LMFDB - Embedded newform 400.2.l.h.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(101,400)]

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([0, 1, 0]))

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

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

chi := DirichletCharacter("400.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.l (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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			101.4
Root			$-1.39563 + 0.228522i$ of defining polynomial
Character	$\chi$	$=$	400.101
Dual form			400.2.l.h.301.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.114638 - 1.40956i) q^{2} +(-1.42313 + 1.42313i) q^{3} +(-1.97372 + 0.323179i) q^{4} +(2.16913 + 1.84284i) q^{6} -0.690576i q^{7} +(0.681804 + 2.74502i) q^{8} -1.05061i q^{9} +O(q^{10})$	\(q+(-0.114638 - 1.40956i) q^{2} +(-1.42313 + 1.42313i) q^{3} +(-1.97372 + 0.323179i) q^{4} +(2.16913 + 1.84284i) q^{6} -0.690576i q^{7} +(0.681804 + 2.74502i) q^{8} -1.05061i q^{9} +(-3.06057 - 3.06057i) q^{11} +(2.34893 - 3.26878i) q^{12} +(2.33686 - 2.33686i) q^{13} +(-0.973408 + 0.0791665i) q^{14} +(3.79111 - 1.27573i) q^{16} +5.28770 q^{17} +(-1.48089 + 0.120440i) q^{18} +(5.38887 - 5.38887i) q^{19} +(0.982780 + 0.982780i) q^{21} +(-3.96320 + 4.66492i) q^{22} -1.60841i q^{23} +(-4.87682 - 2.93623i) q^{24} +(-3.56183 - 3.02605i) q^{26} +(-2.77424 - 2.77424i) q^{27} +(0.223180 + 1.36300i) q^{28} +(1.70319 - 1.70319i) q^{29} -4.69807 q^{31} +(-2.23282 - 5.19755i) q^{32} +8.71119 q^{33} +(-0.606174 - 7.45333i) q^{34} +(0.339534 + 2.07360i) q^{36} +(-7.89871 - 7.89871i) q^{37} +(-8.21371 - 6.97817i) q^{38} +6.65131i q^{39} +5.49891i q^{41} +(1.27262 - 1.49795i) q^{42} +(0.256166 + 0.256166i) q^{43} +(7.02981 + 5.05159i) q^{44} +(-2.26715 + 0.184385i) q^{46} +4.60743 q^{47} +(-3.57972 + 7.21078i) q^{48} +6.52310 q^{49} +(-7.52510 + 7.52510i) q^{51} +(-3.85707 + 5.36752i) q^{52} +(4.99318 + 4.99318i) q^{53} +(-3.59243 + 4.22850i) q^{54} +(1.89565 - 0.470837i) q^{56} +15.3382i q^{57} +(-2.59600 - 2.20549i) q^{58} +(1.46478 + 1.46478i) q^{59} +(9.33004 - 9.33004i) q^{61} +(0.538579 + 6.62221i) q^{62} -0.725523 q^{63} +(-7.07029 + 3.74313i) q^{64} +(-0.998637 - 12.2789i) q^{66} +(1.94797 - 1.94797i) q^{67} +(-10.4364 + 1.70888i) q^{68} +(2.28897 + 2.28897i) q^{69} +2.32246i q^{71} +(2.88394 - 0.716307i) q^{72} -1.29733i q^{73} +(-10.2282 + 12.0392i) q^{74} +(-8.89454 + 12.3777i) q^{76} +(-2.11356 + 2.11356i) q^{77} +(9.37542 - 0.762495i) q^{78} -5.01968 q^{79} +11.0480 q^{81} +(7.75103 - 0.630385i) q^{82} +(-7.30477 + 7.30477i) q^{83} +(-2.25734 - 1.62212i) q^{84} +(0.331715 - 0.390448i) q^{86} +4.84772i q^{87} +(6.31463 - 10.4880i) q^{88} -1.81564i q^{89} +(-1.61378 - 1.61378i) q^{91} +(0.519803 + 3.17454i) q^{92} +(6.68597 - 6.68597i) q^{93} +(-0.528188 - 6.49445i) q^{94} +(10.5744 + 4.21920i) q^{96} -5.27038 q^{97} +(-0.747798 - 9.19470i) q^{98} +(-3.21546 + 3.21546i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 12 q^{6}+O(q^{10}) $ 16 * q - 4 * q^4 - 12 * q^6	$ 16 q - 4 q^{4} - 12 q^{6} - 8 q^{11} + 12 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{19} + 20 q^{22} + 8 q^{24} - 16 q^{26} - 24 q^{27} + 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} + 16 q^{37} - 20 q^{38} - 60 q^{42} - 8 q^{43} + 40 q^{44} - 4 q^{46} + 40 q^{47} + 40 q^{48} - 16 q^{49} - 32 q^{51} - 56 q^{52} - 16 q^{53} + 32 q^{54} + 16 q^{56} + 12 q^{58} - 8 q^{59} + 16 q^{61} + 8 q^{62} - 40 q^{63} - 16 q^{64} - 40 q^{67} + 48 q^{68} + 16 q^{69} + 40 q^{72} - 72 q^{74} - 16 q^{77} + 16 q^{78} + 16 q^{79} - 16 q^{81} + 76 q^{82} - 40 q^{83} - 64 q^{84} + 28 q^{86} + 32 q^{91} + 52 q^{92} + 48 q^{93} - 36 q^{94} + 8 q^{96} - 60 q^{98} - 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 12 * q^6 - 8 * q^11 + 12 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^19 + 20 * q^22 + 8 * q^24 - 16 * q^26 - 24 * q^27 + 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 + 16 * q^37 - 20 * q^38 - 60 * q^42 - 8 * q^43 + 40 * q^44 - 4 * q^46 + 40 * q^47 + 40 * q^48 - 16 * q^49 - 32 * q^51 - 56 * q^52 - 16 * q^53 + 32 * q^54 + 16 * q^56 + 12 * q^58 - 8 * q^59 + 16 * q^61 + 8 * q^62 - 40 * q^63 - 16 * q^64 - 40 * q^67 + 48 * q^68 + 16 * q^69 + 40 * q^72 - 72 * q^74 - 16 * q^77 + 16 * q^78 + 16 * q^79 - 16 * q^81 + 76 * q^82 - 40 * q^83 - 64 * q^84 + 28 * q^86 + 32 * q^91 + 52 * q^92 + 48 * q^93 - 36 * q^94 + 8 * q^96 - 60 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.114638	−	1.40956i	−0.0810615	−	0.996709i
$2$	−0.114638	−	1.40956i	−0.0810615	−	0.996709i
$3$	−1.42313	+	1.42313i	−0.821645	+	0.821645i	−0.986344	−	0.164699i	$-0.947335\pi$
$3$	−1.42313	+	1.42313i	−0.821645	+	0.821645i	0.164699	+	0.986344i	$0.447335\pi$
$4$	−1.97372	+	0.323179i	−0.986858	+	0.161590i
$5$		0			0
$5$		0			0
$6$	2.16913	+	1.84284i	0.885545	+	0.752338i
$7$		−	0.690576i		−	0.261013i	−0.991447	−	0.130507i	$-0.958340\pi$
$7$		−	0.690576i		−	0.261013i	0.991447	−	0.130507i	$-0.0416604\pi$
$8$	0.681804	+	2.74502i	0.241054	+	0.970512i
$9$		−	1.05061i		−	0.350202i
$10$		0			0
$11$	−3.06057	−	3.06057i	−0.922797	−	0.922797i	0.0744292	−	0.997226i	$-0.476287\pi$
$11$	−3.06057	−	3.06057i	−0.922797	−	0.922797i	−0.997226	+	0.0744292i	$0.976287\pi$
$12$	2.34893	−	3.26878i	0.678078	−	0.943617i
$13$	2.33686	−	2.33686i	0.648128	−	0.648128i	−0.304413	−	0.952540i	$-0.598460\pi$
$13$	2.33686	−	2.33686i	0.648128	−	0.648128i	0.952540	+	0.304413i	$0.0984601\pi$
$14$	−0.973408	+	0.0791665i	−0.260154	+	0.0211581i
$15$		0			0
$16$	3.79111	−	1.27573i	0.947778	−	0.318932i
$17$	5.28770			1.28246			0.641228	−	0.767350i	$-0.278425\pi$
$17$	5.28770			1.28246			0.641228	+	0.767350i	$0.278425\pi$
$18$	−1.48089	+	0.120440i	−0.349050	+	0.0283879i
$19$	5.38887	−	5.38887i	1.23629	−	1.23629i	0.274787	−	0.961505i	$-0.411393\pi$
$19$	5.38887	−	5.38887i	1.23629	−	1.23629i	0.961505	−	0.274787i	$-0.0886075\pi$
$20$		0			0
$21$	0.982780	+	0.982780i	0.214460	+	0.214460i
$22$	−3.96320	+	4.66492i	−0.844957	+	0.994564i
$23$		−	1.60841i		−	0.335376i	−0.985840	−	0.167688i	$-0.946370\pi$
$23$		−	1.60841i		−	0.335376i	0.985840	−	0.167688i	$-0.0536301\pi$
$24$	−4.87682	−	2.93623i	−0.995477	−	0.599355i
$25$		0			0
$26$	−3.56183	−	3.02605i	−0.698533	−	0.593457i
$27$	−2.77424	−	2.77424i	−0.533903	−	0.533903i
$28$	0.223180	+	1.36300i	0.0421770	+	0.257583i
$29$	1.70319	−	1.70319i	0.316274	−	0.316274i	−0.531060	−	0.847334i	$-0.678206\pi$
$29$	1.70319	−	1.70319i	0.316274	−	0.316274i	0.847334	+	0.531060i	$0.178206\pi$
$30$		0			0
$31$	−4.69807			−0.843798			−0.421899	−	0.906643i	$-0.638636\pi$
$31$	−4.69807			−0.843798			−0.421899	+	0.906643i	$0.638636\pi$
$32$	−2.23282	−	5.19755i	−0.394711	−	0.918805i
$33$	8.71119			1.51642
$34$	−0.606174	−	7.45333i	−0.103958	−	1.27824i
$35$		0			0
$36$	0.339534	+	2.07360i	0.0565890	+	0.345600i
$37$	−7.89871	−	7.89871i	−1.29854	−	1.29854i	−0.929356	−	0.369185i	$-0.879637\pi$
$37$	−7.89871	−	7.89871i	−1.29854	−	1.29854i	−0.369185	−	0.929356i	$-0.620363\pi$
$38$	−8.21371	−	6.97817i	−1.33244	−	1.13201i
$39$			6.65131i			1.06506i
$40$		0			0
$41$			5.49891i			0.858785i	0.903118	+	0.429392i	$0.141272\pi$
$41$			5.49891i			0.858785i	−0.903118	+	0.429392i	$0.858728\pi$
$42$	1.27262	−	1.49795i	0.196370	−	0.231139i
$43$	0.256166	+	0.256166i	0.0390650	+	0.0390650i	0.726369	−	0.687304i	$-0.241206\pi$
$43$	0.256166	+	0.256166i	0.0390650	+	0.0390650i	−0.687304	+	0.726369i	$0.741206\pi$
$44$	7.02981	+	5.05159i	1.05978	+	0.761555i
$45$		0			0
$46$	−2.26715	+	0.184385i	−0.334272	+	0.0271861i
$47$	4.60743			0.672063			0.336032	−	0.941851i	$-0.390915\pi$
$47$	4.60743			0.672063			0.336032	+	0.941851i	$0.390915\pi$
$48$	−3.57972	+	7.21078i	−0.516688	+	1.04079i
$49$	6.52310			0.931872
$50$		0			0
$51$	−7.52510	+	7.52510i	−1.05372	+	1.05372i
$52$	−3.85707	+	5.36752i	−0.534879	+	0.744341i
$53$	4.99318	+	4.99318i	0.685866	+	0.685866i	0.961316	−	0.275449i	$-0.0888266\pi$
$53$	4.99318	+	4.99318i	0.685866	+	0.685866i	−0.275449	+	0.961316i	$0.588827\pi$
$54$	−3.59243	+	4.22850i	−0.488867	+	0.575425i
$55$		0			0
$56$	1.89565	−	0.470837i	0.253316	−	0.0629183i
$57$			15.3382i			2.03159i
$58$	−2.59600	−	2.20549i	−0.340871	−	0.289596i
$59$	1.46478	+	1.46478i	0.190698	+	0.190698i	0.795998	−	0.605300i	$-0.206947\pi$
$59$	1.46478	+	1.46478i	0.190698	+	0.190698i	−0.605300	+	0.795998i	$0.706947\pi$
$60$		0			0
$61$	9.33004	−	9.33004i	1.19459	−	1.19459i	0.218825	−	0.975764i	$-0.429778\pi$
$61$	9.33004	−	9.33004i	1.19459	−	1.19459i	0.975764	−	0.218825i	$-0.0702224\pi$
$62$	0.538579	+	6.62221i	0.0683996	+	0.841021i
$63$	−0.725523			−0.0914074
$64$	−7.07029	+	3.74313i	−0.883786	+	0.467891i
$65$		0			0
$66$	−0.998637	−	12.2789i	−0.122924	−	1.51143i
$67$	1.94797	−	1.94797i	0.237982	−	0.237982i	−0.578032	−	0.816014i	$-0.696179\pi$
$67$	1.94797	−	1.94797i	0.237982	−	0.237982i	0.816014	+	0.578032i	$0.196179\pi$
$68$	−10.4364	+	1.70888i	−1.26560	+	0.207232i
$69$	2.28897	+	2.28897i	0.275560	+	0.275560i
$70$		0			0
$71$			2.32246i			0.275625i	0.990458	+	0.137813i	$0.0440072\pi$
$71$			2.32246i			0.275625i	−0.990458	+	0.137813i	$0.955993\pi$
$72$	2.88394	−	0.716307i	0.339875	−	0.0844176i
$73$		−	1.29733i		−	0.151841i	−0.997114	−	0.0759206i	$-0.975810\pi$
$73$		−	1.29733i		−	0.151841i	0.997114	−	0.0759206i	$-0.0241896\pi$
$74$	−10.2282	+	12.0392i	−1.18901	+	1.39953i
$75$		0			0
$76$	−8.89454	+	12.3777i	−1.02027	+	1.41982i
$77$	−2.11356	+	2.11356i	−0.240862	+	0.240862i
$78$	9.37542	−	0.762495i	1.06156	−	0.0863356i
$79$	−5.01968			−0.564758			−0.282379	−	0.959303i	$-0.591124\pi$
$79$	−5.01968			−0.564758			−0.282379	+	0.959303i	$0.591124\pi$
$80$		0			0
$81$	11.0480			1.22756
$82$	7.75103	−	0.630385i	0.855959	−	0.0696144i
$83$	−7.30477	+	7.30477i	−0.801802	+	0.801802i	−0.983377	−	0.181575i	$-0.941881\pi$
$83$	−7.30477	+	7.30477i	−0.801802	+	0.801802i	0.181575	+	0.983377i	$0.441881\pi$
$84$	−2.25734	−	1.62212i	−0.246296	−	0.176987i
$85$		0			0
$86$	0.331715	−	0.390448i	0.0357698	−	0.0421031i
$87$			4.84772i			0.519730i
$88$	6.31463	−	10.4880i	0.673141	−	1.11803i
$89$		−	1.81564i		−	0.192458i	−0.995359	−	0.0962290i	$-0.969322\pi$
$89$		−	1.81564i		−	0.192458i	0.995359	−	0.0962290i	$-0.0306781\pi$
$90$		0			0
$91$	−1.61378	−	1.61378i	−0.169170	−	0.169170i
$92$	0.519803	+	3.17454i	0.0541933	+	0.330969i
$93$	6.68597	−	6.68597i	0.693303	−	0.693303i
$94$	−0.528188	−	6.49445i	−0.0544785	−	0.669851i
$95$		0			0
$96$	10.5744	+	4.21920i	1.07924	+	0.430620i
$97$	−5.27038			−0.535126			−0.267563	−	0.963540i	$-0.586218\pi$
$97$	−5.27038			−0.535126			−0.267563	+	0.963540i	$0.586218\pi$
$98$	−0.747798	−	9.19470i	−0.0755390	−	0.928805i
$99$	−3.21546	+	3.21546i	−0.323165	+	0.323165i
$100$		0			0
$101$	−13.4502	−	13.4502i	−1.33834	−	1.33834i	−0.897667	−	0.440675i	$-0.854739\pi$
$101$	−13.4502	−	13.4502i	−1.33834	−	1.33834i	−0.440675	−	0.897667i	$-0.645261\pi$
$102$	11.4697	+	9.74441i	1.13567	+	0.964840i
$103$		−	2.64310i		−	0.260432i	−0.991486	−	0.130216i	$-0.958433\pi$
$103$		−	2.64310i		−	0.260432i	0.991486	−	0.130216i	$-0.0415671\pi$
$104$	8.00800	+	4.82145i	0.785249	+	0.472782i
$105$		0			0
$106$	6.46578	−	7.61060i	0.628012	−	0.739207i
$107$	6.28120	+	6.28120i	0.607227	+	0.607227i	0.942220	−	0.334994i	$-0.108734\pi$
$107$	6.28120	+	6.28120i	0.607227	+	0.607227i	−0.334994	+	0.942220i	$0.608734\pi$
$108$	6.37215	+	4.57899i	0.613160	+	0.440614i
$109$	−6.89216	+	6.89216i	−0.660149	+	0.660149i	−0.955415	−	0.295266i	$-0.904592\pi$
$109$	−6.89216	+	6.89216i	−0.660149	+	0.660149i	0.295266	+	0.955415i	$0.404592\pi$
$110$		0			0
$111$	22.4818			2.13388
$112$	−0.880987	−	2.61805i	−0.0832454	−	0.247382i
$113$	−6.46108			−0.607807			−0.303904	−	0.952703i	$-0.598290\pi$
$113$	−6.46108			−0.607807			−0.303904	+	0.952703i	$0.598290\pi$
$114$	21.6200	−	1.75834i	2.02490	−	0.164684i
$115$		0			0
$116$	−2.81117	+	3.91204i	−0.261011	+	0.363224i
$117$	−2.45512	−	2.45512i	−0.226976	−	0.226976i
$118$	1.89677	−	2.23261i	0.174612	−	0.205528i
$119$		−	3.65156i		−	0.334738i
$120$		0			0
$121$			7.73420i			0.703109i
$122$	−14.2208	−	12.0817i	−1.28749	−	1.09382i
$123$	−7.82566	−	7.82566i	−0.705616	−	0.705616i
$124$	9.27265	−	1.51832i	0.832709	−	0.136349i
$125$		0			0
$126$	0.0831728	+	1.02267i	0.00740962	+	0.0911065i
$127$	16.6123			1.47411			0.737054	−	0.675834i	$-0.236216\pi$
$127$	16.6123			1.47411			0.737054	+	0.675834i	$0.236216\pi$
$128$	6.08669	+	9.53688i	0.537993	+	0.842949i
$129$	−0.729117			−0.0641951
$130$		0			0
$131$	−11.7719	+	11.7719i	−1.02851	+	1.02851i	−0.0289318	+	0.999581i	$0.509211\pi$
$131$	−11.7719	+	11.7719i	−1.02851	+	1.02851i	−0.999581	+	0.0289318i	$0.990789\pi$
$132$	−17.1934	+	2.81528i	−1.49650	+	0.245038i
$133$	−3.72143	−	3.72143i	−0.322689	−	0.322689i
$134$	−2.96909	−	2.52247i	−0.256490	−	0.217908i
$135$		0			0
$136$	3.60518	+	14.5149i	0.309141	+	1.24464i
$137$		−	8.41495i		−	0.718937i	−0.933157	−	0.359469i	$-0.882958\pi$
$137$		−	8.41495i		−	0.718937i	0.933157	−	0.359469i	$-0.117042\pi$
$138$	2.96404	−	3.48885i	0.252316	−	0.296991i
$139$	−1.51845	−	1.51845i	−0.128793	−	0.128793i	0.639772	−	0.768565i	$-0.279029\pi$
$139$	−1.51845	−	1.51845i	−0.128793	−	0.128793i	−0.768565	+	0.639772i	$0.779029\pi$
$140$		0			0
$141$	−6.55698	+	6.55698i	−0.552198	+	0.552198i
$142$	3.27364	−	0.266243i	0.274718	−	0.0223426i
$143$	−14.3042			−1.19618
$144$	−1.34029	−	3.98296i	−0.111691	−	0.331914i
$145$		0			0
$146$	−1.82867	+	0.148724i	−0.151342	+	0.0123085i
$147$	−9.28324	+	9.28324i	−0.765668	+	0.765668i
$148$	18.1425	+	13.0371i	1.49131	+	1.07164i
$149$	−2.61440	−	2.61440i	−0.214180	−	0.214180i	0.591860	−	0.806040i	$-0.298394\pi$
$149$	−2.61440	−	2.61440i	−0.214180	−	0.214180i	−0.806040	+	0.591860i	$0.798394\pi$
$150$		0			0
$151$		−	12.7143i		−	1.03467i	−0.855782	−	0.517337i	$-0.826923\pi$
$151$		−	12.7143i		−	1.03467i	0.855782	−	0.517337i	$-0.173077\pi$
$152$	18.4667	+	11.1184i	1.49785	+	0.901823i
$153$		−	5.55529i		−	0.449119i
$154$	3.22148	+	2.73689i	0.259594	+	0.220545i
$155$		0			0
$156$	−2.14957	−	13.1278i	−0.172103	−	1.05107i
$157$	7.17831	−	7.17831i	0.572891	−	0.572891i	−0.360044	−	0.932935i	$-0.617238\pi$
$157$	7.17831	−	7.17831i	0.572891	−	0.572891i	0.932935	+	0.360044i	$0.117238\pi$
$158$	0.575448	+	7.07554i	0.0457802	+	0.562900i
$159$	−14.2119			−1.12708
$160$		0			0
$161$	−1.11073			−0.0875376
$162$	−1.26653	−	15.5729i	−0.0995080	−	1.22352i
$163$	7.05476	−	7.05476i	0.552572	−	0.552572i	−0.374611	−	0.927182i	$-0.622224\pi$
$163$	7.05476	−	7.05476i	0.552572	−	0.552572i	0.927182	+	0.374611i	$0.122224\pi$
$164$	−1.77713	−	10.8533i	−0.138771	−	0.847499i
$165$		0			0
$166$	11.1339	+	9.45910i	0.864159	+	0.734168i
$167$		−	3.90586i		−	0.302244i	−0.988515	−	0.151122i	$-0.951711\pi$
$167$		−	3.90586i		−	0.302244i	0.988515	−	0.151122i	$-0.0482887\pi$
$168$	−2.02769	+	3.36782i	−0.156440	+	0.259833i
$169$			2.07819i			0.159861i
$170$		0			0
$171$	−5.66158	−	5.66158i	−0.432952	−	0.432952i
$172$	−0.588387	−	0.422812i	−0.0448641	−	0.0322391i
$173$	−8.20139	+	8.20139i	−0.623540	+	0.623540i	−0.946435	−	0.322895i	$-0.895344\pi$
$173$	−8.20139	+	8.20139i	−0.623540	+	0.623540i	0.322895	+	0.946435i	$0.395344\pi$
$174$	6.83315	−	0.555735i	0.518020	−	0.0421301i
$175$		0			0
$176$	−15.5074	−	7.69851i	−1.16892	−	0.580297i
$177$	−4.16914			−0.313372
$178$	−2.55926	+	0.208142i	−0.191825	+	0.0156009i
$179$	−3.10363	+	3.10363i	−0.231976	+	0.231976i	−0.813517	−	0.581541i	$-0.802450\pi$
$179$	−3.10363	+	3.10363i	−0.231976	+	0.231976i	0.581541	+	0.813517i	$0.302450\pi$
$180$		0			0
$181$	−1.91041	−	1.91041i	−0.141999	−	0.141999i	0.632534	−	0.774533i	$-0.282015\pi$
$181$	−1.91041	−	1.91041i	−0.141999	−	0.141999i	−0.774533	+	0.632534i	$0.782015\pi$
$182$	−2.08972	+	2.45972i	−0.154900	+	0.182326i
$183$			26.5557i			1.96306i
$184$	4.41511	−	1.09662i	0.325486	−	0.0808437i
$185$		0			0
$186$	−10.1907	−	8.65780i	−0.747221	−	0.634821i
$187$	−16.1834	−	16.1834i	−1.18345	−	1.18345i
$188$	−9.09376	+	1.48903i	−0.663231	+	0.108598i
$189$	−1.91583	+	1.91583i	−0.139356	+	0.139356i
$190$		0			0
$191$	5.61041			0.405955			0.202977	−	0.979183i	$-0.434938\pi$
$191$	5.61041			0.405955			0.202977	+	0.979183i	$0.434938\pi$
$192$	4.73498	−	15.3889i	0.341718	−	1.11060i
$193$	−3.90696			−0.281229			−0.140615	−	0.990064i	$-0.544908\pi$
$193$	−3.90696			−0.281229			−0.140615	+	0.990064i	$0.544908\pi$
$194$	0.604187	+	7.42891i	0.0433781	+	0.533365i
$195$		0			0
$196$	−12.8748	+	2.10813i	−0.919625	+	0.150581i
$197$	−0.608436	−	0.608436i	−0.0433493	−	0.0433493i	0.685100	−	0.728449i	$-0.259759\pi$
$197$	−0.608436	−	0.608436i	−0.0433493	−	0.0433493i	−0.728449	+	0.685100i	$0.759759\pi$
$198$	4.90099	+	4.16376i	0.348298	+	0.295906i
$199$		−	15.5282i		−	1.10076i	−0.834913	−	0.550382i	$-0.814482\pi$
$199$		−	15.5282i		−	1.10076i	0.834913	−	0.550382i	$-0.185518\pi$
$200$		0			0
$201$			5.54443i			0.391074i
$202$	−17.4169	+	20.5007i	−1.22545	+	1.44243i
$203$	−1.17618	−	1.17618i	−0.0825517	−	0.0825517i
$204$	12.4205	−	17.2844i	0.869606	−	1.21015i
$205$		0			0
$206$	−3.72560	+	0.303000i	−0.259575	+	0.0211110i
$207$	−1.68980			−0.117449
$208$	5.87809	−	11.8405i	0.407572	−	0.820990i
$209$	−32.9861			−2.28169
$210$		0			0
$211$	2.14501	−	2.14501i	0.147669	−	0.147669i	−0.629407	−	0.777076i	$-0.716702\pi$
$211$	2.14501	−	2.14501i	0.147669	−	0.147669i	0.777076	+	0.629407i	$0.216702\pi$
$212$	−11.4688	−	8.24143i	−0.787681	−	0.566024i
$213$	−3.30516	−	3.30516i	−0.226466	−	0.226466i
$214$	8.13366	−	9.57380i	0.556006	−	0.654451i
$215$		0			0
$216$	5.72387	−	9.50685i	0.389460	−	0.646859i
$217$			3.24437i			0.220242i
$218$	10.5050	+	8.92480i	0.711489	+	0.604464i
$219$	1.84627	+	1.84627i	0.124760	+	0.124760i
$220$		0			0
$221$	12.3566	−	12.3566i	0.831196	−	0.831196i
$222$	−2.57728	−	31.6895i	−0.172976	−	2.12686i
$223$	2.34794			0.157230			0.0786148	−	0.996905i	$-0.474950\pi$
$223$	2.34794			0.157230			0.0786148	+	0.996905i	$0.474950\pi$
$224$	−3.58930	+	1.54193i	−0.239820	+	0.103025i
$225$		0			0
$226$	0.740688	+	9.10728i	0.0492698	+	0.605807i
$227$	−13.1881	+	13.1881i	−0.875325	+	0.875325i	−0.993047	−	0.117722i	$-0.962441\pi$
$227$	−13.1881	+	13.1881i	−0.875325	+	0.875325i	0.117722	+	0.993047i	$0.462441\pi$
$228$	−4.95697	−	30.2732i	−0.328283	−	2.00489i
$229$	9.37860	+	9.37860i	0.619755	+	0.619755i	0.945469	−	0.325713i	$-0.105604\pi$
$229$	9.37860	+	9.37860i	0.619755	+	0.619755i	−0.325713	+	0.945469i	$0.605604\pi$
$230$		0			0
$231$		−	6.01574i		−	0.395807i
$232$	5.83653	+	3.51405i	0.383187	+	0.230709i
$233$			16.3435i			1.07070i	0.844630	+	0.535350i	$0.179820\pi$
$233$			16.3435i			1.07070i	−0.844630	+	0.535350i	$0.820180\pi$
$234$	−3.17918	+	3.74208i	−0.207830	+	0.244628i
$235$		0			0
$236$	−3.36444	−	2.41767i	−0.219006	−	0.157377i
$237$	7.14367	−	7.14367i	0.464031	−	0.464031i
$238$	−5.14709	+	0.418609i	−0.333637	+	0.0271344i
$239$	19.3818			1.25371			0.626854	−	0.779137i	$-0.284342\pi$
$239$	19.3818			1.25371			0.626854	+	0.779137i	$0.284342\pi$
$240$		0			0
$241$	7.15965			0.461193			0.230597	−	0.973049i	$-0.425932\pi$
$241$	7.15965			0.461193			0.230597	+	0.973049i	$0.425932\pi$
$242$	10.9018	−	0.886636i	0.700795	−	0.0569951i
$243$	−7.40009	+	7.40009i	−0.474716	+	0.474716i
$244$	−15.3996	+	21.4301i	−0.985857	+	1.37192i
$245$		0			0
$246$	−10.1336	+	11.9279i	−0.646096	+	0.760493i
$247$		−	25.1861i		−	1.60255i
$248$	−3.20316	−	12.8963i	−0.203401	−	0.818916i
$249$		−	20.7913i		−	1.31759i
$250$		0			0
$251$	10.4372	+	10.4372i	0.658787	+	0.658787i	0.955093	−	0.296306i	$-0.0957548\pi$
$251$	10.4372	+	10.4372i	0.658787	+	0.658787i	−0.296306	+	0.955093i	$0.595755\pi$
$252$	1.43198	−	0.234474i	0.0902061	−	0.0147705i
$253$	−4.92264	+	4.92264i	−0.309484	+	0.309484i
$254$	−1.90441	−	23.4161i	−0.119493	−	1.46926i
$255$		0			0
$256$	12.7450	−	9.67285i	0.796565	−	0.604553i
$257$	−5.72152			−0.356899			−0.178449	−	0.983949i	$-0.557108\pi$
$257$	−5.72152			−0.356899			−0.178449	+	0.983949i	$0.557108\pi$
$258$	0.0835847	+	1.02773i	0.00520376	+	0.0639839i
$259$	−5.45466	+	5.45466i	−0.338936	+	0.338936i
$260$		0			0
$261$	−1.78938	−	1.78938i	−0.110760	−	0.110760i
$262$	17.9427	+	15.2436i	1.10850	+	0.941756i
$263$		−	27.1378i		−	1.67339i	−0.547669	−	0.836695i	$-0.684485\pi$
$263$		−	27.1378i		−	1.67339i	0.547669	−	0.836695i	$-0.315515\pi$
$264$	5.93932	+	23.9124i	0.365540	+	1.47171i
$265$		0			0
$266$	−4.81895	+	5.67219i	−0.295469	+	0.347784i
$267$	2.58390	+	2.58390i	0.158132	+	0.158132i
$268$	−3.21519	+	4.47428i	−0.196399	+	0.273310i
$269$	13.0770	−	13.0770i	0.797320	−	0.797320i	−0.185352	−	0.982672i	$-0.559343\pi$
$269$	13.0770	−	13.0770i	0.797320	−	0.797320i	0.982672	+	0.185352i	$0.0593426\pi$
$270$		0			0
$271$	6.55264			0.398044			0.199022	−	0.979995i	$-0.436223\pi$
$271$	6.55264			0.398044			0.199022	+	0.979995i	$0.436223\pi$
$272$	20.0463	−	6.74567i	1.21548	−	0.409016i
$273$	4.59324			0.277995
$274$	−11.8614	+	0.964675i	−0.716571	+	0.0582782i
$275$		0			0
$276$	−5.25753	−	3.77804i	−0.316466	−	0.227411i
$277$	10.2851	+	10.2851i	0.617973	+	0.617973i	0.945011	−	0.327038i	$-0.106051\pi$
$277$	10.2851	+	10.2851i	0.617973	+	0.617973i	−0.327038	+	0.945011i	$0.606051\pi$
$278$	−1.96627	+	2.31442i	−0.117929	+	0.138809i
$279$			4.93582i			0.295500i
$280$		0			0
$281$			29.9714i			1.78794i	0.448124	+	0.893971i	$0.352092\pi$
$281$			29.9714i			1.78794i	−0.448124	+	0.893971i	$0.647908\pi$
$282$	9.99414	+	8.49078i	0.595142	+	0.505618i
$283$	19.1176	+	19.1176i	1.13642	+	1.13642i	0.989087	+	0.147334i	$0.0470691\pi$
$283$	19.1176	+	19.1176i	1.13642	+	1.13642i	0.147334	+	0.989087i	$0.452931\pi$
$284$	−0.750570	−	4.58387i	−0.0445381	−	0.272003i
$285$		0			0
$286$	1.63981	+	20.1627i	0.0969643	+	1.19224i
$287$	3.79741			0.224154
$288$	−5.46058	+	2.34582i	−0.321768	+	0.138228i
$289$	10.9598			0.644695
$290$		0			0
$291$	7.50044	−	7.50044i	0.439684	−	0.439684i
$292$	0.419271	+	2.56056i	0.0245360	+	0.149846i
$293$	−7.27952	−	7.27952i	−0.425274	−	0.425274i	0.461741	−	0.887015i	$-0.347225\pi$
$293$	−7.27952	−	7.27952i	−0.425274	−	0.425274i	−0.887015	+	0.461741i	$0.847225\pi$
$294$	14.1495	+	12.0211i	0.825215	+	0.701082i
$295$		0			0
$296$	16.2968	−	27.0675i	0.947230	−	1.57327i
$297$			16.9815i			0.985369i
$298$	−3.38544	+	3.98486i	−0.196113	+	0.230837i
$299$	−3.75862	−	3.75862i	−0.217366	−	0.217366i
$300$		0			0
$301$	0.176902	−	0.176902i	0.0101965	−	0.0101965i
$302$	−17.9216	+	1.45755i	−1.03127	+	0.0838723i
$303$	38.2827			2.19928
$304$	13.5551	−	27.3046i	0.777437	−	1.56602i
$305$		0			0
$306$	−7.83052	+	0.636850i	−0.447641	+	0.0364063i
$307$	−7.03304	+	7.03304i	−0.401397	+	0.401397i	−0.878725	−	0.477328i	$-0.841605\pi$
$307$	−7.03304	+	7.03304i	−0.401397	+	0.401397i	0.477328	+	0.878725i	$0.341605\pi$
$308$	3.48850	−	4.85462i	0.198776	−	0.276618i
$309$	3.76147	+	3.76147i	0.213983	+	0.213983i
$310$		0			0
$311$			14.2833i			0.809929i	0.914332	+	0.404964i	$0.132716\pi$
$311$			14.2833i			0.809929i	−0.914332	+	0.404964i	$0.867284\pi$
$312$	−18.2580	+	4.53489i	−1.03366	+	0.256738i
$313$			18.4579i			1.04330i	0.853158	+	0.521652i	$0.174684\pi$
$313$			18.4579i			1.04330i	−0.853158	+	0.521652i	$0.825316\pi$
$314$	−10.9412	−	9.29534i	−0.617445	−	0.524567i
$315$		0			0
$316$	9.90743	−	1.62226i	0.557336	−	0.0912590i
$317$	7.21807	−	7.21807i	0.405407	−	0.405407i	−0.474726	−	0.880133i	$-0.657453\pi$
$317$	7.21807	−	7.21807i	0.405407	−	0.405407i	0.880133	+	0.474726i	$0.157453\pi$
$318$	1.62923	+	20.0325i	0.0913626	+	1.12337i
$319$	−10.4255			−0.583714
$320$		0			0
$321$	−17.8780			−0.997850
$322$	0.127332	+	1.56564i	0.00709593	+	0.0872495i
$323$	28.4948	−	28.4948i	1.58549	−	1.58549i
$324$	−21.8057	+	3.57050i	−1.21143	+	0.198361i
$325$		0			0
$326$	−10.7529	−	9.13536i	−0.595545	−	0.505961i
$327$		−	19.6169i		−	1.08482i
$328$	−15.0946	+	3.74917i	−0.833461	+	0.207014i
$329$		−	3.18178i		−	0.175417i
$330$		0			0
$331$	−15.4847	−	15.4847i	−0.851116	−	0.851116i	0.139155	−	0.990271i	$-0.455561\pi$
$331$	−15.4847	−	15.4847i	−0.851116	−	0.851116i	−0.990271	+	0.139155i	$0.955561\pi$
$332$	12.0568	−	16.7783i	0.661702	−	0.920828i
$333$	−8.29844	+	8.29844i	−0.454752	+	0.454752i
$334$	−5.50554	+	0.447761i	−0.301250	+	0.0245004i
$335$		0			0
$336$	4.97959	+	2.47207i	0.271659	+	0.134862i
$337$	26.0210			1.41746			0.708728	−	0.705482i	$-0.249269\pi$
$337$	26.0210			1.41746			0.708728	+	0.705482i	$0.249269\pi$
$338$	2.92933	−	0.238240i	0.159335	−	0.0129586i
$339$	9.19497	−	9.19497i	0.499402	−	0.499402i
$340$		0			0
$341$	14.3788	+	14.3788i	0.778654	+	0.778654i
$342$	−7.33131	+	8.62937i	−0.396432	+	0.466623i
$343$		−	9.33873i		−	0.504244i
$344$	−0.528527	+	0.877837i	−0.0284963	+	0.0473298i
$345$		0			0
$346$	12.5005	+	10.6202i	0.672034	+	0.570943i
$347$	12.8554	+	12.8554i	0.690115	+	0.690115i	0.962257	−	0.272142i	$-0.0877321\pi$
$347$	12.8554	+	12.8554i	0.690115	+	0.690115i	−0.272142	+	0.962257i	$0.587732\pi$
$348$	−1.56668	−	9.56802i	−0.0839830	−	0.512900i
$349$	−20.0227	+	20.0227i	−1.07179	+	1.07179i	−0.0745736	+	0.997216i	$0.523760\pi$
$349$	−20.0227	+	20.0227i	−1.07179	+	1.07179i	−0.997216	+	0.0745736i	$0.976240\pi$
$350$		0			0
$351$	−12.9660			−0.692075
$352$	−9.07376	+	22.7412i	−0.483633	+	1.21211i
$353$	−13.7062			−0.729510			−0.364755	−	0.931104i	$-0.618847\pi$
$353$	−13.7062			−0.729510			−0.364755	+	0.931104i	$0.618847\pi$
$354$	0.477943	+	5.87665i	0.0254024	+	0.312340i
$355$		0			0
$356$	0.586778	+	3.58357i	0.0310992	+	0.189929i
$357$	5.19665	+	5.19665i	0.275036	+	0.275036i
$358$	4.73055	+	4.01896i	0.250017	+	0.212409i
$359$			32.3506i			1.70740i	0.520764	+	0.853700i	$0.325647\pi$
$359$			32.3506i			1.70740i	−0.520764	+	0.853700i	$0.674353\pi$
$360$		0			0
$361$		−	39.0799i		−	2.05684i
$362$	−2.47383	+	2.91184i	−0.130021	+	0.153043i
$363$	−11.0068	−	11.0068i	−0.577706	−	0.577706i
$364$	3.70668	+	2.66360i	0.194283	+	0.139611i
$365$		0			0
$366$	37.4319	−	3.04431i	1.95660	−	0.159128i
$367$	−16.3714			−0.854582			−0.427291	−	0.904114i	$-0.640532\pi$
$367$	−16.3714			−0.854582			−0.427291	+	0.904114i	$0.640532\pi$
$368$	−2.05189	−	6.09765i	−0.106962	−	0.317862i
$369$	5.77718			0.300748
$370$		0			0
$371$	3.44817	−	3.44817i	0.179020	−	0.179020i
$372$	−11.0354	+	15.3570i	−0.572161	+	0.796222i
$373$	−15.5321	−	15.5321i	−0.804222	−	0.804222i	0.179530	−	0.983752i	$-0.442542\pi$
$373$	−15.5321	−	15.5321i	−0.804222	−	0.804222i	−0.983752	+	0.179530i	$0.942542\pi$
$374$	−20.9562	+	24.6667i	−1.08362	+	1.27548i
$375$		0			0
$376$	3.14136	+	12.6475i	0.162004	+	0.652245i
$377$		−	7.96022i		−	0.409972i
$378$	2.92010	+	2.48084i	0.150194	+	0.127601i
$379$	24.9538	+	24.9538i	1.28179	+	1.28179i	0.939647	+	0.342145i	$0.111153\pi$
$379$	24.9538	+	24.9538i	1.28179	+	1.28179i	0.342145	+	0.939647i	$0.388847\pi$
$380$		0			0
$381$	−23.6416	+	23.6416i	−1.21119	+	1.21119i
$382$	−0.643168	−	7.90820i	−0.0329073	−	0.404619i
$383$	−6.24887			−0.319302			−0.159651	−	0.987174i	$-0.551037\pi$
$383$	−6.24887			−0.319302			−0.159651	+	0.987174i	$0.551037\pi$
$384$	−22.2344	−	4.91008i	−1.13464	−	0.250566i
$385$		0			0
$386$	0.447888	+	5.50710i	0.0227969	+	0.280304i
$387$	0.269130	−	0.269130i	0.0136806	−	0.0136806i
$388$	10.4022	−	1.70328i	0.528093	−	0.0864707i
$389$	2.10802	+	2.10802i	0.106881	+	0.106881i	0.758525	−	0.651644i	$-0.225920\pi$
$389$	2.10802	+	2.10802i	0.106881	+	0.106881i	−0.651644	+	0.758525i	$0.725920\pi$
$390$		0			0
$391$		−	8.50478i		−	0.430105i
$392$	4.44748	+	17.9061i	0.224632	+	0.904393i
$393$		−	33.5058i		−	1.69015i
$394$	−0.787876	+	0.927377i	−0.0396926	+	0.0467206i
$395$		0			0
$396$	5.30723	−	7.38556i	0.266698	−	0.371139i
$397$	−23.4977	+	23.4977i	−1.17932	+	1.17932i	−0.199397	+	0.979919i	$0.563898\pi$
$397$	−23.4977	+	23.4977i	−1.17932	+	1.17932i	−0.979919	+	0.199397i	$0.936102\pi$
$398$	−21.8879	+	1.78013i	−1.09714	+	0.0892296i
$399$	10.5922			0.530271
$400$		0			0
$401$	−20.9893			−1.04816			−0.524078	−	0.851670i	$-0.675590\pi$
$401$	−20.9893			−1.04816			−0.524078	+	0.851670i	$0.675590\pi$
$402$	7.81520	−	0.635604i	0.389787	−	0.0317011i
$403$	−10.9787	+	10.9787i	−0.546889	+	0.546889i
$404$	30.8936	+	22.2000i	1.53702	+	1.10449i
$405$		0			0
$406$	−1.52306	+	1.79273i	−0.0755883	+	0.0889718i
$407$			48.3492i			2.39658i
$408$	−25.7872	−	15.5259i	−1.27666	−	0.768647i
$409$			18.4025i			0.909944i	0.890506	+	0.454972i	$0.150351\pi$
$409$			18.4025i			0.909944i	−0.890506	+	0.454972i	$0.849649\pi$
$410$		0			0
$411$	11.9756	+	11.9756i	0.590711	+	0.590711i
$412$	0.854193	+	5.21672i	0.0420831	+	0.257009i
$413$	1.01154	−	1.01154i	0.0497746	−	0.0497746i
$414$	0.193716	+	2.38188i	0.00952063	+	0.117063i
$415$		0			0
$416$	−17.3637	−	6.92815i	−0.851326	−	0.339680i
$417$	4.32190			0.211644
$418$	3.78147	+	46.4958i	0.184958	+	2.27419i
$419$	14.9331	−	14.9331i	0.729530	−	0.729530i	−0.240996	−	0.970526i	$-0.577474\pi$
$419$	14.9331	−	14.9331i	0.729530	−	0.729530i	0.970526	+	0.240996i	$0.0774740\pi$
$420$		0			0
$421$	−16.2680	−	16.2680i	−0.792854	−	0.792854i	0.189103	−	0.981957i	$-0.439442\pi$
$421$	−16.2680	−	16.2680i	−0.792854	−	0.792854i	−0.981957	+	0.189103i	$0.939442\pi$
$422$	−3.26942	−	2.77762i	−0.159153	−	0.135212i
$423$		−	4.84060i		−	0.235358i
$424$	−10.3020	+	17.1108i	−0.500310	+	0.830972i
$425$		0			0
$426$	−4.27993	+	5.03772i	−0.207363	+	0.244078i
$427$	−6.44310	−	6.44310i	−0.311804	−	0.311804i
$428$	−14.4273	−	10.3674i	−0.697368	−	0.501125i
$429$	20.3568	−	20.3568i	0.982836	−	0.982836i
$430$		0			0
$431$	7.05425			0.339791			0.169896	−	0.985462i	$-0.445657\pi$
$431$	7.05425			0.339791			0.169896	+	0.985462i	$0.445657\pi$
$432$	−14.0566	−	6.97829i	−0.676301	−	0.335743i
$433$	14.3192			0.688139			0.344069	−	0.938944i	$-0.388194\pi$
$433$	14.3192			0.688139			0.344069	+	0.938944i	$0.388194\pi$
$434$	4.57314	−	0.371930i	0.219518	−	0.0178532i
$435$		0			0
$436$	11.3758	−	15.8306i	0.544800	−	0.758146i
$437$	−8.66750	−	8.66750i	−0.414623	−	0.414623i
$438$	2.39078	−	2.81409i	0.114236	−	0.134462i
$439$		−	25.9047i		−	1.23637i	−0.786034	−	0.618183i	$-0.787869\pi$
$439$		−	25.9047i		−	1.23637i	0.786034	−	0.618183i	$-0.212131\pi$
$440$		0			0
$441$		−	6.85321i		−	0.326344i
$442$	−18.8339	−	16.0008i	−0.895838	−	0.761082i
$443$	11.1389	+	11.1389i	0.529224	+	0.529224i	0.920341	−	0.391117i	$-0.127911\pi$
$443$	11.1389	+	11.1389i	0.529224	+	0.529224i	−0.391117	+	0.920341i	$0.627911\pi$
$444$	−44.3727	+	7.26565i	−2.10584	+	0.344813i
$445$		0			0
$446$	−0.269164	−	3.30956i	−0.0127453	−	0.156712i
$447$	7.44127			0.351960
$448$	2.58492	+	4.88257i	0.122126	+	0.230680i
$449$	12.6659			0.597740			0.298870	−	0.954294i	$-0.403390\pi$
$449$	12.6659			0.597740			0.298870	+	0.954294i	$0.403390\pi$
$450$		0			0
$451$	16.8298	−	16.8298i	0.792484	−	0.792484i
$452$	12.7523	−	2.08809i	0.599820	−	0.0982153i
$453$	18.0941	+	18.0941i	0.850135	+	0.850135i
$454$	20.1013	+	17.0775i	0.943399	+	0.801489i
$455$		0			0
$456$	−42.1036	+	10.4576i	−1.97168	+	0.489722i
$457$		−	16.9442i		−	0.792617i	−0.918117	−	0.396308i	$-0.870291\pi$
$457$		−	16.9442i		−	0.792617i	0.918117	−	0.396308i	$-0.129709\pi$
$458$	12.1446	−	14.2948i	0.567478	−	0.667954i
$459$	−14.6694	−	14.6694i	−0.684708	−	0.684708i
$460$		0			0
$461$	−13.1888	+	13.1888i	−0.614264	+	0.614264i	−0.944054	−	0.329790i	$-0.893022\pi$
$461$	−13.1888	+	13.1888i	−0.614264	+	0.614264i	0.329790	+	0.944054i	$0.393022\pi$
$462$	−8.47954	+	0.689634i	−0.394504	+	0.0320847i
$463$	14.0955			0.655074			0.327537	−	0.944838i	$-0.393781\pi$
$463$	14.0955			0.655074			0.327537	+	0.944838i	$0.393781\pi$
$464$	4.28417	−	8.62978i	0.198888	−	0.400627i
$465$		0			0
$466$	23.0372	−	1.87360i	1.06718	−	0.0867927i
$467$	12.0918	−	12.0918i	0.559540	−	0.559540i	−0.369636	−	0.929177i	$-0.620518\pi$
$467$	12.0918	−	12.0918i	0.559540	−	0.559540i	0.929177	+	0.369636i	$0.120518\pi$
$468$	5.63915	+	4.05226i	0.260670	+	0.187316i
$469$	−1.34522	−	1.34522i	−0.0621165	−	0.0621165i
$470$		0			0
$471$			20.4313i			0.941427i
$472$	−3.02215	+	5.01953i	−0.139106	+	0.231043i
$473$		−	1.56803i		−	0.0720981i
$474$	−10.8884	−	9.25048i	−0.500119	−	0.424889i
$475$		0			0
$476$	1.18011	+	7.20715i	0.0540902	+	0.330339i
$477$	5.24587	−	5.24587i	0.240192	−	0.240192i
$478$	−2.22190	−	27.3199i	−0.101627	−	1.24958i
$479$	14.2523			0.651202			0.325601	−	0.945507i	$-0.394433\pi$
$479$	14.2523			0.651202			0.325601	+	0.945507i	$0.394433\pi$
$480$		0			0
$481$	−36.9163			−1.68324
$482$	−0.820770	−	10.0919i	−0.0373850	−	0.459676i
$483$	1.58071	−	1.58071i	0.0719248	−	0.0719248i
$484$	−2.49953	−	15.2651i	−0.113615	−	0.693869i
$485$		0			0
$486$	11.2792	+	9.58253i	0.511635	+	0.434672i
$487$			26.0424i			1.18010i	0.807368	+	0.590048i	$0.200891\pi$
$487$			26.0424i			1.18010i	−0.807368	+	0.590048i	$0.799109\pi$
$488$	31.9724	+	19.2499i	1.44732	+	0.871402i
$489$			20.0797i			0.908036i
$490$		0			0
$491$	3.46798	+	3.46798i	0.156508	+	0.156508i	0.781017	−	0.624509i	$-0.214701\pi$
$491$	3.46798	+	3.46798i	0.156508	+	0.156508i	−0.624509	+	0.781017i	$0.714701\pi$
$492$	17.9747	+	12.9165i	0.810364	+	0.582323i
$493$	9.00595	−	9.00595i	0.405608	−	0.405608i
$494$	−35.5013	+	2.88729i	−1.59728	+	0.129905i
$495$		0			0
$496$	−17.8109	+	5.99346i	−0.799733	+	0.269114i
$497$	1.60383			0.0719418
$498$	−29.3066	+	2.38348i	−1.31326	+	0.106806i
$499$	−5.30274	+	5.30274i	−0.237383	+	0.237383i	−0.815766	−	0.578383i	$-0.803684\pi$
$499$	−5.30274	+	5.30274i	−0.237383	+	0.237383i	0.578383	+	0.815766i	$0.303684\pi$
$500$		0			0
$501$	5.55855	+	5.55855i	0.248338	+	0.248338i
$502$	13.5153	−	15.9083i	0.603217	−	0.710021i
$503$			28.8492i			1.28632i	0.765731	+	0.643161i	$0.222378\pi$
$503$			28.8492i			1.28632i	−0.765731	+	0.643161i	$0.777622\pi$
$504$	−0.494665	−	1.99158i	−0.0220341	−	0.0887119i
$505$		0			0
$506$	7.50308	+	6.37444i	0.333553	+	0.283378i
$507$	−2.95754	−	2.95754i	−0.131349	−	0.131349i
$508$	−32.7881	+	5.36876i	−1.45473	+	0.238200i
$509$	12.9968	−	12.9968i	0.576072	−	0.576072i	−0.357747	−	0.933819i	$-0.616455\pi$
$509$	12.9968	−	12.9968i	0.576072	−	0.576072i	0.933819	+	0.357747i	$0.116455\pi$
$510$		0			0
$511$	−0.895906			−0.0396326
$512$	−15.0955	−	16.8560i	−0.667134	−	0.744937i
$513$	−29.9001			−1.32012
$514$	0.655906	+	8.06482i	0.0289308	+	0.355724i
$515$		0			0
$516$	1.43907	−	0.235635i	0.0633515	−	0.0103733i
$517$	−14.1014	−	14.1014i	−0.620178	−	0.620178i
$518$	8.31399	+	7.06336i	0.365296	+	0.310346i
$519$		−	23.3433i		−	1.02466i
$520$		0			0
$521$		−	13.9833i		−	0.612618i	−0.951932	−	0.306309i	$-0.900906\pi$
$521$		−	13.9833i		−	0.612618i	0.951932	−	0.306309i	$-0.0990941\pi$
$522$	−2.31711	+	2.72737i	−0.101417	+	0.119374i
$523$	6.30689	+	6.30689i	0.275781	+	0.275781i	0.831422	−	0.555641i	$-0.187527\pi$
$523$	6.30689	+	6.30689i	0.275781	+	0.275781i	−0.555641	+	0.831422i	$0.687527\pi$
$524$	19.4299	−	27.0388i	0.848800	−	1.18119i
$525$		0			0
$526$	−38.2524	+	3.11104i	−1.66788	+	0.135648i
$527$	−24.8420			−1.08213
$528$	33.0251	−	11.1131i	1.43723	−	0.483636i
$529$	20.4130			0.887523
$530$		0			0
$531$	1.53890	−	1.53890i	0.0667827	−	0.0667827i
$532$	8.54773	+	6.14235i	0.370591	+	0.266305i
$533$	12.8502	+	12.8502i	0.556602	+	0.556602i
$534$	3.34595	−	3.93838i	0.144793	−	0.170430i
$535$		0			0
$536$	6.67535	+	4.01908i	0.288331	+	0.173598i
$537$		−	8.83375i		−	0.381204i
$538$	−19.9320	−	16.9337i	−0.859328	−	0.730064i
$539$	−19.9644	−	19.9644i	−0.859929	−	0.859929i
$540$		0			0
$541$	3.89317	−	3.89317i	0.167381	−	0.167381i	−0.618446	−	0.785827i	$-0.712238\pi$
$541$	3.89317	−	3.89317i	0.167381	−	0.167381i	0.785827	+	0.618446i	$0.212238\pi$
$542$	−0.751184	−	9.23633i	−0.0322661	−	0.396735i
$543$	5.43752			0.233346
$544$	−11.8065	−	27.4831i	−0.506199	−	1.17833i
$545$		0			0
$546$	−0.526561	−	6.47444i	−0.0225347	−	0.277080i
$547$	27.8376	−	27.8376i	1.19025	−	1.19025i	0.213251	−	0.976997i	$-0.431595\pi$
$547$	27.8376	−	27.8376i	1.19025	−	1.19025i	0.976997	−	0.213251i	$-0.0684053\pi$
$548$	2.71953	+	16.6087i	0.116173	+	0.709489i
$549$	−9.80220	−	9.80220i	−0.418348	−	0.418348i
$550$		0			0
$551$		−	18.3565i		−	0.782014i
$552$	−4.72265	+	7.84391i	−0.201009	+	0.333859i
$553$			3.46647i			0.147409i
$554$	13.3184	−	15.6766i	0.565845	−	0.666033i
$555$		0			0
$556$	3.48772	+	2.50625i	0.147912	+	0.106289i
$557$	−1.50454	+	1.50454i	−0.0637492	+	0.0637492i	−0.738263	−	0.674513i	$-0.764353\pi$
$557$	−1.50454	+	1.50454i	−0.0637492	+	0.0637492i	0.674513	+	0.738263i	$0.264353\pi$
$558$	6.95733	−	0.565834i	0.294527	−	0.0239537i
$559$	1.19725			0.0506382
$560$		0			0
$561$	46.0622			1.94475
$562$	42.2465	−	3.43587i	1.78206	−	0.144933i
$563$	6.66663	−	6.66663i	0.280965	−	0.280965i	−0.552529	−	0.833494i	$-0.686337\pi$
$563$	6.66663	−	6.66663i	0.280965	−	0.280965i	0.833494	+	0.552529i	$0.186337\pi$
$564$	10.8225	−	15.0607i	0.455711	−	0.634170i
$565$		0			0
$566$	24.7557	−	29.1389i	1.04056	−	1.22480i
$567$		−	7.62952i		−	0.320410i
$568$	−6.37520	+	1.58346i	−0.267497	+	0.0664405i
$569$			8.38187i			0.351386i	0.984445	+	0.175693i	$0.0562167\pi$
$569$			8.38187i			0.351386i	−0.984445	+	0.175693i	$0.943783\pi$
$570$		0			0
$571$	28.4129	+	28.4129i	1.18904	+	1.18904i	0.977333	+	0.211708i	$0.0679027\pi$
$571$	28.4129	+	28.4129i	1.18904	+	1.18904i	0.211708	+	0.977333i	$0.432097\pi$
$572$	28.2325	−	4.62283i	1.18046	−	0.193290i
$573$	−7.98435	+	7.98435i	−0.333551	+	0.333551i
$574$	−0.435329	−	5.35268i	−0.0181703	−	0.223416i
$575$		0			0
$576$	3.93256	+	7.42809i	0.163857	+	0.309504i
$577$	−23.2045			−0.966014			−0.483007	−	0.875616i	$-0.660455\pi$
$577$	−23.2045			−0.966014			−0.483007	+	0.875616i	$0.660455\pi$
$578$	−1.25642	−	15.4485i	−0.0522600	−	0.642574i
$579$	5.56012	−	5.56012i	0.231071	−	0.231071i
$580$		0			0
$581$	5.04450	+	5.04450i	0.209281	+	0.209281i
$582$	−11.4322	−	9.71248i	−0.473878	−	0.402595i
$583$		−	30.5640i		−	1.26583i
$584$	3.56120	−	0.884526i	0.147364	−	0.0366019i
$585$		0			0
$586$	−9.42640	+	11.0954i	−0.389401	+	0.458348i
$587$	11.0197	+	11.0197i	0.454832	+	0.454832i	0.896955	−	0.442123i	$-0.145774\pi$
$587$	11.0197	+	11.0197i	0.454832	+	0.454832i	−0.442123	+	0.896955i	$0.645774\pi$
$588$	15.3223	−	21.3226i	0.631882	−	0.879330i
$589$	−25.3173	+	25.3173i	−1.04318	+	1.04318i
$590$		0			0
$591$	1.73177			0.0712354
$592$	−40.0215	−	19.8683i	−1.64487	−	0.816582i
$593$	6.98847			0.286982			0.143491	−	0.989652i	$-0.454167\pi$
$593$	6.98847			0.286982			0.143491	+	0.989652i	$0.454167\pi$
$594$	23.9365	−	1.94674i	0.982126	−	0.0798755i
$595$		0			0
$596$	6.00500	+	4.31516i	0.245975	+	0.176756i
$597$	22.0987	+	22.0987i	0.904438	+	0.904438i
$598$	−4.86711	+	5.72888i	−0.199031	+	0.234271i
$599$			39.9642i			1.63289i	0.577420	+	0.816447i	$0.304059\pi$
$599$			39.9642i			1.63289i	−0.577420	+	0.816447i	$0.695941\pi$
$600$		0			0
$601$			21.0830i			0.859993i	0.902831	+	0.429997i	$0.141485\pi$
$601$			21.0830i			0.859993i	−0.902831	+	0.429997i	$0.858515\pi$
$602$	−0.269634	−	0.229075i	−0.0109895	−	0.00933638i
$603$	−2.04655	−	2.04655i	−0.0833418	−	0.0833418i
$604$	4.10899	+	25.0944i	0.167193	+	1.02108i
$605$		0			0
$606$	−4.38867	−	53.9618i	−0.178277	−	2.19205i
$607$	−22.3189			−0.905897			−0.452949	−	0.891537i	$-0.649628\pi$
$607$	−22.3189			−0.905897			−0.452949	+	0.891537i	$0.649628\pi$
$608$	−40.0413	−	15.9765i	−1.62389	−	0.647934i
$609$	3.34772			0.135656
$610$		0			0
$611$	10.7669	−	10.7669i	0.435583	−	0.435583i
$612$	1.79536	+	10.9646i	0.0725729	+	0.443217i
$613$	10.6045	+	10.6045i	0.428312	+	0.428312i	0.888053	−	0.459741i	$-0.152058\pi$
$613$	10.6045	+	10.6045i	0.428312	+	0.428312i	−0.459741	+	0.888053i	$0.652058\pi$
$614$	10.7197	+	9.10724i	0.432614	+	0.367538i
$615$		0			0
$616$	−7.24279	−	4.36073i	−0.291820	−	0.175699i
$617$		−	33.7636i		−	1.35927i	−0.733550	−	0.679635i	$-0.762138\pi$
$617$		−	33.7636i		−	1.35927i	0.733550	−	0.679635i	$-0.237862\pi$
$618$	4.87081	−	5.73323i	0.195933	−	0.230624i
$619$	4.86777	+	4.86777i	0.195652	+	0.195652i	0.798133	−	0.602481i	$-0.205821\pi$
$619$	4.86777	+	4.86777i	0.195652	+	0.195652i	−0.602481	+	0.798133i	$0.705821\pi$
$620$		0			0
$621$	−4.46211	+	4.46211i	−0.179058	+	0.179058i
$622$	20.1331	−	1.63741i	0.807263	−	0.0656541i
$623$	−1.25384			−0.0502341
$624$	8.48526	+	25.2159i	0.339682	+	1.00944i
$625$		0			0
$626$	26.0176	−	2.11599i	1.03987	−	0.0845718i
$627$	46.9435	−	46.9435i	1.87474	−	1.87474i
$628$	−11.8481	+	16.4878i	−0.472789	+	0.657936i
$629$	−41.7661	−	41.7661i	−1.66532	−	1.66532i
$630$		0			0
$631$			16.1348i			0.642315i	0.947026	+	0.321157i	$0.104072\pi$
$631$			16.1348i			0.642315i	−0.947026	+	0.321157i	$0.895928\pi$
$632$	−3.42244	−	13.7791i	−0.136137	−	0.548105i
$633$			6.10526i			0.242662i
$634$	−11.0018	−	9.34683i	−0.436936	−	0.371210i
$635$		0			0
$636$	28.0503	−	4.59299i	1.11227	−	0.182124i
$637$	15.2436	−	15.2436i	0.603972	−	0.603972i
$638$	1.19516	+	14.6953i	0.0473167	+	0.581793i
$639$	2.43999			0.0965245
$640$		0			0
$641$	20.3125			0.802296			0.401148	−	0.916013i	$-0.368611\pi$
$641$	20.3125			0.802296			0.401148	+	0.916013i	$0.368611\pi$
$642$	2.04950	+	25.2000i	0.0808873	+	0.994566i
$643$	−7.78443	+	7.78443i	−0.306988	+	0.306988i	−0.843740	−	0.536752i	$-0.819651\pi$
$643$	−7.78443	+	7.78443i	−0.306988	+	0.306988i	0.536752	+	0.843740i	$0.319651\pi$
$644$	2.19226	−	0.358964i	0.0863871	−	0.0141452i
$645$		0			0
$646$	−43.4317	−	36.8985i	−1.70880	−	1.45175i
$647$			21.7693i			0.855840i	0.903817	+	0.427920i	$0.140754\pi$
$647$			21.7693i			0.855840i	−0.903817	+	0.427920i	$0.859246\pi$
$648$	7.53260	+	30.3271i	0.295908	+	1.19136i
$649$		−	8.96611i		−	0.351951i
$650$		0			0
$651$	−4.61717	−	4.61717i	−0.180961	−	0.180961i
$652$	−11.6441	+	16.2040i	−0.456020	+	0.634600i
$653$	26.3118	−	26.3118i	1.02966	−	1.02966i	0.0301152	−	0.999546i	$-0.490413\pi$
$653$	26.3118	−	26.3118i	1.02966	−	1.02966i	0.999546	−	0.0301152i	$-0.00958743\pi$
$654$	−27.6512	+	2.24885i	−1.08125	+	0.0879369i
$655$		0			0
$656$	7.01511	+	20.8470i	0.273894	+	0.813937i
$657$	−1.36298			−0.0531751
$658$	−4.48491	+	0.364754i	−0.174840	+	0.0142196i
$659$	−20.2389	+	20.2389i	−0.788397	+	0.788397i	−0.981231	−	0.192835i	$-0.938232\pi$
$659$	−20.2389	+	20.2389i	−0.788397	+	0.788397i	0.192835	+	0.981231i	$0.438232\pi$
$660$		0			0
$661$	6.81905	+	6.81905i	0.265230	+	0.265230i	0.827175	−	0.561945i	$-0.189947\pi$
$661$	6.81905	+	6.81905i	0.265230	+	0.265230i	−0.561945	+	0.827175i	$0.689947\pi$
$662$	−20.0515	+	23.6017i	−0.779322	+	0.917308i
$663$			35.1702i			1.36590i
$664$	−25.0322	−	15.0713i	−0.971436	−	0.584881i
$665$		0			0
$666$	12.6485	+	10.7458i	0.490118	+	0.416392i
$667$	−2.73942	−	2.73942i	−0.106071	−	0.106071i
$668$	1.26229	+	7.70905i	0.0488395	+	0.298272i
$669$	−3.34143	+	3.34143i	−0.129187	+	0.129187i
$670$		0			0
$671$	−57.1105			−2.20473
$672$	2.91368	−	7.30242i	0.112398	−	0.281697i
$673$	8.19512			0.315899			0.157949	−	0.987447i	$-0.449512\pi$
$673$	8.19512			0.315899			0.157949	+	0.987447i	$0.449512\pi$
$674$	−2.98301	−	36.6782i	−0.114901	−	1.41279i
$675$		0			0
$676$	−0.671628	−	4.10176i	−0.0258318	−	0.157760i
$677$	−12.8834	−	12.8834i	−0.495151	−	0.495151i	0.414774	−	0.909925i	$-0.363861\pi$
$677$	−12.8834	−	12.8834i	−0.495151	−	0.495151i	−0.909925	+	0.414774i	$0.863861\pi$
$678$	−14.0150	−	11.9068i	−0.538241	−	0.457276i
$679$			3.63960i			0.139675i
$680$		0			0
$681$		−	37.5368i		−	1.43841i
$682$	18.6194	−	21.9161i	0.712973	−	0.839211i
$683$	−15.0673	−	15.0673i	−0.576535	−	0.576535i	0.357412	−	0.933947i	$-0.383659\pi$
$683$	−15.0673	−	15.0673i	−0.576535	−	0.576535i	−0.933947	+	0.357412i	$0.883659\pi$
$684$	13.0041	+	9.34465i	0.497223	+	0.357302i
$685$		0			0
$686$	−13.1635	+	1.07058i	−0.502585	+	0.0408748i
$687$	−26.6940			−1.01844
$688$	1.29795	+	0.644356i	0.0494840	+	0.0245659i
$689$	23.3367			0.889058
$690$		0			0
$691$	−5.23733	+	5.23733i	−0.199237	+	0.199237i	−0.799673	−	0.600436i	$-0.794994\pi$
$691$	−5.23733	+	5.23733i	−0.199237	+	0.199237i	0.600436	+	0.799673i	$0.294994\pi$
$692$	13.5367	−	18.8377i	0.514588	−	0.716104i
$693$	2.22052	+	2.22052i	0.0843504	+	0.0843504i
$694$	16.6467	−	19.5942i	0.631902	−	0.743786i
$695$		0			0
$696$	−13.3071	+	3.30519i	−0.504404	+	0.125283i
$697$			29.0766i			1.10135i
$698$	30.5185	+	25.9278i	1.15514	+	0.981381i
$699$	−23.2590	−	23.2590i	−0.879736	−	0.879736i
$700$		0			0
$701$	21.7664	−	21.7664i	0.822106	−	0.822106i	−0.164303	−	0.986410i	$-0.552538\pi$
$701$	21.7664	−	21.7664i	0.822106	−	0.822106i	0.986410	+	0.164303i	$0.0525376\pi$
$702$	1.48640	+	18.2764i	0.0561007	+	0.689798i
$703$	−85.1304			−3.21075
$704$	33.0952	+	10.1830i	1.24732	+	0.383786i
$705$		0			0
$706$	1.57126	+	19.3198i	0.0591352	+	0.727109i
$707$	−9.28836	+	9.28836i	−0.349325	+	0.349325i
$708$	8.22870	−	1.34738i	0.309253	−	0.0506376i
$709$	−23.9643	−	23.9643i	−0.899997	−	0.899997i	0.0954387	−	0.995435i	$-0.469575\pi$
$709$	−23.9643	−	23.9643i	−0.899997	−	0.899997i	−0.995435	+	0.0954387i	$0.969575\pi$
$710$		0			0
$711$			5.27371i			0.197779i
$712$	4.98398	−	1.23791i	0.186783	−	0.0463928i
$713$			7.55640i			0.282990i
$714$	6.72926	−	7.92073i	0.251836	−	0.296426i
$715$		0			0
$716$	5.12266	−	7.12872i	0.191443	−	0.266413i
$717$	−27.5829	+	27.5829i	−1.03010	+	1.03010i
$718$	45.6001	−	3.70862i	1.70178	−	0.138405i
$719$	−44.4408			−1.65736			−0.828681	−	0.559721i	$-0.810908\pi$
$719$	−44.4408			−1.65736			−0.828681	+	0.559721i	$0.810908\pi$
$720$		0			0
$721$	−1.82526			−0.0679762
$722$	−55.0855	+	4.48006i	−2.05007	+	0.166730i
$723$	−10.1891	+	10.1891i	−0.378937	+	0.378937i
$724$	4.38800	+	3.15320i	0.163079	+	0.117188i
$725$		0			0
$726$	−14.2529	+	16.7765i	−0.528975	+	0.622635i
$727$		−	46.6543i		−	1.73031i	−0.501504	−	0.865155i	$-0.667220\pi$
$727$		−	46.6543i		−	1.73031i	0.501504	−	0.865155i	$-0.332780\pi$
$728$	3.32958	−	5.53014i	0.123402	−	0.204960i
$729$			12.0815i			0.447464i
$730$		0			0
$731$	1.35453	+	1.35453i	0.0500992	+	0.0500992i
$732$	−8.58226	−	52.4135i	−0.317210	−	1.93726i
$733$	−19.4202	+	19.4202i	−0.717303	+	0.717303i	−0.968052	−	0.250749i	$-0.919323\pi$
$733$	−19.4202	+	19.4202i	−0.717303	+	0.717303i	0.250749	+	0.968052i	$0.419323\pi$
$734$	1.87679	+	23.0765i	0.0692737	+	0.851769i
$735$		0			0
$736$	−8.35977	+	3.59128i	−0.308145	+	0.132376i
$737$	−11.9238			−0.439219
$738$	−0.662287	−	8.14328i	−0.0243791	−	0.299758i
$739$	−20.5243	+	20.5243i	−0.754999	+	0.754999i	−0.975408	−	0.220409i	$-0.929261\pi$
$739$	−20.5243	+	20.5243i	−0.754999	+	0.754999i	0.220409	+	0.975408i	$0.429261\pi$
$740$		0			0
$741$	35.8431	+	35.8431i	1.31673	+	1.31673i
$742$	−5.25570	−	4.46511i	−0.192943	−	0.163919i
$743$			12.9245i			0.474154i	0.971491	+	0.237077i	$0.0761893\pi$
$743$			12.9245i			0.474154i	−0.971491	+	0.237077i	$0.923811\pi$
$744$	22.9116	+	13.7946i	0.839982	+	0.505735i
$745$		0			0
$746$	−20.1129	+	23.6740i	−0.736384	+	0.866767i
$747$	7.67443	+	7.67443i	0.280793	+	0.280793i
$748$	37.1716	+	26.7113i	1.35913	+	0.976662i
$749$	4.33765	−	4.33765i	0.158494	−	0.158494i
$750$		0			0
$751$	−52.2694			−1.90734			−0.953668	−	0.300861i	$-0.902726\pi$
$751$	−52.2694			−1.90734			−0.953668	+	0.300861i	$0.902726\pi$
$752$	17.4673	−	5.87783i	0.636966	−	0.214342i
$753$	−29.7069			−1.08258
$754$	−11.2204	+	0.912546i	−0.408623	+	0.0332330i
$755$		0			0
$756$	3.16214	−	4.40045i	0.115006	−	0.160043i
$757$	34.4514	+	34.4514i	1.25216	+	1.25216i	0.954751	+	0.297407i	$0.0961218\pi$
$757$	34.4514	+	34.4514i	1.25216	+	1.25216i	0.297407	+	0.954751i	$0.403878\pi$
$758$	32.3132	−	38.0346i	1.17367	−	1.38148i
$759$		−	14.0111i		−	0.508572i
$760$		0			0
$761$		−	47.7467i		−	1.73082i	−0.501067	−	0.865408i	$-0.667059\pi$
$761$		−	47.7467i		−	1.73082i	0.501067	−	0.865408i	$-0.332941\pi$
$762$	36.0344	+	30.6139i	1.30539	+	1.10903i
$763$	4.75956	+	4.75956i	0.172308	+	0.172308i
$764$	−11.0733	+	1.81317i	−0.400620	+	0.0655980i
$765$		0			0
$766$	0.716360	+	8.80815i	0.0258831	+	0.318251i
$767$	6.84595			0.247193
$768$	−4.37213	+	31.9036i	−0.157766	+	1.15122i
$769$	−17.9108			−0.645882			−0.322941	−	0.946419i	$-0.604671\pi$
$769$	−17.9108			−0.645882			−0.322941	+	0.946419i	$0.604671\pi$
$770$		0			0
$771$	8.14247	−	8.14247i	0.293244	−	0.293244i
$772$	7.71124	−	1.26265i	0.277534	−	0.0454437i
$773$	−3.73170	−	3.73170i	−0.134220	−	0.134220i	0.636805	−	0.771025i	$-0.280256\pi$
$773$	−3.73170	−	3.73170i	−0.134220	−	0.134220i	−0.771025	+	0.636805i	$0.780256\pi$
$774$	−0.410207	−	0.348502i	−0.0147446	−	0.0125266i
$775$		0			0
$776$	−3.59336	−	14.4673i	−0.128994	−	0.519346i
$777$		−	15.5254i		−	0.556971i
$778$	2.72972	−	3.21304i	0.0978652	−	0.115193i
$779$	29.6329	+	29.6329i	1.06171	+	1.06171i
$780$		0			0
$781$	7.10805	−	7.10805i	0.254346	−	0.254346i
$782$	−11.9880	+	0.974974i	−0.428690	+	0.0348650i
$783$	−9.45012			−0.337720
$784$	24.7298	−	8.32170i	0.883208	−	0.297204i
$785$		0			0
$786$	−47.2285	+	3.84105i	−1.68458	+	0.137006i
$787$	−2.40160	+	2.40160i	−0.0856076	+	0.0856076i	−0.748614	−	0.663006i	$-0.769280\pi$
$787$	−2.40160	+	2.40160i	−0.0856076	+	0.0856076i	0.663006	+	0.748614i	$0.269280\pi$
$788$	1.39751	+	1.00425i	0.0497843	+	0.0357748i
$789$	38.6207	+	38.6207i	1.37493	+	1.37493i
$790$		0			0
$791$			4.46187i			0.158646i
$792$	−11.0188	−	6.63419i	−0.391536	−	0.235736i
$793$		−	43.6060i		−	1.54849i
$794$	35.8151	+	30.4277i	1.27103	+	1.07984i
$795$		0			0
$796$	5.01839	+	30.6482i	0.177872	+	1.08630i
$797$	−35.4972	+	35.4972i	−1.25738	+	1.25738i	−0.305035	+	0.952341i	$0.598668\pi$
$797$	−35.4972	+	35.4972i	−1.25738	+	1.25738i	−0.952341	+	0.305035i	$0.901332\pi$
$798$	−1.21427	−	14.9303i	−0.0429846	−	0.528526i
$799$	24.3627			0.861892
$800$		0			0
$801$	−1.90753			−0.0673992
$802$	2.40618	+	29.5857i	0.0849652	+	1.04471i
$803$	−3.97058	+	3.97058i	−0.140119	+	0.140119i
$804$	−1.79184	−	10.9431i	−0.0631935	−	0.385934i
$805$		0			0
$806$	16.7337	+	14.2166i	0.589421	+	0.500757i
$807$			37.2206i			1.31023i
$808$	27.7506	−	46.0914i	0.976264	−	1.62149i
$809$		−	11.9182i		−	0.419021i	−0.977806	−	0.209510i	$-0.932813\pi$
$809$		−	11.9182i		−	0.419021i	0.977806	−	0.209510i	$-0.0671870\pi$
$810$		0			0
$811$	−22.1494	−	22.1494i	−0.777772	−	0.777772i	0.201680	−	0.979452i	$-0.435360\pi$
$811$	−22.1494	−	22.1494i	−0.777772	−	0.777772i	−0.979452	+	0.201680i	$0.935360\pi$
$812$	2.70156	+	1.94133i	0.0948063	+	0.0681273i
$813$	−9.32527	+	9.32527i	−0.327051	+	0.327051i
$814$	68.1510	−	5.54267i	2.38869	−	0.194270i
$815$		0			0
$816$	−18.9285	+	38.1285i	−0.662630	+	1.33476i
$817$	2.76090			0.0965915
$818$	25.9394	−	2.10963i	0.906949	−	0.0737615i
$819$	−1.69545	+	1.69545i	−0.0592436	+	0.0592436i
$820$		0			0
$821$	13.3909	+	13.3909i	0.467344	+	0.467344i	0.901053	−	0.433709i	$-0.142795\pi$
$821$	13.3909	+	13.3909i	0.467344	+	0.467344i	−0.433709	+	0.901053i	$0.642795\pi$
$822$	15.5074	−	18.2531i	0.540884	−	0.636652i
$823$		−	43.9496i		−	1.53199i	−0.642848	−	0.765994i	$-0.722247\pi$
$823$		−	43.9496i		−	1.53199i	0.642848	−	0.765994i	$-0.277753\pi$
$824$	7.25536	−	1.80207i	0.252752	−	0.0627782i
$825$		0			0
$826$	−1.54179	−	1.30986i	−0.0536456	−	0.0455760i
$827$	−1.79096	−	1.79096i	−0.0622777	−	0.0622777i	0.675282	−	0.737560i	$-0.264022\pi$
$827$	−1.79096	−	1.79096i	−0.0622777	−	0.0622777i	−0.737560	+	0.675282i	$0.764022\pi$
$828$	3.33519	−	0.546109i	0.115906	−	0.0189786i
$829$	13.4979	−	13.4979i	0.468801	−	0.468801i	−0.432725	−	0.901526i	$-0.642448\pi$
$829$	13.4979	−	13.4979i	0.468801	−	0.468801i	0.901526	+	0.432725i	$0.142448\pi$
$830$		0			0
$831$	−29.2742			−1.01551
$832$	−7.77509	+	25.2694i	−0.269553	+	0.876060i
$833$	34.4923			1.19509
$834$	−0.495456	−	6.09198i	−0.0171562	−	0.210948i
$835$		0			0
$836$	65.1051	−	10.6604i	2.25171	−	0.368698i
$837$	13.0336	+	13.0336i	0.450507	+	0.450507i
$838$	−22.7610	−	19.3372i	−0.786266	−	0.667993i
$839$		−	14.5332i		−	0.501741i	−0.968021	−	0.250870i	$-0.919283\pi$
$839$		−	14.5332i		−	0.501741i	0.968021	−	0.250870i	$-0.0807168\pi$
$840$		0			0
$841$			23.1983i			0.799941i
$842$	−21.0658	+	24.7956i	−0.725975	+	0.854515i
$843$	−42.6532	−	42.6532i	−1.46905	−	1.46905i
$844$	−3.54042	+	4.92686i	−0.121866	+	0.169590i
$845$		0			0
$846$	−6.82311	+	0.554918i	−0.234583	+	0.0190785i
$847$	5.34105			0.183521
$848$	25.2996	+	12.5598i	0.868793	+	0.431304i
$849$	−54.4136			−1.86747
$850$		0			0
$851$	−12.7043	+	12.7043i	−0.435499	+	0.435499i
$852$	7.59161	+	5.45529i	0.260084	+	0.186895i
$853$	−11.5836	−	11.5836i	−0.396615	−	0.396615i	0.480423	−	0.877037i	$-0.340483\pi$
$853$	−11.5836	−	11.5836i	−0.396615	−	0.396615i	−0.877037	+	0.480423i	$0.840483\pi$
$854$	−8.34331	+	9.82056i	−0.285502	+	0.336053i
$855$		0			0
$856$	−12.9595	+	21.5246i	−0.442946	+	0.735695i
$857$		−	15.6443i		−	0.534399i	−0.963641	−	0.267200i	$-0.913902\pi$
$857$		−	15.6443i		−	0.534399i	0.963641	−	0.267200i	$-0.0860983\pi$
$858$	−31.0278	−	26.3605i	−1.05927	−	0.899932i
$859$	12.0947	+	12.0947i	0.412665	+	0.412665i	0.882666	−	0.470001i	$-0.155746\pi$
$859$	12.0947	+	12.0947i	0.412665	+	0.412665i	−0.470001	+	0.882666i	$0.655746\pi$
$860$		0			0
$861$	−5.40422	+	5.40422i	−0.184175	+	0.184175i
$862$	−0.808687	−	9.94338i	−0.0275440	−	0.338673i
$863$	9.28120			0.315936			0.157968	−	0.987444i	$-0.449506\pi$
$863$	9.28120			0.315936			0.157968	+	0.987444i	$0.449506\pi$
$864$	−8.22488	+	20.6137i	−0.279816	+	0.701291i
$865$		0			0
$866$	−1.64153	−	20.1838i	−0.0557816	−	0.685874i
$867$	−15.5973	+	15.5973i	−0.529711	+	0.529711i
$868$	−1.04851	−	6.40347i	−0.0355889	−	0.217348i
$869$	15.3631	+	15.3631i	0.521157	+	0.521157i
$870$		0			0
$871$		−	9.10425i		−	0.308486i
$872$	−23.6182	−	14.2200i	−0.799814	−	0.481551i
$873$			5.53709i			0.187402i
$874$	−11.2237	+	13.2110i	−0.379648	+	0.446868i
$875$		0			0
$876$	−4.24070	−	3.04734i	−0.143280	−	0.102960i
$877$	2.97610	−	2.97610i	0.100496	−	0.100496i	−0.655071	−	0.755567i	$-0.727361\pi$
$877$	2.97610	−	2.97610i	0.100496	−	0.100496i	0.755567	+	0.655071i	$0.227361\pi$
$878$	−36.5143	+	2.96968i	−1.23230	+	0.100222i
$879$	20.7194			0.698849
$880$		0			0
$881$	29.3318			0.988214			0.494107	−	0.869401i	$-0.335495\pi$
$881$	29.3318			0.988214			0.494107	+	0.869401i	$0.335495\pi$
$882$	−9.66001	+	0.785641i	−0.325270	+	0.0264539i
$883$	−35.5597	+	35.5597i	−1.19668	+	1.19668i	−0.221525	+	0.975155i	$0.571103\pi$
$883$	−35.5597	+	35.5597i	−1.19668	+	1.19668i	−0.975155	+	0.221525i	$0.928897\pi$
$884$	−20.3950	+	28.3818i	−0.685960	+	0.954585i
$885$		0			0
$886$	14.4240	−	16.9778i	0.484583	−	0.570382i
$887$		−	4.51671i		−	0.151656i	−0.997121	−	0.0758282i	$-0.975840\pi$
$887$		−	4.51671i		−	0.151656i	0.997121	−	0.0758282i	$-0.0241601\pi$
$888$	15.3282	+	61.7131i	0.514380	+	2.07096i
$889$		−	11.4721i		−	0.384762i
$890$		0			0
$891$	−33.8133	−	33.8133i	−1.13279	−	1.13279i
$892$	−4.63416	+	0.758805i	−0.155163	+	0.0254067i
$893$	24.8289	−	24.8289i	0.830867	−	0.830867i
$894$	−0.853055	−	10.4889i	−0.0285304	−	0.350802i
$895$		0			0
$896$	6.58594	−	4.20332i	0.220021	−	0.140423i
$897$	10.6980			0.357196
$898$	−1.45200	−	17.8533i	−0.0484537	−	0.595773i
$899$	−8.00169	+	8.00169i	−0.266871	+	0.266871i
$900$		0			0
$901$	26.4025	+	26.4025i	0.879594	+	0.879594i
$902$	−25.6519	−	21.7933i	−0.854116	−	0.725636i
$903$			0.503511i			0.0167558i
$904$	−4.40519	−	17.7358i	−0.146514	−	0.589884i
$905$		0			0
$906$	23.4304	−	27.5790i	0.778424	−	0.916251i
$907$	5.06769	+	5.06769i	0.168270	+	0.168270i	0.786218	−	0.617949i	$-0.212036\pi$
$907$	5.06769	+	5.06769i	0.168270	+	0.168270i	−0.617949	+	0.786218i	$0.712036\pi$
$908$	21.7674	−	30.2917i	0.722378	−	1.00526i
$909$	−14.1308	+	14.1308i	−0.468690	+	0.468690i
$910$		0			0
$911$	36.7140			1.21639			0.608194	−	0.793788i	$-0.291894\pi$
$911$	36.7140			1.21639			0.608194	+	0.793788i	$0.291894\pi$
$912$	19.5673	+	58.1486i	0.647938	+	1.92549i
$913$	44.7135			1.47980
$914$	−23.8839	+	1.94246i	−0.790008	+	0.0642507i
$915$		0			0
$916$	−21.5417	−	15.4797i	−0.711757	−	0.511465i
$917$	8.12937	+	8.12937i	0.268456	+	0.268456i
$918$	−18.9957	+	22.3590i	−0.626951	+	0.737958i
$919$		−	21.5651i		−	0.711365i	−0.934607	−	0.355683i	$-0.884248\pi$
$919$		−	21.5651i		−	0.711365i	0.934607	−	0.355683i	$-0.115752\pi$
$920$		0			0
$921$		−	20.0179i		−	0.659612i
$922$	20.1023	+	17.0785i	0.662035	+	0.562449i
$923$	5.42725	+	5.42725i	0.178640	+	0.178640i
$924$	1.94416	+	11.8734i	0.0639582	+	0.390605i
$925$		0			0
$926$	−1.61589	−	19.8685i	−0.0531013	−	0.652918i
$927$	−2.77685			−0.0912038
$928$	−12.6553	−	5.04949i	−0.415431	−	0.165758i
$929$	−45.6603			−1.49807			−0.749033	−	0.662532i	$-0.769482\pi$
$929$	−45.6603			−1.49807			−0.749033	+	0.662532i	$0.769482\pi$
$930$		0			0
$931$	35.1522	−	35.1522i	1.15207	−	1.15207i
$932$	−5.28189	−	32.2575i	−0.173014	−	1.05663i
$933$	−20.3269	−	20.3269i	−0.665474	−	0.665474i
$934$	−18.4303	−	15.6579i	−0.603056	−	0.512342i
$935$		0			0
$936$	5.06544	−	8.41326i	0.165569	−	0.274996i
$937$		−	2.29807i		−	0.0750746i	−0.999295	−	0.0375373i	$-0.988049\pi$
$937$		−	2.29807i		−	0.0750746i	0.999295	−	0.0375373i	$-0.0119513\pi$
$938$	−1.74195	+	2.05038i	−0.0568768	+	0.0669473i
$939$	−26.2681	−	26.2681i	−0.857226	−	0.857226i
$940$		0			0
$941$	−24.1999	+	24.1999i	−0.788894	+	0.788894i	−0.981313	−	0.192419i	$-0.938367\pi$
$941$	−24.1999	+	24.1999i	−0.788894	+	0.788894i	0.192419	+	0.981313i	$0.438367\pi$
$942$	28.7992	−	2.34222i	0.938329	−	0.0763135i
$943$	8.84448			0.288016
$944$	7.42179	+	3.68447i	0.241559	+	0.119919i
$945$		0			0
$946$	−2.21023	+	0.179756i	−0.0718609	+	0.00584439i
$947$	−24.5182	+	24.5182i	−0.796733	+	0.796733i	−0.982579	−	0.185846i	$-0.940498\pi$
$947$	−24.5182	+	24.5182i	−0.796733	+	0.796733i	0.185846	+	0.982579i	$0.440498\pi$
$948$	−11.7909	+	16.4083i	−0.382950	+	0.532915i
$949$	−3.03168	−	3.03168i	−0.0984125	−	0.0984125i
$950$		0			0
$951$			20.5445i			0.666202i
$952$	10.0236	−	2.48965i	0.324867	−	0.0806900i
$953$			32.3462i			1.04780i	0.851781	+	0.523898i	$0.175523\pi$
$953$			32.3462i			1.04780i	−0.851781	+	0.523898i	$0.824477\pi$
$954$	−7.99574	−	6.79298i	−0.258872	−	0.219931i
$955$		0			0
$956$	−38.2543	+	6.26381i	−1.23723	+	0.202586i
$957$	14.8368	−	14.8368i	0.479605	−	0.479605i
$958$	−1.63385	−	20.0894i	−0.0527874	−	0.649059i
$959$	−5.81116			−0.187652
$960$		0			0
$961$	−8.92816			−0.288005
$962$	4.23203	+	52.0358i	0.136446	+	1.67770i
$963$	6.59907	−	6.59907i	0.212652	−	0.212652i
$964$	−14.1311	+	2.31385i	−0.455132	+	0.0745240i
$965$		0			0
$966$	−2.40932	−	2.04690i	−0.0775185	−	0.0658578i
$967$		−	14.6983i		−	0.472665i	−0.971672	−	0.236333i	$-0.924054\pi$
$967$		−	14.6983i		−	0.472665i	0.971672	−	0.236333i	$-0.0759455\pi$
$968$	−21.2305	+	5.27321i	−0.682376	+	0.169487i
$969$			81.1036i			2.60542i
$970$		0			0
$971$	29.1065	+	29.1065i	0.934073	+	0.934073i	0.997957	−	0.0638845i	$-0.0203489\pi$
$971$	29.1065	+	29.1065i	0.934073	+	0.934073i	−0.0638845	+	0.997957i	$0.520349\pi$
$972$	12.2141	−	16.9972i	0.391768	−	0.545186i
$973$	−1.04860	+	1.04860i	−0.0336167	+	0.0336167i
$974$	36.7084	−	2.98546i	1.17621	−	0.0956604i
$975$		0			0
$976$	23.4686	−	47.2738i	0.751212	−	1.51320i
$977$	−17.3533			−0.555180			−0.277590	−	0.960700i	$-0.589536\pi$
$977$	−17.3533			−0.555180			−0.277590	+	0.960700i	$0.589536\pi$
$978$	28.3035	−	2.30190i	0.905048	−	0.0736068i
$979$	−5.55691	+	5.55691i	−0.177600	+	0.177600i
$980$		0			0
$981$	7.24094	+	7.24094i	0.231186	+	0.231186i
$982$	4.49076	−	5.28589i	0.143306	−	0.168680i
$983$			27.5174i			0.877668i	0.898568	+	0.438834i	$0.144608\pi$
$983$			27.5174i			0.877668i	−0.898568	+	0.438834i	$0.855392\pi$
$984$	16.1461	−	26.8172i	0.514717	−	0.854901i
$985$		0			0
$986$	−13.7269	−	11.6620i	−0.437152	−	0.371394i
$987$	4.52809	+	4.52809i	0.144131	+	0.144131i
$988$	8.13961	+	49.7101i	0.258955	+	1.58149i
$989$	0.412020	−	0.412020i	0.0131015	−	0.0131015i
$990$		0			0
$991$	6.96363			0.221207			0.110604	−	0.993865i	$-0.464722\pi$
$991$	6.96363			0.221207			0.110604	+	0.993865i	$0.464722\pi$
$992$	10.4899	+	24.4184i	0.333056	+	0.775286i
$993$	44.0735			1.39863
$994$	−0.183861	−	2.26070i	−0.00583171	−	0.0717050i
$995$		0			0
$996$	6.71931	+	41.0361i	0.212909	+	1.30028i
$997$	15.7051	+	15.7051i	0.497385	+	0.497385i	0.910623	−	0.413238i	$-0.135602\pi$
$997$	15.7051	+	15.7051i	0.497385	+	0.497385i	−0.413238	+	0.910623i	$0.635602\pi$
$998$	8.08242	+	6.86663i	0.255845	+	0.217359i
$999$			43.8259i			1.38659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.l.h.101.4		16
4.3	odd	2		1600.2.l.i.1201.7		16
5.2	odd	4		400.2.q.h.149.8		16
5.3	odd	4		400.2.q.g.149.1		16
5.4	even	2		80.2.l.a.21.5	✓	16
15.14	odd	2		720.2.t.c.181.4		16
16.3	odd	4		1600.2.l.i.401.7		16
16.13	even	4	inner	400.2.l.h.301.4		16
20.3	even	4		1600.2.q.h.49.7		16
20.7	even	4		1600.2.q.g.49.2		16
20.19	odd	2		320.2.l.a.241.2		16
40.19	odd	2		640.2.l.a.481.7		16
40.29	even	2		640.2.l.b.481.2		16
60.59	even	2		2880.2.t.c.2161.2		16
80.3	even	4		1600.2.q.g.849.2		16
80.13	odd	4		400.2.q.h.349.8		16
80.19	odd	4		320.2.l.a.81.2		16
80.29	even	4		80.2.l.a.61.5	yes	16
80.59	odd	4		640.2.l.a.161.7		16
80.67	even	4		1600.2.q.h.849.7		16
80.69	even	4		640.2.l.b.161.2		16
80.77	odd	4		400.2.q.g.349.1		16
160.19	odd	8		5120.2.a.t.1.7		8
160.29	even	8		5120.2.a.s.1.7		8
160.99	odd	8		5120.2.a.u.1.2		8
160.109	even	8		5120.2.a.v.1.2		8
240.29	odd	4		720.2.t.c.541.4		16
240.179	even	4		2880.2.t.c.721.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.5	✓	16	5.4	even	2
80.2.l.a.61.5	yes	16	80.29	even	4
320.2.l.a.81.2		16	80.19	odd	4
320.2.l.a.241.2		16	20.19	odd	2
400.2.l.h.101.4		16	1.1	even	1	trivial
400.2.l.h.301.4		16	16.13	even	4	inner
400.2.q.g.149.1		16	5.3	odd	4
400.2.q.g.349.1		16	80.77	odd	4
400.2.q.h.149.8		16	5.2	odd	4
400.2.q.h.349.8		16	80.13	odd	4
640.2.l.a.161.7		16	80.59	odd	4
640.2.l.a.481.7		16	40.19	odd	2
640.2.l.b.161.2		16	80.69	even	4
640.2.l.b.481.2		16	40.29	even	2
720.2.t.c.181.4		16	15.14	odd	2
720.2.t.c.541.4		16	240.29	odd	4
1600.2.l.i.401.7		16	16.3	odd	4
1600.2.l.i.1201.7		16	4.3	odd	2
1600.2.q.g.49.2		16	20.7	even	4
1600.2.q.g.849.2		16	80.3	even	4
1600.2.q.h.49.7		16	20.3	even	4
1600.2.q.h.849.7		16	80.67	even	4
2880.2.t.c.721.3		16	240.179	even	4
2880.2.t.c.2161.2		16	60.59	even	2
5120.2.a.s.1.7		8	160.29	even	8
5120.2.a.t.1.7		8	160.19	odd	8
5120.2.a.u.1.2		8	160.99	odd	8
5120.2.a.v.1.2		8	160.109	even	8

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

\(f(q)\)	\(=\)	\(q+(-0.114638 - 1.40956i) q^{2} +(-1.42313 + 1.42313i) q^{3} +(-1.97372 + 0.323179i) q^{4} +(2.16913 + 1.84284i) q^{6} -0.690576i q^{7} +(0.681804 + 2.74502i) q^{8} -1.05061i q^{9} +O(q^{10})\)	\(q+(-0.114638 - 1.40956i) q^{2} +(-1.42313 + 1.42313i) q^{3} +(-1.97372 + 0.323179i) q^{4} +(2.16913 + 1.84284i) q^{6} -0.690576i q^{7} +(0.681804 + 2.74502i) q^{8} -1.05061i q^{9} +(-3.06057 - 3.06057i) q^{11} +(2.34893 - 3.26878i) q^{12} +(2.33686 - 2.33686i) q^{13} +(-0.973408 + 0.0791665i) q^{14} +(3.79111 - 1.27573i) q^{16} +5.28770 q^{17} +(-1.48089 + 0.120440i) q^{18} +(5.38887 - 5.38887i) q^{19} +(0.982780 + 0.982780i) q^{21} +(-3.96320 + 4.66492i) q^{22} -1.60841i q^{23} +(-4.87682 - 2.93623i) q^{24} +(-3.56183 - 3.02605i) q^{26} +(-2.77424 - 2.77424i) q^{27} +(0.223180 + 1.36300i) q^{28} +(1.70319 - 1.70319i) q^{29} -4.69807 q^{31} +(-2.23282 - 5.19755i) q^{32} +8.71119 q^{33} +(-0.606174 - 7.45333i) q^{34} +(0.339534 + 2.07360i) q^{36} +(-7.89871 - 7.89871i) q^{37} +(-8.21371 - 6.97817i) q^{38} +6.65131i q^{39} +5.49891i q^{41} +(1.27262 - 1.49795i) q^{42} +(0.256166 + 0.256166i) q^{43} +(7.02981 + 5.05159i) q^{44} +(-2.26715 + 0.184385i) q^{46} +4.60743 q^{47} +(-3.57972 + 7.21078i) q^{48} +6.52310 q^{49} +(-7.52510 + 7.52510i) q^{51} +(-3.85707 + 5.36752i) q^{52} +(4.99318 + 4.99318i) q^{53} +(-3.59243 + 4.22850i) q^{54} +(1.89565 - 0.470837i) q^{56} +15.3382i q^{57} +(-2.59600 - 2.20549i) q^{58} +(1.46478 + 1.46478i) q^{59} +(9.33004 - 9.33004i) q^{61} +(0.538579 + 6.62221i) q^{62} -0.725523 q^{63} +(-7.07029 + 3.74313i) q^{64} +(-0.998637 - 12.2789i) q^{66} +(1.94797 - 1.94797i) q^{67} +(-10.4364 + 1.70888i) q^{68} +(2.28897 + 2.28897i) q^{69} +2.32246i q^{71} +(2.88394 - 0.716307i) q^{72} -1.29733i q^{73} +(-10.2282 + 12.0392i) q^{74} +(-8.89454 + 12.3777i) q^{76} +(-2.11356 + 2.11356i) q^{77} +(9.37542 - 0.762495i) q^{78} -5.01968 q^{79} +11.0480 q^{81} +(7.75103 - 0.630385i) q^{82} +(-7.30477 + 7.30477i) q^{83} +(-2.25734 - 1.62212i) q^{84} +(0.331715 - 0.390448i) q^{86} +4.84772i q^{87} +(6.31463 - 10.4880i) q^{88} -1.81564i q^{89} +(-1.61378 - 1.61378i) q^{91} +(0.519803 + 3.17454i) q^{92} +(6.68597 - 6.68597i) q^{93} +(-0.528188 - 6.49445i) q^{94} +(10.5744 + 4.21920i) q^{96} -5.27038 q^{97} +(-0.747798 - 9.19470i) q^{98} +(-3.21546 + 3.21546i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 12 q^{6}+O(q^{10}) \) 16 * q - 4 * q^4 - 12 * q^6	\( 16 q - 4 q^{4} - 12 q^{6} - 8 q^{11} + 12 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{19} + 20 q^{22} + 8 q^{24} - 16 q^{26} - 24 q^{27} + 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} + 16 q^{37} - 20 q^{38} - 60 q^{42} - 8 q^{43} + 40 q^{44} - 4 q^{46} + 40 q^{47} + 40 q^{48} - 16 q^{49} - 32 q^{51} - 56 q^{52} - 16 q^{53} + 32 q^{54} + 16 q^{56} + 12 q^{58} - 8 q^{59} + 16 q^{61} + 8 q^{62} - 40 q^{63} - 16 q^{64} - 40 q^{67} + 48 q^{68} + 16 q^{69} + 40 q^{72} - 72 q^{74} - 16 q^{77} + 16 q^{78} + 16 q^{79} - 16 q^{81} + 76 q^{82} - 40 q^{83} - 64 q^{84} + 28 q^{86} + 32 q^{91} + 52 q^{92} + 48 q^{93} - 36 q^{94} + 8 q^{96} - 60 q^{98} - 8 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 12 * q^6 - 8 * q^11 + 12 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^19 + 20 * q^22 + 8 * q^24 - 16 * q^26 - 24 * q^27 + 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 + 16 * q^37 - 20 * q^38 - 60 * q^42 - 8 * q^43 + 40 * q^44 - 4 * q^46 + 40 * q^47 + 40 * q^48 - 16 * q^49 - 32 * q^51 - 56 * q^52 - 16 * q^53 + 32 * q^54 + 16 * q^56 + 12 * q^58 - 8 * q^59 + 16 * q^61 + 8 * q^62 - 40 * q^63 - 16 * q^64 - 40 * q^67 + 48 * q^68 + 16 * q^69 + 40 * q^72 - 72 * q^74 - 16 * q^77 + 16 * q^78 + 16 * q^79 - 16 * q^81 + 76 * q^82 - 40 * q^83 - 64 * q^84 + 28 * q^86 + 32 * q^91 + 52 * q^92 + 48 * q^93 - 36 * q^94 + 8 * q^96 - 60 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

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