LMFDB - Embedded newform 351.2.e.b.235.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(118,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.118"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.487558322307.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 13x^{8} + 43x^{6} + 48x^{4} + 21x^{2} + 3 $ x^10 + 13x^8 + 43x^6 + 48x^4 + 21x^2 + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.5
Root			$-0.858204i$ of defining polynomial
Character	$\chi$	$=$	351.235
Dual form			351.2.e.b.118.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39763 - 2.42077i) q^{2} +(-2.90675 - 5.03463i) q^{4} +(0.413993 + 0.717057i) q^{5} +(1.24323 - 2.15333i) q^{7} -10.6597 q^{8} +2.31444 q^{10} +(-0.459729 + 0.796275i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-3.47514 - 6.01912i) q^{14} +(-9.08484 + 15.7354i) q^{16} +1.53740 q^{17} +3.40028 q^{19} +(2.40675 - 4.16860i) q^{20} +(1.28506 + 2.22580i) q^{22} +(0.490886 + 0.850239i) q^{23} +(2.15722 - 3.73641i) q^{25} -2.79526 q^{26} -14.4550 q^{28} +(-0.595121 + 1.03078i) q^{29} +(3.12690 + 5.41594i) q^{31} +(14.7348 + 25.5214i) q^{32} +(2.14872 - 3.72170i) q^{34} +2.05875 q^{35} +1.83048 q^{37} +(4.75234 - 8.23129i) q^{38} +(-4.41304 - 7.64362i) q^{40} +(-2.86647 - 4.96488i) q^{41} +(-0.792611 + 1.37284i) q^{43} +5.34527 q^{44} +2.74431 q^{46} +(2.68754 - 4.65496i) q^{47} +(0.408777 + 0.708023i) q^{49} +(-6.02999 - 10.4443i) q^{50} +(-2.90675 + 5.03463i) q^{52} +5.82609 q^{53} -0.761299 q^{55} +(-13.2524 + 22.9539i) q^{56} +(1.66352 + 2.88130i) q^{58} +(-0.477338 - 0.826774i) q^{59} +(4.44763 - 7.70353i) q^{61} +17.4810 q^{62} +46.0360 q^{64} +(0.413993 - 0.717057i) q^{65} +(6.56302 + 11.3675i) q^{67} +(-4.46884 - 7.74026i) q^{68} +(2.87737 - 4.98375i) q^{70} -5.27858 q^{71} -10.0187 q^{73} +(2.55834 - 4.43117i) q^{74} +(-9.88375 - 17.1192i) q^{76} +(1.14310 + 1.97990i) q^{77} +(-5.06272 + 8.76888i) q^{79} -15.0443 q^{80} -16.0251 q^{82} +(-1.16257 + 2.01363i) q^{83} +(0.636475 + 1.10241i) q^{85} +(2.21555 + 3.83745i) q^{86} +(4.90058 - 8.48805i) q^{88} -12.5811 q^{89} -2.48645 q^{91} +(2.85376 - 4.94286i) q^{92} +(-7.51238 - 13.0118i) q^{94} +(1.40769 + 2.43820i) q^{95} +(3.94212 - 6.82795i) q^{97} +2.28528 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - 4 q^{4} + q^{5} + 2 q^{7} - 24 q^{8} - 4 q^{10} + 11 q^{11} - 5 q^{13} - 5 q^{14} - 10 q^{16} - 14 q^{17} + 6 q^{19} - q^{20} + 7 q^{22} + 18 q^{23} + 8 q^{25} - 4 q^{26} - 38 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 - 4 * q^4 + q^5 + 2 * q^7 - 24 * q^8 - 4 * q^10 + 11 * q^11 - 5 * q^13 - 5 * q^14 - 10 * q^16 - 14 * q^17 + 6 * q^19 - q^20 + 7 * q^22 + 18 * q^23 + 8 * q^25 - 4 * q^26 - 38 * q^28 + 4 * q^29 + 16 * q^31 + 31 * q^32 - 13 * q^34 - 22 * q^35 + 10 * q^37 + 24 * q^38 - 18 * q^40 + 12 * q^41 - 2 * q^44 + 12 * q^46 + 15 * q^47 - 3 * q^49 - 5 * q^50 - 4 * q^52 + 6 * q^53 - 34 * q^55 - 24 * q^56 + 2 * q^58 + 3 * q^59 + q^61 + 8 * q^62 + 124 * q^64 + q^65 + 4 * q^67 - 16 * q^68 + 25 * q^70 - 30 * q^71 - 10 * q^73 + 11 * q^74 - 9 * q^76 + q^77 - 13 * q^79 - 64 * q^80 - 42 * q^82 + 26 * q^83 + 7 * q^85 - 6 * q^86 - 3 * q^88 - 58 * q^89 - 4 * q^91 - 6 * q^92 - 12 * q^94 + 12 * q^95 + 16 * q^97 + 78 * q^98

Character values

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

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

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 $

$2$	1.39763	−	2.42077i	0.988274	−	1.71174i	0.361905	−	0.932215i	$-0.382126\pi$
$2$	1.39763	−	2.42077i	0.988274	−	1.71174i	0.626369	−	0.779527i	$-0.284540\pi$
$3$		0			0
$3$		0			0
$4$	−2.90675	−	5.03463i	−1.45337	−	2.51732i
$5$	0.413993	+	0.717057i	0.185143	+	0.320678i	0.943625	−	0.331017i	$-0.107392\pi$
$5$	0.413993	+	0.717057i	0.185143	+	0.320678i	−0.758481	+	0.651695i	$0.774058\pi$
$6$		0			0
$7$	1.24323	−	2.15333i	0.469895	−	0.813883i	−0.529512	−	0.848302i	$-0.677625\pi$
$7$	1.24323	−	2.15333i	0.469895	−	0.813883i	0.999407	+	0.0344198i	$0.0109583\pi$
$8$	−10.6597			−3.76877
$9$		0			0
$10$	2.31444			0.731890
$11$	−0.459729	+	0.796275i	−0.138614	+	0.240086i	−0.926972	−	0.375130i	$-0.877598\pi$
$11$	−0.459729	+	0.796275i	−0.138614	+	0.240086i	0.788358	+	0.615216i	$0.210931\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	−3.47514	−	6.01912i	−0.928771	−	1.60868i
$15$		0			0
$16$	−9.08484	+	15.7354i	−2.27121	+	3.93385i
$17$	1.53740			0.372875			0.186438	−	0.982467i	$-0.440306\pi$
$17$	1.53740			0.372875			0.186438	+	0.982467i	$0.440306\pi$
$18$		0			0
$19$	3.40028			0.780078			0.390039	−	0.920798i	$-0.372461\pi$
$19$	3.40028			0.780078			0.390039	+	0.920798i	$0.372461\pi$
$20$	2.40675	−	4.16860i	0.538165	−	0.932128i
$21$		0			0
$22$	1.28506	+	2.22580i	0.273977	+	0.474541i
$23$	0.490886	+	0.850239i	0.102357	+	0.177287i	0.912655	−	0.408730i	$-0.134028\pi$
$23$	0.490886	+	0.850239i	0.102357	+	0.177287i	−0.810298	+	0.586017i	$0.800695\pi$
$24$		0			0
$25$	2.15722	−	3.73641i	0.431444	−	0.747283i
$26$	−2.79526			−0.548196
$27$		0			0
$28$	−14.4550			−2.73173
$29$	−0.595121	+	1.03078i	−0.110511	+	0.191411i	−0.915976	−	0.401232i	$-0.868582\pi$
$29$	−0.595121	+	1.03078i	−0.110511	+	0.191411i	0.805465	+	0.592643i	$0.201915\pi$
$30$		0			0
$31$	3.12690	+	5.41594i	0.561607	+	0.972732i	0.997356	+	0.0726641i	$0.0231501\pi$
$31$	3.12690	+	5.41594i	0.561607	+	0.972732i	−0.435749	+	0.900068i	$0.643517\pi$
$32$	14.7348	+	25.5214i	2.60477	+	4.51160i
$33$		0			0
$34$	2.14872	−	3.72170i	0.368503	−	0.638266i
$35$	2.05875			0.347992
$36$		0			0
$37$	1.83048			0.300929			0.150465	−	0.988615i	$-0.451923\pi$
$37$	1.83048			0.300929			0.150465	+	0.988615i	$0.451923\pi$
$38$	4.75234	−	8.23129i	0.770931	−	1.33529i
$39$		0			0
$40$	−4.41304	−	7.64362i	−0.697764	−	1.20856i
$41$	−2.86647	−	4.96488i	−0.447668	−	0.775384i	0.550566	−	0.834792i	$-0.314412\pi$
$41$	−2.86647	−	4.96488i	−0.447668	−	0.775384i	−0.998234	+	0.0594079i	$0.981079\pi$
$42$		0			0
$43$	−0.792611	+	1.37284i	−0.120872	+	0.209356i	−0.920112	−	0.391656i	$-0.871902\pi$
$43$	−0.792611	+	1.37284i	−0.120872	+	0.209356i	0.799240	+	0.601012i	$0.205236\pi$
$44$	5.34527			0.805829
$45$		0			0
$46$	2.74431			0.404626
$47$	2.68754	−	4.65496i	0.392018	−	0.678996i	−0.600697	−	0.799477i	$-0.705110\pi$
$47$	2.68754	−	4.65496i	0.392018	−	0.678996i	0.992716	+	0.120481i	$0.0384437\pi$
$48$		0			0
$49$	0.408777	+	0.708023i	0.0583967	+	0.101146i
$50$	−6.02999	−	10.4443i	−0.852770	−	1.47704i
$51$		0			0
$52$	−2.90675	+	5.03463i	−0.403093	+	0.698178i
$53$	5.82609			0.800275			0.400137	−	0.916455i	$-0.368962\pi$
$53$	5.82609			0.800275			0.400137	+	0.916455i	$0.368962\pi$
$54$		0			0
$55$	−0.761299			−0.102654
$56$	−13.2524	+	22.9539i	−1.77093	+	3.06734i
$57$		0			0
$58$	1.66352	+	2.88130i	0.218431	+	0.378333i
$59$	−0.477338	−	0.826774i	−0.0621442	−	0.107637i	0.833279	−	0.552852i	$-0.186461\pi$
$59$	−0.477338	−	0.826774i	−0.0621442	−	0.107637i	−0.895424	+	0.445215i	$0.853127\pi$
$60$		0			0
$61$	4.44763	−	7.70353i	0.569461	−	0.986336i	−0.427158	−	0.904177i	$-0.640485\pi$
$61$	4.44763	−	7.70353i	0.569461	−	0.986336i	0.996619	−	0.0821589i	$-0.0261815\pi$
$62$	17.4810			2.22009
$63$		0			0
$64$	46.0360			5.75450
$65$	0.413993	−	0.717057i	0.0513495	−	0.0889400i
$66$		0			0
$67$	6.56302	+	11.3675i	0.801800	+	1.38876i	0.918430	+	0.395583i	$0.129457\pi$
$67$	6.56302	+	11.3675i	0.801800	+	1.38876i	−0.116630	+	0.993175i	$0.537209\pi$
$68$	−4.46884	−	7.74026i	−0.541927	−	0.938645i
$69$		0			0
$70$	2.87737	−	4.98375i	0.343912	−	0.595672i
$71$	−5.27858			−0.626452			−0.313226	−	0.949679i	$-0.601410\pi$
$71$	−5.27858			−0.626452			−0.313226	+	0.949679i	$0.601410\pi$
$72$		0			0
$73$	−10.0187			−1.17260			−0.586302	−	0.810093i	$-0.699417\pi$
$73$	−10.0187			−1.17260			−0.586302	+	0.810093i	$0.699417\pi$
$74$	2.55834	−	4.43117i	0.297400	−	0.515113i
$75$		0			0
$76$	−9.88375	−	17.1192i	−1.13374	−	1.96370i
$77$	1.14310	+	1.97990i	0.130268	+	0.225630i
$78$		0			0
$79$	−5.06272	+	8.76888i	−0.569600	+	0.986577i	0.427005	+	0.904249i	$0.359569\pi$
$79$	−5.06272	+	8.76888i	−0.569600	+	0.986577i	−0.996605	+	0.0823273i	$0.973765\pi$
$80$	−15.0443			−1.68200
$81$		0			0
$82$	−16.0251			−1.76968
$83$	−1.16257	+	2.01363i	−0.127609	+	0.221025i	−0.922750	−	0.385400i	$-0.874063\pi$
$83$	−1.16257	+	2.01363i	−0.127609	+	0.221025i	0.795141	+	0.606425i	$0.207397\pi$
$84$		0			0
$85$	0.636475	+	1.10241i	0.0690354	+	0.119573i
$86$	2.21555	+	3.83745i	0.238909	+	0.413803i
$87$		0			0
$88$	4.90058	−	8.48805i	0.522404	−	0.904830i
$89$	−12.5811			−1.33359			−0.666795	−	0.745241i	$-0.732334\pi$
$89$	−12.5811			−1.33359			−0.666795	+	0.745241i	$0.732334\pi$
$90$		0			0
$91$	−2.48645			−0.260651
$92$	2.85376	−	4.94286i	0.297525	−	0.515329i
$93$		0			0
$94$	−7.51238	−	13.0118i	−0.774843	−	1.34207i
$95$	1.40769	+	2.43820i	0.144426	+	0.250154i
$96$		0			0
$97$	3.94212	−	6.82795i	0.400262	−	0.693274i	−0.593496	−	0.804837i	$-0.702253\pi$
$97$	3.94212	−	6.82795i	0.400262	−	0.693274i	0.993757	+	0.111564i	$0.0355859\pi$
$98$	2.28528			0.230848
$99$		0			0
$100$	−25.0819			−2.50819
$101$	−7.55953	+	13.0935i	−0.752201	+	1.30285i	0.194552	+	0.980892i	$0.437675\pi$
$101$	−7.55953	+	13.0935i	−0.752201	+	1.30285i	−0.946754	+	0.321959i	$0.895659\pi$
$102$		0			0
$103$	−2.25875	−	3.91228i	−0.222562	−	0.385488i	0.733023	−	0.680203i	$-0.238109\pi$
$103$	−2.25875	−	3.91228i	−0.222562	−	0.385488i	−0.955585	+	0.294715i	$0.904775\pi$
$104$	5.32985	+	9.23157i	0.522635	+	0.905230i
$105$		0			0
$106$	8.14272	−	14.1036i	0.790891	−	1.36986i
$107$	−18.5040			−1.78885			−0.894426	−	0.447217i	$-0.852415\pi$
$107$	−18.5040			−1.78885			−0.894426	+	0.447217i	$0.852415\pi$
$108$		0			0
$109$	7.95808			0.762246			0.381123	−	0.924524i	$-0.375537\pi$
$109$	7.95808			0.762246			0.381123	+	0.924524i	$0.375537\pi$
$110$	−1.06402	+	1.84293i	−0.101450	+	0.175716i
$111$		0			0
$112$	22.5890	+	39.1254i	2.13446	+	3.69700i
$113$	6.20325	+	10.7444i	0.583553	+	1.01074i	0.995054	+	0.0993342i	$0.0316713\pi$
$113$	6.20325	+	10.7444i	0.583553	+	1.01074i	−0.411501	+	0.911409i	$0.634995\pi$
$114$		0			0
$115$	−0.406447	+	0.703987i	−0.0379014	+	0.0656471i
$116$	6.91946			0.642456
$117$		0			0
$118$	−2.66857			−0.245662
$119$	1.91134	−	3.31054i	0.175212	−	0.303477i
$120$		0			0
$121$	5.07730	+	8.79414i	0.461573	+	0.799467i
$122$	−12.4323	−	21.5334i	−1.12557	−	1.94954i
$123$		0			0
$124$	18.1782	−	31.4855i	1.63245	−	2.82748i
$125$	7.71223			0.689803
$126$		0			0
$127$	−9.28761			−0.824142			−0.412071	−	0.911152i	$-0.635195\pi$
$127$	−9.28761			−0.824142			−0.412071	+	0.911152i	$0.635195\pi$
$128$	34.8717	−	60.3995i	3.08225	−	5.33861i
$129$		0			0
$130$	−1.15722	−	2.00436i	−0.101495	−	0.175794i
$131$	7.15825	+	12.3985i	0.625419	+	1.08326i	0.988460	+	0.151485i	$0.0484054\pi$
$131$	7.15825	+	12.3985i	0.625419	+	1.08326i	−0.363040	+	0.931773i	$0.618261\pi$
$132$		0			0
$133$	4.22732	−	7.32193i	0.366555	−	0.634892i
$134$	36.6907			3.16959
$135$		0			0
$136$	−16.3883			−1.40528
$137$	6.37199	−	11.0366i	0.544396	−	0.942921i	−0.454249	−	0.890875i	$-0.650092\pi$
$137$	6.37199	−	11.0366i	0.544396	−	0.942921i	0.998645	−	0.0520463i	$-0.0165743\pi$
$138$		0			0
$139$	7.90873	+	13.6983i	0.670809	+	1.16188i	0.977675	+	0.210123i	$0.0673865\pi$
$139$	7.90873	+	13.6983i	0.670809	+	1.16188i	−0.306866	+	0.951753i	$0.599280\pi$
$140$	−5.98426	−	10.3650i	−0.505762	−	0.876006i
$141$		0			0
$142$	−7.37751	+	12.7782i	−0.619107	+	1.07232i
$143$	0.919459			0.0768890
$144$		0			0
$145$	−0.985504			−0.0818416
$146$	−14.0025	+	24.2530i	−1.15885	+	2.00719i
$147$		0			0
$148$	−5.32074	−	9.21579i	−0.437362	−	0.757533i
$149$	1.06496	+	1.84457i	0.0872450	+	0.151113i	0.906346	−	0.422537i	$-0.138860\pi$
$149$	1.06496	+	1.84457i	0.0872450	+	0.151113i	−0.819101	+	0.573650i	$0.805527\pi$
$150$		0			0
$151$	−7.34083	+	12.7147i	−0.597388	+	1.03471i	0.395817	+	0.918330i	$0.370462\pi$
$151$	−7.34083	+	12.7147i	−0.597388	+	1.03471i	−0.993205	+	0.116378i	$0.962872\pi$
$152$	−36.2460			−2.93994
$153$		0			0
$154$	6.39050			0.514961
$155$	−2.58903	+	4.48433i	−0.207956	+	0.360190i
$156$		0			0
$157$	−5.26946	−	9.12697i	−0.420548	−	0.728411i	0.575445	−	0.817841i	$-0.304829\pi$
$157$	−5.26946	−	9.12697i	−0.420548	−	0.728411i	−0.995993	+	0.0894294i	$0.971496\pi$
$158$	14.1516	+	24.5113i	1.12584	+	1.95002i
$159$		0			0
$160$	−12.2002	+	21.1314i	−0.964512	+	1.67058i
$161$	2.44113			0.192388
$162$		0			0
$163$	−2.74398			−0.214925			−0.107463	−	0.994209i	$-0.534273\pi$
$163$	−2.74398			−0.214925			−0.107463	+	0.994209i	$0.534273\pi$
$164$	−16.6642	+	28.8633i	−1.30126	+	2.25384i
$165$		0			0
$166$	3.24969	+	5.62863i	0.252225	+	0.436866i
$167$	5.84319	+	10.1207i	0.452160	+	0.783164i	0.998520	−	0.0543865i	$-0.0173203\pi$
$167$	5.84319	+	10.1207i	0.452160	+	0.783164i	−0.546360	+	0.837550i	$0.683987\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	3.55823			0.272904
$171$		0			0
$172$	9.21567			0.702688
$173$	−0.969058	+	1.67846i	−0.0736761	+	0.127611i	−0.900510	−	0.434836i	$-0.856806\pi$
$173$	−0.969058	+	1.67846i	−0.0736761	+	0.127611i	0.826834	+	0.562446i	$0.190140\pi$
$174$		0			0
$175$	−5.36382	−	9.29041i	−0.405467	−	0.702289i
$176$	−8.35314	−	14.4681i	−0.629642	−	1.09057i
$177$		0			0
$178$	−17.5837	+	30.4558i	−1.31795	+	2.28276i
$179$	−16.3546			−1.22240			−0.611201	−	0.791475i	$-0.709313\pi$
$179$	−16.3546			−1.22240			−0.611201	+	0.791475i	$0.709313\pi$
$180$		0			0
$181$	−14.7968			−1.09984			−0.549920	−	0.835218i	$-0.685342\pi$
$181$	−14.7968			−1.09984			−0.549920	+	0.835218i	$0.685342\pi$
$182$	−3.47514	+	6.01912i	−0.257595	+	0.446167i
$183$		0			0
$184$	−5.23270	−	9.06330i	−0.385760	−	0.668155i
$185$	0.757806	+	1.31256i	0.0557150	+	0.0965012i
$186$		0			0
$187$	−0.706790	+	1.22420i	−0.0516856	+	0.0895221i
$188$	−31.2480			−2.27899
$189$		0			0
$190$	7.86975			0.570931
$191$	11.0198	−	19.0868i	0.797362	−	1.38107i	−0.123966	−	0.992286i	$-0.539561\pi$
$191$	11.0198	−	19.0868i	0.797362	−	1.38107i	0.921328	−	0.388785i	$-0.127105\pi$
$192$		0			0
$193$	−1.51920	−	2.63133i	−0.109354	−	0.189407i	0.806155	−	0.591705i	$-0.201545\pi$
$193$	−1.51920	−	2.63133i	−0.109354	−	0.189407i	−0.915509	+	0.402298i	$0.868212\pi$
$194$	−11.0193	−	19.0859i	−0.791137	−	1.37029i
$195$		0			0
$196$	2.37642	−	4.11608i	0.169744	−	0.294006i
$197$	24.0480			1.71335			0.856674	−	0.515858i	$-0.172527\pi$
$197$	24.0480			1.71335			0.856674	+	0.515858i	$0.172527\pi$
$198$		0			0
$199$	−15.2119			−1.07834			−0.539171	−	0.842197i	$-0.681262\pi$
$199$	−15.2119			−1.07834			−0.539171	+	0.842197i	$0.681262\pi$
$200$	−22.9953	+	39.8291i	−1.62601	+	2.81634i
$201$		0			0
$202$	21.1309	+	36.5997i	1.48676	+	2.57515i
$203$	1.47974	+	2.56298i	0.103857	+	0.179886i
$204$		0			0
$205$	2.37340	−	4.11085i	0.165766	−	0.287114i
$206$	−12.6276			−0.879808
$207$		0			0
$208$	18.1697			1.25984
$209$	−1.56321	+	2.70756i	−0.108130	+	0.187286i
$210$		0			0
$211$	0.697648	+	1.20836i	0.0480280	+	0.0831870i	0.889040	−	0.457829i	$-0.151373\pi$
$211$	0.697648	+	1.20836i	0.0480280	+	0.0831870i	−0.841012	+	0.541017i	$0.818040\pi$
$212$	−16.9350	−	29.3322i	−1.16310	−	2.01454i
$213$		0			0
$214$	−25.8618	+	44.7939i	−1.76788	+	3.06205i
$215$	−1.31254			−0.0895146
$216$		0			0
$217$	15.5498			1.05559
$218$	11.1225	−	19.2647i	0.753308	−	1.30477i
$219$		0			0
$220$	2.21290	+	3.83286i	0.149194	+	0.258411i
$221$	−0.768702	−	1.33143i	−0.0517085	−	0.0895618i
$222$		0			0
$223$	−1.17093	+	2.02811i	−0.0784113	+	0.135812i	−0.902565	−	0.430554i	$-0.858318\pi$
$223$	−1.17093	+	2.02811i	−0.0784113	+	0.135812i	0.824153	+	0.566367i	$0.191651\pi$
$224$	73.2748			4.89588
$225$		0			0
$226$	34.6794			2.30684
$227$	−3.86726	+	6.69829i	−0.256679	+	0.444581i	−0.965350	−	0.260958i	$-0.915962\pi$
$227$	−3.86726	+	6.69829i	−0.256679	+	0.444581i	0.708671	+	0.705539i	$0.249295\pi$
$228$		0			0
$229$	−7.65795	−	13.2640i	−0.506052	−	0.876507i	−0.999975	−	0.00700218i	$-0.997771\pi$
$229$	−7.65795	−	13.2640i	−0.506052	−	0.876507i	0.493924	−	0.869505i	$-0.335562\pi$
$230$	1.13613	+	1.96783i	0.0749139	+	0.129755i
$231$		0			0
$232$	6.34381	−	10.9878i	0.416492	−	0.721385i
$233$	−3.81598			−0.249993			−0.124997	−	0.992157i	$-0.539892\pi$
$233$	−3.81598			−0.249993			−0.124997	+	0.992157i	$0.539892\pi$
$234$		0			0
$235$	4.45050			0.290318
$236$	−2.77500	+	4.80644i	−0.180637	+	0.312873i
$237$		0			0
$238$	−5.34270	−	9.25383i	−0.346316	−	0.599837i
$239$	−5.33578	−	9.24184i	−0.345143	−	0.597805i	0.640237	−	0.768178i	$-0.278836\pi$
$239$	−5.33578	−	9.24184i	−0.345143	−	0.597805i	−0.985380	+	0.170373i	$0.945503\pi$
$240$		0			0
$241$	−0.600452	+	1.04001i	−0.0386785	+	0.0669931i	−0.884717	−	0.466129i	$-0.845648\pi$
$241$	−0.600452	+	1.04001i	−0.0386785	+	0.0669931i	0.846038	+	0.533122i	$0.178981\pi$
$242$	28.3848			1.82464
$243$		0			0
$244$	−51.7126			−3.31056
$245$	−0.338462	+	0.586233i	−0.0216235	+	0.0374531i
$246$		0			0
$247$	−1.70014	−	2.94473i	−0.108177	−	0.187369i
$248$	−33.3318	−	57.7324i	−2.11657	−	3.66601i
$249$		0			0
$250$	10.7788	−	18.6695i	0.681714	−	1.18076i
$251$	−15.6411			−0.987260			−0.493630	−	0.869672i	$-0.664330\pi$
$251$	−15.6411			−0.987260			−0.493630	+	0.869672i	$0.664330\pi$
$252$		0			0
$253$	−0.902699			−0.0567522
$254$	−12.9807	+	22.4832i	−0.814479	+	1.41072i
$255$		0			0
$256$	−51.4395	−	89.0958i	−3.21497	−	5.56849i
$257$	−7.83123	−	13.5641i	−0.488499	−	0.846105i	0.511414	−	0.859335i	$-0.329122\pi$
$257$	−7.83123	−	13.5641i	−0.488499	−	0.846105i	−0.999912	+	0.0132297i	$0.995789\pi$
$258$		0			0
$259$	2.27570	−	3.94163i	0.141405	−	0.244921i
$260$	−4.81349			−0.298520
$261$		0			0
$262$	40.0184			2.47234
$263$	−0.813037	+	1.40822i	−0.0501340	+	0.0868347i	−0.890003	−	0.455954i	$-0.849298\pi$
$263$	−0.813037	+	1.40822i	−0.0501340	+	0.0868347i	0.839869	+	0.542789i	$0.182632\pi$
$264$		0			0
$265$	2.41196	+	4.17764i	0.148166	+	0.256630i
$266$	−11.8165	−	20.4667i	−0.724514	−	1.25490i
$267$		0			0
$268$	38.1540	−	66.0847i	2.33063	−	4.03677i
$269$	18.8883			1.15164			0.575821	−	0.817576i	$-0.304682\pi$
$269$	18.8883			1.15164			0.575821	+	0.817576i	$0.304682\pi$
$270$		0			0
$271$	−10.2390			−0.621977			−0.310988	−	0.950414i	$-0.600660\pi$
$271$	−10.2390			−0.621977			−0.310988	+	0.950414i	$0.600660\pi$
$272$	−13.9671	+	24.1917i	−0.846879	+	1.46684i
$273$		0			0
$274$	−17.8114	−	30.8502i	−1.07602	−	1.86373i
$275$	1.98347	+	3.43548i	0.119608	+	0.207167i
$276$		0			0
$277$	3.65519	−	6.33097i	0.219619	−	0.380391i	−0.735073	−	0.677988i	$-0.762852\pi$
$277$	3.65519	−	6.33097i	0.219619	−	0.380391i	0.954691	+	0.297597i	$0.0961853\pi$
$278$	44.2139			2.65177
$279$		0			0
$280$	−21.9457			−1.31150
$281$	13.0817	−	22.6582i	0.780390	−	1.35168i	−0.151324	−	0.988484i	$-0.548354\pi$
$281$	13.0817	−	22.6582i	0.780390	−	1.35168i	0.931714	−	0.363192i	$-0.118313\pi$
$282$		0			0
$283$	−2.56185	−	4.43725i	−0.152286	−	0.263767i	0.779781	−	0.626052i	$-0.215330\pi$
$283$	−2.56185	−	4.43725i	−0.152286	−	0.263767i	−0.932068	+	0.362285i	$0.881997\pi$
$284$	15.3435	+	26.5757i	0.910468	+	1.57698i
$285$		0			0
$286$	1.28506	−	2.22580i	0.0759875	−	0.131614i
$287$	−14.2547			−0.841429
$288$		0			0
$289$	−14.6364			−0.860964
$290$	−1.37737	+	2.38568i	−0.0808820	+	0.140092i
$291$		0			0
$292$	29.1219	+	50.4406i	1.70423	+	2.95181i
$293$	5.04538	+	8.73886i	0.294755	+	0.510530i	0.974928	−	0.222522i	$-0.0714288\pi$
$293$	5.04538	+	8.73886i	0.294755	+	0.510530i	−0.680173	+	0.733051i	$0.738095\pi$
$294$		0			0
$295$	0.395230	−	0.684558i	0.0230112	−	0.0398565i
$296$	−19.5124			−1.13413
$297$		0			0
$298$	5.95369			0.344888
$299$	0.490886	−	0.850239i	0.0283887	−	0.0491706i
$300$		0			0
$301$	1.97079	+	3.41351i	0.113594	+	0.196751i
$302$	20.5196	+	35.5409i	1.18077	+	2.04515i
$303$		0			0
$304$	−30.8910	+	53.5048i	−1.77172	+	3.06871i
$305$	7.36516			0.421728
$306$		0			0
$307$	14.9405			0.852699			0.426350	−	0.904558i	$-0.359799\pi$
$307$	14.9405			0.852699			0.426350	+	0.904558i	$0.359799\pi$
$308$	6.64537	−	11.5101i	0.378655	−	0.655850i
$309$		0			0
$310$	7.23701	+	12.5349i	0.411035	+	0.711933i
$311$	−3.75769	−	6.50852i	−0.213079	−	0.369064i	0.739597	−	0.673050i	$-0.235016\pi$
$311$	−3.75769	−	6.50852i	−0.213079	−	0.369064i	−0.952677	+	0.303985i	$0.901683\pi$
$312$		0			0
$313$	−3.70826	+	6.42289i	−0.209603	+	0.363043i	−0.951590	−	0.307372i	$-0.900551\pi$
$313$	−3.70826	+	6.42289i	−0.209603	+	0.363043i	0.741986	+	0.670415i	$0.233884\pi$
$314$	−29.4590			−1.66247
$315$		0			0
$316$	58.8641			3.31137
$317$	5.86080	−	10.1512i	0.329175	−	0.570149i	−0.653173	−	0.757209i	$-0.726563\pi$
$317$	5.86080	−	10.1512i	0.329175	−	0.570149i	0.982348	+	0.187060i	$0.0598959\pi$
$318$		0			0
$319$	−0.547189	−	0.947760i	−0.0306367	−	0.0530644i
$320$	19.0586	+	33.0104i	1.06541	+	1.84534i
$321$		0			0
$322$	3.41180	−	5.90941i	0.190132	−	0.329318i
$323$	5.22761			0.290872
$324$		0			0
$325$	−4.31444			−0.239322
$326$	−3.83508	+	6.64255i	−0.212405	+	0.367897i
$327$		0			0
$328$	30.5558	+	52.9242i	1.68716	+	2.92225i
$329$	−6.68245	−	11.5743i	−0.368415	−	0.638114i
$330$		0			0
$331$	1.88362	−	3.26252i	0.103533	−	0.179325i	−0.809605	−	0.586975i	$-0.800319\pi$
$331$	1.88362	−	3.26252i	0.103533	−	0.179325i	0.913138	+	0.407651i	$0.133652\pi$
$332$	13.5172			0.741852
$333$		0			0
$334$	32.6665			1.78743
$335$	−5.43409	+	9.41212i	−0.296896	+	0.514239i
$336$		0			0
$337$	−12.9936	−	22.5056i	−0.707808	−	1.22596i	−0.965669	−	0.259777i	$-0.916351\pi$
$337$	−12.9936	−	22.5056i	−0.707808	−	1.22596i	0.257861	−	0.966182i	$-0.416982\pi$
$338$	1.39763	+	2.42077i	0.0760211	+	0.131672i
$339$		0			0
$340$	3.70014	−	6.40883i	0.200668	−	0.347568i
$341$	−5.75011			−0.311386
$342$		0			0
$343$	19.4380			1.04955
$344$	8.44900	−	14.6341i	0.455539	−	0.789017i
$345$		0			0
$346$	2.70877	+	4.69173i	0.145624	+	0.252229i
$347$	−3.73279	−	6.46538i	−0.200386	−	0.347080i	0.748267	−	0.663398i	$-0.230886\pi$
$347$	−3.73279	−	6.46538i	−0.200386	−	0.347080i	−0.948653	+	0.316319i	$0.897553\pi$
$348$		0			0
$349$	5.63652	−	9.76273i	0.301716	−	0.522587i	−0.674809	−	0.737992i	$-0.735774\pi$
$349$	5.63652	−	9.76273i	0.301716	−	0.522587i	0.976525	+	0.215405i	$0.0691073\pi$
$350$	−29.9866			−1.60285
$351$		0			0
$352$	−27.0961			−1.44423
$353$	10.8052	−	18.7152i	0.575105	−	0.996111i	−0.420925	−	0.907095i	$-0.638294\pi$
$353$	10.8052	−	18.7152i	0.575105	−	0.996111i	0.996030	−	0.0890160i	$-0.0283722\pi$
$354$		0			0
$355$	−2.18530	−	3.78504i	−0.115983	−	0.200889i
$356$	36.5699	+	63.3410i	1.93820	+	3.35707i
$357$		0			0
$358$	−22.8577	+	39.5908i	−1.20807	+	2.09244i
$359$	−27.9681			−1.47610			−0.738050	−	0.674747i	$-0.764253\pi$
$359$	−27.9681			−1.47610			−0.738050	+	0.674747i	$0.764253\pi$
$360$		0			0
$361$	−7.43808			−0.391478
$362$	−20.6805	+	35.8197i	−1.08694	+	1.88264i
$363$		0			0
$364$	7.22748	+	12.5184i	0.378823	+	0.656141i
$365$	−4.14768	−	7.18400i	−0.217100	−	0.376028i
$366$		0			0
$367$	−5.34067	+	9.25031i	−0.278781	+	0.482862i	−0.971082	−	0.238746i	$-0.923264\pi$
$367$	−5.34067	+	9.25031i	−0.278781	+	0.482862i	0.692301	+	0.721609i	$0.256597\pi$
$368$	−17.8385			−0.929896
$369$		0			0
$370$	4.23653			0.220247
$371$	7.24315	−	12.5455i	0.376045	−	0.651330i
$372$		0			0
$373$	7.11158	+	12.3176i	0.368223	+	0.637782i	0.989288	−	0.145978i	$-0.0466328\pi$
$373$	7.11158	+	12.3176i	0.368223	+	0.637782i	−0.621064	+	0.783759i	$0.713299\pi$
$374$	1.97566	+	3.42195i	0.102159	+	0.176945i
$375$		0			0
$376$	−28.6484	+	49.6205i	−1.47743	+	2.55898i
$377$	1.19024			0.0613006
$378$		0			0
$379$	30.2086			1.55171			0.775857	−	0.630909i	$-0.217318\pi$
$379$	30.2086			1.55171			0.775857	+	0.630909i	$0.217318\pi$
$380$	8.18361	−	14.1744i	0.419810	−	0.727133i
$381$		0			0
$382$	−30.8031	−	53.3526i	−1.57603	−	2.72976i
$383$	9.71116	+	16.8202i	0.496217	+	0.859474i	0.999990	−	0.00436238i	$-0.00138859\pi$
$383$	9.71116	+	16.8202i	0.496217	+	0.859474i	−0.503773	+	0.863836i	$0.668055\pi$
$384$		0			0
$385$	−0.946467	+	1.63933i	−0.0482364	+	0.0835480i
$386$	−8.49311			−0.432288
$387$		0			0
$388$	−45.8350			−2.32692
$389$	−1.00577	+	1.74205i	−0.0509947	+	0.0883254i	−0.890396	−	0.455187i	$-0.849572\pi$
$389$	−1.00577	+	1.74205i	−0.0509947	+	0.0883254i	0.839401	+	0.543512i	$0.182906\pi$
$390$		0			0
$391$	0.754690	+	1.30716i	0.0381663	+	0.0661060i
$392$	−4.35744	−	7.54731i	−0.220084	−	0.381197i
$393$		0			0
$394$	33.6102	−	58.2146i	1.69326	−	2.93281i
$395$	−8.38372			−0.421831
$396$		0			0
$397$	20.7184			1.03983			0.519914	−	0.854218i	$-0.325964\pi$
$397$	20.7184			1.03983			0.519914	+	0.854218i	$0.325964\pi$
$398$	−21.2606	+	36.8244i	−1.06570	+	1.84584i
$399$		0			0
$400$	39.1960	+	67.8895i	1.95980	+	3.39447i
$401$	−9.08224	−	15.7309i	−0.453545	−	0.785563i	0.545058	−	0.838398i	$-0.316508\pi$
$401$	−9.08224	−	15.7309i	−0.453545	−	0.785563i	−0.998603	+	0.0528350i	$0.983174\pi$
$402$		0			0
$403$	3.12690	−	5.41594i	0.155762	−	0.269787i
$404$	87.8945			4.37292
$405$		0			0
$406$	8.27252			0.410558
$407$	−0.841526	+	1.45757i	−0.0417129	+	0.0722488i
$408$		0			0
$409$	−16.3177	−	28.2630i	−0.806857	−	1.39752i	−0.915030	−	0.403386i	$-0.867833\pi$
$409$	−16.3177	−	28.2630i	−0.806857	−	1.39752i	0.108173	−	0.994132i	$-0.465500\pi$
$410$	−6.63428	−	11.4909i	−0.327644	−	0.567496i
$411$		0			0
$412$	−13.1312	+	22.7440i	−0.646930	+	1.12052i
$413$	−2.37376			−0.116805
$414$		0			0
$415$	−1.92518			−0.0945036
$416$	14.7348	−	25.5214i	0.722434	−	1.25129i
$417$		0			0
$418$	4.36958	+	7.56834i	0.213723	+	0.370180i
$419$	−13.5292	−	23.4333i	−0.660945	−	1.14479i	−0.980368	−	0.197178i	$-0.936822\pi$
$419$	−13.5292	−	23.4333i	−0.660945	−	1.14479i	0.319423	−	0.947612i	$-0.396511\pi$
$420$		0			0
$421$	−13.3903	+	23.1927i	−0.652603	+	1.13034i	0.329886	+	0.944021i	$0.392990\pi$
$421$	−13.3903	+	23.1927i	−0.652603	+	1.13034i	−0.982489	+	0.186321i	$0.940343\pi$
$422$	3.90022			0.189860
$423$		0			0
$424$	−62.1044			−3.01606
$425$	3.31652	−	5.74438i	0.160875	−	0.278643i
$426$		0			0
$427$	−11.0588	−	19.1545i	−0.535174	−	0.926949i
$428$	53.7865	+	93.1609i	2.59987	+	4.50310i
$429$		0			0
$430$	−1.83445	+	3.17736i	−0.0884650	+	0.153226i
$431$	37.3204			1.79766			0.898830	−	0.438297i	$-0.144418\pi$
$431$	37.3204			1.79766			0.898830	+	0.438297i	$0.144418\pi$
$432$		0			0
$433$	4.67900			0.224859			0.112429	−	0.993660i	$-0.464137\pi$
$433$	4.67900			0.224859			0.112429	+	0.993660i	$0.464137\pi$
$434$	21.7328	−	37.6424i	1.04321	−	1.80689i
$435$		0			0
$436$	−23.1321	−	40.0660i	−1.10783	−	1.91881i
$437$	1.66915	+	2.89105i	0.0798463	+	0.138298i
$438$		0			0
$439$	10.1656	−	17.6074i	0.485179	−	0.840355i	−0.514676	−	0.857385i	$-0.672088\pi$
$439$	10.1656	−	17.6074i	0.485179	−	0.840355i	0.999855	+	0.0170298i	$0.00542101\pi$
$440$	8.11523			0.386878
$441$		0			0
$442$	−4.29745			−0.204409
$443$	0.274181	−	0.474896i	0.0130267	−	0.0225630i	−0.859439	−	0.511239i	$-0.829187\pi$
$443$	0.274181	−	0.474896i	0.0130267	−	0.0225630i	0.872465	+	0.488676i	$0.162520\pi$
$444$		0			0
$445$	−5.20847	−	9.02134i	−0.246905	−	0.427653i
$446$	3.27306	+	5.66910i	0.154984	+	0.268440i
$447$		0			0
$448$	57.2331	−	99.1307i	2.70401	−	4.68348i
$449$	15.7113			0.741460			0.370730	−	0.928741i	$-0.379107\pi$
$449$	15.7113			0.741460			0.370730	+	0.928741i	$0.379107\pi$
$450$		0			0
$451$	5.27121			0.248212
$452$	36.0626	−	62.4622i	1.69624	−	2.93797i
$453$		0			0
$454$	10.8100	+	18.7235i	0.507338	+	0.878736i
$455$	−1.02937	−	1.78293i	−0.0482578	−	0.0835850i
$456$		0			0
$457$	−15.7053	+	27.2023i	−0.734662	+	1.27247i	0.220210	+	0.975453i	$0.429326\pi$
$457$	−15.7053	+	27.2023i	−0.734662	+	1.27247i	−0.954872	+	0.297019i	$0.904007\pi$
$458$	−42.8120			−2.00047
$459$		0			0
$460$	4.72575			0.220339
$461$	16.5562	−	28.6761i	0.771098	−	1.33558i	−0.165864	−	0.986149i	$-0.553041\pi$
$461$	16.5562	−	28.6761i	0.771098	−	1.33558i	0.936962	−	0.349432i	$-0.113625\pi$
$462$		0			0
$463$	8.88057	+	15.3816i	0.412715	+	0.714844i	0.995186	−	0.0980083i	$-0.0312472\pi$
$463$	8.88057	+	15.3816i	0.412715	+	0.714844i	−0.582470	+	0.812852i	$0.697914\pi$
$464$	−10.8132	−	18.7289i	−0.501988	−	0.869469i
$465$		0			0
$466$	−5.33334	+	9.23761i	−0.247062	+	0.427924i
$467$	−25.7033			−1.18941			−0.594704	−	0.803945i	$-0.702731\pi$
$467$	−25.7033			−1.18941			−0.594704	+	0.803945i	$0.702731\pi$
$468$		0			0
$469$	32.6373			1.50705
$470$	6.22015	−	10.7736i	0.286914	−	0.496950i
$471$		0			0
$472$	5.08829	+	8.81317i	0.234207	+	0.405659i
$473$	−0.728773	−	1.26227i	−0.0335090	−	0.0580393i
$474$		0			0
$475$	7.33515	−	12.7049i	0.336560	−	0.582939i
$476$	−22.2231			−1.01860
$477$		0			0
$478$	−29.8298			−1.36438
$479$	−9.29581	+	16.1008i	−0.424736	+	0.735665i	−0.996396	−	0.0848262i	$-0.972967\pi$
$479$	−9.29581	+	16.1008i	−0.424736	+	0.735665i	0.571659	+	0.820491i	$0.306300\pi$
$480$		0			0
$481$	−0.915240	−	1.58524i	−0.0417313	−	0.0722808i
$482$	1.67842	+	2.90711i	0.0764499	+	0.132415i
$483$		0			0
$484$	29.5168	−	51.1246i	1.34167	−	2.32385i
$485$	6.52804			0.296423
$486$		0			0
$487$	27.7070			1.25552			0.627761	−	0.778406i	$-0.283972\pi$
$487$	27.7070			1.25552			0.627761	+	0.778406i	$0.283972\pi$
$488$	−47.4105	+	82.1173i	−2.14617	+	3.71728i
$489$		0			0
$490$	0.946090	+	1.63868i	0.0427400	+	0.0740278i
$491$	8.97484	+	15.5449i	0.405029	+	0.701531i	0.994325	−	0.106386i	$-0.0339281\pi$
$491$	8.97484	+	15.5449i	0.405029	+	0.701531i	−0.589296	+	0.807917i	$0.700595\pi$
$492$		0			0
$493$	−0.914942	+	1.58473i	−0.0412069	+	0.0713724i
$494$	−9.50468			−0.427636
$495$		0			0
$496$	−113.629			−5.10211
$497$	−6.56247	+	11.3665i	−0.294367	+	0.509858i
$498$		0			0
$499$	12.1591	+	21.0601i	0.544315	+	0.942781i	0.998650	+	0.0519502i	$0.0165437\pi$
$499$	12.1591	+	21.0601i	0.544315	+	0.942781i	−0.454335	+	0.890831i	$0.650123\pi$
$500$	−22.4175	−	38.8282i	−1.00254	−	1.73645i
$501$		0			0
$502$	−21.8605	+	37.8636i	−0.975684	+	1.68993i
$503$	39.1695			1.74648			0.873240	−	0.487291i	$-0.162015\pi$
$503$	39.1695			1.74648			0.873240	+	0.487291i	$0.162015\pi$
$504$		0			0
$505$	−12.5184			−0.557060
$506$	−1.26164	+	2.18522i	−0.0560867	+	0.0971451i
$507$		0			0
$508$	26.9967	+	46.7597i	1.19779	+	2.07463i
$509$	−14.9084	−	25.8221i	−0.660803	−	1.14454i	−0.980405	−	0.196993i	$-0.936883\pi$
$509$	−14.9084	−	25.8221i	−0.660803	−	1.14454i	0.319602	−	0.947552i	$-0.396451\pi$
$510$		0			0
$511$	−12.4555	+	21.5736i	−0.551001	+	0.954362i
$512$	−148.087			−6.54458
$513$		0			0
$514$	−43.7807			−1.93108
$515$	1.87022	−	3.23931i	0.0824116	−	0.142741i
$516$		0			0
$517$	2.47108	+	4.28004i	0.108678	+	0.188236i
$518$	−6.36118	−	11.0179i	−0.279494	−	0.484098i
$519$		0			0
$520$	−4.41304	+	7.64362i	−0.193525	+	0.335195i
$521$	−33.7507			−1.47864			−0.739322	−	0.673352i	$-0.764854\pi$
$521$	−33.7507			−1.47864			−0.739322	+	0.673352i	$0.764854\pi$
$522$		0			0
$523$	−39.8074			−1.74065			−0.870327	−	0.492474i	$-0.836093\pi$
$523$	−39.8074			−1.74065			−0.870327	+	0.492474i	$0.836093\pi$
$524$	41.6144	−	72.0783i	1.81793	−	3.14876i
$525$		0			0
$526$	2.27265	+	3.93635i	0.0990923	+	0.171633i
$527$	4.80731	+	8.32650i	0.209410	+	0.362708i
$528$		0			0
$529$	11.0181	−	19.0838i	0.479046	−	0.829732i
$530$	13.4841			0.585713
$531$		0			0
$532$	−49.1510			−2.13096
$533$	−2.86647	+	4.96488i	−0.124161	+	0.215053i
$534$		0			0
$535$	−7.66054	−	13.2684i	−0.331194	−	0.573645i
$536$	−69.9598	−	121.174i	−3.02180	−	5.23392i
$537$		0			0
$538$	26.3989	−	45.7243i	1.13814	−	1.97131i
$539$	−0.751708			−0.0323783
$540$		0			0
$541$	16.4801			0.708533			0.354267	−	0.935144i	$-0.384731\pi$
$541$	16.4801			0.708533			0.354267	+	0.935144i	$0.384731\pi$
$542$	−14.3104	+	24.7863i	−0.614684	+	1.06466i
$543$		0			0
$544$	22.6534	+	39.2368i	0.971255	+	1.68226i
$545$	3.29459	+	5.70640i	0.141125	+	0.244435i
$546$		0			0
$547$	−16.0035	+	27.7189i	−0.684262	+	1.18518i	0.289406	+	0.957206i	$0.406542\pi$
$547$	−16.0035	+	27.7189i	−0.684262	+	1.18518i	−0.973668	+	0.227970i	$0.926791\pi$
$548$	−74.0870			−3.16484
$549$		0			0
$550$	11.0887			0.472822
$551$	−2.02358	+	3.50494i	−0.0862074	+	0.149316i
$552$		0			0
$553$	12.5882	+	21.8034i	0.535305	+	0.927175i
$554$	−10.2172	−	17.6967i	−0.434088	−	0.751862i
$555$		0			0
$556$	45.9773	−	79.6350i	1.94987	−	3.37728i
$557$	−1.65300			−0.0700397			−0.0350198	−	0.999387i	$-0.511149\pi$
$557$	−1.65300			−0.0700397			−0.0350198	+	0.999387i	$0.511149\pi$
$558$		0			0
$559$	1.58522			0.0670477
$560$	−18.7034	+	32.3953i	−0.790363	+	1.36895i
$561$		0			0
$562$	−36.5669	−	63.3357i	−1.54248	−	2.67165i
$563$	15.6527	+	27.1113i	0.659682	+	1.14260i	0.980698	+	0.195529i	$0.0626425\pi$
$563$	15.6527	+	27.1113i	0.659682	+	1.14260i	−0.321016	+	0.947074i	$0.604024\pi$
$564$		0			0
$565$	−5.13621	+	8.89618i	−0.216082	+	0.374265i
$566$	−14.3221			−0.602002
$567$		0			0
$568$	56.2681			2.36096
$569$	−21.8313	+	37.8130i	−0.915217	+	1.58520i	−0.108634	+	0.994082i	$0.534648\pi$
$569$	−21.8313	+	37.8130i	−0.915217	+	1.58520i	−0.806583	+	0.591121i	$0.798686\pi$
$570$		0			0
$571$	0.330617	+	0.572646i	0.0138359	+	0.0239645i	0.872860	−	0.487970i	$-0.162262\pi$
$571$	0.330617	+	0.572646i	0.0138359	+	0.0239645i	−0.859025	+	0.511934i	$0.828929\pi$
$572$	−2.67263	−	4.62914i	−0.111748	−	0.193554i
$573$		0			0
$574$	−19.9228	+	34.5073i	−0.831562	+	1.44031i
$575$	4.23579			0.176645
$576$		0			0
$577$	−26.6761			−1.11054			−0.555270	−	0.831670i	$-0.687385\pi$
$577$	−26.6761			−1.11054			−0.555270	+	0.831670i	$0.687385\pi$
$578$	−20.4563	+	35.4313i	−0.850869	+	1.47375i
$579$		0			0
$580$	2.86461	+	4.96165i	0.118946	+	0.206021i
$581$	2.89068	+	5.00680i	0.119925	+	0.207717i
$582$		0			0
$583$	−2.67843	+	4.63917i	−0.110929	+	0.192135i
$584$	106.797			4.41928
$585$		0			0
$586$	28.2063			1.16519
$587$	−0.954026	+	1.65242i	−0.0393769	+	0.0682028i	−0.885042	−	0.465511i	$-0.845871\pi$
$587$	−0.954026	+	1.65242i	−0.0393769	+	0.0682028i	0.845665	+	0.533714i	$0.179204\pi$
$588$		0			0
$589$	10.6323	+	18.4157i	0.438098	+	0.758807i
$590$	−1.10477	−	1.91352i	−0.0454827	−	0.0787783i
$591$		0			0
$592$	−16.6296	+	28.8034i	−0.683473	+	1.18381i
$593$	15.0838			0.619419			0.309710	−	0.950831i	$-0.399768\pi$
$593$	15.0838			0.619419			0.309710	+	0.950831i	$0.399768\pi$
$594$		0			0
$595$	3.16513			0.129758
$596$	6.19114	−	10.7234i	0.253599	−	0.439246i
$597$		0			0
$598$	−1.37215	−	2.37664i	−0.0561116	−	0.0971881i
$599$	−0.823973	−	1.42716i	−0.0336666	−	0.0583123i	0.848701	−	0.528873i	$-0.177385\pi$
$599$	−0.823973	−	1.42716i	−0.0336666	−	0.0583123i	−0.882368	+	0.470560i	$0.844052\pi$
$600$		0			0
$601$	−4.91508	+	8.51316i	−0.200490	+	0.347259i	−0.948686	−	0.316218i	$-0.897587\pi$
$601$	−4.91508	+	8.51316i	−0.200490	+	0.347259i	0.748196	+	0.663477i	$0.230920\pi$
$602$	11.0177			0.449050
$603$		0			0
$604$	85.3517			3.47291
$605$	−4.20393	+	7.28143i	−0.170914	+	0.296032i
$606$		0			0
$607$	−3.81004	−	6.59918i	−0.154645	−	0.267852i	0.778285	−	0.627911i	$-0.216090\pi$
$607$	−3.81004	−	6.59918i	−0.154645	−	0.267852i	−0.932930	+	0.360059i	$0.882757\pi$
$608$	50.1025	+	86.7801i	2.03193	+	3.51940i
$609$		0			0
$610$	10.2938	−	17.8293i	0.416783	−	0.721889i
$611$	−5.37508			−0.217453
$612$		0			0
$613$	20.7592			0.838458			0.419229	−	0.907881i	$-0.362300\pi$
$613$	20.7592			0.838458			0.419229	+	0.907881i	$0.362300\pi$
$614$	20.8813	−	36.1675i	0.842701	−	1.45960i
$615$		0			0
$616$	−12.1851	−	21.1051i	−0.490950	−	0.850350i
$617$	−10.0058	−	17.3306i	−0.402819	−	0.697702i	0.591246	−	0.806491i	$-0.298636\pi$
$617$	−10.0058	−	17.3306i	−0.402819	−	0.697702i	−0.994065	+	0.108789i	$0.965303\pi$
$618$		0			0
$619$	6.38297	−	11.0556i	0.256553	−	0.444363i	−0.708763	−	0.705447i	$-0.750746\pi$
$619$	6.38297	−	11.0556i	0.256553	−	0.444363i	0.965316	+	0.261083i	$0.0840798\pi$
$620$	30.1026			1.20895
$621$		0			0
$622$	−21.0075			−0.842323
$623$	−15.6411	+	27.0912i	−0.626648	+	1.08539i
$624$		0			0
$625$	−7.59329	−	13.1520i	−0.303731	−	0.526078i
$626$	10.3656	+	17.9537i	0.414291	+	0.717573i
$627$		0			0
$628$	−30.6339	+	53.0595i	−1.22243	+	2.11731i
$629$	2.81419			0.112209
$630$		0			0
$631$	−41.7922			−1.66372			−0.831860	−	0.554985i	$-0.812724\pi$
$631$	−41.7922			−1.66372			−0.831860	+	0.554985i	$0.812724\pi$
$632$	53.9671	−	93.4737i	2.14669	−	3.71818i
$633$		0			0
$634$	−16.3825	−	28.3753i	−0.650631	−	1.12693i
$635$	−3.84501	−	6.65975i	−0.152585	−	0.264284i
$636$		0			0
$637$	0.408777	−	0.708023i	0.0161963	−	0.0280529i
$638$	−3.05907			−0.121110
$639$		0			0
$640$	57.7465			2.28263
$641$	−17.5062	+	30.3216i	−0.691452	+	1.19763i	0.279910	+	0.960026i	$0.409695\pi$
$641$	−17.5062	+	30.3216i	−0.691452	+	1.19763i	−0.971362	+	0.237604i	$0.923638\pi$
$642$		0			0
$643$	−4.63898	−	8.03495i	−0.182944	−	0.316868i	0.759938	−	0.649996i	$-0.225229\pi$
$643$	−4.63898	−	8.03495i	−0.182944	−	0.316868i	−0.942882	+	0.333128i	$0.891896\pi$
$644$	−7.09574	−	12.2902i	−0.279611	−	0.484301i
$645$		0			0
$646$	7.30627	−	12.6548i	0.287461	−	0.497898i
$647$	17.1133			0.672794			0.336397	−	0.941720i	$-0.390792\pi$
$647$	17.1133			0.672794			0.336397	+	0.941720i	$0.390792\pi$
$648$		0			0
$649$	0.877786			0.0344561
$650$	−6.02999	+	10.4443i	−0.236516	+	0.409657i
$651$		0			0
$652$	7.97606	+	13.8149i	0.312367	+	0.541035i
$653$	22.1978	+	38.4478i	0.868668	+	1.50458i	0.863358	+	0.504592i	$0.168357\pi$
$653$	22.1978	+	38.4478i	0.868668	+	1.50458i	0.00531024	+	0.999986i	$0.498310\pi$
$654$		0			0
$655$	−5.92693	+	10.2658i	−0.231584	+	0.401116i
$656$	104.166			4.06699
$657$		0			0
$658$	−37.3584			−1.45638
$659$	8.11972	−	14.0638i	0.316299	−	0.547846i	−0.663414	−	0.748253i	$-0.730893\pi$
$659$	8.11972	−	14.0638i	0.316299	−	0.547846i	0.979713	+	0.200407i	$0.0642263\pi$
$660$		0			0
$661$	−13.3405	−	23.1063i	−0.518883	−	0.898732i	−0.999759	−	0.0219437i	$-0.993015\pi$
$661$	−13.3405	−	23.1063i	−0.518883	−	0.898732i	0.480876	−	0.876789i	$-0.340319\pi$
$662$	−5.26521	−	9.11961i	−0.204638	−	0.354444i
$663$		0			0
$664$	12.3927	−	21.4647i	0.480928	−	0.832992i
$665$	7.00033			0.271461
$666$		0			0
$667$	−1.16855			−0.0452463
$668$	33.9693	−	58.8366i	1.31431	−	2.27646i
$669$		0			0
$670$	15.1897	+	26.3093i	0.586829	+	1.01642i
$671$	4.08942	+	7.08308i	0.157870	+	0.273439i
$672$		0			0
$673$	−9.68028	+	16.7667i	−0.373147	+	0.646310i	−0.990048	−	0.140731i	$-0.955055\pi$
$673$	−9.68028	+	16.7667i	−0.373147	+	0.646310i	0.616901	+	0.787041i	$0.288388\pi$
$674$	−72.6412			−2.79803
$675$		0			0
$676$	5.81349			0.223596
$677$	−8.22920	+	14.2534i	−0.316274	+	0.547802i	−0.979707	−	0.200433i	$-0.935765\pi$
$677$	−8.22920	+	14.2534i	−0.316274	+	0.547802i	0.663434	+	0.748235i	$0.269098\pi$
$678$		0			0
$679$	−9.80190	−	16.9774i	−0.376162	−	0.651532i
$680$	−6.78464	−	11.7513i	−0.260179	−	0.450643i
$681$		0			0
$682$	−8.03653	+	13.9197i	−0.307735	+	0.533012i
$683$	−14.3927			−0.550720			−0.275360	−	0.961341i	$-0.588797\pi$
$683$	−14.3927			−0.550720			−0.275360	+	0.961341i	$0.588797\pi$
$684$		0			0
$685$	10.5518			0.403165
$686$	27.1671	−	47.0548i	1.03725	−	1.79656i
$687$		0			0
$688$	−14.4015	−	24.9441i	−0.549052	−	0.950985i
$689$	−2.91304	−	5.04554i	−0.110978	−	0.192220i
$690$		0			0
$691$	−3.02997	+	5.24806i	−0.115266	+	0.199646i	−0.917886	−	0.396844i	$-0.870105\pi$
$691$	−3.02997	+	5.24806i	−0.115266	+	0.199646i	0.802620	+	0.596490i	$0.203439\pi$
$692$	11.2672			0.428315
$693$		0			0
$694$	−20.8682			−0.792147
$695$	−6.54832	+	11.3420i	−0.248392	+	0.430227i
$696$		0			0
$697$	−4.40693	−	7.63303i	−0.166924	−	0.289122i
$698$	−15.7555	−	27.2894i	−0.596356	−	1.03292i
$699$		0			0
$700$	−31.1825	+	54.0097i	−1.17859	+	2.04138i
$701$	25.7892			0.974045			0.487023	−	0.873389i	$-0.338083\pi$
$701$	25.7892			0.974045			0.487023	+	0.873389i	$0.338083\pi$
$702$		0			0
$703$	6.22415			0.234748
$704$	−21.1641	+	36.6573i	−0.797652	+	1.38157i
$705$		0			0
$706$	−30.2035	−	52.3140i	−1.13672	−	1.96886i
$707$	18.7964	+	32.5563i	0.706912	+	1.22441i
$708$		0			0
$709$	23.3481	−	40.4402i	0.876858	−	1.51876i	0.0220870	−	0.999756i	$-0.492969\pi$
$709$	23.3481	−	40.4402i	0.876858	−	1.51876i	0.854771	−	0.519006i	$-0.173698\pi$
$710$	−12.2169			−0.458494
$711$		0			0
$712$	134.110			5.02600
$713$	−3.06990	+	5.31722i	−0.114969	+	0.199132i
$714$		0			0
$715$	0.380650	+	0.659305i	0.0142355	+	0.0246566i
$716$	47.5387	+	82.3395i	1.77661	+	3.07717i
$717$		0			0
$718$	−39.0891	+	67.7042i	−1.45879	+	2.52670i
$719$	−45.7593			−1.70654			−0.853268	−	0.521473i	$-0.825383\pi$
$719$	−45.7593			−1.70654			−0.853268	+	0.521473i	$0.825383\pi$
$720$		0			0
$721$	−11.2326			−0.418323
$722$	−10.3957	+	18.0059i	−0.386888	+	0.670109i
$723$		0			0
$724$	43.0106	+	74.4966i	1.59848	+	2.76864i
$725$	2.56761	+	4.44724i	0.0953587	+	0.165166i
$726$		0			0
$727$	−2.81788	+	4.88071i	−0.104509	+	0.181016i	−0.913538	−	0.406754i	$-0.866661\pi$
$727$	−2.81788	+	4.88071i	−0.104509	+	0.181016i	0.809028	+	0.587770i	$0.199994\pi$
$728$	26.5048			0.982335
$729$		0			0
$730$	−23.1877			−0.858216
$731$	−1.21856	+	2.11061i	−0.0450702	+	0.0780639i
$732$		0			0
$733$	20.1805	+	34.9536i	0.745383	+	1.29104i	0.950016	+	0.312202i	$0.101067\pi$
$733$	20.1805	+	34.9536i	0.745383	+	1.29104i	−0.204633	+	0.978839i	$0.565600\pi$
$734$	14.9286	+	25.8570i	0.551024	+	0.954401i
$735$		0			0
$736$	−14.4662	+	25.0562i	−0.533232	+	0.923585i
$737$	−12.0688			−0.444562
$738$		0			0
$739$	−22.9326			−0.843590			−0.421795	−	0.906691i	$-0.638600\pi$
$739$	−22.9326			−0.843590			−0.421795	+	0.906691i	$0.638600\pi$
$740$	4.40550	−	7.63055i	0.161949	−	0.280504i
$741$		0			0
$742$	−20.2465	−	35.0680i	−0.743272	−	1.28739i
$743$	2.76237	+	4.78457i	0.101342	+	0.175529i	0.912238	−	0.409661i	$-0.134353\pi$
$743$	2.76237	+	4.78457i	0.101342	+	0.175529i	−0.810896	+	0.585190i	$0.801020\pi$
$744$		0			0
$745$	−0.881773	+	1.52728i	−0.0323057	+	0.0559551i
$746$	39.7574			1.45562
$747$		0			0
$748$	8.21784			0.300474
$749$	−23.0047	+	39.8453i	−0.840573	+	1.45591i
$750$		0			0
$751$	11.4040	+	19.7523i	0.416139	+	0.720773i	0.995547	−	0.0942640i	$-0.0300498\pi$
$751$	11.4040	+	19.7523i	0.416139	+	0.720773i	−0.579409	+	0.815037i	$0.696716\pi$
$752$	48.8318	+	84.5792i	1.78071	+	3.08428i
$753$		0			0
$754$	1.66352	−	2.88130i	0.0605818	−	0.104931i
$755$	−12.1562			−0.442410
$756$		0			0
$757$	−0.0394090			−0.00143235			−0.000716173	−	1.00000i	$-0.500228\pi$
$757$	−0.0394090			−0.00143235			−0.000716173		1.00000i	$0.500228\pi$
$758$	42.2205	−	73.1281i	1.53352	−	2.65613i
$759$		0			0
$760$	−15.0056	−	25.9905i	−0.544310	−	0.942773i
$761$	6.41693	+	11.1145i	0.232614	+	0.402899i	0.958576	−	0.284835i	$-0.0919389\pi$
$761$	6.41693	+	11.1145i	0.232614	+	0.402899i	−0.725963	+	0.687734i	$0.758606\pi$
$762$		0			0
$763$	9.89370	−	17.1364i	0.358176	−	0.620379i
$764$	−128.127			−4.63546
$765$		0			0
$766$	54.2905			1.96160
$767$	−0.477338	+	0.826774i	−0.0172357	+	0.0298531i
$768$		0			0
$769$	−0.424306	−	0.734919i	−0.0153009	−	0.0265019i	0.858274	−	0.513192i	$-0.171537\pi$
$769$	−0.424306	−	0.734919i	−0.0153009	−	0.0265019i	−0.873574	+	0.486691i	$0.838204\pi$
$770$	2.64562	+	4.58236i	0.0953417	+	0.165137i
$771$		0			0
$772$	−8.83184	+	15.2972i	−0.317865	+	0.550558i
$773$	36.0339			1.29605			0.648024	−	0.761620i	$-0.275595\pi$
$773$	36.0339			1.29605			0.648024	+	0.761620i	$0.275595\pi$
$774$		0			0
$775$	26.9816			0.969208
$776$	−42.0218	+	72.7840i	−1.50850	+	2.61279i
$777$		0			0
$778$	2.81140	+	4.86948i	0.100793	+	0.174579i
$779$	−9.74682	−	16.8820i	−0.349216	−	0.604860i
$780$		0			0
$781$	2.42672	−	4.20320i	0.0868348	−	0.150402i
$782$	4.21911			0.150875
$783$		0			0
$784$	−14.8547			−0.530525
$785$	4.36304	−	7.55700i	0.155723	−	0.269721i
$786$		0			0
$787$	8.83804	+	15.3079i	0.315042	+	0.545669i	0.979446	−	0.201704i	$-0.0646480\pi$
$787$	8.83804	+	15.3079i	0.315042	+	0.545669i	−0.664404	+	0.747373i	$0.731315\pi$
$788$	−69.9014	−	121.073i	−2.49013	−	4.31304i
$789$		0			0
$790$	−11.7173	+	20.2950i	−0.416885	+	0.722065i
$791$	30.8482			1.09684
$792$		0			0
$793$	−8.89527			−0.315880
$794$	28.9567	−	50.1545i	1.02764	−	1.77992i
$795$		0			0
$796$	44.2170	+	76.5862i	1.56723	+	2.71452i
$797$	−13.3001	−	23.0365i	−0.471114	−	0.815993i	0.528340	−	0.849033i	$-0.322815\pi$
$797$	−13.3001	−	23.0365i	−0.471114	−	0.815993i	−0.999454	+	0.0330394i	$0.989481\pi$
$798$		0			0
$799$	4.13184	−	7.15656i	0.146174	−	0.253181i
$800$	127.145			4.49525
$801$		0			0
$802$	−50.7745			−1.79291
$803$	4.60590	−	7.97766i	0.162539	−	0.281526i
$804$		0			0
$805$	1.01061	+	1.75043i	0.0356193	+	0.0616945i
$806$	−8.74050	−	15.1390i	−0.307871	−	0.533248i
$807$		0			0
$808$	80.5824	−	139.573i	2.83488	−	4.91015i
$809$	11.8241			0.415713			0.207857	−	0.978159i	$-0.433351\pi$
$809$	11.8241			0.415713			0.207857	+	0.978159i	$0.433351\pi$
$810$		0			0
$811$	−23.5042			−0.825345			−0.412673	−	0.910879i	$-0.635405\pi$
$811$	−23.5042			−0.825345			−0.412673	+	0.910879i	$0.635405\pi$
$812$	8.60245	−	14.8999i	0.301887	−	0.522883i
$813$		0			0
$814$	2.35228	+	4.07428i	0.0824475	+	0.142803i
$815$	−1.13599	−	1.96759i	−0.0397920	−	0.0689218i
$816$		0			0
$817$	−2.69510	+	4.66805i	−0.0942896	+	0.163314i
$818$	−91.2244			−3.18959
$819$		0			0
$820$	−27.5955			−0.963676
$821$	−21.9801	+	38.0706i	−0.767111	+	1.32867i	0.172013	+	0.985095i	$0.444973\pi$
$821$	−21.9801	+	38.0706i	−0.767111	+	1.32867i	−0.939123	+	0.343580i	$0.888360\pi$
$822$		0			0
$823$	16.0977	+	27.8820i	0.561130	+	0.971906i	0.997398	+	0.0720892i	$0.0229666\pi$
$823$	16.0977	+	27.8820i	0.561130	+	0.971906i	−0.436268	+	0.899817i	$0.643700\pi$
$824$	24.0777	+	41.7037i	0.838785	+	1.45282i
$825$		0			0
$826$	−3.31764	+	5.74632i	−0.115435	+	0.199940i
$827$	−10.2409			−0.356112			−0.178056	−	0.984020i	$-0.556981\pi$
$827$	−10.2409			−0.356112			−0.178056	+	0.984020i	$0.556981\pi$
$828$		0			0
$829$	−30.1853			−1.04838			−0.524189	−	0.851602i	$-0.675631\pi$
$829$	−30.1853			−1.04838			−0.524189	+	0.851602i	$0.675631\pi$
$830$	−2.69070	+	4.66043i	−0.0933955	+	0.161766i
$831$		0			0
$832$	−23.0180	−	39.8683i	−0.798005	−	1.38219i
$833$	0.628456	+	1.08852i	0.0217747	+	0.0377149i
$834$		0			0
$835$	−4.83808	+	8.37981i	−0.167429	+	0.289995i
$836$	18.1754			0.628610
$837$		0			0
$838$	−75.6354			−2.61278
$839$	24.4762	−	42.3940i	0.845011	−	1.46360i	−0.0406006	−	0.999175i	$-0.512927\pi$
$839$	24.4762	−	42.3940i	0.845011	−	1.46360i	0.885612	−	0.464427i	$-0.153740\pi$
$840$		0			0
$841$	13.7917	+	23.8879i	0.475575	+	0.823719i
$842$	37.4294	+	64.8296i	1.28990	+	2.23418i
$843$		0			0
$844$	4.05577	−	7.02480i	0.139605	−	0.241803i
$845$	−0.827986			−0.0284836
$846$		0			0
$847$	25.2489			0.867563
$848$	−52.9291	+	91.6759i	−1.81759	+	3.14816i
$849$		0			0
$850$	−9.27054	−	16.0570i	−0.317977	−	0.550752i
$851$	0.898557	+	1.55635i	0.0308021	+	0.0533509i
$852$		0			0
$853$	−1.11612	+	1.93317i	−0.0382151	+	0.0661904i	−0.884500	−	0.466540i	$-0.845501\pi$
$853$	−1.11612	+	1.93317i	−0.0382151	+	0.0661904i	0.846285	+	0.532730i	$0.178834\pi$
$854$	−61.8247			−2.11560
$855$		0			0
$856$	197.247			6.74178
$857$	−15.4333	+	26.7312i	−0.527191	+	0.913121i	0.472307	+	0.881434i	$0.343421\pi$
$857$	−15.4333	+	26.7312i	−0.527191	+	0.913121i	−0.999498	+	0.0316870i	$0.989912\pi$
$858$		0			0
$859$	−15.0620	−	26.0881i	−0.513908	−	0.890115i	−0.999870	−	0.0161347i	$-0.994864\pi$
$859$	−15.0620	−	26.0881i	−0.513908	−	0.890115i	0.485962	−	0.873980i	$-0.338469\pi$
$860$	3.81522	+	6.60816i	0.130098	+	0.225336i
$861$		0			0
$862$	52.1602	−	90.3440i	1.77658	−	3.07713i
$863$	4.66893			0.158932			0.0794661	−	0.996838i	$-0.474678\pi$
$863$	4.66893			0.158932			0.0794661	+	0.996838i	$0.474678\pi$
$864$		0			0
$865$	−1.60473			−0.0545626
$866$	6.53952	−	11.3268i	0.222222	−	0.384900i
$867$		0			0
$868$	−45.1992	−	78.2873i	−1.53416	−	2.65724i
$869$	−4.65496	−	8.06263i	−0.157909	−	0.273506i
$870$		0			0
$871$	6.56302	−	11.3675i	0.222379	−	0.385172i
$872$	−84.8308			−2.87273
$873$		0			0
$874$	9.33143			0.315640
$875$	9.58804	−	16.6070i	0.324135	−	0.561418i
$876$		0			0
$877$	−8.23844	−	14.2694i	−0.278192	−	0.481843i	0.692743	−	0.721184i	$-0.256402\pi$
$877$	−8.23844	−	14.2694i	−0.278192	−	0.481843i	−0.970936	+	0.239341i	$0.923069\pi$
$878$	−28.4156	−	49.2173i	−0.958981	−	1.66100i
$879$		0			0
$880$	6.91629	−	11.9794i	0.233148	−	0.403824i
$881$	−33.5567			−1.13055			−0.565276	−	0.824902i	$-0.691230\pi$
$881$	−33.5567			−1.13055			−0.565276	+	0.824902i	$0.691230\pi$
$882$		0			0
$883$	34.2126			1.15135			0.575673	−	0.817680i	$-0.304740\pi$
$883$	34.2126			1.15135			0.575673	+	0.817680i	$0.304740\pi$
$884$	−4.46884	+	7.74026i	−0.150303	+	0.260333i
$885$		0			0
$886$	−0.766408	−	1.32746i	−0.0257480	−	0.0445968i
$887$	−6.93269	−	12.0078i	−0.232777	−	0.403181i	0.725847	−	0.687856i	$-0.241448\pi$
$887$	−6.93269	−	12.0078i	−0.232777	−	0.403181i	−0.958624	+	0.284674i	$0.908114\pi$
$888$		0			0
$889$	−11.5466	+	19.9993i	−0.387261	+	0.670755i
$890$	−29.1181			−0.976041
$891$		0			0
$892$	13.6144			0.455843
$893$	9.13840	−	15.8282i	0.305805	−	0.529670i
$894$		0			0
$895$	−6.77071	−	11.7272i	−0.226320	−	0.391997i
$896$	−86.7067	−	150.180i	−2.89667	−	5.01718i
$897$		0			0
$898$	21.9585	−	38.0333i	0.732766	−	1.26919i
$899$	−7.44353			−0.248255
$900$		0			0
$901$	8.95706			0.298403
$902$	7.36721	−	12.7604i	0.245301	−	0.424874i
$903$		0			0
$904$	−66.1249	−	114.532i	−2.19928	−	3.80926i
$905$	−6.12578	−	10.6102i	−0.203628	−	0.352694i
$906$		0			0
$907$	−7.85818	+	13.6108i	−0.260927	+	0.451938i	−0.966488	−	0.256710i	$-0.917361\pi$
$907$	−7.85818	+	13.6108i	−0.260927	+	0.451938i	0.705562	+	0.708648i	$0.250695\pi$
$908$	44.9645			1.49220
$909$		0			0
$910$	−5.75474			−0.190768
$911$	13.2464	−	22.9434i	0.438871	−	0.760147i	−0.558732	−	0.829349i	$-0.688712\pi$
$911$	13.2464	−	22.9434i	0.438871	−	0.760147i	0.997603	+	0.0692014i	$0.0220451\pi$
$912$		0			0
$913$	−1.06894	−	1.85145i	−0.0353766	−	0.0612741i
$914$	43.9004	+	76.0377i	1.45210	+	2.51510i
$915$		0			0
$916$	−44.5194	+	77.1099i	−1.47096	+	2.54778i
$917$	35.5973			1.17553
$918$		0			0
$919$	−48.5748			−1.60233			−0.801167	−	0.598440i	$-0.795787\pi$
$919$	−48.5748			−1.60233			−0.801167	+	0.598440i	$0.795787\pi$
$920$	4.33260	−	7.50429i	0.142842	−	0.247409i
$921$		0			0
$922$	−46.2788	−	80.1573i	−1.52411	−	2.63984i
$923$	2.63929	+	4.57138i	0.0868733	+	0.150469i
$924$		0			0
$925$	3.94875	−	6.83943i	0.129834	−	0.224879i
$926$	49.6470			1.63150
$927$		0			0
$928$	−35.0760			−1.15143
$929$	−2.34708	+	4.06526i	−0.0770052	+	0.133377i	−0.901956	−	0.431827i	$-0.857869\pi$
$929$	−2.34708	+	4.06526i	−0.0770052	+	0.133377i	0.824951	+	0.565204i	$0.191202\pi$
$930$		0			0
$931$	1.38996	+	2.40748i	0.0455540	+	0.0789019i
$932$	11.0921	+	19.2121i	0.363334	+	0.629312i
$933$		0			0
$934$	−35.9238	+	62.2218i	−1.17546	+	2.03596i
$935$	−1.17043			−0.0382770
$936$		0			0
$937$	14.2950			0.466998			0.233499	−	0.972357i	$-0.424982\pi$
$937$	14.2950			0.466998			0.233499	+	0.972357i	$0.424982\pi$
$938$	45.6148	−	79.0072i	1.48938	−	2.57968i
$939$		0			0
$940$	−12.9365	−	22.4066i	−0.421941	−	0.730823i
$941$	8.02348	+	13.8971i	0.261558	+	0.453032i	0.966656	−	0.256078i	$-0.0824304\pi$
$941$	8.02348	+	13.8971i	0.261558	+	0.453032i	−0.705098	+	0.709110i	$0.749097\pi$
$942$		0			0
$943$	2.81422	−	4.87438i	0.0916438	−	0.158732i
$944$	17.3462			0.564570
$945$		0			0
$946$	−4.07422			−0.132464
$947$	22.3155	−	38.6516i	0.725156	−	1.25601i	−0.233754	−	0.972296i	$-0.575101\pi$
$947$	22.3155	−	38.6516i	0.725156	−	1.25601i	0.958910	−	0.283711i	$-0.0915657\pi$
$948$		0			0
$949$	5.00936	+	8.67647i	0.162611	+	0.281650i
$950$	−20.5037	−	35.5134i	−0.665227	−	1.15221i
$951$		0			0
$952$	−20.3743	+	35.2894i	−0.660336	+	1.14374i
$953$	−3.70788			−0.120110			−0.0600550	−	0.998195i	$-0.519128\pi$
$953$	−3.70788			−0.120110			−0.0600550	+	0.998195i	$0.519128\pi$
$954$		0			0
$955$	18.2484			0.590505
$956$	−31.0195	+	53.7274i	−1.00324	+	1.73767i
$957$		0			0
$958$	25.9842	+	45.0060i	0.839512	+	1.45408i
$959$	−15.8436	−	27.4420i	−0.511618	−	0.886148i
$960$		0			0
$961$	−4.05496	+	7.02340i	−0.130805	+	0.226561i
$962$	−5.11667			−0.164968
$963$		0			0
$964$	6.98144			0.224857
$965$	1.25787	−	2.17870i	0.0404924	−	0.0701349i
$966$		0			0
$967$	13.5476	+	23.4651i	0.435661	+	0.754587i	0.997349	−	0.0727618i	$-0.0231813\pi$
$967$	13.5476	+	23.4651i	0.435661	+	0.754587i	−0.561688	+	0.827349i	$0.689848\pi$
$968$	−54.1225	−	93.7429i	−1.73956	−	3.01301i
$969$		0			0
$970$	9.12380	−	15.8029i	0.292947	−	0.507400i
$971$	31.9545			1.02547			0.512735	−	0.858547i	$-0.328632\pi$
$971$	31.9545			1.02547			0.512735	+	0.858547i	$0.328632\pi$
$972$		0			0
$973$	39.3293			1.26084
$974$	38.7241	−	67.0721i	1.24080	−	2.14913i
$975$		0			0
$976$	80.8121	+	139.971i	2.58673	+	4.48035i
$977$	−7.78060	−	13.4764i	−0.248924	−	0.431148i	0.714304	−	0.699836i	$-0.246743\pi$
$977$	−7.78060	−	13.4764i	−0.248924	−	0.431148i	−0.963227	+	0.268687i	$0.913410\pi$
$978$		0			0
$979$	5.78388	−	10.0180i	0.184854	−	0.320176i
$980$	3.93529			0.125708
$981$		0			0
$982$	50.1741			1.60112
$983$	−8.57195	+	14.8470i	−0.273403	+	0.473547i	−0.969731	−	0.244176i	$-0.921482\pi$
$983$	−8.57195	+	14.8470i	−0.273403	+	0.473547i	0.696328	+	0.717723i	$0.254816\pi$
$984$		0			0
$985$	9.95570	+	17.2438i	0.317215	+	0.549432i
$986$	2.55750	+	4.42972i	0.0814474	+	0.141071i
$987$		0			0
$988$	−9.88375	+	17.1192i	−0.314444	+	0.544633i
$989$	−1.55633			−0.0494883
$990$		0			0
$991$	25.0309			0.795131			0.397566	−	0.917574i	$-0.369855\pi$
$991$	25.0309			0.795131			0.397566	+	0.917574i	$0.369855\pi$
$992$	−92.1485	+	159.606i	−2.92572	+	5.06749i
$993$		0			0
$994$	18.3438	+	31.7724i	0.581831	+	1.00776i
$995$	−6.29761	−	10.9078i	−0.199648	−	0.345800i
$996$		0			0
$997$	9.17948	−	15.8993i	0.290717	−	0.503537i	−0.683262	−	0.730173i	$-0.739439\pi$
$997$	9.17948	−	15.8993i	0.290717	−	0.503537i	0.973979	+	0.226636i	$0.0727728\pi$
$998$	67.9756			2.15173
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.e.b.235.5		10
3.2	odd	2		117.2.e.b.79.1	yes	10
9.2	odd	6		1053.2.a.k.1.5		5
9.4	even	3	inner	351.2.e.b.118.5		10
9.5	odd	6		117.2.e.b.40.1	✓	10
9.7	even	3		1053.2.a.j.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.e.b.40.1	✓	10	9.5	odd	6
117.2.e.b.79.1	yes	10	3.2	odd	2
351.2.e.b.118.5		10	9.4	even	3	inner
351.2.e.b.235.5		10	1.1	even	1	trivial
1053.2.a.j.1.1		5	9.7	even	3
1053.2.a.k.1.5		5	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.39763 - 2.42077i) q^{2} +(-2.90675 - 5.03463i) q^{4} +(0.413993 + 0.717057i) q^{5} +(1.24323 - 2.15333i) q^{7} -10.6597 q^{8} +2.31444 q^{10} +(-0.459729 + 0.796275i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-3.47514 - 6.01912i) q^{14} +(-9.08484 + 15.7354i) q^{16} +1.53740 q^{17} +3.40028 q^{19} +(2.40675 - 4.16860i) q^{20} +(1.28506 + 2.22580i) q^{22} +(0.490886 + 0.850239i) q^{23} +(2.15722 - 3.73641i) q^{25} -2.79526 q^{26} -14.4550 q^{28} +(-0.595121 + 1.03078i) q^{29} +(3.12690 + 5.41594i) q^{31} +(14.7348 + 25.5214i) q^{32} +(2.14872 - 3.72170i) q^{34} +2.05875 q^{35} +1.83048 q^{37} +(4.75234 - 8.23129i) q^{38} +(-4.41304 - 7.64362i) q^{40} +(-2.86647 - 4.96488i) q^{41} +(-0.792611 + 1.37284i) q^{43} +5.34527 q^{44} +2.74431 q^{46} +(2.68754 - 4.65496i) q^{47} +(0.408777 + 0.708023i) q^{49} +(-6.02999 - 10.4443i) q^{50} +(-2.90675 + 5.03463i) q^{52} +5.82609 q^{53} -0.761299 q^{55} +(-13.2524 + 22.9539i) q^{56} +(1.66352 + 2.88130i) q^{58} +(-0.477338 - 0.826774i) q^{59} +(4.44763 - 7.70353i) q^{61} +17.4810 q^{62} +46.0360 q^{64} +(0.413993 - 0.717057i) q^{65} +(6.56302 + 11.3675i) q^{67} +(-4.46884 - 7.74026i) q^{68} +(2.87737 - 4.98375i) q^{70} -5.27858 q^{71} -10.0187 q^{73} +(2.55834 - 4.43117i) q^{74} +(-9.88375 - 17.1192i) q^{76} +(1.14310 + 1.97990i) q^{77} +(-5.06272 + 8.76888i) q^{79} -15.0443 q^{80} -16.0251 q^{82} +(-1.16257 + 2.01363i) q^{83} +(0.636475 + 1.10241i) q^{85} +(2.21555 + 3.83745i) q^{86} +(4.90058 - 8.48805i) q^{88} -12.5811 q^{89} -2.48645 q^{91} +(2.85376 - 4.94286i) q^{92} +(-7.51238 - 13.0118i) q^{94} +(1.40769 + 2.43820i) q^{95} +(3.94212 - 6.82795i) q^{97} +2.28528 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 4 q^{4} + q^{5} + 2 q^{7} - 24 q^{8} - 4 q^{10} + 11 q^{11} - 5 q^{13} - 5 q^{14} - 10 q^{16} - 14 q^{17} + 6 q^{19} - q^{20} + 7 q^{22} + 18 q^{23} + 8 q^{25} - 4 q^{26} - 38 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 - 4 * q^4 + q^5 + 2 * q^7 - 24 * q^8 - 4 * q^10 + 11 * q^11 - 5 * q^13 - 5 * q^14 - 10 * q^16 - 14 * q^17 + 6 * q^19 - q^20 + 7 * q^22 + 18 * q^23 + 8 * q^25 - 4 * q^26 - 38 * q^28 + 4 * q^29 + 16 * q^31 + 31 * q^32 - 13 * q^34 - 22 * q^35 + 10 * q^37 + 24 * q^38 - 18 * q^40 + 12 * q^41 - 2 * q^44 + 12 * q^46 + 15 * q^47 - 3 * q^49 - 5 * q^50 - 4 * q^52 + 6 * q^53 - 34 * q^55 - 24 * q^56 + 2 * q^58 + 3 * q^59 + q^61 + 8 * q^62 + 124 * q^64 + q^65 + 4 * q^67 - 16 * q^68 + 25 * q^70 - 30 * q^71 - 10 * q^73 + 11 * q^74 - 9 * q^76 + q^77 - 13 * q^79 - 64 * q^80 - 42 * q^82 + 26 * q^83 + 7 * q^85 - 6 * q^86 - 3 * q^88 - 58 * q^89 - 4 * q^91 - 6 * q^92 - 12 * q^94 + 12 * q^95 + 16 * q^97 + 78 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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