LMFDB - Embedded newform 245.4.e.q.226.5

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			226.5
Root			$2.14754 + 3.71965i$ of defining polynomial
Character	$\chi$	$=$	245.226
Dual form			245.4.e.q.116.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44043 - 2.49490i) q^{2} +(-1.44526 - 2.50327i) q^{3} +(-0.149696 - 0.259281i) q^{4} +(-2.50000 + 4.33013i) q^{5} -8.32721 q^{6} +22.1844 q^{8} +(9.32244 - 16.1469i) q^{9} +O(q^{10})$	\(q+(1.44043 - 2.49490i) q^{2} +(-1.44526 - 2.50327i) q^{3} +(-0.149696 - 0.259281i) q^{4} +(-2.50000 + 4.33013i) q^{5} -8.32721 q^{6} +22.1844 q^{8} +(9.32244 - 16.1469i) q^{9} +(7.20217 + 12.4745i) q^{10} +(23.2440 + 40.2598i) q^{11} +(-0.432700 + 0.749459i) q^{12} +31.0537 q^{13} +14.4526 q^{15} +(33.1528 - 57.4223i) q^{16} +(-30.9258 - 53.5651i) q^{17} +(-26.8567 - 46.5172i) q^{18} +(12.3107 - 21.3227i) q^{19} +1.49696 q^{20} +133.926 q^{22} +(77.4708 - 134.183i) q^{23} +(-32.0623 - 55.5335i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(44.7308 - 77.4760i) q^{26} -131.938 q^{27} +200.436 q^{29} +(20.8180 - 36.0579i) q^{30} +(64.6273 + 111.938i) q^{31} +(-6.77096 - 11.7277i) q^{32} +(67.1874 - 116.372i) q^{33} -178.186 q^{34} -5.58213 q^{36} +(38.9831 - 67.5207i) q^{37} +(-35.4654 - 61.4279i) q^{38} +(-44.8808 - 77.7357i) q^{39} +(-55.4611 + 96.0614i) q^{40} -235.479 q^{41} -278.388 q^{43} +(6.95909 - 12.0535i) q^{44} +(46.6122 + 80.7347i) q^{45} +(-223.183 - 386.565i) q^{46} +(184.042 - 318.771i) q^{47} -191.658 q^{48} -72.0217 q^{50} +(-89.3918 + 154.831i) q^{51} +(-4.64862 - 8.05165i) q^{52} +(84.7920 + 146.864i) q^{53} +(-190.047 + 329.172i) q^{54} -232.440 q^{55} -71.1686 q^{57} +(288.714 - 500.068i) q^{58} +(345.745 + 598.847i) q^{59} +(-2.16350 - 3.74730i) q^{60} +(348.286 - 603.249i) q^{61} +372.365 q^{62} +491.432 q^{64} +(-77.6343 + 134.467i) q^{65} +(-193.558 - 335.252i) q^{66} +(-1.16656 - 2.02054i) q^{67} +(-9.25895 + 16.0370i) q^{68} -447.863 q^{69} -866.599 q^{71} +(206.813 - 358.210i) q^{72} +(376.222 + 651.635i) q^{73} +(-112.305 - 194.518i) q^{74} +(-36.1315 + 62.5817i) q^{75} -7.37145 q^{76} -258.591 q^{78} +(-421.391 + 729.871i) q^{79} +(165.764 + 287.111i) q^{80} +(-61.0215 - 105.692i) q^{81} +(-339.192 + 587.497i) q^{82} +1443.44 q^{83} +309.258 q^{85} +(-400.999 + 694.550i) q^{86} +(-289.682 - 501.744i) q^{87} +(515.655 + 893.141i) q^{88} +(-719.031 + 1245.40i) q^{89} +268.567 q^{90} -46.3884 q^{92} +(186.807 - 323.559i) q^{93} +(-530.201 - 918.335i) q^{94} +(61.5534 + 106.614i) q^{95} +(-19.5716 + 33.8990i) q^{96} -23.4509 q^{97} +866.764 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 $

$2$	1.44043	−	2.49490i	0.509270	−	0.882082i	−0.490672	−	0.871344i	$-0.663249\pi$
$2$	1.44043	−	2.49490i	0.509270	−	0.882082i	0.999942	−	0.0107374i	$-0.00341790\pi$
$3$	−1.44526	−	2.50327i	−0.278141	−	0.481754i	0.692782	−	0.721147i	$-0.256385\pi$
$3$	−1.44526	−	2.50327i	−0.278141	−	0.481754i	−0.970923	+	0.239393i	$0.923051\pi$
$4$	−0.149696	−	0.259281i	−0.0187120	−	0.0324102i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$	−8.32721			−0.566595
$7$		0			0
$7$		0			0
$8$	22.1844			0.980422
$9$	9.32244	−	16.1469i	0.345275	−	0.598035i
$10$	7.20217	+	12.4745i	0.227753	+	0.394479i
$11$	23.2440	+	40.2598i	0.637122	+	1.10353i	0.986061	+	0.166382i	$0.0532085\pi$
$11$	23.2440	+	40.2598i	0.637122	+	1.10353i	−0.348940	+	0.937145i	$0.613458\pi$
$12$	−0.432700	+	0.749459i	−0.0104092	+	0.0180292i
$13$	31.0537			0.662519			0.331260	−	0.943540i	$-0.392526\pi$
$13$	31.0537			0.662519			0.331260	+	0.943540i	$0.392526\pi$
$14$		0			0
$15$	14.4526			0.248777
$16$	33.1528	−	57.4223i	0.518012	−	0.897223i
$17$	−30.9258	−	53.5651i	−0.441212	−	0.764202i	0.556567	−	0.830803i	$-0.312118\pi$
$17$	−30.9258	−	53.5651i	−0.441212	−	0.764202i	−0.997780	+	0.0666002i	$0.978785\pi$
$18$	−26.8567	−	46.5172i	−0.351677	−	0.609122i
$19$	12.3107	−	21.3227i	0.148645	−	0.257461i	−0.782082	−	0.623176i	$-0.785842\pi$
$19$	12.3107	−	21.3227i	0.148645	−	0.257461i	0.930727	+	0.365715i	$0.119175\pi$
$20$	1.49696			0.0167365
$21$		0			0
$22$	133.926			1.29787
$23$	77.4708	−	134.183i	0.702339	−	1.21649i	−0.265305	−	0.964165i	$-0.585473\pi$
$23$	77.4708	−	134.183i	0.702339	−	1.21649i	0.967643	−	0.252322i	$-0.0811941\pi$
$24$	−32.0623	−	55.5335i	−0.272695	−	0.472322i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	44.7308	−	77.4760i	0.337401	−	0.584396i
$27$	−131.938			−0.940422
$28$		0			0
$29$	200.436			1.28345			0.641724	−	0.766936i	$-0.278219\pi$
$29$	200.436			1.28345			0.641724	+	0.766936i	$0.278219\pi$
$30$	20.8180	−	36.0579i	0.126694	−	0.219441i
$31$	64.6273	+	111.938i	0.374432	+	0.648536i	0.990242	−	0.139359i	$-0.0445043\pi$
$31$	64.6273	+	111.938i	0.374432	+	0.648536i	−0.615810	+	0.787895i	$0.711171\pi$
$32$	−6.77096	−	11.7277i	−0.0374046	−	0.0647867i
$33$	67.1874	−	116.372i	0.354419	−	0.613872i
$34$	−178.186			−0.898785
$35$		0			0
$36$	−5.58213			−0.0258432
$37$	38.9831	−	67.5207i	0.173210	−	0.300009i	−0.766330	−	0.642447i	$-0.777919\pi$
$37$	38.9831	−	67.5207i	0.173210	−	0.300009i	0.939540	+	0.342438i	$0.111253\pi$
$38$	−35.4654	−	61.4279i	−0.151401	−	0.262235i
$39$	−44.8808	−	77.7357i	−0.184274	−	0.319171i
$40$	−55.4611	+	96.0614i	−0.219229	+	0.379716i
$41$	−235.479			−0.896967			−0.448483	−	0.893791i	$-0.648036\pi$
$41$	−235.479			−0.896967			−0.448483	+	0.893791i	$0.648036\pi$
$42$		0			0
$43$	−278.388			−0.987296			−0.493648	−	0.869662i	$-0.664337\pi$
$43$	−278.388			−0.987296			−0.493648	+	0.869662i	$0.664337\pi$
$44$	6.95909	−	12.0535i	0.0238437	−	0.0412985i
$45$	46.6122	+	80.7347i	0.154412	+	0.267449i
$46$	−223.183	−	386.565i	−0.715360	−	1.23904i
$47$	184.042	−	318.771i	0.571177	−	0.989308i	−0.425268	−	0.905067i	$-0.639820\pi$
$47$	184.042	−	318.771i	0.571177	−	0.989308i	0.996445	−	0.0842404i	$-0.0268464\pi$
$48$	−191.658			−0.576321
$49$		0			0
$50$	−72.0217			−0.203708
$51$	−89.3918	+	154.831i	−0.245438	+	0.425112i
$52$	−4.64862	−	8.05165i	−0.0123971	−	0.0214724i
$53$	84.7920	+	146.864i	0.219756	+	0.380629i	0.954733	−	0.297463i	$-0.0961405\pi$
$53$	84.7920	+	146.864i	0.219756	+	0.380629i	−0.734977	+	0.678092i	$0.762807\pi$
$54$	−190.047	+	329.172i	−0.478929	+	0.829529i
$55$	−232.440			−0.569859
$56$		0			0
$57$	−71.1686			−0.165377
$58$	288.714	−	500.068i	0.653622	−	1.13211i
$59$	345.745	+	598.847i	0.762918	+	1.32141i	0.941341	+	0.337458i	$0.109567\pi$
$59$	345.745	+	598.847i	0.762918	+	1.32141i	−0.178423	+	0.983954i	$0.557100\pi$
$60$	−2.16350	−	3.74730i	−0.00465511	−	0.00806290i
$61$	348.286	−	603.249i	0.731041	−	1.26620i	−0.225398	−	0.974267i	$-0.572368\pi$
$61$	348.286	−	603.249i	0.731041	−	1.26620i	0.956439	−	0.291933i	$-0.0942984\pi$
$62$	372.365			0.762749
$63$		0			0
$64$	491.432			0.959827
$65$	−77.6343	+	134.467i	−0.148144	+	0.256593i
$66$	−193.558	−	335.252i	−0.360990	−	0.625253i
$67$	−1.16656	−	2.02054i	−0.00212713	−	0.00368430i	0.864960	−	0.501841i	$-0.167344\pi$
$67$	−1.16656	−	2.02054i	−0.00212713	−	0.00368430i	−0.867087	+	0.498157i	$0.834010\pi$
$68$	−9.25895	+	16.0370i	−0.0165120	+	0.0285995i
$69$	−447.863			−0.781396
$70$		0			0
$71$	−866.599			−1.44854			−0.724270	−	0.689516i	$-0.757823\pi$
$71$	−866.599			−1.44854			−0.724270	+	0.689516i	$0.757823\pi$
$72$	206.813	−	358.210i	0.338516	−	0.586326i
$73$	376.222	+	651.635i	0.603197	+	1.04477i	0.992334	+	0.123588i	$0.0394402\pi$
$73$	376.222	+	651.635i	0.603197	+	1.04477i	−0.389136	+	0.921180i	$0.627226\pi$
$74$	−112.305	−	194.518i	−0.176422	−	0.305571i
$75$	−36.1315	+	62.5817i	−0.0556281	+	0.0963508i
$76$	−7.37145			−0.0111258
$77$		0			0
$78$	−258.591			−0.375380
$79$	−421.391	+	729.871i	−0.600130	+	1.03945i	0.392671	+	0.919679i	$0.371551\pi$
$79$	−421.391	+	729.871i	−0.600130	+	1.03945i	−0.992801	+	0.119776i	$0.961782\pi$
$80$	165.764	+	287.111i	0.231662	+	0.401250i
$81$	−61.0215	−	105.692i	−0.0837058	−	0.144983i
$82$	−339.192	+	587.497i	−0.456798	+	0.791198i
$83$	1443.44			1.90890			0.954450	−	0.298372i	$-0.0964436\pi$
$83$	1443.44			1.90890			0.954450	+	0.298372i	$0.0964436\pi$
$84$		0			0
$85$	309.258			0.394632
$86$	−400.999	+	694.550i	−0.502800	+	0.870875i
$87$	−289.682	−	501.744i	−0.356979	−	0.618306i
$88$	515.655	+	893.141i	0.624648	+	1.08192i
$89$	−719.031	+	1245.40i	−0.856372	+	1.48328i	0.0189949	+	0.999820i	$0.493953\pi$
$89$	−719.031	+	1245.40i	−0.856372	+	1.48328i	−0.875367	+	0.483460i	$0.839380\pi$
$90$	268.567			0.314549
$91$		0			0
$92$	−46.3884			−0.0525687
$93$	186.807	−	323.559i	0.208290	−	0.360768i
$94$	−530.201	−	918.335i	−0.581767	−	1.00765i
$95$	61.5534	+	106.614i	0.0664763	+	0.115140i
$96$	−19.5716	+	33.8990i	−0.0208075	+	0.0360397i
$97$	−23.4509			−0.0245472			−0.0122736	−	0.999925i	$-0.503907\pi$
$97$	−23.4509			−0.0245472			−0.0122736	+	0.999925i	$0.503907\pi$
$98$		0			0
$99$	866.764			0.879930
$100$	−3.74241	+	6.48204i	−0.00374241	+	0.00648204i
$101$	−738.207	−	1278.61i	−0.727271	−	1.25967i	−0.958032	−	0.286660i	$-0.907455\pi$
$101$	−738.207	−	1278.61i	−0.727271	−	1.25967i	0.230761	−	0.973010i	$-0.425878\pi$
$102$	257.526	+	446.048i	0.249989	+	0.432993i
$103$	504.721	−	874.202i	0.482831	−	0.836289i	−0.516974	−	0.856001i	$-0.672942\pi$
$103$	504.721	−	874.202i	0.482831	−	0.836289i	0.999806	+	0.0197124i	$0.00627504\pi$
$104$	688.909			0.649549
$105$		0			0
$106$	488.549			0.447661
$107$	−709.253	+	1228.46i	−0.640805	+	1.10991i	0.344449	+	0.938805i	$0.388066\pi$
$107$	−709.253	+	1228.46i	−0.640805	+	1.10991i	−0.985253	+	0.171101i	$0.945267\pi$
$108$	19.7506	+	34.2090i	0.0175972	+	0.0304793i
$109$	438.930	+	760.249i	0.385705	+	0.668061i	0.991867	−	0.127281i	$-0.0406249\pi$
$109$	438.930	+	760.249i	0.385705	+	0.668061i	−0.606162	+	0.795341i	$0.707292\pi$
$110$	−334.815	+	579.916i	−0.290212	+	0.502662i
$111$	−225.363			−0.192707
$112$		0			0
$113$	−1500.11			−1.24884			−0.624419	−	0.781090i	$-0.714664\pi$
$113$	−1500.11			−1.24884			−0.624419	+	0.781090i	$0.714664\pi$
$114$	−102.514	+	177.559i	−0.0842218	+	0.145876i
$115$	387.354	+	670.917i	0.314095	+	0.544029i
$116$	−30.0045	−	51.9693i	−0.0240159	−	0.0415968i
$117$	289.496	−	501.422i	0.228752	−	0.396210i
$118$	1992.09			1.55412
$119$		0			0
$120$	320.623			0.243906
$121$	−415.070	+	718.922i	−0.311848	+	0.540137i
$122$	−1003.37	−	1737.88i	−0.744594	−	1.28968i
$123$	340.329	+	589.467i	0.249483	+	0.432117i
$124$	19.3489	−	33.5133i	0.0140128	−	0.0242708i
$125$	125.000			0.0894427
$126$		0			0
$127$	416.639			0.291108			0.145554	−	0.989350i	$-0.453503\pi$
$127$	416.639			0.291108			0.145554	+	0.989350i	$0.453503\pi$
$128$	762.042	−	1319.90i	0.526216	−	0.911433i
$129$	402.343	+	696.878i	0.274607	+	0.475634i
$130$	223.654	+	387.380i	0.150890	+	0.261350i
$131$	−205.248	+	355.500i	−0.136890	+	0.237101i	−0.926318	−	0.376743i	$-0.877044\pi$
$131$	−205.248	+	355.500i	−0.136890	+	0.237101i	0.789428	+	0.613843i	$0.210377\pi$
$132$	−40.2308			−0.0265276
$133$		0			0
$134$	−6.72139			−0.00433313
$135$	329.844	−	571.306i	0.210285	−	0.364224i
$136$	−686.071	−	1188.31i	−0.432574	−	0.749241i
$137$	−880.987	−	1525.91i	−0.549400	−	0.951589i	−0.998316	−	0.0580146i	$-0.981523\pi$
$137$	−880.987	−	1525.91i	−0.549400	−	0.951589i	0.448916	−	0.893574i	$-0.351810\pi$
$138$	−645.116	+	1117.37i	−0.397942	+	0.689255i
$139$	−865.719			−0.528268			−0.264134	−	0.964486i	$-0.585086\pi$
$139$	−865.719			−0.528268			−0.264134	+	0.964486i	$0.585086\pi$
$140$		0			0
$141$	−1063.96			−0.635470
$142$	−1248.28	+	2162.08i	−0.737698	+	1.27773i
$143$	721.814	+	1250.22i	0.422106	+	0.731108i
$144$	−618.129	−	1070.63i	−0.357713	−	0.619578i
$145$	−501.089	+	867.912i	−0.286988	+	0.497077i
$146$	2167.69			1.22876
$147$		0			0
$148$	−23.3425			−0.0129645
$149$	−1509.62	+	2614.73i	−0.830018	+	1.43763i	0.0680059	+	0.997685i	$0.478336\pi$
$149$	−1509.62	+	2614.73i	−0.830018	+	1.43763i	−0.898023	+	0.439948i	$0.854997\pi$
$150$	104.090	+	180.289i	0.0566595	+	0.0981371i
$151$	−270.948	−	469.296i	−0.146023	−	0.252919i	0.783731	−	0.621100i	$-0.213314\pi$
$151$	−270.948	−	469.296i	−0.146023	−	0.252919i	−0.929754	+	0.368181i	$0.879981\pi$
$152$	273.105	−	473.032i	0.145735	−	0.252421i
$153$	−1153.22			−0.609359
$154$		0			0
$155$	−646.273			−0.334902
$156$	−13.4370	+	23.2735i	−0.00689627	+	0.0119447i
$157$	1293.04	+	2239.62i	0.657300	+	1.13848i	0.981312	+	0.192424i	$0.0616350\pi$
$157$	1293.04	+	2239.62i	0.657300	+	1.13848i	−0.324012	+	0.946053i	$0.605032\pi$
$158$	1213.97	+	2102.66i	0.611256	+	1.05873i
$159$	245.093	−	424.514i	0.122246	−	0.211737i
$160$	67.7096			0.0334557
$161$		0			0
$162$	−351.590			−0.170515
$163$	1233.07	−	2135.74i	0.592525	−	1.02628i	−0.401366	−	0.915918i	$-0.631464\pi$
$163$	1233.07	−	2135.74i	0.592525	−	1.02628i	0.993891	−	0.110366i	$-0.0352024\pi$
$164$	35.2503	+	61.0553i	0.0167841	+	0.0290709i
$165$	335.937	+	581.860i	0.158501	+	0.274532i
$166$	2079.19	−	3601.26i	0.972145	−	1.68381i
$167$	−459.020			−0.212695			−0.106347	−	0.994329i	$-0.533916\pi$
$167$	−459.020			−0.212695			−0.106347	+	0.994329i	$0.533916\pi$
$168$		0			0
$169$	−1232.67			−0.561068
$170$	445.466	−	771.569i	0.200974	−	0.348098i
$171$	−229.531	−	397.560i	−0.102647	−	0.177790i
$172$	41.6736	+	72.1807i	0.0184743	+	0.0319984i
$173$	−2250.73	+	3898.38i	−0.989132	+	1.71323i	−0.367233	+	0.930129i	$0.619695\pi$
$173$	−2250.73	+	3898.38i	−0.989132	+	1.71323i	−0.621899	+	0.783097i	$0.713639\pi$
$174$	−1669.07			−0.727195
$175$		0			0
$176$	3082.41			1.32015
$177$	999.383	−	1730.98i	0.424397	−	0.735077i
$178$	2071.43	+	3587.82i	0.872249	+	1.51078i
$179$	−980.055	−	1697.51i	−0.409233	−	0.708813i	0.585571	−	0.810621i	$-0.300870\pi$
$179$	−980.055	−	1697.51i	−0.409233	−	0.708813i	−0.994804	+	0.101808i	$0.967537\pi$
$180$	13.9553	−	24.1714i	0.00577872	−	0.0100090i
$181$	−3645.47			−1.49705			−0.748524	−	0.663108i	$-0.769237\pi$
$181$	−3645.47			−1.49705			−0.748524	+	0.663108i	$0.769237\pi$
$182$		0			0
$183$	−2013.46			−0.813329
$184$	1718.65	−	2976.78i	0.688588	−	1.19267i
$185$	194.915	+	337.604i	0.0774620	+	0.134168i
$186$	−538.165	−	932.129i	−0.212151	−	0.367457i
$187$	1437.68	−	2490.14i	0.562212	−	0.973780i
$188$	−110.202			−0.0427515
$189$		0			0
$190$	354.654			0.135417
$191$	−1257.22	+	2177.57i	−0.476280	+	0.824941i	−0.999631	−	0.0271763i	$-0.991348\pi$
$191$	−1257.22	+	2177.57i	−0.476280	+	0.824941i	0.523351	+	0.852117i	$0.324682\pi$
$192$	−710.247	−	1230.18i	−0.266967	−	0.462400i
$193$	−1094.68	−	1896.05i	−0.408274	−	0.707152i	0.586422	−	0.810006i	$-0.300536\pi$
$193$	−1094.68	−	1896.05i	−0.408274	−	0.707152i	−0.994697	+	0.102854i	$0.967203\pi$
$194$	−33.7795	+	58.5078i	−0.0125012	+	0.0216526i
$195$	448.808			0.164819
$196$		0			0
$197$	−3886.50			−1.40559			−0.702795	−	0.711392i	$-0.748065\pi$
$197$	−3886.50			−1.40559			−0.702795	+	0.711392i	$0.748065\pi$
$198$	1248.52	−	2162.49i	0.448122	−	0.776170i
$199$	484.680	+	839.491i	0.172654	+	0.299045i	0.939347	−	0.342969i	$-0.111433\pi$
$199$	484.680	+	839.491i	0.172654	+	0.299045i	−0.766693	+	0.642014i	$0.778099\pi$
$200$	−277.305	−	480.307i	−0.0980422	−	0.169814i
$201$	−3.37196	+	5.84041i	−0.00118328	+	0.00204951i
$202$	−4253.35			−1.48151
$203$		0			0
$204$	53.5264			0.0183706
$205$	588.697	−	1019.65i	0.200568	−	0.347394i
$206$	−1454.03	−	2518.46i	−0.491783	−	0.851794i
$207$	−1444.43	−	2501.83i	−0.485001	−	0.840046i
$208$	1029.52	−	1783.17i	0.343193	−	0.594427i
$209$	1144.60			0.378821
$210$		0			0
$211$	3079.69			1.00481			0.502404	−	0.864633i	$-0.332449\pi$
$211$	3079.69			1.00481			0.502404	+	0.864633i	$0.332449\pi$
$212$	25.3861	−	43.9700i	0.00822417	−	0.0142447i
$213$	1252.46	+	2169.33i	0.402898	+	0.697840i
$214$	2043.26	+	3539.04i	0.652685	+	1.13048i
$215$	695.969	−	1205.45i	0.220766	−	0.382378i
$216$	−2926.96			−0.922011
$217$		0			0
$218$	2529.00			0.785712
$219$	1087.48	−	1883.57i	0.335547	−	0.581185i
$220$	34.7954	+	60.2675i	0.0106632	+	0.0184692i
$221$	−960.362	−	1663.40i	−0.292312	−	0.506299i
$222$	−324.621	+	562.259i	−0.0981401	+	0.169984i
$223$	162.003			0.0486480			0.0243240	−	0.999704i	$-0.492257\pi$
$223$	162.003			0.0486480			0.0243240	+	0.999704i	$0.492257\pi$
$224$		0			0
$225$	−466.122			−0.138110
$226$	−2160.81	+	3742.63i	−0.635995	+	1.10158i
$227$	−189.976	−	329.048i	−0.0555470	−	0.0962101i	0.836915	−	0.547333i	$-0.184357\pi$
$227$	−189.976	−	329.048i	−0.0555470	−	0.0962101i	−0.892462	+	0.451123i	$0.851024\pi$
$228$	10.6537	+	18.4527i	0.00309455	+	0.00535991i
$229$	2390.75	−	4140.90i	0.689892	−	1.19493i	−0.281980	−	0.959420i	$-0.590991\pi$
$229$	2390.75	−	4140.90i	0.689892	−	1.19493i	0.971872	−	0.235508i	$-0.0756754\pi$
$230$	2231.83			0.639838
$231$		0			0
$232$	4446.55			1.25832
$233$	1262.27	−	2186.31i	0.354910	−	0.614722i	−0.632193	−	0.774811i	$-0.717845\pi$
$233$	1262.27	−	2186.31i	0.354910	−	0.614722i	0.987103	+	0.160090i	$0.0511783\pi$
$234$	−834.000	−	1444.53i	−0.232993	−	0.403555i
$235$	920.211	+	1593.85i	0.255438	+	0.442432i
$236$	103.513	−	179.290i	0.0285515	−	0.0494526i
$237$	2436.08			0.667682
$238$		0			0
$239$	113.452			0.0307053			0.0153527	−	0.999882i	$-0.495113\pi$
$239$	113.452			0.0307053			0.0153527	+	0.999882i	$0.495113\pi$
$240$	479.144	−	829.902i	0.128869	−	0.223208i
$241$	−3362.67	−	5824.32i	−0.898791	−	1.55675i	−0.829041	−	0.559187i	$-0.811113\pi$
$241$	−3362.67	−	5824.32i	−0.898791	−	1.55675i	−0.0697499	−	0.997565i	$-0.522220\pi$
$242$	1195.76	+	2071.12i	0.317630	+	0.550151i
$243$	−1957.54	+	3390.56i	−0.516775	+	0.895081i
$244$	−208.549			−0.0547170
$245$		0			0
$246$	1960.88			0.508217
$247$	382.292	−	662.150i	0.0984805	−	0.170573i
$248$	1433.72	+	2483.27i	0.367102	+	0.635839i
$249$	−2086.16	−	3613.33i	−0.530943	−	0.919620i
$250$	180.054	−	311.863i	0.0455505	−	0.0788958i
$251$	−3815.00			−0.959366			−0.479683	−	0.877442i	$-0.659248\pi$
$251$	−3815.00			−0.959366			−0.479683	+	0.877442i	$0.659248\pi$
$252$		0			0
$253$	7202.94			1.78990
$254$	600.141	−	1039.48i	0.148253	−	0.256781i
$255$	−446.959	−	774.156i	−0.109763	−	0.190116i
$256$	−229.615	−	397.705i	−0.0560584	−	0.0970961i
$257$	−1100.95	+	1906.90i	−0.267220	+	0.462838i	−0.968143	−	0.250399i	$-0.919438\pi$
$257$	−1100.95	+	1906.90i	−0.267220	+	0.462838i	0.700923	+	0.713237i	$0.252772\pi$
$258$	2318.19			0.559397
$259$		0			0
$260$	46.4862			0.0110883
$261$	1868.55	−	3236.42i	0.443143	−	0.767546i
$262$	591.292	+	1024.15i	0.139428	+	0.241496i
$263$	602.090	+	1042.85i	0.141165	+	0.244505i	0.927936	−	0.372740i	$-0.121582\pi$
$263$	602.090	+	1042.85i	0.141165	+	0.244505i	−0.786770	+	0.617246i	$0.788248\pi$
$264$	1490.51	−	2581.65i	0.347480	−	0.601853i
$265$	−847.920			−0.196556
$266$		0			0
$267$	4156.75			0.952767
$268$	−0.349258	+	0.604933i	−7.96058e−5	+	0.000137881i
$269$	−2564.49	−	4441.83i	−0.581263	−	1.00678i	−0.995330	−	0.0965307i	$-0.969225\pi$
$269$	−2564.49	−	4441.83i	−0.581263	−	1.00678i	0.414067	−	0.910246i	$-0.364108\pi$
$270$	−950.236	−	1645.86i	−0.214183	−	0.370977i
$271$	−404.196	+	700.087i	−0.0906020	+	0.156927i	−0.907765	−	0.419480i	$-0.862212\pi$
$271$	−404.196	+	700.087i	−0.0906020	+	0.156927i	0.817163	+	0.576407i	$0.195546\pi$
$272$	−4101.10			−0.914213
$273$		0			0
$274$	−5076.01			−1.11917
$275$	581.101	−	1006.50i	0.127424	−	0.220705i
$276$	67.0433	+	116.122i	0.0146215	+	0.0253252i
$277$	−90.1326	−	156.114i	−0.0195507	−	0.0338628i	0.856085	−	0.516836i	$-0.172890\pi$
$277$	−90.1326	−	156.114i	−0.0195507	−	0.0338628i	−0.875635	+	0.482973i	$0.839557\pi$
$278$	−1247.01	+	2159.88i	−0.269031	+	0.465976i
$279$	2409.93			0.517129
$280$		0			0
$281$	−3068.29			−0.651384			−0.325692	−	0.945476i	$-0.605597\pi$
$281$	−3068.29			−0.651384			−0.325692	+	0.945476i	$0.605597\pi$
$282$	−1532.56	+	2654.47i	−0.323626	+	0.560537i
$283$	1934.09	+	3349.94i	0.406253	+	0.703651i	0.994466	−	0.105055i	$-0.0335019\pi$
$283$	1934.09	+	3349.94i	0.406253	+	0.703651i	−0.588214	+	0.808706i	$0.700169\pi$
$284$	129.727	+	224.693i	0.0271051	+	0.0469475i
$285$	177.922	−	308.169i	0.0369795	−	0.0640504i
$286$	4158.90			0.859863
$287$		0			0
$288$	−252.488			−0.0516596
$289$	543.688	−	941.696i	0.110663	−	0.191674i
$290$	1443.57	+	2500.34i	0.292308	+	0.506293i
$291$	33.8927	+	58.7039i	0.00682758	+	0.0118257i
$292$	112.638	−	195.095i	0.0225741	−	0.0390995i
$293$	−1967.79			−0.392353			−0.196176	−	0.980569i	$-0.562853\pi$
$293$	−1967.79			−0.392353			−0.196176	+	0.980569i	$0.562853\pi$
$294$		0			0
$295$	−3457.45			−0.682374
$296$	864.817	−	1497.91i	0.169819	−	0.294136i
$297$	−3066.76	−	5311.79i	−0.599163	−	1.03778i
$298$	4349.00	+	7532.70i	0.845406	+	1.46429i
$299$	2405.76	−	4166.90i	0.465313	−	0.805946i
$300$	21.6350			0.00416366
$301$		0			0
$302$	−1561.13			−0.297460
$303$	−2133.81	+	3695.86i	−0.404567	+	0.700731i
$304$	−816.266	−	1413.81i	−0.154000	−	0.266736i
$305$	1741.43	+	3016.25i	0.326931	+	0.566262i
$306$	−1661.13	+	2877.16i	−0.310328	+	0.537505i
$307$	5487.54			1.02016			0.510082	−	0.860126i	$-0.329615\pi$
$307$	5487.54			1.02016			0.510082	+	0.860126i	$0.329615\pi$
$308$		0			0
$309$	−2917.82			−0.537180
$310$	−930.913	+	1612.39i	−0.170556	+	0.295411i
$311$	2586.40	+	4479.77i	0.471579	+	0.816799i	0.999471	−	0.0325121i	$-0.0103508\pi$
$311$	2586.40	+	4479.77i	0.471579	+	0.816799i	−0.527892	+	0.849312i	$0.677017\pi$
$312$	−995.654	−	1724.52i	−0.180666	−	0.312923i
$313$	−2881.46	+	4990.83i	−0.520351	+	0.901274i	0.479370	+	0.877613i	$0.340865\pi$
$313$	−2881.46	+	4990.83i	−0.520351	+	0.901274i	−0.999720	+	0.0236604i	$0.992468\pi$
$314$	7450.17			1.33897
$315$		0			0
$316$	252.323			0.0449186
$317$	−1590.44	+	2754.72i	−0.281792	+	0.488077i	−0.971826	−	0.235699i	$-0.924262\pi$
$317$	−1590.44	+	2754.72i	−0.281792	+	0.488077i	0.690035	+	0.723776i	$0.257595\pi$
$318$	−706.081	−	1222.97i	−0.124513	−	0.215662i
$319$	4658.94	+	8069.51i	0.817713	+	1.41632i
$320$	−1228.58	+	2127.96i	−0.214624	+	0.371739i
$321$	4100.23			0.712936
$322$		0			0
$323$	−1522.87			−0.262337
$324$	−18.2694	+	31.6435i	−0.00313261	+	0.00542584i
$325$	−388.172	−	672.333i	−0.0662519	−	0.114752i
$326$	−3552.32	−	6152.79i	−0.603511	−	1.04531i
$327$	1268.74	−	2197.52i	0.214561	−	0.371630i
$328$	−5223.97			−0.879406
$329$		0			0
$330$	1935.58			0.322879
$331$	−4616.51	+	7996.03i	−0.766606	+	1.32780i	0.172788	+	0.984959i	$0.444722\pi$
$331$	−4616.51	+	7996.03i	−0.766606	+	1.32780i	−0.939394	+	0.342841i	$0.888611\pi$
$332$	−216.078	−	374.258i	−0.0357194	−	0.0618678i
$333$	−726.835	−	1258.92i	−0.119611	−	0.207172i
$334$	−661.188	+	1145.21i	−0.108319	+	0.187614i
$335$	11.6656			0.00190256
$336$		0			0
$337$	−3259.50			−0.526874			−0.263437	−	0.964677i	$-0.584856\pi$
$337$	−3259.50			−0.526874			−0.263437	+	0.964677i	$0.584856\pi$
$338$	−1775.57	+	3075.38i	−0.285735	+	0.494908i
$339$	2168.05	+	3755.18i	0.347353	+	0.601632i
$340$	−46.2948	−	80.1849i	−0.00738437	−	0.0127901i
$341$	−3004.40	+	5203.77i	−0.477118	+	0.826392i
$342$	−1322.50			−0.209101
$343$		0			0
$344$	−6175.87			−0.967967
$345$	1119.66	−	1939.30i	0.174725	−	0.302633i
$346$	6484.05	+	11230.7i	1.00747	+	1.74499i
$347$	−925.566	−	1603.13i	−0.143190	−	0.248013i	0.785506	−	0.618854i	$-0.212403\pi$
$347$	−925.566	−	1603.13i	−0.143190	−	0.248013i	−0.928696	+	0.370841i	$0.879069\pi$
$348$	−86.7286	+	150.218i	−0.0133596	+	0.0231395i
$349$	1102.14			0.169043			0.0845216	−	0.996422i	$-0.473064\pi$
$349$	1102.14			0.169043			0.0845216	+	0.996422i	$0.473064\pi$
$350$		0			0
$351$	−4097.15			−0.623048
$352$	314.769	−	545.196i	0.0476626	−	0.0825541i
$353$	−1335.12	−	2312.50i	−0.201307	−	0.348674i	0.747643	−	0.664101i	$-0.231186\pi$
$353$	−1335.12	−	2312.50i	−0.201307	−	0.348674i	−0.948950	+	0.315427i	$0.897852\pi$
$354$	−2879.09	−	4986.73i	−0.432265	−	0.748705i
$355$	2166.50	−	3752.48i	0.323904	−	0.561017i
$356$	430.545			0.0640978
$357$		0			0
$358$	−5646.82			−0.833641
$359$	−217.726	+	377.113i	−0.0320088	+	0.0554409i	−0.881586	−	0.472023i	$-0.843524\pi$
$359$	−217.726	+	377.113i	−0.0320088	+	0.0554409i	0.849577	+	0.527464i	$0.176857\pi$
$360$	1034.06	+	1791.05i	0.151389	+	0.262213i
$361$	3126.39	+	5415.07i	0.455809	+	0.789484i
$362$	−5251.06	+	9095.10i	−0.762402	+	1.32052i
$363$	2399.54			0.346951
$364$		0			0
$365$	−3762.22			−0.539516
$366$	−2900.25	+	5023.39i	−0.414204	+	0.717422i
$367$	1237.33	+	2143.11i	0.175989	+	0.304822i	0.940503	−	0.339785i	$-0.110354\pi$
$367$	1237.33	+	2143.11i	0.175989	+	0.304822i	−0.764514	+	0.644607i	$0.777021\pi$
$368$	−5136.74	−	8897.10i	−0.727639	−	1.26031i
$369$	−2195.24	+	3802.26i	−0.309701	+	0.536417i
$370$	1123.05			0.157796
$371$		0			0
$372$	−111.857			−0.0155901
$373$	−2719.09	+	4709.61i	−0.377451	+	0.653764i	−0.990691	−	0.136133i	$-0.956533\pi$
$373$	−2719.09	+	4709.61i	−0.377451	+	0.653764i	0.613240	+	0.789897i	$0.289866\pi$
$374$	−4141.77	−	7173.75i	−0.572636	−	0.991834i
$375$	−180.658	−	312.908i	−0.0248777	−	0.0430894i
$376$	4082.87	−	7071.74i	0.559995	−	0.969939i
$377$	6224.28			0.850309
$378$		0			0
$379$	10597.1			1.43624			0.718122	−	0.695917i	$-0.245002\pi$
$379$	10597.1			1.43624			0.718122	+	0.695917i	$0.245002\pi$
$380$	18.4286	−	31.9193i	0.00248781	−	0.00430902i
$381$	−602.153	−	1042.96i	−0.0809691	−	0.140243i
$382$	3621.89	+	6273.30i	0.485110	+	0.840236i
$383$	2335.68	−	4045.52i	0.311613	−	0.539729i	−0.667099	−	0.744969i	$-0.732464\pi$
$383$	2335.68	−	4045.52i	0.311613	−	0.539729i	0.978712	+	0.205240i	$0.0657974\pi$
$384$	−4405.40			−0.585448
$385$		0			0
$386$	−6307.27			−0.831688
$387$	−2595.25	+	4495.11i	−0.340889	+	0.590437i
$388$	3.51051	+	6.08039i	0.000459328	+	0.000795580i
$389$	−1778.84	−	3081.05i	−0.231853	−	0.401582i	0.726500	−	0.687166i	$-0.241146\pi$
$389$	−1778.84	−	3081.05i	−0.231853	−	0.401582i	−0.958354	+	0.285585i	$0.907812\pi$
$390$	646.477	−	1119.73i	0.0839376	−	0.145384i
$391$	−9583.40			−1.23952
$392$		0			0
$393$	1186.55			0.152299
$394$	−5598.24	+	9696.43i	−0.715825	+	1.23985i
$395$	−2106.96	−	3649.36i	−0.268386	−	0.464858i
$396$	−129.751	−	224.736i	−0.0164653	−	0.0285187i
$397$	4592.28	−	7954.07i	0.580554	−	1.00555i	−0.414859	−	0.909886i	$-0.636169\pi$
$397$	4592.28	−	7954.07i	0.580554	−	1.00555i	0.995414	−	0.0956642i	$-0.0304975\pi$
$398$	2792.60			0.351709
$399$		0			0
$400$	−1657.64			−0.207205
$401$	4603.26	−	7973.08i	0.573256	−	0.992909i	−0.422972	−	0.906143i	$-0.639013\pi$
$401$	4603.26	−	7973.08i	0.573256	−	0.992909i	0.996229	−	0.0867664i	$-0.0276534\pi$
$402$	9.71417	+	16.8254i	0.00120522	+	0.00208750i
$403$	2006.92	+	3476.08i	0.248069	+	0.429668i
$404$	−221.014	+	382.807i	−0.0272174	+	0.0471420i
$405$	610.215			0.0748687
$406$		0			0
$407$	3624.50			0.441424
$408$	−1983.11	+	3434.84i	−0.240633	+	0.416789i
$409$	3826.83	+	6628.26i	0.462652	+	0.801336i	0.999092	−	0.0426020i	$-0.0135648\pi$
$409$	3826.83	+	6628.26i	0.462652	+	0.801336i	−0.536441	+	0.843938i	$0.680231\pi$
$410$	−1695.96	−	2937.49i	−0.204286	−	0.353834i
$411$	−2546.51	+	4410.69i	−0.305621	+	0.529351i
$412$	−302.219			−0.0361390
$413$		0			0
$414$	−8322.44			−0.987985
$415$	−3608.61	+	6250.30i	−0.426843	+	0.739314i
$416$	−210.264	−	364.187i	−0.0247813	−	0.0429225i
$417$	1251.19	+	2167.12i	0.146933	+	0.254495i
$418$	1648.72	−	2855.66i	0.192922	−	0.334151i
$419$	−370.864			−0.0432408			−0.0216204	−	0.999766i	$-0.506883\pi$
$419$	−370.864			−0.0432408			−0.0216204	+	0.999766i	$0.506883\pi$
$420$		0			0
$421$	1221.96			0.141460			0.0707302	−	0.997495i	$-0.477467\pi$
$421$	1221.96			0.141460			0.0707302	+	0.997495i	$0.477467\pi$
$422$	4436.09	−	7683.53i	0.511719	−	0.886323i
$423$	−3431.44	−	5943.44i	−0.394427	−	0.683167i
$424$	1881.06	+	3258.09i	0.215454	+	0.373177i
$425$	−773.145	+	1339.13i	−0.0882425	+	0.152840i
$426$	7216.35			0.820736
$427$		0			0
$428$	424.690			0.0479630
$429$	2086.42	−	3613.78i	0.234809	−	0.406702i
$430$	−2004.99	−	3472.75i	−0.224859	−	0.389467i
$431$	7464.46	+	12928.8i	0.834224	+	1.44492i	0.894661	+	0.446746i	$0.147417\pi$
$431$	7464.46	+	12928.8i	0.834224	+	1.44492i	−0.0604373	+	0.998172i	$0.519250\pi$
$432$	−4374.09	+	7576.15i	−0.487150	+	0.843768i
$433$	4544.42			0.504367			0.252184	−	0.967679i	$-0.418851\pi$
$433$	4544.42			0.504367			0.252184	+	0.967679i	$0.418851\pi$
$434$		0			0
$435$	2896.82			0.319292
$436$	131.412	−	227.613i	0.0144346	−	0.0250015i
$437$	−1907.44	−	3303.78i	−0.208799	−	0.361650i
$438$	−3132.88	−	5426.30i	−0.341769	−	0.591961i
$439$	−4715.94	+	8168.25i	−0.512710	+	0.888040i	0.487181	+	0.873301i	$0.338025\pi$
$439$	−4715.94	+	8168.25i	−0.512710	+	0.888040i	−0.999891	+	0.0147389i	$0.995308\pi$
$440$	−5156.55			−0.558702
$441$		0			0
$442$	−5533.35			−0.595463
$443$	2771.30	−	4800.04i	0.297220	−	0.514801i	−0.678279	−	0.734805i	$-0.737274\pi$
$443$	2771.30	−	4800.04i	0.297220	−	0.514801i	0.975499	+	0.220004i	$0.0706071\pi$
$444$	33.7360	+	58.4325i	0.00360595	+	0.00624568i
$445$	−3595.15	−	6226.99i	−0.382981	−	0.663343i
$446$	233.354	−	404.181i	0.0247750	−	0.0429115i
$447$	8727.16			0.923447
$448$		0			0
$449$	16311.6			1.71446			0.857229	−	0.514936i	$-0.172184\pi$
$449$	16311.6			1.71446			0.857229	+	0.514936i	$0.172184\pi$
$450$	−671.417	+	1162.93i	−0.0703354	+	0.121824i
$451$	−5473.48	−	9480.35i	−0.571477	−	0.989827i
$452$	224.561	+	388.951i	0.0233683	+	0.0404750i
$453$	−783.181	+	1356.51i	−0.0812297	+	0.140694i
$454$	−1094.59			−0.113154
$455$		0			0
$456$	−1578.83			−0.162140
$457$	7115.54	−	12324.5i	0.728339	−	1.26152i	−0.229246	−	0.973368i	$-0.573626\pi$
$457$	7115.54	−	12324.5i	0.728339	−	1.26152i	0.957585	−	0.288151i	$-0.0930405\pi$
$458$	−6887.44	−	11929.4i	−0.702683	−	1.21708i
$459$	4080.28	+	7067.25i	0.414926	+	0.718673i
$460$	115.971	−	200.868i	0.0117547	−	0.0203598i
$461$	−4960.94			−0.501202			−0.250601	−	0.968090i	$-0.580628\pi$
$461$	−4960.94			−0.501202			−0.250601	+	0.968090i	$0.580628\pi$
$462$		0			0
$463$	15479.5			1.55377			0.776885	−	0.629642i	$-0.216799\pi$
$463$	15479.5			1.55377			0.776885	+	0.629642i	$0.216799\pi$
$464$	6645.00	−	11509.5i	0.664841	−	1.15154i
$465$	934.033	+	1617.79i	0.0931500	+	0.161341i
$466$	−3636.43	−	6298.48i	−0.361490	−	0.626119i
$467$	7407.82	−	12830.7i	0.734033	−	1.27138i	−0.221114	−	0.975248i	$-0.570969\pi$
$467$	7407.82	−	12830.7i	0.734033	−	1.27138i	0.955146	−	0.296134i	$-0.0956974\pi$
$468$	−173.346			−0.0171216
$469$		0			0
$470$	5302.01			0.520348
$471$	3737.57	−	6473.67i	0.365644	−	0.633314i
$472$	7670.15	+	13285.1i	0.747981	+	1.29554i
$473$	−6470.85	−	11207.8i	−0.629027	−	1.08951i
$474$	3509.02	−	6077.79i	0.340030	−	0.588950i
$475$	−615.534			−0.0594582
$476$		0			0
$477$	3161.87			0.303506
$478$	163.419	−	283.051i	0.0156373	−	0.0270846i
$479$	4549.48	+	7879.93i	0.433969	+	0.751656i	0.997211	−	0.0746358i	$-0.0237794\pi$
$479$	4549.48	+	7879.93i	0.433969	+	0.751656i	−0.563242	+	0.826292i	$0.690446\pi$
$480$	−97.8581	−	169.495i	−0.00930540	−	0.0161174i
$481$	1210.57	−	2096.77i	0.114755	−	0.198762i
$482$	−19374.8			−1.83091
$483$		0			0
$484$	248.538			0.0233412
$485$	58.6273	−	101.545i	0.00548892	−	0.00950710i
$486$	5639.42	+	9767.75i	0.526356	+	0.911676i
$487$	7495.72	+	12983.0i	0.697461	+	1.20804i	0.969344	+	0.245707i	$0.0790202\pi$
$487$	7495.72	+	12983.0i	0.697461	+	1.20804i	−0.271883	+	0.962330i	$0.587646\pi$
$488$	7726.53	−	13382.7i	0.716729	−	1.24141i
$489$	−7128.45			−0.659222
$490$		0			0
$491$	8243.61			0.757697			0.378848	−	0.925459i	$-0.376320\pi$
$491$	8243.61			0.757697			0.378848	+	0.925459i	$0.376320\pi$
$492$	101.892	−	176.482i	0.00933667	−	0.0161716i
$493$	−6198.64	−	10736.4i	−0.566273	−	0.980814i
$494$	−1101.33	−	1907.57i	−0.100306	−	0.173736i
$495$	−2166.91	+	3753.20i	−0.196758	+	0.340795i
$496$	8570.29			0.775841
$497$		0			0
$498$	−12019.9			−1.08157
$499$	−4613.74	+	7991.24i	−0.413907	+	0.716908i	−0.995313	−	0.0967057i	$-0.969169\pi$
$499$	−4613.74	+	7991.24i	−0.413907	+	0.716908i	0.581406	+	0.813614i	$0.302503\pi$
$500$	−18.7120	−	32.4102i	−0.00167365	−	0.00289885i
$501$	663.405	+	1149.05i	0.0591591	+	0.102467i
$502$	−5495.26	+	9518.06i	−0.488576	+	0.846239i
$503$	−13750.9			−1.21893			−0.609465	−	0.792813i	$-0.708616\pi$
$503$	−13750.9			−1.21893			−0.609465	+	0.792813i	$0.708616\pi$
$504$		0			0
$505$	7382.07			0.650491
$506$	10375.4	−	17970.6i	0.911543	−	1.57884i
$507$	1781.53	+	3085.69i	0.156056	+	0.270297i
$508$	−62.3693	−	108.027i	−0.00544723	−	0.00943488i
$509$	−7771.98	+	13461.5i	−0.676792	+	1.17224i	0.299150	+	0.954206i	$0.403297\pi$
$509$	−7771.98	+	13461.5i	−0.676792	+	1.17224i	−0.975942	+	0.218032i	$0.930036\pi$
$510$	−2575.26			−0.223597
$511$		0			0
$512$	10869.7			0.938236
$513$	−1624.24	+	2813.27i	−0.139789	+	0.242122i
$514$	3171.69	+	5493.53i	0.272174	+	0.471419i
$515$	2523.61	+	4371.01i	0.215929	+	0.374000i
$516$	120.458	−	208.640i	0.0102769	−	0.0178001i
$517$	17111.5			1.45564
$518$		0			0
$519$	13011.6			1.10047
$520$	−1722.27	+	2983.06i	−0.145244	+	0.251569i
$521$	7623.86	+	13204.9i	0.641089	+	1.11040i	0.985190	+	0.171466i	$0.0548504\pi$
$521$	7623.86	+	13204.9i	0.641089	+	1.11040i	−0.344101	+	0.938933i	$0.611816\pi$
$522$	−5383.04	−	9323.71i	−0.451359	−	0.781777i
$523$	11108.1	−	19239.8i	0.928723	−	1.60860i	0.143263	−	0.989685i	$-0.454241\pi$
$523$	11108.1	−	19239.8i	0.928723	−	1.60860i	0.785461	−	0.618912i	$-0.212426\pi$
$524$	122.899			0.0102460
$525$		0			0
$526$	3469.08			0.287565
$527$	3997.30	−	6923.53i	0.330408	−	0.572284i
$528$	−4454.89	−	7716.10i	−0.367186	−	0.635985i
$529$	−5919.96	−	10253.7i	−0.486559	−	0.842745i
$530$	−1221.37	+	2115.48i	−0.100100	+	0.173378i
$531$	12892.7			1.05367
$532$		0			0
$533$	−7312.50			−0.594258
$534$	5987.52	−	10370.7i	0.485216	−	0.840419i
$535$	−3546.27	−	6142.31i	−0.286577	−	0.496365i
$536$	−25.8794	−	44.8244i	−0.00208548	−	0.00361217i
$537$	−2832.87	+	4906.68i	−0.227649	+	0.394299i
$538$	−14775.9			−1.18408
$539$		0			0
$540$	−197.506			−0.0157394
$541$	6492.65	−	11245.6i	0.515972	−	0.893690i	−0.483856	−	0.875148i	$-0.660764\pi$
$541$	6492.65	−	11245.6i	0.515972	−	0.893690i	0.999828	−	0.0185424i	$-0.00590258\pi$
$542$	1164.43	+	2016.86i	0.0922818	+	0.159837i
$543$	5268.66	+	9125.58i	0.416390	+	0.721208i
$544$	−418.795	+	725.374i	−0.0330068	+	0.0571694i
$545$	−4389.30			−0.344985
$546$		0			0
$547$	−8226.94			−0.643069			−0.321534	−	0.946898i	$-0.604199\pi$
$547$	−8226.94			−0.643069			−0.321534	+	0.946898i	$0.604199\pi$
$548$	−263.761	+	456.847i	−0.0205608	+	0.0356123i
$549$	−6493.75	−	11247.5i	−0.504821	−	0.874375i
$550$	−1674.07	−	2899.58i	−0.129787	−	0.224797i
$551$	2467.50	−	4273.84i	0.190779	−	0.330438i
$552$	−9935.57			−0.766098
$553$		0			0
$554$	−519.320			−0.0398263
$555$	563.408	−	975.851i	0.0430907	−	0.0746352i
$556$	129.595	+	224.465i	0.00988497	+	0.0171213i
$557$	−8920.63	−	15451.0i	−0.678599	−	1.17537i	−0.975403	−	0.220429i	$-0.929254\pi$
$557$	−8920.63	−	15451.0i	−0.678599	−	1.17537i	0.296804	−	0.954938i	$-0.404079\pi$
$558$	3471.35	−	6012.56i	0.263358	−	0.456150i
$559$	−8644.97			−0.654103
$560$		0			0
$561$	−8311.30			−0.625496
$562$	−4419.67	+	7655.09i	−0.331731	+	0.574574i
$563$	−539.199	−	933.919i	−0.0403633	−	0.0699112i	0.845138	−	0.534548i	$-0.179518\pi$
$563$	−539.199	−	933.919i	−0.0403633	−	0.0699112i	−0.885501	+	0.464637i	$0.846185\pi$
$564$	159.270	+	275.864i	0.0118909	+	0.0205957i
$565$	3750.28	−	6495.67i	0.279248	−	0.483673i
$566$	11143.7			0.827570
$567$		0			0
$568$	−19225.0			−1.42018
$569$	−8493.24	+	14710.7i	−0.625756	+	1.08384i	0.362638	+	0.931930i	$0.381876\pi$
$569$	−8493.24	+	14710.7i	−0.625756	+	1.08384i	−0.988394	+	0.151911i	$0.951457\pi$
$570$	−512.568	−	887.794i	−0.0376651	−	0.0652379i
$571$	6131.49	+	10620.1i	0.449378	+	0.778346i	0.998346	−	0.0574980i	$-0.0183123\pi$
$571$	6131.49	+	10620.1i	0.449378	+	0.778346i	−0.548968	+	0.835844i	$0.684979\pi$
$572$	216.106	−	374.306i	0.0157969	−	0.0273610i
$573$	7268.07			0.529891
$574$		0			0
$575$	−3873.54			−0.280935
$576$	4581.34	−	7935.11i	0.331405	−	0.574010i
$577$	3525.25	+	6105.92i	0.254347	+	0.440542i	0.964718	−	0.263286i	$-0.0848062\pi$
$577$	3525.25	+	6105.92i	0.254347	+	0.440542i	−0.710371	+	0.703827i	$0.751473\pi$
$578$	−1566.29	−	2712.90i	−0.112715	−	0.195228i
$579$	−3164.21	+	5480.56i	−0.227116	+	0.393376i
$580$	300.045			0.0214805
$581$		0			0
$582$	195.281			0.0139083
$583$	−3941.82	+	6827.42i	−0.280023	+	0.485014i
$584$	8346.26	+	14456.1i	0.591388	+	1.02431i
$585$	1447.48	+	2507.11i	0.102301	+	0.177190i
$586$	−2834.47	+	4909.44i	−0.199814	+	0.346087i
$587$	−20085.3			−1.41228			−0.706141	−	0.708071i	$-0.749566\pi$
$587$	−20085.3			−1.41228			−0.706141	+	0.708071i	$0.749566\pi$
$588$		0			0
$589$	3182.42			0.222631
$590$	−4980.22	+	8626.00i	−0.347513	+	0.601910i
$591$	5617.00	+	9728.94i	0.390952	+	0.677149i
$592$	−2584.79	−	4476.99i	−0.179450	−	0.310816i
$593$	9487.17	−	16432.3i	0.656984	−	1.13793i	−0.324409	−	0.945917i	$-0.605165\pi$
$593$	9487.17	−	16432.3i	0.656984	−	1.13793i	0.981392	−	0.192013i	$-0.0615014\pi$
$594$	−17669.9			−1.22054
$595$		0			0
$596$	903.936			0.0621252
$597$	1400.98	−	2426.57i	0.0960440	−	0.166353i
$598$	−6930.67	−	12004.3i	−0.473940	−	0.820888i
$599$	−8397.87	−	14545.5i	−0.572834	−	0.992178i	−0.996273	−	0.0862537i	$-0.972510\pi$
$599$	−8397.87	−	14545.5i	−0.572834	−	0.992178i	0.423439	−	0.905925i	$-0.360823\pi$
$600$	−801.557	+	1388.34i	−0.0545391	+	0.0944644i
$601$	−13624.3			−0.924702			−0.462351	−	0.886697i	$-0.652994\pi$
$601$	−13624.3			−0.924702			−0.462351	+	0.886697i	$0.652994\pi$
$602$		0			0
$603$	−43.5006			−0.00293778
$604$	−81.1198	+	140.504i	−0.00546476	+	0.00946525i
$605$	−2075.35	−	3594.61i	−0.139463	−	0.241556i
$606$	6147.21	+	10647.3i	0.412068	+	0.713723i
$607$	4199.75	−	7274.19i	0.280828	−	0.486409i	−0.690761	−	0.723083i	$-0.742724\pi$
$607$	4199.75	−	7274.19i	0.280828	−	0.486409i	0.971589	+	0.236675i	$0.0760575\pi$
$608$	−333.421			−0.0222401
$609$		0			0
$610$	10033.7			0.665985
$611$	5715.20	−	9899.01i	0.378416	−	0.655436i
$612$	172.632	+	299.007i	0.0114023	+	0.0197494i
$613$	−7760.21	−	13441.1i	−0.511308	−	0.885612i	−0.999914	−	0.0131070i	$-0.995828\pi$
$613$	−7760.21	−	13441.1i	−0.511308	−	0.885612i	0.488606	−	0.872505i	$-0.337506\pi$
$614$	7904.43	−	13690.9i	0.519539	−	0.899868i
$615$	−3403.29			−0.223144
$616$		0			0
$617$	−26665.1			−1.73987			−0.869933	−	0.493169i	$-0.835838\pi$
$617$	−26665.1			−1.73987			−0.869933	+	0.493169i	$0.835838\pi$
$618$	−4202.92	+	7279.67i	−0.273570	+	0.473837i
$619$	6115.78	+	10592.8i	0.397114	+	0.687822i	0.993369	−	0.114973i	$-0.0366783\pi$
$619$	6115.78	+	10592.8i	0.397114	+	0.687822i	−0.596254	+	0.802796i	$0.703345\pi$
$620$	96.7446	+	167.567i	0.00626670	+	0.0108542i
$621$	−10221.3	+	17703.8i	−0.660495	+	1.14401i
$622$	14902.1			0.960645
$623$		0			0
$624$	−5951.68			−0.381824
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	8301.10	+	14377.9i	0.529998	+	0.917983i
$627$	−1654.25	−	2865.24i	−0.105366	−	0.182498i
$628$	387.128	−	670.525i	0.0245988	−	0.0426064i
$629$	−4822.34			−0.305690
$630$		0			0
$631$	−7237.27			−0.456595			−0.228297	−	0.973591i	$-0.573316\pi$
$631$	−7237.27			−0.456595			−0.228297	+	0.973591i	$0.573316\pi$
$632$	−9348.33	+	16191.8i	−0.588380	+	1.01910i
$633$	−4450.96	−	7709.29i	−0.279478	−	0.484071i
$634$	4581.84	+	7935.98i	0.287016	+	0.497126i
$635$	−1041.60	+	1804.10i	−0.0650938	+	0.112746i
$636$	−146.758			−0.00914990
$637$		0			0
$638$	26843.5			1.66575
$639$	−8078.82	+	13992.9i	−0.500146	+	0.866278i
$640$	3810.21	+	6599.48i	0.235331	+	0.407605i
$641$	−2452.42	−	4247.71i	−0.151115	−	0.261739i	0.780523	−	0.625127i	$-0.214953\pi$
$641$	−2452.42	−	4247.71i	−0.151115	−	0.261739i	−0.931638	+	0.363389i	$0.881620\pi$
$642$	5906.10	−	10229.7i	0.363077	−	0.628867i
$643$	−8394.46			−0.514845			−0.257422	−	0.966299i	$-0.582873\pi$
$643$	−8394.46			−0.514845			−0.257422	+	0.966299i	$0.582873\pi$
$644$		0			0
$645$	−4023.43			−0.245616
$646$	−2193.59	+	3799.42i	−0.133600	+	0.231403i
$647$	−4763.22	−	8250.15i	−0.289431	−	0.501309i	0.684243	−	0.729254i	$-0.260133\pi$
$647$	−4763.22	−	8250.15i	−0.289431	−	0.501309i	−0.973674	+	0.227945i	$0.926799\pi$
$648$	−1353.73	−	2344.72i	−0.0820670	−	0.142144i
$649$	−16073.0	+	27839.3i	−0.972143	+	1.68380i
$650$	−2236.54			−0.134961
$651$		0			0
$652$	−738.345			−0.0443494
$653$	−7975.03	+	13813.2i	−0.477928	+	0.827796i	−0.999680	−	0.0253017i	$-0.991945\pi$
$653$	−7975.03	+	13813.2i	−0.477928	+	0.827796i	0.521752	+	0.853097i	$0.325279\pi$
$654$	−3655.06	−	6330.75i	−0.218539	−	0.378520i
$655$	−1026.24	−	1777.50i	−0.0612191	−	0.106035i
$656$	−7806.78	+	13521.7i	−0.464639	+	0.804779i
$657$	14029.2			0.833077
$658$		0			0
$659$	−3370.65			−0.199244			−0.0996221	−	0.995025i	$-0.531763\pi$
$659$	−3370.65			−0.199244			−0.0996221	+	0.995025i	$0.531763\pi$
$660$	100.577	−	174.204i	0.00593175	−	0.0102741i
$661$	−12127.0	−	21004.6i	−0.713594	−	1.23598i	−0.963499	−	0.267710i	$-0.913733\pi$
$661$	−12127.0	−	21004.6i	−0.713594	−	1.23598i	0.249906	−	0.968270i	$-0.419600\pi$
$662$	13299.6	+	23035.5i	0.780819	+	1.35242i
$663$	−2775.95	+	4808.08i	−0.162608	+	0.281645i
$664$	32022.0			1.87153
$665$		0			0
$666$	−4187.83			−0.243656
$667$	15527.9	−	26895.2i	0.901415	−	1.56130i
$668$	68.7136	+	119.015i	0.00397995	+	0.00689348i
$669$	−234.136	−	405.536i	−0.0135310	−	0.0234364i
$670$	16.8035	−	29.1045i	0.000968918	−	0.00167821i
$671$	32382.3			1.86305
$672$		0			0
$673$	−3510.41			−0.201064			−0.100532	−	0.994934i	$-0.532055\pi$
$673$	−3510.41			−0.201064			−0.100532	+	0.994934i	$0.532055\pi$
$674$	−4695.10	+	8132.15i	−0.268321	+	0.464746i
$675$	1649.22	+	2856.53i	0.0940422	+	0.162886i
$676$	184.525	+	319.607i	0.0104987	+	0.0181843i
$677$	−4525.59	+	7838.56i	−0.256917	+	0.444993i	−0.965414	−	0.260720i	$-0.916040\pi$
$677$	−4525.59	+	7838.56i	−0.256917	+	0.444993i	0.708498	+	0.705713i	$0.249373\pi$
$678$	12491.7			0.707585
$679$		0			0
$680$	6860.71			0.386906
$681$	−549.130	+	951.122i	−0.0308997	+	0.0535199i
$682$	8655.27	+	14991.4i	0.485964	+	0.841714i
$683$	−3552.86	−	6153.74i	−0.199043	−	0.344753i	0.749175	−	0.662372i	$-0.230450\pi$
$683$	−3552.86	−	6153.74i	−0.199043	−	0.344753i	−0.948219	+	0.317619i	$0.897117\pi$
$684$	−68.7199	+	119.026i	−0.00384148	+	0.00665363i
$685$	8809.87			0.491398
$686$		0			0
$687$	−13821.0			−0.767548
$688$	−9229.32	+	15985.6i	−0.511431	+	0.885824i
$689$	2633.11	+	4560.68i	0.145593	+	0.252174i
$690$	−3225.58	−	5586.87i	−0.177965	−	0.308244i
$691$	6314.70	−	10937.4i	0.347645	−	0.602138i	−0.638186	−	0.769882i	$-0.720315\pi$
$691$	6314.70	−	10937.4i	0.347645	−	0.602138i	0.985831	+	0.167744i	$0.0536483\pi$
$692$	1347.70			0.0740346
$693$		0			0
$694$	−5332.86			−0.291690
$695$	2164.30	−	3748.67i	0.118124	−	0.204597i
$696$	−6426.43	−	11130.9i	−0.349990	−	0.606201i
$697$	7282.38	+	12613.5i	0.395753	+	0.685464i
$698$	1587.56	−	2749.73i	0.0860887	−	0.149110i
$699$	−7297.23			−0.394859
$700$		0			0
$701$	−912.952			−0.0491893			−0.0245947	−	0.999698i	$-0.507830\pi$
$701$	−912.952			−0.0491893			−0.0245947	+	0.999698i	$0.507830\pi$
$702$	−5901.68	+	10222.0i	−0.317300	+	0.549579i
$703$	−959.817	−	1662.45i	−0.0514939	−	0.0891900i
$704$	11422.8	+	19785.0i	0.611527	+	1.05920i
$705$	2659.89	−	4607.07i	0.142096	−	0.246117i
$706$	−7692.63			−0.410079
$707$		0			0
$708$	−598.416			−0.0317653
$709$	10355.2	−	17935.8i	0.548518	−	0.950061i	−0.449858	−	0.893100i	$-0.648525\pi$
$709$	10355.2	−	17935.8i	0.548518	−	0.950061i	0.998376	−	0.0569613i	$-0.0181412\pi$
$710$	−6241.39	−	10810.4i	−0.329909	−	0.571419i
$711$	7856.79	+	13608.4i	0.414420	+	0.717797i
$712$	−15951.3	+	27628.4i	−0.839606	+	1.45424i
$713$	20026.9			1.05191
$714$		0			0
$715$	−7218.14			−0.377543
$716$	−293.421	+	508.220i	−0.0153152	+	0.0265266i
$717$	−163.967	−	283.999i	−0.00854040	−	0.0147924i
$718$	627.241	+	1086.41i	0.0326023	+	0.0564688i
$719$	−1234.88	+	2138.88i	−0.0640518	+	0.110941i	−0.896273	−	0.443503i	$-0.853736\pi$
$719$	−1234.88	+	2138.88i	−0.0640518	+	0.110941i	0.832221	+	0.554444i	$0.187069\pi$
$720$	6181.29			0.319949
$721$		0			0
$722$	18013.4			0.928520
$723$	−9719.88	+	16835.3i	−0.499981	+	0.865992i
$724$	545.713	+	945.203i	0.0280128	+	0.0485196i
$725$	−2505.45	−	4339.56i	−0.128345	−	0.222300i
$726$	3456.37	−	5986.62i	0.176692	−	0.306039i
$727$	10893.4			0.555729			0.277865	−	0.960620i	$-0.410373\pi$
$727$	10893.4			0.555729			0.277865	+	0.960620i	$0.410373\pi$
$728$		0			0
$729$	8021.48			0.407533
$730$	−5419.22	+	9386.37i	−0.274759	+	0.475897i
$731$	8609.36	+	14911.9i	0.435607	+	0.754494i
$732$	301.407	+	522.053i	0.0152190	+	0.0263601i
$733$	−13130.0	+	22741.8i	−0.661619	+	1.14596i	0.318571	+	0.947899i	$0.396797\pi$
$733$	−13130.0	+	22741.8i	−0.661619	+	1.14596i	−0.980190	+	0.198059i	$0.936536\pi$
$734$	7129.14			0.358503
$735$		0			0
$736$	−2098.21			−0.105083
$737$	54.2310	−	93.9308i	0.00271048	−	0.00469469i
$738$	6324.19	+	10953.8i	0.315443	+	0.546363i
$739$	920.414	+	1594.20i	0.0458160	+	0.0793556i	0.888024	−	0.459797i	$-0.152078\pi$
$739$	920.414	+	1594.20i	0.0458160	+	0.0793556i	−0.842208	+	0.539153i	$0.818745\pi$
$740$	58.3562	−	101.076i	0.00289894	−	0.00502112i
$741$	−2210.05			−0.109566
$742$		0			0
$743$	4022.25			0.198603			0.0993015	−	0.995057i	$-0.468339\pi$
$743$	4022.25			0.198603			0.0993015	+	0.995057i	$0.468339\pi$
$744$	4144.20	−	7177.96i	0.204212	−	0.353705i
$745$	−7548.08	−	13073.7i	−0.371195	−	0.642929i
$746$	7833.34	+	13567.7i	0.384449	+	0.665885i
$747$	13456.4	−	23307.2i	0.659096	−	1.14159i
$748$	−860.862			−0.0420805
$749$		0			0
$750$	−1040.90			−0.0506778
$751$	−12862.6	+	22278.7i	−0.624986	+	1.08251i	0.363558	+	0.931572i	$0.381562\pi$
$751$	−12862.6	+	22278.7i	−0.624986	+	1.08251i	−0.988544	+	0.150936i	$0.951771\pi$
$752$	−12203.0	−	21136.2i	−0.591753	−	1.02495i
$753$	5513.68	+	9549.97i	0.266839	+	0.462178i
$754$	8965.66	−	15529.0i	0.433037	−	0.750042i
$755$	2709.48			0.130607
$756$		0			0
$757$	11359.2			0.545385			0.272692	−	0.962101i	$-0.412086\pi$
$757$	11359.2			0.545385			0.272692	+	0.962101i	$0.412086\pi$
$758$	15264.4	−	26438.7i	0.731436	−	1.26688i
$759$	−10410.1	−	18030.9i	−0.497844	−	0.862292i
$760$	1365.53	+	2365.16i	0.0651748	+	0.112886i
$761$	−3921.69	+	6792.56i	−0.186808	+	0.323561i	−0.944184	−	0.329418i	$-0.893148\pi$
$761$	−3921.69	+	6792.56i	−0.186808	+	0.323561i	0.757376	+	0.652979i	$0.226481\pi$
$762$	−3469.45			−0.164941
$763$		0			0
$764$	752.806			0.0356487
$765$	2883.04	−	4993.57i	0.136257	−	0.236004i
$766$	−6728.79	−	11654.6i	−0.317390	−	0.549736i
$767$	10736.7	+	18596.4i	0.505448	+	0.875461i
$768$	−663.709	+	1149.58i	−0.0311843	+	0.0540127i
$769$	29007.8			1.36027			0.680136	−	0.733086i	$-0.261921\pi$
$769$	29007.8			1.36027			0.680136	+	0.733086i	$0.261921\pi$
$770$		0			0
$771$	6364.65			0.297299
$772$	−327.740	+	567.662i	−0.0152793	+	0.0264645i
$773$	339.580	+	588.170i	0.0158006	+	0.0273674i	0.873818	−	0.486254i	$-0.161637\pi$
$773$	339.580	+	588.170i	0.0158006	+	0.0273674i	−0.858017	+	0.513621i	$0.828304\pi$
$774$	7476.57	+	12949.8i	0.347209	+	0.601384i
$775$	1615.68	−	2798.44i	0.0748865	−	0.129707i
$776$	−520.245			−0.0240666
$777$		0			0
$778$	−10249.2			−0.472304
$779$	−2898.91	+	5021.05i	−0.133330	+	0.230934i
$780$	−67.1848	−	116.367i	−0.00308410	−	0.00534183i
$781$	−20143.3	−	34889.1i	−0.922897	−	1.59850i
$782$	−13804.2	+	23909.6i	−0.631252	+	1.09336i
$783$	−26445.0			−1.20698
$784$		0			0
$785$	−12930.4			−0.587907
$786$	1709.14	−	2960.32i	0.0775612	−	0.134340i
$787$	12164.5	+	21069.6i	0.550976	+	0.954318i	0.998204	+	0.0598987i	$0.0190778\pi$
$787$	12164.5	+	21069.6i	0.550976	+	0.954318i	−0.447228	+	0.894420i	$0.647589\pi$
$788$	581.794	+	1007.70i	0.0263015	+	0.0455554i
$789$	1740.35	−	3014.38i	0.0785276	−	0.136014i
$790$	−12139.7			−0.546724
$791$		0			0
$792$	19228.7			0.862703
$793$	10815.6	−	18733.1i	0.484329	−	0.838882i
$794$	−13229.8	−	22914.6i	−0.591318	−	1.02419i
$795$	1225.47	+	2122.57i	0.0546702	+	0.0946916i
$796$	145.110	−	251.337i	0.00646140	−	0.0111915i
$797$	2791.24			0.124054			0.0620269	−	0.998074i	$-0.480244\pi$
$797$	2791.24			0.124054			0.0620269	+	0.998074i	$0.480244\pi$
$798$		0			0
$799$	−22766.6			−1.00804
$800$	−169.274	+	293.191i	−0.00748093	+	0.0129573i
$801$	13406.2	+	23220.3i	0.591368	+	1.02428i
$802$	−13261.4	−	22969.4i	−0.583885	−	1.01132i
$803$	−17489.8	+	30293.2i	−0.768620	+	1.33129i
$804$	2.01908			8.85664e−5
$805$		0			0
$806$	11563.3			0.505336
$807$	−7412.72	+	12839.2i	−0.323346	+	0.560051i
$808$	−16376.7	−	28365.3i	−0.713033	−	1.23501i
$809$	−7847.97	−	13593.1i	−0.341063	−	0.590739i	0.643567	−	0.765390i	$-0.277454\pi$
$809$	−7847.97	−	13593.1i	−0.341063	−	0.590739i	−0.984630	+	0.174651i	$0.944120\pi$
$810$	878.974	−	1522.43i	0.0381284	−	0.0660403i
$811$	−9580.84			−0.414832			−0.207416	−	0.978253i	$-0.566505\pi$
$811$	−9580.84			−0.414832			−0.207416	+	0.978253i	$0.566505\pi$
$812$		0			0
$813$	2336.67			0.100800
$814$	5220.85	−	9042.77i	0.224804	−	0.389372i
$815$	6165.36	+	10678.7i	0.264985	+	0.458968i
$816$	5927.17	+	10266.2i	0.254280	+	0.440426i
$817$	−3427.14	+	5935.98i	−0.146757	+	0.254191i
$818$	22049.2			0.942458
$819$		0			0
$820$	−352.503			−0.0150121
$821$	−13770.5	+	23851.2i	−0.585376	+	1.01390i	0.409452	+	0.912332i	$0.365720\pi$
$821$	−13770.5	+	23851.2i	−0.585376	+	1.01390i	−0.994828	+	0.101570i	$0.967614\pi$
$822$	7336.16	+	12706.6i	0.311287	+	0.539165i
$823$	5873.23	+	10172.7i	0.248758	+	0.430862i	0.963182	−	0.268852i	$-0.0866442\pi$
$823$	5873.23	+	10172.7i	0.248758	+	0.430862i	−0.714423	+	0.699714i	$0.753311\pi$
$824$	11196.9	−	19393.7i	0.473379	−	0.819916i
$825$	−3359.37			−0.141768
$826$		0			0
$827$	−20831.7			−0.875924			−0.437962	−	0.898994i	$-0.644300\pi$
$827$	−20831.7			−0.875924			−0.437962	+	0.898994i	$0.644300\pi$
$828$	−432.453	+	749.030i	−0.0181507	+	0.0314379i
$829$	1795.00	+	3109.03i	0.0752027	+	0.130255i	0.901174	−	0.433457i	$-0.142706\pi$
$829$	1795.00	+	3109.03i	0.0752027	+	0.130255i	−0.825972	+	0.563712i	$0.809373\pi$
$830$	10395.9	+	18006.3i	0.434757	+	0.753021i
$831$	−260.530	+	451.252i	−0.0108757	+	0.0188372i
$832$	15260.8			0.635904
$833$		0			0
$834$	7209.02			0.299314
$835$	1147.55	−	1987.62i	0.0475600	−	0.0823764i
$836$	−171.342	−	296.773i	−0.00708851	−	0.0122777i
$837$	−8526.77	−	14768.8i	−0.352124	−	0.609897i
$838$	−534.205	+	925.271i	−0.0220213	+	0.0381419i
$839$	10917.2			0.449229			0.224614	−	0.974448i	$-0.427888\pi$
$839$	10917.2			0.449229			0.224614	+	0.974448i	$0.427888\pi$
$840$		0			0
$841$	15785.5			0.647239
$842$	1760.16	−	3048.68i	0.0720416	−	0.124780i
$843$	4434.49	+	7680.75i	0.181177	+	0.313807i
$844$	−461.018	−	798.507i	−0.0188020	−	0.0325660i
$845$	3081.67	−	5337.60i	0.125459	−	0.217301i
$846$	−19771.1			−0.803479
$847$		0			0
$848$	11244.4			0.455345
$849$	5590.52	−	9683.07i	0.225991	−	0.391428i
$850$	2227.33	+	3857.85i	0.0898785	+	0.155674i
$851$	−6040.11	−	10461.8i	−0.243305	−	0.421416i
$852$	374.978	−	649.481i	0.0150781	−	0.0261160i
$853$	−35912.9			−1.44154			−0.720770	−	0.693175i	$-0.756211\pi$
$853$	−35912.9			−1.44154			−0.720770	+	0.693175i	$0.756211\pi$
$854$		0			0
$855$	2295.31			0.0918105
$856$	−15734.4	+	27252.7i	−0.628259	+	1.08818i
$857$	−19676.6	−	34080.9i	−0.784295	−	1.35844i	−0.929419	−	0.369025i	$-0.879692\pi$
$857$	−19676.6	−	34080.9i	−0.784295	−	1.35844i	0.145124	−	0.989413i	$-0.453642\pi$
$858$	−6010.70	−	10410.8i	−0.239163	−	0.414242i
$859$	16117.4	−	27916.1i	0.640183	−	1.10883i	−0.345208	−	0.938526i	$-0.612192\pi$
$859$	16117.4	−	27916.1i	0.640183	−	1.10883i	0.985392	−	0.170304i	$-0.0544750\pi$
$860$	−416.736			−0.0165239
$861$		0			0
$862$	43008.2			1.69938
$863$	−21905.7	+	37941.7i	−0.864053	+	1.49658i	0.00393116	+	0.999992i	$0.498749\pi$
$863$	−21905.7	+	37941.7i	−0.864053	+	1.49658i	−0.867984	+	0.496592i	$0.834585\pi$
$864$	893.344	+	1547.32i	0.0351761	+	0.0609269i
$865$	−11253.6	−	19491.9i	−0.442353	−	0.766178i
$866$	6545.94	−	11337.9i	0.256859	−	0.444893i
$867$	−3143.09			−0.123120
$868$		0			0
$869$	−39179.3			−1.52942
$870$	4172.68	−	7227.29i	0.162606	−	0.281641i
$871$	−36.2259	−	62.7452i	−0.00140926	−	0.00244092i
$872$	9737.41	+	16865.7i	0.378154	+	0.654982i
$873$	−218.620	+	378.660i	−0.00847555	+	0.0146801i
$874$	−10990.1			−0.425340
$875$		0			0
$876$	−651.165			−0.0251151
$877$	4570.34	−	7916.06i	0.175974	−	0.304796i	−0.764524	−	0.644596i	$-0.777026\pi$
$877$	4570.34	−	7916.06i	0.175974	−	0.304796i	0.940498	+	0.339799i	$0.110359\pi$
$878$	13586.0	+	23531.6i	0.522216	+	0.904504i
$879$	2843.97	+	4925.90i	0.109129	+	0.189017i
$880$	−7706.04	+	13347.2i	−0.295194	+	0.511290i
$881$	−23013.1			−0.880058			−0.440029	−	0.897984i	$-0.645032\pi$
$881$	−23013.1			−0.880058			−0.440029	+	0.897984i	$0.645032\pi$
$882$		0			0
$883$	7448.15			0.283862			0.141931	−	0.989877i	$-0.454669\pi$
$883$	7448.15			0.283862			0.141931	+	0.989877i	$0.454669\pi$
$884$	−287.525	+	498.008i	−0.0109395	+	0.0189478i
$885$	4996.92	+	8654.91i	0.189796	+	0.328736i
$886$	−7983.76	−	13828.3i	−0.302731	−	0.524345i
$887$	23030.5	−	39890.0i	0.871803	−	1.51001i	0.0116736	−	0.999932i	$-0.496284\pi$
$887$	23030.5	−	39890.0i	0.871803	−	1.51001i	0.860130	−	0.510076i	$-0.170383\pi$
$888$	−4999.55			−0.188935
$889$		0			0
$890$	−20714.3			−0.780163
$891$	2836.77	−	4913.43i	0.106662	−	0.184743i
$892$	−24.2512	−	42.0043i	−0.000910303	−	0.00157669i
$893$	−4531.37	−	7848.56i	−0.169806	−	0.294112i
$894$	12570.9	−	21773.4i	0.470284	−	0.814555i
$895$	9800.55			0.366029
$896$		0			0
$897$	−13907.8			−0.517690
$898$	23495.8	−	40695.8i	0.873122	−	1.51229i
$899$	12953.6	+	22436.3i	0.480564	+	0.832362i
$900$	69.7767	+	120.857i	0.00258432	+	0.00447618i
$901$	5244.52	−	9083.78i	0.193918	−	0.335876i
$902$	−31536.7			−1.16414
$903$		0			0
$904$	−33279.1			−1.22439
$905$	9113.67	−	15785.3i	0.334750	−	0.579804i
$906$	2256.24	+	3907.92i	0.0827358	+	0.143303i
$907$	−19248.0	−	33338.6i	−0.704653	−	1.22050i	−0.966817	−	0.255472i	$-0.917769\pi$
$907$	−19248.0	−	33338.6i	−0.704653	−	1.22050i	0.262163	−	0.965024i	$-0.415564\pi$
$908$	−56.8774	+	98.5146i	−0.00207879	+	0.00360057i
$909$	−27527.6			−1.00444
$910$		0			0
$911$	−18329.1			−0.666596			−0.333298	−	0.942822i	$-0.608162\pi$
$911$	−18329.1			−0.666596			−0.333298	+	0.942822i	$0.608162\pi$
$912$	−2359.44	+	4086.66i	−0.0856674	+	0.148380i
$913$	33551.5	+	58112.9i	1.21620	+	2.10652i
$914$	−20498.9	−	35505.2i	−0.741842	−	1.28491i
$915$	5033.65	−	8718.53i	0.181866	−	0.315001i
$916$	−1431.55			−0.0516371
$917$		0			0
$918$	23509.5			0.845237
$919$	18724.2	−	32431.3i	0.672094	−	1.16410i	−0.305216	−	0.952283i	$-0.598729\pi$
$919$	18724.2	−	32431.3i	0.672094	−	1.16410i	0.977309	−	0.211817i	$-0.0679381\pi$
$920$	8593.23	+	14883.9i	0.307946	+	0.533378i
$921$	−7930.93	−	13736.8i	−0.283749	−	0.491468i
$922$	−7145.91	+	12377.1i	−0.255247	+	0.442101i
$923$	−26911.1			−0.959686
$924$		0			0
$925$	−1949.15			−0.0692841
$926$	22297.3	−	38620.0i	0.791289	−	1.37055i
$927$	−9410.46	−	16299.4i	−0.333420	−	0.577500i
$928$	−1357.14	−	2350.64i	−0.0480069	−	0.0831504i
$929$	−1473.17	+	2551.61i	−0.0520271	+	0.0901136i	−0.890866	−	0.454266i	$-0.849902\pi$
$929$	−1473.17	+	2551.61i	−0.0520271	+	0.0901136i	0.838839	+	0.544380i	$0.183235\pi$
$930$	5381.65			0.189754
$931$		0			0
$932$	−755.827			−0.0265643
$933$	7476.04	−	12948.9i	0.262331	−	0.454370i
$934$	−21341.0	−	36963.6i	−0.747642	−	1.29495i
$935$	7188.41	+	12450.7i	0.251429	+	0.435488i
$936$	6422.31	−	11123.8i	0.224273	−	0.388453i
$937$	−48870.0			−1.70386			−0.851928	−	0.523659i	$-0.824566\pi$
$937$	−48870.0			−1.70386			−0.851928	+	0.523659i	$0.824566\pi$
$938$		0			0
$939$	16657.9			0.578923
$940$	275.504	−	477.187i	0.00955953	−	0.0165576i
$941$	10330.5	+	17892.9i	0.357879	+	0.619864i	0.987606	−	0.156952i	$-0.0501667\pi$
$941$	10330.5	+	17892.9i	0.357879	+	0.619864i	−0.629727	+	0.776816i	$0.716833\pi$
$942$	−10767.5	−	18649.8i	−0.372423	−	0.645056i
$943$	−18242.8	+	31597.4i	−0.629974	+	1.09115i
$944$	45849.6			1.58080
$945$		0			0
$946$	−37283.3			−1.28138
$947$	−6565.16	+	11371.2i	−0.225279	+	0.390194i	−0.956403	−	0.292050i	$-0.905663\pi$
$947$	−6565.16	+	11371.2i	−0.225279	+	0.390194i	0.731124	+	0.682244i	$0.238996\pi$
$948$	−364.672	−	631.631i	−0.0124937	−	0.0216397i
$949$	11683.1	+	20235.7i	0.399630	+	0.692179i
$950$	−886.636	+	1535.70i	−0.0302803	+	0.0524470i
$951$	9194.40			0.313511
$952$		0			0
$953$	16098.9			0.547214			0.273607	−	0.961842i	$-0.411783\pi$
$953$	16098.9			0.547214			0.273607	+	0.961842i	$0.411783\pi$
$954$	4554.47	−	7888.57i	0.154566	−	0.267717i
$955$	−6286.12	−	10887.9i	−0.212999	−	0.368925i
$956$	−16.9833	−	29.4159i	−0.000574559	−	0.000995165i
$957$	13466.8	−	23325.1i	0.454878	−	0.787872i
$958$	26212.9			0.884030
$959$		0			0
$960$	7102.47			0.238783
$961$	6542.13	−	11331.3i	0.219601	−	0.380360i
$962$	−3487.49	−	6040.51i	−0.116883	−	0.202447i
$963$	13223.9	+	22904.5i	0.442508	+	0.766447i
$964$	−1006.76	+	1743.76i	−0.0336364	+	0.0582600i
$965$	10946.8			0.365172
$966$		0			0
$967$	15916.9			0.529320			0.264660	−	0.964342i	$-0.414740\pi$
$967$	15916.9			0.529320			0.264660	+	0.964342i	$0.414740\pi$
$968$	−9208.08	+	15948.9i	−0.305743	+	0.529562i
$969$	2200.95	+	3812.15i	0.0729666	+	0.126382i
$970$	−168.897	−	292.539i	−0.00559069	−	0.00968336i
$971$	−337.954	+	585.354i	−0.0111694	+	0.0193459i	−0.871556	−	0.490296i	$-0.836889\pi$
$971$	−337.954	+	585.354i	−0.0111694	+	0.0193459i	0.860387	+	0.509642i	$0.170222\pi$
$972$	1172.15			0.0386796
$973$		0			0
$974$	43188.3			1.42078
$975$	−1122.02	+	1943.39i	−0.0368547	+	0.0638343i
$976$	−23093.3	−	39998.8i	−0.757375	−	1.31181i
$977$	23084.7	+	39983.8i	0.755931	+	1.30931i	0.944910	+	0.327329i	$0.106149\pi$
$977$	23084.7	+	39983.8i	0.755931	+	1.30931i	−0.188980	+	0.981981i	$0.560518\pi$
$978$	−10268.1	+	17784.8i	−0.335722	+	0.581487i
$979$	−66852.7			−2.18245
$980$		0			0
$981$	16367.6			0.532698
$982$	11874.4	−	20567.0i	0.385872	−	0.668350i
$983$	25168.1	+	43592.4i	0.816620	+	1.41443i	0.908159	+	0.418626i	$0.137488\pi$
$983$	25168.1	+	43592.4i	0.816620	+	1.41443i	−0.0915383	+	0.995802i	$0.529178\pi$
$984$	7550.00	+	13077.0i	0.244599	+	0.423657i
$985$	9716.24	−	16829.0i	0.314300	−	0.544383i
$986$	−35714.9			−1.15354
$987$		0			0
$988$	−228.911			−0.00737108
$989$	−21566.9	+	37355.0i	−0.693416	+	1.20103i
$990$	6242.58	+	10812.5i	0.200406	+	0.347114i
$991$	−20093.5	−	34802.9i	−0.644087	−	1.11559i	−0.984512	−	0.175319i	$-0.943904\pi$
$991$	−20093.5	−	34802.9i	−0.644087	−	1.11559i	0.340425	−	0.940272i	$-0.389429\pi$
$992$	875.178	−	1515.85i	0.0280110	−	0.0485165i
$993$	26688.3			0.852897
$994$		0			0
$995$	−4846.80			−0.154426
$996$	−624.579	+	1081.80i	−0.0198700	+	0.0344159i
$997$	−8875.10	−	15372.1i	−0.281923	−	0.488305i	0.689935	−	0.723871i	$-0.257639\pi$
$997$	−8875.10	−	15372.1i	−0.281923	−	0.488305i	−0.971858	+	0.235566i	$0.924306\pi$
$998$	13291.6	+	23021.7i	0.421581	+	0.730199i
$999$	−5143.34	+	8908.52i	−0.162891	+	0.282135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.q.226.5		12
7.2	even	3		245.4.a.o.1.2	✓	6
7.3	odd	6		245.4.e.p.116.5		12
7.4	even	3	inner	245.4.e.q.116.5		12
7.5	odd	6		245.4.a.p.1.2	yes	6
7.6	odd	2		245.4.e.p.226.5		12
21.2	odd	6		2205.4.a.bz.1.5		6
21.5	even	6		2205.4.a.ca.1.5		6
35.9	even	6		1225.4.a.bj.1.5		6
35.19	odd	6		1225.4.a.bi.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.a.o.1.2	✓	6	7.2	even	3
245.4.a.p.1.2	yes	6	7.5	odd	6
245.4.e.p.116.5		12	7.3	odd	6
245.4.e.p.226.5		12	7.6	odd	2
245.4.e.q.116.5		12	7.4	even	3	inner
245.4.e.q.226.5		12	1.1	even	1	trivial
1225.4.a.bi.1.5		6	35.19	odd	6
1225.4.a.bj.1.5		6	35.9	even	6
2205.4.a.bz.1.5		6	21.2	odd	6
2205.4.a.ca.1.5		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)

\(f(q)\)	\(=\)	\(q+(1.44043 - 2.49490i) q^{2} +(-1.44526 - 2.50327i) q^{3} +(-0.149696 - 0.259281i) q^{4} +(-2.50000 + 4.33013i) q^{5} -8.32721 q^{6} +22.1844 q^{8} +(9.32244 - 16.1469i) q^{9} +O(q^{10})\)	\(q+(1.44043 - 2.49490i) q^{2} +(-1.44526 - 2.50327i) q^{3} +(-0.149696 - 0.259281i) q^{4} +(-2.50000 + 4.33013i) q^{5} -8.32721 q^{6} +22.1844 q^{8} +(9.32244 - 16.1469i) q^{9} +(7.20217 + 12.4745i) q^{10} +(23.2440 + 40.2598i) q^{11} +(-0.432700 + 0.749459i) q^{12} +31.0537 q^{13} +14.4526 q^{15} +(33.1528 - 57.4223i) q^{16} +(-30.9258 - 53.5651i) q^{17} +(-26.8567 - 46.5172i) q^{18} +(12.3107 - 21.3227i) q^{19} +1.49696 q^{20} +133.926 q^{22} +(77.4708 - 134.183i) q^{23} +(-32.0623 - 55.5335i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(44.7308 - 77.4760i) q^{26} -131.938 q^{27} +200.436 q^{29} +(20.8180 - 36.0579i) q^{30} +(64.6273 + 111.938i) q^{31} +(-6.77096 - 11.7277i) q^{32} +(67.1874 - 116.372i) q^{33} -178.186 q^{34} -5.58213 q^{36} +(38.9831 - 67.5207i) q^{37} +(-35.4654 - 61.4279i) q^{38} +(-44.8808 - 77.7357i) q^{39} +(-55.4611 + 96.0614i) q^{40} -235.479 q^{41} -278.388 q^{43} +(6.95909 - 12.0535i) q^{44} +(46.6122 + 80.7347i) q^{45} +(-223.183 - 386.565i) q^{46} +(184.042 - 318.771i) q^{47} -191.658 q^{48} -72.0217 q^{50} +(-89.3918 + 154.831i) q^{51} +(-4.64862 - 8.05165i) q^{52} +(84.7920 + 146.864i) q^{53} +(-190.047 + 329.172i) q^{54} -232.440 q^{55} -71.1686 q^{57} +(288.714 - 500.068i) q^{58} +(345.745 + 598.847i) q^{59} +(-2.16350 - 3.74730i) q^{60} +(348.286 - 603.249i) q^{61} +372.365 q^{62} +491.432 q^{64} +(-77.6343 + 134.467i) q^{65} +(-193.558 - 335.252i) q^{66} +(-1.16656 - 2.02054i) q^{67} +(-9.25895 + 16.0370i) q^{68} -447.863 q^{69} -866.599 q^{71} +(206.813 - 358.210i) q^{72} +(376.222 + 651.635i) q^{73} +(-112.305 - 194.518i) q^{74} +(-36.1315 + 62.5817i) q^{75} -7.37145 q^{76} -258.591 q^{78} +(-421.391 + 729.871i) q^{79} +(165.764 + 287.111i) q^{80} +(-61.0215 - 105.692i) q^{81} +(-339.192 + 587.497i) q^{82} +1443.44 q^{83} +309.258 q^{85} +(-400.999 + 694.550i) q^{86} +(-289.682 - 501.744i) q^{87} +(515.655 + 893.141i) q^{88} +(-719.031 + 1245.40i) q^{89} +268.567 q^{90} -46.3884 q^{92} +(186.807 - 323.559i) q^{93} +(-530.201 - 918.335i) q^{94} +(61.5534 + 106.614i) q^{95} +(-19.5716 + 33.8990i) q^{96} -23.4509 q^{97} +866.764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 16 q^{3} - 14 q^{4} - 30 q^{5} - 48 q^{6} - 132 q^{8} - 70 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 16 * q^3 - 14 * q^4 - 30 * q^5 - 48 * q^6 - 132 * q^8 - 70 * q^9	\( 12 q + 2 q^{2} + 16 q^{3} - 14 q^{4} - 30 q^{5} - 48 q^{6} - 132 q^{8} - 70 q^{9} + 10 q^{10} + 16 q^{11} + 160 q^{12} - 336 q^{13} - 160 q^{15} - 298 q^{16} - 4 q^{17} - 354 q^{18} + 308 q^{19} + 140 q^{20} - 472 q^{22} + 336 q^{23} - 92 q^{24} - 150 q^{25} + 56 q^{26} - 1928 q^{27} + 352 q^{29} + 120 q^{30} + 392 q^{31} + 770 q^{32} + 188 q^{33} - 1624 q^{34} + 460 q^{36} + 140 q^{37} + 20 q^{38} - 140 q^{39} + 330 q^{40} - 1312 q^{41} - 776 q^{43} + 160 q^{44} - 350 q^{45} + 388 q^{46} + 628 q^{47} - 2792 q^{48} - 100 q^{50} - 744 q^{51} + 1520 q^{52} + 676 q^{53} + 2284 q^{54} - 160 q^{55} + 2936 q^{57} + 2012 q^{58} + 996 q^{59} + 800 q^{60} + 740 q^{61} + 728 q^{62} + 2852 q^{64} + 840 q^{65} - 3620 q^{66} - 1768 q^{67} - 2940 q^{68} + 2096 q^{69} - 448 q^{71} - 2858 q^{72} + 2640 q^{73} - 928 q^{74} + 400 q^{75} + 2680 q^{76} + 16 q^{78} - 1636 q^{79} - 1490 q^{80} - 4442 q^{81} - 1756 q^{82} - 280 q^{83} + 40 q^{85} - 1180 q^{86} + 1940 q^{87} + 5652 q^{88} - 1904 q^{89} + 3540 q^{90} - 3904 q^{92} + 1592 q^{93} - 3332 q^{94} + 1540 q^{95} - 6460 q^{96} - 1032 q^{97} - 5608 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 16 * q^3 - 14 * q^4 - 30 * q^5 - 48 * q^6 - 132 * q^8 - 70 * q^9 + 10 * q^10 + 16 * q^11 + 160 * q^12 - 336 * q^13 - 160 * q^15 - 298 * q^16 - 4 * q^17 - 354 * q^18 + 308 * q^19 + 140 * q^20 - 472 * q^22 + 336 * q^23 - 92 * q^24 - 150 * q^25 + 56 * q^26 - 1928 * q^27 + 352 * q^29 + 120 * q^30 + 392 * q^31 + 770 * q^32 + 188 * q^33 - 1624 * q^34 + 460 * q^36 + 140 * q^37 + 20 * q^38 - 140 * q^39 + 330 * q^40 - 1312 * q^41 - 776 * q^43 + 160 * q^44 - 350 * q^45 + 388 * q^46 + 628 * q^47 - 2792 * q^48 - 100 * q^50 - 744 * q^51 + 1520 * q^52 + 676 * q^53 + 2284 * q^54 - 160 * q^55 + 2936 * q^57 + 2012 * q^58 + 996 * q^59 + 800 * q^60 + 740 * q^61 + 728 * q^62 + 2852 * q^64 + 840 * q^65 - 3620 * q^66 - 1768 * q^67 - 2940 * q^68 + 2096 * q^69 - 448 * q^71 - 2858 * q^72 + 2640 * q^73 - 928 * q^74 + 400 * q^75 + 2680 * q^76 + 16 * q^78 - 1636 * q^79 - 1490 * q^80 - 4442 * q^81 - 1756 * q^82 - 280 * q^83 + 40 * q^85 - 1180 * q^86 + 1940 * q^87 + 5652 * q^88 - 1904 * q^89 + 3540 * q^90 - 3904 * q^92 + 1592 * q^93 - 3332 * q^94 + 1540 * q^95 - 6460 * q^96 - 1032 * q^97 - 5608 * q^99

Introduction

L-functions

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