LMFDB - Embedded newform 429.2.m.b.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(109,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("429.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.m (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.1
Character	$\chi$	$=$	429.109
Dual form			429.2.m.b.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92050 - 1.92050i) q^{2} +1.00000 q^{3} +5.37666i q^{4} +(-0.179544 + 0.179544i) q^{5} +(-1.92050 - 1.92050i) q^{6} +(-1.23995 + 1.23995i) q^{7} +(6.48489 - 6.48489i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.92050 - 1.92050i) q^{2} +1.00000 q^{3} +5.37666i q^{4} +(-0.179544 + 0.179544i) q^{5} +(-1.92050 - 1.92050i) q^{6} +(-1.23995 + 1.23995i) q^{7} +(6.48489 - 6.48489i) q^{8} +1.00000 q^{9} +0.689629 q^{10} +(-3.29767 - 0.354039i) q^{11} +5.37666i q^{12} +(-3.59003 + 0.334239i) q^{13} +4.76267 q^{14} +(-0.179544 + 0.179544i) q^{15} -14.1552 q^{16} +5.18603 q^{17} +(-1.92050 - 1.92050i) q^{18} +(5.00964 + 5.00964i) q^{19} +(-0.965347 - 0.965347i) q^{20} +(-1.23995 + 1.23995i) q^{21} +(5.65326 + 7.01313i) q^{22} +2.91402i q^{23} +(6.48489 - 6.48489i) q^{24} +4.93553i q^{25} +(7.53656 + 6.25275i) q^{26} +1.00000 q^{27} +(-6.66682 - 6.66682i) q^{28} +9.44092i q^{29} +0.689629 q^{30} +(-0.0134612 + 0.0134612i) q^{31} +(14.2153 + 14.2153i) q^{32} +(-3.29767 - 0.354039i) q^{33} +(-9.95979 - 9.95979i) q^{34} -0.445253i q^{35} +5.37666i q^{36} +(4.35547 + 4.35547i) q^{37} -19.2420i q^{38} +(-3.59003 + 0.334239i) q^{39} +2.32864i q^{40} +(-3.80943 - 3.80943i) q^{41} +4.76267 q^{42} -3.46108 q^{43} +(1.90355 - 17.7305i) q^{44} +(-0.179544 + 0.179544i) q^{45} +(5.59639 - 5.59639i) q^{46} +(-0.296243 - 0.296243i) q^{47} -14.1552 q^{48} +3.92503i q^{49} +(9.47870 - 9.47870i) q^{50} +5.18603 q^{51} +(-1.79709 - 19.3024i) q^{52} +6.33254 q^{53} +(-1.92050 - 1.92050i) q^{54} +(0.655643 - 0.528512i) q^{55} +16.0819i q^{56} +(5.00964 + 5.00964i) q^{57} +(18.1313 - 18.1313i) q^{58} +(-7.22531 - 7.22531i) q^{59} +(-0.965347 - 0.965347i) q^{60} -2.44346i q^{61} +0.0517045 q^{62} +(-1.23995 + 1.23995i) q^{63} -26.2906i q^{64} +(0.584557 - 0.704578i) q^{65} +(5.65326 + 7.01313i) q^{66} +(6.64309 - 6.64309i) q^{67} +27.8835i q^{68} +2.91402i q^{69} +(-0.855109 + 0.855109i) q^{70} +(-10.7997 + 10.7997i) q^{71} +(6.48489 - 6.48489i) q^{72} +(0.550325 - 0.550325i) q^{73} -16.7294i q^{74} +4.93553i q^{75} +(-26.9351 + 26.9351i) q^{76} +(4.52796 - 3.64997i) q^{77} +(7.53656 + 6.25275i) q^{78} +0.139736i q^{79} +(2.54147 - 2.54147i) q^{80} +1.00000 q^{81} +14.6320i q^{82} +(2.55154 + 2.55154i) q^{83} +(-6.66682 - 6.66682i) q^{84} +(-0.931121 + 0.931121i) q^{85} +(6.64702 + 6.64702i) q^{86} +9.44092i q^{87} +(-23.6810 + 19.0891i) q^{88} +(-7.81316 - 7.81316i) q^{89} +0.689629 q^{90} +(4.03703 - 4.86591i) q^{91} -15.6677 q^{92} +(-0.0134612 + 0.0134612i) q^{93} +1.13787i q^{94} -1.79890 q^{95} +(14.2153 + 14.2153i) q^{96} +(3.14096 - 3.14096i) q^{97} +(7.53802 - 7.53802i) q^{98} +(-3.29767 - 0.354039i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9}+O(q^{10}) $ 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9	$ 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9} - 4 q^{15} - 20 q^{16} - 16 q^{20} - 8 q^{22} + 12 q^{26} + 28 q^{27} + 8 q^{31} - 32 q^{34} - 12 q^{37} + 36 q^{44} - 4 q^{45} - 40 q^{47} - 20 q^{48} + 8 q^{53} - 16 q^{55} + 16 q^{58} - 44 q^{59} - 16 q^{60} - 8 q^{66} - 20 q^{67} - 36 q^{70} - 60 q^{71} + 12 q^{78} - 8 q^{80} + 28 q^{81} + 48 q^{86} + 32 q^{89} + 4 q^{91} + 64 q^{92} + 8 q^{93} + 8 q^{97}+O(q^{100}) $ 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9 - 4 * q^15 - 20 * q^16 - 16 * q^20 - 8 * q^22 + 12 * q^26 + 28 * q^27 + 8 * q^31 - 32 * q^34 - 12 * q^37 + 36 * q^44 - 4 * q^45 - 40 * q^47 - 20 * q^48 + 8 * q^53 - 16 * q^55 + 16 * q^58 - 44 * q^59 - 16 * q^60 - 8 * q^66 - 20 * q^67 - 36 * q^70 - 60 * q^71 + 12 * q^78 - 8 * q^80 + 28 * q^81 + 48 * q^86 + 32 * q^89 + 4 * q^91 + 64 * q^92 + 8 * q^93 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.92050	−	1.92050i	−1.35800	−	1.35800i	−0.876380	−	0.481621i	$-0.840048\pi$
$2$	−1.92050	−	1.92050i	−1.35800	−	1.35800i	−0.481621	−	0.876380i	$-0.659952\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$			5.37666i			2.68833i
$5$	−0.179544	+	0.179544i	−0.0802945	+	0.0802945i	−0.746113	−	0.665819i	$-0.768082\pi$
$5$	−0.179544	+	0.179544i	−0.0802945	+	0.0802945i	0.665819	+	0.746113i	$0.268082\pi$
$6$	−1.92050	−	1.92050i	−0.784042	−	0.784042i
$7$	−1.23995	+	1.23995i	−0.468659	+	0.468659i	−0.901480	−	0.432821i	$-0.857518\pi$
$7$	−1.23995	+	1.23995i	−0.468659	+	0.468659i	0.432821	+	0.901480i	$0.357518\pi$
$8$	6.48489	−	6.48489i	2.29275	−	2.29275i
$9$	1.00000			0.333333
$10$	0.689629			0.218080
$11$	−3.29767	−	0.354039i	−0.994286	−	0.106747i
$11$	−3.29767	−	0.354039i	−0.994286	−	0.106747i
$12$			5.37666i			1.55211i
$13$	−3.59003	+	0.334239i	−0.995694	+	0.0927013i
$13$	−3.59003	+	0.334239i	−0.995694	+	0.0927013i
$14$	4.76267			1.27288
$15$	−0.179544	+	0.179544i	−0.0463580	+	0.0463580i
$16$	−14.1552			−3.53879
$17$	5.18603			1.25780			0.628899	−	0.777487i	$-0.283506\pi$
$17$	5.18603			1.25780			0.628899	+	0.777487i	$0.283506\pi$
$18$	−1.92050	−	1.92050i	−0.452667	−	0.452667i
$19$	5.00964	+	5.00964i	1.14929	+	1.14929i	0.986693	+	0.162597i	$0.0519872\pi$
$19$	5.00964	+	5.00964i	1.14929	+	1.14929i	0.162597	+	0.986693i	$0.448013\pi$
$20$	−0.965347	−	0.965347i	−0.215858	−	0.215858i
$21$	−1.23995	+	1.23995i	−0.270580	+	0.270580i
$22$	5.65326	+	7.01313i	1.20528	+	1.49520i
$23$			2.91402i			0.607616i	0.952733	+	0.303808i	$0.0982581\pi$
$23$			2.91402i			0.607616i	−0.952733	+	0.303808i	$0.901742\pi$
$24$	6.48489	−	6.48489i	1.32372	−	1.32372i
$25$			4.93553i			0.987106i
$26$	7.53656	+	6.25275i	1.47804	+	1.22626i
$27$	1.00000			0.192450
$28$	−6.66682	−	6.66682i	−1.25991	−	1.25991i
$29$			9.44092i			1.75314i	0.481279	+	0.876568i	$0.340173\pi$
$29$			9.44092i			1.75314i	−0.481279	+	0.876568i	$0.659827\pi$
$30$	0.689629			0.125909
$31$	−0.0134612	+	0.0134612i	−0.00241770	+	0.00241770i	−0.708315	−	0.705897i	$-0.750544\pi$
$31$	−0.0134612	+	0.0134612i	−0.00241770	+	0.00241770i	0.705897	+	0.708315i	$0.250544\pi$
$32$	14.2153	+	14.2153i	2.51293	+	2.51293i
$33$	−3.29767	−	0.354039i	−0.574051	−	0.0616302i
$34$	−9.95979	−	9.95979i	−1.70809	−	1.70809i
$35$		−	0.445253i		−	0.0752614i
$36$			5.37666i			0.896110i
$37$	4.35547	+	4.35547i	0.716035	+	0.716035i	0.967791	−	0.251756i	$-0.0810080\pi$
$37$	4.35547	+	4.35547i	0.716035	+	0.716035i	−0.251756	+	0.967791i	$0.581008\pi$
$38$		−	19.2420i		−	3.12147i
$39$	−3.59003	+	0.334239i	−0.574864	+	0.0535211i
$40$			2.32864i			0.368191i
$41$	−3.80943	−	3.80943i	−0.594933	−	0.594933i	0.344027	−	0.938960i	$-0.388209\pi$
$41$	−3.80943	−	3.80943i	−0.594933	−	0.594933i	−0.938960	+	0.344027i	$0.888209\pi$
$42$	4.76267			0.734896
$43$	−3.46108			−0.527810			−0.263905	−	0.964549i	$-0.585011\pi$
$43$	−3.46108			−0.527810			−0.263905	+	0.964549i	$0.585011\pi$
$44$	1.90355	−	17.7305i	0.286970	−	2.67297i
$45$	−0.179544	+	0.179544i	−0.0267648	+	0.0267648i
$46$	5.59639	−	5.59639i	0.825143	−	0.825143i
$47$	−0.296243	−	0.296243i	−0.0432115	−	0.0432115i	0.685171	−	0.728382i	$-0.259728\pi$
$47$	−0.296243	−	0.296243i	−0.0432115	−	0.0432115i	−0.728382	+	0.685171i	$0.759728\pi$
$48$	−14.1552			−2.04312
$49$			3.92503i			0.560718i
$50$	9.47870	−	9.47870i	1.34049	−	1.34049i
$51$	5.18603			0.726190
$52$	−1.79709	−	19.3024i	−0.249212	−	2.67675i
$53$	6.33254			0.869841			0.434921	−	0.900469i	$-0.356776\pi$
$53$	6.33254			0.869841			0.434921	+	0.900469i	$0.356776\pi$
$54$	−1.92050	−	1.92050i	−0.261347	−	0.261347i
$55$	0.655643	−	0.528512i	0.0884069	−	0.0712645i
$56$			16.0819i			2.14904i
$57$	5.00964	+	5.00964i	0.663543	+	0.663543i
$58$	18.1313	−	18.1313i	2.38076	−	2.38076i
$59$	−7.22531	−	7.22531i	−0.940655	−	0.940655i	0.0576799	−	0.998335i	$-0.481630\pi$
$59$	−7.22531	−	7.22531i	−0.940655	−	0.940655i	−0.998335	+	0.0576799i	$0.981630\pi$
$60$	−0.965347	−	0.965347i	−0.124626	−	0.124626i
$61$		−	2.44346i		−	0.312853i	−0.987690	−	0.156426i	$-0.950003\pi$
$61$		−	2.44346i		−	0.312853i	0.987690	−	0.156426i	$-0.0499974\pi$
$62$	0.0517045			0.00656648
$63$	−1.23995	+	1.23995i	−0.156220	+	0.156220i
$64$		−	26.2906i		−	3.28632i
$65$	0.584557	−	0.704578i	0.0725053	−	0.0873921i
$66$	5.65326	+	7.01313i	0.695868	+	0.863256i
$67$	6.64309	−	6.64309i	0.811582	−	0.811582i	−0.173289	−	0.984871i	$-0.555439\pi$
$67$	6.64309	−	6.64309i	0.811582	−	0.811582i	0.984871	+	0.173289i	$0.0554394\pi$
$68$			27.8835i			3.38138i
$69$			2.91402i			0.350807i
$70$	−0.855109	+	0.855109i	−0.102205	+	0.102205i
$71$	−10.7997	+	10.7997i	−1.28169	+	1.28169i	−0.341982	+	0.939707i	$0.611098\pi$
$71$	−10.7997	+	10.7997i	−1.28169	+	1.28169i	−0.939707	+	0.341982i	$0.888902\pi$
$72$	6.48489	−	6.48489i	0.764251	−	0.764251i
$73$	0.550325	−	0.550325i	0.0644107	−	0.0644107i	−0.674168	−	0.738578i	$-0.735497\pi$
$73$	0.550325	−	0.550325i	0.0644107	−	0.0644107i	0.738578	+	0.674168i	$0.235497\pi$
$74$		−	16.7294i		−	1.94475i
$75$			4.93553i			0.569906i
$76$	−26.9351	+	26.9351i	−3.08967	+	3.08967i
$77$	4.52796	−	3.64997i	0.516009	−	0.415953i
$78$	7.53656	+	6.25275i	0.853348	+	0.707984i
$79$			0.139736i			0.0157215i	0.999969	+	0.00786075i	$0.00250218\pi$
$79$			0.139736i			0.0157215i	−0.999969	+	0.00786075i	$0.997498\pi$
$80$	2.54147	−	2.54147i	0.284146	−	0.284146i
$81$	1.00000			0.111111
$82$			14.6320i			1.61584i
$83$	2.55154	+	2.55154i	0.280068	+	0.280068i	0.833136	−	0.553068i	$-0.186543\pi$
$83$	2.55154	+	2.55154i	0.280068	+	0.280068i	−0.553068	+	0.833136i	$0.686543\pi$
$84$	−6.66682	−	6.66682i	−0.727409	−	0.727409i
$85$	−0.931121	+	0.931121i	−0.100994	+	0.100994i
$86$	6.64702	+	6.64702i	0.716766	+	0.716766i
$87$			9.44092i			1.01217i
$88$	−23.6810	+	19.0891i	−2.52440	+	2.03491i
$89$	−7.81316	−	7.81316i	−0.828193	−	0.828193i	0.159073	−	0.987267i	$-0.449149\pi$
$89$	−7.81316	−	7.81316i	−0.828193	−	0.828193i	−0.987267	+	0.159073i	$0.949149\pi$
$90$	0.689629			0.0726933
$91$	4.03703	−	4.86591i	0.423195	−	0.510086i
$92$	−15.6677			−1.63347
$93$	−0.0134612	+	0.0134612i	−0.00139586	+	0.00139586i
$94$			1.13787i			0.117362i
$95$	−1.79890			−0.184563
$96$	14.2153	+	14.2153i	1.45084	+	1.45084i
$97$	3.14096	−	3.14096i	0.318916	−	0.318916i	−0.529435	−	0.848351i	$-0.677596\pi$
$97$	3.14096	−	3.14096i	0.318916	−	0.318916i	0.848351	+	0.529435i	$0.177596\pi$
$98$	7.53802	−	7.53802i	0.761455	−	0.761455i
$99$	−3.29767	−	0.354039i	−0.331429	−	0.0355822i
$100$	−26.5367			−2.65367
$101$	2.97764			0.296286			0.148143	−	0.988966i	$-0.452670\pi$
$101$	2.97764			0.296286			0.148143	+	0.988966i	$0.452670\pi$
$102$	−9.95979	−	9.95979i	−0.986166	−	0.986166i
$103$			5.13357i			0.505825i	0.967489	+	0.252913i	$0.0813885\pi$
$103$			5.13357i			0.505825i	−0.967489	+	0.252913i	$0.918611\pi$
$104$	−21.1134	+	25.4484i	−2.07034	+	2.49542i
$105$		−	0.445253i		−	0.0434522i
$106$	−12.1617	−	12.1617i	−1.18124	−	1.18124i
$107$		−	14.7265i		−	1.42367i	−0.702349	−	0.711833i	$-0.747865\pi$
$107$		−	14.7265i		−	1.42367i	0.702349	−	0.711833i	$-0.252135\pi$
$108$			5.37666i			0.517370i
$109$	2.68699	+	2.68699i	0.257367	+	0.257367i	0.823982	−	0.566616i	$-0.191748\pi$
$109$	2.68699	+	2.68699i	0.257367	+	0.257367i	−0.566616	+	0.823982i	$0.691748\pi$
$110$	−2.27417	−	0.244155i	−0.216834	−	0.0232793i
$111$	4.35547	+	4.35547i	0.413403	+	0.413403i
$112$	17.5518	−	17.5518i	1.65849	−	1.65849i
$113$	−13.5143			−1.27131			−0.635657	−	0.771971i	$-0.719271\pi$
$113$	−13.5143			−1.27131			−0.635657	+	0.771971i	$0.719271\pi$
$114$		−	19.2420i		−	1.80218i
$115$	−0.523195	−	0.523195i	−0.0487882	−	0.0487882i
$116$	−50.7606			−4.71301
$117$	−3.59003	+	0.334239i	−0.331898	+	0.0309004i
$118$			27.7525i			2.55482i
$119$	−6.43044	+	6.43044i	−0.589478	+	0.589478i
$120$			2.32864i			0.212575i
$121$	10.7493	+	2.33501i	0.977210	+	0.212274i
$122$	−4.69267	+	4.69267i	−0.424854	+	0.424854i
$123$	−3.80943	−	3.80943i	−0.343485	−	0.343485i
$124$	−0.0723763	−	0.0723763i	−0.00649958	−	0.00649958i
$125$	−1.78386	−	1.78386i	−0.159554	−	0.159554i
$126$	4.76267			0.424293
$127$	4.43752			0.393766			0.196883	−	0.980427i	$-0.436918\pi$
$127$	4.43752			0.393766			0.196883	+	0.980427i	$0.436918\pi$
$128$	−22.0606	+	22.0606i	−1.94990	+	1.94990i
$129$	−3.46108			−0.304731
$130$	−2.47579	+	0.230501i	−0.217141	+	0.0202163i
$131$		−	2.35034i		−	0.205350i	−0.994715	−	0.102675i	$-0.967260\pi$
$131$		−	2.35034i		−	0.205350i	0.994715	−	0.102675i	$-0.0327402\pi$
$132$	1.90355	−	17.7305i	0.165682	−	1.54324i
$133$	−12.4234			−1.07725
$134$	−25.5161			−2.20426
$135$	−0.179544	+	0.179544i	−0.0154527	+	0.0154527i
$136$	33.6308	−	33.6308i	2.88382	−	2.88382i
$137$	14.0789	+	14.0789i	1.20284	+	1.20284i	0.973299	+	0.229539i	$0.0737218\pi$
$137$	14.0789	+	14.0789i	1.20284	+	1.20284i	0.229539	+	0.973299i	$0.426278\pi$
$138$	5.59639	−	5.59639i	0.476396	−	0.476396i
$139$		−	0.120678i		−	0.0102357i	−0.999987	−	0.00511787i	$-0.998371\pi$
$139$		−	0.120678i		−	0.0102357i	0.999987	−	0.00511787i	$-0.00162908\pi$
$140$	2.39397			0.202328
$141$	−0.296243	−	0.296243i	−0.0249482	−	0.0249482i
$142$	41.4817			3.48107
$143$	11.9571	+	0.168796i	0.999900	+	0.0141154i
$144$	−14.1552			−1.17960
$145$	−1.69506	−	1.69506i	−0.140767	−	0.140767i
$146$	−2.11380			−0.174940
$147$			3.92503i			0.323731i
$148$	−23.4179	+	23.4179i	−1.92494	+	1.92494i
$149$	−3.11109	−	3.11109i	−0.254870	−	0.254870i	0.568094	−	0.822964i	$-0.307681\pi$
$149$	−3.11109	−	3.11109i	−0.254870	−	0.254870i	−0.822964	+	0.568094i	$0.807681\pi$
$150$	9.47870	−	9.47870i	0.773932	−	0.773932i
$151$	−8.25114	+	8.25114i	−0.671468	+	0.671468i	−0.958054	−	0.286586i	$-0.907479\pi$
$151$	−8.25114	+	8.25114i	−0.671468	+	0.671468i	0.286586	+	0.958054i	$0.407479\pi$
$152$	64.9739			5.27008
$153$	5.18603			0.419266
$154$	−15.7057	−	1.68617i	−1.26560	−	0.135875i
$155$		−	0.00483375i		−	0.000388256i
$156$	−1.79709	−	19.3024i	−0.143882	−	1.54543i
$157$	−5.28522			−0.421806			−0.210903	−	0.977507i	$-0.567640\pi$
$157$	−5.28522			−0.421806			−0.210903	+	0.977507i	$0.567640\pi$
$158$	0.268363	−	0.268363i	0.0213498	−	0.0213498i
$159$	6.33254			0.502203
$160$	−5.10453			−0.403548
$161$	−3.61326	−	3.61326i	−0.284765	−	0.284765i
$162$	−1.92050	−	1.92050i	−0.150889	−	0.150889i
$163$	8.29595	+	8.29595i	0.649789	+	0.649789i	0.952942	−	0.303153i	$-0.0980394\pi$
$163$	8.29595	+	8.29595i	0.649789	+	0.649789i	−0.303153	+	0.952942i	$0.598039\pi$
$164$	20.4820	−	20.4820i	1.59938	−	1.59938i
$165$	0.655643	−	0.528512i	0.0510417	−	0.0411446i
$166$		−	9.80049i		−	0.760666i
$167$	−5.64976	+	5.64976i	−0.437192	+	0.437192i	−0.891066	−	0.453874i	$-0.850042\pi$
$167$	−5.64976	+	5.64976i	−0.437192	+	0.437192i	0.453874	+	0.891066i	$0.350042\pi$
$168$			16.0819i			1.24075i
$169$	12.7766	−	2.39985i	0.982813	−	0.184604i
$170$	3.57644			0.274300
$171$	5.00964	+	5.00964i	0.383097	+	0.383097i
$172$		−	18.6091i		−	1.41893i
$173$	12.6825			0.964236			0.482118	−	0.876106i	$-0.339868\pi$
$173$	12.6825			0.964236			0.482118	+	0.876106i	$0.339868\pi$
$174$	18.1313	−	18.1313i	1.37453	−	1.37453i
$175$	−6.11983	−	6.11983i	−0.462616	−	0.462616i
$176$	46.6791	+	5.01148i	3.51857	+	0.377754i
$177$	−7.22531	−	7.22531i	−0.543088	−	0.543088i
$178$			30.0104i			2.24937i
$179$		−	22.5467i		−	1.68522i	−0.538523	−	0.842611i	$-0.681017\pi$
$179$		−	22.5467i		−	1.68522i	0.538523	−	0.842611i	$-0.318983\pi$
$180$	−0.965347	−	0.965347i	−0.0719527	−	0.0719527i
$181$		−	10.1696i		−	0.755897i	−0.925827	−	0.377948i	$-0.876630\pi$
$181$		−	10.1696i		−	0.755897i	0.925827	−	0.377948i	$-0.123370\pi$
$182$	−17.0981	+	1.59187i	−1.26740	+	0.117997i
$183$		−	2.44346i		−	0.180626i
$184$	18.8971	+	18.8971i	1.39311	+	1.39311i
$185$	−1.56400			−0.114987
$186$	0.0517045			0.00379116
$187$	−17.1018	−	1.83606i	−1.25061	−	0.134266i
$188$	1.59280	−	1.59280i	0.116167	−	0.116167i
$189$	−1.23995	+	1.23995i	−0.0901934	+	0.0901934i
$190$	3.45479	+	3.45479i	0.250637	+	0.250637i
$191$	−10.2108			−0.738830			−0.369415	−	0.929265i	$-0.620442\pi$
$191$	−10.2108			−0.738830			−0.369415	+	0.929265i	$0.620442\pi$
$192$		−	26.2906i		−	1.89736i
$193$	6.11830	−	6.11830i	0.440405	−	0.440405i	−0.451743	−	0.892148i	$-0.649198\pi$
$193$	6.11830	−	6.11830i	0.440405	−	0.440405i	0.892148	+	0.451743i	$0.149198\pi$
$194$	−12.0644			−0.866177
$195$	0.584557	−	0.704578i	0.0418610	−	0.0504559i
$196$	−21.1035			−1.50740
$197$	−10.8636	−	10.8636i	−0.773999	−	0.773999i	0.204804	−	0.978803i	$-0.434344\pi$
$197$	−10.8636	−	10.8636i	−0.773999	−	0.773999i	−0.978803	+	0.204804i	$0.934344\pi$
$198$	5.65326	+	7.01313i	0.401760	+	0.498401i
$199$		−	25.5976i		−	1.81456i	−0.420524	−	0.907282i	$-0.638154\pi$
$199$		−	25.5976i		−	1.81456i	0.420524	−	0.907282i	$-0.361846\pi$
$200$	32.0063	+	32.0063i	2.26319	+	2.26319i
$201$	6.64309	−	6.64309i	0.468567	−	0.468567i
$202$	−5.71856	−	5.71856i	−0.402356	−	0.402356i
$203$	−11.7063	−	11.7063i	−0.821622	−	0.821622i
$204$			27.8835i			1.95224i
$205$	1.36792			0.0955397
$206$	9.85903	−	9.85903i	0.686911	−	0.686911i
$207$			2.91402i			0.202539i
$208$	50.8174	−	4.73121i	3.52355	−	0.328051i
$209$	−14.7466	−	18.2938i	−1.02004	−	1.26541i
$210$	−0.855109	+	0.855109i	−0.0590081	+	0.0590081i
$211$		−	24.7167i		−	1.70157i	−0.525514	−	0.850785i	$-0.676127\pi$
$211$		−	24.7167i		−	1.70157i	0.525514	−	0.850785i	$-0.323873\pi$
$212$			34.0479i			2.33842i
$213$	−10.7997	+	10.7997i	−0.739983	+	0.739983i
$214$	−28.2823	+	28.2823i	−1.93334	+	1.93334i
$215$	0.621416	−	0.621416i	0.0423802	−	0.0423802i
$216$	6.48489	−	6.48489i	0.441241	−	0.441241i
$217$		−	0.0333825i		−	0.00226615i
$218$		−	10.3207i		−	0.699008i
$219$	0.550325	−	0.550325i	0.0371875	−	0.0371875i
$220$	2.84163	+	3.52517i	0.191583	+	0.237667i
$221$	−18.6180	+	1.73338i	−1.25238	+	0.116599i
$222$		−	16.7294i		−	1.12280i
$223$	1.47237	−	1.47237i	0.0985972	−	0.0985972i	−0.656088	−	0.754685i	$-0.727790\pi$
$223$	1.47237	−	1.47237i	0.0985972	−	0.0985972i	0.754685	+	0.656088i	$0.227790\pi$
$224$	−35.2526			−2.35541
$225$			4.93553i			0.329035i
$226$	25.9542	+	25.9542i	1.72645	+	1.72645i
$227$	5.70162	+	5.70162i	0.378430	+	0.378430i	0.870535	−	0.492106i	$-0.163773\pi$
$227$	5.70162	+	5.70162i	0.378430	+	0.378430i	−0.492106	+	0.870535i	$0.663773\pi$
$228$	−26.9351	+	26.9351i	−1.78382	+	1.78382i
$229$	17.0678	+	17.0678i	1.12787	+	1.12787i	0.990523	+	0.137348i	$0.0438577\pi$
$229$	17.0678	+	17.0678i	1.12787	+	1.12787i	0.137348	+	0.990523i	$0.456142\pi$
$230$			2.00960i			0.132509i
$231$	4.52796	−	3.64997i	0.297918	−	0.240151i
$232$	61.2233	+	61.2233i	4.01951	+	4.01951i
$233$	9.58947			0.628227			0.314114	−	0.949385i	$-0.398293\pi$
$233$	9.58947			0.628227			0.314114	+	0.949385i	$0.398293\pi$
$234$	7.53656	+	6.25275i	0.492680	+	0.408755i
$235$	0.106377			0.00693929
$236$	38.8480	−	38.8480i	2.52879	−	2.52879i
$237$			0.139736i			0.00907682i
$238$	24.6994			1.60102
$239$	16.8692	+	16.8692i	1.09118	+	1.09118i	0.995403	+	0.0957771i	$0.0305336\pi$
$239$	16.8692	+	16.8692i	1.09118	+	1.09118i	0.0957771	+	0.995403i	$0.469466\pi$
$240$	2.54147	−	2.54147i	0.164052	−	0.164052i
$241$	−1.18063	+	1.18063i	−0.0760513	+	0.0760513i	−0.744109	−	0.668058i	$-0.767126\pi$
$241$	−1.18063	+	1.18063i	−0.0760513	+	0.0760513i	0.668058	+	0.744109i	$0.267126\pi$
$242$	−16.1597	−	25.1285i	−1.03878	−	1.61532i
$243$	1.00000			0.0641500
$244$	13.1377			0.841052
$245$	−0.704715	−	0.704715i	−0.0450226	−	0.0450226i
$246$			14.6320i			0.932905i
$247$	−19.6591	−	16.3103i	−1.25088	−	1.03780i
$248$			0.174589i			0.0110864i
$249$	2.55154	+	2.55154i	0.161697	+	0.161697i
$250$			6.85183i			0.433348i
$251$			12.4101i			0.783317i	0.920111	+	0.391658i	$0.128098\pi$
$251$			12.4101i			0.783317i	−0.920111	+	0.391658i	$0.871902\pi$
$252$	−6.66682	−	6.66682i	−0.419970	−	0.419970i
$253$	1.03168	−	9.60950i	0.0648610	−	0.604144i
$254$	−8.52227	−	8.52227i	−0.534735	−	0.534735i
$255$	−0.931121	+	0.931121i	−0.0583090	+	0.0583090i
$256$	32.1537			2.00961
$257$			17.3718i			1.08362i	0.840501	+	0.541811i	$0.182261\pi$
$257$			17.3718i			1.08362i	−0.840501	+	0.541811i	$0.817739\pi$
$258$	6.64702	+	6.64702i	0.413825	+	0.413825i
$259$	−10.8012			−0.671152
$260$	3.78828	+	3.14296i	0.234939	+	0.194918i
$261$			9.44092i			0.584378i
$262$	−4.51383	+	4.51383i	−0.278865	+	0.278865i
$263$		−	0.670890i		−	0.0413688i	−0.999786	−	0.0206844i	$-0.993415\pi$
$263$		−	0.670890i		−	0.0413688i	0.999786	−	0.0206844i	$-0.00658452\pi$
$264$	−23.6810	+	19.0891i	−1.45746	+	1.17486i
$265$	−1.13697	+	1.13697i	−0.0698435	+	0.0698435i
$266$	23.8593	+	23.8593i	1.46291	+	1.46291i
$267$	−7.81316	−	7.81316i	−0.478158	−	0.478158i
$268$	35.7176	+	35.7176i	2.18180	+	2.18180i
$269$	−4.27988			−0.260949			−0.130475	−	0.991452i	$-0.541650\pi$
$269$	−4.27988			−0.260949			−0.130475	+	0.991452i	$0.541650\pi$
$270$	0.689629			0.0419695
$271$	−18.5288	+	18.5288i	−1.12554	+	1.12554i	−0.134648	+	0.990894i	$0.542990\pi$
$271$	−18.5288	+	18.5288i	−1.12554	+	1.12554i	−0.990894	+	0.134648i	$0.957010\pi$
$272$	−73.4092			−4.45108
$273$	4.03703	−	4.86591i	0.244332	−	0.294498i
$274$		−	54.0770i		−	3.26691i
$275$	1.74737	−	16.2758i	0.105370	−	0.981466i
$276$	−15.6677			−0.943086
$277$	23.7485			1.42691			0.713455	−	0.700701i	$-0.247129\pi$
$277$	23.7485			1.42691			0.713455	+	0.700701i	$0.247129\pi$
$278$	−0.231762	+	0.231762i	−0.0139001	+	0.0139001i
$279$	−0.0134612	+	0.0134612i	−0.000805901	+	0.000805901i
$280$	−2.88741	−	2.88741i	−0.172556	−	0.172556i
$281$	−13.0642	+	13.0642i	−0.779346	+	0.779346i	−0.979720	−	0.200374i	$-0.935784\pi$
$281$	−13.0642	+	13.0642i	−0.779346	+	0.779346i	0.200374	+	0.979720i	$0.435784\pi$
$282$			1.13787i			0.0677592i
$283$	−28.3197			−1.68343			−0.841717	−	0.539919i	$-0.818455\pi$
$283$	−28.3197			−1.68343			−0.841717	+	0.539919i	$0.818455\pi$
$284$	−58.0663	−	58.0663i	−3.44560	−	3.44560i
$285$	−1.79890			−0.106558
$286$	−22.6394	−	23.2878i	−1.33870	−	1.37703i
$287$	9.44704			0.557641
$288$	14.2153	+	14.2153i	0.837643	+	0.837643i
$289$	9.89493			0.582055
$290$			6.51074i			0.382324i
$291$	3.14096	−	3.14096i	0.184126	−	0.184126i
$292$	2.95891	+	2.95891i	0.173157	+	0.173157i
$293$	12.6488	−	12.6488i	0.738951	−	0.738951i	−0.233424	−	0.972375i	$-0.574993\pi$
$293$	12.6488	−	12.6488i	0.738951	−	0.738951i	0.972375	+	0.233424i	$0.0749931\pi$
$294$	7.53802	−	7.53802i	0.439626	−	0.439626i
$295$	2.59452			0.151059
$296$	56.4895			3.28338
$297$	−3.29767	−	0.354039i	−0.191350	−	0.0205434i
$298$			11.9497i			0.692228i
$299$	−0.973981	−	10.4614i	−0.0563268	−	0.605000i
$300$	−26.5367			−1.53210
$301$	4.29158	−	4.29158i	0.247363	−	0.247363i
$302$	31.6927			1.82371
$303$	2.97764			0.171061
$304$	−70.9123	−	70.9123i	−4.06710	−	4.06710i
$305$	0.438708	+	0.438708i	0.0251204	+	0.0251204i
$306$	−9.95979	−	9.95979i	−0.569363	−	0.569363i
$307$	−19.3967	+	19.3967i	−1.10703	+	1.10703i	−0.113487	+	0.993539i	$0.536202\pi$
$307$	−19.3967	+	19.3967i	−1.10703	+	1.10703i	−0.993539	+	0.113487i	$0.963798\pi$
$308$	19.6247	+	24.3453i	1.11822	+	1.38720i
$309$			5.13357i			0.292038i
$310$	−0.00928323	+	0.00928323i	−0.000527252	+	0.000527252i
$311$			11.3761i			0.645081i	0.946556	+	0.322540i	$0.104537\pi$
$311$			11.3761i			0.645081i	−0.946556	+	0.322540i	$0.895463\pi$
$312$	−21.1134	+	25.4484i	−1.19531	+	1.44073i
$313$	18.6866			1.05623			0.528113	−	0.849174i	$-0.322900\pi$
$313$	18.6866			1.05623			0.528113	+	0.849174i	$0.322900\pi$
$314$	10.1503	+	10.1503i	0.572813	+	0.572813i
$315$		−	0.445253i		−	0.0250871i
$316$	−0.751312			−0.0422646
$317$	−7.26868	+	7.26868i	−0.408250	+	0.408250i	−0.881128	−	0.472878i	$-0.843215\pi$
$317$	−7.26868	+	7.26868i	−0.408250	+	0.408250i	0.472878	+	0.881128i	$0.343215\pi$
$318$	−12.1617	−	12.1617i	−0.681992	−	0.681992i
$319$	3.34245	−	31.1331i	0.187141	−	1.74312i
$320$	4.72031	+	4.72031i	0.263874	+	0.263874i
$321$		−	14.7265i		−	0.821954i
$322$			13.8785i			0.773421i
$323$	25.9801	+	25.9801i	1.44557	+	1.44557i
$324$			5.37666i			0.298703i
$325$	−1.64965	−	17.7187i	−0.0915060	−	0.982855i
$326$		−	31.8648i		−	1.76483i
$327$	2.68699	+	2.68699i	0.148591	+	0.148591i
$328$	−49.4074			−2.72807
$329$	0.734655			0.0405029
$330$	−2.27417	−	0.244155i	−0.125189	−	0.0134403i
$331$	−5.64534	+	5.64534i	−0.310296	+	0.310296i	−0.845024	−	0.534728i	$-0.820414\pi$
$331$	−5.64534	+	5.64534i	−0.310296	+	0.310296i	0.534728	+	0.845024i	$0.320414\pi$
$332$	−13.7188	+	13.7188i	−0.752916	+	0.752916i
$333$	4.35547	+	4.35547i	0.238678	+	0.238678i
$334$	21.7008			1.18741
$335$			2.38545i			0.130331i
$336$	17.5518	−	17.5518i	0.957527	−	0.957527i
$337$	24.1748			1.31689			0.658443	−	0.752630i	$-0.271215\pi$
$337$	24.1748			1.31689			0.658443	+	0.752630i	$0.271215\pi$
$338$	−29.1464	−	19.9285i	−1.58535	−	1.08397i
$339$	−13.5143			−0.733994
$340$	−5.00632	−	5.00632i	−0.271506	−	0.271506i
$341$	0.0491564	−	0.0396249i	0.00266197	−	0.00214581i
$342$		−	19.2420i		−	1.04049i
$343$	−13.5465	−	13.5465i	−0.731444	−	0.731444i
$344$	−22.4447	+	22.4447i	−1.21014	+	1.21014i
$345$	−0.523195	−	0.523195i	−0.0281679	−	0.0281679i
$346$	−24.3569	−	24.3569i	−1.30943	−	1.30943i
$347$			10.2980i			0.552826i	0.961039	+	0.276413i	$0.0891458\pi$
$347$			10.2980i			0.552826i	−0.961039	+	0.276413i	$0.910854\pi$
$348$	−50.7606			−2.72106
$349$	13.9071	−	13.9071i	0.744430	−	0.744430i	−0.228997	−	0.973427i	$-0.573545\pi$
$349$	13.9071	−	13.9071i	0.744430	−	0.744430i	0.973427	+	0.228997i	$0.0735446\pi$
$350$			23.5063i			1.25646i
$351$	−3.59003	+	0.334239i	−0.191621	+	0.0178404i
$352$	−41.8446	−	51.9101i	−2.23032	−	2.76682i
$353$	22.3648	−	22.3648i	1.19036	−	1.19036i	0.213393	−	0.976966i	$-0.431548\pi$
$353$	22.3648	−	22.3648i	1.19036	−	1.19036i	0.976966	−	0.213393i	$-0.0684516\pi$
$354$			27.7525i			1.47503i
$355$		−	3.87804i		−	0.205825i
$356$	42.0087	−	42.0087i	2.22646	−	2.22646i
$357$	−6.43044	+	6.43044i	−0.340335	+	0.340335i
$358$	−43.3011	+	43.3011i	−2.28853	+	2.28853i
$359$	−16.6426	+	16.6426i	−0.878361	+	0.878361i	−0.993365	−	0.115004i	$-0.963312\pi$
$359$	−16.6426	+	16.6426i	−0.878361	+	0.878361i	0.115004	+	0.993365i	$0.463312\pi$
$360$			2.32864i			0.122730i
$361$			31.1930i			1.64173i
$362$	−19.5306	+	19.5306i	−1.02651	+	1.02651i
$363$	10.7493	+	2.33501i	0.564193	+	0.122556i
$364$	26.1624	+	21.7057i	1.37128	+	1.13769i
$365$			0.197615i			0.0103436i
$366$	−4.69267	+	4.69267i	−0.245290	+	0.245290i
$367$	−12.4943			−0.652198			−0.326099	−	0.945336i	$-0.605734\pi$
$367$	−12.4943			−0.652198			−0.326099	+	0.945336i	$0.605734\pi$
$368$		−	41.2485i		−	2.15023i
$369$	−3.80943	−	3.80943i	−0.198311	−	0.198311i
$370$	3.00366	+	3.00366i	0.156153	+	0.156153i
$371$	−7.85206	+	7.85206i	−0.407659	+	0.407659i
$372$	−0.0723763	−	0.0723763i	−0.00375254	−	0.00375254i
$373$		−	12.0194i		−	0.622338i	−0.950355	−	0.311169i	$-0.899279\pi$
$373$		−	12.0194i		−	0.622338i	0.950355	−	0.311169i	$-0.100721\pi$
$374$	29.3180	+	36.3703i	1.51600	+	1.88066i
$375$	−1.78386	−	1.78386i	−0.0921183	−	0.0921183i
$376$	−3.84220			−0.198147
$377$	−3.15553	−	33.8932i	−0.162518	−	1.74559i
$378$	4.76267			0.244965
$379$	10.1883	−	10.1883i	0.523340	−	0.523340i	−0.395238	−	0.918579i	$-0.629338\pi$
$379$	10.1883	−	10.1883i	0.523340	−	0.523340i	0.918579	+	0.395238i	$0.129338\pi$
$380$		−	9.67208i		−	0.496167i
$381$	4.43752			0.227341
$382$	19.6099	+	19.6099i	1.00333	+	1.00333i
$383$	17.3442	−	17.3442i	0.886249	−	0.886249i	−0.107911	−	0.994161i	$-0.534416\pi$
$383$	17.3442	−	17.3442i	0.886249	−	0.886249i	0.994161	+	0.107911i	$0.0344162\pi$
$384$	−22.0606	+	22.0606i	−1.12577	+	1.12577i
$385$	−0.157637	+	1.46830i	−0.00803391	+	0.0748314i
$386$	−23.5004			−1.19614
$387$	−3.46108			−0.175937
$388$	16.8879	+	16.8879i	0.857353	+	0.857353i
$389$			10.5429i			0.534545i	0.963621	+	0.267272i	$0.0861223\pi$
$389$			10.5429i			0.534545i	−0.963621	+	0.267272i	$0.913878\pi$
$390$	−2.47579	+	0.230501i	−0.125366	+	0.0116719i
$391$			15.1122i			0.764258i
$392$	25.4534	+	25.4534i	1.28559	+	1.28559i
$393$		−	2.35034i		−	0.118559i
$394$			41.7271i			2.10218i
$395$	−0.0250887	−	0.0250887i	−0.00126235	−	0.00126235i
$396$	1.90355	−	17.7305i	0.0956568	−	0.890990i
$397$	13.0140	+	13.0140i	0.653154	+	0.653154i	0.953751	−	0.300597i	$-0.0971859\pi$
$397$	13.0140	+	13.0140i	0.653154	+	0.653154i	−0.300597	+	0.953751i	$0.597186\pi$
$398$	−49.1602	+	49.1602i	−2.46418	+	2.46418i
$399$	−12.4234			−0.621950
$400$		−	69.8632i		−	3.49316i
$401$	22.2162	+	22.2162i	1.10942	+	1.10942i	0.993226	+	0.116198i	$0.0370706\pi$
$401$	22.2162	+	22.2162i	1.10942	+	1.10942i	0.116198	+	0.993226i	$0.462929\pi$
$402$	−25.5161			−1.27263
$403$	0.0438268	−	0.0528253i	0.00218317	−	0.00263142i
$404$			16.0097i			0.796515i
$405$	−0.179544	+	0.179544i	−0.00892161	+	0.00892161i
$406$			44.9640i			2.23153i
$407$	−12.8209	−	15.9049i	−0.635509	−	0.788378i
$408$	33.6308	−	33.6308i	1.66497	−	1.66497i
$409$	−4.28369	−	4.28369i	−0.211815	−	0.211815i	0.593223	−	0.805038i	$-0.297855\pi$
$409$	−4.28369	−	4.28369i	−0.211815	−	0.211815i	−0.805038	+	0.593223i	$0.797855\pi$
$410$	−2.62709	−	2.62709i	−0.129743	−	0.129743i
$411$	14.0789	+	14.0789i	0.694459	+	0.694459i
$412$	−27.6015			−1.35983
$413$	17.9181			0.881693
$414$	5.59639	−	5.59639i	0.275048	−	0.275048i
$415$	−0.916228			−0.0449759
$416$	−55.7845	−	46.2819i	−2.73506	−	2.26916i
$417$		−	0.120678i		−	0.00590961i
$418$	−6.81243	+	63.4540i	−0.333207	+	3.10364i
$419$	37.3659			1.82544			0.912722	−	0.408582i	$-0.133977\pi$
$419$	37.3659			1.82544			0.912722	+	0.408582i	$0.133977\pi$
$420$	2.39397			0.116814
$421$	8.75013	−	8.75013i	0.426455	−	0.426455i	−0.460964	−	0.887419i	$-0.652496\pi$
$421$	8.75013	−	8.75013i	0.426455	−	0.426455i	0.887419	+	0.460964i	$0.152496\pi$
$422$	−47.4685	+	47.4685i	−2.31073	+	2.31073i
$423$	−0.296243	−	0.296243i	−0.0144038	−	0.0144038i
$424$	41.0658	−	41.0658i	1.99433	−	1.99433i
$425$			25.5958i			1.24158i
$426$	41.4817			2.00980
$427$	3.02978	+	3.02978i	0.146621	+	0.146621i
$428$	79.1795			3.82729
$429$	11.9571	+	0.168796i	0.577293	+	0.00814953i
$430$	−2.38686			−0.115105
$431$	−11.0237	−	11.0237i	−0.530995	−	0.530995i	0.389874	−	0.920868i	$-0.372519\pi$
$431$	−11.0237	−	11.0237i	−0.530995	−	0.530995i	−0.920868	+	0.389874i	$0.872519\pi$
$432$	−14.1552			−0.681041
$433$		−	7.28861i		−	0.350268i	−0.984545	−	0.175134i	$-0.943964\pi$
$433$		−	7.28861i		−	0.350268i	0.984545	−	0.175134i	$-0.0560359\pi$
$434$	−0.0641113	+	0.0641113i	−0.00307744	+	0.00307744i
$435$	−1.69506	−	1.69506i	−0.0812719	−	0.0812719i
$436$	−14.4470	+	14.4470i	−0.691887	+	0.691887i
$437$	−14.5982	+	14.5982i	−0.698327	+	0.698327i
$438$	−2.11380			−0.101001
$439$	17.2018			0.820998			0.410499	−	0.911861i	$-0.365355\pi$
$439$	17.2018			0.820998			0.410499	+	0.911861i	$0.365355\pi$
$440$	0.824430	−	7.67911i	0.0393032	−	0.366087i
$441$			3.92503i			0.186906i
$442$	39.0849	+	32.4269i	1.85908	+	1.54239i
$443$	−2.24486			−0.106656			−0.0533282	−	0.998577i	$-0.516983\pi$
$443$	−2.24486			−0.106656			−0.0533282	+	0.998577i	$0.516983\pi$
$444$	−23.4179	+	23.4179i	−1.11136	+	1.11136i
$445$	2.80561			0.132999
$446$	−5.65538			−0.267790
$447$	−3.11109	−	3.11109i	−0.147149	−	0.147149i
$448$	32.5991	+	32.5991i	1.54016	+	1.54016i
$449$	14.7219	+	14.7219i	0.694771	+	0.694771i	0.963278	−	0.268507i	$-0.0865303\pi$
$449$	14.7219	+	14.7219i	0.694771	+	0.694771i	−0.268507	+	0.963278i	$0.586530\pi$
$450$	9.47870	−	9.47870i	0.446830	−	0.446830i
$451$	11.2136	+	13.9109i	0.528026	+	0.655041i
$452$		−	72.6616i		−	3.41771i
$453$	−8.25114	+	8.25114i	−0.387672	+	0.387672i
$454$		−	21.8999i		−	1.02782i
$455$	0.148821	+	1.59847i	0.00697683	+	0.0749374i
$456$	64.9739			3.04268
$457$	−2.99317	−	2.99317i	−0.140014	−	0.140014i	0.633626	−	0.773640i	$-0.281566\pi$
$457$	−2.99317	−	2.99317i	−0.140014	−	0.140014i	−0.773640	+	0.633626i	$0.781566\pi$
$458$		−	65.5574i		−	3.06330i
$459$	5.18603			0.242063
$460$	2.81304	−	2.81304i	0.131159	−	0.131159i
$461$	11.4712	+	11.4712i	0.534266	+	0.534266i	0.921839	−	0.387573i	$-0.126686\pi$
$461$	11.4712	+	11.4712i	0.534266	+	0.534266i	−0.387573	+	0.921839i	$0.626686\pi$
$462$	−15.7057	−	1.68617i	−0.730697	−	0.0784477i
$463$	−22.9601	−	22.9601i	−1.06705	−	1.06705i	−0.997585	−	0.0694615i	$-0.977872\pi$
$463$	−22.9601	−	22.9601i	−1.06705	−	1.06705i	−0.0694615	−	0.997585i	$-0.522128\pi$
$464$		−	133.638i		−	6.20398i
$465$		−	0.00483375i		−	0.000224160i
$466$	−18.4166	−	18.4166i	−0.853133	−	0.853133i
$467$		−	4.84797i		−	0.224337i	−0.993689	−	0.112169i	$-0.964220\pi$
$467$		−	4.84797i		−	0.224337i	0.993689	−	0.112169i	$-0.0357797\pi$
$468$	−1.79709	−	19.3024i	−0.0830706	−	0.892252i
$469$			16.4742i			0.760710i
$470$	−0.204298	−	0.204298i	−0.00942355	−	0.00942355i
$471$	−5.28522			−0.243530
$472$	−93.7107			−4.31338
$473$	11.4135	+	1.22536i	0.524794	+	0.0563420i
$474$	0.268363	−	0.268363i	0.0123263	−	0.0123263i
$475$	−24.7252	+	24.7252i	−1.13447	+	1.13447i
$476$	−34.5743	−	34.5743i	−1.58471	−	1.58471i
$477$	6.33254			0.289947
$478$		−	64.7948i		−	2.96365i
$479$	17.3837	−	17.3837i	0.794283	−	0.794283i	−0.187904	−	0.982187i	$-0.560170\pi$
$479$	17.3837	−	17.3837i	0.794283	−	0.794283i	0.982187	+	0.187904i	$0.0601695\pi$
$480$	−5.10453			−0.232989
$481$	−17.0920	−	14.1805i	−0.779329	−	0.646574i
$482$	4.53482			0.206556
$483$	−3.61326	−	3.61326i	−0.164409	−	0.164409i
$484$	−12.5546	+	57.7954i	−0.570661	+	2.62706i
$485$			1.12788i			0.0512144i
$486$	−1.92050	−	1.92050i	−0.0871158	−	0.0871158i
$487$	15.2077	−	15.2077i	0.689129	−	0.689129i	−0.272911	−	0.962039i	$-0.587986\pi$
$487$	15.2077	−	15.2077i	0.689129	−	0.689129i	0.962039	+	0.272911i	$0.0879864\pi$
$488$	−15.8456	−	15.8456i	−0.717295	−	0.717295i
$489$	8.29595	+	8.29595i	0.375156	+	0.375156i
$490$			2.70681i			0.122281i
$491$	−24.4397			−1.10295			−0.551474	−	0.834192i	$-0.685934\pi$
$491$	−24.4397			−1.10295			−0.551474	+	0.834192i	$0.685934\pi$
$492$	20.4820	−	20.4820i	0.923400	−	0.923400i
$493$			48.9609i			2.20509i
$494$	6.43145	+	69.0795i	0.289365	+	3.10803i
$495$	0.655643	−	0.528512i	0.0294690	−	0.0237548i
$496$	0.190546	−	0.190546i	0.00855575	−	0.00855575i
$497$		−	26.7823i		−	1.20135i
$498$		−	9.80049i		−	0.439170i
$499$	−2.75483	+	2.75483i	−0.123323	+	0.123323i	−0.766075	−	0.642752i	$-0.777793\pi$
$499$	−2.75483	+	2.75483i	−0.123323	+	0.123323i	0.642752	+	0.766075i	$0.277793\pi$
$500$	9.59123	−	9.59123i	0.428933	−	0.428933i
$501$	−5.64976	+	5.64976i	−0.252413	+	0.252413i
$502$	23.8336	−	23.8336i	1.06374	−	1.06374i
$503$			15.1384i			0.674989i	0.941327	+	0.337495i	$0.109579\pi$
$503$			15.1384i			0.674989i	−0.941327	+	0.337495i	$0.890421\pi$
$504$			16.0819i			0.716346i
$505$	−0.534617	+	0.534617i	−0.0237901	+	0.0237901i
$506$	−20.4364	+	16.4737i	−0.908509	+	0.732347i
$507$	12.7766	−	2.39985i	0.567427	−	0.106581i
$508$			23.8591i			1.05857i
$509$	−8.85081	+	8.85081i	−0.392305	+	0.392305i	−0.875508	−	0.483203i	$-0.839473\pi$
$509$	−8.85081	+	8.85081i	−0.392305	+	0.392305i	0.483203	+	0.875508i	$0.339473\pi$
$510$	3.57644			0.158367
$511$			1.36476i			0.0603733i
$512$	−17.6301	−	17.6301i	−0.779147	−	0.779147i
$513$	5.00964	+	5.00964i	0.221181	+	0.221181i
$514$	33.3625	−	33.3625i	1.47156	−	1.47156i
$515$	−0.921701	−	0.921701i	−0.0406150	−	0.0406150i
$516$		−	18.6091i		−	0.819218i
$517$	0.872031	+	1.08179i	0.0383519	+	0.0475773i
$518$	20.7437	+	20.7437i	0.911425	+	0.911425i
$519$	12.6825			0.556702
$520$	−0.778325	−	8.35990i	−0.0341318	−	0.366606i
$521$	31.0213			1.35907			0.679534	−	0.733644i	$-0.262182\pi$
$521$	31.0213			1.35907			0.679534	+	0.733644i	$0.262182\pi$
$522$	18.1313	−	18.1313i	0.793586	−	0.793586i
$523$		−	34.0058i		−	1.48697i	−0.668753	−	0.743485i	$-0.733172\pi$
$523$		−	34.0058i		−	1.48697i	0.668753	−	0.743485i	$-0.266828\pi$
$524$	12.6370			0.552049
$525$	−6.11983	−	6.11983i	−0.267091	−	0.267091i
$526$	−1.28845	+	1.28845i	−0.0561789	+	0.0561789i
$527$	−0.0698102	+	0.0698102i	−0.00304098	+	0.00304098i
$528$	46.6791	+	5.01148i	2.03145	+	0.218097i
$529$	14.5085			0.630803
$530$	4.36710			0.189695
$531$	−7.22531	−	7.22531i	−0.313552	−	0.313552i
$532$		−	66.7967i		−	2.89600i
$533$	14.9492	+	12.4027i	0.647522	+	0.537220i
$534$			30.0104i			1.29868i
$535$	2.64406	+	2.64406i	0.114313	+	0.114313i
$536$		−	86.1593i		−	3.72152i
$537$		−	22.5467i		−	0.972963i
$538$	8.21953	+	8.21953i	0.354369	+	0.354369i
$539$	1.38961	−	12.9435i	0.0598548	−	0.557514i
$540$	−0.965347	−	0.965347i	−0.0415419	−	0.0415419i
$541$	12.4383	−	12.4383i	0.534763	−	0.534763i	−0.387223	−	0.921986i	$-0.626566\pi$
$541$	12.4383	−	12.4383i	0.534763	−	0.534763i	0.921986	+	0.387223i	$0.126566\pi$
$542$	71.1690			3.05697
$543$		−	10.1696i		−	0.436417i
$544$	73.7208	+	73.7208i	3.16075	+	3.16075i
$545$	−0.964865			−0.0413303
$546$	−17.0981	+	1.59187i	−0.731732	+	0.0681258i
$547$		−	21.2764i		−	0.909715i	−0.890564	−	0.454857i	$-0.849690\pi$
$547$		−	21.2764i		−	0.909715i	0.890564	−	0.454857i	$-0.150310\pi$
$548$	−75.6973	+	75.6973i	−3.23363	+	3.23363i
$549$		−	2.44346i		−	0.104284i
$550$	−34.6135	+	27.9018i	−1.47592	+	1.18974i
$551$	−47.2956	+	47.2956i	−2.01486	+	2.01486i
$552$	18.8971	+	18.8971i	0.804315	+	0.804315i
$553$	−0.173266	−	0.173266i	−0.00736802	−	0.00736802i
$554$	−45.6091	−	45.6091i	−1.93774	−	1.93774i
$555$	−1.56400			−0.0663880
$556$	0.648843			0.0275171
$557$	−16.4189	+	16.4189i	−0.695691	+	0.695691i	−0.963478	−	0.267787i	$-0.913708\pi$
$557$	−16.4189	+	16.4189i	−0.695691	+	0.695691i	0.267787	+	0.963478i	$0.413708\pi$
$558$	0.0517045			0.00218883
$559$	12.4254	−	1.15683i	0.525537	−	0.0489287i
$560$			6.30263i			0.266335i
$561$	−17.1018	−	1.83606i	−0.722041	−	0.0775184i
$562$	50.1797			2.11670
$563$	−4.32837			−0.182419			−0.0912095	−	0.995832i	$-0.529073\pi$
$563$	−4.32837			−0.182419			−0.0912095	+	0.995832i	$0.529073\pi$
$564$	1.59280	−	1.59280i	0.0670689	−	0.0670689i
$565$	2.42640	−	2.42640i	0.102080	−	0.102080i
$566$	54.3881	+	54.3881i	2.28610	+	2.28610i
$567$	−1.23995	+	1.23995i	−0.0520732	+	0.0520732i
$568$			140.070i			5.87719i
$569$	1.42707			0.0598260			0.0299130	−	0.999553i	$-0.490477\pi$
$569$	1.42707			0.0598260			0.0299130	+	0.999553i	$0.490477\pi$
$570$	3.45479	+	3.45479i	0.144705	+	0.144705i
$571$	6.19941			0.259437			0.129719	−	0.991551i	$-0.458593\pi$
$571$	6.19941			0.259437			0.129719	+	0.991551i	$0.458593\pi$
$572$	−0.907558	+	64.2891i	−0.0379469	+	2.68806i
$573$	−10.2108			−0.426564
$574$	−18.1431	−	18.1431i	−0.757277	−	0.757277i
$575$	−14.3822			−0.599781
$576$		−	26.2906i		−	1.09544i
$577$	−18.7005	+	18.7005i	−0.778512	+	0.778512i	−0.979578	−	0.201066i	$-0.935560\pi$
$577$	−18.7005	+	18.7005i	−0.778512	+	0.778512i	0.201066	+	0.979578i	$0.435560\pi$
$578$	−19.0032	−	19.0032i	−0.790431	−	0.790431i
$579$	6.11830	−	6.11830i	0.254268	−	0.254268i
$580$	9.11377	−	9.11377i	0.378429	−	0.378429i
$581$	−6.32759			−0.262513
$582$	−12.0644			−0.500088
$583$	−20.8827	−	2.24196i	−0.864871	−	0.0928527i
$584$		−	7.13760i		−	0.295356i
$585$	0.584557	−	0.704578i	0.0241684	−	0.0291307i
$586$	−48.5841			−2.00699
$587$	15.3702	−	15.3702i	0.634394	−	0.634394i	−0.314773	−	0.949167i	$-0.601928\pi$
$587$	15.3702	−	15.3702i	0.634394	−	0.634394i	0.949167	+	0.314773i	$0.101928\pi$
$588$	−21.1035			−0.870295
$589$	−0.134871			−0.00555728
$590$	−4.98279	−	4.98279i	−0.205138	−	0.205138i
$591$	−10.8636	−	10.8636i	−0.446869	−	0.446869i
$592$	−61.6524	−	61.6524i	−2.53390	−	2.53390i
$593$	−16.4723	+	16.4723i	−0.676435	+	0.676435i	−0.959192	−	0.282757i	$-0.908751\pi$
$593$	−16.4723	+	16.4723i	−0.676435	+	0.676435i	0.282757	+	0.959192i	$0.408751\pi$
$594$	5.65326	+	7.01313i	0.231956	+	0.287752i
$595$		−	2.30909i		−	0.0946637i
$596$	16.7273	−	16.7273i	0.685176	−	0.685176i
$597$		−	25.5976i		−	1.04764i
$598$	−18.2207	+	21.9617i	−0.745098	+	0.898082i
$599$	6.90558			0.282154			0.141077	−	0.989999i	$-0.454943\pi$
$599$	6.90558			0.282154			0.141077	+	0.989999i	$0.454943\pi$
$600$	32.0063	+	32.0063i	1.30665	+	1.30665i
$601$		−	26.4834i		−	1.08028i	−0.841575	−	0.540140i	$-0.818371\pi$
$601$		−	26.4834i		−	1.08028i	0.841575	−	0.540140i	$-0.181629\pi$
$602$	−16.4840			−0.671837
$603$	6.64309	−	6.64309i	0.270527	−	0.270527i
$604$	−44.3636	−	44.3636i	−1.80513	−	1.80513i
$605$	−2.34921	+	1.51074i	−0.0955090	+	0.0614202i
$606$	−5.71856	−	5.71856i	−0.232301	−	0.232301i
$607$			10.8817i			0.441673i	0.975311	+	0.220837i	$0.0708788\pi$
$607$			10.8817i			0.441673i	−0.975311	+	0.220837i	$0.929121\pi$
$608$			142.427i			5.77616i
$609$	−11.7063	−	11.7063i	−0.474364	−	0.474364i
$610$		−	1.68508i		−	0.0682269i
$611$	1.16254	+	0.964504i	0.0470312	+	0.0390196i
$612$			27.8835i			1.12713i
$613$	20.3595	+	20.3595i	0.822314	+	0.822314i	0.986439	−	0.164125i	$-0.0524802\pi$
$613$	20.3595	+	20.3595i	0.822314	+	0.822314i	−0.164125	+	0.986439i	$0.552480\pi$
$614$	74.5027			3.00669
$615$	1.36792			0.0551598
$616$	5.69363	−	53.0330i	0.229403	−	2.13676i
$617$	4.79165	−	4.79165i	0.192905	−	0.192905i	−0.604045	−	0.796950i	$-0.706445\pi$
$617$	4.79165	−	4.79165i	0.192905	−	0.192905i	0.796950	+	0.604045i	$0.206445\pi$
$618$	9.85903	−	9.85903i	0.396588	−	0.396588i
$619$	−28.1908	−	28.1908i	−1.13309	−	1.13309i	−0.989661	−	0.143424i	$-0.954189\pi$
$619$	−28.1908	−	28.1908i	−1.13309	−	1.13309i	−0.143424	−	0.989661i	$-0.545811\pi$
$620$	0.0259895			0.00104376
$621$			2.91402i			0.116936i
$622$	21.8479	−	21.8479i	0.876020	−	0.876020i
$623$	19.3759			0.776280
$624$	50.8174	−	4.73121i	2.03432	−	0.189400i
$625$	−24.0371			−0.961483
$626$	−35.8876	−	35.8876i	−1.43436	−	1.43436i
$627$	−14.7466	−	18.2938i	−0.588921	−	0.730582i
$628$		−	28.4168i		−	1.13395i
$629$	22.5876	+	22.5876i	0.900627	+	0.900627i
$630$	−0.855109	+	0.855109i	−0.0340684	+	0.0340684i
$631$	28.9824	+	28.9824i	1.15377	+	1.15377i	0.985790	+	0.167982i	$0.0537251\pi$
$631$	28.9824	+	28.9824i	1.15377	+	1.15377i	0.167982	+	0.985790i	$0.446275\pi$
$632$	0.906171	+	0.906171i	0.0360456	+	0.0360456i
$633$		−	24.7167i		−	0.982402i
$634$	27.9190			1.10881
$635$	−0.796730	+	0.796730i	−0.0316173	+	0.0316173i
$636$			34.0479i			1.35009i
$637$	−1.31190	−	14.0909i	−0.0519793	−	0.558303i
$638$	−66.2104	+	53.3720i	−2.62129	+	2.11302i
$639$	−10.7997	+	10.7997i	−0.427229	+	0.427229i
$640$		−	7.92169i		−	0.313132i
$641$		−	15.1125i		−	0.596909i	−0.954424	−	0.298455i	$-0.903529\pi$
$641$		−	15.1125i		−	0.596909i	0.954424	−	0.298455i	$-0.0964712\pi$
$642$	−28.2823	+	28.2823i	−1.11621	+	1.11621i
$643$	23.3188	−	23.3188i	0.919602	−	0.919602i	−0.0773983	−	0.997000i	$-0.524661\pi$
$643$	23.3188	−	23.3188i	0.919602	−	0.919602i	0.997000	+	0.0773983i	$0.0246613\pi$
$644$	19.4273	−	19.4273i	0.765541	−	0.765541i
$645$	0.621416	−	0.621416i	0.0244682	−	0.0244682i
$646$		−	99.7899i		−	3.92618i
$647$			14.7708i			0.580700i	0.956921	+	0.290350i	$0.0937717\pi$
$647$			14.7708i			0.580700i	−0.956921	+	0.290350i	$0.906228\pi$
$648$	6.48489	−	6.48489i	0.254750	−	0.254750i
$649$	21.2687	+	26.3848i	0.834869	+	1.03569i
$650$	−30.8606	+	37.1969i	−1.21045	+	1.45898i
$651$		−	0.0333825i		−	0.00130836i
$652$	−44.6045	+	44.6045i	−1.74685	+	1.74685i
$653$	2.43821			0.0954146			0.0477073	−	0.998861i	$-0.484809\pi$
$653$	2.43821			0.0954146			0.0477073	+	0.998861i	$0.484809\pi$
$654$		−	10.3207i		−	0.403573i
$655$	0.421989	+	0.421989i	0.0164885	+	0.0164885i
$656$	53.9231	+	53.9231i	2.10534	+	2.10534i
$657$	0.550325	−	0.550325i	0.0214702	−	0.0214702i
$658$	−1.41091	−	1.41091i	−0.0550029	−	0.0550029i
$659$		−	6.66188i		−	0.259510i	−0.991546	−	0.129755i	$-0.958581\pi$
$659$		−	6.66188i		−	0.259510i	0.991546	−	0.129755i	$-0.0414191\pi$
$660$	2.84163	+	3.52517i	0.110610	+	0.137217i
$661$	−14.6089	−	14.6089i	−0.568219	−	0.568219i	0.363410	−	0.931629i	$-0.381612\pi$
$661$	−14.6089	−	14.6089i	−0.568219	−	0.568219i	−0.931629	+	0.363410i	$0.881612\pi$
$662$	21.6838			0.842764
$663$	−18.6180	+	1.73338i	−0.723063	+	0.0673187i
$664$	33.0929			1.28426
$665$	2.23055	−	2.23055i	0.0864972	−	0.0864972i
$666$		−	16.7294i		−	0.648251i
$667$	−27.5111			−1.06523
$668$	−30.3768	−	30.3768i	−1.17532	−	1.17532i
$669$	1.47237	−	1.47237i	0.0569251	−	0.0569251i
$670$	4.58127	−	4.58127i	0.176990	−	0.176990i
$671$	−0.865079	+	8.05773i	−0.0333960	+	0.311065i
$672$	−35.2526			−1.35990
$673$	37.4402			1.44321			0.721607	−	0.692303i	$-0.243404\pi$
$673$	37.4402			1.44321			0.721607	+	0.692303i	$0.243404\pi$
$674$	−46.4278	−	46.4278i	−1.78833	−	1.78833i
$675$			4.93553i			0.189969i
$676$	12.9032	+	68.6953i	0.496277	+	2.64213i
$677$			8.42149i			0.323664i	0.986818	+	0.161832i	$0.0517403\pi$
$677$			8.42149i			0.323664i	−0.986818	+	0.161832i	$0.948260\pi$
$678$	25.9542	+	25.9542i	0.996764	+	0.996764i
$679$			7.78930i			0.298926i
$680$			12.0764i			0.463110i
$681$	5.70162	+	5.70162i	0.218486	+	0.218486i
$682$	−0.170505	−	0.0183054i	−0.00652896	−	0.000700950i
$683$	−2.83304	−	2.83304i	−0.108403	−	0.108403i	0.650825	−	0.759228i	$-0.274423\pi$
$683$	−2.83304	−	2.83304i	−0.108403	−	0.108403i	−0.759228	+	0.650825i	$0.774423\pi$
$684$	−26.9351	+	26.9351i	−1.02989	+	1.02989i
$685$	−5.05555			−0.193163
$686$			52.0323i			1.98660i
$687$	17.0678	+	17.0678i	0.651176	+	0.651176i
$688$	48.9922			1.86781
$689$	−22.7340	+	2.11658i	−0.866096	+	0.0806354i
$690$			2.00960i			0.0765040i
$691$	−12.8510	+	12.8510i	−0.488874	+	0.488874i	−0.907951	−	0.419077i	$-0.862354\pi$
$691$	−12.8510	+	12.8510i	−0.488874	+	0.488874i	0.419077	+	0.907951i	$0.362354\pi$
$692$			68.1898i			2.59219i
$693$	4.52796	−	3.64997i	0.172003	−	0.138651i
$694$	19.7774	−	19.7774i	0.750738	−	0.750738i
$695$	0.0216669	+	0.0216669i	0.000821874	+	0.000821874i
$696$	61.2233	+	61.2233i	2.32066	+	2.32066i
$697$	−19.7558	−	19.7558i	−0.748305	−	0.748305i
$698$	−53.4172			−2.02187
$699$	9.58947			0.362707
$700$	32.9043	−	32.9043i	1.24366	−	1.24366i
$701$	−13.1073			−0.495056			−0.247528	−	0.968881i	$-0.579618\pi$
$701$	−13.1073			−0.495056			−0.247528	+	0.968881i	$0.579618\pi$
$702$	7.53656	+	6.25275i	0.284449	+	0.235995i
$703$			43.6387i			1.64586i
$704$	−9.30788	+	86.6978i	−0.350804	+	3.26754i
$705$	0.106377			0.00400640
$706$	−85.9034			−3.23302
$707$	−3.69213	+	3.69213i	−0.138857	+	0.138857i
$708$	38.8480	−	38.8480i	1.46000	−	1.46000i
$709$	−37.4272	−	37.4272i	−1.40561	−	1.40561i	−0.780689	−	0.624920i	$-0.785132\pi$
$709$	−37.4272	−	37.4272i	−1.40561	−	1.40561i	−0.624920	−	0.780689i	$-0.714868\pi$
$710$	−7.44779	+	7.44779i	−0.279511	+	0.279511i
$711$			0.139736i			0.00524050i
$712$	−101.335			−3.79769
$713$	−0.0392262	−	0.0392262i	−0.00146903	−	0.00146903i
$714$	24.6994			0.924351
$715$	−2.17713	+	2.11651i	−0.0814199	+	0.0791531i
$716$	121.226			4.53043
$717$	16.8692	+	16.8692i	0.629993	+	0.629993i
$718$	63.9242			2.38563
$719$			21.7393i			0.810738i	0.914153	+	0.405369i	$0.132857\pi$
$719$			21.7393i			0.810738i	−0.914153	+	0.405369i	$0.867143\pi$
$720$	2.54147	−	2.54147i	0.0947152	−	0.0947152i
$721$	−6.36539	−	6.36539i	−0.237060	−	0.237060i
$722$	59.9062	−	59.9062i	2.22948	−	2.22948i
$723$	−1.18063	+	1.18063i	−0.0439083	+	0.0439083i
$724$	54.6782			2.03210
$725$	−46.5959			−1.73053
$726$	−16.1597	−	25.1285i	−0.599743	−	0.932605i
$727$		−	48.8076i		−	1.81018i	−0.425225	−	0.905088i	$-0.639805\pi$
$727$		−	48.8076i		−	1.81018i	0.425225	−	0.905088i	$-0.360195\pi$
$728$	−5.37521	−	57.7346i	−0.199219	−	2.13978i
$729$	1.00000			0.0370370
$730$	0.379520	−	0.379520i	0.0140467	−	0.0140467i
$731$	−17.9493			−0.663878
$732$	13.1377			0.485582
$733$	−3.67772	−	3.67772i	−0.135840	−	0.135840i	0.635917	−	0.771757i	$-0.280622\pi$
$733$	−3.67772	−	3.67772i	−0.135840	−	0.135840i	−0.771757	+	0.635917i	$0.780622\pi$
$734$	23.9954	+	23.9954i	0.885685	+	0.885685i
$735$	−0.704715	−	0.704715i	−0.0259938	−	0.0259938i
$736$	−41.4236	+	41.4236i	−1.52690	+	1.52690i
$737$	−24.2586	+	19.5548i	−0.893579	+	0.720311i
$738$			14.6320i			0.538613i
$739$	−5.70969	+	5.70969i	−0.210034	+	0.210034i	−0.804282	−	0.594248i	$-0.797450\pi$
$739$	−5.70969	+	5.70969i	−0.210034	+	0.210034i	0.594248	+	0.804282i	$0.297450\pi$
$740$		−	8.40908i		−	0.309124i
$741$	−19.6591	−	16.3103i	−0.722197	−	0.599174i
$742$	30.1598			1.10720
$743$	−16.2708	−	16.2708i	−0.596918	−	0.596918i	0.342573	−	0.939491i	$-0.388702\pi$
$743$	−16.2708	−	16.2708i	−0.596918	−	0.596918i	−0.939491	+	0.342573i	$0.888702\pi$
$744$			0.174589i			0.00640073i
$745$	1.11715			0.0409294
$746$	−23.0832	+	23.0832i	−0.845136	+	0.845136i
$747$	2.55154	+	2.55154i	0.0933561	+	0.0933561i
$748$	9.87185	−	91.9509i	0.360951	−	3.36206i
$749$	18.2602	+	18.2602i	0.667213	+	0.667213i
$750$			6.85183i			0.250193i
$751$			40.3477i			1.47231i	0.676813	+	0.736155i	$0.263360\pi$
$751$			40.3477i			1.47231i	−0.676813	+	0.736155i	$0.736640\pi$
$752$	4.19337	+	4.19337i	0.152916	+	0.152916i
$753$			12.4101i			0.452248i
$754$	−59.0317	+	71.1521i	−2.14981	+	2.59121i
$755$		−	2.96288i		−	0.107830i
$756$	−6.66682	−	6.66682i	−0.242470	−	0.242470i
$757$	16.0875			0.584709			0.292354	−	0.956310i	$-0.405561\pi$
$757$	16.0875			0.584709			0.292354	+	0.956310i	$0.405561\pi$
$758$	−39.1335			−1.42139
$759$	1.03168	−	9.60950i	0.0374475	−	0.348803i
$760$	−11.6657	+	11.6657i	−0.423158	+	0.423158i
$761$	22.9980	−	22.9980i	0.833676	−	0.833676i	−0.154341	−	0.988018i	$-0.549325\pi$
$761$	22.9980	−	22.9980i	0.833676	−	0.833676i	0.988018	+	0.154341i	$0.0493255\pi$
$762$	−8.52227	−	8.52227i	−0.308729	−	0.308729i
$763$	−6.66348			−0.241234
$764$		−	54.9002i		−	1.98622i
$765$	−0.931121	+	0.931121i	−0.0336647	+	0.0336647i
$766$	−66.6193			−2.40705
$767$	28.3540	+	23.5241i	1.02380	+	0.849405i
$768$	32.1537			1.16025
$769$	19.3733	+	19.3733i	0.698617	+	0.698617i	0.964112	−	0.265495i	$-0.0855353\pi$
$769$	19.3733	+	19.3733i	0.698617	+	0.698617i	−0.265495	+	0.964112i	$0.585535\pi$
$770$	3.12261	−	2.51713i	0.112531	−	0.0907110i
$771$			17.3718i			0.625629i
$772$	32.8960	+	32.8960i	1.18395	+	1.18395i
$773$	−9.96928	+	9.96928i	−0.358570	+	0.358570i	−0.863286	−	0.504716i	$-0.831597\pi$
$773$	−9.96928	+	9.96928i	−0.358570	+	0.358570i	0.504716	+	0.863286i	$0.331597\pi$
$774$	6.64702	+	6.64702i	0.238922	+	0.238922i
$775$	−0.0664381	−	0.0664381i	−0.00238653	−	0.00238653i
$776$		−	40.7376i		−	1.46239i
$777$	−10.8012			−0.387490
$778$	20.2476	−	20.2476i	0.725912	−	0.725912i
$779$		−	38.1677i		−	1.36750i
$780$	3.78828	+	3.14296i	0.135642	+	0.112536i
$781$	39.4374	−	31.7904i	1.41118	−	1.13755i
$782$	29.0231	−	29.0231i	1.03786	−	1.03786i
$783$			9.44092i			0.337391i
$784$		−	55.5594i		−	1.98426i
$785$	0.948929	−	0.948929i	0.0338687	−	0.0338687i
$786$	−4.51383	+	4.51383i	−0.161003	+	0.161003i
$787$	33.9865	−	33.9865i	1.21149	−	1.21149i	0.240951	−	0.970537i	$-0.422541\pi$
$787$	33.9865	−	33.9865i	1.21149	−	1.21149i	0.970537	−	0.240951i	$-0.0774594\pi$
$788$	58.4099	−	58.4099i	2.08077	−	2.08077i
$789$		−	0.670890i		−	0.0238843i
$790$			0.0963659i			0.00342855i
$791$	16.7571	−	16.7571i	0.595813	−	0.595813i
$792$	−23.6810	+	19.0891i	−0.841466	+	0.678303i
$793$	0.816700	+	8.77208i	0.0290019	+	0.311506i
$794$		−	49.9869i		−	1.77397i
$795$	−1.13697	+	1.13697i	−0.0403241	+	0.0403241i
$796$	137.629			4.87815
$797$		−	32.0436i		−	1.13504i	−0.823359	−	0.567521i	$-0.807903\pi$
$797$		−	32.0436i		−	1.13504i	0.823359	−	0.567521i	$-0.192097\pi$
$798$	23.8593	+	23.8593i	0.844609	+	0.844609i
$799$	−1.53633	−	1.53633i	−0.0543513	−	0.0543513i
$800$	−70.1598	+	70.1598i	−2.48052	+	2.48052i
$801$	−7.81316	−	7.81316i	−0.276064	−	0.276064i
$802$		−	85.3325i		−	3.01320i
$803$	−2.00963	+	1.61996i	−0.0709183	+	0.0571670i
$804$	35.7176	+	35.7176i	1.25966	+	1.25966i
$805$	1.29748			0.0457301
$806$	−0.185621	+	0.0172817i	−0.00653821	+	0.000608721i
$807$	−4.27988			−0.150659
$808$	19.3096	−	19.3096i	0.679311	−	0.679311i
$809$		−	50.4516i		−	1.77378i	−0.461976	−	0.886892i	$-0.652860\pi$
$809$		−	50.4516i		−	1.77378i	0.461976	−	0.886892i	$-0.347140\pi$
$810$	0.689629			0.0242311
$811$	21.0263	+	21.0263i	0.738332	+	0.738332i	0.972255	−	0.233923i	$-0.0751565\pi$
$811$	21.0263	+	21.0263i	0.738332	+	0.738332i	−0.233923	+	0.972255i	$0.575156\pi$
$812$	62.9409	−	62.9409i	2.20879	−	2.20879i
$813$	−18.5288	+	18.5288i	−0.649832	+	0.649832i
$814$	−5.92285	+	55.1681i	−0.207596	+	1.93364i
$815$	−2.97897			−0.104349
$816$	−73.4092			−2.56983
$817$	−17.3388	−	17.3388i	−0.606607	−	0.606607i
$818$			16.4537i			0.575290i
$819$	4.03703	−	4.86591i	0.141065	−	0.170029i
$820$			7.35484i			0.256842i
$821$	5.66898	+	5.66898i	0.197849	+	0.197849i	0.799077	−	0.601228i	$-0.205322\pi$
$821$	5.66898	+	5.66898i	0.197849	+	0.197849i	−0.601228	+	0.799077i	$0.705322\pi$
$822$		−	54.0770i		−	1.88615i
$823$			18.6947i			0.651655i	0.945429	+	0.325827i	$0.105643\pi$
$823$			18.6947i			0.651655i	−0.945429	+	0.325827i	$0.894357\pi$
$824$	33.2906	+	33.2906i	1.15973	+	1.15973i
$825$	1.74737	−	16.2758i	0.0608355	−	0.566649i
$826$	−34.4118	−	34.4118i	−1.19734	−	1.19734i
$827$	22.4518	−	22.4518i	0.780725	−	0.780725i	−0.199228	−	0.979953i	$-0.563844\pi$
$827$	22.4518	−	22.4518i	0.780725	−	0.780725i	0.979953	+	0.199228i	$0.0638435\pi$
$828$	−15.6677			−0.544491
$829$			32.0162i			1.11197i	0.831192	+	0.555985i	$0.187659\pi$
$829$			32.0162i			1.11197i	−0.831192	+	0.555985i	$0.812341\pi$
$830$	1.75962	+	1.75962i	0.0610773	+	0.0610773i
$831$	23.7485			0.823827
$832$	8.78734	+	94.3838i	0.304646	+	3.27217i
$833$			20.3553i			0.705270i
$834$	−0.231762	+	0.231762i	−0.00802525	+	0.00802525i
$835$		−	2.02876i		−	0.0702081i
$836$	98.3594	−	79.2872i	3.40183	−	2.74221i
$837$	−0.0134612	+	0.0134612i	−0.000465287	+	0.000465287i
$838$	−71.7613	−	71.7613i	−2.47895	−	2.47895i
$839$	−3.72404	−	3.72404i	−0.128568	−	0.128568i	0.639895	−	0.768463i	$-0.278978\pi$
$839$	−3.72404	−	3.72404i	−0.128568	−	0.128568i	−0.768463	+	0.639895i	$0.778978\pi$
$840$	−2.88741	−	2.88741i	−0.0996252	−	0.0996252i
$841$	−60.1310			−2.07348
$842$	−33.6093			−1.15825
$843$	−13.0642	+	13.0642i	−0.449955	+	0.449955i
$844$	132.893			4.57438
$845$	−1.86308	+	2.72483i	−0.0640918	+	0.0937372i
$846$			1.13787i			0.0391208i
$847$	−16.2240	+	10.4334i	−0.557462	+	0.358494i
$848$	−89.6382			−3.07819
$849$	−28.3197			−0.971931
$850$	49.1568	−	49.1568i	1.68607	−	1.68607i
$851$	−12.6919	+	12.6919i	−0.435074	+	0.435074i
$852$	−58.0663	−	58.0663i	−1.98932	−	1.98932i
$853$	11.8947	−	11.8947i	0.407266	−	0.407266i	−0.473518	−	0.880784i	$-0.657016\pi$
$853$	11.8947	−	11.8947i	0.407266	−	0.407266i	0.880784	+	0.473518i	$0.157016\pi$
$854$		−	11.6374i		−	0.398223i
$855$	−1.79890			−0.0615211
$856$	−95.4998	−	95.4998i	−3.26412	−	3.26412i
$857$	2.29982			0.0785604			0.0392802	−	0.999228i	$-0.487494\pi$
$857$	2.29982			0.0785604			0.0392802	+	0.999228i	$0.487494\pi$
$858$	−22.6394	−	23.2878i	−0.772897	−	0.795031i
$859$	−36.3298			−1.23956			−0.619778	−	0.784777i	$-0.712778\pi$
$859$	−36.3298			−1.23956			−0.619778	+	0.784777i	$0.712778\pi$
$860$	3.34114	+	3.34114i	0.113932	+	0.113932i
$861$	9.44704			0.321954
$862$			42.3422i			1.44218i
$863$	1.10058	−	1.10058i	0.0374643	−	0.0374643i	−0.688126	−	0.725591i	$-0.741567\pi$
$863$	1.10058	−	1.10058i	0.0374643	−	0.0374643i	0.725591	+	0.688126i	$0.241567\pi$
$864$	14.2153	+	14.2153i	0.483613	+	0.483613i
$865$	−2.27707	+	2.27707i	−0.0774229	+	0.0774229i
$866$	−13.9978	+	13.9978i	−0.475664	+	0.475664i
$867$	9.89493			0.336050
$868$	0.179487			0.00609217
$869$	0.0494719	−	0.460803i	0.00167822	−	0.0156317i
$870$			6.51074i			0.220735i
$871$	−21.6285	+	26.0692i	−0.732853	+	0.883322i
$872$	34.8496			1.18016
$873$	3.14096	−	3.14096i	0.106305	−	0.106305i
$874$	56.0718			1.89666
$875$	4.42382			0.149552
$876$	2.95891	+	2.95891i	0.0999724	+	0.0999724i
$877$	11.3526	+	11.3526i	0.383350	+	0.383350i	0.872308	−	0.488958i	$-0.162623\pi$
$877$	11.3526	+	11.3526i	0.383350	+	0.383350i	−0.488958	+	0.872308i	$0.662623\pi$
$878$	−33.0361	−	33.0361i	−1.11492	−	1.11492i
$879$	12.6488	−	12.6488i	0.426633	−	0.426633i
$880$	−9.28074	+	7.48118i	−0.312854	+	0.252190i
$881$		−	25.9750i		−	0.875120i	−0.899189	−	0.437560i	$-0.855843\pi$
$881$		−	25.9750i		−	0.875120i	0.899189	−	0.437560i	$-0.144157\pi$
$882$	7.53802	−	7.53802i	0.253818	−	0.253818i
$883$			2.29160i			0.0771184i	0.999256	+	0.0385592i	$0.0122768\pi$
$883$			2.29160i			0.0771184i	−0.999256	+	0.0385592i	$0.987723\pi$
$884$	−9.31977	−	100.103i	−0.313458	−	3.36682i
$885$	2.59452			0.0872139
$886$	4.31126	+	4.31126i	0.144840	+	0.144840i
$887$			47.6832i			1.60105i	0.599302	+	0.800523i	$0.295445\pi$
$887$			47.6832i			1.60105i	−0.599302	+	0.800523i	$0.704555\pi$
$888$	56.4895			1.89566
$889$	−5.50233	+	5.50233i	−0.184542	+	0.184542i
$890$	−5.38818	−	5.38818i	−0.180612	−	0.180612i
$891$	−3.29767	−	0.354039i	−0.110476	−	0.0118607i
$892$	7.91643	+	7.91643i	0.265062	+	0.265062i
$893$		−	2.96814i		−	0.0993250i
$894$			11.9497i			0.399658i
$895$	4.04813	+	4.04813i	0.135314	+	0.135314i
$896$		−	54.7083i		−	1.82767i
$897$	−0.973981	−	10.4614i	−0.0325203	−	0.349297i
$898$		−	56.5470i		−	1.88700i
$899$	−0.127086	−	0.127086i	−0.00423856	−	0.00423856i
$900$	−26.5367			−0.884556
$901$	32.8408			1.09408
$902$	5.18031	−	48.2517i	0.172485	−	1.60661i
$903$	4.29158	−	4.29158i	0.142815	−	0.142815i
$904$	−87.6385	+	87.6385i	−2.91481	+	2.91481i
$905$	1.82588	+	1.82588i	0.0606943	+	0.0606943i
$906$	31.6927			1.05292
$907$		−	50.6006i		−	1.68017i	−0.542458	−	0.840083i	$-0.682506\pi$
$907$		−	50.6006i		−	1.68017i	0.542458	−	0.840083i	$-0.317494\pi$
$908$	−30.6557	+	30.6557i	−1.01734	+	1.01734i
$909$	2.97764			0.0987620
$910$	2.78405	−	3.35567i	0.0922904	−	0.111240i
$911$	−15.2286			−0.504548			−0.252274	−	0.967656i	$-0.581178\pi$
$911$	−15.2286			−0.504548			−0.252274	+	0.967656i	$0.581178\pi$
$912$	−70.9123	−	70.9123i	−2.34814	−	2.34814i
$913$	−7.51081	−	9.31750i	−0.248572	−	0.308364i
$914$			11.4968i			0.380279i
$915$	0.438708	+	0.438708i	0.0145032	+	0.0145032i
$916$	−91.7677	+	91.7677i	−3.03209	+	3.03209i
$917$	2.91431	+	2.91431i	0.0962391	+	0.0962391i
$918$	−9.95979	−	9.95979i	−0.328722	−	0.328722i
$919$			52.3841i			1.72799i	0.503498	+	0.863996i	$0.332046\pi$
$919$			52.3841i			1.72799i	−0.503498	+	0.863996i	$0.667954\pi$
$920$	−6.78573			−0.223719
$921$	−19.3967	+	19.3967i	−0.639142	+	0.639142i
$922$		−	44.0609i		−	1.45107i
$923$	35.1615	−	42.3809i	1.15736	−	1.39498i
$924$	19.6247	+	24.3453i	0.645605	+	0.800902i
$925$	−21.4965	+	21.4965i	−0.706802	+	0.706802i
$926$			88.1899i			2.89810i
$927$			5.13357i			0.168608i
$928$	−134.205	+	134.205i	−4.40550	+	4.40550i
$929$	0.794674	−	0.794674i	0.0260724	−	0.0260724i	−0.693950	−	0.720023i	$-0.744131\pi$
$929$	0.794674	−	0.794674i	0.0260724	−	0.0260724i	0.720023	+	0.693950i	$0.244131\pi$
$930$	−0.00928323	+	0.00928323i	−0.000304409	+	0.000304409i
$931$	−19.6630	+	19.6630i	−0.644427	+	0.644427i
$932$			51.5593i			1.68888i
$933$			11.3761i			0.372438i
$934$	−9.31054	+	9.31054i	−0.304650	+	0.304650i
$935$	3.40019	−	2.74088i	0.111198	−	0.0896364i
$936$	−21.1134	+	25.4484i	−0.690113	+	0.831808i
$937$			26.7314i			0.873278i	0.899637	+	0.436639i	$0.143831\pi$
$937$			26.7314i			0.873278i	−0.899637	+	0.436639i	$0.856169\pi$
$938$	31.6388	−	31.6388i	1.03304	−	1.03304i
$939$	18.6866			0.609813
$940$			0.571954i			0.0186551i
$941$	−7.20293	−	7.20293i	−0.234809	−	0.234809i	0.579888	−	0.814696i	$-0.303096\pi$
$941$	−7.20293	−	7.20293i	−0.234809	−	0.234809i	−0.814696	+	0.579888i	$0.803096\pi$
$942$	10.1503	+	10.1503i	0.330714	+	0.330714i
$943$	11.1008	−	11.1008i	0.361491	−	0.361491i
$944$	102.275	+	102.275i	3.32878	+	3.32878i
$945$		−	0.445253i		−	0.0144841i
$946$	−19.5664	−	24.2730i	−0.636158	−	0.789183i
$947$	30.4312	+	30.4312i	0.988881	+	0.988881i	0.999939	−	0.0110578i	$-0.00351988\pi$
$947$	30.4312	+	30.4312i	0.988881	+	0.988881i	−0.0110578	+	0.999939i	$0.503520\pi$
$948$	−0.751312			−0.0244015
$949$	−1.79174	+	2.15962i	−0.0581624	+	0.0701043i
$950$	94.9697			3.08122
$951$	−7.26868	+	7.26868i	−0.235703	+	0.235703i
$952$			83.4014i			2.70306i
$953$	11.3702			0.368317			0.184159	−	0.982897i	$-0.441044\pi$
$953$	11.3702			0.368317			0.184159	+	0.982897i	$0.441044\pi$
$954$	−12.1617	−	12.1617i	−0.393748	−	0.393748i
$955$	1.83329	−	1.83329i	0.0593240	−	0.0593240i
$956$	−90.7002	+	90.7002i	−2.93345	+	2.93345i
$957$	3.34245	−	31.1331i	0.108046	−	1.00639i
$958$	−66.7710			−2.15727
$959$	−34.9143			−1.12744
$960$	4.72031	+	4.72031i	0.152347	+	0.152347i
$961$			30.9996i			0.999988i
$962$	5.59162	+	60.0589i	0.180281	+	1.93638i
$963$		−	14.7265i		−	0.474555i
$964$	−6.34787	−	6.34787i	−0.204451	−	0.204451i
$965$			2.19701i			0.0707241i
$966$			13.8785i			0.446535i
$967$	11.6407	+	11.6407i	0.374339	+	0.374339i	0.869055	−	0.494716i	$-0.164728\pi$
$967$	11.6407	+	11.6407i	0.374339	+	0.374339i	−0.494716	+	0.869055i	$0.664728\pi$
$968$	84.8504	−	54.5658i	2.72719	−	1.75381i
$969$	25.9801	+	25.9801i	0.834603	+	0.834603i
$970$	2.16610	−	2.16610i	0.0695492	−	0.0695492i
$971$	12.4282			0.398839			0.199419	−	0.979914i	$-0.436094\pi$
$971$	12.4282			0.398839			0.199419	+	0.979914i	$0.436094\pi$
$972$			5.37666i			0.172457i
$973$	0.149635	+	0.149635i	0.00479707	+	0.00479707i
$974$	−58.4130			−1.87167
$975$	−1.64965	−	17.7187i	−0.0528310	−	0.567452i
$976$			34.5876i			1.10712i
$977$	−14.0269	+	14.0269i	−0.448760	+	0.448760i	−0.894942	−	0.446182i	$-0.852783\pi$
$977$	−14.0269	+	14.0269i	−0.448760	+	0.448760i	0.446182	+	0.894942i	$0.352783\pi$
$978$		−	31.8648i		−	1.01892i
$979$	22.9991	+	28.5314i	0.735054	+	0.911868i
$980$	3.78901	−	3.78901i	0.121036	−	0.121036i
$981$	2.68699	+	2.68699i	0.0857889	+	0.0857889i
$982$	46.9365	+	46.9365i	1.49780	+	1.49780i
$983$	−20.0582	−	20.0582i	−0.639756	−	0.639756i	0.310739	−	0.950495i	$-0.399423\pi$
$983$	−20.0582	−	20.0582i	−0.639756	−	0.639756i	−0.950495	+	0.310739i	$0.899423\pi$
$984$	−49.4074			−1.57505
$985$	3.90099			0.124296
$986$	94.0296	−	94.0296i	2.99451	−	2.99451i
$987$	0.734655			0.0233843
$988$	87.6950	−	105.701i	2.78995	−	3.36278i
$989$		−	10.0857i		−	0.320706i
$990$	−2.27417	−	0.244155i	−0.0722780	−	0.00775977i
$991$	−17.3813			−0.552135			−0.276067	−	0.961138i	$-0.589031\pi$
$991$	−17.3813			−0.552135			−0.276067	+	0.961138i	$0.589031\pi$
$992$	−0.382709			−0.0121510
$993$	−5.64534	+	5.64534i	−0.179149	+	0.179149i
$994$	−51.4354	+	51.4354i	−1.63143	+	1.63143i
$995$	4.59589	+	4.59589i	0.145699	+	0.145699i
$996$	−13.7188	+	13.7188i	−0.434696	+	0.434696i
$997$			8.27108i			0.261948i	0.991386	+	0.130974i	$0.0418104\pi$
$997$			8.27108i			0.261948i	−0.991386	+	0.130974i	$0.958190\pi$
$998$	10.5813			0.334946
$999$	4.35547	+	4.35547i	0.137801	+	0.137801i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.m.b.109.1	✓	28
11.10	odd	2	inner	429.2.m.b.109.14	yes	28
13.8	odd	4	inner	429.2.m.b.307.14	yes	28
143.21	even	4	inner	429.2.m.b.307.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.m.b.109.1	✓	28	1.1	even	1	trivial
429.2.m.b.109.14	yes	28	11.10	odd	2	inner
429.2.m.b.307.1	yes	28	143.21	even	4	inner
429.2.m.b.307.14	yes	28	13.8	odd	4	inner

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.92050 - 1.92050i) q^{2} +1.00000 q^{3} +5.37666i q^{4} +(-0.179544 + 0.179544i) q^{5} +(-1.92050 - 1.92050i) q^{6} +(-1.23995 + 1.23995i) q^{7} +(6.48489 - 6.48489i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.92050 - 1.92050i) q^{2} +1.00000 q^{3} +5.37666i q^{4} +(-0.179544 + 0.179544i) q^{5} +(-1.92050 - 1.92050i) q^{6} +(-1.23995 + 1.23995i) q^{7} +(6.48489 - 6.48489i) q^{8} +1.00000 q^{9} +0.689629 q^{10} +(-3.29767 - 0.354039i) q^{11} +5.37666i q^{12} +(-3.59003 + 0.334239i) q^{13} +4.76267 q^{14} +(-0.179544 + 0.179544i) q^{15} -14.1552 q^{16} +5.18603 q^{17} +(-1.92050 - 1.92050i) q^{18} +(5.00964 + 5.00964i) q^{19} +(-0.965347 - 0.965347i) q^{20} +(-1.23995 + 1.23995i) q^{21} +(5.65326 + 7.01313i) q^{22} +2.91402i q^{23} +(6.48489 - 6.48489i) q^{24} +4.93553i q^{25} +(7.53656 + 6.25275i) q^{26} +1.00000 q^{27} +(-6.66682 - 6.66682i) q^{28} +9.44092i q^{29} +0.689629 q^{30} +(-0.0134612 + 0.0134612i) q^{31} +(14.2153 + 14.2153i) q^{32} +(-3.29767 - 0.354039i) q^{33} +(-9.95979 - 9.95979i) q^{34} -0.445253i q^{35} +5.37666i q^{36} +(4.35547 + 4.35547i) q^{37} -19.2420i q^{38} +(-3.59003 + 0.334239i) q^{39} +2.32864i q^{40} +(-3.80943 - 3.80943i) q^{41} +4.76267 q^{42} -3.46108 q^{43} +(1.90355 - 17.7305i) q^{44} +(-0.179544 + 0.179544i) q^{45} +(5.59639 - 5.59639i) q^{46} +(-0.296243 - 0.296243i) q^{47} -14.1552 q^{48} +3.92503i q^{49} +(9.47870 - 9.47870i) q^{50} +5.18603 q^{51} +(-1.79709 - 19.3024i) q^{52} +6.33254 q^{53} +(-1.92050 - 1.92050i) q^{54} +(0.655643 - 0.528512i) q^{55} +16.0819i q^{56} +(5.00964 + 5.00964i) q^{57} +(18.1313 - 18.1313i) q^{58} +(-7.22531 - 7.22531i) q^{59} +(-0.965347 - 0.965347i) q^{60} -2.44346i q^{61} +0.0517045 q^{62} +(-1.23995 + 1.23995i) q^{63} -26.2906i q^{64} +(0.584557 - 0.704578i) q^{65} +(5.65326 + 7.01313i) q^{66} +(6.64309 - 6.64309i) q^{67} +27.8835i q^{68} +2.91402i q^{69} +(-0.855109 + 0.855109i) q^{70} +(-10.7997 + 10.7997i) q^{71} +(6.48489 - 6.48489i) q^{72} +(0.550325 - 0.550325i) q^{73} -16.7294i q^{74} +4.93553i q^{75} +(-26.9351 + 26.9351i) q^{76} +(4.52796 - 3.64997i) q^{77} +(7.53656 + 6.25275i) q^{78} +0.139736i q^{79} +(2.54147 - 2.54147i) q^{80} +1.00000 q^{81} +14.6320i q^{82} +(2.55154 + 2.55154i) q^{83} +(-6.66682 - 6.66682i) q^{84} +(-0.931121 + 0.931121i) q^{85} +(6.64702 + 6.64702i) q^{86} +9.44092i q^{87} +(-23.6810 + 19.0891i) q^{88} +(-7.81316 - 7.81316i) q^{89} +0.689629 q^{90} +(4.03703 - 4.86591i) q^{91} -15.6677 q^{92} +(-0.0134612 + 0.0134612i) q^{93} +1.13787i q^{94} -1.79890 q^{95} +(14.2153 + 14.2153i) q^{96} +(3.14096 - 3.14096i) q^{97} +(7.53802 - 7.53802i) q^{98} +(-3.29767 - 0.354039i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9}+O(q^{10}) \) 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9	\( 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9} - 4 q^{15} - 20 q^{16} - 16 q^{20} - 8 q^{22} + 12 q^{26} + 28 q^{27} + 8 q^{31} - 32 q^{34} - 12 q^{37} + 36 q^{44} - 4 q^{45} - 40 q^{47} - 20 q^{48} + 8 q^{53} - 16 q^{55} + 16 q^{58} - 44 q^{59} - 16 q^{60} - 8 q^{66} - 20 q^{67} - 36 q^{70} - 60 q^{71} + 12 q^{78} - 8 q^{80} + 28 q^{81} + 48 q^{86} + 32 q^{89} + 4 q^{91} + 64 q^{92} + 8 q^{93} + 8 q^{97}+O(q^{100}) \) 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9 - 4 * q^15 - 20 * q^16 - 16 * q^20 - 8 * q^22 + 12 * q^26 + 28 * q^27 + 8 * q^31 - 32 * q^34 - 12 * q^37 + 36 * q^44 - 4 * q^45 - 40 * q^47 - 20 * q^48 + 8 * q^53 - 16 * q^55 + 16 * q^58 - 44 * q^59 - 16 * q^60 - 8 * q^66 - 20 * q^67 - 36 * q^70 - 60 * q^71 + 12 * q^78 - 8 * q^80 + 28 * q^81 + 48 * q^86 + 32 * q^89 + 4 * q^91 + 64 * q^92 + 8 * q^93 + 8 * q^97

Introduction

L-functions

Modular forms

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