LMFDB - Embedded newform 252.4.b.d.55.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(55,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("252.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.b (of order $2$, degree $1$, 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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 30x^{6} + 84x^{5} + 493x^{4} - 464x^{3} - 3172x^{2} + 1072x + 8978 $ x^8 - 4x^7 - 30x^6 + 84x^5 + 493x^4 - 464x^3 - 3172x^2 + 1072*x + 8978
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.4
Root			$4.98105 - 1.39897i$ of defining polynomial
Character	$\chi$	$=$	252.55
Dual form			252.4.b.d.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.414214 + 2.79793i) q^{2} +(-7.65685 - 2.31788i) q^{4} +8.74756i q^{5} +(13.8008 - 12.3507i) q^{7} +(9.65685 - 20.4633i) q^{8} +O(q^{10})$	\(q+(-0.414214 + 2.79793i) q^{2} +(-7.65685 - 2.31788i) q^{4} +8.74756i q^{5} +(13.8008 - 12.3507i) q^{7} +(9.65685 - 20.4633i) q^{8} +(-24.4751 - 3.62336i) q^{10} +0.397686i q^{11} -75.7263i q^{13} +(28.8399 + 43.7294i) q^{14} +(53.2548 + 35.4954i) q^{16} -84.4739i q^{17} -20.0536 q^{19} +(20.2758 - 66.9788i) q^{20} +(-1.11270 - 0.164727i) q^{22} +122.382i q^{23} +48.4802 q^{25} +(211.877 + 31.3669i) q^{26} +(-134.298 + 62.5788i) q^{28} +175.823 q^{29} +128.092 q^{31} +(-121.373 + 134.301i) q^{32} +(236.352 + 34.9902i) q^{34} +(108.038 + 120.723i) q^{35} +253.196 q^{37} +(8.30649 - 56.1087i) q^{38} +(179.004 + 84.4739i) q^{40} -81.4722i q^{41} -69.1388i q^{43} +(0.921790 - 3.04502i) q^{44} +(-342.416 - 50.6922i) q^{46} -147.923 q^{47} +(37.9218 - 340.897i) q^{49} +(-20.0812 + 135.644i) q^{50} +(-175.525 + 579.826i) q^{52} -283.921 q^{53} -3.47878 q^{55} +(-119.463 - 401.677i) q^{56} +(-72.8284 + 491.942i) q^{58} +632.911 q^{59} -3.25919i q^{61} +(-53.0574 + 358.392i) q^{62} +(-325.490 - 395.222i) q^{64} +662.420 q^{65} +551.508i q^{67} +(-195.801 + 646.804i) q^{68} +(-382.525 + 252.279i) q^{70} -486.278i q^{71} -165.946i q^{73} +(-104.877 + 708.425i) q^{74} +(153.548 + 46.4820i) q^{76} +(4.91169 + 5.48837i) q^{77} +279.010i q^{79} +(-310.498 + 465.850i) q^{80} +(227.954 + 33.7469i) q^{82} -622.183 q^{83} +738.940 q^{85} +(193.446 + 28.6382i) q^{86} +(8.13795 + 3.84039i) q^{88} -696.803i q^{89} +(-935.271 - 1045.08i) q^{91} +(283.667 - 937.060i) q^{92} +(61.2718 - 413.879i) q^{94} -175.420i q^{95} -1623.01i q^{97} +(938.100 + 247.307i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) $ 8 * q + 8 * q^2 - 16 * q^4 + 32 * q^8	$ 8 q + 8 q^{2} - 16 q^{4} + 32 q^{8} + 152 q^{14} + 64 q^{16} + 240 q^{22} - 472 q^{25} - 48 q^{28} + 592 q^{29} - 1152 q^{32} + 1392 q^{37} + 1184 q^{44} - 816 q^{46} + 1480 q^{49} - 1688 q^{50} + 1168 q^{53} - 800 q^{56} - 560 q^{58} - 3328 q^{64} - 448 q^{65} - 3200 q^{70} + 496 q^{74} - 368 q^{77} + 1024 q^{85} - 240 q^{86} + 3776 q^{88} + 3808 q^{92} + 3144 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 - 16 * q^4 + 32 * q^8 + 152 * q^14 + 64 * q^16 + 240 * q^22 - 472 * q^25 - 48 * q^28 + 592 * q^29 - 1152 * q^32 + 1392 * q^37 + 1184 * q^44 - 816 * q^46 + 1480 * q^49 - 1688 * q^50 + 1168 * q^53 - 800 * q^56 - 560 * q^58 - 3328 * q^64 - 448 * q^65 - 3200 * q^70 + 496 * q^74 - 368 * q^77 + 1024 * q^85 - 240 * q^86 + 3776 * q^88 + 3808 * q^92 + 3144 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.414214	+	2.79793i	−0.146447	+	0.989219i
$2$	−0.414214	+	2.79793i	−0.146447	+	0.989219i
$3$		0			0
$3$		0			0
$4$	−7.65685	−	2.31788i	−0.957107	−	0.289735i
$5$			8.74756i			0.782405i	0.920305	+	0.391203i	$0.127941\pi$
$5$			8.74756i			0.782405i	−0.920305	+	0.391203i	$0.872059\pi$
$6$		0			0
$7$	13.8008	−	12.3507i	0.745171	−	0.666874i
$7$	13.8008	−	12.3507i	0.745171	−	0.666874i
$8$	9.65685	−	20.4633i	0.426777	−	0.904357i
$9$		0			0
$10$	−24.4751	−	3.62336i	−0.773970	−	0.114581i
$11$			0.397686i			0.0109006i	0.999985	+	0.00545031i	$0.00173490\pi$
$11$			0.397686i			0.0109006i	−0.999985	+	0.00545031i	$0.998265\pi$
$12$		0			0
$13$		−	75.7263i		−	1.61559i	−0.589462	−	0.807796i	$-0.700660\pi$
$13$		−	75.7263i		−	1.61559i	0.589462	−	0.807796i	$-0.299340\pi$
$14$	28.8399	+	43.7294i	0.550556	+	0.834798i
$15$		0			0
$16$	53.2548	+	35.4954i	0.832107	+	0.554615i
$17$		−	84.4739i		−	1.20517i	−0.798054	−	0.602586i	$-0.794137\pi$
$17$		−	84.4739i		−	1.20517i	0.798054	−	0.602586i	$-0.205863\pi$
$18$		0			0
$19$	−20.0536			−0.242138			−0.121069	−	0.992644i	$-0.538632\pi$
$19$	−20.0536			−0.242138			−0.121069	+	0.992644i	$0.538632\pi$
$20$	20.2758	−	66.9788i	0.226691	−	0.748845i
$21$		0			0
$22$	−1.11270	−	0.164727i	−0.0107831	−	0.00159636i
$23$			122.382i			1.10950i	0.832019	+	0.554748i	$0.187185\pi$
$23$			122.382i			1.10950i	−0.832019	+	0.554748i	$0.812815\pi$
$24$		0			0
$25$	48.4802			0.387842
$26$	211.877	+	31.3669i	1.59817	+	0.236598i
$27$		0			0
$28$	−134.298	+	62.5788i	−0.906425	+	0.422367i
$29$	175.823			1.12585			0.562924	−	0.826509i	$-0.309676\pi$
$29$	175.823			1.12585			0.562924	+	0.826509i	$0.309676\pi$
$30$		0			0
$31$	128.092			0.742128			0.371064	−	0.928607i	$-0.378993\pi$
$31$	128.092			0.742128			0.371064	+	0.928607i	$0.378993\pi$
$32$	−121.373	+	134.301i	−0.670495	+	0.741914i
$33$		0			0
$34$	236.352	+	34.9902i	1.19218	+	0.176493i
$35$	108.038	+	120.723i	0.521765	+	0.583026i
$36$		0			0
$37$	253.196			1.12500			0.562502	−	0.826796i	$-0.309839\pi$
$37$	253.196			1.12500			0.562502	+	0.826796i	$0.309839\pi$
$38$	8.30649	−	56.1087i	0.0354603	−	0.239527i
$39$		0			0
$40$	179.004	+	84.4739i	0.707574	+	0.333912i
$41$		−	81.4722i		−	0.310337i	−0.987888	−	0.155169i	$-0.950408\pi$
$41$		−	81.4722i		−	0.310337i	0.987888	−	0.155169i	$-0.0495921\pi$
$42$		0			0
$43$		−	69.1388i		−	0.245199i	−0.992456	−	0.122600i	$-0.960877\pi$
$43$		−	69.1388i		−	0.245199i	0.992456	−	0.122600i	$-0.0391231\pi$
$44$	0.921790	−	3.04502i	0.00315830	−	0.0104331i
$45$		0			0
$46$	−342.416	−	50.6922i	−1.09753	−	0.162482i
$47$	−147.923			−0.459081			−0.229541	−	0.973299i	$-0.573722\pi$
$47$	−147.923			−0.459081			−0.229541	+	0.973299i	$0.573722\pi$
$48$		0			0
$49$	37.9218	−	340.897i	0.110559	−	0.993870i
$50$	−20.0812	+	135.644i	−0.0567981	+	0.383660i
$51$		0			0
$52$	−175.525	+	579.826i	−0.468094	+	1.54629i
$53$	−283.921			−0.735840			−0.367920	−	0.929857i	$-0.619930\pi$
$53$	−283.921			−0.735840			−0.367920	+	0.929857i	$0.619930\pi$
$54$		0			0
$55$	−3.47878			−0.00852870
$56$	−119.463	−	401.677i	−0.285070	−	0.958507i
$57$		0			0
$58$	−72.8284	+	491.942i	−0.164877	+	1.11371i
$59$	632.911			1.39658			0.698288	−	0.715816i	$-0.253945\pi$
$59$	632.911			1.39658			0.698288	+	0.715816i	$0.253945\pi$
$60$		0			0
$61$		−	3.25919i		−	0.00684093i	−0.999994	−	0.00342046i	$-0.998911\pi$
$61$		−	3.25919i		−	0.00684093i	0.999994	−	0.00342046i	$-0.00108877\pi$
$62$	−53.0574	+	358.392i	−0.108682	+	0.734127i
$63$		0			0
$64$	−325.490	−	395.222i	−0.635723	−	0.771917i
$65$	662.420			1.26405
$66$		0			0
$67$			551.508i			1.00563i	0.864393	+	0.502817i	$0.167703\pi$
$67$			551.508i			1.00563i	−0.864393	+	0.502817i	$0.832297\pi$
$68$	−195.801	+	646.804i	−0.349181	+	1.15348i
$69$		0			0
$70$	−382.525	+	252.279i	−0.653151	+	0.430758i
$71$		−	486.278i		−	0.812825i	−0.913690	−	0.406412i	$-0.866780\pi$
$71$		−	486.278i		−	0.812825i	0.913690	−	0.406412i	$-0.133220\pi$
$72$		0			0
$73$		−	165.946i		−	0.266062i	−0.991112	−	0.133031i	$-0.957529\pi$
$73$		−	165.946i		−	0.266062i	0.991112	−	0.133031i	$-0.0424710\pi$
$74$	−104.877	+	708.425i	−0.164753	+	1.11288i
$75$		0			0
$76$	153.548	+	46.4820i	0.231752	+	0.0701559i
$77$	4.91169	+	5.48837i	0.00726934	+	0.00812282i
$78$		0			0
$79$			279.010i			0.397355i	0.980065	+	0.198677i	$0.0636646\pi$
$79$			279.010i			0.397355i	−0.980065	+	0.198677i	$0.936335\pi$
$80$	−310.498	+	465.850i	−0.433934	+	0.651045i
$81$		0			0
$82$	227.954	+	33.7469i	0.306991	+	0.0454478i
$83$	−622.183			−0.822813			−0.411406	−	0.911452i	$-0.634962\pi$
$83$	−622.183			−0.822813			−0.411406	+	0.911452i	$0.634962\pi$
$84$		0			0
$85$	738.940			0.942933
$86$	193.446	+	28.6382i	0.242556	+	0.0359086i
$87$		0			0
$88$	8.13795	+	3.84039i	0.00985805	+	0.00465213i
$89$		−	696.803i		−	0.829898i	−0.909845	−	0.414949i	$-0.863799\pi$
$89$		−	696.803i		−	0.829898i	0.909845	−	0.414949i	$-0.136201\pi$
$90$		0			0
$91$	−935.271	−	1045.08i	−1.07740	−	1.20389i
$92$	283.667	−	937.060i	0.321460	−	1.06191i
$93$		0			0
$94$	61.2718	−	413.879i	0.0672309	−	0.454132i
$95$		−	175.420i		−	0.189450i
$96$		0			0
$97$		−	1623.01i		−	1.69889i	−0.527679	−	0.849444i	$-0.676938\pi$
$97$		−	1623.01i		−	1.69889i	0.527679	−	0.849444i	$-0.323062\pi$
$98$	938.100	+	247.307i	0.966963	+	0.254916i
$99$		0			0
$100$	−371.206	−	112.372i	−0.371206	−	0.112372i
$101$		−	774.501i		−	0.763027i	−0.924363	−	0.381513i	$-0.875403\pi$
$101$		−	774.501i		−	0.763027i	0.924363	−	0.381513i	$-0.124597\pi$
$102$		0			0
$103$	28.8584			0.0276068			0.0138034	−	0.999905i	$-0.495606\pi$
$103$	28.8584			0.0276068			0.0138034	+	0.999905i	$0.495606\pi$
$104$	−1549.61	−	731.278i	−1.46107	−	0.689497i
$105$		0			0
$106$	117.604	−	794.392i	0.107761	−	0.727907i
$107$			51.9136i			0.0469035i	0.999725	+	0.0234517i	$0.00746561\pi$
$107$			51.9136i			0.0469035i	−0.999725	+	0.0234517i	$0.992534\pi$
$108$		0			0
$109$	132.197			0.116167			0.0580833	−	0.998312i	$-0.481501\pi$
$109$	132.197			0.116167			0.0580833	+	0.998312i	$0.481501\pi$
$110$	1.44096	−	9.73339i	0.00124900	−	0.00843675i
$111$		0			0
$112$	1173.35	−	167.870i	0.989920	−	0.141627i
$113$	−318.049			−0.264774			−0.132387	−	0.991198i	$-0.542264\pi$
$113$	−318.049			−0.264774			−0.132387	+	0.991198i	$0.542264\pi$
$114$		0			0
$115$	−1070.54			−0.868075
$116$	−1346.25	−	407.538i	−1.07756	−	0.326198i
$117$		0			0
$118$	−262.160	+	1770.84i	−0.204524	+	1.38152i
$119$	−1043.31	−	1165.80i	−0.803698	−	0.898059i
$120$		0			0
$121$	1330.84			0.999881
$122$	9.11900	+	1.35000i	0.00676717	+	0.00100183i
$123$		0			0
$124$	−980.781	−	296.902i	−0.710296	−	0.215021i
$125$			1517.53i			1.08585i
$126$		0			0
$127$		−	845.289i		−	0.590608i	−0.955403	−	0.295304i	$-0.904579\pi$
$127$		−	845.289i		−	0.590608i	0.955403	−	0.295304i	$-0.0954209\pi$
$128$	1240.63	−	746.994i	0.856694	−	0.515825i
$129$		0			0
$130$	−274.384	+	1853.41i	−0.185116	+	1.25042i
$131$	−1464.88			−0.977001			−0.488501	−	0.872564i	$-0.662456\pi$
$131$	−1464.88			−0.977001			−0.488501	+	0.872564i	$0.662456\pi$
$132$		0			0
$133$	−276.755	+	247.676i	−0.180434	+	0.161475i
$134$	−1543.08	−	228.442i	−0.994791	−	0.147272i
$135$		0			0
$136$	−1728.61	−	815.752i	−1.08991	−	0.514339i
$137$	−747.803			−0.466344			−0.233172	−	0.972436i	$-0.574911\pi$
$137$	−747.803			−0.466344			−0.233172	+	0.972436i	$0.574911\pi$
$138$		0			0
$139$	2129.17			1.29924			0.649618	−	0.760261i	$-0.274929\pi$
$139$	2129.17			1.29924			0.649618	+	0.760261i	$0.274929\pi$
$140$	−547.411	−	1174.78i	−0.330462	−	0.709192i
$141$		0			0
$142$	1360.57	+	201.423i	0.804061	+	0.119035i
$143$	30.1153			0.0176110
$144$		0			0
$145$			1538.03i			0.880869i
$146$	464.306	+	68.7371i	0.263193	+	0.0389639i
$147$		0			0
$148$	−1938.68	−	586.879i	−1.07675	−	0.325954i
$149$	843.177			0.463596			0.231798	−	0.972764i	$-0.425539\pi$
$149$	843.177			0.463596			0.231798	+	0.972764i	$0.425539\pi$
$150$		0			0
$151$		−	2088.40i		−	1.12551i	−0.826625	−	0.562753i	$-0.809742\pi$
$151$		−	2088.40i		−	1.12551i	0.826625	−	0.562753i	$-0.190258\pi$
$152$	−193.655	+	410.363i	−0.103339	+	0.218979i
$153$		0			0
$154$	−17.3906	+	11.4692i	−0.00909982	+	0.00600140i
$155$			1120.49i			0.580645i
$156$		0			0
$157$		−	168.690i		−	0.0857513i	−0.999080	−	0.0428756i	$-0.986348\pi$
$157$		−	168.690i		−	0.0857513i	0.999080	−	0.0428756i	$-0.0136519\pi$
$158$	−780.650	−	115.570i	−0.393071	−	0.0581913i
$159$		0			0
$160$	−1174.80	−	1061.71i	−0.580477	−	0.524599i
$161$	1511.50	+	1688.96i	0.739893	+	0.826763i
$162$		0			0
$163$			2882.96i			1.38534i	0.721254	+	0.692670i	$0.243566\pi$
$163$			2882.96i			1.38534i	−0.721254	+	0.692670i	$0.756434\pi$
$164$	−188.843	+	623.821i	−0.0899156	+	0.297026i
$165$		0			0
$166$	257.717	−	1740.83i	0.120498	−	0.813942i
$167$	1988.79			0.921542			0.460771	−	0.887519i	$-0.347573\pi$
$167$	1988.79			0.921542			0.460771	+	0.887519i	$0.347573\pi$
$168$		0			0
$169$	−3537.48			−1.61014
$170$	−306.079	+	2067.51i	−0.138089	+	0.932767i
$171$		0			0
$172$	−160.256	+	529.386i	−0.0710429	+	0.234682i
$173$		−	2516.46i		−	1.10591i	−0.833210	−	0.552957i	$-0.813499\pi$
$173$		−	2516.46i		−	1.10591i	0.833210	−	0.552957i	$-0.186501\pi$
$174$		0			0
$175$	669.064	−	598.763i	0.289008	−	0.258641i
$176$	−14.1160	+	21.1787i	−0.00604565	+	0.00907048i
$177$		0			0
$178$	1949.61	+	288.625i	0.820951	+	0.121536i
$179$			2602.74i			1.08681i	0.839472	+	0.543403i	$0.182864\pi$
$179$			2602.74i			1.08681i	−0.839472	+	0.543403i	$0.817136\pi$
$180$		0			0
$181$			2374.53i			0.975125i	0.873088	+	0.487562i	$0.162114\pi$
$181$			2374.53i			0.975125i	−0.873088	+	0.487562i	$0.837886\pi$
$182$	3311.47	−	2183.94i	1.34869	−	0.889474i
$183$		0			0
$184$	2504.33	+	1181.82i	1.00338	+	0.473507i
$185$			2214.85i			0.880209i
$186$		0			0
$187$	33.5941			0.0131371
$188$	1132.63	+	342.869i	0.439390	+	0.133012i
$189$		0			0
$190$	490.814	+	72.6615i	0.187407	+	0.0277443i
$191$			322.049i			0.122004i	0.998138	+	0.0610018i	$0.0194295\pi$
$191$			322.049i			0.122004i	−0.998138	+	0.0610018i	$0.980570\pi$
$192$		0			0
$193$	−3949.91			−1.47316			−0.736582	−	0.676349i	$-0.763561\pi$
$193$	−3949.91			−1.47316			−0.736582	+	0.676349i	$0.763561\pi$
$194$	4541.08	+	672.274i	1.68057	+	0.248796i
$195$		0			0
$196$	−1080.52	+	2522.30i	−0.393776	+	0.919206i
$197$	−2712.37			−0.980957			−0.490478	−	0.871453i	$-0.663178\pi$
$197$	−2712.37			−0.980957			−0.490478	+	0.871453i	$0.663178\pi$
$198$		0			0
$199$	2828.98			1.00774			0.503872	−	0.863779i	$-0.331908\pi$
$199$	2828.98			1.00774			0.503872	+	0.863779i	$0.331908\pi$
$200$	468.167	−	992.064i	0.165522	−	0.350748i
$201$		0			0
$202$	2167.00	+	320.809i	0.754800	+	0.111743i
$203$	2426.50	−	2171.54i	0.838949	−	0.750798i
$204$		0			0
$205$	712.683			0.242809
$206$	−11.9535	+	80.7439i	−0.00404293	+	0.0273092i
$207$		0			0
$208$	2687.94	−	4032.79i	0.896033	−	1.34435i
$209$		−	7.97505i		−	0.00263945i
$210$		0			0
$211$			4950.07i			1.61506i	0.589828	+	0.807529i	$0.299196\pi$
$211$			4950.07i			1.61506i	−0.589828	+	0.807529i	$0.700804\pi$
$212$	2173.94	+	658.096i	0.704278	+	0.213199i
$213$		0			0
$214$	−145.251	−	21.5033i	−0.0463978	−	0.00686886i
$215$	604.796			0.191845
$216$		0			0
$217$	1767.76	−	1582.02i	0.553012	−	0.494906i
$218$	−54.7577	+	369.878i	−0.0170122	+	0.114914i
$219$		0			0
$220$	26.6365	+	8.06341i	0.00816288	+	0.00247107i
$221$	−6396.90			−1.94707
$222$		0			0
$223$	−5958.68			−1.78934			−0.894669	−	0.446729i	$-0.852589\pi$
$223$	−5958.68			−1.78934			−0.894669	+	0.446729i	$0.852589\pi$
$224$	−16.3288	+	3352.49i	−0.00487059	+	0.999988i
$225$		0			0
$226$	131.740	−	889.879i	0.0387753	−	0.261920i
$227$	817.324			0.238977			0.119488	−	0.992836i	$-0.461875\pi$
$227$	817.324			0.238977			0.119488	+	0.992836i	$0.461875\pi$
$228$		0			0
$229$			3095.86i			0.893364i	0.894693	+	0.446682i	$0.147394\pi$
$229$			3095.86i			0.893364i	−0.894693	+	0.446682i	$0.852606\pi$
$230$	443.433	−	2995.31i	0.127127	−	0.858716i
$231$		0			0
$232$	1697.90	−	3597.92i	0.480486	−	1.01817i
$233$	2649.92			0.745072			0.372536	−	0.928018i	$-0.378488\pi$
$233$	2649.92			0.745072			0.372536	+	0.928018i	$0.378488\pi$
$234$		0			0
$235$		−	1293.97i		−	0.359188i
$236$	−4846.11	−	1467.01i	−1.33667	−	0.404638i
$237$		0			0
$238$	3693.99	−	2436.22i	1.00608	−	0.663515i
$239$			4292.34i			1.16171i	0.814007	+	0.580855i	$0.197282\pi$
$239$			4292.34i			1.16171i	−0.814007	+	0.580855i	$0.802718\pi$
$240$		0			0
$241$			5048.97i			1.34951i	0.738041	+	0.674756i	$0.235751\pi$
$241$			5048.97i			1.34951i	−0.738041	+	0.674756i	$0.764249\pi$
$242$	−551.253	+	3723.61i	−0.146429	+	0.989101i
$243$		0			0
$244$	−7.55443	+	24.9552i	−0.00198206	+	0.00654750i
$245$	2982.02	+	331.723i	0.777609	+	0.0865021i
$246$		0			0
$247$			1518.59i			0.391196i
$248$	1236.96	−	2621.18i	0.316723	−	0.671149i
$249$		0			0
$250$	−4245.94	−	628.581i	−1.07415	−	0.159020i
$251$	478.767			0.120396			0.0601982	−	0.998186i	$-0.480827\pi$
$251$	478.767			0.120396			0.0601982	+	0.998186i	$0.480827\pi$
$252$		0			0
$253$	−48.6696			−0.0120942
$254$	2365.06	+	350.130i	0.584241	+	0.0864926i
$255$		0			0
$256$	1576.15	+	3780.60i	0.384803	+	0.922999i
$257$			2082.43i			0.505442i	0.967539	+	0.252721i	$0.0813255\pi$
$257$			2082.43i			0.505442i	−0.967539	+	0.252721i	$0.918674\pi$
$258$		0			0
$259$	3494.30	−	3127.14i	0.838320	−	0.750236i
$260$	−5072.06	−	1535.41i	−1.20983	−	0.366240i
$261$		0			0
$262$	606.773	−	4098.64i	0.143079	−	0.966468i
$263$		−	4105.49i		−	0.962568i	−0.876565	−	0.481284i	$-0.840171\pi$
$263$		−	4105.49i		−	0.962568i	0.876565	−	0.481284i	$-0.159829\pi$
$264$		0			0
$265$		−	2483.61i		−	0.575725i
$266$	−578.344	−	876.933i	−0.133310	−	0.202136i
$267$		0			0
$268$	1278.33	−	4222.82i	0.291368	−	0.962498i
$269$		−	6020.46i		−	1.36459i	−0.731078	−	0.682294i	$-0.760983\pi$
$269$		−	6020.46i		−	1.36459i	0.731078	−	0.682294i	$-0.239017\pi$
$270$		0			0
$271$	−108.476			−0.0243153			−0.0121577	−	0.999926i	$-0.503870\pi$
$271$	−108.476			−0.0243153			−0.0121577	+	0.999926i	$0.503870\pi$
$272$	2998.43	−	4498.64i	0.668407	−	1.00283i
$273$		0			0
$274$	309.750	−	2092.30i	0.0682945	−	0.461316i
$275$			19.2799i			0.00422772i
$276$		0			0
$277$	−1079.19			−0.234088			−0.117044	−	0.993127i	$-0.537342\pi$
$277$	−1079.19			−0.234088			−0.117044	+	0.993127i	$0.537342\pi$
$278$	−881.931	+	5957.27i	−0.190269	+	1.28523i
$279$		0			0
$280$	3513.69	−	1045.01i	0.749941	−	0.223041i
$281$	−482.626			−0.102459			−0.0512296	−	0.998687i	$-0.516314\pi$
$281$	−482.626			−0.102459			−0.0512296	+	0.998687i	$0.516314\pi$
$282$		0			0
$283$	2476.45			0.520175			0.260088	−	0.965585i	$-0.416249\pi$
$283$	2476.45			0.520175			0.260088	+	0.965585i	$0.416249\pi$
$284$	−1127.14	+	3723.36i	−0.235504	+	0.777960i
$285$		0			0
$286$	−12.4742	+	84.2606i	−0.00257907	+	0.0174211i
$287$	−1006.24	−	1124.38i	−0.206956	−	0.231254i
$288$		0			0
$289$	−2222.84			−0.452440
$290$	−4303.29	−	637.071i	−0.871372	−	0.129000i
$291$		0			0
$292$	−384.644	+	1270.63i	−0.0770876	+	0.254650i
$293$			4641.77i			0.925513i	0.886485	+	0.462757i	$0.153140\pi$
$293$			4641.77i			0.925513i	−0.886485	+	0.462757i	$0.846860\pi$
$294$		0			0
$295$			5536.43i			1.09269i
$296$	2445.08	−	5181.22i	0.480126	−	1.01741i
$297$		0			0
$298$	−349.256	+	2359.15i	−0.0678921	+	0.458598i
$299$	9267.53			1.79249
$300$		0			0
$301$	−853.911	−	954.168i	−0.163517	−	0.182715i
$302$	5843.20	+	865.043i	1.11337	+	0.164827i
$303$		0			0
$304$	−1067.95	−	711.811i	−0.201485	−	0.134293i
$305$	28.5100			0.00535238
$306$		0			0
$307$	−1544.80			−0.287187			−0.143594	−	0.989637i	$-0.545866\pi$
$307$	−1544.80			−0.287187			−0.143594	+	0.989637i	$0.545866\pi$
$308$	−24.8867	−	53.4083i	−0.00460406	−	0.00988059i
$309$		0			0
$310$	−3135.06	−	464.123i	−0.574385	−	0.0850335i
$311$	−8897.39			−1.62227			−0.811133	−	0.584862i	$-0.801149\pi$
$311$	−8897.39			−1.62227			−0.811133	+	0.584862i	$0.801149\pi$
$312$		0			0
$313$			1960.82i			0.354096i	0.984202	+	0.177048i	$0.0566548\pi$
$313$			1960.82i			0.354096i	−0.984202	+	0.177048i	$0.943345\pi$
$314$	471.984	+	69.8738i	0.0848268	+	0.0125580i
$315$		0			0
$316$	646.712	−	2136.34i	0.115128	−	0.380311i
$317$	4234.84			0.750322			0.375161	−	0.926960i	$-0.377587\pi$
$317$	4234.84			0.750322			0.375161	+	0.926960i	$0.377587\pi$
$318$		0			0
$319$			69.9225i			0.0122724i
$320$	3457.22	−	2847.25i	0.603952	−	0.497393i
$321$		0			0
$322$	−5351.69	+	3529.48i	−0.926205	+	0.610839i
$323$			1694.01i			0.291818i
$324$		0			0
$325$		−	3671.23i		−	0.626594i
$326$	−8066.32	−	1194.16i	−1.37040	−	0.202878i
$327$		0			0
$328$	−1667.19	−	786.765i	−0.280656	−	0.132445i
$329$	−2041.45	+	1826.95i	−0.342094	+	0.306149i
$330$		0			0
$331$		−	9859.53i		−	1.63725i	−0.574330	−	0.818624i	$-0.694738\pi$
$331$		−	9859.53i		−	1.63725i	0.574330	−	0.818624i	$-0.305262\pi$
$332$	4763.97	+	1442.15i	0.787520	+	0.238398i
$333$		0			0
$334$	−823.786	+	5564.51i	−0.134957	+	0.911607i
$335$	−4824.35			−0.786813
$336$		0			0
$337$	6869.41			1.11039			0.555194	−	0.831721i	$-0.312644\pi$
$337$	6869.41			1.11039			0.555194	+	0.831721i	$0.312644\pi$
$338$	1465.27	−	9897.62i	0.235800	−	1.59278i
$339$		0			0
$340$	−5657.96	−	1712.78i	−0.902488	−	0.273201i
$341$			50.9403i			0.00808966i
$342$		0			0
$343$	−3686.96	−	5173.00i	−0.580400	−	0.814332i
$344$	−1414.81	−	667.663i	−0.221748	−	0.104645i
$345$		0			0
$346$	7040.90	+	1042.35i	1.09399	+	0.161957i
$347$			257.299i			0.0398055i	0.999802	+	0.0199028i	$0.00633567\pi$
$347$			257.299i			0.0398055i	−0.999802	+	0.0199028i	$0.993664\pi$
$348$		0			0
$349$			2840.72i			0.435703i	0.975982	+	0.217851i	$0.0699048\pi$
$349$			2840.72i			0.435703i	−0.975982	+	0.217851i	$0.930095\pi$
$350$	1398.16	+	2120.01i	0.213529	+	0.323770i
$351$		0			0
$352$	−53.4095	−	48.2682i	−0.00808732	−	0.00730881i
$353$			11322.4i			1.70717i	0.520953	+	0.853585i	$0.325577\pi$
$353$			11322.4i			1.70717i	−0.520953	+	0.853585i	$0.674423\pi$
$354$		0			0
$355$	4253.74			0.635959
$356$	−1615.11	+	5335.32i	−0.240451	+	0.794301i
$357$		0			0
$358$	−7282.30	−	1078.09i	−1.07509	−	0.159159i
$359$		−	5421.36i		−	0.797014i	−0.917165	−	0.398507i	$-0.869528\pi$
$359$		−	5421.36i		−	0.797014i	0.917165	−	0.398507i	$-0.130472\pi$
$360$		0			0
$361$	−6456.85			−0.941369
$362$	−6643.78	−	983.563i	−0.964611	−	0.142804i
$363$		0			0
$364$	4738.86	+	10169.9i	0.682373	+	1.46441i
$365$	1451.62			0.208168
$366$		0			0
$367$	−10941.3			−1.55622			−0.778109	−	0.628129i	$-0.783821\pi$
$367$	−10941.3			−1.55622			−0.778109	+	0.628129i	$0.783821\pi$
$368$	−4343.99	+	6517.43i	−0.615343	+	0.923218i
$369$		0			0
$370$	−6196.99	−	917.419i	−0.870719	−	0.128904i
$371$	−3918.32	+	3506.61i	−0.548327	+	0.490713i
$372$		0			0
$373$	389.936			0.0541290			0.0270645	−	0.999634i	$-0.491384\pi$
$373$	389.936			0.0541290			0.0270645	+	0.999634i	$0.491384\pi$
$374$	−13.9151	+	93.9940i	−0.00192389	+	0.0129955i
$375$		0			0
$376$	−1428.47	+	3026.99i	−0.195925	+	0.415174i
$377$		−	13314.5i		−	1.81891i
$378$		0			0
$379$			12927.3i			1.75207i	0.482252	+	0.876033i	$0.339819\pi$
$379$			12927.3i			1.75207i	−0.482252	+	0.876033i	$0.660181\pi$
$380$	−406.604	+	1343.17i	−0.0548903	+	0.181324i
$381$		0			0
$382$	−901.072	−	133.397i	−0.120688	−	0.0178670i
$383$	−12981.5			−1.73192			−0.865960	−	0.500113i	$-0.833292\pi$
$383$	−12981.5			−1.73192			−0.865960	+	0.500113i	$0.833292\pi$
$384$		0			0
$385$	−48.0098	+	42.9653i	−0.00635534	+	0.00568757i
$386$	1636.11	−	11051.6i	0.215740	−	1.45728i
$387$		0			0
$388$	−3761.96	+	12427.2i	−0.492228	+	1.62602i
$389$	−12562.9			−1.63745			−0.818723	−	0.574188i	$-0.805318\pi$
$389$	−12562.9			−1.63745			−0.818723	+	0.574188i	$0.805318\pi$
$390$		0			0
$391$	10338.1			1.33713
$392$	−6609.67	−	4068.00i	−0.851629	−	0.524145i
$393$		0			0
$394$	1123.50	−	7589.03i	0.143658	−	0.970381i
$395$	−2440.65			−0.310893
$396$		0			0
$397$		−	5874.41i		−	0.742640i	−0.928505	−	0.371320i	$-0.878905\pi$
$397$		−	5874.41i		−	0.742640i	0.928505	−	0.371320i	$-0.121095\pi$
$398$	−1171.80	+	7915.29i	−0.147581	+	0.996878i
$399$		0			0
$400$	2581.81	+	1720.82i	0.322726	+	0.215103i
$401$	−4771.54			−0.594213			−0.297106	−	0.954844i	$-0.596022\pi$
$401$	−4771.54			−0.594213			−0.297106	+	0.954844i	$0.596022\pi$
$402$		0			0
$403$		−	9699.93i		−	1.19898i
$404$	−1795.20	+	5930.24i	−0.221076	+	0.730298i
$405$		0			0
$406$	5070.73	+	7688.65i	0.619842	+	0.939856i
$407$			100.692i			0.0122632i
$408$		0			0
$409$		−	2248.81i		−	0.271874i	−0.990718	−	0.135937i	$-0.956596\pi$
$409$		−	2248.81i		−	0.271874i	0.990718	−	0.135937i	$-0.0434044\pi$
$410$	−295.203	+	1994.04i	−0.0355586	+	0.240192i
$411$		0			0
$412$	−220.965	−	66.8904i	−0.0264227	−	0.00799868i
$413$	8734.66	−	7816.88i	1.04069	−	0.931340i
$414$		0			0
$415$		−	5442.58i		−	0.643773i
$416$	10170.1	+	9191.10i	1.19863	+	1.08325i
$417$		0			0
$418$	22.3136	+	3.30337i	0.00261099	+	0.000386539i
$419$	10323.4			1.20366			0.601829	−	0.798625i	$-0.294439\pi$
$419$	10323.4			1.20366			0.601829	+	0.798625i	$0.294439\pi$
$420$		0			0
$421$	3245.09			0.375668			0.187834	−	0.982201i	$-0.439853\pi$
$421$	3245.09			0.375668			0.187834	+	0.982201i	$0.439853\pi$
$422$	−13850.0	−	2050.39i	−1.59765	−	0.236520i
$423$		0			0
$424$	−2741.78	+	5809.95i	−0.314040	+	0.665462i
$425$		−	4095.31i		−	0.467416i
$426$		0			0
$427$	−40.2532	−	44.9793i	−0.00456204	−	0.00509766i
$428$	120.330	−	397.495i	0.0135896	−	0.0448916i
$429$		0			0
$430$	−250.515	+	1692.18i	−0.0280951	+	0.189777i
$431$		−	9556.09i		−	1.06798i	−0.845490	−	0.533992i	$-0.820691\pi$
$431$		−	9556.09i		−	1.06798i	0.845490	−	0.533992i	$-0.179309\pi$
$432$		0			0
$433$		−	5658.90i		−	0.628058i	−0.949413	−	0.314029i	$-0.898321\pi$
$433$		−	5658.90i		−	0.628058i	0.949413	−	0.314029i	$-0.101679\pi$
$434$	3694.15	+	5601.38i	0.408583	+	0.619527i
$435$		0			0
$436$	−1012.21	−	306.417i	−0.111184	−	0.0336576i
$437$		−	2454.20i		−	0.268651i
$438$		0			0
$439$	−3329.73			−0.362003			−0.181001	−	0.983483i	$-0.557934\pi$
$439$	−3329.73			−0.362003			−0.181001	+	0.983483i	$0.557934\pi$
$440$	−33.5941	+	71.1872i	−0.00363985	+	0.00771299i
$441$		0			0
$442$	2649.68	−	17898.1i	0.285141	−	1.92608i
$443$			6566.55i			0.704257i	0.935952	+	0.352129i	$0.114542\pi$
$443$			6566.55i			0.704257i	−0.935952	+	0.352129i	$0.885458\pi$
$444$		0			0
$445$	6095.32			0.649317
$446$	2468.16	−	16672.0i	0.262043	−	1.77005i
$447$		0			0
$448$	−9373.26	−	1434.33i	−0.988494	−	0.151263i
$449$	15156.4			1.59304			0.796518	−	0.604615i	$-0.206673\pi$
$449$	15156.4			1.59304			0.796518	+	0.604615i	$0.206673\pi$
$450$		0			0
$451$	32.4003			0.00338287
$452$	2435.25	+	737.200i	0.253417	+	0.0767145i
$453$		0			0
$454$	−338.547	+	2286.82i	−0.0349973	+	0.236400i
$455$	9141.90	−	8181.34i	0.941932	−	0.842961i
$456$		0			0
$457$	16572.9			1.69638			0.848191	−	0.529690i	$-0.177692\pi$
$457$	16572.9			1.69638			0.848191	+	0.529690i	$0.177692\pi$
$458$	−8662.02	−	1282.35i	−0.883732	−	0.130830i
$459$		0			0
$460$	8196.99	+	2481.39i	0.830840	+	0.251512i
$461$			5823.47i			0.588343i	0.955753	+	0.294171i	$0.0950436\pi$
$461$			5823.47i			0.588343i	−0.955753	+	0.294171i	$0.904956\pi$
$462$		0			0
$463$			12952.0i			1.30007i	0.759906	+	0.650033i	$0.225245\pi$
$463$			12952.0i			1.30007i	−0.759906	+	0.650033i	$0.774755\pi$
$464$	9363.44	+	6240.92i	0.936825	+	0.624412i
$465$		0			0
$466$	−1097.63	+	7414.29i	−0.109113	+	0.737039i
$467$	7199.70			0.713410			0.356705	−	0.934217i	$-0.383900\pi$
$467$	7199.70			0.713410			0.356705	+	0.934217i	$0.383900\pi$
$468$		0			0
$469$	6811.50	+	7611.23i	0.670630	+	0.749369i
$470$	3620.43	+	535.979i	0.355315	+	0.0526018i
$471$		0			0
$472$	6111.93	−	12951.4i	0.596027	−	1.26300i
$473$	27.4955			0.00267282
$474$		0			0
$475$	−972.205			−0.0939112
$476$	5286.27	+	11344.7i	0.509025	+	1.09240i
$477$		0			0
$478$	−12009.7	−	1777.95i	−1.14918	−	0.170128i
$479$	10505.0			1.00205			0.501027	−	0.865431i	$-0.332956\pi$
$479$	10505.0			1.00205			0.501027	+	0.865431i	$0.332956\pi$
$480$		0			0
$481$		−	19173.6i		−	1.81755i
$482$	−14126.7	−	2091.35i	−1.33496	−	0.197632i
$483$		0			0
$484$	−10190.1	−	3084.74i	−0.956993	−	0.289701i
$485$	14197.4			1.32922
$486$		0			0
$487$		−	14612.5i		−	1.35966i	−0.733369	−	0.679831i	$-0.762053\pi$
$487$		−	14612.5i		−	1.35966i	0.733369	−	0.679831i	$-0.237947\pi$
$488$	−66.6937	−	31.4735i	−0.00618664	−	0.00291955i
$489$		0			0
$490$	−2163.33	+	8206.08i	−0.199448	+	0.756557i
$491$			16952.7i			1.55818i	0.626913	+	0.779089i	$0.284318\pi$
$491$			16952.7i			1.55818i	−0.626913	+	0.779089i	$0.715682\pi$
$492$		0			0
$493$		−	14852.5i		−	1.35684i
$494$	−4248.91	−	629.020i	−0.386978	−	0.0572893i
$495$		0			0
$496$	6821.51	+	4546.67i	0.617530	+	0.411596i
$497$	−6005.86	−	6711.00i	−0.542051	−	0.605693i
$498$		0			0
$499$			17687.3i			1.58676i	0.608727	+	0.793379i	$0.291680\pi$
$499$			17687.3i			1.58676i	−0.608727	+	0.793379i	$0.708320\pi$
$500$	3517.45	−	11619.5i	0.314611	−	1.03928i
$501$		0			0
$502$	−198.312	+	1339.56i	−0.0176316	+	0.119098i
$503$	−14327.9			−1.27008			−0.635038	−	0.772481i	$-0.719016\pi$
$503$	−14327.9			−1.27008			−0.635038	+	0.772481i	$0.719016\pi$
$504$		0			0
$505$	6774.99			0.596996
$506$	20.1596	−	136.174i	0.00177115	−	0.0119638i
$507$		0			0
$508$	−1959.28	+	6472.25i	−0.171120	+	0.565275i
$509$			16759.3i			1.45941i	0.683759	+	0.729707i	$0.260344\pi$
$509$			16759.3i			1.45941i	−0.683759	+	0.729707i	$0.739656\pi$
$510$		0			0
$511$	−2049.55	−	2290.18i	−0.177430	−	0.198262i
$512$	−11230.7	+	2844.00i	−0.969400	+	0.245485i
$513$		0			0
$514$	−5826.51	−	862.572i	−0.499993	−	0.0740203i
$515$			252.441i			0.0215997i
$516$		0			0
$517$		−	58.8270i		−	0.00500427i
$518$	7302.14	+	11072.1i	0.619378	+	0.939152i
$519$		0			0
$520$	6396.90	−	13555.3i	0.539466	−	1.14315i
$521$		−	18219.8i		−	1.53210i	−0.642783	−	0.766049i	$-0.722220\pi$
$521$		−	18219.8i		−	1.53210i	0.642783	−	0.766049i	$-0.277780\pi$
$522$		0			0
$523$	−8500.33			−0.710695			−0.355348	−	0.934734i	$-0.615638\pi$
$523$	−8500.33			−0.710695			−0.355348	+	0.934734i	$0.615638\pi$
$524$	11216.4	+	3395.42i	0.935094	+	0.283072i
$525$		0			0
$526$	11486.9	+	1700.55i	0.952190	+	0.140965i
$527$		−	10820.4i		−	0.894392i
$528$		0			0
$529$	−2810.33			−0.230980
$530$	6948.99	+	1028.75i	0.569518	+	0.0843130i
$531$		0			0
$532$	2693.16	−	1254.93i	0.219480	−	0.102271i
$533$	−6169.59			−0.501378
$534$		0			0
$535$	−454.117			−0.0366975
$536$	11285.7	+	5325.83i	0.909452	+	0.429181i
$537$		0			0
$538$	16844.8	+	2493.76i	1.34988	+	0.199839i
$539$	135.570	+	15.0810i	0.0108338	+	0.00120516i
$540$		0			0
$541$	−18444.5			−1.46579			−0.732895	−	0.680342i	$-0.761831\pi$
$541$	−18444.5			−1.46579			−0.732895	+	0.680342i	$0.761831\pi$
$542$	44.9323	−	303.509i	0.00356090	−	0.0240532i
$543$		0			0
$544$	11344.9	+	10252.8i	0.894134	+	0.808062i
$545$			1156.40i			0.0908894i
$546$		0			0
$547$			16381.3i			1.28046i	0.768182	+	0.640232i	$0.221162\pi$
$547$			16381.3i			1.28046i	−0.768182	+	0.640232i	$0.778838\pi$
$548$	5725.82	+	1733.32i	0.446341	+	0.135116i
$549$		0			0
$550$	−53.9439	−	7.98600i	−0.00418214	−	0.000619135i
$551$	−3525.90			−0.272610
$552$		0			0
$553$	3445.96	+	3850.54i	0.264985	+	0.296097i
$554$	447.015	−	3019.50i	0.0342813	−	0.231564i
$555$		0			0
$556$	−16302.7	−	4935.17i	−1.24351	−	0.376435i
$557$	22097.0			1.68094			0.840468	−	0.541862i	$-0.182280\pi$
$557$	22097.0			1.68094			0.840468	+	0.541862i	$0.182280\pi$
$558$		0			0
$559$	−5235.63			−0.396142
$560$	1468.45	+	10263.9i	0.110810	+	0.774519i
$561$		0			0
$562$	199.910	−	1350.35i	0.0150048	−	0.101355i
$563$	22890.4			1.71353			0.856764	−	0.515709i	$-0.172472\pi$
$563$	22890.4			1.71353			0.856764	+	0.515709i	$0.172472\pi$
$564$		0			0
$565$		−	2782.15i		−	0.207161i
$566$	−1025.78	+	6928.94i	−0.0761779	+	0.514567i
$567$		0			0
$568$	−9950.83	−	4695.91i	−0.735084	−	0.346895i
$569$	−11664.1			−0.859375			−0.429688	−	0.902978i	$-0.641376\pi$
$569$	−11664.1			−0.859375			−0.429688	+	0.902978i	$0.641376\pi$
$570$		0			0
$571$		−	11808.4i		−	0.865439i	−0.901529	−	0.432720i	$-0.857554\pi$
$571$		−	11808.4i		−	0.865439i	0.901529	−	0.432720i	$-0.142446\pi$
$572$	−230.588	−	69.8037i	−0.0168556	−	0.00510252i
$573$		0			0
$574$	3562.73	−	2349.65i	0.259069	−	0.170858i
$575$			5933.10i			0.430309i
$576$		0			0
$577$			14572.9i			1.05144i	0.850659	+	0.525718i	$0.176203\pi$
$577$			14572.9i			1.05144i	−0.850659	+	0.525718i	$0.823797\pi$
$578$	920.730	−	6219.35i	0.0662583	−	0.447562i
$579$		0			0
$580$	3564.96	−	11776.4i	0.255219	−	0.843086i
$581$	−8586.60	+	7684.38i	−0.613136	+	0.548712i
$582$		0			0
$583$		−	112.911i		−	0.00802112i
$584$	−3395.80	−	1602.52i	−0.240615	−	0.113549i
$585$		0			0
$586$	−12987.4	−	1922.69i	−0.915535	−	0.135538i
$587$	−5506.03			−0.387152			−0.193576	−	0.981085i	$-0.562009\pi$
$587$	−5506.03			−0.387152			−0.193576	+	0.981085i	$0.562009\pi$
$588$		0			0
$589$	−2568.71			−0.179697
$590$	−15490.6	−	2293.26i	−1.08091	−	0.160021i
$591$		0			0
$592$	13483.9	+	8987.29i	0.936124	+	0.623945i
$593$		−	7223.08i		−	0.500197i	−0.968220	−	0.250098i	$-0.919537\pi$
$593$		−	7223.08i		−	0.500197i	0.968220	−	0.250098i	$-0.0804629\pi$
$594$		0			0
$595$	10197.9	−	9126.41i	0.702646	−	0.628817i
$596$	−6456.09	−	1954.39i	−0.443711	−	0.134320i
$597$		0			0
$598$	−3838.74	+	25929.9i	−0.262504	+	1.77317i
$599$			11260.6i			0.768107i	0.923311	+	0.384054i	$0.125472\pi$
$599$			11260.6i			0.768107i	−0.923311	+	0.384054i	$0.874528\pi$
$600$		0			0
$601$			25380.2i			1.72259i	0.508103	+	0.861296i	$0.330347\pi$
$601$			25380.2i			1.72259i	−0.508103	+	0.861296i	$0.669653\pi$
$602$	3023.40	−	1993.96i	0.204692	−	0.134996i
$603$		0			0
$604$	−4840.67	+	15990.6i	−0.326099	+	1.07723i
$605$			11641.6i			0.782312i
$606$		0			0
$607$	9071.99			0.606624			0.303312	−	0.952891i	$-0.401908\pi$
$607$	9071.99			0.606624			0.303312	+	0.952891i	$0.401908\pi$
$608$	2433.96	−	2693.22i	0.162352	−	0.179645i
$609$		0			0
$610$	−11.8092	+	79.7690i	−0.000783838	+	0.00529467i
$611$			11201.7i			0.741689i
$612$		0			0
$613$	10393.9			0.684837			0.342419	−	0.939547i	$-0.388754\pi$
$613$	10393.9			0.684837			0.342419	+	0.939547i	$0.388754\pi$
$614$	639.878	−	4322.25i	0.0420576	−	0.284091i
$615$		0			0
$616$	159.741	−	47.5088i	0.0104483	−	0.00310744i
$617$	−16600.4			−1.08316			−0.541578	−	0.840651i	$-0.682173\pi$
$617$	−16600.4			−1.08316			−0.541578	+	0.840651i	$0.682173\pi$
$618$		0			0
$619$	25628.2			1.66411			0.832054	−	0.554695i	$-0.187165\pi$
$619$	25628.2			1.66411			0.832054	+	0.554695i	$0.187165\pi$
$620$	2597.17	−	8579.44i	0.168233	−	0.555739i
$621$		0			0
$622$	3685.42	−	24894.3i	0.237575	−	1.60478i
$623$	−8605.98	−	9616.41i	−0.553437	−	0.618416i
$624$		0			0
$625$	−7214.64			−0.461737
$626$	−5486.25	−	812.199i	−0.350279	−	0.0518562i
$627$		0			0
$628$	−391.004	+	1291.64i	−0.0248452	+	0.0820731i
$629$		−	21388.4i		−	1.35582i
$630$		0			0
$631$			6093.01i			0.384404i	0.981355	+	0.192202i	$0.0615628\pi$
$631$			6093.01i			0.384404i	−0.981355	+	0.192202i	$0.938437\pi$
$632$	5709.45	+	2694.36i	0.359351	+	0.169582i
$633$		0			0
$634$	−1754.13	+	11848.8i	−0.109882	+	0.742233i
$635$	7394.21			0.462095
$636$		0			0
$637$	−25814.9	−	2871.68i	−1.60569	−	0.178619i
$638$	−195.638	−	28.9628i	−0.0121401	−	0.00179726i
$639$		0			0
$640$	6534.37	+	10852.4i	0.403584	+	0.670282i
$641$	9793.98			0.603493			0.301747	−	0.953388i	$-0.402430\pi$
$641$	9793.98			0.603493			0.301747	+	0.953388i	$0.402430\pi$
$642$		0			0
$643$	15275.5			0.936868			0.468434	−	0.883499i	$-0.344818\pi$
$643$	15275.5			0.936868			0.468434	+	0.883499i	$0.344818\pi$
$644$	−7658.51	−	16435.6i	−0.468614	−	1.00567i
$645$		0			0
$646$	−4739.72	−	701.681i	−0.288672	−	0.0427357i
$647$	−10058.4			−0.611184			−0.305592	−	0.952163i	$-0.598854\pi$
$647$	−10058.4			−0.611184			−0.305592	+	0.952163i	$0.598854\pi$
$648$		0			0
$649$			251.700i			0.0152236i
$650$	10271.9	+	1520.67i	0.619839	+	0.0917626i
$651$		0			0
$652$	6682.35	−	22074.4i	0.401382	−	1.32592i
$653$	−24996.0			−1.49796			−0.748981	−	0.662592i	$-0.769456\pi$
$653$	−24996.0			−1.49796			−0.748981	+	0.662592i	$0.769456\pi$
$654$		0			0
$655$		−	12814.1i		−	0.764411i
$656$	2891.89	−	4338.79i	0.172118	−	0.258234i
$657$		0			0
$658$	−4266.09	−	6468.60i	−0.252750	−	0.383240i
$659$			15031.5i			0.888532i	0.895895	+	0.444266i	$0.146536\pi$
$659$			15031.5i			0.888532i	−0.895895	+	0.444266i	$0.853464\pi$
$660$		0			0
$661$			6084.60i			0.358039i	0.983846	+	0.179019i	$0.0572924\pi$
$661$			6084.60i			0.358039i	−0.983846	+	0.179019i	$0.942708\pi$
$662$	27586.3	+	4083.95i	1.61960	+	0.239769i
$663$		0			0
$664$	−6008.33	+	12731.9i	−0.351157	+	0.744117i
$665$	−2166.56	−	2420.93i	−0.126339	−	0.141173i
$666$		0			0
$667$			21517.6i			1.24912i
$668$	−15227.9	−	4609.79i	−0.882014	−	0.267003i
$669$		0			0
$670$	1998.31	−	13498.2i	0.115226	−	0.778330i
$671$	1.29613			7.45704e−5
$672$		0			0
$673$	−9507.60			−0.544563			−0.272282	−	0.962218i	$-0.587778\pi$
$673$	−9507.60			−0.544563			−0.272282	+	0.962218i	$0.587778\pi$
$674$	−2845.40	+	19220.1i	−0.162612	+	1.09842i
$675$		0			0
$676$	27086.0	+	8199.46i	1.54108	+	0.466515i
$677$			19963.6i			1.13333i	0.823948	+	0.566665i	$0.191767\pi$
$677$			19963.6i			1.13333i	−0.823948	+	0.566665i	$0.808233\pi$
$678$		0			0
$679$	−20045.3	−	22398.8i	−1.13294	−	1.26596i
$680$	7135.84	−	15121.1i	0.402422	−	0.852748i
$681$		0			0
$682$	−142.528	−	21.1002i	−0.00800244	−	0.00118470i
$683$		−	21589.2i		−	1.20950i	−0.796415	−	0.604751i	$-0.793273\pi$
$683$		−	21589.2i		−	1.20950i	0.796415	−	0.604751i	$-0.206727\pi$
$684$		0			0
$685$		−	6541.45i		−	0.364870i
$686$	16000.9	−	8173.14i	0.890550	−	0.454886i
$687$		0			0
$688$	2454.11	−	3681.98i	0.135991	−	0.204032i
$689$			21500.3i			1.18882i
$690$		0			0
$691$	−8948.20			−0.492628			−0.246314	−	0.969190i	$-0.579219\pi$
$691$	−8948.20			−0.492628			−0.246314	+	0.969190i	$0.579219\pi$
$692$	−5832.87	+	19268.2i	−0.320423	+	1.05848i
$693$		0			0
$694$	−719.905	−	106.577i	−0.0393764	−	0.00582939i
$695$			18625.0i			1.01653i
$696$		0			0
$697$	−6882.27			−0.374010
$698$	−7948.14	−	1176.66i	−0.431005	−	0.0638072i
$699$		0			0
$700$	−6510.79	+	3033.83i	−0.351550	+	0.163812i
$701$	8280.23			0.446134			0.223067	−	0.974803i	$-0.428393\pi$
$701$	8280.23			0.446134			0.223067	+	0.974803i	$0.428393\pi$
$702$		0			0
$703$	−5077.50			−0.272406
$704$	157.174	−	129.443i	0.00841437	−	0.00692978i
$705$		0			0
$706$	−31679.4	−	4689.90i	−1.68877	−	0.250009i
$707$	−9565.61	−	10688.7i	−0.508843	−	0.568585i
$708$		0			0
$709$	4270.33			0.226200			0.113100	−	0.993584i	$-0.463922\pi$
$709$	4270.33			0.226200			0.113100	+	0.993584i	$0.463922\pi$
$710$	−1761.96	+	11901.7i	−0.0931340	+	0.629102i
$711$		0			0
$712$	−14258.9	−	6728.92i	−0.750525	−	0.354181i
$713$			15676.1i			0.823388i
$714$		0			0
$715$			263.435i			0.0137789i
$716$	6032.85	−	19928.8i	0.314886	−	1.04019i
$717$		0			0
$718$	15168.6	+	2245.60i	0.788422	+	0.116720i
$719$	−24383.1			−1.26472			−0.632362	−	0.774673i	$-0.717915\pi$
$719$	−24383.1			−1.26472			−0.632362	+	0.774673i	$0.717915\pi$
$720$		0			0
$721$	398.268	−	356.421i	0.0205718	−	0.0184103i
$722$	2674.52	−	18065.8i	0.137860	−	0.931220i
$723$		0			0
$724$	5503.89	−	18181.4i	0.282528	−	0.933298i
$725$	8523.96			0.436651
$726$		0			0
$727$	−19046.5			−0.971660			−0.485830	−	0.874053i	$-0.661483\pi$
$727$	−19046.5			−0.971660			−0.485830	+	0.874053i	$0.661483\pi$
$728$	−30417.5	+	9046.51i	−1.54856	+	0.460558i
$729$		0			0
$730$	−601.282	+	4061.54i	−0.0304855	+	0.205924i
$731$	−5840.42			−0.295507
$732$		0			0
$733$			29493.0i			1.48615i	0.669208	+	0.743075i	$0.266633\pi$
$733$			29493.0i			1.48615i	−0.669208	+	0.743075i	$0.733367\pi$
$734$	4532.04	−	30613.1i	0.227903	−	1.53944i
$735$		0			0
$736$	−16436.0	−	14853.8i	−0.823150	−	0.743911i
$737$	−219.327			−0.0109620
$738$		0			0
$739$			4813.56i			0.239607i	0.992798	+	0.119804i	$0.0382265\pi$
$739$			4813.56i			0.239607i	−0.992798	+	0.119804i	$0.961773\pi$
$740$	5133.76	−	16958.8i	0.255028	−	0.842454i
$741$		0			0
$742$	−8188.25	−	12415.7i	−0.405121	−	0.614278i
$743$		−	17606.1i		−	0.869318i	−0.900595	−	0.434659i	$-0.856869\pi$
$743$		−	17606.1i		−	0.869318i	0.900595	−	0.434659i	$-0.143131\pi$
$744$		0			0
$745$			7375.74i			0.362720i
$746$	−161.517	+	1091.01i	−0.00792701	+	0.0535454i
$747$		0			0
$748$	−257.225	−	77.8671i	−0.0125736	−	0.00380629i
$749$	641.167	+	716.446i	0.0312787	+	0.0349511i
$750$		0			0
$751$		−	6572.41i		−	0.319348i	−0.987170	−	0.159674i	$-0.948956\pi$
$751$		−	6572.41i		−	0.319348i	0.987170	−	0.159674i	$-0.0510443\pi$
$752$	−7877.63	−	5250.59i	−0.382005	−	0.254614i
$753$		0			0
$754$	37253.0	+	5515.03i	1.79930	+	0.266373i
$755$	18268.4			0.880602
$756$		0			0
$757$	−10562.7			−0.507146			−0.253573	−	0.967316i	$-0.581606\pi$
$757$	−10562.7			−0.507146			−0.253573	+	0.967316i	$0.581606\pi$
$758$	−36169.8	−	5354.68i	−1.73318	−	0.256584i
$759$		0			0
$760$	−3589.67	−	1694.01i	−0.171330	−	0.0808528i
$761$			15844.6i			0.754750i	0.926061	+	0.377375i	$0.123173\pi$
$761$			15844.6i			0.754750i	−0.926061	+	0.377375i	$0.876827\pi$
$762$		0			0
$763$	1824.42	−	1632.72i	0.0865640	−	0.0774684i
$764$	746.473	−	2465.88i	0.0353487	−	0.116770i
$765$		0			0
$766$	5377.13	−	36321.5i	0.253634	−	1.71325i
$767$		−	47928.1i		−	2.25630i
$768$		0			0
$769$			6030.08i			0.282770i	0.989955	+	0.141385i	$0.0451555\pi$
$769$			6030.08i			0.282770i	−0.989955	+	0.141385i	$0.954844\pi$
$770$	−100.328	−	152.125i	−0.00469553	−	0.00711975i
$771$		0			0
$772$	30243.9	+	9155.42i	1.40997	+	0.426828i
$773$		−	16990.3i		−	0.790556i	−0.918562	−	0.395278i	$-0.870648\pi$
$773$		−	16990.3i		−	0.790556i	0.918562	−	0.395278i	$-0.129352\pi$
$774$		0			0
$775$	6209.92			0.287828
$776$	−33212.2	−	15673.2i	−1.53640	−	0.725046i
$777$		0			0
$778$	5203.74	−	35150.3i	0.239799	−	1.61979i
$779$			1633.81i			0.0751443i
$780$		0			0
$781$	193.386			0.00886029
$782$	−4282.17	+	28925.2i	−0.195819	+	1.32272i
$783$		0			0
$784$	14119.8	−	16808.4i	0.643212	−	0.765688i
$785$	1475.63			0.0670923
$786$		0			0
$787$	−41103.6			−1.86173			−0.930867	−	0.365357i	$-0.880947\pi$
$787$	−41103.6			−1.86173			−0.930867	+	0.365357i	$0.880947\pi$
$788$	20768.2	+	6286.96i	0.938880	+	0.284218i
$789$		0			0
$790$	1010.95	−	6828.78i	0.0455292	−	0.307541i
$791$	−4389.31	+	3928.12i	−0.197302	+	0.176571i
$792$		0			0
$793$	−246.807			−0.0110522
$794$	16436.2	+	2433.26i	0.734633	+	0.108757i
$795$		0			0
$796$	−21661.1	−	6557.24i	−0.964518	−	0.291979i
$797$			6489.74i			0.288430i	0.989546	+	0.144215i	$0.0460656\pi$
$797$			6489.74i			0.288430i	−0.989546	+	0.144215i	$0.953934\pi$
$798$		0			0
$799$			12495.7i			0.553272i
$800$	−5884.17	+	6510.93i	−0.260046	+	0.287745i
$801$		0			0
$802$	1976.44	−	13350.4i	0.0870204	−	0.587806i
$803$	65.9944			0.00290024
$804$		0			0
$805$	−14774.3	+	13221.9i	−0.646864	+	0.578896i
$806$	27139.7	+	4017.84i	1.18605	+	0.175586i
$807$		0			0
$808$	−15848.8	−	7479.24i	−0.690049	−	0.325642i
$809$	2747.19			0.119390			0.0596948	−	0.998217i	$-0.480987\pi$
$809$	2747.19			0.119390			0.0596948	+	0.998217i	$0.480987\pi$
$810$		0			0
$811$	17346.1			0.751053			0.375526	−	0.926812i	$-0.377462\pi$
$811$	17346.1			0.751053			0.375526	+	0.926812i	$0.377462\pi$
$812$	−23612.7	+	11002.8i	−1.02050	+	0.475521i
$813$		0			0
$814$	−281.731	−	41.7082i	−0.0121310	−	0.00179591i
$815$	−25218.8			−1.08390
$816$		0			0
$817$			1386.48i			0.0593720i
$818$	6292.01	+	931.486i	0.268942	+	0.0398150i
$819$		0			0
$820$	−5456.91	−	1651.92i	−0.232395	−	0.0703505i
$821$	1049.07			0.0445956			0.0222978	−	0.999751i	$-0.492902\pi$
$821$	1049.07			0.0445956			0.0222978	+	0.999751i	$0.492902\pi$
$822$		0			0
$823$		−	4120.54i		−	0.174524i	−0.996185	−	0.0872618i	$-0.972188\pi$
$823$		−	4120.54i		−	0.174524i	0.996185	−	0.0872618i	$-0.0278117\pi$
$824$	278.681	−	590.537i	0.0117820	−	0.0249664i
$825$		0			0
$826$	18253.1	+	27676.8i	0.768894	+	1.16586i
$827$		−	493.902i		−	0.0207674i	−0.999946	−	0.0103837i	$-0.996695\pi$
$827$		−	493.902i		−	0.0207674i	0.999946	−	0.0103837i	$-0.00330530\pi$
$828$		0			0
$829$		−	7903.16i		−	0.331108i	−0.986201	−	0.165554i	$-0.947059\pi$
$829$		−	7903.16i		−	0.331108i	0.986201	−	0.165554i	$-0.0529412\pi$
$830$	15228.0	+	2254.39i	0.636832	+	0.0942784i
$831$		0			0
$832$	−29928.7	+	24648.2i	−1.24710	+	1.02707i
$833$	−28796.9	−	3203.40i	−1.19778	−	0.133243i
$834$		0			0
$835$			17397.1i			0.721020i
$836$	−18.4852	+	61.0638i	−0.000764743	+	0.00252624i
$837$		0			0
$838$	−4276.10	+	28884.3i	−0.176272	+	1.19068i
$839$	35079.5			1.44348			0.721739	−	0.692166i	$-0.243343\pi$
$839$	35079.5			1.44348			0.721739	+	0.692166i	$0.243343\pi$
$840$		0			0
$841$	6524.86			0.267533
$842$	−1344.16	+	9079.55i	−0.0550153	+	0.371617i
$843$		0			0
$844$	11473.7	−	37902.0i	0.467939	−	1.54578i
$845$		−	30944.3i		−	1.25978i
$846$		0			0
$847$	18366.6	−	16436.8i	0.745082	−	0.666794i
$848$	−15120.2	−	10077.9i	−0.612298	−	0.408108i
$849$		0			0
$850$	11458.4	+	1696.33i	0.462377	+	0.0684515i
$851$			30986.6i			1.24819i
$852$		0			0
$853$		−	34167.2i		−	1.37147i	−0.727852	−	0.685734i	$-0.759481\pi$
$853$		−	34167.2i		−	1.37147i	0.727852	−	0.685734i	$-0.240519\pi$
$854$	142.522	−	93.9947i	0.00571080	−	0.00376631i
$855$		0			0
$856$	1062.32	+	501.322i	0.0424175	+	0.0200173i
$857$		−	9678.21i		−	0.385766i	−0.981222	−	0.192883i	$-0.938216\pi$
$857$		−	9678.21i		−	0.385766i	0.981222	−	0.192883i	$-0.0617838\pi$
$858$		0			0
$859$	−7458.37			−0.296247			−0.148124	−	0.988969i	$-0.547323\pi$
$859$	−7458.37			−0.296247			−0.148124	+	0.988969i	$0.547323\pi$
$860$	−4630.83	−	1401.85i	−0.183616	−	0.0555844i
$861$		0			0
$862$	26737.3	+	3958.26i	1.05647	+	0.156403i
$863$			2106.36i			0.0830839i	0.999137	+	0.0415420i	$0.0132270\pi$
$863$			2106.36i			0.0830839i	−0.999137	+	0.0415420i	$0.986773\pi$
$864$		0			0
$865$	22012.9			0.865274
$866$	15833.2	+	2343.99i	0.621287	+	0.0919770i
$867$		0			0
$868$	−17202.5	+	8015.83i	−0.672684	+	0.313450i
$869$	−110.958			−0.00433141
$870$		0			0
$871$	41763.7			1.62469
$872$	1276.61	−	2705.18i	0.0495772	−	0.105056i
$873$		0			0
$874$	6866.69	+	1016.56i	0.265754	+	0.0393430i
$875$	18742.5	+	20943.0i	0.724128	+	0.809147i
$876$		0			0
$877$	1942.72			0.0748015			0.0374007	−	0.999300i	$-0.488092\pi$
$877$	1942.72			0.0748015			0.0374007	+	0.999300i	$0.488092\pi$
$878$	1379.22	−	9316.35i	0.0530141	−	0.358100i
$879$		0			0
$880$	−185.262	−	123.481i	−0.00709679	−	0.00473015i
$881$			11938.8i			0.456561i	0.973595	+	0.228280i	$0.0733103\pi$
$881$			11938.8i			0.456561i	−0.973595	+	0.228280i	$0.926690\pi$
$882$		0			0
$883$		−	6631.93i		−	0.252754i	−0.991982	−	0.126377i	$-0.959665\pi$
$883$		−	6631.93i		−	0.252754i	0.991982	−	0.126377i	$-0.0403350\pi$
$884$	48980.1	+	14827.3i	1.86355	+	0.564134i
$885$		0			0
$886$	−18372.8	−	2719.95i	−0.696664	−	0.103136i
$887$	26193.4			0.991530			0.495765	−	0.868457i	$-0.334888\pi$
$887$	26193.4			0.991530			0.495765	+	0.868457i	$0.334888\pi$
$888$		0			0
$889$	−10439.9	−	11665.6i	−0.393861	−	0.440104i
$890$	−2524.77	+	17054.3i	−0.0950903	+	0.642316i
$891$		0			0
$892$	45624.7	+	13811.5i	1.71259	+	0.518435i
$893$	2966.40			0.111161
$894$		0			0
$895$	−22767.6			−0.850322
$896$	7895.70	−	25631.6i	0.294394	−	0.955684i
$897$		0			0
$898$	−6277.97	+	42406.5i	−0.233295	+	1.57586i
$899$	22521.5			0.835523
$900$		0			0
$901$			23983.9i			0.886814i
$902$	−13.4207	+	90.6540i	−0.000495409	+	0.00334639i
$903$		0			0
$904$	−3071.35	+	6508.32i	−0.113000	+	0.239451i
$905$	−20771.4			−0.762943
$906$		0			0
$907$			19976.6i			0.731324i	0.930748	+	0.365662i	$0.119157\pi$
$907$			19976.6i			0.731324i	−0.930748	+	0.365662i	$0.880843\pi$
$908$	−6258.13	−	1894.46i	−0.228726	−	0.0692400i
$909$		0			0
$910$	19104.1	+	28967.3i	0.695929	+	1.05523i
$911$		−	33720.7i		−	1.22636i	−0.789942	−	0.613182i	$-0.789889\pi$
$911$		−	33720.7i		−	1.22636i	0.789942	−	0.613182i	$-0.210111\pi$
$912$		0			0
$913$		−	247.433i		−	0.00896917i
$914$	−6864.71	+	46369.8i	−0.248429	+	1.67809i
$915$		0			0
$916$	7175.85	−	23704.6i	0.258839	−	0.855045i
$917$	−20216.5	+	18092.3i	−0.728033	+	0.651536i
$918$		0			0
$919$			39693.8i			1.42479i	0.701780	+	0.712393i	$0.252389\pi$
$919$			39693.8i			1.42479i	−0.701780	+	0.712393i	$0.747611\pi$
$920$	−10338.1	+	21906.8i	−0.370474	+	0.785050i
$921$		0			0
$922$	−16293.7	−	2412.16i	−0.581999	−	0.0861608i
$923$	−36824.0			−1.31319
$924$		0			0
$925$	12275.0			0.436324
$926$	−36238.8	−	5364.89i	−1.28605	−	0.190390i
$927$		0			0
$928$	−21340.1	+	23613.2i	−0.754875	+	0.835282i
$929$		−	32215.1i		−	1.13772i	−0.822434	−	0.568860i	$-0.807385\pi$
$929$		−	32215.1i		−	1.13772i	0.822434	−	0.568860i	$-0.192615\pi$
$930$		0			0
$931$	−760.470	+	6836.23i	−0.0267705	+	0.240653i
$932$	−20290.0	−	6142.20i	−0.713113	−	0.215874i
$933$		0			0
$934$	−2982.21	+	20144.3i	−0.104476	+	0.705718i
$935$			293.866i			0.0102786i
$936$		0			0
$937$			28308.4i			0.986973i	0.869753	+	0.493487i	$0.164278\pi$
$937$			28308.4i			0.986973i	−0.869753	+	0.493487i	$0.835722\pi$
$938$	−24117.1	+	15905.4i	−0.839501	+	0.553657i
$939$		0			0
$940$	−2999.27	+	9907.72i	−0.104069	+	0.343781i
$941$			35128.7i			1.21696i	0.793568	+	0.608482i	$0.208221\pi$
$941$			35128.7i			1.21696i	−0.793568	+	0.608482i	$0.791779\pi$
$942$		0			0
$943$	9970.72			0.344318
$944$	33705.6	+	22465.4i	1.16210	+	0.774563i
$945$		0			0
$946$	−11.3890	+	76.9306i	−0.000391426	+	0.00264401i
$947$			49095.2i			1.68467i	0.538957	+	0.842333i	$0.318819\pi$
$947$			49095.2i			1.68467i	−0.538957	+	0.842333i	$0.681181\pi$
$948$		0			0
$949$	−12566.5			−0.429848
$950$	402.700	−	2720.16i	0.0137530	−	0.0928987i
$951$		0			0
$952$	−33931.2	+	10091.5i	−1.15517	+	0.343559i
$953$	49122.8			1.66972			0.834860	−	0.550463i	$-0.185549\pi$
$953$	49122.8			1.66972			0.834860	+	0.550463i	$0.185549\pi$
$954$		0			0
$955$	−2817.15			−0.0954562
$956$	9949.15	−	32865.8i	0.336588	−	1.11188i
$957$		0			0
$958$	−4351.30	+	29392.2i	−0.146748	+	0.991251i
$959$	−10320.2	+	9235.87i	−0.347506	+	0.310993i
$960$		0			0
$961$	−13383.5			−0.449246
$962$	53646.4	+	7941.97i	1.79795	+	0.266174i
$963$		0			0
$964$	11702.9	−	38659.2i	0.391002	−	1.29163i
$965$		−	34552.0i		−	1.15261i
$966$		0			0
$967$		−	25958.2i		−	0.863247i	−0.902054	−	0.431624i	$-0.857941\pi$
$967$		−	25958.2i		−	0.863247i	0.902054	−	0.431624i	$-0.142059\pi$
$968$	12851.7	−	27233.4i	0.426726	−	0.904250i
$969$		0			0
$970$	−5880.76	+	39723.4i	−0.194660	+	1.31489i
$971$	29381.4			0.971055			0.485528	−	0.874221i	$-0.338627\pi$
$971$	29381.4			0.971055			0.485528	+	0.874221i	$0.338627\pi$
$972$		0			0
$973$	29384.2	−	26296.7i	0.968153	−	0.866426i
$974$	40884.8	+	6052.70i	1.34500	+	0.199118i
$975$		0			0
$976$	115.686	−	173.568i	0.00379409	−	0.00569238i
$977$	31221.5			1.02238			0.511189	−	0.859468i	$-0.329205\pi$
$977$	31221.5			1.02238			0.511189	+	0.859468i	$0.329205\pi$
$978$		0			0
$979$	277.109			0.00904641
$980$	−22064.0	−	9451.93i	−0.719192	−	0.308093i
$981$		0			0
$982$	−47432.6	−	7022.05i	−1.54138	−	0.228190i
$983$	−19941.1			−0.647021			−0.323511	−	0.946225i	$-0.604863\pi$
$983$	−19941.1			−0.647021			−0.323511	+	0.946225i	$0.604863\pi$
$984$		0			0
$985$		−	23726.6i		−	0.767506i
$986$	41556.3	+	6152.10i	1.34221	+	0.198705i
$987$		0			0
$988$	3519.91	−	11627.6i	0.113343	−	0.374416i
$989$	8461.34			0.272047
$990$		0			0
$991$		−	12092.8i		−	0.387629i	−0.981038	−	0.193815i	$-0.937914\pi$
$991$		−	12092.8i		−	0.387629i	0.981038	−	0.193815i	$-0.0620861\pi$
$992$	−15546.8	+	17202.8i	−0.497593	+	0.550595i
$993$		0			0
$994$	21264.6	−	14024.2i	0.678545	−	0.447506i
$995$			24746.6i			0.788464i
$996$		0			0
$997$		−	13741.5i		−	0.436509i	−0.975892	−	0.218254i	$-0.929964\pi$
$997$		−	13741.5i		−	0.436509i	0.975892	−	0.218254i	$-0.0700362\pi$
$998$	−49487.9	−	7326.32i	−1.56965	−	0.232375i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.b.d.55.4		8
3.2	odd	2		28.4.d.b.27.5	✓	8
4.3	odd	2	inner	252.4.b.d.55.2		8
7.6	odd	2	inner	252.4.b.d.55.3		8
12.11	even	2		28.4.d.b.27.8	yes	8
21.2	odd	6		196.4.f.c.31.2		16
21.5	even	6		196.4.f.c.31.1		16
21.11	odd	6		196.4.f.c.19.6		16
21.17	even	6		196.4.f.c.19.5		16
21.20	even	2		28.4.d.b.27.6	yes	8
24.5	odd	2		448.4.f.d.447.8		8
24.11	even	2		448.4.f.d.447.2		8
28.27	even	2	inner	252.4.b.d.55.1		8
84.11	even	6		196.4.f.c.19.1		16
84.23	even	6		196.4.f.c.31.5		16
84.47	odd	6		196.4.f.c.31.6		16
84.59	odd	6		196.4.f.c.19.2		16
84.83	odd	2		28.4.d.b.27.7	yes	8
168.83	odd	2		448.4.f.d.447.7		8
168.125	even	2		448.4.f.d.447.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.d.b.27.5	✓	8	3.2	odd	2
28.4.d.b.27.6	yes	8	21.20	even	2
28.4.d.b.27.7	yes	8	84.83	odd	2
28.4.d.b.27.8	yes	8	12.11	even	2
196.4.f.c.19.1		16	84.11	even	6
196.4.f.c.19.2		16	84.59	odd	6
196.4.f.c.19.5		16	21.17	even	6
196.4.f.c.19.6		16	21.11	odd	6
196.4.f.c.31.1		16	21.5	even	6
196.4.f.c.31.2		16	21.2	odd	6
196.4.f.c.31.5		16	84.23	even	6
196.4.f.c.31.6		16	84.47	odd	6
252.4.b.d.55.1		8	28.27	even	2	inner
252.4.b.d.55.2		8	4.3	odd	2	inner
252.4.b.d.55.3		8	7.6	odd	2	inner
252.4.b.d.55.4		8	1.1	even	1	trivial
448.4.f.d.447.1		8	168.125	even	2
448.4.f.d.447.2		8	24.11	even	2
448.4.f.d.447.7		8	168.83	odd	2
448.4.f.d.447.8		8	24.5	odd	2

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.414214 + 2.79793i) q^{2} +(-7.65685 - 2.31788i) q^{4} +8.74756i q^{5} +(13.8008 - 12.3507i) q^{7} +(9.65685 - 20.4633i) q^{8} +O(q^{10})\)	\(q+(-0.414214 + 2.79793i) q^{2} +(-7.65685 - 2.31788i) q^{4} +8.74756i q^{5} +(13.8008 - 12.3507i) q^{7} +(9.65685 - 20.4633i) q^{8} +(-24.4751 - 3.62336i) q^{10} +0.397686i q^{11} -75.7263i q^{13} +(28.8399 + 43.7294i) q^{14} +(53.2548 + 35.4954i) q^{16} -84.4739i q^{17} -20.0536 q^{19} +(20.2758 - 66.9788i) q^{20} +(-1.11270 - 0.164727i) q^{22} +122.382i q^{23} +48.4802 q^{25} +(211.877 + 31.3669i) q^{26} +(-134.298 + 62.5788i) q^{28} +175.823 q^{29} +128.092 q^{31} +(-121.373 + 134.301i) q^{32} +(236.352 + 34.9902i) q^{34} +(108.038 + 120.723i) q^{35} +253.196 q^{37} +(8.30649 - 56.1087i) q^{38} +(179.004 + 84.4739i) q^{40} -81.4722i q^{41} -69.1388i q^{43} +(0.921790 - 3.04502i) q^{44} +(-342.416 - 50.6922i) q^{46} -147.923 q^{47} +(37.9218 - 340.897i) q^{49} +(-20.0812 + 135.644i) q^{50} +(-175.525 + 579.826i) q^{52} -283.921 q^{53} -3.47878 q^{55} +(-119.463 - 401.677i) q^{56} +(-72.8284 + 491.942i) q^{58} +632.911 q^{59} -3.25919i q^{61} +(-53.0574 + 358.392i) q^{62} +(-325.490 - 395.222i) q^{64} +662.420 q^{65} +551.508i q^{67} +(-195.801 + 646.804i) q^{68} +(-382.525 + 252.279i) q^{70} -486.278i q^{71} -165.946i q^{73} +(-104.877 + 708.425i) q^{74} +(153.548 + 46.4820i) q^{76} +(4.91169 + 5.48837i) q^{77} +279.010i q^{79} +(-310.498 + 465.850i) q^{80} +(227.954 + 33.7469i) q^{82} -622.183 q^{83} +738.940 q^{85} +(193.446 + 28.6382i) q^{86} +(8.13795 + 3.84039i) q^{88} -696.803i q^{89} +(-935.271 - 1045.08i) q^{91} +(283.667 - 937.060i) q^{92} +(61.2718 - 413.879i) q^{94} -175.420i q^{95} -1623.01i q^{97} +(938.100 + 247.307i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) \) 8 * q + 8 * q^2 - 16 * q^4 + 32 * q^8	\( 8 q + 8 q^{2} - 16 q^{4} + 32 q^{8} + 152 q^{14} + 64 q^{16} + 240 q^{22} - 472 q^{25} - 48 q^{28} + 592 q^{29} - 1152 q^{32} + 1392 q^{37} + 1184 q^{44} - 816 q^{46} + 1480 q^{49} - 1688 q^{50} + 1168 q^{53} - 800 q^{56} - 560 q^{58} - 3328 q^{64} - 448 q^{65} - 3200 q^{70} + 496 q^{74} - 368 q^{77} + 1024 q^{85} - 240 q^{86} + 3776 q^{88} + 3808 q^{92} + 3144 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 - 16 * q^4 + 32 * q^8 + 152 * q^14 + 64 * q^16 + 240 * q^22 - 472 * q^25 - 48 * q^28 + 592 * q^29 - 1152 * q^32 + 1392 * q^37 + 1184 * q^44 - 816 * q^46 + 1480 * q^49 - 1688 * q^50 + 1168 * q^53 - 800 * q^56 - 560 * q^58 - 3328 * q^64 - 448 * q^65 - 3200 * q^70 + 496 * q^74 - 368 * q^77 + 1024 * q^85 - 240 * q^86 + 3776 * q^88 + 3808 * q^92 + 3144 * q^98

Introduction

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