LMFDB - Embedded newform 72.5.m.a.41.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,5,Mod(41,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("72.41");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	72.m (of order $6$, degree $2$, 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:	$7.44263734204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.11
Character	$\chi$	$=$	72.41
Dual form			72.5.m.a.65.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.44225 - 3.11903i) q^{3} +(-14.6470 - 8.45647i) q^{5} +(-42.9574 - 74.4045i) q^{7} +(61.5433 - 52.6632i) q^{9} +O(q^{10})$	\(q+(8.44225 - 3.11903i) q^{3} +(-14.6470 - 8.45647i) q^{5} +(-42.9574 - 74.4045i) q^{7} +(61.5433 - 52.6632i) q^{9} +(44.0796 - 25.4494i) q^{11} +(-79.9617 + 138.498i) q^{13} +(-150.030 - 25.7072i) q^{15} -440.689i q^{17} +237.683 q^{19} +(-594.727 - 494.156i) q^{21} +(518.790 + 299.523i) q^{23} +(-169.476 - 293.541i) q^{25} +(355.306 - 636.552i) q^{27} +(223.437 - 129.001i) q^{29} +(-566.569 + 981.327i) q^{31} +(292.754 - 352.335i) q^{33} +1453.07i q^{35} -1121.13 q^{37} +(-243.079 + 1418.64i) q^{39} +(1776.15 + 1025.46i) q^{41} +(1594.57 + 2761.87i) q^{43} +(-1346.77 + 250.921i) q^{45} +(2237.04 - 1291.56i) q^{47} +(-2490.18 + 4313.13i) q^{49} +(-1374.52 - 3720.41i) q^{51} -2577.10i q^{53} -860.847 q^{55} +(2006.58 - 741.340i) q^{57} +(2479.62 + 1431.61i) q^{59} +(152.465 + 264.077i) q^{61} +(-6562.13 - 2316.82i) q^{63} +(2342.40 - 1352.39i) q^{65} +(1951.56 - 3380.21i) q^{67} +(5313.98 + 910.533i) q^{69} +3660.90i q^{71} -839.584 q^{73} +(-2346.32 - 1949.55i) q^{75} +(-3787.09 - 2186.48i) q^{77} +(-5180.42 - 8972.75i) q^{79} +(1014.17 - 6482.14i) q^{81} +(-4060.91 + 2344.57i) q^{83} +(-3726.68 + 6454.79i) q^{85} +(1483.95 - 1785.97i) q^{87} -1537.03i q^{89} +13739.8 q^{91} +(-1722.34 + 10051.8i) q^{93} +(-3481.35 - 2009.96i) q^{95} +(-3221.04 - 5579.01i) q^{97} +(1372.56 - 3887.61i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 100 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 - 100 * q^9	$ 24 q + 4 q^{3} - 100 q^{9} + 252 q^{11} - 80 q^{15} - 408 q^{19} + 24 q^{21} + 720 q^{23} + 1500 q^{25} - 1280 q^{27} + 2376 q^{29} - 1104 q^{31} - 1412 q^{33} - 4184 q^{39} + 1980 q^{41} + 1476 q^{43} - 4696 q^{45} + 4536 q^{47} - 6084 q^{49} - 7828 q^{51} + 2544 q^{55} - 1204 q^{57} + 10332 q^{59} + 2784 q^{61} + 9072 q^{63} + 17280 q^{65} - 2604 q^{67} + 5680 q^{69} + 5112 q^{73} - 15412 q^{75} - 28368 q^{77} + 3480 q^{79} - 26548 q^{81} - 23400 q^{83} + 7392 q^{85} - 3192 q^{87} - 14208 q^{91} + 39488 q^{93} + 57528 q^{95} - 4020 q^{97} + 50744 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 100 * q^9 + 252 * q^11 - 80 * q^15 - 408 * q^19 + 24 * q^21 + 720 * q^23 + 1500 * q^25 - 1280 * q^27 + 2376 * q^29 - 1104 * q^31 - 1412 * q^33 - 4184 * q^39 + 1980 * q^41 + 1476 * q^43 - 4696 * q^45 + 4536 * q^47 - 6084 * q^49 - 7828 * q^51 + 2544 * q^55 - 1204 * q^57 + 10332 * q^59 + 2784 * q^61 + 9072 * q^63 + 17280 * q^65 - 2604 * q^67 + 5680 * q^69 + 5112 * q^73 - 15412 * q^75 - 28368 * q^77 + 3480 * q^79 - 26548 * q^81 - 23400 * q^83 + 7392 * q^85 - 3192 * q^87 - 14208 * q^91 + 39488 * q^93 + 57528 * q^95 - 4020 * q^97 + 50744 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	8.44225	−	3.11903i	0.938028	−	0.346559i
$3$	8.44225	−	3.11903i	0.938028	−	0.346559i
$4$		0			0
$5$	−14.6470	−	8.45647i	−0.585882	−	0.338259i	0.177586	−	0.984105i	$-0.443171\pi$
$5$	−14.6470	−	8.45647i	−0.585882	−	0.338259i	−0.763467	+	0.645846i	$0.776505\pi$
$6$		0			0
$7$	−42.9574	−	74.4045i	−0.876683	−	1.51846i	−0.854960	−	0.518695i	$-0.826418\pi$
$7$	−42.9574	−	74.4045i	−0.876683	−	1.51846i	−0.0217230	−	0.999764i	$-0.506915\pi$
$8$		0			0
$9$	61.5433	−	52.6632i	0.759794	−	0.650164i
$10$		0			0
$11$	44.0796	−	25.4494i	0.364294	−	0.210325i	−0.306669	−	0.951816i	$-0.599214\pi$
$11$	44.0796	−	25.4494i	0.364294	−	0.210325i	0.670963	+	0.741491i	$0.265881\pi$
$12$		0			0
$13$	−79.9617	+	138.498i	−0.473146	+	0.819513i	−0.999528	−	0.0307357i	$-0.990215\pi$
$13$	−79.9617	+	138.498i	−0.473146	+	0.819513i	0.526382	+	0.850248i	$0.323548\pi$
$14$		0			0
$15$	−150.030	−	25.7072i	−0.666800	−	0.114254i
$16$		0			0
$17$		−	440.689i		−	1.52488i	−0.647061	−	0.762438i	$-0.724002\pi$
$17$		−	440.689i		−	1.52488i	0.647061	−	0.762438i	$-0.275998\pi$
$18$		0			0
$19$	237.683			0.658401			0.329201	−	0.944260i	$-0.393221\pi$
$19$	237.683			0.658401			0.329201	+	0.944260i	$0.393221\pi$
$20$		0			0
$21$	−594.727	−	494.156i	−1.34859	−	1.12054i
$22$		0			0
$23$	518.790	+	299.523i	0.980699	+	0.566207i	0.902481	−	0.430730i	$-0.141744\pi$
$23$	518.790	+	299.523i	0.980699	+	0.566207i	0.0782177	+	0.996936i	$0.475077\pi$
$24$		0			0
$25$	−169.476	−	293.541i	−0.271162	−	0.469666i
$26$		0			0
$27$	355.306	−	636.552i	0.487389	−	0.873185i
$28$		0			0
$29$	223.437	−	129.001i	0.265680	−	0.153390i	−0.361243	−	0.932472i	$-0.617648\pi$
$29$	223.437	−	129.001i	0.265680	−	0.153390i	0.626923	+	0.779082i	$0.284314\pi$
$30$		0			0
$31$	−566.569	+	981.327i	−0.589562	+	1.02115i	0.404728	+	0.914437i	$0.367366\pi$
$31$	−566.569	+	981.327i	−0.589562	+	1.02115i	−0.994290	+	0.106714i	$0.965967\pi$
$32$		0			0
$33$	292.754	−	352.335i	0.268828	−	0.323540i
$34$		0			0
$35$			1453.07i			1.18618i
$36$		0			0
$37$	−1121.13			−0.818941			−0.409471	−	0.912323i	$-0.634287\pi$
$37$	−1121.13			−0.818941			−0.409471	+	0.912323i	$0.634287\pi$
$38$		0			0
$39$	−243.079	+	1418.64i	−0.159815	+	0.932699i
$40$		0			0
$41$	1776.15	+	1025.46i	1.05660	+	0.610029i	0.924490	−	0.381206i	$-0.124491\pi$
$41$	1776.15	+	1025.46i	1.05660	+	0.610029i	0.132111	+	0.991235i	$0.457824\pi$
$42$		0			0
$43$	1594.57	+	2761.87i	0.862394	+	1.49371i	0.869612	+	0.493736i	$0.164369\pi$
$43$	1594.57	+	2761.87i	0.862394	+	1.49371i	−0.00721836	+	0.999974i	$0.502298\pi$
$44$		0			0
$45$	−1346.77	+	250.921i	−0.665073	+	0.123912i
$46$		0			0
$47$	2237.04	−	1291.56i	1.01269	−	0.584679i	0.100714	−	0.994915i	$-0.467887\pi$
$47$	2237.04	−	1291.56i	1.01269	−	0.584679i	0.911979	+	0.410237i	$0.134554\pi$
$48$		0			0
$49$	−2490.18	+	4313.13i	−1.03714	+	1.79639i
$50$		0			0
$51$	−1374.52	−	3720.41i	−0.528459	−	1.43038i
$52$		0			0
$53$		−	2577.10i		−	0.917443i	−0.888580	−	0.458722i	$-0.848308\pi$
$53$		−	2577.10i		−	0.917443i	0.888580	−	0.458722i	$-0.151692\pi$
$54$		0			0
$55$	−860.847			−0.284578
$56$		0			0
$57$	2006.58	−	741.340i	0.617599	−	0.228175i
$58$		0			0
$59$	2479.62	+	1431.61i	0.712330	+	0.411264i	0.811923	−	0.583765i	$-0.198421\pi$
$59$	2479.62	+	1431.61i	0.712330	+	0.411264i	−0.0995934	+	0.995028i	$0.531754\pi$
$60$		0			0
$61$	152.465	+	264.077i	0.0409741	+	0.0709693i	0.885785	−	0.464095i	$-0.153621\pi$
$61$	152.465	+	264.077i	0.0409741	+	0.0709693i	−0.844811	+	0.535065i	$0.820287\pi$
$62$		0			0
$63$	−6562.13	−	2316.82i	−1.65334	−	0.583729i
$64$		0			0
$65$	2342.40	−	1352.39i	0.554415	−	0.320092i
$66$		0			0
$67$	1951.56	−	3380.21i	0.434744	−	0.752998i	−0.562531	−	0.826776i	$-0.690172\pi$
$67$	1951.56	−	3380.21i	0.434744	−	0.752998i	0.997275	+	0.0737781i	$0.0235056\pi$
$68$		0			0
$69$	5313.98	+	910.533i	1.11615	+	0.191248i
$70$		0			0
$71$			3660.90i			0.726224i	0.931745	+	0.363112i	$0.118286\pi$
$71$			3660.90i			0.726224i	−0.931745	+	0.363112i	$0.881714\pi$
$72$		0			0
$73$	−839.584			−0.157550			−0.0787750	−	0.996892i	$-0.525101\pi$
$73$	−839.584			−0.157550			−0.0787750	+	0.996892i	$0.525101\pi$
$74$		0			0
$75$	−2346.32	−	1949.55i	−0.417124	−	0.346587i
$76$		0			0
$77$	−3787.09	−	2186.48i	−0.638741	−	0.368777i
$78$		0			0
$79$	−5180.42	−	8972.75i	−0.830063	−	1.43771i	−0.897988	−	0.440020i	$-0.854971\pi$
$79$	−5180.42	−	8972.75i	−0.830063	−	1.43771i	0.0679254	−	0.997690i	$-0.478362\pi$
$80$		0			0
$81$	1014.17	−	6482.14i	0.154575	−	0.987981i
$82$		0			0
$83$	−4060.91	+	2344.57i	−0.589478	+	0.340335i	−0.764891	−	0.644160i	$-0.777207\pi$
$83$	−4060.91	+	2344.57i	−0.589478	+	0.340335i	0.175413	+	0.984495i	$0.443874\pi$
$84$		0			0
$85$	−3726.68	+	6454.79i	−0.515803	+	0.893397i
$86$		0			0
$87$	1483.95	−	1785.97i	0.196056	−	0.235958i
$88$		0			0
$89$		−	1537.03i		−	0.194046i	−0.995282	−	0.0970228i	$-0.969068\pi$
$89$		−	1537.03i		−	0.194046i	0.995282	−	0.0970228i	$-0.0309320\pi$
$90$		0			0
$91$	13739.8			1.65920
$92$		0			0
$93$	−1722.34	+	10051.8i	−0.199137	+	1.16219i
$94$		0			0
$95$	−3481.35	−	2009.96i	−0.385745	−	0.222710i
$96$		0			0
$97$	−3221.04	−	5579.01i	−0.342336	−	0.592944i	0.642530	−	0.766261i	$-0.277885\pi$
$97$	−3221.04	−	5579.01i	−0.342336	−	0.592944i	−0.984866	+	0.173317i	$0.944552\pi$
$98$		0			0
$99$	1372.56	−	3887.61i	0.140043	−	0.396655i
$100$		0			0
$101$	13975.5	−	8068.78i	1.37002	−	0.790979i	0.379087	−	0.925361i	$-0.376238\pi$
$101$	13975.5	−	8068.78i	1.37002	−	0.790979i	0.990930	+	0.134382i	$0.0429049\pi$
$102$		0			0
$103$	−2190.68	+	3794.38i	−0.206493	+	0.357656i	−0.950607	−	0.310396i	$-0.899538\pi$
$103$	−2190.68	+	3794.38i	−0.206493	+	0.357656i	0.744114	+	0.668052i	$0.232872\pi$
$104$		0			0
$105$	4532.18	+	12267.2i	0.411082	+	1.11267i
$106$		0			0
$107$		−	6517.24i		−	0.569241i	−0.958640	−	0.284621i	$-0.908132\pi$
$107$		−	6517.24i		−	0.569241i	0.958640	−	0.284621i	$-0.0918677\pi$
$108$		0			0
$109$	11311.2			0.952045			0.476022	−	0.879433i	$-0.342078\pi$
$109$	11311.2			0.952045			0.476022	+	0.879433i	$0.342078\pi$
$110$		0			0
$111$	−9464.87	+	3496.84i	−0.768190	+	0.283811i
$112$		0			0
$113$	−13112.7	−	7570.63i	−1.02692	−	0.592891i	−0.110817	−	0.993841i	$-0.535347\pi$
$113$	−13112.7	−	7570.63i	−1.02692	−	0.592891i	−0.916100	+	0.400950i	$0.868680\pi$
$114$		0			0
$115$	−5065.82	−	8774.26i	−0.383049	−	0.663460i
$116$		0			0
$117$	2372.63	+	12734.6i	0.173324	+	0.930283i
$118$		0			0
$119$	−32789.2	+	18930.9i	−2.31546	+	1.33683i
$120$		0			0
$121$	−6025.16	+	10435.9i	−0.411527	+	0.712785i
$122$		0			0
$123$	18193.1	+	3117.34i	1.20253	+	0.206050i
$124$		0			0
$125$			16303.3i			1.04341i
$126$		0			0
$127$	23828.2			1.47735			0.738677	−	0.674059i	$-0.235451\pi$
$127$	23828.2			1.47735			0.738677	+	0.674059i	$0.235451\pi$
$128$		0			0
$129$	22076.1	+	18342.9i	1.32661	+	1.10227i
$130$		0			0
$131$	24358.6	+	14063.5i	1.41942	+	0.819501i	0.996248	−	0.0865490i	$-0.0275839\pi$
$131$	24358.6	+	14063.5i	1.41942	+	0.819501i	0.423170	+	0.906050i	$0.360917\pi$
$132$		0			0
$133$	−10210.3	−	17684.7i	−0.577209	−	0.999755i
$134$		0			0
$135$	−10587.2	+	6318.96i	−0.580915	+	0.346719i
$136$		0			0
$137$	−23817.6	+	13751.1i	−1.26898	+	0.732649i	−0.974796	−	0.223099i	$-0.928383\pi$
$137$	−23817.6	+	13751.1i	−1.26898	+	0.732649i	−0.294189	+	0.955747i	$0.595049\pi$
$138$		0			0
$139$	8759.51	−	15171.9i	0.453367	−	0.785255i	−0.545225	−	0.838290i	$-0.683556\pi$
$139$	8759.51	−	15171.9i	0.453367	−	0.785255i	0.998593	+	0.0530342i	$0.0168892\pi$
$140$		0			0
$141$	14857.3	−	17881.0i	0.747310	−	0.899403i
$142$		0			0
$143$			8139.89i			0.398058i
$144$		0			0
$145$	−4363.58			−0.207542
$146$		0			0
$147$	−7570.01	+	44179.5i	−0.350318	+	2.04449i
$148$		0			0
$149$	−27183.6	−	15694.4i	−1.22443	−	0.706925i	−0.258571	−	0.965992i	$-0.583252\pi$
$149$	−27183.6	−	15694.4i	−1.22443	−	0.706925i	−0.965859	+	0.259067i	$0.916585\pi$
$150$		0			0
$151$	−138.597	−	240.056i	−0.00607853	−	0.0105283i	0.862970	−	0.505255i	$-0.168602\pi$
$151$	−138.597	−	240.056i	−0.00607853	−	0.0105283i	−0.869049	+	0.494727i	$0.835268\pi$
$152$		0			0
$153$	−23208.1	−	27121.5i	−0.991419	−	1.15859i
$154$		0			0
$155$	16597.1	−	9582.35i	0.690827	−	0.398849i
$156$		0			0
$157$	13713.3	−	23752.1i	0.556341	−	0.963611i	−0.441457	−	0.897283i	$-0.645538\pi$
$157$	13713.3	−	23752.1i	0.556341	−	0.963611i	0.997798	−	0.0663288i	$-0.0211286\pi$
$158$		0			0
$159$	−8038.04	−	21756.5i	−0.317948	−	0.860588i
$160$		0			0
$161$		−	51467.0i		−	1.98553i
$162$		0			0
$163$	18355.9			0.690878			0.345439	−	0.938441i	$-0.387730\pi$
$163$	18355.9			0.690878			0.345439	+	0.938441i	$0.387730\pi$
$164$		0			0
$165$	−7267.49	+	2685.01i	−0.266942	+	0.0986228i
$166$		0			0
$167$	−11672.9	−	6739.35i	−0.418548	−	0.241649i	0.275908	−	0.961184i	$-0.411022\pi$
$167$	−11672.9	−	6739.35i	−0.418548	−	0.241649i	−0.694456	+	0.719535i	$0.744355\pi$
$168$		0			0
$169$	1492.77	+	2585.55i	0.0522659	+	0.0905272i
$170$		0			0
$171$	14627.8	−	12517.2i	0.500250	−	0.428069i
$172$		0			0
$173$	19486.8	−	11250.7i	0.651100	−	0.375913i	−0.137778	−	0.990463i	$-0.543996\pi$
$173$	19486.8	−	11250.7i	0.651100	−	0.375913i	0.788877	+	0.614551i	$0.210663\pi$
$174$		0			0
$175$	−14560.5	+	25219.6i	−0.475446	+	0.823496i
$176$		0			0
$177$	25398.8	+	4352.01i	0.810712	+	0.138913i
$178$		0			0
$179$		−	5726.15i		−	0.178713i	−0.996000	−	0.0893567i	$-0.971519\pi$
$179$		−	5726.15i		−	0.178713i	0.996000	−	0.0893567i	$-0.0284811\pi$
$180$		0			0
$181$	−17958.2			−0.548157			−0.274079	−	0.961707i	$-0.588373\pi$
$181$	−17958.2			−0.548157			−0.274079	+	0.961707i	$0.588373\pi$
$182$		0			0
$183$	2110.81	+	1753.86i	0.0630299	+	0.0523712i
$184$		0			0
$185$	16421.2	+	9480.81i	0.479803	+	0.277014i
$186$		0			0
$187$	−11215.3	−	19425.4i	−0.320720	−	0.555503i
$188$		0			0
$189$	−62625.4	+	908.252i	−1.75318	+	0.0254263i
$190$		0			0
$191$	4289.09	−	2476.31i	0.117571	−	0.0678794i	−0.440062	−	0.897968i	$-0.645043\pi$
$191$	4289.09	−	2476.31i	0.117571	−	0.0678794i	0.557632	+	0.830088i	$0.311710\pi$
$192$		0			0
$193$	−9336.66	+	16171.6i	−0.250655	+	0.434148i	−0.963706	−	0.266964i	$-0.913979\pi$
$193$	−9336.66	+	16171.6i	−0.250655	+	0.434148i	0.713051	+	0.701112i	$0.247313\pi$
$194$		0			0
$195$	15557.0	−	18723.2i	0.409126	−	0.492392i
$196$		0			0
$197$			68075.5i			1.75412i	0.480385	+	0.877058i	$0.340497\pi$
$197$			68075.5i			1.75412i	−0.480385	+	0.877058i	$0.659503\pi$
$198$		0			0
$199$	−17840.9			−0.450518			−0.225259	−	0.974299i	$-0.572323\pi$
$199$	−17840.9			−0.450518			−0.225259	+	0.974299i	$0.572323\pi$
$200$		0			0
$201$	5932.64	−	34623.6i	0.146844	−	0.856998i
$202$		0			0
$203$	−19196.5	−	11083.1i	−0.465833	−	0.268949i
$204$		0			0
$205$	−17343.5	−	30039.9i	−0.412696	−	0.714810i
$206$		0			0
$207$	47701.9	−	8887.48i	1.11326	−	0.207414i
$208$		0			0
$209$	10477.0	−	6048.88i	0.239852	−	0.138479i
$210$		0			0
$211$	−39761.2	+	68868.5i	−0.893090	+	1.54688i	−0.0569384	+	0.998378i	$0.518134\pi$
$211$	−39761.2	+	68868.5i	−0.893090	+	1.54688i	−0.836151	+	0.548499i	$0.815199\pi$
$212$		0			0
$213$	11418.4	+	30906.2i	0.251679	+	0.681219i
$214$		0			0
$215$		−	53937.6i		−	1.16685i
$216$		0			0
$217$	97353.5			2.06744
$218$		0			0
$219$	−7087.99	+	2618.69i	−0.147786	+	0.0546003i
$220$		0			0
$221$	61034.4	+	35238.2i	1.24966	+	0.721489i
$222$		0			0
$223$	−12054.9	−	20879.8i	−0.242413	−	0.419871i	0.718988	−	0.695022i	$-0.244606\pi$
$223$	−12054.9	−	20879.8i	−0.242413	−	0.419871i	−0.961401	+	0.275151i	$0.911272\pi$
$224$		0			0
$225$	−25889.0	−	9140.35i	−0.511387	−	0.180550i
$226$		0			0
$227$	7345.71	−	4241.05i	0.142555	−	0.0823041i	−0.427026	−	0.904239i	$-0.640439\pi$
$227$	7345.71	−	4241.05i	0.142555	−	0.0823041i	0.569581	+	0.821935i	$0.307105\pi$
$228$		0			0
$229$	−31504.6	+	54567.6i	−0.600763	+	1.04055i	0.391942	+	0.919990i	$0.371803\pi$
$229$	−31504.6	+	54567.6i	−0.600763	+	1.04055i	−0.992706	+	0.120563i	$0.961530\pi$
$230$		0			0
$231$	−38791.3	−	6646.77i	−0.726960	−	0.124562i
$232$		0			0
$233$			72398.5i			1.33358i	0.745247	+	0.666788i	$0.232331\pi$
$233$			72398.5i			1.33358i	−0.745247	+	0.666788i	$0.767669\pi$
$234$		0			0
$235$	−43688.0			−0.791091
$236$		0			0
$237$	−71720.7	−	59592.4i	−1.27687	−	1.06095i
$238$		0			0
$239$	79975.8	+	46174.0i	1.40011	+	0.808355i	0.994404	−	0.105648i	$-0.0336916\pi$
$239$	79975.8	+	46174.0i	1.40011	+	0.808355i	0.405708	+	0.914003i	$0.367025\pi$
$240$		0			0
$241$	42867.0	+	74247.9i	0.738056	+	1.27835i	0.953370	+	0.301805i	$0.0975893\pi$
$241$	42867.0	+	74247.9i	0.738056	+	1.27835i	−0.215314	+	0.976545i	$0.569077\pi$
$242$		0			0
$243$	−11656.1	−	57887.1i	−0.197398	−	0.980323i
$244$		0			0
$245$	72947.6	−	42116.3i	1.21529	−	0.701647i
$246$		0			0
$247$	−19005.5	+	32918.5i	−0.311520	+	0.539568i
$248$		0			0
$249$	−26970.5	+	32459.5i	−0.435001	+	0.523532i
$250$		0			0
$251$		−	13626.6i		−	0.216291i	−0.994135	−	0.108146i	$-0.965509\pi$
$251$		−	13626.6i		−	0.216291i	0.994135	−	0.108146i	$-0.0344913\pi$
$252$		0			0
$253$	30490.7			0.476350
$254$		0			0
$255$	−11328.9	+	66116.6i	−0.174223	+	1.01679i
$256$		0			0
$257$	−58261.6	−	33637.3i	−0.882097	−	0.509279i	−0.0107474	−	0.999942i	$-0.503421\pi$
$257$	−58261.6	−	33637.3i	−0.882097	−	0.509279i	−0.871349	+	0.490664i	$0.836754\pi$
$258$		0			0
$259$	48160.9	+	83417.1i	0.717952	+	1.24353i
$260$		0			0
$261$	6957.41	−	19706.1i	0.102133	−	0.289280i
$262$		0			0
$263$	29698.4	−	17146.4i	0.429360	−	0.247891i	−0.269714	−	0.962940i	$-0.586929\pi$
$263$	29698.4	−	17146.4i	0.429360	−	0.247891i	0.699074	+	0.715050i	$0.253596\pi$
$264$		0			0
$265$	−21793.2	+	37746.9i	−0.310333	+	0.537513i
$266$		0			0
$267$	−4794.05	−	12976.0i	−0.0672482	−	0.182020i
$268$		0			0
$269$			89581.9i			1.23799i	0.785396	+	0.618993i	$0.212459\pi$
$269$			89581.9i			1.23799i	−0.785396	+	0.618993i	$0.787541\pi$
$270$		0			0
$271$	−85348.4			−1.16214			−0.581068	−	0.813855i	$-0.697365\pi$
$271$	−85348.4			−1.16214			−0.581068	+	0.813855i	$0.697365\pi$
$272$		0			0
$273$	115995.	−	42854.8i	1.55637	−	0.575008i
$274$		0			0
$275$	−14940.9	−	8626.12i	−0.197565	−	0.114064i
$276$		0			0
$277$	−14346.9	−	24849.5i	−0.186981	−	0.323860i	0.757261	−	0.653112i	$-0.226537\pi$
$277$	−14346.9	−	24849.5i	−0.186981	−	0.323860i	−0.944242	+	0.329252i	$0.893204\pi$
$278$		0			0
$279$	16811.3	+	90231.5i	0.215970	+	1.15918i
$280$		0			0
$281$	−33266.2	+	19206.2i	−0.421299	+	0.243237i	−0.695633	−	0.718398i	$-0.744876\pi$
$281$	−33266.2	+	19206.2i	−0.421299	+	0.243237i	0.274334	+	0.961634i	$0.411543\pi$
$282$		0			0
$283$	38050.3	−	65905.0i	0.475100	−	0.822897i	−0.524493	−	0.851415i	$-0.675745\pi$
$283$	38050.3	−	65905.0i	0.475100	−	0.822897i	0.999593	+	0.0285173i	$0.00907856\pi$
$284$		0			0
$285$	−35659.6	−	6110.16i	−0.439022	−	0.0752251i
$286$		0			0
$287$		−	176204.i		−	2.13921i
$288$		0			0
$289$	−110686.			−1.32525
$290$		0			0
$291$	−44594.0	−	37052.9i	−0.526611	−	0.437559i
$292$		0			0
$293$	39767.9	+	22960.0i	0.463231	+	0.267446i	0.713402	−	0.700755i	$-0.247153\pi$
$293$	39767.9	+	22960.0i	0.463231	+	0.267446i	−0.250171	+	0.968202i	$0.580487\pi$
$294$		0			0
$295$	−24212.7	−	41937.7i	−0.278227	−	0.481904i
$296$		0			0
$297$	−538.077	−	37101.3i	−0.00610003	−	0.420606i
$298$		0			0
$299$	−82966.6	+	47900.8i	−0.928027	+	0.535797i
$300$		0			0
$301$	136997.	−	237286.i	1.51209	−	2.61902i
$302$		0			0
$303$	92818.3	−	111709.i	1.01099	−	1.21675i
$304$		0			0
$305$		−	5157.25i		−	0.0554394i
$306$		0			0
$307$	−112176.			−1.19021			−0.595105	−	0.803648i	$-0.702890\pi$
$307$	−112176.			−1.19021			−0.595105	+	0.803648i	$0.702890\pi$
$308$		0			0
$309$	−6659.55	+	38865.9i	−0.0697474	+	0.407054i
$310$		0			0
$311$	56032.9	+	32350.6i	0.579325	+	0.334473i	0.760865	−	0.648910i	$-0.224775\pi$
$311$	56032.9	+	32350.6i	0.579325	+	0.334473i	−0.181540	+	0.983384i	$0.558108\pi$
$312$		0			0
$313$	17656.9	+	30582.6i	0.180229	+	0.312166i	0.941959	−	0.335729i	$-0.108983\pi$
$313$	17656.9	+	30582.6i	0.180229	+	0.312166i	−0.761729	+	0.647895i	$0.775649\pi$
$314$		0			0
$315$	76523.6	+	89427.0i	0.771213	+	0.901255i
$316$		0			0
$317$	1236.84	−	714.087i	0.0123082	−	0.00710612i	−0.493833	−	0.869557i	$-0.664405\pi$
$317$	1236.84	−	714.087i	0.0123082	−	0.00710612i	0.506141	+	0.862450i	$0.331071\pi$
$318$		0			0
$319$	6565.99	−	11372.6i	0.0645237	−	0.111758i
$320$		0			0
$321$	−20327.5	−	55020.2i	−0.197275	−	0.533965i
$322$		0			0
$323$		−	104744.i		−	1.00398i
$324$		0			0
$325$	54206.4			0.513197
$326$		0			0
$327$	95492.4	−	35280.1i	0.893045	−	0.329939i
$328$		0			0
$329$	−192195.	−	110964.i	−1.77562	−	1.02516i
$330$		0			0
$331$	35411.3	+	61334.2i	0.323211	+	0.559818i	0.981149	−	0.193255i	$-0.0619044\pi$
$331$	35411.3	+	61334.2i	0.323211	+	0.559818i	−0.657938	+	0.753072i	$0.728571\pi$
$332$		0			0
$333$	−68998.1	+	59042.4i	−0.622227	+	0.532446i
$334$		0			0
$335$	−57169.3	+	33006.7i	−0.509417	+	0.294112i
$336$		0			0
$337$	18665.7	−	32329.9i	0.164355	−	0.284672i	−0.772071	−	0.635537i	$-0.780779\pi$
$337$	18665.7	−	32329.9i	0.164355	−	0.284672i	0.936426	+	0.350865i	$0.114112\pi$
$338$		0			0
$339$	−134314.	−	23014.3i	−1.16875	−	0.200262i
$340$		0			0
$341$			57675.3i			0.495999i
$342$		0			0
$343$	221606.			1.88362
$344$		0			0
$345$	−70134.1	−	58274.1i	−0.589238	−	0.489595i
$346$		0			0
$347$	−34541.6	−	19942.6i	−0.286869	−	0.165624i	0.349660	−	0.936877i	$-0.386297\pi$
$347$	−34541.6	−	19942.6i	−0.286869	−	0.165624i	−0.636529	+	0.771253i	$0.719630\pi$
$348$		0			0
$349$	−36892.2	−	63899.1i	−0.302889	−	0.524619i	0.673900	−	0.738822i	$-0.264618\pi$
$349$	−36892.2	−	63899.1i	−0.302889	−	0.524619i	−0.976789	+	0.214203i	$0.931284\pi$
$350$		0			0
$351$	59750.1	+	100109.i	0.484980	+	0.812565i
$352$		0			0
$353$	82542.2	−	47655.8i	0.662410	−	0.382442i	−0.130785	−	0.991411i	$-0.541750\pi$
$353$	82542.2	−	47655.8i	0.662410	−	0.382442i	0.793194	+	0.608968i	$0.208416\pi$
$354$		0			0
$355$	30958.3	−	53621.3i	0.245652	−	0.425481i
$356$		0			0
$357$	−217769.	+	262090.i	−1.70868	+	2.05643i
$358$		0			0
$359$			118915.i			0.922671i	0.887226	+	0.461335i	$0.152629\pi$
$359$			118915.i			0.922671i	−0.887226	+	0.461335i	$0.847371\pi$
$360$		0			0
$361$	−73827.8			−0.566508
$362$		0			0
$363$	−18316.1	+	106895.i	−0.139002	+	0.811230i
$364$		0			0
$365$	12297.4	+	7099.92i	0.0923057	+	0.0532927i
$366$		0			0
$367$	73694.2	+	127642.i	0.547143	+	0.947680i	0.998469	+	0.0553207i	$0.0176181\pi$
$367$	73694.2	+	127642.i	0.547143	+	0.947680i	−0.451325	+	0.892360i	$0.649049\pi$
$368$		0			0
$369$	163314.	−	30427.5i	1.19942	−	0.223467i
$370$		0			0
$371$	−191748.	+	110706.i	−1.39310	+	0.804306i
$372$		0			0
$373$	48226.2	−	83530.3i	0.346630	−	0.600380i	−0.639019	−	0.769191i	$-0.720659\pi$
$373$	48226.2	−	83530.3i	0.346630	−	0.600380i	0.985648	+	0.168811i	$0.0539927\pi$
$374$		0			0
$375$	50850.3	+	137636.i	0.361602	+	0.978748i
$376$		0			0
$377$			41260.6i			0.290304i
$378$		0			0
$379$	−147079.			−1.02393			−0.511966	−	0.859006i	$-0.671083\pi$
$379$	−147079.			−1.02393			−0.511966	+	0.859006i	$0.671083\pi$
$380$		0			0
$381$	201164.	−	74320.9i	1.38580	−	0.511990i
$382$		0			0
$383$	70280.9	+	40576.7i	0.479115	+	0.276617i	0.720048	−	0.693925i	$-0.244120\pi$
$383$	70280.9	+	40576.7i	0.479115	+	0.276617i	−0.240932	+	0.970542i	$0.577453\pi$
$384$		0			0
$385$	36979.8	+	64050.9i	0.249484	+	0.432119i
$386$		0			0
$387$	243584.	+	85999.6i	1.62640	+	0.574215i
$388$		0			0
$389$	−45787.5	+	26435.4i	−0.302585	+	0.174698i	−0.643604	−	0.765359i	$-0.722562\pi$
$389$	−45787.5	+	26435.4i	−0.302585	+	0.174698i	0.341018	+	0.940057i	$0.389228\pi$
$390$		0			0
$391$	131997.	−	228625.i	0.863395	−	1.49544i
$392$		0			0
$393$	249506.	+	42752.1i	1.61546	+	0.276804i
$394$		0			0
$395$			175232.i			1.12310i
$396$		0			0
$397$	−44596.1			−0.282954			−0.141477	−	0.989942i	$-0.545185\pi$
$397$	−44596.1			−0.282954			−0.141477	+	0.989942i	$0.545185\pi$
$398$		0			0
$399$	−141357.	−	117452.i	−0.887912	−	0.737762i
$400$		0			0
$401$	−261098.	−	150745.i	−1.62373	−	0.937464i	−0.985909	−	0.167283i	$-0.946501\pi$
$401$	−261098.	−	150745.i	−1.62373	−	0.937464i	−0.637826	−	0.770181i	$-0.720166\pi$
$402$		0			0
$403$	−90607.6	−	156937.i	−0.557898	−	0.966307i
$404$		0			0
$405$	−69670.6	+	86368.0i	−0.424756	+	0.526554i
$406$		0			0
$407$	−49419.0	+	28532.1i	−0.298336	+	0.172244i
$408$		0			0
$409$	−102579.	+	177672.i	−0.613212	+	1.06211i	0.377483	+	0.926016i	$0.376790\pi$
$409$	−102579.	+	177672.i	−0.613212	+	1.06211i	−0.990695	+	0.136098i	$0.956544\pi$
$410$		0			0
$411$	−158184.	+	190378.i	−0.936438	+	1.12702i
$412$		0			0
$413$		−	245993.i		−	1.44219i
$414$		0			0
$415$	79307.1			0.460485
$416$		0			0
$417$	26628.4	−	155406.i	0.153134	−	0.893710i
$418$		0			0
$419$	112039.	+	64685.8i	0.638178	+	0.368452i	0.783912	−	0.620872i	$-0.213221\pi$
$419$	112039.	+	64685.8i	0.638178	+	0.368452i	−0.145735	+	0.989324i	$0.546555\pi$
$420$		0			0
$421$	−10945.6	−	18958.3i	−0.0617555	−	0.106964i	0.833495	−	0.552527i	$-0.186337\pi$
$421$	−10945.6	−	18958.3i	−0.0617555	−	0.106964i	−0.895250	+	0.445564i	$0.853003\pi$
$422$		0			0
$423$	69657.4	−	197296.i	0.389302	−	1.10265i
$424$		0			0
$425$	−129360.	+	74686.3i	−0.716183	+	0.413488i
$426$		0			0
$427$	13099.0	−	22688.1i	0.0718426	−	0.124435i
$428$		0			0
$429$	25388.6	+	68719.1i	0.137951	+	0.373390i
$430$		0			0
$431$			9694.22i			0.0521865i	0.999660	+	0.0260933i	$0.00830668\pi$
$431$			9694.22i			0.0521865i	−0.999660	+	0.0260933i	$0.991693\pi$
$432$		0			0
$433$	−11161.2			−0.0595297			−0.0297649	−	0.999557i	$-0.509476\pi$
$433$	−11161.2			−0.0595297			−0.0297649	+	0.999557i	$0.509476\pi$
$434$		0			0
$435$	−36838.4	+	13610.1i	−0.194681	+	0.0719256i
$436$		0			0
$437$	123307.	+	71191.6i	0.645693	+	0.372791i
$438$		0			0
$439$	50468.2	+	87413.6i	0.261872	+	0.453576i	0.966739	−	0.255763i	$-0.0823268\pi$
$439$	50468.2	+	87413.6i	0.261872	+	0.453576i	−0.704867	+	0.709339i	$0.748993\pi$
$440$		0			0
$441$	73888.9	+	396585.i	0.379929	+	2.03920i
$442$		0			0
$443$	299511.	−	172923.i	1.52618	−	0.881141i	0.526664	−	0.850074i	$-0.323443\pi$
$443$	299511.	−	172923.i	1.52618	−	0.881141i	0.999517	−	0.0310673i	$-0.00989062\pi$
$444$		0			0
$445$	−12997.9	+	22513.0i	−0.0656376	+	0.113688i
$446$		0			0
$447$	−278442.	−	47710.2i	−1.39354	−	0.238779i
$448$		0			0
$449$			38795.3i			0.192436i	0.995360	+	0.0962180i	$0.0306746\pi$
$449$			38795.3i			0.192436i	−0.995360	+	0.0962180i	$0.969325\pi$
$450$		0			0
$451$	104389.			0.513218
$452$		0			0
$453$	−1918.81	−	1594.33i	−0.00935051	−	0.00776930i
$454$		0			0
$455$	−201247.	−	116190.i	−0.972092	−	0.561237i
$456$		0			0
$457$	186004.	+	322168.i	0.890614	+	1.54259i	0.839140	+	0.543915i	$0.183059\pi$
$457$	186004.	+	322168.i	0.890614	+	1.54259i	0.0514741	+	0.998674i	$0.483608\pi$
$458$		0			0
$459$	−280522.	−	156580.i	−1.33150	−	0.743208i
$460$		0			0
$461$	249979.	−	144326.i	1.17626	−	0.679112i	0.221112	−	0.975249i	$-0.429032\pi$
$461$	249979.	−	144326.i	1.17626	−	0.679112i	0.955146	+	0.296136i	$0.0956982\pi$
$462$		0			0
$463$	9713.86	−	16824.9i	0.0453137	−	0.0784857i	−0.842479	−	0.538729i	$-0.818905\pi$
$463$	9713.86	−	16824.9i	0.0453137	−	0.0784857i	0.887793	+	0.460244i	$0.152238\pi$
$464$		0			0
$465$	110230.	−	132664.i	0.509791	−	0.613544i
$466$		0			0
$467$		−	87014.9i		−	0.398988i	−0.979899	−	0.199494i	$-0.936070\pi$
$467$		−	87014.9i		−	0.398988i	0.979899	−	0.199494i	$-0.0639298\pi$
$468$		0			0
$469$	−335337.			−1.52453
$470$		0			0
$471$	41687.5	−	243293.i	0.187916	−	1.09670i
$472$		0			0
$473$	140576.	+	81161.4i	0.628330	+	0.362766i
$474$		0			0
$475$	−40281.6	−	69769.8i	−0.178533	−	0.309229i
$476$		0			0
$477$	−135718.	−	158603.i	−0.596488	−	0.697068i
$478$		0			0
$479$	−139575.	+	80583.7i	−0.608327	+	0.351218i	−0.772310	−	0.635245i	$-0.780899\pi$
$479$	−139575.	+	80583.7i	−0.608327	+	0.351218i	0.163984	+	0.986463i	$0.447566\pi$
$480$		0			0
$481$	89647.5	−	155274.i	0.387479	−	0.671133i
$482$		0			0
$483$	−160527.	−	434498.i	−0.688104	−	1.86249i
$484$		0			0
$485$			108955.i			0.463193i
$486$		0			0
$487$	−148572.			−0.626439			−0.313219	−	0.949681i	$-0.601408\pi$
$487$	−148572.			−0.626439			−0.313219	+	0.949681i	$0.601408\pi$
$488$		0			0
$489$	154966.	−	57252.7i	0.648063	−	0.239430i
$490$		0			0
$491$	−216713.	−	125119.i	−0.898920	−	0.518992i	−0.0220706	−	0.999756i	$-0.507026\pi$
$491$	−216713.	−	125119.i	−0.898920	−	0.518992i	−0.876850	+	0.480765i	$0.840359\pi$
$492$		0			0
$493$	−56849.4	−	98466.1i	−0.233901	−	0.405128i
$494$		0			0
$495$	−52979.4	+	45335.0i	−0.216220	+	0.185022i
$496$		0			0
$497$	272387.	−	157263.i	1.10274	−	0.636668i
$498$		0			0
$499$	28415.2	−	49216.6i	0.114117	−	0.197656i	−0.803310	−	0.595562i	$-0.796929\pi$
$499$	28415.2	−	49216.6i	0.114117	−	0.197656i	0.917426	+	0.397906i	$0.130263\pi$
$500$		0			0
$501$	−119566.	−	20487.2i	−0.476356	−	0.0816221i
$502$		0			0
$503$			123311.i			0.487378i	0.969853	+	0.243689i	$0.0783576\pi$
$503$			123311.i			0.487378i	−0.969853	+	0.243689i	$0.921642\pi$
$504$		0			0
$505$	−272934.			−1.07022
$506$		0			0
$507$	20666.7	+	17171.9i	0.0803999	+	0.0668039i
$508$		0			0
$509$	243848.	+	140785.i	0.941202	+	0.543403i	0.890337	−	0.455302i	$-0.150469\pi$
$509$	243848.	+	140785.i	0.941202	+	0.543403i	0.0508653	+	0.998706i	$0.483802\pi$
$510$		0			0
$511$	36066.4	+	62468.8i	0.138121	+	0.239233i
$512$		0			0
$513$	84450.3	−	151298.i	0.320898	−	0.574906i
$514$		0			0
$515$	64174.1	−	37050.9i	0.241961	−	0.139696i
$516$		0			0
$517$	65738.5	−	113862.i	0.245946	−	0.425990i
$518$		0			0
$519$	129421.	−	155761.i	0.480474	−	0.578261i
$520$		0			0
$521$		−	356570.i		−	1.31362i	−0.754057	−	0.656809i	$-0.771906\pi$
$521$		−	356570.i		−	1.31362i	0.754057	−	0.656809i	$-0.228094\pi$
$522$		0			0
$523$	179066.			0.654650			0.327325	−	0.944912i	$-0.393853\pi$
$523$	179066.			0.654650			0.327325	+	0.944912i	$0.393853\pi$
$524$		0			0
$525$	−44263.2	+	258325.i	−0.160592	+	0.937233i
$526$		0			0
$527$	432460.	+	249681.i	1.55713	+	0.899009i
$528$		0			0
$529$	39507.9	+	68429.8i	0.141180	+	0.244531i
$530$		0			0
$531$	227997.	−	42478.8i	0.808613	−	0.150655i
$532$		0			0
$533$	−284047.	+	163995.i	−0.999854	+	0.577266i
$534$		0			0
$535$	−55112.9	+	95458.3i	−0.192551	+	0.333508i
$536$		0			0
$537$	−17860.0	−	48341.7i	−0.0619346	−	0.167638i
$538$		0			0
$539$			253494.i			0.872551i
$540$		0			0
$541$	−128481.			−0.438980			−0.219490	−	0.975615i	$-0.570439\pi$
$541$	−128481.			−0.438980			−0.219490	+	0.975615i	$0.570439\pi$
$542$		0			0
$543$	−151608.	+	56012.1i	−0.514187	+	0.189969i
$544$		0			0
$545$	−165676.	−	95653.2i	−0.557785	−	0.322038i
$546$		0			0
$547$	141784.	+	245577.i	0.473863	+	0.820755i	0.999552	−	0.0299219i	$-0.00952587\pi$
$547$	141784.	+	245577.i	0.473863	+	0.820755i	−0.525689	+	0.850677i	$0.676193\pi$
$548$		0			0
$549$	23290.3	+	8222.87i	0.0772735	+	0.0272822i
$550$		0			0
$551$	53107.0	−	30661.4i	0.174924	−	0.100992i
$552$		0			0
$553$	−445075.	+	770893.i	−1.45540	+	2.52083i
$554$		0			0
$555$	168203.	+	28821.1i	0.546070	+	0.0935674i
$556$		0			0
$557$		−	174450.i		−	0.562291i	−0.959665	−	0.281145i	$-0.909286\pi$
$557$		−	174450.i		−	0.562291i	0.959665	−	0.281145i	$-0.0907143\pi$
$558$		0			0
$559$	−510017.			−1.63215
$560$		0			0
$561$	−155270.	−	129013.i	−0.493359	−	0.409930i
$562$		0			0
$563$	396004.	+	228633.i	1.24935	+	0.721311i	0.970979	−	0.239164i	$-0.0768733\pi$
$563$	396004.	+	228633.i	1.24935	+	0.721311i	0.278368	+	0.960475i	$0.410207\pi$
$564$		0			0
$565$	128042.	+	221774.i	0.401101	+	0.694728i
$566$		0			0
$567$	−525866.	+	202998.i	−1.63572	+	0.631430i
$568$		0			0
$569$	76101.5	−	43937.2i	0.235054	−	0.135709i	−0.377847	−	0.925868i	$-0.623336\pi$
$569$	76101.5	−	43937.2i	0.235054	−	0.135709i	0.612902	+	0.790159i	$0.290002\pi$
$570$		0			0
$571$	−177941.	+	308203.i	−0.545762	+	0.945288i	0.452796	+	0.891614i	$0.350426\pi$
$571$	−177941.	+	308203.i	−0.545762	+	0.945288i	−0.998559	+	0.0536739i	$0.982907\pi$
$572$		0			0
$573$	28485.9	−	34283.4i	0.0867603	−	0.104418i
$574$		0			0
$575$		−	203048.i		−	0.614135i
$576$		0			0
$577$	478128.			1.43613			0.718063	−	0.695978i	$-0.245029\pi$
$577$	478128.			1.43613			0.718063	+	0.695978i	$0.245029\pi$
$578$		0			0
$579$	−28382.9	+	165646.i	−0.0846642	+	0.494110i
$580$		0			0
$581$	348893.	+	201433.i	1.03357	+	0.596732i
$582$		0			0
$583$	−65585.5	−	113597.i	−0.192962	−	0.334219i
$584$		0			0
$585$	72938.2	−	206589.i	0.213129	−	0.603664i
$586$		0			0
$587$	71409.6	−	41228.3i	0.207243	−	0.119652i	−0.392786	−	0.919630i	$-0.628489\pi$
$587$	71409.6	−	41228.3i	0.207243	−	0.119652i	0.600030	+	0.799978i	$0.295155\pi$
$588$		0			0
$589$	−134664.	+	233245.i	−0.388169	+	0.672328i
$590$		0			0
$591$	212329.	+	574711.i	0.607904	+	1.64541i
$592$		0			0
$593$		−	102109.i		−	0.290371i	−0.989404	−	0.145186i	$-0.953622\pi$
$593$		−	102109.i		−	0.290371i	0.989404	−	0.145186i	$-0.0463780\pi$
$594$		0			0
$595$	640354.			1.80878
$596$		0			0
$597$	−150618.	+	55646.4i	−0.422598	+	0.156131i
$598$		0			0
$599$	−25414.5	−	14673.0i	−0.0708317	−	0.0408947i	0.464166	−	0.885748i	$-0.346354\pi$
$599$	−25414.5	−	14673.0i	−0.0708317	−	0.0408947i	−0.534998	+	0.844854i	$0.679687\pi$
$600$		0			0
$601$	−133411.	−	231075.i	−0.369355	−	0.639742i	0.620110	−	0.784515i	$-0.287088\pi$
$601$	−133411.	−	231075.i	−0.369355	−	0.639742i	−0.989465	+	0.144773i	$0.953755\pi$
$602$		0			0
$603$	−57907.0	−	310805.i	−0.159256	−	0.854778i
$604$		0			0
$605$	176501.	−	101903.i	0.482212	−	0.278405i
$606$		0			0
$607$	47292.2	−	81912.5i	0.128355	−	0.222317i	−0.794685	−	0.607023i	$-0.792364\pi$
$607$	47292.2	−	81912.5i	0.128355	−	0.222317i	0.923039	+	0.384706i	$0.125697\pi$
$608$		0			0
$609$	−196630.	−	33692.0i	−0.530171	−	0.0908432i
$610$		0			0
$611$			413100.i			1.10655i
$612$		0			0
$613$	361645.			0.962412			0.481206	−	0.876608i	$-0.340199\pi$
$613$	361645.			0.962412			0.481206	+	0.876608i	$0.340199\pi$
$614$		0			0
$615$	−240114.	−	199509.i	−0.634844	−	0.527489i
$616$		0			0
$617$	−462957.	−	267288.i	−1.21610	−	0.702117i	−0.252020	−	0.967722i	$-0.581095\pi$
$617$	−462957.	−	267288.i	−1.21610	−	0.702117i	−0.964082	+	0.265605i	$0.914428\pi$
$618$		0			0
$619$	−54852.2	−	95006.7i	−0.143157	−	0.247955i	0.785527	−	0.618828i	$-0.212392\pi$
$619$	−54852.2	−	95006.7i	−0.143157	−	0.247955i	−0.928684	+	0.370872i	$0.879059\pi$
$620$		0			0
$621$	374991.	−	223814.i	0.972385	−	0.580369i
$622$		0			0
$623$	−114362.	+	66027.1i	−0.294650	+	0.170116i
$624$		0			0
$625$	31945.5	−	55331.3i	0.0817806	−	0.141648i
$626$		0			0
$627$	69582.6	−	83744.1i	0.176997	−	0.213019i
$628$		0			0
$629$			494070.i			1.24878i
$630$		0			0
$631$	73200.0			0.183845			0.0919226	−	0.995766i	$-0.470699\pi$
$631$	73200.0			0.183845			0.0919226	+	0.995766i	$0.470699\pi$
$632$		0			0
$633$	−120872.	+	705422.i	−0.301660	+	1.76052i
$634$		0			0
$635$	−349013.	−	201503.i	−0.865555	−	0.499728i
$636$		0			0
$637$	−398239.	−	689769.i	−0.981441	−	1.69991i
$638$		0			0
$639$	192795.	+	225304.i	0.472164	+	0.551781i
$640$		0			0
$641$	−421531.	+	243371.i	−1.02592	+	0.592315i	−0.915813	−	0.401605i	$-0.868452\pi$
$641$	−421531.	+	243371.i	−1.02592	+	0.592315i	−0.110106	+	0.993920i	$0.535119\pi$
$642$		0			0
$643$	6786.60	−	11754.7i	0.0164146	−	0.0284309i	−0.857701	−	0.514148i	$-0.828108\pi$
$643$	6786.60	−	11754.7i	0.0164146	−	0.0284309i	0.874116	+	0.485717i	$0.161442\pi$
$644$		0			0
$645$	−168233.	−	455355.i	−0.404382	−	1.09454i
$646$		0			0
$647$		−	413189.i		−	0.987052i	−0.869731	−	0.493526i	$-0.835708\pi$
$647$		−	413189.i		−	0.987052i	0.869731	−	0.493526i	$-0.164292\pi$
$648$		0			0
$649$	145734.			0.345997
$650$		0			0
$651$	821883.	−	303648.i	1.93931	−	0.716487i
$652$		0			0
$653$	−220837.	−	127500.i	−0.517899	−	0.299009i	0.218176	−	0.975910i	$-0.429989\pi$
$653$	−220837.	−	127500.i	−0.517899	−	0.299009i	−0.736075	+	0.676900i	$0.763323\pi$
$654$		0			0
$655$	−237855.	−	411976.i	−0.554407	−	0.960261i
$656$		0			0
$657$	−51670.8	+	44215.2i	−0.119706	+	0.102433i
$658$		0			0
$659$	90740.7	−	52389.2i	0.208945	−	0.120634i	−0.391876	−	0.920018i	$-0.628174\pi$
$659$	90740.7	−	52389.2i	0.208945	−	0.120634i	0.600821	+	0.799384i	$0.294841\pi$
$660$		0			0
$661$	179854.	−	311517.i	0.411640	−	0.712981i	−0.583429	−	0.812164i	$-0.698289\pi$
$661$	179854.	−	311517.i	0.411640	−	0.712981i	0.995069	+	0.0991825i	$0.0316228\pi$
$662$		0			0
$663$	625177.	+	107122.i	1.42225	+	0.243698i
$664$		0			0
$665$			345371.i			0.780984i
$666$		0			0
$667$	154555.			0.347402
$668$		0			0
$669$	−166896.	−	138673.i	−0.372900	−	0.309841i
$670$		0			0
$671$	13441.2	+	7760.26i	0.0298533	+	0.0172358i
$672$		0			0
$673$	−410683.	−	711324.i	−0.906727	−	1.57050i	−0.818582	−	0.574389i	$-0.805240\pi$
$673$	−410683.	−	711324.i	−0.906727	−	1.57050i	−0.0881443	−	0.996108i	$-0.528094\pi$
$674$		0			0
$675$	−247070.	+	3583.24i	−0.542267	+	0.00786446i
$676$		0			0
$677$	33894.5	−	19569.0i	0.0739523	−	0.0426964i	−0.462568	−	0.886584i	$-0.653072\pi$
$677$	33894.5	−	19569.0i	0.0739523	−	0.0426964i	0.536520	+	0.843887i	$0.319739\pi$
$678$		0			0
$679$	−276736.	+	479320.i	−0.600241	+	1.03965i
$680$		0			0
$681$	48786.4	−	58715.5i	0.105197	−	0.126607i
$682$		0			0
$683$		−	516.462i		−	0.00110713i	−1.00000		0.000553563i	$-0.999824\pi$
$683$		−	516.462i		−	0.00110713i	1.00000		0.000553563i	$-0.000176205\pi$
$684$		0			0
$685$	465142.			0.991299
$686$		0			0
$687$	−95772.2	+	558938.i	−0.202921	+	1.18427i
$688$		0			0
$689$	356922.	+	206069.i	0.751856	+	0.434084i
$690$		0			0
$691$	21026.1	+	36418.3i	0.0440355	+	0.0762718i	0.887203	−	0.461379i	$-0.152645\pi$
$691$	21026.1	+	36418.3i	0.0440355	+	0.0762718i	−0.843168	+	0.537651i	$0.819312\pi$
$692$		0			0
$693$	−348217.	+	64877.4i	−0.725077	+	0.135091i
$694$		0			0
$695$	−256602.	+	148149.i	−0.531239	+	0.306711i
$696$		0			0
$697$	451909.	−	782729.i	0.930219	−	1.61119i
$698$		0			0
$699$	225813.	+	611207.i	0.462162	+	1.25093i
$700$		0			0
$701$		−	530811.i		−	1.08020i	−0.841601	−	0.540099i	$-0.818387\pi$
$701$		−	530811.i		−	1.08020i	0.841601	−	0.540099i	$-0.181613\pi$
$702$		0			0
$703$	−266474.			−0.539192
$704$		0			0
$705$	−368825.	+	136264.i	−0.742066	+	0.274159i
$706$		0			0
$707$	−1.20071e6	−	693228.i	−2.40214	−	1.38688i
$708$		0			0
$709$	76578.1	+	132637.i	0.152339	+	0.263859i	0.932087	−	0.362234i	$-0.117986\pi$
$709$	76578.1	+	132637.i	0.152339	+	0.263859i	−0.779748	+	0.626094i	$0.784653\pi$
$710$		0			0
$711$	−791355.	−	279395.i	−1.56542	−	0.552688i
$712$		0			0
$713$	−587860.	+	339401.i	−1.15637	+	0.667628i
$714$		0			0
$715$	68834.8	−	119225.i	0.134647	−	0.233215i
$716$		0			0
$717$	819194.	+	140366.i	1.59349	+	0.273039i
$718$		0			0
$719$		−	576170.i		−	1.11453i	−0.830334	−	0.557266i	$-0.811850\pi$
$719$		−	576170.i		−	1.11453i	0.830334	−	0.557266i	$-0.188150\pi$
$720$		0			0
$721$	376425.			0.724115
$722$		0			0
$723$	593476.	+	493116.i	1.13534	+	0.943349i
$724$		0			0
$725$	−75734.3	−	43725.2i	−0.144084	−	0.0831871i
$726$		0			0
$727$	274155.	+	474851.i	0.518714	+	0.898439i	0.999764	+	0.0217457i	$0.00692242\pi$
$727$	274155.	+	474851.i	0.518714	+	0.898439i	−0.481049	+	0.876693i	$0.659744\pi$
$728$		0			0
$729$	−278956.	−	452342.i	−0.524904	−	0.851161i
$730$		0			0
$731$	1.21713e6	−	702708.i	2.27772	−	1.31504i
$732$		0			0
$733$	−80630.1	+	139656.i	−0.150068	+	0.259926i	−0.931252	−	0.364375i	$-0.881283\pi$
$733$	−80630.1	+	139656.i	−0.150068	+	0.259926i	0.781184	+	0.624301i	$0.214616\pi$
$734$		0			0
$735$	484481.	−	583083.i	0.896813	−	1.07933i
$736$		0			0
$737$		−	198664.i		−	0.365750i
$738$		0			0
$739$	−220773.			−0.404256			−0.202128	−	0.979359i	$-0.564786\pi$
$739$	−220773.			−0.404256			−0.202128	+	0.979359i	$0.564786\pi$
$740$		0			0
$741$	−57775.7	+	337185.i	−0.105222	+	0.614090i
$742$		0			0
$743$	−685935.	−	396025.i	−1.24252	−	0.717372i	−0.272917	−	0.962037i	$-0.587989\pi$
$743$	−685935.	−	396025.i	−1.24252	−	0.717372i	−0.969608	+	0.244665i	$0.921322\pi$
$744$		0			0
$745$	265439.	+	459754.i	0.478247	+	0.828349i
$746$		0			0
$747$	−126449.	+	358153.i	−0.226608	+	0.641842i
$748$		0			0
$749$	−484912.	+	279964.i	−0.864370	+	0.499044i
$750$		0			0
$751$	40400.3	−	69975.3i	0.0716315	−	0.124069i	−0.827985	−	0.560750i	$-0.810513\pi$
$751$	40400.3	−	69975.3i	0.0716315	−	0.124069i	0.899616	+	0.436681i	$0.143846\pi$
$752$		0			0
$753$	−42501.7	−	115039.i	−0.0749577	−	0.202888i
$754$		0			0
$755$			4688.15i			0.00822447i
$756$		0			0
$757$	24285.2			0.0423788			0.0211894	−	0.999775i	$-0.493255\pi$
$757$	24285.2			0.0423788			0.0211894	+	0.999775i	$0.493255\pi$
$758$		0			0
$759$	257410.	−	95101.4i	0.446830	−	0.165083i
$760$		0			0
$761$	981778.	+	566830.i	1.69529	+	0.978776i	0.950112	+	0.311909i	$0.100969\pi$
$761$	981778.	+	566830.i	1.69529	+	0.978776i	0.745177	+	0.666866i	$0.232365\pi$
$762$		0			0
$763$	−485902.	−	841607.i	−0.834641	−	1.44564i
$764$		0			0
$765$	110578.	+	593508.i	0.188950	+	1.01415i
$766$		0			0
$767$	−396549.	+	228948.i	−0.674072	+	0.389175i
$768$		0			0
$769$	303302.	−	525334.i	0.512888	−	0.888348i	−0.487000	−	0.873402i	$-0.661909\pi$
$769$	303302.	−	525334.i	0.512888	−	0.888348i	0.999888	−	0.0149462i	$-0.00475769\pi$
$770$		0			0
$771$	−596775.	−	102256.i	−1.00393	−	0.172020i
$772$		0			0
$773$			771000.i			1.29031i	0.764050	+	0.645157i	$0.223208\pi$
$773$			771000.i			1.29031i	−0.764050	+	0.645157i	$0.776792\pi$
$774$		0			0
$775$	384080.			0.639467
$776$		0			0
$777$	666767.	+	554014.i	1.10441	+	0.917653i
$778$		0			0
$779$	422160.	+	243734.i	0.695668	+	0.401644i
$780$		0			0
$781$	93167.5	+	161371.i	0.152743	+	0.264559i
$782$		0			0
$783$	−2727.48	−	188064.i	−0.00444875	−	0.306748i
$784$		0			0
$785$	−401717.	+	231932.i	−0.651900	+	0.376375i
$786$		0			0
$787$	59238.0	−	102603.i	0.0956425	−	0.165658i	−0.814234	−	0.580537i	$-0.802843\pi$
$787$	59238.0	−	102603.i	0.0956425	−	0.165658i	0.909877	+	0.414879i	$0.136176\pi$
$788$		0			0
$789$	197241.	−	237384.i	0.316843	−	0.381327i
$790$		0			0
$791$			1.30086e6i			2.07911i
$792$		0			0
$793$	−48765.3			−0.0775469
$794$		0			0
$795$	−66249.9	+	386642.i	−0.104822	+	0.611751i
$796$		0			0
$797$	−589473.	−	340332.i	−0.927999	−	0.535780i	−0.0418206	−	0.999125i	$-0.513316\pi$
$797$	−589473.	−	340332.i	−0.927999	−	0.535780i	−0.886178	+	0.463345i	$0.846649\pi$
$798$		0			0
$799$	−569175.	−	985839.i	−0.891563	−	1.54423i
$800$		0			0
$801$	−80945.2	−	94594.3i	−0.126161	−	0.147435i
$802$		0			0
$803$	−37008.5	+	21366.9i	−0.0573946	+	0.0331368i
$804$		0			0
$805$	−435229.	+	753840.i	−0.671624	+	1.16329i
$806$		0			0
$807$	279408.	+	756274.i	0.429035	+	1.16127i
$808$		0			0
$809$		−	462462.i		−	0.706609i	−0.935508	−	0.353304i	$-0.885058\pi$
$809$		−	462462.i		−	0.706609i	0.935508	−	0.353304i	$-0.114942\pi$
$810$		0			0
$811$	−743003.			−1.12966			−0.564831	−	0.825206i	$-0.691059\pi$
$811$	−743003.			−1.12966			−0.564831	+	0.825206i	$0.691059\pi$
$812$		0			0
$813$	−720533.	+	266204.i	−1.09012	+	0.402748i
$814$		0			0
$815$	−268860.	−	155227.i	−0.404773	−	0.233696i
$816$		0			0
$817$	379001.	+	656449.i	0.567801	+	0.983461i
$818$		0			0
$819$	845593.	−	723582.i	1.26065	−	1.07875i
$820$		0			0
$821$	−534512.	+	308601.i	−0.792996	+	0.457837i	−0.841016	−	0.541010i	$-0.818042\pi$
$821$	−534512.	+	308601.i	−0.792996	+	0.457837i	0.0480200	+	0.998846i	$0.484709\pi$
$822$		0			0
$823$	−309031.	+	535258.i	−0.456250	+	0.790248i	−0.998759	−	0.0498021i	$-0.984141\pi$
$823$	−309031.	+	535258.i	−0.456250	+	0.790248i	0.542509	+	0.840050i	$0.317474\pi$
$824$		0			0
$825$	−153040.	−	26222.9i	−0.224852	−	0.0385277i
$826$		0			0
$827$			562763.i			0.822838i	0.911446	+	0.411419i	$0.134967\pi$
$827$			562763.i			0.822838i	−0.911446	+	0.411419i	$0.865033\pi$
$828$		0			0
$829$	1.26920e6			1.84680			0.923400	−	0.383839i	$-0.125398\pi$
$829$	1.26920e6			1.84680			0.923400	+	0.383839i	$0.125398\pi$
$830$		0			0
$831$	−198626.	−	165037.i	−0.287630	−	0.238990i
$832$		0			0
$833$	1.90075e6	+	1.09740e6i	2.73927	+	1.58152i
$834$		0			0
$835$	113982.	+	197423.i	0.163480	+	0.283155i
$836$		0			0
$837$	423360.	+	709322.i	0.604308	+	1.01249i
$838$		0			0
$839$	246991.	−	142600.i	0.350879	−	0.202580i	−0.314194	−	0.949359i	$-0.601734\pi$
$839$	246991.	−	142600.i	0.350879	−	0.202580i	0.665072	+	0.746779i	$0.268401\pi$
$840$		0			0
$841$	−320358.	+	554876.i	−0.452943	+	0.784520i
$842$		0			0
$843$	−220937.	+	265902.i	−0.310894	+	0.374168i
$844$		0			0
$845$		−	50494.1i		−	0.0707176i
$846$		0			0
$847$	1.03530e6			1.44311
$848$		0			0
$849$	115671.	−	675067.i	0.160475	−	0.936551i
$850$		0			0
$851$	−581631.	−	335805.i	−0.803135	−	0.463690i
$852$		0			0
$853$	135760.	+	235143.i	0.186584	+	0.323172i	0.944109	−	0.329633i	$-0.106925\pi$
$853$	135760.	+	235143.i	0.186584	+	0.323172i	−0.757525	+	0.652806i	$0.773592\pi$
$854$		0			0
$855$	−320105.	+	59639.7i	−0.437885	+	0.0815836i
$856$		0			0
$857$	216815.	−	125178.i	0.295208	−	0.170438i	−0.345080	−	0.938573i	$-0.612148\pi$
$857$	216815.	−	125178.i	0.295208	−	0.170438i	0.640288	+	0.768135i	$0.278815\pi$
$858$		0			0
$859$	−359755.	+	623114.i	−0.487551	+	0.844463i	−0.999898	−	0.0143155i	$-0.995443\pi$
$859$	−359755.	+	623114.i	−0.487551	+	0.844463i	0.512346	+	0.858779i	$0.328776\pi$
$860$		0			0
$861$	−549586.	−	1.48756e6i	−0.741361	−	2.00664i
$862$		0			0
$863$		−	1.26097e6i		−	1.69310i	−0.532307	−	0.846551i	$-0.678675\pi$
$863$		−	1.26097e6i		−	1.69310i	0.532307	−	0.846551i	$-0.321325\pi$
$864$		0			0
$865$	−380564.			−0.508623
$866$		0			0
$867$	−934439.	+	345232.i	−1.24312	+	0.459276i
$868$		0			0
$869$	−456702.	−	263677.i	−0.604774	−	0.349166i
$870$		0			0
$871$	312101.	+	540574.i	0.411394	+	0.712556i
$872$		0			0
$873$	−492043.	−	173720.i	−0.645616	−	0.227941i
$874$		0			0
$875$	1.21304e6	−	700347.i	1.58437	−	0.914739i
$876$		0			0
$877$	62872.9	−	108899.i	0.0817456	−	0.141588i	−0.822254	−	0.569120i	$-0.807284\pi$
$877$	62872.9	−	108899.i	0.0817456	−	0.141588i	0.904000	+	0.427533i	$0.140617\pi$
$878$		0			0
$879$	407344.	+	69797.1i	0.527210	+	0.0903357i
$880$		0			0
$881$		−	347005.i		−	0.447079i	−0.974695	−	0.223540i	$-0.928239\pi$
$881$		−	347005.i		−	0.447079i	0.974695	−	0.223540i	$-0.0717612\pi$
$882$		0			0
$883$	−365890.			−0.469277			−0.234639	−	0.972083i	$-0.575391\pi$
$883$	−365890.			−0.469277			−0.234639	+	0.972083i	$0.575391\pi$
$884$		0			0
$885$	−335215.	−	278528.i	−0.427993	−	0.355617i
$886$		0			0
$887$	844414.	+	487523.i	1.07327	+	0.619652i	0.929073	−	0.369897i	$-0.120607\pi$
$887$	844414.	+	487523.i	1.07327	+	0.619652i	0.144196	+	0.989549i	$0.453941\pi$
$888$		0			0
$889$	−1.02360e6	−	1.77293e6i	−1.29517	−	2.24330i
$890$		0			0
$891$	−120262.	−	311540.i	−0.151487	−	0.392427i
$892$		0			0
$893$	531706.	−	306981.i	0.666759	−	0.384953i
$894$		0			0
$895$	−48423.1	+	83871.2i	−0.0604514	+	0.104705i
$896$		0			0
$897$	−551021.	+	663165.i	−0.684831	+	0.824208i
$898$		0			0
$899$			292352.i			0.361732i
$900$		0			0
$901$	−1.13570e6			−1.39899
$902$		0			0
$903$	416463.	−	2.43052e6i	0.510741	−	2.98074i
$904$		0			0
$905$	263034.	+	151863.i	0.321155	+	0.185419i
$906$		0			0
$907$	135700.	+	235040.i	0.164955	+	0.285711i	0.936639	−	0.350295i	$-0.113919\pi$
$907$	135700.	+	235040.i	0.164955	+	0.285711i	−0.771684	+	0.636006i	$0.780585\pi$
$908$		0			0
$909$	435173.	−	1.23258e6i	0.526665	−	1.49172i
$910$		0			0
$911$	205929.	−	118893.i	0.248130	−	0.143258i	−0.370778	−	0.928722i	$-0.620909\pi$
$911$	205929.	−	118893.i	0.248130	−	0.143258i	0.618908	+	0.785464i	$0.287575\pi$
$912$		0			0
$913$	−119336.	+	206695.i	−0.143162	+	0.247964i
$914$		0			0
$915$	−16085.6	−	43538.8i	−0.0192130	−	0.0520038i
$916$		0			0
$917$		−	2.41652e6i		−	2.87377i
$918$		0			0
$919$	−11632.4			−0.0137734			−0.00688668	−	0.999976i	$-0.502192\pi$
$919$	−11632.4			−0.0137734			−0.00688668	+	0.999976i	$0.502192\pi$
$920$		0			0
$921$	−947019.	+	349880.i	−1.11645	+	0.412478i
$922$		0			0
$923$	−507025.	−	292731.i	−0.595150	−	0.343610i
$924$		0			0
$925$	190005.	+	329098.i	0.222066	+	0.384629i
$926$		0			0
$927$	65002.2	+	348887.i	0.0756429	+	0.406000i
$928$		0			0
$929$	554066.	−	319890.i	0.641993	−	0.370655i	−0.143389	−	0.989666i	$-0.545800\pi$
$929$	554066.	−	319890.i	0.641993	−	0.370655i	0.785382	+	0.619012i	$0.212467\pi$
$930$		0			0
$931$	−591874.	+	1.02516e6i	−0.682858	+	1.18274i
$932$		0			0
$933$	573946.	+	98343.9i	0.659338	+	0.112976i
$934$		0			0
$935$			379366.i			0.433946i
$936$		0			0
$937$	−187338.			−0.213377			−0.106689	−	0.994292i	$-0.534025\pi$
$937$	−187338.			−0.213377			−0.106689	+	0.994292i	$0.534025\pi$
$938$		0			0
$939$	244452.	+	203114.i	0.277244	+	0.230361i
$940$		0			0
$941$	131506.	+	75924.8i	0.148513	+	0.0857441i	0.572415	−	0.819964i	$-0.306007\pi$
$941$	131506.	+	75924.8i	0.148513	+	0.0857441i	−0.423902	+	0.905708i	$0.639340\pi$
$942$		0			0
$943$	614298.	+	1.06400e6i	0.690805	+	1.19651i
$944$		0			0
$945$	924957.	+	516286.i	1.03576	+	0.578132i
$946$		0			0
$947$	−1.16161e6	+	670655.i	−1.29527	+	0.747823i	−0.979583	−	0.201041i	$-0.935568\pi$
$947$	−1.16161e6	+	670655.i	−1.29527	+	0.747823i	−0.315685	+	0.948864i	$0.602234\pi$
$948$		0			0
$949$	67134.6	−	116280.i	0.0745442	−	0.129114i
$950$		0			0
$951$	8214.42	−	9886.23i	0.00908272	−	0.0109312i
$952$		0			0
$953$			1.13325e6i			1.24778i	0.781511	+	0.623891i	$0.214449\pi$
$953$			1.13325e6i			1.24778i	−0.781511	+	0.623891i	$0.785551\pi$
$954$		0			0
$955$	−83763.3			−0.0918432
$956$		0			0
$957$	19960.2	−	116490.i	0.0217942	−	0.127194i
$958$		0			0
$959$	2.04628e6	+	1.18142e6i	2.22499	+	1.28460i
$960$		0			0
$961$	−180241.	−	312186.i	−0.195167	−	0.338039i
$962$		0			0
$963$	−343219.	−	401093.i	−0.370100	−	0.432506i
$964$		0			0
$965$	273509.	−	157910.i	0.293709	−	0.169573i
$966$		0			0
$967$	745559.	−	1.29135e6i	0.797313	−	1.38099i	−0.124046	−	0.992276i	$-0.539587\pi$
$967$	745559.	−	1.29135e6i	0.797313	−	1.38099i	0.921360	−	0.388711i	$-0.127079\pi$
$968$		0			0
$969$	−326700.	−	884278.i	−0.347938	−	0.941762i
$970$		0			0
$971$			157273.i			0.166808i	0.996516	+	0.0834038i	$0.0265791\pi$
$971$			157273.i			0.166808i	−0.996516	+	0.0834038i	$0.973421\pi$
$972$		0			0
$973$	−1.50514e6			−1.58984
$974$		0			0
$975$	457624.	−	169071.i	0.481393	−	0.177853i
$976$		0			0
$977$	−1.60701e6	−	927807.i	−1.68356	−	0.972005i	−0.959261	−	0.282520i	$-0.908830\pi$
$977$	−1.60701e6	−	927807.i	−1.68356	−	0.972005i	−0.724300	−	0.689485i	$-0.757837\pi$
$978$		0			0
$979$	−39116.6	−	67751.9i	−0.0408127	−	0.0706897i
$980$		0			0
$981$	696132.	−	595687.i	0.723358	−	0.618985i
$982$		0			0
$983$	−109587.	+	63270.1i	−0.113410	+	0.0654774i	−0.555632	−	0.831428i	$-0.687524\pi$
$983$	−109587.	+	63270.1i	−0.113410	+	0.0654774i	0.442222	+	0.896906i	$0.354190\pi$
$984$		0			0
$985$	575678.	−	997104.i	0.593345	−	1.02770i
$986$		0			0
$987$	−1.96866e6	−	337324.i	−2.02086	−	0.346268i
$988$		0			0
$989$			1.91044e6i			1.95317i
$990$		0			0
$991$	−818224.			−0.833153			−0.416577	−	0.909101i	$-0.636770\pi$
$991$	−818224.			−0.833153			−0.416577	+	0.909101i	$0.636770\pi$
$992$		0			0
$993$	490254.	+	407350.i	0.497190	+	0.413113i
$994$		0			0
$995$	261317.	+	150871.i	0.263950	+	0.152392i
$996$		0			0
$997$	835707.	+	1.44749e6i	0.840744	+	1.45621i	0.889267	+	0.457389i	$0.151215\pi$
$997$	835707.	+	1.44749e6i	0.840744	+	1.45621i	−0.0485230	+	0.998822i	$0.515451\pi$
$998$		0			0
$999$	−398345.	+	713658.i	−0.399143	+	0.715087i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.5.m.a.41.11	✓	24
3.2	odd	2		216.5.m.a.17.8		24
4.3	odd	2		144.5.q.d.113.2		24
9.2	odd	6	inner	72.5.m.a.65.11	yes	24
9.4	even	3		648.5.e.c.161.16		24
9.5	odd	6		648.5.e.c.161.9		24
9.7	even	3		216.5.m.a.89.8		24
12.11	even	2		432.5.q.d.17.8		24
36.7	odd	6		432.5.q.d.305.8		24
36.11	even	6		144.5.q.d.65.2		24
36.23	even	6		1296.5.e.j.161.9		24
36.31	odd	6		1296.5.e.j.161.16		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.5.m.a.41.11	✓	24	1.1	even	1	trivial
72.5.m.a.65.11	yes	24	9.2	odd	6	inner
144.5.q.d.65.2		24	36.11	even	6
144.5.q.d.113.2		24	4.3	odd	2
216.5.m.a.17.8		24	3.2	odd	2
216.5.m.a.89.8		24	9.7	even	3
432.5.q.d.17.8		24	12.11	even	2
432.5.q.d.305.8		24	36.7	odd	6
648.5.e.c.161.9		24	9.5	odd	6
648.5.e.c.161.16		24	9.4	even	3
1296.5.e.j.161.9		24	36.23	even	6
1296.5.e.j.161.16		24	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	72.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.44225 - 3.11903i) q^{3} +(-14.6470 - 8.45647i) q^{5} +(-42.9574 - 74.4045i) q^{7} +(61.5433 - 52.6632i) q^{9} +O(q^{10})\)	\(q+(8.44225 - 3.11903i) q^{3} +(-14.6470 - 8.45647i) q^{5} +(-42.9574 - 74.4045i) q^{7} +(61.5433 - 52.6632i) q^{9} +(44.0796 - 25.4494i) q^{11} +(-79.9617 + 138.498i) q^{13} +(-150.030 - 25.7072i) q^{15} -440.689i q^{17} +237.683 q^{19} +(-594.727 - 494.156i) q^{21} +(518.790 + 299.523i) q^{23} +(-169.476 - 293.541i) q^{25} +(355.306 - 636.552i) q^{27} +(223.437 - 129.001i) q^{29} +(-566.569 + 981.327i) q^{31} +(292.754 - 352.335i) q^{33} +1453.07i q^{35} -1121.13 q^{37} +(-243.079 + 1418.64i) q^{39} +(1776.15 + 1025.46i) q^{41} +(1594.57 + 2761.87i) q^{43} +(-1346.77 + 250.921i) q^{45} +(2237.04 - 1291.56i) q^{47} +(-2490.18 + 4313.13i) q^{49} +(-1374.52 - 3720.41i) q^{51} -2577.10i q^{53} -860.847 q^{55} +(2006.58 - 741.340i) q^{57} +(2479.62 + 1431.61i) q^{59} +(152.465 + 264.077i) q^{61} +(-6562.13 - 2316.82i) q^{63} +(2342.40 - 1352.39i) q^{65} +(1951.56 - 3380.21i) q^{67} +(5313.98 + 910.533i) q^{69} +3660.90i q^{71} -839.584 q^{73} +(-2346.32 - 1949.55i) q^{75} +(-3787.09 - 2186.48i) q^{77} +(-5180.42 - 8972.75i) q^{79} +(1014.17 - 6482.14i) q^{81} +(-4060.91 + 2344.57i) q^{83} +(-3726.68 + 6454.79i) q^{85} +(1483.95 - 1785.97i) q^{87} -1537.03i q^{89} +13739.8 q^{91} +(-1722.34 + 10051.8i) q^{93} +(-3481.35 - 2009.96i) q^{95} +(-3221.04 - 5579.01i) q^{97} +(1372.56 - 3887.61i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 100 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 - 100 * q^9	\( 24 q + 4 q^{3} - 100 q^{9} + 252 q^{11} - 80 q^{15} - 408 q^{19} + 24 q^{21} + 720 q^{23} + 1500 q^{25} - 1280 q^{27} + 2376 q^{29} - 1104 q^{31} - 1412 q^{33} - 4184 q^{39} + 1980 q^{41} + 1476 q^{43} - 4696 q^{45} + 4536 q^{47} - 6084 q^{49} - 7828 q^{51} + 2544 q^{55} - 1204 q^{57} + 10332 q^{59} + 2784 q^{61} + 9072 q^{63} + 17280 q^{65} - 2604 q^{67} + 5680 q^{69} + 5112 q^{73} - 15412 q^{75} - 28368 q^{77} + 3480 q^{79} - 26548 q^{81} - 23400 q^{83} + 7392 q^{85} - 3192 q^{87} - 14208 q^{91} + 39488 q^{93} + 57528 q^{95} - 4020 q^{97} + 50744 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 100 * q^9 + 252 * q^11 - 80 * q^15 - 408 * q^19 + 24 * q^21 + 720 * q^23 + 1500 * q^25 - 1280 * q^27 + 2376 * q^29 - 1104 * q^31 - 1412 * q^33 - 4184 * q^39 + 1980 * q^41 + 1476 * q^43 - 4696 * q^45 + 4536 * q^47 - 6084 * q^49 - 7828 * q^51 + 2544 * q^55 - 1204 * q^57 + 10332 * q^59 + 2784 * q^61 + 9072 * q^63 + 17280 * q^65 - 2604 * q^67 + 5680 * q^69 + 5112 * q^73 - 15412 * q^75 - 28368 * q^77 + 3480 * q^79 - 26548 * q^81 - 23400 * q^83 + 7392 * q^85 - 3192 * q^87 - 14208 * q^91 + 39488 * q^93 + 57528 * q^95 - 4020 * q^97 + 50744 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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