LMFDB - Embedded newform 245.4.e.q.116.2

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			116.2
Root			$-0.120924 + 0.209447i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.4.e.q.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.828031 - 1.43419i) q^{2} +(-0.166444 + 0.288289i) q^{3} +(2.62873 - 4.55309i) q^{4} +(-2.50000 - 4.33013i) q^{5} +0.551283 q^{6} -21.9552 q^{8} +(13.4446 + 23.2867i) q^{9} +O(q^{10})$	\(q+(-0.828031 - 1.43419i) q^{2} +(-0.166444 + 0.288289i) q^{3} +(2.62873 - 4.55309i) q^{4} +(-2.50000 - 4.33013i) q^{5} +0.551283 q^{6} -21.9552 q^{8} +(13.4446 + 23.2867i) q^{9} +(-4.14016 + 7.17096i) q^{10} +(-34.7863 + 60.2517i) q^{11} +(0.875071 + 1.51567i) q^{12} -68.4326 q^{13} +1.66444 q^{15} +(-2.85026 - 4.93680i) q^{16} +(52.1659 - 90.3539i) q^{17} +(22.2651 - 38.5643i) q^{18} +(35.9465 + 62.2611i) q^{19} -26.2873 q^{20} +115.217 q^{22} +(50.5154 + 87.4952i) q^{23} +(3.65430 - 6.32944i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(56.6643 + 98.1454i) q^{26} -17.9390 q^{27} -114.661 q^{29} +(-1.37821 - 2.38712i) q^{30} +(-36.8252 + 63.7832i) q^{31} +(-92.5409 + 160.286i) q^{32} +(-11.5799 - 20.0570i) q^{33} -172.780 q^{34} +141.369 q^{36} +(100.467 + 174.013i) q^{37} +(59.5296 - 103.108i) q^{38} +(11.3902 - 19.7284i) q^{39} +(54.8879 + 95.0687i) q^{40} -417.308 q^{41} +311.175 q^{43} +(182.888 + 316.771i) q^{44} +(67.2230 - 116.434i) q^{45} +(83.6566 - 144.897i) q^{46} +(74.8485 + 129.641i) q^{47} +1.89763 q^{48} +41.4016 q^{50} +(17.3654 + 30.0777i) q^{51} +(-179.891 + 311.580i) q^{52} +(-135.737 + 235.104i) q^{53} +(14.8541 + 25.7280i) q^{54} +347.863 q^{55} -23.9323 q^{57} +(94.9425 + 164.445i) q^{58} +(-259.014 + 448.625i) q^{59} +(4.37536 - 7.57834i) q^{60} +(-109.963 - 190.461i) q^{61} +121.970 q^{62} +260.903 q^{64} +(171.081 + 296.322i) q^{65} +(-19.1771 + 33.2157i) q^{66} +(-40.3475 + 69.8839i) q^{67} +(-274.260 - 475.032i) q^{68} -33.6319 q^{69} -91.0463 q^{71} +(-295.178 - 511.264i) q^{72} +(441.141 - 764.078i) q^{73} +(166.379 - 288.177i) q^{74} +(-4.16110 - 7.20723i) q^{75} +377.974 q^{76} -37.7257 q^{78} +(-299.939 - 519.509i) q^{79} +(-14.2513 + 24.6840i) q^{80} +(-360.018 + 623.570i) q^{81} +(345.544 + 598.499i) q^{82} -70.8820 q^{83} -521.659 q^{85} +(-257.662 - 446.284i) q^{86} +(19.0845 - 33.0554i) q^{87} +(763.740 - 1322.84i) q^{88} +(401.296 + 695.065i) q^{89} -222.651 q^{90} +531.165 q^{92} +(-12.2587 - 21.2326i) q^{93} +(123.954 - 214.694i) q^{94} +(179.732 - 311.305i) q^{95} +(-30.8057 - 53.3571i) q^{96} -145.648 q^{97} -1870.75 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 $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.828031	−	1.43419i	−0.292753	−	0.507063i	0.681707	−	0.731626i	$-0.261238\pi$
$2$	−0.828031	−	1.43419i	−0.292753	−	0.507063i	−0.974460	+	0.224562i	$0.927905\pi$
$3$	−0.166444	+	0.288289i	−0.0320321	+	0.0554813i	−0.881597	−	0.472003i	$-0.843531\pi$
$3$	−0.166444	+	0.288289i	−0.0320321	+	0.0554813i	0.849565	+	0.527484i	$0.176865\pi$
$4$	2.62873	−	4.55309i	0.328591	−	0.569137i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	0.551283			0.0375100
$7$		0			0
$7$		0			0
$8$	−21.9552			−0.970291
$9$	13.4446	+	23.2867i	0.497948	+	0.862471i
$10$	−4.14016	+	7.17096i	−0.130923	+	0.226766i
$11$	−34.7863	+	60.2517i	−0.953497	+	1.65151i	−0.215727	+	0.976454i	$0.569212\pi$
$11$	−34.7863	+	60.2517i	−0.953497	+	1.65151i	−0.737770	+	0.675052i	$0.764121\pi$
$12$	0.875071	+	1.51567i	0.0210509	+	0.0364613i
$13$	−68.4326			−1.45998			−0.729991	−	0.683456i	$-0.760476\pi$
$13$	−68.4326			−1.45998			−0.729991	+	0.683456i	$0.760476\pi$
$14$		0			0
$15$	1.66444			0.0286504
$16$	−2.85026	−	4.93680i	−0.0445354	−	0.0771375i
$17$	52.1659	−	90.3539i	0.744240	−	1.28906i	−0.206309	−	0.978487i	$-0.566145\pi$
$17$	52.1659	−	90.3539i	0.744240	−	1.28906i	0.950549	−	0.310574i	$-0.100521\pi$
$18$	22.2651	−	38.5643i	0.291552	−	0.504982i
$19$	35.9465	+	62.2611i	0.434036	+	0.751772i	0.997216	−	0.0745616i	$-0.0237557\pi$
$19$	35.9465	+	62.2611i	0.434036	+	0.751772i	−0.563180	+	0.826334i	$0.690422\pi$
$20$	−26.2873			−0.293901
$21$		0			0
$22$	115.217			1.11656
$23$	50.5154	+	87.4952i	0.457964	+	0.793218i	0.998853	−	0.0478764i	$-0.0152453\pi$
$23$	50.5154	+	87.4952i	0.457964	+	0.793218i	−0.540889	+	0.841094i	$0.681912\pi$
$24$	3.65430	−	6.32944i	0.0310805	−	0.0538330i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	56.6643	+	98.1454i	0.427415	+	0.740304i
$27$	−17.9390			−0.127866
$28$		0			0
$29$	−114.661			−0.734205			−0.367102	−	0.930181i	$-0.619650\pi$
$29$	−114.661			−0.734205			−0.367102	+	0.930181i	$0.619650\pi$
$30$	−1.37821	−	2.38712i	−0.00838750	−	0.0145276i
$31$	−36.8252	+	63.7832i	−0.213355	+	0.369542i	−0.952762	−	0.303716i	$-0.901772\pi$
$31$	−36.8252	+	63.7832i	−0.213355	+	0.369542i	0.739407	+	0.673258i	$0.235106\pi$
$32$	−92.5409	+	160.286i	−0.511221	+	0.885461i
$33$	−11.5799	−	20.0570i	−0.0610851	−	0.105802i
$34$	−172.780			−0.871514
$35$		0			0
$36$	141.369			0.654485
$37$	100.467	+	174.013i	0.446395	+	0.773178i	0.998148	−	0.0608289i	$-0.0193744\pi$
$37$	100.467	+	174.013i	0.446395	+	0.773178i	−0.551753	+	0.834007i	$0.686041\pi$
$38$	59.5296	−	103.108i	0.254131	−	0.440168i
$39$	11.3902	−	19.7284i	0.0467663	−	0.0810017i
$40$	54.8879	+	95.0687i	0.216964	+	0.375792i
$41$	−417.308			−1.58957			−0.794786	−	0.606889i	$-0.792417\pi$
$41$	−417.308			−1.58957			−0.794786	+	0.606889i	$0.792417\pi$
$42$		0			0
$43$	311.175			1.10357			0.551787	−	0.833985i	$-0.313946\pi$
$43$	311.175			1.10357			0.551787	+	0.833985i	$0.313946\pi$
$44$	182.888	+	316.771i	0.626621	+	1.08534i
$45$	67.2230	−	116.434i	0.222689	−	0.385709i
$46$	83.6566	−	144.897i	0.268141	−	0.464434i
$47$	74.8485	+	129.641i	0.232293	+	0.402344i	0.958483	−	0.285151i	$-0.0920438\pi$
$47$	74.8485	+	129.641i	0.232293	+	0.402344i	−0.726189	+	0.687495i	$0.758710\pi$
$48$	1.89763			0.00570625
$49$		0			0
$50$	41.4016			0.117101
$51$	17.3654	+	30.0777i	0.0476792	+	0.0825827i
$52$	−179.891	+	311.580i	−0.479737	+	0.830929i
$53$	−135.737	+	235.104i	−0.351791	+	0.609320i	−0.986563	−	0.163379i	$-0.947761\pi$
$53$	−135.737	+	235.104i	−0.351791	+	0.609320i	0.634772	+	0.772699i	$0.281094\pi$
$54$	14.8541	+	25.7280i	0.0374331	+	0.0648360i
$55$	347.863			0.852834
$56$		0			0
$57$	−23.9323			−0.0556124
$58$	94.9425	+	164.445i	0.214941	+	0.372288i
$59$	−259.014	+	448.625i	−0.571538	+	0.989933i	0.424870	+	0.905254i	$0.360320\pi$
$59$	−259.014	+	448.625i	−0.571538	+	0.989933i	−0.996408	+	0.0846788i	$0.973014\pi$
$60$	4.37536	−	7.57834i	0.00941427	−	0.0163060i
$61$	−109.963	−	190.461i	−0.230808	−	0.399771i	0.727238	−	0.686385i	$-0.240804\pi$
$61$	−109.963	−	190.461i	−0.230808	−	0.399771i	−0.958046	+	0.286614i	$0.907470\pi$
$62$	121.970			0.249842
$63$		0			0
$64$	260.903			0.509576
$65$	171.081	+	296.322i	0.326462	+	0.565449i
$66$	−19.1771	+	33.2157i	−0.0357657	+	0.0619480i
$67$	−40.3475	+	69.8839i	−0.0735706	+	0.127428i	−0.900464	−	0.434931i	$-0.856773\pi$
$67$	−40.3475	+	69.8839i	−0.0735706	+	0.127428i	0.826893	+	0.562359i	$0.190106\pi$
$68$	−274.260	−	475.032i	−0.489101	−	0.847148i
$69$	−33.6319			−0.0586783
$70$		0			0
$71$	−91.0463			−0.152186			−0.0760930	−	0.997101i	$-0.524245\pi$
$71$	−91.0463			−0.152186			−0.0760930	+	0.997101i	$0.524245\pi$
$72$	−295.178	−	511.264i	−0.483154	−	0.836848i
$73$	441.141	−	764.078i	0.707283	−	1.22505i	−0.258579	−	0.965990i	$-0.583254\pi$
$73$	441.141	−	764.078i	0.707283	−	1.22505i	0.965861	−	0.259059i	$-0.0834125\pi$
$74$	166.379	−	288.177i	0.261367	−	0.452701i
$75$	−4.16110	−	7.20723i	−0.00640643	−	0.0110963i
$76$	377.974			0.570481
$77$		0			0
$78$	−37.7257			−0.0547640
$79$	−299.939	−	519.509i	−0.427161	−	0.739865i	0.569458	−	0.822020i	$-0.307153\pi$
$79$	−299.939	−	519.509i	−0.427161	−	0.739865i	−0.996620	+	0.0821553i	$0.973820\pi$
$80$	−14.2513	+	24.6840i	−0.0199168	+	0.0344969i
$81$	−360.018	+	623.570i	−0.493852	+	0.855377i
$82$	345.544	+	598.499i	0.465353	+	0.806014i
$83$	−70.8820			−0.0937387			−0.0468694	−	0.998901i	$-0.514924\pi$
$83$	−70.8820			−0.0937387			−0.0468694	+	0.998901i	$0.514924\pi$
$84$		0			0
$85$	−521.659			−0.665668
$86$	−257.662	−	446.284i	−0.323075	−	0.559582i
$87$	19.0845	−	33.0554i	0.0235181	−	0.0407346i
$88$	763.740	−	1322.84i	0.925170	−	1.60244i
$89$	401.296	+	695.065i	0.477947	+	0.827828i	0.999680	−	0.0252802i	$-0.00804778\pi$
$89$	401.296	+	695.065i	0.477947	+	0.827828i	−0.521733	+	0.853109i	$0.674714\pi$
$90$	−222.651			−0.260772
$91$		0			0
$92$	531.165			0.601932
$93$	−12.2587	−	21.2326i	−0.0136684	−	0.0236744i
$94$	123.954	−	214.694i	0.136009	−	0.235575i
$95$	179.732	−	311.305i	0.194107	−	0.336203i
$96$	−30.8057	−	53.3571i	−0.0327510	−	0.0567264i
$97$	−145.648			−0.152457			−0.0762283	−	0.997090i	$-0.524288\pi$
$97$	−145.648			−0.152457			−0.0762283	+	0.997090i	$0.524288\pi$
$98$		0			0
$99$	−1870.75			−1.89917
$100$	65.7182	+	113.827i	0.0657182	+	0.113827i
$101$	−309.718	+	536.447i	−0.305129	+	0.528499i	−0.977290	−	0.211906i	$-0.932033\pi$
$101$	−309.718	+	536.447i	−0.305129	+	0.528499i	0.672161	+	0.740405i	$0.265366\pi$
$102$	28.7581	−	49.8105i	0.0279165	−	0.0483527i
$103$	−911.040	−	1577.97i	−0.871528	−	1.50953i	−0.860416	−	0.509593i	$-0.829796\pi$
$103$	−911.040	−	1577.97i	−0.871528	−	1.50953i	−0.0111125	−	0.999938i	$-0.503537\pi$
$104$	1502.45			1.41661
$105$		0			0
$106$	449.578			0.411952
$107$	−544.851	−	943.709i	−0.492268	−	0.852634i	0.507692	−	0.861539i	$-0.330499\pi$
$107$	−544.851	−	943.709i	−0.492268	−	0.852634i	−0.999960	+	0.00890504i	$0.997165\pi$
$108$	−47.1569	+	81.6781i	−0.0420155	+	0.0727730i
$109$	−294.833	+	510.666i	−0.259082	+	0.448743i	−0.965996	−	0.258556i	$-0.916753\pi$
$109$	−294.833	+	510.666i	−0.259082	+	0.448743i	0.706914	+	0.707299i	$0.250087\pi$
$110$	−288.042	−	498.903i	−0.249670	−	0.432441i
$111$	−66.8882			−0.0571959
$112$		0			0
$113$	−900.358			−0.749544			−0.374772	−	0.927117i	$-0.622279\pi$
$113$	−900.358			−0.749544			−0.374772	+	0.927117i	$0.622279\pi$
$114$	19.8167	+	34.3235i	0.0162807	+	0.0281990i
$115$	252.577	−	437.476i	0.204808	−	0.354738i
$116$	−301.412	+	522.060i	−0.241253	+	0.417863i
$117$	−920.048	−	1593.57i	−0.726995	−	1.25919i
$118$	857.887			0.669279
$119$		0			0
$120$	−36.5430			−0.0277992
$121$	−1754.68	−	3039.19i	−1.31831	−	2.28339i
$122$	−182.105	+	315.415i	−0.135140	+	0.234069i
$123$	69.4583	−	120.305i	0.0509174	−	0.0881915i
$124$	193.607	+	335.337i	0.140213	+	0.242856i
$125$	125.000			0.0894427
$126$		0			0
$127$	−1755.75			−1.22676			−0.613378	−	0.789790i	$-0.710190\pi$
$127$	−1755.75			−1.22676			−0.613378	+	0.789790i	$0.710190\pi$
$128$	524.292	+	908.100i	0.362041	+	0.627074i
$129$	−51.7931	+	89.7083i	−0.0353498	+	0.0612277i
$130$	283.321	−	490.727i	0.191146	−	0.331074i
$131$	904.549	+	1566.72i	0.603289	+	1.04493i	0.992319	+	0.123702i	$0.0394766\pi$
$131$	904.549	+	1566.72i	0.603289	+	1.04493i	−0.389031	+	0.921225i	$0.627190\pi$
$132$	−121.762			−0.0802881
$133$		0			0
$134$	133.636			0.0861521
$135$	44.8476	+	77.6783i	0.0285916	+	0.0495221i
$136$	−1145.31	+	1983.74i	−0.722129	+	1.25076i
$137$	9.25670	−	16.0331i	0.00577265	−	0.00999852i	−0.863125	−	0.504991i	$-0.831496\pi$
$137$	9.25670	−	16.0331i	0.00577265	−	0.00999852i	0.868897	+	0.494992i	$0.164829\pi$
$138$	27.8482	+	48.2346i	0.0171783	+	0.0297536i
$139$	625.608			0.381751			0.190875	−	0.981614i	$-0.438867\pi$
$139$	625.608			0.381751			0.190875	+	0.981614i	$0.438867\pi$
$140$		0			0
$141$	−49.8323			−0.0297634
$142$	75.3892	+	130.578i	0.0445530	+	0.0771680i
$143$	2380.52	−	4123.18i	1.39209	−	2.41117i
$144$	76.6413	−	132.747i	0.0443526	−	0.0768209i
$145$	286.651	+	496.495i	0.164173	+	0.284356i
$146$	−1461.11			−0.828237
$147$		0			0
$148$	1056.40			0.586725
$149$	514.317	+	890.823i	0.282782	+	0.489792i	0.972069	−	0.234696i	$-0.0754095\pi$
$149$	514.317	+	890.823i	0.282782	+	0.489792i	−0.689287	+	0.724488i	$0.742076\pi$
$150$	−6.89103	+	11.9356i	−0.00375100	+	0.00649693i
$151$	−35.5037	+	61.4942i	−0.0191341	+	0.0331412i	−0.875434	−	0.483338i	$-0.839424\pi$
$151$	−35.5037	+	61.4942i	−0.0191341	+	0.0331412i	0.856300	+	0.516479i	$0.172758\pi$
$152$	−789.211	−	1366.95i	−0.421141	−	0.729438i
$153$	2805.39			1.48237
$154$		0			0
$155$	368.252			0.190831
$156$	−59.8834	−	103.721i	−0.0307340	−	0.0532329i
$157$	−1030.66	+	1785.16i	−0.523922	+	0.907459i	0.475691	+	0.879613i	$0.342198\pi$
$157$	−1030.66	+	1785.16i	−0.523922	+	0.907459i	−0.999612	+	0.0278461i	$0.991135\pi$
$158$	−496.717	+	860.339i	−0.250106	+	0.433196i
$159$	−45.1852	−	78.2631i	−0.0225372	−	0.0390356i
$160$	925.409			0.457250
$161$		0			0
$162$	1192.42			0.578307
$163$	981.899	+	1700.70i	0.471830	+	0.817234i	0.999481	−	0.0322280i	$-0.0102603\pi$
$163$	981.899	+	1700.70i	0.471830	+	0.817234i	−0.527651	+	0.849462i	$0.676927\pi$
$164$	−1096.99	+	1900.04i	−0.522320	+	0.904684i
$165$	−57.8997	+	100.285i	−0.0273181	+	0.0473163i
$166$	58.6925	+	101.658i	0.0274423	+	0.0475315i
$167$	−2855.04			−1.32293			−0.661467	−	0.749974i	$-0.730066\pi$
$167$	−2855.04			−1.32293			−0.661467	+	0.749974i	$0.730066\pi$
$168$		0			0
$169$	2486.01			1.13155
$170$	431.950	+	748.158i	0.194877	+	0.337536i
$171$	−966.571	+	1674.15i	−0.432255	+	0.748687i
$172$	817.994	−	1416.81i	0.362625	−	0.628084i
$173$	−776.603	−	1345.12i	−0.341295	−	0.591140i	0.643378	−	0.765548i	$-0.277532\pi$
$173$	−776.603	−	1345.12i	−0.341295	−	0.591140i	−0.984673	+	0.174408i	$0.944199\pi$
$174$	−63.2104			−0.0275400
$175$		0			0
$176$	396.601			0.169857
$177$	−86.2226	−	149.342i	−0.0366152	−	0.0634193i
$178$	664.571	−	1151.07i	0.279841	−	0.484699i
$179$	−134.920	+	233.689i	−0.0563376	+	0.0975795i	−0.892819	−	0.450416i	$-0.851276\pi$
$179$	−134.920	+	233.689i	−0.0563376	+	0.0975795i	0.836481	+	0.547996i	$0.184609\pi$
$180$	−353.422	−	612.145i	−0.146347	−	0.253481i
$181$	−2229.61			−0.915613			−0.457806	−	0.889052i	$-0.651365\pi$
$181$	−2229.61			−0.915613			−0.457806	+	0.889052i	$0.651365\pi$
$182$		0			0
$183$	73.2105			0.0295731
$184$	−1109.07	−	1920.97i	−0.444359	−	0.769652i
$185$	502.333	−	870.066i	0.199634	−	0.345776i
$186$	−20.3011	+	35.1626i	−0.00800296	+	0.0138615i
$187$	3629.32	+	6286.16i	1.41926	+	2.45823i
$188$	787.026			0.305318
$189$		0			0
$190$	−595.296			−0.227302
$191$	232.960	+	403.498i	0.0882533	+	0.152859i	0.906773	−	0.421619i	$-0.138538\pi$
$191$	232.960	+	403.498i	0.0882533	+	0.152859i	−0.818520	+	0.574479i	$0.805205\pi$
$192$	−43.4257	+	75.2154i	−0.0163228	+	0.0282719i
$193$	2207.23	−	3823.04i	0.823212	−	1.42585i	−0.0800657	−	0.996790i	$-0.525513\pi$
$193$	2207.23	−	3823.04i	0.823212	−	1.42585i	0.903278	−	0.429056i	$-0.141154\pi$
$194$	120.601	+	208.887i	0.0446321	+	0.0773051i
$195$	−113.902			−0.0418291
$196$		0			0
$197$	−289.812			−0.104814			−0.0524068	−	0.998626i	$-0.516689\pi$
$197$	−289.812			−0.104814			−0.0524068	+	0.998626i	$0.516689\pi$
$198$	1549.04	+	2683.02i	0.555987	+	0.962998i
$199$	2408.87	−	4172.28i	0.858091	−	1.48626i	−0.0156567	−	0.999877i	$-0.504984\pi$
$199$	2408.87	−	4172.28i	0.858091	−	1.48626i	0.873748	−	0.486380i	$-0.161683\pi$
$200$	274.440	−	475.343i	0.0970291	−	0.168059i
$201$	−13.4312	−	23.2635i	−0.00471324	−	0.00816358i
$202$	1025.82			0.357310
$203$		0			0
$204$	182.595			0.0626678
$205$	1043.27	+	1806.99i	0.355439	+	0.615639i
$206$	−1508.74	+	2613.21i	−0.510285	+	0.883840i
$207$	−1358.32	+	2352.67i	−0.456085	+	0.789962i
$208$	195.051	+	337.838i	0.0650209	+	0.112619i
$209$	−5001.78			−1.65541
$210$		0			0
$211$	2022.01			0.659719			0.329859	−	0.944030i	$-0.392999\pi$
$211$	2022.01			0.659719			0.329859	+	0.944030i	$0.392999\pi$
$212$	713.632	+	1236.05i	0.231191	+	0.400434i
$213$	15.1541	−	26.2477i	0.00487484	−	0.00844347i
$214$	−902.306	+	1562.84i	−0.288226	+	0.499222i
$215$	−777.937	−	1347.43i	−0.246767	−	0.427412i
$216$	393.855			0.124067
$217$		0			0
$218$	976.525			0.303388
$219$	146.850	+	254.352i	0.0453115	+	0.0784819i
$220$	914.438	−	1583.85i	0.280234	−	0.485379i
$221$	−3569.84	+	6183.15i	−1.08658	+	1.88201i
$222$	55.3855	+	95.9305i	0.0167443	+	0.0290019i
$223$	−4343.86			−1.30442			−0.652211	−	0.758037i	$-0.726158\pi$
$223$	−4343.86			−1.30442			−0.652211	+	0.758037i	$0.726158\pi$
$224$		0			0
$225$	−672.230			−0.199179
$226$	745.524	+	1291.29i	0.219432	+	0.380067i
$227$	−1323.80	+	2292.88i	−0.387064	+	0.670414i	−0.992053	−	0.125819i	$-0.959844\pi$
$227$	−1323.80	+	2292.88i	−0.387064	+	0.670414i	0.604989	+	0.796234i	$0.293177\pi$
$228$	−62.9114	+	108.966i	−0.0182737	+	0.0316510i
$229$	−722.545	−	1251.49i	−0.208503	−	0.361137i	0.742740	−	0.669580i	$-0.233526\pi$
$229$	−722.545	−	1251.49i	−0.208503	−	0.361137i	−0.951243	+	0.308442i	$0.900192\pi$
$230$	−836.566			−0.239833
$231$		0			0
$232$	2517.39			0.712392
$233$	3122.96	+	5409.12i	0.878076	+	1.52087i	0.853450	+	0.521175i	$0.174506\pi$
$233$	3122.96	+	5409.12i	0.878076	+	1.52087i	0.0246255	+	0.999697i	$0.492161\pi$
$234$	−1523.66	+	2639.05i	−0.425660	+	0.737265i
$235$	374.243	−	648.207i	0.103885	−	0.179934i
$236$	1361.76	+	2358.63i	0.375605	+	0.650566i
$237$	199.692			0.0547315
$238$		0			0
$239$	1340.24			0.362731			0.181366	−	0.983416i	$-0.441948\pi$
$239$	1340.24			0.362731			0.181366	+	0.983416i	$0.441948\pi$
$240$	−4.74409	−	8.21700i	−0.00127596	−	0.00221002i
$241$	1684.96	−	2918.44i	0.450364	−	0.780054i	−0.548044	−	0.836449i	$-0.684627\pi$
$241$	1684.96	−	2918.44i	0.450364	−	0.780054i	0.998409	+	0.0563953i	$0.0179607\pi$
$242$	−2905.85	+	5033.08i	−0.771881	+	1.33694i
$243$	−362.023	−	627.042i	−0.0955710	−	0.165534i
$244$	−1156.25			−0.303366
$245$		0			0
$246$	−230.054			−0.0596249
$247$	−2459.91	−	4260.69i	−0.633685	−	1.09757i
$248$	808.504	−	1400.37i	0.207016	−	0.358563i
$249$	11.7979	−	20.4345i	0.00300265	−	0.00520074i
$250$	−103.504	−	179.274i	−0.0261846	−	0.0453531i
$251$	3592.64			0.903449			0.451724	−	0.892158i	$-0.350809\pi$
$251$	3592.64			0.903449			0.451724	+	0.892158i	$0.350809\pi$
$252$		0			0
$253$	−7028.97			−1.74667
$254$	1453.82	+	2518.09i	0.359137	+	0.622043i
$255$	86.8268	−	150.388i	0.0213228	−	0.0369321i
$256$	1911.87	−	3311.46i	0.466765	−	0.808461i
$257$	−1.42381	−	2.46612i	−0.000345584	−	0.000598569i	0.865853	−	0.500299i	$-0.166777\pi$
$257$	−1.42381	−	2.46612i	−0.000345584	−	0.000598569i	−0.866198	+	0.499701i	$0.833443\pi$
$258$	171.545			0.0413951
$259$		0			0
$260$	1798.91			0.429090
$261$	−1541.56	−	2670.07i	−0.365596	−	0.633230i
$262$	1497.99	−	2594.59i	0.353229	−	0.611811i
$263$	1408.54	−	2439.66i	0.330244	−	0.571999i	−0.652316	−	0.757947i	$-0.726202\pi$
$263$	1408.54	−	2439.66i	0.330244	−	0.571999i	0.982560	+	0.185948i	$0.0595357\pi$
$264$	254.239	+	440.356i	0.0592703	+	0.102659i
$265$	1357.37			0.314652
$266$		0			0
$267$	−267.173			−0.0612386
$268$	212.125	+	367.412i	0.0483493	+	0.0837434i
$269$	−723.716	+	1253.51i	−0.164036	+	0.284119i	−0.936313	−	0.351168i	$-0.885785\pi$
$269$	−723.716	+	1253.51i	−0.164036	+	0.284119i	0.772276	+	0.635287i	$0.219118\pi$
$270$	74.2704	−	128.640i	0.0167406	−	0.0289955i
$271$	4027.25	+	6975.40i	0.902724	+	1.56356i	0.823944	+	0.566671i	$0.191769\pi$
$271$	4027.25	+	6975.40i	0.902724	+	1.56356i	0.0787797	+	0.996892i	$0.474898\pi$
$272$	−594.746			−0.132580
$273$		0			0
$274$	−30.6593			−0.00675985
$275$	−869.658	−	1506.29i	−0.190699	−	0.330301i
$276$	−88.4091	+	153.129i	−0.0192812	+	0.0333960i
$277$	285.650	−	494.760i	0.0619604	−	0.107319i	−0.833381	−	0.552699i	$-0.813598\pi$
$277$	285.650	−	494.760i	0.0619604	−	0.107319i	0.895342	+	0.445380i	$0.146931\pi$
$278$	−518.023	−	897.242i	−0.111759	−	0.193572i
$279$	−1980.40			−0.424959
$280$		0			0
$281$	−1784.48			−0.378837			−0.189418	−	0.981896i	$-0.560660\pi$
$281$	−1784.48			−0.378837			−0.189418	+	0.981896i	$0.560660\pi$
$282$	41.2627	+	71.4691i	0.00871333	+	0.0150919i
$283$	1660.52	−	2876.11i	0.348791	−	0.604124i	−0.637244	−	0.770662i	$-0.719926\pi$
$283$	1660.52	−	2876.11i	0.348791	−	0.604124i	0.986035	+	0.166538i	$0.0532590\pi$
$284$	−239.336	+	414.542i	−0.0500070	+	0.0866146i
$285$	59.8307	+	103.630i	0.0124353	+	0.0215386i
$286$	−7884.57			−1.63015
$287$		0			0
$288$	−4976.70			−1.01825
$289$	−2986.05	−	5172.00i	−0.607786	−	1.05272i
$290$	474.713	−	822.226i	0.0961244	−	0.166492i
$291$	24.2422	−	41.9887i	0.00488351	−	0.00845848i
$292$	−2319.28	−	4017.11i	−0.464814	−	0.805081i
$293$	5049.54			1.00682			0.503408	−	0.864049i	$-0.332079\pi$
$293$	5049.54			1.00682			0.503408	+	0.864049i	$0.332079\pi$
$294$		0			0
$295$	2590.14			0.511199
$296$	−2205.76	−	3820.49i	−0.433133	−	0.750208i
$297$	624.033	−	1080.86i	0.121919	−	0.211171i
$298$	851.740	−	1475.26i	0.165570	−	0.286776i
$299$	−3456.90	−	5987.52i	−0.668620	−	1.15808i
$300$	−43.7536			−0.00842038
$301$		0			0
$302$	117.593			0.0224063
$303$	−103.101	−	178.576i	−0.0195479	−	0.0338579i
$304$	204.914	−	354.921i	0.0386599	−	0.0669609i
$305$	−549.814	+	952.305i	−0.103220	+	0.178783i
$306$	−2322.95	−	4023.47i	−0.433969	−	0.751656i
$307$	1535.73			0.285500			0.142750	−	0.989759i	$-0.454405\pi$
$307$	1535.73			0.285500			0.142750	+	0.989759i	$0.454405\pi$
$308$		0			0
$309$	606.548			0.111668
$310$	−304.924	−	528.145i	−0.0558663	−	0.0967632i
$311$	−4641.52	+	8039.35i	−0.846291	+	1.46582i	0.0382037	+	0.999270i	$0.487836\pi$
$311$	−4641.52	+	8039.35i	−0.846291	+	1.46582i	−0.884495	+	0.466550i	$0.845497\pi$
$312$	−250.073	+	433.140i	−0.0453770	+	0.0785952i
$313$	3012.72	+	5218.18i	0.544054	+	0.942329i	0.998666	+	0.0516393i	$0.0164446\pi$
$313$	3012.72	+	5218.18i	0.544054	+	0.942329i	−0.454612	+	0.890690i	$0.650222\pi$
$314$	3413.68			0.613519
$315$		0			0
$316$	−3153.83			−0.561445
$317$	3488.79	+	6042.76i	0.618139	+	1.07065i	0.989825	+	0.142289i	$0.0454464\pi$
$317$	3488.79	+	6042.76i	0.618139	+	1.07065i	−0.371686	+	0.928358i	$0.621220\pi$
$318$	−74.8295	+	129.609i	−0.0131957	+	0.0228556i
$319$	3988.62	−	6908.49i	0.700062	−	1.21254i
$320$	−652.257	−	1129.74i	−0.113945	−	0.197358i
$321$	362.748			0.0630736
$322$		0			0
$323$	7500.71			1.29211
$324$	1892.78	+	3278.39i	0.324551	+	0.562139i
$325$	855.407	−	1481.61i	0.145998	−	0.252876i
$326$	1626.09	−	2816.46i	0.276259	−	0.478495i
$327$	−98.1464	−	169.995i	−0.0165979	−	0.0287484i
$328$	9162.06			1.54235
$329$		0			0
$330$	191.771			0.0319898
$331$	−492.439	−	852.930i	−0.0817731	−	0.141635i	0.822239	−	0.569143i	$-0.192725\pi$
$331$	−492.439	−	852.930i	−0.0817731	−	0.141635i	−0.904012	+	0.427508i	$0.859392\pi$
$332$	−186.330	+	322.732i	−0.0308017	+	0.0533501i
$333$	−2701.46	+	4679.07i	−0.444563	+	0.770005i
$334$	2364.07	+	4094.68i	0.387293	+	0.670812i
$335$	403.475			0.0658035
$336$		0			0
$337$	51.9653			0.00839979			0.00419990	−	0.999991i	$-0.498663\pi$
$337$	51.9653			0.00839979			0.00419990	+	0.999991i	$0.498663\pi$
$338$	−2058.50	−	3565.42i	−0.331265	−	0.573767i
$339$	149.859	−	259.563i	0.0240095	−	0.0415857i
$340$	−1371.30	+	2375.16i	−0.218733	+	0.378856i
$341$	−2562.03	−	4437.56i	−0.406867	−	0.704714i
$342$	3201.40			0.506176
$343$		0			0
$344$	−6831.89			−1.07079
$345$	84.0797	+	145.630i	0.0131209	+	0.0227260i
$346$	−1286.10	+	2227.60i	−0.199830	+	0.346116i
$347$	5650.24	−	9786.50i	0.874123	−	1.51403i	0.0164299	−	0.999865i	$-0.494770\pi$
$347$	5650.24	−	9786.50i	0.874123	−	1.51403i	0.857694	−	0.514161i	$-0.171897\pi$
$348$	−100.336	−	173.787i	−0.0154557	−	0.0267701i
$349$	2016.91			0.309349			0.154674	−	0.987966i	$-0.450567\pi$
$349$	2016.91			0.309349			0.154674	+	0.987966i	$0.450567\pi$
$350$		0			0
$351$	1227.61			0.186682
$352$	−6438.31	−	11151.5i	−0.974896	−	1.68857i
$353$	−3794.71	+	6572.62i	−0.572158	+	0.991007i	0.424186	+	0.905575i	$0.360560\pi$
$353$	−3794.71	+	6572.62i	−0.572158	+	0.991007i	−0.996344	+	0.0854319i	$0.972773\pi$
$354$	−142.790	+	247.319i	−0.0214384	+	0.0371324i
$355$	227.616	+	394.242i	0.0340298	+	0.0589414i
$356$	4219.59			0.628196
$357$		0			0
$358$	446.873			0.0659720
$359$	−4367.12	−	7564.08i	−0.642027	−	1.11202i	−0.984980	−	0.172671i	$-0.944760\pi$
$359$	−4367.12	−	7564.08i	−0.642027	−	1.11202i	0.342952	−	0.939353i	$-0.388573\pi$
$360$	−1475.89	+	2556.32i	−0.216073	+	0.374250i
$361$	845.204	−	1463.94i	0.123226	−	0.213433i
$362$	1846.19	+	3197.69i	0.268049	+	0.464274i
$363$	1168.22			0.168914
$364$		0			0
$365$	−4411.41			−0.632613
$366$	−60.6206	−	104.998i	−0.00865762	−	0.0149954i
$367$	−945.271	+	1637.26i	−0.134449	+	0.232872i	−0.925387	−	0.379024i	$-0.876260\pi$
$367$	−945.271	+	1637.26i	−0.134449	+	0.232872i	0.790938	+	0.611896i	$0.209593\pi$
$368$	287.964	−	498.769i	0.0407912	−	0.0706525i
$369$	−5610.53	−	9717.72i	−0.791524	−	1.37096i
$370$	−1663.79			−0.233774
$371$		0			0
$372$	−128.899			−0.0179653
$373$	−1356.94	−	2350.29i	−0.188364	−	0.326256i	0.756341	−	0.654178i	$-0.226985\pi$
$373$	−1356.94	−	2350.29i	−0.188364	−	0.326256i	−0.944705	+	0.327922i	$0.893652\pi$
$374$	6010.37	−	10410.3i	0.830987	−	1.43931i
$375$	−20.8055	+	36.0361i	−0.00286504	+	0.00496240i
$376$	−1643.31	−	2846.30i	−0.225392	−	0.390390i
$377$	7846.52			1.07193
$378$		0			0
$379$	8941.19			1.21182			0.605908	−	0.795535i	$-0.292810\pi$
$379$	8941.19			1.21182			0.605908	+	0.795535i	$0.292810\pi$
$380$	−944.935	−	1636.68i	−0.127564	−	0.220947i
$381$	292.234	−	506.165i	0.0392956	−	0.0680620i
$382$	385.796	−	668.218i	0.0516729	−	0.0895001i
$383$	−4646.94	−	8048.74i	−0.619968	−	1.07382i	−0.989491	−	0.144594i	$-0.953812\pi$
$383$	−4646.94	−	8048.74i	−0.619968	−	1.07382i	0.369524	−	0.929221i	$-0.379521\pi$
$384$	−349.060			−0.0463878
$385$		0			0
$386$	−7310.62			−0.963992
$387$	4183.62	+	7246.24i	0.549522	+	0.951801i
$388$	−382.868	+	663.147i	−0.0500959	+	0.0867686i
$389$	−5227.38	+	9054.08i	−0.681333	+	1.18010i	0.293242	+	0.956038i	$0.405266\pi$
$389$	−5227.38	+	9054.08i	−0.681333	+	1.18010i	−0.974574	+	0.224065i	$0.928067\pi$
$390$	94.3142	+	163.357i	0.0122456	+	0.0212100i
$391$	10540.7			1.36334
$392$		0			0
$393$	−602.226			−0.0772985
$394$	239.974	+	415.646i	0.0306845	+	0.0531471i
$395$	−1499.69	+	2597.54i	−0.191032	+	0.330878i
$396$	−4917.70	+	8517.70i	−0.624050	+	1.08089i
$397$	−1813.01	−	3140.23i	−0.229200	−	0.396987i	0.728371	−	0.685183i	$-0.240278\pi$
$397$	−1813.01	−	3140.23i	−0.229200	−	0.396987i	−0.957571	+	0.288196i	$0.906944\pi$
$398$	−7978.47			−1.00484
$399$		0			0
$400$	142.513			0.0178141
$401$	4211.26	+	7294.12i	0.524440	+	0.908356i	0.999595	+	0.0284542i	$0.00905846\pi$
$401$	4211.26	+	7294.12i	0.524440	+	0.908356i	−0.475156	+	0.879902i	$0.657608\pi$
$402$	−22.2429	+	38.5258i	−0.00275963	+	0.00477983i
$403$	2520.04	−	4364.85i	0.311495	−	0.539525i
$404$	1628.33	+	2820.35i	0.200526	+	0.347320i
$405$	3600.18			0.441715
$406$		0			0
$407$	−13979.5			−1.70254
$408$	−381.260	−	660.361i	−0.0462627	−	0.0801293i
$409$	−7290.34	+	12627.2i	−0.881379	+	1.52659i	−0.0315714	+	0.999502i	$0.510051\pi$
$409$	−7290.34	+	12627.2i	−0.881379	+	1.52659i	−0.849808	+	0.527092i	$0.823282\pi$
$410$	1727.72	−	2992.50i	0.208112	−	0.360461i
$411$	3.08144	+	5.33721i	0.000369820	+	0.000640548i
$412$	−9579.51			−1.14551
$413$		0			0
$414$	4498.92			0.534081
$415$	177.205	+	306.928i	0.0209606	+	0.0363049i
$416$	6332.81	−	10968.8i	0.746374	−	1.29276i
$417$	−104.129	+	180.356i	−0.0122283	+	0.0211800i
$418$	4141.63	+	7173.51i	0.484626	+	0.839397i
$419$	2537.53			0.295863			0.147931	−	0.988998i	$-0.452739\pi$
$419$	2537.53			0.295863			0.147931	+	0.988998i	$0.452739\pi$
$420$		0			0
$421$	9649.52			1.11708			0.558538	−	0.829479i	$-0.311363\pi$
$421$	9649.52			1.11708			0.558538	+	0.829479i	$0.311363\pi$
$422$	−1674.28	−	2899.94i	−0.193135	−	0.334519i
$423$	−2012.62	+	3485.95i	−0.231340	+	0.400692i
$424$	2980.13	−	5161.74i	0.341340	−	0.591218i
$425$	1304.15	+	2258.85i	0.148848	+	0.257812i
$426$	−50.1922			−0.00570850
$427$		0			0
$428$	−5729.06			−0.647020
$429$	792.444	+	1372.55i	0.0891832	+	0.154470i
$430$	−1288.31	+	2231.42i	−0.144483	+	0.250253i
$431$	3631.28	−	6289.57i	0.405830	−	0.702918i	−0.588588	−	0.808433i	$-0.700316\pi$
$431$	3631.28	−	6289.57i	0.405830	−	0.702918i	0.994418	+	0.105515i	$0.0336492\pi$
$432$	51.1310	+	88.5615i	0.00569454	+	0.00986323i
$433$	−11345.0			−1.25914			−0.629570	−	0.776944i	$-0.716769\pi$
$433$	−11345.0			−1.25914			−0.629570	+	0.776944i	$0.716769\pi$
$434$		0			0
$435$	−190.845			−0.0210353
$436$	1550.07	+	2684.81i	0.170264	+	0.294906i
$437$	−3631.70	+	6290.28i	−0.397546	+	0.688570i
$438$	243.193	−	421.223i	0.0265302	−	0.0459516i
$439$	5852.94	+	10137.6i	0.636323	+	1.10214i	0.986233	+	0.165360i	$0.0528786\pi$
$439$	5852.94	+	10137.6i	0.636323	+	1.10214i	−0.349911	+	0.936783i	$0.613788\pi$
$440$	−7637.40			−0.827497
$441$		0			0
$442$	11823.8			1.27240
$443$	−7538.99	−	13057.9i	−0.808551	−	1.40045i	−0.913867	−	0.406013i	$-0.866919\pi$
$443$	−7538.99	−	13057.9i	−0.808551	−	1.40045i	0.105316	−	0.994439i	$-0.466415\pi$
$444$	−175.831	+	304.548i	−0.0187941	+	0.0325523i
$445$	2006.48	−	3475.32i	0.213744	−	0.370216i
$446$	3596.85	+	6229.92i	0.381874	+	0.661425i
$447$	−342.419			−0.0362324
$448$		0			0
$449$	1075.45			0.113037			0.0565185	−	0.998402i	$-0.482000\pi$
$449$	1075.45			0.113037			0.0565185	+	0.998402i	$0.482000\pi$
$450$	556.627	+	964.106i	0.0583103	+	0.100996i
$451$	14516.6	−	25143.5i	1.51565	−	2.62519i
$452$	−2366.80	+	4099.41i	−0.246294	+	0.426593i
$453$	−11.8187	−	20.4706i	−0.00122581	−	0.00212317i
$454$	4384.58			0.453257
$455$		0			0
$456$	525.437			0.0539602
$457$	5368.47	+	9298.47i	0.549511	+	0.951781i	0.998308	+	0.0581472i	$0.0185193\pi$
$457$	5368.47	+	9298.47i	0.549511	+	0.951781i	−0.448797	+	0.893634i	$0.648147\pi$
$458$	−1196.58	+	2072.54i	−0.122080	+	0.211448i
$459$	−935.805	+	1620.86i	−0.0951627	+	0.164827i
$460$	−1327.91	−	2300.01i	−0.134596	−	0.233127i
$461$	−452.568			−0.0457228			−0.0228614	−	0.999739i	$-0.507278\pi$
$461$	−452.568			−0.0457228			−0.0228614	+	0.999739i	$0.507278\pi$
$462$		0			0
$463$	7118.15			0.714489			0.357244	−	0.934011i	$-0.383716\pi$
$463$	7118.15			0.714489			0.357244	+	0.934011i	$0.383716\pi$
$464$	326.813	+	566.057i	0.0326981	+	0.0566347i
$465$	−61.2933	+	106.163i	−0.00611271	+	0.0105875i
$466$	5171.81	−	8957.83i	0.514119	−	0.890480i
$467$	486.900	+	843.335i	0.0482463	+	0.0835651i	0.889140	−	0.457635i	$-0.151303\pi$
$467$	486.900	+	843.335i	0.0482463	+	0.0835651i	−0.840894	+	0.541200i	$0.817970\pi$
$468$	−9674.23			−0.955537
$469$		0			0
$470$	−1239.54			−0.121650
$471$	−343.094	−	594.257i	−0.0335646	−	0.0581357i
$472$	5686.70	−	9849.65i	0.554558	−	0.960523i
$473$	−10824.6	+	18748.8i	−1.05225	+	1.82256i
$474$	−165.351	−	286.396i	−0.0160228	−	0.0277524i
$475$	−1797.32			−0.173614
$476$		0			0
$477$	−7299.72			−0.700695
$478$	−1109.76	−	1922.16i	−0.106191	−	0.183928i
$479$	4857.00	−	8412.57i	0.463303	−	0.802464i	−0.535820	−	0.844332i	$-0.679998\pi$
$479$	4857.00	−	8412.57i	0.463303	−	0.802464i	0.999123	+	0.0418680i	$0.0133309\pi$
$480$	−154.029	+	266.785i	−0.0146467	+	0.0253688i
$481$	−6875.19	−	11908.2i	−0.651729	−	1.12883i
$482$	−5580.80			−0.527383
$483$		0			0
$484$	−18450.3			−1.73274
$485$	364.119	+	630.673i	0.0340903	+	0.0590462i
$486$	−599.532	+	1038.42i	−0.0559575	+	0.0969212i
$487$	−461.694	+	799.678i	−0.0429597	+	0.0744084i	−0.886706	−	0.462334i	$-0.847012\pi$
$487$	−461.694	+	799.678i	−0.0429597	+	0.0744084i	0.843746	+	0.536743i	$0.180345\pi$
$488$	2414.25	+	4181.61i	0.223951	+	0.387894i
$489$	−653.724			−0.0604549
$490$		0			0
$491$	1289.11			0.118486			0.0592430	−	0.998244i	$-0.481131\pi$
$491$	1289.11			0.118486			0.0592430	+	0.998244i	$0.481131\pi$
$492$	−365.174	−	632.500i	−0.0334620	−	0.0579579i
$493$	−5981.37	+	10360.0i	−0.546424	+	0.946435i
$494$	−4073.76	+	7055.96i	−0.371027	+	0.642637i
$495$	4676.88	+	8100.59i	0.424667	+	0.735544i
$496$	419.846			0.0380074
$497$		0			0
$498$	−39.0760			−0.00351614
$499$	9669.15	+	16747.5i	0.867436	+	1.50244i	0.864608	+	0.502447i	$0.167567\pi$
$499$	9669.15	+	16747.5i	0.867436	+	1.50244i	0.00282829	+	0.999996i	$0.499100\pi$
$500$	328.591	−	569.137i	0.0293901	−	0.0509051i
$501$	475.205	−	823.078i	0.0423764	−	0.0733981i
$502$	−2974.82	−	5152.54i	−0.264488	−	0.458106i
$503$	1772.84			0.157151			0.0785757	−	0.996908i	$-0.474963\pi$
$503$	1772.84			0.157151			0.0785757	+	0.996908i	$0.474963\pi$
$504$		0			0
$505$	3097.18			0.272916
$506$	5820.21	+	10080.9i	0.511344	+	0.885673i
$507$	−413.782	+	716.691i	−0.0362459	+	0.0627798i
$508$	−4615.40	+	7994.11i	−0.403101	+	0.698192i
$509$	1575.88	+	2729.50i	0.137229	+	0.237687i	0.926447	−	0.376426i	$-0.122847\pi$
$509$	1575.88	+	2729.50i	0.137229	+	0.237687i	−0.789218	+	0.614113i	$0.789514\pi$
$510$	−287.581			−0.0249692
$511$		0			0
$512$	2056.31			0.177494
$513$	−644.845	−	1116.90i	−0.0554983	−	0.0961258i
$514$	−2.35792	+	4.08404i	−0.000202341	+	0.000350466i
$515$	−4555.20	+	7889.83i	−0.389759	+	0.675083i
$516$	272.300	+	471.637i	0.0232313	+	0.0402377i
$517$	−10414.8			−0.885964
$518$		0			0
$519$	517.043			0.0437296
$520$	−3756.12	−	6505.79i	−0.316763	−	0.548650i
$521$	−5514.69	+	9551.72i	−0.463729	+	0.803202i	−0.999143	−	0.0413875i	$-0.986822\pi$
$521$	−5514.69	+	9551.72i	−0.463729	+	0.803202i	0.535414	+	0.844590i	$0.320156\pi$
$522$	−2552.93	+	4421.80i	−0.214059	+	0.370760i
$523$	7224.21	+	12512.7i	0.604002	+	1.04616i	0.992208	+	0.124589i	$0.0397613\pi$
$523$	7224.21	+	12512.7i	0.604002	+	1.04616i	−0.388207	+	0.921572i	$0.626905\pi$
$524$	9511.26			0.792941
$525$		0			0
$526$	−4665.25			−0.386720
$527$	3842.04	+	6654.61i	0.317575	+	0.550056i
$528$	−66.0117	+	114.336i	−0.00544089	+	0.00942390i
$529$	979.894	−	1697.23i	0.0805371	−	0.139494i
$530$	−1123.95	−	1946.73i	−0.0921153	−	0.159548i
$531$	−13929.4			−1.13838
$532$		0			0
$533$	28557.4			2.32075
$534$	221.227	+	383.177i	0.0179278	+	0.0310519i
$535$	−2724.25	+	4718.54i	−0.220149	+	0.381309i
$536$	885.836	−	1534.31i	0.0713849	−	0.123642i
$537$	−44.9133	−	77.7922i	−0.00360922	−	0.00625136i
$538$	2397.04			0.192089
$539$		0			0
$540$	471.569			0.0375798
$541$	11137.4	+	19290.5i	0.885091	+	1.53302i	0.845609	+	0.533802i	$0.179237\pi$
$541$	11137.4	+	19290.5i	0.885091	+	1.53302i	0.0394817	+	0.999220i	$0.487429\pi$
$542$	6669.38	−	11551.7i	0.528551	−	0.915476i
$543$	371.105	−	642.773i	0.0293290	−	0.0507994i
$544$	9654.95	+	16722.9i	0.760942	+	1.31799i
$545$	2948.33			0.231730
$546$		0			0
$547$	18642.6			1.45722			0.728609	−	0.684930i	$-0.240167\pi$
$547$	18642.6			1.45722			0.728609	+	0.684930i	$0.240167\pi$
$548$	−48.6667	−	84.2932i	−0.00379368	−	0.00657085i
$549$	2956.81	−	5121.34i	0.229861	−	0.398130i
$550$	−1440.21	+	2494.51i	−0.111656	+	0.193393i
$551$	−4121.64	−	7138.89i	−0.318671	−	0.551955i
$552$	738.394			0.0569350
$553$		0			0
$554$	−946.108			−0.0725565
$555$	167.220	+	289.634i	0.0127894	+	0.0221519i
$556$	1644.55	−	2848.45i	0.125440	−	0.217268i
$557$	10715.9	−	18560.5i	0.815165	−	1.41191i	−0.0940446	−	0.995568i	$-0.529980\pi$
$557$	10715.9	−	18560.5i	0.815165	−	1.41191i	0.909209	−	0.416339i	$-0.136687\pi$
$558$	1639.83	+	2840.28i	0.124408	+	0.215481i
$559$	−21294.5			−1.61120
$560$		0			0
$561$	−2416.31			−0.181848
$562$	1477.60	+	2559.29i	0.110906	+	0.192094i
$563$	−3077.43	+	5330.26i	−0.230370	+	0.399012i	−0.957917	−	0.287046i	$-0.907327\pi$
$563$	−3077.43	+	5330.26i	−0.230370	+	0.399012i	0.727547	+	0.686057i	$0.240660\pi$
$564$	−130.996	+	226.891i	−0.00977998	+	0.0169394i
$565$	2250.89	+	3898.66i	0.167603	+	0.290297i
$566$	−5499.86			−0.408439
$567$		0			0
$568$	1998.94			0.147665
$569$	4194.99	+	7265.94i	0.309074	+	0.535333i	0.978160	−	0.207853i	$-0.0666475\pi$
$569$	4194.99	+	7265.94i	0.309074	+	0.535333i	−0.669086	+	0.743185i	$0.733314\pi$
$570$	99.0833	−	171.617i	0.00728095	−	0.0126110i
$571$	300.251	−	520.050i	0.0220055	−	0.0381146i	−0.854813	−	0.518936i	$-0.826328\pi$
$571$	300.251	−	520.050i	0.0220055	−	0.0381146i	0.876818	+	0.480822i	$0.159662\pi$
$572$	−12515.5	−	21677.4i	−0.914856	−	1.58458i
$573$	−155.099			−0.0113078
$574$		0			0
$575$	−2525.77			−0.183186
$576$	3507.73	+	6075.57i	0.253742	+	0.439494i
$577$	2031.17	−	3518.10i	0.146549	−	0.253831i	−0.783401	−	0.621517i	$-0.786517\pi$
$577$	2031.17	−	3518.10i	0.146549	−	0.253831i	0.929950	+	0.367686i	$0.119850\pi$
$578$	−4945.09	+	8565.15i	−0.355863	+	0.616372i
$579$	734.760	+	1272.64i	0.0527385	+	0.0913457i
$580$	3014.12			0.215783
$581$		0			0
$582$	−80.2931			−0.00571865
$583$	−9443.59	−	16356.8i	−0.670864	−	1.16197i
$584$	−9685.32	+	16775.5i	−0.686270	+	1.18865i
$585$	−4600.24	+	7967.85i	−0.325122	+	0.563128i
$586$	−4181.18	−	7242.01i	−0.294749	−	0.510520i
$587$	8387.50			0.589760			0.294880	−	0.955534i	$-0.404720\pi$
$587$	8387.50			0.589760			0.294880	+	0.955534i	$0.404720\pi$
$588$		0			0
$589$	−5294.95			−0.370415
$590$	−2144.72	−	3714.76i	−0.149655	−	0.259210i
$591$	48.2375	−	83.5497i	0.00335740	−	0.00581519i
$592$	572.713	−	991.967i	0.0397607	−	0.0688676i
$593$	−7671.31	−	13287.1i	−0.531236	−	0.920128i	−0.999335	−	0.0364520i	$-0.988394\pi$
$593$	−7671.31	−	13287.1i	−0.531236	−	0.920128i	0.468099	−	0.883676i	$-0.344939\pi$
$594$	−2066.88			−0.142769
$595$		0			0
$596$	5408.00			0.371678
$597$	801.882	+	1388.90i	0.0549730	+	0.0952159i
$598$	−5724.83	+	9915.70i	−0.391481	+	0.678066i
$599$	9854.23	−	17068.0i	0.672175	−	1.16424i	−0.305111	−	0.952317i	$-0.598694\pi$
$599$	9854.23	−	17068.0i	0.672175	−	1.16424i	0.977286	−	0.211925i	$-0.0679731\pi$
$600$	91.3576	+	158.236i	0.00621610	+	0.0107666i
$601$	19002.5			1.28973			0.644866	−	0.764295i	$-0.276913\pi$
$601$	19002.5			1.28973			0.644866	+	0.764295i	$0.276913\pi$
$602$		0			0
$603$	−2169.82			−0.146537
$604$	186.659	+	323.303i	0.0125746	+	0.0217798i
$605$	−8773.38	+	15195.9i	−0.589568	+	1.02116i
$606$	−170.742	+	295.734i	−0.0114454	+	0.0198240i
$607$	14726.6	+	25507.1i	0.984732	+	1.70561i	0.643121	+	0.765765i	$0.277639\pi$
$607$	14726.6	+	25507.1i	0.984732	+	1.70561i	0.341612	+	0.939841i	$0.389027\pi$
$608$	−13306.1			−0.887553
$609$		0			0
$610$	1821.05			0.120873
$611$	−5122.08	−	8871.70i	−0.339144	−	0.587415i
$612$	7374.62	−	12773.2i	0.487094	−	0.843671i
$613$	−4993.63	+	8649.23i	−0.329023	+	0.569884i	−0.982318	−	0.187219i	$-0.940053\pi$
$613$	−4993.63	+	8649.23i	−0.329023	+	0.569884i	0.653295	+	0.757103i	$0.273386\pi$
$614$	−1271.63	−	2202.53i	−0.0835811	−	0.144767i
$615$	−694.583			−0.0455419
$616$		0			0
$617$	−21076.1			−1.37519			−0.687593	−	0.726096i	$-0.741333\pi$
$617$	−21076.1			−1.37519			−0.687593	+	0.726096i	$0.741333\pi$
$618$	−502.240	−	869.906i	−0.0326910	−	0.0566226i
$619$	−157.334	+	272.511i	−0.0102161	+	0.0176949i	−0.871088	−	0.491126i	$-0.836585\pi$
$619$	−157.334	+	272.511i	−0.0102161	+	0.0176949i	0.860872	+	0.508821i	$0.169919\pi$
$620$	968.036	−	1676.69i	0.0627052	−	0.108609i
$621$	−906.197	−	1569.58i	−0.0585579	−	0.101425i
$622$	15373.3			0.991018
$623$		0			0
$624$	−129.860			−0.00833103
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	4989.25	−	8641.63i	0.318547	−	0.551740i
$627$	832.515	−	1441.96i	0.0530262	−	0.0918442i
$628$	5418.66	+	9385.39i	0.344312	+	0.596366i
$629$	20963.7			1.32890
$630$		0			0
$631$	3314.96			0.209138			0.104569	−	0.994518i	$-0.466654\pi$
$631$	3314.96			0.209138			0.104569	+	0.994518i	$0.466654\pi$
$632$	6585.21	+	11405.9i	0.414471	+	0.717884i
$633$	−336.550	+	582.922i	−0.0211322	+	0.0366020i
$634$	5777.65	−	10007.2i	0.361924	−	0.626871i
$635$	4389.39	+	7602.64i	0.274311	+	0.475121i
$636$	−475.119			−0.0296221
$637$		0			0
$638$	−13210.8			−0.819782
$639$	−1224.08	−	2120.17i	−0.0757807	−	0.131256i
$640$	2621.46	−	4540.50i	0.161910	−	0.280436i
$641$	−1502.56	+	2602.51i	−0.0925858	+	0.160363i	−0.908598	−	0.417671i	$-0.862847\pi$
$641$	−1502.56	+	2602.51i	−0.0925858	+	0.160363i	0.816013	+	0.578034i	$0.196180\pi$
$642$	−300.367	−	520.250i	−0.0184650	−	0.0319823i
$643$	−21225.7			−1.30180			−0.650902	−	0.759162i	$-0.725609\pi$
$643$	−21225.7			−1.30180			−0.650902	+	0.759162i	$0.725609\pi$
$644$		0			0
$645$	517.931			0.0316178
$646$	−6210.82	−	10757.5i	−0.378269	−	0.655180i
$647$	−1370.18	+	2373.21i	−0.0832568	+	0.144205i	−0.904647	−	0.426162i	$-0.859866\pi$
$647$	−1370.18	+	2373.21i	−0.0832568	+	0.144205i	0.821390	+	0.570367i	$0.193199\pi$
$648$	7904.26	−	13690.6i	0.479180	−	0.829964i
$649$	−18020.3	−	31212.1i	−1.08992	−	1.88780i
$650$	−2833.21			−0.170966
$651$		0			0
$652$	10324.6			0.620157
$653$	−11395.3	−	19737.3i	−0.682900	−	1.18282i	−0.974092	−	0.226153i	$-0.927385\pi$
$653$	−11395.3	−	19737.3i	−0.682900	−	1.18282i	0.291191	−	0.956665i	$-0.405948\pi$
$654$	−162.536	+	281.521i	−0.00971817	+	0.0168324i
$655$	4522.74	−	7833.62i	0.269799	−	0.467305i
$656$	1189.44	+	2060.16i	0.0707922	+	0.122616i
$657$	23723.8			1.40876
$658$		0			0
$659$	19405.1			1.14706			0.573532	−	0.819183i	$-0.305573\pi$
$659$	19405.1			1.14706			0.573532	+	0.819183i	$0.305573\pi$
$660$	304.405	+	527.245i	0.0179530	+	0.0310954i
$661$	7818.63	−	13542.3i	0.460075	−	0.796873i	−0.538889	−	0.842377i	$-0.681156\pi$
$661$	7818.63	−	13542.3i	0.460075	−	0.796873i	0.998964	+	0.0455035i	$0.0144892\pi$
$662$	−815.510	+	1412.50i	−0.0478787	+	0.0829283i
$663$	−1188.36	−	2058.29i	−0.0696108	−	0.120569i
$664$	1556.23			0.0909538
$665$		0			0
$666$	8947.59			0.520589
$667$	−5792.12	−	10032.3i	−0.336240	−	0.582384i
$668$	−7505.14	+	12999.3i	−0.434704	+	0.752930i
$669$	723.008	−	1252.29i	0.0417834	−	0.0723710i
$670$	−334.090	−	578.660i	−0.0192642	−	0.0333666i
$671$	15300.8			0.880299
$672$		0			0
$673$	−2579.54			−0.147747			−0.0738735	−	0.997268i	$-0.523536\pi$
$673$	−2579.54			−0.147747			−0.0738735	+	0.997268i	$0.523536\pi$
$674$	−43.0289	−	74.5282i	−0.00245907	−	0.00425923i
$675$	224.238	−	388.392i	0.0127866	−	0.0221470i
$676$	6535.06	−	11319.1i	0.371817	−	0.644006i
$677$	4079.78	+	7066.39i	0.231608	+	0.401157i	0.958282	−	0.285826i	$-0.0922680\pi$
$677$	4079.78	+	7066.39i	0.231608	+	0.401157i	−0.726673	+	0.686983i	$0.758935\pi$
$678$	−496.351			−0.0281154
$679$		0			0
$680$	11453.1			0.645892
$681$	−440.676	−	763.272i	−0.0247969	−	0.0429496i
$682$	−4242.88	+	7348.88i	−0.238223	+	0.412615i
$683$	10264.6	−	17778.9i	0.575059	−	0.996032i	−0.420976	−	0.907072i	$-0.638312\pi$
$683$	10264.6	−	17778.9i	0.575059	−	0.996032i	0.996035	−	0.0889598i	$-0.0283543\pi$
$684$	5081.71	+	8801.77i	0.284070	+	0.492024i
$685$	−92.5670			−0.00516321
$686$		0			0
$687$	481.053			0.0267151
$688$	−886.930	−	1536.21i	−0.0491481	−	0.0851270i
$689$	9288.84	−	16088.7i	0.513609	−	0.889597i
$690$	139.241	−	241.173i	0.00768235	−	0.0133062i
$691$	−458.647	−	794.401i	−0.0252500	−	0.0437343i	0.853124	−	0.521708i	$-0.174705\pi$
$691$	−458.647	−	794.401i	−0.0252500	−	0.0437343i	−0.878374	+	0.477973i	$0.841372\pi$
$692$	−8165.92			−0.448586
$693$		0			0
$694$	−18714.3			−1.02361
$695$	−1564.02	−	2708.96i	−0.0853621	−	0.147851i
$696$	−419.005	+	725.737i	−0.0228194	+	0.0395244i
$697$	−21769.2	+	37705.4i	−1.18302	+	2.04906i
$698$	−1670.06	−	2892.63i	−0.0905628	−	0.156859i
$699$	−2079.19			−0.112507
$700$		0			0
$701$	−10491.3			−0.565266			−0.282633	−	0.959228i	$-0.591208\pi$
$701$	−10491.3			−0.565266			−0.282633	+	0.959228i	$0.591208\pi$
$702$	−1016.50	−	1760.63i	−0.0546516	−	0.0946594i
$703$	−7222.84	+	12510.3i	−0.387503	+	0.671175i
$704$	−9075.85	+	15719.8i	−0.485879	+	0.841567i
$705$	124.581	+	215.780i	0.00665530	+	0.0115273i
$706$	12568.5			0.670005
$707$		0			0
$708$	−906.623			−0.0481257
$709$	−11918.8	−	20643.9i	−0.631339	−	1.09351i	−0.987278	−	0.159002i	$-0.949172\pi$
$709$	−11918.8	−	20643.9i	−0.631339	−	1.09351i	0.355939	−	0.934509i	$-0.384161\pi$
$710$	376.946	−	652.889i	0.0199247	−	0.0345106i
$711$	8065.11	−	13969.2i	0.425408	−	0.736828i
$712$	−8810.52	−	15260.3i	−0.463748	−	0.803234i
$713$	−7440.96			−0.390836
$714$		0			0
$715$	−23805.2			−1.24512
$716$	709.338	+	1228.61i	0.0370240	+	0.0641275i
$717$	−223.074	+	386.376i	−0.0116190	+	0.0201248i
$718$	−7232.22	+	12526.6i	−0.375911	+	0.651097i
$719$	−1963.10	−	3400.18i	−0.101824	−	0.176364i	0.810612	−	0.585583i	$-0.199134\pi$
$719$	−1963.10	−	3400.18i	−0.101824	−	0.176364i	−0.912436	+	0.409219i	$0.865801\pi$
$720$	−766.413			−0.0396702
$721$		0			0
$722$	−2799.42			−0.144299
$723$	560.902	+	971.512i	0.0288523	+	0.0499736i
$724$	−5861.05	+	10151.6i	−0.300862	+	0.521109i
$725$	1433.26	−	2482.47i	0.0734205	−	0.127168i
$726$	−967.322	−	1675.45i	−0.0494500	−	0.0856499i
$727$	21071.2			1.07495			0.537474	−	0.843281i	$-0.319379\pi$
$727$	21071.2			1.07495			0.537474	+	0.843281i	$0.319379\pi$
$728$		0			0
$729$	−19200.0			−0.975459
$730$	3652.78	+	6326.81i	0.185199	+	0.320775i
$731$	16232.7	−	28115.8i	0.821324	−	1.42257i
$732$	192.451	−	333.334i	0.00971745	−	0.0168311i
$733$	−11420.3	−	19780.6i	−0.575470	−	0.996744i	−0.995990	−	0.0894605i	$-0.971486\pi$
$733$	−11420.3	−	19780.6i	−0.575470	−	0.996744i	0.420520	−	0.907283i	$-0.361848\pi$
$734$	3130.86			0.157441
$735$		0			0
$736$	−18699.0			−0.936485
$737$	−2807.08	−	4862.01i	−0.140299	−	0.243004i
$738$	−9291.39	+	16093.2i	−0.463443	+	0.802706i
$739$	−5418.67	+	9385.42i	−0.269728	+	0.467183i	−0.968792	−	0.247877i	$-0.920267\pi$
$739$	−5418.67	+	9385.42i	−0.269728	+	0.467183i	0.699063	+	0.715060i	$0.253600\pi$
$740$	−2640.99	−	4574.34i	−0.131196	−	0.227238i
$741$	1637.75			0.0811931
$742$		0			0
$743$	−21631.9			−1.06810			−0.534050	−	0.845453i	$-0.679331\pi$
$743$	−21631.9			−1.06810			−0.534050	+	0.845453i	$0.679331\pi$
$744$	269.141	+	466.166i	0.0132624	+	0.0229711i
$745$	2571.58	−	4454.11i	0.126464	−	0.219042i
$746$	−2247.18	+	3892.23i	−0.110288	+	0.191025i
$747$	−952.980	−	1650.61i	−0.0466770	−	0.0808469i
$748$	38161.9			1.86543
$749$		0			0
$750$	68.9103			0.00335500
$751$	8089.58	+	14011.6i	0.393067	+	0.680812i	0.992852	−	0.119349i	$-0.0380808\pi$
$751$	8089.58	+	14011.6i	0.393067	+	0.680812i	−0.599786	+	0.800161i	$0.704747\pi$
$752$	426.676	−	739.025i	0.0206905	−	0.0358370i
$753$	−597.973	+	1035.72i	−0.0289394	+	0.0501245i
$754$	−6497.16	−	11253.4i	−0.313810	−	0.543535i
$755$	355.037			0.0171140
$756$		0			0
$757$	−40930.9			−1.96520			−0.982601	−	0.185727i	$-0.940536\pi$
$757$	−40930.9			−1.96520			−0.982601	+	0.185727i	$0.940536\pi$
$758$	−7403.59	−	12823.4i	−0.354763	−	0.614467i
$759$	1169.93	−	2026.38i	0.0559496	−	0.0969075i
$760$	−3946.05	+	6834.77i	−0.188340	+	0.326215i
$761$	1591.99	+	2757.40i	0.0758337	+	0.131348i	0.901449	−	0.432886i	$-0.142505\pi$
$761$	1591.99	+	2757.40i	0.0758337	+	0.131348i	−0.825615	+	0.564234i	$0.809172\pi$
$762$	−967.917			−0.0460157
$763$		0			0
$764$	2449.55			0.115997
$765$	−7013.49	−	12147.7i	−0.331468	−	0.574120i
$766$	−7695.62	+	13329.2i	−0.362995	+	0.628726i
$767$	17725.0	−	30700.6i	0.834436	−	1.44529i
$768$	636.438	+	1102.34i	0.0299030	+	0.0517935i
$769$	−33595.8			−1.57542			−0.787708	−	0.616048i	$-0.788733\pi$
$769$	−33595.8			−1.57542			−0.787708	+	0.616048i	$0.788733\pi$
$770$		0			0
$771$	0.947940			4.42791e−5
$772$	−11604.4	−	20099.5i	−0.541000	−	0.937040i
$773$	17193.0	−	29779.1i	0.799986	−	1.38562i	−0.119638	−	0.992818i	$-0.538174\pi$
$773$	17193.0	−	29779.1i	0.799986	−	1.38562i	0.919624	−	0.392799i	$-0.128493\pi$
$774$	6928.33	−	12000.2i	0.321749	−	0.557285i
$775$	−920.631	−	1594.58i	−0.0426710	−	0.0739084i
$776$	3197.72			0.147927
$777$		0			0
$778$	17313.7			0.797849
$779$	−15000.7	−	25982.0i	−0.689932	−	1.19500i
$780$	−299.417	+	518.605i	−0.0137447	+	0.0238065i
$781$	3167.17	−	5485.69i	0.145109	−	0.251336i
$782$	−8728.04	−	15117.4i	−0.399123	−	0.691301i
$783$	2056.90			0.0938795
$784$		0			0
$785$	10306.6			0.468610
$786$	498.662	+	863.708i	0.0226294	+	0.0391952i
$787$	−4106.22	+	7112.18i	−0.185986	+	0.322137i	−0.943908	−	0.330208i	$-0.892881\pi$
$787$	−4106.22	+	7112.18i	−0.185986	+	0.322137i	0.757922	+	0.652345i	$0.226215\pi$
$788$	−761.838	+	1319.54i	−0.0344408	+	0.0596532i
$789$	468.885	+	812.132i	0.0211568	+	0.0366447i
$790$	4967.17			0.223701
$791$		0			0
$792$	41072.7			1.84274
$793$	7525.03	+	13033.7i	0.336976	+	0.583659i
$794$	−3002.46	+	5200.42i	−0.134198	+	0.232438i
$795$	−225.926	+	391.316i	−0.0100790	+	0.0174573i
$796$	−12664.5	−	21935.6i	−0.563922	−	0.976742i
$797$	−36798.3			−1.63546			−0.817732	−	0.575600i	$-0.804769\pi$
$797$	−36798.3			−1.63546			−0.817732	+	0.575600i	$0.804769\pi$
$798$		0			0
$799$	15618.2			0.691528
$800$	−2313.52	−	4007.14i	−0.102244	−	0.177092i
$801$	−10790.5	+	18689.7i	−0.475985	+	0.824431i
$802$	6974.11	−	12079.5i	0.307063	−	0.531848i
$803$	30691.3	+	53158.9i	1.34878	+	2.33616i
$804$	−141.228			−0.00619492
$805$		0			0
$806$	−8346.70			−0.364764
$807$	−240.916	−	417.279i	−0.0105089	−	0.0182019i
$808$	6799.91	−	11777.8i	0.296064	−	0.512798i
$809$	−5093.08	+	8821.48i	−0.221339	+	0.383370i	−0.955215	−	0.295913i	$-0.904376\pi$
$809$	−5093.08	+	8821.48i	−0.221339	+	0.383370i	0.733876	+	0.679284i	$0.237709\pi$
$810$	−2981.06	−	5163.35i	−0.129313	−	0.223977i
$811$	−21196.9			−0.917786			−0.458893	−	0.888492i	$-0.651754\pi$
$811$	−21196.9			−0.917786			−0.458893	+	0.888492i	$0.651754\pi$
$812$		0			0
$813$	−2681.24			−0.115665
$814$	11575.4	+	20049.2i	0.498425	+	0.863298i
$815$	4909.50	−	8503.50i	0.211009	−	0.365478i
$816$	98.9917	−	171.459i	0.00424682	−	0.00735571i
$817$	11185.6	+	19374.1i	0.478991	+	0.829636i
$818$	24146.5			1.03211
$819$		0			0
$820$	10969.9			0.467177
$821$	−3781.97	−	6550.56i	−0.160769	−	0.278461i	0.774376	−	0.632726i	$-0.218064\pi$
$821$	−3781.97	−	6550.56i	−0.160769	−	0.278461i	−0.935145	+	0.354266i	$0.884731\pi$
$822$	5.10306	−	8.83875i	0.000216532	−	0.000375045i
$823$	−4199.90	+	7274.44i	−0.177885	+	0.308106i	−0.941156	−	0.337973i	$-0.890259\pi$
$823$	−4199.90	+	7274.44i	−0.177885	+	0.308106i	0.763271	+	0.646079i	$0.223592\pi$
$824$	20002.0	+	34644.5i	0.845636	+	1.46468i
$825$	578.997			0.0244340
$826$		0			0
$827$	5479.54			0.230402			0.115201	−	0.993342i	$-0.463249\pi$
$827$	5479.54			0.230402			0.115201	+	0.993342i	$0.463249\pi$
$828$	7141.30	+	12369.1i	0.299731	+	0.519149i
$829$	4626.28	−	8012.95i	0.193821	−	0.335707i	−0.752693	−	0.658372i	$-0.771245\pi$
$829$	4626.28	−	8012.95i	0.193821	−	0.335707i	0.946513	+	0.322665i	$0.104579\pi$
$830$	293.463	−	508.292i	0.0122726	−	0.0212567i
$831$	95.0893	+	164.700i	0.00396945	+	0.00687529i
$832$	−17854.2			−0.743972
$833$		0			0
$834$	344.887			0.0143195
$835$	7137.61	+	12362.7i	0.295817	+	0.512370i
$836$	−13148.3	+	22773.6i	−0.543952	+	0.942153i
$837$	660.609	−	1144.21i	0.0272808	−	0.0472517i
$838$	−2101.15	−	3639.31i	−0.0866148	−	0.150021i
$839$	34517.6			1.42036			0.710178	−	0.704022i	$-0.248614\pi$
$839$	34517.6			1.42036			0.710178	+	0.704022i	$0.248614\pi$
$840$		0			0
$841$	−11241.9			−0.460943
$842$	−7990.10	−	13839.3i	−0.327027	−	0.566428i
$843$	297.016	−	514.446i	0.0121349	−	0.0210183i
$844$	5315.31	−	9206.38i	0.216778	−	0.375470i
$845$	−6215.04	−	10764.8i	−0.253022	−	0.438247i
$846$	6666.04			0.270902
$847$		0			0
$848$	1547.55			0.0626686
$849$	552.768	+	957.422i	0.0223450	+	0.0387027i
$850$	2159.75	−	3740.79i	0.0871514	−	0.150951i
$851$	−10150.2	+	17580.7i	−0.408866	+	0.708177i
$852$	−79.6720	−	137.996i	−0.00320366	−	0.00554890i
$853$	1498.57			0.0601525			0.0300763	−	0.999548i	$-0.490425\pi$
$853$	1498.57			0.0601525			0.0300763	+	0.999548i	$0.490425\pi$
$854$		0			0
$855$	9665.71			0.386620
$856$	11962.3	+	20719.3i	0.477643	+	0.827302i
$857$	−4678.51	+	8103.41i	−0.186482	+	0.322996i	−0.944075	−	0.329731i	$-0.893042\pi$
$857$	−4678.51	+	8103.41i	−0.186482	+	0.322996i	0.757593	+	0.652727i	$0.226375\pi$
$858$	1312.34	−	2273.03i	0.0522173	−	0.0904430i
$859$	−14980.5	−	25946.9i	−0.595025	−	1.03061i	−0.993543	−	0.113454i	$-0.963809\pi$
$859$	−14980.5	−	25946.9i	−0.595025	−	1.03061i	0.398518	−	0.917161i	$-0.369525\pi$
$860$	−8179.94			−0.324341
$861$		0			0
$862$	−12027.3			−0.475232
$863$	16970.5	+	29393.8i	0.669389	+	1.15942i	0.978075	+	0.208252i	$0.0667773\pi$
$863$	16970.5	+	29393.8i	0.669389	+	1.15942i	−0.308687	+	0.951164i	$0.599889\pi$
$864$	1660.10	−	2875.37i	0.0653676	−	0.113220i
$865$	−3883.02	+	6725.58i	−0.152632	+	0.264366i
$866$	9394.05	+	16271.0i	0.368617	+	0.638464i
$867$	1988.04			0.0778747
$868$		0			0
$869$	41735.0			1.62919
$870$	158.026	+	273.709i	0.00615814	+	0.0106662i
$871$	2761.08	−	4782.33i	0.107412	−	0.186043i
$872$	6473.12	−	11211.8i	0.251385	−	0.435411i
$873$	−1958.17	−	3391.66i	−0.0759154	−	0.131489i
$874$	12028.6			0.465532
$875$		0			0
$876$	1544.12			0.0595559
$877$	19718.3	+	34153.1i	0.759224	+	1.31501i	0.943247	+	0.332092i	$0.107755\pi$
$877$	19718.3	+	34153.1i	0.759224	+	1.31501i	−0.184023	+	0.982922i	$0.558912\pi$
$878$	9692.84	−	16788.5i	0.372571	−	0.645312i
$879$	−840.465	+	1455.73i	−0.0322505	+	0.0558595i
$880$	−991.502	−	1717.33i	−0.0379813	−	0.0657855i
$881$	−32411.4			−1.23946			−0.619732	−	0.784813i	$-0.712759\pi$
$881$	−32411.4			−1.23946			−0.619732	+	0.784813i	$0.712759\pi$
$882$		0			0
$883$	−17121.4			−0.652526			−0.326263	−	0.945279i	$-0.605790\pi$
$883$	−17121.4			−0.652526			−0.326263	+	0.945279i	$0.605790\pi$
$884$	18768.3	+	32507.6i	0.714079	+	1.23682i
$885$	−431.113	+	746.709i	−0.0163748	+	0.0283620i
$886$	−12485.0	+	21624.7i	−0.473412	+	0.819974i
$887$	−343.899	−	595.650i	−0.0130180	−	0.0225479i	0.859443	−	0.511232i	$-0.170811\pi$
$887$	−343.899	−	595.650i	−0.0130180	−	0.0225479i	−0.872461	+	0.488684i	$0.837477\pi$
$888$	1468.54			0.0554967
$889$		0			0
$890$	−6645.71			−0.250297
$891$	−25047.4	−	43383.4i	−0.941773	−	1.63120i
$892$	−11418.8	+	19778.0i	−0.428621	+	0.742394i
$893$	−5381.08	+	9320.30i	−0.201647	+	0.349263i
$894$	283.534	+	491.095i	0.0106071	+	0.0183721i
$895$	1349.20			0.0503898
$896$		0			0
$897$	2301.52			0.0856693
$898$	−890.506	−	1542.40i	−0.0330919	−	0.0573169i
$899$	4222.40	−	7313.42i	0.156646	−	0.271319i
$900$	−1767.11	+	3060.72i	−0.0654485	+	0.113360i
$901$	14161.7	+	24528.8i	0.523634	+	0.906961i
$902$	−48080.8			−1.77485
$903$		0			0
$904$	19767.5			0.727276
$905$	5574.03	+	9654.51i	0.204737	+	0.354615i
$906$	−19.5726	+	33.9007i	−0.000717720	+	0.00124313i
$907$	−9552.10	+	16544.7i	−0.349694	+	0.605688i	−0.986195	−	0.165588i	$-0.947048\pi$
$907$	−9552.10	+	16544.7i	−0.349694	+	0.605688i	0.636501	+	0.771276i	$0.280381\pi$
$908$	6959.81	+	12054.7i	0.254371	+	0.440584i
$909$	−16656.1			−0.607754
$910$		0			0
$911$	23135.3			0.841390			0.420695	−	0.907202i	$-0.361786\pi$
$911$	23135.3			0.841390			0.420695	+	0.907202i	$0.361786\pi$
$912$	68.2133	+	118.149i	0.00247672	+	0.00428980i
$913$	2465.73	−	4270.76i	0.0893796	−	0.154810i
$914$	8890.52	−	15398.8i	0.321742	−	0.557274i
$915$	−183.026	−	317.011i	−0.00661274	−	0.0114536i
$916$	−7597.50			−0.274049
$917$		0			0
$918$	3099.50			0.111437
$919$	−23687.0	−	41027.0i	−0.850230	−	1.47264i	−0.881001	−	0.473114i	$-0.843130\pi$
$919$	−23687.0	−	41027.0i	−0.850230	−	1.47264i	0.0307713	−	0.999526i	$-0.490204\pi$
$920$	−5545.37	+	9604.86i	−0.198723	+	0.344199i
$921$	−255.612	+	442.733i	−0.00914517	+	0.0158399i
$922$	374.741	+	649.070i	0.0133855	+	0.0231844i
$923$	6230.53			0.222189
$924$		0			0
$925$	−5023.33			−0.178558
$926$	−5894.05	−	10208.8i	−0.209169	−	0.362291i
$927$	24497.1	−	42430.2i	0.867951	−	1.50334i
$928$	10610.8	−	18378.4i	0.375341	−	0.650110i
$929$	−3808.86	−	6597.14i	−0.134515	−	0.232987i	0.790897	−	0.611949i	$-0.209614\pi$
$929$	−3808.86	−	6597.14i	−0.134515	−	0.232987i	−0.925412	+	0.378962i	$0.876281\pi$
$930$	203.011			0.00715806
$931$		0			0
$932$	32837.6			1.15411
$933$	−1545.11	−	2676.20i	−0.0542170	−	0.0939066i
$934$	806.336	−	1396.62i	0.0282485	−	0.0489279i
$935$	18146.6	−	31430.8i	0.634713	−	1.09936i
$936$	20199.8	+	34987.1i	0.705397	+	1.22178i
$937$	52091.2			1.81616			0.908082	−	0.418792i	$-0.137546\pi$
$937$	52091.2			1.81616			0.908082	+	0.418792i	$0.137546\pi$
$938$		0			0
$939$	−2005.79			−0.0697088
$940$	−1967.57	−	3407.92i	−0.0682712	−	0.118249i
$941$	−28382.6	+	49160.0i	−0.983257	+	1.70305i	−0.333817	+	0.942638i	$0.608337\pi$
$941$	−28382.6	+	49160.0i	−0.983257	+	1.70305i	−0.649440	+	0.760413i	$0.724997\pi$
$942$	−568.185	+	984.126i	−0.0196523	+	0.0340388i
$943$	−21080.4	−	36512.4i	−0.727968	−	1.26088i
$944$	2953.03			0.101815
$945$		0			0
$946$	35852.5			1.23220
$947$	23814.6	+	41248.1i	0.817181	+	1.41540i	0.907751	+	0.419510i	$0.137798\pi$
$947$	23814.6	+	41248.1i	0.817181	+	1.41540i	−0.0905695	+	0.995890i	$0.528869\pi$
$948$	524.935	−	909.215i	0.0179843	−	0.0311497i
$949$	−30188.4	+	52287.8i	−1.03262	+	1.78855i
$950$	1488.24	+	2577.71i	0.0508262	+	0.0880335i
$951$	−2322.75			−0.0792012
$952$		0			0
$953$	12893.5			0.438259			0.219129	−	0.975696i	$-0.429678\pi$
$953$	12893.5			0.438259			0.219129	+	0.975696i	$0.429678\pi$
$954$	6044.40	+	10469.2i	0.205131	+	0.355297i
$955$	1164.80	−	2017.49i	0.0394681	−	0.0683607i
$956$	3523.12	−	6102.22i	0.119190	−	0.206443i
$957$	1327.76	+	2299.75i	0.0448490	+	0.0776807i
$958$	−16087.0			−0.542534
$959$		0			0
$960$	434.257			0.0145996
$961$	12183.3	+	21102.1i	0.408959	+	0.708338i
$962$	−11385.7	+	19720.7i	−0.381591	+	0.660936i
$963$	14650.6	−	25375.6i	0.490248	−	0.849134i
$964$	−8858.61	−	15343.6i	−0.295972	−	0.512638i
$965$	−22072.3			−0.736303
$966$		0			0
$967$	−28420.0			−0.945114			−0.472557	−	0.881300i	$-0.656669\pi$
$967$	−28420.0			−0.945114			−0.472557	+	0.881300i	$0.656669\pi$
$968$	38524.2	+	66725.9i	1.27915	+	2.21555i
$969$	−1248.45	+	2162.37i	−0.0413890	+	0.0716878i
$970$	603.004	−	1044.43i	0.0199601	−	0.0345719i
$971$	14636.9	+	25351.8i	0.483749	+	0.837877i	0.999826	−	0.0186650i	$-0.00594160\pi$
$971$	14636.9	+	25351.8i	0.483749	+	0.837877i	−0.516077	+	0.856542i	$0.672608\pi$
$972$	−3806.64			−0.125615
$973$		0			0
$974$	1529.19			0.0503063
$975$	284.754	+	493.209i	0.00935327	+	0.0162003i
$976$	−626.846	+	1085.73i	−0.0205582	+	0.0356079i
$977$	−6027.51	+	10439.9i	−0.197377	+	0.341866i	−0.947677	−	0.319231i	$-0.896576\pi$
$977$	−6027.51	+	10439.9i	−0.197377	+	0.341866i	0.750300	+	0.661097i	$0.229909\pi$
$978$	541.304	+	937.566i	0.0176984	+	0.0306545i
$979$	−55838.4			−1.82288
$980$		0			0
$981$	−15855.7			−0.516037
$982$	−1067.42	−	1848.83i	−0.0346872	−	0.0600799i
$983$	5302.53	−	9184.25i	0.172049	−	0.297998i	−0.767087	−	0.641543i	$-0.778294\pi$
$983$	5302.53	−	9184.25i	0.172049	−	0.297998i	0.939136	+	0.343545i	$0.111628\pi$
$984$	−1524.97	+	2641.32i	−0.0494047	+	0.0855714i
$985$	724.531	+	1254.92i	0.0234370	+	0.0405941i
$986$	19811.0			0.639870
$987$		0			0
$988$	−25865.7			−0.832893
$989$	15719.1	+	27226.3i	0.505398	+	0.875374i
$990$	7745.20	−	13415.1i	0.248645	−	0.430666i
$991$	−22614.5	+	39169.5i	−0.724898	+	1.25556i	0.234117	+	0.972208i	$0.424780\pi$
$991$	−22614.5	+	39169.5i	−0.724898	+	1.25556i	−0.959016	+	0.283352i	$0.908553\pi$
$992$	−6815.68	−	11805.1i	−0.218143	−	0.377835i
$993$	327.854			0.0104775
$994$		0			0
$995$	−24088.7			−0.767500
$996$	−62.0268	−	107.434i	−0.00197329	−	0.00341784i
$997$	−24838.4	+	43021.4i	−0.789008	+	1.36660i	0.137568	+	0.990492i	$0.456072\pi$
$997$	−24838.4	+	43021.4i	−0.789008	+	1.36660i	−0.926575	+	0.376109i	$0.877262\pi$
$998$	16012.7	−	27734.8i	0.507889	−	0.879690i
$999$	−1802.27	−	3121.63i	−0.0570785	−	0.0988629i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.q.116.2		12
7.2	even	3	inner	245.4.e.q.226.2		12
7.3	odd	6		245.4.a.p.1.5	yes	6
7.4	even	3		245.4.a.o.1.5	✓	6
7.5	odd	6		245.4.e.p.226.2		12
7.6	odd	2		245.4.e.p.116.2		12
21.11	odd	6		2205.4.a.bz.1.2		6
21.17	even	6		2205.4.a.ca.1.2		6
35.4	even	6		1225.4.a.bj.1.2		6
35.24	odd	6		1225.4.a.bi.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.a.o.1.5	✓	6	7.4	even	3
245.4.a.p.1.5	yes	6	7.3	odd	6
245.4.e.p.116.2		12	7.6	odd	2
245.4.e.p.226.2		12	7.5	odd	6
245.4.e.q.116.2		12	1.1	even	1	trivial
245.4.e.q.226.2		12	7.2	even	3	inner
1225.4.a.bi.1.2		6	35.24	odd	6
1225.4.a.bj.1.2		6	35.4	even	6
2205.4.a.bz.1.2		6	21.11	odd	6
2205.4.a.ca.1.2		6	21.17	even	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)

\(f(q)\)	\(=\)	\(q+(-0.828031 - 1.43419i) q^{2} +(-0.166444 + 0.288289i) q^{3} +(2.62873 - 4.55309i) q^{4} +(-2.50000 - 4.33013i) q^{5} +0.551283 q^{6} -21.9552 q^{8} +(13.4446 + 23.2867i) q^{9} +O(q^{10})\)	\(q+(-0.828031 - 1.43419i) q^{2} +(-0.166444 + 0.288289i) q^{3} +(2.62873 - 4.55309i) q^{4} +(-2.50000 - 4.33013i) q^{5} +0.551283 q^{6} -21.9552 q^{8} +(13.4446 + 23.2867i) q^{9} +(-4.14016 + 7.17096i) q^{10} +(-34.7863 + 60.2517i) q^{11} +(0.875071 + 1.51567i) q^{12} -68.4326 q^{13} +1.66444 q^{15} +(-2.85026 - 4.93680i) q^{16} +(52.1659 - 90.3539i) q^{17} +(22.2651 - 38.5643i) q^{18} +(35.9465 + 62.2611i) q^{19} -26.2873 q^{20} +115.217 q^{22} +(50.5154 + 87.4952i) q^{23} +(3.65430 - 6.32944i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(56.6643 + 98.1454i) q^{26} -17.9390 q^{27} -114.661 q^{29} +(-1.37821 - 2.38712i) q^{30} +(-36.8252 + 63.7832i) q^{31} +(-92.5409 + 160.286i) q^{32} +(-11.5799 - 20.0570i) q^{33} -172.780 q^{34} +141.369 q^{36} +(100.467 + 174.013i) q^{37} +(59.5296 - 103.108i) q^{38} +(11.3902 - 19.7284i) q^{39} +(54.8879 + 95.0687i) q^{40} -417.308 q^{41} +311.175 q^{43} +(182.888 + 316.771i) q^{44} +(67.2230 - 116.434i) q^{45} +(83.6566 - 144.897i) q^{46} +(74.8485 + 129.641i) q^{47} +1.89763 q^{48} +41.4016 q^{50} +(17.3654 + 30.0777i) q^{51} +(-179.891 + 311.580i) q^{52} +(-135.737 + 235.104i) q^{53} +(14.8541 + 25.7280i) q^{54} +347.863 q^{55} -23.9323 q^{57} +(94.9425 + 164.445i) q^{58} +(-259.014 + 448.625i) q^{59} +(4.37536 - 7.57834i) q^{60} +(-109.963 - 190.461i) q^{61} +121.970 q^{62} +260.903 q^{64} +(171.081 + 296.322i) q^{65} +(-19.1771 + 33.2157i) q^{66} +(-40.3475 + 69.8839i) q^{67} +(-274.260 - 475.032i) q^{68} -33.6319 q^{69} -91.0463 q^{71} +(-295.178 - 511.264i) q^{72} +(441.141 - 764.078i) q^{73} +(166.379 - 288.177i) q^{74} +(-4.16110 - 7.20723i) q^{75} +377.974 q^{76} -37.7257 q^{78} +(-299.939 - 519.509i) q^{79} +(-14.2513 + 24.6840i) q^{80} +(-360.018 + 623.570i) q^{81} +(345.544 + 598.499i) q^{82} -70.8820 q^{83} -521.659 q^{85} +(-257.662 - 446.284i) q^{86} +(19.0845 - 33.0554i) q^{87} +(763.740 - 1322.84i) q^{88} +(401.296 + 695.065i) q^{89} -222.651 q^{90} +531.165 q^{92} +(-12.2587 - 21.2326i) q^{93} +(123.954 - 214.694i) q^{94} +(179.732 - 311.305i) q^{95} +(-30.8057 - 53.3571i) q^{96} -145.648 q^{97} -1870.75 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

Modular forms

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