LMFDB - Embedded newform 6.9.b.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,9,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	6.b (of order $2$, degree $1$, 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:	$2.44427166037$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.1
Root			$-1.41421i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.9.b.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.3137i q^{2} +(-63.0000 - 50.9117i) q^{3} -128.000 q^{4} -576.999i q^{5} +(-576.000 + 712.764i) q^{6} +2786.00 q^{7} +1448.15i q^{8} +(1377.00 + 6414.87i) q^{9} +O(q^{10})$	\(q-11.3137i q^{2} +(-63.0000 - 50.9117i) q^{3} -128.000 q^{4} -576.999i q^{5} +(-576.000 + 712.764i) q^{6} +2786.00 q^{7} +1448.15i q^{8} +(1377.00 + 6414.87i) q^{9} -6528.00 q^{10} -22435.1i q^{11} +(8064.00 + 6516.70i) q^{12} -13150.0 q^{13} -31520.0i q^{14} +(-29376.0 + 36350.9i) q^{15} +16384.0 q^{16} +66388.8i q^{17} +(72576.0 - 15579.0i) q^{18} +144002. q^{19} +73855.9i q^{20} +(-175518. - 141840. i) q^{21} -253824. q^{22} -49350.4i q^{23} +(73728.0 - 91233.7i) q^{24} +57697.0 q^{25} +148775. i q^{26} +(239841. - 474242. i) q^{27} -356608. q^{28} +627402. i q^{29} +(411264. + 332352. i) q^{30} +728738. q^{31} -185364. i q^{32} +(-1.14221e6 + 1.41341e6i) q^{33} +751104. q^{34} -1.60752e6i q^{35} +(-176256. - 821104. i) q^{36} -1.96445e6 q^{37} -1.62920e6i q^{38} +(828450. + 669489. i) q^{39} +835584. q^{40} -986125. i q^{41} +(-1.60474e6 + 1.98576e6i) q^{42} -78142.0 q^{43} +2.87169e6i q^{44} +(3.70138e6 - 794528. i) q^{45} -558336. q^{46} +3.51969e6i q^{47} +(-1.03219e6 - 834137. i) q^{48} +1.99700e6 q^{49} -652767. i q^{50} +(3.37997e6 - 4.18250e6i) q^{51} +1.68320e6 q^{52} -522048. i q^{53} +(-5.36544e6 - 2.71349e6i) q^{54} -1.29450e7 q^{55} +4.03456e6i q^{56} +(-9.07213e6 - 7.33138e6i) q^{57} +7.09824e6 q^{58} +5.00425e6i q^{59} +(3.76013e6 - 4.65292e6i) q^{60} +1.75783e7 q^{61} -8.24473e6i q^{62} +(3.83632e6 + 1.78718e7i) q^{63} -2.09715e6 q^{64} +7.58754e6i q^{65} +(1.59909e7 + 1.29226e7i) q^{66} -1.71368e7 q^{67} -8.49777e6i q^{68} +(-2.51251e6 + 3.10907e6i) q^{69} -1.81870e7 q^{70} -2.58906e7i q^{71} +(-9.28973e6 + 1.99411e6i) q^{72} +2.81393e7 q^{73} +2.22252e7i q^{74} +(-3.63491e6 - 2.93745e6i) q^{75} -1.84323e7 q^{76} -6.25041e7i q^{77} +(7.57440e6 - 9.37284e6i) q^{78} +9.18250e6 q^{79} -9.45355e6i q^{80} +(-3.92545e7 + 1.76666e7i) q^{81} -1.11567e7 q^{82} +8.71084e7i q^{83} +(2.24663e7 + 1.81555e7i) q^{84} +3.83063e7 q^{85} +884076. i q^{86} +(3.19421e7 - 3.95263e7i) q^{87} +3.24895e7 q^{88} +8.12528e7i q^{89} +(-8.98906e6 - 4.18763e7i) q^{90} -3.66359e7 q^{91} +6.31685e6i q^{92} +(-4.59105e7 - 3.71013e7i) q^{93} +3.98208e7 q^{94} -8.30890e7i q^{95} +(-9.43718e6 + 1.16779e7i) q^{96} -1.28723e8 q^{97} -2.25934e7i q^{98} +(1.43918e8 - 3.08931e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 126 q^{3} - 256 q^{4} - 1152 q^{6} + 5572 q^{7} + 2754 q^{9}+O(q^{10}) $ 2 * q - 126 * q^3 - 256 * q^4 - 1152 * q^6 + 5572 * q^7 + 2754 * q^9	\( 2 q - 126 q^{3} - 256 q^{4} - 1152 q^{6} + 5572 q^{7} + 2754 q^{9} - 13056 q^{10} + 16128 q^{12} - 26300 q^{13} - 58752 q^{15} + 32768 q^{16} + 145152 q^{18} + 288004 q^{19} - 351036 q^{21} - 507648 q^{22} + 147456 q^{24} + 115394 q^{25} + 479682 q^{27} - 713216 q^{28} + 822528 q^{30} + 1457476 q^{31} - 2284416 q^{33} + 1502208 q^{34} - 352512 q^{36} - 3928892 q^{37} + 1656900 q^{39} + 1671168 q^{40} - 3209472 q^{42} - 156284 q^{43} + 7402752 q^{45} - 1116672 q^{46} - 2064384 q^{48} + 3993990 q^{49} + 6759936 q^{51} + 3366400 q^{52} - 10730880 q^{54} - 25890048 q^{55} - 18144252 q^{57} + 14196480 q^{58} + 7520256 q^{60} + 35156548 q^{61} + 7672644 q^{63} - 4194304 q^{64} + 31981824 q^{66} - 34273532 q^{67} - 5025024 q^{69} - 36374016 q^{70} - 18579456 q^{72} + 56278660 q^{73} - 7269822 q^{75} - 36864512 q^{76} + 15148800 q^{78} + 18364996 q^{79} - 78508926 q^{81} - 22313472 q^{82} + 44932608 q^{84} + 76612608 q^{85} + 63884160 q^{87} + 64978944 q^{88} - 17978112 q^{90} - 73271800 q^{91} - 91820988 q^{93} + 79641600 q^{94} - 18874368 q^{96} - 257445116 q^{97} + 287836416 q^{99}+O(q^{100}) \) 2 * q - 126 * q^3 - 256 * q^4 - 1152 * q^6 + 5572 * q^7 + 2754 * q^9 - 13056 * q^10 + 16128 * q^12 - 26300 * q^13 - 58752 * q^15 + 32768 * q^16 + 145152 * q^18 + 288004 * q^19 - 351036 * q^21 - 507648 * q^22 + 147456 * q^24 + 115394 * q^25 + 479682 * q^27 - 713216 * q^28 + 822528 * q^30 + 1457476 * q^31 - 2284416 * q^33 + 1502208 * q^34 - 352512 * q^36 - 3928892 * q^37 + 1656900 * q^39 + 1671168 * q^40 - 3209472 * q^42 - 156284 * q^43 + 7402752 * q^45 - 1116672 * q^46 - 2064384 * q^48 + 3993990 * q^49 + 6759936 * q^51 + 3366400 * q^52 - 10730880 * q^54 - 25890048 * q^55 - 18144252 * q^57 + 14196480 * q^58 + 7520256 * q^60 + 35156548 * q^61 + 7672644 * q^63 - 4194304 * q^64 + 31981824 * q^66 - 34273532 * q^67 - 5025024 * q^69 - 36374016 * q^70 - 18579456 * q^72 + 56278660 * q^73 - 7269822 * q^75 - 36864512 * q^76 + 15148800 * q^78 + 18364996 * q^79 - 78508926 * q^81 - 22313472 * q^82 + 44932608 * q^84 + 76612608 * q^85 + 63884160 * q^87 + 64978944 * q^88 - 17978112 * q^90 - 73271800 * q^91 - 91820988 * q^93 + 79641600 * q^94 - 18874368 * q^96 - 257445116 * q^97 + 287836416 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$		−	11.3137i		−	0.707107i
$2$		−	11.3137i		−	0.707107i
$3$	−63.0000	−	50.9117i	−0.777778	−	0.628539i
$3$	−63.0000	−	50.9117i	−0.777778	−	0.628539i
$4$	−128.000			−0.500000
$5$		−	576.999i		−	0.923199i	−0.887089	−	0.461599i	$-0.847276\pi$
$5$		−	576.999i		−	0.923199i	0.887089	−	0.461599i	$-0.152724\pi$
$6$	−576.000	+	712.764i	−0.444444	+	0.549972i
$7$	2786.00			1.16035			0.580175	−	0.814492i	$-0.302984\pi$
$7$	2786.00			1.16035			0.580175	+	0.814492i	$0.302984\pi$
$8$			1448.15i			0.353553i
$9$	1377.00	+	6414.87i	0.209877	+	0.977728i
$10$	−6528.00			−0.652800
$11$		−	22435.1i		−	1.53235i	−0.642634	−	0.766173i	$-0.722158\pi$
$11$		−	22435.1i		−	1.53235i	0.642634	−	0.766173i	$-0.277842\pi$
$12$	8064.00	+	6516.70i	0.388889	+	0.314270i
$13$	−13150.0			−0.460418			−0.230209	−	0.973141i	$-0.573941\pi$
$13$	−13150.0			−0.460418			−0.230209	+	0.973141i	$0.573941\pi$
$14$		−	31520.0i		−	0.820491i
$15$	−29376.0	+	36350.9i	−0.580267	+	0.718043i
$16$	16384.0			0.250000
$17$			66388.8i			0.794876i	0.917629	+	0.397438i	$0.130101\pi$
$17$			66388.8i			0.794876i	−0.917629	+	0.397438i	$0.869899\pi$
$18$	72576.0	−	15579.0i	0.691358	−	0.148405i
$19$	144002.			1.10498			0.552490	−	0.833520i	$-0.313678\pi$
$19$	144002.			1.10498			0.552490	+	0.833520i	$0.313678\pi$
$20$			73855.9i			0.461599i
$21$	−175518.	−	141840.i	−0.902494	−	0.729326i
$22$	−253824.			−1.08353
$23$		−	49350.4i		−	0.176352i	−0.996105	−	0.0881758i	$-0.971896\pi$
$23$		−	49350.4i		−	0.176352i	0.996105	−	0.0881758i	$-0.0281037\pi$
$24$	73728.0	−	91233.7i	0.222222	−	0.274986i
$25$	57697.0			0.147704
$26$			148775.i			0.325565i
$27$	239841.	−	474242.i	0.451303	−	0.892371i
$28$	−356608.			−0.580175
$29$			627402.i			0.887061i	0.896259	+	0.443531i	$0.146274\pi$
$29$			627402.i			0.887061i	−0.896259	+	0.443531i	$0.853726\pi$
$30$	411264.	+	332352.i	0.507733	+	0.410310i
$31$	728738.			0.789087			0.394543	−	0.918877i	$-0.370903\pi$
$31$	728738.			0.789087			0.394543	+	0.918877i	$0.370903\pi$
$32$		−	185364.i		−	0.176777i
$33$	−1.14221e6	+	1.41341e6i	−0.963140	+	1.19182i
$34$	751104.			0.562062
$35$		−	1.60752e6i		−	1.07123i
$36$	−176256.	−	821104.i	−0.104938	−	0.488864i
$37$	−1.96445e6			−1.04817			−0.524087	−	0.851665i	$-0.675593\pi$
$37$	−1.96445e6			−1.04817			−0.524087	+	0.851665i	$0.675593\pi$
$38$		−	1.62920e6i		−	0.781338i
$39$	828450.	+	669489.i	0.358103	+	0.289391i
$40$	835584.			0.326400
$41$		−	986125.i		−	0.348977i	−0.984659	−	0.174488i	$-0.944173\pi$
$41$		−	986125.i		−	0.348977i	0.984659	−	0.174488i	$-0.0558272\pi$
$42$	−1.60474e6	+	1.98576e6i	−0.515711	+	0.638160i
$43$	−78142.0			−0.0228566			−0.0114283	−	0.999935i	$-0.503638\pi$
$43$	−78142.0			−0.0228566			−0.0114283	+	0.999935i	$0.503638\pi$
$44$			2.87169e6i			0.766173i
$45$	3.70138e6	−	794528.i	0.902637	−	0.193758i
$46$	−558336.			−0.124699
$47$			3.51969e6i			0.721296i	0.932702	+	0.360648i	$0.117444\pi$
$47$			3.51969e6i			0.721296i	−0.932702	+	0.360648i	$0.882556\pi$
$48$	−1.03219e6	−	834137.i	−0.194444	−	0.157135i
$49$	1.99700e6			0.346412
$50$		−	652767.i		−	0.104443i
$51$	3.37997e6	−	4.18250e6i	0.499611	−	0.618237i
$52$	1.68320e6			0.230209
$53$		−	522048.i		−	0.0661618i	−0.999453	−	0.0330809i	$-0.989468\pi$
$53$		−	522048.i		−	0.0661618i	0.999453	−	0.0330809i	$-0.0105319\pi$
$54$	−5.36544e6	−	2.71349e6i	−0.631001	−	0.319120i
$55$	−1.29450e7			−1.41466
$56$			4.03456e6i			0.410246i
$57$	−9.07213e6	−	7.33138e6i	−0.859428	−	0.694523i
$58$	7.09824e6			0.627247
$59$			5.00425e6i			0.412981i	0.978449	+	0.206491i	$0.0662043\pi$
$59$			5.00425e6i			0.412981i	−0.978449	+	0.206491i	$0.933796\pi$
$60$	3.76013e6	−	4.65292e6i	0.290133	−	0.359022i
$61$	1.75783e7			1.26957			0.634785	−	0.772689i	$-0.281089\pi$
$61$	1.75783e7			1.26957			0.634785	+	0.772689i	$0.281089\pi$
$62$		−	8.24473e6i		−	0.557968i
$63$	3.83632e6	+	1.78718e7i	0.243530	+	1.13451i
$64$	−2.09715e6			−0.125000
$65$			7.58754e6i			0.425057i
$66$	1.59909e7	+	1.29226e7i	0.842748	+	0.681043i
$67$	−1.71368e7			−0.850413			−0.425206	−	0.905096i	$-0.639798\pi$
$67$	−1.71368e7			−0.850413			−0.425206	+	0.905096i	$0.639798\pi$
$68$		−	8.49777e6i		−	0.397438i
$69$	−2.51251e6	+	3.10907e6i	−0.110844	+	0.137162i
$70$	−1.81870e7			−0.757476
$71$		−	2.58906e7i		−	1.01885i	−0.860516	−	0.509424i	$-0.829859\pi$
$71$		−	2.58906e7i		−	1.01885i	0.860516	−	0.509424i	$-0.170141\pi$
$72$	−9.28973e6	+	1.99411e6i	−0.345679	+	0.0742026i
$73$	2.81393e7			0.990883			0.495441	−	0.868641i	$-0.335006\pi$
$73$	2.81393e7			0.990883			0.495441	+	0.868641i	$0.335006\pi$
$74$			2.22252e7i			0.741171i
$75$	−3.63491e6	−	2.93745e6i	−0.114881	−	0.0928380i
$76$	−1.84323e7			−0.552490
$77$		−	6.25041e7i		−	1.77806i
$78$	7.57440e6	−	9.37284e6i	0.204630	−	0.253217i
$79$	9.18250e6			0.235750			0.117875	−	0.993028i	$-0.462392\pi$
$79$	9.18250e6			0.235750			0.117875	+	0.993028i	$0.462392\pi$
$80$		−	9.45355e6i		−	0.230800i
$81$	−3.92545e7	+	1.76666e7i	−0.911904	+	0.410404i
$82$	−1.11567e7			−0.246764
$83$			8.71084e7i			1.83547i	0.397190	+	0.917736i	$0.369985\pi$
$83$			8.71084e7i			1.83547i	−0.397190	+	0.917736i	$0.630015\pi$
$84$	2.24663e7	+	1.81555e7i	0.451247	+	0.364663i
$85$	3.83063e7			0.733828
$86$			884076.i			0.0161620i
$87$	3.19421e7	−	3.95263e7i	0.557553	−	0.689937i
$88$	3.24895e7			0.541766
$89$			8.12528e7i			1.29503i	0.762055	+	0.647513i	$0.224191\pi$
$89$			8.12528e7i			1.29503i	−0.762055	+	0.647513i	$0.775809\pi$
$90$	−8.98906e6	−	4.18763e7i	−0.137007	−	0.638261i
$91$	−3.66359e7			−0.534246
$92$			6.31685e6i			0.0881758i
$93$	−4.59105e7	−	3.71013e7i	−0.613734	−	0.495972i
$94$	3.98208e7			0.510033
$95$		−	8.30890e7i		−	1.02012i
$96$	−9.43718e6	+	1.16779e7i	−0.111111	+	0.137493i
$97$	−1.28723e8			−1.45401			−0.727006	−	0.686632i	$-0.759089\pi$
$97$	−1.28723e8			−1.45401			−0.727006	+	0.686632i	$0.759089\pi$
$98$		−	2.25934e7i		−	0.244950i
$99$	1.43918e8	−	3.08931e7i	1.49822	−	0.321604i
$100$	−7.38522e6			−0.0738522
$101$			9.37809e7i			0.901216i	0.892722	+	0.450608i	$0.148793\pi$
$101$			9.37809e7i			0.901216i	−0.892722	+	0.450608i	$0.851207\pi$
$102$	−4.73196e7	−	3.82400e7i	−0.437160	−	0.353278i
$103$	−5.30322e7			−0.471184			−0.235592	−	0.971852i	$-0.575703\pi$
$103$	−5.30322e7			−0.471184			−0.235592	+	0.971852i	$0.575703\pi$
$104$		−	1.90432e7i		−	0.162782i
$105$	−8.18415e7	+	1.01274e8i	−0.673312	+	0.833182i
$106$	−5.90630e6			−0.0467835
$107$		−	1.90801e8i		−	1.45561i	−0.685785	−	0.727804i	$-0.740541\pi$
$107$		−	1.90801e8i		−	1.45561i	0.685785	−	0.727804i	$-0.259459\pi$
$108$	−3.06996e7	+	6.07030e7i	−0.225652	+	0.446185i
$109$	2.71959e8			1.92662			0.963312	−	0.268384i	$-0.0864897\pi$
$109$	2.71959e8			1.92662			0.963312	+	0.268384i	$0.0864897\pi$
$110$			1.46456e8i			1.00032i
$111$	1.23760e8	+	1.00013e8i	0.815246	+	0.658818i
$112$	4.56458e7			0.290087
$113$		−	7.69189e7i		−	0.471758i	−0.971782	−	0.235879i	$-0.924203\pi$
$113$		−	7.69189e7i		−	0.471758i	0.971782	−	0.235879i	$-0.0757969\pi$
$114$	−8.29452e7	+	1.02639e8i	−0.491102	+	0.607708i
$115$	−2.84751e7			−0.162808
$116$		−	8.03074e7i		−	0.443531i
$117$	−1.81076e7	−	8.43556e7i	−0.0966309	−	0.450164i
$118$	5.66166e7			0.292022
$119$			1.84959e8i			0.922334i
$120$	−5.26418e7	−	4.25410e7i	−0.253867	−	0.205155i
$121$	−2.88974e8			−1.34809
$122$		−	1.98875e8i		−	0.897722i
$123$	−5.02053e7	+	6.21259e7i	−0.219346	+	0.271427i
$124$	−9.32785e7			−0.394543
$125$		−	2.58681e8i		−	1.05956i
$126$	2.02197e8	−	4.34030e7i	0.802217	−	0.172202i
$127$	−1.25417e8			−0.482104			−0.241052	−	0.970512i	$-0.577492\pi$
$127$	−1.25417e8			−0.482104			−0.241052	+	0.970512i	$0.577492\pi$
$128$			2.37266e7i			0.0883883i
$129$	4.92295e6	+	3.97834e6i	0.0177773	+	0.0143662i
$130$	8.58432e7			0.300561
$131$			1.24051e8i			0.421225i	0.977570	+	0.210612i	$0.0675458\pi$
$131$			1.24051e8i			0.421225i	−0.977570	+	0.210612i	$0.932454\pi$
$132$	1.46203e8	−	1.80917e8i	0.481570	−	0.595912i
$133$	4.01190e8			1.28216
$134$			1.93880e8i			0.601332i
$135$	−2.73637e8	−	1.38388e8i	−0.823835	−	0.416642i
$136$	−9.61413e7			−0.281031
$137$			5.50746e8i			1.56340i	0.623656	+	0.781699i	$0.285647\pi$
$137$			5.50746e8i			1.56340i	−0.623656	+	0.781699i	$0.714353\pi$
$138$	3.51752e7	+	2.84258e7i	0.0969884	+	0.0783785i
$139$	−7.59262e7			−0.203391			−0.101696	−	0.994816i	$-0.532427\pi$
$139$	−7.59262e7			−0.203391			−0.101696	+	0.994816i	$0.532427\pi$
$140$			2.05763e8i			0.535617i
$141$	1.79194e8	−	2.21741e8i	0.453363	−	0.561008i
$142$	−2.92919e8			−0.720434
$143$			2.95021e8i			0.705520i
$144$	2.25608e7	+	1.05101e8i	0.0524691	+	0.244432i
$145$	3.62010e8			0.818934
$146$		−	3.18360e8i		−	0.700660i
$147$	−1.25811e8	−	1.01670e8i	−0.269431	−	0.217733i
$148$	2.51449e8			0.524087
$149$		−	7.35143e8i		−	1.49151i	−0.666219	−	0.745756i	$-0.732088\pi$
$149$		−	7.35143e8i		−	1.49151i	0.666219	−	0.745756i	$-0.267912\pi$
$150$	−3.32335e7	+	4.11243e7i	−0.0656464	+	0.0812332i
$151$	3.01637e8			0.580198			0.290099	−	0.956997i	$-0.406312\pi$
$151$	3.01637e8			0.580198			0.290099	+	0.956997i	$0.406312\pi$
$152$			2.08537e8i			0.390669i
$153$	−4.25876e8	+	9.14174e7i	−0.777172	+	0.166826i
$154$	−7.07154e8			−1.25728
$155$		−	4.20481e8i		−	0.728484i
$156$	−1.06042e8	−	8.56946e7i	−0.179051	−	0.144695i
$157$	−1.61241e8			−0.265386			−0.132693	−	0.991157i	$-0.542362\pi$
$157$	−1.61241e8			−0.265386			−0.132693	+	0.991157i	$0.542362\pi$
$158$		−	1.03888e8i		−	0.166701i
$159$	−2.65784e7	+	3.28891e7i	−0.0415853	+	0.0514592i
$160$	−1.06955e8			−0.163200
$161$		−	1.37490e8i		−	0.204630i
$162$	1.99874e8	+	4.44114e8i	0.290200	+	0.644813i
$163$	−2.21232e8			−0.313399			−0.156700	−	0.987646i	$-0.550085\pi$
$163$	−2.21232e8			−0.313399			−0.156700	+	0.987646i	$0.550085\pi$
$164$			1.26224e8i			0.174488i
$165$	8.15537e8	+	6.59053e8i	1.10029	+	0.889170i
$166$	9.85519e8			1.29787
$167$			4.01854e8i			0.516657i	0.966057	+	0.258328i	$0.0831716\pi$
$167$			4.01854e8i			0.516657i	−0.966057	+	0.258328i	$0.916828\pi$
$168$	2.05406e8	−	2.54177e8i	0.257856	−	0.319080i
$169$	−6.42808e8			−0.788015
$170$		−	4.33386e8i		−	0.518895i
$171$	1.98291e8	+	9.23755e8i	0.231909	+	1.08037i
$172$	1.00022e7			0.0114283
$173$			1.08224e7i			0.0120820i	0.999982	+	0.00604099i	$0.00192292\pi$
$173$			1.08224e7i			0.0120820i	−0.999982	+	0.00604099i	$0.998077\pi$
$174$	−4.47189e8	−	3.61383e8i	−0.487859	−	0.394250i
$175$	1.60744e8			0.171389
$176$		−	3.67576e8i		−	0.383087i
$177$	2.54775e8	−	3.15267e8i	0.259575	−	0.321208i
$178$	9.19271e8			0.915721
$179$		−	2.24822e8i		−	0.218991i	−0.993987	−	0.109495i	$-0.965076\pi$
$179$		−	2.24822e8i		−	0.218991i	0.993987	−	0.109495i	$-0.0349235\pi$
$180$	−4.73776e8	+	1.01700e8i	−0.451319	+	0.0968789i
$181$	−1.31026e9			−1.22080			−0.610398	−	0.792095i	$-0.708990\pi$
$181$	−1.31026e9			−1.22080			−0.610398	+	0.792095i	$0.708990\pi$
$182$			4.14488e8i			0.377769i
$183$	−1.10743e9	−	8.94940e8i	−0.987444	−	0.797975i
$184$	7.14670e7			0.0623497
$185$			1.13348e9i			0.967672i
$186$	−4.19753e8	+	5.19418e8i	−0.350705	+	0.433975i
$187$	1.48944e9			1.21803
$188$		−	4.50521e8i		−	0.360648i
$189$	6.68197e8	−	1.32124e9i	0.523670	−	1.03546i
$190$	−9.40045e8			−0.721330
$191$		−	2.18984e9i		−	1.64543i	−0.568454	−	0.822715i	$-0.692458\pi$
$191$		−	2.18984e9i		−	1.64543i	0.568454	−	0.822715i	$-0.307542\pi$
$192$	1.32121e8	+	1.06770e8i	0.0972222	+	0.0785674i
$193$	−1.71183e9			−1.23376			−0.616881	−	0.787057i	$-0.711604\pi$
$193$	−1.71183e9			−1.23376			−0.616881	+	0.787057i	$0.711604\pi$
$194$			1.45633e9i			1.02814i
$195$	3.86294e8	−	4.78015e8i	0.267165	−	0.330600i
$196$	−2.55615e8			−0.173206
$197$			2.63287e9i			1.74810i	0.485840	+	0.874048i	$0.338514\pi$
$197$			2.63287e9i			1.74810i	−0.485840	+	0.874048i	$0.661486\pi$
$198$	−3.49516e8	−	1.62825e9i	−0.227408	−	1.05940i
$199$	2.95243e9			1.88264			0.941319	−	0.337517i	$-0.109587\pi$
$199$	2.95243e9			1.88264			0.941319	+	0.337517i	$0.109587\pi$
$200$			8.35542e7i			0.0522214i
$201$	1.07962e9	+	8.72462e8i	0.661432	+	0.534518i
$202$	1.06101e9			0.637256
$203$			1.74794e9i			1.02930i
$204$	−4.32636e8	+	5.35360e8i	−0.249805	+	0.309118i
$205$	−5.68994e8			−0.322175
$206$			5.99991e8i			0.333178i
$207$	3.16577e8	−	6.79555e7i	0.172424	−	0.0370121i
$208$	−2.15450e8			−0.115105
$209$		−	3.23070e9i		−	1.69321i
$210$	1.14578e9	+	9.25931e8i	0.589148	+	0.476104i
$211$	−2.66349e9			−1.34376			−0.671880	−	0.740660i	$-0.734513\pi$
$211$	−2.66349e9			−1.34376			−0.671880	+	0.740660i	$0.734513\pi$
$212$			6.68222e7i			0.0330809i
$213$	−1.31814e9	+	1.63111e9i	−0.640386	+	0.792437i
$214$	−2.15866e9			−1.02927
$215$			4.50879e7i			0.0211011i
$216$	6.86776e8	+	3.47327e8i	0.315501	+	0.159560i
$217$	2.03026e9			0.915616
$218$		−	3.07686e9i		−	1.36233i
$219$	−1.77278e9	−	1.43262e9i	−0.770687	−	0.622809i
$220$	1.65696e9			0.707330
$221$		−	8.73013e8i		−	0.365975i
$222$	1.13152e9	−	1.40019e9i	0.465855	−	0.576466i
$223$	−2.04266e8			−0.0825993			−0.0412996	−	0.999147i	$-0.513150\pi$
$223$	−2.04266e8			−0.0825993			−0.0412996	+	0.999147i	$0.513150\pi$
$224$		−	5.16424e8i		−	0.205123i
$225$	7.94488e7	+	3.70119e8i	0.0309997	+	0.144415i
$226$	−8.70238e8			−0.333583
$227$			4.26163e8i			0.160499i	0.996775	+	0.0802495i	$0.0255717\pi$
$227$			4.26163e8i			0.160499i	−0.996775	+	0.0802495i	$0.974428\pi$
$228$	1.16123e9	+	9.38417e8i	0.429714	+	0.347261i
$229$	−3.05784e8			−0.111192			−0.0555960	−	0.998453i	$-0.517706\pi$
$229$	−3.05784e8			−0.111192			−0.0555960	+	0.998453i	$0.517706\pi$
$230$			3.22159e8i			0.115122i
$231$	−3.18219e9	+	3.93776e9i	−1.11758	+	1.38293i
$232$	−9.08575e8			−0.313624
$233$		−	1.40915e9i		−	0.478117i	−0.971005	−	0.239059i	$-0.923161\pi$
$233$		−	1.40915e9i		−	0.478117i	0.971005	−	0.239059i	$-0.0768388\pi$
$234$	−9.54374e8	+	2.04864e8i	−0.318314	+	0.0683284i
$235$	2.03086e9			0.665900
$236$		−	6.40543e8i		−	0.206491i
$237$	−5.78497e8	−	4.67496e8i	−0.183361	−	0.148178i
$238$	2.09258e9			0.652189
$239$			2.28759e9i			0.701109i	0.936542	+	0.350555i	$0.114007\pi$
$239$			2.28759e9i			0.701109i	−0.936542	+	0.350555i	$0.885993\pi$
$240$	−4.81296e8	+	5.95574e8i	−0.145067	+	0.179511i
$241$	4.37370e9			1.29653			0.648263	−	0.761417i	$-0.275496\pi$
$241$	4.37370e9			1.29653			0.648263	+	0.761417i	$0.275496\pi$
$242$			3.26937e9i			0.953240i
$243$	3.37247e9	+	8.85518e8i	0.967214	+	0.253964i
$244$	−2.25002e9			−0.634785
$245$		−	1.15226e9i		−	0.319807i
$246$	7.02874e8	+	5.68008e8i	0.191928	+	0.155101i
$247$	−1.89363e9			−0.508752
$248$			1.05533e9i			0.278984i
$249$	4.43484e9	−	5.48783e9i	1.15367	−	1.42759i
$250$	−2.92665e9			−0.749221
$251$		−	1.78995e9i		−	0.450969i	−0.974247	−	0.225484i	$-0.927604\pi$
$251$		−	1.78995e9i		−	0.450969i	0.974247	−	0.225484i	$-0.0723965\pi$
$252$	−4.91049e8	−	2.28759e9i	−0.121765	−	0.567253i
$253$	−1.10718e9			−0.270232
$254$			1.41893e9i			0.340899i
$255$	−2.41330e9	−	1.95024e9i	−0.570755	−	0.461240i
$256$	2.68435e8			0.0625000
$257$			2.20683e9i			0.505867i	0.967484	+	0.252933i	$0.0813954\pi$
$257$			2.20683e9i			0.505867i	−0.967484	+	0.252933i	$0.918605\pi$
$258$	4.50098e7	−	5.56968e7i	0.0101585	−	0.0125705i
$259$	−5.47295e9			−1.21625
$260$		−	9.71205e8i		−	0.212529i
$261$	−4.02470e9	+	8.63932e8i	−0.867305	+	0.186173i
$262$	1.40347e9			0.297851
$263$			1.77804e9i			0.371636i	0.982584	+	0.185818i	$0.0594935\pi$
$263$			1.77804e9i			0.371636i	−0.982584	+	0.185818i	$0.940506\pi$
$264$	−2.04684e9	−	1.65409e9i	−0.421374	−	0.340521i
$265$	−3.01222e8			−0.0610805
$266$		−	4.53894e9i		−	0.906626i
$267$	4.13672e9	−	5.11893e9i	0.813975	−	1.00724i
$268$	2.19351e9			0.425206
$269$			5.97276e9i			1.14069i	0.821406	+	0.570343i	$0.193190\pi$
$269$			5.97276e9i			1.14069i	−0.821406	+	0.570343i	$0.806810\pi$
$270$	−1.56568e9	+	3.09585e9i	−0.294611	+	0.582540i
$271$	3.24555e9			0.601744			0.300872	−	0.953665i	$-0.402722\pi$
$271$	3.24555e9			0.601744			0.300872	+	0.953665i	$0.402722\pi$
$272$			1.08771e9i			0.198719i
$273$	2.30806e9	+	1.86520e9i	0.415525	+	0.335795i
$274$	6.23098e9			1.10549
$275$		−	1.29444e9i		−	0.226334i
$276$	3.21602e8	−	3.97962e8i	0.0554219	−	0.0685812i
$277$	−1.34137e9			−0.227841			−0.113920	−	0.993490i	$-0.536341\pi$
$277$	−1.34137e9			−0.227841			−0.113920	+	0.993490i	$0.536341\pi$
$278$			8.59007e8i			0.143819i
$279$	1.00347e9	+	4.67476e9i	0.165611	+	0.771512i
$280$	2.32794e9			0.378738
$281$		−	1.89253e9i		−	0.303541i	−0.988416	−	0.151771i	$-0.951502\pi$
$281$		−	1.89253e9i		−	0.303541i	0.988416	−	0.151771i	$-0.0484975\pi$
$282$	−2.50871e9	−	2.02734e9i	−0.396693	−	0.320576i
$283$	−6.88292e9			−1.07307			−0.536534	−	0.843879i	$-0.680267\pi$
$283$	−6.88292e9			−1.07307			−0.536534	+	0.843879i	$0.680267\pi$
$284$			3.31400e9i			0.509424i
$285$	−4.23020e9	+	5.23461e9i	−0.641183	+	0.793423i
$286$	3.33779e9			0.498878
$287$		−	2.74735e9i		−	0.404935i
$288$	1.18909e9	−	2.55246e8i	0.172840	−	0.0371013i
$289$	2.56828e9			0.368172
$290$		−	4.09568e9i		−	0.579074i
$291$	8.10952e9	+	6.55348e9i	1.13090	+	0.913903i
$292$	−3.60183e9			−0.495441
$293$		−	4.31371e9i		−	0.585302i	−0.956219	−	0.292651i	$-0.905463\pi$
$293$		−	4.31371e9i		−	0.585302i	0.956219	−	0.292651i	$-0.0945375\pi$
$294$	−1.15027e9	+	1.42339e9i	−0.153961	+	0.190517i
$295$	2.88745e9			0.381264
$296$		−	2.84482e9i		−	0.370585i
$297$	−1.06397e10	−	5.38085e9i	−1.36742	−	0.691553i
$298$	−8.31719e9			−1.05466
$299$			6.48958e8i			0.0811954i
$300$	4.65269e8	+	3.75994e8i	0.0574406	+	0.0464190i
$301$	−2.17704e8			−0.0265216
$302$		−	3.41263e9i		−	0.410262i
$303$	4.77455e9	−	5.90820e9i	0.566450	−	0.700946i
$304$	2.35933e9			0.276245
$305$		−	1.01426e10i		−	1.17207i
$306$	1.03427e9	+	4.81824e9i	0.117964	+	0.549544i
$307$	−8.32155e9			−0.936809			−0.468404	−	0.883514i	$-0.655171\pi$
$307$	−8.32155e9			−0.936809			−0.468404	+	0.883514i	$0.655171\pi$
$308$			8.00053e9i			0.889029i
$309$	3.34103e9	+	2.69996e9i	0.366477	+	0.296158i
$310$	−4.75720e9			−0.515116
$311$		−	1.09184e10i		−	1.16712i	−0.812069	−	0.583561i	$-0.801659\pi$
$311$		−	1.09184e10i		−	1.16712i	0.812069	−	0.583561i	$-0.198341\pi$
$312$	−9.69523e8	+	1.19972e9i	−0.102315	+	0.126609i
$313$	6.19953e9			0.645924			0.322962	−	0.946412i	$-0.395321\pi$
$313$	6.19953e9			0.645924			0.322962	+	0.946412i	$0.395321\pi$
$314$			1.82424e9i			0.187656i
$315$	1.03120e10	−	2.21355e9i	1.04737	−	0.224827i
$316$	−1.17536e9			−0.117875
$317$			1.86870e10i			1.85056i	0.379289	+	0.925278i	$0.376169\pi$
$317$			1.86870e10i			1.85056i	−0.379289	+	0.925278i	$0.623831\pi$
$318$	3.72097e8	+	3.00700e8i	0.0363871	+	0.0294052i
$319$	1.40758e10			1.35929
$320$			1.21005e9i			0.115400i
$321$	−9.71398e9	+	1.20204e10i	−0.914907	+	1.13214i
$322$	−1.55552e9			−0.144695
$323$			9.56013e9i			0.878322i
$324$	5.02457e9	−	2.26132e9i	0.455952	−	0.205202i
$325$	−7.58716e8			−0.0680057
$326$			2.50296e9i			0.221607i
$327$	−1.71334e10	−	1.38459e10i	−1.49849	−	1.21096i
$328$	1.42806e9			0.123382
$329$			9.80587e9i			0.836956i
$330$	7.45633e9	−	9.22674e9i	0.628738	−	0.778023i
$331$	3.24478e9			0.270317			0.135158	−	0.990824i	$-0.456846\pi$
$331$	3.24478e9			0.270317			0.135158	+	0.990824i	$0.456846\pi$
$332$		−	1.11499e10i		−	0.917736i
$333$	−2.70504e9	−	1.26017e10i	−0.219987	−	1.02483i
$334$	4.54645e9			0.365331
$335$			9.88790e9i			0.785100i
$336$	−2.87569e9	−	2.32391e9i	−0.225624	−	0.182331i
$337$	4.89137e9			0.379237			0.189619	−	0.981858i	$-0.439275\pi$
$337$	4.89137e9			0.379237			0.189619	+	0.981858i	$0.439275\pi$
$338$			7.27254e9i			0.557211i
$339$	−3.91607e9	+	4.84589e9i	−0.296518	+	0.366923i
$340$	−4.90321e9			−0.366914
$341$		−	1.63493e10i		−	1.20915i
$342$	1.04511e10	−	2.24340e9i	0.763936	−	0.163985i
$343$	−1.04971e10			−0.758391
$344$		−	1.13162e8i		−	0.00808101i
$345$	1.79393e9	+	1.44972e9i	0.126628	+	0.102331i
$346$	1.22441e8			0.00854324
$347$		−	1.44263e10i		−	0.995030i	−0.867455	−	0.497515i	$-0.834246\pi$
$347$		−	1.44263e10i		−	0.995030i	0.867455	−	0.497515i	$-0.165754\pi$
$348$	−4.08859e9	+	5.05937e9i	−0.278777	+	0.344968i
$349$	−5.34169e9			−0.360062			−0.180031	−	0.983661i	$-0.557620\pi$
$349$	−5.34169e9			−0.360062			−0.180031	+	0.983661i	$0.557620\pi$
$350$		−	1.81861e9i		−	0.121190i
$351$	−3.15391e9	+	6.23629e9i	−0.207788	+	0.410864i
$352$	−4.15865e9			−0.270883
$353$			7.82366e9i			0.503861i	0.967745	+	0.251931i	$0.0810655\pi$
$353$			7.82366e9i			0.503861i	−0.967745	+	0.251931i	$0.918935\pi$
$354$	−3.56684e9	−	2.88245e9i	−0.227128	−	0.183547i
$355$	−1.49389e10			−0.940599
$356$		−	1.04004e10i		−	0.647513i
$357$	9.41659e9	−	1.16524e10i	0.579723	−	0.717371i
$358$	−2.54357e9			−0.154850
$359$			1.66718e10i			1.00370i	0.864955	+	0.501850i	$0.167347\pi$
$359$			1.66718e10i			1.00370i	−0.864955	+	0.501850i	$0.832653\pi$
$360$	1.15060e9	+	5.36017e9i	0.0685037	+	0.319130i
$361$	3.75301e9			0.220979
$362$			1.48239e10i			0.863233i
$363$	1.82054e10	+	1.47122e10i	1.04851	+	0.847325i
$364$	4.68940e9			0.267123
$365$		−	1.62364e10i		−	0.914782i
$366$	−1.01251e10	+	1.25292e10i	−0.564254	+	0.698228i
$367$	1.86456e10			1.02781			0.513905	−	0.857847i	$-0.328198\pi$
$367$	1.86456e10			1.02781			0.513905	+	0.857847i	$0.328198\pi$
$368$		−	8.08557e8i		−	0.0440879i
$369$	6.32587e9	−	1.35789e9i	0.341205	−	0.0732421i
$370$	1.28239e10			0.684248
$371$		−	1.45443e9i		−	0.0767708i
$372$	5.87654e9	+	4.74896e9i	0.306867	+	0.247986i
$373$	3.38390e10			1.74817			0.874083	−	0.485776i	$-0.161463\pi$
$373$	3.38390e10			1.74817			0.874083	+	0.485776i	$0.161463\pi$
$374$		−	1.68511e10i		−	0.861274i
$375$	−1.31699e10	+	1.62969e10i	−0.665975	+	0.824101i
$376$	−5.09706e9			−0.255017
$377$		−	8.25033e9i		−	0.408419i
$378$	−1.49481e10	−	7.55979e9i	−0.732182	−	0.370290i
$379$	−2.82088e10			−1.36719			−0.683594	−	0.729863i	$-0.739584\pi$
$379$	−2.82088e10			−1.36719			−0.683594	+	0.729863i	$0.739584\pi$
$380$			1.06354e10i			0.510058i
$381$	7.90126e9	+	6.38518e9i	0.374970	+	0.303021i
$382$	−2.47752e10			−1.16349
$383$		−	1.82405e10i		−	0.847698i	−0.905733	−	0.423849i	$-0.860679\pi$
$383$		−	1.82405e10i		−	0.847698i	0.905733	−	0.423849i	$-0.139321\pi$
$384$	1.20796e9	−	1.49477e9i	0.0555556	−	0.0687465i
$385$	−3.60648e10			−1.64150
$386$			1.93671e10i			0.872401i
$387$	−1.07602e8	−	5.01271e8i	−0.00479705	−	0.0223475i
$388$	1.64765e10			0.727006
$389$		−	1.94375e10i		−	0.848871i	−0.905458	−	0.424435i	$-0.860473\pi$
$389$		−	1.94375e10i		−	0.848871i	0.905458	−	0.424435i	$-0.139527\pi$
$390$	−5.40812e9	−	4.37042e9i	−0.233770	−	0.188914i
$391$	3.27632e9			0.140178
$392$			2.89196e9i			0.122475i
$393$	6.31563e9	−	7.81519e9i	0.264756	−	0.327619i
$394$	2.97876e10			1.23609
$395$		−	5.29829e9i		−	0.217644i
$396$	−1.84215e10	+	3.95432e9i	−0.749109	+	0.160802i
$397$	1.66719e10			0.671157			0.335578	−	0.942012i	$-0.391068\pi$
$397$	1.66719e10			0.671157			0.335578	+	0.942012i	$0.391068\pi$
$398$		−	3.34029e10i		−	1.33123i
$399$	−2.52749e10	−	2.04252e10i	−0.997238	−	0.805890i
$400$	9.45308e8			0.0369261
$401$			3.30836e10i			1.27949i	0.768589	+	0.639743i	$0.220959\pi$
$401$			3.30836e10i			1.27949i	−0.768589	+	0.639743i	$0.779041\pi$
$402$	9.87078e9	−	1.22145e10i	0.377961	−	0.467703i
$403$	−9.58290e9			−0.363310
$404$		−	1.20040e10i		−	0.450608i
$405$	1.01936e10	+	2.26498e10i	0.378885	+	0.841868i
$406$	1.97757e10			0.727826
$407$			4.40725e10i			1.60616i
$408$	6.05690e9	+	4.89472e9i	0.218580	+	0.176639i
$409$	−5.03326e10			−1.79869			−0.899345	−	0.437240i	$-0.855956\pi$
$409$	−5.03326e10			−1.79869			−0.899345	+	0.437240i	$0.855956\pi$
$410$			6.43743e9i			0.227812i
$411$	2.80394e10	−	3.46970e10i	0.982657	−	1.21598i
$412$	6.78812e9			0.235592
$413$			1.39418e10i			0.479203i
$414$	−7.68829e8	−	3.58165e9i	−0.0261715	−	0.121922i
$415$	5.02615e10			1.69451
$416$			2.43753e9i			0.0813912i
$417$	4.78335e9	+	3.86553e9i	0.158193	+	0.127839i
$418$	−3.65512e10			−1.19728
$419$			2.94280e10i			0.954782i	0.878691	+	0.477391i	$0.158418\pi$
$419$			2.94280e10i			0.954782i	−0.878691	+	0.477391i	$0.841582\pi$
$420$	1.04757e10	−	1.29630e10i	0.336656	−	0.416591i
$421$	−3.33243e10			−1.06080			−0.530399	−	0.847748i	$-0.677958\pi$
$421$	−3.33243e10			−1.06080			−0.530399	+	0.847748i	$0.677958\pi$
$422$			3.01340e10i			0.950181i
$423$	−2.25784e10	+	4.84662e9i	−0.705231	+	0.151383i
$424$	7.56007e8			0.0233917
$425$			3.83044e9i			0.117407i
$426$	1.84539e10	+	1.49130e10i	0.560338	+	0.452821i
$427$	4.89731e10			1.47315
$428$			2.44225e10i			0.727804i
$429$	1.50200e10	−	1.85863e10i	0.443447	−	0.548738i
$430$	5.10111e8			0.0149208
$431$		−	5.62271e10i		−	1.62943i	−0.579860	−	0.814716i	$-0.696893\pi$
$431$		−	5.62271e10i		−	1.62943i	0.579860	−	0.814716i	$-0.303107\pi$
$432$	3.92955e9	−	7.76999e9i	0.112826	−	0.223093i
$433$	−2.18807e10			−0.622457			−0.311229	−	0.950335i	$-0.600740\pi$
$433$	−2.18807e10			−0.622457			−0.311229	+	0.950335i	$0.600740\pi$
$434$		−	2.29698e10i		−	0.647439i
$435$	−2.28066e10	−	1.84306e10i	−0.636949	−	0.514732i
$436$	−3.48107e10			−0.963312
$437$		−	7.10656e9i		−	0.194865i
$438$	−1.62083e10	+	2.00567e10i	−0.440392	+	0.544958i
$439$	1.87990e10			0.506146			0.253073	−	0.967447i	$-0.418559\pi$
$439$	1.87990e10			0.506146			0.253073	+	0.967447i	$0.418559\pi$
$440$		−	1.87464e10i		−	0.500158i
$441$	2.74986e9	+	1.28105e10i	0.0727037	+	0.338696i
$442$	−9.87702e9			−0.258784
$443$		−	6.53593e10i		−	1.69704i	−0.529163	−	0.848520i	$-0.677494\pi$
$443$		−	6.53593e10i		−	1.69704i	0.529163	−	0.848520i	$-0.322506\pi$
$444$	−1.58413e10	−	1.28017e10i	−0.407623	−	0.329409i
$445$	4.68828e10			1.19557
$446$			2.31100e9i			0.0584065i
$447$	−3.74274e10	+	4.63140e10i	−0.937474	+	1.16006i
$448$	−5.84267e9			−0.145044
$449$			1.58084e10i			0.388959i	0.980907	+	0.194479i	$0.0623017\pi$
$449$			1.58084e10i			0.388959i	−0.980907	+	0.194479i	$0.937698\pi$
$450$	4.18742e9	−	8.98860e8i	0.102117	−	0.0219201i
$451$	−2.21238e10			−0.534754
$452$			9.84562e9i			0.235879i
$453$	−1.90031e10	−	1.53568e10i	−0.451265	−	0.364677i
$454$	4.82148e9			0.113490
$455$			2.11389e10i			0.493215i
$456$	1.06170e10	−	1.31378e10i	0.245551	−	0.303854i
$457$	3.30400e9			0.0757486			0.0378743	−	0.999283i	$-0.487941\pi$
$457$	3.30400e9			0.0757486			0.0378743	+	0.999283i	$0.487941\pi$
$458$			3.45956e9i			0.0786246i
$459$	3.14844e10	+	1.59228e10i	0.709324	+	0.358730i
$460$	3.64482e9			0.0814038
$461$		−	3.30139e10i		−	0.730960i	−0.930819	−	0.365480i	$-0.880905\pi$
$461$		−	3.30139e10i		−	0.730960i	0.930819	−	0.365480i	$-0.119095\pi$
$462$	4.45507e10	+	3.60024e10i	0.977882	+	0.790248i
$463$	5.63117e10			1.22539			0.612696	−	0.790319i	$-0.290085\pi$
$463$	5.63117e10			1.22539			0.612696	+	0.790319i	$0.290085\pi$
$464$			1.02793e10i			0.221765i
$465$	−2.14074e10	+	2.64903e10i	−0.457881	+	0.566598i
$466$	−1.59428e10			−0.338080
$467$			5.38175e10i			1.13150i	0.824576	+	0.565752i	$0.191414\pi$
$467$			5.38175e10i			1.13150i	−0.824576	+	0.565752i	$0.808586\pi$
$468$	2.31777e9	+	1.07975e10i	0.0483155	+	0.225082i
$469$	−4.77430e10			−0.986776
$470$		−	2.29766e10i		−	0.470862i
$471$	1.01582e10	+	8.20907e9i	0.206411	+	0.166805i
$472$	−7.24692e9			−0.146011
$473$			1.75312e9i			0.0350242i
$474$	−5.28912e9	+	6.54495e9i	−0.104778	+	0.129656i
$475$	8.30848e9			0.163210
$476$		−	2.36748e10i		−	0.461167i
$477$	3.34887e9	−	7.18861e8i	0.0646882	−	0.0138858i
$478$	2.58811e10			0.495759
$479$		−	8.02692e10i		−	1.52478i	−0.647119	−	0.762389i	$-0.724026\pi$
$479$		−	8.02692e10i		−	1.52478i	0.647119	−	0.762389i	$-0.275974\pi$
$480$	6.73815e9	+	5.44525e9i	0.126933	+	0.102578i
$481$	2.58325e10			0.482598
$482$		−	4.94828e10i		−	0.916782i
$483$	−6.99986e9	+	8.66188e9i	−0.128618	+	0.159156i
$484$	3.69887e10			0.674043
$485$			7.42728e10i			1.34234i
$486$	1.00185e10	−	3.81551e10i	0.179580	−	0.683923i
$487$	−7.07093e10			−1.25707			−0.628537	−	0.777780i	$-0.716346\pi$
$487$	−7.07093e10			−1.25707			−0.628537	+	0.777780i	$0.716346\pi$
$488$			2.54561e10i			0.448861i
$489$	1.39376e10	+	1.12633e10i	0.243755	+	0.196984i
$490$	−1.30364e10			−0.226138
$491$			6.06876e10i			1.04418i	0.852892	+	0.522088i	$0.174847\pi$
$491$			6.06876e10i			1.04418i	−0.852892	+	0.522088i	$0.825153\pi$
$492$	6.42628e9	−	7.95212e9i	0.109673	−	0.135713i
$493$	−4.16525e10			−0.705104
$494$			2.14239e10i			0.359742i
$495$	−1.78253e10	−	8.30407e10i	−0.296904	−	1.38315i
$496$	1.19396e10			0.197272
$497$		−	7.21313e10i		−	1.18222i
$498$	−6.20877e10	−	5.01745e10i	−1.00946	−	0.815766i
$499$	−1.04926e11			−1.69232			−0.846158	−	0.532932i	$-0.821090\pi$
$499$	−1.04926e11			−1.69232			−0.846158	+	0.532932i	$0.821090\pi$
$500$			3.31112e10i			0.529780i
$501$	2.04590e10	−	2.53168e10i	0.324739	−	0.401844i
$502$	−2.02510e10			−0.318883
$503$			4.73262e9i			0.0739315i	0.999317	+	0.0369657i	$0.0117692\pi$
$503$			4.73262e9i			0.0739315i	−0.999317	+	0.0369657i	$0.988231\pi$
$504$	−2.58812e10	+	5.55559e9i	−0.401109	+	0.0861009i
$505$	5.41115e10			0.832002
$506$			1.25263e10i			0.191083i
$507$	4.04969e10	+	3.27265e10i	0.612901	+	0.495299i
$508$	1.60534e10			0.241052
$509$			8.34402e7i			0.00124309i	1.00000		0.000621547i	$0.000197845\pi$
$509$			8.34402e7i			0.00124309i	−1.00000		0.000621547i	$0.999802\pi$
$510$	−2.20644e10	+	2.73033e10i	−0.326146	+	0.403585i
$511$	7.83962e10			1.14977
$512$		−	3.03700e9i		−	0.0441942i
$513$	3.45376e10	−	6.82919e10i	0.498681	−	0.986051i
$514$	2.49674e10			0.357702
$515$			3.05995e10i			0.434997i
$516$	−6.30137e8	−	5.09228e8i	−0.00888866	−	0.00718312i
$517$	7.89646e10			1.10528
$518$			6.19193e10i			0.860017i
$519$	5.50985e8	−	6.81809e8i	0.00759399	−	0.00939709i
$520$	−1.09879e10			−0.150280
$521$			3.30179e10i			0.448124i	0.974575	+	0.224062i	$0.0719318\pi$
$521$			3.30179e10i			0.448124i	−0.974575	+	0.224062i	$0.928068\pi$
$522$	9.77428e9	+	4.55343e10i	0.131644	+	0.613277i
$523$	−7.60491e9			−0.101645			−0.0508227	−	0.998708i	$-0.516184\pi$
$523$	−7.60491e9			−0.101645			−0.0508227	+	0.998708i	$0.516184\pi$
$524$		−	1.58785e10i		−	0.210612i
$525$	−1.01269e10	−	8.18374e9i	−0.133302	−	0.107725i
$526$	2.01162e10			0.262786
$527$			4.83801e10i			0.627226i
$528$	−1.87139e10	+	2.31573e10i	−0.240785	+	0.297956i
$529$	7.58755e10			0.968900
$530$			3.40793e9i			0.0431904i
$531$	−3.21016e10	+	6.89085e9i	−0.403784	+	0.0866751i
$532$	−5.13523e10			−0.641081
$533$			1.29675e10i			0.160675i
$534$	−5.79141e10	−	4.68016e10i	−0.712228	−	0.575567i
$535$	−1.10092e11			−1.34382
$536$		−	2.48167e10i		−	0.300666i
$537$	−1.14460e10	+	1.41638e10i	−0.137644	+	0.170326i
$538$	6.75741e10			0.806587
$539$		−	4.48028e10i		−	0.530823i
$540$	3.50256e10	+	1.77137e10i	0.411918	+	0.208321i
$541$	−1.18116e11			−1.37885			−0.689427	−	0.724355i	$-0.742138\pi$
$541$	−1.18116e11			−1.37885			−0.689427	+	0.724355i	$0.742138\pi$
$542$		−	3.67192e10i		−	0.425497i
$543$	8.25464e10	+	6.67075e10i	0.949508	+	0.767318i
$544$	1.23061e10			0.140516
$545$		−	1.56920e11i		−	1.77866i
$546$	2.11023e10	−	2.61127e10i	0.237443	−	0.293820i
$547$	−6.60454e10			−0.737723			−0.368862	−	0.929484i	$-0.620252\pi$
$547$	−6.60454e10			−0.737723			−0.368862	+	0.929484i	$0.620252\pi$
$548$		−	7.04955e10i		−	0.781699i
$549$	2.42053e10	+	1.12762e11i	0.266453	+	1.24129i
$550$	−1.46449e10			−0.160042
$551$			9.03471e10i			0.980184i
$552$	−4.50242e9	−	3.63851e9i	−0.0484942	−	0.0391892i
$553$	2.55824e10			0.273553
$554$			1.51759e10i			0.161108i
$555$	5.77076e10	−	7.14095e10i	0.608220	−	0.752634i
$556$	9.71855e9			0.101696
$557$		−	1.38850e11i		−	1.44253i	−0.692659	−	0.721265i	$-0.743561\pi$
$557$		−	1.38850e11i		−	1.44253i	0.692659	−	0.721265i	$-0.256439\pi$
$558$	5.28889e10	−	1.13530e10i	0.545541	−	0.117104i
$559$	1.02757e9			0.0105236
$560$		−	2.63376e10i		−	0.267808i
$561$	−9.38347e10	−	7.58299e10i	−0.947353	−	0.765577i
$562$	−2.14115e10			−0.214636
$563$		−	3.29834e10i		−	0.328294i	−0.986436	−	0.164147i	$-0.947513\pi$
$563$		−	3.29834e10i		−	0.328294i	0.986436	−	0.164147i	$-0.0524871\pi$
$564$	−2.29368e10	+	2.83828e10i	−0.226681	+	0.280504i
$565$	−4.43821e10			−0.435526
$566$			7.78713e10i			0.758773i
$567$	−1.09363e11	+	4.92190e10i	−1.05813	+	0.476213i
$568$	3.74936e10			0.360217
$569$			7.16018e10i			0.683085i	0.939866	+	0.341543i	$0.110949\pi$
$569$			7.16018e10i			0.683085i	−0.939866	+	0.341543i	$0.889051\pi$
$570$	5.92228e10	+	4.78593e10i	0.561035	+	0.453385i
$571$	4.20250e10			0.395333			0.197667	−	0.980269i	$-0.436664\pi$
$571$	4.20250e10			0.395333			0.197667	+	0.980269i	$0.436664\pi$
$572$		−	3.77627e10i		−	0.352760i
$573$	−1.11489e11	+	1.37960e11i	−1.03422	+	1.27978i
$574$	−3.10827e10			−0.286333
$575$		−	2.84737e9i		−	0.0260479i
$576$	−2.88778e9	−	1.34530e10i	−0.0262346	−	0.122216i
$577$	2.19502e11			1.98032			0.990162	−	0.139927i	$-0.0446868\pi$
$577$	2.19502e11			1.98032			0.990162	+	0.139927i	$0.0446868\pi$
$578$		−	2.90568e10i		−	0.260337i
$579$	1.07845e11	+	8.71521e10i	0.959592	+	0.775468i
$580$	−4.63373e10			−0.409467
$581$			2.42684e11i			2.12979i
$582$	7.41442e10	−	9.17488e10i	0.646227	−	0.799665i
$583$	−1.17122e10			−0.101383
$584$			4.07501e10i			0.350330i
$585$	−4.86731e10	+	1.04480e10i	−0.415590	+	0.0892096i
$586$	−4.88040e10			−0.413871
$587$		−	2.05299e11i		−	1.72916i	−0.502496	−	0.864580i	$-0.667585\pi$
$587$		−	2.05299e11i		−	1.72916i	0.502496	−	0.864580i	$-0.332415\pi$
$588$	1.61038e10	+	1.30138e10i	0.134716	+	0.108867i
$589$	1.04940e11			0.871924
$590$		−	3.26677e10i		−	0.269594i
$591$	1.34044e11	−	1.65871e11i	1.09875	−	1.35963i
$592$	−3.21855e10			−0.262043
$593$			1.01405e11i			0.820052i	0.912074	+	0.410026i	$0.134480\pi$
$593$			1.01405e11i			0.820052i	−0.912074	+	0.410026i	$0.865520\pi$
$594$	−6.08774e10	+	1.20374e11i	−0.489002	+	0.966913i
$595$	1.06721e11			0.851498
$596$			9.40983e10i			0.745756i
$597$	−1.86003e11	−	1.50313e11i	−1.46427	−	1.18331i
$598$	7.34212e9			0.0574138
$599$		−	9.27543e10i		−	0.720488i	−0.932858	−	0.360244i	$-0.882693\pi$
$599$		−	9.27543e10i		−	0.720488i	0.932858	−	0.360244i	$-0.117307\pi$
$600$	4.25388e9	−	5.26391e9i	0.0328232	−	0.0406166i
$601$	−1.18263e11			−0.906464			−0.453232	−	0.891393i	$-0.649729\pi$
$601$	−1.18263e11			−0.906464			−0.453232	+	0.891393i	$0.649729\pi$
$602$			2.46304e9i			0.0187536i
$603$	−2.35973e10	−	1.09930e11i	−0.178482	−	0.831472i
$604$	−3.86095e10			−0.290099
$605$			1.66738e11i			1.24455i
$606$	−6.68436e10	−	5.40178e10i	−0.495644	−	0.400541i
$607$	−7.78725e10			−0.573627			−0.286813	−	0.957986i	$-0.592596\pi$
$607$	−7.78725e10			−0.573627			−0.286813	+	0.957986i	$0.592596\pi$
$608$		−	2.66928e10i		−	0.195335i
$609$	8.89906e10	−	1.10120e11i	0.646957	−	0.800568i
$610$	−1.14751e11			−0.828776
$611$		−	4.62840e10i		−	0.332098i
$612$	5.45121e10	−	1.17014e10i	0.388586	−	0.0834129i
$613$	−6.04009e10			−0.427761			−0.213881	−	0.976860i	$-0.568610\pi$
$613$	−6.04009e10			−0.427761			−0.213881	+	0.976860i	$0.568610\pi$
$614$			9.41476e10i			0.662424i
$615$	3.58466e10	+	2.89684e10i	0.250581	+	0.202500i
$616$	9.05157e10			0.628638
$617$		−	1.86030e11i		−	1.28364i	−0.766856	−	0.641819i	$-0.778180\pi$
$617$		−	1.86030e11i		−	1.28364i	0.766856	−	0.641819i	$-0.221820\pi$
$618$	3.05466e10	−	3.77994e10i	0.209415	−	0.259138i
$619$	1.54130e11			1.04984			0.524922	−	0.851151i	$-0.324095\pi$
$619$	1.54130e11			1.04984			0.524922	+	0.851151i	$0.324095\pi$
$620$			5.38216e10i			0.364242i
$621$	−2.34040e10	−	1.18362e10i	−0.157371	−	0.0795880i
$622$	−1.23527e11			−0.825281
$623$			2.26370e11i			1.50268i
$624$	1.35733e10	+	1.09689e10i	0.0895257	+	0.0723477i
$625$	−1.26721e11			−0.830479
$626$		−	7.01397e10i		−	0.456737i
$627$	−1.64480e11	+	2.03534e11i	−1.06425	+	1.31694i
$628$	2.06389e10			0.132693
$629$		−	1.30417e11i		−	0.833168i
$630$	−2.50435e10	−	1.16667e11i	−0.158977	−	0.740606i
$631$	4.35140e10			0.274480			0.137240	−	0.990538i	$-0.456177\pi$
$631$	4.35140e10			0.274480			0.137240	+	0.990538i	$0.456177\pi$
$632$			1.32977e10i			0.0833504i
$633$	1.67800e11	+	1.35603e11i	1.04515	+	0.844606i
$634$	2.11419e11			1.30854
$635$			7.23654e10i			0.445078i
$636$	3.40203e9	−	4.20980e9i	0.0207926	−	0.0257296i
$637$	−2.62605e10			−0.159494
$638$		−	1.59250e11i		−	0.961160i
$639$	1.66085e11	−	3.56514e10i	0.996156	−	0.213832i
$640$	1.36902e10			0.0816000
$641$			1.74736e11i			1.03502i	0.855676	+	0.517512i	$0.173142\pi$
$641$			1.74736e11i			1.03502i	−0.855676	+	0.517512i	$0.826858\pi$
$642$	1.35996e11	+	1.09901e11i	0.800544	+	0.646937i
$643$	−2.46091e11			−1.43963			−0.719817	−	0.694164i	$-0.755774\pi$
$643$	−2.46091e11			−1.43963			−0.719817	+	0.694164i	$0.755774\pi$
$644$			1.75987e10i			0.102315i
$645$	2.29550e9	−	2.84054e9i	0.0132629	−	0.0164120i
$646$	1.08160e11			0.621067
$647$			1.89739e10i			0.108278i	0.998533	+	0.0541390i	$0.0172414\pi$
$647$			1.89739e10i			0.108278i	−0.998533	+	0.0541390i	$0.982759\pi$
$648$	−2.55839e10	−	5.68465e10i	−0.145100	−	0.322407i
$649$	1.12271e11			0.632831
$650$			8.58389e9i			0.0480873i
$651$	−1.27907e11	−	1.03364e11i	−0.712146	−	0.575501i
$652$	2.83177e10			0.156700
$653$		−	1.53366e11i		−	0.843484i	−0.906716	−	0.421742i	$-0.861419\pi$
$653$		−	1.53366e11i		−	0.843484i	0.906716	−	0.421742i	$-0.138581\pi$
$654$	−1.56648e11	+	1.93842e11i	−0.856277	+	1.05959i
$655$	7.15771e10			0.388874
$656$		−	1.61567e10i		−	0.0872442i
$657$	3.87479e10	+	1.80510e11i	0.207963	+	0.968814i
$658$	1.10941e11			0.591817
$659$			1.47234e11i			0.780667i	0.920674	+	0.390333i	$0.127640\pi$
$659$			1.47234e11i			0.780667i	−0.920674	+	0.390333i	$0.872360\pi$
$660$	−1.04389e11	−	8.43588e10i	−0.550146	−	0.444585i
$661$	−6.61159e10			−0.346338			−0.173169	−	0.984892i	$-0.555401\pi$
$661$	−6.61159e10			−0.346338			−0.173169	+	0.984892i	$0.555401\pi$
$662$		−	3.67105e10i		−	0.191143i
$663$	−4.44466e10	+	5.49998e10i	−0.230030	+	0.284647i
$664$	−1.26146e11			−0.648937
$665$		−	2.31486e11i		−	1.18369i
$666$	−1.42572e11	+	3.06041e10i	−0.724663	+	0.155554i
$667$	3.09625e10			0.156435
$668$		−	5.14373e10i		−	0.258328i
$669$	1.28687e10	+	1.03995e10i	0.0642439	+	0.0519169i
$670$	1.11869e11			0.555149
$671$		−	3.94370e11i		−	1.94542i
$672$	−2.62920e10	+	3.25347e10i	−0.128928	+	0.159540i
$673$	−1.67142e11			−0.814753			−0.407377	−	0.913260i	$-0.633556\pi$
$673$	−1.67142e11			−0.814753			−0.407377	+	0.913260i	$0.633556\pi$
$674$		−	5.53395e10i		−	0.268161i
$675$	1.38381e10	−	2.73624e10i	0.0666594	−	0.131807i
$676$	8.22795e10			0.394008
$677$		−	7.82435e10i		−	0.372472i	−0.982505	−	0.186236i	$-0.940371\pi$
$677$		−	7.82435e10i		−	0.372472i	0.982505	−	0.186236i	$-0.0596289\pi$
$678$	5.48250e10	+	4.43053e10i	0.259454	+	0.209670i
$679$	−3.58621e11			−1.68716
$680$			5.54735e10i			0.259448i
$681$	2.16967e10	−	2.68483e10i	0.100880	−	0.124832i
$682$	−1.84971e11			−0.855001
$683$			1.21724e11i			0.559361i	0.960093	+	0.279681i	$0.0902286\pi$
$683$			1.21724e11i			0.559361i	−0.960093	+	0.279681i	$0.909771\pi$
$684$	−2.53812e10	−	1.18241e11i	−0.115955	−	0.540185i
$685$	3.17780e11			1.44333
$686$			1.18761e11i			0.536263i
$687$	1.92644e10	+	1.55680e10i	0.0864827	+	0.0698885i
$688$	−1.28028e9			−0.00571414
$689$			6.86494e9i			0.0304621i
$690$	1.64017e10	−	2.02960e10i	0.0723589	−	0.0895396i
$691$	3.71272e11			1.62847			0.814236	−	0.580535i	$-0.197156\pi$
$691$	3.71272e11			1.62847			0.814236	+	0.580535i	$0.197156\pi$
$692$		−	1.38526e9i		−	0.00604099i
$693$	4.00956e11	−	8.60682e10i	1.73846	−	0.373173i
$694$	−1.63215e11			−0.703592
$695$			4.38094e10i			0.187771i
$696$	5.72402e10	+	4.62571e10i	0.243929	+	0.197125i
$697$	6.54677e10			0.277393
$698$			6.04343e10i			0.254602i
$699$	−7.17424e10	+	8.87767e10i	−0.300516	+	0.371869i
$700$	−2.05752e10			−0.0856943
$701$			2.35914e11i			0.976970i	0.872572	+	0.488485i	$0.162450\pi$
$701$			2.35914e11i			0.976970i	−0.872572	+	0.488485i	$0.837550\pi$
$702$	7.05555e10	+	3.56824e10i	0.290524	+	0.146928i
$703$	−2.82884e11			−1.15821
$704$			4.70498e10i			0.191543i
$705$	−1.27944e11	−	1.03395e11i	−0.517922	−	0.418544i
$706$	8.85146e10			0.356284
$707$			2.61274e11i			1.04573i
$708$	−3.26111e10	+	4.03542e10i	−0.129788	+	0.160604i
$709$	−1.51154e11			−0.598184			−0.299092	−	0.954224i	$-0.596684\pi$
$709$	−1.51154e11			−0.598184			−0.299092	+	0.954224i	$0.596684\pi$
$710$			1.69014e11i			0.665104i
$711$	1.26443e10	+	5.89046e10i	0.0494785	+	0.230500i
$712$	−1.17667e11			−0.457861
$713$		−	3.59635e10i		−	0.139157i
$714$	−1.31832e11	−	1.06537e11i	−0.507258	−	0.409926i
$715$	1.70227e11			0.651335
$716$			2.87772e10i			0.109495i
$717$	1.16465e11	−	1.44118e11i	0.440675	−	0.545307i
$718$	1.88619e11			0.709723
$719$		−	1.57719e10i		−	0.0590158i	−0.999565	−	0.0295079i	$-0.990606\pi$
$719$		−	1.57719e10i		−	0.0590158i	0.999565	−	0.0295079i	$-0.00939402\pi$
$720$	6.06433e10	−	1.30175e10i	0.225659	−	0.0484394i
$721$	−1.47748e11			−0.546739
$722$		−	4.24605e10i		−	0.156256i
$723$	−2.75543e11	−	2.22673e11i	−1.00841	−	0.814918i
$724$	1.67713e11			0.610398
$725$			3.61992e10i			0.131023i
$726$	1.66449e11	−	2.05970e11i	0.599149	−	0.741409i
$727$	3.61913e11			1.29559			0.647794	−	0.761816i	$-0.275692\pi$
$727$	3.61913e11			1.29559			0.647794	+	0.761816i	$0.275692\pi$
$728$		−	5.30545e10i		−	0.188884i
$729$	−1.67382e11	−	2.27486e11i	−0.592651	−	0.805459i
$730$	−1.83694e11			−0.646848
$731$		−	5.18776e9i		−	0.0181681i
$732$	1.41751e11	+	1.14552e11i	0.493722	+	0.398988i
$733$	5.75659e10			0.199411			0.0997056	−	0.995017i	$-0.468210\pi$
$733$	5.75659e10			0.199411			0.0997056	+	0.995017i	$0.468210\pi$
$734$		−	2.10951e11i		−	0.726772i
$735$	−5.86637e10	+	7.25927e10i	−0.201011	+	0.248739i
$736$	−9.14778e9			−0.0311748
$737$			3.84465e11i			1.30313i
$738$	−1.53628e10	−	7.15690e10i	−0.0517900	−	0.241268i
$739$	−2.30778e11			−0.773780			−0.386890	−	0.922126i	$-0.626451\pi$
$739$	−2.30778e11			−0.773780			−0.386890	+	0.922126i	$0.626451\pi$
$740$		−	1.45086e11i		−	0.483836i
$741$	1.19298e11	+	9.64077e10i	0.395696	+	0.319771i
$742$	−1.64550e10			−0.0542852
$743$			4.84430e10i			0.158956i	0.996837	+	0.0794778i	$0.0253253\pi$
$743$			4.84430e10i			0.158956i	−0.996837	+	0.0794778i	$0.974675\pi$
$744$	5.37284e10	−	6.64855e10i	0.175353	−	0.216988i
$745$	−4.24177e11			−1.37696
$746$		−	3.82845e11i		−	1.23614i
$747$	−5.58790e11	+	1.19948e11i	−1.79459	+	0.385223i
$748$	−1.90648e11			−0.609013
$749$		−	5.31571e11i		−	1.68902i
$750$	1.84379e11	+	1.49000e11i	0.582728	+	0.470915i
$751$	1.03467e11			0.325269			0.162635	−	0.986686i	$-0.448001\pi$
$751$	1.03467e11			0.325269			0.162635	+	0.986686i	$0.448001\pi$
$752$			5.76667e10i			0.180324i
$753$	−9.11295e10	+	1.12767e11i	−0.283452	+	0.350753i
$754$	−9.33419e10			−0.288796
$755$		−	1.74044e11i		−	0.535638i
$756$	−8.55292e10	+	1.69119e11i	−0.261835	+	0.517731i
$757$	3.09395e11			0.942170			0.471085	−	0.882088i	$-0.343863\pi$
$757$	3.09395e11			0.942170			0.471085	+	0.882088i	$0.343863\pi$
$758$			3.19146e11i			0.966748i
$759$	6.97524e10	+	5.63684e10i	0.210180	+	0.169851i
$760$	1.20326e11			0.360665
$761$			3.57736e11i			1.06665i	0.845909	+	0.533327i	$0.179059\pi$
$761$			3.57736e11i			1.06665i	−0.845909	+	0.533327i	$0.820941\pi$
$762$	7.22401e10	−	8.93925e10i	0.214268	−	0.265144i
$763$	7.57677e11			2.23556
$764$			2.80300e11i			0.822715i
$765$	5.27478e10	+	2.45730e11i	0.154013	+	0.717485i
$766$	−2.06367e11			−0.599413
$767$		−	6.58058e10i		−	0.190144i
$768$	−1.69114e10	−	1.36665e10i	−0.0486111	−	0.0392837i
$769$	6.91156e10			0.197638			0.0988190	−	0.995105i	$-0.468494\pi$
$769$	6.91156e10			0.197638			0.0988190	+	0.995105i	$0.468494\pi$
$770$			4.08027e11i			1.16072i
$771$	1.12353e11	−	1.39030e11i	0.317957	−	0.393452i
$772$	2.19114e11			0.616881
$773$		−	4.96225e11i		−	1.38983i	−0.719093	−	0.694914i	$-0.755443\pi$
$773$		−	4.96225e11i		−	1.38983i	0.719093	−	0.694914i	$-0.244557\pi$
$774$	−5.67123e9	+	1.21737e9i	−0.0158021	+	0.00339203i
$775$	4.20460e10			0.116551
$776$		−	1.86410e11i		−	0.514071i
$777$	3.44796e11	+	2.78637e11i	0.945971	+	0.764460i
$778$	−2.19910e11			−0.600242
$779$		−	1.42004e11i		−	0.385612i
$780$	−4.94457e10	+	6.11859e10i	−0.133583	+	0.165300i
$781$	−5.80858e11			−1.56123
$782$		−	3.70673e10i		−	0.0991206i
$783$	2.97540e11	+	1.50477e11i	0.791588	+	0.400334i
$784$	3.27188e10			0.0866029
$785$			9.30361e10i			0.245004i
$786$	−8.84188e10	−	7.14532e10i	−0.231662	−	0.187211i
$787$	1.30010e11			0.338906			0.169453	−	0.985538i	$-0.445800\pi$
$787$	1.30010e11			0.338906			0.169453	+	0.985538i	$0.445800\pi$
$788$		−	3.37008e11i		−	0.874048i
$789$	9.05229e10	−	1.12016e11i	0.233588	−	0.289050i
$790$	−5.99433e10			−0.153898
$791$		−	2.14296e11i		−	0.547404i
$792$	4.47380e10	+	2.08416e11i	0.113704	+	0.529700i
$793$	−2.31154e11			−0.584533
$794$		−	1.88621e11i		−	0.474580i
$795$	1.89770e10	+	1.53357e10i	0.0475070	+	0.0383915i
$796$	−3.77911e11			−0.941319
$797$			4.08242e11i			1.01178i	0.862599	+	0.505888i	$0.168835\pi$
$797$			4.08242e11i			1.01178i	−0.862599	+	0.505888i	$0.831165\pi$
$798$	−2.31085e11	+	2.85953e11i	−0.569850	+	0.705153i
$799$	−2.33668e11			−0.573341
$800$		−	1.06949e10i		−	0.0261107i
$801$	−5.21226e11	+	1.11885e11i	−1.26618	+	0.271796i
$802$	3.74299e11			0.904734
$803$		−	6.31308e11i		−	1.51838i
$804$	−1.38191e11	−	1.11675e11i	−0.330716	−	0.267259i
$805$	−7.93317e10			−0.188914
$806$			1.08418e11i			0.256899i
$807$	3.04084e11	−	3.76284e11i	0.716966	−	0.887201i
$808$	−1.35809e11			−0.318628
$809$			2.23269e11i			0.521235i	0.965442	+	0.260618i	$0.0839262\pi$
$809$			2.23269e11i			0.521235i	−0.965442	+	0.260618i	$0.916074\pi$
$810$	2.56253e11	−	1.15327e11i	0.595291	−	0.267912i
$811$	1.75526e11			0.405750			0.202875	−	0.979205i	$-0.434972\pi$
$811$	1.75526e11			0.405750			0.202875	+	0.979205i	$0.434972\pi$
$812$		−	2.23736e11i		−	0.514651i
$813$	−2.04470e11	−	1.65237e11i	−0.468023	−	0.378220i
$814$	4.98624e11			1.13573
$815$			1.27651e11i			0.289330i
$816$	5.53774e10	−	6.85260e10i	0.124903	−	0.154559i
$817$	−1.12526e10			−0.0252560
$818$			5.69449e11i			1.27187i
$819$	−5.04476e10	−	2.35015e11i	−0.112126	−	0.522347i
$820$	7.28312e10			0.161088
$821$		−	8.37441e10i		−	0.184324i	−0.995744	−	0.0921619i	$-0.970622\pi$
$821$		−	8.37441e10i		−	0.184324i	0.995744	−	0.0921619i	$-0.0293777\pi$
$822$	−3.92552e11	−	3.17230e11i	−0.859825	−	0.694843i
$823$	−5.41972e11			−1.18135			−0.590673	−	0.806911i	$-0.701138\pi$
$823$	−5.41972e11			−1.18135			−0.590673	+	0.806911i	$0.701138\pi$
$824$		−	7.67989e10i		−	0.166589i
$825$	−6.59020e10	+	8.15495e10i	−0.142260	+	0.176038i
$826$	1.57734e11			0.338848
$827$			5.30564e11i			1.13427i	0.823626	+	0.567134i	$0.191948\pi$
$827$			5.30564e11i			1.13427i	−0.823626	+	0.567134i	$0.808052\pi$
$828$	−4.05218e10	+	8.69830e9i	−0.0862119	+	0.0185060i
$829$	4.65551e11			0.985710			0.492855	−	0.870111i	$-0.335953\pi$
$829$	4.65551e11			0.985710			0.492855	+	0.870111i	$0.335953\pi$
$830$		−	5.68644e11i		−	1.19820i
$831$	8.45066e10	+	6.82916e10i	0.177209	+	0.143207i
$832$	2.75775e10			0.0575523
$833$			1.32578e11i			0.275354i
$834$	4.37335e10	−	5.41174e10i	0.0903962	−	0.111860i
$835$	2.31869e11			0.476977
$836$			4.13529e11i			0.846605i
$837$	1.74781e11	−	3.45598e11i	0.356117	−	0.704158i
$838$	3.32940e11			0.675133
$839$			7.93304e11i			1.60100i	0.599332	+	0.800501i	$0.295433\pi$
$839$			7.93304e11i			1.60100i	−0.599332	+	0.800501i	$0.704567\pi$
$840$	−1.46660e11	−	1.18519e11i	−0.294574	−	0.238052i
$841$	1.06614e11			0.213122
$842$			3.77021e11i			0.750097i
$843$	−9.63520e10	+	1.19229e11i	−0.190788	+	0.236088i
$844$	3.40927e11			0.671880
$845$			3.70900e11i			0.727495i
$846$	5.48332e10	+	2.55445e11i	0.107044	+	0.498674i
$847$	−8.05082e11			−1.56425
$848$		−	8.55324e9i		−	0.0165405i
$849$	4.33624e11	+	3.50421e11i	0.834608	+	0.674465i
$850$	4.33364e10			0.0830190
$851$			9.69462e10i			0.184847i
$852$	1.68721e11	−	2.08782e11i	0.320193	−	0.396219i
$853$	4.55056e10			0.0859545			0.0429772	−	0.999076i	$-0.486316\pi$
$853$	4.55056e10			0.0859545			0.0429772	+	0.999076i	$0.486316\pi$
$854$		−	5.54067e11i		−	1.04167i
$855$	5.33006e11	−	1.14414e11i	0.997395	−	0.214098i
$856$	2.76309e11			0.514635
$857$		−	8.48487e11i		−	1.57297i	−0.617606	−	0.786487i	$-0.711898\pi$
$857$		−	8.48487e11i		−	1.57297i	0.617606	−	0.786487i	$-0.288102\pi$
$858$	−2.10280e11	−	1.69932e11i	−0.388016	−	0.313564i
$859$	−7.64741e11			−1.40456			−0.702282	−	0.711899i	$-0.747836\pi$
$859$	−7.64741e11			−1.40456			−0.702282	+	0.711899i	$0.747836\pi$
$860$		−	5.77125e9i		−	0.0105506i
$861$	−1.39872e11	+	1.73083e11i	−0.254518	+	0.314950i
$862$	−6.36137e11			−1.15218
$863$			4.55374e11i			0.820966i	0.911868	+	0.410483i	$0.134640\pi$
$863$			4.55374e11i			0.820966i	−0.911868	+	0.410483i	$0.865360\pi$
$864$	−8.79074e10	−	4.44578e10i	−0.157750	−	0.0797799i
$865$	6.24450e9			0.0111541
$866$			2.47552e11i			0.440144i
$867$	−1.61802e11	−	1.30755e11i	−0.286356	−	0.231411i
$868$	−2.59874e11			−0.457808
$869$		−	2.06010e11i		−	0.361251i
$870$	−2.08518e11	+	2.58028e11i	−0.363971	+	0.450391i
$871$	2.25348e11			0.391545
$872$			3.93838e11i			0.681164i
$873$	−1.77251e11	−	8.25739e11i	−0.305163	−	1.42163i
$874$	−8.04015e10			−0.137790
$875$		−	7.20686e11i		−	1.22946i
$876$	2.26916e11	+	1.83375e11i	0.385343	+	0.311404i
$877$	8.42742e11			1.42461			0.712306	−	0.701869i	$-0.247651\pi$
$877$	8.42742e11			1.42461			0.712306	+	0.701869i	$0.247651\pi$
$878$		−	2.12686e11i		−	0.357899i
$879$	−2.19618e11	+	2.71764e11i	−0.367886	+	0.455235i
$880$	−2.12091e11			−0.353665
$881$		−	1.12314e12i		−	1.86436i	−0.361994	−	0.932181i	$-0.617904\pi$
$881$		−	1.12314e12i		−	1.86436i	0.361994	−	0.932181i	$-0.382096\pi$
$882$	1.44934e11	−	3.11111e10i	0.239495	−	0.0514093i
$883$	6.25330e11			1.02865			0.514323	−	0.857596i	$-0.328043\pi$
$883$	6.25330e11			1.02865			0.514323	+	0.857596i	$0.328043\pi$
$884$			1.11746e11i			0.182988i
$885$	−1.81909e11	−	1.47005e11i	−0.296539	−	0.239639i
$886$	−7.39456e11			−1.19999
$887$		−	4.73224e11i		−	0.764491i	−0.924061	−	0.382246i	$-0.875151\pi$
$887$		−	4.73224e11i		−	0.764491i	0.924061	−	0.382246i	$-0.124849\pi$
$888$	−1.44835e11	+	1.79224e11i	−0.232927	+	0.288233i
$889$	−3.49411e11			−0.559409
$890$		−	5.30418e11i		−	0.845393i
$891$	3.96351e11	+	8.80677e11i	0.628882	+	1.39735i
$892$	2.61460e10			0.0412996
$893$			5.06843e11i			0.797017i
$894$	5.23983e11	+	4.23442e11i	0.820290	+	0.662894i
$895$	−1.29722e11			−0.202172
$896$			6.61022e10i			0.102561i
$897$	3.30395e10	−	4.08843e10i	0.0510345	−	0.0631520i
$898$	1.78852e11			0.275035
$899$			4.57211e11i			0.699968i
$900$	−1.01694e10	−	4.73752e10i	−0.0154998	−	0.0722073i
$901$	3.46582e10			0.0525904
$902$			2.50302e11i			0.378128i
$903$	1.37153e10	+	1.10837e10i	0.0206279	+	0.0166699i
$904$	1.11390e11			0.166792
$905$			7.56019e11i			1.12704i
$906$	−1.73743e11	+	2.14996e11i	−0.257866	+	0.319093i
$907$	−9.14524e11			−1.35134			−0.675672	−	0.737202i	$-0.736147\pi$
$907$	−9.14524e11			−1.35134			−0.675672	+	0.737202i	$0.736147\pi$
$908$		−	5.45488e10i		−	0.0802495i
$909$	−6.01593e11	+	1.29136e11i	−0.881144	+	0.189144i
$910$	2.39159e11			0.348756
$911$		−	8.57040e11i		−	1.24431i	−0.782895	−	0.622154i	$-0.786258\pi$
$911$		−	8.57040e11i		−	1.24431i	0.782895	−	0.622154i	$-0.213742\pi$
$912$	−1.48638e11	−	1.20117e11i	−0.214857	−	0.173631i
$913$	1.95429e12			2.81258
$914$		−	3.73805e10i		−	0.0535624i
$915$	−5.16379e11	+	6.38987e11i	−0.736690	+	0.911607i
$916$	3.91404e10			0.0555960
$917$			3.45605e11i			0.488768i
$918$	1.80146e11	−	3.56205e11i	0.253660	−	0.501568i
$919$	9.47490e10			0.132835			0.0664175	−	0.997792i	$-0.478843\pi$
$919$	9.47490e10			0.132835			0.0664175	+	0.997792i	$0.478843\pi$
$920$		−	4.12364e10i		−	0.0575611i
$921$	5.24258e11	+	4.23664e11i	0.728629	+	0.588821i
$922$	−3.73510e11			−0.516867
$923$			3.40462e11i			0.469096i
$924$	4.07321e11	−	5.04033e11i	0.558790	−	0.691467i
$925$	−1.13343e11			−0.154820
$926$		−	6.37095e11i		−	0.866483i
$927$	−7.30254e10	−	3.40195e11i	−0.0988906	−	0.460690i
$928$	1.16298e11			0.156812
$929$			2.06406e11i			0.277115i	0.990354	+	0.138557i	$0.0442466\pi$
$929$			2.06406e11i			0.277115i	−0.990354	+	0.138557i	$0.955753\pi$
$930$	2.99704e11	+	2.42197e11i	0.400646	+	0.323770i
$931$	2.87571e11			0.382778
$932$			1.80372e11i			0.239059i
$933$	−5.55873e11	+	6.87858e11i	−0.733583	+	0.907762i
$934$	6.08875e11			0.800094
$935$		−	8.59405e11i		−	1.12448i
$936$	1.22160e11	−	2.62225e10i	0.159157	−	0.0341642i
$937$	−2.99452e11			−0.388480			−0.194240	−	0.980954i	$-0.562224\pi$
$937$	−2.99452e11			−0.388480			−0.194240	+	0.980954i	$0.562224\pi$
$938$			5.40151e11i			0.697756i
$939$	−3.90571e11	−	3.15629e11i	−0.502386	−	0.405989i
$940$	−2.59950e11			−0.332950
$941$		−	9.75658e11i		−	1.24434i	−0.782882	−	0.622170i	$-0.786251\pi$
$941$		−	9.75658e11i		−	1.24434i	0.782882	−	0.622170i	$-0.213749\pi$
$942$	9.28750e10	−	1.14927e11i	0.117949	−	0.145955i
$943$	−4.86657e10			−0.0615426
$944$			8.19896e10i			0.103245i
$945$	−7.62354e11	−	3.85549e11i	−0.955937	−	0.483451i
$946$	1.98343e10			0.0247658
$947$			6.85570e11i			0.852416i	0.904625	+	0.426208i	$0.140151\pi$
$947$			6.85570e11i			0.852416i	−0.904625	+	0.426208i	$0.859849\pi$
$948$	7.40477e10	+	5.98395e10i	0.0916807	+	0.0740892i
$949$	−3.70032e11			−0.456220
$950$		−	9.39998e10i		−	0.115407i
$951$	9.51386e11	−	1.17728e12i	1.16315	−	1.43932i
$952$	−2.67850e11			−0.326094
$953$			1.81880e11i			0.220502i	0.993904	+	0.110251i	$0.0351655\pi$
$953$			1.81880e11i			0.220502i	−0.993904	+	0.110251i	$0.964835\pi$
$954$	−8.13298e9	−	3.78882e10i	−0.00981875	−	0.0457415i
$955$	−1.26354e12			−1.51906
$956$		−	2.92811e11i		−	0.350555i
$957$	−8.86776e11	−	7.16623e11i	−1.05722	−	0.854364i
$958$	−9.08142e11			−1.07818
$959$			1.53438e12i			1.81409i
$960$	6.16059e10	−	7.62335e10i	0.0725333	−	0.0897554i
$961$	−3.21832e11			−0.377342
$962$		−	2.92261e11i		−	0.341248i
$963$	1.22396e12	−	2.62732e11i	1.42319	−	0.305498i
$964$	−5.59834e11			−0.648263
$965$			9.87724e11i			1.13901i
$966$	9.79980e10	+	7.91944e10i	0.112540	+	0.0909464i
$967$	−1.51799e11			−0.173605			−0.0868024	−	0.996226i	$-0.527665\pi$
$967$	−1.51799e11			−0.173605			−0.0868024	+	0.996226i	$0.527665\pi$
$968$		−	4.18479e11i		−	0.476620i
$969$	4.86722e11	−	6.02288e11i	0.552060	−	0.683139i
$970$	8.40301e11			0.949178
$971$			2.30877e11i			0.259718i	0.991532	+	0.129859i	$0.0414525\pi$
$971$			2.30877e11i			0.259718i	−0.991532	+	0.129859i	$0.958547\pi$
$972$	−4.31676e11	−	1.13346e11i	−0.483607	−	0.126982i
$973$	−2.11530e11			−0.236005
$974$			7.99985e11i			0.888886i
$975$	4.77991e10	+	3.86275e10i	0.0528933	+	0.0427443i
$976$	2.88002e11			0.317393
$977$		−	1.10823e12i		−	1.21633i	−0.793812	−	0.608163i	$-0.791907\pi$
$977$		−	1.10823e12i		−	1.21633i	0.793812	−	0.608163i	$-0.208093\pi$
$978$	1.27430e11	−	1.57686e11i	0.139289	−	0.172361i
$979$	1.82291e12			1.98443
$980$			1.47490e11i			0.159903i
$981$	3.74487e11	+	1.74458e12i	0.404353	+	1.88371i
$982$	6.86602e11			0.738344
$983$			3.64534e11i			0.390413i	0.980762	+	0.195207i	$0.0625377\pi$
$983$			3.64534e11i			0.390413i	−0.980762	+	0.195207i	$0.937462\pi$
$984$	−8.99679e10	−	7.27051e10i	−0.0959638	−	0.0775504i
$985$	1.51917e12			1.61384
$986$			4.71244e11i			0.498584i
$987$	4.99233e11	−	6.17770e11i	0.526060	−	0.650966i
$988$	2.42384e11			0.254376
$989$			3.85634e9i			0.00403079i
$990$	−9.39498e11	+	2.01670e11i	−0.978037	+	0.209943i
$991$	1.27281e10			0.0131968			0.00659842	−	0.999978i	$-0.497900\pi$
$991$	1.27281e10			0.0131968			0.00659842	+	0.999978i	$0.497900\pi$
$992$		−	1.35082e11i		−	0.139492i
$993$	−2.04421e11	−	1.65197e11i	−0.210247	−	0.169905i
$994$	−8.16072e11			−0.835956
$995$		−	1.70355e12i		−	1.73805i
$996$	−5.67659e11	+	7.02442e11i	−0.576833	+	0.713795i
$997$	−1.56439e12			−1.58330			−0.791651	−	0.610973i	$-0.790778\pi$
$997$	−1.56439e12			−1.58330			−0.791651	+	0.610973i	$0.790778\pi$
$998$			1.18710e12i			1.19665i
$999$	−4.71155e11	+	9.31624e11i	−0.473044	+	0.935359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.9.b.a.5.1	✓	2
3.2	odd	2	inner	6.9.b.a.5.2	yes	2
4.3	odd	2		48.9.e.d.17.2		2
5.2	odd	4		150.9.b.a.149.4		4
5.3	odd	4		150.9.b.a.149.1		4
5.4	even	2		150.9.d.a.101.2		2
8.3	odd	2		192.9.e.c.65.1		2
8.5	even	2		192.9.e.h.65.2		2
9.2	odd	6		162.9.d.a.53.2		4
9.4	even	3		162.9.d.a.107.2		4
9.5	odd	6		162.9.d.a.107.1		4
9.7	even	3		162.9.d.a.53.1		4
12.11	even	2		48.9.e.d.17.1		2
15.2	even	4		150.9.b.a.149.2		4
15.8	even	4		150.9.b.a.149.3		4
15.14	odd	2		150.9.d.a.101.1		2
24.5	odd	2		192.9.e.h.65.1		2
24.11	even	2		192.9.e.c.65.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.9.b.a.5.1	✓	2	1.1	even	1	trivial
6.9.b.a.5.2	yes	2	3.2	odd	2	inner
48.9.e.d.17.1		2	12.11	even	2
48.9.e.d.17.2		2	4.3	odd	2
150.9.b.a.149.1		4	5.3	odd	4
150.9.b.a.149.2		4	15.2	even	4
150.9.b.a.149.3		4	15.8	even	4
150.9.b.a.149.4		4	5.2	odd	4
150.9.d.a.101.1		2	15.14	odd	2
150.9.d.a.101.2		2	5.4	even	2
162.9.d.a.53.1		4	9.7	even	3
162.9.d.a.53.2		4	9.2	odd	6
162.9.d.a.107.1		4	9.5	odd	6
162.9.d.a.107.2		4	9.4	even	3
192.9.e.c.65.1		2	8.3	odd	2
192.9.e.c.65.2		2	24.11	even	2
192.9.e.h.65.1		2	24.5	odd	2
192.9.e.h.65.2		2	8.5	even	2

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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-11.3137i q^{2} +(-63.0000 - 50.9117i) q^{3} -128.000 q^{4} -576.999i q^{5} +(-576.000 + 712.764i) q^{6} +2786.00 q^{7} +1448.15i q^{8} +(1377.00 + 6414.87i) q^{9} +O(q^{10})\)	\(q-11.3137i q^{2} +(-63.0000 - 50.9117i) q^{3} -128.000 q^{4} -576.999i q^{5} +(-576.000 + 712.764i) q^{6} +2786.00 q^{7} +1448.15i q^{8} +(1377.00 + 6414.87i) q^{9} -6528.00 q^{10} -22435.1i q^{11} +(8064.00 + 6516.70i) q^{12} -13150.0 q^{13} -31520.0i q^{14} +(-29376.0 + 36350.9i) q^{15} +16384.0 q^{16} +66388.8i q^{17} +(72576.0 - 15579.0i) q^{18} +144002. q^{19} +73855.9i q^{20} +(-175518. - 141840. i) q^{21} -253824. q^{22} -49350.4i q^{23} +(73728.0 - 91233.7i) q^{24} +57697.0 q^{25} +148775. i q^{26} +(239841. - 474242. i) q^{27} -356608. q^{28} +627402. i q^{29} +(411264. + 332352. i) q^{30} +728738. q^{31} -185364. i q^{32} +(-1.14221e6 + 1.41341e6i) q^{33} +751104. q^{34} -1.60752e6i q^{35} +(-176256. - 821104. i) q^{36} -1.96445e6 q^{37} -1.62920e6i q^{38} +(828450. + 669489. i) q^{39} +835584. q^{40} -986125. i q^{41} +(-1.60474e6 + 1.98576e6i) q^{42} -78142.0 q^{43} +2.87169e6i q^{44} +(3.70138e6 - 794528. i) q^{45} -558336. q^{46} +3.51969e6i q^{47} +(-1.03219e6 - 834137. i) q^{48} +1.99700e6 q^{49} -652767. i q^{50} +(3.37997e6 - 4.18250e6i) q^{51} +1.68320e6 q^{52} -522048. i q^{53} +(-5.36544e6 - 2.71349e6i) q^{54} -1.29450e7 q^{55} +4.03456e6i q^{56} +(-9.07213e6 - 7.33138e6i) q^{57} +7.09824e6 q^{58} +5.00425e6i q^{59} +(3.76013e6 - 4.65292e6i) q^{60} +1.75783e7 q^{61} -8.24473e6i q^{62} +(3.83632e6 + 1.78718e7i) q^{63} -2.09715e6 q^{64} +7.58754e6i q^{65} +(1.59909e7 + 1.29226e7i) q^{66} -1.71368e7 q^{67} -8.49777e6i q^{68} +(-2.51251e6 + 3.10907e6i) q^{69} -1.81870e7 q^{70} -2.58906e7i q^{71} +(-9.28973e6 + 1.99411e6i) q^{72} +2.81393e7 q^{73} +2.22252e7i q^{74} +(-3.63491e6 - 2.93745e6i) q^{75} -1.84323e7 q^{76} -6.25041e7i q^{77} +(7.57440e6 - 9.37284e6i) q^{78} +9.18250e6 q^{79} -9.45355e6i q^{80} +(-3.92545e7 + 1.76666e7i) q^{81} -1.11567e7 q^{82} +8.71084e7i q^{83} +(2.24663e7 + 1.81555e7i) q^{84} +3.83063e7 q^{85} +884076. i q^{86} +(3.19421e7 - 3.95263e7i) q^{87} +3.24895e7 q^{88} +8.12528e7i q^{89} +(-8.98906e6 - 4.18763e7i) q^{90} -3.66359e7 q^{91} +6.31685e6i q^{92} +(-4.59105e7 - 3.71013e7i) q^{93} +3.98208e7 q^{94} -8.30890e7i q^{95} +(-9.43718e6 + 1.16779e7i) q^{96} -1.28723e8 q^{97} -2.25934e7i q^{98} +(1.43918e8 - 3.08931e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 126 q^{3} - 256 q^{4} - 1152 q^{6} + 5572 q^{7} + 2754 q^{9}+O(q^{10}) \) 2 * q - 126 * q^3 - 256 * q^4 - 1152 * q^6 + 5572 * q^7 + 2754 * q^9	\( 2 q - 126 q^{3} - 256 q^{4} - 1152 q^{6} + 5572 q^{7} + 2754 q^{9} - 13056 q^{10} + 16128 q^{12} - 26300 q^{13} - 58752 q^{15} + 32768 q^{16} + 145152 q^{18} + 288004 q^{19} - 351036 q^{21} - 507648 q^{22} + 147456 q^{24} + 115394 q^{25} + 479682 q^{27} - 713216 q^{28} + 822528 q^{30} + 1457476 q^{31} - 2284416 q^{33} + 1502208 q^{34} - 352512 q^{36} - 3928892 q^{37} + 1656900 q^{39} + 1671168 q^{40} - 3209472 q^{42} - 156284 q^{43} + 7402752 q^{45} - 1116672 q^{46} - 2064384 q^{48} + 3993990 q^{49} + 6759936 q^{51} + 3366400 q^{52} - 10730880 q^{54} - 25890048 q^{55} - 18144252 q^{57} + 14196480 q^{58} + 7520256 q^{60} + 35156548 q^{61} + 7672644 q^{63} - 4194304 q^{64} + 31981824 q^{66} - 34273532 q^{67} - 5025024 q^{69} - 36374016 q^{70} - 18579456 q^{72} + 56278660 q^{73} - 7269822 q^{75} - 36864512 q^{76} + 15148800 q^{78} + 18364996 q^{79} - 78508926 q^{81} - 22313472 q^{82} + 44932608 q^{84} + 76612608 q^{85} + 63884160 q^{87} + 64978944 q^{88} - 17978112 q^{90} - 73271800 q^{91} - 91820988 q^{93} + 79641600 q^{94} - 18874368 q^{96} - 257445116 q^{97} + 287836416 q^{99}+O(q^{100}) \) 2 * q - 126 * q^3 - 256 * q^4 - 1152 * q^6 + 5572 * q^7 + 2754 * q^9 - 13056 * q^10 + 16128 * q^12 - 26300 * q^13 - 58752 * q^15 + 32768 * q^16 + 145152 * q^18 + 288004 * q^19 - 351036 * q^21 - 507648 * q^22 + 147456 * q^24 + 115394 * q^25 + 479682 * q^27 - 713216 * q^28 + 822528 * q^30 + 1457476 * q^31 - 2284416 * q^33 + 1502208 * q^34 - 352512 * q^36 - 3928892 * q^37 + 1656900 * q^39 + 1671168 * q^40 - 3209472 * q^42 - 156284 * q^43 + 7402752 * q^45 - 1116672 * q^46 - 2064384 * q^48 + 3993990 * q^49 + 6759936 * q^51 + 3366400 * q^52 - 10730880 * q^54 - 25890048 * q^55 - 18144252 * q^57 + 14196480 * q^58 + 7520256 * q^60 + 35156548 * q^61 + 7672644 * q^63 - 4194304 * q^64 + 31981824 * q^66 - 34273532 * q^67 - 5025024 * q^69 - 36374016 * q^70 - 18579456 * q^72 + 56278660 * q^73 - 7269822 * q^75 - 36864512 * q^76 + 15148800 * q^78 + 18364996 * q^79 - 78508926 * q^81 - 22313472 * q^82 + 44932608 * q^84 + 76612608 * q^85 + 63884160 * q^87 + 64978944 * q^88 - 17978112 * q^90 - 73271800 * q^91 - 91820988 * q^93 + 79641600 * q^94 - 18874368 * q^96 - 257445116 * q^97 + 287836416 * q^99

Introduction

L-functions

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