LMFDB - Embedded newform 324.4.b.c.323.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,4,Mod(323,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("324.323");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	324.b (of order $2$, degree $1$, 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:	$19.1166188419$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.16
Character	$\chi$	$=$	324.323
Dual form			324.4.b.c.323.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16011 + 2.57956i) q^{2} +(-5.30829 + 5.98515i) q^{4} -16.7343i q^{5} +19.3037i q^{7} +(-21.5973 - 6.74964i) q^{8} +O(q^{10})$	\(q+(1.16011 + 2.57956i) q^{2} +(-5.30829 + 5.98515i) q^{4} -16.7343i q^{5} +19.3037i q^{7} +(-21.5973 - 6.74964i) q^{8} +(43.1673 - 19.4137i) q^{10} -4.88184 q^{11} -12.0770 q^{13} +(-49.7952 + 22.3944i) q^{14} +(-7.64410 - 63.5419i) q^{16} -71.2528i q^{17} -68.3003i q^{19} +(100.158 + 88.8308i) q^{20} +(-5.66347 - 12.5930i) q^{22} +136.098 q^{23} -155.038 q^{25} +(-14.0106 - 31.1533i) q^{26} +(-115.536 - 102.470i) q^{28} -219.667i q^{29} -329.345i q^{31} +(155.042 - 93.4340i) q^{32} +(183.801 - 82.6611i) q^{34} +323.035 q^{35} -133.618 q^{37} +(176.185 - 79.2359i) q^{38} +(-112.951 + 361.416i) q^{40} -34.1013i q^{41} +0.644564i q^{43} +(25.9142 - 29.2186i) q^{44} +(157.889 + 351.074i) q^{46} -186.951 q^{47} -29.6338 q^{49} +(-179.862 - 399.931i) q^{50} +(64.1080 - 72.2825i) q^{52} +266.453i q^{53} +81.6944i q^{55} +(130.293 - 416.908i) q^{56} +(566.644 - 254.838i) q^{58} +208.694 q^{59} -1.60377 q^{61} +(849.565 - 382.076i) q^{62} +(420.885 + 291.548i) q^{64} +202.100i q^{65} +428.864i q^{67} +(426.459 + 378.231i) q^{68} +(374.756 + 833.290i) q^{70} -386.365 q^{71} -776.832 q^{73} +(-155.011 - 344.676i) q^{74} +(408.788 + 362.558i) q^{76} -94.2377i q^{77} -79.0970i q^{79} +(-1063.33 + 127.919i) q^{80} +(87.9665 - 39.5613i) q^{82} +925.337 q^{83} -1192.37 q^{85} +(-1.66269 + 0.747765i) q^{86} +(105.434 + 32.9506i) q^{88} -1044.26i q^{89} -233.130i q^{91} +(-722.449 + 814.569i) q^{92} +(-216.883 - 482.251i) q^{94} -1142.96 q^{95} -1466.37 q^{97} +(-34.3784 - 76.4422i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4}+O(q^{10}) $ 24 * q + 24 * q^4	$ 24 q + 24 q^{4} + 96 q^{10} + 432 q^{13} + 144 q^{16} + 384 q^{22} - 504 q^{25} - 672 q^{28} + 1320 q^{34} + 1248 q^{37} - 1272 q^{40} + 960 q^{46} - 696 q^{49} - 264 q^{52} - 1032 q^{58} + 528 q^{61} + 960 q^{64} - 1128 q^{70} - 4776 q^{73} + 1200 q^{76} - 4104 q^{82} - 1440 q^{85} - 3912 q^{88} + 2376 q^{94} - 1176 q^{97}+O(q^{100}) $ 24 * q + 24 * q^4 + 96 * q^10 + 432 * q^13 + 144 * q^16 + 384 * q^22 - 504 * q^25 - 672 * q^28 + 1320 * q^34 + 1248 * q^37 - 1272 * q^40 + 960 * q^46 - 696 * q^49 - 264 * q^52 - 1032 * q^58 + 528 * q^61 + 960 * q^64 - 1128 * q^70 - 4776 * q^73 + 1200 * q^76 - 4104 * q^82 - 1440 * q^85 - 3912 * q^88 + 2376 * q^94 - 1176 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.16011	+	2.57956i	0.410161	+	0.912013i
$2$	1.16011	+	2.57956i	0.410161	+	0.912013i
$3$		0			0
$3$		0			0
$4$	−5.30829	+	5.98515i	−0.663536	+	0.748144i
$5$		−	16.7343i		−	1.49677i	−0.663267	−	0.748383i	$-0.730831\pi$
$5$		−	16.7343i		−	1.49677i	0.663267	−	0.748383i	$-0.269169\pi$
$6$		0			0
$7$			19.3037i			1.04230i	0.853464	+	0.521152i	$0.174497\pi$
$7$			19.3037i			1.04230i	−0.853464	+	0.521152i	$0.825503\pi$
$8$	−21.5973	−	6.74964i	−0.954474	−	0.298295i
$9$		0			0
$10$	43.1673	−	19.4137i	1.36507	−	0.613915i
$11$	−4.88184			−0.133812			−0.0669059	−	0.997759i	$-0.521313\pi$
$11$	−4.88184			−0.133812			−0.0669059	+	0.997759i	$0.521313\pi$
$12$		0			0
$13$	−12.0770			−0.257657			−0.128829	−	0.991667i	$-0.541122\pi$
$13$	−12.0770			−0.257657			−0.128829	+	0.991667i	$0.541122\pi$
$14$	−49.7952	+	22.3944i	−0.950594	+	0.427512i
$15$		0			0
$16$	−7.64410	−	63.5419i	−0.119439	−	0.992842i
$17$		−	71.2528i		−	1.01655i	−0.861195	−	0.508275i	$-0.830283\pi$
$17$		−	71.2528i		−	1.01655i	0.861195	−	0.508275i	$-0.169717\pi$
$18$		0			0
$19$		−	68.3003i		−	0.824693i	−0.911027	−	0.412347i	$-0.864709\pi$
$19$		−	68.3003i		−	0.824693i	0.911027	−	0.412347i	$-0.135291\pi$
$20$	100.158	+	88.8308i	1.11980	+	0.993158i
$21$		0			0
$22$	−5.66347	−	12.5930i	−0.0548844	−	0.122038i
$23$	136.098			1.23385			0.616923	−	0.787024i	$-0.288379\pi$
$23$	136.098			1.23385			0.616923	+	0.787024i	$0.288379\pi$
$24$		0			0
$25$	−155.038			−1.24031
$26$	−14.0106	−	31.1533i	−0.105681	−	0.234987i
$27$		0			0
$28$	−115.536	−	102.470i	−0.779793	−	0.691606i
$29$		−	219.667i		−	1.40659i	−0.710899	−	0.703295i	$-0.751712\pi$
$29$		−	219.667i		−	1.40659i	0.710899	−	0.703295i	$-0.248288\pi$
$30$		0			0
$31$		−	329.345i		−	1.90813i	−0.299600	−	0.954065i	$-0.596853\pi$
$31$		−	329.345i		−	1.90813i	0.299600	−	0.954065i	$-0.403147\pi$
$32$	155.042	−	93.4340i	0.856495	−	0.516155i
$33$		0			0
$34$	183.801	−	82.6611i	0.927107	−	0.416949i
$35$	323.035			1.56008
$36$		0			0
$37$	−133.618			−0.593693			−0.296847	−	0.954925i	$-0.595935\pi$
$37$	−133.618			−0.593693			−0.296847	+	0.954925i	$0.595935\pi$
$38$	176.185	−	79.2359i	0.752131	−	0.338257i
$39$		0			0
$40$	−112.951	+	361.416i	−0.446477	+	1.42862i
$41$		−	34.1013i		−	0.129896i	−0.997889	−	0.0649480i	$-0.979312\pi$
$41$		−	34.1013i		−	0.129896i	0.997889	−	0.0649480i	$-0.0206881\pi$
$42$		0			0
$43$			0.644564i			0.00228593i	0.999999	+	0.00114297i	$0.000363817\pi$
$43$			0.644564i			0.00228593i	−0.999999	+	0.00114297i	$0.999636\pi$
$44$	25.9142	−	29.2186i	0.0887890	−	0.100111i
$45$		0			0
$46$	157.889	+	351.074i	0.506075	+	1.12528i
$47$	−186.951			−0.580203			−0.290102	−	0.956996i	$-0.593689\pi$
$47$	−186.951			−0.580203			−0.290102	+	0.956996i	$0.593689\pi$
$48$		0			0
$49$	−29.6338			−0.0863958
$50$	−179.862	−	399.931i	−0.508725	−	1.13118i
$51$		0			0
$52$	64.1080	−	72.2825i	0.170965	−	0.192765i
$53$			266.453i			0.690569i	0.938498	+	0.345284i	$0.112218\pi$
$53$			266.453i			0.690569i	−0.938498	+	0.345284i	$0.887782\pi$
$54$		0			0
$55$			81.6944i			0.200285i
$56$	130.293	−	416.908i	0.310913	−	0.994851i
$57$		0			0
$58$	566.644	−	254.838i	1.28283	−	0.576928i
$59$	208.694			0.460501			0.230251	−	0.973131i	$-0.426045\pi$
$59$	208.694			0.460501			0.230251	+	0.973131i	$0.426045\pi$
$60$		0			0
$61$	−1.60377			−0.00336626			−0.00168313	−	0.999999i	$-0.500536\pi$
$61$	−1.60377			−0.00336626			−0.00168313	+	0.999999i	$0.500536\pi$
$62$	849.565	−	382.076i	1.74024	−	0.782640i
$63$		0			0
$64$	420.885	+	291.548i	0.822041	+	0.569429i
$65$			202.100i			0.385653i
$66$		0			0
$67$			428.864i			0.782001i	0.920390	+	0.391001i	$0.127871\pi$
$67$			428.864i			0.782001i	−0.920390	+	0.391001i	$0.872129\pi$
$68$	426.459	+	378.231i	0.760526	+	0.674518i
$69$		0			0
$70$	374.756	+	833.290i	0.639885	+	1.42282i
$71$	−386.365			−0.645817			−0.322909	−	0.946430i	$-0.604661\pi$
$71$	−386.365			−0.645817			−0.322909	+	0.946430i	$0.604661\pi$
$72$		0			0
$73$	−776.832			−1.24550			−0.622749	−	0.782422i	$-0.713984\pi$
$73$	−776.832			−1.24550			−0.622749	+	0.782422i	$0.713984\pi$
$74$	−155.011	−	344.676i	−0.243510	−	0.541456i
$75$		0			0
$76$	408.788	+	362.558i	0.616989	+	0.547214i
$77$		−	94.2377i		−	0.139472i
$78$		0			0
$79$		−	79.0970i		−	0.112647i	−0.998413	−	0.0563235i	$-0.982062\pi$
$79$		−	79.0970i		−	0.112647i	0.998413	−	0.0563235i	$-0.0179378\pi$
$80$	−1063.33	+	127.919i	−1.48605	+	0.178772i
$81$		0			0
$82$	87.9665	−	39.5613i	0.118467	−	0.0532782i
$83$	925.337			1.22372			0.611861	−	0.790965i	$-0.290421\pi$
$83$	925.337			1.22372			0.611861	+	0.790965i	$0.290421\pi$
$84$		0			0
$85$	−1192.37			−1.52154
$86$	−1.66269	+	0.747765i	−0.00208480	+	0.000937599i
$87$		0			0
$88$	105.434	+	32.9506i	0.127720	+	0.0399154i
$89$		−	1044.26i		−	1.24372i	−0.783128	−	0.621861i	$-0.786377\pi$
$89$		−	1044.26i		−	1.24372i	0.783128	−	0.621861i	$-0.213623\pi$
$90$		0			0
$91$		−	233.130i		−	0.268557i
$92$	−722.449	+	814.569i	−0.818701	+	0.923094i
$93$		0			0
$94$	−216.883	−	482.251i	−0.237977	−	0.529153i
$95$	−1142.96			−1.23437
$96$		0			0
$97$	−1466.37			−1.53492			−0.767460	−	0.641097i	$-0.778479\pi$
$97$	−1466.37			−1.53492			−0.767460	+	0.641097i	$0.778479\pi$
$98$	−34.3784	−	76.4422i	−0.0354362	−	0.0787941i
$99$		0			0
$100$	822.989	−	927.929i	0.822989	−	0.927929i
$101$			362.925i			0.357548i	0.983890	+	0.178774i	$0.0572131\pi$
$101$			362.925i			0.357548i	−0.983890	+	0.178774i	$0.942787\pi$
$102$		0			0
$103$			538.238i			0.514895i	0.966292	+	0.257447i	$0.0828814\pi$
$103$			538.238i			0.514895i	−0.966292	+	0.257447i	$0.917119\pi$
$104$	260.830	+	81.5151i	0.245927	+	0.0768578i
$105$		0			0
$106$	−687.333	+	309.115i	−0.629808	+	0.283244i
$107$	−430.456			−0.388914			−0.194457	−	0.980911i	$-0.562294\pi$
$107$	−430.456			−0.388914			−0.194457	+	0.980911i	$0.562294\pi$
$108$		0			0
$109$	899.324			0.790272			0.395136	−	0.918623i	$-0.370697\pi$
$109$	899.324			0.790272			0.395136	+	0.918623i	$0.370697\pi$
$110$	−210.736	+	94.7745i	−0.182663	+	0.0821490i
$111$		0			0
$112$	1226.59	−	147.560i	1.03484	−	0.124492i
$113$		−	382.044i		−	0.318050i	−0.987275	−	0.159025i	$-0.949165\pi$
$113$		−	382.044i		−	0.318050i	0.987275	−	0.159025i	$-0.0508351\pi$
$114$		0			0
$115$		−	2277.52i		−	1.84678i
$116$	1314.74	+	1166.05i	1.05233	+	0.933323i
$117$		0			0
$118$	242.107	+	538.338i	0.188880	+	0.419983i
$119$	1375.44			1.05955
$120$		0			0
$121$	−1307.17			−0.982094
$122$	−1.86055	−	4.13703i	−0.00138071	−	0.00307008i
$123$		0			0
$124$	1971.18	+	1748.26i	1.42756	+	1.26611i
$125$			502.674i			0.359684i
$126$		0			0
$127$		−	1677.92i		−	1.17237i	−0.810177	−	0.586186i	$-0.800629\pi$
$127$		−	1677.92i		−	1.17237i	0.810177	−	0.586186i	$-0.199371\pi$
$128$	−263.793	+	1423.93i	−0.182158	+	0.983269i
$129$		0			0
$130$	−521.330	+	234.458i	−0.351721	+	0.158180i
$131$	1424.84			0.950294			0.475147	−	0.879906i	$-0.342395\pi$
$131$	1424.84			0.950294			0.475147	+	0.879906i	$0.342395\pi$
$132$		0			0
$133$	1318.45			0.859580
$134$	−1106.28	+	497.529i	−0.713196	+	0.320746i
$135$		0			0
$136$	−480.931	+	1538.87i	−0.303231	+	0.970270i
$137$		−	26.8231i		−	0.0167274i	−0.999965	−	0.00836370i	$-0.997338\pi$
$137$		−	26.8231i		−	0.0167274i	0.999965	−	0.00836370i	$-0.00266228\pi$
$138$		0			0
$139$		−	1656.50i		−	1.01081i	−0.862882	−	0.505406i	$-0.831343\pi$
$139$		−	1656.50i		−	1.01081i	0.862882	−	0.505406i	$-0.168657\pi$
$140$	−1714.77	+	1933.42i	−1.03517	+	1.16717i
$141$		0			0
$142$	−448.225	−	996.652i	−0.264889	−	0.588994i
$143$	58.9578			0.0344776
$144$		0			0
$145$	−3675.98			−2.10533
$146$	−901.211	−	2003.89i	−0.510854	−	1.13591i
$147$		0			0
$148$	709.283	−	799.724i	0.393937	−	0.444168i
$149$			852.498i			0.468720i	0.972150	+	0.234360i	$0.0752995\pi$
$149$			852.498i			0.468720i	−0.972150	+	0.234360i	$0.924700\pi$
$150$		0			0
$151$			1468.84i			0.791608i	0.918335	+	0.395804i	$0.129534\pi$
$151$			1468.84i			0.791608i	−0.918335	+	0.395804i	$0.870466\pi$
$152$	−461.002	+	1475.10i	−0.246002	+	0.787148i
$153$		0			0
$154$	243.092	−	109.326i	0.127201	−	0.0572061i
$155$	−5511.37			−2.85602
$156$		0			0
$157$	2689.05			1.36694			0.683469	−	0.729979i	$-0.260470\pi$
$157$	2689.05			1.36694			0.683469	+	0.729979i	$0.260470\pi$
$158$	204.036	−	91.7612i	0.102736	−	0.0462034i
$159$		0			0
$160$	−1563.56	−	2594.53i	−0.772563	−	1.28197i
$161$			2627.20i			1.28604i
$162$		0			0
$163$			2186.50i			1.05067i	0.850895	+	0.525336i	$0.176060\pi$
$163$			2186.50i			1.05067i	−0.850895	+	0.525336i	$0.823940\pi$
$164$	204.102	+	181.020i	0.0971809	+	0.0861907i
$165$		0			0
$166$	1073.49	+	2386.96i	0.501923	+	1.11605i
$167$	−3581.29			−1.65945			−0.829726	−	0.558171i	$-0.811503\pi$
$167$	−3581.29			−1.65945			−0.829726	+	0.558171i	$0.811503\pi$
$168$		0			0
$169$	−2051.15			−0.933613
$170$	−1383.28	−	3075.79i	−0.624075	−	1.38766i
$171$		0			0
$172$	−3.85781	−	3.42153i	−0.00171021	−	0.00151680i
$173$			109.125i			0.0479574i	0.999712	+	0.0239787i	$0.00763338\pi$
$173$			109.125i			0.0479574i	−0.999712	+	0.0239787i	$0.992367\pi$
$174$		0			0
$175$		−	2992.82i		−	1.29278i
$176$	37.3173	+	310.201i	0.0159824	+	0.132854i
$177$		0			0
$178$	2693.73	−	1211.46i	1.13429	−	0.510126i
$179$	−268.397			−0.112072			−0.0560361	−	0.998429i	$-0.517846\pi$
$179$	−268.397			−0.112072			−0.0560361	+	0.998429i	$0.517846\pi$
$180$		0			0
$181$	898.582			0.369011			0.184506	−	0.982831i	$-0.440932\pi$
$181$	898.582			0.369011			0.184506	+	0.982831i	$0.440932\pi$
$182$	601.375	−	270.457i	0.244928	−	0.110152i
$183$		0			0
$184$	−2939.35	−	918.614i	−1.17767	−	0.368049i
$185$			2236.01i			0.888620i
$186$		0			0
$187$			347.845i			0.136026i
$188$	992.388	−	1118.93i	0.384986	−	0.434076i
$189$		0			0
$190$	−1325.96	−	2948.34i	−0.506291	−	1.12576i
$191$	−514.662			−0.194972			−0.0974860	−	0.995237i	$-0.531080\pi$
$191$	−514.662			−0.194972			−0.0974860	+	0.995237i	$0.531080\pi$
$192$		0			0
$193$	−2459.32			−0.917232			−0.458616	−	0.888635i	$-0.651655\pi$
$193$	−2459.32			−0.917232			−0.458616	+	0.888635i	$0.651655\pi$
$194$	−1701.15	−	3782.59i	−0.629564	−	1.39987i
$195$		0			0
$196$	157.305	−	177.363i	0.0573268	−	0.0646365i
$197$			646.506i			0.233815i	0.993143	+	0.116908i	$0.0372982\pi$
$197$			646.506i			0.233815i	−0.993143	+	0.116908i	$0.962702\pi$
$198$		0			0
$199$		−	1742.98i		−	0.620886i	−0.950592	−	0.310443i	$-0.899523\pi$
$199$		−	1742.98i		−	0.620886i	0.950592	−	0.310443i	$-0.100477\pi$
$200$	3348.41	+	1046.45i	1.18384	+	0.369977i
$201$		0			0
$202$	−936.188	+	421.033i	−0.326089	+	0.146652i
$203$	4240.39			1.46609
$204$		0			0
$205$	−570.664			−0.194424
$206$	−1388.42	+	624.415i	−0.469591	+	0.211190i
$207$		0			0
$208$	92.3175	+	767.393i	0.0307744	+	0.255813i
$209$			333.431i			0.110354i
$210$		0			0
$211$			4212.66i			1.37446i	0.726439	+	0.687231i	$0.241174\pi$
$211$			4212.66i			1.37446i	−0.726439	+	0.687231i	$0.758826\pi$
$212$	−1594.76	−	1414.41i	−0.516645	−	0.458218i
$213$		0			0
$214$	−499.376	−	1110.39i	−0.159517	−	0.354694i
$215$	10.7864			0.00342150
$216$		0			0
$217$	6357.58			1.98885
$218$	1043.31	+	2319.86i	0.324138	+	0.720738i
$219$		0			0
$220$	−488.954	−	433.658i	−0.149842	−	0.132896i
$221$			860.518i			0.261922i
$222$		0			0
$223$			6418.45i			1.92741i	0.266977	+	0.963703i	$0.413975\pi$
$223$			6418.45i			1.92741i	−0.266977	+	0.963703i	$0.586025\pi$
$224$	1803.62	+	2992.89i	0.537990	+	0.892728i
$225$		0			0
$226$	985.507	−	443.213i	0.290066	−	0.130452i
$227$	2249.67			0.657778			0.328889	−	0.944369i	$-0.393326\pi$
$227$	2249.67			0.657778			0.328889	+	0.944369i	$0.393326\pi$
$228$		0			0
$229$	3470.73			1.00154			0.500769	−	0.865581i	$-0.333051\pi$
$229$	3470.73			1.00154			0.500769	+	0.865581i	$0.333051\pi$
$230$	5875.00	−	2642.17i	1.68429	−	0.757476i
$231$		0			0
$232$	−1482.67	+	4744.20i	−0.419578	+	1.34255i
$233$		−	3852.67i		−	1.08325i	−0.840621	−	0.541624i	$-0.817810\pi$
$233$		−	3852.67i		−	1.08325i	0.840621	−	0.541624i	$-0.182190\pi$
$234$		0			0
$235$			3128.50i			0.868428i
$236$	−1107.81	+	1249.06i	−0.305559	+	0.344521i
$237$		0			0
$238$	1595.67	+	3548.05i	0.434587	+	0.966326i
$239$	−39.8668			−0.0107898			−0.00539491	−	0.999985i	$-0.501717\pi$
$239$	−39.8668			−0.0107898			−0.00539491	+	0.999985i	$0.501717\pi$
$240$		0			0
$241$	3458.36			0.924369			0.462184	−	0.886784i	$-0.347066\pi$
$241$	3458.36			0.924369			0.462184	+	0.886784i	$0.347066\pi$
$242$	−1516.46	−	3371.92i	−0.402817	−	0.895683i
$243$		0			0
$244$	8.51329	−	9.59882i	0.00223364	−	0.00251845i
$245$			495.902i			0.129314i
$246$		0			0
$247$			824.861i			0.212488i
$248$	−2222.96	+	7112.95i	−0.569185	+	1.82126i
$249$		0			0
$250$	−1296.68	+	583.156i	−0.328036	+	0.147528i
$251$	2977.61			0.748786			0.374393	−	0.927270i	$-0.377851\pi$
$251$	2977.61			0.748786			0.374393	+	0.927270i	$0.377851\pi$
$252$		0			0
$253$	−664.410			−0.165103
$254$	4328.30	−	1946.57i	1.06922	−	0.480861i
$255$		0			0
$256$	−3979.14	+	971.441i	−0.971469	+	0.237168i
$257$		−	6458.56i		−	1.56760i	−0.621011	−	0.783802i	$-0.713278\pi$
$257$		−	6458.56i		−	1.56760i	0.621011	−	0.783802i	$-0.286722\pi$
$258$		0			0
$259$		−	2579.32i		−	0.618808i
$260$	−1209.60	−	1072.81i	−0.288524	−	0.255895i
$261$		0			0
$262$	1652.97	+	3675.46i	0.389773	+	0.866681i
$263$	5881.98			1.37908			0.689540	−	0.724247i	$-0.257813\pi$
$263$	5881.98			1.37908			0.689540	+	0.724247i	$0.257813\pi$
$264$		0			0
$265$	4458.92			1.03362
$266$	1529.55	+	3401.03i	0.352566	+	0.783949i
$267$		0			0
$268$	−2566.82	−	2276.54i	−0.585050	−	0.518886i
$269$		−	2967.07i		−	0.672510i	−0.941771	−	0.336255i	$-0.890840\pi$
$269$		−	2967.07i		−	0.672510i	0.941771	−	0.336255i	$-0.109160\pi$
$270$		0			0
$271$			1985.78i			0.445121i	0.974919	+	0.222561i	$0.0714415\pi$
$271$			1985.78i			0.445121i	−0.974919	+	0.222561i	$0.928559\pi$
$272$	−4527.54	+	544.664i	−1.00927	+	0.121416i
$273$		0			0
$274$	69.1919	−	31.1178i	0.0152556	−	0.00686092i
$275$	756.873			0.165968
$276$		0			0
$277$	4342.96			0.942034			0.471017	−	0.882124i	$-0.343887\pi$
$277$	4342.96			0.942034			0.471017	+	0.882124i	$0.343887\pi$
$278$	4273.05	−	1921.73i	0.921873	−	0.414595i
$279$		0			0
$280$	−6976.68	−	2180.37i	−1.48906	−	0.465365i
$281$		−	7796.65i		−	1.65519i	−0.561323	−	0.827597i	$-0.689708\pi$
$281$		−	7796.65i		−	1.65519i	0.561323	−	0.827597i	$-0.310292\pi$
$282$		0			0
$283$			2045.51i			0.429658i	0.976652	+	0.214829i	$0.0689194\pi$
$283$			2045.51i			0.429658i	−0.976652	+	0.214829i	$0.931081\pi$
$284$	2050.94	−	2312.45i	0.428523	−	0.483165i
$285$		0			0
$286$	68.3975	+	152.085i	0.0141414	+	0.0314440i
$287$	658.283			0.135391
$288$		0			0
$289$	−163.963			−0.0333732
$290$	−4264.54	−	9482.42i	−0.863525	−	1.92009i
$291$		0			0
$292$	4123.65	−	4649.46i	0.826433	−	0.931812i
$293$		−	2357.43i		−	0.470043i	−0.971990	−	0.235022i	$-0.924484\pi$
$293$		−	2357.43i		−	0.470043i	0.971990	−	0.235022i	$-0.0755161\pi$
$294$		0			0
$295$		−	3492.35i		−	0.689263i
$296$	2885.78	+	901.873i	0.566665	+	0.177096i
$297$		0			0
$298$	−2199.07	+	988.991i	−0.427479	+	0.192251i
$299$	−1643.65			−0.317910
$300$		0			0
$301$	−12.4425			−0.00238263
$302$	−3788.98	+	1704.02i	−0.721957	+	0.324687i
$303$		0			0
$304$	−4339.93	+	522.095i	−0.818790	+	0.0985006i
$305$			26.8381i			0.00503851i
$306$		0			0
$307$		−	5521.27i		−	1.02643i	−0.858259	−	0.513217i	$-0.828454\pi$
$307$		−	5521.27i		−	1.02643i	0.858259	−	0.513217i	$-0.171546\pi$
$308$	564.027	+	500.241i	0.104346	+	0.0925451i
$309$		0			0
$310$	−6393.79	−	14216.9i	−1.17143	−	2.60473i
$311$	1534.66			0.279815			0.139908	−	0.990165i	$-0.455319\pi$
$311$	1534.66			0.279815			0.139908	+	0.990165i	$0.455319\pi$
$312$		0			0
$313$	8766.55			1.58311			0.791557	−	0.611095i	$-0.209271\pi$
$313$	8766.55			1.58311			0.791557	+	0.611095i	$0.209271\pi$
$314$	3119.59	+	6936.57i	0.560664	+	1.24667i
$315$		0			0
$316$	473.408	+	419.870i	0.0842762	+	0.0747454i
$317$			7014.17i			1.24276i	0.783509	+	0.621380i	$0.213428\pi$
$317$			7014.17i			1.24276i	−0.783509	+	0.621380i	$0.786572\pi$
$318$		0			0
$319$			1072.38i			0.188218i
$320$	4878.86	−	7043.23i	0.852302	−	1.23040i
$321$		0			0
$322$	−6777.04	+	3047.84i	−1.17289	+	0.527484i
$323$	−4866.59			−0.838342
$324$		0			0
$325$	1872.39			0.319574
$326$	−5640.20	+	2536.58i	−0.958227	+	0.430945i
$327$		0			0
$328$	−230.172	+	736.496i	−0.0387473	+	0.123982i
$329$		−	3608.84i		−	0.604748i
$330$		0			0
$331$		−	9887.94i		−	1.64196i	−0.570954	−	0.820982i	$-0.693426\pi$
$331$		−	9887.94i		−	1.64196i	0.570954	−	0.820982i	$-0.306574\pi$
$332$	−4911.96	+	5538.28i	−0.811984	+	0.915520i
$333$		0			0
$334$	−4154.69	−	9238.16i	−0.680642	−	1.51344i
$335$	7176.76			1.17047
$336$		0			0
$337$	−5008.19			−0.809536			−0.404768	−	0.914419i	$-0.632648\pi$
$337$	−5008.19			−0.809536			−0.404768	+	0.914419i	$0.632648\pi$
$338$	−2379.56	−	5291.06i	−0.382931	−	0.851467i
$339$		0			0
$340$	6329.44	−	7136.51i	1.00959	−	1.13833i
$341$			1607.81i			0.255330i
$342$		0			0
$343$			6049.14i			0.952252i
$344$	4.35057	−	13.9208i	0.000681881	−	0.00218186i
$345$		0			0
$346$	−281.495	+	126.597i	−0.0437378	+	0.0196702i
$347$	−7795.06			−1.20594			−0.602969	−	0.797764i	$-0.706016\pi$
$347$	−7795.06			−1.20594			−0.602969	+	0.797764i	$0.706016\pi$
$348$		0			0
$349$	−9081.62			−1.39292			−0.696458	−	0.717597i	$-0.745242\pi$
$349$	−9081.62			−1.39292			−0.696458	+	0.717597i	$0.745242\pi$
$350$	7720.17	−	3472.00i	1.17903	−	0.530246i
$351$		0			0
$352$	−756.891	+	456.130i	−0.114609	+	0.0690676i
$353$		−	4554.78i		−	0.686760i	−0.939197	−	0.343380i	$-0.888428\pi$
$353$		−	4554.78i		−	0.686760i	0.939197	−	0.343380i	$-0.111572\pi$
$354$		0			0
$355$			6465.56i			0.966637i
$356$	6250.05	+	5543.23i	0.930483	+	0.825255i
$357$		0			0
$358$	−311.370	−	692.347i	−0.0459676	−	0.102211i
$359$	5415.10			0.796095			0.398047	−	0.917365i	$-0.369688\pi$
$359$	5415.10			0.796095			0.398047	+	0.917365i	$0.369688\pi$
$360$		0			0
$361$	2194.06			0.319881
$362$	1042.45	+	2317.95i	0.151354	+	0.336543i
$363$		0			0
$364$	1395.32	+	1237.52i	0.200919	+	0.178197i
$365$			12999.8i			1.86422i
$366$		0			0
$367$			10656.2i			1.51566i	0.652452	+	0.757830i	$0.273740\pi$
$367$			10656.2i			1.51566i	−0.652452	+	0.757830i	$0.726260\pi$
$368$	−1040.35	−	8647.94i	−0.147369	−	1.22501i
$369$		0			0
$370$	−5767.93	+	2594.02i	−0.810433	+	0.364477i
$371$	−5143.54			−0.719782
$372$		0			0
$373$	2709.97			0.376185			0.188093	−	0.982151i	$-0.439769\pi$
$373$	2709.97			0.376185			0.188093	+	0.982151i	$0.439769\pi$
$374$	−897.288	+	403.538i	−0.124058	+	0.0557927i
$375$		0			0
$376$	4037.63	+	1261.85i	0.553789	+	0.173072i
$377$			2652.91i			0.362418i
$378$		0			0
$379$			6395.35i			0.866774i	0.901208	+	0.433387i	$0.142682\pi$
$379$			6395.35i			0.866774i	−0.901208	+	0.433387i	$0.857318\pi$
$380$	6067.17	−	6840.80i	0.819051	−	0.923489i
$381$		0			0
$382$	−597.065	−	1327.60i	−0.0799699	−	0.177817i
$383$	1365.16			0.182131			0.0910656	−	0.995845i	$-0.470973\pi$
$383$	1365.16			0.182131			0.0910656	+	0.995845i	$0.470973\pi$
$384$		0			0
$385$	−1577.01			−0.208758
$386$	−2853.08	−	6343.97i	−0.376212	−	0.836528i
$387$		0			0
$388$	7783.91	−	8776.44i	1.01847	−	1.14834i
$389$			6213.24i			0.809830i	0.914354	+	0.404915i	$0.132699\pi$
$389$			6213.24i			0.809830i	−0.914354	+	0.404915i	$0.867301\pi$
$390$		0			0
$391$		−	9697.38i		−	1.25427i
$392$	640.009	+	200.017i	0.0824626	+	0.0257714i
$393$		0			0
$394$	−1667.70	+	750.018i	−0.213243	+	0.0959019i
$395$	−1323.64			−0.168606
$396$		0			0
$397$	3291.69			0.416134			0.208067	−	0.978115i	$-0.433283\pi$
$397$	3291.69			0.416134			0.208067	+	0.978115i	$0.433283\pi$
$398$	4496.11	−	2022.04i	0.566256	−	0.254663i
$399$		0			0
$400$	1185.13	+	9851.43i	0.148141	+	1.23143i
$401$			4075.53i			0.507536i	0.967265	+	0.253768i	$0.0816700\pi$
$401$			4075.53i			0.507536i	−0.967265	+	0.253768i	$0.918330\pi$
$402$		0			0
$403$			3977.48i			0.491644i
$404$	−2172.16	−	1926.51i	−0.267498	−	0.237246i
$405$		0			0
$406$	4919.31	+	10938.3i	0.601333	+	1.33710i
$407$	652.301			0.0794432
$408$		0			0
$409$	14109.6			1.70580			0.852900	−	0.522074i	$-0.174841\pi$
$409$	14109.6			1.70580			0.852900	+	0.522074i	$0.174841\pi$
$410$	−662.032	−	1472.06i	−0.0797450	−	0.177317i
$411$		0			0
$412$	−3221.44	−	2857.12i	−0.385216	−	0.341652i
$413$			4028.56i			0.479982i
$414$		0			0
$415$		−	15484.9i		−	1.83162i
$416$	−1872.44	+	1128.40i	−0.220682	+	0.132991i
$417$		0			0
$418$	−860.107	+	386.817i	−0.100644	+	0.0452628i
$419$	6368.39			0.742521			0.371261	−	0.928529i	$-0.378926\pi$
$419$	6368.39			0.742521			0.371261	+	0.928529i	$0.378926\pi$
$420$		0			0
$421$	10812.5			1.25171			0.625853	−	0.779941i	$-0.284751\pi$
$421$	10812.5			1.25171			0.625853	+	0.779941i	$0.284751\pi$
$422$	−10866.8	+	4887.15i	−1.25353	+	0.563750i
$423$		0			0
$424$	1798.46	−	5754.66i	0.205993	−	0.659130i
$425$			11046.9i			1.26083i
$426$		0			0
$427$		−	30.9588i		−	0.00350867i
$428$	2284.99	−	2576.35i	0.258058	−	0.290963i
$429$		0			0
$430$	12.5134	+	27.8241i	0.00140337	+	0.00312046i
$431$	−10968.4			−1.22583			−0.612913	−	0.790150i	$-0.710002\pi$
$431$	−10968.4			−1.22583			−0.612913	+	0.790150i	$0.710002\pi$
$432$		0			0
$433$	−1491.10			−0.165491			−0.0827457	−	0.996571i	$-0.526369\pi$
$433$	−1491.10			−0.165491			−0.0827457	+	0.996571i	$0.526369\pi$
$434$	7375.49	+	16399.8i	0.815748	+	1.81386i
$435$		0			0
$436$	−4773.87	+	5382.59i	−0.524374	+	0.591237i
$437$		−	9295.56i		−	1.01754i
$438$		0			0
$439$			2225.82i			0.241988i	0.992653	+	0.120994i	$0.0386081\pi$
$439$			2225.82i			0.241988i	−0.992653	+	0.120994i	$0.961392\pi$
$440$	551.408	−	1764.38i	0.0597439	−	0.191167i
$441$		0			0
$442$	−2219.76	+	998.295i	−0.238876	+	0.107430i
$443$	−15877.5			−1.70285			−0.851425	−	0.524477i	$-0.824261\pi$
$443$	−15877.5			−1.70285			−0.851425	+	0.524477i	$0.824261\pi$
$444$		0			0
$445$	−17475.0			−1.86156
$446$	−16556.8	+	7446.11i	−1.75782	+	0.790546i
$447$		0			0
$448$	−5627.95	+	8124.64i	−0.593517	+	0.856816i
$449$		−	11558.7i		−	1.21490i	−0.794358	−	0.607450i	$-0.792193\pi$
$449$		−	11558.7i		−	1.21490i	0.794358	−	0.607450i	$-0.207807\pi$
$450$		0			0
$451$			166.477i			0.0173816i
$452$	2286.59	+	2028.00i	0.237947	+	0.211038i
$453$		0			0
$454$	2609.86	+	5803.16i	0.269795	+	0.599902i
$455$	−3901.29			−0.401967
$456$		0			0
$457$	−10889.7			−1.11466			−0.557329	−	0.830292i	$-0.688174\pi$
$457$	−10889.7			−1.11466			−0.557329	+	0.830292i	$0.688174\pi$
$458$	4026.43	+	8952.96i	0.410792	+	0.913416i
$459$		0			0
$460$	13631.3	+	12089.7i	1.38166	+	1.22540i
$461$		−	11775.1i		−	1.18963i	−0.803862	−	0.594816i	$-0.797225\pi$
$461$		−	11775.1i		−	1.18963i	0.803862	−	0.594816i	$-0.202775\pi$
$462$		0			0
$463$			2659.94i			0.266993i	0.991049	+	0.133497i	$0.0426206\pi$
$463$			2659.94i			0.266993i	−0.991049	+	0.133497i	$0.957379\pi$
$464$	−13958.0	+	1679.15i	−1.39652	+	0.168002i
$465$		0			0
$466$	9938.21	−	4469.52i	0.987937	−	0.444306i
$467$	32.9750			0.00326746			0.00163373	−	0.999999i	$-0.499480\pi$
$467$	32.9750			0.00326746			0.00163373	+	0.999999i	$0.499480\pi$
$468$		0			0
$469$	−8278.68			−0.815083
$470$	−8070.16	+	3629.40i	−0.792018	+	0.356195i
$471$		0			0
$472$	−4507.21	−	1408.61i	−0.439537	−	0.137365i
$473$		−	3.14666i		−	0.000305885i
$474$		0			0
$475$			10589.2i			1.02287i
$476$	−7301.26	+	8232.25i	−0.703052	+	0.792698i
$477$		0			0
$478$	−46.2499	−	102.839i	−0.00442556	−	0.00984046i
$479$	−8138.15			−0.776287			−0.388144	−	0.921599i	$-0.626884\pi$
$479$	−8138.15			−0.776287			−0.388144	+	0.921599i	$0.626884\pi$
$480$		0			0
$481$	1613.70			0.152970
$482$	4012.08	+	8921.07i	0.379140	+	0.843036i
$483$		0			0
$484$	6938.83	−	7823.60i	0.651655	−	0.734748i
$485$			24538.7i			2.29741i
$486$		0			0
$487$			1992.29i			0.185378i	0.995695	+	0.0926891i	$0.0295463\pi$
$487$			1992.29i			0.185378i	−0.995695	+	0.0926891i	$0.970454\pi$
$488$	34.6371	+	10.8249i	0.00321301	+	0.00100414i
$489$		0			0
$490$	−1279.21	+	575.301i	−0.117936	+	0.0530396i
$491$	8814.69			0.810186			0.405093	−	0.914275i	$-0.367239\pi$
$491$	8814.69			0.810186			0.405093	+	0.914275i	$0.367239\pi$
$492$		0			0
$493$	−15651.9			−1.42987
$494$	−2127.78	+	956.929i	−0.193792	+	0.0871544i
$495$		0			0
$496$	−20927.2	+	2517.54i	−1.89447	+	0.227905i
$497$		−	7458.28i		−	0.673138i
$498$		0			0
$499$		−	21076.6i		−	1.89082i	−0.325886	−	0.945409i	$-0.605662\pi$
$499$		−	21076.6i		−	1.89082i	0.325886	−	0.945409i	$-0.394338\pi$
$500$	−3008.58	−	2668.34i	−0.269095	−	0.238663i
$501$		0			0
$502$	3454.36	+	7680.94i	0.307123	+	0.682903i
$503$	19011.6			1.68526			0.842629	−	0.538494i	$-0.181006\pi$
$503$	19011.6			1.68526			0.842629	+	0.538494i	$0.181006\pi$
$504$		0			0
$505$	6073.31			0.535166
$506$	−770.788	−	1713.89i	−0.0677188	−	0.150576i
$507$		0			0
$508$	10042.6	+	8906.88i	0.877103	+	0.777911i
$509$			12812.5i			1.11573i	0.829932	+	0.557865i	$0.188379\pi$
$509$			12812.5i			1.11573i	−0.829932	+	0.557865i	$0.811621\pi$
$510$		0			0
$511$		−	14995.8i		−	1.29819i
$512$	−7122.13	−	9137.45i	−0.614759	−	0.788715i
$513$		0			0
$514$	16660.3	−	7492.64i	1.42968	−	0.642970i
$515$	9007.06			0.770677
$516$		0			0
$517$	912.663			0.0776381
$518$	6653.53	−	2992.30i	0.564361	−	0.253811i
$519$		0			0
$520$	1364.10	−	4364.81i	0.115038	−	0.368096i
$521$		−	14455.7i		−	1.21558i	−0.794100	−	0.607788i	$-0.792057\pi$
$521$		−	14455.7i		−	1.21558i	0.794100	−	0.607788i	$-0.207943\pi$
$522$		0			0
$523$			15232.9i			1.27359i	0.771032	+	0.636796i	$0.219741\pi$
$523$			15232.9i			1.27359i	−0.771032	+	0.636796i	$0.780259\pi$
$524$	−7563.45	+	8527.86i	−0.630555	+	0.710957i
$525$		0			0
$526$	6823.74	+	15172.9i	0.565645	+	1.25774i
$527$	−23466.7			−1.93971
$528$		0			0
$529$	6355.73			0.522375
$530$	5172.84	+	11502.1i	0.423950	+	0.942675i
$531$		0			0
$532$	−6998.72	+	7891.13i	−0.570363	+	0.643090i
$533$			411.841i			0.0334687i
$534$		0			0
$535$			7203.40i			0.582113i
$536$	2894.68	−	9262.30i	0.233267	−	0.746400i
$537$		0			0
$538$	7653.73	−	3442.12i	0.613338	−	0.275837i
$539$	144.667			0.0115608
$540$		0			0
$541$	−23075.7			−1.83383			−0.916915	−	0.399083i	$-0.869328\pi$
$541$	−23075.7			−1.83383			−0.916915	+	0.399083i	$0.869328\pi$
$542$	−5122.46	+	2303.73i	−0.405956	+	0.182571i
$543$		0			0
$544$	−6657.43	−	11047.2i	−0.524697	−	0.870670i
$545$		−	15049.6i		−	1.18285i
$546$		0			0
$547$			366.215i			0.0286256i	0.999898	+	0.0143128i	$0.00455607\pi$
$547$			366.215i			0.0286256i	−0.999898	+	0.0143128i	$0.995444\pi$
$548$	160.540	+	142.385i	0.0125145	+	0.0110992i
$549$		0			0
$550$	878.056	+	1952.40i	0.0680735	+	0.151365i
$551$	−15003.3			−1.16000
$552$		0			0
$553$	1526.87			0.117412
$554$	5038.31	+	11202.9i	0.386385	+	0.859147i
$555$		0			0
$556$	9914.42	+	8793.20i	0.756232	+	0.670710i
$557$		−	3402.66i		−	0.258842i	−0.991590	−	0.129421i	$-0.958688\pi$
$557$		−	3402.66i		−	0.258842i	0.991590	−	0.129421i	$-0.0413119\pi$
$558$		0			0
$559$		−	7.78437i		−	0.000588987i
$560$	−2469.31	−	20526.3i	−0.186335	−	1.54892i
$561$		0			0
$562$	20112.0	−	9044.97i	1.50956	−	0.678895i
$563$	4922.90			0.368518			0.184259	−	0.982878i	$-0.441011\pi$
$563$	4922.90			0.368518			0.184259	+	0.982878i	$0.441011\pi$
$564$		0			0
$565$	−6393.26			−0.476047
$566$	−5276.53	+	2373.02i	−0.391854	+	0.176229i
$567$		0			0
$568$	8344.42	+	2607.82i	0.616416	+	0.192644i
$569$		−	12036.3i		−	0.886799i	−0.896324	−	0.443399i	$-0.853772\pi$
$569$		−	12036.3i		−	0.886799i	0.896324	−	0.443399i	$-0.146228\pi$
$570$		0			0
$571$			603.568i			0.0442356i	0.999755	+	0.0221178i	$0.00704090\pi$
$571$			603.568i			0.0442356i	−0.999755	+	0.0221178i	$0.992959\pi$
$572$	−312.965	+	352.871i	−0.0228772	+	0.0257942i
$573$		0			0
$574$	763.680	+	1698.08i	0.0555321	+	0.123478i
$575$	−21100.5			−1.53035
$576$		0			0
$577$	−6971.52			−0.502995			−0.251497	−	0.967858i	$-0.580923\pi$
$577$	−6971.52			−0.502995			−0.251497	+	0.967858i	$0.580923\pi$
$578$	−190.215	−	422.952i	−0.0136884	−	0.0304368i
$579$		0			0
$580$	19513.2	−	22001.3i	1.39697	−	1.57509i
$581$			17862.4i			1.27549i
$582$		0			0
$583$		−	1300.78i		−	0.0924063i
$584$	16777.5	+	5243.34i	1.18880	+	0.371525i
$585$		0			0
$586$	6081.15	−	2734.88i	0.428686	−	0.192793i
$587$	20669.8			1.45338			0.726691	−	0.686964i	$-0.241057\pi$
$587$	20669.8			1.45338			0.726691	+	0.686964i	$0.241057\pi$
$588$		0			0
$589$	−22494.3			−1.57362
$590$	9008.74	−	4051.51i	0.628617	−	0.282709i
$591$		0			0
$592$	1021.39	+	8490.33i	0.0709102	+	0.589443i
$593$			2417.22i			0.167392i	0.996491	+	0.0836958i	$0.0266724\pi$
$593$			2417.22i			0.167392i	−0.996491	+	0.0836958i	$0.973328\pi$
$594$		0			0
$595$		−	23017.2i		−	1.58590i
$596$	−5102.33	−	4525.31i	−0.350670	−	0.311013i
$597$		0			0
$598$	−1906.82	−	4239.91i	−0.130394	−	0.289938i
$599$	28934.9			1.97370			0.986852	−	0.161628i	$-0.0516745\pi$
$599$	28934.9			1.97370			0.986852	+	0.161628i	$0.0516745\pi$
$600$		0			0
$601$	636.493			0.0431998			0.0215999	−	0.999767i	$-0.493124\pi$
$601$	636.493			0.0431998			0.0215999	+	0.999767i	$0.493124\pi$
$602$	−14.4346	−	32.0962i	−0.000977263	−	0.00217299i
$603$		0			0
$604$	−8791.25	−	7797.05i	−0.592237	−	0.525261i
$605$			21874.6i			1.46997i
$606$		0			0
$607$			19186.8i			1.28298i	0.767131	+	0.641490i	$0.221683\pi$
$607$			19186.8i			1.28298i	−0.767131	+	0.641490i	$0.778317\pi$
$608$	−6381.57	−	10589.4i	−0.425669	−	0.706346i
$609$		0			0
$610$	−69.2305	+	31.1351i	−0.00459518	+	0.00206660i
$611$	2257.80			0.149494
$612$		0			0
$613$	6429.22			0.423612			0.211806	−	0.977312i	$-0.432066\pi$
$613$	6429.22			0.423612			0.211806	+	0.977312i	$0.432066\pi$
$614$	14242.5	−	6405.28i	0.936122	−	0.421003i
$615$		0			0
$616$	−636.070	+	2035.28i	−0.0416039	+	0.133123i
$617$		−	6956.82i		−	0.453924i	−0.973904	−	0.226962i	$-0.927121\pi$
$617$		−	6956.82i		−	0.453924i	0.973904	−	0.226962i	$-0.0728794\pi$
$618$		0			0
$619$		−	22202.0i		−	1.44164i	−0.693123	−	0.720819i	$-0.743766\pi$
$619$		−	22202.0i		−	1.44164i	0.693123	−	0.720819i	$-0.256234\pi$
$620$	29255.9	−	32986.4i	1.89508	−	2.13672i
$621$		0			0
$622$	1780.37	+	3958.75i	0.114769	+	0.255195i
$623$	20158.1			1.29634
$624$		0			0
$625$	−10967.9			−0.701945
$626$	10170.2	+	22613.9i	0.649331	+	1.44382i
$627$		0			0
$628$	−14274.2	+	16094.4i	−0.907013	+	1.02267i
$629$			9520.65i			0.603519i
$630$		0			0
$631$			529.250i			0.0333901i	0.999861	+	0.0166950i	$0.00531444\pi$
$631$			529.250i			0.0333901i	−0.999861	+	0.0166950i	$0.994686\pi$
$632$	−533.876	+	1708.28i	−0.0336020	+	0.107519i
$633$		0			0
$634$	−18093.5	+	8137.20i	−1.13341	+	0.509731i
$635$	−28078.9			−1.75477
$636$		0			0
$637$	357.886			0.0222605
$638$	−2766.27	+	1244.08i	−0.171658	+	0.0771997i
$639$		0			0
$640$	23828.5	+	4414.40i	1.47172	+	0.272648i
$641$			22939.6i			1.41351i	0.707458	+	0.706755i	$0.249842\pi$
$641$			22939.6i			1.41351i	−0.707458	+	0.706755i	$0.750158\pi$
$642$		0			0
$643$			2519.76i			0.154540i	0.997010	+	0.0772702i	$0.0246204\pi$
$643$			2519.76i			0.154540i	−0.997010	+	0.0772702i	$0.975380\pi$
$644$	−15724.2	−	13946.0i	−0.962144	−	0.853335i
$645$		0			0
$646$	−5645.78	−	12553.7i	−0.343855	−	0.764579i
$647$	5938.61			0.360851			0.180426	−	0.983589i	$-0.442252\pi$
$647$	5938.61			0.360851			0.180426	+	0.983589i	$0.442252\pi$
$648$		0			0
$649$	−1018.81			−0.0616205
$650$	2172.18	+	4829.96i	0.131077	+	0.291456i
$651$		0			0
$652$	−13086.5	−	11606.6i	−0.786054	−	0.697159i
$653$		−	26052.5i		−	1.56128i	−0.624984	−	0.780638i	$-0.714894\pi$
$653$		−	26052.5i		−	1.56128i	0.624984	−	0.780638i	$-0.285106\pi$
$654$		0			0
$655$		−	23843.7i		−	1.42237i
$656$	−2166.86	+	260.674i	−0.128966	+	0.0155146i
$657$		0			0
$658$	9309.24	−	4186.66i	0.551538	−	0.248044i
$659$	28353.5			1.67602			0.838008	−	0.545659i	$-0.183720\pi$
$659$	28353.5			1.67602			0.838008	+	0.545659i	$0.183720\pi$
$660$		0			0
$661$	−10336.1			−0.608210			−0.304105	−	0.952638i	$-0.598357\pi$
$661$	−10336.1			−0.608210			−0.304105	+	0.952638i	$0.598357\pi$
$662$	25506.6	−	11471.1i	1.49749	−	0.673469i
$663$		0			0
$664$	−19984.8	−	6245.69i	−1.16801	−	0.365030i
$665$		−	22063.4i		−	1.28659i
$666$		0			0
$667$		−	29896.3i		−	1.73551i
$668$	19010.5	−	21434.6i	1.10111	−	1.24151i
$669$		0			0
$670$	8325.83	+	18512.9i	0.480082	+	1.06749i
$671$	7.82936			0.000450446
$672$		0			0
$673$	−15083.9			−0.863957			−0.431979	−	0.901884i	$-0.642184\pi$
$673$	−15083.9			−0.863957			−0.431979	+	0.901884i	$0.642184\pi$
$674$	−5810.05	−	12918.9i	−0.332040	−	0.738307i
$675$		0			0
$676$	10888.1	−	12276.4i	0.619486	−	0.698477i
$677$			13710.5i			0.778343i	0.921165	+	0.389172i	$0.127239\pi$
$677$			13710.5i			0.778343i	−0.921165	+	0.389172i	$0.872761\pi$
$678$		0			0
$679$		−	28306.4i		−	1.59985i
$680$	25751.9	+	8048.06i	1.45227	+	0.453866i
$681$		0			0
$682$	−4147.44	+	1865.23i	−0.232865	+	0.104726i
$683$	−807.274			−0.0452262			−0.0226131	−	0.999744i	$-0.507199\pi$
$683$	−807.274			−0.0452262			−0.0226131	+	0.999744i	$0.507199\pi$
$684$		0			0
$685$	−448.867			−0.0250370
$686$	−15604.1	+	7017.66i	−0.868467	+	0.390577i
$687$		0			0
$688$	40.9568	−	4.92711i	0.00226957	−	0.000273030i
$689$		−	3217.95i		−	0.177930i
$690$		0			0
$691$			21946.7i			1.20824i	0.796894	+	0.604119i	$0.206475\pi$
$691$			21946.7i			1.20824i	−0.796894	+	0.604119i	$0.793525\pi$
$692$	−653.130	−	579.268i	−0.0358790	−	0.0318215i
$693$		0			0
$694$	−9043.13	−	20107.9i	−0.494629	−	1.09983i
$695$	−27720.5			−1.51295
$696$		0			0
$697$	−2429.82			−0.132046
$698$	−10535.7	−	23426.6i	−0.571320	−	1.27036i
$699$		0			0
$700$	17912.5	+	15886.8i	0.967183	+	0.857804i
$701$			3170.45i			0.170822i	0.996346	+	0.0854110i	$0.0272203\pi$
$701$			3170.45i			0.170822i	−0.996346	+	0.0854110i	$0.972780\pi$
$702$		0			0
$703$			9126.15i			0.489615i
$704$	−2054.69	−	1423.29i	−0.109999	−	0.0761963i
$705$		0			0
$706$	11749.3	−	5284.04i	0.626334	−	0.281682i
$707$	−7005.80			−0.372674
$708$		0			0
$709$	2826.07			0.149697			0.0748485	−	0.997195i	$-0.476153\pi$
$709$	2826.07			0.149697			0.0748485	+	0.997195i	$0.476153\pi$
$710$	−16678.3	+	7500.76i	−0.881586	+	0.396477i
$711$		0			0
$712$	−7048.37	+	22553.2i	−0.370996	+	1.18710i
$713$		−	44823.2i		−	2.35434i
$714$		0			0
$715$		−	986.621i		−	0.0516049i
$716$	1424.73	−	1606.40i	0.0743640	−	0.0838462i
$717$		0			0
$718$	6282.11	+	13968.6i	0.326527	+	0.726049i
$719$	−15469.9			−0.802408			−0.401204	−	0.915989i	$-0.631408\pi$
$719$	−15469.9			−0.802408			−0.401204	+	0.915989i	$0.631408\pi$
$720$		0			0
$721$	−10390.0			−0.536677
$722$	2545.35	+	5659.73i	0.131203	+	0.291736i
$723$		0			0
$724$	−4769.93	+	5378.15i	−0.244853	+	0.276074i
$725$			34056.8i			1.74460i
$726$		0			0
$727$		−	7967.56i		−	0.406465i	−0.979130	−	0.203233i	$-0.934855\pi$
$727$		−	7967.56i		−	0.406465i	0.979130	−	0.203233i	$-0.0651448\pi$
$728$	−1573.55	+	5034.98i	−0.0801092	+	0.256331i
$729$		0			0
$730$	−33533.8	+	15081.2i	−1.70019	+	0.764629i
$731$	45.9270			0.00232376
$732$		0			0
$733$	24669.3			1.24308			0.621542	−	0.783381i	$-0.286506\pi$
$733$	24669.3			1.24308			0.621542	+	0.783381i	$0.286506\pi$
$734$	−27488.3	+	12362.3i	−1.38230	+	0.621664i
$735$		0			0
$736$	21101.0	−	12716.2i	1.05678	−	0.636855i
$737$		−	2093.65i		−	0.104641i
$738$		0			0
$739$			1182.09i			0.0588414i	0.999567	+	0.0294207i	$0.00936624\pi$
$739$			1182.09i			0.0588414i	−0.999567	+	0.0294207i	$0.990634\pi$
$740$	−13382.9	−	11869.4i	−0.664816	−	0.589632i
$741$		0			0
$742$	−5967.07	−	13268.1i	−0.295226	−	0.656451i
$743$	27232.9			1.34465			0.672327	−	0.740255i	$-0.265295\pi$
$743$	27232.9			1.34465			0.672327	+	0.740255i	$0.265295\pi$
$744$		0			0
$745$	14266.0			0.701565
$746$	3143.87	+	6990.55i	0.154296	+	0.343086i
$747$		0			0
$748$	−2081.90	−	1846.46i	−0.101767	−	0.0902584i
$749$		−	8309.41i		−	0.405366i
$750$		0			0
$751$			14188.0i			0.689383i	0.938716	+	0.344692i	$0.112017\pi$
$751$			14188.0i			0.689383i	−0.938716	+	0.344692i	$0.887983\pi$
$752$	1429.07	+	11879.2i	0.0692989	+	0.576050i
$753$		0			0
$754$	−6843.34	+	3077.66i	−0.330530	+	0.148650i
$755$	24580.1			1.18485
$756$		0			0
$757$	30482.1			1.46353			0.731764	−	0.681559i	$-0.238698\pi$
$757$	30482.1			1.46353			0.731764	+	0.681559i	$0.238698\pi$
$758$	−16497.2	+	7419.31i	−0.790509	+	0.355517i
$759$		0			0
$760$	24684.9	+	7714.58i	1.17818	+	0.368207i
$761$		−	23077.5i		−	1.09929i	−0.835398	−	0.549645i	$-0.814763\pi$
$761$		−	23077.5i		−	1.09929i	0.835398	−	0.549645i	$-0.185237\pi$
$762$		0			0
$763$			17360.3i			0.823703i
$764$	2731.98	−	3080.33i	0.129371	−	0.145867i
$765$		0			0
$766$	1583.73	+	3521.51i	0.0747031	+	0.166106i
$767$	−2520.38			−0.118652
$768$		0			0
$769$	2070.62			0.0970982			0.0485491	−	0.998821i	$-0.484540\pi$
$769$	2070.62			0.0970982			0.0485491	+	0.998821i	$0.484540\pi$
$770$	−1829.50	−	4067.99i	−0.0856242	−	0.190390i
$771$		0			0
$772$	13054.8	−	14719.4i	0.608617	−	0.686222i
$773$		−	35103.0i		−	1.63333i	−0.577110	−	0.816666i	$-0.695820\pi$
$773$		−	35103.0i		−	1.63333i	0.577110	−	0.816666i	$-0.304180\pi$
$774$		0			0
$775$			51061.1i			2.36667i
$776$	31669.6	+	9897.45i	1.46504	+	0.457858i
$777$		0			0
$778$	−16027.5	+	7208.04i	−0.738576	+	0.332161i
$779$	−2329.13			−0.107124
$780$		0			0
$781$	1886.17			0.0864180
$782$	25015.0	−	11250.0i	1.14391	−	0.514450i
$783$		0			0
$784$	226.523	+	1882.98i	0.0103190	+	0.0857774i
$785$		−	44999.4i		−	2.04599i
$786$		0			0
$787$			23811.0i			1.07849i	0.842149	+	0.539245i	$0.181290\pi$
$787$			23811.0i			1.07849i	−0.842149	+	0.539245i	$0.818710\pi$
$788$	−3869.43	−	3431.84i	−0.174928	−	0.155145i
$789$		0			0
$790$	−1535.56	−	3414.41i	−0.0691556	−	0.153771i
$791$	7374.87			0.331505
$792$		0			0
$793$	19.3687			0.000867343
$794$	3818.72	+	8491.13i	0.170682	+	0.379520i
$795$		0			0
$796$	10432.0	+	9252.22i	0.464512	+	0.411980i
$797$		−	2401.17i		−	0.106718i	−0.998575	−	0.0533588i	$-0.983007\pi$
$797$		−	2401.17i		−	0.106718i	0.998575	−	0.0533588i	$-0.0169927\pi$
$798$		0			0
$799$			13320.8i			0.589805i
$800$	−24037.5	+	14485.9i	−1.06232	+	0.640190i
$801$		0			0
$802$	−10513.1	+	4728.06i	−0.462880	+	0.208171i
$803$	3792.37			0.166662
$804$		0			0
$805$	43964.5			1.92490
$806$	−10260.2	+	4614.32i	−0.448386	+	0.201653i
$807$		0			0
$808$	2449.61	−	7838.19i	0.106655	−	0.341270i
$809$			29338.0i			1.27499i	0.770453	+	0.637497i	$0.220030\pi$
$809$			29338.0i			1.27499i	−0.770453	+	0.637497i	$0.779970\pi$
$810$		0			0
$811$			30884.9i			1.33726i	0.743597	+	0.668629i	$0.233118\pi$
$811$			30884.9i			1.33726i	−0.743597	+	0.668629i	$0.766882\pi$
$812$	−22509.2	+	25379.4i	−0.972806	+	1.09685i
$813$		0			0
$814$	756.741	+	1682.65i	0.0325845	+	0.0724532i
$815$	36589.6			1.57261
$816$		0			0
$817$	44.0239			0.00188519
$818$	16368.6	+	36396.5i	0.699653	+	1.55571i
$819$		0			0
$820$	3029.25	−	3415.51i	0.129007	−	0.145457i
$821$			20041.8i			0.851965i	0.904731	+	0.425983i	$0.140072\pi$
$821$			20041.8i			0.851965i	−0.904731	+	0.425983i	$0.859928\pi$
$822$		0			0
$823$		−	6233.57i		−	0.264020i	−0.991248	−	0.132010i	$-0.957857\pi$
$823$		−	6233.57i		−	0.264020i	0.991248	−	0.132010i	$-0.0421431\pi$
$824$	3632.91	−	11624.5i	0.153590	−	0.491454i
$825$		0			0
$826$	−10391.9	+	4673.57i	−0.437750	+	0.196870i
$827$	43288.8			1.82019			0.910096	−	0.414397i	$-0.136007\pi$
$827$	43288.8			1.82019			0.910096	+	0.414397i	$0.136007\pi$
$828$		0			0
$829$	−15655.6			−0.655902			−0.327951	−	0.944695i	$-0.606358\pi$
$829$	−15655.6			−0.655902			−0.327951	+	0.944695i	$0.606358\pi$
$830$	39944.3	−	17964.2i	1.67047	−	0.751261i
$831$		0			0
$832$	−5083.01	−	3521.01i	−0.211805	−	0.146718i
$833$			2111.49i			0.0878256i
$834$		0			0
$835$			59930.6i			2.48381i
$836$	−1995.64	−	1769.95i	−0.0825605	−	0.0732237i
$837$		0			0
$838$	7388.04	+	16427.7i	0.304553	+	0.677189i
$839$	−45586.9			−1.87585			−0.937924	−	0.346842i	$-0.887254\pi$
$839$	−45586.9			−1.87585			−0.937924	+	0.346842i	$0.887254\pi$
$840$		0			0
$841$	−23864.5			−0.978493
$842$	12543.7	+	27891.5i	0.513401	+	1.14157i
$843$		0			0
$844$	−25213.4	−	22362.0i	−1.02830	−	0.912006i
$845$			34324.6i			1.39740i
$846$		0			0
$847$		−	25233.2i		−	1.02364i
$848$	16930.9	−	2036.79i	0.685626	−	0.0824809i
$849$		0			0
$850$	−28496.2	+	12815.6i	−1.14990	+	0.517145i
$851$	−18185.2			−0.732526
$852$		0			0
$853$	2637.97			0.105888			0.0529439	−	0.998597i	$-0.483140\pi$
$853$	2637.97			0.105888			0.0529439	+	0.998597i	$0.483140\pi$
$854$	79.8601	−	35.9156i	0.00319995	−	0.00143912i
$855$		0			0
$856$	9296.68	+	2905.42i	0.371208	+	0.116011i
$857$			24327.4i			0.969670i	0.874606	+	0.484835i	$0.161120\pi$
$857$			24327.4i			0.969670i	−0.874606	+	0.484835i	$0.838880\pi$
$858$		0			0
$859$		−	44905.2i		−	1.78364i	−0.452391	−	0.891819i	$-0.649429\pi$
$859$		−	44905.2i		−	1.78364i	0.452391	−	0.891819i	$-0.350571\pi$
$860$	−57.2571	+	64.5580i	−0.00227029	+	0.00255978i
$861$		0			0
$862$	−12724.6	−	28293.8i	−0.502786	−	1.11797i
$863$	3830.25			0.151081			0.0755406	−	0.997143i	$-0.475932\pi$
$863$	3830.25			0.151081			0.0755406	+	0.997143i	$0.475932\pi$
$864$		0			0
$865$	1826.14			0.0717809
$866$	−1729.84	−	3846.39i	−0.0678781	−	0.150930i
$867$		0			0
$868$	−33747.9	+	38051.1i	−1.31967	+	1.48795i
$869$			386.139i			0.0150735i
$870$		0			0
$871$		−	5179.38i		−	0.201489i
$872$	−19423.0	−	6070.11i	−0.754294	−	0.235734i
$873$		0			0
$874$	23978.5	−	10783.9i	0.928014	−	0.417357i
$875$	−9703.47			−0.374900
$876$		0			0
$877$	25099.3			0.966412			0.483206	−	0.875507i	$-0.339472\pi$
$877$	25099.3			0.966412			0.483206	+	0.875507i	$0.339472\pi$
$878$	−5741.64	+	2582.19i	−0.220696	+	0.0992538i
$879$		0			0
$880$	5191.02	−	624.480i	0.198851	−	0.0239218i
$881$		−	3336.88i		−	0.127608i	−0.997962	−	0.0638038i	$-0.979677\pi$
$881$		−	3336.88i		−	0.127608i	0.997962	−	0.0638038i	$-0.0203232\pi$
$882$		0			0
$883$		−	26792.8i		−	1.02112i	−0.859841	−	0.510561i	$-0.829438\pi$
$883$		−	26792.8i		−	1.02112i	0.859841	−	0.510561i	$-0.170562\pi$
$884$	−5150.33	−	4567.88i	−0.195955	−	0.173795i
$885$		0			0
$886$	−18419.6	−	40957.0i	−0.698442	−	1.55302i
$887$	−26009.8			−0.984580			−0.492290	−	0.870431i	$-0.663840\pi$
$887$	−26009.8			−0.984580			−0.492290	+	0.870431i	$0.663840\pi$
$888$		0			0
$889$	32390.1			1.22197
$890$	−20272.9	−	45077.9i	−0.763539	−	1.69777i
$891$		0			0
$892$	−38415.4	−	34071.0i	−1.44198	−	1.27890i
$893$			12768.8i			0.478490i
$894$		0			0
$895$			4491.45i			0.167746i
$896$	−27487.1	−	5092.18i	−1.02486	−	0.189864i
$897$		0			0
$898$	29816.5	−	13409.4i	1.10800	−	0.498304i
$899$	−72346.0			−2.68395
$900$		0			0
$901$	18985.5			0.701998
$902$	−429.439	+	193.132i	−0.0158523	+	0.00712926i
$903$		0			0
$904$	−2578.66	+	8251.11i	−0.0948727	+	0.303571i
$905$		−	15037.2i		−	0.552324i
$906$		0			0
$907$		−	27354.8i		−	1.00144i	−0.865610	−	0.500718i	$-0.833069\pi$
$907$		−	27354.8i		−	1.00144i	0.865610	−	0.500718i	$-0.166931\pi$
$908$	−11941.9	+	13464.6i	−0.436460	+	0.492113i
$909$		0			0
$910$	−4525.92	−	10063.6i	−0.164871	−	0.366599i
$911$	−5323.87			−0.193620			−0.0968100	−	0.995303i	$-0.530864\pi$
$911$	−5323.87			−0.193620			−0.0968100	+	0.995303i	$0.530864\pi$
$912$		0			0
$913$	−4517.35			−0.163748
$914$	−12633.2	−	28090.7i	−0.457189	−	1.01658i
$915$		0			0
$916$	−18423.6	+	20772.8i	−0.664557	+	0.749295i
$917$			27504.7i			0.990495i
$918$		0			0
$919$		−	3951.52i		−	0.141837i	−0.997482	−	0.0709187i	$-0.977407\pi$
$919$		−	3951.52i		−	0.141837i	0.997482	−	0.0709187i	$-0.0225931\pi$
$920$	−15372.4	+	49188.1i	−0.550884	+	1.76270i
$921$		0			0
$922$	30374.6	−	13660.4i	1.08496	−	0.487940i
$923$	4666.11			0.166400
$924$		0			0
$925$	20715.9			0.736362
$926$	−6861.49	+	3085.82i	−0.243502	+	0.109510i
$927$		0			0
$928$	−20524.3	−	34057.6i	−0.726017	−	1.20474i
$929$		−	3123.74i		−	0.110319i	−0.998478	−	0.0551597i	$-0.982433\pi$
$929$		−	3123.74i		−	0.110319i	0.998478	−	0.0551597i	$-0.0175668\pi$
$930$		0			0
$931$			2024.00i			0.0712501i
$932$	23058.8	+	20451.1i	0.810426	+	0.718775i
$933$		0			0
$934$	38.2547	+	85.0612i	0.00134018	+	0.00297996i
$935$	5820.96			0.203600
$936$		0			0
$937$	24002.2			0.836838			0.418419	−	0.908254i	$-0.362584\pi$
$937$	24002.2			0.836838			0.418419	+	0.908254i	$0.362584\pi$
$938$	−9604.17	−	21355.4i	−0.334315	−	0.743366i
$939$		0			0
$940$	−18724.5	−	16607.0i	−0.649710	−	0.576234i
$941$			48617.9i			1.68427i	0.539267	+	0.842135i	$0.318701\pi$
$941$			48617.9i			1.68427i	−0.539267	+	0.842135i	$0.681299\pi$
$942$		0			0
$943$		−	4641.13i		−	0.160272i
$944$	−1595.27	−	13260.8i	−0.0550019	−	0.457205i
$945$		0			0
$946$	8.11700	−	3.65047i	0.000278971	−	0.000125462i
$947$	19740.7			0.677388			0.338694	−	0.940897i	$-0.390015\pi$
$947$	19740.7			0.677388			0.338694	+	0.940897i	$0.390015\pi$
$948$		0			0
$949$	9381.78			0.320912
$950$	−27315.5	+	12284.6i	−0.932874	+	0.419542i
$951$		0			0
$952$	−29705.9	−	9283.75i	−1.01132	−	0.316059i
$953$		−	47895.5i		−	1.62800i	−0.580863	−	0.814002i	$-0.697285\pi$
$953$		−	47895.5i		−	1.62800i	0.580863	−	0.814002i	$-0.302715\pi$
$954$		0			0
$955$			8612.54i			0.291827i
$956$	211.625	−	238.609i	0.00715944	−	0.00807234i
$957$		0			0
$958$	−9441.15	−	20992.9i	−0.318403	−	0.707984i
$959$	517.786			0.0174350
$960$		0			0
$961$	−78676.8			−2.64096
$962$	1872.07	+	4162.64i	0.0627421	+	0.139510i
$963$		0			0
$964$	−18358.0	+	20698.8i	−0.613352	+	0.691561i
$965$			41155.1i			1.37288i
$966$		0			0
$967$			46121.5i			1.53378i	0.641776	+	0.766892i	$0.278198\pi$
$967$			46121.5i			1.53378i	−0.641776	+	0.766892i	$0.721802\pi$
$968$	28231.3	+	8822.91i	0.937383	+	0.292953i
$969$		0			0
$970$	−63299.2	+	28467.6i	−2.09527	+	0.942309i
$971$	−51058.5			−1.68748			−0.843741	−	0.536751i	$-0.819651\pi$
$971$	−51058.5			−1.68748			−0.843741	+	0.536751i	$0.819651\pi$
$972$		0			0
$973$	31976.7			1.05357
$974$	−5139.23	+	2311.27i	−0.169067	+	0.0760349i
$975$		0			0
$976$	12.2594	+	101.907i	0.000402063	+	0.00334216i
$977$			22394.9i			0.733342i	0.930351	+	0.366671i	$0.119502\pi$
$977$			22394.9i			0.733342i	−0.930351	+	0.366671i	$0.880498\pi$
$978$		0			0
$979$			5097.91i			0.166425i
$980$	−2968.05	−	2632.39i	−0.0967457	−	0.0858047i
$981$		0			0
$982$	10226.0	+	22738.0i	0.332307	+	0.738900i
$983$	13397.6			0.434706			0.217353	−	0.976093i	$-0.430258\pi$
$983$	13397.6			0.434706			0.217353	+	0.976093i	$0.430258\pi$
$984$		0			0
$985$	10818.9			0.349967
$986$	−18157.9	−	40375.0i	−0.586476	−	1.30406i
$987$		0			0
$988$	−4936.92	−	4378.60i	−0.158972	−	0.140994i
$989$			87.7240i			0.00282049i
$990$		0			0
$991$		−	24672.3i		−	0.790858i	−0.918496	−	0.395429i	$-0.870596\pi$
$991$		−	24672.3i		−	0.790858i	0.918496	−	0.395429i	$-0.129404\pi$
$992$	−30772.0	−	51062.3i	−0.984890	−	1.63430i
$993$		0			0
$994$	19239.1	−	8652.42i	0.613910	−	0.276095i
$995$	−29167.6			−0.929320
$996$		0			0
$997$	58064.2			1.84445			0.922223	−	0.386659i	$-0.126371\pi$
$997$	58064.2			1.84445			0.922223	+	0.386659i	$0.126371\pi$
$998$	54368.4	−	24451.2i	1.72445	−	0.775539i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.4.b.c.323.16		24
3.2	odd	2	inner	324.4.b.c.323.9		24
4.3	odd	2	inner	324.4.b.c.323.10		24
9.2	odd	6		36.4.h.b.23.4	yes	24
9.4	even	3		36.4.h.b.11.1	✓	24
9.5	odd	6		108.4.h.b.35.12		24
9.7	even	3		108.4.h.b.71.9		24
12.11	even	2	inner	324.4.b.c.323.15		24
36.7	odd	6		108.4.h.b.71.12		24
36.11	even	6		36.4.h.b.23.1	yes	24
36.23	even	6		108.4.h.b.35.9		24
36.31	odd	6		36.4.h.b.11.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.1	✓	24	9.4	even	3
36.4.h.b.11.4	yes	24	36.31	odd	6
36.4.h.b.23.1	yes	24	36.11	even	6
36.4.h.b.23.4	yes	24	9.2	odd	6
108.4.h.b.35.9		24	36.23	even	6
108.4.h.b.35.12		24	9.5	odd	6
108.4.h.b.71.9		24	9.7	even	3
108.4.h.b.71.12		24	36.7	odd	6
324.4.b.c.323.9		24	3.2	odd	2	inner
324.4.b.c.323.10		24	4.3	odd	2	inner
324.4.b.c.323.15		24	12.11	even	2	inner
324.4.b.c.323.16		24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	324.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16011 + 2.57956i) q^{2} +(-5.30829 + 5.98515i) q^{4} -16.7343i q^{5} +19.3037i q^{7} +(-21.5973 - 6.74964i) q^{8} +O(q^{10})\)	\(q+(1.16011 + 2.57956i) q^{2} +(-5.30829 + 5.98515i) q^{4} -16.7343i q^{5} +19.3037i q^{7} +(-21.5973 - 6.74964i) q^{8} +(43.1673 - 19.4137i) q^{10} -4.88184 q^{11} -12.0770 q^{13} +(-49.7952 + 22.3944i) q^{14} +(-7.64410 - 63.5419i) q^{16} -71.2528i q^{17} -68.3003i q^{19} +(100.158 + 88.8308i) q^{20} +(-5.66347 - 12.5930i) q^{22} +136.098 q^{23} -155.038 q^{25} +(-14.0106 - 31.1533i) q^{26} +(-115.536 - 102.470i) q^{28} -219.667i q^{29} -329.345i q^{31} +(155.042 - 93.4340i) q^{32} +(183.801 - 82.6611i) q^{34} +323.035 q^{35} -133.618 q^{37} +(176.185 - 79.2359i) q^{38} +(-112.951 + 361.416i) q^{40} -34.1013i q^{41} +0.644564i q^{43} +(25.9142 - 29.2186i) q^{44} +(157.889 + 351.074i) q^{46} -186.951 q^{47} -29.6338 q^{49} +(-179.862 - 399.931i) q^{50} +(64.1080 - 72.2825i) q^{52} +266.453i q^{53} +81.6944i q^{55} +(130.293 - 416.908i) q^{56} +(566.644 - 254.838i) q^{58} +208.694 q^{59} -1.60377 q^{61} +(849.565 - 382.076i) q^{62} +(420.885 + 291.548i) q^{64} +202.100i q^{65} +428.864i q^{67} +(426.459 + 378.231i) q^{68} +(374.756 + 833.290i) q^{70} -386.365 q^{71} -776.832 q^{73} +(-155.011 - 344.676i) q^{74} +(408.788 + 362.558i) q^{76} -94.2377i q^{77} -79.0970i q^{79} +(-1063.33 + 127.919i) q^{80} +(87.9665 - 39.5613i) q^{82} +925.337 q^{83} -1192.37 q^{85} +(-1.66269 + 0.747765i) q^{86} +(105.434 + 32.9506i) q^{88} -1044.26i q^{89} -233.130i q^{91} +(-722.449 + 814.569i) q^{92} +(-216.883 - 482.251i) q^{94} -1142.96 q^{95} -1466.37 q^{97} +(-34.3784 - 76.4422i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4}+O(q^{10}) \) 24 * q + 24 * q^4	\( 24 q + 24 q^{4} + 96 q^{10} + 432 q^{13} + 144 q^{16} + 384 q^{22} - 504 q^{25} - 672 q^{28} + 1320 q^{34} + 1248 q^{37} - 1272 q^{40} + 960 q^{46} - 696 q^{49} - 264 q^{52} - 1032 q^{58} + 528 q^{61} + 960 q^{64} - 1128 q^{70} - 4776 q^{73} + 1200 q^{76} - 4104 q^{82} - 1440 q^{85} - 3912 q^{88} + 2376 q^{94} - 1176 q^{97}+O(q^{100}) \) 24 * q + 24 * q^4 + 96 * q^10 + 432 * q^13 + 144 * q^16 + 384 * q^22 - 504 * q^25 - 672 * q^28 + 1320 * q^34 + 1248 * q^37 - 1272 * q^40 + 960 * q^46 - 696 * q^49 - 264 * q^52 - 1032 * q^58 + 528 * q^61 + 960 * q^64 - 1128 * q^70 - 4776 * q^73 + 1200 * q^76 - 4104 * q^82 - 1440 * q^85 - 3912 * q^88 + 2376 * q^94 - 1176 * q^97

Introduction

L-functions

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