LMFDB - Embedded newform 429.2.f.a.131.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(131,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("429.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.f (of order $2$, degree $1$, 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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.6
Character	$\chi$	$=$	429.131
Dual form			429.2.f.a.131.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23364 q^{2} +(-0.681784 + 1.59222i) q^{3} +2.98915 q^{4} +0.707248i q^{5} +(1.52286 - 3.55645i) q^{6} -2.10340i q^{7} -2.20940 q^{8} +(-2.07034 - 2.17110i) q^{9} +O(q^{10})$	\(q-2.23364 q^{2} +(-0.681784 + 1.59222i) q^{3} +2.98915 q^{4} +0.707248i q^{5} +(1.52286 - 3.55645i) q^{6} -2.10340i q^{7} -2.20940 q^{8} +(-2.07034 - 2.17110i) q^{9} -1.57974i q^{10} +(-0.507391 + 3.27758i) q^{11} +(-2.03795 + 4.75939i) q^{12} +1.00000i q^{13} +4.69823i q^{14} +(-1.12610 - 0.482190i) q^{15} -1.04329 q^{16} -7.18980 q^{17} +(4.62440 + 4.84946i) q^{18} +2.89821i q^{19} +2.11407i q^{20} +(3.34907 + 1.43406i) q^{21} +(1.13333 - 7.32094i) q^{22} -6.04743i q^{23} +(1.50634 - 3.51786i) q^{24} +4.49980 q^{25} -2.23364i q^{26} +(4.86840 - 1.81622i) q^{27} -6.28736i q^{28} +0.109466 q^{29} +(2.51529 + 1.07704i) q^{30} -8.66865 q^{31} +6.74913 q^{32} +(-4.87271 - 3.04248i) q^{33} +16.0594 q^{34} +1.48762 q^{35} +(-6.18856 - 6.48975i) q^{36} -3.35449 q^{37} -6.47356i q^{38} +(-1.59222 - 0.681784i) q^{39} -1.56260i q^{40} -11.1958 q^{41} +(-7.48063 - 3.20318i) q^{42} -9.52062i q^{43} +(-1.51667 + 9.79719i) q^{44} +(1.53551 - 1.46424i) q^{45} +13.5078i q^{46} -8.13373i q^{47} +(0.711296 - 1.66114i) q^{48} +2.57572 q^{49} -10.0509 q^{50} +(4.90189 - 11.4478i) q^{51} +2.98915i q^{52} -9.43684i q^{53} +(-10.8743 + 4.05678i) q^{54} +(-2.31806 - 0.358851i) q^{55} +4.64725i q^{56} +(-4.61460 - 1.97595i) q^{57} -0.244507 q^{58} +0.00192753i q^{59} +(-3.36607 - 1.44134i) q^{60} +2.37336i q^{61} +19.3626 q^{62} +(-4.56669 + 4.35475i) q^{63} -12.9886 q^{64} -0.707248 q^{65} +(10.8839 + 6.79581i) q^{66} -6.90464 q^{67} -21.4914 q^{68} +(9.62884 + 4.12304i) q^{69} -3.32281 q^{70} +0.745113i q^{71} +(4.57422 + 4.79684i) q^{72} +8.85881i q^{73} +7.49272 q^{74} +(-3.06789 + 7.16468i) q^{75} +8.66319i q^{76} +(6.89406 + 1.06724i) q^{77} +(3.55645 + 1.52286i) q^{78} -4.23813i q^{79} -0.737862i q^{80} +(-0.427375 + 8.98985i) q^{81} +25.0073 q^{82} +10.9525 q^{83} +(10.0109 + 4.28662i) q^{84} -5.08497i q^{85} +21.2657i q^{86} +(-0.0746320 + 0.174294i) q^{87} +(1.12103 - 7.24150i) q^{88} -4.12384i q^{89} +(-3.42977 + 3.27059i) q^{90} +2.10340 q^{91} -18.0767i q^{92} +(5.91014 - 13.8024i) q^{93} +18.1678i q^{94} -2.04975 q^{95} +(-4.60145 + 10.7461i) q^{96} -6.03016 q^{97} -5.75324 q^{98} +(8.16644 - 5.68412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) $ 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9	$ 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) $ 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9 - 20 * q^12 - 6 * q^15 + 8 * q^16 - 4 * q^22 - 28 * q^25 - 12 * q^31 + 2 * q^33 - 16 * q^34 + 26 * q^36 + 20 * q^37 - 2 * q^42 - 50 * q^45 - 82 * q^48 - 56 * q^49 - 20 * q^55 - 80 * q^58 + 104 * q^60 + 16 * q^64 - 50 * q^66 + 60 * q^67 + 6 * q^69 + 80 * q^70 + 12 * q^75 + 10 * q^78 + 6 * q^81 - 8 * q^82 - 52 * q^88 - 8 * q^91 + 42 * q^93 - 92 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−2.23364			−1.57942			−0.789711	−	0.613479i	$-0.789770\pi$
$2$	−2.23364			−1.57942			−0.789711	+	0.613479i	$0.789770\pi$
$3$	−0.681784	+	1.59222i	−0.393628	+	0.919270i
$3$	−0.681784	+	1.59222i	−0.393628	+	0.919270i
$4$	2.98915			1.49457
$5$			0.707248i			0.316291i	0.987416	+	0.158145i	$0.0505515\pi$
$5$			0.707248i			0.316291i	−0.987416	+	0.158145i	$0.949449\pi$
$6$	1.52286	−	3.55645i	0.621705	−	1.45192i
$7$		−	2.10340i		−	0.795009i	−0.917600	−	0.397505i	$-0.869876\pi$
$7$		−	2.10340i		−	0.795009i	0.917600	−	0.397505i	$-0.130124\pi$
$8$	−2.20940			−0.781142
$9$	−2.07034	−	2.17110i	−0.690114	−	0.723701i
$10$		−	1.57974i		−	0.499557i
$11$	−0.507391	+	3.27758i	−0.152984	+	0.988229i
$11$	−0.507391	+	3.27758i	−0.152984	+	0.988229i
$12$	−2.03795	+	4.75939i	−0.588307	+	1.37392i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$			4.69823i			1.25565i
$15$	−1.12610	−	0.482190i	−0.290757	−	0.124501i
$16$	−1.04329			−0.260822
$17$	−7.18980			−1.74378			−0.871892	−	0.489699i	$-0.837107\pi$
$17$	−7.18980			−1.74378			−0.871892	+	0.489699i	$0.837107\pi$
$18$	4.62440	+	4.84946i	1.08998	+	1.14303i
$19$			2.89821i			0.664895i	0.943122	+	0.332448i	$0.107874\pi$
$19$			2.89821i			0.664895i	−0.943122	+	0.332448i	$0.892126\pi$
$20$			2.11407i			0.472720i
$21$	3.34907	+	1.43406i	0.730828	+	0.312938i
$22$	1.13333	−	7.32094i	0.241627	−	1.56083i
$23$		−	6.04743i		−	1.26098i	−0.776199	−	0.630488i	$-0.782855\pi$
$23$		−	6.04743i		−	1.26098i	0.776199	−	0.630488i	$-0.217145\pi$
$24$	1.50634	−	3.51786i	0.307479	−	0.718080i
$25$	4.49980			0.899960
$26$		−	2.23364i		−	0.438053i
$27$	4.86840	−	1.81622i	0.936925	−	0.349532i
$28$		−	6.28736i		−	1.18820i
$29$	0.109466			0.0203273			0.0101636	−	0.999948i	$-0.496765\pi$
$29$	0.109466			0.0203273			0.0101636	+	0.999948i	$0.496765\pi$
$30$	2.51529	+	1.07704i	0.459227	+	0.196640i
$31$	−8.66865			−1.55693			−0.778467	−	0.627685i	$-0.784003\pi$
$31$	−8.66865			−1.55693			−0.778467	+	0.627685i	$0.784003\pi$
$32$	6.74913			1.19309
$33$	−4.87271	−	3.04248i	−0.848230	−	0.529628i
$34$	16.0594			2.75417
$35$	1.48762			0.251454
$36$	−6.18856	−	6.48975i	−1.03143	−	1.08162i
$37$	−3.35449			−0.551475			−0.275737	−	0.961233i	$-0.588922\pi$
$37$	−3.35449			−0.551475			−0.275737	+	0.961233i	$0.588922\pi$
$38$		−	6.47356i		−	1.05015i
$39$	−1.59222	−	0.681784i	−0.254960	−	0.109173i
$40$		−	1.56260i		−	0.247068i
$41$	−11.1958			−1.74849			−0.874243	−	0.485489i	$-0.838642\pi$
$41$	−11.1958			−1.74849			−0.874243	+	0.485489i	$0.838642\pi$
$42$	−7.48063	−	3.20318i	−1.15429	−	0.494261i
$43$		−	9.52062i		−	1.45188i	−0.687757	−	0.725941i	$-0.741405\pi$
$43$		−	9.52062i		−	1.45188i	0.687757	−	0.725941i	$-0.258595\pi$
$44$	−1.51667	+	9.79719i	−0.228646	+	1.47698i
$45$	1.53551	−	1.46424i	0.228900	−	0.218277i
$46$			13.5078i			1.99161i
$47$		−	8.13373i		−	1.18643i	−0.805046	−	0.593213i	$-0.797859\pi$
$47$		−	8.13373i		−	1.18643i	0.805046	−	0.593213i	$-0.202141\pi$
$48$	0.711296	−	1.66114i	0.102667	−	0.239765i
$49$	2.57572			0.367961
$50$	−10.0509			−1.42142
$51$	4.90189	−	11.4478i	0.686402	−	1.60301i
$52$			2.98915i			0.414520i
$53$		−	9.43684i		−	1.29625i	−0.761534	−	0.648125i	$-0.775554\pi$
$53$		−	9.43684i		−	1.29625i	0.761534	−	0.648125i	$-0.224446\pi$
$54$	−10.8743	+	4.05678i	−1.47980	+	0.552058i
$55$	−2.31806	−	0.358851i	−0.312568	−	0.0483875i
$56$			4.64725i			0.621015i
$57$	−4.61460	−	1.97595i	−0.611218	−	0.261722i
$58$	−0.244507			−0.0321054
$59$			0.00192753i			0.000250943i	1.00000		0.000125472i	$3.99388e-5\pi$
$59$			0.00192753i			0.000250943i	−1.00000		0.000125472i	$0.999960\pi$
$60$	−3.36607	−	1.44134i	−0.434557	−	0.186076i
$61$			2.37336i			0.303877i	0.988390	+	0.151939i	$0.0485516\pi$
$61$			2.37336i			0.303877i	−0.988390	+	0.151939i	$0.951448\pi$
$62$	19.3626			2.45906
$63$	−4.56669	+	4.35475i	−0.575349	+	0.548647i
$64$	−12.9886			−1.62357
$65$	−0.707248			−0.0877233
$66$	10.8839	+	6.79581i	1.33971	+	0.836507i
$67$	−6.90464			−0.843536			−0.421768	−	0.906704i	$-0.638590\pi$
$67$	−6.90464			−0.843536			−0.421768	+	0.906704i	$0.638590\pi$
$68$	−21.4914			−2.60621
$69$	9.62884	+	4.12304i	1.15918	+	0.496355i
$70$	−3.32281			−0.397152
$71$			0.745113i			0.0884287i	0.999022	+	0.0442143i	$0.0140785\pi$
$71$			0.745113i			0.0884287i	−0.999022	+	0.0442143i	$0.985922\pi$
$72$	4.57422	+	4.79684i	0.539077	+	0.565313i
$73$			8.85881i			1.03685i	0.855125	+	0.518423i	$0.173481\pi$
$73$			8.85881i			1.03685i	−0.855125	+	0.518423i	$0.826519\pi$
$74$	7.49272			0.871011
$75$	−3.06789	+	7.16468i	−0.354250	+	0.827306i
$76$			8.66319i			0.993736i
$77$	6.89406	+	1.06724i	0.785651	+	0.121624i
$78$	3.55645	+	1.52286i	0.402689	+	0.172430i
$79$		−	4.23813i		−	0.476827i	−0.971164	−	0.238414i	$-0.923373\pi$
$79$		−	4.23813i		−	0.476827i	0.971164	−	0.238414i	$-0.0766274\pi$
$80$		−	0.737862i		−	0.0824954i
$81$	−0.427375	+	8.98985i	−0.0474861	+	0.998872i
$82$	25.0073			2.76160
$83$	10.9525			1.20219			0.601095	−	0.799178i	$-0.294732\pi$
$83$	10.9525			1.20219			0.601095	+	0.799178i	$0.294732\pi$
$84$	10.0109	+	4.28662i	1.09228	+	0.467709i
$85$		−	5.08497i		−	0.551543i
$86$			21.2657i			2.29313i
$87$	−0.0746320	+	0.174294i	−0.00800139	+	0.0186863i
$88$	1.12103	−	7.24150i	0.119502	−	0.771947i
$89$		−	4.12384i		−	0.437126i	−0.975823	−	0.218563i	$-0.929863\pi$
$89$		−	4.12384i		−	0.437126i	0.975823	−	0.218563i	$-0.0701369\pi$
$90$	−3.42977	+	3.27059i	−0.361530	+	0.344751i
$91$	2.10340			0.220496
$92$		−	18.0767i		−	1.88462i
$93$	5.91014	−	13.8024i	0.612853	−	1.43124i
$94$			18.1678i			1.87387i
$95$	−2.04975			−0.210300
$96$	−4.60145	+	10.7461i	−0.469634	+	1.09677i
$97$	−6.03016			−0.612270			−0.306135	−	0.951988i	$-0.599036\pi$
$97$	−6.03016			−0.612270			−0.306135	+	0.951988i	$0.599036\pi$
$98$	−5.75324			−0.581165
$99$	8.16644	−	5.68412i	0.820758	−	0.571275i
$100$	13.4506			1.34506
$101$	−0.0732045			−0.00728412			−0.00364206	−	0.999993i	$-0.501159\pi$
$101$	−0.0732045			−0.00728412			−0.00364206	+	0.999993i	$0.501159\pi$
$102$	−10.9491	+	25.5702i	−1.08412	+	2.53183i
$103$	−6.00869			−0.592054			−0.296027	−	0.955180i	$-0.595662\pi$
$103$	−6.00869			−0.592054			−0.296027	+	0.955180i	$0.595662\pi$
$104$		−	2.20940i		−	0.216650i
$105$	−1.01424	+	2.36862i	−0.0989794	+	0.231154i
$106$			21.0785i			2.04732i
$107$	−7.87647			−0.761447			−0.380723	−	0.924689i	$-0.624325\pi$
$107$	−7.87647			−0.761447			−0.380723	+	0.924689i	$0.624325\pi$
$108$	14.5524	−	5.42895i	1.40030	−	0.522401i
$109$			2.41990i			0.231784i	0.993262	+	0.115892i	$0.0369727\pi$
$109$			2.41990i			0.231784i	−0.993262	+	0.115892i	$0.963027\pi$
$110$	5.17772	+	0.801544i	0.493676	+	0.0764243i
$111$	2.28704	−	5.34109i	0.217076	−	0.506954i
$112$			2.19444i			0.207355i
$113$			10.6977i			1.00635i	0.864184	+	0.503176i	$0.167835\pi$
$113$			10.6977i			1.00635i	−0.864184	+	0.503176i	$0.832165\pi$
$114$	10.3073	+	4.41357i	0.965372	+	0.413369i
$115$	4.27703			0.398835
$116$	0.327209			0.0303806
$117$	2.17110	−	2.07034i	0.200719	−	0.191403i
$118$		−	0.00430541i		−	0.000396345i
$119$			15.1230i			1.38632i
$120$	2.48800	+	1.06535i	0.227122	+	0.0972529i
$121$	−10.4851	−	3.32603i	−0.953192	−	0.302367i
$122$		−	5.30123i		−	0.479951i
$123$	7.63310	−	17.8262i	0.688253	−	1.60733i
$124$	−25.9119			−2.32696
$125$			6.71871i			0.600940i
$126$	10.2003	−	9.72694i	0.908719	−	0.866545i
$127$		−	15.1315i		−	1.34270i	−0.741141	−	0.671350i	$-0.765715\pi$
$127$		−	15.1315i		−	1.34270i	0.741141	−	0.671350i	$-0.234285\pi$
$128$	15.5135			1.37121
$129$	15.1589	+	6.49101i	1.33467	+	0.571502i
$130$	1.57974			0.138552
$131$	−13.8748			−1.21225			−0.606124	−	0.795370i	$-0.707277\pi$
$131$	−13.8748			−1.21225			−0.606124	+	0.795370i	$0.707277\pi$
$132$	−14.5653	−	9.09444i	−1.26774	−	0.791569i
$133$	6.09609			0.528598
$134$	15.4225			1.33230
$135$	1.28452	+	3.44317i	0.110554	+	0.296341i
$136$	15.8852			1.36214
$137$			22.4560i			1.91854i	0.282489	+	0.959271i	$0.408840\pi$
$137$			22.4560i			1.91854i	−0.282489	+	0.959271i	$0.591160\pi$
$138$	−21.5074	−	9.20938i	−1.83083	−	0.783955i
$139$			6.63920i			0.563130i	0.959542	+	0.281565i	$0.0908535\pi$
$139$			6.63920i			0.563130i	−0.959542	+	0.281565i	$0.909147\pi$
$140$	4.44672			0.375817
$141$	12.9507	+	5.54544i	1.09065	+	0.467011i
$142$		−	1.66432i		−	0.139666i
$143$	−3.27758	−	0.507391i	−0.274085	−	0.0424302i
$144$	2.15996	+	2.26508i	0.179997	+	0.188757i
$145$			0.0774194i			0.00642933i
$146$		−	19.7874i		−	1.63762i
$147$	−1.75609	+	4.10112i	−0.144840	+	0.338255i
$148$	−10.0271			−0.824220
$149$	17.8633			1.46342			0.731711	−	0.681615i	$-0.238722\pi$
$149$	17.8633			1.46342			0.731711	+	0.681615i	$0.238722\pi$
$150$	6.85257	−	16.0033i	0.559510	−	1.30667i
$151$		−	6.10191i		−	0.496566i	−0.968688	−	0.248283i	$-0.920134\pi$
$151$		−	6.10191i		−	0.496566i	0.968688	−	0.248283i	$-0.0798663\pi$
$152$		−	6.40332i		−	0.519378i
$153$	14.8853	+	15.6098i	1.20341	+	1.26198i
$154$	−15.3988	−	2.38384i	−1.24087	−	0.192095i
$155$		−	6.13088i		−	0.492444i
$156$	−4.75939	−	2.03795i	−0.381056	−	0.163167i
$157$	−15.7285			−1.25527			−0.627637	−	0.778506i	$-0.715978\pi$
$157$	−15.7285			−1.25527			−0.627637	+	0.778506i	$0.715978\pi$
$158$			9.46647i			0.753112i
$159$	15.0255	+	6.43388i	1.19160	+	0.510240i
$160$			4.77331i			0.377363i
$161$	−12.7201			−1.00249
$162$	0.954602	−	20.0801i	0.0750006	−	1.57764i
$163$	−9.97404			−0.781227			−0.390613	−	0.920555i	$-0.627737\pi$
$163$	−9.97404			−0.781227			−0.390613	+	0.920555i	$0.627737\pi$
$164$	−33.4658			−2.61324
$165$	2.15179	−	3.44621i	0.167517	−	0.268287i
$166$	−24.4639			−1.89876
$167$	−20.9068			−1.61782			−0.808908	−	0.587935i	$-0.799941\pi$
$167$	−20.9068			−1.61782			−0.808908	+	0.587935i	$0.799941\pi$
$168$	−7.39945	−	3.16842i	−0.570880	−	0.244449i
$169$	−1.00000			−0.0769231
$170$			11.3580i			0.871118i
$171$	6.29232	−	6.00029i	0.481185	−	0.458853i
$172$		−	28.4586i		−	2.16995i
$173$	2.69979			0.205261			0.102631	−	0.994720i	$-0.467274\pi$
$173$	2.69979			0.205261			0.102631	+	0.994720i	$0.467274\pi$
$174$	0.166701	−	0.389310i	0.0126376	−	0.0295135i
$175$		−	9.46486i		−	0.715476i
$176$	0.529354	−	3.41946i	0.0399016	−	0.257751i
$177$	−0.00306906	−	0.00131416i	−0.000230684	−	9.87783e-5i
$178$			9.21117i			0.690406i
$179$			10.7996i			0.807200i	0.914935	+	0.403600i	$0.132241\pi$
$179$			10.7996i			0.807200i	−0.914935	+	0.403600i	$0.867759\pi$
$180$	4.58986	−	4.37684i	0.342108	−	0.326231i
$181$	0.930469			0.0691612			0.0345806	−	0.999402i	$-0.488990\pi$
$181$	0.930469			0.0691612			0.0345806	+	0.999402i	$0.488990\pi$
$182$	−4.69823			−0.348256
$183$	−3.77891	−	1.61812i	−0.279345	−	0.119615i
$184$			13.3612i			0.985001i
$185$		−	2.37245i		−	0.174426i
$186$	−13.2011	+	30.8296i	−0.967954	+	2.26054i
$187$	3.64804	−	23.5652i	0.266771	−	1.72326i
$188$		−	24.3129i		−	1.77320i
$189$	−3.82023	−	10.2402i	−0.277881	−	0.744864i
$190$	4.57841			0.332153
$191$		−	9.64580i		−	0.697946i	−0.937133	−	0.348973i	$-0.886531\pi$
$191$		−	9.64580i		−	0.697946i	0.937133	−	0.348973i	$-0.113469\pi$
$192$	8.85539	−	20.6807i	0.639083	−	1.49250i
$193$			9.60601i			0.691456i	0.938335	+	0.345728i	$0.112368\pi$
$193$			9.60601i			0.691456i	−0.938335	+	0.345728i	$0.887632\pi$
$194$	13.4692			0.967033
$195$	0.482190	−	1.12610i	0.0345304	−	0.0806414i
$196$	7.69922			0.549945
$197$	−2.84045			−0.202373			−0.101187	−	0.994867i	$-0.532264\pi$
$197$	−2.84045			−0.202373			−0.101187	+	0.994867i	$0.532264\pi$
$198$	−18.2409	+	12.6963i	−1.29632	+	0.902285i
$199$	9.03585			0.640535			0.320267	−	0.947327i	$-0.396227\pi$
$199$	9.03585			0.640535			0.320267	+	0.947327i	$0.396227\pi$
$200$	−9.94187			−0.702997
$201$	4.70747	−	10.9937i	0.332040	−	0.775437i
$202$	0.163513			0.0115047
$203$		−	0.230250i		−	0.0161604i
$204$	14.6525	−	34.2191i	1.02588	−	2.39581i
$205$		−	7.91818i		−	0.553030i
$206$	13.4212			0.935103
$207$	−13.1296	+	12.5202i	−0.912569	+	0.870216i
$208$		−	1.04329i		−	0.0723389i
$209$	−9.49913	−	1.47053i	−0.657069	−	0.101718i
$210$	2.26544	−	5.29065i	0.156330	−	0.365090i
$211$			19.1959i			1.32150i	0.750605	+	0.660751i	$0.229762\pi$
$211$			19.1959i			1.32150i	−0.750605	+	0.660751i	$0.770238\pi$
$212$		−	28.2081i		−	1.93734i
$213$	−1.18639	−	0.508006i	−0.0812898	−	0.0348080i
$214$	17.5932			1.20265
$215$	6.73344			0.459217
$216$	−10.7563	+	4.01276i	−0.731871	+	0.273034i
$217$			18.2336i			1.23778i
$218$		−	5.40519i		−	0.366086i
$219$	−14.1052	−	6.03979i	−0.953140	−	0.408131i
$220$	−6.92904	−	1.07266i	−0.467156	−	0.0723187i
$221$		−	7.18980i		−	0.483638i
$222$	−5.10842	+	11.9301i	−0.342855	+	0.800694i
$223$	7.16022			0.479484			0.239742	−	0.970837i	$-0.422937\pi$
$223$	7.16022			0.479484			0.239742	+	0.970837i	$0.422937\pi$
$224$		−	14.1961i		−	0.948517i
$225$	−9.31612	−	9.76953i	−0.621075	−	0.651302i
$226$		−	23.8947i		−	1.58945i
$227$	6.82394			0.452921			0.226460	−	0.974020i	$-0.427285\pi$
$227$	6.82394			0.452921			0.226460	+	0.974020i	$0.427285\pi$
$228$	−13.7937	−	5.90642i	−0.913511	−	0.391162i
$229$	−21.9402			−1.44985			−0.724925	−	0.688827i	$-0.758126\pi$
$229$	−21.9402			−1.44985			−0.724925	+	0.688827i	$0.758126\pi$
$230$	−9.55334			−0.629929
$231$	−6.39955	+	10.2492i	−0.421059	+	0.674350i
$232$	−0.241854			−0.0158785
$233$	1.81483			0.118894			0.0594468	−	0.998231i	$-0.481066\pi$
$233$	1.81483			0.118894			0.0594468	+	0.998231i	$0.481066\pi$
$234$	−4.84946	+	4.62440i	−0.317019	+	0.302306i
$235$	5.75256			0.375256
$236$			0.00576167i			0.000375053i
$237$	6.74805	+	2.88949i	0.438333	+	0.187693i
$238$		−	33.7793i		−	2.18959i
$239$	4.92380			0.318494			0.159247	−	0.987239i	$-0.449093\pi$
$239$	4.92380			0.318494			0.159247	+	0.987239i	$0.449093\pi$
$240$	1.17484	+	0.503062i	0.0758356	+	0.0324725i
$241$			30.3898i			1.95758i	0.204874	+	0.978788i	$0.434321\pi$
$241$			30.3898i			1.95758i	−0.204874	+	0.978788i	$0.565679\pi$
$242$	23.4200	+	7.42916i	1.50549	+	0.477565i
$243$	−14.0225	−	6.80961i	−0.899541	−	0.436837i
$244$			7.09432i			0.454167i
$245$			1.82168i			0.116383i
$246$	−17.0496	+	39.8172i	−1.08704	+	2.53865i
$247$	−2.89821			−0.184409
$248$	19.1525			1.21619
$249$	−7.46721	+	17.4388i	−0.473216	+	1.10514i
$250$		−	15.0072i		−	0.949138i
$251$		−	2.59266i		−	0.163647i	−0.996647	−	0.0818237i	$-0.973926\pi$
$251$		−	2.59266i		−	0.163647i	0.996647	−	0.0818237i	$-0.0260744\pi$
$252$	−13.6505	+	13.0170i	−0.859902	+	0.819993i
$253$	19.8209	+	3.06841i	1.24613	+	0.192909i
$254$			33.7982i			2.12069i
$255$	8.09640	+	3.46685i	0.507016	+	0.217103i
$256$	−8.67448			−0.542155
$257$		−	16.1555i		−	1.00775i	−0.863775	−	0.503877i	$-0.831906\pi$
$257$		−	16.1555i		−	1.00775i	0.863775	−	0.503877i	$-0.168094\pi$
$258$	−33.8596	−	14.4986i	−2.10801	−	0.902642i
$259$			7.05582i			0.438427i
$260$	−2.11407			−0.131109
$261$	−0.226631	−	0.237661i	−0.0140281	−	0.0147109i
$262$	30.9914			1.91465
$263$	5.61963			0.346521			0.173261	−	0.984876i	$-0.444570\pi$
$263$	5.61963			0.346521			0.173261	+	0.984876i	$0.444570\pi$
$264$	10.7658	+	6.72207i	0.662588	+	0.413715i
$265$	6.67418			0.409992
$266$	−13.6165			−0.834879
$267$	6.56606	+	2.81157i	0.401837	+	0.172065i
$268$	−20.6390			−1.26073
$269$			21.1874i			1.29182i	0.763414	+	0.645909i	$0.223522\pi$
$269$			21.1874i			1.29182i	−0.763414	+	0.645909i	$0.776478\pi$
$270$	−2.86915	−	7.69080i	−0.174611	−	0.468047i
$271$			6.15986i			0.374185i	0.982342	+	0.187092i	$0.0599064\pi$
$271$			6.15986i			0.374185i	−0.982342	+	0.187092i	$0.940094\pi$
$272$	7.50102			0.454816
$273$	−1.43406	+	3.34907i	−0.0867934	+	0.202695i
$274$		−	50.1585i		−	3.03019i
$275$	−2.28316	+	14.7485i	−0.137680	+	0.889366i
$276$	28.7820	+	12.3244i	1.73248	+	0.741840i
$277$			4.27243i			0.256706i	0.991729	+	0.128353i	$0.0409690\pi$
$277$			4.27243i			0.256706i	−0.991729	+	0.128353i	$0.959031\pi$
$278$		−	14.8296i		−	0.889420i
$279$	17.9471	+	18.8205i	1.07446	+	1.12676i
$280$	−3.28676			−0.196421
$281$	8.89147			0.530420			0.265210	−	0.964191i	$-0.414559\pi$
$281$	8.89147			0.530420			0.265210	+	0.964191i	$0.414559\pi$
$282$	−28.9272	−	12.3865i	−1.72259	−	0.737607i
$283$		−	24.2021i		−	1.43866i	−0.694667	−	0.719331i	$-0.744448\pi$
$283$		−	24.2021i		−	1.43866i	0.694667	−	0.719331i	$-0.255552\pi$
$284$			2.22725i			0.132163i
$285$	1.39749	−	3.26366i	0.0827801	−	0.193323i
$286$	7.32094	+	1.13333i	0.432896	+	0.0670152i
$287$			23.5491i			1.39006i
$288$	−13.9730	−	14.6531i	−0.823367	−	0.863440i
$289$	34.6933			2.04078
$290$		−	0.172927i		−	0.0101546i
$291$	4.11127	−	9.60135i	0.241007	−	0.562841i
$292$			26.4803i			1.54964i
$293$	−16.0520			−0.937766			−0.468883	−	0.883260i	$-0.655343\pi$
$293$	−16.0520			−0.937766			−0.468883	+	0.883260i	$0.655343\pi$
$294$	3.92247	−	9.16044i	0.228763	−	0.534248i
$295$	−0.00136324			−7.93710e−5
$296$	7.41142			0.430780
$297$	3.48263	+	16.8781i	0.202082	+	0.979369i
$298$	−39.9003			−2.31136
$299$	6.04743			0.349732
$300$	−9.17039	+	21.4163i	−0.529453	+	1.23647i
$301$	−20.0256			−1.15426
$302$			13.6295i			0.784288i
$303$	0.0499097	−	0.116558i	0.00286723	−	0.00669607i
$304$		−	3.02366i		−	0.173419i
$305$	−1.67855			−0.0961136
$306$	−33.2485	−	34.8667i	−1.90069	−	1.99320i
$307$		−	4.94951i		−	0.282483i	−0.989975	−	0.141242i	$-0.954891\pi$
$307$		−	4.94951i		−	0.282483i	0.989975	−	0.141242i	$-0.0451095\pi$
$308$	20.6074	+	3.19015i	1.17421	+	0.181776i
$309$	4.09663	−	9.56717i	0.233049	−	0.544257i
$310$			13.6942i			0.777777i
$311$		−	29.4037i		−	1.66733i	−0.552268	−	0.833667i	$-0.686238\pi$
$311$		−	29.4037i		−	1.66733i	0.552268	−	0.833667i	$-0.313762\pi$
$312$	3.51786	+	1.50634i	0.199160	+	0.0852795i
$313$	−4.16819			−0.235600			−0.117800	−	0.993037i	$-0.537584\pi$
$313$	−4.16819			−0.235600			−0.117800	+	0.993037i	$0.537584\pi$
$314$	35.1319			1.98261
$315$	−3.07989	−	3.22978i	−0.173532	−	0.181978i
$316$		−	12.6684i		−	0.712654i
$317$			27.6159i			1.55106i	0.631308	+	0.775532i	$0.282518\pi$
$317$			27.6159i			1.55106i	−0.631308	+	0.775532i	$0.717482\pi$
$318$	−33.5616	−	14.3710i	−1.88204	−	0.805885i
$319$	−0.0555419	+	0.358783i	−0.00310975	+	0.0200880i
$320$		−	9.18613i		−	0.513520i
$321$	5.37005	−	12.5411i	0.299727	−	0.699975i
$322$	28.4122			1.58335
$323$		−	20.8376i		−	1.15943i
$324$	−1.27749	+	26.8720i	−0.0709715	+	1.49289i
$325$			4.49980i			0.249604i
$326$	22.2784			1.23389
$327$	−3.85302	−	1.64985i	−0.213072	−	0.0912369i
$328$	24.7360			1.36582
$329$	−17.1084			−0.943219
$330$	−4.80632	+	7.69760i	−0.264579	+	0.423739i
$331$	18.7132			1.02857			0.514284	−	0.857620i	$-0.328058\pi$
$331$	18.7132			1.02857			0.514284	+	0.857620i	$0.328058\pi$
$332$	32.7385			1.79676
$333$	6.94494	+	7.28294i	0.380580	+	0.399103i
$334$	46.6982			2.55521
$335$		−	4.88329i		−	0.266803i
$336$	−3.49404	−	1.49614i	−0.190616	−	0.0816210i
$337$		−	7.57197i		−	0.412472i	−0.978502	−	0.206236i	$-0.933879\pi$
$337$		−	7.57197i		−	0.412472i	0.978502	−	0.206236i	$-0.0661214\pi$
$338$	2.23364			0.121494
$339$	−17.0330	−	7.29349i	−0.925108	−	0.396128i
$340$		−	15.1997i		−	0.824321i
$341$	4.39839	−	28.4122i	0.238186	−	1.53861i
$342$	−14.0548	+	13.4025i	−0.759995	+	0.724723i
$343$		−	20.1415i		−	1.08754i
$344$			21.0349i			1.13413i
$345$	−2.91601	+	6.80998i	−0.156993	+	0.366637i
$346$	−6.03036			−0.324194
$347$	22.1424			1.18866			0.594332	−	0.804219i	$-0.297416\pi$
$347$	22.1424			1.18866			0.594332	+	0.804219i	$0.297416\pi$
$348$	−0.223086	+	0.520990i	−0.0119587	+	0.0279280i
$349$			5.26561i			0.281862i	0.990019	+	0.140931i	$0.0450095\pi$
$349$			5.26561i			0.281862i	−0.990019	+	0.140931i	$0.954990\pi$
$350$			21.1411i			1.13004i
$351$	1.81622	+	4.86840i	0.0969426	+	0.259856i
$352$	−3.42445	+	22.1208i	−0.182524	+	1.17905i
$353$			2.45133i			0.130471i	0.997870	+	0.0652355i	$0.0207799\pi$
$353$			2.45133i			0.130471i	−0.997870	+	0.0652355i	$0.979220\pi$
$354$	0.00685517	+	0.00293536i	0.000364348	+	0.000156013i
$355$	−0.526980			−0.0279692
$356$		−	12.3268i		−	0.653317i
$357$	−24.0792	−	10.3106i	−1.27441	−	0.545696i
$358$		−	24.1224i		−	1.27491i
$359$	23.4831			1.23939			0.619696	−	0.784842i	$-0.287256\pi$
$359$	23.4831			1.23939			0.619696	+	0.784842i	$0.287256\pi$
$360$	−3.39255	+	3.23511i	−0.178803	+	0.170505i
$361$	10.6004			0.557914
$362$	−2.07833			−0.109235
$363$	12.4444	−	14.4270i	0.653160	−	0.757220i
$364$	6.28736			0.329547
$365$	−6.26537			−0.327945
$366$	8.44073	+	3.61429i	0.441204	+	0.188922i
$367$	15.2605			0.796590			0.398295	−	0.917257i	$-0.369602\pi$
$367$	15.2605			0.796590			0.398295	+	0.917257i	$0.369602\pi$
$368$			6.30920i			0.328890i
$369$	23.1791	+	24.3072i	1.20665	+	1.26538i
$370$			5.29921i			0.275493i
$371$	−19.8494			−1.03053
$372$	17.6663	−	41.2575i	0.915955	−	2.13910i
$373$			35.0912i			1.81695i	0.417934	+	0.908477i	$0.362754\pi$
$373$			35.0912i			1.81695i	−0.417934	+	0.908477i	$0.637246\pi$
$374$	−8.14841	+	52.6361i	−0.421344	+	2.72175i
$375$	−10.6977	−	4.58071i	−0.552426	−	0.236547i
$376$			17.9707i			0.926767i
$377$			0.109466i			0.00563777i
$378$	8.53302	+	22.8729i	0.438891	+	1.17645i
$379$	−27.3096			−1.40280			−0.701400	−	0.712768i	$-0.747441\pi$
$379$	−27.3096			−1.40280			−0.701400	+	0.712768i	$0.747441\pi$
$380$	−6.12702			−0.314309
$381$	24.0926	+	10.3164i	1.23430	+	0.528524i
$382$			21.5452i			1.10235i
$383$		−	3.52216i		−	0.179974i	−0.995943	−	0.0899870i	$-0.971317\pi$
$383$		−	3.52216i		−	0.179974i	0.995943	−	0.0899870i	$-0.0286826\pi$
$384$	−10.5769	+	24.7010i	−0.539748	+	1.26052i
$385$	−0.754806	+	4.87581i	−0.0384685	+	0.248494i
$386$		−	21.4564i		−	1.09210i
$387$	−20.6703	+	19.7109i	−1.05073	+	1.00196i
$388$	−18.0250			−0.915083
$389$		−	0.983011i		−	0.0498406i	−0.999689	−	0.0249203i	$-0.992067\pi$
$389$		−	0.983011i		−	0.0498406i	0.999689	−	0.0249203i	$-0.00793320\pi$
$390$	−1.07704	+	2.51529i	−0.0545380	+	0.127367i
$391$			43.4798i			2.19887i
$392$	−5.69081			−0.287429
$393$	9.45963	−	22.0918i	0.477175	−	1.11438i
$394$	6.34454			0.319633
$395$	2.99741			0.150816
$396$	24.4107	−	16.9907i	1.22668	−	0.853814i
$397$	22.8457			1.14659			0.573297	−	0.819348i	$-0.305664\pi$
$397$	22.8457			1.14659			0.573297	+	0.819348i	$0.305664\pi$
$398$	−20.1828			−1.01167
$399$	−4.15621	+	9.70632i	−0.208071	+	0.485924i
$400$	−4.69458			−0.234729
$401$		−	4.65741i		−	0.232580i	−0.993215	−	0.116290i	$-0.962900\pi$
$401$		−	4.65741i		−	0.232580i	0.993215	−	0.116290i	$-0.0371002\pi$
$402$	−10.5148	+	24.5560i	−0.524431	+	1.22474i
$403$		−	8.66865i		−	0.431816i
$404$	−0.218819			−0.0108867
$405$	−6.35805	−	0.302260i	−0.315934	−	0.0150194i
$406$			0.514295i			0.0255240i
$407$	1.70204	−	10.9946i	0.0843669	−	0.544983i
$408$	−10.8303	+	25.2927i	−0.536178	+	1.25218i
$409$			5.53426i			0.273651i	0.990595	+	0.136826i	$0.0436900\pi$
$409$			5.53426i			0.273651i	−0.990595	+	0.136826i	$0.956310\pi$
$410$			17.6864i			0.873468i
$411$	−35.7549	−	15.3101i	−1.76366	−	0.755192i
$412$	−17.9609			−0.884868
$413$	0.00405436			0.000199502
$414$	29.3268	−	27.9657i	1.44133	−	1.37444i
$415$			7.74610i			0.380241i
$416$			6.74913i			0.330903i
$417$	−10.5711	−	4.52650i	−0.517668	−	0.221664i
$418$	21.2176	+	3.28463i	1.03779	+	0.160656i
$419$			24.6341i			1.20345i	0.798702	+	0.601726i	$0.205520\pi$
$419$			24.6341i			1.20345i	−0.798702	+	0.601726i	$0.794480\pi$
$420$	−3.03171	+	7.08017i	−0.147932	+	0.345477i
$421$	17.1808			0.837339			0.418670	−	0.908139i	$-0.362497\pi$
$421$	17.1808			0.837339			0.418670	+	0.908139i	$0.362497\pi$
$422$		−	42.8768i		−	2.08721i
$423$	−17.6592	+	16.8396i	−0.858617	+	0.818769i
$424$			20.8498i			1.01255i
$425$	−32.3527			−1.56934
$426$	2.64996	+	1.13470i	0.128391	+	0.0549766i
$427$	4.99211			0.241585
$428$	−23.5439			−1.13804
$429$	3.04248	−	4.87271i	0.146892	−	0.235257i
$430$	−15.0401			−0.725297
$431$	8.26731			0.398223			0.199111	−	0.979977i	$-0.436194\pi$
$431$	8.26731			0.398223			0.199111	+	0.979977i	$0.436194\pi$
$432$	−5.07914	+	1.89484i	−0.244370	+	0.0911654i
$433$	−20.5989			−0.989921			−0.494961	−	0.868915i	$-0.664817\pi$
$433$	−20.5989			−0.989921			−0.494961	+	0.868915i	$0.664817\pi$
$434$		−	40.7273i		−	1.95497i
$435$	−0.123269	−	0.0527833i	−0.00591029	−	0.00253077i
$436$			7.23345i			0.346419i
$437$	17.5267			0.838417
$438$	31.5059	+	13.4907i	1.50541	+	0.644612i
$439$			9.38533i			0.447938i	0.974596	+	0.223969i	$0.0719014\pi$
$439$			9.38533i			0.447938i	−0.974596	+	0.223969i	$0.928099\pi$
$440$	5.12154	+	0.792847i	0.244160	+	0.0377975i
$441$	−5.33263	−	5.59216i	−0.253935	−	0.266293i
$442$			16.0594i			0.763869i
$443$		−	25.6704i		−	1.21964i	−0.792540	−	0.609820i	$-0.791242\pi$
$443$		−	25.6704i		−	1.21964i	0.792540	−	0.609820i	$-0.208758\pi$
$444$	6.83629	−	15.9653i	0.324436	−	0.757680i
$445$	2.91657			0.138259
$446$	−15.9934			−0.757308
$447$	−12.1789	+	28.4424i	−0.576044	+	1.34528i
$448$			27.3201i			1.29075i
$449$		−	33.7518i		−	1.59285i	−0.604739	−	0.796424i	$-0.706722\pi$
$449$		−	33.7518i		−	1.59285i	0.604739	−	0.796424i	$-0.293278\pi$
$450$	20.8089	+	21.8216i	0.980939	+	1.02868i
$451$	5.68063	−	36.6951i	0.267491	−	1.72790i
$452$			31.9769i			1.50407i
$453$	9.71559	+	4.16018i	0.456478	+	0.195462i
$454$	−15.2422			−0.715353
$455$			1.48762i			0.0697408i
$456$	10.1955	+	4.36568i	0.477448	+	0.204442i
$457$		−	14.2694i		−	0.667494i	−0.942663	−	0.333747i	$-0.891687\pi$
$457$		−	14.2694i		−	0.667494i	0.942663	−	0.333747i	$-0.108313\pi$
$458$	49.0066			2.28993
$459$	−35.0029	+	13.0583i	−1.63379	+	0.609507i
$460$	12.7847			0.596088
$461$	−12.1861			−0.567562			−0.283781	−	0.958889i	$-0.591589\pi$
$461$	−12.1861			−0.567562			−0.283781	+	0.958889i	$0.591589\pi$
$462$	14.2943	−	22.8931i	0.665030	−	1.06508i
$463$	−20.9037			−0.971477			−0.485738	−	0.874104i	$-0.661449\pi$
$463$	−20.9037			−0.971477			−0.485738	+	0.874104i	$0.661449\pi$
$464$	−0.114204			−0.00530179
$465$	9.76172	+	4.17994i	0.452689	+	0.193840i
$466$	−4.05368			−0.187783
$467$			15.3297i			0.709374i	0.934985	+	0.354687i	$0.115413\pi$
$467$			15.3297i			0.709374i	−0.934985	+	0.354687i	$0.884587\pi$
$468$	6.48975	−	6.18856i	0.299989	−	0.286066i
$469$			14.5232i			0.670619i
$470$	−12.8491			−0.592687
$471$	10.7235	−	25.0433i	0.494111	−	1.15394i
$472$		−	0.00425869i		−	0.000196022i
$473$	31.2046	+	4.83068i	1.43479	+	0.222115i
$474$	−15.0727	−	6.45408i	−0.692313	−	0.296446i
$475$			13.0414i			0.598379i
$476$			45.2049i			2.07196i
$477$	−20.4883	+	19.5375i	−0.938097	+	0.894559i
$478$	−10.9980			−0.503037
$479$	−28.3228			−1.29410			−0.647051	−	0.762446i	$-0.723998\pi$
$479$	−28.3228			−1.29410			−0.647051	+	0.762446i	$0.723998\pi$
$480$	−7.60017	−	3.25436i	−0.346899	−	0.148541i
$481$		−	3.35449i		−	0.152952i
$482$		−	67.8798i		−	3.09184i
$483$	8.67238	−	20.2533i	0.394607	−	0.921556i
$484$	−31.3416	−	9.94201i	−1.42462	−	0.451910i
$485$		−	4.26482i		−	0.193655i
$486$	31.3211	+	15.2102i	1.42075	+	0.689950i
$487$	−1.58940			−0.0720226			−0.0360113	−	0.999351i	$-0.511465\pi$
$487$	−1.58940			−0.0720226			−0.0360113	+	0.999351i	$0.511465\pi$
$488$		−	5.24370i		−	0.237371i
$489$	6.80014	−	15.8809i	0.307513	−	0.718158i
$490$		−	4.06897i		−	0.183817i
$491$	−20.4678			−0.923698			−0.461849	−	0.886958i	$-0.652814\pi$
$491$	−20.4678			−0.923698			−0.461849	+	0.886958i	$0.652814\pi$
$492$	22.8165	−	53.2850i	1.02865	−	2.40227i
$493$	−0.787037			−0.0354464
$494$	6.47356			0.291259
$495$	4.02008	+	5.77570i	0.180689	+	0.259598i
$496$	9.04388			0.406082
$497$	1.56727			0.0703016
$498$	16.6791	−	38.9519i	0.747407	−	1.74548i
$499$	−22.7187			−1.01703			−0.508515	−	0.861053i	$-0.669805\pi$
$499$	−22.7187			−1.01703			−0.508515	+	0.861053i	$0.669805\pi$
$500$			20.0832i			0.898149i
$501$	14.2539	−	33.2882i	0.636818	−	1.48721i
$502$			5.79107i			0.258468i
$503$	−41.3858			−1.84530			−0.922651	−	0.385637i	$-0.873982\pi$
$503$	−41.3858			−1.84530			−0.922651	+	0.385637i	$0.873982\pi$
$504$	10.0897	−	9.62139i	0.449429	−	0.428571i
$505$		−	0.0517737i		−	0.00230390i
$506$	−44.2729	−	6.85372i	−1.96817	−	0.304685i
$507$	0.681784	−	1.59222i	0.0302791	−	0.0707131i
$508$		−	45.2302i		−	2.00676i
$509$		−	26.7095i		−	1.18388i	−0.805983	−	0.591938i	$-0.798363\pi$
$509$		−	26.7095i		−	1.18388i	0.805983	−	0.591938i	$-0.201637\pi$
$510$	−18.0844	−	7.74370i	−0.800793	−	0.342897i
$511$	18.6336			0.824301
$512$	−11.6514			−0.514922
$513$	5.26379	+	14.1097i	0.232402	+	0.622957i
$514$			36.0857i			1.59167i
$515$		−	4.24963i		−	0.187261i
$516$	45.3124	+	19.4026i	1.99477	+	0.854152i
$517$	26.6590	+	4.12698i	1.17246	+	0.181504i
$518$		−	15.7602i		−	0.692462i
$519$	−1.84067	+	4.29867i	−0.0807967	+	0.188691i
$520$	1.56260			0.0685243
$521$			16.4168i			0.719234i	0.933100	+	0.359617i	$0.117093\pi$
$521$			16.4168i			0.719234i	−0.933100	+	0.359617i	$0.882907\pi$
$522$	0.506213	+	0.530850i	0.0221563	+	0.0232347i
$523$		−	6.19971i		−	0.271094i	−0.990771	−	0.135547i	$-0.956721\pi$
$523$		−	6.19971i		−	0.271094i	0.990771	−	0.135547i	$-0.0432792\pi$
$524$	−41.4739			−1.81180
$525$	15.0702	+	6.45299i	0.657716	+	0.281632i
$526$	−12.5522			−0.547303
$527$	62.3259			2.71496
$528$	5.08363	+	3.17418i	0.221237	+	0.138138i
$529$	−13.5714			−0.590059
$530$	−14.9077			−0.647550
$531$	0.00418487	−	0.00399064i	0.000181608	−	0.000173179i
$532$	18.2221			0.790029
$533$		−	11.1958i		−	0.484943i
$534$	−14.6662	−	6.28003i	−0.634670	−	0.271763i
$535$		−	5.57061i		−	0.240839i
$536$	15.2551			0.658922
$537$	−17.1954	−	7.36300i	−0.742035	−	0.317737i
$538$		−	47.3250i		−	2.04033i
$539$	−1.30690	+	8.44215i	−0.0562922	+	0.363629i
$540$	3.83961	+	10.2921i	0.165231	+	0.442903i
$541$		−	38.1631i		−	1.64076i	−0.571819	−	0.820380i	$-0.693762\pi$
$541$		−	38.1631i		−	1.64076i	0.571819	−	0.820380i	$-0.306238\pi$
$542$		−	13.7589i		−	0.590996i
$543$	−0.634379	+	1.48151i	−0.0272238	+	0.0635778i
$544$	−48.5249			−2.08049
$545$	−1.71147			−0.0733113
$546$	3.20318	−	7.48063i	0.137083	−	0.320141i
$547$			5.75025i			0.245863i	0.992415	+	0.122931i	$0.0392295\pi$
$547$			5.75025i			0.245863i	−0.992415	+	0.122931i	$0.960770\pi$
$548$			67.1242i			2.86740i
$549$	5.15280	−	4.91366i	0.219916	−	0.209710i
$550$	5.09976	−	32.9428i	0.217454	−	1.40469i
$551$			0.317255i			0.0135155i
$552$	−21.2740	−	9.10945i	−0.905481	−	0.387724i
$553$	−8.91447			−0.379082
$554$		−	9.54308i		−	0.405446i
$555$	3.77747	+	1.61750i	0.160345	+	0.0686591i
$556$			19.8456i			0.841640i
$557$	−18.5398			−0.785556			−0.392778	−	0.919633i	$-0.628486\pi$
$557$	−18.5398			−0.785556			−0.392778	+	0.919633i	$0.628486\pi$
$558$	−40.0873	−	42.0383i	−1.69703	−	1.77962i
$559$	9.52062			0.402680
$560$	−1.55202			−0.0655846
$561$	35.0338	+	21.8749i	1.47913	+	0.923557i
$562$	−19.8603			−0.837758
$563$	18.7416			0.789866			0.394933	−	0.918710i	$-0.370768\pi$
$563$	18.7416			0.789866			0.394933	+	0.918710i	$0.370768\pi$
$564$	38.7116	+	16.5762i	1.63005	+	0.697982i
$565$	−7.56589			−0.318300
$566$			54.0587i			2.27226i
$567$	18.9092	+	0.898939i	0.794112	+	0.0377519i
$568$		−	1.64626i		−	0.0690754i
$569$	−33.4746			−1.40333			−0.701663	−	0.712509i	$-0.747559\pi$
$569$	−33.4746			−1.40333			−0.701663	+	0.712509i	$0.747559\pi$
$570$	−3.12149	+	7.28985i	−0.130745	+	0.305338i
$571$		−	27.0178i		−	1.13066i	−0.824865	−	0.565330i	$-0.808749\pi$
$571$		−	27.0178i		−	1.13066i	0.824865	−	0.565330i	$-0.191251\pi$
$572$	−9.79719	−	1.51667i	−0.409641	−	0.0634151i
$573$	15.3583	+	6.57635i	0.641600	+	0.274731i
$574$		−	52.6003i		−	2.19549i
$575$		−	27.2122i		−	1.13483i
$576$	26.8908	+	28.1995i	1.12045	+	1.17498i
$577$	−27.2745			−1.13545			−0.567725	−	0.823218i	$-0.692176\pi$
$577$	−27.2745			−1.13545			−0.567725	+	0.823218i	$0.692176\pi$
$578$	−77.4923			−3.22325
$579$	−15.2949	−	6.54923i	−0.635635	−	0.272177i
$580$			0.231418i			0.00960911i
$581$		−	23.0374i		−	0.955751i
$582$	−9.18309	+	21.4460i	−0.380651	+	0.888964i
$583$	30.9300	+	4.78817i	1.28099	+	0.198306i
$584$		−	19.5727i		−	0.809923i
$585$	1.46424	+	1.53551i	0.0605390	+	0.0634854i
$586$	35.8543			1.48113
$587$			13.2799i			0.548120i	0.961713	+	0.274060i	$0.0883668\pi$
$587$			13.2799i			0.548120i	−0.961713	+	0.274060i	$0.911633\pi$
$588$	−5.24921	+	12.2589i	−0.216474	+	0.505547i
$589$		−	25.1236i		−	1.03520i
$590$	0.00304499			0.000125360
$591$	1.93657	−	4.52262i	0.0796599	−	0.186036i
$592$	3.49969			0.143836
$593$	29.4035			1.20746			0.603729	−	0.797189i	$-0.293681\pi$
$593$	29.4035			1.20746			0.603729	+	0.797189i	$0.293681\pi$
$594$	−7.77893	−	37.6997i	−0.319174	−	1.54684i
$595$	−10.6957			−0.438481
$596$	53.3962			2.18719
$597$	−6.16050	+	14.3871i	−0.252132	+	0.588824i
$598$	−13.5078			−0.552374
$599$			22.3444i			0.912967i	0.889732	+	0.456483i	$0.150891\pi$
$599$			22.3444i			0.912967i	−0.889732	+	0.456483i	$0.849109\pi$
$600$	6.77821	−	15.8297i	0.276719	−	0.646244i
$601$		−	22.0428i		−	0.899146i	−0.893244	−	0.449573i	$-0.851576\pi$
$601$		−	22.0428i		−	0.899146i	0.893244	−	0.449573i	$-0.148424\pi$
$602$	44.7301			1.82306
$603$	14.2950	+	14.9907i	0.582136	+	0.610468i
$604$		−	18.2395i		−	0.742155i
$605$	2.35233	−	7.41557i	0.0956358	−	0.301486i
$606$	−0.111480	+	0.260348i	−0.00452857	+	0.0105759i
$607$			33.0850i			1.34288i	0.741060	+	0.671439i	$0.234323\pi$
$607$			33.0850i			1.34288i	−0.741060	+	0.671439i	$0.765677\pi$
$608$			19.5604i			0.793280i
$609$	0.366609	+	0.156981i	0.0148557	+	0.00636118i
$610$	3.74928			0.151804
$611$	8.13373			0.329055
$612$	44.4945	+	46.6600i	1.79858	+	1.88612i
$613$			26.9296i			1.08768i	0.839190	+	0.543838i	$0.183029\pi$
$613$			26.9296i			1.08768i	−0.839190	+	0.543838i	$0.816971\pi$
$614$			11.0554i			0.446161i
$615$	12.6075	+	5.39849i	0.508384	+	0.217688i
$616$	−15.2318	−	2.35797i	−0.613705	−	0.0950054i
$617$			13.0760i			0.526420i	0.964739	+	0.263210i	$0.0847813\pi$
$617$			13.0760i			0.526420i	−0.964739	+	0.263210i	$0.915219\pi$
$618$	−9.15039	+	21.3696i	−0.368083	+	0.859612i
$619$	17.5163			0.704040			0.352020	−	0.935992i	$-0.385495\pi$
$619$	17.5163			0.704040			0.352020	+	0.935992i	$0.385495\pi$
$620$		−	18.3261i		−	0.735994i
$621$	−10.9835	−	29.4413i	−0.440751	−	1.18144i
$622$			65.6774i			2.63342i
$623$	−8.67406			−0.347519
$624$	1.66114	+	0.711296i	0.0664989	+	0.0284746i
$625$	17.7472			0.709888
$626$	9.31023			0.372112
$627$	8.81776	−	14.1221i	0.352147	−	0.563984i
$628$	−47.0150			−1.87610
$629$	24.1181			0.961652
$630$	6.87936	+	7.21417i	0.274080	+	0.287419i
$631$	−44.1373			−1.75708			−0.878539	−	0.477670i	$-0.841481\pi$
$631$	−44.1373			−1.75708			−0.878539	+	0.477670i	$0.841481\pi$
$632$			9.36375i			0.372470i
$633$	−30.5642	−	13.0875i	−1.21482	−	0.520180i
$634$		−	61.6840i		−	2.44979i
$635$	10.7017			0.424683
$636$	44.9136	+	19.2318i	1.78094	+	0.762592i
$637$			2.57572i			0.102054i
$638$	0.124061	−	0.801392i	0.00491161	−	0.0317274i
$639$	1.61772	−	1.54264i	0.0639959	−	0.0610259i
$640$			10.9719i			0.433702i
$641$		−	30.2046i		−	1.19301i	−0.802610	−	0.596504i	$-0.796556\pi$
$641$		−	30.2046i		−	1.19301i	0.802610	−	0.596504i	$-0.203444\pi$
$642$	−11.9948	+	28.0123i	−0.473395	+	1.10556i
$643$	−13.3135			−0.525034			−0.262517	−	0.964927i	$-0.584553\pi$
$643$	−13.3135			−0.525034			−0.262517	+	0.964927i	$0.584553\pi$
$644$	−38.0224			−1.49829
$645$	−4.59075	+	10.7211i	−0.180761	+	0.422144i
$646$			46.5436i			1.83123i
$647$			36.3943i			1.43081i	0.698711	+	0.715404i	$0.253757\pi$
$647$			36.3943i			1.43081i	−0.698711	+	0.715404i	$0.746243\pi$
$648$	0.944244	−	19.8622i	0.0370934	−	0.780261i
$649$	−0.00631764		0.000978012i	−0.000247989		3.83903e-5i
$650$		−	10.0509i		−	0.394230i
$651$	−29.0319	−	12.4314i	−1.13785	−	0.487224i
$652$	−29.8139			−1.16760
$653$			11.9487i			0.467589i	0.972286	+	0.233794i	$0.0751142\pi$
$653$			11.9487i			0.467589i	−0.972286	+	0.233794i	$0.924886\pi$
$654$	8.60626	+	3.68517i	0.336531	+	0.144102i
$655$		−	9.81294i		−	0.383423i
$656$	11.6804			0.456043
$657$	19.2334	−	18.3408i	0.750366	−	0.715541i
$658$	38.2141			1.48974
$659$	−36.6627			−1.42818			−0.714088	−	0.700056i	$-0.753158\pi$
$659$	−36.6627			−1.42818			−0.714088	+	0.700056i	$0.753158\pi$
$660$	6.43202	−	10.3012i	0.250366	−	0.400975i
$661$	4.07930			0.158667			0.0793333	−	0.996848i	$-0.474721\pi$
$661$	4.07930			0.158667			0.0793333	+	0.996848i	$0.474721\pi$
$662$	−41.7984			−1.62454
$663$	11.4478	+	4.90189i	0.444594	+	0.190374i
$664$	−24.1984			−0.939080
$665$			4.31144i			0.167191i
$666$	−15.5125	−	16.2675i	−0.601097	−	0.630352i
$667$		−	0.661986i		−	0.0256322i
$668$	−62.4935			−2.41795
$669$	−4.88172	+	11.4007i	−0.188738	+	0.440775i
$670$			10.9075i			0.421394i
$671$	−7.77888	−	1.20422i	−0.300300	−	0.0464884i
$672$	22.6033	+	9.67867i	0.871943	+	0.373363i
$673$			24.5203i			0.945187i	0.881281	+	0.472593i	$0.156682\pi$
$673$			24.5203i			0.945187i	−0.881281	+	0.472593i	$0.843318\pi$
$674$			16.9131i			0.651467i
$675$	21.9068	−	8.17263i	0.843195	−	0.314564i
$676$	−2.98915			−0.114967
$677$	16.8256			0.646659			0.323329	−	0.946286i	$-0.395198\pi$
$677$	16.8256			0.646659			0.323329	+	0.946286i	$0.395198\pi$
$678$	38.0457	+	16.2910i	1.46114	+	0.625654i
$679$			12.6838i			0.486760i
$680$			11.2348i			0.430833i
$681$	−4.65245	+	10.8652i	−0.178282	+	0.416356i
$682$	−9.82443	+	63.4627i	−0.376197	+	2.43011i
$683$			4.82367i			0.184573i	0.995733	+	0.0922863i	$0.0294175\pi$
$683$			4.82367i			0.184573i	−0.995733	+	0.0922863i	$0.970582\pi$
$684$	18.8087	−	17.9358i	0.719167	−	0.685791i
$685$	−15.8819			−0.606817
$686$			44.9890i			1.71769i
$687$	14.9585	−	34.9337i	0.570702	−	1.33280i
$688$			9.93274i			0.378682i
$689$	9.43684			0.359515
$690$	6.51332	−	15.2110i	0.247958	−	0.579074i
$691$	3.94207			0.149963			0.0749817	−	0.997185i	$-0.476110\pi$
$691$	3.94207			0.149963			0.0749817	+	0.997185i	$0.476110\pi$
$692$	8.07008			0.306778
$693$	−11.9560	−	17.1773i	−0.454169	−	0.652510i
$694$	−49.4581			−1.87740
$695$	−4.69556			−0.178113
$696$	0.164892	−	0.385085i	0.00625022	−	0.0145966i
$697$	80.4954			3.04898
$698$		−	11.7615i		−	0.445179i
$699$	−1.23732	+	2.88961i	−0.0467999	+	0.109295i
$700$		−	28.2919i		−	1.06933i
$701$	22.4036			0.846173			0.423087	−	0.906089i	$-0.360947\pi$
$701$	22.4036			0.846173			0.423087	+	0.906089i	$0.360947\pi$
$702$	−4.05678	−	10.8743i	−0.153113	−	0.410423i
$703$		−	9.72202i		−	0.366673i
$704$	6.59028	−	42.5711i	0.248381	−	1.60446i
$705$	−3.92200	+	9.15935i	−0.147711	+	0.344961i
$706$		−	5.47539i		−	0.206069i
$707$			0.153978i			0.00579094i
$708$	−0.00917386	−	0.00392822i	−0.000344775	−	0.000147631i
$709$	31.1086			1.16831			0.584153	−	0.811643i	$-0.301427\pi$
$709$	31.1086			1.16831			0.584153	+	0.811643i	$0.301427\pi$
$710$	1.17708			0.0441751
$711$	−9.20142	+	8.77438i	−0.345080	+	0.329065i
$712$			9.11122i			0.341457i
$713$			52.4230i			1.96326i
$714$	53.7842	+	23.0302i	2.01282	+	0.861884i
$715$	0.358851	−	2.31806i	0.0134203	−	0.0866907i
$716$			32.2816i			1.20642i
$717$	−3.35697	+	7.83978i	−0.125368	+	0.292782i
$718$	−52.4528			−1.95752
$719$			10.4801i			0.390843i	0.980719	+	0.195422i	$0.0626075\pi$
$719$			10.4801i			0.390843i	−0.980719	+	0.195422i	$0.937393\pi$
$720$	−1.60197	+	1.52763i	−0.0597020	+	0.0569312i
$721$			12.6387i			0.470688i
$722$	−23.6774			−0.881182
$723$	−48.3872	−	20.7193i	−1.79954	−	0.770557i
$724$	2.78131			0.103367
$725$	0.492574			0.0182937
$726$	−27.7962	+	32.2247i	−1.03161	+	1.19597i
$727$	30.2274			1.12107			0.560536	−	0.828130i	$-0.310595\pi$
$727$	30.2274			1.12107			0.560536	+	0.828130i	$0.310595\pi$
$728$	−4.64725			−0.172239
$729$	20.4027	−	17.6842i	0.755655	−	0.654969i
$730$	13.9946			0.517963
$731$			68.4514i			2.53177i
$732$	−11.2957	−	4.83679i	−0.417502	−	0.178773i
$733$		−	30.5506i		−	1.12841i	−0.825634	−	0.564206i	$-0.809182\pi$
$733$		−	30.5506i		−	1.12841i	0.825634	−	0.564206i	$-0.190818\pi$
$734$	−34.0864			−1.25815
$735$	−2.90051	−	1.24199i	−0.106987	−	0.0458115i
$736$		−	40.8149i		−	1.50446i
$737$	3.50335	−	22.6305i	0.129048	−	0.833607i
$738$	−51.7737	−	54.2935i	−1.90582	−	1.99857i
$739$		−	32.7561i		−	1.20495i	−0.798137	−	0.602476i	$-0.794181\pi$
$739$		−	32.7561i		−	1.20495i	0.798137	−	0.602476i	$-0.205819\pi$
$740$		−	7.09162i		−	0.260693i
$741$	1.97595	−	4.61460i	0.0725885	−	0.169521i
$742$	44.3364			1.62764
$743$	21.0350			0.771699			0.385850	−	0.922562i	$-0.373908\pi$
$743$	21.0350			0.771699			0.385850	+	0.922562i	$0.373908\pi$
$744$	−13.0579	+	30.4951i	−0.478726	+	1.11800i
$745$			12.6338i			0.462867i
$746$		−	78.3812i		−	2.86974i
$747$	−22.6753	−	23.7789i	−0.829647	−	0.870025i
$748$	10.9045	−	70.4398i	0.398709	−	2.57554i
$749$			16.5673i			0.605357i
$750$	23.8948	+	10.2317i	0.872514	+	0.373607i
$751$	−11.7855			−0.430059			−0.215030	−	0.976607i	$-0.568985\pi$
$751$	−11.7855			−0.430059			−0.215030	+	0.976607i	$0.568985\pi$
$752$			8.48580i			0.309445i
$753$	4.12809	+	1.76763i	0.150436	+	0.0644162i
$754$		−	0.244507i		−	0.00890442i
$755$	4.31556			0.157059
$756$	−11.4192	−	30.6094i	−0.415313	−	1.11325i
$757$	−33.0351			−1.20068			−0.600340	−	0.799745i	$-0.704968\pi$
$757$	−33.0351			−1.20068			−0.600340	+	0.799745i	$0.704968\pi$
$758$	60.9998			2.21561
$759$	−18.3992	+	29.4673i	−0.667848	+	1.06960i
$760$	4.52873			0.164274
$761$	−4.18644			−0.151758			−0.0758792	−	0.997117i	$-0.524176\pi$
$761$	−4.18644			−0.151758			−0.0758792	+	0.997117i	$0.524176\pi$
$762$	−53.8143	−	23.0431i	−1.94949	−	0.834763i
$763$	5.09001			0.184271
$764$		−	28.8327i		−	1.04313i
$765$	−11.0400	+	10.5276i	−0.399152	+	0.380627i
$766$			7.86724i			0.284255i
$767$	−0.00192753			−6.95991e−5
$768$	5.91412	−	13.8117i	0.213407	−	0.498387i
$769$		−	38.2603i		−	1.37970i	−0.723951	−	0.689851i	$-0.757676\pi$
$769$		−	38.2603i		−	1.37970i	0.723951	−	0.689851i	$-0.242324\pi$
$770$	1.68597	−	10.8908i	0.0607580	−	0.392477i
$771$	25.7232	+	11.0146i	0.926399	+	0.396681i
$772$			28.7138i			1.03343i
$773$			31.2358i			1.12347i	0.827316	+	0.561736i	$0.189866\pi$
$773$			31.2358i			1.12347i	−0.827316	+	0.561736i	$0.810134\pi$
$774$	46.1699	−	44.0272i	1.65954	−	1.58252i
$775$	−39.0072			−1.40118
$776$	13.3231			0.478270
$777$	−11.2344	−	4.81054i	−0.403033	−	0.172577i
$778$			2.19569i			0.0787194i
$779$		−	32.4477i		−	1.16256i
$780$	1.44134	−	3.36607i	0.0516082	−	0.120525i
$781$	−2.44217	−	0.378064i	−0.0873878	−	0.0135282i
$782$		−	97.1182i		−	3.47294i
$783$	0.532923	−	0.198814i	0.0190451	−	0.00710503i
$784$	−2.68722			−0.0959721
$785$		−	11.1240i		−	0.397032i
$786$	−21.1294	+	49.3451i	−0.753661	+	1.76008i
$787$		−	7.31521i		−	0.260759i	−0.991464	−	0.130380i	$-0.958380\pi$
$787$		−	7.31521i		−	0.260759i	0.991464	−	0.130380i	$-0.0416196\pi$
$788$	−8.49052			−0.302462
$789$	−3.83137	+	8.94770i	−0.136401	+	0.318546i
$790$	−6.69514			−0.238202
$791$	22.5014			0.800058
$792$	−18.0430	+	12.5585i	−0.641129	+	0.446247i
$793$	−2.37336			−0.0842804
$794$	−51.0291			−1.81096
$795$	−4.55035	+	10.6268i	−0.161384	+	0.376893i
$796$	27.0095			0.957327
$797$			17.4209i			0.617079i	0.951212	+	0.308539i	$0.0998402\pi$
$797$			17.4209i			0.617079i	−0.951212	+	0.308539i	$0.900160\pi$
$798$	9.28349	−	21.6804i	0.328632	−	0.767479i
$799$			58.4799i			2.06887i
$800$	30.3698			1.07373
$801$	−8.95327	+	8.53775i	−0.316348	+	0.301667i
$802$			10.4030i			0.367342i
$803$	−29.0355	−	4.49488i	−1.02464	−	0.158621i
$804$	14.0713	−	32.8619i	0.496258	−	1.15895i
$805$		−	8.99628i		−	0.317077i
$806$			19.3626i			0.682020i
$807$	−33.7350	−	14.4452i	−1.18753	−	0.508496i
$808$	0.161738			0.00568993
$809$	−33.8584			−1.19040			−0.595198	−	0.803579i	$-0.702927\pi$
$809$	−33.8584			−1.19040			−0.595198	+	0.803579i	$0.702927\pi$
$810$	14.2016	+	0.675140i	0.498993	+	0.0237220i
$811$			3.26968i			0.114814i	0.998351	+	0.0574071i	$0.0182833\pi$
$811$			3.26968i			0.114814i	−0.998351	+	0.0574071i	$0.981717\pi$
$812$		−	0.688251i		−	0.0241529i
$813$	−9.80787	−	4.19970i	−0.343977	−	0.147290i
$814$	−3.80174	+	24.5580i	−0.133251	+	0.860758i
$815$		−	7.05411i		−	0.247095i
$816$	−5.11408	+	11.9433i	−0.179028	+	0.418099i
$817$	27.5928			0.965349
$818$		−	12.3615i		−	0.432211i
$819$	−4.35475	−	4.56669i	−0.152167	−	0.159573i
$820$		−	23.6686i		−	0.826544i
$821$	10.6762			0.372603			0.186302	−	0.982493i	$-0.440350\pi$
$821$	10.6762			0.372603			0.186302	+	0.982493i	$0.440350\pi$
$822$	79.8635	+	34.1973i	2.78556	+	1.19277i
$823$	25.0143			0.871942			0.435971	−	0.899961i	$-0.356405\pi$
$823$	25.0143			0.871942			0.435971	+	0.899961i	$0.356405\pi$
$824$	13.2756			0.462478
$825$	−21.9262	−	13.6906i	−0.763373	−	0.476644i
$826$	−0.00905598			−0.000315098
$827$	−24.8263			−0.863294			−0.431647	−	0.902043i	$-0.642067\pi$
$827$	−24.8263			−0.863294			−0.431647	+	0.902043i	$0.642067\pi$
$828$	−39.2463	+	37.4248i	−1.36390	+	1.30060i
$829$	12.0638			0.418994			0.209497	−	0.977809i	$-0.432817\pi$
$829$	12.0638			0.418994			0.209497	+	0.977809i	$0.432817\pi$
$830$		−	17.3020i		−	0.600562i
$831$	−6.80266	−	2.91288i	−0.235982	−	0.101047i
$832$		−	12.9886i		−	0.450297i
$833$	−18.5189			−0.641644
$834$	23.6120	+	10.1106i	0.817617	+	0.350101i
$835$		−	14.7863i		−	0.511700i
$836$	−28.3943	−	4.39562i	−0.982038	−	0.152026i
$837$	−42.2025	+	15.7442i	−1.45873	+	0.544198i
$838$		−	55.0236i		−	1.90076i
$839$		−	31.9559i		−	1.10324i	−0.834096	−	0.551619i	$-0.814010\pi$
$839$		−	31.9559i		−	1.10324i	0.834096	−	0.551619i	$-0.185990\pi$
$840$	2.24086	−	5.23325i	0.0773170	−	0.180564i
$841$	−28.9880			−0.999587
$842$	−38.3757			−1.32251
$843$	−6.06206	+	14.1572i	−0.208788	+	0.487599i
$844$			57.3794i			1.97508i
$845$		−	0.707248i		−	0.0243301i
$846$	39.4442	−	37.6136i	1.35612	−	1.29318i
$847$	−6.99597	+	22.0543i	−0.240384	+	0.757796i
$848$			9.84532i			0.338090i
$849$	38.5350	+	16.5006i	1.32252	+	0.566298i
$850$	72.2642			2.47864
$851$			20.2860i			0.695396i
$852$	−3.54628	−	1.51851i	−0.121494	−	0.0520232i
$853$		−	50.8210i		−	1.74008i	−0.492984	−	0.870039i	$-0.664094\pi$
$853$		−	50.8210i		−	1.74008i	0.492984	−	0.870039i	$-0.335906\pi$
$854$	−11.1506			−0.381565
$855$	4.24369	+	4.45023i	0.145131	+	0.152194i
$856$	17.4023			0.594798
$857$	−16.2214			−0.554113			−0.277056	−	0.960854i	$-0.589359\pi$
$857$	−16.2214			−0.554113			−0.277056	+	0.960854i	$0.589359\pi$
$858$	−6.79581	+	10.8839i	−0.232005	+	0.371570i
$859$	24.9290			0.850567			0.425284	−	0.905060i	$-0.360174\pi$
$859$	24.9290			0.850567			0.425284	+	0.905060i	$0.360174\pi$
$860$	20.1273			0.686334
$861$	−37.4955	−	16.0554i	−1.27784	−	0.547168i
$862$	−18.4662			−0.628962
$863$		−	49.6813i		−	1.69117i	−0.533840	−	0.845585i	$-0.679252\pi$
$863$		−	49.6813i		−	1.69117i	0.533840	−	0.845585i	$-0.320748\pi$
$864$	32.8575	−	12.2579i	1.11783	−	0.417022i
$865$			1.90942i			0.0649223i
$866$	46.0106			1.56350
$867$	−23.6533	+	55.2394i	−0.803308	+	1.87603i
$868$			54.5029i			1.84995i
$869$	13.8908	+	2.15039i	0.471214	+	0.0729470i
$870$	0.275338	+	0.117899i	0.00933484	+	0.00399715i
$871$		−	6.90464i		−	0.233955i
$872$		−	5.34654i		−	0.181057i
$873$	12.4845	+	13.0921i	0.422536	+	0.443100i
$874$	−39.1484			−1.32421
$875$	14.1321			0.477753
$876$	−42.1625	−	18.0538i	−1.42454	−	0.609983i
$877$		−	40.9021i		−	1.38117i	−0.723253	−	0.690583i	$-0.757354\pi$
$877$		−	40.9021i		−	1.38117i	0.723253	−	0.690583i	$-0.242646\pi$
$878$		−	20.9635i		−	0.707483i
$879$	10.9440	−	25.5583i	0.369131	−	0.862060i
$880$	2.41840	+	0.374384i	0.0815244	+	0.0126205i
$881$			1.38442i			0.0466424i	0.999728	+	0.0233212i	$0.00742405\pi$
$881$			1.38442i			0.0466424i	−0.999728	+	0.0233212i	$0.992576\pi$
$882$	11.9112	+	12.4909i	0.401070	+	0.420590i
$883$	−3.63427			−0.122303			−0.0611515	−	0.998128i	$-0.519477\pi$
$883$	−3.63427			−0.122303			−0.0611515	+	0.998128i	$0.519477\pi$
$884$		−	21.4914i		−	0.722834i
$885$	0.000929436	−	0.00217058i	3.12426e−5	−	7.29633e-5i
$886$			57.3385i			1.92633i
$887$	34.0196			1.14227			0.571133	−	0.820857i	$-0.306504\pi$
$887$	34.0196			1.14227			0.571133	+	0.820857i	$0.306504\pi$
$888$	−5.05299	+	11.8006i	−0.169567	+	0.396003i
$889$	−31.8274			−1.06746
$890$	−6.51458			−0.218369
$891$	−29.2481	−	5.96213i	−0.979849	−	0.199739i
$892$	21.4030			0.716624
$893$	23.5733			0.788849
$894$	27.2034	−	63.5301i	0.909817	−	2.12476i
$895$	−7.63800			−0.255310
$896$		−	32.6311i		−	1.09013i
$897$	−4.12304	+	9.62884i	−0.137664	+	0.321498i
$898$			75.3895i			2.51578i
$899$	−0.948920			−0.0316483
$900$	−27.8473	−	29.2026i	−0.928243	−	0.973419i
$901$			67.8490i			2.26038i
$902$	−12.6885	+	81.9636i	−0.422481	+	2.72909i
$903$	13.6532	−	31.8853i	0.454349	−	1.06108i
$904$		−	23.6354i		−	0.786103i
$905$			0.658072i			0.0218750i
$906$	−21.7011	−	9.29235i	−0.720972	−	0.308718i
$907$	14.8398			0.492746			0.246373	−	0.969175i	$-0.420761\pi$
$907$	14.8398			0.492746			0.246373	+	0.969175i	$0.420761\pi$
$908$	20.3978			0.676923
$909$	0.151558	+	0.158934i	0.00502687	+	0.00527152i
$910$		−	3.32281i		−	0.110150i
$911$		−	9.33859i		−	0.309401i	−0.987961	−	0.154701i	$-0.950559\pi$
$911$		−	9.33859i		−	0.309401i	0.987961	−	0.154701i	$-0.0494413\pi$
$912$	4.81434	+	2.06149i	0.159419	+	0.0682626i
$913$	−5.55718	+	35.8976i	−0.183916	+	1.18804i
$914$			31.8727i			1.05426i
$915$	1.14441	−	2.67263i	0.0378330	−	0.0883543i
$916$	−65.5826			−2.16691
$917$			29.1843i			0.963749i
$918$	78.1838	−	29.1675i	2.58045	−	0.962669i
$919$		−	26.1633i		−	0.863047i	−0.902102	−	0.431524i	$-0.857976\pi$
$919$		−	26.1633i		−	0.863047i	0.902102	−	0.431524i	$-0.142024\pi$
$920$	−9.44968			−0.311547
$921$	7.88072	+	3.37450i	0.259678	+	0.111193i
$922$	27.2193			0.896420
$923$	−0.745113			−0.0245257
$924$	−19.1292	+	30.6365i	−0.629305	+	1.00787i
$925$	−15.0945			−0.496305
$926$	46.6913			1.53437
$927$	12.4400	+	13.0455i	0.408584	+	0.428470i
$928$	0.738799			0.0242523
$929$			3.31850i			0.108876i	0.998517	+	0.0544382i	$0.0173368\pi$
$929$			3.31850i			0.108876i	−0.998517	+	0.0544382i	$0.982663\pi$
$930$	−21.8042	−	9.33647i	−0.714987	−	0.306155i
$931$			7.46499i			0.244655i
$932$	5.42480			0.177695
$933$	46.8173	+	20.0470i	1.53273	+	0.656309i
$934$		−	34.2410i		−	1.12040i
$935$	16.6664	+	2.58007i	0.545050	+	0.0843773i
$936$	−4.79684	+	4.57422i	−0.156790	+	0.149513i
$937$		−	53.6189i		−	1.75165i	−0.482625	−	0.875827i	$-0.660316\pi$
$937$		−	53.6189i		−	1.75165i	0.482625	−	0.875827i	$-0.339684\pi$
$938$		−	32.4396i		−	1.05919i
$939$	2.84180	−	6.63668i	0.0927387	−	0.216580i
$940$	17.1953			0.560847
$941$	−52.2502			−1.70331			−0.851654	−	0.524105i	$-0.824400\pi$
$941$	−52.2502			−1.70331			−0.851654	+	0.524105i	$0.824400\pi$
$942$	−23.9524	+	55.9378i	−0.780411	+	1.82255i
$943$			67.7056i			2.20480i
$944$		−	0.00201097i		−	6.54514e-5i
$945$	7.24234	−	2.70185i	0.235593	−	0.0878911i
$946$	−69.7000	−	10.7900i	−2.26614	−	0.350813i
$947$		−	7.99181i		−	0.259699i	−0.991534	−	0.129850i	$-0.958551\pi$
$947$		−	7.99181i		−	0.259699i	0.991534	−	0.129850i	$-0.0414494\pi$
$948$	20.1709	+	8.63712i	0.655121	+	0.280521i
$949$	−8.85881			−0.287569
$950$		−	29.1297i		−	0.945094i
$951$	−43.9707	−	18.8281i	−1.42585	−	0.610543i
$952$		−	33.4128i		−	1.08292i
$953$	−24.5356			−0.794786			−0.397393	−	0.917648i	$-0.630085\pi$
$953$	−24.5356			−0.794786			−0.397393	+	0.917648i	$0.630085\pi$
$954$	45.7636	−	43.6397i	1.48165	−	1.41289i
$955$	6.82197			0.220754
$956$	14.7180			0.476013
$957$	−0.533395	−	0.333048i	−0.0172422	−	0.0107659i
$958$	63.2630			2.04393
$959$	47.2338			1.52526
$960$	14.6264	+	6.26296i	0.472064	+	0.202136i
$961$	44.1454			1.42405
$962$			7.49272i			0.241575i
$963$	16.3070	+	17.1006i	0.525485	+	0.551060i
$964$			90.8395i			2.92574i
$965$	−6.79383			−0.218701
$966$	−19.3710	+	45.2385i	−0.623251	+	1.45553i
$967$			27.4755i			0.883553i	0.897125	+	0.441776i	$0.145652\pi$
$967$			27.4755i			0.883553i	−0.897125	+	0.441776i	$0.854348\pi$
$968$	23.1658	+	7.34855i	0.744578	+	0.236191i
$969$	33.1780	+	14.2067i	1.06583	+	0.456386i
$970$			9.52606i			0.305863i
$971$			11.4405i			0.367142i	0.983006	+	0.183571i	$0.0587657\pi$
$971$			11.4405i			0.367142i	−0.983006	+	0.183571i	$0.941234\pi$
$972$	−41.9152	−	20.3549i	−1.34443	−	0.652885i
$973$	13.9649			0.447693
$974$	3.55015			0.113754
$975$	−7.16468	−	3.06789i	−0.229453	−	0.0982512i
$976$		−	2.47609i		−	0.0792577i
$977$			27.5285i			0.880714i	0.897823	+	0.440357i	$0.145148\pi$
$977$			27.5285i			0.880714i	−0.897823	+	0.440357i	$0.854852\pi$
$978$	−15.1891	+	35.4722i	−0.485693	+	1.13428i
$979$	13.5162	+	2.09240i	0.431980	+	0.0668733i
$980$			5.44526i			0.173942i
$981$	5.25385	−	5.01002i	0.167743	−	0.159958i
$982$	45.7177			1.45891
$983$			6.57392i			0.209676i	0.994489	+	0.104838i	$0.0334323\pi$
$983$			6.57392i			0.209676i	−0.994489	+	0.104838i	$0.966568\pi$
$984$	−16.8646	+	39.3852i	−0.537624	+	1.25555i
$985$		−	2.00890i		−	0.0640089i
$986$	1.75796			0.0559848
$987$	11.6643	−	27.2404i	0.371278	−	0.867073i
$988$	−8.66319			−0.275613
$989$	−57.5753			−1.83079
$990$	−8.97941	−	12.9008i	−0.285384	−	0.410015i
$991$	40.3368			1.28134			0.640671	−	0.767816i	$-0.278656\pi$
$991$	40.3368			1.28134			0.640671	+	0.767816i	$0.278656\pi$
$992$	−58.5058			−1.85756
$993$	−12.7583	+	29.7955i	−0.404873	+	0.945531i
$994$	−3.50071			−0.111036
$995$			6.39059i			0.202595i
$996$	−22.3206	+	52.1270i	−0.707256	+	1.65171i
$997$		−	45.5997i		−	1.44416i	−0.691812	−	0.722078i	$-0.743187\pi$
$997$		−	45.5997i		−	1.44416i	0.691812	−	0.722078i	$-0.256813\pi$
$998$	50.7455			1.60632
$999$	−16.3310	+	6.09249i	−0.516690	+	0.192758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.f.a.131.6	yes	48
3.2	odd	2	inner	429.2.f.a.131.43	yes	48
11.10	odd	2	inner	429.2.f.a.131.44	yes	48
33.32	even	2	inner	429.2.f.a.131.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.f.a.131.5	✓	48	33.32	even	2	inner
429.2.f.a.131.6	yes	48	1.1	even	1	trivial
429.2.f.a.131.43	yes	48	3.2	odd	2	inner
429.2.f.a.131.44	yes	48	11.10	odd	2	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.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.23364 q^{2} +(-0.681784 + 1.59222i) q^{3} +2.98915 q^{4} +0.707248i q^{5} +(1.52286 - 3.55645i) q^{6} -2.10340i q^{7} -2.20940 q^{8} +(-2.07034 - 2.17110i) q^{9} +O(q^{10})\)	\(q-2.23364 q^{2} +(-0.681784 + 1.59222i) q^{3} +2.98915 q^{4} +0.707248i q^{5} +(1.52286 - 3.55645i) q^{6} -2.10340i q^{7} -2.20940 q^{8} +(-2.07034 - 2.17110i) q^{9} -1.57974i q^{10} +(-0.507391 + 3.27758i) q^{11} +(-2.03795 + 4.75939i) q^{12} +1.00000i q^{13} +4.69823i q^{14} +(-1.12610 - 0.482190i) q^{15} -1.04329 q^{16} -7.18980 q^{17} +(4.62440 + 4.84946i) q^{18} +2.89821i q^{19} +2.11407i q^{20} +(3.34907 + 1.43406i) q^{21} +(1.13333 - 7.32094i) q^{22} -6.04743i q^{23} +(1.50634 - 3.51786i) q^{24} +4.49980 q^{25} -2.23364i q^{26} +(4.86840 - 1.81622i) q^{27} -6.28736i q^{28} +0.109466 q^{29} +(2.51529 + 1.07704i) q^{30} -8.66865 q^{31} +6.74913 q^{32} +(-4.87271 - 3.04248i) q^{33} +16.0594 q^{34} +1.48762 q^{35} +(-6.18856 - 6.48975i) q^{36} -3.35449 q^{37} -6.47356i q^{38} +(-1.59222 - 0.681784i) q^{39} -1.56260i q^{40} -11.1958 q^{41} +(-7.48063 - 3.20318i) q^{42} -9.52062i q^{43} +(-1.51667 + 9.79719i) q^{44} +(1.53551 - 1.46424i) q^{45} +13.5078i q^{46} -8.13373i q^{47} +(0.711296 - 1.66114i) q^{48} +2.57572 q^{49} -10.0509 q^{50} +(4.90189 - 11.4478i) q^{51} +2.98915i q^{52} -9.43684i q^{53} +(-10.8743 + 4.05678i) q^{54} +(-2.31806 - 0.358851i) q^{55} +4.64725i q^{56} +(-4.61460 - 1.97595i) q^{57} -0.244507 q^{58} +0.00192753i q^{59} +(-3.36607 - 1.44134i) q^{60} +2.37336i q^{61} +19.3626 q^{62} +(-4.56669 + 4.35475i) q^{63} -12.9886 q^{64} -0.707248 q^{65} +(10.8839 + 6.79581i) q^{66} -6.90464 q^{67} -21.4914 q^{68} +(9.62884 + 4.12304i) q^{69} -3.32281 q^{70} +0.745113i q^{71} +(4.57422 + 4.79684i) q^{72} +8.85881i q^{73} +7.49272 q^{74} +(-3.06789 + 7.16468i) q^{75} +8.66319i q^{76} +(6.89406 + 1.06724i) q^{77} +(3.55645 + 1.52286i) q^{78} -4.23813i q^{79} -0.737862i q^{80} +(-0.427375 + 8.98985i) q^{81} +25.0073 q^{82} +10.9525 q^{83} +(10.0109 + 4.28662i) q^{84} -5.08497i q^{85} +21.2657i q^{86} +(-0.0746320 + 0.174294i) q^{87} +(1.12103 - 7.24150i) q^{88} -4.12384i q^{89} +(-3.42977 + 3.27059i) q^{90} +2.10340 q^{91} -18.0767i q^{92} +(5.91014 - 13.8024i) q^{93} +18.1678i q^{94} -2.04975 q^{95} +(-4.60145 + 10.7461i) q^{96} -6.03016 q^{97} -5.75324 q^{98} +(8.16644 - 5.68412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) \) 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9	\( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) \) 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9 - 20 * q^12 - 6 * q^15 + 8 * q^16 - 4 * q^22 - 28 * q^25 - 12 * q^31 + 2 * q^33 - 16 * q^34 + 26 * q^36 + 20 * q^37 - 2 * q^42 - 50 * q^45 - 82 * q^48 - 56 * q^49 - 20 * q^55 - 80 * q^58 + 104 * q^60 + 16 * q^64 - 50 * q^66 + 60 * q^67 + 6 * q^69 + 80 * q^70 + 12 * q^75 + 10 * q^78 + 6 * q^81 - 8 * q^82 - 52 * q^88 - 8 * q^91 + 42 * q^93 - 92 * q^97 + 18 * q^99

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