LMFDB - Embedded newform 306.4.g.g.217.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [306,4,Mod(55,306)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(306, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("306.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 306 = 2 \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	306.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.0545844618$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 886x^{10} + 292945x^{8} + 42943904x^{6} + 2387634208x^{4} + 5944075264x^{2} + 2089586944 $ x^12 + 886x^10 + 292945x^8 + 42943904x^6 + 2387634208x^4 + 5944075264*x^2 + 2089586944
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 102)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			217.1
Root			$14.8987i$ of defining polynomial
Character	$\chi$	$=$	306.217
Dual form			306.4.g.g.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000i q^{2} -4.00000 q^{4} +(-12.9492 - 12.9492i) q^{5} +(17.3340 - 17.3340i) q^{7} -8.00000i q^{8} +(25.8984 - 25.8984i) q^{10} +(-25.2530 + 25.2530i) q^{11} -13.4149 q^{13} +(34.6680 + 34.6680i) q^{14} +16.0000 q^{16} +(16.8983 + 68.0254i) q^{17} +15.6725i q^{19} +(51.7968 + 51.7968i) q^{20} +(-50.5060 - 50.5060i) q^{22} +(-100.376 + 100.376i) q^{23} +210.364i q^{25} -26.8298i q^{26} +(-69.3360 + 69.3360i) q^{28} +(-94.5834 - 94.5834i) q^{29} +(133.855 + 133.855i) q^{31} +32.0000i q^{32} +(-136.051 + 33.7965i) q^{34} -448.923 q^{35} +(-193.968 - 193.968i) q^{37} -31.3450 q^{38} +(-103.594 + 103.594i) q^{40} +(-171.528 + 171.528i) q^{41} +385.616i q^{43} +(101.012 - 101.012i) q^{44} +(-200.752 - 200.752i) q^{46} +533.009 q^{47} -257.936i q^{49} -420.728 q^{50} +53.6595 q^{52} -403.802i q^{53} +654.012 q^{55} +(-138.672 - 138.672i) q^{56} +(189.167 - 189.167i) q^{58} -266.868i q^{59} +(-484.097 + 484.097i) q^{61} +(-267.710 + 267.710i) q^{62} -64.0000 q^{64} +(173.712 + 173.712i) q^{65} -441.266 q^{67} +(-67.5931 - 272.101i) q^{68} -897.847i q^{70} +(303.839 + 303.839i) q^{71} +(-86.3683 - 86.3683i) q^{73} +(387.936 - 387.936i) q^{74} -62.6901i q^{76} +875.471i q^{77} +(-464.263 + 464.263i) q^{79} +(-207.187 - 207.187i) q^{80} +(-343.057 - 343.057i) q^{82} +1243.94i q^{83} +(662.055 - 1099.69i) q^{85} -771.231 q^{86} +(202.024 + 202.024i) q^{88} -1498.50 q^{89} +(-232.534 + 232.534i) q^{91} +(401.503 - 401.503i) q^{92} +1066.02i q^{94} +(202.947 - 202.947i) q^{95} +(90.0409 + 90.0409i) q^{97} +515.871 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 48 q^{4} - 16 q^{5} - 12 q^{7} + 32 q^{10} + 32 q^{11} - 68 q^{13} - 24 q^{14} + 192 q^{16} - 64 q^{17} + 64 q^{20} + 64 q^{22} + 112 q^{23} + 48 q^{28} + 296 q^{29} + 520 q^{31} + 144 q^{34} - 392 q^{35}+ \cdots + 4168 q^{98}+O(q^{100}) $ 12 * q - 48 * q^4 - 16 * q^5 - 12 * q^7 + 32 * q^10 + 32 * q^11 - 68 * q^13 - 24 * q^14 + 192 * q^16 - 64 * q^17 + 64 * q^20 + 64 * q^22 + 112 * q^23 + 48 * q^28 + 296 * q^29 + 520 * q^31 + 144 * q^34 - 392 * q^35 - 828 * q^37 + 280 * q^38 - 128 * q^40 - 8 * q^41 - 128 * q^44 + 224 * q^46 + 2920 * q^47 - 752 * q^50 + 272 * q^52 + 1156 * q^55 + 96 * q^56 - 592 * q^58 - 1124 * q^61 - 1040 * q^62 - 768 * q^64 - 3288 * q^65 - 2008 * q^67 + 256 * q^68 + 2184 * q^71 + 2456 * q^73 + 1656 * q^74 + 2652 * q^79 - 256 * q^80 - 16 * q^82 + 3444 * q^85 + 184 * q^86 - 256 * q^88 - 5304 * q^89 - 1420 * q^91 - 448 * q^92 + 2920 * q^95 + 2688 * q^97 + 4168 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/306\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−4.00000			−0.500000
$5$	−12.9492	−	12.9492i	−1.15821	−	1.15821i	−0.984860	−	0.173353i	$-0.944540\pi$
$5$	−12.9492	−	12.9492i	−1.15821	−	1.15821i	−0.173353	−	0.984860i	$-0.555460\pi$
$6$		0			0
$7$	17.3340	−	17.3340i	0.935948	−	0.935948i	−0.0621202	−	0.998069i	$-0.519786\pi$
$7$	17.3340	−	17.3340i	0.935948	−	0.935948i	0.998069	+	0.0621202i	$0.0197862\pi$
$8$		−	8.00000i		−	0.353553i
$9$		0			0
$10$	25.8984	−	25.8984i	0.818980	−	0.818980i
$11$	−25.2530	+	25.2530i	−0.692187	+	0.692187i	−0.962713	−	0.270525i	$-0.912803\pi$
$11$	−25.2530	+	25.2530i	−0.692187	+	0.692187i	0.270525	+	0.962713i	$0.412803\pi$
$12$		0			0
$13$	−13.4149			−0.286201			−0.143101	−	0.989708i	$-0.545707\pi$
$13$	−13.4149			−0.286201			−0.143101	+	0.989708i	$0.545707\pi$
$14$	34.6680	+	34.6680i	0.661816	+	0.661816i
$15$		0			0
$16$	16.0000			0.250000
$17$	16.8983	+	68.0254i	0.241084	+	0.970504i
$17$	16.8983	+	68.0254i	0.241084	+	0.970504i
$18$		0			0
$19$			15.6725i			0.189238i	0.995514	+	0.0946190i	$0.0301633\pi$
$19$			15.6725i			0.189238i	−0.995514	+	0.0946190i	$0.969837\pi$
$20$	51.7968	+	51.7968i	0.579106	+	0.579106i
$21$		0			0
$22$	−50.5060	−	50.5060i	−0.489450	−	0.489450i
$23$	−100.376	+	100.376i	−0.909992	+	0.909992i	−0.996271	−	0.0862791i	$-0.972502\pi$
$23$	−100.376	+	100.376i	−0.909992	+	0.909992i	0.0862791	+	0.996271i	$0.472502\pi$
$24$		0			0
$25$			210.364i			1.68291i
$26$		−	26.8298i		−	0.202375i
$27$		0			0
$28$	−69.3360	+	69.3360i	−0.467974	+	0.467974i
$29$	−94.5834	−	94.5834i	−0.605645	−	0.605645i	0.336160	−	0.941805i	$-0.390872\pi$
$29$	−94.5834	−	94.5834i	−0.605645	−	0.605645i	−0.941805	+	0.336160i	$0.890872\pi$
$30$		0			0
$31$	133.855	+	133.855i	0.775520	+	0.775520i	0.979065	−	0.203546i	$-0.0652466\pi$
$31$	133.855	+	133.855i	0.775520	+	0.775520i	−0.203546	+	0.979065i	$0.565247\pi$
$32$			32.0000i			0.176777i
$33$		0			0
$34$	−136.051	+	33.7965i	−0.686250	+	0.170472i
$35$	−448.923			−2.16805
$36$		0			0
$37$	−193.968	−	193.968i	−0.861842	−	0.861842i	0.129710	−	0.991552i	$-0.458595\pi$
$37$	−193.968	−	193.968i	−0.861842	−	0.861842i	−0.991552	+	0.129710i	$0.958595\pi$
$38$	−31.3450			−0.133811
$39$		0			0
$40$	−103.594	+	103.594i	−0.409490	+	0.409490i
$41$	−171.528	+	171.528i	−0.653372	+	0.653372i	−0.953803	−	0.300432i	$-0.902869\pi$
$41$	−171.528	+	171.528i	−0.653372	+	0.653372i	0.300432	+	0.953803i	$0.402869\pi$
$42$		0			0
$43$			385.616i			1.36758i	0.729680	+	0.683789i	$0.239669\pi$
$43$			385.616i			1.36758i	−0.729680	+	0.683789i	$0.760331\pi$
$44$	101.012	−	101.012i	0.346094	−	0.346094i
$45$		0			0
$46$	−200.752	−	200.752i	−0.643461	−	0.643461i
$47$	533.009			1.65420			0.827099	−	0.562056i	$-0.189989\pi$
$47$	533.009			1.65420			0.827099	+	0.562056i	$0.189989\pi$
$48$		0			0
$49$		−	257.936i		−	0.751999i
$50$	−420.728			−1.19000
$51$		0			0
$52$	53.6595			0.143101
$53$		−	403.802i		−	1.04654i	−0.852168	−	0.523268i	$-0.824713\pi$
$53$		−	403.802i		−	1.04654i	0.852168	−	0.523268i	$-0.175287\pi$
$54$		0			0
$55$	654.012			1.60340
$56$	−138.672	−	138.672i	−0.330908	−	0.330908i
$57$		0			0
$58$	189.167	−	189.167i	0.428255	−	0.428255i
$59$		−	266.868i		−	0.588868i	−0.955672	−	0.294434i	$-0.904869\pi$
$59$		−	266.868i		−	0.588868i	0.955672	−	0.294434i	$-0.0951311\pi$
$60$		0			0
$61$	−484.097	+	484.097i	−1.01610	+	1.01610i	−0.0162344	+	0.999868i	$0.505168\pi$
$61$	−484.097	+	484.097i	−1.01610	+	1.01610i	−0.999868	+	0.0162344i	$0.994832\pi$
$62$	−267.710	+	267.710i	−0.548375	+	0.548375i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	173.712	+	173.712i	0.331482	+	0.331482i
$66$		0			0
$67$	−441.266			−0.804615			−0.402308	−	0.915505i	$-0.631792\pi$
$67$	−441.266			−0.804615			−0.402308	+	0.915505i	$0.631792\pi$
$68$	−67.5931	−	272.101i	−0.120542	−	0.485252i
$69$		0			0
$70$		−	897.847i		−	1.53305i
$71$	303.839	+	303.839i	0.507873	+	0.507873i	0.913873	−	0.406000i	$-0.133077\pi$
$71$	303.839	+	303.839i	0.507873	+	0.507873i	−0.406000	+	0.913873i	$0.633077\pi$
$72$		0			0
$73$	−86.3683	−	86.3683i	−0.138475	−	0.138475i	0.634472	−	0.772946i	$-0.281218\pi$
$73$	−86.3683	−	86.3683i	−0.138475	−	0.138475i	−0.772946	+	0.634472i	$0.781218\pi$
$74$	387.936	−	387.936i	0.609414	−	0.609414i
$75$		0			0
$76$		−	62.6901i		−	0.0946190i
$77$			875.471i			1.29570i
$78$		0			0
$79$	−464.263	+	464.263i	−0.661186	+	0.661186i	−0.955660	−	0.294474i	$-0.904856\pi$
$79$	−464.263	+	464.263i	−0.661186	+	0.661186i	0.294474	+	0.955660i	$0.404856\pi$
$80$	−207.187	−	207.187i	−0.289553	−	0.289553i
$81$		0			0
$82$	−343.057	−	343.057i	−0.462004	−	0.462004i
$83$			1243.94i			1.64506i	0.568721	+	0.822530i	$0.307438\pi$
$83$			1243.94i			1.64506i	−0.568721	+	0.822530i	$0.692562\pi$
$84$		0			0
$85$	662.055	−	1099.69i	0.844823	−	1.40328i
$86$	−771.231			−0.967023
$87$		0			0
$88$	202.024	+	202.024i	0.244725	+	0.244725i
$89$	−1498.50			−1.78472			−0.892362	−	0.451320i	$-0.850953\pi$
$89$	−1498.50			−1.78472			−0.892362	+	0.451320i	$0.850953\pi$
$90$		0			0
$91$	−232.534	+	232.534i	−0.267870	+	0.267870i
$92$	401.503	−	401.503i	0.454996	−	0.454996i
$93$		0			0
$94$			1066.02i			1.16970i
$95$	202.947	−	202.947i	0.219178	−	0.219178i
$96$		0			0
$97$	90.0409	+	90.0409i	0.0942502	+	0.0942502i	0.752660	−	0.658410i	$-0.228771\pi$
$97$	90.0409	+	90.0409i	0.0942502	+	0.0942502i	−0.658410	+	0.752660i	$0.728771\pi$
$98$	515.871			0.531744
$99$		0			0
$100$		−	841.456i		−	0.841456i
$101$	1152.65			1.13557			0.567785	−	0.823177i	$-0.307800\pi$
$101$	1152.65			1.13557			0.567785	+	0.823177i	$0.307800\pi$
$102$		0			0
$103$	128.042			0.122489			0.0612445	−	0.998123i	$-0.480493\pi$
$103$	128.042			0.122489			0.0612445	+	0.998123i	$0.480493\pi$
$104$			107.319i			0.101187i
$105$		0			0
$106$	807.603			0.740013
$107$	−1170.71	−	1170.71i	−1.05773	−	1.05773i	−0.998228	−	0.0594973i	$-0.981050\pi$
$107$	−1170.71	−	1170.71i	−1.05773	−	1.05773i	−0.0594973	−	0.998228i	$-0.518950\pi$
$108$		0			0
$109$	−1181.52	+	1181.52i	−1.03825	+	1.03825i	−0.0390141	+	0.999239i	$0.512422\pi$
$109$	−1181.52	+	1181.52i	−1.03825	+	1.03825i	−0.999239	+	0.0390141i	$0.987578\pi$
$110$			1308.02i			1.13378i
$111$		0			0
$112$	277.344	−	277.344i	0.233987	−	0.233987i
$113$	127.056	−	127.056i	0.105773	−	0.105773i	−0.652240	−	0.758013i	$-0.726170\pi$
$113$	127.056	−	127.056i	0.105773	−	0.105773i	0.758013	+	0.652240i	$0.226170\pi$
$114$		0			0
$115$	2599.58			2.10793
$116$	378.334	+	378.334i	0.302822	+	0.302822i
$117$		0			0
$118$	533.735			0.416392
$119$	1472.07	+	886.237i	1.13398	+	0.682700i
$120$		0			0
$121$			55.5736i			0.0417533i
$122$	−968.194	−	968.194i	−0.718493	−	0.718493i
$123$		0			0
$124$	−535.421	−	535.421i	−0.387760	−	0.387760i
$125$	1105.40	−	1105.40i	0.790957	−	0.790957i
$126$		0			0
$127$		−	1988.60i		−	1.38945i	−0.719277	−	0.694723i	$-0.755527\pi$
$127$		−	1988.60i		−	1.38945i	0.719277	−	0.694723i	$-0.244473\pi$
$128$		−	128.000i		−	0.0883883i
$129$		0			0
$130$	−347.424	+	347.424i	−0.234393	+	0.234393i
$131$	−694.086	−	694.086i	−0.462920	−	0.462920i	0.436691	−	0.899611i	$-0.356150\pi$
$131$	−694.086	−	694.086i	−0.462920	−	0.462920i	−0.899611	+	0.436691i	$0.856150\pi$
$132$		0			0
$133$	271.667	+	271.667i	0.177117	+	0.177117i
$134$		−	882.532i		−	0.568949i
$135$		0			0
$136$	544.203	−	135.186i	0.343125	−	0.0852361i
$137$	2788.01			1.73866			0.869328	−	0.494236i	$-0.164552\pi$
$137$	2788.01			1.73866			0.869328	+	0.494236i	$0.164552\pi$
$138$		0			0
$139$	−118.311	−	118.311i	−0.0721944	−	0.0721944i	0.670088	−	0.742282i	$-0.266257\pi$
$139$	−118.311	−	118.311i	−0.0721944	−	0.0721944i	−0.742282	+	0.670088i	$0.766257\pi$
$140$	1795.69			1.08403
$141$		0			0
$142$	−607.677	+	607.677i	−0.359121	+	0.359121i
$143$	338.766	−	338.766i	0.198105	−	0.198105i
$144$		0			0
$145$			2449.56i			1.40293i
$146$	172.737	−	172.737i	0.0979163	−	0.0979163i
$147$		0			0
$148$	775.872	+	775.872i	0.430921	+	0.430921i
$149$	2926.77			1.60920			0.804598	−	0.593820i	$-0.202381\pi$
$149$	2926.77			1.60920			0.804598	+	0.593820i	$0.202381\pi$
$150$		0			0
$151$			2142.40i			1.15461i	0.816528	+	0.577306i	$0.195896\pi$
$151$			2142.40i			1.15461i	−0.816528	+	0.577306i	$0.804104\pi$
$152$	125.380			0.0669057
$153$		0			0
$154$	−1750.94			−0.916201
$155$		−	3466.64i		−	1.79643i
$156$		0			0
$157$	1329.27			0.675714			0.337857	−	0.941197i	$-0.390298\pi$
$157$	1329.27			0.675714			0.337857	+	0.941197i	$0.390298\pi$
$158$	−928.526	−	928.526i	−0.467529	−	0.467529i
$159$		0			0
$160$	414.375	−	414.375i	0.204745	−	0.204745i
$161$			3479.83i			1.70341i
$162$		0			0
$163$	1846.81	−	1846.81i	0.887442	−	0.887442i	−0.106834	−	0.994277i	$-0.534071\pi$
$163$	1846.81	−	1846.81i	0.887442	−	0.887442i	0.994277	+	0.106834i	$0.0340715\pi$
$164$	686.114	−	686.114i	0.326686	−	0.326686i
$165$		0			0
$166$	−2487.88			−1.16323
$167$	−884.150	−	884.150i	−0.409686	−	0.409686i	0.471943	−	0.881629i	$-0.343553\pi$
$167$	−884.150	−	884.150i	−0.409686	−	0.409686i	−0.881629	+	0.471943i	$0.843553\pi$
$168$		0			0
$169$	−2017.04			−0.918089
$170$	2199.39	+	1324.11i	0.992266	+	0.597380i
$171$		0			0
$172$		−	1542.46i		−	0.683789i
$173$	−2434.54	−	2434.54i	−1.06991	−	1.06991i	−0.997365	−	0.0725474i	$-0.976887\pi$
$173$	−2434.54	−	2434.54i	−1.06991	−	1.06991i	−0.0725474	−	0.997365i	$-0.523113\pi$
$174$		0			0
$175$	3646.45	+	3646.45i	1.57512	+	1.57512i
$176$	−404.048	+	404.048i	−0.173047	+	0.173047i
$177$		0			0
$178$		−	2997.00i		−	1.26199i
$179$			1640.52i			0.685019i	0.939514	+	0.342509i	$0.111277\pi$
$179$			1640.52i			0.685019i	−0.939514	+	0.342509i	$0.888723\pi$
$180$		0			0
$181$	185.058	−	185.058i	0.0759958	−	0.0759958i	−0.668087	−	0.744083i	$-0.732887\pi$
$181$	185.058	−	185.058i	0.0759958	−	0.0759958i	0.744083	+	0.668087i	$0.232887\pi$
$182$	−465.067	−	465.067i	−0.189413	−	0.189413i
$183$		0			0
$184$	803.007	+	803.007i	0.321731	+	0.321731i
$185$			5023.46i			1.99639i
$186$		0			0
$187$	−2144.57	−	1291.11i	−0.838646	−	0.504895i
$188$	−2132.04			−0.827099
$189$		0			0
$190$	405.893	+	405.893i	0.154982	+	0.154982i
$191$	−2598.60			−0.984439			−0.492219	−	0.870471i	$-0.663814\pi$
$191$	−2598.60			−0.984439			−0.492219	+	0.870471i	$0.663814\pi$
$192$		0			0
$193$	−2925.77	+	2925.77i	−1.09120	+	1.09120i	−0.0957997	+	0.995401i	$0.530541\pi$
$193$	−2925.77	+	2925.77i	−1.09120	+	1.09120i	−0.995401	+	0.0957997i	$0.969459\pi$
$194$	−180.082	+	180.082i	−0.0666449	+	0.0666449i
$195$		0			0
$196$			1031.74i			0.376000i
$197$	897.733	−	897.733i	0.324674	−	0.324674i	−0.525883	−	0.850557i	$-0.676265\pi$
$197$	897.733	−	897.733i	0.324674	−	0.324674i	0.850557	+	0.525883i	$0.176265\pi$
$198$		0			0
$199$	−3823.88	−	3823.88i	−1.36215	−	1.36215i	−0.871174	−	0.490975i	$-0.836641\pi$
$199$	−3823.88	−	3823.88i	−1.36215	−	1.36215i	−0.490975	−	0.871174i	$-0.663359\pi$
$200$	1682.91			0.594999
$201$		0			0
$202$			2305.29i			0.802970i
$203$	−3279.02			−1.13370
$204$		0			0
$205$	4442.31			1.51349
$206$			256.084i			0.0866128i
$207$		0			0
$208$	−214.638			−0.0715503
$209$	−395.778	−	395.778i	−0.130988	−	0.130988i
$210$		0			0
$211$	2349.49	−	2349.49i	0.766567	−	0.766567i	−0.210933	−	0.977501i	$-0.567650\pi$
$211$	2349.49	−	2349.49i	0.766567	−	0.766567i	0.977501	+	0.210933i	$0.0676502\pi$
$212$			1615.21i			0.523268i
$213$		0			0
$214$	2341.42	−	2341.42i	0.747925	−	0.747925i
$215$	4993.42	−	4993.42i	1.58395	−	1.58395i
$216$		0			0
$217$	4640.49			1.45169
$218$	−2363.05	−	2363.05i	−0.734156	−	0.734156i
$219$		0			0
$220$	−2616.05			−0.801700
$221$	−226.688	−	912.552i	−0.0689986	−	0.277760i
$222$		0			0
$223$		−	2244.32i		−	0.673951i	−0.941513	−	0.336975i	$-0.890596\pi$
$223$		−	2244.32i		−	0.673951i	0.941513	−	0.336975i	$-0.109404\pi$
$224$	554.688	+	554.688i	0.165454	+	0.165454i
$225$		0			0
$226$	254.111	+	254.111i	0.0747930	+	0.0747930i
$227$	−2441.46	+	2441.46i	−0.713856	+	0.713856i	−0.967340	−	0.253484i	$-0.918423\pi$
$227$	−2441.46	+	2441.46i	−0.713856	+	0.713856i	0.253484	+	0.967340i	$0.418423\pi$
$228$		0			0
$229$		−	2682.67i		−	0.774130i	−0.922052	−	0.387065i	$-0.873489\pi$
$229$		−	2682.67i		−	0.774130i	0.922052	−	0.387065i	$-0.126511\pi$
$230$			5199.15i			1.49053i
$231$		0			0
$232$	−756.667	+	756.667i	−0.214128	+	0.214128i
$233$	1116.03	+	1116.03i	0.313791	+	0.313791i	0.846376	−	0.532585i	$-0.178780\pi$
$233$	1116.03	+	1116.03i	0.313791	+	0.313791i	−0.532585	+	0.846376i	$0.678780\pi$
$234$		0			0
$235$	−6902.04	−	6902.04i	−1.91591	−	1.91591i
$236$			1067.47i			0.294434i
$237$		0			0
$238$	−1772.47	+	2944.13i	−0.482742	+	0.801848i
$239$	−5016.20			−1.35762			−0.678810	−	0.734314i	$-0.737504\pi$
$239$	−5016.20			−1.35762			−0.678810	+	0.734314i	$0.737504\pi$
$240$		0			0
$241$	−1150.94	−	1150.94i	−0.307629	−	0.307629i	0.536360	−	0.843989i	$-0.319799\pi$
$241$	−1150.94	−	1150.94i	−0.307629	−	0.307629i	−0.843989	+	0.536360i	$0.819799\pi$
$242$	−111.147			−0.0295240
$243$		0			0
$244$	1936.39	−	1936.39i	0.508051	−	0.508051i
$245$	−3340.06	+	3340.06i	−0.870975	+	0.870975i
$246$		0			0
$247$		−	210.245i		−	0.0541602i
$248$	1070.84	−	1070.84i	0.274188	−	0.274188i
$249$		0			0
$250$	2210.79	+	2210.79i	0.559291	+	0.559291i
$251$	−296.264			−0.0745021			−0.0372510	−	0.999306i	$-0.511860\pi$
$251$	−296.264			−0.0745021			−0.0372510	+	0.999306i	$0.511860\pi$
$252$		0			0
$253$		−	5069.58i		−	1.25977i
$254$	3977.20			0.982487
$255$		0			0
$256$	256.000			0.0625000
$257$			2885.16i			0.700278i	0.936698	+	0.350139i	$0.113866\pi$
$257$			2885.16i			0.700278i	−0.936698	+	0.350139i	$0.886134\pi$
$258$		0			0
$259$	−6724.49			−1.61328
$260$	−694.848	−	694.848i	−0.165741	−	0.165741i
$261$		0			0
$262$	1388.17	−	1388.17i	0.327334	−	0.327334i
$263$		−	2958.63i		−	0.693677i	−0.937925	−	0.346839i	$-0.887255\pi$
$263$		−	2958.63i		−	0.693677i	0.937925	−	0.346839i	$-0.112745\pi$
$264$		0			0
$265$	−5228.91	+	5228.91i	−1.21211	+	1.21211i
$266$	−543.335	+	543.335i	−0.125241	+	0.125241i
$267$		0			0
$268$	1765.06			0.402308
$269$	−1852.83	−	1852.83i	−0.419958	−	0.419958i	0.465231	−	0.885189i	$-0.345971\pi$
$269$	−1852.83	−	1852.83i	−0.419958	−	0.419958i	−0.885189	+	0.465231i	$0.845971\pi$
$270$		0			0
$271$	−2252.27			−0.504856			−0.252428	−	0.967616i	$-0.581229\pi$
$271$	−2252.27			−0.504856			−0.252428	+	0.967616i	$0.581229\pi$
$272$	270.372	+	1088.41i	0.0602710	+	0.242626i
$273$		0			0
$274$			5576.02i			1.22942i
$275$	−5312.32	−	5312.32i	−1.16489	−	1.16489i
$276$		0			0
$277$	3241.37	+	3241.37i	0.703087	+	0.703087i	0.965072	−	0.261985i	$-0.0843771\pi$
$277$	3241.37	+	3241.37i	0.703087	+	0.703087i	−0.261985	+	0.965072i	$0.584377\pi$
$278$	236.622	−	236.622i	0.0510492	−	0.0510492i
$279$		0			0
$280$			3591.39i			0.766523i
$281$		−	5686.53i		−	1.20722i	−0.797278	−	0.603612i	$-0.793728\pi$
$281$		−	5686.53i		−	1.20722i	0.797278	−	0.603612i	$-0.206272\pi$
$282$		0			0
$283$	−389.733	+	389.733i	−0.0818629	+	0.0818629i	−0.746853	−	0.664990i	$-0.768436\pi$
$283$	−389.733	+	389.733i	−0.0818629	+	0.0818629i	0.664990	+	0.746853i	$0.268436\pi$
$284$	−1215.35	−	1215.35i	−0.253937	−	0.253937i
$285$		0			0
$286$	677.531	+	677.531i	0.140081	+	0.140081i
$287$			5946.55i			1.22304i
$288$		0			0
$289$	−4341.90	+	2299.02i	−0.883757	+	0.467946i
$290$	−4899.12			−0.992021
$291$		0			0
$292$	345.473	+	345.473i	0.0692373	+	0.0692373i
$293$	−5505.48			−1.09772			−0.548862	−	0.835913i	$-0.684939\pi$
$293$	−5505.48			−1.09772			−0.548862	+	0.835913i	$0.684939\pi$
$294$		0			0
$295$	−3455.72	+	3455.72i	−0.682034	+	0.682034i
$296$	−1551.74	+	1551.74i	−0.304707	+	0.304707i
$297$		0			0
$298$			5853.54i			1.13787i
$299$	1346.53	−	1346.53i	0.260441	−	0.260441i
$300$		0			0
$301$	6684.27	+	6684.27i	1.27998	+	1.27998i
$302$	−4284.81			−0.816433
$303$		0			0
$304$			250.760i			0.0473095i
$305$	12537.3			2.35373
$306$		0			0
$307$	−3279.39			−0.609657			−0.304829	−	0.952407i	$-0.598599\pi$
$307$	−3279.39			−0.609657			−0.304829	+	0.952407i	$0.598599\pi$
$308$		−	3501.88i		−	0.647852i
$309$		0			0
$310$	6933.28			1.27027
$311$	6043.27	+	6043.27i	1.10187	+	1.10187i	0.994185	+	0.107687i	$0.0343445\pi$
$311$	6043.27	+	6043.27i	1.10187	+	1.10187i	0.107687	+	0.994185i	$0.465656\pi$
$312$		0			0
$313$	−1413.61	+	1413.61i	−0.255277	+	0.255277i	−0.823130	−	0.567853i	$-0.807774\pi$
$313$	−1413.61	+	1413.61i	−0.255277	+	0.255277i	0.567853	+	0.823130i	$0.307774\pi$
$314$			2658.54i			0.477802i
$315$		0			0
$316$	1857.05	−	1857.05i	0.330593	−	0.330593i
$317$	−3348.70	+	3348.70i	−0.593317	+	0.593317i	−0.938526	−	0.345209i	$-0.887808\pi$
$317$	−3348.70	+	3348.70i	−0.593317	+	0.593317i	0.345209	+	0.938526i	$0.387808\pi$
$318$		0			0
$319$	4777.03			0.838439
$320$	828.749	+	828.749i	0.144777	+	0.144777i
$321$		0			0
$322$	−6959.66			−1.20449
$323$	−1066.13	+	264.838i	−0.183656	+	0.0456223i
$324$		0			0
$325$		−	2822.01i		−	0.481652i
$326$	3693.61	+	3693.61i	0.627517	+	0.627517i
$327$		0			0
$328$	1372.23	+	1372.23i	0.231002	+	0.231002i
$329$	9239.18	−	9239.18i	1.54824	−	1.54824i
$330$		0			0
$331$			3878.09i			0.643985i	0.946742	+	0.321993i	$0.104353\pi$
$331$			3878.09i			0.643985i	−0.946742	+	0.321993i	$0.895647\pi$
$332$		−	4975.76i		−	0.822530i
$333$		0			0
$334$	1768.30	−	1768.30i	0.289692	−	0.289692i
$335$	5714.04	+	5714.04i	0.931915	+	0.931915i
$336$		0			0
$337$	−1904.95	−	1904.95i	−0.307921	−	0.307921i	0.536182	−	0.844103i	$-0.319866\pi$
$337$	−1904.95	−	1904.95i	−0.307921	−	0.307921i	−0.844103	+	0.536182i	$0.819866\pi$
$338$		−	4034.08i		−	0.649187i
$339$		0			0
$340$	−2648.22	+	4398.77i	−0.422412	+	0.701638i
$341$	−6760.49			−1.07361
$342$		0			0
$343$	1474.51	+	1474.51i	0.232116	+	0.232116i
$344$	3084.93			0.483512
$345$		0			0
$346$	4869.08	−	4869.08i	0.756542	−	0.756542i
$347$	−5068.32	+	5068.32i	−0.784098	+	0.784098i	−0.980519	−	0.196422i	$-0.937068\pi$
$347$	−5068.32	+	5068.32i	−0.784098	+	0.784098i	0.196422	+	0.980519i	$0.437068\pi$
$348$		0			0
$349$		−	1517.31i		−	0.232722i	−0.993207	−	0.116361i	$-0.962877\pi$
$349$		−	1517.31i		−	0.232722i	0.993207	−	0.116361i	$-0.0371230\pi$
$350$	−7292.90	+	7292.90i	−1.11378	+	1.11378i
$351$		0			0
$352$	−808.095	−	808.095i	−0.122363	−	0.122363i
$353$	−4647.31			−0.700711			−0.350356	−	0.936617i	$-0.613939\pi$
$353$	−4647.31			−0.700711			−0.350356	+	0.936617i	$0.613939\pi$
$354$		0			0
$355$		−	7868.94i		−	1.17645i
$356$	5993.99			0.892362
$357$		0			0
$358$	−3281.04			−0.484381
$359$		−	2365.09i		−	0.347702i	−0.984772	−	0.173851i	$-0.944379\pi$
$359$		−	2365.09i		−	0.347702i	0.984772	−	0.173851i	$-0.0556210\pi$
$360$		0			0
$361$	6613.37			0.964189
$362$	370.116	+	370.116i	0.0537372	+	0.0537372i
$363$		0			0
$364$	930.134	−	930.134i	0.133935	−	0.133935i
$365$			2236.80i			0.320766i
$366$		0			0
$367$	−0.150296	+	0.150296i	−2.13771e−5	+	2.13771e-5i	−0.707117	−	0.707096i	$-0.750005\pi$
$367$	−0.150296	+	0.150296i	−2.13771e−5	+	2.13771e-5i	0.707096	+	0.707117i	$0.250005\pi$
$368$	−1606.01	+	1606.01i	−0.227498	+	0.227498i
$369$		0			0
$370$	−10046.9			−1.41166
$371$	−6999.50	−	6999.50i	−0.979504	−	0.979504i
$372$		0			0
$373$	8478.48			1.17694			0.588471	−	0.808519i	$-0.299730\pi$
$373$	8478.48			1.17694			0.588471	+	0.808519i	$0.299730\pi$
$374$	2582.22	−	4289.15i	0.357015	−	0.593012i
$375$		0			0
$376$		−	4264.07i		−	0.584848i
$377$	1268.82	+	1268.82i	0.173336	+	0.173336i
$378$		0			0
$379$	−4121.44	−	4121.44i	−0.558586	−	0.558586i	0.370319	−	0.928905i	$-0.379248\pi$
$379$	−4121.44	−	4121.44i	−0.558586	−	0.558586i	−0.928905	+	0.370319i	$0.879248\pi$
$380$	−811.787	+	811.787i	−0.109589	+	0.109589i
$381$		0			0
$382$		−	5197.19i		−	0.696103i
$383$			1561.85i			0.208373i	0.994558	+	0.104187i	$0.0332240\pi$
$383$			1561.85i			0.208373i	−0.994558	+	0.104187i	$0.966776\pi$
$384$		0			0
$385$	11336.7	−	11336.7i	1.50070	−	1.50070i
$386$	−5851.54	−	5851.54i	−0.771595	−	0.771595i
$387$		0			0
$388$	−360.164	−	360.164i	−0.0471251	−	0.0471251i
$389$			7043.78i			0.918081i	0.888415	+	0.459041i	$0.151807\pi$
$389$			7043.78i			0.918081i	−0.888415	+	0.459041i	$0.848193\pi$
$390$		0			0
$391$	−8524.28	−	5131.93i	−1.10254	−	0.663766i
$392$	−2063.49			−0.265872
$393$		0			0
$394$	1795.47	+	1795.47i	0.229579	+	0.229579i
$395$	12023.7			1.53159
$396$		0			0
$397$	−8311.58	+	8311.58i	−1.05075	+	1.05075i	−0.0521045	+	0.998642i	$0.516593\pi$
$397$	−8311.58	+	8311.58i	−1.05075	+	1.05075i	−0.998642	+	0.0521045i	$0.983407\pi$
$398$	7647.76	−	7647.76i	0.963185	−	0.963185i
$399$		0			0
$400$			3365.82i			0.420728i
$401$	−191.110	+	191.110i	−0.0237995	+	0.0237995i	−0.718906	−	0.695107i	$-0.755357\pi$
$401$	−191.110	+	191.110i	−0.0237995	+	0.0237995i	0.695107	+	0.718906i	$0.255357\pi$
$402$		0			0
$403$	−1795.65	−	1795.65i	−0.221955	−	0.221955i
$404$	−4610.59			−0.567785
$405$		0			0
$406$		−	6558.04i		−	0.801650i
$407$	9796.54			1.19311
$408$		0			0
$409$	−10961.4			−1.32520			−0.662598	−	0.748975i	$-0.730546\pi$
$409$	−10961.4			−1.32520			−0.662598	+	0.748975i	$0.730546\pi$
$410$			8884.63i			1.07020i
$411$		0			0
$412$	−512.168			−0.0612445
$413$	−4625.88	−	4625.88i	−0.551150	−	0.551150i
$414$		0			0
$415$	16108.0	−	16108.0i	1.90533	−	1.90533i
$416$		−	429.276i		−	0.0505937i
$417$		0			0
$418$	791.555	−	791.555i	0.0926226	−	0.0926226i
$419$	8128.39	−	8128.39i	0.947727	−	0.947727i	−0.0509730	−	0.998700i	$-0.516232\pi$
$419$	8128.39	−	8128.39i	0.947727	−	0.947727i	0.998700	+	0.0509730i	$0.0162322\pi$
$420$		0			0
$421$	11175.3			1.29371			0.646854	−	0.762614i	$-0.276084\pi$
$421$	11175.3			1.29371			0.646854	+	0.762614i	$0.276084\pi$
$422$	4698.99	+	4698.99i	0.542045	+	0.542045i
$423$		0			0
$424$	−3230.41			−0.370006
$425$	−14310.1	+	3554.79i	−1.63327	+	0.405723i
$426$		0			0
$427$			16782.7i			1.90204i
$428$	4682.83	+	4682.83i	0.528863	+	0.528863i
$429$		0			0
$430$	9986.84	+	9986.84i	1.12002	+	1.12002i
$431$	8830.33	−	8830.33i	0.986873	−	0.986873i	−0.0130424	−	0.999915i	$-0.504152\pi$
$431$	8830.33	−	8830.33i	0.986873	−	0.986873i	0.999915	+	0.0130424i	$0.00415165\pi$
$432$		0			0
$433$		−	2035.22i		−	0.225881i	−0.993602	−	0.112940i	$-0.963973\pi$
$433$		−	2035.22i		−	0.225881i	0.993602	−	0.112940i	$-0.0360269\pi$
$434$			9280.99i			1.02650i
$435$		0			0
$436$	4726.10	−	4726.10i	0.519126	−	0.519126i
$437$	−1573.14	−	1573.14i	−0.172205	−	0.172205i
$438$		0			0
$439$	−6948.56	−	6948.56i	−0.755437	−	0.755437i	0.220051	−	0.975488i	$-0.429378\pi$
$439$	−6948.56	−	6948.56i	−0.755437	−	0.755437i	−0.975488	+	0.220051i	$0.929378\pi$
$440$		−	5232.10i		−	0.566888i
$441$		0			0
$442$	1825.10	−	453.376i	0.196406	−	0.0487894i
$443$	1404.92			0.150677			0.0753385	−	0.997158i	$-0.475996\pi$
$443$	1404.92			0.150677			0.0753385	+	0.997158i	$0.475996\pi$
$444$		0			0
$445$	19404.4	+	19404.4i	2.06709	+	2.06709i
$446$	4488.65			0.476555
$447$		0			0
$448$	−1109.38	+	1109.38i	−0.116994	+	0.116994i
$449$	−4441.50	+	4441.50i	−0.466831	+	0.466831i	−0.900886	−	0.434055i	$-0.857082\pi$
$449$	−4441.50	+	4441.50i	−0.466831	+	0.466831i	0.434055	+	0.900886i	$0.357082\pi$
$450$		0			0
$451$		−	8663.21i		−	0.904511i
$452$	−508.222	+	508.222i	−0.0528867	+	0.0528867i
$453$		0			0
$454$	−4882.91	−	4882.91i	−0.504772	−	0.504772i
$455$	6022.25			0.620500
$456$		0			0
$457$			16304.1i			1.66887i	0.551106	+	0.834435i	$0.314206\pi$
$457$			16304.1i			1.66887i	−0.551106	+	0.834435i	$0.685794\pi$
$458$	5365.34			0.547393
$459$		0			0
$460$	−10398.3			−1.05396
$461$		−	80.0065i		−	0.00808302i	−0.999992	−	0.00404151i	$-0.998714\pi$
$461$		−	80.0065i		−	0.00808302i	0.999992	−	0.00404151i	$-0.00128646\pi$
$462$		0			0
$463$	2619.71			0.262955			0.131477	−	0.991319i	$-0.458028\pi$
$463$	2619.71			0.262955			0.131477	+	0.991319i	$0.458028\pi$
$464$	−1513.33	−	1513.33i	−0.151411	−	0.151411i
$465$		0			0
$466$	−2232.05	+	2232.05i	−0.221884	+	0.221884i
$467$		−	1360.07i		−	0.134768i	−0.997727	−	0.0673839i	$-0.978535\pi$
$467$		−	1360.07i		−	0.134768i	0.997727	−	0.0673839i	$-0.0214652\pi$
$468$		0			0
$469$	−7648.91	+	7648.91i	−0.753078	+	0.753078i
$470$	13804.1	−	13804.1i	1.35476	−	1.35476i
$471$		0			0
$472$	−2134.94			−0.208196
$473$	−9737.95	−	9737.95i	−0.946620	−	0.946620i
$474$		0			0
$475$	−3296.93			−0.318471
$476$	−5888.27	−	3544.95i	−0.566992	−	0.341350i
$477$		0			0
$478$		−	10032.4i		−	0.959983i
$479$	6950.26	+	6950.26i	0.662976	+	0.662976i	0.956080	−	0.293105i	$-0.0946884\pi$
$479$	6950.26	+	6950.26i	0.662976	+	0.662976i	−0.293105	+	0.956080i	$0.594688\pi$
$480$		0			0
$481$	2602.06	+	2602.06i	0.246660	+	0.246660i
$482$	2301.88	−	2301.88i	0.217527	−	0.217527i
$483$		0			0
$484$		−	222.294i		−	0.0208766i
$485$		−	2331.92i		−	0.218323i
$486$		0			0
$487$	5165.25	−	5165.25i	0.480616	−	0.480616i	−0.424712	−	0.905328i	$-0.639625\pi$
$487$	5165.25	−	5165.25i	0.480616	−	0.480616i	0.905328	+	0.424712i	$0.139625\pi$
$488$	3872.78	+	3872.78i	0.359247	+	0.359247i
$489$		0			0
$490$	−6680.13	−	6680.13i	−0.615872	−	0.615872i
$491$		−	18687.3i		−	1.71761i	−0.512305	−	0.858803i	$-0.671208\pi$
$491$		−	18687.3i		−	1.71761i	0.512305	−	0.858803i	$-0.328792\pi$
$492$		0			0
$493$	4835.77	−	8032.36i	0.441769	−	0.733792i
$494$	420.490			0.0382970
$495$		0			0
$496$	2141.68	+	2141.68i	0.193880	+	0.193880i
$497$	10533.5			0.950686
$498$		0			0
$499$	5768.60	−	5768.60i	0.517511	−	0.517511i	−0.399307	−	0.916817i	$-0.630749\pi$
$499$	5768.60	−	5768.60i	0.517511	−	0.517511i	0.916817	+	0.399307i	$0.130749\pi$
$500$	−4421.59	+	4421.59i	−0.395479	+	0.395479i
$501$		0			0
$502$		−	592.528i		−	0.0526809i
$503$	−3807.34	+	3807.34i	−0.337497	+	0.337497i	−0.855424	−	0.517928i	$-0.826704\pi$
$503$	−3807.34	+	3807.34i	−0.337497	+	0.337497i	0.517928	+	0.855424i	$0.326704\pi$
$504$		0			0
$505$	−14925.9	−	14925.9i	−1.31523	−	1.31523i
$506$	10139.2			0.890792
$507$		0			0
$508$			7954.40i			0.694723i
$509$	−12438.1			−1.08313			−0.541563	−	0.840660i	$-0.682167\pi$
$509$	−12438.1			−1.08313			−0.541563	+	0.840660i	$0.682167\pi$
$510$		0			0
$511$	−2994.22			−0.259210
$512$			512.000i			0.0441942i
$513$		0			0
$514$	−5770.33			−0.495172
$515$	−1658.04	−	1658.04i	−0.141868	−	0.141868i
$516$		0			0
$517$	−13460.1	+	13460.1i	−1.14502	+	1.14502i
$518$		−	13449.0i		−	1.14076i
$519$		0			0
$520$	1389.70	−	1389.70i	0.117197	−	0.117197i
$521$	1409.93	−	1409.93i	0.118561	−	0.118561i	−0.645337	−	0.763898i	$-0.723283\pi$
$521$	1409.93	−	1409.93i	0.118561	−	0.118561i	0.763898	+	0.645337i	$0.223283\pi$
$522$		0			0
$523$	−171.269			−0.0143194			−0.00715970	−	0.999974i	$-0.502279\pi$
$523$	−171.269			−0.0143194			−0.00715970	+	0.999974i	$0.502279\pi$
$524$	2776.34	+	2776.34i	0.231460	+	0.231460i
$525$		0			0
$526$	5917.27			0.490504
$527$	−6843.63	+	11367.5i	−0.565680	+	0.939610i
$528$		0			0
$529$		−	7983.63i		−	0.656171i
$530$	−10457.8	−	10457.8i	−0.857092	−	0.857092i
$531$		0			0
$532$	−1086.67	−	1086.67i	−0.0885585	−	0.0885585i
$533$	2301.03	−	2301.03i	0.186996	−	0.186996i
$534$		0			0
$535$			30319.5i			2.45014i
$536$			3530.13i			0.284474i
$537$		0			0
$538$	3705.65	−	3705.65i	0.296955	−	0.296955i
$539$	6513.65	+	6513.65i	0.520524	+	0.520524i
$540$		0			0
$541$	11243.1	+	11243.1i	0.893492	+	0.893492i	0.994850	−	0.101358i	$-0.0323187\pi$
$541$	11243.1	+	11243.1i	0.893492	+	0.893492i	−0.101358	+	0.994850i	$0.532319\pi$
$542$		−	4504.55i		−	0.356987i
$543$		0			0
$544$	−2176.81	+	540.744i	−0.171563	+	0.0426181i
$545$	30599.6			2.40503
$546$		0			0
$547$	−598.801	−	598.801i	−0.0468060	−	0.0468060i	0.683316	−	0.730122i	$-0.260537\pi$
$547$	−598.801	−	598.801i	−0.0468060	−	0.0468060i	−0.730122	+	0.683316i	$0.760537\pi$
$548$	−11152.0			−0.869328
$549$		0			0
$550$	10624.6	−	10624.6i	0.823702	−	0.823702i
$551$	1482.36	−	1482.36i	0.114611	−	0.114611i
$552$		0			0
$553$			16095.1i			1.23767i
$554$	−6482.74	+	6482.74i	−0.497158	+	0.497158i
$555$		0			0
$556$	473.245	+	473.245i	0.0360972	+	0.0360972i
$557$	−7243.67			−0.551031			−0.275515	−	0.961297i	$-0.588848\pi$
$557$	−7243.67			−0.551031			−0.275515	+	0.961297i	$0.588848\pi$
$558$		0			0
$559$		−	5172.99i		−	0.391403i
$560$	−7182.77			−0.542014
$561$		0			0
$562$	11373.1			0.853636
$563$			4072.87i			0.304887i	0.988312	+	0.152443i	$0.0487142\pi$
$563$			4072.87i			0.304887i	−0.988312	+	0.152443i	$0.951286\pi$
$564$		0			0
$565$	−3290.54			−0.245016
$566$	−779.466	−	779.466i	−0.0578858	−	0.0578858i
$567$		0			0
$568$	2430.71	−	2430.71i	0.179560	−	0.179560i
$569$			17415.3i			1.28311i	0.767079	+	0.641553i	$0.221709\pi$
$569$			17415.3i			1.28311i	−0.767079	+	0.641553i	$0.778291\pi$
$570$		0			0
$571$	−3510.31	+	3510.31i	−0.257271	+	0.257271i	−0.823943	−	0.566672i	$-0.808231\pi$
$571$	−3510.31	+	3510.31i	−0.257271	+	0.257271i	0.566672	+	0.823943i	$0.308231\pi$
$572$	−1355.06	+	1355.06i	−0.0990525	+	0.0990525i
$573$		0			0
$574$	−11893.1			−0.864823
$575$	−21115.5	−	21115.5i	−1.53144	−	1.53144i
$576$		0			0
$577$	2943.90			0.212402			0.106201	−	0.994345i	$-0.466131\pi$
$577$	2943.90			0.212402			0.106201	+	0.994345i	$0.466131\pi$
$578$	−4598.04	−	8683.79i	−0.330888	−	0.624910i
$579$		0			0
$580$		−	9798.24i		−	0.701465i
$581$	21562.4	+	21562.4i	1.53969	+	1.53969i
$582$		0			0
$583$	10197.2	+	10197.2i	0.724399	+	0.724399i
$584$	−690.946	+	690.946i	−0.0489581	+	0.0489581i
$585$		0			0
$586$		−	11011.0i		−	0.776209i
$587$			3580.59i			0.251767i	0.992045	+	0.125883i	$0.0401765\pi$
$587$			3580.59i			0.251767i	−0.992045	+	0.125883i	$0.959824\pi$
$588$		0			0
$589$	−2097.85	+	2097.85i	−0.146758	+	0.146758i
$590$	−6911.45	−	6911.45i	−0.482271	−	0.482271i
$591$		0			0
$592$	−3103.49	−	3103.49i	−0.215460	−	0.215460i
$593$			23081.4i			1.59838i	0.601077	+	0.799191i	$0.294738\pi$
$593$			23081.4i			1.59838i	−0.601077	+	0.799191i	$0.705262\pi$
$594$		0			0
$595$	−7586.03	−	30538.2i	−0.522684	−	2.10411i
$596$	−11707.1			−0.804598
$597$		0			0
$598$	2693.06	+	2693.06i	0.184160	+	0.184160i
$599$	3524.31			0.240400			0.120200	−	0.992750i	$-0.461646\pi$
$599$	3524.31			0.240400			0.120200	+	0.992750i	$0.461646\pi$
$600$		0			0
$601$	9933.96	−	9933.96i	0.674234	−	0.674234i	−0.284455	−	0.958689i	$-0.591813\pi$
$601$	9933.96	−	9933.96i	0.674234	−	0.674234i	0.958689	+	0.284455i	$0.0918126\pi$
$602$	−13368.5	+	13368.5i	−0.905084	+	0.905084i
$603$		0			0
$604$		−	8569.61i		−	0.577306i
$605$	719.634	−	719.634i	0.0483591	−	0.0483591i
$606$		0			0
$607$	6396.01	+	6396.01i	0.427687	+	0.427687i	0.887840	−	0.460153i	$-0.152205\pi$
$607$	6396.01	+	6396.01i	0.427687	+	0.427687i	−0.460153	+	0.887840i	$0.652205\pi$
$608$	−501.520			−0.0334529
$609$		0			0
$610$			25074.7i			1.66434i
$611$	−7150.25			−0.473434
$612$		0			0
$613$	−17364.1			−1.14409			−0.572047	−	0.820221i	$-0.693851\pi$
$613$	−17364.1			−1.14409			−0.572047	+	0.820221i	$0.693851\pi$
$614$		−	6558.78i		−	0.431093i
$615$		0			0
$616$	7003.77			0.458100
$617$	16029.9	+	16029.9i	1.04593	+	1.04593i	0.998893	+	0.0470409i	$0.0149791\pi$
$617$	16029.9	+	16029.9i	1.04593	+	1.04593i	0.0470409	+	0.998893i	$0.485021\pi$
$618$		0			0
$619$	−664.009	+	664.009i	−0.0431160	+	0.0431160i	−0.728336	−	0.685220i	$-0.759706\pi$
$619$	−664.009	+	664.009i	−0.0431160	+	0.0431160i	0.685220	+	0.728336i	$0.259706\pi$
$620$			13866.6i			0.898216i
$621$		0			0
$622$	−12086.5	+	12086.5i	−0.779141	+	0.779141i
$623$	−25975.0	+	25975.0i	−1.67041	+	1.67041i
$624$		0			0
$625$	−2332.51			−0.149281
$626$	−2827.22	−	2827.22i	−0.180508	−	0.180508i
$627$		0			0
$628$	−5317.07			−0.337857
$629$	9917.02	−	16472.5i	0.628645	−	1.04420i
$630$		0			0
$631$			10145.6i			0.640079i	0.947404	+	0.320040i	$0.103696\pi$
$631$			10145.6i			0.640079i	−0.947404	+	0.320040i	$0.896304\pi$
$632$	3714.10	+	3714.10i	0.233764	+	0.233764i
$633$		0			0
$634$	−6697.40	−	6697.40i	−0.419539	−	0.419539i
$635$	−25750.8	+	25750.8i	−1.60927	+	1.60927i
$636$		0			0
$637$			3460.18i			0.215223i
$638$			9554.05i			0.592866i
$639$		0			0
$640$	−1657.50	+	1657.50i	−0.102372	+	0.102372i
$641$	−2416.01	−	2416.01i	−0.148871	−	0.148871i	0.628742	−	0.777614i	$-0.283570\pi$
$641$	−2416.01	−	2416.01i	−0.148871	−	0.148871i	−0.777614	+	0.628742i	$0.783570\pi$
$642$		0			0
$643$	−11621.0	−	11621.0i	−0.712736	−	0.712736i	0.254371	−	0.967107i	$-0.418132\pi$
$643$	−11621.0	−	11621.0i	−0.712736	−	0.712736i	−0.967107	+	0.254371i	$0.918132\pi$
$644$		−	13919.3i		−	0.851706i
$645$		0			0
$646$	−529.676	−	2132.26i	−0.0322598	−	0.129865i
$647$	−9019.31			−0.548046			−0.274023	−	0.961723i	$-0.588354\pi$
$647$	−9019.31			−0.548046			−0.274023	+	0.961723i	$0.588354\pi$
$648$		0			0
$649$	6739.20	+	6739.20i	0.407607	+	0.407607i
$650$	5644.01			0.340579
$651$		0			0
$652$	−7387.23	+	7387.23i	−0.443721	+	0.443721i
$653$	9946.84	−	9946.84i	0.596095	−	0.596095i	−0.343176	−	0.939271i	$-0.611503\pi$
$653$	9946.84	−	9946.84i	0.596095	−	0.596095i	0.939271	+	0.343176i	$0.111503\pi$
$654$		0			0
$655$			17975.7i			1.07232i
$656$	−2744.45	+	2744.45i	−0.163343	+	0.163343i
$657$		0			0
$658$	18478.4	+	18478.4i	1.09477	+	1.09477i
$659$	−18759.1			−1.10888			−0.554438	−	0.832225i	$-0.687067\pi$
$659$	−18759.1			−1.10888			−0.554438	+	0.832225i	$0.687067\pi$
$660$		0			0
$661$			22941.6i			1.34996i	0.737836	+	0.674980i	$0.235848\pi$
$661$			22941.6i			1.34996i	−0.737836	+	0.674980i	$0.764152\pi$
$662$	−7756.18			−0.455366
$663$		0			0
$664$	9951.51			0.581617
$665$		−	7035.76i		−	0.410278i
$666$		0			0
$667$	18987.8			1.10226
$668$	3536.60	+	3536.60i	0.204843	+	0.204843i
$669$		0			0
$670$	−11428.1	+	11428.1i	−0.658964	+	0.658964i
$671$		−	24449.8i		−	1.40667i
$672$		0			0
$673$	7783.39	−	7783.39i	0.445807	−	0.445807i	−0.448151	−	0.893958i	$-0.647917\pi$
$673$	7783.39	−	7783.39i	0.445807	−	0.445807i	0.893958	+	0.448151i	$0.147917\pi$
$674$	3809.90	−	3809.90i	0.217733	−	0.217733i
$675$		0			0
$676$	8068.16			0.459044
$677$	−6957.54	−	6957.54i	−0.394978	−	0.394978i	0.481480	−	0.876457i	$-0.340100\pi$
$677$	−6957.54	−	6957.54i	−0.394978	−	0.394978i	−0.876457	+	0.481480i	$0.840100\pi$
$678$		0			0
$679$	3121.54			0.176427
$680$	−8797.55	−	5296.44i	−0.496133	−	0.298690i
$681$		0			0
$682$		−	13521.0i		−	0.759157i
$683$	13910.7	+	13910.7i	0.779323	+	0.779323i	0.979716	−	0.200392i	$-0.0642217\pi$
$683$	13910.7	+	13910.7i	0.779323	+	0.779323i	−0.200392	+	0.979716i	$0.564222\pi$
$684$		0			0
$685$	−36102.5	−	36102.5i	−2.01373	−	2.01373i
$686$	−2949.01	+	2949.01i	−0.164131	+	0.164131i
$687$		0			0
$688$			6169.85i			0.341894i
$689$			5416.95i			0.299520i
$690$		0			0
$691$	6593.82	−	6593.82i	0.363011	−	0.363011i	−0.501909	−	0.864920i	$-0.667369\pi$
$691$	6593.82	−	6593.82i	0.363011	−	0.363011i	0.864920	+	0.501909i	$0.167369\pi$
$692$	9738.17	+	9738.17i	0.534956	+	0.534956i
$693$		0			0
$694$	−10136.6	−	10136.6i	−0.554441	−	0.554441i
$695$			3064.07i			0.167233i
$696$		0			0
$697$	−14566.8	−	8769.75i	−0.791618	−	0.476582i
$698$	3034.63			0.164559
$699$		0			0
$700$	−14585.8	−	14585.8i	−0.787559	−	0.787559i
$701$	−4811.86			−0.259260			−0.129630	−	0.991562i	$-0.541379\pi$
$701$	−4811.86			−0.259260			−0.129630	+	0.991562i	$0.541379\pi$
$702$		0			0
$703$	3039.97	−	3039.97i	0.163093	−	0.163093i
$704$	1616.19	−	1616.19i	0.0865234	−	0.0865234i
$705$		0			0
$706$		−	9294.61i		−	0.495478i
$707$	19980.0	−	19980.0i	1.06284	−	1.06284i
$708$		0			0
$709$	19747.1	+	19747.1i	1.04600	+	1.04600i	0.998890	+	0.0471139i	$0.0150024\pi$
$709$	19747.1	+	19747.1i	1.04600	+	1.04600i	0.0471139	+	0.998890i	$0.484998\pi$
$710$	15737.9			0.831876
$711$		0			0
$712$			11988.0i			0.630995i
$713$	−26871.7			−1.41143
$714$		0			0
$715$	−8773.50			−0.458895
$716$		−	6562.09i		−	0.342509i
$717$		0			0
$718$	4730.19			0.245862
$719$	6565.65	+	6565.65i	0.340553	+	0.340553i	0.856575	−	0.516022i	$-0.172588\pi$
$719$	6565.65	+	6565.65i	0.340553	+	0.340553i	−0.516022	+	0.856575i	$0.672588\pi$
$720$		0			0
$721$	2219.48	−	2219.48i	0.114643	−	0.114643i
$722$			13226.7i			0.681785i
$723$		0			0
$724$	−740.232	+	740.232i	−0.0379979	+	0.0379979i
$725$	19896.9	−	19896.9i	1.01925	−	1.01925i
$726$		0			0
$727$	−3740.62			−0.190828			−0.0954140	−	0.995438i	$-0.530418\pi$
$727$	−3740.62			−0.190828			−0.0954140	+	0.995438i	$0.530418\pi$
$728$	1860.27	+	1860.27i	0.0947063	+	0.0947063i
$729$		0			0
$730$	−4473.60			−0.226816
$731$	−26231.6	+	6516.23i	−1.32724	+	0.329701i
$732$		0			0
$733$		−	23222.5i		−	1.17018i	−0.810967	−	0.585092i	$-0.801059\pi$
$733$		−	23222.5i		−	1.17018i	0.810967	−	0.585092i	$-0.198941\pi$
$734$	−0.300592	−	0.300592i	−1.51159e−5	−	1.51159e-5i
$735$		0			0
$736$	−3212.03	−	3212.03i	−0.160865	−	0.160865i
$737$	11143.3	−	11143.3i	0.556944	−	0.556944i
$738$		0			0
$739$		−	9987.91i		−	0.497173i	−0.968610	−	0.248587i	$-0.920034\pi$
$739$		−	9987.91i		−	0.497173i	0.968610	−	0.248587i	$-0.0799661\pi$
$740$		−	20093.9i		−	0.998196i
$741$		0			0
$742$	13999.0	−	13999.0i	0.692614	−	0.692614i
$743$	−25752.7	−	25752.7i	−1.27157	−	1.27157i	−0.945266	−	0.326302i	$-0.894197\pi$
$743$	−25752.7	−	25752.7i	−1.27157	−	1.27157i	−0.326302	−	0.945266i	$-0.605803\pi$
$744$		0			0
$745$	−37899.3	−	37899.3i	−1.86379	−	1.86379i
$746$			16957.0i			0.832223i
$747$		0			0
$748$	8578.30	+	5164.45i	0.419323	+	0.252448i
$749$	−40586.1			−1.97995
$750$		0			0
$751$	−10329.3	−	10329.3i	−0.501894	−	0.501894i	0.410132	−	0.912026i	$-0.365483\pi$
$751$	−10329.3	−	10329.3i	−0.501894	−	0.501894i	−0.912026	+	0.410132i	$0.865483\pi$
$752$	8528.14			0.413550
$753$		0			0
$754$	−2537.65	+	2537.65i	−0.122567	+	0.122567i
$755$	27742.4	−	27742.4i	1.33728	−	1.33728i
$756$		0			0
$757$			25138.4i			1.20696i	0.797378	+	0.603481i	$0.206220\pi$
$757$			25138.4i			1.20696i	−0.797378	+	0.603481i	$0.793780\pi$
$758$	8242.87	−	8242.87i	0.394980	−	0.394980i
$759$		0			0
$760$	−1623.57	−	1623.57i	−0.0774910	−	0.0774910i
$761$	13550.5			0.645473			0.322737	−	0.946489i	$-0.395397\pi$
$761$	13550.5			0.645473			0.322737	+	0.946489i	$0.395397\pi$
$762$		0			0
$763$			40961.1i			1.94350i
$764$	10394.4			0.492219
$765$		0			0
$766$	−3123.71			−0.147342
$767$			3580.00i			0.168535i
$768$		0			0
$769$	30080.8			1.41059			0.705294	−	0.708915i	$-0.250815\pi$
$769$	30080.8			1.41059			0.705294	+	0.708915i	$0.250815\pi$
$770$	22673.3	+	22673.3i	1.06116	+	1.06116i
$771$		0			0
$772$	11703.1	−	11703.1i	0.545600	−	0.545600i
$773$			11588.8i			0.539226i	0.962969	+	0.269613i	$0.0868958\pi$
$773$			11588.8i			0.539226i	−0.962969	+	0.269613i	$0.913104\pi$
$774$		0			0
$775$	−28158.3	+	28158.3i	−1.30513	+	1.30513i
$776$	720.327	−	720.327i	0.0333225	−	0.0333225i
$777$		0			0
$778$	−14087.6			−0.649182
$779$	−2688.28	−	2688.28i	−0.123643	−	0.123643i
$780$		0			0
$781$	−15345.7			−0.703087
$782$	10263.9	−	17048.6i	0.469354	−	0.779610i
$783$		0			0
$784$		−	4126.97i		−	0.188000i
$785$	−17213.0	−	17213.0i	−0.782620	−	0.782620i
$786$		0			0
$787$	3121.23	+	3121.23i	0.141372	+	0.141372i	0.774251	−	0.632879i	$-0.218127\pi$
$787$	3121.23	+	3121.23i	0.141372	+	0.141372i	−0.632879	+	0.774251i	$0.718127\pi$
$788$	−3590.93	+	3590.93i	−0.162337	+	0.162337i
$789$		0			0
$790$			24047.4i			1.08300i
$791$		−	4404.77i		−	0.197997i
$792$		0			0
$793$	6494.10	−	6494.10i	0.290810	−	0.290810i
$794$	−16623.2	−	16623.2i	−0.742990	−	0.742990i
$795$		0			0
$796$	15295.5	+	15295.5i	0.681074	+	0.681074i
$797$			36966.3i			1.64293i	0.570260	+	0.821464i	$0.306843\pi$
$797$			36966.3i			1.64293i	−0.570260	+	0.821464i	$0.693157\pi$
$798$		0			0
$799$	9006.92	+	36258.1i	0.398801	+	1.60541i
$800$	−6731.65			−0.297500
$801$		0			0
$802$	−382.221	−	382.221i	−0.0168288	−	0.0168288i
$803$	4362.11			0.191701
$804$		0			0
$805$	45061.1	−	45061.1i	1.97291	−	1.97291i
$806$	3591.30	−	3591.30i	0.156946	−	0.156946i
$807$		0			0
$808$		−	9221.17i		−	0.401485i
$809$	23264.9	−	23264.9i	1.01106	−	1.01106i	0.0111248	−	0.999938i	$-0.496459\pi$
$809$	23264.9	−	23264.9i	1.01106	−	1.01106i	0.999938	−	0.0111248i	$-0.00354120\pi$
$810$		0			0
$811$	−12867.2	−	12867.2i	−0.557126	−	0.557126i	0.371362	−	0.928488i	$-0.378891\pi$
$811$	−12867.2	−	12867.2i	−0.557126	−	0.557126i	−0.928488	+	0.371362i	$0.878891\pi$
$812$	13116.1			0.566852
$813$		0			0
$814$			19593.1i			0.843658i
$815$	−47829.4			−2.05569
$816$		0			0
$817$	−6043.57			−0.258798
$818$		−	21922.7i		−	0.937055i
$819$		0			0
$820$	−17769.3			−0.756743
$821$	−10846.1	−	10846.1i	−0.461060	−	0.461060i	0.437943	−	0.899003i	$-0.355707\pi$
$821$	−10846.1	−	10846.1i	−0.461060	−	0.461060i	−0.899003	+	0.437943i	$0.855707\pi$
$822$		0			0
$823$	22850.1	−	22850.1i	0.967807	−	0.967807i	−0.0316911	−	0.999498i	$-0.510089\pi$
$823$	22850.1	−	22850.1i	0.967807	−	0.967807i	0.999498	+	0.0316911i	$0.0100893\pi$
$824$		−	1024.34i		−	0.0433064i
$825$		0			0
$826$	9251.77	−	9251.77i	0.389722	−	0.389722i
$827$	−8154.95	+	8154.95i	−0.342896	+	0.342896i	−0.857455	−	0.514559i	$-0.827956\pi$
$827$	−8154.95	+	8154.95i	−0.342896	+	0.342896i	0.514559	+	0.857455i	$0.327956\pi$
$828$		0			0
$829$	28488.7			1.19355			0.596774	−	0.802409i	$-0.296449\pi$
$829$	28488.7			1.19355			0.596774	+	0.802409i	$0.296449\pi$
$830$	32216.1	+	32216.1i	1.34727	+	1.34727i
$831$		0			0
$832$	858.552			0.0357752
$833$	17546.2	−	4358.67i	0.729818	−	0.181295i
$834$		0			0
$835$			22898.1i			0.949007i
$836$	1583.11	+	1583.11i	0.0654941	+	0.0654941i
$837$		0			0
$838$	16256.8	+	16256.8i	0.670144	+	0.670144i
$839$	−13682.6	+	13682.6i	−0.563021	+	0.563021i	−0.930164	−	0.367143i	$-0.880336\pi$
$839$	−13682.6	+	13682.6i	−0.563021	+	0.563021i	0.367143	+	0.930164i	$0.380336\pi$
$840$		0			0
$841$		−	6496.97i		−	0.266389i
$842$			22350.6i			0.914789i
$843$		0			0
$844$	−9397.97	+	9397.97i	−0.383284	+	0.383284i
$845$	26119.1	+	26119.1i	1.06334	+	1.06334i
$846$		0			0
$847$	963.313	+	963.313i	0.0390789	+	0.0390789i
$848$		−	6460.83i		−	0.261634i
$849$		0			0
$850$	−7109.57	−	28620.2i	−0.286890	−	1.15490i
$851$	38939.4			1.56854
$852$		0			0
$853$	−16798.3	−	16798.3i	−0.674281	−	0.674281i	0.284419	−	0.958700i	$-0.408199\pi$
$853$	−16798.3	−	16798.3i	−0.674281	−	0.674281i	−0.958700	+	0.284419i	$0.908199\pi$
$854$	−33565.4			−1.34494
$855$		0			0
$856$	−9365.67	+	9365.67i	−0.373963	+	0.373963i
$857$	−3594.51	+	3594.51i	−0.143274	+	0.143274i	−0.775106	−	0.631831i	$-0.782303\pi$
$857$	−3594.51	+	3594.51i	−0.143274	+	0.143274i	0.631831	+	0.775106i	$0.282303\pi$
$858$		0			0
$859$		−	32488.7i		−	1.29046i	−0.763990	−	0.645228i	$-0.776763\pi$
$859$		−	32488.7i		−	1.29046i	0.763990	−	0.645228i	$-0.223237\pi$
$860$	−19973.7	+	19973.7i	−0.791973	+	0.791973i
$861$		0			0
$862$	17660.7	+	17660.7i	0.697824	+	0.697824i
$863$	30304.2			1.19532			0.597662	−	0.801748i	$-0.296096\pi$
$863$	30304.2			1.19532			0.597662	+	0.801748i	$0.296096\pi$
$864$		0			0
$865$			63050.8i			2.47837i
$866$	4070.44			0.159722
$867$		0			0
$868$	−18562.0			−0.725846
$869$		−	23448.1i		−	0.915329i
$870$		0			0
$871$	5919.53			0.230282
$872$	9452.20	+	9452.20i	0.367078	+	0.367078i
$873$		0			0
$874$	3146.28	−	3146.28i	0.121767	−	0.121767i
$875$		−	38321.9i		−	1.48059i
$876$		0			0
$877$	−15323.5	+	15323.5i	−0.590009	+	0.590009i	−0.937634	−	0.347624i	$-0.886988\pi$
$877$	−15323.5	+	15323.5i	−0.590009	+	0.590009i	0.347624	+	0.937634i	$0.386988\pi$
$878$	13897.1	−	13897.1i	0.534175	−	0.534175i
$879$		0			0
$880$	10464.2			0.400850
$881$	24765.1	+	24765.1i	0.947056	+	0.947056i	0.998667	−	0.0516111i	$-0.0164356\pi$
$881$	24765.1	+	24765.1i	0.947056	+	0.947056i	−0.0516111	+	0.998667i	$0.516436\pi$
$882$		0			0
$883$	35916.7			1.36885			0.684425	−	0.729084i	$-0.260054\pi$
$883$	35916.7			1.36885			0.684425	+	0.729084i	$0.260054\pi$
$884$	906.753	+	3650.21i	0.0344993	+	0.138880i
$885$		0			0
$886$			2809.85i			0.106545i
$887$	17482.6	+	17482.6i	0.661790	+	0.661790i	0.955802	−	0.294012i	$-0.0949904\pi$
$887$	17482.6	+	17482.6i	0.661790	+	0.661790i	−0.294012	+	0.955802i	$0.594990\pi$
$888$		0			0
$889$	−34470.4	−	34470.4i	−1.30045	−	1.30045i
$890$	−38808.7	+	38808.7i	−1.46165	+	1.46165i
$891$		0			0
$892$			8977.29i			0.336975i
$893$			8353.59i			0.313037i
$894$		0			0
$895$	21243.5	−	21243.5i	0.793397	−	0.793397i
$896$	−2218.75	−	2218.75i	−0.0827269	−	0.0827269i
$897$		0			0
$898$	−8882.99	−	8882.99i	−0.330099	−	0.330099i
$899$		−	25321.0i		−	0.939378i
$900$		0			0
$901$	27468.7	−	6823.55i	1.01567	−	0.252303i
$902$	17326.4			0.639586
$903$		0			0
$904$	−1016.44	−	1016.44i	−0.0373965	−	0.0373965i
$905$	−4792.71			−0.176039
$906$		0			0
$907$	−5525.49	+	5525.49i	−0.202283	+	0.202283i	−0.800978	−	0.598694i	$-0.795686\pi$
$907$	−5525.49	+	5525.49i	−0.202283	+	0.202283i	0.598694	+	0.800978i	$0.295686\pi$
$908$	9765.83	−	9765.83i	0.356928	−	0.356928i
$909$		0			0
$910$			12044.5i			0.438760i
$911$	11064.3	−	11064.3i	0.402390	−	0.402390i	−0.476684	−	0.879074i	$-0.658162\pi$
$911$	11064.3	−	11064.3i	0.402390	−	0.402390i	0.879074	+	0.476684i	$0.158162\pi$
$912$		0			0
$913$	−31413.2	−	31413.2i	−1.13869	−	1.13869i
$914$	−32608.2			−1.18007
$915$		0			0
$916$			10730.7i			0.387065i
$917$	−24062.6			−0.866539
$918$		0			0
$919$	−54133.9			−1.94310			−0.971552	−	0.236825i	$-0.923893\pi$
$919$	−54133.9			−1.94310			−0.971552	+	0.236825i	$0.923893\pi$
$920$		−	20796.6i		−	0.745265i
$921$		0			0
$922$	160.013			0.00571556
$923$	−4075.96	−	4075.96i	−0.145354	−	0.145354i
$924$		0			0
$925$	40803.9	−	40803.9i	1.45040	−	1.45040i
$926$			5239.41i			0.185937i
$927$		0			0
$928$	3026.67	−	3026.67i	0.107064	−	0.107064i
$929$	2614.28	−	2614.28i	0.0923270	−	0.0923270i	−0.659435	−	0.751762i	$-0.729204\pi$
$929$	2614.28	−	2614.28i	0.0923270	−	0.0923270i	0.751762	+	0.659435i	$0.229204\pi$
$930$		0			0
$931$	4042.50			0.142307
$932$	−4464.10	−	4464.10i	−0.156895	−	0.156895i
$933$		0			0
$934$	2720.14			0.0952952
$935$	11051.7	+	44489.4i	0.386554	+	1.55611i
$936$		0			0
$937$		−	9888.38i		−	0.344759i	−0.985031	−	0.172380i	$-0.944854\pi$
$937$		−	9888.38i		−	0.344759i	0.985031	−	0.172380i	$-0.0551456\pi$
$938$	−15297.8	−	15297.8i	−0.532507	−	0.532507i
$939$		0			0
$940$	27608.2	+	27608.2i	0.957957	+	0.957957i
$941$	1174.44	−	1174.44i	0.0406860	−	0.0406860i	−0.686471	−	0.727157i	$-0.740841\pi$
$941$	1174.44	−	1174.44i	0.0406860	−	0.0406860i	0.727157	+	0.686471i	$0.240841\pi$
$942$		0			0
$943$		−	34434.6i		−	1.18913i
$944$		−	4269.88i		−	0.147217i
$945$		0			0
$946$	19475.9	−	19475.9i	0.669361	−	0.669361i
$947$	16396.0	+	16396.0i	0.562618	+	0.562618i	0.930050	−	0.367433i	$-0.119763\pi$
$947$	16396.0	+	16396.0i	0.562618	+	0.562618i	−0.367433	+	0.930050i	$0.619763\pi$
$948$		0			0
$949$	1158.62	+	1158.62i	0.0396316	+	0.0396316i
$950$		−	6593.87i		−	0.225193i
$951$		0			0
$952$	7089.90	−	11776.5i	0.241371	−	0.400924i
$953$	1163.54			0.0395495			0.0197748	−	0.999804i	$-0.493705\pi$
$953$	1163.54			0.0395495			0.0197748	+	0.999804i	$0.493705\pi$
$954$		0			0
$955$	33649.8	+	33649.8i	1.14019	+	1.14019i
$956$	20064.8			0.678810
$957$		0			0
$958$	−13900.5	+	13900.5i	−0.468795	+	0.468795i
$959$	48327.4	−	48327.4i	1.62729	−	1.62729i
$960$		0			0
$961$			6043.44i			0.202861i
$962$	−5204.11	+	5204.11i	−0.174415	+	0.174415i
$963$		0			0
$964$	4603.76	+	4603.76i	0.153815	+	0.153815i
$965$	75772.9			2.52768
$966$		0			0
$967$		−	31087.8i		−	1.03383i	−0.856036	−	0.516916i	$-0.827080\pi$
$967$		−	31087.8i		−	1.03383i	0.856036	−	0.516916i	$-0.172920\pi$
$968$	444.589			0.0147620
$969$		0			0
$970$	4663.83			0.154378
$971$			5352.03i			0.176885i	0.996081	+	0.0884423i	$0.0281889\pi$
$971$			5352.03i			0.176885i	−0.996081	+	0.0884423i	$0.971811\pi$
$972$		0			0
$973$	−4101.62			−0.135141
$974$	10330.5	+	10330.5i	0.339847	+	0.339847i
$975$		0			0
$976$	−7745.55	+	7745.55i	−0.254026	+	0.254026i
$977$		−	27767.7i		−	0.909282i	−0.890675	−	0.454641i	$-0.849768\pi$
$977$		−	27767.7i		−	0.909282i	0.890675	−	0.454641i	$-0.150232\pi$
$978$		0			0
$979$	37841.5	−	37841.5i	1.23536	−	1.23536i
$980$	13360.3	−	13360.3i	0.435487	−	0.435487i
$981$		0			0
$982$	37374.6			1.21453
$983$	20541.2	+	20541.2i	0.666492	+	0.666492i	0.956902	−	0.290410i	$-0.0937917\pi$
$983$	20541.2	+	20541.2i	0.666492	+	0.666492i	−0.290410	+	0.956902i	$0.593792\pi$
$984$		0			0
$985$	−23249.9			−0.752083
$986$	16064.7	+	9671.55i	0.518869	+	0.312378i
$987$		0			0
$988$			840.979i			0.0270801i
$989$	−38706.5	−	38706.5i	−1.24448	−	1.24448i
$990$		0			0
$991$	16947.4	+	16947.4i	0.543242	+	0.543242i	0.924478	−	0.381236i	$-0.124501\pi$
$991$	16947.4	+	16947.4i	0.543242	+	0.543242i	−0.381236	+	0.924478i	$0.624501\pi$
$992$	−4283.37	+	4283.37i	−0.137094	+	0.137094i
$993$		0			0
$994$			21067.0i			0.672237i
$995$			99032.4i			3.15532i
$996$		0			0
$997$	−29861.9	+	29861.9i	−0.948582	+	0.948582i	−0.998741	−	0.0501591i	$-0.984027\pi$
$997$	−29861.9	+	29861.9i	−0.948582	+	0.948582i	0.0501591	+	0.998741i	$0.484027\pi$
$998$	11537.2	+	11537.2i	0.365936	+	0.365936i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	306.4.g.g.217.1		12
3.2	odd	2		102.4.f.c.13.3	✓	12
17.4	even	4	inner	306.4.g.g.55.1		12
51.2	odd	8		1734.4.a.bd.1.1		6
51.32	odd	8		1734.4.a.be.1.6		6
51.38	odd	4		102.4.f.c.55.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.4.f.c.13.3	✓	12	3.2	odd	2
102.4.f.c.55.3	yes	12	51.38	odd	4
306.4.g.g.55.1		12	17.4	even	4	inner
306.4.g.g.217.1		12	1.1	even	1	trivial
1734.4.a.bd.1.1		6	51.2	odd	8
1734.4.a.be.1.6		6	51.32	odd	8

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:	\( N \)	\(=\)	\( 306 = 2 \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	306.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -4.00000 q^{4} +(-12.9492 - 12.9492i) q^{5} +(17.3340 - 17.3340i) q^{7} -8.00000i q^{8} +(25.8984 - 25.8984i) q^{10} +(-25.2530 + 25.2530i) q^{11} -13.4149 q^{13} +(34.6680 + 34.6680i) q^{14} +16.0000 q^{16} +(16.8983 + 68.0254i) q^{17} +15.6725i q^{19} +(51.7968 + 51.7968i) q^{20} +(-50.5060 - 50.5060i) q^{22} +(-100.376 + 100.376i) q^{23} +210.364i q^{25} -26.8298i q^{26} +(-69.3360 + 69.3360i) q^{28} +(-94.5834 - 94.5834i) q^{29} +(133.855 + 133.855i) q^{31} +32.0000i q^{32} +(-136.051 + 33.7965i) q^{34} -448.923 q^{35} +(-193.968 - 193.968i) q^{37} -31.3450 q^{38} +(-103.594 + 103.594i) q^{40} +(-171.528 + 171.528i) q^{41} +385.616i q^{43} +(101.012 - 101.012i) q^{44} +(-200.752 - 200.752i) q^{46} +533.009 q^{47} -257.936i q^{49} -420.728 q^{50} +53.6595 q^{52} -403.802i q^{53} +654.012 q^{55} +(-138.672 - 138.672i) q^{56} +(189.167 - 189.167i) q^{58} -266.868i q^{59} +(-484.097 + 484.097i) q^{61} +(-267.710 + 267.710i) q^{62} -64.0000 q^{64} +(173.712 + 173.712i) q^{65} -441.266 q^{67} +(-67.5931 - 272.101i) q^{68} -897.847i q^{70} +(303.839 + 303.839i) q^{71} +(-86.3683 - 86.3683i) q^{73} +(387.936 - 387.936i) q^{74} -62.6901i q^{76} +875.471i q^{77} +(-464.263 + 464.263i) q^{79} +(-207.187 - 207.187i) q^{80} +(-343.057 - 343.057i) q^{82} +1243.94i q^{83} +(662.055 - 1099.69i) q^{85} -771.231 q^{86} +(202.024 + 202.024i) q^{88} -1498.50 q^{89} +(-232.534 + 232.534i) q^{91} +(401.503 - 401.503i) q^{92} +1066.02i q^{94} +(202.947 - 202.947i) q^{95} +(90.0409 + 90.0409i) q^{97} +515.871 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 48 q^{4} - 16 q^{5} - 12 q^{7} + 32 q^{10} + 32 q^{11} - 68 q^{13} - 24 q^{14} + 192 q^{16} - 64 q^{17} + 64 q^{20} + 64 q^{22} + 112 q^{23} + 48 q^{28} + 296 q^{29} + 520 q^{31} + 144 q^{34} - 392 q^{35}+ \cdots + 4168 q^{98}+O(q^{100}) \) 12 * q - 48 * q^4 - 16 * q^5 - 12 * q^7 + 32 * q^10 + 32 * q^11 - 68 * q^13 - 24 * q^14 + 192 * q^16 - 64 * q^17 + 64 * q^20 + 64 * q^22 + 112 * q^23 + 48 * q^28 + 296 * q^29 + 520 * q^31 + 144 * q^34 - 392 * q^35 - 828 * q^37 + 280 * q^38 - 128 * q^40 - 8 * q^41 - 128 * q^44 + 224 * q^46 + 2920 * q^47 - 752 * q^50 + 272 * q^52 + 1156 * q^55 + 96 * q^56 - 592 * q^58 - 1124 * q^61 - 1040 * q^62 - 768 * q^64 - 3288 * q^65 - 2008 * q^67 + 256 * q^68 + 2184 * q^71 + 2456 * q^73 + 1656 * q^74 + 2652 * q^79 - 256 * q^80 - 16 * q^82 + 3444 * q^85 + 184 * q^86 - 256 * q^88 - 5304 * q^89 - 1420 * q^91 - 448 * q^92 + 2920 * q^95 + 2688 * q^97 + 4168 * q^98

Introduction

L-functions

Modular forms

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