LMFDB - Embedded newform 108.4.h.b.35.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.5
Character	$\chi$	$=$	108.35
Dual form			108.4.h.b.71.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.823719 + 2.70582i) q^{2} +(-6.64298 - 4.45768i) q^{4} +(4.71466 - 2.72201i) q^{5} +(20.9358 + 12.0873i) q^{7} +(17.5336 - 14.3029i) q^{8} +O(q^{10})$	\(q+(-0.823719 + 2.70582i) q^{2} +(-6.64298 - 4.45768i) q^{4} +(4.71466 - 2.72201i) q^{5} +(20.9358 + 12.0873i) q^{7} +(17.5336 - 14.3029i) q^{8} +(3.48173 + 14.9992i) q^{10} +(-25.3999 + 43.9939i) q^{11} +(25.0883 + 43.4542i) q^{13} +(-49.9512 + 46.6920i) q^{14} +(24.2582 + 59.2245i) q^{16} -51.7146i q^{17} +27.9305i q^{19} +(-43.4533 - 2.93419i) q^{20} +(-98.1174 - 104.966i) q^{22} +(3.93548 + 6.81645i) q^{23} +(-47.6813 + 82.5864i) q^{25} +(-138.245 + 32.0905i) q^{26} +(-85.1946 - 173.620i) q^{28} +(212.788 + 122.853i) q^{29} +(-51.4009 + 29.6763i) q^{31} +(-180.233 + 16.8542i) q^{32} +(139.931 + 42.5982i) q^{34} +131.607 q^{35} +295.334 q^{37} +(-75.5750 - 23.0069i) q^{38} +(43.7327 - 115.160i) q^{40} +(146.833 - 84.7741i) q^{41} +(-284.968 - 164.526i) q^{43} +(364.841 - 179.026i) q^{44} +(-21.6859 + 5.03388i) q^{46} +(47.9742 - 83.0938i) q^{47} +(120.704 + 209.066i) q^{49} +(-184.188 - 197.045i) q^{50} +(27.0439 - 400.500i) q^{52} -300.751i q^{53} +276.555i q^{55} +(539.963 - 87.5075i) q^{56} +(-507.697 + 474.571i) q^{58} +(-113.273 - 196.195i) q^{59} +(173.722 - 300.896i) q^{61} +(-37.9590 - 163.527i) q^{62} +(102.857 - 501.562i) q^{64} +(236.566 + 136.581i) q^{65} +(904.675 - 522.314i) q^{67} +(-230.527 + 343.538i) q^{68} +(-108.407 + 356.105i) q^{70} -243.524 q^{71} -1094.68 q^{73} +(-243.272 + 799.122i) q^{74} +(124.505 - 185.542i) q^{76} +(-1063.53 + 614.031i) q^{77} +(-530.679 - 306.388i) q^{79} +(275.579 + 213.192i) q^{80} +(108.435 + 467.135i) q^{82} +(-283.063 + 490.280i) q^{83} +(-140.768 - 243.817i) q^{85} +(679.912 - 635.549i) q^{86} +(183.886 + 1134.66i) q^{88} +212.529i q^{89} +1213.00i q^{91} +(4.24224 - 62.8246i) q^{92} +(185.320 + 198.256i) q^{94} +(76.0272 + 131.683i) q^{95} +(234.298 - 405.817i) q^{97} +(-665.122 + 154.393i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) $ 24 * q - 12 * q^4 + 72 * q^5	$ 24 q - 12 q^{4} + 72 q^{5} + 96 q^{10} - 216 q^{13} + 36 q^{14} - 72 q^{16} + 540 q^{20} - 192 q^{22} + 252 q^{25} - 672 q^{28} - 576 q^{29} - 360 q^{32} - 660 q^{34} + 1248 q^{37} + 144 q^{38} + 636 q^{40} - 1116 q^{41} + 960 q^{46} + 348 q^{49} + 648 q^{50} + 132 q^{52} + 1692 q^{56} + 516 q^{58} - 264 q^{61} + 960 q^{64} + 2592 q^{65} - 5688 q^{68} + 564 q^{70} - 4776 q^{73} - 5652 q^{74} - 600 q^{76} - 648 q^{77} - 4104 q^{82} + 720 q^{85} + 9540 q^{86} + 1956 q^{88} + 7416 q^{92} - 1188 q^{94} + 588 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 + 72 * q^5 + 96 * q^10 - 216 * q^13 + 36 * q^14 - 72 * q^16 + 540 * q^20 - 192 * q^22 + 252 * q^25 - 672 * q^28 - 576 * q^29 - 360 * q^32 - 660 * q^34 + 1248 * q^37 + 144 * q^38 + 636 * q^40 - 1116 * q^41 + 960 * q^46 + 348 * q^49 + 648 * q^50 + 132 * q^52 + 1692 * q^56 + 516 * q^58 - 264 * q^61 + 960 * q^64 + 2592 * q^65 - 5688 * q^68 + 564 * q^70 - 4776 * q^73 - 5652 * q^74 - 600 * q^76 - 648 * q^77 - 4104 * q^82 + 720 * q^85 + 9540 * q^86 + 1956 * q^88 + 7416 * q^92 - 1188 * q^94 + 588 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.823719	+	2.70582i	−0.291229	+	0.956654i
$2$	−0.823719	+	2.70582i	−0.291229	+	0.956654i
$3$		0			0
$3$		0			0
$4$	−6.64298	−	4.45768i	−0.830372	−	0.557210i
$5$	4.71466	−	2.72201i	0.421692	−	0.243464i	−0.274109	−	0.961699i	$-0.588383\pi$
$5$	4.71466	−	2.72201i	0.421692	−	0.243464i	0.695801	+	0.718234i	$0.255049\pi$
$6$		0			0
$7$	20.9358	+	12.0873i	1.13043	+	0.652651i	0.944042	−	0.329826i	$-0.106990\pi$
$7$	20.9358	+	12.0873i	1.13043	+	0.652651i	0.186383	+	0.982477i	$0.440323\pi$
$8$	17.5336	−	14.3029i	0.774885	−	0.632103i
$9$		0			0
$10$	3.48173	+	14.9992i	0.110102	+	0.474317i
$11$	−25.3999	+	43.9939i	−0.696214	+	1.20588i	0.273556	+	0.961856i	$0.411800\pi$
$11$	−25.3999	+	43.9939i	−0.696214	+	1.20588i	−0.969770	+	0.244022i	$0.921533\pi$
$12$		0			0
$13$	25.0883	+	43.4542i	0.535249	+	0.927078i	0.999151	+	0.0411921i	$0.0131156\pi$
$13$	25.0883	+	43.4542i	0.535249	+	0.927078i	−0.463902	+	0.885886i	$0.653551\pi$
$14$	−49.9512	+	46.6920i	−0.953573	+	0.891355i
$15$		0			0
$16$	24.2582	+	59.2245i	0.379035	+	0.925382i
$17$		−	51.7146i		−	0.737801i	−0.929469	−	0.368901i	$-0.879734\pi$
$17$		−	51.7146i		−	0.737801i	0.929469	−	0.368901i	$-0.120266\pi$
$18$		0			0
$19$			27.9305i			0.337247i	0.985681	+	0.168624i	$0.0539322\pi$
$19$			27.9305i			0.337247i	−0.985681	+	0.168624i	$0.946068\pi$
$20$	−43.4533	−	2.93419i	−0.485822	−	0.0328052i
$21$		0			0
$22$	−98.1174	−	104.966i	−0.950850	−	1.01722i
$23$	3.93548	+	6.81645i	0.0356785	+	0.0617969i	0.883313	−	0.468783i	$-0.155307\pi$
$23$	3.93548	+	6.81645i	0.0356785	+	0.0617969i	−0.847635	+	0.530580i	$0.821974\pi$
$24$		0			0
$25$	−47.6813	+	82.5864i	−0.381450	+	0.660691i
$26$	−138.245	+	32.0905i	−1.04277	+	0.242056i
$27$		0			0
$28$	−85.1946	−	173.620i	−0.575010	−	1.17183i
$29$	212.788	+	122.853i	1.36254	+	0.786665i	0.989962	−	0.141335i	$-0.0451395\pi$
$29$	212.788	+	122.853i	1.36254	+	0.786665i	0.372581	+	0.928000i	$0.378473\pi$
$30$		0			0
$31$	−51.4009	+	29.6763i	−0.297802	+	0.171936i	−0.641455	−	0.767161i	$-0.721669\pi$
$31$	−51.4009	+	29.6763i	−0.297802	+	0.171936i	0.343653	+	0.939097i	$0.388336\pi$
$32$	−180.233	+	16.8542i	−0.995656	+	0.0931073i
$33$		0			0
$34$	139.931	+	42.5982i	0.705820	+	0.214869i
$35$	131.607			0.635589
$36$		0			0
$37$	295.334			1.31223			0.656116	−	0.754660i	$-0.272198\pi$
$37$	295.334			1.31223			0.656116	+	0.754660i	$0.272198\pi$
$38$	−75.5750	−	23.0069i	−0.322629	−	0.0982160i
$39$		0			0
$40$	43.7327	−	115.160i	0.172868	−	0.455210i
$41$	146.833	−	84.7741i	0.559304	−	0.322915i	−0.193562	−	0.981088i	$-0.562004\pi$
$41$	146.833	−	84.7741i	0.559304	−	0.322915i	0.752866	+	0.658173i	$0.228671\pi$
$42$		0			0
$43$	−284.968	−	164.526i	−1.01063	−	0.583488i	−0.0992550	−	0.995062i	$-0.531646\pi$
$43$	−284.968	−	164.526i	−1.01063	−	0.583488i	−0.911376	+	0.411574i	$0.864979\pi$
$44$	364.841	−	179.026i	1.25004	−	0.613390i
$45$		0			0
$46$	−21.6859	+	5.03388i	−0.0695088	+	0.0161349i
$47$	47.9742	−	83.0938i	0.148888	−	0.257882i	−0.781928	−	0.623368i	$-0.785764\pi$
$47$	47.9742	−	83.0938i	0.148888	−	0.257882i	0.930817	+	0.365486i	$0.119097\pi$
$48$		0			0
$49$	120.704	+	209.066i	0.351908	+	0.609522i
$50$	−184.188	−	197.045i	−0.520964	−	0.557328i
$51$		0			0
$52$	27.0439	−	400.500i	0.0721213	−	1.06807i
$53$		−	300.751i		−	0.779459i	−0.920929	−	0.389729i	$-0.872569\pi$
$53$		−	300.751i		−	0.779459i	0.920929	−	0.389729i	$-0.127431\pi$
$54$		0			0
$55$			276.555i			0.678013i
$56$	539.963	−	87.5075i	1.28849	−	0.208816i
$57$		0			0
$58$	−507.697	+	474.571i	−1.14938	+	1.07438i
$59$	−113.273	−	196.195i	−0.249947	−	0.432921i	0.713564	−	0.700590i	$-0.247080\pi$
$59$	−113.273	−	196.195i	−0.249947	−	0.432921i	−0.963511	+	0.267669i	$0.913747\pi$
$60$		0			0
$61$	173.722	−	300.896i	0.364637	−	0.631570i	−0.624081	−	0.781360i	$-0.714526\pi$
$61$	173.722	−	300.896i	0.364637	−	0.631570i	0.988718	+	0.149790i	$0.0478597\pi$
$62$	−37.9590	−	163.527i	−0.0777548	−	0.334966i
$63$		0			0
$64$	102.857	−	501.562i	0.200892	−	0.979613i
$65$	236.566	+	136.581i	0.451421	+	0.260628i
$66$		0			0
$67$	904.675	−	522.314i	1.64961	−	0.952401i	0.672378	−	0.740208i	$-0.265273\pi$
$67$	904.675	−	522.314i	1.64961	−	0.952401i	0.977228	−	0.212193i	$-0.0680605\pi$
$68$	−230.527	+	343.538i	−0.411110	+	0.612649i
$69$		0			0
$70$	−108.407	+	356.105i	−0.185102	+	0.608038i
$71$	−243.524			−0.407057			−0.203528	−	0.979069i	$-0.565241\pi$
$71$	−243.524			−0.407057			−0.203528	+	0.979069i	$0.565241\pi$
$72$		0			0
$73$	−1094.68			−1.75510			−0.877552	−	0.479481i	$-0.840825\pi$
$73$	−1094.68			−1.75510			−0.877552	+	0.479481i	$0.840825\pi$
$74$	−243.272	+	799.122i	−0.382159	+	1.25535i
$75$		0			0
$76$	124.505	−	185.542i	0.187917	−	0.280041i
$77$	−1063.53	+	614.031i	−1.57404	+	0.908770i
$78$		0			0
$79$	−530.679	−	306.388i	−0.755773	−	0.436346i	0.0720031	−	0.997404i	$-0.477061\pi$
$79$	−530.679	−	306.388i	−0.755773	−	0.436346i	−0.827776	+	0.561059i	$0.810394\pi$
$80$	275.579	+	213.192i	0.385134	+	0.297945i
$81$		0			0
$82$	108.435	+	467.135i	0.146032	+	0.629103i
$83$	−283.063	+	490.280i	−0.374340	+	0.648376i	−0.990228	−	0.139458i	$-0.955464\pi$
$83$	−283.063	+	490.280i	−0.374340	+	0.648376i	0.615888	+	0.787834i	$0.288797\pi$
$84$		0			0
$85$	−140.768	−	243.817i	−0.179628	−	0.311125i
$86$	679.912	−	635.549i	0.852521	−	0.796896i
$87$		0			0
$88$	183.886	+	1134.66i	0.222754	+	1.37450i
$89$			212.529i			0.253124i	0.991959	+	0.126562i	$0.0403943\pi$
$89$			212.529i			0.253124i	−0.991959	+	0.126562i	$0.959606\pi$
$90$		0			0
$91$			1213.00i			1.39732i
$92$	4.24224	−	62.8246i	0.00480744	−	0.0711948i
$93$		0			0
$94$	185.320	+	198.256i	0.203343	+	0.217537i
$95$	76.0272	+	131.683i	0.0821076	+	0.142215i
$96$		0			0
$97$	234.298	−	405.817i	0.245252	−	0.424788i	−0.716951	−	0.697124i	$-0.754463\pi$
$97$	234.298	−	405.817i	0.245252	−	0.424788i	0.962202	+	0.272336i	$0.0877961\pi$
$98$	−665.122	+	154.393i	−0.685587	+	0.159143i
$99$		0			0
$100$	684.889	−	336.072i	0.684889	−	0.336072i
$101$	−1552.98	−	896.613i	−1.52997	−	0.883330i	−0.999362	−	0.0357140i	$-0.988629\pi$
$101$	−1552.98	−	896.613i	−1.52997	−	0.883330i	−0.530610	−	0.847616i	$-0.678037\pi$
$102$		0			0
$103$	119.871	−	69.2074i	0.114672	−	0.0662059i	−0.441567	−	0.897228i	$-0.645577\pi$
$103$	119.871	−	69.2074i	0.114672	−	0.0662059i	0.556239	+	0.831022i	$0.312244\pi$
$104$	1061.41	+	403.076i	1.00077	+	0.380046i
$105$		0			0
$106$	813.779	+	247.734i	0.745672	+	0.227001i
$107$	771.292			0.696857			0.348428	−	0.937335i	$-0.386715\pi$
$107$	771.292			0.696857			0.348428	+	0.937335i	$0.386715\pi$
$108$		0			0
$109$	−275.772			−0.242332			−0.121166	−	0.992632i	$-0.538663\pi$
$109$	−275.772			−0.242332			−0.121166	+	0.992632i	$0.538663\pi$
$110$	−748.310	−	227.804i	−0.648623	−	0.197457i
$111$		0			0
$112$	−207.998	+	1533.13i	−0.175481	+	1.29345i
$113$	542.916	−	313.453i	0.451976	−	0.260948i	−0.256689	−	0.966494i	$-0.582631\pi$
$113$	542.916	−	313.453i	0.451976	−	0.260948i	0.708664	+	0.705546i	$0.249298\pi$
$114$		0			0
$115$	37.1089	+	21.4249i	0.0300907	+	0.0173729i
$116$	−865.906	−	1764.65i	−0.693080	−	1.41245i
$117$		0			0
$118$	624.173	−	144.888i	0.486947	−	0.113034i
$119$	625.088	−	1082.68i	0.481527	−	0.834029i
$120$		0			0
$121$	−624.809	−	1082.20i	−0.469428	−	0.813073i
$122$	671.073	+	717.916i	0.498001	+	0.532762i
$123$		0			0
$124$	473.742	+	31.9895i	0.343091	+	0.0231673i
$125$			1199.66i			0.858406i
$126$		0			0
$127$			71.3408i			0.0498463i	0.999689	+	0.0249231i	$0.00793410\pi$
$127$			71.3408i			0.0498463i	−0.999689	+	0.0249231i	$0.992066\pi$
$128$	1272.41	+	691.458i	0.878645	+	0.477475i
$129$		0			0
$130$	−564.428	+	527.601i	−0.380797	+	0.355951i
$131$	358.903	+	621.638i	0.239370	+	0.414601i	0.960534	−	0.278164i	$-0.0897258\pi$
$131$	358.903	+	621.638i	0.239370	+	0.414601i	−0.721164	+	0.692765i	$0.756392\pi$
$132$		0			0
$133$	−337.604	+	584.747i	−0.220105	+	0.381233i
$134$	668.093	+	2878.13i	0.430705	+	1.85547i
$135$		0			0
$136$	−739.666	−	906.744i	−0.466366	−	0.571711i
$137$	−190.925	−	110.231i	−0.119065	−	0.0687420i	0.439285	−	0.898348i	$-0.355232\pi$
$137$	−190.925	−	110.231i	−0.119065	−	0.0687420i	−0.558350	+	0.829606i	$0.688565\pi$
$138$		0			0
$139$	1214.70	−	701.309i	0.741222	−	0.427945i	−0.0812916	−	0.996690i	$-0.525905\pi$
$139$	1214.70	−	701.309i	0.741222	−	0.427945i	0.822513	+	0.568746i	$0.192571\pi$
$140$	−874.261	−	586.661i	−0.527775	−	0.354156i
$141$		0			0
$142$	200.596	−	658.934i	0.118547	−	0.389412i
$143$	−2548.96			−1.49059
$144$		0			0
$145$	1337.63			0.766099
$146$	901.708	−	2962.01i	0.511136	−	1.67903i
$147$		0			0
$148$	−1961.90	−	1316.50i	−1.08964	−	0.731188i
$149$	1289.36	−	744.413i	0.708917	−	0.409293i	−0.101743	−	0.994811i	$-0.532442\pi$
$149$	1289.36	−	744.413i	0.708917	−	0.409293i	0.810660	+	0.585517i	$0.199109\pi$
$150$		0			0
$151$	−1704.17	−	983.903i	−0.918433	−	0.530257i	−0.0352979	−	0.999377i	$-0.511238\pi$
$151$	−1704.17	−	983.903i	−0.918433	−	0.530257i	−0.883135	+	0.469120i	$0.844571\pi$
$152$	399.486	+	489.723i	0.213175	+	0.261328i
$153$		0			0
$154$	−785.408	−	3383.52i	−0.410974	−	1.77047i
$155$	−161.559	+	279.828i	−0.0837206	+	0.145008i
$156$		0			0
$157$	564.122	+	977.088i	0.286763	+	0.496689i	0.973035	−	0.230656i	$-0.0740874\pi$
$157$	564.122	+	977.088i	0.286763	+	0.496689i	−0.686272	+	0.727345i	$0.740754\pi$
$158$	1266.16	−	1183.55i	0.637534	−	0.595937i
$159$		0			0
$160$	−803.861	+	570.059i	−0.397192	+	0.281669i
$161$			190.277i			0.0931424i
$162$		0			0
$163$		−	1940.05i		−	0.932250i	−0.884719	−	0.466125i	$-0.845650\pi$
$163$		−	1940.05i		−	0.932250i	0.884719	−	0.466125i	$-0.154350\pi$
$164$	−1353.30	−	91.3821i	−0.644362	−	0.0435106i
$165$		0			0
$166$	−1093.45	−	1169.77i	−0.511252	−	0.546939i
$167$	−1242.52	−	2152.11i	−0.575743	−	0.997217i	−0.995960	−	0.0897933i	$-0.971379\pi$
$167$	−1242.52	−	2152.11i	−0.575743	−	0.997217i	0.420217	−	0.907424i	$-0.361954\pi$
$168$		0			0
$169$	−160.344	+	277.723i	−0.0729830	+	0.126410i
$170$	775.678	−	180.056i	0.349952	−	0.0812334i
$171$		0			0
$172$	1159.63	+	2363.24i	0.514075	+	1.04765i
$173$	2492.67	+	1439.15i	1.09546	+	0.632464i	0.935025	−	0.354583i	$-0.115377\pi$
$173$	2492.67	+	1439.15i	1.09546	+	0.632464i	0.160435	+	0.987046i	$0.448710\pi$
$174$		0			0
$175$	−1996.49	+	1152.67i	−0.862402	+	0.497908i
$176$	−3221.67	−	437.081i	−1.37979	−	0.187194i
$177$		0			0
$178$	−575.067	−	175.064i	−0.242152	−	0.0737170i
$179$	2965.78			1.23840			0.619198	−	0.785235i	$-0.287458\pi$
$179$	2965.78			1.23840			0.619198	+	0.785235i	$0.287458\pi$
$180$		0			0
$181$	1250.55			0.513551			0.256776	−	0.966471i	$-0.417340\pi$
$181$	1250.55			0.513551			0.256776	+	0.966471i	$0.417340\pi$
$182$	−3282.15	−	999.167i	−1.33675	−	0.406941i
$183$		0			0
$184$	166.498	+	63.2286i	0.0667087	+	0.0253330i
$185$	1392.40	−	803.902i	0.553358	−	0.319482i
$186$		0			0
$187$	2275.12	+	1313.54i	0.889698	+	0.513668i
$188$	−689.097	+	338.136i	−0.267327	+	0.131176i
$189$		0			0
$190$	−418.936	+	97.2465i	−0.159962	+	0.0371316i
$191$	387.763	−	671.626i	0.146898	−	0.254435i	−0.783181	−	0.621793i	$-0.786404\pi$
$191$	387.763	−	671.626i	0.146898	−	0.254435i	0.930080	+	0.367358i	$0.119738\pi$
$192$		0			0
$193$	2185.71	+	3785.76i	0.815185	+	1.41194i	0.909195	+	0.416370i	$0.136698\pi$
$193$	2185.71	+	3785.76i	0.815185	+	1.41194i	−0.0940101	+	0.995571i	$0.529969\pi$
$194$	905.073	+	968.249i	0.334951	+	0.358331i
$195$		0			0
$196$	130.113	−	1926.88i	0.0474173	−	0.702216i
$197$		−	1648.60i		−	0.596233i	−0.954530	−	0.298116i	$-0.903642\pi$
$197$		−	1648.60i		−	0.596233i	0.954530	−	0.298116i	$-0.0963584\pi$
$198$		0			0
$199$			2946.42i			1.04958i	0.851232	+	0.524790i	$0.175856\pi$
$199$			2946.42i			1.04958i	−0.851232	+	0.524790i	$0.824144\pi$
$200$	345.195	+	2130.02i	0.122045	+	0.753075i
$201$		0			0
$202$	3705.30	−	3463.53i	1.29061	−	1.20640i
$203$	2969.92	+	5144.05i	1.02684	+	1.77853i
$204$		0			0
$205$	461.513	−	799.363i	0.157236	−	0.272341i
$206$	88.5233	+	381.356i	0.0299403	+	0.128982i
$207$		0			0
$208$	−1964.95	+	2539.96i	−0.655024	+	0.846705i
$209$	−1228.77	−	709.432i	−0.406679	−	0.234796i
$210$		0			0
$211$	−477.089	+	275.447i	−0.155659	+	0.0898700i	−0.575806	−	0.817586i	$-0.695312\pi$
$211$	−477.089	+	275.447i	−0.155659	+	0.0898700i	0.420147	+	0.907456i	$0.361979\pi$
$212$	−1340.65	+	1997.88i	−0.434322	+	0.647241i
$213$		0			0
$214$	−635.328	+	2086.98i	−0.202945	+	0.666650i
$215$	−1791.37			−0.568234
$216$		0			0
$217$	−1434.82			−0.448857
$218$	227.159	−	746.192i	0.0705741	−	0.231828i
$219$		0			0
$220$	1232.79	−	1837.15i	0.377795	−	0.563003i
$221$	2247.21	−	1297.43i	0.684000	−	0.394907i
$222$		0			0
$223$	−1564.82	−	903.449i	−0.469902	−	0.271298i	0.246297	−	0.969194i	$-0.420786\pi$
$223$	−1564.82	−	903.449i	−0.469902	−	0.271298i	−0.716199	+	0.697897i	$0.754120\pi$
$224$	−3977.04	−	1825.67i	−1.18628	−	0.544565i
$225$		0			0
$226$	400.938	+	1727.23i	0.118009	+	0.508380i
$227$	−752.796	+	1303.88i	−0.220109	+	0.381241i	−0.954841	−	0.297117i	$-0.903975\pi$
$227$	−752.796	+	1303.88i	−0.220109	+	0.381241i	0.734732	+	0.678358i	$0.237308\pi$
$228$		0			0
$229$	−767.015	−	1328.51i	−0.221335	−	0.383364i	0.733878	−	0.679281i	$-0.237708\pi$
$229$	−767.015	−	1328.51i	−0.221335	−	0.383364i	−0.955214	+	0.295917i	$0.904375\pi$
$230$	−88.5392	+	82.7622i	−0.0253831	+	0.0237269i
$231$		0			0
$232$	5488.10	−	889.413i	1.55307	−	0.251693i
$233$			1257.04i			0.353440i	0.984261	+	0.176720i	$0.0565487\pi$
$233$			1257.04i			0.353440i	−0.984261	+	0.176720i	$0.943451\pi$
$234$		0			0
$235$		−	522.346i		−	0.144996i
$236$	−122.102	+	1808.25i	−0.0336787	+	0.498759i
$237$		0			0
$238$	2414.66	+	2583.21i	0.657643	+	0.703548i
$239$	−916.982	−	1588.26i	−0.248178	−	0.429858i	0.714842	−	0.699286i	$-0.246499\pi$
$239$	−916.982	−	1588.26i	−0.248178	−	0.429858i	−0.963020	+	0.269428i	$0.913165\pi$
$240$		0			0
$241$	−358.771	+	621.410i	−0.0958941	+	0.166094i	−0.909981	−	0.414649i	$-0.863904\pi$
$241$	−358.771	+	621.410i	−0.0958941	+	0.166094i	0.814087	+	0.580743i	$0.197238\pi$
$242$	3442.91	−	799.194i	0.914540	−	0.212290i
$243$		0			0
$244$	−2495.33	+	1224.45i	−0.654701	+	0.321259i
$245$	1138.16	+	657.117i	0.296794	+	0.171354i
$246$		0			0
$247$	−1213.70	+	700.728i	−0.312655	+	0.180511i
$248$	−476.788	+	1255.51i	−0.122081	+	0.321472i
$249$		0			0
$250$	−3246.07	−	988.182i	−0.821198	−	0.249992i
$251$	−1053.84			−0.265010			−0.132505	−	0.991182i	$-0.542302\pi$
$251$	−1053.84			−0.265010			−0.132505	+	0.991182i	$0.542302\pi$
$252$		0			0
$253$	−399.843			−0.0993594
$254$	−193.036	−	58.7648i	−0.0476856	−	0.0145167i
$255$		0			0
$256$	−2919.08	+	2873.36i	−0.712665	+	0.701504i
$257$	−5985.55	+	3455.76i	−1.45280	+	0.838772i	−0.998639	−	0.0521496i	$-0.983393\pi$
$257$	−5985.55	+	3455.76i	−1.45280	+	0.838772i	−0.454157	+	0.890922i	$0.650059\pi$
$258$		0			0
$259$	6183.04	+	3569.78i	1.48338	+	0.856430i
$260$	−962.665	−	1961.84i	−0.229623	−	0.467954i
$261$		0			0
$262$	−1977.68	+	459.073i	−0.466341	+	0.108251i
$263$	−1325.23	+	2295.36i	−0.310712	+	0.538168i	−0.978517	−	0.206168i	$-0.933901\pi$
$263$	−1325.23	+	2295.36i	−0.310712	+	0.538168i	0.667805	+	0.744336i	$0.267234\pi$
$264$		0			0
$265$	−818.648	−	1417.94i	−0.189770	−	0.328692i
$266$	−1304.13	−	1395.16i	−0.300607	−	0.321590i
$267$		0			0
$268$	−8338.04	−	563.027i	−1.90047	−	0.128330i
$269$		−	2386.16i		−	0.540843i	−0.962742	−	0.270422i	$-0.912837\pi$
$269$		−	2386.16i		−	0.540843i	0.962742	−	0.270422i	$-0.0871631\pi$
$270$		0			0
$271$		−	4287.45i		−	0.961048i	−0.876982	−	0.480524i	$-0.840446\pi$
$271$		−	4287.45i		−	0.961048i	0.876982	−	0.480524i	$-0.159554\pi$
$272$	3062.77	−	1254.50i	0.682748	−	0.279652i
$273$		0			0
$274$	455.534	−	425.811i	0.100437	−	0.0938839i
$275$	−2422.20	−	4195.37i	−0.531142	−	0.919965i
$276$		0			0
$277$	−2416.58	+	4185.64i	−0.524181	+	0.907909i	0.475422	+	0.879758i	$0.342295\pi$
$277$	−2416.58	+	4185.64i	−0.524181	+	0.907909i	−0.999604	+	0.0281511i	$0.991038\pi$
$278$	897.046	+	3864.46i	0.193530	+	0.833722i
$279$		0			0
$280$	2307.55	−	1882.35i	0.492508	−	0.401758i
$281$	−1501.29	−	866.770i	−0.318717	−	0.184011i	0.332104	−	0.943243i	$-0.392242\pi$
$281$	−1501.29	−	866.770i	−0.318717	−	0.184011i	−0.650821	+	0.759232i	$0.725575\pi$
$282$		0			0
$283$	3227.63	−	1863.47i	0.677960	−	0.391420i	−0.121126	−	0.992637i	$-0.538650\pi$
$283$	3227.63	−	1863.47i	0.677960	−	0.391420i	0.799086	+	0.601217i	$0.205317\pi$
$284$	1617.73	+	1085.55i	0.338009	+	0.226816i
$285$		0			0
$286$	2099.62	−	6897.03i	0.434103	−	1.42598i
$287$	4098.75			0.843003
$288$		0			0
$289$	2238.61			0.455649
$290$	−1101.83	+	3619.40i	−0.223110	+	0.732891i
$291$		0			0
$292$	7271.93	+	4879.73i	1.45739	+	0.977961i
$293$	−5604.61	+	3235.82i	−1.11749	+	0.645183i	−0.940759	−	0.339076i	$-0.889886\pi$
$293$	−5604.61	+	3235.82i	−1.11749	+	0.645183i	−0.176731	+	0.984259i	$0.556552\pi$
$294$		0			0
$295$	−1068.09	−	616.661i	−0.210802	−	0.121706i
$296$	5178.28	−	4224.12i	1.01683	−	0.829466i
$297$		0			0
$298$	952.180	+	4101.97i	0.185095	+	0.797386i
$299$	−197.469	+	342.026i	−0.0381937	+	0.0661534i
$300$		0			0
$301$	−3977.34	−	6888.96i	−0.761629	−	1.31918i
$302$	4066.02	−	3800.72i	0.774746	−	0.724196i
$303$		0			0
$304$	−1654.17	+	677.545i	−0.312083	+	0.127828i
$305$		−	1891.50i		−	0.355104i
$306$		0			0
$307$		−	7858.86i		−	1.46101i	−0.682909	−	0.730503i	$-0.739285\pi$
$307$		−	7858.86i		−	1.46101i	0.682909	−	0.730503i	$-0.260715\pi$
$308$	9802.17	+	661.893i	1.81341	+	0.122451i
$309$		0			0
$310$	−624.086	−	667.648i	−0.114341	−	0.122322i
$311$	−3745.08	−	6486.66i	−0.682842	−	1.18272i	−0.974110	−	0.226075i	$-0.927410\pi$
$311$	−3745.08	−	6486.66i	−0.682842	−	1.18272i	0.291268	−	0.956642i	$-0.405923\pi$
$312$		0			0
$313$	4304.38	−	7455.41i	0.777310	−	1.34634i	−0.156176	−	0.987729i	$-0.549917\pi$
$313$	4304.38	−	7455.41i	0.777310	−	1.34634i	0.933487	−	0.358612i	$-0.116750\pi$
$314$	−3108.51	+	721.570i	−0.558672	+	0.129683i
$315$		0			0
$316$	2159.51	+	4400.92i	0.384437	+	0.783453i
$317$	4705.42	+	2716.67i	0.833699	+	0.481336i	0.855117	−	0.518434i	$-0.173485\pi$
$317$	4705.42	+	2716.67i	0.833699	+	0.481336i	−0.0214185	+	0.999771i	$0.506818\pi$
$318$		0			0
$319$	−10809.6	+	6240.92i	−1.89724	+	1.09537i
$320$	−880.323	−	2644.67i	−0.153786	−	0.462006i
$321$		0			0
$322$	−514.856	−	156.735i	−0.0891050	−	0.0271257i
$323$	1444.41			0.248821
$324$		0			0
$325$	−4784.97			−0.816684
$326$	5249.44	+	1598.06i	0.891840	+	0.271498i
$327$		0			0
$328$	1362.01	−	3586.53i	0.229281	−	0.603759i
$329$	2008.75	−	1159.75i	0.336615	−	0.194344i
$330$		0			0
$331$	1367.21	+	789.359i	0.227035	+	0.131079i	0.609204	−	0.793014i	$-0.291489\pi$
$331$	1367.21	+	789.359i	0.227035	+	0.131079i	−0.382168	+	0.924093i	$0.624823\pi$
$332$	4065.89	−	1995.11i	0.672122	−	0.329807i
$333$		0			0
$334$	6846.72	−	1589.31i	1.12166	−	0.260369i
$335$	2843.49	−	4925.07i	0.463751	−	0.803240i
$336$		0			0
$337$	−3400.38	−	5889.62i	−0.549645	−	0.952013i	−0.998299	−	0.0583070i	$-0.981430\pi$
$337$	−3400.38	−	5889.62i	−0.549645	−	0.952013i	0.448654	−	0.893706i	$-0.351904\pi$
$338$	−619.393	−	662.628i	−0.0996761	−	0.106634i
$339$		0			0
$340$	−151.740	+	2247.17i	−0.0242037	+	0.358440i
$341$		−	3015.10i		−	0.478818i
$342$		0			0
$343$		−	2455.93i		−	0.386611i
$344$	−7349.71	+	1191.11i	−1.15195	+	0.186687i
$345$		0			0
$346$	−5947.34	+	5559.29i	−0.924078	+	0.863784i
$347$	6228.10	+	10787.4i	0.963522	+	1.66887i	0.713535	+	0.700620i	$0.247093\pi$
$347$	6228.10	+	10787.4i	0.963522	+	1.66887i	0.249987	+	0.968249i	$0.419573\pi$
$348$		0			0
$349$	−910.729	+	1577.43i	−0.139685	+	0.241942i	−0.927378	−	0.374127i	$-0.877942\pi$
$349$	−910.729	+	1577.43i	−0.139685	+	0.241942i	0.787692	+	0.616069i	$0.211276\pi$
$350$	−1474.39	−	6351.63i	−0.225169	−	0.970025i
$351$		0			0
$352$	3836.42	−	8357.25i	0.580914	−	1.26546i
$353$	−6019.52	−	3475.37i	−0.907611	−	0.524010i	−0.0279495	−	0.999609i	$-0.508898\pi$
$353$	−6019.52	−	3475.37i	−0.907611	−	0.524010i	−0.879662	+	0.475600i	$0.842231\pi$
$354$		0			0
$355$	−1148.14	+	662.877i	−0.171653	+	0.0991038i
$356$	947.387	−	1411.83i	0.141043	−	0.210187i
$357$		0			0
$358$	−2442.97	+	8024.88i	−0.360656	+	1.18472i
$359$	318.743			0.0468597			0.0234298	−	0.999725i	$-0.492541\pi$
$359$	318.743			0.0468597			0.0234298	+	0.999725i	$0.492541\pi$
$360$		0			0
$361$	6078.89			0.886264
$362$	−1030.10	+	3383.77i	−0.149561	+	0.491290i
$363$		0			0
$364$	5407.14	−	8057.90i	0.778602	−	1.16030i
$365$	−5161.05	+	2979.73i	−0.740114	+	0.427305i
$366$		0			0
$367$	5425.21	+	3132.25i	0.771645	+	0.445510i	0.833461	−	0.552578i	$-0.186356\pi$
$367$	5425.21	+	3132.25i	0.771645	+	0.445510i	−0.0618160	+	0.998088i	$0.519689\pi$
$368$	−308.233	+	398.432i	−0.0436624	+	0.0564394i
$369$		0			0
$370$	1028.27	+	4429.78i	0.144479	+	0.622414i
$371$	3635.26	−	6296.45i	0.508715	−	0.881120i
$372$		0			0
$373$	6066.19	+	10506.9i	0.842078	+	1.45852i	0.888135	+	0.459583i	$0.152001\pi$
$373$	6066.19	+	10506.9i	0.842078	+	1.45852i	−0.0460564	+	0.998939i	$0.514665\pi$
$374$	−5428.28	+	5074.10i	−0.750508	+	0.701538i
$375$		0			0
$376$	−347.316	−	2143.10i	−0.0476368	−	0.293942i
$377$			12328.7i			1.68425i
$378$		0			0
$379$			1928.72i			0.261402i	0.991422	+	0.130701i	$0.0417229\pi$
$379$			1928.72i			0.261402i	−0.991422	+	0.130701i	$0.958277\pi$
$380$	81.9533	−	1213.67i	0.0110635	−	0.163842i
$381$		0			0
$382$	1497.89	+	1602.45i	0.200625	+	0.214630i
$383$	−2974.93	−	5152.73i	−0.396898	−	0.687448i	0.596443	−	0.802655i	$-0.296580\pi$
$383$	−2974.93	−	5152.73i	−0.396898	−	0.687448i	−0.993341	+	0.115208i	$0.963247\pi$
$384$		0			0
$385$	−3342.80	+	5789.90i	−0.442506	+	0.766443i
$386$	−12044.0	+	2795.74i	−1.58814	+	0.368652i
$387$		0			0
$388$	−3365.44	+	1651.40i	−0.440346	+	0.216076i
$389$	−2023.11	−	1168.05i	−0.263691	−	0.152242i	0.362326	−	0.932051i	$-0.381983\pi$
$389$	−2023.11	−	1168.05i	−0.263691	−	0.152242i	−0.626017	+	0.779809i	$0.715316\pi$
$390$		0			0
$391$	352.510	−	203.522i	0.0455938	−	0.0263236i
$392$	5106.63	+	1939.27i	0.657968	+	0.249867i
$393$		0			0
$394$	4460.82	+	1357.98i	0.570388	+	0.173640i
$395$	−3335.97			−0.424938
$396$		0			0
$397$	−6080.16			−0.768652			−0.384326	−	0.923198i	$-0.625566\pi$
$397$	−6080.16			−0.768652			−0.384326	+	0.923198i	$0.625566\pi$
$398$	−7972.51	−	2427.02i	−1.00408	−	0.305668i
$399$		0			0
$400$	−6047.80	−	820.499i	−0.755975	−	0.102562i
$401$	11997.7	−	6926.90i	1.49411	−	0.862626i	0.494135	−	0.869385i	$-0.335485\pi$
$401$	11997.7	−	6926.90i	1.49411	−	0.862626i	0.999977	+	0.00675957i	$0.00215165\pi$
$402$		0			0
$403$	−2579.12	−	1489.05i	−0.318797	−	0.184057i
$404$	6319.59	+	12878.9i	0.778246	+	1.58601i
$405$		0			0
$406$	−16365.3	+	3798.83i	−2.00048	+	0.464367i
$407$	−7501.45	+	12992.9i	−0.913594	+	1.58239i
$408$		0			0
$409$	135.435	+	234.581i	0.0163737	+	0.0283601i	0.874096	−	0.485753i	$-0.161455\pi$
$409$	135.435	+	234.581i	0.0163737	+	0.0283601i	−0.857722	+	0.514113i	$0.828121\pi$
$410$	1782.78	+	1907.22i	0.214745	+	0.229734i
$411$		0			0
$412$	−1104.80	−	74.6019i	−0.132111	−	0.00892081i
$413$		−	5476.64i		−	0.652513i
$414$		0			0
$415$			3082.01i			0.364553i
$416$	−5254.12	−	7409.03i	−0.619242	−	0.873216i
$417$		0			0
$418$	2931.76	−	2740.47i	0.343055	−	0.320672i
$419$	3950.75	+	6842.90i	0.460637	+	0.797846i	0.998993	−	0.0448712i	$-0.0142877\pi$
$419$	3950.75	+	6842.90i	0.460637	+	0.797846i	−0.538356	+	0.842718i	$0.680954\pi$
$420$		0			0
$421$	3331.91	−	5771.04i	0.385718	−	0.668083i	−0.606150	−	0.795350i	$-0.707287\pi$
$421$	3331.91	−	5771.04i	0.385718	−	0.668083i	0.991869	+	0.127267i	$0.0406204\pi$
$422$	−352.325	−	1517.81i	−0.0406420	−	0.175085i
$423$		0			0
$424$	−4301.60	−	5273.26i	−0.492698	−	0.603991i
$425$	4270.92	+	2465.82i	0.487459	+	0.281435i
$426$		0			0
$427$	7274.02	−	4199.66i	0.824390	−	0.475962i
$428$	−5123.68	−	3438.17i	−0.578650	−	0.388295i
$429$		0			0
$430$	1475.58	−	4847.13i	0.165486	−	0.543603i
$431$	−14773.0			−1.65102			−0.825509	−	0.564388i	$-0.809112\pi$
$431$	−14773.0			−1.65102			−0.825509	+	0.564388i	$0.809112\pi$
$432$		0			0
$433$	−2372.81			−0.263349			−0.131674	−	0.991293i	$-0.542035\pi$
$433$	−2372.81			−0.263349			−0.131674	+	0.991293i	$0.542035\pi$
$434$	1181.89	−	3882.38i	0.130720	−	0.429401i
$435$		0			0
$436$	1831.95	+	1229.30i	0.201226	+	0.135030i
$437$	−190.387	+	109.920i	−0.0208408	+	0.0120325i
$438$		0			0
$439$	2509.56	+	1448.89i	0.272835	+	0.157522i	0.630175	−	0.776453i	$-0.282983\pi$
$439$	2509.56	+	1448.89i	0.272835	+	0.157522i	−0.357340	+	0.933974i	$0.616316\pi$
$440$	3955.53	+	4849.02i	0.428574	+	0.525382i
$441$		0			0
$442$	1659.54	+	7149.28i	0.178589	+	0.769359i
$443$	−3932.06	+	6810.53i	−0.421711	+	0.730425i	−0.996107	−	0.0881526i	$-0.971904\pi$
$443$	−3932.06	+	6810.53i	−0.421711	+	0.730425i	0.574396	+	0.818578i	$0.305237\pi$
$444$		0			0
$445$	578.508	+	1002.00i	0.0616267	+	0.106741i
$446$	3733.55	−	3489.94i	0.396387	−	0.370523i
$447$		0			0
$448$	8215.90	−	9257.33i	0.866439	−	0.976267i
$449$		−	1335.91i		−	0.140413i	−0.997532	−	0.0702064i	$-0.977634\pi$
$449$		−	1335.91i		−	0.140413i	0.997532	−	0.0702064i	$-0.0223658\pi$
$450$		0			0
$451$			8613.02i			0.899271i
$452$	−5003.85	−	337.886i	−0.520711	−	0.0351611i
$453$		0			0
$454$	−2907.98	−	3110.97i	−0.300613	−	0.321597i
$455$	3301.79	+	5718.87i	0.340198	+	0.589241i
$456$		0			0
$457$	−8696.49	+	15062.8i	−0.890164	+	1.54181i	−0.0504849	+	0.998725i	$0.516077\pi$
$457$	−8696.49	+	15062.8i	−0.890164	+	1.54181i	−0.839679	+	0.543084i	$0.817257\pi$
$458$	4226.52	−	981.091i	0.431206	−	0.100095i
$459$		0			0
$460$	−151.009	−	307.744i	−0.0153061	−	0.0311927i
$461$	1933.14	+	1116.10i	0.195304	+	0.112759i	0.594463	−	0.804123i	$-0.297365\pi$
$461$	1933.14	+	1116.10i	0.195304	+	0.112759i	−0.399159	+	0.916882i	$0.630698\pi$
$462$		0			0
$463$	3435.96	−	1983.75i	0.344887	−	0.199121i	−0.317544	−	0.948244i	$-0.602858\pi$
$463$	3435.96	−	1983.75i	0.344887	−	0.199121i	0.662431	+	0.749123i	$0.269525\pi$
$464$	−2114.06	+	15582.5i	−0.211514	+	1.55905i
$465$		0			0
$466$	−3401.33	−	1035.45i	−0.338120	−	0.102932i
$467$	8810.21			0.872993			0.436497	−	0.899706i	$-0.356219\pi$
$467$	8810.21			0.872993			0.436497	+	0.899706i	$0.356219\pi$
$468$		0			0
$469$	25253.4			2.48634
$470$	1413.38	+	430.266i	0.138711	+	0.0422270i
$471$		0			0
$472$	−4792.23	−	1819.88i	−0.467331	−	0.177472i
$473$	14476.3	−	8357.89i	1.40723	−	0.812466i
$474$		0			0
$475$	−2306.68	−	1331.76i	−0.222816	−	0.128643i
$476$	−8978.70	+	4405.80i	−0.864576	+	0.424243i
$477$		0			0
$478$	5052.89	−	1172.91i	0.483502	−	0.112234i
$479$	9734.00	−	16859.8i	0.928513	−	1.60823i	0.142702	−	0.989766i	$-0.454421\pi$
$479$	9734.00	−	16859.8i	0.928513	−	1.60823i	0.785811	−	0.618466i	$-0.212246\pi$
$480$		0			0
$481$	7409.42	+	12833.5i	0.702371	+	1.21654i
$482$	−1385.90	−	1482.64i	−0.130967	−	0.140109i
$483$		0			0
$484$	−673.511	+	9974.23i	−0.0632524	+	0.936723i
$485$		−	2551.05i		−	0.238840i
$486$		0			0
$487$			5226.26i			0.486293i	0.969990	+	0.243146i	$0.0781795\pi$
$487$			5226.26i			0.486293i	−0.969990	+	0.243146i	$0.921820\pi$
$488$	−1257.69	−	7760.52i	−0.116666	−	0.719882i
$489$		0			0
$490$	−2715.57	+	2538.38i	−0.250361	+	0.234025i
$491$	−4793.56	−	8302.69i	−0.440591	−	0.763127i	0.557142	−	0.830417i	$-0.311898\pi$
$491$	−4793.56	−	8302.69i	−0.440591	−	0.763127i	−0.997733	+	0.0672904i	$0.978565\pi$
$492$		0			0
$493$	6353.30	−	11004.2i	0.580402	−	1.00529i
$494$	−896.303	−	3861.25i	−0.0816327	−	0.351672i
$495$		0			0
$496$	−3004.46	−	2324.29i	−0.271984	−	0.210411i
$497$	−5098.37	−	2943.55i	−0.460147	−	0.265666i
$498$		0			0
$499$	2085.65	−	1204.15i	0.187108	−	0.108027i	−0.403520	−	0.914971i	$-0.632213\pi$
$499$	2085.65	−	1204.15i	0.187108	−	0.108027i	0.590628	+	0.806944i	$0.298880\pi$
$500$	5347.69	−	7969.31i	0.478312	−	0.712797i
$501$		0			0
$502$	868.064	−	2851.49i	0.0771785	−	0.253523i
$503$	17192.1			1.52397			0.761985	−	0.647595i	$-0.224225\pi$
$503$	17192.1			1.52397			0.761985	+	0.647595i	$0.224225\pi$
$504$		0			0
$505$	−9762.37			−0.860237
$506$	329.358	−	1081.91i	0.0289363	−	0.0950525i
$507$		0			0
$508$	318.014	−	473.915i	0.0277748	−	0.0413909i
$509$	2562.66	−	1479.55i	0.223159	−	0.128841i	−0.384253	−	0.923228i	$-0.625541\pi$
$509$	2562.66	−	1479.55i	0.223159	−	0.128841i	0.607412	+	0.794387i	$0.292208\pi$
$510$		0			0
$511$	−22918.0	−	13231.7i	−1.98401	−	1.14547i
$512$	−5370.32	−	10265.4i	−0.463548	−	0.886072i
$513$		0			0
$514$	−4420.27	−	19042.4i	−0.379319	−	1.63410i
$515$	376.767	−	652.579i	0.0322375	−	0.0558370i
$516$		0			0
$517$	2437.08	+	4221.14i	0.207316	+	0.359083i
$518$	−14752.3	+	13789.7i	−1.25131	+	1.16966i
$519$		0			0
$520$	6101.36	−	988.798i	0.514543	−	0.0833878i
$521$			12490.4i			1.05032i	0.851004	+	0.525159i	$0.175994\pi$
$521$			12490.4i			1.05032i	−0.851004	+	0.525159i	$0.824006\pi$
$522$		0			0
$523$			13273.1i			1.10974i	0.831939	+	0.554868i	$0.187231\pi$
$523$			13273.1i			1.10974i	−0.831939	+	0.554868i	$0.812769\pi$
$524$	386.878	−	5729.40i	0.0322535	−	0.477652i
$525$		0			0
$526$	−5119.24	−	5476.57i	−0.424352	−	0.453973i
$527$	1534.70	+	2658.17i	0.126855	+	0.219719i
$528$		0			0
$529$	6052.52	−	10483.3i	0.497454	−	0.861616i
$530$	4511.03	−	1047.13i	0.369711	−	0.0858200i
$531$		0			0
$532$	4849.30	−	2379.53i	0.395195	−	0.193920i
$533$	7367.58	+	4253.68i	0.598734	+	0.345679i
$534$		0			0
$535$	3636.38	−	2099.47i	0.293859	−	0.169660i
$536$	8391.65	−	22097.5i	0.676239	−	1.78072i
$537$		0			0
$538$	6456.53	+	1965.53i	0.517400	+	0.157509i
$539$	−12263.5			−0.980012
$540$		0			0
$541$	−12385.8			−0.984302			−0.492151	−	0.870510i	$-0.663789\pi$
$541$	−12385.8			−0.984302			−0.492151	+	0.870510i	$0.663789\pi$
$542$	11601.1	+	3531.65i	0.919390	+	0.279885i
$543$		0			0
$544$	871.609	+	9320.67i	0.0686947	+	0.734596i
$545$	−1300.17	+	750.656i	−0.102190	+	0.0589992i
$546$		0			0
$547$	−15941.6	−	9203.89i	−1.24609	−	0.719433i	−0.275766	−	0.961225i	$-0.588932\pi$
$547$	−15941.6	−	9203.89i	−1.24609	−	0.719433i	−0.970328	+	0.241792i	$0.922265\pi$
$548$	776.939	+	1583.34i	0.0605642	+	0.123425i
$549$		0			0
$550$	13347.2	−	3098.24i	1.03477	−	0.240199i
$551$	−3431.35	+	5943.28i	−0.265300	+	0.459514i
$552$		0			0
$553$	−7406.78	−	12828.9i	−0.569563	−	0.986512i
$554$	−9335.03	−	9986.63i	−0.715898	−	0.765869i
$555$		0			0
$556$	−11195.5	−	755.975i	−0.853944	−	0.0576627i
$557$			13864.9i			1.05472i	0.849643	+	0.527358i	$0.176817\pi$
$557$			13864.9i			1.05472i	−0.849643	+	0.527358i	$0.823183\pi$
$558$		0			0
$559$		−	16510.7i		−	1.24925i
$560$	3192.55	+	7794.35i	0.240910	+	0.588163i
$561$		0			0
$562$	3581.97	−	3348.25i	0.268854	−	0.251312i
$563$	−7442.77	−	12891.3i	−0.557150	−	0.965012i	−0.997733	−	0.0672999i	$-0.978562\pi$
$563$	−7442.77	−	12891.3i	−0.557150	−	0.965012i	0.440583	−	0.897712i	$-0.354772\pi$
$564$		0			0
$565$	1706.44	−	2955.65i	0.127063	−	0.220080i
$566$	2383.57	+	10268.4i	0.177012	+	0.762566i
$567$		0			0
$568$	−4269.87	+	3483.09i	−0.315422	+	0.257302i
$569$	−5893.56	−	3402.65i	−0.434219	−	0.250697i	0.266923	−	0.963718i	$-0.413993\pi$
$569$	−5893.56	−	3402.65i	−0.434219	−	0.250697i	−0.701142	+	0.713021i	$0.747326\pi$
$570$		0			0
$571$	−7163.27	+	4135.72i	−0.524998	+	0.303108i	−0.738977	−	0.673731i	$-0.764691\pi$
$571$	−7163.27	+	4135.72i	−0.524998	+	0.303108i	0.213979	+	0.976838i	$0.431357\pi$
$572$	16932.7	+	11362.4i	1.23775	+	0.830572i
$573$		0			0
$574$	−3376.22	+	11090.5i	−0.245506	+	0.806461i
$575$	−750.595			−0.0544382
$576$		0			0
$577$	−12153.3			−0.876863			−0.438432	−	0.898765i	$-0.644466\pi$
$577$	−12153.3			−0.876863			−0.438432	+	0.898765i	$0.644466\pi$
$578$	−1843.98	+	6057.27i	−0.132698	+	0.435899i
$579$		0			0
$580$	−8885.86	−	5962.73i	−0.636147	−	0.426878i
$581$	−11852.3	+	6842.92i	−0.846327	+	0.488627i
$582$		0			0
$583$	13231.2	+	7639.04i	0.939932	+	0.542670i
$584$	−19193.7	+	15657.0i	−1.36000	+	1.10941i
$585$		0			0
$586$	−4138.95	−	17830.5i	−0.291772	−	1.25695i
$587$	7165.79	−	12411.5i	0.503856	−	0.872705i	−0.496134	−	0.868246i	$-0.665247\pi$
$587$	7165.79	−	12411.5i	0.503856	−	0.872705i	0.999990	−	0.00445871i	$-0.00141926\pi$
$588$		0			0
$589$	−828.874	−	1435.65i	−0.0579850	−	0.100433i
$590$	2548.38	−	2382.10i	0.177822	−	0.166220i
$591$		0			0
$592$	7164.28	+	17491.0i	0.497382	+	1.21432i
$593$		−	17892.9i		−	1.23908i	−0.784966	−	0.619539i	$-0.787319\pi$
$593$		−	17892.9i		−	1.23908i	0.784966	−	0.619539i	$-0.212681\pi$
$594$		0			0
$595$		−	6805.99i		−	0.468938i
$596$	−11883.5	−	802.438i	−0.816727	−	0.0551496i
$597$		0			0
$598$	−762.804	−	816.049i	−0.0521628	−	0.0558039i
$599$	5989.96	+	10374.9i	0.408586	+	0.707692i	0.994732	−	0.102514i	$-0.0326886\pi$
$599$	5989.96	+	10374.9i	0.408586	+	0.707692i	−0.586145	+	0.810206i	$0.699355\pi$
$600$		0			0
$601$	−1473.48	+	2552.14i	−0.100007	+	0.173218i	−0.911687	−	0.410885i	$-0.865220\pi$
$601$	−1473.48	+	2552.14i	−0.100007	+	0.173218i	0.811680	+	0.584102i	$0.198553\pi$
$602$	21916.5	−	5087.43i	1.48381	−	0.344432i
$603$		0			0
$604$	6934.83	+	14132.7i	0.467176	+	0.952070i
$605$	−5891.53	−	3401.48i	−0.395909	−	0.228578i
$606$		0			0
$607$	22272.8	−	12859.2i	1.48933	−	0.859866i	0.489406	−	0.872056i	$-0.337214\pi$
$607$	22272.8	−	12859.2i	1.48933	−	0.859866i	0.999926	+	0.0121903i	$0.00388040\pi$
$608$	−470.747	−	5034.00i	−0.0314002	−	0.335782i
$609$		0			0
$610$	5118.06	+	1558.06i	0.339712	+	0.103417i
$611$	4814.36			0.318770
$612$		0			0
$613$	−1851.43			−0.121988			−0.0609938	−	0.998138i	$-0.519427\pi$
$613$	−1851.43			−0.121988			−0.0609938	+	0.998138i	$0.519427\pi$
$614$	21264.7	+	6473.49i	1.39768	+	0.425487i
$615$		0			0
$616$	−9865.20	+	25977.7i	−0.645260	+	1.69914i
$617$	−17363.4	+	10024.8i	−1.13294	+	0.654103i	−0.944673	−	0.328015i	$-0.893621\pi$
$617$	−17363.4	+	10024.8i	−1.13294	+	0.654103i	−0.188267	+	0.982118i	$0.560287\pi$
$618$		0			0
$619$	19210.5	+	11091.2i	1.24739	+	0.720183i	0.970589	−	0.240743i	$-0.0773911\pi$
$619$	19210.5	+	11091.2i	1.24739	+	0.720183i	0.276805	+	0.960926i	$0.410724\pi$
$620$	2320.61	−	1138.71i	0.150319	−	0.0737609i
$621$		0			0
$622$	20636.7	−	4790.34i	1.33031	−	0.308802i
$623$	−2568.90	+	4449.46i	−0.165202	+	0.286138i
$624$		0			0
$625$	−2694.67	−	4667.31i	−0.172459	−	0.298708i
$626$	16627.4	+	17788.1i	1.06161	+	1.13571i
$627$		0			0
$628$	608.094	−	9005.44i	0.0386395	−	0.572223i
$629$		−	15273.1i		−	0.968166i
$630$		0			0
$631$			28148.1i			1.77584i	0.459994	+	0.887922i	$0.347851\pi$
$631$			28148.1i			1.77584i	−0.459994	+	0.887922i	$0.652149\pi$
$632$	−13687.0	+	2218.14i	−0.861452	+	0.139609i
$633$		0			0
$634$	−11226.8	+	10494.3i	−0.703269	+	0.657382i
$635$	194.191	+	336.348i	0.0121358	+	0.0210198i
$636$		0			0
$637$	−6056.53	+	10490.2i	−0.376716	+	0.652492i
$638$	−7982.77	−	34389.6i	−0.495362	−	2.13401i
$639$		0			0
$640$	7881.16	−	203.534i	0.486766	−	0.0125709i
$641$	−6980.56	−	4030.23i	−0.430134	−	0.248338i	0.269270	−	0.963065i	$-0.413218\pi$
$641$	−6980.56	−	4030.23i	−0.430134	−	0.248338i	−0.699404	+	0.714727i	$0.746551\pi$
$642$		0			0
$643$	−666.166	+	384.611i	−0.0408570	+	0.0235888i	−0.520289	−	0.853990i	$-0.674176\pi$
$643$	−666.166	+	384.611i	−0.0408570	+	0.0235888i	0.479432	+	0.877579i	$0.340843\pi$
$644$	848.193	−	1264.00i	0.0518998	−	0.0773428i
$645$		0			0
$646$	−1189.79	+	3908.33i	−0.0724639	+	0.238036i
$647$	−25155.2			−1.52852			−0.764259	−	0.644909i	$-0.776895\pi$
$647$	−25155.2			−1.52852			−0.764259	+	0.644909i	$0.776895\pi$
$648$		0			0
$649$	11508.5			0.696067
$650$	3941.47	−	12947.3i	0.237842	−	0.781283i
$651$		0			0
$652$	−8648.13	+	12887.7i	−0.519458	+	0.774114i
$653$	−17852.0	+	10306.9i	−1.06984	+	0.617671i	−0.928137	−	0.372238i	$-0.878590\pi$
$653$	−17852.0	+	10306.9i	−1.06984	+	0.617671i	−0.141701	+	0.989910i	$0.545257\pi$
$654$		0			0
$655$	3384.21	+	1953.88i	0.201881	+	0.116556i
$656$	8582.62	+	6639.64i	0.510815	+	0.395175i
$657$		0			0
$658$	1483.44	+	6390.65i	0.0878886	+	0.378622i
$659$	−12082.8	+	20928.0i	−0.714231	+	1.23708i	0.249024	+	0.968497i	$0.419890\pi$
$659$	−12082.8	+	20928.0i	−0.714231	+	1.23708i	−0.963255	+	0.268587i	$0.913443\pi$
$660$		0			0
$661$	−9976.53	−	17279.9i	−0.587053	−	1.01681i	−0.994616	−	0.103629i	$-0.966955\pi$
$661$	−9976.53	−	17279.9i	−0.587053	−	1.01681i	0.407563	−	0.913177i	$-0.366379\pi$
$662$	−3262.06	+	3049.22i	−0.191516	+	0.179020i
$663$		0			0
$664$	2049.27	+	12645.0i	0.119770	+	0.739038i
$665$			3675.84i			0.214351i
$666$		0			0
$667$			1933.95i			0.112268i
$668$	−1339.37	+	19835.2i	−0.0775777	+	1.14887i
$669$		0			0
$670$	10984.1	+	11750.9i	0.633365	+	0.677575i
$671$	8825.05	+	15285.4i	0.507731	+	0.879416i
$672$		0			0
$673$	3449.60	−	5974.88i	0.197581	−	0.342221i	−0.750162	−	0.661254i	$-0.770025\pi$
$673$	3449.60	−	5974.88i	0.197581	−	0.342221i	0.947744	+	0.319033i	$0.103358\pi$
$674$	18737.2	−	4349.43i	1.07082	−	0.248566i
$675$		0			0
$676$	2303.16	−	1130.15i	0.131040	−	0.0643007i
$677$	7812.18	+	4510.37i	0.443496	+	0.256052i	0.705079	−	0.709128i	$-0.250911\pi$
$677$	7812.18	+	4510.37i	0.443496	+	0.256052i	−0.261584	+	0.965181i	$0.584245\pi$
$678$		0			0
$679$	9810.44	−	5664.06i	0.554477	−	0.320128i
$680$	−5955.44	−	2261.61i	−0.335854	−	0.127543i
$681$		0			0
$682$	8158.33	+	2483.59i	0.458062	+	0.139445i
$683$	7388.19			0.413911			0.206956	−	0.978350i	$-0.433644\pi$
$683$	7388.19			0.413911			0.206956	+	0.978350i	$0.433644\pi$
$684$		0			0
$685$	−1200.20			−0.0669448
$686$	6645.30	+	2022.99i	0.369853	+	0.112592i
$687$		0			0
$688$	2831.16	−	20868.2i	0.156885	−	1.15638i
$689$	13068.9	−	7545.32i	0.722620	−	0.417205i
$690$		0			0
$691$	−25972.9	−	14995.5i	−1.42989	−	0.825549i	−0.432781	−	0.901499i	$-0.642468\pi$
$691$	−25972.9	−	14995.5i	−1.42989	−	0.825549i	−0.997112	+	0.0759500i	$0.975801\pi$
$692$	−10143.5	−	20671.7i	−0.557224	−	1.13558i
$693$		0			0
$694$	−34319.0	+	7966.38i	−1.87713	+	0.435734i
$695$	3817.95	−	6612.88i	0.208378	−	0.360922i
$696$		0			0
$697$	−4384.06	−	7593.41i	−0.238247	−	0.412656i
$698$	−3518.06	−	3763.63i	−0.190775	−	0.204091i
$699$		0			0
$700$	18400.9	+	1242.52i	0.993554	+	0.0670899i
$701$		−	23559.3i		−	1.26936i	−0.772774	−	0.634681i	$-0.781131\pi$
$701$		−	23559.3i		−	1.26936i	0.772774	−	0.634681i	$-0.218869\pi$
$702$		0			0
$703$			8248.82i			0.442547i
$704$	19453.1	+	17264.7i	1.04143	+	0.924272i
$705$		0			0
$706$	14362.1	−	13425.0i	0.765618	−	0.715663i
$707$	−21675.2	−	37542.6i	−1.15301	−	1.99708i
$708$		0			0
$709$	−6114.96	+	10591.4i	−0.323910	+	0.561028i	−0.981291	−	0.192530i	$-0.938331\pi$
$709$	−6114.96	+	10591.4i	−0.323910	+	0.561028i	0.657381	+	0.753558i	$0.271664\pi$
$710$	−847.887	−	3652.68i	−0.0448178	−	0.193074i
$711$		0			0
$712$	3039.78	+	3726.41i	0.160001	+	0.196142i
$713$	−404.574	−	233.581i	−0.0212502	−	0.0122688i
$714$		0			0
$715$	−12017.5	+	6938.30i	−0.628571	+	0.362906i
$716$	−19701.6	−	13220.5i	−1.02833	−	0.690046i
$717$		0			0
$718$	−262.555	+	862.464i	−0.0136469	+	0.0448285i
$719$	37718.6			1.95642			0.978211	−	0.207613i	$-0.0665694\pi$
$719$	37718.6			1.95642			0.978211	+	0.207613i	$0.0665694\pi$
$720$		0			0
$721$	3346.11			0.172837
$722$	−5007.29	+	16448.4i	−0.258105	+	0.847848i
$723$		0			0
$724$	−8307.38	−	5574.55i	−0.426438	−	0.286156i
$725$	−20292.0	+	11715.6i	−1.03949	+	0.600147i
$726$		0			0
$727$	7555.48	+	4362.16i	0.385443	+	0.222536i	0.680184	−	0.733041i	$-0.261900\pi$
$727$	7555.48	+	4362.16i	0.385443	+	0.222536i	−0.294741	+	0.955577i	$0.595233\pi$
$728$	17349.3	+	21268.2i	0.883252	+	1.08276i
$729$		0			0
$730$	−3811.38	−	16419.4i	−0.193241	−	0.832476i
$731$	−8508.39	+	14737.0i	−0.430498	+	0.745645i
$732$		0			0
$733$	7960.97	+	13788.8i	0.401153	+	0.694817i	0.993865	−	0.110597i	$-0.0352762\pi$
$733$	7960.97	+	13788.8i	0.401153	+	0.694817i	−0.592712	+	0.805414i	$0.701943\pi$
$734$	−12944.2	+	12099.6i	−0.650923	+	0.608452i
$735$		0			0
$736$	−824.189	−	1162.22i	−0.0412772	−	0.0582065i
$737$			53066.9i			2.65230i
$738$		0			0
$739$		−	21026.0i		−	1.04662i	−0.852141	−	0.523312i	$-0.824696\pi$
$739$		−	21026.0i		−	1.04662i	0.852141	−	0.523312i	$-0.175304\pi$
$740$	−12833.2	−	866.565i	−0.637511	−	0.0430480i
$741$		0			0
$742$	14042.7	+	15022.9i	0.694774	+	0.743271i
$743$	5813.11	+	10068.6i	0.287029	+	0.497148i	0.973099	−	0.230387i	$-0.0739992\pi$
$743$	5813.11	+	10068.6i	0.287029	+	0.497148i	−0.686071	+	0.727535i	$0.740666\pi$
$744$		0			0
$745$	4052.60	−	7019.32i	0.199297	−	0.345192i
$746$	−33426.8	+	7759.27i	−1.64054	+	0.380814i
$747$		0			0
$748$	−9258.24	−	18867.6i	−0.452560	−	0.922284i
$749$	16147.6	+	9322.82i	0.787744	+	0.454804i
$750$		0			0
$751$	6096.06	−	3519.56i	0.296203	−	0.171013i	−0.344533	−	0.938774i	$-0.611963\pi$
$751$	6096.06	−	3519.56i	0.296203	−	0.171013i	0.640736	+	0.767761i	$0.278629\pi$
$752$	6084.95	+	825.539i	0.295074	+	0.0400323i
$753$		0			0
$754$	−33359.3	−	10155.4i	−1.61124	−	0.490500i
$755$	−10712.8			−0.516395
$756$		0			0
$757$	−28354.3			−1.36137			−0.680685	−	0.732577i	$-0.738318\pi$
$757$	−28354.3			−1.36137			−0.680685	+	0.732577i	$0.738318\pi$
$758$	−5218.77	−	1588.72i	−0.250072	−	0.0761279i
$759$		0			0
$760$	3216.47	+	1221.47i	0.153518	+	0.0582994i
$761$	20274.5	−	11705.5i	0.965771	−	0.557588i	0.0678265	−	0.997697i	$-0.478394\pi$
$761$	20274.5	−	11705.5i	0.965771	−	0.557588i	0.897944	+	0.440109i	$0.145060\pi$
$762$		0			0
$763$	−5773.51	−	3333.34i	−0.273939	−	0.158158i
$764$	−5569.79	+	2733.07i	−0.263754	+	0.129423i
$765$		0			0
$766$	16392.9	−	3805.24i	0.773237	−	0.179490i
$767$	5683.65	−	9844.37i	0.267568	−	0.463441i
$768$		0			0
$769$	12632.8	+	21880.6i	0.592392	+	1.02605i	0.993909	+	0.110202i	$0.0351498\pi$
$769$	12632.8	+	21880.6i	0.592392	+	1.02605i	−0.401517	+	0.915852i	$0.631517\pi$
$770$	−12912.9	−	13814.3i	−0.604350	−	0.646535i
$771$		0			0
$772$	2356.08	−	34891.9i	0.109841	−	1.62667i
$773$		−	31081.3i		−	1.44621i	−0.690740	−	0.723103i	$-0.742715\pi$
$773$		−	31081.3i		−	1.44621i	0.690740	−	0.723103i	$-0.257285\pi$
$774$		0			0
$775$		−	5660.02i		−	0.262340i
$776$	−1696.24	−	10466.6i	−0.0784682	−	0.484186i
$777$		0			0
$778$	4827.00	−	4512.05i	0.222438	−	0.207924i
$779$	2367.78	+	4101.12i	0.108902	+	0.188624i
$780$		0			0
$781$	6185.49	−	10713.6i	0.283399	−	0.490861i
$782$	260.325	+	1121.47i	0.0119043	+	0.0512837i
$783$		0			0
$784$	−9453.75	+	12220.2i	−0.430656	+	0.556679i
$785$	5319.29	+	3071.09i	0.241852	+	0.139633i
$786$		0			0
$787$	−29654.1	+	17120.8i	−1.34314	+	0.775463i	−0.987267	−	0.159070i	$-0.949150\pi$
$787$	−29654.1	+	17120.8i	−1.34314	+	0.775463i	−0.355875	+	0.934534i	$0.615817\pi$
$788$	−7348.92	+	10951.6i	−0.332227	+	0.495095i
$789$		0			0
$790$	2747.90	−	9026.54i	0.123754	−	0.406519i
$791$	15155.2			0.681233
$792$		0			0
$793$	17433.6			0.780686
$794$	5008.34	−	16451.9i	0.223853	−	0.735333i
$795$		0			0
$796$	13134.2	−	19573.0i	0.584836	−	0.871542i
$797$	15734.1	−	9084.08i	0.699285	−	0.403732i	−0.107796	−	0.994173i	$-0.534379\pi$
$797$	15734.1	−	9084.08i	0.699285	−	0.403732i	0.807081	+	0.590441i	$0.201046\pi$
$798$		0			0
$799$	−4297.16	−	2480.96i	−0.190266	−	0.109850i
$800$	7201.81	−	15688.4i	0.318278	−	0.693337i
$801$		0			0
$802$	8860.21	+	38169.6i	0.390106	+	1.68057i
$803$	27804.8	−	48159.2i	1.22193	−	2.11644i
$804$		0			0
$805$	517.936	+	897.092i	0.0226768	+	0.0392774i
$806$	6153.59	−	5752.08i	0.268922	−	0.251375i
$807$		0			0
$808$	−40053.5	+	6491.15i	−1.74391	+	0.282621i
$809$		−	24608.1i		−	1.06944i	−0.845029	−	0.534720i	$-0.820417\pi$
$809$		−	24608.1i		−	1.06944i	0.845029	−	0.534720i	$-0.179583\pi$
$810$		0			0
$811$			3293.86i			0.142618i	0.997454	+	0.0713089i	$0.0227176\pi$
$811$			3293.86i			0.142618i	−0.997454	+	0.0713089i	$0.977282\pi$
$812$	3201.42	−	47410.8i	0.138359	−	2.04900i
$813$		0			0
$814$	−28977.4	−	31000.1i	−1.24774	−	1.33483i
$815$	−5280.85	−	9146.70i	−0.226969	−	0.393123i
$816$		0			0
$817$	4595.30	−	7959.29i	0.196780	−	0.340833i
$818$	−746.295	+	173.236i	−0.0318993	+	0.00740470i
$819$		0			0
$820$	−6629.12	+	3252.88i	−0.282316	+	0.138531i
$821$	33264.9	+	19205.5i	1.41407	+	0.816414i	0.995769	−	0.0918946i	$-0.0292923\pi$
$821$	33264.9	+	19205.5i	1.41407	+	0.816414i	0.418301	+	0.908308i	$0.362626\pi$
$822$		0			0
$823$	−531.302	+	306.747i	−0.0225031	+	0.0129922i	−0.511209	−	0.859456i	$-0.670802\pi$
$823$	−531.302	+	306.747i	−0.0225031	+	0.0129922i	0.488706	+	0.872448i	$0.337469\pi$
$824$	1111.91	−	2927.95i	0.0470086	−	0.123786i
$825$		0			0
$826$	14818.8	+	4511.21i	0.624229	+	0.190031i
$827$	−19933.1			−0.838140			−0.419070	−	0.907954i	$-0.637644\pi$
$827$	−19933.1			−0.838140			−0.419070	+	0.907954i	$0.637644\pi$
$828$		0			0
$829$	32209.0			1.34941			0.674707	−	0.738086i	$-0.264270\pi$
$829$	32209.0			1.34941			0.674707	+	0.738086i	$0.264270\pi$
$830$	−8339.37	−	2538.71i	−0.348751	−	0.106168i
$831$		0			0
$832$	24375.5	−	8113.78i	1.01571	−	0.338094i
$833$	10811.8	−	6242.17i	0.449706	−	0.259638i
$834$		0			0
$835$	−11716.1	−	6764.32i	−0.485573	−	0.280346i
$836$	5000.28	+	10190.2i	0.206864	+	0.421574i
$837$		0			0
$838$	−21770.0	+	5053.41i	−0.897413	+	0.208314i
$839$	−21916.3	+	37960.1i	−0.901828	+	1.56201i	−0.0767097	+	0.997053i	$0.524441\pi$
$839$	−21916.3	+	37960.1i	−0.901828	+	1.56201i	−0.825119	+	0.564959i	$0.808892\pi$
$840$		0			0
$841$	17991.3	+	31161.9i	0.737682	+	1.27770i
$842$	12870.9	+	13769.3i	0.526792	+	0.563564i
$843$		0			0
$844$	4397.14	+	296.918i	0.179332	+	0.0121094i
$845$			1745.83i			0.0710750i
$846$		0			0
$847$		−	30208.9i		−	1.22549i
$848$	17811.8	−	7295.69i	0.721297	−	0.295442i
$849$		0			0
$850$	−10190.1	+	9525.22i	−0.411197	+	0.384368i
$851$	1162.28	+	2013.13i	0.0468184	+	0.0810919i
$852$		0			0
$853$	−6391.08	+	11069.7i	−0.256537	+	0.444336i	−0.965312	−	0.261099i	$-0.915915\pi$
$853$	−6391.08	+	11069.7i	−0.256537	+	0.444336i	0.708775	+	0.705435i	$0.249248\pi$
$854$	5371.79	+	23141.6i	0.215245	+	0.927269i
$855$		0			0
$856$	13523.6	−	11031.7i	0.539983	−	0.440485i
$857$	−32179.0	−	18578.6i	−1.28263	−	0.740527i	−0.305302	−	0.952256i	$-0.598757\pi$
$857$	−32179.0	−	18578.6i	−1.28263	−	0.740527i	−0.977329	+	0.211728i	$0.932091\pi$
$858$		0			0
$859$	−7232.93	+	4175.93i	−0.287293	+	0.165869i	−0.636720	−	0.771095i	$-0.719709\pi$
$859$	−7232.93	+	4175.93i	−0.287293	+	0.165869i	0.349428	+	0.936963i	$0.386376\pi$
$860$	11900.0	+	7985.34i	0.471846	+	0.316626i
$861$		0			0
$862$	12168.8	−	39973.1i	0.480824	−	1.57945i
$863$	−11795.5			−0.465265			−0.232633	−	0.972565i	$-0.574734\pi$
$863$	−11795.5			−0.465265			−0.232633	+	0.972565i	$0.574734\pi$
$864$		0			0
$865$	15669.5			0.615929
$866$	1954.53	−	6420.41i	0.0766947	−	0.251934i
$867$		0			0
$868$	9531.49	+	6395.97i	0.372719	+	0.250108i
$869$	26958.4	−	15564.4i	1.05236	−	0.607580i
$870$		0			0
$871$	45393.5	+	26207.9i	1.76590	+	1.01954i
$872$	−4835.29	+	3944.33i	−0.187780	+	0.153179i
$873$		0			0
$874$	−140.599	−	605.697i	−0.00544145	−	0.0234416i
$875$	−14500.6	+	25115.8i	−0.560240	+	0.970364i
$876$		0			0
$877$	7828.97	+	13560.2i	0.301443	+	0.522114i	0.976463	−	0.215685i	$-0.0691984\pi$
$877$	7828.97	+	13560.2i	0.301443	+	0.522114i	−0.675020	+	0.737799i	$0.735865\pi$
$878$	−5987.63	+	5596.95i	−0.230151	+	0.215134i
$879$		0			0
$880$	−16378.8	+	6708.74i	−0.627421	+	0.256991i
$881$			39103.2i			1.49537i	0.664054	+	0.747684i	$0.268834\pi$
$881$			39103.2i			1.49537i	−0.664054	+	0.747684i	$0.731166\pi$
$882$		0			0
$883$			23664.8i			0.901907i	0.892547	+	0.450953i	$0.148916\pi$
$883$			23664.8i			0.901907i	−0.892547	+	0.450953i	$0.851084\pi$
$884$	−20711.7	−	1398.56i	−0.788020	−	0.0532112i
$885$		0			0
$886$	−15189.2	−	16249.4i	−0.575949	−	0.616152i
$887$	22019.4	+	38138.8i	0.833529	+	1.44371i	0.895223	+	0.445619i	$0.147016\pi$
$887$	22019.4	+	38138.8i	0.833529	+	1.44371i	−0.0616939	+	0.998095i	$0.519650\pi$
$888$		0			0
$889$	−862.316	+	1493.58i	−0.0325322	+	0.0563475i
$890$	−3187.78	+	739.970i	−0.120061	+	0.0278695i
$891$		0			0
$892$	6367.77	+	12977.1i	0.239023	+	0.487112i
$893$	2320.85	+	1339.94i	0.0869701	+	0.0502122i
$894$		0			0
$895$	13982.7	−	8072.89i	0.522222	−	0.301505i
$896$	18281.1	+	29856.2i	0.681618	+	1.11320i
$897$		0			0
$898$	3614.73	+	1100.41i	0.134326	+	0.0408922i
$899$	−14583.3			−0.541024
$900$		0			0
$901$	−15553.2			−0.575086
$902$	−23305.3	−	7094.70i	−0.860291	−	0.261893i
$903$		0			0
$904$	5036.02	−	13261.2i	0.185283	−	0.487900i
$905$	5895.93	−	3404.02i	0.216561	−	0.125031i
$906$		0			0
$907$	28310.7	+	16345.2i	1.03643	+	0.598384i	0.918820	−	0.394676i	$-0.129143\pi$
$907$	28310.7	+	16345.2i	1.03643	+	0.598384i	0.117610	+	0.993060i	$0.462477\pi$
$908$	10813.1	−	5305.93i	0.395204	−	0.193925i
$909$		0			0
$910$	−18194.0	+	4223.33i	−0.662775	+	0.153848i
$911$	12749.9	−	22083.5i	0.463693	−	0.803140i	−0.535448	−	0.844568i	$-0.679857\pi$
$911$	12749.9	−	22083.5i	0.463693	−	0.803140i	0.999141	+	0.0414281i	$0.0131907\pi$
$912$		0			0
$913$	−14379.5	−	24906.1i	−0.521241	−	0.902817i
$914$	−33593.7	−	35938.7i	−1.21574	−	1.30060i
$915$		0			0
$916$	−826.802	+	12244.4i	−0.0298235	+	0.441665i
$917$			17352.6i			0.624901i
$918$		0			0
$919$		−	20221.1i		−	0.725825i	−0.931823	−	0.362912i	$-0.881782\pi$
$919$		−	20221.1i		−	0.725825i	0.931823	−	0.362912i	$-0.118218\pi$
$920$	957.091	−	155.108i	0.0342982	−	0.00555844i
$921$		0			0
$922$	−4612.33	+	4311.38i	−0.164749	+	0.154000i
$923$	−6109.61	−	10582.2i	−0.217877	−	0.377374i
$924$		0			0
$925$	−14081.9	+	24390.6i	−0.500551	+	0.866980i
$926$	2537.42	+	10931.2i	0.0900485	+	0.387927i
$927$		0			0
$928$	−40422.0	−	18555.8i	−1.42987	−	0.656385i
$929$	−32318.8	−	18659.3i	−1.14139	−	0.658979i	−0.194612	−	0.980880i	$-0.562345\pi$
$929$	−32318.8	−	18659.3i	−1.14139	−	0.658979i	−0.946773	+	0.321901i	$0.895678\pi$
$930$		0			0
$931$	−5839.32	+	3371.33i	−0.205560	+	0.118680i
$932$	5603.49	−	8350.50i	0.196940	−	0.293487i
$933$		0			0
$934$	−7257.13	+	23838.9i	−0.254241	+	0.835152i
$935$	14301.9			0.500239
$936$		0			0
$937$	−16237.5			−0.566121			−0.283060	−	0.959102i	$-0.591350\pi$
$937$	−16237.5			−0.566121			−0.283060	+	0.959102i	$0.591350\pi$
$938$	−20801.7	+	68331.3i	−0.724094	+	2.37857i
$939$		0			0
$940$	−2328.45	+	3469.93i	−0.0807932	+	0.120401i
$941$	1785.15	−	1030.66i	0.0618429	−	0.0357050i	−0.468760	−	0.883326i	$-0.655299\pi$
$941$	1785.15	−	1030.66i	0.0618429	−	0.0357050i	0.530603	+	0.847621i	$0.321966\pi$
$942$		0			0
$943$	1155.72	+	667.254i	0.0399102	+	0.0230422i
$944$	8871.72	−	11467.9i	0.305879	−	0.395389i
$945$		0			0
$946$	10690.6	+	46054.9i	0.367422	+	1.58285i
$947$	8954.48	−	15509.6i	0.307267	−	0.532202i	−0.670497	−	0.741913i	$-0.733919\pi$
$947$	8954.48	−	15509.6i	0.307267	−	0.532202i	0.977763	+	0.209711i	$0.0672523\pi$
$948$		0			0
$949$	−27463.6	−	47568.4i	−0.939418	−	1.62712i
$950$	5503.57	−	5144.47i	0.187957	−	0.175693i
$951$		0			0
$952$	−4525.41	−	27923.9i	−0.154064	−	0.950651i
$953$		−	10905.6i		−	0.370689i	−0.982674	−	0.185344i	$-0.940660\pi$
$953$		−	10905.6i		−	0.370689i	0.982674	−	0.185344i	$-0.0593400\pi$
$954$		0			0
$955$		−	4221.99i		−	0.143058i
$956$	−988.459	+	14638.4i	−0.0334404	+	0.495229i
$957$		0			0
$958$	37601.5	+	40226.2i	1.26811	+	1.35663i
$959$	−2664.78	−	4615.53i	−0.0897291	−	0.155415i
$960$		0			0
$961$	−13134.1	+	22749.0i	−0.440876	+	0.763619i
$962$	−40828.4	+	9477.40i	−1.36836	+	0.317634i
$963$		0			0
$964$	5153.35	−	2528.72i	0.172177	−	0.0844862i
$965$	20609.8	+	11899.0i	0.687515	+	0.396937i
$966$		0			0
$967$	−42102.8	+	24308.1i	−1.40014	+	0.808370i	−0.994406	−	0.105622i	$-0.966317\pi$
$967$	−42102.8	+	24308.1i	−1.40014	+	0.808370i	−0.405732	+	0.913992i	$0.632983\pi$
$968$	−26433.7	−	10038.4i	−0.877699	−	0.333311i
$969$		0			0
$970$	6902.70	+	2101.35i	0.228487	+	0.0695570i
$971$	−24102.8			−0.796596			−0.398298	−	0.917256i	$-0.630399\pi$
$971$	−24102.8			−0.796596			−0.398298	+	0.917256i	$0.630399\pi$
$972$		0			0
$973$	33907.7			1.11719
$974$	−14141.3	−	4304.97i	−0.465213	−	0.141622i
$975$		0			0
$976$	22034.6	+	2989.41i	0.722654	+	0.0980417i
$977$	−21356.3	+	12330.1i	−0.699333	+	0.403760i	−0.807099	−	0.590416i	$-0.798964\pi$
$977$	−21356.3	+	12330.1i	−0.699333	+	0.403760i	0.107766	+	0.994176i	$0.465630\pi$
$978$		0			0
$979$	−9349.99	−	5398.22i	−0.305237	−	0.176229i
$980$	−4631.56	−	9438.77i	−0.150969	−	0.307664i
$981$		0			0
$982$	26414.2	−	6131.46i	0.858361	−	0.199249i
$983$	−11000.9	+	19054.2i	−0.356943	+	0.618244i	−0.987449	−	0.157941i	$-0.949514\pi$
$983$	−11000.9	+	19054.2i	−0.356943	+	0.618244i	0.630505	+	0.776185i	$0.282848\pi$
$984$		0			0
$985$	−4487.51	−	7772.59i	−0.145161	−	0.251427i
$986$	24542.2	+	26255.3i	0.792681	+	0.848012i
$987$		0			0
$988$	11186.2	+	755.348i	0.360202	+	0.0243227i
$989$		−	2589.96i		−	0.0832718i
$990$		0			0
$991$		−	21100.2i		−	0.676358i	−0.941082	−	0.338179i	$-0.890189\pi$
$991$		−	21100.2i		−	0.676358i	0.941082	−	0.338179i	$-0.109811\pi$
$992$	8763.96	−	6214.97i	0.280500	−	0.198917i
$993$		0			0
$994$	12164.3	−	11370.6i	0.388159	−	0.362832i
$995$	8020.20	+	13891.4i	0.255535	+	0.442600i
$996$		0			0
$997$	−4141.70	+	7173.64i	−0.131564	+	0.227875i	−0.924280	−	0.381716i	$-0.875333\pi$
$997$	−4141.70	+	7173.64i	−0.131564	+	0.227875i	0.792716	+	0.609591i	$0.208666\pi$
$998$	1540.23	+	6635.30i	0.0488530	+	0.210458i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.h.b.35.5		24
3.2	odd	2		36.4.h.b.11.8	yes	24
4.3	odd	2	inner	108.4.h.b.35.10		24
9.2	odd	6		324.4.b.c.323.4		24
9.4	even	3		36.4.h.b.23.3	yes	24
9.5	odd	6	inner	108.4.h.b.71.10		24
9.7	even	3		324.4.b.c.323.21		24
12.11	even	2		36.4.h.b.11.3	✓	24
36.7	odd	6		324.4.b.c.323.3		24
36.11	even	6		324.4.b.c.323.22		24
36.23	even	6	inner	108.4.h.b.71.5		24
36.31	odd	6		36.4.h.b.23.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.3	✓	24	12.11	even	2
36.4.h.b.11.8	yes	24	3.2	odd	2
36.4.h.b.23.3	yes	24	9.4	even	3
36.4.h.b.23.8	yes	24	36.31	odd	6
108.4.h.b.35.5		24	1.1	even	1	trivial
108.4.h.b.35.10		24	4.3	odd	2	inner
108.4.h.b.71.5		24	36.23	even	6	inner
108.4.h.b.71.10		24	9.5	odd	6	inner
324.4.b.c.323.3		24	36.7	odd	6
324.4.b.c.323.4		24	9.2	odd	6
324.4.b.c.323.21		24	9.7	even	3
324.4.b.c.323.22		24	36.11	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.823719 + 2.70582i) q^{2} +(-6.64298 - 4.45768i) q^{4} +(4.71466 - 2.72201i) q^{5} +(20.9358 + 12.0873i) q^{7} +(17.5336 - 14.3029i) q^{8} +O(q^{10})\)	\(q+(-0.823719 + 2.70582i) q^{2} +(-6.64298 - 4.45768i) q^{4} +(4.71466 - 2.72201i) q^{5} +(20.9358 + 12.0873i) q^{7} +(17.5336 - 14.3029i) q^{8} +(3.48173 + 14.9992i) q^{10} +(-25.3999 + 43.9939i) q^{11} +(25.0883 + 43.4542i) q^{13} +(-49.9512 + 46.6920i) q^{14} +(24.2582 + 59.2245i) q^{16} -51.7146i q^{17} +27.9305i q^{19} +(-43.4533 - 2.93419i) q^{20} +(-98.1174 - 104.966i) q^{22} +(3.93548 + 6.81645i) q^{23} +(-47.6813 + 82.5864i) q^{25} +(-138.245 + 32.0905i) q^{26} +(-85.1946 - 173.620i) q^{28} +(212.788 + 122.853i) q^{29} +(-51.4009 + 29.6763i) q^{31} +(-180.233 + 16.8542i) q^{32} +(139.931 + 42.5982i) q^{34} +131.607 q^{35} +295.334 q^{37} +(-75.5750 - 23.0069i) q^{38} +(43.7327 - 115.160i) q^{40} +(146.833 - 84.7741i) q^{41} +(-284.968 - 164.526i) q^{43} +(364.841 - 179.026i) q^{44} +(-21.6859 + 5.03388i) q^{46} +(47.9742 - 83.0938i) q^{47} +(120.704 + 209.066i) q^{49} +(-184.188 - 197.045i) q^{50} +(27.0439 - 400.500i) q^{52} -300.751i q^{53} +276.555i q^{55} +(539.963 - 87.5075i) q^{56} +(-507.697 + 474.571i) q^{58} +(-113.273 - 196.195i) q^{59} +(173.722 - 300.896i) q^{61} +(-37.9590 - 163.527i) q^{62} +(102.857 - 501.562i) q^{64} +(236.566 + 136.581i) q^{65} +(904.675 - 522.314i) q^{67} +(-230.527 + 343.538i) q^{68} +(-108.407 + 356.105i) q^{70} -243.524 q^{71} -1094.68 q^{73} +(-243.272 + 799.122i) q^{74} +(124.505 - 185.542i) q^{76} +(-1063.53 + 614.031i) q^{77} +(-530.679 - 306.388i) q^{79} +(275.579 + 213.192i) q^{80} +(108.435 + 467.135i) q^{82} +(-283.063 + 490.280i) q^{83} +(-140.768 - 243.817i) q^{85} +(679.912 - 635.549i) q^{86} +(183.886 + 1134.66i) q^{88} +212.529i q^{89} +1213.00i q^{91} +(4.24224 - 62.8246i) q^{92} +(185.320 + 198.256i) q^{94} +(76.0272 + 131.683i) q^{95} +(234.298 - 405.817i) q^{97} +(-665.122 + 154.393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) \) 24 * q - 12 * q^4 + 72 * q^5	\( 24 q - 12 q^{4} + 72 q^{5} + 96 q^{10} - 216 q^{13} + 36 q^{14} - 72 q^{16} + 540 q^{20} - 192 q^{22} + 252 q^{25} - 672 q^{28} - 576 q^{29} - 360 q^{32} - 660 q^{34} + 1248 q^{37} + 144 q^{38} + 636 q^{40} - 1116 q^{41} + 960 q^{46} + 348 q^{49} + 648 q^{50} + 132 q^{52} + 1692 q^{56} + 516 q^{58} - 264 q^{61} + 960 q^{64} + 2592 q^{65} - 5688 q^{68} + 564 q^{70} - 4776 q^{73} - 5652 q^{74} - 600 q^{76} - 648 q^{77} - 4104 q^{82} + 720 q^{85} + 9540 q^{86} + 1956 q^{88} + 7416 q^{92} - 1188 q^{94} + 588 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 + 72 * q^5 + 96 * q^10 - 216 * q^13 + 36 * q^14 - 72 * q^16 + 540 * q^20 - 192 * q^22 + 252 * q^25 - 672 * q^28 - 576 * q^29 - 360 * q^32 - 660 * q^34 + 1248 * q^37 + 144 * q^38 + 636 * q^40 - 1116 * q^41 + 960 * q^46 + 348 * q^49 + 648 * q^50 + 132 * q^52 + 1692 * q^56 + 516 * q^58 - 264 * q^61 + 960 * q^64 + 2592 * q^65 - 5688 * q^68 + 564 * q^70 - 4776 * q^73 - 5652 * q^74 - 600 * q^76 - 648 * q^77 - 4104 * q^82 + 720 * q^85 + 9540 * q^86 + 1956 * q^88 + 7416 * q^92 - 1188 * q^94 + 588 * q^97

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