LMFDB - Embedded newform 400.2.q.e.349.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,2,Mod(149,400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [12,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			349.5
Root			$1.22306 + 0.710021i$ of defining polynomial
Character	$\chi$	$=$	400.349
Dual form			400.2.q.e.149.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.710021 + 1.22306i) q^{2} +(-1.09156 + 1.09156i) q^{3} +(-0.991741 + 1.73679i) q^{4} +(-2.11008 - 0.560012i) q^{6} -0.973926 q^{7} +(-2.82835 + 0.0202025i) q^{8} +0.616985i q^{9} +(1.40810 - 1.40810i) q^{11} +(-0.813270 - 2.97836i) q^{12} +(-4.60317 + 4.60317i) q^{13} +(-0.691508 - 1.19117i) q^{14} +(-2.03290 - 3.44490i) q^{16} +0.490104i q^{17} +(-0.754608 + 0.438072i) q^{18} +(-4.54863 - 4.54863i) q^{19} +(1.06310 - 1.06310i) q^{21} +(2.72196 + 0.722406i) q^{22} +1.94308 q^{23} +(3.06527 - 3.10938i) q^{24} +(-8.89828 - 2.36159i) q^{26} +(-3.94816 - 3.94816i) q^{27} +(0.965882 - 1.69151i) q^{28} +(3.74613 + 3.74613i) q^{29} +4.29021 q^{31} +(2.76991 - 4.93230i) q^{32} +3.07405i q^{33} +(-0.599426 + 0.347984i) q^{34} +(-1.07157 - 0.611889i) q^{36} +(4.55320 + 4.55320i) q^{37} +(2.33362 - 8.79286i) q^{38} -10.0493i q^{39} +10.1542i q^{41} +(2.05506 + 0.545410i) q^{42} +(1.79055 + 1.79055i) q^{43} +(1.04911 + 3.84204i) q^{44} +(1.37963 + 2.37650i) q^{46} +10.0162i q^{47} +(5.97936 + 1.54128i) q^{48} -6.05147 q^{49} +(-0.534979 - 0.534979i) q^{51} +(-3.42960 - 12.5599i) q^{52} +(-5.61412 - 5.61412i) q^{53} +(2.02555 - 7.63211i) q^{54} +(2.75461 - 0.0196757i) q^{56} +9.93022 q^{57} +(-1.92191 + 7.24157i) q^{58} +(-8.44185 + 8.44185i) q^{59} +(3.01095 + 3.01095i) q^{61} +(3.04614 + 5.24718i) q^{62} -0.600897i q^{63} +(7.99918 - 0.114280i) q^{64} +(-3.75974 + 2.18264i) q^{66} +(-7.07504 + 7.07504i) q^{67} +(-0.851209 - 0.486056i) q^{68} +(-2.12099 + 2.12099i) q^{69} -0.897891i q^{71} +(-0.0124646 - 1.74505i) q^{72} +9.71555 q^{73} +(-2.33596 + 8.80170i) q^{74} +(12.4111 - 3.38897i) q^{76} +(-1.37138 + 1.37138i) q^{77} +(12.2909 - 7.13520i) q^{78} +14.7857 q^{79} +6.76838 q^{81} +(-12.4192 + 7.20968i) q^{82} +(0.815000 - 0.815000i) q^{83} +(0.792065 + 2.90071i) q^{84} +(-0.918620 + 3.46128i) q^{86} -8.17827 q^{87} +(-3.95415 + 4.01105i) q^{88} +1.12404i q^{89} +(4.48314 - 4.48314i) q^{91} +(-1.92703 + 3.37472i) q^{92} +(-4.68303 + 4.68303i) q^{93} +(-12.2504 + 7.11174i) q^{94} +(2.36039 + 8.40744i) q^{96} -7.54442i q^{97} +(-4.29667 - 7.40130i) q^{98} +(0.868775 + 0.868775i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{8} - 2 q^{11} + 6 q^{12} - 4 q^{13} - 14 q^{14} + 2 q^{16} + 18 q^{18} + 14 q^{19} - 20 q^{21} + 20 q^{22} - 12 q^{23} + 14 q^{24} - 16 q^{26}+ \cdots - 12 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^8 - 2 * q^11 + 6 * q^12 - 4 * q^13 - 14 * q^14 + 2 * q^16 + 18 * q^18 + 14 * q^19 - 20 * q^21 + 20 * q^22 - 12 * q^23 + 14 * q^24 - 16 * q^26 - 10 * q^27 + 10 * q^28 - 4 * q^31 - 2 * q^32 + 6 * q^34 + 2 * q^36 + 8 * q^37 - 28 * q^38 - 10 * q^42 + 44 * q^44 - 10 * q^46 + 58 * q^48 - 4 * q^49 + 10 * q^51 + 16 * q^53 - 10 * q^54 + 6 * q^56 + 16 * q^57 - 4 * q^58 - 20 * q^59 + 4 * q^61 - 22 * q^62 - 38 * q^64 + 32 * q^66 - 50 * q^67 - 50 * q^68 + 54 * q^72 - 40 * q^73 - 10 * q^74 + 60 * q^76 + 8 * q^77 + 48 * q^78 - 12 * q^79 - 8 * q^81 + 12 * q^82 - 2 * q^83 - 34 * q^84 + 6 * q^86 + 64 * q^87 - 56 * q^88 - 50 * q^92 - 44 * q^93 - 32 * q^94 - 34 * q^96 + 30 * q^98 - 12 * q^99

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 $

$2$	0.710021	+	1.22306i	0.502061	+	0.864832i
$2$	0.710021	+	1.22306i	0.502061	+	0.864832i
$3$	−1.09156	+	1.09156i	−0.630214	+	0.630214i	−0.948122	−	0.317908i	$-0.897020\pi$
$3$	−1.09156	+	1.09156i	−0.630214	+	0.630214i	0.317908	+	0.948122i	$0.397020\pi$
$4$	−0.991741	+	1.73679i	−0.495870	+	0.868396i
$5$		0			0
$5$		0			0
$6$	−2.11008	−	0.560012i	−0.861435	−	0.228624i
$7$	−0.973926			−0.368109			−0.184055	−	0.982916i	$-0.558922\pi$
$7$	−0.973926			−0.368109			−0.184055	+	0.982916i	$0.558922\pi$
$8$	−2.82835	+	0.0202025i	−0.999974	+	0.00714267i
$9$			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	$0.152944\pi$
$12$	−0.813270	−	2.97836i	−0.234771	−	0.859780i
$13$	−4.60317	+	4.60317i	−1.27669	+	1.27669i	−0.334179	+	0.942510i	$0.608459\pi$
$13$	−4.60317	+	4.60317i	−1.27669	+	1.27669i	−0.942510	+	0.334179i	$0.891541\pi$
$14$	−0.691508	−	1.19117i	−0.184813	−	0.318353i
$15$		0			0
$16$	−2.03290	−	3.44490i	−0.508225	−	0.861224i
$17$			0.490104i			0.118868i	0.998232	+	0.0594338i	$0.0189295\pi$
$17$			0.490104i			0.118868i	−0.998232	+	0.0594338i	$0.981070\pi$
$18$	−0.754608	+	0.438072i	−0.177863	+	0.103255i
$19$	−4.54863	−	4.54863i	−1.04353	−	1.04353i	−0.999009	−	0.0445187i	$-0.985825\pi$
$19$	−4.54863	−	4.54863i	−1.04353	−	1.04353i	−0.0445187	−	0.999009i	$-0.514175\pi$
$20$		0			0
$21$	1.06310	−	1.06310i	0.231988	−	0.231988i
$22$	2.72196	+	0.722406i	0.580325	+	0.154018i
$23$	1.94308			0.405160			0.202580	−	0.979266i	$-0.435067\pi$
$23$	1.94308			0.405160			0.202580	+	0.979266i	$0.435067\pi$
$24$	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
$28$	0.965882	−	1.69151i	0.182535	−	0.319665i
$29$	3.74613	+	3.74613i	0.695640	+	0.695640i	0.963467	−	0.267827i	$-0.0863057\pi$
$29$	3.74613	+	3.74613i	0.695640	+	0.695640i	−0.267827	+	0.963467i	$0.586306\pi$
$30$		0			0
$31$	4.29021			0.770545			0.385272	−	0.922803i	$-0.374107\pi$
$31$	4.29021			0.770545			0.385272	+	0.922803i	$0.374107\pi$
$32$	2.76991	−	4.93230i	0.489655	−	0.871916i
$33$			3.07405i			0.535124i
$34$	−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	$-0.0724549\pi$
$37$	4.55320	+	4.55320i	0.748542	+	0.748542i	−0.225663	+	0.974205i	$0.572455\pi$
$38$	2.33362	−	8.79286i	0.378562	−	1.42639i
$39$		−	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	$0.708566\pi$
$42$	2.05506	+	0.545410i	0.317102	+	0.0841586i
$43$	1.79055	+	1.79055i	0.273057	+	0.273057i	0.830329	−	0.557273i	$-0.188152\pi$
$43$	1.79055	+	1.79055i	0.273057	+	0.273057i	−0.557273	+	0.830329i	$0.688152\pi$
$44$	1.04911	+	3.84204i	0.158159	+	0.579210i
$45$		0			0
$46$	1.37963	+	2.37650i	0.203415	+	0.350395i
$47$			10.0162i			1.46102i	0.682902	+	0.730510i	$0.260717\pi$
$47$			10.0162i			1.46102i	−0.682902	+	0.730510i	$0.739283\pi$
$48$	5.97936	+	1.54128i	0.863046	+	0.222465i
$49$	−6.05147			−0.864495
$50$		0			0
$51$	−0.534979	−	0.534979i	−0.0749120	−	0.0749120i
$52$	−3.42960	−	12.5599i	−0.475600	−	1.74174i
$53$	−5.61412	−	5.61412i	−0.771158	−	0.771158i	0.207151	−	0.978309i	$-0.433581\pi$
$53$	−5.61412	−	5.61412i	−0.771158	−	0.771158i	−0.978309	+	0.207151i	$0.933581\pi$
$54$	2.02555	−	7.63211i	0.275643	−	1.03860i
$55$		0			0
$56$	2.75461	−	0.0196757i	0.368100	−	0.00262928i
$57$	9.93022			1.31529
$58$	−1.92191	+	7.24157i	−0.252359	+	0.950865i
$59$	−8.44185	+	8.44185i	−1.09904	+	1.09904i	−0.104512	+	0.994524i	$0.533328\pi$
$59$	−8.44185	+	8.44185i	−1.09904	+	1.09904i	−0.994524	+	0.104512i	$0.966672\pi$
$60$		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	$0.662117\pi$
$62$	3.04614	+	5.24718i	0.386860	+	0.666392i
$63$		−	0.600897i		−	0.0757060i
$64$	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	−0.991840	−	0.127486i	$-0.959309\pi$
$67$	−7.07504	+	7.07504i	−0.864354	+	0.864354i	0.127486	+	0.991840i	$0.459309\pi$
$68$	−0.851209	−	0.486056i	−0.103224	−	0.0589430i
$69$	−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	$-0.0169676\pi$
$72$	−0.0124646	−	1.74505i	−0.00146897	−	0.205656i
$73$	9.71555			1.13712			0.568559	−	0.822642i	$-0.307501\pi$
$73$	9.71555			1.13712			0.568559	+	0.822642i	$0.307501\pi$
$74$	−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
$78$	12.2909	−	7.13520i	1.39166	−	0.807902i
$79$	14.7857			1.66352			0.831760	−	0.555135i	$-0.187334\pi$
$79$	14.7857			1.66352			0.831760	+	0.555135i	$0.187334\pi$
$80$		0			0
$81$	6.76838			0.752042
$82$	−12.4192	+	7.20968i	−1.37147	+	0.796176i
$83$	0.815000	−	0.815000i	0.0894579	−	0.0894579i	−0.660962	−	0.750420i	$-0.729851\pi$
$83$	0.815000	−	0.815000i	0.0894579	−	0.0894579i	0.750420	+	0.660962i	$0.229851\pi$
$84$	0.792065	+	2.90071i	0.0864214	+	0.316493i
$85$		0			0
$86$	−0.918620	+	3.46128i	−0.0990573	+	0.373239i
$87$	−8.17827			−0.876803
$88$	−3.95415	+	4.01105i	−0.421514	+	0.427579i
$89$			1.12404i			0.119148i	0.998224	+	0.0595739i	$0.0189742\pi$
$89$			1.12404i			0.119148i	−0.998224	+	0.0595739i	$0.981026\pi$
$90$		0			0
$91$	4.48314	−	4.48314i	0.469961	−	0.469961i
$92$	−1.92703	+	3.37472i	−0.200907	+	0.351839i
$93$	−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
$97$		−	7.54442i		−	0.766019i	−0.923744	−	0.383010i	$-0.874888\pi$
$97$		−	7.54442i		−	0.766019i	0.923744	−	0.383010i	$-0.125112\pi$
$98$	−4.29667	−	7.40130i	−0.434029	−	0.747644i
$99$	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	$0.308682\pi$
$102$	0.274464	−	1.03416i	0.0271760	−	0.102397i
$103$	13.8146			1.36120			0.680598	−	0.732657i	$-0.261720\pi$
$103$	13.8146			1.36120			0.680598	+	0.732657i	$0.261720\pi$
$104$	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	$-0.486353\pi$
$107$	−9.89124	−	9.89124i	−0.956222	−	0.956222i	−0.999081	+	0.0428589i	$0.986353\pi$
$108$	10.7727	−	2.94159i	1.03660	−	0.283054i
$109$	11.5454	+	11.5454i	1.10584	+	1.10584i	0.993691	+	0.112154i	$0.0357750\pi$
$109$	11.5454	+	11.5454i	1.10584	+	1.10584i	0.112154	+	0.993691i	$0.464225\pi$
$110$		0			0
$111$	−9.94021			−0.943483
$112$	1.97989	+	3.35507i	0.187082	+	0.317025i
$113$		−	17.2057i		−	1.61857i	−0.587415	−	0.809286i	$-0.699854\pi$
$113$		−	17.2057i		−	1.61857i	0.587415	−	0.809286i	$-0.300146\pi$
$114$	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
$118$	−16.3188	−	4.33098i	−1.50226	−	0.398699i
$119$		−	0.477325i		−	0.0437563i
$120$		0			0
$121$			7.03452i			0.639502i
$122$	−1.54473	+	5.82041i	−0.139853	+	0.526955i
$123$	−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
$127$		−	1.37608i		−	0.122107i	−0.998134	−	0.0610535i	$-0.980554\pi$
$127$		−	1.37608i		−	0.122107i	0.998134	−	0.0610535i	$-0.0194460\pi$
$128$	5.81936	+	9.70232i	0.514363	+	0.857572i
$129$	−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	$0.938614\pi$
$132$	−5.33899	−	3.04866i	−0.464700	−	0.265352i
$133$	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
$137$	15.3056			1.30764			0.653822	−	0.756649i	$-0.273165\pi$
$137$	15.3056			1.30764			0.653822	+	0.756649i	$0.273165\pi$
$138$	−4.10004	−	1.08815i	−0.349018	−	0.0926291i
$139$	0.346824	−	0.346824i	0.0294173	−	0.0294173i	−0.692245	−	0.721662i	$-0.743378\pi$
$139$	0.346824	−	0.346824i	0.0294173	−	0.0294173i	0.721662	+	0.692245i	$0.243378\pi$
$140$		0			0
$141$	−10.9334	−	10.9334i	−0.920754	−	0.920754i
$142$	1.09817	−	0.637521i	0.0921566	−	0.0534996i
$143$			12.9634i			1.08406i
$144$	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
$148$	−12.4236	+	3.39237i	−1.02121	+	0.278851i
$149$	−4.30028	+	4.30028i	−0.352293	+	0.352293i	−0.860962	−	0.508669i	$-0.830138\pi$
$149$	−4.30028	+	4.30028i	−0.352293	+	0.352293i	0.508669	+	0.860962i	$0.330138\pi$
$150$		0			0
$151$		−	2.02102i		−	0.164468i	−0.996613	−	0.0822341i	$-0.973794\pi$
$151$		−	2.02102i		−	0.164468i	0.996613	−	0.0822341i	$-0.0262055\pi$
$152$	12.9570	+	12.7732i	1.05095	+	1.03605i
$153$	−0.302387			−0.0244465
$154$	−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	−0.580301	−	0.814402i	$-0.697065\pi$
$157$	2.93327	−	2.93327i	0.234101	−	0.234101i	0.814402	+	0.580301i	$0.197065\pi$
$158$	10.4981	+	18.0838i	0.835188	+	1.43867i
$159$	12.2563			0.971989
$160$		0			0
$161$	−1.89241			−0.149143
$162$	4.80569	+	8.27811i	0.377570	+	0.650390i
$163$	5.74697	−	5.74697i	0.450137	−	0.450137i	−0.445263	−	0.895400i	$-0.646890\pi$
$163$	5.74697	−	5.74697i	0.450137	−	0.450137i	0.895400	+	0.445263i	$0.146890\pi$
$164$	−17.6357	−	10.0703i	−1.37712	−	0.786360i
$165$		0			0
$166$	1.57546	+	0.418125i	0.122279	+	0.0324528i
$167$	6.41553			0.496449			0.248224	−	0.968703i	$-0.420153\pi$
$167$	6.41553			0.496449			0.248224	+	0.968703i	$0.420153\pi$
$168$	−2.98535	+	3.02830i	−0.230325	+	0.233639i
$169$		−	29.3783i		−	2.25987i
$170$		0			0
$171$	2.80644	−	2.80644i	0.214613	−	0.214613i
$172$	−4.88558	+	1.33405i	−0.372522	+	0.101721i
$173$	0.545724	−	0.545724i	0.0414907	−	0.0414907i	−0.686057	−	0.727548i	$-0.740660\pi$
$173$	0.545724	−	0.545724i	0.0414907	−	0.0414907i	0.727548	+	0.686057i	$0.240660\pi$
$174$	−5.80674	−	10.0025i	−0.440208	−	0.758288i
$175$		0			0
$176$	−7.71328	−	1.98823i	−0.581410	−	0.149869i
$177$		−	18.4296i		−	1.38525i
$178$	−1.37476	+	0.798090i	−0.103043	+	0.0598194i
$179$	3.57757	+	3.57757i	0.267400	+	0.267400i	0.828052	−	0.560652i	$-0.189449\pi$
$179$	3.57757	+	3.57757i	0.267400	+	0.267400i	−0.560652	+	0.828052i	$0.689449\pi$
$180$		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	$0.277501\pi$
$182$	8.66627	+	2.30002i	0.642386	+	0.170489i
$183$	−6.57328			−0.485911
$184$	−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
$188$	−17.3961	−	9.93352i	−1.26874	−	0.724476i
$189$	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	$0.687219\pi$
$192$	−8.60686	+	8.85635i	−0.621147	+	0.639152i
$193$		−	0.0812703i		−	0.00584996i	−0.999996	−	0.00292498i	$-0.999069\pi$
$193$		−	0.0812703i		−	0.00584996i	0.999996	−	0.00292498i	$-0.000931052\pi$
$194$	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	$-0.272584\pi$
$197$	−1.40711	−	1.40711i	−0.100252	−	0.100252i	−0.755454	+	0.655202i	$0.772584\pi$
$198$	−0.445714	+	1.67941i	−0.0316755	+	0.119351i
$199$		−	14.3046i		−	1.01402i	−0.861939	−	0.507011i	$-0.830750\pi$
$199$		−	14.3046i		−	1.01402i	0.861939	−	0.507011i	$-0.169250\pi$
$200$		0			0
$201$		−	15.4457i		−	1.08946i
$202$	−5.03635	−	1.33664i	−0.354356	−	0.0940458i
$203$	−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
$207$			1.19885i			0.0833258i
$208$	25.2152	+	6.49966i	1.74836	+	0.450670i
$209$	−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	$0.610778\pi$
$212$	15.3183	−	4.18281i	1.05207	−	0.287277i
$213$	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
$217$	−4.17835			−0.283645
$218$	−5.92320	+	22.3181i	−0.401169	+	1.51157i
$219$	−10.6051	+	10.6051i	−0.716628	+	0.716628i
$220$		0			0
$221$	−2.25603	−	2.25603i	−0.151757	−	0.151757i
$222$	−7.05776	−	12.1575i	−0.473686	−	0.815955i
$223$			7.78095i			0.521051i	0.965467	+	0.260525i	$0.0838958\pi$
$223$			7.78095i			0.521051i	−0.965467	+	0.260525i	$0.916104\pi$
$224$	−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	−0.631986	−	0.774980i	$-0.717760\pi$
$227$	2.15443	−	2.15443i	0.142995	−	0.142995i	0.774980	+	0.631986i	$0.217760\pi$
$228$	−9.84821	+	17.2467i	−0.652214	+	1.14219i
$229$	7.63865	−	7.63865i	0.504776	−	0.504776i	−0.408142	−	0.912918i	$-0.633823\pi$
$229$	7.63865	−	7.63865i	0.504776	−	0.504776i	0.912918	+	0.408142i	$0.133823\pi$
$230$		0			0
$231$		−	2.99390i		−	0.196984i
$232$	−10.6711	−	10.5197i	−0.700591	−	0.690653i
$233$	−7.51503			−0.492326			−0.246163	−	0.969228i	$-0.579170\pi$
$233$	−7.51503			−0.492326			−0.246163	+	0.969228i	$0.579170\pi$
$234$	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
$238$	0.583796	−	0.338911i	0.0378419	−	0.0219683i
$239$	−20.5776			−1.33105			−0.665526	−	0.746375i	$-0.731793\pi$
$239$	−20.5776			−1.33105			−0.665526	+	0.746375i	$0.731793\pi$
$240$		0			0
$241$	−23.2914			−1.50033			−0.750166	−	0.661250i	$-0.770026\pi$
$241$	−23.2914			−1.50033			−0.750166	+	0.661250i	$0.770026\pi$
$242$	−8.60362	+	4.99466i	−0.553062	+	0.321069i
$243$	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
$247$	41.8762			2.66452
$248$	−12.1342	+	0.0866731i	−0.770525	+	0.00550375i
$249$			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	$0.297661\pi$
$252$	1.04363	+	0.595935i	0.0657428	+	0.0375404i
$253$	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
$257$			22.4537i			1.40062i	0.713838	+	0.700311i	$0.246955\pi$
$257$			22.4537i			1.40062i	−0.713838	+	0.700311i	$0.753045\pi$
$258$	−2.77547	−	4.78093i	−0.172793	−	0.297648i
$259$	−4.43448	−	4.43448i	−0.275545	−	0.275545i
$260$		0			0
$261$	−2.31131	+	2.31131i	−0.143066	+	0.143066i
$262$	4.63771	−	17.4745i	0.286519	−	1.07958i
$263$	−8.23670			−0.507897			−0.253948	−	0.967218i	$-0.581729\pi$
$263$	−8.23670			−0.507897			−0.253948	+	0.967218i	$0.581729\pi$
$264$	−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
$268$	−5.27128	−	19.3045i	−0.321994	−	1.17921i
$269$	17.2960	+	17.2960i	1.05455	+	1.05455i	0.998423	+	0.0561306i	$0.0178763\pi$
$269$	17.2960	+	17.2960i	1.05455	+	1.05455i	0.0561306	+	0.998423i	$0.482124\pi$
$270$		0			0
$271$	−12.4753			−0.757822			−0.378911	−	0.925433i	$-0.623701\pi$
$271$	−12.4753			−0.757822			−0.378911	+	0.925433i	$0.623701\pi$
$272$	1.68836	−	0.996332i	0.102372	−	0.0604115i
$273$			9.78726i			0.592352i
$274$	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	$-0.393547\pi$
$277$	−10.2583	−	10.2583i	−0.616363	−	0.616363i	−0.944597	+	0.328234i	$0.893547\pi$
$278$	0.670439	+	0.177934i	0.0402103	+	0.0106718i
$279$			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	$-0.220447\pi$
$282$	5.60922	−	21.1350i	0.334024	−	1.25857i
$283$	−7.39635	−	7.39635i	−0.439668	−	0.439668i	0.452232	−	0.891900i	$-0.350628\pi$
$283$	−7.39635	−	7.39635i	−0.439668	−	0.439668i	−0.891900	+	0.452232i	$0.850628\pi$
$284$	1.55945	+	0.890475i	0.0925363	+	0.0528400i
$285$		0			0
$286$	−15.8550	+	9.20430i	−0.937526	+	0.544261i
$287$		−	9.88942i		−	0.583754i
$288$	3.04316	+	1.70899i	0.179320	+	0.100703i
$289$	16.7598			0.985870
$290$		0			0
$291$	8.23520	+	8.23520i	0.482756	+	0.482756i
$292$	−9.63531	+	16.8739i	−0.563864	+	0.987470i
$293$	−0.556728	−	0.556728i	−0.0325244	−	0.0325244i	0.690658	−	0.723182i	$-0.257321\pi$
$293$	−0.556728	−	0.556728i	−0.0325244	−	0.0325244i	−0.723182	+	0.690658i	$0.757321\pi$
$294$	12.7691	+	3.38889i	0.744706	+	0.197644i
$295$		0			0
$296$	−12.9701	−	12.7861i	−0.753870	−	0.743177i
$297$	−11.1188			−0.645178
$298$	−8.31278	−	2.20620i	−0.481546	−	0.127802i
$299$	−8.94430	+	8.94430i	−0.517263	+	0.517263i
$300$		0			0
$301$	−1.74387	−	1.74387i	−0.100515	−	0.100515i
$302$	2.47182	−	1.43497i	0.142238	−	0.0825730i
$303$		−	5.68781i		−	0.326756i
$304$	−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	−0.371082	−	0.928600i	$-0.621013\pi$
$307$	9.76852	−	9.76852i	0.557519	−	0.557519i	0.928600	+	0.371082i	$0.121013\pi$
$308$	−1.02175	−	3.74187i	−0.0582197	−	0.213213i
$309$	−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	$0.664078\pi$
$312$	0.203021	+	28.4229i	0.0114938	+	1.60913i
$313$	−1.71127			−0.0967268			−0.0483634	−	0.998830i	$-0.515401\pi$
$313$	−1.71127			−0.0967268			−0.0483634	+	0.998830i	$0.515401\pi$
$314$	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	−0.930382	−	0.366592i	$-0.880524\pi$
$317$	−10.0380	+	10.0380i	−0.563790	+	0.563790i	0.366592	+	0.930382i	$0.380524\pi$
$318$	8.70224	+	14.9902i	0.487997	+	0.840608i
$319$	10.5498			0.590678
$320$		0			0
$321$	21.5938			1.20525
$322$	−1.34365	−	2.31453i	−0.0748788	−	0.128984i
$323$	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
$327$	−25.2049			−1.39384
$328$	−0.205140	−	28.7196i	−0.0113270	−	1.58578i
$329$		−	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	$0.150698\pi$
$332$	0.607218	+	2.22376i	0.0333254	+	0.122044i
$333$	−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
$337$			3.46077i			0.188520i	0.995548	+	0.0942601i	$0.0300485\pi$
$337$			3.46077i			0.188520i	−0.995548	+	0.0942601i	$0.969951\pi$
$338$	35.9313	−	20.8592i	1.95441	−	1.13459i
$339$	18.7810	+	18.7810i	1.02005	+	1.02005i
$340$		0			0
$341$	6.04104	−	6.04104i	0.327141	−	0.327141i
$342$	5.42506	+	1.43981i	0.293354	+	0.0778558i
$343$	12.7112			0.686338
$344$	−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	$-0.0193205\pi$
$347$	17.4637	+	17.4637i	0.937498	+	0.937498i	−0.0606600	+	0.998158i	$0.519321\pi$
$348$	8.11073	−	14.2040i	0.434781	−	0.761413i
$349$	−24.2159	−	24.2159i	−1.29625	−	1.29625i	−0.930852	−	0.365397i	$-0.880933\pi$
$349$	−24.2159	−	24.2159i	−1.29625	−	1.29625i	−0.365397	−	0.930852i	$-0.619067\pi$
$350$		0			0
$351$	36.3481			1.94012
$352$	−3.04486	−	10.8455i	−0.162292	−	0.578065i
$353$		−	10.7028i		−	0.569650i	−0.958580	−	0.284825i	$-0.908065\pi$
$353$		−	10.7028i		−	0.569650i	0.958580	−	0.284825i	$-0.0919355\pi$
$354$	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
$358$	−1.83543	+	6.91573i	−0.0970053	+	0.365507i
$359$			23.6390i			1.24762i	0.781577	+	0.623809i	$0.214416\pi$
$359$			23.6390i			1.24762i	−0.781577	+	0.623809i	$0.785584\pi$
$360$		0			0
$361$			22.3801i			1.17790i
$362$	−3.17364	−	0.842282i	−0.166803	−	0.0442693i
$363$	−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
$367$			13.7431i			0.717386i	0.933456	+	0.358693i	$0.116777\pi$
$367$			13.7431i			0.717386i	−0.933456	+	0.358693i	$0.883223\pi$
$368$	−3.95008	−	6.69370i	−0.205912	−	0.348933i
$369$	−6.26498			−0.326142
$370$		0			0
$371$	5.46773	+	5.46773i	0.283871	+	0.283871i
$372$	−3.48910	−	12.7778i	−0.180902	−	0.662499i
$373$	18.4703	+	18.4703i	0.956355	+	0.956355i	0.999087	−	0.0427313i	$-0.0136059\pi$
$373$	18.4703	+	18.4703i	0.956355	+	0.956355i	−0.0427313	+	0.999087i	$0.513606\pi$
$374$	−0.354054	+	1.33405i	−0.0183077	+	0.0689819i
$375$		0			0
$376$	−0.202353	−	28.3295i	−0.0104356	−	1.46098i
$377$	−34.4881			−1.77623
$378$	−1.97274	+	7.43311i	−0.101467	+	0.382318i
$379$	16.1028	−	16.1028i	0.827143	−	0.827143i	−0.159978	−	0.987121i	$-0.551142\pi$
$379$	16.1028	−	16.1028i	0.827143	−	0.827143i	0.987121	+	0.159978i	$0.0511423\pi$
$380$		0			0
$381$	1.50207	+	1.50207i	0.0769535	+	0.0769535i
$382$	−10.8888	−	18.7568i	−0.557122	−	0.959679i
$383$			23.1255i			1.18166i	0.806796	+	0.590830i	$0.201200\pi$
$383$			23.1255i			1.18166i	−0.806796	+	0.590830i	$0.798800\pi$
$384$	−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
$388$	13.1031	+	7.48211i	0.665209	+	0.379846i
$389$	19.4044	−	19.4044i	0.983842	−	0.983842i	−0.0160295	−	0.999872i	$-0.505103\pi$
$389$	19.4044	−	19.4044i	0.983842	−	0.983842i	0.999872	+	0.0160295i	$0.00510257\pi$
$390$		0			0
$391$			0.952310i			0.0481604i
$392$	17.1157	−	0.122255i	0.864473	−	0.00617480i
$393$	19.7348			0.995491
$394$	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	−0.800345	−	0.599540i	$-0.795350\pi$
$397$	−4.00102	+	4.00102i	−0.200806	+	0.200806i	0.599540	+	0.800345i	$0.295350\pi$
$398$	17.4953	−	10.1565i	0.876960	−	0.509101i
$399$	−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	$0.0754980\pi$
$402$	18.8910	−	10.9668i	0.942197	−	0.546973i
$403$	−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
$407$	12.8227			0.635598
$408$	1.52392	+	1.50230i	0.0754452	+	0.0743750i
$409$			4.59845i			0.227379i	0.993516	+	0.113689i	$0.0362669\pi$
$409$			4.59845i			0.227379i	−0.993516	+	0.113689i	$0.963733\pi$
$410$		0			0
$411$	−16.7070	+	16.7070i	−0.824095	+	0.824095i
$412$	−13.7005	+	23.9932i	−0.674977	+	1.18206i
$413$	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
$417$			0.757161i			0.0370783i
$418$	−9.09525	−	15.6672i	−0.444863	−	0.766306i
$419$	−16.6774	−	16.6774i	−0.814746	−	0.814746i	0.170595	−	0.985341i	$-0.445431\pi$
$419$	−16.6774	−	16.6774i	−0.814746	−	0.814746i	−0.985341	+	0.170595i	$0.945431\pi$
$420$		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	$0.0717037\pi$
$422$	−4.46401	+	16.8200i	−0.217305	+	0.818786i
$423$	−6.17987			−0.300476
$424$	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
$428$	26.9886	−	7.36949i	1.30454	−	0.356218i
$429$	−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	$0.338068\pi$
$432$	−5.57480	+	21.6272i	−0.268218	+	1.04054i
$433$			0.676118i			0.0324922i	0.999868	+	0.0162461i	$0.00517152\pi$
$433$			0.676118i			0.0324922i	−0.999868	+	0.0162461i	$0.994828\pi$
$434$	−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
$438$	−20.5005	−	5.44082i	−0.979553	−	0.259972i
$439$			13.3550i			0.637400i	0.947856	+	0.318700i	$0.103246\pi$
$439$			13.3550i			0.637400i	−0.947856	+	0.318700i	$0.896754\pi$
$440$		0			0
$441$		−	3.73366i		−	0.177794i
$442$	1.15743	−	4.36108i	0.0550532	−	0.207436i
$443$	28.1262	+	28.1262i	1.33631	+	1.33631i	0.899600	+	0.436714i	$0.143858\pi$
$443$	28.1262	+	28.1262i	1.33631	+	1.33631i	0.436714	+	0.899600i	$0.356142\pi$
$444$	9.85811	−	17.2641i	0.467845	−	0.819317i
$445$		0			0
$446$	−9.51655	+	5.52464i	−0.450622	+	0.261599i
$447$		−	9.38805i		−	0.444039i
$448$	−7.79061	+	0.111300i	−0.368072	+	0.00525843i
$449$	8.37972			0.395464			0.197732	−	0.980256i	$-0.436642\pi$
$449$	8.37972			0.395464			0.197732	+	0.980256i	$0.436642\pi$
$450$		0			0
$451$	14.2981	+	14.2981i	0.673271	+	0.673271i
$452$	29.8827	+	17.0635i	1.40556	+	0.802602i
$453$	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
$457$	5.66561			0.265026			0.132513	−	0.991181i	$-0.457695\pi$
$457$	5.66561			0.265026			0.132513	+	0.991181i	$0.457695\pi$
$458$	14.7661	+	3.91891i	0.689975	+	0.183119i
$459$	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	$0.565417\pi$
$462$	3.66171	−	2.12573i	0.170358	−	0.0988979i
$463$		−	41.6835i		−	1.93720i	−0.248631	−	0.968598i	$-0.579981\pi$
$463$		−	41.6835i		−	1.93720i	0.248631	−	0.968598i	$-0.420019\pi$
$464$	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	−0.631474	−	0.775397i	$-0.717550\pi$
$467$	3.11020	−	3.11020i	0.143923	−	0.143923i	0.775397	+	0.631474i	$0.217550\pi$
$468$	7.74926	−	2.11601i	0.358210	−	0.0978126i
$469$	6.89057	−	6.89057i	0.318177	−	0.318177i
$470$		0			0
$471$			6.40370i			0.295067i
$472$	23.7060	−	24.0471i	1.09116	−	1.10686i
$473$	5.04255			0.231857
$474$	−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
$478$	−14.6105	−	25.1675i	−0.668268	−	1.15114i
$479$	8.32325			0.380299			0.190149	−	0.981755i	$-0.439103\pi$
$479$	8.32325			0.380299			0.190149	+	0.981755i	$0.439103\pi$
$480$		0			0
$481$	−41.9183			−1.91131
$482$	−16.5374	−	28.4868i	−0.753257	−	1.29754i
$483$	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
$487$	−7.29577			−0.330603			−0.165301	−	0.986243i	$-0.552860\pi$
$487$	−7.29577			−0.330603			−0.165301	+	0.986243i	$0.552860\pi$
$488$	−8.57687	−	8.45521i	−0.388257	−	0.382750i
$489$			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	$0.213604\pi$
$492$	30.2429	−	8.25810i	1.36345	−	0.372304i
$493$	−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
$497$			0.874479i			0.0392257i
$498$	−2.17612	+	1.26330i	−0.0975143	+	0.0566099i
$499$	10.8833	+	10.8833i	0.487203	+	0.487203i	0.907422	−	0.420220i	$-0.138047\pi$
$499$	10.8833	+	10.8833i	0.487203	+	0.487203i	−0.420220	+	0.907422i	$0.638047\pi$
$500$		0			0
$501$	−7.00295	+	7.00295i	−0.312869	+	0.312869i
$502$	−6.46093	−	1.71472i	−0.288365	−	0.0765318i
$503$	−29.3781			−1.30991			−0.654953	−	0.755670i	$-0.727312\pi$
$503$	−29.3781			−1.30991			−0.654953	+	0.755670i	$0.727312\pi$
$504$	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
$508$	2.38996	+	1.36471i	0.106037	+	0.0605493i
$509$	−17.4592	−	17.4592i	−0.773863	−	0.773863i	0.204916	−	0.978780i	$-0.434308\pi$
$509$	−17.4592	−	17.4592i	−0.773863	−	0.773863i	−0.978780	+	0.204916i	$0.934308\pi$
$510$		0			0
$511$	−9.46222			−0.418584
$512$	−22.6222	+	0.484827i	−0.999770	+	0.0214265i
$513$			35.9175i			1.58579i
$514$	−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
$518$	2.27505	−	8.57221i	0.0999602	−	0.376641i
$519$			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	$-0.0666270\pi$
$522$	−4.46794	−	1.18579i	−0.195556	−	0.0519005i
$523$	16.2705	+	16.2705i	0.711460	+	0.711460i	0.966841	−	0.255380i	$-0.0822006\pi$
$523$	16.2705	+	16.2705i	0.711460	+	0.711460i	−0.255380	+	0.966841i	$0.582201\pi$
$524$	24.6652	−	6.73507i	1.07750	−	0.294223i
$525$		0			0
$526$	−5.84823	−	10.0740i	−0.254995	−	0.439246i
$527$			2.10265i			0.0915929i
$528$	10.5898	−	6.24924i	0.460862	−	0.271963i
$529$	−19.2245			−0.835846
$530$		0			0
$531$	−5.20849	−	5.20849i	−0.226029	−	0.226029i
$532$	−12.0875	+	3.30060i	−0.524059	+	0.143099i
$533$	−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
$537$	−7.81028			−0.337039
$538$	−8.87348	+	33.4345i	−0.382563	+	1.44146i
$539$	−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	$0.774767\pi$
$542$	−8.85774	−	15.2580i	−0.380472	−	0.655389i
$543$		−	3.58416i		−	0.153811i
$544$	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	−0.998255	−	0.0590579i	$-0.981190\pi$
$547$	−21.9660	+	21.9660i	−0.939197	+	0.939197i	0.0590579	+	0.998255i	$0.481190\pi$
$548$	−15.1792	+	26.5826i	−0.648422	+	1.13555i
$549$	−1.85771	+	1.85771i	−0.0792852	+	0.0792852i
$550$		0			0
$551$		−	34.0796i		−	1.45184i
$552$	5.95606	−	6.04176i	0.253507	−	0.257154i
$553$	−14.4002			−0.612357
$554$	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	−0.229965	−	0.973199i	$-0.573861\pi$
$557$	17.5409	−	17.5409i	0.743234	−	0.743234i	0.973199	+	0.229965i	$0.0738612\pi$
$558$	−3.23743	+	1.87942i	−0.137051	+	0.0795623i
$559$	−16.4844			−0.697217
$560$		0			0
$561$	−1.50661			−0.0636089
$562$	26.1815	−	15.1991i	1.10440	−	0.641136i
$563$	−27.5975	+	27.5975i	−1.16309	+	1.16309i	−0.179300	+	0.983794i	$0.557383\pi$
$563$	−27.5975	+	27.5975i	−1.16309	+	1.16309i	−0.983794	+	0.179300i	$0.942617\pi$
$564$	29.8320	−	8.14592i	1.25615	−	0.343005i
$565$		0			0
$566$	3.79460	−	14.2977i	0.159499	−	0.600979i
$567$	−6.59190			−0.276834
$568$	0.0181396	+	2.53955i	0.000761123	+	0.106557i
$569$			23.6390i			0.990998i	0.868608	+	0.495499i	$0.165015\pi$
$569$			23.6390i			0.990998i	−0.868608	+	0.495499i	$0.834985\pi$
$570$		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	$0.472588\pi$
$572$	−22.5148	−	12.8564i	−0.941390	−	0.537551i
$573$	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
$577$			3.69585i			0.153860i	0.997036	+	0.0769302i	$0.0245119\pi$
$577$			3.69585i			0.153860i	−0.997036	+	0.0769302i	$0.975488\pi$
$578$	11.8998	+	20.4982i	0.494967	+	0.852613i
$579$	0.0887116	+	0.0887116i	0.00368673	+	0.00368673i
$580$		0			0
$581$	−0.793750	+	0.793750i	−0.0329303	+	0.0329303i
$582$	−4.22496	+	15.9193i	−0.175130	+	0.659876i
$583$	−15.8105			−0.654802
$584$	−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	−0.992365	−	0.123335i	$-0.960641\pi$
$587$	−27.0313	−	27.0313i	−1.11570	−	1.11570i	−0.123335	−	0.992365i	$-0.539359\pi$
$588$	4.92148	+	18.0235i	0.202958	+	0.743276i
$589$	−19.5146	−	19.5146i	−0.804085	−	0.804085i
$590$		0			0
$591$	3.07189			0.126361
$592$	6.42912	−	24.9415i	0.264235	−	1.02509i
$593$		−	4.55524i		−	0.187061i	−0.995616	−	0.0935306i	$-0.970185\pi$
$593$		−	4.55524i		−	0.187061i	0.995616	−	0.0935306i	$-0.0298153\pi$
$594$	−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
$598$	−17.2900	−	4.58876i	−0.707043	−	0.187648i
$599$			7.46846i			0.305153i	0.988292	+	0.152576i	$0.0487570\pi$
$599$			7.46846i			0.305153i	−0.988292	+	0.152576i	$0.951243\pi$
$600$		0			0
$601$			12.2638i			0.500250i	0.968214	+	0.250125i	$0.0804717\pi$
$601$			12.2638i			0.500250i	−0.968214	+	0.250125i	$0.919528\pi$
$602$	0.894668	−	3.37103i	0.0364639	−	0.137393i
$603$	−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
$607$		−	5.23884i		−	0.212638i	−0.994332	−	0.106319i	$-0.966094\pi$
$607$		−	5.23884i		−	0.212638i	0.994332	−	0.106319i	$-0.0339065\pi$
$608$	−35.0345	+	9.83593i	−1.42084	+	0.398900i
$609$	7.96503			0.322759
$610$		0			0
$611$	−46.1064	−	46.1064i	−1.86527	−	1.86527i
$612$	0.299889	−	0.525183i	0.0121223	−	0.0212293i
$613$	20.7209	+	20.7209i	0.836910	+	0.836910i	0.988451	−	0.151541i	$-0.0484235\pi$
$613$	20.7209	+	20.7209i	0.836910	+	0.836910i	−0.151541	+	0.988451i	$0.548424\pi$
$614$	18.8833	+	5.01161i	0.762068	+	0.202252i
$615$		0			0
$616$	3.85105	−	3.90646i	0.155163	−	0.157396i
$617$	−2.20286			−0.0886838			−0.0443419	−	0.999016i	$-0.514119\pi$
$617$	−2.20286			−0.0886838			−0.0443419	+	0.999016i	$0.514119\pi$
$618$	−29.1499	−	7.73636i	−1.17258	−	0.311202i
$619$	31.4569	−	31.4569i	1.26436	−	1.26436i	0.315404	−	0.948958i	$-0.397860\pi$
$619$	31.4569	−	31.4569i	1.26436	−	1.26436i	0.948958	−	0.315404i	$-0.102140\pi$
$620$		0			0
$621$	−7.67158	−	7.67158i	−0.307850	−	0.307850i
$622$	−37.5325	+	21.7887i	−1.50492	+	0.873648i
$623$		−	1.09473i		−	0.0438594i
$624$	−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
$628$	2.18544	+	8.00353i	0.0872085	+	0.319376i
$629$	−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	$-0.108678\pi$
$632$	−41.8192	+	0.298708i	−1.66348	+	0.0118820i
$633$	−18.9957			−0.755011
$634$	−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
$638$	7.49061	+	12.9031i	0.296556	+	0.510838i
$639$	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	$0.595209\pi$
$642$	15.3320	+	26.4105i	0.605108	+	1.04234i
$643$	0.541845	−	0.541845i	0.0213683	−	0.0213683i	−0.696342	−	0.717710i	$-0.745190\pi$
$643$	0.541845	−	0.541845i	0.0213683	−	0.0213683i	0.717710	+	0.696342i	$0.245190\pi$
$644$	1.87678	−	3.28673i	0.0739556	−	0.129515i
$645$		0			0
$646$	4.30942	+	1.14371i	0.169552	+	0.0449988i
$647$	−32.6391			−1.28318			−0.641588	−	0.767049i	$-0.721724\pi$
$647$	−32.6391			−1.28318			−0.641588	+	0.767049i	$0.721724\pi$
$648$	−19.1434	+	0.136738i	−0.752023	+	0.00537158i
$649$			23.7739i			0.933208i
$650$		0			0
$651$	4.56093	−	4.56093i	0.178757	−	0.178757i
$652$	4.28179	+	15.6808i	0.167688	+	0.614108i
$653$	−9.73805	+	9.73805i	−0.381079	+	0.381079i	−0.871491	−	0.490412i	$-0.836846\pi$
$653$	−9.73805	+	9.73805i	−0.381079	+	0.381079i	0.490412	+	0.871491i	$0.336846\pi$
$654$	−17.8960	−	30.8271i	−0.699790	−	1.20544i
$655$		0			0
$656$	34.9801	−	20.6424i	1.36574	−	0.805952i
$657$			5.99434i			0.233862i
$658$	11.9310	−	6.92631i	0.465120	−	0.270016i
$659$	−1.26445	−	1.26445i	−0.0492560	−	0.0492560i	0.682050	−	0.731306i	$-0.261089\pi$
$659$	−1.26445	−	1.26445i	−0.0492560	−	0.0492560i	−0.731306	+	0.682050i	$0.761089\pi$
$660$		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	$0.0357099\pi$
$662$	15.2658	+	4.05152i	0.593321	+	0.157467i
$663$	4.92519			0.191279
$664$	−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
$668$	−6.36254	+	11.1424i	−0.246174	+	0.431114i
$669$	−8.49339	−	8.49339i	−0.328373	−	0.328373i
$670$		0			0
$671$	8.47943			0.327345
$672$	−2.29884	−	8.18822i	−0.0886798	−	0.315868i
$673$			3.58765i			0.138294i	0.997606	+	0.0691469i	$0.0220277\pi$
$673$			3.58765i			0.138294i	−0.997606	+	0.0691469i	$0.977972\pi$
$674$	−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	$-0.338962\pi$
$677$	−10.1507	−	10.1507i	−0.390124	−	0.390124i	−0.874731	+	0.484608i	$0.838962\pi$
$678$	−9.63537	+	36.3052i	−0.370044	+	1.39429i
$679$			7.34770i			0.281979i
$680$		0			0
$681$			4.70339i			0.180234i
$682$	11.6778	+	3.09928i	0.447166	+	0.118677i
$683$	16.6805	+	16.6805i	0.638260	+	0.638260i	0.950126	−	0.311866i	$-0.100954\pi$
$683$	16.6805	+	16.6805i	0.638260	+	0.638260i	−0.311866	+	0.950126i	$0.600954\pi$
$684$	2.09094	+	7.65745i	0.0799491	+	0.292790i
$685$		0			0
$686$	9.02519	+	15.5465i	0.344583	+	0.593568i
$687$			16.6761i			0.636234i
$688$	2.52826	−	9.80828i	0.0963889	−	0.373937i
$689$	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	$0.641042\pi$
$692$	0.406593	+	1.48903i	0.0154563	+	0.0566043i
$693$	−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
$697$	−4.97661			−0.188502
$698$	12.4237	−	46.8113i	0.470243	−	1.77183i
$699$	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	$0.695243\pi$
$702$	25.8079	+	44.4558i	0.974057	+	1.67788i
$703$		−	41.4217i		−	1.56225i
$704$	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
$708$	32.0084	+	18.2774i	1.20295	+	0.686907i
$709$	−8.78514	+	8.78514i	−0.329933	+	0.329933i	−0.852561	−	0.522628i	$-0.824952\pi$
$709$	−8.78514	+	8.78514i	−0.329933	+	0.329933i	0.522628	+	0.852561i	$0.324952\pi$
$710$		0			0
$711$			9.12255i			0.342122i
$712$	−0.0227084	−	3.17918i	−0.000851033	−	0.119145i
$713$	8.33621			0.312194
$714$	−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
$718$	−28.9119	+	16.7842i	−1.07898	+	0.626380i
$719$	−46.2329			−1.72420			−0.862099	−	0.506740i	$-0.830850\pi$
$719$	−46.2329			−1.72420			−0.862099	+	0.506740i	$0.830850\pi$
$720$		0			0
$721$	−13.4544			−0.501069
$722$	−27.3721	+	15.8903i	−1.01868	+	0.591376i
$723$	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
$727$	17.4640			0.647703			0.323852	−	0.946108i	$-0.395022\pi$
$727$	17.4640			0.647703			0.323852	+	0.946108i	$0.395022\pi$
$728$	−12.5893	+	12.7705i	−0.466592	+	0.473306i
$729$			30.0340i			1.11237i
$730$		0			0
$731$	−0.877557	+	0.877557i	−0.0324576	+	0.0324576i
$732$	6.51899	−	11.4164i	0.240949	−	0.421963i
$733$	−7.89695	+	7.89695i	−0.291680	+	0.291680i	−0.837744	−	0.546063i	$-0.816126\pi$
$733$	−7.89695	+	7.89695i	−0.291680	+	0.291680i	0.546063	+	0.837744i	$0.316126\pi$
$734$	−16.8086	+	9.75791i	−0.620419	+	0.360171i
$735$		0			0
$736$	5.38214	−	9.58384i	0.198388	−	0.353265i
$737$			19.9247i			0.733936i
$738$	−4.44826	−	7.66243i	−0.163743	−	0.282058i
$739$	−26.1724	−	26.1724i	−0.962769	−	0.962769i	0.0365624	−	0.999331i	$-0.488359\pi$
$739$	−26.1724	−	26.1724i	−0.962769	−	0.962769i	−0.999331	+	0.0365624i	$0.988359\pi$
$740$		0			0
$741$	−45.7105	+	45.7105i	−1.67922	+	1.67922i
$742$	−2.80515	+	10.5696i	−0.102980	+	0.388021i
$743$	49.7660			1.82574			0.912868	−	0.408254i	$-0.133862\pi$
$743$	49.7660			1.82574			0.912868	+	0.408254i	$0.133862\pi$
$744$	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
$748$	−1.88300	+	0.514171i	−0.0688493	+	0.0188000i
$749$	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	$0.645811\pi$
$752$	34.5049	−	20.3620i	1.25827	−	0.742527i
$753$		−	7.29665i		−	0.265905i
$754$	−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	$-0.119696\pi$
$757$	15.4872	+	15.4872i	0.562890	+	0.562890i	−0.367237	+	0.930127i	$0.619696\pi$
$758$	31.1279	+	8.26131i	1.13062	+	0.300064i
$759$			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	$-0.156080\pi$
$762$	−0.770619	+	2.90363i	−0.0279166	+	0.105187i
$763$	−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
$767$		−	77.7185i		−	2.80625i
$768$	−6.84587	−	23.7315i	−0.247029	−	0.856338i
$769$	24.9737			0.900573			0.450287	−	0.892884i	$-0.351322\pi$
$769$	24.9737			0.900573			0.450287	+	0.892884i	$0.351322\pi$
$770$		0			0
$771$	−24.5096	−	24.5096i	−0.882691	−	0.882691i
$772$	0.141150	+	0.0805991i	0.00508009	+	0.00290082i
$773$	−1.32495	−	1.32495i	−0.0476550	−	0.0476550i	0.682878	−	0.730533i	$-0.260728\pi$
$773$	−1.32495	−	1.32495i	−0.0476550	−	0.0476550i	−0.730533	+	0.682878i	$0.760728\pi$
$774$	−2.13556	−	0.566775i	−0.0767610	−	0.0203723i
$775$		0			0
$776$	0.152416	+	21.3383i	0.00547142	+	0.766000i
$777$	9.68103			0.347305
$778$	37.5102	+	9.95518i	1.34481	+	0.356910i
$779$	46.1876	−	46.1876i	1.65484	−	1.65484i
$780$		0			0
$781$	−1.26432	−	1.26432i	−0.0452409	−	0.0452409i
$782$	−1.16473	+	0.676160i	−0.0416507	+	0.0241794i
$783$		−	29.5807i		−	1.05713i
$784$	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	−0.695481	−	0.718545i	$-0.744808\pi$
$787$	0.647036	−	0.647036i	0.0230644	−	0.0230644i	0.718545	+	0.695481i	$0.244808\pi$
$788$	3.83934	−	1.04837i	0.136771	−	0.0373466i
$789$	8.99087	−	8.99087i	0.320084	−	0.320084i
$790$		0			0
$791$			16.7570i			0.595811i
$792$	−2.47476	−	2.43965i	−0.0879366	−	0.0866893i
$793$	−27.7198			−0.984360
$794$	−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	−0.304280	−	0.952583i	$-0.598416\pi$
$797$	18.3024	−	18.3024i	0.648303	−	0.648303i	0.952583	+	0.304280i	$0.0984158\pi$
$798$	−6.86682	−	11.8286i	−0.243083	−	0.418727i
$799$	−4.90900			−0.173668
$800$		0			0
$801$	−0.693514			−0.0245041
$802$	27.6402	+	47.6121i	0.976009	+	1.68124i
$803$	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
$807$	−37.7593			−1.32919
$808$	7.31623	−	7.42150i	0.257384	−	0.261087i
$809$			32.4845i			1.14209i	0.820917	+	0.571047i	$0.193463\pi$
$809$			32.4845i			1.14209i	−0.820917	+	0.571047i	$0.806537\pi$
$810$		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	$0.188834\pi$
$812$	9.95494	−	2.71829i	0.349350	−	0.0953933i
$813$	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
$817$		−	16.2891i		−	0.569884i
$818$	−5.62417	+	3.26499i	−0.196644	+	0.114158i
$819$	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	$0.334082\pi$
$822$	−32.2959	−	8.57130i	−1.12645	−	0.298958i
$823$	−4.85817			−0.169345			−0.0846726	−	0.996409i	$-0.526984\pi$
$823$	−4.85817			−0.169345			−0.0846726	+	0.996409i	$0.526984\pi$
$824$	−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	$-0.313245\pi$
$827$	−8.02757	−	8.02757i	−0.279146	−	0.279146i	−0.832768	+	0.553622i	$0.813245\pi$
$828$	−2.08215	−	1.18895i	−0.0723598	−	0.0413188i
$829$	24.3613	+	24.3613i	0.846102	+	0.846102i	0.989644	−	0.143542i	$-0.0458493\pi$
$829$	24.3613	+	24.3613i	0.846102	+	0.846102i	−0.143542	+	0.989644i	$0.545849\pi$
$830$		0			0
$831$	22.3952			0.776881
$832$	−36.2955	+	37.3476i	−1.25832	+	1.29480i
$833$		−	2.96585i		−	0.102761i
$834$	−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
$838$	8.55615	−	32.2388i	0.295567	−	1.11367i
$839$		−	43.1207i		−	1.48869i	−0.667794	−	0.744346i	$-0.732761\pi$
$839$		−	43.1207i		−	1.48869i	0.667794	−	0.744346i	$-0.267239\pi$
$840$		0			0
$841$		−	0.932964i		−	0.0321712i
$842$	29.8020	+	7.90942i	1.02704	+	0.272577i
$843$	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
$847$		−	6.85110i		−	0.235407i
$848$	−7.92712	+	30.7530i	−0.272219	+	1.05606i
$849$	16.1472			0.554169
$850$		0			0
$851$	8.84723	+	8.84723i	0.303279	+	0.303279i
$852$	−2.67425	+	0.730228i	−0.0916181	+	0.0250172i
$853$	18.0611	+	18.0611i	0.618401	+	0.618401i	0.945121	−	0.326720i	$-0.105943\pi$
$853$	18.0611	+	18.0611i	0.618401	+	0.618401i	−0.326720	+	0.945121i	$0.605943\pi$
$854$	1.50445	−	5.66865i	0.0514813	−	0.193977i
$855$		0			0
$856$	28.1758	+	27.7761i	0.963028	+	0.949368i
$857$	35.8346			1.22409			0.612043	−	0.790825i	$-0.290348\pi$
$857$	35.8346			1.22409			0.612043	+	0.790825i	$0.290348\pi$
$858$	7.25967	−	27.3538i	0.247841	−	0.933843i
$859$	0.619460	−	0.619460i	0.0211357	−	0.0211357i	−0.696460	−	0.717596i	$-0.745243\pi$
$859$	0.619460	−	0.619460i	0.0211357	−	0.0211357i	0.717596	+	0.696460i	$0.245243\pi$
$860$		0			0
$861$	10.7949	+	10.7949i	0.367890	+	0.367890i
$862$	14.3590	+	24.7344i	0.489070	+	0.842456i
$863$			18.8270i			0.640878i	0.947269	+	0.320439i	$0.103830\pi$
$863$			18.8270i			0.640878i	−0.947269	+	0.320439i	$0.896170\pi$
$864$	−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
$868$	4.14384	−	7.25693i	0.140651	−	0.246316i
$869$	20.8197	−	20.8197i	0.706260	−	0.706260i
$870$		0			0
$871$		−	65.1352i		−	2.20702i
$872$	−32.8876	−	32.4211i	−1.11372	−	1.09792i
$873$	4.65479			0.157541
$874$	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	−0.826132	−	0.563476i	$-0.809464\pi$
$877$	−7.77833	+	7.77833i	−0.262656	+	0.262656i	0.563476	+	0.826132i	$0.309464\pi$
$878$	−16.3339	+	9.48233i	−0.551244	+	0.320013i
$879$	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	$0.426119\pi$
$882$	4.56649	−	2.65098i	0.153762	−	0.0892631i
$883$	25.7585	−	25.7585i	0.866844	−	0.866844i	−0.125278	−	0.992122i	$-0.539982\pi$
$883$	25.7585	−	25.7585i	0.866844	−	0.866844i	0.992122	+	0.125278i	$0.0399823\pi$
$884$	6.15565	−	1.68086i	0.207037	−	0.0565334i
$885$		0			0
$886$	−14.4298	+	54.3701i	−0.484777	+	1.82660i
$887$	−38.8982			−1.30607			−0.653037	−	0.757326i	$-0.726505\pi$
$887$	−38.8982			−1.30607			−0.653037	+	0.757326i	$0.726505\pi$
$888$	28.1144	−	0.200817i	0.943459	−	0.00673898i
$889$			1.34020i			0.0449488i
$890$		0			0
$891$	9.53054	−	9.53054i	0.319285	−	0.319285i
$892$	−13.5139	−	7.71669i	−0.452479	−	0.258374i
$893$	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
$897$		−	19.5265i		−	0.651972i
$898$	5.94978	+	10.2489i	0.198547	+	0.342010i
$899$	16.0717	+	16.0717i	0.536022	+	0.536022i
$900$		0			0
$901$	2.75150	−	2.75150i	0.0916658	−	0.0916658i
$902$	−7.33545	+	27.6393i	−0.244244	+	0.920289i
$903$	3.80707			0.126692
$904$	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	$-0.211776\pi$
$907$	5.10220	+	5.10220i	0.169416	+	0.169416i	−0.617307	+	0.786723i	$0.711776\pi$
$908$	1.60516	+	5.87844i	0.0532692	+	0.195083i
$909$	−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	$0.781604\pi$
$912$	−20.1871	−	34.2086i	−0.668463	−	1.13276i
$913$		−	2.29520i		−	0.0759601i
$914$	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
$918$	3.74053	+	0.992732i	0.123456	+	0.0327650i
$919$			53.4692i			1.76379i	0.471449	+	0.881893i	$0.343731\pi$
$919$			53.4692i			1.76379i	−0.471449	+	0.881893i	$0.656269\pi$
$920$		0			0
$921$			21.3259i			0.702712i
$922$	−8.53567	+	32.1617i	−0.281107	+	1.05919i
$923$	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
$927$			8.52342i			0.279946i
$928$	28.8535	−	8.10062i	0.947163	−	0.265916i
$929$	−14.2098			−0.466209			−0.233104	−	0.972452i	$-0.574888\pi$
$929$	−14.2098			−0.466209			−0.233104	+	0.972452i	$0.574888\pi$
$930$		0			0
$931$	27.5259	+	27.5259i	0.902125	+	0.902125i
$932$	7.45297	−	13.0521i	0.244130	−	0.427534i
$933$	−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
$937$	−5.26656			−0.172051			−0.0860255	−	0.996293i	$-0.527417\pi$
$937$	−5.26656			−0.172051			−0.0860255	+	0.996293i	$0.527417\pi$
$938$	13.3200	+	3.53512i	0.434914	+	0.115426i
$939$	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	$0.607507\pi$
$942$	−7.83209	+	4.54676i	−0.255183	+	0.148141i
$943$			19.7304i			0.642509i
$944$	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	−0.651878	−	0.758324i	$-0.726018\pi$
$947$	3.27572	−	3.27572i	0.106447	−	0.106447i	0.758324	+	0.651878i	$0.226018\pi$
$948$	−12.0248	−	44.0372i	−0.390546	−	1.43026i
$949$	−44.7223	+	44.7223i	−1.45175	+	1.45175i
$950$		0			0
$951$		−	21.9142i		−	0.710616i
$952$	0.00964316	+	1.35004i	0.000312537	+	0.0437552i
$953$	−30.0292			−0.972741			−0.486371	−	0.873753i	$-0.661680\pi$
$953$	−30.0292			−0.972741			−0.486371	+	0.873753i	$0.661680\pi$
$954$	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
$958$	5.90968	+	10.1798i	0.190933	+	0.328895i
$959$	−14.9065			−0.481356
$960$		0			0
$961$	−12.5941			−0.406260
$962$	−29.7629	−	51.2685i	−0.959593	−	1.65296i
$963$	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
$967$	−15.2196			−0.489429			−0.244715	−	0.969595i	$-0.578694\pi$
$967$	−15.2196			−0.489429			−0.244715	+	0.969595i	$0.578694\pi$
$968$	−0.142115	−	19.8961i	−0.00456775	−	0.639485i
$969$			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	$0.387772\pi$
$972$	3.32024	+	12.1594i	0.106497	+	0.390013i
$973$	−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
$977$			18.7912i			0.601183i	0.953753	+	0.300592i	$0.0971841\pi$
$977$			18.7912i			0.601183i	−0.953753	+	0.300592i	$0.902816\pi$
$978$	−15.3449	+	8.90817i	−0.490676	+	0.284852i
$979$	1.58276	+	1.58276i	0.0505851	+	0.0505851i
$980$		0			0
$981$	−7.12331	+	7.12331i	−0.227430	+	0.227430i
$982$	6.91129	+	1.83425i	0.220548	+	0.0585333i
$983$	−56.5605			−1.80400			−0.901999	−	0.431738i	$-0.857901\pi$
$983$	−56.5605			−1.80400			−0.901999	+	0.431738i	$0.857901\pi$
$984$	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
$988$	−41.5303	+	72.7303i	−1.32126	+	2.31386i
$989$	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	$0.245920\pi$
$992$	11.8835	−	21.1606i	0.377301	−	0.671851i
$993$			17.2404i			0.547108i
$994$	−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	0.992710	+	0.120528i	$0.0384588\pi$
$997$	35.1508	+	35.1508i	1.11324	+	1.11324i	0.120528	+	0.992710i	$0.461541\pi$
$998$	−5.58353	+	21.0382i	−0.176743	+	0.665954i
$999$		−	35.9536i		−	1.13752i

Twists

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

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

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 $\F_{q}$
Belyi maps

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+(0.710021 + 1.22306i) q^{2} +(-1.09156 + 1.09156i) q^{3} +(-0.991741 + 1.73679i) q^{4} +(-2.11008 - 0.560012i) q^{6} -0.973926 q^{7} +(-2.82835 + 0.0202025i) q^{8} +0.616985i q^{9} +(1.40810 - 1.40810i) q^{11} +(-0.813270 - 2.97836i) q^{12} +(-4.60317 + 4.60317i) q^{13} +(-0.691508 - 1.19117i) q^{14} +(-2.03290 - 3.44490i) q^{16} +0.490104i q^{17} +(-0.754608 + 0.438072i) q^{18} +(-4.54863 - 4.54863i) q^{19} +(1.06310 - 1.06310i) q^{21} +(2.72196 + 0.722406i) q^{22} +1.94308 q^{23} +(3.06527 - 3.10938i) q^{24} +(-8.89828 - 2.36159i) q^{26} +(-3.94816 - 3.94816i) q^{27} +(0.965882 - 1.69151i) q^{28} +(3.74613 + 3.74613i) q^{29} +4.29021 q^{31} +(2.76991 - 4.93230i) q^{32} +3.07405i q^{33} +(-0.599426 + 0.347984i) q^{34} +(-1.07157 - 0.611889i) q^{36} +(4.55320 + 4.55320i) q^{37} +(2.33362 - 8.79286i) q^{38} -10.0493i q^{39} +10.1542i q^{41} +(2.05506 + 0.545410i) q^{42} +(1.79055 + 1.79055i) q^{43} +(1.04911 + 3.84204i) q^{44} +(1.37963 + 2.37650i) q^{46} +10.0162i q^{47} +(5.97936 + 1.54128i) q^{48} -6.05147 q^{49} +(-0.534979 - 0.534979i) q^{51} +(-3.42960 - 12.5599i) q^{52} +(-5.61412 - 5.61412i) q^{53} +(2.02555 - 7.63211i) q^{54} +(2.75461 - 0.0196757i) q^{56} +9.93022 q^{57} +(-1.92191 + 7.24157i) q^{58} +(-8.44185 + 8.44185i) q^{59} +(3.01095 + 3.01095i) q^{61} +(3.04614 + 5.24718i) q^{62} -0.600897i q^{63} +(7.99918 - 0.114280i) q^{64} +(-3.75974 + 2.18264i) q^{66} +(-7.07504 + 7.07504i) q^{67} +(-0.851209 - 0.486056i) q^{68} +(-2.12099 + 2.12099i) q^{69} -0.897891i q^{71} +(-0.0124646 - 1.74505i) q^{72} +9.71555 q^{73} +(-2.33596 + 8.80170i) q^{74} +(12.4111 - 3.38897i) q^{76} +(-1.37138 + 1.37138i) q^{77} +(12.2909 - 7.13520i) q^{78} +14.7857 q^{79} +6.76838 q^{81} +(-12.4192 + 7.20968i) q^{82} +(0.815000 - 0.815000i) q^{83} +(0.792065 + 2.90071i) q^{84} +(-0.918620 + 3.46128i) q^{86} -8.17827 q^{87} +(-3.95415 + 4.01105i) q^{88} +1.12404i q^{89} +(4.48314 - 4.48314i) q^{91} +(-1.92703 + 3.37472i) q^{92} +(-4.68303 + 4.68303i) q^{93} +(-12.2504 + 7.11174i) q^{94} +(2.36039 + 8.40744i) q^{96} -7.54442i q^{97} +(-4.29667 - 7.40130i) q^{98} +(0.868775 + 0.868775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{8} - 2 q^{11} + 6 q^{12} - 4 q^{13} - 14 q^{14} + 2 q^{16} + 18 q^{18} + 14 q^{19} - 20 q^{21} + 20 q^{22} - 12 q^{23} + 14 q^{24} - 16 q^{26}+ \cdots - 12 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^8 - 2 * q^11 + 6 * q^12 - 4 * q^13 - 14 * q^14 + 2 * q^16 + 18 * q^18 + 14 * q^19 - 20 * q^21 + 20 * q^22 - 12 * q^23 + 14 * q^24 - 16 * q^26 - 10 * q^27 + 10 * q^28 - 4 * q^31 - 2 * q^32 + 6 * q^34 + 2 * q^36 + 8 * q^37 - 28 * q^38 - 10 * q^42 + 44 * q^44 - 10 * q^46 + 58 * q^48 - 4 * q^49 + 10 * q^51 + 16 * q^53 - 10 * q^54 + 6 * q^56 + 16 * q^57 - 4 * q^58 - 20 * q^59 + 4 * q^61 - 22 * q^62 - 38 * q^64 + 32 * q^66 - 50 * q^67 - 50 * q^68 + 54 * q^72 - 40 * q^73 - 10 * q^74 + 60 * q^76 + 8 * q^77 + 48 * q^78 - 12 * q^79 - 8 * q^81 + 12 * q^82 - 2 * q^83 - 34 * q^84 + 6 * q^86 + 64 * q^87 - 56 * q^88 - 50 * q^92 - 44 * q^93 - 32 * q^94 - 34 * q^96 + 30 * q^98 - 12 * q^99

Introduction

L-functions

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