LMFDB - Embedded newform 108.4.h.b.71.5

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			71.5
Character	$\chi$	$=$	108.71
Dual form			108.4.h.b.35.5

$q$-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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	0.695801	−	0.718234i	$-0.255049\pi$
$5$	4.71466	+	2.72201i	0.421692	+	0.243464i	−0.274109	+	0.961699i	$0.588383\pi$
$6$		0			0
$7$	20.9358	−	12.0873i	1.13043	−	0.652651i	0.186383	−	0.982477i	$-0.440323\pi$
$7$	20.9358	−	12.0873i	1.13043	−	0.652651i	0.944042	+	0.329826i	$0.106990\pi$
$8$	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	−0.969770	−	0.244022i	$-0.921533\pi$
$11$	−25.3999	−	43.9939i	−0.696214	−	1.20588i	0.273556	−	0.961856i	$-0.411800\pi$
$12$		0			0
$13$	25.0883	−	43.4542i	0.535249	−	0.927078i	−0.463902	−	0.885886i	$-0.653551\pi$
$13$	25.0883	−	43.4542i	0.535249	−	0.927078i	0.999151	−	0.0411921i	$-0.0131156\pi$
$14$	−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	$0.120266\pi$
$17$			51.7146i			0.737801i	−0.929469	+	0.368901i	$0.879734\pi$
$18$		0			0
$19$		−	27.9305i		−	0.337247i	−0.985681	−	0.168624i	$-0.946068\pi$
$19$		−	27.9305i		−	0.337247i	0.985681	−	0.168624i	$-0.0539322\pi$
$20$	−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	−0.847635	−	0.530580i	$-0.821974\pi$
$23$	3.93548	−	6.81645i	0.0356785	−	0.0617969i	0.883313	+	0.468783i	$0.155307\pi$
$24$		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	0.372581	−	0.928000i	$-0.378473\pi$
$29$	212.788	−	122.853i	1.36254	−	0.786665i	0.989962	+	0.141335i	$0.0451395\pi$
$30$		0			0
$31$	−51.4009	−	29.6763i	−0.297802	−	0.171936i	0.343653	−	0.939097i	$-0.388336\pi$
$31$	−51.4009	−	29.6763i	−0.297802	−	0.171936i	−0.641455	+	0.767161i	$0.721669\pi$
$32$	−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	0.752866	−	0.658173i	$-0.228671\pi$
$41$	146.833	+	84.7741i	0.559304	+	0.322915i	−0.193562	+	0.981088i	$0.562004\pi$
$42$		0			0
$43$	−284.968	+	164.526i	−1.01063	+	0.583488i	−0.911376	−	0.411574i	$-0.864979\pi$
$43$	−284.968	+	164.526i	−1.01063	+	0.583488i	−0.0992550	+	0.995062i	$0.531646\pi$
$44$	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	0.930817	−	0.365486i	$-0.119097\pi$
$47$	47.9742	+	83.0938i	0.148888	+	0.257882i	−0.781928	+	0.623368i	$0.785764\pi$
$48$		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	$0.127431\pi$
$53$			300.751i			0.779459i	−0.920929	+	0.389729i	$0.872569\pi$
$54$		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	−0.963511	−	0.267669i	$-0.913747\pi$
$59$	−113.273	+	196.195i	−0.249947	+	0.432921i	0.713564	+	0.700590i	$0.247080\pi$
$60$		0			0
$61$	173.722	+	300.896i	0.364637	+	0.631570i	0.988718	−	0.149790i	$-0.0478597\pi$
$61$	173.722	+	300.896i	0.364637	+	0.631570i	−0.624081	+	0.781360i	$0.714526\pi$
$62$	−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	0.977228	+	0.212193i	$0.0680605\pi$
$67$	904.675	+	522.314i	1.64961	+	0.952401i	0.672378	+	0.740208i	$0.265273\pi$
$68$	−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	−0.827776	−	0.561059i	$-0.810394\pi$
$79$	−530.679	+	306.388i	−0.755773	+	0.436346i	0.0720031	+	0.997404i	$0.477061\pi$
$80$	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	0.615888	−	0.787834i	$-0.288797\pi$
$83$	−283.063	−	490.280i	−0.374340	−	0.648376i	−0.990228	+	0.139458i	$0.955464\pi$
$84$		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	$-0.959606\pi$
$89$		−	212.529i		−	0.253124i	0.991959	−	0.126562i	$-0.0403943\pi$
$90$		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	0.962202	−	0.272336i	$-0.0877961\pi$
$97$	234.298	+	405.817i	0.245252	+	0.424788i	−0.716951	+	0.697124i	$0.754463\pi$
$98$	−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	−0.530610	+	0.847616i	$0.678037\pi$
$101$	−1552.98	+	896.613i	−1.52997	+	0.883330i	−0.999362	+	0.0357140i	$0.988629\pi$
$102$		0			0
$103$	119.871	+	69.2074i	0.114672	+	0.0662059i	0.556239	−	0.831022i	$-0.312244\pi$
$103$	119.871	+	69.2074i	0.114672	+	0.0662059i	−0.441567	+	0.897228i	$0.645577\pi$
$104$	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	0.708664	−	0.705546i	$-0.249298\pi$
$113$	542.916	+	313.453i	0.451976	+	0.260948i	−0.256689	+	0.966494i	$0.582631\pi$
$114$		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	$-0.992066\pi$
$127$		−	71.3408i		−	0.0498463i	0.999689	−	0.0249231i	$-0.00793410\pi$
$128$	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	−0.721164	−	0.692765i	$-0.756392\pi$
$131$	358.903	−	621.638i	0.239370	−	0.414601i	0.960534	+	0.278164i	$0.0897258\pi$
$132$		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	−0.558350	−	0.829606i	$-0.688565\pi$
$137$	−190.925	+	110.231i	−0.119065	+	0.0687420i	0.439285	+	0.898348i	$0.355232\pi$
$138$		0			0
$139$	1214.70	+	701.309i	0.741222	+	0.427945i	0.822513	−	0.568746i	$-0.192571\pi$
$139$	1214.70	+	701.309i	0.741222	+	0.427945i	−0.0812916	+	0.996690i	$0.525905\pi$
$140$	−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	0.810660	−	0.585517i	$-0.199109\pi$
$149$	1289.36	+	744.413i	0.708917	+	0.409293i	−0.101743	+	0.994811i	$0.532442\pi$
$150$		0			0
$151$	−1704.17	+	983.903i	−0.918433	+	0.530257i	−0.883135	−	0.469120i	$-0.844571\pi$
$151$	−1704.17	+	983.903i	−0.918433	+	0.530257i	−0.0352979	+	0.999377i	$0.511238\pi$
$152$	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	−0.686272	−	0.727345i	$-0.740754\pi$
$157$	564.122	−	977.088i	0.286763	−	0.496689i	0.973035	+	0.230656i	$0.0740874\pi$
$158$	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	$0.154350\pi$
$163$			1940.05i			0.932250i	−0.884719	+	0.466125i	$0.845650\pi$
$164$	−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	0.420217	+	0.907424i	$0.361954\pi$
$167$	−1242.52	+	2152.11i	−0.575743	+	0.997217i	−0.995960	+	0.0897933i	$0.971379\pi$
$168$		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	0.160435	−	0.987046i	$-0.448710\pi$
$173$	2492.67	−	1439.15i	1.09546	−	0.632464i	0.935025	+	0.354583i	$0.115377\pi$
$174$		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	0.930080	−	0.367358i	$-0.119738\pi$
$191$	387.763	+	671.626i	0.146898	+	0.254435i	−0.783181	+	0.621793i	$0.786404\pi$
$192$		0			0
$193$	2185.71	−	3785.76i	0.815185	−	1.41194i	−0.0940101	−	0.995571i	$-0.529969\pi$
$193$	2185.71	−	3785.76i	0.815185	−	1.41194i	0.909195	−	0.416370i	$-0.136698\pi$
$194$	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	$0.0963584\pi$
$197$			1648.60i			0.596233i	−0.954530	+	0.298116i	$0.903642\pi$
$198$		0			0
$199$		−	2946.42i		−	1.04958i	−0.851232	−	0.524790i	$-0.824144\pi$
$199$		−	2946.42i		−	1.04958i	0.851232	−	0.524790i	$-0.175856\pi$
$200$	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	0.420147	−	0.907456i	$-0.361979\pi$
$211$	−477.089	−	275.447i	−0.155659	−	0.0898700i	−0.575806	+	0.817586i	$0.695312\pi$
$212$	−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	−0.716199	−	0.697897i	$-0.754120\pi$
$223$	−1564.82	+	903.449i	−0.469902	+	0.271298i	0.246297	+	0.969194i	$0.420786\pi$
$224$	−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	0.734732	−	0.678358i	$-0.237308\pi$
$227$	−752.796	−	1303.88i	−0.220109	−	0.381241i	−0.954841	+	0.297117i	$0.903975\pi$
$228$		0			0
$229$	−767.015	+	1328.51i	−0.221335	+	0.383364i	−0.955214	−	0.295917i	$-0.904375\pi$
$229$	−767.015	+	1328.51i	−0.221335	+	0.383364i	0.733878	+	0.679281i	$0.237708\pi$
$230$	−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	$-0.943451\pi$
$233$		−	1257.04i		−	0.353440i	0.984261	−	0.176720i	$-0.0565487\pi$
$234$		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	−0.963020	−	0.269428i	$-0.913165\pi$
$239$	−916.982	+	1588.26i	−0.248178	+	0.429858i	0.714842	+	0.699286i	$0.246499\pi$
$240$		0			0
$241$	−358.771	−	621.410i	−0.0958941	−	0.166094i	0.814087	−	0.580743i	$-0.197238\pi$
$241$	−358.771	−	621.410i	−0.0958941	−	0.166094i	−0.909981	+	0.414649i	$0.863904\pi$
$242$	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	−0.454157	−	0.890922i	$-0.650059\pi$
$257$	−5985.55	−	3455.76i	−1.45280	−	0.838772i	−0.998639	+	0.0521496i	$0.983393\pi$
$258$		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	0.667805	−	0.744336i	$-0.267234\pi$
$263$	−1325.23	−	2295.36i	−0.310712	−	0.538168i	−0.978517	+	0.206168i	$0.933901\pi$
$264$		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	$0.0871631\pi$
$269$			2386.16i			0.540843i	−0.962742	+	0.270422i	$0.912837\pi$
$270$		0			0
$271$			4287.45i			0.961048i	0.876982	+	0.480524i	$0.159554\pi$
$271$			4287.45i			0.961048i	−0.876982	+	0.480524i	$0.840446\pi$
$272$	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	−0.999604	−	0.0281511i	$-0.991038\pi$
$277$	−2416.58	−	4185.64i	−0.524181	−	0.907909i	0.475422	−	0.879758i	$-0.342295\pi$
$278$	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	−0.650821	−	0.759232i	$-0.725575\pi$
$281$	−1501.29	+	866.770i	−0.318717	+	0.184011i	0.332104	+	0.943243i	$0.392242\pi$
$282$		0			0
$283$	3227.63	+	1863.47i	0.677960	+	0.391420i	0.799086	−	0.601217i	$-0.205317\pi$
$283$	3227.63	+	1863.47i	0.677960	+	0.391420i	−0.121126	+	0.992637i	$0.538650\pi$
$284$	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	−0.176731	−	0.984259i	$-0.556552\pi$
$293$	−5604.61	−	3235.82i	−1.11749	−	0.645183i	−0.940759	+	0.339076i	$0.889886\pi$
$294$		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	$0.260715\pi$
$307$			7858.86i			1.46101i	−0.682909	+	0.730503i	$0.739285\pi$
$308$	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	0.291268	+	0.956642i	$0.405923\pi$
$311$	−3745.08	+	6486.66i	−0.682842	+	1.18272i	−0.974110	+	0.226075i	$0.927410\pi$
$312$		0			0
$313$	4304.38	+	7455.41i	0.777310	+	1.34634i	0.933487	+	0.358612i	$0.116750\pi$
$313$	4304.38	+	7455.41i	0.777310	+	1.34634i	−0.156176	+	0.987729i	$0.549917\pi$
$314$	−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	−0.0214185	−	0.999771i	$-0.506818\pi$
$317$	4705.42	−	2716.67i	0.833699	−	0.481336i	0.855117	+	0.518434i	$0.173485\pi$
$318$		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	−0.382168	−	0.924093i	$-0.624823\pi$
$331$	1367.21	−	789.359i	0.227035	−	0.131079i	0.609204	+	0.793014i	$0.291489\pi$
$332$	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	0.448654	+	0.893706i	$0.351904\pi$
$337$	−3400.38	+	5889.62i	−0.549645	+	0.952013i	−0.998299	+	0.0583070i	$0.981430\pi$
$338$	−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	0.249987	−	0.968249i	$-0.419573\pi$
$347$	6228.10	−	10787.4i	0.963522	−	1.66887i	0.713535	−	0.700620i	$-0.247093\pi$
$348$		0			0
$349$	−910.729	−	1577.43i	−0.139685	−	0.241942i	0.787692	−	0.616069i	$-0.211276\pi$
$349$	−910.729	−	1577.43i	−0.139685	−	0.241942i	−0.927378	+	0.374127i	$0.877942\pi$
$350$	−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	−0.879662	−	0.475600i	$-0.842231\pi$
$353$	−6019.52	+	3475.37i	−0.907611	+	0.524010i	−0.0279495	+	0.999609i	$0.508898\pi$
$354$		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	−0.0618160	−	0.998088i	$-0.519689\pi$
$367$	5425.21	−	3132.25i	0.771645	−	0.445510i	0.833461	+	0.552578i	$0.186356\pi$
$368$	−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	−0.0460564	−	0.998939i	$-0.514665\pi$
$373$	6066.19	−	10506.9i	0.842078	−	1.45852i	0.888135	−	0.459583i	$-0.152001\pi$
$374$	−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	$-0.958277\pi$
$379$		−	1928.72i		−	0.261402i	0.991422	−	0.130701i	$-0.0417229\pi$
$380$	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	−0.993341	−	0.115208i	$-0.963247\pi$
$383$	−2974.93	+	5152.73i	−0.396898	+	0.687448i	0.596443	+	0.802655i	$0.296580\pi$
$384$		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	−0.626017	−	0.779809i	$-0.715316\pi$
$389$	−2023.11	+	1168.05i	−0.263691	+	0.152242i	0.362326	+	0.932051i	$0.381983\pi$
$390$		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	0.999977	−	0.00675957i	$-0.00215165\pi$
$401$	11997.7	+	6926.90i	1.49411	+	0.862626i	0.494135	+	0.869385i	$0.335485\pi$
$402$		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	−0.857722	−	0.514113i	$-0.828121\pi$
$409$	135.435	−	234.581i	0.0163737	−	0.0283601i	0.874096	+	0.485753i	$0.161455\pi$
$410$	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	−0.538356	−	0.842718i	$-0.680954\pi$
$419$	3950.75	−	6842.90i	0.460637	−	0.797846i	0.998993	+	0.0448712i	$0.0142877\pi$
$420$		0			0
$421$	3331.91	+	5771.04i	0.385718	+	0.668083i	0.991869	−	0.127267i	$-0.0406204\pi$
$421$	3331.91	+	5771.04i	0.385718	+	0.668083i	−0.606150	+	0.795350i	$0.707287\pi$
$422$	−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	−0.357340	−	0.933974i	$-0.616316\pi$
$439$	2509.56	−	1448.89i	0.272835	−	0.157522i	0.630175	+	0.776453i	$0.282983\pi$
$440$	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	0.574396	−	0.818578i	$-0.305237\pi$
$443$	−3932.06	−	6810.53i	−0.421711	−	0.730425i	−0.996107	+	0.0881526i	$0.971904\pi$
$444$		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	$0.0223658\pi$
$449$			1335.91i			0.140413i	−0.997532	+	0.0702064i	$0.977634\pi$
$450$		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	−0.839679	−	0.543084i	$-0.817257\pi$
$457$	−8696.49	−	15062.8i	−0.890164	−	1.54181i	−0.0504849	−	0.998725i	$-0.516077\pi$
$458$	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	−0.399159	−	0.916882i	$-0.630698\pi$
$461$	1933.14	−	1116.10i	0.195304	−	0.112759i	0.594463	+	0.804123i	$0.297365\pi$
$462$		0			0
$463$	3435.96	+	1983.75i	0.344887	+	0.199121i	0.662431	−	0.749123i	$-0.269525\pi$
$463$	3435.96	+	1983.75i	0.344887	+	0.199121i	−0.317544	+	0.948244i	$0.602858\pi$
$464$	−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	0.785811	+	0.618466i	$0.212246\pi$
$479$	9734.00	+	16859.8i	0.928513	+	1.60823i	0.142702	+	0.989766i	$0.454421\pi$
$480$		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	$-0.921820\pi$
$487$		−	5226.26i		−	0.486293i	0.969990	−	0.243146i	$-0.0781795\pi$
$488$	−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	−0.997733	−	0.0672904i	$-0.978565\pi$
$491$	−4793.56	+	8302.69i	−0.440591	+	0.763127i	0.557142	+	0.830417i	$0.311898\pi$
$492$		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	0.590628	−	0.806944i	$-0.298880\pi$
$499$	2085.65	+	1204.15i	0.187108	+	0.108027i	−0.403520	+	0.914971i	$0.632213\pi$
$500$	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	0.607412	−	0.794387i	$-0.292208\pi$
$509$	2562.66	+	1479.55i	0.223159	+	0.128841i	−0.384253	+	0.923228i	$0.625541\pi$
$510$		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	$-0.824006\pi$
$521$		−	12490.4i		−	1.05032i	0.851004	−	0.525159i	$-0.175994\pi$
$522$		0			0
$523$		−	13273.1i		−	1.10974i	−0.831939	−	0.554868i	$-0.812769\pi$
$523$		−	13273.1i		−	1.10974i	0.831939	−	0.554868i	$-0.187231\pi$
$524$	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	−0.970328	−	0.241792i	$-0.922265\pi$
$547$	−15941.6	+	9203.89i	−1.24609	+	0.719433i	−0.275766	+	0.961225i	$0.588932\pi$
$548$	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	$-0.823183\pi$
$557$		−	13864.9i		−	1.05472i	0.849643	−	0.527358i	$-0.176817\pi$
$558$		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	0.440583	+	0.897712i	$0.354772\pi$
$563$	−7442.77	+	12891.3i	−0.557150	+	0.965012i	−0.997733	+	0.0672999i	$0.978562\pi$
$564$		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	−0.701142	−	0.713021i	$-0.747326\pi$
$569$	−5893.56	+	3402.65i	−0.434219	+	0.250697i	0.266923	+	0.963718i	$0.413993\pi$
$570$		0			0
$571$	−7163.27	−	4135.72i	−0.524998	−	0.303108i	0.213979	−	0.976838i	$-0.431357\pi$
$571$	−7163.27	−	4135.72i	−0.524998	−	0.303108i	−0.738977	+	0.673731i	$0.764691\pi$
$572$	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	0.999990	+	0.00445871i	$0.00141926\pi$
$587$	7165.79	+	12411.5i	0.503856	+	0.872705i	−0.496134	+	0.868246i	$0.665247\pi$
$588$		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	$0.212681\pi$
$593$			17892.9i			1.23908i	−0.784966	+	0.619539i	$0.787319\pi$
$594$		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	−0.586145	−	0.810206i	$-0.699355\pi$
$599$	5989.96	−	10374.9i	0.408586	−	0.707692i	0.994732	+	0.102514i	$0.0326886\pi$
$600$		0			0
$601$	−1473.48	−	2552.14i	−0.100007	−	0.173218i	0.811680	−	0.584102i	$-0.198553\pi$
$601$	−1473.48	−	2552.14i	−0.100007	−	0.173218i	−0.911687	+	0.410885i	$0.865220\pi$
$602$	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	0.999926	−	0.0121903i	$-0.00388040\pi$
$607$	22272.8	+	12859.2i	1.48933	+	0.859866i	0.489406	+	0.872056i	$0.337214\pi$
$608$	−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	−0.188267	−	0.982118i	$-0.560287\pi$
$617$	−17363.4	−	10024.8i	−1.13294	−	0.654103i	−0.944673	+	0.328015i	$0.893621\pi$
$618$		0			0
$619$	19210.5	−	11091.2i	1.24739	−	0.720183i	0.276805	−	0.960926i	$-0.410724\pi$
$619$	19210.5	−	11091.2i	1.24739	−	0.720183i	0.970589	+	0.240743i	$0.0773911\pi$
$620$	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	$-0.652149\pi$
$631$		−	28148.1i		−	1.77584i	0.459994	−	0.887922i	$-0.347851\pi$
$632$	−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	−0.699404	−	0.714727i	$-0.746551\pi$
$641$	−6980.56	+	4030.23i	−0.430134	+	0.248338i	0.269270	+	0.963065i	$0.413218\pi$
$642$		0			0
$643$	−666.166	−	384.611i	−0.0408570	−	0.0235888i	0.479432	−	0.877579i	$-0.340843\pi$
$643$	−666.166	−	384.611i	−0.0408570	−	0.0235888i	−0.520289	+	0.853990i	$0.674176\pi$
$644$	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	−0.141701	−	0.989910i	$-0.545257\pi$
$653$	−17852.0	−	10306.9i	−1.06984	−	0.617671i	−0.928137	+	0.372238i	$0.878590\pi$
$654$		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	−0.963255	−	0.268587i	$-0.913443\pi$
$659$	−12082.8	−	20928.0i	−0.714231	−	1.23708i	0.249024	−	0.968497i	$-0.419890\pi$
$660$		0			0
$661$	−9976.53	+	17279.9i	−0.587053	+	1.01681i	0.407563	+	0.913177i	$0.366379\pi$
$661$	−9976.53	+	17279.9i	−0.587053	+	1.01681i	−0.994616	+	0.103629i	$0.966955\pi$
$662$	−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	0.947744	−	0.319033i	$-0.103358\pi$
$673$	3449.60	+	5974.88i	0.197581	+	0.342221i	−0.750162	+	0.661254i	$0.770025\pi$
$674$	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	−0.261584	−	0.965181i	$-0.584245\pi$
$677$	7812.18	−	4510.37i	0.443496	−	0.256052i	0.705079	+	0.709128i	$0.250911\pi$
$678$		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	−0.997112	−	0.0759500i	$-0.975801\pi$
$691$	−25972.9	+	14995.5i	−1.42989	+	0.825549i	−0.432781	+	0.901499i	$0.642468\pi$
$692$	−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	$0.218869\pi$
$701$			23559.3i			1.26936i	−0.772774	+	0.634681i	$0.781131\pi$
$702$		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	0.657381	−	0.753558i	$-0.271664\pi$
$709$	−6114.96	−	10591.4i	−0.323910	−	0.561028i	−0.981291	+	0.192530i	$0.938331\pi$
$710$	−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	−0.294741	−	0.955577i	$-0.595233\pi$
$727$	7555.48	−	4362.16i	0.385443	−	0.222536i	0.680184	+	0.733041i	$0.261900\pi$
$728$	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	−0.592712	−	0.805414i	$-0.701943\pi$
$733$	7960.97	−	13788.8i	0.401153	−	0.694817i	0.993865	+	0.110597i	$0.0352762\pi$
$734$	−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	$0.175304\pi$
$739$			21026.0i			1.04662i	−0.852141	+	0.523312i	$0.824696\pi$
$740$	−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	−0.686071	−	0.727535i	$-0.740666\pi$
$743$	5813.11	−	10068.6i	0.287029	−	0.497148i	0.973099	+	0.230387i	$0.0739992\pi$
$744$		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	0.640736	−	0.767761i	$-0.278629\pi$
$751$	6096.06	+	3519.56i	0.296203	+	0.171013i	−0.344533	+	0.938774i	$0.611963\pi$
$752$	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	0.897944	−	0.440109i	$-0.145060\pi$
$761$	20274.5	+	11705.5i	0.965771	+	0.557588i	0.0678265	+	0.997697i	$0.478394\pi$
$762$		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	−0.401517	−	0.915852i	$-0.631517\pi$
$769$	12632.8	−	21880.6i	0.592392	−	1.02605i	0.993909	−	0.110202i	$-0.0351498\pi$
$770$	−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	$0.257285\pi$
$773$			31081.3i			1.44621i	−0.690740	+	0.723103i	$0.742715\pi$
$774$		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	−0.355875	−	0.934534i	$-0.615817\pi$
$787$	−29654.1	−	17120.8i	−1.34314	−	0.775463i	−0.987267	+	0.159070i	$0.949150\pi$
$788$	−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	0.807081	−	0.590441i	$-0.201046\pi$
$797$	15734.1	+	9084.08i	0.699285	+	0.403732i	−0.107796	+	0.994173i	$0.534379\pi$
$798$		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	$0.179583\pi$
$809$			24608.1i			1.06944i	−0.845029	+	0.534720i	$0.820417\pi$
$810$		0			0
$811$		−	3293.86i		−	0.142618i	−0.997454	−	0.0713089i	$-0.977282\pi$
$811$		−	3293.86i		−	0.142618i	0.997454	−	0.0713089i	$-0.0227176\pi$
$812$	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	0.418301	−	0.908308i	$-0.362626\pi$
$821$	33264.9	−	19205.5i	1.41407	−	0.816414i	0.995769	+	0.0918946i	$0.0292923\pi$
$822$		0			0
$823$	−531.302	−	306.747i	−0.0225031	−	0.0129922i	0.488706	−	0.872448i	$-0.337469\pi$
$823$	−531.302	−	306.747i	−0.0225031	−	0.0129922i	−0.511209	+	0.859456i	$0.670802\pi$
$824$	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	−0.825119	−	0.564959i	$-0.808892\pi$
$839$	−21916.3	−	37960.1i	−0.901828	−	1.56201i	−0.0767097	−	0.997053i	$-0.524441\pi$
$840$		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	0.708775	−	0.705435i	$-0.249248\pi$
$853$	−6391.08	−	11069.7i	−0.256537	−	0.444336i	−0.965312	+	0.261099i	$0.915915\pi$
$854$	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	−0.977329	−	0.211728i	$-0.932091\pi$
$857$	−32179.0	+	18578.6i	−1.28263	+	0.740527i	−0.305302	+	0.952256i	$0.598757\pi$
$858$		0			0
$859$	−7232.93	−	4175.93i	−0.287293	−	0.165869i	0.349428	−	0.936963i	$-0.386376\pi$
$859$	−7232.93	−	4175.93i	−0.287293	−	0.165869i	−0.636720	+	0.771095i	$0.719709\pi$
$860$	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	−0.675020	−	0.737799i	$-0.735865\pi$
$877$	7828.97	−	13560.2i	0.301443	−	0.522114i	0.976463	+	0.215685i	$0.0691984\pi$
$878$	−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	$-0.731166\pi$
$881$		−	39103.2i		−	1.49537i	0.664054	−	0.747684i	$-0.268834\pi$
$882$		0			0
$883$		−	23664.8i		−	0.901907i	−0.892547	−	0.450953i	$-0.851084\pi$
$883$		−	23664.8i		−	0.901907i	0.892547	−	0.450953i	$-0.148916\pi$
$884$	−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	−0.0616939	−	0.998095i	$-0.519650\pi$
$887$	22019.4	−	38138.8i	0.833529	−	1.44371i	0.895223	−	0.445619i	$-0.147016\pi$
$888$		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	0.117610	−	0.993060i	$-0.462477\pi$
$907$	28310.7	−	16345.2i	1.03643	−	0.598384i	0.918820	+	0.394676i	$0.129143\pi$
$908$	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	0.999141	−	0.0414281i	$-0.0131907\pi$
$911$	12749.9	+	22083.5i	0.463693	+	0.803140i	−0.535448	+	0.844568i	$0.679857\pi$
$912$		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	$0.118218\pi$
$919$			20221.1i			0.725825i	−0.931823	+	0.362912i	$0.881782\pi$
$920$	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	−0.946773	−	0.321901i	$-0.895678\pi$
$929$	−32318.8	+	18659.3i	−1.14139	+	0.658979i	−0.194612	+	0.980880i	$0.562345\pi$
$930$		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	0.530603	−	0.847621i	$-0.321966\pi$
$941$	1785.15	+	1030.66i	0.0618429	+	0.0357050i	−0.468760	+	0.883326i	$0.655299\pi$
$942$		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	0.977763	−	0.209711i	$-0.0672523\pi$
$947$	8954.48	+	15509.6i	0.307267	+	0.532202i	−0.670497	+	0.741913i	$0.733919\pi$
$948$		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	$0.0593400\pi$
$953$			10905.6i			0.370689i	−0.982674	+	0.185344i	$0.940660\pi$
$954$		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	−0.405732	−	0.913992i	$-0.632983\pi$
$967$	−42102.8	−	24308.1i	−1.40014	−	0.808370i	−0.994406	+	0.105622i	$0.966317\pi$
$968$	−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	0.107766	−	0.994176i	$-0.465630\pi$
$977$	−21356.3	−	12330.1i	−0.699333	−	0.403760i	−0.807099	+	0.590416i	$0.798964\pi$
$978$		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	0.630505	−	0.776185i	$-0.282848\pi$
$983$	−11000.9	−	19054.2i	−0.356943	−	0.618244i	−0.987449	+	0.157941i	$0.949514\pi$
$984$		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	$0.109811\pi$
$991$			21100.2i			0.676358i	−0.941082	+	0.338179i	$0.890189\pi$
$992$	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	0.792716	−	0.609591i	$-0.208666\pi$
$997$	−4141.70	−	7173.64i	−0.131564	−	0.227875i	−0.924280	+	0.381716i	$0.875333\pi$
$998$	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.71.5		24
3.2	odd	2		36.4.h.b.23.8	yes	24
4.3	odd	2	inner	108.4.h.b.71.10		24
9.2	odd	6	inner	108.4.h.b.35.10		24
9.4	even	3		324.4.b.c.323.22		24
9.5	odd	6		324.4.b.c.323.3		24
9.7	even	3		36.4.h.b.11.3	✓	24
12.11	even	2		36.4.h.b.23.3	yes	24
36.7	odd	6		36.4.h.b.11.8	yes	24
36.11	even	6	inner	108.4.h.b.35.5		24
36.23	even	6		324.4.b.c.323.21		24
36.31	odd	6		324.4.b.c.323.4		24

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

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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