LMFDB - Embedded newform 108.4.h.b.35.10

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			35.10
Character	$\chi$	$=$	108.35
Dual form			108.4.h.b.71.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93145 - 2.06627i) q^{2} +(-0.538974 - 7.98182i) q^{4} +(4.71466 - 2.72201i) q^{5} +(-20.9358 - 12.0873i) q^{7} +(-17.5336 - 14.3029i) q^{8} +O(q^{10})$	\(q+(1.93145 - 2.06627i) q^{2} +(-0.538974 - 7.98182i) q^{4} +(4.71466 - 2.72201i) q^{5} +(-20.9358 - 12.0873i) q^{7} +(-17.5336 - 14.3029i) q^{8} +(3.48173 - 14.9992i) q^{10} +(25.3999 - 43.9939i) q^{11} +(25.0883 + 43.4542i) q^{13} +(-65.4121 + 19.9130i) q^{14} +(-63.4190 + 8.60399i) q^{16} -51.7146i q^{17} -27.9305i q^{19} +(-24.2677 - 36.1645i) q^{20} +(-41.8447 - 137.455i) q^{22} +(-3.93548 - 6.81645i) q^{23} +(-47.6813 + 82.5864i) q^{25} +(138.245 + 32.0905i) q^{26} +(-85.1946 + 173.620i) q^{28} +(212.788 + 122.853i) q^{29} +(51.4009 - 29.6763i) q^{31} +(-104.713 + 147.659i) q^{32} +(-106.856 - 99.8843i) q^{34} -131.607 q^{35} +295.334 q^{37} +(-57.7121 - 53.9465i) q^{38} +(-121.598 - 19.7064i) q^{40} +(146.833 - 84.7741i) q^{41} +(284.968 + 164.526i) q^{43} +(-364.841 - 179.026i) q^{44} +(-21.6859 - 5.03388i) q^{46} +(-47.9742 + 83.0938i) q^{47} +(120.704 + 209.066i) q^{49} +(78.5519 + 258.034i) q^{50} +(333.322 - 223.671i) q^{52} -300.751i q^{53} -276.555i q^{55} +(194.198 + 511.375i) q^{56} +(664.839 - 202.393i) q^{58} +(113.273 + 196.195i) q^{59} +(173.722 - 300.896i) q^{61} +(37.9590 - 163.527i) q^{62} +(102.857 + 501.562i) q^{64} +(236.566 + 136.581i) q^{65} +(-904.675 + 522.314i) q^{67} +(-412.776 + 27.8728i) q^{68} +(-254.193 + 271.936i) q^{70} +243.524 q^{71} -1094.68 q^{73} +(570.424 - 610.241i) q^{74} +(-222.936 + 15.0538i) q^{76} +(-1063.53 + 614.031i) q^{77} +(530.679 + 306.388i) q^{79} +(-275.579 + 213.192i) q^{80} +(108.435 - 467.135i) q^{82} +(283.063 - 490.280i) q^{83} +(-140.768 - 243.817i) q^{85} +(890.358 - 271.046i) q^{86} +(-1074.59 + 408.082i) q^{88} +212.529i q^{89} -1213.00i q^{91} +(-52.2866 + 35.0862i) q^{92} +(79.0345 + 259.620i) q^{94} +(-76.0272 - 131.683i) q^{95} +(234.298 - 405.817i) q^{97} +(665.122 + 154.393i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.93145	−	2.06627i	0.682872	−	0.730538i
$2$	1.93145	−	2.06627i	0.682872	−	0.730538i
$3$		0			0
$3$		0			0
$4$	−0.538974	−	7.98182i	−0.0673717	−	0.997728i
$5$	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	−0.186383	−	0.982477i	$-0.559677\pi$
$7$	−20.9358	−	12.0873i	−1.13043	−	0.652651i	−0.944042	+	0.329826i	$0.893010\pi$
$8$	−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	$-0.588200\pi$
$11$	25.3999	−	43.9939i	0.696214	−	1.20588i	0.969770	−	0.244022i	$-0.0784669\pi$
$12$		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	$0.653551\pi$
$14$	−65.4121	+	19.9130i	−1.24872	+	0.380141i
$15$		0			0
$16$	−63.4190	+	8.60399i	−0.990922	+	0.134437i
$17$		−	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	$-0.946068\pi$
$19$		−	27.9305i		−	0.337247i	0.985681	−	0.168624i	$-0.0539322\pi$
$20$	−24.2677	−	36.1645i	−0.271321	−	0.404332i
$21$		0			0
$22$	−41.8447	−	137.455i	−0.405515	−	1.33207i
$23$	−3.93548	−	6.81645i	−0.0356785	−	0.0617969i	0.847635	−	0.530580i	$-0.178026\pi$
$23$	−3.93548	−	6.81645i	−0.0356785	−	0.0617969i	−0.883313	+	0.468783i	$0.844693\pi$
$24$		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	−0.343653	−	0.939097i	$-0.611664\pi$
$31$	51.4009	−	29.6763i	0.297802	−	0.171936i	0.641455	+	0.767161i	$0.278331\pi$
$32$	−104.713	+	147.659i	−0.578461	+	0.815710i
$33$		0			0
$34$	−106.856	−	99.8843i	−0.538992	−	0.503824i
$35$	−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	$0.272198\pi$
$38$	−57.7121	−	53.9465i	−0.246372	−	0.230297i
$39$		0			0
$40$	−121.598	−	19.7064i	−0.480657	−	0.0778963i
$41$	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	0.911376	−	0.411574i	$-0.135021\pi$
$43$	284.968	+	164.526i	1.01063	+	0.583488i	0.0992550	+	0.995062i	$0.468354\pi$
$44$	−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	$-0.880903\pi$
$47$	−47.9742	+	83.0938i	−0.148888	+	0.257882i	0.781928	+	0.623368i	$0.214236\pi$
$48$		0			0
$49$	120.704	+	209.066i	0.351908	+	0.609522i
$50$	78.5519	+	258.034i	0.222178	+	0.729832i
$51$		0			0
$52$	333.322	−	223.671i	0.888911	−	0.596492i
$53$		−	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
$56$	194.198	+	511.375i	0.463406	+	1.22027i
$57$		0			0
$58$	664.839	−	202.393i	1.50513	−	0.458198i
$59$	113.273	+	196.195i	0.249947	+	0.432921i	0.963511	−	0.267669i	$-0.0862534\pi$
$59$	113.273	+	196.195i	0.249947	+	0.432921i	−0.713564	+	0.700590i	$0.752920\pi$
$60$		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	$0.734727\pi$
$67$	−904.675	+	522.314i	−1.64961	+	0.952401i	−0.977228	+	0.212193i	$0.931939\pi$
$68$	−412.776	+	27.8728i	−0.736125	+	0.0497069i
$69$		0			0
$70$	−254.193	+	271.936i	−0.434026	+	0.464322i
$71$	243.524			0.407057			0.203528	−	0.979069i	$-0.434759\pi$
$71$	243.524			0.407057			0.203528	+	0.979069i	$0.434759\pi$
$72$		0			0
$73$	−1094.68			−1.75510			−0.877552	−	0.479481i	$-0.840825\pi$
$73$	−1094.68			−1.75510			−0.877552	+	0.479481i	$0.840825\pi$
$74$	570.424	−	610.241i	0.896086	−	0.958635i
$75$		0			0
$76$	−222.936	+	15.0538i	−0.336481	+	0.0227209i
$77$	−1063.53	+	614.031i	−1.57404	+	0.908770i
$78$		0			0
$79$	530.679	+	306.388i	0.755773	+	0.436346i	0.827776	−	0.561059i	$-0.189606\pi$
$79$	530.679	+	306.388i	0.755773	+	0.436346i	−0.0720031	+	0.997404i	$0.522939\pi$
$80$	−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	$-0.711203\pi$
$83$	283.063	−	490.280i	0.374340	−	0.648376i	0.990228	+	0.139458i	$0.0445360\pi$
$84$		0			0
$85$	−140.768	−	243.817i	−0.179628	−	0.311125i
$86$	890.358	−	271.046i	1.11639	−	0.339857i
$87$		0			0
$88$	−1074.59	+	408.082i	−1.30172	+	0.494337i
$89$			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
$92$	−52.2866	+	35.0862i	−0.0592528	+	0.0397608i
$93$		0			0
$94$	79.0345	+	259.620i	0.0867211	+	0.284869i
$95$	−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	−0.556239	−	0.831022i	$-0.687756\pi$
$103$	−119.871	+	69.2074i	−0.114672	+	0.0662059i	0.441567	+	0.897228i	$0.354423\pi$
$104$	181.630	−	1120.74i	0.171253	−	1.05671i
$105$		0			0
$106$	−621.434	−	580.886i	−0.569424	−	0.532271i
$107$	−771.292			−0.696857			−0.348428	−	0.937335i	$-0.613285\pi$
$107$	−771.292			−0.696857			−0.348428	+	0.937335i	$0.613285\pi$
$108$		0			0
$109$	−275.772			−0.242332			−0.121166	−	0.992632i	$-0.538663\pi$
$109$	−275.772			−0.242332			−0.121166	+	0.992632i	$0.538663\pi$
$110$	−571.439	−	534.154i	−0.495314	−	0.462996i
$111$		0			0
$112$	1431.72	+	586.432i	1.20790	+	0.494755i
$113$	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
$122$	−286.197	−	940.124i	−0.212385	−	0.697663i
$123$		0			0
$124$	−264.575	−	394.278i	−0.191609	−	0.285542i
$125$			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	$-0.00793410\pi$
$128$	1235.03	+	756.214i	0.852828	+	0.522191i
$129$		0			0
$130$	739.130	−	225.009i	0.498661	−	0.151805i
$131$	−358.903	−	621.638i	−0.239370	−	0.414601i	0.721164	−	0.692765i	$-0.243608\pi$
$131$	−358.903	−	621.638i	−0.239370	−	0.414601i	−0.960534	+	0.278164i	$0.910274\pi$
$132$		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	−0.822513	−	0.568746i	$-0.807429\pi$
$139$	−1214.70	+	701.309i	−0.741222	+	0.427945i	0.0812916	+	0.996690i	$0.474095\pi$
$140$	70.9326	+	1050.46i	0.0428207	+	0.634145i
$141$		0			0
$142$	470.356	−	503.188i	0.277968	−	0.297371i
$143$	2548.96			1.49059
$144$		0			0
$145$	1337.63			0.766099
$146$	−2114.32	+	2261.91i	−1.19851	+	1.28217i
$147$		0			0
$148$	−159.177	−	2357.30i	−0.0884073	−	1.30925i
$149$	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	0.883135	−	0.469120i	$-0.155429\pi$
$151$	1704.17	+	983.903i	0.918433	+	0.530257i	0.0352979	+	0.999377i	$0.488762\pi$
$152$	−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	$0.740754\pi$
$158$	1658.06	−	504.755i	0.834863	−	0.254153i
$159$		0			0
$160$	−91.7548	+	981.193i	−0.0453366	+	0.484813i
$161$			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	$0.845650\pi$
$164$	−755.792	−	1126.31i	−0.359862	−	0.536278i
$165$		0			0
$166$	−466.329	−	1531.84i	−0.218037	−	0.716227i
$167$	1242.52	+	2152.11i	0.575743	+	0.997217i	0.995960	+	0.0897933i	$0.0286206\pi$
$167$	1242.52	+	2152.11i	0.575743	+	0.997217i	−0.420217	+	0.907424i	$0.638046\pi$
$168$		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
$176$	−1232.31	+	3008.59i	−0.527779	+	1.28853i
$177$		0			0
$178$	439.144	+	410.491i	0.184917	+	0.172851i
$179$	−2965.78			−1.23840			−0.619198	−	0.785235i	$-0.712542\pi$
$179$	−2965.78			−1.23840			−0.619198	+	0.785235i	$0.712542\pi$
$180$		0			0
$181$	1250.55			0.513551			0.256776	−	0.966471i	$-0.417340\pi$
$181$	1250.55			0.513551			0.256776	+	0.966471i	$0.417340\pi$
$182$	−2506.38	−	2342.84i	−1.02080	−	0.954193i
$183$		0			0
$184$	−28.4914	+	175.806i	−0.0114153	+	0.0704379i
$185$	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	$-0.880262\pi$
$191$	−387.763	+	671.626i	−0.146898	+	0.254435i	0.783181	+	0.621793i	$0.213596\pi$
$192$		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	$0.529969\pi$
$194$	−385.992	−	1267.94i	−0.142848	−	0.469241i
$195$		0			0
$196$	1603.67	−	1076.12i	0.584428	−	0.392173i
$197$		−	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	$-0.824144\pi$
$199$		−	2946.42i		−	1.04958i	0.851232	−	0.524790i	$-0.175856\pi$
$200$	2017.25	−	766.062i	0.713205	−	0.270844i
$201$		0			0
$202$	−4852.15	+	1477.11i	−1.69008	+	0.514502i
$203$	−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	$-0.638021\pi$
$211$	477.089	−	275.447i	0.155659	−	0.0898700i	0.575806	+	0.817586i	$0.304688\pi$
$212$	−2400.54	+	162.097i	−0.777688	+	0.0525135i
$213$		0			0
$214$	−1489.72	+	1593.70i	−0.475864	+	0.509080i
$215$	1791.37			0.568234
$216$		0			0
$217$	−1434.82			−0.448857
$218$	−532.642	+	569.821i	−0.165482	+	0.177033i
$219$		0			0
$220$	−2207.42	+	149.056i	−0.676472	+	0.0456789i
$221$	2247.21	−	1297.43i	0.684000	−	0.394907i
$222$		0			0
$223$	1564.82	+	903.449i	0.469902	+	0.271298i	0.716199	−	0.697897i	$-0.245880\pi$
$223$	1564.82	+	903.449i	0.469902	+	0.271298i	−0.246297	+	0.969194i	$0.579214\pi$
$224$	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	$-0.762692\pi$
$227$	752.796	−	1303.88i	0.220109	−	0.381241i	0.954841	+	0.297117i	$0.0960252\pi$
$228$		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	$0.904375\pi$
$230$	−115.944	+	35.2961i	−0.0332396	+	0.0101189i
$231$		0			0
$232$	−1973.80	−	5197.54i	−0.558561	−	1.47084i
$233$			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
$236$	1504.94	−	1009.87i	0.415098	−	0.278546i
$237$		0			0
$238$	1029.79	+	3382.76i	0.280469	+	0.921309i
$239$	916.982	+	1588.26i	0.248178	+	0.429858i	0.963020	−	0.269428i	$-0.0868347\pi$
$239$	916.982	+	1588.26i	0.248178	+	0.429858i	−0.714842	+	0.699286i	$0.753501\pi$
$240$		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
$248$	−1325.70	−	214.846i	−0.339444	−	0.0550109i
$249$		0			0
$250$	2478.82	+	2317.09i	0.627099	+	0.586182i
$251$	1053.84			0.265010			0.132505	−	0.991182i	$-0.457698\pi$
$251$	1053.84			0.265010			0.132505	+	0.991182i	$0.457698\pi$
$252$		0			0
$253$	−399.843			−0.0993594
$254$	−147.410	−	137.791i	−0.0364146	−	0.0340386i
$255$		0			0
$256$	3947.94	−	1091.31i	0.963853	−	0.266434i
$257$	−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	−0.667805	−	0.744336i	$-0.732766\pi$
$263$	1325.23	−	2295.36i	0.310712	−	0.538168i	0.978517	+	0.206168i	$0.0660993\pi$
$264$		0			0
$265$	−818.648	−	1417.94i	−0.189770	−	0.328692i
$266$	556.181	+	1826.99i	0.128202	+	0.421128i
$267$		0			0
$268$	4656.62	+	6939.44i	1.06137	+	1.58169i
$269$		−	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	$0.159554\pi$
$271$			4287.45i			0.961048i	−0.876982	+	0.480524i	$0.840446\pi$
$272$	444.951	+	3279.69i	0.0991880	+	0.731104i
$273$		0			0
$274$	−596.530	+	181.598i	−0.131524	+	0.0400392i
$275$	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	−0.799086	−	0.601217i	$-0.794683\pi$
$283$	−3227.63	+	1863.47i	−0.677960	+	0.391420i	0.121126	+	0.992637i	$0.461350\pi$
$284$	−131.253	−	1943.77i	−0.0274241	−	0.406132i
$285$		0			0
$286$	4923.19	−	5266.85i	1.01788	−	1.08893i
$287$	−4098.75			−0.843003
$288$		0			0
$289$	2238.61			0.455649
$290$	2583.57	−	2763.91i	0.523147	−	0.559664i
$291$		0			0
$292$	590.004	+	8737.54i	0.118244	+	1.75112i
$293$	−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
$302$	5324.54	−	1620.92i	1.01454	−	0.308852i
$303$		0			0
$304$	240.314	+	1771.32i	0.0453386	+	0.334186i
$305$		−	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	$0.739285\pi$
$308$	5474.30	+	8157.98i	1.01275	+	1.50923i
$309$		0			0
$310$	−266.158	−	874.298i	−0.0487637	−	0.160183i
$311$	3745.08	+	6486.66i	0.682842	+	1.18272i	0.974110	+	0.226075i	$0.0725896\pi$
$311$	3745.08	+	6486.66i	0.682842	+	1.18272i	−0.291268	+	0.956642i	$0.594077\pi$
$312$		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
$320$	1850.19	+	2084.72i	0.323215	+	0.364186i
$321$		0			0
$322$	393.164	+	367.511i	0.0680440	+	0.0636043i
$323$	−1444.41			−0.248821
$324$		0			0
$325$	−4784.97			−0.816684
$326$	4008.68	+	3747.12i	0.681044	+	0.636607i
$327$		0			0
$328$	−3787.03	−	613.734i	−0.637512	−	0.103316i
$329$	2008.75	−	1159.75i	0.336615	−	0.194344i
$330$		0			0
$331$	−1367.21	−	789.359i	−0.227035	−	0.131079i	0.382168	−	0.924093i	$-0.375177\pi$
$331$	−1367.21	−	789.359i	−0.227035	−	0.131079i	−0.609204	+	0.793014i	$0.708511\pi$
$332$	−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	$-0.351904\pi$
$338$	264.156	+	867.724i	0.0425095	+	0.139639i
$339$		0			0
$340$	−1870.23	+	1254.99i	−0.298316	+	0.200181i
$341$		−	3015.10i		−	0.478818i
$342$		0			0
$343$			2455.93i			0.386611i
$344$	−2643.32	−	6960.59i	−0.414298	−	1.09096i
$345$		0			0
$346$	7788.15	−	2370.90i	1.21010	−	0.368383i
$347$	−6228.10	−	10787.4i	−0.963522	−	1.66887i	−0.713535	−	0.700620i	$-0.752907\pi$
$347$	−6228.10	−	10787.4i	−0.963522	−	1.66887i	−0.249987	−	0.968249i	$-0.580427\pi$
$348$		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
$356$	1696.37	−	114.548i	0.252549	−	0.0170534i
$357$		0			0
$358$	−5728.27	+	6128.11i	−0.845666	+	0.904695i
$359$	−318.743			−0.0468597			−0.0234298	−	0.999725i	$-0.507459\pi$
$359$	−318.743			−0.0468597			−0.0234298	+	0.999725i	$0.507459\pi$
$360$		0			0
$361$	6078.89			0.886264
$362$	2415.38	−	2583.98i	0.350690	−	0.375169i
$363$		0			0
$364$	−9681.92	+	653.773i	−1.39415	+	0.0941401i
$365$	−5161.05	+	2979.73i	−0.740114	+	0.427305i
$366$		0			0
$367$	−5425.21	−	3132.25i	−0.771645	−	0.445510i	0.0618160	−	0.998088i	$-0.480311\pi$
$367$	−5425.21	−	3132.25i	−0.771645	−	0.445510i	−0.833461	+	0.552578i	$0.813644\pi$
$368$	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	$0.514665\pi$
$374$	−7108.44	+	2163.98i	−0.982804	+	0.299189i
$375$		0			0
$376$	2029.64	−	770.768i	0.278380	−	0.105716i
$377$			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	$-0.0417229\pi$
$380$	−1010.09	+	677.809i	−0.136360	+	0.0915023i
$381$		0			0
$382$	638.816	+	2098.44i	0.0855619	+	0.281061i
$383$	2974.93	+	5152.73i	0.396898	+	0.687448i	0.993341	−	0.115208i	$-0.0367533\pi$
$383$	2974.93	+	5152.73i	0.396898	+	0.687448i	−0.596443	+	0.802655i	$0.703420\pi$
$384$		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
$392$	873.855	−	5392.10i	0.112593	−	0.694751i
$393$		0			0
$394$	−3406.46	−	3184.19i	−0.435571	−	0.407151i
$395$	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	$0.625566\pi$
$398$	−6088.12	−	5690.88i	−0.766758	−	0.716729i
$399$		0			0
$400$	2313.33	−	5647.80i	0.289166	−	0.705975i
$401$	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	$0.828121\pi$
$410$	−760.313	−	2497.54i	−0.0915834	−	0.300841i
$411$		0			0
$412$	617.008	+	919.486i	0.0737811	+	0.109951i
$413$		−	5476.64i		−	0.652513i
$414$		0			0
$415$		−	3082.01i		−	0.364553i
$416$	−9043.47	−	845.687i	−1.06585	−	0.0996712i
$417$		0			0
$418$	−3839.20	+	1168.74i	−0.449237	+	0.136759i
$419$	−3950.75	−	6842.90i	−0.460637	−	0.797846i	0.538356	−	0.842718i	$-0.319046\pi$
$419$	−3950.75	−	6842.90i	−0.460637	−	0.797846i	−0.998993	+	0.0448712i	$0.985712\pi$
$420$		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
$428$	415.706	+	6156.32i	0.0469484	+	0.695273i
$429$		0			0
$430$	3459.95	−	3701.46i	0.388031	−	0.415117i
$431$	14773.0			1.65102			0.825509	−	0.564388i	$-0.190888\pi$
$431$	14773.0			1.65102			0.825509	+	0.564388i	$0.190888\pi$
$432$		0			0
$433$	−2372.81			−0.263349			−0.131674	−	0.991293i	$-0.542035\pi$
$433$	−2372.81			−0.263349			−0.131674	+	0.991293i	$0.542035\pi$
$434$	−2771.29	+	2964.74i	−0.306512	+	0.327907i
$435$		0			0
$436$	148.634	+	2201.17i	0.0163263	+	0.241782i
$437$	−190.387	+	109.920i	−0.0208408	+	0.0120325i
$438$		0			0
$439$	−2509.56	−	1448.89i	−0.272835	−	0.157522i	0.357340	−	0.933974i	$-0.383684\pi$
$439$	−2509.56	−	1448.89i	−0.272835	−	0.157522i	−0.630175	+	0.776453i	$0.717017\pi$
$440$	−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	$-0.694763\pi$
$443$	3932.06	−	6810.53i	0.421711	−	0.730425i	0.996107	+	0.0881526i	$0.0280963\pi$
$444$		0			0
$445$	578.508	+	1002.00i	0.0616267	+	0.106741i
$446$	4889.15	−	1488.38i	0.519076	−	0.158019i
$447$		0			0
$448$	3909.13	−	11743.8i	0.412253	−	1.23849i
$449$		−	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
$452$	−2794.54	−	4164.52i	−0.290806	−	0.433368i
$453$		0			0
$454$	−1240.18	−	4073.87i	−0.128204	−	0.421137i
$455$	−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	−0.662431	−	0.749123i	$-0.730475\pi$
$463$	−3435.96	+	1983.75i	−0.344887	+	0.199121i	0.317544	+	0.948244i	$0.397142\pi$
$464$	−14551.8	−	5960.41i	−1.45593	−	0.596347i
$465$		0			0
$466$	2597.39	+	2427.92i	0.258201	+	0.241354i
$467$	−8810.21			−0.872993			−0.436497	−	0.899706i	$-0.643781\pi$
$467$	−8810.21			−0.872993			−0.436497	+	0.899706i	$0.643781\pi$
$468$		0			0
$469$	25253.4			2.48634
$470$	1079.31	+	1008.89i	0.105925	+	0.0990137i
$471$		0			0
$472$	820.055	−	5060.13i	0.0799705	−	0.493456i
$473$	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	$0.545579\pi$
$479$	−9734.00	+	16859.8i	−0.928513	+	1.60823i	−0.785811	+	0.618466i	$0.787754\pi$
$480$		0			0
$481$	7409.42	+	12833.5i	0.702371	+	1.21654i
$482$	591.053	+	1941.54i	0.0558542	+	0.183475i
$483$		0			0
$484$	−8301.18	+	5570.39i	−0.779600	+	0.523140i
$485$		−	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	$-0.0781795\pi$
$488$	−7349.65	+	2791.07i	−0.681769	+	0.258906i
$489$		0			0
$490$	3556.09	−	1082.56i	0.327852	−	0.0998063i
$491$	4793.56	+	8302.69i	0.440591	+	0.763127i	0.997733	−	0.0672904i	$-0.0214354\pi$
$491$	4793.56	+	8302.69i	0.440591	+	0.763127i	−0.557142	+	0.830417i	$0.688102\pi$
$492$		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	$-0.701120\pi$
$499$	−2085.65	+	1204.15i	−0.187108	+	0.108027i	0.403520	+	0.914971i	$0.367787\pi$
$500$	9575.47	−	646.585i	0.856456	−	0.0578323i
$501$		0			0
$502$	2035.43	−	2177.51i	0.180968	−	0.193600i
$503$	−17192.1			−1.52397			−0.761985	−	0.647595i	$-0.775775\pi$
$503$	−17192.1			−1.52397			−0.761985	+	0.647595i	$0.775775\pi$
$504$		0			0
$505$	−9762.37			−0.860237
$506$	−772.278	+	826.185i	−0.0678497	+	0.0725858i
$507$		0			0
$508$	−569.430	+	38.4508i	−0.0497330	+	0.00335823i
$509$	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
$518$	−19318.4	+	5880.99i	−1.63861	+	0.498834i
$519$		0			0
$520$	−2194.35	−	5778.33i	−0.185055	−	0.487301i
$521$			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	$-0.812769\pi$
$523$		−	13273.1i		−	1.10974i	0.831939	−	0.554868i	$-0.187231\pi$
$524$	−4768.36	+	3199.74i	−0.397532	+	0.266759i
$525$		0			0
$526$	−2183.23	−	7171.68i	−0.180976	−	0.594487i
$527$	−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
$536$	23332.8	+	3781.36i	1.88027	+	0.304720i
$537$		0			0
$538$	−4930.46	−	4608.76i	−0.395107	−	0.369327i
$539$	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	$0.663789\pi$
$542$	8859.05	+	8281.01i	0.702082	+	0.656273i
$543$		0			0
$544$	7636.13	+	5415.17i	0.601832	+	0.426789i
$545$	−1300.17	+	750.656i	−0.102190	+	0.0589992i
$546$		0			0
$547$	15941.6	+	9203.89i	1.24609	+	0.719433i	0.970328	−	0.241792i	$-0.0777351\pi$
$547$	15941.6	+	9203.89i	1.24609	+	0.719433i	0.275766	+	0.961225i	$0.411068\pi$
$548$	−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
$554$	3981.17	+	13077.7i	0.305313	+	1.00292i
$555$		0			0
$556$	6252.42	+	9317.56i	0.476910	+	0.710706i
$557$			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
$560$	8346.38	−	1132.34i	0.629819	−	0.0854469i
$561$		0			0
$562$	−4690.66	+	1427.95i	−0.352070	+	0.107179i
$563$	7442.77	+	12891.3i	0.557150	+	0.965012i	0.997733	+	0.0672999i	$0.0214384\pi$
$563$	7442.77	+	12891.3i	0.557150	+	0.965012i	−0.440583	+	0.897712i	$0.645228\pi$
$564$		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	−0.213979	−	0.976838i	$-0.568643\pi$
$571$	7163.27	−	4135.72i	0.524998	−	0.303108i	0.738977	+	0.673731i	$0.235309\pi$
$572$	−1373.82	−	20345.3i	−0.100424	−	1.48720i
$573$		0			0
$574$	−7916.55	+	8469.15i	−0.575663	+	0.615845i
$575$	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	$0.644466\pi$
$578$	4323.76	−	4625.57i	0.311150	−	0.332869i
$579$		0			0
$580$	−720.949	−	10676.7i	−0.0516134	−	0.764358i
$581$	−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	$0.334753\pi$
$587$	−7165.79	+	12411.5i	−0.503856	+	0.872705i	−0.999990	+	0.00445871i	$0.998581\pi$
$588$		0			0
$589$	−828.874	−	1435.65i	−0.0579850	−	0.100433i
$590$	3337.15	−	1015.91i	0.232862	−	0.0708887i
$591$		0			0
$592$	−18729.8	+	2541.05i	−1.30032	+	0.176413i
$593$		−	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
$596$	−6636.71	−	9890.23i	−0.456124	−	0.679731i
$597$		0			0
$598$	−325.318	−	1068.63i	−0.0222462	−	0.0730763i
$599$	−5989.96	−	10374.9i	−0.408586	−	0.707692i	0.586145	−	0.810206i	$-0.300645\pi$
$599$	−5989.96	−	10374.9i	−0.408586	−	0.707692i	−0.994732	+	0.102514i	$0.967311\pi$
$600$		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	−0.999926	−	0.0121903i	$-0.996120\pi$
$607$	−22272.8	+	12859.2i	−1.48933	+	0.859866i	−0.489406	+	0.872056i	$0.662786\pi$
$608$	4124.20	+	2924.68i	0.275096	+	0.195084i
$609$		0			0
$610$	−3908.35	−	3653.34i	−0.259417	−	0.242491i
$611$	−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	$0.519427\pi$
$614$	16238.6	+	15179.0i	1.06732	+	0.997681i
$615$		0			0
$616$	27430.0	+	4445.36i	1.79413	+	0.290761i
$617$	−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	−0.276805	−	0.960926i	$-0.589276\pi$
$619$	−19210.5	−	11091.2i	−1.24739	−	0.720183i	−0.970589	+	0.240743i	$0.922609\pi$
$620$	−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
$626$	−7091.20	−	23293.8i	−0.452750	−	1.48723i
$627$		0			0
$628$	7494.90	−	5029.35i	0.476240	−	0.319574i
$629$		−	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	$-0.347851\pi$
$632$	−4922.51	−	12962.3i	−0.309821	−	0.815844i
$633$		0			0
$634$	14701.7	−	4475.55i	0.920944	−	0.280358i
$635$	−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	−0.479432	−	0.877579i	$-0.659157\pi$
$643$	666.166	−	384.611i	0.0408570	−	0.0235888i	0.520289	+	0.853990i	$0.325824\pi$
$644$	1518.76	−	102.554i	0.0929307	−	0.00627516i
$645$		0			0
$646$	−2789.82	+	2984.55i	−0.169913	+	0.181773i
$647$	25155.2			1.52852			0.764259	−	0.644909i	$-0.223105\pi$
$647$	25155.2			1.52852			0.764259	+	0.644909i	$0.223105\pi$
$648$		0			0
$649$	11508.5			0.696067
$650$	−9241.94	+	9887.05i	−0.557690	+	0.596619i
$651$		0			0
$652$	15485.2	−	1045.64i	0.930131	−	0.0628073i
$653$	−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	$-0.580110\pi$
$659$	12082.8	−	20928.0i	0.714231	−	1.23708i	0.963255	−	0.268587i	$-0.0865568\pi$
$660$		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	$-0.366379\pi$
$662$	−4271.73	+	1300.42i	−0.250794	+	0.0763478i
$663$		0			0
$664$	−11975.5	+	4547.77i	−0.699910	+	0.265795i
$665$			3675.84i			0.214351i
$666$		0			0
$667$		−	1933.95i		−	0.112268i
$668$	16508.1	−	11077.5i	0.956162	−	0.641620i
$669$		0			0
$670$	4684.47	+	15388.0i	0.270115	+	0.887298i
$671$	−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
$680$	−1019.11	+	6288.37i	−0.0574720	+	0.354630i
$681$		0			0
$682$	−6230.02	−	5823.52i	−0.349794	−	0.326971i
$683$	−7388.19			−0.413911			−0.206956	−	0.978350i	$-0.566356\pi$
$683$	−7388.19			−0.413911			−0.206956	+	0.978350i	$0.566356\pi$
$684$		0			0
$685$	−1200.20			−0.0669448
$686$	5074.61	+	4743.51i	0.282434	+	0.264006i
$687$		0			0
$688$	−19487.9	−	7982.23i	−1.07990	−	0.442325i
$689$	13068.9	−	7545.32i	0.722620	−	0.417205i
$690$		0			0
$691$	25972.9	+	14995.5i	1.42989	+	0.825549i	0.997112	−	0.0759500i	$-0.0241989\pi$
$691$	25972.9	+	14995.5i	1.42989	+	0.825549i	0.432781	+	0.901499i	$0.357532\pi$
$692$	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
$698$	1500.37	+	4928.55i	0.0813608	+	0.267261i
$699$		0			0
$700$	−10276.5	−	15314.4i	−0.554878	−	0.826898i
$701$		−	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
$704$	24678.2	+	8214.55i	1.32116	+	0.439769i
$705$		0			0
$706$	−18807.5	+	5725.46i	−1.00259	+	0.305213i
$707$	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
$716$	1598.48	+	23672.3i	0.0834329	+	1.23558i
$717$		0			0
$718$	−615.638	+	658.611i	−0.0319992	+	0.0342328i
$719$	−37718.6			−1.95642			−0.978211	−	0.207613i	$-0.933431\pi$
$719$	−37718.6			−1.95642			−0.978211	+	0.207613i	$0.933431\pi$
$720$		0			0
$721$	3346.11			0.172837
$722$	11741.1	−	12560.6i	0.605205	−	0.647450i
$723$		0			0
$724$	−674.014	−	9981.68i	−0.0345988	−	0.512384i
$725$	−20292.0	+	11715.6i	−1.03949	+	0.600147i
$726$		0			0
$727$	−7555.48	−	4362.16i	−0.385443	−	0.222536i	0.294741	−	0.955577i	$-0.404767\pi$
$727$	−7555.48	−	4362.16i	−0.385443	−	0.222536i	−0.680184	+	0.733041i	$0.738100\pi$
$728$	−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	$0.701943\pi$
$734$	−16950.6	+	5160.18i	−0.852397	+	0.259490i
$735$		0			0
$736$	1418.61	+	132.659i	0.0710469	+	0.00664385i
$737$			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	$0.824696\pi$
$740$	−7167.07	−	10680.6i	−0.356036	−	0.530577i
$741$		0			0
$742$	5988.86	+	19672.7i	0.296305	+	0.973328i
$743$	−5813.11	−	10068.6i	−0.287029	−	0.497148i	0.686071	−	0.727535i	$-0.259334\pi$
$743$	−5813.11	−	10068.6i	−0.287029	−	0.497148i	−0.973099	+	0.230387i	$0.926001\pi$
$744$		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	$-0.721371\pi$
$751$	−6096.06	+	3519.56i	−0.296203	+	0.171013i	0.344533	+	0.938774i	$0.388037\pi$
$752$	2327.54	−	5682.49i	0.112868	−	0.275557i
$753$		0			0
$754$	25474.5	+	23812.3i	1.23041	+	1.15012i
$755$	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	$0.738318\pi$
$758$	−3985.26	−	3725.23i	−0.190964	−	0.178504i
$759$		0			0
$760$	−550.409	+	3396.29i	−0.0262703	+	0.162100i
$761$	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	$0.631517\pi$
$770$	5507.05	+	18090.1i	0.257741	+	0.846650i
$771$		0			0
$772$	29039.2	−	19486.4i	1.35381	−	0.908458i
$773$		−	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
$776$	−9912.44	+	3764.31i	−0.458551	+	0.174138i
$777$		0			0
$778$	−6321.05	+	1924.28i	−0.291286	+	0.0886746i
$779$	−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	$-0.384183\pi$
$787$	29654.1	−	17120.8i	1.34314	−	0.775463i	0.987267	+	0.159070i	$0.0508496\pi$
$788$	−13158.8	+	888.552i	−0.594878	+	0.0401692i
$789$		0			0
$790$	6443.26	−	6893.02i	0.290178	−	0.310434i
$791$	−15155.2			−0.681233
$792$		0			0
$793$	17433.6			0.780686
$794$	−11743.6	+	12563.3i	−0.524891	+	0.561529i
$795$		0			0
$796$	−23517.8	+	1588.05i	−1.04720	+	0.0707120i
$797$	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
$806$	8058.24	−	2453.12i	0.352158	−	0.107205i
$807$		0			0
$808$	14405.2	+	37932.9i	0.627196	+	1.65158i
$809$		−	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	$-0.977282\pi$
$811$		−	3293.86i		−	0.142618i	0.997454	−	0.0713089i	$-0.0227176\pi$
$812$	−39458.2	+	26477.9i	−1.70531	+	1.14433i
$813$		0			0
$814$	−12358.2	−	40595.2i	−0.532130	−	1.74799i
$815$	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	−0.488706	−	0.872448i	$-0.662531\pi$
$823$	531.302	−	306.747i	0.0225031	−	0.0129922i	0.511209	+	0.859456i	$0.329198\pi$
$824$	3091.63	+	501.036i	0.130706	+	0.0211825i
$825$		0			0
$826$	−11316.2	−	10577.9i	−0.476686	−	0.445583i
$827$	19933.1			0.838140			0.419070	−	0.907954i	$-0.362356\pi$
$827$	19933.1			0.838140			0.419070	+	0.907954i	$0.362356\pi$
$828$		0			0
$829$	32209.0			1.34941			0.674707	−	0.738086i	$-0.264270\pi$
$829$	32209.0			1.34941			0.674707	+	0.738086i	$0.264270\pi$
$830$	−6368.27	−	5952.75i	−0.266320	−	0.248943i
$831$		0			0
$832$	−19214.5	+	17052.9i	−0.800651	+	0.710580i
$833$	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	$-0.475559\pi$
$839$	21916.3	−	37960.1i	0.901828	−	1.56201i	0.825119	−	0.564959i	$-0.191108\pi$
$840$		0			0
$841$	17991.3	+	31161.9i	0.737682	+	1.27770i
$842$	−5489.11	−	18031.1i	−0.224664	−	0.737997i
$843$		0			0
$844$	−2455.71	−	3659.58i	−0.100153	−	0.149251i
$845$			1745.83i			0.0710750i
$846$		0			0
$847$			30208.9i			1.22549i
$848$	2587.66	+	19073.3i	0.104788	+	0.772383i
$849$		0			0
$850$	13344.1	−	4062.28i	0.538471	−	0.163924i
$851$	−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	−0.349428	−	0.936963i	$-0.613624\pi$
$859$	7232.93	−	4175.93i	0.287293	−	0.165869i	0.636720	+	0.771095i	$0.280291\pi$
$860$	−965.501	−	14298.4i	−0.0382829	−	0.566943i
$861$		0			0
$862$	28533.3	−	30525.0i	1.12743	−	1.20613i
$863$	11795.5			0.465265			0.232633	−	0.972565i	$-0.425266\pi$
$863$	11795.5			0.465265			0.232633	+	0.972565i	$0.425266\pi$
$864$		0			0
$865$	15669.5			0.615929
$866$	−4582.97	+	4902.88i	−0.179833	+	0.192386i
$867$		0			0
$868$	773.332	+	11452.5i	0.0302403	+	0.447838i
$869$	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	$0.735865\pi$
$878$	−7840.91	+	2386.96i	−0.301387	+	0.0917496i
$879$		0			0
$880$	2379.48	+	17538.9i	0.0911502	+	0.671858i
$881$			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	$-0.851084\pi$
$883$		−	23664.8i		−	0.901907i	0.892547	−	0.450953i	$-0.148916\pi$
$884$	−11567.0	−	17237.6i	−0.440092	−	0.655840i
$885$		0			0
$886$	−6477.83	−	21279.0i	−0.245629	−	0.806863i
$887$	−22019.4	−	38138.8i	−0.833529	−	1.44371i	−0.895223	−	0.445619i	$-0.852984\pi$
$887$	−22019.4	−	38138.8i	−0.833529	−	1.44371i	0.0616939	−	0.998095i	$-0.480350\pi$
$888$		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
$896$	−16715.7	−	30760.0i	−0.623250	−	1.14690i
$897$		0			0
$898$	−2760.35	−	2580.24i	−0.102577	−	0.0958839i
$899$	14583.3			0.541024
$900$		0			0
$901$	−15553.2			−0.575086
$902$	−17796.8	−	16635.6i	−0.656952	−	0.614087i
$903$		0			0
$904$	−14002.6	−	2269.28i	−0.515175	−	0.0834903i
$905$	5895.93	−	3404.02i	0.216561	−	0.125031i
$906$		0			0
$907$	−28310.7	−	16345.2i	−1.03643	−	0.598384i	−0.117610	−	0.993060i	$-0.537523\pi$
$907$	−28310.7	−	16345.2i	−1.03643	−	0.598384i	−0.918820	+	0.394676i	$0.870857\pi$
$908$	−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	$-0.986809\pi$
$911$	−12749.9	+	22083.5i	−0.463693	+	0.803140i	0.535448	+	0.844568i	$0.320143\pi$
$912$		0			0
$913$	−14379.5	−	24906.1i	−0.521241	−	0.902817i
$914$	14326.9	+	47062.4i	0.518482	+	1.70316i
$915$		0			0
$916$	−10190.5	+	6838.21i	−0.367581	+	0.246660i
$917$			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	$0.881782\pi$
$920$	344.218	+	906.419i	0.0123354	+	0.0324823i
$921$		0			0
$922$	6039.93	−	1838.70i	0.215742	−	0.0656772i
$923$	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
$932$	10033.5	−	677.513i	0.352637	−	0.0238119i
$933$		0			0
$934$	−17016.5	+	18204.3i	−0.596143	+	0.637755i
$935$	−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	$0.591350\pi$
$938$	48775.8	−	52180.5i	1.69785	−	1.81637i
$939$		0			0
$940$	4169.27	−	281.531i	0.144667	−	0.00976863i
$941$	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	−0.977763	−	0.209711i	$-0.932748\pi$
$947$	−8954.48	+	15509.6i	−0.307267	+	0.532202i	0.670497	+	0.741913i	$0.266081\pi$
$948$		0			0
$949$	−27463.6	−	47568.4i	−0.939418	−	1.62712i
$950$	7207.03	−	2193.99i	0.246134	−	0.0749290i
$951$		0			0
$952$	26445.5	−	10042.8i	0.900320	−	0.341902i
$953$		−	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
$956$	12183.0	−	8175.22i	0.412161	−	0.276575i
$957$		0			0
$958$	16036.2	+	52677.0i	0.540819	+	1.77653i
$959$	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	$-0.367017\pi$
$967$	42102.8	−	24308.1i	1.40014	−	0.808370i	0.994406	+	0.105622i	$0.0336832\pi$
$968$	−4523.39	+	27911.5i	−0.150193	+	0.926765i
$969$		0			0
$970$	−5271.17	−	4927.24i	−0.174482	−	0.163097i
$971$	24102.8			0.796596			0.398298	−	0.917256i	$-0.369601\pi$
$971$	24102.8			0.796596			0.398298	+	0.917256i	$0.369601\pi$
$972$		0			0
$973$	33907.7			1.11719
$974$	−10798.9	−	10094.3i	−0.355255	−	0.332076i
$975$		0			0
$976$	−8428.39	+	20577.2i	−0.276420	+	0.674857i
$977$	−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	−0.630505	−	0.776185i	$-0.717152\pi$
$983$	11000.9	−	19054.2i	0.356943	−	0.618244i	0.987449	+	0.157941i	$0.0504856\pi$
$984$		0			0
$985$	−4487.51	−	7772.59i	−0.145161	−	0.251427i
$986$	−10466.7	−	34381.8i	−0.338059	−	1.11049i
$987$		0			0
$988$	−6247.24	−	9309.84i	−0.201165	−	0.299783i
$989$		−	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	$0.890189\pi$
$992$	−1000.34	+	10697.3i	−0.0320170	+	0.342379i
$993$		0			0
$994$	−15929.4	+	4849.31i	−0.508301	+	0.154739i
$995$	−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.35.10		24
3.2	odd	2		36.4.h.b.11.3	✓	24
4.3	odd	2	inner	108.4.h.b.35.5		24
9.2	odd	6		324.4.b.c.323.22		24
9.4	even	3		36.4.h.b.23.8	yes	24
9.5	odd	6	inner	108.4.h.b.71.5		24
9.7	even	3		324.4.b.c.323.3		24
12.11	even	2		36.4.h.b.11.8	yes	24
36.7	odd	6		324.4.b.c.323.21		24
36.11	even	6		324.4.b.c.323.4		24
36.23	even	6	inner	108.4.h.b.71.10		24
36.31	odd	6		36.4.h.b.23.3	yes	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.93145 - 2.06627i) q^{2} +(-0.538974 - 7.98182i) q^{4} +(4.71466 - 2.72201i) q^{5} +(-20.9358 - 12.0873i) q^{7} +(-17.5336 - 14.3029i) q^{8} +O(q^{10})\)	\(q+(1.93145 - 2.06627i) q^{2} +(-0.538974 - 7.98182i) q^{4} +(4.71466 - 2.72201i) q^{5} +(-20.9358 - 12.0873i) q^{7} +(-17.5336 - 14.3029i) q^{8} +(3.48173 - 14.9992i) q^{10} +(25.3999 - 43.9939i) q^{11} +(25.0883 + 43.4542i) q^{13} +(-65.4121 + 19.9130i) q^{14} +(-63.4190 + 8.60399i) q^{16} -51.7146i q^{17} -27.9305i q^{19} +(-24.2677 - 36.1645i) q^{20} +(-41.8447 - 137.455i) q^{22} +(-3.93548 - 6.81645i) q^{23} +(-47.6813 + 82.5864i) q^{25} +(138.245 + 32.0905i) q^{26} +(-85.1946 + 173.620i) q^{28} +(212.788 + 122.853i) q^{29} +(51.4009 - 29.6763i) q^{31} +(-104.713 + 147.659i) q^{32} +(-106.856 - 99.8843i) q^{34} -131.607 q^{35} +295.334 q^{37} +(-57.7121 - 53.9465i) q^{38} +(-121.598 - 19.7064i) q^{40} +(146.833 - 84.7741i) q^{41} +(284.968 + 164.526i) q^{43} +(-364.841 - 179.026i) q^{44} +(-21.6859 - 5.03388i) q^{46} +(-47.9742 + 83.0938i) q^{47} +(120.704 + 209.066i) q^{49} +(78.5519 + 258.034i) q^{50} +(333.322 - 223.671i) q^{52} -300.751i q^{53} -276.555i q^{55} +(194.198 + 511.375i) q^{56} +(664.839 - 202.393i) q^{58} +(113.273 + 196.195i) q^{59} +(173.722 - 300.896i) q^{61} +(37.9590 - 163.527i) q^{62} +(102.857 + 501.562i) q^{64} +(236.566 + 136.581i) q^{65} +(-904.675 + 522.314i) q^{67} +(-412.776 + 27.8728i) q^{68} +(-254.193 + 271.936i) q^{70} +243.524 q^{71} -1094.68 q^{73} +(570.424 - 610.241i) q^{74} +(-222.936 + 15.0538i) q^{76} +(-1063.53 + 614.031i) q^{77} +(530.679 + 306.388i) q^{79} +(-275.579 + 213.192i) q^{80} +(108.435 - 467.135i) q^{82} +(283.063 - 490.280i) q^{83} +(-140.768 - 243.817i) q^{85} +(890.358 - 271.046i) q^{86} +(-1074.59 + 408.082i) q^{88} +212.529i q^{89} -1213.00i q^{91} +(-52.2866 + 35.0862i) q^{92} +(79.0345 + 259.620i) q^{94} +(-76.0272 - 131.683i) q^{95} +(234.298 - 405.817i) q^{97} +(665.122 + 154.393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) \) 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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