LMFDB - Embedded newform 351.2.r.b.316.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(10,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("351.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.4
Character	$\chi$	$=$	351.316
Dual form			351.2.r.b.10.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.677814 + 0.391336i) q^{2} +(-0.693712 + 1.20154i) q^{4} +(0.0536139 - 0.0309540i) q^{5} -3.75567i q^{7} -2.65124i q^{8} +O(q^{10})$	\(q+(-0.677814 + 0.391336i) q^{2} +(-0.693712 + 1.20154i) q^{4} +(0.0536139 - 0.0309540i) q^{5} -3.75567i q^{7} -2.65124i q^{8} +(-0.0242268 + 0.0419621i) q^{10} +(1.11071 - 0.641267i) q^{11} +(1.65180 - 3.20493i) q^{13} +(1.46973 + 2.54564i) q^{14} +(-0.349898 - 0.606041i) q^{16} +(2.74383 + 4.75245i) q^{17} +(2.72231 - 1.57173i) q^{19} +0.0858927i q^{20} +(-0.501902 + 0.869319i) q^{22} +5.65979 q^{23} +(-2.49808 + 4.32681i) q^{25} +(0.134590 + 2.81875i) q^{26} +(4.51260 + 2.60535i) q^{28} +(-3.56722 - 6.17860i) q^{29} +(3.62246 - 2.09143i) q^{31} +(5.06642 + 2.92510i) q^{32} +(-3.71961 - 2.14752i) q^{34} +(-0.116253 - 0.201356i) q^{35} +(-4.03923 - 2.33205i) q^{37} +(-1.23015 + 2.13067i) q^{38} +(-0.0820666 - 0.142143i) q^{40} -9.88981i q^{41} +4.22761 q^{43} +1.77942i q^{44} +(-3.83628 + 2.21488i) q^{46} +(-2.73495 - 1.57902i) q^{47} -7.10504 q^{49} -3.91036i q^{50} +(2.70499 + 4.20801i) q^{52} +0.752963 q^{53} +(0.0396996 - 0.0687616i) q^{55} -9.95718 q^{56} +(4.83582 + 2.79196i) q^{58} +(0.310908 + 0.179503i) q^{59} +1.65095 q^{61} +(-1.63690 + 2.83520i) q^{62} -3.17919 q^{64} +(-0.0106459 - 0.222958i) q^{65} +1.65785i q^{67} -7.61370 q^{68} +(0.157596 + 0.0909879i) q^{70} +(-11.3838 + 6.57246i) q^{71} +6.09030i q^{73} +3.65046 q^{74} +4.36130i q^{76} +(-2.40838 - 4.17145i) q^{77} +(-0.616191 + 1.06727i) q^{79} +(-0.0375188 - 0.0216615i) q^{80} +(3.87024 + 6.70345i) q^{82} +(11.0538 + 6.38193i) q^{83} +(0.294215 + 0.169865i) q^{85} +(-2.86553 + 1.65442i) q^{86} +(-1.70015 - 2.94475i) q^{88} +(-1.30142 - 0.751374i) q^{89} +(-12.0366 - 6.20361i) q^{91} +(-3.92627 + 6.80049i) q^{92} +2.47172 q^{94} +(0.0973024 - 0.168533i) q^{95} +10.0235i q^{97} +(4.81589 - 2.78046i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 10 q^{4} - 3 q^{5}+O(q^{10}) $ 22 * q + 10 * q^4 - 3 * q^5	$ 22 q + 10 q^{4} - 3 q^{5} - 7 q^{10} - 3 q^{11} + 3 q^{13} + 9 q^{14} - 12 q^{16} - 9 q^{17} - 6 q^{19} - 13 q^{22} + 12 q^{23} + 4 q^{25} + 12 q^{26} + 3 q^{28} + 24 q^{29} + 27 q^{31} - 15 q^{34} + 27 q^{35} + 6 q^{37} - 21 q^{38} + 13 q^{40} + 8 q^{43} - 15 q^{46} - 6 q^{47} - 14 q^{49} - 7 q^{52} + 24 q^{53} - 13 q^{55} - 18 q^{56} + 15 q^{58} + 33 q^{59} - 6 q^{61} - 24 q^{64} - 3 q^{65} - 138 q^{68} + 24 q^{70} - 9 q^{71} - 12 q^{74} - 42 q^{77} - 6 q^{79} - 105 q^{80} - 16 q^{82} + 42 q^{83} - 51 q^{85} + 45 q^{86} - 11 q^{88} + 30 q^{89} + 15 q^{91} + 3 q^{92} - 88 q^{94} + 3 q^{95} - 117 q^{98}+O(q^{100}) $ 22 * q + 10 * q^4 - 3 * q^5 - 7 * q^10 - 3 * q^11 + 3 * q^13 + 9 * q^14 - 12 * q^16 - 9 * q^17 - 6 * q^19 - 13 * q^22 + 12 * q^23 + 4 * q^25 + 12 * q^26 + 3 * q^28 + 24 * q^29 + 27 * q^31 - 15 * q^34 + 27 * q^35 + 6 * q^37 - 21 * q^38 + 13 * q^40 + 8 * q^43 - 15 * q^46 - 6 * q^47 - 14 * q^49 - 7 * q^52 + 24 * q^53 - 13 * q^55 - 18 * q^56 + 15 * q^58 + 33 * q^59 - 6 * q^61 - 24 * q^64 - 3 * q^65 - 138 * q^68 + 24 * q^70 - 9 * q^71 - 12 * q^74 - 42 * q^77 - 6 * q^79 - 105 * q^80 - 16 * q^82 + 42 * q^83 - 51 * q^85 + 45 * q^86 - 11 * q^88 + 30 * q^89 + 15 * q^91 + 3 * q^92 - 88 * q^94 + 3 * q^95 - 117 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.677814	+	0.391336i	−0.479287	+	0.276716i	−0.720119	−	0.693850i	$-0.755913\pi$
$2$	−0.677814	+	0.391336i	−0.479287	+	0.276716i	0.240832	+	0.970567i	$0.422580\pi$
$3$		0			0
$3$		0			0
$4$	−0.693712	+	1.20154i	−0.346856	+	0.600772i
$5$	0.0536139	−	0.0309540i	0.0239769	−	0.0138431i	−0.487964	−	0.872864i	$-0.662260\pi$
$5$	0.0536139	−	0.0309540i	0.0239769	−	0.0138431i	0.511941	+	0.859021i	$0.328927\pi$
$6$		0			0
$7$		−	3.75567i		−	1.41951i	−0.704449	−	0.709754i	$-0.748806\pi$
$7$		−	3.75567i		−	1.41951i	0.704449	−	0.709754i	$-0.251194\pi$
$8$		−	2.65124i		−	0.937356i
$9$		0			0
$10$	−0.0242268	+	0.0419621i	−0.00766120	+	0.0132696i
$11$	1.11071	−	0.641267i	0.334891	−	0.193349i	−0.323120	−	0.946358i	$-0.604732\pi$
$11$	1.11071	−	0.641267i	0.334891	−	0.193349i	0.658010	+	0.753009i	$0.271398\pi$
$12$		0			0
$13$	1.65180	−	3.20493i	0.458127	−	0.888887i
$13$	1.65180	−	3.20493i	0.458127	−	0.888887i
$14$	1.46973	+	2.54564i	0.392801	+	0.680352i
$15$		0			0
$16$	−0.349898	−	0.606041i	−0.0874746	−	0.151510i
$17$	2.74383	+	4.75245i	0.665476	+	1.15264i	0.979156	+	0.203109i	$0.0651046\pi$
$17$	2.74383	+	4.75245i	0.665476	+	1.15264i	−0.313681	+	0.949529i	$0.601562\pi$
$18$		0			0
$19$	2.72231	−	1.57173i	0.624540	−	0.360579i	−0.154094	−	0.988056i	$-0.549246\pi$
$19$	2.72231	−	1.57173i	0.624540	−	0.360579i	0.778635	+	0.627478i	$0.215913\pi$
$20$			0.0858927i			0.0192062i
$21$		0			0
$22$	−0.501902	+	0.869319i	−0.107006	+	0.185339i
$23$	5.65979			1.18015			0.590074	−	0.807349i	$-0.299099\pi$
$23$	5.65979			1.18015			0.590074	+	0.807349i	$0.299099\pi$
$24$		0			0
$25$	−2.49808	+	4.32681i	−0.499617	+	0.865362i
$26$	0.134590	+	2.81875i	0.0263953	+	0.552803i
$27$		0			0
$28$	4.51260	+	2.60535i	0.852802	+	0.492365i
$29$	−3.56722	−	6.17860i	−0.662416	−	1.14734i	−0.979979	−	0.199101i	$-0.936198\pi$
$29$	−3.56722	−	6.17860i	−0.662416	−	1.14734i	0.317563	−	0.948237i	$-0.397135\pi$
$30$		0			0
$31$	3.62246	−	2.09143i	0.650613	−	0.375632i	−0.138078	−	0.990421i	$-0.544092\pi$
$31$	3.62246	−	2.09143i	0.650613	−	0.375632i	0.788691	+	0.614790i	$0.210759\pi$
$32$	5.06642	+	2.92510i	0.895625	+	0.517089i
$33$		0			0
$34$	−3.71961	−	2.14752i	−0.637907	−	0.368296i
$35$	−0.116253	−	0.201356i	−0.0196503	−	0.0340354i
$36$		0			0
$37$	−4.03923	−	2.33205i	−0.664045	−	0.383386i	0.129772	−	0.991544i	$-0.458576\pi$
$37$	−4.03923	−	2.33205i	−0.664045	−	0.383386i	−0.793816	+	0.608158i	$0.791909\pi$
$38$	−1.23015	+	2.13067i	−0.199556	+	0.345641i
$39$		0			0
$40$	−0.0820666	−	0.142143i	−0.0129759	−	0.0224749i
$41$		−	9.88981i		−	1.54453i	−0.635302	−	0.772264i	$-0.719124\pi$
$41$		−	9.88981i		−	1.54453i	0.635302	−	0.772264i	$-0.280876\pi$
$42$		0			0
$43$	4.22761			0.644704			0.322352	−	0.946620i	$-0.395526\pi$
$43$	4.22761			0.644704			0.322352	+	0.946620i	$0.395526\pi$
$44$			1.77942i			0.268257i
$45$		0			0
$46$	−3.83628	+	2.21488i	−0.565629	+	0.326566i
$47$	−2.73495	−	1.57902i	−0.398933	−	0.230324i	0.287090	−	0.957904i	$-0.407312\pi$
$47$	−2.73495	−	1.57902i	−0.398933	−	0.230324i	−0.686024	+	0.727579i	$0.740645\pi$
$48$		0			0
$49$	−7.10504			−1.01501
$50$		−	3.91036i		−	0.553008i
$51$		0			0
$52$	2.70499	+	4.20801i	0.375115	+	0.583546i
$53$	0.752963			0.103427			0.0517137	−	0.998662i	$-0.483532\pi$
$53$	0.752963			0.103427			0.0517137	+	0.998662i	$0.483532\pi$
$54$		0			0
$55$	0.0396996	−	0.0687616i	0.00535309	−	0.00927182i
$56$	−9.95718			−1.33058
$57$		0			0
$58$	4.83582	+	2.79196i	0.634974	+	0.366602i
$59$	0.310908	+	0.179503i	0.0404767	+	0.0233692i	0.520102	−	0.854104i	$-0.325894\pi$
$59$	0.310908	+	0.179503i	0.0404767	+	0.0233692i	−0.479625	+	0.877474i	$0.659227\pi$
$60$		0			0
$61$	1.65095			0.211382			0.105691	−	0.994399i	$-0.466295\pi$
$61$	1.65095			0.211382			0.105691	+	0.994399i	$0.466295\pi$
$62$	−1.63690	+	2.83520i	−0.207887	+	0.360071i
$63$		0			0
$64$	−3.17919			−0.397399
$65$	−0.0106459	−	0.222958i	−0.00132046	−	0.0276546i
$66$		0			0
$67$			1.65785i			0.202539i	0.994859	+	0.101269i	$0.0322904\pi$
$67$			1.65785i			0.202539i	−0.994859	+	0.101269i	$0.967710\pi$
$68$	−7.61370			−0.923297
$69$		0			0
$70$	0.157596	+	0.0909879i	0.0188363	+	0.0108751i
$71$	−11.3838	+	6.57246i	−1.35101	+	0.780008i	−0.988391	−	0.151929i	$-0.951452\pi$
$71$	−11.3838	+	6.57246i	−1.35101	+	0.780008i	−0.362622	+	0.931936i	$0.618118\pi$
$72$		0			0
$73$			6.09030i			0.712816i	0.934330	+	0.356408i	$0.115999\pi$
$73$			6.09030i			0.712816i	−0.934330	+	0.356408i	$0.884001\pi$
$74$	3.65046			0.424357
$75$		0			0
$76$			4.36130i			0.500276i
$77$	−2.40838	−	4.17145i	−0.274461	−	0.475380i
$78$		0			0
$79$	−0.616191	+	1.06727i	−0.0693269	+	0.120078i	−0.898605	−	0.438758i	$-0.855418\pi$
$79$	−0.616191	+	1.06727i	−0.0693269	+	0.120078i	0.829278	+	0.558836i	$0.188752\pi$
$80$	−0.0375188	−	0.0216615i	−0.00419473	−	0.00242183i
$81$		0			0
$82$	3.87024	+	6.70345i	0.427396	+	0.740272i
$83$	11.0538	+	6.38193i	1.21332	+	0.700508i	0.963480	−	0.267781i	$-0.0862903\pi$
$83$	11.0538	+	6.38193i	1.21332	+	0.700508i	0.249835	+	0.968288i	$0.419624\pi$
$84$		0			0
$85$	0.294215	+	0.169865i	0.0319120	+	0.0184244i
$86$	−2.86553	+	1.65442i	−0.308998	+	0.178400i
$87$		0			0
$88$	−1.70015	−	2.94475i	−0.181237	−	0.313912i
$89$	−1.30142	−	0.751374i	−0.137950	−	0.0796455i	0.429437	−	0.903097i	$-0.358712\pi$
$89$	−1.30142	−	0.751374i	−0.137950	−	0.0796455i	−0.567387	+	0.823452i	$0.692045\pi$
$90$		0			0
$91$	−12.0366	−	6.20361i	−1.26178	−	0.650315i
$92$	−3.92627	+	6.80049i	−0.409342	+	0.709000i
$93$		0			0
$94$	2.47172			0.254938
$95$	0.0973024	−	0.168533i	0.00998301	−	0.0172911i
$96$		0			0
$97$			10.0235i			1.01773i	0.860847	+	0.508865i	$0.169935\pi$
$97$			10.0235i			1.01773i	−0.860847	+	0.508865i	$0.830065\pi$
$98$	4.81589	−	2.78046i	0.486479	−	0.280869i
$99$		0			0
$100$	−3.46590	−	6.00312i	−0.346590	−	0.600312i
$101$	−8.60026	−	14.8961i	−0.855758	−	1.48222i	−0.875940	−	0.482420i	$-0.839758\pi$
$101$	−8.60026	−	14.8961i	−0.855758	−	1.48222i	0.0201819	−	0.999796i	$-0.493575\pi$
$102$		0			0
$103$	−8.82611	−	15.2873i	−0.869662	−	1.50630i	−0.862342	−	0.506326i	$-0.831003\pi$
$103$	−8.82611	−	15.2873i	−0.869662	−	1.50630i	−0.00732055	−	0.999973i	$-0.502330\pi$
$104$	−8.49704	−	4.37932i	−0.833203	−	0.429428i
$105$		0			0
$106$	−0.510369	+	0.294661i	−0.0495714	+	0.0286201i
$107$	−5.14019	+	8.90307i	−0.496921	+	0.860692i	−0.999994	−	0.00355197i	$-0.998869\pi$
$107$	−5.14019	+	8.90307i	−0.496921	+	0.860692i	0.503073	+	0.864244i	$0.332203\pi$
$108$		0			0
$109$		−	7.16152i		−	0.685949i	−0.939345	−	0.342975i	$-0.888566\pi$
$109$		−	7.16152i		−	0.685949i	0.939345	−	0.342975i	$-0.111434\pi$
$110$			0.0621435i			0.00592515i
$111$		0			0
$112$	−2.27609	+	1.31410i	−0.215070	+	0.124171i
$113$	1.65216	−	2.86162i	0.155422	−	0.269199i	−0.777791	−	0.628523i	$-0.783660\pi$
$113$	1.65216	−	2.86162i	0.155422	−	0.269199i	0.933213	+	0.359325i	$0.116993\pi$
$114$		0			0
$115$	0.303443	−	0.175193i	0.0282963	−	0.0163368i
$116$	9.89849			0.919052
$117$		0			0
$118$	−0.280983			−0.0258666
$119$	17.8486	−	10.3049i	1.63618	−	0.944649i
$120$		0			0
$121$	−4.67755	+	8.10176i	−0.425232	+	0.736524i
$122$	−1.11903	+	0.646075i	−0.101313	+	0.0584929i
$123$		0			0
$124$			5.80340i			0.521161i
$125$			0.618843i			0.0553510i
$126$		0			0
$127$	−3.56802	+	6.18000i	−0.316611	+	0.548386i	−0.979779	−	0.200085i	$-0.935878\pi$
$127$	−3.56802	+	6.18000i	−0.316611	+	0.548386i	0.663168	+	0.748471i	$0.269212\pi$
$128$	−7.97794	+	4.60606i	−0.705157	+	0.407122i
$129$		0			0
$130$	0.0944676	+	0.146958i	0.00828536	+	0.0128891i
$131$	9.76000	+	16.9048i	0.852735	+	1.47698i	0.878730	+	0.477319i	$0.158391\pi$
$131$	9.76000	+	16.9048i	0.852735	+	1.47698i	−0.0259946	+	0.999662i	$0.508275\pi$
$132$		0			0
$133$	−5.90288	−	10.2241i	−0.511844	−	0.886541i
$134$	−0.648777	−	1.12372i	−0.0560458	−	0.0970742i
$135$		0			0
$136$	12.5999	−	7.27455i	1.08043	−	0.623787i
$137$			8.32371i			0.711143i	0.934649	+	0.355571i	$0.115714\pi$
$137$			8.32371i			0.711143i	−0.934649	+	0.355571i	$0.884286\pi$
$138$		0			0
$139$	−1.91239	+	3.31236i	−0.162207	+	0.280951i	−0.935660	−	0.352903i	$-0.885195\pi$
$139$	−1.91239	+	3.31236i	−0.162207	+	0.280951i	0.773453	+	0.633854i	$0.218528\pi$
$140$	0.322584			0.0272634
$141$		0			0
$142$	5.14408	−	8.90981i	0.431682	−	0.747695i
$143$	−0.220548	−	4.61898i	−0.0184431	−	0.386258i
$144$		0			0
$145$	−0.382505	−	0.220839i	−0.0317653	−	0.0183397i
$146$	−2.38335	−	4.12809i	−0.197248	−	0.341643i
$147$		0			0
$148$	5.60412	−	3.23554i	0.460656	−	0.265960i
$149$	17.3709	+	10.0291i	1.42308	+	0.821614i	0.996561	−	0.0828653i	$-0.0264071\pi$
$149$	17.3709	+	10.0291i	1.42308	+	0.821614i	0.426517	+	0.904480i	$0.359740\pi$
$150$		0			0
$151$	12.0273	+	6.94396i	0.978767	+	0.565092i	0.901898	−	0.431950i	$-0.142174\pi$
$151$	12.0273	+	6.94396i	0.978767	+	0.565092i	0.0768696	+	0.997041i	$0.475507\pi$
$152$	−4.16702	−	7.21750i	−0.337990	−	0.585416i
$153$		0			0
$154$	3.26487	+	1.88498i	0.263091	+	0.151896i
$155$	0.129476	−	0.224259i	0.0103998	−	0.0180129i
$156$		0			0
$157$	7.95334	+	13.7756i	0.634746	+	1.09941i	0.986569	+	0.163346i	$0.0522286\pi$
$157$	7.95334	+	13.7756i	0.634746	+	1.09941i	−0.351823	+	0.936067i	$0.614438\pi$
$158$		−	0.964551i		−	0.0767355i
$159$		0			0
$160$	0.362174			0.0286324
$161$		−	21.2563i		−	1.67523i
$162$		0			0
$163$	11.4205	−	6.59365i	0.894525	−	0.516454i	0.0191051	−	0.999817i	$-0.493918\pi$
$163$	11.4205	−	6.59365i	0.894525	−	0.516454i	0.875420	+	0.483363i	$0.160585\pi$
$164$	11.8830	+	6.86068i	0.927910	+	0.535729i
$165$		0			0
$166$	−9.98991			−0.775368
$167$			1.34960i			0.104435i	0.998636	+	0.0522177i	$0.0166290\pi$
$167$			1.34960i			0.104435i	−0.998636	+	0.0522177i	$0.983371\pi$
$168$		0			0
$169$	−7.54311	−	10.5878i	−0.580239	−	0.814446i
$170$	−0.265897			−0.0203934
$171$		0			0
$172$	−2.93274	+	5.07966i	−0.223620	+	0.387321i
$173$	−14.7144			−1.11871			−0.559356	−	0.828927i	$-0.688952\pi$
$173$	−14.7144			−1.11871			−0.559356	+	0.828927i	$0.688952\pi$
$174$		0			0
$175$	16.2501	+	9.38197i	1.22839	+	0.709210i
$176$	−0.777269	−	0.448756i	−0.0585888	−	0.0338263i
$177$		0			0
$178$	1.17616			0.0881568
$179$	2.60130	−	4.50559i	0.194431	−	0.336764i	−0.752283	−	0.658840i	$-0.771047\pi$
$179$	2.60130	−	4.50559i	0.194431	−	0.336764i	0.946714	+	0.322076i	$0.104381\pi$
$180$		0			0
$181$	10.0948			0.750340			0.375170	−	0.926956i	$-0.377584\pi$
$181$	10.0948			0.750340			0.375170	+	0.926956i	$0.377584\pi$
$182$	10.5863	−	0.505476i	0.784709	−	0.0374684i
$183$		0			0
$184$		−	15.0055i		−	1.10622i
$185$	−0.288745			−0.0212289
$186$		0			0
$187$	6.09517	+	3.51905i	0.445723	+	0.257338i
$188$	3.79454	−	2.19078i	0.276745	−	0.159779i
$189$		0			0
$190$			0.152312i			0.0110499i
$191$	2.71789			0.196659			0.0983297	−	0.995154i	$-0.468650\pi$
$191$	2.71789			0.196659			0.0983297	+	0.995154i	$0.468650\pi$
$192$		0			0
$193$		−	19.0863i		−	1.37386i	−0.726723	−	0.686930i	$-0.758958\pi$
$193$		−	19.0863i		−	1.37386i	0.726723	−	0.686930i	$-0.241042\pi$
$194$	−3.92254	−	6.79405i	−0.281622	−	0.487784i
$195$		0			0
$196$	4.92885	−	8.53702i	0.352061	−	0.609787i
$197$	−1.87976	−	1.08528i	−0.133927	−	0.0773230i	0.431539	−	0.902094i	$-0.357971\pi$
$197$	−1.87976	−	1.08528i	−0.133927	−	0.0773230i	−0.565467	+	0.824771i	$0.691304\pi$
$198$		0			0
$199$	5.21774	+	9.03739i	0.369876	+	0.640644i	0.989546	−	0.144219i	$-0.0460669\pi$
$199$	5.21774	+	9.03739i	0.369876	+	0.640644i	−0.619670	+	0.784862i	$0.712734\pi$
$200$	11.4714	+	6.62302i	0.811152	+	0.468319i
$201$		0			0
$202$	11.6588	+	6.73118i	0.820307	+	0.473604i
$203$	−23.2048	+	13.3973i	−1.62866	+	0.940305i
$204$		0			0
$205$	−0.306129	−	0.530231i	−0.0213810	−	0.0370330i
$206$	11.9649	+	6.90795i	0.833635	+	0.481300i
$207$		0			0
$208$	−2.52028	+	0.120339i	−0.174750	+	0.00834399i
$209$	2.01579	−	3.49145i	0.139435	−	0.241509i
$210$		0			0
$211$	0.386502			0.0266079			0.0133039	−	0.999911i	$-0.495765\pi$
$211$	0.386502			0.0266079			0.0133039	+	0.999911i	$0.495765\pi$
$212$	−0.522340	+	0.904719i	−0.0358744	+	0.0621363i
$213$		0			0
$214$		−	8.04616i		−	0.550024i
$215$	0.226659	−	0.130861i	0.0154580	−	0.00892467i
$216$		0			0
$217$	−7.85471	−	13.6048i	−0.533213	−	0.923551i
$218$	2.80256	+	4.85418i	0.189813	+	0.328766i
$219$		0			0
$220$	0.0550801	+	0.0954016i	0.00371350	+	0.00643197i
$221$	19.7635	−	0.943671i	1.32944	−	0.0634782i
$222$		0			0
$223$	1.75987	−	1.01606i	0.117850	−	0.0680405i	−0.439916	−	0.898039i	$-0.644992\pi$
$223$	1.75987	−	1.01606i	0.117850	−	0.0680405i	0.557766	+	0.829998i	$0.311659\pi$
$224$	10.9857	−	19.0278i	0.734013	−	1.27135i
$225$		0			0
$226$			2.58620i			0.172031i
$227$			26.3044i			1.74588i	0.487826	+	0.872941i	$0.337790\pi$
$227$			26.3044i			1.74588i	−0.487826	+	0.872941i	$0.662210\pi$
$228$		0			0
$229$	−23.2482	+	13.4224i	−1.53629	+	0.886976i	−0.537236	+	0.843432i	$0.680531\pi$
$229$	−23.2482	+	13.4224i	−1.53629	+	0.886976i	−0.999052	+	0.0435436i	$0.986135\pi$
$230$	−0.137119	+	0.237497i	−0.00904134	+	0.0156601i
$231$		0			0
$232$	−16.3810	+	9.45756i	−1.07546	+	0.620919i
$233$	8.15619			0.534330			0.267165	−	0.963651i	$-0.413913\pi$
$233$	8.15619			0.534330			0.267165	+	0.963651i	$0.413913\pi$
$234$		0			0
$235$	−0.195508			−0.0127536
$236$	−0.431361	+	0.249046i	−0.0280792	+	0.0162115i
$237$		0			0
$238$	−8.06536	+	13.9696i	−0.522799	+	0.905515i
$239$	−11.8525	+	6.84307i	−0.766677	+	0.442641i	−0.831688	−	0.555243i	$-0.812625\pi$
$239$	−11.8525	+	6.84307i	−0.766677	+	0.442641i	0.0650107	+	0.997885i	$0.479292\pi$
$240$		0			0
$241$		−	13.2782i		−	0.855325i	−0.903938	−	0.427663i	$-0.859337\pi$
$241$		−	13.2782i		−	0.855325i	0.903938	−	0.427663i	$-0.140663\pi$
$242$		−	7.32198i		−	0.470675i
$243$		0			0
$244$	−1.14528	+	1.98369i	−0.0733192	+	0.126993i
$245$	−0.380929	+	0.219929i	−0.0243367	+	0.0140508i
$246$		0			0
$247$	−0.540556	−	11.3210i	−0.0343947	−	0.720336i
$248$	−5.54488	−	9.60402i	−0.352101	−	0.609856i
$249$		0			0
$250$	−0.242175	−	0.419460i	−0.0153165	−	0.0265290i
$251$	2.59137	+	4.48838i	0.163566	+	0.283304i	0.936145	−	0.351614i	$-0.114367\pi$
$251$	2.59137	+	4.48838i	0.163566	+	0.283304i	−0.772579	+	0.634918i	$0.781034\pi$
$252$		0			0
$253$	6.28637	−	3.62944i	0.395220	−	0.228181i
$254$		−	5.58518i		−	0.350446i
$255$		0			0
$256$	6.78423	−	11.7506i	0.424014	−	0.734414i
$257$	−29.2021			−1.82158			−0.910789	−	0.412873i	$-0.864525\pi$
$257$	−29.2021			−1.82158			−0.910789	+	0.412873i	$0.864525\pi$
$258$		0			0
$259$	−8.75840	+	15.1700i	−0.544220	+	0.942617i
$260$	0.275280	+	0.141878i	0.0170721	+	0.00879887i
$261$		0			0
$262$	−13.2309	−	7.63888i	−0.817410	−	0.471932i
$263$	2.71399	+	4.70077i	0.167352	+	0.289862i	0.937488	−	0.348018i	$-0.113145\pi$
$263$	2.71399	+	4.70077i	0.167352	+	0.289862i	−0.770136	+	0.637880i	$0.779812\pi$
$264$		0			0
$265$	0.0403693	−	0.0233072i	0.00247987	−	0.00143175i
$266$	8.00210	+	4.62002i	0.490640	+	0.283271i
$267$		0			0
$268$	−1.99198	−	1.15007i	−0.121680	−	0.0702519i
$269$	6.85146	+	11.8671i	0.417741	+	0.723549i	0.995712	−	0.0925087i	$-0.0294886\pi$
$269$	6.85146	+	11.8671i	0.417741	+	0.723549i	−0.577971	+	0.816057i	$0.696155\pi$
$270$		0			0
$271$	10.5946	+	6.11677i	0.643573	+	0.371567i	0.785990	−	0.618240i	$-0.212154\pi$
$271$	10.5946	+	6.11677i	0.643573	+	0.371567i	−0.142416	+	0.989807i	$0.545487\pi$
$272$	1.92012	−	3.32575i	0.116424	−	0.201653i
$273$		0			0
$274$	−3.25737	−	5.64193i	−0.196785	−	0.340841i
$275$			6.40775i			0.386402i
$276$		0			0
$277$	−14.0400			−0.843582			−0.421791	−	0.906693i	$-0.638598\pi$
$277$	−14.0400			−0.843582			−0.421791	+	0.906693i	$0.638598\pi$
$278$		−	2.99355i		−	0.179541i
$279$		0			0
$280$	−0.533844	+	0.308215i	−0.0319033	+	0.0184194i
$281$	−18.6400	−	10.7618i	−1.11197	−	0.641997i	−0.172632	−	0.984986i	$-0.555227\pi$
$281$	−18.6400	−	10.7618i	−1.11197	−	0.641997i	−0.939339	+	0.342990i	$0.888560\pi$
$282$		0			0
$283$	23.1108			1.37379			0.686897	−	0.726755i	$-0.258972\pi$
$283$	23.1108			1.37379			0.686897	+	0.726755i	$0.258972\pi$
$284$		−	18.2376i		−	1.08220i
$285$		0			0
$286$	1.95706	+	3.04450i	0.115724	+	0.180025i
$287$	−37.1428			−2.19247
$288$		0			0
$289$	−6.55717	+	11.3573i	−0.385716	+	0.668079i
$290$	0.345690			0.0202996
$291$		0			0
$292$	−7.31777	−	4.22492i	−0.428240	−	0.247245i
$293$	−0.259773	−	0.149980i	−0.0151761	−	0.00876193i	0.492393	−	0.870373i	$-0.336122\pi$
$293$	−0.259773	−	0.149980i	−0.0151761	−	0.00876193i	−0.507569	+	0.861611i	$0.669456\pi$
$294$		0			0
$295$	0.0222253			0.00129401
$296$	−6.18282	+	10.7090i	−0.359369	+	0.622446i
$297$		0			0
$298$	−15.6990			−0.909416
$299$	9.34884	−	18.1392i	0.540658	−	1.04902i
$300$		0			0
$301$		−	15.8775i		−	0.915163i
$302$	−10.8697			−0.625480
$303$		0			0
$304$	−1.90506	−	1.09989i	−0.109263	−	0.0630829i
$305$	0.0885137	−	0.0511034i	0.00506828	−	0.00292617i
$306$		0			0
$307$			13.4090i			0.765291i	0.923895	+	0.382646i	$0.124987\pi$
$307$			13.4090i			0.765291i	−0.923895	+	0.382646i	$0.875013\pi$
$308$	6.68291			0.380794
$309$		0			0
$310$			0.202675i			0.0115112i
$311$	−6.66305	−	11.5407i	−0.377827	−	0.654415i	0.612919	−	0.790146i	$-0.289995\pi$
$311$	−6.66305	−	11.5407i	−0.377827	−	0.654415i	−0.990746	+	0.135731i	$0.956662\pi$
$312$		0			0
$313$	−7.54812	+	13.0737i	−0.426645	+	0.738971i	−0.996572	−	0.0827243i	$-0.973638\pi$
$313$	−7.54812	+	13.0737i	−0.426645	+	0.738971i	0.569928	+	0.821695i	$0.306971\pi$
$314$	−10.7818	−	6.22486i	−0.608451	−	0.351289i
$315$		0			0
$316$	−0.854918	−	1.48076i	−0.0480929	−	0.0832994i
$317$	16.1108	+	9.30158i	0.904873	+	0.522429i	0.878778	−	0.477231i	$-0.158359\pi$
$317$	16.1108	+	9.30158i	0.904873	+	0.522429i	0.0260952	+	0.999659i	$0.491693\pi$
$318$		0			0
$319$	−7.92427	−	4.57508i	−0.443674	−	0.256155i
$320$	−0.170449	+	0.0984087i	−0.00952838	+	0.00550121i
$321$		0			0
$322$	8.31835	+	14.4078i	0.463564	+	0.802916i
$323$	14.9391	+	8.62508i	0.831233	+	0.479912i
$324$		0			0
$325$	9.74077	+	15.1532i	0.540321	+	0.840548i
$326$	−5.16066	+	8.93853i	−0.285823	+	0.495059i
$327$		0			0
$328$	−26.2203			−1.44777
$329$	−5.93029	+	10.2716i	−0.326947	+	0.566290i
$330$		0			0
$331$			5.69806i			0.313194i	0.987663	+	0.156597i	$0.0500524\pi$
$331$			5.69806i			0.313194i	−0.987663	+	0.156597i	$0.949948\pi$
$332$	−15.3364	+	8.85445i	−0.841692	+	0.485951i
$333$		0			0
$334$	−0.528149	−	0.914780i	−0.0288990	−	0.0500545i
$335$	0.0513172	+	0.0888840i	0.00280376	+	0.00485625i
$336$		0			0
$337$	16.0839	+	27.8581i	0.876146	+	1.51753i	0.855537	+	0.517741i	$0.173227\pi$
$337$	16.0839	+	27.8581i	0.876146	+	1.51753i	0.0206081	+	0.999788i	$0.493440\pi$
$338$	9.25621	+	4.22466i	0.503472	+	0.229791i
$339$		0			0
$340$	−0.408200	+	0.235675i	−0.0221378	+	0.0127813i
$341$	2.68233	−	4.64593i	0.145256	−	0.251591i
$342$		0			0
$343$			0.394490i			0.0213005i
$344$		−	11.2084i		−	0.604317i
$345$		0			0
$346$	9.97360	−	5.75826i	0.536184	−	0.309566i
$347$	8.02447	−	13.8988i	0.430776	−	0.746127i	−0.566164	−	0.824293i	$-0.691573\pi$
$347$	8.02447	−	13.8988i	0.430776	−	0.746127i	0.996940	+	0.0781661i	$0.0249065\pi$
$348$		0			0
$349$	23.5647	−	13.6051i	1.26139	−	0.728262i	0.288045	−	0.957617i	$-0.406995\pi$
$349$	23.5647	−	13.6051i	1.26139	−	0.728262i	0.973343	+	0.229355i	$0.0736615\pi$
$350$	−14.6860			−0.785000
$351$		0			0
$352$	7.50307			0.399915
$353$	−4.01185	+	2.31624i	−0.213529	+	0.123281i	−0.602951	−	0.797779i	$-0.706008\pi$
$353$	−4.01185	+	2.31624i	−0.213529	+	0.123281i	0.389421	+	0.921060i	$0.372675\pi$
$354$		0			0
$355$	−0.406888	+	0.704751i	−0.0215954	+	0.0374043i
$356$	1.80562	−	1.04248i	0.0956977	−	0.0552511i
$357$		0			0
$358$			4.07194i			0.215208i
$359$		−	16.1406i		−	0.851870i	−0.904754	−	0.425935i	$-0.859945\pi$
$359$		−	16.1406i		−	0.851870i	0.904754	−	0.425935i	$-0.140055\pi$
$360$		0			0
$361$	−4.55936	+	7.89704i	−0.239966	+	0.415634i
$362$	−6.84239	+	3.95046i	−0.359628	+	0.207631i
$363$		0			0
$364$	15.8039	−	10.1590i	0.828349	−	0.532478i
$365$	0.188519	+	0.326525i	0.00986754	+	0.0170911i
$366$		0			0
$367$	10.3833	+	17.9845i	0.542005	+	0.938781i	0.998789	+	0.0492028i	$0.0156681\pi$
$367$	10.3833	+	17.9845i	0.542005	+	0.938781i	−0.456783	+	0.889578i	$0.650999\pi$
$368$	−1.98035	−	3.43007i	−0.103233	−	0.178805i
$369$		0			0
$370$	0.195715	−	0.112996i	0.0101748	−	0.00587440i
$371$		−	2.82788i		−	0.146816i
$372$		0			0
$373$	−3.03953	+	5.26462i	−0.157381	+	0.272592i	−0.933923	−	0.357473i	$-0.883638\pi$
$373$	−3.03953	+	5.26462i	−0.157381	+	0.272592i	0.776543	+	0.630065i	$0.216972\pi$
$374$	−5.50852			−0.284839
$375$		0			0
$376$	−4.18638	+	7.25101i	−0.215896	+	0.373943i
$377$	−25.6943	+	1.22686i	−1.32332	+	0.0631863i
$378$		0			0
$379$	−13.7130	−	7.91718i	−0.704388	−	0.406678i	0.104592	−	0.994515i	$-0.466646\pi$
$379$	−13.7130	−	7.91718i	−0.704388	−	0.406678i	−0.808979	+	0.587837i	$0.799980\pi$
$380$	0.135000	+	0.233826i	0.00692534	+	0.0119950i
$381$		0			0
$382$	−1.84222	+	1.06361i	−0.0942563	+	0.0544189i
$383$	12.9901	+	7.49986i	0.663765	+	0.383225i	0.793710	−	0.608296i	$-0.208147\pi$
$383$	12.9901	+	7.49986i	0.663765	+	0.383225i	−0.129945	+	0.991521i	$0.541480\pi$
$384$		0			0
$385$	−0.258246	−	0.149098i	−0.0131614	−	0.00759875i
$386$	7.46915	+	12.9369i	0.380170	+	0.658473i
$387$		0			0
$388$	−12.0436	−	6.95340i	−0.611424	−	0.353006i
$389$	−8.69825	+	15.0658i	−0.441019	+	0.763867i	−0.997765	−	0.0668155i	$-0.978716\pi$
$389$	−8.69825	+	15.0658i	−0.441019	+	0.763867i	0.556747	+	0.830682i	$0.312049\pi$
$390$		0			0
$391$	15.5295	+	26.8979i	0.785360	+	1.36028i
$392$			18.8372i			0.951421i
$393$		0			0
$394$	1.69884			0.0855861
$395$			0.0762943i			0.00383878i
$396$		0			0
$397$	−9.89799	+	5.71461i	−0.496766	+	0.286808i	−0.727377	−	0.686238i	$-0.759261\pi$
$397$	−9.89799	+	5.71461i	−0.496766	+	0.286808i	0.230611	+	0.973046i	$0.425928\pi$
$398$	−7.07331	−	4.08378i	−0.354553	−	0.204701i
$399$		0			0
$400$	3.49630			0.174815
$401$		−	12.7790i		−	0.638151i	−0.947729	−	0.319075i	$-0.896628\pi$
$401$		−	12.7790i		−	0.638151i	0.947729	−	0.319075i	$-0.103372\pi$
$402$		0			0
$403$	−0.719295	−	15.0643i	−0.0358306	−	0.750409i
$404$	23.8644			1.18730
$405$		0			0
$406$	10.4857	−	18.1617i	0.520395	−	0.901351i
$407$	−5.98186			−0.296510
$408$		0			0
$409$	−17.1272	−	9.88837i	−0.846884	−	0.488949i	0.0127143	−	0.999919i	$-0.495953\pi$
$409$	−17.1272	−	9.88837i	−0.846884	−	0.488949i	−0.859598	+	0.510971i	$0.829286\pi$
$410$	0.414997	+	0.239599i	0.0204952	+	0.0118329i
$411$		0			0
$412$	24.4911			1.20659
$413$	0.674152	−	1.16767i	0.0331728	−	0.0574571i
$414$		0			0
$415$	0.790185			0.0387887
$416$	17.7434	−	11.4058i	0.869943	−	0.559216i
$417$		0			0
$418$			3.15541i			0.154336i
$419$	−1.02767			−0.0502051			−0.0251025	−	0.999685i	$-0.507991\pi$
$419$	−1.02767			−0.0502051			−0.0251025	+	0.999685i	$0.507991\pi$
$420$		0			0
$421$	−19.3455	−	11.1691i	−0.942843	−	0.544351i	−0.0519927	−	0.998647i	$-0.516557\pi$
$421$	−19.3455	−	11.1691i	−0.942843	−	0.544351i	−0.890850	+	0.454297i	$0.849891\pi$
$422$	−0.261976	+	0.151252i	−0.0127528	+	0.00736283i
$423$		0			0
$424$		−	1.99629i		−	0.0969483i
$425$	−27.4172			−1.32993
$426$		0			0
$427$		−	6.20041i		−	0.300059i
$428$	−7.13162	−	12.3523i	−0.344720	−	0.597073i
$429$		0			0
$430$	−0.102422	+	0.177399i	−0.00493921	+	0.00855496i
$431$	6.38655	+	3.68727i	0.307629	+	0.177610i	0.645865	−	0.763452i	$-0.276497\pi$
$431$	6.38655	+	3.68727i	0.307629	+	0.177610i	−0.338236	+	0.941061i	$0.609830\pi$
$432$		0			0
$433$	2.96921	+	5.14283i	0.142691	+	0.247148i	0.928509	−	0.371309i	$-0.121091\pi$
$433$	2.96921	+	5.14283i	0.142691	+	0.247148i	−0.785818	+	0.618458i	$0.787758\pi$
$434$	10.6481	+	6.14766i	0.511123	+	0.295097i
$435$		0			0
$436$	8.60489	+	4.96804i	0.412099	+	0.237926i
$437$	15.4077	−	8.89564i	0.737050	−	0.425536i
$438$		0			0
$439$	−11.8461	−	20.5180i	−0.565382	−	0.979270i	−0.997014	−	0.0772203i	$-0.975396\pi$
$439$	−11.8461	−	20.5180i	−0.565382	−	0.979270i	0.431632	−	0.902050i	$-0.357938\pi$
$440$	−0.182304	−	0.105253i	−0.00869099	−	0.00501775i
$441$		0			0
$442$	−13.0267	+	8.37380i	−0.619616	+	0.398301i
$443$	19.8468	−	34.3756i	0.942948	−	1.63323i	0.183138	−	0.983087i	$-0.441374\pi$
$443$	19.8468	−	34.3756i	0.942948	−	1.63323i	0.759809	−	0.650146i	$-0.225292\pi$
$444$		0			0
$445$	−0.0930322			−0.00441015
$446$	−0.795243	+	1.37740i	−0.0376558	+	0.0652218i
$447$		0			0
$448$			11.9400i			0.564111i
$449$	7.64958	−	4.41649i	0.361006	−	0.208427i	−0.308516	−	0.951219i	$-0.599832\pi$
$449$	7.64958	−	4.41649i	0.361006	−	0.208427i	0.669522	+	0.742792i	$0.266499\pi$
$450$		0			0
$451$	−6.34200	−	10.9847i	−0.298633	−	0.517248i
$452$	2.29225	+	3.97028i	0.107818	+	0.186746i
$453$		0			0
$454$	−10.2938	−	17.8295i	−0.483114	−	0.836778i
$455$	−0.837358	+	0.0399823i	−0.0392559	+	0.00187440i
$456$		0			0
$457$	−17.9905	+	10.3868i	−0.841559	+	0.485874i	−0.857794	−	0.513994i	$-0.828165\pi$
$457$	−17.9905	+	10.3868i	−0.841559	+	0.485874i	0.0162349	+	0.999868i	$0.494832\pi$
$458$	10.5053	−	18.1957i	0.490881	−	0.850231i
$459$		0			0
$460$			0.486135i			0.0226661i
$461$		−	10.4811i		−	0.488152i	−0.969756	−	0.244076i	$-0.921515\pi$
$461$		−	10.4811i		−	0.488152i	0.969756	−	0.244076i	$-0.0784847\pi$
$462$		0			0
$463$	−17.5850	+	10.1527i	−0.817243	+	0.471835i	−0.849465	−	0.527645i	$-0.823075\pi$
$463$	−17.5850	+	10.1527i	−0.817243	+	0.471835i	0.0322220	+	0.999481i	$0.489742\pi$
$464$	−2.49633	+	4.32376i	−0.115889	+	0.200726i
$465$		0			0
$466$	−5.52838	+	3.19181i	−0.256097	+	0.147858i
$467$	14.0228			0.648897			0.324448	−	0.945903i	$-0.394821\pi$
$467$	14.0228			0.648897			0.324448	+	0.945903i	$0.394821\pi$
$468$		0			0
$469$	6.22634			0.287506
$470$	0.132518	−	0.0765095i	0.00611261	−	0.00352912i
$471$		0			0
$472$	0.475905	−	0.824291i	0.0219053	−	0.0379411i
$473$	4.69563	−	2.71103i	0.215905	−	0.124653i
$474$		0			0
$475$			15.7052i			0.720604i
$476$			28.5945i			1.31063i
$477$		0			0
$478$	5.35588	−	9.27665i	0.244972	−	0.424304i
$479$	−8.56760	+	4.94650i	−0.391464	+	0.226012i	−0.682794	−	0.730611i	$-0.739235\pi$
$479$	−8.56760	+	4.94650i	−0.391464	+	0.226012i	0.291331	+	0.956622i	$0.405902\pi$
$480$		0			0
$481$	−14.1460	+	9.09335i	−0.645004	+	0.414621i
$482$	5.19624	+	9.00016i	0.236682	+	0.409946i
$483$		0			0
$484$	−6.48975	−	11.2406i	−0.294989	−	0.510936i
$485$	0.310267	+	0.537397i	0.0140885	+	0.0244020i
$486$		0			0
$487$	35.6312	−	20.5717i	1.61460	−	0.932192i	0.626320	−	0.779566i	$-0.284560\pi$
$487$	35.6312	−	20.5717i	1.61460	−	0.932192i	0.988284	−	0.152626i	$-0.0487731\pi$
$488$		−	4.37706i		−	0.198140i
$489$		0			0
$490$	0.172133	−	0.298142i	0.00777616	−	0.0134687i
$491$	17.7119			0.799326			0.399663	−	0.916662i	$-0.369127\pi$
$491$	17.7119			0.799326			0.399663	+	0.916662i	$0.369127\pi$
$492$		0			0
$493$	19.5757	−	33.9060i	0.881643	−	1.52705i
$494$	4.79670	+	7.46197i	0.215814	+	0.335730i
$495$		0			0
$496$	−2.53499	−	1.46357i	−0.113824	−	0.0657164i
$497$	24.6840	+	42.7539i	1.10723	+	1.91778i
$498$		0			0
$499$	16.2710	−	9.39408i	0.728391	−	0.420537i	−0.0894423	−	0.995992i	$-0.528508\pi$
$499$	16.2710	−	9.39408i	0.728391	−	0.420537i	0.817833	+	0.575455i	$0.195175\pi$
$500$	−0.743568	−	0.429299i	−0.0332534	−	0.0191988i
$501$		0			0
$502$	−3.51293	−	2.02819i	−0.156790	−	0.0905226i
$503$	7.83131	+	13.5642i	0.349181	+	0.604799i	0.986104	−	0.166128i	$-0.0531266\pi$
$503$	7.83131	+	13.5642i	0.349181	+	0.604799i	−0.636923	+	0.770927i	$0.719793\pi$
$504$		0			0
$505$	−0.922187	−	0.532425i	−0.0410368	−	0.0236926i
$506$	−2.84066	+	4.92016i	−0.126283	+	0.218728i
$507$		0			0
$508$	−4.95036	−	8.57428i	−0.219637	−	0.380422i
$509$			37.6313i			1.66798i	0.551781	+	0.833989i	$0.313948\pi$
$509$			37.6313i			1.66798i	−0.551781	+	0.833989i	$0.686052\pi$
$510$		0			0
$511$	22.8731			1.01185
$512$		−	7.80461i		−	0.344918i
$513$		0			0
$514$	19.7936	−	11.4278i	0.873058	−	0.504060i
$515$	−0.946405	−	0.546407i	−0.0417036	−	0.0240776i
$516$		0			0
$517$	−4.05030			−0.178132
$518$		−	13.7099i		−	0.602379i
$519$		0			0
$520$	−0.591117	+	0.0282247i	−0.0259222	+	0.00123774i
$521$	−3.84164			−0.168305			−0.0841526	−	0.996453i	$-0.526818\pi$
$521$	−3.84164			−0.168305			−0.0841526	+	0.996453i	$0.526818\pi$
$522$		0			0
$523$	−19.6605	+	34.0529i	−0.859692	+	1.48903i	0.0125300	+	0.999921i	$0.496011\pi$
$523$	−19.6605	+	34.0529i	−0.859692	+	1.48903i	−0.872222	+	0.489109i	$0.837322\pi$
$524$	−27.0825			−1.18311
$525$		0			0
$526$	−3.67916	−	2.12417i	−0.160419	−	0.0926181i
$527$	19.8788	+	11.4770i	0.865935	+	0.499948i
$528$		0			0
$529$	9.03323			0.392749
$530$	−0.0182419	+	0.0315959i	−0.000792378	+	0.00137244i
$531$		0			0
$532$	16.3796			0.710146
$533$	−31.6961	−	16.3360i	−1.37291	−	0.707590i
$534$		0			0
$535$			0.636438i			0.0275156i
$536$	4.39537			0.189851
$537$		0			0
$538$	−9.28803	−	5.36245i	−0.400436	−	0.231192i
$539$	−7.89161	+	4.55623i	−0.339916	+	0.196251i
$540$		0			0
$541$		−	45.4115i		−	1.95239i	−0.216885	−	0.976197i	$-0.569590\pi$
$541$		−	45.4115i		−	1.95239i	0.216885	−	0.976197i	$-0.430410\pi$
$542$	−9.57485			−0.411275
$543$		0			0
$544$			32.1038i			1.37644i
$545$	−0.221678	−	0.383957i	−0.00949563	−	0.0164469i
$546$		0			0
$547$	7.70865	−	13.3518i	0.329598	−	0.570881i	−0.652834	−	0.757501i	$-0.726420\pi$
$547$	7.70865	−	13.3518i	0.329598	−	0.570881i	0.982432	+	0.186620i	$0.0597534\pi$
$548$	−10.0013	−	5.77426i	−0.427235	−	0.246664i
$549$		0			0
$550$	−2.50758	−	4.34326i	−0.106924	−	0.185197i
$551$	−19.4221	−	11.2134i	−0.827411	−	0.477706i
$552$		0			0
$553$	4.00833	+	2.31421i	0.170451	+	0.0984101i
$554$	9.51650	−	5.49436i	0.404317	−	0.233433i
$555$		0			0
$556$	−2.65330	−	4.59565i	−0.112525	−	0.194899i
$557$	24.1319	+	13.9325i	1.02250	+	0.590341i	0.914827	−	0.403846i	$-0.132327\pi$
$557$	24.1319	+	13.9325i	1.02250	+	0.590341i	0.107673	+	0.994186i	$0.465660\pi$
$558$		0			0
$559$	6.98316	−	13.5492i	0.295356	−	0.573069i
$560$	−0.0813534	+	0.140908i	−0.00343781	+	0.00595446i
$561$		0			0
$562$	16.8460			0.710604
$563$	13.3491	−	23.1214i	0.562599	−	0.974450i	−0.434669	−	0.900590i	$-0.643135\pi$
$563$	13.3491	−	23.1214i	0.562599	−	0.974450i	0.997269	−	0.0738603i	$-0.0235319\pi$
$564$		0			0
$565$		−	0.204564i		−	0.00860606i
$566$	−15.6648	+	9.04408i	−0.658441	+	0.380151i
$567$		0			0
$568$	17.4252	+	30.1813i	0.731145	+	1.26638i
$569$	−7.92670	−	13.7294i	−0.332305	−	0.575568i	0.650659	−	0.759370i	$-0.274493\pi$
$569$	−7.92670	−	13.7294i	−0.332305	−	0.575568i	−0.982963	+	0.183802i	$0.941160\pi$
$570$		0			0
$571$	−5.89230	−	10.2058i	−0.246585	−	0.427098i	0.715991	−	0.698109i	$-0.245975\pi$
$571$	−5.89230	−	10.2058i	−0.246585	−	0.427098i	−0.962576	+	0.271012i	$0.912642\pi$
$572$	5.70291	+	2.93924i	0.238451	+	0.122896i
$573$		0			0
$574$	25.1759	−	14.5353i	1.05082	−	0.606693i
$575$	−14.1386	+	24.4888i	−0.589622	+	1.02125i
$576$		0			0
$577$		−	3.85716i		−	0.160576i	−0.996772	−	0.0802879i	$-0.974416\pi$
$577$		−	3.85716i		−	0.160576i	0.996772	−	0.0802879i	$-0.0255840\pi$
$578$		−	10.2642i		−	0.426935i
$579$		0			0
$580$	0.530697	−	0.306398i	0.0220360	−	0.0127225i
$581$	23.9684	−	41.5145i	0.994377	−	1.72231i
$582$		0			0
$583$	0.836321	−	0.482850i	0.0346369	−	0.0199976i
$584$	16.1469			0.668162
$585$		0			0
$586$	0.234771			0.00969828
$587$	22.1887	−	12.8107i	0.915827	−	0.528753i	0.0335257	−	0.999438i	$-0.489326\pi$
$587$	22.1887	−	12.8107i	0.915827	−	0.528753i	0.882301	+	0.470685i	$0.155993\pi$
$588$		0			0
$589$	6.57430	−	11.3870i	0.270889	−	0.469194i
$590$	−0.0150646	+	0.00869756i	−0.000620200	+	0.000358073i
$591$		0			0
$592$			3.26392i			0.134146i
$593$			10.1922i			0.418543i	0.977858	+	0.209272i	$0.0671093\pi$
$593$			10.1922i			0.418543i	−0.977858	+	0.209272i	$0.932891\pi$
$594$		0			0
$595$	0.637956	−	1.10497i	0.0261536	−	0.0452994i
$596$	−24.1008	+	13.9146i	−0.987206	+	0.569964i
$597$		0			0
$598$	0.761752	+	15.9535i	0.0311504	+	0.652389i
$599$	6.90176	+	11.9542i	0.281998	+	0.488435i	0.971877	−	0.235490i	$-0.0756694\pi$
$599$	6.90176	+	11.9542i	0.281998	+	0.488435i	−0.689878	+	0.723925i	$0.742336\pi$
$600$		0			0
$601$	5.66423	+	9.81073i	0.231049	+	0.400188i	0.958117	−	0.286377i	$-0.0924510\pi$
$601$	5.66423	+	9.81073i	0.231049	+	0.400188i	−0.727068	+	0.686565i	$0.759118\pi$
$602$	6.21343	+	10.7620i	0.253241	+	0.438626i
$603$		0			0
$604$	−16.6870	+	9.63422i	−0.678983	+	0.392011i
$605$			0.579156i			0.0235460i
$606$		0			0
$607$	−5.44652	+	9.43365i	−0.221067	+	0.382900i	−0.955132	−	0.296179i	$-0.904287\pi$
$607$	−5.44652	+	9.43365i	−0.221067	+	0.382900i	0.734065	+	0.679079i	$0.237621\pi$
$608$	18.3898			0.745805
$609$		0			0
$610$	−0.0399972	+	0.0692772i	−0.00161944	+	0.00280495i
$611$	−9.57825	+	6.15708i	−0.387494	+	0.249089i
$612$		0			0
$613$	27.0132	+	15.5961i	1.09105	+	0.629920i	0.933857	−	0.357647i	$-0.116421\pi$
$613$	27.0132	+	15.5961i	1.09105	+	0.629920i	0.157197	+	0.987567i	$0.449754\pi$
$614$	−5.24742	−	9.08880i	−0.211769	−	0.366794i
$615$		0			0
$616$	−11.0595	+	6.38521i	−0.445600	+	0.257268i
$617$	−29.4907	−	17.0265i	−1.18725	−	0.685460i	−0.229571	−	0.973292i	$-0.573732\pi$
$617$	−29.4907	−	17.0265i	−1.18725	−	0.685460i	−0.957681	+	0.287831i	$0.907066\pi$
$618$		0			0
$619$	−7.48048	−	4.31886i	−0.300666	−	0.173589i	0.342076	−	0.939672i	$-0.388870\pi$
$619$	−7.48048	−	4.31886i	−0.300666	−	0.173589i	−0.642742	+	0.766083i	$0.722203\pi$
$620$	0.179638	+	0.311143i	0.00721446	+	0.0124958i
$621$		0			0
$622$	9.03261	+	5.21498i	0.362175	+	0.209102i
$623$	−2.82191	+	4.88769i	−0.113057	+	0.195821i
$624$		0			0
$625$	−12.4713	−	21.6009i	−0.498851	−	0.864034i
$626$		−	11.8154i		−	0.472238i
$627$		0			0
$628$	−22.0693			−0.880662
$629$		−	25.5949i		−	1.02054i
$630$		0			0
$631$	−34.8576	+	20.1250i	−1.38766	+	0.801165i	−0.993051	−	0.117684i	$-0.962453\pi$
$631$	−34.8576	+	20.1250i	−1.38766	+	0.801165i	−0.394608	+	0.918850i	$0.629120\pi$
$632$	2.82960	+	1.63367i	0.112555	+	0.0649839i
$633$		0			0
$634$	−14.5602			−0.578258
$635$			0.441779i			0.0175314i
$636$		0			0
$637$	−11.7361	+	22.7711i	−0.465001	+	0.902225i
$638$	7.16157			0.283529
$639$		0			0
$640$	−0.285152	+	0.493898i	−0.0112716	+	0.0195230i
$641$	25.7663			1.01771			0.508855	−	0.860852i	$-0.330069\pi$
$641$	25.7663			1.01771			0.508855	+	0.860852i	$0.330069\pi$
$642$		0			0
$643$	3.85976	+	2.22843i	0.152214	+	0.0878809i	0.574173	−	0.818734i	$-0.305324\pi$
$643$	3.85976	+	2.22843i	0.152214	+	0.0878809i	−0.421958	+	0.906615i	$0.638657\pi$
$644$	25.5404	+	14.7458i	1.00643	+	0.581064i
$645$		0			0
$646$	−13.5012			−0.531198
$647$	4.35879	−	7.54964i	0.171362	−	0.296807i	−0.767535	−	0.641008i	$-0.778517\pi$
$647$	4.35879	−	7.54964i	0.171362	−	0.296807i	0.938896	+	0.344201i	$0.111850\pi$
$648$		0			0
$649$	0.460436			0.0180737
$650$	−12.5324	−	6.45913i	−0.491562	−	0.253348i
$651$		0			0
$652$			18.2964i			0.716541i
$653$	−10.9850			−0.429875			−0.214938	−	0.976628i	$-0.568955\pi$
$653$	−10.9850			−0.429875			−0.214938	+	0.976628i	$0.568955\pi$
$654$		0			0
$655$	1.04654	+	0.604222i	0.0408919	+	0.0236089i
$656$	−5.99363	+	3.46043i	−0.234012	+	0.135107i
$657$		0			0
$658$		−	9.28294i		−	0.361887i
$659$	−18.2023			−0.709062			−0.354531	−	0.935044i	$-0.615359\pi$
$659$	−18.2023			−0.709062			−0.354531	+	0.935044i	$0.615359\pi$
$660$		0			0
$661$		−	10.4612i		−	0.406894i	−0.979086	−	0.203447i	$-0.934786\pi$
$661$		−	10.4612i		−	0.406894i	0.979086	−	0.203447i	$-0.0652145\pi$
$662$	−2.22986	−	3.86223i	−0.0866659	−	0.150110i
$663$		0			0
$664$	16.9200	−	29.3064i	0.656625	−	1.13731i
$665$	−0.632953	−	0.365435i	−0.0245449	−	0.0141710i
$666$		0			0
$667$	−20.1897	−	34.9696i	−0.781749	−	1.35403i
$668$	−1.62161	−	0.936237i	−0.0627420	−	0.0362241i
$669$		0			0
$670$	−0.0695670	−	0.0401645i	−0.00268761	−	0.00155169i
$671$	1.83372	−	1.05870i	0.0707899	−	0.0408706i
$672$		0			0
$673$	7.31408	+	12.6684i	0.281937	+	0.488329i	0.971862	−	0.235552i	$-0.0756898\pi$
$673$	7.31408	+	12.6684i	0.281937	+	0.488329i	−0.689925	+	0.723881i	$0.742356\pi$
$674$	−21.8038	−	12.5884i	−0.839850	−	0.484888i
$675$		0			0
$676$	17.9545	−	1.71850i	0.690556	−	0.0660963i
$677$	−5.21183	+	9.02716i	−0.200307	+	0.346942i	−0.948627	−	0.316396i	$-0.897527\pi$
$677$	−5.21183	+	9.02716i	−0.200307	+	0.346942i	0.748320	+	0.663338i	$0.230861\pi$
$678$		0			0
$679$	37.6448			1.44468
$680$	0.450353	−	0.780034i	0.0172702	−	0.0299129i
$681$		0			0
$682$			4.19877i			0.160779i
$683$	−5.83030	+	3.36612i	−0.223090	+	0.128801i	−0.607380	−	0.794411i	$-0.707780\pi$
$683$	−5.83030	+	3.36612i	−0.223090	+	0.128801i	0.384290	+	0.923212i	$0.374446\pi$
$684$		0			0
$685$	0.257652	+	0.446267i	0.00984439	+	0.0170510i
$686$	−0.154378	−	0.267391i	−0.00589419	−	0.0102090i
$687$		0			0
$688$	−1.47923	−	2.56211i	−0.0563952	−	0.0976794i
$689$	1.24374	−	2.41319i	0.0473829	−	0.0919353i
$690$		0			0
$691$	−6.40388	+	3.69728i	−0.243615	+	0.140651i	−0.616837	−	0.787091i	$-0.711586\pi$
$691$	−6.40388	+	3.69728i	−0.243615	+	0.140651i	0.373222	+	0.927742i	$0.378253\pi$
$692$	10.2075	−	17.6800i	0.388032	−	0.672092i
$693$		0			0
$694$			12.5611i			0.476811i
$695$			0.236785i			0.00898176i
$696$		0			0
$697$	47.0008	−	27.1359i	1.78028	−	1.02785i
$698$	−10.6483	+	18.4434i	−0.403044	+	0.698093i
$699$		0			0
$700$	−22.5457	+	13.0168i	−0.852148	+	0.491988i
$701$	30.2665			1.14315			0.571576	−	0.820549i	$-0.306332\pi$
$701$	30.2665			1.14315			0.571576	+	0.820549i	$0.306332\pi$
$702$		0			0
$703$	−14.6614			−0.552963
$704$	−3.53115	+	2.03871i	−0.133085	+	0.0768368i
$705$		0			0
$706$	1.81286	−	3.13996i	0.0682278	−	0.118174i
$707$	−55.9448	+	32.2997i	−2.10402	+	1.21476i
$708$		0			0
$709$		−	0.0660461i		−	0.00248041i	−0.999999	−	0.00124021i	$-0.999605\pi$
$709$		−	0.0660461i		−	0.00248041i	0.999999	−	0.00124021i	$-0.000394770\pi$
$710$		−	0.636920i		−	0.0239032i
$711$		0			0
$712$	−1.99207	+	3.45037i	−0.0746562	+	0.129308i
$713$	20.5024	−	11.8370i	0.767820	−	0.443301i
$714$		0			0
$715$	−0.154800	−	0.240815i	−0.00578920	−	0.00900596i
$716$	3.60911	+	6.25117i	0.134879	+	0.233617i
$717$		0			0
$718$	6.31641	+	10.9403i	0.235726	+	0.408290i
$719$	−1.90007	−	3.29102i	−0.0708607	−	0.122734i	0.828418	−	0.560110i	$-0.189241\pi$
$719$	−1.90007	−	3.29102i	−0.0708607	−	0.122734i	−0.899279	+	0.437376i	$0.855908\pi$
$720$		0			0
$721$	−57.4139	+	33.1479i	−2.13821	+	1.23449i
$722$		−	7.13696i		−	0.265610i
$723$		0			0
$724$	−7.00289	+	12.1294i	−0.260260	+	0.450784i
$725$	35.6448			1.32382
$726$		0			0
$727$	−18.0132	+	31.1997i	−0.668071	+	1.15713i	0.310372	+	0.950615i	$0.399546\pi$
$727$	−18.0132	+	31.1997i	−0.668071	+	1.15713i	−0.978443	+	0.206518i	$0.933787\pi$
$728$	−16.4473	+	31.9120i	−0.609577	+	1.18274i
$729$		0			0
$730$	−0.255562	−	0.147549i	−0.00945877	−	0.00546102i
$731$	11.5998	+	20.0915i	0.429035	+	0.743110i
$732$		0			0
$733$	−6.90293	+	3.98541i	−0.254966	+	0.147204i	−0.622036	−	0.782989i	$-0.713694\pi$
$733$	−6.90293	+	3.98541i	−0.254966	+	0.147204i	0.367070	+	0.930193i	$0.380361\pi$
$734$	−14.0759	−	8.12674i	−0.519552	−	0.299963i
$735$		0			0
$736$	28.6749	+	16.5554i	1.05697	+	0.610242i
$737$	1.06313	+	1.84139i	0.0391607	+	0.0678284i
$738$		0			0
$739$	−8.98365	−	5.18671i	−0.330469	−	0.190796i	0.325580	−	0.945514i	$-0.394440\pi$
$739$	−8.98365	−	5.18671i	−0.330469	−	0.190796i	−0.656049	+	0.754718i	$0.727774\pi$
$740$	0.200306	−	0.346940i	0.00736339	−	0.0127538i
$741$		0			0
$742$	1.10665	+	1.91677i	0.0406264	+	0.0703670i
$743$		−	1.32175i		−	0.0484904i	−0.999706	−	0.0242452i	$-0.992282\pi$
$743$		−	1.32175i		−	0.0484904i	0.999706	−	0.0242452i	$-0.00771824\pi$
$744$		0			0
$745$	1.24176			0.0454946
$746$		−	4.75791i		−	0.174199i
$747$		0			0
$748$	−8.45659	+	4.88242i	−0.309204	+	0.178519i
$749$	33.4370	+	19.3048i	1.22176	+	0.705383i
$750$		0			0
$751$	−13.8895			−0.506834			−0.253417	−	0.967357i	$-0.581555\pi$
$751$	−13.8895			−0.506834			−0.253417	+	0.967357i	$0.581555\pi$
$752$			2.20999i			0.0805901i
$753$		0			0
$754$	16.9358	−	10.8867i	0.616767	−	0.396470i
$755$	0.859774			0.0312904
$756$		0			0
$757$	15.7299	−	27.2450i	0.571712	−	0.990235i	−0.424678	−	0.905344i	$-0.639613\pi$
$757$	15.7299	−	27.2450i	0.571712	−	0.990235i	0.996390	−	0.0848903i	$-0.0270540\pi$
$758$	12.3931			0.450138
$759$		0			0
$760$	−0.446821	−	0.257972i	−0.0162079	−	0.00935764i
$761$	−41.9973	−	24.2472i	−1.52240	−	0.878960i	−0.999649	−	0.0264754i	$-0.991572\pi$
$761$	−41.9973	−	24.2472i	−1.52240	−	0.878960i	−0.522753	−	0.852484i	$-0.675095\pi$
$762$		0			0
$763$	−26.8963			−0.973711
$764$	−1.88543	+	3.26567i	−0.0682126	+	0.118148i
$765$		0			0
$766$	−11.7399			−0.424178
$767$	1.08885	−	0.699934i	0.0393161	−	0.0252731i
$768$		0			0
$769$			11.3355i			0.408770i	0.978891	+	0.204385i	$0.0655194\pi$
$769$			11.3355i			0.408770i	−0.978891	+	0.204385i	$0.934481\pi$
$770$	0.233390			0.00841080
$771$		0			0
$772$	22.9330	+	13.2404i	0.825378	+	0.476532i
$773$	−6.57982	+	3.79886i	−0.236660	+	0.136635i	−0.613640	−	0.789586i	$-0.710296\pi$
$773$	−6.57982	+	3.79886i	−0.236660	+	0.136635i	0.376981	+	0.926221i	$0.376962\pi$
$774$		0			0
$775$			20.8983i			0.750688i
$776$	26.5746			0.953974
$777$		0			0
$778$		−	13.6158i		−	0.488148i
$779$	−15.5441	−	26.9231i	−0.556924	−	0.964620i
$780$		0			0
$781$	−8.42940	+	14.6002i	−0.301628	+	0.522435i
$782$	−21.0522	−	12.1545i	−0.752825	−	0.434644i
$783$		0			0
$784$	2.48604	+	4.30595i	0.0887872	+	0.153784i
$785$	0.852820	+	0.492376i	0.0304384	+	0.0175736i
$786$		0			0
$787$	−32.1986	−	18.5899i	−1.14776	−	0.662658i	−0.199418	−	0.979915i	$-0.563905\pi$
$787$	−32.1986	−	18.5899i	−1.14776	−	0.662658i	−0.948340	+	0.317256i	$0.897238\pi$
$788$	2.60802	−	1.50574i	0.0929070	−	0.0536399i
$789$		0			0
$790$	−0.0298567	−	0.0517133i	−0.00106225	−	0.00183988i
$791$	−10.7473	−	6.20496i	−0.382130	−	0.220623i
$792$		0			0
$793$	2.72703	−	5.29116i	0.0968398	−	0.187895i
$794$	4.47266	−	7.74688i	0.158729	−	0.274927i
$795$		0			0
$796$	−14.4784			−0.513175
$797$	−3.40431	+	5.89644i	−0.120587	+	0.208862i	−0.919999	−	0.391920i	$-0.871811\pi$
$797$	−3.40431	+	5.89644i	−0.120587	+	0.208862i	0.799412	+	0.600783i	$0.205144\pi$
$798$		0			0
$799$		−	17.3303i		−	0.613101i
$800$	−25.3127	+	14.6143i	−0.894938	+	0.516693i
$801$		0			0
$802$	5.00086	+	8.66175i	0.176587	+	0.305857i
$803$	3.90551	+	6.76454i	0.137822	+	0.238715i
$804$		0			0
$805$	−0.657967	−	1.13963i	−0.0231903	−	0.0401668i
$806$	6.38277	+	9.92934i	0.224823	+	0.349746i
$807$		0			0
$808$	−39.4931	+	22.8014i	−1.38936	+	0.802150i
$809$	−8.57387	+	14.8504i	−0.301441	+	0.522112i	−0.976463	−	0.215687i	$-0.930801\pi$
$809$	−8.57387	+	14.8504i	−0.301441	+	0.522112i	0.675021	+	0.737798i	$0.264134\pi$
$810$		0			0
$811$			21.7276i			0.762959i	0.924377	+	0.381480i	$0.124585\pi$
$811$			21.7276i			0.762959i	−0.924377	+	0.381480i	$0.875415\pi$
$812$		−	37.1754i		−	1.30460i
$813$		0			0
$814$	4.05459	−	2.34092i	0.142113	−	0.0820491i
$815$	0.408200	−	0.707022i	0.0142986	−	0.0247659i
$816$		0			0
$817$	11.5089	−	6.64464i	0.402644	−	0.232467i
$818$	15.4787			0.541200
$819$		0			0
$820$	0.849462			0.0296645
$821$	−11.7354	+	6.77542i	−0.409567	+	0.236464i	−0.690604	−	0.723233i	$-0.742655\pi$
$821$	−11.7354	+	6.77542i	−0.409567	+	0.236464i	0.281036	+	0.959697i	$0.409322\pi$
$822$		0			0
$823$	18.3870	−	31.8472i	0.640931	−	1.11012i	−0.344295	−	0.938862i	$-0.611882\pi$
$823$	18.3870	−	31.8472i	0.640931	−	1.11012i	0.985225	−	0.171263i	$-0.0547847\pi$
$824$	−40.5303	+	23.4002i	−1.41194	+	0.815183i
$825$		0			0
$826$			1.05528i			0.0367179i
$827$		−	46.7697i		−	1.62634i	−0.582026	−	0.813170i	$-0.697740\pi$
$827$		−	46.7697i		−	1.62634i	0.582026	−	0.813170i	$-0.302260\pi$
$828$		0			0
$829$	9.45842	−	16.3825i	0.328505	−	0.568987i	−0.653711	−	0.756744i	$-0.726789\pi$
$829$	9.45842	−	16.3825i	0.328505	−	0.568987i	0.982215	+	0.187758i	$0.0601220\pi$
$830$	−0.535598	+	0.309228i	−0.0185909	+	0.0107335i
$831$		0			0
$832$	−5.25139	+	10.1891i	−0.182059	+	0.353243i
$833$	−19.4950	−	33.7663i	−0.675461	−	1.16993i
$834$		0			0
$835$	0.0417757	+	0.0723576i	0.00144571	+	0.00250404i
$836$	2.79676	+	4.84413i	0.0967279	+	0.167538i
$837$		0			0
$838$	0.696571	−	0.402165i	0.0240626	−	0.0138926i
$839$		−	11.8603i		−	0.409464i	−0.978818	−	0.204732i	$-0.934368\pi$
$839$		−	11.8603i		−	0.409464i	0.978818	−	0.204732i	$-0.0656323\pi$
$840$		0			0
$841$	−10.9501	+	18.9661i	−0.377589	+	0.654004i
$842$	17.4836			0.602523
$843$		0			0
$844$	−0.268121	+	0.464399i	−0.00922910	+	0.0159853i
$845$	−0.732150	−	0.334164i	−0.0251867	−	0.0114956i
$846$		0			0
$847$	30.4275	+	17.5673i	1.04550	+	0.603621i
$848$	−0.263460	−	0.456327i	−0.00904727	−	0.0156703i
$849$		0			0
$850$	18.5838	−	10.7293i	0.637418	−	0.368014i
$851$	−22.8612	−	13.1989i	−0.783671	−	0.452453i
$852$		0			0
$853$	−28.3691	−	16.3789i	−0.971340	−	0.560804i	−0.0716956	−	0.997427i	$-0.522841\pi$
$853$	−28.3691	−	16.3789i	−0.971340	−	0.560804i	−0.899645	+	0.436623i	$0.856174\pi$
$854$	2.42644	+	4.20272i	0.0830312	+	0.143814i
$855$		0			0
$856$	23.6042	+	13.6279i	0.806775	+	0.465791i
$857$	−27.4207	+	47.4941i	−0.936674	+	1.62237i	−0.165052	+	0.986285i	$0.552779\pi$
$857$	−27.4207	+	47.4941i	−0.936674	+	1.62237i	−0.771622	+	0.636081i	$0.780554\pi$
$858$		0			0
$859$	−17.3224	−	30.0032i	−0.591031	−	1.02370i	−0.994094	−	0.108524i	$-0.965388\pi$
$859$	−17.3224	−	30.0032i	−0.591031	−	1.02370i	0.403063	−	0.915172i	$-0.367946\pi$
$860$			0.363121i			0.0123823i
$861$		0			0
$862$	−5.77185			−0.196590
$863$		−	8.43673i		−	0.287190i	−0.989637	−	0.143595i	$-0.954134\pi$
$863$		−	8.43673i		−	0.287190i	0.989637	−	0.143595i	$-0.0458662\pi$
$864$		0			0
$865$	−0.788895	+	0.455469i	−0.0268232	+	0.0154864i
$866$	−4.02515	−	2.32392i	−0.136780	−	0.0789700i
$867$		0			0
$868$	21.7956			0.739792
$869$			1.58057i			0.0536172i
$870$		0			0
$871$	5.31330	+	2.73844i	0.180034	+	0.0927885i
$872$	−18.9869			−0.642978
$873$		0			0
$874$	−6.96236	+	12.0592i	−0.235505	+	0.407907i
$875$	2.32417			0.0785712
$876$		0			0
$877$	8.48217	+	4.89718i	0.286423	+	0.165366i	0.636327	−	0.771419i	$-0.280453\pi$
$877$	8.48217	+	4.89718i	0.286423	+	0.165366i	−0.349905	+	0.936785i	$0.613786\pi$
$878$	16.0589	+	9.27158i	0.541960	+	0.312901i
$879$		0			0
$880$	−0.0555632			−0.00187304
$881$	−13.3270	+	23.0831i	−0.448999	+	0.777689i	−0.998321	−	0.0579215i	$-0.981553\pi$
$881$	−13.3270	+	23.0831i	−0.448999	+	0.777689i	0.549322	+	0.835611i	$0.314886\pi$
$882$		0			0
$883$	13.3367			0.448816			0.224408	−	0.974495i	$-0.427955\pi$
$883$	13.3367			0.448816			0.224408	+	0.974495i	$0.427955\pi$
$884$	−12.5763	+	24.4014i	−0.422987	+	0.820707i
$885$		0			0
$886$			31.0670i			1.04372i
$887$	−22.5560			−0.757355			−0.378678	−	0.925529i	$-0.623621\pi$
$887$	−22.5560			−0.757355			−0.378678	+	0.925529i	$0.623621\pi$
$888$		0			0
$889$	23.2100	+	13.4003i	0.778439	+	0.449432i
$890$	0.0630585	−	0.0364068i	0.00211372	−	0.00122036i
$891$		0			0
$892$			2.81942i			0.0944011i
$893$	−9.92717			−0.332200
$894$		0			0
$895$		−	0.322083i		−	0.0107661i
$896$	17.2988	+	29.9625i	0.577914	+	1.00098i
$897$		0			0
$898$	−3.45666	+	5.98711i	−0.115350	+	0.199793i
$899$	−25.8442	−	14.9212i	−0.861953	−	0.497649i
$900$		0			0
$901$	2.06600	+	3.57842i	0.0688284	+	0.119214i
$902$	8.59740	+	4.96371i	0.286262	+	0.165273i
$903$		0			0
$904$	−7.58685	−	4.38027i	−0.252335	−	0.145686i
$905$	0.541222	−	0.312474i	0.0179908	−	0.0103870i
$906$		0			0
$907$	1.51436	+	2.62295i	0.0502835	+	0.0870935i	0.890072	−	0.455821i	$-0.150654\pi$
$907$	1.51436	+	2.62295i	0.0502835	+	0.0870935i	−0.839788	+	0.542914i	$0.817321\pi$
$908$	−31.6059	−	18.2477i	−1.04888	−	0.605570i
$909$		0			0
$910$	0.551926	−	0.354789i	0.0182962	−	0.0117611i
$911$	−8.08483	+	14.0033i	−0.267862	+	0.463951i	−0.968310	−	0.249753i	$-0.919651\pi$
$911$	−8.08483	+	14.0033i	−0.267862	+	0.463951i	0.700447	+	0.713704i	$0.252984\pi$
$912$		0			0
$913$	16.3701			0.541770
$914$	8.12946	−	14.0806i	0.268899	−	0.465746i
$915$		0			0
$916$		−	37.2451i		−	1.23061i
$917$	63.4889	−	36.6553i	2.09659	−	1.21047i
$918$		0			0
$919$	−1.41858	−	2.45706i	−0.0467947	−	0.0810509i	0.841679	−	0.539978i	$-0.181567\pi$
$919$	−1.41858	−	2.45706i	−0.0467947	−	0.0810509i	−0.888474	+	0.458927i	$0.848234\pi$
$920$	−0.464480	−	0.804502i	−0.0153134	−	0.0265237i
$921$		0			0
$922$	4.10162	+	7.10422i	0.135080	+	0.233965i
$923$	2.26043	+	47.3408i	0.0744031	+	1.55824i
$924$		0			0
$925$	20.1806	−	11.6513i	0.663536	−	0.383092i
$926$	7.94622	−	13.7633i	0.261129	−	0.452289i
$927$		0			0
$928$		−	41.7378i		−	1.37011i
$929$		−	37.8966i		−	1.24335i	−0.783276	−	0.621674i	$-0.786453\pi$
$929$		−	37.8966i		−	1.24335i	0.783276	−	0.621674i	$-0.213547\pi$
$930$		0			0
$931$	−19.3421	+	11.1672i	−0.633912	+	0.365989i
$932$	−5.65805	+	9.80003i	−0.185336	+	0.321011i
$933$		0			0
$934$	−9.50483	+	5.48762i	−0.311008	+	0.179560i
$935$	0.435715			0.0142494
$936$		0			0
$937$	−41.8330			−1.36662			−0.683312	−	0.730126i	$-0.739461\pi$
$937$	−41.8330			−1.36662			−0.683312	+	0.730126i	$0.739461\pi$
$938$	−4.22030	+	2.43659i	−0.137798	+	0.0795576i
$939$		0			0
$940$	0.135627	−	0.234912i	0.00442365	−	0.00766199i
$941$	1.89154	−	1.09208i	0.0616623	−	0.0356008i	−0.468852	−	0.883277i	$-0.655332\pi$
$941$	1.89154	−	1.09208i	0.0616623	−	0.0356008i	0.530514	+	0.847676i	$0.321999\pi$
$942$		0			0
$943$		−	55.9742i		−	1.82277i
$944$		−	0.251230i		−	0.00817686i
$945$		0			0
$946$	−2.12184	+	3.67514i	−0.0689871	+	0.119489i
$947$	35.7338	−	20.6309i	1.16119	−	0.670414i	0.209603	−	0.977787i	$-0.432783\pi$
$947$	35.7338	−	20.6309i	1.16119	−	0.670414i	0.951589	+	0.307372i	$0.0994497\pi$
$948$		0			0
$949$	19.5190	+	10.0600i	0.633612	+	0.326560i
$950$	−6.14601	−	10.6452i	−0.199403	−	0.345376i
$951$		0			0
$952$	−27.3208	−	47.3210i	−0.885472	−	1.53368i
$953$	24.5159	+	42.4627i	0.794146	+	1.37550i	0.923380	+	0.383888i	$0.125415\pi$
$953$	24.5159	+	42.4627i	0.794146	+	1.37550i	−0.129233	+	0.991614i	$0.541252\pi$
$954$		0			0
$955$	0.145717	−	0.0841295i	0.00471528	−	0.00272237i
$956$		−	18.9885i		−	0.614132i
$957$		0			0
$958$	3.87149	−	6.70562i	0.125082	−	0.216649i
$959$	31.2611			1.00947
$960$		0			0
$961$	−6.75185	+	11.6945i	−0.217802	+	0.377243i
$962$	6.02983	−	11.6994i	0.194409	−	0.377205i
$963$		0			0
$964$	15.9544	+	9.21126i	0.513856	+	0.296675i
$965$	−0.590797	−	1.02329i	−0.0190184	−	0.0329409i
$966$		0			0
$967$	−48.5763	+	28.0455i	−1.56211	+	0.901884i	−0.565064	+	0.825047i	$0.691149\pi$
$967$	−48.5763	+	28.0455i	−1.56211	+	0.901884i	−0.997044	+	0.0768368i	$0.975518\pi$
$968$	21.4797	+	12.4013i	0.690385	+	0.398594i
$969$		0			0
$970$	−0.420606	−	0.242837i	−0.0135048	−	0.00779702i
$971$	−16.5122	−	28.6000i	−0.529903	−	0.917819i	−0.999391	−	0.0348805i	$-0.988895\pi$
$971$	−16.5122	−	28.6000i	−0.529903	−	0.917819i	0.469488	−	0.882939i	$-0.344438\pi$
$972$		0			0
$973$	12.4401	+	7.18231i	0.398812	+	0.230254i
$974$	−16.1009	+	27.8875i	−0.515906	+	0.893575i
$975$		0			0
$976$	−0.577663	−	1.00054i	−0.0184906	−	0.0320266i
$977$		−	33.4220i		−	1.06927i	−0.845084	−	0.534633i	$-0.820450\pi$
$977$		−	33.4220i		−	1.06927i	0.845084	−	0.534633i	$-0.179550\pi$
$978$		0			0
$979$	−1.92733			−0.0615976
$980$		−	0.610271i		−	0.0194944i
$981$		0			0
$982$	−12.0054	+	6.93129i	−0.383106	+	0.221186i
$983$	31.4108	+	18.1350i	1.00185	+	0.578418i	0.908795	−	0.417243i	$-0.137004\pi$
$983$	31.4108	+	18.1350i	1.00185	+	0.578418i	0.0930545	+	0.995661i	$0.470337\pi$
$984$		0			0
$985$	−0.134375			−0.00428154
$986$			30.6426i			0.975860i
$987$		0			0
$988$	13.9777	+	7.20400i	0.444688	+	0.229190i
$989$	23.9274			0.760846
$990$		0			0
$991$	20.1550	−	34.9095i	0.640244	−	1.10894i	−0.345134	−	0.938554i	$-0.612166\pi$
$991$	20.1550	−	34.9095i	0.640244	−	1.10894i	0.985378	−	0.170382i	$-0.0545003\pi$
$992$	24.4705			0.776940
$993$		0			0
$994$	−33.4623	−	19.3195i	−1.06136	−	0.612776i
$995$	0.559487	+	0.323020i	0.0177369	+	0.0102404i
$996$		0			0
$997$	32.7202			1.03626			0.518129	−	0.855303i	$-0.326629\pi$
$997$	32.7202			1.03626			0.518129	+	0.855303i	$0.326629\pi$
$998$	−7.35248	+	12.7349i	−0.232739	+	0.403115i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.r.b.316.4		22
3.2	odd	2		117.2.r.b.43.8	yes	22
9.4	even	3		351.2.l.b.199.4		22
9.5	odd	6		117.2.l.b.4.8	✓	22
13.10	even	6		351.2.l.b.127.8		22
39.23	odd	6		117.2.l.b.88.4	yes	22
117.23	odd	6		117.2.r.b.49.8	yes	22
117.49	even	6	inner	351.2.r.b.10.4		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.8	✓	22	9.5	odd	6
117.2.l.b.88.4	yes	22	39.23	odd	6
117.2.r.b.43.8	yes	22	3.2	odd	2
117.2.r.b.49.8	yes	22	117.23	odd	6
351.2.l.b.127.8		22	13.10	even	6
351.2.l.b.199.4		22	9.4	even	3
351.2.r.b.10.4		22	117.49	even	6	inner
351.2.r.b.316.4		22	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.677814 + 0.391336i) q^{2} +(-0.693712 + 1.20154i) q^{4} +(0.0536139 - 0.0309540i) q^{5} -3.75567i q^{7} -2.65124i q^{8} +O(q^{10})\)	\(q+(-0.677814 + 0.391336i) q^{2} +(-0.693712 + 1.20154i) q^{4} +(0.0536139 - 0.0309540i) q^{5} -3.75567i q^{7} -2.65124i q^{8} +(-0.0242268 + 0.0419621i) q^{10} +(1.11071 - 0.641267i) q^{11} +(1.65180 - 3.20493i) q^{13} +(1.46973 + 2.54564i) q^{14} +(-0.349898 - 0.606041i) q^{16} +(2.74383 + 4.75245i) q^{17} +(2.72231 - 1.57173i) q^{19} +0.0858927i q^{20} +(-0.501902 + 0.869319i) q^{22} +5.65979 q^{23} +(-2.49808 + 4.32681i) q^{25} +(0.134590 + 2.81875i) q^{26} +(4.51260 + 2.60535i) q^{28} +(-3.56722 - 6.17860i) q^{29} +(3.62246 - 2.09143i) q^{31} +(5.06642 + 2.92510i) q^{32} +(-3.71961 - 2.14752i) q^{34} +(-0.116253 - 0.201356i) q^{35} +(-4.03923 - 2.33205i) q^{37} +(-1.23015 + 2.13067i) q^{38} +(-0.0820666 - 0.142143i) q^{40} -9.88981i q^{41} +4.22761 q^{43} +1.77942i q^{44} +(-3.83628 + 2.21488i) q^{46} +(-2.73495 - 1.57902i) q^{47} -7.10504 q^{49} -3.91036i q^{50} +(2.70499 + 4.20801i) q^{52} +0.752963 q^{53} +(0.0396996 - 0.0687616i) q^{55} -9.95718 q^{56} +(4.83582 + 2.79196i) q^{58} +(0.310908 + 0.179503i) q^{59} +1.65095 q^{61} +(-1.63690 + 2.83520i) q^{62} -3.17919 q^{64} +(-0.0106459 - 0.222958i) q^{65} +1.65785i q^{67} -7.61370 q^{68} +(0.157596 + 0.0909879i) q^{70} +(-11.3838 + 6.57246i) q^{71} +6.09030i q^{73} +3.65046 q^{74} +4.36130i q^{76} +(-2.40838 - 4.17145i) q^{77} +(-0.616191 + 1.06727i) q^{79} +(-0.0375188 - 0.0216615i) q^{80} +(3.87024 + 6.70345i) q^{82} +(11.0538 + 6.38193i) q^{83} +(0.294215 + 0.169865i) q^{85} +(-2.86553 + 1.65442i) q^{86} +(-1.70015 - 2.94475i) q^{88} +(-1.30142 - 0.751374i) q^{89} +(-12.0366 - 6.20361i) q^{91} +(-3.92627 + 6.80049i) q^{92} +2.47172 q^{94} +(0.0973024 - 0.168533i) q^{95} +10.0235i q^{97} +(4.81589 - 2.78046i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 10 q^{4} - 3 q^{5}+O(q^{10}) \) 22 * q + 10 * q^4 - 3 * q^5	\( 22 q + 10 q^{4} - 3 q^{5} - 7 q^{10} - 3 q^{11} + 3 q^{13} + 9 q^{14} - 12 q^{16} - 9 q^{17} - 6 q^{19} - 13 q^{22} + 12 q^{23} + 4 q^{25} + 12 q^{26} + 3 q^{28} + 24 q^{29} + 27 q^{31} - 15 q^{34} + 27 q^{35} + 6 q^{37} - 21 q^{38} + 13 q^{40} + 8 q^{43} - 15 q^{46} - 6 q^{47} - 14 q^{49} - 7 q^{52} + 24 q^{53} - 13 q^{55} - 18 q^{56} + 15 q^{58} + 33 q^{59} - 6 q^{61} - 24 q^{64} - 3 q^{65} - 138 q^{68} + 24 q^{70} - 9 q^{71} - 12 q^{74} - 42 q^{77} - 6 q^{79} - 105 q^{80} - 16 q^{82} + 42 q^{83} - 51 q^{85} + 45 q^{86} - 11 q^{88} + 30 q^{89} + 15 q^{91} + 3 q^{92} - 88 q^{94} + 3 q^{95} - 117 q^{98}+O(q^{100}) \) 22 * q + 10 * q^4 - 3 * q^5 - 7 * q^10 - 3 * q^11 + 3 * q^13 + 9 * q^14 - 12 * q^16 - 9 * q^17 - 6 * q^19 - 13 * q^22 + 12 * q^23 + 4 * q^25 + 12 * q^26 + 3 * q^28 + 24 * q^29 + 27 * q^31 - 15 * q^34 + 27 * q^35 + 6 * q^37 - 21 * q^38 + 13 * q^40 + 8 * q^43 - 15 * q^46 - 6 * q^47 - 14 * q^49 - 7 * q^52 + 24 * q^53 - 13 * q^55 - 18 * q^56 + 15 * q^58 + 33 * q^59 - 6 * q^61 - 24 * q^64 - 3 * q^65 - 138 * q^68 + 24 * q^70 - 9 * q^71 - 12 * q^74 - 42 * q^77 - 6 * q^79 - 105 * q^80 - 16 * q^82 + 42 * q^83 - 51 * q^85 + 45 * q^86 - 11 * q^88 + 30 * q^89 + 15 * q^91 + 3 * q^92 - 88 * q^94 + 3 * q^95 - 117 * q^98

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