LMFDB - Embedded newform 245.4.e.h.226.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,4,Mod(116,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [4,-8,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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.h.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} +(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} + 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}+ \cdots + 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

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	$-0.945371\pi$
$3$	−3.32843	−	5.76500i	−0.640556	−	1.10948i	0.344753	−	0.938694i	$-0.387963\pi$
$4$	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	$-0.433845\pi$
$13$	19.3431			0.412679			0.206339	+	0.978480i	$0.433845\pi$
$14$		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	$0.0470998\pi$
$17$	43.6127	+	75.5394i	0.622214	+	1.07771i	−0.366859	+	0.930277i	$0.619567\pi$
$18$	−22.3848	−	38.7716i	−0.293119	−	0.507697i
$19$	22.1127	−	38.3003i	0.267000	−	0.462458i	−0.701086	−	0.713077i	$-0.747301\pi$
$19$	22.1127	−	38.3003i	0.267000	−	0.462458i	0.968086	+	0.250619i	$0.0806343\pi$
$20$	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	$-0.976079\pi$
$31$	−97.2792	−	168.493i	−0.563609	−	0.976199i	0.433569	−	0.901120i	$-0.357254\pi$
$32$	−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	$-0.723699\pi$
$41$	−339.362			−1.29267			−0.646336	+	0.763053i	$0.723699\pi$
$42$		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	−0.874943	−	0.484227i	$-0.839101\pi$
$47$	−5.83810	+	10.1119i	−0.0181186	+	0.0313823i	0.856824	+	0.515609i	$0.172434\pi$
$48$	−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	$0.0711931\pi$
$59$	308.000	+	533.472i	0.679630	+	1.17715i	−0.295462	+	0.955354i	$0.595474\pi$
$60$	−21.8629	−	37.8677i	−0.0470415	−	0.0814783i
$61$	−160.368	+	277.765i	−0.336606	+	0.583018i	−0.983792	−	0.179314i	$-0.942612\pi$
$61$	−160.368	+	277.765i	−0.336606	+	0.583018i	0.647186	+	0.762332i	$0.275946\pi$
$62$	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	$-0.936819\pi$
$73$	−412.245	−	714.029i	−0.660953	−	1.14480i	0.319412	−	0.947616i	$-0.396515\pi$
$74$	−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	$-0.740366\pi$
$83$	−1036.53			−1.37077			−0.685384	+	0.728182i	$0.740366\pi$
$84$		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	−0.810879	−	0.585213i	$-0.801011\pi$
$89$	85.1127	−	147.420i	0.101370	−	0.175578i	0.912249	+	0.409635i	$0.134344\pi$
$90$	−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	$-0.312829\pi$
$97$	1059.87			1.10942			0.554710	+	0.832044i	$0.312829\pi$
$98$		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	0.919421	−	0.393274i	$-0.128658\pi$
$101$	120.917	+	209.434i	0.119125	+	0.206331i	−0.800296	+	0.599605i	$0.795324\pi$
$102$	750.714	+	1300.28i	0.728743	+	1.26222i
$103$	839.788	−	1454.56i	0.803367	−	1.39147i	−0.114021	−	0.993478i	$-0.536373\pi$
$103$	839.788	−	1454.56i	0.803367	−	1.39147i	0.917388	−	0.397994i	$-0.130294\pi$
$104$	−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	$-0.603429\pi$
$131$	991.209	−	1716.83i	0.661087	−	1.14504i	0.980330	−	0.197363i	$-0.0632378\pi$
$132$	−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	$-0.448494\pi$
$139$	528.039			0.322213			0.161107	+	0.986937i	$0.448494\pi$
$140$		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	0.791546	−	0.611109i	$-0.209276\pi$
$157$	−262.549	−	454.749i	−0.133463	−	0.231165i	−0.925009	+	0.379944i	$0.875943\pi$
$158$	−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	$-0.526537\pi$
$167$	−359.422			−0.166544			−0.0832722	+	0.996527i	$0.526537\pi$
$168$		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	$0.424242\pi$
$173$	−1646.83	+	2852.39i	−0.723733	+	1.25354i	−0.959493	+	0.281732i	$0.909091\pi$
$174$	−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	$-0.402928\pi$
$181$	1462.31			0.600514			0.300257	+	0.953858i	$0.402928\pi$
$182$		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	$-0.996203\pi$
$199$	−1432.52	−	2481.20i	−0.510295	−	0.883856i	0.489634	−	0.871928i	$-0.337130\pi$
$200$	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	$-0.905552\pi$
$223$	−6369.16			−1.91260			−0.956302	+	0.292381i	$0.905552\pi$
$224$		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	0.930668	−	0.365865i	$-0.119227\pi$
$227$	507.837	+	879.600i	0.148486	+	0.257185i	−0.782182	+	0.623050i	$0.785893\pi$
$228$	−193.379	−	334.943i	−0.0561704	−	0.0972900i
$229$	−2054.18	+	3557.94i	−0.592768	+	1.02670i	0.401090	+	0.916039i	$0.368632\pi$
$229$	−2054.18	+	3557.94i	−0.592768	+	1.02670i	−0.993858	+	0.110665i	$0.964702\pi$
$230$	−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	0.865700	−	0.500563i	$-0.166874\pi$
$241$	−2.43391	−	4.21565i	−0.000650547	−	0.00112678i	−0.866350	+	0.499437i	$0.833540\pi$
$242$	−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	$-0.521947\pi$
$251$	−547.921			−0.137787			−0.0688934	+	0.997624i	$0.521947\pi$
$252$		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	−0.738021	−	0.674778i	$-0.764239\pi$
$257$	887.306	−	1536.86i	0.215364	−	0.373022i	0.953385	+	0.301756i	$0.0975728\pi$
$258$	−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	0.620955	−	0.783846i	$-0.286745\pi$
$269$	−1625.15	−	2814.84i	−0.368353	−	0.638006i	−0.989308	+	0.145840i	$0.953411\pi$
$270$	−416.830	−	721.971i	−0.0939536	−	0.162732i
$271$	448.071	−	776.082i	0.100437	−	0.173962i	−0.811428	−	0.584453i	$-0.801309\pi$
$271$	448.071	−	776.082i	0.100437	−	0.173962i	0.911865	+	0.410491i	$0.134643\pi$
$272$	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	$-0.974222\pi$
$283$	−2706.13	−	4687.15i	−0.568419	−	0.984531i	0.428303	−	0.903635i	$-0.359111\pi$
$284$	−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	$-0.491043\pi$
$293$	282.211			0.0562695			0.0281347	+	0.999604i	$0.491043\pi$
$294$		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	$-0.442895\pi$
$307$	1919.67			0.356878			0.178439	+	0.983951i	$0.442895\pi$
$308$		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	0.805405	−	0.592724i	$-0.201948\pi$
$311$	−606.654	−	1050.76i	−0.110612	−	0.191585i	−0.916017	+	0.401139i	$0.868614\pi$
$312$	1550.53	+	2685.60i	0.281352	+	0.487315i
$313$	717.001	−	1241.88i	0.129480	−	0.224266i	−0.793995	−	0.607924i	$-0.792002\pi$
$313$	717.001	−	1241.88i	0.129480	−	0.224266i	0.923475	+	0.383658i	$0.125336\pi$
$314$	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	$-0.788659\pi$
$349$	−10269.6			−1.57513			−0.787567	+	0.616229i	$0.788659\pi$
$350$		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	0.740970	−	0.671538i	$-0.234366\pi$
$353$	−1399.97	−	2424.81i	−0.211084	−	0.365609i	−0.952054	+	0.305930i	$0.901033\pi$
$354$	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	0.730371	−	0.683050i	$-0.239347\pi$
$367$	−1591.42	−	2756.42i	−0.226353	−	0.392055i	−0.956725	+	0.290995i	$0.906014\pi$
$368$	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	−0.902403	−	0.430893i	$-0.858199\pi$
$383$	−584.928	+	1013.13i	−0.0780377	+	0.135165i	0.824366	+	0.566058i	$0.191532\pi$
$384$	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	−0.796410	−	0.604757i	$-0.793270\pi$
$397$	992.963	−	1719.86i	0.125530	−	0.217424i	0.921940	+	0.387333i	$0.126604\pi$
$398$	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	$0.0834180\pi$
$409$	5850.40	+	10133.2i	0.707295	+	1.22507i	−0.258562	+	0.965995i	$0.583249\pi$
$410$	−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	$-0.449064\pi$
$419$	2733.20			0.318677			0.159339	+	0.987224i	$0.449064\pi$
$420$		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	$-0.353145\pi$
$433$	8022.03			0.890333			0.445166	+	0.895448i	$0.353145\pi$
$434$		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	−0.673989	−	0.738741i	$-0.735420\pi$
$439$	2784.94	−	4823.66i	0.302774	−	0.524421i	0.976763	+	0.214321i	$0.0687538\pi$
$440$	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	$-0.400740\pi$
$461$	6073.57			0.613611			0.306805	+	0.951772i	$0.400740\pi$
$462$		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	−0.647880	−	0.761742i	$-0.724344\pi$
$467$	3388.35	−	5868.80i	0.335748	−	0.581532i	0.983628	+	0.180210i	$0.0576777\pi$
$468$	−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	0.803177	−	0.595741i	$-0.203141\pi$
$479$	−1198.66	−	2076.14i	−0.114338	−	0.198040i	−0.917515	+	0.397701i	$0.869808\pi$
$480$	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	$-0.437139\pi$
$503$	4426.76			0.392405			0.196202	+	0.980563i	$0.437139\pi$
$504$		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	$0.447346\pi$
$509$	−8863.84	+	15352.6i	−0.771872	+	1.33692i	−0.936536	+	0.350571i	$0.885987\pi$
$510$	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	0.624425	−	0.781084i	$-0.285333\pi$
$521$	−4331.40	−	7502.20i	−0.364226	−	0.630858i	−0.988652	+	0.150226i	$0.952000\pi$
$522$	1050.77	+	1819.98i	0.0881050	+	0.152602i
$523$	3885.20	−	6729.36i	0.324833	−	0.562628i	−0.656645	−	0.754200i	$-0.728025\pi$
$523$	3885.20	−	6729.36i	0.324833	−	0.562628i	0.981479	+	0.191572i	$0.0613584\pi$
$524$	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	$-0.967296\pi$
$563$	−7830.65	−	13563.1i	−0.586186	−	1.01530i	0.408541	−	0.912740i	$-0.366038\pi$
$564$	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	0.876565	−	0.481284i	$-0.159829\pi$
$577$	297.689	+	515.613i	0.0214783	+	0.0372015i	−0.855086	+	0.518485i	$0.826496\pi$
$578$	−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	$-0.686798\pi$
$587$	−15750.3			−1.10747			−0.553736	+	0.832693i	$0.686798\pi$
$588$		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	−0.858700	−	0.512478i	$-0.828728\pi$
$593$	208.939	−	361.893i	0.0144690	−	0.0250610i	0.873169	+	0.487417i	$0.162061\pi$
$594$	−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	$-0.682607\pi$
$601$	−15992.6			−1.08545			−0.542723	+	0.839912i	$0.682607\pi$
$602$		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	−0.999536	−	0.0304515i	$-0.990306\pi$
$607$	−7079.59	+	12262.2i	−0.473396	+	0.819947i	0.526140	+	0.850398i	$0.323639\pi$
$608$	−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	0.592294	−	0.805722i	$-0.298222\pi$
$619$	−6185.30	−	10713.3i	−0.401629	−	0.695641i	−0.993923	+	0.110081i	$0.964889\pi$
$620$	−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	$-0.544087\pi$
$643$	−4502.17			−0.276125			−0.138063	+	0.990424i	$0.544087\pi$
$644$		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	$-0.814785\pi$
$647$	−14707.4	−	25474.0i	−0.893675	−	1.54789i	−0.0582393	−	0.998303i	$-0.518549\pi$
$648$	−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	0.969535	−	0.244953i	$-0.0787724\pi$
$661$	4633.18	+	8024.91i	0.272632	+	0.472213i	−0.696903	+	0.717166i	$0.745439\pi$
$662$	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	$-0.613883\pi$
$677$	11204.8	−	19407.3i	0.636093	−	1.10174i	0.986283	−	0.165066i	$-0.0527838\pi$
$678$	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	−0.958721	−	0.284349i	$-0.908223\pi$
$691$	−4234.21	+	7333.87i	−0.233107	+	0.403753i	0.725614	+	0.688102i	$0.241556\pi$
$692$	−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	−0.685960	−	0.727639i	$-0.740618\pi$
$719$	5536.53	−	9589.56i	0.287174	−	0.497399i	0.973134	+	0.230240i	$0.0739510\pi$
$720$	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	$-0.200884\pi$
$727$	31652.7			1.61476			0.807382	+	0.590029i	$0.200884\pi$
$728$		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	−0.996629	−	0.0820419i	$-0.973856\pi$
$733$	−8479.15	+	14686.3i	−0.427264	+	0.740043i	0.569365	+	0.822085i	$0.307189\pi$
$734$	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	$-0.588541\pi$
$761$	14599.5	−	25287.1i	0.695444	−	1.20454i	0.970031	−	0.242982i	$-0.0781257\pi$
$762$	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	$-0.328892\pi$
$769$	21838.2			1.02407			0.512033	+	0.858966i	$0.328892\pi$
$770$		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	$0.0359027\pi$
$773$	12772.4	+	22122.4i	0.594296	+	1.02935i	−0.399349	+	0.916799i	$0.630764\pi$
$774$	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	$0.152539\pi$
$787$	18611.6	+	32236.2i	0.842989	+	1.46010i	−0.0443677	+	0.999015i	$0.514127\pi$
$788$	−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	$-0.854564\pi$
$797$	−40384.6			−1.79485			−0.897425	+	0.441168i	$0.854564\pi$
$798$		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	$-0.766408\pi$
$811$	−34301.8			−1.48520			−0.742600	+	0.669735i	$0.766408\pi$
$812$		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	$-0.938476\pi$
$829$	−15682.8	−	27163.3i	−0.657039	−	1.13802i	0.324340	−	0.945941i	$-0.394858\pi$
$830$	−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	$-0.697726\pi$
$839$	−28287.1			−1.16398			−0.581990	+	0.813196i	$0.697726\pi$
$840$		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	$-0.439551\pi$
$853$	9405.41			0.377533			0.188766	+	0.982022i	$0.439551\pi$
$854$		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	$0.0215223\pi$
$857$	13983.4	+	24220.0i	0.557369	+	0.965391i	−0.440346	+	0.897828i	$0.645144\pi$
$858$	−6368.62	−	11030.8i	−0.253404	−	0.438909i
$859$	−3140.55	+	5439.60i	−0.124743	+	0.216061i	−0.921632	−	0.388064i	$-0.873144\pi$
$859$	−3140.55	+	5439.60i	−0.124743	+	0.216061i	0.796889	+	0.604125i	$0.206477\pi$
$860$	−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	$-0.171672\pi$
$881$	44875.5			1.71611			0.858056	+	0.513556i	$0.171672\pi$
$882$		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	−0.882213	−	0.470850i	$-0.843947\pi$
$887$	−880.700	+	1525.42i	−0.0333382	+	0.0577435i	0.848875	+	0.528594i	$0.177281\pi$
$888$	−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	−0.974830	−	0.222950i	$-0.928431\pi$
$929$	−8334.21	+	14435.3i	−0.294334	+	0.509802i	0.680496	+	0.732752i	$0.261765\pi$
$930$	−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	$-0.322310\pi$
$937$	30384.9			1.05937			0.529685	+	0.848194i	$0.322310\pi$
$938$		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	0.876201	−	0.481946i	$-0.160070\pi$
$941$	598.176	+	1036.07i	0.0207226	+	0.0358926i	−0.855478	+	0.517839i	$0.826737\pi$
$942$	−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	−0.988669	−	0.150115i	$-0.952036\pi$
$971$	−11023.6	+	19093.5i	−0.364331	+	0.631039i	0.624338	+	0.781155i	$0.285369\pi$
$972$	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	0.795623	−	0.605792i	$-0.207144\pi$
$983$	−3908.55	−	6769.81i	−0.126819	−	0.219658i	−0.922443	+	0.386134i	$0.873810\pi$
$984$	−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	$0.131273\pi$
$997$	25348.0	+	43904.0i	0.805195	+	1.39464i	−0.110964	+	0.993824i	$0.535394\pi$
$998$	−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.h.226.2		4
7.2	even	3		35.4.a.b.1.1	✓	2
7.3	odd	6		245.4.e.i.116.2		4
7.4	even	3	inner	245.4.e.h.116.2		4
7.5	odd	6		245.4.a.k.1.1		2
7.6	odd	2		245.4.e.i.226.2		4
21.2	odd	6		315.4.a.f.1.2		2
21.5	even	6		2205.4.a.u.1.2		2
28.23	odd	6		560.4.a.r.1.1		2
35.2	odd	12		175.4.b.c.99.3		4
35.9	even	6		175.4.a.c.1.2		2
35.19	odd	6		1225.4.a.m.1.2		2
35.23	odd	12		175.4.b.c.99.2		4
56.37	even	6		2240.4.a.bn.1.1		2
56.51	odd	6		2240.4.a.bo.1.2		2
105.44	odd	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	7.2	even	3
175.4.a.c.1.2		2	35.9	even	6
175.4.b.c.99.2		4	35.23	odd	12
175.4.b.c.99.3		4	35.2	odd	12
245.4.a.k.1.1		2	7.5	odd	6
245.4.e.h.116.2		4	7.4	even	3	inner
245.4.e.h.226.2		4	1.1	even	1	trivial
245.4.e.i.116.2		4	7.3	odd	6
245.4.e.i.226.2		4	7.6	odd	2
315.4.a.f.1.2		2	21.2	odd	6
560.4.a.r.1.1		2	28.23	odd	6
1225.4.a.m.1.2		2	35.19	odd	6
1575.4.a.z.1.1		2	105.44	odd	6
2205.4.a.u.1.2		2	21.5	even	6
2240.4.a.bn.1.1		2	56.37	even	6
2240.4.a.bo.1.2		2	56.51	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - 2 q^{3} - 20 q^{4} + 10 q^{5} - 16 q^{6} + 96 q^{8} - 12 q^{9} + 40 q^{10} + 14 q^{11} + 108 q^{12} + 100 q^{13} - 20 q^{15} - 168 q^{16} + 50 q^{17} - 16 q^{18} - 36 q^{19} - 200 q^{20}+ \cdots + 1880 q^{99}+O(q^{100}) \) 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

Introduction

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