LMFDB - Embedded newform 252.4.j.b.85.5

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			85.5
Root			$-0.0672952 - 5.08536i$ of defining polynomial
Character	$\chi$	$=$	252.85
Dual form			252.4.j.b.169.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06730 - 5.08536i) q^{3} +(1.60891 - 2.78671i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-24.7218 - 10.8552i) q^{9} +O(q^{10})$	\(q+(1.06730 - 5.08536i) q^{3} +(1.60891 - 2.78671i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-24.7218 - 10.8552i) q^{9} +(7.86210 + 13.6176i) q^{11} +(35.9532 - 62.2727i) q^{13} +(-12.4543 - 11.1561i) q^{15} -92.2719 q^{17} -113.849 q^{19} +(-34.5639 + 11.3286i) q^{21} +(85.3800 - 147.882i) q^{23} +(57.3228 + 99.2860i) q^{25} +(-81.5878 + 114.133i) q^{27} +(-11.9097 - 20.6282i) q^{29} +(-58.7390 + 101.739i) q^{31} +(77.6413 - 25.4476i) q^{33} -22.5247 q^{35} -211.000 q^{37} +(-278.307 - 249.298i) q^{39} +(-222.028 + 384.563i) q^{41} +(-278.264 - 481.967i) q^{43} +(-70.0253 + 51.4275i) q^{45} +(-48.0208 - 83.1744i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(-98.4814 + 469.236i) q^{51} +620.809 q^{53} +50.5976 q^{55} +(-121.510 + 578.962i) q^{57} +(151.584 - 262.551i) q^{59} +(-300.021 - 519.651i) q^{61} +(20.7203 + 187.861i) q^{63} +(-115.691 - 200.382i) q^{65} +(388.715 - 673.275i) q^{67} +(-660.910 - 592.022i) q^{69} +209.219 q^{71} -337.528 q^{73} +(566.086 - 185.540i) q^{75} +(55.0347 - 95.3229i) q^{77} +(200.708 + 347.637i) q^{79} +(493.331 + 536.717i) q^{81} +(-186.412 - 322.875i) q^{83} +(-148.457 + 257.135i) q^{85} +(-117.613 + 38.5487i) q^{87} +937.562 q^{89} -503.344 q^{91} +(454.687 + 407.295i) q^{93} +(-183.172 + 317.264i) q^{95} +(-290.865 - 503.793i) q^{97} +(-46.5442 - 421.994i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.06730	−	5.08536i	0.205401	−	0.978678i
$3$	1.06730	−	5.08536i	0.205401	−	0.978678i
$4$		0			0
$5$	1.60891	−	2.78671i	0.143905	−	0.249251i	−0.785059	−	0.619421i	$-0.787367\pi$
$5$	1.60891	−	2.78671i	0.143905	−	0.249251i	0.928964	+	0.370170i	$0.120701\pi$
$6$		0			0
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$8$		0			0
$9$	−24.7218	−	10.8552i	−0.915621	−	0.402043i
$10$		0			0
$11$	7.86210	+	13.6176i	0.215501	+	0.373259i	0.953427	−	0.301622i	$-0.0975282\pi$
$11$	7.86210	+	13.6176i	0.215501	+	0.373259i	−0.737926	+	0.674881i	$0.764195\pi$
$12$		0			0
$13$	35.9532	−	62.2727i	0.767047	−	1.32857i	−0.172110	−	0.985078i	$-0.555058\pi$
$13$	35.9532	−	62.2727i	0.767047	−	1.32857i	0.939157	−	0.343487i	$-0.111608\pi$
$14$		0			0
$15$	−12.4543	−	11.1561i	−0.214378	−	0.192033i
$16$		0			0
$17$	−92.2719			−1.31643			−0.658213	−	0.752832i	$-0.728687\pi$
$17$	−92.2719			−1.31643			−0.658213	+	0.752832i	$0.728687\pi$
$18$		0			0
$19$	−113.849			−1.37467			−0.687335	−	0.726341i	$-0.741219\pi$
$19$	−113.849			−1.37467			−0.687335	+	0.726341i	$0.741219\pi$
$20$		0			0
$21$	−34.5639	+	11.3286i	−0.359165	+	0.117719i
$22$		0			0
$23$	85.3800	−	147.882i	0.774042	−	1.34068i	−0.161290	−	0.986907i	$-0.551565\pi$
$23$	85.3800	−	147.882i	0.774042	−	1.34068i	0.935331	−	0.353773i	$-0.115101\pi$
$24$		0			0
$25$	57.3228	+	99.2860i	0.458583	+	0.794288i
$26$		0			0
$27$	−81.5878	+	114.133i	−0.581540	+	0.813518i
$28$		0			0
$29$	−11.9097	−	20.6282i	−0.0762612	−	0.132088i	0.825373	−	0.564588i	$-0.190965\pi$
$29$	−11.9097	−	20.6282i	−0.0762612	−	0.132088i	−0.901634	+	0.432500i	$0.857632\pi$
$30$		0			0
$31$	−58.7390	+	101.739i	−0.340317	+	0.589447i	−0.984492	−	0.175432i	$-0.943868\pi$
$31$	−58.7390	+	101.739i	−0.340317	+	0.589447i	0.644174	+	0.764879i	$0.277201\pi$
$32$		0			0
$33$	77.6413	−	25.4476i	0.409564	−	0.134238i
$34$		0			0
$35$	−22.5247			−0.108782
$36$		0			0
$37$	−211.000			−0.937518			−0.468759	−	0.883326i	$-0.655299\pi$
$37$	−211.000			−0.937518			−0.468759	+	0.883326i	$0.655299\pi$
$38$		0			0
$39$	−278.307	−	249.298i	−1.14268	−	1.02358i
$40$		0			0
$41$	−222.028	+	384.563i	−0.845729	+	1.46485i	0.0392580	+	0.999229i	$0.487501\pi$
$41$	−222.028	+	384.563i	−0.845729	+	1.46485i	−0.884987	+	0.465616i	$0.845833\pi$
$42$		0			0
$43$	−278.264	−	481.967i	−0.986857	−	1.70929i	−0.633373	−	0.773847i	$-0.718330\pi$
$43$	−278.264	−	481.967i	−0.986857	−	1.70929i	−0.353484	−	0.935440i	$-0.615003\pi$
$44$		0			0
$45$	−70.0253	+	51.4275i	−0.231972	+	0.170363i
$46$		0			0
$47$	−48.0208	−	83.1744i	−0.149033	−	0.258133i	0.781837	−	0.623482i	$-0.214283\pi$
$47$	−48.0208	−	83.1744i	−0.149033	−	0.258133i	−0.930870	+	0.365350i	$0.880949\pi$
$48$		0			0
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$		0			0
$51$	−98.4814	+	469.236i	−0.270395	+	1.28836i
$52$		0			0
$53$	620.809			1.60896			0.804478	−	0.593983i	$-0.202445\pi$
$53$	620.809			1.60896			0.804478	+	0.593983i	$0.202445\pi$
$54$		0			0
$55$	50.5976			0.124047
$56$		0			0
$57$	−121.510	+	578.962i	−0.282359	+	1.34536i
$58$		0			0
$59$	151.584	−	262.551i	0.334484	−	0.579343i	−0.648902	−	0.760872i	$-0.724771\pi$
$59$	151.584	−	262.551i	0.334484	−	0.579343i	0.983386	+	0.181529i	$0.0581047\pi$
$60$		0			0
$61$	−300.021	−	519.651i	−0.629733	−	1.09073i	−0.987605	−	0.156959i	$-0.949831\pi$
$61$	−300.021	−	519.651i	−0.629733	−	1.09073i	0.357872	−	0.933771i	$-0.383503\pi$
$62$		0			0
$63$	20.7203	+	187.861i	0.0414366	+	0.375686i
$64$		0			0
$65$	−115.691	−	200.382i	−0.220764	−	0.382375i
$66$		0			0
$67$	388.715	−	673.275i	0.708793	−	1.22767i	−0.256512	−	0.966541i	$-0.582573\pi$
$67$	388.715	−	673.275i	0.708793	−	1.22767i	0.965305	−	0.261125i	$-0.0840933\pi$
$68$		0			0
$69$	−660.910	−	592.022i	−1.15310	−	1.03291i
$70$		0			0
$71$	209.219			0.349714			0.174857	−	0.984594i	$-0.444054\pi$
$71$	209.219			0.349714			0.174857	+	0.984594i	$0.444054\pi$
$72$		0			0
$73$	−337.528			−0.541160			−0.270580	−	0.962698i	$-0.587215\pi$
$73$	−337.528			−0.541160			−0.270580	+	0.962698i	$0.587215\pi$
$74$		0			0
$75$	566.086	−	185.540i	0.871546	−	0.285657i
$76$		0			0
$77$	55.0347	−	95.3229i	0.0814518	−	0.141079i
$78$		0			0
$79$	200.708	+	347.637i	0.285841	+	0.495092i	0.972813	−	0.231593i	$-0.0743936\pi$
$79$	200.708	+	347.637i	0.285841	+	0.495092i	−0.686972	+	0.726684i	$0.741060\pi$
$80$		0			0
$81$	493.331	+	536.717i	0.676723	+	0.736238i
$82$		0			0
$83$	−186.412	−	322.875i	−0.246522	−	0.426989i	0.716036	−	0.698063i	$-0.245955\pi$
$83$	−186.412	−	322.875i	−0.246522	−	0.426989i	−0.962559	+	0.271074i	$0.912621\pi$
$84$		0			0
$85$	−148.457	+	257.135i	−0.189441	+	0.328121i
$86$		0			0
$87$	−117.613	+	38.5487i	−0.144936	+	0.0475041i
$88$		0			0
$89$	937.562			1.11664			0.558322	−	0.829624i	$-0.311445\pi$
$89$	937.562			1.11664			0.558322	+	0.829624i	$0.311445\pi$
$90$		0			0
$91$	−503.344			−0.579833
$92$		0			0
$93$	454.687	+	407.295i	0.506977	+	0.454134i
$94$		0			0
$95$	−183.172	+	317.264i	−0.197822	+	0.342638i
$96$		0			0
$97$	−290.865	−	503.793i	−0.304462	−	0.527344i	0.672679	−	0.739934i	$-0.265143\pi$
$97$	−290.865	−	503.793i	−0.304462	−	0.527344i	−0.977141	+	0.212590i	$0.931810\pi$
$98$		0			0
$99$	−46.5442	−	421.994i	−0.0472512	−	0.428404i
$100$		0			0
$101$	961.123	+	1664.71i	0.946884	+	1.64005i	0.751934	+	0.659238i	$0.229121\pi$
$101$	961.123	+	1664.71i	0.946884	+	1.64005i	0.194950	+	0.980813i	$0.437546\pi$
$102$		0			0
$103$	380.685	−	659.366i	0.364175	−	0.630769i	−0.624468	−	0.781050i	$-0.714684\pi$
$103$	380.685	−	659.366i	0.364175	−	0.630769i	0.988643	+	0.150281i	$0.0480177\pi$
$104$		0			0
$105$	−24.0405	+	114.546i	−0.0223440	+	0.106463i
$106$		0			0
$107$	2042.46			1.84535			0.922675	−	0.385579i	$-0.125998\pi$
$107$	2042.46			1.84535			0.922675	+	0.385579i	$0.125998\pi$
$108$		0			0
$109$	403.310			0.354405			0.177202	−	0.984174i	$-0.443295\pi$
$109$	403.310			0.354405			0.177202	+	0.984174i	$0.443295\pi$
$110$		0			0
$111$	−225.199	+	1073.01i	−0.192567	+	0.917529i
$112$		0			0
$113$	361.790	−	626.639i	0.301189	−	0.521674i	−0.675217	−	0.737619i	$-0.735950\pi$
$113$	361.790	−	626.639i	0.301189	−	0.521674i	0.976406	+	0.215945i	$0.0692832\pi$
$114$		0			0
$115$	−274.737	−	475.859i	−0.222777	−	0.385862i
$116$		0			0
$117$	−1564.81	+	1149.21i	−1.23646	+	0.908076i
$118$		0			0
$119$	322.952	+	559.369i	0.248781	+	0.430901i
$120$		0			0
$121$	541.875	−	938.555i	0.407119	−	0.705150i
$122$		0			0
$123$	1718.67	+	1539.53i	1.25990	+	1.12858i
$124$		0			0
$125$	771.136			0.551780
$126$		0			0
$127$	617.764			0.431635			0.215818	−	0.976434i	$-0.430758\pi$
$127$	617.764			0.431635			0.215818	+	0.976434i	$0.430758\pi$
$128$		0			0
$129$	−2747.97	+	900.671i	−1.87554	+	0.614726i
$130$		0			0
$131$	1022.91	−	1771.73i	0.682228	−	1.18165i	−0.292071	−	0.956397i	$-0.594344\pi$
$131$	1022.91	−	1771.73i	0.682228	−	1.18165i	0.974299	−	0.225258i	$-0.0723224\pi$
$132$		0			0
$133$	398.471	+	690.172i	0.259788	+	0.449966i
$134$		0			0
$135$	186.790	+	410.992i	0.119084	+	0.262019i
$136$		0			0
$137$	19.3129	+	33.4509i	0.0120439	+	0.0208606i	0.871985	−	0.489533i	$-0.162833\pi$
$137$	19.3129	+	33.4509i	0.0120439	+	0.0208606i	−0.859941	+	0.510394i	$0.829500\pi$
$138$		0			0
$139$	−248.579	+	430.552i	−0.151685	+	0.262726i	−0.931847	−	0.362851i	$-0.881803\pi$
$139$	−248.579	+	430.552i	−0.151685	+	0.262726i	0.780162	+	0.625578i	$0.215137\pi$
$140$		0			0
$141$	−474.224	+	155.431i	−0.283240	+	0.0928345i
$142$		0			0
$143$	1130.67			0.661198
$144$		0			0
$145$	−76.6465			−0.0438976
$146$		0			0
$147$	189.650	+	169.882i	0.106408	+	0.0953174i
$148$		0			0
$149$	−1472.88	+	2551.11i	−0.809820	+	1.40265i	0.103169	+	0.994664i	$0.467102\pi$
$149$	−1472.88	+	2551.11i	−0.809820	+	1.40265i	−0.912989	+	0.407985i	$0.866231\pi$
$150$		0			0
$151$	−436.975	−	756.863i	−0.235500	−	0.407898i	0.723918	−	0.689886i	$-0.242340\pi$
$151$	−436.975	−	756.863i	−0.235500	−	0.407898i	−0.959418	+	0.281988i	$0.909006\pi$
$152$		0			0
$153$	2281.13	+	1001.63i	1.20535	+	0.529260i
$154$		0			0
$155$	189.012	+	327.378i	0.0979469	+	0.169649i
$156$		0			0
$157$	−79.1992	+	137.177i	−0.0402598	+	0.0697320i	−0.885453	−	0.464729i	$-0.846152\pi$
$157$	−79.1992	+	137.177i	−0.0402598	+	0.0697320i	0.845193	+	0.534461i	$0.179485\pi$
$158$		0			0
$159$	662.586	−	3157.04i	0.330481	−	1.57465i
$160$		0			0
$161$	−1195.32			−0.585121
$162$		0			0
$163$	−928.654			−0.446244			−0.223122	−	0.974791i	$-0.571625\pi$
$163$	−928.654			−0.446244			−0.223122	+	0.974791i	$0.571625\pi$
$164$		0			0
$165$	54.0026	−	257.307i	0.0254794	−	0.121402i
$166$		0			0
$167$	1380.00	−	2390.24i	0.639448	−	1.10756i	−0.346106	−	0.938195i	$-0.612496\pi$
$167$	1380.00	−	2390.24i	0.639448	−	1.10756i	0.985554	−	0.169361i	$-0.0541704\pi$
$168$		0			0
$169$	−1486.76	−	2575.15i	−0.676724	−	1.17212i
$170$		0			0
$171$	2814.54	+	1235.85i	1.25868	+	0.552676i
$172$		0			0
$173$	−1793.22	−	3105.94i	−0.788068	−	1.36497i	−0.927149	−	0.374693i	$-0.877748\pi$
$173$	−1793.22	−	3105.94i	−0.788068	−	1.36497i	0.139081	−	0.990281i	$-0.455585\pi$
$174$		0			0
$175$	401.260	−	695.002i	0.173328	−	0.300213i
$176$		0			0
$177$	−1173.38	−	1051.08i	−0.498287	−	0.446349i
$178$		0			0
$179$	3541.36			1.47874			0.739368	−	0.673301i	$-0.235124\pi$
$179$	3541.36			1.47874			0.739368	+	0.673301i	$0.235124\pi$
$180$		0			0
$181$	−2317.46			−0.951688			−0.475844	−	0.879530i	$-0.657857\pi$
$181$	−2317.46			−0.951688			−0.475844	+	0.879530i	$0.657857\pi$
$182$		0			0
$183$	−2962.82	+	971.092i	−1.19682	+	0.392269i
$184$		0			0
$185$	−339.480	+	587.996i	−0.134914	+	0.233678i
$186$		0			0
$187$	−725.451	−	1256.52i	−0.283691	−	0.491367i
$188$		0			0
$189$	977.454	+	95.1330i	0.376187	+	0.0366133i
$190$		0			0
$191$	114.758	+	198.767i	0.0434744	+	0.0752999i	0.886944	−	0.461877i	$-0.152824\pi$
$191$	114.758	+	198.767i	0.0434744	+	0.0752999i	−0.843469	+	0.537177i	$0.819491\pi$
$192$		0			0
$193$	−1904.01	+	3297.85i	−0.710124	+	1.22997i	0.254687	+	0.967024i	$0.418028\pi$
$193$	−1904.01	+	3297.85i	−0.710124	+	1.22997i	−0.964810	+	0.262947i	$0.915306\pi$
$194$		0			0
$195$	−1142.49	+	374.462i	−0.419567	+	0.137517i
$196$		0			0
$197$	−431.378			−0.156012			−0.0780061	−	0.996953i	$-0.524855\pi$
$197$	−431.378			−0.156012			−0.0780061	+	0.996953i	$0.524855\pi$
$198$		0			0
$199$	288.253			0.102682			0.0513410	−	0.998681i	$-0.483650\pi$
$199$	288.253			0.102682			0.0513410	+	0.998681i	$0.483650\pi$
$200$		0			0
$201$	−3008.97	−	2695.34i	−1.05590	−	0.945844i
$202$		0			0
$203$	−83.3679	+	144.397i	−0.0288240	+	0.0499247i
$204$		0			0
$205$	714.444	+	1237.45i	0.243410	+	0.421598i
$206$		0			0
$207$	−3716.03	+	2729.10i	−1.24774	+	0.916356i
$208$		0			0
$209$	−895.091	−	1550.34i	−0.296243	−	0.513107i
$210$		0			0
$211$	2298.19	−	3980.59i	0.749830	−	1.29874i	−0.198074	−	0.980187i	$-0.563468\pi$
$211$	2298.19	−	3980.59i	0.749830	−	1.29874i	0.947904	−	0.318557i	$-0.103198\pi$
$212$		0			0
$213$	223.298	−	1063.95i	0.0718317	−	0.342258i
$214$		0			0
$215$	−1790.81			−0.568056
$216$		0			0
$217$	822.346			0.257256
$218$		0			0
$219$	−360.242	+	1716.45i	−0.111155	+	0.529621i
$220$		0			0
$221$	−3317.47	+	5746.03i	−1.00976	+	1.74896i
$222$		0			0
$223$	−1097.32	−	1900.62i	−0.329517	−	0.570740i	0.652899	−	0.757445i	$-0.273552\pi$
$223$	−1097.32	−	1900.62i	−0.329517	−	0.570740i	−0.982416	+	0.186705i	$0.940219\pi$
$224$		0			0
$225$	−339.355	−	3076.77i	−0.100550	−	0.911637i
$226$		0			0
$227$	−1165.22	−	2018.22i	−0.340698	−	0.590105i	0.643865	−	0.765139i	$-0.277330\pi$
$227$	−1165.22	−	2018.22i	−0.340698	−	0.590105i	−0.984562	+	0.175034i	$0.943997\pi$
$228$		0			0
$229$	1080.52	−	1871.51i	0.311802	−	0.540056i	−0.666951	−	0.745102i	$-0.732401\pi$
$229$	1080.52	−	1871.51i	0.311802	−	0.540056i	0.978752	+	0.205046i	$0.0657343\pi$
$230$		0			0
$231$	−426.013	−	381.609i	−0.121340	−	0.108693i
$232$		0			0
$233$	779.022			0.219036			0.109518	−	0.993985i	$-0.465069\pi$
$233$	779.022			0.219036			0.109518	+	0.993985i	$0.465069\pi$
$234$		0			0
$235$	−309.044			−0.0857865
$236$		0			0
$237$	1982.08	−	649.643i	0.543247	−	0.178054i
$238$		0			0
$239$	−1934.12	+	3350.00i	−0.523465	+	0.906667i	0.476162	+	0.879357i	$0.342027\pi$
$239$	−1934.12	+	3350.00i	−0.523465	+	0.906667i	−0.999627	+	0.0273100i	$0.991306\pi$
$240$		0			0
$241$	1383.83	+	2396.87i	0.369878	+	0.640647i	0.989546	−	0.144217i	$-0.0460662\pi$
$241$	1383.83	+	2396.87i	0.369878	+	0.640647i	−0.619668	+	0.784864i	$0.712733\pi$
$242$		0			0
$243$	3255.93	−	1935.93i	0.859539	−	0.511070i
$244$		0			0
$245$	78.8366	+	136.549i	0.0205579	+	0.0356073i
$246$		0			0
$247$	−4093.23	+	7089.68i	−1.05444	+	1.82634i
$248$		0			0
$249$	−1840.89	+	603.368i	−0.468521	+	0.153562i
$250$		0			0
$251$	−2766.40			−0.695671			−0.347836	−	0.937555i	$-0.613083\pi$
$251$	−2766.40			−0.695671			−0.347836	+	0.937555i	$0.613083\pi$
$252$		0			0
$253$	2685.06			0.667227
$254$		0			0
$255$	1149.18	+	1029.40i	0.282213	+	0.252798i
$256$		0			0
$257$	−1609.31	+	2787.40i	−0.390607	+	0.676551i	−0.992530	−	0.122004i	$-0.961068\pi$
$257$	−1609.31	+	2787.40i	−0.390607	+	0.676551i	0.601923	+	0.798554i	$0.294401\pi$
$258$		0			0
$259$	738.500	+	1279.12i	0.177174	+	0.306875i
$260$		0			0
$261$	70.5063	+	639.247i	0.0167212	+	0.151603i
$262$		0			0
$263$	−1944.04	−	3367.18i	−0.455798	−	0.789465i	0.542936	−	0.839774i	$-0.317313\pi$
$263$	−1944.04	−	3367.18i	−0.455798	−	0.789465i	−0.998734	+	0.0503094i	$0.983979\pi$
$264$		0			0
$265$	998.825	−	1730.02i	0.231537	−	0.401034i
$266$		0			0
$267$	1000.66	−	4767.84i	0.229360	−	1.09284i
$268$		0			0
$269$	1006.60			0.228155			0.114077	−	0.993472i	$-0.463609\pi$
$269$	1006.60			0.228155			0.114077	+	0.993472i	$0.463609\pi$
$270$		0			0
$271$	−7489.46			−1.67879			−0.839395	−	0.543521i	$-0.817091\pi$
$271$	−7489.46			−1.67879			−0.839395	+	0.543521i	$0.817091\pi$
$272$		0			0
$273$	−537.217	+	2559.69i	−0.119098	+	0.567470i
$274$		0			0
$275$	−901.355	+	1561.19i	−0.197650	+	0.342340i
$276$		0			0
$277$	2162.66	+	3745.84i	0.469104	+	0.812513i	0.999376	−	0.0353151i	$-0.0112435\pi$
$277$	2162.66	+	3745.84i	0.469104	+	0.812513i	−0.530272	+	0.847828i	$0.677910\pi$
$278$		0			0
$279$	2556.52	−	1877.55i	0.548585	−	0.402888i
$280$		0			0
$281$	−808.587	−	1400.51i	−0.171659	−	0.297323i	0.767341	−	0.641240i	$-0.221580\pi$
$281$	−808.587	−	1400.51i	−0.171659	−	0.297323i	−0.939000	+	0.343917i	$0.888246\pi$
$282$		0			0
$283$	−1247.32	+	2160.42i	−0.261998	+	0.453793i	−0.966773	−	0.255638i	$-0.917715\pi$
$283$	−1247.32	+	2160.42i	−0.261998	+	0.453793i	0.704775	+	0.709431i	$0.251048\pi$
$284$		0			0
$285$	1417.90	+	1270.11i	0.294699	+	0.263982i
$286$		0			0
$287$	3108.39			0.639311
$288$		0			0
$289$	3601.11			0.732976
$290$		0			0
$291$	−2872.41	+	941.457i	−0.578637	+	0.189654i
$292$		0			0
$293$	−324.364	+	561.815i	−0.0646742	+	0.112019i	−0.896549	−	0.442944i	$-0.853934\pi$
$293$	−324.364	+	561.815i	−0.0646742	+	0.112019i	0.831875	+	0.554963i	$0.187267\pi$
$294$		0			0
$295$	−487.769	−	844.841i	−0.0962679	−	0.166741i
$296$		0			0
$297$	−2195.67	−	213.698i	−0.428975	−	0.0417510i
$298$		0			0
$299$	−6139.36	−	10633.7i	−1.18745	−	2.05673i
$300$		0			0
$301$	−1947.85	+	3373.77i	−0.372997	+	0.646050i
$302$		0			0
$303$	9491.47	−	3110.91i	1.79957	−	0.589826i
$304$		0			0
$305$	−1930.83			−0.362488
$306$		0			0
$307$	5162.70			0.959775			0.479887	−	0.877330i	$-0.340677\pi$
$307$	5162.70			0.959775			0.479887	+	0.877330i	$0.340677\pi$
$308$		0			0
$309$	−2946.81	−	2639.66i	−0.542518	−	0.485971i
$310$		0			0
$311$	−139.590	+	241.777i	−0.0254515	+	0.0440833i	−0.878471	−	0.477796i	$-0.841436\pi$
$311$	−139.590	+	241.777i	−0.0254515	+	0.0440833i	0.853019	+	0.521880i	$0.174769\pi$
$312$		0			0
$313$	39.1994	+	67.8954i	0.00707886	+	0.0122609i	0.869543	−	0.493857i	$-0.164413\pi$
$313$	39.1994	+	67.8954i	0.00707886	+	0.0122609i	−0.862464	+	0.506118i	$0.831080\pi$
$314$		0			0
$315$	556.851	+	244.510i	0.0996032	+	0.0437351i
$316$		0			0
$317$	−1852.03	−	3207.81i	−0.328140	−	0.568356i	0.654003	−	0.756492i	$-0.273089\pi$
$317$	−1852.03	−	3207.81i	−0.328140	−	0.568356i	−0.982143	+	0.188137i	$0.939755\pi$
$318$		0			0
$319$	187.271	−	324.362i	0.0328688	−	0.0569304i
$320$		0			0
$321$	2179.91	−	10386.7i	0.379037	−	1.80600i
$322$		0			0
$323$	10505.1			1.80965
$324$		0			0
$325$	8243.75			1.40702
$326$		0			0
$327$	430.451	−	2050.98i	0.0727951	−	0.346848i
$328$		0			0
$329$	−336.145	+	582.221i	−0.0563291	+	0.0975649i
$330$		0			0
$331$	3201.46	+	5545.10i	0.531626	+	0.920804i	0.999319	+	0.0369124i	$0.0117522\pi$
$331$	3201.46	+	5545.10i	0.531626	+	0.920804i	−0.467692	+	0.883891i	$0.654914\pi$
$332$		0			0
$333$	5216.29	+	2290.44i	0.858411	+	0.376923i
$334$		0			0
$335$	−1250.82	−	2166.48i	−0.203998	−	0.353335i
$336$		0			0
$337$	3422.84	−	5928.54i	0.553276	−	0.958303i	−0.444759	−	0.895650i	$-0.646711\pi$
$337$	3422.84	−	5928.54i	0.553276	−	0.958303i	0.998035	−	0.0626525i	$-0.0199560\pi$
$338$		0			0
$339$	−2800.55	−	2508.64i	−0.448687	−	0.401919i
$340$		0			0
$341$	−1847.25			−0.293355
$342$		0			0
$343$	343.000			0.0539949
$344$		0			0
$345$	−2713.14	+	889.256i	−0.423393	+	0.138771i
$346$		0			0
$347$	−4551.72	+	7883.80i	−0.704175	+	1.21967i	0.262813	+	0.964847i	$0.415350\pi$
$347$	−4551.72	+	7883.80i	−0.704175	+	1.21967i	−0.966988	+	0.254821i	$0.917983\pi$
$348$		0			0
$349$	4829.49	+	8364.93i	0.740736	+	1.28299i	0.952161	+	0.305598i	$0.0988565\pi$
$349$	4829.49	+	8364.93i	0.740736	+	1.28299i	−0.211424	+	0.977394i	$0.567810\pi$
$350$		0			0
$351$	4174.06	+	9184.15i	0.634743	+	1.39662i
$352$		0			0
$353$	5970.59	+	10341.4i	0.900234	+	1.55925i	0.827190	+	0.561923i	$0.189938\pi$
$353$	5970.59	+	10341.4i	0.900234	+	1.55925i	0.0730446	+	0.997329i	$0.476728\pi$
$354$		0			0
$355$	336.614	−	583.033i	0.0503257	−	0.0871667i
$356$		0			0
$357$	3189.28	−	1045.31i	0.472814	−	0.154969i
$358$		0			0
$359$	−6451.82			−0.948507			−0.474254	−	0.880388i	$-0.657282\pi$
$359$	−6451.82			−0.948507			−0.474254	+	0.880388i	$0.657282\pi$
$360$		0			0
$361$	6102.56			0.889716
$362$		0			0
$363$	−4194.55	−	3757.34i	−0.606492	−	0.543276i
$364$		0			0
$365$	−543.052	+	940.594i	−0.0778757	+	0.134885i
$366$		0			0
$367$	144.387	+	250.085i	0.0205366	+	0.0355704i	0.876111	−	0.482109i	$-0.160129\pi$
$367$	144.387	+	250.085i	0.0205366	+	0.0355704i	−0.855574	+	0.517680i	$0.826796\pi$
$368$		0			0
$369$	9663.41	−	7096.93i	1.36330	−	1.00122i
$370$		0			0
$371$	−2172.83	−	3763.45i	−0.304064	−	0.526654i
$372$		0			0
$373$	−1192.34	+	2065.19i	−0.165515	+	0.286680i	−0.936838	−	0.349764i	$-0.886262\pi$
$373$	−1192.34	+	2065.19i	−0.165515	+	0.286680i	0.771323	+	0.636444i	$0.219595\pi$
$374$		0			0
$375$	823.030	−	3921.51i	0.113336	−	0.540015i
$376$		0			0
$377$	−1712.77			−0.233984
$378$		0			0
$379$	−5188.78			−0.703245			−0.351622	−	0.936142i	$-0.614370\pi$
$379$	−5188.78			−0.703245			−0.351622	+	0.936142i	$0.614370\pi$
$380$		0			0
$381$	659.336	−	3141.55i	0.0886583	−	0.422432i
$382$		0			0
$383$	2198.44	−	3807.81i	0.293303	−	0.508015i	−0.681286	−	0.732017i	$-0.738579\pi$
$383$	2198.44	−	3807.81i	0.293303	−	0.508015i	0.974589	+	0.224002i	$0.0719123\pi$
$384$		0			0
$385$	−177.092	−	306.732i	−0.0234427	−	0.0406039i
$386$		0			0
$387$	1647.34	+	14935.7i	0.216380	+	1.96182i
$388$		0			0
$389$	4820.75	+	8349.79i	0.628334	+	1.08831i	0.987886	+	0.155181i	$0.0495962\pi$
$389$	4820.75	+	8349.79i	0.628334	+	1.08831i	−0.359552	+	0.933125i	$0.617070\pi$
$390$		0			0
$391$	−7878.18	+	13645.4i	−1.01897	+	1.76490i
$392$		0			0
$393$	−7918.14	−	7092.82i	−1.01633	−	0.910395i
$394$		0			0
$395$	1291.69			0.164536
$396$		0			0
$397$	2274.29			0.287515			0.143758	−	0.989613i	$-0.454081\pi$
$397$	2274.29			0.287515			0.143758	+	0.989613i	$0.454081\pi$
$398$		0			0
$399$	3935.06	−	1289.75i	0.493733	−	0.161825i
$400$		0			0
$401$	1280.66	−	2218.17i	0.159484	−	0.276235i	−0.775199	−	0.631718i	$-0.782350\pi$
$401$	1280.66	−	2218.17i	0.159484	−	0.276235i	0.934683	+	0.355483i	$0.115684\pi$
$402$		0			0
$403$	4223.71	+	7315.68i	0.522079	+	0.904268i
$404$		0			0
$405$	2289.40	−	511.242i	0.280892	−	0.0627255i
$406$		0			0
$407$	−1658.90	−	2873.30i	−0.202036	−	0.349937i
$408$		0			0
$409$	6474.75	−	11214.6i	0.782777	−	1.35581i	−0.147540	−	0.989056i	$-0.547136\pi$
$409$	6474.75	−	11214.6i	0.782777	−	1.35581i	0.930318	−	0.366754i	$-0.119531\pi$
$410$		0			0
$411$	190.723	−	62.5110i	0.0228897	−	0.00750229i
$412$		0			0
$413$	−2122.17			−0.252846
$414$		0			0
$415$	−1199.68			−0.141903
$416$		0			0
$417$	1924.20	+	1723.64i	0.225968	+	0.202415i
$418$		0			0
$419$	−3417.03	+	5918.47i	−0.398408	+	0.690063i	−0.993530	−	0.113573i	$-0.963771\pi$
$419$	−3417.03	+	5918.47i	−0.398408	+	0.690063i	0.595122	+	0.803636i	$0.297104\pi$
$420$		0			0
$421$	2927.95	+	5071.37i	0.338954	+	0.587086i	0.984236	−	0.176858i	$-0.0565935\pi$
$421$	2927.95	+	5071.37i	0.338954	+	0.587086i	−0.645282	+	0.763944i	$0.723260\pi$
$422$		0			0
$423$	284.286	+	2577.49i	0.0326772	+	0.296269i
$424$		0			0
$425$	−5289.29	−	9161.32i	−0.603690	−	1.04562i
$426$		0			0
$427$	−2100.15	+	3637.56i	−0.238017	+	0.412257i
$428$		0			0
$429$	1206.76	−	5749.86i	0.135811	−	0.647100i
$430$		0			0
$431$	3527.61			0.394243			0.197122	−	0.980379i	$-0.436841\pi$
$431$	3527.61			0.394243			0.197122	+	0.980379i	$0.436841\pi$
$432$		0			0
$433$	8876.41			0.985157			0.492579	−	0.870268i	$-0.336054\pi$
$433$	8876.41			0.985157			0.492579	+	0.870268i	$0.336054\pi$
$434$		0			0
$435$	−81.8045	+	389.775i	−0.00901661	+	0.0429616i
$436$		0			0
$437$	−9720.41	+	16836.3i	−1.06405	+	1.84299i
$438$		0			0
$439$	3326.74	+	5762.09i	0.361679	+	0.626446i	0.988237	−	0.152929i	$-0.0488705\pi$
$439$	3326.74	+	5762.09i	0.361679	+	0.626446i	−0.626559	+	0.779374i	$0.715537\pi$
$440$		0			0
$441$	1066.32	−	783.123i	0.115141	−	0.0845613i
$442$		0			0
$443$	2739.68	+	4745.26i	0.293828	+	0.508926i	0.974712	−	0.223466i	$-0.0717372\pi$
$443$	2739.68	+	4745.26i	0.293828	+	0.508926i	−0.680883	+	0.732392i	$0.738404\pi$
$444$		0			0
$445$	1508.45	−	2612.72i	0.160691	−	0.278325i
$446$		0			0
$447$	11401.3	+	10212.9i	1.20640	+	1.08066i
$448$		0			0
$449$	−4263.60			−0.448133			−0.224067	−	0.974574i	$-0.571933\pi$
$449$	−4263.60			−0.448133			−0.224067	+	0.974574i	$0.571933\pi$
$450$		0			0
$451$	−6982.41			−0.729022
$452$		0			0
$453$	−4315.30	+	1414.38i	−0.447573	+	0.146696i
$454$		0			0
$455$	−809.836	+	1402.68i	−0.0834411	+	0.144524i
$456$		0			0
$457$	−5239.52	−	9075.12i	−0.536312	−	0.928920i	−0.999099	−	0.0424500i	$-0.986484\pi$
$457$	−5239.52	−	9075.12i	−0.536312	−	0.928920i	0.462787	−	0.886470i	$-0.346850\pi$
$458$		0			0
$459$	7528.27	−	10531.3i	0.765554	−	1.07094i
$460$		0			0
$461$	−8876.25	−	15374.1i	−0.896764	−	1.55324i	−0.831606	−	0.555365i	$-0.812578\pi$
$461$	−8876.25	−	15374.1i	−0.896764	−	1.55324i	−0.0651573	−	0.997875i	$-0.520755\pi$
$462$		0			0
$463$	5679.93	−	9837.93i	0.570127	−	0.987489i	−0.426425	−	0.904523i	$-0.640227\pi$
$463$	5679.93	−	9837.93i	0.570127	−	0.987489i	0.996552	−	0.0829661i	$-0.0264393\pi$
$464$		0			0
$465$	1866.56	−	611.783i	0.186150	−	0.0610124i
$466$		0			0
$467$	6950.56			0.688723			0.344362	−	0.938837i	$-0.388095\pi$
$467$	6950.56			0.688723			0.344362	+	0.938837i	$0.388095\pi$
$468$		0			0
$469$	−5442.01			−0.535797
$470$		0			0
$471$	613.066	+	549.165i	0.0599758	+	0.0537244i
$472$		0			0
$473$	4375.48	−	7578.55i	0.425338	−	0.736706i
$474$		0			0
$475$	−6526.14	−	11303.6i	−0.630399	−	1.09188i
$476$		0			0
$477$	−15347.5	−	6738.98i	−1.47319	−	0.646869i
$478$		0			0
$479$	−6043.95	−	10468.4i	−0.576524	−	0.998570i	−0.995874	−	0.0907448i	$-0.971075\pi$
$479$	−6043.95	−	10468.4i	−0.576524	−	0.998570i	0.419350	−	0.907825i	$-0.362258\pi$
$480$		0			0
$481$	−7586.12	+	13139.5i	−0.719121	+	1.24555i
$482$		0			0
$483$	−1275.76	+	6078.63i	−0.120184	+	0.572645i
$484$		0			0
$485$	−1871.90			−0.175255
$486$		0			0
$487$	−8547.51			−0.795328			−0.397664	−	0.917531i	$-0.630179\pi$
$487$	−8547.51			−0.795328			−0.397664	+	0.917531i	$0.630179\pi$
$488$		0			0
$489$	−991.148	+	4722.54i	−0.0916590	+	0.436729i
$490$		0			0
$491$	−5090.25	+	8816.57i	−0.467861	+	0.810359i	−0.999326	−	0.0367217i	$-0.988308\pi$
$491$	−5090.25	+	8816.57i	−0.467861	+	0.810359i	0.531465	+	0.847080i	$0.321642\pi$
$492$		0			0
$493$	1098.93	+	1903.41i	0.100392	+	0.173884i
$494$		0			0
$495$	−1250.86	−	549.245i	−0.113580	−	0.0498722i
$496$		0			0
$497$	−732.266	−	1268.32i	−0.0660898	−	0.114471i
$498$		0			0
$499$	−741.029	+	1283.50i	−0.0664790	+	0.115145i	−0.897349	−	0.441321i	$-0.854510\pi$
$499$	−741.029	+	1283.50i	−0.0664790	+	0.115145i	0.830870	+	0.556466i	$0.187843\pi$
$500$		0			0
$501$	−10682.3	−	9568.90i	−0.952598	−	0.853307i
$502$		0			0
$503$	1988.61			0.176277			0.0881387	−	0.996108i	$-0.471908\pi$
$503$	1988.61			0.176277			0.0881387	+	0.996108i	$0.471908\pi$
$504$		0			0
$505$	6185.44			0.545046
$506$		0			0
$507$	−14682.4	+	4812.28i	−1.28613	+	0.421540i
$508$		0			0
$509$	3250.95	−	5630.81i	0.283096	−	0.490337i	−0.689050	−	0.724714i	$-0.741972\pi$
$509$	3250.95	−	5630.81i	0.283096	−	0.490337i	0.972146	+	0.234377i	$0.0753051\pi$
$510$		0			0
$511$	1181.35	+	2046.16i	0.102270	+	0.177136i
$512$		0			0
$513$	9288.68	−	12994.0i	0.799425	−	1.11832i
$514$		0			0
$515$	−1224.98	−	2121.72i	−0.104813	−	0.181542i
$516$		0			0
$517$	755.088	−	1307.85i	0.0642335	−	0.111256i
$518$		0			0
$519$	−17708.7	+	5804.20i	−1.49774	+	0.490898i
$520$		0			0
$521$	1667.96			0.140258			0.0701290	−	0.997538i	$-0.477659\pi$
$521$	1667.96			0.140258			0.0701290	+	0.997538i	$0.477659\pi$
$522$		0			0
$523$	2097.89			0.175400			0.0877002	−	0.996147i	$-0.472048\pi$
$523$	2097.89			0.175400			0.0877002	+	0.996147i	$0.472048\pi$
$524$		0			0
$525$	−3106.07	−	2782.32i	−0.258210	−	0.231296i
$526$		0			0
$527$	5419.96	−	9387.65i	0.448003	−	0.775963i
$528$		0			0
$529$	−8495.99	−	14715.5i	−0.698281	−	1.20946i
$530$		0			0
$531$	−6597.45	+	4845.26i	−0.539181	+	0.395981i
$532$		0			0
$533$	15965.2	+	27652.5i	1.29743	+	2.24721i
$534$		0			0
$535$	3286.14	−	5691.76i	0.265556	−	0.459956i
$536$		0			0
$537$	3779.68	−	18009.1i	0.303734	−	1.44721i
$538$		0			0
$539$	−770.486			−0.0615717
$540$		0			0
$541$	6221.74			0.494442			0.247221	−	0.968959i	$-0.420483\pi$
$541$	6221.74			0.494442			0.247221	+	0.968959i	$0.420483\pi$
$542$		0			0
$543$	−2473.41	+	11785.1i	−0.195478	+	0.931396i
$544$		0			0
$545$	648.889	−	1123.91i	0.0510007	−	0.0883357i
$546$		0			0
$547$	−8110.97	−	14048.6i	−0.634003	−	1.09813i	−0.986725	−	0.162398i	$-0.948077\pi$
$547$	−8110.97	−	14048.6i	−0.634003	−	1.09813i	0.352722	−	0.935728i	$-0.385256\pi$
$548$		0			0
$549$	1776.15	+	16103.5i	0.138077	+	1.25188i
$550$		0			0
$551$	1355.91	+	2348.50i	0.104834	+	0.181578i
$552$		0			0
$553$	1404.96	−	2433.46i	0.108038	−	0.187127i
$554$		0			0
$555$	2627.85	+	2353.94i	0.200984	+	0.180035i
$556$		0			0
$557$	13231.8			1.00655			0.503276	−	0.864126i	$-0.332128\pi$
$557$	13231.8			1.00655			0.503276	+	0.864126i	$0.332128\pi$
$558$		0			0
$559$	−40017.9			−3.02787
$560$		0			0
$561$	−7164.12	+	2348.10i	−0.539161	+	0.176715i
$562$		0			0
$563$	−2153.81	+	3730.52i	−0.161230	+	0.279258i	−0.935310	−	0.353829i	$-0.884879\pi$
$563$	−2153.81	+	3730.52i	−0.161230	+	0.279258i	0.774080	+	0.633088i	$0.218213\pi$
$564$		0			0
$565$	−1164.17	−	2016.41i	−0.0866853	−	0.150143i
$566$		0			0
$567$	1527.02	−	4869.17i	0.113102	−	0.360645i
$568$		0			0
$569$	−8808.89	−	15257.4i	−0.649012	−	1.12412i	−0.983359	−	0.181672i	$-0.941849\pi$
$569$	−8808.89	−	15257.4i	−0.649012	−	1.12412i	0.334347	−	0.942450i	$-0.391484\pi$
$570$		0			0
$571$	3648.04	−	6318.59i	0.267366	−	0.463091i	−0.700815	−	0.713343i	$-0.747180\pi$
$571$	3648.04	−	6318.59i	0.267366	−	0.463091i	0.968181	+	0.250252i	$0.0805135\pi$
$572$		0			0
$573$	1133.28	−	371.444i	0.0826241	−	0.0270808i
$574$		0			0
$575$	19576.9			1.41985
$576$		0			0
$577$	−16357.0			−1.18015			−0.590077	−	0.807347i	$-0.700903\pi$
$577$	−16357.0			−1.18015			−0.590077	+	0.807347i	$0.700903\pi$
$578$		0			0
$579$	14738.6	+	13202.4i	1.05788	+	0.947620i
$580$		0			0
$581$	−1304.88	+	2260.12i	−0.0931767	+	0.161387i
$582$		0			0
$583$	4880.86	+	8453.90i	0.346732	+	0.600557i
$584$		0			0
$585$	684.898	+	6209.65i	0.0484052	+	0.438867i
$586$		0			0
$587$	−10203.8	−	17673.4i	−0.717469	−	1.24269i	−0.962000	−	0.273051i	$-0.911967\pi$
$587$	−10203.8	−	17673.4i	−0.717469	−	1.24269i	0.244531	−	0.969641i	$-0.421366\pi$
$588$		0			0
$589$	6687.37	−	11582.9i	0.467824	−	0.810295i
$590$		0			0
$591$	−460.407	+	2193.71i	−0.0320451	+	0.152686i
$592$		0			0
$593$	−23409.0			−1.62106			−0.810532	−	0.585695i	$-0.800822\pi$
$593$	−23409.0			−1.62106			−0.810532	+	0.585695i	$0.800822\pi$
$594$		0			0
$595$	2078.40			0.143204
$596$		0			0
$597$	307.651	−	1465.87i	0.0210910	−	0.100493i
$598$		0			0
$599$	9138.25	−	15827.9i	0.623337	−	1.07965i	−0.365523	−	0.930802i	$-0.619110\pi$
$599$	9138.25	−	15827.9i	0.623337	−	1.07965i	0.988860	−	0.148849i	$-0.0475568\pi$
$600$		0			0
$601$	8632.32	+	14951.6i	0.585889	+	1.01479i	0.994764	+	0.102200i	$0.0325881\pi$
$601$	8632.32	+	14951.6i	0.585889	+	1.01479i	−0.408874	+	0.912591i	$0.634079\pi$
$602$		0			0
$603$	−16918.2	+	12425.0i	−1.14256	+	0.839111i
$604$		0			0
$605$	−1743.65	−	3020.10i	−0.117173	−	0.202950i
$606$		0			0
$607$	−5619.29	+	9732.90i	−0.375750	+	0.650817i	−0.990439	−	0.137952i	$-0.955948\pi$
$607$	−5619.29	+	9732.90i	−0.375750	+	0.650817i	0.614689	+	0.788769i	$0.289281\pi$
$608$		0			0
$609$	645.335	+	578.071i	0.0429397	+	0.0384640i
$610$		0			0
$611$	−6905.99			−0.457261
$612$		0			0
$613$	11276.9			0.743018			0.371509	−	0.928429i	$-0.378840\pi$
$613$	11276.9			0.743018			0.371509	+	0.928429i	$0.378840\pi$
$614$		0			0
$615$	7055.42	−	2312.48i	0.462605	−	0.151623i
$616$		0			0
$617$	−10637.1	+	18424.0i	−0.694057	+	1.20214i	0.276441	+	0.961031i	$0.410845\pi$
$617$	−10637.1	+	18424.0i	−0.694057	+	1.20214i	−0.970498	+	0.241111i	$0.922488\pi$
$618$		0			0
$619$	−10395.9	−	18006.3i	−0.675037	−	1.16920i	−0.976458	−	0.215707i	$-0.930794\pi$
$619$	−10395.9	−	18006.3i	−0.675037	−	1.16920i	0.301421	−	0.953491i	$-0.402539\pi$
$620$		0			0
$621$	9912.36	+	21810.1i	0.640530	+	1.40936i
$622$		0			0
$623$	−3281.47	−	5683.67i	−0.211026	−	0.365508i
$624$		0			0
$625$	−5924.66	+	10261.8i	−0.379179	+	0.656756i
$626$		0			0
$627$	−8839.38	+	2897.19i	−0.563015	+	0.184533i
$628$		0			0
$629$	19469.4			1.23417
$630$		0			0
$631$	24359.7			1.53683			0.768417	−	0.639949i	$-0.221045\pi$
$631$	24359.7			1.53683			0.768417	+	0.639949i	$0.221045\pi$
$632$		0			0
$633$	−17789.9	−	15935.6i	−1.11704	−	1.00061i
$634$		0			0
$635$	993.926	−	1721.53i	0.0621146	−	0.107586i
$636$		0			0
$637$	1761.71	+	3051.36i	0.109578	+	0.189795i
$638$		0			0
$639$	−5172.26	−	2271.11i	−0.320206	−	0.140600i
$640$		0			0
$641$	7384.96	+	12791.1i	0.455052	+	0.788173i	0.998691	−	0.0511460i	$-0.0162874\pi$
$641$	7384.96	+	12791.1i	0.455052	+	0.788173i	−0.543639	+	0.839319i	$0.682954\pi$
$642$		0			0
$643$	−10060.2	+	17424.7i	−0.617005	+	1.06868i	0.373024	+	0.927822i	$0.378321\pi$
$643$	−10060.2	+	17424.7i	−0.617005	+	1.06868i	−0.990029	+	0.140862i	$0.955013\pi$
$644$		0			0
$645$	−1911.32	+	9106.89i	−0.116679	+	0.555944i
$646$		0			0
$647$	21010.2			1.27666			0.638329	−	0.769764i	$-0.279626\pi$
$647$	21010.2			1.27666			0.638329	+	0.769764i	$0.279626\pi$
$648$		0			0
$649$	4767.07			0.288326
$650$		0			0
$651$	877.686	−	4181.93i	0.0528406	−	0.251771i
$652$		0			0
$653$	−6631.65	+	11486.4i	−0.397422	+	0.688355i	−0.993407	−	0.114640i	$-0.963428\pi$
$653$	−6631.65	+	11486.4i	−0.397422	+	0.688355i	0.595985	+	0.802996i	$0.296762\pi$
$654$		0			0
$655$	−3291.53	−	5701.10i	−0.196352	−	0.340092i
$656$		0			0
$657$	8344.29	+	3663.92i	0.495497	+	0.217570i
$658$		0			0
$659$	10931.2	+	18933.4i	0.646160	+	1.11918i	0.984032	+	0.177990i	$0.0569596\pi$
$659$	10931.2	+	18933.4i	0.646160	+	1.11918i	−0.337872	+	0.941192i	$0.609707\pi$
$660$		0			0
$661$	4441.82	−	7693.45i	0.261372	−	0.452709i	−0.705235	−	0.708974i	$-0.749159\pi$
$661$	4441.82	−	7693.45i	0.261372	−	0.452709i	0.966607	+	0.256265i	$0.0824919\pi$
$662$		0			0
$663$	25679.9	+	23003.2i	1.50426	+	1.34747i
$664$		0			0
$665$	2564.41			0.149539
$666$		0			0
$667$	−4067.40			−0.236118
$668$		0			0
$669$	−10836.5	+	3551.76i	−0.626253	+	0.205260i
$670$		0			0
$671$	4717.59	−	8171.10i	0.271416	−	0.470107i
$672$		0			0
$673$	−15589.9	−	27002.4i	−0.892934	−	1.54661i	−0.836341	−	0.548210i	$-0.815310\pi$
$673$	−15589.9	−	27002.4i	−0.892934	−	1.54661i	−0.0565933	−	0.998397i	$-0.518024\pi$
$674$		0			0
$675$	−16008.7	−	1558.08i	−0.912852	−	0.0888454i
$676$		0			0
$677$	14788.1	+	25613.7i	0.839517	+	1.45409i	0.890299	+	0.455376i	$0.150495\pi$
$677$	14788.1	+	25613.7i	0.839517	+	1.45409i	−0.0507828	+	0.998710i	$0.516172\pi$
$678$		0			0
$679$	−2036.05	+	3526.55i	−0.115076	+	0.199317i
$680$		0			0
$681$	−11507.0	+	3771.52i	−0.647503	+	0.212225i
$682$		0			0
$683$	−6576.68			−0.368448			−0.184224	−	0.982884i	$-0.558977\pi$
$683$	−6576.68			−0.368448			−0.184224	+	0.982884i	$0.558977\pi$
$684$		0			0
$685$	124.291			0.00693272
$686$		0			0
$687$	−8364.07	−	7492.27i	−0.464497	−	0.416081i
$688$		0			0
$689$	22320.0	−	38659.5i	1.23415	−	2.13760i
$690$		0			0
$691$	−4204.38	−	7282.20i	−0.231465	−	0.400909i	0.726775	−	0.686876i	$-0.241019\pi$
$691$	−4204.38	−	7282.20i	−0.231465	−	0.400909i	−0.958239	+	0.285967i	$0.907685\pi$
$692$		0			0
$693$	−2395.30	+	1759.14i	−0.131299	+	0.0964274i
$694$		0			0
$695$	799.883	+	1385.44i	0.0436566	+	0.0756154i
$696$		0			0
$697$	20486.9	−	35484.4i	1.11334	−	1.92836i
$698$		0			0
$699$	831.446	−	3961.61i	0.0449902	−	0.214366i
$700$		0			0
$701$	28843.2			1.55406			0.777028	−	0.629466i	$-0.216726\pi$
$701$	28843.2			1.55406			0.777028	+	0.629466i	$0.216726\pi$
$702$		0			0
$703$	24022.1			1.28878
$704$		0			0
$705$	−329.841	+	1571.60i	−0.0176206	+	0.0839573i
$706$		0			0
$707$	6727.86	−	11653.0i	0.357889	−	0.619881i
$708$		0			0
$709$	−8838.72	−	15309.1i	−0.468188	−	0.810925i	0.531151	−	0.847277i	$-0.321760\pi$
$709$	−8838.72	−	15309.1i	−0.468188	−	0.810925i	−0.999339	+	0.0363520i	$0.988426\pi$
$710$		0			0
$711$	−1188.21	−	10772.9i	−0.0626741	−	0.568237i
$712$		0			0
$713$	10030.3	+	17372.9i	0.526840	+	0.912513i
$714$		0			0
$715$	1819.15	−	3150.85i	0.0951499	−	0.164804i
$716$		0			0
$717$	14971.7	+	13411.2i	0.779815	+	0.698534i
$718$		0			0
$719$	−3184.07			−0.165154			−0.0825770	−	0.996585i	$-0.526315\pi$
$719$	−3184.07			−0.165154			−0.0825770	+	0.996585i	$0.526315\pi$
$720$		0			0
$721$	−5329.59			−0.275290
$722$		0			0
$723$	13665.9	−	4479.12i	0.702961	−	0.230402i
$724$		0			0
$725$	1365.40	−	2364.93i	0.0699442	−	0.121147i
$726$		0			0
$727$	−1192.19	−	2064.94i	−0.0608197	−	0.105343i	0.834012	−	0.551746i	$-0.186038\pi$
$727$	−1192.19	−	2064.94i	−0.0608197	−	0.105343i	−0.894832	+	0.446403i	$0.852705\pi$
$728$		0			0
$729$	−6369.86	−	18623.8i	−0.323622	−	0.946186i
$730$		0			0
$731$	25676.0	+	44472.1i	1.29912	+	2.25015i
$732$		0			0
$733$	−11899.9	+	20611.3i	−0.599636	+	1.03860i	0.393239	+	0.919437i	$0.371355\pi$
$733$	−11899.9	+	20611.3i	−0.599636	+	1.03860i	−0.992875	+	0.119164i	$0.961979\pi$
$734$		0			0
$735$	778.542	−	255.174i	0.0390707	−	0.0128058i
$736$		0			0
$737$	12224.5			0.610983
$738$		0			0
$739$	−19122.2			−0.951855			−0.475928	−	0.879485i	$-0.657888\pi$
$739$	−19122.2			−0.951855			−0.475928	+	0.879485i	$0.657888\pi$
$740$		0			0
$741$	31684.9	+	28382.3i	1.57081	+	1.40709i
$742$		0			0
$743$	−8491.25	+	14707.3i	−0.419265	+	0.726188i	−0.995866	−	0.0908381i	$-0.971045\pi$
$743$	−8491.25	+	14707.3i	−0.419265	+	0.726188i	0.576601	+	0.817026i	$0.304379\pi$
$744$		0			0
$745$	4739.47	+	8209.00i	0.233075	+	0.403697i
$746$		0			0
$747$	1103.57	+	10005.6i	0.0540530	+	0.490073i
$748$		0			0
$749$	−7148.62	−	12381.8i	−0.348738	−	0.604033i
$750$		0			0
$751$	9729.75	−	16852.4i	0.472761	−	0.818846i	−0.526753	−	0.850018i	$-0.676591\pi$
$751$	9729.75	−	16852.4i	0.472761	−	0.818846i	0.999514	+	0.0311721i	$0.00992400\pi$
$752$		0			0
$753$	−2952.56	+	14068.1i	−0.142892	+	0.680838i
$754$		0			0
$755$	−2812.21			−0.135559
$756$		0			0
$757$	10578.0			0.507880			0.253940	−	0.967220i	$-0.418273\pi$
$757$	10578.0			0.507880			0.253940	+	0.967220i	$0.418273\pi$
$758$		0			0
$759$	2865.76	−	13654.5i	0.137049	−	0.653001i
$760$		0			0
$761$	9158.95	−	15863.8i	0.436283	−	0.755665i	−0.561116	−	0.827737i	$-0.689628\pi$
$761$	9158.95	−	15863.8i	0.436283	−	0.755665i	0.997399	+	0.0720721i	$0.0229612\pi$
$762$		0			0
$763$	−1411.59	−	2444.94i	−0.0669762	−	0.116006i
$764$		0			0
$765$	6461.37	−	4745.31i	0.305374	−	0.224271i
$766$		0			0
$767$	−10899.8	−	18879.1i	−0.513130	−	0.888767i
$768$		0			0
$769$	519.213	−	899.303i	0.0243476	−	0.0421713i	−0.853595	−	0.520937i	$-0.825582\pi$
$769$	519.213	−	899.303i	0.0243476	−	0.0421713i	0.877942	+	0.478766i	$0.158916\pi$
$770$		0			0
$771$	12457.3	+	11158.9i	0.581894	+	0.521242i
$772$		0			0
$773$	−34901.7			−1.62397			−0.811985	−	0.583679i	$-0.801613\pi$
$773$	−34901.7			−1.62397			−0.811985	+	0.583679i	$0.801613\pi$
$774$		0			0
$775$	−13468.3			−0.624255
$776$		0			0
$777$	7292.98	−	2390.34i	0.336724	−	0.110364i
$778$		0			0
$779$	25277.6	−	43782.1i	1.16260	−	2.01368i
$780$		0			0
$781$	1644.90	+	2849.05i	0.0753638	+	0.130534i
$782$		0			0
$783$	3326.05	+	323.716i	0.151805	+	0.0147748i
$784$		0			0
$785$	254.849	+	441.411i	0.0115872	+	0.0200696i
$786$		0			0
$787$	15556.0	−	26943.8i	0.704588	−	1.22038i	−0.262251	−	0.965000i	$-0.584465\pi$
$787$	15556.0	−	26943.8i	0.704588	−	1.22038i	0.966840	−	0.255383i	$-0.0822017\pi$
$788$		0			0
$789$	−19198.2	+	6292.38i	−0.866253	+	0.283922i
$790$		0			0
$791$	−5065.06			−0.227677
$792$		0			0
$793$	−43146.8			−1.93214
$794$		0			0
$795$	−7731.71	−	6925.82i	−0.344925	−	0.308973i
$796$		0			0
$797$	−7268.39	+	12589.2i	−0.323036	+	0.559515i	−0.981113	−	0.193436i	$-0.938037\pi$
$797$	−7268.39	+	12589.2i	−0.323036	+	0.559515i	0.658077	+	0.752951i	$0.271370\pi$
$798$		0			0
$799$	4430.97	+	7674.66i	0.196191	+	0.339812i
$800$		0			0
$801$	−23178.2	−	10177.4i	−1.02242	−	0.448939i
$802$		0			0
$803$	−2653.68	−	4596.31i	−0.116621	−	0.201993i
$804$		0			0
$805$	−1923.16	+	3331.01i	−0.0842019	+	0.145842i
$806$		0			0
$807$	1074.34	−	5118.93i	0.0468632	−	0.223290i
$808$		0			0
$809$	−9852.04			−0.428157			−0.214079	−	0.976816i	$-0.568675\pi$
$809$	−9852.04			−0.428157			−0.214079	+	0.976816i	$0.568675\pi$
$810$		0			0
$811$	25319.9			1.09630			0.548152	−	0.836378i	$-0.315331\pi$
$811$	25319.9			1.09630			0.548152	+	0.836378i	$0.315331\pi$
$812$		0			0
$813$	−7993.46	+	38086.6i	−0.344825	+	1.64300i
$814$		0			0
$815$	−1494.12	+	2587.89i	−0.0642169	+	0.111227i
$816$		0			0
$817$	31680.0	+	54871.4i	1.35660	+	2.34970i
$818$		0			0
$819$	12443.6	+	5463.88i	0.530907	+	0.233118i
$820$		0			0
$821$	−8448.26	−	14632.8i	−0.359131	−	0.622033i	0.628685	−	0.777660i	$-0.283593\pi$
$821$	−8448.26	−	14632.8i	−0.359131	−	0.622033i	−0.987816	+	0.155627i	$0.950260\pi$
$822$		0			0
$823$	−10073.8	+	17448.3i	−0.426670	+	0.739014i	−0.996575	−	0.0826970i	$-0.973647\pi$
$823$	−10073.8	+	17448.3i	−0.426670	+	0.739014i	0.569905	+	0.821711i	$0.306980\pi$
$824$		0			0
$825$	6977.22	+	6249.97i	0.294443	+	0.263753i
$826$		0			0
$827$	43947.5			1.84789			0.923944	−	0.382528i	$-0.124946\pi$
$827$	43947.5			1.84789			0.923944	+	0.382528i	$0.124946\pi$
$828$		0			0
$829$	22233.5			0.931485			0.465742	−	0.884920i	$-0.345787\pi$
$829$	22233.5			0.931485			0.465742	+	0.884920i	$0.345787\pi$
$830$		0			0
$831$	21357.2	−	7000.00i	0.891543	−	0.292211i
$832$		0			0
$833$	2260.66	−	3915.58i	0.0940304	−	0.162865i
$834$		0			0
$835$	−4440.60	−	7691.34i	−0.184040	−	0.318766i
$836$		0			0
$837$	−6819.43	−	15004.7i	−0.281617	−	0.619641i
$838$		0			0
$839$	−14171.1	−	24545.1i	−0.583125	−	1.01000i	−0.995106	−	0.0988095i	$-0.968497\pi$
$839$	−14171.1	−	24545.1i	−0.583125	−	1.01000i	0.411982	−	0.911192i	$-0.364837\pi$
$840$		0			0
$841$	11910.8	−	20630.1i	0.488368	−	0.845879i
$842$		0			0
$843$	−7985.12	+	2617.20i	−0.326242	+	0.106929i
$844$		0			0
$845$	−9568.26			−0.389536
$846$		0			0
$847$	−7586.25			−0.307753
$848$		0			0
$849$	9655.25	+	8648.87i	0.390303	+	0.349621i
$850$		0			0
$851$	−18015.2	+	31203.2i	−0.725678	+	1.25691i
$852$		0			0
$853$	13986.1	+	24224.6i	0.561399	+	0.972372i	0.997375	+	0.0724137i	$0.0230702\pi$
$853$	13986.1	+	24224.6i	0.561399	+	0.972372i	−0.435975	+	0.899959i	$0.643596\pi$
$854$		0			0
$855$	7972.30	−	5854.96i	0.318885	−	0.234193i
$856$		0			0
$857$	22699.2	+	39316.2i	0.904773	+	1.56711i	0.821221	+	0.570610i	$0.193293\pi$
$857$	22699.2	+	39316.2i	0.904773	+	1.56711i	0.0835520	+	0.996503i	$0.473374\pi$
$858$		0			0
$859$	−12874.1	+	22298.6i	−0.511360	+	0.885701i	0.488554	+	0.872534i	$0.337525\pi$
$859$	−12874.1	+	22298.6i	−0.511360	+	0.885701i	−0.999913	+	0.0131670i	$0.995809\pi$
$860$		0			0
$861$	3317.57	−	15807.3i	0.131315	−	0.625679i
$862$		0			0
$863$	4753.06			0.187481			0.0937405	−	0.995597i	$-0.470118\pi$
$863$	4753.06			0.187481			0.0937405	+	0.995597i	$0.470118\pi$
$864$		0			0
$865$	−11540.5			−0.453628
$866$		0			0
$867$	3843.45	−	18313.0i	0.150554	−	0.717348i
$868$		0			0
$869$	−3155.98	+	5466.32i	−0.123198	+	0.213386i
$870$		0			0
$871$	−27951.1	−	48412.7i	−1.08736	−	1.88336i
$872$		0			0
$873$	1721.94	+	15612.0i	0.0667570	+	0.605254i
$874$		0			0
$875$	−2698.98	−	4674.77i	−0.104277	−	0.180612i
$876$		0			0
$877$	−10976.1	+	19011.2i	−0.422619	+	0.731998i	−0.996195	−	0.0871549i	$-0.972223\pi$
$877$	−10976.1	+	19011.2i	−0.422619	+	0.731998i	0.573576	+	0.819153i	$0.305556\pi$
$878$		0			0
$879$	2510.84	+	2249.13i	0.0963464	+	0.0863040i
$880$		0			0
$881$	−22781.1			−0.871187			−0.435593	−	0.900144i	$-0.643461\pi$
$881$	−22781.1			−0.871187			−0.435593	+	0.900144i	$0.643461\pi$
$882$		0			0
$883$	11670.4			0.444780			0.222390	−	0.974958i	$-0.428614\pi$
$883$	11670.4			0.444780			0.222390	+	0.974958i	$0.428614\pi$
$884$		0			0
$885$	−4816.92	+	1578.79i	−0.182959	+	0.0599665i
$886$		0			0
$887$	−13025.6	+	22561.0i	−0.493074	+	0.854030i	−0.999968	−	0.00797889i	$-0.997460\pi$
$887$	−13025.6	+	22561.0i	−0.493074	+	0.854030i	0.506894	+	0.862008i	$0.330794\pi$
$888$		0			0
$889$	−2162.17	−	3744.99i	−0.0815714	−	0.141286i
$890$		0			0
$891$	−3430.16	+	10937.7i	−0.128973	+	0.411253i
$892$		0			0
$893$	5467.11	+	9469.31i	0.204871	+	0.354847i
$894$		0			0
$895$	5697.73	−	9868.76i	0.212798	−	0.368577i
$896$		0			0
$897$	−60628.7	+	19871.6i	−2.25678	+	0.739680i
$898$		0			0
$899$	2798.26			0.103812
$900$		0			0
$901$	−57283.2			−2.11807
$902$		0			0
$903$	15077.9	+	13506.3i	0.555661	+	0.497743i
$904$		0			0
$905$	−3728.58	+	6458.10i	−0.136953	+	0.237209i
$906$		0			0
$907$	−11163.3	−	19335.4i	−0.408678	−	0.707852i	0.586064	−	0.810265i	$-0.300677\pi$
$907$	−11163.3	−	19335.4i	−0.408678	−	0.707852i	−0.994742	+	0.102413i	$0.967344\pi$
$908$		0			0
$909$	−5689.92	−	51587.8i	−0.207616	−	1.88235i
$910$		0			0
$911$	12527.9	+	21698.9i	0.455617	+	0.789152i	0.998723	−	0.0505120i	$-0.0160853\pi$
$911$	12527.9	+	21698.9i	0.455617	+	0.789152i	−0.543106	+	0.839664i	$0.682752\pi$
$912$		0			0
$913$	2931.18	−	5076.95i	0.106252	−	0.184033i
$914$		0			0
$915$	−2060.76	+	9818.94i	−0.0744554	+	0.354759i
$916$		0			0
$917$	−14320.7			−0.515716
$918$		0			0
$919$	15968.9			0.573194			0.286597	−	0.958051i	$-0.407476\pi$
$919$	15968.9			0.573194			0.286597	+	0.958051i	$0.407476\pi$
$920$		0			0
$921$	5510.13	−	26254.2i	0.197139	−	0.939310i
$922$		0			0
$923$	7522.09	−	13028.6i	0.268248	−	0.464618i
$924$		0			0
$925$	−12095.1	−	20949.4i	−0.429930	−	0.744660i
$926$		0			0
$927$	−16568.7	+	12168.3i	−0.587043	+	0.431132i
$928$		0			0
$929$	−7757.18	−	13435.8i	−0.273956	−	0.474505i	0.695915	−	0.718124i	$-0.254999\pi$
$929$	−7757.18	−	13435.8i	−0.273956	−	0.474505i	−0.969871	+	0.243618i	$0.921666\pi$
$930$		0			0
$931$	2789.30	−	4831.20i	0.0981907	−	0.170071i
$932$		0			0
$933$	1080.54	+	967.912i	0.0379156	+	0.0339636i
$934$		0			0
$935$	−4668.74			−0.163299
$936$		0			0
$937$	10661.1			0.371700			0.185850	−	0.982578i	$-0.440496\pi$
$937$	10661.1			0.371700			0.185850	+	0.982578i	$0.440496\pi$
$938$		0			0
$939$	387.110	−	126.879i	0.0134535	−	0.00440951i
$940$		0			0
$941$	14789.0	−	25615.3i	0.512335	−	0.887391i	−0.487562	−	0.873088i	$-0.662114\pi$
$941$	14789.0	−	25615.3i	0.512335	−	0.887391i	0.999898	−	0.0143026i	$-0.00455280\pi$
$942$		0			0
$943$	37913.4	+	65668.0i	1.30926	+	2.26770i
$944$		0			0
$945$	1837.74	−	2570.82i	0.0632612	−	0.0884962i
$946$		0			0
$947$	−5943.81	−	10295.0i	−0.203958	−	0.353265i	0.745842	−	0.666122i	$-0.232047\pi$
$947$	−5943.81	−	10295.0i	−0.203958	−	0.353265i	−0.949800	+	0.312857i	$0.898714\pi$
$948$		0			0
$949$	−12135.2	+	21018.8i	−0.415095	+	0.718966i
$950$		0			0
$951$	−18289.5	+	5994.56i	−0.623637	+	0.204403i
$952$		0			0
$953$	−40462.3			−1.37534			−0.687672	−	0.726021i	$-0.741367\pi$
$953$	−40462.3			−1.37534			−0.687672	+	0.726021i	$0.741367\pi$
$954$		0			0
$955$	738.543			0.0250248
$956$		0			0
$957$	−1449.62	−	1298.53i	−0.0489652	−	0.0438615i
$958$		0			0
$959$	135.190	−	234.157i	0.00455216	−	0.00788458i
$960$		0			0
$961$	7994.95	+	13847.7i	0.268368	+	0.464827i
$962$		0			0
$963$	−50493.3	−	22171.3i	−1.68964	−	0.741910i
$964$		0			0
$965$	6126.77	+	10611.9i	0.204381	+	0.353998i
$966$		0			0
$967$	12862.9	−	22279.3i	0.427760	−	0.740903i	−0.568913	−	0.822397i	$-0.692636\pi$
$967$	12862.9	−	22279.3i	0.427760	−	0.740903i	0.996674	+	0.0814946i	$0.0259694\pi$
$968$		0			0
$969$	11212.0	−	53422.0i	0.371704	−	1.77106i
$970$		0			0
$971$	−2071.32			−0.0684571			−0.0342286	−	0.999414i	$-0.510897\pi$
$971$	−2071.32			−0.0684571			−0.0342286	+	0.999414i	$0.510897\pi$
$972$		0			0
$973$	3480.11			0.114663
$974$		0			0
$975$	8798.51	−	41922.4i	0.289003	−	1.37702i
$976$		0			0
$977$	3872.56	−	6707.48i	0.126811	−	0.219643i	−0.795628	−	0.605785i	$-0.792859\pi$
$977$	3872.56	−	6707.48i	0.126811	−	0.219643i	0.922439	+	0.386142i	$0.126193\pi$
$978$		0			0
$979$	7371.20	+	12767.3i	0.240638	+	0.416797i
$980$		0			0
$981$	−9970.53	−	4377.99i	−0.324500	−	0.142486i
$982$		0			0
$983$	−9119.10	−	15794.8i	−0.295884	−	0.512487i	0.679306	−	0.733855i	$-0.262281\pi$
$983$	−9119.10	−	15794.8i	−0.295884	−	0.512487i	−0.975190	+	0.221369i	$0.928948\pi$
$984$		0			0
$985$	−694.048	+	1202.13i	−0.0224510	+	0.0388862i
$986$		0			0
$987$	2602.04	+	2330.82i	0.0839146	+	0.0751680i
$988$		0			0
$989$	−95032.7			−3.05548
$990$		0			0
$991$	35444.9			1.13617			0.568085	−	0.822970i	$-0.307684\pi$
$991$	35444.9			1.13617			0.568085	+	0.822970i	$0.307684\pi$
$992$		0			0
$993$	31615.7	−	10362.3i	1.01037	−	0.331157i
$994$		0			0
$995$	463.773	−	803.278i	0.0147765	−	0.0255936i
$996$		0			0
$997$	3548.67	+	6146.47i	0.112726	+	0.195247i	0.916868	−	0.399190i	$-0.130709\pi$
$997$	3548.67	+	6146.47i	0.112726	+	0.195247i	−0.804143	+	0.594436i	$0.797375\pi$
$998$		0			0
$999$	17215.0	−	24082.1i	0.545205	−	0.762688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.j.b.85.5	✓	18
3.2	odd	2		756.4.j.b.253.4		18
9.2	odd	6		756.4.j.b.505.4		18
9.4	even	3		2268.4.a.i.1.4		9
9.5	odd	6		2268.4.a.h.1.6		9
9.7	even	3	inner	252.4.j.b.169.5	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.j.b.85.5	✓	18	1.1	even	1	trivial
252.4.j.b.169.5	yes	18	9.7	even	3	inner
756.4.j.b.253.4		18	3.2	odd	2
756.4.j.b.505.4		18	9.2	odd	6
2268.4.a.h.1.6		9	9.5	odd	6
2268.4.a.i.1.4		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)

\(f(q)\)	\(=\)	\(q+(1.06730 - 5.08536i) q^{3} +(1.60891 - 2.78671i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-24.7218 - 10.8552i) q^{9} +O(q^{10})\)	\(q+(1.06730 - 5.08536i) q^{3} +(1.60891 - 2.78671i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-24.7218 - 10.8552i) q^{9} +(7.86210 + 13.6176i) q^{11} +(35.9532 - 62.2727i) q^{13} +(-12.4543 - 11.1561i) q^{15} -92.2719 q^{17} -113.849 q^{19} +(-34.5639 + 11.3286i) q^{21} +(85.3800 - 147.882i) q^{23} +(57.3228 + 99.2860i) q^{25} +(-81.5878 + 114.133i) q^{27} +(-11.9097 - 20.6282i) q^{29} +(-58.7390 + 101.739i) q^{31} +(77.6413 - 25.4476i) q^{33} -22.5247 q^{35} -211.000 q^{37} +(-278.307 - 249.298i) q^{39} +(-222.028 + 384.563i) q^{41} +(-278.264 - 481.967i) q^{43} +(-70.0253 + 51.4275i) q^{45} +(-48.0208 - 83.1744i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(-98.4814 + 469.236i) q^{51} +620.809 q^{53} +50.5976 q^{55} +(-121.510 + 578.962i) q^{57} +(151.584 - 262.551i) q^{59} +(-300.021 - 519.651i) q^{61} +(20.7203 + 187.861i) q^{63} +(-115.691 - 200.382i) q^{65} +(388.715 - 673.275i) q^{67} +(-660.910 - 592.022i) q^{69} +209.219 q^{71} -337.528 q^{73} +(566.086 - 185.540i) q^{75} +(55.0347 - 95.3229i) q^{77} +(200.708 + 347.637i) q^{79} +(493.331 + 536.717i) q^{81} +(-186.412 - 322.875i) q^{83} +(-148.457 + 257.135i) q^{85} +(-117.613 + 38.5487i) q^{87} +937.562 q^{89} -503.344 q^{91} +(454.687 + 407.295i) q^{93} +(-183.172 + 317.264i) q^{95} +(-290.865 - 503.793i) q^{97} +(-46.5442 - 421.994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9}+O(q^{10}) \) 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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