LMFDB - Embedded newform 108.4.h.b.71.10

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			71.10
Character	$\chi$	$=$	108.71
Dual form			108.4.h.b.35.10

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

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

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 $

$2$	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	0.695801	−	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	−0.944042	−	0.329826i	$-0.893010\pi$
$7$	−20.9358	+	12.0873i	−1.13043	+	0.652651i	−0.186383	+	0.982477i	$0.559677\pi$
$8$	−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	$0.0784669\pi$
$11$	25.3999	+	43.9939i	0.696214	+	1.20588i	−0.273556	+	0.961856i	$0.588200\pi$
$12$		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	$-0.0131156\pi$
$14$	−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	$0.120266\pi$
$17$			51.7146i			0.737801i	−0.929469	+	0.368901i	$0.879734\pi$
$18$		0			0
$19$			27.9305i			0.337247i	0.985681	+	0.168624i	$0.0539322\pi$
$19$			27.9305i			0.337247i	−0.985681	+	0.168624i	$0.946068\pi$
$20$	−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	−0.883313	−	0.468783i	$-0.844693\pi$
$23$	−3.93548	+	6.81645i	−0.0356785	+	0.0617969i	0.847635	+	0.530580i	$0.178026\pi$
$24$		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	0.641455	−	0.767161i	$-0.278331\pi$
$31$	51.4009	+	29.6763i	0.297802	+	0.171936i	−0.343653	+	0.939097i	$0.611664\pi$
$32$	−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	0.752866	−	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	0.0992550	−	0.995062i	$-0.468354\pi$
$43$	284.968	−	164.526i	1.01063	−	0.583488i	0.911376	+	0.411574i	$0.135021\pi$
$44$	−364.841	+	179.026i	−1.25004	+	0.613390i
$45$		0			0
$46$	−21.6859	+	5.03388i	−0.0695088	+	0.0161349i
$47$	−47.9742	−	83.0938i	−0.148888	−	0.257882i	0.781928	−	0.623368i	$-0.214236\pi$
$47$	−47.9742	−	83.0938i	−0.148888	−	0.257882i	−0.930817	+	0.365486i	$0.880903\pi$
$48$		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	$0.127431\pi$
$53$			300.751i			0.779459i	−0.920929	+	0.389729i	$0.872569\pi$
$54$		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	−0.713564	−	0.700590i	$-0.752920\pi$
$59$	113.273	−	196.195i	0.249947	−	0.432921i	0.963511	+	0.267669i	$0.0862534\pi$
$60$		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	$-0.931939\pi$
$67$	−904.675	−	522.314i	−1.64961	−	0.952401i	−0.672378	−	0.740208i	$-0.734727\pi$
$68$	−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	−0.0720031	−	0.997404i	$-0.522939\pi$
$79$	530.679	−	306.388i	0.755773	−	0.436346i	0.827776	+	0.561059i	$0.189606\pi$
$80$	−275.579	−	213.192i	−0.385134	−	0.297945i
$81$		0			0
$82$	108.435	+	467.135i	0.146032	+	0.629103i
$83$	283.063	+	490.280i	0.374340	+	0.648376i	0.990228	−	0.139458i	$-0.0445360\pi$
$83$	283.063	+	490.280i	0.374340	+	0.648376i	−0.615888	+	0.787834i	$0.711203\pi$
$84$		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	$-0.959606\pi$
$89$		−	212.529i		−	0.253124i	0.991959	−	0.126562i	$-0.0403943\pi$
$90$		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	0.962202	−	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	0.441567	−	0.897228i	$-0.354423\pi$
$103$	−119.871	−	69.2074i	−0.114672	−	0.0662059i	−0.556239	+	0.831022i	$0.687756\pi$
$104$	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	0.708664	−	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
$122$	−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	$0.00793410\pi$
$127$			71.3408i			0.0498463i	−0.999689	+	0.0249231i	$0.992066\pi$
$128$	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	−0.960534	−	0.278164i	$-0.910274\pi$
$131$	−358.903	+	621.638i	−0.239370	+	0.414601i	0.721164	+	0.692765i	$0.243608\pi$
$132$		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	0.0812916	−	0.996690i	$-0.474095\pi$
$139$	−1214.70	−	701.309i	−0.741222	−	0.427945i	−0.822513	+	0.568746i	$0.807429\pi$
$140$	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	0.810660	−	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	0.0352979	−	0.999377i	$-0.488762\pi$
$151$	1704.17	−	983.903i	0.918433	−	0.530257i	0.883135	+	0.469120i	$0.155429\pi$
$152$	−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	$0.0740874\pi$
$158$	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	$-0.845650\pi$
$163$		−	1940.05i		−	0.932250i	0.884719	−	0.466125i	$-0.154350\pi$
$164$	−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	−0.420217	−	0.907424i	$-0.638046\pi$
$167$	1242.52	−	2152.11i	0.575743	−	0.997217i	0.995960	−	0.0897933i	$-0.0286206\pi$
$168$		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
$176$	−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	0.783181	−	0.621793i	$-0.213596\pi$
$191$	−387.763	−	671.626i	−0.146898	−	0.254435i	−0.930080	+	0.367358i	$0.880262\pi$
$192$		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	$-0.136698\pi$
$194$	−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	$0.0963584\pi$
$197$			1648.60i			0.596233i	−0.954530	+	0.298116i	$0.903642\pi$
$198$		0			0
$199$			2946.42i			1.04958i	0.851232	+	0.524790i	$0.175856\pi$
$199$			2946.42i			1.04958i	−0.851232	+	0.524790i	$0.824144\pi$
$200$	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	0.575806	−	0.817586i	$-0.304688\pi$
$211$	477.089	+	275.447i	0.155659	+	0.0898700i	−0.420147	+	0.907456i	$0.638021\pi$
$212$	−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	−0.246297	−	0.969194i	$-0.579214\pi$
$223$	1564.82	−	903.449i	0.469902	−	0.271298i	0.716199	+	0.697897i	$0.245880\pi$
$224$	3977.04	+	1825.67i	1.18628	+	0.544565i
$225$		0			0
$226$	400.938	+	1727.23i	0.118009	+	0.508380i
$227$	752.796	+	1303.88i	0.220109	+	0.381241i	0.954841	−	0.297117i	$-0.0960252\pi$
$227$	752.796	+	1303.88i	0.220109	+	0.381241i	−0.734732	+	0.678358i	$0.762692\pi$
$228$		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	$0.237708\pi$
$230$	−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	$-0.943451\pi$
$233$		−	1257.04i		−	0.353440i	0.984261	−	0.176720i	$-0.0565487\pi$
$234$		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	−0.714842	−	0.699286i	$-0.753501\pi$
$239$	916.982	−	1588.26i	0.248178	−	0.429858i	0.963020	+	0.269428i	$0.0868347\pi$
$240$		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
$248$	−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	−0.454157	−	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	0.978517	−	0.206168i	$-0.0660993\pi$
$263$	1325.23	+	2295.36i	0.310712	+	0.538168i	−0.667805	+	0.744336i	$0.732766\pi$
$264$		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	$0.0871631\pi$
$269$			2386.16i			0.540843i	−0.962742	+	0.270422i	$0.912837\pi$
$270$		0			0
$271$		−	4287.45i		−	0.961048i	−0.876982	−	0.480524i	$-0.840446\pi$
$271$		−	4287.45i		−	0.961048i	0.876982	−	0.480524i	$-0.159554\pi$
$272$	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	−0.999604	−	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	0.121126	−	0.992637i	$-0.461350\pi$
$283$	−3227.63	−	1863.47i	−0.677960	−	0.391420i	−0.799086	+	0.601217i	$0.794683\pi$
$284$	−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	−0.176731	−	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
$302$	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	$-0.739285\pi$
$307$		−	7858.86i		−	1.46101i	0.682909	−	0.730503i	$-0.260715\pi$
$308$	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	−0.291268	−	0.956642i	$-0.594077\pi$
$311$	3745.08	−	6486.66i	0.682842	−	1.18272i	0.974110	−	0.226075i	$-0.0725896\pi$
$312$		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
$320$	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	−0.609204	−	0.793014i	$-0.708511\pi$
$331$	−1367.21	+	789.359i	−0.227035	+	0.131079i	0.382168	+	0.924093i	$0.375177\pi$
$332$	−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	$0.981430\pi$
$338$	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	−0.249987	+	0.968249i	$0.580427\pi$
$347$	−6228.10	+	10787.4i	−0.963522	+	1.66887i	−0.713535	+	0.700620i	$0.752907\pi$
$348$		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
$356$	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	−0.833461	−	0.552578i	$-0.813644\pi$
$367$	−5425.21	+	3132.25i	−0.771645	+	0.445510i	0.0618160	+	0.998088i	$0.480311\pi$
$368$	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	$-0.152001\pi$
$374$	−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	$0.0417229\pi$
$379$			1928.72i			0.261402i	−0.991422	+	0.130701i	$0.958277\pi$
$380$	−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	−0.596443	−	0.802655i	$-0.703420\pi$
$383$	2974.93	−	5152.73i	0.396898	−	0.687448i	0.993341	+	0.115208i	$0.0367533\pi$
$384$		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
$392$	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	0.999977	−	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	$0.161455\pi$
$410$	−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	−0.998993	−	0.0448712i	$-0.985712\pi$
$419$	−3950.75	+	6842.90i	−0.460637	+	0.797846i	0.538356	+	0.842718i	$0.319046\pi$
$420$		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
$428$	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	−0.630175	−	0.776453i	$-0.717017\pi$
$439$	−2509.56	+	1448.89i	−0.272835	+	0.157522i	0.357340	+	0.933974i	$0.383684\pi$
$440$	−3955.53	−	4849.02i	−0.428574	−	0.525382i
$441$		0			0
$442$	1659.54	+	7149.28i	0.178589	+	0.769359i
$443$	3932.06	+	6810.53i	0.421711	+	0.730425i	0.996107	−	0.0881526i	$-0.0280963\pi$
$443$	3932.06	+	6810.53i	0.421711	+	0.730425i	−0.574396	+	0.818578i	$0.694763\pi$
$444$		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	$0.0223658\pi$
$449$			1335.91i			0.140413i	−0.997532	+	0.0702064i	$0.977634\pi$
$450$		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	−0.839679	−	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	0.317544	−	0.948244i	$-0.397142\pi$
$463$	−3435.96	−	1983.75i	−0.344887	−	0.199121i	−0.662431	+	0.749123i	$0.730475\pi$
$464$	−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	−0.785811	−	0.618466i	$-0.787754\pi$
$479$	−9734.00	−	16859.8i	−0.928513	−	1.60823i	−0.142702	−	0.989766i	$-0.545579\pi$
$480$		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	$0.0781795\pi$
$487$			5226.26i			0.486293i	−0.969990	+	0.243146i	$0.921820\pi$
$488$	−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	−0.557142	−	0.830417i	$-0.688102\pi$
$491$	4793.56	−	8302.69i	0.440591	−	0.763127i	0.997733	+	0.0672904i	$0.0214354\pi$
$492$		0			0
$493$	6353.30	+	11004.2i	0.580402	+	1.00529i
$494$	896.303	+	3861.25i	0.0816327	+	0.351672i
$495$		0			0
$496$	−3004.46	−	2324.29i	−0.271984	−	0.210411i
$497$	−5098.37	+	2943.55i	−0.460147	+	0.265666i
$498$		0			0
$499$	−2085.65	−	1204.15i	−0.187108	−	0.108027i	0.403520	−	0.914971i	$-0.367787\pi$
$499$	−2085.65	−	1204.15i	−0.187108	−	0.108027i	−0.590628	+	0.806944i	$0.701120\pi$
$500$	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	0.607412	−	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
$518$	−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	$-0.824006\pi$
$521$		−	12490.4i		−	1.05032i	0.851004	−	0.525159i	$-0.175994\pi$
$522$		0			0
$523$			13273.1i			1.10974i	0.831939	+	0.554868i	$0.187231\pi$
$523$			13273.1i			1.10974i	−0.831939	+	0.554868i	$0.812769\pi$
$524$	−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	0.275766	−	0.961225i	$-0.411068\pi$
$547$	15941.6	−	9203.89i	1.24609	−	0.719433i	0.970328	+	0.241792i	$0.0777351\pi$
$548$	−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	$-0.823183\pi$
$557$		−	13864.9i		−	1.05472i	0.849643	−	0.527358i	$-0.176817\pi$
$558$		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	−0.440583	−	0.897712i	$-0.645228\pi$
$563$	7442.77	−	12891.3i	0.557150	−	0.965012i	0.997733	−	0.0672999i	$-0.0214384\pi$
$564$		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	0.738977	−	0.673731i	$-0.235309\pi$
$571$	7163.27	+	4135.72i	0.524998	+	0.303108i	−0.213979	+	0.976838i	$0.568643\pi$
$572$	−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	−0.999990	−	0.00445871i	$-0.998581\pi$
$587$	−7165.79	−	12411.5i	−0.503856	−	0.872705i	0.496134	−	0.868246i	$-0.334753\pi$
$588$		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	$0.212681\pi$
$593$			17892.9i			1.23908i	−0.784966	+	0.619539i	$0.787319\pi$
$594$		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	−0.994732	−	0.102514i	$-0.967311\pi$
$599$	−5989.96	+	10374.9i	−0.408586	+	0.707692i	0.586145	+	0.810206i	$0.300645\pi$
$600$		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	−0.489406	−	0.872056i	$-0.662786\pi$
$607$	−22272.8	−	12859.2i	−1.48933	−	0.859866i	−0.999926	+	0.0121903i	$0.996120\pi$
$608$	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	−0.188267	−	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	−0.970589	−	0.240743i	$-0.922609\pi$
$619$	−19210.5	+	11091.2i	−1.24739	+	0.720183i	−0.276805	+	0.960926i	$0.589276\pi$
$620$	−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	$0.347851\pi$
$631$			28148.1i			1.77584i	−0.459994	+	0.887922i	$0.652149\pi$
$632$	−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	−0.699404	−	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	0.520289	−	0.853990i	$-0.325824\pi$
$643$	666.166	+	384.611i	0.0408570	+	0.0235888i	−0.479432	+	0.877579i	$0.659157\pi$
$644$	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	−0.141701	−	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	$0.0865568\pi$
$659$	12082.8	+	20928.0i	0.714231	+	1.23708i	−0.249024	+	0.968497i	$0.580110\pi$
$660$		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	$0.966955\pi$
$662$	−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	0.947744	−	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
$680$	−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	0.432781	−	0.901499i	$-0.357532\pi$
$691$	25972.9	−	14995.5i	1.42989	−	0.825549i	0.997112	+	0.0759500i	$0.0241989\pi$
$692$	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	$0.218869\pi$
$701$			23559.3i			1.26936i	−0.772774	+	0.634681i	$0.781131\pi$
$702$		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	0.657381	−	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
$716$	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	−0.680184	−	0.733041i	$-0.738100\pi$
$727$	−7555.48	+	4362.16i	−0.385443	+	0.222536i	0.294741	+	0.955577i	$0.404767\pi$
$728$	−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	$0.0352762\pi$
$734$	−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	$-0.824696\pi$
$739$		−	21026.0i		−	1.04662i	0.852141	−	0.523312i	$-0.175304\pi$
$740$	−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	−0.973099	−	0.230387i	$-0.926001\pi$
$743$	−5813.11	+	10068.6i	−0.287029	+	0.497148i	0.686071	+	0.727535i	$0.259334\pi$
$744$		0			0
$745$	4052.60	+	7019.32i	0.199297	+	0.345192i
$746$	33426.8	−	7759.27i	1.64054	−	0.380814i
$747$		0			0
$748$	−9258.24	−	18867.6i	−0.452560	−	0.922284i
$749$	16147.6	−	9322.82i	0.787744	−	0.454804i
$750$		0			0
$751$	−6096.06	−	3519.56i	−0.296203	−	0.171013i	0.344533	−	0.938774i	$-0.388037\pi$
$751$	−6096.06	−	3519.56i	−0.296203	−	0.171013i	−0.640736	+	0.767761i	$0.721371\pi$
$752$	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	0.897944	−	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	$-0.0351498\pi$
$770$	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	$0.257285\pi$
$773$			31081.3i			1.44621i	−0.690740	+	0.723103i	$0.742715\pi$
$774$		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	0.987267	−	0.159070i	$-0.0508496\pi$
$787$	29654.1	+	17120.8i	1.34314	+	0.775463i	0.355875	+	0.934534i	$0.384183\pi$
$788$	−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	0.807081	−	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
$806$	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	$0.179583\pi$
$809$			24608.1i			1.06944i	−0.845029	+	0.534720i	$0.820417\pi$
$810$		0			0
$811$			3293.86i			0.142618i	0.997454	+	0.0713089i	$0.0227176\pi$
$811$			3293.86i			0.142618i	−0.997454	+	0.0713089i	$0.977282\pi$
$812$	−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	0.418301	−	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	0.511209	−	0.859456i	$-0.329198\pi$
$823$	531.302	+	306.747i	0.0225031	+	0.0129922i	−0.488706	+	0.872448i	$0.662531\pi$
$824$	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	0.825119	+	0.564959i	$0.191108\pi$
$839$	21916.3	+	37960.1i	0.901828	+	1.56201i	0.0767097	+	0.997053i	$0.475559\pi$
$840$		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	0.708775	−	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	0.636720	−	0.771095i	$-0.280291\pi$
$859$	7232.93	+	4175.93i	0.287293	+	0.165869i	−0.349428	+	0.936963i	$0.613624\pi$
$860$	−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	−0.675020	−	0.737799i	$-0.735865\pi$
$877$	7828.97	−	13560.2i	0.301443	−	0.522114i	0.976463	+	0.215685i	$0.0691984\pi$
$878$	−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	$-0.731166\pi$
$881$		−	39103.2i		−	1.49537i	0.664054	−	0.747684i	$-0.268834\pi$
$882$		0			0
$883$			23664.8i			0.901907i	0.892547	+	0.450953i	$0.148916\pi$
$883$			23664.8i			0.901907i	−0.892547	+	0.450953i	$0.851084\pi$
$884$	−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	0.0616939	+	0.998095i	$0.480350\pi$
$887$	−22019.4	+	38138.8i	−0.833529	+	1.44371i	−0.895223	+	0.445619i	$0.852984\pi$
$888$		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	−0.918820	−	0.394676i	$-0.870857\pi$
$907$	−28310.7	+	16345.2i	−1.03643	+	0.598384i	−0.117610	+	0.993060i	$0.537523\pi$
$908$	−10813.1	+	5305.93i	−0.395204	+	0.193925i
$909$		0			0
$910$	−18194.0	+	4223.33i	−0.662775	+	0.153848i
$911$	−12749.9	−	22083.5i	−0.463693	−	0.803140i	0.535448	−	0.844568i	$-0.320143\pi$
$911$	−12749.9	−	22083.5i	−0.463693	−	0.803140i	−0.999141	+	0.0414281i	$0.986809\pi$
$912$		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	$-0.881782\pi$
$919$		−	20221.1i		−	0.725825i	0.931823	−	0.362912i	$-0.118218\pi$
$920$	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	−0.946773	−	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
$932$	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	0.530603	−	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	0.670497	−	0.741913i	$-0.266081\pi$
$947$	−8954.48	−	15509.6i	−0.307267	−	0.532202i	−0.977763	+	0.209711i	$0.932748\pi$
$948$		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	$0.0593400\pi$
$953$			10905.6i			0.370689i	−0.982674	+	0.185344i	$0.940660\pi$
$954$		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	0.994406	−	0.105622i	$-0.0336832\pi$
$967$	42102.8	+	24308.1i	1.40014	+	0.808370i	0.405732	+	0.913992i	$0.367017\pi$
$968$	−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	0.107766	−	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	0.987449	−	0.157941i	$-0.0504856\pi$
$983$	11000.9	+	19054.2i	0.356943	+	0.618244i	−0.630505	+	0.776185i	$0.717152\pi$
$984$		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	$-0.890189\pi$
$991$		−	21100.2i		−	0.676358i	0.941082	−	0.338179i	$-0.109811\pi$
$992$	−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	0.792716	−	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.71.10		24
3.2	odd	2		36.4.h.b.23.3	yes	24
4.3	odd	2	inner	108.4.h.b.71.5		24
9.2	odd	6	inner	108.4.h.b.35.5		24
9.4	even	3		324.4.b.c.323.4		24
9.5	odd	6		324.4.b.c.323.21		24
9.7	even	3		36.4.h.b.11.8	yes	24
12.11	even	2		36.4.h.b.23.8	yes	24
36.7	odd	6		36.4.h.b.11.3	✓	24
36.11	even	6	inner	108.4.h.b.35.10		24
36.23	even	6		324.4.b.c.323.3		24
36.31	odd	6		324.4.b.c.323.22		24

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