LMFDB - Embedded newform 252.4.j.b.85.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(85,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, 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("252.85");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.j (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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 7 x^{17} + 81 x^{16} - 470 x^{15} + 2687 x^{14} - 12243 x^{13} + 43732 x^{12} + \cdots + 5500612092612 $ x^18 - 7x^17 + 81x^16 - 470x^15 + 2687x^14 - 12243x^13 + 43732x^12 - 169303x^11 + 166449x^10 - 57172x^9 - 3758051x^8 + 73649097x^7 + 358194386x^6 + 3599409199x^5 + 26802380109x^4 + 114591208112x^3 + 655546044172x^2 + 1324018291596*x + 5500612092612
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			85.6
Root			$-0.208655 - 5.05363i$ of defining polynomial
Character	$\chi$	$=$	252.85
Dual form			252.4.j.b.169.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20866 - 5.05363i) q^{3} +(7.66838 - 13.2820i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-24.0783 - 12.2162i) q^{9} +O(q^{10})$	\(q+(1.20866 - 5.05363i) q^{3} +(7.66838 - 13.2820i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-24.0783 - 12.2162i) q^{9} +(-33.5187 - 58.0562i) q^{11} +(-40.7808 + 70.6345i) q^{13} +(-57.8540 - 54.8066i) q^{15} +101.984 q^{17} +86.0055 q^{19} +(-34.8663 + 10.3606i) q^{21} +(-64.5509 + 111.805i) q^{23} +(-55.1082 - 95.4503i) q^{25} +(-90.8384 + 106.918i) q^{27} +(-45.2228 - 78.3281i) q^{29} +(47.8658 - 82.9060i) q^{31} +(-333.907 + 99.2214i) q^{33} -107.357 q^{35} -207.875 q^{37} +(307.670 + 291.464i) q^{39} +(65.0713 - 112.707i) q^{41} +(-36.6422 - 63.4662i) q^{43} +(-346.897 + 226.130i) q^{45} +(-165.521 - 286.690i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(123.264 - 515.392i) q^{51} +120.105 q^{53} -1028.14 q^{55} +(103.951 - 434.640i) q^{57} +(97.6534 - 169.141i) q^{59} +(29.8757 + 51.7462i) q^{61} +(10.2174 + 188.724i) q^{63} +(625.446 + 1083.30i) q^{65} +(402.981 - 697.984i) q^{67} +(487.003 + 461.350i) q^{69} +391.162 q^{71} -729.424 q^{73} +(-548.977 + 163.130i) q^{75} +(-234.631 + 406.393i) q^{77} +(-327.833 - 567.824i) q^{79} +(430.530 + 588.290i) q^{81} +(6.15385 + 10.6588i) q^{83} +(782.056 - 1354.56i) q^{85} +(-450.500 + 133.867i) q^{87} +716.679 q^{89} +570.932 q^{91} +(-361.123 - 342.101i) q^{93} +(659.524 - 1142.33i) q^{95} +(-375.694 - 650.721i) q^{97} +(97.8497 + 1807.36i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9}+O(q^{10}) $ 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9	$ 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9} - 93 q^{11} - 18 q^{13} + 162 q^{15} - 54 q^{17} - 90 q^{19} - 49 q^{21} - 246 q^{23} - 315 q^{25} - 394 q^{27} - 318 q^{29} - 18 q^{31} + 33 q^{33} + 84 q^{35} - 72 q^{37} + 268 q^{39} - 57 q^{41} - 171 q^{43} - 318 q^{45} - 1056 q^{47} - 441 q^{49} + 705 q^{51} + 1512 q^{53} - 1800 q^{55} - 1271 q^{57} - 411 q^{59} - 198 q^{61} + 308 q^{63} - 1326 q^{65} - 441 q^{67} + 642 q^{69} + 3516 q^{71} + 54 q^{73} - 2497 q^{75} - 651 q^{77} + 72 q^{79} + 1163 q^{81} - 558 q^{83} - 1008 q^{85} + 2766 q^{87} + 2784 q^{89} + 252 q^{91} - 2618 q^{93} - 156 q^{95} + 909 q^{97} + 6318 q^{99}+O(q^{100}) $ 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9 - 93 * q^11 - 18 * q^13 + 162 * q^15 - 54 * q^17 - 90 * q^19 - 49 * q^21 - 246 * q^23 - 315 * q^25 - 394 * q^27 - 318 * q^29 - 18 * q^31 + 33 * q^33 + 84 * q^35 - 72 * q^37 + 268 * q^39 - 57 * q^41 - 171 * q^43 - 318 * q^45 - 1056 * q^47 - 441 * q^49 + 705 * q^51 + 1512 * q^53 - 1800 * q^55 - 1271 * q^57 - 411 * q^59 - 198 * q^61 + 308 * q^63 - 1326 * q^65 - 441 * q^67 + 642 * q^69 + 3516 * q^71 + 54 * q^73 - 2497 * q^75 - 651 * q^77 + 72 * q^79 + 1163 * q^81 - 558 * q^83 - 1008 * q^85 + 2766 * q^87 + 2784 * q^89 + 252 * q^91 - 2618 * q^93 - 156 * q^95 + 909 * q^97 + 6318 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	1.20866	−	5.05363i	0.232606	−	0.972571i
$3$	1.20866	−	5.05363i	0.232606	−	0.972571i
$4$		0			0
$5$	7.66838	−	13.2820i	0.685881	−	1.18798i	−0.287278	−	0.957847i	$-0.592750\pi$
$5$	7.66838	−	13.2820i	0.685881	−	1.18798i	0.973159	−	0.230134i	$-0.0739163\pi$
$6$		0			0
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$8$		0			0
$9$	−24.0783	−	12.2162i	−0.891789	−	0.452451i
$10$		0			0
$11$	−33.5187	−	58.0562i	−0.918753	−	1.59133i	−0.801312	−	0.598246i	$-0.795864\pi$
$11$	−33.5187	−	58.0562i	−0.918753	−	1.59133i	−0.117440	−	0.993080i	$-0.537469\pi$
$12$		0			0
$13$	−40.7808	+	70.6345i	−0.870044	+	1.50696i	−0.00809305	+	0.999967i	$0.502576\pi$
$13$	−40.7808	+	70.6345i	−0.870044	+	1.50696i	−0.861951	+	0.506992i	$0.830757\pi$
$14$		0			0
$15$	−57.8540	−	54.8066i	−0.995856	−	0.943399i
$16$		0			0
$17$	101.984			1.45499			0.727496	−	0.686112i	$-0.240684\pi$
$17$	101.984			1.45499			0.727496	+	0.686112i	$0.240684\pi$
$18$		0			0
$19$	86.0055			1.03848			0.519238	−	0.854630i	$-0.326216\pi$
$19$	86.0055			1.03848			0.519238	+	0.854630i	$0.326216\pi$
$20$		0			0
$21$	−34.8663	+	10.3606i	−0.362307	+	0.107661i
$22$		0			0
$23$	−64.5509	+	111.805i	−0.585208	+	1.01361i	0.409641	+	0.912247i	$0.365654\pi$
$23$	−64.5509	+	111.805i	−0.585208	+	1.01361i	−0.994849	+	0.101363i	$0.967680\pi$
$24$		0			0
$25$	−55.1082	−	95.4503i	−0.440866	−	0.763602i
$26$		0			0
$27$	−90.8384	+	106.918i	−0.647476	+	0.762086i
$28$		0			0
$29$	−45.2228	−	78.3281i	−0.289574	−	0.501558i	0.684134	−	0.729357i	$-0.260180\pi$
$29$	−45.2228	−	78.3281i	−0.289574	−	0.501558i	−0.973708	+	0.227799i	$0.926847\pi$
$30$		0			0
$31$	47.8658	−	82.9060i	0.277321	−	0.480334i	−0.693397	−	0.720556i	$-0.743887\pi$
$31$	47.8658	−	82.9060i	0.277321	−	0.480334i	0.970718	+	0.240222i	$0.0772201\pi$
$32$		0			0
$33$	−333.907	+	99.2214i	−1.76139	+	0.523401i
$34$		0			0
$35$	−107.357			−0.518477
$36$		0			0
$37$	−207.875			−0.923635			−0.461817	−	0.886975i	$-0.652802\pi$
$37$	−207.875			−0.923635			−0.461817	+	0.886975i	$0.652802\pi$
$38$		0			0
$39$	307.670	+	291.464i	1.26325	+	1.19671i
$40$		0			0
$41$	65.0713	−	112.707i	0.247864	−	0.429313i	−0.715069	−	0.699054i	$-0.753605\pi$
$41$	65.0713	−	112.707i	0.247864	−	0.429313i	0.962933	+	0.269741i	$0.0869380\pi$
$42$		0			0
$43$	−36.6422	−	63.4662i	−0.129951	−	0.225082i	0.793706	−	0.608301i	$-0.208149\pi$
$43$	−36.6422	−	63.4662i	−0.129951	−	0.225082i	−0.923657	+	0.383219i	$0.874815\pi$
$44$		0			0
$45$	−346.897	+	226.130i	−1.14916	+	0.749101i
$46$		0			0
$47$	−165.521	−	286.690i	−0.513695	−	0.889746i	−0.999874	−	0.0158869i	$-0.994943\pi$
$47$	−165.521	−	286.690i	−0.513695	−	0.889746i	0.486178	−	0.873860i	$-0.338391\pi$
$48$		0			0
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$		0			0
$51$	123.264	−	515.392i	0.338440	−	1.41508i
$52$		0			0
$53$	120.105			0.311276			0.155638	−	0.987814i	$-0.450257\pi$
$53$	120.105			0.311276			0.155638	+	0.987814i	$0.450257\pi$
$54$		0			0
$55$	−1028.14			−2.52062
$56$		0			0
$57$	103.951	−	434.640i	0.241555	−	1.00999i
$58$		0			0
$59$	97.6534	−	169.141i	0.215481	−	0.373224i	−0.737940	−	0.674866i	$-0.764201\pi$
$59$	97.6534	−	169.141i	0.215481	−	0.373224i	0.953421	+	0.301642i	$0.0975347\pi$
$60$		0			0
$61$	29.8757	+	51.7462i	0.0627080	+	0.108613i	0.895675	−	0.444709i	$-0.146693\pi$
$61$	29.8757	+	51.7462i	0.0627080	+	0.108613i	−0.832967	+	0.553323i	$0.813360\pi$
$62$		0			0
$63$	10.2174	+	188.724i	0.0204329	+	0.377412i
$64$		0			0
$65$	625.446	+	1083.30i	1.19349	+	2.06719i
$66$		0			0
$67$	402.981	−	697.984i	0.734806	−	1.27272i	−0.220003	−	0.975499i	$-0.570607\pi$
$67$	402.981	−	697.984i	0.734806	−	1.27272i	0.954808	−	0.297222i	$-0.0960601\pi$
$68$		0			0
$69$	487.003	+	461.350i	0.849685	+	0.804928i
$70$		0			0
$71$	391.162			0.653837			0.326918	−	0.945053i	$-0.393990\pi$
$71$	391.162			0.653837			0.326918	+	0.945053i	$0.393990\pi$
$72$		0			0
$73$	−729.424			−1.16949			−0.584744	−	0.811218i	$-0.698805\pi$
$73$	−729.424			−1.16949			−0.584744	+	0.811218i	$0.698805\pi$
$74$		0			0
$75$	−548.977	+	163.130i	−0.845205	+	0.251155i
$76$		0			0
$77$	−234.631	+	406.393i	−0.347256	+	0.601465i
$78$		0			0
$79$	−327.833	−	567.824i	−0.466888	−	0.808673i	0.532397	−	0.846495i	$-0.321291\pi$
$79$	−327.833	−	567.824i	−0.466888	−	0.808673i	−0.999285	+	0.0378217i	$0.987958\pi$
$80$		0			0
$81$	430.530	+	588.290i	0.590576	+	0.806982i
$82$		0			0
$83$	6.15385	+	10.6588i	0.00813822	+	0.0140958i	0.870066	−	0.492936i	$-0.164076\pi$
$83$	6.15385	+	10.6588i	0.00813822	+	0.0140958i	−0.861928	+	0.507031i	$0.830743\pi$
$84$		0			0
$85$	782.056	−	1354.56i	0.997952	−	1.72850i
$86$		0			0
$87$	−450.500	+	133.867i	−0.555157	+	0.164967i
$88$		0			0
$89$	716.679			0.853571			0.426785	−	0.904353i	$-0.359646\pi$
$89$	716.679			0.853571			0.426785	+	0.904353i	$0.359646\pi$
$90$		0			0
$91$	570.932			0.657691
$92$		0			0
$93$	−361.123	−	342.101i	−0.402653	−	0.381443i
$94$		0			0
$95$	659.524	−	1142.33i	0.712270	−	1.23369i
$96$		0			0
$97$	−375.694	−	650.721i	−0.393257	−	0.681142i	0.599620	−	0.800285i	$-0.295319\pi$
$97$	−375.694	−	650.721i	−0.393257	−	0.681142i	−0.992877	+	0.119143i	$0.961985\pi$
$98$		0			0
$99$	97.8497	+	1807.36i	0.0993360	+	1.83482i
$100$		0			0
$101$	−133.001	−	230.365i	−0.131031	−	0.226952i	0.793043	−	0.609165i	$-0.208495\pi$
$101$	−133.001	−	230.365i	−0.131031	−	0.226952i	−0.924074	+	0.382213i	$0.875162\pi$
$102$		0			0
$103$	580.953	−	1006.24i	0.555757	−	0.962600i	−0.442087	−	0.896972i	$-0.645762\pi$
$103$	580.953	−	1006.24i	0.555757	−	0.962600i	0.997844	−	0.0656275i	$-0.0209049\pi$
$104$		0			0
$105$	−129.758	+	542.544i	−0.120601	+	0.504256i
$106$		0			0
$107$	1672.22			1.51084			0.755418	−	0.655243i	$-0.227434\pi$
$107$	1672.22			1.51084			0.755418	+	0.655243i	$0.227434\pi$
$108$		0			0
$109$	686.800			0.603519			0.301759	−	0.953384i	$-0.402426\pi$
$109$	686.800			0.603519			0.301759	+	0.953384i	$0.402426\pi$
$110$		0			0
$111$	−251.249	+	1050.52i	−0.214843	+	0.898300i
$112$		0			0
$113$	−821.318	+	1422.56i	−0.683744	+	1.18428i	0.290086	+	0.957001i	$0.406316\pi$
$113$	−821.318	+	1422.56i	−0.683744	+	1.18428i	−0.973830	+	0.227279i	$0.927017\pi$
$114$		0			0
$115$	990.001	+	1714.73i	0.802766	+	1.39043i
$116$		0			0
$117$	1844.82	−	1202.57i	1.45772	−	0.950238i
$118$		0			0
$119$	−356.946	−	618.248i	−0.274968	−	0.476258i
$120$		0			0
$121$	−1581.51	+	2739.26i	−1.18821	+	2.05805i
$122$		0			0
$123$	−490.930	−	465.070i	−0.359883	−	0.340926i
$124$		0			0
$125$	226.732			0.162236
$126$		0			0
$127$	−1149.15			−0.802917			−0.401459	−	0.915877i	$-0.631497\pi$
$127$	−1149.15			−0.802917			−0.401459	+	0.915877i	$0.631497\pi$
$128$		0			0
$129$	−365.022	+	108.467i	−0.249135	+	0.0740312i
$130$		0			0
$131$	1060.42	−	1836.70i	0.707247	−	1.22499i	−0.258628	−	0.965977i	$-0.583270\pi$
$131$	1060.42	−	1836.70i	0.707247	−	1.22499i	0.965875	−	0.259010i	$-0.0833964\pi$
$132$		0			0
$133$	−301.019	−	521.381i	−0.196253	−	0.339921i
$134$		0			0
$135$	723.500	+	2026.40i	0.461251	+	1.29189i
$136$		0			0
$137$	1272.68	+	2204.35i	0.793669	+	1.37467i	0.923681	+	0.383162i	$0.125165\pi$
$137$	1272.68	+	2204.35i	0.793669	+	1.37467i	−0.130013	+	0.991512i	$0.541502\pi$
$138$		0			0
$139$	1118.77	−	1937.77i	0.682685	−	1.18245i	−0.291473	−	0.956579i	$-0.594145\pi$
$139$	1118.77	−	1937.77i	0.682685	−	1.18245i	0.974158	−	0.225866i	$-0.0725213\pi$
$140$		0			0
$141$	−1648.88	+	489.971i	−0.984830	+	0.292645i
$142$		0			0
$143$	5467.69			3.19742
$144$		0			0
$145$	−1387.14			−0.794454
$146$		0			0
$147$	184.840	+	175.103i	0.103710	+	0.0982469i
$148$		0			0
$149$	1356.73	−	2349.92i	0.745955	−	1.29203i	−0.203792	−	0.979014i	$-0.565326\pi$
$149$	1356.73	−	2349.92i	0.745955	−	1.29203i	0.949747	−	0.313018i	$-0.101340\pi$
$150$		0			0
$151$	501.502	+	868.627i	0.270276	+	0.468132i	0.968932	−	0.247326i	$-0.0795518\pi$
$151$	501.502	+	868.627i	0.270276	+	0.468132i	−0.698657	+	0.715457i	$0.746218\pi$
$152$		0			0
$153$	−2455.61	−	1245.86i	−1.29755	−	0.658313i
$154$		0			0
$155$	−734.107	−	1271.51i	−0.380418	−	0.658904i
$156$		0			0
$157$	−1255.51	+	2174.61i	−0.638222	+	1.10543i	0.347601	+	0.937642i	$0.386996\pi$
$157$	−1255.51	+	2174.61i	−0.638222	+	1.10543i	−0.985823	+	0.167790i	$0.946337\pi$
$158$		0			0
$159$	145.165	−	606.964i	0.0724046	−	0.302738i
$160$		0			0
$161$	903.712			0.442376
$162$		0			0
$163$	3600.11			1.72995			0.864977	−	0.501812i	$-0.167333\pi$
$163$	3600.11			1.72995			0.864977	+	0.501812i	$0.167333\pi$
$164$		0			0
$165$	−1242.66	+	5195.83i	−0.586311	+	2.45148i
$166$		0			0
$167$	−1122.49	+	1944.22i	−0.520127	+	0.900887i	0.479599	+	0.877488i	$0.340782\pi$
$167$	−1122.49	+	1944.22i	−0.520127	+	0.900887i	−0.999726	+	0.0233989i	$0.992551\pi$
$168$		0			0
$169$	−2227.65	−	3858.41i	−1.01395	−	1.75622i
$170$		0			0
$171$	−2070.87	−	1050.66i	−0.926101	−	0.469859i
$172$		0			0
$173$	−734.325	−	1271.89i	−0.322715	−	0.558959i	0.658332	−	0.752728i	$-0.271262\pi$
$173$	−734.325	−	1271.89i	−0.322715	−	0.558959i	−0.981047	+	0.193769i	$0.937929\pi$
$174$		0			0
$175$	−385.758	+	668.152i	−0.166632	+	0.288614i
$176$		0			0
$177$	−736.745	−	697.937i	−0.312865	−	0.296385i
$178$		0			0
$179$	−2121.48			−0.885847			−0.442923	−	0.896559i	$-0.646059\pi$
$179$	−2121.48			−0.885847			−0.442923	+	0.896559i	$0.646059\pi$
$180$		0			0
$181$	3103.09			1.27431			0.637157	−	0.770734i	$-0.280110\pi$
$181$	3103.09			1.27431			0.637157	+	0.770734i	$0.280110\pi$
$182$		0			0
$183$	297.615	−	88.4373i	0.120221	−	0.0357239i
$184$		0			0
$185$	−1594.07	+	2761.01i	−0.633504	+	1.09726i
$186$		0			0
$187$	−3418.39	−	5920.83i	−1.33678	−	2.31537i
$188$		0			0
$189$	966.088	+	176.467i	0.371813	+	0.0679158i
$190$		0			0
$191$	−967.933	−	1676.51i	−0.366687	−	0.635120i	0.622359	−	0.782732i	$-0.286175\pi$
$191$	−967.933	−	1676.51i	−0.366687	−	0.635120i	−0.989045	+	0.147612i	$0.952841\pi$
$192$		0			0
$193$	1360.86	−	2357.08i	0.507549	−	0.879100i	−0.492413	−	0.870362i	$-0.663885\pi$
$193$	1360.86	−	2357.08i	0.507549	−	0.879100i	0.999962	−	0.00873849i	$-0.00278158\pi$
$194$		0			0
$195$	6230.57	−	1851.43i	2.28810	−	0.679916i
$196$		0			0
$197$	−1198.22			−0.433350			−0.216675	−	0.976244i	$-0.569521\pi$
$197$	−1198.22			−0.433350			−0.216675	+	0.976244i	$0.569521\pi$
$198$		0			0
$199$	−4258.24			−1.51688			−0.758439	−	0.651744i	$-0.774038\pi$
$199$	−4258.24			−1.51688			−0.758439	+	0.651744i	$0.774038\pi$
$200$		0			0
$201$	−3040.29	−	2880.14i	−1.06689	−	1.01069i
$202$		0			0
$203$	−316.559	+	548.297i	−0.109449	+	0.189571i
$204$		0			0
$205$	−997.984	−	1728.56i	−0.340011	−	0.588916i
$206$		0			0
$207$	2920.11	−	1903.52i	0.980491	−	0.639148i
$208$		0			0
$209$	−2882.80	−	4993.15i	−0.954102	−	1.65255i
$210$		0			0
$211$	292.865	−	507.257i	0.0955528	−	0.165502i	−0.814286	−	0.580463i	$-0.802871\pi$
$211$	292.865	−	507.257i	0.0955528	−	0.165502i	0.909839	+	0.414961i	$0.136205\pi$
$212$		0			0
$213$	472.780	−	1976.79i	0.152086	−	0.635903i
$214$		0			0
$215$	−1123.95			−0.356523
$216$		0			0
$217$	−670.121			−0.209635
$218$		0			0
$219$	−881.622	+	3686.24i	−0.272030	+	1.13741i
$220$		0			0
$221$	−4159.01	+	7203.62i	−1.26591	+	2.19261i
$222$		0			0
$223$	1093.48	+	1893.96i	0.328363	+	0.568741i	0.982187	−	0.187905i	$-0.0601698\pi$
$223$	1093.48	+	1893.96i	0.328363	+	0.568741i	−0.653824	+	0.756646i	$0.726836\pi$
$224$		0			0
$225$	160.875	+	2971.49i	0.0476666	+	0.880442i
$226$		0			0
$227$	2421.60	+	4194.33i	0.708050	+	1.22638i	0.965580	+	0.260108i	$0.0837580\pi$
$227$	2421.60	+	4194.33i	0.708050	+	1.22638i	−0.257530	+	0.966270i	$0.582909\pi$
$228$		0			0
$229$	−2628.28	+	4552.32i	−0.758436	+	1.31365i	0.185212	+	0.982699i	$0.440703\pi$
$229$	−2628.28	+	4552.32i	−0.758436	+	1.31365i	−0.943648	+	0.330951i	$0.892630\pi$
$230$		0			0
$231$	1770.17	+	1676.93i	0.504194	+	0.477635i
$232$		0			0
$233$	−2434.53			−0.684511			−0.342256	−	0.939607i	$-0.611191\pi$
$233$	−2434.53			−0.684511			−0.342256	+	0.939607i	$0.611191\pi$
$234$		0			0
$235$	−5077.11			−1.40934
$236$		0			0
$237$	−3265.81	+	970.444i	−0.895093	+	0.265979i
$238$		0			0
$239$	1109.20	−	1921.19i	0.300202	−	0.519965i	−0.675980	−	0.736920i	$-0.736279\pi$
$239$	1109.20	−	1921.19i	0.300202	−	0.519965i	0.976182	+	0.216955i	$0.0696126\pi$
$240$		0			0
$241$	829.281	+	1436.36i	0.221654	+	0.383917i	0.955310	−	0.295604i	$-0.0955210\pi$
$241$	829.281	+	1436.36i	0.221654	+	0.383917i	−0.733656	+	0.679521i	$0.762188\pi$
$242$		0			0
$243$	3493.36	−	1464.70i	0.922219	−	0.386668i
$244$		0			0
$245$	375.751	+	650.820i	0.0979830	+	0.169712i
$246$		0			0
$247$	−3507.38	+	6074.96i	−0.903518	+	1.56494i
$248$		0			0
$249$	61.3033	−	18.2165i	0.0156022	−	0.00463623i
$250$		0			0
$251$	297.180			0.0747323			0.0373662	−	0.999302i	$-0.488103\pi$
$251$	297.180			0.0747323			0.0373662	+	0.999302i	$0.488103\pi$
$252$		0			0
$253$	8654.65			2.15065
$254$		0			0
$255$	−5900.21	−	5589.42i	−1.44896	−	1.37264i
$256$		0			0
$257$	1160.26	−	2009.63i	0.281614	−	0.487771i	−0.690168	−	0.723649i	$-0.742463\pi$
$257$	1160.26	−	2009.63i	0.281614	−	0.487771i	0.971783	+	0.235879i	$0.0757967\pi$
$258$		0			0
$259$	727.563	+	1260.18i	0.174551	+	0.302330i
$260$		0			0
$261$	132.017	+	2438.46i	0.0313089	+	0.578302i
$262$		0			0
$263$	−47.4532	−	82.1914i	−0.0111258	−	0.0192705i	0.860409	−	0.509604i	$-0.170208\pi$
$263$	−47.4532	−	82.1914i	−0.0111258	−	0.0192705i	−0.871535	+	0.490334i	$0.836875\pi$
$264$		0			0
$265$	921.008	−	1595.23i	0.213498	−	0.369790i
$266$		0			0
$267$	866.217	−	3621.83i	0.198545	−	0.830158i
$268$		0			0
$269$	2243.74			0.508563			0.254281	−	0.967130i	$-0.418161\pi$
$269$	2243.74			0.508563			0.254281	+	0.967130i	$0.418161\pi$
$270$		0			0
$271$	−1740.35			−0.390105			−0.195053	−	0.980793i	$-0.562488\pi$
$271$	−1740.35			−0.390105			−0.195053	+	0.980793i	$0.562488\pi$
$272$		0			0
$273$	690.059	−	2885.28i	0.152983	−	0.639651i
$274$		0			0
$275$	−3694.32	+	6398.74i	−0.810093	+	1.40312i
$276$		0			0
$277$	3248.96	+	5627.37i	0.704733	+	1.22063i	0.966788	+	0.255581i	$0.0822668\pi$
$277$	3248.96	+	5627.37i	0.704733	+	1.22063i	−0.262054	+	0.965053i	$0.584400\pi$
$278$		0			0
$279$	−2165.32	+	1411.50i	−0.464640	+	0.302882i
$280$		0			0
$281$	−1969.62	−	3411.47i	−0.418140	−	0.724240i	0.577612	−	0.816311i	$-0.303985\pi$
$281$	−1969.62	−	3411.47i	−0.418140	−	0.724240i	−0.995752	+	0.0920712i	$0.970651\pi$
$282$		0			0
$283$	3287.14	−	5693.49i	0.690460	−	1.19591i	−0.281227	−	0.959641i	$-0.590741\pi$
$283$	3287.14	−	5693.49i	0.690460	−	1.19591i	0.971687	−	0.236271i	$-0.0759252\pi$
$284$		0			0
$285$	−4975.77	−	4713.67i	−1.03417	−	0.979697i
$286$		0			0
$287$	−910.999			−0.187368
$288$		0			0
$289$	5487.83			1.11700
$290$		0			0
$291$	−3742.59	+	1112.12i	−0.753933	+	0.224033i
$292$		0			0
$293$	12.1321	−	21.0135i	0.00241900	−	0.00418983i	−0.864813	−	0.502093i	$-0.832563\pi$
$293$	12.1321	−	21.0135i	0.00241900	−	0.00418983i	0.867232	+	0.497904i	$0.165897\pi$
$294$		0			0
$295$	−1497.69	−	2594.07i	−0.295589	−	0.511975i
$296$		0			0
$297$	9252.02	+	1689.98i	1.80760	+	0.330178i
$298$		0			0
$299$	−5264.87	−	9119.03i	−1.01831	−	1.76377i
$300$		0			0
$301$	−256.496	+	444.263i	−0.0491168	+	0.0850728i
$302$		0			0
$303$	−1324.93	+	393.707i	−0.251205	+	0.0746464i
$304$		0			0
$305$	916.393			0.172041
$306$		0			0
$307$	−8877.90			−1.65045			−0.825226	−	0.564803i	$-0.808952\pi$
$307$	−8877.90			−1.65045			−0.825226	+	0.564803i	$0.808952\pi$
$308$		0			0
$309$	−4382.99	−	4152.12i	−0.806924	−	0.764420i
$310$		0			0
$311$	381.724	−	661.165i	0.0695999	−	0.120551i	−0.829125	−	0.559063i	$-0.811161\pi$
$311$	381.724	−	661.165i	0.0695999	−	0.120551i	0.898725	+	0.438512i	$0.144494\pi$
$312$		0			0
$313$	5012.93	+	8682.66i	0.905264	+	1.56796i	0.820562	+	0.571558i	$0.193661\pi$
$313$	5012.93	+	8682.66i	0.905264	+	1.56796i	0.0847025	+	0.996406i	$0.473006\pi$
$314$		0			0
$315$	2584.98	+	1311.50i	0.462372	+	0.234586i
$316$		0			0
$317$	635.164	+	1100.14i	0.112537	+	0.194920i	0.916793	−	0.399364i	$-0.130769\pi$
$317$	635.164	+	1100.14i	0.112537	+	0.194920i	−0.804255	+	0.594284i	$0.797436\pi$
$318$		0			0
$319$	−3031.62	+	5250.92i	−0.532094	+	0.921615i
$320$		0			0
$321$	2021.14	−	8450.77i	0.351429	−	1.46940i
$322$		0			0
$323$	8771.23			1.51097
$324$		0			0
$325$	8989.44			1.53429
$326$		0			0
$327$	830.105	−	3470.83i	0.140382	−	0.586965i
$328$		0			0
$329$	−1158.65	+	2006.83i	−0.194159	+	0.336293i
$330$		0			0
$331$	3032.15	+	5251.85i	0.503511	+	0.872107i	0.999992	+	0.00405934i	$0.00129213\pi$
$331$	3032.15	+	5251.85i	0.503511	+	0.872107i	−0.496480	+	0.868048i	$0.665375\pi$
$332$		0			0
$333$	5005.28	+	2539.44i	0.823687	+	0.417900i
$334$		0			0
$335$	−6180.43	−	10704.8i	−1.00798	−	1.74587i
$336$		0			0
$337$	4432.30	−	7676.96i	0.716447	−	1.24092i	−0.245952	−	0.969282i	$-0.579101\pi$
$337$	4432.30	−	7676.96i	0.716447	−	1.24092i	0.962399	−	0.271640i	$-0.0875661\pi$
$338$		0			0
$339$	6196.42	+	5870.02i	0.992753	+	0.940460i
$340$		0			0
$341$	−6417.60			−1.01916
$342$		0			0
$343$	343.000			0.0539949
$344$		0			0
$345$	9862.19	−	2930.58i	1.53902	−	0.457325i
$346$		0			0
$347$	1677.41	−	2905.36i	0.259505	−	0.449476i	−0.706604	−	0.707609i	$-0.749774\pi$
$347$	1677.41	−	2905.36i	0.259505	−	0.449476i	0.966109	+	0.258133i	$0.0831073\pi$
$348$		0			0
$349$	2692.00	+	4662.68i	0.412892	+	0.715150i	0.995205	−	0.0978151i	$-0.0311854\pi$
$349$	2692.00	+	4662.68i	0.412892	+	0.715150i	−0.582313	+	0.812965i	$0.697852\pi$
$350$		0			0
$351$	−3847.60	−	10776.5i	−0.585100	−	1.63877i
$352$		0			0
$353$	−2280.85	−	3950.55i	−0.343902	−	0.595656i	0.641252	−	0.767331i	$-0.278415\pi$
$353$	−2280.85	−	3950.55i	−0.343902	−	0.595656i	−0.985154	+	0.171675i	$0.945082\pi$
$354$		0			0
$355$	2999.58	−	5195.43i	0.448454	−	0.776746i
$356$		0			0
$357$	−3555.82	+	1056.62i	−0.527154	+	0.156645i
$358$		0			0
$359$	4104.70			0.603448			0.301724	−	0.953395i	$-0.402438\pi$
$359$	4104.70			0.603448			0.301724	+	0.953395i	$0.402438\pi$
$360$		0			0
$361$	537.954			0.0784303
$362$		0			0
$363$	11931.7	+	11303.2i	1.72521	+	1.63433i
$364$		0			0
$365$	−5593.51	+	9688.24i	−0.802130	+	1.38933i
$366$		0			0
$367$	4096.00	+	7094.48i	0.582587	+	1.00907i	0.995172	+	0.0981509i	$0.0312928\pi$
$367$	4096.00	+	7094.48i	0.582587	+	1.00907i	−0.412585	+	0.910919i	$0.635374\pi$
$368$		0			0
$369$	−2943.66	+	1918.87i	−0.415286	+	0.270711i
$370$		0			0
$371$	−420.366	−	728.095i	−0.0588257	−	0.101889i
$372$		0			0
$373$	−2800.38	+	4850.40i	−0.388735	+	0.673309i	−0.992280	−	0.124020i	$-0.960421\pi$
$373$	−2800.38	+	4850.40i	−0.388735	+	0.673309i	0.603545	+	0.797329i	$0.293754\pi$
$374$		0			0
$375$	274.041	−	1145.82i	0.0377370	−	0.157786i
$376$		0			0
$377$	7376.89			1.00777
$378$		0			0
$379$	6164.97			0.835549			0.417774	−	0.908551i	$-0.362810\pi$
$379$	6164.97			0.835549			0.417774	+	0.908551i	$0.362810\pi$
$380$		0			0
$381$	−1388.92	+	5807.37i	−0.186763	+	0.780894i
$382$		0			0
$383$	−3120.36	+	5404.62i	−0.416300	+	0.721053i	−0.995564	−	0.0940873i	$-0.970007\pi$
$383$	−3120.36	+	5404.62i	−0.416300	+	0.721053i	0.579264	+	0.815140i	$0.303340\pi$
$384$		0			0
$385$	3598.48	+	6232.76i	0.476352	+	0.825067i
$386$		0			0
$387$	106.968	+	1975.79i	0.0140504	+	0.259522i
$388$		0			0
$389$	2278.55	+	3946.57i	0.296985	+	0.514393i	0.975445	−	0.220245i	$-0.0706856\pi$
$389$	2278.55	+	3946.57i	0.296985	+	0.514393i	−0.678460	+	0.734638i	$0.737352\pi$
$390$		0			0
$391$	−6583.18	+	11402.4i	−0.851473	+	1.47479i
$392$		0			0
$393$	−8000.32	−	7578.91i	−1.02688	−	0.972787i
$394$		0			0
$395$	−10055.8			−1.28092
$396$		0			0
$397$	−1518.01			−0.191906			−0.0959531	−	0.995386i	$-0.530590\pi$
$397$	−1518.01			−0.191906			−0.0959531	+	0.995386i	$0.530590\pi$
$398$		0			0
$399$	−2998.69	+	891.070i	−0.376247	+	0.111803i
$400$		0			0
$401$	−4778.45	+	8276.52i	−0.595074	+	1.03070i	0.398463	+	0.917185i	$0.369544\pi$
$401$	−4778.45	+	8276.52i	−0.595074	+	1.03070i	−0.993536	+	0.113513i	$0.963789\pi$
$402$		0			0
$403$	3904.01	+	6761.95i	0.482563	+	0.835823i
$404$		0			0
$405$	11115.2	−	1207.07i	1.36374	−	0.148099i
$406$		0			0
$407$	6967.72	+	12068.4i	0.848592	+	1.46980i
$408$		0			0
$409$	4527.37	−	7841.63i	0.547345	−	0.948029i	−0.451111	−	0.892468i	$-0.648972\pi$
$409$	4527.37	−	7841.63i	0.547345	−	0.948029i	0.998455	−	0.0555606i	$-0.0176946\pi$
$410$		0			0
$411$	12678.2	−	3767.36i	1.52158	−	0.452142i
$412$		0			0
$413$	−1367.15			−0.162889
$414$		0			0
$415$	188.760			0.0223274
$416$		0			0
$417$	−8440.58	−	7995.97i	−0.991216	−	0.939003i
$418$		0			0
$419$	−453.649	+	785.744i	−0.0528931	+	0.0916136i	−0.891260	−	0.453493i	$-0.850178\pi$
$419$	−453.649	+	785.744i	−0.0528931	+	0.0916136i	0.838367	+	0.545107i	$0.183511\pi$
$420$		0			0
$421$	−4036.65	−	6991.69i	−0.467303	−	0.809392i	0.531999	−	0.846745i	$-0.321441\pi$
$421$	−4036.65	−	6991.69i	−0.467303	−	0.809392i	−0.999302	+	0.0373527i	$0.988107\pi$
$422$		0			0
$423$	483.197	+	8925.05i	0.0555410	+	1.02589i
$424$		0			0
$425$	−5620.18	−	9734.44i	−0.641456	−	1.11103i
$426$		0			0
$427$	209.130	−	362.223i	0.0237014	−	0.0410520i
$428$		0			0
$429$	6608.55	−	27631.7i	0.743738	−	3.10972i
$430$		0			0
$431$	13087.2			1.46261			0.731307	−	0.682049i	$-0.238911\pi$
$431$	13087.2			1.46261			0.731307	+	0.682049i	$0.238911\pi$
$432$		0			0
$433$	184.294			0.0204540			0.0102270	−	0.999948i	$-0.496745\pi$
$433$	184.294			0.0204540			0.0102270	+	0.999948i	$0.496745\pi$
$434$		0			0
$435$	−1676.58	+	7010.10i	−0.184795	+	0.772663i
$436$		0			0
$437$	−5551.73	+	9615.88i	−0.607724	+	1.05261i
$438$		0			0
$439$	−1238.41	−	2144.99i	−0.134638	−	0.233200i	0.790821	−	0.612047i	$-0.209654\pi$
$439$	−1238.41	−	2144.99i	−0.134638	−	0.233200i	−0.925459	+	0.378848i	$0.876320\pi$
$440$		0			0
$441$	1108.32	−	722.472i	0.119676	−	0.0780123i
$442$		0			0
$443$	−3420.79	−	5924.99i	−0.366878	−	0.635451i	0.622198	−	0.782860i	$-0.286240\pi$
$443$	−3420.79	−	5924.99i	−0.366878	−	0.635451i	−0.989076	+	0.147409i	$0.952907\pi$
$444$		0			0
$445$	5495.77	−	9518.95i	0.585448	−	1.01403i
$446$		0			0
$447$	−10235.8	−	9696.63i	−1.08308	−	1.02603i
$448$		0			0
$449$	8977.61			0.943607			0.471803	−	0.881704i	$-0.343603\pi$
$449$	8977.61			0.943607			0.471803	+	0.881704i	$0.343603\pi$
$450$		0			0
$451$	−8724.44			−0.910904
$452$		0			0
$453$	4995.86	−	1484.53i	0.518159	−	0.153972i
$454$		0			0
$455$	4378.12	−	7583.13i	0.451098	−	0.781325i
$456$		0			0
$457$	−5497.08	−	9521.23i	−0.562676	−	0.974583i	−0.997262	−	0.0739524i	$-0.976439\pi$
$457$	−5497.08	−	9521.23i	−0.562676	−	0.974583i	0.434586	−	0.900630i	$-0.356895\pi$
$458$		0			0
$459$	−9264.11	+	10903.9i	−0.942073	+	1.10883i
$460$		0			0
$461$	5854.46	+	10140.2i	0.591474	+	1.02446i	0.994034	+	0.109070i	$0.0347871\pi$
$461$	5854.46	+	10140.2i	0.591474	+	1.02446i	−0.402560	+	0.915394i	$0.631880\pi$
$462$		0			0
$463$	−7426.41	+	12862.9i	−0.745431	+	1.29112i	0.204562	+	0.978854i	$0.434423\pi$
$463$	−7426.41	+	12862.9i	−0.745431	+	1.29112i	−0.949993	+	0.312271i	$0.898910\pi$
$464$		0			0
$465$	−7313.02	+	2173.08i	−0.729319	+	0.216719i
$466$		0			0
$467$	−9614.01			−0.952641			−0.476321	−	0.879272i	$-0.658030\pi$
$467$	−9614.01			−0.952641			−0.476321	+	0.879272i	$0.658030\pi$
$468$		0			0
$469$	−5641.74			−0.555461
$470$		0			0
$471$	9472.19	+	8973.25i	0.926657	+	0.877846i
$472$		0			0
$473$	−2456.40	+	4254.61i	−0.238785	+	0.413589i
$474$		0			0
$475$	−4739.61	−	8209.25i	−0.457828	−	0.792982i
$476$		0			0
$477$	−2891.92	−	1467.22i	−0.277593	−	0.140837i
$478$		0			0
$479$	−2131.47	−	3691.82i	−0.203318	−	0.352158i	0.746277	−	0.665635i	$-0.231839\pi$
$479$	−2131.47	−	3691.82i	−0.203318	−	0.352158i	−0.949596	+	0.313478i	$0.898506\pi$
$480$		0			0
$481$	8477.32	−	14683.2i	0.803602	−	1.39188i
$482$		0			0
$483$	1092.28	−	4567.02i	0.102899	−	0.430242i
$484$		0			0
$485$	−11523.9			−1.07891
$486$		0			0
$487$	12531.7			1.16605			0.583025	−	0.812454i	$-0.301869\pi$
$487$	12531.7			1.16605			0.583025	+	0.812454i	$0.301869\pi$
$488$		0			0
$489$	4351.29	−	18193.6i	0.402397	−	1.68250i
$490$		0			0
$491$	−6129.54	+	10616.7i	−0.563386	+	0.975812i	0.433812	+	0.901003i	$0.357168\pi$
$491$	−6129.54	+	10616.7i	−0.563386	+	0.975812i	−0.997198	+	0.0748092i	$0.976165\pi$
$492$		0			0
$493$	−4612.02	−	7988.25i	−0.421328	−	0.729762i
$494$		0			0
$495$	24755.8	+	12559.9i	2.24786	+	1.14046i
$496$		0			0
$497$	−1369.07	−	2371.30i	−0.123564	−	0.214018i
$498$		0			0
$499$	−4700.04	+	8140.71i	−0.421649	+	0.730317i	−0.996101	−	0.0882210i	$-0.971882\pi$
$499$	−4700.04	+	8140.71i	−0.421649	+	0.730317i	0.574452	+	0.818538i	$0.305215\pi$
$500$		0			0
$501$	8468.64	+	8022.56i	0.755192	+	0.715412i
$502$		0			0
$503$	−10688.3			−0.947455			−0.473728	−	0.880671i	$-0.657092\pi$
$503$	−10688.3			−0.947455			−0.473728	+	0.880671i	$0.657092\pi$
$504$		0			0
$505$	−4079.62			−0.359486
$506$		0			0
$507$	−22191.4	+	6594.24i	−1.94390	+	0.577634i
$508$		0			0
$509$	8427.86	−	14597.5i	0.733906	−	1.27116i	−0.221295	−	0.975207i	$-0.571028\pi$
$509$	8427.86	−	14597.5i	0.733906	−	1.27116i	0.955202	−	0.295956i	$-0.0956382\pi$
$510$		0			0
$511$	2552.98	+	4421.90i	0.221013	+	0.382805i
$512$		0			0
$513$	−7812.61	+	9195.51i	−0.672388	+	0.791407i
$514$		0			0
$515$	−8909.94	−	15432.5i	−0.762367	−	1.32046i
$516$		0			0
$517$	−11096.1	+	19219.0i	−0.943918	+	1.63491i
$518$		0			0
$519$	−7315.20	+	2173.73i	−0.618693	+	0.183846i
$520$		0			0
$521$	−19657.4			−1.65299			−0.826494	−	0.562946i	$-0.809668\pi$
$521$	−19657.4			−1.65299			−0.826494	+	0.562946i	$0.809668\pi$
$522$		0			0
$523$	−17874.8			−1.49448			−0.747238	−	0.664557i	$-0.768620\pi$
$523$	−17874.8			−1.49448			−0.747238	+	0.664557i	$0.768620\pi$
$524$		0			0
$525$	2910.34	+	2757.04i	0.241939	+	0.229194i
$526$		0			0
$527$	4881.57	−	8455.12i	0.403500	−	0.698882i
$528$		0			0
$529$	−2250.13	−	3897.33i	−0.184937	−	0.320320i
$530$		0			0
$531$	−4417.58	+	2879.67i	−0.361030	+	0.235343i
$532$		0			0
$533$	5307.33	+	9192.56i	0.431305	+	0.747043i
$534$		0			0
$535$	12823.2	−	22210.5i	1.03625	−	1.79485i
$536$		0			0
$537$	−2564.13	+	10721.2i	−0.206053	+	0.861549i
$538$		0			0
$539$	3284.84			0.262501
$540$		0			0
$541$	−2697.58			−0.214377			−0.107189	−	0.994239i	$-0.534185\pi$
$541$	−2697.58			−0.214377			−0.107189	+	0.994239i	$0.534185\pi$
$542$		0			0
$543$	3750.56	−	15681.9i	0.296413	−	1.23936i
$544$		0			0
$545$	5266.65	−	9122.10i	0.413942	−	0.716969i
$546$		0			0
$547$	−6594.98	−	11422.8i	−0.515505	−	0.892881i	−0.999838	−	0.0179970i	$-0.994271\pi$
$547$	−6594.98	−	11422.8i	−0.515505	−	0.892881i	0.484333	−	0.874884i	$-0.339062\pi$
$548$		0			0
$549$	−87.2147	−	1610.93i	−0.00678002	−	0.125233i
$550$		0			0
$551$	−3889.41	−	6736.65i	−0.300716	−	0.520855i
$552$		0			0
$553$	−2294.83	+	3974.77i	−0.176467	+	0.305650i
$554$		0			0
$555$	12026.4	+	11392.9i	0.919807	+	0.871356i
$556$		0			0
$557$	20815.7			1.58346			0.791731	−	0.610869i	$-0.209180\pi$
$557$	20815.7			1.58346			0.791731	+	0.610869i	$0.209180\pi$
$558$		0			0
$559$	5977.20			0.452252
$560$		0			0
$561$	−34053.3	+	10119.0i	−2.56280	+	0.761544i
$562$		0			0
$563$	3715.46	−	6435.37i	0.278132	−	0.481738i	−0.692789	−	0.721140i	$-0.743618\pi$
$563$	3715.46	−	6435.37i	0.278132	−	0.481738i	0.970920	+	0.239403i	$0.0769516\pi$
$564$		0			0
$565$	12596.4	+	21817.5i	0.937934	+	1.62455i
$566$		0			0
$567$	2059.47	−	4668.96i	0.152539	−	0.345817i
$568$		0			0
$569$	−5698.36	−	9869.85i	−0.419838	−	0.727180i	0.576085	−	0.817390i	$-0.304580\pi$
$569$	−5698.36	−	9869.85i	−0.419838	−	0.727180i	−0.995923	+	0.0902095i	$0.971246\pi$
$570$		0			0
$571$	−3106.40	+	5380.44i	−0.227668	+	0.394333i	−0.957117	−	0.289703i	$-0.906444\pi$
$571$	−3106.40	+	5380.44i	−0.227668	+	0.394333i	0.729448	+	0.684036i	$0.239777\pi$
$572$		0			0
$573$	−9642.35	+	2865.25i	−0.702993	+	0.208896i
$574$		0			0
$575$	14229.1			1.03199
$576$		0			0
$577$	15646.5			1.12890			0.564448	−	0.825469i	$-0.309089\pi$
$577$	15646.5			1.12890			0.564448	+	0.825469i	$0.309089\pi$
$578$		0			0
$579$	−10267.0	−	9726.18i	−0.736929	−	0.698111i
$580$		0			0
$581$	43.0769	−	74.6114i	0.00307596	−	0.00532772i
$582$		0			0
$583$	−4025.75	−	6972.81i	−0.285986	−	0.495342i
$584$		0			0
$585$	−1825.84	−	33724.7i	−0.129041	−	2.38350i
$586$		0			0
$587$	−5926.95	−	10265.8i	−0.416749	−	0.721830i	0.578861	−	0.815426i	$-0.303497\pi$
$587$	−5926.95	−	10265.8i	−0.416749	−	0.721830i	−0.995610	+	0.0935957i	$0.970164\pi$
$588$		0			0
$589$	4116.72	−	7130.38i	0.287991	−	0.498815i
$590$		0			0
$591$	−1448.24	+	6055.38i	−0.100800	+	0.421464i
$592$		0			0
$593$	24339.6			1.68551			0.842755	−	0.538297i	$-0.180932\pi$
$593$	24339.6			1.68551			0.842755	+	0.538297i	$0.180932\pi$
$594$		0			0
$595$	−10948.8			−0.754381
$596$		0			0
$597$	−5146.75	+	21519.6i	−0.352835	+	1.47527i
$598$		0			0
$599$	−6093.55	+	10554.3i	−0.415652	+	0.719931i	−0.995497	−	0.0947963i	$-0.969780\pi$
$599$	−6093.55	+	10554.3i	−0.415652	+	0.719931i	0.579844	+	0.814727i	$0.303113\pi$
$600$		0			0
$601$	661.282	+	1145.37i	0.0448823	+	0.0777384i	0.887594	−	0.460627i	$-0.152375\pi$
$601$	661.282	+	1145.37i	0.0448823	+	0.0777384i	−0.842712	+	0.538365i	$0.819042\pi$
$602$		0			0
$603$	−18229.8	+	11883.4i	−1.23114	+	0.802535i
$604$		0			0
$605$	24255.3	+	42011.4i	1.62995	+	2.82315i
$606$		0			0
$607$	−9192.12	+	15921.2i	−0.614657	+	1.06462i	0.375788	+	0.926706i	$0.377372\pi$
$607$	−9192.12	+	15921.2i	−0.614657	+	1.06462i	−0.990445	+	0.137911i	$0.955961\pi$
$608$		0			0
$609$	2388.28	+	2262.48i	0.158913	+	0.150542i
$610$		0			0
$611$	27000.3			1.78775
$612$		0			0
$613$	−14174.8			−0.933959			−0.466979	−	0.884268i	$-0.654658\pi$
$613$	−14174.8			−0.933959			−0.466979	+	0.884268i	$0.654658\pi$
$614$		0			0
$615$	−9941.71	+	2954.21i	−0.651851	+	0.193699i
$616$		0			0
$617$	8636.48	−	14958.8i	0.563519	−	0.976044i	−0.433666	−	0.901074i	$-0.642780\pi$
$617$	8636.48	−	14958.8i	0.563519	−	0.976044i	0.997186	−	0.0749707i	$-0.0238863\pi$
$618$		0			0
$619$	−8781.84	−	15210.6i	−0.570229	−	0.987666i	−0.996542	−	0.0830904i	$-0.973521\pi$
$619$	−8781.84	−	15210.6i	−0.570229	−	0.987666i	0.426313	−	0.904576i	$-0.359812\pi$
$620$		0			0
$621$	−6090.27	−	17057.8i	−0.393549	−	1.10227i
$622$		0			0
$623$	−2508.38	−	4344.63i	−0.161310	−	0.279397i
$624$		0			0
$625$	8627.19	−	14942.7i	0.552140	−	0.956335i
$626$		0			0
$627$	−28717.8	+	8533.59i	−1.82915	+	0.543538i
$628$		0			0
$629$	−21200.0			−1.34388
$630$		0			0
$631$	−7749.44			−0.488907			−0.244454	−	0.969661i	$-0.578609\pi$
$631$	−7749.44			−0.488907			−0.244454	+	0.969661i	$0.578609\pi$
$632$		0			0
$633$	−2209.51	−	2093.13i	−0.138737	−	0.131429i
$634$		0			0
$635$	−8812.12	+	15263.0i	−0.550706	+	0.953850i
$636$		0			0
$637$	−1998.26	−	3461.09i	−0.124292	−	0.215280i
$638$		0			0
$639$	−9418.53	−	4778.51i	−0.583085	−	0.295829i
$640$		0			0
$641$	980.662	+	1698.56i	0.0604272	+	0.104663i	0.894656	−	0.446755i	$-0.147420\pi$
$641$	980.662	+	1698.56i	0.0604272	+	0.104663i	−0.834229	+	0.551418i	$0.814087\pi$
$642$		0			0
$643$	−4815.35	+	8340.43i	−0.295333	+	0.511531i	−0.975062	−	0.221932i	$-0.928764\pi$
$643$	−4815.35	+	8340.43i	−0.295333	+	0.511531i	0.679730	+	0.733463i	$0.262097\pi$
$644$		0			0
$645$	−1358.46	+	5680.01i	−0.0829294	+	0.346744i
$646$		0			0
$647$	10126.3			0.615313			0.307656	−	0.951498i	$-0.400455\pi$
$647$	10126.3			0.615313			0.307656	+	0.951498i	$0.400455\pi$
$648$		0			0
$649$	−13092.9			−0.791896
$650$		0			0
$651$	−809.945	+	3386.54i	−0.0487623	+	0.203885i
$652$		0			0
$653$	9784.04	−	16946.4i	0.586338	−	1.01557i	−0.408369	−	0.912817i	$-0.633902\pi$
$653$	9784.04	−	16946.4i	0.586338	−	1.01557i	0.994707	−	0.102751i	$-0.0327644\pi$
$654$		0			0
$655$	−16263.4	−	28169.1i	−0.970175	−	1.68039i
$656$		0			0
$657$	17563.3	+	8910.78i	1.04294	+	0.529137i
$658$		0			0
$659$	13035.4	+	22578.0i	0.770542	+	1.33462i	0.937266	+	0.348614i	$0.113348\pi$
$659$	13035.4	+	22578.0i	0.770542	+	1.33462i	−0.166725	+	0.986003i	$0.553319\pi$
$660$		0			0
$661$	−311.100	+	538.842i	−0.0183062	+	0.0317073i	−0.875033	−	0.484063i	$-0.839161\pi$
$661$	−311.100	+	538.842i	−0.0183062	+	0.0317073i	0.856727	+	0.515770i	$0.172494\pi$
$662$		0			0
$663$	31377.6	+	29724.8i	1.83802	+	1.74120i
$664$		0			0
$665$	−9233.33			−0.538426
$666$		0			0
$667$	11676.7			0.677845
$668$		0			0
$669$	10893.0	−	3236.90i	0.629520	−	0.187064i
$670$		0			0
$671$	2002.79	−	3468.93i	0.115226	−	0.199578i
$672$		0			0
$673$	11972.3	+	20736.6i	0.685732	+	1.18772i	0.973206	+	0.229934i	$0.0738511\pi$
$673$	11972.3	+	20736.6i	0.685732	+	1.18772i	−0.287474	+	0.957788i	$0.592816\pi$
$674$		0			0
$675$	15211.3	+	2778.51i	0.867380	+	0.158437i
$676$		0			0
$677$	−2149.61	−	3723.23i	−0.122033	−	0.211367i	0.798536	−	0.601947i	$-0.205608\pi$
$677$	−2149.61	−	3723.23i	−0.122033	−	0.211367i	−0.920569	+	0.390580i	$0.872275\pi$
$678$		0			0
$679$	−2629.86	+	4555.05i	−0.148637	+	0.257447i
$680$		0			0
$681$	24123.5	−	7168.36i	1.35744	−	0.403366i
$682$		0			0
$683$	19177.7			1.07440			0.537200	−	0.843455i	$-0.319482\pi$
$683$	19177.7			1.07440			0.537200	+	0.843455i	$0.319482\pi$
$684$		0			0
$685$	39037.7			2.17745
$686$		0			0
$687$	19829.0	+	18784.6i	1.10120	+	1.04320i
$688$		0			0
$689$	−4897.96	+	8483.52i	−0.270824	+	0.469081i
$690$		0			0
$691$	13750.1	+	23815.9i	0.756990	+	1.31114i	0.944379	+	0.328859i	$0.106664\pi$
$691$	13750.1	+	23815.9i	0.756990	+	1.31114i	−0.187389	+	0.982286i	$0.560003\pi$
$692$		0			0
$693$	10614.1	−	6918.96i	0.581813	−	0.379263i
$694$		0			0
$695$	−17158.4	−	29719.2i	−0.936482	−	1.62203i
$696$		0			0
$697$	6636.26	−	11494.3i	0.360641	−	0.624648i
$698$		0			0
$699$	−2942.50	+	12303.2i	−0.159221	+	0.665736i
$700$		0			0
$701$	17920.6			0.965550			0.482775	−	0.875744i	$-0.339629\pi$
$701$	17920.6			0.965550			0.482775	+	0.875744i	$0.339629\pi$
$702$		0			0
$703$	−17878.4			−0.959171
$704$		0			0
$705$	−6136.47	+	25657.8i	−0.327820	+	1.37068i
$706$		0			0
$707$	−931.008	+	1612.55i	−0.0495250	+	0.0857798i
$708$		0			0
$709$	−10259.3	−	17769.6i	−0.543436	−	0.941258i	−0.998704	−	0.0509038i	$-0.983790\pi$
$709$	−10259.3	−	17769.6i	−0.543436	−	0.941258i	0.455268	−	0.890355i	$-0.349544\pi$
$710$		0			0
$711$	957.028	+	17677.1i	0.0504801	+	0.932410i
$712$		0			0
$713$	6179.56	+	10703.3i	0.324581	+	0.562191i
$714$		0			0
$715$	41928.3	−	72622.0i	2.19305	−	3.79847i
$716$		0			0
$717$	−8368.35	−	7927.55i	−0.435874	−	0.412915i
$718$		0			0
$719$	14773.2			0.766268			0.383134	−	0.923693i	$-0.374845\pi$
$719$	14773.2			0.766268			0.383134	+	0.923693i	$0.374845\pi$
$720$		0			0
$721$	−8133.34			−0.420113
$722$		0			0
$723$	8261.13	−	2454.82i	0.424944	−	0.126273i
$724$		0			0
$725$	−4984.29	+	8633.05i	−0.255327	+	0.442239i
$726$		0			0
$727$	−9320.43	−	16143.5i	−0.475482	−	0.823560i	0.524123	−	0.851642i	$-0.324393\pi$
$727$	−9320.43	−	16143.5i	−0.475482	−	0.823560i	−0.999606	+	0.0280827i	$0.991060\pi$
$728$		0			0
$729$	−3179.76	−	19424.5i	−0.161549	−	0.986865i
$730$		0			0
$731$	−3736.94	−	6472.57i	−0.189078	−	0.327492i
$732$		0			0
$733$	−18145.4	+	31428.7i	−0.914344	+	1.58369i	−0.106486	+	0.994314i	$0.533960\pi$
$733$	−18145.4	+	31428.7i	−0.914344	+	1.58369i	−0.807858	+	0.589377i	$0.799373\pi$
$734$		0			0
$735$	3743.15	−	1112.29i	0.187848	−	0.0558196i
$736$		0			0
$737$	−54029.7			−2.70042
$738$		0			0
$739$	15137.4			0.753503			0.376751	−	0.926314i	$-0.377041\pi$
$739$	15137.4			0.753503			0.376751	+	0.926314i	$0.377041\pi$
$740$		0			0
$741$	26461.4	+	25067.5i	1.31185	+	1.24275i
$742$		0			0
$743$	−5581.16	+	9666.85i	−0.275576	+	0.477311i	−0.970280	−	0.241984i	$-0.922202\pi$
$743$	−5581.16	+	9666.85i	−0.275576	+	0.477311i	0.694704	+	0.719295i	$0.255535\pi$
$744$		0			0
$745$	−20807.8	−	36040.2i	−1.02327	−	1.77236i
$746$		0			0
$747$	−17.9646	−	331.822i	−0.000879908	−	0.0162526i
$748$		0			0
$749$	−5852.77	−	10137.3i	−0.285521	−	0.494537i
$750$		0			0
$751$	−12634.5	+	21883.7i	−0.613903	+	1.06331i	0.376673	+	0.926346i	$0.377068\pi$
$751$	−12634.5	+	21883.7i	−0.613903	+	1.06331i	−0.990576	+	0.136965i	$0.956265\pi$
$752$		0			0
$753$	359.188	−	1501.84i	0.0173832	−	0.0726825i
$754$		0			0
$755$	15382.8			0.741509
$756$		0			0
$757$	27731.0			1.33144			0.665721	−	0.746200i	$-0.268124\pi$
$757$	27731.0			1.33144			0.665721	+	0.746200i	$0.268124\pi$
$758$		0			0
$759$	10460.5	−	43737.4i	0.500253	−	2.09166i
$760$		0			0
$761$	−1219.04	+	2111.44i	−0.0580686	+	0.100578i	−0.893598	−	0.448867i	$-0.851828\pi$
$761$	−1219.04	+	2111.44i	−0.0580686	+	0.100578i	0.835530	+	0.549445i	$0.185161\pi$
$762$		0			0
$763$	−2403.80	−	4163.51i	−0.114054	−	0.197548i
$764$		0			0
$765$	−35378.1	+	23061.8i	−1.67203	+	1.08994i
$766$		0			0
$767$	7964.78	+	13795.4i	0.374956	+	0.649443i
$768$		0			0
$769$	−14186.9	+	24572.4i	−0.665269	+	1.15228i	0.313943	+	0.949442i	$0.398350\pi$
$769$	−14186.9	+	24572.4i	−0.665269	+	1.15228i	−0.979212	+	0.202839i	$0.934983\pi$
$770$		0			0
$771$	−8753.55	−	8292.46i	−0.408886	−	0.387348i
$772$		0			0
$773$	40257.5			1.87317			0.936585	−	0.350439i	$-0.113968\pi$
$773$	40257.5			1.87317			0.936585	+	0.350439i	$0.113968\pi$
$774$		0			0
$775$	−10551.2			−0.489045
$776$		0			0
$777$	7247.84	−	2153.72i	0.334639	−	0.0994390i
$778$		0			0
$779$	5596.50	−	9693.41i	0.257401	−	0.445831i
$780$		0			0
$781$	−13111.3	−	22709.4i	−0.600714	−	1.04047i
$782$		0			0
$783$	12482.6	+	2280.09i	0.569722	+	0.104066i
$784$		0			0
$785$	19255.5	+	33351.5i	0.875488	+	1.51639i
$786$		0			0
$787$	2538.82	−	4397.36i	0.114992	−	0.199173i	−0.802784	−	0.596270i	$-0.796649\pi$
$787$	2538.82	−	4397.36i	0.114992	−	0.199173i	0.917777	+	0.397097i	$0.129982\pi$
$788$		0			0
$789$	−472.719	+	140.470i	−0.0213298	+	0.00633822i
$790$		0			0
$791$	11498.5			0.516862
$792$		0			0
$793$	−4873.42			−0.218235
$794$		0			0
$795$	−6948.53	−	6582.52i	−0.309986	−	0.293658i
$796$		0			0
$797$	12920.2	−	22378.5i	0.574226	−	0.994589i	−0.421899	−	0.906643i	$-0.638636\pi$
$797$	12920.2	−	22378.5i	0.574226	−	0.994589i	0.996125	−	0.0879461i	$-0.0280303\pi$
$798$		0			0
$799$	−16880.5	−	29238.0i	−0.747423	−	1.29457i
$800$		0			0
$801$	−17256.4	−	8755.08i	−0.761205	−	0.386199i
$802$		0			0
$803$	24449.4	+	42347.6i	1.07447	+	1.86104i
$804$		0			0
$805$	6930.01	−	12003.1i	0.303417	−	0.525534i
$806$		0			0
$807$	2711.91	−	11339.0i	0.118295	−	0.494613i
$808$		0			0
$809$	−8475.12			−0.368318			−0.184159	−	0.982896i	$-0.558956\pi$
$809$	−8475.12			−0.368318			−0.184159	+	0.982896i	$0.558956\pi$
$810$		0			0
$811$	−25028.1			−1.08367			−0.541833	−	0.840486i	$-0.682270\pi$
$811$	−25028.1			−1.08367			−0.541833	+	0.840486i	$0.682270\pi$
$812$		0			0
$813$	−2103.48	+	8795.06i	−0.0907407	+	0.379405i
$814$		0			0
$815$	27607.0	−	47816.8i	1.18654	−	2.05515i
$816$		0			0
$817$	−3151.44	−	5458.45i	−0.134951	−	0.233742i
$818$		0			0
$819$	−13747.1	−	6974.61i	−0.586522	−	0.297573i
$820$		0			0
$821$	19333.1	+	33485.9i	0.821840	+	1.42347i	0.904311	+	0.426875i	$0.140385\pi$
$821$	19333.1	+	33485.9i	0.821840	+	1.42347i	−0.0824712	+	0.996593i	$0.526281\pi$
$822$		0			0
$823$	1275.85	−	2209.83i	0.0540380	−	0.0935966i	−0.837741	−	0.546068i	$-0.816124\pi$
$823$	1275.85	−	2209.83i	0.0540380	−	0.0935966i	0.891779	+	0.452471i	$0.149457\pi$
$824$		0			0
$825$	27871.7	+	26403.6i	1.17620	+	1.11425i
$826$		0			0
$827$	20418.3			0.858540			0.429270	−	0.903176i	$-0.358771\pi$
$827$	20418.3			0.858540			0.429270	+	0.903176i	$0.358771\pi$
$828$		0			0
$829$	6122.36			0.256500			0.128250	−	0.991742i	$-0.459064\pi$
$829$	6122.36			0.256500			0.128250	+	0.991742i	$0.459064\pi$
$830$		0			0
$831$	32365.5	−	9617.50i	1.35108	−	0.401477i
$832$		0			0
$833$	−2498.62	+	4327.74i	−0.103928	+	0.180009i
$834$		0			0
$835$	17215.4	+	29818.0i	0.713491	+	1.23580i
$836$		0			0
$837$	4516.06	+	12648.7i	0.186497	+	0.522347i
$838$		0			0
$839$	−19550.9	−	33863.2i	−0.804496	−	1.39343i	−0.916631	−	0.399735i	$-0.869102\pi$
$839$	−19550.9	−	33863.2i	−0.804496	−	1.39343i	0.112135	−	0.993693i	$-0.464231\pi$
$840$		0			0
$841$	8104.30	−	14037.1i	0.332293	−	0.575549i
$842$		0			0
$843$	−19620.9	+	5830.41i	−0.801637	+	0.238209i
$844$		0			0
$845$	−68330.0			−2.78180
$846$		0			0
$847$	22141.2			0.898205
$848$		0			0
$849$	−24799.8	−	23493.5i	−1.00250	−	0.949698i
$850$		0			0
$851$	13418.5	−	23241.6i	0.540518	−	0.936205i
$852$		0			0
$853$	10271.3	+	17790.4i	0.412289	+	0.714106i	0.995140	−	0.0984735i	$-0.0313960\pi$
$853$	10271.3	+	17790.4i	0.412289	+	0.714106i	−0.582850	+	0.812580i	$0.698063\pi$
$854$		0			0
$855$	−29835.1	+	19448.5i	−1.19338	+	0.777922i
$856$		0			0
$857$	7889.43	+	13664.9i	0.314466	+	0.544672i	0.979324	−	0.202298i	$-0.0648411\pi$
$857$	7889.43	+	13664.9i	0.314466	+	0.544672i	−0.664858	+	0.746970i	$0.731508\pi$
$858$		0			0
$859$	−18708.4	+	32403.9i	−0.743098	+	1.28708i	0.207980	+	0.978133i	$0.433311\pi$
$859$	−18708.4	+	32403.9i	−0.743098	+	1.28708i	−0.951078	+	0.308951i	$0.900022\pi$
$860$		0			0
$861$	−1101.08	+	4603.85i	−0.0435828	+	0.182228i
$862$		0			0
$863$	−26182.8			−1.03276			−0.516380	−	0.856360i	$-0.672721\pi$
$863$	−26182.8			−1.03276			−0.516380	+	0.856360i	$0.672721\pi$
$864$		0			0
$865$	−22524.4			−0.885377
$866$		0			0
$867$	6632.89	−	27733.5i	0.259821	−	1.08636i
$868$		0			0
$869$	−21977.1	+	38065.5i	−0.857909	+	1.48594i
$870$		0			0
$871$	32867.8	+	56928.7i	1.27863	+	2.21465i
$872$		0			0
$873$	1096.75	+	20257.8i	0.0425192	+	0.785365i
$874$		0			0
$875$	−793.561	−	1374.49i	−0.0306597	−	0.0531042i
$876$		0			0
$877$	−10083.5	+	17465.1i	−0.388249	+	0.672467i	−0.992214	−	0.124544i	$-0.960253\pi$
$877$	−10083.5	+	17465.1i	−0.388249	+	0.672467i	0.603965	+	0.797011i	$0.293587\pi$
$878$		0			0
$879$	−91.5307	−	86.7094i	−0.00351224	−	0.00332723i
$880$		0			0
$881$	3159.11			0.120809			0.0604047	−	0.998174i	$-0.480761\pi$
$881$	3159.11			0.120809			0.0604047	+	0.998174i	$0.480761\pi$
$882$		0			0
$883$	32379.2			1.23403			0.617015	−	0.786952i	$-0.288342\pi$
$883$	32379.2			1.23403			0.617015	+	0.786952i	$0.288342\pi$
$884$		0			0
$885$	−14919.7	+	4433.42i	−0.566688	+	0.168393i
$886$		0			0
$887$	7531.75	−	13045.4i	0.285109	−	0.493823i	−0.687527	−	0.726159i	$-0.741304\pi$
$887$	7531.75	−	13045.4i	0.285109	−	0.493823i	0.972636	+	0.232336i	$0.0746370\pi$
$888$		0			0
$889$	4022.02	+	6966.35i	0.151737	+	0.262816i
$890$		0			0
$891$	19723.0	−	44713.6i	0.741579	−	1.68122i
$892$		0			0
$893$	−14235.7	−	24657.0i	−0.533460	−	0.923979i
$894$		0			0
$895$	−16268.3	+	28177.5i	−0.607586	+	1.05237i
$896$		0			0
$897$	−52447.6	+	15585.0i	−1.95226	+	0.580119i
$898$		0			0
$899$	−8658.50			−0.321220
$900$		0			0
$901$	12248.8			0.452904
$902$		0			0
$903$	1935.13	+	1833.19i	0.0713145	+	0.0675580i
$904$		0			0
$905$	23795.7	−	41215.3i	0.874027	−	1.51386i
$906$		0			0
$907$	7179.62	+	12435.5i	0.262839	+	0.455251i	0.966995	−	0.254794i	$-0.0820077\pi$
$907$	7179.62	+	12435.5i	0.262839	+	0.455251i	−0.704156	+	0.710045i	$0.748674\pi$
$908$		0			0
$909$	388.264	+	7171.56i	0.0141671	+	0.261678i
$910$		0			0
$911$	8286.66	+	14352.9i	0.301371	+	0.521990i	0.976447	−	0.215758i	$-0.0692223\pi$
$911$	8286.66	+	14352.9i	0.301371	+	0.521990i	−0.675076	+	0.737749i	$0.735889\pi$
$912$		0			0
$913$	412.538	−	714.537i	0.0149540	−	0.0259011i
$914$		0			0
$915$	1107.60	−	4631.11i	0.0400177	−	0.167322i
$916$		0			0
$917$	−14845.9			−0.534628
$918$		0			0
$919$	−9972.35			−0.357952			−0.178976	−	0.983853i	$-0.557278\pi$
$919$	−9972.35			−0.357952			−0.178976	+	0.983853i	$0.557278\pi$
$920$		0			0
$921$	−10730.3	+	44865.6i	−0.383905	+	1.60518i
$922$		0			0
$923$	−15951.9	+	27629.5i	−0.568867	+	0.985306i
$924$		0			0
$925$	11455.6	+	19841.7i	0.407199	+	0.705289i
$926$		0			0
$927$	−26280.8	+	17131.5i	−0.931148	+	0.606983i
$928$		0			0
$929$	−8829.76	−	15293.6i	−0.311835	−	0.540115i	0.666924	−	0.745125i	$-0.267610\pi$
$929$	−8829.76	−	15293.6i	−0.311835	−	0.540115i	−0.978760	+	0.205011i	$0.934277\pi$
$930$		0			0
$931$	−2107.14	+	3649.67i	−0.0741768	+	0.128478i
$932$		0			0
$933$	−2879.91	−	2728.21i	−0.101055	−	0.0957316i
$934$		0			0
$935$	−104854.			−3.66748
$936$		0			0
$937$	−16521.2			−0.576012			−0.288006	−	0.957629i	$-0.592992\pi$
$937$	−16521.2			−0.576012			−0.288006	+	0.957629i	$0.592992\pi$
$938$		0			0
$939$	49937.8	−	14839.2i	1.73553	−	0.515717i
$940$		0			0
$941$	20148.0	−	34897.4i	0.697988	−	1.20895i	−0.271175	−	0.962530i	$-0.587412\pi$
$941$	20148.0	−	34897.4i	0.697988	−	1.20895i	0.969163	−	0.246421i	$-0.0792546\pi$
$942$		0			0
$943$	8400.82	+	14550.6i	0.290104	+	0.502475i
$944$		0			0
$945$	9752.17	−	11478.4i	0.335702	−	0.395124i
$946$		0			0
$947$	11015.7	+	19079.8i	0.377997	+	0.654710i	0.990771	−	0.135548i	$-0.0432796\pi$
$947$	11015.7	+	19079.8i	0.377997	+	0.654710i	−0.612774	+	0.790258i	$0.709946\pi$
$948$		0			0
$949$	29746.5	−	51522.5i	1.01751	−	1.76237i
$950$		0			0
$951$	6327.37	−	1880.20i	0.215751	−	0.0641110i
$952$		0			0
$953$	−31578.2			−1.07337			−0.536683	−	0.843784i	$-0.680323\pi$
$953$	−31578.2			−1.07337			−0.536683	+	0.843784i	$0.680323\pi$
$954$		0			0
$955$	−29689.9			−1.00601
$956$		0			0
$957$	22872.0	+	21667.2i	0.772568	+	0.731873i
$958$		0			0
$959$	8908.78	−	15430.5i	0.299979	−	0.519578i
$960$		0			0
$961$	10313.2	+	17863.0i	0.346186	+	0.599612i
$962$		0			0
$963$	−40264.2	−	20428.1i	−1.34735	−	0.683580i
$964$		0			0
$965$	−20871.2	−	36150.0i	−0.696236	−	1.20592i
$966$		0			0
$967$	23825.7	−	41267.4i	0.792331	−	1.37236i	−0.132190	−	0.991224i	$-0.542201\pi$
$967$	23825.7	−	41267.4i	0.792331	−	1.37236i	0.924520	−	0.381132i	$-0.124466\pi$
$968$		0			0
$969$	10601.4	−	44326.5i	0.351461	−	1.46953i
$970$		0			0
$971$	−11343.0			−0.374885			−0.187443	−	0.982276i	$-0.560020\pi$
$971$	−11343.0			−0.374885			−0.187443	+	0.982276i	$0.560020\pi$
$972$		0			0
$973$	−15662.8			−0.516061
$974$		0			0
$975$	10865.1	−	45429.3i	0.356885	−	1.49221i
$976$		0			0
$977$	8038.74	−	13923.5i	0.263237	−	0.455939i	−0.703864	−	0.710335i	$-0.748543\pi$
$977$	8038.74	−	13923.5i	0.263237	−	0.455939i	0.967100	+	0.254396i	$0.0818767\pi$
$978$		0			0
$979$	−24022.2	−	41607.6i	−0.784220	−	1.35831i
$980$		0			0
$981$	−16537.0	−	8390.08i	−0.538211	−	0.273063i
$982$		0			0
$983$	23662.5	+	40984.6i	0.767767	+	1.32981i	0.938771	+	0.344541i	$0.111966\pi$
$983$	23662.5	+	40984.6i	0.767767	+	1.32981i	−0.171004	+	0.985270i	$0.554701\pi$
$984$		0			0
$985$	−9188.45	+	15914.9i	−0.297227	+	0.514812i
$986$		0			0
$987$	8741.38	+	8280.93i	0.281906	+	0.267057i
$988$		0			0
$989$	9461.15			0.304193
$990$		0			0
$991$	−12416.7			−0.398011			−0.199005	−	0.979998i	$-0.563771\pi$
$991$	−12416.7			−0.398011			−0.199005	+	0.979998i	$0.563771\pi$
$992$		0			0
$993$	30205.7	−	8975.71i	0.965306	−	0.286843i
$994$		0			0
$995$	−32653.8	+	56558.1i	−1.04040	+	1.80202i
$996$		0			0
$997$	12818.5	+	22202.3i	0.407188	+	0.705270i	0.994573	−	0.104037i	$-0.0331761\pi$
$997$	12818.5	+	22202.3i	0.407188	+	0.705270i	−0.587385	+	0.809307i	$0.699843\pi$
$998$		0			0
$999$	18883.1	−	22225.5i	0.598032	−	0.703889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.j.b.85.6	✓	18
3.2	odd	2		756.4.j.b.253.2		18
9.2	odd	6		756.4.j.b.505.2		18
9.4	even	3		2268.4.a.i.1.2		9
9.5	odd	6		2268.4.a.h.1.8		9
9.7	even	3	inner	252.4.j.b.169.6	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.j.b.85.6	✓	18	1.1	even	1	trivial
252.4.j.b.169.6	yes	18	9.7	even	3	inner
756.4.j.b.253.2		18	3.2	odd	2
756.4.j.b.505.2		18	9.2	odd	6
2268.4.a.h.1.8		9	9.5	odd	6
2268.4.a.i.1.2		9	9.4	even	3

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20866 - 5.05363i) q^{3} +(7.66838 - 13.2820i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-24.0783 - 12.2162i) q^{9} +O(q^{10})\)	\(q+(1.20866 - 5.05363i) q^{3} +(7.66838 - 13.2820i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-24.0783 - 12.2162i) q^{9} +(-33.5187 - 58.0562i) q^{11} +(-40.7808 + 70.6345i) q^{13} +(-57.8540 - 54.8066i) q^{15} +101.984 q^{17} +86.0055 q^{19} +(-34.8663 + 10.3606i) q^{21} +(-64.5509 + 111.805i) q^{23} +(-55.1082 - 95.4503i) q^{25} +(-90.8384 + 106.918i) q^{27} +(-45.2228 - 78.3281i) q^{29} +(47.8658 - 82.9060i) q^{31} +(-333.907 + 99.2214i) q^{33} -107.357 q^{35} -207.875 q^{37} +(307.670 + 291.464i) q^{39} +(65.0713 - 112.707i) q^{41} +(-36.6422 - 63.4662i) q^{43} +(-346.897 + 226.130i) q^{45} +(-165.521 - 286.690i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(123.264 - 515.392i) q^{51} +120.105 q^{53} -1028.14 q^{55} +(103.951 - 434.640i) q^{57} +(97.6534 - 169.141i) q^{59} +(29.8757 + 51.7462i) q^{61} +(10.2174 + 188.724i) q^{63} +(625.446 + 1083.30i) q^{65} +(402.981 - 697.984i) q^{67} +(487.003 + 461.350i) q^{69} +391.162 q^{71} -729.424 q^{73} +(-548.977 + 163.130i) q^{75} +(-234.631 + 406.393i) q^{77} +(-327.833 - 567.824i) q^{79} +(430.530 + 588.290i) q^{81} +(6.15385 + 10.6588i) q^{83} +(782.056 - 1354.56i) q^{85} +(-450.500 + 133.867i) q^{87} +716.679 q^{89} +570.932 q^{91} +(-361.123 - 342.101i) q^{93} +(659.524 - 1142.33i) q^{95} +(-375.694 - 650.721i) q^{97} +(97.8497 + 1807.36i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9}+O(q^{10}) \) 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9	\( 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9} - 93 q^{11} - 18 q^{13} + 162 q^{15} - 54 q^{17} - 90 q^{19} - 49 q^{21} - 246 q^{23} - 315 q^{25} - 394 q^{27} - 318 q^{29} - 18 q^{31} + 33 q^{33} + 84 q^{35} - 72 q^{37} + 268 q^{39} - 57 q^{41} - 171 q^{43} - 318 q^{45} - 1056 q^{47} - 441 q^{49} + 705 q^{51} + 1512 q^{53} - 1800 q^{55} - 1271 q^{57} - 411 q^{59} - 198 q^{61} + 308 q^{63} - 1326 q^{65} - 441 q^{67} + 642 q^{69} + 3516 q^{71} + 54 q^{73} - 2497 q^{75} - 651 q^{77} + 72 q^{79} + 1163 q^{81} - 558 q^{83} - 1008 q^{85} + 2766 q^{87} + 2784 q^{89} + 252 q^{91} - 2618 q^{93} - 156 q^{95} + 909 q^{97} + 6318 q^{99}+O(q^{100}) \) 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9 - 93 * q^11 - 18 * q^13 + 162 * q^15 - 54 * q^17 - 90 * q^19 - 49 * q^21 - 246 * q^23 - 315 * q^25 - 394 * q^27 - 318 * q^29 - 18 * q^31 + 33 * q^33 + 84 * q^35 - 72 * q^37 + 268 * q^39 - 57 * q^41 - 171 * q^43 - 318 * q^45 - 1056 * q^47 - 441 * q^49 + 705 * q^51 + 1512 * q^53 - 1800 * q^55 - 1271 * q^57 - 411 * q^59 - 198 * q^61 + 308 * q^63 - 1326 * q^65 - 441 * q^67 + 642 * q^69 + 3516 * q^71 + 54 * q^73 - 2497 * q^75 - 651 * q^77 + 72 * q^79 + 1163 * q^81 - 558 * q^83 - 1008 * q^85 + 2766 * q^87 + 2784 * q^89 + 252 * q^91 - 2618 * q^93 - 156 * q^95 + 909 * q^97 + 6318 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more