i) q^{11} +(-3.43831 - 4.83296i) q^{12} -1.55822 q^{13} +(0.204588 + 0.105530i) q^{14} +(1.31162 - 3.77884i) q^{16} +(-0.299668 - 0.299668i) q^{17} +(-7.80658 + 2.49359i) q^{18} +(2.26261 + 2.26261i) q^{19} +(0.341344 - 0.341344i) q^{21} +(5.26071 + 2.71356i) q^{22} +(-4.14573 + 4.14573i) q^{23} +(-6.71162 - 5.03121i) q^{24} +(-2.09917 + 0.670518i) q^{26} +8.28846i q^{27} +(0.321023 + 0.0541288i) q^{28} +(-0.289656 + 0.289656i) q^{29} +4.18508i q^{31} +(0.140879 - 5.65510i) q^{32} +(8.77721 - 8.77721i) q^{33} +(-0.532650 - 0.274749i) q^{34} +(-9.44368 + 6.71851i) q^{36} -1.63643 q^{37} +(4.02172 + 2.07447i) q^{38} +4.62107i q^{39} -7.61648i q^{41} +(0.312960 - 0.606729i) q^{42} +6.72651 q^{43} +(8.25467 + 1.39185i) q^{44} +(-3.80100 + 7.36890i) q^{46} +(4.38366 - 4.38366i) q^{47} +(-11.2066 - 3.88975i) q^{48} -6.97350i q^{49} +(-0.888698 + 0.888698i) q^{51} +(-2.53938 + 1.80659i) q^{52} +11.4324i q^{53} +(3.56661 + 11.1659i) q^{54} +(0.455760 - 0.0652196i) q^{56} +(6.71003 - 6.71003i) q^{57} +(-0.265570 + 0.514854i) q^{58} +(-1.63497 + 1.63497i) q^{59} +(-1.23034 - 1.23034i) q^{61} +(1.80089 + 5.63796i) q^{62} +(-0.666993 - 0.666993i) q^{63} +(-2.24366 - 7.67893i) q^{64} +(8.04736 - 15.6012i) q^{66} -2.49337 q^{67} +(-0.835791 - 0.140926i) q^{68} +(12.2946 + 12.2946i) q^{69} +8.00096 q^{71} +(-9.83107 + 13.1146i) q^{72} +(-1.12102 - 1.12102i) q^{73} +(-2.20453 + 0.704173i) q^{74} +(6.31056 + 1.06405i) q^{76} +0.681319i q^{77} +(1.98850 + 6.22531i) q^{78} -3.62218 q^{79} +7.19579 q^{81} +(-3.27745 - 10.2606i) q^{82} +1.62629i q^{83} +(0.160525 - 0.952029i) q^{84} +(9.06167 - 2.89449i) q^{86} +(0.859007 + 0.859007i) q^{87} +(11.7193 - 1.67703i) q^{88} +15.7149 q^{89} +(-0.179352 - 0.179352i) q^{91} +(-1.94962 + 11.5627i) q^{92} +12.4113 q^{93} +(4.01915 - 7.79182i) q^{94} +(-16.7708 - 0.417792i) q^{96} +(-9.69217 - 9.69217i) q^{97} +(-3.00077 - 9.39441i) q^{98} +(-17.1508 - 17.1508i) 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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