LMFDB - Embedded newform 644.4.i.b.93.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,4,Mod(93,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("644.93");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	644.i (of order $3$, 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:	$37.9972300437$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.2
Character	$\chi$	$=$	644.93
Dual form			644.4.i.b.277.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.53140 - 7.84862i) q^{3} +(7.01387 - 12.1484i) q^{5} +(18.1867 - 3.49896i) q^{7} +(-27.5672 + 47.7478i) q^{9} +O(q^{10})$	\(q+(-4.53140 - 7.84862i) q^{3} +(7.01387 - 12.1484i) q^{5} +(18.1867 - 3.49896i) q^{7} +(-27.5672 + 47.7478i) q^{9} +(16.5579 + 28.6792i) q^{11} +38.7753 q^{13} -127.131 q^{15} +(-54.7836 - 94.8880i) q^{17} +(37.1510 - 64.3474i) q^{19} +(-109.873 - 126.886i) q^{21} +(11.5000 - 19.9186i) q^{23} +(-35.8887 - 62.1610i) q^{25} +254.977 q^{27} -245.176 q^{29} +(-117.817 - 204.065i) q^{31} +(150.061 - 259.914i) q^{33} +(85.0527 - 245.481i) q^{35} +(125.796 - 217.884i) q^{37} +(-175.707 - 304.333i) q^{39} +109.856 q^{41} -380.631 q^{43} +(386.706 + 669.794i) q^{45} +(-113.010 + 195.739i) q^{47} +(318.515 - 127.269i) q^{49} +(-496.493 + 859.951i) q^{51} +(307.607 + 532.791i) q^{53} +464.541 q^{55} -673.384 q^{57} +(-32.5545 - 56.3861i) q^{59} +(6.45160 - 11.1745i) q^{61} +(-334.290 + 964.833i) q^{63} +(271.965 - 471.057i) q^{65} +(-357.710 - 619.572i) q^{67} -208.444 q^{69} -22.4989 q^{71} +(3.41405 + 5.91332i) q^{73} +(-325.252 + 563.353i) q^{75} +(401.482 + 463.645i) q^{77} +(-23.3449 + 40.4346i) q^{79} +(-411.087 - 712.024i) q^{81} -664.248 q^{83} -1536.98 q^{85} +(1110.99 + 1924.30i) q^{87} +(297.282 - 514.907i) q^{89} +(705.197 - 135.673i) q^{91} +(-1067.75 + 1849.40i) q^{93} +(-521.144 - 902.648i) q^{95} +79.5901 q^{97} -1825.82 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9}+O(q^{10}) $ 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9	$ 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9} + 28 q^{11} - 152 q^{13} + 208 q^{15} - 52 q^{17} + 38 q^{19} - 10 q^{21} + 506 q^{23} - 516 q^{25} - 876 q^{27} - 100 q^{29} + 230 q^{31} + 424 q^{33} + 98 q^{35} + 18 q^{37} - 350 q^{39} + 784 q^{41} - 336 q^{43} + 1156 q^{45} + 452 q^{47} + 546 q^{49} - 498 q^{51} - 508 q^{53} - 3084 q^{55} - 1916 q^{57} + 508 q^{59} + 1386 q^{61} + 1290 q^{63} + 360 q^{65} - 1896 q^{67} + 552 q^{69} - 3352 q^{71} + 990 q^{73} + 3328 q^{75} + 1328 q^{77} + 524 q^{79} - 4486 q^{81} - 1120 q^{83} - 5296 q^{85} + 3700 q^{87} + 1216 q^{89} + 1438 q^{91} + 366 q^{93} + 90 q^{95} + 716 q^{97} + 5716 q^{99}+O(q^{100}) $ 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9 + 28 * q^11 - 152 * q^13 + 208 * q^15 - 52 * q^17 + 38 * q^19 - 10 * q^21 + 506 * q^23 - 516 * q^25 - 876 * q^27 - 100 * q^29 + 230 * q^31 + 424 * q^33 + 98 * q^35 + 18 * q^37 - 350 * q^39 + 784 * q^41 - 336 * q^43 + 1156 * q^45 + 452 * q^47 + 546 * q^49 - 498 * q^51 - 508 * q^53 - 3084 * q^55 - 1916 * q^57 + 508 * q^59 + 1386 * q^61 + 1290 * q^63 + 360 * q^65 - 1896 * q^67 + 552 * q^69 - 3352 * q^71 + 990 * q^73 + 3328 * q^75 + 1328 * q^77 + 524 * q^79 - 4486 * q^81 - 1120 * q^83 - 5296 * q^85 + 3700 * q^87 + 1216 * q^89 + 1438 * q^91 + 366 * q^93 + 90 * q^95 + 716 * q^97 + 5716 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−4.53140	−	7.84862i	−0.872069	−	1.51047i	−0.859853	−	0.510542i	$-0.829445\pi$
$3$	−4.53140	−	7.84862i	−0.872069	−	1.51047i	−0.0122159	−	0.999925i	$-0.503889\pi$
$4$		0			0
$5$	7.01387	−	12.1484i	0.627339	−	1.08658i	−0.360744	−	0.932665i	$-0.617477\pi$
$5$	7.01387	−	12.1484i	0.627339	−	1.08658i	0.988083	−	0.153919i	$-0.0491895\pi$
$6$		0			0
$7$	18.1867	−	3.49896i	0.981991	−	0.188926i
$7$	18.1867	−	3.49896i	0.981991	−	0.188926i
$8$		0			0
$9$	−27.5672	+	47.7478i	−1.02101	+	1.76844i
$10$		0			0
$11$	16.5579	+	28.6792i	0.453855	+	0.786100i	0.998622	−	0.0524880i	$-0.0167151\pi$
$11$	16.5579	+	28.6792i	0.453855	+	0.786100i	−0.544767	+	0.838588i	$0.683382\pi$
$12$		0			0
$13$	38.7753			0.827257			0.413629	−	0.910446i	$-0.364261\pi$
$13$	38.7753			0.827257			0.413629	+	0.910446i	$0.364261\pi$
$14$		0			0
$15$	−127.131			−2.18833
$16$		0			0
$17$	−54.7836	−	94.8880i	−0.781587	−	1.35375i	−0.931017	−	0.364976i	$-0.881077\pi$
$17$	−54.7836	−	94.8880i	−0.781587	−	1.35375i	0.149430	−	0.988772i	$-0.452256\pi$
$18$		0			0
$19$	37.1510	−	64.3474i	0.448580	−	0.776963i	−0.549714	−	0.835353i	$-0.685263\pi$
$19$	37.1510	−	64.3474i	0.448580	−	0.776963i	0.998294	+	0.0583896i	$0.0185966\pi$
$20$		0			0
$21$	−109.873	−	126.886i	−1.14173	−	1.31851i
$22$		0			0
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$24$		0			0
$25$	−35.8887	−	62.1610i	−0.287110	−	0.497288i
$26$		0			0
$27$	254.977			1.81742
$28$		0			0
$29$	−245.176			−1.56993			−0.784967	−	0.619537i	$-0.787320\pi$
$29$	−245.176			−1.56993			−0.784967	+	0.619537i	$0.787320\pi$
$30$		0			0
$31$	−117.817	−	204.065i	−0.682599	−	1.18230i	−0.974185	−	0.225751i	$-0.927516\pi$
$31$	−117.817	−	204.065i	−0.682599	−	1.18230i	0.291586	−	0.956545i	$-0.405817\pi$
$32$		0			0
$33$	150.061	−	259.914i	0.791585	−	1.37107i
$34$		0			0
$35$	85.0527	−	245.481i	0.410758	−	1.18554i
$36$		0			0
$37$	125.796	−	217.884i	0.558937	−	0.968107i	−0.438648	−	0.898659i	$-0.644543\pi$
$37$	125.796	−	217.884i	0.558937	−	0.968107i	0.997586	−	0.0694487i	$-0.0221240\pi$
$38$		0			0
$39$	−175.707	−	304.333i	−0.721425	−	1.24954i
$40$		0			0
$41$	109.856			0.418455			0.209228	−	0.977867i	$-0.432905\pi$
$41$	109.856			0.418455			0.209228	+	0.977867i	$0.432905\pi$
$42$		0			0
$43$	−380.631			−1.34990			−0.674950	−	0.737863i	$-0.735835\pi$
$43$	−380.631			−1.34990			−0.674950	+	0.737863i	$0.735835\pi$
$44$		0			0
$45$	386.706	+	669.794i	1.28104	+	2.21882i
$46$		0			0
$47$	−113.010	+	195.739i	−0.350728	+	0.607478i	−0.986377	−	0.164500i	$-0.947399\pi$
$47$	−113.010	+	195.739i	−0.350728	+	0.607478i	0.635650	+	0.771978i	$0.280732\pi$
$48$		0			0
$49$	318.515	−	127.269i	0.928614	−	0.371047i
$50$		0			0
$51$	−496.493	+	859.951i	−1.36320	+	2.36112i
$52$		0			0
$53$	307.607	+	532.791i	0.797228	+	1.38084i	0.921415	+	0.388580i	$0.127034\pi$
$53$	307.607	+	532.791i	0.797228	+	1.38084i	−0.124187	+	0.992259i	$0.539632\pi$
$54$		0			0
$55$	464.541			1.13888
$56$		0			0
$57$	−673.384			−1.56477
$58$		0			0
$59$	−32.5545	−	56.3861i	−0.0718345	−	0.124421i	0.827871	−	0.560919i	$-0.189552\pi$
$59$	−32.5545	−	56.3861i	−0.0718345	−	0.124421i	−0.899705	+	0.436498i	$0.856219\pi$
$60$		0			0
$61$	6.45160	−	11.1745i	0.0135417	−	0.0234549i	−0.859175	−	0.511682i	$-0.829023\pi$
$61$	6.45160	−	11.1745i	0.0135417	−	0.0234549i	0.872717	+	0.488227i	$0.162356\pi$
$62$		0			0
$63$	−334.290	+	964.833i	−0.668517	+	1.92948i
$64$		0			0
$65$	271.965	−	471.057i	0.518971	−	0.898884i
$66$		0			0
$67$	−357.710	−	619.572i	−0.652257	−	1.12974i	−0.982574	−	0.185873i	$-0.940489\pi$
$67$	−357.710	−	619.572i	−0.652257	−	1.12974i	0.330317	−	0.943870i	$-0.392845\pi$
$68$		0			0
$69$	−208.444			−0.363678
$70$		0			0
$71$	−22.4989			−0.0376074			−0.0188037	−	0.999823i	$-0.505986\pi$
$71$	−22.4989			−0.0376074			−0.0188037	+	0.999823i	$0.505986\pi$
$72$		0			0
$73$	3.41405	+	5.91332i	0.00547377	+	0.00948084i	0.868749	−	0.495252i	$-0.164924\pi$
$73$	3.41405	+	5.91332i	0.00547377	+	0.00948084i	−0.863276	+	0.504733i	$0.831591\pi$
$74$		0			0
$75$	−325.252	+	563.353i	−0.500759	+	0.867339i
$76$		0			0
$77$	401.482	+	463.645i	0.594196	+	0.686198i
$78$		0			0
$79$	−23.3449	+	40.4346i	−0.0332470	+	0.0575854i	−0.882170	−	0.470931i	$-0.843918\pi$
$79$	−23.3449	+	40.4346i	−0.0332470	+	0.0575854i	0.848923	+	0.528516i	$0.177251\pi$
$80$		0			0
$81$	−411.087	−	712.024i	−0.563906	−	0.976713i
$82$		0			0
$83$	−664.248			−0.878441			−0.439221	−	0.898379i	$-0.644745\pi$
$83$	−664.248			−0.878441			−0.439221	+	0.898379i	$0.644745\pi$
$84$		0			0
$85$	−1536.98			−1.96128
$86$		0			0
$87$	1110.99	+	1924.30i	1.36909	+	2.37133i
$88$		0			0
$89$	297.282	−	514.907i	0.354065	−	0.613259i	−0.632892	−	0.774240i	$-0.718132\pi$
$89$	297.282	−	514.907i	0.354065	−	0.613259i	0.986957	+	0.160981i	$0.0514658\pi$
$90$		0			0
$91$	705.197	−	135.673i	0.812359	−	0.156290i
$92$		0			0
$93$	−1067.75	+	1849.40i	−1.19055	+	2.06209i
$94$		0			0
$95$	−521.144	−	902.648i	−0.562824	−	0.974840i
$96$		0			0
$97$	79.5901			0.0833108			0.0416554	−	0.999132i	$-0.486737\pi$
$97$	79.5901			0.0833108			0.0416554	+	0.999132i	$0.486737\pi$
$98$		0			0
$99$	−1825.82			−1.85356
$100$		0			0
$101$	−498.824	−	863.988i	−0.491434	−	0.851189i	0.508517	−	0.861052i	$-0.330194\pi$
$101$	−498.824	−	863.988i	−0.491434	−	0.851189i	−0.999951	+	0.00986314i	$0.996860\pi$
$102$		0			0
$103$	589.823	−	1021.60i	0.564243	−	0.977297i	−0.432877	−	0.901453i	$-0.642502\pi$
$103$	589.823	−	1021.60i	0.564243	−	0.977297i	0.997120	−	0.0758439i	$-0.0241651\pi$
$104$		0			0
$105$	−2312.09	+	444.825i	−2.14892	+	0.413433i
$106$		0			0
$107$	−1043.51	+	1807.41i	−0.942802	+	1.63298i	−0.182709	+	0.983167i	$0.558486\pi$
$107$	−1043.51	+	1807.41i	−0.942802	+	1.63298i	−0.760093	+	0.649814i	$0.774847\pi$
$108$		0			0
$109$	153.693	+	266.204i	0.135056	+	0.233924i	0.925619	−	0.378457i	$-0.123545\pi$
$109$	153.693	+	266.204i	0.135056	+	0.233924i	−0.790563	+	0.612381i	$0.790212\pi$
$110$		0			0
$111$	−2280.12			−1.94973
$112$		0			0
$113$	1500.34			1.24903			0.624513	−	0.781015i	$-0.285298\pi$
$113$	1500.34			1.24903			0.624513	+	0.781015i	$0.285298\pi$
$114$		0			0
$115$	−161.319	−	279.413i	−0.130809	−	0.226568i
$116$		0			0
$117$	−1068.93	+	1851.44i	−0.844636	+	1.46295i
$118$		0			0
$119$	−1328.34	−	1534.02i	−1.02327	−	1.18171i
$120$		0			0
$121$	117.170	−	202.944i	0.0880315	−	0.152475i
$122$		0			0
$123$	−497.803	−	862.219i	−0.364922	−	0.632063i
$124$		0			0
$125$	746.593			0.534218
$126$		0			0
$127$	−931.648			−0.650948			−0.325474	−	0.945551i	$-0.605524\pi$
$127$	−931.648			−0.650948			−0.325474	+	0.945551i	$0.605524\pi$
$128$		0			0
$129$	1724.79	+	2987.43i	1.17721	+	2.03898i
$130$		0			0
$131$	−361.180	+	625.582i	−0.240889	+	0.417232i	−0.960968	−	0.276660i	$-0.910772\pi$
$131$	−361.180	+	625.582i	−0.240889	+	0.417232i	0.720079	+	0.693892i	$0.244106\pi$
$132$		0			0
$133$	450.506	−	1300.26i	0.293713	−	0.847720i
$134$		0			0
$135$	1788.37	−	3097.55i	1.14014	−	1.97478i
$136$		0			0
$137$	1168.00	+	2023.04i	0.728389	+	1.26161i	0.957564	+	0.288221i	$0.0930638\pi$
$137$	1168.00	+	2023.04i	0.728389	+	1.26161i	−0.229175	+	0.973385i	$0.573603\pi$
$138$		0			0
$139$	−2722.08			−1.66104			−0.830518	−	0.556992i	$-0.811955\pi$
$139$	−2722.08			−1.66104			−0.830518	+	0.556992i	$0.811955\pi$
$140$		0			0
$141$	2048.37			1.22343
$142$		0			0
$143$	642.039	+	1112.04i	0.375455	+	0.650307i
$144$		0			0
$145$	−1719.63	+	2978.49i	−0.984882	+	1.70587i
$146$		0			0
$147$	−2442.21	−	1923.19i	−1.37027	−	1.07906i
$148$		0			0
$149$	1095.27	−	1897.07i	0.602203	−	1.04305i	−0.390284	−	0.920695i	$-0.627623\pi$
$149$	1095.27	−	1897.07i	0.602203	−	1.04305i	0.992487	−	0.122351i	$-0.0390435\pi$
$150$		0			0
$151$	381.071	+	660.034i	0.205371	+	0.355714i	0.950251	−	0.311485i	$-0.100826\pi$
$151$	381.071	+	660.034i	0.205371	+	0.355714i	−0.744880	+	0.667199i	$0.767493\pi$
$152$		0			0
$153$	6040.92			3.19202
$154$		0			0
$155$	−3305.41			−1.71288
$156$		0			0
$157$	1831.16	+	3171.65i	0.930841	+	1.61226i	0.781887	+	0.623421i	$0.214258\pi$
$157$	1831.16	+	3171.65i	0.930841	+	1.61226i	0.148955	+	0.988844i	$0.452409\pi$
$158$		0			0
$159$	2787.78	−	4828.58i	1.39047	−	2.40837i
$160$		0			0
$161$	139.453	−	402.492i	0.0682636	−	0.197024i
$162$		0			0
$163$	−618.766	+	1071.73i	−0.297334	+	0.514998i	−0.975525	−	0.219888i	$-0.929431\pi$
$163$	−618.766	+	1071.73i	−0.297334	+	0.514998i	0.678191	+	0.734886i	$0.262764\pi$
$164$		0			0
$165$	−2105.02	−	3646.00i	−0.993185	−	1.72025i
$166$		0			0
$167$	1438.08			0.666357			0.333179	−	0.942864i	$-0.391879\pi$
$167$	1438.08			0.666357			0.333179	+	0.942864i	$0.391879\pi$
$168$		0			0
$169$	−693.473			−0.315645
$170$		0			0
$171$	2048.30	+	3547.76i	0.916007	+	1.58657i
$172$		0			0
$173$	272.890	−	472.659i	0.119927	−	0.207720i	−0.799811	−	0.600252i	$-0.795067\pi$
$173$	272.890	−	472.659i	0.119927	−	0.207720i	0.919739	+	0.392531i	$0.128400\pi$
$174$		0			0
$175$	−870.197	−	1004.93i	−0.375890	−	0.434090i
$176$		0			0
$177$	−295.035	+	511.016i	−0.125289	+	0.217007i
$178$		0			0
$179$	1078.82	+	1868.58i	0.450475	+	0.780245i	0.998415	−	0.0562718i	$-0.0179213\pi$
$179$	1078.82	+	1868.58i	0.450475	+	0.780245i	−0.547941	+	0.836517i	$0.684588\pi$
$180$		0			0
$181$	2052.21			0.842759			0.421379	−	0.906884i	$-0.361546\pi$
$181$	2052.21			0.842759			0.421379	+	0.906884i	$0.361546\pi$
$182$		0			0
$183$	−116.939			−0.0472371
$184$		0			0
$185$	−1764.63	−	3056.43i	−0.701287	−	1.21466i
$186$		0			0
$187$	1814.21	−	3142.30i	0.709454	−	1.22881i
$188$		0			0
$189$	4637.19	−	892.153i	1.78469	−	0.343358i
$190$		0			0
$191$	1897.69	−	3286.90i	0.718912	−	1.24519i	−0.242520	−	0.970146i	$-0.577974\pi$
$191$	1897.69	−	3286.90i	0.718912	−	1.24519i	0.961431	−	0.275045i	$-0.0886928\pi$
$192$		0			0
$193$	−1289.52	−	2233.52i	−0.480942	−	0.833015i	0.518819	−	0.854884i	$-0.326372\pi$
$193$	−1289.52	−	2233.52i	−0.480942	−	0.833015i	−0.999761	+	0.0218686i	$0.993038\pi$
$194$		0			0
$195$	−4929.53			−1.81031
$196$		0			0
$197$	462.329			0.167206			0.0836030	−	0.996499i	$-0.473357\pi$
$197$	462.329			0.167206			0.0836030	+	0.996499i	$0.473357\pi$
$198$		0			0
$199$	−1675.42	−	2901.91i	−0.596820	−	1.03372i	−0.993287	−	0.115674i	$-0.963097\pi$
$199$	−1675.42	−	2901.91i	−0.596820	−	1.03372i	0.396467	−	0.918049i	$-0.370236\pi$
$200$		0			0
$201$	−3241.86	+	5615.06i	−1.13763	+	1.97043i
$202$		0			0
$203$	−4458.96	+	857.862i	−1.54166	+	0.296602i
$204$		0			0
$205$	770.517	−	1334.57i	0.262513	−	0.454686i
$206$		0			0
$207$	634.046	+	1098.20i	0.212895	+	0.368745i
$208$		0			0
$209$	2460.57			0.814361
$210$		0			0
$211$	−900.224			−0.293715			−0.146858	−	0.989158i	$-0.546916\pi$
$211$	−900.224			−0.293715			−0.146858	+	0.989158i	$0.546916\pi$
$212$		0			0
$213$	101.952	+	176.585i	0.0327963	+	0.0568048i
$214$		0			0
$215$	−2669.70	+	4624.05i	−0.846846	+	1.46678i
$216$		0			0
$217$	−2856.72	−	3299.04i	−0.893673	−	1.03204i
$218$		0			0
$219$	30.9409	−	53.5912i	0.00954700	−	0.0165359i
$220$		0			0
$221$	−2124.25	−	3679.31i	−0.646573	−	1.11990i
$222$		0			0
$223$	−5976.79			−1.79478			−0.897389	−	0.441240i	$-0.854539\pi$
$223$	−5976.79			−1.79478			−0.897389	+	0.441240i	$0.854539\pi$
$224$		0			0
$225$	3957.40			1.17256
$226$		0			0
$227$	791.883	+	1371.58i	0.231538	+	0.401035i	0.958261	−	0.285895i	$-0.0922909\pi$
$227$	791.883	+	1371.58i	0.231538	+	0.401035i	−0.726723	+	0.686931i	$0.758958\pi$
$228$		0			0
$229$	1853.55	−	3210.44i	0.534872	−	0.926426i	−0.464297	−	0.885680i	$-0.653693\pi$
$229$	1853.55	−	3210.44i	0.534872	−	0.926426i	0.999170	−	0.0407466i	$-0.0129737\pi$
$230$		0			0
$231$	1819.70	−	5252.04i	0.518300	−	1.49593i
$232$		0			0
$233$	505.209	−	875.048i	0.142049	−	0.246036i	−0.786219	−	0.617948i	$-0.787964\pi$
$233$	505.209	−	875.048i	0.142049	−	0.246036i	0.928268	+	0.371912i	$0.121298\pi$
$234$		0			0
$235$	1585.27	+	2745.77i	0.440050	+	0.762190i
$236$		0			0
$237$	423.141			0.115975
$238$		0			0
$239$	5595.12			1.51430			0.757151	−	0.653240i	$-0.226591\pi$
$239$	5595.12			1.51430			0.757151	+	0.653240i	$0.226591\pi$
$240$		0			0
$241$	237.821	+	411.917i	0.0635659	+	0.110099i	0.896057	−	0.443939i	$-0.146419\pi$
$241$	237.821	+	411.917i	0.0635659	+	0.110099i	−0.832491	+	0.554038i	$0.813086\pi$
$242$		0			0
$243$	−283.418	+	490.894i	−0.0748200	+	0.129592i
$244$		0			0
$245$	687.904	−	4762.08i	0.179382	−	1.24179i
$246$		0			0
$247$	1440.54	−	2495.09i	0.371091	−	0.642749i
$248$		0			0
$249$	3009.97	+	5213.43i	0.766061	+	1.32686i
$250$		0			0
$251$	6174.50			1.55271			0.776356	−	0.630294i	$-0.217066\pi$
$251$	6174.50			1.55271			0.776356	+	0.630294i	$0.217066\pi$
$252$		0			0
$253$	761.665			0.189271
$254$		0			0
$255$	6964.67	+	12063.2i	1.71037	+	2.96245i
$256$		0			0
$257$	−1369.33	+	2371.75i	−0.332360	+	0.575664i	−0.982974	−	0.183744i	$-0.941178\pi$
$257$	−1369.33	+	2371.75i	−0.332360	+	0.575664i	0.650614	+	0.759408i	$0.274511\pi$
$258$		0			0
$259$	1525.44	−	4402.76i	0.365971	−	1.05627i
$260$		0			0
$261$	6758.83	−	11706.6i	1.60292	−	2.77633i
$262$		0			0
$263$	2310.90	+	4002.60i	0.541812	+	0.938445i	0.998800	+	0.0489725i	$0.0155947\pi$
$263$	2310.90	+	4002.60i	0.541812	+	0.938445i	−0.456989	+	0.889473i	$0.651072\pi$
$264$		0			0
$265$	8630.06			2.00053
$266$		0			0
$267$	−5388.41			−1.23508
$268$		0			0
$269$	−1021.00	−	1768.42i	−0.231418	−	0.400827i	0.726808	−	0.686841i	$-0.241003\pi$
$269$	−1021.00	−	1768.42i	−0.231418	−	0.400827i	−0.958226	+	0.286014i	$0.907670\pi$
$270$		0			0
$271$	−3224.62	+	5585.21i	−0.722811	+	1.25195i	0.237057	+	0.971496i	$0.423817\pi$
$271$	−3224.62	+	5585.21i	−0.722811	+	1.25195i	−0.959869	+	0.280450i	$0.909516\pi$
$272$		0			0
$273$	−4260.38	−	4920.03i	−0.944505	−	1.09075i
$274$		0			0
$275$	1188.48	−	2058.52i	0.260612	−	0.451393i
$276$		0			0
$277$	1969.18	+	3410.72i	0.427136	+	0.739821i	0.996617	−	0.0821831i	$-0.0261892\pi$
$277$	1969.18	+	3410.72i	0.427136	+	0.739821i	−0.569481	+	0.822004i	$0.692856\pi$
$278$		0			0
$279$	12991.5			2.78775
$280$		0			0
$281$	−1997.04			−0.423963			−0.211981	−	0.977274i	$-0.567992\pi$
$281$	−1997.04			−0.423963			−0.211981	+	0.977274i	$0.567992\pi$
$282$		0			0
$283$	−2706.17	−	4687.22i	−0.568427	−	0.984545i	−0.996722	−	0.0809056i	$-0.974219\pi$
$283$	−2706.17	−	4687.22i	−0.568427	−	0.984545i	0.428295	−	0.903639i	$-0.359115\pi$
$284$		0			0
$285$	−4723.03	+	8180.52i	−0.981642	+	1.70025i
$286$		0			0
$287$	1997.93	−	384.382i	0.410919	−	0.0790570i
$288$		0			0
$289$	−3545.99	+	6141.83i	−0.721756	+	1.25012i
$290$		0			0
$291$	−360.655	−	624.672i	−0.0726527	−	0.125838i
$292$		0			0
$293$	−4846.72			−0.966377			−0.483189	−	0.875516i	$-0.660521\pi$
$293$	−4846.72			−0.966377			−0.483189	+	0.875516i	$0.660521\pi$
$294$		0			0
$295$	−913.332			−0.180258
$296$		0			0
$297$	4221.89	+	7312.52i	0.824844	+	1.42867i
$298$		0			0
$299$	445.916	−	772.350i	0.0862475	−	0.149385i
$300$		0			0
$301$	−6922.44	+	1331.81i	−1.32559	+	0.255031i
$302$		0			0
$303$	−4520.74	+	7830.16i	−0.857128	+	1.48459i
$304$		0			0
$305$	−90.5014	−	156.753i	−0.0169905	−	0.0294284i
$306$		0			0
$307$	−9943.94			−1.84863			−0.924317	−	0.381626i	$-0.875364\pi$
$307$	−9943.94			−1.84863			−0.924317	+	0.381626i	$0.875364\pi$
$308$		0			0
$309$	−10690.9			−1.96823
$310$		0			0
$311$	1976.04	+	3422.61i	0.360293	+	0.624046i	0.988009	−	0.154396i	$-0.0493433\pi$
$311$	1976.04	+	3422.61i	0.360293	+	0.624046i	−0.627716	+	0.778443i	$0.716010\pi$
$312$		0			0
$313$	2799.99	−	4849.72i	0.505638	−	0.875791i	−0.494341	−	0.869268i	$-0.664590\pi$
$313$	2799.99	−	4849.72i	0.505638	−	0.875791i	0.999979	−	0.00652272i	$-0.00207626\pi$
$314$		0			0
$315$	9376.49	+	10828.3i	1.67716	+	1.93684i
$316$		0			0
$317$	4584.26	−	7940.17i	0.812232	−	1.40683i	−0.0990658	−	0.995081i	$-0.531585\pi$
$317$	4584.26	−	7940.17i	0.812232	−	1.40683i	0.911298	−	0.411747i	$-0.135081\pi$
$318$		0			0
$319$	−4059.61	−	7031.46i	−0.712522	−	1.23413i
$320$		0			0
$321$	18914.2			3.28875
$322$		0			0
$323$	−8141.06			−1.40242
$324$		0			0
$325$	−1391.60	−	2410.32i	−0.237513	−	0.411385i
$326$		0			0
$327$	1392.89	−	2412.56i	0.235557	−	0.407996i
$328$		0			0
$329$	−1370.40	+	3955.27i	−0.229643	+	0.662800i
$330$		0			0
$331$	4711.67	−	8160.85i	0.782407	−	1.35517i	−0.148129	−	0.988968i	$-0.547325\pi$
$331$	4711.67	−	8160.85i	0.782407	−	1.35517i	0.930536	−	0.366201i	$-0.119342\pi$
$332$		0			0
$333$	6935.67	+	12012.9i	1.14136	+	1.97689i
$334$		0			0
$335$	−10035.7			−1.63675
$336$		0			0
$337$	−8051.62			−1.30148			−0.650742	−	0.759299i	$-0.725542\pi$
$337$	−8051.62			−1.30148			−0.650742	+	0.759299i	$0.725542\pi$
$338$		0			0
$339$	−6798.63	−	11775.6i	−1.08924	−	1.88661i
$340$		0			0
$341$	3901.61	−	6757.79i	0.619602	−	1.07318i
$342$		0			0
$343$	5347.43	−	3429.08i	0.841790	−	0.539805i
$344$		0			0
$345$	−1462.00	+	2532.26i	−0.228149	+	0.395166i
$346$		0			0
$347$	1025.05	+	1775.44i	0.158581	+	0.274670i	0.934357	−	0.356338i	$-0.115975\pi$
$347$	1025.05	+	1775.44i	0.158581	+	0.274670i	−0.775776	+	0.631008i	$0.782641\pi$
$348$		0			0
$349$	−3899.99			−0.598171			−0.299086	−	0.954226i	$-0.596682\pi$
$349$	−3899.99			−0.598171			−0.299086	+	0.954226i	$0.596682\pi$
$350$		0			0
$351$	9886.81			1.50347
$352$		0			0
$353$	4669.61	+	8088.01i	0.704075	+	1.21949i	0.967024	+	0.254684i	$0.0819715\pi$
$353$	4669.61	+	8088.01i	0.704075	+	1.21949i	−0.262949	+	0.964810i	$0.584695\pi$
$354$		0			0
$355$	−157.804	+	273.325i	−0.0235926	+	0.0408636i
$356$		0			0
$357$	−6020.65	+	17376.9i	−0.892568	+	2.57615i
$358$		0			0
$359$	2665.23	−	4616.32i	0.391826	−	0.678663i	−0.600864	−	0.799351i	$-0.705177\pi$
$359$	2665.23	−	4616.32i	0.391826	−	0.678663i	0.992690	+	0.120688i	$0.0385101\pi$
$360$		0			0
$361$	669.109	+	1158.93i	0.0975519	+	0.168965i
$362$		0			0
$363$	−2123.78			−0.307078
$364$		0			0
$365$	95.7829			0.0137356
$366$		0			0
$367$	6399.61	+	11084.4i	0.910236	+	1.57658i	0.813730	+	0.581243i	$0.197433\pi$
$367$	6399.61	+	11084.4i	0.910236	+	1.57658i	0.0965061	+	0.995332i	$0.469233\pi$
$368$		0			0
$369$	−3028.43	+	5245.39i	−0.427246	+	0.740011i
$370$		0			0
$371$	7458.58	+	8613.42i	1.04375	+	1.20535i
$372$		0			0
$373$	6621.53	−	11468.8i	0.919169	−	1.59205i	0.118489	−	0.992955i	$-0.462195\pi$
$373$	6621.53	−	11468.8i	0.919169	−	1.59205i	0.800680	−	0.599092i	$-0.204472\pi$
$374$		0			0
$375$	−3383.11	−	5859.72i	−0.465875	−	0.806919i
$376$		0			0
$377$	−9506.80			−1.29874
$378$		0			0
$379$	−243.277			−0.0329718			−0.0164859	−	0.999864i	$-0.505248\pi$
$379$	−243.277			−0.0329718			−0.0164859	+	0.999864i	$0.505248\pi$
$380$		0			0
$381$	4221.67	+	7312.15i	0.567671	+	0.983235i
$382$		0			0
$383$	3632.52	−	6291.70i	0.484629	−	0.839402i	−0.515215	−	0.857061i	$-0.672288\pi$
$383$	3632.52	−	6291.70i	0.484629	−	0.839402i	0.999844	+	0.0176590i	$0.00562134\pi$
$384$		0			0
$385$	8448.47	−	1625.41i	1.11837	−	0.215165i
$386$		0			0
$387$	10492.9	−	18174.3i	1.37826	−	2.38721i
$388$		0			0
$389$	−3535.81	−	6124.20i	−0.460855	−	0.798224i	0.538149	−	0.842850i	$-0.319124\pi$
$389$	−3535.81	−	6124.20i	−0.460855	−	0.798224i	−0.999004	+	0.0446258i	$0.985790\pi$
$390$		0			0
$391$	−2520.05			−0.325944
$392$		0			0
$393$	6546.61			0.840287
$394$		0			0
$395$	327.477	+	567.206i	0.0417143	+	0.0722512i
$396$		0			0
$397$	−600.251	+	1039.67i	−0.0758835	+	0.131434i	−0.901470	−	0.432841i	$-0.857511\pi$
$397$	−600.251	+	1039.67i	−0.0758835	+	0.131434i	0.825587	+	0.564275i	$0.190844\pi$
$398$		0			0
$399$	−12246.7	+	2356.14i	−1.53659	+	0.295626i
$400$		0			0
$401$	−3452.90	+	5980.60i	−0.429999	+	0.744780i	−0.996873	−	0.0790245i	$-0.974819\pi$
$401$	−3452.90	+	5980.60i	−0.429999	+	0.744780i	0.566874	+	0.823805i	$0.308153\pi$
$402$		0			0
$403$	−4568.40	−	7912.69i	−0.564685	−	0.978063i
$404$		0			0
$405$	−11533.2			−1.41504
$406$		0			0
$407$	8331.66			1.01471
$408$		0			0
$409$	413.568	+	716.321i	0.0499991	+	0.0866009i	0.889942	−	0.456074i	$-0.150745\pi$
$409$	413.568	+	716.321i	0.0499991	+	0.0866009i	−0.839943	+	0.542675i	$0.817411\pi$
$410$		0			0
$411$	10585.4	−	18334.4i	1.27041	−	2.20041i
$412$		0			0
$413$	−789.353	−	911.571i	−0.0940472	−	0.108609i
$414$		0			0
$415$	−4658.94	+	8069.53i	−0.551081	+	0.954500i
$416$		0			0
$417$	12334.8	+	21364.6i	1.44854	+	2.50894i
$418$		0			0
$419$	−15658.5			−1.82570			−0.912851	−	0.408292i	$-0.866125\pi$
$419$	−15658.5			−1.82570			−0.912851	+	0.408292i	$0.866125\pi$
$420$		0			0
$421$	7991.78			0.925168			0.462584	−	0.886575i	$-0.346922\pi$
$421$	7991.78			0.925168			0.462584	+	0.886575i	$0.346922\pi$
$422$		0			0
$423$	−6230.74	−	10792.0i	−0.716191	−	1.24048i
$424$		0			0
$425$	−3932.22	+	6810.81i	−0.448802	+	0.777348i
$426$		0			0
$427$	78.2344	−	225.802i	0.00886658	−	0.0255909i
$428$		0			0
$429$	5818.68	−	10078.2i	0.654845	−	1.13422i
$430$		0			0
$431$	2922.11	+	5061.25i	0.326574	+	0.565642i	0.981830	−	0.189765i	$-0.0607725\pi$
$431$	2922.11	+	5061.25i	0.326574	+	0.565642i	−0.655256	+	0.755407i	$0.727439\pi$
$432$		0			0
$433$	9547.81			1.05967			0.529837	−	0.848100i	$-0.322253\pi$
$433$	9547.81			1.05967			0.529837	+	0.848100i	$0.322253\pi$
$434$		0			0
$435$	31169.4			3.43554
$436$		0			0
$437$	−854.473	−	1479.99i	−0.0935354	−	0.162008i
$438$		0			0
$439$	7168.61	−	12416.4i	0.779360	−	1.34989i	−0.152952	−	0.988234i	$-0.548878\pi$
$439$	7168.61	−	12416.4i	0.779360	−	1.34989i	0.932311	−	0.361657i	$-0.117789\pi$
$440$		0			0
$441$	−2703.73	+	18716.8i	−0.291948	+	2.02104i
$442$		0			0
$443$	−3548.73	+	6146.58i	−0.380599	+	0.659217i	−0.991148	−	0.132762i	$-0.957615\pi$
$443$	−3548.73	+	6146.58i	−0.380599	+	0.659217i	0.610549	+	0.791978i	$0.290949\pi$
$444$		0			0
$445$	−4170.19	−	7222.98i	−0.444238	−	0.769443i
$446$		0			0
$447$	−19852.5			−2.10065
$448$		0			0
$449$	−11883.7			−1.24906			−0.624528	−	0.781003i	$-0.714709\pi$
$449$	−11883.7			−1.24906			−0.624528	+	0.781003i	$0.714709\pi$
$450$		0			0
$451$	1818.99	+	3150.59i	0.189918	+	0.328947i
$452$		0			0
$453$	3453.57	−	5981.76i	0.358196	−	0.620414i
$454$		0			0
$455$	3297.95	−	9518.59i	0.339802	−	0.980744i
$456$		0			0
$457$	−2307.93	+	3997.45i	−0.236237	+	0.409174i	−0.959631	−	0.281261i	$-0.909247\pi$
$457$	−2307.93	+	3997.45i	−0.236237	+	0.409174i	0.723395	+	0.690435i	$0.242581\pi$
$458$		0			0
$459$	−13968.5	−	24194.2i	−1.42047	−	2.46033i
$460$		0			0
$461$	−8312.05			−0.839763			−0.419882	−	0.907579i	$-0.637928\pi$
$461$	−8312.05			−0.839763			−0.419882	+	0.907579i	$0.637928\pi$
$462$		0			0
$463$	15130.9			1.51878			0.759388	−	0.650638i	$-0.225498\pi$
$463$	15130.9			1.51878			0.759388	+	0.650638i	$0.225498\pi$
$464$		0			0
$465$	14978.2	+	25942.9i	1.49375	+	2.58726i
$466$		0			0
$467$	−1395.26	+	2416.66i	−0.138255	+	0.239464i	−0.926836	−	0.375466i	$-0.877483\pi$
$467$	−1395.26	+	2416.66i	−0.138255	+	0.239464i	0.788581	+	0.614930i	$0.210816\pi$
$468$		0			0
$469$	−8673.44	−	10016.4i	−0.853949	−	0.986169i
$470$		0			0
$471$	16595.4	−	28744.1i	1.62352	−	2.81201i
$472$		0			0
$473$	−6302.47	−	10916.2i	−0.612659	−	1.06116i
$474$		0			0
$475$	−5333.20			−0.515166
$476$		0			0
$477$	−33919.5			−3.25590
$478$		0			0
$479$	−9093.18	−	15749.9i	−0.867387	−	1.50236i	−0.864658	−	0.502361i	$-0.832465\pi$
$479$	−9093.18	−	15749.9i	−0.867387	−	1.50236i	−0.00272871	−	0.999996i	$-0.500869\pi$
$480$		0			0
$481$	4877.77	−	8448.54i	0.462385	−	0.800874i
$482$		0			0
$483$	−3790.92	+	729.339i	−0.357128	+	0.0687082i
$484$		0			0
$485$	558.234	−	966.890i	0.0522641	−	0.0905242i
$486$		0			0
$487$	−4784.82	−	8287.56i	−0.445218	−	0.771140i	0.552850	−	0.833281i	$-0.313540\pi$
$487$	−4784.82	−	8287.56i	−0.445218	−	0.771140i	−0.998067	+	0.0621413i	$0.980207\pi$
$488$		0			0
$489$	11215.5			1.03718
$490$		0			0
$491$	15181.5			1.39538			0.697688	−	0.716402i	$-0.254212\pi$
$491$	15181.5			1.39538			0.697688	+	0.716402i	$0.254212\pi$
$492$		0			0
$493$	13431.6	+	23264.3i	1.22704	+	2.12530i
$494$		0			0
$495$	−12806.1	+	22180.8i	−1.16281	+	2.01405i
$496$		0			0
$497$	−409.182	+	78.7227i	−0.0369302	+	0.00710503i
$498$		0			0
$499$	2223.21	−	3850.72i	0.199448	−	0.345454i	−0.748901	−	0.662681i	$-0.769418\pi$
$499$	2223.21	−	3850.72i	0.199448	−	0.345454i	0.948350	+	0.317227i	$0.102752\pi$
$500$		0			0
$501$	−6516.50	−	11286.9i	−0.581109	−	1.00651i
$502$		0			0
$503$	−15705.5			−1.39219			−0.696095	−	0.717949i	$-0.745081\pi$
$503$	−15705.5			−1.39219			−0.696095	+	0.717949i	$0.745081\pi$
$504$		0			0
$505$	−13994.7			−1.23318
$506$		0			0
$507$	3142.41	+	5442.81i	0.275265	+	0.476772i
$508$		0			0
$509$	−5308.01	+	9193.75i	−0.462227	+	0.800601i	−0.999072	−	0.0430803i	$-0.986283\pi$
$509$	−5308.01	+	9193.75i	−0.462227	+	0.800601i	0.536844	+	0.843681i	$0.319616\pi$
$510$		0			0
$511$	82.7810	+	95.5983i	0.00716637	+	0.00827597i
$512$		0			0
$513$	9472.63	−	16407.1i	0.815257	−	1.41207i
$514$		0			0
$515$	−8273.88	−	14330.8i	−0.707943	−	1.22619i
$516$		0			0
$517$	−7484.84			−0.636718
$518$		0			0
$519$	−4946.30			−0.418340
$520$		0			0
$521$	−8251.65	−	14292.3i	−0.693880	−	1.20183i	−0.970557	−	0.240872i	$-0.922567\pi$
$521$	−8251.65	−	14292.3i	−0.693880	−	1.20183i	0.276677	−	0.960963i	$-0.410767\pi$
$522$		0			0
$523$	6349.27	−	10997.3i	0.530849	−	0.919458i	−0.468502	−	0.883462i	$-0.655206\pi$
$523$	6349.27	−	10997.3i	0.530849	−	0.919458i	0.999352	−	0.0359961i	$-0.0114604\pi$
$524$		0			0
$525$	−3944.12	+	11383.6i	−0.327878	+	0.946326i
$526$		0			0
$527$	−12908.9	+	22358.8i	−1.06702	+	1.84813i
$528$		0			0
$529$	−264.500	−	458.127i	−0.0217391	−	0.0376533i
$530$		0			0
$531$	3589.75			0.293374
$532$		0			0
$533$	4259.71			0.346170
$534$		0			0
$535$	14638.1	+	25353.9i	1.18291	+	2.04887i
$536$		0			0
$537$	9777.16	−	16934.5i	0.785690	−	1.36086i
$538$		0			0
$539$	8923.92	+	7027.42i	0.713136	+	0.561581i
$540$		0			0
$541$	1037.13	−	1796.36i	0.0824207	−	0.142757i	−0.821868	−	0.569677i	$-0.807068\pi$
$541$	1037.13	−	1796.36i	0.0824207	−	0.142757i	0.904289	+	0.426920i	$0.140402\pi$
$542$		0			0
$543$	−9299.37	−	16107.0i	−0.734943	−	1.27296i
$544$		0			0
$545$	4311.93			0.338904
$546$		0			0
$547$	−5959.49			−0.465831			−0.232915	−	0.972497i	$-0.574827\pi$
$547$	−5959.49			−0.465831			−0.232915	+	0.972497i	$0.574827\pi$
$548$		0			0
$549$	355.705	+	616.100i	0.0276523	+	0.0478952i
$550$		0			0
$551$	−9108.54	+	15776.5i	−0.704241	+	1.21978i
$552$		0			0
$553$	−283.089	+	817.056i	−0.0217688	+	0.0628296i
$554$		0			0
$555$	−15992.5	+	27699.8i	−1.22314	+	2.11854i
$556$		0			0
$557$	843.154	+	1460.39i	0.0641393	+	0.111093i	0.896312	−	0.443424i	$-0.146236\pi$
$557$	843.154	+	1460.39i	0.0641393	+	0.111093i	−0.832173	+	0.554517i	$0.812903\pi$
$558$		0			0
$559$	−14759.1			−1.11671
$560$		0			0
$561$	−32883.6			−2.47477
$562$		0			0
$563$	−1129.40	−	1956.18i	−0.0845447	−	0.146436i	0.820652	−	0.571428i	$-0.193610\pi$
$563$	−1129.40	−	1956.18i	−0.0845447	−	0.146436i	−0.905197	+	0.424992i	$0.860277\pi$
$564$		0			0
$565$	10523.2	−	18226.7i	0.783563	−	1.35717i
$566$		0			0
$567$	−9967.68	−	11511.0i	−0.738277	−	0.852587i
$568$		0			0
$569$	3590.53	−	6218.98i	0.264539	−	0.458196i	−0.702904	−	0.711285i	$-0.748113\pi$
$569$	3590.53	−	6218.98i	0.264539	−	0.458196i	0.967443	+	0.253090i	$0.0814468\pi$
$570$		0			0
$571$	3654.69	+	6330.11i	0.267853	+	0.463935i	0.968307	−	0.249762i	$-0.0803525\pi$
$571$	3654.69	+	6330.11i	0.267853	+	0.463935i	−0.700454	+	0.713697i	$0.747019\pi$
$572$		0			0
$573$	−34396.8			−2.50776
$574$		0			0
$575$	−1650.88			−0.119733
$576$		0			0
$577$	−6917.35	−	11981.2i	−0.499087	−	0.864444i	0.500913	−	0.865498i	$-0.332998\pi$
$577$	−6917.35	−	11981.2i	−0.499087	−	0.864444i	−0.999999	+	0.00105405i	$0.999664\pi$
$578$		0			0
$579$	−11686.7	+	20241.9i	−0.838828	+	1.45289i
$580$		0			0
$581$	−12080.5	+	2324.18i	−0.862622	+	0.165960i
$582$		0			0
$583$	−10186.7	+	17643.8i	−0.723651	+	1.25340i
$584$		0			0
$585$	14994.6	+	25971.5i	1.05975	+	1.83554i
$586$		0			0
$587$	10955.7			0.770340			0.385170	−	0.922846i	$-0.374143\pi$
$587$	10955.7			0.770340			0.385170	+	0.922846i	$0.374143\pi$
$588$		0			0
$589$	−17508.1			−1.22480
$590$		0			0
$591$	−2095.00	−	3628.64i	−0.145815	−	0.252559i
$592$		0			0
$593$	−5873.02	+	10172.4i	−0.406705	+	0.704433i	−0.994518	−	0.104563i	$-0.966656\pi$
$593$	−5873.02	+	10172.4i	−0.406705	+	0.704433i	0.587814	+	0.808996i	$0.299989\pi$
$594$		0			0
$595$	−27952.6	+	5377.83i	−1.92596	+	0.370537i
$596$		0			0
$597$	−15184.0	+	26299.4i	−1.04094	+	1.80295i
$598$		0			0
$599$	10775.7	+	18664.1i	0.735033	+	1.27311i	0.954709	+	0.297541i	$0.0961666\pi$
$599$	10775.7	+	18664.1i	0.735033	+	1.27311i	−0.219676	+	0.975573i	$0.570500\pi$
$600$		0			0
$601$	11009.6			0.747241			0.373621	−	0.927582i	$-0.378116\pi$
$601$	11009.6			0.747241			0.373621	+	0.927582i	$0.378116\pi$
$602$		0			0
$603$	39444.3			2.66384
$604$		0			0
$605$	−1643.63	−	2846.85i	−0.110451	−	0.191307i
$606$		0			0
$607$	3773.43	−	6535.78i	0.252321	−	0.437033i	−0.711843	−	0.702338i	$-0.752139\pi$
$607$	3773.43	−	6535.78i	0.252321	−	0.437033i	0.964164	+	0.265305i	$0.0854728\pi$
$608$		0			0
$609$	26938.4	+	31109.3i	1.79244	+	2.06997i
$610$		0			0
$611$	−4382.00	+	7589.84i	−0.290142	+	0.502540i
$612$		0			0
$613$	4417.72	+	7651.71i	0.291077	+	0.504159i	0.974065	−	0.226270i	$-0.0726532\pi$
$613$	4417.72	+	7651.71i	0.291077	+	0.504159i	−0.682988	+	0.730430i	$0.739320\pi$
$614$		0			0
$615$	−13966.1			−0.915719
$616$		0			0
$617$	24178.7			1.57763			0.788816	−	0.614629i	$-0.210694\pi$
$617$	24178.7			1.57763			0.788816	+	0.614629i	$0.210694\pi$
$618$		0			0
$619$	−11923.6	−	20652.2i	−0.774229	−	1.34100i	−0.935227	−	0.354050i	$-0.884804\pi$
$619$	−11923.6	−	20652.2i	−0.774229	−	1.34100i	0.160997	−	0.986955i	$-0.448529\pi$
$620$		0			0
$621$	2932.23	−	5078.77i	0.189479	−	0.328187i
$622$		0			0
$623$	3604.94	−	10404.6i	0.231828	−	0.669107i
$624$		0			0
$625$	9722.59	−	16840.0i	0.622246	−	1.07776i
$626$		0			0
$627$	−11149.8	−	19312.1i	−0.710179	−	1.23007i
$628$		0			0
$629$	−27566.2			−1.74743
$630$		0			0
$631$	20585.3			1.29872			0.649358	−	0.760483i	$-0.275038\pi$
$631$	20585.3			1.29872			0.649358	+	0.760483i	$0.275038\pi$
$632$		0			0
$633$	4079.27	+	7065.51i	0.256140	+	0.443647i
$634$		0			0
$635$	−6534.45	+	11318.0i	−0.408365	+	0.707309i
$636$		0			0
$637$	12350.5	−	4934.91i	0.768203	−	0.306952i
$638$		0			0
$639$	620.232	−	1074.27i	0.0383975	−	0.0665064i
$640$		0			0
$641$	12145.2	+	21036.1i	0.748373	+	1.29622i	0.948602	+	0.316471i	$0.102498\pi$
$641$	12145.2	+	21036.1i	0.748373	+	1.29622i	−0.200229	+	0.979749i	$0.564169\pi$
$642$		0			0
$643$	20041.4			1.22917			0.614584	−	0.788851i	$-0.289324\pi$
$643$	20041.4			1.22917			0.614584	+	0.788851i	$0.289324\pi$
$644$		0			0
$645$	48389.9			2.95403
$646$		0			0
$647$	−3349.07	−	5800.76i	−0.203502	−	0.352475i	0.746153	−	0.665775i	$-0.231899\pi$
$647$	−3349.07	−	5800.76i	−0.203502	−	0.352475i	−0.949654	+	0.313300i	$0.898566\pi$
$648$		0			0
$649$	1078.07	−	1867.27i	0.0652049	−	0.112938i
$650$		0			0
$651$	−12948.0	+	37370.6i	−0.779524	+	2.24988i
$652$		0			0
$653$	−10338.8	+	17907.3i	−0.619585	+	1.07315i	0.369977	+	0.929041i	$0.379366\pi$
$653$	−10338.8	+	17907.3i	−0.619585	+	1.07315i	−0.989562	+	0.144111i	$0.953968\pi$
$654$		0			0
$655$	5066.54	+	8775.50i	0.302238	+	0.523492i
$656$		0			0
$657$	−376.464			−0.0223550
$658$		0			0
$659$	−8818.84			−0.521294			−0.260647	−	0.965434i	$-0.583936\pi$
$659$	−8818.84			−0.521294			−0.260647	+	0.965434i	$0.583936\pi$
$660$		0			0
$661$	−4094.09	−	7091.17i	−0.240910	−	0.417269i	0.720064	−	0.693908i	$-0.244113\pi$
$661$	−4094.09	−	7091.17i	−0.240910	−	0.417269i	−0.960974	+	0.276639i	$0.910779\pi$
$662$		0			0
$663$	−19251.7	+	33344.9i	−1.12771	+	1.95326i
$664$		0			0
$665$	−12636.2	−	14592.8i	−0.736861	−	0.850952i
$666$		0			0
$667$	−2819.53	+	4883.57i	−0.163677	+	0.283497i
$668$		0			0
$669$	27083.2	+	46909.6i	1.56517	+	2.71095i
$670$		0			0
$671$	427.301			0.0245838
$672$		0			0
$673$	31554.9			1.80736			0.903678	−	0.428213i	$-0.140857\pi$
$673$	31554.9			1.80736			0.903678	+	0.428213i	$0.140857\pi$
$674$		0			0
$675$	−9150.78	−	15849.6i	−0.521798	−	0.903781i
$676$		0			0
$677$	3518.75	−	6094.66i	0.199759	−	0.345992i	−0.748691	−	0.662919i	$-0.769317\pi$
$677$	3518.75	−	6094.66i	0.199759	−	0.345992i	0.948450	+	0.316926i	$0.102651\pi$
$678$		0			0
$679$	1447.48	−	278.482i	0.0818105	−	0.0157396i
$680$		0			0
$681$	7176.68	−	12430.4i	0.403834	−	0.699461i
$682$		0			0
$683$	4529.35	+	7845.06i	0.253749	+	0.439506i	0.964555	−	0.263882i	$-0.0850029\pi$
$683$	4529.35	+	7845.06i	0.253749	+	0.439506i	−0.710806	+	0.703388i	$0.751670\pi$
$684$		0			0
$685$	32768.9			1.82779
$686$		0			0
$687$	−33596.7			−1.86578
$688$		0			0
$689$	11927.6	+	20659.2i	0.659512	+	1.14231i
$690$		0			0
$691$	2353.99	−	4077.23i	0.129595	−	0.224464i	−0.793925	−	0.608016i	$-0.791966\pi$
$691$	2353.99	−	4077.23i	0.129595	−	0.224464i	0.923520	+	0.383551i	$0.125299\pi$
$692$		0			0
$693$	−33205.8	+	6388.48i	−1.82018	+	0.350185i
$694$		0			0
$695$	−19092.3	+	33068.9i	−1.04203	+	1.80485i
$696$		0			0
$697$	−6018.32	−	10424.0i	−0.327059	−	0.566483i
$698$		0			0
$699$	−9157.22			−0.495505
$700$		0			0
$701$	36312.6			1.95650			0.978251	−	0.207423i	$-0.0665076\pi$
$701$	36312.6			1.95650			0.978251	+	0.207423i	$0.0665076\pi$
$702$		0			0
$703$	−9346.86	−	16189.2i	−0.501456	−	0.868547i
$704$		0			0
$705$	14367.0	−	24884.4i	0.767508	−	1.32936i
$706$		0			0
$707$	−12095.0	−	13967.8i	−0.643396	−	0.743015i
$708$		0			0
$709$	−9459.87	+	16385.0i	−0.501090	+	0.867913i	0.498909	+	0.866654i	$0.333734\pi$
$709$	−9459.87	+	16385.0i	−0.501090	+	0.867913i	−0.999999	+	0.00125911i	$0.999599\pi$
$710$		0			0
$711$	−1287.11	−	2229.34i	−0.0678908	−	0.117590i
$712$		0			0
$713$	−5419.58			−0.284663
$714$		0			0
$715$	18012.7			0.942150
$716$		0			0
$717$	−25353.7	−	43913.9i	−1.32057	−	2.28730i
$718$		0			0
$719$	−5923.94	+	10260.6i	−0.307268	+	0.532204i	−0.977764	−	0.209710i	$-0.932748\pi$
$719$	−5923.94	+	10260.6i	−0.307268	+	0.532204i	0.670496	+	0.741913i	$0.266081\pi$
$720$		0			0
$721$	7152.41	−	20643.4i	0.369445	−	1.06630i
$722$		0			0
$723$	2155.32	−	3733.13i	0.110868	−	0.192028i
$724$		0			0
$725$	8799.06	+	15240.4i	0.450743	+	0.780710i
$726$		0			0
$727$	−14338.6			−0.731485			−0.365743	−	0.930716i	$-0.619185\pi$
$727$	−14338.6			−0.731485			−0.365743	+	0.930716i	$0.619185\pi$
$728$		0			0
$729$	−17061.6			−0.866819
$730$		0			0
$731$	20852.4	+	36117.3i	1.05506	+	1.82743i
$732$		0			0
$733$	12302.4	−	21308.3i	0.619916	−	1.07373i	−0.369585	−	0.929197i	$-0.620500\pi$
$733$	12302.4	−	21308.3i	0.619916	−	1.07373i	0.989501	−	0.144529i	$-0.0461667\pi$
$734$		0			0
$735$	−40493.0	+	16179.8i	−2.03212	+	0.811975i
$736$		0			0
$737$	11845.9	−	20517.7i	0.592060	−	1.02548i
$738$		0			0
$739$	−15578.3	−	26982.5i	−0.775452	−	1.34312i	−0.934540	−	0.355858i	$-0.884189\pi$
$739$	−15578.3	−	26982.5i	−0.775452	−	1.34312i	0.159088	−	0.987264i	$-0.449144\pi$
$740$		0			0
$741$	−26110.7			−1.29447
$742$		0			0
$743$	1151.65			0.0568639			0.0284320	−	0.999596i	$-0.490949\pi$
$743$	1151.65			0.0568639			0.0284320	+	0.999596i	$0.490949\pi$
$744$		0			0
$745$	−15364.2	−	26611.6i	−0.755571	−	1.30869i
$746$		0			0
$747$	18311.5	−	31716.4i	0.896895	−	1.55347i
$748$		0			0
$749$	−12654.0	+	36522.1i	−0.617311	+	1.78169i
$750$		0			0
$751$	12760.7	−	22102.2i	0.620034	−	1.07393i	−0.369445	−	0.929253i	$-0.620452\pi$
$751$	12760.7	−	22102.2i	0.620034	−	1.07393i	0.989479	−	0.144677i	$-0.0462144\pi$
$752$		0			0
$753$	−27979.1	−	48461.3i	−1.35407	−	2.34532i
$754$		0			0
$755$	10691.1			0.515350
$756$		0			0
$757$	−30191.6			−1.44958			−0.724790	−	0.688970i	$-0.758063\pi$
$757$	−30191.6			−1.44958			−0.724790	+	0.688970i	$0.758063\pi$
$758$		0			0
$759$	−3451.41	−	5978.02i	−0.165057	−	0.285887i
$760$		0			0
$761$	−3059.78	+	5299.70i	−0.145752	+	0.252449i	−0.929653	−	0.368436i	$-0.879893\pi$
$761$	−3059.78	+	5299.70i	−0.145752	+	0.252449i	0.783901	+	0.620885i	$0.213227\pi$
$762$		0			0
$763$	3726.61	+	4303.62i	0.176818	+	0.204196i
$764$		0			0
$765$	42370.3	−	73387.4i	2.00248	−	3.46840i
$766$		0			0
$767$	−1262.31	−	2186.39i	−0.0594256	−	0.102928i
$768$		0			0
$769$	15158.9			0.710852			0.355426	−	0.934704i	$-0.384336\pi$
$769$	15158.9			0.710852			0.355426	+	0.934704i	$0.384336\pi$
$770$		0			0
$771$	24819.9			1.15936
$772$		0			0
$773$	3163.15	+	5478.74i	0.147181	+	0.254924i	0.930184	−	0.367093i	$-0.119647\pi$
$773$	3163.15	+	5478.74i	0.147181	+	0.254924i	−0.783004	+	0.622017i	$0.786313\pi$
$774$		0			0
$775$	−8456.60	+	14647.3i	−0.391961	+	0.678897i
$776$		0			0
$777$	−41468.0	+	7978.05i	−1.91461	+	0.368354i
$778$		0			0
$779$	4081.27	−	7068.96i	0.187711	−	0.325124i
$780$		0			0
$781$	−372.535	−	645.250i	−0.0170683	−	0.0295632i
$782$		0			0
$783$	−62514.2			−2.85323
$784$		0			0
$785$	51373.9			2.33581
$786$		0			0
$787$	5669.15	+	9819.25i	0.256777	+	0.444750i	0.965377	−	0.260860i	$-0.0840061\pi$
$787$	5669.15	+	9819.25i	0.256777	+	0.444750i	−0.708600	+	0.705611i	$0.750673\pi$
$788$		0			0
$789$	20943.3	−	36274.8i	0.944994	−	1.63678i
$790$		0			0
$791$	27286.2	−	5249.62i	1.22653	−	0.235973i
$792$		0			0
$793$	250.163	−	433.295i	0.0112025	−	0.0194032i
$794$		0			0
$795$	−39106.3	−	67734.1i	−1.74460	−	3.02174i
$796$		0			0
$797$	−4014.31			−0.178412			−0.0892060	−	0.996013i	$-0.528433\pi$
$797$	−4014.31			−0.178412			−0.0892060	+	0.996013i	$0.528433\pi$
$798$		0			0
$799$	24764.4			1.09650
$800$		0			0
$801$	16390.4	+	28389.1i	0.723006	+	1.25228i
$802$		0			0
$803$	−113.059	+	195.825i	−0.00496859	+	0.00860585i
$804$		0			0
$805$	−3911.52	−	4517.15i	−0.171258	−	0.197775i
$806$		0			0
$807$	−9253.11	+	16026.9i	−0.403624	+	0.699098i
$808$		0			0
$809$	−18228.8	−	31573.1i	−0.792199	−	1.37213i	−0.924603	−	0.380933i	$-0.875603\pi$
$809$	−18228.8	−	31573.1i	−0.792199	−	1.37213i	0.132403	−	0.991196i	$-0.457731\pi$
$810$		0			0
$811$	−1307.84			−0.0566269			−0.0283134	−	0.999599i	$-0.509014\pi$
$811$	−1307.84			−0.0566269			−0.0283134	+	0.999599i	$0.509014\pi$
$812$		0			0
$813$	58448.2			2.52136
$814$		0			0
$815$	8679.89	+	15034.0i	0.373059	+	0.646157i
$816$		0			0
$817$	−14140.8	+	24492.6i	−0.605538	+	1.04882i
$818$		0			0
$819$	−12962.2	+	37411.7i	−0.553035	+	1.59618i
$820$		0			0
$821$	−10826.0	+	18751.1i	−0.460206	+	0.797100i	−0.998971	−	0.0453564i	$-0.985558\pi$
$821$	−10826.0	+	18751.1i	−0.460206	+	0.797100i	0.538765	+	0.842456i	$0.318891\pi$
$822$		0			0
$823$	−11443.0	−	19819.9i	−0.484664	−	0.839464i	0.515180	−	0.857082i	$-0.327725\pi$
$823$	−11443.0	−	19819.9i	−0.484664	−	0.839464i	−0.999845	+	0.0176183i	$0.994392\pi$
$824$		0			0
$825$	−21542.0			−0.909087
$826$		0			0
$827$	18260.6			0.767816			0.383908	−	0.923371i	$-0.374578\pi$
$827$	18260.6			0.767816			0.383908	+	0.923371i	$0.374578\pi$
$828$		0			0
$829$	15545.3	+	26925.2i	0.651277	+	1.12805i	0.982813	+	0.184603i	$0.0590999\pi$
$829$	15545.3	+	26925.2i	0.651277	+	1.12805i	−0.331536	+	0.943443i	$0.607567\pi$
$830$		0			0
$831$	17846.3	−	30910.7i	0.744984	−	1.29035i
$832$		0			0
$833$	−29525.7	−	23250.9i	−1.22810	−	0.967104i
$834$		0			0
$835$	10086.5	−	17470.3i	0.418032	−	0.724053i
$836$		0			0
$837$	−30040.6	−	52031.8i	−1.24057	−	2.14873i
$838$		0			0
$839$	45195.2			1.85973			0.929863	−	0.367906i	$-0.119925\pi$
$839$	45195.2			1.85973			0.929863	+	0.367906i	$0.119925\pi$
$840$		0			0
$841$	35722.4			1.46469
$842$		0			0
$843$	9049.40	+	15674.0i	0.369725	+	0.640382i
$844$		0			0
$845$	−4863.93	+	8424.57i	−0.198017	+	0.342975i
$846$		0			0
$847$	1420.84	−	4100.87i	0.0576397	−	0.166361i
$848$		0			0
$849$	−24525.5	+	42479.3i	−0.991415	+	1.71718i
$850$		0			0
$851$	−2893.30	−	5011.34i	−0.116546	−	0.201864i
$852$		0			0
$853$	14557.8			0.584350			0.292175	−	0.956365i	$-0.405621\pi$
$853$	14557.8			0.584350			0.292175	+	0.956365i	$0.405621\pi$
$854$		0			0
$855$	57466.0			2.29859
$856$		0			0
$857$	−15847.9	−	27449.4i	−0.631687	−	1.09411i	−0.987207	−	0.159445i	$-0.949030\pi$
$857$	−15847.9	−	27449.4i	−0.631687	−	1.09411i	0.355520	−	0.934669i	$-0.384304\pi$
$858$		0			0
$859$	−3501.76	+	6065.23i	−0.139090	+	0.240911i	−0.927153	−	0.374684i	$-0.877751\pi$
$859$	−3501.76	+	6065.23i	−0.139090	+	0.240911i	0.788062	+	0.615596i	$0.211084\pi$
$860$		0			0
$861$	−12070.3	−	13939.2i	−0.477763	−	0.551737i
$862$		0			0
$863$	−18212.0	+	31544.1i	−0.718359	+	1.24423i	0.243290	+	0.969954i	$0.421773\pi$
$863$	−18212.0	+	31544.1i	−0.718359	+	1.24423i	−0.961650	+	0.274281i	$0.911560\pi$
$864$		0			0
$865$	−3828.03	−	6630.34i	−0.150470	−	0.260622i
$866$		0			0
$867$	64273.2			2.51768
$868$		0			0
$869$	−1546.17			−0.0603572
$870$		0			0
$871$	−13870.3	−	24024.1i	−0.539585	−	0.934588i
$872$		0			0
$873$	−2194.08	+	3800.25i	−0.0850610	+	0.147330i
$874$		0			0
$875$	13578.1	−	2612.30i	0.524598	−	0.100928i
$876$		0			0
$877$	10076.0	−	17452.1i	0.387960	−	0.671966i	−0.604215	−	0.796821i	$-0.706513\pi$
$877$	10076.0	−	17452.1i	0.387960	−	0.671966i	0.992175	+	0.124855i	$0.0398466\pi$
$878$		0			0
$879$	21962.4	+	38040.1i	0.842747	+	1.45968i
$880$		0			0
$881$	−818.719			−0.0313091			−0.0156546	−	0.999877i	$-0.504983\pi$
$881$	−818.719			−0.0313091			−0.0156546	+	0.999877i	$0.504983\pi$
$882$		0			0
$883$	−34813.8			−1.32681			−0.663407	−	0.748259i	$-0.730890\pi$
$883$	−34813.8			−1.32681			−0.663407	+	0.748259i	$0.730890\pi$
$884$		0			0
$885$	4138.68	+	7168.40i	0.157198	+	0.272275i
$886$		0			0
$887$	13863.0	−	24011.4i	0.524774	−	0.908935i	−0.474810	−	0.880088i	$-0.657483\pi$
$887$	13863.0	−	24011.4i	0.524774	−	0.908935i	0.999584	−	0.0288468i	$-0.00918351\pi$
$888$		0			0
$889$	−16943.6	+	3259.80i	−0.639225	+	0.122981i
$890$		0			0
$891$	13613.5	−	23579.3i	0.511863	−	0.886572i
$892$		0			0
$893$	8396.86	+	14543.8i	0.314659	+	0.545005i
$894$		0			0
$895$	30266.9			1.13040
$896$		0			0
$897$	−8082.51			−0.300855
$898$		0			0
$899$	28885.9	+	50031.9i	1.07164	+	1.85613i
$900$		0			0
$901$	33703.6	−	58376.4i	1.24621	−	2.15849i
$902$		0			0
$903$	41821.2	+	48296.6i	1.54122	+	1.77986i
$904$		0			0
$905$	14393.9	−	24931.0i	0.528696	−	0.915728i
$906$		0			0
$907$	18444.8	+	31947.3i	0.675247	+	1.16956i	0.976397	+	0.215986i	$0.0692965\pi$
$907$	18444.8	+	31947.3i	0.675247	+	1.16956i	−0.301149	+	0.953577i	$0.597370\pi$
$908$		0			0
$909$	55004.7			2.00703
$910$		0			0
$911$	26304.3			0.956642			0.478321	−	0.878185i	$-0.341245\pi$
$911$	26304.3			0.956642			0.478321	+	0.878185i	$0.341245\pi$
$912$		0			0
$913$	−10998.6	−	19050.1i	−0.398685	−	0.690543i
$914$		0			0
$915$	−820.196	+	1420.62i	−0.0296337	+	0.0513271i
$916$		0			0
$917$	−4379.80	+	12641.0i	−0.157725	+	0.455228i
$918$		0			0
$919$	15728.5	−	27242.5i	0.564564	−	0.977853i	−0.432526	−	0.901621i	$-0.642378\pi$
$919$	15728.5	−	27242.5i	0.564564	−	0.977853i	0.997090	−	0.0762318i	$-0.0242889\pi$
$920$		0			0
$921$	45060.0	+	78046.2i	1.61214	+	2.79230i
$922$		0			0
$923$	−872.403			−0.0311110
$924$		0			0
$925$	−18058.6			−0.641905
$926$		0			0
$927$	32519.5	+	56325.5i	1.15219	+	1.99566i
$928$		0			0
$929$	2746.37	−	4756.85i	0.0969919	−	0.167995i	−0.813446	−	0.581640i	$-0.802411\pi$
$929$	2746.37	−	4756.85i	0.0969919	−	0.167995i	0.910438	+	0.413645i	$0.135745\pi$
$930$		0			0
$931$	3643.68	−	25223.8i	0.128267	−	0.887943i
$932$		0			0
$933$	17908.5	−	31018.4i	0.628401	−	1.08842i
$934$		0			0
$935$	−25449.2	−	44079.3i	−0.890137	−	1.54176i
$936$		0			0
$937$	47063.7			1.64088			0.820440	−	0.571732i	$-0.193728\pi$
$937$	47063.7			1.64088			0.820440	+	0.571732i	$0.193728\pi$
$938$		0			0
$939$	−50751.5			−1.76381
$940$		0			0
$941$	6770.47	+	11726.8i	0.234550	+	0.406252i	0.959142	−	0.282926i	$-0.0913052\pi$
$941$	6770.47	+	11726.8i	0.234550	+	0.406252i	−0.724592	+	0.689178i	$0.757972\pi$
$942$		0			0
$943$	1263.35	−	2188.18i	0.0436270	−	0.0755641i
$944$		0			0
$945$	21686.5	−	62591.8i	0.746519	−	2.15462i
$946$		0			0
$947$	19974.5	−	34596.9i	0.685412	−	1.18717i	−0.287896	−	0.957662i	$-0.592956\pi$
$947$	19974.5	−	34596.9i	0.685412	−	1.18717i	0.973307	−	0.229506i	$-0.0737110\pi$
$948$		0			0
$949$	132.381	+	229.291i	0.00452821	+	0.00784309i
$950$		0			0
$951$	−83092.5			−2.83329
$952$		0			0
$953$	19145.9			0.650784			0.325392	−	0.945579i	$-0.394504\pi$
$953$	19145.9			0.650784			0.325392	+	0.945579i	$0.394504\pi$
$954$		0			0
$955$	−26620.3	−	46107.7i	−0.902003	−	1.56232i
$956$		0			0
$957$	−36791.5	+	63724.7i	−1.24274	+	2.15248i
$958$		0			0
$959$	28320.7	+	32705.7i	0.953622	+	1.10127i
$960$		0			0
$961$	−12866.2	+	22284.9i	−0.431882	+	0.748042i
$962$		0			0
$963$	−57533.3	−	99650.5i	−1.92522	−	3.33457i
$964$		0			0
$965$	−36178.1			−1.20685
$966$		0			0
$967$	−10223.1			−0.339973			−0.169986	−	0.985446i	$-0.554372\pi$
$967$	−10223.1			−0.339973			−0.169986	+	0.985446i	$0.554372\pi$
$968$		0			0
$969$	36890.4	+	63896.1i	1.22300	+	2.11831i
$970$		0			0
$971$	−9637.88	+	16693.3i	−0.318532	+	0.551713i	−0.980182	−	0.198100i	$-0.936523\pi$
$971$	−9637.88	+	16693.3i	−0.318532	+	0.551713i	0.661650	+	0.749813i	$0.269856\pi$
$972$		0			0
$973$	−49505.8	+	9524.45i	−1.63112	+	0.313813i
$974$		0			0
$975$	−12611.8	+	21844.2i	−0.414256	+	0.717513i
$976$		0			0
$977$	−2148.96	−	3722.10i	−0.0703697	−	0.121884i	0.828694	−	0.559702i	$-0.189085\pi$
$977$	−2148.96	−	3722.10i	−0.0703697	−	0.121884i	−0.899063	+	0.437819i	$0.855751\pi$
$978$		0			0
$979$	19689.5			0.642776
$980$		0			0
$981$	−16947.6			−0.551574
$982$		0			0
$983$	16610.6	+	28770.5i	0.538960	+	0.933506i	0.998960	+	0.0455871i	$0.0145158\pi$
$983$	16610.6	+	28770.5i	0.538960	+	0.933506i	−0.460001	+	0.887919i	$0.652151\pi$
$984$		0			0
$985$	3242.71	−	5616.55i	0.104895	−	0.181683i
$986$		0			0
$987$	37253.2	−	7167.18i	1.20140	−	0.231139i
$988$		0			0
$989$	−4377.26	+	7581.64i	−0.140737	+	0.243763i
$990$		0			0
$991$	18080.7	+	31316.7i	0.579568	+	1.00384i	0.995529	+	0.0944589i	$0.0301121\pi$
$991$	18080.7	+	31316.7i	0.579568	+	1.00384i	−0.415961	+	0.909383i	$0.636555\pi$
$992$		0			0
$993$	−85401.9			−2.72925
$994$		0			0
$995$	−47004.6			−1.49764
$996$		0			0
$997$	−4012.62	−	6950.06i	−0.127463	−	0.220773i	0.795230	−	0.606308i	$-0.207350\pi$
$997$	−4012.62	−	6950.06i	−0.127463	−	0.220773i	−0.922693	+	0.385535i	$0.874017\pi$
$998$		0			0
$999$	32074.9	−	55555.4i	1.01582	−	1.75946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.4.i.b.93.2	✓	44
7.4	even	3	inner	644.4.i.b.277.2	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.4.i.b.93.2	✓	44	1.1	even	1	trivial
644.4.i.b.277.2	yes	44	7.4	even	3	inner

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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	644.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.53140 - 7.84862i) q^{3} +(7.01387 - 12.1484i) q^{5} +(18.1867 - 3.49896i) q^{7} +(-27.5672 + 47.7478i) q^{9} +O(q^{10})\)	\(q+(-4.53140 - 7.84862i) q^{3} +(7.01387 - 12.1484i) q^{5} +(18.1867 - 3.49896i) q^{7} +(-27.5672 + 47.7478i) q^{9} +(16.5579 + 28.6792i) q^{11} +38.7753 q^{13} -127.131 q^{15} +(-54.7836 - 94.8880i) q^{17} +(37.1510 - 64.3474i) q^{19} +(-109.873 - 126.886i) q^{21} +(11.5000 - 19.9186i) q^{23} +(-35.8887 - 62.1610i) q^{25} +254.977 q^{27} -245.176 q^{29} +(-117.817 - 204.065i) q^{31} +(150.061 - 259.914i) q^{33} +(85.0527 - 245.481i) q^{35} +(125.796 - 217.884i) q^{37} +(-175.707 - 304.333i) q^{39} +109.856 q^{41} -380.631 q^{43} +(386.706 + 669.794i) q^{45} +(-113.010 + 195.739i) q^{47} +(318.515 - 127.269i) q^{49} +(-496.493 + 859.951i) q^{51} +(307.607 + 532.791i) q^{53} +464.541 q^{55} -673.384 q^{57} +(-32.5545 - 56.3861i) q^{59} +(6.45160 - 11.1745i) q^{61} +(-334.290 + 964.833i) q^{63} +(271.965 - 471.057i) q^{65} +(-357.710 - 619.572i) q^{67} -208.444 q^{69} -22.4989 q^{71} +(3.41405 + 5.91332i) q^{73} +(-325.252 + 563.353i) q^{75} +(401.482 + 463.645i) q^{77} +(-23.3449 + 40.4346i) q^{79} +(-411.087 - 712.024i) q^{81} -664.248 q^{83} -1536.98 q^{85} +(1110.99 + 1924.30i) q^{87} +(297.282 - 514.907i) q^{89} +(705.197 - 135.673i) q^{91} +(-1067.75 + 1849.40i) q^{93} +(-521.144 - 902.648i) q^{95} +79.5901 q^{97} -1825.82 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9}+O(q^{10}) \) 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9	\( 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9} + 28 q^{11} - 152 q^{13} + 208 q^{15} - 52 q^{17} + 38 q^{19} - 10 q^{21} + 506 q^{23} - 516 q^{25} - 876 q^{27} - 100 q^{29} + 230 q^{31} + 424 q^{33} + 98 q^{35} + 18 q^{37} - 350 q^{39} + 784 q^{41} - 336 q^{43} + 1156 q^{45} + 452 q^{47} + 546 q^{49} - 498 q^{51} - 508 q^{53} - 3084 q^{55} - 1916 q^{57} + 508 q^{59} + 1386 q^{61} + 1290 q^{63} + 360 q^{65} - 1896 q^{67} + 552 q^{69} - 3352 q^{71} + 990 q^{73} + 3328 q^{75} + 1328 q^{77} + 524 q^{79} - 4486 q^{81} - 1120 q^{83} - 5296 q^{85} + 3700 q^{87} + 1216 q^{89} + 1438 q^{91} + 366 q^{93} + 90 q^{95} + 716 q^{97} + 5716 q^{99}+O(q^{100}) \) 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9 + 28 * q^11 - 152 * q^13 + 208 * q^15 - 52 * q^17 + 38 * q^19 - 10 * q^21 + 506 * q^23 - 516 * q^25 - 876 * q^27 - 100 * q^29 + 230 * q^31 + 424 * q^33 + 98 * q^35 + 18 * q^37 - 350 * q^39 + 784 * q^41 - 336 * q^43 + 1156 * q^45 + 452 * q^47 + 546 * q^49 - 498 * q^51 - 508 * q^53 - 3084 * q^55 - 1916 * q^57 + 508 * q^59 + 1386 * q^61 + 1290 * q^63 + 360 * q^65 - 1896 * q^67 + 552 * q^69 - 3352 * q^71 + 990 * q^73 + 3328 * q^75 + 1328 * q^77 + 524 * q^79 - 4486 * q^81 - 1120 * q^83 - 5296 * q^85 + 3700 * q^87 + 1216 * q^89 + 1438 * q^91 + 366 * q^93 + 90 * q^95 + 716 * q^97 + 5716 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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