LMFDB - Embedded newform 400.2.l.f.301.2

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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.4767670494822400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 $ x^12 - 4x^11 + 7x^10 - 4x^9 - 8x^8 + 24x^7 - 38x^6 + 48x^5 - 32x^4 - 32x^3 + 112x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			301.2
Root			$1.22306 - 0.710021i$ of defining polynomial
Character	$\chi$	$=$	400.301
Dual form			400.2.l.f.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22306 + 0.710021i) q^{2} +(1.09156 + 1.09156i) q^{3} +(0.991741 - 1.73679i) q^{4} +(-2.11008 - 0.560012i) q^{6} -0.973926i q^{7} +(0.0202025 + 2.82835i) q^{8} -0.616985i q^{9} +O(q^{10})$	\(q+(-1.22306 + 0.710021i) q^{2} +(1.09156 + 1.09156i) q^{3} +(0.991741 - 1.73679i) q^{4} +(-2.11008 - 0.560012i) q^{6} -0.973926i q^{7} +(0.0202025 + 2.82835i) q^{8} -0.616985i q^{9} +(1.40810 - 1.40810i) q^{11} +(2.97836 - 0.813270i) q^{12} +(4.60317 + 4.60317i) q^{13} +(0.691508 + 1.19117i) q^{14} +(-2.03290 - 3.44490i) q^{16} -0.490104 q^{17} +(0.438072 + 0.754608i) q^{18} +(4.54863 + 4.54863i) q^{19} +(1.06310 - 1.06310i) q^{21} +(-0.722406 + 2.72196i) q^{22} -1.94308i q^{23} +(-3.06527 + 3.10938i) q^{24} +(-8.89828 - 2.36159i) q^{26} +(3.94816 - 3.94816i) q^{27} +(-1.69151 - 0.965882i) q^{28} +(-3.74613 - 3.74613i) q^{29} +4.29021 q^{31} +(4.93230 + 2.76991i) q^{32} +3.07405 q^{33} +(0.599426 - 0.347984i) q^{34} +(-1.07157 - 0.611889i) q^{36} +(-4.55320 + 4.55320i) q^{37} +(-8.79286 - 2.33362i) q^{38} +10.0493i q^{39} +10.1542i q^{41} +(-0.545410 + 2.05506i) q^{42} +(1.79055 - 1.79055i) q^{43} +(-1.04911 - 3.84204i) q^{44} +(1.37963 + 2.37650i) q^{46} -10.0162 q^{47} +(1.54128 - 5.97936i) q^{48} +6.05147 q^{49} +(-0.534979 - 0.534979i) q^{51} +(12.5599 - 3.42960i) q^{52} +(-5.61412 + 5.61412i) q^{53} +(-2.02555 + 7.63211i) q^{54} +(2.75461 - 0.0196757i) q^{56} +9.93022i q^{57} +(7.24157 + 1.92191i) q^{58} +(8.44185 - 8.44185i) q^{59} +(3.01095 + 3.01095i) q^{61} +(-5.24718 + 3.04614i) q^{62} -0.600897 q^{63} +(-7.99918 + 0.114280i) q^{64} +(-3.75974 + 2.18264i) q^{66} +(-7.07504 - 7.07504i) q^{67} +(-0.486056 + 0.851209i) q^{68} +(2.12099 - 2.12099i) q^{69} -0.897891i q^{71} +(1.74505 - 0.0124646i) q^{72} -9.71555i q^{73} +(2.33596 - 8.80170i) q^{74} +(12.4111 - 3.38897i) q^{76} +(-1.37138 - 1.37138i) q^{77} +(-7.13520 - 12.2909i) q^{78} -14.7857 q^{79} +6.76838 q^{81} +(-7.20968 - 12.4192i) q^{82} +(-0.815000 - 0.815000i) q^{83} +(-0.792065 - 2.90071i) q^{84} +(-0.918620 + 3.46128i) q^{86} -8.17827i q^{87} +(4.01105 + 3.95415i) q^{88} -1.12404i q^{89} +(4.48314 - 4.48314i) q^{91} +(-3.37472 - 1.92703i) q^{92} +(4.68303 + 4.68303i) q^{93} +(12.2504 - 7.11174i) q^{94} +(2.36039 + 8.40744i) q^{96} +7.54442 q^{97} +(-7.40130 + 4.29667i) q^{98} +(-0.868775 - 0.868775i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} + 8 q^{8}+O(q^{10}) $ 12 * q - 4 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 + 8 * q^8	$ 12 q - 4 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} + 8 q^{8} - 2 q^{11} - 8 q^{12} + 4 q^{13} + 14 q^{14} + 2 q^{16} + 8 q^{17} - 18 q^{18} - 14 q^{19} - 20 q^{21} - 2 q^{22} - 14 q^{24} - 16 q^{26} + 10 q^{27} - 26 q^{28} - 4 q^{31} + 16 q^{32} - 28 q^{33} - 6 q^{34} + 2 q^{36} - 8 q^{37} - 10 q^{38} - 10 q^{42} - 44 q^{44} - 10 q^{46} - 8 q^{47} + 28 q^{48} + 4 q^{49} + 10 q^{51} + 12 q^{52} + 16 q^{53} + 10 q^{54} + 6 q^{56} + 60 q^{58} + 20 q^{59} + 4 q^{61} + 18 q^{62} + 8 q^{63} + 38 q^{64} + 32 q^{66} - 50 q^{67} + 60 q^{68} + 14 q^{72} + 10 q^{74} + 60 q^{76} + 8 q^{77} - 4 q^{78} + 12 q^{79} - 8 q^{81} - 42 q^{82} + 2 q^{83} + 34 q^{84} + 6 q^{86} - 30 q^{88} + 2 q^{92} + 44 q^{93} + 32 q^{94} - 34 q^{96} - 64 q^{98} + 12 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 + 8 * q^8 - 2 * q^11 - 8 * q^12 + 4 * q^13 + 14 * q^14 + 2 * q^16 + 8 * q^17 - 18 * q^18 - 14 * q^19 - 20 * q^21 - 2 * q^22 - 14 * q^24 - 16 * q^26 + 10 * q^27 - 26 * q^28 - 4 * q^31 + 16 * q^32 - 28 * q^33 - 6 * q^34 + 2 * q^36 - 8 * q^37 - 10 * q^38 - 10 * q^42 - 44 * q^44 - 10 * q^46 - 8 * q^47 + 28 * q^48 + 4 * q^49 + 10 * q^51 + 12 * q^52 + 16 * q^53 + 10 * q^54 + 6 * q^56 + 60 * q^58 + 20 * q^59 + 4 * q^61 + 18 * q^62 + 8 * q^63 + 38 * q^64 + 32 * q^66 - 50 * q^67 + 60 * q^68 + 14 * q^72 + 10 * q^74 + 60 * q^76 + 8 * q^77 - 4 * q^78 + 12 * q^79 - 8 * q^81 - 42 * q^82 + 2 * q^83 + 34 * q^84 + 6 * q^86 - 30 * q^88 + 2 * q^92 + 44 * q^93 + 32 * q^94 - 34 * q^96 - 64 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.22306	+	0.710021i	−0.864832	+	0.502061i
$2$	−1.22306	+	0.710021i	−0.864832	+	0.502061i
$3$	1.09156	+	1.09156i	0.630214	+	0.630214i	0.948122	−	0.317908i	$-0.102980\pi$
$3$	1.09156	+	1.09156i	0.630214	+	0.630214i	−0.317908	+	0.948122i	$0.602980\pi$
$4$	0.991741	−	1.73679i	0.495870	−	0.868396i
$5$		0			0
$5$		0			0
$6$	−2.11008	−	0.560012i	−0.861435	−	0.228624i
$7$		−	0.973926i		−	0.368109i	−0.982916	−	0.184055i	$-0.941078\pi$
$7$		−	0.973926i		−	0.368109i	0.982916	−	0.184055i	$-0.0589224\pi$
$8$	0.0202025	+	2.82835i	0.00714267	+	0.999974i
$9$		−	0.616985i		−	0.205662i
$10$		0			0
$11$	1.40810	−	1.40810i	0.424558	−	0.424558i	−0.462212	−	0.886769i	$-0.652944\pi$
$11$	1.40810	−	1.40810i	0.424558	−	0.424558i	0.886769	+	0.462212i	$0.152944\pi$
$12$	2.97836	−	0.813270i	0.859780	−	0.234771i
$13$	4.60317	+	4.60317i	1.27669	+	1.27669i	0.942510	+	0.334179i	$0.108459\pi$
$13$	4.60317	+	4.60317i	1.27669	+	1.27669i	0.334179	+	0.942510i	$0.391541\pi$
$14$	0.691508	+	1.19117i	0.184813	+	0.318353i
$15$		0			0
$16$	−2.03290	−	3.44490i	−0.508225	−	0.861224i
$17$	−0.490104			−0.118868			−0.0594338	−	0.998232i	$-0.518930\pi$
$17$	−0.490104			−0.118868			−0.0594338	+	0.998232i	$0.518930\pi$
$18$	0.438072	+	0.754608i	0.103255	+	0.177863i
$19$	4.54863	+	4.54863i	1.04353	+	1.04353i	0.999009	+	0.0445187i	$0.0141754\pi$
$19$	4.54863	+	4.54863i	1.04353	+	1.04353i	0.0445187	+	0.999009i	$0.485825\pi$
$20$		0			0
$21$	1.06310	−	1.06310i	0.231988	−	0.231988i
$22$	−0.722406	+	2.72196i	−0.154018	+	0.580325i
$23$		−	1.94308i		−	0.405160i	−0.979266	−	0.202580i	$-0.935067\pi$
$23$		−	1.94308i		−	0.405160i	0.979266	−	0.202580i	$-0.0649325\pi$
$24$	−3.06527	+	3.10938i	−0.625696	+	0.634699i
$25$		0			0
$26$	−8.89828	−	2.36159i	−1.74510	−	0.463147i
$27$	3.94816	−	3.94816i	0.759824	−	0.759824i
$28$	−1.69151	−	0.965882i	−0.319665	−	0.182535i
$29$	−3.74613	−	3.74613i	−0.695640	−	0.695640i	0.267827	−	0.963467i	$-0.413694\pi$
$29$	−3.74613	−	3.74613i	−0.695640	−	0.695640i	−0.963467	+	0.267827i	$0.913694\pi$
$30$		0			0
$31$	4.29021			0.770545			0.385272	−	0.922803i	$-0.374107\pi$
$31$	4.29021			0.770545			0.385272	+	0.922803i	$0.374107\pi$
$32$	4.93230	+	2.76991i	0.871916	+	0.489655i
$33$	3.07405			0.535124
$34$	0.599426	−	0.347984i	0.102801	−	0.0596788i
$35$		0			0
$36$	−1.07157	−	0.611889i	−0.178596	−	0.101982i
$37$	−4.55320	+	4.55320i	−0.748542	+	0.748542i	−0.974205	−	0.225663i	$-0.927545\pi$
$37$	−4.55320	+	4.55320i	−0.748542	+	0.748542i	0.225663	+	0.974205i	$0.427545\pi$
$38$	−8.79286	−	2.33362i	−1.42639	−	0.378562i
$39$			10.0493i			1.60917i
$40$		0			0
$41$			10.1542i			1.58582i	0.609341	+	0.792908i	$0.291434\pi$
$41$			10.1542i			1.58582i	−0.609341	+	0.792908i	$0.708566\pi$
$42$	−0.545410	+	2.05506i	−0.0841586	+	0.317102i
$43$	1.79055	−	1.79055i	0.273057	−	0.273057i	−0.557273	−	0.830329i	$-0.688152\pi$
$43$	1.79055	−	1.79055i	0.273057	−	0.273057i	0.830329	+	0.557273i	$0.188152\pi$
$44$	−1.04911	−	3.84204i	−0.158159	−	0.579210i
$45$		0			0
$46$	1.37963	+	2.37650i	0.203415	+	0.350395i
$47$	−10.0162			−1.46102			−0.730510	−	0.682902i	$-0.760717\pi$
$47$	−10.0162			−1.46102			−0.730510	+	0.682902i	$0.760717\pi$
$48$	1.54128	−	5.97936i	0.222465	−	0.863046i
$49$	6.05147			0.864495
$50$		0			0
$51$	−0.534979	−	0.534979i	−0.0749120	−	0.0749120i
$52$	12.5599	−	3.42960i	1.74174	−	0.475600i
$53$	−5.61412	+	5.61412i	−0.771158	+	0.771158i	−0.978309	−	0.207151i	$-0.933581\pi$
$53$	−5.61412	+	5.61412i	−0.771158	+	0.771158i	0.207151	+	0.978309i	$0.433581\pi$
$54$	−2.02555	+	7.63211i	−0.275643	+	1.03860i
$55$		0			0
$56$	2.75461	−	0.0196757i	0.368100	−	0.00262928i
$57$			9.93022i			1.31529i
$58$	7.24157	+	1.92191i	0.950865	+	0.252359i
$59$	8.44185	−	8.44185i	1.09904	−	1.09904i	0.104512	−	0.994524i	$-0.466672\pi$
$59$	8.44185	−	8.44185i	1.09904	−	1.09904i	0.994524	−	0.104512i	$-0.0333281\pi$
$60$		0			0
$61$	3.01095	+	3.01095i	0.385513	+	0.385513i	0.873084	−	0.487571i	$-0.162117\pi$
$61$	3.01095	+	3.01095i	0.385513	+	0.385513i	−0.487571	+	0.873084i	$0.662117\pi$
$62$	−5.24718	+	3.04614i	−0.666392	+	0.386860i
$63$	−0.600897			−0.0757060
$64$	−7.99918	+	0.114280i	−0.999898	+	0.0142850i
$65$		0			0
$66$	−3.75974	+	2.18264i	−0.462793	+	0.268665i
$67$	−7.07504	−	7.07504i	−0.864354	−	0.864354i	0.127486	−	0.991840i	$-0.459309\pi$
$67$	−7.07504	−	7.07504i	−0.864354	−	0.864354i	−0.991840	+	0.127486i	$0.959309\pi$
$68$	−0.486056	+	0.851209i	−0.0589430	+	0.103224i
$69$	2.12099	−	2.12099i	0.255337	−	0.255337i
$70$		0			0
$71$		−	0.897891i		−	0.106560i	−0.998580	−	0.0532800i	$-0.983032\pi$
$71$		−	0.897891i		−	0.106560i	0.998580	−	0.0532800i	$-0.0169676\pi$
$72$	1.74505	−	0.0124646i	0.205656	−	0.00146897i
$73$		−	9.71555i		−	1.13712i	−0.822642	−	0.568559i	$-0.807501\pi$
$73$		−	9.71555i		−	1.13712i	0.822642	−	0.568559i	$-0.192499\pi$
$74$	2.33596	−	8.80170i	0.271550	−	1.02318i
$75$		0			0
$76$	12.4111	−	3.38897i	1.42365	−	0.388741i
$77$	−1.37138	−	1.37138i	−0.156284	−	0.156284i
$78$	−7.13520	−	12.2909i	−0.807902	−	1.39166i
$79$	−14.7857			−1.66352			−0.831760	−	0.555135i	$-0.812666\pi$
$79$	−14.7857			−1.66352			−0.831760	+	0.555135i	$0.812666\pi$
$80$		0			0
$81$	6.76838			0.752042
$82$	−7.20968	−	12.4192i	−0.796176	−	1.37147i
$83$	−0.815000	−	0.815000i	−0.0894579	−	0.0894579i	0.660962	−	0.750420i	$-0.270149\pi$
$83$	−0.815000	−	0.815000i	−0.0894579	−	0.0894579i	−0.750420	+	0.660962i	$0.770149\pi$
$84$	−0.792065	−	2.90071i	−0.0864214	−	0.316493i
$85$		0			0
$86$	−0.918620	+	3.46128i	−0.0990573	+	0.373239i
$87$		−	8.17827i		−	0.876803i
$88$	4.01105	+	3.95415i	0.427579	+	0.421514i
$89$		−	1.12404i		−	0.119148i	−0.998224	−	0.0595739i	$-0.981026\pi$
$89$		−	1.12404i		−	0.119148i	0.998224	−	0.0595739i	$-0.0189742\pi$
$90$		0			0
$91$	4.48314	−	4.48314i	0.469961	−	0.469961i
$92$	−3.37472	−	1.92703i	−0.351839	−	0.200907i
$93$	4.68303	+	4.68303i	0.485608	+	0.485608i
$94$	12.2504	−	7.11174i	1.26354	−	0.733520i
$95$		0			0
$96$	2.36039	+	8.40744i	0.240906	+	0.858081i
$97$	7.54442			0.766019			0.383010	−	0.923744i	$-0.374888\pi$
$97$	7.54442			0.766019			0.383010	+	0.923744i	$0.374888\pi$
$98$	−7.40130	+	4.29667i	−0.747644	+	0.434029i
$99$	−0.868775	−	0.868775i	−0.0873152	−	0.0873152i
$100$		0			0
$101$	−2.60535	+	2.60535i	−0.259242	+	0.259242i	−0.824746	−	0.565504i	$-0.808682\pi$
$101$	−2.60535	+	2.60535i	−0.259242	+	0.259242i	0.565504	+	0.824746i	$0.308682\pi$
$102$	1.03416	+	0.274464i	0.102397	+	0.0271760i
$103$		−	13.8146i		−	1.36120i	−0.732657	−	0.680598i	$-0.761720\pi$
$103$		−	13.8146i		−	1.36120i	0.732657	−	0.680598i	$-0.238280\pi$
$104$	−12.9264	+	13.1124i	−1.26754	+	1.28577i
$105$		0			0
$106$	2.88025	−	10.8525i	0.279755	−	1.05409i
$107$	9.89124	−	9.89124i	0.956222	−	0.956222i	−0.0428589	−	0.999081i	$-0.513647\pi$
$107$	9.89124	−	9.89124i	0.956222	−	0.956222i	0.999081	+	0.0428589i	$0.0136466\pi$
$108$	−2.94159	−	10.7727i	−0.283054	−	1.03660i
$109$	−11.5454	−	11.5454i	−1.10584	−	1.10584i	−0.993691	−	0.112154i	$-0.964225\pi$
$109$	−11.5454	−	11.5454i	−1.10584	−	1.10584i	−0.112154	−	0.993691i	$-0.535775\pi$
$110$		0			0
$111$	−9.94021			−0.943483
$112$	−3.35507	+	1.97989i	−0.317025	+	0.187082i
$113$	−17.2057			−1.61857			−0.809286	−	0.587415i	$-0.800146\pi$
$113$	−17.2057			−1.61857			−0.809286	+	0.587415i	$0.800146\pi$
$114$	−7.05066	−	12.1452i	−0.660355	−	1.13751i
$115$		0			0
$116$	−10.2215	+	2.79106i	−0.949038	+	0.259144i
$117$	2.84008	−	2.84008i	0.262566	−	0.262566i
$118$	−4.33098	+	16.3188i	−0.398699	+	1.50226i
$119$			0.477325i			0.0437563i
$120$		0			0
$121$			7.03452i			0.639502i
$122$	−5.82041	−	1.54473i	−0.526955	−	0.139853i
$123$	−11.0839	+	11.0839i	−0.999403	+	0.999403i
$124$	4.25478	−	7.45121i	0.382091	−	0.669139i
$125$		0			0
$126$	0.734932	−	0.426650i	0.0654730	−	0.0380090i
$127$	1.37608			0.122107			0.0610535	−	0.998134i	$-0.480554\pi$
$127$	1.37608			0.122107			0.0610535	+	0.998134i	$0.480554\pi$
$128$	9.70232	−	5.81936i	0.857572	−	0.514363i
$129$	3.90900			0.344168
$130$		0			0
$131$	−9.03973	−	9.03973i	−0.789804	−	0.789804i	0.191657	−	0.981462i	$-0.438614\pi$
$131$	−9.03973	−	9.03973i	−0.789804	−	0.789804i	−0.981462	+	0.191657i	$0.938614\pi$
$132$	3.04866	−	5.33899i	0.265352	−	0.464700i
$133$	4.43003	−	4.43003i	0.384132	−	0.384132i
$134$	13.6766	+	3.62976i	1.18148	+	0.313563i
$135$		0			0
$136$	−0.00990133	−	1.38619i	−0.000849032	−	0.118865i
$137$			15.3056i			1.30764i	0.756649	+	0.653822i	$0.226835\pi$
$137$			15.3056i			1.30764i	−0.756649	+	0.653822i	$0.773165\pi$
$138$	−1.08815	+	4.10004i	−0.0926291	+	0.349018i
$139$	−0.346824	+	0.346824i	−0.0294173	+	0.0294173i	−0.721662	−	0.692245i	$-0.756622\pi$
$139$	−0.346824	+	0.346824i	−0.0294173	+	0.0294173i	0.692245	+	0.721662i	$0.256622\pi$
$140$		0			0
$141$	−10.9334	−	10.9334i	−0.920754	−	0.920754i
$142$	0.637521	+	1.09817i	0.0534996	+	0.0921566i
$143$	12.9634			1.08406
$144$	−2.12545	+	1.25427i	−0.177121	+	0.104522i
$145$		0			0
$146$	6.89824	+	11.8827i	0.570902	+	0.983417i
$147$	6.60555	+	6.60555i	0.544817	+	0.544817i
$148$	3.39237	+	12.4236i	0.278851	+	1.02121i
$149$	4.30028	−	4.30028i	0.352293	−	0.352293i	−0.508669	−	0.860962i	$-0.669862\pi$
$149$	4.30028	−	4.30028i	0.352293	−	0.352293i	0.860962	+	0.508669i	$0.169862\pi$
$150$		0			0
$151$		−	2.02102i		−	0.164468i	−0.996613	−	0.0822341i	$-0.973794\pi$
$151$		−	2.02102i		−	0.164468i	0.996613	−	0.0822341i	$-0.0262055\pi$
$152$	−12.7732	+	12.9570i	−1.03605	+	1.05095i
$153$			0.302387i			0.0244465i
$154$	2.65099	+	0.703570i	0.213623	+	0.0566953i
$155$		0			0
$156$	17.4535	+	9.96628i	1.39740	+	0.797941i
$157$	2.93327	+	2.93327i	0.234101	+	0.234101i	0.814402	−	0.580301i	$-0.197065\pi$
$157$	2.93327	+	2.93327i	0.234101	+	0.234101i	−0.580301	+	0.814402i	$0.697065\pi$
$158$	18.0838	−	10.4981i	1.43867	−	0.835188i
$159$	−12.2563			−0.971989
$160$		0			0
$161$	−1.89241			−0.149143
$162$	−8.27811	+	4.80569i	−0.650390	+	0.377570i
$163$	−5.74697	−	5.74697i	−0.450137	−	0.450137i	0.445263	−	0.895400i	$-0.353110\pi$
$163$	−5.74697	−	5.74697i	−0.450137	−	0.450137i	−0.895400	+	0.445263i	$0.853110\pi$
$164$	17.6357	+	10.0703i	1.37712	+	0.786360i
$165$		0			0
$166$	1.57546	+	0.418125i	0.122279	+	0.0324528i
$167$			6.41553i			0.496449i	0.968703	+	0.248224i	$0.0798470\pi$
$167$			6.41553i			0.496449i	−0.968703	+	0.248224i	$0.920153\pi$
$168$	3.02830	+	2.98535i	0.233639	+	0.230325i
$169$			29.3783i			2.25987i
$170$		0			0
$171$	2.80644	−	2.80644i	0.214613	−	0.214613i
$172$	−1.33405	−	4.88558i	−0.101721	−	0.372522i
$173$	−0.545724	−	0.545724i	−0.0414907	−	0.0414907i	0.686057	−	0.727548i	$-0.259340\pi$
$173$	−0.545724	−	0.545724i	−0.0414907	−	0.0414907i	−0.727548	+	0.686057i	$0.759340\pi$
$174$	5.80674	+	10.0025i	0.440208	+	0.758288i
$175$		0			0
$176$	−7.71328	−	1.98823i	−0.581410	−	0.149869i
$177$	18.4296			1.38525
$178$	0.798090	+	1.37476i	0.0598194	+	0.103043i
$179$	−3.57757	−	3.57757i	−0.267400	−	0.267400i	0.560652	−	0.828052i	$-0.310551\pi$
$179$	−3.57757	−	3.57757i	−0.267400	−	0.267400i	−0.828052	+	0.560652i	$0.810551\pi$
$180$		0			0
$181$	−1.64176	+	1.64176i	−0.122031	+	0.122031i	−0.765485	−	0.643454i	$-0.777501\pi$
$181$	−1.64176	+	1.64176i	−0.122031	+	0.122031i	0.643454	+	0.765485i	$0.277501\pi$
$182$	−2.30002	+	8.66627i	−0.170489	+	0.642386i
$183$			6.57328i			0.485911i
$184$	5.49571	−	0.0392550i	0.405149	−	0.00289392i
$185$		0			0
$186$	−9.05267	−	2.40257i	−0.663774	−	0.176165i
$187$	−0.690114	+	0.690114i	−0.0504662	+	0.0504662i
$188$	−9.93352	+	17.3961i	−0.724476	+	1.26874i
$189$	−3.84522	−	3.84522i	−0.279698	−	0.279698i
$190$		0			0
$191$	−15.3359			−1.10967			−0.554835	−	0.831960i	$-0.687219\pi$
$191$	−15.3359			−1.10967			−0.554835	+	0.831960i	$0.687219\pi$
$192$	−8.85635	−	8.60686i	−0.639152	−	0.621147i
$193$	−0.0812703			−0.00584996			−0.00292498	−	0.999996i	$-0.500931\pi$
$193$	−0.0812703			−0.00584996			−0.00292498	+	0.999996i	$0.500931\pi$
$194$	−9.22726	+	5.35669i	−0.662478	+	0.384588i
$195$		0			0
$196$	6.00149	−	10.5101i	0.428678	−	0.750725i
$197$	1.40711	−	1.40711i	0.100252	−	0.100252i	−0.655202	−	0.755454i	$-0.727416\pi$
$197$	1.40711	−	1.40711i	0.100252	−	0.100252i	0.755454	+	0.655202i	$0.227416\pi$
$198$	1.67941	+	0.445714i	0.119351	+	0.0316755i
$199$			14.3046i			1.01402i	0.861939	+	0.507011i	$0.169250\pi$
$199$			14.3046i			1.01402i	−0.861939	+	0.507011i	$0.830750\pi$
$200$		0			0
$201$		−	15.4457i		−	1.08946i
$202$	1.33664	−	5.03635i	0.0940458	−	0.354356i
$203$	−3.64846	+	3.64846i	−0.256071	+	0.256071i
$204$	−1.45971	+	0.398587i	−0.102200	+	0.0279067i
$205$		0			0
$206$	9.80868	+	16.8961i	0.683403	+	1.17721i
$207$	−1.19885			−0.0833258
$208$	6.49966	−	25.2152i	0.450670	−	1.74836i
$209$	12.8098			0.886075
$210$		0			0
$211$	8.70115	+	8.70115i	0.599012	+	0.599012i	0.940050	−	0.341038i	$-0.110778\pi$
$211$	8.70115	+	8.70115i	0.599012	+	0.599012i	−0.341038	+	0.940050i	$0.610778\pi$
$212$	4.18281	+	15.3183i	0.287277	+	1.05207i
$213$	0.980103	−	0.980103i	0.0671556	−	0.0671556i
$214$	−5.07457	+	19.1205i	−0.346891	+	1.30705i
$215$		0			0
$216$	11.2466	+	11.0870i	0.765232	+	0.754378i
$217$		−	4.17835i		−	0.283645i
$218$	22.3181	+	5.92320i	1.51157	+	0.401169i
$219$	10.6051	−	10.6051i	0.716628	−	0.716628i
$220$		0			0
$221$	−2.25603	−	2.25603i	−0.151757	−	0.151757i
$222$	12.1575	−	7.05776i	0.815955	−	0.473686i
$223$	7.78095			0.521051			0.260525	−	0.965467i	$-0.416104\pi$
$223$	7.78095			0.521051			0.260525	+	0.965467i	$0.416104\pi$
$224$	2.69769	−	4.80370i	0.180247	−	0.320961i
$225$		0			0
$226$	21.0435	−	12.2164i	1.39979	−	0.812621i
$227$	2.15443	+	2.15443i	0.142995	+	0.142995i	0.774980	−	0.631986i	$-0.217760\pi$
$227$	2.15443	+	2.15443i	0.142995	+	0.142995i	−0.631986	+	0.774980i	$0.717760\pi$
$228$	17.2467	+	9.84821i	1.14219	+	0.652214i
$229$	−7.63865	+	7.63865i	−0.504776	+	0.504776i	−0.912918	−	0.408142i	$-0.866177\pi$
$229$	−7.63865	+	7.63865i	−0.504776	+	0.504776i	0.408142	+	0.912918i	$0.366177\pi$
$230$		0			0
$231$		−	2.99390i		−	0.196984i
$232$	10.5197	−	10.6711i	0.690653	−	0.700591i
$233$			7.51503i			0.492326i	0.969228	+	0.246163i	$0.0791699\pi$
$233$			7.51503i			0.492326i	−0.969228	+	0.246163i	$0.920830\pi$
$234$	−1.45707	+	5.49010i	−0.0952515	+	0.358899i
$235$		0			0
$236$	−6.28962	−	23.0339i	−0.409419	−	1.49938i
$237$	−16.1395	−	16.1395i	−1.04837	−	1.04837i
$238$	−0.338911	−	0.583796i	−0.0219683	−	0.0378419i
$239$	20.5776			1.33105			0.665526	−	0.746375i	$-0.268207\pi$
$239$	20.5776			1.33105			0.665526	+	0.746375i	$0.268207\pi$
$240$		0			0
$241$	−23.2914			−1.50033			−0.750166	−	0.661250i	$-0.770026\pi$
$241$	−23.2914			−1.50033			−0.750166	+	0.661250i	$0.770026\pi$
$242$	−4.99466	−	8.60362i	−0.321069	−	0.553062i
$243$	−4.45639	−	4.45639i	−0.285877	−	0.285877i
$244$	8.21549	−	2.24332i	0.525943	−	0.143614i
$245$		0			0
$246$	5.68646	−	21.4261i	0.362556	−	1.36608i
$247$			41.8762i			2.66452i
$248$	0.0866731	+	12.1342i	0.00550375	+	0.770525i
$249$		−	1.77925i		−	0.112755i
$250$		0			0
$251$	−3.34230	+	3.34230i	−0.210964	+	0.210964i	−0.804677	−	0.593713i	$-0.797661\pi$
$251$	−3.34230	+	3.34230i	−0.210964	+	0.210964i	0.593713	+	0.804677i	$0.297661\pi$
$252$	−0.595935	+	1.04363i	−0.0375404	+	0.0657428i
$253$	−2.73604	−	2.73604i	−0.172014	−	0.172014i
$254$	−1.68302	+	0.977043i	−0.105602	+	0.0613051i
$255$		0			0
$256$	−7.73464	+	14.0063i	−0.483415	+	0.875391i
$257$	−22.4537			−1.40062			−0.700311	−	0.713838i	$-0.746955\pi$
$257$	−22.4537			−1.40062			−0.700311	+	0.713838i	$0.746955\pi$
$258$	−4.78093	+	2.77547i	−0.297648	+	0.172793i
$259$	4.43448	+	4.43448i	0.275545	+	0.275545i
$260$		0			0
$261$	−2.31131	+	2.31131i	−0.143066	+	0.143066i
$262$	17.4745	+	4.63771i	1.07958	+	0.286519i
$263$			8.23670i			0.507897i	0.967218	+	0.253948i	$0.0817294\pi$
$263$			8.23670i			0.507897i	−0.967218	+	0.253948i	$0.918271\pi$
$264$	0.0621036	+	8.69451i	0.00382221	+	0.535110i
$265$		0			0
$266$	−2.27277	+	8.56359i	−0.139352	+	0.525068i
$267$	1.22696	−	1.22696i	0.0750885	−	0.0750885i
$268$	−19.3045	+	5.27128i	−1.17921	+	0.321994i
$269$	−17.2960	−	17.2960i	−1.05455	−	1.05455i	−0.998423	−	0.0561306i	$-0.982124\pi$
$269$	−17.2960	−	17.2960i	−1.05455	−	1.05455i	−0.0561306	−	0.998423i	$-0.517876\pi$
$270$		0			0
$271$	−12.4753			−0.757822			−0.378911	−	0.925433i	$-0.623701\pi$
$271$	−12.4753			−0.757822			−0.378911	+	0.925433i	$0.623701\pi$
$272$	0.996332	+	1.68836i	0.0604115	+	0.102372i
$273$	9.78726			0.592352
$274$	−10.8673	−	18.7196i	−0.656516	−	1.13089i
$275$		0			0
$276$	−1.58025	−	5.78719i	−0.0951197	−	0.348348i
$277$	10.2583	−	10.2583i	0.616363	−	0.616363i	−0.328234	−	0.944597i	$-0.606453\pi$
$277$	10.2583	−	10.2583i	0.616363	−	0.616363i	0.944597	+	0.328234i	$0.106453\pi$
$278$	0.177934	−	0.670439i	0.0106718	−	0.0402103i
$279$		−	2.64700i		−	0.158472i
$280$		0			0
$281$		−	21.4066i		−	1.27701i	−0.769618	−	0.638505i	$-0.779553\pi$
$281$		−	21.4066i		−	1.27701i	0.769618	−	0.638505i	$-0.220447\pi$
$282$	21.1350	+	5.60922i	1.25857	+	0.334024i
$283$	−7.39635	+	7.39635i	−0.439668	+	0.439668i	−0.891900	−	0.452232i	$-0.850628\pi$
$283$	−7.39635	+	7.39635i	−0.439668	+	0.439668i	0.452232	+	0.891900i	$0.350628\pi$
$284$	−1.55945	−	0.890475i	−0.0925363	−	0.0528400i
$285$		0			0
$286$	−15.8550	+	9.20430i	−0.937526	+	0.544261i
$287$	9.88942			0.583754
$288$	1.70899	−	3.04316i	0.100703	−	0.179320i
$289$	−16.7598			−0.985870
$290$		0			0
$291$	8.23520	+	8.23520i	0.482756	+	0.482756i
$292$	−16.8739	−	9.63531i	−0.987470	−	0.563864i
$293$	−0.556728	+	0.556728i	−0.0325244	+	0.0325244i	−0.723182	−	0.690658i	$-0.757321\pi$
$293$	−0.556728	+	0.556728i	−0.0325244	+	0.0325244i	0.690658	+	0.723182i	$0.257321\pi$
$294$	−12.7691	−	3.38889i	−0.744706	−	0.197644i
$295$		0			0
$296$	−12.9701	−	12.7861i	−0.753870	−	0.743177i
$297$		−	11.1188i		−	0.645178i
$298$	−2.20620	+	8.31278i	−0.127802	+	0.481546i
$299$	8.94430	−	8.94430i	0.517263	−	0.517263i
$300$		0			0
$301$	−1.74387	−	1.74387i	−0.100515	−	0.100515i
$302$	1.43497	+	2.47182i	0.0825730	+	0.142238i
$303$	−5.68781			−0.326756
$304$	6.42266	−	24.9165i	0.368365	−	1.42906i
$305$		0			0
$306$	−0.214701	−	0.369836i	−0.0122736	−	0.0211421i
$307$	9.76852	+	9.76852i	0.557519	+	0.557519i	0.928600	−	0.371082i	$-0.121013\pi$
$307$	9.76852	+	9.76852i	0.557519	+	0.557519i	−0.371082	+	0.928600i	$0.621013\pi$
$308$	−3.74187	+	1.02175i	−0.213213	+	0.0582197i
$309$	15.0795	−	15.0795i	0.857844	−	0.857844i
$310$		0			0
$311$			30.6874i			1.74013i	0.492941	+	0.870063i	$0.335922\pi$
$311$			30.6874i			1.74013i	−0.492941	+	0.870063i	$0.664078\pi$
$312$	−28.4229	+	0.203021i	−1.60913	+	0.0114938i
$313$			1.71127i			0.0967268i	0.998830	+	0.0483634i	$0.0154006\pi$
$313$			1.71127i			0.0967268i	−0.998830	+	0.0483634i	$0.984599\pi$
$314$	−5.67024	−	1.50488i	−0.319990	−	0.0849251i
$315$		0			0
$316$	−14.6636	+	25.6797i	−0.824891	+	1.44460i
$317$	−10.0380	−	10.0380i	−0.563790	−	0.563790i	0.366592	−	0.930382i	$-0.380524\pi$
$317$	−10.0380	−	10.0380i	−0.563790	−	0.563790i	−0.930382	+	0.366592i	$0.880524\pi$
$318$	14.9902	−	8.70224i	0.840608	−	0.487997i
$319$	−10.5498			−0.590678
$320$		0			0
$321$	21.5938			1.20525
$322$	2.31453	−	1.34365i	0.128984	−	0.0748788i
$323$	−2.22930	−	2.22930i	−0.124042	−	0.124042i
$324$	6.71248	−	11.7553i	0.372915	−	0.653070i
$325$		0			0
$326$	11.1093	+	2.94841i	0.615290	+	0.163297i
$327$		−	25.2049i		−	1.39384i
$328$	−28.7196	+	0.205140i	−1.58578	+	0.0113270i
$329$			9.75508i			0.537815i
$330$		0			0
$331$	7.89713	−	7.89713i	0.434066	−	0.434066i	−0.455943	−	0.890009i	$-0.650698\pi$
$331$	7.89713	−	7.89713i	0.434066	−	0.434066i	0.890009	+	0.455943i	$0.150698\pi$
$332$	−2.22376	+	0.607218i	−0.122044	+	0.0333254i
$333$	2.80926	+	2.80926i	0.153946	+	0.153946i
$334$	−4.55516	−	7.84656i	−0.249247	−	0.429345i
$335$		0			0
$336$	−5.82345	−	1.50110i	−0.317695	−	0.0818915i
$337$	−3.46077			−0.188520			−0.0942601	−	0.995548i	$-0.530049\pi$
$337$	−3.46077			−0.188520			−0.0942601	+	0.995548i	$0.530049\pi$
$338$	−20.8592	−	35.9313i	−1.13459	−	1.95441i
$339$	−18.7810	−	18.7810i	−1.02005	−	1.02005i
$340$		0			0
$341$	6.04104	−	6.04104i	0.327141	−	0.327141i
$342$	−1.43981	+	5.42506i	−0.0778558	+	0.293354i
$343$		−	12.7112i		−	0.686338i
$344$	5.10049	+	5.02814i	0.275000	+	0.271099i
$345$		0			0
$346$	1.05493	+	0.279977i	0.0567133	+	0.0150516i
$347$	−17.4637	+	17.4637i	−0.937498	+	0.937498i	−0.998158	−	0.0606600i	$-0.980679\pi$
$347$	−17.4637	+	17.4637i	−0.937498	+	0.937498i	0.0606600	+	0.998158i	$0.480679\pi$
$348$	−14.2040	−	8.11073i	−0.761413	−	0.434781i
$349$	24.2159	+	24.2159i	1.29625	+	1.29625i	0.930852	+	0.365397i	$0.119067\pi$
$349$	24.2159	+	24.2159i	1.29625	+	1.29625i	0.365397	+	0.930852i	$0.380933\pi$
$350$		0			0
$351$	36.3481			1.94012
$352$	10.8455	−	3.04486i	0.578065	−	0.162292i
$353$	−10.7028			−0.569650			−0.284825	−	0.958580i	$-0.591935\pi$
$353$	−10.7028			−0.569650			−0.284825	+	0.958580i	$0.591935\pi$
$354$	−22.5405	+	13.0854i	−1.19801	+	0.695482i
$355$		0			0
$356$	−1.95222	−	1.11475i	−0.103467	−	0.0590818i
$357$	−0.521030	+	0.521030i	−0.0275758	+	0.0275758i
$358$	6.91573	+	1.83543i	0.365507	+	0.0970053i
$359$		−	23.6390i		−	1.24762i	−0.781577	−	0.623809i	$-0.785584\pi$
$359$		−	23.6390i		−	1.24762i	0.781577	−	0.623809i	$-0.214416\pi$
$360$		0			0
$361$			22.3801i			1.17790i
$362$	0.842282	−	3.17364i	0.0442693	−	0.166803i
$363$	−7.67861	+	7.67861i	−0.403023	+	0.403023i
$364$	−3.34017	−	12.2324i	−0.175073	−	0.641152i
$365$		0			0
$366$	−4.66717	−	8.03950i	−0.243957	−	0.420232i
$367$	−13.7431			−0.717386			−0.358693	−	0.933456i	$-0.616777\pi$
$367$	−13.7431			−0.717386			−0.358693	+	0.933456i	$0.616777\pi$
$368$	−6.69370	+	3.95008i	−0.348933	+	0.205912i
$369$	6.26498			0.326142
$370$		0			0
$371$	5.46773	+	5.46773i	0.283871	+	0.283871i
$372$	12.7778	−	3.48910i	0.662499	−	0.180902i
$373$	18.4703	−	18.4703i	0.956355	−	0.956355i	−0.0427313	−	0.999087i	$-0.513606\pi$
$373$	18.4703	−	18.4703i	0.956355	−	0.956355i	0.999087	+	0.0427313i	$0.0136059\pi$
$374$	0.354054	−	1.33405i	0.0183077	−	0.0689819i
$375$		0			0
$376$	−0.202353	−	28.3295i	−0.0104356	−	1.46098i
$377$		−	34.4881i		−	1.77623i
$378$	7.43311	+	1.97274i	0.382318	+	0.101467i
$379$	−16.1028	+	16.1028i	−0.827143	+	0.827143i	−0.987121	−	0.159978i	$-0.948858\pi$
$379$	−16.1028	+	16.1028i	−0.827143	+	0.827143i	0.159978	+	0.987121i	$0.448858\pi$
$380$		0			0
$381$	1.50207	+	1.50207i	0.0769535	+	0.0769535i
$382$	18.7568	−	10.8888i	0.959679	−	0.557122i
$383$	23.1255			1.18166			0.590830	−	0.806796i	$-0.298800\pi$
$383$	23.1255			1.18166			0.590830	+	0.806796i	$0.298800\pi$
$384$	16.9429	+	4.23850i	0.864613	+	0.216295i
$385$		0			0
$386$	0.0993983	−	0.0577036i	0.00505924	−	0.00293704i
$387$	−1.10474	−	1.10474i	−0.0561573	−	0.0561573i
$388$	7.48211	−	13.1031i	0.379846	−	0.665209i
$389$	−19.4044	+	19.4044i	−0.983842	+	0.983842i	−0.999872	−	0.0160295i	$-0.994897\pi$
$389$	−19.4044	+	19.4044i	−0.983842	+	0.983842i	0.0160295	+	0.999872i	$0.494897\pi$
$390$		0			0
$391$			0.952310i			0.0481604i
$392$	0.122255	+	17.1157i	0.00617480	+	0.864473i
$393$		−	19.7348i		−	0.995491i
$394$	−0.721898	+	2.72005i	−0.0363687	+	0.137034i
$395$		0			0
$396$	−2.37048	+	0.647283i	−0.119121	+	0.0325272i
$397$	−4.00102	−	4.00102i	−0.200806	−	0.200806i	0.599540	−	0.800345i	$-0.295350\pi$
$397$	−4.00102	−	4.00102i	−0.200806	−	0.200806i	−0.800345	+	0.599540i	$0.795350\pi$
$398$	−10.1565	−	17.4953i	−0.509101	−	0.876960i
$399$	9.67130			0.484171
$400$		0			0
$401$	38.9287			1.94401			0.972003	−	0.234967i	$-0.0754980\pi$
$401$	38.9287			1.94401			0.972003	+	0.234967i	$0.0754980\pi$
$402$	10.9668	+	18.8910i	0.546973	+	0.942197i
$403$	19.7486	+	19.7486i	0.983746	+	0.983746i
$404$	1.94112	+	7.10879i	0.0965745	+	0.353676i
$405$		0			0
$406$	1.87179	−	7.05275i	0.0928955	−	0.350022i
$407$			12.8227i			0.635598i
$408$	1.50230	−	1.52392i	0.0743750	−	0.0754452i
$409$		−	4.59845i		−	0.227379i	−0.993516	−	0.113689i	$-0.963733\pi$
$409$		−	4.59845i		−	0.227379i	0.993516	−	0.113689i	$-0.0362669\pi$
$410$		0			0
$411$	−16.7070	+	16.7070i	−0.824095	+	0.824095i
$412$	−23.9932	−	13.7005i	−1.18206	−	0.674977i
$413$	−8.22174	−	8.22174i	−0.404565	−	0.404565i
$414$	1.46626	−	0.851208i	0.0720628	−	0.0418346i
$415$		0			0
$416$	9.95386	+	35.4546i	0.488028	+	1.73830i
$417$	−0.757161			−0.0370783
$418$	−15.6672	+	9.09525i	−0.766306	+	0.444863i
$419$	16.6774	+	16.6774i	0.814746	+	0.814746i	0.985341	−	0.170595i	$-0.0545689\pi$
$419$	16.6774	+	16.6774i	0.814746	+	0.814746i	−0.170595	+	0.985341i	$0.554569\pi$
$420$		0			0
$421$	15.4169	−	15.4169i	0.751372	−	0.751372i	−0.223364	−	0.974735i	$-0.571704\pi$
$421$	15.4169	−	15.4169i	0.751372	−	0.751372i	0.974735	+	0.223364i	$0.0717037\pi$
$422$	−16.8200	−	4.46401i	−0.818786	−	0.217305i
$423$			6.17987i			0.300476i
$424$	−15.9921	−	15.7653i	−0.776647	−	0.765631i
$425$		0			0
$426$	−0.502829	+	1.89462i	−0.0243622	+	0.0917945i
$427$	2.93244	−	2.93244i	0.141911	−	0.141911i
$428$	−7.36949	−	26.9886i	−0.356218	−	1.30454i
$429$	14.1504	+	14.1504i	0.683186	+	0.683186i
$430$		0			0
$431$	20.2234			0.974126			0.487063	−	0.873367i	$-0.338068\pi$
$431$	20.2234			0.974126			0.487063	+	0.873367i	$0.338068\pi$
$432$	−21.6272	−	5.57480i	−1.04054	−	0.268218i
$433$	0.676118			0.0324922			0.0162461	−	0.999868i	$-0.494828\pi$
$433$	0.676118			0.0324922			0.0162461	+	0.999868i	$0.494828\pi$
$434$	2.96671	+	5.11036i	0.142407	+	0.245305i
$435$		0			0
$436$	−31.5019	+	8.60189i	−1.50867	+	0.411956i
$437$	8.83834	−	8.83834i	0.422795	−	0.422795i
$438$	−5.44082	+	20.5005i	−0.259972	+	0.979553i
$439$		−	13.3550i		−	0.637400i	−0.947856	−	0.318700i	$-0.896754\pi$
$439$		−	13.3550i		−	0.637400i	0.947856	−	0.318700i	$-0.103246\pi$
$440$		0			0
$441$		−	3.73366i		−	0.177794i
$442$	4.36108	+	1.15743i	0.207436	+	0.0550532i
$443$	28.1262	−	28.1262i	1.33631	−	1.33631i	0.436714	−	0.899600i	$-0.356142\pi$
$443$	28.1262	−	28.1262i	1.33631	−	1.33631i	0.899600	−	0.436714i	$-0.143858\pi$
$444$	−9.85811	+	17.2641i	−0.467845	+	0.819317i
$445$		0			0
$446$	−9.51655	+	5.52464i	−0.450622	+	0.261599i
$447$	9.38805			0.444039
$448$	0.111300	+	7.79061i	0.00525843	+	0.368072i
$449$	−8.37972			−0.395464			−0.197732	−	0.980256i	$-0.563358\pi$
$449$	−8.37972			−0.395464			−0.197732	+	0.980256i	$0.563358\pi$
$450$		0			0
$451$	14.2981	+	14.2981i	0.673271	+	0.673271i
$452$	−17.0635	+	29.8827i	−0.802602	+	1.40556i
$453$	2.20607	−	2.20607i	0.103650	−	0.103650i
$454$	−4.16469	−	1.10530i	−0.195458	−	0.0518745i
$455$		0			0
$456$	−28.0862	+	0.200615i	−1.31526	+	0.00939468i
$457$			5.66561i			0.265026i	0.991181	+	0.132513i	$0.0423046\pi$
$457$			5.66561i			0.265026i	−0.991181	+	0.132513i	$0.957695\pi$
$458$	3.91891	−	14.7661i	0.183119	−	0.689975i
$459$	−1.93501	+	1.93501i	−0.0903186	+	0.0903186i
$460$		0			0
$461$	16.6375	+	16.6375i	0.774887	+	0.774887i	0.978956	−	0.204069i	$-0.0654168\pi$
$461$	16.6375	+	16.6375i	0.774887	+	0.774887i	−0.204069	+	0.978956i	$0.565417\pi$
$462$	2.12573	+	3.66171i	0.0988979	+	0.170358i
$463$	−41.6835			−1.93720			−0.968598	−	0.248631i	$-0.920019\pi$
$463$	−41.6835			−1.93720			−0.968598	+	0.248631i	$0.920019\pi$
$464$	−5.28953	+	20.5206i	−0.245560	+	0.952643i
$465$		0			0
$466$	−5.33583	−	9.19132i	−0.247178	−	0.425780i
$467$	3.11020	+	3.11020i	0.143923	+	0.143923i	0.775397	−	0.631474i	$-0.217550\pi$
$467$	3.11020	+	3.11020i	0.143923	+	0.143923i	−0.631474	+	0.775397i	$0.717550\pi$
$468$	−2.11601	−	7.74926i	−0.0978126	−	0.358210i
$469$	−6.89057	+	6.89057i	−0.318177	+	0.318177i
$470$		0			0
$471$			6.40370i			0.295067i
$472$	24.0471	+	23.7060i	1.10686	+	1.09116i
$473$		−	5.04255i		−	0.231857i
$474$	31.1989	+	8.28016i	1.43301	+	0.380320i
$475$		0			0
$476$	0.829015	+	0.473383i	0.0379978	+	0.0216975i
$477$	3.46383	+	3.46383i	0.158598	+	0.158598i
$478$	−25.1675	+	14.6105i	−1.15114	+	0.668268i
$479$	−8.32325			−0.380299			−0.190149	−	0.981755i	$-0.560897\pi$
$479$	−8.32325			−0.380299			−0.190149	+	0.981755i	$0.560897\pi$
$480$		0			0
$481$	−41.9183			−1.91131
$482$	28.4868	−	16.5374i	1.29754	−	0.753257i
$483$	−2.06569	−	2.06569i	−0.0939920	−	0.0939920i
$484$	12.2175	+	6.97642i	0.555341	+	0.317110i
$485$		0			0
$486$	8.61455	+	2.28629i	0.390764	+	0.103708i
$487$		−	7.29577i		−	0.330603i	−0.986243	−	0.165301i	$-0.947140\pi$
$487$		−	7.29577i		−	0.330603i	0.986243	−	0.165301i	$-0.0528597\pi$
$488$	−8.45521	+	8.57687i	−0.382750	+	0.388257i
$489$		−	12.5463i		−	0.567365i
$490$		0			0
$491$	3.57528	−	3.57528i	0.161350	−	0.161350i	−0.621815	−	0.783165i	$-0.713604\pi$
$491$	3.57528	−	3.57528i	0.161350	−	0.161350i	0.783165	+	0.621815i	$0.213604\pi$
$492$	8.25810	+	30.2429i	0.372304	+	1.36345i
$493$	1.83600	+	1.83600i	0.0826891	+	0.0826891i
$494$	−29.7330	−	51.2170i	−1.33775	−	2.30436i
$495$		0			0
$496$	−8.72157	−	14.7793i	−0.391610	−	0.663612i
$497$	−0.874479			−0.0392257
$498$	1.26330	+	2.17612i	0.0566099	+	0.0975143i
$499$	−10.8833	−	10.8833i	−0.487203	−	0.487203i	0.420220	−	0.907422i	$-0.361953\pi$
$499$	−10.8833	−	10.8833i	−0.487203	−	0.487203i	−0.907422	+	0.420220i	$0.861953\pi$
$500$		0			0
$501$	−7.00295	+	7.00295i	−0.312869	+	0.312869i
$502$	1.71472	−	6.46093i	0.0765318	−	0.288365i
$503$			29.3781i			1.30991i	0.755670	+	0.654953i	$0.227312\pi$
$503$			29.3781i			1.30991i	−0.755670	+	0.654953i	$0.772688\pi$
$504$	−0.0121396	−	1.69955i	−0.000540742	−	0.0757040i
$505$		0			0
$506$	5.28899	+	1.40369i	0.235124	+	0.0624017i
$507$	−32.0682	+	32.0682i	−1.42420	+	1.42420i
$508$	1.36471	−	2.38996i	0.0605493	−	0.106037i
$509$	17.4592	+	17.4592i	0.773863	+	0.773863i	0.978780	−	0.204916i	$-0.0656922\pi$
$509$	17.4592	+	17.4592i	0.773863	+	0.773863i	−0.204916	+	0.978780i	$0.565692\pi$
$510$		0			0
$511$	−9.46222			−0.418584
$512$	−0.484827	−	22.6222i	−0.0214265	−	0.999770i
$513$	35.9175			1.58579
$514$	27.4621	−	15.9426i	1.21130	−	0.703197i
$515$		0			0
$516$	3.87671	−	6.78912i	0.170663	−	0.298874i
$517$	−14.1039	+	14.1039i	−0.620287	+	0.620287i
$518$	−8.57221	−	2.27505i	−0.376641	−	0.0999602i
$519$		−	1.19138i		−	0.0522959i
$520$		0			0
$521$		−	9.48578i		−	0.415580i	−0.978174	−	0.207790i	$-0.933373\pi$
$521$		−	9.48578i		−	0.415580i	0.978174	−	0.207790i	$-0.0666270\pi$
$522$	1.18579	−	4.46794i	0.0519005	−	0.195556i
$523$	16.2705	−	16.2705i	0.711460	−	0.711460i	−0.255380	−	0.966841i	$-0.582201\pi$
$523$	16.2705	−	16.2705i	0.711460	−	0.711460i	0.966841	+	0.255380i	$0.0822006\pi$
$524$	−24.6652	+	6.73507i	−1.07750	+	0.294223i
$525$		0			0
$526$	−5.84823	−	10.0740i	−0.254995	−	0.439246i
$527$	−2.10265			−0.0915929
$528$	−6.24924	−	10.5898i	−0.271963	−	0.460862i
$529$	19.2245			0.835846
$530$		0			0
$531$	−5.20849	−	5.20849i	−0.226029	−	0.226029i
$532$	−3.30060	−	12.0875i	−0.143099	−	0.524059i
$533$	−46.7414	+	46.7414i	−2.02459	+	2.02459i
$534$	−0.629474	+	2.37180i	−0.0272400	+	0.102638i
$535$		0			0
$536$	19.8678	−	20.1537i	0.858158	−	0.870506i
$537$		−	7.81028i		−	0.337039i
$538$	33.4345	+	8.87348i	1.44146	+	0.382563i
$539$	8.52106	−	8.52106i	0.367028	−	0.367028i
$540$		0			0
$541$	−2.55686	−	2.55686i	−0.109928	−	0.109928i	0.650003	−	0.759931i	$-0.274767\pi$
$541$	−2.55686	−	2.55686i	−0.109928	−	0.109928i	−0.759931	+	0.650003i	$0.774767\pi$
$542$	15.2580	−	8.85774i	0.655389	−	0.380472i
$543$	−3.58416			−0.153811
$544$	−2.41734	−	1.35754i	−0.103643	−	0.0582042i
$545$		0			0
$546$	−11.9704	+	6.94915i	−0.512285	+	0.297396i
$547$	−21.9660	−	21.9660i	−0.939197	−	0.939197i	0.0590579	−	0.998255i	$-0.481190\pi$
$547$	−21.9660	−	21.9660i	−0.939197	−	0.939197i	−0.998255	+	0.0590579i	$0.981190\pi$
$548$	26.5826	+	15.1792i	1.13555	+	0.648422i
$549$	1.85771	−	1.85771i	0.0792852	−	0.0792852i
$550$		0			0
$551$		−	34.0796i		−	1.45184i
$552$	6.04176	+	5.95606i	0.257154	+	0.253507i
$553$			14.4002i			0.612357i
$554$	−5.26290	+	19.8301i	−0.223599	+	0.842502i
$555$		0			0
$556$	0.258402	+	0.946322i	0.0109587	+	0.0401330i
$557$	17.5409	+	17.5409i	0.743234	+	0.743234i	0.973199	−	0.229965i	$-0.0738612\pi$
$557$	17.5409	+	17.5409i	0.743234	+	0.743234i	−0.229965	+	0.973199i	$0.573861\pi$
$558$	1.87942	+	3.23743i	0.0795623	+	0.137051i
$559$	16.4844			0.697217
$560$		0			0
$561$	−1.50661			−0.0636089
$562$	15.1991	+	26.1815i	0.641136	+	1.10440i
$563$	27.5975	+	27.5975i	1.16309	+	1.16309i	0.983794	+	0.179300i	$0.0573833\pi$
$563$	27.5975	+	27.5975i	1.16309	+	1.16309i	0.179300	+	0.983794i	$0.442617\pi$
$564$	−29.8320	+	8.14592i	−1.25615	+	0.343005i
$565$		0			0
$566$	3.79460	−	14.2977i	0.159499	−	0.600979i
$567$		−	6.59190i		−	0.276834i
$568$	2.53955	−	0.0181396i	0.106557	−	0.000761123i
$569$		−	23.6390i		−	0.990998i	−0.868608	−	0.495499i	$-0.834985\pi$
$569$		−	23.6390i		−	0.990998i	0.868608	−	0.495499i	$-0.165015\pi$
$570$		0			0
$571$	−21.7518	+	21.7518i	−0.910284	+	0.910284i	−0.996294	−	0.0860105i	$-0.972588\pi$
$571$	−21.7518	+	21.7518i	−0.910284	+	0.910284i	0.0860105	+	0.996294i	$0.472588\pi$
$572$	12.8564	−	22.5148i	0.537551	−	0.941390i
$573$	−16.7401	−	16.7401i	−0.699329	−	0.699329i
$574$	−12.0953	+	7.02169i	−0.504850	+	0.293080i
$575$		0			0
$576$	0.0705089	+	4.93537i	0.00293787	+	0.205641i
$577$	−3.69585			−0.153860			−0.0769302	−	0.997036i	$-0.524512\pi$
$577$	−3.69585			−0.153860			−0.0769302	+	0.997036i	$0.524512\pi$
$578$	20.4982	−	11.8998i	0.852613	−	0.494967i
$579$	−0.0887116	−	0.0887116i	−0.00368673	−	0.00368673i
$580$		0			0
$581$	−0.793750	+	0.793750i	−0.0329303	+	0.0329303i
$582$	−15.9193	−	4.22496i	−0.659876	−	0.175130i
$583$			15.8105i			0.654802i
$584$	27.4790	−	0.196278i	1.13709	−	0.00812206i
$585$		0			0
$586$	0.285622	−	1.07620i	0.0117989	−	0.0444573i
$587$	27.0313	−	27.0313i	1.11570	−	1.11570i	0.123335	−	0.992365i	$-0.460641\pi$
$587$	27.0313	−	27.0313i	1.11570	−	1.11570i	0.992365	−	0.123335i	$-0.0393590\pi$
$588$	18.0235	−	4.92148i	0.743276	−	0.202958i
$589$	19.5146	+	19.5146i	0.804085	+	0.804085i
$590$		0			0
$591$	3.07189			0.126361
$592$	24.9415	+	6.42912i	1.02509	+	0.264235i
$593$	−4.55524			−0.187061			−0.0935306	−	0.995616i	$-0.529815\pi$
$593$	−4.55524			−0.187061			−0.0935306	+	0.995616i	$0.529815\pi$
$594$	7.89458	+	13.5989i	0.323919	+	0.557971i
$595$		0			0
$596$	−3.20393	−	11.7335i	−0.131238	−	0.480621i
$597$	−15.6143	+	15.6143i	−0.639051	+	0.639051i
$598$	−4.58876	+	17.2900i	−0.187648	+	0.707043i
$599$		−	7.46846i		−	0.305153i	−0.988292	−	0.152576i	$-0.951243\pi$
$599$		−	7.46846i		−	0.305153i	0.988292	−	0.152576i	$-0.0487570\pi$
$600$		0			0
$601$			12.2638i			0.500250i	0.968214	+	0.250125i	$0.0804717\pi$
$601$			12.2638i			0.500250i	−0.968214	+	0.250125i	$0.919528\pi$
$602$	3.37103	+	0.894668i	0.137393	+	0.0364639i
$603$	−4.36519	+	4.36519i	−0.177764	+	0.177764i
$604$	−3.51009	−	2.00433i	−0.142824	−	0.0815550i
$605$		0			0
$606$	6.95652	−	4.03846i	0.282589	−	0.164051i
$607$	5.23884			0.212638			0.106319	−	0.994332i	$-0.466094\pi$
$607$	5.23884			0.212638			0.106319	+	0.994332i	$0.466094\pi$
$608$	9.83593	+	35.0345i	0.398900	+	1.42084i
$609$	−7.96503			−0.322759
$610$		0			0
$611$	−46.1064	−	46.1064i	−1.86527	−	1.86527i
$612$	0.525183	+	0.299889i	0.0212293	+	0.0121223i
$613$	20.7209	−	20.7209i	0.836910	−	0.836910i	−0.151541	−	0.988451i	$-0.548424\pi$
$613$	20.7209	−	20.7209i	0.836910	−	0.836910i	0.988451	+	0.151541i	$0.0484235\pi$
$614$	−18.8833	−	5.01161i	−0.762068	−	0.202252i
$615$		0			0
$616$	3.85105	−	3.90646i	0.155163	−	0.157396i
$617$		−	2.20286i		−	0.0886838i	−0.999016	−	0.0443419i	$-0.985881\pi$
$617$		−	2.20286i		−	0.0886838i	0.999016	−	0.0443419i	$-0.0141191\pi$
$618$	−7.73636	+	29.1499i	−0.311202	+	1.17258i
$619$	−31.4569	+	31.4569i	−1.26436	+	1.26436i	−0.315404	+	0.948958i	$0.602140\pi$
$619$	−31.4569	+	31.4569i	−1.26436	+	1.26436i	−0.948958	+	0.315404i	$0.897860\pi$
$620$		0			0
$621$	−7.67158	−	7.67158i	−0.307850	−	0.307850i
$622$	−21.7887	−	37.5325i	−0.873648	−	1.50492i
$623$	−1.09473			−0.0438594
$624$	34.6187	−	20.4292i	1.38586	−	0.817822i
$625$		0			0
$626$	−1.21504	−	2.09298i	−0.0485627	−	0.0836525i
$627$	13.9827	+	13.9827i	0.558416	+	0.558416i
$628$	8.00353	−	2.18544i	0.319376	−	0.0872085i
$629$	2.23154	−	2.23154i	0.0889775	−	0.0889775i
$630$		0			0
$631$		−	16.8215i		−	0.669655i	−0.942279	−	0.334828i	$-0.891322\pi$
$631$		−	16.8215i		−	0.669655i	0.942279	−	0.334828i	$-0.108678\pi$
$632$	−0.298708	−	41.8192i	−0.0118820	−	1.66348i
$633$			18.9957i			0.755011i
$634$	19.4042	+	5.14986i	0.770640	+	0.204527i
$635$		0			0
$636$	−12.1551	+	21.2867i	−0.481981	+	0.844072i
$637$	27.8559	+	27.8559i	1.10369	+	1.10369i
$638$	12.9031	−	7.49061i	0.510838	−	0.296556i
$639$	−0.553985			−0.0219153
$640$		0			0
$641$	−14.9208			−0.589336			−0.294668	−	0.955600i	$-0.595209\pi$
$641$	−14.9208			−0.589336			−0.294668	+	0.955600i	$0.595209\pi$
$642$	−26.4105	+	15.3320i	−1.04234	+	0.605108i
$643$	−0.541845	−	0.541845i	−0.0213683	−	0.0213683i	0.696342	−	0.717710i	$-0.254810\pi$
$643$	−0.541845	−	0.541845i	−0.0213683	−	0.0213683i	−0.717710	+	0.696342i	$0.754810\pi$
$644$	−1.87678	+	3.28673i	−0.0739556	+	0.129515i
$645$		0			0
$646$	4.30942	+	1.14371i	0.169552	+	0.0449988i
$647$		−	32.6391i		−	1.28318i	−0.767049	−	0.641588i	$-0.778276\pi$
$647$		−	32.6391i		−	1.28318i	0.767049	−	0.641588i	$-0.221724\pi$
$648$	0.136738	+	19.1434i	0.00537158	+	0.752023i
$649$		−	23.7739i		−	0.933208i
$650$		0			0
$651$	4.56093	−	4.56093i	0.178757	−	0.178757i
$652$	−15.6808	+	4.28179i	−0.614108	+	0.167688i
$653$	9.73805	+	9.73805i	0.381079	+	0.381079i	0.871491	−	0.490412i	$-0.163154\pi$
$653$	9.73805	+	9.73805i	0.381079	+	0.381079i	−0.490412	+	0.871491i	$0.663154\pi$
$654$	17.8960	+	30.8271i	0.699790	+	1.20544i
$655$		0			0
$656$	34.9801	−	20.6424i	1.36574	−	0.805952i
$657$	−5.99434			−0.233862
$658$	−6.92631	−	11.9310i	−0.270016	−	0.465120i
$659$	1.26445	+	1.26445i	0.0492560	+	0.0492560i	0.731306	−	0.682050i	$-0.238911\pi$
$659$	1.26445	+	1.26445i	0.0492560	+	0.0492560i	−0.682050	+	0.731306i	$0.738911\pi$
$660$		0			0
$661$	22.6701	−	22.6701i	0.881763	−	0.881763i	−0.111951	−	0.993714i	$-0.535710\pi$
$661$	22.6701	−	22.6701i	0.881763	−	0.881763i	0.993714	+	0.111951i	$0.0357099\pi$
$662$	−4.05152	+	15.2658i	−0.157467	+	0.593321i
$663$		−	4.92519i		−	0.191279i
$664$	2.28865	−	2.32158i	0.0888167	−	0.0900946i
$665$		0			0
$666$	−5.43052	−	1.44125i	−0.210428	−	0.0558474i
$667$	−7.27903	+	7.27903i	−0.281845	+	0.281845i
$668$	11.1424	+	6.36254i	0.431114	+	0.246174i
$669$	8.49339	+	8.49339i	0.328373	+	0.328373i
$670$		0			0
$671$	8.47943			0.327345
$672$	8.18822	−	2.29884i	0.315868	−	0.0886798i
$673$	3.58765			0.138294			0.0691469	−	0.997606i	$-0.477972\pi$
$673$	3.58765			0.138294			0.0691469	+	0.997606i	$0.477972\pi$
$674$	4.23273	−	2.45722i	0.163038	−	0.0946486i
$675$		0			0
$676$	51.0240	+	29.1356i	1.96246	+	1.12060i
$677$	10.1507	−	10.1507i	0.390124	−	0.390124i	−0.484608	−	0.874731i	$-0.661038\pi$
$677$	10.1507	−	10.1507i	0.390124	−	0.390124i	0.874731	+	0.484608i	$0.161038\pi$
$678$	36.3052	+	9.63537i	1.39429	+	0.370044i
$679$		−	7.34770i		−	0.281979i
$680$		0			0
$681$			4.70339i			0.180234i
$682$	−3.09928	+	11.6778i	−0.118677	+	0.447166i
$683$	16.6805	−	16.6805i	0.638260	−	0.638260i	−0.311866	−	0.950126i	$-0.600954\pi$
$683$	16.6805	−	16.6805i	0.638260	−	0.638260i	0.950126	+	0.311866i	$0.100954\pi$
$684$	−2.09094	−	7.65745i	−0.0799491	−	0.292790i
$685$		0			0
$686$	9.02519	+	15.5465i	0.344583	+	0.593568i
$687$	−16.6761			−0.636234
$688$	−9.80828	−	2.52826i	−0.373937	−	0.0963889i
$689$	−51.6854			−1.96906
$690$		0			0
$691$	12.4781	+	12.4781i	0.474689	+	0.474689i	0.903428	−	0.428739i	$-0.141042\pi$
$691$	12.4781	+	12.4781i	0.474689	+	0.474689i	−0.428739	+	0.903428i	$0.641042\pi$
$692$	−1.48903	+	0.406593i	−0.0566043	+	0.0154563i
$693$	−0.846123	+	0.846123i	−0.0321415	+	0.0321415i
$694$	8.95951	−	33.7586i	0.340098	−	1.28146i
$695$		0			0
$696$	23.1311	−	0.165222i	0.876781	−	0.00626271i
$697$		−	4.97661i		−	0.188502i
$698$	−46.8113	−	12.4237i	−1.77183	−	0.470243i
$699$	−8.20312	+	8.20312i	−0.310271	+	0.310271i
$700$		0			0
$701$	6.40945	+	6.40945i	0.242082	+	0.242082i	0.817711	−	0.575629i	$-0.195243\pi$
$701$	6.40945	+	6.40945i	0.242082	+	0.242082i	−0.575629	+	0.817711i	$0.695243\pi$
$702$	−44.4558	+	25.8079i	−1.67788	+	0.974057i
$703$	−41.4217			−1.56225
$704$	−11.1027	+	11.4246i	−0.418449	+	0.430579i
$705$		0			0
$706$	13.0901	−	7.59918i	0.492652	−	0.285999i
$707$	2.53742	+	2.53742i	0.0954295	+	0.0954295i
$708$	18.2774	−	32.0084i	0.686907	−	1.20295i
$709$	8.78514	−	8.78514i	0.329933	−	0.329933i	−0.522628	−	0.852561i	$-0.675048\pi$
$709$	8.78514	−	8.78514i	0.329933	−	0.329933i	0.852561	+	0.522628i	$0.175048\pi$
$710$		0			0
$711$			9.12255i			0.342122i
$712$	3.17918	−	0.0227084i	0.119145	−	0.000851033i
$713$		−	8.33621i		−	0.312194i
$714$	0.267308	−	1.00719i	0.0100037	−	0.0376932i
$715$		0			0
$716$	−9.76152	+	2.66548i	−0.364805	+	0.0996135i
$717$	22.4617	+	22.4617i	0.838847	+	0.838847i
$718$	16.7842	+	28.9119i	0.626380	+	1.07898i
$719$	46.2329			1.72420			0.862099	−	0.506740i	$-0.169150\pi$
$719$	46.2329			1.72420			0.862099	+	0.506740i	$0.169150\pi$
$720$		0			0
$721$	−13.4544			−0.501069
$722$	−15.8903	−	27.3721i	−0.591376	−	1.01868i
$723$	−25.4240	−	25.4240i	−0.945530	−	0.945530i
$724$	1.22319	+	4.47959i	0.0454596	+	0.166483i
$725$		0			0
$726$	3.93941	−	14.8434i	0.146205	−	0.550889i
$727$			17.4640i			0.647703i	0.946108	+	0.323852i	$0.104978\pi$
$727$			17.4640i			0.647703i	−0.946108	+	0.323852i	$0.895022\pi$
$728$	12.7705	+	12.5893i	0.473306	+	0.466592i
$729$		−	30.0340i		−	1.11237i
$730$		0			0
$731$	−0.877557	+	0.877557i	−0.0324576	+	0.0324576i
$732$	11.4164	+	6.51899i	0.421963	+	0.240949i
$733$	7.89695	+	7.89695i	0.291680	+	0.291680i	0.837744	−	0.546063i	$-0.183874\pi$
$733$	7.89695	+	7.89695i	0.291680	+	0.291680i	−0.546063	+	0.837744i	$0.683874\pi$
$734$	16.8086	−	9.75791i	0.620419	−	0.360171i
$735$		0			0
$736$	5.38214	−	9.58384i	0.198388	−	0.353265i
$737$	−19.9247			−0.733936
$738$	−7.66243	+	4.44826i	−0.282058	+	0.163743i
$739$	26.1724	+	26.1724i	0.962769	+	0.962769i	0.999331	−	0.0365624i	$-0.0116408\pi$
$739$	26.1724	+	26.1724i	0.962769	+	0.962769i	−0.0365624	+	0.999331i	$0.511641\pi$
$740$		0			0
$741$	−45.7105	+	45.7105i	−1.67922	+	1.67922i
$742$	−10.5696	−	2.80515i	−0.388021	−	0.102980i
$743$		−	49.7660i		−	1.82574i	−0.408254	−	0.912868i	$-0.633862\pi$
$743$		−	49.7660i		−	1.82574i	0.408254	−	0.912868i	$-0.366138\pi$
$744$	−13.1507	+	13.3399i	−0.482127	+	0.489064i
$745$		0			0
$746$	−9.47594	+	35.7045i	−0.346939	+	1.30724i
$747$	−0.502843	+	0.502843i	−0.0183981	+	0.0183981i
$748$	0.514171	+	1.88300i	0.0188000	+	0.0688493i
$749$	−9.63333	−	9.63333i	−0.351994	−	0.351994i
$750$		0			0
$751$	−24.2379			−0.884454			−0.442227	−	0.896903i	$-0.645811\pi$
$751$	−24.2379			−0.884454			−0.442227	+	0.896903i	$0.645811\pi$
$752$	20.3620	+	34.5049i	0.742527	+	1.25827i
$753$	−7.29665			−0.265905
$754$	24.4873	+	42.1810i	0.891775	+	1.53614i
$755$		0			0
$756$	−10.4918	+	2.86489i	−0.381583	+	0.104195i
$757$	−15.4872	+	15.4872i	−0.562890	+	0.562890i	−0.930127	−	0.367237i	$-0.880304\pi$
$757$	−15.4872	+	15.4872i	−0.562890	+	0.562890i	0.367237	+	0.930127i	$0.380304\pi$
$758$	8.26131	−	31.1279i	0.300064	−	1.13062i
$759$		−	5.97312i		−	0.216811i
$760$		0			0
$761$		−	25.9821i		−	0.941849i	−0.882174	−	0.470924i	$-0.843920\pi$
$761$		−	25.9821i		−	0.941849i	0.882174	−	0.470924i	$-0.156080\pi$
$762$	−2.90363	−	0.770619i	−0.105187	−	0.0279166i
$763$	−11.2443	+	11.2443i	−0.407072	+	0.407072i
$764$	−15.2093	+	26.6354i	−0.550253	+	0.963634i
$765$		0			0
$766$	−28.2839	+	16.4196i	−1.02194	+	0.593265i
$767$	77.7185			2.80625
$768$	−23.7315	+	6.84587i	−0.856338	+	0.247029i
$769$	−24.9737			−0.900573			−0.450287	−	0.892884i	$-0.648678\pi$
$769$	−24.9737			−0.900573			−0.450287	+	0.892884i	$0.648678\pi$
$770$		0			0
$771$	−24.5096	−	24.5096i	−0.882691	−	0.882691i
$772$	−0.0805991	+	0.141150i	−0.00290082	+	0.00508009i
$773$	−1.32495	+	1.32495i	−0.0476550	+	0.0476550i	−0.730533	−	0.682878i	$-0.760728\pi$
$773$	−1.32495	+	1.32495i	−0.0476550	+	0.0476550i	0.682878	+	0.730533i	$0.260728\pi$
$774$	2.13556	+	0.566775i	0.0767610	+	0.0203723i
$775$		0			0
$776$	0.152416	+	21.3383i	0.00547142	+	0.766000i
$777$			9.68103i			0.347305i
$778$	9.95518	−	37.5102i	0.356910	−	1.34481i
$779$	−46.1876	+	46.1876i	−1.65484	+	1.65484i
$780$		0			0
$781$	−1.26432	−	1.26432i	−0.0452409	−	0.0452409i
$782$	−0.676160	−	1.16473i	−0.0241794	−	0.0416507i
$783$	−29.5807			−1.05713
$784$	−12.3020	−	20.8467i	−0.439358	−	0.744525i
$785$		0			0
$786$	14.0121	+	24.1369i	0.499797	+	0.860933i
$787$	0.647036	+	0.647036i	0.0230644	+	0.0230644i	0.718545	−	0.695481i	$-0.244808\pi$
$787$	0.647036	+	0.647036i	0.0230644	+	0.0230644i	−0.695481	+	0.718545i	$0.744808\pi$
$788$	−1.04837	−	3.83934i	−0.0373466	−	0.136771i
$789$	−8.99087	+	8.99087i	−0.320084	+	0.320084i
$790$		0			0
$791$			16.7570i			0.595811i
$792$	2.43965	−	2.47476i	0.0866893	−	0.0879366i
$793$			27.7198i			0.984360i
$794$	7.73429	+	2.05267i	0.274480	+	0.0728466i
$795$		0			0
$796$	24.8440	+	14.1864i	0.880574	+	0.502824i
$797$	18.3024	+	18.3024i	0.648303	+	0.648303i	0.952583	−	0.304280i	$-0.0984158\pi$
$797$	18.3024	+	18.3024i	0.648303	+	0.648303i	−0.304280	+	0.952583i	$0.598416\pi$
$798$	−11.8286	+	6.86682i	−0.418727	+	0.243083i
$799$	4.90900			0.173668
$800$		0			0
$801$	−0.693514			−0.0245041
$802$	−47.6121	+	27.6402i	−1.68124	+	0.976009i
$803$	−13.6804	−	13.6804i	−0.482772	−	0.482772i
$804$	−26.8260	−	15.3181i	−0.946079	−	0.540229i
$805$		0			0
$806$	−38.1755	−	10.1317i	−1.34468	−	0.356875i
$807$		−	37.7593i		−	1.32919i
$808$	−7.42150	−	7.31623i	−0.261087	−	0.257384i
$809$		−	32.4845i		−	1.14209i	−0.820917	−	0.571047i	$-0.806537\pi$
$809$		−	32.4845i		−	1.14209i	0.820917	−	0.571047i	$-0.193463\pi$
$810$		0			0
$811$	7.69149	−	7.69149i	0.270085	−	0.270085i	−0.559049	−	0.829134i	$-0.688834\pi$
$811$	7.69149	−	7.69149i	0.270085	−	0.270085i	0.829134	+	0.559049i	$0.188834\pi$
$812$	2.71829	+	9.95494i	0.0953933	+	0.349350i
$813$	−13.6176	−	13.6176i	−0.477590	−	0.477590i
$814$	−9.10440	−	15.6829i	−0.319109	−	0.549686i
$815$		0			0
$816$	−0.755389	+	2.93051i	−0.0264439	+	0.102588i
$817$	16.2891			0.569884
$818$	3.26499	+	5.62417i	0.114158	+	0.196644i
$819$	−2.76603	−	2.76603i	−0.0966529	−	0.0966529i
$820$		0			0
$821$	−10.5798	+	10.5798i	−0.369238	+	0.369238i	−0.867199	−	0.497961i	$-0.834082\pi$
$821$	−10.5798	+	10.5798i	−0.369238	+	0.369238i	0.497961	+	0.867199i	$0.334082\pi$
$822$	8.57130	−	32.2959i	0.298958	−	1.12645i
$823$			4.85817i			0.169345i	0.996409	+	0.0846726i	$0.0269844\pi$
$823$			4.85817i			0.169345i	−0.996409	+	0.0846726i	$0.973016\pi$
$824$	39.0727	−	0.279090i	1.36116	−	0.00972257i
$825$		0			0
$826$	15.8933	+	4.21806i	0.552997	+	0.146765i
$827$	8.02757	−	8.02757i	0.279146	−	0.279146i	−0.553622	−	0.832768i	$-0.686755\pi$
$827$	8.02757	−	8.02757i	0.279146	−	0.279146i	0.832768	+	0.553622i	$0.186755\pi$
$828$	−1.18895	+	2.08215i	−0.0413188	+	0.0723598i
$829$	−24.3613	−	24.3613i	−0.846102	−	0.846102i	0.143542	−	0.989644i	$-0.454151\pi$
$829$	−24.3613	−	24.3613i	−0.846102	−	0.846102i	−0.989644	+	0.143542i	$0.954151\pi$
$830$		0			0
$831$	22.3952			0.776881
$832$	−37.3476	−	36.2955i	−1.29480	−	1.25832i
$833$	−2.96585			−0.102761
$834$	0.926051	−	0.537600i	0.0320665	−	0.0186156i
$835$		0			0
$836$	12.7040	−	22.2480i	0.439378	−	0.769464i
$837$	16.9385	−	16.9385i	0.585479	−	0.585479i
$838$	−32.2388	−	8.55615i	−1.11367	−	0.295567i
$839$			43.1207i			1.48869i	0.667794	+	0.744346i	$0.267239\pi$
$839$			43.1207i			1.48869i	−0.667794	+	0.744346i	$0.732761\pi$
$840$		0			0
$841$		−	0.932964i		−	0.0321712i
$842$	−7.90942	+	29.8020i	−0.272577	+	1.02704i
$843$	23.3666	−	23.3666i	0.804789	−	0.804789i
$844$	23.7414	−	6.48281i	0.817213	−	0.223148i
$845$		0			0
$846$	−4.38784	−	7.55834i	−0.150857	−	0.259861i
$847$	6.85110			0.235407
$848$	30.7530	+	7.92712i	1.05606	+	0.272219i
$849$	−16.1472			−0.554169
$850$		0			0
$851$	8.84723	+	8.84723i	0.303279	+	0.303279i
$852$	−0.730228	−	2.67425i	−0.0250172	−	0.0916181i
$853$	18.0611	−	18.0611i	0.618401	−	0.618401i	−0.326720	−	0.945121i	$-0.605943\pi$
$853$	18.0611	−	18.0611i	0.618401	−	0.618401i	0.945121	+	0.326720i	$0.105943\pi$
$854$	−1.50445	+	5.66865i	−0.0514813	+	0.193977i
$855$		0			0
$856$	28.1758	+	27.7761i	0.963028	+	0.949368i
$857$			35.8346i			1.22409i	0.790825	+	0.612043i	$0.209652\pi$
$857$			35.8346i			1.22409i	−0.790825	+	0.612043i	$0.790348\pi$
$858$	−27.3538	−	7.25967i	−0.933843	−	0.247841i
$859$	−0.619460	+	0.619460i	−0.0211357	+	0.0211357i	−0.717596	−	0.696460i	$-0.754757\pi$
$859$	−0.619460	+	0.619460i	−0.0211357	+	0.0211357i	0.696460	+	0.717596i	$0.254757\pi$
$860$		0			0
$861$	10.7949	+	10.7949i	0.367890	+	0.367890i
$862$	−24.7344	+	14.3590i	−0.842456	+	0.489070i
$863$	18.8270			0.640878			0.320439	−	0.947269i	$-0.396170\pi$
$863$	18.8270			0.640878			0.320439	+	0.947269i	$0.396170\pi$
$864$	30.4096	−	8.53749i	1.03456	−	0.290451i
$865$		0			0
$866$	−0.826931	+	0.480058i	−0.0281003	+	0.0163130i
$867$	−18.2944	−	18.2944i	−0.621309	−	0.621309i
$868$	−7.25693	−	4.14384i	−0.246316	−	0.140651i
$869$	−20.8197	+	20.8197i	−0.706260	+	0.706260i
$870$		0			0
$871$		−	65.1352i		−	2.20702i
$872$	32.4211	−	32.8876i	1.09792	−	1.11372i
$873$		−	4.65479i		−	0.157541i
$874$	−4.53439	+	17.0852i	−0.153378	+	0.577916i
$875$		0			0
$876$	−7.90137	−	28.9364i	−0.266962	−	0.977672i
$877$	−7.77833	−	7.77833i	−0.262656	−	0.262656i	0.563476	−	0.826132i	$-0.309464\pi$
$877$	−7.77833	−	7.77833i	−0.262656	−	0.262656i	−0.826132	+	0.563476i	$0.809464\pi$
$878$	9.48233	+	16.3339i	0.320013	+	0.551244i
$879$	−1.21541			−0.0409946
$880$		0			0
$881$	13.6551			0.460052			0.230026	−	0.973184i	$-0.426119\pi$
$881$	13.6551			0.460052			0.230026	+	0.973184i	$0.426119\pi$
$882$	2.65098	+	4.56649i	0.0892631	+	0.153762i
$883$	−25.7585	−	25.7585i	−0.866844	−	0.866844i	0.125278	−	0.992122i	$-0.460018\pi$
$883$	−25.7585	−	25.7585i	−0.866844	−	0.866844i	−0.992122	+	0.125278i	$0.960018\pi$
$884$	−6.15565	+	1.68086i	−0.207037	+	0.0565334i
$885$		0			0
$886$	−14.4298	+	54.3701i	−0.484777	+	1.82660i
$887$		−	38.8982i		−	1.30607i	−0.757326	−	0.653037i	$-0.773495\pi$
$887$		−	38.8982i		−	1.30607i	0.757326	−	0.653037i	$-0.226505\pi$
$888$	−0.200817	−	28.1144i	−0.00673898	−	0.943459i
$889$		−	1.34020i		−	0.0449488i
$890$		0			0
$891$	9.53054	−	9.53054i	0.319285	−	0.319285i
$892$	7.71669	−	13.5139i	0.258374	−	0.452479i
$893$	−45.5602	−	45.5602i	−1.52461	−	1.52461i
$894$	−11.4821	+	6.66571i	−0.384020	+	0.222935i
$895$		0			0
$896$	−5.66762	−	9.44934i	−0.189342	−	0.315680i
$897$	19.5265			0.651972
$898$	10.2489	−	5.94978i	0.342010	−	0.198547i
$899$	−16.0717	−	16.0717i	−0.536022	−	0.536022i
$900$		0			0
$901$	2.75150	−	2.75150i	0.0916658	−	0.0916658i
$902$	−27.6393	−	7.33545i	−0.920289	−	0.244244i
$903$		−	3.80707i		−	0.126692i
$904$	−0.347597	−	48.6637i	−0.0115609	−	1.61853i
$905$		0			0
$906$	−1.13179	+	4.26450i	−0.0376014	+	0.141679i
$907$	−5.10220	+	5.10220i	−0.169416	+	0.169416i	−0.786723	−	0.617307i	$-0.788224\pi$
$907$	−5.10220	+	5.10220i	−0.169416	+	0.169416i	0.617307	+	0.786723i	$0.288224\pi$
$908$	5.87844	−	1.60516i	0.195083	−	0.0532692i
$909$	1.60746	+	1.60746i	0.0533162	+	0.0533162i
$910$		0			0
$911$	−46.7058			−1.54743			−0.773716	−	0.633533i	$-0.781604\pi$
$911$	−46.7058			−1.54743			−0.773716	+	0.633533i	$0.781604\pi$
$912$	34.2086	−	20.1871i	1.13276	−	0.668463i
$913$	−2.29520			−0.0759601
$914$	−4.02270	−	6.92937i	−0.133059	−	0.229203i
$915$		0			0
$916$	5.69119	+	20.8423i	0.188042	+	0.688650i
$917$	−8.80402	+	8.80402i	−0.290734	+	0.290734i
$918$	0.992732	−	3.74053i	0.0327650	−	0.123456i
$919$		−	53.4692i		−	1.76379i	−0.471449	−	0.881893i	$-0.656269\pi$
$919$		−	53.4692i		−	1.76379i	0.471449	−	0.881893i	$-0.343731\pi$
$920$		0			0
$921$			21.3259i			0.702712i
$922$	−32.1617	−	8.53567i	−1.05919	−	0.281107i
$923$	4.13314	−	4.13314i	0.136044	−	0.136044i
$924$	−5.19978	−	2.96917i	−0.171060	−	0.0976786i
$925$		0			0
$926$	50.9813	−	29.5961i	1.67535	−	0.972590i
$927$	−8.52342			−0.279946
$928$	−8.10062	−	28.8535i	−0.265916	−	0.947163i
$929$	14.2098			0.466209			0.233104	−	0.972452i	$-0.425112\pi$
$929$	14.2098			0.466209			0.233104	+	0.972452i	$0.425112\pi$
$930$		0			0
$931$	27.5259	+	27.5259i	0.902125	+	0.902125i
$932$	13.0521	+	7.45297i	0.427534	+	0.244130i
$933$	−33.4972	+	33.4972i	−1.09665	+	1.09665i
$934$	−6.01227	−	1.59565i	−0.196728	−	0.0522113i
$935$		0			0
$936$	8.09014	+	7.97539i	0.264434	+	0.260684i
$937$		−	5.26656i		−	0.172051i	−0.996293	−	0.0860255i	$-0.972583\pi$
$937$		−	5.26656i		−	0.172051i	0.996293	−	0.0860255i	$-0.0274166\pi$
$938$	3.53512	−	13.3200i	0.115426	−	0.434914i
$939$	−1.86796	+	1.86796i	−0.0609585	+	0.0609585i
$940$		0			0
$941$	18.7780	+	18.7780i	0.612145	+	0.612145i	0.943505	−	0.331359i	$-0.107507\pi$
$941$	18.7780	+	18.7780i	0.612145	+	0.612145i	−0.331359	+	0.943505i	$0.607507\pi$
$942$	−4.54676	−	7.83209i	−0.148141	−	0.255183i
$943$	19.7304			0.642509
$944$	−46.2428	−	11.9199i	−1.50507	−	0.387959i
$945$		0			0
$946$	3.58031	+	6.16733i	0.116406	+	0.200517i
$947$	3.27572	+	3.27572i	0.106447	+	0.106447i	0.758324	−	0.651878i	$-0.226018\pi$
$947$	3.27572	+	3.27572i	0.106447	+	0.106447i	−0.651878	+	0.758324i	$0.726018\pi$
$948$	−44.0372	+	12.0248i	−1.43026	+	0.390546i
$949$	44.7223	−	44.7223i	1.45175	−	1.45175i
$950$		0			0
$951$		−	21.9142i		−	0.710616i
$952$	−1.35004	+	0.00964316i	−0.0437552	+	0.000312537i
$953$			30.0292i			0.972741i	0.873753	+	0.486371i	$0.161680\pi$
$953$			30.0292i			0.972741i	−0.873753	+	0.486371i	$0.838320\pi$
$954$	−6.69585	−	1.77707i	−0.216786	−	0.0575348i
$955$		0			0
$956$	20.4076	−	35.7390i	0.660029	−	1.15588i
$957$	−11.5158	−	11.5158i	−0.372253	−	0.372253i
$958$	10.1798	−	5.90968i	0.328895	−	0.190933i
$959$	14.9065			0.481356
$960$		0			0
$961$	−12.5941			−0.406260
$962$	51.2685	−	29.7629i	1.65296	−	0.959593i
$963$	−6.10274	−	6.10274i	−0.196658	−	0.196658i
$964$	−23.0991	+	40.4524i	−0.743970	+	1.30288i
$965$		0			0
$966$	3.99313	+	1.05977i	0.128477	+	0.0340977i
$967$		−	15.2196i		−	0.489429i	−0.969595	−	0.244715i	$-0.921306\pi$
$967$		−	15.2196i		−	0.489429i	0.969595	−	0.244715i	$-0.0786943\pi$
$968$	−19.8961	+	0.142115i	−0.639485	+	0.00456775i
$969$		−	4.86684i		−	0.156345i
$970$		0			0
$971$	−18.4838	+	18.4838i	−0.593173	+	0.593173i	−0.938487	−	0.345314i	$-0.887772\pi$
$971$	−18.4838	+	18.4838i	−0.593173	+	0.593173i	0.345314	+	0.938487i	$0.387772\pi$
$972$	−12.1594	+	3.32024i	−0.390013	+	0.106497i
$973$	0.337781	+	0.337781i	0.0108288	+	0.0108288i
$974$	5.18014	+	8.92314i	0.165983	+	0.285916i
$975$		0			0
$976$	4.25146	−	16.4934i	0.136086	−	0.527940i
$977$	−18.7912			−0.601183			−0.300592	−	0.953753i	$-0.597184\pi$
$977$	−18.7912			−0.601183			−0.300592	+	0.953753i	$0.597184\pi$
$978$	8.90817	+	15.3449i	0.284852	+	0.490676i
$979$	−1.58276	−	1.58276i	−0.0505851	−	0.0505851i
$980$		0			0
$981$	−7.12331	+	7.12331i	−0.227430	+	0.227430i
$982$	−1.83425	+	6.91129i	−0.0585333	+	0.220548i
$983$			56.5605i			1.80400i	0.431738	+	0.901999i	$0.357901\pi$
$983$			56.5605i			1.80400i	−0.431738	+	0.901999i	$0.642099\pi$
$984$	−31.5732	−	31.1253i	−1.00652	−	0.992240i
$985$		0			0
$986$	−3.54912	−	0.941933i	−0.113027	−	0.0299973i
$987$	−10.6483	+	10.6483i	−0.338938	+	0.338938i
$988$	72.7303	+	41.5303i	2.31386	+	1.32126i
$989$	−3.47918	−	3.47918i	−0.110632	−	0.110632i
$990$		0			0
$991$	45.0866			1.43222			0.716112	−	0.697985i	$-0.245920\pi$
$991$	45.0866			1.43222			0.716112	+	0.697985i	$0.245920\pi$
$992$	21.1606	+	11.8835i	0.671851	+	0.377301i
$993$	17.2404			0.547108
$994$	1.06954	−	0.620898i	0.0339237	−	0.0196937i
$995$		0			0
$996$	−3.09018	−	1.76455i	−0.0979162	−	0.0559120i
$997$	−35.1508	+	35.1508i	−1.11324	+	1.11324i	−0.120528	+	0.992710i	$0.538459\pi$
$997$	−35.1508	+	35.1508i	−1.11324	+	1.11324i	−0.992710	+	0.120528i	$0.961541\pi$
$998$	21.0382	+	5.58353i	0.665954	+	0.176743i
$999$			35.9536i			1.13752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.l.f.301.2	yes	12
4.3	odd	2		1600.2.l.g.401.2		12
5.2	odd	4		400.2.q.f.349.2		12
5.3	odd	4		400.2.q.e.349.5		12
5.4	even	2		400.2.l.g.301.5	yes	12
16.5	even	4	inner	400.2.l.f.101.2	✓	12
16.11	odd	4		1600.2.l.g.1201.2		12
20.3	even	4		1600.2.q.e.849.5		12
20.7	even	4		1600.2.q.f.849.2		12
20.19	odd	2		1600.2.l.f.401.5		12
80.27	even	4		1600.2.q.e.49.5		12
80.37	odd	4		400.2.q.e.149.5		12
80.43	even	4		1600.2.q.f.49.2		12
80.53	odd	4		400.2.q.f.149.2		12
80.59	odd	4		1600.2.l.f.1201.5		12
80.69	even	4		400.2.l.g.101.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.2	✓	12	16.5	even	4	inner
400.2.l.f.301.2	yes	12	1.1	even	1	trivial
400.2.l.g.101.5	yes	12	80.69	even	4
400.2.l.g.301.5	yes	12	5.4	even	2
400.2.q.e.149.5		12	80.37	odd	4
400.2.q.e.349.5		12	5.3	odd	4
400.2.q.f.149.2		12	80.53	odd	4
400.2.q.f.349.2		12	5.2	odd	4
1600.2.l.f.401.5		12	20.19	odd	2
1600.2.l.f.1201.5		12	80.59	odd	4
1600.2.l.g.401.2		12	4.3	odd	2
1600.2.l.g.1201.2		12	16.11	odd	4
1600.2.q.e.49.5		12	80.27	even	4
1600.2.q.e.849.5		12	20.3	even	4
1600.2.q.f.49.2		12	80.43	even	4
1600.2.q.f.849.2		12	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.22306 + 0.710021i) q^{2} +(1.09156 + 1.09156i) q^{3} +(0.991741 - 1.73679i) q^{4} +(-2.11008 - 0.560012i) q^{6} -0.973926i q^{7} +(0.0202025 + 2.82835i) q^{8} -0.616985i q^{9} +O(q^{10})\)	\(q+(-1.22306 + 0.710021i) q^{2} +(1.09156 + 1.09156i) q^{3} +(0.991741 - 1.73679i) q^{4} +(-2.11008 - 0.560012i) q^{6} -0.973926i q^{7} +(0.0202025 + 2.82835i) q^{8} -0.616985i q^{9} +(1.40810 - 1.40810i) q^{11} +(2.97836 - 0.813270i) q^{12} +(4.60317 + 4.60317i) q^{13} +(0.691508 + 1.19117i) q^{14} +(-2.03290 - 3.44490i) q^{16} -0.490104 q^{17} +(0.438072 + 0.754608i) q^{18} +(4.54863 + 4.54863i) q^{19} +(1.06310 - 1.06310i) q^{21} +(-0.722406 + 2.72196i) q^{22} -1.94308i q^{23} +(-3.06527 + 3.10938i) q^{24} +(-8.89828 - 2.36159i) q^{26} +(3.94816 - 3.94816i) q^{27} +(-1.69151 - 0.965882i) q^{28} +(-3.74613 - 3.74613i) q^{29} +4.29021 q^{31} +(4.93230 + 2.76991i) q^{32} +3.07405 q^{33} +(0.599426 - 0.347984i) q^{34} +(-1.07157 - 0.611889i) q^{36} +(-4.55320 + 4.55320i) q^{37} +(-8.79286 - 2.33362i) q^{38} +10.0493i q^{39} +10.1542i q^{41} +(-0.545410 + 2.05506i) q^{42} +(1.79055 - 1.79055i) q^{43} +(-1.04911 - 3.84204i) q^{44} +(1.37963 + 2.37650i) q^{46} -10.0162 q^{47} +(1.54128 - 5.97936i) q^{48} +6.05147 q^{49} +(-0.534979 - 0.534979i) q^{51} +(12.5599 - 3.42960i) q^{52} +(-5.61412 + 5.61412i) q^{53} +(-2.02555 + 7.63211i) q^{54} +(2.75461 - 0.0196757i) q^{56} +9.93022i q^{57} +(7.24157 + 1.92191i) q^{58} +(8.44185 - 8.44185i) q^{59} +(3.01095 + 3.01095i) q^{61} +(-5.24718 + 3.04614i) q^{62} -0.600897 q^{63} +(-7.99918 + 0.114280i) q^{64} +(-3.75974 + 2.18264i) q^{66} +(-7.07504 - 7.07504i) q^{67} +(-0.486056 + 0.851209i) q^{68} +(2.12099 - 2.12099i) q^{69} -0.897891i q^{71} +(1.74505 - 0.0124646i) q^{72} -9.71555i q^{73} +(2.33596 - 8.80170i) q^{74} +(12.4111 - 3.38897i) q^{76} +(-1.37138 - 1.37138i) q^{77} +(-7.13520 - 12.2909i) q^{78} -14.7857 q^{79} +6.76838 q^{81} +(-7.20968 - 12.4192i) q^{82} +(-0.815000 - 0.815000i) q^{83} +(-0.792065 - 2.90071i) q^{84} +(-0.918620 + 3.46128i) q^{86} -8.17827i q^{87} +(4.01105 + 3.95415i) q^{88} -1.12404i q^{89} +(4.48314 - 4.48314i) q^{91} +(-3.37472 - 1.92703i) q^{92} +(4.68303 + 4.68303i) q^{93} +(12.2504 - 7.11174i) q^{94} +(2.36039 + 8.40744i) q^{96} +7.54442 q^{97} +(-7.40130 + 4.29667i) q^{98} +(-0.868775 - 0.868775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} + 8 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 + 8 * q^8	\( 12 q - 4 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} + 8 q^{8} - 2 q^{11} - 8 q^{12} + 4 q^{13} + 14 q^{14} + 2 q^{16} + 8 q^{17} - 18 q^{18} - 14 q^{19} - 20 q^{21} - 2 q^{22} - 14 q^{24} - 16 q^{26} + 10 q^{27} - 26 q^{28} - 4 q^{31} + 16 q^{32} - 28 q^{33} - 6 q^{34} + 2 q^{36} - 8 q^{37} - 10 q^{38} - 10 q^{42} - 44 q^{44} - 10 q^{46} - 8 q^{47} + 28 q^{48} + 4 q^{49} + 10 q^{51} + 12 q^{52} + 16 q^{53} + 10 q^{54} + 6 q^{56} + 60 q^{58} + 20 q^{59} + 4 q^{61} + 18 q^{62} + 8 q^{63} + 38 q^{64} + 32 q^{66} - 50 q^{67} + 60 q^{68} + 14 q^{72} + 10 q^{74} + 60 q^{76} + 8 q^{77} - 4 q^{78} + 12 q^{79} - 8 q^{81} - 42 q^{82} + 2 q^{83} + 34 q^{84} + 6 q^{86} - 30 q^{88} + 2 q^{92} + 44 q^{93} + 32 q^{94} - 34 q^{96} - 64 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 + 8 * q^8 - 2 * q^11 - 8 * q^12 + 4 * q^13 + 14 * q^14 + 2 * q^16 + 8 * q^17 - 18 * q^18 - 14 * q^19 - 20 * q^21 - 2 * q^22 - 14 * q^24 - 16 * q^26 + 10 * q^27 - 26 * q^28 - 4 * q^31 + 16 * q^32 - 28 * q^33 - 6 * q^34 + 2 * q^36 - 8 * q^37 - 10 * q^38 - 10 * q^42 - 44 * q^44 - 10 * q^46 - 8 * q^47 + 28 * q^48 + 4 * q^49 + 10 * q^51 + 12 * q^52 + 16 * q^53 + 10 * q^54 + 6 * q^56 + 60 * q^58 + 20 * q^59 + 4 * q^61 + 18 * q^62 + 8 * q^63 + 38 * q^64 + 32 * q^66 - 50 * q^67 + 60 * q^68 + 14 * q^72 + 10 * q^74 + 60 * q^76 + 8 * q^77 - 4 * q^78 + 12 * q^79 - 8 * q^81 - 42 * q^82 + 2 * q^83 + 34 * q^84 + 6 * q^86 - 30 * q^88 + 2 * q^92 + 44 * q^93 + 32 * q^94 - 34 * q^96 - 64 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

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