LMFDB - Embedded newform 324.4.b.c.323.18

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			323.18
Character	$\chi$	$=$	324.323
Dual form			324.4.b.c.323.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.04896 + 1.94981i) q^{2} +(0.396477 + 7.99017i) q^{4} +16.5019i q^{5} +22.2418i q^{7} +(-14.7670 + 17.1446i) q^{8} +O(q^{10})$	\(q+(2.04896 + 1.94981i) q^{2} +(0.396477 + 7.99017i) q^{4} +16.5019i q^{5} +22.2418i q^{7} +(-14.7670 + 17.1446i) q^{8} +(-32.1756 + 33.8118i) q^{10} +12.7531 q^{11} +22.3532 q^{13} +(-43.3674 + 45.5727i) q^{14} +(-63.6856 + 6.33583i) q^{16} -117.295i q^{17} -27.7307i q^{19} +(-131.853 + 6.54262i) q^{20} +(26.1306 + 24.8661i) q^{22} +35.1671 q^{23} -147.313 q^{25} +(45.8008 + 43.5845i) q^{26} +(-177.716 + 8.81837i) q^{28} +1.16843i q^{29} +137.826i q^{31} +(-142.843 - 111.193i) q^{32} +(228.704 - 240.333i) q^{34} -367.033 q^{35} +233.596 q^{37} +(54.0696 - 56.8191i) q^{38} +(-282.919 - 243.683i) q^{40} -15.3068i q^{41} +417.378i q^{43} +(5.05631 + 101.900i) q^{44} +(72.0561 + 68.5693i) q^{46} -232.987 q^{47} -151.700 q^{49} +(-301.839 - 287.233i) q^{50} +(8.86252 + 178.606i) q^{52} +180.951i q^{53} +210.451i q^{55} +(-381.327 - 328.444i) q^{56} +(-2.27823 + 2.39408i) q^{58} -627.433 q^{59} +764.220 q^{61} +(-268.735 + 282.400i) q^{62} +(-75.8742 - 506.347i) q^{64} +368.871i q^{65} +131.015i q^{67} +(937.210 - 46.5048i) q^{68} +(-752.036 - 715.645i) q^{70} -22.6910 q^{71} +387.864 q^{73} +(478.630 + 455.469i) q^{74} +(221.573 - 10.9946i) q^{76} +283.653i q^{77} -561.659i q^{79} +(-104.553 - 1050.93i) q^{80} +(29.8454 - 31.3630i) q^{82} -684.222 q^{83} +1935.60 q^{85} +(-813.809 + 855.192i) q^{86} +(-188.325 + 218.647i) q^{88} +278.003i q^{89} +497.177i q^{91} +(13.9429 + 280.991i) q^{92} +(-477.382 - 454.281i) q^{94} +457.610 q^{95} +528.886 q^{97} +(-310.827 - 295.786i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.04896	+	1.94981i	0.724417	+	0.689362i
$2$	2.04896	+	1.94981i	0.724417	+	0.689362i
$3$		0			0
$3$		0			0
$4$	0.396477	+	7.99017i	0.0495596	+	0.998771i
$5$			16.5019i			1.47598i	0.674813	+	0.737988i	$0.264224\pi$
$5$			16.5019i			1.47598i	−0.674813	+	0.737988i	$0.735776\pi$
$6$		0			0
$7$			22.2418i			1.20095i	0.799645	+	0.600473i	$0.205021\pi$
$7$			22.2418i			1.20095i	−0.799645	+	0.600473i	$0.794979\pi$
$8$	−14.7670	+	17.1446i	−0.652613	+	0.757691i
$9$		0			0
$10$	−32.1756	+	33.8118i	−1.01748	+	1.06922i
$11$	12.7531			0.349564			0.174782	−	0.984607i	$-0.444078\pi$
$11$	12.7531			0.349564			0.174782	+	0.984607i	$0.444078\pi$
$12$		0			0
$13$	22.3532			0.476897			0.238449	−	0.971155i	$-0.423361\pi$
$13$	22.3532			0.476897			0.238449	+	0.971155i	$0.423361\pi$
$14$	−43.3674	+	45.5727i	−0.827887	+	0.869986i
$15$		0			0
$16$	−63.6856	+	6.33583i	−0.995088	+	0.0989973i
$17$		−	117.295i		−	1.67343i	−0.547639	−	0.836715i	$-0.684473\pi$
$17$		−	117.295i		−	1.67343i	0.547639	−	0.836715i	$-0.315527\pi$
$18$		0			0
$19$		−	27.7307i		−	0.334835i	−0.985886	−	0.167417i	$-0.946457\pi$
$19$		−	27.7307i		−	0.334835i	0.985886	−	0.167417i	$-0.0535427\pi$
$20$	−131.853	+	6.54262i	−1.47416	+	0.0731488i
$21$		0			0
$22$	26.1306	+	24.8661i	0.253230	+	0.240976i
$23$	35.1671			0.318820			0.159410	−	0.987212i	$-0.449041\pi$
$23$	35.1671			0.318820			0.159410	+	0.987212i	$0.449041\pi$
$24$		0			0
$25$	−147.313			−1.17851
$26$	45.8008	+	43.5845i	0.345472	+	0.328755i
$27$		0			0
$28$	−177.716	+	8.81837i	−1.19947	+	0.0595184i
$29$			1.16843i			0.00748182i	0.999993	+	0.00374091i	$0.00119077\pi$
$29$			1.16843i			0.00748182i	−0.999993	+	0.00374091i	$0.998809\pi$
$30$		0			0
$31$			137.826i			0.798525i	0.916837	+	0.399263i	$0.130734\pi$
$31$			137.826i			0.798525i	−0.916837	+	0.399263i	$0.869266\pi$
$32$	−142.843	−	111.193i	−0.789103	−	0.614260i
$33$		0			0
$34$	228.704	−	240.333i	1.15360	−	1.21226i
$35$	−367.033			−1.77257
$36$		0			0
$37$	233.596			1.03792			0.518959	−	0.854799i	$-0.326320\pi$
$37$	233.596			1.03792			0.518959	+	0.854799i	$0.326320\pi$
$38$	54.0696	−	56.8191i	0.230822	−	0.242560i
$39$		0			0
$40$	−282.919	−	243.683i	−1.11833	−	0.963242i
$41$		−	15.3068i		−	0.0583054i	−0.999575	−	0.0291527i	$-0.990719\pi$
$41$		−	15.3068i		−	0.0583054i	0.999575	−	0.0291527i	$-0.00928091\pi$
$42$		0			0
$43$			417.378i			1.48022i	0.672484	+	0.740112i	$0.265227\pi$
$43$			417.378i			1.48022i	−0.672484	+	0.740112i	$0.734773\pi$
$44$	5.05631	+	101.900i	0.0173243	+	0.349135i
$45$		0			0
$46$	72.0561	+	68.5693i	0.230958	+	0.219782i
$47$	−232.987			−0.723079			−0.361539	−	0.932357i	$-0.617749\pi$
$47$	−232.987			−0.723079			−0.361539	+	0.932357i	$0.617749\pi$
$48$		0			0
$49$	−151.700			−0.442273
$50$	−301.839	−	287.233i	−0.853730	−	0.812418i
$51$		0			0
$52$	8.86252	+	178.606i	0.0236348	+	0.476311i
$53$			180.951i			0.468972i	0.972120	+	0.234486i	$0.0753407\pi$
$53$			180.951i			0.468972i	−0.972120	+	0.234486i	$0.924659\pi$
$54$		0			0
$55$			210.451i			0.515949i
$56$	−381.327	−	328.444i	−0.909947	−	0.783754i
$57$		0			0
$58$	−2.27823	+	2.39408i	−0.00515768	+	0.00541996i
$59$	−627.433			−1.38449			−0.692244	−	0.721663i	$-0.743378\pi$
$59$	−627.433			−1.38449			−0.692244	+	0.721663i	$0.743378\pi$
$60$		0			0
$61$	764.220			1.60407			0.802035	−	0.597276i	$-0.203750\pi$
$61$	764.220			1.60407			0.802035	+	0.597276i	$0.203750\pi$
$62$	−268.735	+	282.400i	−0.550473	+	0.578465i
$63$		0			0
$64$	−75.8742	−	506.347i	−0.148192	−	0.988959i
$65$			368.871i			0.703889i
$66$		0			0
$67$			131.015i			0.238897i	0.992840	+	0.119448i	$0.0381126\pi$
$67$			131.015i			0.238897i	−0.992840	+	0.119448i	$0.961887\pi$
$68$	937.210	−	46.5048i	1.67137	−	0.0829344i
$69$		0			0
$70$	−752.036	−	715.645i	−1.28408	−	1.22194i
$71$	−22.6910			−0.0379285			−0.0189643	−	0.999820i	$-0.506037\pi$
$71$	−22.6910			−0.0379285			−0.0189643	+	0.999820i	$0.506037\pi$
$72$		0			0
$73$	387.864			0.621863			0.310932	−	0.950432i	$-0.399359\pi$
$73$	387.864			0.621863			0.310932	+	0.950432i	$0.399359\pi$
$74$	478.630	+	455.469i	0.751886	+	0.715502i
$75$		0			0
$76$	221.573	−	10.9946i	0.334423	−	0.0165943i
$77$			283.653i			0.419808i
$78$		0			0
$79$		−	561.659i		−	0.799894i	−0.916538	−	0.399947i	$-0.869029\pi$
$79$		−	561.659i		−	0.799894i	0.916538	−	0.399947i	$-0.130971\pi$
$80$	−104.553	−	1050.93i	−0.146118	−	1.46873i
$81$		0			0
$82$	29.8454	−	31.3630i	0.0401935	−	0.0422374i
$83$	−684.222			−0.904857			−0.452429	−	0.891801i	$-0.649442\pi$
$83$	−684.222			−0.904857			−0.452429	+	0.891801i	$0.649442\pi$
$84$		0			0
$85$	1935.60			2.46994
$86$	−813.809	+	855.192i	−1.02041	+	1.07230i
$87$		0			0
$88$	−188.325	+	218.647i	−0.228130	+	0.264862i
$89$			278.003i			0.331103i	0.986201	+	0.165552i	$0.0529405\pi$
$89$			278.003i			0.331103i	−0.986201	+	0.165552i	$0.947060\pi$
$90$		0			0
$91$			497.177i			0.572728i
$92$	13.9429	+	280.991i	0.0158006	+	0.318428i
$93$		0			0
$94$	−477.382	−	454.281i	−0.523810	−	0.498463i
$95$	457.610			0.494208
$96$		0			0
$97$	528.886			0.553610			0.276805	−	0.960926i	$-0.410724\pi$
$97$	528.886			0.553610			0.276805	+	0.960926i	$0.410724\pi$
$98$	−310.827	−	295.786i	−0.320390	−	0.304887i
$99$		0			0
$100$	−58.4063	−	1177.06i	−0.0584063	−	1.17706i
$101$		−	1433.95i		−	1.41271i	−0.707857	−	0.706355i	$-0.750338\pi$
$101$		−	1433.95i		−	1.41271i	0.707857	−	0.706355i	$-0.249662\pi$
$102$		0			0
$103$			229.895i			0.219925i	0.993936	+	0.109962i	$0.0350730\pi$
$103$			229.895i			0.219925i	−0.993936	+	0.109962i	$0.964927\pi$
$104$	−330.089	+	383.237i	−0.311230	+	0.361341i
$105$		0			0
$106$	−352.820	+	370.761i	−0.323291	+	0.339731i
$107$	1676.13			1.51437			0.757184	−	0.653201i	$-0.226574\pi$
$107$	1676.13			1.51437			0.757184	+	0.653201i	$0.226574\pi$
$108$		0			0
$109$	−540.666			−0.475104			−0.237552	−	0.971375i	$-0.576345\pi$
$109$	−540.666			−0.475104			−0.237552	+	0.971375i	$0.576345\pi$
$110$	−410.339	+	431.205i	−0.355676	+	0.373762i
$111$		0			0
$112$	−140.921	−	1416.49i	−0.118891	−	1.19505i
$113$		−	1282.68i		−	1.06783i	−0.845540	−	0.533913i	$-0.820721\pi$
$113$		−	1282.68i		−	1.06783i	0.845540	−	0.533913i	$-0.179279\pi$
$114$		0			0
$115$			580.325i			0.470571i
$116$	−9.33599	+	0.463257i	−0.00747263	+	0.000370796i
$117$		0			0
$118$	−1285.59	−	1223.38i	−1.00295	−	0.954414i
$119$	2608.86			2.00970
$120$		0			0
$121$	−1168.36			−0.877805
$122$	1565.86	+	1490.08i	1.16202	+	1.10579i
$123$		0			0
$124$	−1101.25	+	54.6448i	−0.797544	+	0.0395746i
$125$		−	368.214i		−	0.263472i
$126$		0			0
$127$			2674.79i			1.86889i	0.356109	+	0.934444i	$0.384103\pi$
$127$			2674.79i			1.86889i	−0.356109	+	0.934444i	$0.615897\pi$
$128$	831.817	−	1185.42i	0.574398	−	0.818576i
$129$		0			0
$130$	−719.228	+	755.802i	−0.485235	+	0.509909i
$131$	826.801			0.551435			0.275717	−	0.961239i	$-0.411085\pi$
$131$	826.801			0.551435			0.275717	+	0.961239i	$0.411085\pi$
$132$		0			0
$133$	616.782			0.402118
$134$	−255.455	+	268.446i	−0.164686	+	0.173061i
$135$		0			0
$136$	2010.98	+	1732.09i	1.26794	+	1.09210i
$137$			647.705i			0.403921i	0.979394	+	0.201960i	$0.0647313\pi$
$137$			647.705i			0.403921i	−0.979394	+	0.201960i	$0.935269\pi$
$138$		0			0
$139$			2670.49i			1.62955i	0.579775	+	0.814777i	$0.303141\pi$
$139$			2670.49i			1.62955i	−0.579775	+	0.814777i	$0.696859\pi$
$140$	−145.520	−	2932.66i	−0.0878478	−	1.77039i
$141$		0			0
$142$	−46.4930	−	44.2432i	−0.0274761	−	0.0261465i
$143$	285.073			0.166706
$144$		0			0
$145$	−19.2814			−0.0110430
$146$	794.718	+	756.261i	0.450488	+	0.428689i
$147$		0			0
$148$	92.6154	+	1866.47i	0.0514388	+	1.03664i
$149$			104.210i			0.0572967i	0.999590	+	0.0286484i	$0.00912031\pi$
$149$			104.210i			0.0572967i	−0.999590	+	0.0286484i	$0.990880\pi$
$150$		0			0
$151$			2751.39i			1.48281i	0.671056	+	0.741407i	$0.265841\pi$
$151$			2751.39i			1.48281i	−0.671056	+	0.741407i	$0.734159\pi$
$152$	475.431	+	409.498i	0.253701	+	0.218517i
$153$		0			0
$154$	−553.069	+	581.193i	−0.289400	+	0.304116i
$155$	−2274.39			−1.17860
$156$		0			0
$157$	−1163.09			−0.591241			−0.295620	−	0.955306i	$-0.595526\pi$
$157$	−1163.09			−0.591241			−0.295620	+	0.955306i	$0.595526\pi$
$158$	1095.13	−	1150.82i	0.551417	−	0.579457i
$159$		0			0
$160$	1834.90	−	2357.18i	0.906634	−	1.16470i
$161$			782.182i			0.382886i
$162$		0			0
$163$		−	2930.45i		−	1.40816i	−0.710120	−	0.704081i	$-0.751359\pi$
$163$		−	2930.45i		−	1.40816i	0.710120	−	0.704081i	$-0.248641\pi$
$164$	122.304	−	6.06879i	0.0582337	−	0.00288959i
$165$		0			0
$166$	−1401.94	−	1334.10i	−0.655494	−	0.623774i
$167$	871.920			0.404019			0.202010	−	0.979384i	$-0.435253\pi$
$167$	871.920			0.404019			0.202010	+	0.979384i	$0.435253\pi$
$168$		0			0
$169$	−1697.33			−0.772569
$170$	3965.96	+	3774.05i	1.78927	+	1.70268i
$171$		0			0
$172$	−3334.92	+	165.481i	−1.47840	+	0.0733592i
$173$			2332.71i			1.02516i	0.858639	+	0.512581i	$0.171310\pi$
$173$			2332.71i			1.02516i	−0.858639	+	0.512581i	$0.828690\pi$
$174$		0			0
$175$		−	3276.52i		−	1.41532i
$176$	−812.190	+	80.8015i	−0.347847	+	0.0346059i
$177$		0			0
$178$	−542.052	+	569.616i	−0.228250	+	0.239857i
$179$	−638.773			−0.266727			−0.133364	−	0.991067i	$-0.542578\pi$
$179$	−638.773			−0.266727			−0.133364	+	0.991067i	$0.542578\pi$
$180$		0			0
$181$	4031.01			1.65537			0.827686	−	0.561192i	$-0.189657\pi$
$181$	4031.01			1.65537			0.827686	+	0.561192i	$0.189657\pi$
$182$	−969.400	+	1018.70i	−0.394817	+	0.414894i
$183$		0			0
$184$	−519.311	+	602.926i	−0.208066	+	0.241567i
$185$			3854.79i			1.53194i
$186$		0			0
$187$		−	1495.88i		−	0.584971i
$188$	−92.3740	−	1861.61i	−0.0358355	−	0.722190i
$189$		0			0
$190$	937.624	+	892.252i	0.358013	+	0.340688i
$191$	3663.43			1.38784			0.693918	−	0.720054i	$-0.255883\pi$
$191$	3663.43			1.38784			0.693918	+	0.720054i	$0.255883\pi$
$192$		0			0
$193$	1417.66			0.528731			0.264366	−	0.964423i	$-0.414837\pi$
$193$	1417.66			0.528731			0.264366	+	0.964423i	$0.414837\pi$
$194$	1083.67	+	1031.23i	0.401045	+	0.381638i
$195$		0			0
$196$	−60.1454	−	1212.11i	−0.0219189	−	0.441730i
$197$		−	876.917i		−	0.317146i	−0.987347	−	0.158573i	$-0.949311\pi$
$197$		−	876.917i		−	0.317146i	0.987347	−	0.158573i	$-0.0506893\pi$
$198$		0			0
$199$		−	1485.45i		−	0.529149i	−0.964365	−	0.264574i	$-0.914769\pi$
$199$		−	1485.45i		−	0.529149i	0.964365	−	0.264574i	$-0.0852315\pi$
$200$	2175.37	−	2525.63i	0.769109	−	0.892944i
$201$		0			0
$202$	2795.94	−	2938.12i	0.973869	−	1.02339i
$203$	−25.9881			−0.00898527
$204$		0			0
$205$	252.592			0.0860574
$206$	−448.252	+	471.046i	−0.151608	+	0.159317i
$207$		0			0
$208$	−1423.58	+	141.626i	−0.474555	+	0.0472116i
$209$		−	353.652i		−	0.117046i
$210$		0			0
$211$			307.652i			0.100377i	0.998740	+	0.0501887i	$0.0159823\pi$
$211$			307.652i			0.100377i	−0.998740	+	0.0501887i	$0.984018\pi$
$212$	−1445.83	+	71.7428i	−0.468396	+	0.0232420i
$213$		0			0
$214$	3434.32	+	3268.13i	1.09703	+	1.04395i
$215$	−6887.55			−2.18478
$216$		0			0
$217$	−3065.50			−0.958986
$218$	−1107.80	−	1054.20i	−0.344174	−	0.327519i
$219$		0			0
$220$	−1681.54	+	83.4388i	−0.515315	+	0.0255702i
$221$		−	2621.93i		−	0.798054i
$222$		0			0
$223$		−	3903.48i		−	1.17218i	−0.810245	−	0.586091i	$-0.800666\pi$
$223$		−	3903.48i		−	1.17218i	0.810245	−	0.586091i	$-0.199334\pi$
$224$	2473.14	−	3177.09i	0.737694	−	0.947671i
$225$		0			0
$226$	2500.98	−	2628.16i	0.736119	−	0.773551i
$227$	−1928.76			−0.563949			−0.281975	−	0.959422i	$-0.590989\pi$
$227$	−1928.76			−0.563949			−0.281975	+	0.959422i	$0.590989\pi$
$228$		0			0
$229$	2297.42			0.662958			0.331479	−	0.943463i	$-0.392452\pi$
$229$	2297.42			0.662958			0.331479	+	0.943463i	$0.392452\pi$
$230$	−1131.52	+	1189.06i	−0.324394	+	0.340889i
$231$		0			0
$232$	−20.0323	−	17.2542i	−0.00566891	−	0.00488274i
$233$		−	3366.60i		−	0.946580i	−0.880907	−	0.473290i	$-0.843066\pi$
$233$		−	3366.60i		−	0.946580i	0.880907	−	0.473290i	$-0.156934\pi$
$234$		0			0
$235$		−	3844.74i		−	1.06725i
$236$	−248.762	−	5013.30i	−0.0686146	−	1.38279i
$237$		0			0
$238$	5345.46	+	5086.79i	1.45586	+	1.38541i
$239$	−615.143			−0.166486			−0.0832432	−	0.996529i	$-0.526528\pi$
$239$	−615.143			−0.166486			−0.0832432	+	0.996529i	$0.526528\pi$
$240$		0			0
$241$	−4391.55			−1.17380			−0.586898	−	0.809661i	$-0.699651\pi$
$241$	−4391.55			−1.17380			−0.586898	+	0.809661i	$0.699651\pi$
$242$	−2393.92	−	2278.08i	−0.635897	−	0.605125i
$243$		0			0
$244$	302.995	+	6106.25i	0.0794971	+	1.60210i
$245$		−	2503.34i		−	0.652785i
$246$		0			0
$247$		−	619.870i		−	0.159682i
$248$	−2362.97	−	2035.27i	−0.605035	−	0.521128i
$249$		0			0
$250$	717.947	−	754.455i	0.181628	−	0.190864i
$251$	7726.08			1.94289			0.971446	−	0.237259i	$-0.0762489\pi$
$251$	7726.08			1.94289			0.971446	+	0.237259i	$0.0762489\pi$
$252$		0			0
$253$	448.490			0.111448
$254$	−5215.33	+	5480.53i	−1.28834	+	1.35385i
$255$		0			0
$256$	4015.71	−	807.002i	0.980399	−	0.197022i
$257$			2566.70i			0.622982i	0.950249	+	0.311491i	$0.100828\pi$
$257$			2566.70i			0.622982i	−0.950249	+	0.311491i	$0.899172\pi$
$258$		0			0
$259$			5195.61i			1.24649i
$260$	−2947.34	+	146.249i	−0.703024	+	0.0348844i
$261$		0			0
$262$	1694.08	+	1612.11i	0.399469	+	0.380138i
$263$	−4007.84			−0.939673			−0.469837	−	0.882753i	$-0.655687\pi$
$263$	−4007.84			−0.939673			−0.469837	+	0.882753i	$0.655687\pi$
$264$		0			0
$265$	−2986.04			−0.692192
$266$	1263.76	+	1202.61i	0.291301	+	0.277205i
$267$		0			0
$268$	−1046.84	+	51.9446i	−0.238603	+	0.0118396i
$269$		−	2242.21i		−	0.508214i	−0.967176	−	0.254107i	$-0.918218\pi$
$269$		−	2242.21i		−	0.508214i	0.967176	−	0.254107i	$-0.0817816\pi$
$270$		0			0
$271$			6324.08i			1.41757i	0.705426	+	0.708784i	$0.250756\pi$
$271$			6324.08i			1.41757i	−0.705426	+	0.708784i	$0.749244\pi$
$272$	743.163	+	7470.02i	0.165665	+	1.66521i
$273$		0			0
$274$	−1262.90	+	1327.12i	−0.278448	+	0.292607i
$275$	−1878.70			−0.411964
$276$		0			0
$277$	1251.70			0.271508			0.135754	−	0.990743i	$-0.456654\pi$
$277$	1251.70			0.271508			0.135754	+	0.990743i	$0.456654\pi$
$278$	−5206.95	+	5471.73i	−1.12335	+	1.18048i
$279$		0			0
$280$	5419.96	−	6292.64i	1.15680	−	1.34306i
$281$		−	1374.48i		−	0.291796i	−0.989300	−	0.145898i	$-0.953393\pi$
$281$		−	1374.48i		−	0.291796i	0.989300	−	0.145898i	$-0.0466071\pi$
$282$		0			0
$283$		−	4625.92i		−	0.971669i	−0.874051	−	0.485835i	$-0.838516\pi$
$283$		−	4625.92i		−	0.971669i	0.874051	−	0.485835i	$-0.161484\pi$
$284$	−8.99645	−	181.305i	−0.00187972	−	0.0378819i
$285$		0			0
$286$	584.103	+	555.838i	0.120765	+	0.114921i
$287$	340.452			0.0700217
$288$		0			0
$289$	−8845.19			−1.80037
$290$	−39.5068	−	37.5951i	−0.00799973	−	0.00761262i
$291$		0			0
$292$	153.779	+	3099.10i	0.0308193	+	0.621099i
$293$		−	6377.04i		−	1.27150i	−0.771893	−	0.635752i	$-0.780690\pi$
$293$		−	6377.04i		−	1.27150i	0.771893	−	0.635752i	$-0.219310\pi$
$294$		0			0
$295$		−	10353.8i		−	2.04347i
$296$	−3449.51	+	4004.91i	−0.677360	+	0.786422i
$297$		0			0
$298$	−203.190	+	213.522i	−0.0394982	+	0.0415067i
$299$	786.098			0.152044
$300$		0			0
$301$	−9283.27			−1.77767
$302$	−5364.69	+	5637.48i	−1.02220	+	1.07417i
$303$		0			0
$304$	175.697	+	1766.05i	0.0331477	+	0.333190i
$305$			12611.1i			2.36757i
$306$		0			0
$307$		−	6609.36i		−	1.22872i	−0.789027	−	0.614359i	$-0.789415\pi$
$307$		−	6609.36i		−	1.22872i	0.789027	−	0.614359i	$-0.210585\pi$
$308$	−2266.43	+	112.462i	−0.419292	+	0.0208055i
$309$		0			0
$310$	−4660.14	−	4434.64i	−0.853801	−	0.812485i
$311$	−5136.69			−0.936576			−0.468288	−	0.883576i	$-0.655129\pi$
$311$	−5136.69			−0.936576			−0.468288	+	0.883576i	$0.655129\pi$
$312$		0			0
$313$	6202.84			1.12014			0.560072	−	0.828444i	$-0.310773\pi$
$313$	6202.84			1.12014			0.560072	+	0.828444i	$0.310773\pi$
$314$	−2383.13	−	2267.81i	−0.428305	−	0.407579i
$315$		0			0
$316$	4487.75	−	222.685i	0.798911	−	0.0396424i
$317$			1825.15i			0.323377i	0.986842	+	0.161689i	$0.0516940\pi$
$317$			1825.15i			0.323377i	−0.986842	+	0.161689i	$0.948306\pi$
$318$		0			0
$319$			14.9012i			0.00261538i
$320$	8355.70	−	1252.07i	1.45968	−	0.218728i
$321$		0			0
$322$	−1525.11	+	1602.66i	−0.263947	+	0.277369i
$323$	−3252.68			−0.560322
$324$		0			0
$325$	−3292.93			−0.562027
$326$	5713.82	−	6004.37i	0.970733	−	1.02010i
$327$		0			0
$328$	262.429	+	226.035i	0.0441775	+	0.0380509i
$329$		−	5182.07i		−	0.868379i
$330$		0			0
$331$		−	3977.22i		−	0.660447i	−0.943903	−	0.330223i	$-0.892876\pi$
$331$		−	3977.22i		−	0.660447i	0.943903	−	0.330223i	$-0.107124\pi$
$332$	−271.278	−	5467.05i	−0.0448443	−	0.903745i
$333$		0			0
$334$	1786.53	+	1700.08i	0.292678	+	0.278516i
$335$	−2162.01			−0.352606
$336$		0			0
$337$	−1157.69			−0.187132			−0.0935662	−	0.995613i	$-0.529827\pi$
$337$	−1157.69			−0.187132			−0.0935662	+	0.995613i	$0.529827\pi$
$338$	−3477.77	−	3309.48i	−0.559662	−	0.532580i
$339$		0			0
$340$	767.419	+	15465.8i	0.122409	+	2.46691i
$341$			1757.71i			0.279136i
$342$		0			0
$343$			4254.87i			0.669800i
$344$	−7155.78	−	6163.41i	−1.12155	−	0.966013i
$345$		0			0
$346$	−4548.35	+	4779.64i	−0.706707	+	0.742644i
$347$	−2483.25			−0.384173			−0.192086	−	0.981378i	$-0.561525\pi$
$347$	−2483.25			−0.384173			−0.192086	+	0.981378i	$0.561525\pi$
$348$		0			0
$349$	−5973.80			−0.916248			−0.458124	−	0.888888i	$-0.651478\pi$
$349$	−5973.80			−0.916248			−0.458124	+	0.888888i	$0.651478\pi$
$350$	6388.60	−	6713.46i	0.975671	−	1.02528i
$351$		0			0
$352$	−1821.69	−	1418.06i	−0.275842	−	0.214724i
$353$		−	1031.33i		−	0.155502i	−0.996973	−	0.0777511i	$-0.975226\pi$
$353$		−	1031.33i		−	0.155502i	0.996973	−	0.0777511i	$-0.0247740\pi$
$354$		0			0
$355$		−	374.445i		−	0.0559816i
$356$	−2221.29	+	110.221i	−0.330697	+	0.0164093i
$357$		0			0
$358$	−1308.82	−	1245.49i	−0.193222	−	0.183872i
$359$	−4218.99			−0.620249			−0.310125	−	0.950696i	$-0.600371\pi$
$359$	−4218.99			−0.620249			−0.310125	+	0.950696i	$0.600371\pi$
$360$		0			0
$361$	6090.01			0.887886
$362$	8259.37	+	7859.70i	1.19918	+	1.14115i
$363$		0			0
$364$	−3972.53	+	197.119i	−0.572025	+	0.0283842i
$365$			6400.50i			0.917856i
$366$		0			0
$367$			3040.22i			0.432421i	0.976347	+	0.216210i	$0.0693697\pi$
$367$			3040.22i			0.432421i	−0.976347	+	0.216210i	$0.930630\pi$
$368$	−2239.64	+	222.813i	−0.317254	+	0.0315623i
$369$		0			0
$370$	−7516.11	+	7898.31i	−1.05606	+	1.10977i
$371$	−4024.68			−0.563210
$372$		0			0
$373$	5117.83			0.710433			0.355216	−	0.934784i	$-0.384407\pi$
$373$	5117.83			0.710433			0.355216	+	0.934784i	$0.384407\pi$
$374$	2916.68	−	3065.00i	0.403257	−	0.423763i
$375$		0			0
$376$	3440.51	−	3994.47i	0.471891	−	0.547870i
$377$			26.1183i			0.00356806i
$378$		0			0
$379$			2840.61i			0.384993i	0.981298	+	0.192497i	$0.0616585\pi$
$379$			2840.61i			0.384993i	−0.981298	+	0.192497i	$0.938342\pi$
$380$	181.431	+	3656.38i	0.0244927	+	0.493601i
$381$		0			0
$382$	7506.23	+	7143.00i	1.00537	+	0.956722i
$383$	5628.66			0.750943			0.375472	−	0.926834i	$-0.377481\pi$
$383$	5628.66			0.750943			0.375472	+	0.926834i	$0.377481\pi$
$384$		0			0
$385$	−4680.81			−0.619627
$386$	2904.72	+	2764.16i	0.383022	+	0.364487i
$387$		0			0
$388$	209.691	+	4225.88i	0.0274367	+	0.552930i
$389$		−	3561.97i		−	0.464265i	−0.972684	−	0.232132i	$-0.925430\pi$
$389$		−	3561.97i		−	0.464265i	0.972684	−	0.232132i	$-0.0745703\pi$
$390$		0			0
$391$		−	4124.94i		−	0.533522i
$392$	2240.14	−	2600.83i	0.288633	−	0.335107i
$393$		0			0
$394$	1709.82	−	1796.77i	0.218628	−	0.229746i
$395$	9268.46			1.18062
$396$		0			0
$397$	−9427.52			−1.19182			−0.595911	−	0.803050i	$-0.703209\pi$
$397$	−9427.52			−1.19182			−0.595911	+	0.803050i	$0.703209\pi$
$398$	2896.34	−	3043.62i	0.364775	−	0.383324i
$399$		0			0
$400$	9381.74	−	933.352i	1.17272	−	0.116669i
$401$			8631.58i			1.07491i	0.843291	+	0.537457i	$0.180615\pi$
$401$			8631.58i			1.07491i	−0.843291	+	0.537457i	$0.819385\pi$
$402$		0			0
$403$			3080.85i			0.380814i
$404$	11457.5	−	568.529i	1.41097	−	0.0700133i
$405$		0			0
$406$	−53.2487	−	50.6719i	−0.00650908	−	0.00619410i
$407$	2979.08			0.362819
$408$		0			0
$409$	5864.81			0.709037			0.354518	−	0.935049i	$-0.384645\pi$
$409$	5864.81			0.709037			0.354518	+	0.935049i	$0.384645\pi$
$410$	517.550	+	492.506i	0.0623414	+	0.0593247i
$411$		0			0
$412$	−1836.90	+	91.1481i	−0.219654	+	0.0108994i
$413$		−	13955.3i		−	1.66270i
$414$		0			0
$415$		−	11291.0i		−	1.33555i
$416$	−3193.00	−	2485.52i	−0.376321	−	0.292939i
$417$		0			0
$418$	689.555	−	724.620i	0.0806872	−	0.0847902i
$419$	6955.71			0.810999			0.405500	−	0.914095i	$-0.367098\pi$
$419$	6955.71			0.810999			0.405500	+	0.914095i	$0.367098\pi$
$420$		0			0
$421$	−9395.79			−1.08770			−0.543851	−	0.839182i	$-0.683034\pi$
$421$	−9395.79			−1.08770			−0.543851	+	0.839182i	$0.683034\pi$
$422$	−599.863	+	630.366i	−0.0691964	+	0.0727151i
$423$		0			0
$424$	−3102.33	−	2672.09i	−0.355336	−	0.306057i
$425$			17279.2i			1.97215i
$426$		0			0
$427$			16997.7i			1.92640i
$428$	664.546	+	13392.6i	0.0750515	+	1.51251i
$429$		0			0
$430$	−14112.3	−	13429.4i	−1.58269	−	1.50610i
$431$	−7346.03			−0.820988			−0.410494	−	0.911863i	$-0.634644\pi$
$431$	−7346.03			−0.820988			−0.410494	+	0.911863i	$0.634644\pi$
$432$		0			0
$433$	13673.0			1.51751			0.758755	−	0.651376i	$-0.225808\pi$
$433$	13673.0			1.51751			0.758755	+	0.651376i	$0.225808\pi$
$434$	−6281.10	−	5977.15i	−0.694706	−	0.661089i
$435$		0			0
$436$	−214.361	−	4320.01i	−0.0235460	−	0.474521i
$437$		−	975.209i		−	0.106752i
$438$		0			0
$439$			5768.74i			0.627168i	0.949560	+	0.313584i	$0.101530\pi$
$439$			5768.74i			0.627168i	−0.949560	+	0.313584i	$0.898470\pi$
$440$	−3608.09	−	3107.72i	−0.390930	−	0.336715i
$441$		0			0
$442$	5112.26	−	5372.22i	0.550148	−	0.578124i
$443$	9652.91			1.03527			0.517634	−	0.855602i	$-0.326813\pi$
$443$	9652.91			1.03527			0.517634	+	0.855602i	$0.326813\pi$
$444$		0			0
$445$	−4587.58			−0.488701
$446$	7611.06	−	7998.08i	0.808058	−	0.849149i
$447$		0			0
$448$	11262.1	−	1687.58i	1.18769	−	0.177970i
$449$		−	11492.2i		−	1.20791i	−0.797018	−	0.603955i	$-0.793590\pi$
$449$		−	11492.2i		−	1.20791i	0.797018	−	0.603955i	$-0.206410\pi$
$450$		0			0
$451$		−	195.209i		−	0.0203815i
$452$	10248.8	−	508.552i	1.06651	−	0.0529210i
$453$		0			0
$454$	−3951.96	−	3760.72i	−0.408534	−	0.388765i
$455$	−8204.37			−0.845334
$456$		0			0
$457$	17642.1			1.80583			0.902914	−	0.429821i	$-0.141423\pi$
$457$	17642.1			1.80583			0.902914	+	0.429821i	$0.141423\pi$
$458$	4707.31	+	4479.53i	0.480258	+	0.457018i
$459$		0			0
$460$	−4636.90	+	230.085i	−0.469992	+	0.0233213i
$461$		−	12865.9i		−	1.29984i	−0.760004	−	0.649918i	$-0.774803\pi$
$461$		−	12865.9i		−	1.29984i	0.760004	−	0.649918i	$-0.225197\pi$
$462$		0			0
$463$		−	13838.7i		−	1.38907i	−0.719460	−	0.694534i	$-0.755611\pi$
$463$		−	13838.7i		−	1.38907i	0.719460	−	0.694534i	$-0.244389\pi$
$464$	−7.40300	−	74.4124i	−0.000740680	−	0.00744507i
$465$		0			0
$466$	6564.23	−	6898.02i	0.652536	−	0.685718i
$467$	81.1441			0.00804047			0.00402024	−	0.999992i	$-0.498720\pi$
$467$	81.1441			0.00804047			0.00402024	+	0.999992i	$0.498720\pi$
$468$		0			0
$469$	−2914.03			−0.286902
$470$	7496.51	−	7877.72i	0.735720	−	0.773132i
$471$		0			0
$472$	9265.27	−	10757.1i	0.903536	−	1.04901i
$473$			5322.87i			0.517433i
$474$		0			0
$475$			4085.10i			0.394605i
$476$	1034.35	+	20845.3i	0.0995998	+	2.00723i
$477$		0			0
$478$	−1260.40	−	1199.41i	−0.120606	−	0.114769i
$479$	14944.1			1.42550			0.712750	−	0.701418i	$-0.247450\pi$
$479$	14944.1			1.42550			0.712750	+	0.701418i	$0.247450\pi$
$480$		0			0
$481$	5221.63			0.494981
$482$	−8998.12	−	8562.70i	−0.850318	−	0.809171i
$483$		0			0
$484$	−463.227	−	9335.38i	−0.0435036	−	0.876726i
$485$			8727.63i			0.817116i
$486$		0			0
$487$			5934.04i			0.552150i	0.961136	+	0.276075i	$0.0890338\pi$
$487$			5934.04i			0.552150i	−0.961136	+	0.276075i	$0.910966\pi$
$488$	−11285.2	+	13102.2i	−1.04684	+	1.21539i
$489$		0			0
$490$	4881.03	−	5129.24i	0.450005	−	0.472889i
$491$	20064.8			1.84422			0.922110	−	0.386929i	$-0.126464\pi$
$491$	20064.8			1.84422			0.922110	+	0.386929i	$0.126464\pi$
$492$		0			0
$493$	137.052			0.0125203
$494$	1208.63	−	1270.09i	0.110079	−	0.115676i
$495$		0			0
$496$	−873.242	−	8777.53i	−0.0790519	−	0.794602i
$497$		−	504.690i		−	0.0455502i
$498$		0			0
$499$		−	9408.60i		−	0.844062i	−0.906581	−	0.422031i	$-0.861317\pi$
$499$		−	9408.60i		−	0.844062i	0.906581	−	0.422031i	$-0.138683\pi$
$500$	2942.09	−	145.988i	0.263149	−	0.0130576i
$501$		0			0
$502$	15830.4	+	15064.4i	1.40746	+	1.33936i
$503$	12736.4			1.12900			0.564501	−	0.825432i	$-0.309069\pi$
$503$	12736.4			1.12900			0.564501	+	0.825432i	$0.309069\pi$
$504$		0			0
$505$	23663.0			2.08513
$506$	918.939	+	874.471i	0.0807348	+	0.0768280i
$507$		0			0
$508$	−21372.0	+	1060.49i	−1.86659	+	0.0926213i
$509$		−	9147.07i		−	0.796536i	−0.917269	−	0.398268i	$-0.869611\pi$
$509$		−	9147.07i		−	0.796536i	0.917269	−	0.398268i	$-0.130389\pi$
$510$		0			0
$511$			8626.81i			0.746825i
$512$	9801.54	+	6176.37i	0.846037	+	0.533124i
$513$		0			0
$514$	−5004.58	+	5259.07i	−0.429460	+	0.451299i
$515$	−3793.71			−0.324604
$516$		0			0
$517$	−2971.31			−0.252762
$518$	−10130.5	+	10645.6i	−0.859280	+	0.902975i
$519$		0			0
$520$	−6324.14	−	5447.10i	−0.533331	−	0.459368i
$521$			7691.78i			0.646801i	0.946262	+	0.323400i	$0.104826\pi$
$521$			7691.78i			0.646801i	−0.946262	+	0.323400i	$0.895174\pi$
$522$		0			0
$523$		−	9967.82i		−	0.833389i	−0.909047	−	0.416694i	$-0.863189\pi$
$523$		−	9967.82i		−	0.833389i	0.909047	−	0.416694i	$-0.136811\pi$
$524$	327.807	+	6606.28i	0.0273289	+	0.550757i
$525$		0			0
$526$	−8211.91	−	7814.53i	−0.680715	−	0.647775i
$527$	16166.3			1.33628
$528$		0			0
$529$	−10930.3			−0.898354
$530$	−6118.27	−	5822.21i	−0.501435	−	0.477171i
$531$		0			0
$532$	244.539	+	4928.19i	0.0199288	+	0.401624i
$533$		−	342.156i		−	0.0278057i
$534$		0			0
$535$			27659.3i			2.23517i
$536$	−2246.21	−	1934.70i	−0.181010	−	0.155907i
$537$		0			0
$538$	4371.88	−	4594.19i	0.350344	−	0.368159i
$539$	−1934.64			−0.154603
$540$		0			0
$541$	6050.08			0.480801			0.240400	−	0.970674i	$-0.422721\pi$
$541$	6050.08			0.480801			0.240400	+	0.970674i	$0.422721\pi$
$542$	−12330.8	+	12957.8i	−0.977217	+	1.02691i
$543$		0			0
$544$	−13042.4	+	16754.8i	−1.02792	+	1.32051i
$545$		−	8922.02i		−	0.701243i
$546$		0			0
$547$		−	12969.7i		−	1.01380i	−0.862006	−	0.506898i	$-0.830792\pi$
$547$		−	12969.7i		−	1.01380i	0.862006	−	0.506898i	$-0.169208\pi$
$548$	−5175.27	+	256.800i	−0.403425	+	0.0200181i
$549$		0			0
$550$	−3849.39	−	3663.12i	−0.298434	−	0.283992i
$551$	32.4015			0.00250517
$552$		0			0
$553$	12492.3			0.960630
$554$	2564.69	+	2440.59i	0.196685	+	0.187167i
$555$		0			0
$556$	−21337.7	+	1058.79i	−1.62755	+	0.0807600i
$557$		−	2223.88i		−	0.169172i	−0.996416	−	0.0845859i	$-0.973043\pi$
$557$		−	2223.88i		−	0.169172i	0.996416	−	0.0845859i	$-0.0269567\pi$
$558$		0			0
$559$			9329.75i			0.705915i
$560$	23374.7	−	2325.46i	1.76386	−	0.175480i
$561$		0			0
$562$	2679.98	−	2816.26i	0.201153	−	0.211382i
$563$	−17827.6			−1.33453			−0.667267	−	0.744818i	$-0.732536\pi$
$563$	−17827.6			−1.33453			−0.667267	+	0.744818i	$0.732536\pi$
$564$		0			0
$565$	21166.7			1.57609
$566$	9019.67	−	9478.33i	0.669832	−	0.703894i
$567$		0			0
$568$	335.077	−	389.028i	0.0247527	−	0.0287381i
$569$			11276.5i			0.830820i	0.909634	+	0.415410i	$0.136362\pi$
$569$			11276.5i			0.830820i	−0.909634	+	0.415410i	$0.863638\pi$
$570$		0			0
$571$			7536.73i			0.552369i	0.961105	+	0.276184i	$0.0890700\pi$
$571$			7536.73i			0.552369i	−0.961105	+	0.276184i	$0.910930\pi$
$572$	113.025	+	2277.78i	0.00826189	+	0.166501i
$573$		0			0
$574$	697.572	+	663.816i	0.0507249	+	0.0482703i
$575$	−5180.59			−0.375731
$576$		0			0
$577$	−16888.0			−1.21847			−0.609233	−	0.792991i	$-0.708523\pi$
$577$	−16888.0			−1.21847			−0.609233	+	0.792991i	$0.708523\pi$
$578$	−18123.5	−	17246.5i	−1.30421	−	1.24110i
$579$		0			0
$580$	−7.64463	−	154.062i	−0.000547286	−	0.0110294i
$581$		−	15218.4i		−	1.08669i
$582$		0			0
$583$			2307.69i			0.163936i
$584$	−5727.57	+	6649.77i	−0.405836	+	0.471180i
$585$		0			0
$586$	12434.0	−	13066.3i	0.876527	−	0.921099i
$587$	−16207.7			−1.13963			−0.569814	−	0.821773i	$-0.692985\pi$
$587$	−16207.7			−1.13963			−0.569814	+	0.821773i	$0.692985\pi$
$588$		0			0
$589$	3822.01			0.267374
$590$	20188.0	−	21214.6i	1.40869	−	1.48033i
$591$		0			0
$592$	−14876.7	+	1480.03i	−1.03282	+	0.102751i
$593$			22320.8i			1.54571i	0.634583	+	0.772855i	$0.281172\pi$
$593$			22320.8i			1.54571i	−0.634583	+	0.772855i	$0.718828\pi$
$594$		0			0
$595$			43051.3i			2.96627i
$596$	−832.655	+	41.3168i	−0.0572263	+	0.00283960i
$597$		0			0
$598$	1610.68	+	1532.74i	0.110143	+	0.104814i
$599$	−9767.43			−0.666254			−0.333127	−	0.942882i	$-0.608104\pi$
$599$	−9767.43			−0.666254			−0.333127	+	0.942882i	$0.608104\pi$
$600$		0			0
$601$	18633.6			1.26469			0.632347	−	0.774685i	$-0.282092\pi$
$601$	18633.6			1.26469			0.632347	+	0.774685i	$0.282092\pi$
$602$	−19021.0	−	18100.6i	−1.28777	−	1.22546i
$603$		0			0
$604$	−21984.1	+	1090.86i	−1.48099	+	0.0734876i
$605$		−	19280.2i		−	1.29562i
$606$		0			0
$607$			429.023i			0.0286878i	0.999897	+	0.0143439i	$0.00456597\pi$
$607$			429.023i			0.0286878i	−0.999897	+	0.0143439i	$0.995434\pi$
$608$	−3083.46	+	3961.13i	−0.205676	+	0.264219i
$609$		0			0
$610$	−24589.2	+	25839.6i	−1.63211	+	1.71511i
$611$	−5208.01			−0.344834
$612$		0			0
$613$	−4211.54			−0.277492			−0.138746	−	0.990328i	$-0.544307\pi$
$613$	−4211.54			−0.277492			−0.138746	+	0.990328i	$0.544307\pi$
$614$	12887.0	−	13542.3i	0.847031	−	0.890104i
$615$		0			0
$616$	−4863.11	−	4188.69i	−0.318085	−	0.273972i
$617$			27042.6i			1.76450i	0.470786	+	0.882248i	$0.343970\pi$
$617$			27042.6i			1.76450i	−0.470786	+	0.882248i	$0.656030\pi$
$618$		0			0
$619$			9662.70i			0.627426i	0.949518	+	0.313713i	$0.101573\pi$
$619$			9662.70i			0.627426i	−0.949518	+	0.313713i	$0.898427\pi$
$620$	−901.744	−	18172.8i	−0.0584111	−	1.17716i
$621$		0			0
$622$	−10524.9	−	10015.6i	−0.678471	−	0.645640i
$623$	−6183.29			−0.397638
$624$		0			0
$625$	−12337.9			−0.789628
$626$	12709.4	+	12094.4i	0.811452	+	0.772185i
$627$		0			0
$628$	−461.138	−	9293.29i	−0.0293016	−	0.590514i
$629$		−	27399.8i		−	1.73688i
$630$		0			0
$631$		−	10846.5i		−	0.684297i	−0.939646	−	0.342149i	$-0.888845\pi$
$631$		−	10846.5i		−	0.684297i	0.939646	−	0.342149i	$-0.111155\pi$
$632$	9629.42	+	8294.00i	0.606073	+	0.522021i
$633$		0			0
$634$	−3558.69	+	3739.66i	−0.222924	+	0.234260i
$635$	−44139.1			−2.75844
$636$		0			0
$637$	−3390.98			−0.210919
$638$	−29.0545	+	30.5319i	−0.00180294	+	0.00189462i
$639$		0			0
$640$	19561.8	+	13726.6i	1.20820	+	0.847798i
$641$			14748.4i			0.908776i	0.890804	+	0.454388i	$0.150142\pi$
$641$			14748.4i			0.908776i	−0.890804	+	0.454388i	$0.849858\pi$
$642$		0			0
$643$		−	14765.6i		−	0.905598i	−0.891613	−	0.452799i	$-0.850425\pi$
$643$		−	14765.6i		−	0.905598i	0.891613	−	0.452799i	$-0.149575\pi$
$644$	−6249.77	+	310.117i	−0.382415	+	0.0189756i
$645$		0			0
$646$	−6664.61	−	6342.11i	−0.405907	−	0.386265i
$647$	27157.4			1.65018			0.825090	−	0.565002i	$-0.191125\pi$
$647$	27157.4			1.65018			0.825090	+	0.565002i	$0.191125\pi$
$648$		0			0
$649$	−8001.72			−0.483968
$650$	−6747.08	−	6420.58i	−0.407142	−	0.387440i
$651$		0			0
$652$	23414.8	−	1161.85i	1.40643	−	0.0697879i
$653$			3069.88i			0.183972i	0.995760	+	0.0919861i	$0.0293215\pi$
$653$			3069.88i			0.183972i	−0.995760	+	0.0919861i	$0.970678\pi$
$654$		0			0
$655$			13643.8i			0.813905i
$656$	96.9813	+	974.823i	0.00577208	+	0.0580190i
$657$		0			0
$658$	10104.1	−	10617.9i	0.598628	−	0.629068i
$659$	−1159.53			−0.0685417			−0.0342709	−	0.999413i	$-0.510911\pi$
$659$	−1159.53			−0.0685417			−0.0342709	+	0.999413i	$0.510911\pi$
$660$		0			0
$661$	17839.5			1.04974			0.524868	−	0.851184i	$-0.324115\pi$
$661$	17839.5			1.04974			0.524868	+	0.851184i	$0.324115\pi$
$662$	7754.83	−	8149.17i	0.455287	−	0.478439i
$663$		0			0
$664$	10103.9	−	11730.7i	0.590522	−	0.685602i
$665$			10178.1i			0.593517i
$666$		0			0
$667$			41.0905i			0.00238535i
$668$	345.696	+	6966.79i	0.0200230	+	0.403523i
$669$		0			0
$670$	−4429.87	−	4215.50i	−0.255434	−	0.243073i
$671$	9746.18			0.560726
$672$		0			0
$673$	−12116.6			−0.693998			−0.346999	−	0.937865i	$-0.612799\pi$
$673$	−12116.6			−0.693998			−0.346999	+	0.937865i	$0.612799\pi$
$674$	−2372.07	−	2257.28i	−0.135562	−	0.129002i
$675$		0			0
$676$	−672.953	−	13562.0i	−0.0382882	−	0.771620i
$677$		−	21508.1i		−	1.22101i	−0.792013	−	0.610504i	$-0.790967\pi$
$677$		−	21508.1i		−	1.22101i	0.792013	−	0.610504i	$-0.209033\pi$
$678$		0			0
$679$			11763.4i			0.664856i
$680$	−28582.9	+	33185.0i	−1.61192	+	1.87145i
$681$		0			0
$682$	−3427.20	+	3601.48i	−0.192426	+	0.202211i
$683$	−33849.4			−1.89636			−0.948179	−	0.317738i	$-0.897077\pi$
$683$	−33849.4			−1.89636			−0.948179	+	0.317738i	$0.897077\pi$
$684$		0			0
$685$	−10688.4			−0.596178
$686$	−8296.19	+	8718.06i	−0.461735	+	0.485214i
$687$		0			0
$688$	−2644.44	−	26581.0i	−0.146538	−	1.47295i
$689$			4044.83i			0.223651i
$690$		0			0
$691$			2063.38i			0.113596i	0.998386	+	0.0567980i	$0.0180891\pi$
$691$			2063.38i			0.113596i	−0.998386	+	0.0567980i	$0.981911\pi$
$692$	−18638.8	+	924.866i	−1.02390	+	0.0508065i
$693$		0			0
$694$	−5088.08	−	4841.87i	−0.278301	−	0.264834i
$695$	−44068.2			−2.40518
$696$		0			0
$697$	−1795.42			−0.0975699
$698$	−12240.1	−	11647.8i	−0.663745	−	0.631627i
$699$		0			0
$700$	26180.0	−	1299.06i	1.41359	−	0.0701429i
$701$			19641.7i			1.05828i	0.848534	+	0.529141i	$0.177486\pi$
$701$			19641.7i			1.05828i	−0.848534	+	0.529141i	$0.822514\pi$
$702$		0			0
$703$		−	6477.79i		−	0.347531i
$704$	−967.632	−	6457.50i	−0.0518026	−	0.345705i
$705$		0			0
$706$	2010.90	−	2113.16i	0.107197	−	0.112648i
$707$	31893.8			1.69659
$708$		0			0
$709$	−5371.97			−0.284554			−0.142277	−	0.989827i	$-0.545442\pi$
$709$	−5371.97			−0.284554			−0.142277	+	0.989827i	$0.545442\pi$
$710$	730.097	−	767.223i	0.0385916	−	0.0405540i
$711$		0			0
$712$	−4766.24	−	4105.25i	−0.250874	−	0.216083i
$713$			4846.95i			0.254586i
$714$		0			0
$715$			4704.25i			0.246055i
$716$	−253.259	−	5103.91i	−0.0132189	−	0.266399i
$717$		0			0
$718$	−8644.53	−	8226.22i	−0.449319	−	0.427576i
$719$	12836.0			0.665788			0.332894	−	0.942964i	$-0.391975\pi$
$719$	12836.0			0.665788			0.332894	+	0.942964i	$0.391975\pi$
$720$		0			0
$721$	−5113.29			−0.264118
$722$	12478.2	+	11874.4i	0.643199	+	0.612075i
$723$		0			0
$724$	1598.20	+	32208.4i	0.0820395	+	1.65334i
$725$		−	172.126i		−	0.00881738i
$726$		0			0
$727$		−	34346.9i		−	1.75221i	−0.482119	−	0.876106i	$-0.660133\pi$
$727$		−	34346.9i		−	1.75221i	0.482119	−	0.876106i	$-0.339867\pi$
$728$	−8523.89	−	7341.78i	−0.433951	−	0.373770i
$729$		0			0
$730$	−12479.8	+	13114.4i	−0.632735	+	0.664910i
$731$	48956.5			2.47705
$732$		0			0
$733$	9075.02			0.457290			0.228645	−	0.973510i	$-0.426571\pi$
$733$	9075.02			0.457290			0.228645	+	0.973510i	$0.426571\pi$
$734$	−5927.86	+	6229.30i	−0.298094	+	0.313253i
$735$		0			0
$736$	−5023.38	−	3910.34i	−0.251582	−	0.195838i
$737$			1670.85i			0.0835098i
$738$		0			0
$739$			16863.2i			0.839410i	0.907661	+	0.419705i	$0.137866\pi$
$739$			16863.2i			0.839410i	−0.907661	+	0.419705i	$0.862134\pi$
$740$	−30800.4	+	1528.33i	−1.53006	+	0.0759225i
$741$		0			0
$742$	−8246.41	−	7847.37i	−0.407999	−	0.388256i
$743$	−30043.7			−1.48344			−0.741721	−	0.670709i	$-0.765990\pi$
$743$	−30043.7			−1.48344			−0.741721	+	0.670709i	$0.765990\pi$
$744$		0			0
$745$	−1719.66			−0.0845686
$746$	10486.2	+	9978.81i	0.514649	+	0.489745i
$747$		0			0
$748$	11952.3	−	593.081i	0.584252	−	0.0289909i
$749$			37280.2i			1.81868i
$750$		0			0
$751$			8444.33i			0.410304i	0.978730	+	0.205152i	$0.0657688\pi$
$751$			8444.33i			0.410304i	−0.978730	+	0.205152i	$0.934231\pi$
$752$	14837.9	−	1476.17i	0.719527	−	0.0715829i
$753$		0			0
$754$	−50.9257	+	53.5153i	−0.00245969	+	0.00258476i
$755$	−45403.2			−2.18860
$756$		0			0
$757$	35193.1			1.68971			0.844857	−	0.534992i	$-0.179685\pi$
$757$	35193.1			1.68971			0.844857	+	0.534992i	$0.179685\pi$
$758$	−5538.66	+	5820.30i	−0.265400	+	0.278896i
$759$		0			0
$760$	−6757.50	+	7845.53i	−0.322527	+	0.374457i
$761$		−	15773.0i		−	0.751342i	−0.926753	−	0.375671i	$-0.877412\pi$
$761$		−	15773.0i		−	0.751342i	0.926753	−	0.375671i	$-0.122588\pi$
$762$		0			0
$763$		−	12025.4i		−	0.570575i
$764$	1452.47	+	29271.5i	0.0687806	+	1.38613i
$765$		0			0
$766$	11532.9	+	10974.8i	0.543996	+	0.517672i
$767$	−14025.1			−0.660259
$768$		0			0
$769$	−20741.8			−0.972651			−0.486325	−	0.873778i	$-0.661663\pi$
$769$	−20741.8			−0.972651			−0.486325	+	0.873778i	$0.661663\pi$
$770$	−9590.80	−	9126.70i	−0.448868	−	0.427147i
$771$		0			0
$772$	562.067	+	11327.3i	0.0262037	+	0.528081i
$773$		−	35223.1i		−	1.63892i	−0.573133	−	0.819462i	$-0.694272\pi$
$773$		−	35223.1i		−	1.63892i	0.573133	−	0.819462i	$-0.305728\pi$
$774$		0			0
$775$		−	20303.6i		−	0.941067i
$776$	−7810.03	+	9067.53i	−0.361293	+	0.419466i
$777$		0			0
$778$	6945.17	−	7298.34i	0.320047	−	0.336321i
$779$	−424.468			−0.0195227
$780$		0			0
$781$	−289.381			−0.0132585
$782$	8042.85	−	8451.84i	0.367790	−	0.386493i
$783$		0			0
$784$	9661.09	−	961.144i	0.440101	−	0.0437839i
$785$		−	19193.2i		−	0.872657i
$786$		0			0
$787$		−	22691.9i		−	1.02780i	−0.857850	−	0.513901i	$-0.828200\pi$
$787$		−	22691.9i		−	1.02780i	0.857850	−	0.513901i	$-0.171800\pi$
$788$	7006.71	−	347.677i	0.316756	−	0.0157176i
$789$		0			0
$790$	18990.7	+	18071.7i	0.855265	+	0.813878i
$791$	28529.2			1.28240
$792$		0			0
$793$	17082.8			0.764977
$794$	−19316.6	−	18381.9i	−0.863377	−	0.821598i
$795$		0			0
$796$	11869.0	−	588.945i	0.528499	−	0.0262244i
$797$		−	31732.1i		−	1.41030i	−0.709058	−	0.705150i	$-0.750880\pi$
$797$		−	31732.1i		−	1.41030i	0.709058	−	0.705150i	$-0.249120\pi$
$798$		0			0
$799$			27328.3i			1.21002i
$800$	21042.7	+	16380.2i	0.929964	+	0.723910i
$801$		0			0
$802$	−16829.9	+	17685.8i	−0.741005	+	0.778686i
$803$	4946.47			0.217381
$804$		0			0
$805$	−12907.5			−0.565130
$806$	−6007.08	+	6312.55i	−0.262519	+	0.275868i
$807$		0			0
$808$	24584.6	+	21175.1i	1.07040	+	0.921954i
$809$			18376.4i			0.798613i	0.916817	+	0.399307i	$0.130749\pi$
$809$			18376.4i			0.798613i	−0.916817	+	0.399307i	$0.869251\pi$
$810$		0			0
$811$		−	28834.7i		−	1.24849i	−0.781229	−	0.624244i	$-0.785407\pi$
$811$		−	28834.7i		−	1.24849i	0.781229	−	0.624244i	$-0.214593\pi$
$812$	−10.3037	−	207.650i	−0.000445306	−	0.00897423i
$813$		0			0
$814$	6104.01	+	5808.64i	0.262832	+	0.250114i
$815$	48358.0			2.07841
$816$		0			0
$817$	11574.2			0.495630
$818$	12016.8	+	11435.3i	0.513638	+	0.488783i
$819$		0			0
$820$	100.147	+	2018.25i	0.00426497	+	0.0859517i
$821$		−	16710.2i		−	0.710339i	−0.934802	−	0.355170i	$-0.884423\pi$
$821$		−	16710.2i		−	0.710339i	0.934802	−	0.355170i	$-0.115577\pi$
$822$		0			0
$823$			523.667i			0.0221797i	0.999939	+	0.0110898i	$0.00353008\pi$
$823$			523.667i			0.0221797i	−0.999939	+	0.0110898i	$0.996470\pi$
$824$	−3941.46	−	3394.85i	−0.166635	−	0.143526i
$825$		0			0
$826$	27210.1	−	28593.8i	1.14620	−	1.20449i
$827$	28676.4			1.20577			0.602887	−	0.797826i	$-0.294017\pi$
$827$	28676.4			1.20577			0.602887	+	0.797826i	$0.294017\pi$
$828$		0			0
$829$	14521.0			0.608365			0.304183	−	0.952614i	$-0.401617\pi$
$829$	14521.0			0.608365			0.304183	+	0.952614i	$0.401617\pi$
$830$	22015.3	−	23134.8i	0.920676	−	0.967494i
$831$		0			0
$832$	−1696.03	−	11318.5i	−0.0706723	−	0.471632i
$833$			17793.7i			0.740113i
$834$		0			0
$835$			14388.4i			0.596323i
$836$	2825.74	−	140.215i	0.116902	−	0.00580076i
$837$		0			0
$838$	14252.0	+	13562.3i	0.587501	+	0.559072i
$839$	31189.5			1.28341			0.641706	−	0.766951i	$-0.278227\pi$
$839$	31189.5			1.28341			0.641706	+	0.766951i	$0.278227\pi$
$840$		0			0
$841$	24387.6			0.999944
$842$	−19251.6	−	18320.0i	−0.787950	−	0.749821i
$843$		0			0
$844$	−2458.19	+	121.977i	−0.100254	+	0.00497466i
$845$		−	28009.3i		−	1.14029i
$846$		0			0
$847$		−	25986.4i		−	1.05420i
$848$	−1146.47	−	11524.0i	−0.0464270	−	0.466668i
$849$		0			0
$850$	−33691.1	+	35404.3i	−1.35952	+	1.42866i
$851$	8214.91			0.330909
$852$		0			0
$853$	13089.9			0.525426			0.262713	−	0.964874i	$-0.415383\pi$
$853$	13089.9			0.525426			0.262713	+	0.964874i	$0.415383\pi$
$854$	−33142.2	+	34827.5i	−1.32799	+	1.39552i
$855$		0			0
$856$	−24751.3	+	28736.5i	−0.988297	+	1.14742i
$857$		−	17799.5i		−	0.709472i	−0.934966	−	0.354736i	$-0.884571\pi$
$857$		−	17799.5i		−	0.709472i	0.934966	−	0.354736i	$-0.115429\pi$
$858$		0			0
$859$		−	42346.5i		−	1.68201i	−0.541029	−	0.841004i	$-0.681965\pi$
$859$		−	42346.5i		−	1.68201i	0.541029	−	0.841004i	$-0.318035\pi$
$860$	−2730.75	−	55032.7i	−0.108277	−	2.18209i
$861$		0			0
$862$	−15051.7	−	14323.4i	−0.594738	−	0.565958i
$863$	−41963.9			−1.65524			−0.827618	−	0.561291i	$-0.810305\pi$
$863$	−41963.9			−1.65524			−0.827618	+	0.561291i	$0.810305\pi$
$864$		0			0
$865$	−38494.2			−1.51311
$866$	28015.4	+	26659.7i	1.09931	+	1.04611i
$867$		0			0
$868$	−1215.40	−	24493.9i	−0.0475269	−	0.957808i
$869$		−	7162.90i		−	0.279614i
$870$		0			0
$871$			2928.62i			0.113929i
$872$	7983.99	−	9269.50i	0.310060	−	0.359982i
$873$		0			0
$874$	1901.47	−	1998.16i	0.0735907	−	0.0773328i
$875$	8189.76			0.316416
$876$		0			0
$877$	−43331.4			−1.66841			−0.834206	−	0.551453i	$-0.814074\pi$
$877$	−43331.4			−1.66841			−0.834206	+	0.551453i	$0.814074\pi$
$878$	−11247.9	+	11819.9i	−0.432346	+	0.454331i
$879$		0			0
$880$	−1333.38	−	13402.7i	−0.0510775	−	0.513414i
$881$		−	38532.4i		−	1.47354i	−0.676142	−	0.736771i	$-0.736349\pi$
$881$		−	38532.4i		−	1.47354i	0.676142	−	0.736771i	$-0.263651\pi$
$882$		0			0
$883$		−	7198.92i		−	0.274364i	−0.990546	−	0.137182i	$-0.956196\pi$
$883$		−	7198.92i		−	0.274364i	0.990546	−	0.137182i	$-0.0438045\pi$
$884$	20949.6	−	1039.53i	0.797073	−	0.0395512i
$885$		0			0
$886$	19778.4	+	18821.3i	0.749965	+	0.713674i
$887$	−14220.1			−0.538291			−0.269145	−	0.963100i	$-0.586741\pi$
$887$	−14220.1			−0.538291			−0.269145	+	0.963100i	$0.586741\pi$
$888$		0			0
$889$	−59492.2			−2.24444
$890$	−9399.76	−	8944.90i	−0.354023	−	0.336892i
$891$		0			0
$892$	31189.5	−	1547.64i	1.17074	−	0.0580928i
$893$			6460.90i			0.242112i
$894$		0			0
$895$		−	10541.0i		−	0.393683i
$896$	26366.0	+	18501.2i	0.983066	+	0.689822i
$897$		0			0
$898$	22407.7	−	23547.1i	0.832688	−	0.875031i
$899$	−161.041			−0.00597442
$900$		0			0
$901$	21224.7			0.784791
$902$	380.621	−	399.976i	0.0140502	−	0.0147647i
$903$		0			0
$904$	21991.0	+	18941.3i	0.809082	+	0.696877i
$905$			66519.3i			2.44329i
$906$		0			0
$907$		−	49979.1i		−	1.82969i	−0.403804	−	0.914845i	$-0.632312\pi$
$907$		−	49979.1i		−	1.82969i	0.403804	−	0.914845i	$-0.367688\pi$
$908$	−764.709	−	15411.1i	−0.0279491	−	0.563256i
$909$		0			0
$910$	−16810.4	−	15997.0i	−0.612374	−	0.582741i
$911$	−14612.6			−0.531436			−0.265718	−	0.964051i	$-0.585609\pi$
$911$	−14612.6			−0.531436			−0.265718	+	0.964051i	$0.585609\pi$
$912$		0			0
$913$	−8725.96			−0.316306
$914$	36148.0	+	34398.8i	1.30817	+	1.24487i
$915$		0			0
$916$	910.871	+	18356.7i	0.0328559	+	0.662144i
$917$			18389.6i			0.662244i
$918$		0			0
$919$		−	45594.4i		−	1.63658i	−0.574804	−	0.818291i	$-0.694922\pi$
$919$		−	45594.4i		−	1.63658i	0.574804	−	0.818291i	$-0.305078\pi$
$920$	−9949.44	−	8569.64i	−0.356547	−	0.307101i
$921$		0			0
$922$	25086.1	−	26361.7i	0.896058	−	0.941623i
$923$	−507.217			−0.0180880
$924$		0			0
$925$	−34411.9			−1.22319
$926$	26982.8	−	28354.9i	0.957571	−	1.00626i
$927$		0			0
$928$	129.922	−	166.903i	0.00459579	−	0.00590393i
$929$			51720.3i			1.82657i	0.407316	+	0.913287i	$0.366465\pi$
$929$			51720.3i			1.82657i	−0.407316	+	0.913287i	$0.633535\pi$
$930$		0			0
$931$			4206.74i			0.148088i
$932$	26899.7	−	1334.78i	0.945417	−	0.0469121i
$933$		0			0
$934$	166.261	+	158.216i	0.00582466	+	0.00554280i
$935$	24684.9			0.863404
$936$		0			0
$937$	−42197.0			−1.47120			−0.735601	−	0.677415i	$-0.763100\pi$
$937$	−42197.0			−1.47120			−0.735601	+	0.677415i	$0.763100\pi$
$938$	−5970.72	−	5681.80i	−0.207837	−	0.197780i
$939$		0			0
$940$	30720.1	−	1524.35i	1.06594	−	0.0528923i
$941$			10808.1i			0.374424i	0.982320	+	0.187212i	$0.0599451\pi$
$941$			10808.1i			0.374424i	−0.982320	+	0.187212i	$0.940055\pi$
$942$		0			0
$943$		−	538.296i		−	0.0185889i
$944$	39958.5	−	3975.31i	1.37769	−	0.137061i
$945$		0			0
$946$	−10378.6	+	10906.4i	−0.356699	+	0.374837i
$947$	745.664			0.0255869			0.0127935	−	0.999918i	$-0.495928\pi$
$947$	745.664			0.0255869			0.0127935	+	0.999918i	$0.495928\pi$
$948$		0			0
$949$	8670.00			0.296565
$950$	−7965.17	+	8370.21i	−0.272026	+	0.285858i
$951$		0			0
$952$	−38525.0	+	44727.9i	−1.31156	+	1.52273i
$953$			49163.3i			1.67110i	0.549417	+	0.835548i	$0.314850\pi$
$953$			49163.3i			1.67110i	−0.549417	+	0.835548i	$0.685150\pi$
$954$		0			0
$955$			60453.7i			2.04841i
$956$	−243.890	−	4915.09i	−0.00825100	−	0.166282i
$957$		0			0
$958$	30619.9	+	29138.2i	1.03266	+	0.982685i
$959$	−14406.2			−0.485088
$960$		0			0
$961$	10795.0			0.362358
$962$	10698.9	+	10181.2i	0.358572	+	0.341221i
$963$		0			0
$964$	−1741.15	−	35089.3i	−0.0581728	−	1.17235i
$965$			23394.0i			0.780395i
$966$		0			0
$967$			16888.4i			0.561627i	0.959762	+	0.280813i	$0.0906042\pi$
$967$			16888.4i			0.561627i	−0.959762	+	0.280813i	$0.909396\pi$
$968$	17253.1	−	20031.0i	0.572867	−	0.665105i
$969$		0			0
$970$	−17017.2	+	17882.6i	−0.563289	+	0.591932i
$971$	22501.6			0.743677			0.371838	−	0.928297i	$-0.378728\pi$
$971$	22501.6			0.743677			0.371838	+	0.928297i	$0.378728\pi$
$972$		0			0
$973$	−59396.6			−1.95701
$974$	−11570.2	+	12158.6i	−0.380631	+	0.399987i
$975$		0			0
$976$	−48669.8	+	4841.97i	−1.59619	+	0.158799i
$977$		−	13764.1i		−	0.450720i	−0.974276	−	0.225360i	$-0.927644\pi$
$977$		−	13764.1i		−	0.450720i	0.974276	−	0.225360i	$-0.0723558\pi$
$978$		0			0
$979$			3545.40i			0.115742i
$980$	20002.1	−	992.515i	0.651983	−	0.0323518i
$981$		0			0
$982$	41112.0	+	39122.6i	1.33598	+	1.27134i
$983$	7784.49			0.252581			0.126290	−	0.991993i	$-0.459693\pi$
$983$	7784.49			0.252581			0.126290	+	0.991993i	$0.459693\pi$
$984$		0			0
$985$	14470.8			0.468100
$986$	280.814	+	267.225i	0.00906991	+	0.00863102i
$987$		0			0
$988$	4952.87	−	245.764i	0.159485	−	0.00791375i
$989$			14678.0i			0.471925i
$990$		0			0
$991$			47880.3i			1.53478i	0.641179	+	0.767391i	$0.278445\pi$
$991$			47880.3i			1.53478i	−0.641179	+	0.767391i	$0.721555\pi$
$992$	15325.3	−	19687.5i	0.490502	−	0.630119i
$993$		0			0
$994$	984.049	−	1034.09i	0.0314006	−	0.0329973i
$995$	24512.7			0.781011
$996$		0			0
$997$	2491.15			0.0791328			0.0395664	−	0.999217i	$-0.487402\pi$
$997$	2491.15			0.0791328			0.0395664	+	0.999217i	$0.487402\pi$
$998$	18345.0	−	19277.9i	0.581864	−	0.611453i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.4.b.c.323.18		24
3.2	odd	2	inner	324.4.b.c.323.7		24
4.3	odd	2	inner	324.4.b.c.323.8		24
9.2	odd	6		108.4.h.b.71.6		24
9.4	even	3		108.4.h.b.35.1		24
9.5	odd	6		36.4.h.b.11.12	yes	24
9.7	even	3		36.4.h.b.23.7	yes	24
12.11	even	2	inner	324.4.b.c.323.17		24
36.7	odd	6		36.4.h.b.23.12	yes	24
36.11	even	6		108.4.h.b.71.1		24
36.23	even	6		36.4.h.b.11.7	✓	24
36.31	odd	6		108.4.h.b.35.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.7	✓	24	36.23	even	6
36.4.h.b.11.12	yes	24	9.5	odd	6
36.4.h.b.23.7	yes	24	9.7	even	3
36.4.h.b.23.12	yes	24	36.7	odd	6
108.4.h.b.35.1		24	9.4	even	3
108.4.h.b.35.6		24	36.31	odd	6
108.4.h.b.71.1		24	36.11	even	6
108.4.h.b.71.6		24	9.2	odd	6
324.4.b.c.323.7		24	3.2	odd	2	inner
324.4.b.c.323.8		24	4.3	odd	2	inner
324.4.b.c.323.17		24	12.11	even	2	inner
324.4.b.c.323.18		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)

\(f(q)\)	\(=\)	\(q+(2.04896 + 1.94981i) q^{2} +(0.396477 + 7.99017i) q^{4} +16.5019i q^{5} +22.2418i q^{7} +(-14.7670 + 17.1446i) q^{8} +O(q^{10})\)	\(q+(2.04896 + 1.94981i) q^{2} +(0.396477 + 7.99017i) q^{4} +16.5019i q^{5} +22.2418i q^{7} +(-14.7670 + 17.1446i) q^{8} +(-32.1756 + 33.8118i) q^{10} +12.7531 q^{11} +22.3532 q^{13} +(-43.3674 + 45.5727i) q^{14} +(-63.6856 + 6.33583i) q^{16} -117.295i q^{17} -27.7307i q^{19} +(-131.853 + 6.54262i) q^{20} +(26.1306 + 24.8661i) q^{22} +35.1671 q^{23} -147.313 q^{25} +(45.8008 + 43.5845i) q^{26} +(-177.716 + 8.81837i) q^{28} +1.16843i q^{29} +137.826i q^{31} +(-142.843 - 111.193i) q^{32} +(228.704 - 240.333i) q^{34} -367.033 q^{35} +233.596 q^{37} +(54.0696 - 56.8191i) q^{38} +(-282.919 - 243.683i) q^{40} -15.3068i q^{41} +417.378i q^{43} +(5.05631 + 101.900i) q^{44} +(72.0561 + 68.5693i) q^{46} -232.987 q^{47} -151.700 q^{49} +(-301.839 - 287.233i) q^{50} +(8.86252 + 178.606i) q^{52} +180.951i q^{53} +210.451i q^{55} +(-381.327 - 328.444i) q^{56} +(-2.27823 + 2.39408i) q^{58} -627.433 q^{59} +764.220 q^{61} +(-268.735 + 282.400i) q^{62} +(-75.8742 - 506.347i) q^{64} +368.871i q^{65} +131.015i q^{67} +(937.210 - 46.5048i) q^{68} +(-752.036 - 715.645i) q^{70} -22.6910 q^{71} +387.864 q^{73} +(478.630 + 455.469i) q^{74} +(221.573 - 10.9946i) q^{76} +283.653i q^{77} -561.659i q^{79} +(-104.553 - 1050.93i) q^{80} +(29.8454 - 31.3630i) q^{82} -684.222 q^{83} +1935.60 q^{85} +(-813.809 + 855.192i) q^{86} +(-188.325 + 218.647i) q^{88} +278.003i q^{89} +497.177i q^{91} +(13.9429 + 280.991i) q^{92} +(-477.382 - 454.281i) q^{94} +457.610 q^{95} +528.886 q^{97} +(-310.827 - 295.786i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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