LMFDB - Embedded newform 245.4.e.i.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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	245.226
Dual form			245.4.e.i.116.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29289 + 2.23936i) q^{2} +(3.32843 + 5.76500i) q^{3} +(0.656854 + 1.13770i) q^{4} +(-2.50000 + 4.33013i) q^{5} -17.2132 q^{6} -24.0833 q^{8} +(-8.65685 + 14.9941i) q^{9} +O(q^{10})$	\(q+(-1.29289 + 2.23936i) q^{2} +(3.32843 + 5.76500i) q^{3} +(0.656854 + 1.13770i) q^{4} +(-2.50000 + 4.33013i) q^{5} -17.2132 q^{6} -24.0833 q^{8} +(-8.65685 + 14.9941i) q^{9} +(-6.46447 - 11.1968i) q^{10} +(-19.1274 - 33.1297i) q^{11} +(-4.37258 + 7.57354i) q^{12} -19.3431 q^{13} -33.2843 q^{15} +(25.8823 - 44.8294i) q^{16} +(-43.6127 - 75.5394i) q^{17} +(-22.3848 - 38.7716i) q^{18} +(-22.1127 + 38.3003i) q^{19} -6.56854 q^{20} +98.9188 q^{22} +(-109.083 + 188.938i) q^{23} +(-80.1594 - 138.840i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(25.0086 - 43.3162i) q^{26} +64.4802 q^{27} -46.9411 q^{29} +(43.0330 - 74.5354i) q^{30} +(97.2792 + 168.493i) q^{31} +(-29.4071 - 50.9345i) q^{32} +(127.328 - 220.539i) q^{33} +225.546 q^{34} -22.7452 q^{36} +(-183.426 + 317.704i) q^{37} +(-57.1787 - 99.0364i) q^{38} +(-64.3823 - 111.513i) q^{39} +(60.2082 - 104.284i) q^{40} +339.362 q^{41} -226.167 q^{43} +(25.1279 - 43.5227i) q^{44} +(-43.2843 - 74.9706i) q^{45} +(-282.066 - 488.553i) q^{46} +(5.83810 - 10.1119i) q^{47} +344.589 q^{48} +64.6447 q^{50} +(290.323 - 502.855i) q^{51} +(-12.7056 - 22.0068i) q^{52} +(104.510 + 181.016i) q^{53} +(-83.3661 + 144.394i) q^{54} +191.274 q^{55} -294.402 q^{57} +(60.6899 - 105.118i) q^{58} +(-308.000 - 533.472i) q^{59} +(-21.8629 - 37.8677i) q^{60} +(160.368 - 277.765i) q^{61} -503.087 q^{62} +566.197 q^{64} +(48.3579 - 83.7583i) q^{65} +(329.244 + 570.268i) q^{66} +(-7.25483 - 12.5657i) q^{67} +(57.2944 - 99.2368i) q^{68} -1452.30 q^{69} -952.000 q^{71} +(208.485 - 361.107i) q^{72} +(412.245 + 714.029i) q^{73} +(-474.302 - 821.514i) q^{74} +(83.2107 - 144.125i) q^{75} -58.0993 q^{76} +332.958 q^{78} +(-78.1375 + 135.338i) q^{79} +(129.411 + 224.147i) q^{80} +(448.353 + 776.570i) q^{81} +(-438.759 + 759.954i) q^{82} +1036.53 q^{83} +436.127 q^{85} +(292.409 - 506.468i) q^{86} +(-156.240 - 270.616i) q^{87} +(460.651 + 797.870i) q^{88} +(-85.1127 + 147.420i) q^{89} +223.848 q^{90} -286.607 q^{92} +(-647.574 + 1121.63i) q^{93} +(15.0961 + 26.1472i) q^{94} +(-110.563 - 191.502i) q^{95} +(195.759 - 339.064i) q^{96} -1059.87 q^{97} +662.333 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} + 2 q^{3} - 20 q^{4} - 10 q^{5} + 16 q^{6} + 96 q^{8} - 12 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 + 2 * q^3 - 20 * q^4 - 10 * q^5 + 16 * q^6 + 96 * q^8 - 12 * q^9	\( 4 q - 8 q^{2} + 2 q^{3} - 20 q^{4} - 10 q^{5} + 16 q^{6} + 96 q^{8} - 12 q^{9} - 40 q^{10} + 14 q^{11} - 108 q^{12} - 100 q^{13} - 20 q^{15} - 168 q^{16} - 50 q^{17} - 16 q^{18} + 36 q^{19} + 200 q^{20} - 368 q^{22} - 244 q^{23} - 496 q^{24} - 50 q^{25} + 216 q^{26} - 172 q^{27} - 52 q^{29} - 40 q^{30} - 120 q^{31} - 672 q^{32} + 498 q^{33} + 48 q^{34} - 272 q^{36} - 564 q^{37} + 320 q^{38} + 14 q^{39} - 240 q^{40} + 656 q^{41} - 520 q^{43} + 1164 q^{44} - 60 q^{45} - 704 q^{46} - 350 q^{47} + 2736 q^{48} + 400 q^{50} + 754 q^{51} + 628 q^{52} + 56 q^{53} + 648 q^{54} - 140 q^{55} - 1336 q^{57} + 8 q^{58} - 1232 q^{59} - 540 q^{60} + 336 q^{61} + 2400 q^{62} + 4256 q^{64} + 250 q^{65} + 1976 q^{66} + 152 q^{67} + 908 q^{68} - 2664 q^{69} - 3808 q^{71} + 800 q^{72} + 676 q^{73} - 2016 q^{74} + 50 q^{75} - 3536 q^{76} - 880 q^{78} - 1014 q^{79} - 840 q^{80} + 1454 q^{81} - 816 q^{82} + 752 q^{83} + 500 q^{85} + 768 q^{86} - 410 q^{87} + 4688 q^{88} - 216 q^{89} + 160 q^{90} + 528 q^{92} - 2760 q^{93} - 1928 q^{94} + 180 q^{95} - 2464 q^{96} - 5484 q^{97} + 1880 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 2 * q^3 - 20 * q^4 - 10 * q^5 + 16 * q^6 + 96 * q^8 - 12 * q^9 - 40 * q^10 + 14 * q^11 - 108 * q^12 - 100 * q^13 - 20 * q^15 - 168 * q^16 - 50 * q^17 - 16 * q^18 + 36 * q^19 + 200 * q^20 - 368 * q^22 - 244 * q^23 - 496 * q^24 - 50 * q^25 + 216 * q^26 - 172 * q^27 - 52 * q^29 - 40 * q^30 - 120 * q^31 - 672 * q^32 + 498 * q^33 + 48 * q^34 - 272 * q^36 - 564 * q^37 + 320 * q^38 + 14 * q^39 - 240 * q^40 + 656 * q^41 - 520 * q^43 + 1164 * q^44 - 60 * q^45 - 704 * q^46 - 350 * q^47 + 2736 * q^48 + 400 * q^50 + 754 * q^51 + 628 * q^52 + 56 * q^53 + 648 * q^54 - 140 * q^55 - 1336 * q^57 + 8 * q^58 - 1232 * q^59 - 540 * q^60 + 336 * q^61 + 2400 * q^62 + 4256 * q^64 + 250 * q^65 + 1976 * q^66 + 152 * q^67 + 908 * q^68 - 2664 * q^69 - 3808 * q^71 + 800 * q^72 + 676 * q^73 - 2016 * q^74 + 50 * q^75 - 3536 * q^76 - 880 * q^78 - 1014 * q^79 - 840 * q^80 + 1454 * q^81 - 816 * q^82 + 752 * q^83 + 500 * q^85 + 768 * q^86 - 410 * q^87 + 4688 * q^88 - 216 * q^89 + 160 * q^90 + 528 * q^92 - 2760 * q^93 - 1928 * q^94 + 180 * q^95 - 2464 * q^96 - 5484 * q^97 + 1880 * 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 $

$2$	−1.29289	+	2.23936i	−0.457107	+	0.791732i	−0.998807	−	0.0488398i	$-0.984448\pi$
$2$	−1.29289	+	2.23936i	−0.457107	+	0.791732i	0.541700	+	0.840572i	$0.317781\pi$
$3$	3.32843	+	5.76500i	0.640556	+	1.10948i	0.985309	+	0.170782i	$0.0546294\pi$
$3$	3.32843	+	5.76500i	0.640556	+	1.10948i	−0.344753	+	0.938694i	$0.612037\pi$
$4$	0.656854	+	1.13770i	0.0821068	+	0.142213i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$	−17.2132			−1.17121
$7$		0			0
$7$		0			0
$8$	−24.0833			−1.06434
$9$	−8.65685	+	14.9941i	−0.320624	+	0.555337i
$10$	−6.46447	−	11.1968i	−0.204424	−	0.354073i
$11$	−19.1274	−	33.1297i	−0.524285	−	0.908088i	−0.999600	−	0.0282725i	$-0.990999\pi$
$11$	−19.1274	−	33.1297i	−0.524285	−	0.908088i	0.475315	−	0.879815i	$-0.342334\pi$
$12$	−4.37258	+	7.57354i	−0.105188	+	0.182191i
$13$	−19.3431			−0.412679			−0.206339	−	0.978480i	$-0.566155\pi$
$13$	−19.3431			−0.412679			−0.206339	+	0.978480i	$0.566155\pi$
$14$		0			0
$15$	−33.2843			−0.572931
$16$	25.8823	−	44.8294i	0.404410	−	0.700459i
$17$	−43.6127	−	75.5394i	−0.622214	−	1.07771i	−0.989073	−	0.147429i	$-0.952900\pi$
$17$	−43.6127	−	75.5394i	−0.622214	−	1.07771i	0.366859	−	0.930277i	$-0.380433\pi$
$18$	−22.3848	−	38.7716i	−0.293119	−	0.507697i
$19$	−22.1127	+	38.3003i	−0.267000	+	0.462458i	−0.968086	−	0.250619i	$-0.919366\pi$
$19$	−22.1127	+	38.3003i	−0.267000	+	0.462458i	0.701086	+	0.713077i	$0.252699\pi$
$20$	−6.56854			−0.0734385
$21$		0			0
$22$	98.9188			0.958617
$23$	−109.083	+	188.938i	−0.988932	+	1.71288i	−0.365973	+	0.930625i	$0.619264\pi$
$23$	−109.083	+	188.938i	−0.988932	+	1.71288i	−0.622959	+	0.782255i	$0.714069\pi$
$24$	−80.1594	−	138.840i	−0.681769	−	1.18086i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	25.0086	−	43.3162i	0.188638	−	0.326731i
$27$	64.4802			0.459601
$28$		0			0
$29$	−46.9411			−0.300578			−0.150289	−	0.988642i	$-0.548020\pi$
$29$	−46.9411			−0.300578			−0.150289	+	0.988642i	$0.548020\pi$
$30$	43.0330	−	74.5354i	0.261891	−	0.453608i
$31$	97.2792	+	168.493i	0.563609	+	0.976199i	0.997178	+	0.0750783i	$0.0239207\pi$
$31$	97.2792	+	168.493i	0.563609	+	0.976199i	−0.433569	+	0.901120i	$0.642746\pi$
$32$	−29.4071	−	50.9345i	−0.162453	−	0.281376i
$33$	127.328	−	220.539i	0.671668	−	1.16336i
$34$	225.546			1.13767
$35$		0			0
$36$	−22.7452			−0.105302
$37$	−183.426	+	317.704i	−0.815003	+	1.41163i	0.0943225	+	0.995542i	$0.469932\pi$
$37$	−183.426	+	317.704i	−0.815003	+	1.41163i	−0.909326	+	0.416085i	$0.863402\pi$
$38$	−57.1787	−	99.0364i	−0.244095	−	0.422785i
$39$	−64.3823	−	111.513i	−0.264344	−	0.457857i
$40$	60.2082	−	104.284i	0.237994	−	0.412217i
$41$	339.362			1.29267			0.646336	−	0.763053i	$-0.276301\pi$
$41$	339.362			1.29267			0.646336	+	0.763053i	$0.276301\pi$
$42$		0			0
$43$	−226.167			−0.802095			−0.401047	−	0.916057i	$-0.631354\pi$
$43$	−226.167			−0.802095			−0.401047	+	0.916057i	$0.631354\pi$
$44$	25.1279	−	43.5227i	0.0860947	−	0.149120i
$45$	−43.2843	−	74.9706i	−0.143388	−	0.248354i
$46$	−282.066	−	488.553i	−0.904095	−	1.56594i
$47$	5.83810	−	10.1119i	0.0181186	−	0.0313823i	−0.856824	−	0.515609i	$-0.827566\pi$
$47$	5.83810	−	10.1119i	0.0181186	−	0.0313823i	0.874943	+	0.484227i	$0.160899\pi$
$48$	344.589			1.03619
$49$		0			0
$50$	64.6447			0.182843
$51$	290.323	−	502.855i	0.797126	−	1.38066i
$52$	−12.7056	−	22.0068i	−0.0338837	−	0.0586883i
$53$	104.510	+	181.016i	0.270859	+	0.469141i	0.969082	−	0.246739i	$-0.0793591\pi$
$53$	104.510	+	181.016i	0.270859	+	0.469141i	−0.698223	+	0.715880i	$0.746026\pi$
$54$	−83.3661	+	144.394i	−0.210087	+	0.363881i
$55$	191.274			0.468935
$56$		0			0
$57$	−294.402			−0.684114
$58$	60.6899	−	105.118i	0.137396	−	0.237977i
$59$	−308.000	−	533.472i	−0.679630	−	1.17715i	−0.975092	−	0.221800i	$-0.928807\pi$
$59$	−308.000	−	533.472i	−0.679630	−	1.17715i	0.295462	−	0.955354i	$-0.404526\pi$
$60$	−21.8629	−	37.8677i	−0.0470415	−	0.0814783i
$61$	160.368	−	277.765i	0.336606	−	0.583018i	−0.647186	−	0.762332i	$-0.724054\pi$
$61$	160.368	−	277.765i	0.336606	−	0.583018i	0.983792	+	0.179314i	$0.0573877\pi$
$62$	−503.087			−1.03052
$63$		0			0
$64$	566.197			1.10585
$65$	48.3579	−	83.7583i	0.0922778	−	0.159830i
$66$	329.244	+	570.268i	0.614048	+	1.06356i
$67$	−7.25483	−	12.5657i	−0.0132286	−	0.0229127i	0.859335	−	0.511413i	$-0.170878\pi$
$67$	−7.25483	−	12.5657i	−0.0132286	−	0.0229127i	−0.872564	+	0.488500i	$0.837544\pi$
$68$	57.2944	−	99.2368i	0.102176	−	0.176974i
$69$	−1452.30			−2.53387
$70$		0			0
$71$	−952.000			−1.59129			−0.795645	−	0.605763i	$-0.792868\pi$
$71$	−952.000			−1.59129			−0.795645	+	0.605763i	$0.792868\pi$
$72$	208.485	−	361.107i	0.341253	−	0.591068i
$73$	412.245	+	714.029i	0.660953	+	1.14480i	0.980366	+	0.197189i	$0.0631812\pi$
$73$	412.245	+	714.029i	0.660953	+	1.14480i	−0.319412	+	0.947616i	$0.603485\pi$
$74$	−474.302	−	821.514i	−0.745087	−	1.29053i
$75$	83.2107	−	144.125i	0.128111	−	0.221895i
$76$	−58.0993			−0.0876901
$77$		0			0
$78$	332.958			0.483334
$79$	−78.1375	+	135.338i	−0.111280	+	0.192743i	−0.916287	−	0.400523i	$-0.868829\pi$
$79$	−78.1375	+	135.338i	−0.111280	+	0.192743i	0.805006	+	0.593266i	$0.202162\pi$
$80$	129.411	+	224.147i	0.180858	+	0.313255i
$81$	448.353	+	776.570i	0.615024	+	1.06525i
$82$	−438.759	+	759.954i	−0.590889	+	1.02345i
$83$	1036.53			1.37077			0.685384	−	0.728182i	$-0.259634\pi$
$83$	1036.53			1.37077			0.685384	+	0.728182i	$0.259634\pi$
$84$		0			0
$85$	436.127			0.556525
$86$	292.409	−	506.468i	0.366643	−	0.635044i
$87$	−156.240	−	270.616i	−0.192537	−	0.333483i
$88$	460.651	+	797.870i	0.558017	+	0.966514i
$89$	−85.1127	+	147.420i	−0.101370	+	0.175578i	−0.912249	−	0.409635i	$-0.865656\pi$
$89$	−85.1127	+	147.420i	−0.101370	+	0.175578i	0.810879	+	0.585213i	$0.198989\pi$
$90$	223.848			0.262174
$91$		0			0
$92$	−286.607			−0.324792
$93$	−647.574	+	1121.63i	−0.722046	+	1.25062i
$94$	15.0961	+	26.1472i	0.0165643	+	0.0286901i
$95$	−110.563	−	191.502i	−0.119406	−	0.206817i
$96$	195.759	−	339.064i	0.208120	−	0.360475i
$97$	−1059.87			−1.10942			−0.554710	−	0.832044i	$-0.687171\pi$
$97$	−1059.87			−1.10942			−0.554710	+	0.832044i	$0.687171\pi$
$98$		0			0
$99$	662.333			0.672394
$100$	16.4214	−	28.4426i	0.0164214	−	0.0284426i
$101$	−120.917	−	209.434i	−0.119125	−	0.206331i	0.800296	−	0.599605i	$-0.204676\pi$
$101$	−120.917	−	209.434i	−0.119125	−	0.206331i	−0.919421	+	0.393274i	$0.871342\pi$
$102$	750.714	+	1300.28i	0.728743	+	1.26222i
$103$	−839.788	+	1454.56i	−0.803367	+	1.39147i	0.114021	+	0.993478i	$0.463627\pi$
$103$	−839.788	+	1454.56i	−0.803367	+	1.39147i	−0.917388	+	0.397994i	$0.869706\pi$
$104$	465.846			0.439230
$105$		0			0
$106$	−540.479			−0.495245
$107$	−753.441	+	1305.00i	−0.680728	+	1.17905i	0.294031	+	0.955796i	$0.405003\pi$
$107$	−753.441	+	1305.00i	−0.680728	+	1.17905i	−0.974759	+	0.223259i	$0.928330\pi$
$108$	42.3541	+	73.3595i	0.0377364	+	0.0653613i
$109$	626.205	+	1084.62i	0.550271	+	0.953097i	0.998255	+	0.0590556i	$0.0188089\pi$
$109$	626.205	+	1084.62i	0.550271	+	0.953097i	−0.447984	+	0.894042i	$0.647858\pi$
$110$	−247.297	+	428.331i	−0.214353	+	0.371271i
$111$	−2442.09			−2.08822
$112$		0			0
$113$	1370.20			1.14069			0.570345	−	0.821405i	$-0.306810\pi$
$113$	1370.20			1.14069			0.570345	+	0.821405i	$0.306810\pi$
$114$	380.630	−	659.271i	0.312713	−	0.541635i
$115$	−545.416	−	944.689i	−0.442264	−	0.766023i
$116$	−30.8335	−	53.4052i	−0.0246795	−	0.0427461i
$117$	167.451	−	290.033i	0.132315	−	0.229176i
$118$	1592.84			1.24265
$119$		0			0
$120$	801.594			0.609793
$121$	−66.2162	+	114.690i	−0.0497492	+	0.0861681i
$122$	414.676	+	718.240i	0.307730	+	0.533003i
$123$	1129.54	+	1956.43i	0.828028	+	1.43419i
$124$	−127.797	+	221.350i	−0.0925522	+	0.160305i
$125$	125.000			0.0894427
$126$		0			0
$127$	1213.49			0.847873			0.423936	−	0.905692i	$-0.360648\pi$
$127$	1213.49			0.847873			0.423936	+	0.905692i	$0.360648\pi$
$128$	−496.775	+	860.440i	−0.343040	+	0.594163i
$129$	−752.779	−	1303.85i	−0.513787	−	0.889905i
$130$	125.043	+	216.581i	0.0843616	+	0.146119i
$131$	−991.209	+	1716.83i	−0.661087	+	1.14504i	0.319244	+	0.947673i	$0.396571\pi$
$131$	−991.209	+	1716.83i	−0.661087	+	1.14504i	−0.980330	+	0.197363i	$0.936762\pi$
$132$	334.545			0.220594
$133$		0			0
$134$	37.5189			0.0241876
$135$	−161.201	+	279.208i	−0.102770	+	0.178003i
$136$	1050.34	+	1819.24i	0.662247	+	1.14705i
$137$	−1105.47	−	1914.74i	−0.689394	−	1.19407i	−0.972034	−	0.234840i	$-0.924543\pi$
$137$	−1105.47	−	1914.74i	−0.689394	−	1.19407i	0.282640	−	0.959226i	$-0.408790\pi$
$138$	1877.67	−	3252.22i	1.15825	−	2.00614i
$139$	−528.039			−0.322213			−0.161107	−	0.986937i	$-0.551506\pi$
$139$	−528.039			−0.322213			−0.161107	+	0.986937i	$0.551506\pi$
$140$		0			0
$141$	77.7267			0.0464239
$142$	1230.83	−	2131.87i	0.727390	−	1.25988i
$143$	369.984	+	640.832i	0.216361	+	0.374749i
$144$	448.118	+	776.163i	0.259327	+	0.449168i
$145$	117.353	−	203.261i	0.0672112	−	0.116413i
$146$	−2131.95			−1.20851
$147$		0			0
$148$	−481.938			−0.267669
$149$	164.186	−	284.378i	0.0902727	−	0.156357i	−0.817353	−	0.576137i	$-0.804559\pi$
$149$	164.186	−	284.378i	0.0902727	−	0.156357i	0.907626	+	0.419780i	$0.137893\pi$
$150$	215.165	+	372.677i	0.117121	+	0.202860i
$151$	−514.714	−	891.512i	−0.277396	−	0.480465i	0.693340	−	0.720610i	$-0.256138\pi$
$151$	−514.714	−	891.512i	−0.277396	−	0.480465i	−0.970737	+	0.240145i	$0.922805\pi$
$152$	532.546	−	922.397i	0.284179	−	0.492212i
$153$	1510.20			0.797987
$154$		0			0
$155$	−972.792			−0.504107
$156$	84.5795	−	146.496i	0.0434088	−	0.0751863i
$157$	262.549	+	454.749i	0.133463	+	0.231165i	0.925009	−	0.379944i	$-0.124057\pi$
$157$	262.549	+	454.749i	0.133463	+	0.231165i	−0.791546	+	0.611109i	$0.790724\pi$
$158$	−202.047	−	349.956i	−0.101734	−	0.176209i
$159$	−695.706	+	1205.00i	−0.347000	+	0.601022i
$160$	294.071			0.145302
$161$		0			0
$162$	−2318.69			−1.12453
$163$	−501.313	+	868.299i	−0.240895	+	0.417242i	−0.960969	−	0.276655i	$-0.910774\pi$
$163$	−501.313	+	868.299i	−0.240895	+	0.417242i	0.720075	+	0.693897i	$0.244108\pi$
$164$	222.912	+	386.094i	0.106137	+	0.183835i
$165$	636.642	+	1102.70i	0.300379	+	0.520272i
$166$	−1340.12	+	2321.16i	−0.626587	+	1.08528i
$167$	359.422			0.166544			0.0832722	−	0.996527i	$-0.473463\pi$
$167$	359.422			0.166544			0.0832722	+	0.996527i	$0.473463\pi$
$168$		0			0
$169$	−1822.84			−0.829696
$170$	−563.866	+	976.644i	−0.254391	+	0.440619i
$171$	−382.853	−	663.121i	−0.171213	−	0.296550i
$172$	−148.558	−	257.311i	−0.0658574	−	0.114068i
$173$	1646.83	−	2852.39i	0.723733	−	1.25354i	−0.235760	−	0.971811i	$-0.575758\pi$
$173$	1646.83	−	2852.39i	0.723733	−	1.25354i	0.959493	−	0.281732i	$-0.0909088\pi$
$174$	808.007			0.352039
$175$		0			0
$176$	−1980.24			−0.848104
$177$	2050.31	−	3551.24i	0.870683	−	1.50807i
$178$	−220.083	−	381.195i	−0.0926738	−	0.160516i
$179$	−1489.41	−	2579.74i	−0.621921	−	1.07720i	−0.989128	−	0.147059i	$-0.953019\pi$
$179$	−1489.41	−	2579.74i	−0.621921	−	1.07720i	0.367207	−	0.930139i	$-0.380314\pi$
$180$	56.8629	−	98.4895i	0.0235462	−	0.0407832i
$181$	−1462.31			−0.600514			−0.300257	−	0.953858i	$-0.597072\pi$
$181$	−1462.31			−0.600514			−0.300257	+	0.953858i	$0.597072\pi$
$182$		0			0
$183$	2135.09			0.862460
$184$	2627.08	−	4550.24i	1.05256	−	1.82309i
$185$	−917.132	−	1588.52i	−0.364480	−	0.631299i
$186$	−1674.49	−	2900.30i	−0.660104	−	1.14333i
$187$	−1668.40	+	2889.75i	−0.652434	+	1.13005i
$188$	15.3391			0.00595064
$189$		0			0
$190$	571.787			0.218325
$191$	187.461	−	324.693i	0.0710169	−	0.123005i	−0.828330	−	0.560240i	$-0.810709\pi$
$191$	187.461	−	324.693i	0.0710169	−	0.123005i	0.899347	+	0.437235i	$0.144042\pi$
$192$	1884.54	+	3264.13i	0.708361	+	1.22692i
$193$	−366.514	−	634.821i	−0.136696	−	0.236764i	0.789548	−	0.613688i	$-0.210315\pi$
$193$	−366.514	−	634.821i	−0.136696	−	0.236764i	−0.926244	+	0.376925i	$0.876982\pi$
$194$	1370.30	−	2373.43i	0.507124	−	0.878364i
$195$	643.823			0.236436
$196$		0			0
$197$	−2093.24			−0.757043			−0.378521	−	0.925593i	$-0.623567\pi$
$197$	−2093.24			−0.757043			−0.378521	+	0.925593i	$0.623567\pi$
$198$	−856.326	+	1483.20i	−0.307356	+	0.532356i
$199$	1432.52	+	2481.20i	0.510295	+	0.883856i	0.999929	+	0.0119283i	$0.00379699\pi$
$199$	1432.52	+	2481.20i	0.510295	+	0.883856i	−0.489634	+	0.871928i	$0.662870\pi$
$200$	301.041	+	521.418i	0.106434	+	0.184349i
$201$	48.2944	−	83.6483i	0.0169474	−	0.0293537i
$202$	625.330			0.217812
$203$		0			0
$204$	762.801			0.261798
$205$	−848.406	+	1469.48i	−0.289050	+	0.500649i
$206$	−2171.51	−	3761.17i	−0.734449	−	1.27210i
$207$	−1888.64	−	3271.21i	−0.634151	−	1.09838i
$208$	−500.644	+	867.141i	−0.166891	+	0.289065i
$209$	1691.84			0.559936
$210$		0			0
$211$	5643.65			1.84135			0.920674	−	0.390331i	$-0.127640\pi$
$211$	5643.65			1.84135			0.920674	+	0.390331i	$0.127640\pi$
$212$	−137.295	+	237.802i	−0.0444787	+	0.0770393i
$213$	−3168.66	−	5488.28i	−1.01931	−	1.76550i
$214$	−1948.24	−	3374.44i	−0.622330	−	1.07791i
$215$	565.416	−	979.330i	0.179354	−	0.310650i
$216$	−1552.89			−0.489172
$217$		0			0
$218$	−3238.46			−1.00613
$219$	−2744.25	+	4753.19i	−0.846755	+	1.46662i
$220$	125.639	+	217.614i	0.0385027	+	0.0666887i
$221$	843.607	+	1461.17i	0.256774	+	0.444746i
$222$	3157.36	−	5468.70i	0.954540	−	1.65331i
$223$	6369.16			1.91260			0.956302	−	0.292381i	$-0.0944477\pi$
$223$	6369.16			1.91260			0.956302	+	0.292381i	$0.0944477\pi$
$224$		0			0
$225$	432.843			0.128250
$226$	−1771.53	+	3068.37i	−0.521417	+	0.903120i
$227$	−507.837	−	879.600i	−0.148486	−	0.257185i	0.782182	−	0.623050i	$-0.214107\pi$
$227$	−507.837	−	879.600i	−0.148486	−	0.257185i	−0.930668	+	0.365865i	$0.880773\pi$
$228$	−193.379	−	334.943i	−0.0561704	−	0.0972900i
$229$	2054.18	−	3557.94i	0.592768	−	1.02670i	−0.401090	−	0.916039i	$-0.631368\pi$
$229$	2054.18	−	3557.94i	0.592768	−	1.02670i	0.993858	−	0.110665i	$-0.0352982\pi$
$230$	2820.66			0.808647
$231$		0			0
$232$	1130.50			0.319917
$233$	−304.215	+	526.916i	−0.0855357	+	0.148152i	−0.905619	−	0.424092i	$-0.860593\pi$
$233$	−304.215	+	526.916i	−0.0855357	+	0.148152i	0.820084	+	0.572244i	$0.193927\pi$
$234$	432.992	+	749.964i	0.120964	+	0.209516i
$235$	29.1905	+	50.5594i	0.00810288	+	0.0140346i
$236$	404.622	−	700.826i	0.111605	−	0.193305i
$237$	−1040.30			−0.285126
$238$		0			0
$239$	−5054.44			−1.36797			−0.683985	−	0.729496i	$-0.739755\pi$
$239$	−5054.44			−1.36797			−0.683985	+	0.729496i	$0.739755\pi$
$240$	−861.472	+	1492.11i	−0.231699	+	0.401315i
$241$	2.43391	+	4.21565i	0.000650547	+	0.00112678i	0.866350	−	0.499437i	$-0.166460\pi$
$241$	2.43391	+	4.21565i	0.000650547	+	0.00112678i	−0.865700	+	0.500563i	$0.833126\pi$
$242$	−171.221	−	296.563i	−0.0454814	−	0.0787761i
$243$	−2114.14	+	3661.79i	−0.558115	+	0.966683i
$244$	421.352			0.110551
$245$		0			0
$246$	−5841.52			−1.51399
$247$	427.729	−	740.849i	0.110185	−	0.190846i
$248$	−2342.80	−	4057.85i	−0.599871	−	1.03901i
$249$	3450.01	+	5975.59i	0.878054	+	1.52083i
$250$	−161.612	+	279.920i	−0.0408849	+	0.0708147i
$251$	547.921			0.137787			0.0688934	−	0.997624i	$-0.478053\pi$
$251$	547.921			0.137787			0.0688934	+	0.997624i	$0.478053\pi$
$252$		0			0
$253$	8345.92			2.07393
$254$	−1568.91	+	2717.44i	−0.387568	+	0.671288i
$255$	1451.62	+	2514.27i	0.356485	+	0.617451i
$256$	980.232	+	1697.81i	0.239314	+	0.414505i
$257$	−887.306	+	1536.86i	−0.215364	+	0.373022i	−0.953385	−	0.301756i	$-0.902427\pi$
$257$	−887.306	+	1536.86i	−0.215364	+	0.373022i	0.738021	+	0.674778i	$0.235761\pi$
$258$	3893.05			0.939421
$259$		0			0
$260$	127.056			0.0303065
$261$	406.362	−	703.840i	0.0963724	−	0.166922i
$262$	−2563.06	−	4439.34i	−0.604374	−	1.04681i
$263$	599.547	+	1038.45i	0.140569	+	0.243473i	0.927711	−	0.373299i	$-0.121774\pi$
$263$	599.547	+	1038.45i	0.140569	+	0.243473i	−0.787142	+	0.616772i	$0.788440\pi$
$264$	−3066.48	+	5311.31i	−0.714883	+	1.23821i
$265$	−1045.10			−0.242263
$266$		0			0
$267$	−1133.17			−0.259733
$268$	9.53074	−	16.5077i	0.00217232	−	0.00376257i
$269$	1625.15	+	2814.84i	0.368353	+	0.638006i	0.989308	−	0.145840i	$-0.0465885\pi$
$269$	1625.15	+	2814.84i	0.368353	+	0.638006i	−0.620955	+	0.783846i	$0.713255\pi$
$270$	−416.830	−	721.971i	−0.0939536	−	0.162732i
$271$	−448.071	+	776.082i	−0.100437	+	0.173962i	−0.911865	−	0.410491i	$-0.865357\pi$
$271$	−448.071	+	776.082i	−0.100437	+	0.173962i	0.811428	+	0.584453i	$0.198691\pi$
$272$	−4515.18			−1.00652
$273$		0			0
$274$	5717.04			1.26051
$275$	−478.185	+	828.241i	−0.104857	+	0.181618i
$276$	−953.951	−	1652.29i	−0.208048	−	0.360349i
$277$	193.281	+	334.772i	0.0419246	+	0.0726156i	0.886226	−	0.463253i	$-0.153318\pi$
$277$	193.281	+	334.772i	0.0419246	+	0.0726156i	−0.844302	+	0.535868i	$0.819984\pi$
$278$	682.698	−	1182.47i	0.147286	−	0.255107i
$279$	−3368.53			−0.722826
$280$		0			0
$281$	−3335.10			−0.708025			−0.354013	−	0.935241i	$-0.615183\pi$
$281$	−3335.10			−0.708025			−0.354013	+	0.935241i	$0.615183\pi$
$282$	−100.492	+	174.058i	−0.0212207	+	0.0367553i
$283$	2706.13	+	4687.15i	0.568419	+	0.984531i	0.996723	+	0.0808959i	$0.0257781\pi$
$283$	2706.13	+	4687.15i	0.568419	+	0.984531i	−0.428303	+	0.903635i	$0.640889\pi$
$284$	−625.325	−	1083.10i	−0.130656	−	0.226302i
$285$	736.005	−	1274.80i	0.152973	−	0.264956i
$286$	−1913.40			−0.395601
$287$		0			0
$288$	1018.29			0.208345
$289$	−1347.63	+	2334.17i	−0.274300	+	0.475101i
$290$	303.449	+	525.590i	0.0614454	+	0.106427i
$291$	−3527.71	−	6110.17i	−0.710646	−	1.23088i
$292$	−541.569	+	938.026i	−0.108538	+	0.187992i
$293$	−282.211			−0.0562695			−0.0281347	−	0.999604i	$-0.508957\pi$
$293$	−282.211			−0.0562695			−0.0281347	+	0.999604i	$0.508957\pi$
$294$		0			0
$295$	3080.00			0.607880
$296$	4417.51	−	7651.34i	0.867440	−	1.50245i
$297$	−1233.34	−	2136.21i	−0.240962	−	0.417358i
$298$	424.550	+	735.341i	0.0825285	+	0.142944i
$299$	2110.01	−	3654.65i	0.408111	−	0.706869i
$300$	218.629			0.0420752
$301$		0			0
$302$	2661.88			0.507199
$303$	804.925	−	1394.17i	0.152613	−	0.264333i
$304$	1144.65	+	1982.60i	0.215955	+	0.374045i
$305$	801.838	+	1388.82i	0.150535	+	0.260734i
$306$	−1952.52	+	3381.87i	−0.364765	+	0.631792i
$307$	−1919.67			−0.356878			−0.178439	−	0.983951i	$-0.557105\pi$
$307$	−1919.67			−0.356878			−0.178439	+	0.983951i	$0.557105\pi$
$308$		0			0
$309$	−11180.7			−2.05841
$310$	1257.72	−	2178.43i	0.230431	−	0.399118i
$311$	606.654	+	1050.76i	0.110612	+	0.191585i	0.916017	−	0.401139i	$-0.131386\pi$
$311$	606.654	+	1050.76i	0.110612	+	0.191585i	−0.805405	+	0.592724i	$0.798052\pi$
$312$	1550.53	+	2685.60i	0.281352	+	0.487315i
$313$	−717.001	+	1241.88i	−0.129480	+	0.224266i	−0.923475	−	0.383658i	$-0.874664\pi$
$313$	−717.001	+	1241.88i	−0.129480	+	0.224266i	0.793995	+	0.607924i	$0.207998\pi$
$314$	−1357.79			−0.244028
$315$		0			0
$316$	−205.300			−0.0365475
$317$	−3248.48	+	5626.52i	−0.575560	+	0.996899i	0.420420	+	0.907329i	$0.361883\pi$
$317$	−3248.48	+	5626.52i	−0.575560	+	0.996899i	−0.995981	+	0.0895699i	$0.971451\pi$
$318$	−1798.95	−	3115.87i	−0.317232	−	0.549463i
$319$	897.862	+	1555.14i	0.157588	+	0.272951i
$320$	−1415.49	+	2451.70i	−0.247276	+	0.428295i
$321$	−10031.1			−1.74418
$322$		0			0
$323$	3857.58			0.664524
$324$	−589.005	+	1020.19i	−0.100995	+	0.174929i
$325$	241.789	+	418.791i	0.0412679	+	0.0714781i
$326$	−1296.29	−	2245.24i	−0.220229	−	0.381448i
$327$	−4168.55	+	7220.15i	−0.704959	+	1.22102i
$328$	−8172.96			−1.37584
$329$		0			0
$330$	−3292.44			−0.549221
$331$	4841.94	−	8386.49i	0.804039	−	1.39264i	−0.112898	−	0.993607i	$-0.536013\pi$
$331$	4841.94	−	8386.49i	0.804039	−	1.39264i	0.916938	−	0.399031i	$-0.130653\pi$
$332$	680.848	+	1179.26i	0.112549	+	0.194941i
$333$	−3175.79	−	5500.63i	−0.522619	−	0.905204i
$334$	−464.695	+	804.875i	−0.0761286	+	0.131859i
$335$	72.5483			0.0118321
$336$		0			0
$337$	29.1319			0.00470895			0.00235447	−	0.999997i	$-0.499251\pi$
$337$	29.1319			0.00470895			0.00235447	+	0.999997i	$0.499251\pi$
$338$	2356.74	−	4082.00i	0.379260	−	0.656897i
$339$	4560.62	+	7899.23i	0.730676	+	1.26557i
$340$	286.472	+	496.184i	0.0456945	+	0.0791451i
$341$	3721.40	−	6445.65i	0.590983	−	1.02361i
$342$	1979.95			0.313051
$343$		0			0
$344$	5446.83			0.853701
$345$	3630.76	−	6288.66i	0.566590	−	0.981362i
$346$	4258.34	+	7375.66i	0.661647	+	1.14601i
$347$	3924.29	+	6797.07i	0.607110	+	1.05154i	0.991714	+	0.128463i	$0.0410045\pi$
$347$	3924.29	+	6797.07i	0.607110	+	1.05154i	−0.384605	+	0.923081i	$0.625662\pi$
$348$	205.254	−	355.510i	0.0316171	−	0.0547625i
$349$	10269.6			1.57513			0.787567	−	0.616229i	$-0.211341\pi$
$349$	10269.6			1.57513			0.787567	+	0.616229i	$0.211341\pi$
$350$		0			0
$351$	−1247.25			−0.189668
$352$	−1124.96	+	1948.49i	−0.170343	+	0.295043i
$353$	1399.97	+	2424.81i	0.211084	+	0.365609i	0.952054	−	0.305930i	$-0.0989672\pi$
$353$	1399.97	+	2424.81i	0.211084	+	0.365609i	−0.740970	+	0.671538i	$0.765634\pi$
$354$	5301.67	+	9182.76i	0.795990	+	1.37869i
$355$	2380.00	−	4122.28i	0.355823	−	0.616304i
$356$	−223.627			−0.0332927
$357$		0			0
$358$	7702.60			1.13714
$359$	1581.65	−	2739.49i	0.232524	−	0.402743i	−0.726026	−	0.687667i	$-0.758635\pi$
$359$	1581.65	−	2739.49i	0.232524	−	0.402743i	0.958550	+	0.284924i	$0.0919683\pi$
$360$	1042.43	+	1805.54i	0.152613	+	0.264334i
$361$	2451.56	+	4246.22i	0.357422	+	0.619073i
$362$	1890.62	−	3274.64i	0.274499	−	0.475446i
$363$	−881.583			−0.127469
$364$		0			0
$365$	−4122.45			−0.591175
$366$	−2760.44	+	4781.22i	−0.394236	+	0.682837i
$367$	1591.42	+	2756.42i	0.226353	+	0.392055i	0.956725	−	0.290995i	$-0.0939864\pi$
$367$	1591.42	+	2756.42i	0.226353	+	0.392055i	−0.730371	+	0.683050i	$0.760653\pi$
$368$	5646.64	+	9780.27i	0.799868	+	1.38541i
$369$	−2937.81	+	5088.44i	−0.414462	+	0.717869i
$370$	4743.02			0.666426
$371$		0			0
$372$	−1701.45			−0.237139
$373$	1307.57	−	2264.78i	0.181510	−	0.314385i	−0.760885	−	0.648887i	$-0.775235\pi$
$373$	1307.57	−	2264.78i	0.181510	−	0.314385i	0.942395	+	0.334502i	$0.108568\pi$
$374$	−4314.12	−	7472.27i	−0.596464	−	1.03311i
$375$	416.053	+	720.626i	0.0572931	+	0.0992345i
$376$	−140.600	+	243.527i	−0.0192843	+	0.0334015i
$377$	907.989			0.124042
$378$		0			0
$379$	−672.434			−0.0911362			−0.0455681	−	0.998961i	$-0.514510\pi$
$379$	−672.434			−0.0911362			−0.0455681	+	0.998961i	$0.514510\pi$
$380$	145.248	−	251.577i	0.0196081	−	0.0339622i
$381$	4039.01	+	6995.78i	0.543110	+	0.940694i
$382$	484.735	+	839.586i	0.0649246	+	0.112453i
$383$	584.928	−	1013.13i	0.0780377	−	0.135165i	−0.824366	−	0.566058i	$-0.808468\pi$
$383$	584.928	−	1013.13i	0.0780377	−	0.135165i	0.902403	+	0.430893i	$0.141801\pi$
$384$	−6613.92			−0.878946
$385$		0			0
$386$	1895.45			0.249938
$387$	1957.89	−	3391.17i	0.257171	−	0.445433i
$388$	−696.182	−	1205.82i	−0.0910910	−	0.157774i
$389$	561.110	+	971.871i	0.0731347	+	0.126673i	0.900274	−	0.435325i	$-0.143366\pi$
$389$	561.110	+	971.871i	0.0731347	+	0.126673i	−0.827139	+	0.561998i	$0.810033\pi$
$390$	−832.394	+	1441.75i	−0.108077	+	0.187194i
$391$	19029.7			2.46131
$392$		0			0
$393$	−13196.7			−1.69385
$394$	2706.34	−	4687.52i	0.346049	−	0.599375i
$395$	−390.688	−	676.691i	−0.0497661	−	0.0861975i
$396$	435.056	+	753.540i	0.0552081	+	0.0956232i
$397$	−992.963	+	1719.86i	−0.125530	+	0.217424i	−0.921940	−	0.387333i	$-0.873396\pi$
$397$	−992.963	+	1719.86i	−0.125530	+	0.217424i	0.796410	+	0.604757i	$0.206730\pi$
$398$	−7408.38			−0.933037
$399$		0			0
$400$	−1294.11			−0.161764
$401$	2086.19	−	3613.38i	0.259799	−	0.449984i	−0.706389	−	0.707824i	$-0.749677\pi$
$401$	2086.19	−	3613.38i	0.259799	−	0.449984i	0.966188	+	0.257839i	$0.0830105\pi$
$402$	124.879	+	216.297i	0.0154935	+	0.0268356i
$403$	−1881.69	−	3259.18i	−0.232589	−	0.402856i
$404$	158.849	−	275.135i	0.0195620	−	0.0338824i
$405$	−4483.53			−0.550095
$406$		0			0
$407$	14033.9			1.70918
$408$	−6991.93	+	12110.4i	−0.848412	+	1.46949i
$409$	−5850.40	−	10133.2i	−0.707295	−	1.22507i	−0.965857	−	0.259076i	$-0.916582\pi$
$409$	−5850.40	−	10133.2i	−0.707295	−	1.22507i	0.258562	−	0.965995i	$-0.416751\pi$
$410$	−2193.80	−	3799.77i	−0.264253	−	0.457700i
$411$	7358.98	−	12746.1i	0.883192	−	1.52973i
$412$	−2206.47			−0.263848
$413$		0			0
$414$	9767.22			1.15950
$415$	−2591.32	+	4488.30i	−0.306513	+	0.530896i
$416$	568.825	+	985.234i	0.0670408	+	0.116118i
$417$	−1757.54	−	3044.15i	−0.206396	−	0.357488i
$418$	−2187.36	+	3788.62i	−0.255951	+	0.443320i
$419$	−2733.20			−0.318677			−0.159339	−	0.987224i	$-0.550936\pi$
$419$	−2733.20			−0.318677			−0.159339	+	0.987224i	$0.550936\pi$
$420$		0			0
$421$	13549.4			1.56854			0.784272	−	0.620417i	$-0.213037\pi$
$421$	13549.4			1.56854			0.784272	+	0.620417i	$0.213037\pi$
$422$	−7296.63	+	12638.1i	−0.841693	+	1.45786i
$423$	101.079	+	175.074i	0.0116185	+	0.0201239i
$424$	−2516.93	−	4359.46i	−0.288286	−	0.499325i
$425$	−1090.32	+	1888.49i	−0.124443	+	0.215541i
$426$	16387.0			1.86374
$427$		0			0
$428$	−1979.60			−0.223569
$429$	−2462.93	+	4265.92i	−0.277183	+	0.480095i
$430$	1462.05	+	2532.34i	0.163968	+	0.284000i
$431$	3214.63	+	5567.90i	0.359265	+	0.622265i	0.987838	−	0.155485i	$-0.0496942\pi$
$431$	3214.63	+	5567.90i	0.359265	+	0.622265i	−0.628573	+	0.777750i	$0.716361\pi$
$432$	1668.89	−	2890.61i	0.185867	−	0.321932i
$433$	−8022.03			−0.890333			−0.445166	−	0.895448i	$-0.646855\pi$
$433$	−8022.03			−0.890333			−0.445166	+	0.895448i	$0.646855\pi$
$434$		0			0
$435$	1562.40			0.172210
$436$	−822.651	+	1424.87i	−0.0903620	+	0.156512i
$437$	−4824.25	−	8355.85i	−0.528090	−	0.914678i
$438$	−7096.05	−	12290.7i	−0.774115	−	1.34081i
$439$	−2784.94	+	4823.66i	−0.302774	+	0.524421i	−0.976763	−	0.214321i	$-0.931246\pi$
$439$	−2784.94	+	4823.66i	−0.302774	+	0.524421i	0.673989	+	0.738741i	$0.264580\pi$
$440$	−4606.51			−0.499106
$441$		0			0
$442$	−4362.77			−0.469493
$443$	2743.11	−	4751.20i	0.294196	−	0.509563i	−0.680601	−	0.732654i	$-0.738281\pi$
$443$	2743.11	−	4751.20i	0.294196	−	0.509563i	0.974798	+	0.223091i	$0.0716148\pi$
$444$	−1604.09	−	2778.37i	−0.171457	−	0.296972i
$445$	−425.563	−	737.098i	−0.0453340	−	0.0785208i
$446$	−8234.65	+	14262.8i	−0.874264	+	1.51427i
$447$	2185.92			0.231299
$448$		0			0
$449$	−7232.67			−0.760203			−0.380101	−	0.924945i	$-0.624111\pi$
$449$	−7232.67			−0.760203			−0.380101	+	0.924945i	$0.624111\pi$
$450$	−559.619	+	969.289i	−0.0586238	+	0.101539i
$451$	−6491.13	−	11243.0i	−0.677728	−	1.17386i
$452$	900.024	+	1558.89i	0.0936583	+	0.162221i
$453$	3426.38	−	5934.66i	0.355376	−	0.615529i
$454$	2626.32			0.271496
$455$		0			0
$456$	7090.16			0.728130
$457$	1450.25	−	2511.91i	0.148446	−	0.257117i	−0.782207	−	0.623019i	$-0.785906\pi$
$457$	1450.25	−	2511.91i	0.148446	−	0.257117i	0.930653	+	0.365902i	$0.119239\pi$
$458$	5311.66	+	9200.07i	0.541916	+	0.938627i
$459$	−2812.16	−	4870.80i	−0.285970	−	0.495315i
$460$	716.518	−	1241.05i	0.0726257	−	0.125791i
$461$	−6073.57			−0.613611			−0.306805	−	0.951772i	$-0.599260\pi$
$461$	−6073.57			−0.613611			−0.306805	+	0.951772i	$0.599260\pi$
$462$		0			0
$463$	−18922.8			−1.89939			−0.949693	−	0.313183i	$-0.898605\pi$
$463$	−18922.8			−1.89939			−0.949693	+	0.313183i	$0.898605\pi$
$464$	−1214.94	+	2104.34i	−0.121557	+	0.210542i
$465$	−3237.87	−	5608.15i	−0.322909	−	0.559294i
$466$	−786.636	−	1362.49i	−0.0781979	−	0.135443i
$467$	−3388.35	+	5868.80i	−0.335748	+	0.581532i	−0.983628	−	0.180210i	$-0.942322\pi$
$467$	−3388.35	+	5868.80i	−0.335748	+	0.581532i	0.647880	+	0.761742i	$0.275656\pi$
$468$	439.963			0.0434558
$469$		0			0
$470$	−150.961			−0.0148155
$471$	−1747.75	+	3027.19i	−0.170981	+	0.296148i
$472$	7417.64	+	12847.7i	0.723358	+	1.25289i
$473$	4325.98	+	7492.82i	0.420526	+	0.728373i
$474$	1345.00	−	2329.60i	0.130333	−	0.225743i
$475$	1105.63			0.106800
$476$		0			0
$477$	−3618.90			−0.347375
$478$	6534.86	−	11318.7i	0.625308	−	1.08307i
$479$	1198.66	+	2076.14i	0.114338	+	0.198040i	0.917515	−	0.397701i	$-0.130192\pi$
$479$	1198.66	+	2076.14i	0.114338	+	0.198040i	−0.803177	+	0.595741i	$0.796859\pi$
$480$	978.793	+	1695.32i	0.0930741	+	0.161209i
$481$	3548.04	−	6145.39i	0.336334	−	0.582548i
$482$	−12.5871			−0.00118948
$483$		0			0
$484$	−173.977			−0.0163390
$485$	2649.68	−	4589.38i	0.248074	−	0.429677i
$486$	−5466.70	−	9468.61i	−0.510236	−	0.883755i
$487$	−2793.08	−	4837.76i	−0.259890	−	0.450143i	0.706322	−	0.707891i	$-0.250353\pi$
$487$	−2793.08	−	4837.76i	−0.259890	−	0.450143i	−0.966212	+	0.257747i	$0.917020\pi$
$488$	−3862.17	+	6689.48i	−0.358263	+	0.620530i
$489$	−6674.33			−0.617227
$490$		0			0
$491$	537.392			0.0493934			0.0246967	−	0.999695i	$-0.492138\pi$
$491$	537.392			0.0493934			0.0246967	+	0.999695i	$0.492138\pi$
$492$	−1483.89	+	2570.17i	−0.135973	+	0.235513i
$493$	2047.23	+	3545.90i	0.187023	+	0.323934i
$494$	1106.02	+	1915.68i	0.100733	+	0.174474i
$495$	−1655.83	+	2867.99i	−0.150352	+	0.260417i
$496$	10071.2			0.911716
$497$		0			0
$498$	−17842.0			−1.60546
$499$	−299.482	+	518.719i	−0.0268671	+	0.0465351i	−0.879146	−	0.476552i	$-0.841886\pi$
$499$	−299.482	+	518.719i	−0.0268671	+	0.0465351i	0.852279	+	0.523087i	$0.175220\pi$
$500$	82.1068	+	142.213i	0.00734385	+	0.0127199i
$501$	1196.31	+	2072.07i	0.106681	+	0.184777i
$502$	−708.403	+	1226.99i	−0.0629832	+	0.109090i
$503$	−4426.76			−0.392405			−0.196202	−	0.980563i	$-0.562861\pi$
$503$	−4426.76			−0.392405			−0.196202	+	0.980563i	$0.562861\pi$
$504$		0			0
$505$	1209.17			0.106549
$506$	−10790.4	+	18689.5i	−0.948006	+	1.64200i
$507$	−6067.20	−	10508.7i	−0.531467	−	0.920528i
$508$	797.086	+	1380.59i	0.0696161	+	0.120579i
$509$	8863.84	−	15352.6i	0.771872	−	1.33692i	−0.164665	−	0.986350i	$-0.552654\pi$
$509$	8863.84	−	15352.6i	0.771872	−	1.33692i	0.936536	−	0.350571i	$-0.114013\pi$
$510$	−7507.14			−0.651808
$511$		0			0
$512$	−13017.7			−1.12365
$513$	−1425.83	+	2469.61i	−0.122713	+	0.212546i
$514$	−2294.38	−	3973.99i	−0.196889	−	0.341022i
$515$	−4198.94	−	7272.78i	−0.359277	−	0.622286i
$516$	988.932	−	1712.88i	0.0843707	−	0.146134i
$517$	−446.671			−0.0379972
$518$		0			0
$519$	21925.4			1.85437
$520$	−1164.62	+	2017.17i	−0.0982149	+	0.170113i
$521$	4331.40	+	7502.20i	0.364226	+	0.630858i	0.988652	−	0.150226i	$-0.0480001\pi$
$521$	4331.40	+	7502.20i	0.364226	+	0.630858i	−0.624425	+	0.781084i	$0.714667\pi$
$522$	1050.77	+	1819.98i	0.0881050	+	0.152602i
$523$	−3885.20	+	6729.36i	−0.324833	+	0.562628i	−0.981479	−	0.191572i	$-0.938642\pi$
$523$	−3885.20	+	6729.36i	−0.324833	+	0.562628i	0.656645	+	0.754200i	$0.271975\pi$
$524$	−2604.32			−0.217119
$525$		0			0
$526$	−3100.60			−0.257020
$527$	8485.22	−	14696.8i	0.701370	−	1.21481i
$528$	−6591.09	−	11416.1i	−0.543259	−	0.940951i
$529$	−17714.8	−	30683.0i	−1.45597	−	2.52182i
$530$	1351.20	−	2340.34i	0.110740	−	0.191808i
$531$	10665.2			0.871624
$532$		0			0
$533$	−6564.34			−0.533458
$534$	1465.06	−	2537.56i	0.118726	−	0.205639i
$535$	−3767.20	−	6524.99i	−0.304431	−	0.527289i
$536$	174.720	+	302.624i	0.0140798	+	0.0243869i
$537$	9914.79	−	17172.9i	0.796750	−	1.38001i
$538$	−8404.56			−0.673506
$539$		0			0
$540$	−423.541			−0.0337524
$541$	−10820.5	+	18741.6i	−0.859906	+	1.48940i	0.0121123	+	0.999927i	$0.496144\pi$
$541$	−10820.5	+	18741.6i	−0.859906	+	1.48940i	−0.872018	+	0.489474i	$0.837189\pi$
$542$	−1158.62	−	2006.78i	−0.0918208	−	0.159038i
$543$	−4867.21	−	8430.25i	−0.384663	−	0.666255i
$544$	−2565.04	+	4442.79i	−0.202161	+	0.350152i
$545$	−6262.05			−0.492177
$546$		0			0
$547$	7489.29			0.585409			0.292705	−	0.956203i	$-0.405445\pi$
$547$	7489.29			0.585409			0.292705	+	0.956203i	$0.405445\pi$
$548$	1452.27	−	2515.41i	0.113208	−	0.196082i
$549$	2776.56	+	4809.14i	0.215848	+	0.373860i
$550$	−1236.49	−	2141.66i	−0.0958617	−	0.166037i
$551$	1037.99	−	1797.86i	0.0802542	−	0.139004i
$552$	34976.2			2.69689
$553$		0			0
$554$	−999.566			−0.0766561
$555$	6105.21	−	10574.5i	0.466940	−	0.808764i
$556$	−346.844	−	600.752i	−0.0264559	−	0.0458230i
$557$	−12648.9	−	21908.6i	−0.962214	−	1.66660i	−0.716921	−	0.697154i	$-0.754449\pi$
$557$	−12648.9	−	21908.6i	−0.962214	−	1.66660i	−0.245293	−	0.969449i	$-0.578884\pi$
$558$	4355.15	−	7543.34i	0.330409	−	0.572285i
$559$	4374.77			0.331007
$560$		0			0
$561$	−22212.5			−1.67168
$562$	4311.92	−	7468.47i	0.323643	−	0.560566i
$563$	7830.65	+	13563.1i	0.586186	+	1.01530i	0.994726	+	0.102563i	$0.0327044\pi$
$563$	7830.65	+	13563.1i	0.586186	+	1.01530i	−0.408541	+	0.912740i	$0.633962\pi$
$564$	51.0551	+	88.4300i	0.00381172	+	0.00660209i
$565$	−3425.51	+	5933.16i	−0.255066	+	0.441787i
$566$	−13994.9			−1.03931
$567$		0			0
$568$	22927.3			1.69367
$569$	4991.37	−	8645.31i	0.367749	−	0.636960i	−0.621464	−	0.783443i	$-0.713462\pi$
$569$	4991.37	−	8645.31i	0.367749	−	0.636960i	0.989213	+	0.146482i	$0.0467952\pi$
$570$	1903.15	+	3296.36i	0.139850	+	0.242227i
$571$	5791.81	+	10031.7i	0.424483	+	0.735226i	0.996372	−	0.0851049i	$-0.0271226\pi$
$571$	5791.81	+	10031.7i	0.424483	+	0.735226i	−0.571889	+	0.820331i	$0.693789\pi$
$572$	−486.052	+	841.866i	−0.0355294	+	0.0615388i
$573$	2495.81			0.181961
$574$		0			0
$575$	5454.16			0.395573
$576$	−4901.48	+	8489.62i	−0.354563	+	0.614122i
$577$	−297.689	−	515.613i	−0.0214783	−	0.0372015i	0.855086	−	0.518485i	$-0.173504\pi$
$577$	−297.689	−	515.613i	−0.0214783	−	0.0372015i	−0.876565	+	0.481284i	$0.840171\pi$
$578$	−3484.70	−	6035.67i	−0.250769	−	0.434344i
$579$	2439.83	−	4225.91i	0.175122	−	0.303321i
$580$	308.335			0.0220740
$581$		0			0
$582$	18243.8			1.29936
$583$	3998.00	−	6924.74i	0.284014	−	0.491927i
$584$	−9928.20	−	17196.1i	−0.703479	−	1.21846i
$585$	837.254	+	1450.17i	0.0591730	+	0.102491i
$586$	364.869	−	631.972i	0.0257212	−	0.0445504i
$587$	15750.3			1.10747			0.553736	−	0.832693i	$-0.313202\pi$
$587$	15750.3			1.10747			0.553736	+	0.832693i	$0.313202\pi$
$588$		0			0
$589$	−8604.42			−0.601934
$590$	−3982.11	+	6897.22i	−0.277866	+	0.481278i
$591$	−6967.21	−	12067.6i	−0.484928	−	0.839920i
$592$	9494.98	+	16445.8i	0.659191	+	1.14175i
$593$	−208.939	+	361.893i	−0.0144690	+	0.0250610i	−0.873169	−	0.487417i	$-0.837939\pi$
$593$	−208.939	+	361.893i	−0.0144690	+	0.0250610i	0.858700	+	0.512478i	$0.171272\pi$
$594$	6378.31			0.440581
$595$		0			0
$596$	431.385			0.0296480
$597$	−9536.08	+	16517.0i	−0.653745	+	1.13232i
$598$	5456.04	+	9450.15i	0.373101	+	0.646229i
$599$	9998.67	+	17318.2i	0.682028	+	1.18131i	0.974361	+	0.224990i	$0.0722350\pi$
$599$	9998.67	+	17318.2i	0.682028	+	1.18131i	−0.292333	+	0.956316i	$0.594432\pi$
$600$	−2003.98	+	3471.00i	−0.136354	+	0.236172i
$601$	15992.6			1.08545			0.542723	−	0.839912i	$-0.317393\pi$
$601$	15992.6			1.08545			0.542723	+	0.839912i	$0.317393\pi$
$602$		0			0
$603$	251.216			0.0169657
$604$	676.185	−	1171.19i	0.0455523	−	0.0788988i
$605$	−331.081	−	573.449i	−0.0222485	−	0.0385356i
$606$	2081.36	+	3605.03i	0.139521	+	0.241657i
$607$	7079.59	−	12262.2i	0.473396	−	0.819947i	−0.526140	−	0.850398i	$-0.676361\pi$
$607$	7079.59	−	12262.2i	0.473396	−	0.819947i	0.999536	+	0.0304515i	$0.00969450\pi$
$608$	2601.08			0.173499
$609$		0			0
$610$	−4146.76			−0.275242
$611$	−112.927	+	195.596i	−0.00747716	+	0.0129508i
$612$	991.978	+	1718.16i	0.0655202	+	0.113484i
$613$	2314.70	+	4009.18i	0.152512	+	0.264159i	0.932150	−	0.362071i	$-0.117930\pi$
$613$	2314.70	+	4009.18i	0.152512	+	0.264159i	−0.779638	+	0.626230i	$0.784597\pi$
$614$	2481.93	−	4298.84i	0.163131	−	0.282552i
$615$	−11295.4			−0.740611
$616$		0			0
$617$	−23165.3			−1.51151			−0.755753	−	0.654857i	$-0.772729\pi$
$617$	−23165.3			−1.51151			−0.755753	+	0.654857i	$0.772729\pi$
$618$	14455.4	−	25037.6i	0.940912	−	1.62971i
$619$	6185.30	+	10713.3i	0.401629	+	0.695641i	0.993923	−	0.110081i	$-0.0351109\pi$
$619$	6185.30	+	10713.3i	0.401629	+	0.695641i	−0.592294	+	0.805722i	$0.701778\pi$
$620$	−638.983	−	1106.75i	−0.0413906	−	0.0716906i
$621$	−7033.71	+	12182.7i	−0.454514	+	0.787241i
$622$	−3137.36			−0.202245
$623$		0			0
$624$	−6665.43			−0.427613
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−1854.01	−	3211.24i	−0.118373	−	0.205027i
$627$	5631.15	+	9753.44i	0.358671	+	0.621236i
$628$	−344.913	+	597.407i	−0.0219165	+	0.0379604i
$629$	31998.9			2.02842
$630$		0			0
$631$	13980.2			0.882002			0.441001	−	0.897507i	$-0.354623\pi$
$631$	13980.2			0.882002			0.441001	+	0.897507i	$0.354623\pi$
$632$	1881.81	−	3259.38i	0.118440	−	0.205145i
$633$	18784.5	+	32535.6i	1.17949	+	2.04293i
$634$	−8399.86	−	14549.0i	−0.526185	−	0.911379i
$635$	−3033.73	+	5254.57i	−0.189590	+	0.328380i
$636$	−1827.91			−0.113964
$637$		0			0
$638$	−4643.36			−0.288139
$639$	8241.33	−	14274.4i	0.510206	−	0.883703i
$640$	−2483.88	−	4302.20i	−0.153412	−	0.265718i
$641$	8030.47	+	13909.2i	0.494828	+	0.857067i	0.999982	−	0.00596217i	$-0.00189783\pi$
$641$	8030.47	+	13909.2i	0.494828	+	0.857067i	−0.505155	+	0.863029i	$0.668564\pi$
$642$	12969.1	−	22463.2i	0.797275	−	1.38092i
$643$	4502.17			0.276125			0.138063	−	0.990424i	$-0.455913\pi$
$643$	4502.17			0.276125			0.138063	+	0.990424i	$0.455913\pi$
$644$		0			0
$645$	7527.79			0.459545
$646$	−4987.44	+	8638.49i	−0.303759	+	0.526125i
$647$	14707.4	+	25474.0i	0.893675	+	1.54789i	0.835436	+	0.549588i	$0.185215\pi$
$647$	14707.4	+	25474.0i	0.893675	+	1.54789i	0.0582393	+	0.998303i	$0.481451\pi$
$648$	−10797.8	−	18702.3i	−0.654595	−	1.13379i
$649$	−11782.5	+	20407.9i	−0.712640	+	1.23433i
$650$	−1250.43			−0.0754553
$651$		0			0
$652$	−1317.16			−0.0791164
$653$	−6506.82	+	11270.1i	−0.389941	+	0.675398i	−0.992441	−	0.122721i	$-0.960838\pi$
$653$	−6506.82	+	11270.1i	−0.389941	+	0.675398i	0.602500	+	0.798119i	$0.294171\pi$
$654$	−10779.0	−	18669.8i	−0.644483	−	1.11628i
$655$	−4956.05	−	8584.13i	−0.295647	−	0.512076i
$656$	8783.46	−	15213.4i	0.522769	−	0.905463i
$657$	−14275.0			−0.847671
$658$		0			0
$659$	23474.2			1.38759			0.693797	−	0.720171i	$-0.255937\pi$
$659$	23474.2			1.38759			0.693797	+	0.720171i	$0.255937\pi$
$660$	−836.362	+	1448.62i	−0.0493263	+	0.0854356i
$661$	−4633.18	−	8024.91i	−0.272632	−	0.472213i	0.696903	−	0.717166i	$-0.254561\pi$
$661$	−4633.18	−	8024.91i	−0.272632	−	0.472213i	−0.969535	+	0.244953i	$0.921228\pi$
$662$	12520.2	+	21685.7i	0.735064	+	1.27317i
$663$	−5615.77	+	9726.79i	−0.328957	+	0.569770i
$664$	−24963.0			−1.45896
$665$		0			0
$666$	16423.8			0.955572
$667$	5120.49	−	8868.95i	0.297251	−	0.514853i
$668$	236.088	+	408.916i	0.0136744	+	0.0236848i
$669$	21199.3	+	36718.2i	1.22513	+	2.12199i
$670$	−93.7973	+	162.462i	−0.00540851	+	0.00936782i
$671$	−12269.7			−0.705909
$672$		0			0
$673$	−25067.2			−1.43576			−0.717882	−	0.696164i	$-0.754888\pi$
$673$	−25067.2			−1.43576			−0.717882	+	0.696164i	$0.754888\pi$
$674$	−37.6644	+	65.2367i	−0.00215249	+	0.00372822i
$675$	−806.003	−	1396.04i	−0.0459601	−	0.0796052i
$676$	−1197.34	−	2073.86i	−0.0681237	−	0.117994i
$677$	−11204.8	+	19407.3i	−0.636093	+	1.10174i	0.350190	+	0.936679i	$0.386117\pi$
$677$	−11204.8	+	19407.3i	−0.636093	+	1.10174i	−0.986283	+	0.165066i	$0.947216\pi$
$678$	−23585.6			−1.33599
$679$		0			0
$680$	−10503.4			−0.592332
$681$	3380.60	−	5855.37i	0.190227	−	0.329483i
$682$	9622.75	+	16667.1i	0.540284	+	0.935800i
$683$	4378.77	+	7584.24i	0.245313	+	0.424895i	0.962220	−	0.272275i	$-0.0877759\pi$
$683$	4378.77	+	7584.24i	0.245313	+	0.424895i	−0.716907	+	0.697169i	$0.754443\pi$
$684$	502.957	−	871.147i	0.0281156	−	0.0486976i
$685$	11054.7			0.616613
$686$		0			0
$687$	27348.7			1.51880
$688$	−5853.70	+	10138.9i	−0.324375	+	0.561834i
$689$	−2021.55	−	3501.42i	−0.111778	−	0.193604i
$690$	9388.36	+	16261.1i	0.517984	+	0.897174i
$691$	4234.21	−	7333.87i	0.233107	−	0.403753i	−0.725614	−	0.688102i	$-0.758444\pi$
$691$	4234.21	−	7333.87i	0.233107	−	0.403753i	0.958721	+	0.284349i	$0.0917774\pi$
$692$	4326.90			0.237694
$693$		0			0
$694$	−20294.8			−1.11006
$695$	1320.10	−	2286.47i	0.0720491	−	0.124793i
$696$	3762.77	+	6517.31i	0.204925	+	0.354940i
$697$	−14800.5	−	25635.2i	−0.804318	−	1.39312i
$698$	−13277.6	+	22997.4i	−0.720004	+	1.24708i
$699$	−4050.23			−0.219162
$700$		0			0
$701$	15996.9			0.861906			0.430953	−	0.902374i	$-0.358177\pi$
$701$	15996.9			0.861906			0.430953	+	0.902374i	$0.358177\pi$
$702$	1612.56	−	2793.04i	0.0866983	−	0.150166i
$703$	−8112.11	−	14050.6i	−0.435212	−	0.753809i
$704$	−10829.9	−	18757.9i	−0.579782	−	1.00421i
$705$	−194.317	+	336.566i	−0.0103807	+	0.0179799i
$706$	−7240.03			−0.385952
$707$		0			0
$708$	5387.02			0.285956
$709$	−9951.48	+	17236.5i	−0.527131	+	0.913017i	0.472369	+	0.881401i	$0.343399\pi$
$709$	−9951.48	+	17236.5i	−0.527131	+	0.913017i	−0.999500	+	0.0316164i	$0.989935\pi$
$710$	6154.17	+	10659.3i	0.325299	+	0.563434i
$711$	−1352.85	−	2343.21i	−0.0713584	−	0.123596i
$712$	2049.79	−	3550.34i	0.107892	−	0.186875i
$713$	−42446.1			−2.22948
$714$		0			0
$715$	−3699.84			−0.193519
$716$	1956.65	−	3389.02i	0.102128	−	0.176891i
$717$	−16823.3	−	29138.9i	−0.876261	−	1.51773i
$718$	4089.80	+	7083.73i	0.212576	+	0.368193i
$719$	−5536.53	+	9589.56i	−0.287174	+	0.497399i	−0.973134	−	0.230240i	$-0.926049\pi$
$719$	−5536.53	+	9589.56i	−0.287174	+	0.497399i	0.685960	+	0.727639i	$0.259382\pi$
$720$	−4481.18			−0.231949
$721$		0			0
$722$	−12678.4			−0.653520
$723$	−16.2022	+	28.0630i	−0.000833424	+	0.00144353i
$724$	−960.528	−	1663.68i	−0.0493062	−	0.0854009i
$725$	586.764	+	1016.31i	0.0300578	+	0.0520616i
$726$	1139.79	−	1974.18i	0.0582667	−	0.100921i
$727$	−31652.7			−1.61476			−0.807382	−	0.590029i	$-0.799116\pi$
$727$	−31652.7			−1.61476			−0.807382	+	0.590029i	$0.799116\pi$
$728$		0			0
$729$	−3935.94			−0.199967
$730$	5329.88	−	9231.63i	0.270230	−	0.468052i
$731$	9863.73	+	17084.5i	0.499074	+	0.864422i
$732$	1402.44	+	2429.10i	0.0708138	+	0.122653i
$733$	8479.15	−	14686.3i	0.427264	−	0.740043i	−0.569365	−	0.822085i	$-0.692811\pi$
$733$	8479.15	−	14686.3i	0.427264	−	0.740043i	0.996629	+	0.0820419i	$0.0261441\pi$
$734$	−8230.16			−0.413870
$735$		0			0
$736$	12831.3			0.642618
$737$	−277.532	+	480.700i	−0.0138712	+	0.0240255i
$738$	−7596.55	−	13157.6i	−0.378906	−	0.656285i
$739$	5808.30	+	10060.3i	0.289123	+	0.500775i	0.973601	−	0.228258i	$-0.0733031\pi$
$739$	5808.30	+	10060.3i	0.289123	+	0.500775i	−0.684478	+	0.729034i	$0.739970\pi$
$740$	1204.84	−	2086.85i	0.0598526	−	0.103668i
$741$	5694.66			0.282319
$742$		0			0
$743$	15928.0			0.786464			0.393232	−	0.919439i	$-0.371357\pi$
$743$	15928.0			0.786464			0.393232	+	0.919439i	$0.371357\pi$
$744$	15595.7	−	27012.5i	0.768502	−	1.33108i
$745$	820.929	+	1421.89i	0.0403712	+	0.0699249i
$746$	3381.10	+	5856.23i	0.165939	+	0.287415i
$747$	−8973.07	+	15541.8i	−0.439501	+	0.761239i
$748$	−4383.57			−0.214277
$749$		0			0
$750$	−2151.65			−0.104756
$751$	−12786.0	+	22145.9i	−0.621260	+	1.07605i	0.367991	+	0.929829i	$0.380046\pi$
$751$	−12786.0	+	22145.9i	−0.621260	+	1.07605i	−0.989251	+	0.146225i	$0.953288\pi$
$752$	−302.206	−	523.436i	−0.0146547	−	0.0253827i
$753$	1823.71	+	3158.77i	0.0882601	+	0.152871i
$754$	−1173.93	+	2033.31i	−0.0567004	+	0.0982080i
$755$	5147.14			0.248111
$756$		0			0
$757$	6202.41			0.297794			0.148897	−	0.988853i	$-0.452428\pi$
$757$	6202.41			0.297794			0.148897	+	0.988853i	$0.452428\pi$
$758$	869.385	−	1505.82i	0.0416590	−	0.0721555i
$759$	27778.8	+	48114.3i	1.32847	+	2.30097i
$760$	2662.73	+	4611.98i	0.127089	+	0.220124i
$761$	−14599.5	+	25287.1i	−0.695444	+	1.20454i	0.274587	+	0.961562i	$0.411459\pi$
$761$	−14599.5	+	25287.1i	−0.695444	+	1.20454i	−0.970031	+	0.242982i	$0.921874\pi$
$762$	−20888.1			−0.993037
$763$		0			0
$764$	492.539			0.0233239
$765$	−3775.49	+	6539.34i	−0.178435	+	0.309059i
$766$	1512.50	+	2619.73i	0.0713431	+	0.123570i
$767$	5957.69	+	10319.0i	0.280469	+	0.485786i
$768$	−6525.26	+	11302.1i	−0.306589	+	0.531027i
$769$	−21838.2			−1.02407			−0.512033	−	0.858966i	$-0.671108\pi$
$769$	−21838.2			−1.02407			−0.512033	+	0.858966i	$0.671108\pi$
$770$		0			0
$771$	−11813.3			−0.551812
$772$	481.492	−	833.969i	0.0224473	−	0.0388798i
$773$	−12772.4	−	22122.4i	−0.594296	−	1.02935i	−0.993646	−	0.112553i	$-0.964097\pi$
$773$	−12772.4	−	22122.4i	−0.594296	−	1.02935i	0.399349	−	0.916799i	$-0.369236\pi$
$774$	5062.69	+	8768.83i	0.235109	+	0.407221i
$775$	2431.98	−	4212.31i	0.112722	−	0.195240i
$776$	25525.2			1.18080
$777$		0			0
$778$	−2901.82			−0.133721
$779$	−7504.22	+	12997.7i	−0.345143	+	0.597806i
$780$	422.898	+	732.480i	0.0194130	+	0.0336243i
$781$	18209.3	+	31539.4i	0.834289	+	1.44503i
$782$	−24603.3	+	42614.2i	−1.12508	+	1.94870i
$783$	−3026.77			−0.138146
$784$		0			0
$785$	−2625.49			−0.119373
$786$	17061.9	−	29552.1i	0.774272	−	1.34108i
$787$	−18611.6	−	32236.2i	−0.842989	−	1.46010i	−0.887356	−	0.461084i	$-0.847461\pi$
$787$	−18611.6	−	32236.2i	−0.842989	−	1.46010i	0.0443677	−	0.999015i	$-0.485873\pi$
$788$	−1374.96	−	2381.49i	−0.0621583	−	0.107661i
$789$	−3991.09	+	6912.78i	−0.180085	+	0.311916i
$790$	2020.47			0.0909938
$791$		0			0
$792$	−15951.1			−0.715655
$793$	−3102.01	+	5372.84i	−0.138910	+	0.240599i
$794$	−2567.59	−	4447.20i	−0.114761	−	0.198772i
$795$	−3478.53	−	6024.99i	−0.155183	−	0.268785i
$796$	−1881.91	+	3259.57i	−0.0837973	+	0.145141i
$797$	40384.6			1.79485			0.897425	−	0.441168i	$-0.145436\pi$
$797$	40384.6			1.79485			0.897425	+	0.441168i	$0.145436\pi$
$798$		0			0
$799$	−1018.46			−0.0450945
$800$	−735.177	+	1273.36i	−0.0324905	+	0.0562752i
$801$	−1473.62	−	2552.38i	−0.0650033	−	0.112589i
$802$	5394.44	+	9343.44i	0.237511	+	0.411382i
$803$	15770.4	−	27315.1i	0.693056	−	1.20041i
$804$	126.889			0.00556598
$805$		0			0
$806$	9731.28			0.425272
$807$	−10818.4	+	18738.0i	−0.471901	+	0.817357i
$808$	2912.07	+	5043.85i	0.126790	+	0.219607i
$809$	977.879	+	1693.74i	0.0424974	+	0.0736076i	0.886492	−	0.462744i	$-0.153135\pi$
$809$	977.879	+	1693.74i	0.0424974	+	0.0736076i	−0.843994	+	0.536352i	$0.819802\pi$
$810$	5796.72	−	10040.2i	0.251452	−	0.435528i
$811$	34301.8			1.48520			0.742600	−	0.669735i	$-0.233592\pi$
$811$	34301.8			1.48520			0.742600	+	0.669735i	$0.233592\pi$
$812$		0			0
$813$	−5965.49			−0.257342
$814$	−18144.3	+	31426.9i	−0.781276	+	1.35321i
$815$	−2506.56	−	4341.50i	−0.107731	−	0.186596i
$816$	−15028.4	−	26030.0i	−0.644731	−	1.11671i
$817$	5001.15	−	8662.25i	0.214159	−	0.370935i
$818$	30255.8			1.29324
$819$		0			0
$820$	−2229.12			−0.0949319
$821$	6832.81	−	11834.8i	0.290459	−	0.503090i	−0.683459	−	0.729989i	$-0.739525\pi$
$821$	6832.81	−	11834.8i	0.290459	−	0.503090i	0.973918	+	0.226899i	$0.0728587\pi$
$822$	19028.8	+	32958.8i	0.807426	+	1.39850i
$823$	10759.7	+	18636.4i	0.455724	+	0.789338i	0.998730	−	0.0503916i	$-0.0160469\pi$
$823$	10759.7	+	18636.4i	0.455724	+	0.789338i	−0.543005	+	0.839729i	$0.682714\pi$
$824$	20224.8	−	35030.5i	0.855056	−	1.48100i
$825$	−6366.42			−0.268667
$826$		0			0
$827$	35220.6			1.48094			0.740471	−	0.672088i	$-0.234602\pi$
$827$	35220.6			1.48094			0.740471	+	0.672088i	$0.234602\pi$
$828$	2481.12	−	4297.42i	0.104136	−	0.180369i
$829$	15682.8	+	27163.3i	0.657039	+	1.13802i	0.981379	+	0.192084i	$0.0615245\pi$
$829$	15682.8	+	27163.3i	0.657039	+	1.13802i	−0.324340	+	0.945941i	$0.605142\pi$
$830$	−6700.60	−	11605.8i	−0.280218	−	0.485352i
$831$	−1286.64	+	2228.53i	−0.0537101	+	0.0930287i
$832$	−10952.0			−0.456362
$833$		0			0
$834$	9089.24			0.377380
$835$	−898.556	+	1556.34i	−0.0372405	+	0.0645024i
$836$	1111.29	+	1924.81i	0.0459746	+	0.0796303i
$837$	6272.59	+	10864.4i	0.259035	+	0.448662i
$838$	3533.74	−	6120.62i	0.145670	−	0.252307i
$839$	28287.1			1.16398			0.581990	−	0.813196i	$-0.302274\pi$
$839$	28287.1			1.16398			0.581990	+	0.813196i	$0.302274\pi$
$840$		0			0
$841$	−22185.5			−0.909653
$842$	−17517.9	+	30341.9i	−0.716992	+	1.24187i
$843$	−11100.6	−	19226.8i	−0.453530	−	0.785537i
$844$	3707.05	+	6420.80i	0.151187	+	0.261864i
$845$	4557.11	−	7893.14i	0.185526	−	0.321340i
$846$	−522.738			−0.0212436
$847$		0			0
$848$	10819.8			0.438152
$849$	−18014.3	+	31201.7i	−0.728209	+	1.26129i
$850$	−2819.33	−	4883.22i	−0.113767	−	0.197051i
$851$	−40017.5	−	69312.3i	−1.61197	−	2.79201i
$852$	4162.70	−	7210.01i	0.167385	−	0.289919i
$853$	−9405.41			−0.377533			−0.188766	−	0.982022i	$-0.560449\pi$
$853$	−9405.41			−0.377533			−0.188766	+	0.982022i	$0.560449\pi$
$854$		0			0
$855$	3828.53			0.153138
$856$	18145.3	−	31428.6i	0.724526	−	1.25492i
$857$	−13983.4	−	24220.0i	−0.557369	−	0.965391i	−0.997715	−	0.0675629i	$-0.978478\pi$
$857$	−13983.4	−	24220.0i	−0.557369	−	0.965391i	0.440346	−	0.897828i	$-0.354856\pi$
$858$	−6368.62	−	11030.8i	−0.253404	−	0.438909i
$859$	3140.55	−	5439.60i	0.124743	−	0.216061i	−0.796889	−	0.604125i	$-0.793523\pi$
$859$	3140.55	−	5439.60i	0.124743	−	0.216061i	0.921632	+	0.388064i	$0.126856\pi$
$860$	1485.58			0.0589047
$861$		0			0
$862$	−16624.7			−0.656890
$863$	2378.57	−	4119.80i	0.0938208	−	0.162502i	−0.815295	−	0.579046i	$-0.803425\pi$
$863$	2378.57	−	4119.80i	0.0938208	−	0.162502i	0.909116	+	0.416543i	$0.136759\pi$
$864$	−1896.17	−	3284.27i	−0.0746634	−	0.129321i
$865$	8234.13	+	14261.9i	0.323663	+	0.560601i
$866$	10371.6	−	17964.2i	0.406977	−	0.704905i
$867$	−17942.0			−0.702818
$868$		0			0
$869$	5978.28			0.233371
$870$	−2020.02	+	3498.77i	−0.0787184	+	0.136344i
$871$	140.331	+	243.061i	0.00545918	+	0.00945558i
$872$	−15081.1	−	26121.1i	−0.585675	−	1.01442i
$873$	9175.17	−	15891.9i	0.355707	−	0.616103i
$874$	24949.0			0.965574
$875$		0			0
$876$	−7210.30			−0.278097
$877$	15120.3	−	26189.1i	0.582184	−	1.00837i	−0.413036	−	0.910715i	$-0.635532\pi$
$877$	15120.3	−	26189.1i	0.582184	−	1.00837i	0.995220	−	0.0976572i	$-0.0311349\pi$
$878$	−7201.26	−	12473.0i	−0.276801	−	0.479433i
$879$	−939.320	−	1626.95i	−0.0360438	−	0.0624296i
$880$	4950.61	−	8574.70i	0.189642	−	0.328469i
$881$	−44875.5			−1.71611			−0.858056	−	0.513556i	$-0.828328\pi$
$881$	−44875.5			−1.71611			−0.858056	+	0.513556i	$0.828328\pi$
$882$		0			0
$883$	4892.13			0.186448			0.0932238	−	0.995645i	$-0.470283\pi$
$883$	4892.13			0.186448			0.0932238	+	0.995645i	$0.470283\pi$
$884$	−1108.25	+	1919.55i	−0.0421658	+	0.0730334i
$885$	10251.6	+	17756.2i	0.389381	+	0.674428i
$886$	7093.08	+	12285.6i	0.268958	+	0.465849i
$887$	880.700	−	1525.42i	0.0333382	−	0.0577435i	−0.848875	−	0.528594i	$-0.822719\pi$
$887$	880.700	−	1525.42i	0.0333382	−	0.0577435i	0.882213	+	0.470850i	$0.156053\pi$
$888$	58813.4			2.22258
$889$		0			0
$890$	2200.83			0.0828900
$891$	17151.7	−	29707.6i	0.644896	−	1.11699i
$892$	4183.61	+	7246.23i	0.157038	+	0.271997i
$893$	258.192	+	447.202i	0.00967533	+	0.0167582i
$894$	−2826.16	+	4895.06i	−0.105728	+	0.183127i
$895$	14894.1			0.556263
$896$		0			0
$897$	28092.1			1.04567
$898$	9351.08	−	16196.5i	0.347494	−	0.601877i
$899$	−4566.40	−	7909.23i	−0.169408	−	0.293423i
$900$	284.315	+	492.447i	0.0105302	+	0.0182388i
$901$	9115.90	−	15789.2i	0.337064	−	0.583812i
$902$	33569.3			1.23918
$903$		0			0
$904$	−32999.0			−1.21408
$905$	3655.79	−	6332.01i	0.134279	−	0.232578i
$906$	8859.88	+	15345.8i	0.324890	+	0.562725i
$907$	−11844.6	−	20515.4i	−0.433619	−	0.751050i	0.563563	−	0.826073i	$-0.309430\pi$
$907$	−11844.6	−	20515.4i	−0.433619	−	0.751050i	−0.997182	+	0.0750229i	$0.976097\pi$
$908$	667.150	−	1155.54i	0.0243834	−	0.0422333i
$909$	4187.03			0.152778
$910$		0			0
$911$	−13877.3			−0.504692			−0.252346	−	0.967637i	$-0.581202\pi$
$911$	−13877.3			−0.504692			−0.252346	+	0.967637i	$0.581202\pi$
$912$	−7619.79	+	13197.9i	−0.276663	+	0.479194i
$913$	−19826.1	−	34339.8i	−0.718673	−	1.24478i
$914$	3750.04	+	6495.27i	0.135712	+	0.235059i
$915$	−5337.72	+	9245.20i	−0.192852	+	0.334029i
$916$	5397.18			0.194681
$917$		0			0
$918$	14543.3			0.522875
$919$	−7165.82	+	12411.6i	−0.257213	+	0.445506i	−0.965494	−	0.260425i	$-0.916137\pi$
$919$	−7165.82	+	12411.6i	−0.257213	+	0.445506i	0.708281	+	0.705930i	$0.249471\pi$
$920$	13135.4	+	22751.2i	0.470719	+	0.815309i
$921$	−6389.50	−	11066.9i	−0.228601	−	0.395948i
$922$	7852.48	−	13600.9i	0.280486	−	0.485815i
$923$	18414.7			0.656692
$924$		0			0
$925$	9171.32			0.326001
$926$	24465.1	−	42374.8i	0.868222	−	1.50380i
$927$	−14539.9	−	25183.8i	−0.515158	−	0.892280i
$928$	1380.40	+	2390.92i	0.0488296	+	0.0845754i
$929$	8334.21	−	14435.3i	0.294334	−	0.509802i	−0.680496	−	0.732752i	$-0.738235\pi$
$929$	8334.21	−	14435.3i	0.294334	−	0.509802i	0.974830	+	0.222950i	$0.0715688\pi$
$930$	16744.9			0.590415
$931$		0			0
$932$	−799.300			−0.0280922
$933$	−4038.41	+	6994.73i	−0.141706	+	0.245442i
$934$	−8761.56	−	15175.5i	−0.306945	−	0.531645i
$935$	−8341.98	−	14448.7i	−0.291778	−	0.505374i
$936$	−4032.76	+	6984.95i	−0.140828	+	0.243921i
$937$	−30384.9			−1.05937			−0.529685	−	0.848194i	$-0.677690\pi$
$937$	−30384.9			−1.05937			−0.529685	+	0.848194i	$0.677690\pi$
$938$		0			0
$939$	−9545.94			−0.331757
$940$	−38.3478	+	66.4203i	−0.00133060	+	0.00230467i
$941$	−598.176	−	1036.07i	−0.0207226	−	0.0358926i	0.855478	−	0.517839i	$-0.173263\pi$
$941$	−598.176	−	1036.07i	−0.0207226	−	0.0358926i	−0.876201	+	0.481946i	$0.839930\pi$
$942$	−4519.31	−	7827.68i	−0.156313	−	0.270743i
$943$	−37018.8	+	64118.4i	−1.27836	+	2.21419i
$944$	−31886.9			−1.09940
$945$		0			0
$946$	−22372.1			−0.768901
$947$	−894.206	+	1548.81i	−0.0306840	+	0.0531463i	−0.880960	−	0.473191i	$-0.843102\pi$
$947$	−894.206	+	1548.81i	−0.0306840	+	0.0531463i	0.850276	+	0.526338i	$0.176435\pi$
$948$	−683.326	−	1183.55i	−0.0234107	−	0.0405486i
$949$	−7974.11	−	13811.6i	−0.272761	−	0.472437i
$950$	−1429.47	+	2475.91i	−0.0488190	+	0.0845570i
$951$	−43249.2			−1.47471
$952$		0			0
$953$	8578.60			0.291593			0.145796	−	0.989315i	$-0.453426\pi$
$953$	8578.60			0.291593			0.145796	+	0.989315i	$0.453426\pi$
$954$	4678.85	−	8104.01i	0.158788	−	0.275028i
$955$	937.307	+	1623.46i	0.0317597	+	0.0550094i
$956$	−3320.03	−	5750.46i	−0.112320	−	0.194543i
$957$	−5976.94	+	10352.4i	−0.201888	+	0.349681i
$958$	−6198.95			−0.209059
$959$		0			0
$960$	−18845.4			−0.633577
$961$	−4030.99	+	6981.89i	−0.135309	+	0.234362i
$962$	9174.48	+	15890.7i	0.307482	+	0.532574i
$963$	−13044.9	−	22594.3i	−0.436516	−	0.756067i
$964$	−3.19745	+	5.53814i	−0.000106829	+	0.000185033i
$965$	3665.14			0.122264
$966$		0			0
$967$	−55459.3			−1.84431			−0.922156	−	0.386818i	$-0.873574\pi$
$967$	−55459.3			−1.84431			−0.922156	+	0.386818i	$0.873574\pi$
$968$	1594.70	−	2762.10i	0.0529500	−	0.0917122i
$969$	12839.7	+	22239.0i	0.425665	+	0.737274i
$970$	6851.51	+	11867.2i	0.226793	+	0.392816i
$971$	11023.6	−	19093.5i	0.364331	−	0.631039i	−0.624338	−	0.781155i	$-0.714631\pi$
$971$	11023.6	−	19093.5i	0.364331	−	0.631039i	0.988669	+	0.150115i	$0.0479644\pi$
$972$	−5554.72			−0.183300
$973$		0			0
$974$	14444.6			0.475191
$975$	−1609.56	+	2787.83i	−0.0528688	+	0.0915714i
$976$	−8301.35	−	14378.4i	−0.272254	−	0.471557i
$977$	−7201.14	−	12472.7i	−0.235809	−	0.408432i	0.723699	−	0.690116i	$-0.242440\pi$
$977$	−7201.14	−	12472.7i	−0.235809	−	0.408432i	−0.959507	+	0.281684i	$0.909107\pi$
$978$	8629.20	−	14946.2i	0.282138	−	0.488678i
$979$	6511.94			0.212587
$980$		0			0
$981$	−21683.9			−0.705721
$982$	−694.790	+	1203.41i	−0.0225781	+	0.0391063i
$983$	3908.55	+	6769.81i	0.126819	+	0.219658i	0.922443	−	0.386134i	$-0.126190\pi$
$983$	3908.55	+	6769.81i	0.126819	+	0.219658i	−0.795623	+	0.605792i	$0.792856\pi$
$984$	−27203.1	−	47117.1i	−0.881304	−	1.52646i
$985$	5233.11	−	9064.01i	0.169280	−	0.293201i
$986$	−10587.4			−0.341959
$987$		0			0
$988$	1123.82			0.0361878
$989$	24671.0	−	42731.4i	0.793217	−	1.37389i
$990$	−4281.63	−	7416.00i	−0.137454	−	0.238077i
$991$	−12250.8	−	21219.0i	−0.392693	−	0.680164i	0.600111	−	0.799917i	$-0.295123\pi$
$991$	−12250.8	−	21219.0i	−0.392693	−	0.680164i	−0.992804	+	0.119753i	$0.961790\pi$
$992$	5721.39	−	9909.74i	0.183119	−	0.317172i
$993$	64464.2			2.06013
$994$		0			0
$995$	−14325.2			−0.456421
$996$	−4532.31	+	7850.18i	−0.144188	+	0.249742i
$997$	−25348.0	−	43904.0i	−0.805195	−	1.39464i	−0.916159	−	0.400815i	$-0.868727\pi$
$997$	−25348.0	−	43904.0i	−0.805195	−	1.39464i	0.110964	−	0.993824i	$-0.464606\pi$
$998$	−774.398	−	1341.30i	−0.0245622	−	0.0425431i
$999$	−11827.4	+	20485.6i	−0.374576	+	0.648785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.i.226.2		4
7.2	even	3		245.4.a.k.1.1		2
7.3	odd	6		245.4.e.h.116.2		4
7.4	even	3	inner	245.4.e.i.116.2		4
7.5	odd	6		35.4.a.b.1.1	✓	2
7.6	odd	2		245.4.e.h.226.2		4
21.2	odd	6		2205.4.a.u.1.2		2
21.5	even	6		315.4.a.f.1.2		2
28.19	even	6		560.4.a.r.1.1		2
35.9	even	6		1225.4.a.m.1.2		2
35.12	even	12		175.4.b.c.99.3		4
35.19	odd	6		175.4.a.c.1.2		2
35.33	even	12		175.4.b.c.99.2		4
56.5	odd	6		2240.4.a.bn.1.1		2
56.19	even	6		2240.4.a.bo.1.2		2
105.89	even	6		1575.4.a.z.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.b.1.1	✓	2	7.5	odd	6
175.4.a.c.1.2		2	35.19	odd	6
175.4.b.c.99.2		4	35.33	even	12
175.4.b.c.99.3		4	35.12	even	12
245.4.a.k.1.1		2	7.2	even	3
245.4.e.h.116.2		4	7.3	odd	6
245.4.e.h.226.2		4	7.6	odd	2
245.4.e.i.116.2		4	7.4	even	3	inner
245.4.e.i.226.2		4	1.1	even	1	trivial
315.4.a.f.1.2		2	21.5	even	6
560.4.a.r.1.1		2	28.19	even	6
1225.4.a.m.1.2		2	35.9	even	6
1575.4.a.z.1.1		2	105.89	even	6
2205.4.a.u.1.2		2	21.2	odd	6
2240.4.a.bn.1.1		2	56.5	odd	6
2240.4.a.bo.1.2		2	56.19	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)

\(f(q)\)	\(=\)	\(q+(-1.29289 + 2.23936i) q^{2} +(3.32843 + 5.76500i) q^{3} +(0.656854 + 1.13770i) q^{4} +(-2.50000 + 4.33013i) q^{5} -17.2132 q^{6} -24.0833 q^{8} +(-8.65685 + 14.9941i) q^{9} +O(q^{10})\)	\(q+(-1.29289 + 2.23936i) q^{2} +(3.32843 + 5.76500i) q^{3} +(0.656854 + 1.13770i) q^{4} +(-2.50000 + 4.33013i) q^{5} -17.2132 q^{6} -24.0833 q^{8} +(-8.65685 + 14.9941i) q^{9} +(-6.46447 - 11.1968i) q^{10} +(-19.1274 - 33.1297i) q^{11} +(-4.37258 + 7.57354i) q^{12} -19.3431 q^{13} -33.2843 q^{15} +(25.8823 - 44.8294i) q^{16} +(-43.6127 - 75.5394i) q^{17} +(-22.3848 - 38.7716i) q^{18} +(-22.1127 + 38.3003i) q^{19} -6.56854 q^{20} +98.9188 q^{22} +(-109.083 + 188.938i) q^{23} +(-80.1594 - 138.840i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(25.0086 - 43.3162i) q^{26} +64.4802 q^{27} -46.9411 q^{29} +(43.0330 - 74.5354i) q^{30} +(97.2792 + 168.493i) q^{31} +(-29.4071 - 50.9345i) q^{32} +(127.328 - 220.539i) q^{33} +225.546 q^{34} -22.7452 q^{36} +(-183.426 + 317.704i) q^{37} +(-57.1787 - 99.0364i) q^{38} +(-64.3823 - 111.513i) q^{39} +(60.2082 - 104.284i) q^{40} +339.362 q^{41} -226.167 q^{43} +(25.1279 - 43.5227i) q^{44} +(-43.2843 - 74.9706i) q^{45} +(-282.066 - 488.553i) q^{46} +(5.83810 - 10.1119i) q^{47} +344.589 q^{48} +64.6447 q^{50} +(290.323 - 502.855i) q^{51} +(-12.7056 - 22.0068i) q^{52} +(104.510 + 181.016i) q^{53} +(-83.3661 + 144.394i) q^{54} +191.274 q^{55} -294.402 q^{57} +(60.6899 - 105.118i) q^{58} +(-308.000 - 533.472i) q^{59} +(-21.8629 - 37.8677i) q^{60} +(160.368 - 277.765i) q^{61} -503.087 q^{62} +566.197 q^{64} +(48.3579 - 83.7583i) q^{65} +(329.244 + 570.268i) q^{66} +(-7.25483 - 12.5657i) q^{67} +(57.2944 - 99.2368i) q^{68} -1452.30 q^{69} -952.000 q^{71} +(208.485 - 361.107i) q^{72} +(412.245 + 714.029i) q^{73} +(-474.302 - 821.514i) q^{74} +(83.2107 - 144.125i) q^{75} -58.0993 q^{76} +332.958 q^{78} +(-78.1375 + 135.338i) q^{79} +(129.411 + 224.147i) q^{80} +(448.353 + 776.570i) q^{81} +(-438.759 + 759.954i) q^{82} +1036.53 q^{83} +436.127 q^{85} +(292.409 - 506.468i) q^{86} +(-156.240 - 270.616i) q^{87} +(460.651 + 797.870i) q^{88} +(-85.1127 + 147.420i) q^{89} +223.848 q^{90} -286.607 q^{92} +(-647.574 + 1121.63i) q^{93} +(15.0961 + 26.1472i) q^{94} +(-110.563 - 191.502i) q^{95} +(195.759 - 339.064i) q^{96} -1059.87 q^{97} +662.333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 2 q^{3} - 20 q^{4} - 10 q^{5} + 16 q^{6} + 96 q^{8} - 12 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 + 2 * q^3 - 20 * q^4 - 10 * q^5 + 16 * q^6 + 96 * q^8 - 12 * q^9	\( 4 q - 8 q^{2} + 2 q^{3} - 20 q^{4} - 10 q^{5} + 16 q^{6} + 96 q^{8} - 12 q^{9} - 40 q^{10} + 14 q^{11} - 108 q^{12} - 100 q^{13} - 20 q^{15} - 168 q^{16} - 50 q^{17} - 16 q^{18} + 36 q^{19} + 200 q^{20} - 368 q^{22} - 244 q^{23} - 496 q^{24} - 50 q^{25} + 216 q^{26} - 172 q^{27} - 52 q^{29} - 40 q^{30} - 120 q^{31} - 672 q^{32} + 498 q^{33} + 48 q^{34} - 272 q^{36} - 564 q^{37} + 320 q^{38} + 14 q^{39} - 240 q^{40} + 656 q^{41} - 520 q^{43} + 1164 q^{44} - 60 q^{45} - 704 q^{46} - 350 q^{47} + 2736 q^{48} + 400 q^{50} + 754 q^{51} + 628 q^{52} + 56 q^{53} + 648 q^{54} - 140 q^{55} - 1336 q^{57} + 8 q^{58} - 1232 q^{59} - 540 q^{60} + 336 q^{61} + 2400 q^{62} + 4256 q^{64} + 250 q^{65} + 1976 q^{66} + 152 q^{67} + 908 q^{68} - 2664 q^{69} - 3808 q^{71} + 800 q^{72} + 676 q^{73} - 2016 q^{74} + 50 q^{75} - 3536 q^{76} - 880 q^{78} - 1014 q^{79} - 840 q^{80} + 1454 q^{81} - 816 q^{82} + 752 q^{83} + 500 q^{85} + 768 q^{86} - 410 q^{87} + 4688 q^{88} - 216 q^{89} + 160 q^{90} + 528 q^{92} - 2760 q^{93} - 1928 q^{94} + 180 q^{95} - 2464 q^{96} - 5484 q^{97} + 1880 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 2 * q^3 - 20 * q^4 - 10 * q^5 + 16 * q^6 + 96 * q^8 - 12 * q^9 - 40 * q^10 + 14 * q^11 - 108 * q^12 - 100 * q^13 - 20 * q^15 - 168 * q^16 - 50 * q^17 - 16 * q^18 + 36 * q^19 + 200 * q^20 - 368 * q^22 - 244 * q^23 - 496 * q^24 - 50 * q^25 + 216 * q^26 - 172 * q^27 - 52 * q^29 - 40 * q^30 - 120 * q^31 - 672 * q^32 + 498 * q^33 + 48 * q^34 - 272 * q^36 - 564 * q^37 + 320 * q^38 + 14 * q^39 - 240 * q^40 + 656 * q^41 - 520 * q^43 + 1164 * q^44 - 60 * q^45 - 704 * q^46 - 350 * q^47 + 2736 * q^48 + 400 * q^50 + 754 * q^51 + 628 * q^52 + 56 * q^53 + 648 * q^54 - 140 * q^55 - 1336 * q^57 + 8 * q^58 - 1232 * q^59 - 540 * q^60 + 336 * q^61 + 2400 * q^62 + 4256 * q^64 + 250 * q^65 + 1976 * q^66 + 152 * q^67 + 908 * q^68 - 2664 * q^69 - 3808 * q^71 + 800 * q^72 + 676 * q^73 - 2016 * q^74 + 50 * q^75 - 3536 * q^76 - 880 * q^78 - 1014 * q^79 - 840 * q^80 + 1454 * q^81 - 816 * q^82 + 752 * q^83 + 500 * q^85 + 768 * q^86 - 410 * q^87 + 4688 * q^88 - 216 * q^89 + 160 * q^90 + 528 * q^92 - 2760 * q^93 - 1928 * q^94 + 180 * q^95 - 2464 * q^96 - 5484 * q^97 + 1880 * q^99

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