LMFDB - Embedded newform 245.4.e.p.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(116,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("245.116");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, degree $2$, not 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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 27 x^{10} + 22 x^{9} + 399 x^{8} + 492 x^{7} + 4046 x^{6} + 8784 x^{5} + 22536 x^{4} + \cdots + 784 $ x^12 - 2x^11 + 27x^10 + 22x^9 + 399x^8 + 492x^7 + 4046x^6 + 8784x^5 + 22536x^4 + 22736x^3 + 18792x^2 + 4256*x + 784
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$-1.52662 - 2.64418i$ of defining polynomial
Character	$\chi$	$=$	245.226
Dual form			245.4.e.p.116.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23372 + 3.86892i) q^{2} +(-4.90460 - 8.49501i) q^{3} +(-5.97903 - 10.3560i) q^{4} +(2.50000 - 4.33013i) q^{5} +43.8221 q^{6} +17.6824 q^{8} +(-34.6102 + 59.9466i) q^{9} +O(q^{10})$	\(q+(-2.23372 + 3.86892i) q^{2} +(-4.90460 - 8.49501i) q^{3} +(-5.97903 - 10.3560i) q^{4} +(2.50000 - 4.33013i) q^{5} +43.8221 q^{6} +17.6824 q^{8} +(-34.6102 + 59.9466i) q^{9} +(11.1686 + 19.3446i) q^{10} +(28.2702 + 48.9654i) q^{11} +(-58.6495 + 101.584i) q^{12} +40.9643 q^{13} -49.0460 q^{15} +(8.33460 - 14.4359i) q^{16} +(-1.09448 - 1.89570i) q^{17} +(-154.619 - 267.808i) q^{18} +(-8.23676 + 14.2665i) q^{19} -59.7903 q^{20} -252.591 q^{22} +(77.6361 - 134.470i) q^{23} +(-86.7253 - 150.213i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-91.5029 + 158.488i) q^{26} +414.148 q^{27} -6.26048 q^{29} +(109.555 - 189.755i) q^{30} +(-84.3401 - 146.081i) q^{31} +(107.964 + 186.999i) q^{32} +(277.308 - 480.312i) q^{33} +9.77908 q^{34} +827.742 q^{36} +(18.5869 - 32.1934i) q^{37} +(-36.7973 - 63.7348i) q^{38} +(-200.914 - 347.992i) q^{39} +(44.2061 - 76.5672i) q^{40} -266.804 q^{41} -14.6549 q^{43} +(338.057 - 585.532i) q^{44} +(173.051 + 299.733i) q^{45} +(346.835 + 600.736i) q^{46} +(84.9202 - 147.086i) q^{47} -163.511 q^{48} +111.686 q^{50} +(-10.7360 + 18.5953i) q^{51} +(-244.927 - 424.226i) q^{52} +(75.6954 + 131.108i) q^{53} +(-925.091 + 1602.30i) q^{54} +282.702 q^{55} +161.592 q^{57} +(13.9842 - 24.2213i) q^{58} +(117.038 + 202.716i) q^{59} +(293.248 + 507.920i) q^{60} +(121.206 - 209.934i) q^{61} +753.569 q^{62} -831.294 q^{64} +(102.411 - 177.381i) q^{65} +(1238.86 + 2145.77i) q^{66} +(-410.385 - 710.808i) q^{67} +(-13.0879 + 22.6689i) q^{68} -1523.10 q^{69} +961.611 q^{71} +(-611.992 + 1060.00i) q^{72} +(-467.013 - 808.890i) q^{73} +(83.0359 + 143.822i) q^{74} +(-122.615 + 212.375i) q^{75} +196.992 q^{76} +1795.14 q^{78} +(-150.118 + 260.012i) q^{79} +(-41.6730 - 72.1797i) q^{80} +(-1096.75 - 1899.63i) q^{81} +(595.966 - 1032.24i) q^{82} +1087.60 q^{83} -10.9448 q^{85} +(32.7351 - 56.6988i) q^{86} +(30.7051 + 53.1828i) q^{87} +(499.886 + 865.828i) q^{88} +(562.023 - 973.453i) q^{89} -1546.19 q^{90} -1856.76 q^{92} +(-827.309 + 1432.94i) q^{93} +(379.376 + 657.099i) q^{94} +(41.1838 + 71.3325i) q^{95} +(1059.04 - 1834.31i) q^{96} +752.168 q^{97} -3913.75 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 16 q^{3} - 14 q^{4} + 30 q^{5} + 48 q^{6} - 132 q^{8} - 70 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 - 16 * q^3 - 14 * q^4 + 30 * q^5 + 48 * q^6 - 132 * q^8 - 70 * q^9	\( 12 q + 2 q^{2} - 16 q^{3} - 14 q^{4} + 30 q^{5} + 48 q^{6} - 132 q^{8} - 70 q^{9} - 10 q^{10} + 16 q^{11} - 160 q^{12} + 336 q^{13} - 160 q^{15} - 298 q^{16} + 4 q^{17} - 354 q^{18} - 308 q^{19} - 140 q^{20} - 472 q^{22} + 336 q^{23} + 92 q^{24} - 150 q^{25} - 56 q^{26} + 1928 q^{27} + 352 q^{29} + 120 q^{30} - 392 q^{31} + 770 q^{32} - 188 q^{33} + 1624 q^{34} + 460 q^{36} + 140 q^{37} - 20 q^{38} - 140 q^{39} - 330 q^{40} + 1312 q^{41} - 776 q^{43} + 160 q^{44} + 350 q^{45} + 388 q^{46} - 628 q^{47} + 2792 q^{48} - 100 q^{50} - 744 q^{51} - 1520 q^{52} + 676 q^{53} - 2284 q^{54} + 160 q^{55} + 2936 q^{57} + 2012 q^{58} - 996 q^{59} + 800 q^{60} - 740 q^{61} - 728 q^{62} + 2852 q^{64} + 840 q^{65} + 3620 q^{66} - 1768 q^{67} + 2940 q^{68} - 2096 q^{69} - 448 q^{71} - 2858 q^{72} - 2640 q^{73} - 928 q^{74} - 400 q^{75} - 2680 q^{76} + 16 q^{78} - 1636 q^{79} + 1490 q^{80} - 4442 q^{81} + 1756 q^{82} + 280 q^{83} + 40 q^{85} - 1180 q^{86} - 1940 q^{87} + 5652 q^{88} + 1904 q^{89} - 3540 q^{90} - 3904 q^{92} + 1592 q^{93} + 3332 q^{94} + 1540 q^{95} + 6460 q^{96} + 1032 q^{97} - 5608 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 16 * q^3 - 14 * q^4 + 30 * q^5 + 48 * q^6 - 132 * q^8 - 70 * q^9 - 10 * q^10 + 16 * q^11 - 160 * q^12 + 336 * q^13 - 160 * q^15 - 298 * q^16 + 4 * q^17 - 354 * q^18 - 308 * q^19 - 140 * q^20 - 472 * q^22 + 336 * q^23 + 92 * q^24 - 150 * q^25 - 56 * q^26 + 1928 * q^27 + 352 * q^29 + 120 * q^30 - 392 * q^31 + 770 * q^32 - 188 * q^33 + 1624 * q^34 + 460 * q^36 + 140 * q^37 - 20 * q^38 - 140 * q^39 - 330 * q^40 + 1312 * q^41 - 776 * q^43 + 160 * q^44 + 350 * q^45 + 388 * q^46 - 628 * q^47 + 2792 * q^48 - 100 * q^50 - 744 * q^51 - 1520 * q^52 + 676 * q^53 - 2284 * q^54 + 160 * q^55 + 2936 * q^57 + 2012 * q^58 - 996 * q^59 + 800 * q^60 - 740 * q^61 - 728 * q^62 + 2852 * q^64 + 840 * q^65 + 3620 * q^66 - 1768 * q^67 + 2940 * q^68 - 2096 * q^69 - 448 * q^71 - 2858 * q^72 - 2640 * q^73 - 928 * q^74 - 400 * q^75 - 2680 * q^76 + 16 * q^78 - 1636 * q^79 + 1490 * q^80 - 4442 * q^81 + 1756 * q^82 + 280 * q^83 + 40 * q^85 - 1180 * q^86 - 1940 * q^87 + 5652 * q^88 + 1904 * q^89 - 3540 * q^90 - 3904 * q^92 + 1592 * q^93 + 3332 * q^94 + 1540 * q^95 + 6460 * q^96 + 1032 * q^97 - 5608 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−2.23372	+	3.86892i	−0.789740	+	1.36787i	0.136386	+	0.990656i	$0.456451\pi$
$2$	−2.23372	+	3.86892i	−0.789740	+	1.36787i	−0.926126	+	0.377214i	$0.876882\pi$
$3$	−4.90460	−	8.49501i	−0.943890	−	1.63487i	−0.757958	−	0.652304i	$-0.773803\pi$
$3$	−4.90460	−	8.49501i	−0.943890	−	1.63487i	−0.185933	−	0.982562i	$-0.559531\pi$
$4$	−5.97903	−	10.3560i	−0.747379	−	1.29450i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$	43.8221			2.98171
$7$		0			0
$7$		0			0
$8$	17.6824			0.781461
$9$	−34.6102	+	59.9466i	−1.28186	+	2.22024i
$10$	11.1686	+	19.3446i	0.353183	+	0.611730i
$11$	28.2702	+	48.9654i	0.774890	+	1.34215i	0.934856	+	0.355026i	$0.115528\pi$
$11$	28.2702	+	48.9654i	0.774890	+	1.34215i	−0.159966	+	0.987122i	$0.551139\pi$
$12$	−58.6495	+	101.584i	−1.41089	+	2.44373i
$13$	40.9643			0.873958			0.436979	−	0.899472i	$-0.356048\pi$
$13$	40.9643			0.873958			0.436979	+	0.899472i	$0.356048\pi$
$14$		0			0
$15$	−49.0460			−0.844241
$16$	8.33460	−	14.4359i	0.130228	−	0.225562i
$17$	−1.09448	−	1.89570i	−0.0156148	−	0.0270456i	0.858112	−	0.513462i	$-0.171637\pi$
$17$	−1.09448	−	1.89570i	−0.0156148	−	0.0270456i	−0.873727	+	0.486416i	$0.838304\pi$
$18$	−154.619	−	267.808i	−2.02467	−	3.50683i
$19$	−8.23676	+	14.2665i	−0.0994549	+	0.172261i	−0.911459	−	0.411391i	$-0.865043\pi$
$19$	−8.23676	+	14.2665i	−0.0994549	+	0.172261i	0.812004	+	0.583652i	$0.198377\pi$
$20$	−59.7903			−0.668476
$21$		0			0
$22$	−252.591			−2.44785
$23$	77.6361	−	134.470i	0.703837	−	1.21908i	−0.263272	−	0.964722i	$-0.584802\pi$
$23$	77.6361	−	134.470i	0.703837	−	1.21908i	0.967110	−	0.254360i	$-0.0818649\pi$
$24$	−86.7253	−	150.213i	−0.737613	−	1.27758i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−91.5029	+	158.488i	−0.690200	+	1.19546i
$27$	414.148			2.95195
$28$		0			0
$29$	−6.26048			−0.0400876			−0.0200438	−	0.999799i	$-0.506381\pi$
$29$	−6.26048			−0.0400876			−0.0200438	+	0.999799i	$0.506381\pi$
$30$	109.555	−	189.755i	0.666731	−	1.15481i
$31$	−84.3401	−	146.081i	−0.488643	−	0.846354i	0.511272	−	0.859419i	$-0.329175\pi$
$31$	−84.3401	−	146.081i	−0.488643	−	0.846354i	−0.999915	+	0.0130648i	$0.995841\pi$
$32$	107.964	+	186.999i	0.596423	+	1.03304i
$33$	277.308	−	480.312i	1.46282	−	2.53368i
$34$	9.77908			0.0493264
$35$		0			0
$36$	827.742			3.83214
$37$	18.5869	−	32.1934i	0.0825856	−	0.143042i	−0.821774	−	0.569813i	$-0.807016\pi$
$37$	18.5869	−	32.1934i	0.0825856	−	0.143042i	0.904360	+	0.426771i	$0.140349\pi$
$38$	−36.7973	−	63.7348i	−0.157087	−	0.272083i
$39$	−200.914	−	347.992i	−0.824921	−	1.42880i
$40$	44.2061	−	76.5672i	0.174740	−	0.302658i
$41$	−266.804			−1.01629			−0.508143	−	0.861273i	$-0.669668\pi$
$41$	−266.804			−1.01629			−0.508143	+	0.861273i	$0.669668\pi$
$42$		0			0
$43$	−14.6549			−0.0519735			−0.0259867	−	0.999662i	$-0.508273\pi$
$43$	−14.6549			−0.0519735			−0.0259867	+	0.999662i	$0.508273\pi$
$44$	338.057	−	585.532i	1.15827	−	2.00619i
$45$	173.051	+	299.733i	0.573264	+	0.992923i
$46$	346.835	+	600.736i	1.11170	+	1.92552i
$47$	84.9202	−	147.086i	0.263551	−	0.456483i	−0.703632	−	0.710564i	$-0.748440\pi$
$47$	84.9202	−	147.086i	0.263551	−	0.456483i	0.967183	+	0.254081i	$0.0817730\pi$
$48$	−163.511			−0.491684
$49$		0			0
$50$	111.686			0.315896
$51$	−10.7360	+	18.5953i	−0.0294773	+	0.0510561i
$52$	−244.927	−	424.226i	−0.653178	−	1.13134i
$53$	75.6954	+	131.108i	0.196180	+	0.339794i	0.947287	−	0.320387i	$-0.103813\pi$
$53$	75.6954	+	131.108i	0.196180	+	0.339794i	−0.751106	+	0.660181i	$0.770480\pi$
$54$	−925.091	+	1602.30i	−2.33128	+	4.03789i
$55$	282.702			0.693083
$56$		0			0
$57$	161.592			0.375498
$58$	13.9842	−	24.2213i	0.0316588	−	0.0548347i
$59$	117.038	+	202.716i	0.258255	+	0.447311i	0.965775	−	0.259383i	$-0.0835192\pi$
$59$	117.038	+	202.716i	0.258255	+	0.447311i	−0.707520	+	0.706694i	$0.750186\pi$
$60$	293.248	+	507.920i	0.630968	+	1.09287i
$61$	121.206	−	209.934i	0.254407	−	0.440645i	−0.710328	−	0.703871i	$-0.751453\pi$
$61$	121.206	−	209.934i	0.254407	−	0.440645i	0.964734	+	0.263226i	$0.0847865\pi$
$62$	753.569			1.54360
$63$		0			0
$64$	−831.294			−1.62362
$65$	102.411	−	177.381i	0.195423	−	0.338483i
$66$	1238.86	+	2145.77i	2.31050	+	4.00190i
$67$	−410.385	−	710.808i	−0.748307	−	1.29611i	−0.948634	−	0.316376i	$-0.897534\pi$
$67$	−410.385	−	710.808i	−0.748307	−	1.29611i	0.200327	−	0.979729i	$-0.435800\pi$
$68$	−13.0879	+	22.6689i	−0.0233403	+	0.0404266i
$69$	−1523.10			−2.65738
$70$		0			0
$71$	961.611			1.60736			0.803678	−	0.595065i	$-0.202874\pi$
$71$	961.611			1.60736			0.803678	+	0.595065i	$0.202874\pi$
$72$	−611.992	+	1060.00i	−1.00172	+	1.73503i
$73$	−467.013	−	808.890i	−0.748763	−	1.29690i	−0.948416	−	0.317029i	$-0.897315\pi$
$73$	−467.013	−	808.890i	−0.748763	−	1.29690i	0.199652	−	0.979867i	$-0.436019\pi$
$74$	83.0359	+	143.822i	0.130442	+	0.225933i
$75$	−122.615	+	212.375i	−0.188778	+	0.326973i
$76$	196.992			0.297322
$77$		0			0
$78$	1795.14			2.60589
$79$	−150.118	+	260.012i	−0.213792	+	0.370299i	−0.952898	−	0.303290i	$-0.901915\pi$
$79$	−150.118	+	260.012i	−0.213792	+	0.370299i	0.739106	+	0.673589i	$0.235248\pi$
$80$	−41.6730	−	72.1797i	−0.0582398	−	0.100874i
$81$	−1096.75	−	1899.63i	−1.50446	−	2.60581i
$82$	595.966	−	1032.24i	0.802602	−	1.39015i
$83$	1087.60			1.43830			0.719151	−	0.694854i	$-0.244531\pi$
$83$	1087.60			1.43830			0.719151	+	0.694854i	$0.244531\pi$
$84$		0			0
$85$	−10.9448			−0.0139663
$86$	32.7351	−	56.6988i	0.0410455	−	0.0710929i
$87$	30.7051	+	53.1828i	0.0378383	+	0.0655379i
$88$	499.886	+	865.828i	0.605546	+	1.04884i
$89$	562.023	−	973.453i	0.669375	−	1.15939i	−0.308704	−	0.951158i	$-0.599895\pi$
$89$	562.023	−	973.453i	0.669375	−	1.15939i	0.978079	−	0.208233i	$-0.0667713\pi$
$90$	−1546.19			−1.81092
$91$		0			0
$92$	−1856.76			−2.10413
$93$	−827.309	+	1432.94i	−0.922451	+	1.59773i
$94$	379.376	+	657.099i	0.416273	+	0.721007i
$95$	41.1838	+	71.3325i	0.0444776	+	0.0770374i
$96$	1059.04	−	1834.31i	1.12592	−	1.95014i
$97$	752.168			0.787330			0.393665	−	0.919254i	$-0.371207\pi$
$97$	752.168			0.787330			0.393665	+	0.919254i	$0.371207\pi$
$98$		0			0
$99$	−3913.75			−3.97320
$100$	−149.476	+	258.900i	−0.149476	+	0.258900i
$101$	−279.613	−	484.304i	−0.275471	−	0.477129i	0.694783	−	0.719219i	$-0.255500\pi$
$101$	−279.613	−	484.304i	−0.275471	−	0.477129i	−0.970254	+	0.242090i	$0.922167\pi$
$102$	−47.9625	−	83.0734i	−0.0465587	−	0.0806421i
$103$	102.665	−	177.822i	0.0982128	−	0.170110i	−0.812732	−	0.582637i	$-0.802021\pi$
$103$	102.665	−	177.822i	0.0982128	−	0.170110i	0.910945	+	0.412528i	$0.135354\pi$
$104$	724.349			0.682964
$105$		0			0
$106$	−676.330			−0.619726
$107$	735.086	−	1273.21i	0.664145	−	1.15033i	−0.315372	−	0.948968i	$-0.602129\pi$
$107$	735.086	−	1273.21i	0.664145	−	1.15033i	0.979516	−	0.201364i	$-0.0645375\pi$
$108$	−2476.20	−	4288.91i	−2.20623	−	3.82130i
$109$	387.096	+	670.471i	0.340157	+	0.589169i	0.984462	−	0.175600i	$-0.0561864\pi$
$109$	387.096	+	670.471i	0.340157	+	0.589169i	−0.644305	+	0.764769i	$0.722853\pi$
$110$	−631.478	+	1093.75i	−0.547355	+	0.948047i
$111$	−364.645			−0.311807
$112$		0			0
$113$	−406.121			−0.338094			−0.169047	−	0.985608i	$-0.554069\pi$
$113$	−406.121			−0.338094			−0.169047	+	0.985608i	$0.554069\pi$
$114$	−360.952	+	625.187i	−0.296546	+	0.513633i
$115$	−388.181	−	672.349i	−0.314766	−	0.545190i
$116$	37.4316	+	64.8334i	0.0299607	+	0.0518934i
$117$	−1417.78	+	2455.67i	−1.12029	+	1.94040i
$118$	−1045.72			−0.815817
$119$		0			0
$120$	−867.253			−0.659742
$121$	−932.909	+	1615.85i	−0.700909	+	1.21401i
$122$	541.480	+	937.871i	0.401830	+	0.695990i
$123$	1308.57	+	2266.50i	0.959263	+	1.66149i
$124$	−1008.54	+	1746.85i	−0.730403	+	1.26509i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−451.639			−0.315563			−0.157781	−	0.987474i	$-0.550434\pi$
$127$	−451.639			−0.315563			−0.157781	+	0.987474i	$0.550434\pi$
$128$	993.167	−	1720.22i	0.685816	−	1.18787i
$129$	71.8766	+	124.494i	0.0490572	+	0.0849696i
$130$	457.515	+	792.439i	0.308667	+	0.534627i
$131$	−180.966	+	313.442i	−0.120695	+	0.209050i	−0.920042	−	0.391820i	$-0.871846\pi$
$131$	−180.966	+	313.442i	−0.120695	+	0.209050i	0.799347	+	0.600870i	$0.205179\pi$
$132$	−6632.14			−4.37313
$133$		0			0
$134$	3666.75			2.36387
$135$	1035.37	−	1793.31i	0.660077	−	1.14329i
$136$	−19.3531	−	33.5206i	−0.0122023	−	0.0211350i
$137$	−1256.36	−	2176.08i	−0.783490	−	1.35705i	−0.929897	−	0.367821i	$-0.880104\pi$
$137$	−1256.36	−	2176.08i	−0.783490	−	1.35705i	0.146406	−	0.989225i	$-0.453229\pi$
$138$	3402.18	−	5892.74i	2.09864	−	3.63495i
$139$	1165.71			0.711324			0.355662	−	0.934615i	$-0.384255\pi$
$139$	1165.71			0.711324			0.355662	+	0.934615i	$0.384255\pi$
$140$		0			0
$141$	−1666.00			−0.995052
$142$	−2147.97	+	3720.40i	−1.26939	+	2.19865i
$143$	1158.07	+	2005.84i	0.677221	+	1.17298i
$144$	576.924	+	999.261i	0.333868	+	0.578276i
$145$	−15.6512	+	27.1087i	−0.00896387	+	0.0155259i
$146$	4172.71			2.36531
$147$		0			0
$148$	−444.526			−0.246891
$149$	1318.74	−	2284.13i	0.725072	−	1.25586i	−0.233872	−	0.972267i	$-0.575140\pi$
$149$	1318.74	−	2284.13i	0.725072	−	1.25586i	0.958944	−	0.283595i	$-0.0915271\pi$
$150$	−547.776	−	948.775i	−0.298171	−	0.516448i
$151$	1291.16	+	2236.36i	0.695849	+	1.20525i	0.969894	+	0.243529i	$0.0783051\pi$
$151$	1291.16	+	2236.36i	0.695849	+	1.20525i	−0.274044	+	0.961717i	$0.588362\pi$
$152$	−145.646	+	252.266i	−0.0777201	+	0.134615i
$153$	151.521			0.0800637
$154$		0			0
$155$	−843.401			−0.437055
$156$	−2402.54	+	4161.32i	−1.23306	+	2.13572i
$157$	−112.894	−	195.538i	−0.0573880	−	0.0993989i	0.835904	−	0.548875i	$-0.184944\pi$
$157$	−112.894	−	195.538i	−0.0573880	−	0.0993989i	−0.893292	+	0.449477i	$0.851611\pi$
$158$	−670.643	−	1161.59i	−0.337680	−	0.584879i
$159$	742.511	−	1286.07i	0.370346	−	0.641457i
$160$	1079.64			0.533457
$161$		0			0
$162$	9799.38			4.75254
$163$	−744.504	+	1289.52i	−0.357755	+	0.619649i	−0.987585	−	0.157083i	$-0.949791\pi$
$163$	−744.504	+	1289.52i	−0.357755	+	0.619649i	0.629831	+	0.776732i	$0.283124\pi$
$164$	1595.23	+	2763.02i	0.759551	+	1.31558i
$165$	−1386.54	−	2401.56i	−0.654194	−	1.13310i
$166$	−2429.39	+	4207.82i	−1.13588	+	1.96741i
$167$	2858.73			1.32464			0.662322	−	0.749220i	$-0.269571\pi$
$167$	2858.73			1.32464			0.662322	+	0.749220i	$0.269571\pi$
$168$		0			0
$169$	−518.925			−0.236197
$170$	24.4477	−	42.3447i	0.0110297	−	0.0191040i
$171$	−570.152	−	987.532i	−0.254974	−	0.441628i
$172$	87.6224	+	151.766i	0.0388439	+	0.0672796i
$173$	16.0020	−	27.7163i	0.00703242	−	0.0121805i	−0.862488	−	0.506078i	$-0.831095\pi$
$173$	16.0020	−	27.7163i	0.00703242	−	0.0121805i	0.869520	+	0.493897i	$0.164428\pi$
$174$	−274.347			−0.119530
$175$		0			0
$176$	942.483			0.403650
$177$	1148.05	−	1988.48i	0.487529	−	0.844425i
$178$	2510.81	+	4348.85i	1.05726	+	1.83124i
$179$	−369.222	−	639.511i	−0.154173	−	0.267035i	0.778585	−	0.627540i	$-0.215938\pi$
$179$	−369.222	−	639.511i	−0.154173	−	0.267035i	−0.932758	+	0.360504i	$0.882605\pi$
$180$	2069.35	−	3584.23i	0.856892	−	1.48418i
$181$	−1991.91			−0.817997			−0.408998	−	0.912535i	$-0.634122\pi$
$181$	−1991.91			−0.817997			−0.408998	+	0.912535i	$0.634122\pi$
$182$		0			0
$183$	−2377.86			−0.960528
$184$	1372.80	−	2377.75i	0.550021	−	0.952665i
$185$	−92.9344	−	160.967i	−0.0369334	−	0.0639705i
$186$	−3695.96	−	6401.58i	−1.45699	−	2.52359i
$187$	61.8825	−	107.184i	0.0241994	−	0.0419147i
$188$	−2030.96			−0.787890
$189$		0			0
$190$	−367.973			−0.140503
$191$	−1076.84	+	1865.14i	−0.407945	+	0.706582i	−0.994659	−	0.103212i	$-0.967088\pi$
$191$	−1076.84	+	1865.14i	−0.407945	+	0.706582i	0.586714	+	0.809794i	$0.300421\pi$
$192$	4077.16	+	7061.85i	1.53252	+	2.65440i
$193$	−501.970	−	869.437i	−0.187215	−	0.324267i	0.757105	−	0.653293i	$-0.226613\pi$
$193$	−501.970	−	869.437i	−0.187215	−	0.324267i	−0.944321	+	0.329026i	$0.893280\pi$
$194$	−1680.13	+	2910.08i	−0.621786	+	1.07697i
$195$	−2009.14			−0.737832
$196$		0			0
$197$	1716.80			0.620899			0.310449	−	0.950590i	$-0.399521\pi$
$197$	1716.80			0.620899			0.310449	+	0.950590i	$0.399521\pi$
$198$	8742.23	−	15142.0i	3.13779	−	5.43482i
$199$	2668.93	+	4622.72i	0.950730	+	1.64671i	0.743849	+	0.668347i	$0.232998\pi$
$199$	2668.93	+	4622.72i	0.950730	+	1.64671i	0.206881	+	0.978366i	$0.433669\pi$
$200$	−221.031	−	382.836i	−0.0781461	−	0.135353i
$201$	−4025.55	+	6972.46i	−1.41264	+	2.44676i
$202$	2498.31			0.870201
$203$		0			0
$204$	256.763			0.0881227
$205$	−667.009	+	1155.29i	−0.227249	+	0.393606i
$206$	458.652	+	794.408i	0.155125	+	0.268685i
$207$	5374.00	+	9308.04i	1.80444	+	3.12538i
$208$	341.421	−	591.359i	0.113814	−	0.197131i
$209$	−931.420			−0.308266
$210$		0			0
$211$	860.589			0.280784			0.140392	−	0.990096i	$-0.455164\pi$
$211$	860.589			0.280784			0.140392	+	0.990096i	$0.455164\pi$
$212$	905.170	−	1567.80i	0.293242	−	0.507911i
$213$	−4716.32	−	8168.90i	−1.51717	−	2.62781i
$214$	3283.96	+	5687.98i	1.04900	+	1.81693i
$215$	−36.6374	+	63.4578i	−0.0116216	+	0.0201292i
$216$	7323.14			2.30684
$217$		0			0
$218$	−3458.66			−1.07454
$219$	−4581.02	+	7934.56i	−1.41350	+	2.44826i
$220$	−1690.29	−	2927.66i	−0.517995	−	0.897194i
$221$	−44.8347	−	77.6560i	−0.0136467	−	0.0236367i
$222$	814.516	−	1410.78i	0.246246	−	0.426511i
$223$	−3661.12			−1.09940			−0.549701	−	0.835361i	$-0.685259\pi$
$223$	−3661.12			−1.09940			−0.549701	+	0.835361i	$0.685259\pi$
$224$		0			0
$225$	1730.51			0.512743
$226$	907.161	−	1571.25i	0.267006	−	0.462468i
$227$	−3016.19	−	5224.20i	−0.881902	−	1.52750i	−0.849224	−	0.528032i	$-0.822930\pi$
$227$	−3016.19	−	5224.20i	−0.881902	−	1.52750i	−0.0326773	−	0.999466i	$-0.510403\pi$
$228$	−966.164	−	1673.45i	−0.280639	−	0.486082i
$229$	1924.82	−	3333.88i	0.555439	−	0.962049i	−0.442430	−	0.896803i	$-0.645883\pi$
$229$	1924.82	−	3333.88i	0.555439	−	0.962049i	0.997869	−	0.0652460i	$-0.0207832\pi$
$230$	3468.35			0.994332
$231$		0			0
$232$	−110.701			−0.0313269
$233$	852.600	−	1476.75i	0.239724	−	0.415214i	−0.720911	−	0.693028i	$-0.756276\pi$
$233$	852.600	−	1476.75i	0.239724	−	0.415214i	0.960635	+	0.277813i	$0.0896097\pi$
$234$	−6333.86	−	10970.6i	−1.76948	−	3.06482i
$235$	−424.601	−	735.431i	−0.117864	−	0.204146i
$236$	1399.55	−	2424.09i	0.386029	−	0.668621i
$237$	2945.07			0.807185
$238$		0			0
$239$	6804.54			1.84163			0.920814	−	0.390001i	$-0.127525\pi$
$239$	6804.54			1.84163			0.920814	+	0.390001i	$0.127525\pi$
$240$	−408.779	+	708.025i	−0.109944	+	0.190428i
$241$	−2321.49	−	4020.94i	−0.620499	−	1.07474i	−0.989393	−	0.145264i	$-0.953597\pi$
$241$	−2321.49	−	4020.94i	−0.620499	−	1.07474i	0.368894	−	0.929472i	$-0.379737\pi$
$242$	−4167.72	−	7218.70i	−1.10707	−	1.91750i
$243$	−5167.28	+	8949.99i	−1.36412	+	2.36273i
$244$	−2898.77			−0.760553
$245$		0			0
$246$	−11691.9			−3.03027
$247$	−337.413	+	584.417i	−0.0869194	+	0.150549i
$248$	−1491.34	−	2583.07i	−0.381855	−	0.661393i
$249$	−5334.22	−	9239.14i	−1.35760	−	2.35143i
$250$	279.215	−	483.615i	0.0706365	−	0.122346i
$251$	5912.64			1.48686			0.743431	−	0.668813i	$-0.233197\pi$
$251$	5912.64			1.48686			0.743431	+	0.668813i	$0.233197\pi$
$252$		0			0
$253$	8779.16			2.18159
$254$	1008.84	−	1747.35i	0.249212	−	0.431649i
$255$	53.6800	+	92.9764i	0.0131826	+	0.0228330i
$256$	1111.74	+	1925.60i	0.271422	+	0.470116i
$257$	848.917	−	1470.37i	0.206047	−	0.356883i	−0.744419	−	0.667713i	$-0.767273\pi$
$257$	848.917	−	1470.37i	0.206047	−	0.356883i	0.950466	+	0.310829i	$0.100607\pi$
$258$	−642.210			−0.154970
$259$		0			0
$260$	−2449.27			−0.584220
$261$	216.676	−	375.294i	0.0513867	−	0.0890043i
$262$	−808.455	−	1400.28i	−0.190635	−	0.330190i
$263$	2830.89	+	4903.24i	0.663727	+	1.14961i	0.979629	+	0.200816i	$0.0643594\pi$
$263$	2830.89	+	4903.24i	0.663727	+	1.14961i	−0.315902	+	0.948792i	$0.602307\pi$
$264$	4903.48	−	8493.08i	1.14314	−	1.97997i
$265$	756.954			0.175469
$266$		0			0
$267$	−11026.0			−2.52727
$268$	−4907.42	+	8499.89i	−1.11854	+	1.93736i
$269$	−2665.01	−	4615.93i	−0.604046	−	1.04624i	−0.992202	−	0.124644i	$-0.960221\pi$
$269$	−2665.01	−	4615.93i	−0.604046	−	1.04624i	0.388156	−	0.921594i	$-0.373112\pi$
$270$	4625.46	+	8011.52i	1.04258	+	1.80580i
$271$	1017.47	−	1762.31i	0.228069	−	0.395028i	−0.729166	−	0.684336i	$-0.760092\pi$
$271$	1017.47	−	1762.31i	0.228069	−	0.395028i	0.957236	+	0.289308i	$0.0934253\pi$
$272$	−36.4883			−0.00813392
$273$		0			0
$274$	11225.5			2.47502
$275$	706.755	−	1224.14i	0.154978	−	0.268430i
$276$	9106.64	+	15773.2i	1.98607	+	3.43998i
$277$	433.828	+	751.413i	0.0941019	+	0.162989i	0.909233	−	0.416287i	$-0.136669\pi$
$277$	433.828	+	751.413i	0.0941019	+	0.162989i	−0.815132	+	0.579276i	$0.803335\pi$
$278$	−2603.87	+	4510.03i	−0.561761	+	0.972999i
$279$	11676.1			2.50548
$280$		0			0
$281$	2049.70			0.435142			0.217571	−	0.976045i	$-0.430187\pi$
$281$	2049.70			0.435142			0.217571	+	0.976045i	$0.430187\pi$
$282$	3721.38	−	6445.62i	0.785833	−	1.36110i
$283$	−3312.56	−	5737.51i	−0.695799	−	1.20516i	−0.969911	−	0.243461i	$-0.921717\pi$
$283$	−3312.56	−	5737.51i	−0.695799	−	1.20516i	0.274112	−	0.961698i	$-0.411616\pi$
$284$	−5749.50	−	9958.43i	−1.20130	−	2.08072i
$285$	403.980	−	699.714i	0.0839639	−	0.145430i
$286$	−10347.2			−2.13932
$287$		0			0
$288$	−14946.6			−3.05812
$289$	2454.10	−	4250.63i	0.499512	−	0.865181i
$290$	−69.9209	−	121.106i	−0.0141583	−	0.0245228i
$291$	−3689.08	−	6389.67i	−0.743154	−	1.28718i
$292$	−5584.57	+	9672.76i	−1.11922	+	1.93855i
$293$	−5670.84			−1.13070			−0.565348	−	0.824852i	$-0.691258\pi$
$293$	−5670.84			−1.13070			−0.565348	+	0.824852i	$0.691258\pi$
$294$		0			0
$295$	1170.38			0.230990
$296$	328.662	−	569.258i	0.0645374	−	0.111782i
$297$	11708.0	+	20278.9i	2.28744	+	3.96196i
$298$	5891.42	+	10204.2i	1.14524	+	1.98361i
$299$	3180.31	−	5508.46i	0.615124	−	1.06543i
$300$	2932.48			0.564355
$301$		0			0
$302$	−11536.4			−2.19816
$303$	−2742.78	+	4750.63i	−0.520028	+	0.900715i
$304$	137.300	+	237.811i	0.0259036	+	0.0448664i
$305$	−606.029	−	1049.67i	−0.113774	−	0.197063i
$306$	−338.456	+	586.222i	−0.0632295	+	0.109517i
$307$	−272.638			−0.0506849			−0.0253424	−	0.999679i	$-0.508068\pi$
$307$	−272.638			−0.0506849			−0.0253424	+	0.999679i	$0.508068\pi$
$308$		0			0
$309$	−2014.13			−0.370808
$310$	1883.92	−	3263.05i	0.345160	−	0.597835i
$311$	610.417	+	1057.27i	0.111298	+	0.192773i	0.916294	−	0.400507i	$-0.131166\pi$
$311$	610.417	+	1057.27i	0.111298	+	0.192773i	−0.804996	+	0.593280i	$0.797833\pi$
$312$	−3552.64	−	6153.36i	−0.644643	−	1.11656i
$313$	−387.598	+	671.339i	−0.0699946	+	0.121234i	−0.898899	−	0.438157i	$-0.855632\pi$
$313$	−387.598	+	671.339i	−0.0699946	+	0.121234i	0.828904	+	0.559391i	$0.188965\pi$
$314$	1008.69			0.181286
$315$		0			0
$316$	3590.24			0.639135
$317$	−3696.62	+	6402.73i	−0.654962	+	1.13443i	0.326942	+	0.945044i	$0.393982\pi$
$317$	−3696.62	+	6402.73i	−0.654962	+	1.13443i	−0.981903	+	0.189382i	$0.939351\pi$
$318$	3317.13	+	5745.43i	0.584954	+	1.01317i
$319$	−176.985	−	306.547i	−0.0310635	−	0.0538036i
$320$	−2078.23	+	3599.61i	−0.363053	+	0.628826i
$321$	−14421.2			−2.50752
$322$		0			0
$323$	36.0600			0.00621186
$324$	−13115.1	+	22715.9i	−2.24881	+	3.89505i
$325$	−512.054	−	886.903i	−0.0873958	−	0.151374i
$326$	−3326.03	−	5760.85i	−0.565067	−	0.978724i
$327$	3797.11	−	6576.78i	0.642142	−	1.11222i
$328$	−4717.74			−0.794188
$329$		0			0
$330$	12388.6			2.06657
$331$	1868.48	−	3236.30i	0.310274	−	0.537410i	−0.668148	−	0.744029i	$-0.732913\pi$
$331$	1868.48	−	3236.30i	0.310274	−	0.537410i	0.978422	+	0.206618i	$0.0662458\pi$
$332$	−6502.77	−	11263.1i	−1.07496	−	1.86188i
$333$	1286.59	+	2228.44i	0.211726	+	0.366720i
$334$	−6385.62	+	11060.2i	−1.04612	+	1.81194i
$335$	−4103.85			−0.669306
$336$		0			0
$337$	−8230.24			−1.33036			−0.665178	−	0.746685i	$-0.731644\pi$
$337$	−8230.24			−1.33036			−0.665178	+	0.746685i	$0.731644\pi$
$338$	1159.13	−	2007.68i	0.186534	−	0.323087i
$339$	1991.86	+	3450.00i	0.319124	+	0.552738i
$340$	65.4395	+	113.344i	0.0104381	+	0.0180793i
$341$	4768.62	−	8259.50i	0.757289	−	1.31166i
$342$	5094.24			0.805453
$343$		0			0
$344$	−259.135			−0.0406152
$345$	−3807.74	+	6595.20i	−0.594208	+	1.02920i
$346$	71.4880	+	123.821i	0.0111076	+	0.0192389i
$347$	6365.25	+	11024.9i	0.984739	+	1.70562i	0.643089	+	0.765791i	$0.277652\pi$
$347$	6365.25	+	11024.9i	0.984739	+	1.70562i	0.341650	+	0.939827i	$0.389014\pi$
$348$	367.174	−	635.964i	0.0565592	−	0.0979634i
$349$	4487.30			0.688252			0.344126	−	0.938924i	$-0.388175\pi$
$349$	4487.30			0.688252			0.344126	+	0.938924i	$0.388175\pi$
$350$		0			0
$351$	16965.3			2.57989
$352$	−6104.34	+	10573.0i	−0.924324	+	1.60098i
$353$	6131.74	+	10620.5i	0.924532	+	1.60134i	0.792313	+	0.610115i	$0.208877\pi$
$353$	6131.74	+	10620.5i	0.924532	+	1.60134i	0.132219	+	0.991221i	$0.457790\pi$
$354$	5128.84	+	8883.41i	0.770042	+	1.33375i
$355$	2404.03	−	4163.90i	0.359416	−	0.622526i
$356$	−13441.4			−2.00111
$357$		0			0
$358$	3298.96			0.487026
$359$	5536.60	−	9589.67i	0.813957	−	1.40982i	−0.0961171	−	0.995370i	$-0.530642\pi$
$359$	5536.60	−	9589.67i	0.813957	−	1.40982i	0.910074	−	0.414445i	$-0.136024\pi$
$360$	3059.96	+	5300.01i	0.447984	+	0.775931i
$361$	3293.81	+	5705.05i	0.480217	+	0.831761i
$362$	4449.37	−	7706.54i	0.646005	−	1.11891i
$363$	18302.2			2.64632
$364$		0			0
$365$	−4670.13			−0.669714
$366$	5311.48	−	9199.76i	0.758567	−	1.31388i
$367$	−2932.36	−	5078.99i	−0.417079	−	0.722401i	0.578566	−	0.815636i	$-0.303613\pi$
$367$	−2932.36	−	5078.99i	−0.417079	−	0.722401i	−0.995644	+	0.0932345i	$0.970279\pi$
$368$	−1294.13	−	2241.50i	−0.183319	−	0.317517i
$369$	9234.13	−	15994.0i	1.30274	−	2.25640i
$370$	830.359			0.116671
$371$		0			0
$372$	19786.0			2.75768
$373$	4684.09	−	8113.08i	0.650222	−	1.12622i	−0.332847	−	0.942981i	$-0.608009\pi$
$373$	4684.09	−	8113.08i	0.650222	−	1.12622i	0.983069	−	0.183237i	$-0.0586575\pi$
$374$	276.457	+	478.837i	0.0382225	+	0.0662034i
$375$	613.075	+	1061.88i	0.0844241	+	0.146227i
$376$	1501.60	−	2600.84i	0.205955	−	0.356724i
$377$	−256.456			−0.0350349
$378$		0			0
$379$	5537.81			0.750549			0.375275	−	0.926914i	$-0.377548\pi$
$379$	5537.81			0.750549			0.375275	+	0.926914i	$0.377548\pi$
$380$	492.479	−	852.998i	0.0664832	−	0.115152i
$381$	2215.11	+	3836.68i	0.297857	+	0.515903i
$382$	−4810.73	−	8332.43i	−0.644341	−	1.11603i
$383$	−2621.58	+	4540.72i	−0.349756	+	0.605796i	−0.986206	−	0.165522i	$-0.947069\pi$
$383$	−2621.58	+	4540.72i	−0.349756	+	0.605796i	0.636450	+	0.771318i	$0.280402\pi$
$384$	−19484.3			−2.58934
$385$		0			0
$386$	4485.05			0.591406
$387$	507.210	−	878.514i	0.0666226	−	0.115394i
$388$	−4497.23	−	7789.44i	−0.588434	−	1.01920i
$389$	5445.27	+	9431.48i	0.709733	+	1.22929i	0.964956	+	0.262411i	$0.0845177\pi$
$389$	5445.27	+	9431.48i	0.709733	+	1.22929i	−0.255223	+	0.966882i	$0.582149\pi$
$390$	4487.85	−	7773.19i	0.582695	−	1.00926i
$391$	−339.886			−0.0439610
$392$		0			0
$393$	3550.26			0.455692
$394$	−3834.86	+	6642.17i	−0.490349	+	0.849309i
$395$	750.589	+	1300.06i	0.0956107	+	0.165603i
$396$	23400.4	+	40530.7i	2.96948	+	5.14330i
$397$	−6653.52	+	11524.2i	−0.841135	+	1.45689i	0.0478017	+	0.998857i	$0.484778\pi$
$397$	−6653.52	+	11524.2i	−0.841135	+	1.45689i	−0.888936	+	0.458031i	$0.848555\pi$
$398$	−23846.6			−3.00332
$399$		0			0
$400$	−416.730			−0.0520912
$401$	−3613.51	+	6258.79i	−0.450000	+	0.779423i	−0.998385	−	0.0568024i	$-0.981909\pi$
$401$	−3613.51	+	6258.79i	−0.450000	+	0.779423i	0.548385	+	0.836226i	$0.315243\pi$
$402$	−17983.9	−	31149.1i	−2.23124	−	3.86461i
$403$	−3454.93	−	5984.12i	−0.427053	−	0.739678i
$404$	−3343.63	+	5791.34i	−0.411762	+	0.713192i
$405$	−10967.5			−1.34563
$406$		0			0
$407$	2101.82			0.255979
$408$	−189.839	+	328.810i	−0.0230353	+	0.0398983i
$409$	−2926.32	−	5068.53i	−0.353783	−	0.612769i	0.633126	−	0.774049i	$-0.281771\pi$
$409$	−2926.32	−	5068.53i	−0.353783	−	0.612769i	−0.986909	+	0.161279i	$0.948438\pi$
$410$	−2979.83	−	5161.21i	−0.358935	−	0.621693i
$411$	−12323.9	+	21345.6i	−1.47906	+	2.56180i
$412$	−2455.36			−0.293609
$413$		0			0
$414$	−48016.1			−5.70015
$415$	2718.99	−	4709.42i	0.321614	−	0.557052i
$416$	4422.68	+	7660.30i	0.521249	+	0.902830i
$417$	−5717.33	−	9902.70i	−0.671412	−	1.16292i
$418$	2080.53	−	3603.59i	0.243450	−	0.421668i
$419$	−8344.19			−0.972889			−0.486444	−	0.873712i	$-0.661706\pi$
$419$	−8344.19			−0.972889			−0.486444	+	0.873712i	$0.661706\pi$
$420$		0			0
$421$	−10955.3			−1.26824			−0.634122	−	0.773233i	$-0.718638\pi$
$421$	−10955.3			−1.26824			−0.634122	+	0.773233i	$0.718638\pi$
$422$	−1922.32	+	3329.55i	−0.221746	+	0.384076i
$423$	5878.21	+	10181.4i	0.675670	+	1.17029i
$424$	1338.48	+	2318.31i	0.153307	+	0.265536i
$425$	−27.3621	+	47.3925i	−0.00312295	+	0.00540911i
$426$	42139.8			4.79267
$427$		0			0
$428$	−17580.4			−1.98547
$429$	11359.7	−	19675.6i	1.27845	−	2.21433i
$430$	−163.675	−	283.494i	−0.0183561	−	0.0317937i
$431$	−4708.72	−	8155.73i	−0.526243	−	0.911480i	−0.999533	−	0.0305730i	$-0.990267\pi$
$431$	−4708.72	−	8155.73i	−0.526243	−	0.911480i	0.473289	−	0.880907i	$-0.343067\pi$
$432$	3451.75	−	5978.61i	0.384427	−	0.665848i
$433$	8783.79			0.974878			0.487439	−	0.873157i	$-0.337931\pi$
$433$	8783.79			0.974878			0.487439	+	0.873157i	$0.337931\pi$
$434$		0			0
$435$	307.051			0.0338436
$436$	4628.92	−	8017.53i	0.508452	−	0.880666i
$437$	1278.94	+	2215.19i	0.140000	+	0.242487i
$438$	−20465.5	−	35447.2i	−2.23260	−	3.86697i
$439$	−5279.80	+	9144.88i	−0.574011	+	0.994217i	0.422137	+	0.906532i	$0.361280\pi$
$439$	−5279.80	+	9144.88i	−0.574011	+	0.994217i	−0.996148	+	0.0876849i	$0.972053\pi$
$440$	4998.86			0.541617
$441$		0			0
$442$	400.593			0.0431092
$443$	2439.07	−	4224.60i	0.261589	−	0.453085i	−0.705076	−	0.709132i	$-0.749087\pi$
$443$	2439.07	−	4224.60i	0.261589	−	0.453085i	0.966664	+	0.256047i	$0.0824203\pi$
$444$	2180.22	+	3776.26i	0.233038	+	0.403634i
$445$	−2810.12	−	4867.26i	−0.299353	−	0.518495i
$446$	8177.93	−	14164.6i	0.868243	−	1.50384i
$447$	−25871.7			−2.73756
$448$		0			0
$449$	43.7917			0.00460280			0.00230140	−	0.999997i	$-0.499267\pi$
$449$	43.7917			0.00460280			0.00230140	+	0.999997i	$0.499267\pi$
$450$	−3865.48	+	6695.20i	−0.404934	+	0.701366i
$451$	−7542.60	−	13064.2i	−0.787510	−	1.36401i
$452$	2428.21	+	4205.78i	0.252684	+	0.437662i
$453$	12665.3	−	21936.9i	1.31361	−	2.27524i
$454$	26949.3			2.78589
$455$		0			0
$456$	2857.34			0.293437
$457$	−1434.88	+	2485.28i	−0.146873	+	0.254391i	−0.930070	−	0.367382i	$-0.880254\pi$
$457$	−1434.88	+	2485.28i	−0.146873	+	0.254391i	0.783197	+	0.621773i	$0.213587\pi$
$458$	8599.02	+	14893.9i	0.877305	+	1.51954i
$459$	−453.277	−	785.100i	−0.0460941	−	0.0798373i
$460$	−4641.89	+	8039.99i	−0.470498	+	0.814927i
$461$	−17910.1			−1.80945			−0.904723	−	0.426001i	$-0.859922\pi$
$461$	−17910.1			−1.80945			−0.904723	+	0.426001i	$0.859922\pi$
$462$		0			0
$463$	−7630.72			−0.765938			−0.382969	−	0.923761i	$-0.625098\pi$
$463$	−7630.72			−0.765938			−0.382969	+	0.923761i	$0.625098\pi$
$464$	−52.1786	+	90.3759i	−0.00522054	+	0.00904223i
$465$	4136.54	+	7164.70i	0.412532	+	0.714527i
$466$	3808.95	+	6597.29i	0.378640	+	0.655823i
$467$	3123.15	−	5409.46i	0.309469	−	0.536017i	−0.668777	−	0.743463i	$-0.733182\pi$
$467$	3123.15	−	5409.46i	0.309469	−	0.536017i	0.978246	+	0.207446i	$0.0665152\pi$
$468$	33907.9			3.34913
$469$		0			0
$470$	3793.76			0.372326
$471$	−1107.40	+	1918.07i	−0.108336	+	0.187643i
$472$	2069.52	+	3584.51i	0.201816	+	0.349556i
$473$	−414.298	−	717.586i	−0.0402737	−	0.0697561i
$474$	−6578.47	+	11394.2i	−0.637466	+	1.10412i
$475$	411.838			0.0397820
$476$		0			0
$477$	−10479.3			−1.00590
$478$	−15199.5	+	26326.2i	−1.45441	+	2.51911i
$479$	2059.79	+	3567.66i	0.196480	+	0.340314i	0.947385	−	0.320097i	$-0.103715\pi$
$479$	2059.79	+	3567.66i	0.196480	+	0.340314i	−0.750904	+	0.660411i	$0.770382\pi$
$480$	−5295.21	−	9171.57i	−0.503525	−	0.872131i
$481$	761.399	−	1318.78i	0.0721763	−	0.125013i
$482$	20742.2			1.96013
$483$		0			0
$484$	22311.6			2.09538
$485$	1880.42	−	3256.98i	0.176052	−	0.304932i
$486$	−23084.5	−	39983.6i	−2.15460	−	3.73188i
$487$	710.731	+	1231.02i	0.0661320	+	0.114544i	0.897196	−	0.441633i	$-0.145601\pi$
$487$	710.731	+	1231.02i	0.0661320	+	0.114544i	−0.831064	+	0.556177i	$0.812267\pi$
$488$	2143.21	−	3712.15i	0.198809	−	0.344347i
$489$	14606.0			1.35073
$490$		0			0
$491$	19241.1			1.76851			0.884253	−	0.467007i	$-0.154668\pi$
$491$	19241.1			1.76851			0.884253	+	0.467007i	$0.154668\pi$
$492$	15647.9	−	27103.0i	1.43387	−	2.48353i
$493$	6.85198	+	11.8680i	0.000625959	+	0.00108419i
$494$	−1507.38	−	2610.85i	−0.137288	−	0.237789i
$495$	−9784.37	+	16947.0i	−0.888434	+	1.53881i
$496$	−2811.76			−0.254540
$497$		0			0
$498$	47660.6			4.28860
$499$	−4788.24	+	8293.48i	−0.429561	+	0.744022i	−0.996834	−	0.0795077i	$-0.974665\pi$
$499$	−4788.24	+	8293.48i	−0.429561	+	0.744022i	0.567273	+	0.823530i	$0.307998\pi$
$500$	747.379	+	1294.50i	0.0668476	+	0.115783i
$501$	−14020.9	−	24285.0i	−1.25032	−	2.16561i
$502$	−13207.2	+	22875.5i	−1.17423	+	2.03383i
$503$	−10581.9			−0.938019			−0.469009	−	0.883193i	$-0.655389\pi$
$503$	−10581.9			−0.938019			−0.469009	+	0.883193i	$0.655389\pi$
$504$		0			0
$505$	−2796.13			−0.246388
$506$	−19610.2	+	33965.9i	−1.72289	+	2.98413i
$507$	2545.12	+	4408.27i	0.222944	+	0.386150i
$508$	2700.36	+	4677.16i	0.235845	+	0.408495i
$509$	−3541.43	+	6133.94i	−0.308391	+	0.534149i	−0.978011	−	0.208555i	$-0.933124\pi$
$509$	−3541.43	+	6133.94i	−0.308391	+	0.534149i	0.669619	+	0.742704i	$0.266457\pi$
$510$	−479.625			−0.0416434
$511$		0			0
$512$	5957.37			0.514220
$513$	−3411.24	+	5908.44i	−0.293586	+	0.508506i
$514$	3792.49	+	6568.79i	0.325447	+	0.563690i
$515$	−513.327	−	889.108i	−0.0439221	−	0.0760753i
$516$	859.506	−	1488.71i	0.0733287	−	0.127009i
$517$	9602.85			0.816891
$518$		0			0
$519$	−313.933			−0.0265513
$520$	1810.87	−	3136.52i	0.152715	−	0.264511i
$521$	3576.96	+	6195.48i	0.300786	+	0.520976i	0.976314	−	0.216358i	$-0.0694177\pi$
$521$	3576.96	+	6195.48i	0.300786	+	0.520976i	−0.675528	+	0.737334i	$0.736084\pi$
$522$	967.989	+	1676.61i	0.0811642	+	0.140581i
$523$	7890.65	−	13667.0i	0.659721	−	1.14267i	−0.320967	−	0.947090i	$-0.604008\pi$
$523$	7890.65	−	13667.0i	0.659721	−	1.14267i	0.980688	−	0.195580i	$-0.0626589\pi$
$524$	4328.00			0.360820
$525$		0			0
$526$	−25293.7			−2.09669
$527$	−184.618	+	319.767i	−0.0152601	+	0.0264312i
$528$	−4622.50	−	8006.41i	−0.381001	−	0.659913i
$529$	−5971.24	−	10342.5i	−0.490774	−	0.850045i
$530$	−1690.83	+	2928.59i	−0.138575	+	0.240019i
$531$	−16202.8			−1.32418
$532$		0			0
$533$	−10929.4			−0.888192
$534$	24629.0	−	42658.7i	1.99588	−	3.45697i
$535$	−3675.43	−	6366.03i	−0.297015	−	0.514444i
$536$	−7256.62	−	12568.8i	−0.584773	−	1.01286i
$537$	−3621.77	+	6273.09i	−0.291045	+	0.504104i
$538$	23811.5			1.90816
$539$		0			0
$540$	−24762.0			−1.97331
$541$	12138.6	−	21024.7i	0.964656	−	1.67083i	0.254121	−	0.967173i	$-0.418214\pi$
$541$	12138.6	−	21024.7i	0.964656	−	1.67083i	0.710536	−	0.703661i	$-0.248453\pi$
$542$	4545.49	+	7873.01i	0.360231	+	0.623939i
$543$	9769.52	+	16921.3i	0.772099	+	1.33732i
$544$	236.330	−	409.335i	0.0186260	−	0.0322612i
$545$	3870.96			0.304246
$546$		0			0
$547$	−191.079			−0.0149359			−0.00746796	−	0.999972i	$-0.502377\pi$
$547$	−191.079			−0.0149359			−0.00746796	+	0.999972i	$0.502377\pi$
$548$	−15023.7	+	26021.7i	−1.17113	+	2.02845i
$549$	8389.90	+	14531.7i	0.652226	+	1.12969i
$550$	3157.39	+	5468.76i	0.244785	+	0.423979i
$551$	51.5661	−	89.3151i	0.00398691	−	0.00690553i
$552$	−26932.1			−2.07664
$553$		0			0
$554$	−3876.21			−0.297264
$555$	−911.612	+	1578.96i	−0.0697221	+	0.120762i
$556$	−6969.80	−	12072.1i	−0.531629	−	0.920808i
$557$	7860.78	+	13615.3i	0.597974	+	1.03572i	0.993120	+	0.117103i	$0.0373609\pi$
$557$	7860.78	+	13615.3i	0.597974	+	1.03572i	−0.395145	+	0.918619i	$0.629306\pi$
$558$	−26081.2	+	45173.9i	−1.97868	+	3.42718i
$559$	−600.330			−0.0454226
$560$		0			0
$561$	−1214.04			−0.0913665
$562$	−4578.46	+	7930.12i	−0.343649	+	0.595217i
$563$	−1522.25	−	2636.61i	−0.113952	−	0.197371i	0.803408	−	0.595429i	$-0.203018\pi$
$563$	−1522.25	−	2636.61i	−0.113952	−	0.197371i	−0.917360	+	0.398057i	$0.869684\pi$
$564$	9961.06	+	17253.1i	0.743681	+	1.28809i
$565$	−1015.30	+	1758.55i	−0.0756001	+	0.130943i
$566$	29597.3			2.19800
$567$		0			0
$568$	17003.6			1.25609
$569$	−6526.10	+	11303.5i	−0.480823	+	0.832810i	−0.999758	−	0.0220035i	$-0.992996\pi$
$569$	−6526.10	+	11303.5i	−0.480823	+	0.832810i	0.518935	+	0.854814i	$0.326329\pi$
$570$	1804.76	+	3125.93i	0.132619	+	0.229704i
$571$	2905.53	+	5032.52i	0.212946	+	0.368834i	0.952635	−	0.304115i	$-0.0983607\pi$
$571$	2905.53	+	5032.52i	0.212946	+	0.368834i	−0.739689	+	0.672949i	$0.765027\pi$
$572$	13848.3	−	23985.9i	1.01228	−	1.75332i
$573$	21125.9			1.54022
$574$		0			0
$575$	−3881.81			−0.281535
$576$	28771.2	−	49833.2i	2.08125	−	3.60483i
$577$	11395.2	+	19737.0i	0.822162	+	1.42403i	0.904069	+	0.427386i	$0.140565\pi$
$577$	11395.2	+	19737.0i	0.822162	+	1.42403i	−0.0819076	+	0.996640i	$0.526101\pi$
$578$	10963.6	+	18989.5i	0.788970	+	1.36654i
$579$	−4923.92	+	8528.48i	−0.353422	+	0.612145i
$580$	374.316			0.0267976
$581$		0			0
$582$	32961.5			2.34759
$583$	−4279.85	+	7412.92i	−0.304036	+	0.526607i
$584$	−8257.93	−	14303.2i	−0.585129	−	1.01347i
$585$	7088.91	+	12278.4i	0.501009	+	0.867773i
$586$	12667.1	−	21940.0i	0.892957	−	1.54665i
$587$	−20600.3			−1.44850			−0.724248	−	0.689540i	$-0.757813\pi$
$587$	−20600.3			−1.44850			−0.724248	+	0.689540i	$0.757813\pi$
$588$		0			0
$589$	2778.76			0.194392
$590$	−2614.30	+	4528.10i	−0.182422	+	0.315965i
$591$	−8420.22	−	14584.2i	−0.586060	−	1.01509i
$592$	−309.828	−	536.639i	−0.0215099	−	0.0372563i
$593$	−386.915	+	670.157i	−0.0267938	+	0.0464081i	−0.879111	−	0.476616i	$-0.841863\pi$
$593$	−386.915	+	670.157i	−0.0267938	+	0.0464081i	0.852318	+	0.523025i	$0.175196\pi$
$594$	−104610.			−7.22593
$595$		0			0
$596$	−31539.3			−2.16762
$597$	26180.0	−	45345.2i	1.79477	−	3.10863i
$598$	14207.9	+	24608.7i	0.971577	+	1.68282i
$599$	6820.51	+	11813.5i	0.465239	+	0.805818i	0.999212	−	0.0396835i	$-0.0126350\pi$
$599$	6820.51	+	11813.5i	0.465239	+	0.805818i	−0.533973	+	0.845501i	$0.679302\pi$
$600$	−2168.13	+	3755.31i	−0.147523	+	0.255517i
$601$	14271.8			0.968650			0.484325	−	0.874888i	$-0.339065\pi$
$601$	14271.8			0.968650			0.484325	+	0.874888i	$0.339065\pi$
$602$		0			0
$603$	56814.1			3.83689
$604$	15439.8	−	26742.5i	1.04013	−	1.80155i
$605$	4664.55	+	8079.23i	0.313456	+	0.542921i
$606$	−12253.2	−	21223.2i	−0.821374	−	1.42266i
$607$	−1617.45	+	2801.51i	−0.108155	+	0.187331i	−0.915023	−	0.403402i	$-0.867828\pi$
$607$	−1617.45	+	2801.51i	−0.108155	+	0.187331i	0.806868	+	0.590732i	$0.201161\pi$
$608$	−3557.10			−0.237269
$609$		0			0
$610$	5414.80			0.359408
$611$	3478.70	−	6025.28i	0.230332	−	0.398947i
$612$	−905.949	−	1569.15i	−0.0598379	−	0.103642i
$613$	−4206.76	−	7286.32i	−0.277177	−	0.480084i	0.693505	−	0.720452i	$-0.256065\pi$
$613$	−4206.76	−	7286.32i	−0.277177	−	0.480084i	−0.970682	+	0.240367i	$0.922732\pi$
$614$	608.997	−	1054.81i	0.0400279	−	0.0693303i
$615$	13085.7			0.857991
$616$		0			0
$617$	7077.93			0.461826			0.230913	−	0.972974i	$-0.425829\pi$
$617$	7077.93			0.461826			0.230913	+	0.972974i	$0.425829\pi$
$618$	4499.01	−	7792.51i	0.292842	−	0.507218i
$619$	−2732.37	−	4732.61i	−0.177420	−	0.307301i	0.763576	−	0.645718i	$-0.223442\pi$
$619$	−2732.37	−	4732.61i	−0.177420	−	0.307301i	−0.940996	+	0.338417i	$0.890109\pi$
$620$	5042.72	+	8734.25i	0.326646	+	0.565768i
$621$	32152.8	−	55690.3i	2.07770	−	3.59867i
$622$	−5454.01			−0.351585
$623$		0			0
$624$	−6698.13			−0.429711
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−1731.57	−	2999.17i	−0.110555	−	0.191487i
$627$	4568.24	+	7912.43i	0.290970	+	0.503974i
$628$	−1349.99	+	2338.26i	−0.0857812	+	0.148577i
$629$	−81.3721			−0.00515822
$630$		0			0
$631$	−1569.98			−0.0990492			−0.0495246	−	0.998773i	$-0.515771\pi$
$631$	−1569.98			−0.0990492			−0.0495246	+	0.998773i	$0.515771\pi$
$632$	−2654.45	+	4597.64i	−0.167070	+	0.289374i
$633$	−4220.84	−	7310.71i	−0.265029	−	0.459044i
$634$	−16514.4	−	28603.9i	−1.03450	−	1.79180i
$635$	−1129.10	+	1955.65i	−0.0705619	+	0.122217i
$636$	−17758.0			−1.10715
$637$		0			0
$638$	1581.34			0.0981284
$639$	−33281.5	+	57645.3i	−2.06040	+	3.56872i
$640$	−4965.84	−	8601.08i	−0.306706	−	0.531231i
$641$	7289.16	+	12625.2i	0.449149	+	0.777949i	0.998331	−	0.0577537i	$-0.0183938\pi$
$641$	7289.16	+	12625.2i	0.449149	+	0.777949i	−0.549182	+	0.835703i	$0.685060\pi$
$642$	32213.0	−	55794.5i	1.98029	−	3.42996i
$643$	−11980.0			−0.734750			−0.367375	−	0.930073i	$-0.619744\pi$
$643$	−11980.0			−0.734750			−0.367375	+	0.930073i	$0.619744\pi$
$644$		0			0
$645$	718.766			0.0438781
$646$	−80.5480	+	139.513i	−0.00490575	+	0.00849702i
$647$	2825.90	+	4894.61i	0.171712	+	0.297414i	0.939019	−	0.343867i	$-0.111737\pi$
$647$	2825.90	+	4894.61i	0.171712	+	0.297414i	−0.767306	+	0.641281i	$0.778403\pi$
$648$	−19393.3	−	33590.2i	−1.17568	−	2.03634i
$649$	−6617.37	+	11461.6i	−0.400238	+	0.693233i
$650$	4575.15			0.276080
$651$		0			0
$652$	17805.6			1.06951
$653$	1185.43	−	2053.22i	0.0710405	−	0.123046i	−0.828317	−	0.560260i	$-0.810701\pi$
$653$	1185.43	−	2053.22i	0.0710405	−	0.123046i	0.899358	+	0.437214i	$0.144035\pi$
$654$	16963.4	+	29381.4i	1.01425	+	1.75673i
$655$	904.829	+	1567.21i	0.0539765	+	0.0934900i
$656$	−2223.70	+	3851.56i	−0.132349	+	0.229235i
$657$	64653.6			3.83923
$658$		0			0
$659$	5233.92			0.309385			0.154692	−	0.987963i	$-0.450561\pi$
$659$	5233.92			0.309385			0.154692	+	0.987963i	$0.450561\pi$
$660$	−16580.3	+	28718.0i	−0.977862	+	1.69371i
$661$	−5227.99	−	9055.14i	−0.307633	−	0.532835i	0.670211	−	0.742170i	$-0.266203\pi$
$661$	−5227.99	−	9055.14i	−0.307633	−	0.532835i	−0.977844	+	0.209335i	$0.932870\pi$
$662$	8347.31	+	14458.0i	0.490072	+	0.848829i
$663$	−439.793	+	761.743i	−0.0257619	+	0.0446209i
$664$	19231.3			1.12398
$665$		0			0
$666$	−11495.5			−0.668834
$667$	−486.039	+	841.845i	−0.0282152	+	0.0488701i
$668$	−17092.5	−	29605.0i	−0.990011	−	1.71475i
$669$	17956.3	+	31101.3i	1.03772	+	1.79738i
$670$	9166.87	−	15877.5i	0.528578	−	0.915524i
$671$	13706.0			0.788548
$672$		0			0
$673$	−17658.6			−1.01143			−0.505714	−	0.862701i	$-0.668771\pi$
$673$	−17658.6			−1.01143			−0.505714	+	0.862701i	$0.668771\pi$
$674$	18384.1	−	31842.1i	1.05064	−	1.81975i
$675$	−5176.85	−	8966.56i	−0.295195	−	0.511294i
$676$	3102.67	+	5373.98i	0.176529	+	0.305757i
$677$	4562.02	−	7901.64i	0.258984	−	0.448574i	−0.706986	−	0.707228i	$-0.749945\pi$
$677$	4562.02	−	7901.64i	0.258984	−	0.448574i	0.965970	+	0.258654i	$0.0832788\pi$
$678$	−17797.0			−1.00810
$679$		0			0
$680$	−193.531			−0.0109141
$681$	−29586.4	+	51245.2i	−1.66484	+	2.88358i
$682$	21303.6	+	36898.9i	1.19612	+	2.07175i
$683$	−5261.83	−	9113.75i	−0.294785	−	0.510583i	0.680150	−	0.733073i	$-0.261915\pi$
$683$	−5261.83	−	9113.75i	−0.294785	−	0.510583i	−0.974935	+	0.222490i	$0.928581\pi$
$684$	−6817.91	+	11809.0i	−0.381125	+	0.660127i
$685$	−12563.6			−0.700775
$686$		0			0
$687$	−37761.9			−2.09710
$688$	−122.143	+	211.558i	−0.00676840	+	0.0117232i
$689$	3100.81	+	5370.76i	0.171453	+	0.296966i
$690$	−17010.9	−	29463.7i	−0.938541	−	1.62560i
$691$	−16464.1	+	28516.6i	−0.906400	+	1.56993i	−0.0873735	+	0.996176i	$0.527847\pi$
$691$	−16464.1	+	28516.6i	−0.906400	+	1.56993i	−0.819027	+	0.573755i	$0.805486\pi$
$692$	−382.706			−0.0210235
$693$		0			0
$694$	−56872.8			−3.11075
$695$	2914.27	−	5047.66i	0.159057	−	0.275495i
$696$	542.942	+	940.403i	0.0295692	+	0.0512153i
$697$	292.012	+	505.780i	0.0158691	+	0.0274860i
$698$	−10023.4	+	17361.0i	−0.543540	+	0.941439i
$699$	−16726.7			−0.905093
$700$		0			0
$701$	−2582.50			−0.139144			−0.0695719	−	0.997577i	$-0.522163\pi$
$701$	−2582.50			−0.139144			−0.0695719	+	0.997577i	$0.522163\pi$
$702$	−37895.7	+	65637.3i	−2.03744	+	3.52895i
$703$	306.192	+	530.339i	0.0164271	+	0.0284525i
$704$	−23500.9	−	40704.7i	−1.25813	−	2.17914i
$705$	−4165.00	+	7213.99i	−0.222501	+	0.385382i
$706$	−54786.4			−2.92056
$707$		0			0
$708$	−27456.9			−1.45748
$709$	3433.00	−	5946.13i	0.181846	−	0.314967i	−0.760663	−	0.649147i	$-0.775126\pi$
$709$	3433.00	−	5946.13i	0.181846	−	0.314967i	0.942509	+	0.334180i	$0.108459\pi$
$710$	10739.9	+	18602.0i	0.567690	+	0.983268i
$711$	−10391.2	−	17998.1i	−0.548102	−	0.949341i
$712$	9937.94	−	17213.0i	0.523090	−	0.906019i
$713$	−26191.4			−1.37570
$714$		0			0
$715$	11580.7			0.605725
$716$	−4415.18	+	7647.32i	−0.230451	+	0.399153i
$717$	−33373.6	−	57804.7i	−1.73830	−	3.01082i
$718$	24734.5	+	42841.3i	1.28563	+	2.22678i
$719$	3290.92	−	5700.05i	0.170696	−	0.295655i	−0.767967	−	0.640489i	$-0.778732\pi$
$719$	3290.92	−	5700.05i	0.170696	−	0.295655i	0.938664	+	0.344834i	$0.112065\pi$
$720$	5769.24			0.298621
$721$		0			0
$722$	−29429.8			−1.51699
$723$	−22771.9	+	39442.2i	−1.17137	+	2.02887i
$724$	11909.7	+	20628.2i	0.611354	+	1.05890i
$725$	78.2560	+	135.543i	0.00400876	+	0.00694338i
$726$	−40882.0	+	70809.7i	−2.08991	+	3.61983i
$727$	15527.2			0.792119			0.396060	−	0.918225i	$-0.370377\pi$
$727$	15527.2			0.792119			0.396060	+	0.918225i	$0.370377\pi$
$728$		0			0
$729$	42149.0			2.14139
$730$	10431.8	−	18068.4i	0.528900	−	0.916082i
$731$	16.0396	+	27.7814i	0.000811553	+	0.00140565i
$732$	14217.3	+	24625.1i	0.717878	+	1.24340i
$733$	1695.66	−	2936.97i	0.0854443	−	0.147994i	−0.820136	−	0.572168i	$-0.806102\pi$
$733$	1695.66	−	2936.97i	0.0854443	−	0.147994i	0.905580	+	0.424175i	$0.139436\pi$
$734$	26200.3			1.31754
$735$		0			0
$736$	33527.7			1.67914
$737$	23203.4	−	40189.4i	1.15971	−	2.00868i
$738$	41252.9	+	71452.2i	2.05764	+	3.56395i
$739$	7167.51	+	12414.5i	0.356781	+	0.617962i	0.987421	−	0.158113i	$-0.0505410\pi$
$739$	7167.51	+	12414.5i	0.356781	+	0.617962i	−0.630640	+	0.776075i	$0.717208\pi$
$740$	−1111.32	+	1924.86i	−0.0552065	+	0.0956204i
$741$	6619.51			0.328170
$742$		0			0
$743$	−27668.2			−1.36615			−0.683073	−	0.730350i	$-0.739357\pi$
$743$	−27668.2			−1.36615			−0.683073	+	0.730350i	$0.739357\pi$
$744$	−14628.8	+	25337.9i	−0.720859	+	1.24856i
$745$	−6593.72	−	11420.7i	−0.324262	−	0.561639i
$746$	20925.9	+	36244.7i	1.02701	+	1.77884i
$747$	−37641.9	+	65197.6i	−1.84370	+	3.19338i
$748$	−1479.99			−0.0723446
$749$		0			0
$750$	−5477.76			−0.266693
$751$	8464.93	−	14661.7i	0.411305	−	0.712401i	−0.583728	−	0.811949i	$-0.698407\pi$
$751$	8464.93	−	14661.7i	0.411305	−	0.712401i	0.995033	+	0.0995486i	$0.0317399\pi$
$752$	−1415.55	−	2451.81i	−0.0686434	−	0.118894i
$753$	−28999.1	−	50227.9i	−1.40343	−	2.43082i
$754$	572.852	−	992.209i	0.0276685	−	0.0479232i
$755$	12911.6			0.622386
$756$		0			0
$757$	19445.3			0.933622			0.466811	−	0.884357i	$-0.345403\pi$
$757$	19445.3			0.933622			0.466811	+	0.884357i	$0.345403\pi$
$758$	−12369.9	+	21425.4i	−0.592739	+	1.02665i
$759$	−43058.3	−	74579.1i	−2.05918	−	3.56660i
$760$	728.230	+	1261.33i	0.0347575	+	0.0602017i
$761$	−4998.49	+	8657.63i	−0.238101	+	0.412403i	−0.960169	−	0.279418i	$-0.909858\pi$
$761$	−4998.49	+	8657.63i	−0.238101	+	0.412403i	0.722068	+	0.691822i	$0.243192\pi$
$762$	−19791.7			−0.940917
$763$		0			0
$764$	25753.9			1.21956
$765$	378.802	−	656.105i	0.0179028	−	0.0310085i
$766$	−11711.8	−	20285.4i	−0.552433	−	0.956842i
$767$	4794.38	+	8304.11i	0.225704	+	0.390931i
$768$	10905.3	−	18888.6i	0.512385	−	0.887477i
$769$	8382.34			0.393075			0.196538	−	0.980496i	$-0.437030\pi$
$769$	8382.34			0.393075			0.196538	+	0.980496i	$0.437030\pi$
$770$		0			0
$771$	−16654.4			−0.777942
$772$	−6002.59	+	10396.8i	−0.279842	+	0.484700i
$773$	5648.73	+	9783.89i	0.262834	+	0.455242i	0.966994	−	0.254799i	$-0.0820094\pi$
$773$	5648.73	+	9783.89i	0.262834	+	0.455242i	−0.704160	+	0.710042i	$0.748676\pi$
$774$	2265.93	+	3924.71i	0.105229	+	0.182262i
$775$	−2108.50	+	3652.03i	−0.0977286	+	0.169271i
$776$	13300.2			0.615268
$777$		0			0
$778$	−48652.9			−2.24202
$779$	2197.60	−	3806.35i	0.101075	−	0.175066i
$780$	12012.7	+	20806.6i	0.551440	+	0.955122i
$781$	27184.9	+	47085.7i	1.24552	+	2.15731i
$782$	759.210	−	1314.99i	0.0347178	−	0.0601330i
$783$	−2592.76			−0.118337
$784$		0			0
$785$	−1128.94			−0.0513294
$786$	−7930.29	+	13735.7i	−0.359878	+	0.623327i
$787$	12587.2	+	21801.6i	0.570120	+	0.987477i	0.996553	+	0.0829580i	$0.0264367\pi$
$787$	12587.2	+	21801.6i	0.570120	+	0.987477i	−0.426433	+	0.904519i	$0.640230\pi$
$788$	−10264.8	−	17779.2i	−0.464047	−	0.803752i
$789$	27768.7	−	48096.9i	1.25297	−	2.17021i
$790$	−6706.43			−0.302030
$791$		0			0
$792$	−69204.6			−3.10490
$793$	4965.11	−	8599.82i	0.222341	−	0.385105i
$794$	−29724.2	−	51483.9i	−1.32856	−	2.30113i
$795$	−3712.56	−	6430.33i	−0.165624	−	0.286868i
$796$	31915.2	−	55278.8i	1.42111	−	2.46144i
$797$	−26277.4			−1.16787			−0.583936	−	0.811800i	$-0.698488\pi$
$797$	−26277.4			−1.16787			−0.583936	+	0.811800i	$0.698488\pi$
$798$		0			0
$799$	−371.775			−0.0164611
$800$	2699.10	−	4674.98i	0.119285	−	0.206607i
$801$	38903.5	+	67382.8i	1.71609	+	2.97235i
$802$	−16143.2	−	27960.8i	−0.710767	−	1.23108i
$803$	26405.1	−	45735.0i	1.16042	−	2.00990i
$804$	96275.6			4.22311
$805$		0			0
$806$	30869.5			1.34905
$807$	−26141.6	+	45278.5i	−1.14031	+	1.97507i
$808$	−4944.24	−	8563.67i	−0.215269	−	0.372858i
$809$	−7838.44	−	13576.6i	−0.340649	−	0.590021i	0.643905	−	0.765106i	$-0.277313\pi$
$809$	−7838.44	−	13576.6i	−0.340649	−	0.590021i	−0.984553	+	0.175085i	$0.943980\pi$
$810$	24498.4	−	42432.5i	1.06270	−	1.84065i
$811$	26600.5			1.15175			0.575876	−	0.817537i	$-0.304661\pi$
$811$	26600.5			1.15175			0.575876	+	0.817537i	$0.304661\pi$
$812$		0			0
$813$	−19961.1			−0.861090
$814$	−4694.88	+	8131.78i	−0.202157	+	0.350146i
$815$	3722.52	+	6447.59i	0.159993	+	0.277116i
$816$	178.960	+	309.968i	0.00767753	+	0.0132979i
$817$	120.709	−	209.075i	0.00516901	−	0.00895300i
$818$	26146.3			1.11759
$819$		0			0
$820$	15952.3			0.679363
$821$	−17800.7	+	30831.6i	−0.756696	+	1.31064i	0.187831	+	0.982201i	$0.439854\pi$
$821$	−17800.7	+	30831.6i	−0.756696	+	1.31064i	−0.944527	+	0.328434i	$0.893479\pi$
$822$	−55056.3	−	95360.4i	−2.33614	−	4.04632i
$823$	−20987.5	−	36351.4i	−0.888916	−	1.53965i	−0.841159	−	0.540788i	$-0.818126\pi$
$823$	−20987.5	−	36351.4i	−0.888916	−	1.53965i	−0.0477569	−	0.998859i	$-0.515207\pi$
$824$	1815.37	−	3144.32i	0.0767495	−	0.132934i
$825$	−13865.4			−0.585129
$826$		0			0
$827$	27719.4			1.16554			0.582768	−	0.812639i	$-0.301970\pi$
$827$	27719.4			1.16554			0.582768	+	0.812639i	$0.301970\pi$
$828$	64262.7	−	111306.i	2.69720	−	4.67169i
$829$	−13611.1	−	23575.2i	−0.570246	−	0.987696i	−0.996540	−	0.0831109i	$-0.973514\pi$
$829$	−13611.1	−	23575.2i	−0.570246	−	0.987696i	0.426294	−	0.904585i	$-0.359819\pi$
$830$	12146.9	+	21039.1i	0.507983	+	0.879853i
$831$	4255.51	−	7370.75i	0.177644	−	0.307688i
$832$	−34053.4			−1.41898
$833$		0			0
$834$	51083.7			2.12096
$835$	7146.83	−	12378.7i	0.296199	−	0.513032i
$836$	5568.99	+	9645.78i	0.230392	+	0.399050i
$837$	−34929.3	−	60499.3i	−1.44245	−	2.49840i
$838$	18638.6	−	32283.0i	0.768329	−	1.33079i
$839$	−24081.1			−0.990909			−0.495454	−	0.868634i	$-0.664998\pi$
$839$	−24081.1			−0.990909			−0.495454	+	0.868634i	$0.664998\pi$
$840$		0			0
$841$	−24349.8			−0.998393
$842$	24471.2	−	42385.3i	1.00158	−	1.73479i
$843$	−10053.0	−	17412.2i	−0.410726	−	0.711398i
$844$	−5145.49	−	8912.25i	−0.209852	−	0.363474i
$845$	−1297.31	+	2247.01i	−0.0528153	+	0.0914787i
$846$	−52521.1			−2.13441
$847$		0			0
$848$	2523.56			0.102193
$849$	−32493.5	+	56280.4i	−1.31352	+	2.27507i
$850$	−122.239	−	211.723i	−0.00493264	−	0.00854359i
$851$	−2886.03	−	4998.75i	−0.116254	−	0.201357i
$852$	−56398.0	+	97684.2i	−2.26780	+	3.92794i
$853$	−18493.0			−0.742309			−0.371155	−	0.928571i	$-0.621038\pi$
$853$	−18493.0			−0.742309			−0.371155	+	0.928571i	$0.621038\pi$
$854$		0			0
$855$	−5701.52			−0.228056
$856$	12998.1	−	22513.4i	0.519003	−	0.898940i
$857$	1749.63	+	3030.44i	0.0697387	+	0.120791i	0.898786	−	0.438387i	$-0.144450\pi$
$857$	1749.63	+	3030.44i	0.0697387	+	0.120791i	−0.829048	+	0.559178i	$0.811117\pi$
$858$	50749.0	+	87899.8i	2.01928	+	3.49750i
$859$	16079.0	−	27849.7i	0.638660	−	1.10619i	−0.347067	−	0.937840i	$-0.612822\pi$
$859$	16079.0	−	27849.7i	0.638660	−	1.10619i	0.985727	−	0.168352i	$-0.0538444\pi$
$860$	876.224			0.0347430
$861$		0			0
$862$	42071.9			1.66238
$863$	23852.3	−	41313.5i	0.940838	−	1.62958i	0.176960	−	0.984218i	$-0.443374\pi$
$863$	23852.3	−	41313.5i	0.940838	−	1.62958i	0.763878	−	0.645361i	$-0.223293\pi$
$864$	44713.1	+	77445.4i	1.76061	+	3.04947i
$865$	−80.0099	−	138.581i	−0.00314499	−	0.00544729i
$866$	−19620.6	+	33983.8i	−0.769900	+	1.33351i
$867$	−48145.6			−1.88594
$868$		0			0
$869$	−16975.4			−0.662661
$870$	−685.867	+	1187.96i	−0.0267277	+	0.0462937i
$871$	−16811.2	−	29117.8i	−0.653989	−	1.13274i
$872$	6844.81	+	11855.6i	0.265819	+	0.460413i
$873$	−26032.7	+	45089.9i	−1.00925	+	1.74807i
$874$	−11427.2			−0.442255
$875$		0			0
$876$	109560.			4.22569
$877$	12218.7	−	21163.3i	0.470461	−	0.814863i	−0.528968	−	0.848642i	$-0.677421\pi$
$877$	12218.7	−	21163.3i	0.470461	−	0.814863i	0.999429	+	0.0337787i	$0.0107541\pi$
$878$	−23587.2	−	40854.2i	−0.906640	−	1.57035i
$879$	27813.2	+	48173.9i	1.06725	+	1.84854i
$880$	2356.21	−	4081.07i	0.0902588	−	0.156333i
$881$	−13975.8			−0.534458			−0.267229	−	0.963633i	$-0.586108\pi$
$881$	−13975.8			−0.534458			−0.267229	+	0.963633i	$0.586108\pi$
$882$		0			0
$883$	3193.55			0.121712			0.0608558	−	0.998147i	$-0.480617\pi$
$883$	3193.55			0.121712			0.0608558	+	0.998147i	$0.480617\pi$
$884$	−536.137	+	928.616i	−0.0203984	+	0.0353311i
$885$	−5740.24	−	9942.39i	−0.218029	−	0.377638i
$886$	10896.4	+	18873.1i	0.413174	+	0.715639i
$887$	−10049.6	+	17406.5i	−0.380422	+	0.658909i	−0.991122	−	0.132952i	$-0.957554\pi$
$887$	−10049.6	+	17406.5i	−0.380422	+	0.658909i	0.610701	+	0.791861i	$0.290888\pi$
$888$	−6447.81			−0.243665
$889$		0			0
$890$	25108.1			0.945646
$891$	62010.9	−	107406.i	2.33159	−	4.03843i
$892$	21890.0	+	37914.5i	0.821671	+	1.42318i
$893$	1398.94	+	2423.03i	0.0524228	+	0.0907990i
$894$	57790.1	−	100095.i	2.16196	−	3.74462i
$895$	−3692.22			−0.137896
$896$		0			0
$897$	−62392.6			−2.32244
$898$	−97.8185	+	169.427i	−0.00363502	+	0.00629604i
$899$	528.009	+	914.539i	0.0195885	+	0.0339283i
$900$	−10346.8	−	17921.1i	−0.383214	−	0.663746i
$901$	165.695	−	286.991i	0.00612662	−	0.0106116i
$902$	67392.3			2.48771
$903$		0			0
$904$	−7181.20			−0.264207
$905$	−4979.77	+	8625.22i	−0.182910	+	0.316809i
$906$	56581.3	+	98001.8i	2.07482	+	3.59370i
$907$	−11606.3	−	20102.7i	−0.424896	−	0.735941i	0.571515	−	0.820592i	$-0.306356\pi$
$907$	−11606.3	−	20102.7i	−0.424896	−	0.735941i	−0.996411	+	0.0846504i	$0.973023\pi$
$908$	−36067.8	+	62471.3i	−1.31823	+	2.28324i
$909$	38709.8			1.41246
$910$		0			0
$911$	2754.63			0.100181			0.0500905	−	0.998745i	$-0.484049\pi$
$911$	2754.63			0.100181			0.0500905	+	0.998745i	$0.484049\pi$
$912$	1346.80	−	2332.73i	0.0489004	−	0.0846980i
$913$	30746.5	+	53254.6i	1.11453	+	1.93042i
$914$	−6410.24	−	11102.9i	−0.231982	−	0.401805i
$915$	−5944.65	+	10296.4i	−0.214781	+	0.372011i
$916$	−46034.2			−1.66049
$917$		0			0
$918$	4049.98			0.145609
$919$	−8109.02	+	14045.2i	−0.291068	+	0.504145i	−0.974063	−	0.226279i	$-0.927344\pi$
$919$	−8109.02	+	14045.2i	−0.291068	+	0.504145i	0.682994	+	0.730424i	$0.260677\pi$
$920$	−6863.98	−	11888.8i	−0.245977	−	0.426045i
$921$	1337.18	+	2316.06i	0.0478410	+	0.0828630i
$922$	40006.1	−	69292.6i	1.42899	−	2.47509i
$923$	39391.7			1.40476
$924$		0			0
$925$	−929.344			−0.0330342
$926$	17044.9	−	29522.6i	0.604892	−	1.04770i
$927$	7106.53	+	12308.9i	0.251790	+	0.436113i
$928$	−675.907	−	1170.71i	−0.0239092	−	0.0414119i
$929$	−21296.3	+	36886.3i	−0.752109	+	1.30269i	0.194689	+	0.980865i	$0.437630\pi$
$929$	−21296.3	+	36886.3i	−0.752109	+	1.30269i	−0.946799	+	0.321827i	$0.895703\pi$
$930$	−36959.6			−1.30317
$931$		0			0
$932$	−20390.9			−0.716659
$933$	5987.70	−	10371.0i	0.210106	−	0.363914i
$934$	13952.5	+	24166.5i	0.488801	+	0.846628i
$935$	−309.412	−	535.918i	−0.0108223	−	0.0187448i
$936$	−25069.8	+	43422.3i	−0.875463	+	1.51635i
$937$	−4670.79			−0.162848			−0.0814238	−	0.996680i	$-0.525947\pi$
$937$	−4670.79			−0.162848			−0.0814238	+	0.996680i	$0.525947\pi$
$938$		0			0
$939$	7604.04			0.264269
$940$	−5077.41	+	8794.33i	−0.176177	+	0.305148i
$941$	−5518.26	−	9557.90i	−0.191169	−	0.331115i	0.754469	−	0.656336i	$-0.227895\pi$
$941$	−5518.26	−	9557.90i	−0.191169	−	0.331115i	−0.945638	+	0.325221i	$0.894561\pi$
$942$	−4947.24	−	8568.87i	−0.171114	−	0.296379i
$943$	−20713.6	+	35877.0i	−0.715300	+	1.23894i
$944$	3901.86			0.134528
$945$		0			0
$946$	3701.71			0.127223
$947$	−14109.5	+	24438.3i	−0.484157	+	0.838584i	−0.999834	−	0.0181984i	$-0.994207\pi$
$947$	−14109.5	+	24438.3i	−0.484157	+	0.838584i	0.515678	+	0.856783i	$0.327540\pi$
$948$	−17608.7	−	30499.1i	−0.603273	−	1.04490i
$949$	−19130.9	−	33135.6i	−0.654388	−	1.13343i
$950$	−919.932	+	1593.37i	−0.0314174	+	0.0544166i
$951$	72521.7			2.47285
$952$		0			0
$953$	42209.7			1.43474			0.717370	−	0.696693i	$-0.245346\pi$
$953$	42209.7			1.43474			0.717370	+	0.696693i	$0.245346\pi$
$954$	23407.9	−	40543.7i	0.794401	−	1.37594i
$955$	5384.21	+	9325.72i	0.182439	+	0.315993i
$956$	−40684.6	−	70467.8i	−1.37640	−	2.38399i
$957$	−1736.08	+	3006.98i	−0.0586411	+	0.101569i
$958$	−18404.0			−0.620674
$959$		0			0
$960$	40771.6			1.37073
$961$	668.996	−	1158.74i	0.0224563	−	0.0388955i
$962$	3401.51	+	5891.59i	0.114001	+	0.197456i
$963$	50882.9	+	88131.8i	1.70268	+	2.94913i
$964$	−27760.5	+	48082.6i	−0.927496	+	1.60647i
$965$	−5019.70			−0.167451
$966$		0			0
$967$	11522.8			0.383193			0.191596	−	0.981474i	$-0.438634\pi$
$967$	11522.8			0.383193			0.191596	+	0.981474i	$0.438634\pi$
$968$	−16496.1	+	28572.1i	−0.547733	+	0.948701i
$969$	−176.860	−	306.330i	−0.00586331	−	0.0101556i
$970$	8400.67	+	14550.4i	0.278071	+	0.481634i
$971$	−21330.1	+	36944.9i	−0.704961	+	1.22103i	0.261745	+	0.965137i	$0.415702\pi$
$971$	−21330.1	+	36944.9i	−0.704961	+	1.22103i	−0.966706	+	0.255891i	$0.917631\pi$
$972$	123581.			4.07806
$973$		0			0
$974$	−6350.30			−0.208908
$975$	−5022.84	+	8699.81i	−0.164984	+	0.285761i
$976$	−2020.40	−	3499.44i	−0.0662618	−	0.114769i
$977$	6995.83	+	12117.1i	0.229085	+	0.396787i	0.957537	−	0.288309i	$-0.0930932\pi$
$977$	6995.83	+	12117.1i	0.229085	+	0.396787i	−0.728452	+	0.685097i	$0.759760\pi$
$978$	−32625.7	+	56509.3i	−1.06672	+	1.84762i
$979$	63554.1			2.07477
$980$		0			0
$981$	−53589.9			−1.74413
$982$	−42979.2	+	74442.1i	−1.39666	+	2.41909i
$983$	−12981.6	−	22484.8i	−0.421210	−	0.729557i	0.574848	−	0.818260i	$-0.305061\pi$
$983$	−12981.6	−	22484.8i	−0.421210	−	0.729557i	−0.996058	+	0.0887029i	$0.971728\pi$
$984$	23138.6	+	40077.3i	0.749627	+	1.29839i
$985$	4292.00	−	7433.97i	0.138837	−	0.240473i
$986$	−61.2217			−0.00197738
$987$		0			0
$988$	8069.62			0.259847
$989$	−1137.75	+	1970.65i	−0.0365809	+	0.0633599i
$990$	−43711.1	−	75709.9i	−1.40326	−	2.43052i
$991$	−7241.15	−	12542.0i	−0.232112	−	0.402029i	0.726318	−	0.687359i	$-0.241230\pi$
$991$	−7241.15	−	12542.0i	−0.232112	−	0.402029i	−0.958429	+	0.285330i	$0.907897\pi$
$992$	18211.4	−	31543.1i	0.582876	−	1.00957i
$993$	−36656.5			−1.17146
$994$		0			0
$995$	26689.3			0.850359
$996$	−63786.9	+	110482.i	−2.02928	+	3.51482i
$997$	2092.23	+	3623.84i	0.0664609	+	0.115114i	0.897341	−	0.441338i	$-0.145496\pi$
$997$	2092.23	+	3623.84i	0.0664609	+	0.115114i	−0.830880	+	0.556451i	$0.812163\pi$
$998$	−21391.2	−	37050.7i	−0.678484	−	1.17517i
$999$	7697.72	−	13332.8i	0.243789	−	0.422255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.p.226.1		12
7.2	even	3		245.4.a.p.1.6	yes	6
7.3	odd	6		245.4.e.q.116.1		12
7.4	even	3	inner	245.4.e.p.116.1		12
7.5	odd	6		245.4.a.o.1.6	✓	6
7.6	odd	2		245.4.e.q.226.1		12
21.2	odd	6		2205.4.a.ca.1.1		6
21.5	even	6		2205.4.a.bz.1.1		6
35.9	even	6		1225.4.a.bi.1.1		6
35.19	odd	6		1225.4.a.bj.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.a.o.1.6	✓	6	7.5	odd	6
245.4.a.p.1.6	yes	6	7.2	even	3
245.4.e.p.116.1		12	7.4	even	3	inner
245.4.e.p.226.1		12	1.1	even	1	trivial
245.4.e.q.116.1		12	7.3	odd	6
245.4.e.q.226.1		12	7.6	odd	2
1225.4.a.bi.1.1		6	35.9	even	6
1225.4.a.bj.1.1		6	35.19	odd	6
2205.4.a.bz.1.1		6	21.5	even	6
2205.4.a.ca.1.1		6	21.2	odd	6

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.23372 + 3.86892i) q^{2} +(-4.90460 - 8.49501i) q^{3} +(-5.97903 - 10.3560i) q^{4} +(2.50000 - 4.33013i) q^{5} +43.8221 q^{6} +17.6824 q^{8} +(-34.6102 + 59.9466i) q^{9} +O(q^{10})\)	\(q+(-2.23372 + 3.86892i) q^{2} +(-4.90460 - 8.49501i) q^{3} +(-5.97903 - 10.3560i) q^{4} +(2.50000 - 4.33013i) q^{5} +43.8221 q^{6} +17.6824 q^{8} +(-34.6102 + 59.9466i) q^{9} +(11.1686 + 19.3446i) q^{10} +(28.2702 + 48.9654i) q^{11} +(-58.6495 + 101.584i) q^{12} +40.9643 q^{13} -49.0460 q^{15} +(8.33460 - 14.4359i) q^{16} +(-1.09448 - 1.89570i) q^{17} +(-154.619 - 267.808i) q^{18} +(-8.23676 + 14.2665i) q^{19} -59.7903 q^{20} -252.591 q^{22} +(77.6361 - 134.470i) q^{23} +(-86.7253 - 150.213i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-91.5029 + 158.488i) q^{26} +414.148 q^{27} -6.26048 q^{29} +(109.555 - 189.755i) q^{30} +(-84.3401 - 146.081i) q^{31} +(107.964 + 186.999i) q^{32} +(277.308 - 480.312i) q^{33} +9.77908 q^{34} +827.742 q^{36} +(18.5869 - 32.1934i) q^{37} +(-36.7973 - 63.7348i) q^{38} +(-200.914 - 347.992i) q^{39} +(44.2061 - 76.5672i) q^{40} -266.804 q^{41} -14.6549 q^{43} +(338.057 - 585.532i) q^{44} +(173.051 + 299.733i) q^{45} +(346.835 + 600.736i) q^{46} +(84.9202 - 147.086i) q^{47} -163.511 q^{48} +111.686 q^{50} +(-10.7360 + 18.5953i) q^{51} +(-244.927 - 424.226i) q^{52} +(75.6954 + 131.108i) q^{53} +(-925.091 + 1602.30i) q^{54} +282.702 q^{55} +161.592 q^{57} +(13.9842 - 24.2213i) q^{58} +(117.038 + 202.716i) q^{59} +(293.248 + 507.920i) q^{60} +(121.206 - 209.934i) q^{61} +753.569 q^{62} -831.294 q^{64} +(102.411 - 177.381i) q^{65} +(1238.86 + 2145.77i) q^{66} +(-410.385 - 710.808i) q^{67} +(-13.0879 + 22.6689i) q^{68} -1523.10 q^{69} +961.611 q^{71} +(-611.992 + 1060.00i) q^{72} +(-467.013 - 808.890i) q^{73} +(83.0359 + 143.822i) q^{74} +(-122.615 + 212.375i) q^{75} +196.992 q^{76} +1795.14 q^{78} +(-150.118 + 260.012i) q^{79} +(-41.6730 - 72.1797i) q^{80} +(-1096.75 - 1899.63i) q^{81} +(595.966 - 1032.24i) q^{82} +1087.60 q^{83} -10.9448 q^{85} +(32.7351 - 56.6988i) q^{86} +(30.7051 + 53.1828i) q^{87} +(499.886 + 865.828i) q^{88} +(562.023 - 973.453i) q^{89} -1546.19 q^{90} -1856.76 q^{92} +(-827.309 + 1432.94i) q^{93} +(379.376 + 657.099i) q^{94} +(41.1838 + 71.3325i) q^{95} +(1059.04 - 1834.31i) q^{96} +752.168 q^{97} -3913.75 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 16 q^{3} - 14 q^{4} + 30 q^{5} + 48 q^{6} - 132 q^{8} - 70 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 - 16 * q^3 - 14 * q^4 + 30 * q^5 + 48 * q^6 - 132 * q^8 - 70 * q^9	\( 12 q + 2 q^{2} - 16 q^{3} - 14 q^{4} + 30 q^{5} + 48 q^{6} - 132 q^{8} - 70 q^{9} - 10 q^{10} + 16 q^{11} - 160 q^{12} + 336 q^{13} - 160 q^{15} - 298 q^{16} + 4 q^{17} - 354 q^{18} - 308 q^{19} - 140 q^{20} - 472 q^{22} + 336 q^{23} + 92 q^{24} - 150 q^{25} - 56 q^{26} + 1928 q^{27} + 352 q^{29} + 120 q^{30} - 392 q^{31} + 770 q^{32} - 188 q^{33} + 1624 q^{34} + 460 q^{36} + 140 q^{37} - 20 q^{38} - 140 q^{39} - 330 q^{40} + 1312 q^{41} - 776 q^{43} + 160 q^{44} + 350 q^{45} + 388 q^{46} - 628 q^{47} + 2792 q^{48} - 100 q^{50} - 744 q^{51} - 1520 q^{52} + 676 q^{53} - 2284 q^{54} + 160 q^{55} + 2936 q^{57} + 2012 q^{58} - 996 q^{59} + 800 q^{60} - 740 q^{61} - 728 q^{62} + 2852 q^{64} + 840 q^{65} + 3620 q^{66} - 1768 q^{67} + 2940 q^{68} - 2096 q^{69} - 448 q^{71} - 2858 q^{72} - 2640 q^{73} - 928 q^{74} - 400 q^{75} - 2680 q^{76} + 16 q^{78} - 1636 q^{79} + 1490 q^{80} - 4442 q^{81} + 1756 q^{82} + 280 q^{83} + 40 q^{85} - 1180 q^{86} - 1940 q^{87} + 5652 q^{88} + 1904 q^{89} - 3540 q^{90} - 3904 q^{92} + 1592 q^{93} + 3332 q^{94} + 1540 q^{95} + 6460 q^{96} + 1032 q^{97} - 5608 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 16 * q^3 - 14 * q^4 + 30 * q^5 + 48 * q^6 - 132 * q^8 - 70 * q^9 - 10 * q^10 + 16 * q^11 - 160 * q^12 + 336 * q^13 - 160 * q^15 - 298 * q^16 + 4 * q^17 - 354 * q^18 - 308 * q^19 - 140 * q^20 - 472 * q^22 + 336 * q^23 + 92 * q^24 - 150 * q^25 - 56 * q^26 + 1928 * q^27 + 352 * q^29 + 120 * q^30 - 392 * q^31 + 770 * q^32 - 188 * q^33 + 1624 * q^34 + 460 * q^36 + 140 * q^37 - 20 * q^38 - 140 * q^39 - 330 * q^40 + 1312 * q^41 - 776 * q^43 + 160 * q^44 + 350 * q^45 + 388 * q^46 - 628 * q^47 + 2792 * q^48 - 100 * q^50 - 744 * q^51 - 1520 * q^52 + 676 * q^53 - 2284 * q^54 + 160 * q^55 + 2936 * q^57 + 2012 * q^58 - 996 * q^59 + 800 * q^60 - 740 * q^61 - 728 * q^62 + 2852 * q^64 + 840 * q^65 + 3620 * q^66 - 1768 * q^67 + 2940 * q^68 - 2096 * q^69 - 448 * q^71 - 2858 * q^72 - 2640 * q^73 - 928 * q^74 - 400 * q^75 - 2680 * q^76 + 16 * q^78 - 1636 * q^79 + 1490 * q^80 - 4442 * q^81 + 1756 * q^82 + 280 * q^83 + 40 * q^85 - 1180 * q^86 - 1940 * q^87 + 5652 * q^88 + 1904 * q^89 - 3540 * q^90 - 3904 * q^92 + 1592 * q^93 + 3332 * q^94 + 1540 * q^95 + 6460 * q^96 + 1032 * q^97 - 5608 * q^99

Introduction

L-functions

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