LMFDB - Embedded newform 99.6.f.b.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,6,Mod(37,99)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, 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:	$15.8779981615$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 78 x^{18} + 79 x^{17} + 10573 x^{16} - 33409 x^{15} + 1262953 x^{14} + \cdots + 25599187870096 $ x^20 - x^19 + 78x^18 + 79x^17 + 10573x^16 - 33409x^15 + 1262953x^14 - 1581925x^13 + 89291182x^12 - 100741271x^11 + 2277268901x^10 - 1144062486x^9 + 70677624924x^8 + 93641098134x^7 + 1732079176577x^6 + 1113900934906x^5 + 27749747552381x^4 + 4154923377746x^3 + 57625758470132x^2 + 60036938210920x + 25599187870096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 11^{2} $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.1
Root			$7.96653 - 5.78803i$ of defining polynomial
Character	$\chi$	$=$	99.37
Dual form			99.6.f.b.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.77555 - 6.37581i) q^{2} +(26.4708 + 81.4687i) q^{4} +(-31.3852 + 22.8027i) q^{5} +(-67.6896 - 208.327i) q^{7} +(179.871 - 553.584i) q^{8} +O(q^{10})$	\(q+(-8.77555 - 6.37581i) q^{2} +(26.4708 + 81.4687i) q^{4} +(-31.3852 + 22.8027i) q^{5} +(-67.6896 - 208.327i) q^{7} +(179.871 - 553.584i) q^{8} +420.808 q^{10} +(-313.554 - 250.469i) q^{11} +(32.8450 + 23.8633i) q^{13} +(-734.241 + 2259.76i) q^{14} +(-2890.37 + 2099.97i) q^{16} +(-516.753 + 375.443i) q^{17} +(427.464 - 1315.60i) q^{19} +(-2688.50 - 1953.31i) q^{20} +(1154.67 + 4197.17i) q^{22} +799.310 q^{23} +(-500.610 + 1540.72i) q^{25} +(-136.085 - 418.826i) q^{26} +(15180.3 - 11029.2i) q^{28} +(1319.88 + 4062.16i) q^{29} +(-4931.04 - 3582.61i) q^{31} +20127.3 q^{32} +6928.55 q^{34} +(6874.87 + 4994.88i) q^{35} +(3018.37 + 9289.60i) q^{37} +(-12139.2 + 8819.67i) q^{38} +(6977.94 + 21475.9i) q^{40} +(1351.42 - 4159.25i) q^{41} +2017.22 q^{43} +(12105.3 - 32175.0i) q^{44} +(-7014.39 - 5096.25i) q^{46} +(-110.244 + 339.295i) q^{47} +(-25221.1 + 18324.2i) q^{49} +(14216.5 - 10328.9i) q^{50} +(-1074.68 + 3307.52i) q^{52} +(28795.3 + 20921.0i) q^{53} +(15552.3 + 711.130i) q^{55} -127502. q^{56} +(14316.9 - 44063.0i) q^{58} +(3667.59 + 11287.7i) q^{59} +(-22766.8 + 16541.0i) q^{61} +(20430.6 + 62878.8i) q^{62} +(-84136.1 - 61128.5i) q^{64} -1574.99 q^{65} +21369.8 q^{67} +(-44265.7 - 32160.9i) q^{68} +(-28484.3 - 87665.7i) q^{70} +(1968.99 - 1430.56i) q^{71} +(20773.7 + 63934.8i) q^{73} +(32740.8 - 100766. i) q^{74} +118495. q^{76} +(-30955.1 + 82276.0i) q^{77} +(-26787.6 - 19462.3i) q^{79} +(42829.7 - 131816. i) q^{80} +(-38378.0 + 27883.3i) q^{82} +(-54821.4 + 39830.1i) q^{83} +(7657.29 - 23566.7i) q^{85} +(-17702.2 - 12861.4i) q^{86} +(-195055. + 128527. i) q^{88} -69719.1 q^{89} +(2748.10 - 8457.79i) q^{91} +(21158.4 + 65118.8i) q^{92} +(3130.73 - 2274.61i) q^{94} +(16583.1 + 51037.6i) q^{95} +(136758. + 99360.2i) q^{97} +338161. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{2} + 8 q^{4} + 11 q^{5} - 139 q^{7} + 76 q^{8}+O(q^{10}) $ 20 * q - 6 * q^2 + 8 * q^4 + 11 * q^5 - 139 * q^7 + 76 * q^8	$ 20 q - 6 q^{2} + 8 q^{4} + 11 q^{5} - 139 q^{7} + 76 q^{8} - 424 q^{10} - 2289 q^{11} - 847 q^{13} - 2022 q^{14} - 7148 q^{16} - 2482 q^{17} + 2958 q^{19} - 8037 q^{20} + 7441 q^{22} - 8140 q^{23} - 13120 q^{25} + 13508 q^{26} + 27819 q^{28} + 20210 q^{29} + 5540 q^{31} + 4626 q^{32} + 16540 q^{34} + 34101 q^{35} - 25173 q^{37} + 55878 q^{38} + 22689 q^{40} - 54349 q^{41} - 21688 q^{43} - 24587 q^{44} + 44155 q^{46} + 48387 q^{47} - 78880 q^{49} - 19956 q^{50} + 109051 q^{52} + 74382 q^{53} - 47630 q^{55} - 168894 q^{56} + 1501 q^{58} + 108412 q^{59} + 16737 q^{61} - 132685 q^{62} - 157030 q^{64} + 134194 q^{65} + 20178 q^{67} - 387013 q^{68} - 411988 q^{70} - 143157 q^{71} + 164980 q^{73} - 286114 q^{74} + 46868 q^{76} + 367461 q^{77} + 369613 q^{79} + 107448 q^{80} - 184129 q^{82} - 267741 q^{83} + 379937 q^{85} + 290531 q^{86} - 740846 q^{88} - 205492 q^{89} + 394559 q^{91} + 483181 q^{92} + 561327 q^{94} - 267881 q^{95} - 300567 q^{97} + 2296174 q^{98}+O(q^{100}) $ 20 * q - 6 * q^2 + 8 * q^4 + 11 * q^5 - 139 * q^7 + 76 * q^8 - 424 * q^10 - 2289 * q^11 - 847 * q^13 - 2022 * q^14 - 7148 * q^16 - 2482 * q^17 + 2958 * q^19 - 8037 * q^20 + 7441 * q^22 - 8140 * q^23 - 13120 * q^25 + 13508 * q^26 + 27819 * q^28 + 20210 * q^29 + 5540 * q^31 + 4626 * q^32 + 16540 * q^34 + 34101 * q^35 - 25173 * q^37 + 55878 * q^38 + 22689 * q^40 - 54349 * q^41 - 21688 * q^43 - 24587 * q^44 + 44155 * q^46 + 48387 * q^47 - 78880 * q^49 - 19956 * q^50 + 109051 * q^52 + 74382 * q^53 - 47630 * q^55 - 168894 * q^56 + 1501 * q^58 + 108412 * q^59 + 16737 * q^61 - 132685 * q^62 - 157030 * q^64 + 134194 * q^65 + 20178 * q^67 - 387013 * q^68 - 411988 * q^70 - 143157 * q^71 + 164980 * q^73 - 286114 * q^74 + 46868 * q^76 + 367461 * q^77 + 369613 * q^79 + 107448 * q^80 - 184129 * q^82 - 267741 * q^83 + 379937 * q^85 + 290531 * q^86 - 740846 * q^88 - 205492 * q^89 + 394559 * q^91 + 483181 * q^92 + 561327 * q^94 - 267881 * q^95 - 300567 * q^97 + 2296174 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−8.77555	−	6.37581i	−1.55131	−	1.12709i	−0.942707	−	0.333622i	$-0.891729\pi$
$2$	−8.77555	−	6.37581i	−1.55131	−	1.12709i	−0.608606	−	0.793473i	$-0.708271\pi$
$3$		0			0
$3$		0			0
$4$	26.4708	+	81.4687i	0.827212	+	2.54590i
$5$	−31.3852	+	22.8027i	−0.561436	+	0.407907i	−0.831984	−	0.554800i	$-0.812795\pi$
$5$	−31.3852	+	22.8027i	−0.561436	+	0.407907i	0.270548	+	0.962706i	$0.412795\pi$
$6$		0			0
$7$	−67.6896	−	208.327i	−0.522128	−	1.60694i	−0.769927	−	0.638132i	$-0.779707\pi$
$7$	−67.6896	−	208.327i	−0.522128	−	1.60694i	0.247799	−	0.968811i	$-0.420293\pi$
$8$	179.871	−	553.584i	0.993654	−	3.05815i
$9$		0			0
$10$	420.808			1.33071
$11$	−313.554	−	250.469i	−0.781324	−	0.624125i
$11$	−313.554	−	250.469i	−0.781324	−	0.624125i
$12$		0			0
$13$	32.8450	+	23.8633i	0.0539027	+	0.0391626i	0.614410	−	0.788987i	$-0.289394\pi$
$13$	32.8450	+	23.8633i	0.0539027	+	0.0391626i	−0.560508	+	0.828149i	$0.689394\pi$
$14$	−734.241	+	2259.76i	−1.00119	+	3.08136i
$15$		0			0
$16$	−2890.37	+	2099.97i	−2.82262	+	2.05076i
$17$	−516.753	+	375.443i	−0.433672	+	0.315081i	−0.783115	−	0.621876i	$-0.786371\pi$
$17$	−516.753	+	375.443i	−0.433672	+	0.315081i	0.349444	+	0.936957i	$0.386371\pi$
$18$		0			0
$19$	427.464	−	1315.60i	0.271653	−	0.836063i	−0.718432	−	0.695597i	$-0.755140\pi$
$19$	427.464	−	1315.60i	0.271653	−	0.836063i	0.990086	−	0.140466i	$-0.0448601\pi$
$20$	−2688.50	−	1953.31i	−1.50291	−	1.09193i
$21$		0			0
$22$	1154.67	+	4197.17i	0.508630	+	1.84884i
$23$	799.310			0.315062			0.157531	−	0.987514i	$-0.449647\pi$
$23$	799.310			0.315062			0.157531	+	0.987514i	$0.449647\pi$
$24$		0			0
$25$	−500.610	+	1540.72i	−0.160195	+	0.493030i
$26$	−136.085	−	418.826i	−0.0394800	−	0.121507i
$27$		0			0
$28$	15180.3	−	11029.2i	3.65920	−	2.65857i
$29$	1319.88	+	4062.16i	0.291433	+	0.896937i	0.984396	+	0.175965i	$0.0563045\pi$
$29$	1319.88	+	4062.16i	0.291433	+	0.896937i	−0.692964	+	0.720972i	$0.743695\pi$
$30$		0			0
$31$	−4931.04	−	3582.61i	−0.921583	−	0.669569i	0.0223345	−	0.999751i	$-0.492890\pi$
$31$	−4931.04	−	3582.61i	−0.921583	−	0.669569i	−0.943918	+	0.330181i	$0.892890\pi$
$32$	20127.3			3.47464
$33$		0			0
$34$	6928.55			1.02789
$35$	6874.87	+	4994.88i	0.948624	+	0.689216i
$36$		0			0
$37$	3018.37	+	9289.60i	0.362467	+	1.11556i	0.951552	+	0.307488i	$0.0994884\pi$
$37$	3018.37	+	9289.60i	0.362467	+	1.11556i	−0.589085	+	0.808071i	$0.700512\pi$
$38$	−12139.2	+	8819.67i	−1.36374	+	0.990816i
$39$		0			0
$40$	6977.94	+	21475.9i	0.689568	+	2.12227i
$41$	1351.42	−	4159.25i	0.125554	−	0.386416i	−0.868448	−	0.495781i	$-0.834882\pi$
$41$	1351.42	−	4159.25i	0.125554	−	0.386416i	0.994002	+	0.109365i	$0.0348818\pi$
$42$		0			0
$43$	2017.22			0.166373			0.0831864	−	0.996534i	$-0.473490\pi$
$43$	2017.22			0.166373			0.0831864	+	0.996534i	$0.473490\pi$
$44$	12105.3	−	32175.0i	0.942638	−	2.50545i
$45$		0			0
$46$	−7014.39	−	5096.25i	−0.488759	−	0.355105i
$47$	−110.244	+	339.295i	−0.00727961	+	0.0224043i	−0.954630	−	0.297793i	$-0.903749\pi$
$47$	−110.244	+	339.295i	−0.00727961	+	0.0224043i	0.947351	+	0.320198i	$0.103749\pi$
$48$		0			0
$49$	−25221.1	+	18324.2i	−1.50063	+	1.09027i
$50$	14216.5	−	10328.9i	0.804204	−	0.584288i
$51$		0			0
$52$	−1074.68	+	3307.52i	−0.0551150	+	0.169626i
$53$	28795.3	+	20921.0i	1.40810	+	1.02304i	0.993596	+	0.112992i	$0.0360435\pi$
$53$	28795.3	+	20921.0i	1.40810	+	1.02304i	0.414500	+	0.910049i	$0.363956\pi$
$54$		0			0
$55$	15552.3	+	711.130i	0.693248	+	0.0316988i
$56$	−127502.			−5.43309
$57$		0			0
$58$	14316.9	−	44063.0i	0.558830	−	1.71990i
$59$	3667.59	+	11287.7i	0.137167	+	0.422158i	0.995921	−	0.0902311i	$-0.0287606\pi$
$59$	3667.59	+	11287.7i	0.137167	+	0.422158i	−0.858753	+	0.512389i	$0.828761\pi$
$60$		0			0
$61$	−22766.8	+	16541.0i	−0.783388	+	0.569164i	−0.905994	−	0.423291i	$-0.860875\pi$
$61$	−22766.8	+	16541.0i	−0.783388	+	0.569164i	0.122606	+	0.992455i	$0.460875\pi$
$62$	20430.6	+	62878.8i	0.674996	+	2.07742i
$63$		0			0
$64$	−84136.1	−	61128.5i	−2.56763	−	1.86549i
$65$	−1574.99			−0.0462376
$66$		0			0
$67$	21369.8			0.581586			0.290793	−	0.956786i	$-0.406081\pi$
$67$	21369.8			0.581586			0.290793	+	0.956786i	$0.406081\pi$
$68$	−44265.7	−	32160.9i	−1.16090	−	0.843444i
$69$		0			0
$70$	−28484.3	−	87665.7i	−0.694801	−	2.13838i
$71$	1968.99	−	1430.56i	0.0463551	−	0.0336790i	−0.564366	−	0.825524i	$-0.690879\pi$
$71$	1968.99	−	1430.56i	0.0463551	−	0.0336790i	0.610722	+	0.791845i	$0.290879\pi$
$72$		0			0
$73$	20773.7	+	63934.8i	0.456253	+	1.40420i	0.869657	+	0.493656i	$0.164340\pi$
$73$	20773.7	+	63934.8i	0.456253	+	1.40420i	−0.413404	+	0.910548i	$0.635660\pi$
$74$	32740.8	−	100766.i	0.695041	−	2.13912i
$75$		0			0
$76$	118495.			2.35324
$77$	−30955.1	+	82276.0i	−0.594983	+	1.58142i
$78$		0			0
$79$	−26787.6	−	19462.3i	−0.482910	−	0.350854i	0.319542	−	0.947572i	$-0.396471\pi$
$79$	−26787.6	−	19462.3i	−0.482910	−	0.350854i	−0.802451	+	0.596718i	$0.796471\pi$
$80$	42829.7	−	131816.i	0.748204	−	2.30274i
$81$		0			0
$82$	−38378.0	+	27883.3i	−0.630301	+	0.457941i
$83$	−54821.4	+	39830.1i	−0.873484	+	0.634623i	−0.931520	−	0.363691i	$-0.881516\pi$
$83$	−54821.4	+	39830.1i	−0.873484	+	0.634623i	0.0580356	+	0.998315i	$0.481516\pi$
$84$		0			0
$85$	7657.29	−	23566.7i	0.114955	−	0.353795i
$86$	−17702.2	−	12861.4i	−0.258096	−	0.187518i
$87$		0			0
$88$	−195055.	+	128527.i	−2.68504	+	1.76924i
$89$	−69719.1			−0.932989			−0.466495	−	0.884524i	$-0.654483\pi$
$89$	−69719.1			−0.932989			−0.466495	+	0.884524i	$0.654483\pi$
$90$		0			0
$91$	2748.10	−	8457.79i	0.0347880	−	0.107066i
$92$	21158.4	+	65118.8i	0.260623	+	0.802115i
$93$		0			0
$94$	3130.73	−	2274.61i	0.0365448	−	0.0265513i
$95$	16583.1	+	51037.6i	0.188520	+	0.580205i
$96$		0			0
$97$	136758.	+	99360.2i	1.47578	+	1.07222i	0.978886	+	0.204407i	$0.0655267\pi$
$97$	136758.	+	99360.2i	1.47578	+	1.07222i	0.496895	+	0.867811i	$0.334473\pi$
$98$	338161.			3.55679
$99$		0			0
$100$	−138772.			−1.38772
$101$	51456.8	+	37385.6i	0.501926	+	0.364671i	0.809752	−	0.586772i	$-0.199602\pi$
$101$	51456.8	+	37385.6i	0.501926	+	0.364671i	−0.307826	+	0.951443i	$0.599602\pi$
$102$		0			0
$103$	−22346.7	−	68775.9i	−0.207548	−	0.638768i	−0.999599	−	0.0283130i	$-0.990986\pi$
$103$	−22346.7	−	68775.9i	−0.207548	−	0.638768i	0.792051	−	0.610455i	$-0.209014\pi$
$104$	19118.2	−	13890.2i	0.173326	−	0.125928i
$105$		0			0
$106$	−119306.	−	367187.i	−1.03133	−	3.17411i
$107$	22166.4	−	68221.1i	0.187170	−	0.576049i	−0.812809	−	0.582530i	$-0.802063\pi$
$107$	22166.4	−	68221.1i	0.187170	−	0.576049i	0.999979	+	0.00648071i	$0.00206289\pi$
$108$		0			0
$109$	87556.4			0.705865			0.352932	−	0.935649i	$-0.385185\pi$
$109$	87556.4			0.705865			0.352932	+	0.935649i	$0.385185\pi$
$110$	−131946.	−	105399.i	−1.03972	−	0.830531i
$111$		0			0
$112$	633129.	+	459995.i	4.76922	+	3.46504i
$113$	60708.7	−	186842.i	0.447255	−	1.37651i	−0.432737	−	0.901520i	$-0.642452\pi$
$113$	60708.7	−	186842.i	0.447255	−	1.37651i	0.879992	−	0.474988i	$-0.157548\pi$
$114$		0			0
$115$	−25086.5	+	18226.4i	−0.176887	+	0.128516i
$116$	−296001.	+	215057.i	−2.04243	+	1.48391i
$117$		0			0
$118$	39783.0	−	122440.i	0.263022	−	0.809500i
$119$	113194.	+	82240.1i	0.732749	+	0.532373i
$120$		0			0
$121$	35581.8	+	157071.i	0.220935	+	0.975289i
$122$	305253.			1.85678
$123$		0			0
$124$	161342.	−	496560.i	0.942310	−	2.90013i
$125$	−56883.5	−	175069.i	−0.325620	−	1.00216i
$126$		0			0
$127$	−152225.	+	110598.i	−0.837484	+	0.608468i	−0.921667	−	0.387982i	$-0.873172\pi$
$127$	−152225.	+	110598.i	−0.837484	+	0.608468i	0.0841825	+	0.996450i	$0.473172\pi$
$128$	149568.	+	460322.i	0.806888	+	2.48335i
$129$		0			0
$130$	13821.4	+	10041.9i	0.0717289	+	0.0521141i
$131$	−345605.			−1.75955			−0.879776	−	0.475388i	$-0.842308\pi$
$131$	−345605.			−1.75955			−0.879776	+	0.475388i	$0.842308\pi$
$132$		0			0
$133$	−303009.			−1.48534
$134$	−187532.	−	136250.i	−0.902221	−	0.655502i
$135$		0			0
$136$	114891.	+	353598.i	0.532646	+	1.63931i
$137$	−36871.0	+	26788.3i	−0.167835	+	0.121939i	−0.668532	−	0.743683i	$-0.733077\pi$
$137$	−36871.0	+	26788.3i	−0.167835	+	0.121939i	0.500697	+	0.865623i	$0.333077\pi$
$138$		0			0
$139$	−19547.2	−	60160.1i	−0.0858119	−	0.264102i	0.898939	−	0.438075i	$-0.144339\pi$
$139$	−19547.2	−	60160.1i	−0.0858119	−	0.264102i	−0.984750	+	0.173973i	$0.944339\pi$
$140$	−224943.	+	692305.i	−0.969959	+	2.98523i
$141$		0			0
$142$	−26399.9			−0.109871
$143$	−4321.68	−	15709.1i	−0.0176731	−	0.0642407i
$144$		0			0
$145$	−134053.	−	97395.0i	−0.529487	−	0.384695i
$146$	225336.	−	693512.i	0.874879	−	2.69260i
$147$		0			0
$148$	−676913.	+	491806.i	−2.54026	+	1.84561i
$149$	−60321.5	+	43826.1i	−0.222590	+	0.161721i	−0.693492	−	0.720464i	$-0.743929\pi$
$149$	−60321.5	+	43826.1i	−0.222590	+	0.161721i	0.470902	+	0.882186i	$0.343929\pi$
$150$		0			0
$151$	−11587.9	+	35663.9i	−0.0413583	+	0.127288i	−0.969604	−	0.244680i	$-0.921317\pi$
$151$	−11587.9	+	35663.9i	−0.0413583	+	0.127288i	0.928245	+	0.371968i	$0.121317\pi$
$152$	−651406.	−	473274.i	−2.28688	−	1.66151i
$153$		0			0
$154$	796224.	−	524654.i	2.70541	−	1.78267i
$155$	236455.			0.790531
$156$		0			0
$157$	−120640.	+	371290.i	−0.390608	+	1.20217i	0.541722	+	0.840557i	$0.317772\pi$
$157$	−120640.	+	371290.i	−0.390608	+	1.20217i	−0.932330	+	0.361609i	$0.882228\pi$
$158$	110988.	+	341585.i	0.353698	+	1.08857i
$159$		0			0
$160$	−631698.	+	458956.i	−1.95079	+	1.41733i
$161$	−54105.0	−	166518.i	−0.164502	−	0.506286i
$162$		0			0
$163$	−274567.	−	199485.i	−0.809431	−	0.588086i	0.104234	−	0.994553i	$-0.466761\pi$
$163$	−274567.	−	199485.i	−0.809431	−	0.588086i	−0.913666	+	0.406467i	$0.866761\pi$
$164$	374622.			1.08763
$165$		0			0
$166$	735037.			2.07033
$167$	50921.1	+	36996.3i	0.141288	+	0.102652i	0.656184	−	0.754601i	$-0.272169\pi$
$167$	50921.1	+	36996.3i	0.141288	+	0.102652i	−0.514896	+	0.857253i	$0.672169\pi$
$168$		0			0
$169$	−114227.	−	351553.i	−0.307645	−	0.946835i
$170$	−217454.	+	157990.i	−0.577092	+	0.419282i
$171$		0			0
$172$	53397.4	+	164340.i	0.137626	+	0.423568i
$173$	146159.	−	449831.i	0.371287	−	1.14270i	−0.574662	−	0.818391i	$-0.694867\pi$
$173$	146159.	−	449831.i	0.371287	−	1.14270i	0.945950	−	0.324314i	$-0.105133\pi$
$174$		0			0
$175$	354859.			0.875913
$176$	1.43227e6	+	65490.3i	3.48531	+	0.159366i
$177$		0			0
$178$	611823.	+	444516.i	1.44736	+	1.05157i
$179$	−89865.8	+	276578.i	−0.209634	+	0.645187i	0.789857	+	0.613291i	$0.210155\pi$
$179$	−89865.8	+	276578.i	−0.209634	+	0.645187i	−0.999491	+	0.0318964i	$0.989845\pi$
$180$		0			0
$181$	313275.	−	227608.i	0.710771	−	0.516406i	−0.172651	−	0.984983i	$-0.555233\pi$
$181$	313275.	−	227608.i	0.710771	−	0.516406i	0.883422	+	0.468578i	$0.155233\pi$
$182$	−78041.4	+	56700.4i	−0.174641	+	0.126884i
$183$		0			0
$184$	143772.	−	442486.i	0.313062	−	0.963507i
$185$	−306560.	−	222729.i	−0.658546	−	0.478462i
$186$		0			0
$187$	256067.	+	11708.7i	0.535488	+	0.0244852i
$188$	−30560.1			−0.0630609
$189$		0			0
$190$	179880.	−	553614.i	0.361492	−	1.11256i
$191$	254984.	+	784759.i	0.505742	+	1.55651i	0.799520	+	0.600640i	$0.205087\pi$
$191$	254984.	+	784759.i	0.505742	+	1.55651i	−0.293778	+	0.955874i	$0.594913\pi$
$192$		0			0
$193$	390657.	−	283829.i	0.754923	−	0.548484i	−0.142426	−	0.989805i	$-0.545490\pi$
$193$	390657.	−	283829.i	0.754923	−	0.548484i	0.897349	+	0.441322i	$0.145490\pi$
$194$	−566621.	−	1.74388e6i	−1.08091	−	3.32669i
$195$		0			0
$196$	−2.16047e6	−	1.56968e6i	−4.01706	−	2.91857i
$197$	−300533.			−0.551730			−0.275865	−	0.961196i	$-0.588964\pi$
$197$	−300533.			−0.551730			−0.275865	+	0.961196i	$0.588964\pi$
$198$		0			0
$199$	−946020.			−1.69343			−0.846716	−	0.532045i	$-0.821424\pi$
$199$	−946020.			−1.69343			−0.846716	+	0.532045i	$0.821424\pi$
$200$	762873.	+	554259.i	1.34858	+	0.979801i
$201$		0			0
$202$	−213199.	−	656158.i	−0.367626	−	1.13144i
$203$	756916.	−	549932.i	1.28916	−	0.936631i
$204$		0			0
$205$	52427.4	+	161355.i	0.0871311	+	0.268162i
$206$	−242398.	+	746025.i	−0.397980	+	1.22486i
$207$		0			0
$208$	−145046.			−0.232460
$209$	−463549.	+	305445.i	−0.734057	+	0.483690i
$210$		0			0
$211$	850656.	+	618038.i	1.31537	+	0.955672i	0.999977	+	0.00671130i	$0.00213629\pi$
$211$	850656.	+	618038.i	1.31537	+	0.955672i	0.315393	+	0.948961i	$0.397864\pi$
$212$	−942174.	+	2.89971e6i	−1.43976	+	4.43114i
$213$		0			0
$214$	−629487.	+	457349.i	−0.939621	+	0.682674i
$215$	−63310.9	+	45998.1i	−0.0934077	+	0.0678646i
$216$		0			0
$217$	−412575.	+	1.26977e6i	−0.594776	+	1.83053i
$218$	−768355.	−	558243.i	−1.09502	−	0.795576i
$219$		0			0
$220$	353748.	+	1.28585e6i	0.492761	+	1.79116i
$221$	−25932.0			−0.0357154
$222$		0			0
$223$	169535.	−	521775.i	0.228296	−	0.702621i	−0.769645	−	0.638472i	$-0.779567\pi$
$223$	169535.	−	521775.i	0.228296	−	0.702621i	0.997940	−	0.0641491i	$-0.0204333\pi$
$224$	−1.36241e6	−	4.19305e6i	−1.81421	−	5.58355i
$225$		0			0
$226$	−1.72402e6	+	1.25258e6i	−2.24529	+	1.63130i
$227$	124962.	+	384593.i	0.160958	+	0.495378i	0.998716	−	0.0506643i	$-0.0161338\pi$
$227$	124962.	+	384593.i	0.160958	+	0.495378i	−0.837758	+	0.546042i	$0.816134\pi$
$228$		0			0
$229$	−76471.5	−	55559.8i	−0.0963632	−	0.0700119i	0.538560	−	0.842587i	$-0.318968\pi$
$229$	−76471.5	−	55559.8i	−0.0963632	−	0.0700119i	−0.634924	+	0.772575i	$0.718968\pi$
$230$	336356.			0.419257
$231$		0			0
$232$	2.48616e6			3.03255
$233$	581255.	+	422306.i	0.701418	+	0.509610i	0.880394	−	0.474244i	$-0.157278\pi$
$233$	581255.	+	422306.i	0.701418	+	0.509610i	−0.178976	+	0.983853i	$0.557278\pi$
$234$		0			0
$235$	−4276.81	−	13162.7i	−0.00505185	−	0.0155480i
$236$	−822509.	+	597588.i	−0.961304	+	0.698428i
$237$		0			0
$238$	−468991.	−	1.44340e6i	−0.536688	−	1.65176i
$239$	22144.1	−	68152.6i	0.0250763	−	0.0771770i	−0.937735	−	0.347351i	$-0.887081\pi$
$239$	22144.1	−	68152.6i	0.0250763	−	0.0771770i	0.962811	+	0.270174i	$0.0870812\pi$
$240$		0			0
$241$	237149.			0.263014			0.131507	−	0.991315i	$-0.458018\pi$
$241$	237149.			0.263014			0.131507	+	0.991315i	$0.458018\pi$
$242$	689206.	−	1.60525e6i	0.756503	−	1.76199i
$243$		0			0
$244$	−1.95023e6	−	1.41692e6i	−2.09706	−	1.52360i
$245$	373729.	−	1.15022e6i	0.397779	−	1.22424i
$246$		0			0
$247$	45434.5	−	33010.1i	0.0473852	−	0.0344274i
$248$	−2.87023e6	+	2.08534e6i	−2.96338	+	2.15302i
$249$		0			0
$250$	−617026.	+	1.89901e6i	−0.624386	+	1.92166i
$251$	826366.	+	600390.i	0.827919	+	0.601518i	0.918970	−	0.394328i	$-0.129023\pi$
$251$	826366.	+	600390.i	0.827919	+	0.601518i	−0.0910507	+	0.995846i	$0.529023\pi$
$252$		0			0
$253$	−250627.	−	200202.i	−0.246165	−	0.196638i
$254$	2.04101e6			1.98500
$255$		0			0
$256$	594000.	−	1.82814e6i	0.566483	−	1.74345i
$257$	109152.	+	335936.i	0.103086	+	0.317266i	0.989276	−	0.146055i	$-0.0466576\pi$
$257$	109152.	+	335936.i	0.103086	+	0.317266i	−0.886190	+	0.463321i	$0.846658\pi$
$258$		0			0
$259$	1.73096e6	−	1.25762e6i	1.60339	−	1.16493i
$260$	−41691.3	−	128313.i	−0.0382483	−	0.117716i
$261$		0			0
$262$	3.03288e6	+	2.20351e6i	2.72962	+	1.98318i
$263$	−1.20912e6			−1.07790			−0.538950	−	0.842338i	$-0.681179\pi$
$263$	−1.20912e6			−1.07790			−0.538950	+	0.842338i	$0.681179\pi$
$264$		0			0
$265$	−1.38080e6			−1.20786
$266$	2.65907e6	+	1.93193e6i	2.30423	+	1.67412i
$267$		0			0
$268$	565676.	+	1.74097e6i	0.481095	+	1.48066i
$269$	81918.1	−	59517.0i	0.0690238	−	0.0501488i	−0.552738	−	0.833355i	$-0.686417\pi$
$269$	81918.1	−	59517.0i	0.0690238	−	0.0501488i	0.621762	+	0.783206i	$0.286417\pi$
$270$		0			0
$271$	−11458.8	−	35266.5i	−0.00947796	−	0.0291702i	0.946206	−	0.323566i	$-0.104882\pi$
$271$	−11458.8	−	35266.5i	−0.00947796	−	0.0291702i	−0.955684	+	0.294396i	$0.904882\pi$
$272$	705186.	−	2.17034e6i	0.577938	−	1.77871i
$273$		0			0
$274$	494360.			0.397802
$275$	542870.	−	357712.i	0.432877	−	0.285234i
$276$		0			0
$277$	−520856.	−	378424.i	−0.407867	−	0.296333i	0.364871	−	0.931058i	$-0.381113\pi$
$277$	−520856.	−	378424.i	−0.407867	−	0.296333i	−0.772738	+	0.634725i	$0.781113\pi$
$278$	−212032.	+	652567.i	−0.164547	+	0.506423i
$279$		0			0
$280$	4.00168e6	−	2.90739e6i	3.05033	−	2.21619i
$281$	−1.84764e6	+	1.34239e6i	−1.39589	+	1.01417i	−0.400698	+	0.916210i	$0.631232\pi$
$281$	−1.84764e6	+	1.34239e6i	−1.39589	+	1.01417i	−0.995190	+	0.0979624i	$0.968768\pi$
$282$		0			0
$283$	43539.5	−	134001.i	0.0323160	−	0.0994584i	−0.933598	−	0.358323i	$-0.883349\pi$
$283$	43539.5	−	134001.i	0.0323160	−	0.0994584i	0.965913	+	0.258865i	$0.0833485\pi$
$284$	168666.	+	122543.i	0.124089	+	0.0901558i
$285$		0			0
$286$	−62232.9	+	165410.i	−0.0449889	+	0.119577i
$287$	−957960.			−0.686504
$288$		0			0
$289$	−312684.	+	962341.i	−0.220222	+	0.677773i
$290$	555414.	+	1.70939e6i	0.387813	+	1.19357i
$291$		0			0
$292$	−4.65879e6	+	3.38481e6i	−3.19754	+	2.32315i
$293$	88335.2	+	271868.i	0.0601125	+	0.185007i	0.976603	−	0.215048i	$-0.0689909\pi$
$293$	88335.2	+	271868.i	0.0601125	+	0.185007i	−0.916491	+	0.400055i	$0.868991\pi$
$294$		0			0
$295$	−372498.	−	270635.i	−0.249212	−	0.181063i
$296$	5.68550e6			3.77172
$297$		0			0
$298$	808781.			0.527582
$299$	26253.3	+	19074.1i	0.0169827	+	0.0123386i
$300$		0			0
$301$	−136545.	−	420242.i	−0.0868679	−	0.267352i
$302$	329077.	−	239088.i	0.207625	−	0.150848i
$303$		0			0
$304$	1.52719e6	+	4.70022e6i	0.947786	+	2.91699i
$305$	337360.	−	1.03829e6i	0.207656	−	0.639098i
$306$		0			0
$307$	2.62633e6			1.59039			0.795194	−	0.606355i	$-0.207369\pi$
$307$	2.62633e6			1.59039			0.795194	+	0.606355i	$0.207369\pi$
$308$	−7.52232e6	−	343958.i	−4.51830	−	0.206599i
$309$		0			0
$310$	−2.07502e6	−	1.50759e6i	−1.22636	−	0.891004i
$311$	92222.2	−	283831.i	0.0540673	−	0.166402i	−0.920377	−	0.391033i	$-0.872118\pi$
$311$	92222.2	−	283831.i	0.0540673	−	0.166402i	0.974444	+	0.224631i	$0.0721177\pi$
$312$		0			0
$313$	913041.	−	663363.i	0.526780	−	0.382728i	−0.292372	−	0.956305i	$-0.594444\pi$
$313$	913041.	−	663363.i	0.526780	−	0.382728i	0.819152	+	0.573577i	$0.194444\pi$
$314$	3.42596e6	−	2.48910e6i	1.96091	−	1.42468i
$315$		0			0
$316$	876481.	−	2.69753e6i	0.493770	−	1.51967i
$317$	91772.5	+	66676.7i	0.0512938	+	0.0372671i	0.613137	−	0.789977i	$-0.289907\pi$
$317$	91772.5	+	66676.7i	0.0512938	+	0.0372671i	−0.561843	+	0.827244i	$0.689907\pi$
$318$		0			0
$319$	603591.	−	1.60430e6i	0.332098	−	0.882689i
$320$	4.03452e6			2.20251
$321$		0			0
$322$	−586886.	+	1.80625e6i	−0.315438	+	0.970819i
$323$	273039.	+	840328.i	0.145619	+	0.448170i
$324$		0			0
$325$	−53209.0	+	38658.6i	−0.0279433	+	0.0203020i
$326$	1.13760e6	+	3.50118e6i	0.592852	+	1.82461i
$327$		0			0
$328$	−2.05941e6	−	1.49625e6i	−1.05696	−	0.767927i
$329$	78146.6			0.0398034
$330$		0			0
$331$	−993938.			−0.498643			−0.249321	−	0.968421i	$-0.580208\pi$
$331$	−993938.			−0.498643			−0.249321	+	0.968421i	$0.580208\pi$
$332$	−4.69607e6	−	3.41189e6i	−2.33824	−	1.69883i
$333$		0			0
$334$	−210979.	−	649327.i	−0.103484	−	0.318491i
$335$	−670696.	+	487289.i	−0.326523	+	0.237233i
$336$		0			0
$337$	−168894.	−	519802.i	−0.0810101	−	0.249324i	0.902346	−	0.431013i	$-0.141844\pi$
$337$	−168894.	−	519802.i	−0.0810101	−	0.249324i	−0.983356	+	0.181689i	$0.941844\pi$
$338$	−1.23904e6	+	3.81336e6i	−0.589918	+	1.81558i
$339$		0			0
$340$	2.12265e6			0.995818
$341$	648818.	+	2.35842e6i	0.302160	+	1.09833i
$342$		0			0
$343$	2.54621e6	+	1.84993e6i	1.16858	+	0.849024i
$344$	362839.	−	1.11670e6i	0.165317	−	0.508793i
$345$		0			0
$346$	−4.15066e6	+	3.01563e6i	−1.86392	+	1.35422i
$347$	2.94835e6	−	2.14210e6i	1.31448	−	0.955029i	0.314501	−	0.949257i	$-0.398163\pi$
$347$	2.94835e6	−	2.14210e6i	1.31448	−	0.955029i	0.999983	−	0.00577194i	$-0.00183728\pi$
$348$		0			0
$349$	599671.	−	1.84560e6i	0.263542	−	0.811098i	−0.728484	−	0.685063i	$-0.759775\pi$
$349$	599671.	−	1.84560e6i	0.263542	−	0.811098i	0.992026	−	0.126035i	$-0.0402253\pi$
$350$	−3.11409e6	−	2.26252e6i	−1.35882	−	0.987237i
$351$		0			0
$352$	−6.31099e6	−	5.04125e6i	−2.71482	−	2.16861i
$353$	106849.			0.0456386			0.0228193	−	0.999740i	$-0.492736\pi$
$353$	106849.			0.0456386			0.0228193	+	0.999740i	$0.492736\pi$
$354$		0			0
$355$	−29176.7	+	89796.6i	−0.0122875	+	0.0378172i
$356$	−1.84552e6	−	5.67992e6i	−0.771780	−	2.37529i
$357$		0			0
$358$	2.55203e6	−	1.85416e6i	1.05240	−	0.764610i
$359$	−67012.4	−	206243.i	−0.0274422	−	0.0844585i	0.936397	−	0.350941i	$-0.114138\pi$
$359$	−67012.4	−	206243.i	−0.0274422	−	0.0844585i	−0.963840	+	0.266483i	$0.914138\pi$
$360$		0			0
$361$	455135.	+	330675.i	0.183811	+	0.133547i
$362$	−4.20035e6			−1.68467
$363$		0			0
$364$	761789.			0.301357
$365$	−2.10987e6	−	1.53291e6i	−0.828941	−	0.602261i
$366$		0			0
$367$	−56705.9	−	174523.i	−0.0219767	−	0.0676374i	0.939467	−	0.342640i	$-0.111321\pi$
$367$	−56705.9	−	174523.i	−0.0219767	−	0.0676374i	−0.961443	+	0.275003i	$0.911321\pi$
$368$	−2.31030e6	+	1.67853e6i	−0.889301	+	0.646115i
$369$		0			0
$370$	1.27016e6	+	3.90914e6i	0.482339	+	1.48449i
$371$	2.40927e6	−	7.41498e6i	0.908764	−	2.79689i
$372$		0			0
$373$	−4.72995e6			−1.76029			−0.880145	−	0.474705i	$-0.842555\pi$
$373$	−4.72995e6			−1.76029			−0.880145	+	0.474705i	$0.842555\pi$
$374$	−2.17248e6	−	1.73539e6i	−0.803112	−	0.641530i
$375$		0			0
$376$	167999.	+	122058.i	0.0612825	+	0.0445243i
$377$	−53585.1	+	164918.i	−0.0194174	+	0.0597606i
$378$		0			0
$379$	−3.49564e6	+	2.53973e6i	−1.25005	+	0.908217i	−0.998225	−	0.0595551i	$-0.981032\pi$
$379$	−3.49564e6	+	2.53973e6i	−1.25005	+	0.908217i	−0.251828	+	0.967772i	$0.581032\pi$
$380$	−3.71900e6	+	2.70201e6i	−1.32120	+	0.959905i
$381$		0			0
$382$	2.76585e6	−	8.51242e6i	0.969774	−	2.98466i
$383$	−280423.	−	203739.i	−0.0976824	−	0.0709704i	0.537872	−	0.843027i	$-0.319228\pi$
$383$	−280423.	−	203739.i	−0.0976824	−	0.0709704i	−0.635554	+	0.772056i	$0.719228\pi$
$384$		0			0
$385$	−904583.	−	3.28811e6i	−0.311026	−	1.13056i
$386$	−5.23787e6			−1.78931
$387$		0			0
$388$	−4.47466e6	+	1.37716e7i	−1.50897	+	4.64414i
$389$	245745.	+	756324.i	0.0823398	+	0.253416i	0.983748	−	0.179554i	$-0.0574655\pi$
$389$	245745.	+	756324.i	0.0823398	+	0.253416i	−0.901408	+	0.432970i	$0.857466\pi$
$390$		0			0
$391$	−413046.	+	300096.i	−0.136633	+	0.0992700i
$392$	5.60747e6	+	1.72580e7i	1.84311	+	5.67252i
$393$		0			0
$394$	2.63734e6	+	1.91614e6i	0.855905	+	0.621852i
$395$	1.28453e6			0.414238
$396$		0			0
$397$	−3.25240e6			−1.03568			−0.517842	−	0.855476i	$-0.673265\pi$
$397$	−3.25240e6			−1.03568			−0.517842	+	0.855476i	$0.673265\pi$
$398$	8.30185e6	+	6.03165e6i	2.62704	+	1.90866i
$399$		0			0
$400$	−1.78852e6	−	5.50451e6i	−0.558913	−	1.72016i
$401$	−3.24218e6	+	2.35558e6i	−1.00688	+	0.731538i	−0.963551	−	0.267523i	$-0.913795\pi$
$401$	−3.24218e6	+	2.35558e6i	−1.00688	+	0.731538i	−0.0433238	+	0.999061i	$0.513795\pi$
$402$		0			0
$403$	−76467.1	−	235341.i	−0.0234537	−	0.0721832i
$404$	−1.68365e6	+	5.18175e6i	−0.513214	+	1.57951i
$405$		0			0
$406$	−1.01486e7			−3.05557
$407$	1.38033e6	−	3.66880e6i	0.413045	−	1.09784i
$408$		0			0
$409$	−2.39161e6	−	1.73761e6i	−0.706940	−	0.513622i	0.175245	−	0.984525i	$-0.443928\pi$
$409$	−2.39161e6	−	1.73761e6i	−0.706940	−	0.513622i	−0.882185	+	0.470903i	$0.843928\pi$
$410$	568689.	−	1.75024e6i	0.167076	−	0.514208i
$411$		0			0
$412$	5.01155e6	−	3.64111e6i	1.45455	−	1.05679i
$413$	2.10327e6	−	1.52812e6i	0.606765	−	0.440841i
$414$		0			0
$415$	812348.	−	2.50015e6i	0.231538	−	0.712600i
$416$	661079.	+	480302.i	0.187292	+	0.136076i
$417$		0			0
$418$	6.01536e6	+	275052.i	1.68392	+	0.0769971i
$419$	693679.			0.193029			0.0965147	−	0.995332i	$-0.469231\pi$
$419$	693679.			0.193029			0.0965147	+	0.995332i	$0.469231\pi$
$420$		0			0
$421$	914792.	−	2.81544e6i	0.251546	−	0.774179i	−0.742945	−	0.669353i	$-0.766571\pi$
$421$	914792.	−	2.81544e6i	0.251546	−	0.774179i	0.994491	−	0.104826i	$-0.0334285\pi$
$422$	−3.52448e6	−	1.08472e7i	−0.963417	−	2.96509i
$423$		0			0
$424$	1.67610e7	−	1.21776e7i	4.52777	−	3.28962i
$425$	−319760.	−	984122.i	−0.0858722	−	0.264287i
$426$		0			0
$427$	4.98702e6	+	3.62328e6i	1.32364	+	0.961683i
$428$	6.14465e6			1.62139
$429$		0			0
$430$	848863.			0.221394
$431$	−4.87092e6	−	3.53893e6i	−1.26304	−	0.917653i	−0.264138	−	0.964485i	$-0.585088\pi$
$431$	−4.87092e6	−	3.53893e6i	−1.26304	−	0.917653i	−0.998903	+	0.0468317i	$0.985088\pi$
$432$		0			0
$433$	1.25654e6	+	3.86724e6i	0.322075	+	0.991245i	0.972744	+	0.231883i	$0.0744887\pi$
$433$	1.25654e6	+	3.86724e6i	0.322075	+	0.991245i	−0.650669	+	0.759362i	$0.725511\pi$
$434$	1.17164e7	−	8.51247e6i	2.98587	−	2.16936i
$435$		0			0
$436$	2.31769e6	+	7.13310e6i	0.583900	+	1.79706i
$437$	341676.	−	1.05157e6i	0.0855876	−	0.263412i
$438$		0			0
$439$	4.07619e6			1.00947			0.504735	−	0.863274i	$-0.331590\pi$
$439$	4.07619e6			1.00947			0.504735	+	0.863274i	$0.331590\pi$
$440$	3.19108e6	−	8.48162e6i	0.785788	−	2.08856i
$441$		0			0
$442$	227568.	+	165338.i	0.0554058	+	0.0402547i
$443$	−1.16621e6	+	3.58924e6i	−0.282338	+	0.868946i	0.704846	+	0.709360i	$0.251016\pi$
$443$	−1.16621e6	+	3.58924e6i	−0.282338	+	0.868946i	−0.987184	+	0.159586i	$0.948984\pi$
$444$		0			0
$445$	2.18815e6	−	1.58978e6i	0.523813	−	0.380573i
$446$	−4.81450e6	+	3.49794e6i	−1.14608	+	0.832675i
$447$		0			0
$448$	−7.03958e6	+	2.16656e7i	−1.65711	+	5.10006i
$449$	6.03269e6	+	4.38301e6i	1.41220	+	1.02602i	0.992998	+	0.118127i	$0.0376890\pi$
$449$	6.03269e6	+	4.38301e6i	1.41220	+	1.02602i	0.419199	+	0.907894i	$0.362311\pi$
$450$		0			0
$451$	−1.46551e6	+	965661.i	−0.339270	+	0.223555i
$452$	1.68288e7			3.87442
$453$		0			0
$454$	1.35548e6	−	4.17175e6i	0.308642	−	0.949901i
$455$	106611.	+	328113.i	0.0241419	+	0.0743011i
$456$		0			0
$457$	−3.94251e6	+	2.86440e6i	−0.883044	+	0.641569i	−0.934055	−	0.357129i	$-0.883756\pi$
$457$	−3.94251e6	+	2.86440e6i	−0.883044	+	0.641569i	0.0510108	+	0.998698i	$0.483756\pi$
$458$	316841.	+	975136.i	0.0705793	+	0.217221i
$459$		0			0
$460$	−2.14894e6	−	1.56130e6i	−0.473511	−	0.344026i
$461$	142994.			0.0313376			0.0156688	−	0.999877i	$-0.495012\pi$
$461$	142994.			0.0313376			0.0156688	+	0.999877i	$0.495012\pi$
$462$		0			0
$463$	1.04836e6			0.227279			0.113639	−	0.993522i	$-0.463749\pi$
$463$	1.04836e6			0.227279			0.113639	+	0.993522i	$0.463749\pi$
$464$	−1.23454e7	−	8.96943e6i	−2.66200	−	1.93406i
$465$		0			0
$466$	−2.40829e6	−	7.41194e6i	−0.513740	−	1.58113i
$467$	−4.70506e6	+	3.41843e6i	−0.998328	+	0.725328i	−0.961729	−	0.274002i	$-0.911653\pi$
$467$	−4.70506e6	+	3.41843e6i	−0.998328	+	0.725328i	−0.0365993	+	0.999330i	$0.511653\pi$
$468$		0			0
$469$	−1.44651e6	−	4.45191e6i	−0.303662	−	0.934575i
$470$	−46391.4	+	142778.i	−0.00968707	+	0.0298137i
$471$		0			0
$472$	6.90838e6			1.42732
$473$	−632509.	−	505251.i	−0.129991	−	0.103838i
$474$		0			0
$475$	1.81297e6	+	1.31720e6i	0.368686	+	0.267866i
$476$	−3.70367e6	+	1.13987e7i	−0.749229	+	2.30589i
$477$		0			0
$478$	−628855.	+	456890.i	−0.125887	+	0.0914622i
$479$	−6.20512e6	+	4.50829e6i	−1.23570	+	0.897786i	−0.997304	−	0.0733832i	$-0.976620\pi$
$479$	−6.20512e6	+	4.50829e6i	−1.23570	+	0.897786i	−0.238392	+	0.971169i	$0.576620\pi$
$480$		0			0
$481$	−122542.	+	377145.i	−0.0241502	+	0.0743268i
$482$	−2.08111e6	−	1.51202e6i	−0.408016	−	0.296441i
$483$		0			0
$484$	−1.18545e7	+	7.05660e6i	−2.30022	+	1.36925i
$485$	−6.55784e6			−1.26592
$486$		0			0
$487$	−2.30524e6	+	7.09479e6i	−0.440446	+	1.35555i	0.446955	+	0.894556i	$0.352508\pi$
$487$	−2.30524e6	+	7.09479e6i	−0.440446	+	1.35555i	−0.887401	+	0.460998i	$0.847492\pi$
$488$	5.06178e6	+	1.55786e7i	0.962175	+	2.96127i
$489$		0			0
$490$	−1.06133e7	+	7.71098e6i	−1.99691	+	1.45084i
$491$	−1.12782e6	−	3.47108e6i	−0.211124	−	0.649772i	−0.999406	−	0.0344582i	$-0.989029\pi$
$491$	−1.12782e6	−	3.47108e6i	−0.211124	−	0.649772i	0.788283	−	0.615313i	$-0.210971\pi$
$492$		0			0
$493$	−2.20716e6	−	1.60360e6i	−0.408994	−	0.297151i
$494$	−609178.			−0.112312
$495$		0			0
$496$	2.17759e7			3.97441
$497$	−431304.	−	313360.i	−0.0783235	−	0.0569054i
$498$		0			0
$499$	2.61645e6	+	8.05260e6i	0.470393	+	1.44772i	0.852072	+	0.523425i	$0.175346\pi$
$499$	2.61645e6	+	8.05260e6i	0.470393	+	1.44772i	−0.381679	+	0.924295i	$0.624654\pi$
$500$	1.27569e7	−	9.26845e6i	2.28203	−	1.65799i
$501$		0			0
$502$	−3.42384e6	−	1.05375e7i	−0.606393	−	1.86629i
$503$	−3.02546e6	+	9.31141e6i	−0.533177	+	1.64095i	0.214378	+	0.976751i	$0.431228\pi$
$503$	−3.02546e6	+	9.31141e6i	−0.533177	+	1.64095i	−0.747555	+	0.664200i	$0.768772\pi$
$504$		0			0
$505$	−2.46747e6			−0.430551
$506$	922941.	+	3.35484e6i	0.160250	+	0.582499i
$507$		0			0
$508$	−1.30398e7	−	9.47396e6i	−2.24187	−	1.62882i
$509$	−1.56152e6	+	4.80588e6i	−0.267149	+	0.822201i	0.724041	+	0.689757i	$0.242283\pi$
$509$	−1.56152e6	+	4.80588e6i	−0.267149	+	0.822201i	−0.991190	+	0.132444i	$0.957717\pi$
$510$		0			0
$511$	1.19132e7	−	8.65544e6i	2.01825	−	1.46635i
$512$	−4.33823e6	+	3.15191e6i	−0.731371	+	0.531372i
$513$		0			0
$514$	1.18399e6	−	3.64396e6i	0.197671	−	0.608367i
$515$	2.26963e6	+	1.64898e6i	0.377083	+	0.273967i
$516$		0			0
$517$	119550.	−	78774.8i	0.0196709	−	0.0129617i
$518$	−2.32085e7			−3.80034
$519$		0			0
$520$	−283295.	+	871891.i	−0.0459441	+	0.141401i
$521$	−815918.	−	2.51114e6i	−0.131690	−	0.405300i	0.863371	−	0.504570i	$-0.168349\pi$
$521$	−815918.	−	2.51114e6i	−0.131690	−	0.405300i	−0.995060	+	0.0992706i	$0.968349\pi$
$522$		0			0
$523$	−587362.	+	426743.i	−0.0938969	+	0.0682201i	−0.633743	−	0.773544i	$-0.718482\pi$
$523$	−587362.	+	426743.i	−0.0938969	+	0.0682201i	0.539846	+	0.841764i	$0.318482\pi$
$524$	−9.14845e6	−	2.81560e7i	−1.45552	−	4.47964i
$525$		0			0
$526$	1.06107e7	+	7.70910e6i	1.67216	+	1.21490i
$527$	3.89320e6			0.610633
$528$		0			0
$529$	−5.79745e6			−0.900736
$530$	1.21173e7	+	8.80374e6i	1.87377	+	1.36137i
$531$		0			0
$532$	−8.02089e6	−	2.46858e7i	−1.22869	−	3.78153i
$533$	143641.	−	104361.i	0.0219007	−	0.0159118i
$534$		0			0
$535$	859929.	+	2.64659e6i	0.129891	+	0.399762i
$536$	3.84380e6	−	1.18300e7i	0.577895	−	1.77858i
$537$		0			0
$538$	−1.09835e6			−0.163600
$539$	1.24978e7	+	571464.i	1.85295	+	0.0847260i
$540$		0			0
$541$	8.62074e6	+	6.26334e6i	1.26634	+	0.920052i	0.999051	−	0.0435631i	$-0.0138709\pi$
$541$	8.62074e6	+	6.26334e6i	1.26634	+	0.920052i	0.267293	+	0.963615i	$0.413871\pi$
$542$	−124295.	+	382542.i	−0.0181743	+	0.0559346i
$543$		0			0
$544$	−1.04008e7	+	7.55665e6i	−1.50685	+	1.09479i
$545$	−2.74797e6	+	1.99652e6i	−0.396298	+	0.287927i
$546$		0			0
$547$	−506090.	+	1.55758e6i	−0.0723201	+	0.222578i	−0.980683	−	0.195605i	$-0.937333\pi$
$547$	−506090.	+	1.55758e6i	−0.0723201	+	0.222578i	0.908363	+	0.418183i	$0.137333\pi$
$548$	−3.15841e6	−	2.29472e6i	−0.449280	−	0.326421i
$549$		0			0
$550$	−7.04469e6	−	322118.i	−0.993013	−	0.0454055i
$551$	5.90837e6			0.829065
$552$		0			0
$553$	−2.24129e6	+	6.89797e6i	−0.311663	+	0.959199i
$554$	2.15804e6	+	6.64176e6i	0.298734	+	0.919410i
$555$		0			0
$556$	4.38373e6	−	3.18497e6i	0.601391	−	0.436936i
$557$	−3.83067e6	−	1.17896e7i	−0.523163	−	1.61013i	−0.767920	−	0.640546i	$-0.778708\pi$
$557$	−3.83067e6	−	1.17896e7i	−0.523163	−	1.61013i	0.244757	−	0.969585i	$-0.421292\pi$
$558$		0			0
$559$	66255.6	+	48137.5i	0.00896794	+	0.00651559i
$560$	−3.03600e7			−4.09102
$561$		0			0
$562$	2.47728e7			3.30853
$563$	7.26569e6	+	5.27883e6i	0.966064	+	0.701887i	0.954551	−	0.298047i	$-0.0963352\pi$
$563$	7.26569e6	+	5.27883e6i	0.966064	+	0.701887i	0.0115130	+	0.999934i	$0.496335\pi$
$564$		0			0
$565$	2.35515e6	+	7.24840e6i	0.310383	+	0.955259i
$566$	−1.23645e6	+	898331.i	−0.162231	+	0.117868i
$567$		0			0
$568$	−437770.	−	1.34732e6i	−0.0569345	−	0.175226i
$569$	−2.87829e6	+	8.85847e6i	−0.372695	+	1.14704i	0.572325	+	0.820027i	$0.306042\pi$
$569$	−2.87829e6	+	8.85847e6i	−0.372695	+	1.14704i	−0.945020	+	0.327012i	$0.893958\pi$
$570$		0			0
$571$	−5.89599e6			−0.756774			−0.378387	−	0.925647i	$-0.623521\pi$
$571$	−5.89599e6			−0.756774			−0.378387	+	0.925647i	$0.623521\pi$
$572$	1.16540e6	−	767913.i	0.148931	−	0.0981346i
$573$		0			0
$574$	8.40663e6	+	6.10777e6i	1.06498	+	0.773755i
$575$	−400142.	+	1.23151e6i	−0.0504713	+	0.155335i
$576$		0			0
$577$	−4.51904e6	+	3.28327e6i	−0.565075	+	0.410551i	−0.833313	−	0.552801i	$-0.813559\pi$
$577$	−4.51904e6	+	3.28327e6i	−0.565075	+	0.410551i	0.268238	+	0.963353i	$0.413559\pi$
$578$	8.87968e6	−	6.45146e6i	1.10555	−	0.803227i
$579$		0			0
$580$	4.38616e6	−	1.34992e7i	0.541396	−	1.66624i
$581$	1.20085e7	+	8.72470e6i	1.47587	+	1.07228i
$582$		0			0
$583$	−3.78884e6	−	1.37722e7i	−0.461673	−	1.67816i
$584$	3.91299e7			4.74763
$585$		0			0
$586$	958187.	−	2.94900e6i	0.115267	−	0.354756i
$587$	−1.50232e6	−	4.62366e6i	−0.179956	−	0.553848i	0.819869	−	0.572551i	$-0.194046\pi$
$587$	−1.50232e6	−	4.62366e6i	−0.179956	−	0.553848i	−0.999825	+	0.0187034i	$0.994046\pi$
$588$		0			0
$589$	−6.82112e6	+	4.95583e6i	−0.810153	+	0.588611i
$590$	1.54335e6	+	4.74995e6i	0.182530	+	0.561771i
$591$		0			0
$592$	−2.82321e7	−	2.05118e7i	−3.31085	−	2.40547i
$593$	7.37203e6			0.860896			0.430448	−	0.902615i	$-0.358356\pi$
$593$	7.37203e6			0.860896			0.430448	+	0.902615i	$0.358356\pi$
$594$		0			0
$595$	−5.42791e6			−0.628550
$596$	−5.16721e6	−	3.75420e6i	−0.595855	−	0.432914i
$597$		0			0
$598$	−108774.	−	334772.i	−0.0124386	−	0.0382822i
$599$	3.41614e6	−	2.48197e6i	0.389017	−	0.282638i	−0.376035	−	0.926605i	$-0.622713\pi$
$599$	3.41614e6	−	2.48197e6i	0.389017	−	0.282638i	0.765053	+	0.643968i	$0.222713\pi$
$600$		0			0
$601$	−4.36395e6	−	1.34309e7i	−0.492826	−	1.51676i	−0.820317	−	0.571909i	$-0.806203\pi$
$601$	−4.36395e6	−	1.34309e7i	−0.492826	−	1.51676i	0.327491	−	0.944854i	$-0.393797\pi$
$602$	−1.48113e6	+	4.55844e6i	−0.166572	+	0.512655i
$603$		0			0
$604$	−3.21224e6			−0.358274
$605$	−4.69839e6	−	4.11835e6i	−0.521868	−	0.457441i
$606$		0			0
$607$	8.29504e6	+	6.02670e6i	0.913791	+	0.663908i	0.941971	−	0.335695i	$-0.108971\pi$
$607$	8.29504e6	+	6.02670e6i	0.913791	+	0.663908i	−0.0281797	+	0.999603i	$0.508971\pi$
$608$	8.60367e6	−	2.64794e7i	0.943898	−	2.90502i
$609$		0			0
$610$	−9.58044e6	+	6.96060e6i	−1.04246	+	0.757394i
$611$	−11717.6	+	8513.35i	−0.00126980	+	0.000922566i
$612$		0			0
$613$	−4.44460e6	+	1.36791e7i	−0.477728	+	1.47030i	0.364514	+	0.931198i	$0.381235\pi$
$613$	−4.44460e6	+	1.36791e7i	−0.477728	+	1.47030i	−0.842242	+	0.539099i	$0.818765\pi$
$614$	−2.30475e7	−	1.67450e7i	−2.46719	−	1.79252i
$615$		0			0
$616$	3.99788e7	+	3.19353e7i	4.24500	+	3.39093i
$617$	−8.26153e6			−0.873670			−0.436835	−	0.899542i	$-0.643901\pi$
$617$	−8.26153e6			−0.873670			−0.436835	+	0.899542i	$0.643901\pi$
$618$		0			0
$619$	1.51440e6	−	4.66085e6i	0.158860	−	0.488921i	−0.839672	−	0.543094i	$-0.817253\pi$
$619$	1.51440e6	−	4.66085e6i	0.158860	−	0.488921i	0.998532	+	0.0541739i	$0.0172525\pi$
$620$	6.25915e6	+	1.92637e7i	0.653937	+	2.01261i
$621$		0			0
$622$	−2.61895e6	+	1.90278e6i	−0.271426	+	0.197203i
$623$	4.71925e6	+	1.45244e7i	0.487139	+	1.49926i
$624$		0			0
$625$	1.68169e6	+	1.22182e6i	0.172205	+	0.125114i
$626$	−1.22419e7			−1.24857
$627$		0			0
$628$	−3.34420e7			−3.38371
$629$	−5.04747e6	−	3.66720e6i	−0.508683	−	0.369580i
$630$		0			0
$631$	4.93563e6	+	1.51903e7i	0.493479	+	1.51877i	0.819313	+	0.573346i	$0.194355\pi$
$631$	4.93563e6	+	1.51903e7i	0.493479	+	1.51877i	−0.325834	+	0.945427i	$0.605645\pi$
$632$	−1.55923e7	+	1.13285e7i	−1.55281	+	1.12818i
$633$		0			0
$634$	−380237.	−	1.17025e6i	−0.0375691	−	0.115626i
$635$	2.25568e6	−	6.94228e6i	0.221995	−	0.683231i
$636$		0			0
$637$	−1.26566e6			−0.123586
$638$	−1.55255e7	+	1.02302e7i	−1.51006	+	0.995021i
$639$		0			0
$640$	−1.51908e7	−	1.10368e7i	−1.46599	−	1.06510i
$641$	−3.33477e6	+	1.02634e7i	−0.320569	+	0.986609i	0.652833	+	0.757502i	$0.273580\pi$
$641$	−3.33477e6	+	1.02634e7i	−0.320569	+	0.986609i	−0.973401	+	0.229107i	$0.926420\pi$
$642$		0			0
$643$	−414230.	+	300956.i	−0.0395107	+	0.0287062i	−0.607365	−	0.794423i	$-0.707774\pi$
$643$	−414230.	+	300956.i	−0.0395107	+	0.0287062i	0.567855	+	0.823129i	$0.307774\pi$
$644$	1.21338e7	−	8.81572e6i	1.15287	−	0.837612i
$645$		0			0
$646$	2.96170e6	−	9.11518e6i	0.279229	−	0.859378i
$647$	−9.25546e6	−	6.72449e6i	−0.869236	−	0.631537i	0.0611461	−	0.998129i	$-0.480524\pi$
$647$	−9.25546e6	−	6.72449e6i	−0.869236	−	0.631537i	−0.930382	+	0.366592i	$0.880524\pi$
$648$		0			0
$649$	1.67722e6	−	4.45792e6i	0.156307	−	0.415452i
$650$	713419.			0.0662310
$651$		0			0
$652$	8.98376e6	−	2.76492e7i	0.827636	−	2.54720i
$653$	−3.06087e6	−	9.42040e6i	−0.280907	−	0.864543i	−0.987596	−	0.157018i	$-0.949812\pi$
$653$	−3.06087e6	−	9.42040e6i	−0.280907	−	0.864543i	0.706689	−	0.707525i	$-0.250188\pi$
$654$		0			0
$655$	1.08469e7	−	7.88073e6i	0.987875	−	0.717734i
$656$	4.82821e6	+	1.48597e7i	0.438053	+	1.34819i
$657$		0			0
$658$	−685779.	−	498248.i	−0.0617475	−	0.0448622i
$659$	3.43885e6			0.308461			0.154231	−	0.988035i	$-0.450710\pi$
$659$	3.43885e6			0.308461			0.154231	+	0.988035i	$0.450710\pi$
$660$		0			0
$661$	−1.76956e7			−1.57529			−0.787646	−	0.616128i	$-0.788701\pi$
$661$	−1.76956e7			−1.57529			−0.787646	+	0.616128i	$0.788701\pi$
$662$	8.72236e6	+	6.33716e6i	0.773551	+	0.562018i
$663$		0			0
$664$	1.21886e7	+	3.75125e7i	1.07283	+	3.30184i
$665$	9.51001e6	−	6.90943e6i	0.833925	−	0.605882i
$666$		0			0
$667$	1.05499e6	+	3.24693e6i	0.0918193	+	0.282591i
$668$	−1.66612e6	+	5.12780e6i	−0.144466	+	0.444621i
$669$		0			0
$670$	8.99259e6			0.773923
$671$	1.12816e7	+	515852.i	0.967310	+	0.0442302i
$672$		0			0
$673$	1.20083e7	+	8.72452e6i	1.02198	+	0.742512i	0.966688	−	0.255958i	$-0.0823908\pi$
$673$	1.20083e7	+	8.72452e6i	1.02198	+	0.742512i	0.0552927	+	0.998470i	$0.482391\pi$
$674$	−1.83202e6	+	5.63839e6i	−0.155339	+	0.478085i
$675$		0			0
$676$	2.56169e7	−	1.86118e7i	2.15606	−	1.56647i
$677$	−1.53492e7	+	1.11518e7i	−1.28710	+	0.935135i	−0.999743	−	0.0226869i	$-0.992778\pi$
$677$	−1.53492e7	+	1.11518e7i	−1.28710	+	0.935135i	−0.287361	+	0.957822i	$0.592778\pi$
$678$		0			0
$679$	1.14424e7	−	3.52159e7i	0.952447	−	2.93133i
$680$	−1.16689e7	−	8.47792e6i	−0.967734	−	0.703100i
$681$		0			0
$682$	9.34308e6	−	2.48331e7i	0.769182	−	2.04442i
$683$	−1.23287e7			−1.01127			−0.505633	−	0.862749i	$-0.668741\pi$
$683$	−1.23287e7			−1.01127			−0.505633	+	0.862749i	$0.668741\pi$
$684$		0			0
$685$	546357.	−	1.68151e6i	0.0444887	−	0.136922i
$686$	−1.05496e7	−	3.24683e7i	−0.855905	−	2.63420i
$687$		0			0
$688$	−5.83051e6	+	4.23612e6i	−0.469608	+	0.341190i
$689$	446537.	+	1.37430e6i	0.0358352	+	0.110289i
$690$		0			0
$691$	−1.71200e7	−	1.24384e7i	−1.36398	−	0.990990i	−0.998181	−	0.0602961i	$-0.980796\pi$
$691$	−1.71200e7	−	1.24384e7i	−1.36398	−	0.990990i	−0.365800	−	0.930694i	$-0.619204\pi$
$692$	4.05161e7			3.21634
$693$		0			0
$694$	−3.95310e7			−3.11559
$695$	1.98530e6	+	1.44241e6i	0.155907	+	0.113273i
$696$		0			0
$697$	863210.	+	2.65669e6i	0.0673030	+	0.207137i
$698$	−1.70296e7	+	1.23727e7i	−1.32302	+	0.961231i
$699$		0			0
$700$	9.39340e6	+	2.89099e7i	0.724566	+	2.22998i
$701$	4.81363e6	−	1.48148e7i	0.369980	−	1.13868i	−0.576824	−	0.816868i	$-0.695708\pi$
$701$	4.81363e6	−	1.48148e7i	0.369980	−	1.13868i	0.946804	−	0.321812i	$-0.104292\pi$
$702$		0			0
$703$	1.35116e7			1.03114
$704$	1.10705e7	+	4.02406e7i	0.841850	+	3.06008i
$705$		0			0
$706$	−937655.	−	681246.i	−0.0707997	−	0.0514390i
$707$	4.30534e6	−	1.32505e7i	0.323936	−	0.996971i
$708$		0			0
$709$	8.62245e6	−	6.26458e6i	0.644192	−	0.468033i	−0.217096	−	0.976150i	$-0.569658\pi$
$709$	8.62245e6	−	6.26458e6i	0.644192	−	0.468033i	0.861288	+	0.508117i	$0.169658\pi$
$710$	828567.	−	601989.i	0.0616853	−	0.0448170i
$711$		0			0
$712$	−1.25404e7	+	3.85954e7i	−0.927068	+	2.85322i
$713$	−3.94143e6	−	2.86362e6i	−0.290356	−	0.210956i
$714$		0			0
$715$	493846.	+	394486.i	0.0361265	+	0.0288580i
$716$	−2.49113e7			−1.81599
$717$		0			0
$718$	−726896.	+	2.23715e6i	−0.0526212	+	0.161951i
$719$	6.47603e6	+	1.99312e7i	0.467183	+	1.43784i	0.856217	+	0.516617i	$0.172809\pi$
$719$	6.47603e6	+	1.99312e7i	0.467183	+	1.43784i	−0.389034	+	0.921223i	$0.627191\pi$
$720$		0			0
$721$	−1.28152e7	+	9.31082e6i	−0.918098	+	0.667037i
$722$	−1.88574e6	−	5.80371e6i	−0.134629	−	0.414345i
$723$		0			0
$724$	2.68356e7	+	1.94972e7i	1.90267	+	1.38237i
$725$	−6.91939e6			−0.488903
$726$		0			0
$727$	−296119.			−0.0207793			−0.0103896	−	0.999946i	$-0.503307\pi$
$727$	−296119.			−0.0207793			−0.0103896	+	0.999946i	$0.503307\pi$
$728$	−4.18780e6	−	3.04261e6i	−0.292858	−	0.212774i
$729$		0			0
$730$	8.74173e6	+	2.69043e7i	0.607142	+	1.86859i
$731$	−1.04241e6	+	757352.i	−0.0721512	+	0.0524209i
$732$		0			0
$733$	−8.05044e6	−	2.47767e7i	−0.553426	−	1.70327i	−0.700064	−	0.714080i	$-0.746845\pi$
$733$	−8.05044e6	−	2.47767e7i	−0.553426	−	1.70327i	0.146638	−	0.989190i	$-0.453155\pi$
$734$	−615099.	+	1.89308e6i	−0.0421410	+	0.129697i
$735$		0			0
$736$	1.60879e7			1.09473
$737$	−6.70060e6	−	5.35247e6i	−0.454407	−	0.362982i
$738$		0			0
$739$	−1.08943e7	−	7.91517e6i	−0.733818	−	0.533150i	0.156951	−	0.987606i	$-0.449834\pi$
$739$	−1.08943e7	−	7.91517e6i	−0.733818	−	0.533150i	−0.890769	+	0.454456i	$0.849834\pi$
$740$	1.00306e7	−	3.08709e7i	0.673357	−	2.07238i
$741$		0			0
$742$	−6.84192e7	+	4.97095e7i	−4.56214	+	3.31459i
$743$	1.34801e7	−	9.79390e6i	0.895824	−	0.650854i	−0.0415661	−	0.999136i	$-0.513235\pi$
$743$	1.34801e7	−	9.79390e6i	0.895824	−	0.650854i	0.937390	+	0.348282i	$0.113235\pi$
$744$		0			0
$745$	893848.	−	2.75098e6i	0.0590029	−	0.181592i
$746$	4.15079e7	+	3.01572e7i	2.73076	+	1.98401i
$747$		0			0
$748$	5.82441e6	+	2.11714e7i	0.380625	+	1.38355i
$749$	−1.57127e7			−1.02340
$750$		0			0
$751$	−3.78148e6	+	1.16382e7i	−0.244660	+	0.752985i	0.751032	+	0.660265i	$0.229556\pi$
$751$	−3.78148e6	+	1.16382e7i	−0.244660	+	0.752985i	−0.995692	+	0.0927200i	$0.970444\pi$
$752$	−393866.	−	1.21219e6i	−0.0253983	−	0.0781678i
$753$		0			0
$754$	1.52173e6	−	1.10560e6i	0.0974783	−	0.0708221i
$755$	−449544.	−	1.38356e6i	−0.0287015	−	0.0883343i
$756$		0			0
$757$	1.44776e7	+	1.05186e7i	0.918244	+	0.667143i	0.943086	−	0.332548i	$-0.107908\pi$
$757$	1.44776e7	+	1.05186e7i	0.918244	+	0.667143i	−0.0248427	+	0.999691i	$0.507908\pi$
$758$	4.68690e7			2.96287
$759$		0			0
$760$	3.12364e7			1.96168
$761$	−1.23126e7	−	8.94561e6i	−0.770703	−	0.559949i	0.131471	−	0.991320i	$-0.458030\pi$
$761$	−1.23126e7	−	8.94561e6i	−0.770703	−	0.559949i	−0.902174	+	0.431371i	$0.858030\pi$
$762$		0			0
$763$	−5.92665e6	−	1.82404e7i	−0.368551	−	1.13428i
$764$	−5.71837e7	+	4.15464e7i	−3.54437	+	2.57513i
$765$		0			0
$766$	1.16186e6	+	3.57584e6i	0.0715455	+	0.220195i
$767$	−148899.	+	458264.i	−0.00913910	+	0.0281273i
$768$		0			0
$769$	9.90796e6			0.604183			0.302091	−	0.953279i	$-0.402315\pi$
$769$	9.90796e6			0.604183			0.302091	+	0.953279i	$0.402315\pi$
$770$	−1.30261e7	+	3.46224e7i	−0.791751	+	2.10441i
$771$		0			0
$772$	3.34642e7	+	2.43132e7i	2.02086	+	1.46824i
$773$	8.90154e6	−	2.73961e7i	0.535817	−	1.64907i	−0.206061	−	0.978539i	$-0.566065\pi$
$773$	8.90154e6	−	2.73961e7i	0.535817	−	1.64907i	0.741878	−	0.670535i	$-0.233935\pi$
$774$		0			0
$775$	7.98832e6	−	5.80385e6i	0.477751	−	0.347106i
$776$	7.96029e7	−	5.78349e7i	4.74542	−	3.44775i
$777$		0			0
$778$	2.66564e6	−	8.20398e6i	0.157889	−	0.485932i
$779$	−4.89421e6	−	3.55585e6i	−0.288961	−	0.209942i
$780$		0			0
$781$	−975696.	−	44613.7i	−0.0572383	−	0.00261722i
$782$	5.53806e6			0.323848
$783$		0			0
$784$	3.44179e7	−	1.05927e8i	1.99984	−	6.15487i
$785$	−4.68012e6	−	1.44039e7i	−0.271071	−	0.834270i
$786$		0			0
$787$	−2.38068e7	+	1.72967e7i	−1.37014	+	0.995463i	−0.372411	+	0.928068i	$0.621469\pi$
$787$	−2.38068e7	+	1.72967e7i	−1.37014	+	0.995463i	−0.997726	+	0.0673957i	$0.978531\pi$
$788$	−7.95534e6	−	2.44840e7i	−0.456397	−	1.40465i
$789$		0			0
$790$	−1.12724e7	−	8.18990e6i	−0.642613	−	0.466886i
$791$	−4.30336e7			−2.44550
$792$		0			0
$793$	−1.14250e6			−0.0645166
$794$	2.85416e7	+	2.07367e7i	1.60667	+	1.16732i
$795$		0			0
$796$	−2.50419e7	−	7.70710e7i	−1.40083	−	4.31130i
$797$	2.08999e7	−	1.51847e7i	1.16546	−	0.846758i	0.175004	−	0.984568i	$-0.444006\pi$
$797$	2.08999e7	−	1.51847e7i	1.16546	−	0.846758i	0.990459	+	0.137810i	$0.0440063\pi$
$798$		0			0
$799$	−70417.2	−	216722.i	−0.00390222	−	0.0120098i
$800$	−1.00759e7	+	3.10104e7i	−0.556620	+	1.71310i
$801$		0			0
$802$	4.34706e7			2.38649
$803$	9.49999e6	−	2.52502e7i	0.519917	−	1.38190i
$804$		0			0
$805$	5.49515e6	+	3.99246e6i	0.298875	+	0.217146i
$806$	−829452.	+	2.55279e6i	−0.0449732	+	0.138413i
$807$		0			0
$808$	2.99516e7	−	2.17611e7i	1.61396	−	1.17261i
$809$	−27132.3	+	19712.8i	−0.00145753	+	0.00105895i	−0.588514	−	0.808487i	$-0.700287\pi$
$809$	−27132.3	+	19712.8i	−0.00145753	+	0.00105895i	0.587056	+	0.809546i	$0.300287\pi$
$810$		0			0
$811$	−446267.	+	1.37347e6i	−0.0238255	+	0.0733274i	−0.962262	−	0.272124i	$-0.912274\pi$
$811$	−446267.	+	1.37347e6i	−0.0238255	+	0.0733274i	0.938437	+	0.345451i	$0.112274\pi$
$812$	6.48384e7	+	4.71078e7i	3.45098	+	2.50728i
$813$		0			0
$814$	−3.55048e7	+	2.33951e7i	−1.87813	+	1.23755i
$815$	1.31661e7			0.694328
$816$		0			0
$817$	862289.	−	2.65385e6i	0.0451957	−	0.139098i
$818$	9.90905e6	+	3.04969e7i	0.517784	+	1.59358i
$819$		0			0
$820$	−1.17576e7	+	8.54238e6i	−0.610637	+	0.443654i
$821$	6.13945e6	+	1.88953e7i	0.317886	+	0.978353i	0.974550	+	0.224170i	$0.0719670\pi$
$821$	6.13945e6	+	1.88953e7i	0.317886	+	0.978353i	−0.656664	+	0.754183i	$0.728033\pi$
$822$		0			0
$823$	1.57265e7	+	1.14260e7i	0.809342	+	0.588021i	0.913640	−	0.406525i	$-0.133260\pi$
$823$	1.57265e7	+	1.14260e7i	0.809342	+	0.588021i	−0.104298	+	0.994546i	$0.533260\pi$
$824$	−4.20928e7			−2.15968
$825$		0			0
$826$	−2.82004e7			−1.43815
$827$	1.50937e7	+	1.09662e7i	0.767420	+	0.557563i	0.901177	−	0.433451i	$-0.142704\pi$
$827$	1.50937e7	+	1.09662e7i	0.767420	+	0.557563i	−0.133757	+	0.991014i	$0.542704\pi$
$828$		0			0
$829$	−9.19628e6	−	2.83032e7i	−0.464757	−	1.43037i	−0.859288	−	0.511492i	$-0.829093\pi$
$829$	−9.19628e6	−	2.83032e7i	−0.464757	−	1.43037i	0.394531	−	0.918883i	$-0.370907\pi$
$830$	−2.30693e7	+	1.67608e7i	−1.16236	+	0.844501i
$831$		0			0
$832$	−1.30472e6	−	4.01552e6i	−0.0653446	−	0.201110i
$833$	6.15340e6	−	1.89382e7i	0.307257	−	0.945641i
$834$		0			0
$835$	−2.44178e6			−0.121197
$836$	−3.71547e7	−	2.96794e7i	−1.83865	−	1.46872i
$837$		0			0
$838$	−6.08741e6	−	4.42276e6i	−0.299449	−	0.217562i
$839$	−7.32237e6	+	2.25359e7i	−0.359126	+	1.10528i	0.594452	+	0.804131i	$0.297369\pi$
$839$	−7.32237e6	+	2.25359e7i	−0.359126	+	1.10528i	−0.953578	+	0.301145i	$0.902631\pi$
$840$		0			0
$841$	1.83479e6	−	1.33306e6i	0.0894534	−	0.0649917i
$842$	−2.59785e7	+	1.88745e7i	−1.26280	+	0.917477i
$843$		0			0
$844$	−2.78332e7	+	8.56618e7i	−1.34495	+	4.13934i
$845$	1.16014e7	+	8.42889e6i	0.558943	+	0.406096i
$846$		0			0
$847$	3.03137e7	−	1.80447e7i	1.45188	−	0.864255i
$848$	−1.27163e8			−6.07254
$849$		0			0
$850$	−3.46850e6	+	1.06749e7i	−0.164662	+	0.506779i
$851$	2.41262e6	+	7.42527e6i	0.114200	+	0.351470i
$852$		0			0
$853$	9.84443e6	−	7.15240e6i	0.463253	−	0.336573i	−0.331553	−	0.943437i	$-0.607573\pi$
$853$	9.84443e6	−	7.15240e6i	0.463253	−	0.336573i	0.794806	+	0.606864i	$0.207573\pi$
$854$	−2.06625e7	−	6.35925e7i	−0.969477	−	2.98374i
$855$		0			0
$856$	−3.37791e7	−	2.45419e7i	−1.57566	−	1.14479i
$857$	3.92879e7			1.82729			0.913645	−	0.406514i	$-0.133256\pi$
$857$	3.92879e7			1.82729			0.913645	+	0.406514i	$0.133256\pi$
$858$		0			0
$859$	−6.06087e6			−0.280254			−0.140127	−	0.990134i	$-0.544751\pi$
$859$	−6.06087e6			−0.280254			−0.140127	+	0.990134i	$0.544751\pi$
$860$	−5.42329e6	−	3.94025e6i	−0.250044	−	0.181668i
$861$		0			0
$862$	2.01814e7	+	6.21121e7i	0.925090	+	2.84713i
$863$	−1.28679e7	+	9.34907e6i	−0.588139	+	0.427308i	−0.841649	−	0.540025i	$-0.818415\pi$
$863$	−1.28679e7	+	9.34907e6i	−0.588139	+	0.427308i	0.253510	+	0.967333i	$0.418415\pi$
$864$		0			0
$865$	5.67012e6	+	1.74508e7i	0.257663	+	0.793006i
$866$	1.36299e7	−	4.19486e7i	0.617588	−	1.90074i
$867$		0			0
$868$	−1.14368e8			−5.15235
$869$	3.52466e6	+	1.28119e7i	0.158332	+	0.575527i
$870$		0			0
$871$	701890.	+	509953.i	0.0313490	+	0.0227764i
$872$	1.57488e7	−	4.84698e7i	0.701385	−	2.15864i
$873$		0			0
$874$	−9.70301e6	+	7.04965e6i	−0.429663	+	0.312168i
$875$	−3.26213e7	+	2.37008e7i	−1.44039	+	1.04651i
$876$		0			0
$877$	1.10432e7	−	3.39876e7i	0.484838	−	1.49218i	−0.347377	−	0.937726i	$-0.612927\pi$
$877$	1.10432e7	−	3.39876e7i	0.484838	−	1.49218i	0.832215	−	0.554453i	$-0.187073\pi$
$878$	−3.57708e7	−	2.59890e7i	−1.56600	−	1.13777i
$879$		0			0
$880$	−4.64453e7	+	3.06041e7i	−2.02179	+	1.33221i
$881$	−1.72470e7			−0.748642			−0.374321	−	0.927299i	$-0.622124\pi$
$881$	−1.72470e7			−0.748642			−0.374321	+	0.927299i	$0.622124\pi$
$882$		0			0
$883$	−7.29629e6	+	2.24557e7i	−0.314920	+	0.969225i	0.660867	+	0.750503i	$0.270189\pi$
$883$	−7.29629e6	+	2.24557e7i	−0.314920	+	0.969225i	−0.975787	+	0.218722i	$0.929811\pi$
$884$	−686441.	−	2.11265e6i	−0.0295442	−	0.0909278i
$885$		0			0
$886$	3.31185e7	−	2.40620e7i	1.41738	−	1.02979i
$887$	3.32904e6	+	1.02457e7i	0.142073	+	0.437255i	0.996623	−	0.0821140i	$-0.0261672\pi$
$887$	3.32904e6	+	1.02457e7i	0.142073	+	0.437255i	−0.854550	+	0.519369i	$0.826167\pi$
$888$		0			0
$889$	3.33446e7	+	2.42263e7i	1.41505	+	1.02809i
$890$	−2.93384e7			−1.24154
$891$		0			0
$892$	4.69961e7			1.97765
$893$	399250.	+	290072.i	0.0167539	+	0.0121724i
$894$		0			0
$895$	−3.48628e6	−	1.07297e7i	−0.145480	−	0.447742i
$896$	8.57734e7	−	6.23180e7i	3.56930	−	2.59325i
$897$		0			0
$898$	−2.49950e7	−	7.69266e7i	−1.03434	−	3.18336i
$899$	8.04478e6	−	2.47593e7i	0.331982	−	1.02174i
$900$		0			0
$901$	−2.27347e7			−0.932992
$902$	1.90175e7	+	869574.i	0.778282	+	0.0355869i
$903$		0			0
$904$	−9.25132e7	−	6.72148e7i	−3.76515	−	2.73555i
$905$	−4.64214e6	+	1.42870e7i	−0.188407	+	0.579857i
$906$		0			0
$907$	−1.00345e7	+	7.29046e6i	−0.405019	+	0.294264i	−0.771582	−	0.636130i	$-0.780534\pi$
$907$	−1.00345e7	+	7.29046e6i	−0.405019	+	0.294264i	0.366563	+	0.930393i	$0.380534\pi$
$908$	−2.80244e7	+	2.03610e7i	−1.12803	+	0.819565i
$909$		0			0
$910$	1.15642e6	−	3.55910e6i	0.0462928	−	0.142475i
$911$	−2.90502e7	−	2.11062e7i	−1.15972	−	0.842586i	−0.169978	−	0.985448i	$-0.554370\pi$
$911$	−2.90502e7	−	2.11062e7i	−1.15972	−	0.842586i	−0.989743	+	0.142861i	$0.954370\pi$
$912$		0			0
$913$	2.71657e7	+	1.24215e6i	1.07856	+	0.0493171i
$914$	5.28606e7			2.09299
$915$		0			0
$916$	2.50212e6	−	7.70075e6i	0.0985304	−	0.303245i
$917$	2.33939e7	+	7.19989e7i	0.918711	+	2.82750i
$918$		0			0
$919$	−1.11992e6	+	813669.i	−0.0437419	+	0.0317804i	−0.609441	−	0.792831i	$-0.708606\pi$
$919$	−1.11992e6	+	813669.i	−0.0437419	+	0.0317804i	0.565699	+	0.824611i	$0.308606\pi$
$920$	5.57754e6	+	1.71659e7i	0.217257	+	0.668647i
$921$		0			0
$922$	−1.25485e6	−	911704.i	−0.0486144	−	0.0353205i
$923$	98809.2			0.00381762
$924$		0			0
$925$	−1.58237e7			−0.608069
$926$	−9.19995e6	−	6.68416e6i	−0.352580	−	0.256165i
$927$		0			0
$928$	2.65655e7	+	8.17602e7i	1.01262	+	3.11653i
$929$	2.16777e7	−	1.57498e7i	0.824090	−	0.598736i	−0.0937911	−	0.995592i	$-0.529899\pi$
$929$	2.16777e7	−	1.57498e7i	0.824090	−	0.598736i	0.917881	+	0.396855i	$0.129899\pi$
$930$		0			0
$931$	1.33262e7	+	4.10138e7i	0.503885	+	1.55080i
$932$	−1.90185e7	+	5.85328e7i	−0.717193	+	2.20729i
$933$		0			0
$934$	6.30848e7			2.36623
$935$	−8.30371e6	+	5.47154e6i	−0.310630	+	0.204682i
$936$		0			0
$937$	−2.48929e7	−	1.80857e7i	−0.926246	−	0.672957i	0.0188250	−	0.999823i	$-0.494007\pi$
$937$	−2.48929e7	−	1.80857e7i	−0.926246	−	0.672957i	−0.945071	+	0.326866i	$0.894007\pi$
$938$	−1.56906e7	+	4.82906e7i	−0.582280	+	1.79207i
$939$		0			0
$940$	959136.	−	696853.i	0.0354047	−	0.0257230i
$941$	−2.25683e7	+	1.63968e7i	−0.830853	+	0.603650i	−0.919801	−	0.392386i	$-0.871650\pi$
$941$	−2.25683e7	+	1.63968e7i	−0.830853	+	0.603650i	0.0889474	+	0.996036i	$0.471650\pi$
$942$		0			0
$943$	1.08020e6	−	3.32453e6i	0.0395573	−	0.121745i
$944$	−3.43045e7	−	2.49237e7i	−1.25292	−	0.910296i
$945$		0			0
$946$	2.32923e6	+	8.46661e6i	0.0846222	+	0.307597i
$947$	1.01024e7			0.366059			0.183030	−	0.983107i	$-0.441410\pi$
$947$	1.01024e7			0.366059			0.183030	+	0.983107i	$0.441410\pi$
$948$		0			0
$949$	−843382.	+	2.59566e6i	−0.0303990	+	0.0935584i
$950$	−7.51160e6	−	2.31183e7i	−0.270037	−	0.831089i
$951$		0			0
$952$	6.58871e7	−	4.78698e7i	2.35618	−	1.71186i
$953$	−5.72799e6	−	1.76289e7i	−0.204301	−	0.628773i	−0.999741	−	0.0227417i	$-0.992760\pi$
$953$	−5.72799e6	−	1.76289e7i	−0.204301	−	0.628773i	0.795441	−	0.606032i	$-0.207240\pi$
$954$		0			0
$955$	−2.58973e7	−	1.88155e7i	−0.918854	−	0.667586i
$956$	6.13848e6			0.217228
$957$		0			0
$958$	8.31974e7			2.92884
$959$	8.07651e6	+	5.86793e6i	0.283581	+	0.206034i
$960$		0			0
$961$	2.63317e6	+	8.10408e6i	0.0919753	+	0.283071i
$962$	3.47998e6	−	2.52835e6i	0.121238	−	0.0880845i
$963$		0			0
$964$	6.27751e6	+	1.93202e7i	0.217568	+	0.669605i
$965$	−5.78879e6	+	1.78161e7i	−0.200110	+	0.615876i
$966$		0			0
$967$	1.43629e6			0.0493941			0.0246970	−	0.999695i	$-0.492138\pi$
$967$	1.43629e6			0.0493941			0.0246970	+	0.999695i	$0.492138\pi$
$968$	9.33523e7	+	8.55495e6i	3.20211	+	0.293447i
$969$		0			0
$970$	5.75487e7	+	4.18116e7i	1.96384	+	1.42681i
$971$	−3.70003e6	+	1.13875e7i	−0.125938	+	0.387597i	−0.994071	−	0.108735i	$-0.965320\pi$
$971$	−3.70003e6	+	1.13875e7i	−0.125938	+	0.387597i	0.868133	+	0.496332i	$0.165320\pi$
$972$		0			0
$973$	−1.12098e7	+	8.14442e6i	−0.379592	+	0.275790i
$974$	6.54647e7	−	4.75629e7i	2.21111	−	1.60646i
$975$		0			0
$976$	3.10686e7	−	9.56193e7i	1.04399	−	3.21308i
$977$	1.80022e7	+	1.30794e7i	0.603379	+	0.438381i	0.847077	−	0.531471i	$-0.178360\pi$
$977$	1.80022e7	+	1.30794e7i	0.603379	+	0.438381i	−0.243698	+	0.969851i	$0.578360\pi$
$978$		0			0
$979$	2.18607e7	+	1.74625e7i	0.728967	+	0.582302i
$980$	1.03600e8			3.44583
$981$		0			0
$982$	−1.22337e7	+	3.76514e7i	−0.404835	+	1.24596i
$983$	−9.20976e6	−	2.83447e7i	−0.303994	−	0.935596i	−0.980051	−	0.198747i	$-0.936313\pi$
$983$	−9.20976e6	−	2.83447e7i	−0.303994	−	0.935596i	0.676057	−	0.736849i	$-0.263687\pi$
$984$		0			0
$985$	9.43228e6	−	6.85296e6i	0.309761	−	0.225054i
$986$	9.14483e6	+	2.81449e7i	0.299560	+	0.921950i
$987$		0			0
$988$	3.89197e6	+	2.82768e6i	0.126846	+	0.0921592i
$989$	1.61239e6			0.0524177
$990$		0			0
$991$	−5.77652e7			−1.86845			−0.934227	−	0.356680i	$-0.883909\pi$
$991$	−5.77652e7			−1.86845			−0.934227	+	0.356680i	$0.883909\pi$
$992$	−9.92484e7	−	7.21082e7i	−3.20217	−	2.32651i
$993$		0			0
$994$	1.78700e6	+	5.49982e6i	0.0573665	+	0.176556i
$995$	2.96910e7	−	2.15718e7i	0.950753	−	0.690763i
$996$		0			0
$997$	3.04621e6	+	9.37526e6i	0.0970558	+	0.298707i	0.987784	−	0.155829i	$-0.0498050\pi$
$997$	3.04621e6	+	9.37526e6i	0.0970558	+	0.298707i	−0.890728	+	0.454536i	$0.849805\pi$
$998$	2.83811e7	−	8.73480e7i	0.901991	−	2.77604i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.6.f.b.37.1		20
3.2	odd	2		33.6.e.b.4.5	✓	20
11.3	even	5	inner	99.6.f.b.91.1		20
11.5	even	5		1089.6.a.bk.1.10		10
11.6	odd	10		1089.6.a.bi.1.1		10
33.5	odd	10		363.6.a.r.1.1		10
33.14	odd	10		33.6.e.b.25.5	yes	20
33.17	even	10		363.6.a.t.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.e.b.4.5	✓	20	3.2	odd	2
33.6.e.b.25.5	yes	20	33.14	odd	10
99.6.f.b.37.1		20	1.1	even	1	trivial
99.6.f.b.91.1		20	11.3	even	5	inner
363.6.a.r.1.1		10	33.5	odd	10
363.6.a.t.1.10		10	33.17	even	10
1089.6.a.bi.1.1		10	11.6	odd	10
1089.6.a.bk.1.10		10	11.5	even	5

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.77555 - 6.37581i) q^{2} +(26.4708 + 81.4687i) q^{4} +(-31.3852 + 22.8027i) q^{5} +(-67.6896 - 208.327i) q^{7} +(179.871 - 553.584i) q^{8} +O(q^{10})\)	\(q+(-8.77555 - 6.37581i) q^{2} +(26.4708 + 81.4687i) q^{4} +(-31.3852 + 22.8027i) q^{5} +(-67.6896 - 208.327i) q^{7} +(179.871 - 553.584i) q^{8} +420.808 q^{10} +(-313.554 - 250.469i) q^{11} +(32.8450 + 23.8633i) q^{13} +(-734.241 + 2259.76i) q^{14} +(-2890.37 + 2099.97i) q^{16} +(-516.753 + 375.443i) q^{17} +(427.464 - 1315.60i) q^{19} +(-2688.50 - 1953.31i) q^{20} +(1154.67 + 4197.17i) q^{22} +799.310 q^{23} +(-500.610 + 1540.72i) q^{25} +(-136.085 - 418.826i) q^{26} +(15180.3 - 11029.2i) q^{28} +(1319.88 + 4062.16i) q^{29} +(-4931.04 - 3582.61i) q^{31} +20127.3 q^{32} +6928.55 q^{34} +(6874.87 + 4994.88i) q^{35} +(3018.37 + 9289.60i) q^{37} +(-12139.2 + 8819.67i) q^{38} +(6977.94 + 21475.9i) q^{40} +(1351.42 - 4159.25i) q^{41} +2017.22 q^{43} +(12105.3 - 32175.0i) q^{44} +(-7014.39 - 5096.25i) q^{46} +(-110.244 + 339.295i) q^{47} +(-25221.1 + 18324.2i) q^{49} +(14216.5 - 10328.9i) q^{50} +(-1074.68 + 3307.52i) q^{52} +(28795.3 + 20921.0i) q^{53} +(15552.3 + 711.130i) q^{55} -127502. q^{56} +(14316.9 - 44063.0i) q^{58} +(3667.59 + 11287.7i) q^{59} +(-22766.8 + 16541.0i) q^{61} +(20430.6 + 62878.8i) q^{62} +(-84136.1 - 61128.5i) q^{64} -1574.99 q^{65} +21369.8 q^{67} +(-44265.7 - 32160.9i) q^{68} +(-28484.3 - 87665.7i) q^{70} +(1968.99 - 1430.56i) q^{71} +(20773.7 + 63934.8i) q^{73} +(32740.8 - 100766. i) q^{74} +118495. q^{76} +(-30955.1 + 82276.0i) q^{77} +(-26787.6 - 19462.3i) q^{79} +(42829.7 - 131816. i) q^{80} +(-38378.0 + 27883.3i) q^{82} +(-54821.4 + 39830.1i) q^{83} +(7657.29 - 23566.7i) q^{85} +(-17702.2 - 12861.4i) q^{86} +(-195055. + 128527. i) q^{88} -69719.1 q^{89} +(2748.10 - 8457.79i) q^{91} +(21158.4 + 65118.8i) q^{92} +(3130.73 - 2274.61i) q^{94} +(16583.1 + 51037.6i) q^{95} +(136758. + 99360.2i) q^{97} +338161. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{2} + 8 q^{4} + 11 q^{5} - 139 q^{7} + 76 q^{8}+O(q^{10}) \) 20 * q - 6 * q^2 + 8 * q^4 + 11 * q^5 - 139 * q^7 + 76 * q^8	\( 20 q - 6 q^{2} + 8 q^{4} + 11 q^{5} - 139 q^{7} + 76 q^{8} - 424 q^{10} - 2289 q^{11} - 847 q^{13} - 2022 q^{14} - 7148 q^{16} - 2482 q^{17} + 2958 q^{19} - 8037 q^{20} + 7441 q^{22} - 8140 q^{23} - 13120 q^{25} + 13508 q^{26} + 27819 q^{28} + 20210 q^{29} + 5540 q^{31} + 4626 q^{32} + 16540 q^{34} + 34101 q^{35} - 25173 q^{37} + 55878 q^{38} + 22689 q^{40} - 54349 q^{41} - 21688 q^{43} - 24587 q^{44} + 44155 q^{46} + 48387 q^{47} - 78880 q^{49} - 19956 q^{50} + 109051 q^{52} + 74382 q^{53} - 47630 q^{55} - 168894 q^{56} + 1501 q^{58} + 108412 q^{59} + 16737 q^{61} - 132685 q^{62} - 157030 q^{64} + 134194 q^{65} + 20178 q^{67} - 387013 q^{68} - 411988 q^{70} - 143157 q^{71} + 164980 q^{73} - 286114 q^{74} + 46868 q^{76} + 367461 q^{77} + 369613 q^{79} + 107448 q^{80} - 184129 q^{82} - 267741 q^{83} + 379937 q^{85} + 290531 q^{86} - 740846 q^{88} - 205492 q^{89} + 394559 q^{91} + 483181 q^{92} + 561327 q^{94} - 267881 q^{95} - 300567 q^{97} + 2296174 q^{98}+O(q^{100}) \) 20 * q - 6 * q^2 + 8 * q^4 + 11 * q^5 - 139 * q^7 + 76 * q^8 - 424 * q^10 - 2289 * q^11 - 847 * q^13 - 2022 * q^14 - 7148 * q^16 - 2482 * q^17 + 2958 * q^19 - 8037 * q^20 + 7441 * q^22 - 8140 * q^23 - 13120 * q^25 + 13508 * q^26 + 27819 * q^28 + 20210 * q^29 + 5540 * q^31 + 4626 * q^32 + 16540 * q^34 + 34101 * q^35 - 25173 * q^37 + 55878 * q^38 + 22689 * q^40 - 54349 * q^41 - 21688 * q^43 - 24587 * q^44 + 44155 * q^46 + 48387 * q^47 - 78880 * q^49 - 19956 * q^50 + 109051 * q^52 + 74382 * q^53 - 47630 * q^55 - 168894 * q^56 + 1501 * q^58 + 108412 * q^59 + 16737 * q^61 - 132685 * q^62 - 157030 * q^64 + 134194 * q^65 + 20178 * q^67 - 387013 * q^68 - 411988 * q^70 - 143157 * q^71 + 164980 * q^73 - 286114 * q^74 + 46868 * q^76 + 367461 * q^77 + 369613 * q^79 + 107448 * q^80 - 184129 * q^82 - 267741 * q^83 + 379937 * q^85 + 290531 * q^86 - 740846 * q^88 - 205492 * q^89 + 394559 * q^91 + 483181 * q^92 + 561327 * q^94 - 267881 * q^95 - 300567 * q^97 + 2296174 * q^98

Introduction

L-functions

Modular forms

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Database

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