LMFDB - Embedded newform 252.4.j.b.169.9

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			169.9
Root			$-4.09635 - 1.01354i$ of defining polynomial
Character	$\chi$	$=$	252.169
Dual form			252.4.j.b.85.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.09635 - 1.01354i) q^{3} +(0.184423 + 0.319430i) q^{5} +(-3.50000 + 6.06218i) q^{7} +(24.9455 - 10.3307i) q^{9} +O(q^{10})$	\(q+(5.09635 - 1.01354i) q^{3} +(0.184423 + 0.319430i) q^{5} +(-3.50000 + 6.06218i) q^{7} +(24.9455 - 10.3307i) q^{9} +(16.1092 - 27.9020i) q^{11} +(4.62663 + 8.01356i) q^{13} +(1.26364 + 1.44101i) q^{15} +87.0444 q^{17} +66.5327 q^{19} +(-11.6929 + 34.4423i) q^{21} +(21.4225 + 37.1049i) q^{23} +(62.4320 - 108.135i) q^{25} +(116.660 - 77.9321i) q^{27} +(-48.3348 + 83.7183i) q^{29} +(-11.7252 - 20.3086i) q^{31} +(53.8183 - 158.525i) q^{33} -2.58192 q^{35} -147.986 q^{37} +(31.7010 + 36.1506i) q^{39} +(-12.7866 - 22.1471i) q^{41} +(11.0164 - 19.0809i) q^{43} +(7.90046 + 6.06312i) q^{45} +(-54.6744 + 94.6988i) q^{47} +(-24.5000 - 42.4352i) q^{49} +(443.608 - 88.2230i) q^{51} +328.433 q^{53} +11.8836 q^{55} +(339.074 - 67.4336i) q^{57} +(194.501 + 336.885i) q^{59} +(183.696 - 318.171i) q^{61} +(-24.6826 + 187.381i) q^{63} +(-1.70652 + 2.95577i) q^{65} +(-239.963 - 415.629i) q^{67} +(146.784 + 167.387i) q^{69} -186.194 q^{71} -722.479 q^{73} +(208.575 - 614.372i) q^{75} +(112.764 + 195.314i) q^{77} +(-87.2813 + 151.176i) q^{79} +(515.553 - 515.409i) q^{81} +(-455.339 + 788.670i) q^{83} +(16.0530 + 27.8046i) q^{85} +(-161.479 + 475.647i) q^{87} +592.104 q^{89} -64.7728 q^{91} +(-80.3390 - 91.6155i) q^{93} +(12.2702 + 21.2526i) q^{95} +(-604.703 + 1047.38i) q^{97} +(113.605 - 862.447i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	5.09635	−	1.01354i	0.980792	−	0.195056i
$3$	5.09635	−	1.01354i	0.980792	−	0.195056i
$4$		0			0
$5$	0.184423	+	0.319430i	0.0164953	+	0.0285707i	0.874155	−	0.485647i	$-0.161416\pi$
$5$	0.184423	+	0.319430i	0.0164953	+	0.0285707i	−0.857660	+	0.514217i	$0.828082\pi$
$6$		0			0
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$8$		0			0
$9$	24.9455	−	10.3307i	0.923906	−	0.382619i
$10$		0			0
$11$	16.1092	−	27.9020i	0.441555	−	0.764796i	−0.556250	−	0.831015i	$-0.687760\pi$
$11$	16.1092	−	27.9020i	0.441555	−	0.764796i	0.997805	+	0.0662189i	$0.0210936\pi$
$12$		0			0
$13$	4.62663	+	8.01356i	0.0987074	+	0.170966i	0.911150	−	0.412075i	$-0.135196\pi$
$13$	4.62663	+	8.01356i	0.0987074	+	0.170966i	−0.812442	+	0.583041i	$0.801863\pi$
$14$		0			0
$15$	1.26364	+	1.44101i	0.0217514	+	0.0248044i
$16$		0			0
$17$	87.0444			1.24184			0.620922	−	0.783872i	$-0.286758\pi$
$17$	87.0444			1.24184			0.620922	+	0.783872i	$0.286758\pi$
$18$		0			0
$19$	66.5327			0.803350			0.401675	−	0.915782i	$-0.368428\pi$
$19$	66.5327			0.803350			0.401675	+	0.915782i	$0.368428\pi$
$20$		0			0
$21$	−11.6929	+	34.4423i	−0.121505	+	0.357902i
$22$		0			0
$23$	21.4225	+	37.1049i	0.194213	+	0.336387i	0.946642	−	0.322286i	$-0.104451\pi$
$23$	21.4225	+	37.1049i	0.194213	+	0.336387i	−0.752429	+	0.658673i	$0.771118\pi$
$24$		0			0
$25$	62.4320	−	108.135i	0.499456	−	0.865083i
$26$		0			0
$27$	116.660	−	77.9321i	0.831528	−	0.555483i
$28$		0			0
$29$	−48.3348	+	83.7183i	−0.309502	+	0.536072i	−0.978253	−	0.207413i	$-0.933496\pi$
$29$	−48.3348	+	83.7183i	−0.309502	+	0.536072i	0.668752	+	0.743486i	$0.266829\pi$
$30$		0			0
$31$	−11.7252	−	20.3086i	−0.0679323	−	0.117662i	0.830059	−	0.557676i	$-0.188307\pi$
$31$	−11.7252	−	20.3086i	−0.0679323	−	0.117662i	−0.897991	+	0.440014i	$0.854974\pi$
$32$		0			0
$33$	53.8183	−	158.525i	0.283896	−	0.836234i
$34$		0			0
$35$	−2.58192			−0.0124693
$36$		0			0
$37$	−147.986			−0.657535			−0.328767	−	0.944411i	$-0.606633\pi$
$37$	−147.986			−0.657535			−0.328767	+	0.944411i	$0.606633\pi$
$38$		0			0
$39$	31.7010	+	36.1506i	0.130159	+	0.148429i
$40$		0			0
$41$	−12.7866	−	22.1471i	−0.0487058	−	0.0843609i	0.840645	−	0.541587i	$-0.182176\pi$
$41$	−12.7866	−	22.1471i	−0.0487058	−	0.0843609i	−0.889350	+	0.457226i	$0.848843\pi$
$42$		0			0
$43$	11.0164	−	19.0809i	0.0390693	−	0.0676700i	−0.845830	−	0.533453i	$-0.820894\pi$
$43$	11.0164	−	19.0809i	0.0390693	−	0.0676700i	0.884899	+	0.465783i	$0.154227\pi$
$44$		0			0
$45$	7.90046	+	6.06312i	0.0261718	+	0.0200852i
$46$		0			0
$47$	−54.6744	+	94.6988i	−0.169683	+	0.293899i	−0.938308	−	0.345800i	$-0.887608\pi$
$47$	−54.6744	+	94.6988i	−0.169683	+	0.293899i	0.768626	+	0.639699i	$0.220941\pi$
$48$		0			0
$49$	−24.5000	−	42.4352i	−0.0714286	−	0.123718i
$50$		0			0
$51$	443.608	−	88.2230i	1.21799	−	0.242229i
$52$		0			0
$53$	328.433			0.851204			0.425602	−	0.904911i	$-0.360062\pi$
$53$	328.433			0.851204			0.425602	+	0.904911i	$0.360062\pi$
$54$		0			0
$55$	11.8836			0.0291344
$56$		0			0
$57$	339.074	−	67.4336i	0.787919	−	0.156698i
$58$		0			0
$59$	194.501	+	336.885i	0.429184	+	0.743369i	0.996801	−	0.0799241i	$-0.0254678\pi$
$59$	194.501	+	336.885i	0.429184	+	0.743369i	−0.567617	+	0.823293i	$0.692134\pi$
$60$		0			0
$61$	183.696	−	318.171i	0.385572	−	0.667831i	−0.606276	−	0.795254i	$-0.707337\pi$
$61$	183.696	−	318.171i	0.385572	−	0.667831i	0.991848	+	0.127423i	$0.0406707\pi$
$62$		0			0
$63$	−24.6826	+	187.381i	−0.0493605	+	0.374727i
$64$		0			0
$65$	−1.70652	+	2.95577i	−0.00325642	+	0.00564028i
$66$		0			0
$67$	−239.963	−	415.629i	−0.437555	−	0.757868i	0.559945	−	0.828530i	$-0.310822\pi$
$67$	−239.963	−	415.629i	−0.437555	−	0.757868i	−0.997500	+	0.0706620i	$0.977489\pi$
$68$		0			0
$69$	146.784	+	167.387i	0.256097	+	0.292043i
$70$		0			0
$71$	−186.194			−0.311228			−0.155614	−	0.987818i	$-0.549736\pi$
$71$	−186.194			−0.311228			−0.155614	+	0.987818i	$0.549736\pi$
$72$		0			0
$73$	−722.479			−1.15835			−0.579177	−	0.815202i	$-0.696626\pi$
$73$	−722.479			−1.15835			−0.579177	+	0.815202i	$0.696626\pi$
$74$		0			0
$75$	208.575	−	614.372i	0.321123	−	0.945888i
$76$		0			0
$77$	112.764	+	195.314i	0.166892	+	0.289066i
$78$		0			0
$79$	−87.2813	+	151.176i	−0.124303	+	0.215299i	−0.921460	−	0.388473i	$-0.873003\pi$
$79$	−87.2813	+	151.176i	−0.124303	+	0.215299i	0.797157	+	0.603772i	$0.206336\pi$
$80$		0			0
$81$	515.553	−	515.409i	0.707206	−	0.707008i
$82$		0			0
$83$	−455.339	+	788.670i	−0.602168	+	1.04298i	0.390325	+	0.920677i	$0.372363\pi$
$83$	−455.339	+	788.670i	−0.602168	+	1.04298i	−0.992492	+	0.122307i	$0.960971\pi$
$84$		0			0
$85$	16.0530	+	27.8046i	0.0204846	+	0.0354804i
$86$		0			0
$87$	−161.479	+	475.647i	−0.198993	+	0.586146i
$88$		0			0
$89$	592.104			0.705201			0.352600	−	0.935774i	$-0.385298\pi$
$89$	592.104			0.705201			0.352600	+	0.935774i	$0.385298\pi$
$90$		0			0
$91$	−64.7728			−0.0746158
$92$		0			0
$93$	−80.3390	−	91.6155i	−0.0895781	−	0.102151i
$94$		0			0
$95$	12.2702	+	21.2526i	0.0132515	+	0.0229523i
$96$		0			0
$97$	−604.703	+	1047.38i	−0.632972	+	1.09634i	0.353969	+	0.935257i	$0.384832\pi$
$97$	−604.703	+	1047.38i	−0.632972	+	1.09634i	−0.986941	+	0.161082i	$0.948501\pi$
$98$		0			0
$99$	113.605	−	862.447i	0.115330	−	0.875547i
$100$		0			0
$101$	−851.737	+	1475.25i	−0.839119	+	1.45340i	0.0515130	+	0.998672i	$0.483596\pi$
$101$	−851.737	+	1475.25i	−0.839119	+	1.45340i	−0.890632	+	0.454725i	$0.849738\pi$
$102$		0			0
$103$	−1001.08	−	1733.91i	−0.957660	−	1.65872i	−0.728161	−	0.685407i	$-0.759624\pi$
$103$	−1001.08	−	1733.91i	−0.957660	−	1.65872i	−0.229499	−	0.973309i	$-0.573709\pi$
$104$		0			0
$105$	−13.1584	+	2.61689i	−0.0122298	+	0.00243221i
$106$		0			0
$107$	−1197.02			−1.08150			−0.540751	−	0.841183i	$-0.681860\pi$
$107$	−1197.02			−1.08150			−0.540751	+	0.841183i	$0.681860\pi$
$108$		0			0
$109$	−556.035			−0.488610			−0.244305	−	0.969698i	$-0.578560\pi$
$109$	−556.035			−0.488610			−0.244305	+	0.969698i	$0.578560\pi$
$110$		0			0
$111$	−754.189	+	149.990i	−0.644905	+	0.128256i
$112$		0			0
$113$	446.270	+	772.962i	0.371518	+	0.643488i	0.989799	−	0.142469i	$-0.0455040\pi$
$113$	446.270	+	772.962i	0.371518	+	0.643488i	−0.618281	+	0.785957i	$0.712171\pi$
$114$		0			0
$115$	−7.90162	+	13.6860i	−0.00640722	+	0.0110976i
$116$		0			0
$117$	198.199	+	152.106i	0.156611	+	0.120189i
$118$		0			0
$119$	−304.655	+	527.678i	−0.234687	+	0.406489i
$120$		0			0
$121$	146.487	+	253.723i	0.110058	+	0.190626i
$122$		0			0
$123$	−87.6121	−	99.9096i	−0.0642254	−	0.0732402i
$124$		0			0
$125$	92.1614			0.0659453
$126$		0			0
$127$	−2702.61			−1.88833			−0.944164	−	0.329476i	$-0.893128\pi$
$127$	−2702.61			−1.88833			−0.944164	+	0.329476i	$0.893128\pi$
$128$		0			0
$129$	36.8039	−	108.408i	0.0251194	−	0.0739909i
$130$		0			0
$131$	−658.242	−	1140.11i	−0.439014	−	0.760395i	0.558600	−	0.829437i	$-0.311339\pi$
$131$	−658.242	−	1140.11i	−0.439014	−	0.760395i	−0.997614	+	0.0690428i	$0.978005\pi$
$132$		0			0
$133$	−232.864	+	403.333i	−0.151819	+	0.262958i
$134$		0			0
$135$	46.4087	+	22.8923i	0.0295869	+	0.0145945i
$136$		0			0
$137$	−1197.55	+	2074.22i	−0.746816	+	1.29352i	0.202526	+	0.979277i	$0.435085\pi$
$137$	−1197.55	+	2074.22i	−0.746816	+	1.29352i	−0.949342	+	0.314246i	$0.898248\pi$
$138$		0			0
$139$	−1373.34	−	2378.69i	−0.838021	−	1.45149i	−0.891547	−	0.452928i	$-0.850379\pi$
$139$	−1373.34	−	2378.69i	−0.838021	−	1.45149i	0.0535264	−	0.998566i	$-0.482954\pi$
$140$		0			0
$141$	−182.658	+	538.033i	−0.109097	+	0.321351i
$142$		0			0
$143$	298.125			0.174339
$144$		0			0
$145$	−35.6562			−0.0204213
$146$		0			0
$147$	−167.870	−	191.433i	−0.0941885	−	0.107409i
$148$		0			0
$149$	870.416	+	1507.60i	0.478572	+	0.828911i	0.999698	−	0.0245684i	$-0.00782114\pi$
$149$	870.416	+	1507.60i	0.478572	+	0.828911i	−0.521126	+	0.853480i	$0.674488\pi$
$150$		0			0
$151$	−481.764	+	834.439i	−0.259638	+	0.449707i	−0.966145	−	0.258000i	$-0.916937\pi$
$151$	−481.764	+	834.439i	−0.259638	+	0.449707i	0.706507	+	0.707706i	$0.250270\pi$
$152$		0			0
$153$	2171.36	−	899.230i	1.14735	−	0.475153i
$154$		0			0
$155$	4.32478	−	7.49074i	0.00224113	−	0.00388175i
$156$		0			0
$157$	373.098	+	646.224i	0.189659	+	0.328499i	0.945136	−	0.326676i	$-0.105928\pi$
$157$	373.098	+	646.224i	0.189659	+	0.328499i	−0.755478	+	0.655174i	$0.772595\pi$
$158$		0			0
$159$	1673.81	−	332.881i	0.834854	−	0.166032i
$160$		0			0
$161$	−299.915			−0.146811
$162$		0			0
$163$	−810.012			−0.389233			−0.194617	−	0.980879i	$-0.562346\pi$
$163$	−810.012			−0.389233			−0.194617	+	0.980879i	$0.562346\pi$
$164$		0			0
$165$	60.5631	−	12.0446i	0.0285748	−	0.00568283i
$166$		0			0
$167$	−112.694	−	195.191i	−0.0522186	−	0.0904452i	0.838735	−	0.544540i	$-0.183296\pi$
$167$	−112.694	−	195.191i	−0.0522186	−	0.0904452i	−0.890953	+	0.454095i	$0.849963\pi$
$168$		0			0
$169$	1055.69	−	1828.51i	0.480514	−	0.832274i
$170$		0			0
$171$	1659.69	−	687.330i	0.742220	−	0.307377i
$172$		0			0
$173$	975.759	−	1690.06i	0.428819	−	0.742736i	−0.567950	−	0.823063i	$-0.692263\pi$
$173$	975.759	−	1690.06i	0.428819	−	0.742736i	0.996769	+	0.0803275i	$0.0255966\pi$
$174$		0			0
$175$	437.024	+	756.947i	0.188777	+	0.326971i
$176$		0			0
$177$	1332.69	+	1519.75i	0.565939	+	0.645375i
$178$		0			0
$179$	928.859			0.387856			0.193928	−	0.981016i	$-0.437877\pi$
$179$	928.859			0.387856			0.193928	+	0.981016i	$0.437877\pi$
$180$		0			0
$181$	2136.89			0.877537			0.438768	−	0.898600i	$-0.355415\pi$
$181$	2136.89			0.877537			0.438768	+	0.898600i	$0.355415\pi$
$182$		0			0
$183$	613.700	−	1807.70i	0.247902	−	0.730211i
$184$		0			0
$185$	−27.2921	−	47.2713i	−0.0108462	−	0.0187862i
$186$		0			0
$187$	1402.22	−	2428.71i	0.548343	−	0.949758i
$188$		0			0
$189$	64.1277	+	979.977i	0.0246805	+	0.377158i
$190$		0			0
$191$	−1805.36	+	3126.97i	−0.683933	+	1.18461i	0.289838	+	0.957076i	$0.406399\pi$
$191$	−1805.36	+	3126.97i	−0.683933	+	1.18461i	−0.973771	+	0.227531i	$0.926935\pi$
$192$		0			0
$193$	1053.37	+	1824.50i	0.392868	+	0.680467i	0.992827	−	0.119564i	$-0.0381496\pi$
$193$	1053.37	+	1824.50i	0.392868	+	0.680467i	−0.599958	+	0.800031i	$0.704816\pi$
$194$		0			0
$195$	−5.70120	+	16.7933i	−0.00209370	+	0.00616713i
$196$		0			0
$197$	3911.47			1.41462			0.707311	−	0.706902i	$-0.249908\pi$
$197$	3911.47			1.41462			0.707311	+	0.706902i	$0.249908\pi$
$198$		0			0
$199$	−262.394			−0.0934705			−0.0467353	−	0.998907i	$-0.514882\pi$
$199$	−262.394			−0.0934705			−0.0467353	+	0.998907i	$0.514882\pi$
$200$		0			0
$201$	−1644.19	−	1874.97i	−0.576977	−	0.657963i
$202$		0			0
$203$	−338.343	−	586.028i	−0.116981	−	0.202616i
$204$		0			0
$205$	4.71631	−	8.16888i	0.00160683	−	0.00278312i
$206$		0			0
$207$	917.715	+	704.289i	0.308143	+	0.236481i
$208$		0			0
$209$	1071.79	−	1856.39i	0.354723	−	0.614399i
$210$		0			0
$211$	43.0493	+	74.5635i	0.0140457	+	0.0243278i	0.872963	−	0.487787i	$-0.162196\pi$
$211$	43.0493	+	74.5635i	0.0140457	+	0.0243278i	−0.858917	+	0.512115i	$0.828862\pi$
$212$		0			0
$213$	−948.911	+	188.716i	−0.305250	+	0.0607070i
$214$		0			0
$215$	8.12669			0.00257784
$216$		0			0
$217$	164.152			0.0513520
$218$		0			0
$219$	−3682.00	+	732.262i	−1.13610	+	0.225944i
$220$		0			0
$221$	402.722	+	697.535i	0.122579	+	0.212314i
$222$		0			0
$223$	1908.94	−	3306.37i	0.573237	−	0.992875i	−0.422994	−	0.906132i	$-0.639021\pi$
$223$	1908.94	−	3306.37i	0.573237	−	0.992875i	0.996231	−	0.0867425i	$-0.0276457\pi$
$224$		0			0
$225$	440.280	−	3342.45i	0.130453	−	0.990357i
$226$		0			0
$227$	58.2326	−	100.862i	0.0170266	−	0.0294909i	−0.857387	−	0.514673i	$-0.827913\pi$
$227$	58.2326	−	100.862i	0.0170266	−	0.0294909i	0.874413	+	0.485182i	$0.161247\pi$
$228$		0			0
$229$	304.731	+	527.810i	0.0879354	+	0.152309i	0.906638	−	0.421909i	$-0.138640\pi$
$229$	304.731	+	527.810i	0.0879354	+	0.152309i	−0.818703	+	0.574217i	$0.805306\pi$
$230$		0			0
$231$	772.645	+	881.095i	0.220071	+	0.250960i
$232$		0			0
$233$	5153.48			1.44900			0.724498	−	0.689277i	$-0.242072\pi$
$233$	5153.48			1.44900			0.724498	+	0.689277i	$0.242072\pi$
$234$		0			0
$235$	−40.3329			−0.0111959
$236$		0			0
$237$	−291.593	+	858.907i	−0.0799199	+	0.235409i
$238$		0			0
$239$	−1830.64	−	3170.77i	−0.495458	−	0.858158i	0.504529	−	0.863395i	$-0.331666\pi$
$239$	−1830.64	−	3170.77i	−0.495458	−	0.858158i	−0.999986	+	0.00523701i	$0.998333\pi$
$240$		0			0
$241$	−2180.05	+	3775.97i	−0.582696	+	1.00926i	0.412463	+	0.910974i	$0.364669\pi$
$241$	−2180.05	+	3775.97i	−0.582696	+	1.00926i	−0.995158	+	0.0982840i	$0.968665\pi$
$242$		0			0
$243$	2105.05	−	3149.23i	0.555716	−	0.831372i
$244$		0			0
$245$	9.03674	−	15.6521i	0.00235647	−	0.00408153i
$246$		0			0
$247$	307.822	+	533.163i	0.0792966	+	0.137346i
$248$		0			0
$249$	−1521.21	+	4480.84i	−0.387161	+	1.14041i
$250$		0			0
$251$	603.942			0.151874			0.0759372	−	0.997113i	$-0.475805\pi$
$251$	603.942			0.151874			0.0759372	+	0.997113i	$0.475805\pi$
$252$		0			0
$253$	1380.40			0.343023
$254$		0			0
$255$	109.993	+	125.432i	0.0270118	+	0.0308032i
$256$		0			0
$257$	−3729.10	−	6458.99i	−0.905117	−	1.56771i	−0.820761	−	0.571272i	$-0.806450\pi$
$257$	−3729.10	−	6458.99i	−0.905117	−	1.56771i	−0.0843559	−	0.996436i	$-0.526883\pi$
$258$		0			0
$259$	517.952	−	897.119i	0.124262	−	0.215229i
$260$		0			0
$261$	−340.865	+	2587.72i	−0.0808391	+	0.613702i
$262$		0			0
$263$	−2379.97	+	4122.23i	−0.558005	+	0.966494i	0.439657	+	0.898166i	$0.355100\pi$
$263$	−2379.97	+	4122.23i	−0.558005	+	0.966494i	−0.997663	+	0.0683283i	$0.978233\pi$
$264$		0			0
$265$	60.5707	+	104.912i	0.0140409	+	0.0243195i
$266$		0			0
$267$	3017.57	−	600.121i	0.691655	−	0.137554i
$268$		0			0
$269$	3184.34			0.721757			0.360878	−	0.932613i	$-0.382477\pi$
$269$	3184.34			0.721757			0.360878	+	0.932613i	$0.382477\pi$
$270$		0			0
$271$	5434.12			1.21808			0.609039	−	0.793140i	$-0.291555\pi$
$271$	5434.12			1.21808			0.609039	+	0.793140i	$0.291555\pi$
$272$		0			0
$273$	−330.105	+	65.6499i	−0.0731826	+	0.0145543i
$274$		0			0
$275$	−2011.46	−	3483.95i	−0.441075	−	0.763964i
$276$		0			0
$277$	−4311.82	+	7468.29i	−0.935278	+	1.61995i	−0.161141	+	0.986931i	$0.551517\pi$
$277$	−4311.82	+	7468.29i	−0.935278	+	1.61995i	−0.774137	+	0.633018i	$0.781816\pi$
$278$		0			0
$279$	−502.291	−	385.478i	−0.107783	−	0.0827166i
$280$		0			0
$281$	934.204	−	1618.09i	0.198327	−	0.343513i	−0.749659	−	0.661824i	$-0.769782\pi$
$281$	934.204	−	1618.09i	0.198327	−	0.343513i	0.947986	+	0.318312i	$0.103116\pi$
$282$		0			0
$283$	−203.460	−	352.403i	−0.0427365	−	0.0740219i	0.843866	−	0.536554i	$-0.180274\pi$
$283$	−203.460	−	352.403i	−0.0427365	−	0.0740219i	−0.886602	+	0.462532i	$0.846941\pi$
$284$		0			0
$285$	84.0733	+	95.8740i	0.0174739	+	0.0199266i
$286$		0			0
$287$	179.013			0.0368181
$288$		0			0
$289$	2663.72			0.542178
$290$		0			0
$291$	−2020.22	+	5950.68i	−0.406966	+	1.19875i
$292$		0			0
$293$	−3843.57	−	6657.25i	−0.766360	−	1.32738i	−0.939524	−	0.342482i	$-0.888732\pi$
$293$	−3843.57	−	6657.25i	−0.766360	−	1.32738i	0.173164	−	0.984893i	$-0.444601\pi$
$294$		0			0
$295$	−71.7410	+	124.259i	−0.0141591	+	0.0245242i
$296$		0			0
$297$	−295.156	−	4510.47i	−0.0576657	−	0.881226i
$298$		0			0
$299$	−198.228	+	343.341i	−0.0383406	+	0.0664078i
$300$		0			0
$301$	77.1146	+	133.566i	0.0147668	+	0.0255769i
$302$		0			0
$303$	−2845.52	+	8381.67i	−0.539508	+	1.58916i
$304$		0			0
$305$	135.511			0.0254405
$306$		0			0
$307$	5629.82			1.04661			0.523307	−	0.852144i	$-0.324698\pi$
$307$	5629.82			1.04661			0.523307	+	0.852144i	$0.324698\pi$
$308$		0			0
$309$	−6859.22	−	7822.00i	−1.26281	−	1.44006i
$310$		0			0
$311$	411.333	+	712.450i	0.0749986	+	0.129901i	0.901086	−	0.433641i	$-0.142771\pi$
$311$	411.333	+	712.450i	0.0749986	+	0.129901i	−0.826087	+	0.563542i	$0.809438\pi$
$312$		0			0
$313$	3290.92	−	5700.04i	0.594293	−	1.02935i	−0.399354	−	0.916797i	$-0.630765\pi$
$313$	3290.92	−	5700.04i	0.594293	−	1.02935i	0.993646	−	0.112548i	$-0.0359013\pi$
$314$		0			0
$315$	−64.4073	+	26.6731i	−0.0115204	+	0.00477098i
$316$		0			0
$317$	−368.356	+	638.012i	−0.0652649	+	0.113042i	−0.896811	−	0.442413i	$-0.854123\pi$
$317$	−368.356	+	638.012i	−0.0652649	+	0.113042i	0.831547	+	0.555455i	$0.187456\pi$
$318$		0			0
$319$	1557.27	+	2697.27i	0.273324	+	0.473411i
$320$		0			0
$321$	−6100.45	+	1213.23i	−1.06073	+	0.210953i
$322$		0			0
$323$	5791.30			0.997636
$324$		0			0
$325$	1155.40			0.197200
$326$		0			0
$327$	−2833.74	+	563.564i	−0.479225	+	0.0953063i
$328$		0			0
$329$	−382.721	−	662.892i	−0.0641340	−	0.111083i
$330$		0			0
$331$	−945.921	+	1638.38i	−0.157077	+	0.272066i	−0.933813	−	0.357760i	$-0.883540\pi$
$331$	−945.921	+	1638.38i	−0.157077	+	0.272066i	0.776736	+	0.629826i	$0.216874\pi$
$332$		0			0
$333$	−3691.59	+	1528.80i	−0.607500	+	0.251585i
$334$		0			0
$335$	88.5096	−	153.303i	0.0144352	−	0.0250025i
$336$		0			0
$337$	−39.6888	−	68.7430i	−0.00641539	−	0.0111118i	0.862800	−	0.505546i	$-0.168709\pi$
$337$	−39.6888	−	68.7430i	−0.00641539	−	0.0111118i	−0.869215	+	0.494434i	$0.835375\pi$
$338$		0			0
$339$	3057.78	+	3486.97i	0.489898	+	0.558661i
$340$		0			0
$341$	−755.532			−0.119983
$342$		0			0
$343$	343.000			0.0539949
$344$		0			0
$345$	−26.3981	+	77.7572i	−0.00411949	+	0.0121342i
$346$		0			0
$347$	284.152	+	492.166i	0.0439599	+	0.0761408i	0.887168	−	0.461446i	$-0.152669\pi$
$347$	284.152	+	492.166i	0.0439599	+	0.0761408i	−0.843208	+	0.537587i	$0.819336\pi$
$348$		0			0
$349$	75.3608	−	130.529i	0.0115587	−	0.0200202i	−0.860188	−	0.509977i	$-0.829654\pi$
$349$	75.3608	−	130.529i	0.0115587	−	0.0200202i	0.871747	+	0.489957i	$0.162987\pi$
$350$		0			0
$351$	1164.26	+	574.300i	0.177047	+	0.0873329i
$352$		0			0
$353$	423.706	−	733.880i	0.0638855	−	0.110653i	−0.832314	−	0.554305i	$-0.812984\pi$
$353$	423.706	−	733.880i	0.0638855	−	0.110653i	0.896199	+	0.443652i	$0.146317\pi$
$354$		0			0
$355$	−34.3386	−	59.4762i	−0.00513381	−	0.00889202i
$356$		0			0
$357$	−1017.81	+	2998.01i	−0.150891	+	0.444458i
$358$		0			0
$359$	−7460.57			−1.09681			−0.548404	−	0.836214i	$-0.684764\pi$
$359$	−7460.57			−1.09681			−0.548404	+	0.836214i	$0.684764\pi$
$360$		0			0
$361$	−2432.40			−0.354629
$362$		0			0
$363$	1003.71	+	1144.59i	0.145127	+	0.165497i
$364$		0			0
$365$	−133.242	−	230.782i	−0.0191074	−	0.0330950i
$366$		0			0
$367$	−442.984	+	767.271i	−0.0630070	+	0.109131i	−0.895808	−	0.444441i	$-0.853402\pi$
$367$	−442.984	+	767.271i	−0.0630070	+	0.109131i	0.832801	+	0.553572i	$0.186736\pi$
$368$		0			0
$369$	−547.764	−	420.375i	−0.0772777	−	0.0593058i
$370$		0			0
$371$	−1149.52	+	1991.02i	−0.160862	+	0.278622i
$372$		0			0
$373$	5758.79	+	9974.52i	0.799407	+	1.38461i	0.920003	+	0.391912i	$0.128186\pi$
$373$	5758.79	+	9974.52i	0.799407	+	1.38461i	−0.120596	+	0.992702i	$0.538480\pi$
$374$		0			0
$375$	469.686	−	93.4093i	0.0646787	−	0.0128630i
$376$		0			0
$377$	−894.509			−0.122200
$378$		0			0
$379$	−7392.74			−1.00195			−0.500975	−	0.865462i	$-0.667025\pi$
$379$	−7392.74			−1.00195			−0.500975	+	0.865462i	$0.667025\pi$
$380$		0			0
$381$	−13773.4	+	2739.20i	−1.85206	+	0.368330i
$382$		0			0
$383$	−5562.06	−	9633.78i	−0.742058	−	1.28528i	−0.951557	−	0.307473i	$-0.900517\pi$
$383$	−5562.06	−	9633.78i	−0.742058	−	1.28528i	0.209499	−	0.977809i	$-0.432817\pi$
$384$		0			0
$385$	−41.5928	+	72.0408i	−0.00550588	+	0.00953646i
$386$		0			0
$387$	77.6892	−	589.789i	0.0102046	−	0.0774694i
$388$		0			0
$389$	435.654	−	754.574i	0.0567828	−	0.0983507i	−0.836237	−	0.548369i	$-0.815249\pi$
$389$	435.654	−	754.574i	0.0567828	−	0.0983507i	0.893020	+	0.450018i	$0.148582\pi$
$390$		0			0
$391$	1864.71	+	3229.77i	0.241183	+	0.417741i
$392$		0			0
$393$	−4510.17	−	5143.23i	−0.578901	−	0.660157i
$394$		0			0
$395$	−64.3868			−0.00820165
$396$		0			0
$397$	−2085.84			−0.263691			−0.131845	−	0.991270i	$-0.542090\pi$
$397$	−2085.84			−0.263691			−0.131845	+	0.991270i	$0.542090\pi$
$398$		0			0
$399$	−777.963	+	2291.54i	−0.0976112	+	0.287520i
$400$		0			0
$401$	−4756.69	−	8238.83i	−0.592364	−	1.02600i	−0.993913	−	0.110166i	$-0.964862\pi$
$401$	−4756.69	−	8238.83i	−0.592364	−	1.02600i	0.401550	−	0.915837i	$-0.368472\pi$
$402$		0			0
$403$	108.496	−	187.920i	0.0134108	−	0.0232282i
$404$		0			0
$405$	259.717	+	69.6300i	0.0318653	+	0.00854306i
$406$		0			0
$407$	−2383.94	+	4129.10i	−0.290338	+	0.502880i
$408$		0			0
$409$	1619.04	+	2804.27i	0.195737	+	0.339027i	0.947142	−	0.320815i	$-0.103957\pi$
$409$	1619.04	+	2804.27i	0.195737	+	0.339027i	−0.751405	+	0.659842i	$0.770623\pi$
$410$		0			0
$411$	−4000.83	+	11784.7i	−0.480162	+	1.41435i
$412$		0			0
$413$	−2723.01			−0.324433
$414$		0			0
$415$	−335.900			−0.0397318
$416$		0			0
$417$	−9409.89	−	10730.7i	−1.10505	−	1.26015i
$418$		0			0
$419$	−5467.96	−	9470.79i	−0.637536	−	1.10424i	−0.985972	−	0.166911i	$-0.946621\pi$
$419$	−5467.96	−	9470.79i	−0.637536	−	1.10424i	0.348436	−	0.937332i	$-0.386713\pi$
$420$		0			0
$421$	−8173.08	+	14156.2i	−0.946156	+	1.63879i	−0.192736	+	0.981251i	$0.561736\pi$
$421$	−8173.08	+	14156.2i	−0.946156	+	1.63879i	−0.753420	+	0.657540i	$0.771597\pi$
$422$		0			0
$423$	−385.573	+	2927.13i	−0.0443196	+	0.336459i
$424$		0			0
$425$	5434.35	−	9412.57i	0.620247	−	1.07430i
$426$		0			0
$427$	1285.87	+	2227.20i	0.145733	+	0.252416i
$428$		0			0
$429$	1519.35	−	302.162i	0.170990	−	0.0340059i
$430$		0			0
$431$	7323.52			0.818472			0.409236	−	0.912429i	$-0.365795\pi$
$431$	7323.52			0.818472			0.409236	+	0.912429i	$0.365795\pi$
$432$		0			0
$433$	92.7438			0.0102933			0.00514663	−	0.999987i	$-0.498362\pi$
$433$	92.7438			0.0102933			0.00514663	+	0.999987i	$0.498362\pi$
$434$		0			0
$435$	−181.716	+	36.1390i	−0.0200290	+	0.00398330i
$436$		0			0
$437$	1425.30	+	2468.69i	0.156021	+	0.270237i
$438$		0			0
$439$	7589.57	−	13145.5i	0.825127	−	1.42916i	−0.0766957	−	0.997055i	$-0.524437\pi$
$439$	7589.57	−	13145.5i	0.825127	−	1.42916i	0.901822	−	0.432107i	$-0.142230\pi$
$440$		0			0
$441$	−1049.55	−	805.465i	−0.113330	−	0.0869739i
$442$		0			0
$443$	−5045.05	+	8738.28i	−0.541078	+	0.937174i	0.457765	+	0.889073i	$0.348650\pi$
$443$	−5045.05	+	8738.28i	−0.541078	+	0.937174i	−0.998842	+	0.0481009i	$0.984683\pi$
$444$		0			0
$445$	109.198	+	189.136i	0.0116325	+	0.0201481i
$446$		0			0
$447$	5963.96	+	6801.07i	0.631064	+	0.719641i
$448$		0			0
$449$	17180.0			1.80573			0.902866	−	0.429922i	$-0.141459\pi$
$449$	17180.0			1.80573			0.902866	+	0.429922i	$0.141459\pi$
$450$		0			0
$451$	−823.931			−0.0860252
$452$		0			0
$453$	−1609.50	+	4740.88i	−0.166933	+	0.491713i
$454$		0			0
$455$	−11.9456	−	20.6904i	−0.00123081	−	0.00213183i
$456$		0			0
$457$	1757.85	−	3044.68i	0.179931	−	0.311650i	−0.761925	−	0.647665i	$-0.775746\pi$
$457$	1757.85	−	3044.68i	0.179931	−	0.311650i	0.941857	+	0.336014i	$0.109079\pi$
$458$		0			0
$459$	10154.6	−	6783.55i	1.03263	−	0.689824i
$460$		0			0
$461$	−1382.37	+	2394.34i	−0.139661	+	0.241899i	−0.927368	−	0.374150i	$-0.877934\pi$
$461$	−1382.37	+	2394.34i	−0.139661	+	0.241899i	0.787708	+	0.616049i	$0.211268\pi$
$462$		0			0
$463$	−3398.82	−	5886.93i	−0.341159	−	0.590904i	0.643489	−	0.765455i	$-0.277486\pi$
$463$	−3398.82	−	5886.93i	−0.341159	−	0.590904i	−0.984648	+	0.174551i	$0.944153\pi$
$464$		0			0
$465$	14.4484	−	42.5587i	0.00144092	−	0.00424433i
$466$		0			0
$467$	1709.04			0.169346			0.0846732	−	0.996409i	$-0.473015\pi$
$467$	1709.04			0.169346			0.0846732	+	0.996409i	$0.473015\pi$
$468$		0			0
$469$	3359.49			0.330761
$470$		0			0
$471$	2556.41	+	2915.23i	0.250091	+	0.285195i
$472$		0			0
$473$	−354.930	−	614.756i	−0.0345025	−	0.0597601i
$474$		0			0
$475$	4153.77	−	7194.54i	0.401238	−	0.694964i
$476$		0			0
$477$	8192.93	−	3392.95i	0.786432	−	0.325687i
$478$		0			0
$479$	−1449.25	+	2510.18i	−0.138242	+	0.239443i	−0.926831	−	0.375478i	$-0.877479\pi$
$479$	−1449.25	+	2510.18i	−0.138242	+	0.239443i	0.788589	+	0.614921i	$0.210812\pi$
$480$		0			0
$481$	−684.677	−	1185.90i	−0.0649035	−	0.112416i
$482$		0			0
$483$	−1528.47	+	303.976i	−0.143991	+	0.0286364i
$484$		0			0
$485$	−446.085			−0.0417643
$486$		0			0
$487$	11568.4			1.07642			0.538210	−	0.842811i	$-0.319101\pi$
$487$	11568.4			1.07642			0.538210	+	0.842811i	$0.319101\pi$
$488$		0			0
$489$	−4128.10	+	820.980i	−0.381757	+	0.0759223i
$490$		0			0
$491$	5226.96	+	9053.35i	0.480426	+	0.832123i	0.999748	−	0.0224563i	$-0.00714866\pi$
$491$	5226.96	+	9053.35i	0.480426	+	0.832123i	−0.519322	+	0.854579i	$0.673815\pi$
$492$		0			0
$493$	−4207.27	+	7287.21i	−0.384353	+	0.665719i
$494$		0			0
$495$	296.443	−	122.766i	0.0269174	−	0.0111474i
$496$		0			0
$497$	651.681	−	1128.74i	0.0588166	−	0.101873i
$498$		0			0
$499$	−3397.06	−	5883.87i	−0.304756	−	0.527852i	0.672451	−	0.740141i	$-0.265241\pi$
$499$	−3397.06	−	5883.87i	−0.304756	−	0.527852i	−0.977207	+	0.212289i	$0.931908\pi$
$500$		0			0
$501$	−772.161	−	880.543i	−0.0688575	−	0.0785224i
$502$		0			0
$503$	386.796			0.0342871			0.0171435	−	0.999853i	$-0.494543\pi$
$503$	386.796			0.0342871			0.0171435	+	0.999853i	$0.494543\pi$
$504$		0			0
$505$	−628.320			−0.0553661
$506$		0			0
$507$	3526.89	−	10388.7i	0.308944	−	0.910015i
$508$		0			0
$509$	1412.26	+	2446.10i	0.122981	+	0.213009i	0.920942	−	0.389700i	$-0.127421\pi$
$509$	1412.26	+	2446.10i	0.122981	+	0.213009i	−0.797961	+	0.602709i	$0.794088\pi$
$510$		0			0
$511$	2528.68	−	4379.80i	0.218908	−	0.379160i
$512$		0			0
$513$	7761.71	−	5185.03i	0.668008	−	0.446247i
$514$		0			0
$515$	369.243	−	639.548i	0.0315938	−	0.0547221i
$516$		0			0
$517$	1761.52	+	3051.05i	0.149848	+	0.259545i
$518$		0			0
$519$	3259.86	−	9602.13i	0.275707	−	0.812113i
$520$		0			0
$521$	6472.10			0.544237			0.272119	−	0.962264i	$-0.412276\pi$
$521$	6472.10			0.544237			0.272119	+	0.962264i	$0.412276\pi$
$522$		0			0
$523$	11260.3			0.941450			0.470725	−	0.882280i	$-0.343992\pi$
$523$	11260.3			0.941450			0.470725	+	0.882280i	$0.343992\pi$
$524$		0			0
$525$	2994.42	+	3414.72i	0.248928	+	0.283868i
$526$		0			0
$527$	−1020.61	−	1767.75i	−0.0843613	−	0.146118i
$528$		0			0
$529$	5165.65	−	8947.17i	0.424562	−	0.735364i
$530$		0			0
$531$	8332.18	+	6394.44i	0.680953	+	0.522589i
$532$		0			0
$533$	118.318	−	204.933i	0.00961525	−	0.0166541i
$534$		0			0
$535$	−220.759	−	382.366i	−0.0178397	−	0.0308993i
$536$		0			0
$537$	4733.79	−	941.436i	0.380406	−	0.0756536i
$538$		0			0
$539$	−1578.70			−0.126159
$540$		0			0
$541$	13109.7			1.04183			0.520913	−	0.853610i	$-0.325592\pi$
$541$	13109.7			1.04183			0.520913	+	0.853610i	$0.325592\pi$
$542$		0			0
$543$	10890.4	−	2165.83i	0.860681	−	0.171169i
$544$		0			0
$545$	−102.546	−	177.614i	−0.00805977	−	0.0139599i
$546$		0			0
$547$	−9005.60	+	15598.2i	−0.703933	+	1.21925i	0.263142	+	0.964757i	$0.415241\pi$
$547$	−9005.60	+	15598.2i	−0.703933	+	1.21925i	−0.967075	+	0.254491i	$0.918092\pi$
$548$		0			0
$549$	1295.46	−	9834.65i	0.100708	−	0.764540i
$550$		0			0
$551$	−3215.84	+	5570.00i	−0.248638	+	0.430654i
$552$		0			0
$553$	−610.969	−	1058.23i	−0.0469820	−	0.0813753i
$554$		0			0
$555$	−187.001	−	213.249i	−0.0143023	−	0.0163098i
$556$		0			0
$557$	7576.43			0.576344			0.288172	−	0.957579i	$-0.406953\pi$
$557$	7576.43			0.576344			0.288172	+	0.957579i	$0.406953\pi$
$558$		0			0
$559$	203.875			0.0154257
$560$		0			0
$561$	4684.58	−	13798.7i	0.352555	−	1.03847i
$562$		0			0
$563$	9514.47	+	16479.5i	0.712233	+	1.23362i	0.964017	+	0.265840i	$0.0856493\pi$
$563$	9514.47	+	16479.5i	0.712233	+	1.23362i	−0.251784	+	0.967783i	$0.581017\pi$
$564$		0			0
$565$	−164.605	+	285.104i	−0.0122566	+	0.0212291i
$566$		0			0
$567$	1320.06	+	4929.30i	0.0977733	+	0.365099i
$568$		0			0
$569$	11257.7	−	19498.8i	0.829430	−	1.43662i	−0.0690554	−	0.997613i	$-0.521999\pi$
$569$	11257.7	−	19498.8i	0.829430	−	1.43662i	0.898486	−	0.439003i	$-0.144668\pi$
$570$		0			0
$571$	−6659.01	−	11533.7i	−0.488040	−	0.845310i	0.511865	−	0.859066i	$-0.328955\pi$
$571$	−6659.01	−	11533.7i	−0.488040	−	0.845310i	−0.999905	+	0.0137554i	$0.995621\pi$
$572$		0			0
$573$	−6031.42	+	17765.9i	−0.439732	+	1.29526i
$574$		0			0
$575$	5349.80			0.388004
$576$		0			0
$577$	−23673.3			−1.70803			−0.854014	−	0.520251i	$-0.825838\pi$
$577$	−23673.3			−1.70803			−0.854014	+	0.520251i	$0.825838\pi$
$578$		0			0
$579$	7217.56	+	8230.63i	0.518051	+	0.590766i
$580$		0			0
$581$	−3187.37	−	5520.69i	−0.227598	−	0.394211i
$582$		0			0
$583$	5290.80	−	9163.94i	0.375853	−	0.650997i
$584$		0			0
$585$	−12.0346	+	91.3626i	−0.000850548	+	0.00645706i
$586$		0			0
$587$	−11960.4	+	20716.1i	−0.840988	+	1.45663i	0.0480722	+	0.998844i	$0.484692\pi$
$587$	−11960.4	+	20716.1i	−0.840988	+	1.45663i	−0.889060	+	0.457790i	$0.848641\pi$
$588$		0			0
$589$	−780.106	−	1351.18i	−0.0545734	−	0.0945238i
$590$		0			0
$591$	19934.2	−	3964.43i	1.38745	−	0.275931i
$592$		0			0
$593$	−17549.9			−1.21532			−0.607662	−	0.794196i	$-0.707893\pi$
$593$	−17549.9			−1.21532			−0.607662	+	0.794196i	$0.707893\pi$
$594$		0			0
$595$	−224.742			−0.0154849
$596$		0			0
$597$	−1337.25	+	265.947i	−0.0916751	+	0.0182320i
$598$		0			0
$599$	−4393.46	−	7609.70i	−0.299686	−	0.519072i	0.676378	−	0.736555i	$-0.263549\pi$
$599$	−4393.46	−	7609.70i	−0.299686	−	0.519072i	−0.976064	+	0.217483i	$0.930215\pi$
$600$		0			0
$601$	2483.40	−	4301.37i	0.168552	−	0.291941i	−0.769359	−	0.638817i	$-0.779424\pi$
$601$	2483.40	−	4301.37i	0.168552	−	0.291941i	0.937911	+	0.346876i	$0.112757\pi$
$602$		0			0
$603$	−10279.7	−	7889.06i	−0.694234	−	0.532782i
$604$		0			0
$605$	−54.0312	+	93.5848i	−0.00363088	+	0.00628887i
$606$		0			0
$607$	−2228.34	−	3859.60i	−0.149004	−	0.258083i	0.781855	−	0.623460i	$-0.214274\pi$
$607$	−2228.34	−	3859.60i	−0.149004	−	0.258083i	−0.930860	+	0.365377i	$0.880940\pi$
$608$		0			0
$609$	−2318.28	−	2643.68i	−0.154255	−	0.175907i
$610$		0			0
$611$	−1011.83			−0.0669957
$612$		0			0
$613$	−26168.3			−1.72419			−0.862093	−	0.506749i	$-0.830847\pi$
$613$	−26168.3			−1.72419			−0.862093	+	0.506749i	$0.830847\pi$
$614$		0			0
$615$	15.7564	−	46.4116i	0.00103311	−	0.00304308i
$616$		0			0
$617$	12892.9	+	22331.1i	0.841243	+	1.45708i	0.888844	+	0.458209i	$0.151509\pi$
$617$	12892.9	+	22331.1i	0.841243	+	1.45708i	−0.0476016	+	0.998866i	$0.515158\pi$
$618$		0			0
$619$	−1522.21	+	2636.54i	−0.0988413	+	0.171198i	−0.911205	−	0.411953i	$-0.864847\pi$
$619$	−1522.21	+	2636.54i	−0.0988413	+	0.171198i	0.812364	+	0.583151i	$0.198180\pi$
$620$		0			0
$621$	5390.82	+	2659.16i	0.348351	+	0.171833i
$622$		0			0
$623$	−2072.36	+	3589.44i	−0.133270	+	0.230831i
$624$		0			0
$625$	−7787.00	−	13487.5i	−0.498368	−	0.863199i
$626$		0			0
$627$	3580.68	−	10547.1i	0.228068	−	0.671788i
$628$		0			0
$629$	−12881.4			−0.816556
$630$		0			0
$631$	−22163.7			−1.39829			−0.699146	−	0.714979i	$-0.746436\pi$
$631$	−22163.7			−1.39829			−0.699146	+	0.714979i	$0.746436\pi$
$632$		0			0
$633$	294.967	+	336.369i	0.0185212	+	0.0211208i
$634$		0			0
$635$	−498.424	−	863.295i	−0.0311486	−	0.0539509i
$636$		0			0
$637$	226.705	−	392.664i	0.0141011	−	0.0244237i
$638$		0			0
$639$	−4644.71	+	1923.52i	−0.287546	+	0.119082i
$640$		0			0
$641$	−181.616	+	314.568i	−0.0111910	+	0.0193833i	−0.871567	−	0.490277i	$-0.836896\pi$
$641$	−181.616	+	314.568i	−0.0111910	+	0.0193833i	0.860376	+	0.509660i	$0.170229\pi$
$642$		0			0
$643$	2664.31	+	4614.71i	0.163406	+	0.283027i	0.936088	−	0.351766i	$-0.114419\pi$
$643$	2664.31	+	4614.71i	0.163406	+	0.283027i	−0.772682	+	0.634793i	$0.781085\pi$
$644$		0			0
$645$	41.4164	−	8.23673i	0.00252833	−	0.000502823i
$646$		0			0
$647$	11876.8			0.721679			0.360839	−	0.932628i	$-0.382490\pi$
$647$	11876.8			0.721679			0.360839	+	0.932628i	$0.382490\pi$
$648$		0			0
$649$	12533.0			0.758034
$650$		0			0
$651$	836.576	−	166.375i	0.0503656	−	0.0100165i
$652$		0			0
$653$	5967.73	+	10336.4i	0.357635	+	0.619441i	0.987565	−	0.157210i	$-0.0502500\pi$
$653$	5967.73	+	10336.4i	0.357635	+	0.619441i	−0.629931	+	0.776651i	$0.716917\pi$
$654$		0			0
$655$	242.790	−	420.525i	0.0144833	−	0.0250859i
$656$		0			0
$657$	−18022.6	+	7463.72i	−1.07021	+	0.443208i
$658$		0			0
$659$	−11728.4	+	20314.1i	−0.693282	+	1.20080i	0.277475	+	0.960733i	$0.410503\pi$
$659$	−11728.4	+	20314.1i	−0.693282	+	1.20080i	−0.970756	+	0.240066i	$0.922831\pi$
$660$		0			0
$661$	−3096.72	−	5363.68i	−0.182222	−	0.315617i	0.760415	−	0.649437i	$-0.224995\pi$
$661$	−3096.72	−	5363.68i	−0.182222	−	0.315617i	−0.942637	+	0.333820i	$0.891662\pi$
$662$		0			0
$663$	2759.39	+	3146.70i	0.161638	+	0.184326i
$664$		0			0
$665$	−171.782			−0.0100172
$666$		0			0
$667$	−4141.81			−0.240437
$668$		0			0
$669$	6377.45	−	18785.2i	0.368560	−	1.08562i
$670$		0			0
$671$	−5918.40	−	10251.0i	−0.340503	−	0.589768i
$672$		0			0
$673$	−10536.5	+	18249.8i	−0.603496	+	1.04529i	0.388791	+	0.921326i	$0.372893\pi$
$673$	−10536.5	+	18249.8i	−0.603496	+	1.04529i	−0.992287	+	0.123960i	$0.960441\pi$
$674$		0			0
$675$	−1143.89	−	17480.5i	−0.0652273	−	0.996780i
$676$		0			0
$677$	−12634.4	+	21883.3i	−0.717249	+	1.24231i	0.244837	+	0.969564i	$0.421266\pi$
$677$	−12634.4	+	21883.3i	−0.717249	+	1.24231i	−0.962086	+	0.272747i	$0.912068\pi$
$678$		0			0
$679$	−4232.92	−	7331.63i	−0.239241	−	0.414377i
$680$		0			0
$681$	194.546	−	573.048i	0.0109472	−	0.0322456i
$682$		0			0
$683$	10047.8			0.562909			0.281454	−	0.959575i	$-0.409183\pi$
$683$	10047.8			0.562909			0.281454	+	0.959575i	$0.409183\pi$
$684$		0			0
$685$	−883.425			−0.0492758
$686$		0			0
$687$	2087.97	+	2381.04i	0.115955	+	0.132231i
$688$		0			0
$689$	1519.54	+	2631.92i	0.0840201	+	0.145527i
$690$		0			0
$691$	−13704.2	+	23736.5i	−0.754463	+	1.30677i	0.191177	+	0.981556i	$0.438769\pi$
$691$	−13704.2	+	23736.5i	−0.754463	+	1.30677i	−0.945641	+	0.325213i	$0.894564\pi$
$692$		0			0
$693$	4830.69	+	3707.26i	0.264795	+	0.203214i
$694$		0			0
$695$	506.550	−	877.371i	0.0276468	−	0.0478857i
$696$		0			0
$697$	−1113.01	−	1927.78i	−0.0604850	−	0.104763i
$698$		0			0
$699$	26263.9	−	5223.27i	1.42116	−	0.282635i
$700$		0			0
$701$	16824.7			0.906507			0.453253	−	0.891382i	$-0.350263\pi$
$701$	16824.7			0.906507			0.453253	+	0.891382i	$0.350263\pi$
$702$		0			0
$703$	−9845.92			−0.528230
$704$		0			0
$705$	−205.550	+	40.8790i	−0.0109808	+	0.00218382i
$706$		0			0
$707$	−5962.16	−	10326.8i	−0.317157	−	0.549332i
$708$		0			0
$709$	5580.19	−	9665.18i	0.295583	−	0.511965i	−0.679537	−	0.733641i	$-0.737819\pi$
$709$	5580.19	−	9665.18i	0.295583	−	0.511965i	0.975120	+	0.221676i	$0.0711527\pi$
$710$		0			0
$711$	−615.522	+	4672.83i	−0.0324668	+	0.246476i
$712$		0			0
$713$	502.365	−	870.121i	0.0263867	−	0.0457031i
$714$		0			0
$715$	54.9812	+	95.2303i	0.00287578	+	0.00498099i
$716$		0			0
$717$	−12543.3	−	14303.9i	−0.653330	−	0.745033i
$718$		0			0
$719$	−37045.3			−1.92149			−0.960747	−	0.277425i	$-0.910519\pi$
$719$	−37045.3			−1.92149			−0.960747	+	0.277425i	$0.910519\pi$
$720$		0			0
$721$	14015.1			0.723923
$722$		0			0
$723$	−7283.22	+	21453.2i	−0.374641	+	1.10353i
$724$		0			0
$725$	6035.27	+	10453.4i	0.309165	+	0.535489i
$726$		0			0
$727$	15649.2	−	27105.2i	0.798344	−	1.38277i	−0.122349	−	0.992487i	$-0.539043\pi$
$727$	15649.2	−	27105.2i	0.798344	−	1.38277i	0.920694	−	0.390286i	$-0.127624\pi$
$728$		0			0
$729$	7536.18	−	18183.1i	0.382877	−	0.923799i
$730$		0			0
$731$	958.913	−	1660.89i	0.0485180	−	0.0840356i
$732$		0			0
$733$	11227.0	+	19445.7i	0.565728	+	0.979870i	0.996982	+	0.0776389i	$0.0247381\pi$
$733$	11227.0	+	19445.7i	0.565728	+	0.979870i	−0.431254	+	0.902231i	$0.641929\pi$
$734$		0			0
$735$	30.1903	−	88.9275i	0.00151508	−	0.00446278i
$736$		0			0
$737$	−15462.5			−0.772819
$738$		0			0
$739$	−16620.2			−0.827312			−0.413656	−	0.910433i	$-0.635748\pi$
$739$	−16620.2			−0.827312			−0.413656	+	0.910433i	$0.635748\pi$
$740$		0			0
$741$	2109.15	+	2405.20i	0.104564	+	0.119240i
$742$		0			0
$743$	17096.8	+	29612.5i	0.844172	+	1.46215i	0.886339	+	0.463038i	$0.153241\pi$
$743$	17096.8	+	29612.5i	0.844172	+	1.46215i	−0.0421667	+	0.999111i	$0.513426\pi$
$744$		0			0
$745$	−321.050	+	556.075i	−0.0157884	+	0.0273463i
$746$		0			0
$747$	−3211.12	+	24377.7i	−0.157281	+	1.19402i
$748$		0			0
$749$	4189.58	−	7256.57i	0.204385	−	0.354005i
$750$		0			0
$751$	−12770.5	−	22119.2i	−0.620511	−	1.07476i	−0.989391	−	0.145279i	$-0.953592\pi$
$751$	−12770.5	−	22119.2i	−0.620511	−	1.07476i	0.368880	−	0.929477i	$-0.379741\pi$
$752$		0			0
$753$	3077.90	−	612.120i	0.148957	−	0.0296240i
$754$		0			0
$755$	−355.394			−0.0171313
$756$		0			0
$757$	−35951.4			−1.72612			−0.863061	−	0.505099i	$-0.831456\pi$
$757$	−35951.4			−1.72612			−0.863061	+	0.505099i	$0.831456\pi$
$758$		0			0
$759$	7034.99	−	1399.09i	0.336435	−	0.0669088i
$760$		0			0
$761$	5269.05	+	9126.26i	0.250989	+	0.434726i	0.963798	−	0.266632i	$-0.0859107\pi$
$761$	5269.05	+	9126.26i	0.250989	+	0.434726i	−0.712809	+	0.701358i	$0.752577\pi$
$762$		0			0
$763$	1946.12	−	3370.78i	0.0923386	−	0.159935i
$764$		0			0
$765$	687.691	+	527.760i	0.0325013	+	0.0249428i
$766$		0			0
$767$	−1799.77	+	3117.29i	−0.0847273	+	0.146752i
$768$		0			0
$769$	−7697.28	−	13332.1i	−0.360951	−	0.625185i	0.627167	−	0.778885i	$-0.284214\pi$
$769$	−7697.28	−	13332.1i	−0.360951	−	0.625185i	−0.988118	+	0.153700i	$0.950881\pi$
$770$		0			0
$771$	−25551.2	−	29137.7i	−1.19352	−	1.36105i
$772$		0			0
$773$	−19598.2			−0.911899			−0.455949	−	0.890006i	$-0.650700\pi$
$773$	−19598.2			−0.911899			−0.455949	+	0.890006i	$0.650700\pi$
$774$		0			0
$775$	−2928.10			−0.135717
$776$		0			0
$777$	1730.39	−	5096.99i	0.0798939	−	0.235333i
$778$		0			0
$779$	−850.730	−	1473.51i	−0.0391278	−	0.0677713i
$780$		0			0
$781$	−2999.44	+	5195.19i	−0.137425	+	0.238026i
$782$		0			0
$783$	885.600	+	13533.4i	0.0404199	+	0.617682i
$784$		0			0
$785$	−137.616	+	238.357i	−0.00625696	+	0.0108374i
$786$		0			0
$787$	−8388.76	−	14529.8i	−0.379958	−	0.658106i	0.611098	−	0.791555i	$-0.290728\pi$
$787$	−8388.76	−	14529.8i	−0.379958	−	0.658106i	−0.991056	+	0.133449i	$0.957395\pi$
$788$		0			0
$789$	−7951.11	+	23420.5i	−0.358767	+	1.05677i
$790$		0			0
$791$	−6247.78			−0.280841
$792$		0			0
$793$	3399.58			0.152235
$794$		0			0
$795$	415.022	+	473.275i	0.0185148	+	0.0211136i
$796$		0			0
$797$	6902.44	+	11955.4i	0.306771	+	0.531344i	0.977654	−	0.210220i	$-0.0674179\pi$
$797$	6902.44	+	11955.4i	0.306771	+	0.531344i	−0.670883	+	0.741564i	$0.734085\pi$
$798$		0			0
$799$	−4759.10	+	8243.00i	−0.210719	+	0.364977i
$800$		0			0
$801$	14770.3	−	6116.85i	0.651539	−	0.269823i
$802$		0			0
$803$	−11638.6	+	20158.6i	−0.511477	+	0.885904i
$804$		0			0
$805$	−55.3113	−	95.8020i	−0.00242170	−	0.00419451i
$806$		0			0
$807$	16228.5	−	3227.46i	0.707893	−	0.140783i
$808$		0			0
$809$	−2582.51			−0.112232			−0.0561162	−	0.998424i	$-0.517872\pi$
$809$	−2582.51			−0.112232			−0.0561162	+	0.998424i	$0.517872\pi$
$810$		0			0
$811$	13372.8			0.579017			0.289508	−	0.957175i	$-0.406508\pi$
$811$	13372.8			0.579017			0.289508	+	0.957175i	$0.406508\pi$
$812$		0			0
$813$	27694.2	−	5507.70i	1.19468	−	0.237594i
$814$		0			0
$815$	−149.385	−	258.742i	−0.00642053	−	0.0111207i
$816$		0			0
$817$	732.948	−	1269.50i	0.0313863	−	0.0543627i
$818$		0			0
$819$	−1615.79	+	669.149i	−0.0689380	+	0.0285494i
$820$		0			0
$821$	−753.429	+	1304.98i	−0.0320278	+	0.0554738i	−0.881595	−	0.472007i	$-0.843530\pi$
$821$	−753.429	+	1304.98i	−0.0320278	+	0.0554738i	0.849567	+	0.527480i	$0.176863\pi$
$822$		0			0
$823$	8529.74	+	14773.9i	0.361273	+	0.625744i	0.988171	−	0.153358i	$-0.0490088\pi$
$823$	8529.74	+	14773.9i	0.361273	+	0.625744i	−0.626897	+	0.779102i	$0.715675\pi$
$824$		0			0
$825$	−13782.2	−	15716.7i	−0.581618	−	0.663255i
$826$		0			0
$827$	29547.7			1.24241			0.621205	−	0.783648i	$-0.286643\pi$
$827$	29547.7			1.24241			0.621205	+	0.783648i	$0.286643\pi$
$828$		0			0
$829$	3404.72			0.142643			0.0713214	−	0.997453i	$-0.477278\pi$
$829$	3404.72			0.142643			0.0713214	+	0.997453i	$0.477278\pi$
$830$		0			0
$831$	−14405.1	+	42431.2i	−0.601333	+	1.77126i
$832$		0			0
$833$	−2132.59	−	3693.75i	−0.0887032	−	0.153638i
$834$		0			0
$835$	41.5667	−	71.9956i	0.00172272	−	0.00298384i
$836$		0			0
$837$	−2950.55	−	1455.43i	−0.121847	−	0.0601041i
$838$		0			0
$839$	17529.5	−	30362.0i	0.721318	−	1.24936i	−0.239153	−	0.970982i	$-0.576870\pi$
$839$	17529.5	−	30362.0i	0.721318	−	1.24936i	0.960472	−	0.278378i	$-0.0897969\pi$
$840$		0			0
$841$	7522.00	+	13028.5i	0.308418	+	0.534195i
$842$		0			0
$843$	3121.03	−	9193.19i	0.127513	−	0.375599i
$844$		0			0
$845$	778.774			0.0317049
$846$		0			0
$847$	−2050.82			−0.0831959
$848$		0			0
$849$	−1394.08	−	1589.75i	−0.0563541	−	0.0642640i
$850$		0			0
$851$	−3170.24	−	5491.01i	−0.127702	−	0.221186i
$852$		0			0
$853$	−11505.4	+	19928.0i	−0.461827	+	0.799908i	−0.999052	−	0.0435308i	$-0.986139\pi$
$853$	−11505.4	+	19928.0i	−0.461827	+	0.799908i	0.537225	+	0.843439i	$0.319473\pi$
$854$		0			0
$855$	525.639	+	403.395i	0.0210251	+	0.0161355i
$856$		0			0
$857$	23875.3	−	41353.3i	0.951652	−	1.64831i	0.209802	−	0.977744i	$-0.432718\pi$
$857$	23875.3	−	41353.3i	0.951652	−	1.64831i	0.741850	−	0.670566i	$-0.233949\pi$
$858$		0			0
$859$	−4747.43	−	8222.80i	−0.188569	−	0.326610i	0.756205	−	0.654335i	$-0.227051\pi$
$859$	−4747.43	−	8222.80i	−0.188569	−	0.326610i	−0.944773	+	0.327725i	$0.893718\pi$
$860$		0			0
$861$	912.312	−	181.437i	0.0361109	−	0.00718160i
$862$		0			0
$863$	−40189.7			−1.58525			−0.792627	−	0.609707i	$-0.791287\pi$
$863$	−40189.7			−1.58525			−0.792627	+	0.609707i	$0.791287\pi$
$864$		0			0
$865$	719.811			0.0282940
$866$		0			0
$867$	13575.2	−	2699.79i	0.531764	−	0.105755i
$868$		0			0
$869$	2812.07	+	4870.64i	0.109773	+	0.190133i
$870$		0			0
$871$	2220.44	−	3845.92i	0.0863798	−	0.149614i
$872$		0			0
$873$	−4264.46	+	32374.3i	−0.165327	+	1.25510i
$874$		0			0
$875$	−322.565	+	558.699i	−0.0124625	+	0.0215857i
$876$		0			0
$877$	2479.94	+	4295.39i	0.0954866	+	0.165388i	0.909812	−	0.415022i	$-0.136226\pi$
$877$	2479.94	+	4295.39i	0.0954866	+	0.165388i	−0.814325	+	0.580409i	$0.802893\pi$
$878$		0			0
$879$	−26335.5	−	30032.1i	−1.01055	−	1.15240i
$880$		0			0
$881$	−43851.8			−1.67696			−0.838482	−	0.544929i	$-0.816556\pi$
$881$	−43851.8			−1.67696			−0.838482	+	0.544929i	$0.816556\pi$
$882$		0			0
$883$	−48080.7			−1.83244			−0.916220	−	0.400676i	$-0.868775\pi$
$883$	−48080.7			−1.83244			−0.916220	+	0.400676i	$0.868775\pi$
$884$		0			0
$885$	−239.675	+	705.979i	−0.00910349	+	0.0268149i
$886$		0			0
$887$	−6369.39	−	11032.1i	−0.241108	−	0.417612i	0.719922	−	0.694055i	$-0.244178\pi$
$887$	−6369.39	−	11032.1i	−0.241108	−	0.417612i	−0.961030	+	0.276443i	$0.910844\pi$
$888$		0			0
$889$	9459.13	−	16383.7i	0.356860	−	0.618100i
$890$		0			0
$891$	−6075.76	−	22687.8i	−0.228446	−	0.853051i
$892$		0			0
$893$	−3637.63	+	6300.57i	−0.136314	+	0.236104i
$894$		0			0
$895$	171.303	+	296.706i	0.00639780	+	0.0110813i
$896$		0			0
$897$	−662.249	+	1950.70i	−0.0246509	+	0.0726108i
$898$		0			0
$899$	2266.93			0.0841005
$900$		0			0
$901$	28588.3			1.05706
$902$		0			0
$903$	528.377	+	602.541i	0.0194721	+	0.0222052i
$904$		0			0
$905$	394.093	+	682.589i	0.0144752	+	0.0250719i
$906$		0			0
$907$	4330.10	−	7499.96i	0.158521	−	0.274567i	−0.775814	−	0.630961i	$-0.782661\pi$
$907$	4330.10	−	7499.96i	0.158521	−	0.274567i	0.934336	+	0.356394i	$0.115994\pi$
$908$		0			0
$909$	−6006.59	+	45599.9i	−0.219171	+	1.66387i
$910$		0			0
$911$	−3207.30	+	5555.21i	−0.116644	+	0.202033i	−0.918436	−	0.395570i	$-0.870547\pi$
$911$	−3207.30	+	5555.21i	−0.116644	+	0.202033i	0.801792	+	0.597604i	$0.203880\pi$
$912$		0			0
$913$	14670.3	+	25409.7i	0.531780	+	0.921071i
$914$		0			0
$915$	690.613	−	137.346i	0.0249519	−	0.00496233i
$916$		0			0
$917$	9215.38			0.331863
$918$		0			0
$919$	53285.2			1.91264			0.956320	−	0.292323i	$-0.0944284\pi$
$919$	53285.2			1.91264			0.956320	+	0.292323i	$0.0944284\pi$
$920$		0			0
$921$	28691.5	−	5706.05i	1.02651	−	0.204148i
$922$		0			0
$923$	−861.453	−	1492.08i	−0.0307205	−	0.0532095i
$924$		0			0
$925$	−9239.07	+	16002.5i	−0.328409	+	0.568822i
$926$		0			0
$927$	−42884.9	−	32911.5i	−1.51944	−	1.16608i
$928$		0			0
$929$	16788.4	−	29078.4i	0.592907	−	1.02694i	−0.400932	−	0.916108i	$-0.631314\pi$
$929$	16788.4	−	29078.4i	0.592907	−	1.02694i	0.993839	−	0.110837i	$-0.0353531\pi$
$930$		0			0
$931$	−1630.05	−	2823.33i	−0.0573821	−	0.0993887i
$932$		0			0
$933$	2818.39	+	3213.99i	0.0988960	+	0.112777i
$934$		0			0
$935$	1034.40			0.0361804
$936$		0			0
$937$	22555.2			0.786389			0.393194	−	0.919455i	$-0.371370\pi$
$937$	22555.2			0.786389			0.393194	+	0.919455i	$0.371370\pi$
$938$		0			0
$939$	10994.4	−	32384.8i	0.382098	−	1.12549i
$940$		0			0
$941$	27076.8	+	46898.4i	0.938021	+	1.62470i	0.769156	+	0.639061i	$0.220677\pi$
$941$	27076.8	+	46898.4i	0.938021	+	1.62470i	0.168865	+	0.985639i	$0.445990\pi$
$942$		0			0
$943$	547.844	−	948.894i	0.0189186	−	0.0327680i
$944$		0			0
$945$	−301.208	+	201.215i	−0.0103686	+	0.00692647i
$946$		0			0
$947$	25271.0	−	43770.6i	0.867156	−	1.50196i	0.00226600	−	0.999997i	$-0.499279\pi$
$947$	25271.0	−	43770.6i	0.867156	−	1.50196i	0.864890	−	0.501961i	$-0.167388\pi$
$948$		0			0
$949$	−3342.64	−	5789.63i	−0.114338	−	0.198039i
$950$		0			0
$951$	−1230.62	+	3624.87i	−0.0419617	+	0.123601i
$952$		0			0
$953$	35582.5			1.20947			0.604737	−	0.796425i	$-0.293278\pi$
$953$	35582.5			1.20947			0.604737	+	0.796425i	$0.293278\pi$
$954$		0			0
$955$	−1331.80			−0.0451268
$956$		0			0
$957$	10670.2	+	12167.9i	0.360416	+	0.411004i
$958$		0			0
$959$	−8382.86	−	14519.5i	−0.282270	−	0.488906i
$960$		0			0
$961$	14620.5	−	25323.5i	0.490770	−	0.850039i
$962$		0			0
$963$	−29860.3	+	12366.1i	−0.999206	+	0.413803i
$964$		0			0
$965$	−388.533	+	672.959i	−0.0129610	+	0.0224490i
$966$		0			0
$967$	14049.5	+	24334.4i	0.467219	+	0.809247i	0.999299	−	0.0374474i	$-0.0119227\pi$
$967$	14049.5	+	24334.4i	0.467219	+	0.809247i	−0.532080	+	0.846694i	$0.678589\pi$
$968$		0			0
$969$	29514.4	−	5869.71i	0.978473	−	0.194595i
$970$		0			0
$971$	3990.19			0.131876			0.0659378	−	0.997824i	$-0.478996\pi$
$971$	3990.19			0.131876			0.0659378	+	0.997824i	$0.478996\pi$
$972$		0			0
$973$	19226.7			0.633484
$974$		0			0
$975$	5888.31	−	1171.04i	0.193412	−	0.0384650i
$976$		0			0
$977$	14137.5	+	24486.9i	0.462947	+	0.801848i	0.999106	−	0.0422692i	$-0.0134587\pi$
$977$	14137.5	+	24486.9i	0.462947	+	0.801848i	−0.536159	+	0.844117i	$0.680125\pi$
$978$		0			0
$979$	9538.32	−	16520.9i	0.311385	−	0.539335i
$980$		0			0
$981$	−13870.5	+	5744.23i	−0.451430	+	0.186951i
$982$		0			0
$983$	14161.4	−	24528.3i	0.459491	−	0.795862i	−0.539443	−	0.842022i	$-0.681365\pi$
$983$	14161.4	−	24528.3i	0.459491	−	0.795862i	0.998934	+	0.0461604i	$0.0146985\pi$
$984$		0			0
$985$	721.366	+	1249.44i	0.0233346	+	0.0404168i
$986$		0			0
$987$	−2622.35	−	2990.42i	−0.0845696	−	0.0964399i
$988$		0			0
$989$	943.993			0.0303511
$990$		0			0
$991$	32720.7			1.04885			0.524424	−	0.851457i	$-0.324281\pi$
$991$	32720.7			1.04885			0.524424	+	0.851457i	$0.324281\pi$
$992$		0			0
$993$	−3160.17	+	9308.50i	−0.100992	+	0.297479i
$994$		0			0
$995$	−48.3916	−	83.8167i	−0.00154183	−	0.00267052i
$996$		0			0
$997$	9429.18	−	16331.8i	0.299524	−	0.518790i	−0.676503	−	0.736440i	$-0.736506\pi$
$997$	9429.18	−	16331.8i	0.299524	−	0.518790i	0.976027	+	0.217649i	$0.0698389\pi$
$998$		0			0
$999$	−17264.1	+	11532.9i	−0.546758	+	0.365249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.j.b.169.9	yes	18
3.2	odd	2		756.4.j.b.505.5		18
9.2	odd	6		2268.4.a.h.1.5		9
9.4	even	3	inner	252.4.j.b.85.9	✓	18
9.5	odd	6		756.4.j.b.253.5		18
9.7	even	3		2268.4.a.i.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.j.b.85.9	✓	18	9.4	even	3	inner
252.4.j.b.169.9	yes	18	1.1	even	1	trivial
756.4.j.b.253.5		18	9.5	odd	6
756.4.j.b.505.5		18	3.2	odd	2
2268.4.a.h.1.5		9	9.2	odd	6
2268.4.a.i.1.5		9	9.7	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)

\(f(q)\)	\(=\)	\(q+(5.09635 - 1.01354i) q^{3} +(0.184423 + 0.319430i) q^{5} +(-3.50000 + 6.06218i) q^{7} +(24.9455 - 10.3307i) q^{9} +O(q^{10})\)	\(q+(5.09635 - 1.01354i) q^{3} +(0.184423 + 0.319430i) q^{5} +(-3.50000 + 6.06218i) q^{7} +(24.9455 - 10.3307i) q^{9} +(16.1092 - 27.9020i) q^{11} +(4.62663 + 8.01356i) q^{13} +(1.26364 + 1.44101i) q^{15} +87.0444 q^{17} +66.5327 q^{19} +(-11.6929 + 34.4423i) q^{21} +(21.4225 + 37.1049i) q^{23} +(62.4320 - 108.135i) q^{25} +(116.660 - 77.9321i) q^{27} +(-48.3348 + 83.7183i) q^{29} +(-11.7252 - 20.3086i) q^{31} +(53.8183 - 158.525i) q^{33} -2.58192 q^{35} -147.986 q^{37} +(31.7010 + 36.1506i) q^{39} +(-12.7866 - 22.1471i) q^{41} +(11.0164 - 19.0809i) q^{43} +(7.90046 + 6.06312i) q^{45} +(-54.6744 + 94.6988i) q^{47} +(-24.5000 - 42.4352i) q^{49} +(443.608 - 88.2230i) q^{51} +328.433 q^{53} +11.8836 q^{55} +(339.074 - 67.4336i) q^{57} +(194.501 + 336.885i) q^{59} +(183.696 - 318.171i) q^{61} +(-24.6826 + 187.381i) q^{63} +(-1.70652 + 2.95577i) q^{65} +(-239.963 - 415.629i) q^{67} +(146.784 + 167.387i) q^{69} -186.194 q^{71} -722.479 q^{73} +(208.575 - 614.372i) q^{75} +(112.764 + 195.314i) q^{77} +(-87.2813 + 151.176i) q^{79} +(515.553 - 515.409i) q^{81} +(-455.339 + 788.670i) q^{83} +(16.0530 + 27.8046i) q^{85} +(-161.479 + 475.647i) q^{87} +592.104 q^{89} -64.7728 q^{91} +(-80.3390 - 91.6155i) q^{93} +(12.2702 + 21.2526i) q^{95} +(-604.703 + 1047.38i) q^{97} +(113.605 - 862.447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9}+O(q^{10}) \) 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

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