LMFDB - Embedded newform 400.2.q.g.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(149,400)]

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, 2]))

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

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

chi := DirichletCharacter("400.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.q (of order $4$, degree $2$, not 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			149.1
Root			$-1.39563 - 0.228522i$ of defining polynomial
Character	$\chi$	$=$	400.149
Dual form			400.2.q.g.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	−1.40956	+	0.114638i	−0.996709	+	0.0810615i
$2$	−1.40956	+	0.114638i	−0.996709	+	0.0810615i
$3$	−1.42313	−	1.42313i	−0.821645	−	0.821645i	0.164699	−	0.986344i	$-0.447335\pi$
$3$	−1.42313	−	1.42313i	−0.821645	−	0.821645i	−0.986344	+	0.164699i	$0.947335\pi$
$4$	1.97372	−	0.323179i	0.986858	−	0.161590i
$5$		0			0
$5$		0			0
$6$	2.16913	+	1.84284i	0.885545	+	0.752338i
$7$	−0.690576			−0.261013			−0.130507	−	0.991447i	$-0.541660\pi$
$7$	−0.690576			−0.261013			−0.130507	+	0.991447i	$0.541660\pi$
$8$	−2.74502	+	0.681804i	−0.970512	+	0.241054i
$9$			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	$0.976287\pi$
$12$	−3.26878	−	2.34893i	−0.943617	−	0.678078i
$13$	2.33686	+	2.33686i	0.648128	+	0.648128i	0.952540	−	0.304413i	$-0.0984601\pi$
$13$	2.33686	+	2.33686i	0.648128	+	0.648128i	−0.304413	+	0.952540i	$0.598460\pi$
$14$	0.973408	−	0.0791665i	0.260154	−	0.0211581i
$15$		0			0
$16$	3.79111	−	1.27573i	0.947778	−	0.318932i
$17$		−	5.28770i		−	1.28246i	−0.767350	−	0.641228i	$-0.778425\pi$
$17$		−	5.28770i		−	1.28246i	0.767350	−	0.641228i	$-0.221575\pi$
$18$	−0.120440	−	1.48089i	−0.0283879	−	0.349050i
$19$	−5.38887	+	5.38887i	−1.23629	+	1.23629i	−0.274787	+	0.961505i	$0.588607\pi$
$19$	−5.38887	+	5.38887i	−1.23629	+	1.23629i	−0.961505	+	0.274787i	$0.911393\pi$
$20$		0			0
$21$	0.982780	+	0.982780i	0.214460	+	0.214460i
$22$	4.66492	+	3.96320i	0.994564	+	0.844957i
$23$	1.60841			0.335376			0.167688	−	0.985840i	$-0.446370\pi$
$23$	1.60841			0.335376			0.167688	+	0.985840i	$0.446370\pi$
$24$	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
$28$	−1.36300	+	0.223180i	−0.257583	+	0.0421770i
$29$	−1.70319	+	1.70319i	−0.316274	+	0.316274i	−0.847334	−	0.531060i	$-0.821794\pi$
$29$	−1.70319	+	1.70319i	−0.316274	+	0.316274i	0.531060	+	0.847334i	$0.321794\pi$
$30$		0			0
$31$	−4.69807			−0.843798			−0.421899	−	0.906643i	$-0.638636\pi$
$31$	−4.69807			−0.843798			−0.421899	+	0.906643i	$0.638636\pi$
$32$	−5.19755	+	2.23282i	−0.918805	+	0.394711i
$33$			8.71119i			1.51642i
$34$	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	−0.369185	+	0.929356i	$0.620363\pi$
$37$	−7.89871	+	7.89871i	−1.29854	+	1.29854i	−0.929356	+	0.369185i	$0.879637\pi$
$38$	6.97817	−	8.21371i	1.13201	−	1.33244i
$39$		−	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	$0.858728\pi$
$42$	−1.49795	−	1.27262i	−0.231139	−	0.196370i
$43$	−0.256166	+	0.256166i	−0.0390650	+	0.0390650i	−0.726369	−	0.687304i	$-0.758794\pi$
$43$	−0.256166	+	0.256166i	−0.0390650	+	0.0390650i	0.687304	+	0.726369i	$0.258794\pi$
$44$	−7.02981	−	5.05159i	−1.05978	−	0.761555i
$45$		0			0
$46$	−2.26715	+	0.184385i	−0.334272	+	0.0271861i
$47$		−	4.60743i		−	0.672063i	−0.941851	−	0.336032i	$-0.890915\pi$
$47$		−	4.60743i		−	0.672063i	0.941851	−	0.336032i	$-0.109085\pi$
$48$	−7.21078	−	3.57972i	−1.04079	−	0.516688i
$49$	−6.52310			−0.931872
$50$		0			0
$51$	−7.52510	+	7.52510i	−1.05372	+	1.05372i
$52$	5.36752	+	3.85707i	0.744341	+	0.534879i
$53$	−4.99318	+	4.99318i	−0.685866	+	0.685866i	−0.961316	−	0.275449i	$-0.911173\pi$
$53$	−4.99318	+	4.99318i	−0.685866	+	0.685866i	0.275449	+	0.961316i	$0.411173\pi$
$54$	3.59243	−	4.22850i	0.488867	−	0.575425i
$55$		0			0
$56$	1.89565	−	0.470837i	0.253316	−	0.0629183i
$57$	15.3382			2.03159
$58$	2.20549	−	2.59600i	0.289596	−	0.340871i
$59$	−1.46478	−	1.46478i	−0.190698	−	0.190698i	0.605300	−	0.795998i	$-0.293053\pi$
$59$	−1.46478	−	1.46478i	−0.190698	−	0.190698i	−0.795998	+	0.605300i	$0.793053\pi$
$60$		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	$-0.0702224\pi$
$62$	6.62221	−	0.538579i	0.841021	−	0.0683996i
$63$		−	0.725523i		−	0.0914074i
$64$	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	$-0.303821\pi$
$67$	−1.94797	−	1.94797i	−0.237982	−	0.237982i	−0.816014	+	0.578032i	$0.803821\pi$
$68$	−1.70888	−	10.4364i	−0.207232	−	1.26560i
$69$	−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	$0.955993\pi$
$72$	−0.716307	−	2.88394i	−0.0844176	−	0.339875i
$73$	1.29733			0.151841			0.0759206	−	0.997114i	$-0.475810\pi$
$73$	1.29733			0.151841			0.0759206	+	0.997114i	$0.475810\pi$
$74$	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
$78$	0.762495	+	9.37542i	0.0863356	+	1.06156i
$79$	5.01968			0.564758			0.282379	−	0.959303i	$-0.408876\pi$
$79$	5.01968			0.564758			0.282379	+	0.959303i	$0.408876\pi$
$80$		0			0
$81$	11.0480			1.22756
$82$	−0.630385	−	7.75103i	−0.0696144	−	0.855959i
$83$	−7.30477	−	7.30477i	−0.801802	−	0.801802i	0.181575	−	0.983377i	$-0.441881\pi$
$83$	−7.30477	−	7.30477i	−0.801802	−	0.801802i	−0.983377	+	0.181575i	$0.941881\pi$
$84$	2.25734	+	1.62212i	0.246296	+	0.176987i
$85$		0			0
$86$	0.331715	−	0.390448i	0.0357698	−	0.0421031i
$87$	4.84772			0.519730
$88$	10.4880	+	6.31463i	1.11803	+	0.673141i
$89$			1.81564i			0.192458i	0.995359	+	0.0962290i	$0.0306781\pi$
$89$			1.81564i			0.192458i	−0.995359	+	0.0962290i	$0.969322\pi$
$90$		0			0
$91$	−1.61378	−	1.61378i	−0.169170	−	0.169170i
$92$	3.17454	−	0.519803i	0.330969	−	0.0541933i
$93$	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
$97$			5.27038i			0.535126i	0.963540	+	0.267563i	$0.0862183\pi$
$97$			5.27038i			0.535126i	−0.963540	+	0.267563i	$0.913782\pi$
$98$	9.19470	−	0.747798i	0.928805	−	0.0755390i
$99$	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	$-0.645261\pi$
$102$	9.74441	−	11.4697i	0.964840	−	1.13567i
$103$	2.64310			0.260432			0.130216	−	0.991486i	$-0.458433\pi$
$103$	2.64310			0.260432			0.130216	+	0.991486i	$0.458433\pi$
$104$	−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	−0.334994	−	0.942220i	$-0.608734\pi$
$107$	6.28120	−	6.28120i	0.607227	−	0.607227i	0.942220	+	0.334994i	$0.108734\pi$
$108$	−4.57899	+	6.37215i	−0.440614	+	0.613160i
$109$	6.89216	−	6.89216i	0.660149	−	0.660149i	−0.295266	−	0.955415i	$-0.595408\pi$
$109$	6.89216	−	6.89216i	0.660149	−	0.660149i	0.955415	+	0.295266i	$0.0954083\pi$
$110$		0			0
$111$	22.4818			2.13388
$112$	−2.61805	+	0.880987i	−0.247382	+	0.0832454i
$113$		−	6.46108i		−	0.607807i	−0.952703	−	0.303904i	$-0.901710\pi$
$113$		−	6.46108i		−	0.607807i	0.952703	−	0.303904i	$-0.0982901\pi$
$114$	−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
$118$	2.23261	+	1.89677i	0.205528	+	0.174612i
$119$			3.65156i			0.334738i
$120$		0			0
$121$			7.73420i			0.703109i
$122$	−12.0817	+	14.2208i	−1.09382	+	1.28749i
$123$	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
$127$		−	16.6123i		−	1.47411i	−0.675834	−	0.737054i	$-0.736216\pi$
$127$		−	16.6123i		−	1.47411i	0.675834	−	0.737054i	$-0.263784\pi$
$128$	−9.53688	+	6.08669i	−0.842949	+	0.537993i
$129$	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	$0.990789\pi$
$132$	2.81528	+	17.1934i	0.245038	+	1.49650i
$133$	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
$137$	−8.41495			−0.718937			−0.359469	−	0.933157i	$-0.617042\pi$
$137$	−8.41495			−0.718937			−0.359469	+	0.933157i	$0.617042\pi$
$138$	3.48885	+	2.96404i	0.296991	+	0.252316i
$139$	1.51845	+	1.51845i	0.128793	+	0.128793i	0.768565	−	0.639772i	$-0.220971\pi$
$139$	1.51845	+	1.51845i	0.128793	+	0.128793i	−0.639772	+	0.768565i	$0.720971\pi$
$140$		0			0
$141$	−6.55698	+	6.55698i	−0.552198	+	0.552198i
$142$	−0.266243	−	3.27364i	−0.0223426	−	0.274718i
$143$		−	14.3042i		−	1.19618i
$144$	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
$148$	−13.0371	+	18.1425i	−1.07164	+	1.49131i
$149$	2.61440	+	2.61440i	0.214180	+	0.214180i	0.806040	−	0.591860i	$-0.201606\pi$
$149$	2.61440	+	2.61440i	0.214180	+	0.214180i	−0.591860	+	0.806040i	$0.701606\pi$
$150$		0			0
$151$		−	12.7143i		−	1.03467i	−0.855782	−	0.517337i	$-0.826923\pi$
$151$		−	12.7143i		−	1.03467i	0.855782	−	0.517337i	$-0.173077\pi$
$152$	11.1184	−	18.4667i	0.901823	−	1.49785i
$153$	5.55529			0.449119
$154$	−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	$-0.382762\pi$
$157$	−7.17831	−	7.17831i	−0.572891	−	0.572891i	−0.932935	+	0.360044i	$0.882762\pi$
$158$	−7.07554	+	0.575448i	−0.562900	+	0.0457802i
$159$	14.2119			1.12708
$160$		0			0
$161$	−1.11073			−0.0875376
$162$	−15.5729	+	1.26653i	−1.22352	+	0.0995080i
$163$	7.05476	+	7.05476i	0.552572	+	0.552572i	0.927182	−	0.374611i	$-0.122224\pi$
$163$	7.05476	+	7.05476i	0.552572	+	0.552572i	−0.374611	+	0.927182i	$0.622224\pi$
$164$	1.77713	+	10.8533i	0.138771	+	0.847499i
$165$		0			0
$166$	11.1339	+	9.45910i	0.864159	+	0.734168i
$167$	−3.90586			−0.302244			−0.151122	−	0.988515i	$-0.548289\pi$
$167$	−3.90586			−0.302244			−0.151122	+	0.988515i	$0.548289\pi$
$168$	−3.36782	−	2.02769i	−0.259833	−	0.156440i
$169$		−	2.07819i		−	0.159861i
$170$		0			0
$171$	−5.66158	−	5.66158i	−0.432952	−	0.432952i
$172$	−0.422812	+	0.588387i	−0.0322391	+	0.0448641i
$173$	−8.20139	−	8.20139i	−0.623540	−	0.623540i	0.322895	−	0.946435i	$-0.395344\pi$
$173$	−8.20139	−	8.20139i	−0.623540	−	0.623540i	−0.946435	+	0.322895i	$0.895344\pi$
$174$	−6.83315	+	0.555735i	−0.518020	+	0.0421301i
$175$		0			0
$176$	−15.5074	−	7.69851i	−1.16892	−	0.580297i
$177$			4.16914i			0.313372i
$178$	−0.208142	−	2.55926i	−0.0156009	−	0.191825i
$179$	3.10363	−	3.10363i	0.231976	−	0.231976i	−0.581541	−	0.813517i	$-0.697550\pi$
$179$	3.10363	−	3.10363i	0.231976	−	0.231976i	0.813517	+	0.581541i	$0.197550\pi$
$180$		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	$0.782015\pi$
$182$	2.45972	+	2.08972i	0.182326	+	0.154900i
$183$	−26.5557			−1.96306
$184$	−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
$188$	−1.48903	−	9.09376i	−0.108598	−	0.663231i
$189$	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	$0.434938\pi$
$192$	−15.3889	−	4.73498i	−1.11060	−	0.341718i
$193$		−	3.90696i		−	0.281229i	−0.990064	−	0.140615i	$-0.955092\pi$
$193$		−	3.90696i		−	0.281229i	0.990064	−	0.140615i	$-0.0449079\pi$
$194$	−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	−0.728449	−	0.685100i	$-0.759759\pi$
$197$	−0.608436	+	0.608436i	−0.0433493	+	0.0433493i	0.685100	+	0.728449i	$0.259759\pi$
$198$	−4.16376	+	4.90099i	−0.295906	+	0.348298i
$199$			15.5282i			1.10076i	0.834913	+	0.550382i	$0.185518\pi$
$199$			15.5282i			1.10076i	−0.834913	+	0.550382i	$0.814482\pi$
$200$		0			0
$201$			5.54443i			0.391074i
$202$	20.5007	+	17.4169i	1.44243	+	1.22545i
$203$	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
$207$			1.68980i			0.117449i
$208$	11.8405	+	5.87809i	0.820990	+	0.407572i
$209$	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	$0.216702\pi$
$212$	−8.24143	+	11.4688i	−0.566024	+	0.787681i
$213$	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
$217$	3.24437			0.220242
$218$	−8.92480	+	10.5050i	−0.604464	+	0.711489i
$219$	−1.84627	−	1.84627i	−0.124760	−	0.124760i
$220$		0			0
$221$	12.3566	−	12.3566i	0.831196	−	0.831196i
$222$	−31.6895	+	2.57728i	−2.12686	+	0.172976i
$223$			2.34794i			0.157230i	0.996905	+	0.0786148i	$0.0250497\pi$
$223$			2.34794i			0.157230i	−0.996905	+	0.0786148i	$0.974950\pi$
$224$	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	$-0.0375591\pi$
$227$	13.1881	+	13.1881i	0.875325	+	0.875325i	−0.117722	+	0.993047i	$0.537559\pi$
$228$	30.2732	−	4.95697i	2.00489	−	0.328283i
$229$	−9.37860	−	9.37860i	−0.619755	−	0.619755i	0.325713	−	0.945469i	$-0.394396\pi$
$229$	−9.37860	−	9.37860i	−0.619755	−	0.619755i	−0.945469	+	0.325713i	$0.894396\pi$
$230$		0			0
$231$		−	6.01574i		−	0.395807i
$232$	3.51405	−	5.83653i	0.230709	−	0.383187i
$233$	−16.3435			−1.07070			−0.535350	−	0.844630i	$-0.679820\pi$
$233$	−16.3435			−1.07070			−0.535350	+	0.844630i	$0.679820\pi$
$234$	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
$238$	−0.418609	−	5.14709i	−0.0271344	−	0.333637i
$239$	−19.3818			−1.25371			−0.626854	−	0.779137i	$-0.715658\pi$
$239$	−19.3818			−1.25371			−0.626854	+	0.779137i	$0.715658\pi$
$240$		0			0
$241$	7.15965			0.461193			0.230597	−	0.973049i	$-0.425932\pi$
$241$	7.15965			0.461193			0.230597	+	0.973049i	$0.425932\pi$
$242$	−0.886636	−	10.9018i	−0.0569951	−	0.700795i
$243$	−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
$247$	−25.1861			−1.60255
$248$	12.8963	−	3.20316i	0.818916	−	0.203401i
$249$			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	$0.595755\pi$
$252$	−0.234474	−	1.43198i	−0.0147705	−	0.0902061i
$253$	−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
$257$			5.72152i			0.356899i	0.983949	+	0.178449i	$0.0571081\pi$
$257$			5.72152i			0.356899i	−0.983949	+	0.178449i	$0.942892\pi$
$258$	−1.02773	+	0.0835847i	−0.0639839	+	0.00520376i
$259$	5.45466	−	5.45466i	0.338936	−	0.338936i
$260$		0			0
$261$	−1.78938	−	1.78938i	−0.110760	−	0.110760i
$262$	15.2436	−	17.9427i	0.941756	−	1.10850i
$263$	27.1378			1.67339			0.836695	−	0.547669i	$-0.184485\pi$
$263$	27.1378			1.67339			0.836695	+	0.547669i	$0.184485\pi$
$264$	−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
$268$	−4.47428	−	3.21519i	−0.273310	−	0.196399i
$269$	−13.0770	+	13.0770i	−0.797320	+	0.797320i	−0.982672	−	0.185352i	$-0.940657\pi$
$269$	−13.0770	+	13.0770i	−0.797320	+	0.797320i	0.185352	+	0.982672i	$0.440657\pi$
$270$		0			0
$271$	6.55264			0.398044			0.199022	−	0.979995i	$-0.436223\pi$
$271$	6.55264			0.398044			0.199022	+	0.979995i	$0.436223\pi$
$272$	−6.74567	−	20.0463i	−0.409016	−	1.21548i
$273$			4.59324i			0.277995i
$274$	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	−0.327038	−	0.945011i	$-0.606051\pi$
$277$	10.2851	−	10.2851i	0.617973	−	0.617973i	0.945011	+	0.327038i	$0.106051\pi$
$278$	−2.31442	−	1.96627i	−0.138809	−	0.117929i
$279$		−	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	$0.647908\pi$
$282$	8.49078	−	9.99414i	0.505618	−	0.595142i
$283$	−19.1176	+	19.1176i	−1.13642	+	1.13642i	−0.147334	+	0.989087i	$0.547069\pi$
$283$	−19.1176	+	19.1176i	−1.13642	+	1.13642i	−0.989087	+	0.147334i	$0.952931\pi$
$284$	0.750570	+	4.58387i	0.0445381	+	0.272003i
$285$		0			0
$286$	1.63981	+	20.1627i	0.0969643	+	1.19224i
$287$		−	3.79741i		−	0.224154i
$288$	−2.34582	−	5.46058i	−0.138228	−	0.321768i
$289$	−10.9598			−0.644695
$290$		0			0
$291$	7.50044	−	7.50044i	0.439684	−	0.439684i
$292$	2.56056	−	0.419271i	0.149846	−	0.0245360i
$293$	7.27952	−	7.27952i	0.425274	−	0.425274i	−0.461741	−	0.887015i	$-0.652775\pi$
$293$	7.27952	−	7.27952i	0.425274	−	0.425274i	0.887015	+	0.461741i	$0.152775\pi$
$294$	−14.1495	−	12.0211i	−0.825215	−	0.701082i
$295$		0			0
$296$	16.2968	−	27.0675i	0.947230	−	1.57327i
$297$	16.9815			0.985369
$298$	−3.98486	−	3.38544i	−0.230837	−	0.196113i
$299$	3.75862	+	3.75862i	0.217366	+	0.217366i
$300$		0			0
$301$	0.176902	−	0.176902i	0.0101965	−	0.0101965i
$302$	1.45755	+	17.9216i	0.0838723	+	1.03127i
$303$			38.2827i			2.19928i
$304$	−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	$-0.158395\pi$
$307$	7.03304	+	7.03304i	0.401397	+	0.401397i	−0.477328	+	0.878725i	$0.658395\pi$
$308$	4.85462	+	3.48850i	0.276618	+	0.198776i
$309$	−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	$0.867284\pi$
$312$	4.53489	+	18.2580i	0.256738	+	1.03366i
$313$	−18.4579			−1.04330			−0.521652	−	0.853158i	$-0.674684\pi$
$313$	−18.4579			−1.04330			−0.521652	+	0.853158i	$0.674684\pi$
$314$	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	$-0.342547\pi$
$317$	−7.21807	−	7.21807i	−0.405407	−	0.405407i	−0.880133	+	0.474726i	$0.842547\pi$
$318$	−20.0325	+	1.62923i	−1.12337	+	0.0913626i
$319$	10.4255			0.583714
$320$		0			0
$321$	−17.8780			−0.997850
$322$	1.56564	−	0.127332i	0.0872495	−	0.00709593i
$323$	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
$327$	−19.6169			−1.08482
$328$	−3.74917	−	15.0946i	−0.207014	−	0.833461i
$329$			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	$0.955561\pi$
$332$	−16.7783	−	12.0568i	−0.920828	−	0.661702i
$333$	−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
$337$		−	26.0210i		−	1.41746i	−0.705482	−	0.708728i	$-0.749269\pi$
$337$		−	26.0210i		−	1.41746i	0.705482	−	0.708728i	$-0.250731\pi$
$338$	0.238240	+	2.92933i	0.0129586	+	0.159335i
$339$	−9.19497	+	9.19497i	−0.499402	+	0.499402i
$340$		0			0
$341$	14.3788	+	14.3788i	0.778654	+	0.778654i
$342$	8.62937	+	7.33131i	0.466623	+	0.396432i
$343$	9.33873			0.504244
$344$	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	−0.272142	−	0.962257i	$-0.587732\pi$
$347$	12.8554	−	12.8554i	0.690115	−	0.690115i	0.962257	+	0.272142i	$0.0877321\pi$
$348$	9.56802	−	1.56668i	0.512900	−	0.0839830i
$349$	20.0227	−	20.0227i	1.07179	−	1.07179i	0.0745736	−	0.997216i	$-0.476240\pi$
$349$	20.0227	−	20.0227i	1.07179	−	1.07179i	0.997216	−	0.0745736i	$-0.0237596\pi$
$350$		0			0
$351$	−12.9660			−0.692075
$352$	22.7412	+	9.07376i	1.21211	+	0.483633i
$353$		−	13.7062i		−	0.729510i	−0.931104	−	0.364755i	$-0.881153\pi$
$353$		−	13.7062i		−	0.729510i	0.931104	−	0.364755i	$-0.118847\pi$
$354$	−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
$358$	−4.01896	+	4.73055i	−0.212409	+	0.250017i
$359$		−	32.3506i		−	1.70740i	−0.520764	−	0.853700i	$-0.674353\pi$
$359$		−	32.3506i		−	1.70740i	0.520764	−	0.853700i	$-0.325647\pi$
$360$		0			0
$361$		−	39.0799i		−	2.05684i
$362$	2.91184	+	2.47383i	0.153043	+	0.130021i
$363$	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
$367$			16.3714i			0.854582i	0.904114	+	0.427291i	$0.140532\pi$
$367$			16.3714i			0.854582i	−0.904114	+	0.427291i	$0.859468\pi$
$368$	6.09765	−	2.05189i	0.317862	−	0.106962i
$369$	−5.77718			−0.300748
$370$		0			0
$371$	3.44817	−	3.44817i	0.179020	−	0.179020i
$372$	15.3570	+	11.0354i	0.796222	+	0.572161i
$373$	15.5321	−	15.5321i	0.804222	−	0.804222i	−0.179530	−	0.983752i	$-0.557458\pi$
$373$	15.5321	−	15.5321i	0.804222	−	0.804222i	0.983752	+	0.179530i	$0.0574578\pi$
$374$	20.9562	−	24.6667i	1.08362	−	1.27548i
$375$		0			0
$376$	3.14136	+	12.6475i	0.162004	+	0.652245i
$377$	−7.96022			−0.409972
$378$	−2.48084	+	2.92010i	−0.127601	+	0.150194i
$379$	−24.9538	−	24.9538i	−1.28179	−	1.28179i	−0.939647	−	0.342145i	$-0.888847\pi$
$379$	−24.9538	−	24.9538i	−1.28179	−	1.28179i	−0.342145	−	0.939647i	$-0.611153\pi$
$380$		0			0
$381$	−23.6416	+	23.6416i	−1.21119	+	1.21119i
$382$	−7.90820	+	0.643168i	−0.404619	+	0.0329073i
$383$		−	6.24887i		−	0.319302i	−0.987174	−	0.159651i	$-0.948963\pi$
$383$		−	6.24887i		−	0.319302i	0.987174	−	0.159651i	$-0.0510369\pi$
$384$	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
$388$	1.70328	+	10.4022i	0.0864707	+	0.528093i
$389$	−2.10802	−	2.10802i	−0.106881	−	0.106881i	0.651644	−	0.758525i	$-0.274080\pi$
$389$	−2.10802	−	2.10802i	−0.106881	−	0.106881i	−0.758525	+	0.651644i	$0.774080\pi$
$390$		0			0
$391$		−	8.50478i		−	0.430105i
$392$	17.9061	−	4.44748i	0.904393	−	0.224632i
$393$	33.5058			1.69015
$394$	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	0.979919	+	0.199397i	$0.0638983\pi$
$397$	23.4977	+	23.4977i	1.17932	+	1.17932i	0.199397	+	0.979919i	$0.436102\pi$
$398$	−1.78013	−	21.8879i	−0.0892296	−	1.09714i
$399$	−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	$0.675590\pi$
$402$	−0.635604	−	7.81520i	−0.0317011	−	0.389787i
$403$	−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
$407$	48.3492			2.39658
$408$	15.5259	−	25.7872i	0.768647	−	1.27666i
$409$		−	18.4025i		−	0.909944i	−0.890506	−	0.454972i	$-0.849649\pi$
$409$		−	18.4025i		−	0.909944i	0.890506	−	0.454972i	$-0.150351\pi$
$410$		0			0
$411$	11.9756	+	11.9756i	0.590711	+	0.590711i
$412$	5.21672	−	0.854193i	0.257009	−	0.0420831i
$413$	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
$417$		−	4.32190i		−	0.211644i
$418$	−46.4958	+	3.78147i	−2.27419	+	0.184958i
$419$	−14.9331	+	14.9331i	−0.729530	+	0.729530i	−0.970526	−	0.240996i	$-0.922526\pi$
$419$	−14.9331	+	14.9331i	−0.729530	+	0.729530i	0.240996	+	0.970526i	$0.422526\pi$
$420$		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	$0.939442\pi$
$422$	−2.77762	+	3.26942i	−0.135212	+	0.159153i
$423$	4.84060			0.235358
$424$	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
$428$	10.3674	−	14.4273i	0.501125	−	0.697368i
$429$	−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	$0.445657\pi$
$432$	−6.97829	+	14.0566i	−0.335743	+	0.676301i
$433$			14.3192i			0.688139i	0.938944	+	0.344069i	$0.111806\pi$
$433$			14.3192i			0.688139i	−0.938944	+	0.344069i	$0.888194\pi$
$434$	−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
$438$	2.81409	+	2.39078i	0.134462	+	0.114236i
$439$			25.9047i			1.23637i	0.786034	+	0.618183i	$0.212131\pi$
$439$			25.9047i			1.23637i	−0.786034	+	0.618183i	$0.787869\pi$
$440$		0			0
$441$		−	6.85321i		−	0.326344i
$442$	−16.0008	+	18.8339i	−0.761082	+	0.895838i
$443$	−11.1389	+	11.1389i	−0.529224	+	0.529224i	−0.920341	−	0.391117i	$-0.872089\pi$
$443$	−11.1389	+	11.1389i	−0.529224	+	0.529224i	0.391117	+	0.920341i	$0.372089\pi$
$444$	44.3727	−	7.26565i	2.10584	−	0.344813i
$445$		0			0
$446$	−0.269164	−	3.30956i	−0.0127453	−	0.156712i
$447$		−	7.44127i		−	0.351960i
$448$	−4.88257	+	2.58492i	−0.230680	+	0.122126i
$449$	−12.6659			−0.597740			−0.298870	−	0.954294i	$-0.596610\pi$
$449$	−12.6659			−0.597740			−0.298870	+	0.954294i	$0.596610\pi$
$450$		0			0
$451$	16.8298	−	16.8298i	0.792484	−	0.792484i
$452$	−2.08809	−	12.7523i	−0.0982153	−	0.599820i
$453$	−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
$457$	−16.9442			−0.792617			−0.396308	−	0.918117i	$-0.629709\pi$
$457$	−16.9442			−0.792617			−0.396308	+	0.918117i	$0.629709\pi$
$458$	14.2948	+	12.1446i	0.667954	+	0.567478i
$459$	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	$0.393022\pi$
$462$	0.689634	+	8.47954i	0.0320847	+	0.394504i
$463$			14.0955i			0.655074i	0.944838	+	0.327537i	$0.106219\pi$
$463$			14.0955i			0.655074i	−0.944838	+	0.327537i	$0.893781\pi$
$464$	−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	$-0.379482\pi$
$467$	−12.0918	−	12.0918i	−0.559540	−	0.559540i	−0.929177	+	0.369636i	$0.879482\pi$
$468$	−4.05226	+	5.63915i	−0.187316	+	0.260670i
$469$	1.34522	+	1.34522i	0.0621165	+	0.0621165i
$470$		0			0
$471$			20.4313i			0.941427i
$472$	5.01953	+	3.02215i	0.231043	+	0.139106i
$473$	1.56803			0.0720981
$474$	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
$478$	27.3199	−	2.22190i	1.24958	−	0.101627i
$479$	−14.2523			−0.651202			−0.325601	−	0.945507i	$-0.605567\pi$
$479$	−14.2523			−0.651202			−0.325601	+	0.945507i	$0.605567\pi$
$480$		0			0
$481$	−36.9163			−1.68324
$482$	−10.0919	+	0.820770i	−0.459676	+	0.0373850i
$483$	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
$487$	26.0424			1.18010			0.590048	−	0.807368i	$-0.299109\pi$
$487$	26.0424			1.18010			0.590048	+	0.807368i	$0.299109\pi$
$488$	−19.2499	+	31.9724i	−0.871402	+	1.44732i
$489$		−	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	$0.714701\pi$
$492$	12.9165	−	17.9747i	0.582323	−	0.810364i
$493$	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
$497$		−	1.60383i		−	0.0719418i
$498$	−2.38348	−	29.3066i	−0.106806	−	1.31326i
$499$	5.30274	−	5.30274i	0.237383	−	0.237383i	−0.578383	−	0.815766i	$-0.696316\pi$
$499$	5.30274	−	5.30274i	0.237383	−	0.237383i	0.815766	+	0.578383i	$0.196316\pi$
$500$		0			0
$501$	5.55855	+	5.55855i	0.248338	+	0.248338i
$502$	−15.9083	−	13.5153i	−0.710021	−	0.603217i
$503$	−28.8492			−1.28632			−0.643161	−	0.765731i	$-0.722378\pi$
$503$	−28.8492			−1.28632			−0.643161	+	0.765731i	$0.722378\pi$
$504$	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
$508$	−5.36876	−	32.7881i	−0.238200	−	1.45473i
$509$	−12.9968	+	12.9968i	−0.576072	+	0.576072i	−0.933819	−	0.357747i	$-0.883545\pi$
$509$	−12.9968	+	12.9968i	−0.576072	+	0.576072i	0.357747	+	0.933819i	$0.383545\pi$
$510$		0			0
$511$	−0.895906			−0.0396326
$512$	−16.8560	+	15.0955i	−0.744937	+	0.667134i
$513$		−	29.9001i		−	1.32012i
$514$	−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
$518$	−7.06336	+	8.31399i	−0.310346	+	0.365296i
$519$			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	$-0.0990941\pi$
$522$	2.72737	+	2.31711i	0.119374	+	0.101417i
$523$	−6.30689	+	6.30689i	−0.275781	+	0.275781i	−0.831422	−	0.555641i	$-0.812473\pi$
$523$	−6.30689	+	6.30689i	−0.275781	+	0.275781i	0.555641	+	0.831422i	$0.312473\pi$
$524$	−19.4299	+	27.0388i	−0.848800	+	1.18119i
$525$		0			0
$526$	−38.2524	+	3.11104i	−1.66788	+	0.135648i
$527$			24.8420i			1.08213i
$528$	11.1131	+	33.0251i	0.483636	+	1.43723i
$529$	−20.4130			−0.887523
$530$		0			0
$531$	1.53890	−	1.53890i	0.0667827	−	0.0667827i
$532$	6.14235	−	8.54773i	0.266305	−	0.370591i
$533$	−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
$537$	−8.83375			−0.381204
$538$	16.9337	−	19.9320i	0.730064	−	0.859328i
$539$	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	$0.212238\pi$
$542$	−9.23633	+	0.751184i	−0.396735	+	0.0322661i
$543$			5.43752i			0.233346i
$544$	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	−0.976997	−	0.213251i	$-0.931595\pi$
$547$	−27.8376	−	27.8376i	−1.19025	−	1.19025i	−0.213251	−	0.976997i	$-0.568405\pi$
$548$	−16.6087	+	2.71953i	−0.709489	+	0.116173i
$549$	9.80220	+	9.80220i	0.418348	+	0.418348i
$550$		0			0
$551$		−	18.3565i		−	0.782014i
$552$	7.84391	+	4.72265i	0.333859	+	0.201009i
$553$	−3.46647			−0.147409
$554$	−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	$-0.235647\pi$
$557$	1.50454	+	1.50454i	0.0637492	+	0.0637492i	−0.674513	+	0.738263i	$0.735647\pi$
$558$	0.565834	+	6.95733i	0.0239537	+	0.294527i
$559$	−1.19725			−0.0506382
$560$		0			0
$561$	46.0622			1.94475
$562$	−3.43587	−	42.2465i	−0.144933	−	1.78206i
$563$	6.66663	+	6.66663i	0.280965	+	0.280965i	0.833494	−	0.552529i	$-0.186337\pi$
$563$	6.66663	+	6.66663i	0.280965	+	0.280965i	−0.552529	+	0.833494i	$0.686337\pi$
$564$	−10.8225	+	15.0607i	−0.455711	+	0.634170i
$565$		0			0
$566$	24.7557	−	29.1389i	1.04056	−	1.22480i
$567$	−7.62952			−0.320410
$568$	−1.58346	−	6.37520i	−0.0664405	−	0.267497i
$569$		−	8.38187i		−	0.351386i	−0.984445	−	0.175693i	$-0.943783\pi$
$569$		−	8.38187i		−	0.351386i	0.984445	−	0.175693i	$-0.0562167\pi$
$570$		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	$0.432097\pi$
$572$	−4.62283	−	28.2325i	−0.193290	−	1.18046i
$573$	−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
$577$			23.2045i			0.966014i	0.875616	+	0.483007i	$0.160455\pi$
$577$			23.2045i			0.966014i	−0.875616	+	0.483007i	$0.839545\pi$
$578$	15.4485	−	1.25642i	0.642574	−	0.0522600i
$579$	−5.56012	+	5.56012i	−0.231071	+	0.231071i
$580$		0			0
$581$	5.04450	+	5.04450i	0.209281	+	0.209281i
$582$	−9.71248	+	11.4322i	−0.402595	+	0.473878i
$583$	30.5640			1.26583
$584$	−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	−0.442123	−	0.896955i	$-0.645774\pi$
$587$	11.0197	−	11.0197i	0.454832	−	0.454832i	0.896955	+	0.442123i	$0.145774\pi$
$588$	21.3226	+	15.3223i	0.879330	+	0.631882i
$589$	25.3173	−	25.3173i	1.04318	−	1.04318i
$590$		0			0
$591$	1.73177			0.0712354
$592$	−19.8683	+	40.0215i	−0.816582	+	1.64487i
$593$			6.98847i			0.286982i	0.989652	+	0.143491i	$0.0458328\pi$
$593$			6.98847i			0.286982i	−0.989652	+	0.143491i	$0.954167\pi$
$594$	−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
$598$	−5.72888	−	4.86711i	−0.234271	−	0.199031i
$599$		−	39.9642i		−	1.63289i	−0.577420	−	0.816447i	$-0.695941\pi$
$599$		−	39.9642i		−	1.63289i	0.577420	−	0.816447i	$-0.304059\pi$
$600$		0			0
$601$			21.0830i			0.859993i	0.902831	+	0.429997i	$0.141485\pi$
$601$			21.0830i			0.859993i	−0.902831	+	0.429997i	$0.858515\pi$
$602$	−0.229075	+	0.269634i	−0.00933638	+	0.0109895i
$603$	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
$607$			22.3189i			0.905897i	0.891537	+	0.452949i	$0.149628\pi$
$607$			22.3189i			0.905897i	−0.891537	+	0.452949i	$0.850372\pi$
$608$	15.9765	−	40.0413i	0.647934	−	1.62389i
$609$	−3.34772			−0.135656
$610$		0			0
$611$	10.7669	−	10.7669i	0.435583	−	0.435583i
$612$	10.9646	−	1.79536i	0.443217	−	0.0725729i
$613$	−10.6045	+	10.6045i	−0.428312	+	0.428312i	−0.888053	−	0.459741i	$-0.847942\pi$
$613$	−10.6045	+	10.6045i	−0.428312	+	0.428312i	0.459741	+	0.888053i	$0.347942\pi$
$614$	−10.7197	−	9.10724i	−0.432614	−	0.367538i
$615$		0			0
$616$	−7.24279	−	4.36073i	−0.291820	−	0.175699i
$617$	−33.7636			−1.35927			−0.679635	−	0.733550i	$-0.737862\pi$
$617$	−33.7636			−1.35927			−0.679635	+	0.733550i	$0.737862\pi$
$618$	5.73323	+	4.87081i	0.230624	+	0.195933i
$619$	−4.86777	−	4.86777i	−0.195652	−	0.195652i	0.602481	−	0.798133i	$-0.294179\pi$
$619$	−4.86777	−	4.86777i	−0.195652	−	0.195652i	−0.798133	+	0.602481i	$0.794179\pi$
$620$		0			0
$621$	−4.46211	+	4.46211i	−0.179058	+	0.179058i
$622$	−1.63741	−	20.1331i	−0.0656541	−	0.807263i
$623$		−	1.25384i		−	0.0502341i
$624$	−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
$628$	−16.4878	−	11.8481i	−0.657936	−	0.472789i
$629$	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	$0.895928\pi$
$632$	−13.7791	+	3.42244i	−0.548105	+	0.136137i
$633$	−6.10526			−0.242662
$634$	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
$638$	−14.6953	+	1.19516i	−0.581793	+	0.0473167i
$639$	−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	$0.368611\pi$
$642$	25.2000	−	2.04950i	0.994566	−	0.0808873i
$643$	−7.78443	−	7.78443i	−0.306988	−	0.306988i	0.536752	−	0.843740i	$-0.319651\pi$
$643$	−7.78443	−	7.78443i	−0.306988	−	0.306988i	−0.843740	+	0.536752i	$0.819651\pi$
$644$	−2.19226	+	0.358964i	−0.0863871	+	0.0141452i
$645$		0			0
$646$	−43.4317	−	36.8985i	−1.70880	−	1.45175i
$647$	21.7693			0.855840			0.427920	−	0.903817i	$-0.359246\pi$
$647$	21.7693			0.855840			0.427920	+	0.903817i	$0.359246\pi$
$648$	−30.3271	+	7.53260i	−1.19136	+	0.295908i
$649$			8.96611i			0.351951i
$650$		0			0
$651$	−4.61717	−	4.61717i	−0.180961	−	0.180961i
$652$	16.2040	+	11.6441i	0.634600	+	0.456020i
$653$	26.3118	+	26.3118i	1.02966	+	1.02966i	0.999546	+	0.0301152i	$0.00958743\pi$
$653$	26.3118	+	26.3118i	1.02966	+	1.02966i	0.0301152	+	0.999546i	$0.490413\pi$
$654$	27.6512	−	2.24885i	1.08125	−	0.0879369i
$655$		0			0
$656$	7.01511	+	20.8470i	0.273894	+	0.813937i
$657$			1.36298i			0.0531751i
$658$	−0.364754	−	4.48491i	−0.0142196	−	0.174840i
$659$	20.2389	−	20.2389i	0.788397	−	0.788397i	−0.192835	−	0.981231i	$-0.561768\pi$
$659$	20.2389	−	20.2389i	0.788397	−	0.788397i	0.981231	+	0.192835i	$0.0617681\pi$
$660$		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	$0.689947\pi$
$662$	23.6017	+	20.0515i	0.917308	+	0.779322i
$663$	−35.1702			−1.36590
$664$	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
$668$	−7.70905	+	1.26229i	−0.298272	+	0.0488395i
$669$	3.34143	−	3.34143i	0.129187	−	0.129187i
$670$		0			0
$671$	−57.1105			−2.20473
$672$	−7.30242	−	2.91368i	−0.281697	−	0.112398i
$673$			8.19512i			0.315899i	0.987447	+	0.157949i	$0.0504883\pi$
$673$			8.19512i			0.315899i	−0.987447	+	0.157949i	$0.949512\pi$
$674$	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	−0.909925	−	0.414774i	$-0.863861\pi$
$677$	−12.8834	+	12.8834i	−0.495151	+	0.495151i	0.414774	+	0.909925i	$0.363861\pi$
$678$	11.9068	−	14.0150i	0.457276	−	0.538241i
$679$		−	3.63960i		−	0.139675i
$680$		0			0
$681$		−	37.5368i		−	1.43841i
$682$	−21.9161	−	18.6194i	−0.839211	−	0.712973i
$683$	15.0673	−	15.0673i	0.576535	−	0.576535i	−0.357412	−	0.933947i	$-0.616341\pi$
$683$	15.0673	−	15.0673i	0.576535	−	0.576535i	0.933947	+	0.357412i	$0.116341\pi$
$684$	−13.0041	−	9.34465i	−0.497223	−	0.357302i
$685$		0			0
$686$	−13.1635	+	1.07058i	−0.502585	+	0.0408748i
$687$			26.6940i			1.01844i
$688$	−0.644356	+	1.29795i	−0.0245659	+	0.0494840i
$689$	−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	$0.294994\pi$
$692$	−18.8377	−	13.5367i	−0.716104	−	0.514588i
$693$	−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
$697$	29.0766			1.10135
$698$	−25.9278	+	30.5185i	−0.981381	+	1.15514i
$699$	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	$0.0525376\pi$
$702$	18.2764	−	1.48640i	0.689798	−	0.0561007i
$703$		−	85.1304i		−	3.21075i
$704$	−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
$708$	1.34738	+	8.22870i	0.0506376	+	0.309253i
$709$	23.9643	+	23.9643i	0.899997	+	0.899997i	0.995435	−	0.0954387i	$-0.0304254\pi$
$709$	23.9643	+	23.9643i	0.899997	+	0.899997i	−0.0954387	+	0.995435i	$0.530425\pi$
$710$		0			0
$711$			5.27371i			0.197779i
$712$	−1.23791	−	4.98398i	−0.0463928	−	0.186783i
$713$	−7.55640			−0.282990
$714$	−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
$718$	3.70862	+	45.6001i	0.138405	+	1.70178i
$719$	44.4408			1.65736			0.828681	−	0.559721i	$-0.189092\pi$
$719$	44.4408			1.65736			0.828681	+	0.559721i	$0.189092\pi$
$720$		0			0
$721$	−1.82526			−0.0679762
$722$	4.48006	+	55.0855i	0.166730	+	2.05007i
$723$	−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
$727$	−46.6543			−1.73031			−0.865155	−	0.501504i	$-0.832780\pi$
$727$	−46.6543			−1.73031			−0.865155	+	0.501504i	$0.832780\pi$
$728$	5.53014	+	3.32958i	0.204960	+	0.123402i
$729$		−	12.0815i		−	0.447464i
$730$		0			0
$731$	1.35453	+	1.35453i	0.0500992	+	0.0500992i
$732$	−52.4135	+	8.58226i	−1.93726	+	0.317210i
$733$	−19.4202	−	19.4202i	−0.717303	−	0.717303i	0.250749	−	0.968052i	$-0.419323\pi$
$733$	−19.4202	−	19.4202i	−0.717303	−	0.717303i	−0.968052	+	0.250749i	$0.919323\pi$
$734$	−1.87679	−	23.0765i	−0.0692737	−	0.851769i
$735$		0			0
$736$	−8.35977	+	3.59128i	−0.308145	+	0.132376i
$737$			11.9238i			0.439219i
$738$	8.14328	−	0.662287i	0.299758	−	0.0243791i
$739$	20.5243	−	20.5243i	0.754999	−	0.754999i	−0.220409	−	0.975408i	$-0.570739\pi$
$739$	20.5243	−	20.5243i	0.754999	−	0.754999i	0.975408	+	0.220409i	$0.0707392\pi$
$740$		0			0
$741$	35.8431	+	35.8431i	1.31673	+	1.31673i
$742$	−4.46511	+	5.25570i	−0.163919	+	0.192943i
$743$	−12.9245			−0.474154			−0.237077	−	0.971491i	$-0.576189\pi$
$743$	−12.9245			−0.474154			−0.237077	+	0.971491i	$0.576189\pi$
$744$	−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
$748$	−26.7113	+	37.1716i	−0.976662	+	1.35913i
$749$	−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	$0.902726\pi$
$752$	−5.87783	−	17.4673i	−0.214342	−	0.636966i
$753$		−	29.7069i		−	1.08258i
$754$	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	0.297407	−	0.954751i	$-0.403878\pi$
$757$	34.4514	−	34.4514i	1.25216	−	1.25216i	0.954751	−	0.297407i	$-0.0961218\pi$
$758$	38.0346	+	32.3132i	1.38148	+	1.17367i
$759$			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	$-0.332941\pi$
$762$	30.6139	−	36.0344i	1.10903	−	1.30539i
$763$	−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
$767$		−	6.84595i		−	0.247193i
$768$	−31.9036	−	4.37213i	−1.15122	−	0.157766i
$769$	17.9108			0.645882			0.322941	−	0.946419i	$-0.395329\pi$
$769$	17.9108			0.645882			0.322941	+	0.946419i	$0.395329\pi$
$770$		0			0
$771$	8.14247	−	8.14247i	0.293244	−	0.293244i
$772$	−1.26265	−	7.71124i	−0.0454437	−	0.277534i
$773$	3.73170	−	3.73170i	0.134220	−	0.134220i	−0.636805	−	0.771025i	$-0.719744\pi$
$773$	3.73170	−	3.73170i	0.134220	−	0.134220i	0.771025	+	0.636805i	$0.219744\pi$
$774$	0.410207	+	0.348502i	0.0147446	+	0.0125266i
$775$		0			0
$776$	−3.59336	−	14.4673i	−0.128994	−	0.519346i
$777$	−15.5254			−0.556971
$778$	3.21304	+	2.72972i	0.115193	+	0.0978652i
$779$	−29.6329	−	29.6329i	−1.06171	−	1.06171i
$780$		0			0
$781$	7.10805	−	7.10805i	0.254346	−	0.254346i
$782$	0.974974	+	11.9880i	0.0348650	+	0.428690i
$783$		−	9.45012i		−	0.337720i
$784$	−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	$-0.230720\pi$
$787$	2.40160	+	2.40160i	0.0856076	+	0.0856076i	−0.663006	+	0.748614i	$0.730720\pi$
$788$	−1.00425	+	1.39751i	−0.0357748	+	0.0497843i
$789$	−38.6207	−	38.6207i	−1.37493	−	1.37493i
$790$		0			0
$791$			4.46187i			0.158646i
$792$	−6.63419	+	11.0188i	−0.235736	+	0.391536i
$793$	43.6060			1.54849
$794$	−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	0.952341	+	0.305035i	$0.0986682\pi$
$797$	35.4972	+	35.4972i	1.25738	+	1.25738i	0.305035	+	0.952341i	$0.401332\pi$
$798$	14.9303	−	1.21427i	0.528526	−	0.0429846i
$799$	−24.3627			−0.861892
$800$		0			0
$801$	−1.90753			−0.0673992
$802$	29.5857	−	2.40618i	1.04471	−	0.0849652i
$803$	−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
$807$	37.2206			1.31023
$808$	46.0914	+	27.7506i	1.62149	+	0.976264i
$809$			11.9182i			0.419021i	0.977806	+	0.209510i	$0.0671870\pi$
$809$			11.9182i			0.419021i	−0.977806	+	0.209510i	$0.932813\pi$
$810$		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	$0.935360\pi$
$812$	1.94133	−	2.70156i	0.0681273	−	0.0948063i
$813$	−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
$817$		−	2.76090i		−	0.0965915i
$818$	2.10963	+	25.9394i	0.0737615	+	0.906949i
$819$	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	$0.642795\pi$
$822$	−18.2531	−	15.5074i	−0.636652	−	0.540884i
$823$	43.9496			1.53199			0.765994	−	0.642848i	$-0.222247\pi$
$823$	43.9496			1.53199			0.765994	+	0.642848i	$0.222247\pi$
$824$	−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	−0.737560	−	0.675282i	$-0.764022\pi$
$827$	−1.79096	+	1.79096i	−0.0622777	+	0.0622777i	0.675282	+	0.737560i	$0.264022\pi$
$828$	0.546109	+	3.33519i	0.0189786	+	0.115906i
$829$	−13.4979	+	13.4979i	−0.468801	+	0.468801i	−0.901526	−	0.432725i	$-0.857552\pi$
$829$	−13.4979	+	13.4979i	−0.468801	+	0.468801i	0.432725	+	0.901526i	$0.357552\pi$
$830$		0			0
$831$	−29.2742			−1.01551
$832$	25.2694	+	7.77509i	0.876060	+	0.269553i
$833$			34.4923i			1.19509i
$834$	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
$838$	19.3372	−	22.7610i	0.667993	−	0.786266i
$839$			14.5332i			0.501741i	0.968021	+	0.250870i	$0.0807168\pi$
$839$			14.5332i			0.501741i	−0.968021	+	0.250870i	$0.919283\pi$
$840$		0			0
$841$			23.1983i			0.799941i
$842$	24.7956	+	21.0658i	0.854515	+	0.725975i
$843$	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
$847$		−	5.34105i		−	0.183521i
$848$	−12.5598	+	25.2996i	−0.431304	+	0.868793i
$849$	54.4136			1.86747
$850$		0			0
$851$	−12.7043	+	12.7043i	−0.435499	+	0.435499i
$852$	5.45529	−	7.59161i	0.186895	−	0.260084i
$853$	11.5836	−	11.5836i	0.396615	−	0.396615i	−0.480423	−	0.877037i	$-0.659517\pi$
$853$	11.5836	−	11.5836i	0.396615	−	0.396615i	0.877037	+	0.480423i	$0.159517\pi$
$854$	8.34331	−	9.82056i	0.285502	−	0.336053i
$855$		0			0
$856$	−12.9595	+	21.5246i	−0.442946	+	0.735695i
$857$	−15.6443			−0.534399			−0.267200	−	0.963641i	$-0.586098\pi$
$857$	−15.6443			−0.534399			−0.267200	+	0.963641i	$0.586098\pi$
$858$	26.3605	−	31.0278i	0.899932	−	1.05927i
$859$	−12.0947	−	12.0947i	−0.412665	−	0.412665i	0.470001	−	0.882666i	$-0.344254\pi$
$859$	−12.0947	−	12.0947i	−0.412665	−	0.412665i	−0.882666	+	0.470001i	$0.844254\pi$
$860$		0			0
$861$	−5.40422	+	5.40422i	−0.184175	+	0.184175i
$862$	−9.94338	+	0.808687i	−0.338673	+	0.0275440i
$863$			9.28120i			0.315936i	0.987444	+	0.157968i	$0.0504942\pi$
$863$			9.28120i			0.315936i	−0.987444	+	0.157968i	$0.949506\pi$
$864$	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
$868$	6.40347	−	1.04851i	0.217348	−	0.0355889i
$869$	−15.3631	−	15.3631i	−0.521157	−	0.521157i
$870$		0			0
$871$		−	9.10425i		−	0.308486i
$872$	−14.2200	+	23.6182i	−0.481551	+	0.799814i
$873$	−5.53709			−0.187402
$874$	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	$-0.272639\pi$
$877$	−2.97610	−	2.97610i	−0.100496	−	0.100496i	−0.755567	+	0.655071i	$0.772639\pi$
$878$	−2.96968	−	36.5143i	−0.100222	−	1.23230i
$879$	−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	$0.335495\pi$
$882$	0.785641	+	9.66001i	0.0264539	+	0.325270i
$883$	−35.5597	−	35.5597i	−1.19668	−	1.19668i	−0.975155	−	0.221525i	$-0.928897\pi$
$883$	−35.5597	−	35.5597i	−1.19668	−	1.19668i	−0.221525	−	0.975155i	$-0.571103\pi$
$884$	20.3950	−	28.3818i	0.685960	−	0.954585i
$885$		0			0
$886$	14.4240	−	16.9778i	0.484583	−	0.570382i
$887$	−4.51671			−0.151656			−0.0758282	−	0.997121i	$-0.524160\pi$
$887$	−4.51671			−0.151656			−0.0758282	+	0.997121i	$0.524160\pi$
$888$	−61.7131	+	15.3282i	−2.07096	+	0.514380i
$889$			11.4721i			0.384762i
$890$		0			0
$891$	−33.8133	−	33.8133i	−1.13279	−	1.13279i
$892$	0.758805	+	4.63416i	0.0254067	+	0.155163i
$893$	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
$897$		−	10.6980i		−	0.357196i
$898$	17.8533	−	1.45200i	0.595773	−	0.0484537i
$899$	8.00169	−	8.00169i	0.266871	−	0.266871i
$900$		0			0
$901$	26.4025	+	26.4025i	0.879594	+	0.879594i
$902$	−21.7933	+	25.6519i	−0.725636	+	0.854116i
$903$	−0.503511			−0.0167558
$904$	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	−0.617949	−	0.786218i	$-0.712036\pi$
$907$	5.06769	−	5.06769i	0.168270	−	0.168270i	0.786218	+	0.617949i	$0.212036\pi$
$908$	30.2917	+	21.7674i	1.00526	+	0.722378i
$909$	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	$0.291894\pi$
$912$	58.1486	−	19.5673i	1.92549	−	0.647938i
$913$			44.7135i			1.47980i
$914$	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
$918$	−22.3590	−	18.9957i	−0.737958	−	0.626951i
$919$			21.5651i			0.711365i	0.934607	+	0.355683i	$0.115752\pi$
$919$			21.5651i			0.711365i	−0.934607	+	0.355683i	$0.884248\pi$
$920$		0			0
$921$		−	20.0179i		−	0.659612i
$922$	17.0785	−	20.1023i	0.562449	−	0.662035i
$923$	−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
$927$			2.77685i			0.0912038i
$928$	5.04949	−	12.6553i	0.165758	−	0.415431i
$929$	45.6603			1.49807			0.749033	−	0.662532i	$-0.230518\pi$
$929$	45.6603			1.49807			0.749033	+	0.662532i	$0.230518\pi$
$930$		0			0
$931$	35.1522	−	35.1522i	1.15207	−	1.15207i
$932$	−32.2575	+	5.28189i	−1.05663	+	0.173014i
$933$	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
$937$	−2.29807			−0.0750746			−0.0375373	−	0.999295i	$-0.511951\pi$
$937$	−2.29807			−0.0750746			−0.0375373	+	0.999295i	$0.511951\pi$
$938$	−2.05038	−	1.74195i	−0.0669473	−	0.0568768i
$939$	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	$0.438367\pi$
$942$	−2.34222	−	28.7992i	−0.0763135	−	0.938329i
$943$			8.84448i			0.288016i
$944$	−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	$-0.0595025\pi$
$947$	24.5182	+	24.5182i	0.796733	+	0.796733i	−0.185846	+	0.982579i	$0.559502\pi$
$948$	−16.4083	−	11.7909i	−0.532915	−	0.382950i
$949$	3.03168	+	3.03168i	0.0984125	+	0.0984125i
$950$		0			0
$951$			20.5445i			0.666202i
$952$	−2.48965	−	10.0236i	−0.0806900	−	0.324867i
$953$	−32.3462			−1.04780			−0.523898	−	0.851781i	$-0.675523\pi$
$953$	−32.3462			−1.04780			−0.523898	+	0.851781i	$0.675523\pi$
$954$	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
$958$	20.0894	−	1.63385i	0.649059	−	0.0527874i
$959$	5.81116			0.187652
$960$		0			0
$961$	−8.92816			−0.288005
$962$	52.0358	−	4.23203i	1.67770	−	0.136446i
$963$	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
$967$	−14.6983			−0.472665			−0.236333	−	0.971672i	$-0.575946\pi$
$967$	−14.6983			−0.472665			−0.236333	+	0.971672i	$0.575946\pi$
$968$	−5.27321	−	21.2305i	−0.169487	−	0.682376i
$969$		−	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	$0.520349\pi$
$972$	−16.9972	−	12.2141i	−0.545186	−	0.391768i
$973$	−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
$977$			17.3533i			0.555180i	0.960700	+	0.277590i	$0.0895357\pi$
$977$			17.3533i			0.555180i	−0.960700	+	0.277590i	$0.910464\pi$
$978$	2.30190	+	28.3035i	0.0736068	+	0.905048i
$979$	5.55691	−	5.55691i	0.177600	−	0.177600i
$980$		0			0
$981$	7.24094	+	7.24094i	0.231186	+	0.231186i
$982$	−5.28589	−	4.49076i	−0.168680	−	0.143306i
$983$	−27.5174			−0.877668			−0.438834	−	0.898568i	$-0.644608\pi$
$983$	−27.5174			−0.877668			−0.438834	+	0.898568i	$0.644608\pi$
$984$	−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
$988$	−49.7101	+	8.13961i	−1.58149	+	0.258955i
$989$	−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	$0.464722\pi$
$992$	24.4184	−	10.4899i	0.775286	−	0.333056i
$993$			44.0735i			1.39863i
$994$	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	−0.413238	−	0.910623i	$-0.635602\pi$
$997$	15.7051	−	15.7051i	0.497385	−	0.497385i	0.910623	+	0.413238i	$0.135602\pi$
$998$	−6.86663	+	8.08242i	−0.217359	+	0.255845i
$999$		−	43.8259i		−	1.38659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.q.g.149.1		16
4.3	odd	2		1600.2.q.h.49.7		16
5.2	odd	4		400.2.l.h.101.4		16
5.3	odd	4		80.2.l.a.21.5	✓	16
5.4	even	2		400.2.q.h.149.8		16
15.8	even	4		720.2.t.c.181.4		16
16.3	odd	4		1600.2.q.g.849.2		16
16.13	even	4		400.2.q.h.349.8		16
20.3	even	4		320.2.l.a.241.2		16
20.7	even	4		1600.2.l.i.1201.7		16
20.19	odd	2		1600.2.q.g.49.2		16
40.3	even	4		640.2.l.a.481.7		16
40.13	odd	4		640.2.l.b.481.2		16
60.23	odd	4		2880.2.t.c.2161.2		16
80.3	even	4		320.2.l.a.81.2		16
80.13	odd	4		80.2.l.a.61.5	yes	16
80.19	odd	4		1600.2.q.h.849.7		16
80.29	even	4	inner	400.2.q.g.349.1		16
80.43	even	4		640.2.l.a.161.7		16
80.53	odd	4		640.2.l.b.161.2		16
80.67	even	4		1600.2.l.i.401.7		16
80.77	odd	4		400.2.l.h.301.4		16
160.3	even	8		5120.2.a.u.1.2		8
160.13	odd	8		5120.2.a.v.1.2		8
160.83	even	8		5120.2.a.t.1.7		8
160.93	odd	8		5120.2.a.s.1.7		8
240.83	odd	4		2880.2.t.c.721.3		16
240.173	even	4		720.2.t.c.541.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.5	✓	16	5.3	odd	4
80.2.l.a.61.5	yes	16	80.13	odd	4
320.2.l.a.81.2		16	80.3	even	4
320.2.l.a.241.2		16	20.3	even	4
400.2.l.h.101.4		16	5.2	odd	4
400.2.l.h.301.4		16	80.77	odd	4
400.2.q.g.149.1		16	1.1	even	1	trivial
400.2.q.g.349.1		16	80.29	even	4	inner
400.2.q.h.149.8		16	5.4	even	2
400.2.q.h.349.8		16	16.13	even	4
640.2.l.a.161.7		16	80.43	even	4
640.2.l.a.481.7		16	40.3	even	4
640.2.l.b.161.2		16	80.53	odd	4
640.2.l.b.481.2		16	40.13	odd	4
720.2.t.c.181.4		16	15.8	even	4
720.2.t.c.541.4		16	240.173	even	4
1600.2.l.i.401.7		16	80.67	even	4
1600.2.l.i.1201.7		16	20.7	even	4
1600.2.q.g.49.2		16	20.19	odd	2
1600.2.q.g.849.2		16	16.3	odd	4
1600.2.q.h.49.7		16	4.3	odd	2
1600.2.q.h.849.7		16	80.19	odd	4
2880.2.t.c.721.3		16	240.83	odd	4
2880.2.t.c.2161.2		16	60.23	odd	4
5120.2.a.s.1.7		8	160.93	odd	8
5120.2.a.t.1.7		8	160.83	even	8
5120.2.a.u.1.2		8	160.3	even	8
5120.2.a.v.1.2		8	160.13	odd	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.q (of order \(4\), degree \(2\), not minimal)

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

Introduction

L-functions

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