LMFDB - Embedded newform 245.4.e.q.226.2

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			226.2
Root			$-0.120924 - 0.209447i$ of defining polynomial
Character	$\chi$	$=$	245.226
Dual form			245.4.e.q.116.2

$q$-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 $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.828031	+	1.43419i	−0.292753	+	0.507063i	−0.974460	−	0.224562i	$-0.927905\pi$
$2$	−0.828031	+	1.43419i	−0.292753	+	0.507063i	0.681707	+	0.731626i	$0.261238\pi$
$3$	−0.166444	−	0.288289i	−0.0320321	−	0.0554813i	0.849565	−	0.527484i	$-0.176865\pi$
$3$	−0.166444	−	0.288289i	−0.0320321	−	0.0554813i	−0.881597	+	0.472003i	$0.843531\pi$
$4$	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	−0.737770	−	0.675052i	$-0.764121\pi$
$11$	−34.7863	−	60.2517i	−0.953497	−	1.65151i	−0.215727	−	0.976454i	$-0.569212\pi$
$12$	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	0.950549	+	0.310574i	$0.100521\pi$
$17$	52.1659	+	90.3539i	0.744240	+	1.28906i	−0.206309	+	0.978487i	$0.566145\pi$
$18$	22.2651	+	38.5643i	0.291552	+	0.504982i
$19$	35.9465	−	62.2611i	0.434036	−	0.751772i	−0.563180	−	0.826334i	$-0.690422\pi$
$19$	35.9465	−	62.2611i	0.434036	−	0.751772i	0.997216	+	0.0745616i	$0.0237557\pi$
$20$	−26.2873			−0.293901
$21$		0			0
$22$	115.217			1.11656
$23$	50.5154	−	87.4952i	0.457964	−	0.793218i	−0.540889	−	0.841094i	$-0.681912\pi$
$23$	50.5154	−	87.4952i	0.457964	−	0.793218i	0.998853	+	0.0478764i	$0.0152453\pi$
$24$	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	0.739407	−	0.673258i	$-0.235106\pi$
$31$	−36.8252	−	63.7832i	−0.213355	−	0.369542i	−0.952762	+	0.303716i	$0.901772\pi$
$32$	−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	−0.551753	−	0.834007i	$-0.686041\pi$
$37$	100.467	−	174.013i	0.446395	−	0.773178i	0.998148	+	0.0608289i	$0.0193744\pi$
$38$	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	−0.726189	−	0.687495i	$-0.758710\pi$
$47$	74.8485	−	129.641i	0.232293	−	0.402344i	0.958483	+	0.285151i	$0.0920438\pi$
$48$	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	0.634772	−	0.772699i	$-0.281094\pi$
$53$	−135.737	−	235.104i	−0.351791	−	0.609320i	−0.986563	+	0.163379i	$0.947761\pi$
$54$	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	−0.996408	−	0.0846788i	$-0.973014\pi$
$59$	−259.014	−	448.625i	−0.571538	−	0.989933i	0.424870	−	0.905254i	$-0.360320\pi$
$60$	4.37536	+	7.57834i	0.00941427	+	0.0163060i
$61$	−109.963	+	190.461i	−0.230808	+	0.399771i	−0.958046	−	0.286614i	$-0.907470\pi$
$61$	−109.963	+	190.461i	−0.230808	+	0.399771i	0.727238	+	0.686385i	$0.240804\pi$
$62$	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	0.826893	−	0.562359i	$-0.190106\pi$
$67$	−40.3475	−	69.8839i	−0.0735706	−	0.127428i	−0.900464	+	0.434931i	$0.856773\pi$
$68$	−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	0.965861	+	0.259059i	$0.0834125\pi$
$73$	441.141	+	764.078i	0.707283	+	1.22505i	−0.258579	+	0.965990i	$0.583254\pi$
$74$	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	−0.996620	−	0.0821553i	$-0.973820\pi$
$79$	−299.939	+	519.509i	−0.427161	+	0.739865i	0.569458	+	0.822020i	$0.307153\pi$
$80$	−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	−0.521733	−	0.853109i	$-0.674714\pi$
$89$	401.296	−	695.065i	0.477947	−	0.827828i	0.999680	+	0.0252802i	$0.00804778\pi$
$90$	−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	0.672161	−	0.740405i	$-0.265366\pi$
$101$	−309.718	−	536.447i	−0.305129	−	0.528499i	−0.977290	+	0.211906i	$0.932033\pi$
$102$	28.7581	+	49.8105i	0.0279165	+	0.0483527i
$103$	−911.040	+	1577.97i	−0.871528	+	1.50953i	−0.0111125	+	0.999938i	$0.503537\pi$
$103$	−911.040	+	1577.97i	−0.871528	+	1.50953i	−0.860416	+	0.509593i	$0.829796\pi$
$104$	1502.45			1.41661
$105$		0			0
$106$	449.578			0.411952
$107$	−544.851	+	943.709i	−0.492268	+	0.852634i	−0.999960	−	0.00890504i	$-0.997165\pi$
$107$	−544.851	+	943.709i	−0.492268	+	0.852634i	0.507692	+	0.861539i	$0.330499\pi$
$108$	−47.1569	−	81.6781i	−0.0420155	−	0.0727730i
$109$	−294.833	−	510.666i	−0.259082	−	0.448743i	0.706914	−	0.707299i	$-0.250087\pi$
$109$	−294.833	−	510.666i	−0.259082	−	0.448743i	−0.965996	+	0.258556i	$0.916753\pi$
$110$	−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	−0.389031	−	0.921225i	$-0.627190\pi$
$131$	904.549	−	1566.72i	0.603289	−	1.04493i	0.992319	−	0.123702i	$-0.0394766\pi$
$132$	−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	0.868897	−	0.494992i	$-0.164829\pi$
$137$	9.25670	+	16.0331i	0.00577265	+	0.00999852i	−0.863125	+	0.504991i	$0.831496\pi$
$138$	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	−0.689287	−	0.724488i	$-0.742076\pi$
$149$	514.317	−	890.823i	0.282782	−	0.489792i	0.972069	+	0.234696i	$0.0754095\pi$
$150$	−6.89103	−	11.9356i	−0.00375100	−	0.00649693i
$151$	−35.5037	−	61.4942i	−0.0191341	−	0.0331412i	0.856300	−	0.516479i	$-0.172758\pi$
$151$	−35.5037	−	61.4942i	−0.0191341	−	0.0331412i	−0.875434	+	0.483338i	$0.839424\pi$
$152$	−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	−0.999612	−	0.0278461i	$-0.991135\pi$
$157$	−1030.66	−	1785.16i	−0.523922	−	0.907459i	0.475691	−	0.879613i	$-0.342198\pi$
$158$	−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	−0.527651	−	0.849462i	$-0.676927\pi$
$163$	981.899	−	1700.70i	0.471830	−	0.817234i	0.999481	+	0.0322280i	$0.0102603\pi$
$164$	−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	−0.984673	−	0.174408i	$-0.944199\pi$
$173$	−776.603	+	1345.12i	−0.341295	+	0.591140i	0.643378	+	0.765548i	$0.277532\pi$
$174$	−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	0.836481	−	0.547996i	$-0.184609\pi$
$179$	−134.920	−	233.689i	−0.0563376	−	0.0975795i	−0.892819	+	0.450416i	$0.851276\pi$
$180$	−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	−0.818520	−	0.574479i	$-0.805205\pi$
$191$	232.960	−	403.498i	0.0882533	−	0.152859i	0.906773	+	0.421619i	$0.138538\pi$
$192$	−43.4257	−	75.2154i	−0.0163228	−	0.0282719i
$193$	2207.23	+	3823.04i	0.823212	+	1.42585i	0.903278	+	0.429056i	$0.141154\pi$
$193$	2207.23	+	3823.04i	0.823212	+	1.42585i	−0.0800657	+	0.996790i	$0.525513\pi$
$194$	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	0.873748	+	0.486380i	$0.161683\pi$
$199$	2408.87	+	4172.28i	0.858091	+	1.48626i	−0.0156567	+	0.999877i	$0.504984\pi$
$200$	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	0.604989	−	0.796234i	$-0.293177\pi$
$227$	−1323.80	−	2292.88i	−0.387064	−	0.670414i	−0.992053	+	0.125819i	$0.959844\pi$
$228$	−62.9114	−	108.966i	−0.0182737	−	0.0316510i
$229$	−722.545	+	1251.49i	−0.208503	+	0.361137i	−0.951243	−	0.308442i	$-0.900192\pi$
$229$	−722.545	+	1251.49i	−0.208503	+	0.361137i	0.742740	+	0.669580i	$0.233526\pi$
$230$	−836.566			−0.239833
$231$		0			0
$232$	2517.39			0.712392
$233$	3122.96	−	5409.12i	0.878076	−	1.52087i	0.0246255	−	0.999697i	$-0.492161\pi$
$233$	3122.96	−	5409.12i	0.878076	−	1.52087i	0.853450	−	0.521175i	$-0.174506\pi$
$234$	−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	0.998409	−	0.0563953i	$-0.0179607\pi$
$241$	1684.96	+	2918.44i	0.450364	+	0.780054i	−0.548044	+	0.836449i	$0.684627\pi$
$242$	−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	−0.866198	−	0.499701i	$-0.833443\pi$
$257$	−1.42381	+	2.46612i	−0.000345584	+	0.000598569i	0.865853	+	0.500299i	$0.166777\pi$
$258$	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	0.982560	−	0.185948i	$-0.0595357\pi$
$263$	1408.54	+	2439.66i	0.330244	+	0.571999i	−0.652316	+	0.757947i	$0.726202\pi$
$264$	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	0.772276	−	0.635287i	$-0.219118\pi$
$269$	−723.716	−	1253.51i	−0.164036	−	0.284119i	−0.936313	+	0.351168i	$0.885785\pi$
$270$	74.2704	+	128.640i	0.0167406	+	0.0289955i
$271$	4027.25	−	6975.40i	0.902724	−	1.56356i	0.0787797	−	0.996892i	$-0.474898\pi$
$271$	4027.25	−	6975.40i	0.902724	−	1.56356i	0.823944	−	0.566671i	$-0.191769\pi$
$272$	−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	0.895342	−	0.445380i	$-0.146931\pi$
$277$	285.650	+	494.760i	0.0619604	+	0.107319i	−0.833381	+	0.552699i	$0.813598\pi$
$278$	−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	0.986035	−	0.166538i	$-0.0532590\pi$
$283$	1660.52	+	2876.11i	0.348791	+	0.604124i	−0.637244	+	0.770662i	$0.719926\pi$
$284$	−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	−0.884495	−	0.466550i	$-0.845497\pi$
$311$	−4641.52	−	8039.35i	−0.846291	−	1.46582i	0.0382037	−	0.999270i	$-0.487836\pi$
$312$	−250.073	−	433.140i	−0.0453770	−	0.0785952i
$313$	3012.72	−	5218.18i	0.544054	−	0.942329i	−0.454612	−	0.890690i	$-0.650222\pi$
$313$	3012.72	−	5218.18i	0.544054	−	0.942329i	0.998666	−	0.0516393i	$-0.0164446\pi$
$314$	3413.68			0.613519
$315$		0			0
$316$	−3153.83			−0.561445
$317$	3488.79	−	6042.76i	0.618139	−	1.07065i	−0.371686	−	0.928358i	$-0.621220\pi$
$317$	3488.79	−	6042.76i	0.618139	−	1.07065i	0.989825	−	0.142289i	$-0.0454464\pi$
$318$	−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	−0.904012	−	0.427508i	$-0.859392\pi$
$331$	−492.439	+	852.930i	−0.0817731	+	0.141635i	0.822239	+	0.569143i	$0.192725\pi$
$332$	−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	0.857694	+	0.514161i	$0.171897\pi$
$347$	5650.24	+	9786.50i	0.874123	+	1.51403i	0.0164299	+	0.999865i	$0.494770\pi$
$348$	−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	−0.996344	−	0.0854319i	$-0.972773\pi$
$353$	−3794.71	−	6572.62i	−0.572158	−	0.991007i	0.424186	−	0.905575i	$-0.360560\pi$
$354$	−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	0.342952	+	0.939353i	$0.388573\pi$
$359$	−4367.12	+	7564.08i	−0.642027	+	1.11202i	−0.984980	+	0.172671i	$0.944760\pi$
$360$	−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	0.790938	−	0.611896i	$-0.209593\pi$
$367$	−945.271	−	1637.26i	−0.134449	−	0.232872i	−0.925387	+	0.379024i	$0.876260\pi$
$368$	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	−0.944705	−	0.327922i	$-0.893652\pi$
$373$	−1356.94	+	2350.29i	−0.188364	+	0.326256i	0.756341	+	0.654178i	$0.226985\pi$
$374$	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	0.369524	+	0.929221i	$0.379521\pi$
$383$	−4646.94	+	8048.74i	−0.619968	+	1.07382i	−0.989491	+	0.144594i	$0.953812\pi$
$384$	−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	−0.974574	−	0.224065i	$-0.928067\pi$
$389$	−5227.38	−	9054.08i	−0.681333	−	1.18010i	0.293242	−	0.956038i	$-0.405266\pi$
$390$	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	−0.957571	−	0.288196i	$-0.906944\pi$
$397$	−1813.01	+	3140.23i	−0.229200	+	0.396987i	0.728371	+	0.685183i	$0.240278\pi$
$398$	−7978.47			−1.00484
$399$		0			0
$400$	142.513			0.0178141
$401$	4211.26	−	7294.12i	0.524440	−	0.908356i	−0.475156	−	0.879902i	$-0.657608\pi$
$401$	4211.26	−	7294.12i	0.524440	−	0.908356i	0.999595	−	0.0284542i	$-0.00905846\pi$
$402$	−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	−0.849808	−	0.527092i	$-0.823282\pi$
$409$	−7290.34	−	12627.2i	−0.881379	−	1.52659i	−0.0315714	−	0.999502i	$-0.510051\pi$
$410$	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	0.994418	−	0.105515i	$-0.0336492\pi$
$431$	3631.28	+	6289.57i	0.405830	+	0.702918i	−0.588588	+	0.808433i	$0.700316\pi$
$432$	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	−0.349911	−	0.936783i	$-0.613788\pi$
$439$	5852.94	−	10137.6i	0.636323	−	1.10214i	0.986233	−	0.165360i	$-0.0528786\pi$
$440$	−7637.40			−0.827497
$441$		0			0
$442$	11823.8			1.27240
$443$	−7538.99	+	13057.9i	−0.808551	+	1.40045i	0.105316	+	0.994439i	$0.466415\pi$
$443$	−7538.99	+	13057.9i	−0.808551	+	1.40045i	−0.913867	+	0.406013i	$0.866919\pi$
$444$	−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	−0.448797	−	0.893634i	$-0.648147\pi$
$457$	5368.47	−	9298.47i	0.549511	−	0.951781i	0.998308	−	0.0581472i	$-0.0185193\pi$
$458$	−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	−0.840894	−	0.541200i	$-0.817970\pi$
$467$	486.900	−	843.335i	0.0482463	−	0.0835651i	0.889140	+	0.457635i	$0.151303\pi$
$468$	−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	0.999123	−	0.0418680i	$-0.0133309\pi$
$479$	4857.00	+	8412.57i	0.463303	+	0.802464i	−0.535820	+	0.844332i	$0.679998\pi$
$480$	−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	0.843746	−	0.536743i	$-0.180345\pi$
$487$	−461.694	−	799.678i	−0.0429597	−	0.0744084i	−0.886706	+	0.462334i	$0.847012\pi$
$488$	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	0.00282829	−	0.999996i	$-0.499100\pi$
$499$	9669.15	−	16747.5i	0.867436	−	1.50244i	0.864608	−	0.502447i	$-0.167567\pi$
$500$	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	−0.789218	−	0.614113i	$-0.789514\pi$
$509$	1575.88	−	2729.50i	0.137229	−	0.237687i	0.926447	+	0.376426i	$0.122847\pi$
$510$	−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	0.535414	−	0.844590i	$-0.320156\pi$
$521$	−5514.69	−	9551.72i	−0.463729	−	0.803202i	−0.999143	+	0.0413875i	$0.986822\pi$
$522$	−2552.93	−	4421.80i	−0.214059	−	0.370760i
$523$	7224.21	−	12512.7i	0.604002	−	1.04616i	−0.388207	−	0.921572i	$-0.626905\pi$
$523$	7224.21	−	12512.7i	0.604002	−	1.04616i	0.992208	−	0.124589i	$-0.0397613\pi$
$524$	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	0.0394817	−	0.999220i	$-0.487429\pi$
$541$	11137.4	−	19290.5i	0.885091	−	1.53302i	0.845609	−	0.533802i	$-0.179237\pi$
$542$	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	0.909209	+	0.416339i	$0.136687\pi$
$557$	10715.9	+	18560.5i	0.815165	+	1.41191i	−0.0940446	+	0.995568i	$0.529980\pi$
$558$	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	0.727547	−	0.686057i	$-0.240660\pi$
$563$	−3077.43	−	5330.26i	−0.230370	−	0.399012i	−0.957917	+	0.287046i	$0.907327\pi$
$564$	−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	−0.669086	−	0.743185i	$-0.733314\pi$
$569$	4194.99	−	7265.94i	0.309074	−	0.535333i	0.978160	+	0.207853i	$0.0666475\pi$
$570$	99.0833	+	171.617i	0.00728095	+	0.0126110i
$571$	300.251	+	520.050i	0.0220055	+	0.0381146i	0.876818	−	0.480822i	$-0.159662\pi$
$571$	300.251	+	520.050i	0.0220055	+	0.0381146i	−0.854813	+	0.518936i	$0.826328\pi$
$572$	−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	0.929950	−	0.367686i	$-0.119850\pi$
$577$	2031.17	+	3518.10i	0.146549	+	0.253831i	−0.783401	+	0.621517i	$0.786517\pi$
$578$	−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	0.468099	+	0.883676i	$0.344939\pi$
$593$	−7671.31	+	13287.1i	−0.531236	+	0.920128i	−0.999335	+	0.0364520i	$0.988394\pi$
$594$	−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	0.977286	+	0.211925i	$0.0679731\pi$
$599$	9854.23	+	17068.0i	0.672175	+	1.16424i	−0.305111	+	0.952317i	$0.598694\pi$
$600$	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	0.341612	−	0.939841i	$-0.389027\pi$
$607$	14726.6	−	25507.1i	0.984732	−	1.70561i	0.643121	−	0.765765i	$-0.277639\pi$
$608$	−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	0.653295	−	0.757103i	$-0.273386\pi$
$613$	−4993.63	−	8649.23i	−0.329023	−	0.569884i	−0.982318	+	0.187219i	$0.940053\pi$
$614$	−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	0.860872	−	0.508821i	$-0.169919\pi$
$619$	−157.334	−	272.511i	−0.0102161	−	0.0176949i	−0.871088	+	0.491126i	$0.836585\pi$
$620$	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	0.816013	−	0.578034i	$-0.196180\pi$
$641$	−1502.56	−	2602.51i	−0.0925858	−	0.160363i	−0.908598	+	0.417671i	$0.862847\pi$
$642$	−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	0.821390	−	0.570367i	$-0.193199\pi$
$647$	−1370.18	−	2373.21i	−0.0832568	−	0.144205i	−0.904647	+	0.426162i	$0.859866\pi$
$648$	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	0.291191	+	0.956665i	$0.405948\pi$
$653$	−11395.3	+	19737.3i	−0.682900	+	1.18282i	−0.974092	+	0.226153i	$0.927385\pi$
$654$	−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	0.998964	−	0.0455035i	$-0.0144892\pi$
$661$	7818.63	+	13542.3i	0.460075	+	0.796873i	−0.538889	+	0.842377i	$0.681156\pi$
$662$	−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	−0.726673	−	0.686983i	$-0.758935\pi$
$677$	4079.78	−	7066.39i	0.231608	−	0.401157i	0.958282	+	0.285826i	$0.0922680\pi$
$678$	−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	0.996035	+	0.0889598i	$0.0283543\pi$
$683$	10264.6	+	17778.9i	0.575059	+	0.996032i	−0.420976	+	0.907072i	$0.638312\pi$
$684$	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	−0.878374	−	0.477973i	$-0.841372\pi$
$691$	−458.647	+	794.401i	−0.0252500	+	0.0437343i	0.853124	+	0.521708i	$0.174705\pi$
$692$	−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	0.355939	+	0.934509i	$0.384161\pi$
$709$	−11918.8	+	20643.9i	−0.631339	+	1.09351i	−0.987278	+	0.159002i	$0.949172\pi$
$710$	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	−0.912436	−	0.409219i	$-0.865801\pi$
$719$	−1963.10	+	3400.18i	−0.101824	+	0.176364i	0.810612	+	0.585583i	$0.199134\pi$
$720$	−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	0.420520	+	0.907283i	$0.361848\pi$
$733$	−11420.3	+	19780.6i	−0.575470	+	0.996744i	−0.995990	+	0.0894605i	$0.971486\pi$
$734$	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	0.699063	−	0.715060i	$-0.253600\pi$
$739$	−5418.67	−	9385.42i	−0.269728	−	0.467183i	−0.968792	+	0.247877i	$0.920267\pi$
$740$	−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	−0.599786	−	0.800161i	$-0.704747\pi$
$751$	8089.58	−	14011.6i	0.393067	−	0.680812i	0.992852	+	0.119349i	$0.0380808\pi$
$752$	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	−0.825615	−	0.564234i	$-0.809172\pi$
$761$	1591.99	−	2757.40i	0.0758337	−	0.131348i	0.901449	+	0.432886i	$0.142505\pi$
$762$	−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	0.919624	+	0.392799i	$0.128493\pi$
$773$	17193.0	+	29779.1i	0.799986	+	1.38562i	−0.119638	+	0.992818i	$0.538174\pi$
$774$	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	0.757922	−	0.652345i	$-0.226215\pi$
$787$	−4106.22	−	7112.18i	−0.185986	−	0.322137i	−0.943908	+	0.330208i	$0.892881\pi$
$788$	−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	0.733876	−	0.679284i	$-0.237709\pi$
$809$	−5093.08	−	8821.48i	−0.221339	−	0.383370i	−0.955215	+	0.295913i	$0.904376\pi$
$810$	−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	−0.935145	−	0.354266i	$-0.884731\pi$
$821$	−3781.97	+	6550.56i	−0.160769	+	0.278461i	0.774376	+	0.632726i	$0.218064\pi$
$822$	5.10306	+	8.83875i	0.000216532	+	0.000375045i
$823$	−4199.90	−	7274.44i	−0.177885	−	0.308106i	0.763271	−	0.646079i	$-0.223592\pi$
$823$	−4199.90	−	7274.44i	−0.177885	−	0.308106i	−0.941156	+	0.337973i	$0.890259\pi$
$824$	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	0.946513	−	0.322665i	$-0.104579\pi$
$829$	4626.28	+	8012.95i	0.193821	+	0.335707i	−0.752693	+	0.658372i	$0.771245\pi$
$830$	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	0.757593	−	0.652727i	$-0.226375\pi$
$857$	−4678.51	−	8103.41i	−0.186482	−	0.322996i	−0.944075	+	0.329731i	$0.893042\pi$
$858$	1312.34	+	2273.03i	0.0522173	+	0.0904430i
$859$	−14980.5	+	25946.9i	−0.595025	+	1.03061i	0.398518	+	0.917161i	$0.369525\pi$
$859$	−14980.5	+	25946.9i	−0.595025	+	1.03061i	−0.993543	+	0.113454i	$0.963809\pi$
$860$	−8179.94			−0.324341
$861$		0			0
$862$	−12027.3			−0.475232
$863$	16970.5	−	29393.8i	0.669389	−	1.15942i	−0.308687	−	0.951164i	$-0.599889\pi$
$863$	16970.5	−	29393.8i	0.669389	−	1.15942i	0.978075	−	0.208252i	$-0.0667773\pi$
$864$	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	−0.184023	−	0.982922i	$-0.558912\pi$
$877$	19718.3	−	34153.1i	0.759224	−	1.31501i	0.943247	−	0.332092i	$-0.107755\pi$
$878$	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	−0.872461	−	0.488684i	$-0.837477\pi$
$887$	−343.899	+	595.650i	−0.0130180	+	0.0225479i	0.859443	+	0.511232i	$0.170811\pi$
$888$	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	0.636501	−	0.771276i	$-0.280381\pi$
$907$	−9552.10	−	16544.7i	−0.349694	−	0.605688i	−0.986195	+	0.165588i	$0.947048\pi$
$908$	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	0.0307713	+	0.999526i	$0.490204\pi$
$919$	−23687.0	+	41027.0i	−0.850230	+	1.47264i	−0.881001	+	0.473114i	$0.843130\pi$
$920$	−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	−0.925412	−	0.378962i	$-0.876281\pi$
$929$	−3808.86	+	6597.14i	−0.134515	+	0.232987i	0.790897	+	0.611949i	$0.209614\pi$
$930$	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	−0.649440	−	0.760413i	$-0.724997\pi$
$941$	−28382.6	−	49160.0i	−0.983257	−	1.70305i	−0.333817	−	0.942638i	$-0.608337\pi$
$942$	−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	−0.0905695	−	0.995890i	$-0.528869\pi$
$947$	23814.6	−	41248.1i	0.817181	−	1.41540i	0.907751	−	0.419510i	$-0.137798\pi$
$948$	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	−0.516077	−	0.856542i	$-0.672608\pi$
$971$	14636.9	−	25351.8i	0.483749	−	0.837877i	0.999826	+	0.0186650i	$0.00594160\pi$
$972$	−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	0.750300	−	0.661097i	$-0.229909\pi$
$977$	−6027.51	−	10439.9i	−0.197377	−	0.341866i	−0.947677	+	0.319231i	$0.896576\pi$
$978$	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	0.939136	−	0.343545i	$-0.111628\pi$
$983$	5302.53	+	9184.25i	0.172049	+	0.297998i	−0.767087	+	0.641543i	$0.778294\pi$
$984$	−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	−0.959016	−	0.283352i	$-0.908553\pi$
$991$	−22614.5	−	39169.5i	−0.724898	−	1.25556i	0.234117	−	0.972208i	$-0.424780\pi$
$992$	−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	−0.926575	−	0.376109i	$-0.877262\pi$
$997$	−24838.4	−	43021.4i	−0.789008	−	1.36660i	0.137568	−	0.990492i	$-0.456072\pi$
$998$	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.226.2		12
7.2	even	3		245.4.a.o.1.5	✓	6
7.3	odd	6		245.4.e.p.116.2		12
7.4	even	3	inner	245.4.e.q.116.2		12
7.5	odd	6		245.4.a.p.1.5	yes	6
7.6	odd	2		245.4.e.p.226.2		12
21.2	odd	6		2205.4.a.bz.1.2		6
21.5	even	6		2205.4.a.ca.1.2		6
35.9	even	6		1225.4.a.bj.1.2		6
35.19	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	7.2	even	3
245.4.a.p.1.5	yes	6	7.5	odd	6
245.4.e.p.116.2		12	7.3	odd	6
245.4.e.p.226.2		12	7.6	odd	2
245.4.e.q.116.2		12	7.4	even	3	inner
245.4.e.q.226.2		12	1.1	even	1	trivial
1225.4.a.bi.1.2		6	35.19	odd	6
1225.4.a.bj.1.2		6	35.9	even	6
2205.4.a.bz.1.2		6	21.2	odd	6
2205.4.a.ca.1.2		6	21.5	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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